LMFDB - Embedded newform 108.3.j.a.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(7,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("108.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.j (of order $18$, degree $6$, 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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	108.31
Dual form			108.3.j.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95123 + 0.438997i) q^{2} +(-1.49386 + 2.60161i) q^{3} +(3.61456 - 1.71316i) q^{4} +(0.0372686 - 0.211361i) q^{5} +(1.77277 - 5.73213i) q^{6} +(7.43930 + 8.86581i) q^{7} +(-6.30076 + 4.92955i) q^{8} +(-4.53674 - 7.77290i) q^{9} +O(q^{10})$	\(q+(-1.95123 + 0.438997i) q^{2} +(-1.49386 + 2.60161i) q^{3} +(3.61456 - 1.71316i) q^{4} +(0.0372686 - 0.211361i) q^{5} +(1.77277 - 5.73213i) q^{6} +(7.43930 + 8.86581i) q^{7} +(-6.30076 + 4.92955i) q^{8} +(-4.53674 - 7.77290i) q^{9} +(0.0200672 + 0.428773i) q^{10} +(-9.50415 + 1.67584i) q^{11} +(-0.942686 + 11.9629i) q^{12} +(-18.7145 + 6.81150i) q^{13} +(-18.4078 - 14.0334i) q^{14} +(0.494204 + 0.412703i) q^{15} +(10.1301 - 12.3847i) q^{16} +(-0.856471 + 1.48345i) q^{17} +(12.2645 + 13.1751i) q^{18} +(-5.28896 + 3.05358i) q^{19} +(-0.227386 - 0.827824i) q^{20} +(-34.1787 + 6.10984i) q^{21} +(17.8091 - 7.44223i) q^{22} +(-20.2195 + 24.0967i) q^{23} +(-3.41229 - 23.7562i) q^{24} +(23.4490 + 8.53475i) q^{25} +(33.5259 - 21.5064i) q^{26} +(26.9993 - 0.191178i) q^{27} +(42.0784 + 19.3013i) q^{28} +(8.13847 + 2.96216i) q^{29} +(-1.14548 - 0.588322i) q^{30} +(-0.101324 + 0.120753i) q^{31} +(-14.3294 + 28.6124i) q^{32} +(9.83803 - 27.2296i) q^{33} +(1.01994 - 3.27054i) q^{34} +(2.15114 - 1.24196i) q^{35} +(-29.7146 - 20.3235i) q^{36} +(24.1007 - 41.7436i) q^{37} +(8.97943 - 8.28006i) q^{38} +(10.2360 - 58.8632i) q^{39} +(0.807093 + 1.51545i) q^{40} +(19.2926 - 7.02193i) q^{41} +(64.0081 - 26.9260i) q^{42} +(-45.0838 + 7.94949i) q^{43} +(-31.4824 + 22.3396i) q^{44} +(-1.81196 + 0.669204i) q^{45} +(28.8744 - 55.8943i) q^{46} +(23.9050 + 28.4889i) q^{47} +(17.0870 + 44.8557i) q^{48} +(-14.7507 + 83.6553i) q^{49} +(-49.5011 - 6.35918i) q^{50} +(-2.57991 - 4.44428i) q^{51} +(-55.9754 + 56.6815i) q^{52} +98.4809 q^{53} +(-52.5978 + 12.2256i) q^{54} +2.07126i q^{55} +(-90.5777 - 19.1890i) q^{56} +(-0.0432430 - 18.3214i) q^{57} +(-17.1804 - 2.20708i) q^{58} +(-12.4095 - 2.18814i) q^{59} +(2.49336 + 0.645088i) q^{60} +(-62.8227 + 52.7145i) q^{61} +(0.144696 - 0.280098i) q^{62} +(35.1629 - 98.0469i) q^{63} +(15.3991 - 62.1198i) q^{64} +(0.742223 + 4.20936i) q^{65} +(-7.24254 + 57.4499i) q^{66} +(18.1950 + 49.9905i) q^{67} +(-0.554376 + 6.82930i) q^{68} +(-32.4849 - 88.6003i) q^{69} +(-3.65214 + 3.36769i) q^{70} +(65.5561 + 37.8488i) q^{71} +(66.9018 + 26.6111i) q^{72} +(13.3902 + 23.1924i) q^{73} +(-28.7005 + 92.0312i) q^{74} +(-57.2337 + 48.2555i) q^{75} +(-13.8860 + 20.0982i) q^{76} +(-85.5619 - 71.7950i) q^{77} +(5.86803 + 119.349i) q^{78} +(39.9006 - 109.626i) q^{79} +(-2.24010 - 2.60268i) q^{80} +(-39.8359 + 70.5273i) q^{81} +(-34.5616 + 22.1707i) q^{82} +(38.5038 - 105.788i) q^{83} +(-113.074 + 80.6381i) q^{84} +(0.281624 + 0.236311i) q^{85} +(84.4788 - 35.3029i) q^{86} +(-19.8642 + 16.7481i) q^{87} +(51.6222 - 57.4102i) q^{88} +(59.4575 + 102.983i) q^{89} +(3.24177 - 2.10121i) q^{90} +(-199.612 - 115.246i) q^{91} +(-31.8032 + 121.738i) q^{92} +(-0.162789 - 0.443995i) q^{93} +(-59.1506 - 45.0941i) q^{94} +(0.448295 + 1.23168i) q^{95} +(-53.0321 - 80.0225i) q^{96} +(-4.27138 - 24.2242i) q^{97} +(-7.94247 - 169.706i) q^{98} +(56.1440 + 66.2720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25} - 174 q^{26} - 12 q^{28} + 60 q^{29} - 153 q^{30} - 96 q^{32} + 48 q^{33} + 6 q^{34} + 24 q^{36} - 6 q^{37} + 72 q^{38} + 69 q^{40} - 192 q^{41} - 126 q^{42} - 219 q^{44} - 132 q^{45} - 3 q^{46} - 219 q^{48} - 12 q^{49} - 165 q^{50} + 21 q^{52} - 24 q^{53} + 78 q^{54} + 99 q^{56} - 150 q^{57} - 141 q^{58} + 210 q^{60} - 12 q^{61} + 294 q^{62} - 3 q^{64} - 156 q^{65} + 393 q^{66} + 375 q^{68} - 60 q^{69} - 165 q^{70} + 228 q^{72} - 6 q^{73} + 447 q^{74} - 54 q^{76} + 132 q^{77} + 750 q^{78} + 798 q^{80} + 228 q^{81} - 12 q^{82} + 762 q^{84} + 138 q^{85} + 606 q^{86} - 198 q^{88} - 114 q^{89} + 894 q^{90} + 723 q^{92} - 1020 q^{93} - 357 q^{94} + 474 q^{96} + 168 q^{97} + 510 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$

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 $

$2$	−1.95123	+	0.438997i	−0.975613	+	0.219498i
$2$	−1.95123	+	0.438997i	−0.975613	+	0.219498i
$3$	−1.49386	+	2.60161i	−0.497955	+	0.867203i
$3$	−1.49386	+	2.60161i	−0.497955	+	0.867203i
$4$	3.61456	−	1.71316i	0.903641	−	0.428291i
$5$	0.0372686	−	0.211361i	0.00745372	−	0.0422722i	−0.980854	−	0.194744i	$-0.937612\pi$
$5$	0.0372686	−	0.211361i	0.00745372	−	0.0422722i	0.988308	+	0.152472i	$0.0487234\pi$
$6$	1.77277	−	5.73213i	0.295461	−	0.955355i
$7$	7.43930	+	8.86581i	1.06276	+	1.26654i	0.962412	+	0.271592i	$0.0875502\pi$
$7$	7.43930	+	8.86581i	1.06276	+	1.26654i	0.100345	+	0.994953i	$0.468005\pi$
$8$	−6.30076	+	4.92955i	−0.787595	+	0.616194i
$9$	−4.53674	−	7.77290i	−0.504082	−	0.863656i
$10$	0.0200672	+	0.428773i	0.00200672	+	0.0428773i
$11$	−9.50415	+	1.67584i	−0.864014	+	0.152349i	−0.588055	−	0.808821i	$-0.700106\pi$
$11$	−9.50415	+	1.67584i	−0.864014	+	0.152349i	−0.275958	+	0.961170i	$0.588995\pi$
$12$	−0.942686	+	11.9629i	−0.0785572	+	0.996910i
$13$	−18.7145	+	6.81150i	−1.43957	+	0.523962i	−0.939659	−	0.342113i	$-0.888858\pi$
$13$	−18.7145	+	6.81150i	−1.43957	+	0.523962i	−0.499915	+	0.866075i	$0.666635\pi$
$14$	−18.4078	−	14.0334i	−1.31484	−	1.00238i
$15$	0.494204	+	0.412703i	0.0329469	+	0.0275135i
$16$	10.1301	−	12.3847i	0.633134	−	0.774042i
$17$	−0.856471	+	1.48345i	−0.0503806	+	0.0872618i	−0.890116	−	0.455734i	$-0.849377\pi$
$17$	−0.856471	+	1.48345i	−0.0503806	+	0.0872618i	0.839735	+	0.542996i	$0.182710\pi$
$18$	12.2645	+	13.1751i	0.681360	+	0.731948i
$19$	−5.28896	+	3.05358i	−0.278366	+	0.160715i	−0.632683	−	0.774410i	$-0.718047\pi$
$19$	−5.28896	+	3.05358i	−0.278366	+	0.160715i	0.354317	+	0.935125i	$0.384713\pi$
$20$	−0.227386	−	0.827824i	−0.0113693	−	0.0413912i
$21$	−34.1787	+	6.10984i	−1.62756	+	0.290945i
$22$	17.8091	−	7.44223i	0.809503	−	0.338283i
$23$	−20.2195	+	24.0967i	−0.879108	+	1.04768i	0.119387	+	0.992848i	$0.461907\pi$
$23$	−20.2195	+	24.0967i	−0.879108	+	1.04768i	−0.998496	+	0.0548328i	$0.982537\pi$
$24$	−3.41229	−	23.7562i	−0.142179	−	0.989841i
$25$	23.4490	+	8.53475i	0.937961	+	0.341390i
$26$	33.5259	−	21.5064i	1.28946	−	0.827168i
$27$	26.9993	−	0.191178i	0.999975	−	0.00708065i
$28$	42.0784	+	19.3013i	1.50280	+	0.689333i
$29$	8.13847	+	2.96216i	0.280637	+	0.102144i	0.478504	−	0.878085i	$-0.341179\pi$
$29$	8.13847	+	2.96216i	0.280637	+	0.102144i	−0.197867	+	0.980229i	$0.563401\pi$
$30$	−1.14548	−	0.588322i	−0.0381826	−	0.0196107i
$31$	−0.101324	+	0.120753i	−0.00326852	+	0.00389527i	−0.767676	−	0.640838i	$-0.778587\pi$
$31$	−0.101324	+	0.120753i	−0.00326852	+	0.00389527i	0.764408	+	0.644733i	$0.223032\pi$
$32$	−14.3294	+	28.6124i	−0.447793	+	0.894137i
$33$	9.83803	−	27.2296i	0.298122	−	0.825138i
$34$	1.01994	−	3.27054i	0.0299982	−	0.0961922i
$35$	2.15114	−	1.24196i	0.0614611	−	0.0354846i
$36$	−29.7146	−	20.3235i	−0.825405	−	0.564541i
$37$	24.1007	−	41.7436i	0.651369	−	1.12820i	−0.331422	−	0.943483i	$-0.607528\pi$
$37$	24.1007	−	41.7436i	0.651369	−	1.12820i	0.982791	−	0.184722i	$-0.0591383\pi$
$38$	8.97943	−	8.28006i	0.236301	−	0.217896i
$39$	10.2360	−	58.8632i	0.262461	−	1.50931i
$40$	0.807093	+	1.51545i	0.0201773	+	0.0378863i
$41$	19.2926	−	7.02193i	0.470551	−	0.171267i	−0.0958510	−	0.995396i	$-0.530557\pi$
$41$	19.2926	−	7.02193i	0.470551	−	0.171267i	0.566402	+	0.824129i	$0.308335\pi$
$42$	64.0081	−	26.9260i	1.52400	−	0.641095i
$43$	−45.0838	+	7.94949i	−1.04846	+	0.184872i	−0.671231	−	0.741248i	$-0.734234\pi$
$43$	−45.0838	+	7.94949i	−1.04846	+	0.184872i	−0.377229	+	0.926120i	$0.623123\pi$
$44$	−31.4824	+	22.3396i	−0.715509	+	0.507718i
$45$	−1.81196	+	0.669204i	−0.0402659	+	0.0148712i
$46$	28.8744	−	55.8943i	0.627705	−	1.21509i
$47$	23.9050	+	28.4889i	0.508618	+	0.606147i	0.957850	−	0.287268i	$-0.0927470\pi$
$47$	23.9050	+	28.4889i	0.508618	+	0.606147i	−0.449233	+	0.893415i	$0.648303\pi$
$48$	17.0870	+	44.8557i	0.355980	+	0.934494i
$49$	−14.7507	+	83.6553i	−0.301035	+	1.70725i
$50$	−49.5011	−	6.35918i	−0.990022	−	0.127184i
$51$	−2.57991	−	4.44428i	−0.0505865	−	0.0871427i
$52$	−55.9754	+	56.6815i	−1.07645	+	1.09003i
$53$	98.4809			1.85813			0.929065	−	0.369917i	$-0.120614\pi$
$53$	98.4809			1.85813			0.929065	+	0.369917i	$0.120614\pi$
$54$	−52.5978	+	12.2256i	−0.974034	+	0.226401i
$55$			2.07126i			0.0376593i
$56$	−90.5777	−	19.1890i	−1.61746	−	0.342660i
$57$	−0.0432430	−	18.3214i	−0.000758649	−	0.321429i
$58$	−17.1804	−	2.20708i	−0.296213	−	0.0380532i
$59$	−12.4095	−	2.18814i	−0.210331	−	0.0370871i	0.0674896	−	0.997720i	$-0.478501\pi$
$59$	−12.4095	−	2.18814i	−0.210331	−	0.0370871i	−0.277821	+	0.960633i	$0.589612\pi$
$60$	2.49336	+	0.645088i	0.0415560	+	0.0107515i
$61$	−62.8227	+	52.7145i	−1.02988	+	0.864172i	−0.990837	−	0.135065i	$-0.956876\pi$
$61$	−62.8227	+	52.7145i	−1.02988	+	0.864172i	−0.0390434	+	0.999238i	$0.512431\pi$
$62$	0.144696	−	0.280098i	0.00233381	−	0.00451771i
$63$	35.1629	−	98.0469i	0.558141	−	1.55630i
$64$	15.3991	−	62.1198i	0.240611	−	0.970622i
$65$	0.742223	+	4.20936i	0.0114188	+	0.0647593i
$66$	−7.24254	+	57.4499i	−0.109735	+	0.870453i
$67$	18.1950	+	49.9905i	0.271568	+	0.746126i	0.998249	+	0.0591515i	$0.0188395\pi$
$67$	18.1950	+	49.9905i	0.271568	+	0.746126i	−0.726681	+	0.686975i	$0.758938\pi$
$68$	−0.554376	+	6.82930i	−0.00815259	+	0.100431i
$69$	−32.4849	−	88.6003i	−0.470796	−	1.28406i
$70$	−3.65214	+	3.36769i	−0.0521734	+	0.0481098i
$71$	65.5561	+	37.8488i	0.923325	+	0.533082i	0.884694	−	0.466172i	$-0.154367\pi$
$71$	65.5561	+	37.8488i	0.923325	+	0.533082i	0.0386308	+	0.999254i	$0.487700\pi$
$72$	66.9018	+	26.6111i	0.929192	+	0.369598i
$73$	13.3902	+	23.1924i	0.183427	+	0.317705i	0.943045	−	0.332664i	$-0.107948\pi$
$73$	13.3902	+	23.1924i	0.183427	+	0.317705i	−0.759618	+	0.650369i	$0.774614\pi$
$74$	−28.7005	+	92.0312i	−0.387845	+	1.24367i
$75$	−57.2337	+	48.2555i	−0.763117	+	0.643406i
$76$	−13.8860	+	20.0982i	−0.182710	+	0.264450i
$77$	−85.5619	−	71.7950i	−1.11119	−	0.932402i
$78$	5.86803	+	119.349i	0.0752312	+	1.53011i
$79$	39.9006	−	109.626i	0.505071	−	1.38767i	−0.381194	−	0.924495i	$-0.624487\pi$
$79$	39.9006	−	109.626i	0.505071	−	1.38767i	0.886266	−	0.463177i	$-0.153291\pi$
$80$	−2.24010	−	2.60268i	−0.0280012	−	0.0325334i
$81$	−39.8359	+	70.5273i	−0.491802	+	0.870707i
$82$	−34.5616	+	22.1707i	−0.421483	+	0.270375i
$83$	38.5038	−	105.788i	0.463901	−	1.27456i	−0.458628	−	0.888628i	$-0.651659\pi$
$83$	38.5038	−	105.788i	0.463901	−	1.27456i	0.922529	−	0.385928i	$-0.126119\pi$
$84$	−113.074	+	80.6381i	−1.34612	+	0.959977i
$85$	0.281624	+	0.236311i	0.00331322	+	0.00278012i
$86$	84.4788	−	35.3029i	0.982312	−	0.410498i
$87$	−19.8642	+	16.7481i	−0.228324	+	0.192506i
$88$	51.6222	−	57.4102i	0.586616	−	0.652389i
$89$	59.4575	+	102.983i	0.668061	+	1.15712i	0.978446	+	0.206505i	$0.0662089\pi$
$89$	59.4575	+	102.983i	0.668061	+	1.15712i	−0.310384	+	0.950611i	$0.600458\pi$
$90$	3.24177	−	2.10121i	0.0360197	−	0.0233468i
$91$	−199.612	−	115.246i	−2.19354	−	1.26644i
$92$	−31.8032	+	121.738i	−0.345687	+	1.32324i
$93$	−0.162789	−	0.443995i	−0.00175042	−	0.00477414i
$94$	−59.1506	−	45.0941i	−0.629262	−	0.479724i
$95$	0.448295	+	1.23168i	0.00471889	+	0.0129651i
$96$	−53.0321	−	80.0225i	−0.552418	−	0.833567i
$97$	−4.27138	−	24.2242i	−0.0440349	−	0.249734i	0.954842	−	0.297114i	$-0.0960241\pi$
$97$	−4.27138	−	24.2242i	−0.0440349	−	0.249734i	−0.998877	+	0.0473796i	$0.984913\pi$
$98$	−7.94247	−	169.706i	−0.0810456	−	1.73169i
$99$	56.1440	+	66.2720i	0.567111	+	0.669414i
$100$	99.3794	−	9.32261i	0.993794	−	0.0932261i
$101$	36.2218	−	30.3937i	0.358632	−	0.300928i	−0.445613	−	0.895226i	$-0.647014\pi$
$101$	36.2218	−	30.3937i	0.358632	−	0.300928i	0.804245	+	0.594298i	$0.202570\pi$
$102$	6.98501	+	7.53922i	0.0684805	+	0.0739139i
$103$	52.3436	+	9.22958i	0.508190	+	0.0896076i	0.421864	−	0.906659i	$-0.361376\pi$
$103$	52.3436	+	9.22958i	0.508190	+	0.0896076i	0.0863264	+	0.996267i	$0.472487\pi$
$104$	84.3376	−	135.171i	0.810939	−	1.29973i
$105$	0.0175879	+	7.45174i	0.000167504	+	0.0709689i
$106$	−192.158	+	43.2328i	−1.81282	+	0.407856i
$107$			31.1755i			0.291360i	0.989332	+	0.145680i	$0.0465369\pi$
$107$			31.1755i			0.291360i	−0.989332	+	0.145680i	$0.953463\pi$
$108$	97.2633	−	46.9453i	0.900586	−	0.434678i
$109$	62.5881			0.574203			0.287101	−	0.957900i	$-0.407308\pi$
$109$	62.5881			0.574203			0.287101	+	0.957900i	$0.407308\pi$
$110$	−0.909277	−	4.04150i	−0.00826615	−	0.0367409i
$111$	72.5973	+	125.060i	0.654030	+	1.12666i
$112$	185.161	−	2.32132i	1.65323	−	0.0207260i
$113$	22.6665	−	128.548i	0.200589	−	1.13760i	−0.703643	−	0.710554i	$-0.748445\pi$
$113$	22.6665	−	128.548i	0.200589	−	1.13760i	0.904232	−	0.427042i	$-0.140444\pi$
$114$	8.12742	+	35.7303i	0.0712932	+	0.313423i
$115$	4.33953	+	5.17166i	0.0377351	+	0.0449709i
$116$	34.4917	−	3.23560i	0.297342	−	0.0278931i
$117$	137.848	+	114.564i	1.17819	+	0.979176i
$118$	25.1744	−	1.17820i	0.213342	−	0.00998471i
$119$	−19.5236	+	3.44253i	−0.164063	+	0.0289288i
$120$	−5.14830	−	0.164137i	−0.0429025	−	0.00136781i
$121$	−26.1823	+	9.52958i	−0.216383	+	0.0787569i
$122$	99.4398	−	130.437i	0.815080	−	1.06915i
$123$	−10.5522	+	60.6816i	−0.0857901	+	0.493346i
$124$	−0.159372	+	0.610056i	−0.00128526	+	0.00491980i
$125$	5.36059	−	9.28482i	0.0428847	−	0.0742785i
$126$	−25.5685	+	206.748i	−0.202925	+	1.64086i
$127$	26.2396	−	15.1494i	0.206611	−	0.119287i	−0.393124	−	0.919485i	$-0.628606\pi$
$127$	26.2396	−	15.1494i	0.206611	−	0.119287i	0.599735	+	0.800198i	$0.295273\pi$
$128$	−2.77676	+	127.970i	−0.0216934	+	0.999765i
$129$	46.6676	−	129.166i	0.361764	−	1.00129i
$130$	−3.29614	−	7.88757i	−0.0253549	−	0.0606736i
$131$	−118.464	+	141.179i	−0.904302	+	1.07770i	0.0923324	+	0.995728i	$0.470568\pi$
$131$	−118.464	+	141.179i	−0.904302	+	1.07770i	−0.996634	+	0.0819767i	$0.973877\pi$
$132$	−11.0885	−	115.277i	−0.0840037	−	0.873312i
$133$	−66.4186	−	24.1744i	−0.499388	−	0.181762i
$134$	−57.4483	−	89.5551i	−0.428718	−	0.668322i
$135$	0.965820	−	5.71372i	0.00715422	−	0.0423239i
$136$	−1.91633	−	13.5689i	−0.0140907	−	0.0997712i
$137$	−23.6048	−	8.59145i	−0.172298	−	0.0627113i	0.254431	−	0.967091i	$-0.418112\pi$
$137$	−23.6048	−	8.59145i	−0.172298	−	0.0627113i	−0.426729	+	0.904380i	$0.640334\pi$
$138$	102.281	+	158.618i	0.741164	+	1.14941i
$139$	5.61100	−	6.68693i	0.0403669	−	0.0481074i	−0.745483	−	0.666524i	$-0.767781\pi$
$139$	5.61100	−	6.68693i	0.0403669	−	0.0481074i	0.785850	+	0.618417i	$0.212226\pi$
$140$	5.64775	−	8.17439i	0.0403410	−	0.0583885i
$141$	−109.828	+	19.6330i	−0.778921	+	0.139241i
$142$	−144.530	−	45.0727i	−1.01782	−	0.317413i
$143$	166.450	−	96.1000i	1.16399	−	0.672028i
$144$	−142.223	−	22.5545i	−0.987658	−	0.156629i
$145$	0.929394	−	1.60976i	0.00640962	−	0.0111018i
$146$	−36.3086	−	39.3755i	−0.248689	−	0.269695i
$147$	−195.603	−	163.345i	−1.33063	−	1.11119i
$148$	15.5999	−	192.173i	0.105404	−	1.29847i
$149$	−9.12132	+	3.31989i	−0.0612169	+	0.0222811i	−0.372447	−	0.928053i	$-0.621481\pi$
$149$	−9.12132	+	3.31989i	−0.0612169	+	0.0222811i	0.311230	+	0.950335i	$0.399259\pi$
$150$	90.4920	−	119.283i	0.603280	−	0.795218i
$151$	92.5096	−	16.3119i	0.612646	−	0.108026i	0.141289	−	0.989968i	$-0.454875\pi$
$151$	92.5096	−	16.3119i	0.612646	−	0.108026i	0.471357	+	0.881942i	$0.343764\pi$
$152$	18.2717	−	45.3120i	0.120208	−	0.298105i
$153$	15.4163	−	0.0727728i	0.100760	−	0.000475639i
$154$	198.468	+	102.527i	1.28876	+	0.665759i
$155$	0.0217463	+	0.0259163i	0.000140299	+	0.000167202i
$156$	−63.8436	−	230.301i	−0.409254	−	1.47629i
$157$	−23.4101	+	132.765i	−0.149109	+	0.845639i	0.814867	+	0.579649i	$0.196810\pi$
$157$	−23.4101	+	132.765i	−0.149109	+	0.845639i	−0.963976	+	0.265991i	$0.914301\pi$
$158$	−29.7297	+	231.422i	−0.188163	+	1.46469i
$159$	−147.117	+	256.209i	−0.925264	+	1.61138i
$160$	5.51350	+	4.09501i	0.0344594	+	0.0255938i
$161$	−364.055			−2.26121
$162$	46.7677	−	155.102i	0.288689	−	0.957423i
$163$			202.543i			1.24260i	0.783575	+	0.621298i	$0.213394\pi$
$163$			202.543i			1.24260i	−0.783575	+	0.621298i	$0.786606\pi$
$164$	57.7046	−	58.4326i	0.351857	−	0.356296i
$165$	−5.38861	−	3.09418i	−0.0326583	−	0.0187526i
$166$	−28.6889	+	223.320i	−0.172824	+	1.34530i
$167$	−147.033	−	25.9260i	−0.880440	−	0.155245i	−0.284887	−	0.958561i	$-0.591956\pi$
$167$	−147.033	−	25.9260i	−0.880440	−	0.155245i	−0.595553	+	0.803316i	$0.703067\pi$
$168$	185.233	−	206.982i	1.10258	−	1.23204i
$169$	174.373	−	146.316i	1.03179	−	0.865776i
$170$	−0.653251	−	0.337463i	−0.00384266	−	0.00198508i
$171$	47.7298	+	27.2572i	0.279122	+	0.159399i
$172$	−149.339	+	105.970i	−0.868252	+	0.616103i
$173$	54.2893	+	307.890i	0.313811	+	1.77971i	0.578809	+	0.815463i	$0.303518\pi$
$173$	54.2893	+	307.890i	0.313811	+	1.77971i	−0.264998	+	0.964249i	$0.585371\pi$
$174$	31.4071	−	41.3995i	0.180501	−	0.237928i
$175$	98.7769	+	271.387i	0.564439	+	1.55078i
$176$	−75.5238	+	134.682i	−0.429112	+	0.765240i
$177$	24.2308	−	29.0160i	0.136897	−	0.163932i
$178$	−161.224	−	174.842i	−0.905754	−	0.982259i
$179$	23.2554	+	13.4265i	0.129919	+	0.0750086i	0.563551	−	0.826081i	$-0.309435\pi$
$179$	23.2554	+	13.4265i	0.129919	+	0.0750086i	−0.433632	+	0.901090i	$0.642768\pi$
$180$	−5.40300	+	5.52307i	−0.0300167	+	0.0306837i
$181$	−144.044	−	249.492i	−0.795823	−	1.37841i	−0.922315	−	0.386439i	$-0.873705\pi$
$181$	−144.044	−	249.492i	−0.795823	−	1.37841i	0.126492	−	0.991968i	$-0.459628\pi$
$182$	440.081	+	137.242i	2.41803	+	0.754077i
$183$	−43.2940	−	242.188i	−0.236579	−	1.32343i
$184$	8.61251	−	251.500i	0.0468071	−	1.36685i
$185$	−7.92475	−	6.64966i	−0.0428365	−	0.0359441i
$186$	0.512550	+	0.794871i	0.00275564	+	0.00427350i
$187$	5.65401	−	15.5343i	0.0302353	−	0.0830709i
$188$	135.212	+	62.0218i	0.719215	+	0.329903i
$189$	202.551	+	237.949i	1.07170	+	1.25899i
$190$	−1.41543	−	2.20649i	−0.00744962	−	0.0116131i
$191$	77.1124	−	211.865i	0.403730	−	1.10924i	−0.556699	−	0.830714i	$-0.687932\pi$
$191$	77.1124	−	211.865i	0.403730	−	1.10924i	0.960429	−	0.278525i	$-0.0898454\pi$
$192$	138.607	+	132.861i	0.721913	+	0.691984i
$193$	−157.892	−	132.487i	−0.818095	−	0.686463i	0.134430	−	0.990923i	$-0.457080\pi$
$193$	−157.892	−	132.487i	−0.818095	−	0.686463i	−0.952525	+	0.304460i	$0.901524\pi$
$194$	18.9688	+	45.3918i	0.0977772	+	0.233978i
$195$	−12.0599	−	4.35723i	−0.0618456	−	0.0223448i
$196$	89.9979	+	327.648i	0.459173	+	1.67167i
$197$	−63.0398	−	109.188i	−0.319999	−	0.554255i	0.660488	−	0.750836i	$-0.270349\pi$
$197$	−63.0398	−	109.188i	−0.319999	−	0.554255i	−0.980487	+	0.196581i	$0.937016\pi$
$198$	−138.643	−	104.665i	−0.700216	−	0.528609i
$199$	−64.5454	−	37.2653i	−0.324348	−	0.187263i	0.328981	−	0.944337i	$-0.393295\pi$
$199$	−64.5454	−	37.2653i	−0.324348	−	0.187263i	−0.653329	+	0.757074i	$0.726628\pi$
$200$	−189.819	+	61.8177i	−0.949096	+	0.309089i
$201$	−157.237	−	27.3426i	−0.782272	−	0.136033i
$202$	−57.3343	+	75.2063i	−0.283833	+	0.372308i
$203$	34.2826	+	94.1906i	0.168880	+	0.463993i
$204$	−16.9390	−	11.6443i	−0.0830344	−	0.0570800i
$205$	−0.765152	−	4.33939i	−0.00373245	−	0.0211678i
$206$	−106.186	+	4.96965i	−0.515465	+	0.0241245i
$207$	279.031	+	47.8438i	1.34798	+	0.231129i
$208$	−105.222	+	300.774i	−0.505875	+	1.44603i
$209$	45.1497	−	37.8851i	0.216027	−	0.181269i
$210$	−3.30561	−	14.5323i	−0.0157410	−	0.0692014i
$211$	−26.9666	−	4.75493i	−0.127804	−	0.0225352i	0.109380	−	0.994000i	$-0.465113\pi$
$211$	−26.9666	−	4.75493i	−0.127804	−	0.0225352i	−0.237184	+	0.971465i	$0.576224\pi$
$212$	355.965	−	168.714i	1.67908	−	0.795820i
$213$	−196.400	+	114.010i	−0.922064	+	0.535260i
$214$	−13.6859	−	60.8304i	−0.0639529	−	0.284254i
$215$			9.82521i			0.0456986i
$216$	−169.174	+	134.299i	−0.783212	+	0.621755i
$217$	−1.82436			−0.00840718
$218$	−122.123	+	27.4760i	−0.560200	+	0.126036i
$219$	−80.3408	+	0.189624i	−0.366853	+	0.000865861i
$220$	3.54841	+	7.48671i	0.0161291	+	0.0340305i
$221$	5.92385	−	33.5958i	0.0268048	−	0.152017i
$222$	−196.555	−	212.150i	−0.885381	−	0.955629i
$223$	−25.4525	−	30.3332i	−0.114137	−	0.136023i	0.705951	−	0.708261i	$-0.250520\pi$
$223$	−25.4525	−	30.3332i	−0.114137	−	0.136023i	−0.820088	+	0.572238i	$0.806075\pi$
$224$	−360.273	+	85.8146i	−1.60836	+	0.383101i
$225$	−40.0425	−	220.987i	−0.177966	−	0.982164i
$226$	12.2047	+	260.777i	0.0540033	+	1.15388i
$227$	−367.121	+	64.7334i	−1.61727	+	0.285169i	−0.907750	−	0.419512i	$-0.862201\pi$
$227$	−367.121	+	64.7334i	−1.61727	+	0.285169i	−0.709524	+	0.704681i	$0.751090\pi$
$228$	−31.5439	−	66.1499i	−0.138350	−	0.290131i
$229$	270.130	−	98.3193i	1.17961	−	0.429342i	0.323544	−	0.946213i	$-0.395126\pi$
$229$	270.130	−	98.3193i	1.17961	−	0.429342i	0.856063	+	0.516871i	$0.172903\pi$
$230$	−10.7378	−	8.18603i	−0.0466859	−	0.0355914i
$231$	314.600	−	115.347i	1.36191	−	0.499337i
$232$	−65.8807	+	21.4551i	−0.283968	+	0.0924790i
$233$	−183.876	+	318.482i	−0.789166	+	1.36688i	0.137312	+	0.990528i	$0.456154\pi$
$233$	−183.876	+	318.482i	−0.789166	+	1.36688i	−0.926478	+	0.376348i	$0.877180\pi$
$234$	−319.265	−	163.025i	−1.36438	−	0.696686i
$235$	6.91234	−	3.99084i	0.0294142	−	0.0169823i
$236$	−48.6037	+	13.3504i	−0.205948	+	0.0565695i
$237$	225.598	+	267.572i	0.951891	+	1.12900i
$238$	36.5836	−	15.2879i	0.153713	−	0.0642350i
$239$	114.381	−	136.314i	0.478581	−	0.570350i	−0.471694	−	0.881762i	$-0.656357\pi$
$239$	114.381	−	136.314i	0.478581	−	0.570350i	0.950275	+	0.311412i	$0.100802\pi$
$240$	10.1175	−	1.93982i	0.0421564	−	0.00808257i
$241$	327.606	+	119.239i	1.35936	+	0.494766i	0.915856	−	0.401507i	$-0.131513\pi$
$241$	327.606	+	119.239i	1.35936	+	0.494766i	0.443503	+	0.896273i	$0.353736\pi$
$242$	46.9041	−	30.0883i	0.193819	−	0.124332i
$243$	−123.975	−	208.996i	−0.510185	−	0.860065i
$244$	−136.768	+	298.165i	−0.560525	+	1.22199i
$245$	17.1317	+	6.23544i	0.0699254	+	0.0254508i
$246$	−6.04931	−	123.036i	−0.0245907	−	0.500146i
$247$	78.1804	−	93.1718i	0.316520	−	0.377214i
$248$	0.0431591	−	1.26032i	0.000174029	−	0.00508194i
$249$	217.700	+	258.205i	0.874298	+	1.03697i
$250$	−6.38372	+	20.4701i	−0.0255349	+	0.0818802i
$251$	−110.893	+	64.0244i	−0.441806	+	0.255077i	−0.704364	−	0.709839i	$-0.748768\pi$
$251$	−110.893	+	64.0244i	−0.441806	+	0.255077i	0.262557	+	0.964916i	$0.415434\pi$
$252$	−40.8717	−	414.636i	−0.162189	−	1.64538i
$253$	151.787	−	262.903i	0.599949	−	1.03914i
$254$	−44.5488	+	41.0790i	−0.175389	+	0.161729i
$255$	−1.03550	+	0.379660i	−0.00406077	+	0.00148886i
$256$	−50.7603	−	250.917i	−0.198282	−	0.980145i
$257$	−251.532	+	91.5503i	−0.978725	+	0.356227i	−0.781344	−	0.624100i	$-0.785466\pi$
$257$	−251.532	+	91.5503i	−0.978725	+	0.356227i	−0.197381	+	0.980327i	$0.563244\pi$
$258$	−34.3556	+	272.519i	−0.133161	+	1.05627i
$259$	549.383	−	96.8710i	2.12117	−	0.374019i
$260$	9.89413	+	13.9434i	0.0380543	+	0.0536286i
$261$	−13.8976	−	76.6981i	−0.0532474	−	0.293862i
$262$	169.172	−	327.478i	0.645694	−	1.24992i
$263$	−167.815	−	199.995i	−0.638081	−	0.760436i	0.345985	−	0.938240i	$-0.387545\pi$
$263$	−167.815	−	199.995i	−0.638081	−	0.760436i	−0.984066	+	0.177805i	$0.943101\pi$
$264$	72.2424	+	220.064i	0.273646	+	0.833576i
$265$	3.67024	−	20.8150i	0.0138500	−	0.0785471i
$266$	140.210	+	18.0122i	0.527106	+	0.0677149i
$267$	−356.744	+	0.842001i	−1.33612	+	0.00315356i
$268$	151.409	+	149.523i	0.564959	+	0.557920i
$269$	316.834			1.17782			0.588910	−	0.808199i	$-0.299557\pi$
$269$	316.834			1.17782			0.588910	+	0.808199i	$0.299557\pi$
$270$	0.623772	+	11.5728i	0.00231027	+	0.0428621i
$271$		−	175.899i		−	0.649072i	−0.945873	−	0.324536i	$-0.894792\pi$
$271$		−	175.899i		−	0.649072i	0.945873	−	0.324536i	$-0.105208\pi$
$272$	9.69588	+	25.6347i	0.0356466	+	0.0942452i
$273$	598.018	−	347.151i	2.19054	−	1.27161i
$274$	49.8300	+	6.40143i	0.181861	+	0.0233629i
$275$	−237.166	−	41.8188i	−0.862422	−	0.152068i
$276$	−269.206	−	264.600i	−0.975383	−	0.958694i
$277$	12.2521	−	10.2807i	0.0442313	−	0.0371144i	−0.620404	−	0.784282i	$-0.713031\pi$
$277$	12.2521	−	10.2807i	0.0442313	−	0.0371144i	0.664635	+	0.747168i	$0.268587\pi$
$278$	−8.01279	+	15.5109i	−0.0288230	+	0.0557947i
$279$	1.39829	+	0.239755i	0.00501178	+	0.000859338i
$280$	−7.43150	+	18.4294i	−0.0265411	+	0.0658194i
$281$	−55.2824	−	313.522i	−0.196734	−	1.11574i	−0.909927	−	0.414768i	$-0.863863\pi$
$281$	−55.2824	−	313.522i	−0.196734	−	1.11574i	0.713193	−	0.700968i	$-0.247248\pi$
$282$	205.680	−	86.5225i	0.729362	−	0.306817i
$283$	70.4466	+	193.550i	0.248928	+	0.683924i	0.999726	+	0.0233925i	$0.00744673\pi$
$283$	70.4466	+	193.550i	0.248928	+	0.683924i	−0.750798	+	0.660531i	$0.770331\pi$
$284$	301.798	+	24.4988i	1.06267	+	0.0862632i
$285$	−3.87404	−	0.673674i	−0.0135931	−	0.00236377i
$286$	−282.594	+	260.584i	−0.988091	+	0.911132i
$287$	205.778	+	118.806i	0.716998	+	0.413959i
$288$	287.410	−	18.4263i	0.997951	−	0.0639801i
$289$	143.033	+	247.740i	0.494924	+	0.857233i
$290$	−1.10678	+	3.54900i	−0.00381648	+	0.0122379i
$291$	69.4028	+	25.0752i	0.238498	+	0.0861691i
$292$	88.1320	+	60.8911i	0.301822	+	0.208531i
$293$	74.1234	+	62.1969i	0.252981	+	0.212276i	0.760455	−	0.649391i	$-0.224976\pi$
$293$	74.1234	+	62.1969i	0.252981	+	0.212276i	−0.507474	+	0.861667i	$0.669421\pi$
$294$	453.374	+	232.854i	1.54209	+	0.792022i
$295$	−0.924972	+	2.54134i	−0.00313550	+	0.00861471i
$296$	53.9245	+	381.821i	0.182177	+	1.28994i
$297$	−256.285	+	47.0635i	−0.862914	+	0.158463i
$298$	16.3403	−	10.4821i	0.0548333	−	0.0351748i
$299$	214.262	−	588.681i	0.716596	−	1.96883i
$300$	−124.206	+	272.473i	−0.414019	+	0.908244i
$301$	−405.870	−	340.566i	−1.34841	−	1.13145i
$302$	−173.346	+	72.4397i	−0.573994	+	0.239866i
$303$	24.9621	+	139.639i	0.0823833	+	0.460855i
$304$	−15.7603	+	96.4352i	−0.0518431	+	0.317221i
$305$	8.80046	+	15.2428i	0.0288540	+	0.0499765i
$306$	−30.0487	+	6.90970i	−0.0981985	+	0.0225807i
$307$	234.193	+	135.212i	0.762845	+	0.440429i	0.830316	−	0.557293i	$-0.188160\pi$
$307$	234.193	+	135.212i	0.762845	+	0.440429i	−0.0674715	+	0.997721i	$0.521493\pi$
$308$	−432.266	−	112.926i	−1.40346	−	0.366643i
$309$	−102.206	+	122.390i	−0.330764	+	0.396083i
$310$	−0.0538091	−	0.0410219i	−0.000173578	−	0.000132329i
$311$	6.59888	+	18.1303i	0.0212183	+	0.0582967i	0.949850	−	0.312707i	$-0.101236\pi$
$311$	6.59888	+	18.1303i	0.0212183	+	0.0582967i	−0.928631	+	0.371004i	$0.879014\pi$
$312$	225.674	+	421.341i	0.723315	+	1.35045i
$313$	84.3023	+	478.102i	0.269337	+	1.52748i	0.756396	+	0.654114i	$0.226959\pi$
$313$	84.3023	+	478.102i	0.269337	+	1.52748i	−0.487059	+	0.873369i	$0.661930\pi$
$314$	−12.6051	−	269.332i	−0.0401437	−	0.857746i
$315$	−19.4128	−	11.0861i	−0.0616279	−	0.0351941i
$316$	−43.5839	−	464.607i	−0.137924	−	1.47028i
$317$	420.029	−	352.446i	1.32501	−	1.11182i	0.339796	−	0.940499i	$-0.389642\pi$
$317$	420.029	−	352.446i	1.32501	−	1.11182i	0.985216	−	0.171318i	$-0.0548024\pi$
$318$	174.584	−	564.505i	0.549005	−	1.77517i
$319$	−82.3134	−	14.5141i	−0.258036	−	0.0454987i
$320$	−12.5558	−	5.56988i	−0.0392368	−	0.0174059i
$321$	−81.1064	−	46.5719i	−0.252668	−	0.145084i
$322$	710.354	−	159.819i	2.20607	−	0.496332i
$323$		−	10.4612i		−	0.0323876i
$324$	−23.1648	+	323.171i	−0.0714964	+	0.997441i
$325$	−496.970			−1.52914
$326$	−88.9157	−	395.207i	−0.272748	−	1.21229i
$327$	−93.4981	+	162.830i	−0.285927	+	0.497950i
$328$	−86.9430	+	139.347i	−0.265070	+	0.424839i
$329$	−74.7406	+	423.875i	−0.227175	+	1.28837i
$330$	11.8727	+	3.67187i	0.0359780	+	0.0111269i
$331$	−349.160	−	416.112i	−1.05486	−	1.25714i	−0.965297	−	0.261156i	$-0.915896\pi$
$331$	−349.160	−	416.112i	−1.05486	−	1.25714i	−0.0895664	−	0.995981i	$-0.528548\pi$
$332$	−42.0581	−	448.341i	−0.126681	−	1.35043i
$333$	−433.807	+	2.04779i	−1.30272	+	0.00614952i
$334$	298.277	−	13.9598i	0.893045	−	0.0417957i
$335$	11.2441	−	1.98264i	0.0335646	−	0.00591834i
$336$	−270.567	+	485.185i	−0.805258	+	1.44400i
$337$	187.444	−	68.2240i	0.556214	−	0.202445i	−0.0485915	−	0.998819i	$-0.515473\pi$
$337$	187.444	−	68.2240i	0.556214	−	0.202445i	0.604805	+	0.796374i	$0.293251\pi$
$338$	−276.008	+	362.045i	−0.816593	+	1.07114i
$339$	300.572	+	251.003i	0.886643	+	0.740422i
$340$	1.42279	+	0.371692i	0.00418467	+	0.00109321i
$341$	0.760637	−	1.31746i	0.00223061	−	0.00386352i
$342$	−105.097	−	32.2318i	−0.307302	−	0.0942449i
$343$	−360.283	+	208.010i	−1.05039	+	0.606442i
$344$	244.875	−	272.330i	0.711845	−	0.791658i
$345$	−19.9373	+	3.56402i	−0.0577893	+	0.0103305i
$346$	−241.094	−	576.930i	−0.696802	−	1.66743i
$347$	−19.9944	+	23.8284i	−0.0576208	+	0.0686697i	−0.794085	−	0.607807i	$-0.792050\pi$
$347$	−19.9944	+	23.8284i	−0.0576208	+	0.0686697i	0.736464	+	0.676477i	$0.236494\pi$
$348$	−43.1081	+	94.5675i	−0.123874	+	0.271746i
$349$	−181.722	−	66.1414i	−0.520694	−	0.189517i	0.0682846	−	0.997666i	$-0.478247\pi$
$349$	−181.722	−	66.1414i	−0.520694	−	0.189517i	−0.588978	+	0.808149i	$0.700470\pi$
$350$	−311.874	−	486.175i	−0.891069	−	1.38907i
$351$	−503.975	+	187.484i	−1.43583	+	0.534142i
$352$	88.2388	−	295.950i	0.250678	−	0.840768i
$353$	−247.782	−	90.1852i	−0.701932	−	0.255482i	−0.0336962	−	0.999432i	$-0.510728\pi$
$353$	−247.782	−	90.1852i	−0.701932	−	0.255482i	−0.668235	+	0.743950i	$0.732950\pi$
$354$	−34.5419	+	67.2540i	−0.0975760	+	0.189983i
$355$	10.4429	−	12.4454i	0.0294167	−	0.0350575i
$356$	391.340	+	270.380i	1.09927	+	0.759493i
$357$	20.2094	−	55.9353i	0.0566090	−	0.156682i
$358$	−51.2708	−	15.9891i	−0.143215	−	0.0446624i
$359$	−250.254	+	144.484i	−0.697086	+	0.402463i	−0.806261	−	0.591560i	$-0.798512\pi$
$359$	−250.254	+	144.484i	−0.697086	+	0.402463i	0.109175	+	0.994023i	$0.465179\pi$
$360$	8.11787	−	13.1487i	0.0225496	−	0.0365241i
$361$	−161.851	+	280.335i	−0.448342	+	0.776550i
$362$	390.588	+	423.580i	1.07897	+	1.17011i
$363$	14.3206	−	82.3520i	0.0394506	−	0.226865i
$364$	−918.946	−	74.5964i	−2.52458	−	0.204935i
$365$	5.40101	−	1.96581i	0.0147973	−	0.00538577i
$366$	190.796	+	453.558i	0.521301	+	1.23923i
$367$	−443.020	+	78.1163i	−1.20714	+	0.212851i	−0.740782	−	0.671746i	$-0.765545\pi$
$367$	−443.020	+	78.1163i	−1.20714	+	0.212851i	−0.466356	+	0.884597i	$0.654434\pi$
$368$	93.6027	+	494.514i	0.254355	+	1.34379i
$369$	−142.106	−	118.103i	−0.385112	−	0.320061i
$370$	18.3822	+	9.49604i	0.0496815	+	0.0256650i
$371$	732.629	+	873.113i	1.97474	+	2.35340i
$372$	−1.34905	−	1.32596i	−0.00362647	−	0.00356442i
$373$	−40.7778	+	231.262i	−0.109324	+	0.620006i	0.880081	+	0.474824i	$0.157488\pi$
$373$	−40.7778	+	231.262i	−0.109324	+	0.620006i	−0.989405	+	0.145183i	$0.953623\pi$
$374$	−4.21276	+	32.7929i	−0.0112641	+	0.0876816i
$375$	16.1475	+	27.8164i	0.0430599	+	0.0741771i
$376$	−291.057	−	61.6607i	−0.774088	−	0.163991i
$377$	−172.484			−0.457517
$378$	−499.682	−	375.373i	−1.32191	−	0.993049i
$379$		−	24.5603i		−	0.0648028i	−0.999475	−	0.0324014i	$-0.989685\pi$
$379$		−	24.5603i		−	0.0648028i	0.999475	−	0.0324014i	$-0.0103155\pi$
$380$	3.73046	+	3.68399i	0.00981700	+	0.00969470i
$381$	0.214537	+	90.8963i	0.000563090	+	0.238573i
$382$	−57.4559	+	447.248i	−0.150408	+	1.17081i
$383$	586.109	+	103.347i	1.53031	+	0.269835i	0.874475	−	0.485070i	$-0.161206\pi$
$383$	586.109	+	103.347i	1.53031	+	0.269835i	0.655835	+	0.754905i	$0.272317\pi$
$384$	−328.780	−	198.394i	−0.856197	−	0.516650i
$385$	−18.3634	+	15.4087i	−0.0476972	+	0.0400227i
$386$	366.245	+	189.199i	0.948822	+	0.490152i
$387$	266.324	+	314.367i	0.688176	+	0.812317i
$388$	−56.9392	−	80.2424i	−0.146751	−	0.206810i
$389$	−57.6262	−	326.814i	−0.148139	−	0.840139i	−0.964793	−	0.263011i	$-0.915284\pi$
$389$	−57.6262	−	326.814i	−0.148139	−	0.840139i	0.816654	−	0.577128i	$-0.195827\pi$
$390$	25.4444	+	3.20769i	0.0652420	+	0.00822486i
$391$	−18.4288	−	50.6327i	−0.0471325	−	0.129495i
$392$	−319.443	−	599.806i	−0.814904	−	1.53012i
$393$	−190.325	−	519.099i	−0.484288	−	1.32086i
$394$	170.938	+	185.377i	0.433853	+	0.470499i
$395$	−21.6836	−	12.5190i	−0.0548952	−	0.0316938i
$396$	316.471	+	143.360i	0.799169	+	0.362021i
$397$	−42.7323	−	74.0146i	−0.107638	−	0.186435i	0.807175	−	0.590312i	$-0.200995\pi$
$397$	−42.7323	−	74.0146i	−0.107638	−	0.186435i	−0.914813	+	0.403878i	$0.867662\pi$
$398$	142.302	+	44.3778i	0.357542	+	0.111502i
$399$	162.113	−	136.682i	0.406297	−	0.342561i
$400$	343.242	−	203.950i	0.858106	−	0.509876i
$401$	129.017	+	108.258i	0.321738	+	0.269970i	0.789323	−	0.613978i	$-0.210432\pi$
$401$	129.017	+	108.258i	0.321738	+	0.269970i	−0.467586	+	0.883948i	$0.654876\pi$
$402$	318.807	−	15.6748i	0.793053	−	0.0389921i
$403$	1.07371	−	2.95000i	0.00266430	−	0.00732011i
$404$	78.8568	−	171.914i	0.195190	−	0.425530i
$405$	13.4221	+	11.0482i	0.0331409	+	0.0272795i
$406$	−108.242	−	168.737i	−0.266607	−	0.415609i
$407$	−159.101	+	437.126i	−0.390911	+	1.07402i
$408$	38.1637	+	15.2845i	0.0935384	+	0.0374621i
$409$	−106.572	−	89.4245i	−0.260567	−	0.218642i	0.503139	−	0.864205i	$-0.332178\pi$
$409$	−106.572	−	89.4245i	−0.260567	−	0.218642i	−0.763707	+	0.645563i	$0.776623\pi$
$410$	3.39796	+	8.13124i	0.00828772	+	0.0198323i
$411$	57.6140	−	48.5761i	0.140180	−	0.118190i
$412$	205.011	−	56.3121i	0.497599	−	0.136680i
$413$	−72.9187	−	126.299i	−0.176559	−	0.305808i
$414$	−565.457	+	29.1398i	−1.36584	+	0.0703861i
$415$	−20.9245	−	12.0808i	−0.0504205	−	0.0291103i
$416$	73.2730	−	633.070i	0.176137	−	1.52180i
$417$	9.01471	+	24.5870i	0.0216180	+	0.0589616i
$418$	−71.4659	+	93.7430i	−0.170971	+	0.224266i
$419$	−48.4909	−	133.228i	−0.115730	−	0.317966i	0.868281	−	0.496073i	$-0.165225\pi$
$419$	−48.4909	−	133.228i	−0.115730	−	0.317966i	−0.984011	+	0.178107i	$0.943003\pi$
$420$	12.8296	+	26.9047i	0.0305467	+	0.0640587i
$421$	18.5532	+	105.220i	0.0440694	+	0.249930i	0.998882	−	0.0472796i	$-0.0150552\pi$
$421$	18.5532	+	105.220i	0.0440694	+	0.249930i	−0.954812	+	0.297209i	$0.903944\pi$
$422$	54.7053	−	2.56028i	0.129633	−	0.00606702i
$423$	112.990	−	315.058i	0.267117	−	0.744818i
$424$	−620.504	+	485.466i	−1.46345	+	1.14497i
$425$	−32.7443	+	27.4757i	−0.0770454	+	0.0646488i
$426$	333.170	−	308.679i	0.782089	−	0.724598i
$427$	−934.714	−	164.815i	−2.18903	−	0.385984i
$428$	53.4087	+	112.686i	0.124787	+	0.263284i
$429$	1.36091	+	576.598i	0.00317229	+	1.34405i
$430$	−4.31323	−	19.1712i	−0.0100308	−	0.0445842i
$431$			560.222i			1.29982i	0.760012	+	0.649910i	$0.225193\pi$
$431$			560.222i			1.29982i	−0.760012	+	0.649910i	$0.774807\pi$
$432$	271.139	−	336.314i	0.627638	−	0.778506i
$433$	381.789			0.881731			0.440865	−	0.897573i	$-0.354672\pi$
$433$	381.789			0.881731			0.440865	+	0.897573i	$0.354672\pi$
$434$	3.55973	−	0.800887i	0.00820215	−	0.00184536i
$435$	2.79957	+	4.82268i	0.00643580	+	0.0110866i
$436$	226.229	−	107.224i	0.518873	−	0.245926i
$437$	33.3589	−	189.188i	0.0763362	−	0.432924i
$438$	156.680	−	35.6393i	0.357716	−	0.0813683i
$439$	310.625	+	370.189i	0.707575	+	0.843255i	0.993361	−	0.115038i	$-0.0366991\pi$
$439$	310.625	+	370.189i	0.707575	+	0.843255i	−0.285786	+	0.958293i	$0.592255\pi$
$440$	−10.2104	−	13.0505i	−0.0232054	−	0.0296603i
$441$	717.165	−	264.867i	1.62622	−	0.600606i
$442$	3.18968	+	68.1536i	0.00721648	+	0.154194i
$443$	−310.302	+	54.7146i	−0.700456	+	0.123509i	−0.512524	−	0.858673i	$-0.671289\pi$
$443$	−310.302	+	54.7146i	−0.700456	+	0.123509i	−0.187932	+	0.982182i	$0.560178\pi$
$444$	476.655	+	327.665i	1.07355	+	0.737985i
$445$	23.9825	−	8.72893i	0.0538933	−	0.0196156i
$446$	62.9798	+	48.0133i	0.141210	+	0.107653i
$447$	4.98895	−	28.6896i	0.0111610	−	0.0641825i
$448$	665.301	−	325.602i	1.48505	−	0.726791i
$449$	408.322	−	707.234i	0.909402	−	1.57513i	0.0945056	−	0.995524i	$-0.469873\pi$
$449$	408.322	−	707.234i	0.909402	−	1.57513i	0.814897	−	0.579606i	$-0.196794\pi$
$450$	175.144	+	413.617i	0.389210	+	0.919149i
$451$	−171.592	+	99.0687i	−0.380470	+	0.219665i
$452$	−138.295	−	503.478i	−0.305961	−	1.11389i
$453$	−95.7595	+	265.042i	−0.211390	+	0.585081i
$454$	687.919	−	287.474i	1.51524	−	0.633204i
$455$	−31.7978	+	37.8951i	−0.0698852	+	0.0832859i
$456$	90.5888	+	115.226i	0.198660	+	0.252688i
$457$	48.2527	+	17.5625i	0.105586	+	0.0384301i	0.394273	−	0.918993i	$-0.370996\pi$
$457$	48.2527	+	17.5625i	0.105586	+	0.0384301i	−0.288687	+	0.957424i	$0.593219\pi$
$458$	−483.923	+	310.429i	−1.05660	+	0.677793i
$459$	−22.8405	+	40.2159i	−0.0497615	+	0.0876164i
$460$	24.5454	+	11.2590i	0.0533596	+	0.0244760i
$461$	559.359	+	203.590i	1.21336	+	0.441627i	0.867868	−	0.496795i	$-0.165490\pi$
$461$	559.359	+	203.590i	1.21336	+	0.441627i	0.345492	+	0.938422i	$0.387712\pi$
$462$	−563.220	+	363.176i	−1.21909	+	0.786096i
$463$	277.457	−	330.660i	0.599259	−	0.714169i	−0.378098	−	0.925766i	$-0.623422\pi$
$463$	277.457	−	330.660i	0.599259	−	0.714169i	0.977357	+	0.211597i	$0.0678663\pi$
$464$	119.129	−	70.7852i	0.256744	−	0.152554i
$465$	−0.0999100	+	0.0178601i	−0.000214860	+	3.84088e-5i
$466$	218.970	−	702.151i	0.469894	−	1.50676i
$467$	654.186	−	377.694i	1.40083	−	0.808767i	0.406349	−	0.913718i	$-0.366802\pi$
$467$	654.186	−	377.694i	1.40083	−	0.808767i	0.994477	+	0.104951i	$0.0334685\pi$
$468$	694.526	+	177.942i	1.48403	+	0.380217i
$469$	−307.848	+	533.208i	−0.656392	+	1.13690i
$470$	−11.7356	+	10.8215i	−0.0249693	+	0.0230245i
$471$	−310.432	−	259.237i	−0.659091	−	0.550398i
$472$	88.9760	−	47.3865i	0.188509	−	0.100395i
$473$	415.161	−	151.106i	0.877719	−	0.319464i
$474$	−557.656	−	423.057i	−1.17649	−	0.892526i
$475$	−150.082	+	26.4636i	−0.315963	+	0.0557128i
$476$	−64.6715	+	45.8903i	−0.135865	+	0.0964081i
$477$	−446.782	−	765.482i	−0.936651	−	1.60478i
$478$	−163.342	+	316.192i	−0.341719	+	0.661489i
$479$	−379.355	−	452.098i	−0.791974	−	0.943837i	0.207434	−	0.978249i	$-0.433489\pi$
$479$	−379.355	−	452.098i	−0.791974	−	0.943837i	−0.999408	+	0.0344117i	$0.989044\pi$
$480$	−18.8900	+	8.22659i	−0.0393543	+	0.0171387i
$481$	−166.694	+	945.370i	−0.346558	+	1.96543i
$482$	−691.578	−	88.8439i	−1.43481	−	0.184323i
$483$	543.849	−	947.130i	1.12598	−	1.96093i
$484$	−78.3119	+	79.2998i	−0.161801	+	0.163843i
$485$	−5.27924			−0.0108850
$486$	333.652	+	353.373i	0.686526	+	0.727105i
$487$		−	474.186i		−	0.973688i	−0.873489	−	0.486844i	$-0.838148\pi$
$487$		−	474.186i		−	0.973688i	0.873489	−	0.486844i	$-0.161852\pi$
$488$	135.972	−	641.829i	0.278631	−	1.31522i
$489$	−526.938	−	302.572i	−1.07758	−	0.618756i
$490$	−36.1652	−	4.64598i	−0.0738065	−	0.00948159i
$491$	280.087	+	49.3868i	0.570441	+	0.100584i	0.451427	−	0.892308i	$-0.350915\pi$
$491$	280.087	+	49.3868i	0.570441	+	0.100584i	0.119015	+	0.992892i	$0.462026\pi$
$492$	65.8159	+	237.415i	0.133772	+	0.482551i
$493$	−11.3646	+	9.53602i	−0.0230519	+	0.0193428i
$494$	−111.646	+	216.120i	−0.226003	+	0.437490i
$495$	16.0997	−	9.39678i	0.0325247	−	0.0189834i
$496$	0.469063	+	2.47812i	0.000945692	+	0.00499620i
$497$	152.131	+	862.777i	0.306098	+	1.73597i
$498$	−538.133	−	408.246i	−1.08059	−	0.819772i
$499$	−128.475	−	352.983i	−0.257465	−	0.707380i	−0.999322	−	0.0368216i	$-0.988277\pi$
$499$	−128.475	−	352.983i	−0.257465	−	0.707380i	0.741857	−	0.670559i	$-0.233946\pi$
$500$	3.46980	−	42.7441i	0.00693960	−	0.0854883i
$501$	287.097	−	343.794i	0.573048	−	0.686215i
$502$	188.272	−	173.608i	0.375043	−	0.345832i
$503$	−461.157	−	266.249i	−0.916814	−	0.529323i	−0.0341967	−	0.999415i	$-0.510887\pi$
$503$	−461.157	−	266.249i	−0.916814	−	0.529323i	−0.882617	+	0.470092i	$0.844221\pi$
$504$	261.774	+	791.107i	0.519393	+	1.56966i
$505$	−5.07411	−	8.78861i	−0.0100477	−	0.0174032i
$506$	−180.757	+	579.617i	−0.357228	+	1.14549i
$507$	120.168	+	672.226i	0.237018	+	1.32589i
$508$	68.8912	−	99.7113i	0.135613	−	0.196282i
$509$	142.299	+	119.403i	0.279565	+	0.234583i	0.771778	−	0.635892i	$-0.219367\pi$
$509$	142.299	+	119.403i	0.279565	+	0.234583i	−0.492213	+	0.870475i	$0.663812\pi$
$510$	1.85382	−	1.19538i	0.00363493	−	0.00234388i
$511$	−106.006	+	291.250i	−0.207449	+	0.569962i
$512$	209.196	+	467.312i	0.408587	+	0.912719i
$513$	−142.214	+	83.4557i	−0.277221	+	0.162682i
$514$	450.606	−	289.057i	0.876666	−	0.562368i
$515$	3.90154	−	10.7194i	0.00757581	−	0.0208144i
$516$	−52.5992	−	546.827i	−0.101936	−	1.05974i
$517$	−274.940	−	230.702i	−0.531799	−	0.446232i
$518$	−1029.44	+	430.194i	−1.98734	+	0.830491i
$519$	−882.111	−	318.706i	−1.69964	−	0.614078i
$520$	−25.4268	−	22.8633i	−0.0488977	−	0.0439679i
$521$	87.3646	+	151.320i	0.167686	+	0.290441i	0.937606	−	0.347700i	$-0.113037\pi$
$521$	87.3646	+	151.320i	0.167686	+	0.290441i	−0.769920	+	0.638141i	$0.779704\pi$
$522$	60.7875	+	143.554i	0.116451	+	0.275008i
$523$	721.777	+	416.718i	1.38007	+	0.796784i	0.992167	−	0.124916i	$-0.0398662\pi$
$523$	721.777	+	416.718i	1.38007	+	0.796784i	0.387903	+	0.921700i	$0.373200\pi$
$524$	−186.331	+	713.249i	−0.355593	+	1.36116i
$525$	−853.603	−	148.437i	−1.62591	−	0.282737i
$526$	415.243	+	316.564i	0.789435	+	0.601833i
$527$	−0.0923506	−	0.253731i	−0.000175238	−	0.000481463i
$528$	−237.569	−	397.680i	−0.449941	−	0.753182i
$529$	−79.9609	−	453.481i	−0.151155	−	0.857242i
$530$	1.97623	+	42.2260i	0.00372874	+	0.0796716i
$531$	39.2907	+	106.385i	0.0739938	+	0.200349i
$532$	−281.489	+	26.4060i	−0.529115	+	0.0496353i
$533$	−313.220	+	262.823i	−0.587656	+	0.493102i
$534$	695.718	−	158.252i	1.30284	−	0.296352i
$535$	6.58927	+	1.16187i	0.0123164	+	0.00217171i
$536$	−361.073	−	225.284i	−0.673644	−	0.420307i
$537$	−69.6711	+	40.4442i	−0.129741	+	0.0753150i
$538$	−618.214	+	139.089i	−1.14910	+	0.258530i
$539$		−	819.793i		−	1.52095i
$540$	−6.29752	−	22.3072i	−0.0116621	−	0.0413097i
$541$	313.109			0.578760			0.289380	−	0.957214i	$-0.406551\pi$
$541$	313.109			0.578760			0.289380	+	0.957214i	$0.406551\pi$
$542$	77.2189	+	343.218i	0.142470	+	0.633243i
$543$	864.262	−	2.03987i	1.59164	−	0.00375666i
$544$	−30.1724	−	45.7626i	−0.0554640	−	0.0841225i
$545$	2.33257	−	13.2287i	0.00427995	−	0.0242728i
$546$	−1014.47	+	939.897i	−1.85801	+	1.72142i
$547$	372.771	+	444.251i	0.681482	+	0.812158i	0.990297	−	0.138964i	$-0.0443771\pi$
$547$	372.771	+	444.251i	0.681482	+	0.812158i	−0.308816	+	0.951122i	$0.599933\pi$
$548$	−100.040	+	9.38455i	−0.182554	+	0.0171251i
$549$	694.755	+	249.162i	1.26549	+	0.453848i
$550$	481.123	−	22.5172i	0.874769	−	0.0409404i
$551$	−52.0892	+	9.18473i	−0.0945358	+	0.0166692i
$552$	641.439	+	398.113i	1.16203	+	0.721220i
$553$	1268.76	−	461.790i	2.29432	−	0.835063i
$554$	−19.3933	+	25.4386i	−0.0350060	+	0.0459180i
$555$	29.1383	−	10.6834i	0.0525015	−	0.0192494i
$556$	8.82552	−	33.7829i	0.0158732	−	0.0607606i
$557$	−39.2530	+	67.9882i	−0.0704722	+	0.122061i	−0.899108	−	0.437726i	$-0.855784\pi$
$557$	−39.2530	+	67.9882i	−0.0704722	+	0.122061i	0.828636	+	0.559788i	$0.189117\pi$
$558$	−2.83362	+	0.146026i	−0.00507818	+	0.000261695i
$559$	789.570	−	455.859i	1.41247	−	0.815489i
$560$	6.41007	−	39.2224i	0.0114466	−	0.0700400i
$561$	31.9678	+	37.9156i	0.0569835	+	0.0675857i
$562$	245.503	+	587.483i	0.436839	+	1.04534i
$563$	28.0423	−	33.4195i	0.0498087	−	0.0593597i	−0.740565	−	0.671985i	$-0.765442\pi$
$563$	28.0423	−	33.4195i	0.0498087	−	0.0593597i	0.790374	+	0.612625i	$0.209886\pi$
$564$	−363.345	+	259.118i	−0.644229	+	0.459429i
$565$	−26.3253	−	9.58163i	−0.0465935	−	0.0169586i
$566$	−222.425	−	346.735i	−0.392977	−	0.612606i
$567$	−921.633	+	171.496i	−1.62546	+	0.302462i
$568$	−599.631	+	84.6856i	−1.05569	+	0.149094i
$569$	−623.877	−	227.073i	−1.09645	−	0.399074i	−0.270441	−	0.962737i	$-0.587169\pi$
$569$	−623.877	−	227.073i	−1.09645	−	0.399074i	−0.826005	+	0.563663i	$0.809392\pi$
$570$	7.85487	−	0.386201i	0.0137805	−	0.000677545i
$571$	316.761	−	377.501i	0.554747	−	0.661122i	−0.413679	−	0.910423i	$-0.635756\pi$
$571$	316.761	−	377.501i	0.554747	−	0.661122i	0.968426	+	0.249301i	$0.0802009\pi$
$572$	437.010	−	632.516i	0.764003	−	1.10580i
$573$	435.994	+	517.113i	0.760896	+	0.902467i
$574$	−453.676	−	141.482i	−0.790376	−	0.246484i
$575$	−679.786	+	392.475i	−1.18224	+	0.682565i
$576$	−552.713	+	162.126i	−0.959571	+	0.281468i
$577$	−4.25933	+	7.37738i	−0.00738186	+	0.0127858i	−0.869693	−	0.493594i	$-0.835683\pi$
$577$	−4.25933	+	7.37738i	−0.00738186	+	0.0127858i	0.862311	+	0.506379i	$0.169016\pi$
$578$	−387.847	−	420.606i	−0.671015	−	0.727692i
$579$	580.550	−	212.856i	1.00268	−	0.367627i
$580$	0.601578	−	7.41078i	0.00103720	−	0.0127772i
$581$	1224.34	−	445.623i	2.10730	−	0.766993i
$582$	−146.428	−	18.4598i	−0.251595	−	0.0317179i
$583$	−935.977	+	165.038i	−1.60545	+	0.283084i
$584$	−198.696	−	80.1225i	−0.340234	−	0.137196i
$585$	29.3516	−	24.8660i	0.0501737	−	0.0425060i
$586$	−171.936	−	88.8203i	−0.293406	−	0.151571i
$587$	265.990	+	316.994i	0.453134	+	0.540024i	0.943447	−	0.331522i	$-0.107562\pi$
$587$	265.990	+	316.994i	0.453134	+	0.540024i	−0.490313	+	0.871546i	$0.663118\pi$
$588$	−986.857	−	255.322i	−1.67833	−	0.434221i
$589$	0.167169	−	0.948061i	0.000283818	−	0.00160961i
$590$	0.689190	−	5.36479i	0.00116812	−	0.00909286i
$591$	378.238	−	0.892733i	0.639997	−	0.00151055i
$592$	−272.837	−	721.347i	−0.460874	−	1.21849i
$593$	−105.821			−0.178450			−0.0892252	−	0.996011i	$-0.528439\pi$
$593$	−105.821			−0.178450			−0.0892252	+	0.996011i	$0.528439\pi$
$594$	479.410	−	204.340i	0.807087	−	0.344007i
$595$			4.25481i			0.00715094i
$596$	−27.2821	+	27.6263i	−0.0457753	+	0.0463528i
$597$	193.372	−	112.253i	0.323906	−	0.188028i
$598$	−159.645	+	1242.71i	−0.266965	+	2.07811i
$599$	−430.103	−	75.8387i	−0.718035	−	0.126609i	−0.197319	−	0.980339i	$-0.563224\pi$
$599$	−430.103	−	75.8387i	−0.718035	−	0.126609i	−0.520715	+	0.853730i	$0.674335\pi$
$600$	122.738	−	586.183i	0.204564	−	0.976971i
$601$	−756.042	+	634.394i	−1.25797	+	1.05556i	−0.262078	+	0.965047i	$0.584408\pi$
$601$	−756.042	+	634.394i	−1.25797	+	1.05556i	−0.995895	+	0.0905178i	$0.971148\pi$
$602$	941.452	+	486.345i	1.56387	+	0.807882i
$603$	306.025	−	368.222i	0.507504	−	0.610650i
$604$	306.437	−	217.445i	0.507346	−	0.360008i
$605$	1.03840	+	5.88907i	0.00171637	+	0.00973400i
$606$	−110.008	−	261.509i	−0.181531	−	0.431533i
$607$	258.006	+	708.866i	0.425051	+	1.16782i	0.948781	+	0.315934i	$0.102318\pi$
$607$	258.006	+	708.866i	0.425051	+	1.16782i	−0.523730	+	0.851884i	$0.675460\pi$
$608$	−11.5828	−	195.086i	−0.0190507	−	0.320864i
$609$	−296.261	−	51.5181i	−0.486471	−	0.0845945i
$610$	−23.8632	−	25.8789i	−0.0391201	−	0.0424244i
$611$	−641.422	−	370.325i	−1.04979	−	0.606097i
$612$	55.5986	−	26.6737i	0.0908473	−	0.0435845i
$613$	88.3953	+	153.105i	0.144201	+	0.249764i	0.929075	−	0.369892i	$-0.120605\pi$
$613$	88.3953	+	153.105i	0.144201	+	0.249764i	−0.784874	+	0.619656i	$0.787272\pi$
$614$	−516.321	−	161.018i	−0.840914	−	0.262245i
$615$	12.4324	+	4.49184i	0.0202154	+	0.00730380i
$616$	893.022	+	30.5811i	1.44971	+	0.0496447i
$617$	−385.320	−	323.322i	−0.624506	−	0.524023i	0.274710	−	0.961527i	$-0.411418\pi$
$617$	−385.320	−	323.322i	−0.624506	−	0.524023i	−0.899216	+	0.437504i	$0.855862\pi$
$618$	145.698	−	283.678i	0.235758	−	0.459026i
$619$	82.2498	−	225.980i	0.132875	−	0.365072i	−0.855356	−	0.518041i	$-0.826661\pi$
$619$	82.2498	−	225.980i	0.132875	−	0.365072i	0.988231	+	0.152969i	$0.0488836\pi$
$620$	0.123002	+	0.0564210i	0.000198391	+	9.10016e-5i
$621$	−541.306	+	654.459i	−0.871668	+	1.05388i
$622$	−20.8350	−	32.4794i	−0.0334968	−	0.0522177i
$623$	−470.709	+	1293.26i	−0.755552	+	2.07586i
$624$	−625.309	−	723.062i	−1.00210	−	1.15875i
$625$	476.133	+	399.523i	0.761813	+	0.639237i
$626$	−374.378	−	895.877i	−0.598048	−	1.43111i
$627$	31.1147	+	174.057i	0.0496248	+	0.277603i
$628$	142.831	+	519.994i	0.227438	+	0.828016i
$629$	41.2830	+	71.5043i	0.0656328	+	0.113679i
$630$	42.7455	+	13.1094i	0.0678500	+	0.0208086i
$631$	−72.3715	−	41.7837i	−0.114693	−	0.0662182i	0.441556	−	0.897234i	$-0.354427\pi$
$631$	−72.3715	−	41.7837i	−0.114693	−	0.0662182i	−0.556249	+	0.831016i	$0.687760\pi$
$632$	289.003	+	887.420i	0.457283	+	1.40415i
$633$	52.6549	−	63.0533i	0.0831830	−	0.0996102i
$634$	−664.848	+	872.093i	−1.04866	+	1.37554i
$635$	−2.22408	−	6.11062i	−0.00350249	−	0.00962302i
$636$	−92.8365	+	1178.12i	−0.145969	+	1.85239i
$637$	−293.768	−	1666.04i	−0.461174	−	2.61545i
$638$	166.984	−	7.81506i	0.261730	−	0.0122493i
$639$	−3.21595	−	681.271i	−0.00503278	−	1.06615i
$640$	26.9443	+	5.35616i	0.0421005	+	0.00836899i
$641$	−709.440	+	595.291i	−1.10677	+	0.928691i	−0.997862	−	0.0653607i	$-0.979180\pi$
$641$	−709.440	+	595.291i	−1.10677	+	0.928691i	−0.108909	+	0.994052i	$0.534736\pi$
$642$	178.702	+	55.2669i	0.278352	+	0.0860855i
$643$	−0.379828	−	0.0669739i	−0.000590712	−	0.000104159i	0.173353	−	0.984860i	$-0.444540\pi$
$643$	−0.379828	−	0.0669739i	−0.000590712	−	0.000104159i	−0.173944	+	0.984756i	$0.555651\pi$
$644$	−1315.90	+	623.686i	−2.04333	+	0.968457i
$645$	−25.5613	−	14.6775i	−0.0396300	−	0.0227558i
$646$	4.59244	+	20.4122i	0.00710903	+	0.0315978i
$647$		−	295.175i		−	0.456222i	−0.973635	−	0.228111i	$-0.926745\pi$
$647$		−	295.175i		−	0.456222i	0.973635	−	0.228111i	$-0.0732549\pi$
$648$	−96.6710	−	640.749i	−0.149184	−	0.988809i
$649$	121.609			0.187379
$650$	969.701	−	218.168i	1.49185	−	0.335643i
$651$	2.72534	−	4.74627i	0.00418639	−	0.00729073i
$652$	346.989	+	732.105i	0.532192	+	1.12286i
$653$	−19.2754	+	109.316i	−0.0295182	+	0.167406i	−0.996003	−	0.0893167i	$-0.971532\pi$
$653$	−19.2754	+	109.316i	−0.0295182	+	0.167406i	0.966485	+	0.256723i	$0.0826428\pi$
$654$	110.954	−	358.763i	0.169655	−	0.548567i
$655$	25.4248	+	30.3001i	0.0388165	+	0.0462597i
$656$	108.472	−	310.066i	0.165354	−	0.472661i
$657$	119.525	−	209.299i	0.181925	−	0.318567i
$658$	−40.2439	−	859.887i	−0.0611609	−	1.30682i
$659$	1084.88	−	191.294i	1.64626	−	0.290280i	0.727797	−	0.685792i	$-0.240544\pi$
$659$	1084.88	−	191.294i	1.64626	−	0.290280i	0.918461	+	0.395512i	$0.129433\pi$
$660$	−24.7783	−	1.95255i	−0.0375429	−	0.00295841i
$661$	471.148	−	171.484i	0.712781	−	0.259431i	0.0399230	−	0.999203i	$-0.487289\pi$
$661$	471.148	−	171.484i	0.712781	−	0.259431i	0.672858	+	0.739772i	$0.265067\pi$
$662$	863.961	+	658.649i	1.30508	+	0.994938i
$663$	78.5538	+	65.5992i	0.118482	+	0.0989429i
$664$	278.885	+	856.352i	0.420008	+	1.28969i
$665$	−7.58485	+	13.1373i	−0.0114058	+	0.0197554i
$666$	845.556	−	194.435i	1.26960	−	0.291945i
$667$	−235.934	+	136.217i	−0.353724	+	0.204223i
$668$	−575.877	+	158.181i	−0.862092	+	0.236798i
$669$	116.938	−	20.9040i	0.174795	−	0.0312466i
$670$	−21.0695	+	8.80472i	−0.0314470	+	0.0131414i
$671$	508.735	−	606.287i	0.758175	−	0.903558i
$672$	314.942	−	1065.48i	0.468664	−	1.58554i
$673$	−745.558	−	271.361i	−1.10781	−	0.403211i	−0.277622	−	0.960690i	$-0.589546\pi$
$673$	−745.558	−	271.361i	−1.10781	−	0.403211i	−0.830190	+	0.557480i	$0.811768\pi$
$674$	−335.795	+	215.408i	−0.498213	+	0.319596i
$675$	634.740	+	225.950i	0.940355	+	0.334740i
$676$	379.618	−	827.598i	0.561565	−	1.22426i
$677$	−524.604	−	190.940i	−0.774896	−	0.282039i	−0.0758531	−	0.997119i	$-0.524168\pi$
$677$	−524.604	−	190.940i	−0.774896	−	0.282039i	−0.699043	+	0.715080i	$0.746390\pi$
$678$	−696.673	−	357.814i	−1.02754	−	0.527749i
$679$	182.991	−	218.080i	0.269501	−	0.321179i
$680$	−2.93935	−	0.100657i	−0.00432257	−	0.000148025i
$681$	380.018	−	1051.81i	0.558030	−	1.54451i
$682$	−0.905813	+	2.90458i	−0.00132817	+	0.00425892i
$683$	−921.593	+	532.082i	−1.34933	+	0.779037i	−0.988155	−	0.153461i	$-0.950958\pi$
$683$	−921.593	+	532.082i	−1.34933	+	0.779037i	−0.361176	+	0.932498i	$0.617625\pi$
$684$	219.218	+	16.7540i	0.320495	+	0.0244942i
$685$	−2.69562	+	4.66894i	−0.00393520	+	0.00681597i
$686$	611.679	−	564.037i	0.891660	−	0.822211i
$687$	−147.749	+	849.648i	−0.215064	+	1.23675i
$688$	−358.253	+	638.877i	−0.520717	+	0.928601i
$689$	−1843.02	+	670.803i	−2.67491	+	0.973589i
$690$	37.3376	−	15.7066i	0.0541124	−	0.0227632i
$691$	−135.724	+	23.9318i	−0.196417	+	0.0346336i	−0.270991	−	0.962582i	$-0.587351\pi$
$691$	−135.724	+	23.9318i	−0.196417	+	0.0346336i	0.0745742	+	0.997215i	$0.476240\pi$
$692$	723.698	+	1019.88i	1.04581	+	1.47382i
$693$	−169.883	+	990.780i	−0.245141	+	1.42970i
$694$	28.5530	−	55.2721i	0.0411427	−	0.0796427i
$695$	−1.20424	−	1.43516i	−0.00173272	−	0.00206497i
$696$	42.5989	−	203.447i	0.0612053	−	0.292309i
$697$	−6.10685	+	34.6337i	−0.00876163	+	0.0496897i
$698$	383.617	+	49.2815i	0.549594	+	0.0706039i
$699$	−553.881	−	954.141i	−0.792390	−	1.36501i
$700$	821.966	+	811.726i	1.17424	+	1.15961i
$701$	1148.72			1.63869			0.819347	−	0.573298i	$-0.194336\pi$
$701$	1148.72			1.63869			0.819347	+	0.573298i	$0.194336\pi$
$702$	901.065	−	587.067i	1.28357	−	0.836277i
$703$			294.373i			0.418738i
$704$	−42.2527	+	616.202i	−0.0600181	+	0.875287i
$705$	0.0565160	+	23.9450i	8.01645e−5	+	0.0339645i
$706$	523.069	+	67.1963i	0.740891	+	0.0951789i
$707$	538.930	+	95.0280i	0.762278	+	0.134410i
$708$	37.8748	−	146.392i	0.0534955	−	0.206768i
$709$	166.685	−	139.866i	0.235099	−	0.197272i	−0.517625	−	0.855608i	$-0.673184\pi$
$709$	166.685	−	139.866i	0.235099	−	0.197272i	0.752724	+	0.658336i	$0.228739\pi$
$710$	−14.9130	+	28.8682i	−0.0210043	+	0.0406595i
$711$	−1033.13	+	187.202i	−1.45307	+	0.263294i
$712$	−882.288	−	355.775i	−1.23917	−	0.499683i
$713$	−0.861030	−	4.88315i	−0.00120762	−	0.00684873i
$714$	−14.8777	+	118.014i	−0.0208371	+	0.165286i
$715$	−14.1084	−	38.7625i	−0.0197320	−	0.0542133i
$716$	107.060	+	8.69072i	0.149525	+	0.0121379i
$717$	183.766	+	501.208i	0.256298	+	0.699035i
$718$	424.874	−	391.782i	0.591746	−	0.545657i
$719$	532.823	+	307.625i	0.741061	+	0.427852i	0.822455	−	0.568830i	$-0.192604\pi$
$719$	532.823	+	307.625i	0.741061	+	0.427852i	−0.0813939	+	0.996682i	$0.525937\pi$
$720$	−10.0676	+	29.2197i	−0.0139828	+	0.0405829i
$721$	307.572	+	532.730i	0.426591	+	0.738877i
$722$	192.742	−	618.048i	0.266956	−	0.856023i
$723$	−799.611	+	674.175i	−1.10596	+	0.932469i
$724$	−948.076	−	655.032i	−1.30950	−	0.904741i
$725$	165.558	+	138.920i	0.228356	+	0.191613i
$726$	8.20962	+	166.974i	0.0113080	+	0.229992i
$727$	−263.701	+	724.511i	−0.362724	+	0.996577i	0.615338	+	0.788264i	$0.289020\pi$
$727$	−263.701	+	724.511i	−0.362724	+	0.996577i	−0.978062	+	0.208313i	$0.933203\pi$
$728$	1825.82	−	257.860i	2.50799	−	0.354203i
$729$	728.927	−	10.3233i	0.999900	−	0.0141609i
$730$	−9.67560	+	6.20675i	−0.0132542	+	0.00850240i
$731$	26.8203	−	73.6881i	0.0366898	−	0.100804i
$732$	−571.397	−	801.236i	−0.780597	−	1.09458i
$733$	−542.102	−	454.878i	−0.739566	−	0.620570i	0.193155	−	0.981168i	$-0.438128\pi$
$733$	−542.102	−	454.878i	−0.739566	−	0.620570i	−0.932721	+	0.360598i	$0.882572\pi$
$734$	830.139	−	346.907i	1.13098	−	0.472625i
$735$	−41.8146	+	35.2552i	−0.0568906	+	0.0479662i
$736$	−399.730	−	923.818i	−0.543112	−	1.25519i
$737$	−256.704	−	444.625i	−0.348310	−	0.603291i
$738$	329.128	+	168.061i	0.445973	+	0.227725i
$739$	328.811	+	189.839i	0.444940	+	0.256887i	0.705691	−	0.708520i	$-0.250637\pi$
$739$	328.811	+	189.839i	0.444940	+	0.256887i	−0.260751	+	0.965406i	$0.583970\pi$
$740$	−40.0365	−	10.4592i	−0.0541033	−	0.0141341i
$741$	125.606	+	342.581i	0.169508	+	0.462323i
$742$	−1812.82	−	1382.02i	−2.44315	−	1.86256i
$743$	−410.605	−	1128.13i	−0.552631	−	1.51834i	−0.830104	−	0.557608i	$-0.811719\pi$
$743$	−410.605	−	1128.13i	−0.552631	−	1.51834i	0.277473	−	0.960733i	$-0.410503\pi$
$744$	3.21439	+	1.99503i	0.00432041	+	0.00268149i
$745$	0.361755	+	2.05162i	0.000485578	+	0.00275385i
$746$	−21.9567	−	469.146i	−0.0294326	−	0.628883i
$747$	−996.963	+	180.648i	−1.33462	+	0.241831i
$748$	−6.17594	−	65.8358i	−0.00825660	−	0.0880158i
$749$	−276.396	+	231.924i	−0.369020	+	0.309644i
$750$	−43.7187	−	47.1874i	−0.0582916	−	0.0629166i
$751$	−338.515	−	59.6894i	−0.450753	−	0.0794799i	−0.0563366	−	0.998412i	$-0.517942\pi$
$751$	−338.515	−	59.6894i	−0.450753	−	0.0794799i	−0.394416	+	0.918932i	$0.629053\pi$
$752$	594.987	−	7.45919i	0.791206	−	0.00991913i
$753$	−0.906675	−	384.145i	−0.00120408	−	0.510153i
$754$	336.555	−	75.7198i	0.446359	−	0.100424i
$755$		−	20.1608i		−	0.0267031i
$756$	1139.78	+	513.078i	1.50764	+	0.678675i
$757$	−185.105			−0.244525			−0.122262	−	0.992498i	$-0.539015\pi$
$757$	−185.105			−0.244525			−0.122262	+	0.992498i	$0.539015\pi$
$758$	10.7819	+	47.9226i	0.0142241	+	0.0632225i
$759$	457.221	+	787.632i	0.602400	+	1.03772i
$760$	−8.89623	−	5.55063i	−0.0117056	−	0.00730346i
$761$	107.060	−	607.165i	0.140683	−	0.797851i	−0.830050	−	0.557689i	$-0.811688\pi$
$761$	107.060	−	607.165i	0.140683	−	0.797851i	0.970733	−	0.240162i	$-0.0772006\pi$
$762$	−40.3218	−	177.265i	−0.0529157	−	0.232631i
$763$	465.612	+	554.894i	0.610238	+	0.727253i
$764$	−84.2308	−	897.904i	−0.110250	−	1.17527i
$765$	0.559163	−	3.26111i	0.000730932	−	0.00426290i
$766$	−1189.00	+	55.6468i	−1.55222	+	0.0726460i
$767$	247.142	−	43.5778i	0.322219	−	0.0568160i
$768$	728.617	+	242.778i	0.948720	+	0.316117i
$769$	120.247	−	43.7664i	0.156368	−	0.0569134i	−0.262650	−	0.964891i	$-0.584596\pi$
$769$	120.247	−	43.7664i	0.156368	−	0.0569134i	0.419018	+	0.907978i	$0.362374\pi$
$770$	29.0668	−	38.1274i	0.0377491	−	0.0495161i
$771$	137.577	−	791.153i	0.178440	−	1.02614i
$772$	−797.684	−	208.389i	−1.03327	−	0.269934i
$773$	−156.807	+	271.599i	−0.202856	+	0.351356i	−0.949447	−	0.313926i	$-0.898356\pi$
$773$	−156.807	+	271.599i	−0.202856	+	0.351356i	0.746592	+	0.665283i	$0.231689\pi$
$774$	−657.664	−	496.485i	−0.849695	−	0.641454i
$775$	−3.40655	+	1.96677i	−0.00439555	+	0.00253777i
$776$	146.327	+	131.575i	0.188566	+	0.169555i
$777$	−568.682	+	1573.99i	−0.731895	+	2.02573i
$778$	255.912	+	612.391i	0.328936	+	0.787135i
$779$	−80.5956	+	96.0501i	−0.103460	+	0.123299i
$780$	−51.0559	+	4.91105i	−0.0654562	+	0.00629622i
$781$	−686.484	−	249.860i	−0.878980	−	0.319923i
$782$	58.1863	+	90.7057i	0.0744071	+	0.115992i
$783$	220.300	+	78.4205i	0.281353	+	0.100154i
$784$	886.617	+	1030.12i	1.13089	+	1.31393i
$785$	27.1889	+	9.89596i	0.0346356	+	0.0126063i
$786$	599.250	+	929.326i	0.762404	+	1.18235i
$787$	335.127	−	399.389i	0.425828	−	0.507483i	−0.509886	−	0.860242i	$-0.670312\pi$
$787$	335.127	−	399.389i	0.425828	−	0.507483i	0.935714	+	0.352760i	$0.114757\pi$
$788$	−414.919	−	286.670i	−0.526547	−	0.363795i
$789$	771.001	−	137.825i	0.977188	−	0.174684i
$790$	47.8055	+	14.9084i	0.0605132	+	0.0188715i
$791$	1308.31	−	755.352i	1.65399	−	0.954934i
$792$	−680.441	−	140.799i	−0.859142	−	0.177777i
$793$	816.627	−	1414.44i	1.02979	−	1.78366i
$794$	115.873	+	125.660i	0.145935	+	0.158262i
$795$	48.6696	+	40.6433i	0.0612197	+	0.0511237i
$796$	−297.145	−	24.1210i	−0.373297	−	0.0303028i
$797$	−260.173	+	94.6953i	−0.326441	+	0.118815i	−0.500041	−	0.866001i	$-0.666682\pi$
$797$	−260.173	+	94.6953i	−0.326441	+	0.118815i	0.173601	+	0.984816i	$0.444460\pi$
$798$	−256.315	+	337.864i	−0.321197	+	0.423389i
$799$	−62.7359	+	11.0620i	−0.0785180	+	0.0138448i
$800$	−580.210	+	548.635i	−0.725262	+	0.685794i
$801$	530.736	−	929.366i	0.662592	−	1.16026i
$802$	−299.266	−	154.598i	−0.373149	−	0.192765i
$803$	−166.129	−	197.985i	−0.206885	−	0.246556i
$804$	−615.184	+	170.540i	−0.765154	+	0.212115i
$805$	−13.5678	+	76.9470i	−0.0168545	+	0.0955864i
$806$	−0.800016	+	6.22748i	−0.000992576	+	0.00772640i
$807$	−473.306	+	824.277i	−0.586501	+	1.02141i
$808$	−78.3977	+	370.061i	−0.0970268	+	0.457996i
$809$	638.629			0.789405			0.394702	−	0.918809i	$-0.370848\pi$
$809$	638.629			0.789405			0.394702	+	0.918809i	$0.370848\pi$
$810$	−31.0396	−	15.6653i	−0.0383205	−	0.0193399i
$811$		−	260.263i		−	0.320916i	−0.987043	−	0.160458i	$-0.948703\pi$
$811$		−	260.263i		−	0.320916i	0.987043	−	0.160458i	$-0.0512971\pi$
$812$	285.280	+	281.726i	0.351331	+	0.346954i
$813$	457.619	+	262.768i	0.562877	+	0.323208i
$814$	118.545	−	922.776i	0.145633	−	1.13363i
$815$	42.8097	+	7.54850i	0.0525272	+	0.00926196i
$816$	−81.1758	−	13.0698i	−0.0994801	−	0.0160170i
$817$	214.172	−	179.711i	0.262144	−	0.219965i
$818$	247.203	+	127.703i	0.302204	+	0.156116i
$819$	9.79225	+	2074.41i	0.0119563	+	2.53285i
$820$	−10.1998	−	14.3742i	−0.0124388	−	0.0175295i
$821$	−179.659	−	1018.90i	−0.218830	−	1.24104i	−0.874136	−	0.485681i	$-0.838572\pi$
$821$	−179.659	−	1018.90i	−0.218830	−	1.24104i	0.655307	−	0.755363i	$-0.272539\pi$
$822$	−91.0932	+	120.075i	−0.110819	+	0.146077i
$823$	−206.443	−	567.198i	−0.250842	−	0.689183i	−0.999652	−	0.0263979i	$-0.991596\pi$
$823$	−206.443	−	567.198i	−0.250842	−	0.689183i	0.748809	−	0.662786i	$-0.230626\pi$
$824$	−375.302	+	199.877i	−0.455463	+	0.242569i
$825$	463.090	−	554.542i	0.561321	−	0.672172i
$826$	197.726	+	214.427i	0.239377	+	0.259596i
$827$	−584.555	−	337.493i	−0.706838	−	0.408093i	0.103051	−	0.994676i	$-0.467140\pi$
$827$	−584.555	−	337.493i	−0.706838	−	0.408093i	−0.809889	+	0.586583i	$0.800473\pi$
$828$	1090.54	−	305.092i	1.31708	−	0.368468i
$829$	109.326	+	189.359i	0.131877	+	0.228418i	0.924400	−	0.381424i	$-0.124566\pi$
$829$	109.326	+	189.359i	0.131877	+	0.228418i	−0.792523	+	0.609842i	$0.791233\pi$
$830$	46.1318	+	14.3865i	0.0555805	+	0.0173331i
$831$	8.44346	+	47.2331i	0.0101606	+	0.0568388i
$832$	134.943	+	1267.43i	0.162192	+	1.52335i
$833$	−111.465	−	93.5303i	−0.133812	−	0.112281i
$834$	−28.3833	−	44.0173i	−0.0340328	−	0.0527786i
$835$	−10.9595	+	30.1109i	−0.0131251	+	0.0360609i
$836$	98.2932	−	214.287i	0.117576	−	0.256324i
$837$	−2.71260	+	3.27963i	−0.00324086	+	0.00391832i
$838$	153.103	+	238.670i	0.182701	+	0.284809i
$839$	−257.800	+	708.300i	−0.307270	+	0.844219i	0.685916	+	0.727681i	$0.259402\pi$
$839$	−257.800	+	708.300i	−0.307270	+	0.844219i	−0.993186	+	0.116538i	$0.962820\pi$
$840$	−36.8445	−	46.8649i	−0.0438625	−	0.0557916i
$841$	−586.783	−	492.369i	−0.697721	−	0.585457i
$842$	−82.3929	−	197.164i	−0.0978538	−	0.234162i
$843$	898.246	+	324.536i	1.06553	+	0.384977i
$844$	−105.618	+	29.0111i	−0.125140	+	0.0343734i
$845$	−24.4269	−	42.3086i	−0.0289075	−	0.0500693i
$846$	−82.1604	+	664.352i	−0.0971163	+	0.785286i
$847$	−279.266	−	161.234i	−0.329711	−	0.190359i
$848$	997.626	−	1219.65i	1.17645	−	1.43827i
$849$	−608.780	−	105.863i	−0.717056	−	0.124692i
$850$	51.8298	−	67.9860i	0.0609762	−	0.0799835i
$851$	518.577	+	1424.78i	0.609374	+	1.67424i
$852$	−514.581	+	748.562i	−0.603968	+	0.878594i
$853$	198.372	+	1125.02i	0.232558	+	1.31890i	0.847696	+	0.530482i	$0.177989\pi$
$853$	198.372	+	1125.02i	0.232558	+	1.31890i	−0.615138	+	0.788419i	$0.710900\pi$
$854$	1896.19	−	88.7443i	2.22036	−	0.103916i
$855$	7.53993	−	9.07237i	0.00881863	−	0.0106110i
$856$	−153.681	−	196.429i	−0.179534	−	0.229473i
$857$	−226.349	+	189.929i	−0.264117	+	0.221621i	−0.765223	−	0.643765i	$-0.777371\pi$
$857$	−226.349	+	189.929i	−0.264117	+	0.221621i	0.501106	+	0.865386i	$0.332927\pi$
$858$	−255.780	−	1124.48i	−0.298112	−	1.31058i
$859$	−156.184	−	27.5395i	−0.181821	−	0.0320600i	0.0819961	−	0.996633i	$-0.473870\pi$
$859$	−156.184	−	27.5395i	−0.181821	−	0.0320600i	−0.263817	+	0.964573i	$0.584982\pi$
$860$	16.8322	+	35.5138i	0.0195723	+	0.0412952i
$861$	−616.492	+	357.875i	−0.716019	+	0.415650i
$862$	−245.936	−	1093.12i	−0.285308	−	1.26812i
$863$		−	222.807i		−	0.258177i	−0.991633	−	0.129089i	$-0.958795\pi$
$863$		−	222.807i		−	0.258177i	0.991633	−	0.129089i	$-0.0412052\pi$
$864$	−381.413	+	775.255i	−0.441451	+	0.897286i
$865$	67.0992			0.0775713
$866$	−744.957	+	167.604i	−0.860228	+	0.193538i
$867$	−858.195	+	2.02555i	−0.989844	+	0.00233627i
$868$	−6.59426	+	3.12542i	−0.00759707	+	0.00360072i
$869$	−195.506	+	1108.77i	−0.224978	+	1.27592i
$870$	−7.57974	−	8.18113i	−0.00871234	−	0.00940360i
$871$	−681.021	−	811.609i	−0.781884	−	0.931813i
$872$	−394.352	+	308.531i	−0.452239	+	0.353820i
$873$	−168.914	+	143.100i	−0.193487	+	0.163918i
$874$	17.9620	+	383.793i	0.0205515	+	0.439122i
$875$	122.197	−	21.5465i	0.139653	−	0.0246246i
$876$	−290.072	+	138.322i	−0.331132	+	0.157902i
$877$	−443.850	+	161.548i	−0.506100	+	0.184205i	−0.582436	−	0.812877i	$-0.697900\pi$
$877$	−443.850	+	161.548i	−0.506100	+	0.184205i	0.0763355	+	0.997082i	$0.475678\pi$
$878$	−768.612	−	585.959i	−0.875412	−	0.667379i
$879$	−272.542	+	99.9264i	−0.310060	+	0.113682i
$880$	25.6519	+	20.9822i	0.0291499	+	0.0238434i
$881$	40.2626	−	69.7369i	0.0457010	−	0.0791565i	−0.842270	−	0.539056i	$-0.818781\pi$
$881$	40.2626	−	69.7369i	0.0457010	−	0.0791565i	0.887971	+	0.459899i	$0.152115\pi$
$882$	−1283.07	+	831.648i	−1.45473	+	0.942912i
$883$	820.367	−	473.639i	0.929068	−	0.536398i	0.0425516	−	0.999094i	$-0.486451\pi$
$883$	820.367	−	473.639i	0.929068	−	0.536398i	0.886517	+	0.462696i	$0.153118\pi$
$884$	−36.1430	−	131.583i	−0.0408857	−	0.148849i
$885$	−5.22979	−	6.20283i	−0.00590937	−	0.00700885i
$886$	581.449	−	242.982i	0.656264	−	0.274246i
$887$	422.053	−	502.984i	0.475821	−	0.567062i	−0.473731	−	0.880669i	$-0.657093\pi$
$887$	422.053	−	502.984i	0.475821	−	0.567062i	0.949553	+	0.313608i	$0.101538\pi$
$888$	−1073.91	−	430.099i	−1.20935	−	0.484345i
$889$	329.516	+	119.934i	0.370659	+	0.134909i
$890$	−42.9634	+	27.5604i	−0.0482734	+	0.0309667i
$891$	260.415	−	737.061i	0.292272	−	0.827229i
$892$	−143.966	−	66.0368i	−0.161396	−	0.0740323i
$893$	−213.426	−	77.6806i	−0.238999	−	0.0869884i
$894$	2.86005	+	58.1700i	0.00319916	+	0.0650671i
$895$	3.70454	−	4.41490i	0.00413915	−	0.00493285i
$896$	−1155.21	+	927.388i	−1.28930	+	1.03503i
$897$	1211.44	+	1436.84i	1.35055	+	1.60182i
$898$	−486.254	+	1559.22i	−0.541486	+	1.73633i
$899$	−1.18231	+	0.682610i	−0.00131514	+	0.000759299i
$900$	−523.323	−	730.172i	−0.581470	−	0.811302i
$901$	−84.3460	+	146.092i	−0.0936138	+	0.162144i
$902$	291.324	−	268.634i	0.322976	−	0.297820i
$903$	1492.33	−	547.157i	1.65264	−	0.605933i
$904$	490.869	+	921.688i	0.542997	+	1.01957i
$905$	−58.1010	+	21.1471i	−0.0642001	+	0.0233669i
$906$	70.4959	−	559.194i	0.0778101	−	0.617212i
$907$	1463.07	−	257.979i	1.61309	−	0.284431i	0.706902	−	0.707312i	$-0.250092\pi$
$907$	1463.07	−	257.979i	1.61309	−	0.284431i	0.906185	+	0.422881i	$0.138981\pi$
$908$	−1216.08	+	862.921i	−1.33930	+	0.950354i
$909$	−400.577	−	143.660i	−0.440678	−	0.158042i
$910$	45.4088	−	87.9010i	0.0498998	−	0.0965945i
$911$	−654.039	−	779.454i	−0.717936	−	0.855603i	0.276493	−	0.961016i	$-0.410828\pi$
$911$	−654.039	−	779.454i	−0.717936	−	0.855603i	−0.994428	+	0.105413i	$0.966383\pi$
$912$	−227.343	−	185.063i	−0.249280	−	0.202920i
$913$	−188.662	+	1069.95i	−0.206639	+	1.17191i
$914$	−101.862	−	13.0857i	−0.111446	−	0.0143170i
$915$	−52.8026	+	0.124627i	−0.0577078	+	0.000136204i
$916$	807.965	−	818.158i	0.882058	−	0.893186i
$917$	−2132.96			−2.32602
$918$	26.9124	−	88.4973i	0.0293163	−	0.0964022i
$919$		−	320.861i		−	0.349141i	−0.984645	−	0.174571i	$-0.944146\pi$
$919$		−	320.861i		−	0.349141i	0.984645	−	0.174571i	$-0.0558537\pi$
$920$	−52.8363	−	11.1934i	−0.0574307	−	0.0121667i
$921$	−701.621	+	407.292i	−0.761803	+	0.442228i
$922$	−1180.81	−	151.693i	−1.28071	−	0.164526i
$923$	−1484.65	−	261.785i	−1.60851	−	0.283624i
$924$	939.535	−	955.890i	1.01681	−	1.03451i
$925$	921.408	−	773.153i	0.996117	−	0.835841i
$926$	−396.222	+	766.995i	−0.427886	+	0.828289i
$927$	−165.729	−	448.734i	−0.178780	−	0.484071i
$928$	−201.374	+	190.415i	−0.216998	+	0.205189i
$929$	−57.4894	−	326.039i	−0.0618831	−	0.350957i	−0.999989	−	0.00460898i	$-0.998533\pi$
$929$	−57.4894	−	326.039i	−0.0618831	−	0.350957i	0.938106	−	0.346348i	$-0.112578\pi$
$930$	0.187107	−	0.0787092i	0.000201190	−	8.46336e-5i
$931$	−177.433	−	487.492i	−0.190583	−	0.523622i
$932$	−119.019	+	1466.18i	−0.127703	+	1.57316i
$933$	−57.0257	−	9.91645i	−0.0611208	−	0.0106286i
$934$	−1110.66	+	1024.15i	−1.18914	+	1.09652i
$935$	−3.07262	−	1.77398i	−0.00328622	−	0.00189730i
$936$	−1433.29	−	42.3098i	−1.53130	−	0.0452027i
$937$	−663.749	−	1149.65i	−0.708376	−	1.22694i	−0.965459	−	0.260554i	$-0.916095\pi$
$937$	−663.749	−	1149.65i	−0.708376	−	1.22694i	0.257083	−	0.966389i	$-0.417239\pi$
$938$	366.604	−	1175.55i	0.390836	−	1.25326i
$939$	−1369.77	−	494.898i	−1.45876	−	0.527048i
$940$	18.1481	−	26.2671i	0.0193065	−	0.0279438i
$941$	292.985	+	245.844i	0.311355	+	0.261258i	0.785052	−	0.619430i	$-0.212636\pi$
$941$	292.985	+	245.844i	0.311355	+	0.261258i	−0.473697	+	0.880688i	$0.657081\pi$
$942$	719.527	+	369.552i	0.763830	+	0.392306i
$943$	−220.881	+	606.867i	−0.234233	+	0.643549i
$944$	−152.810	+	131.522i	−0.161875	+	0.139324i
$945$	57.8418	−	33.9433i	0.0612083	−	0.0359189i
$946$	−743.738	+	477.097i	−0.786192	+	0.504331i
$947$	108.937	−	299.302i	0.115034	−	0.316053i	−0.868793	−	0.495176i	$-0.835104\pi$
$947$	108.937	−	299.302i	0.115034	−	0.316053i	0.983827	+	0.179123i	$0.0573260\pi$
$948$	1273.83	+	580.671i	1.34371	+	0.612522i
$949$	−408.565	−	342.827i	−0.430522	−	0.361251i
$950$	281.227	−	117.522i	0.296029	−	0.123707i
$951$	289.461	+	1619.26i	0.304375	+	1.70269i
$952$	106.043	−	117.933i	0.111390	−	0.123879i
$953$	61.8869	+	107.191i	0.0649391	+	0.112478i	0.896667	−	0.442706i	$-0.145981\pi$
$953$	61.8869	+	107.191i	0.0649391	+	0.112478i	−0.831728	+	0.555183i	$0.812648\pi$
$954$	1207.82	+	1297.49i	1.26606	+	1.36005i
$955$	−41.9060	−	24.1944i	−0.0438806	−	0.0253345i
$956$	179.909	−	688.668i	0.188189	−	0.720364i
$957$	160.725	−	192.465i	0.167947	−	0.201113i
$958$	938.677	+	715.610i	0.979830	+	0.746983i
$959$	−99.4332	−	273.190i	−0.103684	−	0.284870i
$960$	33.2473	−	24.3446i	0.0346326	−	0.0253590i
$961$	166.872	+	946.376i	0.173644	+	0.984782i
$962$	−89.7560	−	1917.81i	−0.0933015	−	1.99356i
$963$	242.324	−	141.435i	0.251634	−	0.146869i
$964$	1388.43	−	130.246i	1.44028	−	0.135110i
$965$	−33.8871	+	28.4346i	−0.0351161	+	0.0294659i
$966$	−645.386	+	2086.81i	−0.668101	+	2.16026i
$967$	59.4973	+	10.4910i	0.0615277	+	0.0108490i	0.204327	−	0.978903i	$-0.434499\pi$
$967$	59.4973	+	10.4910i	0.0615277	+	0.0108490i	−0.142800	+	0.989752i	$0.545610\pi$
$968$	117.992	−	189.111i	0.121892	−	0.195362i
$969$	27.2160	+	15.6276i	0.0280867	+	0.0161276i
$970$	10.3010	−	2.31757i	0.0106196	−	0.00238924i
$971$		−	670.687i		−	0.690718i	−0.938471	−	0.345359i	$-0.887757\pi$
$971$		−	670.687i		−	0.690718i	0.938471	−	0.345359i	$-0.112243\pi$
$972$	−806.159	−	543.039i	−0.829382	−	0.558682i
$973$	101.027			0.103830
$974$	208.166	+	925.244i	0.213723	+	0.949943i
$975$	742.406	−	1292.92i	0.761442	−	1.32607i
$976$	16.4487	+	1312.04i	0.0168532	+	1.34431i
$977$	123.095	−	698.106i	0.125993	−	0.714540i	−0.854721	−	0.519088i	$-0.826272\pi$
$977$	123.095	−	698.106i	0.125993	−	0.714540i	0.980713	−	0.195452i	$-0.0626173\pi$
$978$	1161.00	+	359.062i	1.18712	+	0.367139i
$979$	−737.676	−	879.128i	−0.753500	−	0.897986i
$980$	72.6060	−	6.81104i	0.0740878	−	0.00695004i
$981$	−283.946	−	486.491i	−0.289446	−	0.495913i
$982$	−568.193	+	26.5922i	−0.578608	+	0.0270796i
$983$	668.074	−	117.799i	0.679628	−	0.119837i	0.176831	−	0.984241i	$-0.443415\pi$
$983$	668.074	−	117.799i	0.679628	−	0.119837i	0.502797	+	0.864405i	$0.332304\pi$
$984$	−232.646	−	434.357i	−0.236429	−	0.441420i
$985$	−25.4275	+	9.25486i	−0.0258147	+	0.00939579i
$986$	17.9886	−	23.5959i	0.0182440	−	0.0239310i
$987$	−991.105	−	827.658i	−1.00416	−	0.838559i
$988$	122.970	−	470.711i	0.124463	−	0.476429i
$989$	720.015	−	1247.10i	0.728023	−	1.26097i
$990$	−27.2890	+	25.4030i	−0.0275647	+	0.0256595i
$991$	1062.37	−	613.362i	1.07202	−	0.618932i	0.143289	−	0.989681i	$-0.454232\pi$
$991$	1062.37	−	613.362i	1.07202	−	0.618932i	0.928733	+	0.370749i	$0.120899\pi$
$992$	−2.00313	−	4.62945i	−0.00201929	−	0.00466678i
$993$	1604.16	−	286.762i	1.61547	−	0.288783i
$994$	−675.598	−	1616.69i	−0.679676	−	1.62645i
$995$	−10.2819	+	12.2535i	−0.0103336	+	0.0123151i
$996$	1229.24	+	560.342i	1.23417	+	0.562593i
$997$	1118.16	+	406.977i	1.12152	+	0.408202i	0.835209	−	0.549933i	$-0.185347\pi$
$997$	1118.16	+	406.977i	1.12152	+	0.408202i	0.286316	+	0.958135i	$0.407569\pi$
$998$	405.642	+	632.349i	0.406455	+	0.633616i
$999$	642.721	−	1131.66i	0.643364	−	1.13279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.j.a.31.2	yes	204
3.2	odd	2		324.3.j.a.307.33		204
4.3	odd	2	inner	108.3.j.a.31.9	yes	204
12.11	even	2		324.3.j.a.307.26		204
27.7	even	9	inner	108.3.j.a.7.9	yes	204
27.20	odd	18		324.3.j.a.19.26		204
108.7	odd	18	inner	108.3.j.a.7.2	✓	204
108.47	even	18		324.3.j.a.19.33		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.2	✓	204	108.7	odd	18	inner
108.3.j.a.7.9	yes	204	27.7	even	9	inner
108.3.j.a.31.2	yes	204	1.1	even	1	trivial
108.3.j.a.31.9	yes	204	4.3	odd	2	inner
324.3.j.a.19.26		204	27.20	odd	18
324.3.j.a.19.33		204	108.47	even	18
324.3.j.a.307.26		204	12.11	even	2
324.3.j.a.307.33		204	3.2	odd	2

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95123 + 0.438997i) q^{2} +(-1.49386 + 2.60161i) q^{3} +(3.61456 - 1.71316i) q^{4} +(0.0372686 - 0.211361i) q^{5} +(1.77277 - 5.73213i) q^{6} +(7.43930 + 8.86581i) q^{7} +(-6.30076 + 4.92955i) q^{8} +(-4.53674 - 7.77290i) q^{9} +O(q^{10})\)	\(q+(-1.95123 + 0.438997i) q^{2} +(-1.49386 + 2.60161i) q^{3} +(3.61456 - 1.71316i) q^{4} +(0.0372686 - 0.211361i) q^{5} +(1.77277 - 5.73213i) q^{6} +(7.43930 + 8.86581i) q^{7} +(-6.30076 + 4.92955i) q^{8} +(-4.53674 - 7.77290i) q^{9} +(0.0200672 + 0.428773i) q^{10} +(-9.50415 + 1.67584i) q^{11} +(-0.942686 + 11.9629i) q^{12} +(-18.7145 + 6.81150i) q^{13} +(-18.4078 - 14.0334i) q^{14} +(0.494204 + 0.412703i) q^{15} +(10.1301 - 12.3847i) q^{16} +(-0.856471 + 1.48345i) q^{17} +(12.2645 + 13.1751i) q^{18} +(-5.28896 + 3.05358i) q^{19} +(-0.227386 - 0.827824i) q^{20} +(-34.1787 + 6.10984i) q^{21} +(17.8091 - 7.44223i) q^{22} +(-20.2195 + 24.0967i) q^{23} +(-3.41229 - 23.7562i) q^{24} +(23.4490 + 8.53475i) q^{25} +(33.5259 - 21.5064i) q^{26} +(26.9993 - 0.191178i) q^{27} +(42.0784 + 19.3013i) q^{28} +(8.13847 + 2.96216i) q^{29} +(-1.14548 - 0.588322i) q^{30} +(-0.101324 + 0.120753i) q^{31} +(-14.3294 + 28.6124i) q^{32} +(9.83803 - 27.2296i) q^{33} +(1.01994 - 3.27054i) q^{34} +(2.15114 - 1.24196i) q^{35} +(-29.7146 - 20.3235i) q^{36} +(24.1007 - 41.7436i) q^{37} +(8.97943 - 8.28006i) q^{38} +(10.2360 - 58.8632i) q^{39} +(0.807093 + 1.51545i) q^{40} +(19.2926 - 7.02193i) q^{41} +(64.0081 - 26.9260i) q^{42} +(-45.0838 + 7.94949i) q^{43} +(-31.4824 + 22.3396i) q^{44} +(-1.81196 + 0.669204i) q^{45} +(28.8744 - 55.8943i) q^{46} +(23.9050 + 28.4889i) q^{47} +(17.0870 + 44.8557i) q^{48} +(-14.7507 + 83.6553i) q^{49} +(-49.5011 - 6.35918i) q^{50} +(-2.57991 - 4.44428i) q^{51} +(-55.9754 + 56.6815i) q^{52} +98.4809 q^{53} +(-52.5978 + 12.2256i) q^{54} +2.07126i q^{55} +(-90.5777 - 19.1890i) q^{56} +(-0.0432430 - 18.3214i) q^{57} +(-17.1804 - 2.20708i) q^{58} +(-12.4095 - 2.18814i) q^{59} +(2.49336 + 0.645088i) q^{60} +(-62.8227 + 52.7145i) q^{61} +(0.144696 - 0.280098i) q^{62} +(35.1629 - 98.0469i) q^{63} +(15.3991 - 62.1198i) q^{64} +(0.742223 + 4.20936i) q^{65} +(-7.24254 + 57.4499i) q^{66} +(18.1950 + 49.9905i) q^{67} +(-0.554376 + 6.82930i) q^{68} +(-32.4849 - 88.6003i) q^{69} +(-3.65214 + 3.36769i) q^{70} +(65.5561 + 37.8488i) q^{71} +(66.9018 + 26.6111i) q^{72} +(13.3902 + 23.1924i) q^{73} +(-28.7005 + 92.0312i) q^{74} +(-57.2337 + 48.2555i) q^{75} +(-13.8860 + 20.0982i) q^{76} +(-85.5619 - 71.7950i) q^{77} +(5.86803 + 119.349i) q^{78} +(39.9006 - 109.626i) q^{79} +(-2.24010 - 2.60268i) q^{80} +(-39.8359 + 70.5273i) q^{81} +(-34.5616 + 22.1707i) q^{82} +(38.5038 - 105.788i) q^{83} +(-113.074 + 80.6381i) q^{84} +(0.281624 + 0.236311i) q^{85} +(84.4788 - 35.3029i) q^{86} +(-19.8642 + 16.7481i) q^{87} +(51.6222 - 57.4102i) q^{88} +(59.4575 + 102.983i) q^{89} +(3.24177 - 2.10121i) q^{90} +(-199.612 - 115.246i) q^{91} +(-31.8032 + 121.738i) q^{92} +(-0.162789 - 0.443995i) q^{93} +(-59.1506 - 45.0941i) q^{94} +(0.448295 + 1.23168i) q^{95} +(-53.0321 - 80.0225i) q^{96} +(-4.27138 - 24.2242i) q^{97} +(-7.94247 - 169.706i) q^{98} +(56.1440 + 66.2720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25} - 174 q^{26} - 12 q^{28} + 60 q^{29} - 153 q^{30} - 96 q^{32} + 48 q^{33} + 6 q^{34} + 24 q^{36} - 6 q^{37} + 72 q^{38} + 69 q^{40} - 192 q^{41} - 126 q^{42} - 219 q^{44} - 132 q^{45} - 3 q^{46} - 219 q^{48} - 12 q^{49} - 165 q^{50} + 21 q^{52} - 24 q^{53} + 78 q^{54} + 99 q^{56} - 150 q^{57} - 141 q^{58} + 210 q^{60} - 12 q^{61} + 294 q^{62} - 3 q^{64} - 156 q^{65} + 393 q^{66} + 375 q^{68} - 60 q^{69} - 165 q^{70} + 228 q^{72} - 6 q^{73} + 447 q^{74} - 54 q^{76} + 132 q^{77} + 750 q^{78} + 798 q^{80} + 228 q^{81} - 12 q^{82} + 762 q^{84} + 138 q^{85} + 606 q^{86} - 198 q^{88} - 114 q^{89} + 894 q^{90} + 723 q^{92} - 1020 q^{93} - 357 q^{94} + 474 q^{96} + 168 q^{97} + 510 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

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