LMFDB - Embedded newform 804.2.u.a.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(43,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 3]))

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

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

chi := DirichletCharacter("804.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.u (of order $22$, degree $10$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$340$
Relative dimension:	$34$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			43.2
Character	$\chi$	$=$	804.43
Dual form			804.2.u.a.187.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38258 - 0.297428i) q^{2} +(0.841254 - 0.540641i) q^{3} +(1.82307 + 0.822439i) q^{4} +(-2.84397 - 0.408902i) q^{5} +(-1.32390 + 0.497268i) q^{6} +(0.447300 - 0.979450i) q^{7} +(-2.27593 - 1.67932i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-1.38258 - 0.297428i) q^{2} +(0.841254 - 0.540641i) q^{3} +(1.82307 + 0.822439i) q^{4} +(-2.84397 - 0.408902i) q^{5} +(-1.32390 + 0.497268i) q^{6} +(0.447300 - 0.979450i) q^{7} +(-2.27593 - 1.67932i) q^{8} +(0.415415 - 0.909632i) q^{9} +(3.81041 + 1.41122i) q^{10} +(-0.565094 + 3.93031i) q^{11} +(1.97831 - 0.293748i) q^{12} +(-0.369419 + 1.25812i) q^{13} +(-0.909745 + 1.22113i) q^{14} +(-2.61357 + 1.19358i) q^{15} +(2.64719 + 2.99873i) q^{16} +(-2.97900 + 3.43795i) q^{17} +(-0.844896 + 1.13409i) q^{18} +(3.25991 - 1.48875i) q^{19} +(-4.84847 - 3.08445i) q^{20} +(-0.153238 - 1.06579i) q^{21} +(1.95028 - 5.26591i) q^{22} +(2.21304 + 3.44355i) q^{23} +(-2.82255 - 0.182275i) q^{24} +(3.12352 + 0.917149i) q^{25} +(0.884954 - 1.62959i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(1.62100 - 1.41773i) q^{28} +7.93353 q^{29} +(3.96849 - 0.872871i) q^{30} +(-1.37356 + 0.403315i) q^{31} +(-2.76805 - 4.93335i) q^{32} +(1.64950 + 3.61190i) q^{33} +(5.14126 - 3.86721i) q^{34} +(-1.67261 + 2.60263i) q^{35} +(1.50545 - 1.31667i) q^{36} +5.00214 q^{37} +(-4.94989 + 1.08873i) q^{38} +(0.369419 + 1.25812i) q^{39} +(5.78602 + 5.70659i) q^{40} +(4.58146 + 3.96986i) q^{41} +(-0.105133 + 1.51913i) q^{42} +(-5.15466 + 5.94879i) q^{43} +(-4.26265 + 6.70049i) q^{44} +(-1.55338 + 2.41711i) q^{45} +(-2.03550 - 5.41922i) q^{46} +(-0.617896 - 0.961465i) q^{47} +(3.84819 + 1.09152i) q^{48} +(3.82478 + 4.41403i) q^{49} +(-4.04574 - 2.19706i) q^{50} +(-0.647398 + 4.50275i) q^{51} +(-1.70821 + 1.98983i) q^{52} +(2.54216 - 2.20279i) q^{53} +(-0.0976390 + 1.41084i) q^{54} +(3.21422 - 10.9466i) q^{55} +(-2.66284 + 1.47800i) q^{56} +(1.93753 - 3.01486i) q^{57} +(-10.9688 - 2.35966i) q^{58} +(-1.41876 - 4.83184i) q^{59} +(-5.74638 + 0.0264759i) q^{60} +(5.52691 - 0.794650i) q^{61} +(2.01902 - 0.149079i) q^{62} +(-0.705124 - 0.813756i) q^{63} +(2.35974 + 7.64406i) q^{64} +(1.56507 - 3.42702i) q^{65} +(-1.20629 - 5.48436i) q^{66} +(-7.64970 + 2.91240i) q^{67} +(-8.25843 + 3.81758i) q^{68} +(3.72345 + 1.70044i) q^{69} +(3.08661 - 3.10087i) q^{70} +(-3.05082 + 2.64355i) q^{71} +(-2.47302 + 1.37264i) q^{72} +(1.71458 + 11.9252i) q^{73} +(-6.91588 - 1.48778i) q^{74} +(3.12352 - 0.917149i) q^{75} +(7.16746 - 0.0330234i) q^{76} +(3.59678 + 2.31151i) q^{77} +(-0.136550 - 1.84934i) q^{78} +(-3.07103 - 0.901736i) q^{79} +(-6.30235 - 9.61076i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-5.15350 - 6.85131i) q^{82} +(3.69057 + 0.530624i) q^{83} +(0.597187 - 2.06905i) q^{84} +(9.87798 - 8.55932i) q^{85} +(8.89608 - 6.69156i) q^{86} +(6.67411 - 4.28919i) q^{87} +(7.88639 - 7.99615i) q^{88} +(5.82628 + 3.74432i) q^{89} +(2.86659 - 2.87983i) q^{90} +(1.06703 + 0.924586i) q^{91} +(1.20242 + 8.09794i) q^{92} +(-0.937467 + 1.08189i) q^{93} +(0.568326 + 1.51308i) q^{94} +(-9.87985 + 2.90098i) q^{95} +(-4.99580 - 2.65368i) q^{96} +13.0246i q^{97} +(-3.97522 - 7.24036i) q^{98} +(3.34039 + 2.14674i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 340 q - 34 q^{3} - 2 q^{4} + 11 q^{6} - 4 q^{7} + 39 q^{8} - 34 q^{9}+O(q^{10}) $ 340 * q - 34 * q^3 - 2 * q^4 + 11 * q^6 - 4 * q^7 + 39 * q^8 - 34 * q^9	$ 340 q - 34 q^{3} - 2 q^{4} + 11 q^{6} - 4 q^{7} + 39 q^{8} - 34 q^{9} - 27 q^{10} + 9 q^{12} + 4 q^{14} - 2 q^{16} + 12 q^{20} - 4 q^{21} - 3 q^{22} + 6 q^{24} + 34 q^{25} - 10 q^{26} - 34 q^{27} - 25 q^{28} + 16 q^{29} + 6 q^{30} + 4 q^{31} - 55 q^{32} + 9 q^{36} - 12 q^{37} - 26 q^{38} - 37 q^{40} + 4 q^{42} + 4 q^{43} + 51 q^{44} + 81 q^{46} - 2 q^{48} - 46 q^{49} - 15 q^{50} - 32 q^{52} - 14 q^{56} + 66 q^{57} - 92 q^{58} - 43 q^{60} + 2 q^{62} + 18 q^{63} + 7 q^{64} + 8 q^{66} + 18 q^{67} - 208 q^{68} - 56 q^{70} + 6 q^{72} + 54 q^{73} - 22 q^{74} + 34 q^{75} + 120 q^{76} + 8 q^{77} - 10 q^{78} - 10 q^{79} + 68 q^{80} - 34 q^{81} + 84 q^{82} + 8 q^{84} + 104 q^{86} + 16 q^{87} + 138 q^{88} - 27 q^{90} - 42 q^{92} + 4 q^{93} - 32 q^{94} + 40 q^{95} + 7 q^{98}+O(q^{100}) $ 340 * q - 34 * q^3 - 2 * q^4 + 11 * q^6 - 4 * q^7 + 39 * q^8 - 34 * q^9 - 27 * q^10 + 9 * q^12 + 4 * q^14 - 2 * q^16 + 12 * q^20 - 4 * q^21 - 3 * q^22 + 6 * q^24 + 34 * q^25 - 10 * q^26 - 34 * q^27 - 25 * q^28 + 16 * q^29 + 6 * q^30 + 4 * q^31 - 55 * q^32 + 9 * q^36 - 12 * q^37 - 26 * q^38 - 37 * q^40 + 4 * q^42 + 4 * q^43 + 51 * q^44 + 81 * q^46 - 2 * q^48 - 46 * q^49 - 15 * q^50 - 32 * q^52 - 14 * q^56 + 66 * q^57 - 92 * q^58 - 43 * q^60 + 2 * q^62 + 18 * q^63 + 7 * q^64 + 8 * q^66 + 18 * q^67 - 208 * q^68 - 56 * q^70 + 6 * q^72 + 54 * q^73 - 22 * q^74 + 34 * q^75 + 120 * q^76 + 8 * q^77 - 10 * q^78 - 10 * q^79 + 68 * q^80 - 34 * q^81 + 84 * q^82 + 8 * q^84 + 104 * q^86 + 16 * q^87 + 138 * q^88 - 27 * q^90 - 42 * q^92 + 4 * q^93 - 32 * q^94 + 40 * q^95 + 7 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$	$-1$

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 $

$2$	−1.38258	−	0.297428i	−0.977634	−	0.210314i
$2$	−1.38258	−	0.297428i	−0.977634	−	0.210314i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$	1.82307	+	0.822439i	0.911536	+	0.411220i
$5$	−2.84397	−	0.408902i	−1.27186	−	0.182866i	−0.526875	−	0.849943i	$-0.676636\pi$
$5$	−2.84397	−	0.408902i	−1.27186	−	0.182866i	−0.744989	+	0.667077i	$0.767545\pi$
$6$	−1.32390	+	0.497268i	−0.540482	+	0.203009i
$7$	0.447300	−	0.979450i	0.169063	−	0.370197i	−0.806069	−	0.591822i	$-0.798409\pi$
$7$	0.447300	−	0.979450i	0.169063	−	0.370197i	0.975132	+	0.221625i	$0.0711361\pi$
$8$	−2.27593	−	1.67932i	−0.804664	−	0.593731i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	3.81041	+	1.41122i	1.20496	+	0.446267i
$11$	−0.565094	+	3.93031i	−0.170382	+	1.18503i	0.707696	+	0.706517i	$0.249735\pi$
$11$	−0.565094	+	3.93031i	−0.170382	+	1.18503i	−0.878078	+	0.478517i	$0.841175\pi$
$12$	1.97831	−	0.293748i	0.571089	−	0.0847976i
$13$	−0.369419	+	1.25812i	−0.102458	+	0.348941i	−0.994726	−	0.102565i	$-0.967295\pi$
$13$	−0.369419	+	1.25812i	−0.102458	+	0.348941i	0.892268	+	0.451506i	$0.149113\pi$
$14$	−0.909745	+	1.22113i	−0.243140	+	0.326361i
$15$	−2.61357	+	1.19358i	−0.674821	+	0.308181i
$16$	2.64719	+	2.99873i	0.661797	+	0.749683i
$17$	−2.97900	+	3.43795i	−0.722513	+	0.833825i	−0.991607	−	0.129289i	$-0.958730\pi$
$17$	−2.97900	+	3.43795i	−0.722513	+	0.833825i	0.269094	+	0.963114i	$0.413276\pi$
$18$	−0.844896	+	1.13409i	−0.199144	+	0.267307i
$19$	3.25991	−	1.48875i	0.747874	−	0.341543i	−0.00475376	−	0.999989i	$-0.501513\pi$
$19$	3.25991	−	1.48875i	0.747874	−	0.341543i	0.752628	+	0.658446i	$0.228786\pi$
$20$	−4.84847	−	3.08445i	−1.08415	−	0.689705i
$21$	−0.153238	−	1.06579i	−0.0334393	−	0.232575i
$22$	1.95028	−	5.26591i	0.415800	−	1.12270i
$23$	2.21304	+	3.44355i	0.461450	+	0.718031i	0.991524	−	0.129921i	$-0.0414722\pi$
$23$	2.21304	+	3.44355i	0.461450	+	0.718031i	−0.530074	+	0.847951i	$0.677836\pi$
$24$	−2.82255	−	0.182275i	−0.576150	−	0.0372068i
$25$	3.12352	+	0.917149i	0.624705	+	0.183430i
$26$	0.884954	−	1.62959i	0.173554	−	0.319588i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	1.62100	−	1.41773i	0.306340	−	0.267926i
$29$	7.93353			1.47322			0.736610	−	0.676318i	$-0.236425\pi$
$29$	7.93353			1.47322			0.736610	+	0.676318i	$0.236425\pi$
$30$	3.96849	−	0.872871i	0.724543	−	0.159364i
$31$	−1.37356	+	0.403315i	−0.246699	+	0.0724375i	−0.402744	−	0.915312i	$-0.631944\pi$
$31$	−1.37356	+	0.403315i	−0.246699	+	0.0724375i	0.156045	+	0.987750i	$0.450125\pi$
$32$	−2.76805	−	4.93335i	−0.489326	−	0.872101i
$33$	1.64950	+	3.61190i	0.287141	+	0.628751i
$34$	5.14126	−	3.86721i	0.881718	−	0.663221i
$35$	−1.67261	+	2.60263i	−0.282722	+	0.439924i
$36$	1.50545	−	1.31667i	0.250908	−	0.219445i
$37$	5.00214			0.822347			0.411173	−	0.911557i	$-0.365119\pi$
$37$	5.00214			0.822347			0.411173	+	0.911557i	$0.365119\pi$
$38$	−4.94989	+	1.08873i	−0.802978	+	0.176616i
$39$	0.369419	+	1.25812i	0.0591543	+	0.201461i
$40$	5.78602	+	5.70659i	0.914849	+	0.902291i
$41$	4.58146	+	3.96986i	0.715504	+	0.619988i	0.934594	−	0.355717i	$-0.115763\pi$
$41$	4.58146	+	3.96986i	0.715504	+	0.619988i	−0.219090	+	0.975705i	$0.570309\pi$
$42$	−0.105133	+	1.51913i	−0.0162224	+	0.234406i
$43$	−5.15466	+	5.94879i	−0.786078	+	0.907182i	−0.997533	−	0.0702055i	$-0.977634\pi$
$43$	−5.15466	+	5.94879i	−0.786078	+	0.907182i	0.211455	+	0.977388i	$0.432180\pi$
$44$	−4.26265	+	6.70049i	−0.642619	+	1.01014i
$45$	−1.55338	+	2.41711i	−0.231564	+	0.360321i
$46$	−2.03550	−	5.41922i	−0.300118	−	0.799021i
$47$	−0.617896	−	0.961465i	−0.0901294	−	0.140244i	0.793261	−	0.608881i	$-0.208381\pi$
$47$	−0.617896	−	0.961465i	−0.0901294	−	0.140244i	−0.883391	+	0.468637i	$0.844745\pi$
$48$	3.84819	+	1.09152i	0.555439	+	0.157547i
$49$	3.82478	+	4.41403i	0.546397	+	0.630576i
$50$	−4.04574	−	2.19706i	−0.572155	−	0.310711i
$51$	−0.647398	+	4.50275i	−0.0906539	+	0.630512i
$52$	−1.70821	+	1.98983i	−0.236886	+	0.275939i
$53$	2.54216	−	2.20279i	0.349192	−	0.302577i	−0.462550	−	0.886593i	$-0.653065\pi$
$53$	2.54216	−	2.20279i	0.349192	−	0.302577i	0.811742	+	0.584017i	$0.198520\pi$
$54$	−0.0976390	+	1.41084i	−0.0132870	+	0.191991i
$55$	3.21422	−	10.9466i	0.433406	−	1.47604i
$56$	−2.66284	+	1.47800i	−0.355837	+	0.197506i
$57$	1.93753	−	3.01486i	0.256632	−	0.399327i
$58$	−10.9688	−	2.35966i	−1.44027	−	0.309838i
$59$	−1.41876	−	4.83184i	−0.184706	−	0.629052i	−0.998830	−	0.0483603i	$-0.984600\pi$
$59$	−1.41876	−	4.83184i	−0.184706	−	0.629052i	0.814124	−	0.580692i	$-0.197218\pi$
$60$	−5.74638	+	0.0264759i	−0.741854	+	0.00341803i
$61$	5.52691	−	0.794650i	0.707648	−	0.101744i	0.220912	−	0.975294i	$-0.429096\pi$
$61$	5.52691	−	0.794650i	0.707648	−	0.101744i	0.486736	+	0.873549i	$0.338187\pi$
$62$	2.01902	−	0.149079i	0.256416	−	0.0189331i
$63$	−0.705124	−	0.813756i	−0.0888373	−	0.102524i
$64$	2.35974	+	7.64406i	0.294967	+	0.955507i
$65$	1.56507	−	3.42702i	0.194123	−	0.425069i
$66$	−1.20629	−	5.48436i	−0.148484	−	0.675079i
$67$	−7.64970	+	2.91240i	−0.934560	+	0.355806i
$67$	−7.64970	+	2.91240i	−0.934560	+	0.355806i
$68$	−8.25843	+	3.81758i	−1.00148	+	0.462950i
$69$	3.72345	+	1.70044i	0.448251	+	0.204709i
$70$	3.08661	−	3.10087i	0.368921	−	0.370625i
$71$	−3.05082	+	2.64355i	−0.362066	+	0.313732i	−0.816828	−	0.576881i	$-0.804270\pi$
$71$	−3.05082	+	2.64355i	−0.362066	+	0.313732i	0.454762	+	0.890613i	$0.349724\pi$
$72$	−2.47302	+	1.37264i	−0.291449	+	0.161768i
$73$	1.71458	+	11.9252i	0.200677	+	1.39574i	0.802282	+	0.596945i	$0.203619\pi$
$73$	1.71458	+	11.9252i	0.200677	+	1.39574i	−0.601605	+	0.798794i	$0.705472\pi$
$74$	−6.91588	−	1.48778i	−0.803954	−	0.172951i
$75$	3.12352	−	0.917149i	0.360673	−	0.105903i
$76$	7.16746	−	0.0330234i	0.822164	−	0.00378805i
$77$	3.59678	+	2.31151i	0.409891	+	0.263421i
$78$	−0.136550	−	1.84934i	−0.0154612	−	0.209396i
$79$	−3.07103	−	0.901736i	−0.345518	−	0.101453i	0.104369	−	0.994539i	$-0.466718\pi$
$79$	−3.07103	−	0.901736i	−0.345518	−	0.101453i	−0.449887	+	0.893085i	$0.648536\pi$
$80$	−6.30235	−	9.61076i	−0.704624	−	1.07452i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−5.15350	−	6.85131i	−0.569109	−	0.756601i
$83$	3.69057	+	0.530624i	0.405093	+	0.0582436i	0.341850	−	0.939755i	$-0.388947\pi$
$83$	3.69057	+	0.530624i	0.405093	+	0.0582436i	0.0632431	+	0.997998i	$0.479856\pi$
$84$	0.597187	−	2.06905i	0.0651584	−	0.225752i
$85$	9.87798	−	8.55932i	1.07142	−	0.928388i
$86$	8.89608	−	6.69156i	0.959289	−	0.721569i
$87$	6.67411	−	4.28919i	0.715540	−	0.459850i
$88$	7.88639	−	7.99615i	0.840691	−	0.852393i
$89$	5.82628	+	3.74432i	0.617584	+	0.396897i	0.811694	−	0.584082i	$-0.198546\pi$
$89$	5.82628	+	3.74432i	0.617584	+	0.396897i	−0.194110	+	0.980980i	$0.562182\pi$
$90$	2.86659	−	2.87983i	0.302165	−	0.303561i
$91$	1.06703	+	0.924586i	0.111855	+	0.0969229i
$92$	1.20242	+	8.09794i	0.125360	+	0.844269i
$93$	−0.937467	+	1.08189i	−0.0972108	+	0.112187i
$94$	0.568326	+	1.51308i	0.0586183	+	0.156063i
$95$	−9.87985	+	2.90098i	−1.01365	+	0.297635i
$96$	−4.99580	−	2.65368i	−0.509882	−	0.270840i
$97$			13.0246i			1.32245i	0.750187	+	0.661226i	$0.229964\pi$
$97$			13.0246i			1.32245i	−0.750187	+	0.661226i	$0.770036\pi$
$98$	−3.97522	−	7.24036i	−0.401558	−	0.731387i
$99$	3.34039	+	2.14674i	0.335722	+	0.215755i
$100$	4.94011	+	4.24094i	0.494011	+	0.424094i
$101$	6.23115	−	2.84567i	0.620022	−	0.283155i	−0.0805339	−	0.996752i	$-0.525663\pi$
$101$	6.23115	−	2.84567i	0.620022	−	0.283155i	0.700556	+	0.713597i	$0.252935\pi$
$102$	2.23433	−	6.03288i	0.221232	−	0.597344i
$103$	3.97229	+	13.5284i	0.391402	+	1.33299i	0.885925	+	0.463828i	$0.153524\pi$
$103$	3.97229	+	13.5284i	0.391402	+	1.33299i	−0.494524	+	0.869164i	$0.664658\pi$
$104$	2.95357	−	2.24303i	0.289621	−	0.219947i
$105$			3.09375i			0.301919i
$106$	−4.16992	+	2.28943i	−0.405018	+	0.222369i
$107$	10.8256	−	1.55649i	1.04655	−	0.150471i	0.402473	−	0.915432i	$-0.368151\pi$
$107$	10.8256	−	1.55649i	1.04655	−	0.150471i	0.644077	+	0.764961i	$0.277242\pi$
$108$	0.554618	−	1.92156i	0.0533681	−	0.184902i
$109$	2.33107	−	7.93889i	0.223276	−	0.760408i	−0.769311	−	0.638874i	$-0.779400\pi$
$109$	2.33107	−	7.93889i	0.223276	−	0.760408i	0.992587	−	0.121534i	$-0.0387814\pi$
$110$	−7.69977	+	14.1786i	−0.734145	+	1.35188i
$111$	4.20807	−	2.70436i	0.399412	−	0.256687i
$112$	4.12119	−	1.25145i	0.389416	−	0.118251i
$113$	−9.60775	+	1.38139i	−0.903821	+	0.129950i	−0.578527	−	0.815663i	$-0.696372\pi$
$113$	−9.60775	+	1.38139i	−0.903821	+	0.129950i	−0.325294	+	0.945613i	$0.605463\pi$
$114$	−3.57550	+	3.59201i	−0.334876	+	0.336423i
$115$	−4.88575	−	10.6983i	−0.455598	−	0.997621i
$116$	14.4634	+	6.52485i	1.34289	+	0.605817i
$117$	0.990968	+	0.858679i	0.0916150	+	0.0793849i
$118$	0.524422	+	7.10240i	0.0482769	+	0.653829i
$119$	2.03479	+	4.45557i	0.186529	+	0.408442i
$120$	7.95272	+	1.67253i	0.725981	+	0.152681i
$121$	−4.57361	−	1.34293i	−0.415782	−	0.122085i
$122$	−7.87777	−	0.545191i	−0.713219	−	0.0493593i
$123$	6.00044	+	0.862732i	0.541041	+	0.0777900i
$124$	−2.83581	−	0.394401i	−0.254663	−	0.0354182i
$125$	4.55967	+	2.08233i	0.407829	+	0.186249i
$126$	0.732858	+	1.33481i	0.0652882	+	0.118914i
$127$	−13.7424	−	6.27597i	−1.21945	−	0.556902i	−0.301446	−	0.953483i	$-0.597469\pi$
$127$	−13.7424	−	6.27597i	−1.21945	−	0.556902i	−0.918000	+	0.396581i	$0.870196\pi$
$128$	−0.988976	−	11.2704i	−0.0874140	−	0.996172i
$129$	−1.12021	+	7.79126i	−0.0986294	+	0.685982i
$130$	−3.18313	+	4.27264i	−0.279179	+	0.374735i
$131$	4.73909	+	7.37417i	0.414056	+	0.644284i	0.984159	−	0.177290i	$-0.0567329\pi$
$131$	4.73909	+	7.37417i	0.414056	+	0.644284i	−0.570103	+	0.821574i	$0.693097\pi$
$132$	0.0365892	+	7.94137i	0.00318468	+	0.691208i
$133$		−	3.85883i		−	0.334603i
$134$	11.4426	−	1.75140i	0.988488	−	0.151298i
$135$			2.87322i			0.247287i
$136$	12.5534	−	2.82183i	1.07645	−	0.241970i
$137$	−1.41950	−	2.20879i	−0.121276	−	0.188709i	0.775307	−	0.631584i	$-0.217595\pi$
$137$	−1.41950	−	2.20879i	−0.121276	−	0.188709i	−0.896583	+	0.442875i	$0.853959\pi$
$138$	−4.64222	−	3.45847i	−0.395172	−	0.294404i
$139$	−3.15781	+	21.9630i	−0.267842	+	1.86288i	0.200992	+	0.979593i	$0.435583\pi$
$139$	−3.15781	+	21.9630i	−0.267842	+	1.86288i	−0.468834	+	0.883286i	$0.655326\pi$
$140$	−5.18979	+	3.36916i	−0.438617	+	0.284746i
$141$	−1.03961	−	0.474776i	−0.0875513	−	0.0399833i
$142$	5.00428	−	2.74753i	0.419950	−	0.230567i
$143$	−4.73607	−	2.16289i	−0.396050	−	0.180870i
$144$	3.82742	−	1.16225i	0.318952	−	0.0968540i
$145$	−22.5628	−	3.24404i	−1.87374	−	0.269402i
$146$	1.17634	−	16.9975i	0.0973544	−	1.40673i
$147$	5.60402	+	1.64549i	0.462211	+	0.135718i
$148$	9.11927	+	4.11396i	0.749599	+	0.338165i
$149$	−9.45018	−	20.6930i	−0.774189	−	1.69524i	−0.717204	−	0.696863i	$-0.754579\pi$
$149$	−9.45018	−	20.6930i	−0.774189	−	1.69524i	−0.0569850	−	0.998375i	$-0.518149\pi$
$150$	−4.59132	+	0.339010i	−0.374879	+	0.0276801i
$151$	−8.39969	−	7.27838i	−0.683557	−	0.592306i	0.242290	−	0.970204i	$-0.422101\pi$
$151$	−8.39969	−	7.27838i	−0.683557	−	0.592306i	−0.925847	+	0.377898i	$0.876647\pi$
$152$	−9.91943	−	2.08615i	−0.804572	−	0.169209i
$153$	1.88975	+	4.13797i	0.152777	+	0.334535i
$154$	−4.28534	−	4.26564i	−0.345322	−	0.343735i
$155$	4.07130	−	0.585364i	0.327014	−	0.0470176i
$156$	−0.361254	+	2.59748i	−0.0289235	+	0.207965i
$157$	−0.556731	+	0.357789i	−0.0444320	+	0.0285547i	−0.562668	−	0.826683i	$-0.690225\pi$
$157$	−0.556731	+	0.357789i	−0.0444320	+	0.0285547i	0.518236	+	0.855237i	$0.326589\pi$
$158$	3.97775	+	2.16014i	0.316453	+	0.171851i
$159$	0.947679	−	3.22750i	0.0751559	−	0.255957i
$160$	5.85500	+	15.1622i	0.462879	+	1.19867i
$161$	4.36268	−	0.627259i	0.343827	−	0.0494349i
$162$	0.680618	+	1.23966i	0.0534744	+	0.0973970i
$163$		−	18.9808i		−	1.48669i	−0.668909	−	0.743345i	$-0.733238\pi$
$163$		−	18.9808i		−	1.48669i	0.668909	−	0.743345i	$-0.266762\pi$
$164$	5.08737	+	11.0053i	0.397257	+	0.859370i
$165$	−3.21422	−	10.9466i	−0.250227	−	0.852195i
$166$	−4.94470	−	1.83131i	−0.383783	−	0.142138i
$167$	−4.51530	+	2.06207i	−0.349405	+	0.159568i	−0.582384	−	0.812914i	$-0.697880\pi$
$167$	−4.51530	+	2.06207i	−0.349405	+	0.159568i	0.232979	+	0.972482i	$0.425153\pi$
$168$	−1.44105	+	2.68301i	−0.111180	+	0.206999i
$169$	9.48989	+	6.09878i	0.729991	+	0.469137i
$170$	−16.2029	+	8.89597i	−1.24271	+	0.682290i
$171$		−	3.58377i		−	0.274057i
$172$	−14.2898	+	6.60569i	−1.08959	+	0.503679i
$173$	−14.8753	+	4.36779i	−1.13095	+	0.332077i	−0.793081	−	0.609117i	$-0.791524\pi$
$173$	−14.8753	+	4.36779i	−1.13095	+	0.332077i	−0.337869	+	0.941193i	$0.609706\pi$
$174$	−10.5032	+	3.94509i	−0.796249	+	0.299077i
$175$	2.29545	−	2.64909i	0.173520	−	0.200253i
$176$	−13.2819	+	8.70971i	−1.00116	+	0.656519i
$177$	−3.80582	−	3.29776i	−0.286063	−	0.247875i
$178$	−6.94165	−	6.90974i	−0.520298	−	0.517907i
$179$	−19.3910	−	12.4618i	−1.44935	−	0.931441i	−0.999260	−	0.0384587i	$-0.987755\pi$
$179$	−19.3910	−	12.4618i	−1.44935	−	0.931441i	−0.450091	−	0.892983i	$-0.648608\pi$
$180$	−4.81985	+	3.12900i	−0.359250	+	0.233222i
$181$	4.37303	−	2.81037i	0.325044	−	0.208893i	−0.367934	−	0.929852i	$-0.619935\pi$
$181$	4.37303	−	2.81037i	0.325044	−	0.208893i	0.692978	+	0.720959i	$0.256298\pi$
$182$	−1.20026	−	1.59568i	−0.0889690	−	0.118280i
$183$	4.21991	−	3.65658i	0.311945	−	0.270302i
$184$	0.746119	−	11.5537i	0.0550046	−	0.851751i
$185$	−14.2260	−	2.04538i	−1.04591	−	0.150380i
$186$	1.61791	−	1.21698i	0.118631	−	0.0892333i
$187$	−11.8288	−	13.6512i	−0.865007	−	0.998271i
$188$	−0.335723	−	2.26100i	−0.0244851	−	0.164901i
$189$	−1.03314	−	0.303357i	−0.0751497	−	0.0220659i
$190$	14.5225	−	1.07231i	1.05358	−	0.0777932i
$191$	−1.51626	−	0.974441i	−0.109713	−	0.0705081i	0.484634	−	0.874717i	$-0.338953\pi$
$191$	−1.51626	−	0.974441i	−0.109713	−	0.0705081i	−0.594347	+	0.804209i	$0.702589\pi$
$192$	6.11783	+	5.15482i	0.441516	+	0.372017i
$193$	−19.9006	+	5.84333i	−1.43247	+	0.420612i	−0.903706	−	0.428154i	$-0.859164\pi$
$193$	−19.9006	+	5.84333i	−1.43247	+	0.420612i	−0.528768	+	0.848766i	$0.677346\pi$
$194$	3.87390	−	18.0077i	0.278130	−	1.29287i
$195$	−0.536168	−	3.72913i	−0.0383958	−	0.267048i
$196$	3.34258	+	11.1927i	0.238756	+	0.799482i
$197$	−9.80330	+	8.49461i	−0.698456	+	0.605216i	−0.929979	−	0.367614i	$-0.880175\pi$
$197$	−9.80330	+	8.49461i	−0.698456	+	0.605216i	0.231522	+	0.972830i	$0.425629\pi$
$198$	−3.97987	−	3.96157i	−0.282837	−	0.281537i
$199$	18.5754	+	8.48310i	1.31677	+	0.601351i	0.945030	−	0.326984i	$-0.106032\pi$
$199$	18.5754	+	8.48310i	1.31677	+	0.601351i	0.371745	+	0.928335i	$0.378760\pi$
$200$	−5.56874	−	7.33278i	−0.393769	−	0.518506i
$201$	−4.86078	+	6.58581i	−0.342853	+	0.464527i
$202$	−9.46146	+	2.08105i	−0.665706	+	0.146423i
$203$	3.54867	−	7.77050i	0.249068	−	0.545382i
$204$	−4.88349	+	7.67640i	−0.341913	+	0.537456i
$205$	−11.4063	−	13.1635i	−0.796649	−	0.919381i
$206$	−1.46830	−	19.8856i	−0.102301	−	1.38550i
$207$	4.05170	−	0.582546i	0.281612	−	0.0404898i
$208$	−4.75070	+	2.22270i	−0.329402	+	0.154117i
$209$	4.00910	+	13.6537i	0.277315	+	0.944449i
$210$	0.920169	−	4.27737i	0.0634977	−	0.295166i
$211$	−0.253916	+	0.395101i	−0.0174803	+	0.0271999i	−0.849884	−	0.526970i	$-0.823328\pi$
$211$	−0.253916	+	0.395101i	−0.0174803	+	0.0271999i	0.832403	+	0.554170i	$0.186964\pi$
$212$	6.44620	−	1.92508i	0.442727	−	0.132215i
$213$	−1.13730	+	3.87329i	−0.0779266	+	0.265394i
$214$	−15.4302	−	1.06787i	−1.05479	−	0.0729980i
$215$	17.0922	−	14.8105i	1.16568	−	1.01007i
$216$	−1.33833	+	2.49176i	−0.0910620	+	0.169543i
$217$	−0.219368	+	1.52574i	−0.0148917	+	0.103574i
$218$	−5.58415	+	10.2829i	−0.378206	+	0.696443i
$219$	7.88965	+	9.10514i	0.533133	+	0.615268i
$220$	14.8627	−	17.3130i	1.00204	−	1.16724i
$221$	−3.22487	−	5.01799i	−0.216928	−	0.337547i
$222$	−6.62236	+	2.48741i	−0.444464	+	0.166944i
$223$	4.76054	−	7.40755i	0.318790	−	0.496046i	−0.644466	−	0.764633i	$-0.722920\pi$
$223$	4.76054	−	7.40755i	0.318790	−	0.496046i	0.963256	+	0.268587i	$0.0865566\pi$
$224$	−6.07011	+	0.504480i	−0.405576	+	0.0337070i
$225$	2.13183	−	2.46026i	0.142122	−	0.164017i
$226$	13.6944	+	0.947738i	0.910937	+	0.0630426i
$227$	−13.7358	−	11.9022i	−0.911680	−	0.789975i	0.0664890	−	0.997787i	$-0.478820\pi$
$227$	−13.7358	−	11.9022i	−0.911680	−	0.789975i	−0.978169	+	0.207812i	$0.933366\pi$
$228$	6.01179	−	3.90280i	0.398141	−	0.258469i
$229$	−1.94646	−	6.62904i	−0.128626	−	0.438059i	0.869846	−	0.493323i	$-0.164218\pi$
$229$	−1.94646	−	6.62904i	−0.128626	−	0.438059i	−0.998472	+	0.0552641i	$0.982400\pi$
$230$	3.57298	+	16.2444i	0.235595	+	1.07113i
$231$	4.27550			0.281307
$232$	−18.0562	−	13.3230i	−1.18545	−	0.874696i
$233$	5.41212	−	8.42142i	0.354560	−	0.551705i	−0.617461	−	0.786602i	$-0.711839\pi$
$233$	5.41212	−	8.42142i	0.354560	−	0.551705i	0.972020	+	0.234896i	$0.0754750\pi$
$234$	−1.11470	−	1.48194i	−0.0728702	−	0.0968773i
$235$	1.36414	+	2.98704i	0.0889864	+	0.194853i
$236$	1.38740	−	9.97563i	0.0903120	−	0.649358i
$237$	−3.07103	+	0.901736i	−0.199485	+	0.0585740i
$238$	−1.48805	−	6.76540i	−0.0964563	−	0.438536i
$239$	0.749120			0.0484566			0.0242283	−	0.999706i	$-0.492287\pi$
$239$	0.749120			0.0484566			0.0242283	+	0.999706i	$0.492287\pi$
$240$	−10.4978	−	4.67778i	−0.677633	−	0.301949i
$241$	−3.27103	−	22.7505i	−0.210706	−	1.46549i	−0.770808	−	0.637067i	$-0.780147\pi$
$241$	−3.27103	−	22.7505i	−0.210706	−	1.46549i	0.560103	−	0.828423i	$-0.310762\pi$
$242$	5.92396	+	3.21704i	0.380807	+	0.206799i
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$	10.7295	+	3.09684i	0.686887	+	0.198255i
$245$	−9.07267	−	14.1174i	−0.579632	−	0.901925i
$246$	−8.03950	−	2.97750i	−0.512580	−	0.189838i
$247$	0.668762	+	4.65134i	0.0425523	+	0.295958i
$248$	3.80343	+	1.38874i	0.241518	+	0.0881852i
$249$	3.39158	−	1.54888i	0.214933	−	0.0981566i
$250$	−5.68477	−	4.23517i	−0.359537	−	0.267856i
$251$	−9.35785	+	10.7995i	−0.590662	+	0.681660i	−0.969862	−	0.243654i	$-0.921654\pi$
$251$	−9.35785	+	10.7995i	−0.590662	+	0.681660i	0.379200	+	0.925315i	$0.376199\pi$
$252$	−0.616227	−	2.06346i	−0.0388186	−	0.129986i
$253$	−14.7848	+	6.75200i	−0.929514	+	0.424495i
$254$	17.1334	+	12.7644i	1.07505	+	0.800912i
$255$	3.68237	−	12.5410i	0.230599	−	0.785347i
$256$	−1.98480	+	15.8764i	−0.124050	+	0.992276i
$257$	−3.30871	+	23.0126i	−0.206392	+	1.43549i	0.578413	+	0.815744i	$0.303672\pi$
$257$	−3.30871	+	23.0126i	−0.206392	+	1.43549i	−0.784805	+	0.619743i	$0.787237\pi$
$258$	3.86613	−	10.4389i	0.240695	−	0.649896i
$259$	2.23746	−	4.89935i	0.139029	−	0.304431i
$260$	5.67174	−	4.96053i	0.351747	−	0.307639i
$261$	3.29571	−	7.21660i	0.203999	−	0.446696i
$262$	−4.35890	−	11.6049i	−0.269294	−	0.716956i
$263$	6.88599	+	0.990056i	0.424608	+	0.0610495i	0.351307	−	0.936260i	$-0.385737\pi$
$263$	6.88599	+	0.990056i	0.424608	+	0.0610495i	0.0733015	+	0.997310i	$0.476646\pi$
$264$	2.31140	−	10.9905i	0.142257	−	0.676418i
$265$	−8.13055	+	5.22519i	−0.499456	+	0.320981i
$266$	−1.14773	+	5.33516i	−0.0703717	+	0.327120i
$267$	6.92571			0.423847
$268$	−16.3412	−	0.981896i	−0.998200	−	0.0599789i
$269$	16.7698			1.02247			0.511236	−	0.859440i	$-0.329188\pi$
$269$	16.7698			1.02247			0.511236	+	0.859440i	$0.329188\pi$
$270$	0.854577	−	3.97246i	0.0520079	−	0.241757i
$271$	−12.8777	+	8.27599i	−0.782264	+	0.502731i	−0.869784	−	0.493432i	$-0.835742\pi$
$271$	−12.8777	+	8.27599i	−0.782264	+	0.502731i	0.0875202	+	0.996163i	$0.472106\pi$
$272$	−18.1955	+	0.167672i	−1.10326	+	0.0101666i
$273$	1.39751	+	0.200932i	0.0845812	+	0.0121609i
$274$	1.30562	+	3.47603i	0.0788755	+	0.209995i
$275$	−5.36977	+	11.7581i	−0.323809	+	0.709043i
$276$	5.38961	+	6.16235i	0.324417	+	0.370930i
$277$	5.03987	−	11.0358i	0.302817	−	0.663076i	−0.695653	−	0.718378i	$-0.744885\pi$
$277$	5.03987	−	11.0358i	0.302817	−	0.663076i	0.998470	+	0.0553021i	$0.0176122\pi$
$278$	10.8984	−	29.4265i	0.653640	−	1.76488i
$279$	−0.203731	+	1.41698i	−0.0121971	+	0.0848324i
$280$	8.17740	−	3.11456i	0.488693	−	0.186130i
$281$	−1.19518	+	4.07041i	−0.0712985	+	0.242820i	−0.987430	−	0.158058i	$-0.949477\pi$
$281$	−1.19518	+	4.07041i	−0.0712985	+	0.242820i	0.916131	+	0.400878i	$0.131295\pi$
$282$	1.29614	+	0.965628i	0.0771841	+	0.0575023i
$283$	−22.3044	+	10.1861i	−1.32586	+	0.605500i	−0.947381	−	0.320109i	$-0.896280\pi$
$283$	−22.3044	+	10.1861i	−1.32586	+	0.605500i	−0.378480	+	0.925609i	$0.623553\pi$
$284$	−7.73603	+	2.31027i	−0.459049	+	0.137089i
$285$	−6.74307	+	7.78191i	−0.399425	+	0.460961i
$286$	5.90470	+	4.39902i	0.349152	+	0.260119i
$287$	5.93756	−	2.71159i	0.350483	−	0.160060i
$288$	−5.63742	+	0.468519i	−0.332188	+	0.0276078i
$289$	−0.525698	−	3.65631i	−0.0309234	−	0.215077i
$290$	30.2300	+	11.1960i	1.77517	+	0.657449i
$291$	7.04165	+	10.9570i	0.412789	+	0.642312i
$292$	−6.68194	+	23.1506i	−0.391031	+	1.35479i
$293$	10.5823	+	3.10726i	0.618227	+	0.181528i	0.575825	−	0.817573i	$-0.304681\pi$
$293$	10.5823	+	3.10726i	0.618227	+	0.181528i	0.0424018	+	0.999101i	$0.486499\pi$
$294$	−7.25860	−	3.94182i	−0.423330	−	0.229891i
$295$	2.05916	+	14.3218i	0.119889	+	0.833845i
$296$	−11.3845	−	8.40022i	−0.661713	−	0.488253i
$297$	3.97073			0.230405
$298$	6.91097	+	31.4206i	0.400342	+	1.82014i
$299$	−5.14996	+	1.51216i	−0.297830	+	0.0874507i
$300$	6.44871	+	0.896878i	0.372316	+	0.0517813i
$301$	3.52087	+	7.70962i	0.202939	+	0.444375i
$302$	9.44848	+	12.5613i	0.543699	+	0.722820i
$303$	3.70349	−	5.76274i	0.212760	−	0.331061i
$304$	13.0940	+	5.83459i	0.750990	+	0.334637i
$305$	−16.0433			−0.918638
$306$	−1.38198	−	6.28315i	−0.0790027	−	0.359184i
$307$	−2.10258	−	7.16072i	−0.120000	−	0.408684i	0.877481	−	0.479611i	$-0.159222\pi$
$307$	−2.10258	−	7.16072i	−0.120000	−	0.408684i	−0.997481	+	0.0709273i	$0.977404\pi$
$308$	4.65611	+	7.17218i	0.265307	+	0.408673i
$309$	10.6557	+	9.23322i	0.606182	+	0.525260i
$310$	−5.80301	−	0.401605i	−0.329589	−	0.0228096i
$311$	−5.67589	+	6.55033i	−0.321850	+	0.371435i	−0.893500	−	0.449062i	$-0.851758\pi$
$311$	−5.67589	+	6.55033i	−0.321850	+	0.371435i	0.571650	+	0.820498i	$0.306304\pi$
$312$	1.27203	−	3.48378i	0.0720143	−	0.197230i
$313$	6.63939	−	10.3311i	0.375281	−	0.583948i	−0.601320	−	0.799008i	$-0.705358\pi$
$313$	6.63939	−	10.3311i	0.375281	−	0.583948i	0.976601	+	0.215060i	$0.0689947\pi$
$314$	0.876144	−	0.329086i	0.0494436	−	0.0185714i
$315$	1.67261	+	2.60263i	0.0942408	+	0.146641i
$316$	−4.85709	−	4.16967i	−0.273233	−	0.234562i
$317$	−7.19634	−	8.30502i	−0.404187	−	0.466456i	0.516768	−	0.856125i	$-0.327135\pi$
$317$	−7.19634	−	8.30502i	−0.404187	−	0.466456i	−0.920955	+	0.389669i	$0.872589\pi$
$318$	−2.27020	+	4.18042i	−0.127306	+	0.234426i
$319$	−4.48319	+	31.1813i	−0.251010	+	1.74582i
$320$	−3.58537	−	22.7044i	−0.200428	−	1.26921i
$321$	8.26557	−	7.16216i	0.461339	−	0.399753i
$322$	−6.21833	−	0.430348i	−0.346534	−	0.0239824i
$323$	−4.59302	+	15.6424i	−0.255562	+	0.870365i
$324$	−0.572301	−	1.91637i	−0.0317945	−	0.106465i
$325$	−2.30778	+	3.59097i	−0.128012	+	0.199191i
$326$	−5.64542	+	26.2425i	−0.312671	+	1.45344i
$327$	−2.33107	−	7.93889i	−0.128908	−	0.439022i
$328$	−3.76042	−	16.7289i	−0.207634	−	0.923698i
$329$	−1.21809	+	0.175135i	−0.0671555	+	0.00965551i
$330$	1.18809	+	16.0906i	0.0654022	+	0.885761i
$331$	−17.4552	−	20.1444i	−0.959427	−	1.10724i	−0.994168	−	0.107841i	$-0.965606\pi$
$331$	−17.4552	−	20.1444i	−0.959427	−	1.10724i	0.0347412	−	0.999396i	$-0.488939\pi$
$332$	6.29178	+	4.00264i	0.345306	+	0.219673i
$333$	2.07796	−	4.55011i	0.113872	−	0.249344i
$334$	6.85610	−	1.50800i	0.375149	−	0.0825143i
$335$	22.9464	−	5.15482i	1.25370	−	0.281638i
$336$	2.79038	−	3.28088i	0.152228	−	0.178986i
$337$	27.6406	+	12.6231i	1.50568	+	0.687622i	0.986001	−	0.166739i	$-0.0533237\pi$
$337$	27.6406	+	12.6231i	1.50568	+	0.687622i	0.519680	+	0.854361i	$0.326051\pi$
$338$	−11.3066	−	11.2546i	−0.614999	−	0.612171i
$339$	−7.33572	+	6.35644i	−0.398422	+	0.345234i
$340$	25.0478	−	7.48022i	1.35841	−	0.405672i
$341$	−0.808961	−	5.62645i	−0.0438077	−	0.304689i
$342$	−1.06591	+	4.95485i	−0.0576380	+	0.267928i
$343$	13.2661	−	3.89528i	0.716303	−	0.210325i
$344$	21.7216	−	4.88271i	1.17115	−	0.263258i
$345$	−9.89409	−	6.35854i	−0.532680	−	0.342333i
$346$	21.8655	−	1.61449i	1.17549	−	0.0867953i
$347$	20.3046	+	5.96198i	1.09001	+	0.320056i	0.776876	−	0.629653i	$-0.216803\pi$
$347$	20.3046	+	5.96198i	1.09001	+	0.320056i	0.313134	+	0.949709i	$0.398621\pi$
$348$	15.6950	−	2.33046i	0.841340	−	0.124926i
$349$	10.5856	+	12.2164i	0.566632	+	0.653929i	0.964676	−	0.263438i	$-0.0848563\pi$
$349$	10.5856	+	12.2164i	0.566632	+	0.653929i	−0.398044	+	0.917366i	$0.630311\pi$
$350$	−3.96157	+	2.97986i	−0.211755	+	0.159280i
$351$	1.29789	+	0.186609i	0.0692764	+	0.00996044i
$352$	20.9538	−	8.09149i	1.11684	−	0.431278i
$353$	14.4334	−	12.5066i	0.768212	−	0.665660i	−0.179868	−	0.983691i	$-0.557567\pi$
$353$	14.4334	−	12.5066i	0.768212	−	0.665660i	0.948080	+	0.318031i	$0.103022\pi$
$354$	4.28102	+	5.69139i	0.227534	+	0.302494i
$355$	9.75740	−	6.27070i	0.517869	−	0.332814i
$356$	7.54225	+	11.6179i	0.399739	+	0.615749i
$357$	4.12064	+	2.64817i	0.218087	+	0.140156i
$358$	23.1032	+	22.9970i	1.22104	+	1.21543i
$359$	23.7926	+	20.6164i	1.25573	+	1.08809i	0.992357	+	0.123398i	$0.0393792\pi$
$359$	23.7926	+	20.6164i	1.25573	+	1.08809i	0.263369	+	0.964695i	$0.415166\pi$
$360$	7.59449	−	2.89254i	0.400265	−	0.152450i
$361$	−4.03173	+	4.65286i	−0.212196	+	0.244888i
$362$	−6.88196	+	2.58491i	−0.361708	+	0.135860i
$363$	−4.57361	+	1.34293i	−0.240052	+	0.0704856i
$364$	1.18486	+	2.56315i	0.0621033	+	0.134346i
$365$		−	34.6161i		−	1.81189i
$366$	−6.92195	+	3.80040i	−0.361816	+	0.198650i
$367$	8.03803	+	5.16573i	0.419582	+	0.269649i	0.733351	−	0.679851i	$-0.237955\pi$
$367$	8.03803	+	5.16573i	0.419582	+	0.269649i	−0.313769	+	0.949499i	$0.601592\pi$
$368$	−4.46797	+	15.7520i	−0.232909	+	0.821132i
$369$	5.51432	−	2.51830i	0.287064	−	0.131098i
$370$	19.0602	+	7.05912i	0.990893	+	0.366986i
$371$	−1.02042	−	3.47522i	−0.0529774	−	0.180425i
$372$	−2.59886	+	1.20136i	−0.134745	+	0.0622878i
$373$		−	22.3437i		−	1.15691i	−0.815714	−	0.578456i	$-0.803656\pi$
$373$		−	22.3437i		−	1.15691i	0.815714	−	0.578456i	$-0.196344\pi$
$374$	12.2941	+	22.3921i	0.635710	+	1.15787i
$375$	4.96163	−	0.713374i	0.256217	−	0.0368385i
$376$	−0.208322	+	3.22588i	−0.0107434	+	0.166362i
$377$	−2.93079	+	9.98137i	−0.150944	+	0.514067i
$378$	1.33817	+	0.726700i	0.0688281	+	0.0373774i
$379$	−24.1395	+	15.5135i	−1.23996	+	0.796874i	−0.985412	−	0.170186i	$-0.945563\pi$
$379$	−24.1395	+	15.5135i	−1.23996	+	0.796874i	−0.254548	+	0.967060i	$0.581927\pi$
$380$	−20.3976	−	2.83687i	−1.04637	−	0.145528i
$381$	−14.9539	+	2.15005i	−0.766113	+	0.110150i
$382$	1.80653	+	1.79823i	0.0924301	+	0.0920052i
$383$	−3.52198	−	7.71206i	−0.179965	−	0.394068i	0.798054	−	0.602586i	$-0.205863\pi$
$383$	−3.52198	−	7.71206i	−0.179965	−	0.394068i	−0.978018	+	0.208518i	$0.933136\pi$
$384$	−6.92522	−	8.94658i	−0.353401	−	0.456553i
$385$	−9.28396	−	8.04460i	−0.473155	−	0.409991i
$386$	29.2522	−	2.15990i	1.48890	−	0.109936i
$387$	3.26989	+	7.16006i	0.166218	+	0.363966i
$388$	−10.7120	+	23.7449i	−0.543818	+	1.20546i
$389$	30.3261	+	8.90455i	1.53759	+	0.451479i	0.937365	−	0.348349i	$-0.113258\pi$
$389$	30.3261	+	8.90455i	1.53759	+	0.451479i	0.600230	+	0.799828i	$0.295076\pi$
$390$	−0.367853	+	5.31530i	−0.0186269	+	0.269151i
$391$	−18.4314	−	2.65003i	−0.932116	−	0.134018i
$392$	−1.29235	−	16.4691i	−0.0652736	−	0.831814i
$393$	7.97355	+	3.64140i	0.402212	+	0.183684i
$394$	16.0804	−	8.82872i	0.810120	−	0.444785i
$395$	8.36521	+	3.82026i	0.420899	+	0.192218i
$396$	4.32421	+	6.66093i	0.217300	+	0.334724i
$397$	2.91813	−	20.2960i	0.146457	−	1.01863i	−0.775504	−	0.631343i	$-0.782504\pi$
$397$	2.91813	−	20.2960i	0.146457	−	1.01863i	0.921960	−	0.387285i	$-0.126587\pi$
$398$	−23.1589	−	17.2534i	−1.16085	−	0.864837i
$399$	−2.08624	−	3.24626i	−0.104443	−	0.162516i
$400$	5.51827	+	11.7945i	0.275913	+	0.589724i
$401$			26.6055i			1.32861i	0.747460	+	0.664307i	$0.231273\pi$
$401$			26.6055i			1.32861i	−0.747460	+	0.664307i	$0.768727\pi$
$402$	8.67923	−	7.65969i	0.432881	−	0.382031i
$403$		−	1.87711i		−	0.0935053i
$404$	13.7002	−	0.0631226i	0.681612	−	0.00314047i
$405$	1.55338	+	2.41711i	0.0771881	+	0.120107i
$406$	−7.21749	+	9.68788i	−0.358198	+	0.480802i
$407$	−2.82668	+	19.6600i	−0.140113	+	0.974509i
$408$	9.03502	−	9.16077i	0.447300	−	0.453526i
$409$	3.93391	+	1.79655i	0.194519	+	0.0888339i	0.510293	−	0.860001i	$-0.329537\pi$
$409$	3.93391	+	1.79655i	0.194519	+	0.0888339i	−0.315774	+	0.948834i	$0.602264\pi$
$410$	11.8549	+	21.5922i	0.585472	+	1.06636i
$411$	−2.38832	−	1.09071i	−0.117807	−	0.0538007i
$412$	−3.88450	+	27.9302i	−0.191375	+	1.37602i
$413$	−5.36715	−	0.771680i	−0.264100	−	0.0379719i
$414$	−5.77507	−	0.399672i	−0.283829	−	0.0196428i
$415$	−10.2789	−	3.01816i	−0.504572	−	0.148156i
$416$	7.22933	−	1.66008i	0.354447	−	0.0813921i
$417$	9.21759	+	20.1837i	0.451387	+	0.988401i
$418$	−1.48190	−	20.0699i	−0.0724823	−	0.981649i
$419$	28.7617	+	24.9221i	1.40510	+	1.21753i	0.943901	+	0.330228i	$0.107126\pi$
$419$	28.7617	+	24.9221i	1.40510	+	1.21753i	0.461198	+	0.887297i	$0.347420\pi$
$420$	−2.54442	+	5.64013i	−0.124155	+	0.275210i
$421$	−4.29962	−	9.41486i	−0.209551	−	0.458852i	0.775449	−	0.631411i	$-0.217524\pi$
$421$	−4.29962	−	9.41486i	−0.209551	−	0.458852i	−0.984999	+	0.172559i	$0.944797\pi$
$422$	0.468575	−	0.470739i	0.0228099	−	0.0229152i
$423$	−1.13126	+	0.162651i	−0.0550039	+	0.00790836i
$424$	−9.48498	+	0.744299i	−0.460631	+	0.0361464i
$425$	−12.4581	+	8.00632i	−0.604306	+	0.388364i
$426$	2.72444	−	5.01688i	0.132000	−	0.243069i
$427$	1.69387	−	5.76878i	0.0819719	−	0.279171i
$428$	21.0160	+	6.06581i	1.01584	+	0.293202i
$429$	−5.15358	+	0.740973i	−0.248817	+	0.0357745i
$430$	−28.0364	+	15.3930i	−1.35204	+	0.742316i
$431$		−	31.3631i		−	1.51071i	−0.655318	−	0.755353i	$-0.727465\pi$
$431$		−	31.3631i		−	1.51071i	0.655318	−	0.755353i	$-0.272535\pi$
$432$	2.59148	−	3.04701i	0.124682	−	0.146599i
$433$	−8.15134	−	27.7609i	−0.391728	−	1.33410i	−0.885551	−	0.464542i	$-0.846219\pi$
$433$	−8.15134	−	27.7609i	−0.391728	−	1.33410i	0.493823	−	0.869563i	$-0.335599\pi$
$434$	0.757093	−	2.04422i	0.0363416	−	0.0981255i
$435$	−20.7349	+	9.46929i	−0.994160	+	0.454018i
$436$	10.7790	−	12.5560i	0.516219	−	0.601324i
$437$	12.3409	+	7.93101i	0.590345	+	0.379392i
$438$	−8.19997	−	14.9352i	−0.391810	−	0.713632i
$439$		−	18.9803i		−	0.905878i	−0.891541	−	0.452939i	$-0.850375\pi$
$439$		−	18.9803i		−	0.905878i	0.891541	−	0.452939i	$-0.149625\pi$
$440$	−25.6983	+	19.5161i	−1.22512	+	0.930393i
$441$	5.60402	−	1.64549i	0.266858	−	0.0783565i
$442$	2.96615	+	7.89696i	0.141086	+	0.375620i
$443$	21.6950	−	25.0374i	1.03076	−	1.18956i	0.0491260	−	0.998793i	$-0.484356\pi$
$443$	21.6950	−	25.0374i	1.03076	−	1.18956i	0.981635	−	0.190769i	$-0.0610981\pi$
$444$	9.89579	−	1.46937i	0.469633	−	0.0697331i
$445$	−15.0387	−	13.0311i	−0.712904	−	0.617735i
$446$	−8.78506	+	8.82563i	−0.415985	+	0.417906i
$447$	−19.1375	−	12.2989i	−0.905172	−	0.581719i
$448$	8.54248	+	1.10794i	0.403594	+	0.0523452i
$449$	−4.40088	+	2.82828i	−0.207691	+	0.133475i	−0.640351	−	0.768082i	$-0.721211\pi$
$449$	−4.40088	+	2.82828i	−0.207691	+	0.133475i	0.432661	+	0.901557i	$0.357575\pi$
$450$	−3.67918	+	2.76745i	−0.173438	+	0.130459i
$451$	−18.1917	+	15.7632i	−0.856615	+	0.742261i
$452$	−18.6517	−	5.38342i	−0.877304	−	0.253215i
$453$	−11.0013	−	1.58174i	−0.516884	−	0.0743167i
$454$	15.4509	+	20.5412i	0.725147	+	0.964045i
$455$	−2.65654	−	3.06581i	−0.124540	−	0.143727i
$456$	−9.47261	+	3.60787i	−0.443596	+	0.168954i
$457$	3.13601	+	0.920815i	0.146696	+	0.0430739i	0.354256	−	0.935148i	$-0.384734\pi$
$457$	3.13601	+	0.920815i	0.146696	+	0.0430739i	−0.207560	+	0.978222i	$0.566552\pi$
$458$	0.719480	+	9.74413i	0.0336191	+	0.455313i
$459$	3.82691	+	2.45941i	0.178625	+	0.114795i
$460$	−0.108376	−	23.5220i	−0.00505304	−	1.09672i
$461$	−21.3433	+	6.26694i	−0.994054	+	0.291881i	−0.738014	−	0.674785i	$-0.764236\pi$
$461$	−21.3433	+	6.26694i	−0.994054	+	0.291881i	−0.256040	+	0.966666i	$0.582418\pi$
$462$	−5.91123	−	1.27165i	−0.275015	−	0.0591627i
$463$	0.620427	+	4.31517i	0.0288337	+	0.200543i	0.999146	−	0.0413113i	$-0.0131535\pi$
$463$	0.620427	+	4.31517i	0.0288337	+	0.200543i	−0.970313	+	0.241854i	$0.922244\pi$
$464$	21.0015	+	23.7905i	0.974972	+	1.10445i
$465$	3.10852	−	2.69355i	0.144154	−	0.124910i
$466$	−9.98747	+	10.0336i	−0.462661	+	0.464797i
$467$	9.52327	+	4.34913i	0.440685	+	0.201254i	0.623386	−	0.781915i	$-0.285757\pi$
$467$	9.52327	+	4.34913i	0.440685	+	0.201254i	−0.182701	+	0.983169i	$0.558484\pi$
$468$	1.10040	+	2.38044i	0.0508658	+	0.110036i
$469$	−0.569159	+	8.79521i	−0.0262813	+	0.406125i
$470$	−0.997600	−	4.53556i	−0.0460159	−	0.209210i
$471$	−0.274916	+	0.601983i	−0.0126675	+	0.0277379i
$472$	−4.88523	+	13.3795i	−0.224861	+	0.615841i
$473$	−20.4677	−	23.6210i	−0.941108	−	1.08610i
$474$	4.51416	−	0.333313i	0.207342	−	0.0153096i
$475$	11.5478	−	1.66032i	0.529850	−	0.0761809i
$476$	0.0451357	+	9.79632i	0.00206879	+	0.449014i
$477$	−0.947679	−	3.22750i	−0.0433913	−	0.147777i
$478$	−1.03572	−	0.222810i	−0.0473728	−	0.0101911i
$479$	9.28479	−	14.4474i	0.424233	−	0.660119i	−0.561685	−	0.827351i	$-0.689847\pi$
$479$	9.28479	−	14.4474i	0.424233	−	0.660119i	0.985918	+	0.167232i	$0.0534829\pi$
$480$	13.1228	+	9.58977i	0.598973	+	0.437711i
$481$	−1.84788	+	6.29332i	−0.0842563	+	0.286950i
$482$	−2.24418	+	32.4274i	−0.102220	+	1.47703i
$483$	3.33100	−	2.88633i	0.151566	−	0.131332i
$484$	−7.23353	−	6.20977i	−0.328797	−	0.282262i
$485$	5.32580	−	37.0417i	0.241832	−	1.68198i
$486$	1.24278	+	0.674899i	0.0563738	+	0.0306141i
$487$	−4.63872	−	5.35337i	−0.210200	−	0.242584i	0.640853	−	0.767664i	$-0.278581\pi$
$487$	−4.63872	−	5.35337i	−0.210200	−	0.242584i	−0.851053	+	0.525080i	$0.824035\pi$
$488$	−13.9134	−	7.47291i	−0.629828	−	0.338283i
$489$	−10.2618	−	15.9676i	−0.464054	−	0.722082i
$490$	8.34482	+	22.2169i	0.376981	+	1.00366i
$491$	10.5404	−	16.4011i	0.475680	−	0.740173i	−0.517636	−	0.855601i	$-0.673188\pi$
$491$	10.5404	−	16.4011i	0.475680	−	0.740173i	0.993316	+	0.115428i	$0.0368241\pi$
$492$	10.2297	+	6.50782i	0.461190	+	0.293395i
$493$	−23.6340	+	27.2751i	−1.06442	+	1.22841i
$494$	0.458822	−	6.62978i	0.0206434	−	0.298288i
$495$	−8.62218	−	7.47116i	−0.387538	−	0.335804i
$496$	−4.84551	−	3.05130i	−0.217570	−	0.137007i
$497$	1.22459	+	4.17058i	0.0549305	+	0.187076i
$498$	−5.14983	+	1.13271i	−0.230769	+	0.0507579i
$499$	−6.97296			−0.312152			−0.156076	−	0.987745i	$-0.549885\pi$
$499$	−6.97296			−0.312152			−0.156076	+	0.987745i	$0.549885\pi$
$500$	6.60001	+	7.54629i	0.295162	+	0.337480i
$501$	−2.68368	+	4.17588i	−0.119898	+	0.186565i
$502$	16.1501	−	12.1480i	0.720814	−	0.542190i
$503$	−3.00064	−	6.57050i	−0.133792	−	0.292964i	0.830864	−	0.556475i	$-0.187847\pi$
$503$	−3.00064	−	6.57050i	−0.133792	−	0.292964i	−0.964656	+	0.263511i	$0.915119\pi$
$504$	0.238254	+	3.03619i	0.0106127	+	0.135242i
$505$	−18.8848	+	5.54508i	−0.840364	+	0.246753i
$506$	22.4495	−	4.93778i	0.998001	−	0.219511i
$507$	11.2807			0.500991
$508$	−19.8919	−	22.7439i	−0.882560	−	1.00910i
$509$	3.89208	+	27.0700i	0.172514	+	1.19986i	0.873551	+	0.486733i	$0.161812\pi$
$509$	3.89208	+	27.0700i	0.172514	+	1.19986i	−0.701037	+	0.713125i	$0.747279\pi$
$510$	−8.82123	+	16.2437i	−0.390610	+	0.719284i
$511$	12.4471	+	3.65479i	0.550626	+	0.161678i
$512$	7.46624	−	21.3601i	0.329964	−	0.943993i
$513$	−1.93753	−	3.01486i	−0.0855440	−	0.133109i
$514$	11.4192	−	30.8327i	0.503678	−	1.35997i
$515$	−5.76532	−	40.0987i	−0.254050	−	1.76696i
$516$	−8.45007	+	13.2827i	−0.371994	+	0.584739i
$517$	4.12803	−	1.88521i	0.181550	−	0.0829113i
$518$	−4.55067	+	6.10827i	−0.199945	+	0.268382i
$519$	−10.1525	+	11.7166i	−0.445646	+	0.514303i
$520$	−9.31706	+	5.17141i	−0.408580	+	0.226781i
$521$	21.5117	−	9.82404i	0.942443	−	0.430399i	0.115892	−	0.993262i	$-0.463027\pi$
$521$	21.5117	−	9.82404i	0.942443	−	0.430399i	0.826550	+	0.562863i	$0.190300\pi$
$522$	−6.70301	+	8.99731i	−0.293383	+	0.393801i
$523$	11.4960	−	39.1517i	0.502684	−	1.71198i	−0.182137	−	0.983273i	$-0.558301\pi$
$523$	11.4960	−	39.1517i	0.502684	−	1.71198i	0.684821	−	0.728711i	$-0.259880\pi$
$524$	2.57490	+	17.3413i	0.112485	+	0.757556i
$525$	0.498849	−	3.46957i	0.0217716	−	0.151425i
$526$	−9.22598	−	3.41692i	−0.402272	−	0.148985i
$527$	2.70527	−	5.92371i	0.117843	−	0.258041i
$528$	−6.46459	+	14.5078i	−0.281335	+	0.631371i
$529$	2.59401	−	5.68010i	0.112783	−	0.246961i
$530$	12.7953	−	4.80600i	0.555792	−	0.208759i
$531$	−4.98457	−	0.716673i	−0.216312	−	0.0311009i
$532$	3.17366	−	7.03493i	0.137595	−	0.305003i
$533$	−6.68705	+	4.29751i	−0.289648	+	0.186146i
$534$	−9.57537	−	2.05990i	−0.414367	−	0.0891407i
$535$	−31.4242			−1.35859
$536$	22.3011	+	6.21790i	0.963259	+	0.268572i
$537$	−23.0501			−0.994686
$538$	−23.1856	−	4.98781i	−0.999604	−	0.215040i
$539$	−19.5099	+	12.5382i	−0.840350	+	0.540060i
$540$	−2.36305	+	5.23809i	−0.101689	+	0.225411i
$541$	18.4430	+	2.65171i	0.792927	+	0.114006i	0.526864	−	0.849950i	$-0.323368\pi$
$541$	18.4430	+	2.65171i	0.792927	+	0.114006i	0.266064	+	0.963955i	$0.414277\pi$
$542$	20.2660	−	7.61205i	0.870499	−	0.326966i
$543$	2.15942	−	4.72847i	0.0926696	−	0.202918i
$544$	25.2066	+	5.18003i	1.08072	+	0.222092i
$545$	−9.87573	+	21.6248i	−0.423030	+	0.926306i
$546$	−1.87241	−	0.693464i	−0.0801318	−	0.0296775i
$547$	−2.17735	+	15.1438i	−0.0930968	+	0.647502i	0.888829	+	0.458238i	$0.151519\pi$
$547$	−2.17735	+	15.1438i	−0.0930968	+	0.647502i	−0.981926	+	0.189264i	$0.939390\pi$
$548$	−0.771261	−	5.19423i	−0.0329466	−	0.221887i
$549$	1.57312	−	5.35756i	0.0671392	−	0.228655i
$550$	10.9214	−	14.6595i	0.465688	−	0.625083i
$551$	25.8626	−	11.8110i	1.10178	−	0.503168i
$552$	−5.61873	−	10.1230i	−0.239149	−	0.430863i
$553$	−2.25688	+	2.60457i	−0.0959721	+	0.110758i
$554$	−10.2504	+	13.7589i	−0.435498	+	0.584559i
$555$	−13.0735	+	5.97045i	−0.554937	+	0.253431i
$556$	−23.8202	+	37.4431i	−1.01020	+	1.58794i
$557$	0.746008	+	5.18860i	0.0316094	+	0.219848i	0.999503	−	0.0315106i	$-0.0100318\pi$
$557$	0.746008	+	5.18860i	0.0316094	+	0.219848i	−0.967894	+	0.251358i	$0.919123\pi$
$558$	0.703125	−	1.89850i	0.0297657	−	0.0803698i
$559$	−5.58009	−	8.68280i	−0.236013	−	0.367243i
$560$	−12.2323	+	1.87394i	−0.516909	+	0.0791885i
$561$	−17.3314	−	5.08895i	−0.731732	−	0.214856i
$562$	2.86309	−	5.27220i	0.120772	−	0.222394i
$563$	−1.04456	−	7.26510i	−0.0440231	−	0.306188i	−0.999922	−	0.0124915i	$-0.996024\pi$
$563$	−1.04456	−	7.26510i	−0.0440231	−	0.306188i	0.955899	−	0.293696i	$-0.0948854\pi$
$564$	−1.50482	−	1.72057i	−0.0633643	−	0.0724491i
$565$	27.8890			1.17330
$566$	33.8674	−	7.44915i	1.42355	−	0.313111i
$567$	−1.03314	+	0.303357i	−0.0433877	+	0.0127398i
$568$	11.3828	−	0.893227i	0.477613	−	0.0374790i
$569$	1.83106	+	4.00946i	0.0767619	+	0.168085i	0.944122	−	0.329596i	$-0.106912\pi$
$569$	1.83106	+	4.00946i	0.0767619	+	0.168085i	−0.867360	+	0.497681i	$0.834185\pi$
$570$	11.6374	−	8.75356i	0.487438	−	0.366646i
$571$	−12.2957	+	19.1325i	−0.514558	+	0.800668i	−0.997171	−	0.0751656i	$-0.976051\pi$
$571$	−12.2957	+	19.1325i	−0.514558	+	0.800668i	0.482613	+	0.875834i	$0.339688\pi$
$572$	−6.85535	−	7.83823i	−0.286637	−	0.327733i
$573$	−1.80238			−0.0752956
$574$	−9.01568	+	1.98300i	−0.376307	+	0.0827690i
$575$	3.75422	+	12.7857i	0.156562	+	0.533201i
$576$	7.93355	+	1.02896i	0.330565	+	0.0428734i
$577$	20.7429	+	17.9739i	0.863540	+	0.748261i	0.969235	−	0.246137i	$-0.0791614\pi$
$577$	20.7429	+	17.9739i	0.863540	+	0.748261i	−0.105695	+	0.994399i	$0.533707\pi$
$578$	−0.360670	+	5.21151i	−0.0150019	+	0.216770i
$579$	−13.5823	+	15.6748i	−0.564460	+	0.651422i
$580$	−38.4655	−	24.4706i	−1.59719	−	1.01609i
$581$	2.17051	−	3.37738i	0.0900480	−	0.140117i
$582$	−6.47674	−	17.2434i	−0.268470	−	0.714762i
$583$	7.22110	+	11.2363i	0.299067	+	0.465358i
$584$	16.1240	−	30.0203i	0.667216	−	1.24225i
$585$	−2.46717	−	2.84727i	−0.102005	−	0.117720i
$586$	−13.7068	−	7.44353i	−0.566222	−	0.307489i
$587$	2.78623	−	19.3786i	0.115000	−	0.799841i	−0.847934	−	0.530102i	$-0.822153\pi$
$587$	2.78623	−	19.3786i	0.115000	−	0.799841i	0.962933	−	0.269739i	$-0.0869374\pi$
$588$	8.86321	+	7.60881i	0.365513	+	0.313782i
$589$	−3.87726	+	3.35966i	−0.159760	+	0.138432i
$590$	1.41274	−	20.4135i	0.0581616	−	0.840409i
$591$	−3.65453	+	12.4462i	−0.150327	+	0.511968i
$592$	13.2416	+	15.0001i	0.544227	+	0.616500i
$593$	13.1639	−	20.4834i	0.540576	−	0.841153i	−0.458288	−	0.888804i	$-0.651537\pi$
$593$	13.1639	−	20.4834i	0.540576	−	0.841153i	0.998864	+	0.0476511i	$0.0151736\pi$
$594$	−5.48986	−	1.18101i	−0.225252	−	0.0484573i
$595$	−3.96500	−	13.5036i	−0.162549	−	0.553592i
$596$	−0.209624	−	45.4971i	−0.00858653	−	1.86363i
$597$	20.2129	−	2.90618i	0.827260	−	0.118942i
$598$	7.57001	−	0.558949i	0.309561	−	0.0228571i
$599$	13.9028	+	16.0447i	0.568055	+	0.655570i	0.964993	−	0.262275i	$-0.0844728\pi$
$599$	13.9028	+	16.0447i	0.568055	+	0.655570i	−0.396938	+	0.917845i	$0.629927\pi$
$600$	−8.64912	−	3.15804i	−0.353099	−	0.128926i
$601$	3.63586	−	7.96142i	0.148310	−	0.324753i	−0.820867	−	0.571119i	$-0.806509\pi$
$601$	3.63586	−	7.96142i	0.148310	−	0.324753i	0.969177	+	0.246366i	$0.0792366\pi$
$602$	−2.57483	−	11.7064i	−0.104942	−	0.477117i
$603$	−0.528588	+	8.16827i	−0.0215258	+	0.332638i
$604$	−9.32723	−	20.1772i	−0.379520	−	0.821000i
$605$	12.4581	+	5.68942i	0.506493	+	0.231308i
$606$	−6.83439	+	6.86595i	−0.277628	+	0.278910i
$607$	−31.3062	+	27.1270i	−1.27068	+	1.10105i	−0.280707	+	0.959794i	$0.590569\pi$
$607$	−31.3062	+	27.1270i	−1.27068	+	1.10105i	−0.989973	+	0.141257i	$0.954886\pi$
$608$	−16.3681	−	11.9613i	−0.663814	−	0.485096i
$609$	−1.21572	−	8.45551i	−0.0492634	−	0.342635i
$610$	22.1812	+	4.77174i	0.898092	+	0.193202i
$611$	1.43790	−	0.422207i	0.0581714	−	0.0170807i
$612$	0.0419183	+	9.09802i	0.00169445	+	0.367765i
$613$	21.3283	+	13.7069i	0.861441	+	0.553615i	0.895124	−	0.445818i	$-0.147087\pi$
$613$	21.3283	+	13.7069i	0.861441	+	0.553615i	−0.0336825	+	0.999433i	$0.510724\pi$
$614$	0.777186	+	10.5257i	0.0313647	+	0.424781i
$615$	−16.7123	−	4.90718i	−0.673905	−	0.197877i
$616$	−4.30425	−	11.3010i	−0.173423	−	0.455330i
$617$	25.4546	+	29.3762i	1.02476	+	1.18264i	0.983017	+	0.183512i	$0.0587468\pi$
$617$	25.4546	+	29.3762i	1.02476	+	1.18264i	0.0417466	+	0.999128i	$0.486708\pi$
$618$	−11.9862	−	15.9350i	−0.482155	−	0.641000i
$619$	21.6805	+	3.11718i	0.871413	+	0.125290i	0.563492	−	0.826122i	$-0.309458\pi$
$619$	21.6805	+	3.11718i	0.871413	+	0.125290i	0.307921	+	0.951412i	$0.400367\pi$
$620$	7.90369	+	2.28123i	0.317420	+	0.0916165i
$621$	3.09356	−	2.68058i	0.124140	−	0.107568i
$622$	9.79565	−	7.36820i	0.392770	−	0.295438i
$623$	6.27347	−	4.03171i	0.251341	−	0.161527i
$624$	−2.79486	+	4.43828i	−0.111884	+	0.177673i
$625$	−25.8091	−	16.5865i	−1.03237	−	0.663461i
$626$	−12.2523	+	12.3089i	−0.489700	+	0.491961i
$627$	10.7544	+	9.31878i	0.429491	+	0.372156i
$628$	−1.30922	+	0.194398i	−0.0522436	+	0.00775734i
$629$	−14.9014	+	17.1971i	−0.594156	+	0.685693i
$630$	−1.53842	−	4.09583i	−0.0612923	−	0.163182i
$631$	13.1838	−	3.87113i	0.524841	−	0.154107i	−0.00857040	−	0.999963i	$-0.502728\pi$
$631$	13.1838	−	3.87113i	0.524841	−	0.154107i	0.533411	+	0.845856i	$0.320910\pi$
$632$	5.47515	+	7.20955i	0.217790	+	0.286780i
$633$			0.469658i			0.0186672i
$634$	7.47939	+	13.6228i	0.297044	+	0.541029i
$635$	36.5169	+	23.4680i	1.44913	+	0.931299i
$636$	4.38211	−	5.10456i	0.173762	−	0.202409i
$637$	−6.96635	+	3.18142i	−0.276017	+	0.126053i
$638$	15.4726	−	41.7773i	0.612565	−	1.65398i
$639$	1.13730	+	3.87329i	0.0449910	+	0.153225i
$640$	−1.79586	+	32.4571i	−0.0709878	+	1.28298i
$641$		−	5.39690i		−	0.213165i	−0.994304	−	0.106582i	$-0.966009\pi$
$641$		−	5.39690i		−	0.213165i	0.994304	−	0.106582i	$-0.0339908\pi$
$642$	−13.5581	+	7.44386i	−0.535094	+	0.293786i
$643$	23.2908	−	3.34871i	0.918500	−	0.132060i	0.333181	−	0.942863i	$-0.391878\pi$
$643$	23.2908	−	3.34871i	0.918500	−	0.132060i	0.585320	+	0.810803i	$0.300969\pi$
$644$	8.46937	+	2.44450i	0.333740	+	0.0963268i
$645$	6.37172	−	21.7001i	0.250886	−	0.854440i
$646$	11.0027	−	20.2608i	0.432896	−	0.797150i
$647$	−40.8866	+	26.2762i	−1.60742	+	1.03303i	−0.644001	+	0.765025i	$0.722727\pi$
$647$	−40.8866	+	26.2762i	−1.60742	+	1.03303i	−0.963419	+	0.268001i	$0.913637\pi$
$648$	0.221270	+	2.81976i	0.00869232	+	0.110771i
$649$	19.7924	−	2.84571i	0.776918	−	0.111704i
$650$	4.25875	−	4.27841i	0.167042	−	0.167813i
$651$	0.640333	+	1.40213i	0.0250966	+	0.0549539i
$652$	15.6105	−	34.6033i	0.611356	−	1.35517i
$653$	−31.4049	−	27.2125i	−1.22897	−	1.06491i	−0.995713	−	0.0924913i	$-0.970517\pi$
$653$	−31.4049	−	27.2125i	−1.22897	−	1.06491i	−0.233255	−	0.972416i	$-0.574938\pi$
$654$	0.861645	+	11.6695i	0.0336930	+	0.456314i
$655$	−10.4625	−	22.9098i	−0.408805	−	0.895158i
$656$	0.223442	+	24.2475i	0.00872393	+	0.946707i
$657$	11.5598	+	3.39427i	0.450991	+	0.132423i
$658$	1.73620	+	0.120156i	0.0676842	+	0.00468418i
$659$	−23.0758	−	3.31779i	−0.898904	−	0.129243i	−0.322655	−	0.946517i	$-0.604575\pi$
$659$	−23.0758	−	3.31779i	−0.898904	−	0.129243i	−0.576249	+	0.817274i	$0.695484\pi$
$660$	3.14318	−	22.6000i	0.122348	−	0.879705i
$661$	−20.8165	−	9.50658i	−0.809668	−	0.369763i	−0.0328280	−	0.999461i	$-0.510451\pi$
$661$	−20.8165	−	9.50658i	−0.809668	−	0.369763i	−0.776840	+	0.629698i	$0.783179\pi$
$662$	18.1418	+	33.0430i	0.705101	+	1.28425i
$663$	−5.42586	−	2.47791i	−0.210723	−	0.0962340i
$664$	−7.50841	−	7.40533i	−0.291383	−	0.287383i
$665$	−1.57788	+	10.9744i	−0.0611877	+	0.425570i
$666$	−4.22629	+	5.67286i	−0.163765	+	0.219819i
$667$	17.5572	+	27.3196i	0.679818	+	1.05782i
$668$	−9.92766	+	0.0457408i	−0.384113	+	0.00176977i
$669$		−	8.80537i		−	0.340435i
$670$	−33.2585	+	0.302038i	−1.28489	+	0.0116687i
$671$			22.1715i			0.855923i
$672$	−4.83376	+	3.70615i	−0.186466	+	0.142968i
$673$	1.00807	+	1.56859i	0.0388583	+	0.0604646i	0.860139	−	0.510059i	$-0.170377\pi$
$673$	1.00807	+	1.56859i	0.0388583	+	0.0604646i	−0.821281	+	0.570524i	$0.806740\pi$
$674$	−34.4610	−	25.6735i	−1.32739	−	0.988908i
$675$	0.463290	−	3.22225i	0.0178320	−	0.124025i
$676$	12.2849	+	18.9234i	0.472495	+	0.727822i
$677$	28.0665	+	12.8175i	1.07868	+	0.492618i	0.873858	−	0.486181i	$-0.161610\pi$
$677$	28.0665	+	12.8175i	1.07868	+	0.492618i	0.204825	+	0.978799i	$0.434338\pi$
$678$	12.0328	−	6.60645i	0.462118	−	0.253719i
$679$	12.7570	+	5.82592i	0.489568	+	0.223578i
$680$	−36.8555	+	2.89210i	−1.41334	+	0.110907i
$681$	−17.9901	−	2.58659i	−0.689383	−	0.0991183i
$682$	−0.555010	+	8.01964i	−0.0212524	+	0.307088i
$683$	−33.3637	−	9.79648i	−1.27663	−	0.374852i	−0.427969	−	0.903793i	$-0.640771\pi$
$683$	−33.3637	−	9.79648i	−1.27663	−	0.374852i	−0.848658	+	0.528941i	$0.822589\pi$
$684$	2.94743	−	6.53347i	0.112698	−	0.249813i
$685$	3.13385	+	6.86217i	0.119738	+	0.262190i
$686$	−19.5001	+	1.43983i	−0.744516	+	0.0549730i
$687$	−5.22140	−	4.52437i	−0.199209	−	0.172615i
$688$	−31.4842	+	0.290127i	−1.20032	+	0.0110610i
$689$	1.83227	+	4.01210i	0.0698037	+	0.152849i
$690$	11.7882	+	11.7340i	0.448769	+	0.446706i
$691$	43.3061	−	6.22648i	1.64744	−	0.236867i	0.744810	−	0.667277i	$-0.232540\pi$
$691$	43.3061	−	6.22648i	1.64744	−	0.236867i	0.902633	+	0.430410i	$0.141631\pi$
$692$	−30.7110	−	4.27125i	−1.16746	−	0.162369i
$693$	3.59678	−	2.31151i	0.136630	−	0.0878070i
$694$	−26.2996	−	14.2821i	−0.998318	−	0.542141i
$695$	17.9614	−	61.1710i	0.681316	−	2.32035i
$696$	−22.3928	−	1.44609i	−0.848796	−	0.0548138i
$697$	−27.2963	+	3.92462i	−1.03392	+	0.148656i
$698$	−11.0019	−	20.0386i	−0.416429	−	0.758473i
$699$		−	10.0106i		−	0.378634i
$700$	6.36349	−	2.94162i	0.240517	−	0.111183i
$701$	12.0454	+	41.0228i	0.454947	+	1.54941i	0.793566	+	0.608485i	$0.208222\pi$
$701$	12.0454	+	41.0228i	0.454947	+	1.54941i	−0.338618	+	0.940924i	$0.609959\pi$
$702$	−1.73894	−	0.644032i	−0.0656321	−	0.0243074i
$703$	16.3065	−	7.44694i	0.615012	−	0.280867i
$704$	−31.3770	+	4.95491i	−1.18257	+	0.186745i
$705$	2.76250	+	1.77535i	0.104042	+	0.0668636i
$706$	−23.6752	+	12.9985i	−0.891028	+	0.489206i
$707$		−	7.37596i		−	0.277402i
$708$	−4.22608	−	9.14212i	−0.158826	−	0.343582i
$709$	22.6565	−	6.65254i	0.850882	−	0.249841i	0.172917	−	0.984936i	$-0.444681\pi$
$709$	22.6565	−	6.65254i	0.850882	−	0.249841i	0.677964	+	0.735095i	$0.262862\pi$
$710$	−15.3555	+	5.76764i	−0.576282	+	0.216456i
$711$	−2.09600	+	2.41891i	−0.0786061	+	0.0907163i
$712$	−6.97229	−	18.3060i	−0.261298	−	0.686048i
$713$	−4.42859	−	3.83739i	−0.165852	−	0.143711i
$714$	−4.90948	−	4.88692i	−0.183733	−	0.182888i
$715$	12.5848	+	8.08779i	0.470646	+	0.302466i
$716$	−25.1021	−	38.6667i	−0.938109	−	1.44504i
$717$	0.630200	−	0.405005i	0.0235352	−	0.0151252i
$718$	−26.7634	−	35.5805i	−0.998800	−	1.32785i
$719$	−36.3884	+	31.5307i	−1.35706	+	1.17590i	−0.390157	+	0.920748i	$0.627579\pi$
$719$	−36.3884	+	31.5307i	−1.35706	+	1.17590i	−0.966902	+	0.255150i	$0.917875\pi$
$720$	−11.3603	+	1.74036i	−0.423375	+	0.0648595i
$721$	15.0272	+	2.16058i	0.559642	+	0.0804643i
$722$	6.95810	−	5.23382i	0.258954	−	0.194783i
$723$	−15.0516	−	17.3705i	−0.559776	−	0.646016i
$724$	10.2837	−	1.52697i	0.382191	−	0.0567493i
$725$	24.7806	+	7.27623i	0.920327	+	0.270232i
$726$	6.72282	−	0.496394i	0.249507	−	0.0184229i
$727$	−5.53354	−	3.55619i	−0.205227	−	0.131892i	0.433990	−	0.900918i	$-0.357105\pi$
$727$	−5.53354	−	3.55619i	−0.205227	−	0.131892i	−0.639218	+	0.769026i	$0.720742\pi$
$728$	−0.875807	−	3.89618i	−0.0324595	−	0.144402i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−10.2958	+	47.8596i	−0.381065	+	1.77136i
$731$	−5.09592	−	35.4429i	−0.188479	−	1.31090i
$732$	10.7005	−	3.19558i	0.395503	−	0.118112i
$733$	−21.3782	+	18.5243i	−0.789620	+	0.684210i	−0.953207	−	0.302319i	$-0.902239\pi$
$733$	−21.3782	+	18.5243i	−0.789620	+	0.684210i	0.163586	+	0.986529i	$0.447694\pi$
$734$	−9.57681	−	9.53279i	−0.353486	−	0.351862i
$735$	−15.2648	−	6.97122i	−0.563052	−	0.257137i
$736$	10.8625	−	20.4496i	0.400395	−	0.753783i
$737$	−7.12385	−	31.7115i	−0.262410	−	1.16811i
$738$	−8.37302	+	1.84165i	−0.308215	+	0.0677921i
$739$	16.8468	−	36.8893i	0.619719	−	1.35700i	−0.296004	−	0.955187i	$-0.595654\pi$
$739$	16.8468	−	36.8893i	0.619719	−	1.35700i	0.915723	−	0.401809i	$-0.131619\pi$
$740$	−24.2528	−	15.4289i	−0.891549	−	0.567177i
$741$	3.07730	+	3.55140i	0.113048	+	0.130464i
$742$	0.377182	+	5.10829i	0.0138468	+	0.187531i
$743$	−39.5851	+	5.69148i	−1.45224	+	0.208800i	−0.822835	−	0.568280i	$-0.807609\pi$
$743$	−39.5851	+	5.69148i	−1.45224	+	0.208800i	−0.629402	+	0.777080i	$0.716700\pi$
$744$	3.95046	−	0.888008i	0.144831	−	0.0325560i
$745$	18.4147	+	62.7146i	0.674661	+	2.29769i
$746$	−6.64564	+	30.8920i	−0.243314	+	1.13104i
$747$	2.01579	−	3.13663i	0.0737540	−	0.114763i
$748$	−10.3375	−	34.6155i	−0.377977	−	1.26567i
$749$	3.31779	−	11.2993i	0.121229	−	0.412869i
$750$	−7.07204	−	0.489430i	−0.258234	−	0.0178715i
$751$	21.9270	−	18.9998i	0.800126	−	0.693313i	−0.155519	−	0.987833i	$-0.549705\pi$
$751$	21.9270	−	18.9998i	0.800126	−	0.693313i	0.955645	+	0.294519i	$0.0951596\pi$
$752$	1.24749	−	4.39808i	0.0454913	−	0.160382i
$753$	−2.03365	+	14.1444i	−0.0741105	+	0.515450i
$754$	7.02081	−	12.9284i	0.255683	−	0.470824i
$755$	20.9124	+	24.1342i	0.761079	+	0.878332i
$756$	−1.63399	−	1.40273i	−0.0594277	−	0.0510169i
$757$	9.59512	+	14.9303i	0.348741	+	0.542651i	0.970668	−	0.240424i	$-0.0772865\pi$
$757$	9.59512	+	14.9303i	0.348741	+	0.542651i	−0.621927	+	0.783075i	$0.713650\pi$
$758$	37.9890	−	14.2689i	1.37982	−	0.518271i
$759$	−8.78738	+	13.6734i	−0.318962	+	0.496314i
$760$	27.3576	+	9.98902i	0.992363	+	0.362340i
$761$	−28.0391	+	32.3589i	−1.01642	+	1.17301i	−0.0315844	+	0.999501i	$0.510055\pi$
$761$	−28.0391	+	32.3589i	−1.01642	+	1.17301i	−0.984833	+	0.173507i	$0.944490\pi$
$762$	21.3145	+	1.47510i	0.772144	+	0.0534373i
$763$	−6.73306	−	5.83423i	−0.243753	−	0.211213i
$764$	−1.96283	−	3.02351i	−0.0710128	−	0.109387i
$765$	−3.68237	−	12.5410i	−0.133136	−	0.453421i
$766$	2.57565	+	11.7101i	0.0930618	+	0.423103i
$767$	6.60317			0.238427
$768$	6.91372	+	14.4292i	0.249477	+	0.520667i
$769$	−8.45739	+	13.1600i	−0.304981	+	0.474560i	−0.959588	−	0.281410i	$-0.909198\pi$
$769$	−8.45739	+	13.1600i	−0.304981	+	0.474560i	0.654606	+	0.755970i	$0.272834\pi$
$770$	10.4432	+	13.8836i	0.376345	+	0.500332i
$771$	9.65809	+	21.1483i	0.347828	+	0.761636i
$772$	−41.0860	−	5.71418i	−1.47872	−	0.205658i
$773$	21.0526	−	6.18161i	0.757210	−	0.222337i	0.119733	−	0.992806i	$-0.461796\pi$
$773$	21.0526	−	6.18161i	0.757210	−	0.222337i	0.637477	+	0.770469i	$0.279978\pi$
$774$	−2.39129	−	10.8719i	−0.0859531	−	0.390784i
$775$	−4.66026			−0.167401
$776$	21.8726	−	29.6432i	0.785181	−	1.06413i
$777$	−0.766518	−	5.33125i	−0.0274987	−	0.191258i
$778$	−39.2799	−	21.3311i	−1.40825	−	0.764758i
$779$	20.8453	+	6.12072i	0.746859	+	0.219298i
$780$	2.08951	−	7.23944i	0.0748164	−	0.259213i
$781$	−8.66598	−	13.4845i	−0.310093	−	0.482514i
$782$	24.6947	+	9.14592i	0.883082	+	0.327057i
$783$	−1.12906	−	7.85278i	−0.0403493	−	0.280635i
$784$	−3.11159	+	23.1543i	−0.111128	+	0.826938i
$785$	1.72963	−	0.789895i	0.0617331	−	0.0281926i
$786$	−9.94104	−	7.40610i	−0.354585	−	0.264167i
$787$	−3.50553	+	4.04560i	−0.124959	+	0.144210i	−0.814781	−	0.579768i	$-0.803143\pi$
$787$	−3.50553	+	4.04560i	−0.124959	+	0.144210i	0.689823	+	0.723978i	$0.257688\pi$
$788$	−24.8584	+	7.42367i	−0.885545	+	0.264457i
$789$	6.32813	−	2.88996i	0.225287	−	0.102885i
$790$	−10.4293	−	7.76988i	−0.371059	−	0.276440i
$791$	−2.94455	+	10.0282i	−0.104696	+	0.356562i
$792$	−3.99743	−	10.4954i	−0.142043	−	0.372939i
$793$	−1.04198	+	7.24710i	−0.0370016	+	0.257352i
$794$	−10.0712	+	27.1930i	−0.357412	+	0.965044i
$795$	−4.01491	+	8.79142i	−0.142394	+	0.311799i
$796$	26.8875	+	30.7424i	0.953001	+	1.08964i
$797$	1.47049	−	3.21993i	0.0520875	−	0.114056i	−0.881799	−	0.471626i	$-0.843667\pi$
$797$	1.47049	−	3.21993i	0.0520875	−	0.114056i	0.933886	+	0.357570i	$0.116395\pi$
$798$	1.91888	+	5.10873i	0.0679274	+	0.180847i
$799$	5.14618	+	0.739908i	0.182059	+	0.0261761i
$800$	−4.12145	−	17.9481i	−0.145715	−	0.634562i
$801$	5.82628	−	3.74432i	0.205861	−	0.132299i
$802$	7.91322	−	36.7843i	0.279426	−	1.29890i
$803$	−47.8387			−1.68819
$804$	−14.2780	+	8.00871i	−0.503545	+	0.282446i
$805$	−12.6638			−0.446342
$806$	−0.558305	+	2.59526i	−0.0196654	+	0.0914140i
$807$	14.1076	−	9.06643i	0.496613	−	0.319154i
$808$	−18.9605	−	3.98757i	−0.667027	−	0.140282i
$809$	−49.6434	−	7.13765i	−1.74537	−	0.250946i	−0.805529	−	0.592557i	$-0.798119\pi$
$809$	−49.6434	−	7.13765i	−1.74537	−	0.250946i	−0.939842	+	0.341610i	$0.889028\pi$
$810$	−1.42876	−	3.80387i	−0.0502015	−	0.133654i
$811$	14.4653	−	31.6745i	0.507944	−	1.11224i	−0.465862	−	0.884858i	$-0.654256\pi$
$811$	14.4653	−	31.6745i	0.507944	−	1.11224i	0.973805	−	0.227384i	$-0.0730172\pi$
$812$	12.8602	−	11.2476i	0.451306	−	0.394714i
$813$	−6.35907	+	13.9244i	−0.223022	+	0.488350i
$814$	9.75555	−	26.3408i	0.341932	−	0.923245i
$815$	−7.76127	+	53.9808i	−0.271866	+	1.89087i
$816$	−15.2163	+	9.97826i	−0.532678	+	0.349309i
$817$	−7.94745	+	27.0665i	−0.278046	+	0.946937i
$818$	−4.90461	−	3.65394i	−0.171486	−	0.127757i
$819$	1.28429	−	0.586517i	0.0448768	−	0.0204946i
$820$	−9.96825	−	33.3791i	−0.348106	−	1.16565i
$821$	2.14864	−	2.47967i	0.0749882	−	0.0865410i	−0.717016	−	0.697057i	$-0.754492\pi$
$821$	2.14864	−	2.47967i	0.0749882	−	0.0865410i	0.792004	+	0.610516i	$0.209038\pi$
$822$	2.97764	+	2.21835i	0.103857	+	0.0773739i
$823$	13.1199	−	5.99167i	0.457332	−	0.208856i	−0.173409	−	0.984850i	$-0.555478\pi$
$823$	13.1199	−	5.99167i	0.457332	−	0.208856i	0.630741	+	0.775994i	$0.282751\pi$
$824$	13.6779	−	37.4605i	0.476492	−	1.30500i
$825$	1.83960	+	12.7947i	0.0640466	+	0.445454i
$826$	7.19102	+	2.66326i	0.250207	+	0.0926665i
$827$	−16.3273	−	25.4058i	−0.567757	−	0.883448i	0.432074	−	0.901838i	$-0.357782\pi$
$827$	−16.3273	−	25.4058i	−0.567757	−	0.883448i	−0.999831	+	0.0183908i	$0.994146\pi$
$828$	7.86565	+	2.27025i	0.273350	+	0.0788967i
$829$	30.7709	+	9.03515i	1.06872	+	0.313804i	0.768357	−	0.640022i	$-0.221075\pi$
$829$	30.7709	+	9.03515i	1.06872	+	0.313804i	0.300361	+	0.953826i	$0.402893\pi$
$830$	13.3138	+	7.23011i	0.462128	+	0.250961i
$831$	−1.72658	−	12.0086i	−0.0598945	−	0.416575i
$832$	−10.4889	+	0.144988i	−0.363637	+	0.00502657i
$833$	−26.5692			−0.920569
$834$	−6.74088	−	30.6472i	−0.233417	−	1.06123i
$835$	13.6846	−	4.01816i	0.473575	−	0.139054i
$836$	−3.92049	+	28.1890i	−0.135593	+	0.974937i
$837$	0.594688	+	1.30219i	0.0205554	+	0.0450101i
$838$	−32.3528	−	43.0114i	−1.11761	−	1.48581i
$839$	−9.12908	+	14.2051i	−0.315171	+	0.490415i	−0.962309	−	0.271957i	$-0.912329\pi$
$839$	−9.12908	+	14.2051i	−0.315171	+	0.490415i	0.647139	+	0.762372i	$0.275965\pi$
$840$	5.19541	−	7.04117i	0.179259	−	0.242943i
$841$	33.9409			1.17038
$842$	3.14434	+	14.2957i	0.108361	+	0.492661i
$843$	1.19518	+	4.07041i	0.0411642	+	0.140192i
$844$	−0.787855	+	0.511468i	−0.0271191	+	0.0176054i
$845$	−24.4952	−	21.2252i	−0.842660	−	0.730169i
$846$	1.61244	+	0.111591i	0.0554369	+	0.00383658i
$847$	−3.36111	+	3.87892i	−0.115489	+	0.133281i
$848$	13.3351	+	1.79205i	0.457931	+	0.0615391i
$849$	−13.2567	+	20.6278i	−0.454968	+	0.707943i
$850$	19.6056	−	7.36402i	0.672468	−	0.252584i
$851$	11.0699	+	17.2251i	0.379472	+	0.590470i
$852$	−5.25893	+	6.12593i	−0.180168	+	0.209871i
$853$	−29.7899	−	34.3794i	−1.01999	−	1.17713i	−0.984071	−	0.177774i	$-0.943110\pi$
$853$	−29.7899	−	34.3794i	−1.01999	−	1.17713i	−0.0359163	−	0.999355i	$-0.511435\pi$
$854$	−4.05771	+	7.47201i	−0.138852	+	0.255687i
$855$	−1.46541	+	10.1921i	−0.0501159	+	0.348564i
$856$	−27.2522	−	14.6372i	−0.931460	−	0.500290i
$857$	19.8407	−	17.1920i	0.677744	−	0.587269i	−0.246467	−	0.969151i	$-0.579270\pi$
$857$	19.8407	−	17.1920i	0.677744	−	0.587269i	0.924211	+	0.381883i	$0.124724\pi$
$858$	7.34564	+	0.508365i	0.250776	+	0.0173553i
$859$	−15.3300	+	52.2093i	−0.523054	+	1.78136i	0.0952875	+	0.995450i	$0.469623\pi$
$859$	−15.3300	+	52.2093i	−0.523054	+	1.78136i	−0.618342	+	0.785909i	$0.712195\pi$
$860$	43.3410	−	12.9433i	1.47792	−	0.441362i
$861$	3.52900	−	5.49123i	0.120268	−	0.187140i
$862$	−9.32827	+	43.3621i	−0.317722	+	1.47692i
$863$	11.5415	+	39.3068i	0.392878	+	1.33802i	0.884227	+	0.467057i	$0.154686\pi$
$863$	11.5415	+	39.3068i	0.392878	+	1.33802i	−0.491349	+	0.870963i	$0.663496\pi$
$864$	−4.48920	+	3.44196i	−0.152726	+	0.117098i
$865$	44.0910	−	6.33933i	1.49914	−	0.215544i
$866$	3.01302	+	40.8062i	0.102387	+	1.38665i
$867$	−2.41900	−	2.79167i	−0.0821535	−	0.0948102i
$868$	−1.65475	+	2.60112i	−0.0561659	+	0.0882876i
$869$	5.27952	−	11.5605i	0.179096	−	0.392165i
$870$	31.4841	−	6.92495i	1.06741	−	0.234778i
$871$	−0.838220	−	10.7002i	−0.0284020	−	0.362561i
$872$	−18.6373	+	14.1538i	−0.631140	+	0.479307i
$873$	11.8476	+	5.41063i	0.400982	+	0.183122i
$874$	−14.7034	−	14.6358i	−0.497350	−	0.495064i
$875$	4.07907	−	3.53454i	0.137898	−	0.119489i
$876$	6.89498	+	23.0881i	0.232960	+	0.780074i
$877$	−4.38473	−	30.4965i	−0.148062	−	1.02979i	−0.919388	−	0.393353i	$-0.871315\pi$
$877$	−4.38473	−	30.4965i	−0.148062	−	1.02979i	0.771326	−	0.636441i	$-0.219594\pi$
$878$	−5.64527	+	26.2418i	−0.190519	+	0.885617i
$879$	10.5823	−	3.10726i	0.356934	−	0.104805i
$880$	41.3347	−	19.3392i	1.39339	−	0.651925i
$881$	39.1034	+	25.1302i	1.31743	+	0.846659i	0.994994	−	0.0999335i	$-0.0318630\pi$
$881$	39.1034	+	25.1302i	1.31743	+	0.846659i	0.322433	+	0.946592i	$0.395499\pi$
$882$	−8.23743	+	0.608230i	−0.277369	+	0.0204802i
$883$	36.3998	+	10.6880i	1.22495	+	0.359678i	0.829343	−	0.558740i	$-0.188715\pi$
$883$	36.3998	+	10.6880i	1.22495	+	0.359678i	0.395610	+	0.918419i	$0.370533\pi$
$884$	−1.75217	−	11.8004i	−0.0589320	−	0.396891i
$885$	9.47520	+	10.9350i	0.318505	+	0.367575i
$886$	−37.4420	+	28.1635i	−1.25789	+	0.946173i
$887$	6.52768	+	0.938538i	0.219178	+	0.0315130i	0.251029	−	0.967980i	$-0.419231\pi$
$887$	6.52768	+	0.938538i	0.219178	+	0.0315130i	−0.0318510	+	0.999493i	$0.510140\pi$
$888$	−14.1188	−	0.911767i	−0.473795	−	0.0305969i
$889$	−12.2940	+	10.6528i	−0.412327	+	0.357283i
$890$	16.9165	+	22.4896i	0.567041	+	0.753852i
$891$	3.34039	−	2.14674i	0.111907	−	0.0719184i
$892$	14.7711	−	9.58925i	0.494572	−	0.321072i
$893$	−3.44566	−	2.21439i	−0.115305	−	0.0741019i
$894$	22.8011	+	22.6963i	0.762584	+	0.759078i
$895$	50.0518	+	43.3702i	1.67305	+	1.44970i
$896$	−11.4812	−	4.07259i	−0.383559	−	0.136056i
$897$	−3.51488	+	4.05639i	−0.117359	+	0.135439i
$898$	6.92580	−	2.60138i	0.231117	−	0.0868091i
$899$	−10.8972	+	3.19971i	−0.363442	+	0.106716i
$900$	5.90989	−	2.73193i	0.196996	−	0.0910644i
$901$			15.3019i			0.509781i
$902$	29.8400	−	16.3832i	0.993564	−	0.545502i
$903$	7.13008	+	4.58222i	0.237274	+	0.152487i
$904$	24.1864	+	12.9906i	0.804427	+	0.432061i
$905$	−13.5859	+	6.20449i	−0.451612	+	0.206244i
$906$	14.7397	+	5.45898i	0.489694	+	0.181362i
$907$	5.04266	+	17.1737i	0.167439	+	0.570244i	0.999870	+	0.0161160i	$0.00513011\pi$
$907$	5.04266	+	17.1737i	0.167439	+	0.570244i	−0.832431	+	0.554128i	$0.813052\pi$
$908$	−15.2526	−	32.9954i	−0.506176	−	1.09499i
$909$		−	6.85019i		−	0.227206i
$910$	2.76103	+	5.02886i	0.0915271	+	0.166705i
$911$	−37.6151	+	5.40823i	−1.24624	+	0.179183i	−0.733697	−	0.679477i	$-0.762207\pi$
$911$	−37.6151	+	5.40823i	−1.24624	+	0.179183i	−0.512547	+	0.858659i	$0.671298\pi$
$912$	14.1698	−	2.17075i	0.469207	−	0.0718808i
$913$	−4.17104	+	14.2053i	−0.138041	+	0.470125i
$914$	−4.06191	−	2.20584i	−0.134356	−	0.0729627i
$915$	−13.4965	+	8.67368i	−0.446181	+	0.286743i
$916$	1.90344	−	13.6861i	0.0628915	−	0.452200i
$917$	9.34242	−	1.34324i	0.308514	−	0.0443576i
$918$	−4.55952	−	4.53856i	−0.150487	−	0.149795i
$919$	−21.4234	−	46.9108i	−0.706694	−	1.54744i	−0.831662	−	0.555283i	$-0.812610\pi$
$919$	−21.4234	−	46.9108i	−0.706694	−	1.54744i	0.124968	−	0.992161i	$-0.460117\pi$
$920$	−6.84627	+	32.5534i	−0.225715	+	1.07325i
$921$	−5.64018	−	4.88724i	−0.185850	−	0.161040i
$922$	31.3728	−	2.31648i	1.03321	−	0.0762892i
$923$	−2.19889	−	4.81489i	−0.0723772	−	0.158484i
$924$	7.79454	+	3.51634i	0.256422	+	0.115679i
$925$	15.6243	+	4.58771i	0.513724	+	0.150843i
$926$	0.425661	−	6.15061i	0.0139881	−	0.202122i
$927$	13.9560	+	2.00657i	0.458375	+	0.0659044i
$928$	−21.9604	−	39.1389i	−0.720886	−	1.28480i
$929$	11.7043	+	5.34516i	0.384004	+	0.175369i	0.598058	−	0.801453i	$-0.295939\pi$
$929$	11.7043	+	5.34516i	0.384004	+	0.175369i	−0.214053	+	0.976822i	$0.568667\pi$
$930$	−5.09893	+	2.79949i	−0.167200	+	0.0917990i
$931$	19.0398	+	8.69520i	0.624005	+	0.284974i
$932$	16.7928	−	10.9017i	0.550066	−	0.357098i
$933$	−1.23349	+	8.57911i	−0.0403826	+	0.280867i
$934$	−11.8732	−	8.84553i	−0.388502	−	0.289435i
$935$	28.0588	+	43.6604i	0.917621	+	1.42785i
$936$	−0.813377	−	3.61845i	−0.0265860	−	0.118273i
$937$		−	44.5623i		−	1.45579i	−0.685690	−	0.727894i	$-0.740499\pi$
$937$		−	44.5623i		−	1.45579i	0.685690	−	0.727894i	$-0.259501\pi$
$938$	3.40286	−	11.9908i	0.111107	−	0.391514i
$939$		−	12.2806i		−	0.400762i
$940$	0.0302592	+	6.56751i	0.000986947	+	0.214209i
$941$	−15.0351	−	23.3950i	−0.490130	−	0.762657i	0.504799	−	0.863237i	$-0.331567\pi$
$941$	−15.0351	−	23.3950i	−0.490130	−	0.762657i	−0.994929	+	0.100580i	$0.967930\pi$
$942$	0.559142	−	0.750524i	0.0182178	−	0.0244534i
$943$	−3.53148	+	24.5620i	−0.115001	+	0.799847i
$944$	10.7337	−	17.0453i	0.349352	−	0.554776i
$945$	2.81417	+	1.28519i	0.0915451	+	0.0418072i
$946$	21.2728	+	38.7457i	0.691638	+	1.25973i
$947$	−47.6602	−	21.7657i	−1.54875	−	0.707290i	−0.556418	−	0.830902i	$-0.687825\pi$
$947$	−47.6602	−	21.7657i	−1.54875	−	0.707290i	−0.992331	+	0.123613i	$0.960552\pi$
$948$	−6.34033	−	0.881806i	−0.205925	−	0.0286397i
$949$	−15.6368	−	2.24823i	−0.507591	−	0.0729806i
$950$	−16.4596	−	1.13911i	−0.534021	−	0.0369576i
$951$	−10.5440	−	3.09599i	−0.341912	−	0.100394i
$952$	2.85130	−	13.5577i	0.0924112	−	0.439406i
$953$	−8.26439	−	18.0965i	−0.267710	−	0.586203i	0.727262	−	0.686360i	$-0.240793\pi$
$953$	−8.26439	−	18.0965i	−0.267710	−	0.586203i	−0.994972	+	0.100158i	$0.968065\pi$
$954$	0.350295	+	4.74415i	0.0113412	+	0.153598i
$955$	3.91375	+	3.39129i	0.126646	+	0.109739i
$956$	1.36570	+	0.616106i	0.0441699	+	0.0199263i
$957$	13.0864	+	28.6551i	0.423022	+	0.926289i
$958$	−17.1341	+	17.2132i	−0.553577	+	0.556133i
$959$	−2.79834	+	0.402340i	−0.0903631	+	0.0129922i
$960$	−15.2911	−	17.1618i	−0.493519	−	0.553894i
$961$	−24.3548	+	15.6519i	−0.785640	+	0.504900i
$962$	4.42666	−	8.15142i	0.142721	−	0.262812i
$963$	3.08129	−	10.4939i	0.0992931	−	0.338161i
$964$	12.7476	−	44.1661i	0.410572	−	1.42249i
$965$	58.9860	−	8.48091i	1.89883	−	0.273010i
$966$	−5.46386	+	2.99985i	−0.175797	+	0.0965187i
$967$		−	4.40554i		−	0.141673i	−0.997488	−	0.0708364i	$-0.977433\pi$
$967$		−	4.40554i		−	0.141673i	0.997488	−	0.0708364i	$-0.0225668\pi$
$968$	8.15400	+	10.7370i	0.262079	+	0.345100i
$969$	4.59302	+	15.6424i	0.147549	+	0.502506i
$970$	−18.3806	+	49.6293i	−0.590167	+	1.59350i
$971$	20.9267	−	9.55691i	0.671570	−	0.306696i	−0.0502901	−	0.998735i	$-0.516015\pi$
$971$	20.9267	−	9.55691i	0.671570	−	0.306696i	0.721860	+	0.692039i	$0.243287\pi$
$972$	−1.51752	−	1.30274i	−0.0486744	−	0.0417855i
$973$	20.0992	+	12.9170i	0.644351	+	0.414099i
$974$	4.82117	+	8.78116i	0.154480	+	0.281366i
$975$			4.26859i			0.136704i
$976$	17.0137	+	14.4701i	0.544596	+	0.463178i
$977$	8.33007	−	2.44593i	0.266502	−	0.0782522i	−0.145751	−	0.989321i	$-0.546560\pi$
$977$	8.33007	−	2.44593i	0.266502	−	0.0782522i	0.412254	+	0.911069i	$0.364742\pi$
$978$	9.43854	+	25.1287i	0.301811	+	0.803529i
$979$	−18.0088	+	20.7832i	−0.575562	+	0.664234i
$980$	−4.92947	−	33.1987i	−0.157466	−	1.06049i
$981$	−6.25311	−	5.41835i	−0.199646	−	0.172995i
$982$	−19.4511	+	19.5409i	−0.620709	+	0.623576i
$983$	23.9608	+	15.3987i	0.764231	+	0.491141i	0.863766	−	0.503893i	$-0.168099\pi$
$983$	23.9608	+	15.3987i	0.764231	+	0.491141i	−0.0995354	+	0.995034i	$0.531736\pi$
$984$	−12.2078	−	12.0402i	−0.389170	−	0.383828i
$985$	31.3538	−	20.1499i	0.999015	−	0.642028i
$986$	40.7883	−	30.6806i	1.29896	−	0.977070i
$987$	−0.930038	+	0.805883i	−0.0296034	+	0.0256515i
$988$	−2.60624	+	9.02975i	−0.0829157	+	0.287275i
$989$	−31.8924	−	4.58544i	−1.01412	−	0.145809i
$990$	9.69874	+	12.8940i	0.308246	+	0.409798i
$991$	−29.9565	−	34.5717i	−0.951601	−	1.09821i	−0.995072	−	0.0991509i	$-0.968387\pi$
$991$	−29.9565	−	34.5717i	−0.951601	−	1.09821i	0.0434719	−	0.999055i	$-0.486158\pi$
$992$	5.79178	+	5.65987i	0.183889	+	0.179701i
$993$	−25.5752	−	7.50955i	−0.811604	−	0.238308i
$994$	−0.452653	−	6.13041i	−0.0143573	−	0.194445i
$995$	−49.3592	−	31.7212i	−1.56479	−	1.00563i
$996$	7.45697	−	0.0343573i	0.236283	−	0.00108865i
$997$	16.0350	−	4.70829i	0.507833	−	0.149113i	−0.0177719	−	0.999842i	$-0.505657\pi$
$997$	16.0350	−	4.70829i	0.507833	−	0.149113i	0.525605	+	0.850729i	$0.323839\pi$
$998$	9.64069	+	2.07396i	0.305171	+	0.0656499i
$999$	−0.711879	−	4.95123i	−0.0225228	−	0.156650i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.u.a.43.2	✓	340
4.3	odd	2		804.2.u.b.43.7	yes	340
67.53	odd	22		804.2.u.b.187.7	yes	340
268.187	even	22	inner	804.2.u.a.187.2	yes	340

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.u.a.43.2	✓	340	1.1	even	1	trivial
804.2.u.a.187.2	yes	340	268.187	even	22	inner
804.2.u.b.43.7	yes	340	4.3	odd	2
804.2.u.b.187.7	yes	340	67.53	odd	22

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38258 - 0.297428i) q^{2} +(0.841254 - 0.540641i) q^{3} +(1.82307 + 0.822439i) q^{4} +(-2.84397 - 0.408902i) q^{5} +(-1.32390 + 0.497268i) q^{6} +(0.447300 - 0.979450i) q^{7} +(-2.27593 - 1.67932i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-1.38258 - 0.297428i) q^{2} +(0.841254 - 0.540641i) q^{3} +(1.82307 + 0.822439i) q^{4} +(-2.84397 - 0.408902i) q^{5} +(-1.32390 + 0.497268i) q^{6} +(0.447300 - 0.979450i) q^{7} +(-2.27593 - 1.67932i) q^{8} +(0.415415 - 0.909632i) q^{9} +(3.81041 + 1.41122i) q^{10} +(-0.565094 + 3.93031i) q^{11} +(1.97831 - 0.293748i) q^{12} +(-0.369419 + 1.25812i) q^{13} +(-0.909745 + 1.22113i) q^{14} +(-2.61357 + 1.19358i) q^{15} +(2.64719 + 2.99873i) q^{16} +(-2.97900 + 3.43795i) q^{17} +(-0.844896 + 1.13409i) q^{18} +(3.25991 - 1.48875i) q^{19} +(-4.84847 - 3.08445i) q^{20} +(-0.153238 - 1.06579i) q^{21} +(1.95028 - 5.26591i) q^{22} +(2.21304 + 3.44355i) q^{23} +(-2.82255 - 0.182275i) q^{24} +(3.12352 + 0.917149i) q^{25} +(0.884954 - 1.62959i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(1.62100 - 1.41773i) q^{28} +7.93353 q^{29} +(3.96849 - 0.872871i) q^{30} +(-1.37356 + 0.403315i) q^{31} +(-2.76805 - 4.93335i) q^{32} +(1.64950 + 3.61190i) q^{33} +(5.14126 - 3.86721i) q^{34} +(-1.67261 + 2.60263i) q^{35} +(1.50545 - 1.31667i) q^{36} +5.00214 q^{37} +(-4.94989 + 1.08873i) q^{38} +(0.369419 + 1.25812i) q^{39} +(5.78602 + 5.70659i) q^{40} +(4.58146 + 3.96986i) q^{41} +(-0.105133 + 1.51913i) q^{42} +(-5.15466 + 5.94879i) q^{43} +(-4.26265 + 6.70049i) q^{44} +(-1.55338 + 2.41711i) q^{45} +(-2.03550 - 5.41922i) q^{46} +(-0.617896 - 0.961465i) q^{47} +(3.84819 + 1.09152i) q^{48} +(3.82478 + 4.41403i) q^{49} +(-4.04574 - 2.19706i) q^{50} +(-0.647398 + 4.50275i) q^{51} +(-1.70821 + 1.98983i) q^{52} +(2.54216 - 2.20279i) q^{53} +(-0.0976390 + 1.41084i) q^{54} +(3.21422 - 10.9466i) q^{55} +(-2.66284 + 1.47800i) q^{56} +(1.93753 - 3.01486i) q^{57} +(-10.9688 - 2.35966i) q^{58} +(-1.41876 - 4.83184i) q^{59} +(-5.74638 + 0.0264759i) q^{60} +(5.52691 - 0.794650i) q^{61} +(2.01902 - 0.149079i) q^{62} +(-0.705124 - 0.813756i) q^{63} +(2.35974 + 7.64406i) q^{64} +(1.56507 - 3.42702i) q^{65} +(-1.20629 - 5.48436i) q^{66} +(-7.64970 + 2.91240i) q^{67} +(-8.25843 + 3.81758i) q^{68} +(3.72345 + 1.70044i) q^{69} +(3.08661 - 3.10087i) q^{70} +(-3.05082 + 2.64355i) q^{71} +(-2.47302 + 1.37264i) q^{72} +(1.71458 + 11.9252i) q^{73} +(-6.91588 - 1.48778i) q^{74} +(3.12352 - 0.917149i) q^{75} +(7.16746 - 0.0330234i) q^{76} +(3.59678 + 2.31151i) q^{77} +(-0.136550 - 1.84934i) q^{78} +(-3.07103 - 0.901736i) q^{79} +(-6.30235 - 9.61076i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-5.15350 - 6.85131i) q^{82} +(3.69057 + 0.530624i) q^{83} +(0.597187 - 2.06905i) q^{84} +(9.87798 - 8.55932i) q^{85} +(8.89608 - 6.69156i) q^{86} +(6.67411 - 4.28919i) q^{87} +(7.88639 - 7.99615i) q^{88} +(5.82628 + 3.74432i) q^{89} +(2.86659 - 2.87983i) q^{90} +(1.06703 + 0.924586i) q^{91} +(1.20242 + 8.09794i) q^{92} +(-0.937467 + 1.08189i) q^{93} +(0.568326 + 1.51308i) q^{94} +(-9.87985 + 2.90098i) q^{95} +(-4.99580 - 2.65368i) q^{96} +13.0246i q^{97} +(-3.97522 - 7.24036i) q^{98} +(3.34039 + 2.14674i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 340 q - 34 q^{3} - 2 q^{4} + 11 q^{6} - 4 q^{7} + 39 q^{8} - 34 q^{9}+O(q^{10}) \) 340 * q - 34 * q^3 - 2 * q^4 + 11 * q^6 - 4 * q^7 + 39 * q^8 - 34 * q^9	\( 340 q - 34 q^{3} - 2 q^{4} + 11 q^{6} - 4 q^{7} + 39 q^{8} - 34 q^{9} - 27 q^{10} + 9 q^{12} + 4 q^{14} - 2 q^{16} + 12 q^{20} - 4 q^{21} - 3 q^{22} + 6 q^{24} + 34 q^{25} - 10 q^{26} - 34 q^{27} - 25 q^{28} + 16 q^{29} + 6 q^{30} + 4 q^{31} - 55 q^{32} + 9 q^{36} - 12 q^{37} - 26 q^{38} - 37 q^{40} + 4 q^{42} + 4 q^{43} + 51 q^{44} + 81 q^{46} - 2 q^{48} - 46 q^{49} - 15 q^{50} - 32 q^{52} - 14 q^{56} + 66 q^{57} - 92 q^{58} - 43 q^{60} + 2 q^{62} + 18 q^{63} + 7 q^{64} + 8 q^{66} + 18 q^{67} - 208 q^{68} - 56 q^{70} + 6 q^{72} + 54 q^{73} - 22 q^{74} + 34 q^{75} + 120 q^{76} + 8 q^{77} - 10 q^{78} - 10 q^{79} + 68 q^{80} - 34 q^{81} + 84 q^{82} + 8 q^{84} + 104 q^{86} + 16 q^{87} + 138 q^{88} - 27 q^{90} - 42 q^{92} + 4 q^{93} - 32 q^{94} + 40 q^{95} + 7 q^{98}+O(q^{100}) \) 340 * q - 34 * q^3 - 2 * q^4 + 11 * q^6 - 4 * q^7 + 39 * q^8 - 34 * q^9 - 27 * q^10 + 9 * q^12 + 4 * q^14 - 2 * q^16 + 12 * q^20 - 4 * q^21 - 3 * q^22 + 6 * q^24 + 34 * q^25 - 10 * q^26 - 34 * q^27 - 25 * q^28 + 16 * q^29 + 6 * q^30 + 4 * q^31 - 55 * q^32 + 9 * q^36 - 12 * q^37 - 26 * q^38 - 37 * q^40 + 4 * q^42 + 4 * q^43 + 51 * q^44 + 81 * q^46 - 2 * q^48 - 46 * q^49 - 15 * q^50 - 32 * q^52 - 14 * q^56 + 66 * q^57 - 92 * q^58 - 43 * q^60 + 2 * q^62 + 18 * q^63 + 7 * q^64 + 8 * q^66 + 18 * q^67 - 208 * q^68 - 56 * q^70 + 6 * q^72 + 54 * q^73 - 22 * q^74 + 34 * q^75 + 120 * q^76 + 8 * q^77 - 10 * q^78 - 10 * q^79 + 68 * q^80 - 34 * q^81 + 84 * q^82 + 8 * q^84 + 104 * q^86 + 16 * q^87 + 138 * q^88 - 27 * q^90 - 42 * q^92 + 4 * q^93 - 32 * q^94 + 40 * q^95 + 7 * q^98

Introduction

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