LMFDB - Embedded newform 722.2.e.m.415.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, not 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			415.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	722.415
Dual form			722.2.e.m.595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(1.76604 - 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.347296 - 1.96962i) q^{5} +(1.76604 + 0.642788i) q^{6} +(-2.53209 - 4.38571i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.407604 - 0.342020i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(1.76604 - 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.347296 - 1.96962i) q^{5} +(1.76604 + 0.642788i) q^{6} +(-2.53209 - 4.38571i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.407604 - 0.342020i) q^{9} +(1.53209 - 1.28558i) q^{10} +(0.705737 - 1.22237i) q^{11} +(0.939693 + 1.62760i) q^{12} +(1.22668 + 0.446476i) q^{13} +(0.879385 - 4.98724i) q^{14} +(-0.652704 - 3.70167i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.83022 + 1.53574i) q^{17} +0.532089 q^{18} +2.00000 q^{20} +(-7.29086 - 6.11776i) q^{21} +(1.32635 - 0.482753i) q^{22} +(-0.532089 - 3.01763i) q^{23} +(-0.326352 + 1.85083i) q^{24} +(0.939693 + 0.342020i) q^{25} +(0.652704 + 1.13052i) q^{26} +(-2.31908 + 4.01676i) q^{27} +(3.87939 - 3.25519i) q^{28} +(6.47565 - 5.43372i) q^{29} +(1.87939 - 3.25519i) q^{30} +(-0.184793 - 0.320070i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.460637 - 2.61240i) q^{33} +(0.414878 + 2.35289i) q^{34} +(-9.51754 + 3.46410i) q^{35} +(0.407604 + 0.342020i) q^{36} +4.82295 q^{37} +2.45336 q^{39} +(1.53209 + 1.28558i) q^{40} +(1.43969 - 0.524005i) q^{41} +(-1.65270 - 9.37295i) q^{42} +(-0.131759 + 0.747243i) q^{43} +(1.32635 + 0.482753i) q^{44} +(-0.532089 - 0.921605i) q^{45} +(1.53209 - 2.65366i) q^{46} +(-7.82295 + 6.56423i) q^{47} +(-1.43969 + 1.20805i) q^{48} +(-9.32295 + 16.1478i) q^{49} +(0.500000 + 0.866025i) q^{50} +(4.21941 + 1.53574i) q^{51} +(-0.226682 + 1.28558i) q^{52} +(0.290859 + 1.64955i) q^{53} +(-4.35844 + 1.58634i) q^{54} +(-2.16250 - 1.81456i) q^{55} +5.06418 q^{56} +8.45336 q^{58} +(0.549163 + 0.460802i) q^{59} +(3.53209 - 1.28558i) q^{60} +(1.69459 + 9.61051i) q^{61} +(0.0641778 - 0.363970i) q^{62} +(-2.53209 - 0.921605i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.30541 - 2.26103i) q^{65} +(2.03209 - 1.70513i) q^{66} +(-1.07532 + 0.902302i) q^{67} +(-1.19459 + 2.06910i) q^{68} +(-2.87939 - 4.98724i) q^{69} +(-9.51754 - 3.46410i) q^{70} +(-1.10607 + 6.27282i) q^{71} +(0.0923963 + 0.524005i) q^{72} +(4.28446 - 1.55942i) q^{73} +(3.69459 + 3.10013i) q^{74} +1.87939 q^{75} -7.14796 q^{77} +(1.87939 + 1.57699i) q^{78} +(2.10607 - 0.766546i) q^{79} +(0.347296 + 1.96962i) q^{80} +(-1.79086 + 10.1565i) q^{81} +(1.43969 + 0.524005i) q^{82} +(1.99273 + 3.45150i) q^{83} +(4.75877 - 8.24243i) q^{84} +(3.66044 - 3.07148i) q^{85} +(-0.581252 + 0.487728i) q^{86} +(7.94356 - 13.7587i) q^{87} +(0.705737 + 1.22237i) q^{88} +(10.0039 + 3.64111i) q^{89} +(0.184793 - 1.04801i) q^{90} +(-1.14796 - 6.51038i) q^{91} +(2.87939 - 1.04801i) q^{92} +(-0.532089 - 0.446476i) q^{93} -10.2121 q^{94} -1.87939 q^{96} +(-1.17365 - 0.984808i) q^{97} +(-17.5214 + 6.37727i) q^{98} +(-0.130415 - 0.739620i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} + 6 q^{6} - 6 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^3 + 6 * q^6 - 6 * q^7 - 3 * q^8 + 6 * q^9	$ 6 q + 6 q^{3} + 6 q^{6} - 6 q^{7} - 3 q^{8} + 6 q^{9} - 6 q^{11} - 6 q^{13} - 6 q^{14} - 6 q^{15} - 12 q^{17} - 6 q^{18} + 12 q^{20} - 12 q^{21} + 9 q^{22} + 6 q^{23} - 3 q^{24} + 6 q^{26} + 3 q^{27} + 12 q^{28} + 6 q^{31} - 6 q^{33} + 24 q^{34} - 12 q^{35} + 6 q^{36} - 12 q^{37} - 12 q^{39} + 3 q^{41} - 12 q^{42} - 6 q^{43} + 9 q^{44} + 6 q^{45} - 6 q^{47} - 3 q^{48} - 15 q^{49} + 3 q^{50} - 6 q^{51} + 12 q^{52} - 30 q^{53} - 18 q^{54} - 18 q^{55} + 12 q^{56} + 24 q^{58} + 15 q^{59} + 12 q^{60} + 6 q^{61} - 18 q^{62} - 6 q^{63} - 3 q^{64} + 12 q^{65} + 3 q^{66} + 18 q^{67} - 3 q^{68} - 6 q^{69} - 12 q^{70} + 18 q^{71} - 3 q^{72} + 33 q^{73} + 18 q^{74} - 12 q^{77} - 12 q^{79} + 21 q^{81} + 3 q^{82} - 6 q^{83} + 6 q^{84} - 24 q^{85} - 6 q^{86} + 18 q^{87} - 6 q^{88} + 36 q^{89} - 6 q^{90} + 24 q^{91} + 6 q^{92} + 6 q^{93} - 12 q^{94} - 6 q^{97} - 36 q^{98} - 15 q^{99}+O(q^{100}) $ 6 * q + 6 * q^3 + 6 * q^6 - 6 * q^7 - 3 * q^8 + 6 * q^9 - 6 * q^11 - 6 * q^13 - 6 * q^14 - 6 * q^15 - 12 * q^17 - 6 * q^18 + 12 * q^20 - 12 * q^21 + 9 * q^22 + 6 * q^23 - 3 * q^24 + 6 * q^26 + 3 * q^27 + 12 * q^28 + 6 * q^31 - 6 * q^33 + 24 * q^34 - 12 * q^35 + 6 * q^36 - 12 * q^37 - 12 * q^39 + 3 * q^41 - 12 * q^42 - 6 * q^43 + 9 * q^44 + 6 * q^45 - 6 * q^47 - 3 * q^48 - 15 * q^49 + 3 * q^50 - 6 * q^51 + 12 * q^52 - 30 * q^53 - 18 * q^54 - 18 * q^55 + 12 * q^56 + 24 * q^58 + 15 * q^59 + 12 * q^60 + 6 * q^61 - 18 * q^62 - 6 * q^63 - 3 * q^64 + 12 * q^65 + 3 * q^66 + 18 * q^67 - 3 * q^68 - 6 * q^69 - 12 * q^70 + 18 * q^71 - 3 * q^72 + 33 * q^73 + 18 * q^74 - 12 * q^77 - 12 * q^79 + 21 * q^81 + 3 * q^82 - 6 * q^83 + 6 * q^84 - 24 * q^85 - 6 * q^86 + 18 * q^87 - 6 * q^88 + 36 * q^89 - 6 * q^90 + 24 * q^91 + 6 * q^92 + 6 * q^93 - 12 * q^94 - 6 * q^97 - 36 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	1.76604	−	0.642788i	1.01963	−	0.371114i	0.222504	−	0.974932i	$-0.428577\pi$
$3$	1.76604	−	0.642788i	1.01963	−	0.371114i	0.797122	+	0.603818i	$0.206355\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.347296	−	1.96962i	0.155316	−	0.880839i	−0.803181	−	0.595735i	$-0.796861\pi$
$5$	0.347296	−	1.96962i	0.155316	−	0.880839i	0.958497	−	0.285104i	$-0.0920281\pi$
$6$	1.76604	+	0.642788i	0.720985	+	0.262417i
$7$	−2.53209	−	4.38571i	−0.957040	−	1.65764i	−0.729630	−	0.683842i	$-0.760308\pi$
$7$	−2.53209	−	4.38571i	−0.957040	−	1.65764i	−0.227410	−	0.973799i	$-0.573026\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.407604	−	0.342020i	0.135868	−	0.114007i
$10$	1.53209	−	1.28558i	0.484489	−	0.406535i
$11$	0.705737	−	1.22237i	0.212788	−	0.368559i	−0.739798	−	0.672829i	$-0.765079\pi$
$11$	0.705737	−	1.22237i	0.212788	−	0.368559i	0.952586	+	0.304270i	$0.0984124\pi$
$12$	0.939693	+	1.62760i	0.271266	+	0.469846i
$13$	1.22668	+	0.446476i	0.340220	+	0.123830i	0.506479	−	0.862252i	$-0.330947\pi$
$13$	1.22668	+	0.446476i	0.340220	+	0.123830i	−0.166259	+	0.986082i	$0.553169\pi$
$14$	0.879385	−	4.98724i	0.235026	−	1.33290i
$15$	−0.652704	−	3.70167i	−0.168527	−	0.955766i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	1.83022	+	1.53574i	0.443894	+	0.372471i	0.837164	−	0.546952i	$-0.184212\pi$
$17$	1.83022	+	1.53574i	0.443894	+	0.372471i	−0.393270	+	0.919423i	$0.628656\pi$
$18$	0.532089			0.125415
$19$		0			0
$19$		0			0
$20$	2.00000			0.447214
$21$	−7.29086	−	6.11776i	−1.59100	−	1.33500i
$22$	1.32635	−	0.482753i	0.282779	−	0.102923i
$23$	−0.532089	−	3.01763i	−0.110948	−	0.629219i	−0.988677	−	0.150060i	$-0.952053\pi$
$23$	−0.532089	−	3.01763i	−0.110948	−	0.629219i	0.877729	−	0.479158i	$-0.159058\pi$
$24$	−0.326352	+	1.85083i	−0.0666163	+	0.377800i
$25$	0.939693	+	0.342020i	0.187939	+	0.0684040i
$26$	0.652704	+	1.13052i	0.128006	+	0.221712i
$27$	−2.31908	+	4.01676i	−0.446307	+	0.773026i
$28$	3.87939	−	3.25519i	0.733135	−	0.615173i
$29$	6.47565	−	5.43372i	1.20250	−	1.00902i	0.202943	−	0.979191i	$-0.434949\pi$
$29$	6.47565	−	5.43372i	1.20250	−	1.00902i	0.999555	−	0.0298254i	$-0.00949514\pi$
$30$	1.87939	−	3.25519i	0.343127	−	0.594314i
$31$	−0.184793	−	0.320070i	−0.0331897	−	0.0574863i	0.848953	−	0.528468i	$-0.177233\pi$
$31$	−0.184793	−	0.320070i	−0.0331897	−	0.0574863i	−0.882143	+	0.470981i	$0.843900\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	0.460637	−	2.61240i	0.0801866	−	0.454761i
$34$	0.414878	+	2.35289i	0.0711509	+	0.403517i
$35$	−9.51754	+	3.46410i	−1.60876	+	0.585540i
$36$	0.407604	+	0.342020i	0.0679340	+	0.0570034i
$37$	4.82295			0.792888			0.396444	−	0.918059i	$-0.370244\pi$
$37$	4.82295			0.792888			0.396444	+	0.918059i	$0.370244\pi$
$38$		0			0
$39$	2.45336			0.392853
$40$	1.53209	+	1.28558i	0.242245	+	0.203267i
$41$	1.43969	−	0.524005i	0.224842	−	0.0818359i	−0.227143	−	0.973862i	$-0.572938\pi$
$41$	1.43969	−	0.524005i	0.224842	−	0.0818359i	0.451985	+	0.892026i	$0.350716\pi$
$42$	−1.65270	−	9.37295i	−0.255018	−	1.44628i
$43$	−0.131759	+	0.747243i	−0.0200931	+	0.113953i	−0.993205	−	0.116381i	$-0.962871\pi$
$43$	−0.131759	+	0.747243i	−0.0200931	+	0.113953i	0.973112	+	0.230334i	$0.0739819\pi$
$44$	1.32635	+	0.482753i	0.199955	+	0.0727777i
$45$	−0.532089	−	0.921605i	−0.0793191	−	0.137385i
$46$	1.53209	−	2.65366i	0.225894	−	0.391260i
$47$	−7.82295	+	6.56423i	−1.14109	+	0.957492i	−0.999474	−	0.0324293i	$-0.989676\pi$
$47$	−7.82295	+	6.56423i	−1.14109	+	0.957492i	−0.141620	+	0.989921i	$0.545231\pi$
$48$	−1.43969	+	1.20805i	−0.207802	+	0.174366i
$49$	−9.32295	+	16.1478i	−1.33185	+	2.30683i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	4.21941	+	1.53574i	0.590835	+	0.215046i
$52$	−0.226682	+	1.28558i	−0.0314351	+	0.178277i
$53$	0.290859	+	1.64955i	0.0399526	+	0.226582i	0.998246	−	0.0592041i	$-0.0188563\pi$
$53$	0.290859	+	1.64955i	0.0399526	+	0.226582i	−0.958293	+	0.285787i	$0.907745\pi$
$54$	−4.35844	+	1.58634i	−0.593109	+	0.215874i
$55$	−2.16250	−	1.81456i	−0.291592	−	0.244675i
$56$	5.06418			0.676729
$57$		0			0
$58$	8.45336			1.10998
$59$	0.549163	+	0.460802i	0.0714949	+	0.0599914i	0.677835	−	0.735214i	$-0.262918\pi$
$59$	0.549163	+	0.460802i	0.0714949	+	0.0599914i	−0.606340	+	0.795206i	$0.707363\pi$
$60$	3.53209	−	1.28558i	0.455991	−	0.165967i
$61$	1.69459	+	9.61051i	0.216970	+	1.23050i	0.877454	+	0.479660i	$0.159240\pi$
$61$	1.69459	+	9.61051i	0.216970	+	1.23050i	−0.660484	+	0.750840i	$0.729649\pi$
$62$	0.0641778	−	0.363970i	0.00815059	−	0.0462243i
$63$	−2.53209	−	0.921605i	−0.319013	−	0.116111i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.30541	−	2.26103i	0.161916	−	0.280446i
$66$	2.03209	−	1.70513i	0.250133	−	0.209886i
$67$	−1.07532	+	0.902302i	−0.131372	+	0.110234i	−0.706106	−	0.708106i	$-0.749550\pi$
$67$	−1.07532	+	0.902302i	−0.131372	+	0.110234i	0.574734	+	0.818340i	$0.305105\pi$
$68$	−1.19459	+	2.06910i	−0.144866	+	0.250915i
$69$	−2.87939	−	4.98724i	−0.346637	−	0.600393i
$70$	−9.51754	−	3.46410i	−1.13756	−	0.414039i
$71$	−1.10607	+	6.27282i	−0.131266	+	0.744446i	0.846121	+	0.532990i	$0.178932\pi$
$71$	−1.10607	+	6.27282i	−0.131266	+	0.744446i	−0.977387	+	0.211456i	$0.932179\pi$
$72$	0.0923963	+	0.524005i	0.0108890	+	0.0617546i
$73$	4.28446	−	1.55942i	0.501458	−	0.182516i	−0.0788914	−	0.996883i	$-0.525138\pi$
$73$	4.28446	−	1.55942i	0.501458	−	0.182516i	0.580350	+	0.814367i	$0.302916\pi$
$74$	3.69459	+	3.10013i	0.429488	+	0.360383i
$75$	1.87939			0.217013
$76$		0			0
$77$	−7.14796			−0.814585
$78$	1.87939	+	1.57699i	0.212798	+	0.178559i
$79$	2.10607	−	0.766546i	0.236951	−	0.0862431i	−0.220815	−	0.975316i	$-0.570872\pi$
$79$	2.10607	−	0.766546i	0.236951	−	0.0862431i	0.457766	+	0.889073i	$0.348650\pi$
$80$	0.347296	+	1.96962i	0.0388289	+	0.220210i
$81$	−1.79086	+	10.1565i	−0.198984	+	1.12850i
$82$	1.43969	+	0.524005i	0.158987	+	0.0578667i
$83$	1.99273	+	3.45150i	0.218730	+	0.378852i	0.954420	−	0.298467i	$-0.0964752\pi$
$83$	1.99273	+	3.45150i	0.218730	+	0.378852i	−0.735690	+	0.677319i	$0.763142\pi$
$84$	4.75877	−	8.24243i	0.519224	−	0.899323i
$85$	3.66044	−	3.07148i	0.397031	−	0.333149i
$86$	−0.581252	+	0.487728i	−0.0626780	+	0.0525931i
$87$	7.94356	−	13.7587i	0.851639	−	1.47508i
$88$	0.705737	+	1.22237i	0.0752318	+	0.130305i
$89$	10.0039	+	3.64111i	1.06041	+	0.385957i	0.812582	−	0.582847i	$-0.198061\pi$
$89$	10.0039	+	3.64111i	1.06041	+	0.385957i	0.247827	+	0.968804i	$0.420284\pi$
$90$	0.184793	−	1.04801i	0.0194788	−	0.110470i
$91$	−1.14796	−	6.51038i	−0.120338	−	0.682473i
$92$	2.87939	−	1.04801i	0.300197	−	0.109263i
$93$	−0.532089	−	0.446476i	−0.0551750	−	0.0462974i
$94$	−10.2121			−1.05330
$95$		0			0
$96$	−1.87939			−0.191814
$97$	−1.17365	−	0.984808i	−0.119166	−	0.0999921i	0.581257	−	0.813720i	$-0.302561\pi$
$97$	−1.17365	−	0.984808i	−0.119166	−	0.0999921i	−0.700423	+	0.713728i	$0.747005\pi$
$98$	−17.5214	+	6.37727i	−1.76993	+	0.644202i
$99$	−0.130415	−	0.739620i	−0.0131072	−	0.0743346i
$100$	−0.173648	+	0.984808i	−0.0173648	+	0.0984808i
$101$	−8.29086	−	3.01763i	−0.824971	−	0.300265i	−0.105178	−	0.994453i	$-0.533541\pi$
$101$	−8.29086	−	3.01763i	−0.824971	−	0.300265i	−0.719793	+	0.694188i	$0.755763\pi$
$102$	2.24510	+	3.88863i	0.222298	+	0.385031i
$103$	3.57398	−	6.19031i	0.352155	−	0.609950i	−0.634472	−	0.772946i	$-0.718782\pi$
$103$	3.57398	−	6.19031i	0.352155	−	0.609950i	0.986627	+	0.162996i	$0.0521158\pi$
$104$	−1.00000	+	0.839100i	−0.0980581	+	0.0822805i
$105$	−14.5817	+	12.2355i	−1.42303	+	1.19406i
$106$	−0.837496	+	1.45059i	−0.0813448	+	0.140893i
$107$	4.68479	+	8.11430i	0.452896	+	0.784439i	0.998565	−	0.0535622i	$-0.0170576\pi$
$107$	4.68479	+	8.11430i	0.452896	+	0.784439i	−0.545669	+	0.838001i	$0.683724\pi$
$108$	−4.35844	−	1.58634i	−0.419391	−	0.152646i
$109$	1.92127	−	10.8961i	0.184025	−	1.04366i	−0.743177	−	0.669094i	$-0.766682\pi$
$109$	1.92127	−	10.8961i	0.184025	−	1.04366i	0.927202	−	0.374561i	$-0.122207\pi$
$110$	−0.490200	−	2.78006i	−0.0467387	−	0.265068i
$111$	8.51754	−	3.10013i	0.808449	−	0.294251i
$112$	3.87939	+	3.25519i	0.366567	+	0.307587i
$113$	−13.2986			−1.25103			−0.625514	−	0.780213i	$-0.715110\pi$
$113$	−13.2986			−1.25103			−0.625514	+	0.780213i	$0.715110\pi$
$114$		0			0
$115$	−6.12836			−0.571472
$116$	6.47565	+	5.43372i	0.601249	+	0.504508i
$117$	0.652704	−	0.237565i	0.0603425	−	0.0219629i
$118$	0.124485	+	0.705990i	0.0114598	+	0.0649917i
$119$	2.10101	−	11.9154i	0.192600	−	1.09229i
$120$	3.53209	+	1.28558i	0.322434	+	0.117356i
$121$	4.50387	+	7.80093i	0.409443	+	0.709176i
$122$	−4.87939	+	8.45134i	−0.441759	+	0.765149i
$123$	2.20574	−	1.85083i	0.198885	−	0.166884i
$124$	0.283119	−	0.237565i	0.0254248	−	0.0213339i
$125$	6.00000	−	10.3923i	0.536656	−	0.929516i
$126$	−1.34730	−	2.33359i	−0.120027	−	0.207892i
$127$	5.36959	+	1.95437i	0.476474	+	0.173422i	0.569083	−	0.822280i	$-0.307298\pi$
$127$	5.36959	+	1.95437i	0.476474	+	0.173422i	−0.0926090	+	0.995703i	$0.529521\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	0.247626	+	1.40436i	0.0218023	+	0.123647i
$130$	2.45336	−	0.892951i	0.215174	−	0.0783170i
$131$	−7.56805	−	6.35035i	−0.661223	−	0.554832i	0.249230	−	0.968444i	$-0.419823\pi$
$131$	−7.56805	−	6.35035i	−0.661223	−	0.554832i	−0.910453	+	0.413612i	$0.864267\pi$
$132$	2.65270			0.230888
$133$		0			0
$134$	−1.40373			−0.121264
$135$	7.10607	+	5.96270i	0.611593	+	0.513187i
$136$	−2.24510	+	0.817150i	−0.192516	+	0.0700700i
$137$	0.937166	+	5.31493i	0.0800675	+	0.454086i	0.998312	+	0.0580724i	$0.0184954\pi$
$137$	0.937166	+	5.31493i	0.0800675	+	0.454086i	−0.918245	+	0.396013i	$0.870393\pi$
$138$	1.00000	−	5.67128i	0.0851257	−	0.482772i
$139$	2.19846	+	0.800175i	0.186471	+	0.0678700i	0.433568	−	0.901121i	$-0.357254\pi$
$139$	2.19846	+	0.800175i	0.186471	+	0.0678700i	−0.247097	+	0.968991i	$0.579477\pi$
$140$	−5.06418	−	8.77141i	−0.428001	−	0.741320i
$141$	−9.59627	+	16.6212i	−0.808151	+	1.39976i
$142$	−4.87939	+	4.09429i	−0.409469	+	0.343585i
$143$	1.41147	−	1.18437i	0.118033	−	0.0990418i
$144$	−0.266044	+	0.460802i	−0.0221704	+	0.0384002i
$145$	−8.45336	−	14.6417i	−0.702014	−	1.21592i
$146$	4.28446	+	1.55942i	0.354585	+	0.129058i
$147$	−6.08512	+	34.5104i	−0.501892	+	2.84637i
$148$	0.837496	+	4.74968i	0.0688418	+	0.390421i
$149$	13.5030	−	4.91469i	1.10621	−	0.402627i	0.276607	−	0.960983i	$-0.410790\pi$
$149$	13.5030	−	4.91469i	1.10621	−	0.402627i	0.829601	+	0.558356i	$0.188568\pi$
$150$	1.43969	+	1.20805i	0.117550	+	0.0986365i
$151$	−20.8384			−1.69581			−0.847904	−	0.530150i	$-0.822135\pi$
$151$	−20.8384			−1.69581			−0.847904	+	0.530150i	$0.822135\pi$
$152$		0			0
$153$	1.27126			0.102775
$154$	−5.47565	−	4.59462i	−0.441241	−	0.370245i
$155$	−0.694593	+	0.252811i	−0.0557910	+	0.0203063i
$156$	0.426022	+	2.41609i	0.0341091	+	0.193442i
$157$	1.10607	−	6.27282i	0.0882737	−	0.500625i	−0.908328	−	0.418258i	$-0.862641\pi$
$157$	1.10607	−	6.27282i	0.0882737	−	0.500625i	0.996602	−	0.0823673i	$-0.0262481\pi$
$158$	2.10607	+	0.766546i	0.167550	+	0.0609831i
$159$	1.57398	+	2.72621i	0.124825	+	0.216202i
$160$	−1.00000	+	1.73205i	−0.0790569	+	0.136931i
$161$	−11.8871	+	9.97448i	−0.936837	+	0.786099i
$162$	−7.90033	+	6.62916i	−0.620709	+	0.520836i
$163$	−2.36571	+	4.09754i	−0.185297	+	0.320944i	−0.943677	−	0.330869i	$-0.892658\pi$
$163$	−2.36571	+	4.09754i	−0.185297	+	0.320944i	0.758380	+	0.651813i	$0.225991\pi$
$164$	0.766044	+	1.32683i	0.0598180	+	0.103608i
$165$	−4.98545	−	1.81456i	−0.388117	−	0.141263i
$166$	−0.692066	+	3.92490i	−0.0537148	+	0.304632i
$167$	3.00000	+	17.0138i	0.232147	+	1.31657i	0.848540	+	0.529132i	$0.177482\pi$
$167$	3.00000	+	17.0138i	0.232147	+	1.31657i	−0.616393	+	0.787439i	$0.711407\pi$
$168$	8.94356	−	3.25519i	0.690011	−	0.251143i
$169$	−8.65317	−	7.26087i	−0.665628	−	0.558529i
$170$	4.77837			0.366484
$171$		0			0
$172$	−0.758770			−0.0578557
$173$	14.4192	+	12.0992i	1.09627	+	0.919882i	0.997169	−	0.0751952i	$-0.0239580\pi$
$173$	14.4192	+	12.0992i	1.09627	+	0.919882i	0.0991038	+	0.995077i	$0.468402\pi$
$174$	14.9290	−	5.43372i	1.13177	−	0.411929i
$175$	−0.879385	−	4.98724i	−0.0664753	−	0.377000i
$176$	−0.245100	+	1.39003i	−0.0184751	+	0.104778i
$177$	1.26604	+	0.460802i	0.0951617	+	0.0346360i
$178$	5.32295	+	9.21962i	0.398972	+	0.691039i
$179$	6.91400	−	11.9754i	0.516777	−	0.895083i	−0.483034	−	0.875602i	$-0.660465\pi$
$179$	6.91400	−	11.9754i	0.516777	−	0.895083i	0.999810	−	0.0194816i	$-0.00620157\pi$
$180$	0.815207	−	0.684040i	0.0607620	−	0.0509854i
$181$	9.38919	−	7.87846i	0.697893	−	0.585601i	−0.223281	−	0.974754i	$-0.571677\pi$
$181$	9.38919	−	7.87846i	0.697893	−	0.585601i	0.921173	+	0.389153i	$0.127232\pi$
$182$	3.30541	−	5.72513i	0.245013	−	0.424375i
$183$	9.17024	+	15.8833i	0.677884	+	1.17413i
$184$	2.87939	+	1.04801i	0.212271	+	0.0772604i
$185$	1.67499	−	9.49935i	0.123148	−	0.698406i
$186$	−0.120615	−	0.684040i	−0.00884390	−	0.0501563i
$187$	3.16890	−	1.15339i	0.231733	−	0.0843439i
$188$	−7.82295	−	6.56423i	−0.570547	−	0.478746i
$189$	23.4884			1.70853
$190$		0			0
$191$	−20.0993			−1.45433			−0.727166	−	0.686462i	$-0.759163\pi$
$191$	−20.0993			−1.45433			−0.727166	+	0.686462i	$0.759163\pi$
$192$	−1.43969	−	1.20805i	−0.103901	−	0.0871832i
$193$	−15.6789	+	5.70664i	−1.12859	+	0.410773i	−0.837780	−	0.546008i	$-0.816147\pi$
$193$	−15.6789	+	5.70664i	−1.12859	+	0.410773i	−0.290809	+	0.956781i	$0.593925\pi$
$194$	−0.266044	−	1.50881i	−0.0191009	−	0.108326i
$195$	0.852044	−	4.83218i	0.0610161	−	0.346040i
$196$	−17.5214	−	6.37727i	−1.25153	−	0.455519i
$197$	−6.49525	−	11.2501i	−0.462768	−	0.801537i	0.536330	−	0.844008i	$-0.319810\pi$
$197$	−6.49525	−	11.2501i	−0.462768	−	0.801537i	−0.999098	+	0.0424714i	$0.986477\pi$
$198$	0.375515	−	0.650411i	0.0266867	−	0.0462227i
$199$	13.1702	−	11.0511i	0.933614	−	0.783395i	−0.0428488	−	0.999082i	$-0.513643\pi$
$199$	13.1702	−	11.0511i	0.933614	−	0.783395i	0.976463	+	0.215687i	$0.0691989\pi$
$200$	−0.766044	+	0.642788i	−0.0541675	+	0.0454519i
$201$	−1.31908	+	2.28471i	−0.0930406	+	0.161151i
$202$	−4.41147	−	7.64090i	−0.310390	−	0.537612i
$203$	−40.2276	−	14.6417i	−2.82343	−	1.02764i
$204$	−0.779715	+	4.42198i	−0.0545910	+	0.309601i
$205$	−0.532089	−	3.01763i	−0.0371627	−	0.210760i
$206$	6.71688	−	2.44474i	0.467987	−	0.170333i
$207$	−1.24897	−	1.04801i	−0.0868094	−	0.0728418i
$208$	−1.30541			−0.0905137
$209$		0			0
$210$	−19.0351			−1.31355
$211$	−12.3400	−	10.3545i	−0.849522	−	0.712834i	0.110162	−	0.993914i	$-0.464863\pi$
$211$	−12.3400	−	10.3545i	−0.849522	−	0.712834i	−0.959684	+	0.281080i	$0.909307\pi$
$212$	−1.57398	+	0.572881i	−0.108101	+	0.0393456i
$213$	2.07873	+	11.7890i	0.142432	+	0.807772i
$214$	−1.62701	+	9.22724i	−0.111220	+	0.630761i
$215$	1.42602	+	0.519030i	0.0972539	+	0.0353975i
$216$	−2.31908	−	4.01676i	−0.157793	−	0.273306i
$217$	−0.935822	+	1.62089i	−0.0635278	+	0.110033i
$218$	8.47565	−	7.11192i	0.574044	−	0.481680i
$219$	6.56418	−	5.50800i	0.443566	−	0.372196i
$220$	1.41147	−	2.44474i	0.0951616	−	0.164825i
$221$	1.55943	+	2.70101i	0.104899	+	0.181690i
$222$	8.51754	+	3.10013i	0.571660	+	0.208067i
$223$	0.709141	−	4.02174i	0.0474876	−	0.269315i	−0.951814	−	0.306675i	$-0.900784\pi$
$223$	0.709141	−	4.02174i	0.0474876	−	0.269315i	0.999302	+	0.0373595i	$0.0118947\pi$
$224$	0.879385	+	4.98724i	0.0587564	+	0.333224i
$225$	0.500000	−	0.181985i	0.0333333	−	0.0121323i
$226$	−10.1873	−	8.54818i	−0.677650	−	0.568616i
$227$	13.6604			0.906676			0.453338	−	0.891339i	$-0.350233\pi$
$227$	13.6604			0.906676			0.453338	+	0.891339i	$0.350233\pi$
$228$		0			0
$229$	−5.22163			−0.345055			−0.172527	−	0.985005i	$-0.555193\pi$
$229$	−5.22163			−0.345055			−0.172527	+	0.985005i	$0.555193\pi$
$230$	−4.69459	−	3.93923i	−0.309552	−	0.259745i
$231$	−12.6236	+	4.59462i	−0.830572	+	0.302304i
$232$	1.46791	+	8.32494i	0.0963731	+	0.546559i
$233$	−4.69594	+	26.6320i	−0.307641	+	1.74472i	0.303164	+	0.952938i	$0.401957\pi$
$233$	−4.69594	+	26.6320i	−0.307641	+	1.74472i	−0.610805	+	0.791781i	$0.709154\pi$
$234$	0.652704	+	0.237565i	0.0426686	+	0.0155301i
$235$	10.2121	+	17.6879i	0.666166	+	1.15383i
$236$	−0.358441	+	0.620838i	−0.0233325	+	0.0404131i
$237$	3.22668	−	2.70751i	0.209595	−	0.175872i
$238$	9.26857	−	7.77725i	0.600792	−	0.504125i
$239$	0.142903	−	0.247516i	0.00924366	−	0.0160105i	−0.861367	−	0.507984i	$-0.830391\pi$
$239$	0.142903	−	0.247516i	0.00924366	−	0.0160105i	0.870610	+	0.491973i	$0.163724\pi$
$240$	1.87939	+	3.25519i	0.121314	+	0.210122i
$241$	−2.91400	−	1.06061i	−0.187707	−	0.0683199i	0.246456	−	0.969154i	$-0.420734\pi$
$241$	−2.91400	−	1.06061i	−0.187707	−	0.0683199i	−0.434164	+	0.900834i	$0.642956\pi$
$242$	−1.56418	+	8.87089i	−0.100549	+	0.570243i
$243$	0.949493	+	5.38484i	0.0609100	+	0.345438i
$244$	−9.17024	+	3.33770i	−0.587065	+	0.213674i
$245$	28.5672	+	23.9707i	1.82509	+	1.53143i
$246$	2.87939			0.183583
$247$		0			0
$248$	0.369585			0.0234687
$249$	5.73783	+	4.81461i	0.363620	+	0.305113i
$250$	11.2763	−	4.10424i	0.713177	−	0.259575i
$251$	−2.19800	−	12.4655i	−0.138736	−	0.786813i	−0.972185	−	0.234215i	$-0.924748\pi$
$251$	−2.19800	−	12.4655i	−0.138736	−	0.786813i	0.833448	−	0.552597i	$-0.186363\pi$
$252$	0.467911	−	2.65366i	0.0294756	−	0.167165i
$253$	−4.06418	−	1.47924i	−0.255513	−	0.0929990i
$254$	2.85710	+	4.94864i	0.179270	+	0.310505i
$255$	4.49020	−	7.77725i	0.281187	−	0.487031i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−23.2822	+	19.5361i	−1.45231	+	1.21863i	−0.521431	+	0.853294i	$0.674601\pi$
$257$	−23.2822	+	19.5361i	−1.45231	+	1.21863i	−0.930876	+	0.365336i	$0.880954\pi$
$258$	−0.713011	+	1.23497i	−0.0443901	+	0.0768860i
$259$	−12.2121	−	21.1520i	−0.758825	−	1.31432i
$260$	2.45336	+	0.892951i	0.152151	+	0.0553785i
$261$	0.781059	−	4.42961i	0.0483464	−	0.274186i
$262$	−1.71554	−	9.72930i	−0.105986	−	0.601078i
$263$	−20.5817	+	7.49113i	−1.26912	+	0.461923i	−0.886820	−	0.462114i	$-0.847091\pi$
$263$	−20.5817	+	7.49113i	−1.26912	+	0.461923i	−0.382303	+	0.924037i	$0.624869\pi$
$264$	2.03209	+	1.70513i	0.125066	+	0.104943i
$265$	3.34998			0.205788
$266$		0			0
$267$	20.0077			1.22445
$268$	−1.07532	−	0.902302i	−0.0656858	−	0.0551169i
$269$	1.34730	−	0.490376i	0.0821461	−	0.0298987i	−0.300620	−	0.953744i	$-0.597194\pi$
$269$	1.34730	−	0.490376i	0.0821461	−	0.0298987i	0.382766	+	0.923845i	$0.374971\pi$
$270$	1.61081	+	9.13538i	0.0980311	+	0.555962i
$271$	2.80840	−	15.9272i	0.170598	−	0.967510i	−0.772505	−	0.635009i	$-0.780996\pi$
$271$	2.80840	−	15.9272i	0.170598	−	0.967510i	0.943103	−	0.332501i	$-0.107893\pi$
$272$	−2.24510	−	0.817150i	−0.136129	−	0.0495470i
$273$	−6.21213	−	10.7597i	−0.375975	−	0.651209i
$274$	−2.69846	+	4.67388i	−0.163020	+	0.282359i
$275$	1.08125	−	0.907278i	0.0652019	−	0.0547109i
$276$	4.41147	−	3.70167i	0.265540	−	0.222814i
$277$	−5.55438	+	9.62046i	−0.333730	+	0.578038i	−0.983240	−	0.182315i	$-0.941641\pi$
$277$	−5.55438	+	9.62046i	−0.333730	+	0.578038i	0.649510	+	0.760353i	$0.274974\pi$
$278$	1.16978	+	2.02611i	0.0701586	+	0.121518i
$279$	−0.184793	−	0.0672590i	−0.0110632	−	0.00402669i
$280$	1.75877	−	9.97448i	0.105107	−	0.596089i
$281$	0.737826	+	4.18442i	0.0440150	+	0.249622i	0.998874	−	0.0474372i	$-0.0151054\pi$
$281$	0.737826	+	4.18442i	0.0440150	+	0.249622i	−0.954859	+	0.297059i	$0.903994\pi$
$282$	−18.0351	+	6.56423i	−1.07397	+	0.390894i
$283$	−4.17958	−	3.50708i	−0.248450	−	0.208474i	0.510054	−	0.860142i	$-0.329625\pi$
$283$	−4.17958	−	3.50708i	−0.248450	−	0.208474i	−0.758505	+	0.651668i	$0.774070\pi$
$284$	−6.36959			−0.377965
$285$		0			0
$286$	1.84255			0.108952
$287$	−5.94356	−	4.98724i	−0.350837	−	0.294388i
$288$	−0.500000	+	0.181985i	−0.0294628	+	0.0107236i
$289$	−1.96080	−	11.1202i	−0.115341	−	0.654132i
$290$	2.93582	−	16.6499i	0.172397	−	0.977714i
$291$	−2.70574	−	0.984808i	−0.158613	−	0.0577305i
$292$	2.27972	+	3.94858i	0.133410	+	0.231073i
$293$	−8.90673	+	15.4269i	−0.520337	+	0.901249i	0.479384	+	0.877605i	$0.340860\pi$
$293$	−8.90673	+	15.4269i	−0.520337	+	0.901249i	−0.999720	+	0.0236440i	$0.992473\pi$
$294$	−26.8444	+	22.5251i	−1.56559	+	1.31369i
$295$	1.09833	−	0.921605i	0.0639470	−	0.0536579i
$296$	−2.41147	+	4.17680i	−0.140164	+	0.242771i
$297$	3.27332	+	5.66955i	0.189937	+	0.328981i
$298$	13.5030	+	4.91469i	0.782207	+	0.284700i
$299$	0.694593	−	3.93923i	0.0401693	−	0.227812i
$300$	0.326352	+	1.85083i	0.0188419	+	0.106858i
$301$	3.61081	−	1.31423i	0.208124	−	0.0757509i
$302$	−15.9632	−	13.3947i	−0.918577	−	0.770777i
$303$	−16.5817			−0.952595
$304$		0			0
$305$	19.5175			1.11757
$306$	0.973841	+	0.817150i	0.0556708	+	0.0467133i
$307$	26.9304	−	9.80185i	1.53700	−	0.559421i	0.571674	−	0.820481i	$-0.306294\pi$
$307$	26.9304	−	9.80185i	1.53700	−	0.559421i	0.965323	+	0.261060i	$0.0840719\pi$
$308$	−1.24123	−	7.03936i	−0.0707256	−	0.401105i
$309$	2.33275	−	13.2297i	0.132705	−	0.752610i
$310$	−0.694593	−	0.252811i	−0.0394502	−	0.0143587i
$311$	−7.90673	−	13.6949i	−0.448349	−	0.776564i	0.549929	−	0.835211i	$-0.314655\pi$
$311$	−7.90673	−	13.6949i	−0.448349	−	0.776564i	−0.998279	+	0.0586473i	$0.981321\pi$
$312$	−1.22668	+	2.12467i	−0.0694472	+	0.120286i
$313$	10.0660	−	8.44637i	0.568963	−	0.477417i	−0.312338	−	0.949971i	$-0.601112\pi$
$313$	10.0660	−	8.44637i	0.568963	−	0.477417i	0.881302	+	0.472554i	$0.156668\pi$
$314$	4.87939	−	4.09429i	0.275360	−	0.231054i
$315$	−2.69459	+	4.66717i	−0.151823	+	0.262965i
$316$	1.12061	+	1.94096i	0.0630395	+	0.109188i
$317$	20.1138	+	7.32083i	1.12970	+	0.411179i	0.838185	−	0.545386i	$-0.183617\pi$
$317$	20.1138	+	7.32083i	1.12970	+	0.411179i	0.291519	+	0.956565i	$0.405839\pi$
$318$	−0.546637	+	3.10013i	−0.0306539	+	0.173847i
$319$	−2.07192	−	11.7504i	−0.116005	−	0.657898i
$320$	−1.87939	+	0.684040i	−0.105061	+	0.0382390i
$321$	13.4893	+	11.3189i	0.752901	+	0.631759i
$322$	−15.5175			−0.864759
$323$		0			0
$324$	−10.3131			−0.572953
$325$	1.00000	+	0.839100i	0.0554700	+	0.0465449i
$326$	−4.44609	+	1.61824i	−0.246246	+	0.0896263i
$327$	−3.61081	−	20.4779i	−0.199679	−	1.13243i
$328$	−0.266044	+	1.50881i	−0.0146898	+	0.0833103i
$329$	48.5972	+	17.6879i	2.67925	+	0.975167i
$330$	−2.65270	−	4.59462i	−0.146027	−	0.252925i
$331$	12.6989	−	21.9952i	0.697996	−	1.20897i	−0.271164	−	0.962533i	$-0.587409\pi$
$331$	12.6989	−	21.9952i	0.697996	−	1.20897i	0.969160	−	0.246432i	$-0.0792582\pi$
$332$	−3.05303	+	2.56180i	−0.167557	+	0.140597i
$333$	1.96585	−	1.64955i	0.107728	−	0.0903945i
$334$	−8.63816	+	14.9617i	−0.472659	+	0.818669i
$335$	1.40373	+	2.43134i	0.0766941	+	0.132838i
$336$	8.94356	+	3.25519i	0.487911	+	0.177585i
$337$	4.58037	−	25.9766i	0.249509	−	1.41504i	−0.560275	−	0.828307i	$-0.689304\pi$
$337$	4.58037	−	25.9766i	0.249509	−	1.41504i	0.809784	−	0.586729i	$-0.199584\pi$
$338$	−1.96151	−	11.1243i	−0.106692	−	0.605082i
$339$	−23.4859	+	8.54818i	−1.27558	+	0.464273i
$340$	3.66044	+	3.07148i	0.198515	+	0.166574i
$341$	−0.521660			−0.0282495
$342$		0			0
$343$	58.9769			3.18445
$344$	−0.581252	−	0.487728i	−0.0313390	−	0.0262965i
$345$	−10.8229	+	3.93923i	−0.582688	+	0.212081i
$346$	3.26857	+	18.5370i	0.175719	+	0.996555i
$347$	−4.45084	+	25.2420i	−0.238933	+	1.35506i	0.595236	+	0.803551i	$0.297059\pi$
$347$	−4.45084	+	25.2420i	−0.238933	+	1.35506i	−0.834170	+	0.551508i	$0.814053\pi$
$348$	14.9290	+	5.43372i	0.800279	+	0.291278i
$349$	2.92127	+	5.05980i	0.156372	+	0.270845i	0.933558	−	0.358427i	$-0.116687\pi$
$349$	2.92127	+	5.05980i	0.156372	+	0.270845i	−0.777186	+	0.629271i	$0.783353\pi$
$350$	2.53209	−	4.38571i	0.135346	−	0.234426i
$351$	−4.63816	+	3.89187i	−0.247566	+	0.207733i
$352$	−1.08125	+	0.907278i	−0.0576309	+	0.0483581i
$353$	11.2049	−	19.4074i	0.596375	−	1.03295i	−0.396977	−	0.917829i	$-0.629941\pi$
$353$	11.2049	−	19.4074i	0.596375	−	1.03295i	0.993351	−	0.115122i	$-0.0367260\pi$
$354$	0.673648	+	1.16679i	0.0358040	+	0.0620143i
$355$	11.9709	+	4.35705i	0.635350	+	0.231248i
$356$	−1.84864	+	10.4842i	−0.0979778	+	0.555659i
$357$	−3.94862	−	22.3937i	−0.208983	−	1.18520i
$358$	12.9941	−	4.72945i	0.686758	−	0.249959i
$359$	7.36690	+	6.18156i	0.388810	+	0.326250i	0.816149	−	0.577841i	$-0.196105\pi$
$359$	7.36690	+	6.18156i	0.388810	+	0.326250i	−0.427339	+	0.904091i	$0.640549\pi$
$360$	1.06418			0.0560871
$361$		0			0
$362$	12.2567			0.644198
$363$	12.9684	+	10.8818i	0.680663	+	0.571144i
$364$	6.21213	−	2.26103i	0.325604	−	0.118510i
$365$	−1.58347	−	8.98032i	−0.0828828	−	0.470052i
$366$	−3.18479	+	18.0619i	−0.166472	+	0.944108i
$367$	−21.9513	−	7.98962i	−1.14585	−	0.417055i	−0.301826	−	0.953363i	$-0.597596\pi$
$367$	−21.9513	−	7.98962i	−1.14585	−	0.417055i	−0.844022	+	0.536308i	$0.819819\pi$
$368$	1.53209	+	2.65366i	0.0798657	+	0.138331i
$369$	0.407604	−	0.705990i	0.0212190	−	0.0367524i
$370$	7.38919	−	6.20026i	0.384145	−	0.322336i
$371$	6.49794	−	5.45242i	0.337356	−	0.283076i
$372$	0.347296	−	0.601535i	0.0180065	−	0.0311881i
$373$	12.9709	+	22.4663i	0.671608	+	1.16326i	0.977448	+	0.211176i	$0.0677294\pi$
$373$	12.9709	+	22.4663i	0.671608	+	1.16326i	−0.305840	+	0.952083i	$0.598937\pi$
$374$	3.16890	+	1.15339i	0.163860	+	0.0596401i
$375$	3.91622	−	22.2100i	0.202233	−	1.14692i
$376$	−1.77332	−	10.0570i	−0.0914519	−	0.518650i
$377$	10.3696	−	3.77422i	0.534061	−	0.194382i
$378$	17.9932	+	15.0981i	0.925470	+	0.776562i
$379$	9.47834			0.486870			0.243435	−	0.969917i	$-0.421726\pi$
$379$	9.47834			0.486870			0.243435	+	0.969917i	$0.421726\pi$
$380$		0			0
$381$	10.7392			0.550184
$382$	−15.3969	−	12.9196i	−0.787775	−	0.661022i
$383$	12.6750	−	4.61332i	0.647662	−	0.235730i	0.00276137	−	0.999996i	$-0.499121\pi$
$383$	12.6750	−	4.61332i	0.647662	−	0.235730i	0.644900	+	0.764267i	$0.276899\pi$
$384$	−0.326352	−	1.85083i	−0.0166541	−	0.0944499i
$385$	−2.48246	+	14.0787i	−0.126518	+	0.717518i
$386$	−15.6789	−	5.70664i	−0.798033	−	0.290460i
$387$	0.201867	+	0.349643i	0.0102615	+	0.0177734i
$388$	0.766044	−	1.32683i	0.0388900	−	0.0673595i
$389$	−19.2645	+	16.1648i	−0.976746	+	0.819588i	−0.983595	−	0.180389i	$-0.942264\pi$
$389$	−19.2645	+	16.1648i	−0.976746	+	0.819588i	0.00684888	+	0.999977i	$0.497820\pi$
$390$	3.75877	−	3.15398i	0.190333	−	0.159708i
$391$	3.66044	−	6.34008i	0.185117	−	0.320631i
$392$	−9.32295	−	16.1478i	−0.470880	−	0.815588i
$393$	−17.4474	−	6.35035i	−0.880107	−	0.320333i
$394$	2.25578	−	12.7931i	0.113644	−	0.644510i
$395$	−0.778371	−	4.41436i	−0.0391641	−	0.222111i
$396$	0.705737	−	0.256867i	0.0354646	−	0.0129081i
$397$	5.03003	+	4.22070i	0.252450	+	0.211831i	0.760226	−	0.649658i	$-0.225088\pi$
$397$	5.03003	+	4.22070i	0.252450	+	0.211831i	−0.507776	+	0.861489i	$0.669532\pi$
$398$	17.1925			0.861784
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−22.6065	−	18.9691i	−1.12892	−	0.947273i	−0.129896	−	0.991528i	$-0.541464\pi$
$401$	−22.6065	−	18.9691i	−1.12892	−	0.947273i	−0.999020	+	0.0442543i	$0.985909\pi$
$402$	−2.47906	+	0.902302i	−0.123644	+	0.0450028i
$403$	−0.0837781	−	0.475129i	−0.00417329	−	0.0236679i
$404$	1.53209	−	8.68891i	0.0762243	−	0.432289i
$405$	19.3824	+	7.05461i	0.963118	+	0.350546i
$406$	−21.4047	−	37.0740i	−1.06230	−	1.83995i
$407$	3.40373	−	5.89544i	0.168717	−	0.292226i
$408$	−3.43969	+	2.88624i	−0.170290	+	0.142890i
$409$	16.1873	−	13.5828i	0.800411	−	0.671625i	−0.147887	−	0.989004i	$-0.547247\pi$
$409$	16.1873	−	13.5828i	0.800411	−	0.671625i	0.948299	+	0.317379i	$0.102803\pi$
$410$	1.53209	−	2.65366i	0.0756645	−	0.131055i
$411$	5.07145	+	8.78401i	0.250156	+	0.433283i
$412$	6.71688	+	2.44474i	0.330917	+	0.120444i
$413$	0.630415	−	3.57526i	0.0310207	−	0.175927i
$414$	−0.283119	−	1.60565i	−0.0139145	−	0.0789132i
$415$	7.49020	−	2.72621i	0.367679	−	0.133824i
$416$	−1.00000	−	0.839100i	−0.0490290	−	0.0411402i
$417$	4.39693			0.215318
$418$		0			0
$419$	−27.8830			−1.36217			−0.681087	−	0.732202i	$-0.738492\pi$
$419$	−27.8830			−1.36217			−0.681087	+	0.732202i	$0.738492\pi$
$420$	−14.5817	−	12.2355i	−0.711515	−	0.597032i
$421$	0.0418891	−	0.0152464i	0.00204155	−	0.000743063i	−0.340999	−	0.940064i	$-0.610765\pi$
$421$	0.0418891	−	0.0152464i	0.00204155	−	0.000743063i	0.343041	+	0.939321i	$0.388543\pi$
$422$	−2.79726	−	15.8640i	−0.136168	−	0.772249i
$423$	−0.943563	+	5.35121i	−0.0458776	+	0.260185i
$424$	−1.57398	−	0.572881i	−0.0764391	−	0.0278216i
$425$	1.19459	+	2.06910i	0.0579463	+	0.100366i
$426$	−5.98545	+	10.3671i	−0.289996	+	0.502288i
$427$	37.8580	−	31.7667i	1.83208	−	1.53730i
$428$	−7.17752	+	6.02265i	−0.346938	+	0.291116i
$429$	1.73143	−	2.99892i	0.0835942	−	0.144789i
$430$	0.758770	+	1.31423i	0.0365912	+	0.0633778i
$431$	11.0770	+	4.03169i	0.533559	+	0.194200i	0.594727	−	0.803928i	$-0.297260\pi$
$431$	11.0770	+	4.03169i	0.533559	+	0.194200i	−0.0611678	+	0.998127i	$0.519482\pi$
$432$	0.805407	−	4.56769i	0.0387502	−	0.219763i
$433$	4.80066	+	27.2259i	0.230705	+	1.30839i	0.851473	+	0.524399i	$0.175710\pi$
$433$	4.80066	+	27.2259i	0.230705	+	1.30839i	−0.620768	+	0.783994i	$0.713179\pi$
$434$	−1.75877	+	0.640140i	−0.0844237	+	0.0307277i
$435$	−24.3405	−	20.4241i	−1.16704	−	0.979260i
$436$	11.0642			0.529878
$437$		0			0
$438$	8.56893			0.409439
$439$	28.6878	+	24.0719i	1.36919	+	1.14889i	0.973022	+	0.230713i	$0.0741059\pi$
$439$	28.6878	+	24.0719i	1.36919	+	1.14889i	0.396171	+	0.918177i	$0.370339\pi$
$440$	2.65270	−	0.965505i	0.126463	−	0.0460287i
$441$	1.72281	+	9.77055i	0.0820386	+	0.465264i
$442$	−0.541584	+	3.07148i	−0.0257605	+	0.146095i
$443$	−19.7224	−	7.17837i	−0.937040	−	0.341054i	−0.172043	−	0.985089i	$-0.555037\pi$
$443$	−19.7224	−	7.17837i	−0.937040	−	0.341054i	−0.764996	+	0.644035i	$0.777259\pi$
$444$	4.53209	+	7.84981i	0.215083	+	0.372535i
$445$	10.6459	−	18.4392i	0.504664	−	0.874104i
$446$	3.12836	−	2.62500i	0.148132	−	0.124297i
$447$	20.6878	−	17.3591i	0.978499	−	0.821058i
$448$	−2.53209	+	4.38571i	−0.119630	+	0.207205i
$449$	10.9474	+	18.9615i	0.516641	+	0.894849i	0.999813	+	0.0193235i	$0.00615126\pi$
$449$	10.9474	+	18.9615i	0.516641	+	0.894849i	−0.483172	+	0.875525i	$0.660515\pi$
$450$	0.500000	+	0.181985i	0.0235702	+	0.00857886i
$451$	0.375515	−	2.12965i	0.0176823	−	0.100281i
$452$	−2.30928	−	13.0966i	−0.108619	−	0.616011i
$453$	−36.8016	+	13.3947i	−1.72909	+	0.629337i
$454$	10.4645	+	8.78076i	0.491124	+	0.412102i
$455$	−13.2216			−0.619840
$456$		0			0
$457$	−13.0496			−0.610436			−0.305218	−	0.952283i	$-0.598729\pi$
$457$	−13.0496			−0.610436			−0.305218	+	0.952283i	$0.598729\pi$
$458$	−4.00000	−	3.35640i	−0.186908	−	0.156834i
$459$	−10.4131	+	3.79007i	−0.486043	+	0.176905i
$460$	−1.06418	−	6.03525i	−0.0496175	−	0.281395i
$461$	0.765578	−	4.34181i	0.0356565	−	0.202218i	−0.961775	−	0.273840i	$-0.911706\pi$
$461$	0.765578	−	4.34181i	0.0356565	−	0.202218i	0.997432	+	0.0716215i	$0.0228174\pi$
$462$	−12.6236	−	4.59462i	−0.587303	−	0.213761i
$463$	−13.3327	−	23.0930i	−0.619625	−	1.07322i	−0.989554	−	0.144162i	$-0.953951\pi$
$463$	−13.3327	−	23.0930i	−0.619625	−	1.07322i	0.369929	−	0.929060i	$-0.379382\pi$
$464$	−4.22668	+	7.32083i	−0.196219	+	0.339861i
$465$	−1.06418	+	0.892951i	−0.0493501	+	0.0414096i
$466$	−20.7160	+	17.3828i	−0.959650	+	0.805242i
$467$	−15.0569	+	26.0793i	−0.696750	+	1.20681i	0.272837	+	0.962060i	$0.412038\pi$
$467$	−15.0569	+	26.0793i	−0.696750	+	1.20681i	−0.969587	+	0.244747i	$0.921295\pi$
$468$	0.347296	+	0.601535i	0.0160538	+	0.0278060i
$469$	6.68004	+	2.43134i	0.308456	+	0.112269i
$470$	−3.54664	+	20.1140i	−0.163594	+	0.927789i
$471$	−2.07873	−	11.7890i	−0.0957826	−	0.543210i
$472$	−0.673648	+	0.245188i	−0.0310072	+	0.0112857i
$473$	0.820422	+	0.688416i	0.0377230	+	0.0316534i
$474$	4.21213			0.193470
$475$		0			0
$476$	12.0993			0.554569
$477$	0.682733	+	0.572881i	0.0312602	+	0.0262304i
$478$	0.268571	−	0.0977517i	0.0122841	−	0.00447106i
$479$	1.41828	+	8.04347i	0.0648029	+	0.367516i	0.999913	+	0.0131594i	$0.00418888\pi$
$479$	1.41828	+	8.04347i	0.0648029	+	0.367516i	−0.935110	+	0.354356i	$0.884700\pi$
$480$	−0.652704	+	3.70167i	−0.0297917	+	0.168957i
$481$	5.91622	+	2.15333i	0.269756	+	0.0981833i
$482$	−1.55051	−	2.68556i	−0.0706237	−	0.122324i
$483$	−14.5817	+	25.2563i	−0.663491	+	1.14920i
$484$	−6.90033	+	5.79006i	−0.313651	+	0.263185i
$485$	−2.34730	+	1.96962i	−0.106585	+	0.0894356i
$486$	−2.73396	+	4.73535i	−0.124015	+	0.214800i
$487$	−13.2935	−	23.0251i	−0.602388	−	1.04337i	−0.992458	−	0.122582i	$-0.960883\pi$
$487$	−13.2935	−	23.0251i	−0.602388	−	1.04337i	0.390070	−	0.920785i	$-0.372451\pi$
$488$	−9.17024	−	3.33770i	−0.415117	−	0.151090i
$489$	−1.54411	+	8.75709i	−0.0698271	+	0.396009i
$490$	6.47565	+	36.7252i	0.292540	+	1.65908i
$491$	−36.4873	+	13.2803i	−1.64665	+	0.599331i	−0.988183	−	0.153281i	$-0.951016\pi$
$491$	−36.4873	+	13.2803i	−1.64665	+	0.599331i	−0.658465	+	0.752612i	$0.728794\pi$
$492$	2.20574	+	1.85083i	0.0994423	+	0.0834420i
$493$	20.1967			0.909611
$494$		0			0
$495$	−1.50206			−0.0675125
$496$	0.283119	+	0.237565i	0.0127124	+	0.0106670i
$497$	30.3114	−	11.0324i	1.35965	−	0.494873i
$498$	1.30066	+	7.37641i	0.0582839	+	0.330545i
$499$	3.58734	−	20.3448i	0.160592	−	0.910760i	−0.792903	−	0.609348i	$-0.791431\pi$
$499$	3.58734	−	20.3448i	0.160592	−	0.910760i	0.953494	−	0.301412i	$-0.0974578\pi$
$500$	11.2763	+	4.10424i	0.504292	+	0.183547i
$501$	16.2344	+	28.1188i	0.725301	+	1.25626i
$502$	6.32888	−	10.9619i	0.282472	−	0.489255i
$503$	0.0564370	−	0.0473563i	0.00251640	−	0.00211151i	−0.641529	−	0.767099i	$-0.721699\pi$
$503$	0.0564370	−	0.0473563i	0.00251640	−	0.00211151i	0.644045	+	0.764988i	$0.277255\pi$
$504$	2.06418	−	1.73205i	0.0919458	−	0.0771517i
$505$	−8.82295	+	15.2818i	−0.392616	+	0.680031i
$506$	−2.16250	−	3.74557i	−0.0961350	−	0.166511i
$507$	−19.9491	−	7.26087i	−0.885970	−	0.322467i
$508$	−0.992259	+	5.62738i	−0.0440244	+	0.249675i
$509$	2.60813	+	14.7914i	0.115603	+	0.655618i	0.986450	+	0.164063i	$0.0524601\pi$
$509$	2.60813	+	14.7914i	0.115603	+	0.655618i	−0.870847	+	0.491555i	$0.836429\pi$
$510$	8.43882	−	3.07148i	0.373677	−	0.136007i
$511$	−17.6878	−	14.8418i	−0.782462	−	0.656563i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−30.3928			−1.34057
$515$	−10.9513	−	9.18923i	−0.482572	−	0.404926i
$516$	−1.34002	+	0.487728i	−0.0589912	+	0.0214710i
$517$	2.50299	+	14.1952i	0.110082	+	0.624303i
$518$	4.24123	−	24.0532i	0.186349	−	1.05684i
$519$	33.2422	+	12.0992i	1.45917	+	0.531094i
$520$	1.30541	+	2.26103i	0.0572459	+	0.0991528i
$521$	−22.5856	+	39.1194i	−0.989493	+	1.71385i	−0.369533	+	0.929217i	$0.620482\pi$
$521$	−22.5856	+	39.1194i	−0.989493	+	1.71385i	−0.619959	+	0.784634i	$0.712851\pi$
$522$	3.44562	−	2.89122i	0.150811	−	0.126545i
$523$	0.128356	−	0.107703i	0.00561260	−	0.00470953i	−0.639977	−	0.768394i	$-0.721056\pi$
$523$	0.128356	−	0.107703i	0.00561260	−	0.00470953i	0.645590	+	0.763685i	$0.276612\pi$
$524$	4.93969	−	8.55580i	0.215791	−	0.373762i
$525$	−4.75877	−	8.24243i	−0.207690	−	0.359729i
$526$	−20.5817	−	7.49113i	−0.897406	−	0.326629i
$527$	0.153333	−	0.869592i	0.00667927	−	0.0378800i
$528$	0.460637	+	2.61240i	0.0200467	+	0.113690i
$529$	12.7900	−	4.65517i	0.556086	−	0.202399i
$530$	2.56624	+	2.15333i	0.111470	+	0.0935346i
$531$	0.381445			0.0165533
$532$		0			0
$533$	2.00000			0.0866296
$534$	15.3268	+	12.8607i	0.663256	+	0.556538i
$535$	17.6091	−	6.40917i	0.761306	−	0.277093i
$536$	−0.243756	−	1.38241i	−0.0105286	−	0.0597109i
$537$	4.51279	−	25.5933i	0.194741	−	1.10443i
$538$	1.34730	+	0.490376i	0.0580861	+	0.0211416i
$539$	13.1591	+	22.7922i	0.566803	+	0.981731i
$540$	−4.63816	+	8.03352i	−0.199594	+	0.345708i
$541$	−0.751030	+	0.630189i	−0.0322893	+	0.0270939i	−0.658789	−	0.752327i	$-0.728931\pi$
$541$	−0.751030	+	0.630189i	−0.0322893	+	0.0270939i	0.626500	+	0.779421i	$0.284487\pi$
$542$	12.3892	−	10.3958i	0.532161	−	0.446536i
$543$	11.5175	−	19.9490i	0.494265	−	0.856092i
$544$	−1.19459	−	2.06910i	−0.0512177	−	0.0887117i
$545$	−20.7939	−	7.56834i	−0.890711	−	0.324192i
$546$	2.15745	−	12.2355i	0.0923304	−	0.523632i
$547$	4.93242	+	27.9731i	0.210895	+	1.19604i	0.887889	+	0.460057i	$0.152171\pi$
$547$	4.93242	+	27.9731i	0.210895	+	1.19604i	−0.676994	+	0.735988i	$0.736718\pi$
$548$	−5.07145	+	1.84586i	−0.216642	+	0.0788511i
$549$	3.97771	+	3.33770i	0.169765	+	0.142449i
$550$	1.41147			0.0601855
$551$		0			0
$552$	5.75877			0.245110
$553$	−8.69459	−	7.29563i	−0.369732	−	0.310242i
$554$	−10.4388	+	3.79942i	−0.443503	+	0.161422i
$555$	−3.14796	−	17.8529i	−0.133623	−	0.757815i
$556$	−0.406260	+	2.30401i	−0.0172292	+	0.0977119i
$557$	−33.4834	−	12.1870i	−1.41874	−	0.516378i	−0.485056	−	0.874483i	$-0.661201\pi$
$557$	−33.4834	−	12.1870i	−1.41874	−	0.516378i	−0.933681	+	0.358105i	$0.883423\pi$
$558$	−0.0983261	−	0.170306i	−0.00416247	−	0.00720962i
$559$	−0.495252	+	0.857802i	−0.0209469	+	0.0362812i
$560$	7.75877	−	6.51038i	0.327868	−	0.275114i
$561$	4.85504	−	4.07386i	0.204980	−	0.171998i
$562$	−2.12449	+	3.67972i	−0.0896160	+	0.155219i
$563$	−4.31386	−	7.47183i	−0.181808	−	0.314900i	0.760688	−	0.649117i	$-0.224861\pi$
$563$	−4.31386	−	7.47183i	−0.181808	−	0.314900i	−0.942496	+	0.334217i	$0.891528\pi$
$564$	−18.0351	−	6.56423i	−0.759414	−	0.276404i
$565$	−4.61856	+	26.1931i	−0.194304	+	1.10195i
$566$	−0.947433	−	5.37316i	−0.0398236	−	0.225851i
$567$	49.0779	−	17.8629i	2.06108	−	0.750171i
$568$	−4.87939	−	4.09429i	−0.204734	−	0.171793i
$569$	22.3310			0.936164			0.468082	−	0.883685i	$-0.344945\pi$
$569$	22.3310			0.936164			0.468082	+	0.883685i	$0.344945\pi$
$570$		0			0
$571$	−9.56448			−0.400261			−0.200131	−	0.979769i	$-0.564137\pi$
$571$	−9.56448			−0.400261			−0.200131	+	0.979769i	$0.564137\pi$
$572$	1.41147	+	1.18437i	0.0590167	+	0.0495209i
$573$	−35.4962	+	12.9196i	−1.48287	+	0.539722i
$574$	−1.34730	−	7.64090i	−0.0562351	−	0.318925i
$575$	0.532089	−	3.01763i	0.0221896	−	0.125844i
$576$	−0.500000	−	0.181985i	−0.0208333	−	0.00758271i
$577$	−11.2378	−	19.4645i	−0.467837	−	0.810317i	0.531488	−	0.847066i	$-0.321633\pi$
$577$	−11.2378	−	19.4645i	−0.467837	−	0.810317i	−0.999325	+	0.0367489i	$0.988300\pi$
$578$	5.64590	−	9.77898i	0.234838	−	0.406752i
$579$	−24.0214	+	20.1564i	−0.998296	+	0.837670i
$580$	12.9513	−	10.8674i	0.537774	−	0.451246i
$581$	10.0915	−	17.4790i	0.418667	−	0.725152i
$582$	−1.43969	−	2.49362i	−0.0596772	−	0.103364i
$583$	2.22163	+	0.808607i	0.0920105	+	0.0334891i
$584$	−0.791737	+	4.49016i	−0.0327623	+	0.185804i
$585$	−0.241230	−	1.36808i	−0.00997361	−	0.0565632i
$586$	−16.7392	+	6.09256i	−0.691489	+	0.251681i
$587$	3.17752	+	2.66625i	0.131150	+	0.110048i	0.706003	−	0.708209i	$-0.250496\pi$
$587$	3.17752	+	2.66625i	0.131150	+	0.110048i	−0.574853	+	0.818257i	$0.694941\pi$
$588$	−35.0428			−1.44514
$589$		0			0
$590$	1.43376			0.0590271
$591$	−18.7023	−	15.6931i	−0.769311	−	0.645529i
$592$	−4.53209	+	1.64955i	−0.186268	+	0.0677959i
$593$	1.80897	+	10.2592i	0.0742856	+	0.421295i	0.999158	+	0.0410180i	$0.0130601\pi$
$593$	1.80897	+	10.2592i	0.0742856	+	0.421295i	−0.924873	+	0.380277i	$0.875829\pi$
$594$	−1.13681	+	6.44718i	−0.0466439	+	0.264531i
$595$	−22.7392	−	8.27638i	−0.932215	−	0.339299i
$596$	7.18479	+	12.4444i	0.294301	+	0.509744i
$597$	16.1557	−	27.9825i	0.661209	−	1.14525i
$598$	3.06418	−	2.57115i	0.125304	−	0.105142i
$599$	−30.3783	+	25.4904i	−1.24122	+	1.04151i	−0.243794	+	0.969827i	$0.578392\pi$
$599$	−30.3783	+	25.4904i	−1.24122	+	1.04151i	−0.997428	+	0.0716820i	$0.977163\pi$
$600$	−0.939693	+	1.62760i	−0.0383628	+	0.0664463i
$601$	−11.9324	−	20.6676i	−0.486734	−	0.843047i	0.513150	−	0.858299i	$-0.328478\pi$
$601$	−11.9324	−	20.6676i	−0.486734	−	0.843047i	−0.999884	+	0.0152517i	$0.995145\pi$
$602$	3.61081	+	1.31423i	0.147166	+	0.0535640i
$603$	−0.129700	+	0.735564i	−0.00528178	+	0.0299545i
$604$	−3.61856	−	20.5218i	−0.147237	−	0.835022i
$605$	16.9290	−	6.16166i	0.688262	−	0.250507i
$606$	−12.7023	−	10.6585i	−0.515997	−	0.432973i
$607$	−29.9317			−1.21489			−0.607445	−	0.794362i	$-0.707806\pi$
$607$	−29.9317			−1.21489			−0.607445	+	0.794362i	$0.707806\pi$
$608$		0			0
$609$	−80.4552			−3.26021
$610$	14.9513	+	12.5456i	0.605361	+	0.507958i
$611$	−12.5270	+	4.55947i	−0.506790	+	0.184456i
$612$	0.220752	+	1.25195i	0.00892336	+	0.0506069i
$613$	−6.17799	+	35.0371i	−0.249526	+	1.41513i	0.560215	+	0.828348i	$0.310719\pi$
$613$	−6.17799	+	35.0371i	−0.249526	+	1.41513i	−0.809741	+	0.586787i	$0.800392\pi$
$614$	26.9304	+	9.80185i	1.08682	+	0.395570i
$615$	−2.87939	−	4.98724i	−0.116108	−	0.201105i
$616$	3.57398	−	6.19031i	0.144000	−	0.249415i
$617$	9.21735	−	7.73427i	0.371076	−	0.311370i	−0.438111	−	0.898921i	$-0.644352\pi$
$617$	9.21735	−	7.73427i	0.371076	−	0.311370i	0.809187	+	0.587551i	$0.199908\pi$
$618$	10.2909	−	8.63506i	0.413959	−	0.347353i
$619$	8.55644	−	14.8202i	0.343912	−	0.595673i	−0.641243	−	0.767338i	$-0.721581\pi$
$619$	8.55644	−	14.8202i	0.343912	−	0.595673i	0.985156	+	0.171664i	$0.0549144\pi$
$620$	−0.369585	−	0.640140i	−0.0148429	−	0.0257086i
$621$	13.3550	+	4.86084i	0.535919	+	0.195059i
$622$	2.74598	−	15.5732i	0.110104	−	0.624429i
$623$	−9.36184	−	53.0937i	−0.375074	−	2.12715i
$624$	−2.30541	+	0.839100i	−0.0922902	+	0.0335909i
$625$	−14.5548	−	12.2130i	−0.582194	−	0.488519i
$626$	13.1402			0.525189
$627$		0			0
$628$	6.36959			0.254174
$629$	8.82707	+	7.40679i	0.351958	+	0.295328i
$630$	−5.06418	+	1.84321i	−0.201762	+	0.0734352i
$631$	3.18479	+	18.0619i	0.126785	+	0.719031i	0.980232	+	0.197852i	$0.0633965\pi$
$631$	3.18479	+	18.0619i	0.126785	+	0.719031i	−0.853447	+	0.521179i	$0.825492\pi$
$632$	−0.389185	+	2.20718i	−0.0154810	+	0.0877969i
$633$	−28.4488	−	10.3545i	−1.13074	−	0.411555i
$634$	10.7023	+	18.5370i	0.425044	+	0.736198i
$635$	5.71419	−	9.89727i	0.226761	−	0.392761i
$636$	−2.41147	+	2.02347i	−0.0956212	+	0.0802357i
$637$	−18.6459	+	15.6458i	−0.738777	+	0.619908i
$638$	5.96585	−	10.3332i	0.236190	−	0.409094i
$639$	1.69459	+	2.93512i	0.0670371	+	0.116112i
$640$	−1.87939	−	0.684040i	−0.0742892	−	0.0270391i
$641$	−5.41400	+	30.7043i	−0.213840	+	1.21275i	0.669068	+	0.743201i	$0.266694\pi$
$641$	−5.41400	+	30.7043i	−0.213840	+	1.21275i	−0.882908	+	0.469546i	$0.844417\pi$
$642$	3.05778	+	17.3415i	0.120681	+	0.684416i
$643$	30.0228	−	10.9274i	1.18398	−	0.430934i	0.326375	−	0.945240i	$-0.394173\pi$
$643$	30.0228	−	10.9274i	1.18398	−	0.430934i	0.857607	+	0.514306i	$0.171950\pi$
$644$	−11.8871	−	9.97448i	−0.468418	−	0.393050i
$645$	2.85204			0.112299
$646$		0			0
$647$	2.99588			0.117780			0.0588901	−	0.998264i	$-0.481244\pi$
$647$	2.99588			0.117780			0.0588901	+	0.998264i	$0.481244\pi$
$648$	−7.90033	−	6.62916i	−0.310354	−	0.260418i
$649$	0.950837	−	0.346076i	0.0373236	−	0.0135847i
$650$	0.226682	+	1.28558i	0.00889118	+	0.0504244i
$651$	−0.610815	+	3.46410i	−0.0239397	+	0.135769i
$652$	−4.44609	−	1.61824i	−0.174122	−	0.0633753i
$653$	−0.467911	−	0.810446i	−0.0183108	−	0.0317152i	0.856725	−	0.515774i	$-0.172495\pi$
$653$	−0.467911	−	0.810446i	−0.0183108	−	0.0317152i	−0.875036	+	0.484059i	$0.839162\pi$
$654$	10.3969	−	18.0080i	0.406552	−	0.704169i
$655$	−15.1361	+	12.7007i	−0.591416	+	0.496257i
$656$	−1.17365	+	0.984808i	−0.0458233	+	0.0384503i
$657$	1.21301	−	2.10100i	0.0473241	−	0.0819677i
$658$	25.8580	+	44.7874i	1.00805	+	1.74600i
$659$	11.4991	+	4.18534i	0.447942	+	0.163038i	0.556134	−	0.831092i	$-0.312284\pi$
$659$	11.4991	+	4.18534i	0.447942	+	0.163038i	−0.108192	+	0.994130i	$0.534506\pi$
$660$	0.921274	−	5.22481i	0.0358606	−	0.203375i
$661$	−2.07604	−	11.7738i	−0.0807485	−	0.457947i	−0.998193	−	0.0600844i	$-0.980863\pi$
$661$	−2.07604	−	11.7738i	−0.0807485	−	0.457947i	0.917445	−	0.397863i	$-0.130248\pi$
$662$	23.8662	−	8.68658i	0.927585	−	0.337614i
$663$	4.49020	+	3.76773i	0.174385	+	0.146326i
$664$	−3.98545			−0.154666
$665$		0			0
$666$	2.56624			0.0994397
$667$	−19.8425	−	16.6499i	−0.768307	−	0.644686i
$668$	−16.2344	+	5.90885i	−0.628129	+	0.228620i
$669$	−1.33275	−	7.55839i	−0.0515270	−	0.292224i
$670$	−0.487511	+	2.76481i	−0.0188342	+	0.106814i
$671$	12.9436	+	4.71107i	0.499681	+	0.181869i
$672$	4.75877	+	8.24243i	0.183574	+	0.317959i
$673$	−22.4317	+	38.8529i	−0.864679	+	1.49767i	0.00268731	+	0.999996i	$0.499145\pi$
$673$	−22.4317	+	38.8529i	−0.864679	+	1.49767i	−0.867366	+	0.497671i	$0.834189\pi$
$674$	20.2062	−	16.9550i	0.778314	−	0.653083i
$675$	−3.55303	+	2.98135i	−0.136756	+	0.114752i
$676$	5.64796	−	9.78255i	0.217229	−	0.376252i
$677$	−0.472964	−	0.819197i	−0.0181775	−	0.0314843i	0.856794	−	0.515660i	$-0.172453\pi$
$677$	−0.472964	−	0.819197i	−0.0181775	−	0.0314843i	−0.874971	+	0.484175i	$0.839120\pi$
$678$	−23.4859	−	8.54818i	−0.901971	−	0.328291i
$679$	−1.34730	+	7.64090i	−0.0517045	+	0.293231i
$680$	0.829755	+	4.70578i	0.0318197	+	0.180458i
$681$	24.1250	−	8.78076i	0.924470	−	0.336480i
$682$	−0.399615	−	0.335316i	−0.0153020	−	0.0128399i
$683$	−5.92221			−0.226607			−0.113303	−	0.993560i	$-0.536143\pi$
$683$	−5.92221			−0.226607			−0.113303	+	0.993560i	$0.536143\pi$
$684$		0			0
$685$	10.7939			0.412412
$686$	45.1789	+	37.9096i	1.72494	+	1.44740i
$687$	−9.22163	+	3.35640i	−0.351827	+	0.128055i
$688$	−0.131759	−	0.747243i	−0.00502327	−	0.0284884i
$689$	−0.379690	+	2.15333i	−0.0144650	+	0.0820353i
$690$	−10.8229	−	3.93923i	−0.412023	−	0.149964i
$691$	−0.103074	−	0.178529i	−0.00392111	−	0.00679156i	0.864058	−	0.503392i	$-0.167915\pi$
$691$	−0.103074	−	0.178529i	−0.00392111	−	0.00679156i	−0.867979	+	0.496600i	$0.834581\pi$
$692$	−9.41147	+	16.3012i	−0.357771	+	0.619677i
$693$	−2.91353	+	2.44474i	−0.110676	+	0.0928682i
$694$	−19.6348	+	16.4755i	−0.745325	+	0.625402i
$695$	2.33956	−	4.05223i	0.0887444	−	0.153710i
$696$	7.94356	+	13.7587i	0.301100	+	0.521520i
$697$	3.43969	+	1.25195i	0.130288	+	0.0474208i
$698$	−1.01455	+	5.75379i	−0.0384012	+	0.217784i
$699$	8.82547	+	50.0518i	0.333810	+	1.89313i
$700$	4.75877	−	1.73205i	0.179865	−	0.0654654i
$701$	3.34730	+	2.80872i	0.126426	+	0.106084i	0.703808	−	0.710390i	$-0.251481\pi$
$701$	3.34730	+	2.80872i	0.126426	+	0.106084i	−0.577383	+	0.816474i	$0.695926\pi$
$702$	−6.05468			−0.228519
$703$		0			0
$704$	−1.41147			−0.0531969
$705$	29.4047	+	24.6734i	1.10744	+	0.929256i
$706$	21.0582	−	7.66458i	0.792538	−	0.288460i
$707$	7.75877	+	44.0022i	0.291799	+	1.65487i
$708$	−0.233956	+	1.32683i	−0.00879259	+	0.0498652i
$709$	−8.22668	−	2.99427i	−0.308960	−	0.112452i	0.182887	−	0.983134i	$-0.441456\pi$
$709$	−8.22668	−	2.99427i	−0.308960	−	0.112452i	−0.491847	+	0.870682i	$0.663678\pi$
$710$	6.36959	+	11.0324i	0.239046	+	0.414040i
$711$	0.596267	−	1.03276i	0.0223617	−	0.0387317i
$712$	−8.15523	+	6.84305i	−0.305630	+	0.256454i
$713$	−0.867526	+	0.727940i	−0.0324891	+	0.0272616i
$714$	11.3696	−	19.6927i	0.425496	−	0.736981i
$715$	−1.84255	−	3.19139i	−0.0689074	−	0.119351i
$716$	12.9941	+	4.72945i	0.485611	+	0.176748i
$717$	0.0932736	−	0.528981i	0.00348337	−	0.0197552i
$718$	1.66994	+	9.47070i	0.0623216	+	0.353443i
$719$	25.9418	−	9.44205i	0.967466	−	0.352129i	0.190511	−	0.981685i	$-0.438985\pi$
$719$	25.9418	−	9.44205i	0.967466	−	0.352129i	0.776955	+	0.629556i	$0.216763\pi$
$720$	0.815207	+	0.684040i	0.0303810	+	0.0254927i
$721$	−36.1985			−1.34810
$722$		0			0
$723$	−5.82800			−0.216746
$724$	9.38919	+	7.87846i	0.348946	+	0.292801i
$725$	7.94356	−	2.89122i	0.295017	−	0.107377i
$726$	2.93969	+	16.6718i	0.109102	+	0.618749i
$727$	4.97266	−	28.2013i	0.184426	−	1.04593i	−0.742265	−	0.670106i	$-0.766249\pi$
$727$	4.97266	−	28.2013i	0.184426	−	1.04593i	0.926691	−	0.375824i	$-0.122640\pi$
$728$	6.21213	+	2.26103i	0.230237	+	0.0837994i
$729$	−10.3316	−	17.8948i	−0.382651	−	0.662770i
$730$	4.55943	−	7.89716i	0.168752	−	0.292287i
$731$	−1.38872	+	1.16527i	−0.0513636	+	0.0430992i
$732$	−14.0496	+	11.7890i	−0.519289	+	0.435735i
$733$	−18.4807	+	32.0095i	−0.682600	+	1.18230i	0.291584	+	0.956545i	$0.405818\pi$
$733$	−18.4807	+	32.0095i	−0.682600	+	1.18230i	−0.974184	+	0.225753i	$0.927516\pi$
$734$	−11.6800	−	20.2304i	−0.431118	−	0.746719i
$735$	65.8590	+	23.9707i	2.42924	+	0.884173i
$736$	−0.532089	+	3.01763i	−0.0196131	+	0.111231i
$737$	0.344055	+	1.95123i	0.0126734	+	0.0718746i
$738$	0.766044	−	0.278817i	0.0281985	−	0.0102634i
$739$	35.2584	+	29.5853i	1.29700	+	1.08831i	0.990655	+	0.136391i	$0.0435505\pi$
$739$	35.2584	+	29.5853i	1.29700	+	1.08831i	0.306345	+	0.951921i	$0.400894\pi$
$740$	9.64590			0.354590
$741$		0			0
$742$	8.48246			0.311401
$743$	20.2317	+	16.9764i	0.742230	+	0.622805i	0.933436	−	0.358745i	$-0.116795\pi$
$743$	20.2317	+	16.9764i	0.742230	+	0.622805i	−0.191205	+	0.981550i	$0.561240\pi$
$744$	0.652704	−	0.237565i	0.0239293	−	0.00870954i
$745$	−4.99050	−	28.3026i	−0.182838	−	1.03693i
$746$	−4.50475	+	25.5477i	−0.164931	+	0.935368i
$747$	1.99273	+	0.725293i	0.0729100	+	0.0265371i
$748$	1.68614	+	2.92047i	0.0616513	+	0.106783i
$749$	23.7246	−	41.0923i	0.866879	−	1.50148i
$750$	17.2763	−	14.4965i	0.630842	−	0.529339i
$751$	−20.8188	+	17.4691i	−0.759690	+	0.637455i	−0.938046	−	0.346510i	$-0.887367\pi$
$751$	−20.8188	+	17.4691i	−0.759690	+	0.637455i	0.178356	+	0.983966i	$0.442922\pi$
$752$	5.10607	−	8.84397i	0.186199	−	0.322506i
$753$	−11.8944	−	20.6017i	−0.433456	−	0.750768i
$754$	10.3696	+	3.77422i	0.377638	+	0.137449i
$755$	−7.23711	+	41.0437i	−0.263385	+	1.49373i
$756$	4.07873	+	23.1316i	0.148342	+	0.841288i
$757$	−18.2344	+	6.63679i	−0.662741	+	0.241218i	−0.651419	−	0.758718i	$-0.725826\pi$
$757$	−18.2344	+	6.63679i	−0.662741	+	0.241218i	−0.0113219	+	0.999936i	$0.503604\pi$
$758$	7.26083	+	6.09256i	0.263725	+	0.221292i
$759$	−8.12836			−0.295041
$760$		0			0
$761$	40.2645			1.45959			0.729793	−	0.683669i	$-0.239617\pi$
$761$	40.2645			1.45959			0.729793	+	0.683669i	$0.239617\pi$
$762$	8.22668	+	6.90301i	0.298021	+	0.250070i
$763$	−52.6519	+	19.1637i	−1.90613	+	0.693773i
$764$	−3.49020	−	19.7939i	−0.126271	−	0.716118i
$765$	0.441504	−	2.50389i	0.0159626	−	0.0905284i
$766$	12.6750	+	4.61332i	0.457966	+	0.166686i
$767$	0.467911	+	0.810446i	0.0168953	+	0.0292635i
$768$	0.939693	−	1.62760i	0.0339082	−	0.0587308i
$769$	−29.8312	+	25.0313i	−1.07574	+	0.902652i	−0.995560	−	0.0941283i	$-0.969994\pi$
$769$	−29.8312	+	25.0313i	−1.07574	+	0.902652i	−0.0801789	+	0.996780i	$0.525549\pi$
$770$	−10.9513	+	9.18923i	−0.394658	+	0.331157i
$771$	−28.5599	+	49.4672i	−1.02856	+	1.78152i
$772$	−8.34255	−	14.4497i	−0.300255	−	0.520057i
$773$	6.35504	+	2.31304i	0.228575	+	0.0831944i	0.453769	−	0.891120i	$-0.350079\pi$
$773$	6.35504	+	2.31304i	0.228575	+	0.0831944i	−0.225194	+	0.974314i	$0.572302\pi$
$774$	−0.0701076	+	0.397600i	−0.00251996	+	0.0142914i
$775$	−0.0641778	−	0.363970i	−0.00230533	−	0.0130742i
$776$	1.43969	−	0.524005i	0.0516820	−	0.0188107i
$777$	−35.1634	−	29.5056i	−1.26148	−	1.05851i
$778$	−25.1480			−0.901598
$779$		0			0
$780$	4.90673			0.175689
$781$	6.88713	+	5.77898i	0.246441	+	0.206788i
$782$	6.87939	−	2.50389i	0.246006	−	0.0895390i
$783$	6.80840	+	38.6124i	0.243312	+	1.37989i
$784$	3.23783	−	18.3626i	0.115637	−	0.655808i
$785$	−11.9709	−	4.35705i	−0.427260	−	0.155510i
$786$	−9.28359	−	16.0796i	−0.331135	−	0.573542i
$787$	−2.90239	+	5.02709i	−0.103459	+	0.179196i	−0.913108	−	0.407719i	$-0.866324\pi$
$787$	−2.90239	+	5.02709i	−0.103459	+	0.179196i	0.809649	+	0.586915i	$0.199658\pi$
$788$	9.95130	−	8.35014i	0.354501	−	0.297461i
$789$	−31.5330	+	26.4593i	−1.12261	+	0.941978i
$790$	2.24123	−	3.88192i	0.0797394	−	0.138113i
$791$	33.6732	+	58.3238i	1.19728	+	2.07375i
$792$	0.705737	+	0.256867i	0.0250773	+	0.00912738i
$793$	−2.21213	+	12.5456i	−0.0785552	+	0.445509i
$794$	1.14022	+	6.46648i	0.0404647	+	0.229487i
$795$	5.91622	−	2.15333i	0.209827	−	0.0763707i
$796$	13.1702	+	11.0511i	0.466807	+	0.391698i
$797$	−39.2181			−1.38918			−0.694589	−	0.719407i	$-0.744414\pi$
$797$	−39.2181			−1.38918			−0.694589	+	0.719407i	$0.744414\pi$
$798$		0			0
$799$	−24.3987			−0.863163
$800$	−0.766044	−	0.642788i	−0.0270838	−	0.0227260i
$801$	5.32295	−	1.93739i	0.188077	−	0.0684545i
$802$	−5.12449	−	29.0624i	−0.180952	−	1.02623i
$803$	1.11752	−	6.33775i	0.0394363	−	0.223654i
$804$	−2.47906	−	0.902302i	−0.0874295	−	0.0318218i
$805$	15.5175	+	26.8772i	0.546921	+	0.947296i
$806$	0.241230	−	0.417822i	0.00849695	−	0.0147171i
$807$	2.06418	−	1.73205i	0.0726625	−	0.0609711i
$808$	6.75877	−	5.67128i	0.237773	−	0.199515i
$809$	−3.50134	+	6.06451i	−0.123101	+	0.213217i	−0.920989	−	0.389589i	$-0.872617\pi$
$809$	−3.50134	+	6.06451i	−0.123101	+	0.213217i	0.797888	+	0.602805i	$0.205950\pi$
$810$	10.3131	+	17.8629i	0.362367	+	0.627638i
$811$	−41.0506	−	14.9412i	−1.44148	−	0.524656i	−0.501282	−	0.865284i	$-0.667138\pi$
$811$	−41.0506	−	14.9412i	−1.44148	−	0.524656i	−0.940198	+	0.340628i	$0.889360\pi$
$812$	7.43376	−	42.1590i	0.260874	−	1.47949i
$813$	−5.27807	−	29.9334i	−0.185110	−	1.04981i
$814$	6.39693	−	2.32829i	0.224212	−	0.0816065i
$815$	7.24897	+	6.08261i	0.253920	+	0.213064i
$816$	−4.49020			−0.157188
$817$		0			0
$818$	21.1310			0.738830
$819$	−2.69459	−	2.26103i	−0.0941567	−	0.0790068i
$820$	2.87939	−	1.04801i	0.100552	−	0.0365981i
$821$	2.15064	+	12.1969i	0.0750580	+	0.425675i	0.999062	+	0.0432933i	$0.0137850\pi$
$821$	2.15064	+	12.1969i	0.0750580	+	0.425675i	−0.924004	+	0.382382i	$0.875104\pi$
$822$	−1.76130	+	9.98881i	−0.0614323	+	0.348400i
$823$	12.0547	+	4.38755i	0.420200	+	0.152940i	0.543462	−	0.839434i	$-0.317113\pi$
$823$	12.0547	+	4.38755i	0.420200	+	0.152940i	−0.123262	+	0.992374i	$0.539336\pi$
$824$	3.57398	+	6.19031i	0.124505	+	0.215650i
$825$	1.32635	−	2.29731i	0.0461776	−	0.0799820i
$826$	2.78106	−	2.33359i	0.0967654	−	0.0811958i
$827$	19.2251	−	16.1318i	0.668522	−	0.560956i	−0.244106	−	0.969749i	$-0.578494\pi$
$827$	19.2251	−	16.1318i	0.668522	−	0.560956i	0.912627	+	0.408792i	$0.134050\pi$
$828$	0.815207	−	1.41198i	0.0283304	−	0.0490697i
$829$	−14.1634	−	24.5318i	−0.491917	−	0.852024i	0.508040	−	0.861333i	$-0.330370\pi$
$829$	−14.1634	−	24.5318i	−0.491917	−	0.852024i	−0.999957	+	0.00930899i	$0.997037\pi$
$830$	7.49020	+	2.72621i	0.259989	+	0.0946281i
$831$	−3.62536	+	20.5605i	−0.125762	+	0.713234i
$832$	−0.226682	−	1.28558i	−0.00785877	−	0.0445693i
$833$	−41.8619	+	15.2365i	−1.45043	+	0.527913i
$834$	3.36824	+	2.82629i	0.116633	+	0.0978664i
$835$	34.5526			1.19574
$836$		0			0
$837$	1.71419			0.0592512
$838$	−21.3596	−	17.9229i	−0.737856	−	0.619135i
$839$	28.5012	−	10.3736i	0.983972	−	0.358137i	0.200589	−	0.979676i	$-0.435714\pi$
$839$	28.5012	−	10.3736i	0.983972	−	0.358137i	0.783383	+	0.621539i	$0.213492\pi$
$840$	−3.30541	−	18.7459i	−0.114047	−	0.646795i
$841$	7.37299	−	41.8143i	0.254241	−	1.44187i
$842$	0.0418891	+	0.0152464i	0.00144359	+	0.000525425i
$843$	3.99273	+	6.91560i	0.137517	+	0.238186i
$844$	8.05438	−	13.9506i	0.277243	−	0.480199i
$845$	−17.3063	+	14.5217i	−0.595356	+	0.499563i
$846$	−4.16250	+	3.49276i	−0.143110	+	0.120083i
$847$	22.8084	−	39.5053i	0.783706	−	1.35742i
$848$	−0.837496	−	1.45059i	−0.0287597	−	0.0498133i
$849$	−9.63563	−	3.50708i	−0.330694	−	0.120363i
$850$	−0.414878	+	2.35289i	−0.0142302	+	0.0807034i
$851$	−2.56624	−	14.5539i	−0.0879695	−	0.498900i
$852$	−11.2490	+	4.09429i	−0.385383	+	0.140268i
$853$	−33.4243	−	28.0463i	−1.14443	−	0.960287i	−0.144851	−	0.989454i	$-0.546270\pi$
$853$	−33.4243	−	28.0463i	−1.14443	−	0.960287i	−0.999575	+	0.0291668i	$0.990715\pi$
$854$	49.4201			1.69112
$855$		0			0
$856$	−9.36959			−0.320246
$857$	−24.1379	−	20.2541i	−0.824535	−	0.691867i	0.129494	−	0.991580i	$-0.458665\pi$
$857$	−24.1379	−	20.2541i	−0.824535	−	0.691867i	−0.954029	+	0.299713i	$0.903109\pi$
$858$	3.25402	−	1.18437i	0.111091	−	0.0404336i
$859$	−3.24685	−	18.4138i	−0.110781	−	0.628272i	−0.988753	−	0.149559i	$-0.952215\pi$
$859$	−3.24685	−	18.4138i	−0.110781	−	0.628272i	0.877972	−	0.478713i	$-0.158896\pi$
$860$	−0.263518	+	1.49449i	−0.00898590	+	0.0509616i
$861$	−13.7023	−	4.98724i	−0.466974	−	0.169965i
$862$	5.89393	+	10.2086i	0.200748	+	0.347706i
$863$	−5.31315	+	9.20264i	−0.180862	+	0.313262i	−0.942174	−	0.335123i	$-0.891222\pi$
$863$	−5.31315	+	9.20264i	−0.180862	+	0.313262i	0.761313	+	0.648385i	$0.224555\pi$
$864$	3.55303	−	2.98135i	0.120877	−	0.101428i
$865$	28.8384	−	24.1983i	0.980536	−	0.822767i
$866$	−13.8229	+	23.9420i	−0.469723	+	0.813584i
$867$	−10.6108	−	18.3785i	−0.360362	−	0.624166i
$868$	−1.75877	−	0.640140i	−0.0596966	−	0.0217278i
$869$	0.549325	−	3.11538i	0.0186346	−	0.105682i
$870$	−5.51754	−	31.2915i	−0.187062	−	1.06088i
$871$	−1.72193	+	0.626733i	−0.0583455	+	0.0212360i
$872$	8.47565	+	7.11192i	0.287022	+	0.240840i
$873$	−0.815207			−0.0275906
$874$		0			0
$875$	−60.7701			−2.05441
$876$	6.56418	+	5.50800i	0.221783	+	0.186098i
$877$	−42.1908	+	15.3562i	−1.42468	+	0.518542i	−0.935402	−	0.353586i	$-0.884962\pi$
$877$	−42.1908	+	15.3562i	−1.42468	+	0.518542i	−0.489279	+	0.872127i	$0.662740\pi$
$878$	6.50299	+	36.8803i	0.219465	+	1.24465i
$879$	−5.81345	+	32.9697i	−0.196083	+	1.11204i
$880$	2.65270	+	0.965505i	0.0894226	+	0.0325472i
$881$	9.00821	+	15.6027i	0.303494	+	0.525667i	0.976925	−	0.213583i	$-0.0685134\pi$
$881$	9.00821	+	15.6027i	0.303494	+	0.525667i	−0.673431	+	0.739250i	$0.735180\pi$
$882$	−4.96064	+	8.59208i	−0.167033	+	0.289310i
$883$	−35.6962	+	29.9527i	−1.20127	+	1.00799i	−0.201681	+	0.979451i	$0.564641\pi$
$883$	−35.6962	+	29.9527i	−1.20127	+	1.00799i	−0.999593	+	0.0285375i	$0.990915\pi$
$884$	−2.38919	+	2.00476i	−0.0803570	+	0.0674275i
$885$	1.34730	−	2.33359i	0.0452889	−	0.0784426i
$886$	−10.4941	−	18.1763i	−0.352555	−	0.610643i
$887$	−6.65270	−	2.42139i	−0.223376	−	0.0813022i	0.227908	−	0.973683i	$-0.426812\pi$
$887$	−6.65270	−	2.42139i	−0.223376	−	0.0813022i	−0.451284	+	0.892381i	$0.649034\pi$
$888$	−1.57398	+	8.92647i	−0.0528192	+	0.299553i
$889$	−5.02498	−	28.4981i	−0.168532	−	0.955794i
$890$	20.0077	−	7.28222i	0.670661	−	0.244101i
$891$	11.1511	+	9.35689i	0.373576	+	0.313468i
$892$	4.08378			0.136735
$893$		0			0
$894$	27.0060			0.903215
$895$	−21.1857	−	17.7769i	−0.708161	−	0.594217i
$896$	−4.75877	+	1.73205i	−0.158979	+	0.0578638i
$897$	−1.30541	−	7.40333i	−0.0435863	−	0.247190i
$898$	−3.80200	+	21.5622i	−0.126875	+	0.719541i
$899$	−2.93582	−	1.06855i	−0.0979152	−	0.0356382i
$900$	0.266044	+	0.460802i	0.00886815	+	0.0153601i
$901$	−2.00093	+	3.46572i	−0.0666608	+	0.115460i
$902$	1.65657	−	1.39003i	0.0551579	−	0.0462830i
$903$	5.53209	−	4.64197i	0.184096	−	0.154475i
$904$	6.64930	−	11.5169i	0.221152	−	0.383047i
$905$	−12.2567	−	21.2292i	−0.407427	−	0.705684i
$906$	−36.8016	−	13.3947i	−1.22265	−	0.445009i
$907$	2.62479	−	14.8859i	0.0871547	−	0.494279i	−0.909716	−	0.415231i	$-0.863701\pi$
$907$	2.62479	−	14.8859i	0.0871547	−	0.494279i	0.996871	−	0.0790481i	$-0.0251881\pi$
$908$	2.37211	+	13.4529i	0.0787213	+	0.446451i
$909$	−4.41147	+	1.60565i	−0.146319	+	0.0532559i
$910$	−10.1284	−	8.49870i	−0.335752	−	0.281729i
$911$	−12.8366			−0.425294			−0.212647	−	0.977129i	$-0.568208\pi$
$911$	−12.8366			−0.425294			−0.212647	+	0.977129i	$0.568208\pi$
$912$		0			0
$913$	5.62536			0.186172
$914$	−9.99660	−	8.38814i	−0.330658	−	0.277455i
$915$	34.4688	−	12.5456i	1.13950	−	0.414746i
$916$	−0.906726	−	5.14230i	−0.0299591	−	0.169906i
$917$	−8.68779	+	49.2709i	−0.286896	+	1.62707i
$918$	−10.4131	−	3.79007i	−0.343684	−	0.125091i
$919$	10.3396	+	17.9086i	0.341070	+	0.590751i	0.984632	−	0.174643i	$-0.0558772\pi$
$919$	10.3396	+	17.9086i	0.341070	+	0.590751i	−0.643561	+	0.765395i	$0.722544\pi$
$920$	3.06418	−	5.30731i	0.101023	−	0.174977i
$921$	41.2597	−	34.6210i	1.35955	−	1.14080i
$922$	3.37733	−	2.83391i	0.111226	−	0.0933300i
$923$	−4.15745	+	7.20092i	−0.136844	+	0.237021i
$924$	−6.71688	−	11.6340i	−0.220969	−	0.382730i
$925$	4.53209	+	1.64955i	0.149014	+	0.0542367i
$926$	4.63041	−	26.2604i	0.152165	−	0.862970i
$927$	−0.660444	−	3.74557i	−0.0216918	−	0.123021i
$928$	−7.94356	+	2.89122i	−0.260760	+	0.0949090i
$929$	−13.9802	−	11.7308i	−0.458677	−	0.384875i	0.383967	−	0.923347i	$-0.374558\pi$
$929$	−13.9802	−	11.7308i	−0.458677	−	0.384875i	−0.842644	+	0.538471i	$0.819002\pi$
$930$	−1.38919			−0.0455532
$931$		0			0
$932$	−27.0428			−0.885817
$933$	−22.7665	−	19.1034i	−0.745342	−	0.625416i
$934$	−28.2977	+	10.2995i	−0.925930	+	0.337011i
$935$	−1.17118	−	6.64208i	−0.0383016	−	0.217219i
$936$	−0.120615	+	0.684040i	−0.00394242	+	0.0223586i
$937$	4.46064	+	1.62354i	0.145723	+	0.0530387i	0.413852	−	0.910344i	$-0.364183\pi$
$937$	4.46064	+	1.62354i	0.145723	+	0.0530387i	−0.268129	+	0.963383i	$0.586405\pi$
$938$	3.55438	+	6.15636i	0.116055	+	0.201012i
$939$	12.3478	−	21.3870i	0.402954	−	0.697937i
$940$	−15.6459	+	13.1285i	−0.510313	+	0.428203i
$941$	36.0205	−	30.2248i	1.17424	−	0.985301i	0.174236	−	0.984704i	$-0.444254\pi$
$941$	36.0205	−	30.2248i	1.17424	−	0.985301i	1.00000		0.000596950i	$-0.000190015\pi$
$942$	5.98545	−	10.3671i	0.195017	−	0.337779i
$943$	−2.34730	−	4.06564i	−0.0764385	−	0.132395i
$944$	−0.673648	−	0.245188i	−0.0219254	−	0.00798019i
$945$	8.15745	−	46.2632i	0.265362	−	1.50494i
$946$	0.185975	+	1.05471i	0.00604656	+	0.0342917i
$947$	−34.7648	+	12.6533i	−1.12970	+	0.411178i	−0.838184	−	0.545387i	$-0.816383\pi$
$947$	−34.7648	+	12.6533i	−1.12970	+	0.411178i	−0.291518	+	0.956565i	$0.594160\pi$
$948$	3.22668	+	2.70751i	0.104798	+	0.0879358i
$949$	5.95191			0.193207
$950$		0			0
$951$	40.2276			1.30447
$952$	9.26857	+	7.77725i	0.300396	+	0.252062i
$953$	35.4351	−	12.8973i	1.14786	−	0.417785i	0.303111	−	0.952955i	$-0.401975\pi$
$953$	35.4351	−	12.8973i	1.14786	−	0.417785i	0.844744	+	0.535170i	$0.179752\pi$
$954$	0.154763	+	0.877705i	0.00501064	+	0.0284167i
$955$	−6.98040	+	39.5878i	−0.225880	+	1.28103i
$956$	0.268571	+	0.0977517i	0.00868620	+	0.00316152i
$957$	−11.2121	−	19.4200i	−0.362437	−	0.627759i
$958$	−4.08378	+	7.07331i	−0.131941	+	0.228528i
$959$	20.9368	−	17.5680i	0.676083	−	0.567301i
$960$	−2.87939	+	2.41609i	−0.0929318	+	0.0779790i
$961$	15.4317	−	26.7285i	0.497797	−	0.862209i
$962$	3.14796	+	5.45242i	0.101494	+	0.175793i
$963$	4.68479	+	1.70513i	0.150965	+	0.0549469i
$964$	0.538485	−	3.05390i	0.0173435	−	0.0983596i
$965$	5.79467	+	32.8632i	0.186537	+	1.05790i
$966$	−27.4047	+	9.97448i	−0.881731	+	0.320924i
$967$	31.0351	+	26.0415i	0.998021	+	0.837439i	0.986709	−	0.162497i	$-0.0519548\pi$
$967$	31.0351	+	26.0415i	0.998021	+	0.837439i	0.0113119	+	0.999936i	$0.496399\pi$
$968$	−9.00774			−0.289520
$969$		0			0
$970$	−3.06418			−0.0983848
$971$	−10.7843	−	9.04910i	−0.346085	−	0.290400i	0.453131	−	0.891444i	$-0.350307\pi$
$971$	−10.7843	−	9.04910i	−0.346085	−	0.290400i	−0.799216	+	0.601044i	$0.794751\pi$
$972$	−5.13816	+	1.87014i	−0.164806	+	0.0599846i
$973$	−2.05737	−	11.6679i	−0.0659563	−	0.374057i
$974$	4.61680	−	26.1832i	0.147932	−	0.838963i
$975$	2.30541	+	0.839100i	0.0738321	+	0.0268727i
$976$	−4.87939	−	8.45134i	−0.156185	−	0.270521i
$977$	17.6028	−	30.4890i	0.563164	−	0.975429i	−0.434054	−	0.900887i	$-0.642917\pi$
$977$	17.6028	−	30.4890i	0.563164	−	0.975429i	0.997218	−	0.0745421i	$-0.0237495\pi$
$978$	−6.81180	+	5.71578i	−0.217817	+	0.182771i
$979$	11.5109	−	9.65879i	0.367890	−	0.308696i
$980$	−18.6459	+	32.2956i	−0.595621	+	1.03165i
$981$	−2.94356	−	5.09840i	−0.0939807	−	0.162779i
$982$	−36.4873	−	13.2803i	−1.16436	−	0.423791i
$983$	3.89662	−	22.0988i	0.124283	−	0.704843i	−0.857448	−	0.514570i	$-0.827951\pi$
$983$	3.89662	−	22.0988i	0.124283	−	0.704843i	0.981731	−	0.190273i	$-0.0609374\pi$
$984$	0.500000	+	2.83564i	0.0159394	+	0.0903969i
$985$	−24.4142	+	8.88603i	−0.777900	+	0.283132i
$986$	15.4715	+	12.9822i	0.492714	+	0.413436i
$987$	97.1944			3.09373
$988$		0			0
$989$	2.32501			0.0739309
$990$	−1.15064	−	0.965505i	−0.0365699	−	0.0306858i
$991$	−25.4688	+	9.26990i	−0.809045	+	0.294468i	−0.713229	−	0.700931i	$-0.752768\pi$
$991$	−25.4688	+	9.26990i	−0.809045	+	0.294468i	−0.0958154	+	0.995399i	$0.530546\pi$
$992$	0.0641778	+	0.363970i	0.00203765	+	0.0115561i
$993$	8.28864	−	47.0072i	0.263032	−	1.49173i
$994$	30.3114	+	11.0324i	0.961419	+	0.349928i
$995$	−17.1925	−	29.7783i	−0.545040	−	0.944037i
$996$	−3.74510	+	6.48670i	−0.118668	+	0.205539i
$997$	21.4088	−	17.9641i	0.678023	−	0.568929i	−0.237405	−	0.971411i	$-0.576297\pi$
$997$	21.4088	−	17.9641i	0.678023	−	0.568929i	0.915428	+	0.402482i	$0.131852\pi$
$998$	15.8255	−	13.2791i	0.500947	−	0.420344i
$999$	−11.1848	+	19.3726i	−0.353871	+	0.612923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.m.415.1		6
19.2	odd	18		722.2.c.l.653.1		6
19.3	odd	18		722.2.c.l.429.1		6
19.4	even	9		722.2.e.b.389.1		6
19.5	even	9		722.2.a.l.1.1		3
19.6	even	9	inner	722.2.e.m.595.1		6
19.7	even	3		38.2.e.a.5.1	✓	6
19.8	odd	6		722.2.e.l.245.1		6
19.9	even	9		38.2.e.a.23.1	yes	6
19.10	odd	18		722.2.e.k.99.1		6
19.11	even	3		722.2.e.b.245.1		6
19.12	odd	6		722.2.e.k.423.1		6
19.13	odd	18		722.2.e.a.595.1		6
19.14	odd	18		722.2.a.k.1.3		3
19.15	odd	18		722.2.e.l.389.1		6
19.16	even	9		722.2.c.k.429.3		6
19.17	even	9		722.2.c.k.653.3		6
19.18	odd	2		722.2.e.a.415.1		6
57.5	odd	18		6498.2.a.bl.1.3		3
57.14	even	18		6498.2.a.bq.1.3		3
57.26	odd	6		342.2.u.c.271.1		6
57.47	odd	18		342.2.u.c.289.1		6
76.7	odd	6		304.2.u.c.81.1		6
76.43	odd	18		5776.2.a.bn.1.3		3
76.47	odd	18		304.2.u.c.289.1		6
76.71	even	18		5776.2.a.bo.1.1		3
95.7	odd	12		950.2.u.b.499.1		12
95.9	even	18		950.2.l.d.251.1		6
95.28	odd	36		950.2.u.b.99.1		12
95.47	odd	36		950.2.u.b.99.2		12
95.64	even	6		950.2.l.d.651.1		6
95.83	odd	12		950.2.u.b.499.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.5.1	✓	6	19.7	even	3
38.2.e.a.23.1	yes	6	19.9	even	9
304.2.u.c.81.1		6	76.7	odd	6
304.2.u.c.289.1		6	76.47	odd	18
342.2.u.c.271.1		6	57.26	odd	6
342.2.u.c.289.1		6	57.47	odd	18
722.2.a.k.1.3		3	19.14	odd	18
722.2.a.l.1.1		3	19.5	even	9
722.2.c.k.429.3		6	19.16	even	9
722.2.c.k.653.3		6	19.17	even	9
722.2.c.l.429.1		6	19.3	odd	18
722.2.c.l.653.1		6	19.2	odd	18
722.2.e.a.415.1		6	19.18	odd	2
722.2.e.a.595.1		6	19.13	odd	18
722.2.e.b.245.1		6	19.11	even	3
722.2.e.b.389.1		6	19.4	even	9
722.2.e.k.99.1		6	19.10	odd	18
722.2.e.k.423.1		6	19.12	odd	6
722.2.e.l.245.1		6	19.8	odd	6
722.2.e.l.389.1		6	19.15	odd	18
722.2.e.m.415.1		6	1.1	even	1	trivial
722.2.e.m.595.1		6	19.6	even	9	inner
950.2.l.d.251.1		6	95.9	even	18
950.2.l.d.651.1		6	95.64	even	6
950.2.u.b.99.1		12	95.28	odd	36
950.2.u.b.99.2		12	95.47	odd	36
950.2.u.b.499.1		12	95.7	odd	12
950.2.u.b.499.2		12	95.83	odd	12
5776.2.a.bn.1.3		3	76.43	odd	18
5776.2.a.bo.1.1		3	76.71	even	18
6498.2.a.bl.1.3		3	57.5	odd	18
6498.2.a.bq.1.3		3	57.14	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(1.76604 - 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.347296 - 1.96962i) q^{5} +(1.76604 + 0.642788i) q^{6} +(-2.53209 - 4.38571i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.407604 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(1.76604 - 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.347296 - 1.96962i) q^{5} +(1.76604 + 0.642788i) q^{6} +(-2.53209 - 4.38571i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.407604 - 0.342020i) q^{9} +(1.53209 - 1.28558i) q^{10} +(0.705737 - 1.22237i) q^{11} +(0.939693 + 1.62760i) q^{12} +(1.22668 + 0.446476i) q^{13} +(0.879385 - 4.98724i) q^{14} +(-0.652704 - 3.70167i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.83022 + 1.53574i) q^{17} +0.532089 q^{18} +2.00000 q^{20} +(-7.29086 - 6.11776i) q^{21} +(1.32635 - 0.482753i) q^{22} +(-0.532089 - 3.01763i) q^{23} +(-0.326352 + 1.85083i) q^{24} +(0.939693 + 0.342020i) q^{25} +(0.652704 + 1.13052i) q^{26} +(-2.31908 + 4.01676i) q^{27} +(3.87939 - 3.25519i) q^{28} +(6.47565 - 5.43372i) q^{29} +(1.87939 - 3.25519i) q^{30} +(-0.184793 - 0.320070i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.460637 - 2.61240i) q^{33} +(0.414878 + 2.35289i) q^{34} +(-9.51754 + 3.46410i) q^{35} +(0.407604 + 0.342020i) q^{36} +4.82295 q^{37} +2.45336 q^{39} +(1.53209 + 1.28558i) q^{40} +(1.43969 - 0.524005i) q^{41} +(-1.65270 - 9.37295i) q^{42} +(-0.131759 + 0.747243i) q^{43} +(1.32635 + 0.482753i) q^{44} +(-0.532089 - 0.921605i) q^{45} +(1.53209 - 2.65366i) q^{46} +(-7.82295 + 6.56423i) q^{47} +(-1.43969 + 1.20805i) q^{48} +(-9.32295 + 16.1478i) q^{49} +(0.500000 + 0.866025i) q^{50} +(4.21941 + 1.53574i) q^{51} +(-0.226682 + 1.28558i) q^{52} +(0.290859 + 1.64955i) q^{53} +(-4.35844 + 1.58634i) q^{54} +(-2.16250 - 1.81456i) q^{55} +5.06418 q^{56} +8.45336 q^{58} +(0.549163 + 0.460802i) q^{59} +(3.53209 - 1.28558i) q^{60} +(1.69459 + 9.61051i) q^{61} +(0.0641778 - 0.363970i) q^{62} +(-2.53209 - 0.921605i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.30541 - 2.26103i) q^{65} +(2.03209 - 1.70513i) q^{66} +(-1.07532 + 0.902302i) q^{67} +(-1.19459 + 2.06910i) q^{68} +(-2.87939 - 4.98724i) q^{69} +(-9.51754 - 3.46410i) q^{70} +(-1.10607 + 6.27282i) q^{71} +(0.0923963 + 0.524005i) q^{72} +(4.28446 - 1.55942i) q^{73} +(3.69459 + 3.10013i) q^{74} +1.87939 q^{75} -7.14796 q^{77} +(1.87939 + 1.57699i) q^{78} +(2.10607 - 0.766546i) q^{79} +(0.347296 + 1.96962i) q^{80} +(-1.79086 + 10.1565i) q^{81} +(1.43969 + 0.524005i) q^{82} +(1.99273 + 3.45150i) q^{83} +(4.75877 - 8.24243i) q^{84} +(3.66044 - 3.07148i) q^{85} +(-0.581252 + 0.487728i) q^{86} +(7.94356 - 13.7587i) q^{87} +(0.705737 + 1.22237i) q^{88} +(10.0039 + 3.64111i) q^{89} +(0.184793 - 1.04801i) q^{90} +(-1.14796 - 6.51038i) q^{91} +(2.87939 - 1.04801i) q^{92} +(-0.532089 - 0.446476i) q^{93} -10.2121 q^{94} -1.87939 q^{96} +(-1.17365 - 0.984808i) q^{97} +(-17.5214 + 6.37727i) q^{98} +(-0.130415 - 0.739620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} + 6 q^{6} - 6 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^3 + 6 * q^6 - 6 * q^7 - 3 * q^8 + 6 * q^9	\( 6 q + 6 q^{3} + 6 q^{6} - 6 q^{7} - 3 q^{8} + 6 q^{9} - 6 q^{11} - 6 q^{13} - 6 q^{14} - 6 q^{15} - 12 q^{17} - 6 q^{18} + 12 q^{20} - 12 q^{21} + 9 q^{22} + 6 q^{23} - 3 q^{24} + 6 q^{26} + 3 q^{27} + 12 q^{28} + 6 q^{31} - 6 q^{33} + 24 q^{34} - 12 q^{35} + 6 q^{36} - 12 q^{37} - 12 q^{39} + 3 q^{41} - 12 q^{42} - 6 q^{43} + 9 q^{44} + 6 q^{45} - 6 q^{47} - 3 q^{48} - 15 q^{49} + 3 q^{50} - 6 q^{51} + 12 q^{52} - 30 q^{53} - 18 q^{54} - 18 q^{55} + 12 q^{56} + 24 q^{58} + 15 q^{59} + 12 q^{60} + 6 q^{61} - 18 q^{62} - 6 q^{63} - 3 q^{64} + 12 q^{65} + 3 q^{66} + 18 q^{67} - 3 q^{68} - 6 q^{69} - 12 q^{70} + 18 q^{71} - 3 q^{72} + 33 q^{73} + 18 q^{74} - 12 q^{77} - 12 q^{79} + 21 q^{81} + 3 q^{82} - 6 q^{83} + 6 q^{84} - 24 q^{85} - 6 q^{86} + 18 q^{87} - 6 q^{88} + 36 q^{89} - 6 q^{90} + 24 q^{91} + 6 q^{92} + 6 q^{93} - 12 q^{94} - 6 q^{97} - 36 q^{98} - 15 q^{99}+O(q^{100}) \) 6 * q + 6 * q^3 + 6 * q^6 - 6 * q^7 - 3 * q^8 + 6 * q^9 - 6 * q^11 - 6 * q^13 - 6 * q^14 - 6 * q^15 - 12 * q^17 - 6 * q^18 + 12 * q^20 - 12 * q^21 + 9 * q^22 + 6 * q^23 - 3 * q^24 + 6 * q^26 + 3 * q^27 + 12 * q^28 + 6 * q^31 - 6 * q^33 + 24 * q^34 - 12 * q^35 + 6 * q^36 - 12 * q^37 - 12 * q^39 + 3 * q^41 - 12 * q^42 - 6 * q^43 + 9 * q^44 + 6 * q^45 - 6 * q^47 - 3 * q^48 - 15 * q^49 + 3 * q^50 - 6 * q^51 + 12 * q^52 - 30 * q^53 - 18 * q^54 - 18 * q^55 + 12 * q^56 + 24 * q^58 + 15 * q^59 + 12 * q^60 + 6 * q^61 - 18 * q^62 - 6 * q^63 - 3 * q^64 + 12 * q^65 + 3 * q^66 + 18 * q^67 - 3 * q^68 - 6 * q^69 - 12 * q^70 + 18 * q^71 - 3 * q^72 + 33 * q^73 + 18 * q^74 - 12 * q^77 - 12 * q^79 + 21 * q^81 + 3 * q^82 - 6 * q^83 + 6 * q^84 - 24 * q^85 - 6 * q^86 + 18 * q^87 - 6 * q^88 + 36 * q^89 - 6 * q^90 + 24 * q^91 + 6 * q^92 + 6 * q^93 - 12 * q^94 - 6 * q^97 - 36 * q^98 - 15 * q^99

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