LMFDB - Embedded newform 121.2.e.a.12.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,2,Mod(12,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([18]))

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

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

chi := DirichletCharacter("121.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	121.e (of order $11$, degree $10$, 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:	$0.966189864457$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			12.1
Character	$\chi$	$=$	121.12
Dual form			121.2.e.a.111.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.28929 + 1.47124i) q^{2} -1.98337 q^{3} +(2.24548 - 4.91691i) q^{4} +(0.00109106 - 0.00758846i) q^{5} +(4.54050 - 2.91800i) q^{6} +(1.07261 - 1.23786i) q^{7} +(1.31883 + 9.17268i) q^{8} +0.933746 q^{9} +O(q^{10})$	\(q+(-2.28929 + 1.47124i) q^{2} -1.98337 q^{3} +(2.24548 - 4.91691i) q^{4} +(0.00109106 - 0.00758846i) q^{5} +(4.54050 - 2.91800i) q^{6} +(1.07261 - 1.23786i) q^{7} +(1.31883 + 9.17268i) q^{8} +0.933746 q^{9} +(0.00866667 + 0.0189774i) q^{10} +(3.26984 + 0.555122i) q^{11} +(-4.45360 + 9.75203i) q^{12} +(-0.784057 + 1.71684i) q^{13} +(-0.634332 + 4.41187i) q^{14} +(-0.00216396 + 0.0150507i) q^{15} +(-9.43482 - 10.8884i) q^{16} +(5.32085 + 1.56234i) q^{17} +(-2.13761 + 1.37376i) q^{18} +(7.08022 - 2.07894i) q^{19} +(-0.0348618 - 0.0224043i) q^{20} +(-2.12738 + 2.45512i) q^{21} +(-8.30232 + 3.53987i) q^{22} +(-4.02142 - 4.64097i) q^{23} +(-2.61573 - 18.1928i) q^{24} +(4.79741 + 1.40865i) q^{25} +(-0.730952 - 5.08389i) q^{26} +4.09814 q^{27} +(-3.67791 - 8.05349i) q^{28} +(0.687061 - 0.201739i) q^{29} +(-0.0171892 - 0.0376391i) q^{30} +(-2.57634 - 5.64140i) q^{31} +(19.8351 + 5.82412i) q^{32} +(-6.48529 - 1.10101i) q^{33} +(-14.4795 + 4.25158i) q^{34} +(-0.00822315 - 0.00949002i) q^{35} +(2.09670 - 4.59114i) q^{36} +(2.37491 + 5.20034i) q^{37} +(-13.1501 + 15.1760i) q^{38} +(1.55507 - 3.40513i) q^{39} +0.0710454 q^{40} +(-2.42919 + 1.56115i) q^{41} +(1.25811 - 8.75036i) q^{42} +(-0.101783 - 0.707916i) q^{43} +(10.0718 - 14.8310i) q^{44} +(0.00101877 - 0.00708569i) q^{45} +(16.0341 + 4.70805i) q^{46} +(-5.27039 - 3.38707i) q^{47} +(18.7127 + 21.5956i) q^{48} +(0.614405 + 4.27328i) q^{49} +(-13.0551 + 3.83332i) q^{50} +(-10.5532 - 3.09870i) q^{51} +(6.68098 + 7.71027i) q^{52} +(0.518272 - 0.598117i) q^{53} +(-9.38183 + 6.02934i) q^{54} +(0.00778009 - 0.0242074i) q^{55} +(12.7690 + 8.20617i) q^{56} +(-14.0427 + 4.12330i) q^{57} +(-1.27608 + 1.47267i) q^{58} +(-1.52057 - 0.977210i) q^{59} +(0.0691437 + 0.0444360i) q^{60} +(2.61318 + 1.67939i) q^{61} +(14.1978 + 9.12439i) q^{62} +(1.00154 - 1.15584i) q^{63} +(-26.3295 + 7.73103i) q^{64} +(0.0121728 + 0.00782295i) q^{65} +(16.4665 - 7.02086i) q^{66} +(7.42985 - 4.77488i) q^{67} +(19.6297 - 22.6539i) q^{68} +(7.97595 + 9.20474i) q^{69} +(0.0327872 + 0.00962719i) q^{70} +(3.92323 - 1.15196i) q^{71} +(1.23145 + 8.56495i) q^{72} +(-7.48365 - 8.63660i) q^{73} +(-13.0878 - 8.41101i) q^{74} +(-9.51502 - 2.79386i) q^{75} +(5.67651 - 39.4810i) q^{76} +(4.19442 - 3.45216i) q^{77} +(1.44975 + 10.0832i) q^{78} +(-1.95144 + 13.5726i) q^{79} +(-0.0929198 + 0.0597159i) q^{80} -10.9294 q^{81} +(3.26430 - 7.14783i) q^{82} +(3.82759 - 4.41727i) q^{83} +(7.29464 + 15.9730i) q^{84} +(0.0176611 - 0.0386724i) q^{85} +(1.27452 + 1.47088i) q^{86} +(-1.36270 + 0.400123i) q^{87} +(-0.779588 + 30.7253i) q^{88} +(-1.80100 - 0.528820i) q^{89} +(0.00809247 + 0.0177200i) q^{90} +(1.28422 + 2.81205i) q^{91} +(-31.8492 + 9.35177i) q^{92} +(5.10983 + 11.1890i) q^{93} +17.0486 q^{94} +(-0.00805104 - 0.0559962i) q^{95} +(-39.3404 - 11.5514i) q^{96} +(-0.709923 - 4.93763i) q^{97} +(-7.69355 - 8.87883i) q^{98} +(3.05320 + 0.518343i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 6 q^{2} - 18 q^{3} - 16 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} + 4 q^{8} + 70 q^{9}+O(q^{10}) $ 100 * q - 6 * q^2 - 18 * q^3 - 16 * q^4 - 7 * q^5 - 23 * q^6 - q^7 + 4 * q^8 + 70 * q^9	\( 100 q - 6 q^{2} - 18 q^{3} - 16 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} + 4 q^{8} + 70 q^{9} - 13 q^{10} - 12 q^{11} - 51 q^{12} - 34 q^{13} - 17 q^{14} - 46 q^{15} + 10 q^{16} + 9 q^{17} - 31 q^{18} + 9 q^{19} + 21 q^{20} - 14 q^{21} - 20 q^{22} - 11 q^{23} - 72 q^{24} + 11 q^{25} + 33 q^{26} - 60 q^{27} + 49 q^{28} + 19 q^{29} + 26 q^{30} - 13 q^{31} + 44 q^{32} + q^{33} + 31 q^{34} + 39 q^{35} - 17 q^{36} - 16 q^{37} - 29 q^{38} + 16 q^{39} + 2 q^{40} + 39 q^{41} + 42 q^{42} + 39 q^{43} + 53 q^{44} - 33 q^{45} + 59 q^{46} + 21 q^{47} + 56 q^{48} - 11 q^{49} - 58 q^{50} - 139 q^{51} - 75 q^{52} - 73 q^{53} - 156 q^{54} - 34 q^{55} + 10 q^{56} - 41 q^{57} - 38 q^{58} + 33 q^{59} + 100 q^{60} + 39 q^{61} + 44 q^{62} - 76 q^{63} - 16 q^{64} + 36 q^{65} + 75 q^{66} - 4 q^{67} + 119 q^{68} + 32 q^{69} + 61 q^{70} + 5 q^{71} + 63 q^{72} + 37 q^{73} + 109 q^{74} + 58 q^{75} - 91 q^{76} - 53 q^{77} - 24 q^{78} - 9 q^{79} - 36 q^{80} + 28 q^{81} + 33 q^{82} + 79 q^{83} + 176 q^{84} - 11 q^{85} + 85 q^{86} + 76 q^{87} + 33 q^{88} - 48 q^{89} - 89 q^{90} - 14 q^{91} - 113 q^{92} + 31 q^{93} - 38 q^{94} + 21 q^{95} + 84 q^{96} + 40 q^{97} - 22 q^{98} - 53 q^{99}+O(q^{100}) \) 100 * q - 6 * q^2 - 18 * q^3 - 16 * q^4 - 7 * q^5 - 23 * q^6 - q^7 + 4 * q^8 + 70 * q^9 - 13 * q^10 - 12 * q^11 - 51 * q^12 - 34 * q^13 - 17 * q^14 - 46 * q^15 + 10 * q^16 + 9 * q^17 - 31 * q^18 + 9 * q^19 + 21 * q^20 - 14 * q^21 - 20 * q^22 - 11 * q^23 - 72 * q^24 + 11 * q^25 + 33 * q^26 - 60 * q^27 + 49 * q^28 + 19 * q^29 + 26 * q^30 - 13 * q^31 + 44 * q^32 + q^33 + 31 * q^34 + 39 * q^35 - 17 * q^36 - 16 * q^37 - 29 * q^38 + 16 * q^39 + 2 * q^40 + 39 * q^41 + 42 * q^42 + 39 * q^43 + 53 * q^44 - 33 * q^45 + 59 * q^46 + 21 * q^47 + 56 * q^48 - 11 * q^49 - 58 * q^50 - 139 * q^51 - 75 * q^52 - 73 * q^53 - 156 * q^54 - 34 * q^55 + 10 * q^56 - 41 * q^57 - 38 * q^58 + 33 * q^59 + 100 * q^60 + 39 * q^61 + 44 * q^62 - 76 * q^63 - 16 * q^64 + 36 * q^65 + 75 * q^66 - 4 * q^67 + 119 * q^68 + 32 * q^69 + 61 * q^70 + 5 * q^71 + 63 * q^72 + 37 * q^73 + 109 * q^74 + 58 * q^75 - 91 * q^76 - 53 * q^77 - 24 * q^78 - 9 * q^79 - 36 * q^80 + 28 * q^81 + 33 * q^82 + 79 * q^83 + 176 * q^84 - 11 * q^85 + 85 * q^86 + 76 * q^87 + 33 * q^88 - 48 * q^89 - 89 * q^90 - 14 * q^91 - 113 * q^92 + 31 * q^93 - 38 * q^94 + 21 * q^95 + 84 * q^96 + 40 * q^97 - 22 * q^98 - 53 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−2.28929	+	1.47124i	−1.61877	+	1.04032i	−0.661990	+	0.749512i	$0.730288\pi$
$2$	−2.28929	+	1.47124i	−1.61877	+	1.04032i	−0.956781	+	0.290809i	$0.906076\pi$
$3$	−1.98337			−1.14510			−0.572549	−	0.819871i	$-0.694045\pi$
$3$	−1.98337			−1.14510			−0.572549	+	0.819871i	$0.694045\pi$
$4$	2.24548	−	4.91691i	1.12274	−	2.45845i
$5$	0.00109106	−	0.00758846i	0.000487935	−	0.00339366i	−0.989576	−	0.144011i	$-0.954000\pi$
$5$	0.00109106	−	0.00758846i	0.000487935	−	0.00339366i	0.990064	+	0.140618i	$0.0449089\pi$
$6$	4.54050	−	2.91800i	1.85365	−	1.19127i
$7$	1.07261	−	1.23786i	0.405408	−	0.467866i	−0.515929	−	0.856632i	$-0.672553\pi$
$7$	1.07261	−	1.23786i	0.405408	−	0.467866i	0.921337	+	0.388766i	$0.127098\pi$
$8$	1.31883	+	9.17268i	0.466277	+	3.24303i
$9$	0.933746			0.311249
$10$	0.00866667	+	0.0189774i	0.00274064	+	0.00600117i
$11$	3.26984	+	0.555122i	0.985893	+	0.167376i
$11$	3.26984	+	0.555122i	0.985893	+	0.167376i
$12$	−4.45360	+	9.75203i	−1.28564	+	2.81517i
$13$	−0.784057	+	1.71684i	−0.217458	+	0.476167i	−0.986651	−	0.162850i	$-0.947931\pi$
$13$	−0.784057	+	1.71684i	−0.217458	+	0.476167i	0.769193	+	0.639017i	$0.220659\pi$
$14$	−0.634332	+	4.41187i	−0.169532	+	1.17912i
$15$	−0.00216396	+	0.0150507i	−0.000558733	+	0.00388607i
$16$	−9.43482	−	10.8884i	−2.35871	−	2.72209i
$17$	5.32085	+	1.56234i	1.29050	+	0.378924i	0.853760	−	0.520666i	$-0.174316\pi$
$17$	5.32085	+	1.56234i	1.29050	+	0.378924i	0.436735	+	0.899590i	$0.356135\pi$
$18$	−2.13761	+	1.37376i	−0.503840	+	0.323798i
$19$	7.08022	−	2.07894i	1.62431	−	0.476942i	0.662141	−	0.749379i	$-0.269648\pi$
$19$	7.08022	−	2.07894i	1.62431	−	0.476942i	0.962173	+	0.272438i	$0.0878299\pi$
$20$	−0.0348618	−	0.0224043i	−0.00779533	−	0.00500976i
$21$	−2.12738	+	2.45512i	−0.464232	+	0.535752i
$22$	−8.30232	+	3.53987i	−1.77006	+	0.754703i
$23$	−4.02142	−	4.64097i	−0.838524	−	0.967708i	0.161292	−	0.986907i	$-0.448434\pi$
$23$	−4.02142	−	4.64097i	−0.838524	−	0.967708i	−0.999816	+	0.0191986i	$0.993889\pi$
$24$	−2.61573	−	18.1928i	−0.533933	−	3.71359i
$25$	4.79741	+	1.40865i	0.959482	+	0.281729i
$26$	−0.730952	−	5.08389i	−0.143352	−	0.997032i
$27$	4.09814			0.788688
$28$	−3.67791	−	8.05349i	−0.695059	−	1.52197i
$29$	0.687061	−	0.201739i	0.127584	−	0.0374621i	−0.217317	−	0.976101i	$-0.569731\pi$
$29$	0.687061	−	0.201739i	0.127584	−	0.0374621i	0.344901	+	0.938639i	$0.387912\pi$
$30$	−0.0171892	−	0.0376391i	−0.00313830	−	0.00687193i
$31$	−2.57634	−	5.64140i	−0.462725	−	1.01323i	−0.986858	−	0.161589i	$-0.948338\pi$
$31$	−2.57634	−	5.64140i	−0.462725	−	1.01323i	0.524134	−	0.851636i	$-0.324389\pi$
$32$	19.8351	+	5.82412i	3.50639	+	1.02957i
$33$	−6.48529	−	1.10101i	−1.12894	−	0.191661i
$34$	−14.4795	+	4.25158i	−2.48322	+	0.729139i
$35$	−0.00822315	−	0.00949002i	−0.00138997	−	0.00160411i
$36$	2.09670	−	4.59114i	0.349451	−	0.765190i
$37$	2.37491	+	5.20034i	0.390433	+	0.854930i	0.998151	+	0.0607771i	$0.0193579\pi$
$37$	2.37491	+	5.20034i	0.390433	+	0.854930i	−0.607718	+	0.794153i	$0.707915\pi$
$38$	−13.1501	+	15.1760i	−2.13322	+	2.46187i
$39$	1.55507	−	3.40513i	0.249011	−	0.545258i
$40$	0.0710454			0.0112333
$41$	−2.42919	+	1.56115i	−0.379376	+	0.243810i	−0.716406	−	0.697684i	$-0.754214\pi$
$41$	−2.42919	+	1.56115i	−0.379376	+	0.243810i	0.337030	+	0.941494i	$0.390578\pi$
$42$	1.25811	−	8.75036i	0.194131	−	1.35021i
$43$	−0.101783	−	0.707916i	−0.0155218	−	0.107956i	0.980588	−	0.196081i	$-0.0628216\pi$
$43$	−0.101783	−	0.707916i	−0.0155218	−	0.107956i	−0.996109	+	0.0881250i	$0.971913\pi$
$44$	10.0718	−	14.8310i	1.51838	−	2.23585i
$45$	0.00101877	−	0.00708569i	0.000151869	−	0.00105627i
$46$	16.0341	+	4.70805i	2.36411	+	0.694164i
$47$	−5.27039	−	3.38707i	−0.768765	−	0.494055i	0.0965228	−	0.995331i	$-0.469228\pi$
$47$	−5.27039	−	3.38707i	−0.768765	−	0.494055i	−0.865288	+	0.501276i	$0.832864\pi$
$48$	18.7127	+	21.5956i	2.70095	+	3.11706i
$49$	0.614405	+	4.27328i	0.0877721	+	0.610468i
$50$	−13.0551	+	3.83332i	−1.84627	+	0.542114i
$51$	−10.5532	−	3.09870i	−1.47774	−	0.433905i
$52$	6.68098	+	7.71027i	0.926486	+	1.06922i
$53$	0.518272	−	0.598117i	0.0711901	−	0.0821577i	−0.719037	−	0.694971i	$-0.755417\pi$
$53$	0.518272	−	0.598117i	0.0711901	−	0.0821577i	0.790227	+	0.612814i	$0.209962\pi$
$54$	−9.38183	+	6.02934i	−1.27671	+	0.820489i
$55$	0.00778009	−	0.0242074i	0.00104907	−	0.00326412i
$56$	12.7690	+	8.20617i	1.70634	+	1.09660i
$57$	−14.0427	+	4.12330i	−1.86000	+	0.546145i
$58$	−1.27608	+	1.47267i	−0.167557	+	0.193371i
$59$	−1.52057	−	0.977210i	−0.197961	−	0.127222i	0.437905	−	0.899021i	$-0.355721\pi$
$59$	−1.52057	−	0.977210i	−0.197961	−	0.127222i	−0.635866	+	0.771799i	$0.719357\pi$
$60$	0.0691437	+	0.0444360i	0.00892642	+	0.00573666i
$61$	2.61318	+	1.67939i	0.334583	+	0.215024i	0.697135	−	0.716940i	$-0.254458\pi$
$61$	2.61318	+	1.67939i	0.334583	+	0.215024i	−0.362551	+	0.931964i	$0.618094\pi$
$62$	14.1978	+	9.12439i	1.80313	+	1.15880i
$63$	1.00154	−	1.15584i	0.126183	−	0.145623i
$64$	−26.3295	+	7.73103i	−3.29119	+	0.966379i
$65$	0.0121728	+	0.00782295i	0.00150984	+	0.000970318i
$66$	16.4665	−	7.02086i	2.02689	−	0.864208i
$67$	7.42985	−	4.77488i	0.907701	−	0.583344i	−0.00136360	−	0.999999i	$-0.500434\pi$
$67$	7.42985	−	4.77488i	0.907701	−	0.583344i	0.909065	+	0.416655i	$0.136798\pi$
$68$	19.6297	−	22.6539i	2.38045	−	2.74719i
$69$	7.97595	+	9.20474i	0.960192	+	1.10812i
$70$	0.0327872	+	0.00962719i	0.00391882	+	0.00115067i
$71$	3.92323	−	1.15196i	0.465601	−	0.136713i	−0.0405135	−	0.999179i	$-0.512899\pi$
$71$	3.92323	−	1.15196i	0.465601	−	0.136713i	0.506115	+	0.862466i	$0.331081\pi$
$72$	1.23145	+	8.56495i	0.145128	+	1.00939i
$73$	−7.48365	−	8.63660i	−0.875896	−	1.01084i	−0.999828	−	0.0185467i	$-0.994096\pi$
$73$	−7.48365	−	8.63660i	−0.875896	−	1.01084i	0.123932	−	0.992291i	$-0.460449\pi$
$74$	−13.0878	−	8.41101i	−1.52142	−	0.977760i
$75$	−9.51502	−	2.79386i	−1.09870	−	0.322607i
$76$	5.67651	−	39.4810i	0.651140	−	4.52878i
$77$	4.19442	−	3.45216i	0.477998	−	0.393410i
$78$	1.44975	+	10.0832i	0.164152	+	1.14170i
$79$	−1.95144	+	13.5726i	−0.219555	+	1.52704i	0.520133	+	0.854085i	$0.325882\pi$
$79$	−1.95144	+	13.5726i	−0.219555	+	1.52704i	−0.739688	+	0.672950i	$0.765027\pi$
$80$	−0.0929198	+	0.0597159i	−0.0103887	+	0.00667644i
$81$	−10.9294			−1.21437
$82$	3.26430	−	7.14783i	0.360482	−	0.789346i
$83$	3.82759	−	4.41727i	0.420133	−	0.484859i	−0.505745	−	0.862683i	$-0.668782\pi$
$83$	3.82759	−	4.41727i	0.420133	−	0.484859i	0.925877	+	0.377824i	$0.123328\pi$
$84$	7.29464	+	15.9730i	0.795911	+	1.74280i
$85$	0.0176611	−	0.0386724i	0.00191562	−	0.00419461i
$86$	1.27452	+	1.47088i	0.137435	+	0.158609i
$87$	−1.36270	+	0.400123i	−0.146096	+	0.0428977i
$88$	−0.779588	+	30.7253i	−0.0831044	+	3.27533i
$89$	−1.80100	−	0.528820i	−0.190905	−	0.0560548i	0.184882	−	0.982761i	$-0.440810\pi$
$89$	−1.80100	−	0.528820i	−0.190905	−	0.0560548i	−0.375788	+	0.926706i	$0.622628\pi$
$90$	0.00809247	+	0.0177200i	0.000853021	+	0.00186786i
$91$	1.28422	+	2.81205i	0.134623	+	0.294783i
$92$	−31.8492	+	9.35177i	−3.32051	+	0.974989i
$93$	5.10983	+	11.1890i	0.529865	+	1.16024i
$94$	17.0486			1.75843
$95$	−0.00805104	−	0.0559962i	−0.000826019	−	0.00574509i
$96$	−39.3404	−	11.5514i	−4.01516	−	1.17896i
$97$	−0.709923	−	4.93763i	−0.0720818	−	0.501340i	−0.993596	−	0.112994i	$-0.963956\pi$
$97$	−0.709923	−	4.93763i	−0.0720818	−	0.501340i	0.921514	−	0.388346i	$-0.126953\pi$
$98$	−7.69355	−	8.87883i	−0.777166	−	0.896897i
$99$	3.05320	+	0.518343i	0.306858	+	0.0520954i
$100$	17.6986	−	20.4253i	1.76986	−	2.04253i
$101$	1.00940	+	0.648700i	0.100439	+	0.0645480i	0.589896	−	0.807479i	$-0.299169\pi$
$101$	1.00940	+	0.648700i	0.100439	+	0.0645480i	−0.489457	+	0.872027i	$0.662805\pi$
$102$	28.7182	−	8.43244i	2.84353	−	0.834936i
$103$	−2.64020	+	1.69676i	−0.260147	+	0.167186i	−0.664213	−	0.747544i	$-0.731233\pi$
$103$	−2.64020	+	1.69676i	−0.260147	+	0.167186i	0.404066	+	0.914730i	$0.367597\pi$
$104$	−16.7821	−	4.92767i	−1.64562	−	0.483198i
$105$	0.0163095	+	0.0188222i	0.00159165	+	0.00183686i
$106$	−0.306501	+	2.13176i	−0.0297700	+	0.207055i
$107$	−2.21585	+	15.4116i	−0.214214	+	1.48989i	0.544661	+	0.838657i	$0.316658\pi$
$107$	−2.21585	+	15.4116i	−0.214214	+	1.48989i	−0.758875	+	0.651236i	$0.774251\pi$
$108$	9.20228	−	20.1502i	0.885490	−	1.93895i
$109$	−6.01811	+	13.1778i	−0.576430	+	1.26221i	0.366872	+	0.930272i	$0.380429\pi$
$109$	−6.01811	+	13.1778i	−0.576430	+	1.26221i	−0.943302	+	0.331935i	$0.892298\pi$
$110$	0.0178039	+	0.0668640i	0.00169753	+	0.00637523i
$111$	−4.71033	−	10.3142i	−0.447084	−	0.978978i
$112$	−23.5981			−2.22981
$113$	−1.16016	−	8.06912i	−0.109139	−	0.759079i	−0.968734	−	0.248103i	$-0.920193\pi$
$113$	−1.16016	−	8.06912i	−0.109139	−	0.759079i	0.859595	−	0.510976i	$-0.170716\pi$
$114$	26.0814	−	30.0995i	2.44275	−	2.81908i
$115$	−0.0396054	+	0.0254528i	−0.00369322	+	0.00237349i
$116$	0.550846	−	3.83122i	0.0511448	−	0.355720i
$117$	−0.732109	+	1.60310i	−0.0676835	+	0.148206i
$118$	4.91873			0.452805
$119$	7.64115	−	4.91067i	0.700463	−	0.450160i
$120$	−0.140909			−0.0128632
$121$	10.3837	+	3.63032i	0.943971	+	0.330029i
$122$	−8.45310			−0.765308
$123$	4.81798	−	3.09633i	0.434422	−	0.279186i
$124$	−33.5233			−3.01049
$125$	0.0318476	−	0.0697364i	0.00284853	−	0.00623742i
$126$	−0.592304	+	4.11957i	−0.0527667	+	0.367000i
$127$	−0.701716	+	0.450966i	−0.0622672	+	0.0400167i	−0.571404	−	0.820669i	$-0.693601\pi$
$127$	−0.701716	+	0.450966i	−0.0622672	+	0.0400167i	0.509137	+	0.860686i	$0.329965\pi$
$128$	21.8264	−	25.1890i	1.92920	−	2.22641i
$129$	0.201873	+	1.40406i	0.0177739	+	0.123620i
$130$	−0.0393764			−0.00345353
$131$	0.270701	+	0.592752i	0.0236513	+	0.0517890i	0.921089	−	0.389352i	$-0.127301\pi$
$131$	0.270701	+	0.592752i	0.0236513	+	0.0517890i	−0.897438	+	0.441141i	$0.854574\pi$
$132$	−19.9761	+	29.4153i	−1.73870	+	2.56027i
$133$	5.02088	−	10.9942i	0.435365	−	0.953317i
$134$	−9.98411	+	21.8621i	−0.862495	+	1.88860i
$135$	0.00447130	−	0.0310986i	0.000384828	−	0.00267654i
$136$	−7.31356	+	50.8669i	−0.627132	+	4.36180i
$137$	−1.44632	−	1.66915i	−0.123568	−	0.142605i	0.690595	−	0.723242i	$-0.257349\pi$
$137$	−1.44632	−	1.66915i	−0.123568	−	0.142605i	−0.814162	+	0.580637i	$0.802803\pi$
$138$	−31.8016	−	9.33779i	−2.70713	−	0.794886i
$139$	−0.221914	+	0.142615i	−0.0188225	+	0.0120965i	−0.550018	−	0.835153i	$-0.685379\pi$
$139$	−0.221914	+	0.142615i	−0.0188225	+	0.0120965i	0.531196	+	0.847249i	$0.321743\pi$
$140$	−0.0651264	+	0.0191228i	−0.00550418	+	0.00161617i
$141$	10.4531	+	6.71781i	0.880311	+	0.565741i
$142$	−7.28659	+	8.40917i	−0.611477	+	0.705682i
$143$	−3.51680	+	5.17856i	−0.294089	+	0.433053i
$144$	−8.80972	−	10.1670i	−0.734143	−	0.847247i
$145$	−0.000781269	−	0.00543384i	−6.48809e−5	−	0.000451256i
$146$	29.8387	+	8.76144i	2.46947	+	0.725102i
$147$	−1.21859	−	8.47548i	−0.100508	−	0.699046i
$148$	30.9024			2.54016
$149$	−0.166868	−	0.365389i	−0.0136703	−	0.0299338i	0.902674	−	0.430326i	$-0.141601\pi$
$149$	−0.166868	−	0.365389i	−0.0136703	−	0.0299338i	−0.916344	+	0.400392i	$0.868874\pi$
$150$	25.8931	−	7.60289i	2.11416	−	0.620773i
$151$	4.17486	+	9.14166i	0.339745	+	0.743938i	0.999975	−	0.00712610i	$-0.00226833\pi$
$151$	4.17486	+	9.14166i	0.339745	+	0.743938i	−0.660230	+	0.751064i	$0.729541\pi$
$152$	28.4071	+	62.2028i	2.30412	+	5.04531i
$153$	4.96832	+	1.45883i	0.401665	+	0.117939i
$154$	−4.52329	+	14.0740i	−0.364497	+	1.13411i
$155$	−0.0456204	+	0.0133954i	−0.00366432	+	0.00107594i
$156$	−13.2508	−	15.2923i	−1.06092	−	1.22436i
$157$	8.45278	−	18.5090i	0.674606	−	1.47718i	−0.193654	−	0.981070i	$-0.562034\pi$
$157$	8.45278	−	18.5090i	0.674606	−	1.47718i	0.868260	−	0.496110i	$-0.165239\pi$
$158$	−15.5011	−	33.9426i	−1.23320	−	2.70033i
$159$	−1.02792	+	1.18629i	−0.0815196	+	0.0940786i
$160$	0.0658373	−	0.144164i	0.00520490	−	0.0113971i
$161$	−10.0583			−0.792702
$162$	25.0205	−	16.0797i	1.96579	−	1.26334i
$163$	−3.08035	+	21.4243i	−0.241272	+	1.67808i	0.404491	+	0.914542i	$0.367449\pi$
$163$	−3.08035	+	21.4243i	−0.241272	+	1.67808i	−0.645762	+	0.763538i	$0.723460\pi$
$164$	2.22132	+	15.4496i	0.173456	+	1.20641i
$165$	−0.0154308	+	0.0480121i	−0.00120128	+	0.00373773i
$166$	−2.26360	+	15.7437i	−0.175690	+	1.22195i
$167$	−10.9201	−	3.20644i	−0.845024	−	0.248122i	−0.169565	−	0.985519i	$-0.554236\pi$
$167$	−10.9201	−	3.20644i	−0.845024	−	0.248122i	−0.675459	+	0.737397i	$0.736055\pi$
$168$	−25.3257	−	16.2758i	−1.95392	−	1.25571i
$169$	6.18038	+	7.13254i	0.475414	+	0.548657i
$170$	0.0164649	+	0.114516i	0.00126280	+	0.00878298i
$171$	6.61113	−	1.94120i	0.505565	−	0.148447i
$172$	−3.70931	−	1.08915i	−0.282832	−	0.0830470i
$173$	−0.312091	−	0.360172i	−0.0237278	−	0.0273834i	0.743762	−	0.668445i	$-0.233040\pi$
$173$	−0.312091	−	0.360172i	−0.0237278	−	0.0273834i	−0.767489	+	0.641062i	$0.778494\pi$
$174$	2.53093	−	2.92084i	0.191869	−	0.221429i
$175$	6.88945	−	4.42758i	0.520793	−	0.334693i
$176$	−24.8060	−	40.8407i	−1.86982	−	3.07848i
$177$	3.01585	+	1.93817i	0.226685	+	0.145681i
$178$	4.90102	−	1.43907i	0.367347	−	0.107863i
$179$	11.1009	−	12.8112i	0.829723	−	0.957552i	−0.169887	−	0.985464i	$-0.554340\pi$
$179$	11.1009	−	12.8112i	0.829723	−	0.957552i	0.999610	+	0.0279118i	$0.00888577\pi$
$180$	−0.0325520	−	0.0209199i	−0.00242629	−	0.00155928i
$181$	−10.6312	−	6.83229i	−0.790214	−	0.507840i	0.0821947	−	0.996616i	$-0.473807\pi$
$181$	−10.6312	−	6.83229i	−0.790214	−	0.507840i	−0.872409	+	0.488776i	$0.837443\pi$
$182$	−7.07715	−	4.54821i	−0.524593	−	0.337136i
$183$	−5.18289	−	3.33084i	−0.383131	−	0.246223i
$184$	37.2665	−	43.0078i	2.74732	−	3.17058i
$185$	0.0420537	−	0.0123481i	0.00309185	−	0.000907849i
$186$	−28.1595	−	18.0970i	−2.06475	−	1.32694i
$187$	16.5310	+	8.06233i	1.20887	+	0.589576i
$188$	−28.4884	+	18.3084i	−2.07773	+	1.33528i
$189$	4.39570	−	5.07291i	0.319740	−	0.369000i
$190$	0.100815	+	0.116346i	0.00731387	+	0.00844066i
$191$	−11.1070	−	3.26132i	−0.803678	−	0.235981i	−0.146004	−	0.989284i	$-0.546641\pi$
$191$	−11.1070	−	3.26132i	−0.803678	−	0.235981i	−0.657674	+	0.753303i	$0.728459\pi$
$192$	52.2210	−	15.3335i	3.76873	−	1.10660i
$193$	−1.99173	−	13.8528i	−0.143368	−	0.997148i	−0.926769	−	0.375631i	$-0.877426\pi$
$193$	−1.99173	−	13.8528i	−0.143368	−	0.997148i	0.783401	−	0.621517i	$-0.213483\pi$
$194$	8.88963	+	10.2592i	0.638239	+	0.736567i
$195$	−0.0241430	−	0.0155158i	−0.00172892	−	0.00111111i
$196$	22.3909	+	6.57457i	1.59935	+	0.469612i
$197$	−2.16792	+	15.0782i	−0.154458	+	1.07428i	0.754173	+	0.656676i	$0.228038\pi$
$197$	−2.16792	+	15.0782i	−0.154458	+	1.07428i	−0.908631	+	0.417601i	$0.862871\pi$
$198$	−7.75225	+	3.30534i	−0.550929	+	0.234900i
$199$	−2.64855	−	18.4211i	−0.187751	−	1.30584i	−0.837814	−	0.545956i	$-0.816167\pi$
$199$	−2.64855	−	18.4211i	−0.187751	−	1.30584i	0.650063	−	0.759880i	$-0.274742\pi$
$200$	−6.59408	+	45.8628i	−0.466272	+	3.24299i
$201$	−14.7361	+	9.47033i	−1.03941	+	0.667986i
$202$	−3.26519			−0.229738
$203$	0.487224	−	1.06687i	0.0341964	−	0.0748797i
$204$	−38.9330	+	44.9310i	−2.72585	+	3.14580i
$205$	0.00919631	+	0.0201371i	0.000642298	+	0.00140644i
$206$	3.54786	−	7.76873i	0.247191	−	0.541273i
$207$	−3.75498	−	4.33348i	−0.260989	−	0.301198i
$208$	26.0911	−	7.66103i	1.80909	−	0.531197i
$209$	24.3052	−	2.86741i	1.68123	−	0.198343i
$210$	−0.0650291	−	0.0190943i	−0.00448743	−	0.00131763i
$211$	−0.889046	−	1.94674i	−0.0612045	−	0.134019i	0.876558	−	0.481296i	$-0.159834\pi$
$211$	−0.889046	−	1.94674i	−0.0612045	−	0.134019i	−0.937763	+	0.347277i	$0.887106\pi$
$212$	−1.77712	−	3.89135i	−0.122053	−	0.267259i
$213$	−7.78120	+	2.28477i	−0.533159	+	0.156550i
$214$	−17.6013	−	38.5416i	−1.20320	−	2.63465i
$215$	−0.00548304			−0.000373940
$216$	5.40476	+	37.5909i	0.367747	+	2.55774i
$217$	−9.74665	−	2.86188i	−0.661646	−	0.194277i
$218$	−5.61050	−	39.0219i	−0.379991	−	2.64290i
$219$	14.8428	+	17.1295i	1.00299	+	1.15751i
$220$	−0.101555	−	0.0926110i	−0.00684685	−	0.00624383i
$221$	−6.85415	+	7.91011i	−0.461060	+	0.532091i
$222$	25.9579	+	16.6821i	1.74218	+	1.11963i
$223$	−23.8697	+	7.00876i	−1.59843	+	0.469342i	−0.955109	−	0.296255i	$-0.904262\pi$
$223$	−23.8697	+	7.00876i	−1.59843	+	0.469342i	−0.643321	+	0.765596i	$0.722444\pi$
$224$	28.4848	−	18.3061i	1.90322	−	1.22312i
$225$	4.47956	+	1.31532i	0.298637	+	0.0876878i
$226$	14.5275	+	16.7657i	0.966357	+	1.11524i
$227$	1.41173	−	9.81879i	0.0936998	−	0.651696i	−0.887800	−	0.460230i	$-0.847767\pi$
$227$	1.41173	−	9.81879i	0.0936998	−	0.651696i	0.981499	−	0.191466i	$-0.0613241\pi$
$228$	−11.2586	+	78.3053i	−0.745619	+	5.18590i
$229$	−3.51107	+	7.68817i	−0.232018	+	0.508049i	−0.989452	−	0.144864i	$-0.953726\pi$
$229$	−3.51107	+	7.68817i	−0.232018	+	0.508049i	0.757434	+	0.652912i	$0.226453\pi$
$230$	0.0532210	−	0.116538i	0.00350929	−	0.00768427i
$231$	−8.31907	+	6.84690i	−0.547355	+	0.450493i
$232$	2.75661	+	6.03613i	0.180980	+	0.396291i
$233$	−3.67656			−0.240859			−0.120430	−	0.992722i	$-0.538427\pi$
$233$	−3.67656			−0.240859			−0.120430	+	0.992722i	$0.538427\pi$
$234$	−0.682524	−	4.74706i	−0.0446180	−	0.310325i
$235$	−0.0314529	+	0.0362986i	−0.00205176	+	0.00236786i
$236$	−8.21925	+	5.28219i	−0.535027	+	0.343841i
$237$	3.87043	−	26.9194i	0.251411	−	1.74860i
$238$	−10.2680	+	22.4839i	−0.665578	+	1.45741i
$239$	−16.0396			−1.03751			−0.518756	−	0.854922i	$-0.673605\pi$
$239$	−16.0396			−1.03751			−0.518756	+	0.854922i	$0.673605\pi$
$240$	0.184294	−	0.118439i	0.0118961	−	0.00764518i
$241$	−12.8134			−0.825381			−0.412690	−	0.910871i	$-0.635411\pi$
$241$	−12.8134			−0.825381			−0.412690	+	0.910871i	$0.635411\pi$
$242$	−29.1123	+	6.96600i	−1.87141	+	0.447792i
$243$	9.38250			0.601888
$244$	14.1252	−	9.07773i	0.904275	−	0.581142i
$245$	0.0330979			0.00211455
$246$	−6.47431	+	14.1768i	−0.412787	+	0.903878i
$247$	−1.98208	+	13.7856i	−0.126117	+	0.877160i
$248$	48.3490	−	31.0720i	3.07016	−	1.97307i
$249$	−7.59152	+	8.76108i	−0.481093	+	0.555211i
$250$	0.0296905	+	0.206502i	0.00187779	+	0.0130603i
$251$	−18.9422			−1.19562			−0.597811	−	0.801637i	$-0.703963\pi$
$251$	−18.9422			−1.19562			−0.597811	+	0.801637i	$0.703963\pi$
$252$	−3.43423	−	7.51992i	−0.216336	−	0.473710i
$253$	−10.5731	−	17.4076i	−0.664724	−	1.09441i
$254$	0.942954	−	2.06478i	0.0591662	−	0.129556i
$255$	−0.0350285	+	0.0767016i	−0.00219357	+	0.00480324i
$256$	−5.09739	+	35.4531i	−0.318587	+	2.21582i
$257$	−0.583468	+	4.05811i	−0.0363958	+	0.253138i	−0.999894	−	0.0145775i	$-0.995360\pi$
$257$	−0.583468	+	4.05811i	−0.0363958	+	0.253138i	0.963498	+	0.267716i	$0.0862688\pi$
$258$	−2.52785	−	2.91729i	−0.157377	−	0.181622i
$259$	8.98463	+	2.63812i	0.558277	+	0.163925i
$260$	0.0657983	−	0.0422860i	0.00408064	−	0.00262247i
$261$	0.641541	−	0.188373i	0.0397104	−	0.0116600i
$262$	−1.49179	−	0.958716i	−0.0921632	−	0.0592297i
$263$	21.2189	−	24.4879i	1.30841	−	1.50999i	0.620444	−	0.784251i	$-0.286952\pi$
$263$	21.2189	−	24.4879i	1.30841	−	1.50999i	0.687970	−	0.725739i	$-0.258502\pi$
$264$	1.54621	−	60.9395i	0.0951626	−	3.75057i
$265$	−0.00397332	−	0.00458546i	−0.000244079	−	0.000281683i
$266$	4.68081	+	32.5558i	0.286999	+	1.99612i
$267$	3.57204	+	1.04884i	0.218605	+	0.0641883i
$268$	−6.79407	−	47.2538i	−0.415014	−	2.88648i
$269$	20.2194			1.23280			0.616398	−	0.787435i	$-0.288591\pi$
$269$	20.2194			1.23280			0.616398	+	0.787435i	$0.288591\pi$
$270$	0.0355172	+	0.0777719i	0.00216151	+	0.00473305i
$271$	−4.54903	+	1.33572i	−0.276334	+	0.0811389i	−0.416963	−	0.908923i	$-0.636906\pi$
$271$	−4.54903	+	1.33572i	−0.276334	+	0.0811389i	0.140629	+	0.990062i	$0.455087\pi$
$272$	−33.1899	−	72.6758i	−2.01243	−	4.40662i
$273$	−2.54708	−	5.57733i	−0.154156	−	0.337556i
$274$	5.76676	+	1.69327i	0.348383	+	0.102294i
$275$	14.9048	+	7.26919i	0.898792	+	0.438349i
$276$	63.1686	−	18.5480i	3.80231	−	1.11646i
$277$	−7.73025	−	8.92119i	−0.464466	−	0.536022i	0.474398	−	0.880310i	$-0.342666\pi$
$277$	−7.73025	−	8.92119i	−0.464466	−	0.536022i	−0.938864	+	0.344288i	$0.888120\pi$
$278$	0.298204	−	0.652975i	0.0178851	−	0.0391628i
$279$	−2.40565	−	5.26763i	−0.144022	−	0.315365i
$280$	0.0762039	−	0.0879440i	0.00455405	−	0.00525566i
$281$	−3.12627	+	6.84558i	−0.186498	+	0.408373i	−0.979668	−	0.200628i	$-0.935702\pi$
$281$	−3.12627	+	6.84558i	−0.186498	+	0.408373i	0.793170	+	0.609000i	$0.208429\pi$
$282$	−33.8137			−2.01358
$283$	−11.5705	+	7.43592i	−0.687795	+	0.442019i	−0.837301	−	0.546742i	$-0.815868\pi$
$283$	−11.5705	+	7.43592i	−0.687795	+	0.442019i	0.149506	+	0.988761i	$0.452232\pi$
$284$	3.14542	−	21.8768i	0.186646	−	1.29815i
$285$	0.0159682	+	0.111061i	0.000945872	+	0.00657869i
$286$	0.432081	−	17.0292i	0.0255495	−	1.00696i
$287$	−0.673097	+	4.68149i	−0.0397316	+	0.276340i
$288$	18.5210	+	5.43825i	1.09136	+	0.320452i
$289$	11.5692	+	7.43509i	0.680543	+	0.437358i
$290$	0.00978302	+	0.0112902i	0.000574479	+	0.000662984i
$291$	1.40804	+	9.79312i	0.0825407	+	0.574083i
$292$	−59.2697	+	17.4032i	−3.46850	+	1.01844i
$293$	12.6684	+	3.71978i	0.740096	+	0.217312i	0.629985	−	0.776607i	$-0.283061\pi$
$293$	12.6684	+	3.71978i	0.740096	+	0.217312i	0.110111	+	0.993919i	$0.464879\pi$
$294$	15.2591	+	17.6100i	0.889931	+	1.02704i
$295$	−0.00907454	+	0.0104726i	−0.000528340	+	0.000609737i
$296$	−44.5689	+	28.6427i	−2.59051	+	1.66482i
$297$	13.4003	+	2.27497i	0.777562	+	0.132007i
$298$	0.919582	+	0.590980i	0.0532700	+	0.0342345i
$299$	11.1208	−	3.26537i	0.643135	−	0.188841i
$300$	−35.1029	+	40.5109i	−2.02667	+	2.33890i
$301$	−0.985472	−	0.633324i	−0.0568016	−	0.0365042i
$302$	−23.0070	−	14.7857i	−1.32390	−	0.850821i
$303$	−2.00200	−	1.28661i	−0.115012	−	0.0739138i
$304$	−89.4369	−	57.4776i	−5.12956	−	3.29657i
$305$	0.0155951	−	0.0179977i	0.000892972	−	0.00103054i
$306$	−13.5202	+	3.96989i	−0.772899	+	0.226944i
$307$	−16.8993	−	10.8605i	−0.964494	−	0.619842i	−0.0392554	−	0.999229i	$-0.512499\pi$
$307$	−16.8993	−	10.8605i	−0.964494	−	0.619842i	−0.925238	+	0.379387i	$0.876135\pi$
$308$	−7.55549	−	28.3753i	−0.430514	−	1.61683i
$309$	5.23649	−	3.36529i	0.297894	−	0.191445i
$310$	0.0847306	−	0.0977843i	0.00481238	−	0.00555378i
$311$	10.0337	+	11.5795i	0.568957	+	0.656612i	0.965193	−	0.261537i	$-0.0842293\pi$
$311$	10.0337	+	11.5795i	0.568957	+	0.656612i	−0.396236	+	0.918149i	$0.629684\pi$
$312$	33.2851	+	9.77338i	1.88440	+	0.553308i
$313$	4.33929	−	1.27413i	0.245271	−	0.0720181i	−0.156786	−	0.987633i	$-0.550113\pi$
$313$	4.33929	−	1.27413i	0.245271	−	0.0720181i	0.402057	+	0.915614i	$0.368295\pi$
$314$	7.88028	+	54.8085i	0.444710	+	3.09302i
$315$	−0.00767833	−	0.00886126i	−0.000432625	−	0.000499275i
$316$	62.3532	+	40.0720i	3.50764	+	2.25423i
$317$	8.50179	+	2.49635i	0.477508	+	0.140209i	0.511625	−	0.859209i	$-0.329044\pi$
$317$	8.50179	+	2.49635i	0.477508	+	0.140209i	−0.0341170	+	0.999418i	$0.510862\pi$
$318$	0.607905	−	4.22807i	0.0340896	−	0.237098i
$319$	2.35857	−	0.278252i	0.132055	−	0.0155791i
$320$	0.0299397	+	0.208235i	0.00167368	+	0.0116407i
$321$	4.39484	−	30.5668i	0.245296	−	1.70607i
$322$	23.0263	−	14.7981i	1.28320	−	0.824665i
$323$	40.9208			2.27690
$324$	−24.5416	+	53.7386i	−1.36342	+	2.98548i
$325$	−6.17987	+	7.13195i	−0.342797	+	0.395609i
$326$	−24.4684	−	53.5783i	−1.35518	−	2.96743i
$327$	11.9361	−	26.1365i	0.660069	−	1.44535i
$328$	−17.5236	−	20.2233i	−0.967578	−	1.11664i
$329$	−9.84577	+	2.89098i	−0.542815	+	0.159385i
$330$	−0.0353116	−	0.132616i	−0.00194384	−	0.00730026i
$331$	−8.86390	−	2.60268i	−0.487204	−	0.143056i	0.0288994	−	0.999582i	$-0.490800\pi$
$331$	−8.86390	−	2.60268i	−0.487204	−	0.143056i	−0.516103	+	0.856526i	$0.672618\pi$
$332$	−13.1246	−	28.7388i	−0.720304	−	1.57725i
$333$	2.21757	+	4.85579i	0.121522	+	0.266096i
$334$	29.7167	−	8.72562i	1.62603	−	0.477445i
$335$	−0.0281276	−	0.0615908i	−0.00153677	−	0.00336506i
$336$	46.8037			2.55335
$337$	1.57461	+	10.9517i	0.0857747	+	0.596576i	0.986694	+	0.162589i	$0.0519846\pi$
$337$	1.57461	+	10.9517i	0.0857747	+	0.596576i	−0.900919	+	0.433987i	$0.857106\pi$
$338$	−24.6423	−	7.23564i	−1.34037	−	0.393567i
$339$	2.30103	+	16.0040i	0.124975	+	0.869220i
$340$	−0.150491	−	0.173676i	−0.00816153	−	0.00941891i
$341$	−5.29255	−	19.8766i	−0.286608	−	1.07638i
$342$	−12.2788	+	14.1705i	−0.663962	+	0.766253i
$343$	15.5941	+	10.0217i	0.842000	+	0.541121i
$344$	6.35925	−	1.86724i	0.342868	−	0.100675i
$345$	0.0785520	−	0.0504823i	0.00422910	−	0.00271787i
$346$	1.24437	+	0.365379i	0.0668975	+	0.0196429i
$347$	12.7884	+	14.7586i	0.686517	+	0.792283i	0.986865	−	0.161547i	$-0.0516483\pi$
$347$	12.7884	+	14.7586i	0.686517	+	0.792283i	−0.300348	+	0.953830i	$0.597103\pi$
$348$	−1.09253	+	7.59871i	−0.0585657	+	0.407334i
$349$	−0.819025	+	5.69644i	−0.0438414	+	0.304924i	0.956088	+	0.293078i	$0.0946797\pi$
$349$	−0.819025	+	5.69644i	−0.0438414	+	0.304924i	−0.999930	+	0.0118453i	$0.996229\pi$
$350$	−9.25792	+	20.2720i	−0.494856	+	1.08358i
$351$	−3.21317	+	7.03587i	−0.171507	+	0.375547i
$352$	61.6246	+	30.0549i	3.28460	+	1.60193i
$353$	10.8525	+	23.7636i	0.577620	+	1.26481i	0.942640	+	0.333811i	$0.108335\pi$
$353$	10.8525	+	23.7636i	0.577620	+	1.26481i	−0.365021	+	0.930999i	$0.618938\pi$
$354$	−9.75564			−0.518506
$355$	−0.00446117	−	0.0310281i	−0.000236774	−	0.00164680i
$356$	−6.64425	+	7.66788i	−0.352145	+	0.406397i
$357$	−15.1552	+	9.73966i	−0.802098	+	0.515477i
$358$	−6.56500	+	45.6606i	−0.346971	+	2.41324i
$359$	14.4933	−	31.7360i	0.764930	−	1.67496i	0.0274213	−	0.999624i	$-0.491270\pi$
$359$	14.4933	−	31.7360i	0.764930	−	1.67496i	0.737508	−	0.675338i	$-0.236002\pi$
$360$	0.0663383			0.00349634
$361$	29.8237	−	19.1665i	1.56967	−	1.00877i
$362$	34.3899			1.80749
$363$	−20.5946	−	7.20025i	−1.08094	−	0.377915i
$364$	16.7103			0.875857
$365$	−0.0737035	+	0.0473664i	−0.00385782	+	0.00247927i
$366$	16.7656			0.876352
$367$	−5.46319	+	11.9627i	−0.285176	+	0.624449i	−0.996957	−	0.0779526i	$-0.975162\pi$
$367$	−5.46319	+	11.9627i	−0.285176	+	0.624449i	0.711781	+	0.702402i	$0.247889\pi$
$368$	−12.5911	+	87.5733i	−0.656359	+	4.56508i
$369$	−2.26825	+	1.45771i	−0.118080	+	0.0758855i
$370$	−0.0781061	+	0.0901392i	−0.00406054	+	0.00468612i
$371$	−0.184481	−	1.28309i	−0.00957776	−	0.0666148i
$372$	66.4891			3.44730
$373$	4.61996	+	10.1163i	0.239212	+	0.523802i	0.990719	−	0.135923i	$-0.0434000\pi$
$373$	4.61996	+	10.1163i	0.239212	+	0.523802i	−0.751507	+	0.659725i	$0.770673\pi$
$374$	−49.7059	+	5.86405i	−2.57023	+	0.303223i
$375$	−0.0631654	+	0.138313i	−0.00326185	+	0.00714245i
$376$	24.1178	−	52.8105i	1.24378	−	2.72350i
$377$	−0.192340	+	1.33775i	−0.00990601	+	0.0688978i
$378$	−2.59958	+	18.0805i	−0.133708	+	0.929959i
$379$	−6.93771	−	8.00654i	−0.356366	−	0.411268i	0.549053	−	0.835788i	$-0.314989\pi$
$379$	−6.93771	−	8.00654i	−0.356366	−	0.411268i	−0.905419	+	0.424519i	$0.860443\pi$
$380$	−0.293406	−	0.0861519i	−0.0150514	−	0.00441950i
$381$	1.39176	−	0.894430i	0.0713021	−	0.0458231i
$382$	30.2254	−	8.87498i	1.54647	−	0.454084i
$383$	−13.0153	−	8.36446i	−0.665053	−	0.427404i	0.164086	−	0.986446i	$-0.447533\pi$
$383$	−13.0153	−	8.36446i	−0.665053	−	0.427404i	−0.829139	+	0.559042i	$0.811169\pi$
$384$	−43.2897	+	49.9590i	−2.20912	+	2.54946i
$385$	−0.0216202	−	0.0355957i	−0.00110187	−	0.00181412i
$386$	24.9404	+	28.7828i	1.26943	+	1.46501i
$387$	−0.0950394	−	0.661013i	−0.00483112	−	0.0336012i
$388$	−25.8720	−	7.59669i	−1.31345	−	0.385664i
$389$	2.57874	+	17.9355i	0.130747	+	0.909367i	0.944583	+	0.328272i	$0.106466\pi$
$389$	2.57874	+	17.9355i	0.130747	+	0.909367i	−0.813836	+	0.581095i	$0.802625\pi$
$390$	0.0780978			0.00395463
$391$	−14.1466	−	30.9767i	−0.715424	−	1.56656i
$392$	−38.3871	+	11.2715i	−1.93884	+	0.569295i
$393$	−0.536899	−	1.17565i	−0.0270830	−	0.0593035i
$394$	−17.2206	−	37.7078i	−0.867561	−	1.89969i
$395$	0.100866	+	0.0296169i	0.00507511	+	0.00149019i
$396$	9.40452	−	13.8484i	0.472595	−	0.695906i
$397$	−11.6798	+	3.42950i	−0.586192	+	0.172122i	−0.561362	−	0.827570i	$-0.689723\pi$
$397$	−11.6798	+	3.42950i	−0.586192	+	0.172122i	−0.0248300	+	0.999692i	$0.507904\pi$
$398$	33.1651	+	38.2745i	1.66241	+	1.91853i
$399$	−9.95825	+	21.8055i	−0.498536	+	1.09164i
$400$	−29.9248	−	65.5262i	−1.49624	−	3.27631i
$401$	6.94342	−	8.01313i	0.346738	−	0.400157i	−0.555415	−	0.831573i	$-0.687441\pi$
$401$	6.94342	−	8.01313i	0.346738	−	0.400157i	0.902153	+	0.431417i	$0.141986\pi$
$402$	19.8021	−	43.3607i	0.987641	−	2.16263i
$403$	11.7054			0.583088
$404$	5.45617	−	3.50647i	0.271455	−	0.174453i
$405$	−0.0119245	+	0.0829369i	−0.000592535	+	0.00412117i
$406$	0.454224	+	3.15920i	0.0225428	+	0.156788i
$407$	4.87876	+	18.3226i	0.241831	+	0.908219i
$408$	14.5055	−	100.888i	0.718128	−	4.99469i
$409$	−27.5597	−	8.09226i	−1.36274	−	0.400137i	−0.483012	−	0.875614i	$-0.660457\pi$
$409$	−27.5597	−	8.09226i	−1.36274	−	0.400137i	−0.879728	+	0.475477i	$0.842276\pi$
$410$	−0.0506794	−	0.0325697i	−0.00250288	−	0.00160850i
$411$	2.86859	+	3.31053i	0.141497	+	0.163296i
$412$	2.41428	+	16.7917i	0.118943	+	0.827265i
$413$	−2.84062	+	0.834082i	−0.139778	+	0.0410425i
$414$	14.9718	+	4.39612i	0.735825	+	0.216058i
$415$	−0.0293442	−	0.0338650i	−0.00144045	−	0.00166237i
$416$	−25.5510	+	29.4874i	−1.25274	+	1.44574i
$417$	0.440136	−	0.282858i	0.0215536	−	0.0138516i
$418$	−51.4231	+	42.3231i	−2.51518	+	2.07009i
$419$	−18.8872	−	12.1381i	−0.922701	−	0.592984i	−0.00926094	−	0.999957i	$-0.502948\pi$
$419$	−18.8872	−	12.1381i	−0.922701	−	0.592984i	−0.913440	+	0.406973i	$0.866584\pi$
$420$	0.129170	−	0.0379276i	0.00630283	−	0.00185068i
$421$	1.63573	−	1.88774i	0.0797208	−	0.0920027i	−0.714488	−	0.699648i	$-0.753340\pi$
$421$	1.63573	−	1.88774i	0.0797208	−	0.0920027i	0.794209	+	0.607645i	$0.207886\pi$
$422$	4.89940	+	3.14865i	0.238499	+	0.153274i
$423$	−4.92120	−	3.16266i	−0.239277	−	0.153774i
$424$	6.16985	+	3.96512i	0.299634	+	0.192563i
$425$	23.3255	+	14.9904i	1.13145	+	0.727141i
$426$	14.4520	−	16.6785i	0.700201	−	0.808075i
$427$	4.88176	−	1.43341i	0.236245	−	0.0693678i
$428$	70.8016	+	45.5014i	3.42233	+	2.19940i
$429$	6.97510	−	10.2710i	0.336761	−	0.495888i
$430$	0.0125523	−	0.00806685i	0.000605324	−	0.000389018i
$431$	−21.5036	+	24.8165i	−1.03579	+	1.19537i	−0.0553677	+	0.998466i	$0.517633\pi$
$431$	−21.5036	+	24.8165i	−1.03579	+	1.19537i	−0.980423	+	0.196901i	$0.936912\pi$
$432$	−38.6652	−	44.6220i	−1.86028	−	2.14688i
$433$	6.70632	+	1.96915i	0.322285	+	0.0946315i	0.438874	−	0.898549i	$-0.355378\pi$
$433$	6.70632	+	1.96915i	0.322285	+	0.0946315i	−0.116588	+	0.993180i	$0.537196\pi$
$434$	26.5234	−	7.78797i	1.27316	−	0.373835i
$435$	0.00154954	+	0.0107773i	7.42949e−5	+	0.000516732i
$436$	51.2806	+	59.1810i	2.45590	+	2.83425i
$437$	−38.1208	−	24.4988i	−1.82357	−	1.17194i
$438$	−59.1811	−	17.3772i	−2.82778	−	0.830312i
$439$	0.225857	−	1.57087i	0.0107796	−	0.0749735i	−0.983722	−	0.179699i	$-0.942487\pi$
$439$	0.225857	−	1.57087i	0.0107796	−	0.0749735i	0.994501	+	0.104726i	$0.0333966\pi$
$440$	0.232307	+	0.0394388i	0.0110748	+	0.00188017i
$441$	0.573698	+	3.99015i	0.0273189	+	0.190007i
$442$	4.05348	−	28.1926i	0.192805	−	1.34098i
$443$	−31.8541	+	20.4714i	−1.51343	+	0.972624i	−0.520511	+	0.853855i	$0.674259\pi$
$443$	−31.8541	+	20.4714i	−1.51343	+	0.972624i	−0.992922	+	0.118769i	$0.962105\pi$
$444$	−61.2908			−2.90873
$445$	−0.00597792	+	0.0130898i	−0.000283380	+	0.000620517i
$446$	44.3330	−	51.1630i	2.09923	−	2.42264i
$447$	0.330960	+	0.724701i	0.0156539	+	0.0342772i
$448$	−18.6713	+	40.8845i	−0.882137	+	1.93161i
$449$	−3.86640	−	4.46206i	−0.182467	−	0.210578i	0.657146	−	0.753763i	$-0.271763\pi$
$449$	−3.86640	−	4.46206i	−0.182467	−	0.210578i	−0.839613	+	0.543185i	$0.817218\pi$
$450$	−12.1901	+	3.57935i	−0.574649	+	0.168732i
$451$	−8.80969	+	3.75620i	−0.414832	+	0.176872i
$452$	−42.2802	−	12.4146i	−1.98869	−	0.583933i
$453$	−8.28027	−	18.1313i	−0.389041	−	0.851881i
$454$	11.2139	+	24.5550i	0.526295	+	1.15243i
$455$	0.0227403	−	0.00667715i	0.00106608	−	0.000313030i
$456$	−56.3416	−	123.371i	−2.63844	−	5.77738i
$457$	1.13779			0.0532237			0.0266118	−	0.999646i	$-0.491528\pi$
$457$	1.13779			0.0532237			0.0266118	+	0.999646i	$0.491528\pi$
$458$	−3.27326	−	22.7661i	−0.152950	−	1.06379i
$459$	21.8056	+	6.40270i	1.01780	+	0.298852i
$460$	0.0362162	+	0.251889i	0.00168859	+	0.0117444i
$461$	−3.09203	−	3.56839i	−0.144010	−	0.166196i	0.679162	−	0.733988i	$-0.262343\pi$
$461$	−3.09203	−	3.56839i	−0.144010	−	0.166196i	−0.823172	+	0.567792i	$0.807798\pi$
$462$	8.97134	−	27.9139i	0.417385	−	1.29867i
$463$	−15.0525	+	17.3716i	−0.699551	+	0.807325i	−0.988692	−	0.149962i	$-0.952085\pi$
$463$	−15.0525	+	17.3716i	−0.699551	+	0.807325i	0.289141	+	0.957287i	$0.406630\pi$
$464$	−8.67891	−	5.57760i	−0.402908	−	0.258934i
$465$	0.0904821	−	0.0265679i	0.00419601	−	0.00123206i
$466$	8.41670	−	5.40908i	0.389896	−	0.250571i
$467$	34.9624	+	10.2659i	1.61787	+	0.475048i	0.960444	−	0.278475i	$-0.0898288\pi$
$467$	34.9624	+	10.2659i	1.61787	+	0.475048i	0.657422	+	0.753523i	$0.271647\pi$
$468$	6.23834	+	7.19943i	0.288367	+	0.332794i
$469$	2.05871	−	14.3187i	0.0950626	−	0.661175i
$470$	0.0186010	−	0.129373i	0.000858000	−	0.00596752i
$471$	−16.7650	+	36.7102i	−0.772489	+	1.69152i
$472$	6.95826	−	15.2365i	0.320280	−	0.701315i
$473$	0.0601660	−	2.37127i	0.00276643	−	0.109031i
$474$	30.7443	+	67.3207i	1.41213	+	3.09214i
$475$	36.8952			1.69287
$476$	−6.98728	−	48.5976i	−0.320261	−	2.22747i
$477$	0.483934	−	0.558489i	0.0221578	−	0.0255715i
$478$	36.7192	−	23.5980i	1.67950	−	1.07935i
$479$	−1.26278	+	8.78283i	−0.0576979	+	0.401298i	0.940422	+	0.340009i	$0.110430\pi$
$479$	−1.26278	+	8.78283i	−0.0576979	+	0.401298i	−0.998120	+	0.0612887i	$0.980479\pi$
$480$	−0.130580	+	0.285929i	−0.00596012	+	0.0130508i
$481$	−10.7902			−0.491992
$482$	29.3335	−	18.8515i	1.33610	−	0.858661i
$483$	19.9492			0.907721
$484$	41.1662	−	42.9038i	1.87119	−	1.95017i
$485$	−0.0382435			−0.00173655
$486$	−21.4793	+	13.8039i	−0.974319	+	0.626157i
$487$	−36.1868			−1.63978			−0.819891	−	0.572520i	$-0.805966\pi$
$487$	−36.1868			−1.63978			−0.819891	+	0.572520i	$0.805966\pi$
$488$	−11.9581	+	26.1847i	−0.541320	+	1.18532i
$489$	6.10946	−	42.4923i	0.276279	−	1.92157i
$490$	−0.0757707	+	0.0486949i	−0.00342297	+	0.00219981i
$491$	−23.5416	+	27.1684i	−1.06242	+	1.22609i	−0.0892449	+	0.996010i	$0.528445\pi$
$491$	−23.5416	+	27.1684i	−1.06242	+	1.22609i	−0.973171	+	0.230083i	$0.926100\pi$
$492$	−4.40569	−	30.6423i	−0.198624	−	1.38146i
$493$	3.97094			0.178842
$494$	−15.7444	−	34.4754i	−0.708374	−	1.55112i
$495$	0.00726463	−	0.0226035i	0.000326521	−	0.00101595i
$496$	−37.1183	+	81.2777i	−1.66666	+	3.64948i
$497$	2.78212	−	6.09200i	0.124795	−	0.273263i
$498$	4.48956	−	31.2255i	0.201182	−	1.39925i
$499$	−3.36282	+	23.3889i	−0.150540	+	1.04703i	0.764776	+	0.644296i	$0.222850\pi$
$499$	−3.36282	+	23.3889i	−0.150540	+	1.04703i	−0.915316	+	0.402736i	$0.868059\pi$
$500$	−0.271375	−	0.313183i	−0.0121362	−	0.0140060i
$501$	21.6586	+	6.35954i	0.967635	+	0.284123i
$502$	43.3642	−	27.8685i	1.93544	−	1.24383i
$503$	9.33241	−	2.74024i	0.416111	−	0.122181i	−0.0669737	−	0.997755i	$-0.521334\pi$
$503$	9.33241	−	2.74024i	0.416111	−	0.122181i	0.483085	+	0.875573i	$0.339516\pi$
$504$	11.9230	+	7.66247i	0.531095	+	0.341314i
$505$	0.00602394	−	0.00695199i	0.000268062	−	0.000309360i
$506$	49.8155	+	24.2955i	2.21457	+	1.08007i
$507$	−12.2580	−	14.1464i	−0.544395	−	0.628266i
$508$	0.641669	+	4.46290i	0.0284695	+	0.198009i
$509$	−27.0805	−	7.95155i	−1.20032	−	0.352446i	−0.380345	−	0.924844i	$-0.624195\pi$
$509$	−27.0805	−	7.95155i	−1.20032	−	0.352446i	−0.819976	+	0.572398i	$0.806013\pi$
$510$	−0.0326560	−	0.227127i	−0.00144603	−	0.0100574i
$511$	−18.7179			−0.828031
$512$	−12.7991	−	28.0262i	−0.565647	−	1.23859i
$513$	29.0157	−	8.51979i	1.28108	−	0.376158i
$514$	−4.63472	−	10.1486i	−0.204429	−	0.447636i
$515$	0.00999515	+	0.0218863i	0.000440439	+	0.000964426i
$516$	7.35692	+	2.16019i	0.323870	+	0.0950969i
$517$	−15.3531	−	14.0009i	−0.675227	−	0.615758i
$518$	−24.4497	+	7.17908i	−1.07426	+	0.315431i
$519$	0.618991	+	0.714354i	0.0271707	+	0.0313567i
$520$	−0.0557036	+	0.121974i	−0.00244276	+	0.00534891i
$521$	−14.1746	−	31.0380i	−0.620999	−	1.35980i	−0.914791	−	0.403928i	$-0.867645\pi$
$521$	−14.1746	−	31.0380i	−0.620999	−	1.35980i	0.293792	−	0.955869i	$-0.405083\pi$
$522$	−1.19153	+	1.37510i	−0.0521519	+	0.0601864i
$523$	−12.4769	+	27.3205i	−0.545576	+	1.19464i	0.413242	+	0.910621i	$0.364396\pi$
$523$	−12.4769	+	27.3205i	−0.545576	+	1.19464i	−0.958818	+	0.284023i	$0.908331\pi$
$524$	3.52236			0.153875
$525$	−13.6643	+	8.78151i	−0.596359	+	0.383257i
$526$	−12.5487	+	87.2780i	−0.547148	+	3.80550i
$527$	−4.89453	−	34.0422i	−0.213209	−	1.48290i
$528$	49.1993	+	81.0020i	2.14113	+	3.52516i
$529$	−2.09350	+	14.5606i	−0.0910219	+	0.633072i
$530$	0.0158424	+	0.00465174i	0.000688149	+	0.000202059i
$531$	−1.41982	−	0.912465i	−0.0616151	−	0.0395976i
$532$	−42.7831	−	49.3744i	−1.85488	−	2.14065i
$533$	−0.775622	−	5.39457i	−0.0335959	−	0.233665i
$534$	−9.72052	+	2.85420i	−0.420648	+	0.123513i
$535$	0.114532	+	0.0336298i	0.00495167	+	0.00145394i
$536$	53.5971	+	61.8544i	2.31504	+	2.67170i
$537$	−22.0172	+	25.4093i	−0.950114	+	1.09649i
$538$	−46.2879	+	29.7474i	−1.99561	+	1.28250i
$539$	−0.363187	+	14.3140i	−0.0156436	+	0.616547i
$540$	−0.142869	−	0.0918160i	−0.00614808	−	0.00395113i
$541$	−34.7652	+	10.2080i	−1.49467	+	0.438876i	−0.924029	−	0.382322i	$-0.875125\pi$
$541$	−34.7652	+	10.2080i	−1.49467	+	0.438876i	−0.570644	+	0.821198i	$0.693306\pi$
$542$	8.44889	−	9.75054i	0.362911	−	0.418821i
$543$	21.0857	+	13.5509i	0.904873	+	0.581526i
$544$	96.4405	+	61.9786i	4.13485	+	2.65731i
$545$	0.0934332	+	0.0600459i	0.00400224	+	0.00257208i
$546$	14.0366	+	9.02076i	0.600710	+	0.386053i
$547$	−0.916081	+	1.05721i	−0.0391688	+	0.0452032i	−0.774996	−	0.631966i	$-0.782248\pi$
$547$	−0.916081	+	1.05721i	−0.0391688	+	0.0452032i	0.735827	+	0.677169i	$0.236794\pi$
$548$	−11.4547	+	3.36341i	−0.489322	+	0.143678i
$549$	2.44004	+	1.56812i	0.104139	+	0.0669258i
$550$	−44.8160	+	5.28717i	−1.91096	+	0.225446i
$551$	4.44514	−	2.85672i	0.189369	−	0.121700i
$552$	−73.9131	+	85.3003i	−3.14595	+	3.63062i
$553$	14.7078	+	16.9737i	0.625439	+	0.721795i
$554$	30.8220	+	9.05015i	1.30950	+	0.384504i
$555$	−0.0834079	+	0.0244908i	−0.00354047	+	0.00103958i
$556$	0.202924	+	1.41137i	0.00860590	+	0.0598553i
$557$	1.24335	+	1.43490i	0.0526823	+	0.0607986i	0.781479	−	0.623931i	$-0.214466\pi$
$557$	1.24335	+	1.43490i	0.0526823	+	0.0607986i	−0.728797	+	0.684730i	$0.759920\pi$
$558$	13.2572	+	8.51986i	0.561220	+	0.360674i
$559$	1.29518	+	0.380301i	0.0547805	+	0.0160850i
$560$	−0.0257468	+	0.179073i	−0.00108800	+	0.00756722i
$561$	−32.7871	−	15.9906i	−1.38427	−	0.675122i
$562$	−2.91453	−	20.2710i	−0.122942	−	0.855080i
$563$	2.84962	−	19.8195i	0.120097	−	0.835294i	−0.837346	−	0.546673i	$-0.815894\pi$
$563$	2.84962	−	19.8195i	0.120097	−	0.835294i	0.957443	−	0.288621i	$-0.0931967\pi$
$564$	56.5030	−	36.3123i	2.37921	−	1.52902i
$565$	−0.0624980			−0.00262931
$566$	15.5482	−	34.0459i	0.653542	−	1.43106i
$567$	−11.7229	+	13.5290i	−0.492317	+	0.568164i
$568$	15.7407	+	34.4672i	0.660463	+	1.44621i
$569$	−0.294418	+	0.644685i	−0.0123426	+	0.0270266i	−0.915703	−	0.401856i	$-0.868365\pi$
$569$	−0.294418	+	0.644685i	−0.0123426	+	0.0270266i	0.903360	+	0.428882i	$0.141093\pi$
$570$	−0.199953	−	0.230758i	−0.00837510	−	0.00966538i
$571$	−9.37763	+	2.75352i	−0.392442	+	0.115231i	−0.471999	−	0.881599i	$-0.656467\pi$
$571$	−9.37763	+	2.75352i	−0.392442	+	0.115231i	0.0795574	+	0.996830i	$0.474649\pi$
$572$	17.5656	+	28.9201i	0.734454	+	1.20921i
$573$	22.0294	+	6.46840i	0.920289	+	0.270221i
$574$	−5.34667	−	11.7076i	−0.223166	−	0.488664i
$575$	−12.7549	−	27.9294i	−0.531917	−	1.16474i
$576$	−24.5850	+	7.21882i	−1.02438	+	0.300784i
$577$	17.1054	+	37.4556i	0.712108	+	1.55930i	0.824645	+	0.565651i	$0.191375\pi$
$577$	17.1054	+	37.4556i	0.712108	+	1.55930i	−0.112537	+	0.993648i	$0.535898\pi$
$578$	−37.4241			−1.55664
$579$	3.95034	+	27.4752i	0.164171	+	1.14183i
$580$	−0.0284720	−	0.00836014i	−0.00118224	−	0.000347136i
$581$	−1.36245	−	9.47602i	−0.0565238	−	0.393131i
$582$	−17.6314	−	20.3477i	−0.730845	−	0.843441i
$583$	2.02669	−	1.66804i	0.0839370	−	0.0690833i
$584$	69.3510	−	80.0354i	2.86977	−	3.31189i
$585$	0.0113663	+	0.00730465i	0.000469937	+	0.000302010i
$586$	−34.4743	+	10.1226i	−1.42412	+	0.418159i
$587$	29.8418	−	19.1782i	1.23170	−	0.791568i	0.247548	−	0.968876i	$-0.420375\pi$
$587$	29.8418	−	19.1782i	1.23170	−	0.791568i	0.984155	+	0.177308i	$0.0567389\pi$
$588$	−44.4095	−	13.0398i	−1.83141	−	0.537752i
$589$	−29.9692	−	34.5863i	−1.23486	−	1.42510i
$590$	0.00536660	−	0.0373255i	0.000220940	−	0.00153667i
$591$	4.29977	−	29.9056i	0.176869	−	1.23015i
$592$	34.2163	−	74.9232i	1.40628	−	3.07932i
$593$	7.72606	−	16.9177i	0.317271	−	0.694727i	−0.682060	−	0.731296i	$-0.738916\pi$
$593$	7.72606	−	16.9177i	0.317271	−	0.694727i	0.999331	+	0.0365693i	$0.0116430\pi$
$594$	−34.0241	+	14.5069i	−1.39602	+	0.595225i
$595$	−0.0289275	−	0.0633423i	−0.00118591	−	0.00259678i
$596$	−2.17128			−0.0889392
$597$	5.25305	+	36.5358i	0.214993	+	1.49531i
$598$	−20.6547	+	23.8368i	−0.844632	+	0.974758i
$599$	−8.75254	+	5.62491i	−0.357619	+	0.229828i	−0.707097	−	0.707117i	$-0.749995\pi$
$599$	−8.75254	+	5.62491i	−0.357619	+	0.229828i	0.349478	+	0.936945i	$0.386359\pi$
$600$	13.0785	−	90.9629i	0.533927	−	3.71354i
$601$	14.6286	−	32.0321i	0.596712	−	1.30662i	−0.334589	−	0.942364i	$-0.608597\pi$
$601$	14.6286	−	32.0321i	0.596712	−	1.30662i	0.931300	−	0.364252i	$-0.118675\pi$
$602$	3.18780			0.129925
$603$	6.93759	−	4.45852i	0.282521	−	0.181565i
$604$	54.3232			2.21038
$605$	0.0388777	−	0.0748352i	0.00158060	−	0.00304248i
$606$	6.47607			0.263072
$607$	19.2348	−	12.3614i	0.780715	−	0.501735i	−0.0885556	−	0.996071i	$-0.528225\pi$
$607$	19.2348	−	12.3614i	0.780715	−	0.501735i	0.869271	+	0.494336i	$0.164589\pi$
$608$	152.545			6.18652
$609$	−0.966344	+	2.11600i	−0.0391582	+	0.0857445i
$610$	−0.00922280	+	0.0641460i	−0.000373420	+	0.00259719i
$611$	9.94736	−	6.39278i	0.402427	−	0.258624i
$612$	18.3292	−	21.1530i	0.740913	−	0.855059i
$613$	−6.82704	−	47.4831i	−0.275742	−	1.91783i	−0.383295	−	0.923626i	$-0.625211\pi$
$613$	−6.82704	−	47.4831i	−0.275742	−	1.91783i	0.107553	−	0.994199i	$-0.465699\pi$
$614$	54.6657			2.20613
$615$	−0.0182397	−	0.0399393i	−0.000735494	−	0.00161051i
$616$	37.1973	+	33.9212i	1.49872	+	1.36673i
$617$	−5.10108	+	11.1698i	−0.205362	+	0.449679i	−0.984087	−	0.177685i	$-0.943139\pi$
$617$	−5.10108	+	11.1698i	−0.205362	+	0.449679i	0.778726	+	0.627365i	$0.215866\pi$
$618$	−7.03671	+	15.4082i	−0.283058	+	0.619810i
$619$	3.03971	−	21.1417i	0.122176	−	0.849756i	−0.832906	−	0.553415i	$-0.813324\pi$
$619$	3.03971	−	21.1417i	0.122176	−	0.849756i	0.955082	−	0.296341i	$-0.0957665\pi$
$620$	−0.0365758	+	0.254390i	−0.00146892	+	0.0102166i
$621$	−16.4803	−	19.0193i	−0.661333	−	0.763220i
$622$	−40.0061	−	11.7469i	−1.60410	−	0.471006i
$623$	−2.58637	+	1.66216i	−0.103621	+	0.0665930i
$624$	−51.7482	+	15.1946i	−2.07158	+	0.608272i
$625$	21.0306	+	13.5155i	0.841224	+	0.540622i
$626$	−8.05934	+	9.30097i	−0.322116	+	0.371742i
$627$	−48.2062	+	5.68713i	−1.92517	+	0.227122i
$628$	−72.0266	−	83.1231i	−2.87417	−	3.31697i
$629$	4.51186	+	31.3806i	0.179899	+	1.25123i
$630$	0.0306149	+	0.00898935i	0.00121973	+	0.000358144i
$631$	2.39044	+	16.6259i	0.0951621	+	0.661867i	0.980442	+	0.196808i	$0.0630576\pi$
$631$	2.39044	+	16.6259i	0.0951621	+	0.661867i	−0.885280	+	0.465059i	$0.846033\pi$
$632$	−127.071			−5.05460
$633$	1.76331	+	3.86110i	0.0700851	+	0.153465i
$634$	−23.1358	+	6.79327i	−0.918839	+	0.269795i
$635$	0.00265652	+	0.00581697i	0.000105421	+	0.000230839i
$636$	3.52468	+	7.71798i	0.139763	+	0.306038i
$637$	−7.81828	−	2.29565i	−0.309772	−	0.0909571i
$638$	−4.99007	+	4.10701i	−0.197559	+	0.162598i
$639$	3.66330	−	1.07564i	0.144918	−	0.0425517i
$640$	−0.167332	−	0.193111i	−0.00661436	−	0.00763338i
$641$	2.45044	−	5.36571i	0.0967865	−	0.211933i	−0.855045	−	0.518553i	$-0.826471\pi$
$641$	2.45044	−	5.36571i	0.0967865	−	0.211933i	0.951832	+	0.306620i	$0.0991981\pi$
$642$	34.9099	+	76.4421i	1.37779	+	3.01693i
$643$	−2.23317	+	2.57721i	−0.0880676	+	0.101635i	−0.798073	−	0.602561i	$-0.794147\pi$
$643$	−2.23317	+	2.57721i	−0.0880676	+	0.101635i	0.710005	+	0.704196i	$0.248693\pi$
$644$	−22.5856	+	49.4555i	−0.889997	+	1.94882i
$645$	0.0108749			0.000428198
$646$	−93.6796	+	60.2042i	−3.68577	+	2.36870i
$647$	−2.42670	+	16.8781i	−0.0954035	+	0.663546i	0.884861	+	0.465855i	$0.154253\pi$
$647$	−2.42670	+	16.8781i	−0.0954035	+	0.663546i	−0.980264	+	0.197691i	$0.936656\pi$
$648$	−14.4140	−	100.251i	−0.566235	−	3.93825i
$649$	−4.42954	−	4.03942i	−0.173875	−	0.158561i
$650$	3.65472	−	25.4191i	0.143350	−	0.997020i
$651$	19.3312	+	5.67615i	0.757649	+	0.222466i
$652$	98.4244	+	63.2535i	3.85460	+	2.47720i
$653$	−10.7804	−	12.4412i	−0.421868	−	0.486862i	0.504537	−	0.863390i	$-0.331663\pi$
$653$	−10.7804	−	12.4412i	−0.421868	−	0.486862i	−0.926405	+	0.376528i	$0.877118\pi$
$654$	11.1277	+	77.3948i	0.435127	+	3.02638i
$655$	0.00479342	−	0.00140748i	0.000187295	−	5.49947e-5i
$656$	39.9173	+	11.7208i	1.55851	+	0.457620i
$657$	−6.98783	−	8.06439i	−0.272621	−	0.314622i
$658$	18.2865	−	21.1038i	0.712882	−	0.822710i
$659$	22.8216	−	14.6666i	0.889004	−	0.571328i	−0.0145062	−	0.999895i	$-0.504618\pi$
$659$	22.8216	−	14.6666i	0.889004	−	0.571328i	0.903510	+	0.428567i	$0.140981\pi$
$660$	0.201421	+	0.183682i	0.00784032	+	0.00714980i
$661$	33.4652	+	21.5068i	1.30165	+	0.836518i	0.993390	−	0.114785i	$-0.0366180\pi$
$661$	33.4652	+	21.5068i	1.30165	+	0.836518i	0.308257	+	0.951303i	$0.400254\pi$
$662$	24.1212	−	7.08262i	0.937496	−	0.275274i
$663$	13.5943	−	15.6886i	0.527959	−	0.609297i
$664$	45.5662	+	29.2836i	1.76831	+	1.13642i
$665$	−0.0779509	−	0.0500960i	−0.00302280	−	0.00194264i
$666$	−12.2207	−	7.85375i	−0.473541	−	0.304326i
$667$	−3.69923	−	2.37735i	−0.143235	−	0.0920513i
$668$	−40.2866	+	46.4932i	−1.55874	+	1.79888i
$669$	47.3423	−	13.9010i	1.83036	−	0.537442i
$670$	0.155007	+	0.0996168i	0.00598843	+	0.00384853i
$671$	7.61241	+	6.94196i	0.293874	+	0.267991i
$672$	−56.4958	+	36.3076i	−2.17937	+	1.40060i
$673$	28.0232	−	32.3405i	1.08022	−	1.24663i	0.112752	−	0.993623i	$-0.464033\pi$
$673$	28.0232	−	32.3405i	1.08022	−	1.24663i	0.967463	−	0.253012i	$-0.0814211\pi$
$674$	−19.7173	−	22.7549i	−0.759481	−	0.876488i
$675$	19.6605	+	5.77283i	0.756731	+	0.222196i
$676$	48.9479	−	14.3724i	1.88261	−	0.552785i
$677$	6.05076	+	42.0840i	0.232550	+	1.61742i	0.687008	+	0.726650i	$0.258924\pi$
$677$	6.05076	+	42.0840i	0.232550	+	1.61742i	−0.454459	+	0.890768i	$0.650167\pi$
$678$	−28.8134	−	33.2525i	−1.10657	−	1.27705i
$679$	−6.87354	−	4.41736i	−0.263782	−	0.169523i
$680$	0.378022	+	0.110997i	0.0144965	+	0.00425655i
$681$	−2.79998	+	19.4743i	−0.107295	+	0.746256i
$682$	41.3594	+	37.7168i	1.58373	+	1.44425i
$683$	0.212771	+	1.47986i	0.00814146	+	0.0566251i	0.993487	−	0.113944i	$-0.0363485\pi$
$683$	0.212771	+	1.47986i	0.00814146	+	0.0566251i	−0.985346	+	0.170569i	$0.945439\pi$
$684$	5.30042	−	36.8652i	0.202666	−	1.40958i
$685$	−0.0142443	+	0.00915423i	−0.000544245	+	0.000349765i
$686$	−50.4436			−1.92594
$687$	6.96374	−	15.2485i	0.265683	−	0.581765i
$688$	−6.74774	+	7.78731i	−0.257255	+	0.296888i
$689$	0.620520	+	1.35875i	0.0236399	+	0.0517642i
$690$	−0.105557	+	0.231137i	−0.00401848	+	0.00879924i
$691$	−14.9827	−	17.2910i	−0.569970	−	0.657780i	0.395448	−	0.918488i	$-0.370589\pi$
$691$	−14.9827	−	17.2910i	−0.569970	−	0.657780i	−0.965418	+	0.260708i	$0.916044\pi$
$692$	−2.47173	+	0.725764i	−0.0939609	+	0.0275894i
$693$	3.91652	−	3.22344i	0.148776	−	0.122448i
$694$	−50.9897	−	14.9719i	−1.93554	−	0.568327i
$695$	0.000840110		0.00183958i	3.18672e−5		6.97794e-5i
$696$	−5.46737	−	11.9719i	−0.207240	−	0.453792i
$697$	−15.3644	+	4.51140i	−0.581968	+	0.170881i
$698$	−6.50583	−	14.2458i	−0.246249	−	0.539211i
$699$	7.29196			0.275807
$700$	−6.29990	−	43.8168i	−0.238114	−	1.65612i
$701$	22.6930	+	6.66328i	0.857105	+	0.251669i	0.680622	−	0.732635i	$-0.261710\pi$
$701$	22.6930	+	6.66328i	0.857105	+	0.251669i	0.176483	+	0.984304i	$0.443528\pi$
$702$	−2.99555	−	20.8345i	−0.113060	−	0.786347i
$703$	27.6261	+	31.8822i	1.04194	+	1.20246i
$704$	−90.3848	+	10.6632i	−3.40651	+	0.401883i
$705$	0.0623827	−	0.0719935i	0.00234947	−	0.00271143i
$706$	−59.8064	−	38.4352i	−2.25084	−	1.44653i
$707$	1.88569	−	0.553687i	0.0709185	−	0.0208235i
$708$	16.3018	−	10.4765i	0.612659	−	0.393732i
$709$	−13.6931	−	4.02067i	−0.514256	−	0.150999i	0.0142997	−	0.999898i	$-0.495448\pi$
$709$	−13.6931	−	4.02067i	−0.514256	−	0.150999i	−0.528556	+	0.848899i	$0.677266\pi$
$710$	0.0558626	+	0.0644688i	0.00209648	+	0.00241947i
$711$	−1.82215	+	12.6733i	−0.0683360	+	0.475288i
$712$	2.47549	−	17.2174i	0.0927728	−	0.645249i
$713$	−15.8210	+	34.6431i	−0.592501	+	1.29740i
$714$	20.3653	−	44.5938i	0.762152	−	1.66888i
$715$	0.0354602	+	0.0323371i	0.00132614	+	0.00120934i
$716$	−38.0644	−	83.3495i	−1.42253	−	3.11492i
$717$	31.8123			1.18805
$718$	13.5117	+	93.9760i	0.504253	+	3.50715i
$719$	−13.2010	+	15.2348i	−0.492315	+	0.568161i	−0.946483	−	0.322755i	$-0.895391\pi$
$719$	−13.2010	+	15.2348i	−0.492315	+	0.568161i	0.454168	+	0.890916i	$0.349937\pi$
$720$	−0.0867634	+	0.0557595i	−0.00323348	+	0.00207803i
$721$	−0.731565	+	5.08815i	−0.0272449	+	0.189493i
$722$	−40.0766	+	87.7555i	−1.49150	+	3.26592i
$723$	25.4136			0.945142
$724$	−57.4659	+	36.9311i	−2.13570	+	1.37253i
$725$	3.58029			0.132969
$726$	57.7404	−	13.8161i	2.14295	−	0.512765i
$727$	38.3382			1.42189			0.710943	−	0.703250i	$-0.248268\pi$
$727$	38.3382			1.42189			0.710943	+	0.703250i	$0.248268\pi$
$728$	−24.1004	+	15.4884i	−0.893219	+	0.574037i
$729$	14.1791			0.525153
$730$	0.0990415	−	0.216871i	0.00366569	−	0.00802674i
$731$	0.564435	−	3.92573i	0.0208764	−	0.145199i
$732$	−28.0155	+	18.0045i	−1.03548	+	0.665465i
$733$	23.3893	−	26.9926i	0.863902	−	0.996996i	−0.136078	−	0.990698i	$-0.543450\pi$
$733$	23.3893	−	26.9926i	0.863902	−	0.996996i	0.999980	−	0.00629791i	$-0.00200470\pi$
$734$	−5.09317	−	35.4238i	−0.187992	−	1.30752i
$735$	−0.0656453			−0.00242137
$736$	−52.7359	−	115.475i	−1.94387	−	4.25648i
$737$	26.9451	−	11.4886i	0.992534	−	0.423188i
$738$	3.04803	−	6.67425i	0.112200	−	0.245683i
$739$	−6.04002	+	13.2258i	−0.222186	+	0.486519i	−0.987595	−	0.157026i	$-0.949809\pi$
$739$	−6.04002	+	13.2258i	−0.222186	+	0.486519i	0.765409	+	0.643544i	$0.222537\pi$
$740$	0.0337162	−	0.234501i	0.00123943	−	0.00862044i
$741$	3.93119	−	27.3420i	0.144416	−	1.00443i
$742$	2.31006	+	2.66595i	0.0848050	+	0.0978702i
$743$	−25.2172	−	7.40444i	−0.925130	−	0.271643i	−0.215733	−	0.976452i	$-0.569214\pi$
$743$	−25.2172	−	7.40444i	−0.925130	−	0.271643i	−0.709397	+	0.704810i	$0.751032\pi$
$744$	−95.8938	+	61.6272i	−3.51564	+	2.25936i
$745$	−0.00295480		0.000867608i	−0.000108256		3.17867e-5i
$746$	−25.4599	−	16.3621i	−0.932153	−	0.599058i
$747$	3.57400	−	4.12461i	0.130766	−	0.150912i
$748$	76.7617	−	63.1777i	2.80669	−	2.31001i
$749$	16.7006	+	19.2735i	0.610226	+	0.704238i
$750$	−0.0588872	−	0.409570i	−0.00215026	−	0.0149554i
$751$	31.1002	+	9.13185i	1.13486	+	0.333226i	0.794617	−	0.607111i	$-0.207671\pi$
$751$	31.1002	+	9.13185i	1.13486	+	0.333226i	0.340246	+	0.940336i	$0.389490\pi$
$752$	12.8455	+	89.3423i	0.468427	+	3.25798i
$753$	37.5694			1.36910
$754$	−1.52783	−	3.34548i	−0.0556403	−	0.121835i
$755$	0.0739261	−	0.0217067i	0.00269045	−	0.000789986i
$756$	−15.0726	−	33.0044i	−0.548185	−	1.20036i
$757$	−10.2063	−	22.3488i	−0.370956	−	0.812279i	−0.999407	−	0.0344307i	$-0.989038\pi$
$757$	−10.2063	−	22.3488i	−0.370956	−	0.812279i	0.628451	−	0.777849i	$-0.283689\pi$
$758$	27.6619	+	8.12228i	1.00473	+	0.295014i
$759$	20.9703	+	34.5256i	0.761174	+	1.25320i
$760$	0.503017	−	0.147699i	0.0182463	−	0.00535761i
$761$	1.69261	+	1.95337i	0.0613569	+	0.0708097i	0.785598	−	0.618737i	$-0.212355\pi$
$761$	1.69261	+	1.95337i	0.0613569	+	0.0708097i	−0.724241	+	0.689547i	$0.757810\pi$
$762$	−1.87022	+	4.09522i	−0.0677511	+	0.148354i
$763$	9.85718	+	21.5842i	0.356854	+	0.781401i
$764$	−40.9762	+	47.2891i	−1.48247	+	1.71086i
$765$	0.0164910	−	0.0361102i	0.000596233	−	0.00130557i
$766$	42.1020			1.52121
$767$	2.86993	−	1.84439i	0.103627	−	0.0665971i
$768$	10.1100	−	70.3165i	0.364813	−	2.53733i
$769$	−4.52126	−	31.4460i	−0.163041	−	1.13397i	−0.892861	−	0.450333i	$-0.851305\pi$
$769$	−4.52126	−	31.4460i	−0.163041	−	1.13397i	0.729820	−	0.683639i	$-0.239604\pi$
$770$	0.101865	+	0.0496803i	0.00367095	+	0.00179035i
$771$	1.15723	−	8.04873i	0.0416767	−	0.289868i
$772$	−72.5854	−	21.3130i	−2.61241	−	0.767072i
$773$	−24.2102	−	15.5589i	−0.870780	−	0.559616i	0.0272114	−	0.999630i	$-0.491337\pi$
$773$	−24.2102	−	15.5589i	−0.870780	−	0.559616i	−0.897991	+	0.440014i	$0.854974\pi$
$774$	1.19008	+	1.37342i	0.0427765	+	0.0493667i
$775$	−4.41302	−	30.6933i	−0.158520	−	1.10253i
$776$	44.3550	−	13.0238i	1.59225	−	0.467527i
$777$	−17.8198	−	5.23237i	−0.639282	−	0.187710i
$778$	−32.2909	−	37.2657i	−1.15768	−	1.33604i
$779$	−13.9537	+	16.1034i	−0.499942	+	0.576964i
$780$	−0.130502	+	0.0838687i	−0.00467273	+	0.00300298i
$781$	13.4678	−	1.58886i	0.481916	−	0.0568540i
$782$	77.9597	+	50.1017i	2.78783	+	1.79163i
$783$	2.81567	−	0.826757i	0.100624	−	0.0295459i
$784$	40.7322	−	47.0075i	1.45472	−	1.67884i
$785$	−0.131232	−	0.0843379i	−0.00468388	−	0.00301015i
$786$	2.95877	+	1.90149i	0.105536	+	0.0678238i
$787$	13.6264	+	8.75716i	0.485729	+	0.312159i	0.760486	−	0.649355i	$-0.224961\pi$
$787$	13.6264	+	8.75716i	0.485729	+	0.312159i	−0.274757	+	0.961514i	$0.588597\pi$
$788$	69.2700	+	44.5171i	2.46764	+	1.58586i
$789$	−42.0849	+	48.5685i	−1.49826	+	1.72909i
$790$	−0.274485	+	0.0805959i	−0.00976572	+	0.00286747i
$791$	−11.2328	−	7.21889i	−0.399393	−	0.256674i
$792$	−0.727937	+	28.6896i	−0.0258661	+	1.01944i
$793$	−4.93213	+	3.16969i	−0.175145	+	0.112559i
$794$	21.6928	−	25.0349i	0.769850	−	0.888454i
$795$	0.00788056	+	0.00909465i	0.000279495	+	0.000322554i
$796$	−96.5220	−	28.3414i	−3.42113	−	1.00453i
$797$	8.20899	−	2.41038i	0.290777	−	0.0853800i	−0.133091	−	0.991104i	$-0.542490\pi$
$797$	8.20899	−	2.41038i	0.290777	−	0.0853800i	0.423868	+	0.905724i	$0.360672\pi$
$798$	−9.28377	−	64.5701i	−0.328642	−	2.28576i
$799$	−22.7512	−	26.2563i	−0.804879	−	0.928879i
$800$	86.9531	+	55.8814i	3.07426	+	1.97571i
$801$	−1.68167	−	0.493784i	−0.0594190	−	0.0174470i
$802$	−4.10628	+	28.5598i	−0.144998	+	1.00848i
$803$	−19.6760	−	32.3946i	−0.694350	−	1.14318i
$804$	13.4751	+	93.7216i	0.475231	+	3.30530i
$805$	−0.0109741	+	0.0763267i	−0.000386787	+	0.00269016i
$806$	−26.7970	+	17.2214i	−0.943886	+	0.606599i
$807$	−40.1024			−1.41167
$808$	−4.61909	+	10.1144i	−0.162499	+	0.355823i
$809$	−20.3089	+	23.4377i	−0.714022	+	0.824026i	−0.990575	−	0.136973i	$-0.956263\pi$
$809$	−20.3089	+	23.4377i	−0.714022	+	0.824026i	0.276553	+	0.960999i	$0.410808\pi$
$810$	−0.0947212	−	0.207410i	−0.00332816	−	0.00728766i
$811$	−5.46178	+	11.9596i	−0.191789	+	0.419959i	−0.980959	−	0.194216i	$-0.937784\pi$
$811$	−5.46178	+	11.9596i	−0.191789	+	0.419959i	0.789170	+	0.614175i	$0.210511\pi$
$812$	−4.15166	−	4.79127i	−0.145695	−	0.168141i
$813$	9.02240	−	2.64921i	0.316429	−	0.0929120i
$814$	−38.1258	−	34.7680i	−1.33631	−	1.21862i
$815$	0.159217	+	0.0467502i	0.00557711	+	0.00163759i
$816$	65.8278	+	144.143i	2.30443	+	5.04601i
$817$	−2.19236	−	4.80060i	−0.0767010	−	0.167952i
$818$	74.9978	−	22.0213i	2.62224	−	0.769958i
$819$	1.19914	+	2.62574i	0.0419012	+	0.0917508i
$820$	0.119662			0.00417879
$821$	7.64054	+	53.1411i	0.266657	+	1.85464i	0.479487	+	0.877549i	$0.340823\pi$
$821$	7.64054	+	53.1411i	0.266657	+	1.85464i	−0.212831	+	0.977089i	$0.568268\pi$
$822$	−11.4376	−	3.35838i	−0.398932	−	0.117137i
$823$	3.00641	+	20.9100i	0.104797	+	0.728878i	0.972687	+	0.232121i	$0.0745666\pi$
$823$	3.00641	+	20.9100i	0.104797	+	0.728878i	−0.867890	+	0.496756i	$0.834524\pi$
$824$	−19.0458	−	21.9800i	−0.663491	−	0.765709i
$825$	−29.5616	−	14.4175i	−1.02920	−	0.501952i
$826$	5.27587	−	6.08868i	0.183571	−	0.211852i
$827$	−15.1390	−	9.72925i	−0.526435	−	0.338319i	0.250278	−	0.968174i	$-0.419478\pi$
$827$	−15.1390	−	9.72925i	−0.526435	−	0.338319i	−0.776713	+	0.629855i	$0.783114\pi$
$828$	−29.7390	+	8.73217i	−1.03350	+	0.303464i
$829$	8.09920	−	5.20504i	0.281297	−	0.180778i	−0.392383	−	0.919802i	$-0.628349\pi$
$829$	8.09920	−	5.20504i	0.281297	−	0.180778i	0.673680	+	0.739024i	$0.264713\pi$
$830$	0.117001	+	0.0343545i	0.00406115	+	0.00119246i
$831$	15.3319	+	17.6940i	0.531859	+	0.613798i
$832$	7.37082	−	51.2652i	0.255537	−	1.77730i
$833$	−3.40717	+	23.6974i	−0.118051	+	0.821066i
$834$	−0.591447	+	1.29509i	−0.0204801	+	0.0448453i
$835$	−0.0362464	+	0.0793685i	−0.00125436	+	0.00274666i
$836$	40.4780	−	125.945i	1.39996	−	4.35591i
$837$	−10.5582	−	23.1193i	−0.364945	−	0.799118i
$838$	61.0963			2.11054
$839$	−7.68751	−	53.4678i	−0.265402	−	1.84591i	−0.490327	−	0.871538i	$-0.663123\pi$
$839$	−7.68751	−	53.4678i	−0.265402	−	1.84591i	0.224925	−	0.974376i	$-0.427786\pi$
$840$	−0.151140	+	0.174425i	−0.00521484	+	0.00601824i
$841$	−23.9650	+	15.4014i	−0.826379	+	0.531082i
$842$	−0.967358	+	6.72812i	−0.0333374	+	0.231866i
$843$	6.20054	−	13.5773i	0.213558	−	0.467627i
$844$	−11.5683			−0.398196
$845$	0.0608681	−	0.0391175i	0.00209393	−	0.00134568i
$846$	15.9191			0.547309
$847$	15.6314	−	8.95960i	0.537103	−	0.307855i
$848$	−11.4023			−0.391557
$849$	22.9486	−	14.7482i	0.787593	−	0.506155i
$850$	−75.4532			−2.58802
$851$	14.5841	−	31.9346i	0.499935	−	1.09471i
$852$	−6.23851	+	43.3898i	−0.213728	+	1.48651i
$853$	−29.9455	+	19.2448i	−1.02531	+	0.658929i	−0.941312	−	0.337537i	$-0.890406\pi$
$853$	−29.9455	+	19.2448i	−1.02531	+	0.658929i	−0.0840010	+	0.996466i	$0.526770\pi$
$854$	−9.06687	+	10.4637i	−0.310262	+	0.358061i
$855$	−0.00751762	−	0.0522862i	−0.000257097	−	0.00178815i
$856$	−144.288			−4.93165
$857$	18.4728	+	40.4498i	0.631019	+	1.38174i	0.907227	+	0.420640i	$0.138195\pi$
$857$	18.4728	+	40.4498i	0.631019	+	1.38174i	−0.276209	+	0.961098i	$0.589078\pi$
$858$	−0.856975	+	33.7753i	−0.0292566	+	1.15307i
$859$	13.7387	−	30.0837i	0.468760	−	1.02644i	−0.516643	−	0.856201i	$-0.672818\pi$
$859$	13.7387	−	30.0837i	0.468760	−	1.02644i	0.985403	−	0.170240i	$-0.0544543\pi$
$860$	−0.0123120	+	0.0269596i	−0.000419837	+	0.000919314i
$861$	1.33500	−	9.28511i	0.0454966	−	0.316436i
$862$	12.7170	−	88.4489i	0.433144	−	3.01258i
$863$	−35.6610	−	41.1550i	−1.21392	−	1.40093i	−0.890690	−	0.454612i	$-0.849778\pi$
$863$	−35.6610	−	41.1550i	−1.21392	−	1.40093i	−0.323226	−	0.946322i	$-0.604767\pi$
$864$	81.2872	+	23.8681i	2.76545	+	0.812008i
$865$	−0.00307366	+	0.00197532i	−0.000104508	+	6.71629e-5i
$866$	−18.2498	+	5.35863i	−0.620154	+	0.182094i
$867$	−22.9460	−	14.7465i	−0.779288	−	0.500818i
$868$	−35.9574	+	41.4971i	−1.22048	+	1.40850i
$869$	−13.9153	+	43.2969i	−0.472046	+	1.46875i
$870$	−0.0194033	−	0.0223926i	−0.000657834	−	0.000759181i
$871$	2.37230	+	16.4997i	0.0803822	+	0.559070i
$872$	−128.813	−	37.8228i	−4.36215	−	1.28084i
$873$	−0.662888	−	4.61049i	−0.0224354	−	0.156041i
$874$	123.313			4.17113
$875$	−0.0521637	−	0.114223i	−0.00176346	−	0.00386143i
$876$	117.554	−	34.5169i	3.97177	−	1.16622i
$877$	8.31136	+	18.1993i	0.280655	+	0.614548i	0.996489	−	0.0837220i	$-0.0266808\pi$
$877$	8.31136	+	18.1993i	0.280655	+	0.614548i	−0.715834	+	0.698270i	$0.753953\pi$
$878$	1.79407	+	3.92846i	0.0605469	+	0.132579i
$879$	−25.1261	−	7.37769i	−0.847482	−	0.248843i
$880$	−0.336982	+	0.143680i	−0.0113597	+	0.00484344i
$881$	3.33159	−	0.978242i	0.112244	−	0.0329578i	−0.225128	−	0.974329i	$-0.572280\pi$
$881$	3.33159	−	0.978242i	0.112244	−	0.0329578i	0.337372	+	0.941371i	$0.390462\pi$
$882$	−7.18382	−	8.29057i	−0.241892	−	0.279158i
$883$	−3.69739	+	8.09615i	−0.124427	+	0.272457i	−0.961587	−	0.274501i	$-0.911487\pi$
$883$	−3.69739	+	8.09615i	−0.124427	+	0.272457i	0.837160	+	0.546959i	$0.184214\pi$
$884$	23.5024	+	51.4632i	0.790472	+	1.73089i
$885$	0.0179981	−	0.0207710i	0.000605001	−	0.000698208i
$886$	42.8049	−	93.7298i	1.43806	−	3.14891i
$887$	−39.9669			−1.34196			−0.670979	−	0.741477i	$-0.734126\pi$
$887$	−39.9669			−1.34196			−0.670979	+	0.741477i	$0.734126\pi$
$888$	88.3965	−	56.8090i	2.96639	−	1.90638i
$889$	−0.194436	+	1.35233i	−0.00652118	+	0.0453558i
$890$	−0.00557303	−	0.0387613i	−0.000186808	−	0.00129928i
$891$	−35.7372	−	6.06713i	−1.19724	−	0.203256i
$892$	−19.1373	+	133.103i	−0.640764	+	4.45661i
$893$	−44.3570	−	13.0244i	−1.48435	−	0.435845i
$894$	−1.82387	−	1.17213i	−0.0609993	−	0.0392019i
$895$	−0.0851052	−	0.0982167i	−0.00284475	−	0.00328302i
$896$	−7.76918	−	54.0358i	−0.259550	−	1.80521i
$897$	−22.0567	+	6.47643i	−0.736452	+	0.216242i
$898$	15.4161	+	4.52656i	0.514441	+	0.151053i
$899$	−2.90820	−	3.35624i	−0.0969938	−	0.111937i
$900$	16.5260	−	19.0721i	0.550868	−	0.635735i
$901$	3.69211	−	2.37277i	0.123002	−	0.0790486i
$902$	14.6417	−	21.5602i	0.487514	−	0.717875i
$903$	1.95455	+	1.25611i	0.0650434	+	0.0418009i
$904$	72.4854	−	21.2836i	2.41083	−	0.707883i
$905$	−0.0634458	+	0.0732204i	−0.00210901	+	0.00243393i
$906$	45.6313	+	29.3255i	1.51600	+	0.974273i
$907$	−32.7211	−	21.0286i	−1.08649	−	0.698243i	−0.130440	−	0.991456i	$-0.541639\pi$
$907$	−32.7211	−	21.0286i	−1.08649	−	0.698243i	−0.956047	+	0.293213i	$0.905275\pi$
$908$	−45.1081	−	28.9892i	−1.49696	−	0.962040i
$909$	0.942520	+	0.605721i	0.0312614	+	0.0200905i
$910$	−0.0422354	+	0.0487423i	−0.00140009	+	0.00161579i
$911$	46.9239	−	13.7781i	1.55466	−	0.456489i	0.612171	−	0.790726i	$-0.290297\pi$
$911$	46.9239	−	13.7781i	1.55466	−	0.456489i	0.942489	+	0.334236i	$0.108478\pi$
$912$	177.386	+	113.999i	5.87384	+	3.77489i
$913$	14.9677	−	12.3190i	0.495359	−	0.407699i
$914$	−2.60474	+	1.67396i	−0.0861570	+	0.0553697i
$915$	−0.0309308	+	0.0356960i	−0.00102254	+	0.00118007i
$916$	29.9180	+	34.5272i	0.988518	+	1.14081i
$917$	1.02410	+	0.300703i	0.0338187	+	0.00993007i
$918$	−59.3392	+	17.4236i	−1.95849	+	0.575063i
$919$	−3.01310	−	20.9565i	−0.0993928	−	0.691292i	−0.977207	−	0.212290i	$-0.931908\pi$
$919$	−3.01310	−	20.9565i	−0.0993928	−	0.691292i	0.877814	−	0.479002i	$-0.159001\pi$
$920$	−0.285703	−	0.329719i	−0.00941936	−	0.0108705i
$921$	33.5175	+	21.5404i	1.10444	+	0.709780i
$922$	12.3285	+	3.61997i	0.406017	+	0.119217i
$923$	−1.09829	+	7.63877i	−0.0361507	+	0.251433i
$924$	14.9853	+	56.2787i	0.492981	+	1.85143i
$925$	4.06800	+	28.2936i	0.133755	+	0.930286i
$926$	8.90194	−	61.9144i	0.292536	−	2.03463i
$927$	−2.46528	+	1.58434i	−0.0809703	+	0.0520365i
$928$	14.8029			0.485930
$929$	8.78720	−	19.2413i	0.288299	−	0.631286i	−0.708963	−	0.705246i	$-0.750836\pi$
$929$	8.78720	−	19.2413i	0.288299	−	0.631286i	0.997261	+	0.0739602i	$0.0235638\pi$
$930$	−0.168052	+	0.193942i	−0.00551064	+	0.00635962i
$931$	13.2340	+	28.9784i	0.433727	+	0.949730i
$932$	−8.25562	+	18.0773i	−0.270422	+	0.592141i
$933$	−19.9005	−	22.9663i	−0.651512	−	0.751884i
$934$	−95.1425	+	27.9364i	−3.11316	+	0.914105i
$935$	0.0792169	−	0.116649i	0.00259067	−	0.00381481i
$936$	−15.6702	−	4.60119i	−0.512197	−	0.150395i
$937$	15.0501	+	32.9551i	0.491665	+	1.07660i	0.979089	+	0.203430i	$0.0652090\pi$
$937$	15.0501	+	32.9551i	0.491665	+	1.07660i	−0.487425	+	0.873165i	$0.662064\pi$
$938$	16.3532	+	35.8084i	0.533950	+	1.16919i
$939$	−8.60641	+	2.52707i	−0.280859	+	0.0824678i
$940$	0.107850	+	0.236159i	0.00351768	+	0.00770265i
$941$	14.4693			0.471686			0.235843	−	0.971791i	$-0.424215\pi$
$941$	14.4693			0.471686			0.235843	+	0.971791i	$0.424215\pi$
$942$	−15.6295	−	108.705i	−0.509236	−	3.54181i
$943$	17.0140	+	4.99577i	0.554053	+	0.162685i
$944$	3.70607	+	25.7763i	0.120622	+	0.838947i
$945$	−0.0336996	−	0.0388914i	−0.00109625	−	0.00126514i
$946$	3.35096	+	5.51704i	0.108949	+	0.179375i
$947$	11.9291	−	13.7669i	0.387643	−	0.447364i	−0.528068	−	0.849202i	$-0.677083\pi$
$947$	11.9291	−	13.7669i	0.387643	−	0.447364i	0.915711	+	0.401838i	$0.131629\pi$
$948$	−123.669	−	79.4775i	−4.01659	−	2.58131i
$949$	20.6953	−	6.07669i	0.671798	−	0.197258i
$950$	−84.4638	+	54.2816i	−2.74037	+	1.76113i
$951$	−16.8622	−	4.95118i	−0.546793	−	0.160553i
$952$	55.1213	+	63.6134i	1.78649	+	2.06172i
$953$	−4.63619	+	32.2454i	−0.150181	+	1.04453i	0.765734	+	0.643158i	$0.222376\pi$
$953$	−4.63619	+	32.2454i	−0.150181	+	1.04453i	−0.915915	+	0.401373i	$0.868533\pi$
$954$	−0.286194	+	1.99052i	−0.00926588	+	0.0644456i
$955$	−0.0368668	+	0.0807271i	−0.00119298	+	0.00261227i
$956$	−36.0164	+	78.8650i	−1.16485	+	2.55068i
$957$	−4.67791	+	0.551877i	−0.151215	+	0.0178396i
$958$	−10.0307	−	21.9643i	−0.324079	−	0.709634i
$959$	−3.61750			−0.116815
$960$	−0.0593814	−	0.413007i	−0.00191653	−	0.0133297i
$961$	−4.88718	+	5.64010i	−0.157651	+	0.181939i
$962$	24.7020	−	15.8750i	0.796423	−	0.511830i
$963$	−2.06904	+	14.3905i	−0.0666739	+	0.463727i
$964$	−28.7721	+	63.0021i	−0.926686	+	2.02916i
$965$	−0.107295			−0.00345394
$966$	−45.6695	+	29.3500i	−1.46939	+	0.944322i
$967$	36.3247			1.16812			0.584062	−	0.811709i	$-0.301462\pi$
$967$	36.3247			1.16812			0.584062	+	0.811709i	$0.301462\pi$
$968$	−19.6054	+	100.034i	−0.630142	+	3.21521i
$969$	−81.1610			−2.60727
$970$	0.0875505	−	0.0562653i	0.00281108	−	0.00180657i
$971$	25.1586			0.807379			0.403689	−	0.914896i	$-0.367728\pi$
$971$	25.1586			0.807379			0.403689	+	0.914896i	$0.367728\pi$
$972$	21.0682	−	46.1329i	0.675762	−	1.47971i
$973$	−0.0614893	+	0.427668i	−0.00197126	+	0.0137104i
$974$	82.8421	−	53.2394i	2.65443	−	1.70590i
$975$	12.2569	−	14.1453i	0.392536	−	0.453011i
$976$	−6.36909	−	44.2980i	−0.203869	−	1.41794i
$977$	0.138623			0.00443496			0.00221748	−	0.999998i	$-0.499294\pi$
$977$	0.138623			0.00443496			0.00221748	+	0.999998i	$0.499294\pi$
$978$	48.5298	+	106.265i	1.55181	+	3.39800i
$979$	−5.59541	−	2.72893i	−0.178830	−	0.0872170i
$980$	0.0743206	−	0.162739i	0.00237408	−	0.00519852i
$981$	−5.61938	+	12.3047i	−0.179413	+	0.392860i
$982$	13.9223	−	96.8315i	0.444278	−	3.09002i
$983$	5.25449	−	36.5458i	0.167592	−	1.16563i	−0.716250	−	0.697844i	$-0.754143\pi$
$983$	5.25449	−	36.5458i	0.167592	−	1.16563i	0.883842	−	0.467786i	$-0.154948\pi$
$984$	34.7557	+	40.1102i	1.10797	+	1.27867i
$985$	0.112055	+	0.0329023i	0.00357036	+	0.00104835i
$986$	−9.09062	+	5.84219i	−0.289504	+	0.186053i
$987$	19.5278	−	5.73388i	0.621576	−	0.182511i
$988$	63.3320	+	40.7010i	2.01486	+	1.29487i
$989$	−2.87610	+	3.31920i	−0.0914547	+	0.105544i
$990$	0.0166243	+	0.0624339i	0.000528354	+	0.00198428i
$991$	14.0789	+	16.2480i	0.447232	+	0.516133i	0.933939	−	0.357432i	$-0.116348\pi$
$991$	14.0789	+	16.2480i	0.447232	+	0.516133i	−0.486707	+	0.873565i	$0.661802\pi$
$992$	−18.2459	−	126.903i	−0.579307	−	4.02917i
$993$	17.5804	+	5.16206i	0.557896	+	0.163813i
$994$	2.59369	+	18.0395i	0.0822668	+	0.572178i
$995$	−0.142677			−0.00452317
$996$	26.0308	+	56.9996i	0.824818	+	1.80610i
$997$	−25.7215	+	7.55252i	−0.814609	+	0.239191i	−0.662393	−	0.749157i	$-0.730459\pi$
$997$	−25.7215	+	7.55252i	−0.814609	+	0.239191i	−0.152216	+	0.988347i	$0.548641\pi$
$998$	−26.7122	−	58.4915i	−0.845559	−	1.85152i
$999$	9.73273	+	21.3117i	0.307930	+	0.674273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.2.e.a.12.1	✓	100
121.111	even	11	inner	121.2.e.a.111.1	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.2.e.a.12.1	✓	100	1.1	even	1	trivial
121.2.e.a.111.1	yes	100	121.111	even	11	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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	121.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.28929 + 1.47124i) q^{2} -1.98337 q^{3} +(2.24548 - 4.91691i) q^{4} +(0.00109106 - 0.00758846i) q^{5} +(4.54050 - 2.91800i) q^{6} +(1.07261 - 1.23786i) q^{7} +(1.31883 + 9.17268i) q^{8} +0.933746 q^{9} +O(q^{10})\)	\(q+(-2.28929 + 1.47124i) q^{2} -1.98337 q^{3} +(2.24548 - 4.91691i) q^{4} +(0.00109106 - 0.00758846i) q^{5} +(4.54050 - 2.91800i) q^{6} +(1.07261 - 1.23786i) q^{7} +(1.31883 + 9.17268i) q^{8} +0.933746 q^{9} +(0.00866667 + 0.0189774i) q^{10} +(3.26984 + 0.555122i) q^{11} +(-4.45360 + 9.75203i) q^{12} +(-0.784057 + 1.71684i) q^{13} +(-0.634332 + 4.41187i) q^{14} +(-0.00216396 + 0.0150507i) q^{15} +(-9.43482 - 10.8884i) q^{16} +(5.32085 + 1.56234i) q^{17} +(-2.13761 + 1.37376i) q^{18} +(7.08022 - 2.07894i) q^{19} +(-0.0348618 - 0.0224043i) q^{20} +(-2.12738 + 2.45512i) q^{21} +(-8.30232 + 3.53987i) q^{22} +(-4.02142 - 4.64097i) q^{23} +(-2.61573 - 18.1928i) q^{24} +(4.79741 + 1.40865i) q^{25} +(-0.730952 - 5.08389i) q^{26} +4.09814 q^{27} +(-3.67791 - 8.05349i) q^{28} +(0.687061 - 0.201739i) q^{29} +(-0.0171892 - 0.0376391i) q^{30} +(-2.57634 - 5.64140i) q^{31} +(19.8351 + 5.82412i) q^{32} +(-6.48529 - 1.10101i) q^{33} +(-14.4795 + 4.25158i) q^{34} +(-0.00822315 - 0.00949002i) q^{35} +(2.09670 - 4.59114i) q^{36} +(2.37491 + 5.20034i) q^{37} +(-13.1501 + 15.1760i) q^{38} +(1.55507 - 3.40513i) q^{39} +0.0710454 q^{40} +(-2.42919 + 1.56115i) q^{41} +(1.25811 - 8.75036i) q^{42} +(-0.101783 - 0.707916i) q^{43} +(10.0718 - 14.8310i) q^{44} +(0.00101877 - 0.00708569i) q^{45} +(16.0341 + 4.70805i) q^{46} +(-5.27039 - 3.38707i) q^{47} +(18.7127 + 21.5956i) q^{48} +(0.614405 + 4.27328i) q^{49} +(-13.0551 + 3.83332i) q^{50} +(-10.5532 - 3.09870i) q^{51} +(6.68098 + 7.71027i) q^{52} +(0.518272 - 0.598117i) q^{53} +(-9.38183 + 6.02934i) q^{54} +(0.00778009 - 0.0242074i) q^{55} +(12.7690 + 8.20617i) q^{56} +(-14.0427 + 4.12330i) q^{57} +(-1.27608 + 1.47267i) q^{58} +(-1.52057 - 0.977210i) q^{59} +(0.0691437 + 0.0444360i) q^{60} +(2.61318 + 1.67939i) q^{61} +(14.1978 + 9.12439i) q^{62} +(1.00154 - 1.15584i) q^{63} +(-26.3295 + 7.73103i) q^{64} +(0.0121728 + 0.00782295i) q^{65} +(16.4665 - 7.02086i) q^{66} +(7.42985 - 4.77488i) q^{67} +(19.6297 - 22.6539i) q^{68} +(7.97595 + 9.20474i) q^{69} +(0.0327872 + 0.00962719i) q^{70} +(3.92323 - 1.15196i) q^{71} +(1.23145 + 8.56495i) q^{72} +(-7.48365 - 8.63660i) q^{73} +(-13.0878 - 8.41101i) q^{74} +(-9.51502 - 2.79386i) q^{75} +(5.67651 - 39.4810i) q^{76} +(4.19442 - 3.45216i) q^{77} +(1.44975 + 10.0832i) q^{78} +(-1.95144 + 13.5726i) q^{79} +(-0.0929198 + 0.0597159i) q^{80} -10.9294 q^{81} +(3.26430 - 7.14783i) q^{82} +(3.82759 - 4.41727i) q^{83} +(7.29464 + 15.9730i) q^{84} +(0.0176611 - 0.0386724i) q^{85} +(1.27452 + 1.47088i) q^{86} +(-1.36270 + 0.400123i) q^{87} +(-0.779588 + 30.7253i) q^{88} +(-1.80100 - 0.528820i) q^{89} +(0.00809247 + 0.0177200i) q^{90} +(1.28422 + 2.81205i) q^{91} +(-31.8492 + 9.35177i) q^{92} +(5.10983 + 11.1890i) q^{93} +17.0486 q^{94} +(-0.00805104 - 0.0559962i) q^{95} +(-39.3404 - 11.5514i) q^{96} +(-0.709923 - 4.93763i) q^{97} +(-7.69355 - 8.87883i) q^{98} +(3.05320 + 0.518343i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 6 q^{2} - 18 q^{3} - 16 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} + 4 q^{8} + 70 q^{9}+O(q^{10}) \) 100 * q - 6 * q^2 - 18 * q^3 - 16 * q^4 - 7 * q^5 - 23 * q^6 - q^7 + 4 * q^8 + 70 * q^9	\( 100 q - 6 q^{2} - 18 q^{3} - 16 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} + 4 q^{8} + 70 q^{9} - 13 q^{10} - 12 q^{11} - 51 q^{12} - 34 q^{13} - 17 q^{14} - 46 q^{15} + 10 q^{16} + 9 q^{17} - 31 q^{18} + 9 q^{19} + 21 q^{20} - 14 q^{21} - 20 q^{22} - 11 q^{23} - 72 q^{24} + 11 q^{25} + 33 q^{26} - 60 q^{27} + 49 q^{28} + 19 q^{29} + 26 q^{30} - 13 q^{31} + 44 q^{32} + q^{33} + 31 q^{34} + 39 q^{35} - 17 q^{36} - 16 q^{37} - 29 q^{38} + 16 q^{39} + 2 q^{40} + 39 q^{41} + 42 q^{42} + 39 q^{43} + 53 q^{44} - 33 q^{45} + 59 q^{46} + 21 q^{47} + 56 q^{48} - 11 q^{49} - 58 q^{50} - 139 q^{51} - 75 q^{52} - 73 q^{53} - 156 q^{54} - 34 q^{55} + 10 q^{56} - 41 q^{57} - 38 q^{58} + 33 q^{59} + 100 q^{60} + 39 q^{61} + 44 q^{62} - 76 q^{63} - 16 q^{64} + 36 q^{65} + 75 q^{66} - 4 q^{67} + 119 q^{68} + 32 q^{69} + 61 q^{70} + 5 q^{71} + 63 q^{72} + 37 q^{73} + 109 q^{74} + 58 q^{75} - 91 q^{76} - 53 q^{77} - 24 q^{78} - 9 q^{79} - 36 q^{80} + 28 q^{81} + 33 q^{82} + 79 q^{83} + 176 q^{84} - 11 q^{85} + 85 q^{86} + 76 q^{87} + 33 q^{88} - 48 q^{89} - 89 q^{90} - 14 q^{91} - 113 q^{92} + 31 q^{93} - 38 q^{94} + 21 q^{95} + 84 q^{96} + 40 q^{97} - 22 q^{98} - 53 q^{99}+O(q^{100}) \) 100 * q - 6 * q^2 - 18 * q^3 - 16 * q^4 - 7 * q^5 - 23 * q^6 - q^7 + 4 * q^8 + 70 * q^9 - 13 * q^10 - 12 * q^11 - 51 * q^12 - 34 * q^13 - 17 * q^14 - 46 * q^15 + 10 * q^16 + 9 * q^17 - 31 * q^18 + 9 * q^19 + 21 * q^20 - 14 * q^21 - 20 * q^22 - 11 * q^23 - 72 * q^24 + 11 * q^25 + 33 * q^26 - 60 * q^27 + 49 * q^28 + 19 * q^29 + 26 * q^30 - 13 * q^31 + 44 * q^32 + q^33 + 31 * q^34 + 39 * q^35 - 17 * q^36 - 16 * q^37 - 29 * q^38 + 16 * q^39 + 2 * q^40 + 39 * q^41 + 42 * q^42 + 39 * q^43 + 53 * q^44 - 33 * q^45 + 59 * q^46 + 21 * q^47 + 56 * q^48 - 11 * q^49 - 58 * q^50 - 139 * q^51 - 75 * q^52 - 73 * q^53 - 156 * q^54 - 34 * q^55 + 10 * q^56 - 41 * q^57 - 38 * q^58 + 33 * q^59 + 100 * q^60 + 39 * q^61 + 44 * q^62 - 76 * q^63 - 16 * q^64 + 36 * q^65 + 75 * q^66 - 4 * q^67 + 119 * q^68 + 32 * q^69 + 61 * q^70 + 5 * q^71 + 63 * q^72 + 37 * q^73 + 109 * q^74 + 58 * q^75 - 91 * q^76 - 53 * q^77 - 24 * q^78 - 9 * q^79 - 36 * q^80 + 28 * q^81 + 33 * q^82 + 79 * q^83 + 176 * q^84 - 11 * q^85 + 85 * q^86 + 76 * q^87 + 33 * q^88 - 48 * q^89 - 89 * q^90 - 14 * q^91 - 113 * q^92 + 31 * q^93 - 38 * q^94 + 21 * q^95 + 84 * q^96 + 40 * q^97 - 22 * q^98 - 53 * q^99

Introduction

L-functions

Modular forms

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