LMFDB - Embedded newform 288.2.bf.a.275.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			275.9
Character	$\chi$	$=$	288.275
Dual form			288.2.bf.a.155.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17575 - 0.785882i) q^{2} +(-1.01508 - 1.40343i) q^{3} +(0.764778 + 1.84800i) q^{4} +(2.85653 + 0.376069i) q^{5} +(0.0905582 + 2.44782i) q^{6} +(-0.838984 + 3.13113i) q^{7} +(0.553125 - 2.77382i) q^{8} +(-0.939208 + 2.84919i) q^{9} +O(q^{10})$	\(q+(-1.17575 - 0.785882i) q^{2} +(-1.01508 - 1.40343i) q^{3} +(0.764778 + 1.84800i) q^{4} +(2.85653 + 0.376069i) q^{5} +(0.0905582 + 2.44782i) q^{6} +(-0.838984 + 3.13113i) q^{7} +(0.553125 - 2.77382i) q^{8} +(-0.939208 + 2.84919i) q^{9} +(-3.06302 - 2.68706i) q^{10} +(-3.69421 + 4.81439i) q^{11} +(1.81722 - 2.94919i) q^{12} +(-3.49913 + 2.68498i) q^{13} +(3.44714 - 3.02209i) q^{14} +(-2.37183 - 4.39067i) q^{15} +(-2.83023 + 2.82662i) q^{16} +4.67934 q^{17} +(3.34340 - 2.61183i) q^{18} +(-1.17593 + 2.83895i) q^{19} +(1.48963 + 5.56649i) q^{20} +(5.24595 - 2.00091i) q^{21} +(8.12702 - 2.75731i) q^{22} +(3.57188 - 0.957081i) q^{23} +(-4.45431 + 2.03939i) q^{24} +(3.18871 + 0.854412i) q^{25} +(6.22418 - 0.406959i) q^{26} +(4.95200 - 1.57406i) q^{27} +(-6.42797 + 0.844175i) q^{28} +(-0.568252 - 4.31631i) q^{29} +(-0.661866 + 7.02631i) q^{30} +(-3.52849 - 2.03717i) q^{31} +(5.54904 - 1.09918i) q^{32} +(10.5066 + 0.297540i) q^{33} +(-5.50174 - 3.67741i) q^{34} +(-3.57410 + 8.62865i) q^{35} +(-5.98360 + 0.443340i) q^{36} +(1.98078 - 0.820466i) q^{37} +(3.61369 - 2.41376i) q^{38} +(7.32008 + 2.18529i) q^{39} +(2.62316 - 7.71547i) q^{40} +(0.0956623 + 0.357017i) q^{41} +(-7.74041 - 1.77013i) q^{42} +(0.627411 + 0.481429i) q^{43} +(-11.7223 - 3.14498i) q^{44} +(-3.75437 + 7.78559i) q^{45} +(-4.95179 - 1.68179i) q^{46} +(2.98300 - 1.72224i) q^{47} +(6.83988 + 1.10276i) q^{48} +(-3.03790 - 1.75394i) q^{49} +(-3.07766 - 3.51052i) q^{50} +(-4.74992 - 6.56711i) q^{51} +(-7.63791 - 4.41300i) q^{52} +(-6.59478 + 2.73165i) q^{53} +(-7.05935 - 2.04099i) q^{54} +(-12.3632 + 12.3632i) q^{55} +(8.22112 + 4.05909i) q^{56} +(5.17793 - 1.23144i) q^{57} +(-2.72399 + 5.52148i) q^{58} +(0.174758 - 1.32742i) q^{59} +(6.30005 - 7.74104i) q^{60} +(-2.52080 + 0.331870i) q^{61} +(2.54764 + 5.16818i) q^{62} +(-8.13321 - 5.33121i) q^{63} +(-7.38811 - 3.06853i) q^{64} +(-11.0051 + 6.35381i) q^{65} +(-12.1193 - 8.60677i) q^{66} +(8.04333 - 6.17187i) q^{67} +(3.57866 + 8.64743i) q^{68} +(-4.96895 - 4.04134i) q^{69} +(10.9834 - 7.33632i) q^{70} +(5.75858 - 5.75858i) q^{71} +(7.38363 + 4.18115i) q^{72} +(11.3191 + 11.3191i) q^{73} +(-2.97369 - 0.591997i) q^{74} +(-2.03770 - 5.34241i) q^{75} +(-6.14572 - 0.00195846i) q^{76} +(-11.9751 - 15.6063i) q^{77} +(-6.88921 - 8.32208i) q^{78} +(7.01043 + 12.1424i) q^{79} +(-9.14764 + 7.00997i) q^{80} +(-7.23578 - 5.35196i) q^{81} +(0.168098 - 0.494942i) q^{82} +(-2.31862 - 17.6117i) q^{83} +(7.70967 + 8.16428i) q^{84} +(13.3667 + 1.75976i) q^{85} +(-0.359332 - 1.05911i) q^{86} +(-5.48079 + 5.17891i) q^{87} +(11.3109 + 12.9100i) q^{88} +(2.22386 + 2.22386i) q^{89} +(10.5328 - 6.20342i) q^{90} +(-5.47130 - 13.2089i) q^{91} +(4.50038 + 5.86888i) q^{92} +(0.722690 + 7.01987i) q^{93} +(-4.86074 - 0.319367i) q^{94} +(-4.42673 + 7.66732i) q^{95} +(-7.17535 - 6.67190i) q^{96} +(0.970710 + 1.68132i) q^{97} +(2.19343 + 4.44963i) q^{98} +(-10.2475 - 15.0472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.17575	−	0.785882i	−0.831381	−	0.555703i
$2$	−1.17575	−	0.785882i	−0.831381	−	0.555703i
$3$	−1.01508	−	1.40343i	−0.586059	−	0.810268i
$3$	−1.01508	−	1.40343i	−0.586059	−	0.810268i
$4$	0.764778	+	1.84800i	0.382389	+	0.924001i
$5$	2.85653	+	0.376069i	1.27748	+	0.168183i	0.738568	−	0.674179i	$-0.235502\pi$
$5$	2.85653	+	0.376069i	1.27748	+	0.168183i	0.538911	+	0.842362i	$0.318836\pi$
$6$	0.0905582	+	2.44782i	0.0369702	+	0.999316i
$7$	−0.838984	+	3.13113i	−0.317106	+	1.18346i	0.604907	+	0.796296i	$0.293210\pi$
$7$	−0.838984	+	3.13113i	−0.317106	+	1.18346i	−0.922013	+	0.387160i	$0.873456\pi$
$8$	0.553125	−	2.77382i	0.195559	−	0.980692i
$9$	−0.939208	+	2.84919i	−0.313069	+	0.949730i
$10$	−3.06302	−	2.68706i	−0.968612	−	0.849723i
$11$	−3.69421	+	4.81439i	−1.11385	+	1.45159i	−0.236568	+	0.971615i	$0.576023\pi$
$11$	−3.69421	+	4.81439i	−1.11385	+	1.45159i	−0.877280	+	0.479980i	$0.840644\pi$
$12$	1.81722	−	2.94919i	0.524586	−	0.851357i
$13$	−3.49913	+	2.68498i	−0.970485	+	0.744679i	−0.966858	−	0.255314i	$-0.917821\pi$
$13$	−3.49913	+	2.68498i	−0.970485	+	0.744679i	−0.00362678	+	0.999993i	$0.501154\pi$
$14$	3.44714	−	3.02209i	0.921286	−	0.807686i
$15$	−2.37183	−	4.39067i	−0.612405	−	1.13367i
$16$	−2.83023	+	2.82662i	−0.707557	+	0.706656i
$17$	4.67934			1.13491			0.567453	−	0.823406i	$-0.307929\pi$
$17$	4.67934			1.13491			0.567453	+	0.823406i	$0.307929\pi$
$18$	3.34340	−	2.61183i	0.788048	−	0.615614i
$19$	−1.17593	+	2.83895i	−0.269778	+	0.651301i	−0.999473	−	0.0324721i	$-0.989662\pi$
$19$	−1.17593	+	2.83895i	−0.269778	+	0.651301i	0.729695	+	0.683773i	$0.239662\pi$
$20$	1.48963	+	5.56649i	0.333092	+	1.24470i
$21$	5.24595	−	2.00091i	1.14476	−	0.436634i
$22$	8.12702	−	2.75731i	1.73269	−	0.587860i
$23$	3.57188	−	0.957081i	0.744788	−	0.199565i	0.133583	−	0.991038i	$-0.457352\pi$
$23$	3.57188	−	0.957081i	0.744788	−	0.199565i	0.611205	+	0.791472i	$0.290685\pi$
$24$	−4.45431	+	2.03939i	−0.909233	+	0.416288i
$25$	3.18871	+	0.854412i	0.637742	+	0.170882i
$26$	6.22418	−	0.406959i	1.22066	−	0.0798112i
$27$	4.95200	−	1.57406i	0.953013	−	0.302928i
$28$	−6.42797	+	0.844175i	−1.21477	+	0.159534i
$29$	−0.568252	−	4.31631i	−0.105522	−	0.801518i	−0.959599	−	0.281371i	$-0.909211\pi$
$29$	−0.568252	−	4.31631i	−0.105522	−	0.801518i	0.854077	−	0.520146i	$-0.174123\pi$
$30$	−0.661866	+	7.02631i	−0.120840	+	1.28282i
$31$	−3.52849	−	2.03717i	−0.633735	−	0.365887i	0.148462	−	0.988918i	$-0.452568\pi$
$31$	−3.52849	−	2.03717i	−0.633735	−	0.365887i	−0.782197	+	0.623031i	$0.785901\pi$
$32$	5.54904	−	1.09918i	0.980940	−	0.194309i
$33$	10.5066	+	0.297540i	1.82896	+	0.0517951i
$34$	−5.50174	−	3.67741i	−0.943540	−	0.630671i
$35$	−3.57410	+	8.62865i	−0.604134	+	1.45851i
$36$	−5.98360	+	0.443340i	−0.997266	+	0.0738899i
$37$	1.98078	−	0.820466i	0.325638	−	0.134884i	−0.213875	−	0.976861i	$-0.568608\pi$
$37$	1.98078	−	0.820466i	0.325638	−	0.134884i	0.539513	+	0.841977i	$0.318608\pi$
$38$	3.61369	−	2.41376i	0.586217	−	0.391563i
$39$	7.32008	+	2.18529i	1.17215	+	0.349927i
$40$	2.62316	−	7.71547i	0.414759	−	1.21992i
$41$	0.0956623	+	0.357017i	0.0149399	+	0.0557566i	0.972993	−	0.230833i	$-0.0741451\pi$
$41$	0.0956623	+	0.357017i	0.0149399	+	0.0557566i	−0.958053	+	0.286590i	$0.907478\pi$
$42$	−7.74041	−	1.77013i	−1.19437	−	0.273137i
$43$	0.627411	+	0.481429i	0.0956793	+	0.0734173i	0.655493	−	0.755201i	$-0.272461\pi$
$43$	0.627411	+	0.481429i	0.0956793	+	0.0734173i	−0.559814	+	0.828618i	$0.689127\pi$
$44$	−11.7223	−	3.14498i	−1.76720	−	0.474123i
$45$	−3.75437	+	7.78559i	−0.559668	+	1.16061i
$46$	−4.95179	−	1.68179i	−0.730101	−	0.247966i
$47$	2.98300	−	1.72224i	0.435115	−	0.251214i	−0.266408	−	0.963860i	$-0.585837\pi$
$47$	2.98300	−	1.72224i	0.435115	−	0.251214i	0.701523	+	0.712646i	$0.252504\pi$
$48$	6.83988	+	1.10276i	0.987251	+	0.159169i
$49$	−3.03790	−	1.75394i	−0.433986	−	0.250562i
$50$	−3.07766	−	3.51052i	−0.435246	−	0.496463i
$51$	−4.74992	−	6.56711i	−0.665122	−	0.919579i
$52$	−7.63791	−	4.41300i	−1.05919	−	0.611972i
$53$	−6.59478	+	2.73165i	−0.905863	+	0.375221i	−0.786471	−	0.617627i	$-0.788094\pi$
$53$	−6.59478	+	2.73165i	−0.905863	+	0.375221i	−0.119391	+	0.992847i	$0.538094\pi$
$54$	−7.05935	−	2.04099i	−0.960655	−	0.277743i
$55$	−12.3632	+	12.3632i	−1.66705	+	1.66705i
$56$	8.22112	+	4.05909i	1.09859	+	0.542419i
$57$	5.17793	−	1.23144i	0.685834	−	0.163108i
$58$	−2.72399	+	5.52148i	−0.357677	+	0.725006i
$59$	0.174758	−	1.32742i	0.0227515	−	0.172815i	−0.976297	−	0.216437i	$-0.930556\pi$
$59$	0.174758	−	1.32742i	0.0227515	−	0.172815i	0.999048	+	0.0436220i	$0.0138897\pi$
$60$	6.30005	−	7.74104i	0.813332	−	0.999364i
$61$	−2.52080	+	0.331870i	−0.322756	+	0.0424916i	−0.290163	−	0.956977i	$-0.593710\pi$
$61$	−2.52080	+	0.331870i	−0.322756	+	0.0424916i	−0.0325924	+	0.999469i	$0.510376\pi$
$62$	2.54764	+	5.16818i	0.323551	+	0.656359i
$63$	−8.13321	−	5.33121i	−1.02469	−	0.671669i
$64$	−7.38811	−	3.06853i	−0.923513	−	0.383566i
$65$	−11.0051	+	6.35381i	−1.36502	+	0.788093i
$66$	−12.1193	−	8.60677i	−1.49178	−	1.05942i
$67$	8.04333	−	6.17187i	0.982650	−	0.754014i	0.0133538	−	0.999911i	$-0.495749\pi$
$67$	8.04333	−	6.17187i	0.982650	−	0.754014i	0.969296	+	0.245897i	$0.0790825\pi$
$68$	3.57866	+	8.64743i	0.433976	+	1.04866i
$69$	−4.96895	−	4.04134i	−0.598191	−	0.486521i
$70$	10.9834	−	7.33632i	1.31276	−	0.876857i
$71$	5.75858	−	5.75858i	0.683418	−	0.683418i	−0.277351	−	0.960769i	$-0.589456\pi$
$71$	5.75858	−	5.75858i	0.683418	−	0.683418i	0.960769	+	0.277351i	$0.0894564\pi$
$72$	7.38363	+	4.18115i	0.870169	+	0.492753i
$73$	11.3191	+	11.3191i	1.32480	+	1.32480i	0.909843	+	0.414952i	$0.136202\pi$
$73$	11.3191	+	11.3191i	1.32480	+	1.32480i	0.414952	+	0.909843i	$0.363798\pi$
$74$	−2.97369	−	0.591997i	−0.345685	−	0.0688183i
$75$	−2.03770	−	5.34241i	−0.235294	−	0.616889i
$76$	−6.14572	−	0.00195846i	−0.704963	−	0.000224651i
$77$	−11.9751	−	15.6063i	−1.36469	−	1.77850i
$78$	−6.88921	−	8.32208i	−0.780049	−	0.942290i
$79$	7.01043	+	12.1424i	0.788735	+	1.36613i	0.926742	+	0.375697i	$0.122597\pi$
$79$	7.01043	+	12.1424i	0.788735	+	1.36613i	−0.138008	+	0.990431i	$0.544070\pi$
$80$	−9.14764	+	7.00997i	−1.02274	+	0.783739i
$81$	−7.23578	−	5.35196i	−0.803975	−	0.594663i
$82$	0.168098	−	0.494942i	0.0185633	−	0.0546572i
$83$	−2.31862	−	17.6117i	−0.254502	−	1.93313i	−0.347957	−	0.937510i	$-0.613125\pi$
$83$	−2.31862	−	17.6117i	−0.254502	−	1.93313i	0.0934556	−	0.995623i	$-0.470209\pi$
$84$	7.70967	+	8.16428i	0.841194	+	0.890796i
$85$	13.3667	+	1.75976i	1.44982	+	0.190872i
$86$	−0.359332	−	1.05911i	−0.0387478	−	0.114207i
$87$	−5.48079	+	5.17891i	−0.587602	+	0.555238i
$88$	11.3109	+	12.9100i	1.20574	+	1.37621i
$89$	2.22386	+	2.22386i	0.235728	+	0.235728i	0.815079	−	0.579350i	$-0.196694\pi$
$89$	2.22386	+	2.22386i	0.235728	+	0.235728i	−0.579350	+	0.815079i	$0.696694\pi$
$90$	10.5328	−	6.20342i	1.11025	−	0.653898i
$91$	−5.47130	−	13.2089i	−0.573548	−	1.38467i
$92$	4.50038	+	5.86888i	0.469197	+	0.611873i
$93$	0.722690	+	7.01987i	0.0749395	+	0.727926i
$94$	−4.86074	−	0.319367i	−0.501347	−	0.0329402i
$95$	−4.42673	+	7.66732i	−0.454173	+	0.786651i
$96$	−7.17535	−	6.67190i	−0.732331	−	0.680948i
$97$	0.970710	+	1.68132i	0.0985606	+	0.170712i	0.911089	−	0.412210i	$-0.135243\pi$
$97$	0.970710	+	1.68132i	0.0985606	+	0.170712i	−0.812528	+	0.582922i	$0.801909\pi$
$98$	2.19343	+	4.44963i	0.221570	+	0.449480i
$99$	−10.2475	−	15.0472i	−1.02991	−	1.51230i
$100$	0.859698	+	6.54618i	0.0859698	+	0.654618i
$101$	−7.65091	+	9.97086i	−0.761294	+	0.992138i	0.238485	+	0.971146i	$0.423349\pi$
$101$	−7.65091	+	9.97086i	−0.761294	+	0.992138i	−0.999780	+	0.0209918i	$0.993318\pi$
$102$	0.423753	+	11.4542i	0.0419578	+	1.13413i
$103$	−3.04623	+	0.816235i	−0.300154	+	0.0804261i	−0.405753	−	0.913983i	$-0.632991\pi$
$103$	−3.04623	+	0.816235i	−0.300154	+	0.0804261i	0.105599	+	0.994409i	$0.466324\pi$
$104$	5.51218	+	11.1911i	0.540514	+	1.09738i
$105$	15.7377	−	3.74282i	1.53584	−	0.365262i
$106$	9.90057	+	1.97099i	0.961628	+	0.191439i
$107$	−1.96372	−	4.74085i	−0.189840	−	0.458315i	0.800088	−	0.599882i	$-0.204786\pi$
$107$	−1.96372	−	4.74085i	−0.189840	−	0.458315i	−0.989929	+	0.141567i	$0.954786\pi$
$108$	6.69605	+	7.94751i	0.644328	+	0.764749i
$109$	6.27216	+	2.59801i	0.600764	+	0.248845i	0.662274	−	0.749262i	$-0.269592\pi$
$109$	6.27216	+	2.59801i	0.600764	+	0.248845i	−0.0615097	+	0.998106i	$0.519592\pi$
$110$	24.2520	−	4.82001i	2.31234	−	0.459570i
$111$	−3.16212	−	1.94704i	−0.300135	−	0.184805i
$112$	−6.47601	−	11.2333i	−0.611926	−	1.06145i
$113$	0.221857	−	0.384268i	0.0208706	−	0.0361489i	−0.855401	−	0.517966i	$-0.826690\pi$
$113$	0.221857	−	0.384268i	0.0208706	−	0.0361489i	0.876272	+	0.481817i	$0.160023\pi$
$114$	−7.05572	−	2.62138i	−0.660829	−	0.245514i
$115$	10.5631	−	1.39066i	0.985014	−	0.129680i
$116$	7.54196	−	4.35115i	0.700253	−	0.403994i
$117$	−4.36361	−	12.4915i	−0.403415	−	1.15484i
$118$	−1.24867	+	1.42337i	−0.114949	+	0.131032i
$119$	−3.92589	+	14.6516i	−0.359886	+	1.34311i
$120$	−13.4908	+	4.15044i	−1.23154	+	0.378882i
$121$	−6.68416	−	24.9456i	−0.607651	−	2.26778i
$122$	3.22465	+	1.59086i	0.291946	+	0.144030i
$123$	0.403941	−	0.496657i	0.0364221	−	0.0447821i
$124$	1.06619	−	8.07864i	0.0957468	−	0.725483i
$125$	−4.52199	−	1.87307i	−0.404459	−	0.167532i
$126$	5.37292	+	12.6599i	0.478658	+	1.12783i
$127$		−	0.759969i		−	0.0674364i	−0.999431	−	0.0337182i	$-0.989265\pi$
$127$		−	0.759969i		−	0.0674364i	0.999431	−	0.0337182i	$-0.0107349\pi$
$128$	6.27506	+	9.41401i	0.554643	+	0.832089i
$129$	0.0387754	−	1.36922i	0.00341398	−	0.120553i
$130$	17.9326	+	1.17824i	1.57279	+	0.103338i
$131$	3.83035	+	4.99180i	0.334659	+	0.436136i	0.930124	−	0.367245i	$-0.119699\pi$
$131$	3.83035	+	4.99180i	0.334659	+	0.436136i	−0.595465	+	0.803381i	$0.703032\pi$
$132$	7.48535	+	19.6438i	0.651516	+	1.70977i
$133$	−7.90254	−	6.06383i	−0.685237	−	0.525801i
$134$	−14.3073	+	0.935462i	−1.23596	+	0.0808116i
$135$	14.7375	−	2.63405i	1.26840	−	0.226703i
$136$	2.58826	−	12.9796i	0.221941	−	1.11299i
$137$	13.8441	+	3.70952i	1.18278	+	0.316926i	0.796030	−	0.605257i	$-0.206930\pi$
$137$	13.8441	+	3.70952i	1.18278	+	0.316926i	0.386754	+	0.922183i	$0.373596\pi$
$138$	2.66622	+	8.65662i	0.226964	+	0.736900i
$139$	−1.77167	+	13.4571i	−0.150271	+	1.14142i	0.735576	+	0.677442i	$0.236912\pi$
$139$	−1.77167	+	13.4571i	−0.150271	+	1.14142i	−0.885847	+	0.463978i	$0.846422\pi$
$140$	−18.6792	−	0.00595250i	−1.57868	−	0.000503078i
$141$	−5.44503	−	2.43820i	−0.458554	−	0.205334i
$142$	−11.2962	+	2.24509i	−0.947958	+	0.188404i
$143$		−	26.7651i		−	2.23821i
$144$	−5.39542	−	10.7187i	−0.449618	−	0.893221i
$145$		−	12.5434i		−	1.04167i
$146$	−4.41294	−	22.2038i	−0.365217	−	1.83760i
$147$	0.622212	+	6.04387i	0.0513191	+	0.498490i
$148$	3.03108	+	3.03301i	0.249153	+	0.249312i
$149$	−1.08494	+	8.24090i	−0.0888814	+	0.675121i	0.887770	+	0.460288i	$0.152254\pi$
$149$	−1.08494	+	8.24090i	−0.0888814	+	0.675121i	−0.976651	+	0.214833i	$0.931079\pi$
$150$	−1.80268	+	7.88274i	−0.147188	+	0.643623i
$151$	0.395426	+	0.105954i	0.0321793	+	0.00862241i	0.274873	−	0.961481i	$-0.411364\pi$
$151$	0.395426	+	0.105954i	0.0321793	+	0.00862241i	−0.242693	+	0.970103i	$0.578031\pi$
$152$	7.22430	+	4.83212i	0.585968	+	0.391936i
$153$	−4.39487	+	13.3323i	−0.355304	+	1.07786i
$154$	1.81505	+	27.7601i	0.146261	+	2.23697i
$155$	−9.31311	−	7.14620i	−0.748047	−	0.573996i
$156$	1.55981	+	15.1988i	0.124885	+	1.21688i
$157$	8.63965	+	11.2594i	0.689519	+	0.898599i	0.998625	−	0.0524290i	$-0.0166963\pi$
$157$	8.63965	+	11.2594i	0.689519	+	0.898599i	−0.309106	+	0.951028i	$0.600030\pi$
$158$	1.30000	−	19.7858i	0.103422	−	1.57408i
$159$	10.5279	+	6.48243i	0.834918	+	0.514090i
$160$	16.2644	−	1.05301i	1.28581	−	0.0832477i
$161$			11.9870i			0.944707i
$162$	4.30145	+	11.9790i	0.337954	+	0.941163i
$163$	7.16640	+	2.96842i	0.561316	+	0.232505i	0.645256	−	0.763966i	$-0.276751\pi$
$163$	7.16640	+	2.96842i	0.561316	+	0.232505i	−0.0839407	+	0.996471i	$0.526751\pi$
$164$	−0.586608	+	0.449823i	−0.0458064	+	0.0351253i
$165$	29.9005	+	4.80114i	2.32775	+	0.373768i
$166$	−11.1146	+	22.5291i	−0.862660	+	1.74860i
$167$	3.88696	+	14.5063i	0.300782	+	1.12253i	0.936516	+	0.350625i	$0.114031\pi$
$167$	3.88696	+	14.5063i	0.300782	+	1.12253i	−0.635734	+	0.771908i	$0.719302\pi$
$168$	−2.64849	−	15.6580i	−0.204335	−	1.20804i
$169$	1.67017	−	6.23316i	0.128475	−	0.479474i
$170$	−14.3329	−	12.5737i	−1.09928	−	0.964356i
$171$	−6.98427	−	6.01682i	−0.534101	−	0.460118i
$172$	−0.409853	+	1.52764i	−0.0312510	+	0.116482i
$173$	−11.4938	+	1.51319i	−0.873861	+	0.115046i	−0.554098	−	0.832451i	$-0.686937\pi$
$173$	−11.4938	+	1.51319i	−0.873861	+	0.115046i	−0.319763	+	0.947497i	$0.603603\pi$
$174$	10.5141	−	1.78185i	0.797069	−	0.135082i
$175$	−5.35055	+	9.26742i	−0.404463	+	0.700551i
$176$	−3.15301	−	24.0680i	−0.237667	−	1.81419i
$177$	−2.04033	+	1.10218i	−0.153360	+	0.0828451i
$178$	−0.867011	−	4.36239i	−0.0649852	−	0.326975i
$179$	19.6993	+	8.15971i	1.47239	+	0.609886i	0.967404	−	0.253239i	$-0.0814960\pi$
$179$	19.6993	+	8.15971i	1.47239	+	0.609886i	0.504990	+	0.863125i	$0.331496\pi$
$180$	−17.2591	−	0.983835i	−1.28641	−	0.0733307i
$181$	−0.746186	−	1.80145i	−0.0554636	−	0.133901i	0.893719	−	0.448628i	$-0.148087\pi$
$181$	−0.746186	−	1.80145i	−0.0554636	−	0.133901i	−0.949182	+	0.314727i	$0.898087\pi$
$182$	−3.94775	+	19.8302i	−0.292627	+	1.46991i
$183$	3.02458	+	3.20088i	0.223584	+	0.236616i
$184$	−0.679074	−	10.4371i	−0.0500620	−	0.769434i
$185$	5.96671	−	1.59878i	0.438681	−	0.117544i
$186$	4.66709	−	8.82156i	0.342207	−	0.646828i
$187$	−17.2865	+	22.5282i	−1.26411	+	1.64742i
$188$	5.46403	+	4.19546i	0.398505	+	0.305986i
$189$	0.773937	+	16.8260i	0.0562957	+	1.22391i
$190$	11.2303	−	5.53597i	0.814735	−	0.401621i
$191$	−6.06876	−	10.5114i	−0.439120	−	0.760578i	0.558502	−	0.829503i	$-0.311376\pi$
$191$	−6.06876	−	10.5114i	−0.439120	−	0.760578i	−0.997622	+	0.0689251i	$0.978043\pi$
$192$	3.19309	+	13.4835i	0.230442	+	0.973086i
$193$	1.87855	−	3.25374i	0.135221	−	0.234210i	−0.790461	−	0.612512i	$-0.790159\pi$
$193$	1.87855	−	3.25374i	0.135221	−	0.234210i	0.925682	+	0.378303i	$0.123492\pi$
$194$	0.180006	−	2.73967i	0.0129237	−	0.196697i
$195$	20.0882	+	8.99522i	1.43855	+	0.644161i
$196$	0.917954	−	6.95543i	0.0655682	−	0.496816i
$197$	−8.91962	−	21.5339i	−0.635497	−	1.53422i	−0.832619	−	0.553846i	$-0.813160\pi$
$197$	−8.91962	−	21.5339i	−0.635497	−	1.53422i	0.197122	−	0.980379i	$-0.436840\pi$
$198$	0.223134	+	25.7451i	0.0158575	+	1.82963i
$199$	−13.5124	−	13.5124i	−0.957872	−	0.957872i	0.0412759	−	0.999148i	$-0.486858\pi$
$199$	−13.5124	−	13.5124i	−0.957872	−	0.957872i	−0.999148	+	0.0412759i	$0.986858\pi$
$200$	4.13373	−	8.37229i	0.292299	−	0.592010i
$201$	−16.8264	−	5.02326i	−1.18684	−	0.354313i
$202$	16.8315	−	5.71053i	1.18426	−	0.401791i
$203$	13.9917	+	1.84204i	0.982023	+	0.129286i
$204$	8.50339	−	13.8003i	0.595357	−	0.966211i
$205$	0.138999	+	1.05580i	0.00970814	+	0.0737406i
$206$	4.22307	+	1.43429i	0.294235	+	0.0999318i
$207$	−0.627827	+	11.0759i	−0.0436370	+	0.769825i
$208$	2.31392	−	17.4898i	0.160442	−	1.21270i
$209$	−9.32369	−	16.1491i	−0.644933	−	1.11706i
$210$	−21.4450	−	7.96735i	−1.47985	−	0.549800i
$211$	−2.02558	−	2.63979i	−0.139447	−	0.181730i	0.718409	−	0.695621i	$-0.244871\pi$
$211$	−2.02558	−	2.63979i	−0.139447	−	0.181730i	−0.857856	+	0.513890i	$0.828204\pi$
$212$	−10.0916	−	10.0981i	−0.693096	−	0.693538i
$213$	−13.9272	−	2.23630i	−0.954275	−	0.153229i
$214$	−1.41690	+	7.11731i	−0.0968573	+	0.486529i
$215$	1.61117	+	1.61117i	0.109881	+	0.109881i
$216$	−1.62708	−	14.6066i	−0.110709	−	0.993853i
$217$	9.33899	−	9.33899i	0.633972	−	0.633972i
$218$	−5.33276	−	7.98380i	−0.361180	−	0.540731i
$219$	4.39566	−	27.3753i	0.297031	−	1.84985i
$220$	−32.3023	−	13.3921i	−2.17782	−	0.902896i
$221$	−16.3736	+	12.5639i	−1.10141	+	0.845142i
$222$	2.18773	+	4.77429i	0.146831	+	0.320429i
$223$	8.66983	−	5.00553i	0.580574	−	0.335195i	−0.180787	−	0.983522i	$-0.557865\pi$
$223$	8.66983	−	5.00553i	0.580574	−	0.335195i	0.761362	+	0.648327i	$0.224531\pi$
$224$	−1.21389	+	18.2969i	−0.0811061	+	1.22252i
$225$	−5.42924	+	8.28277i	−0.361949	+	0.552184i
$226$	−0.562839	+	0.277450i	−0.0374395	+	0.0184557i
$227$	14.9664	−	1.97036i	0.993352	−	0.130777i	0.383710	−	0.923454i	$-0.374646\pi$
$227$	14.9664	−	1.97036i	0.993352	−	0.130777i	0.609642	+	0.792677i	$0.291313\pi$
$228$	6.23568	+	8.62705i	0.412968	+	0.571340i
$229$	2.27583	−	17.2867i	0.150391	−	1.14234i	−0.735193	−	0.677857i	$-0.762909\pi$
$229$	2.27583	−	17.2867i	0.150391	−	1.14234i	0.885585	−	0.464478i	$-0.153758\pi$
$230$	−13.5125	−	6.66629i	−0.890985	−	0.439562i
$231$	−9.74649	+	32.6479i	−0.641272	+	2.14807i
$232$	−12.2870	−	0.811228i	−0.806678	−	0.0532597i
$233$	15.6723	−	15.6723i	1.02673	−	1.02673i	0.0270935	−	0.999633i	$-0.491375\pi$
$233$	15.6723	−	15.6723i	1.02673	−	1.02673i	0.999633	−	0.0270935i	$-0.00862519\pi$
$234$	−4.68630	+	18.1161i	−0.306353	+	1.18429i
$235$	9.16871	−	3.79780i	0.598101	−	0.247741i
$236$	2.58672	−	0.692227i	0.168381	−	0.0450602i
$237$	9.92480	−	22.1642i	0.644685	−	1.43972i
$238$	16.1303	−	14.1414i	1.04557	−	0.916648i
$239$	14.9128	+	8.60993i	0.964632	+	0.556930i	0.897595	−	0.440820i	$-0.145312\pi$
$239$	14.9128	+	8.60993i	0.964632	+	0.556930i	0.0670362	+	0.997751i	$0.478646\pi$
$240$	19.1236	+	5.72232i	1.23442	+	0.369374i
$241$	10.9425	−	6.31766i	0.704869	−	0.406956i	−0.104290	−	0.994547i	$-0.533257\pi$
$241$	10.9425	−	6.31766i	0.704869	−	0.406956i	0.809158	+	0.587591i	$0.199924\pi$
$242$	−11.7454	+	34.5828i	−0.755025	+	2.22307i
$243$	−0.166162	+	15.5876i	−0.0106593	+	0.999943i
$244$	−2.54115	−	4.40464i	−0.162681	−	0.281978i
$245$	−8.01827	−	6.15263i	−0.512268	−	0.393077i
$246$	−0.865248	+	0.266495i	−0.0551662	+	0.0169911i
$247$	−3.50778	−	13.0912i	−0.223195	−	0.832975i
$248$	−7.60243	+	8.66056i	−0.482755	+	0.549946i
$249$	−22.3631	+	21.1314i	−1.41720	+	1.33915i
$250$	3.84472	+	5.75601i	0.243161	+	0.364042i
$251$	6.30328	−	2.61090i	0.397859	−	0.164799i	−0.174777	−	0.984608i	$-0.555921\pi$
$251$	6.30328	−	2.61090i	0.397859	−	0.164799i	0.572637	+	0.819809i	$0.305921\pi$
$252$	3.63199	−	19.1074i	0.228794	−	1.20365i
$253$	−8.58751	+	20.7321i	−0.539892	+	1.30341i
$254$	−0.597246	+	0.893534i	−0.0374746	+	0.0560653i
$255$	−11.0986	−	20.5454i	−0.695022	−	1.28661i
$256$	0.0203949	−	16.0000i	0.00127468	−	0.999999i
$257$	−24.2199	−	13.9834i	−1.51079	−	0.872258i	−0.999921	−	0.0126022i	$-0.995988\pi$
$257$	−24.2199	−	13.9834i	−1.51079	−	0.872258i	−0.510874	−	0.859656i	$-0.670678\pi$
$258$	−1.12163	+	1.57938i	−0.0698298	+	0.0983281i
$259$	0.907144	+	6.89044i	0.0563672	+	0.428151i
$260$	−20.1583	−	15.4782i	−1.25017	−	0.959920i
$261$	12.8317	+	2.43485i	0.794261	+	0.150713i
$262$	−0.580560	−	8.87932i	−0.0358671	−	0.548566i
$263$	−0.270431	−	0.0724618i	−0.0166755	−	0.00446819i	0.250472	−	0.968124i	$-0.419414\pi$
$263$	−0.270431	−	0.0724618i	−0.0166755	−	0.00446819i	−0.267147	+	0.963656i	$0.586081\pi$
$264$	6.63677	−	28.9788i	0.408465	−	1.78352i
$265$	−19.8655	+	5.32294i	−1.22033	+	0.326986i
$266$	4.52596	+	13.3400i	0.277504	+	0.817929i
$267$	0.863616	−	5.37842i	0.0528524	−	0.329154i
$268$	17.5570	+	10.1440i	1.07246	+	0.619643i
$269$	2.02799	−	4.89600i	0.123649	−	0.298515i	−0.849919	−	0.526914i	$-0.823349\pi$
$269$	2.02799	−	4.89600i	0.123649	−	0.298515i	0.973568	+	0.228399i	$0.0733491\pi$
$270$	−19.3977	−	8.48495i	−1.18051	−	0.516378i
$271$	−22.5843			−1.37190			−0.685949	−	0.727649i	$-0.740613\pi$
$271$	−22.5843			−1.37190			−0.685949	+	0.727649i	$0.740613\pi$
$272$	−13.2436	+	13.2267i	−0.803012	+	0.801989i
$273$	−12.9839	+	21.0867i	−0.785820	+	1.27623i
$274$	−13.3620	−	15.2413i	−0.807227	−	0.920762i
$275$	−15.8932	+	12.1953i	−0.958399	+	0.735405i
$276$	3.66827	−	12.2734i	0.220804	−	0.738769i
$277$	−8.06669	+	10.5127i	−0.484680	+	0.631648i	−0.970121	−	0.242622i	$-0.921993\pi$
$277$	−8.06669	+	10.5127i	−0.484680	+	0.631648i	0.485440	+	0.874270i	$0.338659\pi$
$278$	12.6588	−	14.4299i	0.759223	−	0.865449i
$279$	9.11827	−	8.14000i	0.545897	−	0.487329i
$280$	21.9574	+	14.6866i	1.31220	+	0.877694i
$281$	−4.05619	+	15.1379i	−0.241972	+	0.903053i	0.732909	+	0.680327i	$0.238162\pi$
$281$	−4.05619	+	15.1379i	−0.241972	+	0.903053i	−0.974881	+	0.222726i	$0.928504\pi$
$282$	4.48585	+	7.14587i	0.267129	+	0.425530i
$283$	−0.743339	−	0.0978624i	−0.0441869	−	0.00581732i	0.108400	−	0.994107i	$-0.465427\pi$
$283$	−0.743339	−	0.0978624i	−0.0441869	−	0.00581732i	−0.152587	+	0.988290i	$0.548761\pi$
$284$	15.0459	+	6.23784i	0.892811	+	0.370148i
$285$	15.2540	−	1.57039i	0.903570	−	0.0930219i
$286$	−21.0342	+	31.4691i	−1.24378	+	1.86081i
$287$	−1.19813			−0.0707231
$288$	−2.07993	+	16.8426i	−0.122561	+	0.992461i
$289$	4.89622			0.288013
$290$	−9.85761	+	14.7479i	−0.578859	+	0.866024i
$291$	1.37425	−	3.06900i	0.0805602	−	0.179908i
$292$	−12.2611	+	29.5742i	−0.717526	+	1.73070i
$293$	1.09834	+	0.144599i	0.0641658	+	0.00844758i	0.162541	−	0.986702i	$-0.448031\pi$
$293$	1.09834	+	0.144599i	0.0641658	+	0.00844758i	−0.0983750	+	0.995149i	$0.531364\pi$
$294$	4.01820	−	7.59506i	0.234346	−	0.442953i
$295$	0.998403	−	3.72609i	0.0581293	−	0.216941i
$296$	−1.18020	−	5.94814i	−0.0685979	−	0.345729i
$297$	−10.7156	+	29.6558i	−0.621783	+	1.72080i
$298$	7.75199	−	8.83661i	0.449061	−	0.511891i
$299$	−9.92873	+	12.9394i	−0.574193	+	0.748303i
$300$	8.31441	−	7.85144i	0.480032	−	0.453303i
$301$	−2.03381	+	1.56059i	−0.117227	+	0.0899511i
$302$	−0.381654	−	0.435333i	−0.0219617	−	0.0250506i
$303$	21.7597	+	0.616221i	1.25006	+	0.0354010i
$304$	−4.69649	−	11.3588i	−0.269362	−	0.651472i
$305$	−7.32556			−0.419460
$306$	15.6449	−	12.2216i	0.894360	−	0.698665i
$307$	5.62180	−	13.5722i	0.320853	−	0.774607i	−0.678352	−	0.734737i	$-0.737306\pi$
$307$	5.62180	−	13.5722i	0.320853	−	0.774607i	0.999205	−	0.0398702i	$-0.0126944\pi$
$308$	19.6821	−	34.0654i	1.12149	−	1.94105i
$309$	4.23771	+	3.44661i	0.241075	+	0.196071i
$310$	5.33382	+	15.7212i	0.302941	+	0.892901i
$311$	15.9966	−	4.28627i	0.907083	−	0.243052i	0.225027	−	0.974352i	$-0.427753\pi$
$311$	15.9966	−	4.28627i	0.907083	−	0.243052i	0.682056	+	0.731300i	$0.261086\pi$
$312$	10.1105	−	19.0958i	0.572396	−	1.08109i
$313$	2.04004	+	0.546628i	0.115310	+	0.0308972i	0.316013	−	0.948755i	$-0.397656\pi$
$313$	2.04004	+	0.546628i	0.115310	+	0.0308972i	−0.200703	+	0.979652i	$0.564322\pi$
$314$	−1.30950	−	20.0280i	−0.0738994	−	1.13025i
$315$	−21.2278	−	18.2874i	−1.19605	−	1.03038i
$316$	−17.0778	+	22.2415i	−0.960701	+	1.25118i
$317$	−2.28300	−	17.3411i	−0.128226	−	0.973974i	−0.927714	−	0.373292i	$-0.878229\pi$
$317$	−2.28300	−	17.3411i	−0.128226	−	0.973974i	0.799488	−	0.600682i	$-0.205104\pi$
$318$	−7.28378	−	15.8954i	−0.408454	−	0.891371i
$319$	22.8796	+	13.2096i	1.28101	+	0.739594i
$320$	−19.9504	−	11.5438i	−1.11526	−	0.645318i
$321$	−4.66008	+	7.56830i	−0.260101	+	0.422421i
$322$	9.42036	−	14.0937i	0.524976	−	0.785411i
$323$	−5.50259	+	13.2844i	−0.306172	+	0.739165i
$324$	4.35668	−	17.4648i	0.242038	−	0.970267i
$325$	−13.4518	+	5.57191i	−0.746171	+	0.309074i
$326$	−6.09307	−	9.12206i	−0.337464	−	0.505224i
$327$	−2.72065	−	11.4397i	−0.150452	−	0.632618i
$328$	1.04321	−	0.0678749i	0.0576017	−	0.00374777i
$329$	2.88986	+	10.7851i	0.159323	+	0.594601i
$330$	−31.3824	−	29.1432i	−1.72754	−	1.60428i
$331$	−6.80198	−	5.21934i	−0.373871	−	0.286881i	0.404686	−	0.914456i	$-0.367381\pi$
$331$	−6.80198	−	5.21934i	−0.373871	−	0.286881i	−0.778556	+	0.627575i	$0.784048\pi$
$332$	30.7732	−	17.7539i	1.68890	−	0.974369i
$333$	0.477300	+	6.41421i	0.0261559	+	0.351497i
$334$	6.83017	−	20.1105i	0.373730	−	1.10040i
$335$	25.2971	−	14.6053i	1.38213	−	0.797971i
$336$	−9.19142	+	20.4914i	−0.501433	+	1.11790i
$337$	9.96360	+	5.75249i	0.542752	+	0.313358i	0.746193	−	0.665729i	$-0.231879\pi$
$337$	9.96360	+	5.75249i	0.542752	+	0.313358i	−0.203442	+	0.979087i	$0.565213\pi$
$338$	−6.86224	+	6.01609i	−0.373257	+	0.327232i
$339$	−0.764496	+	0.0787043i	−0.0415217	+	0.00427463i
$340$	6.97051	+	26.0475i	0.378029	+	1.41262i
$341$	22.8427	−	9.46177i	1.23700	−	0.512384i
$342$	3.48325	+	12.5631i	0.188352	+	0.679335i
$343$	−8.00447	+	8.00447i	−0.432201	+	0.432201i
$344$	1.68243	−	1.47403i	0.0907107	−	0.0794745i
$345$	−12.6741	−	13.4129i	−0.682352	−	0.722126i
$346$	14.7031	+	7.25367i	0.790443	+	0.389960i
$347$	−2.84116	+	21.5808i	−0.152521	+	1.15852i	0.728366	+	0.685189i	$0.240280\pi$
$347$	−2.84116	+	21.5808i	−0.152521	+	1.15852i	−0.880887	+	0.473327i	$0.843053\pi$
$348$	−13.7622	−	6.16780i	−0.737733	−	0.330629i
$349$	24.0250	−	3.16295i	1.28603	−	0.169309i	0.543663	−	0.839304i	$-0.317037\pi$
$349$	24.0250	−	3.16295i	1.28603	−	0.169309i	0.742366	+	0.669995i	$0.233704\pi$
$350$	13.5740	−	6.69127i	0.725561	−	0.357664i
$351$	−13.1014	+	18.8039i	−0.699301	+	1.00368i
$352$	−15.2075	+	30.7758i	−0.810560	+	1.64036i
$353$	15.5162	−	8.95827i	0.825843	−	0.476801i	−0.0265842	−	0.999647i	$-0.508463\pi$
$353$	15.5162	−	8.95827i	0.825843	−	0.476801i	0.852427	+	0.522846i	$0.175130\pi$
$354$	3.26510	+	0.307566i	0.173538	+	0.0163470i
$355$	18.6152	−	14.2839i	0.987992	−	0.758113i
$356$	−2.40894	+	5.81045i	−0.127673	+	0.307953i
$357$	24.5476	−	9.36294i	1.29920	−	0.495539i
$358$	−16.7489	−	25.0751i	−0.885205	−	1.32526i
$359$	−4.22376	+	4.22376i	−0.222921	+	0.222921i	−0.809727	−	0.586806i	$-0.800385\pi$
$359$	−4.22376	+	4.22376i	−0.222921	+	0.222921i	0.586806	+	0.809727i	$0.300385\pi$
$360$	19.5192	+	14.7203i	1.02875	+	0.775830i
$361$	6.75819	+	6.75819i	0.355694	+	0.355694i
$362$	−0.538401	+	2.70447i	−0.0282977	+	0.142144i
$363$	−28.2244	+	34.7026i	−1.48139	+	1.82142i
$364$	20.2257	−	20.2129i	1.06012	−	1.05944i
$365$	28.0765	+	36.5900i	1.46959	+	1.91521i
$366$	−1.04064	−	6.14041i	−0.0543949	−	0.320964i
$367$	1.50986	+	2.61515i	0.0788140	+	0.136510i	0.902738	−	0.430190i	$-0.141553\pi$
$367$	1.50986	+	2.61515i	0.0788140	+	0.136510i	−0.823925	+	0.566700i	$0.808220\pi$
$368$	−7.40392	+	12.8051i	−0.385956	+	0.667512i
$369$	−1.10706	−	0.0627526i	−0.0576310	−	0.00326677i
$370$	−8.27181	−	2.80937i	−0.430031	−	0.146052i
$371$	−3.02023	−	22.9409i	−0.156803	−	1.19103i
$372$	−12.4200	+	6.70417i	−0.643949	+	0.347595i
$373$	−19.5198	−	2.56982i	−1.01069	−	0.133060i	−0.393049	−	0.919517i	$-0.628580\pi$
$373$	−19.5198	−	2.56982i	−1.01069	−	0.133060i	−0.617645	+	0.786457i	$0.711913\pi$
$374$	38.0291	−	12.9024i	1.96644	−	0.667166i
$375$	1.96149	+	8.24760i	0.101291	+	0.425904i
$376$	−3.12719	−	9.22690i	−0.161273	−	0.475841i
$377$	13.5776	+	13.5776i	0.699281	+	0.699281i
$378$	12.3133	−	20.3914i	0.633327	−	1.04882i
$379$	12.4650	+	30.0933i	0.640286	+	1.54579i	0.826294	+	0.563239i	$0.190445\pi$
$379$	12.4650	+	30.0933i	0.640286	+	1.54579i	−0.186008	+	0.982548i	$0.559555\pi$
$380$	−17.5547	−	2.31681i	−0.900537	−	0.118850i
$381$	−1.06656	+	0.771433i	−0.0546416	+	0.0395217i
$382$	−1.12538	+	17.1281i	−0.0575793	+	0.876351i
$383$	11.8673	−	20.5548i	0.606392	−	1.05030i	−0.385437	−	0.922734i	$-0.625949\pi$
$383$	11.8673	−	20.5548i	0.606392	−	1.05030i	0.991830	−	0.127568i	$-0.0407172\pi$
$384$	6.84215	−	18.3626i	0.349162	−	0.937062i
$385$	−28.3382	−	49.0832i	−1.44425	−	2.50151i
$386$	−4.76576	+	2.34927i	−0.242571	+	0.119575i
$387$	−1.96095	+	1.33545i	−0.0996809	+	0.0678848i
$388$	−2.36470	+	3.07971i	−0.120050	+	0.156349i
$389$	−3.54858	+	4.62460i	−0.179920	+	0.234476i	−0.874603	−	0.484840i	$-0.838878\pi$
$389$	−3.54858	+	4.62460i	−0.179920	+	0.234476i	0.694683	+	0.719316i	$0.255545\pi$
$390$	−16.5496	−	26.3631i	−0.838019	−	1.33495i
$391$	16.7140	−	4.47851i	0.845264	−	0.226488i
$392$	−6.54543	+	7.45644i	−0.330594	+	0.376607i
$393$	3.11750	−	10.4427i	0.157257	−	0.526765i
$394$	−6.43584	+	32.3282i	−0.324233	+	1.62867i
$395$	15.4591	+	37.3216i	0.777832	+	1.87785i
$396$	19.9703	−	30.4452i	1.00354	−	1.52993i
$397$	−17.4731	−	7.23758i	−0.876948	−	0.363244i	−0.101636	−	0.994822i	$-0.532408\pi$
$397$	−17.4731	−	7.23758i	−0.876948	−	0.363244i	−0.775312	+	0.631578i	$0.782408\pi$
$398$	5.26807	+	26.5065i	0.264065	+	1.32865i
$399$	−0.488395	+	17.2459i	−0.0244503	+	0.863377i
$400$	−11.4399	+	6.59510i	−0.571994	+	0.329755i
$401$	6.30036	−	10.9125i	0.314625	−	0.544947i	−0.664733	−	0.747081i	$-0.731455\pi$
$401$	6.30036	−	10.9125i	0.314625	−	0.544947i	0.979358	+	0.202135i	$0.0647879\pi$
$402$	15.8360	+	19.1297i	0.789827	+	0.954102i
$403$	17.8164	−	2.34557i	0.887498	−	0.116841i
$404$	−24.2774	−	6.51341i	−1.20785	−	0.324054i
$405$	−18.6565	−	18.0092i	−0.927049	−	0.894885i
$406$	−15.0031	−	13.1616i	−0.744591	−	0.653198i
$407$	−3.36738	+	12.5672i	−0.166915	+	0.622935i
$408$	−20.8432	+	9.54299i	−1.03189	+	0.472448i
$409$	8.06455	+	30.0973i	0.398766	+	1.48822i	0.815269	+	0.579082i	$0.196589\pi$
$409$	8.06455	+	30.0973i	0.398766	+	1.48822i	−0.416503	+	0.909134i	$0.636744\pi$
$410$	0.666310	−	1.35060i	0.0329067	−	0.0667014i
$411$	−8.84692	−	23.1947i	−0.436386	−	1.14411i
$412$	−3.83810	−	5.00521i	−0.189089	−	0.246589i
$413$	4.00970	+	1.66087i	0.197304	+	0.0817262i
$414$	9.44249	−	12.5290i	0.464073	−	0.615769i
$415$		−	51.1803i		−	2.51234i
$416$	−16.4656	+	18.7452i	−0.807290	+	0.919060i
$417$	20.6845	−	11.1737i	1.01292	−	0.547180i
$418$	−1.72896	+	26.3146i	−0.0845664	+	1.28709i
$419$	2.70599	+	3.52651i	0.132196	+	0.172282i	0.854761	−	0.519022i	$-0.173704\pi$
$419$	2.70599	+	3.52651i	0.132196	+	0.172282i	−0.722565	+	0.691303i	$0.757037\pi$
$420$	18.9526	+	26.2209i	0.924791	+	1.27945i
$421$	−20.6981	−	15.8822i	−1.00877	−	0.774053i	−0.0344885	−	0.999405i	$-0.510980\pi$
$421$	−20.6981	−	15.8822i	−1.00877	−	0.774053i	−0.974277	+	0.225352i	$0.927647\pi$
$422$	0.307014	+	4.69560i	0.0149452	+	0.228578i
$423$	2.10532	+	10.1167i	0.102364	+	0.491890i
$424$	3.92935	+	19.8036i	0.190826	+	0.961750i
$425$	14.9210	+	3.99808i	0.723777	+	0.193936i
$426$	14.6174	+	13.5745i	0.708217	+	0.657685i
$427$	1.07578	−	8.17140i	0.0520609	−	0.395442i
$428$	7.25929	−	7.25466i	0.350891	−	0.350667i
$429$	−37.5628	+	27.1688i	−1.81355	+	1.31172i
$430$	−0.628143	−	3.16052i	−0.0302917	−	0.152414i
$431$			3.86711i			0.186272i	0.995653	+	0.0931362i	$0.0296892\pi$
$431$			3.86711i			0.186272i	−0.995653	+	0.0931362i	$0.970311\pi$
$432$	−9.56603	+	18.4524i	−0.460246	+	0.887792i
$433$		−	33.7121i		−	1.62010i	−0.586360	−	0.810050i	$-0.699440\pi$
$433$		−	33.7121i		−	1.62010i	0.586360	−	0.810050i	$-0.300560\pi$
$434$	−18.3197	+	3.64098i	−0.879372	+	0.174772i
$435$	−17.6037	+	12.7326i	−0.844032	+	0.610480i
$436$	−0.00432687	+	13.5779i	−0.000207220	+	0.650262i
$437$	−1.48318	+	11.2659i	−0.0709500	+	0.538919i
$438$	−26.6819	+	28.7320i	−1.27491	+	1.37287i
$439$	3.17739	+	0.851379i	0.151648	+	0.0406341i	0.333845	−	0.942628i	$-0.391654\pi$
$439$	3.17739	+	0.851379i	0.151648	+	0.0406341i	−0.182196	+	0.983262i	$0.558321\pi$
$440$	27.4548	+	41.1316i	1.30886	+	1.96087i
$441$	7.85052	−	7.00826i	0.373834	−	0.333727i
$442$	29.1251	−	1.90430i	1.38534	−	0.0905782i
$443$	24.0366	+	18.4439i	1.14201	+	0.876297i	0.993637	−	0.112634i	$-0.0359288\pi$
$443$	24.0366	+	18.4439i	1.14201	+	0.876297i	0.148376	+	0.988931i	$0.452595\pi$
$444$	1.17981	−	7.33266i	0.0559912	−	0.347993i
$445$	5.51619	+	7.18884i	0.261493	+	0.340784i
$446$	−14.1273	−	0.928213i	−0.668947	−	0.0439522i
$447$	12.6668	−	6.84258i	0.599119	−	0.323643i
$448$	15.8065	−	20.5587i	0.746786	−	0.971306i
$449$			15.8644i			0.748686i	0.927290	+	0.374343i	$0.122132\pi$
$449$			15.8644i			0.748686i	−0.927290	+	0.374343i	$0.877868\pi$
$450$	12.8927	−	5.47172i	0.607768	−	0.257939i
$451$	−2.07222	−	0.858340i	−0.0975769	−	0.0404177i
$452$	0.879800	+	0.116113i	0.0413823	+	0.00546150i
$453$	−0.252692	−	0.662503i	−0.0118725	−	0.0311271i
$454$	−19.1452	−	9.44515i	−0.898527	−	0.443283i
$455$	−10.6615	−	39.7892i	−0.499818	−	1.86535i
$456$	−0.551752	−	15.0438i	−0.0258381	−	0.704489i
$457$	−0.391338	+	1.46049i	−0.0183060	+	0.0683191i	−0.974475	−	0.224498i	$-0.927926\pi$
$457$	−0.391338	+	1.46049i	−0.0183060	+	0.0683191i	0.956169	+	0.292817i	$0.0945926\pi$
$458$	−16.2611	+	18.5363i	−0.759831	+	0.866143i
$459$	23.1721	−	7.36556i	1.08158	−	0.343795i
$460$	10.6484	+	18.4571i	0.496483	+	0.860566i
$461$	2.13606	−	0.281217i	0.0994860	−	0.0130976i	−0.0806188	−	0.996745i	$-0.525690\pi$
$461$	2.13606	−	0.281217i	0.0994860	−	0.0130976i	0.180105	+	0.983647i	$0.442356\pi$
$462$	37.1168	−	30.7261i	1.72683	−	1.42951i
$463$	−9.17201	+	15.8864i	−0.426259	+	0.738303i	−0.996537	−	0.0831491i	$-0.973502\pi$
$463$	−9.17201	+	15.8864i	−0.426259	+	0.738303i	0.570278	+	0.821452i	$0.306836\pi$
$464$	13.8089	+	10.6099i	0.641060	+	0.492552i
$465$	−0.575571	+	20.3242i	−0.0266914	+	0.942514i
$466$	−30.7433	+	6.11013i	−1.42416	+	0.283046i
$467$	−32.6812	−	13.5370i	−1.51230	−	0.626417i	−0.536272	−	0.844045i	$-0.680168\pi$
$467$	−32.6812	−	13.5370i	−1.51230	−	0.626417i	−0.976032	+	0.217629i	$0.930168\pi$
$468$	19.7470	−	17.6171i	0.912808	−	0.814353i
$469$	12.5767	+	30.3628i	0.580738	+	1.40203i
$470$	−13.7647	−	2.74026i	−0.634920	−	0.126399i
$471$	7.03177	−	23.5544i	0.324007	−	1.08533i
$472$	−3.58535	−	1.21897i	−0.165029	−	0.0561078i
$473$	−4.63558	+	1.24210i	−0.213144	+	0.0571118i
$474$	−29.0875	+	18.2598i	−1.33603	+	0.838701i
$475$	−6.17534	+	8.04786i	−0.283344	+	0.369261i
$476$	−30.0787	+	3.95018i	−1.37865	+	0.181056i
$477$	−1.58912	−	21.3554i	−0.0727606	−	0.977795i
$478$	−10.7674	−	21.8429i	−0.492489	−	0.999070i
$479$	3.52666	+	6.10836i	0.161137	+	0.279098i	0.935277	−	0.353917i	$-0.115150\pi$
$479$	3.52666	+	6.10836i	0.161137	+	0.279098i	−0.774139	+	0.633015i	$0.781817\pi$
$480$	−17.9875	−	21.7569i	−0.821014	−	0.993063i
$481$	−4.72808	+	8.18928i	−0.215582	+	0.373399i
$482$	−17.8306	−	1.17153i	−0.812161	−	0.0533618i
$483$	16.8228	−	12.1678i	0.765466	−	0.553654i
$484$	40.9877	−	31.4302i	1.86308	−	1.42865i
$485$	2.14057	+	5.16779i	0.0971982	+	0.234657i
$486$	12.4454	−	18.1965i	0.564533	−	0.825410i
$487$	−0.127493	−	0.127493i	−0.00577726	−	0.00577726i	0.704212	−	0.709990i	$-0.251300\pi$
$487$	−0.127493	−	0.127493i	−0.00577726	−	0.00577726i	−0.709990	+	0.704212i	$0.751300\pi$
$488$	−0.473772	+	7.17581i	−0.0214467	+	0.324834i
$489$	−3.10854	−	13.0707i	−0.140573	−	0.591078i
$490$	4.59223	+	13.5354i	0.207456	+	0.611466i
$491$	−20.3157	−	2.67461i	−0.916833	−	0.120703i	−0.342681	−	0.939452i	$-0.611335\pi$
$491$	−20.3157	−	2.67461i	−0.916833	−	0.120703i	−0.574152	+	0.818749i	$0.694668\pi$
$492$	1.22675	+	0.366652i	0.0553061	+	0.0165299i
$493$	−2.65905	−	20.1975i	−0.119757	−	0.909648i
$494$	−6.16389	+	18.1487i	−0.277326	+	0.816550i
$495$	−23.6135	−	46.8367i	−1.06135	−	2.10515i
$496$	15.7447	−	4.20804i	0.706960	−	0.188946i
$497$	13.1995	+	22.8622i	0.592079	+	1.02551i
$498$	42.9002	−	7.27044i	1.92240	−	0.325796i
$499$	6.83554	+	8.90825i	0.306001	+	0.398788i	0.920888	−	0.389827i	$-0.127465\pi$
$499$	6.83554	+	8.90825i	0.306001	+	0.398788i	−0.614887	+	0.788615i	$0.710798\pi$
$500$	0.00311951	−	9.78913i	0.000139509	−	0.437783i
$501$	16.4130	−	20.1802i	0.733277	−	0.901585i
$502$	−9.46294	−	1.88386i	−0.422352	−	0.0840809i
$503$	−23.8196	−	23.8196i	−1.06206	−	1.06206i	−0.997942	−	0.0641209i	$-0.979576\pi$
$503$	−23.8196	−	23.8196i	−1.06206	−	1.06206i	−0.0641209	−	0.997942i	$-0.520424\pi$
$504$	−19.2865	+	19.6112i	−0.859087	+	0.873552i
$505$	−25.6048	+	25.6048i	−1.13940	+	1.13940i
$506$	26.3897	−	17.6270i	1.17317	−	0.783615i
$507$	−10.4431	+	3.98323i	−0.463797	+	0.176901i
$508$	1.40443	−	0.581208i	0.0623113	−	0.0257869i
$509$	−8.91776	+	6.84284i	−0.395273	+	0.303304i	−0.787206	−	0.616690i	$-0.788473\pi$
$509$	−8.91776	+	6.84284i	−0.395273	+	0.303304i	0.391933	+	0.919994i	$0.371806\pi$
$510$	−3.09710	+	32.8785i	−0.137142	+	1.45589i
$511$	−44.9379	+	25.9449i	−1.98794	+	1.14774i
$512$	−12.5981	+	18.7960i	−0.556762	+	0.830672i
$513$	−1.35454	+	15.9095i	−0.0598044	+	0.702421i
$514$	17.4873	+	35.4749i	0.771330	+	1.56473i
$515$	−9.00862	+	1.18601i	−0.396967	+	0.0522617i
$516$	2.55997	−	0.975489i	0.112696	−	0.0429435i
$517$	−2.72832	+	20.7236i	−0.119991	+	0.911425i
$518$	4.34850	−	8.81435i	0.191062	−	0.387280i
$519$	13.7909	+	14.5947i	0.605352	+	0.640638i
$520$	11.5371	+	34.0406i	0.505935	+	1.49278i
$521$	21.7451	−	21.7451i	0.952672	−	0.952672i	−0.0462579	−	0.998930i	$-0.514730\pi$
$521$	21.7451	−	21.7451i	0.952672	−	0.952672i	0.998930	+	0.0462579i	$0.0147296\pi$
$522$	−13.1734	−	12.9470i	−0.576582	−	0.566673i
$523$	−20.4000	+	8.44994i	−0.892028	+	0.369490i	−0.781150	−	0.624344i	$-0.785366\pi$
$523$	−20.4000	+	8.44994i	−0.892028	+	0.369490i	−0.110879	+	0.993834i	$0.535366\pi$
$524$	−6.29550	+	10.8961i	−0.275020	+	0.475999i
$525$	18.4374	−	1.89812i	0.804674	−	0.0828406i
$526$	0.261013	+	0.297724i	0.0113807	+	0.0129814i
$527$	−16.5110	−	9.53262i	−0.719230	−	0.415247i
$528$	−30.5771	+	28.8561i	−1.33070	+	1.25580i
$529$	−8.07629	+	4.66285i	−0.351143	+	0.202733i
$530$	27.5400	+	9.35348i	1.19626	+	0.406289i
$531$	3.61793	+	1.74464i	0.157005	+	0.0757110i
$532$	5.16229	−	19.2414i	0.223814	−	0.834221i
$533$	−1.29332	−	0.992398i	−0.0560198	−	0.0429855i
$534$	−5.24220	+	5.64498i	−0.226852	+	0.244282i
$535$	−3.82655	−	14.2809i	−0.165436	−	0.617416i
$536$	−12.6707	−	25.7245i	−0.547289	−	1.11113i
$537$	−8.54489	−	35.9293i	−0.368739	−	1.55046i
$538$	−6.23209	+	4.16272i	−0.268685	+	0.179467i
$539$	19.6668	−	8.14626i	0.847109	−	0.350884i
$540$	16.1387	+	25.2205i	0.694497	+	1.08532i
$541$	9.30148	−	22.4558i	0.399902	−	0.965449i	−0.587787	−	0.809016i	$-0.700001\pi$
$541$	9.30148	−	22.4558i	0.399902	−	0.965449i	0.987689	−	0.156433i	$-0.0499995\pi$
$542$	26.5535	+	17.7486i	1.14057	+	0.762368i
$543$	−1.77076	+	2.87584i	−0.0759907	+	0.123414i
$544$	25.9658	−	5.14342i	1.11328	−	0.220522i
$545$	16.9396	+	9.78007i	0.725612	+	0.418932i
$546$	31.8375	−	14.5889i	1.36252	−	0.624348i
$547$	−5.35307	−	40.6606i	−0.228881	−	1.73852i	−0.591252	−	0.806487i	$-0.701366\pi$
$547$	−5.35307	−	40.6606i	−0.228881	−	1.73852i	0.362372	−	0.932034i	$-0.381967\pi$
$548$	3.73248	+	28.4210i	0.159443	+	1.21408i
$549$	1.42200	−	7.49394i	0.0606894	−	0.319834i
$550$	28.2706	−	1.84843i	1.20546	−	0.0788172i
$551$	12.9220	+	3.46244i	0.550496	+	0.147505i
$552$	−13.9584	+	11.5476i	−0.594109	+	0.491497i
$553$	−43.9011	+	11.7633i	−1.86687	+	0.500225i
$554$	17.7462	−	6.02086i	0.753963	−	0.255802i
$555$	−8.30048	−	6.75095i	−0.352336	−	0.286562i
$556$	−26.2238	+	7.01768i	−1.11214	+	0.297616i
$557$	5.08956	−	12.2873i	0.215651	−	0.520628i	−0.778622	−	0.627493i	$-0.784081\pi$
$557$	5.08956	−	12.2873i	0.215651	−	0.520628i	0.994274	+	0.106865i	$0.0340811\pi$
$558$	−17.1179	+	2.40472i	−0.724658	+	0.101800i
$559$	−3.48802			−0.147528
$560$	−14.2744	−	34.5237i	−0.603204	−	1.45889i
$561$	49.1639	+	1.39229i	2.07570	+	0.0587826i
$562$	16.6657	−	14.6107i	0.703000	−	0.616316i
$563$	−5.98768	+	4.59451i	−0.252351	+	0.193635i	−0.727188	−	0.686438i	$-0.759173\pi$
$563$	−5.98768	+	4.59451i	−0.252351	+	0.193635i	0.474838	+	0.880073i	$0.342507\pi$
$564$	0.341573	−	11.9271i	0.0143828	−	0.502222i
$565$	0.778254	−	1.01424i	0.0327414	−	0.0426694i
$566$	0.797073	+	0.699239i	0.0335035	+	0.0293912i
$567$	22.8284	−	18.1659i	0.958703	−	0.762898i
$568$	−12.7880	−	19.1585i	−0.536574	−	0.803871i
$569$	−0.558495	+	2.08433i	−0.0234133	+	0.0873797i	−0.976644	−	0.214864i	$-0.931069\pi$
$569$	−0.558495	+	2.08433i	−0.0234133	+	0.0873797i	0.953231	+	0.302244i	$0.0977357\pi$
$570$	−19.1691	−	10.1415i	−0.802904	−	0.424780i
$571$	20.1241	+	2.64939i	0.842167	+	0.110873i	0.539252	−	0.842144i	$-0.318707\pi$
$571$	20.1241	+	2.64939i	0.842167	+	0.110873i	0.302915	+	0.953018i	$0.402040\pi$
$572$	49.4620	−	20.4694i	2.06811	−	0.855867i
$573$	−8.59167	+	19.1870i	−0.358922	+	0.801549i
$574$	1.40870	+	0.941585i	0.0587978	+	0.0393010i
$575$	12.2074			0.509084
$576$	15.6818	−	18.1681i	0.653408	−	0.757006i
$577$	22.7617			0.947583			0.473791	−	0.880637i	$-0.342885\pi$
$577$	22.7617			0.947583			0.473791	+	0.880637i	$0.342885\pi$
$578$	−5.75674	−	3.84786i	−0.239449	−	0.160050i
$579$	−6.47327	+	0.666419i	−0.269020	+	0.0276954i
$580$	23.1802	−	9.59289i	0.962504	−	0.398323i
$581$	57.0898	+	7.51601i	2.36848	+	0.311817i
$582$	−4.02765	+	2.52838i	−0.166952	+	0.104805i
$583$	11.2113	−	41.8412i	0.464325	−	1.73288i
$584$	37.6578	−	25.1361i	1.55829	−	1.04014i
$585$	−7.76712	−	37.3232i	−0.321131	−	1.54313i
$586$	−1.17774	−	1.03318i	−0.0486519	−	0.0426802i
$587$	4.11805	−	5.36674i	0.169970	−	0.221509i	−0.700599	−	0.713555i	$-0.747084\pi$
$587$	4.11805	−	5.36674i	0.169970	−	0.221509i	0.870569	+	0.492046i	$0.163751\pi$
$588$	−10.6932	+	5.77206i	−0.440981	+	0.238036i
$589$	9.93270	−	7.62163i	0.409270	−	0.314044i
$590$	−4.10214	+	3.59632i	−0.168882	+	0.148058i
$591$	−21.1670	+	34.3767i	−0.870695	+	1.41407i
$592$	−3.28691	+	7.92103i	−0.135091	+	0.325552i
$593$	−24.0199			−0.986380			−0.493190	−	0.869922i	$-0.664169\pi$
$593$	−24.0199			−0.986380			−0.493190	+	0.869922i	$0.664169\pi$
$594$	35.9049	−	26.4466i	1.47319	−	1.08512i
$595$	−16.7245	+	40.3764i	−0.685636	+	1.65527i
$596$	−16.0589	+	4.29750i	−0.657800	+	0.176032i
$597$	−5.24744	+	32.6800i	−0.214764	+	1.33750i
$598$	21.8425	−	7.41066i	0.893207	−	0.303044i
$599$	−30.5456	+	8.18468i	−1.24806	+	0.334417i	−0.821587	−	0.570083i	$-0.806911\pi$
$599$	−30.5456	+	8.18468i	−1.24806	+	0.334417i	−0.426474	+	0.904500i	$0.640244\pi$
$600$	−15.9460	+	2.69719i	−0.650992	+	0.110112i
$601$	20.0266	+	5.36611i	0.816901	+	0.218888i	0.642991	−	0.765873i	$-0.277693\pi$
$601$	20.0266	+	5.36611i	0.816901	+	0.218888i	0.173910	+	0.984762i	$0.444360\pi$
$602$	3.61769	−	0.236537i	0.147446	−	0.00964053i
$603$	10.0305	+	28.7137i	0.408472	+	1.16931i
$604$	0.106610	+	0.811779i	0.00433788	+	0.0330308i
$605$	−9.71222	−	73.7717i	−0.394858	−	2.99924i
$606$	−25.0997	−	17.8251i	−1.01960	−	0.724094i
$607$	−35.8101	−	20.6750i	−1.45349	−	0.839172i	−0.454812	−	0.890588i	$-0.650293\pi$
$607$	−35.8101	−	20.6750i	−1.45349	−	0.839172i	−0.998677	+	0.0514155i	$0.983627\pi$
$608$	−3.40478	+	17.0460i	−0.138082	+	0.691307i
$609$	−11.6176	−	21.5061i	−0.470767	−	0.871471i
$610$	8.61303	+	5.75703i	0.348731	+	0.233095i
$611$	−5.81375	+	14.0356i	−0.235199	+	0.567821i
$612$	−27.9993	+	2.07454i	−1.13180	+	0.0838582i
$613$	39.4122	−	16.3251i	1.59185	−	0.659364i	0.601612	−	0.798788i	$-0.294525\pi$
$613$	39.4122	−	16.3251i	1.59185	−	0.659364i	0.990233	+	0.139424i	$0.0445252\pi$
$614$	−17.2760	+	11.5395i	−0.697202	+	0.465695i
$615$	1.34065	−	1.26681i	0.0540601	−	0.0510826i
$616$	−49.9126	+	24.5845i	−2.01104	+	0.990539i
$617$	−2.15431	−	8.04000i	−0.0867293	−	0.323678i	0.908907	−	0.416999i	$-0.136918\pi$
$617$	−2.15431	−	8.04000i	−0.0867293	−	0.323678i	−0.995636	+	0.0933213i	$0.970252\pi$
$618$	−2.27386	−	7.38270i	−0.0914679	−	0.296976i
$619$	−19.3738	−	14.8660i	−0.778697	−	0.597516i	0.141061	−	0.990001i	$-0.454949\pi$
$619$	−19.3738	−	14.8660i	−0.778697	−	0.597516i	−0.919758	+	0.392485i	$0.871615\pi$
$620$	6.08374	−	22.6759i	0.244329	−	0.910686i
$621$	16.1814	−	10.3618i	0.649339	−	0.415805i
$622$	−22.1765	−	7.53184i	−0.889196	−	0.301999i
$623$	−8.82897	+	5.09741i	−0.353725	+	0.204223i
$624$	−26.8945	+	14.5062i	−1.07664	+	0.580715i
$625$	−26.5074	−	15.3040i	−1.06030	−	0.612162i
$626$	−1.96900	−	2.24593i	−0.0786969	−	0.0897655i
$627$	−13.1997	+	29.4778i	−0.527147	+	1.17723i
$628$	−14.2000	+	24.5770i	−0.566642	+	0.980731i
$629$	9.26875	−	3.83924i	0.369569	−	0.153081i
$630$	10.5869	+	38.1840i	0.421792	+	1.52129i
$631$	−3.80915	+	3.80915i	−0.151640	+	0.151640i	−0.778850	−	0.627210i	$-0.784197\pi$
$631$	−3.80915	+	3.80915i	−0.151640	+	0.151640i	0.627210	+	0.778850i	$0.284197\pi$
$632$	37.5585	−	12.7294i	1.49400	−	0.506347i
$633$	−1.64861	+	5.52235i	−0.0655264	+	0.219494i
$634$	−10.9438	+	22.1830i	−0.434635	+	0.880999i
$635$	0.285801	−	2.17088i	0.0113417	−	0.0861486i
$636$	−3.92803	+	24.4133i	−0.155757	+	0.968048i
$637$	15.3393	−	2.01946i	0.607766	−	0.0800139i
$638$	−16.5196	−	33.5119i	−0.654017	−	1.32675i
$639$	10.9988	+	21.8158i	0.435106	+	0.863020i
$640$	14.3846	+	29.2513i	0.568601	+	1.15626i
$641$	−18.5594	+	10.7153i	−0.733051	+	0.423227i	−0.819537	−	0.573026i	$-0.805769\pi$
$641$	−18.5594	+	10.7153i	−0.733051	+	0.423227i	0.0864863	+	0.996253i	$0.472436\pi$
$642$	11.4269	−	5.23616i	0.450983	−	0.206655i
$643$	−20.0541	+	15.3880i	−0.790855	+	0.606845i	−0.923183	−	0.384361i	$-0.874422\pi$
$643$	−20.0541	+	15.3880i	−0.790855	+	0.606845i	0.132327	+	0.991206i	$0.457755\pi$
$644$	−22.1520	+	9.16738i	−0.872910	+	0.361245i
$645$	0.625683	−	3.89663i	0.0246363	−	0.153429i
$646$	16.9097	−	11.2948i	0.665302	−	0.444387i
$647$	−1.32295	+	1.32295i	−0.0520104	+	0.0520104i	−0.732634	−	0.680623i	$-0.761709\pi$
$647$	−1.32295	+	1.32295i	−0.0520104	+	0.0520104i	0.680623	+	0.732634i	$0.261709\pi$
$648$	−18.8477	+	17.1104i	−0.740406	+	0.672160i
$649$	5.74512	+	5.74512i	0.225516	+	0.225516i
$650$	20.1948	+	4.02034i	0.792106	+	0.157691i
$651$	−22.5864	−	3.62672i	−0.885233	−	0.142142i
$652$	−0.00494376	+	15.5137i	−0.000193613	+	0.607564i
$653$	15.5873	+	20.3137i	0.609977	+	0.794937i	0.991595	−	0.129383i	$-0.0412996\pi$
$653$	15.5873	+	20.3137i	0.609977	+	0.794937i	−0.381618	+	0.924320i	$0.624633\pi$
$654$	−5.79146	+	15.5884i	−0.226464	+	0.609553i
$655$	9.06424	+	15.6997i	0.354169	+	0.613439i
$656$	−1.27990	−	0.740038i	−0.0499716	−	0.0288936i
$657$	−42.8811	+	21.6192i	−1.67295	+	0.843446i
$658$	5.07806	−	14.9517i	0.197963	−	0.582876i
$659$	−0.168711	−	1.28149i	−0.00657206	−	0.0499197i	0.987845	−	0.155445i	$-0.0496810\pi$
$659$	−0.168711	−	1.28149i	−0.00657206	−	0.0499197i	−0.994417	+	0.105525i	$0.966348\pi$
$660$	13.9947	+	58.9280i	0.544744	+	2.29377i
$661$	−24.1790	−	3.18323i	−0.940456	−	0.123813i	−0.355316	−	0.934746i	$-0.615627\pi$
$661$	−24.1790	−	3.18323i	−0.940456	−	0.123813i	−0.585139	+	0.810933i	$0.698960\pi$
$662$	3.89564	+	11.4822i	0.151408	+	0.446268i
$663$	34.2532	+	10.2257i	1.33028	+	0.397135i
$664$	−50.1341	−	3.31003i	−1.94558	−	0.128454i
$665$	−20.2934	−	20.2934i	−0.786946	−	0.786946i
$666$	4.47963	−	7.91661i	0.173582	−	0.306763i
$667$	−6.16078	−	14.8734i	−0.238546	−	0.575902i
$668$	−23.8351	+	18.2772i	−0.922207	+	0.707167i
$669$	−15.8255	−	7.08643i	−0.611849	−	0.273977i
$670$	−41.2211	−	2.70837i	−1.59251	−	0.104633i
$671$	7.71463	−	13.3621i	0.297820	−	0.515840i
$672$	26.9106	−	16.8693i	1.03810	−	0.650749i
$673$	1.54203	+	2.67087i	0.0594407	+	0.102954i	0.894214	−	0.447639i	$-0.147735\pi$
$673$	1.54203	+	2.67087i	0.0594407	+	0.102954i	−0.834774	+	0.550593i	$0.814402\pi$
$674$	−7.19393	−	14.5937i	−0.277100	−	0.562129i
$675$	17.1354	−	0.788169i	0.659541	−	0.0303366i
$676$	12.7962	−	1.68051i	0.492162	−	0.0646348i
$677$	−14.1128	+	18.3921i	−0.542397	+	0.706866i	−0.981477	−	0.191582i	$-0.938638\pi$
$677$	−14.1128	+	18.3921i	−0.542397	+	0.706866i	0.439079	+	0.898448i	$0.355305\pi$
$678$	0.960709	+	0.508267i	0.0368958	+	0.0195199i
$679$	−6.07884	+	1.62882i	−0.233284	+	0.0625084i
$680$	12.2747	−	36.1033i	0.470712	−	1.38450i
$681$	−17.9574	−	19.0041i	−0.688128	−	0.728238i
$682$	−34.2932	−	6.82702i	−1.31315	−	0.261420i
$683$	−8.07633	−	19.4980i	−0.309032	−	0.746070i	−0.999737	−	0.0229330i	$-0.992700\pi$
$683$	−8.07633	−	19.4980i	−0.309032	−	0.746070i	0.690705	−	0.723137i	$-0.257300\pi$
$684$	5.77769	−	17.5085i	0.220915	−	0.669454i
$685$	38.1511	+	15.8027i	1.45768	+	0.603791i
$686$	15.7018	−	3.12069i	0.599499	−	0.119148i
$687$	−26.5707	+	14.3535i	−1.01374	+	0.547619i
$688$	−3.13654	+	0.410899i	−0.119579	+	0.0156654i
$689$	15.7416	−	27.2652i	0.599707	−	1.03872i
$690$	4.36065	+	25.7306i	0.166007	+	0.979547i
$691$	30.9251	−	4.07137i	1.17645	−	0.154882i	0.483152	−	0.875537i	$-0.339492\pi$
$691$	30.9251	−	4.07137i	1.17645	−	0.154882i	0.693294	+	0.720655i	$0.256159\pi$
$692$	−11.5866	−	20.0834i	−0.440458	−	0.763457i
$693$	55.7124	−	19.4618i	2.11634	−	0.739294i
$694$	20.3004	−	23.1408i	0.770594	−	0.878411i
$695$	−10.1216	+	37.7745i	−0.383936	+	1.43287i
$696$	11.3338	+	18.0673i	0.429606	+	0.684839i
$697$	0.447637	+	1.67060i	0.0169554	+	0.0632786i
$698$	−30.7331	−	15.1620i	−1.16327	−	0.573889i
$699$	−37.9036	−	6.08620i	−1.43365	−	0.230201i
$700$	−21.2182	−	2.80031i	−0.801973	−	0.105842i
$701$	−33.4570	−	13.8584i	−1.26365	−	0.523423i	−0.352626	−	0.935765i	$-0.614711\pi$
$701$	−33.4570	−	13.8584i	−1.26365	−	0.523423i	−0.911029	+	0.412341i	$0.864711\pi$
$702$	30.1816	−	11.8125i	1.13913	−	0.445834i
$703$			6.58816i			0.248477i
$704$	42.0664	−	24.2334i	1.58544	−	0.913332i
$705$	−14.6369	−	9.01251i	−0.551259	−	0.339431i
$706$	−25.2833	−	1.66120i	−0.951550	−	0.0625201i
$707$	−24.8011	−	32.3214i	−0.932740	−	1.21557i
$708$	−3.59723	−	2.92761i	−0.135192	−	0.110026i
$709$	4.18727	+	3.21300i	0.157256	+	0.120667i	0.684392	−	0.729114i	$-0.260068\pi$
$709$	4.18727	+	3.21300i	0.157256	+	0.120667i	−0.527136	+	0.849781i	$0.676734\pi$
$710$	−33.1123	+	2.16500i	−1.24268	+	0.0812509i
$711$	−41.1803	+	8.56979i	−1.54438	+	0.321392i
$712$	7.39864	−	4.93850i	0.277276	−	0.185078i
$713$	−14.5531	−	3.89948i	−0.545016	−	0.146037i
$714$	−36.2200	−	8.28303i	−1.35550	−	0.309985i
$715$	10.0655	−	76.4553i	0.376430	−	2.85927i
$716$	−0.0135896	+	42.6447i	−0.000507868	+	1.59371i
$717$	−3.05439	−	29.6689i	−0.114068	−	1.10800i
$718$	8.28546	−	1.64671i	0.309211	−	0.0614546i
$719$		−	40.9430i		−	1.52691i	−0.645858	−	0.763457i	$-0.723500\pi$
$719$		−	40.9430i		−	1.52691i	0.645858	−	0.763457i	$-0.276500\pi$
$720$	−11.3812	−	32.6472i	−0.424153	−	1.21669i
$721$		−	10.2230i		−	0.380723i
$722$	−2.63480	−	13.2571i	−0.0980572	−	0.493378i
$723$	−19.9739	−	8.94404i	−0.742838	−	0.332632i
$724$	2.75842	−	2.75666i	0.102516	−	0.102451i
$725$	1.87591	−	14.2490i	0.0696696	−	0.529193i
$726$	60.4570	−	18.6206i	2.24377	−	0.691076i
$727$	−18.2625	−	4.89343i	−0.677320	−	0.181487i	−0.0962700	−	0.995355i	$-0.530691\pi$
$727$	−18.2625	−	4.89343i	−0.677320	−	0.181487i	−0.581050	+	0.813868i	$0.697358\pi$
$728$	−39.6654	+	7.87022i	−1.47010	+	0.291690i
$729$	22.0447	−	15.5895i	0.816469	−	0.577389i
$730$	−4.25551	−	65.0855i	−0.157504	−	2.40892i
$731$	2.93587	+	2.25277i	0.108587	+	0.0833218i
$732$	−3.60211	+	8.03740i	−0.133138	+	0.297071i
$733$	30.1492	+	39.2912i	1.11359	+	1.45125i	0.877534	+	0.479515i	$0.159187\pi$
$733$	30.1492	+	39.2912i	1.11359	+	1.45125i	0.236053	+	0.971740i	$0.424146\pi$
$734$	0.279985	−	4.26134i	0.0103344	−	0.157289i
$735$	−0.495547	+	17.4985i	−0.0182785	+	0.645441i
$736$	18.7685	−	9.23700i	0.691815	−	0.340480i
$737$			61.5240i			2.26627i
$738$	1.25230	+	0.943797i	0.0460980	+	0.0347416i
$739$	24.3973	+	10.1057i	0.897468	+	0.371743i	0.783246	−	0.621712i	$-0.213563\pi$
$739$	24.3973	+	10.1057i	0.897468	+	0.371743i	0.114222	+	0.993455i	$0.463563\pi$
$740$	7.51775	+	9.80379i	0.276358	+	0.360395i
$741$	−14.8119	+	18.2116i	−0.544128	+	0.669021i
$742$	−14.4778	+	29.3463i	−0.531498	+	1.07734i
$743$	−6.18952	−	23.0996i	−0.227072	−	0.847443i	−0.981564	−	0.191134i	$-0.938784\pi$
$743$	−6.18952	−	23.0996i	−0.227072	−	0.847443i	0.754492	−	0.656309i	$-0.227883\pi$
$744$	19.8716	+	1.87825i	0.728527	+	0.0688601i
$745$	−6.19830	+	23.1324i	−0.227088	+	0.847505i
$746$	20.9308	+	18.3617i	0.766330	+	0.672270i
$747$	52.3567	+	9.93484i	1.91563	+	0.363497i
$748$	−54.8525	−	14.7164i	−2.00561	−	0.538085i
$749$	16.4917	−	2.17118i	0.602595	−	0.0793332i
$750$	4.17542	−	11.2386i	0.152465	−	0.410376i
$751$	9.25320	−	16.0270i	0.337654	−	0.584834i	−0.646337	−	0.763052i	$-0.723700\pi$
$751$	9.25320	−	16.0270i	0.337654	−	0.584834i	0.983991	+	0.178218i	$0.0570332\pi$
$752$	−3.57446	+	13.3061i	−0.130347	+	0.485225i
$753$	−10.0626	−	6.19589i	−0.366700	−	0.225791i
$754$	−5.29347	−	26.6342i	−0.192777	−	0.969962i
$755$	1.08970	+	0.451368i	0.0396582	+	0.0164270i
$756$	−30.5026	+	14.2984i	−1.10937	+	0.520027i
$757$	19.5190	+	47.1230i	0.709430	+	1.71272i	0.701420	+	0.712748i	$0.252550\pi$
$757$	19.5190	+	47.1230i	0.709430	+	1.71272i	0.00801046	+	0.999968i	$0.497450\pi$
$758$	8.99399	−	45.1782i	0.326676	−	1.64095i
$759$	37.8130	−	8.99288i	1.37252	−	0.326421i
$760$	18.8192	+	16.5199i	0.682644	+	0.599241i
$761$	15.5130	−	4.15670i	0.562346	−	0.150680i	0.0335620	−	0.999437i	$-0.489315\pi$
$761$	15.5130	−	4.15670i	0.562346	−	0.150680i	0.528784	+	0.848757i	$0.322648\pi$
$762$	1.86026	−	0.0688215i	0.0673903	−	0.00249314i
$763$	−13.3970	+	17.4593i	−0.485003	+	0.632068i
$764$	14.7838	−	19.2540i	0.534861	−	0.696584i
$765$	−17.5680	+	36.4314i	−0.635171	+	1.31718i
$766$	−30.1067	+	14.8410i	−1.08780	+	0.536228i
$767$	2.95259	+	5.11404i	0.106612	+	0.184657i
$768$	−22.4755	+	16.2127i	−0.811015	+	0.585026i
$769$	−0.485057	+	0.840144i	−0.0174916	+	0.0302964i	−0.874639	−	0.484775i	$-0.838901\pi$
$769$	−0.485057	+	0.840144i	−0.0174916	+	0.0302964i	0.857147	+	0.515072i	$0.172235\pi$
$770$	−5.25497	+	79.9802i	−0.189376	+	2.88228i
$771$	4.96062	+	48.1851i	0.178652	+	1.73534i
$772$	7.44960	+	0.983174i	0.268117	+	0.0353852i
$773$	11.5933	+	27.9886i	0.416980	+	1.00668i	0.983218	+	0.182437i	$0.0583986\pi$
$773$	11.5933	+	27.9886i	0.416980	+	1.00668i	−0.566237	+	0.824242i	$0.691601\pi$
$774$	3.35510	−	0.0290788i	0.120597	−	0.00104522i
$775$	−9.51072	−	9.51072i	−0.341635	−	0.341635i
$776$	5.20059	−	1.76259i	0.186690	−	0.0632733i
$777$	8.74940	−	8.26749i	0.313883	−	0.296594i
$778$	7.80663	−	2.64861i	0.279881	−	0.0949572i
$779$	−1.12605	−	0.148247i	−0.0403448	−	0.00531149i
$780$	−1.26016	+	44.0024i	−0.0451208	+	1.57554i
$781$	6.45065	+	48.9975i	0.230822	+	1.75327i
$782$	−23.1711	−	7.86965i	−0.828597	−	0.281418i
$783$	−9.60811	−	20.4799i	−0.343366	−	0.731892i
$784$	13.5557	−	3.62298i	0.484131	−	0.129392i
$785$	20.4451	+	35.4120i	0.729717	+	1.26391i
$786$	−11.8721	+	9.82803i	−0.423465	+	0.350554i
$787$	−2.22969	−	2.90579i	−0.0794799	−	0.103580i	0.751921	−	0.659253i	$-0.229127\pi$
$787$	−2.22969	−	2.90579i	−0.0794799	−	0.103580i	−0.831401	+	0.555673i	$0.812461\pi$
$788$	32.9731	−	32.9521i	1.17462	−	1.17387i
$789$	0.172816	+	0.453085i	0.00615240	+	0.0161302i
$790$	11.1543	−	56.0299i	0.396853	−	1.99345i
$791$	1.01706	+	1.01706i	0.0361625	+	0.0361625i
$792$	−47.4064	+	20.1017i	−1.68451	+	0.714281i
$793$	7.92956	−	7.92956i	0.281587	−	0.281587i
$794$	14.8561	+	22.2414i	0.527223	+	0.789317i
$795$	27.6355	+	22.4765i	0.980130	+	0.797159i
$796$	14.6370	−	35.3051i	0.518795	−	1.25135i
$797$	3.87216	−	2.97121i	0.137159	−	0.105246i	−0.537903	−	0.843007i	$-0.680783\pi$
$797$	3.87216	−	2.97121i	0.137159	−	0.105246i	0.675062	+	0.737761i	$0.264117\pi$
$798$	14.1275	−	19.8931i	0.500108	−	0.704208i
$799$	13.9585	−	8.05893i	0.493815	−	0.285104i
$800$	18.6334	+	1.23621i	0.658790	+	0.0437065i
$801$	−8.42486	+	4.24753i	−0.297678	+	0.150079i
$802$	−15.9836	+	7.87909i	−0.564402	+	0.278220i
$803$	−96.3094	+	12.6794i	−3.39869	+	0.447445i
$804$	−3.58548	−	34.9370i	−0.126450	−	1.23213i
$805$	−4.50794	+	34.2412i	−0.158884	+	1.20684i
$806$	−22.7910	−	11.2438i	−0.802778	−	0.396046i
$807$	−8.92976	+	2.12372i	−0.314342	+	0.0747585i
$808$	23.4254	+	26.7373i	0.824104	+	0.940617i
$809$	−28.0570	+	28.0570i	−0.986431	+	0.986431i	−0.999909	−	0.0134785i	$-0.995710\pi$
$809$	−28.0570	+	28.0570i	−0.986431	+	0.986431i	0.0134785	+	0.999909i	$0.495710\pi$
$810$	7.78228	+	35.8361i	0.273441	+	1.25915i
$811$	29.9705	−	12.4142i	1.05240	−	0.435920i	0.211655	−	0.977344i	$-0.432115\pi$
$811$	29.9705	−	12.4142i	1.05240	−	0.435920i	0.840750	+	0.541424i	$0.182115\pi$
$812$	7.29643	+	27.2654i	0.256054	+	0.956828i
$813$	22.9250	+	31.6954i	0.804014	+	1.11161i
$814$	13.8356	−	12.1296i	0.484937	−	0.425141i
$815$	19.3547	+	11.1744i	0.677966	+	0.391424i
$816$	32.0061	+	5.16017i	1.12044	+	0.180642i
$817$	−2.10455	+	1.21506i	−0.0736288	+	0.0425096i
$818$	14.1710	−	41.7247i	0.495479	−	1.45887i
$819$	42.7734	−	3.18289i	1.49462	−	0.111219i
$820$	−1.84483	+	1.06433i	−0.0644241	+	0.0371679i
$821$	22.2068	+	17.0399i	0.775022	+	0.594695i	0.918712	−	0.394927i	$-0.129230\pi$
$821$	22.2068	+	17.0399i	0.775022	+	0.594695i	−0.143690	+	0.989623i	$0.545897\pi$
$822$	−7.82653	+	34.2238i	−0.272981	+	1.19369i
$823$	2.78458	+	10.3922i	0.0970645	+	0.362250i	0.997324	−	0.0731033i	$-0.0232903\pi$
$823$	2.78458	+	10.3922i	0.0970645	+	0.362250i	−0.900260	+	0.435353i	$0.856624\pi$
$824$	0.579140	+	8.90117i	0.0201753	+	0.310087i
$825$	33.2482	+	9.92572i	1.15755	+	0.345569i
$826$	−3.40916	−	5.10392i	−0.118620	−	0.177588i
$827$	13.0122	−	5.38984i	0.452480	−	0.187423i	−0.144792	−	0.989462i	$-0.546251\pi$
$827$	13.0122	−	5.38984i	0.452480	−	0.187423i	0.597272	+	0.802039i	$0.296251\pi$
$828$	−20.9484	+	7.31034i	−0.728006	+	0.254052i
$829$	11.6899	−	28.2220i	0.406009	−	0.980191i	−0.580169	−	0.814496i	$-0.697013\pi$
$829$	11.6899	−	28.2220i	0.406009	−	0.980191i	0.986177	−	0.165695i	$-0.0529867\pi$
$830$	−40.2217	+	60.1752i	−1.39611	+	2.08871i
$831$	22.9422	+	0.649709i	0.795856	+	0.0225382i
$832$	34.0909	−	9.09971i	1.18189	−	0.315476i
$833$	−14.2154	−	8.20726i	−0.492534	−	0.284365i
$834$	−33.1010	−	3.11806i	−1.14620	−	0.107970i
$835$	5.64783	+	42.8995i	0.195451	+	1.48460i
$836$	22.7130	−	29.5807i	0.785547	−	1.02307i
$837$	−20.6797	−	4.53403i	−0.714795	−	0.156719i
$838$	−0.410143	−	6.27289i	−0.0141682	−	0.216693i
$839$	−23.1112	−	6.19264i	−0.797889	−	0.213794i	−0.163232	−	0.986588i	$-0.552192\pi$
$839$	−23.1112	−	6.19264i	−0.797889	−	0.213794i	−0.634657	+	0.772794i	$0.718859\pi$
$840$	−1.67698	−	45.7237i	−0.0578614	−	1.57762i
$841$	9.70426	−	2.60025i	0.334630	−	0.0896638i
$842$	11.8543	+	34.9399i	0.408525	+	1.20411i
$843$	25.3623	−	9.67370i	0.873525	−	0.333180i
$844$	3.32921	−	5.76213i	0.114596	−	0.198341i
$845$	7.11500	−	17.1771i	0.244763	−	0.590911i
$846$	5.47518	−	13.5492i	0.188241	−	0.465832i
$847$	83.7159			2.87651
$848$	10.9434	−	26.3721i	0.375798	−	0.905623i
$849$	0.617209	+	1.14256i	0.0211826	+	0.0392125i
$850$	−14.4014	−	16.4269i	−0.493964	−	0.563439i
$851$	6.28985	−	4.82637i	0.215613	−	0.165446i
$852$	−6.51853	−	27.4478i	−0.223321	−	0.940345i
$853$	26.1872	−	34.1278i	0.896631	−	1.16851i	−0.0883910	−	0.996086i	$-0.528172\pi$
$853$	26.1872	−	34.1278i	0.896631	−	1.16851i	0.985022	−	0.172427i	$-0.0551608\pi$
$854$	−7.68661	+	8.76208i	−0.263030	+	0.299832i
$855$	−17.6880	−	19.8138i	−0.604918	−	0.677618i
$856$	−14.2364	+	2.82473i	−0.486591	+	0.0965472i
$857$	6.49577	−	24.2426i	0.221891	−	0.828110i	−0.761735	−	0.647889i	$-0.775652\pi$
$857$	6.49577	−	24.2426i	0.221891	−	0.828110i	0.983626	−	0.180221i	$-0.0576813\pi$
$858$	65.5160	−	2.42380i	2.23668	−	0.0827472i
$859$	21.5218	+	2.83339i	0.734313	+	0.0966741i	0.488403	−	0.872618i	$-0.337580\pi$
$859$	21.5218	+	2.83339i	0.734313	+	0.0966741i	0.245910	+	0.969293i	$0.420913\pi$
$860$	−1.74526	+	4.20963i	−0.0595128	+	0.143547i
$861$	1.21620	+	1.68148i	0.0414479	+	0.0573047i
$862$	3.03910	−	4.54676i	0.103512	−	0.154863i
$863$	7.05846			0.240273			0.120136	−	0.992757i	$-0.461667\pi$
$863$	7.05846			0.240273			0.120136	+	0.992757i	$0.461667\pi$
$864$	25.7487	−	14.1776i	0.875988	−	0.482333i
$865$	−33.4016			−1.13569
$866$	−26.4938	+	39.6370i	−0.900294	+	1.34692i
$867$	−4.97008	−	6.87149i	−0.168793	−	0.233368i
$868$	24.4007	+	10.1162i	0.828215	+	0.343367i
$869$	−84.3564	−	11.1057i	−2.86159	−	0.376736i
$870$	30.7038	−	1.13590i	1.04096	−	0.0385108i
$871$	−11.5734	+	43.1924i	−0.392148	+	1.46352i
$872$	10.6757	−	15.9608i	0.361525	−	0.540501i
$873$	−5.70210	+	1.18663i	−0.192987	+	0.0401613i
$874$	10.5975	−	12.0802i	0.358465	−	0.408620i
$875$	9.65870	−	12.5875i	0.326524	−	0.425534i
$876$	53.9512	−	12.8128i	1.82284	−	0.432904i
$877$	−31.8089	+	24.4079i	−1.07411	+	0.824195i	−0.985125	−	0.171838i	$-0.945029\pi$
$877$	−31.8089	+	24.4079i	−1.07411	+	0.824195i	−0.0889861	+	0.996033i	$0.528363\pi$
$878$	−3.06673	−	3.49806i	−0.103497	−	0.118054i
$879$	−0.911974	−	1.68822i	−0.0307601	−	0.0569423i
$880$	0.0445736	−	69.9367i	0.00150257	−	2.35757i
$881$	−13.6983			−0.461509			−0.230754	−	0.973012i	$-0.574119\pi$
$881$	−13.6983			−0.461509			−0.230754	+	0.973012i	$0.574119\pi$
$882$	−14.7379	+	2.07038i	−0.496252	+	0.0697133i
$883$	20.9737	−	50.6349i	0.705820	−	1.70400i	−0.00436881	−	0.999990i	$-0.501391\pi$
$883$	20.9737	−	50.6349i	0.705820	−	1.70400i	0.710189	−	0.704011i	$-0.248609\pi$
$884$	−35.7404	−	20.6499i	−1.20208	−	0.694531i
$885$	−6.24275	+	2.38111i	−0.209848	+	0.0800402i
$886$	−13.7663	−	40.5754i	−0.462487	−	1.36316i
$887$	27.8064	−	7.45071i	0.933649	−	0.250170i	0.240239	−	0.970714i	$-0.422774\pi$
$887$	27.8064	−	7.45071i	0.933649	−	0.250170i	0.693410	+	0.720543i	$0.256108\pi$
$888$	−7.14977	+	7.69419i	−0.239931	+	0.258200i
$889$	2.37956	+	0.637602i	0.0798080	+	0.0213845i
$890$	−0.836082	−	12.7874i	−0.0280255	−	0.428633i
$891$	52.4970	−	15.0646i	1.75872	−	0.504682i
$892$	15.8807	+	12.1937i	0.531726	+	0.408277i
$893$	1.38154	+	10.4938i	0.0462314	+	0.351163i
$894$	−20.2705	−	1.90944i	−0.677945	−	0.0638612i
$895$	53.2030	+	30.7168i	1.77838	+	1.02675i
$896$	−34.7412	+	11.7498i	−1.16062	+	0.392535i
$897$	28.2379	+	0.799681i	0.942837	+	0.0267006i
$898$	12.4675	−	18.6525i	0.416047	−	0.622443i
$899$	−6.78799	+	16.3877i	−0.226392	+	0.546559i
$900$	−19.4587	−	3.69878i	−0.648625	−	0.123293i
$901$	−30.8592	+	12.7823i	−1.02807	+	0.425840i
$902$	1.76186	+	2.63771i	0.0586634	+	0.0878262i
$903$	4.25466	+	1.27016i	0.141586	+	0.0422683i
$904$	−0.943174	−	0.827940i	−0.0313695	−	0.0275369i
$905$	−1.45403	−	5.42652i	−0.0483336	−	0.180384i
$906$	−0.223547	+	0.977524i	−0.00742684	+	0.0324761i
$907$	40.4805	+	31.0618i	1.34413	+	1.03139i	0.995562	+	0.0941078i	$0.0299998\pi$
$907$	40.4805	+	31.0618i	1.34413	+	1.03139i	0.348572	+	0.937282i	$0.386667\pi$
$908$	15.0872	+	26.1510i	0.500685	+	0.867851i
$909$	−21.2231	−	31.1636i	−0.703926	−	1.03363i
$910$	−18.7344	+	55.1608i	−0.621039	+	1.82856i
$911$	−3.77486	+	2.17941i	−0.125067	+	0.0722072i	−0.561228	−	0.827661i	$-0.689671\pi$
$911$	−3.77486	+	2.17941i	−0.125067	+	0.0722072i	0.436162	+	0.899868i	$0.356338\pi$
$912$	−11.1739	+	18.1213i	−0.370005	+	0.600057i
$913$	93.3551	+	53.8986i	3.08960	+	1.78378i
$914$	1.60789	−	1.40963i	0.0531844	−	0.0466265i
$915$	7.43606	+	10.2809i	0.245828	+	0.339875i
$916$	33.6863	−	9.01472i	1.11303	−	0.297855i
$917$	−18.8436	+	7.80527i	−0.622270	+	0.257753i
$918$	−33.0331	−	9.55048i	−1.09025	−	0.315213i
$919$	−6.43591	+	6.43591i	−0.212301	+	0.212301i	−0.805244	−	0.592943i	$-0.797966\pi$
$919$	−6.43591	+	6.43591i	−0.212301	+	0.212301i	0.592943	+	0.805244i	$0.297966\pi$
$920$	1.98528	−	30.0693i	0.0654528	−	0.991355i
$921$	−24.7542	+	5.88717i	−0.815678	+	0.193989i
$922$	−2.73247	−	1.34805i	−0.0899892	−	0.0443956i
$923$	−4.68837	+	35.6117i	−0.154320	+	1.17217i
$924$	−67.7872	+	6.95682i	−2.23004	+	0.228862i
$925$	7.01715	−	0.923825i	0.230722	−	0.0303752i
$926$	23.2688	−	11.4703i	0.764661	−	0.376938i
$927$	0.535435	−	9.44591i	0.0175860	−	0.310244i
$928$	−7.89764	−	23.3267i	−0.259253	−	0.765737i
$929$	19.6087	−	11.3211i	0.643341	−	0.371433i	−0.142559	−	0.989786i	$-0.545533\pi$
$929$	19.6087	−	11.3211i	0.643341	−	0.371433i	0.785900	+	0.618353i	$0.212200\pi$
$930$	16.6492	−	23.4439i	0.545949	−	0.768756i
$931$	8.55171	−	6.56196i	0.280271	−	0.215060i
$932$	40.9483	+	16.9766i	1.34131	+	0.556088i
$933$	−22.2533	−	18.0991i	−0.728542	−	0.592537i
$934$	27.7864	+	41.5996i	0.909199	+	1.36118i
$935$	−57.8515	+	57.8515i	−1.89195	+	1.89195i
$936$	−37.0626	+	5.19451i	−1.21143	+	0.169788i
$937$	−14.5093	−	14.5093i	−0.473998	−	0.473998i	0.429207	−	0.903206i	$-0.358793\pi$
$937$	−14.5093	−	14.5093i	−0.473998	−	0.473998i	−0.903206	+	0.429207i	$0.858793\pi$
$938$	9.07455	−	45.5829i	0.296295	−	1.48833i
$939$	−1.30366	−	3.41792i	−0.0425435	−	0.111540i
$940$	14.0304	+	14.0393i	0.457621	+	0.457912i
$941$	−3.50418	−	4.56674i	−0.114233	−	0.148871i	0.732737	−	0.680512i	$-0.238242\pi$
$941$	−3.50418	−	4.56674i	−0.114233	−	0.148871i	−0.846970	+	0.531640i	$0.821576\pi$
$942$	−26.7786	+	22.1679i	−0.872493	+	0.722269i
$943$	0.683388	+	1.18366i	0.0222542	+	0.0385454i
$944$	3.25751	+	4.25087i	0.106023	+	0.138354i
$945$	−4.11696	+	48.3550i	−0.133925	+	1.57299i
$946$	6.42643	+	2.18262i	0.208941	+	0.0709632i
$947$	1.94795	+	14.7961i	0.0632998	+	0.480810i	0.993507	+	0.113774i	$0.0362940\pi$
$947$	1.94795	+	14.7961i	0.0632998	+	0.480810i	−0.930207	+	0.367036i	$0.880373\pi$
$948$	48.5498	+	1.39038i	1.57682	+	0.0451576i
$949$	−69.9983	−	9.21545i	−2.27224	−	0.299146i
$950$	13.5853	−	4.60918i	0.440766	−	0.149542i
$951$	−22.0195	+	20.8067i	−0.714032	+	0.674704i
$952$	38.4694	+	18.9939i	1.24680	+	0.615595i
$953$	−17.8843	−	17.8843i	−0.579330	−	0.579330i	0.355389	−	0.934719i	$-0.384348\pi$
$953$	−17.8843	−	17.8843i	−0.579330	−	0.579330i	−0.934719	+	0.355389i	$0.884348\pi$
$954$	−14.9144	+	26.3574i	−0.482872	+	0.853354i
$955$	−13.3826	−	32.3084i	−0.433050	−	1.04548i
$956$	−4.50617	+	34.1437i	−0.145740	+	1.10429i
$957$	−4.68612	−	45.5187i	−0.151481	−	1.47141i
$958$	0.653976	−	9.95345i	0.0211290	−	0.321581i
$959$	−23.2300	+	40.2355i	−0.750136	+	1.29927i
$960$	4.05045	+	39.7168i	0.130728	+	1.28185i
$961$	−7.19986	−	12.4705i	−0.232254	−	0.402275i
$962$	11.9949	−	5.91283i	0.386730	−	0.190637i
$963$	15.3519	−	1.14238i	0.494709	−	0.0368127i
$964$	20.0436	+	15.3902i	0.645562	+	0.495684i
$965$	6.58977	−	8.58795i	0.212132	−	0.276456i
$966$	−29.3419	+	1.08552i	−0.944061	+	0.0349260i
$967$	27.7620	−	7.43881i	0.892767	−	0.239216i	0.216859	−	0.976203i	$-0.430419\pi$
$967$	27.7620	−	7.43881i	0.892767	−	0.239216i	0.675907	+	0.736987i	$0.263752\pi$
$968$	−72.8918	+	4.74259i	−2.34283	+	0.152433i
$969$	24.2293	−	5.76234i	0.778357	−	0.185113i
$970$	1.54450	−	7.75827i	0.0495909	−	0.249103i
$971$	3.64747	+	8.80578i	0.117053	+	0.282591i	0.971537	−	0.236886i	$-0.0761268\pi$
$971$	3.64747	+	8.80578i	0.117053	+	0.282591i	−0.854484	+	0.519477i	$0.826127\pi$
$972$	−28.9330	+	11.6140i	−0.928025	+	0.372518i
$973$	−40.6497	−	16.8376i	−1.30317	−	0.539790i
$974$	0.0497055	+	0.250095i	0.00159267	+	0.00801355i
$975$	21.4745	+	13.2226i	0.687733	+	0.423463i
$976$	6.19638	−	8.06463i	0.198341	−	0.258143i
$977$	23.9495	−	41.4818i	0.766214	−	1.32712i	−0.173388	−	0.984854i	$-0.555472\pi$
$977$	23.9495	−	41.4818i	0.766214	−	1.32712i	0.939602	−	0.342268i	$-0.111195\pi$
$978$	−6.61716	+	17.8108i	−0.211594	+	0.569528i
$979$	−18.9219	+	2.49112i	−0.604748	+	0.0796165i
$980$	5.23789	−	19.5232i	0.167318	−	0.623645i
$981$	−13.2931	+	15.4305i	−0.424416	+	0.492658i
$982$	21.7842	+	19.1104i	0.695162	+	0.609837i
$983$	1.15926	−	4.32640i	0.0369745	−	0.137991i	−0.944971	−	0.327153i	$-0.893911\pi$
$983$	1.15926	−	4.32640i	0.0369745	−	0.137991i	0.981946	+	0.189163i	$0.0605773\pi$
$984$	−1.15421	−	1.39517i	−0.0367947	−	0.0444764i
$985$	−17.3809	−	64.8665i	−0.553803	−	2.06682i
$986$	−12.7465	+	25.8369i	−0.405930	+	0.822814i
$987$	12.2026	−	15.0035i	0.388414	−	0.477566i
$988$	21.5100	−	16.4943i	0.684323	−	0.524753i
$989$	2.70180	+	1.11912i	0.0859123	+	0.0355860i
$990$	−9.04456	+	73.6256i	−0.287455	+	2.33998i
$991$			61.1681i			1.94307i	0.236901	+	0.971534i	$0.423868\pi$
$991$			61.1681i			1.94307i	−0.236901	+	0.971534i	$0.576132\pi$
$992$	−21.8189	−	7.42591i	−0.692751	−	0.235773i
$993$	−0.420377	+	14.8441i	−0.0133403	+	0.471065i
$994$	2.44769	−	37.2535i	0.0776359	−	1.18161i
$995$	−33.5171	−	43.6803i	−1.06256	−	1.38476i
$996$	−56.1536	−	25.1663i	−1.77930	−	0.797424i
$997$	−45.7959	−	35.1404i	−1.45037	−	1.11291i	−0.972064	−	0.234716i	$-0.924584\pi$
$997$	−45.7959	−	35.1404i	−1.45037	−	1.11291i	−0.478307	−	0.878193i	$-0.658749\pi$
$998$	−1.03605	−	15.8458i	−0.0327957	−	0.501590i
$999$	8.51737	−	7.18082i	0.269478	−	0.227191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.275.9	yes	368
3.2	odd	2		864.2.bn.a.179.38		368
9.2	odd	6	inner	288.2.bf.a.83.25	yes	368
9.7	even	3		864.2.bn.a.467.22		368
32.27	odd	8	inner	288.2.bf.a.59.25	✓	368
96.59	even	8		864.2.bn.a.827.22		368
288.155	even	24	inner	288.2.bf.a.155.9	yes	368
288.187	odd	24		864.2.bn.a.251.38		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.59.25	✓	368	32.27	odd	8	inner
288.2.bf.a.83.25	yes	368	9.2	odd	6	inner
288.2.bf.a.155.9	yes	368	288.155	even	24	inner
288.2.bf.a.275.9	yes	368	1.1	even	1	trivial
864.2.bn.a.179.38		368	3.2	odd	2
864.2.bn.a.251.38		368	288.187	odd	24
864.2.bn.a.467.22		368	9.7	even	3
864.2.bn.a.827.22		368	96.59	even	8

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17575 - 0.785882i) q^{2} +(-1.01508 - 1.40343i) q^{3} +(0.764778 + 1.84800i) q^{4} +(2.85653 + 0.376069i) q^{5} +(0.0905582 + 2.44782i) q^{6} +(-0.838984 + 3.13113i) q^{7} +(0.553125 - 2.77382i) q^{8} +(-0.939208 + 2.84919i) q^{9} +O(q^{10})\)	\(q+(-1.17575 - 0.785882i) q^{2} +(-1.01508 - 1.40343i) q^{3} +(0.764778 + 1.84800i) q^{4} +(2.85653 + 0.376069i) q^{5} +(0.0905582 + 2.44782i) q^{6} +(-0.838984 + 3.13113i) q^{7} +(0.553125 - 2.77382i) q^{8} +(-0.939208 + 2.84919i) q^{9} +(-3.06302 - 2.68706i) q^{10} +(-3.69421 + 4.81439i) q^{11} +(1.81722 - 2.94919i) q^{12} +(-3.49913 + 2.68498i) q^{13} +(3.44714 - 3.02209i) q^{14} +(-2.37183 - 4.39067i) q^{15} +(-2.83023 + 2.82662i) q^{16} +4.67934 q^{17} +(3.34340 - 2.61183i) q^{18} +(-1.17593 + 2.83895i) q^{19} +(1.48963 + 5.56649i) q^{20} +(5.24595 - 2.00091i) q^{21} +(8.12702 - 2.75731i) q^{22} +(3.57188 - 0.957081i) q^{23} +(-4.45431 + 2.03939i) q^{24} +(3.18871 + 0.854412i) q^{25} +(6.22418 - 0.406959i) q^{26} +(4.95200 - 1.57406i) q^{27} +(-6.42797 + 0.844175i) q^{28} +(-0.568252 - 4.31631i) q^{29} +(-0.661866 + 7.02631i) q^{30} +(-3.52849 - 2.03717i) q^{31} +(5.54904 - 1.09918i) q^{32} +(10.5066 + 0.297540i) q^{33} +(-5.50174 - 3.67741i) q^{34} +(-3.57410 + 8.62865i) q^{35} +(-5.98360 + 0.443340i) q^{36} +(1.98078 - 0.820466i) q^{37} +(3.61369 - 2.41376i) q^{38} +(7.32008 + 2.18529i) q^{39} +(2.62316 - 7.71547i) q^{40} +(0.0956623 + 0.357017i) q^{41} +(-7.74041 - 1.77013i) q^{42} +(0.627411 + 0.481429i) q^{43} +(-11.7223 - 3.14498i) q^{44} +(-3.75437 + 7.78559i) q^{45} +(-4.95179 - 1.68179i) q^{46} +(2.98300 - 1.72224i) q^{47} +(6.83988 + 1.10276i) q^{48} +(-3.03790 - 1.75394i) q^{49} +(-3.07766 - 3.51052i) q^{50} +(-4.74992 - 6.56711i) q^{51} +(-7.63791 - 4.41300i) q^{52} +(-6.59478 + 2.73165i) q^{53} +(-7.05935 - 2.04099i) q^{54} +(-12.3632 + 12.3632i) q^{55} +(8.22112 + 4.05909i) q^{56} +(5.17793 - 1.23144i) q^{57} +(-2.72399 + 5.52148i) q^{58} +(0.174758 - 1.32742i) q^{59} +(6.30005 - 7.74104i) q^{60} +(-2.52080 + 0.331870i) q^{61} +(2.54764 + 5.16818i) q^{62} +(-8.13321 - 5.33121i) q^{63} +(-7.38811 - 3.06853i) q^{64} +(-11.0051 + 6.35381i) q^{65} +(-12.1193 - 8.60677i) q^{66} +(8.04333 - 6.17187i) q^{67} +(3.57866 + 8.64743i) q^{68} +(-4.96895 - 4.04134i) q^{69} +(10.9834 - 7.33632i) q^{70} +(5.75858 - 5.75858i) q^{71} +(7.38363 + 4.18115i) q^{72} +(11.3191 + 11.3191i) q^{73} +(-2.97369 - 0.591997i) q^{74} +(-2.03770 - 5.34241i) q^{75} +(-6.14572 - 0.00195846i) q^{76} +(-11.9751 - 15.6063i) q^{77} +(-6.88921 - 8.32208i) q^{78} +(7.01043 + 12.1424i) q^{79} +(-9.14764 + 7.00997i) q^{80} +(-7.23578 - 5.35196i) q^{81} +(0.168098 - 0.494942i) q^{82} +(-2.31862 - 17.6117i) q^{83} +(7.70967 + 8.16428i) q^{84} +(13.3667 + 1.75976i) q^{85} +(-0.359332 - 1.05911i) q^{86} +(-5.48079 + 5.17891i) q^{87} +(11.3109 + 12.9100i) q^{88} +(2.22386 + 2.22386i) q^{89} +(10.5328 - 6.20342i) q^{90} +(-5.47130 - 13.2089i) q^{91} +(4.50038 + 5.86888i) q^{92} +(0.722690 + 7.01987i) q^{93} +(-4.86074 - 0.319367i) q^{94} +(-4.42673 + 7.66732i) q^{95} +(-7.17535 - 6.67190i) q^{96} +(0.970710 + 1.68132i) q^{97} +(2.19343 + 4.44963i) q^{98} +(-10.2475 - 15.0472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

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