LMFDB - Embedded newform 637.2.bl.a.53.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.8
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.a.625.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31734 - 0.898146i) q^{2} +(-1.50703 - 1.39832i) q^{3} +(0.198032 + 0.504577i) q^{4} +(0.675664 - 0.208415i) q^{5} +(0.729374 + 3.19559i) q^{6} +(-1.94868 - 1.78960i) q^{7} +(-0.517257 + 2.26625i) q^{8} +(0.0916520 + 1.22301i) q^{9} +O(q^{10})$	\(q+(-1.31734 - 0.898146i) q^{2} +(-1.50703 - 1.39832i) q^{3} +(0.198032 + 0.504577i) q^{4} +(0.675664 - 0.208415i) q^{5} +(0.729374 + 3.19559i) q^{6} +(-1.94868 - 1.78960i) q^{7} +(-0.517257 + 2.26625i) q^{8} +(0.0916520 + 1.22301i) q^{9} +(-1.07726 - 0.332292i) q^{10} +(-0.293184 + 3.91227i) q^{11} +(0.407120 - 1.03732i) q^{12} +(0.900969 - 0.433884i) q^{13} +(0.959745 + 4.10770i) q^{14} +(-1.30968 - 0.630707i) q^{15} +(3.51152 - 3.25822i) q^{16} +(-2.99095 + 0.450814i) q^{17} +(0.977706 - 1.69344i) q^{18} +(3.45636 + 5.98659i) q^{19} +(0.238964 + 0.299652i) q^{20} +(0.434284 + 5.42185i) q^{21} +(3.90001 - 4.89046i) q^{22} +(-0.475891 - 0.0717290i) q^{23} +(3.94847 - 2.69202i) q^{24} +(-3.71811 + 2.53496i) q^{25} +(-1.57657 - 0.237630i) q^{26} +(-2.27333 + 2.85067i) q^{27} +(0.517090 - 1.33765i) q^{28} +(0.0971907 + 0.121873i) q^{29} +(1.15882 + 2.00714i) q^{30} +(-2.05887 + 3.56607i) q^{31} +(-2.95508 + 0.445407i) q^{32} +(5.91245 - 5.48595i) q^{33} +(4.34499 + 2.09244i) q^{34} +(-1.68963 - 0.803034i) q^{35} +(-0.598953 + 0.288441i) q^{36} +(4.15109 - 10.5768i) q^{37} +(0.823638 - 10.9907i) q^{38} +(-1.96450 - 0.605967i) q^{39} +(0.122828 + 1.63903i) q^{40} +(-0.0987303 + 0.432565i) q^{41} +(4.29752 - 7.53246i) q^{42} +(-0.519363 - 2.27548i) q^{43} +(-2.03210 + 0.626820i) q^{44} +(0.316820 + 0.807243i) q^{45} +(0.562486 + 0.521911i) q^{46} +(7.95351 + 5.42261i) q^{47} -9.84800 q^{48} +(0.594678 + 6.97469i) q^{49} +7.17477 q^{50} +(5.13784 + 3.50292i) q^{51} +(0.397348 + 0.368685i) q^{52} +(1.80035 + 4.58721i) q^{53} +(5.55506 - 1.71351i) q^{54} +(0.617281 + 2.70448i) q^{55} +(5.06364 - 3.49051i) q^{56} +(3.16233 - 13.8551i) q^{57} +(-0.0185730 - 0.247840i) q^{58} +(0.183834 + 0.0567051i) q^{59} +(0.0588825 - 0.785733i) q^{60} +(4.12357 - 10.5067i) q^{61} +(5.91509 - 2.84856i) q^{62} +(2.01010 - 2.54727i) q^{63} +(-4.33890 - 2.08950i) q^{64} +(0.518324 - 0.480935i) q^{65} +(-12.7159 + 1.91661i) q^{66} +(2.78911 - 4.83089i) q^{67} +(-0.819774 - 1.41989i) q^{68} +(0.616882 + 0.773546i) q^{69} +(1.50457 + 2.57540i) q^{70} +(1.20249 - 1.50788i) q^{71} +(-2.81906 - 0.424905i) q^{72} +(-4.38662 + 2.99075i) q^{73} +(-14.9679 + 10.2050i) q^{74} +(9.14800 + 1.37884i) q^{75} +(-2.33623 + 2.92954i) q^{76} +(7.57271 - 7.09907i) q^{77} +(2.04366 + 2.56267i) q^{78} +(5.15296 + 8.92519i) q^{79} +(1.69355 - 2.93331i) q^{80} +(11.0503 - 1.66557i) q^{81} +(0.518568 - 0.481161i) q^{82} +(4.87321 + 2.34681i) q^{83} +(-2.64974 + 1.29283i) q^{84} +(-1.92692 + 0.927957i) q^{85} +(-1.35954 + 3.46404i) q^{86} +(0.0239485 - 0.319571i) q^{87} +(-8.71454 - 2.68808i) q^{88} +(0.408336 + 5.44887i) q^{89} +(0.307664 - 1.34796i) q^{90} +(-2.53217 - 0.766873i) q^{91} +(-0.0580488 - 0.254328i) q^{92} +(8.08930 - 2.49522i) q^{93} +(-5.60717 - 14.2868i) q^{94} +(3.58303 + 3.32457i) q^{95} +(5.07622 + 3.46091i) q^{96} -17.6039 q^{97} +(5.48090 - 9.72214i) q^{98} -4.81162 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

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 $

$2$	−1.31734	−	0.898146i	−0.931499	−	0.635085i	−0.000457913	−	1.00000i	$-0.500146\pi$
$2$	−1.31734	−	0.898146i	−0.931499	−	0.635085i	−0.931041	+	0.364915i	$0.881098\pi$
$3$	−1.50703	−	1.39832i	−0.870085	−	0.807321i	0.112400	−	0.993663i	$-0.464146\pi$
$3$	−1.50703	−	1.39832i	−0.870085	−	0.807321i	−0.982485	+	0.186342i	$0.940337\pi$
$4$	0.198032	+	0.504577i	0.0990159	+	0.252288i
$5$	0.675664	−	0.208415i	0.302166	−	0.0932059i	−0.139965	−	0.990156i	$-0.544699\pi$
$5$	0.675664	−	0.208415i	0.302166	−	0.0932059i	0.442131	+	0.896951i	$0.354223\pi$
$6$	0.729374	+	3.19559i	0.297766	+	1.30460i
$7$	−1.94868	−	1.78960i	−0.736530	−	0.676404i
$7$	−1.94868	−	1.78960i	−0.736530	−	0.676404i
$8$	−0.517257	+	2.26625i	−0.182878	+	0.801241i
$9$	0.0916520	+	1.22301i	0.0305507	+	0.407670i
$10$	−1.07726	−	0.332292i	−0.340661	−	0.105080i
$11$	−0.293184	+	3.91227i	−0.0883984	+	1.17959i	0.759887	+	0.650055i	$0.225254\pi$
$11$	−0.293184	+	3.91227i	−0.0883984	+	1.17959i	−0.848285	+	0.529539i	$0.822365\pi$
$12$	0.407120	−	1.03732i	0.117525	−	0.299450i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$14$	0.959745	+	4.10770i	0.256503	+	1.09783i
$15$	−1.30968	−	0.630707i	−0.338157	−	0.162848i
$16$	3.51152	−	3.25822i	0.877881	−	0.814554i
$17$	−2.99095	+	0.450814i	−0.725413	+	0.109338i	−0.501360	−	0.865239i	$-0.667167\pi$
$17$	−2.99095	+	0.450814i	−0.725413	+	0.109338i	−0.224053	+	0.974577i	$0.571929\pi$
$18$	0.977706	−	1.69344i	0.230448	−	0.399147i
$19$	3.45636	+	5.98659i	0.792943	+	1.37342i	0.924137	+	0.382061i	$0.124786\pi$
$19$	3.45636	+	5.98659i	0.792943	+	1.37342i	−0.131194	+	0.991357i	$0.541881\pi$
$20$	0.238964	+	0.299652i	0.0534340	+	0.0670042i
$21$	0.434284	+	5.42185i	0.0947685	+	1.18315i
$22$	3.90001	−	4.89046i	0.831486	−	1.04265i
$23$	−0.475891	−	0.0717290i	−0.0992301	−	0.0149565i	0.0992395	−	0.995064i	$-0.468359\pi$
$23$	−0.475891	−	0.0717290i	−0.0992301	−	0.0149565i	−0.198470	+	0.980107i	$0.563597\pi$
$24$	3.94847	−	2.69202i	0.805977	−	0.549506i
$25$	−3.71811	+	2.53496i	−0.743622	+	0.506993i
$26$	−1.57657	−	0.237630i	−0.309191	−	0.0466031i
$27$	−2.27333	+	2.85067i	−0.437503	+	0.548611i
$28$	0.517090	−	1.33765i	0.0977208	−	0.252793i
$29$	0.0971907	+	0.121873i	0.0180479	+	0.0226313i	0.790774	−	0.612109i	$-0.209679\pi$
$29$	0.0971907	+	0.121873i	0.0180479	+	0.0226313i	−0.772726	+	0.634740i	$0.781107\pi$
$30$	1.15882	+	2.00714i	0.211571	+	0.366451i
$31$	−2.05887	+	3.56607i	−0.369785	+	0.640486i	−0.989532	−	0.144316i	$-0.953902\pi$
$31$	−2.05887	+	3.56607i	−0.369785	+	0.640486i	0.619747	+	0.784802i	$0.287235\pi$
$32$	−2.95508	+	0.445407i	−0.522390	+	0.0787376i
$33$	5.91245	−	5.48595i	1.02922	−	0.954981i
$34$	4.34499	+	2.09244i	0.745160	+	0.358850i
$35$	−1.68963	−	0.803034i	−0.285599	−	0.135738i
$36$	−0.598953	+	0.288441i	−0.0998256	+	0.0480735i
$37$	4.15109	−	10.5768i	0.682436	−	1.73882i	0.00857006	−	0.999963i	$-0.497272\pi$
$37$	4.15109	−	10.5768i	0.682436	−	1.73882i	0.673865	−	0.738854i	$-0.264633\pi$
$38$	0.823638	−	10.9907i	0.133612	−	1.78292i
$39$	−1.96450	−	0.605967i	−0.314571	−	0.0970323i
$40$	0.122828	+	1.63903i	0.0194208	+	0.259153i
$41$	−0.0987303	+	0.432565i	−0.0154191	+	0.0675554i	−0.982052	−	0.188610i	$-0.939602\pi$
$41$	−0.0987303	+	0.432565i	−0.0154191	+	0.0675554i	0.966633	+	0.256165i	$0.0824591\pi$
$42$	4.29752	−	7.53246i	0.663121	−	1.16228i
$43$	−0.519363	−	2.27548i	−0.0792022	−	0.347007i	0.919764	−	0.392472i	$-0.128380\pi$
$43$	−0.519363	−	2.27548i	−0.0792022	−	0.347007i	−0.998966	+	0.0454651i	$0.985523\pi$
$44$	−2.03210	+	0.626820i	−0.306351	+	0.0944967i
$45$	0.316820	+	0.807243i	0.0472287	+	0.120337i
$46$	0.562486	+	0.521911i	0.0829341	+	0.0769516i
$47$	7.95351	+	5.42261i	1.16014	+	0.790969i	0.981219	−	0.192895i	$-0.0617876\pi$
$47$	7.95351	+	5.42261i	1.16014	+	0.790969i	0.178919	+	0.983864i	$0.442740\pi$
$48$	−9.84800			−1.42144
$49$	0.594678	+	6.97469i	0.0849539	+	0.996385i
$50$	7.17477			1.01467
$51$	5.13784	+	3.50292i	0.719442	+	0.490507i
$52$	0.397348	+	0.368685i	0.0551023	+	0.0511275i
$53$	1.80035	+	4.58721i	0.247297	+	0.630101i	0.999587	−	0.0287299i	$-0.00914629\pi$
$53$	1.80035	+	4.58721i	0.247297	+	0.630101i	−0.752291	+	0.658831i	$0.771051\pi$
$54$	5.55506	−	1.71351i	0.755948	−	0.233179i
$55$	0.617281	+	2.70448i	0.0832341	+	0.364673i
$56$	5.06364	−	3.49051i	0.676658	−	0.466439i
$57$	3.16233	−	13.8551i	0.418861	−	1.83515i
$58$	−0.0185730	−	0.247840i	−0.00243876	−	0.0325430i
$59$	0.183834	+	0.0567051i	0.0239331	+	0.00738238i	0.306699	−	0.951807i	$-0.400776\pi$
$59$	0.183834	+	0.0567051i	0.0239331	+	0.00738238i	−0.282766	+	0.959189i	$0.591252\pi$
$60$	0.0588825	−	0.785733i	0.00760170	−	0.101438i
$61$	4.12357	−	10.5067i	0.527969	−	1.34524i	−0.379526	−	0.925181i	$-0.623913\pi$
$61$	4.12357	−	10.5067i	0.527969	−	1.34524i	0.907495	−	0.420063i	$-0.137992\pi$
$62$	5.91509	−	2.84856i	0.751217	−	0.361767i
$63$	2.01010	−	2.54727i	0.253249	−	0.320926i
$64$	−4.33890	−	2.08950i	−0.542363	−	0.261188i
$65$	0.518324	−	0.480935i	0.0642902	−	0.0596526i
$66$	−12.7159	+	1.91661i	−1.56522	+	0.235918i
$67$	2.78911	−	4.83089i	0.340745	−	0.590187i	−0.643827	−	0.765171i	$-0.722654\pi$
$67$	2.78911	−	4.83089i	0.340745	−	0.590187i	0.984571	+	0.174984i	$0.0559875\pi$
$68$	−0.819774	−	1.41989i	−0.0994122	−	0.172187i
$69$	0.616882	+	0.773546i	0.0742639	+	0.0931240i
$70$	1.50457	+	2.57540i	0.179831	+	0.307819i
$71$	1.20249	−	1.50788i	0.142710	−	0.178952i	−0.705340	−	0.708869i	$-0.749206\pi$
$71$	1.20249	−	1.50788i	0.142710	−	0.178952i	0.848049	+	0.529917i	$0.177777\pi$
$72$	−2.81906	−	0.424905i	−0.332229	−	0.0500755i
$73$	−4.38662	+	2.99075i	−0.513415	+	0.350040i	−0.792149	−	0.610328i	$-0.791038\pi$
$73$	−4.38662	+	2.99075i	−0.513415	+	0.350040i	0.278734	+	0.960368i	$0.410085\pi$
$74$	−14.9679	+	10.2050i	−1.73999	+	1.18630i
$75$	9.14800	+	1.37884i	1.05632	+	0.159215i
$76$	−2.33623	+	2.92954i	−0.267984	+	0.336041i
$77$	7.57271	−	7.09907i	0.862991	−	0.809014i
$78$	2.04366	+	2.56267i	0.231399	+	0.290165i
$79$	5.15296	+	8.92519i	0.579753	+	1.00416i	0.995507	+	0.0946850i	$0.0301844\pi$
$79$	5.15296	+	8.92519i	0.579753	+	1.00416i	−0.415754	+	0.909477i	$0.636482\pi$
$80$	1.69355	−	2.93331i	0.189345	−	0.327954i
$81$	11.0503	−	1.66557i	1.22782	−	0.185064i
$82$	0.518568	−	0.481161i	0.0572663	−	0.0531353i
$83$	4.87321	+	2.34681i	0.534904	+	0.257596i	0.681778	−	0.731559i	$-0.261207\pi$
$83$	4.87321	+	2.34681i	0.534904	+	0.257596i	−0.146874	+	0.989155i	$0.546921\pi$
$84$	−2.64974	+	1.29283i	−0.289110	+	0.141059i
$85$	−1.92692	+	0.927957i	−0.209004	+	0.100651i
$86$	−1.35954	+	3.46404i	−0.146603	+	0.373537i
$87$	0.0239485	−	0.319571i	0.00256755	−	0.0342616i
$88$	−8.71454	−	2.68808i	−0.928973	−	0.286550i
$89$	0.408336	+	5.44887i	0.0432835	+	0.577579i	0.976113	+	0.217262i	$0.0697125\pi$
$89$	0.408336	+	5.44887i	0.0432835	+	0.577579i	−0.932830	+	0.360317i	$0.882668\pi$
$90$	0.307664	−	1.34796i	0.0324306	−	0.142088i
$91$	−2.53217	−	0.766873i	−0.265444	−	0.0803902i
$92$	−0.0580488	−	0.254328i	−0.00605200	−	0.0265156i
$93$	8.08930	−	2.49522i	0.838821	−	0.258742i
$94$	−5.60717	−	14.2868i	−0.578335	−	1.47357i
$95$	3.58303	+	3.32457i	0.367611	+	0.341093i
$96$	5.07622	+	3.46091i	0.518090	+	0.353227i
$97$	−17.6039			−1.78740			−0.893700	−	0.448664i	$-0.851900\pi$
$97$	−17.6039			−1.78740			−0.893700	+	0.448664i	$0.851900\pi$
$98$	5.48090	−	9.72214i	0.553655	−	0.982084i
$99$	−4.81162			−0.483586
$100$	−2.01539	−	1.37407i	−0.201539	−	0.137407i
$101$	−4.23330	−	3.92793i	−0.421229	−	0.390843i	0.440880	−	0.897566i	$-0.354666\pi$
$101$	−4.23330	−	3.92793i	−0.421229	−	0.390843i	−0.862109	+	0.506723i	$0.830857\pi$
$102$	−3.62214	−	9.22906i	−0.358645	−	0.913813i
$103$	−14.9227	+	4.60304i	−1.47038	+	0.453551i	−0.923479	−	0.383649i	$-0.874667\pi$
$103$	−14.9227	+	4.60304i	−1.47038	+	0.453551i	−0.546897	+	0.837200i	$0.684191\pi$
$104$	0.517257	+	2.26625i	0.0507212	+	0.222224i
$105$	1.42342	+	3.57284i	0.138912	+	0.348673i
$106$	1.74832	−	7.65988i	0.169812	−	0.743993i
$107$	1.30489	+	17.4126i	0.126149	+	1.68334i	0.597872	+	0.801592i	$0.296013\pi$
$107$	1.30489	+	17.4126i	0.126149	+	1.68334i	−0.471723	+	0.881747i	$0.656368\pi$
$108$	−1.88857	−	0.582547i	−0.181728	−	0.0560556i
$109$	−0.0349174	+	0.465940i	−0.00334448	+	0.0446290i	−0.998626	−	0.0523969i	$-0.983314\pi$
$109$	−0.0349174	+	0.465940i	−0.00334448	+	0.0446290i	0.995282	+	0.0970259i	$0.0309330\pi$
$110$	1.61585	−	4.11713i	0.154066	−	0.392553i
$111$	−21.0456	+	10.1350i	−1.99756	+	0.961974i
$112$	−12.6737	+	0.0649955i	−1.19755	+	0.00614149i
$113$	16.6007	+	7.99447i	1.56166	+	0.752057i	0.997297	−	0.0734692i	$-0.0234071\pi$
$113$	16.6007	+	7.99447i	1.56166	+	0.752057i	0.564364	+	0.825526i	$0.309121\pi$
$114$	−16.6097	+	15.4116i	−1.55564	+	1.44343i
$115$	−0.336492	+	0.0507180i	−0.0313780	+	0.00472948i
$116$	−0.0422476	+	0.0731750i	−0.00392259	+	0.00679413i
$117$	0.613220	+	1.06213i	0.0566922	+	0.0981939i
$118$	−0.191242	−	0.239809i	−0.0176052	−	0.0220762i
$119$	6.63517	+	4.47411i	0.608245	+	0.410141i
$120$	2.10678	−	2.64182i	0.192322	−	0.241164i
$121$	−4.34277	−	0.654568i	−0.394798	−	0.0595062i
$122$	−14.8687	+	10.1373i	−1.34615	+	0.917788i
$123$	0.753655	−	0.513833i	0.0679547	−	0.0463308i
$124$	−2.20708	−	0.332664i	−0.198202	−	0.0298741i
$125$	−4.18815	+	5.25177i	−0.374599	+	0.469732i
$126$	−4.93580	+	1.55026i	−0.439716	+	0.138108i
$127$	−9.59198	−	12.0280i	−0.851151	−	1.06731i	−0.996954	−	0.0779956i	$-0.975148\pi$
$127$	−9.59198	−	12.0280i	−0.851151	−	1.06731i	0.145803	−	0.989314i	$-0.453423\pi$
$128$	6.82758	+	11.8257i	0.603479	+	1.04526i
$129$	−2.39915	+	4.15545i	−0.211234	+	0.365867i
$130$	−1.11476	+	0.168023i	−0.0977708	+	0.0147366i
$131$	−13.4763	+	12.5042i	−1.17743	+	1.09249i	−0.183438	+	0.983031i	$0.558723\pi$
$131$	−13.4763	+	12.5042i	−1.17743	+	1.09249i	−0.993991	+	0.109463i	$0.965087\pi$
$132$	3.93894	+	1.89689i	0.342840	+	0.165103i
$133$	3.97827	−	17.8514i	0.344959	−	1.54791i
$134$	−8.01305	+	3.85888i	−0.692222	+	0.333357i
$135$	−0.941886	+	2.39989i	−0.0810647	+	0.206549i
$136$	0.525434	−	7.01144i	0.0450556	−	0.601226i
$137$	2.32199	+	0.716240i	0.198381	+	0.0611925i	0.392353	−	0.919815i	$-0.371661\pi$
$137$	2.32199	+	0.716240i	0.198381	+	0.0611925i	−0.193972	+	0.981007i	$0.562137\pi$
$138$	−0.117885	−	1.57307i	−0.0100351	−	0.133909i
$139$	−4.69578	+	20.5736i	−0.398291	+	1.74503i	0.235832	+	0.971794i	$0.424219\pi$
$139$	−4.69578	+	20.5736i	−0.398291	+	1.74503i	−0.634123	+	0.773232i	$0.718639\pi$
$140$	0.0705921	−	1.01157i	0.00596612	−	0.0854936i
$141$	−4.40364	−	19.2936i	−0.370853	−	1.62481i
$142$	−2.93839	+	0.906372i	−0.246584	+	0.0760611i
$143$	1.43332	+	3.65204i	0.119860	+	0.305399i
$144$	4.30667	+	3.99601i	0.358890	+	0.333001i
$145$	0.0910685	+	0.0620894i	0.00756283	+	0.00515625i
$146$	8.46479			0.700551
$147$	8.85666	−	11.3426i	0.730485	−	0.935524i
$148$	6.15886			0.506256
$149$	5.89373	+	4.01828i	0.482833	+	0.329190i	0.780154	−	0.625588i	$-0.215141\pi$
$149$	5.89373	+	4.01828i	0.482833	+	0.329190i	−0.297321	+	0.954778i	$0.596093\pi$
$150$	−10.8126	−	10.0326i	−0.882846	−	0.819161i
$151$	5.86066	+	14.9327i	0.476934	+	1.21521i	0.943693	+	0.330823i	$0.107326\pi$
$151$	5.86066	+	14.9327i	0.476934	+	1.21521i	−0.466759	+	0.884385i	$0.654578\pi$
$152$	−15.3549	+	4.73637i	−1.24545	+	0.384170i
$153$	−0.825477	−	3.61665i	−0.0667359	−	0.292389i
$154$	−16.3518	+	2.55047i	−1.31767	+	0.205523i
$155$	−0.647885	+	2.83857i	−0.0520393	+	0.227999i
$156$	−0.0832759	−	1.11124i	−0.00666741	−	0.0889704i
$157$	0.760075	+	0.234452i	0.0606606	+	0.0187113i	0.324937	−	0.945736i	$-0.394657\pi$
$157$	0.760075	+	0.234452i	0.0606606	+	0.0187113i	−0.264276	+	0.964447i	$0.585133\pi$
$158$	1.22793	−	16.3856i	0.0976890	−	1.30357i
$159$	3.70121	−	9.43052i	0.293525	−	0.747889i
$160$	−1.90381	+	0.916828i	−0.150510	+	0.0724816i
$161$	0.798991	+	0.991430i	0.0629693	+	0.0781357i
$162$	−16.0530	−	7.73070i	−1.26124	−	0.607382i
$163$	−0.207274	+	0.192322i	−0.0162349	+	0.0150638i	−0.688248	−	0.725475i	$-0.741620\pi$
$163$	−0.207274	+	0.192322i	−0.0162349	+	0.0150638i	0.672014	+	0.740539i	$0.265430\pi$
$164$	−0.237814	+	0.0358447i	−0.0185702	+	0.00279900i
$165$	2.85147	−	4.93890i	0.221987	−	0.384493i
$166$	−4.31188	−	7.46840i	−0.334667	−	0.579661i
$167$	3.28557	+	4.11998i	0.254245	+	0.318814i	0.892531	−	0.450986i	$-0.148928\pi$
$167$	3.28557	+	4.11998i	0.254245	+	0.318814i	−0.638286	+	0.769800i	$0.720356\pi$
$168$	−12.5119	−	1.82029i	−0.965315	−	0.140439i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	3.37185	+	0.508225i	0.258609	+	0.0389791i
$171$	−7.00489	+	4.77585i	−0.535677	+	0.365218i
$172$	1.04530	−	0.712676i	0.0797037	−	0.0543410i
$173$	9.52393	+	1.43550i	0.724091	+	0.109139i	0.500739	−	0.865599i	$-0.333062\pi$
$173$	9.52393	+	1.43550i	0.724091	+	0.109139i	0.223353	+	0.974738i	$0.428300\pi$
$174$	−0.318569	+	0.399473i	−0.0241507	+	0.0302840i
$175$	11.7820	+	1.71410i	0.890632	+	0.129574i
$176$	11.7175	+	14.6933i	0.883240	+	1.10755i
$177$	−0.197751	−	0.342515i	−0.0148639	−	0.0257450i
$178$	4.35596	−	7.54475i	0.326493	−	0.565503i
$179$	−19.1305	+	2.88345i	−1.42988	+	0.215519i	−0.817902	−	0.575357i	$-0.804863\pi$
$179$	−19.1305	+	2.88345i	−1.42988	+	0.215519i	−0.611976	+	0.790877i	$0.709625\pi$
$180$	−0.344576	+	0.319720i	−0.0256832	+	0.0238305i
$181$	7.47716	+	3.60081i	0.555773	+	0.267646i	0.690617	−	0.723221i	$-0.257339\pi$
$181$	7.47716	+	3.60081i	0.555773	+	0.267646i	−0.134844	+	0.990867i	$0.543053\pi$
$182$	2.64697	+	3.28449i	0.196206	+	0.243463i
$183$	−20.9061	+	10.0678i	−1.54542	+	0.744236i
$184$	0.408714	−	1.04139i	0.0301308	−	0.0767720i
$185$	0.600380	−	8.01152i	0.0441408	−	0.589019i
$186$	−12.8974	−	3.97833i	−0.945685	−	0.291705i
$187$	−0.886805	−	11.8336i	−0.0648496	−	0.865358i
$188$	−1.16108	+	5.08701i	−0.0846802	+	0.371008i
$189$	9.53153	−	1.48668i	0.693317	−	0.108140i
$190$	−1.73412	−	7.59766i	−0.125806	−	0.551193i
$191$	12.4084	−	3.82749i	0.897843	−	0.276948i	0.188718	−	0.982031i	$-0.439567\pi$
$191$	12.4084	−	3.82749i	0.897843	−	0.276948i	0.709124	+	0.705083i	$0.249090\pi$
$192$	3.61706	+	9.21612i	0.261039	+	0.665116i
$193$	−9.76362	−	9.05932i	−0.702801	−	0.652104i	0.245529	−	0.969389i	$-0.421038\pi$
$193$	−9.76362	−	9.05932i	−0.702801	−	0.652104i	−0.948330	+	0.317285i	$0.897229\pi$
$194$	23.1902	+	15.8108i	1.66496	+	1.13515i
$195$	−1.45363			−0.104097
$196$	−3.40150	+	1.68127i	−0.242965	+	0.120091i
$197$	−3.63332			−0.258863			−0.129432	−	0.991588i	$-0.541315\pi$
$197$	−3.63332			−0.258863			−0.129432	+	0.991588i	$0.541315\pi$
$198$	6.33854	+	4.32154i	0.450460	+	0.307119i
$199$	−1.75235	−	1.62594i	−0.124221	−	0.115260i	0.615617	−	0.788046i	$-0.288907\pi$
$199$	−1.75235	−	1.62594i	−0.124221	−	0.115260i	−0.739837	+	0.672786i	$0.765097\pi$
$200$	−3.82165	−	9.73739i	−0.270231	−	0.688538i
$201$	−10.9584	+	3.38022i	−0.772947	+	0.238422i
$202$	2.04883	+	8.97653i	0.144155	+	0.631586i
$203$	0.0287110	−	0.411424i	0.00201512	−	0.0288763i
$204$	−0.750037	+	3.28613i	−0.0525131	+	0.230075i
$205$	0.0234445	+	0.312846i	0.00163744	+	0.0218501i
$206$	23.7924	+	7.33899i	1.65770	+	0.511332i
$207$	0.0441090	−	0.588594i	0.00306579	−	0.0409101i
$208$	1.75009	−	4.45914i	0.121347	−	0.309186i
$209$	−24.4345	+	11.7670i	−1.69017	+	0.813943i
$210$	1.33380	−	5.98508i	0.0920410	−	0.413010i
$211$	10.0718	+	4.85031i	0.693369	+	0.333909i	0.747161	−	0.664643i	$-0.231416\pi$
$211$	10.0718	+	4.85031i	0.693369	+	0.333909i	−0.0537917	+	0.998552i	$0.517131\pi$
$212$	−1.95807	+	1.81683i	−0.134481	+	0.124780i
$213$	−3.92069	+	0.590949i	−0.268641	+	0.0404912i
$214$	13.9201	−	24.1103i	0.951556	−	1.64814i
$215$	−0.825158	−	1.42922i	−0.0562753	−	0.0974717i
$216$	−5.28443	−	6.62646i	−0.359560	−	0.450874i
$217$	10.3939	−	3.26457i	0.705585	−	0.221613i
$218$	0.464480	−	0.582440i	0.0314586	−	0.0394478i
$219$	10.7928	+	1.62675i	0.729309	+	0.109926i
$220$	−1.24238	+	0.847040i	−0.0837612	+	0.0571074i
$221$	−2.49916	+	1.70390i	−0.168111	+	0.114616i
$222$	36.8269	+	5.55076i	2.47166	+	0.372543i
$223$	3.20901	−	4.02397i	0.214891	−	0.269465i	−0.662689	−	0.748894i	$-0.730585\pi$
$223$	3.20901	−	4.02397i	0.214891	−	0.269465i	0.877580	+	0.479430i	$0.159156\pi$
$224$	6.55560	+	4.42045i	0.438014	+	0.295354i
$225$	−3.44106	−	4.31496i	−0.229404	−	0.287664i
$226$	−14.6885	−	25.4413i	−0.977066	−	1.69233i
$227$	−4.62799	+	8.01592i	−0.307171	+	0.532035i	−0.977742	−	0.209810i	$-0.932716\pi$
$227$	−4.62799	+	8.01592i	−0.307171	+	0.532035i	0.670572	+	0.741845i	$0.266049\pi$
$228$	7.61719	−	1.14811i	0.504461	−	0.0760352i
$229$	0.111881	−	0.103811i	0.00739333	−	0.00686001i	−0.676467	−	0.736473i	$-0.736490\pi$
$229$	0.111881	−	0.103811i	0.00739333	−	0.00686001i	0.683861	+	0.729613i	$0.260300\pi$
$230$	0.488826	+	0.235406i	0.0322322	+	0.0155222i
$231$	−21.3391	+	0.109435i	−1.40401	+	0.00720027i
$232$	−0.326468	+	0.157219i	−0.0214337	+	0.0103219i
$233$	−3.16570	+	8.06608i	−0.207392	+	0.528426i	−0.996286	−	0.0861026i	$-0.972559\pi$
$233$	−3.16570	+	8.06608i	−0.207392	+	0.528426i	0.788894	+	0.614529i	$0.210654\pi$
$234$	0.146128	−	1.94994i	0.00955270	−	0.127472i
$235$	6.50405	+	2.00623i	0.424278	+	0.130872i
$236$	0.00779279	+	0.103988i	0.000507268	+	0.00676902i
$237$	4.71460	−	20.6560i	0.306246	−	1.34175i
$238$	−4.72236	−	11.8533i	−0.306105	−	0.768334i
$239$	1.76049	+	7.71323i	0.113877	+	0.498927i	0.999410	+	0.0343508i	$0.0109363\pi$
$239$	1.76049	+	7.71323i	0.113877	+	0.498927i	−0.885533	+	0.464577i	$0.846207\pi$
$240$	−6.65394	+	2.05247i	−0.429510	+	0.132486i
$241$	4.74294	+	12.0848i	0.305520	+	0.778451i	0.998354	+	0.0573543i	$0.0182665\pi$
$241$	4.74294	+	12.0848i	0.305520	+	0.778451i	−0.692834	+	0.721097i	$0.743638\pi$
$242$	5.13300	+	4.76273i	0.329962	+	0.306160i
$243$	−9.94448	−	6.78003i	−0.637938	−	0.434939i
$244$	6.11803			0.391667
$245$	1.85543	+	4.58861i	0.118539	+	0.293156i
$246$	−1.45432			−0.0927237
$247$	5.71156	+	3.89407i	0.363418	+	0.247774i
$248$	−7.01665	−	6.51050i	−0.445558	−	0.413417i
$249$	−4.06248	−	10.3510i	−0.257449	−	0.655970i
$250$	10.2341	−	3.15679i	0.647259	−	0.199653i
$251$	−1.48664	−	6.51338i	−0.0938357	−	0.411121i	0.906093	−	0.423079i	$-0.139051\pi$
$251$	−1.48664	−	6.51338i	−0.0938357	−	0.411121i	−0.999929	+	0.0119580i	$0.996194\pi$
$252$	1.68336	+	0.509808i	0.106042	+	0.0321149i
$253$	0.420147	−	1.84079i	0.0264144	−	0.115729i
$254$	1.83302	+	24.4599i	0.115014	+	1.53475i
$255$	4.20151	+	1.29600i	0.263109	+	0.0811584i
$256$	0.907214	−	12.1059i	0.0567009	−	0.756621i
$257$	0.0509032	−	0.129699i	0.00317525	−	0.00809041i	−0.929277	−	0.369383i	$-0.879569\pi$
$257$	0.0509032	−	0.129699i	0.00317525	−	0.00809041i	0.932453	+	0.361292i	$0.117664\pi$
$258$	6.89270	−	3.31935i	0.429121	−	0.206654i
$259$	−27.0174	+	13.1820i	−1.67878	+	0.819089i
$260$	0.345313	+	0.166294i	0.0214154	+	0.0103131i
$261$	−0.140145	+	0.130035i	−0.00867474	+	0.00804898i
$262$	28.9834	−	4.36854i	1.79060	−	0.269890i
$263$	15.7867	−	27.3435i	0.973453	−	1.68607i	0.288503	−	0.957479i	$-0.406842\pi$
$263$	15.7867	−	27.3435i	0.973453	−	1.68607i	0.684950	−	0.728590i	$-0.259824\pi$
$264$	9.37428	+	16.2367i	0.576947	+	0.999302i
$265$	2.17247	+	2.72419i	0.133454	+	0.167346i
$266$	−21.2739	+	19.9433i	−1.30439	+	1.22280i
$267$	7.00388	−	8.78259i	0.428631	−	0.537486i
$268$	2.98989	+	0.450653i	0.182636	+	0.0275280i
$269$	−10.8336	+	7.38619i	−0.660533	+	0.450344i	−0.846626	−	0.532188i	$-0.821370\pi$
$269$	−10.8336	+	7.38619i	−0.660533	+	0.450344i	0.186093	+	0.982532i	$0.440418\pi$
$270$	3.39623	−	2.31551i	0.206688	−	0.140918i
$271$	8.61371	+	1.29831i	0.523246	+	0.0788666i	0.405354	−	0.914160i	$-0.367148\pi$
$271$	8.61371	+	1.29831i	0.523246	+	0.0788666i	0.117892	+	0.993026i	$0.462386\pi$
$272$	−9.03395	+	11.3282i	−0.547764	+	0.686874i
$273$	2.74373	+	4.69649i	0.166058	+	0.284245i
$274$	−2.41556	−	3.02902i	−0.145929	−	0.182990i
$275$	−8.82738	−	15.2895i	−0.532311	−	0.921989i
$276$	−0.268151	+	0.464451i	−0.0161408	+	0.0279567i
$277$	−12.0501	+	1.81627i	−0.724023	+	0.109129i	−0.500706	−	0.865617i	$-0.666926\pi$
$277$	−12.0501	+	1.81627i	−0.724023	+	0.109129i	−0.223316	+	0.974746i	$0.571688\pi$
$278$	24.6640	−	22.8848i	1.47925	−	1.37254i
$279$	−4.55005	−	2.19119i	−0.272404	−	0.131183i
$280$	2.69385	−	3.41375i	0.160988	−	0.204010i
$281$	25.1744	−	12.1233i	1.50178	−	0.723217i	0.511109	−	0.859516i	$-0.329235\pi$
$281$	25.1744	−	12.1233i	1.50178	−	0.723217i	0.990668	+	0.136299i	$0.0435207\pi$
$282$	−11.5274	+	29.3713i	−0.686446	+	1.74904i
$283$	−1.93026	+	25.7576i	−0.114742	+	1.53113i	0.581634	+	0.813451i	$0.302414\pi$
$283$	−1.93026	+	25.7576i	−0.114742	+	1.53113i	−0.696376	+	0.717677i	$0.745205\pi$
$284$	0.998973	+	0.308142i	0.0592781	+	0.0182849i
$285$	−0.750929	−	10.0204i	−0.0444812	−	0.593560i
$286$	1.39190	−	6.09831i	0.0823047	−	0.360600i
$287$	0.966512	−	0.666243i	0.0570514	−	0.0393271i
$288$	−0.815577	−	3.57328i	−0.0480583	−	0.210557i
$289$	−7.50217	+	2.31411i	−0.441304	+	0.136124i
$290$	−0.0642026	−	0.163586i	−0.00377011	−	0.00960608i
$291$	26.5296	+	24.6158i	1.55519	+	1.44301i
$292$	−2.37775	−	1.62112i	−0.139147	−	0.0948691i
$293$	−30.2357			−1.76639			−0.883193	−	0.469009i	$-0.844611\pi$
$293$	−30.2357			−1.76639			−0.883193	+	0.469009i	$0.844611\pi$
$294$	−21.8546	+	6.98751i	−1.27458	+	0.407520i
$295$	0.136028			0.00791985
$296$	21.8225	+	14.8783i	1.26841	+	0.864786i
$297$	−10.4861	−	9.72965i	−0.608464	−	0.564572i
$298$	−4.15504	−	10.5869i	−0.240695	−	0.613280i
$299$	−0.459885	+	0.141856i	−0.0265958	+	0.00820373i
$300$	1.11586	+	4.88892i	0.0644245	+	0.282262i
$301$	−3.06012	+	5.36362i	−0.176383	+	0.309154i
$302$	5.69129	−	24.9352i	0.327497	−	1.43486i
$303$	0.887211	+	11.8390i	0.0509689	+	0.680133i
$304$	31.6427	+	9.76048i	1.81483	+	0.559802i
$305$	0.596400	−	7.95841i	0.0341498	−	0.455697i
$306$	−2.16085	+	5.50575i	−0.123528	+	0.314743i
$307$	25.8887	−	12.4673i	1.47754	−	0.711548i	0.490418	−	0.871488i	$-0.336844\pi$
$307$	25.8887	−	12.4673i	1.47754	−	0.711548i	0.987127	+	0.159940i	$0.0511299\pi$
$308$	5.08167	+	2.41518i	0.289555	+	0.137617i
$309$	28.9255	+	13.9298i	1.64551	+	0.792437i
$310$	3.40293	−	3.15746i	0.193274	−	0.179332i
$311$	−26.5347	+	3.99946i	−1.50465	+	0.226789i	−0.849045	−	0.528320i	$-0.822822\pi$
$311$	−26.5347	+	3.99946i	−1.50465	+	0.226789i	−0.655600	+	0.755109i	$0.727584\pi$
$312$	2.38942	−	4.13860i	0.135274	−	0.234302i
$313$	3.06213	+	5.30376i	0.173082	+	0.299786i	0.939496	−	0.342561i	$-0.111294\pi$
$313$	3.06213	+	5.30376i	0.173082	+	0.299786i	−0.766414	+	0.642347i	$0.777961\pi$
$314$	−0.790703	−	0.991511i	−0.0446220	−	0.0559542i
$315$	0.827262	−	2.14003i	0.0466109	−	0.120577i
$316$	−3.48299	+	4.36754i	−0.195934	+	0.245693i
$317$	5.96336	+	0.898832i	0.334936	+	0.0504834i	0.314357	−	0.949305i	$-0.398211\pi$
$317$	5.96336	+	0.898832i	0.334936	+	0.0504834i	0.0205786	+	0.999788i	$0.493449\pi$
$318$	−13.3457	+	9.09897i	−0.748391	+	0.510245i
$319$	−0.505296	+	0.344505i	−0.0282912	+	0.0192886i
$320$	−3.36712	−	0.507512i	−0.188228	−	0.0283708i
$321$	22.3819	−	28.0660i	1.24923	−	1.56649i
$322$	−0.162093	−	2.02366i	−0.00903307	−	0.112774i
$323$	−13.0366	−	16.3474i	−0.725378	−	0.909596i
$324$	3.02873	+	5.24591i	0.168263	+	0.291440i
$325$	−2.25002	+	3.89715i	−0.124809	+	0.216175i
$326$	0.445783	−	0.0671909i	0.0246896	−	0.00372136i
$327$	0.704155	−	0.653361i	0.0389399	−	0.0361309i
$328$	−0.929233	−	0.447495i	−0.0513083	−	0.0247088i
$329$	−5.79452	−	24.8005i	−0.319462	−	1.36730i
$330$	−8.19221	+	3.94516i	−0.450966	+	0.217174i
$331$	10.1748	−	25.9250i	0.559259	−	1.42497i	−0.319447	−	0.947604i	$-0.603497\pi$
$331$	10.1748	−	25.9250i	0.559259	−	1.42497i	0.878706	−	0.477364i	$-0.158408\pi$
$332$	−0.219098	+	2.92365i	−0.0120245	+	0.160456i
$333$	13.3160	+	4.10745i	0.729713	+	0.225087i
$334$	−0.627869	−	8.37833i	−0.0343555	−	0.458442i
$335$	0.877676	−	3.84535i	0.0479526	−	0.210094i
$336$	19.1906	+	17.6240i	1.04693	+	0.961466i
$337$	4.19095	+	18.3618i	0.228296	+	1.00023i	0.951029	+	0.309102i	$0.100028\pi$
$337$	4.19095	+	18.3618i	0.228296	+	1.00023i	−0.722733	+	0.691127i	$0.757114\pi$
$338$	−1.52355	+	0.469952i	−0.0828700	+	0.0255620i
$339$	−13.8389	−	35.2610i	−0.751627	−	1.91511i
$340$	−0.849818	−	0.788516i	−0.0460878	−	0.0427633i
$341$	−13.3478	−	9.10039i	−0.722825	−	0.492814i
$342$	13.5172			0.730927
$343$	11.3231	−	14.6557i	0.611388	−	0.791331i
$344$	5.42545			0.292521
$345$	0.578023	+	0.394090i	0.0311197	+	0.0212171i
$346$	−11.2569	−	10.4449i	−0.605177	−	0.561523i
$347$	8.36147	+	21.3047i	0.448867	+	1.14369i	0.958951	+	0.283570i	$0.0915190\pi$
$347$	8.36147	+	21.3047i	0.448867	+	1.14369i	−0.510084	+	0.860124i	$0.670386\pi$
$348$	0.165991	−	0.0512013i	0.00889803	−	0.00274468i
$349$	−0.491653	−	2.15407i	−0.0263176	−	0.115305i	0.960063	−	0.279784i	$-0.0902628\pi$
$349$	−0.491653	−	2.15407i	−0.0263176	−	0.115305i	−0.986381	+	0.164479i	$0.947406\pi$
$350$	−13.9813	−	12.8400i	−0.747333	−	0.686325i
$351$	−0.811342	+	3.55472i	−0.0433062	+	0.189737i
$352$	−0.876169	−	11.6917i	−0.0467000	−	0.623168i
$353$	26.6382	+	8.21679i	1.41781	+	0.437335i	0.906552	−	0.422094i	$-0.138705\pi$
$353$	26.6382	+	8.21679i	1.41781	+	0.437335i	0.511254	+	0.859429i	$0.329181\pi$
$354$	−0.0471233	+	0.628817i	−0.00250458	+	0.0334212i
$355$	0.498217	−	1.26944i	0.0264426	−	0.0673747i
$356$	−2.66851	+	1.28509i	−0.141431	+	0.0681094i
$357$	−3.74317	−	16.0207i	−0.198109	−	0.847907i
$358$	27.7911	+	13.3835i	1.46880	+	0.707338i
$359$	8.99293	−	8.34422i	0.474629	−	0.440391i	−0.406230	−	0.913771i	$-0.633157\pi$
$359$	8.99293	−	8.34422i	0.474629	−	0.440391i	0.880858	+	0.473380i	$0.156966\pi$
$360$	−1.99329	+	0.300440i	−0.105056	+	0.0158346i
$361$	−14.3928	+	24.9291i	−0.757518	+	1.31206i
$362$	−6.61589	−	11.4591i	−0.347724	−	0.602275i
$363$	5.62940	+	7.05904i	0.295467	+	0.370504i
$364$	−0.114505	−	1.42954i	−0.00600167	−	0.0749284i
$365$	−2.34056	+	2.93497i	−0.122511	+	0.153624i
$366$	36.5828	+	5.51396i	1.91221	+	0.288219i
$367$	9.27944	−	6.32661i	0.484383	−	0.330247i	−0.296384	−	0.955069i	$-0.595781\pi$
$367$	9.27944	−	6.32661i	0.484383	−	0.330247i	0.780767	+	0.624822i	$0.214829\pi$
$368$	−1.90481	+	1.29868i	−0.0992951	+	0.0676983i
$369$	−0.538081	−	0.0811027i	−0.0280114	−	0.00422204i
$370$	−7.98642	+	10.0147i	−0.415194	+	0.520637i
$371$	4.70097	−	12.1609i	0.244062	−	0.631361i
$372$	2.86097	+	3.58754i	0.148334	+	0.186005i
$373$	6.06543	+	10.5056i	0.314056	+	0.543961i	0.979236	−	0.202722i	$-0.0649787\pi$
$373$	6.06543	+	10.5056i	0.314056	+	0.543961i	−0.665180	+	0.746683i	$0.731645\pi$
$374$	−9.46007	+	16.3853i	−0.489169	+	0.847265i
$375$	13.6553	−	2.05821i	0.705158	−	0.106285i
$376$	−16.4030	+	15.2198i	−0.845920	+	0.784899i
$377$	0.140445	+	0.0676346i	0.00723327	+	0.00348336i
$378$	−13.8915	−	6.60225i	−0.714502	−	0.339583i
$379$	−15.4877	+	7.45848i	−0.795549	+	0.383116i	−0.787082	−	0.616848i	$-0.788409\pi$
$379$	−15.4877	+	7.45848i	−0.795549	+	0.383116i	−0.00846685	+	0.999964i	$0.502695\pi$
$380$	−0.967946	+	2.46629i	−0.0496546	+	0.126518i
$381$	−2.36353	+	31.5392i	−0.121088	+	1.61580i
$382$	−19.7838	−	6.10248i	−1.01222	−	0.312230i
$383$	−0.0214900	−	0.286765i	−0.00109809	−	0.0146530i	0.996628	−	0.0820546i	$-0.0261482\pi$
$383$	−0.0214900	−	0.286765i	−0.00109809	−	0.0146530i	−0.997726	+	0.0674016i	$0.978529\pi$
$384$	6.24676	−	27.3689i	0.318779	−	1.39666i
$385$	3.63706	−	6.37485i	0.185362	−	0.324892i
$386$	4.72540	+	20.7033i	0.240517	+	1.05377i
$387$	2.73534	−	0.843740i	0.139045	−	0.0428897i
$388$	−3.48612	−	8.88250i	−0.176981	−	0.450941i
$389$	4.73281	+	4.39141i	0.239963	+	0.222653i	0.790982	−	0.611840i	$-0.209570\pi$
$389$	4.73281	+	4.39141i	0.239963	+	0.222653i	−0.551019	+	0.834493i	$0.685761\pi$
$390$	1.91492	+	1.30557i	0.0969660	+	0.0661103i
$391$	1.45570			0.0736181
$392$	−16.1140	−	2.26002i	−0.813880	−	0.114148i
$393$	37.7940			1.90646
$394$	4.78631	+	3.26325i	0.241131	+	0.164400i
$395$	5.34181	+	4.95647i	0.268776	+	0.249387i
$396$	−0.952855	−	2.42783i	−0.0478828	−	0.122003i
$397$	−13.3728	+	4.12497i	−0.671163	+	0.207027i	−0.611563	−	0.791196i	$-0.709459\pi$
$397$	−13.3728	+	4.12497i	−0.671163	+	0.207027i	−0.0596005	+	0.998222i	$0.518983\pi$
$398$	0.848102	+	3.71578i	0.0425115	+	0.186255i
$399$	−30.9574	+	21.3398i	−1.54981	+	1.06832i
$400$	−4.79676	+	21.0160i	−0.239838	+	1.05080i
$401$	−1.00651	−	13.4309i	−0.0502625	−	0.670706i	−0.964255	−	0.264976i	$-0.914636\pi$
$401$	−1.00651	−	13.4309i	−0.0502625	−	0.670706i	0.913993	−	0.405731i	$-0.132983\pi$
$402$	17.4719	+	5.38936i	0.871417	+	0.268797i
$403$	−0.307720	+	4.10623i	−0.0153286	+	0.204546i
$404$	1.14361	−	2.91388i	0.0568969	−	0.144971i
$405$	7.11919	−	3.42842i	0.353755	−	0.170360i
$406$	−0.407341	+	0.516198i	−0.0202160	+	0.0256185i
$407$	40.1623	+	19.3412i	1.99077	+	0.958706i
$408$	−10.5961	+	9.83172i	−0.524584	+	0.486743i
$409$	13.3485	−	2.01196i	0.660040	−	0.0994851i	0.189524	−	0.981876i	$-0.439306\pi$
$409$	13.3485	−	2.01196i	0.660040	−	0.0994851i	0.470517	+	0.882391i	$0.344068\pi$
$410$	0.250097	−	0.433180i	0.0123514	−	0.0213932i
$411$	−2.49778	−	4.32628i	−0.123206	−	0.213400i
$412$	−5.27776	−	6.61810i	−0.260016	−	0.326050i
$413$	−0.256753	−	0.439488i	−0.0126340	−	0.0216258i
$414$	−0.586750	+	0.735761i	−0.0288372	+	0.0361607i
$415$	3.78176	+	0.570009i	0.185639	+	0.0279806i
$416$	−2.46918	+	1.68346i	−0.121062	+	0.0825384i
$417$	35.8451	−	24.4388i	1.75534	−	1.19677i
$418$	42.7571	+	6.44459i	2.09132	+	0.315215i
$419$	−23.5215	+	29.4950i	−1.14910	+	1.44093i	−0.270918	+	0.962602i	$0.587327\pi$
$419$	−23.5215	+	29.4950i	−1.14910	+	1.44093i	−0.878183	+	0.478325i	$0.841244\pi$
$420$	−1.52089	+	1.42576i	−0.0742118	+	0.0695701i
$421$	−20.9694	−	26.2948i	−1.02199	−	1.28153i	−0.958966	−	0.283520i	$-0.908498\pi$
$421$	−20.9694	−	26.2948i	−1.02199	−	1.28153i	−0.0630214	−	0.998012i	$-0.520074\pi$
$422$	−8.91164	−	15.4354i	−0.433812	−	0.751384i
$423$	−5.90296	+	10.2242i	−0.287012	+	0.497119i
$424$	−11.3270	+	1.70727i	−0.550088	+	0.0829124i
$425$	9.97789	−	9.25813i	0.483999	−	0.449085i
$426$	5.69564	+	2.74287i	0.275955	+	0.132893i
$427$	−26.8383	+	13.0946i	−1.29879	+	0.633692i
$428$	−8.52758	+	4.10667i	−0.412196	+	0.198503i
$429$	2.94667	−	7.50798i	0.142266	−	0.362489i
$430$	−0.196632	+	2.62387i	−0.00948245	+	0.126534i
$431$	−11.8575	−	3.65757i	−0.571158	−	0.176179i	−0.00429465	−	0.999991i	$-0.501367\pi$
$431$	−11.8575	−	3.65757i	−0.571158	−	0.176179i	−0.566863	+	0.823812i	$0.691843\pi$
$432$	1.30524	+	17.4172i	0.0627982	+	0.837984i
$433$	−0.00519781	+	0.0227731i	−0.000249791	+	0.00109441i	−0.975053	−	0.221974i	$-0.928750\pi$
$433$	−0.00519781	+	0.0227731i	−0.000249791	+	0.00109441i	0.974803	+	0.223068i	$0.0716072\pi$
$434$	−16.6244	−	5.03472i	−0.797995	−	0.241674i
$435$	−0.0504221	−	0.220914i	−0.00241755	−	0.0105920i
$436$	−0.242017	+	0.0746525i	−0.0115905	+	0.00357521i
$437$	−1.21544	−	3.09689i	−0.0581423	−	0.148144i
$438$	−12.7567	−	11.8365i	−0.609538	−	0.565569i
$439$	−34.0393	−	23.2076i	−1.62461	−	1.10764i	−0.915325	−	0.402716i	$-0.868066\pi$
$439$	−34.0393	−	23.2076i	−1.62461	−	1.10764i	−0.709283	−	0.704923i	$-0.750981\pi$
$440$	−6.44833			−0.307412
$441$	−8.47563	+	1.36654i	−0.403601	+	0.0650734i
$442$	4.82258			0.229387
$443$	−34.2036	−	23.3196i	−1.62506	−	1.10795i	−0.914718	−	0.404093i	$-0.867587\pi$
$443$	−34.2036	−	23.3196i	−1.62506	−	1.10795i	−0.710344	−	0.703855i	$-0.751460\pi$
$444$	−9.28160	−	8.61206i	−0.440485	−	0.408710i
$445$	1.41152	+	3.59650i	0.0669126	+	0.170490i
$446$	−7.84145	+	2.41877i	−0.371304	+	0.114532i
$447$	−3.26319	−	14.2970i	−0.154344	−	0.676224i
$448$	4.71574	+	11.8367i	0.222798	+	0.559229i
$449$	−5.20350	+	22.7980i	−0.245568	+	1.07591i	0.690291	+	0.723532i	$0.257483\pi$
$449$	−5.20350	+	22.7980i	−0.245568	+	1.07591i	−0.935859	+	0.352374i	$0.885375\pi$
$450$	0.657583	+	8.77483i	0.0309987	+	0.413650i
$451$	−1.66337	−	0.513081i	−0.0783249	−	0.0241600i
$452$	−0.746360	+	9.95949i	−0.0351058	+	0.468455i
$453$	12.0485	−	30.6992i	0.566089	−	1.44237i
$454$	13.2961	−	6.40306i	0.624017	−	0.300511i
$455$	−1.87073	+	0.00959377i	−0.0877010	+	0.000449763i
$456$	29.7633	+	14.3333i	1.39380	+	0.671217i
$457$	5.33406	−	4.94929i	0.249517	−	0.231518i	−0.545491	−	0.838116i	$-0.683657\pi$
$457$	5.33406	−	4.94929i	0.249517	−	0.231518i	0.795008	+	0.606599i	$0.207466\pi$
$458$	−0.240623	+	0.0362681i	−0.0112436	+	0.00169469i
$459$	5.51430	−	9.55106i	0.257386	−	0.445805i
$460$	−0.0922272	−	0.159742i	−0.00430012	−	0.00744802i
$461$	7.21007	+	9.04114i	0.335806	+	0.421088i	0.920852	−	0.389913i	$-0.127495\pi$
$461$	7.21007	+	9.04114i	0.335806	+	0.421088i	−0.585045	+	0.811001i	$0.698923\pi$
$462$	28.2091	+	19.0215i	1.31241	+	0.884958i
$463$	7.42090	−	9.30552i	0.344879	−	0.432464i	−0.578896	−	0.815402i	$-0.696516\pi$
$463$	7.42090	−	9.30552i	0.344879	−	0.432464i	0.923774	+	0.382938i	$0.125088\pi$
$464$	0.738377	+	0.111292i	0.0342783	+	0.00516662i
$465$	4.94561	−	3.37186i	0.229347	−	0.156366i
$466$	11.4148	−	7.78249i	0.528781	−	0.360517i
$467$	−37.6963	−	5.68180i	−1.74438	−	0.262922i	−0.801963	−	0.597374i	$-0.796211\pi$
$467$	−37.6963	−	5.68180i	−1.74438	−	0.262922i	−0.942413	+	0.334452i	$0.891449\pi$
$468$	−0.414489	+	0.519752i	−0.0191597	+	0.0240256i
$469$	−14.0804	+	4.42244i	−0.650174	+	0.204209i
$470$	−6.76614	−	8.48448i	−0.312099	−	0.391360i
$471$	−0.817617	−	1.41615i	−0.0376738	−	0.0652529i
$472$	−0.223597	+	0.387282i	−0.0102919	+	0.0178261i
$473$	9.05456	−	1.36476i	0.416329	−	0.0627515i
$474$	−24.7628	+	22.9766i	−1.13740	+	1.05535i
$475$	−28.0269	−	13.4970i	−1.28596	−	0.619287i
$476$	−0.943559	+	4.23397i	−0.0432480	+	0.194064i
$477$	−5.44520	+	2.62227i	−0.249319	+	0.120066i
$478$	4.60844	−	11.7421i	0.210785	−	0.537072i
$479$	−1.79427	+	23.9428i	−0.0819821	+	1.09398i	0.792807	+	0.609472i	$0.208619\pi$
$479$	−1.79427	+	23.9428i	−0.0819821	+	1.09398i	−0.874790	+	0.484503i	$0.839000\pi$
$480$	4.15112	+	1.28045i	0.189472	+	0.0584444i
$481$	−0.849101	−	11.3305i	−0.0387157	−	0.516625i
$482$	4.60587	−	20.1796i	0.209792	−	0.919157i
$483$	0.182232	−	2.61136i	0.00829186	−	0.118821i
$484$	−0.529728	−	2.32089i	−0.0240785	−	0.105495i
$485$	−11.8943	+	3.66890i	−0.540092	+	0.166596i
$486$	7.01078	+	17.8632i	0.318016	+	0.810290i
$487$	4.91688	+	4.56219i	0.222805	+	0.206733i	0.783675	−	0.621171i	$-0.213343\pi$
$487$	4.91688	+	4.56219i	0.222805	+	0.206733i	−0.560870	+	0.827904i	$0.689533\pi$
$488$	21.6778	+	14.7797i	0.981310	+	0.669046i
$489$	0.581295			0.0262871
$490$	1.67701	−	7.71120i	0.0757596	−	0.348356i
$491$	−17.0475			−0.769341			−0.384671	−	0.923054i	$-0.625685\pi$
$491$	−17.0475			−0.769341			−0.384671	+	0.923054i	$0.625685\pi$
$492$	0.408516	+	0.278521i	0.0184173	+	0.0125567i
$493$	−0.345635	−	0.320703i	−0.0155666	−	0.0144437i
$494$	−4.02661	−	10.2596i	−0.181166	−	0.461602i
$495$	−3.25104	+	1.00281i	−0.146123	+	0.0450731i
$496$	4.38926	+	19.2306i	0.197084	+	0.863480i
$497$	−5.04177	+	0.786388i	−0.226154	+	0.0352743i
$498$	−3.94508	+	17.2845i	−0.176783	+	0.774537i
$499$	−1.51442	−	20.2085i	−0.0677945	−	0.904655i	−0.922613	−	0.385728i	$-0.873950\pi$
$499$	−1.51442	−	20.2085i	−0.0677945	−	0.904655i	0.854818	−	0.518928i	$-0.173669\pi$
$500$	−3.47931	−	1.07322i	−0.155599	−	0.0479960i
$501$	0.809590	−	10.8032i	0.0361698	−	0.482652i
$502$	−3.89156	+	9.91554i	−0.173689	+	0.442552i
$503$	23.7721	−	11.4481i	1.05995	−	0.510444i	0.179094	−	0.983832i	$-0.442683\pi$
$503$	23.7721	−	11.4481i	1.05995	−	0.510444i	0.880854	+	0.473388i	$0.156969\pi$
$504$	4.73302	+	5.87298i	0.210826	+	0.261603i
$505$	−3.67892	−	1.77168i	−0.163710	−	0.0788386i
$506$	−2.20677	+	2.04758i	−0.0981029	+	0.0910262i
$507$	−2.03287	+	0.306406i	−0.0902829	+	0.0136080i
$508$	4.16952	−	7.22181i	0.184992	−	0.320416i
$509$	6.76862	+	11.7236i	0.300014	+	0.519639i	0.976139	−	0.217148i	$-0.0696754\pi$
$509$	6.76862	+	11.7236i	0.300014	+	0.519639i	−0.676125	+	0.736787i	$0.736342\pi$
$510$	−4.37082	−	5.48084i	−0.193543	−	0.242696i
$511$	13.9003	+	2.02229i	0.614914	+	0.0894608i
$512$	4.95970	−	6.21927i	0.219190	−	0.274856i
$513$	−24.9232	−	3.75657i	−1.10039	−	0.165857i
$514$	−0.183546	+	0.125139i	−0.00809585	+	0.00551965i
$515$	−9.12338	+	6.22022i	−0.402024	+	0.274095i
$516$	−2.57185	−	0.387645i	−0.113220	−	0.0170651i
$517$	−23.5466	+	29.5265i	−1.03558	+	1.29857i
$518$	47.4304	+	6.90041i	2.08397	+	0.303186i
$519$	−12.3456	−	15.4809i	−0.541910	−	0.679534i
$520$	0.821812	+	1.42342i	0.0360388	+	0.0624211i
$521$	6.02493	−	10.4355i	0.263957	−	0.457187i	−0.703333	−	0.710861i	$-0.748306\pi$
$521$	6.02493	−	10.4355i	0.263957	−	0.457187i	0.967290	+	0.253674i	$0.0816389\pi$
$522$	0.301409	−	0.0454301i	0.0131923	−	0.00198842i
$523$	−16.1612	+	14.9954i	−0.706678	+	0.655702i	−0.949283	−	0.314424i	$-0.898189\pi$
$523$	−16.1612	+	14.9954i	−0.706678	+	0.655702i	0.242604	+	0.970125i	$0.421998\pi$
$524$	−8.97805	−	4.32360i	−0.392208	−	0.188877i
$525$	−15.3589	−	19.0581i	−0.670318	−	0.831766i
$526$	−45.3549	+	21.8418i	−1.97757	+	0.952346i
$527$	4.55036	−	11.5941i	0.198217	−	0.505048i
$528$	2.88728	−	38.5281i	0.125653	−	1.67672i
$529$	−21.7568	−	6.71110i	−0.945950	−	0.291787i
$530$	−0.415157	−	5.53988i	−0.0180332	−	0.240637i
$531$	−0.0525023	+	0.230028i	−0.00227841	+	0.00998235i
$532$	9.79524	−	1.52781i	0.424677	−	0.0662389i
$533$	0.0987303	+	0.432565i	0.00427648	+	0.0187365i
$534$	−17.1145	+	5.27914i	−0.740618	+	0.228451i
$535$	4.51071	+	11.4931i	0.195015	+	0.496890i
$536$	9.50531	+	8.81964i	0.410567	+	0.380951i
$537$	32.8622	+	22.4051i	1.41811	+	0.966850i
$538$	20.9053			0.901293
$539$	−27.4612	+	0.281670i	−1.18284	+	0.0121324i
$540$	−1.39745			−0.0601367
$541$	21.7946	+	14.8593i	0.937024	+	0.638852i	0.932512	−	0.361138i	$-0.117612\pi$
$541$	21.7946	+	14.8593i	0.937024	+	0.638852i	0.00451119	+	0.999990i	$0.498564\pi$
$542$	−10.1811	−	9.44668i	−0.437316	−	0.405770i
$543$	−6.23322	−	15.8820i	−0.267493	−	0.681561i
$544$	8.63772	−	2.66438i	0.370339	−	0.114234i
$545$	0.0735164	+	0.322096i	0.00314910	+	0.0137971i
$546$	0.603715	−	8.65114i	0.0258366	−	0.370235i
$547$	2.26605	−	9.92820i	0.0968892	−	0.424499i	−0.903099	−	0.429433i	$-0.858713\pi$
$547$	2.26605	−	9.92820i	0.0968892	−	0.424499i	0.999988	+	0.00493396i	$0.00157054\pi$
$548$	0.0984304	+	1.31346i	0.00420474	+	0.0561083i
$549$	13.2277	+	4.08022i	0.564546	+	0.174139i
$550$	−2.10353	+	28.0697i	−0.0896949	+	1.19689i
$551$	−0.393680	+	1.00308i	−0.0167713	+	0.0427326i
$552$	−2.07214	+	0.997888i	−0.0881959	+	0.0424729i
$553$	5.93105	−	26.6140i	0.252214	−	1.13174i
$554$	17.5054	+	8.43015i	0.743732	+	0.358163i
$555$	−12.1075	+	11.2341i	−0.513933	+	0.476860i
$556$	−11.3109	+	1.70484i	−0.479687	+	0.0723012i
$557$	−3.51345	+	6.08547i	−0.148870	+	0.257850i	−0.930810	−	0.365504i	$-0.880897\pi$
$557$	−3.51345	+	6.08547i	−0.148870	+	0.257850i	0.781940	+	0.623353i	$0.214230\pi$
$558$	4.02595	+	6.97315i	0.170432	+	0.295197i
$559$	−1.45522	−	1.82479i	−0.0615494	−	0.0771805i
$560$	−8.54963	+	2.68530i	−0.361288	+	0.113475i
$561$	−15.2107	+	19.0736i	−0.642197	+	0.805289i
$562$	−44.0517	−	6.63972i	−1.85821	−	0.280080i
$563$	−19.0229	+	12.9696i	−0.801718	+	0.546602i	−0.893440	−	0.449182i	$-0.851715\pi$
$563$	−19.0229	+	12.9696i	−0.801718	+	0.546602i	0.0917219	+	0.995785i	$0.470763\pi$
$564$	8.86304	−	6.04272i	0.373201	−	0.254444i
$565$	12.8827	+	1.94175i	0.541977	+	0.0816899i
$566$	25.6769	−	32.1978i	1.07928	−	1.35337i
$567$	−24.5143	−	16.5300i	−1.02950	−	0.694196i
$568$	2.79523	+	3.50511i	0.117285	+	0.147071i
$569$	−16.7614	−	29.0317i	−0.702676	−	1.21707i	−0.967524	−	0.252781i	$-0.918655\pi$
$569$	−16.7614	−	29.0317i	−0.702676	−	1.21707i	0.264847	−	0.964290i	$-0.414679\pi$
$570$	−8.01060	+	13.8748i	−0.335527	+	0.581150i
$571$	22.8841	−	3.44922i	0.957669	−	0.144345i	0.348432	−	0.937334i	$-0.386714\pi$
$571$	22.8841	−	3.44922i	0.957669	−	0.144345i	0.609236	+	0.792989i	$0.291476\pi$
$572$	−1.55889	+	1.44644i	−0.0651806	+	0.0604788i
$573$	−24.0519	−	11.5828i	−1.00478	−	0.483879i
$574$	−1.87161	+	0.00959828i	−0.0781193	+	0.000400624i
$575$	1.95125	−	0.939670i	0.0813725	−	0.0391870i
$576$	2.15782	−	5.49803i	0.0899091	−	0.229085i
$577$	−0.768643	+	10.2568i	−0.0319990	+	0.426997i	0.958081	+	0.286496i	$0.0924905\pi$
$577$	−0.768643	+	10.2568i	−0.0319990	+	0.426997i	−0.990081	+	0.140501i	$0.955129\pi$
$578$	11.9613	+	3.68957i	0.497525	+	0.153466i
$579$	2.04625	+	27.3053i	0.0850393	+	1.13477i
$580$	−0.0132944	+	0.0582467i	−0.000552021	+	0.00241856i
$581$	−5.29645	−	13.2943i	−0.219734	−	0.551539i
$582$	−12.8398	−	56.2548i	−0.532226	−	2.33184i
$583$	−18.4742	+	5.69855i	−0.765125	+	0.236010i
$584$	−4.50877	−	11.4882i	−0.186574	−	0.475383i
$585$	0.635694	+	0.589838i	0.0262827	+	0.0243868i
$586$	39.8306	+	27.1560i	1.64539	+	1.12181i
$587$	−16.1363			−0.666018			−0.333009	−	0.942924i	$-0.608064\pi$
$587$	−16.1363			−0.666018			−0.333009	+	0.942924i	$0.608064\pi$
$588$	7.47713	+	2.22266i	0.308352	+	0.0916611i
$589$	−28.4648			−1.17287
$590$	−0.179195	−	0.122173i	−0.00737733	−	0.00502978i
$591$	5.47552	+	5.08054i	0.225233	+	0.208986i
$592$	−19.8849	−	50.6659i	−0.817264	−	2.08235i
$593$	7.71927	−	2.38108i	0.316992	−	0.0977792i	−0.132176	−	0.991226i	$-0.542196\pi$
$593$	7.71927	−	2.38108i	0.316992	−	0.0977792i	0.449168	+	0.893447i	$0.351720\pi$
$594$	5.07506	+	22.2353i	0.208232	+	0.912324i
$595$	5.41562	+	1.64013i	0.222019	+	0.0672388i
$596$	−0.860384	+	3.76959i	−0.0352427	+	0.154408i
$597$	0.367255	+	4.90068i	0.0150308	+	0.200572i
$598$	0.733231	+	0.226172i	0.0299841	+	0.00924886i
$599$	−2.68898	+	35.8820i	−0.109869	+	1.46610i	0.621123	+	0.783713i	$0.286677\pi$
$599$	−2.68898	+	35.8820i	−0.109869	+	1.46610i	−0.730992	+	0.682386i	$0.760942\pi$
$600$	−7.85666	+	20.0184i	−0.320747	+	0.817249i
$601$	22.9983	−	11.0754i	0.938122	−	0.451776i	0.0986154	−	0.995126i	$-0.468559\pi$
$601$	22.9983	−	11.0754i	0.938122	−	0.451776i	0.839506	+	0.543350i	$0.182844\pi$
$602$	8.84853	−	4.31727i	0.360639	−	0.175959i
$603$	6.16386	+	2.96836i	0.251012	+	0.120881i
$604$	−6.37411	+	5.91431i	−0.259359	+	0.240650i
$605$	−3.07068	+	0.462830i	−0.124841	+	0.0188167i
$606$	9.46440	−	16.3928i	0.384465	−	0.665913i
$607$	−8.09850	−	14.0270i	−0.328708	−	0.569339i	0.653548	−	0.756885i	$-0.273280\pi$
$607$	−8.09850	−	14.0270i	−0.328708	−	0.569339i	−0.982256	+	0.187546i	$0.939946\pi$
$608$	−12.8803	−	16.1514i	−0.522365	−	0.655025i
$609$	−0.618571	+	0.579881i	−0.0250658	+	0.0234980i
$610$	−7.93347	+	9.94826i	−0.321217	+	0.402793i
$611$	9.51865	+	1.43471i	0.385083	+	0.0580420i
$612$	1.66141	−	1.13273i	0.0671585	−	0.0457879i
$613$	−16.4988	+	11.2487i	−0.666381	+	0.454331i	−0.848676	−	0.528913i	$-0.822600\pi$
$613$	−16.4988	+	11.2487i	−0.666381	+	0.454331i	0.182295	+	0.983244i	$0.441647\pi$
$614$	−45.3016	−	6.82812i	−1.82822	−	0.275561i
$615$	0.402127	−	0.504251i	0.0162153	−	0.0203334i
$616$	12.1712	+	20.8337i	0.490393	+	0.839414i
$617$	13.7465	+	17.2376i	0.553415	+	0.693960i	0.977325	−	0.211744i	$-0.0679143\pi$
$617$	13.7465	+	17.2376i	0.553415	+	0.693960i	−0.423910	+	0.905704i	$0.639343\pi$
$618$	−25.5937	−	44.3295i	−1.02953	−	1.78320i
$619$	19.5810	−	33.9152i	0.787026	−	1.36317i	−0.140755	−	0.990044i	$-0.544953\pi$
$619$	19.5810	−	33.9152i	0.787026	−	1.36317i	0.927781	−	0.373124i	$-0.121714\pi$
$620$	−1.56058	+	0.235219i	−0.0626743	+	0.00944663i
$621$	1.28633	−	1.19354i	0.0516188	−	0.0478952i
$622$	38.5473	+	18.5634i	1.54561	+	0.744324i
$623$	8.95557	−	11.3488i	0.358797	−	0.454681i
$624$	−8.87274	+	4.27289i	−0.355194	+	0.171052i
$625$	6.48502	−	16.5236i	0.259401	−	0.660942i
$626$	0.729694	−	9.73709i	0.0291644	−	0.389172i
$627$	53.2777	+	16.4340i	2.12771	+	0.656310i
$628$	0.0322199	+	0.429945i	0.00128572	+	0.0171567i
$629$	−7.64755	+	33.5061i	−0.304928	+	1.33598i
$630$	−3.01185	+	2.07615i	−0.119995	+	0.0827157i
$631$	3.93150	+	17.2250i	0.156511	+	0.685717i	0.990907	+	0.134552i	$0.0429595\pi$
$631$	3.93150	+	17.2250i	0.156511	+	0.685717i	−0.834396	+	0.551165i	$0.814183\pi$
$632$	−22.8921	+	7.06128i	−0.910599	+	0.280883i
$633$	−8.39618	−	21.3931i	−0.333718	−	0.850300i
$634$	−7.04848	−	6.54004i	−0.279931	−	0.259738i
$635$	−8.98776	−	6.12775i	−0.356668	−	0.243172i
$636$	5.49138			0.217747
$637$	3.56199	+	6.02596i	0.141131	+	0.238757i
$638$	0.975062			0.0386031
$639$	1.95436	+	1.33246i	0.0773135	+	0.0527114i
$640$	7.07780	+	6.56724i	0.279775	+	0.259593i
$641$	−12.8427	−	32.7227i	−0.507256	−	1.29247i	−0.923634	−	0.383276i	$-0.874796\pi$
$641$	−12.8427	−	32.7227i	−0.507256	−	1.29247i	0.416377	−	0.909192i	$-0.363299\pi$
$642$	−54.6918	+	16.8702i	−2.15851	+	0.665813i
$643$	10.1293	+	44.3795i	0.399462	+	1.75016i	0.629524	+	0.776981i	$0.283250\pi$
$643$	10.1293	+	44.3795i	0.399462	+	1.75016i	−0.230062	+	0.973176i	$0.573893\pi$
$644$	−0.342027	+	0.599487i	−0.0134778	+	0.0236231i
$645$	−0.754963	+	3.30771i	−0.0297266	+	0.130241i
$646$	2.49129	+	33.2439i	0.0980184	+	1.30796i
$647$	−10.4521	−	3.22404i	−0.410914	−	0.126750i	0.0824045	−	0.996599i	$-0.473740\pi$
$647$	−10.4521	−	3.22404i	−0.410914	−	0.126750i	−0.493318	+	0.869849i	$0.664216\pi$
$648$	−1.94127	+	25.9044i	−0.0762601	+	1.01762i
$649$	−0.275743	+	0.702582i	−0.0108239	+	0.0275787i
$650$	6.46425	−	3.11302i	0.253549	−	0.122103i
$651$	−20.2289	−	9.61422i	−0.792832	−	0.376811i
$652$	−0.138088	−	0.0664996i	−0.00540794	−	0.00260433i
$653$	−32.4071	+	30.0694i	−1.26819	+	1.17671i	−0.292809	+	0.956171i	$0.594590\pi$
$653$	−32.4071	+	30.0694i	−1.26819	+	1.17671i	−0.975379	+	0.220535i	$0.929220\pi$
$654$	−1.51442	+	0.228263i	−0.0592187	+	0.00892578i
$655$	−6.49939	+	11.2573i	−0.253952	+	0.439858i
$656$	1.06270	+	1.84065i	0.0414914	+	0.0718652i
$657$	−4.05976	−	5.09078i	−0.158386	−	0.198610i
$658$	−14.6411	+	37.8750i	−0.570770	+	1.47652i
$659$	30.3858	−	38.1025i	1.18366	−	1.48426i	0.345862	−	0.938285i	$-0.387586\pi$
$659$	30.3858	−	38.1025i	1.18366	−	1.48426i	0.837799	−	0.545979i	$-0.183842\pi$
$660$	3.05674	+	0.460729i	0.118983	+	0.0179338i
$661$	−17.6586	+	12.0394i	−0.686841	+	0.468280i	−0.855776	−	0.517347i	$-0.826920\pi$
$661$	−17.6586	+	12.0394i	−0.686841	+	0.468280i	0.168935	+	0.985627i	$0.445967\pi$
$662$	−36.6881	+	25.0135i	−1.42592	+	0.972179i
$663$	6.14889	+	0.926797i	0.238803	+	0.0359938i
$664$	−7.83917	+	9.83001i	−0.304219	+	0.381478i
$665$	−1.03253	−	12.8907i	−0.0400397	−	0.499880i
$666$	−13.8526	−	17.3706i	−0.536778	−	0.673098i
$667$	−0.0375103	−	0.0649698i	−0.00145241	−	0.00251564i
$668$	−1.42820	+	2.47371i	−0.0552587	+	0.0957108i
$669$	−10.4629	+	1.57702i	−0.404518	+	0.0609712i
$670$	−4.60988	+	4.27734i	−0.178095	+	0.165248i
$671$	39.8961	+	19.2129i	1.54017	+	0.741707i
$672$	−3.69827	−	15.8286i	−0.142664	−	0.610601i
$673$	−13.1278	+	6.32204i	−0.506041	+	0.243697i	−0.669444	−	0.742863i	$-0.733467\pi$
$673$	−13.1278	+	6.32204i	−0.506041	+	0.243697i	0.163402	+	0.986560i	$0.447753\pi$
$674$	10.9706	−	27.9527i	0.422573	−	1.07670i
$675$	1.22615	−	16.3619i	0.0471947	−	0.629770i
$676$	0.517965	+	0.159771i	0.0199217	+	0.00614504i
$677$	0.220589	+	2.94355i	0.00847791	+	0.113130i	0.999837	−	0.0180448i	$-0.00574416\pi$
$677$	0.220589	+	2.94355i	0.00847791	+	0.113130i	−0.991359	+	0.131175i	$0.958125\pi$
$678$	−13.4390	+	58.8800i	−0.516121	+	2.26127i
$679$	34.3042	+	31.5038i	1.31647	+	1.20901i
$680$	−1.10627	−	4.84688i	−0.0424235	−	0.185869i
$681$	18.1833	−	5.60882i	0.696787	−	0.214930i
$682$	9.41012	+	23.9766i	0.360332	+	0.918111i
$683$	−26.6985	−	24.7726i	−1.02159	−	0.947897i	−0.0229344	−	0.999737i	$-0.507301\pi$
$683$	−26.6985	−	24.7726i	−1.02159	−	0.947897i	−0.998655	+	0.0518401i	$0.983491\pi$
$684$	−3.79697	−	2.58873i	−0.145181	−	0.0989827i
$685$	1.71816			0.0656476
$686$	−28.0792	+	9.13669i	−1.07207	+	0.348840i
$687$	−0.313769			−0.0119710
$688$	−9.23776	−	6.29820i	−0.352186	−	0.240117i
$689$	3.61237	+	3.35179i	0.137620	+	0.127693i
$690$	−0.407502	−	1.03830i	−0.0155133	−	0.0395274i
$691$	−10.5927	+	3.26742i	−0.402966	+	0.124299i	−0.489612	−	0.871941i	$-0.662861\pi$
$691$	−10.5927	+	3.26742i	−0.402966	+	0.124299i	0.0866455	+	0.996239i	$0.472385\pi$
$692$	1.16172	+	5.08983i	0.0441620	+	0.193486i
$693$	9.37630	+	8.61087i	0.356176	+	0.327100i
$694$	8.11983	−	35.5753i	0.308224	−	1.35042i
$695$	1.11506	+	14.8795i	0.0422967	+	0.564411i
$696$	0.711840	+	0.219573i	0.0269822	+	0.00832291i
$697$	0.100291	−	1.33829i	0.00379880	−	0.0506914i
$698$	−1.28700	+	3.27922i	−0.0487136	+	0.124120i
$699$	16.0498	−	7.72916i	0.607058	−	0.292344i
$700$	1.46831	+	6.28435i	0.0554969	+	0.237526i
$701$	29.4954	+	14.2042i	1.11402	+	0.536486i	0.898041	−	0.439911i	$-0.144990\pi$
$701$	29.4954	+	14.2042i	1.11402	+	0.536486i	0.215983	+	0.976397i	$0.430704\pi$
$702$	4.26147	−	3.95407i	0.160839	−	0.149237i
$703$	77.6667	−	11.7064i	2.92926	−	0.441514i
$704$	9.44681	−	16.3623i	0.356040	−	0.616679i
$705$	−6.99645	−	12.1182i	−0.263501	−	0.456398i
$706$	−27.7116	−	34.7493i	−1.04294	−	1.30781i
$707$	1.21992	+	15.2302i	0.0458797	+	0.572789i
$708$	0.133664	−	0.167609i	0.00502340	−	0.00629914i
$709$	−14.5654	−	2.19539i	−0.547017	−	0.0824495i	−0.130281	−	0.991477i	$-0.541588\pi$
$709$	−14.5654	−	2.19539i	−0.547017	−	0.0824495i	−0.416736	+	0.909028i	$0.636826\pi$
$710$	−1.79646	+	1.22481i	−0.0674200	+	0.0459662i
$711$	−10.4433	+	7.12014i	−0.391655	+	0.267026i
$712$	−12.5597	−	1.89307i	−0.470695	−	0.0709459i
$713$	1.23559	−	1.54938i	0.0462732	−	0.0580248i
$714$	−9.45793	+	24.4666i	−0.353954	+	0.915641i
$715$	1.72958	+	2.16883i	0.0646827	+	0.0811096i
$716$	−5.24337	−	9.08178i	−0.195954	−	0.339402i
$717$	8.13245	−	14.0858i	0.303712	−	0.526044i
$718$	−19.3411	+	2.91520i	−0.721802	+	0.108794i
$719$	−28.1576	+	26.1264i	−1.05010	+	0.974351i	−0.999703	−	0.0243778i	$-0.992240\pi$
$719$	−28.1576	+	26.1264i	−1.05010	+	0.974351i	−0.0503983	+	0.998729i	$0.516049\pi$
$720$	3.74269	+	1.80239i	0.139482	+	0.0671709i
$721$	37.3171	+	17.7358i	1.38976	+	0.660515i
$722$	41.3503	−	19.9132i	1.53890	−	0.741094i
$723$	9.75068	−	24.8443i	0.362632	−	0.923970i
$724$	−0.336170	+	4.48587i	−0.0124937	+	0.166716i
$725$	−0.670310	−	0.206763i	−0.0248947	−	0.00767900i
$726$	−1.07577	−	14.3552i	−0.0399256	−	0.532770i
$727$	5.43248	−	23.8013i	0.201480	−	0.882740i	−0.768557	−	0.639781i	$-0.779025\pi$
$727$	5.43248	−	23.8013i	0.201480	−	0.882740i	0.970037	−	0.242959i	$-0.0781180\pi$
$728$	3.04771	−	5.34187i	0.112956	−	0.197983i
$729$	−1.95415	−	8.56167i	−0.0723758	−	0.317099i
$730$	5.71935	−	1.76419i	0.211683	−	0.0652954i
$731$	2.57921	+	6.57172i	0.0953955	+	0.243064i
$732$	−9.22006	−	8.55497i	−0.340783	−	0.316201i
$733$	−15.1146	−	10.3049i	−0.558270	−	0.380622i	0.251064	−	0.967970i	$-0.419219\pi$
$733$	−15.1146	−	10.3049i	−0.558270	−	0.380622i	−0.809334	+	0.587349i	$0.800172\pi$
$734$	−17.9064			−0.660937
$735$	3.62015	−	9.50966i	0.133531	−	0.350769i
$736$	1.43825			0.0530144
$737$	18.0820	+	12.3281i	0.666060	+	0.454112i
$738$	0.635993	+	0.590115i	0.0234112	+	0.0217224i
$739$	14.8674	+	37.8814i	0.546905	+	1.39349i	0.890763	+	0.454469i	$0.150171\pi$
$739$	14.8674	+	37.8814i	0.546905	+	1.39349i	−0.343858	+	0.939022i	$0.611734\pi$
$740$	4.16132	−	1.28360i	0.152973	−	0.0471860i
$741$	−3.16233	−	13.8551i	−0.116171	−	0.508979i
$742$	−17.1150	+	11.7978i	−0.628312	+	0.433112i
$743$	−4.39587	+	19.2596i	−0.161269	+	0.706566i	0.828032	+	0.560680i	$0.189460\pi$
$743$	−4.39587	+	19.2596i	−0.161269	+	0.706566i	−0.989301	+	0.145886i	$0.953397\pi$
$744$	1.47054	+	19.6231i	0.0539128	+	0.719416i
$745$	4.81965	+	1.48667i	0.176578	+	0.0544672i
$746$	1.44537	−	19.2871i	0.0529187	−	0.706151i
$747$	−2.42354	+	6.17508i	−0.0886727	+	0.225934i
$748$	5.79534	−	2.79089i	0.211899	−	0.102045i
$749$	28.6187	−	36.2667i	1.04571	−	1.32516i
$750$	−19.8372	−	9.55311i	−0.724354	−	0.348830i
$751$	31.9773	−	29.6706i	1.16687	−	1.08270i	0.171636	−	0.985160i	$-0.445095\pi$
$751$	31.9773	−	29.6706i	1.16687	−	1.08270i	0.995232	−	0.0975351i	$-0.0310958\pi$
$752$	45.5970	−	6.87264i	1.66275	−	0.250619i
$753$	−6.86739	+	11.8947i	−0.250261	+	0.433466i
$754$	−0.124267	−	0.215237i	−0.00452555	−	0.00783849i
$755$	7.07204	+	8.86806i	0.257378	+	0.322742i
$756$	2.63769	+	4.51498i	0.0959318	+	0.164208i
$757$	4.61420	−	5.78602i	0.167706	−	0.210297i	−0.690876	−	0.722974i	$-0.742775\pi$
$757$	4.61420	−	5.78602i	0.167706	−	0.210297i	0.858582	+	0.512677i	$0.171346\pi$
$758$	27.1013	+	4.08487i	0.984365	+	0.148369i
$759$	−3.20718	+	2.18662i	−0.116413	+	0.0793693i
$760$	−9.38765	+	6.40039i	−0.340526	+	0.232167i
$761$	−14.1550	−	2.13353i	−0.513120	−	0.0773403i	−0.112622	−	0.993638i	$-0.535925\pi$
$761$	−14.1550	−	2.13353i	−0.513120	−	0.0773403i	−0.400498	+	0.916298i	$0.631163\pi$
$762$	31.4404	−	39.4250i	1.13896	−	1.42822i
$763$	0.901889	−	0.845479i	0.0326506	−	0.0306084i
$764$	4.38853	+	5.50304i	0.158771	+	0.199093i
$765$	−1.31151	−	2.27160i	−0.0474177	−	0.0821299i
$766$	−0.229247	+	0.397067i	−0.00828303	+	0.0143466i
$767$	0.190232	−	0.0286728i	0.00686887	−	0.00103532i
$768$	−18.2952	+	16.9754i	−0.660170	+	0.612548i
$769$	29.8794	+	14.3892i	1.07748	+	0.518887i	0.886510	−	0.462709i	$-0.153122\pi$
$769$	29.8794	+	14.3892i	1.07748	+	0.518887i	0.190970	+	0.981596i	$0.438837\pi$
$770$	−10.5168	+	5.13122i	−0.378999	+	0.184916i
$771$	−0.258074	+	0.124282i	−0.00929430	+	0.00447590i
$772$	2.63761	−	6.72053i	0.0949298	−	0.241877i
$773$	−0.609049	+	8.12719i	−0.0219060	+	0.292315i	0.975482	+	0.220080i	$0.0706320\pi$
$773$	−0.609049	+	8.12719i	−0.0219060	+	0.292315i	−0.997388	+	0.0722342i	$0.976987\pi$
$774$	−4.36117	−	1.34524i	−0.156759	−	0.0483537i
$775$	−1.38475	−	18.4782i	−0.0497417	−	0.663757i
$776$	9.10572	−	39.8947i	0.326876	−	1.43214i
$777$	59.1487	+	17.9133i	2.12195	+	0.642635i
$778$	−2.29059	−	10.0357i	−0.0821216	−	0.359798i
$779$	−2.93084	+	0.904044i	−0.105008	+	0.0323908i
$780$	−0.287865	−	0.733469i	−0.0103072	−	0.0262624i
$781$	5.54668	+	5.14657i	0.198476	+	0.184159i
$782$	−1.91765	−	1.30744i	−0.0685752	−	0.0467538i
$783$	−0.568367			−0.0203118
$784$	24.8133	+	22.5542i	0.886189	+	0.805507i
$785$	0.562418			0.0200736
$786$	−49.7875	−	33.9445i	−1.77586	−	1.21076i
$787$	−30.6246	−	28.4155i	−1.09165	−	1.01290i	−0.999853	−	0.0171240i	$-0.994549\pi$
$787$	−30.6246	−	28.4155i	−1.09165	−	1.01290i	−0.0917953	−	0.995778i	$-0.529261\pi$
$788$	−0.719513	−	1.83329i	−0.0256316	−	0.0653082i
$789$	−62.0260	+	19.1325i	−2.20818	+	0.681135i
$790$	−2.58533	−	11.3271i	−0.0919820	−	0.402999i
$791$	−18.0425	−	45.2872i	−0.641517	−	1.61023i
$792$	2.48885	−	10.9043i	0.0884373	−	0.387469i
$793$	−0.843472	−	11.2554i	−0.0299526	−	0.399689i
$794$	21.3214	+	6.57677i	0.756667	+	0.233401i
$795$	0.535313	−	7.14325i	0.0189856	−	0.253345i
$796$	0.473391	−	1.20618i	0.0167789	−	0.0427520i
$797$	26.0858	−	12.5622i	0.924005	−	0.444977i	0.0895058	−	0.995986i	$-0.471471\pi$
$797$	26.0858	−	12.5622i	0.924005	−	0.444977i	0.834499	+	0.551009i	$0.185757\pi$
$798$	59.9475	−	0.307433i	2.12212	−	0.0108830i
$799$	−26.2332	−	12.6332i	−0.928063	−	0.446931i
$800$	9.85823	−	9.14710i	0.348541	−	0.323399i
$801$	−6.62660	+	0.998799i	−0.234139	+	0.0352908i
$802$	−10.7370	+	18.5970i	−0.379136	+	0.656683i
$803$	−10.4145	−	18.0385i	−0.367520	−	0.636564i
$804$	−3.87570	−	4.85997i	−0.136685	−	0.171398i
$805$	0.746478	+	0.503352i	0.0263099	+	0.0177408i
$806$	4.09337	−	5.13292i	0.144183	−	0.180799i
$807$	26.6548	+	4.01756i	0.938292	+	0.141425i
$808$	11.0914	−	7.56197i	0.390193	−	0.266029i
$809$	26.1401	−	17.8220i	0.919038	−	0.626590i	−0.00864298	−	0.999963i	$-0.502751\pi$
$809$	26.1401	−	17.8220i	0.919038	−	0.626590i	0.927681	+	0.373373i	$0.121799\pi$
$810$	−12.4576	−	1.87768i	−0.437716	−	0.0659750i
$811$	9.76041	−	12.2392i	0.342734	−	0.429775i	−0.580353	−	0.814365i	$-0.697086\pi$
$811$	9.76041	−	12.2392i	0.342734	−	0.429775i	0.923088	+	0.384589i	$0.125657\pi$
$812$	0.213281	−	0.0669882i	0.00748469	−	0.00235082i
$813$	−11.1657	−	14.0013i	−0.391597	−	0.491048i
$814$	−35.5362	−	61.5505i	−1.24554	−	2.15734i
$815$	−0.0999646	+	0.173144i	−0.00350161	+	0.00606496i
$816$	29.4549	−	4.43961i	1.03113	−	0.155418i
$817$	11.8273	−	10.9741i	0.413783	−	0.383935i
$818$	−19.3915	−	9.33846i	−0.678008	−	0.326512i
$819$	0.705816	−	3.16716i	0.0246632	−	0.110670i
$820$	−0.153212	+	0.0737830i	−0.00535039	+	0.00257661i
$821$	17.1334	−	43.6553i	0.597961	−	1.52358i	−0.235998	−	0.971754i	$-0.575836\pi$
$821$	17.1334	−	43.6553i	0.597961	−	1.52358i	0.833959	−	0.551827i	$-0.186069\pi$
$822$	−0.595212	+	7.94255i	−0.0207604	+	0.277028i
$823$	−20.8586	−	6.43403i	−0.727085	−	0.224276i	−0.0909519	−	0.995855i	$-0.528991\pi$
$823$	−20.8586	−	6.43403i	−0.727085	−	0.224276i	−0.636133	+	0.771579i	$0.719467\pi$
$824$	−2.71278	−	36.1995i	−0.0945041	−	1.26107i
$825$	−8.07644	+	35.3852i	−0.281185	+	1.23195i
$826$	−0.0564944	+	0.809556i	−0.00196569	+	0.0281681i
$827$	−4.51549	−	19.7837i	−0.157019	−	0.687945i	−0.990742	−	0.135762i	$-0.956652\pi$
$827$	−4.51549	−	19.7837i	−0.157019	−	0.687945i	0.833723	−	0.552184i	$-0.186205\pi$
$828$	0.305726	−	0.0943040i	0.0106247	−	0.00327729i
$829$	−3.47492	−	8.85395i	−0.120689	−	0.307510i	0.857743	−	0.514078i	$-0.171866\pi$
$829$	−3.47492	−	8.85395i	−0.120689	−	0.307510i	−0.978432	+	0.206568i	$0.933771\pi$
$830$	−4.46991	−	4.14747i	−0.155153	−	0.143961i
$831$	20.6996	+	14.1128i	0.718063	+	0.489567i
$832$	−4.81582			−0.166958
$833$	−4.92294	−	20.5929i	−0.170570	−	0.713502i
$834$	−69.1697			−2.39515
$835$	3.07861	+	2.09896i	0.106540	+	0.0726375i
$836$	−10.7762	−	9.99885i	−0.372702	−	0.345817i
$837$	−5.48519	−	13.9760i	−0.189596	−	0.483082i
$838$	57.4766	−	17.7292i	1.98550	−	0.612445i
$839$	1.34584	+	5.89653i	0.0464637	+	0.203571i	0.992832	−	0.119519i	$-0.0381354\pi$
$839$	1.34584	+	5.89653i	0.0464637	+	0.203571i	−0.946368	+	0.323090i	$0.895278\pi$
$840$	−8.83322	+	1.37776i	−0.304775	+	0.0475372i
$841$	6.44770	−	28.2492i	0.222334	−	0.974111i
$842$	4.00723	+	53.4728i	0.138098	+	1.84279i
$843$	−54.8908	−	16.9316i	−1.89054	−	0.583155i
$844$	−0.452823	+	6.04250i	−0.0155868	+	0.207991i
$845$	0.258324	−	0.658200i	0.00888663	−	0.0226428i
$846$	16.9590	−	8.16704i	0.583064	−	0.280789i
$847$	7.29125	+	9.04736i	0.250530	+	0.310871i
$848$	21.2681	+	10.2422i	0.730349	+	0.351717i
$849$	38.9263	−	36.1183i	1.33595	−	1.23958i
$850$	−21.4594	+	3.23449i	−0.736052	+	0.110942i
$851$	−2.73413	+	4.73566i	−0.0937249	+	0.162336i
$852$	−1.07460	−	1.86126i	−0.0368152	−	0.0637659i
$853$	28.8113	+	36.1282i	0.986479	+	1.23701i	0.971481	+	0.237118i	$0.0762027\pi$
$853$	28.8113	+	36.1282i	0.986479	+	1.23701i	0.0149977	+	0.999888i	$0.495226\pi$
$854$	47.1159	+	6.85466i	1.61227	+	0.234562i
$855$	−3.73759	+	4.68679i	−0.127823	+	0.160285i
$856$	−40.1363	−	6.04957i	−1.37183	−	0.206770i
$857$	−5.77171	+	3.93508i	−0.197158	+	0.134420i	−0.657875	−	0.753127i	$-0.728545\pi$
$857$	−5.77171	+	3.93508i	−0.197158	+	0.134420i	0.460717	+	0.887547i	$0.347592\pi$
$858$	−10.6250	+	7.24402i	−0.362732	+	0.247307i
$859$	27.7654	+	4.18495i	0.947342	+	0.142789i	0.604501	−	0.796605i	$-0.293373\pi$
$859$	27.7654	+	4.18495i	0.947342	+	0.142789i	0.342841	+	0.939393i	$0.388611\pi$
$860$	0.557742	−	0.699386i	0.0190188	−	0.0238489i
$861$	−2.38818	−	0.347445i	−0.0813891	−	0.0118409i
$862$	12.3354	+	15.4681i	0.420144	+	0.526844i
$863$	23.8260	+	41.2679i	0.811047	+	1.40478i	0.912132	+	0.409898i	$0.134436\pi$
$863$	23.8260	+	41.2679i	0.811047	+	1.40478i	−0.101084	+	0.994878i	$0.532231\pi$
$864$	5.44817	−	9.43651i	0.185350	−	0.321036i
$865$	6.73416	−	1.01501i	0.228968	−	0.0345114i
$866$	0.0273008	−	0.0253315i	0.000927720	−	0.000860799i
$867$	14.5419	+	7.00299i	0.493868	+	0.237834i
$868$	3.70555	+	4.59804i	0.125775	+	0.156068i
$869$	−36.4285	+	17.5431i	−1.23575	+	0.595107i
$870$	−0.131990	+	0.336304i	−0.00447487	+	0.0114018i
$871$	0.416862	−	5.56263i	0.0141248	−	0.188483i
$872$	−1.03788	−	0.320142i	−0.0351469	−	0.0108414i
$873$	−1.61343	−	21.5297i	−0.0546063	−	0.728670i
$874$	−1.18031	+	5.17129i	−0.0399247	+	0.174921i
$875$	17.5599	−	2.73890i	0.593633	−	0.0925917i
$876$	1.31649	+	5.76794i	0.0444802	+	0.194881i
$877$	−9.18461	+	2.83308i	−0.310142	+	0.0956662i	−0.445919	−	0.895073i	$-0.647123\pi$
$877$	−9.18461	+	2.83308i	−0.310142	+	0.0956662i	0.135777	+	0.990739i	$0.456647\pi$
$878$	23.9975	+	61.1446i	0.809876	+	2.06353i
$879$	45.5661	+	42.2791i	1.53691	+	1.42604i
$880$	10.9794	+	7.48562i	0.370115	+	0.252340i
$881$	17.7719			0.598751			0.299376	−	0.954135i	$-0.403222\pi$
$881$	17.7719			0.598751			0.299376	+	0.954135i	$0.403222\pi$
$882$	12.3926	+	5.81215i	0.417281	+	0.195705i
$883$	29.3209			0.986725			0.493363	−	0.869824i	$-0.335768\pi$
$883$	29.3209			0.986725			0.493363	+	0.869824i	$0.335768\pi$
$884$	−1.35466	−	0.923591i	−0.0455621	−	0.0310637i
$885$	−0.204998	−	0.190211i	−0.00689094	−	0.00639386i
$886$	24.1133	+	61.4396i	0.810101	+	2.06410i
$887$	−30.2007	+	9.31567i	−1.01404	+	0.312790i	−0.756862	−	0.653575i	$-0.773269\pi$
$887$	−30.2007	+	9.31567i	−1.01404	+	0.312790i	−0.257177	+	0.966364i	$0.582792\pi$
$888$	−12.0825	−	52.9370i	−0.405463	−	1.77645i
$889$	−2.83356	+	40.6044i	−0.0950344	+	1.36183i
$890$	1.37073	−	6.00556i	0.0459470	−	0.201307i
$891$	3.27638	+	43.7203i	0.109763	+	1.46468i
$892$	2.66589	+	0.822317i	0.0892604	+	0.0275332i
$893$	−4.97276	+	66.3569i	−0.166407	+	2.22055i
$894$	−8.54205	+	21.7648i	−0.285689	+	0.727924i
$895$	−12.3248	+	5.93532i	−0.411973	+	0.198396i
$896$	7.85854	−	35.2631i	0.262535	−	1.17806i
$897$	0.891421	+	0.429286i	0.0297637	+	0.0143334i
$898$	27.3307	−	25.3592i	0.912038	−	0.846248i
$899$	−0.634713	+	0.0956676i	−0.0211689	+	0.00319069i
$900$	1.49579	−	2.59078i	0.0498596	−	0.0863593i
$901$	−7.45273	−	12.9085i	−0.248286	−	0.430045i
$902$	1.73040	+	2.16985i	0.0576159	+	0.0722480i
$903$	12.1118	−	3.80412i	0.403054	−	0.126593i
$904$	−26.7043	+	33.4861i	−0.888172	+	1.11373i
$905$	5.80251	+	0.874587i	0.192882	+	0.0290723i
$906$	−43.4443	+	29.6198i	−1.44334	+	0.984053i
$907$	−5.06007	+	3.44990i	−0.168017	+	0.114552i	−0.644409	−	0.764681i	$-0.722897\pi$
$907$	−5.06007	+	3.44990i	−0.168017	+	0.114552i	0.476392	+	0.879233i	$0.341944\pi$
$908$	−4.96114	−	0.747771i	−0.164641	−	0.0248157i
$909$	4.41591	−	5.53737i	0.146466	−	0.183663i
$910$	2.47300	+	1.66755i	0.0819790	+	0.0552787i
$911$	−11.1190	−	13.9428i	−0.368388	−	0.461944i	0.562741	−	0.826633i	$-0.309747\pi$
$911$	−11.1190	−	13.9428i	−0.368388	−	0.461944i	−0.931129	+	0.364689i	$0.881175\pi$
$912$	−34.0382	−	58.9560i	−1.12712	−	1.95223i
$913$	−10.6101	+	18.3773i	−0.351144	+	0.608199i
$914$	−11.4720	+	1.72912i	−0.379458	+	0.0571942i
$915$	−12.0272	+	11.1596i	−0.397607	+	0.368925i
$916$	0.0745366	+	0.0358949i	0.00246276	+	0.00118600i
$917$	48.6384	−	0.249435i	1.60618	−	0.00823708i
$918$	−15.8424	+	7.62932i	−0.522879	+	0.251805i
$919$	−1.45968	+	3.71922i	−0.0481505	+	0.122686i	−0.952926	−	0.303204i	$-0.901944\pi$
$919$	−1.45968	+	3.71922i	−0.0481505	+	0.122686i	0.904775	+	0.425890i	$0.140039\pi$
$920$	0.0591131	−	0.788809i	0.00194890	−	0.0260063i
$921$	−56.4483	−	17.4120i	−1.86004	−	0.573745i
$922$	−1.37784	−	18.3859i	−0.0453766	−	0.605509i
$923$	0.429165	−	1.88029i	0.0141261	−	0.0618907i
$924$	−4.28104	−	10.7455i	−0.140836	−	0.353502i
$925$	11.3776	+	49.8486i	0.374094	+	1.63901i
$926$	−18.1336	+	5.59346i	−0.595906	+	0.183813i
$927$	−6.99727	−	17.8287i	−0.229820	−	0.585573i
$928$	−0.341490	−	0.316856i	−0.0112100	−	0.0104013i
$929$	22.2796	+	15.1900i	0.730970	+	0.498367i	0.870695	−	0.491823i	$-0.163669\pi$
$929$	22.2796	+	15.1900i	0.730970	+	0.498367i	−0.139725	+	0.990190i	$0.544622\pi$
$930$	−9.54346			−0.312942
$931$	−39.6992	+	27.6671i	−1.30109	+	0.906754i
$932$	−4.69687			−0.153851
$933$	45.5811	+	31.0767i	1.49226	+	1.01741i
$934$	44.5557	+	41.3416i	1.45791	+	1.35274i
$935$	−3.06548	−	7.81071i	−0.100252	−	0.255437i
$936$	−2.72424	+	0.840318i	−0.0890447	+	0.0274666i
$937$	5.11449	+	22.4081i	0.167083	+	0.732040i	0.987153	+	0.159776i	$0.0510773\pi$
$937$	5.11449	+	22.4081i	0.167083	+	0.732040i	−0.820070	+	0.572263i	$0.806066\pi$
$938$	22.5207	+	6.82043i	0.735327	+	0.222695i
$939$	2.80164	−	12.2748i	0.0914279	−	0.400572i
$940$	0.275710	+	3.67909i	0.00899266	+	0.119999i
$941$	13.0517	+	4.02591i	0.425473	+	0.131241i	0.500094	−	0.865971i	$-0.333299\pi$
$941$	13.0517	+	4.02591i	0.425473	+	0.131241i	−0.0746215	+	0.997212i	$0.523775\pi$
$942$	−0.194835	+	2.59989i	−0.00634807	+	0.0847091i
$943$	0.0780123	−	0.198772i	0.00254043	−	0.00647291i
$944$	0.830293	−	0.399848i	0.0270237	−	0.0130140i
$945$	6.13026	−	2.99100i	0.199418	−	0.0972974i
$946$	−13.1537	−	6.33447i	−0.427663	−	0.205952i
$947$	−4.77186	+	4.42764i	−0.155065	+	0.143879i	−0.753890	−	0.657001i	$-0.771825\pi$
$947$	−4.77186	+	4.42764i	−0.155065	+	0.143879i	0.598825	+	0.800880i	$0.295634\pi$
$948$	11.3562	−	1.71167i	0.368832	−	0.0555925i
$949$	−2.65457	+	4.59785i	−0.0861710	+	0.149253i
$950$	24.7986	+	42.9524i	0.804573	+	1.39356i
$951$	−7.73011	−	9.69326i	−0.250666	−	0.314325i
$952$	−13.5716	+	12.7227i	−0.439857	+	0.412345i
$953$	−17.6876	+	22.1795i	−0.572957	+	0.718466i	−0.980894	−	0.194545i	$-0.937677\pi$
$953$	−17.6876	+	22.1795i	−0.572957	+	0.718466i	0.407937	+	0.913010i	$0.366248\pi$
$954$	9.52836	+	1.43617i	0.308492	+	0.0464977i
$955$	7.58622	−	5.17220i	0.245484	−	0.167368i
$956$	−3.54328	+	2.41577i	−0.114598	+	0.0781316i
$957$	1.24323	+	0.187386i	0.0401878	+	0.00605733i
$958$	23.8678	−	29.9293i	0.771134	−	0.966971i
$959$	−3.24303	−	5.55115i	−0.104723	−	0.179256i
$960$	4.36469	+	5.47315i	0.140870	+	0.176645i
$961$	7.02207	+	12.1626i	0.226518	+	0.392342i
$962$	−9.05786	+	15.6887i	−0.292037	+	0.505823i
$963$	−21.1762	+	3.19180i	−0.682394	+	0.102854i
$964$	−5.15846	+	4.78635i	−0.166143	+	0.154158i
$965$	−8.48502	−	4.08617i	−0.273143	−	0.131539i
$966$	−2.58545	+	3.27638i	−0.0831854	+	0.105416i
$967$	−32.8819	+	15.8351i	−1.05741	+	0.509222i	−0.880029	−	0.474920i	$-0.842477\pi$
$967$	−32.8819	+	15.8351i	−1.05741	+	0.509222i	−0.177382	+	0.984142i	$0.556763\pi$
$968$	3.72974	−	9.50323i	0.119879	−	0.305445i
$969$	−3.21233	+	42.8655i	−0.103195	+	1.37704i
$970$	18.9640	+	5.84962i	0.608898	+	0.187820i
$971$	−2.80322	−	37.4064i	−0.0899596	−	1.20043i	−0.841321	−	0.540536i	$-0.818221\pi$
$971$	−2.80322	−	37.4064i	−0.0899596	−	1.20043i	0.751361	−	0.659891i	$-0.229398\pi$
$972$	1.45172	−	6.36041i	0.0465640	−	0.204010i
$973$	45.9690	−	31.6876i	1.47370	−	1.01586i
$974$	−2.37967	−	10.4260i	−0.0762496	−	0.334071i
$975$	8.84031	−	2.72688i	0.283117	−	0.0873299i
$976$	−19.7531	−	50.3300i	−0.632280	−	1.61102i
$977$	−7.02258	−	6.51600i	−0.224672	−	0.208465i	0.559803	−	0.828626i	$-0.310877\pi$
$977$	−7.02258	−	6.51600i	−0.224672	−	0.208465i	−0.784475	+	0.620161i	$0.787067\pi$
$978$	−0.765762	−	0.522088i	−0.0244864	−	0.0166945i
$979$	−21.4372			−0.685135
$980$	−1.94787	+	1.84490i	−0.0622225	+	0.0589331i
$981$	−0.573051			−0.0182961
$982$	22.4573	+	15.3111i	0.716640	+	0.488597i
$983$	−23.2099	−	21.5356i	−0.740280	−	0.686880i	0.216958	−	0.976181i	$-0.430387\pi$
$983$	−23.2099	−	21.5356i	−0.740280	−	0.686880i	−0.957238	+	0.289301i	$0.906577\pi$
$984$	0.774641	+	1.97375i	0.0246947	+	0.0629210i
$985$	−2.45490	+	0.757237i	−0.0782197	+	0.0241276i
$986$	0.167281	+	0.732905i	0.00532730	+	0.0233404i
$987$	−25.9465	+	45.4777i	−0.825887	+	1.44757i
$988$	−0.833790	+	3.65307i	−0.0265264	+	0.116220i
$989$	0.0839424	+	1.12013i	0.00266921	+	0.0356182i
$990$	5.18339	+	1.59887i	0.164739	+	0.0508153i
$991$	−2.72987	+	36.4276i	−0.0867172	+	1.15716i	0.768836	+	0.639446i	$0.220836\pi$
$991$	−2.72987	+	36.4276i	−0.0867172	+	1.15716i	−0.855553	+	0.517715i	$0.826783\pi$
$992$	4.49579	−	11.4551i	0.142741	−	0.363699i
$993$	−51.5852	+	24.8421i	−1.63701	+	0.788342i
$994$	7.34801	+	3.49231i	0.233065	+	0.110769i
$995$	−1.52287	−	0.733374i	−0.0482781	−	0.0232495i
$996$	4.41839	−	4.09967i	0.140002	−	0.129903i
$997$	44.4990	−	6.70714i	1.40930	−	0.212417i	0.600086	−	0.799936i	$-0.295133\pi$
$997$	44.4990	−	6.70714i	1.40930	−	0.212417i	0.809211	+	0.587518i	$0.199895\pi$
$998$	−16.1552	+	27.9816i	−0.511383	+	0.885741i
$999$	20.7142	+	35.8780i	0.655367	+	1.13513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.53.8	✓	324
49.37	even	21	inner	637.2.bl.a.625.8	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.53.8	✓	324	1.1	even	1	trivial
637.2.bl.a.625.8	yes	324	49.37	even	21	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31734 - 0.898146i) q^{2} +(-1.50703 - 1.39832i) q^{3} +(0.198032 + 0.504577i) q^{4} +(0.675664 - 0.208415i) q^{5} +(0.729374 + 3.19559i) q^{6} +(-1.94868 - 1.78960i) q^{7} +(-0.517257 + 2.26625i) q^{8} +(0.0916520 + 1.22301i) q^{9} +O(q^{10})\)	\(q+(-1.31734 - 0.898146i) q^{2} +(-1.50703 - 1.39832i) q^{3} +(0.198032 + 0.504577i) q^{4} +(0.675664 - 0.208415i) q^{5} +(0.729374 + 3.19559i) q^{6} +(-1.94868 - 1.78960i) q^{7} +(-0.517257 + 2.26625i) q^{8} +(0.0916520 + 1.22301i) q^{9} +(-1.07726 - 0.332292i) q^{10} +(-0.293184 + 3.91227i) q^{11} +(0.407120 - 1.03732i) q^{12} +(0.900969 - 0.433884i) q^{13} +(0.959745 + 4.10770i) q^{14} +(-1.30968 - 0.630707i) q^{15} +(3.51152 - 3.25822i) q^{16} +(-2.99095 + 0.450814i) q^{17} +(0.977706 - 1.69344i) q^{18} +(3.45636 + 5.98659i) q^{19} +(0.238964 + 0.299652i) q^{20} +(0.434284 + 5.42185i) q^{21} +(3.90001 - 4.89046i) q^{22} +(-0.475891 - 0.0717290i) q^{23} +(3.94847 - 2.69202i) q^{24} +(-3.71811 + 2.53496i) q^{25} +(-1.57657 - 0.237630i) q^{26} +(-2.27333 + 2.85067i) q^{27} +(0.517090 - 1.33765i) q^{28} +(0.0971907 + 0.121873i) q^{29} +(1.15882 + 2.00714i) q^{30} +(-2.05887 + 3.56607i) q^{31} +(-2.95508 + 0.445407i) q^{32} +(5.91245 - 5.48595i) q^{33} +(4.34499 + 2.09244i) q^{34} +(-1.68963 - 0.803034i) q^{35} +(-0.598953 + 0.288441i) q^{36} +(4.15109 - 10.5768i) q^{37} +(0.823638 - 10.9907i) q^{38} +(-1.96450 - 0.605967i) q^{39} +(0.122828 + 1.63903i) q^{40} +(-0.0987303 + 0.432565i) q^{41} +(4.29752 - 7.53246i) q^{42} +(-0.519363 - 2.27548i) q^{43} +(-2.03210 + 0.626820i) q^{44} +(0.316820 + 0.807243i) q^{45} +(0.562486 + 0.521911i) q^{46} +(7.95351 + 5.42261i) q^{47} -9.84800 q^{48} +(0.594678 + 6.97469i) q^{49} +7.17477 q^{50} +(5.13784 + 3.50292i) q^{51} +(0.397348 + 0.368685i) q^{52} +(1.80035 + 4.58721i) q^{53} +(5.55506 - 1.71351i) q^{54} +(0.617281 + 2.70448i) q^{55} +(5.06364 - 3.49051i) q^{56} +(3.16233 - 13.8551i) q^{57} +(-0.0185730 - 0.247840i) q^{58} +(0.183834 + 0.0567051i) q^{59} +(0.0588825 - 0.785733i) q^{60} +(4.12357 - 10.5067i) q^{61} +(5.91509 - 2.84856i) q^{62} +(2.01010 - 2.54727i) q^{63} +(-4.33890 - 2.08950i) q^{64} +(0.518324 - 0.480935i) q^{65} +(-12.7159 + 1.91661i) q^{66} +(2.78911 - 4.83089i) q^{67} +(-0.819774 - 1.41989i) q^{68} +(0.616882 + 0.773546i) q^{69} +(1.50457 + 2.57540i) q^{70} +(1.20249 - 1.50788i) q^{71} +(-2.81906 - 0.424905i) q^{72} +(-4.38662 + 2.99075i) q^{73} +(-14.9679 + 10.2050i) q^{74} +(9.14800 + 1.37884i) q^{75} +(-2.33623 + 2.92954i) q^{76} +(7.57271 - 7.09907i) q^{77} +(2.04366 + 2.56267i) q^{78} +(5.15296 + 8.92519i) q^{79} +(1.69355 - 2.93331i) q^{80} +(11.0503 - 1.66557i) q^{81} +(0.518568 - 0.481161i) q^{82} +(4.87321 + 2.34681i) q^{83} +(-2.64974 + 1.29283i) q^{84} +(-1.92692 + 0.927957i) q^{85} +(-1.35954 + 3.46404i) q^{86} +(0.0239485 - 0.319571i) q^{87} +(-8.71454 - 2.68808i) q^{88} +(0.408336 + 5.44887i) q^{89} +(0.307664 - 1.34796i) q^{90} +(-2.53217 - 0.766873i) q^{91} +(-0.0580488 - 0.254328i) q^{92} +(8.08930 - 2.49522i) q^{93} +(-5.60717 - 14.2868i) q^{94} +(3.58303 + 3.32457i) q^{95} +(5.07622 + 3.46091i) q^{96} -17.6039 q^{97} +(5.48090 - 9.72214i) q^{98} -4.81162 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

Modular forms

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Database

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