LMFDB - Embedded newform 547.2.m.a.10.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(10,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(182))

chi = DirichletCharacter(H, H._module([60]))

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

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

chi := DirichletCharacter("547.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.m (of order $91$, degree $72$, 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:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$3168$
Relative dimension:	$44$ over $\Q(\zeta_{91})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{91}]$

Embedding invariants

Embedding label			10.12
Character	$\chi$	$=$	547.10
Dual form			547.2.m.a.383.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.807206 - 1.36169i) q^{2} +(0.219615 + 0.962195i) q^{3} +(-0.242743 + 0.443723i) q^{4} +(-0.516600 - 0.0178417i) q^{5} +(1.13294 - 1.07574i) q^{6} +(-2.71722 + 0.377630i) q^{7} +(-2.36389 + 0.0816410i) q^{8} +(1.82532 - 0.879027i) q^{9} +O(q^{10})$	\(q+(-0.807206 - 1.36169i) q^{2} +(0.219615 + 0.962195i) q^{3} +(-0.242743 + 0.443723i) q^{4} +(-0.516600 - 0.0178417i) q^{5} +(1.13294 - 1.07574i) q^{6} +(-2.71722 + 0.377630i) q^{7} +(-2.36389 + 0.0816410i) q^{8} +(1.82532 - 0.879027i) q^{9} +(0.392708 + 0.717851i) q^{10} +(-4.77600 - 1.17718i) q^{11} +(-0.480258 - 0.136118i) q^{12} +(3.35023 + 4.20106i) q^{13} +(2.70757 + 3.39519i) q^{14} +(-0.0962857 - 0.500988i) q^{15} +(2.56487 + 4.00482i) q^{16} +(-3.18087 + 2.62775i) q^{17} +(-2.67037 - 1.77596i) q^{18} +(4.65439 - 2.86882i) q^{19} +(0.133318 - 0.224896i) q^{20} +(-0.960096 - 2.53156i) q^{21} +(2.25226 + 7.45365i) q^{22} +(-1.76583 + 5.84385i) q^{23} +(-0.597699 - 2.25659i) q^{24} +(-4.72153 - 0.326522i) q^{25} +(3.01621 - 7.95310i) q^{26} +(3.09270 + 3.87813i) q^{27} +(0.492024 - 1.29736i) q^{28} +(-5.48537 + 3.12503i) q^{29} +(-0.604468 + 0.535512i) q^{30} +(-8.19059 + 2.94560i) q^{31} +(1.25715 - 2.49921i) q^{32} +(0.0837950 - 4.85396i) q^{33} +(6.14580 + 2.21023i) q^{34} +(1.41045 - 0.146604i) q^{35} +(-0.0530392 + 1.02331i) q^{36} +(0.493360 - 3.15014i) q^{37} +(-7.66349 - 4.02211i) q^{38} +(-3.30648 + 4.14619i) q^{39} +1.22264 q^{40} +7.18495 q^{41} +(-2.67221 + 3.35085i) q^{42} +(-3.38014 + 2.42034i) q^{43} +(1.68168 - 1.83347i) q^{44} +(-0.958642 + 0.421538i) q^{45} +(9.38291 - 2.31268i) q^{46} +(-5.18260 + 7.50829i) q^{47} +(-3.29013 + 3.34742i) q^{48} +(0.505971 - 0.143406i) q^{49} +(3.36662 + 6.69283i) q^{50} +(-3.22697 - 2.48353i) q^{51} +(-2.67735 + 0.466797i) q^{52} +(-0.410455 - 2.13566i) q^{53} +(2.78436 - 7.34175i) q^{54} +(2.44628 + 0.693341i) q^{55} +(6.39238 - 1.11451i) q^{56} +(3.78253 + 3.84839i) q^{57} +(8.68315 + 4.94682i) q^{58} +(-0.640233 - 5.27279i) q^{59} +(0.245673 + 0.0788872i) q^{60} +(-0.296651 - 3.42860i) q^{61} +(10.6225 + 8.77533i) q^{62} +(-4.62785 + 3.07781i) q^{63} +(5.07089 - 0.350682i) q^{64} +(-1.65578 - 2.23004i) q^{65} +(-6.67723 + 3.80405i) q^{66} +(11.5711 + 3.27956i) q^{67} +(-0.393858 - 2.04929i) q^{68} +(-6.01073 - 0.415678i) q^{69} +(-1.33816 - 1.80226i) q^{70} +(1.29943 + 3.81898i) q^{71} +(-4.24308 + 2.22694i) q^{72} +(1.80035 - 9.36749i) q^{73} +(-4.68775 + 1.87100i) q^{74} +(-0.722740 - 4.61474i) q^{75} +(0.143138 + 2.76164i) q^{76} +(13.4220 + 1.39509i) q^{77} +(8.31483 + 1.15557i) q^{78} +(-6.20239 + 4.44119i) q^{79} +(-1.25356 - 2.11465i) q^{80} +(0.737168 - 0.924380i) q^{81} +(-5.79973 - 9.78368i) q^{82} +(-13.8724 - 7.28078i) q^{83} +(1.35637 + 0.188504i) q^{84} +(1.69012 - 1.30074i) q^{85} +(6.02422 + 2.64899i) q^{86} +(-4.21156 - 4.59169i) q^{87} +(11.3860 + 2.39280i) q^{88} +(0.131599 - 1.52098i) q^{89} +(1.34783 + 0.965105i) q^{90} +(-10.6898 - 10.1501i) q^{91} +(-2.16441 - 2.20210i) q^{92} +(-4.63301 - 7.23404i) q^{93} +(14.4074 + 0.996357i) q^{94} +(-2.45564 + 1.39899i) q^{95} +(2.68082 + 0.660763i) q^{96} +(5.24115 + 4.03367i) q^{97} +(-0.603697 - 0.573217i) q^{98} +(-9.75248 + 2.04951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9}+O(q^{10}) $ 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9} - 91 q^{10} - 61 q^{11} - 31 q^{12} - 72 q^{13} - 21 q^{14} - 46 q^{15} + 24 q^{16} - 91 q^{17} + 9 q^{18} - 89 q^{19} - 108 q^{20} - 81 q^{21} - 50 q^{22} - 86 q^{23} - 33 q^{24} - 15 q^{25} + 137 q^{26} + 163 q^{27} - 47 q^{28} - 12 q^{29} + 29 q^{30} - 53 q^{31} - 122 q^{32} - 21 q^{33} - 80 q^{34} - 75 q^{35} - 8 q^{36} - 49 q^{37} - 47 q^{38} + 128 q^{39} - 246 q^{40} - 686 q^{41} - 466 q^{42} - 9 q^{43} - 43 q^{44} + 156 q^{45} - 91 q^{46} - 72 q^{47} + 21 q^{48} - 8 q^{49} - 84 q^{50} + 93 q^{51} + 4 q^{52} - 32 q^{53} - 71 q^{54} - 34 q^{55} - 263 q^{56} - 61 q^{57} - 36 q^{58} - 23 q^{59} + 87 q^{60} + 38 q^{61} + 26 q^{62} + 133 q^{63} + 343 q^{64} + 143 q^{65} - 65 q^{66} - 50 q^{67} - 213 q^{68} - 140 q^{69} + 372 q^{70} - 75 q^{71} + 147 q^{72} - 18 q^{73} - 85 q^{74} + 97 q^{75} - 47 q^{76} + 11 q^{77} + 55 q^{78} - 37 q^{79} - 142 q^{80} - 532 q^{81} - 94 q^{82} - 279 q^{83} + 395 q^{84} - 75 q^{85} - 147 q^{86} + 84 q^{87} + 345 q^{88} + 8 q^{89} + 278 q^{90} - 38 q^{91} - 78 q^{92} - 83 q^{93} - 540 q^{94} + 35 q^{95} + 123 q^{96} - 735 q^{97} - 90 q^{98} + 351 q^{99}+O(q^{100}) \) 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9 - 91 * q^10 - 61 * q^11 - 31 * q^12 - 72 * q^13 - 21 * q^14 - 46 * q^15 + 24 * q^16 - 91 * q^17 + 9 * q^18 - 89 * q^19 - 108 * q^20 - 81 * q^21 - 50 * q^22 - 86 * q^23 - 33 * q^24 - 15 * q^25 + 137 * q^26 + 163 * q^27 - 47 * q^28 - 12 * q^29 + 29 * q^30 - 53 * q^31 - 122 * q^32 - 21 * q^33 - 80 * q^34 - 75 * q^35 - 8 * q^36 - 49 * q^37 - 47 * q^38 + 128 * q^39 - 246 * q^40 - 686 * q^41 - 466 * q^42 - 9 * q^43 - 43 * q^44 + 156 * q^45 - 91 * q^46 - 72 * q^47 + 21 * q^48 - 8 * q^49 - 84 * q^50 + 93 * q^51 + 4 * q^52 - 32 * q^53 - 71 * q^54 - 34 * q^55 - 263 * q^56 - 61 * q^57 - 36 * q^58 - 23 * q^59 + 87 * q^60 + 38 * q^61 + 26 * q^62 + 133 * q^63 + 343 * q^64 + 143 * q^65 - 65 * q^66 - 50 * q^67 - 213 * q^68 - 140 * q^69 + 372 * q^70 - 75 * q^71 + 147 * q^72 - 18 * q^73 - 85 * q^74 + 97 * q^75 - 47 * q^76 + 11 * q^77 + 55 * q^78 - 37 * q^79 - 142 * q^80 - 532 * q^81 - 94 * q^82 - 279 * q^83 + 395 * q^84 - 75 * q^85 - 147 * q^86 + 84 * q^87 + 345 * q^88 + 8 * q^89 + 278 * q^90 - 38 * q^91 - 78 * q^92 - 83 * q^93 - 540 * q^94 + 35 * q^95 + 123 * q^96 - 735 * q^97 - 90 * q^98 + 351 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{30}{91}\right)$

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 $

$2$	−0.807206	−	1.36169i	−0.570781	−	0.962860i	−0.998268	−	0.0588386i	$-0.981260\pi$
$2$	−0.807206	−	1.36169i	−0.570781	−	0.962860i	0.427487	−	0.904022i	$-0.359399\pi$
$3$	0.219615	+	0.962195i	0.126795	+	0.555523i	0.997920	+	0.0644630i	$0.0205335\pi$
$3$	0.219615	+	0.962195i	0.126795	+	0.555523i	−0.871125	+	0.491060i	$0.836609\pi$
$4$	−0.242743	+	0.443723i	−0.121372	+	0.221861i
$5$	−0.516600	−	0.0178417i	−0.231030	−	0.00797903i	−0.0812304	−	0.996695i	$-0.525885\pi$
$5$	−0.516600	−	0.0178417i	−0.231030	−	0.00797903i	−0.149800	+	0.988716i	$0.547863\pi$
$6$	1.13294	−	1.07574i	0.462520	−	0.439168i
$7$	−2.71722	+	0.377630i	−1.02701	+	0.142731i	−0.631216	−	0.775607i	$-0.717444\pi$
$7$	−2.71722	+	0.377630i	−1.02701	+	0.142731i	−0.395797	+	0.918338i	$0.629532\pi$
$8$	−2.36389	+	0.0816410i	−0.835761	+	0.0288644i
$9$	1.82532	−	0.879027i	0.608439	−	0.293009i
$10$	0.392708	+	0.717851i	0.124185	+	0.227004i
$11$	−4.77600	−	1.17718i	−1.44002	−	0.354932i	−0.559454	−	0.828861i	$-0.688989\pi$
$11$	−4.77600	−	1.17718i	−1.44002	−	0.354932i	−0.880563	+	0.473929i	$0.842835\pi$
$12$	−0.480258	−	0.136118i	−0.138639	−	0.0392939i
$13$	3.35023	+	4.20106i	0.929187	+	1.16516i	0.985994	+	0.166779i	$0.0533366\pi$
$13$	3.35023	+	4.20106i	0.929187	+	1.16516i	−0.0568069	+	0.998385i	$0.518092\pi$
$14$	2.70757	+	3.39519i	0.723629	+	0.907402i
$15$	−0.0962857	−	0.500988i	−0.0248609	−	0.129355i
$16$	2.56487	+	4.00482i	0.641217	+	1.00120i
$17$	−3.18087	+	2.62775i	−0.771475	+	0.637323i	−0.937178	−	0.348853i	$-0.886571\pi$
$17$	−3.18087	+	2.62775i	−0.771475	+	0.637323i	0.165702	+	0.986176i	$0.447011\pi$
$18$	−2.67037	−	1.77596i	−0.629412	−	0.418598i
$19$	4.65439	−	2.86882i	1.06779	−	0.658152i	0.125209	−	0.992130i	$-0.460040\pi$
$19$	4.65439	−	2.86882i	1.06779	−	0.658152i	0.942581	+	0.333979i	$0.108391\pi$
$20$	0.133318	−	0.224896i	0.0298108	−	0.0502883i
$21$	−0.960096	−	2.53156i	−0.209510	−	0.552433i
$22$	2.25226	+	7.45365i	0.480184	+	1.58912i
$23$	−1.76583	+	5.84385i	−0.368201	+	1.21853i	0.554229	+	0.832364i	$0.313013\pi$
$23$	−1.76583	+	5.84385i	−0.368201	+	1.21853i	−0.922430	+	0.386164i	$0.873800\pi$
$24$	−0.597699	−	2.25659i	−0.122005	−	0.460625i
$25$	−4.72153	−	0.326522i	−0.944306	−	0.0653043i
$26$	3.01621	−	7.95310i	0.591528	−	1.55973i
$27$	3.09270	+	3.87813i	0.595191	+	0.746346i
$28$	0.492024	−	1.29736i	0.0929838	−	0.245178i
$29$	−5.48537	+	3.12503i	−1.01861	+	0.580304i	−0.910359	−	0.413820i	$-0.864194\pi$
$29$	−5.48537	+	3.12503i	−1.01861	+	0.580304i	−0.108248	+	0.994124i	$0.534524\pi$
$30$	−0.604468	+	0.535512i	−0.110360	+	0.0977706i
$31$	−8.19059	+	2.94560i	−1.47107	+	0.529045i	−0.946608	−	0.322387i	$-0.895515\pi$
$31$	−8.19059	+	2.94560i	−1.47107	+	0.529045i	−0.524465	+	0.851432i	$0.675735\pi$
$32$	1.25715	−	2.49921i	0.222236	−	0.441803i
$33$	0.0837950	−	4.85396i	0.0145868	−	0.844967i
$34$	6.14580	+	2.21023i	1.05400	+	0.379051i
$35$	1.41045	−	0.146604i	0.238410	−	0.0247806i
$36$	−0.0530392	+	1.02331i	−0.00883986	+	0.170552i
$37$	0.493360	−	3.15014i	0.0811079	−	0.517879i	−0.912866	−	0.408260i	$-0.866136\pi$
$37$	0.493360	−	3.15014i	0.0811079	−	0.517879i	0.993974	−	0.109619i	$-0.0349632\pi$
$38$	−7.66349	−	4.02211i	−1.24318	−	0.652472i
$39$	−3.30648	+	4.14619i	−0.529460	+	0.663922i
$40$	1.22264			0.193316
$41$	7.18495			1.12210			0.561050	−	0.827782i	$-0.310397\pi$
$41$	7.18495			1.12210			0.561050	+	0.827782i	$0.310397\pi$
$42$	−2.67221	+	3.35085i	−0.412331	+	0.517047i
$43$	−3.38014	+	2.42034i	−0.515467	+	0.369098i	−0.809894	−	0.586576i	$-0.800475\pi$
$43$	−3.38014	+	2.42034i	−0.515467	+	0.369098i	0.294427	+	0.955674i	$0.404871\pi$
$44$	1.68168	−	1.83347i	0.253523	−	0.276406i
$45$	−0.958642	+	0.421538i	−0.142906	+	0.0628392i
$46$	9.38291	−	2.31268i	1.38343	−	0.340986i
$47$	−5.18260	+	7.50829i	−0.755960	+	1.09520i	0.236380	+	0.971661i	$0.424039\pi$
$47$	−5.18260	+	7.50829i	−0.755960	+	1.09520i	−0.992340	+	0.123536i	$0.960576\pi$
$48$	−3.29013	+	3.34742i	−0.474890	+	0.483159i
$49$	0.505971	−	0.143406i	0.0722815	−	0.0204865i
$50$	3.36662	+	6.69283i	0.476113	+	0.946509i
$51$	−3.22697	−	2.48353i	−0.451867	−	0.347763i
$52$	−2.67735	+	0.466797i	−0.371282	+	0.0647330i
$53$	−0.410455	−	2.13566i	−0.0563804	−	0.293355i	0.942822	−	0.333298i	$-0.108161\pi$
$53$	−0.410455	−	2.13566i	−0.0563804	−	0.293355i	−0.999202	+	0.0399430i	$0.987282\pi$
$54$	2.78436	−	7.34175i	0.378903	−	0.999085i
$55$	2.44628	+	0.693341i	0.329856	+	0.0934901i
$56$	6.39238	−	1.11451i	0.854218	−	0.148933i
$57$	3.78253	+	3.84839i	0.501009	+	0.509732i
$58$	8.68315	+	4.94682i	1.14015	+	0.649549i
$59$	−0.640233	−	5.27279i	−0.0833512	−	0.686459i	−0.973161	−	0.230127i	$-0.926086\pi$
$59$	−0.640233	−	5.27279i	−0.0833512	−	0.686459i	0.889809	−	0.456332i	$-0.150837\pi$
$60$	0.245673	+	0.0788872i	0.0317162	+	0.0101843i
$61$	−0.296651	−	3.42860i	−0.0379823	−	0.438987i	−0.990789	−	0.135411i	$-0.956764\pi$
$61$	−0.296651	−	3.42860i	−0.0379823	−	0.438987i	0.952807	−	0.303576i	$-0.0981806\pi$
$62$	10.6225	+	8.77533i	1.34906	+	1.11447i
$63$	−4.62785	+	3.07781i	−0.583054	+	0.387767i
$64$	5.07089	−	0.350682i	0.633862	−	0.0438353i
$65$	−1.65578	−	2.23004i	−0.205374	−	0.276602i
$66$	−6.67723	+	3.80405i	−0.821911	+	0.468246i
$67$	11.5711	+	3.27956i	1.41363	+	0.400662i	0.891817	−	0.452396i	$-0.149431\pi$
$67$	11.5711	+	3.27956i	1.41363	+	0.400662i	0.521816	+	0.853058i	$0.325255\pi$
$68$	−0.393858	−	2.04929i	−0.0477622	−	0.248513i
$69$	−6.01073	−	0.415678i	−0.723607	−	0.0500417i
$70$	−1.33816	−	1.80226i	−0.159940	−	0.215411i
$71$	1.29943	+	3.81898i	0.154214	+	0.453229i	0.996283	−	0.0861411i	$-0.0274536\pi$
$71$	1.29943	+	3.81898i	0.154214	+	0.453229i	−0.842069	+	0.539370i	$0.818662\pi$
$72$	−4.24308	+	2.22694i	−0.500052	+	0.262448i
$73$	1.80035	−	9.36749i	0.210716	−	1.09638i	−0.709421	−	0.704785i	$-0.751044\pi$
$73$	1.80035	−	9.36749i	0.210716	−	1.09638i	0.920137	−	0.391597i	$-0.128077\pi$
$74$	−4.68775	+	1.87100i	−0.544940	+	0.217500i
$75$	−0.722740	−	4.61474i	−0.0834548	−	0.532864i
$76$	0.143138	+	2.76164i	0.0164191	+	0.316782i
$77$	13.4220	+	1.39509i	1.52958	+	0.158986i
$78$	8.31483	+	1.15557i	0.941470	+	0.130842i
$79$	−6.20239	+	4.44119i	−0.697823	+	0.499673i	−0.874765	−	0.484548i	$-0.838984\pi$
$79$	−6.20239	+	4.44119i	−0.697823	+	0.499673i	0.176942	+	0.984221i	$0.443380\pi$
$80$	−1.25356	−	2.11465i	−0.140152	−	0.236425i
$81$	0.737168	−	0.924380i	0.0819076	−	0.102709i
$82$	−5.79973	−	9.78368i	−0.640474	−	1.08043i
$83$	−13.8724	−	7.28078i	−1.52269	−	0.799170i	−0.524070	−	0.851675i	$-0.675587\pi$
$83$	−13.8724	−	7.28078i	−1.52269	−	0.799170i	−0.998621	+	0.0525057i	$0.983279\pi$
$84$	1.35637	+	0.188504i	0.147992	+	0.0205674i
$85$	1.69012	−	1.30074i	0.183319	−	0.141085i
$86$	6.02422	+	2.64899i	0.649608	+	0.285648i
$87$	−4.21156	−	4.59169i	−0.451526	−	0.492281i
$88$	11.3860	+	2.39280i	1.21375	+	0.255073i
$89$	0.131599	−	1.52098i	0.0139495	−	0.161224i	−0.986036	−	0.166530i	$-0.946744\pi$
$89$	0.131599	−	1.52098i	0.0139495	−	0.161224i	0.999986	+	0.00530572i	$0.00168887\pi$
$90$	1.34783	+	0.965105i	0.142073	+	0.101731i
$91$	−10.6898	−	10.1501i	−1.12059	−	1.06402i
$92$	−2.16441	−	2.20210i	−0.225655	−	0.229584i
$93$	−4.63301	−	7.23404i	−0.480421	−	0.750135i
$94$	14.4074	+	0.996357i	1.48601	+	0.102766i
$95$	−2.45564	+	1.39899i	−0.251943	+	0.143533i
$96$	2.68082	+	0.660763i	0.273610	+	0.0674388i
$97$	5.24115	+	4.03367i	0.532159	+	0.409557i	0.840576	−	0.541694i	$-0.182217\pi$
$97$	5.24115	+	4.03367i	0.532159	+	0.409557i	−0.308417	+	0.951251i	$0.599799\pi$
$98$	−0.603697	−	0.573217i	−0.0609826	−	0.0579037i
$99$	−9.75248	+	2.04951i	−0.980161	+	0.205983i
$100$	1.29100	−	2.01579i	0.129100	−	0.201579i
$101$	1.42716	−	1.92213i	0.142007	−	0.191259i	−0.726167	−	0.687518i	$-0.758700\pi$
$101$	1.42716	−	1.92213i	0.142007	−	0.191259i	0.868174	+	0.496259i	$0.165293\pi$
$102$	−0.776962	+	6.39886i	−0.0769307	+	0.633581i
$103$	2.02787	−	4.40380i	0.199812	−	0.433919i	−0.782126	−	0.623120i	$-0.785865\pi$
$103$	2.02787	−	4.40380i	0.199812	−	0.433919i	0.981938	+	0.189202i	$0.0605899\pi$
$104$	−8.26256	−	9.65732i	−0.810210	−	0.946978i
$105$	0.450818	+	1.32494i	0.0439953	+	0.129300i
$106$	−2.57678	+	2.28283i	−0.250279	+	0.221728i
$107$	10.3967	+	2.56257i	1.00509	+	0.247733i	0.707311	−	0.706902i	$-0.249908\pi$
$107$	10.3967	+	2.56257i	1.00509	+	0.247733i	0.297779	+	0.954635i	$0.403754\pi$
$108$	−2.47155	+	0.430914i	−0.237825	+	0.0414647i
$109$	−0.187648	−	0.292995i	−0.0179734	−	0.0280638i	0.832997	−	0.553277i	$-0.186623\pi$
$109$	−0.187648	−	0.292995i	−0.0179734	−	0.0280638i	−0.850971	+	0.525213i	$0.823986\pi$
$110$	−1.03053	−	3.89074i	−0.0982574	−	0.370967i
$111$	3.13939	−	0.217108i	0.297978	−	0.0206069i
$112$	−8.48166	−	9.91341i	−0.801442	−	0.936729i
$113$	−2.70189	−	1.66536i	−0.254173	−	0.156664i	0.391738	−	0.920077i	$-0.371874\pi$
$113$	−2.70189	−	1.66536i	−0.254173	−	0.156664i	−0.645911	+	0.763413i	$0.723522\pi$
$114$	2.18704	−	8.25708i	0.204835	−	0.773347i
$115$	1.01649	−	2.98743i	0.0947884	−	0.278579i
$116$	−0.0551139	−	3.19256i	−0.00511720	−	0.296422i
$117$	9.80808	+	4.72332i	0.906758	+	0.436672i
$118$	−6.66311	+	5.12803i	−0.613389	+	0.472073i
$119$	7.65082	−	8.34137i	0.701350	−	0.764653i
$120$	0.268510	+	1.17642i	0.0245115	+	0.107392i
$121$	11.6844	+	6.13243i	1.06222	+	0.557494i
$122$	−4.42923	+	3.17153i	−0.401004	+	0.287137i
$123$	1.57792	+	6.91332i	0.142276	+	0.623353i
$124$	0.681179	−	4.34937i	0.0611717	−	0.390585i
$125$	5.00400	+	0.520121i	0.447572	+	0.0465210i
$126$	7.92664	+	3.81727i	0.706162	+	0.340069i
$127$	0.877043	+	0.152912i	0.0778249	+	0.0135688i	0.210537	−	0.977586i	$-0.432479\pi$
$127$	0.877043	+	0.152912i	0.0778249	+	0.0135688i	−0.132713	+	0.991155i	$0.542369\pi$
$128$	−7.74920	−	11.2267i	−0.684939	−	0.992306i
$129$	−3.07116	−	2.72081i	−0.270401	−	0.239554i
$130$	−1.70007	+	4.05475i	−0.149106	+	0.355625i
$131$	−18.5031	+	3.88846i	−1.61662	+	0.339736i	−0.924245	−	0.381801i	$-0.875304\pi$
$131$	−18.5031	+	3.88846i	−1.61662	+	0.339736i	−0.692376	+	0.721537i	$0.743436\pi$
$132$	2.13347	+	1.21545i	0.185695	+	0.105791i
$133$	−11.5637	+	9.55285i	−1.00270	+	0.828337i
$134$	−4.87450	−	18.4035i	−0.421093	−	1.58982i
$135$	−1.52850	−	2.05862i	−0.131552	−	0.177178i
$136$	7.30470	−	6.47140i	0.626373	−	0.554918i
$137$	−0.615800	−	1.12565i	−0.0526113	−	0.0961710i	0.849678	−	0.527302i	$-0.176796\pi$
$137$	−0.615800	−	1.12565i	−0.0526113	−	0.0961710i	−0.902290	+	0.431131i	$0.858115\pi$
$138$	4.28587	+	8.52029i	0.364838	+	0.725295i
$139$	−16.3377	−	11.6985i	−1.38574	−	0.992257i	−0.997498	−	0.0707012i	$-0.977476\pi$
$139$	−16.3377	−	11.6985i	−1.38574	−	0.992257i	−0.388247	−	0.921555i	$-0.626919\pi$
$140$	−0.277327	+	0.661438i	−0.0234384	+	0.0559017i
$141$	−8.36262	−	3.33774i	−0.704259	−	0.281088i
$142$	4.15135	−	4.85212i	0.348374	−	0.407181i
$143$	−11.0553	−	24.0081i	−0.924491	−	2.00765i
$144$	8.20205	+	5.05548i	0.683504	+	0.421290i
$145$	2.88949	−	1.51652i	0.239959	−	0.125940i
$146$	−14.2089	+	5.10997i	−1.17593	+	0.422904i
$147$	0.249103	+	0.455348i	0.0205457	+	0.0375565i
$148$	1.27803	+	0.983589i	0.105053	+	0.0808505i
$149$	−10.2596	−	10.4383i	−0.840501	−	0.855136i	0.150552	−	0.988602i	$-0.451895\pi$
$149$	−10.2596	−	10.4383i	−0.840501	−	0.855136i	−0.991053	+	0.133466i	$0.957389\pi$
$150$	−5.70045	+	4.70919i	−0.465439	+	0.384504i
$151$	1.09097	−	3.61047i	0.0887820	−	0.293816i	−0.901522	−	0.432733i	$-0.857549\pi$
$151$	1.09097	−	3.61047i	0.0887820	−	0.293816i	0.990304	+	0.138918i	$0.0443623\pi$
$152$	−10.7682	+	7.16155i	−0.873420	+	0.580878i
$153$	−3.49624	+	7.59255i	−0.282655	+	0.613822i
$154$	−8.93462	−	19.4027i	−0.719972	−	1.56351i
$155$	4.28381	−	1.37556i	0.344084	−	0.110488i
$156$	−1.03714	−	2.47362i	−0.0830373	−	0.198048i
$157$	−2.29215	−	0.399637i	−0.182934	−	0.0318945i	0.0795503	−	0.996831i	$-0.474652\pi$
$157$	−2.29215	−	0.399637i	−0.182934	−	0.0318945i	−0.262484	+	0.964936i	$0.584542\pi$
$158$	11.0541	+	4.86077i	0.879419	+	0.386702i
$159$	1.96477	−	0.863959i	0.155817	−	0.0685164i
$160$	−0.694036	+	1.26866i	−0.0548683	+	0.100297i
$161$	2.59134	−	16.5459i	0.204226	−	1.30400i
$162$	−1.85376	−	0.257630i	−0.145646	−	0.0202413i
$163$	−16.1606	+	17.6193i	−1.26580	+	1.38005i	−0.374121	+	0.927380i	$0.622055\pi$
$163$	−16.1606	+	17.6193i	−1.26580	+	1.38005i	−0.891679	+	0.452669i	$0.850472\pi$
$164$	−1.74410	+	3.18813i	−0.136191	+	0.248951i
$165$	−0.129891	+	2.50606i	−0.0101120	+	0.195097i
$166$	1.28369	+	24.7670i	0.0996338	+	1.92229i
$167$	−0.365312	−	21.1613i	−0.0282687	−	1.63751i	−0.588018	−	0.808848i	$-0.700092\pi$
$167$	−0.365312	−	21.1613i	−0.0282687	−	1.63751i	0.559750	−	0.828662i	$-0.310897\pi$
$168$	2.47624	+	5.90595i	0.191046	+	0.455654i
$169$	−3.53207	+	15.4750i	−0.271697	+	1.19038i
$170$	−3.13548	−	1.25145i	−0.240481	−	0.0959822i
$171$	5.97397	−	9.32783i	0.456841	−	0.713317i
$172$	−0.253452	−	2.08737i	−0.0193255	−	0.159160i
$173$	−0.825202	−	0.548811i	−0.0627390	−	0.0417253i	0.522012	−	0.852938i	$-0.325182\pi$
$173$	−0.825202	−	0.548811i	−0.0627390	−	0.0417253i	−0.584751	+	0.811213i	$0.698808\pi$
$174$	−2.85286	+	9.44127i	−0.216275	+	0.715741i
$175$	12.9527	−	0.895759i	0.979136	−	0.0677130i
$176$	−7.53543	−	22.1463i	−0.568004	−	1.66934i
$177$	4.93285	−	1.77401i	0.370776	−	0.133343i
$178$	−2.17734	+	1.04855i	−0.163198	+	0.0785922i
$179$	9.14978	−	2.59330i	0.683886	−	0.193832i	0.0870607	−	0.996203i	$-0.472253\pi$
$179$	9.14978	−	2.59330i	0.683886	−	0.193832i	0.596826	+	0.802371i	$0.296428\pi$
$180$	0.0456576	−	0.527697i	0.00340312	−	0.0393322i
$181$	18.4536	+	16.3485i	1.37165	+	1.21517i	0.951474	+	0.307728i	$0.0995686\pi$
$181$	18.4536	+	16.3485i	1.37165	+	1.21517i	0.420172	+	0.907445i	$0.361970\pi$
$182$	−5.19239	+	22.7493i	−0.384886	+	1.68629i
$183$	3.23383	−	1.03841i	0.239052	−	0.0767613i
$184$	3.69713	−	13.9584i	0.272556	−	1.02903i
$185$	−0.311073	+	1.61856i	−0.0228706	+	0.118999i
$186$	−6.11073	+	12.1481i	−0.448060	+	0.890741i
$187$	18.2852	−	8.80567i	1.33714	−	0.643934i
$188$	−2.07356	−	4.12223i	−0.151230	−	0.300644i
$189$	−9.86806	−	9.36983i	−0.717795	−	0.681555i
$190$	3.88719	+	2.21455i	0.282007	+	0.160660i
$191$	−5.32735	−	3.54302i	−0.385473	−	0.256364i	0.345999	−	0.938235i	$-0.387540\pi$
$191$	−5.32735	−	3.54302i	−0.385473	−	0.256364i	−0.731472	+	0.681871i	$0.761166\pi$
$192$	1.45107	+	4.80217i	0.104722	+	0.346567i
$193$	−5.20137	−	4.29690i	−0.374403	−	0.309298i	0.430630	−	0.902529i	$-0.358292\pi$
$193$	−5.20137	−	4.29690i	−0.374403	−	0.309298i	−0.805032	+	0.593231i	$0.797852\pi$
$194$	1.26192	−	10.3928i	0.0906004	−	0.746162i
$195$	1.78210	−	2.08293i	0.127619	−	0.149162i
$196$	−0.0591884	+	0.259322i	−0.00422775	+	0.0185230i
$197$	9.68141	+	14.0259i	0.689772	+	0.999307i	0.998835	+	0.0482655i	$0.0153694\pi$
$197$	9.68141	+	14.0259i	0.689772	+	0.999307i	−0.309063	+	0.951042i	$0.600015\pi$
$198$	10.6631	+	11.6255i	0.757790	+	0.826187i
$199$	13.1483	−	3.24077i	0.932060	−	0.229732i	0.256083	−	0.966655i	$-0.417568\pi$
$199$	13.1483	−	3.24077i	0.932060	−	0.229732i	0.675977	+	0.736923i	$0.263722\pi$
$200$	11.1878	+	0.386391i	0.791099	+	0.0273220i
$201$	−0.614397	+	11.8539i	−0.0433362	+	0.836108i
$202$	−3.76936	−	0.391790i	−0.265211	−	0.0275663i
$203$	13.7248	−	10.5628i	0.963296	−	0.741367i
$204$	1.88532	−	0.829023i	0.131999	−	0.0580432i
$205$	−3.71174	−	0.128191i	−0.259239	−	0.00895328i
$206$	−7.63352	+	0.793434i	−0.531852	+	0.0552812i
$207$	1.91370	+	12.2191i	0.133011	+	0.849287i
$208$	−8.23157	+	24.1922i	−0.570757	+	1.67743i
$209$	−25.6064	+	8.22241i	−1.77123	+	0.568756i
$210$	1.44025	−	1.68337i	0.0993865	−	0.116164i
$211$	−8.19233	+	11.0336i	−0.563984	+	0.759587i	−0.989369	−	0.145425i	$-0.953545\pi$
$211$	−8.19233	+	11.0336i	−0.563984	+	0.759587i	0.425386	+	0.905012i	$0.360138\pi$
$212$	1.04727	+	0.336287i	0.0719271	+	0.0230963i
$213$	−3.38922	+	2.08901i	−0.232226	+	0.143137i
$214$	−4.90289	−	16.2257i	−0.335155	−	1.10916i
$215$	1.78936	−	1.19004i	0.122034	−	0.0811599i
$216$	−7.62742	−	8.91497i	−0.518980	−	0.606587i
$217$	21.1433	−	11.0969i	1.43530	−	0.753304i
$218$	−0.247498	+	0.492025i	−0.0167627	+	0.0333241i
$219$	9.40874	−	0.324947i	0.635783	−	0.0219579i
$220$	−0.901468	+	0.917164i	−0.0607770	+	0.0618352i
$221$	−21.6960	−	4.55946i	−1.45943	−	0.306703i
$222$	−2.82977	−	4.09963i	−0.189922	−	0.275149i
$223$	−0.266863	−	0.636482i	−0.0178705	−	0.0426220i	0.913038	−	0.407874i	$-0.133730\pi$
$223$	−0.266863	−	0.636482i	−0.0178705	−	0.0426220i	−0.930908	+	0.365252i	$0.880983\pi$
$224$	−2.47219	+	7.26566i	−0.165180	+	0.485457i
$225$	−8.90531	+	3.55435i	−0.593688	+	0.236956i
$226$	−0.0867205	+	5.02343i	−0.00576856	+	0.334153i
$227$	4.44426	−	0.153490i	0.294976	−	0.0101875i	0.113350	−	0.993555i	$-0.463842\pi$
$227$	4.44426	−	0.153490i	0.294976	−	0.0101875i	0.181626	+	0.983368i	$0.441864\pi$
$228$	−2.62580	+	0.744225i	−0.173898	+	0.0492875i
$229$	19.0540	+	13.6436i	1.25913	+	0.901591i	0.997969	−	0.0637053i	$-0.0202918\pi$
$229$	19.0540	+	13.6436i	1.25913	+	0.901591i	0.261156	+	0.965297i	$0.415896\pi$
$230$	−4.88847	+	1.02732i	−0.322336	+	0.0677397i
$231$	1.60531	+	13.2209i	0.105622	+	0.869874i
$232$	12.7117	−	7.83506i	0.834561	−	0.514397i
$233$	5.89038	+	15.5317i	0.385892	+	1.01751i	0.977434	+	0.211239i	$0.0677500\pi$
$233$	5.89038	+	15.5317i	0.385892	+	1.01751i	−0.591543	+	0.806274i	$0.701481\pi$
$234$	−1.48544	−	17.1683i	−0.0971063	−	1.12232i
$235$	2.81129	−	3.78632i	0.183388	−	0.246992i
$236$	2.49507	+	0.995848i	0.162415	+	0.0648242i
$237$	−5.63543	−	4.99255i	−0.366060	−	0.324301i
$238$	−17.5342	−	3.68484i	−1.13657	−	0.238853i
$239$	6.87734	−	9.96355i	0.444858	−	0.644488i	−0.534843	−	0.844951i	$-0.679629\pi$
$239$	6.87734	−	9.96355i	0.444858	−	0.644488i	0.979701	+	0.200463i	$0.0642447\pi$
$240$	1.75941	−	1.67058i	0.113569	−	0.107835i
$241$	−9.59544	+	0.997359i	−0.618097	+	0.0642455i	−0.407315	−	0.913288i	$-0.633535\pi$
$241$	−9.59544	+	0.997359i	−0.618097	+	0.0642455i	−0.210782	+	0.977533i	$0.567601\pi$
$242$	−1.08122	−	20.8606i	−0.0695037	−	1.34097i
$243$	14.4586	+	6.96288i	0.927518	+	0.446669i
$244$	1.59336	+	0.700639i	0.102004	+	0.0448538i
$245$	−0.263943	+	0.0650561i	−0.0168627	+	0.00415628i
$246$	8.14010	−	7.72911i	0.518994	−	0.492790i
$247$	27.6453	+	9.94216i	1.75903	+	0.632604i
$248$	19.1211	−	7.63175i	1.21419	−	0.484617i
$249$	3.95895	−	14.9469i	0.250889	−	0.947221i
$250$	−3.33102	−	7.23375i	−0.210672	−	0.457502i
$251$	−0.170857	+	1.40713i	−0.0107844	+	0.0888173i	−0.997107	−	0.0760074i	$-0.975783\pi$
$251$	−0.170857	+	1.40713i	−0.0107844	+	0.0888173i	0.986323	+	0.164825i	$0.0527058\pi$
$252$	−0.242315	−	2.80060i	−0.0152644	−	0.176421i
$253$	15.3129	−	25.8315i	0.962711	−	1.62401i
$254$	−0.499735	−	1.31769i	−0.0313561	−	0.0826793i
$255$	1.62274	+	1.34056i	0.101620	+	0.0839494i
$256$	−4.77991	+	10.3802i	−0.298744	+	0.648763i
$257$	7.27784	+	4.48583i	0.453979	+	0.279818i	0.732697	−	0.680555i	$-0.238261\pi$
$257$	7.27784	+	4.48583i	0.453979	+	0.279818i	−0.278718	+	0.960373i	$0.589909\pi$
$258$	−1.22584	+	6.37823i	−0.0763176	+	0.397091i
$259$	−0.150983	+	8.74593i	−0.00938161	+	0.543445i
$260$	1.39145	−	0.193379i	0.0862939	−	0.0119928i
$261$	−7.26555	+	10.5260i	−0.449726	+	0.651541i
$262$	20.2307	+	22.0566i	1.24985	+	1.36266i
$263$	−18.4077	−	3.20938i	−1.13507	−	0.197899i	−0.427140	−	0.904185i	$-0.640479\pi$
$263$	−18.4077	−	3.20938i	−1.13507	−	0.197899i	−0.707926	+	0.706286i	$0.750369\pi$
$264$	0.198200	+	11.4811i	0.0121984	+	0.706611i
$265$	0.173937	+	1.11060i	0.0106849	+	0.0682238i
$266$	22.3423	+	8.03500i	1.36989	+	0.492657i
$267$	1.49238	−	0.207406i	0.0913325	−	0.0126931i
$268$	−4.26402	+	4.33827i	−0.260466	+	0.265002i
$269$	−2.51528	+	29.0709i	−0.153360	+	1.77248i	0.378452	+	0.925621i	$0.376457\pi$
$269$	−2.51528	+	29.0709i	−0.153360	+	1.77248i	−0.531812	+	0.846863i	$0.678489\pi$
$270$	−1.56939	+	3.74307i	−0.0955099	+	0.227796i
$271$	−10.4369	+	16.2962i	−0.633994	+	0.989926i	0.364285	+	0.931288i	$0.381313\pi$
$271$	−10.4369	+	16.2962i	−0.633994	+	0.989926i	−0.998279	+	0.0586389i	$0.981324\pi$
$272$	−18.6822	−	5.99899i	−1.13277	−	0.363742i
$273$	7.41871	−	12.5147i	0.449001	−	0.757427i
$274$	−1.03571	+	1.74716i	−0.0625697	+	0.105550i
$275$	22.1656	+	7.11754i	1.33664	+	0.429204i
$276$	1.64351	−	2.56620i	0.0989276	−	0.154467i
$277$	1.91344	−	4.56364i	0.114967	−	0.274203i	−0.854488	−	0.519471i	$-0.826129\pi$
$277$	1.91344	−	4.56364i	0.114967	−	0.274203i	0.969455	+	0.245269i	$0.0788762\pi$
$278$	−2.74189	+	31.6900i	−0.164448	+	1.90064i
$279$	−12.3612	+	12.5764i	−0.740044	+	0.752929i
$280$	−3.32219	+	0.461706i	−0.198539	+	0.0275922i
$281$	25.7943	+	9.27644i	1.53876	+	0.553386i	0.964222	−	0.265095i	$-0.0854032\pi$
$281$	25.7943	+	9.27644i	1.53876	+	0.553386i	0.574534	+	0.818481i	$0.305183\pi$
$282$	2.20539	+	14.0815i	0.131329	+	0.838543i
$283$	0.410472	+	23.7773i	0.0244000	+	1.41341i	0.719497	+	0.694495i	$0.244372\pi$
$283$	0.410472	+	23.7773i	0.0244000	+	1.41341i	−0.695097	+	0.718916i	$0.744639\pi$
$284$	−2.00999	−	0.350443i	−0.119271	−	0.0207950i
$285$	−1.88539	−	2.05557i	−0.111681	−	0.121761i
$286$	−23.7676	+	34.4333i	−1.40541	+	2.03609i
$287$	−19.5231	+	2.71325i	−1.15241	+	0.160158i
$288$	0.0978295	−	5.66693i	0.00576466	−	0.333927i
$289$	0.00434604	−	0.0226131i	0.000255650	−	0.00133018i
$290$	−4.39745	−	2.71045i	−0.258227	−	0.159163i
$291$	−2.73014	+	5.92886i	−0.160044	+	0.347556i
$292$	3.71955	+	3.07275i	0.217670	+	0.179819i
$293$	3.23072	+	8.51870i	0.188740	+	0.497668i	0.995668	−	0.0929832i	$-0.0296403\pi$
$293$	3.23072	+	8.51870i	0.188740	+	0.497668i	−0.806927	+	0.590651i	$0.798871\pi$
$294$	0.418966	−	0.706761i	0.0244346	−	0.0412191i
$295$	0.236669	+	2.73535i	0.0137794	+	0.159258i
$296$	−0.909068	+	7.48685i	−0.0528385	+	0.435164i
$297$	−10.2055	−	22.1626i	−0.592183	−	1.28600i
$298$	−5.93206	+	22.3963i	−0.343635	+	1.29738i
$299$	−30.4663	+	12.1599i	−1.76191	+	0.703226i
$300$	2.22311	+	0.799501i	0.128351	+	0.0461592i
$301$	8.27060	−	7.85303i	0.476710	−	0.452641i
$302$	−5.79698	+	1.42883i	−0.333579	+	0.0822197i
$303$	2.16289	+	0.951075i	0.124255	+	0.0546378i
$304$	23.4270	+	11.2818i	1.34363	+	0.647058i
$305$	0.0920778	+	1.77651i	0.00527236	+	0.101723i
$306$	13.1609	−	1.36795i	0.752358	−	0.0782008i
$307$	−4.09106	+	3.88450i	−0.233489	+	0.221700i	−0.796326	−	0.604867i	$-0.793226\pi$
$307$	−4.09106	+	3.88450i	−0.233489	+	0.221700i	0.562837	+	0.826568i	$0.309710\pi$
$308$	−3.87713	+	5.61699i	−0.220920	+	0.320058i
$309$	4.68266	+	0.984071i	0.266387	+	0.0559819i
$310$	−5.33100	−	4.72286i	−0.302781	−	0.268240i
$311$	3.70681	+	1.47949i	0.210194	+	0.0838940i	0.473407	−	0.880844i	$-0.343024\pi$
$311$	3.70681	+	1.47949i	0.210194	+	0.0838940i	−0.263213	+	0.964738i	$0.584782\pi$
$312$	7.47764	−	10.0711i	0.423338	−	0.570163i
$313$	−1.99926	−	23.1068i	−0.113005	−	1.30607i	−0.808907	−	0.587937i	$-0.799940\pi$
$313$	−1.99926	−	23.1068i	−0.113005	−	1.30607i	0.695902	−	0.718137i	$-0.255005\pi$
$314$	1.30606	+	3.44379i	0.0737051	+	0.194344i
$315$	2.44566	−	1.50743i	0.137797	−	0.0849338i
$316$	−0.465072	−	3.83021i	−0.0261623	−	0.215466i
$317$	9.67222	−	2.03264i	0.543246	−	0.114164i	0.0740436	−	0.997255i	$-0.476410\pi$
$317$	9.67222	−	2.03264i	0.543246	−	0.114164i	0.469202	+	0.883091i	$0.344541\pi$
$318$	−2.76242	−	1.97802i	−0.154909	−	0.110922i
$319$	29.8768	−	8.46790i	1.67278	−	0.474111i
$320$	−2.62588	+	0.0906893i	−0.146791	+	0.00506968i
$321$	−0.182411	+	10.5665i	−0.0101812	+	0.589763i
$322$	−24.6221	+	9.82733i	−1.37214	+	0.547656i
$323$	−7.26649	+	21.3559i	−0.404318	+	1.18827i
$324$	0.231226	+	0.551485i	0.0128459	+	0.0306381i
$325$	−14.4465	−	20.9293i	−0.801347	−	1.16095i
$326$	37.0370	+	7.78340i	2.05129	+	0.431083i
$327$	0.240708	−	0.244900i	0.0133112	−	0.0135430i
$328$	−16.9844	+	0.586586i	−0.937808	+	0.0323888i
$329$	11.2469	−	22.3588i	0.620063	−	1.23268i
$330$	3.51733	−	1.84604i	0.193623	−	0.101621i
$331$	−16.5489	−	19.3425i	−0.909612	−	1.06316i	−0.997750	−	0.0670516i	$-0.978641\pi$
$331$	−16.5489	−	19.3425i	−0.909612	−	1.06316i	0.0881370	−	0.996108i	$-0.471909\pi$
$332$	6.59807	−	4.38813i	0.362116	−	0.240830i
$333$	−1.86852	−	6.18368i	−0.102394	−	0.338863i
$334$	−28.5202	+	17.5790i	−1.56056	+	0.961878i
$335$	−5.91911	−	1.90067i	−0.323395	−	0.103845i
$336$	7.67594	−	10.3381i	0.418757	−	0.563992i
$337$	13.1532	−	15.3735i	0.716501	−	0.837450i	−0.275811	−	0.961212i	$-0.588946\pi$
$337$	13.1532	−	15.3735i	0.716501	−	0.837450i	0.992312	+	0.123762i	$0.0394959\pi$
$338$	23.9232	−	7.68192i	1.30125	−	0.417842i
$339$	1.00903	−	2.96548i	0.0548027	−	0.161063i
$340$	0.166904	+	1.06569i	0.00905163	+	0.0577953i
$341$	42.5857	−	4.42639i	2.30614	−	0.239703i
$342$	−17.5238	−	0.605216i	−0.947581	−	0.0327263i
$343$	16.2582	−	7.14914i	0.877862	−	0.386017i
$344$	7.79268	−	5.99736i	0.420153	−	0.323356i
$345$	3.09773	+	0.321980i	0.166776	+	0.0173348i
$346$	−0.0812019	+	1.56667i	−0.00436544	+	0.0842248i
$347$	−29.3012	−	1.01197i	−1.57297	−	0.0543252i	−0.765188	−	0.643807i	$-0.777354\pi$
$347$	−29.3012	−	1.01197i	−1.57297	−	0.0543252i	−0.807782	+	0.589482i	$0.799332\pi$
$348$	3.05976	−	0.754164i	0.164021	−	0.0404274i
$349$	−0.0688920	−	0.0751101i	−0.00368770	−	0.00402055i	0.735107	−	0.677951i	$-0.237132\pi$
$349$	−0.0688920	−	0.0751101i	−0.00368770	−	0.00402055i	−0.738794	+	0.673931i	$0.764605\pi$
$350$	−11.6753	−	16.9146i	−0.624070	−	0.904122i
$351$	−5.93096	+	25.9852i	−0.316571	+	1.38699i
$352$	−8.94618	+	10.4563i	−0.476833	+	0.557325i
$353$	1.90002	−	15.6481i	0.101128	−	0.832863i	−0.850577	−	0.525850i	$-0.823747\pi$
$353$	1.90002	−	15.6481i	0.101128	−	0.832863i	0.951705	−	0.307013i	$-0.0993296\pi$
$354$	−6.39748	−	5.28502i	−0.340022	−	0.280896i
$355$	−0.603149	−	1.99607i	−0.0320118	−	0.105940i
$356$	0.642951	+	0.427602i	0.0340763	+	0.0226629i
$357$	9.70626	+	5.52969i	0.513710	+	0.292662i
$358$	−10.9170	−	10.3658i	−0.576982	−	0.547851i
$359$	−7.70524	−	15.3180i	−0.406667	−	0.808451i	−0.999994	−	0.00348984i	$-0.998889\pi$
$359$	−7.70524	−	15.3180i	−0.406667	−	0.808451i	0.593327	−	0.804962i	$-0.297814\pi$
$360$	2.23171	−	1.07473i	0.117621	−	0.0566435i
$361$	4.89519	−	9.73160i	0.257641	−	0.512190i
$362$	7.36569	−	38.3247i	0.387132	−	2.01430i
$363$	−3.33453	+	12.5894i	−0.175018	+	0.660773i
$364$	7.09868	−	2.27944i	0.372072	−	0.119475i
$365$	−1.09719	+	4.80712i	−0.0574298	+	0.251616i
$366$	−4.02436	−	3.56527i	−0.210357	−	0.186360i
$367$	−3.22279	+	37.2480i	−0.168228	+	1.94433i	0.133746	+	0.991016i	$0.457299\pi$
$367$	−3.22279	+	37.2480i	−0.168228	+	1.94433i	−0.301975	+	0.953316i	$0.597646\pi$
$368$	−27.9327	+	7.91689i	−1.45609	+	0.412697i
$369$	13.1148	−	6.31577i	0.682730	−	0.328786i
$370$	2.45507	−	0.882923i	0.127633	−	0.0459010i
$371$	1.92179	+	5.64805i	0.0997742	+	0.293232i
$372$	4.33454	−	0.299759i	0.224736	−	0.0155418i
$373$	−10.8661	+	35.9604i	−0.562626	+	1.86196i	−0.0585782	+	0.998283i	$0.518657\pi$
$373$	−10.8661	+	35.9604i	−0.562626	+	1.86196i	−0.504048	+	0.863676i	$0.668156\pi$
$374$	−26.7505	−	17.7907i	−1.38323	−	0.919937i
$375$	0.598496	+	4.92905i	0.0309062	+	0.254535i
$376$	11.6381	−	18.1719i	0.600189	−	0.937143i
$377$	−31.5057	−	12.5748i	−1.62263	−	0.647633i
$378$	−4.79325	+	21.0006i	−0.246538	+	1.08016i
$379$	−4.59262	−	10.9536i	−0.235907	−	0.562650i	0.760309	−	0.649561i	$-0.225047\pi$
$379$	−4.59262	−	10.9536i	−0.235907	−	0.562650i	−0.996216	+	0.0869117i	$0.972300\pi$
$380$	−0.0246729	−	1.42922i	−0.00126569	−	0.0733174i
$381$	0.0454799	+	0.877468i	0.00233001	+	0.0449540i
$382$	−0.524224	+	10.1141i	−0.0268216	+	0.517484i
$383$	13.4737	−	24.6292i	0.688472	−	1.25849i	−0.267081	−	0.963674i	$-0.586059\pi$
$383$	13.4737	−	24.6292i	0.688472	−	1.25849i	0.955553	−	0.294819i	$-0.0952594\pi$
$384$	9.10039	−	9.92178i	0.464402	−	0.506319i
$385$	−6.90890	−	0.960175i	−0.352110	−	0.0489350i
$386$	−1.65247	+	10.5511i	−0.0841085	+	0.537038i
$387$	−4.04229	+	7.38912i	−0.205481	+	0.375610i
$388$	−3.06209	+	1.34647i	−0.155454	+	0.0683569i
$389$	−10.8734	−	4.78131i	−0.551304	−	0.242422i	0.108192	−	0.994130i	$-0.465494\pi$
$389$	−10.8734	−	4.78131i	−0.551304	−	0.242422i	−0.659496	+	0.751708i	$0.729230\pi$
$390$	−4.27482	−	0.745316i	−0.216464	−	0.0377405i
$391$	−9.73930	−	23.2287i	−0.492538	−	1.17473i
$392$	−1.18435	+	0.380303i	−0.0598187	+	0.0192082i
$393$	−7.80500	−	16.9496i	−0.393710	−	0.854994i
$394$	11.2841	−	24.5049i	0.568485	−	1.23454i
$395$	3.28339	−	2.18366i	0.165205	−	0.109872i
$396$	1.45794	−	4.82490i	0.0732640	−	0.242460i
$397$	−17.9513	+	14.8298i	−0.900952	+	0.744285i	−0.967333	−	0.253509i	$-0.918415\pi$
$397$	−17.9513	+	14.8298i	−0.900952	+	0.744285i	0.0663811	+	0.997794i	$0.478855\pi$
$398$	−15.0263	−	15.2880i	−0.753202	−	0.766317i
$399$	−11.7312	−	9.02854i	−0.587297	−	0.451993i
$400$	−10.8024	−	19.7464i	−0.540122	−	0.987318i
$401$	−21.2936	+	7.65786i	−1.06335	+	0.382415i	−0.810894	−	0.585193i	$-0.801019\pi$
$401$	−21.2936	+	7.65786i	−1.06335	+	0.382415i	−0.252457	+	0.967608i	$0.581239\pi$
$402$	16.6373	−	8.73191i	0.829791	−	0.435508i
$403$	−39.8150	−	24.5407i	−1.98333	−	1.22246i
$404$	0.506461	+	1.09985i	0.0251974	+	0.0547194i
$405$	−0.397313	+	0.464382i	−0.0197427	+	0.0230753i
$406$	−25.4621	−	10.1626i	−1.26366	−	0.504361i
$407$	−6.06455	+	14.4643i	−0.300609	+	0.716967i
$408$	7.83097	+	5.60733i	0.387691	+	0.277604i
$409$	−0.0306795	−	0.0609907i	−0.00151701	−	0.00301580i	0.892586	−	0.450878i	$-0.148889\pi$
$409$	−0.0306795	−	0.0609907i	−0.00151701	−	0.00301580i	−0.894103	+	0.447862i	$0.852186\pi$
$410$	2.82158	+	5.15772i	0.139348	+	0.254722i
$411$	0.947858	−	0.839729i	0.0467544	−	0.0414208i
$412$	1.46181	+	1.96881i	0.0720183	+	0.0969961i
$413$	3.73082	+	14.0856i	0.183582	+	0.693106i
$414$	15.0939	−	12.4692i	0.741824	−	0.612828i
$415$	7.03656	+	4.00876i	0.345411	+	0.196782i
$416$	14.7111	−	3.09157i	0.721271	−	0.151577i
$417$	7.66827	−	18.2892i	0.375517	−	0.895626i
$418$	31.8660	+	28.2309i	1.55862	+	1.38082i
$419$	5.46094	+	7.91153i	0.266784	+	0.386504i	0.933365	−	0.358929i	$-0.116858\pi$
$419$	5.46094	+	7.91153i	0.266784	+	0.386504i	−0.666580	+	0.745433i	$0.732243\pi$
$420$	−0.697337	−	0.121581i	−0.0340266	−	0.00593253i
$421$	12.8124	+	6.17013i	0.624439	+	0.300714i	0.719218	−	0.694784i	$-0.244500\pi$
$421$	12.8124	+	6.17013i	0.624439	+	0.300714i	−0.0947793	+	0.995498i	$0.530215\pi$
$422$	21.6373	+	2.24900i	1.05329	+	0.109480i
$423$	−2.85990	+	18.2607i	−0.139053	+	0.887864i
$424$	1.14463	+	5.01494i	0.0555880	+	0.243547i
$425$	15.8766	−	11.3684i	0.770128	−	0.551447i
$426$	5.58038	+	2.92881i	0.270371	+	0.141901i
$427$	2.10081	+	9.20425i	0.101665	+	0.445425i
$428$	−3.66081	+	3.99123i	−0.176952	+	0.192923i
$429$	20.6725	−	15.9099i	0.998079	−	0.768136i
$430$	−3.06485	−	1.47595i	−0.147800	−	0.0711767i
$431$	0.530985	+	30.7582i	0.0255766	+	1.48157i	0.684309	+	0.729192i	$0.260104\pi$
$431$	0.530985	+	30.7582i	0.0255766	+	1.48157i	−0.658733	+	0.752377i	$0.728907\pi$
$432$	−7.59881	+	22.3326i	−0.365598	+	1.07448i
$433$	3.45942	−	13.0609i	0.166249	−	0.627668i	−0.831180	−	0.556004i	$-0.812334\pi$
$433$	3.45942	−	13.0609i	0.166249	−	0.627668i	0.997429	−	0.0716639i	$-0.0228309\pi$
$434$	−32.1775	−	19.8332i	−1.54457	−	0.952022i
$435$	2.09377	+	2.44721i	0.100388	+	0.117335i
$436$	0.175559	−	0.0121409i	0.00840774	−	0.000581445i
$437$	8.54608	+	32.2654i	0.408814	+	1.54346i
$438$	−8.03726	−	12.5495i	−0.384035	−	0.599637i
$439$	7.24665	−	1.26345i	0.345863	−	0.0603013i	0.00383973	−	0.999993i	$-0.498778\pi$
$439$	7.24665	−	1.26345i	0.345863	−	0.0603013i	0.342024	+	0.939691i	$0.388888\pi$
$440$	−5.83933	−	1.43926i	−0.278379	−	0.0686143i
$441$	0.797500	−	0.706523i	0.0379762	−	0.0336440i
$442$	11.3046	+	33.2237i	0.537703	+	1.58029i
$443$	21.2000	+	24.7786i	1.00724	+	1.17727i	0.984114	+	0.177535i	$0.0568123\pi$
$443$	21.2000	+	24.7786i	1.00724	+	1.17727i	0.0231256	+	0.999733i	$0.492638\pi$
$444$	−0.665731	+	1.44572i	−0.0315942	+	0.0686109i
$445$	−0.0951210	+	0.783392i	−0.00450917	+	0.0371364i
$446$	−0.651278	+	0.877157i	−0.0308389	+	0.0415346i
$447$	7.79049	−	12.1642i	0.368477	−	0.575345i
$448$	−13.6463	+	2.86780i	−0.644728	+	0.135491i
$449$	9.18281	+	8.71919i	0.433364	+	0.411484i	0.873789	−	0.486305i	$-0.161656\pi$
$449$	9.18281	+	8.71919i	0.433364	+	0.411484i	−0.440425	+	0.897789i	$0.645172\pi$
$450$	12.0283	+	9.25719i	0.567021	+	0.436388i
$451$	−34.3153	−	8.45796i	−1.61584	−	0.398270i
$452$	1.39482	−	0.794636i	0.0656070	−	0.0373766i
$453$	3.71357	+	0.256815i	0.174479	+	0.0120662i
$454$	−3.79644	−	5.92781i	−0.178176	−	0.278206i
$455$	5.34124	+	5.43424i	0.250401	+	0.254761i
$456$	−9.25567	−	8.78837i	−0.433437	−	0.411553i
$457$	1.12510	+	0.805623i	0.0526300	+	0.0376855i	0.608195	−	0.793787i	$-0.291894\pi$
$457$	1.12510	+	0.805623i	0.0526300	+	0.0376855i	−0.555565	+	0.831473i	$0.687498\pi$
$458$	3.19777	−	36.9588i	0.149422	−	1.72697i
$459$	−20.0282	−	4.20898i	−0.934838	−	0.196458i
$460$	1.07884	+	1.17622i	0.0503014	+	0.0548415i
$461$	4.11669	+	1.81021i	0.191733	+	0.0843099i	0.496181	−	0.868219i	$-0.334735\pi$
$461$	4.11669	+	1.81021i	0.191733	+	0.0843099i	−0.304447	+	0.952529i	$0.598472\pi$
$462$	16.7070	−	12.8580i	0.777280	−	0.598206i
$463$	−40.9745	−	5.69449i	−1.90425	−	0.264645i	−0.914187	−	0.405294i	$-0.867169\pi$
$463$	−40.9745	−	5.69449i	−1.90425	−	0.264645i	−0.990060	+	0.140648i	$0.955081\pi$
$464$	−26.5844	−	13.9526i	−1.23415	−	0.647733i
$465$	2.26435	+	3.81977i	0.105007	+	0.177137i
$466$	16.3946	−	20.5581i	0.759463	−	0.952337i
$467$	5.46819	+	9.22439i	0.253038	+	0.426854i	0.959836	−	0.280561i	$-0.0905206\pi$
$467$	5.46819	+	9.22439i	0.253038	+	0.426854i	−0.706798	+	0.707415i	$0.749861\pi$
$468$	−4.47669	+	3.20552i	−0.206935	+	0.148175i
$469$	−32.6797	−	4.54171i	−1.50901	−	0.209717i
$470$	−7.42508	−	0.771769i	−0.342493	−	0.0355991i
$471$	−0.118862	−	2.29326i	−0.00547686	−	0.105668i
$472$	1.94391	+	12.4120i	0.0894759	+	0.571310i
$473$	18.9927	−	7.58049i	0.873285	−	0.348551i
$474$	−2.24936	+	11.7037i	−0.103317	+	0.537570i
$475$	−22.9126	+	12.0254i	−1.05130	+	0.551765i
$476$	1.84407	+	5.41966i	0.0845230	+	0.248410i
$477$	−2.62651	−	3.53745i	−0.120260	−	0.161969i
$478$	−19.1187	−	1.32217i	−0.874468	−	0.0604747i
$479$	4.19529	+	21.8287i	0.191688	+	0.997378i	0.941827	+	0.336098i	$0.109107\pi$
$479$	4.19529	+	21.8287i	0.191688	+	0.997378i	−0.750139	+	0.661280i	$0.770013\pi$
$480$	−1.37312	−	0.389180i	−0.0626742	−	0.0177636i
$481$	14.8868	−	8.48105i	0.678779	−	0.386703i
$482$	9.10359	+	12.2609i	0.414657	+	0.558471i
$483$	16.4895	−	1.14034i	0.750296	−	0.0518874i
$484$	−5.55740	+	3.69602i	−0.252609	+	0.168001i
$485$	−2.63561	−	2.17730i	−0.119677	−	0.0988663i
$486$	−2.18976	−	25.3086i	−0.0993295	−	1.14802i
$487$	−2.12462	−	0.682232i	−0.0962759	−	0.0309149i	0.257203	−	0.966357i	$-0.417199\pi$
$487$	−2.12462	−	0.682232i	−0.0962759	−	0.0309149i	−0.353479	+	0.935443i	$0.615001\pi$
$488$	0.981164	+	8.08061i	0.0444152	+	0.365792i
$489$	−20.5023	−	11.6802i	−0.927146	−	0.528199i
$490$	0.301642	+	0.306895i	0.0136268	+	0.0138641i
$491$	27.8362	−	4.85325i	1.25623	−	0.219024i	0.495797	−	0.868438i	$-0.334876\pi$
$491$	27.8362	−	4.85325i	1.25623	−	0.219024i	0.760435	+	0.649414i	$0.224986\pi$
$492$	−3.45063	−	0.978002i	−0.155566	−	0.0440918i
$493$	9.23645	−	24.3545i	0.415989	−	1.09687i
$494$	−8.77735	−	45.6698i	−0.394912	−	2.05478i
$495$	5.07470	−	0.884774i	0.228091	−	0.0397676i
$496$	−32.8044	−	25.2467i	−1.47296	−	1.13361i
$497$	−4.97300	−	9.88630i	−0.223070	−	0.443461i
$498$	−23.5487	+	6.67435i	−1.05524	+	0.299085i
$499$	6.44175	−	6.55392i	0.288372	−	0.293394i	−0.553747	−	0.832685i	$-0.686802\pi$
$499$	6.44175	−	6.55392i	0.288372	−	0.293394i	0.842119	+	0.539292i	$0.181308\pi$
$500$	−1.44548	+	2.09414i	−0.0646437	+	0.0936526i
$501$	20.2811	−	4.99883i	0.906091	−	0.223331i
$502$	2.05399	−	0.903190i	0.0916741	−	0.0403113i
$503$	7.76597	−	8.46692i	0.346268	−	0.377521i	−0.539235	−	0.842155i	$-0.681287\pi$
$503$	7.76597	−	8.46692i	0.346268	−	0.377521i	0.885503	+	0.464634i	$0.153814\pi$
$504$	10.6884	−	7.65341i	0.476101	−	0.340910i
$505$	−0.771563	+	0.967510i	−0.0343341	+	0.0430536i
$506$	−47.5352			−2.11320
$507$	−15.6656			−0.695736
$508$	−0.280747	+	0.352045i	−0.0124561	+	0.0156195i
$509$	−0.934135	−	0.490272i	−0.0414048	−	0.0217309i	0.443894	−	0.896079i	$-0.353597\pi$
$509$	−0.934135	−	0.490272i	−0.0414048	−	0.0217309i	−0.485299	+	0.874349i	$0.661289\pi$
$510$	0.515545	−	3.29179i	0.0228287	−	0.145763i
$511$	−1.35452	+	26.1334i	−0.0599203	+	1.15607i
$512$	−9.14363	+	0.950397i	−0.404095	+	0.0420020i
$513$	25.5203	+	9.17791i	1.12675	+	0.405215i
$514$	0.233591	−	13.5312i	0.0103033	−	0.596834i
$515$	−1.12617	+	2.23882i	−0.0496250	+	0.0986541i
$516$	1.95279	−	0.702287i	0.0859668	−	0.0309164i
$517$	33.5907	−	29.7587i	1.47732	−	1.30879i
$518$	12.0311	−	6.85417i	0.528617	−	0.301155i
$519$	0.346836	−	0.914532i	0.0152244	−	0.0401435i
$520$	4.09613	+	5.13639i	0.179627	+	0.225245i
$521$	−1.35917	+	3.58384i	−0.0595463	+	0.157011i	−0.961488	−	0.274847i	$-0.911373\pi$
$521$	−1.35917	+	3.58384i	−0.0595463	+	0.157011i	0.901942	+	0.431858i	$0.142142\pi$
$522$	20.1979	+	1.39680i	0.884038	+	0.0611364i
$523$	3.13733	+	11.8449i	0.137186	+	0.517940i	0.999924	+	0.0122897i	$0.00391204\pi$
$523$	3.13733	+	11.8449i	0.137186	+	0.517940i	−0.862739	+	0.505650i	$0.831253\pi$
$524$	2.76609	−	9.15413i	0.120837	−	0.399900i
$525$	3.70651	+	12.2663i	0.161765	+	0.535347i
$526$	10.4886	+	27.6562i	0.457325	+	1.20587i
$527$	18.3129	−	30.8924i	0.797723	−	1.34569i
$528$	19.6542	−	12.1142i	0.855338	−	0.527203i
$529$	−11.8812	−	7.90170i	−0.516572	−	0.343552i
$530$	1.37189	−	1.13333i	0.0595912	−	0.0492289i
$531$	−5.80355	−	9.06174i	−0.251853	−	0.393246i
$532$	−1.43182	−	7.44995i	−0.0620772	−	0.322996i
$533$	24.0713	+	30.1844i	1.04264	+	1.30743i
$534$	−1.48708	−	1.86475i	−0.0643525	−	0.0806954i
$535$	−5.32523	−	1.50932i	−0.230230	−	0.0652534i
$536$	−27.6205	−	6.80784i	−1.19302	−	0.294054i
$537$	4.50468	+	8.23434i	0.194391	+	0.355338i
$538$	41.6159	−	20.0412i	1.79419	−	0.864036i
$539$	−2.58533	+	0.0892887i	−0.111358	+	0.00384594i
$540$	1.28449	−	0.178514i	0.0552756	−	0.00768200i
$541$	7.78529	−	7.39222i	0.334716	−	0.317817i	−0.502618	−	0.864509i	$-0.667630\pi$
$541$	7.78529	−	7.39222i	0.334716	−	0.317817i	0.837334	+	0.546692i	$0.184113\pi$
$542$	30.6151	+	1.05735i	1.31503	+	0.0454169i
$543$	−11.6777	+	21.3463i	−0.501139	+	0.916059i
$544$	2.56846	+	11.2532i	0.110122	+	0.482476i
$545$	0.0917111	+	0.154709i	0.00392847	+	0.00662701i
$546$	−23.0296			−0.985577
$547$	−16.6654	+	16.4093i	−0.712562	+	0.701609i
$547$	−16.6654	+	16.4093i	−0.712562	+	0.701609i
$548$	0.648959			0.0277221
$549$	−3.55531	−	5.99752i	−0.151737	−	0.255968i
$550$	−8.20034	−	35.9280i	−0.349664	−	1.53198i
$551$	−16.5659	+	30.2816i	−0.705730	+	1.29004i
$552$	14.2426	+	0.491894i	0.606207	+	0.0209364i
$553$	15.1761	−	14.4099i	0.645355	−	0.612772i
$554$	−7.75880	+	1.07829i	−0.329640	+	0.0458122i
$555$	−1.62568	+	0.0561458i	−0.0690064	+	0.00238326i
$556$	9.15677	−	4.40967i	0.388333	−	0.187012i
$557$	10.5288	+	19.2461i	0.446118	+	0.815482i	0.999852	−	0.0172116i	$-0.00547888\pi$
$557$	10.5288	+	19.2461i	0.446118	+	0.815482i	−0.553734	+	0.832694i	$0.686798\pi$
$558$	27.1032	+	6.68033i	1.14737	+	0.282801i
$559$	−21.4922	−	6.09148i	−0.909024	−	0.257642i
$560$	4.20475	+	5.27259i	0.177683	+	0.222808i
$561$	12.4885	+	15.6600i	0.527263	+	0.661167i
$562$	−8.18963	−	42.6118i	−0.345459	−	1.79747i
$563$	−12.6202	−	19.7054i	−0.531879	−	0.830483i	0.466664	−	0.884434i	$-0.345456\pi$
$563$	−12.6202	−	19.7054i	−0.531879	−	0.830483i	−0.998544	+	0.0539519i	$0.982818\pi$
$564$	3.51100	−	2.90047i	0.147840	−	0.122132i
$565$	1.36608	+	0.908530i	0.0574716	+	0.0382222i
$566$	32.0459	−	19.7521i	1.34699	−	0.830242i
$567$	−1.65398	+	2.79012i	−0.0694605	+	0.117174i
$568$	−3.38350	−	8.92154i	−0.141968	−	0.374340i
$569$	−7.43327	−	24.5997i	−0.311619	−	1.03127i	−0.962315	−	0.271936i	$-0.912336\pi$
$569$	−7.43327	−	24.5997i	−0.311619	−	1.03127i	0.650696	−	0.759338i	$-0.274477\pi$
$570$	−1.27714	+	4.22659i	−0.0534936	+	0.177032i
$571$	−10.5903	−	39.9833i	−0.443191	−	1.67325i	−0.705850	−	0.708362i	$-0.749435\pi$
$571$	−10.5903	−	39.9833i	−0.443191	−	1.67325i	0.262659	−	0.964889i	$-0.415401\pi$
$572$	13.3365	+	0.922300i	0.557628	+	0.0385633i
$573$	2.23911	−	5.90405i	0.0935401	−	0.246645i
$574$	19.4538	+	24.3943i	0.811985	+	1.01820i
$575$	10.2456	−	27.0154i	0.427270	−	1.12662i
$576$	8.94774	−	5.09756i	0.372822	−	0.212398i
$577$	−10.2208	+	9.05487i	−0.425499	+	0.376959i	−0.848522	−	0.529160i	$-0.822507\pi$
$577$	−10.2208	+	9.05487i	−0.425499	+	0.376959i	0.423023	+	0.906119i	$0.360969\pi$
$578$	−0.0343001	+	0.0123354i	−0.00142670	+	0.000513086i
$579$	2.99216	−	5.94839i	0.124350	−	0.247207i
$580$	−0.0284888	+	1.65026i	−0.00118293	+	0.0685233i
$581$	40.4438	+	14.5449i	1.67789	+	0.603423i
$582$	10.2771	−	1.06821i	0.425998	−	0.0442786i
$583$	−0.553712	+	10.6831i	−0.0229324	+	0.442447i
$584$	−3.49107	+	22.2907i	−0.144461	+	0.922395i
$585$	−4.98258	−	2.61506i	−0.206004	−	0.108119i
$586$	8.99197	−	11.2756i	0.371455	−	0.465790i
$587$	36.1967			1.49400			0.746998	−	0.664826i	$-0.231494\pi$
$587$	36.1967			1.49400			0.746998	+	0.664826i	$0.231494\pi$
$588$	−0.262516			−0.0108260
$589$	−29.6718	+	37.2072i	−1.22260	+	1.53310i
$590$	3.53365	−	2.53026i	0.145478	−	0.104169i
$591$	−11.3695	+	12.3957i	−0.467679	+	0.509891i
$592$	13.8811	−	6.10387i	0.570511	−	0.250868i
$593$	−11.7083	+	2.88583i	−0.480801	+	0.118507i	−0.472265	−	0.881457i	$-0.656563\pi$
$593$	−11.7083	+	2.88583i	−0.480801	+	0.118507i	−0.00853606	+	0.999964i	$0.502717\pi$
$594$	−21.9406	+	31.7865i	−0.900234	+	1.30421i
$595$	−4.10124	+	4.17265i	−0.168134	+	0.171062i
$596$	7.12215	−	2.01861i	0.291735	−	0.0826856i
$597$	6.00582	+	11.9395i	0.245802	+	0.488652i
$598$	41.1506	+	31.6701i	1.68277	+	1.29509i
$599$	19.9286	−	3.47455i	0.814260	−	0.141966i	0.250725	−	0.968058i	$-0.419331\pi$
$599$	19.9286	−	3.47455i	0.814260	−	0.141966i	0.563535	+	0.826092i	$0.309441\pi$
$600$	2.08523	+	10.8497i	0.0851291	+	0.442938i
$601$	6.22617	−	16.4171i	0.253971	−	0.669666i	−0.746022	−	0.665921i	$-0.768039\pi$
$601$	6.22617	−	16.4171i	0.253971	−	0.669666i	0.999993	−	0.00374484i	$-0.00119202\pi$
$602$	−17.3695	−	4.92298i	−0.707927	−	0.200646i
$603$	24.0037	−	4.18505i	0.977508	−	0.170429i
$604$	1.33722	+	1.36051i	0.0544108	+	0.0553582i
$605$	−5.92673	−	3.37648i	−0.240956	−	0.137273i
$606$	−0.450827	−	3.71290i	−0.0183136	−	0.150826i
$607$	38.2768	+	12.2909i	1.55361	+	0.498874i	0.953589	−	0.301112i	$-0.0973579\pi$
$607$	38.2768	+	12.2909i	1.55361	+	0.498874i	0.600018	+	0.799987i	$0.295160\pi$
$608$	−1.31850	−	15.2389i	−0.0534724	−	0.618017i
$609$	13.1777	+	10.8862i	0.533987	+	0.441132i
$610$	2.34473	−	1.55939i	0.0949352	−	0.0631378i
$611$	−48.9057	+	3.38212i	−1.97851	+	0.136826i
$612$	−2.52030	−	3.39440i	−0.101877	−	0.137211i
$613$	−32.4399	+	18.4811i	−1.31023	+	0.746446i	−0.980292	−	0.197555i	$-0.936700\pi$
$613$	−32.4399	+	18.4811i	−1.31023	+	0.746446i	−0.329943	+	0.944001i	$0.607030\pi$
$614$	8.59181	+	2.43515i	0.346737	+	0.0982748i
$615$	−0.691808	−	3.59957i	−0.0278964	−	0.145149i
$616$	−31.8420	−	2.20206i	−1.28295	−	0.0887235i
$617$	21.1678	+	28.5094i	0.852185	+	1.14774i	0.987606	+	0.156956i	$0.0501682\pi$
$617$	21.1678	+	28.5094i	0.852185	+	1.14774i	−0.135420	+	0.990788i	$0.543238\pi$
$618$	−2.43987	−	7.17068i	−0.0981460	−	0.288447i
$619$	3.18659	−	1.67245i	0.128080	−	0.0672214i	−0.399466	−	0.916748i	$-0.630805\pi$
$619$	3.18659	−	1.67245i	0.128080	−	0.0672214i	0.527546	+	0.849526i	$0.323112\pi$
$620$	−0.429497	+	2.23473i	−0.0172490	+	0.0897490i
$621$	−28.1244	+	11.2252i	−1.12859	+	0.450451i
$622$	−0.977560	−	6.24178i	−0.0391966	−	0.250273i
$623$	0.216785	+	4.18255i	0.00868531	+	0.167570i
$624$	−25.0854	−	2.60740i	−1.00422	−	0.104380i
$625$	20.8630	+	2.89946i	0.834519	+	0.115979i
$626$	−29.8505	+	21.3743i	−1.19307	+	0.854290i
$627$	−13.5351	−	22.8326i	−0.540540	−	0.911847i
$628$	0.733733	−	0.920072i	0.0292791	−	0.0367149i
$629$	6.70845	+	11.3166i	0.267484	+	0.451223i
$630$	−4.02680	−	2.11343i	−0.160431	−	0.0842009i
$631$	29.1300	+	4.04839i	1.15965	+	0.161164i	0.691426	−	0.722447i	$-0.256983\pi$
$631$	29.1300	+	4.04839i	1.15965	+	0.161164i	0.468222	+	0.883611i	$0.344895\pi$
$632$	14.2992	−	11.0049i	0.568790	−	0.437750i
$633$	−12.4157	−	5.45947i	−0.493479	−	0.216995i
$634$	−10.5753	−	11.5298i	−0.419999	−	0.457907i
$635$	−0.450352	−	0.0946424i	−0.0178717	−	0.00375577i
$636$	−0.0935771	+	1.08154i	−0.00371057	+	0.0428857i
$637$	2.29758	+	1.64517i	0.0910333	+	0.0651840i
$638$	−35.6474	−	33.8476i	−1.41129	−	1.34004i
$639$	5.72886	+	5.82861i	0.226630	+	0.230576i
$640$	3.80293	+	5.93795i	0.150324	+	0.234718i
$641$	−0.637907	−	0.0441151i	−0.0251958	−	0.00174244i	0.0563877	−	0.998409i	$-0.482042\pi$
$641$	−0.637907	−	0.0441151i	−0.0251958	−	0.00174244i	−0.0815836	+	0.996667i	$0.525998\pi$
$642$	14.5355	−	8.28093i	0.573670	−	0.326822i
$643$	−4.71196	−	1.16139i	−0.185822	−	0.0458009i	0.145307	−	0.989387i	$-0.453583\pi$
$643$	−4.71196	−	1.16139i	−0.185822	−	0.0458009i	−0.331128	+	0.943586i	$0.607429\pi$
$644$	6.71276	+	5.16624i	0.264520	+	0.203578i
$645$	1.53802	+	1.46037i	0.0605594	+	0.0575019i
$646$	34.9457	−	7.34391i	1.37492	−	0.288942i
$647$	−15.3315	+	23.9388i	−0.602744	+	0.941133i	0.396984	+	0.917826i	$0.370057\pi$
$647$	−15.3315	+	23.9388i	−0.602744	+	0.941133i	−0.999728	+	0.0233070i	$0.992580\pi$
$648$	−1.66712	+	2.24531i	−0.0654905	+	0.0882042i
$649$	−3.14926	+	25.9365i	−0.123619	+	1.01810i
$650$	−16.8380	+	36.5659i	−0.660440	+	1.43423i
$651$	15.3207	+	17.9069i	0.600466	+	0.701828i
$652$	−3.89519	−	11.4478i	−0.152548	−	0.448331i
$653$	−15.6933	+	13.9031i	−0.614128	+	0.544070i	−0.911819	−	0.410592i	$-0.865322\pi$
$653$	−15.6933	+	13.9031i	−0.614128	+	0.544070i	0.297691	+	0.954662i	$0.403784\pi$
$654$	−0.527778	−	0.130086i	−0.0206378	−	0.00508675i
$655$	9.62805	−	1.67865i	0.376199	−	0.0655904i
$656$	18.4285	+	28.7744i	0.719511	+	1.12345i
$657$	−4.94806	−	18.6812i	−0.193042	−	0.728823i
$658$	−39.5243	+	2.73334i	−1.54082	+	0.106557i
$659$	14.3297	+	16.7486i	0.558205	+	0.652433i	0.965359	−	0.260926i	$-0.0840280\pi$
$659$	14.3297	+	16.7486i	0.558205	+	0.652433i	−0.407153	+	0.913360i	$0.633479\pi$
$660$	−1.08047	−	0.665965i	−0.0420571	−	0.0259227i
$661$	5.29052	−	19.9742i	0.205777	−	0.776905i	−0.782294	−	0.622909i	$-0.785951\pi$
$661$	5.29052	−	19.9742i	0.205777	−	0.776905i	0.988072	−	0.153996i	$-0.0492142\pi$
$662$	−12.9801	+	38.1479i	−0.504485	+	1.48266i
$663$	−0.377669	−	21.8771i	−0.0146675	−	0.849636i
$664$	33.3871	+	16.0784i	1.29567	+	0.623963i
$665$	6.14422	−	4.72868i	0.238263	−	0.183370i
$666$	−6.91197	+	7.53584i	−0.267834	+	0.292008i
$667$	−8.57601	−	37.5740i	−0.332064	−	1.45487i
$668$	9.47842	+	4.97466i	0.366731	+	0.192475i
$669$	0.553813	−	0.396555i	0.0214116	−	0.0153317i
$670$	2.18982	+	9.59422i	0.0846001	+	0.370657i
$671$	−2.61927	+	16.7242i	−0.101116	+	0.645630i
$672$	−7.53391	−	0.783081i	−0.290627	−	0.0302080i
$673$	13.0995	+	6.30840i	0.504950	+	0.243171i	0.668975	−	0.743285i	$-0.266733\pi$
$673$	13.0995	+	6.30840i	0.504950	+	0.243171i	−0.164025	+	0.986456i	$0.552448\pi$
$674$	−31.5513	−	5.50098i	−1.21531	−	0.211890i
$675$	−13.3360	−	19.3205i	−0.513303	−	0.743647i
$676$	−6.00922	−	5.32371i	−0.231124	−	0.204758i
$677$	4.87482	−	11.6267i	0.187355	−	0.446850i	−0.801068	−	0.598573i	$-0.795735\pi$
$677$	4.87482	−	11.6267i	0.187355	−	0.446850i	0.988423	+	0.151722i	$0.0484820\pi$
$678$	−4.85256	+	1.01978i	−0.186361	+	0.0391643i
$679$	−15.7646	−	8.98116i	−0.604990	−	0.344665i
$680$	−3.88907	+	3.21279i	−0.149139	+	0.123205i
$681$	1.12371	+	4.24254i	0.0430608	+	0.162574i
$682$	−40.4028	−	54.4155i	−1.54710	−	2.08368i
$683$	33.7370	−	29.8883i	1.29091	−	1.14365i	0.309671	−	0.950844i	$-0.399781\pi$
$683$	33.7370	−	29.8883i	1.29091	−	1.14365i	0.981238	−	0.192801i	$-0.0617573\pi$
$684$	2.68883	+	4.91506i	0.102810	+	0.187932i
$685$	0.298038	+	0.592499i	0.0113875	+	0.0226382i
$686$	−22.8587	−	16.3678i	−0.872747	−	0.624927i
$687$	−8.94321	+	21.3300i	−0.341205	+	0.813791i
$688$	−18.3626	−	7.32901i	−0.700069	−	0.279416i
$689$	7.59689	−	8.87929i	0.289419	−	0.338274i
$690$	−2.06206	−	4.47805i	−0.0785015	−	0.170476i
$691$	8.86114	+	5.46172i	0.337094	+	0.207774i	0.682864	−	0.730545i	$-0.260734\pi$
$691$	8.86114	+	5.46172i	0.337094	+	0.207774i	−0.345770	+	0.938319i	$0.612382\pi$
$692$	0.443832	−	0.232941i	0.0168720	−	0.00885509i
$693$	25.7257	−	9.25179i	0.977239	−	0.351447i
$694$	22.2741	+	40.7160i	0.845513	+	1.54556i
$695$	8.23132	+	6.33495i	0.312232	+	0.240298i
$696$	10.3305	+	10.5104i	0.391577	+	0.398396i
$697$	−22.8544	+	18.8803i	−0.865673	+	0.715141i
$698$	−0.0466666	+	0.154439i	−0.00176636	+	0.00584560i
$699$	−13.6509	+	9.07868i	−0.516323	+	0.343387i
$700$	−2.74672	+	5.96487i	−0.103816	+	0.225451i
$701$	−16.4866	−	35.8029i	−0.622692	−	1.35226i	−0.917895	−	0.396823i	$-0.870113\pi$
$701$	−16.4866	−	35.8029i	−0.622692	−	1.35226i	0.295204	−	0.955434i	$-0.404612\pi$
$702$	40.1714	−	12.8993i	1.51617	−	0.486853i
$703$	−6.74087	−	16.0773i	−0.254237	−	0.606367i
$704$	−24.6314	−	4.29448i	−0.928330	−	0.161854i
$705$	4.26057	+	1.87348i	0.160463	+	0.0705593i
$706$	−22.8415	+	10.0440i	−0.859653	+	0.378010i
$707$	−3.15205	+	5.76179i	−0.118545	+	0.216695i
$708$	−0.410246	+	2.61945i	−0.0154180	+	0.0984449i
$709$	3.81481	+	0.530168i	0.143268	+	0.0199109i	0.208927	−	0.977931i	$-0.433003\pi$
$709$	3.81481	+	0.530168i	0.143268	+	0.0199109i	−0.0656590	+	0.997842i	$0.520915\pi$
$710$	−2.23116	+	2.43254i	−0.0837338	+	0.0912915i
$711$	−7.41740	+	13.5587i	−0.278174	+	0.508489i
$712$	−0.186911	+	3.60618i	−0.00700480	+	0.135147i
$713$	−2.75046	−	53.0660i	−0.103005	−	1.98734i
$714$	−0.305223	−	17.6805i	−0.0114227	−	0.661677i
$715$	5.28282	+	12.5998i	0.197566	+	0.471206i
$716$	−1.07034	+	4.68947i	−0.0400005	+	0.175254i
$717$	11.0972	+	4.42920i	0.414434	+	0.165411i
$718$	−14.6386	+	22.8569i	−0.546308	+	0.853012i
$719$	0.381446	+	3.14149i	0.0142255	+	0.117158i	0.998092	−	0.0617478i	$-0.0196674\pi$
$719$	0.381446	+	3.14149i	0.0142255	+	0.117158i	−0.983866	+	0.178905i	$0.942744\pi$
$720$	−4.14698	−	2.75800i	−0.154549	−	0.102784i
$721$	−3.84718	+	12.7319i	−0.143276	+	0.474160i
$722$	−17.2028	+	1.18968i	−0.640224	+	0.0442753i
$723$	−3.06695	−	9.01365i	−0.114061	−	0.335221i
$724$	−11.7337	+	4.21981i	−0.436079	+	0.156828i
$725$	26.9197	−	12.9638i	0.999773	−	0.481465i
$726$	19.8345	−	5.62165i	0.736129	−	0.208639i
$727$	−2.39155	+	27.6408i	−0.0886977	+	1.02514i	0.809958	+	0.586487i	$0.199490\pi$
$727$	−2.39155	+	27.6408i	−0.0886977	+	1.02514i	−0.898656	+	0.438654i	$0.855455\pi$
$728$	26.0981	+	23.1209i	0.967260	+	0.856917i
$729$	−2.73506	+	11.9831i	−0.101298	+	0.443818i
$730$	7.43147	−	2.38630i	0.275051	−	0.0883209i
$731$	4.39176	−	16.5809i	0.162435	−	0.613268i
$732$	−0.324226	+	1.68699i	−0.0119837	+	0.0623530i
$733$	3.42765	−	6.81414i	0.126603	−	0.251686i	−0.821136	−	0.570733i	$-0.806659\pi$
$733$	3.42765	−	6.81414i	0.126603	−	0.251686i	0.947739	+	0.319046i	$0.103363\pi$
$734$	53.3217	−	25.6784i	1.96814	−	0.947807i
$735$	−0.120562	−	0.239677i	−0.00444701	−	0.00884063i
$736$	12.3851	+	11.7598i	0.456522	+	0.433473i
$737$	−51.4028	−	29.2844i	−1.89345	−	1.07870i
$738$	−19.1865	−	12.7602i	−0.706264	−	0.469709i
$739$	3.21677	+	10.6456i	0.118331	+	0.391605i	0.996179	−	0.0873339i	$-0.0278347\pi$
$739$	3.21677	+	10.6456i	0.118331	+	0.391605i	−0.877848	+	0.478939i	$0.841022\pi$
$740$	−0.642680	−	0.530924i	−0.0236254	−	0.0195172i
$741$	−3.49497	+	28.7837i	−0.128391	+	1.05739i
$742$	6.13962	−	7.17602i	0.225392	−	0.263440i
$743$	0.457473	−	2.00432i	0.0167830	−	0.0735313i	−0.965843	−	0.259128i	$-0.916565\pi$
$743$	0.457473	−	2.00432i	0.0167830	−	0.0735313i	0.982626	+	0.185597i	$0.0594219\pi$
$744$	11.5425	+	16.7222i	0.423169	+	0.613067i
$745$	5.11389	+	5.57546i	0.187358	+	0.204269i
$746$	57.7381	−	14.2312i	2.11394	−	0.521040i
$747$	−31.7215	−	1.09556i	−1.16063	−	0.0400843i
$748$	−0.531321	+	10.2511i	−0.0194270	+	0.374816i
$749$	−29.2180	−	3.03694i	−1.06760	−	0.110967i
$750$	6.22873	−	4.79373i	0.227441	−	0.175042i
$751$	−5.02572	+	2.20993i	−0.183391	+	0.0806415i	−0.492198	−	0.870483i	$-0.663806\pi$
$751$	−5.02572	+	2.20993i	−0.183391	+	0.0806415i	0.308807	+	0.951125i	$0.400070\pi$
$752$	−43.3621	−	1.49758i	−1.58125	−	0.0546112i
$753$	−1.39146	+	0.144629i	−0.0507075	+	0.00527058i
$754$	8.30867	+	53.0514i	0.302584	+	1.93202i
$755$	−0.628012	+	1.84570i	−0.0228557	+	0.0671720i
$756$	6.55301	−	2.10422i	0.238331	−	0.0765297i
$757$	−11.2025	+	13.0935i	−0.407161	+	0.475892i	−0.925208	−	0.379460i	$-0.876110\pi$
$757$	−11.2025	+	13.0935i	−0.407161	+	0.475892i	0.518047	+	0.855352i	$0.326659\pi$
$758$	−11.2082	+	15.0955i	−0.407102	+	0.548295i
$759$	28.2179	+	9.06097i	1.02424	+	0.328892i
$760$	5.69064	−	3.50753i	0.206421	−	0.127232i
$761$	−9.69650	−	32.0897i	−0.351498	−	1.16325i	−0.936042	−	0.351888i	$-0.885540\pi$
$761$	−9.69650	−	32.0897i	−0.351498	−	1.16325i	0.584544	−	0.811362i	$-0.301273\pi$
$762$	1.15813	−	0.770227i	0.0419545	−	0.0279024i
$763$	0.620524	+	0.725272i	0.0224645	+	0.0262566i
$764$	2.86530	−	1.50382i	0.103663	−	0.0544064i
$765$	1.94162	−	3.85993i	0.0701995	−	0.139556i
$766$	−44.4133	+	1.53389i	−1.60472	+	0.0554217i
$767$	20.0064	−	20.3547i	0.722389	−	0.734967i
$768$	−11.0375	−	2.31956i	−0.398282	−	0.0836999i
$769$	−23.0846	−	33.4438i	−0.832451	−	1.20601i	−0.976302	−	0.216414i	$-0.930564\pi$
$769$	−23.0846	−	33.4438i	−0.832451	−	1.20601i	0.143851	−	0.989599i	$-0.454051\pi$
$770$	4.26944	+	10.1828i	0.153860	+	0.366964i
$771$	−2.71792	+	7.98786i	−0.0978835	+	0.287676i
$772$	3.16923	−	1.26492i	0.114063	−	0.0455256i
$773$	−0.842689	+	48.8142i	−0.0303094	+	1.75572i	0.463449	+	0.886124i	$0.346612\pi$
$773$	−0.842689	+	48.8142i	−0.0303094	+	1.75572i	−0.493758	+	0.869599i	$0.664377\pi$
$774$	13.3246	−	0.460190i	0.478945	−	0.0165412i
$775$	39.6339	−	11.2333i	1.42369	−	0.403513i
$776$	−12.7188	−	9.10725i	−0.456579	−	0.326931i
$777$	−8.44844	+	1.77546i	−0.303086	+	0.0636942i
$778$	2.26643	+	18.6657i	0.0812554	+	0.669198i
$779$	33.4416	−	20.6123i	1.19817	−	0.738512i
$780$	0.491650	+	1.29638i	0.0176039	+	0.0464177i
$781$	−1.71047	−	19.7691i	−0.0612054	−	0.707393i
$782$	−23.7687	+	32.0123i	−0.849967	+	1.14476i
$783$	−29.0839	−	11.6081i	−1.03937	−	0.414841i
$784$	1.87206	+	1.65850i	0.0668594	+	0.0592323i
$785$	1.17700	+	0.247348i	0.0420088	+	0.00882824i
$786$	−16.7798	+	24.3098i	−0.598517	+	0.867102i
$787$	−12.1784	+	11.5636i	−0.434114	+	0.412196i	−0.874052	−	0.485832i	$-0.838517\pi$
$787$	−12.1784	+	11.5636i	−0.434114	+	0.412196i	0.439938	+	0.898028i	$0.355000\pi$
$788$	−8.57373	+	0.891161i	−0.305426	+	0.0317463i
$789$	−0.954548	−	18.4166i	−0.0339828	−	0.655649i
$790$	−5.62384	−	2.70830i	−0.200087	−	0.0963569i
$791$	7.97053	+	3.50484i	0.283399	+	0.124618i
$792$	22.8865	−	5.64100i	0.813235	−	0.200444i
$793$	13.4099	−	12.7329i	0.476200	−	0.452157i
$794$	34.6840	+	12.4735i	1.23089	+	0.442667i
$795$	−1.03042	+	0.411266i	−0.0365451	+	0.0145861i
$796$	−1.75366	+	6.62089i	−0.0621569	+	0.234671i
$797$	10.4356	+	22.6622i	0.369646	+	0.802736i	0.999658	+	0.0261502i	$0.00832480\pi$
$797$	10.4356	+	22.6622i	0.369646	+	0.802736i	−0.630012	+	0.776586i	$0.716950\pi$
$798$	−2.82454	+	23.2622i	−0.0999878	+	0.823474i
$799$	−3.24472	−	37.5015i	−0.114790	−	1.32671i
$800$	−6.75174	+	11.3896i	−0.238710	+	0.402684i
$801$	−1.09678	−	2.89196i	−0.0387527	−	0.102182i
$802$	27.6159	+	22.8138i	0.975153	+	0.805583i
$803$	−19.6257	+	42.6198i	−0.692575	+	1.50402i
$804$	−5.11070	−	3.15007i	−0.180240	−	0.111094i
$805$	−1.63389	+	8.50136i	−0.0575871	+	0.299634i
$806$	−1.27791	+	74.0251i	−0.0450125	+	2.60742i
$807$	−28.5243	+	3.96420i	−1.00410	+	0.139547i
$808$	−3.21672	+	4.66022i	−0.113164	+	0.163946i
$809$	−1.92119	−	2.09460i	−0.0675456	−	0.0736422i	0.702260	−	0.711920i	$-0.252174\pi$
$809$	−1.92119	−	2.09460i	−0.0675456	−	0.0736422i	−0.769806	+	0.638278i	$0.779647\pi$
$810$	0.953058	+	0.166166i	0.0334870	+	0.00583847i
$811$	−0.598422	−	34.6646i	−0.0210134	−	1.21724i	−0.803782	−	0.594924i	$-0.797182\pi$
$811$	−0.598422	−	34.6646i	−0.0210134	−	1.21724i	0.782768	−	0.622313i	$-0.213807\pi$
$812$	1.35536	+	8.65409i	0.0475640	+	0.303699i
$813$	−17.9723	−	6.46340i	−0.630314	−	0.226681i
$814$	24.5912	−	3.41760i	0.861921	−	0.119787i
$815$	8.66294	−	8.81378i	0.303450	−	0.308733i
$816$	1.66931	−	19.2934i	0.0584375	−	0.675403i
$817$	−8.78899	+	20.9622i	−0.307488	+	0.733374i
$818$	−0.0582858	+	0.0910081i	−0.00203791	+	0.00318202i
$819$	−28.4344	−	9.13050i	−0.993579	−	0.319045i
$820$	0.957882	−	1.61587i	0.0334507	−	0.0564286i
$821$	8.70738	−	14.6886i	0.303890	−	0.512637i	−0.669194	−	0.743087i	$-0.733361\pi$
$821$	8.70738	−	14.6886i	0.303890	−	0.512637i	0.973084	+	0.230450i	$0.0740199\pi$
$822$	−1.90857	−	0.612855i	−0.0665689	−	0.0213758i
$823$	−25.3286	+	39.5484i	−0.882901	+	1.37857i	0.0423046	+	0.999105i	$0.486530\pi$
$823$	−25.3286	+	39.5484i	−0.882901	+	1.37857i	−0.925205	+	0.379467i	$0.876107\pi$
$824$	−4.43414	+	10.5756i	−0.154470	+	0.368420i
$825$	−1.98057	+	22.8908i	−0.0689544	+	0.796954i
$826$	16.1686	−	16.4502i	0.562579	−	0.572375i
$827$	34.4690	−	4.79038i	1.19860	−	0.166578i	0.489706	−	0.871888i	$-0.337104\pi$
$827$	34.4690	−	4.79038i	1.19860	−	0.166578i	0.708899	+	0.705310i	$0.249192\pi$
$828$	−5.88644	−	2.11695i	−0.204568	−	0.0735692i
$829$	−8.18822	−	52.2823i	−0.284389	−	1.81584i	−0.531732	−	0.846913i	$-0.678459\pi$
$829$	−8.18822	−	52.2823i	−0.284389	−	1.81584i	0.247343	−	0.968928i	$-0.420442\pi$
$830$	−0.221271	−	12.8175i	−0.00768044	−	0.444902i
$831$	4.81133	+	0.838856i	0.166903	+	0.0290996i
$832$	18.4619	+	20.1283i	0.640052	+	0.697822i
$833$	−1.23259	+	1.78572i	−0.0427068	+	0.0618715i
$834$	−31.0941	+	4.32135i	−1.07670	+	0.149636i
$835$	−0.188832	+	10.9384i	−0.00653482	+	0.378540i
$836$	2.56732	−	13.3581i	0.0887925	−	0.462000i
$837$	−36.7544	−	22.6543i	−1.27042	−	0.783046i
$838$	6.36495	−	13.8223i	0.219874	−	0.477485i
$839$	−11.6772	−	9.64661i	−0.403140	−	0.333038i	0.413168	−	0.910655i	$-0.364422\pi$
$839$	−11.6772	−	9.64661i	−0.403140	−	0.333038i	−0.816308	+	0.577617i	$0.803983\pi$
$840$	−1.17385	−	3.09519i	−0.0405017	−	0.106794i
$841$	5.53535	−	9.33768i	0.190874	−	0.321989i
$842$	−1.94045	−	22.4271i	−0.0668722	−	0.772889i
$843$	−3.26095	+	26.8563i	−0.112313	+	0.924982i
$844$	−2.90725	−	6.31347i	−0.100072	−	0.217319i
$845$	2.10076	−	7.93136i	0.0722685	−	0.272847i
$846$	27.1739	−	10.8458i	0.934258	−	0.372887i
$847$	−34.0648	−	12.2508i	−1.17048	−	0.420943i
$848$	7.50015	−	7.12148i	0.257556	−	0.244553i
$849$	−22.7882	+	5.61679i	−0.782089	+	0.192768i
$850$	−28.2959	−	12.4424i	−0.970541	−	0.426771i
$851$	17.5377	+	8.44573i	0.601186	+	0.289516i
$852$	−0.104230	−	2.01097i	−0.00357087	−	0.0688947i
$853$	−51.2024	+	5.32202i	−1.75314	+	0.182223i	−0.925425	−	0.378931i	$-0.876292\pi$
$853$	−51.2024	+	5.32202i	−1.75314	+	0.182223i	−0.827712	+	0.561153i	$0.810358\pi$
$854$	10.8375	−	10.2904i	0.370853	−	0.352129i
$855$	−3.25258	+	4.71217i	−0.111236	+	0.161153i
$856$	−24.7859	−	5.20882i	−0.847166	−	0.178034i
$857$	−13.6306	−	12.0756i	−0.465611	−	0.412496i	0.397427	−	0.917634i	$-0.369903\pi$
$857$	−13.6306	−	12.0756i	−0.465611	−	0.412496i	−0.863039	+	0.505138i	$0.831442\pi$
$858$	−38.3513	−	15.3070i	−1.30929	−	0.522573i
$859$	−4.27749	+	5.76103i	−0.145946	+	0.196564i	−0.869821	−	0.493367i	$-0.835766\pi$
$859$	−4.27749	+	5.76103i	−0.145946	+	0.196564i	0.723875	+	0.689931i	$0.242359\pi$
$860$	0.0936912	+	1.08285i	0.00319484	+	0.0369250i
$861$	−6.89824	−	18.1892i	−0.235091	−	0.619885i
$862$	41.4545	−	25.5512i	1.41195	−	0.870278i
$863$	−0.722065	−	5.94674i	−0.0245794	−	0.202429i	0.975246	−	0.221123i	$-0.0709723\pi$
$863$	−0.722065	−	5.94674i	−0.0245794	−	0.202429i	−0.999825	+	0.0186938i	$0.994049\pi$
$864$	13.5803	−	2.85392i	0.462010	−	0.0970925i
$865$	0.416508	+	0.298238i	0.0141617	+	0.0101404i
$866$	−20.5774	+	5.83219i	−0.699248	+	0.198186i
$867$	0.0227126		0.000784420i	0.000771361		2.66403e-5i
$868$	−0.208461	+	12.0754i	−0.00707563	+	0.409867i
$869$	34.8506	−	13.9098i	1.18223	−	0.471858i
$870$	1.64223	−	4.82646i	0.0556770	−	0.163632i
$871$	24.9882	+	59.5981i	0.846693	+	2.01941i
$872$	0.467498	+	0.677288i	0.0158315	+	0.0229359i
$873$	13.1125	+	2.75562i	0.443790	+	0.0932635i
$874$	37.0370	−	37.6819i	1.25280	−	1.27461i
$875$	−13.7934	+	0.476379i	−0.466302	+	0.0161045i
$876$	−2.13972	+	4.25375i	−0.0722944	+	0.143721i
$877$	−25.7516	+	13.5155i	−0.869568	+	0.456385i	−0.839625	−	0.543167i	$-0.817225\pi$
$877$	−25.7516	+	13.5155i	−0.869568	+	0.456385i	−0.0299436	+	0.999552i	$0.509533\pi$
$878$	−7.56997	−	8.84782i	−0.255474	−	0.298599i
$879$	−7.48713	+	4.97941i	−0.252535	+	0.167951i
$880$	3.49767	+	11.5752i	0.117906	+	0.390201i
$881$	−47.7584	+	29.4367i	−1.60902	+	0.991749i	−0.632977	+	0.774170i	$0.718167\pi$
$881$	−47.7584	+	29.4367i	−1.60902	+	0.991749i	−0.976043	+	0.217578i	$0.930184\pi$
$882$	−1.60581	−	0.515638i	−0.0540705	−	0.0173624i
$883$	22.7969	−	30.7035i	0.767178	−	1.03325i	−0.231002	−	0.972953i	$-0.574201\pi$
$883$	22.7969	−	30.7035i	0.767178	−	1.03325i	0.998180	−	0.0603011i	$-0.0192061\pi$
$884$	7.28969	−	8.52023i	0.245179	−	0.286566i
$885$	−2.57996	+	0.828444i	−0.0867244	+	0.0278478i
$886$	16.6281	−	48.8692i	0.558631	−	1.64179i
$887$	3.45507	+	22.0608i	0.116010	+	0.740730i	0.973913	+	0.226920i	$0.0728655\pi$
$887$	3.45507	+	22.0608i	0.116010	+	0.740730i	−0.857904	+	0.513811i	$0.828233\pi$
$888$	−7.40345	+	0.769521i	−0.248444	+	0.0258234i
$889$	−2.44086	−	0.0842994i	−0.0818639	−	0.00282731i
$890$	1.14352	−	0.502833i	0.0383309	−	0.0168550i
$891$	−4.60887	+	3.54706i	−0.154403	+	0.118831i
$892$	0.347201	+	0.0360884i	0.0116251	+	0.00120833i
$893$	−2.58192	+	49.8144i	−0.0864008	+	1.66698i
$894$	−22.8523	−	0.789245i	−0.764297	−	0.0263963i
$895$	−4.77304	+	1.17645i	−0.159545	+	0.0393243i
$896$	25.2958	+	27.5790i	0.845074	+	0.921349i
$897$	−18.3911	−	26.6440i	−0.614060	−	0.889619i
$898$	4.46041	−	19.5423i	0.148846	−	0.652136i
$899$	35.7233	−	41.7535i	1.19144	−	1.39256i
$900$	0.584560	−	4.81429i	0.0194853	−	0.160476i
$901$	6.91758	+	5.71468i	0.230458	+	0.190383i
$902$	16.1824	+	53.5541i	0.538815	+	1.78316i
$903$	9.37249	+	6.23329i	0.311897	+	0.207431i
$904$	6.52293	+	3.71614i	0.216949	+	0.123597i
$905$	−9.24145	−	8.77486i	−0.307196	−	0.291686i
$906$	−2.64791	−	5.26403i	−0.0879710	−	0.174886i
$907$	−30.6074	+	14.7398i	−1.01630	+	0.489426i	−0.866440	−	0.499281i	$-0.833597\pi$
$907$	−30.6074	+	14.7398i	−1.01630	+	0.489426i	−0.149863	+	0.988707i	$0.547883\pi$
$908$	−1.01071	+	2.00928i	−0.0335415	+	0.0666803i
$909$	0.915411	−	4.76301i	0.0303623	−	0.157979i
$910$	3.08827	−	11.6597i	0.102375	−	0.386514i
$911$	32.4469	−	10.4189i	1.07501	−	0.345194i	0.285153	−	0.958482i	$-0.407955\pi$
$911$	32.4469	−	10.4189i	1.07501	−	0.345194i	0.789860	+	0.613287i	$0.210153\pi$
$912$	−5.71042	+	25.0190i	−0.189091	+	0.828461i
$913$	57.6836	+	51.1032i	1.90905	+	1.69127i
$914$	0.188821	−	2.18234i	0.00624566	−	0.0721854i
$915$	−1.68912	+	0.478744i	−0.0558407	+	0.0158268i
$916$	−10.6792	+	5.14283i	−0.352850	+	0.169924i
$917$	48.8085	−	17.5531i	1.61180	−	0.579655i
$918$	10.4356	+	30.6698i	0.344426	+	1.01225i
$919$	41.6835	−	2.88266i	1.37501	−	0.0950901i	0.637513	−	0.770440i	$-0.279963\pi$
$919$	41.6835	−	2.88266i	1.37501	−	0.0950901i	0.737498	+	0.675350i	$0.236007\pi$
$920$	−2.15898	+	7.14494i	−0.0711794	+	0.235562i
$921$	−4.63611	−	3.08330i	−0.152765	−	0.101598i
$922$	−0.858073	−	7.06687i	−0.0282591	−	0.232735i
$923$	−11.6903	+	18.2534i	−0.384792	+	0.600819i
$924$	−6.25611	−	2.49698i	−0.205811	−	0.0821446i
$925$	−3.35800	+	14.7124i	−0.110410	+	0.483740i
$926$	25.3207	+	60.3912i	0.832090	+	1.98458i
$927$	−0.169540	−	9.82088i	−0.00556842	−	0.322560i
$928$	0.914179	+	17.6378i	0.0300094	+	0.578988i
$929$	−2.69641	+	52.0233i	−0.0884663	+	1.70683i	0.474424	+	0.880297i	$0.342656\pi$
$929$	−2.69641	+	52.0233i	−0.0884663	+	1.70683i	−0.562890	+	0.826532i	$0.690311\pi$
$930$	3.37354	−	6.16667i	0.110623	−	0.202213i
$931$	1.94358	−	2.11900i	0.0636982	−	0.0694475i
$932$	−8.32161	−	1.15651i	−0.272583	−	0.0378827i
$933$	−0.609484	+	3.89160i	−0.0199536	+	0.127405i
$934$	8.14680	−	14.8920i	0.266571	−	0.487280i
$935$	−9.60322	+	4.22277i	−0.314059	+	0.138099i
$936$	−23.5708	−	10.3647i	−0.770437	−	0.338780i
$937$	−43.9597	−	7.66438i	−1.43610	−	0.250385i	−0.600458	−	0.799656i	$-0.705015\pi$
$937$	−43.9597	−	7.66438i	−1.43610	−	0.250385i	−0.835644	+	0.549272i	$0.814905\pi$
$938$	20.1948	+	48.1657i	0.659385	+	1.57267i
$939$	21.7942	−	6.99827i	0.711227	−	0.228380i
$940$	0.997653	+	2.16654i	0.0325399	+	0.0706646i
$941$	−11.8341	+	25.6994i	−0.385782	+	0.837777i	0.613077	+	0.790023i	$0.289932\pi$
$941$	−11.8341	+	25.6994i	−0.385782	+	0.837777i	−0.998859	+	0.0477538i	$0.984794\pi$
$942$	−3.02677	+	2.01299i	−0.0986175	+	0.0655867i
$943$	−12.6874	+	41.9878i	−0.413159	+	1.36731i
$944$	19.4745	−	16.0880i	0.633840	−	0.523621i
$945$	4.93066	+	5.01652i	0.160394	+	0.163187i
$946$	−25.6533	−	19.7432i	−0.834060	−	0.641905i
$947$	−23.5933	−	43.1275i	−0.766680	−	1.40145i	−0.911205	−	0.411953i	$-0.864847\pi$
$947$	−23.5933	−	43.1275i	−0.766680	−	1.40145i	0.144525	−	0.989501i	$-0.453835\pi$
$948$	3.58327	−	1.28866i	0.116379	−	0.0418537i
$949$	45.3850	−	23.8199i	1.47326	−	0.773226i
$950$	34.8701	+	21.4928i	1.13133	+	0.697318i
$951$	4.07996	+	8.86016i	0.132302	+	0.287310i
$952$	−17.4047	+	20.3427i	−0.564089	+	0.659311i
$953$	30.9420	+	12.3498i	1.00231	+	0.400048i	0.813248	−	0.581917i	$-0.197697\pi$
$953$	30.9420	+	12.3498i	1.00231	+	0.400048i	0.189062	+	0.981965i	$0.439455\pi$
$954$	−2.69677	+	6.43194i	−0.0873113	+	0.208242i
$955$	2.68889	+	1.92537i	0.0870105	+	0.0623035i
$956$	2.75163	+	5.47022i	0.0889940	+	0.176919i
$957$	14.7092	+	26.8876i	0.475479	+	0.869154i
$958$	26.3374	−	23.3329i	0.850924	−	0.753853i
$959$	2.09834	+	2.82610i	0.0677591	+	0.0912596i
$960$	−0.663942	−	2.50669i	−0.0214287	−	0.0809031i
$961$	34.5096	−	28.5087i	1.11321	−	0.919636i
$962$	−23.5653	−	13.4252i	−0.759774	−	0.432846i
$963$	21.2299	−	4.46152i	0.684125	−	0.143770i
$964$	1.88668	−	4.49982i	0.0607658	−	0.144929i
$965$	2.61036	+	2.31258i	0.0840305	+	0.0744445i
$966$	−14.8632	−	21.5330i	−0.478215	−	0.692814i
$967$	−45.3254	−	7.90249i	−1.45757	−	0.254127i	−0.613216	−	0.789915i	$-0.710124\pi$
$967$	−45.3254	−	7.90249i	−1.45757	−	0.254127i	−0.844352	+	0.535788i	$0.820014\pi$
$968$	−28.1212	−	13.5425i	−0.903850	−	0.435271i
$969$	−22.1444	−	2.30171i	−0.711380	−	0.0739415i
$970$	−0.837332	+	5.34642i	−0.0268851	+	0.171663i
$971$	0.856990	+	3.75472i	0.0275021	+	0.120495i	0.986816	−	0.161848i	$-0.0517455\pi$
$971$	0.856990	+	3.75472i	0.0275021	+	0.120495i	−0.959314	+	0.282343i	$0.908888\pi$
$972$	−6.59931	+	4.72541i	−0.211673	+	0.151568i
$973$	48.8108	+	25.6179i	1.56480	+	0.821272i
$974$	0.786021	+	3.44378i	0.0251857	+	0.110346i
$975$	16.9655	−	18.4967i	0.543329	−	0.592369i
$976$	12.9701	−	9.98195i	0.415161	−	0.319514i
$977$	−31.2071	−	15.0285i	−0.998403	−	0.480806i	−0.138007	−	0.990431i	$-0.544070\pi$
$977$	−31.2071	−	15.0285i	−0.998403	−	0.480806i	−0.860396	+	0.509626i	$0.829784\pi$
$978$	0.644714	+	37.3461i	0.0206157	+	1.19420i
$979$	−2.41899	+	7.10930i	−0.0773111	+	0.227214i
$980$	0.0352035	−	0.132909i	0.00112453	−	0.00424564i
$981$	−0.600067	−	0.369862i	−0.0191587	−	0.0118088i
$982$	−29.0782	−	33.9868i	−0.927923	−	1.08456i
$983$	12.2658	−	0.848251i	0.391217	−	0.0270550i	0.127957	−	0.991780i	$-0.459158\pi$
$983$	12.2658	−	0.848251i	0.391217	−	0.0270550i	0.263261	+	0.964725i	$0.415202\pi$
$984$	−4.29444	−	16.2135i	−0.136902	−	0.516868i
$985$	−4.75117	−	7.41853i	−0.151385	−	0.236374i
$986$	−40.6190	+	7.08193i	−1.29357	+	0.225534i
$987$	23.9835	+	5.91141i	0.763404	+	0.188162i
$988$	−11.1223	+	9.85348i	−0.353847	+	0.313481i
$989$	−8.17533	−	24.0270i	−0.259960	−	0.764013i
$990$	−5.30111	−	6.19597i	−0.168480	−	0.196921i
$991$	22.0298	−	47.8406i	0.699799	−	1.51971i	−0.147770	−	0.989022i	$-0.547209\pi$
$991$	22.0298	−	47.8406i	0.699799	−	1.51971i	0.847569	−	0.530685i	$-0.178065\pi$
$992$	−2.93515	+	24.1731i	−0.0931910	+	0.767497i
$993$	14.9769	−	20.1712i	0.475276	−	0.640114i
$994$	−9.44784	+	14.7520i	−0.299667	+	0.467904i
$995$	−6.85024	+	1.43959i	−0.217167	+	0.0456382i
$996$	5.67127	+	5.38493i	0.179701	+	0.170628i
$997$	−36.5433	−	28.1243i	−1.15734	−	0.890704i	−0.161965	−	0.986797i	$-0.551783\pi$
$997$	−36.5433	−	28.1243i	−1.15734	−	0.890704i	−0.995372	+	0.0960925i	$0.969366\pi$
$998$	−14.1242	−	3.48131i	−0.447095	−	0.110199i
$999$	13.7424	−	7.82912i	0.434792	−	0.247702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.m.a.10.12	✓	3168
547.383	even	91	inner	547.2.m.a.383.12	yes	3168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.m.a.10.12	✓	3168	1.1	even	1	trivial
547.2.m.a.383.12	yes	3168	547.383	even	91	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.m (of order \(91\), degree \(72\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.807206 - 1.36169i) q^{2} +(0.219615 + 0.962195i) q^{3} +(-0.242743 + 0.443723i) q^{4} +(-0.516600 - 0.0178417i) q^{5} +(1.13294 - 1.07574i) q^{6} +(-2.71722 + 0.377630i) q^{7} +(-2.36389 + 0.0816410i) q^{8} +(1.82532 - 0.879027i) q^{9} +O(q^{10})\)	\(q+(-0.807206 - 1.36169i) q^{2} +(0.219615 + 0.962195i) q^{3} +(-0.242743 + 0.443723i) q^{4} +(-0.516600 - 0.0178417i) q^{5} +(1.13294 - 1.07574i) q^{6} +(-2.71722 + 0.377630i) q^{7} +(-2.36389 + 0.0816410i) q^{8} +(1.82532 - 0.879027i) q^{9} +(0.392708 + 0.717851i) q^{10} +(-4.77600 - 1.17718i) q^{11} +(-0.480258 - 0.136118i) q^{12} +(3.35023 + 4.20106i) q^{13} +(2.70757 + 3.39519i) q^{14} +(-0.0962857 - 0.500988i) q^{15} +(2.56487 + 4.00482i) q^{16} +(-3.18087 + 2.62775i) q^{17} +(-2.67037 - 1.77596i) q^{18} +(4.65439 - 2.86882i) q^{19} +(0.133318 - 0.224896i) q^{20} +(-0.960096 - 2.53156i) q^{21} +(2.25226 + 7.45365i) q^{22} +(-1.76583 + 5.84385i) q^{23} +(-0.597699 - 2.25659i) q^{24} +(-4.72153 - 0.326522i) q^{25} +(3.01621 - 7.95310i) q^{26} +(3.09270 + 3.87813i) q^{27} +(0.492024 - 1.29736i) q^{28} +(-5.48537 + 3.12503i) q^{29} +(-0.604468 + 0.535512i) q^{30} +(-8.19059 + 2.94560i) q^{31} +(1.25715 - 2.49921i) q^{32} +(0.0837950 - 4.85396i) q^{33} +(6.14580 + 2.21023i) q^{34} +(1.41045 - 0.146604i) q^{35} +(-0.0530392 + 1.02331i) q^{36} +(0.493360 - 3.15014i) q^{37} +(-7.66349 - 4.02211i) q^{38} +(-3.30648 + 4.14619i) q^{39} +1.22264 q^{40} +7.18495 q^{41} +(-2.67221 + 3.35085i) q^{42} +(-3.38014 + 2.42034i) q^{43} +(1.68168 - 1.83347i) q^{44} +(-0.958642 + 0.421538i) q^{45} +(9.38291 - 2.31268i) q^{46} +(-5.18260 + 7.50829i) q^{47} +(-3.29013 + 3.34742i) q^{48} +(0.505971 - 0.143406i) q^{49} +(3.36662 + 6.69283i) q^{50} +(-3.22697 - 2.48353i) q^{51} +(-2.67735 + 0.466797i) q^{52} +(-0.410455 - 2.13566i) q^{53} +(2.78436 - 7.34175i) q^{54} +(2.44628 + 0.693341i) q^{55} +(6.39238 - 1.11451i) q^{56} +(3.78253 + 3.84839i) q^{57} +(8.68315 + 4.94682i) q^{58} +(-0.640233 - 5.27279i) q^{59} +(0.245673 + 0.0788872i) q^{60} +(-0.296651 - 3.42860i) q^{61} +(10.6225 + 8.77533i) q^{62} +(-4.62785 + 3.07781i) q^{63} +(5.07089 - 0.350682i) q^{64} +(-1.65578 - 2.23004i) q^{65} +(-6.67723 + 3.80405i) q^{66} +(11.5711 + 3.27956i) q^{67} +(-0.393858 - 2.04929i) q^{68} +(-6.01073 - 0.415678i) q^{69} +(-1.33816 - 1.80226i) q^{70} +(1.29943 + 3.81898i) q^{71} +(-4.24308 + 2.22694i) q^{72} +(1.80035 - 9.36749i) q^{73} +(-4.68775 + 1.87100i) q^{74} +(-0.722740 - 4.61474i) q^{75} +(0.143138 + 2.76164i) q^{76} +(13.4220 + 1.39509i) q^{77} +(8.31483 + 1.15557i) q^{78} +(-6.20239 + 4.44119i) q^{79} +(-1.25356 - 2.11465i) q^{80} +(0.737168 - 0.924380i) q^{81} +(-5.79973 - 9.78368i) q^{82} +(-13.8724 - 7.28078i) q^{83} +(1.35637 + 0.188504i) q^{84} +(1.69012 - 1.30074i) q^{85} +(6.02422 + 2.64899i) q^{86} +(-4.21156 - 4.59169i) q^{87} +(11.3860 + 2.39280i) q^{88} +(0.131599 - 1.52098i) q^{89} +(1.34783 + 0.965105i) q^{90} +(-10.6898 - 10.1501i) q^{91} +(-2.16441 - 2.20210i) q^{92} +(-4.63301 - 7.23404i) q^{93} +(14.4074 + 0.996357i) q^{94} +(-2.45564 + 1.39899i) q^{95} +(2.68082 + 0.660763i) q^{96} +(5.24115 + 4.03367i) q^{97} +(-0.603697 - 0.573217i) q^{98} +(-9.75248 + 2.04951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9}+O(q^{10}) \) 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9} - 91 q^{10} - 61 q^{11} - 31 q^{12} - 72 q^{13} - 21 q^{14} - 46 q^{15} + 24 q^{16} - 91 q^{17} + 9 q^{18} - 89 q^{19} - 108 q^{20} - 81 q^{21} - 50 q^{22} - 86 q^{23} - 33 q^{24} - 15 q^{25} + 137 q^{26} + 163 q^{27} - 47 q^{28} - 12 q^{29} + 29 q^{30} - 53 q^{31} - 122 q^{32} - 21 q^{33} - 80 q^{34} - 75 q^{35} - 8 q^{36} - 49 q^{37} - 47 q^{38} + 128 q^{39} - 246 q^{40} - 686 q^{41} - 466 q^{42} - 9 q^{43} - 43 q^{44} + 156 q^{45} - 91 q^{46} - 72 q^{47} + 21 q^{48} - 8 q^{49} - 84 q^{50} + 93 q^{51} + 4 q^{52} - 32 q^{53} - 71 q^{54} - 34 q^{55} - 263 q^{56} - 61 q^{57} - 36 q^{58} - 23 q^{59} + 87 q^{60} + 38 q^{61} + 26 q^{62} + 133 q^{63} + 343 q^{64} + 143 q^{65} - 65 q^{66} - 50 q^{67} - 213 q^{68} - 140 q^{69} + 372 q^{70} - 75 q^{71} + 147 q^{72} - 18 q^{73} - 85 q^{74} + 97 q^{75} - 47 q^{76} + 11 q^{77} + 55 q^{78} - 37 q^{79} - 142 q^{80} - 532 q^{81} - 94 q^{82} - 279 q^{83} + 395 q^{84} - 75 q^{85} - 147 q^{86} + 84 q^{87} + 345 q^{88} + 8 q^{89} + 278 q^{90} - 38 q^{91} - 78 q^{92} - 83 q^{93} - 540 q^{94} + 35 q^{95} + 123 q^{96} - 735 q^{97} - 90 q^{98} + 351 q^{99}+O(q^{100}) \) 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9 - 91 * q^10 - 61 * q^11 - 31 * q^12 - 72 * q^13 - 21 * q^14 - 46 * q^15 + 24 * q^16 - 91 * q^17 + 9 * q^18 - 89 * q^19 - 108 * q^20 - 81 * q^21 - 50 * q^22 - 86 * q^23 - 33 * q^24 - 15 * q^25 + 137 * q^26 + 163 * q^27 - 47 * q^28 - 12 * q^29 + 29 * q^30 - 53 * q^31 - 122 * q^32 - 21 * q^33 - 80 * q^34 - 75 * q^35 - 8 * q^36 - 49 * q^37 - 47 * q^38 + 128 * q^39 - 246 * q^40 - 686 * q^41 - 466 * q^42 - 9 * q^43 - 43 * q^44 + 156 * q^45 - 91 * q^46 - 72 * q^47 + 21 * q^48 - 8 * q^49 - 84 * q^50 + 93 * q^51 + 4 * q^52 - 32 * q^53 - 71 * q^54 - 34 * q^55 - 263 * q^56 - 61 * q^57 - 36 * q^58 - 23 * q^59 + 87 * q^60 + 38 * q^61 + 26 * q^62 + 133 * q^63 + 343 * q^64 + 143 * q^65 - 65 * q^66 - 50 * q^67 - 213 * q^68 - 140 * q^69 + 372 * q^70 - 75 * q^71 + 147 * q^72 - 18 * q^73 - 85 * q^74 + 97 * q^75 - 47 * q^76 + 11 * q^77 + 55 * q^78 - 37 * q^79 - 142 * q^80 - 532 * q^81 - 94 * q^82 - 279 * q^83 + 395 * q^84 - 75 * q^85 - 147 * q^86 + 84 * q^87 + 345 * q^88 + 8 * q^89 + 278 * q^90 - 38 * q^91 - 78 * q^92 - 83 * q^93 - 540 * q^94 + 35 * q^95 + 123 * q^96 - 735 * q^97 - 90 * q^98 + 351 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more