LMFDB - Embedded newform 76.2.k.a.59.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.k (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:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.6
Character	$\chi$	$=$	76.59
Dual form			76.2.k.a.67.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.343391 - 1.37189i) q^{2} +(-1.20007 - 1.00697i) q^{3} +(-1.76416 - 0.942190i) q^{4} +(0.709721 - 0.258317i) q^{5} +(-1.79355 + 1.30057i) q^{6} +(0.937645 - 0.541349i) q^{7} +(-1.89838 + 2.09670i) q^{8} +(-0.0947852 - 0.537553i) q^{9} +O(q^{10})$	\(q+(0.343391 - 1.37189i) q^{2} +(-1.20007 - 1.00697i) q^{3} +(-1.76416 - 0.942190i) q^{4} +(0.709721 - 0.258317i) q^{5} +(-1.79355 + 1.30057i) q^{6} +(0.937645 - 0.541349i) q^{7} +(-1.89838 + 2.09670i) q^{8} +(-0.0947852 - 0.537553i) q^{9} +(-0.110671 - 1.06236i) q^{10} +(2.64713 + 1.52832i) q^{11} +(1.16835 + 2.90716i) q^{12} +(2.97626 + 3.54697i) q^{13} +(-0.420693 - 1.47224i) q^{14} +(-1.11183 - 0.404673i) q^{15} +(2.22456 + 3.32436i) q^{16} +(0.837695 - 4.75081i) q^{17} +(-0.770013 - 0.0545563i) q^{18} +(-1.62987 + 4.04271i) q^{19} +(-1.49545 - 0.212978i) q^{20} +(-1.67036 - 0.294530i) q^{21} +(3.00569 - 3.10676i) q^{22} +(1.30131 - 3.57533i) q^{23} +(4.38950 - 0.604558i) q^{24} +(-3.39325 + 2.84727i) q^{25} +(5.88807 - 2.86510i) q^{26} +(-2.77742 + 4.81062i) q^{27} +(-2.16421 + 0.0715903i) q^{28} +(-6.38295 + 1.12549i) q^{29} +(-0.936960 + 1.38635i) q^{30} +(0.249223 + 0.431666i) q^{31} +(5.32455 - 1.91029i) q^{32} +(-1.63775 - 4.49968i) q^{33} +(-6.22993 - 2.78061i) q^{34} +(0.525626 - 0.626417i) q^{35} +(-0.339261 + 1.03764i) q^{36} +2.70604i q^{37} +(4.98648 + 3.62423i) q^{38} -7.25360i q^{39} +(-0.805706 + 1.97846i) q^{40} +(-3.63013 + 4.32622i) q^{41} +(-0.977649 + 2.19041i) q^{42} +(-2.40019 - 6.59447i) q^{43} +(-3.23001 - 5.19031i) q^{44} +(-0.206130 - 0.357028i) q^{45} +(-4.45810 - 3.01300i) q^{46} +(8.31690 - 1.46649i) q^{47} +(0.677930 - 6.22952i) q^{48} +(-2.91388 + 5.04699i) q^{49} +(2.74093 + 5.63289i) q^{50} +(-5.78923 + 4.85774i) q^{51} +(-1.90869 - 9.06163i) q^{52} +(4.64782 - 12.7698i) q^{53} +(5.64591 + 5.46223i) q^{54} +(2.27352 + 0.400882i) q^{55} +(-0.644958 + 2.99365i) q^{56} +(6.02685 - 3.21029i) q^{57} +(-0.647805 + 9.14318i) q^{58} +(-0.185976 + 1.05472i) q^{59} +(1.58017 + 1.76146i) q^{60} +(5.54306 + 2.01751i) q^{61} +(0.677779 - 0.193676i) q^{62} +(-0.379879 - 0.452722i) q^{63} +(-0.792308 - 7.96067i) q^{64} +(3.02855 + 1.74854i) q^{65} +(-6.73545 + 0.701662i) q^{66} +(2.28900 + 12.9816i) q^{67} +(-5.95399 + 7.59194i) q^{68} +(-5.16193 + 2.98024i) q^{69} +(-0.678880 - 0.936207i) q^{70} +(-2.22740 + 0.810707i) q^{71} +(1.30703 + 0.821744i) q^{72} +(4.77080 + 4.00317i) q^{73} +(3.71238 + 0.929229i) q^{74} +6.93925 q^{75} +(6.68436 - 5.59637i) q^{76} +3.30942 q^{77} +(-9.95115 - 2.49082i) q^{78} +(-10.7050 - 8.98260i) q^{79} +(2.43755 + 1.78472i) q^{80} +(6.63847 - 2.41621i) q^{81} +(4.68854 + 6.46572i) q^{82} +(-10.7411 + 6.20140i) q^{83} +(2.66929 + 2.09340i) q^{84} +(-0.632685 - 3.58814i) q^{85} +(-9.87109 + 1.02832i) q^{86} +(8.79329 + 5.07681i) q^{87} +(-8.22969 + 2.64891i) q^{88} +(3.51946 + 4.19433i) q^{89} +(-0.560587 + 0.160188i) q^{90} +(4.71082 + 1.71460i) q^{91} +(-5.66437 + 5.08139i) q^{92} +(0.135593 - 0.768988i) q^{93} +(0.844082 - 11.9135i) q^{94} +(-0.112447 + 3.29022i) q^{95} +(-8.31342 - 3.06921i) q^{96} +(-3.44962 - 0.608262i) q^{97} +(5.92332 + 5.73062i) q^{98} +(0.570646 - 1.56784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$

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 $

$2$	0.343391	−	1.37189i	0.242814	−	0.970073i
$2$	0.343391	−	1.37189i	0.242814	−	0.970073i
$3$	−1.20007	−	1.00697i	−0.692858	−	0.581377i	0.226874	−	0.973924i	$-0.427149\pi$
$3$	−1.20007	−	1.00697i	−0.692858	−	0.581377i	−0.919732	+	0.392547i	$0.871594\pi$
$4$	−1.76416	−	0.942190i	−0.882082	−	0.471095i
$5$	0.709721	−	0.258317i	0.317397	−	0.115523i	−0.178409	−	0.983956i	$-0.557095\pi$
$5$	0.709721	−	0.258317i	0.317397	−	0.115523i	0.495806	+	0.868433i	$0.334873\pi$
$6$	−1.79355	+	1.30057i	−0.732214	+	0.530956i
$7$	0.937645	−	0.541349i	0.354396	−	0.204611i	−0.312223	−	0.950009i	$-0.601074\pi$
$7$	0.937645	−	0.541349i	0.354396	−	0.204611i	0.666620	+	0.745398i	$0.267740\pi$
$8$	−1.89838	+	2.09670i	−0.671179	+	0.741296i
$9$	−0.0947852	−	0.537553i	−0.0315951	−	0.179184i
$10$	−0.110671	−	1.06236i	−0.0349972	−	0.335949i
$11$	2.64713	+	1.52832i	0.798140	+	0.460806i	0.842820	−	0.538195i	$-0.180894\pi$
$11$	2.64713	+	1.52832i	0.798140	+	0.460806i	−0.0446804	+	0.999001i	$0.514227\pi$
$12$	1.16835	+	2.90716i	0.337274	+	0.839224i
$13$	2.97626	+	3.54697i	0.825465	+	0.983751i	1.00000		0.000899967i	$-0.000286468\pi$
$13$	2.97626	+	3.54697i	0.825465	+	0.983751i	−0.174534	+	0.984651i	$0.555842\pi$
$14$	−0.420693	−	1.47224i	−0.112435	−	0.393473i
$15$	−1.11183	−	0.404673i	−0.287073	−	0.104486i
$16$	2.22456	+	3.32436i	0.556139	+	0.831089i
$17$	0.837695	−	4.75081i	0.203171	−	1.15224i	−0.697121	−	0.716953i	$-0.745536\pi$
$17$	0.837695	−	4.75081i	0.203171	−	1.15224i	0.900292	−	0.435286i	$-0.143353\pi$
$18$	−0.770013	−	0.0545563i	−0.181494	−	0.0128590i
$19$	−1.62987	+	4.04271i	−0.373917	+	0.927462i
$19$	−1.62987	+	4.04271i	−0.373917	+	0.927462i
$20$	−1.49545	−	0.212978i	−0.334392	−	0.0476232i
$21$	−1.67036	−	0.294530i	−0.364502	−	0.0642716i
$22$	3.00569	−	3.10676i	0.640815	−	0.662363i
$23$	1.30131	−	3.57533i	0.271343	−	0.745508i	−0.726927	−	0.686714i	$-0.759052\pi$
$23$	1.30131	−	3.57533i	0.271343	−	0.745508i	0.998270	−	0.0587937i	$-0.0187254\pi$
$24$	4.38950	−	0.604558i	0.896004	−	0.123405i
$25$	−3.39325	+	2.84727i	−0.678649	+	0.569454i
$26$	5.88807	−	2.86510i	1.15474	−	0.561893i
$27$	−2.77742	+	4.81062i	−0.534514	+	0.925805i
$28$	−2.16421	+	0.0715903i	−0.408998	+	0.0135293i
$29$	−6.38295	+	1.12549i	−1.18528	+	0.208997i	−0.731327	−	0.682027i	$-0.761099\pi$
$29$	−6.38295	+	1.12549i	−1.18528	+	0.208997i	−0.453956	+	0.891024i	$0.649988\pi$
$30$	−0.936960	+	1.38635i	−0.171065	+	0.253111i
$31$	0.249223	+	0.431666i	0.0447617	+	0.0775295i	0.887538	−	0.460734i	$-0.152414\pi$
$31$	0.249223	+	0.431666i	0.0447617	+	0.0775295i	−0.842777	+	0.538264i	$0.819080\pi$
$32$	5.32455	−	1.91029i	0.941256	−	0.337695i
$33$	−1.63775	−	4.49968i	−0.285095	−	0.783293i
$34$	−6.22993	−	2.78061i	−1.06842	−	0.476871i
$35$	0.525626	−	0.626417i	0.0888470	−	0.105884i
$36$	−0.339261	+	1.03764i	−0.0565435	+	0.172940i
$37$			2.70604i			0.444870i	0.974948	+	0.222435i	$0.0714005\pi$
$37$			2.70604i			0.444870i	−0.974948	+	0.222435i	$0.928600\pi$
$38$	4.98648	+	3.62423i	0.808914	+	0.587928i
$39$		−	7.25360i		−	1.16151i
$40$	−0.805706	+	1.97846i	−0.127393	+	0.312821i
$41$	−3.63013	+	4.32622i	−0.566930	+	0.675641i	−0.970998	−	0.239088i	$-0.923152\pi$
$41$	−3.63013	+	4.32622i	−0.566930	+	0.675641i	0.404068	+	0.914729i	$0.367596\pi$
$42$	−0.977649	+	2.19041i	−0.150855	+	0.337988i
$43$	−2.40019	−	6.59447i	−0.366026	−	1.00565i	−0.976858	−	0.213888i	$-0.931387\pi$
$43$	−2.40019	−	6.59447i	−0.366026	−	1.00565i	0.610833	−	0.791760i	$-0.290835\pi$
$44$	−3.23001	−	5.19031i	−0.486942	−	0.782469i
$45$	−0.206130	−	0.357028i	−0.0307281	−	0.0532226i
$46$	−4.45810	−	3.01300i	−0.657311	−	0.444242i
$47$	8.31690	−	1.46649i	1.21314	−	0.213910i	0.469772	−	0.882788i	$-0.344336\pi$
$47$	8.31690	−	1.46649i	1.21314	−	0.213910i	0.743373	+	0.668877i	$0.233225\pi$
$48$	0.677930	−	6.22952i	0.0978507	−	0.899153i
$49$	−2.91388	+	5.04699i	−0.416269	+	0.720999i
$50$	2.74093	+	5.63289i	0.387626	+	0.796611i
$51$	−5.78923	+	4.85774i	−0.810654	+	0.680219i
$52$	−1.90869	−	9.06163i	−0.264688	−	1.25662i
$53$	4.64782	−	12.7698i	0.638427	−	1.75406i	−0.0181838	−	0.999835i	$-0.505788\pi$
$53$	4.64782	−	12.7698i	0.638427	−	1.75406i	0.656611	−	0.754229i	$-0.271989\pi$
$54$	5.64591	+	5.46223i	0.768311	+	0.743316i
$55$	2.27352	+	0.400882i	0.306561	+	0.0540549i
$56$	−0.644958	+	2.99365i	−0.0861862	+	0.400043i
$57$	6.02685	−	3.21029i	0.798276	−	0.425213i
$58$	−0.647805	+	9.14318i	−0.0850609	+	1.20056i
$59$	−0.185976	+	1.05472i	−0.0242121	+	0.137313i	−0.994518	−	0.104569i	$-0.966654\pi$
$59$	−0.185976	+	1.05472i	−0.0242121	+	0.137313i	0.970306	+	0.241882i	$0.0777648\pi$
$60$	1.58017	+	1.76146i	0.203999	+	0.227404i
$61$	5.54306	+	2.01751i	0.709715	+	0.258315i	0.671553	−	0.740956i	$-0.265627\pi$
$61$	5.54306	+	2.01751i	0.709715	+	0.258315i	0.0381622	+	0.999272i	$0.487850\pi$
$62$	0.677779	−	0.193676i	0.0860781	−	0.0245968i
$63$	−0.379879	−	0.452722i	−0.0478603	−	0.0570376i
$64$	−0.792308	−	7.96067i	−0.0990385	−	0.995084i
$65$	3.02855	+	1.74854i	0.375646	+	0.216879i
$66$	−6.73545	+	0.701662i	−0.829077	+	0.0863686i
$67$	2.28900	+	12.9816i	0.279646	+	1.58595i	0.723806	+	0.690003i	$0.242391\pi$
$67$	2.28900	+	12.9816i	0.279646	+	1.58595i	−0.444160	+	0.895947i	$0.646498\pi$
$68$	−5.95399	+	7.59194i	−0.722028	+	0.920657i
$69$	−5.16193	+	2.98024i	−0.621423	+	0.358779i
$70$	−0.678880	−	0.936207i	−0.0811416	−	0.111898i
$71$	−2.22740	+	0.810707i	−0.264344	+	0.0962132i	−0.470792	−	0.882244i	$-0.656032\pi$
$71$	−2.22740	+	0.810707i	−0.264344	+	0.0962132i	0.206448	+	0.978458i	$0.433809\pi$
$72$	1.30703	+	0.821744i	0.154035	+	0.0968435i
$73$	4.77080	+	4.00317i	0.558380	+	0.468536i	0.877767	−	0.479088i	$-0.159033\pi$
$73$	4.77080	+	4.00317i	0.558380	+	0.468536i	−0.319387	+	0.947624i	$0.603477\pi$
$74$	3.71238	+	0.929229i	0.431556	+	0.108021i
$75$	6.93925			0.801275
$76$	6.68436	−	5.59637i	0.766748	−	0.641948i
$77$	3.30942			0.377144
$78$	−9.95115	−	2.49082i	−1.12675	−	0.282030i
$79$	−10.7050	−	8.98260i	−1.20441	−	1.01062i	−0.999493	−	0.0318423i	$-0.989863\pi$
$79$	−10.7050	−	8.98260i	−1.20441	−	1.01062i	−0.204919	−	0.978779i	$-0.565693\pi$
$80$	2.43755	+	1.78472i	0.272527	+	0.199538i
$81$	6.63847	−	2.41621i	0.737608	−	0.268467i
$82$	4.68854	+	6.46572i	0.517763	+	0.714019i
$83$	−10.7411	+	6.20140i	−1.17899	+	0.680692i	−0.955782	−	0.294077i	$-0.904988\pi$
$83$	−10.7411	+	6.20140i	−1.17899	+	0.680692i	−0.223212	+	0.974770i	$0.571654\pi$
$84$	2.66929	+	2.09340i	0.291243	+	0.228408i
$85$	−0.632685	−	3.58814i	−0.0686243	−	0.389188i
$86$	−9.87109	+	1.02832i	−1.06443	+	0.110886i
$87$	8.79329	+	5.07681i	0.942739	+	0.544291i
$88$	−8.22969	+	2.64891i	−0.877288	+	0.282374i
$89$	3.51946	+	4.19433i	0.373062	+	0.444598i	0.919612	−	0.392828i	$-0.128503\pi$
$89$	3.51946	+	4.19433i	0.373062	+	0.444598i	−0.546549	+	0.837427i	$0.684059\pi$
$90$	−0.560587	+	0.160188i	−0.0590910	+	0.0168853i
$91$	4.71082	+	1.71460i	0.493828	+	0.179739i
$92$	−5.66437	+	5.08139i	−0.590552	+	0.529771i
$93$	0.135593	−	0.768988i	0.0140604	−	0.0797404i
$94$	0.844082	−	11.9135i	0.0870604	−	1.22878i
$95$	−0.112447	+	3.29022i	−0.0115368	+	0.337569i
$96$	−8.31342	−	3.06921i	−0.848485	−	0.313250i
$97$	−3.44962	−	0.608262i	−0.350256	−	0.0617596i	−0.00424764	−	0.999991i	$-0.501352\pi$
$97$	−3.44962	−	0.608262i	−0.350256	−	0.0617596i	−0.346009	+	0.938231i	$0.612463\pi$
$98$	5.92332	+	5.73062i	0.598345	+	0.578880i
$99$	0.570646	−	1.56784i	0.0573520	−	0.157573i
$100$	8.66892	−	1.82597i	0.866892	−	0.182597i
$101$	−0.588423	+	0.493745i	−0.0585502	+	0.0491295i	−0.671593	−	0.740920i	$-0.734390\pi$
$101$	−0.588423	+	0.493745i	−0.0585502	+	0.0491295i	0.613043	+	0.790050i	$0.289945\pi$
$102$	4.67631	+	9.61029i	0.463024	+	0.951560i
$103$	7.50991	−	13.0075i	0.739973	−	1.28167i	−0.212533	−	0.977154i	$-0.568171\pi$
$103$	7.50991	−	13.0075i	0.739973	−	1.28167i	0.952507	−	0.304518i	$-0.0984953\pi$
$104$	−13.0870	−	0.493166i	−1.28329	−	0.0483589i
$105$	−1.26157	+	0.222449i	−0.123117	+	0.0217088i
$106$	−15.9227	−	10.7613i	−1.54655	−	1.04523i
$107$	−7.48422	−	12.9630i	−0.723527	−	1.25319i	−0.959578	−	0.281444i	$-0.909187\pi$
$107$	−7.48422	−	12.9630i	−0.723527	−	1.25319i	0.236051	−	0.971741i	$-0.424147\pi$
$108$	9.43234	−	5.86988i	0.907627	−	0.564830i
$109$	−1.20073	−	3.29897i	−0.115009	−	0.315984i	0.868811	−	0.495143i	$-0.164884\pi$
$109$	−1.20073	−	3.29897i	−0.115009	−	0.315984i	−0.983820	+	0.179160i	$0.942662\pi$
$110$	1.33067	−	2.98135i	0.126875	−	0.284261i
$111$	2.72491	−	3.24742i	0.258637	−	0.308231i
$112$	3.88548	+	1.91280i	0.367144	+	0.180743i
$113$		−	4.87099i		−	0.458224i	−0.973400	−	0.229112i	$-0.926418\pi$
$113$		−	4.87099i		−	0.458224i	0.973400	−	0.229112i	$-0.0735823\pi$
$114$	−2.33459	−	9.37057i	−0.218655	−	0.877634i
$115$		−	2.87364i		−	0.267968i
$116$	12.3210	+	4.02841i	1.14398	+	0.374028i
$117$	1.62458	−	1.93610i	0.150192	−	0.178992i
$118$	1.38310	+	0.617322i	0.127325	+	0.0568291i
$119$	−1.78639	−	4.90805i	−0.163758	−	0.449921i
$120$	2.95915	−	1.56295i	0.270133	−	0.142677i
$121$	−0.828467	−	1.43495i	−0.0753151	−	0.130450i
$122$	4.67123	−	6.91167i	0.422914	−	0.625753i
$123$	8.71278	−	1.53630i	0.785605	−	0.138523i
$124$	−0.0329582	−	0.996345i	−0.00295973	−	0.0894744i
$125$	−3.56093	+	6.16771i	−0.318499	+	0.551657i
$126$	−0.751532	+	0.365691i	−0.0669518	+	0.0325784i
$127$	−8.42048	+	7.06562i	−0.747197	+	0.626973i	−0.934760	−	0.355280i	$-0.884386\pi$
$127$	−8.42048	+	7.06562i	−0.747197	+	0.626973i	0.187563	+	0.982253i	$0.439941\pi$
$128$	−11.1932	−	1.64666i	−0.989352	−	0.145546i
$129$	−3.76008	+	10.3307i	−0.331056	+	0.909570i
$130$	3.43878	−	3.55441i	0.301601	−	0.311742i
$131$	−10.7902	−	1.90260i	−0.942741	−	0.166231i	−0.318906	−	0.947786i	$-0.603315\pi$
$131$	−10.7902	−	1.90260i	−0.942741	−	0.166231i	−0.623835	+	0.781556i	$0.714426\pi$
$132$	−1.35029	+	9.48125i	−0.117528	+	0.825236i
$133$	0.660287	+	4.67296i	0.0572541	+	0.405197i
$134$	18.5953	+	1.31750i	1.60639	+	0.113815i
$135$	−0.728522	+	4.13165i	−0.0627012	+	0.355596i
$136$	8.37075	+	10.7752i	0.717786	+	0.923968i
$137$	−11.6234	−	4.23059i	−0.993057	−	0.361443i	−0.206154	−	0.978520i	$-0.566095\pi$
$137$	−11.6234	−	4.23059i	−0.993057	−	0.361443i	−0.786903	+	0.617076i	$0.788317\pi$
$138$	2.31600	+	8.10499i	0.197151	+	0.689942i
$139$	5.97171	+	7.11681i	0.506514	+	0.603640i	0.957337	−	0.288974i	$-0.0933140\pi$
$139$	5.97171	+	7.11681i	0.506514	+	0.603640i	−0.450823	+	0.892613i	$0.648870\pi$
$140$	−1.51749	+	0.609863i	−0.128252	+	0.0515428i
$141$	−11.4575	−	6.61502i	−0.964900	−	0.557085i
$142$	0.347332	+	3.33414i	0.0291474	+	0.279794i
$143$	2.45764	+	13.9380i	0.205518	+	1.16555i
$144$	1.57616	−	1.51092i	0.131347	−	0.125910i
$145$	−4.23938	+	2.44760i	−0.352061	+	0.203263i
$146$	7.13017	−	5.17036i	0.590097	−	0.427902i
$147$	8.57904	−	3.12251i	0.707587	−	0.257541i
$148$	2.54960	−	4.77389i	0.209576	−	0.392412i
$149$	−0.921936	−	0.773596i	−0.0755280	−	0.0633755i	0.604242	−	0.796801i	$-0.293476\pi$
$149$	−0.921936	−	0.773596i	−0.0755280	−	0.0633755i	−0.679770	+	0.733425i	$0.737920\pi$
$150$	2.38288	−	9.51988i	0.194561	−	0.777295i
$151$	−2.35305			−0.191489			−0.0957444	−	0.995406i	$-0.530523\pi$
$151$	−2.35305			−0.191489			−0.0957444	+	0.995406i	$0.530523\pi$
$152$	−5.38226	−	11.0919i	−0.436559	−	0.899676i
$153$	−2.63321			−0.212883
$154$	1.13643	−	4.54017i	0.0915759	−	0.365857i
$155$	0.288385	+	0.241984i	0.0231637	+	0.0194366i
$156$	−6.83427	+	12.7966i	−0.547180	+	1.02454i
$157$	−3.10209	+	1.12907i	−0.247573	+	0.0901093i	−0.462826	−	0.886449i	$-0.653165\pi$
$157$	−3.10209	+	1.12907i	−0.247573	+	0.0901093i	0.215253	+	0.976558i	$0.430942\pi$
$158$	−15.9992	+	11.6016i	−1.27282	+	0.922974i
$159$	−18.4365	+	10.6443i	−1.46211	+	0.844151i
$160$	3.28548	−	2.73120i	0.259740	−	0.215920i
$161$	−0.715333	−	4.05686i	−0.0563762	−	0.319725i
$162$	−1.03518	−	9.93696i	−0.0813312	−	0.780721i
$163$	0.156238	+	0.0902042i	0.0122375	+	0.00706534i	0.506106	−	0.862471i	$-0.331084\pi$
$163$	0.156238	+	0.0902042i	0.0122375	+	0.00706534i	−0.493869	+	0.869536i	$0.664418\pi$
$164$	10.4803	−	4.21189i	0.818371	−	0.328893i
$165$	−2.32469	−	2.77046i	−0.180977	−	0.215680i
$166$	4.81923	+	16.8652i	0.374045	+	1.30899i
$167$	12.2782	+	4.46888i	0.950112	+	0.345813i	0.770151	−	0.637861i	$-0.220181\pi$
$167$	12.2782	+	4.46888i	0.950112	+	0.345813i	0.179961	+	0.983674i	$0.442403\pi$
$168$	3.78852	−	2.94312i	0.292291	−	0.227066i
$169$	−1.46543	+	8.31086i	−0.112725	+	0.639297i
$170$	−5.13979	−	0.364160i	−0.394204	−	0.0279298i
$171$	2.32766	+	0.492950i	0.178001	+	0.0376968i
$172$	−1.97891	+	13.8952i	−0.150891	+	1.05950i
$173$	1.30043	+	0.229300i	0.0988695	+	0.0174334i	0.222864	−	0.974850i	$-0.428459\pi$
$173$	1.30043	+	0.229300i	0.0988695	+	0.0174334i	−0.123995	+	0.992283i	$0.539571\pi$
$174$	9.98436	−	10.3201i	0.756912	−	0.782364i
$175$	−1.64029	+	4.50666i	−0.123994	+	0.340672i
$176$	0.808004	+	12.1998i	0.0609056	+	0.919598i
$177$	1.28526	−	1.07846i	0.0966064	−	0.0810624i
$178$	6.96272	−	3.38802i	0.521878	−	0.253943i
$179$	−4.15946	+	7.20439i	−0.310892	+	0.538481i	−0.978556	−	0.205982i	$-0.933961\pi$
$179$	−4.15946	+	7.20439i	−0.310892	+	0.538481i	0.667663	+	0.744463i	$0.267295\pi$
$180$	0.0272595	+	0.824070i	0.00203180	+	0.0614226i
$181$	14.1155	−	2.48894i	1.04920	−	0.185001i	0.377637	−	0.925954i	$-0.376737\pi$
$181$	14.1155	−	2.48894i	1.04920	−	0.185001i	0.671558	+	0.740952i	$0.265625\pi$
$182$	3.96989	−	5.87395i	0.294268	−	0.435406i
$183$	−4.62045	−	8.00285i	−0.341554	−	0.591588i
$184$	5.02601	+	9.51580i	0.370522	+	0.701514i
$185$	0.699016	+	1.92053i	0.0513927	+	0.141200i
$186$	−1.00841	−	0.450083i	−0.0739399	−	0.0330017i
$187$	9.47825	−	11.2957i	0.693118	−	0.826026i
$188$	−16.0541	−	5.24896i	−1.17087	−	0.382820i
$189$			6.01421i			0.437469i
$190$	4.47521	+	1.28410i	0.324666	+	0.0931582i
$191$		−	3.41758i		−	0.247287i	−0.992327	−	0.123644i	$-0.960542\pi$
$191$		−	3.41758i		−	0.247287i	0.992327	−	0.123644i	$-0.0394580\pi$
$192$	−7.06537	+	10.3512i	−0.509899	+	0.747030i
$193$	12.8703	−	15.3383i	0.926428	−	1.10407i	−0.0678973	−	0.997692i	$-0.521629\pi$
$193$	12.8703	−	15.3383i	0.926428	−	1.10407i	0.994325	−	0.106382i	$-0.0339265\pi$
$194$	−2.01904	+	4.52363i	−0.144959	+	0.324778i
$195$	−1.87373	−	5.14803i	−0.134181	−	0.368658i
$196$	9.89579	−	6.15829i	0.706842	−	0.439878i
$197$	6.96502	+	12.0638i	0.496237	+	0.859508i	0.999991	−	0.00433940i	$-0.00138128\pi$
$197$	6.96502	+	12.0638i	0.496237	+	0.859508i	−0.503753	+	0.863848i	$0.668048\pi$
$198$	−1.95494	−	1.32124i	−0.138932	−	0.0938967i
$199$	24.0045	−	4.23264i	1.70164	−	0.300044i	0.763370	−	0.645961i	$-0.223543\pi$
$199$	24.0045	−	4.23264i	1.70164	−	0.300044i	0.938265	+	0.345917i	$0.112432\pi$
$200$	0.471794	−	12.5198i	0.0333608	−	0.885285i
$201$	10.3252	−	17.8837i	0.728280	−	1.26142i
$202$	0.475305	+	0.976799i	0.0334423	+	0.0687273i
$203$	−5.37565	+	4.51071i	−0.377297	+	0.316590i
$204$	14.7901	−	3.11530i	1.03551	−	0.218115i
$205$	−1.45884	+	4.00813i	−0.101890	+	0.279940i
$206$	−15.2661	−	14.7694i	−1.06364	−	1.02904i
$207$	−2.04528	−	0.360637i	−0.142157	−	0.0250660i
$208$	−5.17053	+	17.7846i	−0.358512	+	1.23314i
$209$	−10.4930	+	8.21063i	−0.725818	+	0.567941i
$210$	−0.128037	+	1.80712i	−0.00883538	+	0.124703i
$211$	2.02045	−	11.4585i	0.139093	−	0.788837i	−0.832828	−	0.553531i	$-0.813280\pi$
$211$	2.02045	−	11.4585i	0.139093	−	0.788837i	0.971921	−	0.235305i	$-0.0756090\pi$
$212$	−20.2311	+	18.1489i	−1.38948	+	1.24647i
$213$	3.48938	+	1.27003i	0.239089	+	0.0870212i
$214$	−20.3539	+	5.81613i	−1.39136	+	0.397582i
$215$	−3.40693	−	4.06022i	−0.232351	−	0.276905i
$216$	−4.81385	−	14.9558i	−0.327541	−	1.01761i
$217$	0.467364	+	0.269833i	0.0317268	+	0.0183175i
$218$	−4.93814	+	0.514427i	−0.334453	+	0.0348414i
$219$	−1.69417	−	9.60814i	−0.114482	−	0.649258i
$220$	−3.63315	−	2.84931i	−0.244947	−	0.192100i
$221$	19.3441	−	11.1683i	1.30123	−	0.751264i
$222$	−3.51939	−	4.85341i	−0.236206	−	0.325740i
$223$	−18.9595	+	6.90070i	−1.26962	+	0.462105i	−0.886987	−	0.461794i	$-0.847206\pi$
$223$	−18.9595	+	6.90070i	−1.26962	+	0.462105i	−0.382636	+	0.923899i	$0.624984\pi$
$224$	3.95840	−	4.67362i	0.264482	−	0.312269i
$225$	1.85219	+	1.55417i	0.123479	+	0.103611i
$226$	−6.68247	−	1.67266i	−0.444511	−	0.111263i
$227$	−4.00906			−0.266091			−0.133045	−	0.991110i	$-0.542476\pi$
$227$	−4.00906			−0.266091			−0.133045	+	0.991110i	$0.542476\pi$
$228$	−13.6571	−	0.0149632i	−0.904461	−	0.000990962i
$229$	−21.5588			−1.42465			−0.712324	−	0.701851i	$-0.752357\pi$
$229$	−21.5588			−1.42465			−0.712324	+	0.701851i	$0.752357\pi$
$230$	−3.94232	−	0.986782i	−0.259949	−	0.0650665i
$231$	−3.97153	−	3.33251i	−0.261307	−	0.219263i
$232$	9.75745	−	15.5197i	0.640608	−	1.01892i
$233$	0.862546	−	0.313941i	0.0565073	−	0.0205670i	−0.313612	−	0.949551i	$-0.601539\pi$
$233$	0.862546	−	0.313941i	0.0565073	−	0.0205670i	0.370119	+	0.928984i	$0.379317\pi$
$234$	−2.09825	−	2.89358i	−0.137167	−	0.189159i
$235$	5.52386	−	3.18920i	0.360337	−	0.208040i
$236$	1.32184	−	1.68548i	0.0860447	−	0.109716i
$237$	3.80151	+	21.5594i	0.246934	+	1.40043i
$238$	−7.34674	+	0.765342i	−0.476218	+	0.0496098i
$239$	11.7324	+	6.77369i	0.758904	+	0.438154i	0.828902	−	0.559394i	$-0.188966\pi$
$239$	11.7324	+	6.77369i	0.758904	+	0.438154i	−0.0699979	+	0.997547i	$0.522299\pi$
$240$	−1.12805	−	4.59634i	−0.0728153	−	0.296692i
$241$	−7.78203	−	9.27426i	−0.501284	−	0.597408i	0.454766	−	0.890611i	$-0.349723\pi$
$241$	−7.78203	−	9.27426i	−0.501284	−	0.597408i	−0.956050	+	0.293204i	$0.905279\pi$
$242$	−2.25308	+	0.643817i	−0.144833	+	0.0413861i
$243$	5.25984	+	1.91443i	0.337419	+	0.122810i
$244$	−7.87799	−	8.78183i	−0.504337	−	0.562199i
$245$	−0.764317	+	4.33466i	−0.0488304	+	0.276931i
$246$	0.884259	−	12.4805i	0.0563783	−	0.795729i
$247$	−19.1903	+	6.25108i	−1.22105	+	0.397747i
$248$	−1.37819	−	0.296921i	−0.0875154	−	0.0188545i
$249$	19.1347	+	3.37397i	1.21261	+	0.213817i
$250$	7.23863	+	7.00314i	0.457811	+	0.442918i
$251$	6.39165	−	17.5609i	0.403437	−	1.10843i	−0.557139	−	0.830419i	$-0.688101\pi$
$251$	6.39165	−	17.5609i	0.403437	−	1.10843i	0.960577	−	0.278016i	$-0.0896768\pi$
$252$	0.243619	+	1.15659i	0.0153466	+	0.0728586i
$253$	8.90900	−	7.47554i	0.560104	−	0.469983i
$254$	6.80174	+	13.9783i	0.426779	+	0.877073i
$255$	−2.85390	+	4.94309i	−0.178718	+	0.309549i
$256$	−6.10270	+	14.7904i	−0.381419	+	0.924402i
$257$	9.08137	−	1.60129i	0.566481	−	0.0998858i	0.116929	−	0.993140i	$-0.462695\pi$
$257$	9.08137	−	1.60129i	0.566481	−	0.0998858i	0.449551	+	0.893254i	$0.351584\pi$
$258$	12.8814	+	8.70589i	0.801964	+	0.542005i
$259$	1.46491	+	2.53730i	0.0910252	+	0.157660i
$260$	−3.69541	−	5.93818i	−0.229180	−	0.368270i
$261$	1.21002	+	3.32449i	0.0748982	+	0.205781i
$262$	−6.31540	+	14.1496i	−0.390167	+	0.874164i
$263$	−5.04261	+	6.00955i	−0.310941	+	0.370565i	−0.898770	−	0.438420i	$-0.855538\pi$
$263$	−5.04261	+	6.00955i	−0.310941	+	0.370565i	0.587829	+	0.808985i	$0.299983\pi$
$264$	12.5435	+	5.10823i	0.772002	+	0.314390i
$265$		−	10.2636i		−	0.630487i
$266$	6.63752	+	0.698812i	0.406972	+	0.0428469i
$267$		−	8.57748i		−	0.524933i
$268$	8.19293	−	25.0583i	0.500463	−	1.53068i
$269$	−7.71584	+	9.19538i	−0.470443	+	0.560652i	−0.948132	−	0.317877i	$-0.897030\pi$
$269$	−7.71584	+	9.19538i	−0.470443	+	0.560652i	0.477689	+	0.878529i	$0.341475\pi$
$270$	5.41801	+	2.41823i	0.329729	+	0.147169i
$271$	9.12276	+	25.0646i	0.554168	+	1.52256i	0.827967	+	0.560777i	$0.189498\pi$
$271$	9.12276	+	25.0646i	0.554168	+	1.52256i	−0.273799	+	0.961787i	$0.588280\pi$
$272$	17.6569	−	7.78364i	1.07061	−	0.471952i
$273$	−3.92673	−	6.80130i	−0.237657	−	0.411634i
$274$	−9.79529	+	14.4933i	−0.591755	+	0.875574i
$275$	−13.3339	+	2.35113i	−0.804065	+	0.141778i
$276$	11.9144	−	0.394119i	0.717165	−	0.0237232i
$277$	8.66220	−	15.0034i	0.520461	−	0.901465i	−0.479256	−	0.877675i	$-0.659093\pi$
$277$	8.66220	−	15.0034i	0.520461	−	0.901465i	0.999717	−	0.0237896i	$-0.00757318\pi$
$278$	11.8141	−	5.74868i	0.708563	−	0.344783i
$279$	0.208421	−	0.174886i	0.0124778	−	0.0104701i
$280$	0.315571	+	2.29126i	0.0188589	+	0.136929i
$281$	−5.38466	+	14.7942i	−0.321222	+	0.882549i	0.669027	+	0.743238i	$0.266711\pi$
$281$	−5.38466	+	14.7942i	−0.321222	+	0.882549i	−0.990249	+	0.139311i	$0.955511\pi$
$282$	−13.0095	+	13.4470i	−0.774704	+	0.800755i
$283$	3.40324	+	0.600082i	0.202301	+	0.0356712i	0.273880	−	0.961764i	$-0.411693\pi$
$283$	3.40324	+	0.600082i	0.202301	+	0.0356712i	−0.0715791	+	0.997435i	$0.522804\pi$
$284$	4.69334	+	0.668412i	0.278498	+	0.0396630i
$285$	3.44811	−	3.83525i	0.204248	−	0.227181i
$286$	19.9653	+	1.41456i	1.18057	+	0.0836448i
$287$	−1.06177	+	6.02162i	−0.0626745	+	0.355445i
$288$	−1.53157	−	2.68116i	−0.0902487	−	0.157989i
$289$	−5.89364	−	2.14511i	−0.346685	−	0.126183i
$290$	1.90208	+	6.65644i	0.111694	+	0.390880i
$291$	3.52727	+	4.20364i	0.206772	+	0.246421i
$292$	−4.64472	−	11.5573i	−0.271812	−	0.676337i
$293$	12.9386	+	7.47010i	0.755881	+	0.436408i	0.827815	−	0.561001i	$-0.189584\pi$
$293$	12.9386	+	7.47010i	0.755881	+	0.436408i	−0.0719340	+	0.997409i	$0.522917\pi$
$294$	−1.33778	−	12.8417i	−0.0780210	−	0.748946i
$295$	0.140462	+	0.796601i	0.00817802	+	0.0463799i
$296$	−5.67375	−	5.13708i	−0.329780	−	0.298587i
$297$	−14.7044	+	8.48957i	−0.853234	+	0.492615i
$298$	−1.37787	+	0.999149i	−0.0798181	+	0.0578791i
$299$	16.5546	−	6.02539i	0.957378	−	0.348457i
$300$	−12.2420	−	6.53809i	−0.706791	−	0.377477i
$301$	−5.82044	−	4.88393i	−0.335485	−	0.281505i
$302$	−0.808018	+	3.22813i	−0.0464962	+	0.185758i
$303$	1.20333			0.0691297
$304$	−17.0652	+	3.57499i	−0.978754	+	0.205040i
$305$	4.45518			0.255103
$306$	−0.904222	+	3.61248i	−0.0516909	+	0.206512i
$307$	−2.10257	−	1.76426i	−0.120000	−	0.100692i	0.580813	−	0.814037i	$-0.302735\pi$
$307$	−2.10257	−	1.76426i	−0.120000	−	0.100692i	−0.700813	+	0.713345i	$0.747179\pi$
$308$	−5.83837	−	3.11811i	−0.332672	−	0.177671i
$309$	−22.1106	+	8.04762i	−1.25783	+	0.457813i
$310$	0.431004	−	0.312538i	0.0244794	−	0.0177509i
$311$	17.7003	−	10.2193i	1.00369	−	0.579481i	0.0943518	−	0.995539i	$-0.469922\pi$
$311$	17.7003	−	10.2193i	1.00369	−	0.579481i	0.909338	+	0.416058i	$0.136589\pi$
$312$	15.2086	+	13.7701i	0.861020	+	0.779578i
$313$	−3.53964	−	20.0743i	−0.200072	−	1.13467i	−0.905008	−	0.425395i	$-0.860135\pi$
$313$	−3.53964	−	20.0743i	−0.200072	−	1.13467i	0.704936	−	0.709271i	$-0.250976\pi$
$314$	0.483727	+	4.64343i	0.0272983	+	0.262044i
$315$	−0.386554	−	0.223177i	−0.0217798	−	0.0125746i
$316$	10.4221	+	25.9330i	0.586292	+	1.45884i
$317$	−18.5300	−	22.0832i	−1.04075	−	1.24032i	−0.970072	−	0.242818i	$-0.921928\pi$
$317$	−18.5300	−	22.0832i	−1.04075	−	1.24032i	−0.0706777	−	0.997499i	$-0.522516\pi$
$318$	8.27192	+	28.9481i	0.463866	+	1.62333i
$319$	−18.6166	−	6.77589i	−1.04233	−	0.379377i
$320$	−2.61870	−	5.44518i	−0.146390	−	0.304395i
$321$	−4.07190	+	23.0929i	−0.227272	+	1.28892i
$322$	−5.81120	−	0.411730i	−0.323846	−	0.0229448i
$323$	17.8408	+	11.1297i	0.992690	+	0.619275i
$324$	−13.9879	−	1.99212i	−0.777105	−	0.110673i
$325$	−20.1983	−	3.56151i	−1.12040	−	0.197557i
$326$	0.177401	−	0.183366i	0.00982534	−	0.0101557i
$327$	−1.88103	+	5.16807i	−0.104021	+	0.285795i
$328$	−2.17942	−	15.8241i	−0.120338	−	0.873739i
$329$	7.00441	−	5.87740i	0.386166	−	0.324032i
$330$	−4.59904	+	2.23787i	−0.253169	+	0.123191i
$331$	1.83809	−	3.18366i	0.101030	−	0.174990i	−0.811079	−	0.584937i	$-0.801119\pi$
$331$	1.83809	−	3.18366i	0.101030	−	0.174990i	0.912109	+	0.409947i	$0.134453\pi$
$332$	24.7921	−	0.820099i	1.36064	−	0.0450088i
$333$	1.45464	−	0.256492i	0.0797137	−	0.0140557i
$334$	10.3470	−	15.3097i	0.566164	−	0.837710i
$335$	4.97791	+	8.62200i	0.271972	+	0.471070i
$336$	−2.73669	−	6.20807i	−0.149299	−	0.338678i
$337$	10.2016	+	28.0286i	0.555716	+	1.52682i	0.825790	+	0.563978i	$0.190730\pi$
$337$	10.2016	+	28.0286i	0.555716	+	1.52682i	−0.270074	+	0.962840i	$0.587048\pi$
$338$	10.8984	+	4.86428i	0.592793	+	0.264582i
$339$	−4.90496	+	5.84551i	−0.266401	+	0.317484i
$340$	−2.26454	+	6.92617i	−0.122812	+	0.375624i
$341$			1.52357i			0.0825059i
$342$	1.47557	−	3.02402i	0.0797898	−	0.163520i
$343$			13.8886i			0.749914i
$344$	18.3831	+	7.48633i	0.991151	+	0.403636i
$345$	−2.89368	+	3.44855i	−0.155790	+	0.185664i
$346$	0.761129	−	1.70530i	0.0409186	−	0.0916776i
$347$	−9.95707	−	27.3568i	−0.534524	−	1.46859i	−0.853634	−	0.520874i	$-0.825606\pi$
$347$	−9.95707	−	27.3568i	−0.534524	−	1.46859i	0.319110	−	0.947718i	$-0.396616\pi$
$348$	−10.7295	−	17.2413i	−0.575161	−	0.924229i
$349$	−9.01897	−	15.6213i	−0.482774	−	0.836189i	0.517030	−	0.855967i	$-0.327037\pi$
$349$	−9.01897	−	15.6213i	−0.482774	−	0.836189i	−0.999804	+	0.0197778i	$0.993704\pi$
$350$	5.61938	+	3.79785i	0.300369	+	0.203003i
$351$	−25.3294	+	4.46626i	−1.35198	+	0.238391i
$352$	17.0143	+	3.08083i	0.906866	+	0.164209i
$353$	−13.3944	+	23.1997i	−0.712910	+	1.23480i	0.250850	+	0.968026i	$0.419290\pi$
$353$	−13.3944	+	23.1997i	−0.712910	+	1.23480i	−0.963760	+	0.266770i	$0.914044\pi$
$354$	−1.03819	−	2.13358i	−0.0551790	−	0.113398i
$355$	−1.37141	+	1.15075i	−0.0727870	+	0.0610755i
$356$	−2.25706	−	10.7155i	−0.119624	−	0.567920i
$357$	−2.79850	+	7.68883i	−0.148113	+	0.406936i
$358$	8.45531	+	8.18024i	0.446877	+	0.432339i
$359$	17.0891	+	3.01327i	0.901929	+	0.159034i	0.605337	−	0.795970i	$-0.293039\pi$
$359$	17.0891	+	3.01327i	0.901929	+	0.159034i	0.296593	+	0.955004i	$0.404150\pi$
$360$	1.13989	+	0.245581i	0.0600777	+	0.0129433i
$361$	−13.6871	−	13.1782i	−0.720373	−	0.693587i
$362$	1.43258	−	20.2196i	0.0752947	−	1.06272i
$363$	−0.450740	+	2.55627i	−0.0236577	+	0.134170i
$364$	−6.69519	−	7.46332i	−0.350923	−	0.391184i
$365$	4.42002	+	1.60876i	0.231355	+	0.0842062i
$366$	−12.5657	+	3.59064i	−0.656818	+	0.187686i
$367$	−14.8155	−	17.6564i	−0.773361	−	0.921656i	0.225252	−	0.974300i	$-0.427679\pi$
$367$	−14.8155	−	17.6564i	−0.773361	−	0.921656i	−0.998613	+	0.0526448i	$0.983235\pi$
$368$	14.7805	−	3.62749i	0.770488	−	0.189096i
$369$	2.66965	+	1.54133i	0.138977	+	0.0802382i
$370$	2.87479	−	0.299480i	0.149453	−	0.0155692i
$371$	−2.55491	−	14.4896i	−0.132644	−	0.752263i
$372$	−0.963742	+	1.22887i	−0.0499677	+	0.0637138i
$373$	12.3630	−	7.13780i	0.640133	−	0.369581i	−0.144533	−	0.989500i	$-0.546168\pi$
$373$	12.3630	−	7.13780i	0.640133	−	0.369581i	0.784666	+	0.619919i	$0.212835\pi$
$374$	−12.2418	−	16.8820i	−0.633006	−	0.872946i
$375$	10.4841	−	3.81589i	0.541395	−	0.197052i
$376$	−12.7138	+	20.2220i	−0.655666	+	1.04287i
$377$	−22.9893	−	19.2904i	−1.18401	−	0.993504i
$378$	8.25083	+	2.06523i	0.424377	+	0.106224i
$379$	3.94639			0.202713			0.101356	−	0.994850i	$-0.467682\pi$
$379$	3.94639			0.202713			0.101356	+	0.994850i	$0.467682\pi$
$380$	3.29839	−	5.69855i	0.169204	−	0.292329i
$381$	17.2200			0.882209
$382$	−4.68855	−	1.17357i	−0.239887	−	0.0600449i
$383$	2.54527	+	2.13574i	0.130057	+	0.109131i	0.705496	−	0.708714i	$-0.250724\pi$
$383$	2.54527	+	2.13574i	0.130057	+	0.109131i	−0.575439	+	0.817845i	$0.695169\pi$
$384$	11.7745	+	13.2474i	0.600863	+	0.676029i
$385$	2.34877	−	0.854881i	0.119704	−	0.0435688i
$386$	−16.6229	−	22.9237i	−0.846082	−	1.16679i
$387$	−3.31738	+	1.91529i	−0.168632	+	0.0973596i
$388$	5.51261	+	4.32327i	0.279860	+	0.219481i
$389$	1.28952	+	7.31325i	0.0653814	+	0.370797i	0.999890	+	0.0148550i	$0.00472867\pi$
$389$	1.28952	+	7.31325i	0.0653814	+	0.370797i	−0.934508	+	0.355942i	$0.884160\pi$
$390$	−7.70596	+	0.802764i	−0.390206	+	0.0406495i
$391$	−15.8956	−	9.17733i	−0.803875	−	0.464117i
$392$	−5.05038	−	15.6906i	−0.255082	−	0.792497i
$393$	11.0330	+	13.1487i	0.556543	+	0.663262i
$394$	18.9419	−	5.41265i	0.954279	−	0.272685i
$395$	−9.91795	−	3.60984i	−0.499026	−	0.181631i
$396$	−2.48391	+	2.22826i	−0.124821	+	0.111975i
$397$	3.75365	−	21.2880i	0.188390	−	1.06841i	−0.733132	−	0.680087i	$-0.761942\pi$
$397$	3.75365	−	21.2880i	0.188390	−	1.06841i	0.921522	−	0.388327i	$-0.126947\pi$
$398$	2.43622	−	34.3850i	0.122117	−	1.72357i
$399$	3.91316	−	6.27274i	0.195903	−	0.314030i
$400$	−17.0138	−	4.94645i	−0.850691	−	0.247322i
$401$	20.7532	+	3.65934i	1.03636	+	0.182739i	0.665848	−	0.746088i	$-0.268070\pi$
$401$	20.7532	+	3.65934i	1.03636	+	0.182739i	0.370515	+	0.928826i	$0.379181\pi$
$402$	−20.9889	−	20.3061i	−1.04683	−	1.01278i
$403$	−0.789354	+	2.16873i	−0.0393205	+	0.108032i
$404$	1.50328	−	0.316642i	0.0747908	−	0.0157535i
$405$	4.08731	−	3.42966i	0.203100	−	0.170421i
$406$	4.34225	+	8.92375i	0.215502	+	0.442878i
$407$	−4.13569	+	7.16323i	−0.204999	+	0.355068i
$408$	0.804928	−	21.3601i	0.0398499	−	1.05748i
$409$	−0.265891	+	0.0468838i	−0.0131475	+	0.00231825i	−0.180218	−	0.983627i	$-0.557680\pi$
$409$	−0.265891	+	0.0468838i	−0.0131475	+	0.00231825i	0.167071	+	0.985945i	$0.446569\pi$
$410$	4.99776	+	3.37772i	0.246822	+	0.166814i
$411$	9.68879	+	16.7815i	0.477913	+	0.827770i
$412$	−25.5043	+	15.8717i	−1.25651	+	0.781942i
$413$	0.396595	+	1.08964i	0.0195152	+	0.0536174i
$414$	−1.19708	+	2.68205i	−0.0588335	+	0.131816i
$415$	−6.02128	+	7.17589i	−0.295573	+	0.352250i
$416$	22.6230	+	13.2005i	1.10918	+	0.647206i
$417$		−	14.5540i		−	0.712712i
$418$	7.66087	+	17.2147i	0.374706	+	0.842001i
$419$		−	4.30895i		−	0.210506i	−0.994445	−	0.105253i	$-0.966435\pi$
$419$		−	4.30895i		−	0.210506i	0.994445	−	0.105253i	$-0.0335652\pi$
$420$	2.43521	+	0.796203i	0.118826	+	0.0388507i
$421$	−7.34047	+	8.74803i	−0.357753	+	0.426353i	−0.914661	−	0.404221i	$-0.867543\pi$
$421$	−7.34047	+	8.74803i	−0.357753	+	0.426353i	0.556909	+	0.830574i	$0.311987\pi$
$422$	−15.0260	−	6.70658i	−0.731455	−	0.326471i
$423$	−1.57664	−	4.33178i	−0.0766588	−	0.210618i
$424$	17.9511	+	33.9870i	0.871781	+	1.65055i
$425$	10.6843	+	18.5058i	0.518266	+	0.897663i
$426$	2.94057	−	4.35093i	0.142471	−	0.210803i
$427$	6.28959	−	1.10903i	0.304375	−	0.0536695i
$428$	0.989744	+	29.9205i	0.0478411	+	1.44626i
$429$	11.0858	−	19.2012i	0.535229	−	0.927044i
$430$	−6.74009	+	3.27969i	−0.325036	+	0.158161i
$431$	18.5249	−	15.5443i	0.892315	−	0.748741i	−0.0763579	−	0.997080i	$-0.524329\pi$
$431$	18.5249	−	15.5443i	0.892315	−	0.748741i	0.968673	+	0.248339i	$0.0798847\pi$
$432$	−22.1707	+	1.46838i	−1.06669	+	0.0706476i
$433$	−0.996702	+	2.73842i	−0.0478984	+	0.131600i	−0.961335	−	0.275381i	$-0.911196\pi$
$433$	−0.996702	+	2.73842i	−0.0478984	+	0.131600i	0.913437	+	0.406981i	$0.133418\pi$
$434$	0.530670	−	0.548514i	0.0254730	−	0.0263295i
$435$	7.55220	+	1.33166i	0.362100	+	0.0638481i
$436$	−0.989975	+	6.95123i	−0.0474112	+	0.332904i
$437$	12.3331	+	11.0881i	0.589971	+	0.530418i
$438$	−13.7631	−	0.975130i	−0.657625	−	0.0465935i
$439$	−1.63239	+	9.25775i	−0.0779098	+	0.441848i	0.920753	+	0.390147i	$0.127576\pi$
$439$	−1.63239	+	9.25775i	−0.0779098	+	0.441848i	−0.998663	+	0.0517018i	$0.983535\pi$
$440$	−5.15652	+	4.00585i	−0.245828	+	0.190972i
$441$	2.98922	+	1.08799i	0.142344	+	0.0518089i
$442$	−8.67913	−	30.3731i	−0.412824	−	1.44470i
$443$	5.87925	+	7.00661i	0.279331	+	0.332894i	0.887409	−	0.460984i	$-0.152503\pi$
$443$	5.87925	+	7.00661i	0.279331	+	0.332894i	−0.608077	+	0.793878i	$0.708059\pi$
$444$	−7.86688	+	3.16160i	−0.373345	+	0.150043i
$445$	3.58130	+	2.06767i	0.169770	+	0.0980168i
$446$	2.95647	+	28.3800i	0.139993	+	1.34383i
$447$	0.327392	+	1.85673i	0.0154851	+	0.0878204i
$448$	−5.05241	−	7.03536i	−0.238704	−	0.332390i
$449$	11.1663	−	6.44689i	0.526973	−	0.304248i	−0.212810	−	0.977094i	$-0.568262\pi$
$449$	11.1663	−	6.44689i	0.526973	−	0.304248i	0.739783	+	0.672846i	$0.234928\pi$
$450$	2.76818	−	2.00731i	0.130493	−	0.0946256i
$451$	−16.2213	+	5.90406i	−0.763830	+	0.278011i
$452$	−4.58940	+	8.59323i	−0.215867	+	0.404192i
$453$	2.82382	+	2.36947i	0.132675	+	0.111327i
$454$	−1.37668	+	5.49999i	−0.0646106	+	0.258127i
$455$	3.78628			0.177503
$456$	−4.71024	+	18.7309i	−0.220577	+	0.877153i
$457$	24.3871			1.14078			0.570390	−	0.821374i	$-0.306792\pi$
$457$	24.3871			1.14078			0.570390	+	0.821374i	$0.306792\pi$
$458$	−7.40312	+	29.5764i	−0.345925	+	1.38201i
$459$	20.5277	+	17.2248i	0.958151	+	0.803985i
$460$	−2.70751	+	5.06957i	−0.126238	+	0.236370i
$461$	−17.8483	+	6.49625i	−0.831278	+	0.302561i	−0.722383	−	0.691493i	$-0.756953\pi$
$461$	−17.8483	+	6.49625i	−0.831278	+	0.302561i	−0.108895	+	0.994053i	$0.534731\pi$
$462$	−5.93562	+	4.30414i	−0.276150	+	0.200247i
$463$	34.9271	−	20.1652i	1.62320	−	0.937155i	0.637143	−	0.770746i	$-0.280116\pi$
$463$	34.9271	−	20.1652i	1.62320	−	0.937155i	0.986057	−	0.166409i	$-0.0532171\pi$
$464$	−17.9407	−	18.7155i	−0.832878	−	0.868845i
$465$	−0.102409	−	0.580793i	−0.00474913	−	0.0269336i
$466$	−0.134502	−	1.29112i	−0.00623068	−	0.0598101i
$467$	−22.7989	−	13.1630i	−1.05501	−	0.609109i	−0.130961	−	0.991388i	$-0.541806\pi$
$467$	−22.7989	−	13.1630i	−1.05501	−	0.609109i	−0.924047	+	0.382278i	$0.875140\pi$
$468$	−4.69019	+	1.88493i	−0.216804	+	0.0871310i
$469$	9.17383	+	10.9329i	0.423608	+	0.504837i
$470$	−2.47839	−	8.67327i	−0.114320	−	0.400068i
$471$	4.85965	+	1.76877i	0.223921	+	0.0815005i
$472$	−1.85839	−	2.39220i	−0.0855392	−	0.110110i
$473$	3.72485	−	21.1247i	0.171269	−	0.971314i
$474$	30.8825	+	2.18806i	1.41848	+	0.100501i
$475$	−5.98017	−	18.3586i	−0.274389	−	0.842350i
$476$	−1.47284	+	10.3417i	−0.0675075	+	0.474012i
$477$	−7.30498	−	1.28807i	−0.334472	−	0.0589765i
$478$	13.3216	−	13.7695i	0.609314	−	0.629803i
$479$	−8.12858	+	22.3331i	−0.371404	+	1.02042i	0.603415	+	0.797428i	$0.293806\pi$
$479$	−8.12858	+	22.3331i	−0.371404	+	1.02042i	−0.974819	+	0.222997i	$0.928416\pi$
$480$	−6.69303	−	0.0307804i	−0.305494	−	0.00140493i
$481$	−9.59822	+	8.05386i	−0.437641	+	0.367224i
$482$	−15.3955	+	7.49139i	−0.701248	+	0.341223i
$483$	−3.22670	+	5.58881i	−0.146820	+	0.254300i
$484$	0.109560	+	3.31205i	0.00497999	+	0.150548i
$485$	−2.60539	+	0.459401i	−0.118305	+	0.0208603i
$486$	4.43256	−	6.55853i	0.201065	−	0.297501i
$487$	0.348135	+	0.602987i	0.0157755	+	0.0273240i	0.873805	−	0.486276i	$-0.161645\pi$
$487$	0.348135	+	0.602987i	0.0157755	+	0.0273240i	−0.858030	+	0.513600i	$0.828312\pi$
$488$	−14.7529	+	7.79213i	−0.667834	+	0.352733i
$489$	−0.0966628	−	0.265579i	−0.00437124	−	0.0120099i
$490$	5.68422	+	2.53704i	0.256787	+	0.114612i
$491$	−20.8082	+	24.7982i	−0.939061	+	1.11913i	0.0536445	+	0.998560i	$0.482916\pi$
$491$	−20.8082	+	24.7982i	−0.939061	+	1.11913i	−0.992705	+	0.120569i	$0.961528\pi$
$492$	−16.8183	−	5.49881i	−0.758226	−	0.247905i
$493$			31.2669i			1.40819i
$494$	1.98603	+	28.4735i	0.0893557	+	1.28108i
$495$		−	1.26013i		−	0.0566388i
$496$	−0.880603	+	1.78877i	−0.0395402	+	0.0803182i
$497$	−1.64963	+	1.96596i	−0.0739962	+	0.0881852i
$498$	11.1994	−	25.0922i	0.501858	−	1.12441i
$499$	10.2442	+	28.1458i	0.458595	+	1.25998i	0.926531	+	0.376218i	$0.122776\pi$
$499$	10.2442	+	28.1458i	0.458595	+	1.25998i	−0.467936	+	0.883762i	$0.655002\pi$
$500$	12.0932	−	7.52579i	0.540825	−	0.336564i
$501$	−10.2345	−	17.7267i	−0.457245	−	0.791972i
$502$	−21.8968	−	14.7989i	−0.977302	−	0.660507i
$503$	−14.2238	+	2.50804i	−0.634208	+	0.111828i	−0.481504	−	0.876444i	$-0.659909\pi$
$503$	−14.2238	+	2.50804i	−0.634208	+	0.111828i	−0.152704	+	0.988272i	$0.548798\pi$
$504$	1.67038	+	0.0629460i	0.0744045	+	0.00280384i
$505$	−0.290073	+	0.502421i	−0.0129081	+	0.0223574i
$506$	−7.19635	−	14.7892i	−0.319917	−	0.657460i
$507$	10.1274	−	8.49792i	0.449775	−	0.377406i
$508$	21.5123	−	4.53123i	0.954453	−	0.201041i
$509$	14.4187	−	39.6151i	0.639098	−	1.75591i	−0.0154441	−	0.999881i	$-0.504916\pi$
$509$	14.4187	−	39.6151i	0.639098	−	1.75591i	0.654542	−	0.756026i	$-0.272862\pi$
$510$	5.80138	+	5.61265i	0.256889	+	0.248532i
$511$	6.64043	+	1.17089i	0.293755	+	0.0517970i
$512$	18.1952	+	13.4511i	0.804124	+	0.594462i
$513$	−14.9212	−	19.0690i	−0.658786	−	0.841915i
$514$	0.921668	−	13.0085i	0.0406530	−	0.573781i
$515$	1.96987	−	11.1717i	0.0868027	−	0.492282i
$516$	16.3669	−	14.6824i	0.720513	−	0.646357i
$517$	24.2572	+	8.82890i	1.06683	+	0.388295i
$518$	3.98394	−	1.13841i	0.175044	−	0.0500189i
$519$	−1.32970	−	1.58467i	−0.0583672	−	0.0695593i
$520$	−9.41550	+	3.03058i	−0.412897	+	0.132900i
$521$	8.57677	+	4.95180i	0.375755	+	0.216942i	0.675970	−	0.736929i	$-0.263725\pi$
$521$	8.57677	+	4.95180i	0.375755	+	0.216942i	−0.300215	+	0.953872i	$0.597058\pi$
$522$	4.97635	−	0.518408i	0.217809	−	0.0226901i
$523$	−0.677373	−	3.84158i	−0.0296195	−	0.167980i	0.966410	−	0.257006i	$-0.0827359\pi$
$523$	−0.677373	−	3.84158i	−0.0296195	−	0.167980i	−0.996029	+	0.0890253i	$0.971625\pi$
$524$	17.2430	+	13.5229i	0.753265	+	0.590750i
$525$	6.50655	−	3.75656i	0.283969	−	0.163950i
$526$	6.51285	+	8.98153i	0.283974	+	0.391614i
$527$	2.25953	−	0.822403i	0.0984269	−	0.0358244i
$528$	11.3153	−	15.4542i	0.492434	−	0.672560i
$529$	6.52945	+	5.47886i	0.283889	+	0.238211i
$530$	−14.0805	−	3.52443i	−0.611619	−	0.153091i
$531$	0.584598			0.0253694
$532$	3.23796	−	8.86598i	0.140383	−	0.384389i
$533$	−26.1491			−1.13264
$534$	−11.7674	−	2.94543i	−0.509224	−	0.127461i
$535$	−8.66028	−	7.26684i	−0.374417	−	0.314173i
$536$	−31.5638	−	19.8446i	−1.36335	−	0.857156i
$537$	12.2463	−	4.45727i	0.528465	−	0.192346i
$538$	9.96550	+	13.7429i	0.429643	+	0.592498i
$539$	−15.4268	+	8.90670i	−0.664481	+	0.383639i
$540$	5.17804	−	6.60251i	0.222827	−	0.284127i
$541$	4.35056	+	24.6733i	0.187045	+	1.06079i	0.923299	+	0.384081i	$0.125482\pi$
$541$	4.35056	+	24.6733i	0.187045	+	1.06079i	−0.736254	+	0.676705i	$0.763407\pi$
$542$	37.5185	−	3.90847i	1.61156	−	0.167883i
$543$	−19.4458	−	11.2270i	−0.834499	−	0.481798i
$544$	−4.61508	−	26.8961i	−0.197870	−	1.15316i
$545$	−1.70436	−	2.03118i	−0.0730067	−	0.0870060i
$546$	−10.6790	+	3.05154i	−0.457021	+	0.130594i
$547$	−15.2865	−	5.56383i	−0.653604	−	0.237892i	−0.00613128	−	0.999981i	$-0.501952\pi$
$547$	−15.2865	−	5.56383i	−0.653604	−	0.237892i	−0.647472	+	0.762089i	$0.724174\pi$
$548$	16.5196	+	18.4149i	0.705684	+	0.786647i
$549$	0.559118	−	3.17092i	0.0238626	−	0.135331i
$550$	−1.35326	+	19.1000i	−0.0577031	+	0.814428i
$551$	5.85333	−	27.6388i	0.249360	−	1.17745i
$552$	3.55063	−	16.4806i	0.151125	−	0.701463i
$553$	−14.9003	−	2.62732i	−0.633623	−	0.111725i
$554$	−17.6084	−	17.0356i	−0.748111	−	0.723773i
$555$	1.09506	−	3.00865i	0.0464827	−	0.127710i
$556$	−3.82970	−	18.1817i	−0.162415	−	0.771076i
$557$	−16.5072	+	13.8512i	−0.699432	+	0.586893i	−0.921612	−	0.388112i	$-0.873127\pi$
$557$	−16.5072	+	13.8512i	−0.699432	+	0.586893i	0.222180	+	0.975006i	$0.428683\pi$
$558$	−0.168354	−	0.345985i	−0.00712701	−	0.0146467i
$559$	16.2468	−	28.1402i	0.687165	−	1.19021i
$560$	3.25172	+	0.353869i	0.137410	+	0.0149537i
$561$	−22.7490	+	4.01127i	−0.960465	+	0.169356i
$562$	18.4470	+	12.4674i	0.778140	+	0.525904i
$563$	5.48942	+	9.50796i	0.231352	+	0.400713i	0.958206	−	0.286079i	$-0.0923519\pi$
$563$	5.48942	+	9.50796i	0.231352	+	0.400713i	−0.726855	+	0.686791i	$0.759019\pi$
$564$	13.9804	+	22.4652i	0.588681	+	0.945954i
$565$	−1.25826	−	3.45704i	−0.0529354	−	0.145439i
$566$	1.99189	−	4.46280i	0.0837253	−	0.187586i
$567$	4.91652	−	5.85928i	0.206474	−	0.246066i
$568$	2.52864	−	6.20922i	0.106099	−	0.260533i
$569$			0.529264i			0.0221879i	0.999938	+	0.0110940i	$0.00353139\pi$
$569$			0.529264i			0.0221879i	−0.999938	+	0.0110940i	$0.996469\pi$
$570$	−4.07749	−	6.04742i	−0.170787	−	0.253299i
$571$			42.0314i			1.75896i	0.475935	+	0.879480i	$0.342110\pi$
$571$			42.0314i			1.75896i	−0.475935	+	0.879480i	$0.657890\pi$
$572$	8.79652	−	26.9044i	0.367801	−	1.12493i
$573$	−3.44142	+	4.10132i	−0.143767	+	0.171335i
$574$	7.89640	+	3.52441i	0.329589	+	0.147106i
$575$	5.76426	+	15.8372i	0.240386	+	0.660456i
$576$	−4.20419	+	1.18046i	−0.175174	+	0.0491859i
$577$	6.38905	+	11.0662i	0.265980	+	0.460691i	0.967820	−	0.251644i	$-0.0809712\pi$
$577$	6.38905	+	11.0662i	0.265980	+	0.460691i	−0.701840	+	0.712335i	$0.747638\pi$
$578$	−4.96668	+	7.34882i	−0.206587	+	0.305670i
$579$	−30.8905	+	5.44683i	−1.28377	+	0.226363i
$580$	9.78507	−	0.323681i	0.406303	−	0.0134401i
$581$	−6.71425	+	11.6294i	−0.278554	+	0.482470i
$582$	6.97816	−	3.39553i	0.289254	−	0.140749i
$583$	31.8197	−	26.6999i	1.31784	−	1.10580i
$584$	−17.4502	+	2.40339i	−0.722096	+	0.0994530i
$585$	0.652869	−	1.79374i	0.0269928	−	0.0741622i
$586$	14.6912	−	15.1852i	0.606886	−	0.627293i
$587$	−20.8963	−	3.68458i	−0.862483	−	0.152079i	−0.275127	−	0.961408i	$-0.588720\pi$
$587$	−20.8963	−	3.68458i	−0.862483	−	0.152079i	−0.587356	+	0.809329i	$0.699831\pi$
$588$	−18.0768	−	2.57445i	−0.745476	−	0.106169i
$589$	−2.15130	+	0.303978i	−0.0886429	+	0.0125252i
$590$	1.14108	+	0.0808470i	0.0469776	+	0.00332842i
$591$	3.78943	−	21.4909i	0.155876	−	0.884018i
$592$	−8.99583	+	6.01973i	−0.369726	+	0.247409i
$593$	−33.1969	−	12.0827i	−1.36323	−	0.496176i	−0.446180	−	0.894943i	$-0.647216\pi$
$593$	−33.1969	−	12.0827i	−1.36323	−	0.496176i	−0.917052	+	0.398767i	$0.869438\pi$
$594$	6.59740	+	23.0880i	0.270695	+	0.947312i
$595$	−2.53567	−	3.02189i	−0.103952	−	0.123886i
$596$	0.897573	+	2.23339i	0.0367660	+	0.0914832i
$597$	−33.0692	−	19.0925i	−1.35343	−	0.781404i
$598$	−2.58146	−	24.7802i	−0.105564	−	1.01334i
$599$	−5.24954	−	29.7716i	−0.214490	−	1.21644i	−0.881789	−	0.471645i	$-0.843660\pi$
$599$	−5.24954	−	29.7716i	−0.214490	−	1.21644i	0.667298	−	0.744791i	$-0.267451\pi$
$600$	−13.1733	+	14.5495i	−0.537799	+	0.593982i
$601$	−30.8900	+	17.8343i	−1.26003	+	0.727478i	−0.973080	−	0.230468i	$-0.925974\pi$
$601$	−30.8900	+	17.8343i	−1.26003	+	0.727478i	−0.286949	+	0.957946i	$0.592641\pi$
$602$	−8.69890	+	6.30791i	−0.354541	+	0.257091i
$603$	6.76132	−	2.46092i	0.275342	−	0.100216i
$604$	4.15118	+	2.21702i	0.168909	+	0.0902094i
$605$	−0.958651	−	0.804404i	−0.0389747	−	0.0327037i
$606$	0.413214	−	1.65084i	0.0167857	−	0.0670609i
$607$	−3.61581			−0.146761			−0.0733806	−	0.997304i	$-0.523379\pi$
$607$	−3.61581			−0.146761			−0.0733806	+	0.997304i	$0.523379\pi$
$608$	−0.955529	+	24.6391i	−0.0387518	+	0.999249i
$609$	10.9933			0.445471
$610$	1.52987	−	6.11201i	0.0619426	−	0.247468i
$611$	29.9548	+	25.1351i	1.21184	+	1.01686i
$612$	4.64542	+	2.48099i	0.187780	+	0.100288i
$613$	−1.15127	+	0.419027i	−0.0464992	+	0.0169243i	−0.365165	−	0.930943i	$-0.618987\pi$
$613$	−1.15127	+	0.419027i	−0.0464992	+	0.0169243i	0.318666	+	0.947867i	$0.396765\pi$
$614$	−3.14238	+	2.27866i	−0.126816	+	0.0919592i
$615$	5.78679	−	3.34100i	0.233346	−	0.134722i
$616$	−6.28254	+	6.93887i	−0.253131	+	0.279575i
$617$	−3.68259	−	20.8850i	−0.148256	−	0.840799i	−0.964695	−	0.263368i	$-0.915167\pi$
$617$	−3.68259	−	20.8850i	−0.148256	−	0.840799i	0.816440	−	0.577431i	$-0.195945\pi$
$618$	3.44785	+	33.0969i	0.138693	+	1.33135i
$619$	9.34154	+	5.39334i	0.375468	+	0.216777i	0.675845	−	0.737044i	$-0.263779\pi$
$619$	9.34154	+	5.39334i	0.375468	+	0.216777i	−0.300376	+	0.953821i	$0.597112\pi$
$620$	−0.280764	−	0.698613i	−0.0112758	−	0.0280570i
$621$	13.5853	+	16.1903i	0.545159	+	0.649695i
$622$	−7.94158	−	27.7920i	−0.318428	−	1.11436i
$623$	5.57061	+	2.02754i	0.223182	+	0.0812315i
$624$	24.1136	−	16.1360i	0.965315	−	0.645959i
$625$	2.91189	−	16.5142i	0.116476	−	0.660567i
$626$	−28.7552	−	2.03734i	−1.14929	−	0.0814285i
$627$	20.8602	+	0.712919i	0.833077	+	0.0284712i
$628$	6.53639	+	0.930894i	0.260830	+	0.0371467i
$629$	12.8559	+	2.26683i	0.512596	+	0.0903846i
$630$	−0.438914	+	0.453673i	−0.0174867	+	0.0180747i
$631$	−7.69640	+	21.1457i	−0.306389	+	0.841796i	0.686965	+	0.726691i	$0.258943\pi$
$631$	−7.69640	+	21.1457i	−0.306389	+	0.841796i	−0.993353	+	0.115105i	$0.963279\pi$
$632$	39.1561	−	5.39289i	1.55754	−	0.214518i
$633$	−13.9631	+	11.7164i	−0.554983	+	0.465686i
$634$	−36.6588	+	17.8380i	−1.45591	+	0.708436i
$635$	−4.15102	+	7.18978i	−0.164728	+	0.285318i
$636$	42.5541	−	1.40765i	1.68738	−	0.0558170i
$637$	−26.5740	+	4.68571i	−1.05290	+	0.185654i
$638$	−15.6885	+	23.2131i	−0.621115	+	0.919017i
$639$	0.646923	+	1.12050i	0.0255919	+	0.0443264i
$640$	−8.36943	+	1.72273i	−0.330831	+	0.0680970i
$641$	−13.3995	−	36.8148i	−0.529248	−	1.45410i	−0.859958	−	0.510364i	$-0.829511\pi$
$641$	−13.3995	−	36.8148i	−0.529248	−	1.45410i	0.330710	−	0.943732i	$-0.392712\pi$
$642$	30.2827	+	13.5161i	1.19516	+	0.533438i
$643$	12.1261	−	14.4513i	0.478207	−	0.569905i	−0.471970	−	0.881614i	$-0.656457\pi$
$643$	12.1261	−	14.4513i	0.478207	−	0.569905i	0.950177	+	0.311709i	$0.100902\pi$
$644$	−2.56036	+	7.83094i	−0.100892	+	0.308582i
$645$			8.30322i			0.326939i
$646$	21.3952	−	20.6538i	0.841781	−	0.812612i
$647$			20.3440i			0.799806i	0.916557	+	0.399903i	$0.130956\pi$
$647$			20.3440i			0.799806i	−0.916557	+	0.399903i	$0.869044\pi$
$648$	−7.53628	+	18.5058i	−0.296053	+	0.726975i
$649$	−2.10426	+	2.50776i	−0.0825995	+	0.0984383i
$650$	−11.8219	+	26.4869i	−0.463695	+	1.03890i
$651$	−0.289153	−	0.794441i	−0.0113328	−	0.0311366i
$652$	−0.190641	−	0.306341i	−0.00746606	−	0.0119972i
$653$	11.1928	+	19.3865i	0.438008	+	0.758651i	0.997536	−	0.0701600i	$-0.0223510\pi$
$653$	11.1928	+	19.3865i	0.438008	+	0.758651i	−0.559528	+	0.828811i	$0.689018\pi$
$654$	6.44410	+	4.35523i	0.251984	+	0.170303i
$655$	−8.14948	+	1.43697i	−0.318426	+	0.0561472i
$656$	−22.4573	−	2.44393i	−0.876810	−	0.0954193i
$657$	1.69972	−	2.94400i	0.0663124	−	0.114856i
$658$	−5.65790	−	11.6275i	−0.220568	−	0.453289i
$659$	−10.9733	+	9.20773i	−0.427461	+	0.358682i	−0.830993	−	0.556283i	$-0.812227\pi$
$659$	−10.9733	+	9.20773i	−0.427461	+	0.358682i	0.403532	+	0.914966i	$0.367782\pi$
$660$	1.49084	+	7.07784i	0.0580308	+	0.275505i
$661$	5.54631	−	15.2384i	0.215726	−	0.592703i	−0.783876	−	0.620918i	$-0.786760\pi$
$661$	5.54631	−	15.2384i	0.215726	−	0.592703i	0.999602	+	0.0282147i	$0.00898221\pi$
$662$	−3.73645	−	3.61490i	−0.145221	−	0.140497i
$663$	−34.4605	−	6.07631i	−1.33833	−	0.235984i
$664$	7.38829	−	34.2936i	0.286721	−	1.33085i
$665$	1.67572	+	3.14593i	0.0649818	+	0.121994i
$666$	0.147631	−	2.08368i	0.00572059	−	0.0807410i
$667$	−4.28223	+	24.2858i	−0.165809	+	0.940348i
$668$	−17.4502	−	19.4522i	−0.675167	−	0.752628i
$669$	29.7015	+	10.8105i	1.14833	+	0.417956i
$670$	13.5378	−	3.86843i	0.523011	−	0.149451i
$671$	11.5898	+	13.8122i	0.447419	+	0.533213i
$672$	−9.45655	+	1.62264i	−0.364794	+	0.0625947i
$673$	24.7321	+	14.2791i	0.953352	+	0.550418i	0.894121	−	0.447826i	$-0.147802\pi$
$673$	24.7321	+	14.2791i	0.953352	+	0.550418i	0.0592314	+	0.998244i	$0.481135\pi$
$674$	41.9554	−	4.37067i	1.61606	−	0.168352i
$675$	−4.27270	−	24.2317i	−0.164456	−	0.932678i
$676$	10.4157	−	13.2810i	0.400603	−	0.510808i
$677$	8.84921	−	5.10909i	0.340103	−	0.196358i	−0.320215	−	0.947345i	$-0.603755\pi$
$677$	8.84921	−	5.10909i	0.340103	−	0.196358i	0.660318	+	0.750987i	$0.270422\pi$
$678$	6.33507	+	8.73637i	0.243297	+	0.335518i
$679$	−3.56380	+	1.29712i	−0.136766	+	0.0497788i
$680$	8.72432	+	5.48509i	0.334563	+	0.210344i
$681$	4.81113	+	4.03702i	0.184363	+	0.154699i
$682$	2.09017	+	0.523180i	0.0800367	+	0.0200336i
$683$	−40.4675			−1.54844			−0.774222	−	0.632914i	$-0.781859\pi$
$683$	−40.4675			−1.54844			−0.774222	+	0.632914i	$0.781859\pi$
$684$	−3.64193	−	3.06275i	−0.139253	−	0.117107i
$685$	−9.34223			−0.356948
$686$	19.0536	+	4.76922i	0.727471	+	0.182090i
$687$	25.8720	+	21.7092i	0.987079	+	0.828258i
$688$	16.5830	−	22.6489i	0.632222	−	0.863480i
$689$	59.1271	−	21.5205i	2.25256	−	0.819865i
$690$	3.73737	+	5.15401i	0.142279	+	0.196210i
$691$	12.7642	−	7.36940i	0.485572	−	0.280345i	−0.237163	−	0.971470i	$-0.576218\pi$
$691$	12.7642	−	7.36940i	0.485572	−	0.280345i	0.722736	+	0.691124i	$0.242884\pi$
$692$	−2.07812	−	1.62977i	−0.0789983	−	0.0619546i
$693$	−0.313684	−	1.77899i	−0.0119159	−	0.0675783i
$694$	−40.9497	+	4.26591i	−1.55443	+	0.161932i
$695$	6.07664	+	3.50835i	0.230500	+	0.133079i
$696$	−27.3375	+	8.79918i	−1.03623	+	0.333532i
$697$	17.5121	+	20.8701i	0.663317	+	0.790510i
$698$	−24.5277	+	7.00881i	−0.928389	+	0.265287i
$699$	−1.35124	−	0.491812i	−0.0511087	−	0.0186020i
$700$	7.13988	−	6.40503i	0.269862	−	0.242087i
$701$	−3.61494	+	20.5013i	−0.136534	+	0.774325i	0.837244	+	0.546829i	$0.184165\pi$
$701$	−3.61494	+	20.5013i	−0.136534	+	0.774325i	−0.973779	+	0.227496i	$0.926946\pi$
$702$	−2.57068	+	36.2828i	−0.0970241	+	1.36941i
$703$	−10.9397	−	4.41047i	−0.412600	−	0.166344i
$704$	10.0691	−	22.2838i	0.379494	−	0.839853i
$705$	−9.84043	−	1.73513i	−0.370612	−	0.0653489i
$706$	27.2279	+	26.3422i	1.02474	+	0.991400i
$707$	−0.284443	+	0.781500i	−0.0106976	+	0.0293913i
$708$	−3.28354	+	0.691627i	−0.123403	+	0.0259929i
$709$	21.7284	−	18.2323i	0.816027	−	0.684728i	−0.136011	−	0.990707i	$-0.543428\pi$
$709$	21.7284	−	18.2323i	0.816027	−	0.684728i	0.952038	+	0.305979i	$0.0989838\pi$
$710$	1.10777	+	2.27658i	0.0415740	+	0.0854387i
$711$	−3.81395	+	6.60595i	−0.143034	+	0.247742i
$712$	−15.4755	−	0.583176i	−0.579970	−	0.0218554i
$713$	1.86767	−	0.329320i	0.0699446	−	0.0123331i
$714$	9.58725	+	6.47952i	0.358794	+	0.242490i
$715$	5.34465	+	9.25721i	0.199879	+	0.346200i
$716$	14.1259	−	8.79073i	0.527909	−	0.328525i
$717$	−7.25868	−	19.9431i	−0.271081	−	0.744788i
$718$	10.0021	−	22.4097i	0.373276	−	0.836321i
$719$	31.1096	−	37.0750i	1.16019	−	1.38266i	0.250119	−	0.968215i	$-0.419530\pi$
$719$	31.1096	−	37.0750i	1.16019	−	1.38266i	0.910073	−	0.414448i	$-0.136025\pi$
$720$	0.728341	−	1.47948i	0.0271436	−	0.0551369i
$721$		−	16.2619i		−	0.605626i
$722$	−22.7790	+	14.2519i	−0.847747	+	0.530401i
$723$			18.9660i			0.705354i
$724$	−27.2471	−	8.90856i	−1.01263	−	0.331084i
$725$	18.4543	−	21.9930i	0.685377	−	0.816801i
$726$	3.35215	+	1.49617i	0.124410	+	0.0555280i
$727$	11.1784	+	30.7123i	0.414582	+	1.13906i	0.954727	+	0.297483i	$0.0961472\pi$
$727$	11.1784	+	30.7123i	0.414582	+	1.13906i	−0.540145	+	0.841572i	$0.681631\pi$
$728$	−12.5379	+	6.62222i	−0.464686	+	0.245436i
$729$	−14.9811	−	25.9481i	−0.554857	−	0.961041i
$730$	3.72483	−	5.51135i	0.137862	−	0.203984i
$731$	−33.3397	+	5.87868i	−1.23311	+	0.217431i
$732$	0.611027	+	18.4717i	0.0225842	+	0.682734i
$733$	−17.3930	+	30.1256i	−0.642427	+	1.11272i	0.342463	+	0.939531i	$0.388739\pi$
$733$	−17.3930	+	30.1256i	−0.642427	+	1.11272i	−0.984889	+	0.173184i	$0.944594\pi$
$734$	−29.3101	+	14.2621i	−1.08186	+	0.526425i
$735$	5.28212	−	4.43223i	0.194834	−	0.163485i
$736$	0.0989812	−	21.5229i	0.00364850	−	0.793345i
$737$	−13.7807	+	37.8622i	−0.507619	+	1.39467i
$738$	3.03126	−	3.13319i	0.111582	−	0.115334i
$739$	11.2136	+	1.97726i	0.412499	+	0.0727346i	0.376047	−	0.926601i	$-0.377283\pi$
$739$	11.2136	+	1.97726i	0.412499	+	0.0727346i	0.0364520	+	0.999335i	$0.488394\pi$
$740$	0.576325	−	4.04674i	0.0211861	−	0.148761i
$741$	29.3242	+	11.8224i	1.07725	+	0.434307i
$742$	−20.7555	−	1.47055i	−0.761958	−	0.0539856i
$743$	1.31475	−	7.45634i	0.0482337	−	0.273547i	−0.951147	−	0.308739i	$-0.900093\pi$
$743$	1.31475	−	7.45634i	0.0482337	−	0.273547i	0.999381	+	0.0351919i	$0.0112043\pi$
$744$	1.35493	+	1.74413i	0.0496742	+	0.0639429i
$745$	−0.854150	−	0.310885i	−0.0312936	−	0.0113900i
$746$	−5.54692	−	19.4118i	−0.203087	−	0.710715i
$747$	4.35169	+	5.18614i	0.159220	+	0.189751i
$748$	−27.3639	+	10.9972i	−1.00052	+	0.402099i
$749$	−14.0351	−	8.10316i	−0.512831	−	0.296083i
$750$	−1.63484	−	15.6933i	−0.0596961	−	0.573040i
$751$	−3.02587	−	17.1606i	−0.110416	−	0.626198i	−0.988918	−	0.148461i	$-0.952568\pi$
$751$	−3.02587	−	17.1606i	−0.110416	−	0.626198i	0.878503	−	0.477738i	$-0.158543\pi$
$752$	23.3766	+	24.3861i	0.852456	+	0.889268i
$753$	−25.3538	+	14.6380i	−0.923943	+	0.533439i
$754$	−34.3586	+	24.9147i	−1.25127	+	0.907341i
$755$	−1.67001	+	0.607834i	−0.0607779	+	0.0221214i
$756$	5.66653	−	10.6101i	0.206090	−	0.385884i
$757$	25.6276	+	21.5041i	0.931452	+	0.781581i	0.976077	−	0.217423i	$-0.0697651\pi$
$757$	25.6276	+	21.5041i	0.931452	+	0.781581i	−0.0446258	+	0.999004i	$0.514210\pi$
$758$	1.35516	−	5.41402i	0.0492215	−	0.196646i
$759$	−18.2191			−0.661310
$760$	−6.68514	−	6.48185i	−0.242496	−	0.235122i
$761$	26.3077			0.953654			0.476827	−	0.878997i	$-0.341787\pi$
$761$	26.3077			0.953654			0.476827	+	0.878997i	$0.341787\pi$
$762$	5.91321	−	23.6240i	0.214213	−	0.855807i
$763$	−2.91175	−	2.44325i	−0.105412	−	0.0884515i
$764$	−3.22001	+	6.02918i	−0.116496	+	0.218128i
$765$	−1.86885	+	0.680204i	−0.0675682	+	0.0245928i
$766$	3.80402	−	2.75844i	0.137445	−	0.0996664i
$767$	−4.29458	+	2.47948i	−0.155068	+	0.0895288i
$768$	22.2172	−	11.6042i	0.801695	−	0.418732i
$769$	−4.38426	−	24.8644i	−0.158100	−	0.896632i	−0.955896	−	0.293704i	$-0.905112\pi$
$769$	−4.38426	−	24.8644i	−0.158100	−	0.896632i	0.797796	−	0.602928i	$-0.205999\pi$
$770$	−0.366257	−	3.51581i	−0.0131990	−	0.126701i
$771$	−12.5107	−	7.22306i	−0.450562	−	0.260132i
$772$	−37.1570	+	14.9330i	−1.33731	+	0.537449i
$773$	−18.0924	−	21.5617i	−0.650738	−	0.775520i	0.335287	−	0.942116i	$-0.391167\pi$
$773$	−18.0924	−	21.5617i	−0.650738	−	0.775520i	−0.986025	+	0.166597i	$0.946722\pi$
$774$	1.48841	+	5.20877i	0.0534997	+	0.187225i
$775$	−2.07474	−	0.755145i	−0.0745270	−	0.0271256i
$776$	7.82404	−	6.07812i	0.280867	−	0.218192i
$777$	0.797008	−	4.52006i	0.0285925	−	0.162156i
$778$	10.4758	+	0.742222i	0.375575	+	0.0266099i
$779$	−11.5730	−	21.7267i	−0.414647	−	0.778440i
$780$	−1.54485	+	10.8474i	−0.0553147	+	0.388399i
$781$	−7.13524	−	1.25813i	−0.255319	−	0.0450196i
$782$	−18.0487	+	18.6556i	−0.645420	+	0.667123i
$783$	12.3138	−	33.8319i	0.440059	−	1.20905i
$784$	−23.2601	+	1.54053i	−0.830718	+	0.0550190i
$785$	−1.90996	+	1.60264i	−0.0681693	+	0.0572008i
$786$	21.8272	−	10.6210i	0.778549	−	0.378838i
$787$	13.2989	−	23.0343i	0.474053	−	0.821085i	−0.525505	−	0.850790i	$-0.676124\pi$
$787$	13.2989	−	23.0343i	0.474053	−	0.821085i	0.999559	+	0.0297057i	$0.00945702\pi$
$788$	−0.921083	−	27.8449i	−0.0328122	−	0.991932i
$789$	12.1029	−	2.13407i	0.430876	−	0.0759750i
$790$	−8.35804	+	12.3668i	−0.297366	+	0.439989i
$791$	−2.63691	−	4.56726i	−0.0937577	−	0.162393i
$792$	2.20398	+	4.17282i	0.0783151	+	0.148275i
$793$	9.34153	+	25.6656i	0.331727	+	0.911414i
$794$	−27.9158	−	12.4597i	−0.990695	−	0.442178i
$795$	−10.3352	+	12.3170i	−0.366551	+	0.436838i
$796$	−46.3359	−	15.1497i	−1.64233	−	0.536968i
$797$		−	18.1641i		−	0.643405i	−0.946841	−	0.321702i	$-0.895745\pi$
$797$		−	18.1641i		−	0.643405i	0.946841	−	0.321702i	$-0.104255\pi$
$798$	−7.26177	−	7.52243i	−0.257064	−	0.266291i
$799$		−	40.7405i		−	1.44129i
$800$	−12.6284	+	21.6425i	−0.446481	+	0.765179i
$801$	1.92109	−	2.28946i	0.0678782	−	0.0808941i
$802$	12.1467	−	27.2145i	0.428914	−	0.960976i
$803$	6.51079	+	17.8882i	0.229761	+	0.631262i
$804$	−35.0651	+	21.8215i	−1.23665	+	0.769586i
$805$	−1.55564	−	2.69445i	−0.0548292	−	0.0949669i
$806$	2.70421	+	1.82763i	0.0952516	+	0.0643756i
$807$	18.5190	−	3.26540i	0.651900	−	0.114948i
$808$	0.0818137	−	2.17106i	0.00287820	−	0.0763777i
$809$	−19.2576	+	33.3551i	−0.677061	+	1.17270i	0.298801	+	0.954315i	$0.403413\pi$
$809$	−19.2576	+	33.3551i	−0.677061	+	1.17270i	−0.975862	+	0.218388i	$0.929920\pi$
$810$	−3.30157	−	6.78506i	−0.116005	−	0.238403i
$811$	30.7794	−	25.8270i	1.08081	−	0.906907i	0.0848219	−	0.996396i	$-0.472968\pi$
$811$	30.7794	−	25.8270i	1.08081	−	0.906907i	0.995988	+	0.0894891i	$0.0285234\pi$
$812$	13.7335	−	2.89275i	0.481951	−	0.101516i
$813$	14.2915	−	39.2655i	0.501224	−	1.37710i
$814$	8.40701	+	8.13351i	0.294665	+	0.285079i
$815$	0.134187	+	0.0236608i	0.00470036	+	0.000828800i
$816$	−29.0273	−	8.43915i	−1.01616	−	0.295429i
$817$	30.5716	+	1.04481i	1.06956	+	0.0365534i
$818$	−0.0269853	+	0.380873i	−0.000943518	+	0.0133169i
$819$	0.475172	−	2.69484i	0.0166039	−	0.0941652i
$820$	6.35005	−	5.69650i	0.221753	−	0.198930i
$821$	−9.74851	−	3.54817i	−0.340225	−	0.123832i	0.166256	−	0.986083i	$-0.446832\pi$
$821$	−9.74851	−	3.54817i	−0.340225	−	0.123832i	−0.506482	+	0.862251i	$0.669054\pi$
$822$	26.3494	−	7.52935i	0.919041	−	0.262616i
$823$	−13.6432	−	16.2594i	−0.475573	−	0.566766i	0.473914	−	0.880571i	$-0.342841\pi$
$823$	−13.6432	−	16.2594i	−0.475573	−	0.566766i	−0.949488	+	0.313805i	$0.898396\pi$
$824$	13.0163	+	40.4393i	0.453443	+	1.40877i
$825$	18.3691	+	10.6054i	0.639530	+	0.369233i
$826$	1.63105	−	0.169913i	0.0567514	−	0.00591204i
$827$	−0.820127	−	4.65117i	−0.0285186	−	0.161737i	0.967223	−	0.253930i	$-0.0817234\pi$
$827$	−0.820127	−	4.65117i	−0.0285186	−	0.161737i	−0.995741	+	0.0921932i	$0.970612\pi$
$828$	3.26842	+	2.56326i	0.113585	+	0.0890795i
$829$	−7.40704	+	4.27646i	−0.257257	+	0.148527i	−0.623083	−	0.782156i	$-0.714120\pi$
$829$	−7.40704	+	4.27646i	−0.257257	+	0.148527i	0.365826	+	0.930683i	$0.380787\pi$
$830$	7.77687	+	10.7247i	0.269939	+	0.372259i
$831$	−25.5032	+	9.28241i	−0.884696	+	0.322003i
$832$	25.8781	−	26.5033i	0.897162	−	0.918836i
$833$	21.5363	+	18.0711i	0.746189	+	0.626127i
$834$	−19.9665	−	4.99771i	−0.691383	−	0.173057i
$835$	9.86845			0.341512
$836$	26.2474	−	4.59848i	0.907786	−	0.159042i
$837$	−2.76878			−0.0957030
$838$	−5.91140	−	1.47965i	−0.204206	−	0.0511138i
$839$	17.4577	+	14.6488i	0.602707	+	0.505732i	0.892315	−	0.451414i	$-0.149080\pi$
$839$	17.4577	+	14.6488i	0.602707	+	0.505732i	−0.289607	+	0.957146i	$0.593525\pi$
$840$	1.92853	−	3.06743i	0.0665407	−	0.105836i
$841$	12.2242	−	4.44924i	0.421524	−	0.153422i
$842$	9.48068	+	13.0743i	0.326726	+	0.450571i
$843$	21.3593	−	12.3318i	0.735655	−	0.424730i
$844$	−14.3605	+	18.3111i	−0.494309	+	0.630293i
$845$	1.10679	+	6.27693i	0.0380748	+	0.215933i
$846$	−6.48413	+	0.675480i	−0.222929	+	0.0232235i
$847$	−1.55361	−	0.896980i	−0.0533828	−	0.0308206i
$848$	52.7906	−	12.9561i	1.81284	−	0.444914i
$849$	−3.47984	−	4.14711i	−0.119428	−	0.142328i
$850$	29.0568	−	8.30300i	0.996641	−	0.284790i
$851$	9.67498	+	3.52140i	0.331654	+	0.120712i
$852$	−4.95924	−	5.52821i	−0.169901	−	0.189393i
$853$	−4.72752	+	26.8111i	−0.161867	+	0.917994i	0.790369	+	0.612631i	$0.209889\pi$
$853$	−4.72752	+	26.8111i	−0.161867	+	0.917994i	−0.952236	+	0.305363i	$0.901222\pi$
$854$	0.638331	−	9.00946i	0.0218432	−	0.308297i
$855$	1.77933	−	0.251418i	0.0608517	−	0.00859832i
$856$	41.3875	+	8.91662i	1.41460	+	0.304764i
$857$	−13.6996	−	2.41560i	−0.467968	−	0.0825153i	−0.0653082	−	0.997865i	$-0.520803\pi$
$857$	−13.6996	−	2.41560i	−0.467968	−	0.0825153i	−0.402660	+	0.915350i	$0.631914\pi$
$858$	−22.5352	−	21.8021i	−0.769339	−	0.744311i
$859$	−17.2191	+	47.3090i	−0.587507	+	1.61416i	0.187539	+	0.982257i	$0.439949\pi$
$859$	−17.2191	+	47.3090i	−0.587507	+	1.61416i	−0.775046	+	0.631905i	$0.782273\pi$
$860$	2.18489	+	10.3729i	0.0745040	+	0.353712i
$861$	7.33782	−	6.15716i	0.250072	−	0.209835i
$862$	−14.9637	−	30.7520i	−0.509667	−	1.04742i
$863$	−6.57791	+	11.3933i	−0.223915	+	0.387831i	−0.955993	−	0.293389i	$-0.905217\pi$
$863$	−6.57791	+	11.3933i	−0.223915	+	0.387831i	0.732079	+	0.681220i	$0.238550\pi$
$864$	−5.59878	+	30.9201i	−0.190474	+	1.05192i
$865$	0.982171	−	0.173183i	0.0333948	−	0.00588841i
$866$	3.41455	+	2.30771i	0.116031	+	0.0784193i
$867$	4.91268	+	8.50902i	0.166843	+	0.288981i
$868$	−0.570274	−	0.916376i	−0.0193564	−	0.0311038i
$869$	−14.6094	−	40.1389i	−0.495588	−	1.36162i
$870$	4.42025	−	9.90351i	0.149860	−	0.335761i
$871$	−39.2325	+	46.7555i	−1.32934	+	1.58425i
$872$	9.19638	+	3.74513i	0.311429	+	0.126826i
$873$			1.91201i			0.0647118i
$874$	19.4468	−	13.1121i	0.657797	−	0.443522i
$875$			7.71083i			0.260674i
$876$	−6.06389	+	18.5466i	−0.204880	+	0.626631i
$877$	9.75081	−	11.6206i	0.329261	−	0.392399i	−0.575862	−	0.817547i	$-0.695334\pi$
$877$	9.75081	−	11.6206i	0.329261	−	0.392399i	0.905124	+	0.425148i	$0.139778\pi$
$878$	12.1401	+	5.41849i	0.409707	+	0.182865i
$879$	−8.00496	−	21.9934i	−0.270001	−	0.741821i
$880$	3.72489	+	8.44976i	0.125566	+	0.284841i
$881$	−3.34310	−	5.79042i	−0.112632	−	0.195084i	0.804199	−	0.594360i	$-0.202595\pi$
$881$	−3.34310	−	5.79042i	−0.112632	−	0.195084i	−0.916831	+	0.399276i	$0.869261\pi$
$882$	2.51907	−	3.72728i	0.0848215	−	0.125504i
$883$	1.04288	−	0.183888i	0.0350957	−	0.00618833i	−0.156073	−	0.987746i	$-0.549883\pi$
$883$	1.04288	−	0.183888i	0.0350957	−	0.00618833i	0.191168	+	0.981557i	$0.438772\pi$
$884$	−44.6489	+	1.47695i	−1.50171	+	0.0496751i
$885$	0.633593	−	1.09741i	0.0212980	−	0.0368892i
$886$	11.6312	−	5.65967i	0.390757	−	0.190140i
$887$	−16.0418	+	13.4607i	−0.538632	+	0.451966i	−0.871070	−	0.491159i	$-0.836573\pi$
$887$	−16.0418	+	13.4607i	−0.538632	+	0.451966i	0.332438	+	0.943125i	$0.392129\pi$
$888$	1.63596	+	11.8782i	0.0548991	+	0.398605i
$889$	−4.07045	+	11.1835i	−0.136519	+	0.375082i
$890$	4.06640	−	4.20314i	0.136306	−	0.140890i
$891$	21.2656	+	3.74971i	0.712426	+	0.125620i
$892$	39.9495	+	5.68949i	1.33761	+	0.190498i
$893$	−7.62681	+	36.0131i	−0.255222	+	1.20513i
$894$	2.65966	+	0.188440i	0.0889522	+	0.00630236i
$895$	−1.09103	+	6.18756i	−0.0364693	+	0.206827i
$896$	−11.3867	+	4.51547i	−0.380403	+	0.150851i
$897$	−25.9340	−	9.43922i	−0.865912	−	0.315166i
$898$	−5.01000	−	17.5328i	−0.167186	−	0.585077i
$899$	−2.07661	−	2.47481i	−0.0692588	−	0.0825394i
$900$	−1.80324	−	4.48693i	−0.0601081	−	0.149564i
$901$	−56.7733	−	32.7781i	−1.89139	−	1.09200i
$902$	2.52948	+	24.2812i	0.0842224	+	0.808475i
$903$	2.06692	+	11.7221i	0.0687827	+	0.390086i
$904$	10.2130	+	9.24699i	0.339680	+	0.307550i
$905$	9.37511	−	5.41272i	0.311639	−	0.179925i
$906$	4.22032	−	3.06032i	0.140211	−	0.101672i
$907$	−14.5374	+	5.29118i	−0.482706	+	0.175691i	−0.571899	−	0.820324i	$-0.693793\pi$
$907$	−14.5374	+	5.29118i	−0.482706	+	0.175691i	0.0891935	+	0.996014i	$0.471571\pi$
$908$	7.07264	+	3.77730i	0.234714	+	0.125354i
$909$	0.321188	+	0.269509i	0.0106531	+	0.00893904i
$910$	1.30017	−	5.19436i	0.0431003	−	0.172191i
$911$	45.0630			1.49300			0.746501	−	0.665384i	$-0.231732\pi$
$911$	45.0630			1.49300			0.746501	+	0.665384i	$0.231732\pi$
$912$	24.0792	+	12.8939i	0.797343	+	0.426961i
$913$	−37.9110			−1.25467
$914$	8.37431	−	33.4564i	0.276998	−	1.10664i
$915$	−5.34650	−	4.48625i	−0.176750	−	0.148311i
$916$	38.0334	+	20.3125i	1.25666	+	0.671145i
$917$	−11.1473	+	4.05729i	−0.368117	+	0.133984i
$918$	30.6796	−	22.2469i	1.01258	−	0.734258i
$919$	−13.8026	+	7.96894i	−0.455306	+	0.262871i	−0.710069	−	0.704133i	$-0.751336\pi$
$919$	−13.8026	+	7.96894i	−0.455306	+	0.262871i	0.254762	+	0.967004i	$0.418003\pi$
$920$	6.02516	+	5.45526i	0.198644	+	0.179854i
$921$	0.746650	+	4.23446i	0.0246029	+	0.139530i
$922$	2.78319	+	26.7167i	0.0916596	+	0.879867i
$923$	−9.50486	−	5.48763i	−0.312856	−	0.180628i
$924$	3.86657	+	9.62102i	0.127201	+	0.316508i
$925$	−7.70482	−	9.18225i	−0.253333	−	0.301910i
$926$	−15.6707	−	54.8407i	−0.514972	−	1.80218i
$927$	−7.70408	−	2.80406i	−0.253035	−	0.0920973i
$928$	−31.8363	+	18.1860i	−1.04508	+	0.596984i
$929$	−3.18405	+	18.0577i	−0.104465	+	0.592453i	0.886967	+	0.461833i	$0.152808\pi$
$929$	−3.18405	+	18.0577i	−0.104465	+	0.592453i	−0.991432	+	0.130620i	$0.958303\pi$
$930$	−0.831951	−	0.0589447i	−0.0272807	−	0.00193287i
$931$	−15.6543	−	20.0059i	−0.513049	−	0.655667i
$932$	−1.81747	−	0.258838i	−0.0595330	−	0.00847853i
$933$	−31.5320	−	5.55994i	−1.03231	−	0.182024i
$934$	−25.8871	+	26.7576i	−0.847051	+	0.875534i
$935$	3.80902	−	10.4652i	0.124568	−	0.342249i
$936$	0.975349	+	7.08170i	0.0318803	+	0.231473i
$937$	−33.1396	+	27.8074i	−1.08262	+	0.908428i	−0.996136	−	0.0878249i	$-0.972008\pi$
$937$	−33.1396	+	27.8074i	−1.08262	+	0.908428i	−0.0864865	+	0.996253i	$0.527564\pi$
$938$	18.1490	−	8.83121i	0.592586	−	0.288349i
$939$	−15.9665	+	27.6548i	−0.521047	+	0.902480i
$940$	−12.7498	+	0.421753i	−0.415854	+	0.0137561i
$941$	4.91527	−	0.866695i	0.160233	−	0.0282534i	−0.0929560	−	0.995670i	$-0.529632\pi$
$941$	4.91527	−	0.866695i	0.160233	−	0.0282534i	0.253189	+	0.967417i	$0.418520\pi$
$942$	4.09531	−	6.05952i	0.133433	−	0.197430i
$943$	10.7437	+	18.6087i	0.349864	+	0.605982i
$944$	−3.92000	+	1.72804i	−0.127585	+	0.0562430i
$945$	1.55357	+	4.26841i	0.0505378	+	0.138851i
$946$	−27.7017	−	12.3641i	−0.900659	−	0.401992i
$947$	17.2136	−	20.5144i	0.559367	−	0.666627i	−0.410046	−	0.912065i	$-0.634487\pi$
$947$	17.2136	−	20.5144i	0.559367	−	0.666627i	0.969412	+	0.245438i	$0.0789317\pi$
$948$	13.6066	−	41.6161i	0.441921	−	1.35163i
$949$			28.8363i			0.936067i
$950$	−27.2395	+	1.89996i	−0.883767	+	0.0616428i
$951$			45.1606i			1.46443i
$952$	13.6820	+	5.57183i	0.443435	+	0.180584i
$953$	0.108118	−	0.128850i	0.00350228	−	0.00417386i	−0.764290	−	0.644872i	$-0.776911\pi$
$953$	0.108118	−	0.128850i	0.00350228	−	0.00417386i	0.767793	+	0.640698i	$0.221355\pi$
$954$	−4.27555	+	9.57932i	−0.138426	+	0.310142i
$955$	−0.882820	−	2.42553i	−0.0285674	−	0.0784882i
$956$	−14.3157	−	23.0040i	−0.463004	−	0.744004i
$957$	15.5180	+	26.8779i	0.501625	+	0.868840i
$958$	27.8473	+	18.8205i	0.899704	+	0.608063i
$959$	−13.1889	+	2.32556i	−0.425891	+	0.0750961i
$960$	−2.34056	+	9.17154i	−0.0755411	+	0.296010i
$961$	15.3758	−	26.6316i	0.495993	−	0.859085i
$962$	7.75307	+	15.9333i	0.249969	+	0.513711i
$963$	−6.25894	+	5.25187i	−0.201691	+	0.169239i
$964$	4.99067	+	23.6935i	0.160739	+	0.763115i
$965$	5.17221	−	14.2105i	0.166499	−	0.457453i
$966$	6.55922	+	6.34583i	0.211039	+	0.204174i
$967$	39.0081	+	6.87817i	1.25441	+	0.221187i	0.761083	−	0.648654i	$-0.224668\pi$
$967$	39.0081	+	6.87817i	1.25441	+	0.221187i	0.493331	+	0.869841i	$0.335779\pi$
$968$	4.58140	+	0.987026i	0.147252	+	0.0317242i
$969$	−10.2028	−	31.3217i	−0.327761	−	1.00620i
$970$	−0.264421	+	3.73207i	−0.00849005	+	0.119829i
$971$	2.86243	−	16.2336i	0.0918597	−	0.520962i	−0.903805	−	0.427945i	$-0.859238\pi$
$971$	2.86243	−	16.2336i	0.0918597	−	0.520962i	0.995664	−	0.0930173i	$-0.0296512\pi$
$972$	−7.47547	−	8.33313i	−0.239776	−	0.267285i
$973$	9.45202	+	3.44025i	0.303018	+	0.110290i
$974$	0.946779	−	0.270542i	0.0303368	−	0.00866873i
$975$	20.6530	+	24.6133i	0.661425	+	0.788255i
$976$	5.62392	+	22.9152i	0.180017	+	0.733496i
$977$	−13.5649	−	7.83168i	−0.433978	−	0.250558i	0.267062	−	0.963679i	$-0.413947\pi$
$977$	−13.5649	−	7.83168i	−0.433978	−	0.250558i	−0.701040	+	0.713122i	$0.747281\pi$
$978$	−0.397538	+	0.0414133i	−0.0127119	+	0.00132425i
$979$	2.90619	+	16.4818i	0.0928822	+	0.526761i
$980$	5.43245	−	6.92692i	0.173533	−	0.221272i
$981$	−1.65956	+	0.958147i	−0.0529857	+	0.0305913i
$982$	26.8751	+	37.0620i	0.857619	+	1.18270i
$983$	17.2444	−	6.27645i	0.550011	−	0.200188i	−0.0520403	−	0.998645i	$-0.516572\pi$
$983$	17.2444	−	6.27645i	0.550011	−	0.200188i	0.602051	+	0.798457i	$0.294350\pi$
$984$	−13.3190	+	21.1846i	−0.424594	+	0.675339i
$985$	8.05950	+	6.76272i	0.256797	+	0.215478i
$986$	42.8948	+	10.7368i	1.36605	+	0.341929i
$987$	−14.3241			−0.455943
$988$	39.7445	+	7.05294i	1.26444	+	0.224384i
$989$	−26.7008			−0.849037
$990$	−1.72876	−	0.432719i	−0.0549437	−	0.0137527i
$991$	−40.1167	−	33.6619i	−1.27435	−	1.06931i	−0.993997	−	0.109409i	$-0.965104\pi$
$991$	−40.1167	−	33.6619i	−1.27435	−	1.06931i	−0.280353	−	0.959897i	$-0.590451\pi$
$992$	2.15161	+	1.82234i	0.0683135	+	0.0578593i
$993$	−5.41169	+	1.96969i	−0.171735	+	0.0625064i
$994$	2.13061	+	2.93821i	0.0675787	+	0.0931943i
$995$	15.9431	−	9.20478i	0.505432	−	0.291811i
$996$	−30.5779	−	23.9808i	−0.968898	−	0.759860i
$997$	6.70707	+	38.0377i	0.212415	+	1.20467i	0.885336	+	0.464951i	$0.153928\pi$
$997$	6.70707	+	38.0377i	0.212415	+	1.20467i	−0.672921	+	0.739714i	$0.734961\pi$
$998$	42.1308	−	4.38895i	1.33363	−	0.138930i
$999$	−13.0177	−	7.51579i	−0.411863	−	0.237789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.k.a.59.6	yes	48
3.2	odd	2		684.2.cf.a.667.3		48
4.3	odd	2	inner	76.2.k.a.59.5	✓	48
12.11	even	2		684.2.cf.a.667.4		48
19.10	odd	18	inner	76.2.k.a.67.5	yes	48
57.29	even	18		684.2.cf.a.523.4		48
76.67	even	18	inner	76.2.k.a.67.6	yes	48
228.143	odd	18		684.2.cf.a.523.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.59.5	✓	48	4.3	odd	2	inner
76.2.k.a.59.6	yes	48	1.1	even	1	trivial
76.2.k.a.67.5	yes	48	19.10	odd	18	inner
76.2.k.a.67.6	yes	48	76.67	even	18	inner
684.2.cf.a.523.3		48	228.143	odd	18
684.2.cf.a.523.4		48	57.29	even	18
684.2.cf.a.667.3		48	3.2	odd	2
684.2.cf.a.667.4		48	12.11	even	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.343391 - 1.37189i) q^{2} +(-1.20007 - 1.00697i) q^{3} +(-1.76416 - 0.942190i) q^{4} +(0.709721 - 0.258317i) q^{5} +(-1.79355 + 1.30057i) q^{6} +(0.937645 - 0.541349i) q^{7} +(-1.89838 + 2.09670i) q^{8} +(-0.0947852 - 0.537553i) q^{9} +O(q^{10})\)	\(q+(0.343391 - 1.37189i) q^{2} +(-1.20007 - 1.00697i) q^{3} +(-1.76416 - 0.942190i) q^{4} +(0.709721 - 0.258317i) q^{5} +(-1.79355 + 1.30057i) q^{6} +(0.937645 - 0.541349i) q^{7} +(-1.89838 + 2.09670i) q^{8} +(-0.0947852 - 0.537553i) q^{9} +(-0.110671 - 1.06236i) q^{10} +(2.64713 + 1.52832i) q^{11} +(1.16835 + 2.90716i) q^{12} +(2.97626 + 3.54697i) q^{13} +(-0.420693 - 1.47224i) q^{14} +(-1.11183 - 0.404673i) q^{15} +(2.22456 + 3.32436i) q^{16} +(0.837695 - 4.75081i) q^{17} +(-0.770013 - 0.0545563i) q^{18} +(-1.62987 + 4.04271i) q^{19} +(-1.49545 - 0.212978i) q^{20} +(-1.67036 - 0.294530i) q^{21} +(3.00569 - 3.10676i) q^{22} +(1.30131 - 3.57533i) q^{23} +(4.38950 - 0.604558i) q^{24} +(-3.39325 + 2.84727i) q^{25} +(5.88807 - 2.86510i) q^{26} +(-2.77742 + 4.81062i) q^{27} +(-2.16421 + 0.0715903i) q^{28} +(-6.38295 + 1.12549i) q^{29} +(-0.936960 + 1.38635i) q^{30} +(0.249223 + 0.431666i) q^{31} +(5.32455 - 1.91029i) q^{32} +(-1.63775 - 4.49968i) q^{33} +(-6.22993 - 2.78061i) q^{34} +(0.525626 - 0.626417i) q^{35} +(-0.339261 + 1.03764i) q^{36} +2.70604i q^{37} +(4.98648 + 3.62423i) q^{38} -7.25360i q^{39} +(-0.805706 + 1.97846i) q^{40} +(-3.63013 + 4.32622i) q^{41} +(-0.977649 + 2.19041i) q^{42} +(-2.40019 - 6.59447i) q^{43} +(-3.23001 - 5.19031i) q^{44} +(-0.206130 - 0.357028i) q^{45} +(-4.45810 - 3.01300i) q^{46} +(8.31690 - 1.46649i) q^{47} +(0.677930 - 6.22952i) q^{48} +(-2.91388 + 5.04699i) q^{49} +(2.74093 + 5.63289i) q^{50} +(-5.78923 + 4.85774i) q^{51} +(-1.90869 - 9.06163i) q^{52} +(4.64782 - 12.7698i) q^{53} +(5.64591 + 5.46223i) q^{54} +(2.27352 + 0.400882i) q^{55} +(-0.644958 + 2.99365i) q^{56} +(6.02685 - 3.21029i) q^{57} +(-0.647805 + 9.14318i) q^{58} +(-0.185976 + 1.05472i) q^{59} +(1.58017 + 1.76146i) q^{60} +(5.54306 + 2.01751i) q^{61} +(0.677779 - 0.193676i) q^{62} +(-0.379879 - 0.452722i) q^{63} +(-0.792308 - 7.96067i) q^{64} +(3.02855 + 1.74854i) q^{65} +(-6.73545 + 0.701662i) q^{66} +(2.28900 + 12.9816i) q^{67} +(-5.95399 + 7.59194i) q^{68} +(-5.16193 + 2.98024i) q^{69} +(-0.678880 - 0.936207i) q^{70} +(-2.22740 + 0.810707i) q^{71} +(1.30703 + 0.821744i) q^{72} +(4.77080 + 4.00317i) q^{73} +(3.71238 + 0.929229i) q^{74} +6.93925 q^{75} +(6.68436 - 5.59637i) q^{76} +3.30942 q^{77} +(-9.95115 - 2.49082i) q^{78} +(-10.7050 - 8.98260i) q^{79} +(2.43755 + 1.78472i) q^{80} +(6.63847 - 2.41621i) q^{81} +(4.68854 + 6.46572i) q^{82} +(-10.7411 + 6.20140i) q^{83} +(2.66929 + 2.09340i) q^{84} +(-0.632685 - 3.58814i) q^{85} +(-9.87109 + 1.02832i) q^{86} +(8.79329 + 5.07681i) q^{87} +(-8.22969 + 2.64891i) q^{88} +(3.51946 + 4.19433i) q^{89} +(-0.560587 + 0.160188i) q^{90} +(4.71082 + 1.71460i) q^{91} +(-5.66437 + 5.08139i) q^{92} +(0.135593 - 0.768988i) q^{93} +(0.844082 - 11.9135i) q^{94} +(-0.112447 + 3.29022i) q^{95} +(-8.31342 - 3.06921i) q^{96} +(-3.44962 - 0.608262i) q^{97} +(5.92332 + 5.73062i) q^{98} +(0.570646 - 1.56784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

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