LMFDB - Embedded newform 546.2.bx.b.97.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(97,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("546.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bx (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	546.97
Dual form			546.2.bx.b.349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.201763 + 0.201763i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-0.864369 - 2.50057i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.201763 + 0.201763i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-0.864369 - 2.50057i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.142668 - 0.247108i) q^{10} +(3.76078 - 1.00770i) q^{11} -1.00000 q^{12} +(3.08839 + 1.86060i) q^{13} +(-2.19165 + 1.48211i) q^{14} +(0.0738503 + 0.275613i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.53360 - 2.65627i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-0.152440 + 0.568913i) q^{19} +(-0.275613 - 0.0738503i) q^{20} +(0.501721 - 2.59774i) q^{21} +(-1.94672 - 3.37183i) q^{22} +(-0.501757 - 0.289689i) q^{23} +(0.258819 + 0.965926i) q^{24} -4.91858i q^{25} +(0.997865 - 3.46472i) q^{26} +1.00000i q^{27} +(1.99885 + 1.73338i) q^{28} +(5.10417 - 8.84068i) q^{29} +(0.247108 - 0.142668i) q^{30} +(6.91577 + 6.91577i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(3.76078 + 1.00770i) q^{33} +(-2.16884 + 2.16884i) q^{34} +(0.330125 - 0.678920i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-7.62705 + 2.04366i) q^{37} +0.588982 q^{38} +(1.74433 + 3.15552i) q^{39} +0.285336i q^{40} +(7.90367 - 2.11778i) q^{41} +(-2.63908 + 0.187721i) q^{42} +(0.751692 - 0.433989i) q^{43} +(-2.75308 + 2.75308i) q^{44} +(-0.0738503 + 0.275613i) q^{45} +(-0.149954 + 0.559637i) q^{46} +(1.05225 - 1.05225i) q^{47} +(0.866025 - 0.500000i) q^{48} +(-5.50573 + 4.32284i) q^{49} +(-4.75099 + 1.27302i) q^{50} -3.06720i q^{51} +(-3.60493 - 0.0671284i) q^{52} +9.83949 q^{53} +(0.965926 - 0.258819i) q^{54} +(0.962102 + 0.555470i) q^{55} +(1.15697 - 2.37937i) q^{56} +(-0.416473 + 0.416473i) q^{57} +(-9.86049 - 2.64211i) q^{58} +(-12.2057 - 3.27051i) q^{59} +(-0.201763 - 0.201763i) q^{60} +(2.76356 - 1.59554i) q^{61} +(4.89019 - 8.47005i) q^{62} +(1.73338 - 1.99885i) q^{63} +1.00000i q^{64} +(0.247723 + 0.998522i) q^{65} -3.89345i q^{66} +(3.37501 + 12.5957i) q^{67} +(2.65627 + 1.53360i) q^{68} +(-0.289689 - 0.501757i) q^{69} +(-0.741229 - 0.143159i) q^{70} +(-7.43034 - 1.99095i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-10.7299 + 10.7299i) q^{73} +(3.94805 + 6.83823i) q^{74} +(2.45929 - 4.25962i) q^{75} +(-0.152440 - 0.568913i) q^{76} +(-5.77053 - 8.53309i) q^{77} +(2.59653 - 2.50160i) q^{78} -9.59166 q^{79} +(0.275613 - 0.0738503i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.09124 - 7.08624i) q^{82} +(-10.2349 - 10.2349i) q^{83} +(0.864369 + 2.50057i) q^{84} +(0.226513 - 0.845359i) q^{85} +(-0.613754 - 0.613754i) q^{86} +(8.84068 - 5.10417i) q^{87} +(3.37183 + 1.94672i) q^{88} +(3.58656 + 13.3852i) q^{89} +0.285336 q^{90} +(1.98305 - 9.33100i) q^{91} +0.579379 q^{92} +(2.53135 + 9.44711i) q^{93} +(-1.28873 - 0.744051i) q^{94} +(-0.145542 + 0.0840288i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-2.65996 + 9.92712i) q^{97} +(5.60053 + 4.19930i) q^{98} +(2.75308 + 2.75308i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 8 * q^7 + 20 * q^9	$ 40 q + 8 q^{7} + 20 q^{9} + 8 q^{11} - 40 q^{12} - 8 q^{14} + 20 q^{16} - 16 q^{17} - 16 q^{19} + 4 q^{21} + 8 q^{22} - 32 q^{26} - 8 q^{28} + 8 q^{33} - 16 q^{34} + 40 q^{35} + 40 q^{37} + 16 q^{38} - 16 q^{39} + 4 q^{41} - 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} - 16 q^{50} + 8 q^{52} + 32 q^{53} + 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} - 84 q^{59} + 48 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} - 20 q^{70} - 40 q^{71} + 48 q^{73} + 8 q^{74} - 36 q^{75} - 16 q^{76} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} - 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} - 12 q^{89} + 32 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} - 8 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q + 8 * q^7 + 20 * q^9 + 8 * q^11 - 40 * q^12 - 8 * q^14 + 20 * q^16 - 16 * q^17 - 16 * q^19 + 4 * q^21 + 8 * q^22 - 32 * q^26 - 8 * q^28 + 8 * q^33 - 16 * q^34 + 40 * q^35 + 40 * q^37 + 16 * q^38 - 16 * q^39 + 4 * q^41 - 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 - 16 * q^50 + 8 * q^52 + 32 * q^53 + 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 - 84 * q^59 + 48 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 - 20 * q^70 - 40 * q^71 + 48 * q^73 + 8 * q^74 - 36 * q^75 - 16 * q^76 + 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 - 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 - 12 * q^89 + 32 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 - 8 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.201763	+	0.201763i	0.0902310	+	0.0902310i	0.750782	−	0.660551i	$-0.229677\pi$
$5$	0.201763	+	0.201763i	0.0902310	+	0.0902310i	−0.660551	+	0.750782i	$0.729677\pi$
$6$	0.258819	−	0.965926i	0.105662	−	0.394338i
$7$	−0.864369	−	2.50057i	−0.326701	−	0.945128i
$7$	−0.864369	−	2.50057i	−0.326701	−	0.945128i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.142668	−	0.247108i	0.0451155	−	0.0781424i
$11$	3.76078	−	1.00770i	1.13392	−	0.303833i	0.357415	−	0.933946i	$-0.383658\pi$
$11$	3.76078	−	1.00770i	1.13392	−	0.303833i	0.776503	+	0.630113i	$0.216991\pi$
$12$	−1.00000			−0.288675
$13$	3.08839	+	1.86060i	0.856566	+	0.516037i
$13$	3.08839	+	1.86060i	0.856566	+	0.516037i
$14$	−2.19165	+	1.48211i	−0.585744	+	0.396111i
$15$	0.0738503	+	0.275613i	0.0190681	+	0.0711630i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.53360	−	2.65627i	−0.371952	−	0.644240i	0.617914	−	0.786246i	$-0.287978\pi$
$17$	−1.53360	−	2.65627i	−0.371952	−	0.644240i	−0.989866	+	0.142006i	$0.954645\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−0.152440	+	0.568913i	−0.0349721	+	0.130518i	−0.981205	−	0.192969i	$-0.938188\pi$
$19$	−0.152440	+	0.568913i	−0.0349721	+	0.130518i	0.946233	+	0.323486i	$0.104855\pi$
$20$	−0.275613	−	0.0738503i	−0.0616289	−	0.0165134i
$21$	0.501721	−	2.59774i	0.109484	−	0.566874i
$22$	−1.94672	−	3.37183i	−0.415043	−	0.718876i
$23$	−0.501757	−	0.289689i	−0.104624	−	0.0604044i	0.446775	−	0.894646i	$-0.352572\pi$
$23$	−0.501757	−	0.289689i	−0.104624	−	0.0604044i	−0.551399	+	0.834242i	$0.685906\pi$
$24$	0.258819	+	0.965926i	0.0528312	+	0.197169i
$25$		−	4.91858i		−	0.983717i
$26$	0.997865	−	3.46472i	0.195697	−	0.679487i
$27$			1.00000i			0.192450i
$28$	1.99885	+	1.73338i	0.377748	+	0.327577i
$29$	5.10417	−	8.84068i	0.947820	−	1.64167i	0.197816	−	0.980239i	$-0.436615\pi$
$29$	5.10417	−	8.84068i	0.947820	−	1.64167i	0.750004	−	0.661434i	$-0.230052\pi$
$30$	0.247108	−	0.142668i	0.0451155	−	0.0260475i
$31$	6.91577	+	6.91577i	1.24211	+	1.24211i	0.959125	+	0.282984i	$0.0913242\pi$
$31$	6.91577	+	6.91577i	1.24211	+	1.24211i	0.282984	+	0.959125i	$0.408676\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	3.76078	+	1.00770i	0.654668	+	0.175418i
$34$	−2.16884	+	2.16884i	−0.371952	+	0.371952i
$35$	0.330125	−	0.678920i	0.0558013	−	0.114758i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	−7.62705	+	2.04366i	−1.25388	+	0.335976i	−0.823834	−	0.566831i	$-0.808169\pi$
$37$	−7.62705	+	2.04366i	−1.25388	+	0.335976i	−0.430046	+	0.902807i	$0.641503\pi$
$38$	0.588982			0.0955455
$39$	1.74433	+	3.15552i	0.279316	+	0.505288i
$40$			0.285336i			0.0451155i
$41$	7.90367	−	2.11778i	1.23435	−	0.330742i	0.418076	−	0.908412i	$-0.362705\pi$
$41$	7.90367	−	2.11778i	1.23435	−	0.330742i	0.816270	+	0.577670i	$0.196038\pi$
$42$	−2.63908	+	0.187721i	−0.407219	+	0.0289659i
$43$	0.751692	−	0.433989i	0.114632	−	0.0661828i	−0.441588	−	0.897218i	$-0.645585\pi$
$43$	0.751692	−	0.433989i	0.114632	−	0.0661828i	0.556220	+	0.831035i	$0.312251\pi$
$44$	−2.75308	+	2.75308i	−0.415043	+	0.415043i
$45$	−0.0738503	+	0.275613i	−0.0110090	+	0.0410860i
$46$	−0.149954	+	0.559637i	−0.0221096	+	0.0825140i
$47$	1.05225	−	1.05225i	0.153486	−	0.153486i	−0.626187	−	0.779673i	$-0.715385\pi$
$47$	1.05225	−	1.05225i	0.153486	−	0.153486i	0.779673	+	0.626187i	$0.215385\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−5.50573	+	4.32284i	−0.786533	+	0.617548i
$50$	−4.75099	+	1.27302i	−0.671891	+	0.180033i
$51$		−	3.06720i		−	0.429493i
$52$	−3.60493	−	0.0671284i	−0.499913	−	0.00930904i
$53$	9.83949			1.35156			0.675779	−	0.737105i	$-0.263808\pi$
$53$	9.83949			1.35156			0.675779	+	0.737105i	$0.263808\pi$
$54$	0.965926	−	0.258819i	0.131446	−	0.0352208i
$55$	0.962102	+	0.555470i	0.129730	+	0.0748995i
$56$	1.15697	−	2.37937i	0.154607	−	0.317957i
$57$	−0.416473	+	0.416473i	−0.0551632	+	0.0551632i
$58$	−9.86049	−	2.64211i	−1.29475	−	0.346926i
$59$	−12.2057	−	3.27051i	−1.58905	−	0.425784i	−0.647335	−	0.762206i	$-0.724117\pi$
$59$	−12.2057	−	3.27051i	−1.58905	−	0.425784i	−0.941711	+	0.336422i	$0.890783\pi$
$60$	−0.201763	−	0.201763i	−0.0260475	−	0.0260475i
$61$	2.76356	−	1.59554i	0.353838	−	0.204288i	−0.312536	−	0.949906i	$-0.601179\pi$
$61$	2.76356	−	1.59554i	0.353838	−	0.204288i	0.666374	+	0.745617i	$0.267845\pi$
$62$	4.89019	−	8.47005i	0.621054	−	1.07570i
$63$	1.73338	−	1.99885i	0.218385	−	0.251832i
$64$			1.00000i			0.125000i
$65$	0.247723	+	0.998522i	0.0307263	+	0.123851i
$66$		−	3.89345i		−	0.479250i
$67$	3.37501	+	12.5957i	0.412323	+	1.53881i	0.790139	+	0.612928i	$0.210008\pi$
$67$	3.37501	+	12.5957i	0.412323	+	1.53881i	−0.377816	+	0.925881i	$0.623325\pi$
$68$	2.65627	+	1.53360i	0.322120	+	0.185976i
$69$	−0.289689	−	0.501757i	−0.0348745	−	0.0604044i
$70$	−0.741229	−	0.143159i	−0.0885938	−	0.0171107i
$71$	−7.43034	−	1.99095i	−0.881820	−	0.236283i	−0.210628	−	0.977566i	$-0.567551\pi$
$71$	−7.43034	−	1.99095i	−0.881820	−	0.236283i	−0.671192	+	0.741284i	$0.734217\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	−10.7299	+	10.7299i	−1.25584	+	1.25584i	−0.302781	+	0.953060i	$0.597915\pi$
$73$	−10.7299	+	10.7299i	−1.25584	+	1.25584i	−0.953060	+	0.302781i	$0.902085\pi$
$74$	3.94805	+	6.83823i	0.458952	+	0.794928i
$75$	2.45929	−	4.25962i	0.283975	−	0.491858i
$76$	−0.152440	−	0.568913i	−0.0174860	−	0.0652588i
$77$	−5.77053	−	8.53309i	−0.657613	−	0.972436i
$78$	2.59653	−	2.50160i	0.294000	−	0.283251i
$79$	−9.59166			−1.07915			−0.539573	−	0.841939i	$-0.681414\pi$
$79$	−9.59166			−1.07915			−0.539573	+	0.841939i	$0.681414\pi$
$80$	0.275613	−	0.0738503i	0.0308145	−	0.00825671i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.09124	−	7.08624i	−0.451802	−	0.782544i
$83$	−10.2349	−	10.2349i	−1.12343	−	1.12343i	−0.991222	−	0.132206i	$-0.957794\pi$
$83$	−10.2349	−	10.2349i	−1.12343	−	1.12343i	−0.132206	−	0.991222i	$-0.542206\pi$
$84$	0.864369	+	2.50057i	0.0943104	+	0.272835i
$85$	0.226513	−	0.845359i	0.0245688	−	0.0916921i
$86$	−0.613754	−	0.613754i	−0.0661828	−	0.0661828i
$87$	8.84068	−	5.10417i	0.947820	−	0.547224i
$88$	3.37183	+	1.94672i	0.359438	+	0.207521i
$89$	3.58656	+	13.3852i	0.380175	+	1.41883i	0.845634	+	0.533763i	$0.179223\pi$
$89$	3.58656	+	13.3852i	0.380175	+	1.41883i	−0.465459	+	0.885069i	$0.654111\pi$
$90$	0.285336			0.0300770
$91$	1.98305	−	9.33100i	0.207880	−	0.978154i
$92$	0.579379			0.0604044
$93$	2.53135	+	9.44711i	0.262488	+	0.979620i
$94$	−1.28873	−	0.744051i	−0.132923	−	0.0767430i
$95$	−0.145542	+	0.0840288i	−0.0149323	+	0.00862117i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−2.65996	+	9.92712i	−0.270078	+	1.00795i	0.688990	+	0.724771i	$0.258055\pi$
$97$	−2.65996	+	9.92712i	−0.270078	+	1.00795i	−0.959068	+	0.283175i	$0.908612\pi$
$98$	5.60053	+	4.19930i	0.565739	+	0.424193i
$99$	2.75308	+	2.75308i	0.276695	+	0.276695i
$100$	2.45929	+	4.25962i	0.245929	+	0.425962i
$101$	1.77247	−	3.07001i	0.176368	−	0.305478i	−0.764266	−	0.644901i	$-0.776899\pi$
$101$	1.77247	−	3.07001i	0.176368	−	0.305478i	0.940634	+	0.339423i	$0.110232\pi$
$102$	−2.96268	+	0.793849i	−0.293349	+	0.0786028i
$103$	−14.7414			−1.45251			−0.726257	−	0.687423i	$-0.758742\pi$
$103$	−14.7414			−1.45251			−0.726257	+	0.687423i	$0.758742\pi$
$104$	0.868182	+	3.49947i	0.0851323	+	0.343151i
$105$	0.625357	−	0.422900i	0.0610286	−	0.0412708i
$106$	−2.54665	−	9.50421i	−0.247352	−	0.923131i
$107$	−6.94326	+	12.0261i	−0.671230	+	1.16260i	0.306325	+	0.951927i	$0.400900\pi$
$107$	−6.94326	+	12.0261i	−0.671230	+	1.16260i	−0.977556	+	0.210678i	$0.932433\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	9.08175	−	9.08175i	0.869874	−	0.869874i	−0.122584	−	0.992458i	$-0.539118\pi$
$109$	9.08175	−	9.08175i	0.869874	−	0.869874i	0.992458	+	0.122584i	$0.0391182\pi$
$110$	0.287532	−	1.07309i	0.0274151	−	0.102315i
$111$	−7.62705	−	2.04366i	−0.723928	−	0.193976i
$112$	−2.59774	−	0.501721i	−0.245464	−	0.0474081i
$113$	9.94827	+	17.2309i	0.935854	+	1.62095i	0.773103	+	0.634280i	$0.218703\pi$
$113$	9.94827	+	17.2309i	0.935854	+	1.62095i	0.162751	+	0.986667i	$0.447963\pi$
$114$	0.510073	+	0.294491i	0.0477728	+	0.0275816i
$115$	−0.0427873	−	0.159684i	−0.00398994	−	0.0148906i
$116$			10.2083i			0.947820i
$117$	−0.0671284	+	3.60493i	−0.00620603	+	0.333276i
$118$			12.6363i			1.16326i
$119$	−5.31660	+	6.13087i	−0.487372	+	0.562016i
$120$	−0.142668	+	0.247108i	−0.0130237	+	0.0225578i
$121$	3.60175	−	2.07947i	0.327432	−	0.189043i
$122$	−2.25644	−	2.25644i	−0.204288	−	0.204288i
$123$	7.90367	+	2.11778i	0.712650	+	0.190954i
$124$	−9.44711	−	2.53135i	−0.848376	−	0.227322i
$125$	2.00120	−	2.00120i	0.178993	−	0.178993i
$126$	−2.37937	−	1.15697i	−0.211971	−	0.103071i
$127$	3.79239	+	2.18954i	0.336520	+	0.194290i	0.658732	−	0.752378i	$-0.271093\pi$
$127$	3.79239	+	2.18954i	0.336520	+	0.194290i	−0.322212	+	0.946667i	$0.604426\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	0.867979			0.0764213
$130$	0.900383	−	0.497719i	0.0789688	−	0.0436528i
$131$			3.90543i			0.341219i	0.985339	+	0.170609i	$0.0545736\pi$
$131$			3.90543i			0.341219i	−0.985339	+	0.170609i	$0.945426\pi$
$132$	−3.76078	+	1.00770i	−0.327334	+	0.0877089i
$133$	1.55437	−	0.110564i	0.134781	−	0.00958713i
$134$	11.2930	−	6.52001i	0.975566	−	0.563243i
$135$	−0.201763	+	0.201763i	−0.0173650	+	0.0173650i
$136$	0.793849	−	2.96268i	0.0680720	−	0.254048i
$137$	1.67780	−	6.26163i	0.143344	−	0.534967i	−0.856479	−	0.516181i	$-0.827353\pi$
$137$	1.67780	−	6.26163i	0.143344	−	0.534967i	0.999824	−	0.0187862i	$-0.00598018\pi$
$138$	−0.409683	+	0.409683i	−0.0348745	+	0.0348745i
$139$	0.776781	−	0.448475i	0.0658857	−	0.0380391i	−0.466695	−	0.884418i	$-0.654556\pi$
$139$	0.776781	−	0.448475i	0.0658857	−	0.0380391i	0.532581	+	0.846379i	$0.321222\pi$
$140$	0.0535634	+	0.753024i	0.00452694	+	0.0636422i
$141$	1.43740	−	0.385149i	0.121051	−	0.0324354i
$142$			7.69246i			0.645537i
$143$	13.4897	+	3.88513i	1.12807	+	0.324891i
$144$	1.00000			0.0833333
$145$	2.81355	−	0.753889i	0.233653	−	0.0626070i
$146$	13.1414	+	7.58719i	1.08759	+	0.627921i
$147$	−6.92952	+	0.990822i	−0.571537	+	0.0817216i
$148$	5.58339	−	5.58339i	0.458952	−	0.458952i
$149$	−9.68110	−	2.59404i	−0.793107	−	0.212512i	−0.160552	−	0.987027i	$-0.551327\pi$
$149$	−9.68110	−	2.59404i	−0.793107	−	0.212512i	−0.632555	+	0.774515i	$0.717994\pi$
$150$	−4.75099	−	1.27302i	−0.387916	−	0.103942i
$151$	4.20040	+	4.20040i	0.341823	+	0.341823i	0.857052	−	0.515229i	$-0.172293\pi$
$151$	4.20040	+	4.20040i	0.341823	+	0.341823i	−0.515229	+	0.857052i	$0.672293\pi$
$152$	−0.510073	+	0.294491i	−0.0413724	+	0.0238864i
$153$	1.53360	−	2.65627i	0.123984	−	0.214747i
$154$	−6.74881	+	7.78243i	−0.543834	+	0.627126i
$155$			2.79069i			0.224153i
$156$	−3.08839	−	1.86060i	−0.247269	−	0.148967i
$157$			1.49857i			0.119599i	0.998210	+	0.0597995i	$0.0190461\pi$
$157$			1.49857i			0.119599i	−0.998210	+	0.0597995i	$0.980954\pi$
$158$	2.48250	+	9.26483i	0.197497	+	0.737070i
$159$	8.52125	+	4.91974i	0.675779	+	0.390161i
$160$	−0.142668	−	0.247108i	−0.0112789	−	0.0195356i
$161$	−0.290686	+	1.50508i	−0.0229093	+	0.118617i
$162$	0.965926	+	0.258819i	0.0758903	+	0.0203347i
$163$	−1.74039	+	6.49523i	−0.136318	+	0.508746i	0.863671	+	0.504056i	$0.168159\pi$
$163$	−1.74039	+	6.49523i	−0.136318	+	0.508746i	−0.999989	+	0.00468978i	$0.998507\pi$
$164$	−5.78589	+	5.78589i	−0.451802	+	0.451802i
$165$	0.555470	+	0.962102i	0.0432433	+	0.0748995i
$166$	−7.23718	+	12.5352i	−0.561714	+	0.972917i
$167$	−2.01049	−	7.50324i	−0.155576	−	0.580618i	−0.999055	−	0.0434561i	$-0.986163\pi$
$167$	−2.01049	−	7.50324i	−0.155576	−	0.580618i	0.843479	−	0.537162i	$-0.180504\pi$
$168$	2.19165	−	1.48211i	0.169090	−	0.114347i
$169$	6.07635	+	11.4925i	0.467411	+	0.884040i
$170$	−0.875181			−0.0671233
$171$	−0.568913	+	0.152440i	−0.0435059	+	0.0116574i
$172$	−0.433989	+	0.751692i	−0.0330914	+	0.0573159i
$173$	−6.10424	−	10.5728i	−0.464096	−	0.803839i	0.535064	−	0.844812i	$-0.320288\pi$
$173$	−6.10424	−	10.5728i	−0.464096	−	0.803839i	−0.999160	+	0.0409730i	$0.986954\pi$
$174$	−7.21838	−	7.21838i	−0.547224	−	0.547224i
$175$	−12.2993	+	4.25147i	−0.929738	+	0.321381i
$176$	1.00770	−	3.76078i	0.0759581	−	0.283480i
$177$	−8.93519	−	8.93519i	−0.671610	−	0.671610i
$178$	12.0009	−	6.92871i	0.899504	−	0.519329i
$179$	2.26143	+	1.30564i	0.169027	+	0.0975880i	0.582127	−	0.813098i	$-0.302221\pi$
$179$	2.26143	+	1.30564i	0.169027	+	0.0975880i	−0.413100	+	0.910686i	$0.635554\pi$
$180$	−0.0738503	−	0.275613i	−0.00550448	−	0.0205430i
$181$	−0.0134817			−0.00100209			−0.000501043	−	1.00000i	$-0.500159\pi$
$181$	−0.0134817			−0.00100209			−0.000501043		1.00000i	$0.500159\pi$
$182$	−9.52630	+	0.499562i	−0.706137	+	0.0370300i
$183$	3.19109			0.235892
$184$	−0.149954	−	0.559637i	−0.0110548	−	0.0412570i
$185$	−1.95119	−	1.12652i	−0.143454	−	0.0828234i
$186$	8.47005	−	4.89019i	0.621054	−	0.358566i
$187$	−8.44425	−	8.44425i	−0.617505	−	0.617505i
$188$	−0.385149	+	1.43740i	−0.0280899	+	0.104833i
$189$	2.50057	−	0.864369i	0.181890	−	0.0628736i
$190$	0.118835	+	0.118835i	0.00862117	+	0.00862117i
$191$	−1.09040	−	1.88863i	−0.0788988	−	0.136657i	0.823876	−	0.566770i	$-0.191807\pi$
$191$	−1.09040	−	1.88863i	−0.0788988	−	0.136657i	−0.902775	+	0.430113i	$0.858474\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−7.19589	+	1.92813i	−0.517971	+	0.138790i	−0.508328	−	0.861164i	$-0.669736\pi$
$193$	−7.19589	+	1.92813i	−0.517971	+	0.138790i	−0.00964322	+	0.999954i	$0.503070\pi$
$194$	10.2773			0.737868
$195$	−0.284726	+	0.988607i	−0.0203897	+	0.0707956i
$196$	2.60668	−	6.49655i	0.186192	−	0.464039i
$197$	4.39763	+	16.4122i	0.313318	+	1.16932i	0.925545	+	0.378637i	$0.123607\pi$
$197$	4.39763	+	16.4122i	0.313318	+	1.16932i	−0.612227	+	0.790682i	$0.709726\pi$
$198$	1.94672	−	3.37183i	0.138348	−	0.239625i
$199$	−11.0233	−	19.0929i	−0.781421	−	1.35346i	−0.931114	−	0.364728i	$-0.881162\pi$
$199$	−11.0233	−	19.0929i	−0.781421	−	1.35346i	0.149693	−	0.988732i	$-0.452171\pi$
$200$	3.47796	−	3.47796i	0.245929	−	0.245929i
$201$	−3.37501	+	12.5957i	−0.238055	+	0.888432i
$202$	−3.42416	−	0.917500i	−0.240923	−	0.0645551i
$203$	−26.5186	−	5.12173i	−1.86124	−	0.359475i
$204$	1.53360	+	2.65627i	0.107373	+	0.185976i
$205$	2.02196	+	1.16738i	0.141220	+	0.0815331i
$206$	3.81536	+	14.2391i	0.265829	+	0.992086i
$207$		−	0.579379i		−	0.0402696i
$208$	3.15552	−	1.74433i	0.218796	−	0.120947i
$209$			2.29317i			0.158622i
$210$	−0.570344	−	0.494594i	−0.0393575	−	0.0341302i
$211$	−8.77636	+	15.2011i	−0.604190	+	1.04649i	0.387989	+	0.921664i	$0.373170\pi$
$211$	−8.77636	+	15.2011i	−0.604190	+	1.04649i	−0.992179	+	0.124823i	$0.960164\pi$
$212$	−8.52125	+	4.91974i	−0.585242	+	0.337889i
$213$	−5.43939	−	5.43939i	−0.372701	−	0.372701i
$214$	13.4133	+	3.59410i	0.916918	+	0.245687i
$215$	0.239226	+	0.0641005i	0.0163151	+	0.00437162i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	11.3156	−	23.2712i	0.768153	−	1.57975i
$218$	−11.1228	−	6.42177i	−0.753333	−	0.434937i
$219$	−14.6573	+	3.92742i	−0.990451	+	0.265390i
$220$	−1.11094			−0.0748995
$221$	0.205896	−	11.0570i	0.0138501	−	0.743776i
$222$			7.89611i			0.529952i
$223$	17.4443	−	4.67419i	1.16816	−	0.313007i	0.377938	−	0.925831i	$-0.376633\pi$
$223$	17.4443	−	4.67419i	1.16816	−	0.313007i	0.790219	+	0.612824i	$0.209967\pi$
$224$	0.187721	+	2.63908i	0.0125426	+	0.176331i
$225$	4.25962	−	2.45929i	0.283975	−	0.163953i
$226$	14.0690	−	14.0690i	0.935854	−	0.935854i
$227$	−3.44569	+	12.8595i	−0.228698	+	0.853514i	0.752191	+	0.658945i	$0.228997\pi$
$227$	−3.44569	+	12.8595i	−0.228698	+	0.853514i	−0.980889	+	0.194568i	$0.937669\pi$
$228$	0.152440	−	0.568913i	0.0100956	−	0.0376772i
$229$	5.57218	−	5.57218i	0.368220	−	0.368220i	−0.498608	−	0.866828i	$-0.666155\pi$
$229$	5.57218	−	5.57218i	0.368220	−	0.368220i	0.866828	+	0.498608i	$0.166155\pi$
$230$	−0.143169	+	0.0826587i	−0.00944029	+	0.00545036i
$231$	−0.730881	−	10.2751i	−0.0480885	−	0.676054i
$232$	9.86049	−	2.64211i	0.647373	−	0.173463i
$233$		−	8.06554i		−	0.528391i	−0.964469	−	0.264195i	$-0.914894\pi$
$233$		−	8.06554i		−	0.528391i	0.964469	−	0.264195i	$-0.0851064\pi$
$234$	3.49947	−	0.868182i	0.228767	−	0.0567549i
$235$	0.424608			0.0276984
$236$	12.2057	−	3.27051i	0.794523	−	0.212892i
$237$	−8.30662	−	4.79583i	−0.539573	−	0.311522i
$238$	7.29801	+	3.54866i	0.473060	+	0.230025i
$239$	7.09809	−	7.09809i	0.459137	−	0.459137i	−0.439235	−	0.898372i	$-0.644750\pi$
$239$	7.09809	−	7.09809i	0.459137	−	0.459137i	0.898372	+	0.439235i	$0.144750\pi$
$240$	0.275613	+	0.0738503i	0.0177907	+	0.00476702i
$241$	12.8835	+	3.45212i	0.829899	+	0.222371i	0.648670	−	0.761070i	$-0.275326\pi$
$241$	12.8835	+	3.45212i	0.829899	+	0.222371i	0.181230	+	0.983441i	$0.441992\pi$
$242$	−2.94081	−	2.94081i	−0.189043	−	0.189043i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−1.59554	+	2.76356i	−0.102144	+	0.176919i
$245$	−1.98304	−	0.238664i	−0.126692	−	0.0152477i
$246$		−	8.18248i		−	0.521696i
$247$	−1.52931	+	1.47340i	−0.0973078	+	0.0937501i
$248$			9.78037i			0.621054i
$249$	−3.74624	−	13.9812i	−0.237408	−	0.886020i
$250$	−2.45096	−	1.41506i	−0.155012	−	0.0894964i
$251$	−0.834005	−	1.44454i	−0.0526419	−	0.0911785i	0.838504	−	0.544896i	$-0.183431\pi$
$251$	−0.834005	−	1.44454i	−0.0526419	−	0.0911785i	−0.891146	+	0.453717i	$0.850098\pi$
$252$	−0.501721	+	2.59774i	−0.0316054	+	0.163643i
$253$	−2.17892	−	0.583839i	−0.136987	−	0.0367057i
$254$	1.13339	−	4.22986i	0.0711150	−	0.265405i
$255$	0.618846	−	0.618846i	0.0387536	−	0.0387536i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.317610	+	0.550117i	−0.0198120	+	0.0343153i	−0.875761	−	0.482744i	$-0.839640\pi$
$257$	−0.317610	+	0.550117i	−0.0198120	+	0.0343153i	0.855949	+	0.517060i	$0.172973\pi$
$258$	−0.224649	−	0.838403i	−0.0139861	−	0.0521967i
$259$	11.7029	+	17.3055i	0.727184	+	1.07531i
$260$	−0.713796	−	0.740884i	−0.0442677	−	0.0459477i
$261$	10.2083			0.631880
$262$	3.77235	−	1.01080i	0.233057	−	0.0624474i
$263$	2.37411	−	4.11207i	0.146394	−	0.253561i	−0.783498	−	0.621394i	$-0.786567\pi$
$263$	2.37411	−	4.11207i	0.146394	−	0.253561i	0.929892	+	0.367832i	$0.119900\pi$
$264$	1.94672	+	3.37183i	0.119813	+	0.207521i
$265$	1.98524	+	1.98524i	0.121952	+	0.121952i
$266$	−0.509098	−	1.47279i	−0.0312148	−	0.0903027i
$267$	−3.58656	+	13.3852i	−0.219494	+	0.819163i
$268$	−9.22069	−	9.22069i	−0.563243	−	0.563243i
$269$	14.6914	−	8.48207i	0.895749	−	0.517161i	0.0199305	−	0.999801i	$-0.493656\pi$
$269$	14.6914	−	8.48207i	0.895749	−	0.517161i	0.875819	+	0.482640i	$0.160322\pi$
$270$	0.247108	+	0.142668i	0.0150385	+	0.00868249i
$271$	−2.31119	−	8.62547i	−0.140395	−	0.523960i	−0.999917	−	0.0128623i	$-0.995906\pi$
$271$	−2.31119	−	8.62547i	−0.140395	−	0.523960i	0.859523	−	0.511098i	$-0.170761\pi$
$272$	−3.06720			−0.185976
$273$	6.38287	−	7.08936i	0.386309	−	0.429067i
$274$	−6.48252			−0.391623
$275$	−4.95645	−	18.4977i	−0.298885	−	1.11545i
$276$	0.501757	+	0.289689i	0.0302022	+	0.0174373i
$277$	11.5675	−	6.67850i	0.695023	−	0.401272i	−0.110468	−	0.993880i	$-0.535235\pi$
$277$	11.5675	−	6.67850i	0.695023	−	0.401272i	0.805491	+	0.592608i	$0.201902\pi$
$278$	−0.634239	−	0.634239i	−0.0380391	−	0.0380391i
$279$	−2.53135	+	9.44711i	−0.151548	+	0.565584i
$280$	0.713503	−	0.246635i	0.0426399	−	0.0147393i
$281$	−9.26988	−	9.26988i	−0.552994	−	0.552994i	0.374309	−	0.927304i	$-0.377880\pi$
$281$	−9.26988	−	9.26988i	−0.552994	−	0.552994i	−0.927304	+	0.374309i	$0.877880\pi$
$282$	−0.744051	−	1.28873i	−0.0443076	−	0.0767430i
$283$	6.40543	−	11.0945i	0.380763	−	0.659502i	−0.610408	−	0.792087i	$-0.708995\pi$
$283$	6.40543	−	11.0945i	0.380763	−	0.659502i	0.991172	+	0.132585i	$0.0423279\pi$
$284$	7.43034	−	1.99095i	0.440910	−	0.118141i
$285$	−0.168058			−0.00995487
$286$	0.261361	−	14.0356i	0.0154546	−	0.829942i
$287$	−12.1274	−	17.9332i	−0.715855	−	1.05856i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	3.79615	−	6.57513i	0.223303	−	0.386772i
$290$	−1.45640	−	2.52256i	−0.0855228	−	0.148130i
$291$	−7.26716	+	7.26716i	−0.426008	+	0.426008i
$292$	3.92742	−	14.6573i	0.229835	−	0.857755i
$293$	−3.73867	−	1.00177i	−0.218415	−	0.0585243i	0.147952	−	0.988995i	$-0.452732\pi$
$293$	−3.73867	−	1.00177i	−0.218415	−	0.0585243i	−0.366367	+	0.930470i	$0.619399\pi$
$294$	2.75055	+	6.43696i	0.160415	+	0.375411i
$295$	−1.80279	−	3.12252i	−0.104962	−	0.181800i
$296$	−6.83823	−	3.94805i	−0.397464	−	0.229476i
$297$	1.00770	+	3.76078i	0.0584726	+	0.218223i
$298$			10.0226i			0.580595i
$299$	−1.01063	−	1.82824i	−0.0584461	−	0.105730i
$300$			4.91858i			0.283975i
$301$	−1.73496	−	1.50453i	−0.100001	−	0.0867198i
$302$	2.97013	−	5.14441i	0.170912	−	0.296028i
$303$	3.07001	−	1.77247i	0.176368	−	0.101826i
$304$	0.416473	+	0.416473i	0.0238864	+	0.0238864i
$305$	0.879505	+	0.235663i	0.0503603	+	0.0134940i
$306$	−2.96268	−	0.793849i	−0.169365	−	0.0453813i
$307$	−16.9410	+	16.9410i	−0.966872	+	0.966872i	−0.999469	−	0.0325969i	$-0.989622\pi$
$307$	−16.9410	+	16.9410i	−0.966872	+	0.966872i	0.0325969	+	0.999469i	$0.489622\pi$
$308$	9.26397	+	4.50461i	0.527864	+	0.256674i
$309$	−12.7664	−	7.37071i	−0.726257	−	0.419305i
$310$	2.69560	−	0.722283i	0.153100	−	0.0410229i
$311$	−21.1282			−1.19807			−0.599034	−	0.800724i	$-0.704449\pi$
$311$	−21.1282			−1.19807			−0.599034	+	0.800724i	$0.704449\pi$
$312$	−0.997865	+	3.46472i	−0.0564930	+	0.196151i
$313$		−	28.4235i		−	1.60659i	−0.595580	−	0.803296i	$-0.703078\pi$
$313$		−	28.4235i		−	1.60659i	0.595580	−	0.803296i	$-0.296922\pi$
$314$	1.44751	−	0.387858i	0.0816876	−	0.0218881i
$315$	0.753024	−	0.0535634i	0.0424281	−	0.00301796i
$316$	8.30662	−	4.79583i	0.467284	−	0.269786i
$317$	−10.3506	+	10.3506i	−0.581349	+	0.581349i	−0.935274	−	0.353925i	$-0.884847\pi$
$317$	−10.3506	+	10.3506i	−0.581349	+	0.581349i	0.353925	+	0.935274i	$0.384847\pi$
$318$	2.54665	−	9.50421i	0.142809	−	0.532970i
$319$	10.2869	−	38.3913i	0.575957	−	2.14950i
$320$	−0.201763	+	0.201763i	−0.0112789	+	0.0112789i
$321$	−12.0261	+	6.94326i	−0.671230	+	0.387535i
$322$	1.52903	−	0.108761i	0.0852095	−	0.00606104i
$323$	1.74497	−	0.467563i	0.0970926	−	0.0260159i
$324$		−	1.00000i		−	0.0555556i
$325$	9.15151	−	15.1905i	0.507634	−	0.842619i
$326$	6.72436			0.372428
$327$	12.4059	−	3.32415i	0.686048	−	0.183826i
$328$	7.08624	+	4.09124i	0.391272	+	0.225901i
$329$	−3.54075	−	1.72169i	−0.195208	−	0.0949198i
$330$	0.785553	−	0.785553i	0.0432433	−	0.0432433i
$331$	−15.1557	−	4.06095i	−0.833031	−	0.223210i	−0.182995	−	0.983114i	$-0.558579\pi$
$331$	−15.1557	−	4.06095i	−0.833031	−	0.223210i	−0.650036	+	0.759904i	$0.725246\pi$
$332$	13.9812	+	3.74624i	0.767316	+	0.205602i
$333$	−5.58339	−	5.58339i	−0.305968	−	0.305968i
$334$	−6.72722	+	3.88396i	−0.368097	+	0.212521i
$335$	−1.86039	+	3.22229i	−0.101644	+	0.176053i
$336$	−1.99885	−	1.73338i	−0.109046	−	0.0945634i
$337$		−	9.01866i		−	0.491278i	−0.969361	−	0.245639i	$-0.921002\pi$
$337$		−	9.01866i		−	0.491278i	0.969361	−	0.245639i	$-0.0789977\pi$
$338$	9.52825	−	8.84379i	0.518268	−	0.481039i
$339$			19.8965i			1.08063i
$340$	0.226513	+	0.845359i	0.0122844	+	0.0458461i
$341$	32.9777	+	19.0397i	1.78584	+	1.03106i
$342$	0.294491	+	0.510073i	0.0159243	+	0.0275816i
$343$	15.5686	+	10.0310i	0.840623	+	0.541621i
$344$	0.838403	+	0.224649i	0.0452037	+	0.0121123i
$345$	0.0427873	−	0.159684i	0.00230359	−	0.00859712i
$346$	−8.63269	+	8.63269i	−0.464096	+	0.464096i
$347$	6.95315	+	12.0432i	0.373265	+	0.646514i	0.990066	−	0.140606i	$-0.0449049\pi$
$347$	6.95315	+	12.0432i	0.373265	+	0.646514i	−0.616801	+	0.787119i	$0.711572\pi$
$348$	−5.10417	+	8.84068i	−0.273612	+	0.473910i
$349$	1.14060	+	4.25677i	0.0610549	+	0.227860i	0.989711	−	0.143082i	$-0.0457014\pi$
$349$	1.14060	+	4.25677i	0.0610549	+	0.227860i	−0.928656	+	0.370942i	$0.879035\pi$
$350$	7.28989	+	10.7798i	0.389661	+	0.576206i
$351$	−1.86060	+	3.08839i	−0.0993114	+	0.164846i
$352$	−3.89345			−0.207521
$353$	0.199351	−	0.0534159i	0.0106104	−	0.00284304i	−0.253510	−	0.967333i	$-0.581585\pi$
$353$	0.199351	−	0.0534159i	0.0106104	−	0.00284304i	0.264120	+	0.964490i	$0.414918\pi$
$354$	−6.31813	+	10.9433i	−0.335805	+	0.581631i
$355$	−1.09747	−	1.90087i	−0.0582475	−	0.100888i
$356$	−9.79868	−	9.79868i	−0.519329	−	0.519329i
$357$	−7.66975	+	2.65119i	−0.405926	+	0.140316i
$358$	0.675848	−	2.52230i	0.0357197	−	0.133308i
$359$	3.67379	+	3.67379i	0.193895	+	0.193895i	0.797377	−	0.603482i	$-0.206220\pi$
$359$	3.67379	+	3.67379i	0.193895	+	0.193895i	−0.603482	+	0.797377i	$0.706220\pi$
$360$	−0.247108	+	0.142668i	−0.0130237	+	0.00751925i
$361$	16.1541	+	9.32655i	0.850214	+	0.490871i
$362$	0.00348932	+	0.0130223i	0.000183394	+	0.000684438i
$363$	4.15894			0.218288
$364$	2.94813	+	9.07241i	0.154524	+	0.475523i
$365$	−4.32979			−0.226632
$366$	−0.825914	−	3.08235i	−0.0431712	−	0.161117i
$367$	1.01384	+	0.585342i	0.0529221	+	0.0305546i	0.526228	−	0.850344i	$-0.323606\pi$
$367$	1.01384	+	0.585342i	0.0529221	+	0.0305546i	−0.473305	+	0.880898i	$0.656939\pi$
$368$	−0.501757	+	0.289689i	−0.0261559	+	0.0151011i
$369$	5.78589	+	5.78589i	0.301201	+	0.301201i
$370$	−0.583130	+	2.17627i	−0.0303155	+	0.113139i
$371$	−8.50495	−	24.6044i	−0.441555	−	1.27739i
$372$	−6.91577	−	6.91577i	−0.358566	−	0.358566i
$373$	−0.107766	−	0.186656i	−0.00557989	−	0.00966466i	0.863222	−	0.504825i	$-0.168443\pi$
$373$	−0.107766	−	0.186656i	−0.00557989	−	0.00966466i	−0.868802	+	0.495160i	$0.835109\pi$
$374$	−5.97099	+	10.3421i	−0.308752	+	0.534775i
$375$	2.73369	−	0.732490i	0.141167	−	0.0378256i
$376$	1.48810			0.0767430
$377$	32.2126	−	17.8067i	1.65903	−	0.917091i
$378$	−1.48211	−	2.19165i	−0.0762316	−	0.112726i
$379$	5.60278	+	20.9098i	0.287795	+	1.07407i	0.946772	+	0.321904i	$0.104323\pi$
$379$	5.60278	+	20.9098i	0.287795	+	1.07407i	−0.658977	+	0.752163i	$0.729011\pi$
$380$	0.0840288	−	0.145542i	0.00431059	−	0.00746615i
$381$	2.18954	+	3.79239i	0.112173	+	0.194290i
$382$	−1.54206	+	1.54206i	−0.0788988	+	0.0788988i
$383$	−7.64834	+	28.5440i	−0.390812	+	1.45853i	0.437986	+	0.898982i	$0.355692\pi$
$383$	−7.64834	+	28.5440i	−0.390812	+	1.45853i	−0.828798	+	0.559548i	$0.810975\pi$
$384$	0.965926	+	0.258819i	0.0492922	+	0.0132078i
$385$	0.557381	−	2.88594i	0.0284068	−	0.147081i
$386$	3.72486	+	6.45166i	0.189591	+	0.328381i
$387$	0.751692	+	0.433989i	0.0382106	+	0.0220609i
$388$	−2.65996	−	9.92712i	−0.135039	−	0.503973i
$389$		−	13.6644i		−	0.692810i	−0.938085	−	0.346405i	$-0.887402\pi$
$389$		−	13.6644i		−	0.692810i	0.938085	−	0.346405i	$-0.112598\pi$
$390$	1.02861	+	0.0191541i	0.0520859	+	0.000969907i
$391$			1.77707i			0.0898703i
$392$	−6.94985	−	0.836432i	−0.351020	−	0.0422462i
$393$	−1.95271	+	3.38220i	−0.0985014	+	0.170609i
$394$	14.7147	−	8.49556i	0.741318	−	0.428000i
$395$	−1.93524	−	1.93524i	−0.0973724	−	0.0973724i
$396$	−3.76078	−	1.00770i	−0.188986	−	0.0506388i
$397$	−32.9002	−	8.81558i	−1.65121	−	0.442441i	−0.691261	−	0.722605i	$-0.742944\pi$
$397$	−32.9002	−	8.81558i	−1.65121	−	0.442441i	−0.959952	+	0.280164i	$0.909611\pi$
$398$	−15.5893	+	15.5893i	−0.781421	+	0.781421i
$399$	1.40141	+	0.681435i	0.0701582	+	0.0341144i
$400$	−4.25962	−	2.45929i	−0.212981	−	0.122965i
$401$	18.3691	−	4.92198i	0.917309	−	0.245792i	0.230874	−	0.972984i	$-0.425841\pi$
$401$	18.3691	−	4.92198i	0.917309	−	0.245792i	0.686435	+	0.727192i	$0.259175\pi$
$402$	13.0400			0.650377
$403$	8.49115	+	34.2261i	0.422974	+	1.70492i
$404$			3.54495i			0.176368i
$405$	−0.275613	+	0.0738503i	−0.0136953	+	0.00366965i
$406$	1.91632	+	26.9406i	0.0951052	+	1.33704i
$407$	−26.6243	+	15.3715i	−1.31972	+	0.761939i
$408$	2.16884	−	2.16884i	0.107373	−	0.107373i
$409$	−5.77217	+	21.5420i	−0.285416	+	1.06519i	0.663120	+	0.748514i	$0.269232\pi$
$409$	−5.77217	+	21.5420i	−0.285416	+	1.06519i	−0.948535	+	0.316672i	$0.897435\pi$
$410$	0.604279	−	2.25520i	0.0298432	−	0.111376i
$411$	4.58383	−	4.58383i	0.226104	−	0.226104i
$412$	12.7664	−	7.37071i	0.628957	−	0.363129i
$413$	2.37209	+	33.3482i	0.116723	+	1.64096i
$414$	−0.559637	+	0.149954i	−0.0275047	+	0.00736985i
$415$		−	4.13005i		−	0.202736i
$416$	−2.50160	−	2.59653i	−0.122651	−	0.127306i
$417$	0.896950			0.0439238
$418$	2.21503	−	0.593516i	0.108341	−	0.0290298i
$419$	−26.5034	−	15.3017i	−1.29477	−	0.747538i	−0.315278	−	0.948999i	$-0.602098\pi$
$419$	−26.5034	−	15.3017i	−1.29477	−	0.747538i	−0.979497	+	0.201461i	$0.935431\pi$
$420$	−0.330125	+	0.678920i	−0.0161084	+	0.0331279i
$421$	1.73584	−	1.73584i	0.0845995	−	0.0845995i	−0.663541	−	0.748140i	$-0.730947\pi$
$421$	1.73584	−	1.73584i	0.0845995	−	0.0845995i	0.748140	+	0.663541i	$0.230947\pi$
$422$	16.9546	+	4.54298i	0.825339	+	0.221149i
$423$	1.43740	+	0.385149i	0.0698886	+	0.0187266i
$424$	6.95757	+	6.95757i	0.337889	+	0.337889i
$425$	−13.0651	+	7.54313i	−0.633750	+	0.365896i
$426$	−3.84623	+	6.66186i	−0.186350	+	0.322768i
$427$	−6.37851	−	5.53135i	−0.308678	−	0.267681i
$428$		−	13.8865i		−	0.671230i
$429$	9.73985	+	10.1095i	0.470245	+	0.488090i
$430$		−	0.247665i		−	0.0119435i
$431$	1.55048	+	5.78645i	0.0746838	+	0.278724i	0.993161	−	0.116749i	$-0.0372474\pi$
$431$	1.55048	+	5.78645i	0.0746838	+	0.278724i	−0.918478	+	0.395473i	$0.870581\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	15.1373	+	26.2186i	0.727454	+	1.25999i	0.957956	+	0.286916i	$0.0926300\pi$
$433$	15.1373	+	26.2186i	0.727454	+	1.25999i	−0.230502	+	0.973072i	$0.574037\pi$
$434$	−25.4069	−	4.90701i	−1.21957	−	0.235544i
$435$	2.81355	+	0.753889i	0.134899	+	0.0361462i
$436$	−3.32415	+	12.4059i	−0.159198	+	0.594135i
$437$	0.241296	−	0.241296i	0.0115427	−	0.0115427i
$438$	7.58719	+	13.1414i	0.362530	+	0.627921i
$439$	4.46966	−	7.74168i	0.213325	−	0.369490i	−0.739428	−	0.673236i	$-0.764904\pi$
$439$	4.46966	−	7.74168i	0.213325	−	0.369490i	0.952753	+	0.303746i	$0.0982373\pi$
$440$	0.287532	+	1.07309i	0.0137076	+	0.0511573i
$441$	−6.49655	−	2.60668i	−0.309360	−	0.124128i
$442$	−10.7335	+	2.66289i	−0.510543	+	0.126661i
$443$	−9.10779			−0.432724			−0.216362	−	0.976313i	$-0.569419\pi$
$443$	−9.10779			−0.432724			−0.216362	+	0.976313i	$0.569419\pi$
$444$	7.62705	−	2.04366i	0.361964	−	0.0969879i
$445$	−1.97701	+	3.42428i	−0.0937192	+	0.162326i
$446$	−9.02984	−	15.6401i	−0.427575	−	0.740582i
$447$	−7.08706	−	7.08706i	−0.335206	−	0.335206i
$448$	2.50057	−	0.864369i	0.118141	−	0.0408376i
$449$	−3.88150	+	14.4860i	−0.183179	+	0.683635i	0.811834	+	0.583889i	$0.198470\pi$
$449$	−3.88150	+	14.4860i	−0.183179	+	0.683635i	−0.995013	+	0.0997458i	$0.968197\pi$
$450$	−3.47796	−	3.47796i	−0.163953	−	0.163953i
$451$	27.5899	−	15.9290i	1.29916	−	0.750069i
$452$	−17.2309	−	9.94827i	−0.810474	−	0.467927i
$453$	1.53745	+	5.73785i	0.0722358	+	0.269588i
$454$	13.3131			0.624815
$455$	2.28275	−	1.48254i	0.107017	−	0.0695027i
$456$	−0.588982			−0.0275816
$457$	3.76383	+	14.0468i	0.176065	+	0.657082i	0.996368	+	0.0851531i	$0.0271379\pi$
$457$	3.76383	+	14.0468i	0.176065	+	0.657082i	−0.820303	+	0.571929i	$0.806195\pi$
$458$	−6.82450	−	3.94012i	−0.318888	−	0.184110i
$459$	2.65627	−	1.53360i	0.123984	−	0.0715822i
$460$	0.116897	+	0.116897i	0.00545036	+	0.00545036i
$461$	0.0716253	−	0.267309i	0.00333592	−	0.0124498i	−0.964238	−	0.265039i	$-0.914615\pi$
$461$	0.0716253	−	0.267309i	0.00333592	−	0.0124498i	0.967574	+	0.252589i	$0.0812820\pi$
$462$	−9.73585	+	3.36538i	−0.452953	+	0.156572i
$463$	25.0656	+	25.0656i	1.16490	+	1.16490i	0.983390	+	0.181507i	$0.0580976\pi$
$463$	25.0656	+	25.0656i	1.16490	+	1.16490i	0.181507	+	0.983390i	$0.441902\pi$
$464$	−5.10417	−	8.84068i	−0.236955	−	0.410418i
$465$	−1.39534	+	2.41681i	−0.0647075	+	0.112077i
$466$	−7.79071	+	2.08751i	−0.360898	+	0.0967023i
$467$	−4.84704			−0.224294			−0.112147	−	0.993692i	$-0.535773\pi$
$467$	−4.84704			−0.224294			−0.112147	+	0.993692i	$0.535773\pi$
$468$	−1.74433	−	3.15552i	−0.0806316	−	0.145864i
$469$	28.5792	−	19.3268i	1.31966	−	0.892428i
$470$	−0.109897	−	0.410140i	−0.00506916	−	0.0189184i
$471$	−0.749285	+	1.29780i	−0.0345252	+	0.0597995i
$472$	−6.31813	−	10.9433i	−0.290816	−	0.503708i
$473$	2.38962	−	2.38962i	0.109875	−	0.109875i
$474$	−2.48250	+	9.26483i	−0.114025	+	0.425548i
$475$	2.79825	+	0.749788i	0.128392	+	0.0344026i
$476$	1.53888	−	7.96779i	0.0705343	−	0.365203i
$477$	4.91974	+	8.52125i	0.225260	+	0.390161i
$478$	−8.69335	−	5.01911i	−0.397624	−	0.229569i
$479$	5.51712	+	20.5902i	0.252084	+	0.940789i	0.969690	+	0.244340i	$0.0785711\pi$
$479$	5.51712	+	20.5902i	0.252084	+	0.940789i	−0.717606	+	0.696449i	$0.754762\pi$
$480$		−	0.285336i		−	0.0130237i
$481$	−27.3578	−	7.87925i	−1.24741	−	0.359263i
$482$		−	13.3380i		−	0.607528i
$483$	−1.00428	+	1.15809i	−0.0456964	+	0.0526951i
$484$	−2.07947	+	3.60175i	−0.0945214	+	0.163716i
$485$	−2.53961	+	1.46624i	−0.115318	+	0.0665786i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−38.7212	−	10.3753i	−1.75462	−	0.470150i	−0.769020	−	0.639224i	$-0.779256\pi$
$487$	−38.7212	−	10.3753i	−1.75462	−	0.470150i	−0.985603	+	0.169074i	$0.945922\pi$
$488$	3.08235	+	0.825914i	0.139532	+	0.0373874i
$489$	−4.75484	+	4.75484i	−0.215021	+	0.215021i
$490$	0.282717	+	1.97724i	0.0127718	+	0.0893226i
$491$	13.8208	+	7.97941i	0.623722	+	0.360106i	0.778317	−	0.627872i	$-0.216074\pi$
$491$	13.8208	+	7.97941i	0.623722	+	0.360106i	−0.154595	+	0.987978i	$0.549407\pi$
$492$	−7.90367	+	2.11778i	−0.356325	+	0.0954770i
$493$	−31.3110			−1.41018
$494$	1.81901	+	1.09586i	0.0818411	+	0.0493050i
$495$			1.11094i			0.0499330i
$496$	9.44711	−	2.53135i	0.424188	−	0.113661i
$497$	1.44403	+	20.3010i	0.0647738	+	0.910626i
$498$	−12.5352	+	7.23718i	−0.561714	+	0.324306i
$499$	12.9148	−	12.9148i	0.578146	−	0.578146i	−0.356246	−	0.934392i	$-0.615944\pi$
$499$	12.9148	−	12.9148i	0.578146	−	0.578146i	0.934392	+	0.356246i	$0.115944\pi$
$500$	−0.732490	+	2.73369i	−0.0327580	+	0.122254i
$501$	2.01049	−	7.50324i	0.0898219	−	0.335220i
$502$	−1.17946	+	1.17946i	−0.0526419	+	0.0526419i
$503$	−9.93163	+	5.73403i	−0.442830	+	0.255668i	−0.704797	−	0.709409i	$-0.748962\pi$
$503$	−9.93163	+	5.73403i	−0.442830	+	0.255668i	0.261968	+	0.965077i	$0.415629\pi$
$504$	2.63908	−	0.187721i	0.117554	−	0.00836175i
$505$	0.977034	−	0.261795i	0.0434774	−	0.0116497i
$506$			2.25578i			0.100282i
$507$	−0.483986	+	12.9910i	−0.0214946	+	0.576950i
$508$	−4.37907			−0.194290
$509$	8.49293	−	2.27567i	0.376442	−	0.100867i	−0.0656365	−	0.997844i	$-0.520908\pi$
$509$	8.49293	−	2.27567i	0.376442	−	0.100867i	0.442079	+	0.896976i	$0.354241\pi$
$510$	−0.757929	−	0.437590i	−0.0335616	−	0.0193768i
$511$	36.1055	+	17.5563i	1.59721	+	0.776646i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−0.568913	−	0.152440i	−0.0251181	−	0.00673038i
$514$	0.613575	+	0.164407i	0.0270637	+	0.00725168i
$515$	−2.97427	−	2.97427i	−0.131062	−	0.131062i
$516$	−0.751692	+	0.433989i	−0.0330914	+	0.0191053i
$517$	2.89692	−	5.01762i	0.127407	−	0.220675i
$518$	13.6869	−	15.7832i	0.601368	−	0.693472i
$519$		−	12.2085i		−	0.535892i
$520$	−0.530895	+	0.881229i	−0.0232813	+	0.0386444i
$521$		−	32.0483i		−	1.40406i	−0.712147	−	0.702031i	$-0.752277\pi$
$521$		−	32.0483i		−	1.40406i	0.712147	−	0.702031i	$-0.247723\pi$
$522$	−2.64211	−	9.86049i	−0.115642	−	0.431582i
$523$	−7.60861	−	4.39284i	−0.332701	−	0.192085i	0.324338	−	0.945941i	$-0.394858\pi$
$523$	−7.60861	−	4.39284i	−0.332701	−	0.192085i	−0.657040	+	0.753856i	$0.728192\pi$
$524$	−1.95271	−	3.38220i	−0.0853047	−	0.147752i
$525$	−12.7772	−	2.46776i	−0.557644	−	0.107702i
$526$	−4.58642	−	1.22893i	−0.199978	−	0.0535838i
$527$	7.76414	−	28.9762i	0.338211	−	1.26222i
$528$	2.75308	−	2.75308i	0.119813	−	0.119813i
$529$	−11.3322	−	19.6279i	−0.492703	−	0.853386i
$530$	1.40378	−	2.43141i	0.0609762	−	0.105614i
$531$	−3.27051	−	12.2057i	−0.141928	−	0.529682i
$532$	−1.29084	+	0.872938i	−0.0559652	+	0.0378467i
$533$	28.3500	+	8.16501i	1.22797	+	0.353666i
$534$	13.8574			0.599669
$535$	−3.82731	+	1.02552i	−0.165469	+	0.0443372i
$536$	−6.52001	+	11.2930i	−0.281622	+	0.487783i
$537$	1.30564	+	2.26143i	0.0563425	+	0.0975880i
$538$	−11.9955	−	11.9955i	−0.517161	−	0.517161i
$539$	−16.3497	+	21.8054i	−0.704233	+	0.939224i
$540$	0.0738503	−	0.275613i	0.00317801	−	0.0118605i
$541$	19.2259	+	19.2259i	0.826585	+	0.826585i	0.987043	−	0.160458i	$-0.0512971\pi$
$541$	19.2259	+	19.2259i	0.826585	+	0.826585i	−0.160458	+	0.987043i	$0.551297\pi$
$542$	−7.73339	+	4.46487i	−0.332177	+	0.191783i
$543$	−0.0116755	−	0.00674084i	−0.000501043	−	0.000289277i
$544$	0.793849	+	2.96268i	0.0340360	+	0.127024i
$545$	3.66472			0.156979
$546$	−8.49980	−	4.33052i	−0.363758	−	0.185329i
$547$	−14.1507			−0.605042			−0.302521	−	0.953143i	$-0.597828\pi$
$547$	−14.1507			−0.605042			−0.302521	+	0.953143i	$0.597828\pi$
$548$	1.67780	+	6.26163i	0.0716720	+	0.267484i
$549$	2.76356	+	1.59554i	0.117946	+	0.0680961i
$550$	−16.5846	+	9.57513i	−0.707170	+	0.408285i
$551$	4.25150	+	4.25150i	0.181120	+	0.181120i
$552$	0.149954	−	0.559637i	0.00638248	−	0.0238197i
$553$	8.29073	+	23.9846i	0.352558	+	1.01993i
$554$	−9.44482	−	9.44482i	−0.401272	−	0.401272i
$555$	−1.12652	−	1.95119i	−0.0478181	−	0.0828234i
$556$	−0.448475	+	0.776781i	−0.0190196	+	0.0329429i
$557$	−29.7591	+	7.97394i	−1.26093	+	0.337866i	−0.826551	−	0.562861i	$-0.809700\pi$
$557$	−29.7591	+	7.97394i	−1.26093	+	0.337866i	−0.434384	+	0.900728i	$0.643034\pi$
$558$	9.78037			0.414036
$559$	3.12900	+	0.0582661i	0.132343	+	0.00246439i
$560$	−0.422900	−	0.625357i	−0.0178708	−	0.0264261i
$561$	−3.09081	−	11.5351i	−0.130494	−	0.487011i
$562$	−6.55479	+	11.3532i	−0.276497	+	0.478907i
$563$	−11.4052	−	19.7545i	−0.480674	−	0.832551i	0.519081	−	0.854725i	$-0.326274\pi$
$563$	−11.4052	−	19.7545i	−0.480674	−	0.832551i	−0.999754	+	0.0221743i	$0.992941\pi$
$564$	−1.05225	+	1.05225i	−0.0443076	+	0.0443076i
$565$	−1.46936	+	5.48374i	−0.0618166	+	0.230703i
$566$	−12.3743	−	3.31570i	−0.520133	−	0.139369i
$567$	2.59774	+	0.501721i	0.109095	+	0.0210703i
$568$	−3.84623	−	6.66186i	−0.161384	−	0.279526i
$569$	36.3088	+	20.9629i	1.52214	+	0.878810i	0.999658	+	0.0261630i	$0.00832888\pi$
$569$	36.3088	+	20.9629i	1.52214	+	0.878810i	0.522487	+	0.852647i	$0.325004\pi$
$570$	0.0434965	+	0.162331i	0.00182187	+	0.00679930i
$571$			16.3137i			0.682708i	0.939935	+	0.341354i	$0.110885\pi$
$571$			16.3137i			0.682708i	−0.939935	+	0.341354i	$0.889115\pi$
$572$	−13.6250	+	3.38022i	−0.569689	+	0.141334i
$573$		−	2.18081i		−	0.0911045i
$574$	−14.1833	+	16.3556i	−0.592000	+	0.682668i
$575$	−1.42486	+	2.46793i	−0.0594208	+	0.102920i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	−26.5956	−	26.5956i	−1.10719	−	1.10719i	−0.993518	−	0.113671i	$-0.963739\pi$
$577$	−26.5956	−	26.5956i	−1.10719	−	1.10719i	−0.113671	−	0.993518i	$-0.536261\pi$
$578$	−7.33360	−	1.96503i	−0.305038	−	0.0817346i
$579$	−7.19589	−	1.92813i	−0.299051	−	0.0801304i
$580$	−2.05966	+	2.05966i	−0.0855228	+	0.0855228i
$581$	−16.7464	+	34.4399i	−0.694758	+	1.42881i
$582$	8.90042	+	5.13866i	0.368934	+	0.213004i
$583$	37.0042	−	9.91524i	1.53256	−	0.410647i
$584$	−15.1744			−0.627921
$585$	−0.740884	+	0.713796i	−0.0306318	+	0.0295118i
$586$			3.87056i			0.159891i
$587$	14.2718	−	3.82411i	0.589058	−	0.157838i	0.0480356	−	0.998846i	$-0.484704\pi$
$587$	14.2718	−	3.82411i	0.589058	−	0.157838i	0.541023	+	0.841008i	$0.318037\pi$
$588$	5.50573	−	4.32284i	0.227053	−	0.178271i
$589$	−4.98871	+	2.88023i	−0.205556	+	0.118678i
$590$	−2.54953	+	2.54953i	−0.104962	+	0.104962i
$591$	−4.39763	+	16.4122i	−0.180894	+	0.675106i
$592$	−2.04366	+	7.62705i	−0.0839940	+	0.313470i
$593$	28.5401	−	28.5401i	1.17200	−	1.17200i	0.190271	−	0.981732i	$-0.439063\pi$
$593$	28.5401	−	28.5401i	1.17200	−	1.17200i	0.981732	−	0.190271i	$-0.0609366\pi$
$594$	3.37183	−	1.94672i	0.138348	−	0.0798751i
$595$	−2.30967	+	0.164290i	−0.0946874	+	0.00673522i
$596$	9.68110	−	2.59404i	0.396554	−	0.106256i
$597$		−	22.0466i		−	0.902307i
$598$	−1.50438	+	1.44937i	−0.0615186	+	0.0592693i
$599$	31.6671			1.29388			0.646942	−	0.762539i	$-0.276048\pi$
$599$	31.6671			1.29388			0.646942	+	0.762539i	$0.276048\pi$
$600$	4.75099	−	1.27302i	0.193958	−	0.0519710i
$601$	23.8399	+	13.7640i	0.972452	+	0.561445i	0.899983	−	0.435925i	$-0.143579\pi$
$601$	23.8399	+	13.7640i	0.972452	+	0.561445i	0.0724689	+	0.997371i	$0.476912\pi$
$602$	−1.00423	+	2.06525i	−0.0409292	+	0.0841731i
$603$	−9.22069	+	9.22069i	−0.375495	+	0.375495i
$604$	−5.73785	−	1.53745i	−0.233470	−	0.0625580i
$605$	1.14626	+	0.307139i	0.0466020	+	0.0124870i
$606$	−2.50666	−	2.50666i	−0.101826	−	0.101826i
$607$	28.4588	−	16.4307i	1.15511	−	0.666901i	0.204980	−	0.978766i	$-0.434287\pi$
$607$	28.4588	−	16.4307i	1.15511	−	0.666901i	0.950126	+	0.311865i	$0.100954\pi$
$608$	0.294491	−	0.510073i	0.0119432	−	0.0206862i
$609$	−20.4050	−	17.6949i	−0.826851	−	0.717032i
$610$		−	0.910531i		−	0.0368663i
$611$	5.20756	−	1.29194i	0.210675	−	0.0522664i
$612$			3.06720i			0.123984i
$613$	−7.36682	−	27.4933i	−0.297543	−	1.11045i	−0.939177	−	0.343434i	$-0.888410\pi$
$613$	−7.36682	−	27.4933i	−0.297543	−	1.11045i	0.641634	−	0.767011i	$-0.278257\pi$
$614$	20.7484	+	11.9791i	0.837335	+	0.483436i
$615$	1.16738	+	2.02196i	0.0470732	+	0.0815331i
$616$	1.95342	−	10.1142i	0.0787057	−	0.407512i
$617$	−27.5592	−	7.38447i	−1.10949	−	0.297288i	−0.342868	−	0.939383i	$-0.611399\pi$
$617$	−27.5592	−	7.38447i	−1.10949	−	0.297288i	−0.766625	+	0.642096i	$0.778065\pi$
$618$	−3.81536	+	14.2391i	−0.153476	+	0.572781i
$619$	−4.44570	+	4.44570i	−0.178688	+	0.178688i	−0.790784	−	0.612096i	$-0.790327\pi$
$619$	−4.44570	+	4.44570i	−0.178688	+	0.178688i	0.612096	+	0.790784i	$0.290327\pi$
$620$	−1.39534	−	2.41681i	−0.0560384	−	0.0970613i
$621$	0.289689	−	0.501757i	0.0116248	−	0.0201348i
$622$	5.46837	+	20.4082i	0.219262	+	0.818296i
$623$	30.3707	−	20.5383i	1.21677	−	0.822848i
$624$	3.60493	+	0.0671284i	0.144313	+	0.00268729i
$625$	−23.7854			−0.951415
$626$	−27.4550	+	7.35655i	−1.09732	+	0.294027i
$627$	−1.14659	+	1.98594i	−0.0457902	+	0.0793110i
$628$	−0.749285	−	1.29780i	−0.0298997	−	0.0517879i
$629$	17.1254	+	17.1254i	0.682833	+	0.682833i
$630$	−0.246635	−	0.713503i	−0.00982619	−	0.0284266i
$631$	−1.93884	+	7.23584i	−0.0771839	+	0.288054i	−0.993720	−	0.111899i	$-0.964307\pi$
$631$	−1.93884	+	7.23584i	−0.0771839	+	0.288054i	0.916536	+	0.399953i	$0.130974\pi$
$632$	−6.78232	−	6.78232i	−0.269786	−	0.269786i
$633$	−15.2011	+	8.77636i	−0.604190	+	0.348829i
$634$	12.6769	+	7.31900i	0.503463	+	0.290675i
$635$	0.323396	+	1.20693i	0.0128336	+	0.0478955i
$636$	−9.83949			−0.390161
$637$	−25.0469	+	3.10667i	−0.992395	+	0.123091i
$638$	−39.7456			−1.57354
$639$	−1.99095	−	7.43034i	−0.0787610	−	0.293940i
$640$	0.247108	+	0.142668i	0.00976780	+	0.00563944i
$641$	−16.7622	+	9.67764i	−0.662066	+	0.382244i	−0.793064	−	0.609139i	$-0.791515\pi$
$641$	−16.7622	+	9.67764i	−0.662066	+	0.382244i	0.130998	+	0.991383i	$0.458182\pi$
$642$	9.81925	+	9.81925i	0.387535	+	0.387535i
$643$	2.36325	−	8.81976i	0.0931973	−	0.347817i	−0.903543	−	0.428498i	$-0.859043\pi$
$643$	2.36325	−	8.81976i	0.0931973	−	0.347817i	0.996740	+	0.0806810i	$0.0257095\pi$
$644$	−0.500797	−	1.44878i	−0.0197342	−	0.0570899i
$645$	0.175126	+	0.175126i	0.00689557	+	0.00689557i
$646$	−0.903262	−	1.56450i	−0.0355384	−	0.0615543i
$647$	10.2528	−	17.7584i	0.403080	−	0.698154i	−0.591016	−	0.806660i	$-0.701273\pi$
$647$	10.2528	−	17.7584i	0.403080	−	0.698154i	0.994096	+	0.108505i	$0.0346065\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	−49.1987			−1.93122
$650$	−17.0415	−	4.90808i	−0.668423	−	0.192511i
$651$	21.4352	−	14.4956i	0.840111	−	0.568128i
$652$	−1.74039	−	6.49523i	−0.0681590	−	0.254373i
$653$	−1.92718	+	3.33797i	−0.0754163	+	0.130625i	−0.901267	−	0.433264i	$-0.857362\pi$
$653$	−1.92718	+	3.33797i	−0.0754163	+	0.130625i	0.825851	+	0.563889i	$0.190695\pi$
$654$	−6.42177	−	11.1228i	−0.251111	−	0.434937i
$655$	−0.787970	+	0.787970i	−0.0307885	+	0.0307885i
$656$	2.11778	−	7.90367i	0.0826855	−	0.308586i
$657$	−14.6573	−	3.92742i	−0.571837	−	0.153223i
$658$	−0.746611	+	3.86571i	−0.0291059	+	0.150701i
$659$	9.28933	+	16.0896i	0.361861	+	0.626761i	0.988267	−	0.152735i	$-0.0488082\pi$
$659$	9.28933	+	16.0896i	0.361861	+	0.626761i	−0.626406	+	0.779497i	$0.715475\pi$
$660$	−0.962102	−	0.555470i	−0.0374498	−	0.0216216i
$661$	10.9763	+	40.9640i	0.426927	+	1.59331i	0.759678	+	0.650299i	$0.225356\pi$
$661$	10.9763	+	40.9640i	0.426927	+	1.59331i	−0.332751	+	0.943015i	$0.607977\pi$
$662$			15.6903i			0.609821i
$663$	5.70682	−	9.47271i	0.221635	−	0.367890i
$664$		−	14.4744i		−	0.561714i
$665$	0.335922	+	0.291307i	0.0130265	+	0.0112964i
$666$	−3.94805	+	6.83823i	−0.152984	+	0.264976i
$667$	−5.12210	+	2.95725i	−0.198329	+	0.114505i
$668$	5.49275	+	5.49275i	0.212521	+	0.212521i
$669$	17.4443	+	4.67419i	0.674436	+	0.180715i
$670$	3.59400	+	0.963009i	0.138848	+	0.0372043i
$671$	8.78533	−	8.78533i	0.339154	−	0.339154i
$672$	−1.15697	+	2.37937i	−0.0446311	+	0.0917863i
$673$	−19.2726	−	11.1270i	−0.742903	−	0.428915i	0.0802212	−	0.996777i	$-0.474437\pi$
$673$	−19.2726	−	11.1270i	−0.742903	−	0.428915i	−0.823124	+	0.567862i	$0.807771\pi$
$674$	−8.71135	+	2.33420i	−0.335549	+	0.0899100i
$675$	4.91858			0.189316
$676$	−11.0085	−	6.91464i	−0.423405	−	0.265948i
$677$			6.32224i			0.242983i	0.992592	+	0.121492i	$0.0387678\pi$
$677$			6.32224i			0.242983i	−0.992592	+	0.121492i	$0.961232\pi$
$678$	19.2186	−	5.14960i	0.738085	−	0.197769i
$679$	27.1227	−	1.92927i	1.04087	−	0.0740384i
$680$	0.757929	−	0.437590i	0.0290652	−	0.0167808i
$681$	−9.41379	+	9.41379i	−0.360737	+	0.360737i
$682$	9.85567	−	36.7818i	0.377393	−	1.40845i
$683$	−3.44207	+	12.8460i	−0.131707	+	0.491537i	−0.999990	−	0.00453243i	$-0.998557\pi$
$683$	−3.44207	+	12.8460i	−0.131707	+	0.491537i	0.868283	+	0.496070i	$0.165224\pi$
$684$	0.416473	−	0.416473i	0.0159243	−	0.0159243i
$685$	1.60188	−	0.924847i	0.0612047	−	0.0353366i
$686$	5.65972	−	17.6343i	0.216089	−	0.673280i
$687$	7.61174	−	2.03956i	0.290406	−	0.0778140i
$688$		−	0.867979i		−	0.0330914i
$689$	30.3882	+	18.3073i	1.15770	+	0.697454i
$690$	−0.165317			−0.00629353
$691$	−33.1131	+	8.87264i	−1.25968	+	0.337531i	−0.826070	−	0.563568i	$-0.809428\pi$
$691$	−33.1131	+	8.87264i	−1.25968	+	0.337531i	−0.433613	+	0.901099i	$0.642762\pi$
$692$	10.5728	+	6.10424i	0.401919	+	0.232048i
$693$	4.50461	−	9.26397i	0.171116	−	0.351909i
$694$	9.83324	−	9.83324i	0.373265	−	0.373265i
$695$	0.247211	+	0.0662400i	0.00937725	+	0.00251263i
$696$	9.86049	+	2.64211i	0.373761	+	0.100149i
$697$	−17.7465	−	17.7465i	−0.672195	−	0.672195i
$698$	3.81652	−	2.20347i	0.144457	−	0.0834025i
$699$	4.03277	−	6.98496i	0.152533	−	0.264195i
$700$	8.52575	−	9.83152i	0.322243	−	0.371597i
$701$			7.35078i			0.277635i	0.990318	+	0.138817i	$0.0443301\pi$
$701$			7.35078i			0.277635i	−0.990318	+	0.138817i	$0.955670\pi$
$702$	3.46472	+	0.997865i	0.130767	+	0.0376620i
$703$		−	4.65067i		−	0.175403i
$704$	1.00770	+	3.76078i	0.0379791	+	0.141740i
$705$	0.367722	+	0.212304i	0.0138492	+	0.00799584i
$706$	−0.103192	−	0.178733i	−0.00388366	−	0.00672670i
$707$	−9.20887	−	1.77857i	−0.346335	−	0.0668901i
$708$	12.2057	+	3.27051i	0.458718	+	0.122913i
$709$	6.88955	−	25.7122i	0.258743	−	0.965640i	−0.707227	−	0.706986i	$-0.750054\pi$
$709$	6.88955	−	25.7122i	0.258743	−	0.965640i	0.965970	−	0.258654i	$-0.0832790\pi$
$710$	−1.55205	+	1.55205i	−0.0582475	+	0.0582475i
$711$	−4.79583	−	8.30662i	−0.179858	−	0.311522i
$712$	−6.92871	+	12.0009i	−0.259664	+	0.449752i
$713$	−1.46661	−	5.47346i	−0.0549249	−	0.204983i
$714$	4.54593	+	6.72223i	0.170127	+	0.251573i
$715$	1.93784	+	3.50559i	0.0724712	+	0.131102i
$716$	−2.61128			−0.0975880
$717$	9.69617	−	2.59808i	0.362110	−	0.0970271i
$718$	2.59777	−	4.49946i	0.0969477	−	0.167918i
$719$	18.9490	+	32.8206i	0.706677	+	1.22400i	0.966083	+	0.258232i	$0.0831400\pi$
$719$	18.9490	+	32.8206i	0.706677	+	1.22400i	−0.259406	+	0.965768i	$0.583527\pi$
$720$	0.201763	+	0.201763i	0.00751925	+	0.00751925i
$721$	12.7420	+	36.8620i	0.474538	+	1.37281i
$722$	4.82778	−	18.0175i	0.179671	−	0.670542i
$723$	9.43138	+	9.43138i	0.350757	+	0.350757i
$724$	0.0116755	−	0.00674084i	0.000433916	−	0.000250522i
$725$	−43.4836	−	25.1053i	−1.61494	−	0.932387i
$726$	−1.07641	−	4.01723i	−0.0399494	−	0.149093i
$727$	−14.8900			−0.552238			−0.276119	−	0.961123i	$-0.589048\pi$
$727$	−14.8900			−0.552238			−0.276119	+	0.961123i	$0.589048\pi$
$728$	8.00024	−	5.19578i	0.296509	−	0.192569i
$729$	−1.00000			−0.0370370
$730$	1.12063	+	4.18226i	0.0414765	+	0.154792i
$731$	−2.30559	−	1.33113i	−0.0852752	−	0.0492336i
$732$	−2.76356	+	1.59554i	−0.102144	+	0.0589730i
$733$	28.2755	+	28.2755i	1.04438	+	1.04438i	0.998968	+	0.0454095i	$0.0144593\pi$
$733$	28.2755	+	28.2755i	1.04438	+	1.04438i	0.0454095	+	0.998968i	$0.485541\pi$
$734$	0.302995	−	1.13079i	0.0111838	−	0.0417384i
$735$	−1.59803	−	1.19821i	−0.0589442	−	0.0441966i
$736$	0.409683	+	0.409683i	0.0151011	+	0.0151011i
$737$	25.3853	+	43.9687i	0.935080	+	1.61961i
$738$	4.09124	−	7.08624i	0.150601	−	0.260848i
$739$	47.2984	−	12.6736i	1.73990	−	0.466204i	0.757474	−	0.652866i	$-0.226433\pi$
$739$	47.2984	−	12.6736i	1.73990	−	0.466204i	0.982424	+	0.186661i	$0.0597667\pi$
$740$	2.25304			0.0828234
$741$	−2.06112	+	0.511344i	−0.0757172	+	0.0187847i
$742$	−21.5647	+	14.5832i	−0.791666	+	0.535367i
$743$	−11.3699	−	42.4331i	−0.417121	−	1.55672i	−0.780548	−	0.625096i	$-0.785060\pi$
$743$	−11.3699	−	42.4331i	−0.417121	−	1.55672i	0.363427	−	0.931623i	$-0.381607\pi$
$744$	−4.89019	+	8.47005i	−0.179283	+	0.310527i
$745$	−1.42990	−	2.47667i	−0.0523877	−	0.0907381i
$746$	−0.152404	+	0.152404i	−0.00557989	+	0.00557989i
$747$	3.74624	−	13.9812i	0.137068	−	0.511544i
$748$	11.5351	+	3.09081i	0.421764	+	0.113011i
$749$	36.0736	+	6.96715i	1.31810	+	0.254574i
$750$	−1.41506	−	2.45096i	−0.0516708	−	0.0894964i
$751$	−6.47070	−	3.73586i	−0.236119	−	0.136323i	0.377273	−	0.926102i	$-0.376862\pi$
$751$	−6.47070	−	3.73586i	−0.236119	−	0.136323i	−0.613392	+	0.789779i	$0.710195\pi$
$752$	−0.385149	−	1.43740i	−0.0140449	−	0.0524164i
$753$		−	1.66801i		−	0.0607857i
$754$	−25.5372	−	26.5063i	−0.930009	−	0.965302i
$755$			1.69497i			0.0616862i
$756$	−1.73338	+	1.99885i	−0.0630422	+	0.0726976i
$757$	1.73336	−	3.00227i	0.0630001	−	0.109119i	−0.832805	−	0.553566i	$-0.813266\pi$
$757$	1.73336	−	3.00227i	0.0630001	−	0.109119i	0.895805	+	0.444447i	$0.146600\pi$
$758$	18.7473	−	10.8237i	0.680931	−	0.393136i
$759$	−1.59508	−	1.59508i	−0.0578977	−	0.0578977i
$760$	−0.162331	−	0.0434965i	−0.00588837	−	0.00157778i
$761$	−0.764237	−	0.204777i	−0.0277036	−	0.00742315i	0.244941	−	0.969538i	$-0.421232\pi$
$761$	−0.764237	−	0.204777i	−0.0277036	−	0.00742315i	−0.272644	+	0.962115i	$0.587898\pi$
$762$	3.09647	−	3.09647i	0.112173	−	0.112173i
$763$	−30.5596	−	14.8596i	−1.10633	−	0.537953i
$764$	1.88863	+	1.09040i	0.0683284	+	0.0394494i
$765$	0.845359	−	0.226513i	0.0305640	−	0.00818961i
$766$	29.5509			1.06772
$767$	−31.6109	−	32.8105i	−1.14140	−	1.18472i
$768$		−	1.00000i		−	0.0360844i
$769$	−27.6477	+	7.40819i	−0.997003	+	0.267146i	−0.720190	−	0.693777i	$-0.755945\pi$
$769$	−27.6477	+	7.40819i	−0.997003	+	0.267146i	−0.276814	+	0.960924i	$0.589279\pi$
$770$	−2.93186	+	0.208546i	−0.105657	+	0.00751549i
$771$	−0.550117	+	0.317610i	−0.0198120	+	0.0114384i
$772$	5.26775	−	5.26775i	0.189591	−	0.189591i
$773$	−0.348381	+	1.30018i	−0.0125304	+	0.0467641i	−0.971908	−	0.235361i	$-0.924373\pi$
$773$	−0.348381	+	1.30018i	−0.0125304	+	0.0467641i	0.959378	+	0.282125i	$0.0910394\pi$
$774$	0.224649	−	0.838403i	0.00807486	−	0.0301358i
$775$	34.0158	−	34.0158i	1.22188	−	1.22188i
$776$	−8.90042	+	5.13866i	−0.319506	+	0.184467i
$777$	1.48226	+	20.8385i	0.0531759	+	0.747576i
$778$	−13.1988	+	3.53660i	−0.473198	+	0.126793i
$779$			4.81934i			0.172671i
$780$	−0.247723	−	0.998522i	−0.00886992	−	0.0357528i
$781$	−29.9502			−1.07170
$782$	1.71652	−	0.459939i	0.0613825	−	0.0164474i
$783$	8.84068	+	5.10417i	0.315940	+	0.182408i
$784$	0.990822	+	6.92952i	0.0353865	+	0.247483i
$785$	−0.302356	+	0.302356i	−0.0107915	+	0.0107915i
$786$	3.77235	+	1.01080i	0.134555	+	0.0360540i
$787$	−40.5529	−	10.8661i	−1.44556	−	0.387335i	−0.551080	−	0.834452i	$-0.685784\pi$
$787$	−40.5529	−	10.8661i	−1.44556	−	0.387335i	−0.894476	+	0.447117i	$0.852451\pi$
$788$	−12.0145	−	12.0145i	−0.428000	−	0.428000i
$789$	4.11207	−	2.37411i	0.146394	−	0.0845205i
$790$	−1.36842	+	2.37017i	−0.0486862	+	0.0843270i
$791$	34.4882	−	39.7702i	1.22626	−	1.41407i
$792$			3.89345i			0.138348i
$793$	11.5036	+	0.214213i	0.408506	+	0.00760692i
$794$			34.0608i			1.20877i
$795$	0.726649	+	2.71189i	0.0257716	+	0.0961809i
$796$	19.0929	+	11.0233i	0.676730	+	0.390710i
$797$	6.62293	+	11.4712i	0.234596	+	0.406332i	0.959155	−	0.282880i	$-0.0912899\pi$
$797$	6.62293	+	11.4712i	0.234596	+	0.406332i	−0.724559	+	0.689213i	$0.757957\pi$
$798$	0.295505	−	1.53003i	0.0104607	−	0.0541623i
$799$	−4.40877	−	1.18133i	−0.155971	−	0.0417924i
$800$	−1.27302	+	4.75099i	−0.0450082	+	0.167973i
$801$	−9.79868	+	9.79868i	−0.346219	+	0.346219i
$802$	−9.50854	−	16.4693i	−0.335758	−	0.581550i
$803$	−29.5403	+	51.1654i	−1.04246	+	1.80559i
$804$	−3.37501	−	12.5957i	−0.119027	−	0.444216i
$805$	−0.362318	+	0.245019i	−0.0127700	+	0.00863579i
$806$	30.8622	−	17.0602i	1.08707	−	0.600919i
$807$	16.9641			0.597166
$808$	3.42416	−	0.917500i	0.120461	−	0.0322775i
$809$	−2.48078	+	4.29683i	−0.0872194	+	0.151068i	−0.906335	−	0.422560i	$-0.861131\pi$
$809$	−2.48078	+	4.29683i	−0.0872194	+	0.151068i	0.819115	+	0.573629i	$0.194465\pi$
$810$	0.142668	+	0.247108i	0.00501284	+	0.00868249i
$811$	35.5676	+	35.5676i	1.24895	+	1.24895i	0.956185	+	0.292762i	$0.0945743\pi$
$811$	35.5676	+	35.5676i	1.24895	+	1.24895i	0.292762	+	0.956185i	$0.405426\pi$
$812$	25.5267	−	8.82377i	0.895811	−	0.309654i
$813$	2.31119	−	8.62547i	0.0810569	−	0.302508i
$814$	21.7386	+	21.7386i	0.761939	+	0.761939i
$815$	−1.66164	+	0.959349i	−0.0582048	+	0.0336045i
$816$	−2.65627	−	1.53360i	−0.0929881	−	0.0536867i
$817$	0.132314	+	0.493804i	0.00462910	+	0.0172760i
$818$	22.3020			0.779770
$819$	9.07241	−	2.94813i	0.317015	−	0.103016i
$820$	−2.33475			−0.0815331
$821$	−5.35611	−	19.9893i	−0.186929	−	0.697630i	−0.994209	−	0.107461i	$-0.965728\pi$
$821$	−5.35611	−	19.9893i	−0.186929	−	0.697630i	0.807280	−	0.590169i	$-0.200939\pi$
$822$	−5.61402	−	3.24126i	−0.195812	−	0.113052i
$823$	−1.96934	+	1.13700i	−0.0686470	+	0.0396333i	−0.533931	−	0.845528i	$-0.679286\pi$
$823$	−1.96934	+	1.13700i	−0.0686470	+	0.0396333i	0.465284	+	0.885162i	$0.345952\pi$
$824$	−10.4238	−	10.4238i	−0.363129	−	0.363129i
$825$	4.95645	−	18.4977i	0.172561	−	0.644008i
$826$	31.5979	−	10.9224i	1.09943	−	0.380039i
$827$	30.8200	+	30.8200i	1.07172	+	1.07172i	0.997221	+	0.0744952i	$0.0237346\pi$
$827$	30.8200	+	30.8200i	1.07172	+	1.07172i	0.0744952	+	0.997221i	$0.476265\pi$
$828$	0.289689	+	0.501757i	0.0100674	+	0.0174373i
$829$	−5.13161	+	8.88820i	−0.178228	+	0.308700i	−0.941274	−	0.337645i	$-0.890370\pi$
$829$	−5.13161	+	8.88820i	−0.178228	+	0.308700i	0.763046	+	0.646345i	$0.223703\pi$
$830$	−3.98932	+	1.06894i	−0.138471	+	0.0371033i
$831$	13.3570			0.463349
$832$	−1.86060	+	3.08839i	−0.0645046	+	0.107071i
$833$	19.9262	+	7.99521i	0.690402	+	0.277018i
$834$	−0.232148	−	0.866387i	−0.00803861	−	0.0300005i
$835$	1.10823	−	1.91951i	0.0383520	−	0.0664275i
$836$	−1.14659	−	1.98594i	−0.0396555	−	0.0686853i
$837$	−6.91577	+	6.91577i	−0.239044	+	0.239044i
$838$	−7.92076	+	29.5607i	−0.273618	+	1.02116i
$839$	23.9971	+	6.42999i	0.828471	+	0.221988i	0.648046	−	0.761601i	$-0.275586\pi$
$839$	23.9971	+	6.42999i	0.828471	+	0.221988i	0.180424	+	0.983589i	$0.442253\pi$
$840$	0.741229	+	0.143159i	0.0255748	+	0.00493945i
$841$	−37.6051	−	65.1339i	−1.29673	−	2.24600i
$842$	−2.12596	−	1.22742i	−0.0732653	−	0.0422997i
$843$	−3.39301	−	12.6629i	−0.116861	−	0.436133i
$844$		−	17.5527i		−	0.604190i
$845$	−1.09278	+	3.54474i	−0.0375928	+	0.121943i
$846$		−	1.48810i		−	0.0511620i
$847$	−8.31311	−	7.20900i	−0.285642	−	0.247704i
$848$	4.91974	−	8.52125i	0.168945	−	0.292621i
$849$	11.0945	−	6.40543i	0.380763	−	0.219834i
$850$	10.6676	+	10.6676i	0.365896	+	0.365896i
$851$	4.41895	+	1.18406i	0.151480	+	0.0405889i
$852$	7.43034	+	1.99095i	0.254559	+	0.0682090i
$853$	−9.46714	+	9.46714i	−0.324149	+	0.324149i	−0.850356	−	0.526207i	$-0.823614\pi$
$853$	−9.46714	+	9.46714i	−0.324149	+	0.324149i	0.526207	+	0.850356i	$0.323614\pi$
$854$	−3.69199	+	7.59279i	−0.126337	+	0.259820i
$855$	−0.145542	−	0.0840288i	−0.00497744	−	0.00287372i
$856$	−13.4133	+	3.59410i	−0.458459	+	0.122844i
$857$	37.1295			1.26832			0.634160	−	0.773202i	$-0.281346\pi$
$857$	37.1295			1.26832			0.634160	+	0.773202i	$0.281346\pi$
$858$	7.24414	−	12.0245i	0.247311	−	0.410510i
$859$		−	4.12816i		−	0.140851i	−0.997517	−	0.0704254i	$-0.977564\pi$
$859$		−	4.12816i		−	0.140851i	0.997517	−	0.0704254i	$-0.0224357\pi$
$860$	−0.239226	+	0.0641005i	−0.00815755	+	0.00218581i
$861$	−1.53602	−	21.5943i	−0.0523475	−	0.735930i
$862$	5.18799	−	2.99529i	0.176704	−	0.102020i
$863$	−14.4952	+	14.4952i	−0.493423	+	0.493423i	−0.909383	−	0.415960i	$-0.863446\pi$
$863$	−14.4952	+	14.4952i	−0.493423	+	0.493423i	0.415960	+	0.909383i	$0.363446\pi$
$864$	0.258819	−	0.965926i	0.00880520	−	0.0328615i
$865$	0.901599	−	3.36481i	0.0306553	−	0.114407i
$866$	21.4074	−	21.4074i	0.727454	−	0.727454i
$867$	6.57513	−	3.79615i	0.223303	−	0.128924i
$868$	1.83598	+	25.8112i	0.0623172	+	0.876090i
$869$	−36.0721	+	9.66550i	−1.22366	+	0.327880i
$870$		−	2.91280i		−	0.0987532i
$871$	−13.0122	+	45.1800i	−0.440901	+	1.53087i
$872$	12.8435			0.434937
$873$	−9.92712	+	2.65996i	−0.335982	+	0.0900262i
$874$	−0.295526	−	0.170622i	−0.00999631	−	0.00577137i
$875$	−6.73393	−	3.27437i	−0.227648	−	0.110694i
$876$	10.7299	−	10.7299i	0.362530	−	0.362530i
$877$	7.28324	+	1.95154i	0.245938	+	0.0658988i	0.379682	−	0.925117i	$-0.376033\pi$
$877$	7.28324	+	1.95154i	0.245938	+	0.0658988i	−0.133744	+	0.991016i	$0.542700\pi$
$878$	−8.63472	−	2.31367i	−0.291408	−	0.0780825i
$879$	−2.73690	−	2.73690i	−0.0923132	−	0.0923132i
$880$	0.962102	−	0.555470i	0.0324324	−	0.0187249i
$881$	22.0267	−	38.1514i	0.742098	−	1.28535i	−0.209440	−	0.977821i	$-0.567164\pi$
$881$	22.0267	−	38.1514i	0.742098	−	1.28535i	0.951538	−	0.307530i	$-0.0995025\pi$
$882$	−0.836432	+	6.94985i	−0.0281641	+	0.234014i
$883$		−	23.5415i		−	0.792236i	−0.918200	−	0.396118i	$-0.870357\pi$
$883$		−	23.5415i		−	0.792236i	0.918200	−	0.396118i	$-0.129643\pi$
$884$	5.35020	+	9.67861i	0.179947	+	0.325527i
$885$		−	3.60558i		−	0.121200i
$886$	2.35727	+	8.79745i	0.0791941	+	0.295556i
$887$	−6.50491	−	3.75561i	−0.218413	−	0.126101i	0.386802	−	0.922163i	$-0.373580\pi$
$887$	−6.50491	−	3.75561i	−0.218413	−	0.126101i	−0.605215	+	0.796062i	$0.706913\pi$
$888$	−3.94805	−	6.83823i	−0.132488	−	0.229476i
$889$	2.19707	−	11.3757i	0.0736874	−	0.381529i
$890$	3.81929	+	1.02337i	0.128023	+	0.0343036i
$891$	−1.00770	+	3.76078i	−0.0337592	+	0.125991i
$892$	−12.7701	+	12.7701i	−0.427575	+	0.427575i
$893$	0.438233	+	0.759041i	0.0146649	+	0.0254003i
$894$	−5.01131	+	8.67984i	−0.167603	+	0.290297i
$895$	0.192844	+	0.719702i	0.00644605	+	0.0240570i
$896$	−1.48211	−	2.19165i	−0.0495139	−	0.0732180i
$897$	0.0388928	−	2.08862i	0.00129859	−	0.0697369i
$898$	14.9970			0.500455
$899$	96.4393	−	25.8408i	3.21643	−	0.861840i
$900$	−2.45929	+	4.25962i	−0.0819764	+	0.141987i
$901$	−15.0898	−	26.1363i	−0.502715	−	0.870728i
$902$	−22.5271	−	22.5271i	−0.750069	−	0.750069i
$903$	−0.750254	−	2.17044i	−0.0249669	−	0.0722279i
$904$	−5.14960	+	19.2186i	−0.171273	+	0.639200i
$905$	−0.00272010	−	0.00272010i	−9.04193e−5	−	9.04193e-5i
$906$	5.14441	−	2.97013i	0.170912	−	0.0986759i
$907$	−29.7223	−	17.1602i	−0.986914	−	0.569795i	−0.0825632	−	0.996586i	$-0.526311\pi$
$907$	−29.7223	−	17.1602i	−0.986914	−	0.569795i	−0.904350	+	0.426791i	$0.859644\pi$
$908$	−3.44569	−	12.8595i	−0.114349	−	0.426757i
$909$	3.54495			0.117578
$910$	−2.02285	−	1.82126i	−0.0670567	−	0.0603742i
$911$	12.9731			0.429818			0.214909	−	0.976634i	$-0.431054\pi$
$911$	12.9731			0.429818			0.214909	+	0.976634i	$0.431054\pi$
$912$	0.152440	+	0.568913i	0.00504779	+	0.0188386i
$913$	−48.8050	−	28.1776i	−1.61521	−	0.932542i
$914$	12.5940	−	7.27116i	0.416573	−	0.240509i
$915$	0.643842	+	0.643842i	0.0212848	+	0.0212848i
$916$	−2.03956	+	7.61174i	−0.0673889	+	0.251499i
$917$	9.76581	−	3.37573i	0.322495	−	0.111476i
$918$	−2.16884	−	2.16884i	−0.0715822	−	0.0715822i
$919$	−7.67594	−	13.2951i	−0.253206	−	0.438566i	0.711201	−	0.702989i	$-0.248152\pi$
$919$	−7.67594	−	13.2951i	−0.253206	−	0.438566i	−0.964407	+	0.264423i	$0.914818\pi$
$920$	0.0826587	−	0.143169i	0.00272518	−	0.00472015i
$921$	−23.1418	+	6.20082i	−0.762548	+	0.204324i
$922$	−0.276739			−0.00911391
$923$	−19.2435	−	19.9737i	−0.633406	−	0.657444i
$924$	5.77053	+	8.53309i	0.189836	+	0.280718i
$925$	10.0519	+	37.5143i	0.330505	+	1.23346i
$926$	17.7241	−	30.6990i	0.582448	−	1.00883i
$927$	−7.37071	−	12.7664i	−0.242086	−	0.419305i
$928$	−7.21838	+	7.21838i	−0.236955	+	0.236955i
$929$	12.1178	−	45.2244i	0.397574	−	1.48376i	−0.419779	−	0.907627i	$-0.637892\pi$
$929$	12.1178	−	45.2244i	0.397574	−	1.48376i	0.817352	−	0.576138i	$-0.195441\pi$
$930$	2.69560	+	0.722283i	0.0883921	+	0.0236846i
$931$	−1.62003	−	3.79125i	−0.0530942	−	0.124253i
$932$	4.03277	+	6.98496i	0.132098	+	0.228800i
$933$	−18.2975	−	10.5641i	−0.599034	−	0.345852i
$934$	1.25451	+	4.68188i	0.0410487	+	0.153196i
$935$		−	3.40747i		−	0.111436i
$936$	−2.59653	+	2.50160i	−0.0848704	+	0.0817674i
$937$		−	29.6494i		−	0.968605i	−0.874901	−	0.484303i	$-0.839073\pi$
$937$		−	29.6494i		−	0.968605i	0.874901	−	0.484303i	$-0.160927\pi$
$938$	−26.0651	−	22.6032i	−0.851055	−	0.738022i
$939$	14.2118	−	24.6155i	0.463783	−	0.803296i
$940$	−0.367722	+	0.212304i	−0.0119938	+	0.00692460i
$941$	2.61702	+	2.61702i	0.0853126	+	0.0853126i	0.748475	−	0.663163i	$-0.230786\pi$
$941$	2.61702	+	2.61702i	0.0853126	+	0.0853126i	−0.663163	+	0.748475i	$0.730786\pi$
$942$	1.44751	+	0.387858i	0.0471623	+	0.0126371i
$943$	−4.57922	−	1.22700i	−0.149120	−	0.0399566i
$944$	−8.93519	+	8.93519i	−0.290816	+	0.290816i
$945$	0.678920	+	0.330125i	0.0220853	+	0.0107390i
$946$	−2.92667	−	1.68971i	−0.0951543	−	0.0549374i
$947$	−6.02298	+	1.61385i	−0.195721	+	0.0524432i	−0.355348	−	0.934734i	$-0.615638\pi$
$947$	−6.02298	+	1.61385i	−0.195721	+	0.0524432i	0.159627	+	0.987177i	$0.448971\pi$
$948$	9.59166			0.311522
$949$	−53.1022	+	13.1741i	−1.72377	+	0.427651i
$950$		−	2.89696i		−	0.0939897i
$951$	−14.1392	+	3.78859i	−0.458496	+	0.122854i
$952$	−8.09459	+	0.575777i	−0.262347	+	0.0186610i
$953$	18.2600	−	10.5424i	0.591498	−	0.341501i	−0.174192	−	0.984712i	$-0.555731\pi$
$953$	18.2600	−	10.5424i	0.591498	−	0.341501i	0.765690	+	0.643210i	$0.222398\pi$
$954$	6.95757	−	6.95757i	0.225260	−	0.225260i
$955$	0.161053	−	0.601059i	0.00521156	−	0.0194498i
$956$	−2.59808	+	9.69617i	−0.0840279	+	0.313596i
$957$	28.1044	−	28.1044i	0.908486	−	0.908486i
$958$	18.4606	−	10.6583i	0.596436	−	0.344353i
$959$	−17.1079	+	1.21690i	−0.552443	+	0.0392959i
$960$	−0.275613	+	0.0738503i	−0.00889537	+	0.00238351i
$961$			64.6557i			2.08567i
$962$	−0.530053	+	28.4649i	−0.0170896	+	0.917745i
$963$	−13.8865			−0.447487
$964$	−12.8835	+	3.45212i	−0.414950	+	0.111185i
$965$	−1.84089	−	1.06284i	−0.0592603	−	0.0342139i
$966$	1.37856	+	0.670324i	0.0443544	+	0.0215673i
$967$	34.3086	−	34.3086i	1.10329	−	1.10329i	0.109280	−	0.994011i	$-0.465145\pi$
$967$	34.3086	−	34.3086i	1.10329	−	1.10329i	0.994011	−	0.109280i	$-0.0348547\pi$
$968$	4.01723	+	1.07641i	0.129119	+	0.0345972i
$969$	1.74497	+	0.467563i	0.0560565	+	0.0150203i
$970$	2.07358	+	2.07358i	0.0665786	+	0.0665786i
$971$	−15.6579	+	9.04011i	−0.502487	+	0.290111i	−0.729740	−	0.683725i	$-0.760359\pi$
$971$	−15.6579	+	9.04011i	−0.502487	+	0.290111i	0.227253	+	0.973836i	$0.427026\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−1.79287	−	1.55475i	−0.0574768	−	0.0498430i
$974$			40.0871i			1.28447i
$975$	15.5207	−	8.57962i	0.497060	−	0.274768i
$976$		−	3.19109i		−	0.102144i
$977$	3.46786	+	12.9422i	0.110947	+	0.414059i	0.998952	−	0.0457747i	$-0.0145756\pi$
$977$	3.46786	+	12.9422i	0.110947	+	0.414059i	−0.888005	+	0.459834i	$0.847909\pi$
$978$	5.82346	+	3.36218i	0.186214	+	0.107511i
$979$	26.9766	+	46.7248i	0.862175	+	1.49333i
$980$	1.83669	−	0.784831i	0.0586710	−	0.0250705i
$981$	12.4059	+	3.32415i	0.396090	+	0.106132i
$982$	4.13045	−	15.4150i	0.131808	−	0.491914i
$983$	−10.0429	+	10.0429i	−0.320318	+	0.320318i	−0.848889	−	0.528571i	$-0.822728\pi$
$983$	−10.0429	+	10.0429i	−0.320318	+	0.320318i	0.528571	+	0.848889i	$0.322728\pi$
$984$	4.09124	+	7.08624i	0.130424	+	0.225901i
$985$	−2.42409	+	4.19864i	−0.0772378	+	0.133780i
$986$	8.10388	+	30.2441i	0.258080	+	0.963168i
$987$	−2.20553	−	3.26140i	−0.0702029	−	0.103812i
$988$	0.587724	−	2.04066i	0.0186980	−	0.0649219i
$989$	−0.502889			−0.0159909
$990$	1.07309	−	0.287532i	0.0341049	−	0.00913838i
$991$	−24.0870	+	41.7198i	−0.765147	+	1.32527i	0.175021	+	0.984565i	$0.444001\pi$
$991$	−24.0870	+	41.7198i	−0.765147	+	1.32527i	−0.940169	+	0.340709i	$0.889333\pi$
$992$	−4.89019	−	8.47005i	−0.155264	−	0.268924i
$993$	−11.0947	−	11.0947i	−0.352080	−	0.352080i
$994$	19.2356	−	6.64913i	0.610115	−	0.210897i
$995$	1.62815	−	6.07633i	0.0516157	−	0.192633i
$996$	10.2349	+	10.2349i	0.324306	+	0.324306i
$997$	2.64767	−	1.52863i	0.0838526	−	0.0484123i	−0.457487	−	0.889216i	$-0.651251\pi$
$997$	2.64767	−	1.52863i	0.0838526	−	0.0484123i	0.541340	+	0.840804i	$0.317917\pi$
$998$	−15.8173	−	9.13215i	−0.500689	−	0.289073i
$999$	−2.04366	−	7.62705i	−0.0646586	−	0.241309i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bx.b.97.4	yes	40
7.6	odd	2		546.2.bx.a.97.2	✓	40
13.11	odd	12		546.2.bx.a.349.2	yes	40
91.76	even	12	inner	546.2.bx.b.349.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bx.a.97.2	✓	40	7.6	odd	2
546.2.bx.a.349.2	yes	40	13.11	odd	12
546.2.bx.b.97.4	yes	40	1.1	even	1	trivial
546.2.bx.b.349.4	yes	40	91.76	even	12	inner

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bx (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.201763 + 0.201763i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-0.864369 - 2.50057i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.201763 + 0.201763i) q^{5} +(0.258819 - 0.965926i) q^{6} +(-0.864369 - 2.50057i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.142668 - 0.247108i) q^{10} +(3.76078 - 1.00770i) q^{11} -1.00000 q^{12} +(3.08839 + 1.86060i) q^{13} +(-2.19165 + 1.48211i) q^{14} +(0.0738503 + 0.275613i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.53360 - 2.65627i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-0.152440 + 0.568913i) q^{19} +(-0.275613 - 0.0738503i) q^{20} +(0.501721 - 2.59774i) q^{21} +(-1.94672 - 3.37183i) q^{22} +(-0.501757 - 0.289689i) q^{23} +(0.258819 + 0.965926i) q^{24} -4.91858i q^{25} +(0.997865 - 3.46472i) q^{26} +1.00000i q^{27} +(1.99885 + 1.73338i) q^{28} +(5.10417 - 8.84068i) q^{29} +(0.247108 - 0.142668i) q^{30} +(6.91577 + 6.91577i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(3.76078 + 1.00770i) q^{33} +(-2.16884 + 2.16884i) q^{34} +(0.330125 - 0.678920i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-7.62705 + 2.04366i) q^{37} +0.588982 q^{38} +(1.74433 + 3.15552i) q^{39} +0.285336i q^{40} +(7.90367 - 2.11778i) q^{41} +(-2.63908 + 0.187721i) q^{42} +(0.751692 - 0.433989i) q^{43} +(-2.75308 + 2.75308i) q^{44} +(-0.0738503 + 0.275613i) q^{45} +(-0.149954 + 0.559637i) q^{46} +(1.05225 - 1.05225i) q^{47} +(0.866025 - 0.500000i) q^{48} +(-5.50573 + 4.32284i) q^{49} +(-4.75099 + 1.27302i) q^{50} -3.06720i q^{51} +(-3.60493 - 0.0671284i) q^{52} +9.83949 q^{53} +(0.965926 - 0.258819i) q^{54} +(0.962102 + 0.555470i) q^{55} +(1.15697 - 2.37937i) q^{56} +(-0.416473 + 0.416473i) q^{57} +(-9.86049 - 2.64211i) q^{58} +(-12.2057 - 3.27051i) q^{59} +(-0.201763 - 0.201763i) q^{60} +(2.76356 - 1.59554i) q^{61} +(4.89019 - 8.47005i) q^{62} +(1.73338 - 1.99885i) q^{63} +1.00000i q^{64} +(0.247723 + 0.998522i) q^{65} -3.89345i q^{66} +(3.37501 + 12.5957i) q^{67} +(2.65627 + 1.53360i) q^{68} +(-0.289689 - 0.501757i) q^{69} +(-0.741229 - 0.143159i) q^{70} +(-7.43034 - 1.99095i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(-10.7299 + 10.7299i) q^{73} +(3.94805 + 6.83823i) q^{74} +(2.45929 - 4.25962i) q^{75} +(-0.152440 - 0.568913i) q^{76} +(-5.77053 - 8.53309i) q^{77} +(2.59653 - 2.50160i) q^{78} -9.59166 q^{79} +(0.275613 - 0.0738503i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.09124 - 7.08624i) q^{82} +(-10.2349 - 10.2349i) q^{83} +(0.864369 + 2.50057i) q^{84} +(0.226513 - 0.845359i) q^{85} +(-0.613754 - 0.613754i) q^{86} +(8.84068 - 5.10417i) q^{87} +(3.37183 + 1.94672i) q^{88} +(3.58656 + 13.3852i) q^{89} +0.285336 q^{90} +(1.98305 - 9.33100i) q^{91} +0.579379 q^{92} +(2.53135 + 9.44711i) q^{93} +(-1.28873 - 0.744051i) q^{94} +(-0.145542 + 0.0840288i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-2.65996 + 9.92712i) q^{97} +(5.60053 + 4.19930i) q^{98} +(2.75308 + 2.75308i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 8 * q^7 + 20 * q^9	\( 40 q + 8 q^{7} + 20 q^{9} + 8 q^{11} - 40 q^{12} - 8 q^{14} + 20 q^{16} - 16 q^{17} - 16 q^{19} + 4 q^{21} + 8 q^{22} - 32 q^{26} - 8 q^{28} + 8 q^{33} - 16 q^{34} + 40 q^{35} + 40 q^{37} + 16 q^{38} - 16 q^{39} + 4 q^{41} - 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} - 16 q^{50} + 8 q^{52} + 32 q^{53} + 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} - 84 q^{59} + 48 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} - 20 q^{70} - 40 q^{71} + 48 q^{73} + 8 q^{74} - 36 q^{75} - 16 q^{76} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} - 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} - 12 q^{89} + 32 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} - 8 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q + 8 * q^7 + 20 * q^9 + 8 * q^11 - 40 * q^12 - 8 * q^14 + 20 * q^16 - 16 * q^17 - 16 * q^19 + 4 * q^21 + 8 * q^22 - 32 * q^26 - 8 * q^28 + 8 * q^33 - 16 * q^34 + 40 * q^35 + 40 * q^37 + 16 * q^38 - 16 * q^39 + 4 * q^41 - 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 - 16 * q^50 + 8 * q^52 + 32 * q^53 + 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 - 84 * q^59 + 48 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 - 20 * q^70 - 40 * q^71 + 48 * q^73 + 8 * q^74 - 36 * q^75 - 16 * q^76 + 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 - 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 - 12 * q^89 + 32 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 - 8 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

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Database

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