LMFDB - Embedded newform 256.2.m.a.101.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, 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:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			101.15
Character	$\chi$	$=$	256.101
Dual form			256.2.m.a.109.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.375382 - 1.36348i) q^{2} +(1.08486 - 0.271743i) q^{3} +(-1.71818 + 1.02365i) q^{4} +(2.65917 + 1.25769i) q^{5} +(-0.777754 - 1.37718i) q^{6} +(-0.202472 - 0.667460i) q^{7} +(2.04071 + 1.95845i) q^{8} +(-1.54269 + 0.824584i) q^{9} +O(q^{10})$	\(q+(-0.375382 - 1.36348i) q^{2} +(1.08486 - 0.271743i) q^{3} +(-1.71818 + 1.02365i) q^{4} +(2.65917 + 1.25769i) q^{5} +(-0.777754 - 1.37718i) q^{6} +(-0.202472 - 0.667460i) q^{7} +(2.04071 + 1.95845i) q^{8} +(-1.54269 + 0.824584i) q^{9} +(0.716640 - 4.09784i) q^{10} +(6.06673 - 0.899914i) q^{11} +(-1.58581 + 1.57742i) q^{12} +(0.659432 - 1.84299i) q^{13} +(-0.834067 + 0.526620i) q^{14} +(3.22659 + 0.641809i) q^{15} +(1.90426 - 3.51764i) q^{16} +(-5.72839 + 1.13945i) q^{17} +(1.70340 + 1.79390i) q^{18} +(0.138829 + 0.125828i) q^{19} +(-5.85636 + 0.561129i) q^{20} +(-0.401031 - 0.669080i) q^{21} +(-3.50436 - 7.93408i) q^{22} +(3.65657 - 0.360141i) q^{23} +(2.74608 + 1.57009i) q^{24} +(2.31741 + 2.82377i) q^{25} +(-2.76042 - 0.207300i) q^{26} +(-3.93551 + 3.56694i) q^{27} +(1.03113 + 0.939554i) q^{28} +(-4.22087 - 5.69119i) q^{29} +(-0.336108 - 4.64033i) q^{30} +(-3.64060 - 1.50799i) q^{31} +(-5.51107 - 1.27598i) q^{32} +(6.33700 - 2.62487i) q^{33} +(3.70395 + 7.38284i) q^{34} +(0.301053 - 2.02953i) q^{35} +(1.80652 - 2.99596i) q^{36} +(-0.0316262 + 0.643767i) q^{37} +(0.119450 - 0.236525i) q^{38} +(0.214571 - 2.17858i) q^{39} +(2.96346 + 7.77441i) q^{40} +(-3.93122 + 4.79020i) q^{41} +(-0.761741 + 0.797961i) q^{42} +(-1.54023 + 6.14894i) q^{43} +(-9.50251 + 7.75644i) q^{44} +(-5.13933 + 0.252479i) q^{45} +(-1.86366 - 4.85049i) q^{46} +(-1.06023 - 0.708426i) q^{47} +(1.10996 - 4.33362i) q^{48} +(5.41578 - 3.61871i) q^{49} +(2.98025 - 4.21974i) q^{50} +(-5.90486 + 2.79279i) q^{51} +(0.753562 + 3.84161i) q^{52} +(1.04002 - 1.40231i) q^{53} +(6.34078 + 4.02704i) q^{54} +(17.2642 + 5.23705i) q^{55} +(0.893998 - 1.75862i) q^{56} +(0.184803 + 0.0987793i) q^{57} +(-6.17540 + 7.89146i) q^{58} +(-0.553538 - 1.54704i) q^{59} +(-6.20084 + 2.20017i) q^{60} +(-5.98148 + 9.97950i) q^{61} +(-0.689500 + 5.52998i) q^{62} +(0.862728 + 0.862728i) q^{63} +(0.328984 + 7.99323i) q^{64} +(4.07145 - 4.07145i) q^{65} +(-5.95777 - 7.65507i) q^{66} +(10.1735 + 6.09778i) q^{67} +(8.67598 - 7.82166i) q^{68} +(3.86900 - 1.38435i) q^{69} +(-2.88025 + 0.351370i) q^{70} +(2.06844 - 3.86978i) q^{71} +(-4.76308 - 1.33853i) q^{72} +(-4.46300 + 14.7126i) q^{73} +(0.889638 - 0.198537i) q^{74} +(3.28140 + 2.43365i) q^{75} +(-0.367337 - 0.0740808i) q^{76} +(-1.82900 - 3.86709i) q^{77} +(-3.05100 + 0.525235i) q^{78} +(-7.70630 - 11.5333i) q^{79} +(9.48786 - 6.95901i) q^{80} +(-0.384717 + 0.575770i) q^{81} +(8.00707 + 3.56200i) q^{82} +(0.220427 + 4.48690i) q^{83} +(1.37395 + 0.739081i) q^{84} +(-16.6658 - 4.17457i) q^{85} +(8.96215 - 0.208123i) q^{86} +(-6.12560 - 5.02715i) q^{87} +(14.1429 + 10.0449i) q^{88} +(-12.4959 - 1.23074i) q^{89} +(2.27346 + 6.91262i) q^{90} +(-1.36364 - 0.0669912i) q^{91} +(-5.91398 + 4.36185i) q^{92} +(-4.35933 - 0.646646i) q^{93} +(-0.567935 + 1.71154i) q^{94} +(0.210918 + 0.509201i) q^{95} +(-6.32548 + 0.113341i) q^{96} +(0.123173 - 0.297367i) q^{97} +(-6.96704 - 6.02593i) q^{98} +(-8.61701 + 6.39081i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{9}{64}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.375382	−	1.36348i	−0.265435	−	0.964129i
$2$	−0.375382	−	1.36348i	−0.265435	−	0.964129i
$3$	1.08486	−	0.271743i	0.626344	−	0.156891i	0.0832032	−	0.996533i	$-0.473485\pi$
$3$	1.08486	−	0.271743i	0.626344	−	0.156891i	0.543141	+	0.839642i	$0.317235\pi$
$4$	−1.71818	+	1.02365i	−0.859088	+	0.511827i
$5$	2.65917	+	1.25769i	1.18921	+	0.562457i	0.916654	−	0.399682i	$-0.130879\pi$
$5$	2.65917	+	1.25769i	1.18921	+	0.562457i	0.272561	+	0.962139i	$0.412129\pi$
$6$	−0.777754	−	1.37718i	−0.317517	−	0.562232i
$7$	−0.202472	−	0.667460i	−0.0765272	−	0.252276i	0.910327	−	0.413890i	$-0.135830\pi$
$7$	−0.202472	−	0.667460i	−0.0765272	−	0.252276i	−0.986854	+	0.161614i	$0.948330\pi$
$8$	2.04071	+	1.95845i	0.721499	+	0.692415i
$9$	−1.54269	+	0.824584i	−0.514229	+	0.274861i
$10$	0.716640	−	4.09784i	0.226621	−	1.29585i
$11$	6.06673	−	0.899914i	1.82919	−	0.271334i	0.858699	−	0.512481i	$-0.171273\pi$
$11$	6.06673	−	0.899914i	1.82919	−	0.271334i	0.970489	+	0.241146i	$0.0775234\pi$
$12$	−1.58581	+	1.57742i	−0.457784	+	0.455363i
$13$	0.659432	−	1.84299i	0.182893	−	0.511153i	−0.814746	−	0.579818i	$-0.803124\pi$
$13$	0.659432	−	1.84299i	0.182893	−	0.511153i	0.997640	+	0.0686646i	$0.0218738\pi$
$14$	−0.834067	+	0.526620i	−0.222914	+	0.140745i
$15$	3.22659	+	0.641809i	0.833102	+	0.165714i
$16$	1.90426	−	3.51764i	0.476066	−	0.879410i
$17$	−5.72839	+	1.13945i	−1.38934	+	0.276357i	−0.832390	−	0.554191i	$-0.813028\pi$
$17$	−5.72839	+	1.13945i	−1.38934	+	0.276357i	−0.556948	+	0.830547i	$0.688028\pi$
$18$	1.70340	+	1.79390i	0.401496	+	0.422825i
$19$	0.138829	+	0.125828i	0.0318496	+	0.0288668i	0.687329	−	0.726347i	$-0.258783\pi$
$19$	0.138829	+	0.125828i	0.0318496	+	0.0288668i	−0.655479	+	0.755213i	$0.727533\pi$
$20$	−5.85636	+	0.561129i	−1.30952	+	0.125472i
$21$	−0.401031	−	0.669080i	−0.0875122	−	0.146005i
$22$	−3.50436	−	7.93408i	−0.747132	−	1.69155i
$23$	3.65657	−	0.360141i	0.762448	−	0.0750946i	0.290684	−	0.956819i	$-0.406117\pi$
$23$	3.65657	−	0.360141i	0.762448	−	0.0750946i	0.471764	+	0.881725i	$0.343617\pi$
$24$	2.74608	+	1.57009i	0.560541	+	0.320493i
$25$	2.31741	+	2.82377i	0.463481	+	0.564753i
$26$	−2.76042	−	0.207300i	−0.541364	−	0.0406549i
$27$	−3.93551	+	3.56694i	−0.757389	+	0.686458i
$28$	1.03113	+	0.939554i	0.194865	+	0.177559i
$29$	−4.22087	−	5.69119i	−0.783796	−	1.05683i	−0.996813	−	0.0797783i	$-0.974579\pi$
$29$	−4.22087	−	5.69119i	−0.783796	−	1.05683i	0.213016	−	0.977049i	$-0.431671\pi$
$30$	−0.336108	−	4.64033i	−0.0613646	−	0.847204i
$31$	−3.64060	−	1.50799i	−0.653872	−	0.270843i	0.0309855	−	0.999520i	$-0.490135\pi$
$31$	−3.64060	−	1.50799i	−0.653872	−	0.270843i	−0.684857	+	0.728677i	$0.740135\pi$
$32$	−5.51107	−	1.27598i	−0.974229	−	0.225563i
$33$	6.33700	−	2.62487i	1.10313	−	0.456932i
$34$	3.70395	+	7.38284i	0.635222	+	1.26615i
$35$	0.301053	−	2.02953i	0.0508872	−	0.343054i
$36$	1.80652	−	2.99596i	0.301087	−	0.499327i
$37$	−0.0316262	+	0.643767i	−0.00519932	+	0.105835i	0.994793	+	0.101916i	$0.0324973\pi$
$37$	−0.0316262	+	0.643767i	−0.00519932	+	0.105835i	−0.999992	+	0.00391856i	$0.998753\pi$
$38$	0.119450	−	0.236525i	0.0193773	−	0.0383694i
$39$	0.214571	−	2.17858i	0.0343589	−	0.348852i
$40$	2.96346	+	7.77441i	0.468564	+	1.22924i
$41$	−3.93122	+	4.79020i	−0.613953	+	0.748104i	−0.983460	−	0.181124i	$-0.942026\pi$
$41$	−3.93122	+	4.79020i	−0.613953	+	0.748104i	0.369507	+	0.929228i	$0.379526\pi$
$42$	−0.761741	+	0.797961i	−0.117539	+	0.123128i
$43$	−1.54023	+	6.14894i	−0.234883	+	0.937704i	0.731757	+	0.681565i	$0.238700\pi$
$43$	−1.54023	+	6.14894i	−0.234883	+	0.937704i	−0.966640	+	0.256139i	$0.917550\pi$
$44$	−9.50251	+	7.75644i	−1.43256	+	1.16933i
$45$	−5.13933	+	0.252479i	−0.766127	+	0.0376374i
$46$	−1.86366	−	4.85049i	−0.274781	−	0.715165i
$47$	−1.06023	−	0.708426i	−0.154651	−	0.103335i	0.475837	−	0.879534i	$-0.342145\pi$
$47$	−1.06023	−	0.708426i	−0.154651	−	0.103335i	−0.630488	+	0.776199i	$0.717145\pi$
$48$	1.10996	−	4.33362i	0.160210	−	0.625503i
$49$	5.41578	−	3.61871i	0.773683	−	0.516958i
$50$	2.98025	−	4.21974i	0.421471	−	0.596761i
$51$	−5.90486	+	2.79279i	−0.826846	+	0.391069i
$52$	0.753562	+	3.84161i	0.104500	+	0.532735i
$53$	1.04002	−	1.40231i	0.142858	−	0.192622i	−0.725983	−	0.687712i	$-0.758615\pi$
$53$	1.04002	−	1.40231i	0.142858	−	0.192622i	0.868841	+	0.495090i	$0.164865\pi$
$54$	6.34078	+	4.02704i	0.862871	+	0.548011i
$55$	17.2642	+	5.23705i	2.32791	+	0.706164i
$56$	0.893998	−	1.75862i	0.119466	−	0.235006i
$57$	0.184803	+	0.0987793i	0.0244778	+	0.0130836i
$58$	−6.17540	+	7.89146i	−0.810870	+	1.03620i
$59$	−0.553538	−	1.54704i	−0.0720645	−	0.201407i	0.900111	−	0.435661i	$-0.143485\pi$
$59$	−0.553538	−	1.54704i	−0.0720645	−	0.201407i	−0.972175	+	0.234254i	$0.924735\pi$
$60$	−6.20084	+	2.20017i	−0.800525	+	0.284041i
$61$	−5.98148	+	9.97950i	−0.765851	+	1.27774i	0.189386	+	0.981903i	$0.439350\pi$
$61$	−5.98148	+	9.97950i	−0.765851	+	1.27774i	−0.955237	+	0.295842i	$0.904400\pi$
$62$	−0.689500	+	5.52998i	−0.0875666	+	0.702308i
$63$	0.862728	+	0.862728i	0.108693	+	0.108693i
$64$	0.328984	+	7.99323i	0.0411230	+	0.999154i
$65$	4.07145	−	4.07145i	0.505001	−	0.505001i
$66$	−5.95777	−	7.65507i	−0.733351	−	0.942274i
$67$	10.1735	+	6.09778i	1.24289	+	0.744962i	0.975791	−	0.218706i	$-0.0701834\pi$
$67$	10.1735	+	6.09778i	1.24289	+	0.744962i	0.267104	+	0.963668i	$0.413933\pi$
$68$	8.67598	−	7.82166i	1.05212	−	0.948516i
$69$	3.86900	−	1.38435i	0.465773	−	0.166656i
$70$	−2.88025	+	0.351370i	−0.344255	+	0.0419967i
$71$	2.06844	−	3.86978i	0.245479	−	0.459258i	−0.728763	−	0.684766i	$-0.759904\pi$
$71$	2.06844	−	3.86978i	0.245479	−	0.459258i	0.974241	+	0.225508i	$0.0724042\pi$
$72$	−4.76308	−	1.33853i	−0.561334	−	0.157748i
$73$	−4.46300	+	14.7126i	−0.522355	+	1.72197i	0.156478	+	0.987681i	$0.449986\pi$
$73$	−4.46300	+	14.7126i	−0.522355	+	1.72197i	−0.678833	+	0.734293i	$0.737514\pi$
$74$	0.889638	−	0.198537i	0.103418	−	0.0230794i
$75$	3.28140	+	2.43365i	0.378903	+	0.281014i
$76$	−0.367337	−	0.0740808i	−0.0421365	−	0.00849765i
$77$	−1.82900	−	3.86709i	−0.208434	−	0.440696i
$78$	−3.05100	+	0.525235i	−0.345458	+	0.0594711i
$79$	−7.70630	−	11.5333i	−0.867027	−	1.29760i	−0.953515	−	0.301344i	$-0.902565\pi$
$79$	−7.70630	−	11.5333i	−0.867027	−	1.29760i	0.0864889	−	0.996253i	$-0.472435\pi$
$80$	9.48786	−	6.95901i	1.06077	−	0.778040i
$81$	−0.384717	+	0.575770i	−0.0427463	+	0.0639744i
$82$	8.00707	+	3.56200i	0.884233	+	0.393357i
$83$	0.220427	+	4.48690i	0.0241951	+	0.492502i	0.980061	+	0.198698i	$0.0636713\pi$
$83$	0.220427	+	4.48690i	0.0241951	+	0.492502i	−0.955866	+	0.293804i	$0.905079\pi$
$84$	1.37395	+	0.739081i	0.149910	+	0.0806404i
$85$	−16.6658	−	4.17457i	−1.80766	−	0.452795i
$86$	8.96215	−	0.208123i	0.966414	−	0.0224424i
$87$	−6.12560	−	5.02715i	−0.656733	−	0.538967i
$88$	14.1429	+	10.0449i	1.50763	+	1.07079i
$89$	−12.4959	−	1.23074i	−1.32457	−	0.130458i	−0.589122	−	0.808044i	$-0.700526\pi$
$89$	−12.4959	−	1.23074i	−1.32457	−	0.130458i	−0.735444	+	0.677586i	$0.763026\pi$
$90$	2.27346	+	6.91262i	0.239644	+	0.728654i
$91$	−1.36364	−	0.0669912i	−0.142948	−	0.00702259i
$92$	−5.91398	+	4.36185i	−0.616575	+	0.454754i
$93$	−4.35933	−	0.646646i	−0.452041	−	0.0670540i
$94$	−0.567935	+	1.71154i	−0.0585780	+	0.176532i
$95$	0.210918	+	0.509201i	0.0216397	+	0.0522429i
$96$	−6.32548	+	0.113341i	−0.645591	+	0.0115679i
$97$	0.123173	−	0.297367i	0.0125064	−	0.0301930i	−0.917503	−	0.397729i	$-0.869798\pi$
$97$	0.123173	−	0.297367i	0.0125064	−	0.0301930i	0.930009	+	0.367536i	$0.119798\pi$
$98$	−6.96704	−	6.02593i	−0.703777	−	0.608711i
$99$	−8.61701	+	6.39081i	−0.866042	+	0.642301i
$100$	−6.87228	−	2.47951i	−0.687228	−	0.247951i
$101$	−13.2561	−	14.6259i	−1.31903	−	1.45533i	−0.799204	−	0.601059i	$-0.794746\pi$
$101$	−13.2561	−	14.6259i	−1.31903	−	1.45533i	−0.519829	−	0.854270i	$-0.674004\pi$
$102$	6.02450	+	7.00282i	0.596515	+	0.693382i
$103$	13.6279	−	11.1841i	1.34280	−	1.10201i	0.356993	−	0.934107i	$-0.383802\pi$
$103$	13.6279	−	11.1841i	1.34280	−	1.10201i	0.985804	−	0.167898i	$-0.0536980\pi$
$104$	4.95510	−	2.46954i	0.485887	−	0.242158i
$105$	−0.224912	−	2.28357i	−0.0219492	−	0.222854i
$106$	−2.30243	−	0.891653i	−0.223632	−	0.0866050i
$107$	−7.08482	+	4.24648i	−0.684915	+	0.410522i	−0.813806	−	0.581136i	$-0.802608\pi$
$107$	−7.08482	+	4.24648i	−0.684915	+	0.410522i	0.128891	+	0.991659i	$0.458858\pi$
$108$	3.11059	−	10.1572i	0.299317	−	0.977380i
$109$	−3.94952	+	4.35762i	−0.378295	+	0.417385i	−0.900102	−	0.435679i	$-0.856508\pi$
$109$	−3.94952	+	4.35762i	−0.378295	+	0.417385i	0.521807	+	0.853064i	$0.325258\pi$
$110$	0.659951	−	25.5054i	0.0629239	−	2.43185i
$111$	0.140629	+	0.706991i	0.0133479	+	0.0671046i
$112$	−2.73344	−	0.558798i	−0.258286	−	0.0528014i
$113$	−0.725094	+	3.64529i	−0.0682111	+	0.342920i	−0.999787	−	0.0206258i	$-0.993434\pi$
$113$	−0.725094	+	3.64529i	−0.0682111	+	0.342920i	0.931576	+	0.363546i	$0.118434\pi$
$114$	0.0653123	−	0.289056i	0.00611706	−	0.0270726i
$115$	10.1764	+	3.64116i	0.948952	+	0.339540i
$116$	13.0780	+	5.45775i	1.21426	+	0.506740i
$117$	0.502401	+	3.38691i	0.0464470	+	0.313120i
$118$	−1.90157	+	1.33547i	−0.175054	+	0.122940i
$119$	1.92037	+	3.59277i	0.176040	+	0.329348i
$120$	5.32758	+	7.62885i	0.486340	+	0.696415i
$121$	25.4690	−	7.72594i	2.31536	−	0.702358i
$122$	15.8522	+	4.40953i	1.43519	+	0.399220i
$123$	−2.96311	+	6.26498i	−0.267175	+	0.564894i
$124$	7.79886	−	1.13573i	0.700358	−	0.101992i
$125$	−0.962802	−	3.84372i	−0.0861156	−	0.343793i
$126$	0.852463	−	1.50017i	0.0759434	−	0.133646i
$127$		−	10.1340i		−	0.899247i	−0.893218	−	0.449624i	$-0.851558\pi$
$127$		−	10.1340i		−	0.899247i	0.893218	−	0.449624i	$-0.148442\pi$
$128$	10.7751	−	3.44908i	0.952398	−	0.304858i
$129$			7.08928i			0.624176i
$130$	−7.07970	−	4.02301i	−0.620931	−	0.352841i
$131$	−4.51342	−	18.0186i	−0.394339	−	1.57429i	−0.764059	−	0.645147i	$-0.776796\pi$
$131$	−4.51342	−	18.0186i	−0.394339	−	1.57429i	0.369719	−	0.929143i	$-0.379454\pi$
$132$	−8.20113	+	10.9969i	−0.713817	+	0.957157i
$133$	0.0558759	−	0.118140i	0.00484505	−	0.0102440i
$134$	4.49527	−	16.1604i	0.388332	−	1.39605i
$135$	−14.9513	+	4.53542i	−1.28680	+	0.390347i
$136$	−13.9215	−	8.89346i	−1.19376	−	0.762607i
$137$	5.33574	+	9.98246i	0.455863	+	0.852859i	0.999905	+	0.0138013i	$0.00439322\pi$
$137$	5.33574	+	9.98246i	0.455863	+	0.852859i	−0.544042	+	0.839058i	$0.683107\pi$
$138$	−3.33989	−	4.75566i	−0.284311	−	0.404829i
$139$	−0.890165	−	6.00100i	−0.0755028	−	0.508998i	−0.993628	−	0.112708i	$-0.964047\pi$
$139$	−0.890165	−	6.00100i	−0.0755028	−	0.508998i	0.918125	−	0.396290i	$-0.129703\pi$
$140$	1.56028	+	3.79527i	0.131868	+	0.320759i
$141$	−1.34272	−	0.480432i	−0.113077	−	0.0404596i
$142$	−6.05284	−	1.36764i	−0.507943	−	0.114770i
$143$	2.34206	−	11.7743i	0.195853	−	0.984620i
$144$	−0.0370968	+	6.99684i	−0.00309140	+	0.583070i
$145$	−4.06624	−	20.4424i	−0.337683	−	1.69765i
$146$	21.7357	+	0.562409i	1.79886	+	0.0465453i
$147$	4.89200	−	5.39749i	0.403485	−	0.445178i
$148$	−0.604655	−	1.13848i	−0.0497024	−	0.0935825i
$149$	7.09279	−	4.25125i	0.581064	−	0.348276i	−0.193180	−	0.981163i	$-0.561880\pi$
$149$	7.09279	−	4.25125i	0.581064	−	0.348276i	0.774244	+	0.632887i	$0.218130\pi$
$150$	2.08647	−	5.38769i	0.170359	−	0.439903i
$151$	1.49637	+	15.1929i	0.121773	+	1.23638i	0.840778	+	0.541379i	$0.182098\pi$
$151$	1.49637	+	15.1929i	0.121773	+	1.23638i	−0.719005	+	0.695005i	$0.755402\pi$
$152$	0.0368838	+	0.528667i	0.00299167	+	0.0428806i
$153$	7.89754	−	6.48135i	0.638479	−	0.523986i
$154$	−4.58615	+	3.94545i	−0.369562	+	0.317933i
$155$	−7.78438	−	8.58874i	−0.625257	−	0.689865i
$156$	1.86144	+	3.96283i	0.149035	+	0.317281i
$157$	3.31592	−	2.45925i	0.264639	−	0.196270i	−0.455241	−	0.890368i	$-0.650447\pi$
$157$	3.31592	−	2.45925i	0.264639	−	0.196270i	0.719880	+	0.694099i	$0.244197\pi$
$158$	−12.8327	+	14.8368i	−1.02091	+	1.18035i
$159$	0.747211	−	1.80393i	0.0592577	−	0.143061i
$160$	−13.0501	−	10.3243i	−1.03170	−	0.816204i
$161$	−0.980733	−	2.36770i	−0.0772926	−	0.186601i
$162$	0.929468	+	0.308422i	0.0730259	+	0.0242319i
$163$	−16.2010	−	2.40319i	−1.26896	−	0.188232i	−0.521909	−	0.853001i	$-0.674780\pi$
$163$	−16.2010	−	2.40319i	−1.26896	−	0.188232i	−0.747049	+	0.664769i	$0.768530\pi$
$164$	1.85102	−	12.2546i	0.144540	−	0.956925i
$165$	20.1524	+	0.990025i	1.56886	+	0.0770733i
$166$	6.03508	−	1.98485i	0.468413	−	0.154054i
$167$	−0.496329	−	0.0488842i	−0.0384071	−	0.00378277i	0.0787953	−	0.996891i	$-0.474893\pi$
$167$	−0.496329	−	0.0488842i	−0.0384071	−	0.00378277i	−0.117202	+	0.993108i	$0.537393\pi$
$168$	0.491969	−	2.15080i	0.0379563	−	0.165938i
$169$	7.08738	+	5.81646i	0.545183	+	0.447420i
$170$	0.564086	+	24.2906i	0.0432634	+	1.86301i
$171$	−0.317926	−	0.0796362i	−0.0243124	−	0.00608993i
$172$	−3.64800	−	12.1416i	−0.278157	−	0.925790i
$173$	0.0676564	+	1.37718i	0.00514382	+	0.104705i	0.999994	+	0.00335223i	$0.00106705\pi$
$173$	0.0676564	+	1.37718i	0.00514382	+	0.104705i	−0.994851	+	0.101353i	$0.967683\pi$
$174$	−4.55500	+	10.2393i	−0.345313	+	0.776236i
$175$	1.41554	−	2.11851i	0.107005	−	0.160144i
$176$	8.38708	−	23.0542i	0.632200	−	1.73778i
$177$	−1.02091	−	1.52790i	−0.0767361	−	0.114844i
$178$	3.01265	+	17.5000i	0.225808	+	1.31168i
$179$	−4.15709	−	8.78943i	−0.310716	−	0.656953i	0.686842	−	0.726807i	$-0.258997\pi$
$179$	−4.15709	−	8.78943i	−0.310716	−	0.656953i	−0.997557	+	0.0698543i	$0.977747\pi$
$180$	8.57183	−	5.69470i	0.638907	−	0.424458i
$181$	4.80406	+	3.56293i	0.357083	+	0.264831i	0.759337	−	0.650697i	$-0.225523\pi$
$181$	4.80406	+	3.56293i	0.357083	+	0.264831i	−0.402254	+	0.915528i	$0.631773\pi$
$182$	0.420543	+	1.88445i	0.0311728	+	0.139684i
$183$	−3.77721	+	12.4518i	−0.279219	+	0.920463i
$184$	8.16731	+	6.42625i	0.602102	+	0.473750i
$185$	−0.893760	+	1.67211i	−0.0657105	+	0.122936i
$186$	0.754723	+	6.18662i	0.0553390	+	0.453625i
$187$	−33.7272	+	12.0678i	−2.46637	+	0.882483i
$188$	2.54685	+	0.131888i	0.185748	+	0.00961890i
$189$	3.17762	+	1.90459i	0.231138	+	0.138539i
$190$	0.615112	−	0.478728i	0.0446249	−	0.0347306i
$191$	−10.7982	+	10.7982i	−0.781328	+	0.781328i	−0.980055	−	0.198727i	$-0.936319\pi$
$191$	−10.7982	+	10.7982i	−0.781328	+	0.781328i	0.198727	+	0.980055i	$0.436319\pi$
$192$	2.52901	+	8.58214i	0.182515	+	0.619362i
$193$	2.60126	+	2.60126i	0.187243	+	0.187243i	0.794503	−	0.607260i	$-0.207731\pi$
$193$	2.60126	+	2.60126i	0.187243	+	0.187243i	−0.607260	+	0.794503i	$0.707731\pi$
$194$	−0.451692	−	0.0563188i	−0.0324296	−	0.00404345i
$195$	3.31056	−	5.52334i	0.237074	−	0.395535i
$196$	−5.60096	+	11.7615i	−0.400069	+	0.840105i
$197$	7.99440	+	22.3429i	0.569577	+	1.59186i	0.787779	+	0.615959i	$0.211231\pi$
$197$	7.99440	+	22.3429i	0.569577	+	1.59186i	−0.218201	+	0.975904i	$0.570019\pi$
$198$	11.9484	+	9.35016i	0.849139	+	0.664487i
$199$	6.26988	+	3.35132i	0.444460	+	0.237569i	0.678416	−	0.734678i	$-0.262667\pi$
$199$	6.26988	+	3.35132i	0.444460	+	0.237569i	−0.233955	+	0.972247i	$0.575167\pi$
$200$	−0.801044	+	10.3010i	−0.0566423	+	0.728391i
$201$	12.6939	+	3.85065i	0.895357	+	0.271604i
$202$	−14.9660	+	23.5648i	−1.05301	+	1.65801i
$203$	−2.94403	+	3.96957i	−0.206631	+	0.278609i
$204$	7.28674	−	10.8430i	0.510174	−	0.759165i
$205$	−16.4784	+	7.79368i	−1.15090	+	0.544334i
$206$	−20.3651	−	14.3831i	−1.41890	−	1.00212i
$207$	−5.34398	+	3.57073i	−0.371432	+	0.248183i
$208$	−5.22723	−	5.82918i	−0.362443	−	0.404181i
$209$	0.955474	+	0.638427i	0.0660915	+	0.0441609i
$210$	−3.02918	+	1.16387i	−0.209033	+	0.0803150i
$211$	23.2337	−	1.14140i	1.59948	−	0.0785773i	0.770344	−	0.637629i	$-0.220085\pi$
$211$	23.2337	−	1.14140i	1.59948	−	0.0785773i	0.829133	+	0.559051i	$0.188835\pi$
$212$	−0.351464	+	3.47404i	−0.0241386	+	0.238598i
$213$	1.19238	−	4.76025i	0.0817006	−	0.326167i
$214$	8.44952	+	8.06599i	0.577597	+	0.551380i
$215$	−11.8292	+	14.4139i	−0.806744	+	0.983021i
$216$	−15.0169	−	0.428399i	−1.02177	−	0.0291489i
$217$	−0.269402	+	2.73528i	−0.0182882	+	0.185683i
$218$	7.42413	+	3.74933i	0.502825	+	0.253937i
$219$	−0.843697	+	17.1738i	−0.0570118	+	1.16050i
$220$	−35.0240	+	8.67444i	−2.36132	+	0.584831i
$221$	−1.67749	+	11.3087i	−0.112840	+	0.760708i
$222$	0.911181	−	0.457137i	0.0611545	−	0.0306811i
$223$	1.74582	−	0.723142i	0.116909	−	0.0484252i	−0.323462	−	0.946241i	$-0.604847\pi$
$223$	1.74582	−	0.723142i	0.116909	−	0.0484252i	0.440371	+	0.897816i	$0.354847\pi$
$224$	0.264174	+	3.93677i	0.0176508	+	0.263036i
$225$	−5.90347	−	2.44530i	−0.393564	−	0.163020i
$226$	5.24249	−	0.379723i	0.348725	−	0.0252588i
$227$	−2.48757	−	3.35411i	−0.165106	−	0.222620i	0.712904	−	0.701261i	$-0.247379\pi$
$227$	−2.48757	−	3.35411i	−0.165106	−	0.222620i	−0.878010	+	0.478642i	$0.841129\pi$
$228$	−0.418640	+	0.0194542i	−0.0277251	+	0.00128838i
$229$	11.4023	−	10.3344i	0.753482	−	0.682916i	−0.201530	−	0.979482i	$-0.564591\pi$
$229$	11.4023	−	10.3344i	0.753482	−	0.682916i	0.955012	+	0.296566i	$0.0958415\pi$
$230$	1.14464	−	15.2421i	0.0754756	−	1.00504i
$231$	−3.03506	−	3.69824i	−0.199693	−	0.243326i
$232$	2.53231	−	19.8804i	0.166254	−	1.30521i
$233$	−3.13277	+	0.308551i	−0.205235	+	0.0202138i	−0.200112	−	0.979773i	$-0.564131\pi$
$233$	−3.13277	+	0.308551i	−0.205235	+	0.0202138i	−0.00512259	+	0.999987i	$0.501631\pi$
$234$	4.42941	−	1.95640i	0.289559	−	0.127894i
$235$	−1.92836	−	3.21727i	−0.125792	−	0.209872i
$236$	2.53471	+	2.09145i	0.164995	+	0.136142i
$237$	−11.4943	−	10.4179i	−0.746638	−	0.676713i
$238$	4.17781	−	3.96706i	0.270807	−	0.257146i
$239$	24.4807	−	4.86951i	1.58352	−	0.314982i	0.676624	−	0.736329i	$-0.263442\pi$
$239$	24.4807	−	4.86951i	1.58352	−	0.314982i	0.906900	+	0.421347i	$0.138442\pi$
$240$	8.40193	−	10.1278i	0.542342	−	0.653747i
$241$	6.51386	+	1.29569i	0.419595	+	0.0834626i	0.400372	−	0.916353i	$-0.368881\pi$
$241$	6.51386	+	1.29569i	0.419595	+	0.0834626i	0.0192227	+	0.999815i	$0.493881\pi$
$242$	−20.0948	−	31.8264i	−1.29174	−	2.04588i
$243$	5.10720	−	14.2737i	0.327627	−	0.915656i
$244$	0.0616864	−	23.2695i	0.00394906	−	1.48968i
$245$	18.9527	−	2.81136i	1.21084	−	0.179611i
$246$	9.65450	+	1.68840i	0.615548	+	0.107648i
$247$	0.323447	−	0.172886i	0.0205805	−	0.0110005i
$248$	−4.47610	−	10.2073i	−0.284233	−	0.648163i
$249$	1.45842	+	4.80776i	0.0924235	+	0.304680i
$250$	−4.87943	+	2.75563i	−0.308603	+	0.174281i
$251$	12.2125	+	5.77610i	0.770848	+	0.364584i	0.772171	−	0.635415i	$-0.219171\pi$
$251$	12.2125	+	5.77610i	0.770848	+	0.364584i	−0.00132250	+	0.999999i	$0.500421\pi$
$252$	−2.36545	−	0.599184i	−0.149010	−	0.0377450i
$253$	21.8593	−	5.47548i	1.37428	−	0.344240i
$254$	−13.8175	+	3.80412i	−0.866990	+	0.238692i
$255$	−19.2145			−1.20326
$256$	−8.74756	−	13.3970i	−0.546722	−	0.837314i
$257$	−1.30080			−0.0811420			−0.0405710	−	0.999177i	$-0.512918\pi$
$257$	−1.30080			−0.0811420			−0.0405710	+	0.999177i	$0.512918\pi$
$258$	9.66612	−	2.66119i	0.601786	−	0.165678i
$259$	0.436092	−	0.109235i	0.0270975	−	0.00678756i
$260$	−2.82771	+	11.1632i	−0.175367	+	0.692314i
$261$	11.2043	+	5.29926i	0.693532	+	0.328016i
$262$	−22.8738	+	12.9178i	−1.41315	+	0.798066i
$263$	0.377771	+	1.24535i	0.0232944	+	0.0767913i	0.967817	−	0.251655i	$-0.0809749\pi$
$263$	0.377771	+	1.24535i	0.0232944	+	0.0767913i	−0.944523	+	0.328447i	$0.893475\pi$
$264$	18.0726	+	7.05407i	1.11229	+	0.434148i
$265$	4.52926	−	2.42094i	0.278230	−	0.148717i
$266$	−0.182056	−	0.0318384i	−0.0111626	−	0.00195214i
$267$	−13.8908	+	2.06050i	−0.850102	+	0.126101i
$268$	−23.7219	−	0.0628857i	−1.44905	−	0.00384136i
$269$	−1.37195	+	3.83435i	−0.0836494	+	0.233784i	−0.976085	−	0.217391i	$-0.930245\pi$
$269$	−1.37195	+	3.83435i	−0.0836494	+	0.233784i	0.892435	+	0.451176i	$0.148995\pi$
$270$	11.7964	+	18.6833i	0.717907	+	1.13703i
$271$	−2.07495	−	0.412733i	−0.126044	−	0.0250717i	0.131665	−	0.991294i	$-0.457968\pi$
$271$	−2.07495	−	0.412733i	−0.126044	−	0.0250717i	−0.257709	+	0.966223i	$0.582968\pi$
$272$	−6.90020	+	22.3202i	−0.418386	+	1.35336i
$273$	−1.49756	+	0.297883i	−0.0906365	+	0.0180287i
$274$	11.6080	−	11.0224i	0.701264	−	0.665889i
$275$	16.6002	+	15.0456i	1.00103	+	0.907282i
$276$	−5.23053	+	6.33908i	−0.314841	+	0.381568i
$277$	−4.66292	−	7.77962i	−0.280168	−	0.467432i	0.685189	−	0.728365i	$-0.259720\pi$
$277$	−4.66292	−	7.77962i	−0.280168	−	0.467432i	−0.965357	+	0.260934i	$0.915970\pi$
$278$	−7.84812	+	3.46639i	−0.470699	+	0.207900i
$279$	6.85978	−	0.675629i	0.410684	−	0.0404488i
$280$	4.58909	−	3.55209i	0.274251	−	0.212278i
$281$	−13.5994	−	16.5709i	−0.811271	−	0.988537i	−0.999979	−	0.00650344i	$-0.997930\pi$
$281$	−13.5994	−	16.5709i	−0.811271	−	0.988537i	0.188708	−	0.982033i	$-0.439570\pi$
$282$	−0.151029	+	2.01112i	−0.00899367	+	0.119760i
$283$	4.59531	−	4.16495i	0.273163	−	0.247580i	−0.523470	−	0.852044i	$-0.675363\pi$
$283$	4.59531	−	4.16495i	0.273163	−	0.247580i	0.796632	+	0.604464i	$0.206613\pi$
$284$	0.407370	+	8.76633i	0.0241730	+	0.520186i
$285$	0.367188	+	0.495096i	0.0217503	+	0.0293270i
$286$	−16.9333	+	1.22651i	−1.00129	+	0.0725251i
$287$	3.99323	+	1.65405i	0.235713	+	0.0976355i
$288$	9.55401	−	2.57591i	0.562975	−	0.151787i
$289$	15.8101	−	6.54877i	0.930008	−	0.385222i
$290$	−26.3464	+	13.2179i	−1.54712	+	0.776184i
$291$	0.0528184	−	0.356073i	0.00309627	−	0.0208734i
$292$	−7.39234	−	29.8473i	−0.432604	−	1.74668i
$293$	−1.55933	+	31.7409i	−0.0910972	+	1.85433i	0.325883	+	0.945410i	$0.394338\pi$
$293$	−1.55933	+	31.7409i	−0.0910972	+	1.85433i	−0.416980	+	0.908915i	$0.636912\pi$
$294$	−9.19576	−	4.64404i	−0.536308	−	0.270846i
$295$	0.473744	−	4.81000i	0.0275824	−	0.280049i
$296$	−1.32532	+	1.25180i	−0.0770328	+	0.0727595i
$297$	−20.6657	+	25.1813i	−1.19915	+	1.46117i
$298$	−8.45902	−	8.07506i	−0.490018	−	0.467776i
$299$	1.74752	−	6.97651i	0.101062	−	0.403462i
$300$	−8.12924	−	0.822426i	−0.469342	−	0.0474828i
$301$	4.41603	−	0.216945i	0.254535	−	0.0125045i
$302$	20.1536	−	7.74344i	1.15971	−	0.445585i
$303$	−18.3555	−	12.2648i	−1.05450	−	0.704592i
$304$	0.706983	−	0.248742i	0.0405483	−	0.0142664i
$305$	−28.4569	+	19.0143i	−1.62944	+	1.08875i
$306$	−11.8018	−	8.33519i	−0.674664	−	0.476491i
$307$	4.87796	−	2.30710i	0.278400	−	0.131673i	−0.283256	−	0.959044i	$-0.591415\pi$
$307$	4.87796	−	2.30710i	0.278400	−	0.131673i	0.561656	+	0.827371i	$0.310165\pi$
$308$	7.10111	+	4.77209i	0.404623	+	0.271915i
$309$	11.7452	−	15.8365i	0.668158	−	0.900907i
$310$	−8.78850	+	13.8379i	−0.499153	+	0.785942i
$311$	12.7204	+	3.85869i	0.721308	+	0.218807i	0.629534	−	0.776973i	$-0.283246\pi$
$311$	12.7204	+	3.85869i	0.721308	+	0.218807i	0.0917748	+	0.995780i	$0.470746\pi$
$312$	4.70451	−	4.02562i	0.266340	−	0.227906i
$313$	9.26363	+	4.95152i	0.523612	+	0.279876i	0.711953	−	0.702227i	$-0.247811\pi$
$313$	9.26363	+	4.95152i	0.523612	+	0.279876i	−0.188341	+	0.982104i	$0.560311\pi$
$314$	−4.59789	−	3.59804i	−0.259474	−	0.203049i
$315$	1.20909	+	3.37918i	0.0681245	+	0.190395i
$316$	25.0469	+	11.9277i	1.40900	+	0.670983i
$317$	12.7100	−	21.2054i	0.713866	−	1.19101i	−0.260376	−	0.965507i	$-0.583846\pi$
$317$	12.7100	−	21.2054i	0.713866	−	1.19101i	0.974242	−	0.225506i	$-0.0724036\pi$
$318$	−2.74011	−	0.341649i	−0.153658	−	0.0191587i
$319$	−30.7285	−	30.7285i	−1.72046	−	1.72046i
$320$	−9.17820	+	21.6691i	−0.513077	+	1.21134i
$321$	−6.53208	+	6.53208i	−0.364585	+	0.364585i
$322$	−2.86017	+	2.22600i	−0.159391	+	0.124050i
$323$	−0.938642	−	0.562600i	−0.0522274	−	0.0313039i
$324$	0.0716228	−	1.38309i	0.00397904	−	0.0768384i
$325$	6.73234	−	2.40887i	0.373443	−	0.133620i
$326$	2.80485	+	22.9919i	0.155346	+	1.27340i
$327$	−3.10052	+	5.80067i	−0.171459	+	0.320778i
$328$	−17.4038	+	2.07633i	−0.960965	+	0.114646i
$329$	−0.258179	+	0.851101i	−0.0142339	+	0.0469227i
$330$	−6.21497	−	27.8491i	−0.342123	−	1.53304i
$331$	16.2427	+	12.0464i	0.892779	+	0.662130i	0.941620	−	0.336677i	$-0.109303\pi$
$331$	16.2427	+	12.0464i	0.892779	+	0.662130i	−0.0488414	+	0.998807i	$0.515553\pi$
$332$	−4.97177	−	7.48365i	−0.272861	−	0.410719i
$333$	−0.482050	−	1.01921i	−0.0264162	−	0.0558523i
$334$	0.119660	+	0.695087i	0.00654752	+	0.0380335i
$335$	19.3840	+	29.0102i	1.05906	+	1.58499i
$336$	−3.11725	+	0.136578i	−0.170060	+	0.00745093i
$337$	−3.14951	+	4.71357i	−0.171564	+	0.256764i	−0.907281	−	0.420526i	$-0.861846\pi$
$337$	−3.14951	+	4.71357i	−0.171564	+	0.256764i	0.735716	+	0.677290i	$0.236846\pi$
$338$	5.27018	−	11.8469i	0.286660	−	0.644388i
$339$	0.203959	+	4.15167i	0.0110775	+	0.225488i
$340$	32.9081	−	9.88738i	1.78469	−	0.536218i
$341$	−23.4436	−	5.87232i	−1.26954	−	0.318004i
$342$	0.0107608	+	0.463380i	0.000581878	+	0.0250567i
$343$	−7.28608	−	5.97953i	−0.393411	−	0.322864i
$344$	−15.1855	+	9.53174i	−0.818748	+	0.513917i
$345$	12.0294	+	1.18479i	0.647641	+	0.0637871i
$346$	1.85236	−	0.609216i	0.0995837	−	0.0327517i
$347$	13.8899	+	0.682366i	0.745647	+	0.0366313i	0.418345	−	0.908288i	$-0.362610\pi$
$347$	13.8899	+	0.682366i	0.745647	+	0.0366313i	0.327303	+	0.944920i	$0.393860\pi$
$348$	15.6709	+	2.36703i	0.840049	+	0.126886i
$349$	21.9087	+	3.24985i	1.17275	+	0.173960i	0.704544	−	0.709661i	$-0.251152\pi$
$349$	21.9087	+	3.24985i	1.17275	+	0.173960i	0.468203	+	0.883621i	$0.344902\pi$
$350$	−3.41992	−	1.13482i	−0.182803	−	0.0606587i
$351$	3.97863	+	9.60525i	0.212363	+	0.512690i
$352$	−34.5824	−	2.78151i	−1.84325	−	0.148255i
$353$	8.56599	−	20.6801i	0.455922	−	1.10069i	−0.514112	−	0.857723i	$-0.671879\pi$
$353$	8.56599	−	20.6801i	0.455922	−	1.10069i	0.970034	−	0.242969i	$-0.0781214\pi$
$354$	−1.70003	+	1.96554i	−0.0903557	+	0.104467i
$355$	10.3673	−	7.68892i	0.550240	−	0.408086i
$356$	22.7301	−	10.6769i	1.20469	−	0.565874i
$357$	3.05965	+	3.37580i	0.161934	+	0.178666i
$358$	−10.4237	+	8.96752i	−0.550912	+	0.473948i
$359$	19.6843	−	16.1545i	1.03890	−	0.852602i	0.0496384	−	0.998767i	$-0.484193\pi$
$359$	19.6843	−	16.1545i	1.03890	−	0.852602i	0.989260	+	0.146165i	$0.0466931\pi$
$360$	−10.9823	−	9.54987i	−0.578821	−	0.503322i
$361$	−1.85888	−	18.8736i	−0.0978360	−	0.993346i
$362$	3.05465	−	7.88772i	0.160549	−	0.414569i
$363$	25.5308	−	15.3026i	1.34002	−	0.803178i
$364$	2.41155	−	1.28079i	0.126399	−	0.0671317i
$365$	−30.3717	+	33.5100i	−1.58973	+	1.75400i
$366$	18.3957	+	0.475988i	0.961559	+	0.0248803i
$367$	5.87714	+	29.5464i	0.306784	+	1.54231i	0.759413	+	0.650609i	$0.225486\pi$
$367$	5.87714	+	29.5464i	0.306784	+	1.54231i	−0.452628	+	0.891699i	$0.649514\pi$
$368$	5.69623	−	13.5483i	0.296937	−	0.706254i
$369$	2.11472	−	10.6314i	0.110088	−	0.553449i
$370$	2.61539	+	0.590948i	0.135968	+	0.0307219i
$371$	−1.14656	−	0.410246i	−0.0595264	−	0.0212989i
$372$	8.15204	−	3.35140i	0.422664	−	0.173762i
$373$	−0.993236	−	6.69586i	−0.0514278	−	0.346698i	−0.999583	−	0.0288894i	$-0.990803\pi$
$373$	−0.993236	−	6.69586i	−0.0514278	−	0.346698i	0.948155	−	0.317809i	$-0.102947\pi$
$374$	29.1148	+	41.4564i	1.50549	+	2.14366i
$375$	−2.08901	−	3.90826i	−0.107876	−	0.201822i
$376$	−0.776216	−	3.52210i	−0.0400303	−	0.181639i
$377$	−13.2722	+	4.02607i	−0.683551	+	0.207353i
$378$	1.40406	−	5.04758i	0.0722171	−	0.259620i
$379$	−7.96273	+	16.8358i	−0.409018	+	0.864795i	0.589361	+	0.807870i	$0.299380\pi$
$379$	−7.96273	+	16.8358i	−0.409018	+	0.864795i	−0.998378	+	0.0569254i	$0.981870\pi$
$380$	−0.883640	−	0.658990i	−0.0453298	−	0.0338055i
$381$	−2.75385	−	10.9940i	−0.141084	−	0.563238i
$382$	18.7766	+	10.6697i	0.960693	+	0.545909i
$383$		−	5.61591i		−	0.286960i	−0.989653	−	0.143480i	$-0.954171\pi$
$383$		−	5.61591i		−	0.286960i	0.989653	−	0.143480i	$-0.0458292\pi$
$384$	10.7523	−	6.66984i	0.548699	−	0.340369i
$385$		−	12.5836i		−	0.641317i
$386$	2.57031	−	4.52324i	0.130825	−	0.230227i
$387$	−2.69422	−	10.7559i	−0.136955	−	0.546755i
$388$	0.0927672	+	0.637016i	0.00470954	+	0.0323396i
$389$	−11.9869	+	25.3441i	−0.607759	+	1.28500i	0.332038	+	0.943266i	$0.392264\pi$
$389$	−11.9869	+	25.3441i	−0.607759	+	1.28500i	−0.939797	+	0.341733i	$0.888986\pi$
$390$	−8.77371	−	2.44054i	−0.444274	−	0.123581i
$391$	−20.5359	+	6.22950i	−1.03855	+	0.315039i
$392$	18.1391	+	3.22178i	0.916161	+	0.162724i
$393$	−9.79285	−	18.3211i	−0.493984	−	0.924179i
$394$	27.4632	−	19.2873i	1.38357	−	0.971682i
$395$	−5.98700	−	40.3611i	−0.301239	−	2.03079i
$396$	8.26357	−	19.8014i	0.415260	−	0.995057i
$397$	−4.37738	−	1.56625i	−0.219694	−	0.0786079i	0.224742	−	0.974418i	$-0.427846\pi$
$397$	−4.37738	−	1.56625i	−0.219694	−	0.0786079i	−0.444436	+	0.895810i	$0.646596\pi$
$398$	2.21587	−	9.80691i	0.111072	−	0.491576i
$399$	0.0285138	−	0.143349i	0.00142748	−	0.00717642i
$400$	14.3459	−	2.77460i	0.717297	−	0.138730i
$401$	−6.70390	−	33.7028i	−0.334777	−	1.68304i	−0.671161	−	0.741312i	$-0.734204\pi$
$401$	−6.70390	−	33.7028i	−0.334777	−	1.68304i	0.336384	−	0.941725i	$-0.390796\pi$
$402$	0.485242	−	18.7534i	0.0242017	−	0.935333i
$403$	−5.17993	+	5.71518i	−0.258031	+	0.284693i
$404$	37.7482	+	11.5602i	1.87804	+	0.575139i
$405$	−1.74717	+	1.04721i	−0.0868174	+	0.0520364i
$406$	6.51758	+	2.52404i	0.323462	+	0.125266i
$407$	0.387467	+	3.93402i	0.0192060	+	0.195002i
$408$	−17.5196	−	5.86507i	−0.867351	−	0.290364i
$409$	−5.97401	+	4.90274i	−0.295396	+	0.242425i	−0.770404	−	0.637557i	$-0.779945\pi$
$409$	−5.97401	+	4.90274i	−0.295396	+	0.242425i	0.475008	+	0.879982i	$0.342445\pi$
$410$	16.8122	+	19.5424i	0.830297	+	0.965128i
$411$	8.50119	+	9.37962i	0.419333	+	0.462663i
$412$	−11.9665	+	33.1666i	−0.589545	+	1.63400i
$413$	−0.920509	+	0.682696i	−0.0452953	+	0.0335933i
$414$	6.87467	+	5.94604i	0.337872	+	0.292232i
$415$	−5.05699	+	12.2087i	−0.248238	+	0.599299i
$416$	−5.98578	+	9.31542i	−0.293477	+	0.456726i
$417$	−2.59644	−	6.26835i	−0.127148	−	0.306962i
$418$	0.511818	−	1.54243i	0.0250338	−	0.0754426i
$419$	−26.0456	−	3.86349i	−1.27241	−	0.188744i	−0.523849	−	0.851811i	$-0.675504\pi$
$419$	−26.0456	−	3.86349i	−1.27241	−	0.188744i	−0.748560	+	0.663067i	$0.769254\pi$
$420$	2.72402	+	3.69334i	0.132919	+	0.180217i
$421$	4.19652	+	0.206162i	0.204526	+	0.0100477i	0.151073	−	0.988523i	$-0.451727\pi$
$421$	4.19652	+	0.206162i	0.204526	+	0.0100477i	0.0534531	+	0.998570i	$0.482977\pi$
$422$	−10.2778	−	31.2504i	−0.500316	−	1.52124i
$423$	2.21977	+	0.218628i	0.107929	+	0.0106301i
$424$	4.86873	−	0.824875i	0.236446	−	0.0400595i
$425$	−16.4925	−	13.5351i	−0.800005	−	0.656548i
$426$	−6.93812	+	0.161120i	−0.336153	+	0.00780628i
$427$	7.87200	+	1.97183i	0.380953	+	0.0954238i
$428$	7.82605	−	14.5486i	0.378286	−	0.703233i
$429$	−0.658788	−	13.4099i	−0.0318066	−	0.647438i
$430$	24.0936	+	10.7182i	1.16190	+	0.516877i
$431$	5.17159	−	7.73983i	0.249107	−	0.372815i	−0.685751	−	0.727836i	$-0.740526\pi$
$431$	5.17159	−	7.73983i	0.249107	−	0.372815i	0.934858	+	0.355021i	$0.115526\pi$
$432$	5.05295	+	20.6361i	0.243110	+	0.992855i
$433$	15.2737	+	22.8588i	0.734009	+	1.09852i	0.991227	+	0.132168i	$0.0421940\pi$
$433$	15.2737	+	22.8588i	0.734009	+	1.09852i	−0.257218	+	0.966353i	$0.582806\pi$
$434$	3.83064	−	0.659451i	0.183877	−	0.0316546i
$435$	−9.96637	−	21.0721i	−0.477851	−	1.01033i
$436$	2.32527	−	11.5301i	0.111360	−	0.552192i
$437$	0.552955	+	0.410099i	0.0264514	+	0.0196177i
$438$	23.7330	−	5.29638i	1.13401	−	0.253071i
$439$	5.80080	−	19.1227i	0.276857	−	0.912676i	−0.702696	−	0.711490i	$-0.748021\pi$
$439$	5.80080	−	19.1227i	0.276857	−	0.912676i	0.979553	−	0.201186i	$-0.0644795\pi$
$440$	24.9748	+	44.4984i	1.19063	+	2.12138i
$441$	−5.37093	+	10.0483i	−0.255758	+	0.478490i
$442$	16.0490	−	1.95786i	0.763372	−	0.0931259i
$443$	−11.2127	+	4.01197i	−0.532731	+	0.190614i	−0.589493	−	0.807773i	$-0.700672\pi$
$443$	−11.2127	+	4.01197i	−0.532731	+	0.190614i	0.0567617	+	0.998388i	$0.481922\pi$
$444$	−0.965340	−	1.07078i	−0.0458130	−	0.0508170i
$445$	−31.6809	−	18.9888i	−1.50182	−	0.900154i
$446$	−1.64134	−	2.10894i	−0.0777198	−	0.0998613i
$447$	6.53943	−	6.53943i	0.309304	−	0.309304i
$448$	5.26856	−	1.83799i	0.248916	−	0.0868368i
$449$	12.4636	+	12.4636i	0.588192	+	0.588192i	0.937141	−	0.348950i	$-0.113462\pi$
$449$	12.4636	+	12.4636i	0.588192	+	0.588192i	−0.348950	+	0.937141i	$0.613462\pi$
$450$	−1.11807	+	8.96720i	−0.0527062	+	0.422718i
$451$	−19.5389	+	32.5986i	−0.920049	+	1.53501i
$452$	−2.48568	−	7.00551i	−0.116917	−	0.329511i
$453$	5.75193	+	16.0756i	0.270249	+	0.755297i
$454$	−3.63948	+	4.65084i	−0.170809	+	0.218275i
$455$	−3.54188	−	1.89318i	−0.166046	−	0.0887535i
$456$	0.183675	+	0.563507i	0.00860139	+	0.0263886i
$457$	37.1461	+	11.2681i	1.73762	+	0.527101i	0.990491	−	0.137578i	$-0.0439317\pi$
$457$	37.1461	+	11.2681i	1.73762	+	0.527101i	0.747129	+	0.664679i	$0.231432\pi$
$458$	−18.3710	−	11.6674i	−0.858420	−	0.545184i
$459$	18.4798	−	24.9171i	0.862563	−	1.16303i
$460$	−21.2121	+	4.16092i	−0.989019	+	0.194004i
$461$	28.6433	−	13.5473i	1.33405	−	0.630960i	0.378450	−	0.925622i	$-0.376457\pi$
$461$	28.6433	−	13.5473i	1.33405	−	0.630960i	0.955602	+	0.294662i	$0.0952071\pi$
$462$	−3.90318	+	5.52651i	−0.181592	+	0.257117i
$463$	−1.17573	+	0.785597i	−0.0546407	+	0.0365098i	−0.582591	−	0.812766i	$-0.697961\pi$
$463$	−1.17573	+	0.785597i	−0.0546407	+	0.0365098i	0.527950	+	0.849276i	$0.322961\pi$
$464$	−28.0572	+	4.00998i	−1.30252	+	0.186159i
$465$	−10.7789	−	7.20223i	−0.499859	−	0.333995i
$466$	1.59669	+	4.15566i	0.0739652	+	0.192507i
$467$	−14.3533	+	0.705131i	−0.664191	+	0.0326296i	−0.378371	−	0.925654i	$-0.623516\pi$
$467$	−14.3533	+	0.705131i	−0.664191	+	0.0326296i	−0.285819	+	0.958284i	$0.592266\pi$
$468$	−4.33024	−	5.30503i	−0.200165	−	0.245225i
$469$	2.01017	−	8.02506i	0.0928211	−	0.370563i
$470$	−3.66283	+	3.83699i	−0.168954	+	0.176987i
$471$	2.92902	−	3.56902i	0.134962	−	0.164452i
$472$	1.90017	−	4.24112i	0.0874626	−	0.195214i
$473$	−3.81063	+	38.6900i	−0.175213	+	1.77897i
$474$	−9.88983	+	19.5830i	−0.454255	+	0.899479i
$475$	−0.0335839	+	0.683615i	−0.00154093	+	0.0313664i
$476$	−6.97729	−	4.20721i	−0.319804	−	0.192837i
$477$	−0.448109	+	3.02091i	−0.0205175	+	0.138318i
$478$	−15.8291	−	31.5511i	−0.724006	−	1.44311i
$479$	−17.3703	+	7.19502i	−0.793670	+	0.328749i	−0.742418	−	0.669937i	$-0.766321\pi$
$479$	−17.3703	+	7.19502i	−0.793670	+	0.328749i	−0.0512521	+	0.998686i	$0.516321\pi$
$480$	−16.9630	−	7.65410i	−0.774253	−	0.349360i
$481$	1.16560	+	0.482807i	0.0531468	+	0.0220141i
$482$	−0.678537	−	9.36793i	−0.0309065	−	0.426697i
$483$	−1.70736	−	2.30211i	−0.0776877	−	0.104750i
$484$	−35.8516	+	39.3460i	−1.62962	+	1.78845i
$485$	0.701534	−	0.635833i	0.0318550	−	0.0288717i
$486$	−21.3791	−	1.60551i	−0.969774	−	0.0728274i
$487$	0.871792	+	1.06228i	0.0395047	+	0.0481366i	0.792388	−	0.610017i	$-0.208838\pi$
$487$	0.871792	+	1.06228i	0.0395047	+	0.0481366i	−0.752883	+	0.658154i	$0.771338\pi$
$488$	−31.7508	+	8.65085i	−1.43729	+	0.391606i
$489$	−18.2288	+	1.79538i	−0.824337	+	0.0811901i
$490$	−10.9477	−	24.7863i	−0.494568	−	1.11973i
$491$	9.08843	+	15.1631i	0.410155	+	0.684303i	0.991609	−	0.129277i	$-0.0412657\pi$
$491$	9.08843	+	15.1631i	0.410155	+	0.684303i	−0.581453	+	0.813580i	$0.697516\pi$
$492$	−1.32202	−	13.7975i	−0.0596012	−	0.622041i
$493$	30.6636	+	27.7919i	1.38102	+	1.25168i
$494$	−0.357144	−	0.376117i	−0.0160687	−	0.0169223i
$495$	−30.9517	+	6.15668i	−1.39118	+	0.276722i
$496$	−12.2372	+	9.93472i	−0.549468	+	0.446082i
$497$	−3.00172	−	0.597080i	−0.134646	−	0.0267827i
$498$	6.00784	−	3.79328i	0.269218	−	0.169981i
$499$	−5.21321	+	14.5699i	−0.233375	+	0.652240i	0.766574	+	0.642156i	$0.221960\pi$
$499$	−5.21321	+	14.5699i	−0.233375	+	0.652240i	−0.999949	+	0.0100842i	$0.996790\pi$
$500$	5.58891	+	5.61862i	0.249944	+	0.251272i
$501$	−0.551732	+	0.0818416i	−0.0246495	+	0.00365642i
$502$	3.29125	−	18.8198i	0.146896	−	0.839970i
$503$	−28.3784	+	15.1686i	−1.26533	+	0.676333i	−0.961083	−	0.276260i	$-0.910905\pi$
$503$	−28.3784	+	15.1686i	−1.26533	+	0.676333i	−0.304247	+	0.952593i	$0.598405\pi$
$504$	0.0709708	+	3.45018i	0.00316129	+	0.153683i
$505$	−16.8554	−	55.5647i	−0.750055	−	2.47260i
$506$	−15.6713	−	27.7494i	−0.696675	−	1.23361i
$507$	9.26940	+	4.38410i	0.411668	+	0.194705i
$508$	10.3737	+	17.4120i	0.460259	+	0.772533i
$509$	−6.98616	+	1.74994i	−0.309656	+	0.0775648i	−0.394693	−	0.918813i	$-0.629149\pi$
$509$	−6.98616	+	1.74994i	−0.309656	+	0.0775648i	0.0850371	+	0.996378i	$0.472899\pi$
$510$	7.21276	+	26.1986i	0.319387	+	1.16009i
$511$	10.7237			0.474388
$512$	−14.9829	+	16.9562i	−0.662159	+	0.749363i
$513$	−0.995183			−0.0439384
$514$	0.488299	+	1.77363i	0.0215379	+	0.0782313i
$515$	50.3050	−	12.6008i	2.21671	−	0.555256i
$516$	−7.25697	−	12.1806i	−0.319470	−	0.536223i
$517$	−7.06968	−	3.34371i	−0.310924	−	0.147056i
$518$	−0.312642	−	0.553600i	−0.0137367	−	0.0243238i
$519$	0.447637	+	1.47566i	0.0196491	+	0.0647743i
$520$	16.2824	−	0.334931i	0.714028	−	0.0146877i
$521$	1.82505	−	0.975510i	0.0799569	−	0.0427379i	−0.430934	−	0.902384i	$-0.641816\pi$
$521$	1.82505	−	0.975510i	0.0799569	−	0.0427379i	0.510891	+	0.859646i	$0.329316\pi$
$522$	3.01955	−	17.2662i	0.132162	−	0.755721i
$523$	−37.5513	+	5.57021i	−1.64200	+	0.243568i	−0.902846	−	0.429964i	$-0.858526\pi$
$523$	−37.5513	+	5.57021i	−1.64200	+	0.243568i	−0.739158	+	0.673533i	$0.764776\pi$
$524$	26.1996	+	26.3389i	1.14454	+	1.15062i
$525$	0.959975	−	2.68295i	0.0418967	−	0.117094i
$526$	1.55620	−	0.982565i	0.0678535	−	0.0428419i
$527$	22.5731	+	4.49006i	0.983298	+	0.195590i
$528$	2.83397	−	27.2897i	0.123333	−	1.18763i
$529$	−9.31725	+	1.85332i	−0.405098	+	0.0805790i
$530$	−5.00112	−	5.26680i	−0.217235	−	0.228775i
$531$	2.12960	+	1.93015i	0.0924166	+	0.0837616i
$532$	0.0249295	+	0.260182i	0.00108083	+	0.0112803i
$533$	6.23592	+	10.4040i	0.270107	+	0.450647i
$534$	8.02381	+	18.1664i	0.347224	+	0.786136i
$535$	−24.1805	+	2.38157i	−1.04541	+	0.102964i
$536$	8.81904	+	32.3681i	0.380925	+	1.39809i
$537$	−6.89833	−	8.40564i	−0.297685	−	0.362730i
$538$	5.74308	+	0.431290i	0.247602	+	0.0185942i
$539$	29.5995	−	26.8275i	1.27494	−	1.15554i
$540$	21.0462	−	23.0976i	0.905686	−	0.993963i
$541$	−11.9065	−	16.0540i	−0.511898	−	0.690215i	0.469339	−	0.883018i	$-0.344492\pi$
$541$	−11.9065	−	16.0540i	−0.511898	−	0.690215i	−0.981237	+	0.192803i	$0.938242\pi$
$542$	0.216143	+	2.98409i	0.00928415	+	0.128178i
$543$	6.17993	+	2.55981i	0.265206	+	0.109852i
$544$	33.0235	+	1.02971i	1.41587	+	0.0441484i
$545$	−15.9830	+	6.62037i	−0.684635	+	0.283585i
$546$	0.968316	+	1.93008i	0.0414401	+	0.0825998i
$547$	5.77096	−	38.9047i	0.246749	−	1.66344i	−0.412078	−	0.911149i	$-0.635197\pi$
$547$	5.77096	−	38.9047i	0.246749	−	1.66344i	0.658826	−	0.752295i	$-0.271053\pi$
$548$	−19.3863	−	11.6897i	−0.828143	−	0.499359i
$549$	0.998625	−	20.3275i	0.0426203	−	0.867556i
$550$	14.2830	−	28.2820i	0.609028	−	1.20595i
$551$	0.130127	−	1.32121i	0.00554361	−	0.0562853i
$552$	10.6067	+	4.75217i	0.451450	+	0.202266i
$553$	−6.13771	+	7.47882i	−0.261002	+	0.318032i
$554$	−8.85700	+	9.27815i	−0.376298	+	0.394191i
$555$	−0.515220	+	2.05687i	−0.0218699	+	0.0873095i
$556$	7.67241	+	9.39956i	0.325383	+	0.398630i
$557$	−45.7873	+	2.24939i	−1.94007	+	0.0953096i	−0.981726	−	0.190300i	$-0.939054\pi$
$557$	−45.7873	+	2.24939i	−1.94007	+	0.0953096i	−0.958346	+	0.285609i	$0.907804\pi$
$558$	−3.49624	−	9.09958i	−0.148008	−	0.385216i
$559$	10.3167	+	6.89343i	0.436352	+	0.291561i
$560$	−6.56588	−	4.92376i	−0.277459	−	0.208067i
$561$	−33.3099	+	22.2570i	−1.40635	+	0.939690i
$562$	−17.4892	+	24.7630i	−0.737737	+	1.04456i
$563$	33.6867	−	15.9326i	1.41972	−	0.671479i	0.445131	−	0.895465i	$-0.353157\pi$
$563$	33.6867	−	15.9326i	1.41972	−	0.671479i	0.974592	+	0.223986i	$0.0719070\pi$
$564$	2.79882	−	0.549011i	0.117852	−	0.0231175i
$565$	−6.51280	+	8.78150i	−0.273996	+	0.369440i
$566$	−7.40383	−	4.70219i	−0.311206	−	0.197648i
$567$	0.462198	+	0.140206i	0.0194105	+	0.00588811i
$568$	11.7998	−	3.84616i	0.495110	−	0.161381i
$569$	−35.6088	−	19.0333i	−1.49280	−	0.797917i	−0.495307	−	0.868718i	$-0.664945\pi$
$569$	−35.6088	−	19.0333i	−1.49280	−	0.797917i	−0.997490	+	0.0708006i	$0.977445\pi$
$570$	0.537220	−	0.686505i	0.0225017	−	0.0287545i
$571$	12.1132	+	33.8542i	0.506922	+	1.41675i	0.873710	+	0.486448i	$0.161708\pi$
$571$	12.1132	+	33.8542i	0.506922	+	1.41675i	−0.366788	+	0.930305i	$0.619542\pi$
$572$	8.02878	+	22.6279i	0.335700	+	0.946118i
$573$	−8.78017	+	14.6488i	−0.366797	+	0.611964i
$574$	0.756284	−	6.06561i	0.0315667	−	0.253173i
$575$	9.49071	+	9.49071i	0.395790	+	0.395790i
$576$	−7.09861	−	12.0598i	−0.295775	−	0.502491i
$577$	−13.7706	+	13.7706i	−0.573276	+	0.573276i	−0.933042	−	0.359766i	$-0.882856\pi$
$577$	−13.7706	+	13.7706i	−0.573276	+	0.573276i	0.359766	+	0.933042i	$0.382856\pi$
$578$	−14.8640	−	19.0986i	−0.618260	−	0.794396i
$579$	3.52888	+	2.11513i	0.146655	+	0.0879017i
$580$	27.9124	+	30.9612i	1.15900	+	1.28559i
$581$	2.95020	−	1.05560i	0.122395	−	0.0437936i
$582$	−0.505326	+	0.0616462i	−0.0209465	+	0.00255532i
$583$	5.04758	−	9.44335i	0.209049	−	0.391104i
$584$	−37.9214	+	21.2835i	−1.56920	+	0.880717i
$585$	−2.92372	+	9.63822i	−0.120881	+	0.398491i
$586$	43.8636	−	9.78885i	1.81199	−	0.404374i
$587$	−17.3678	−	12.8808i	−0.716845	−	0.531648i	0.174677	−	0.984626i	$-0.444112\pi$
$587$	−17.3678	−	12.8808i	−0.716845	−	0.531648i	−0.891522	+	0.452977i	$0.850362\pi$
$588$	−2.88016	+	14.2816i	−0.118776	+	0.588962i
$589$	−0.315676	−	0.667441i	−0.0130072	−	0.0275014i
$590$	−6.73620	+	1.15965i	−0.277325	+	0.0477419i
$591$	14.7443	+	22.0664i	0.606500	+	0.907692i
$592$	2.20431	+	1.33715i	0.0905968	+	0.0549566i
$593$	−4.85201	+	7.26155i	−0.199248	+	0.298196i	−0.917616	−	0.397467i	$-0.869889\pi$
$593$	−4.85201	+	7.26155i	−0.199248	+	0.298196i	0.718368	+	0.695663i	$0.244889\pi$
$594$	42.0918	+	18.7248i	1.72705	+	0.768288i
$595$	0.587999	+	11.9690i	0.0241056	+	0.490681i
$596$	−7.83485	+	14.5650i	−0.320928	+	0.596604i
$597$	7.71264	+	1.93192i	0.315657	+	0.0790681i
$598$	−10.1683	+	0.236133i	−0.415814	+	0.00965621i
$599$	−3.49676	−	2.86972i	−0.142874	−	0.117254i	0.560242	−	0.828329i	$-0.310708\pi$
$599$	−3.49676	−	2.86972i	−0.142874	−	0.117254i	−0.703115	+	0.711076i	$0.748208\pi$
$600$	1.93021	+	11.3928i	0.0788004	+	0.465110i
$601$	−14.9283	−	1.47031i	−0.608938	−	0.0599751i	−0.211152	−	0.977453i	$-0.567721\pi$
$601$	−14.9283	−	1.47031i	−0.608938	−	0.0599751i	−0.397786	+	0.917478i	$0.630221\pi$
$602$	−1.95350	−	5.93974i	−0.0796186	−	0.242086i
$603$	−20.7227	−	1.01804i	−0.843894	−	0.0414578i
$604$	−18.1234	−	24.5724i	−0.737429	−	0.999836i
$605$	77.4431	+	11.4876i	3.14851	+	0.467038i
$606$	−9.83248	+	29.6314i	−0.399417	+	1.20369i
$607$	−1.44950	−	3.49941i	−0.0588335	−	0.142037i	0.891729	−	0.452569i	$-0.149493\pi$
$607$	−1.44950	−	3.49941i	−0.0588335	−	0.142037i	−0.950563	+	0.310533i	$0.899493\pi$
$608$	−0.604545	−	0.870587i	−0.0245175	−	0.0353070i
$609$	−2.11516	+	5.10645i	−0.0857106	+	0.206924i
$610$	36.6079	+	31.6629i	1.48221	+	1.28199i
$611$	−2.00477	+	1.48684i	−0.0811045	+	0.0601512i
$612$	−6.93472	+	19.2205i	−0.280319	+	0.776941i
$613$	9.58745	+	10.5781i	0.387234	+	0.427246i	0.903105	−	0.429420i	$-0.141282\pi$
$613$	9.58745	+	10.5781i	0.387234	+	0.427246i	−0.515872	+	0.856666i	$0.672532\pi$
$614$	−4.97680	−	5.78498i	−0.200847	−	0.233463i
$615$	−15.7588	+	12.9329i	−0.635457	+	0.521506i
$616$	3.84104	−	11.4736i	0.154760	−	0.462285i
$617$	1.54334	+	15.6698i	0.0621325	+	0.630842i	0.974942	+	0.222457i	$0.0714077\pi$
$617$	1.54334	+	15.6698i	0.0621325	+	0.630842i	−0.912810	+	0.408384i	$0.866092\pi$
$618$	−26.0017	−	10.0696i	−1.04594	−	0.405058i
$619$	5.66360	−	3.39463i	0.227639	−	0.136442i	−0.395737	−	0.918364i	$-0.629511\pi$
$619$	5.66360	−	3.39463i	0.227639	−	0.136442i	0.623376	+	0.781922i	$0.285761\pi$
$620$	22.1669	+	6.78846i	0.890242	+	0.272631i
$621$	−13.1059	+	14.4601i	−0.525921	+	0.580264i
$622$	0.486256	−	18.7926i	0.0194971	−	0.753513i
$623$	1.70860	+	8.58973i	0.0684538	+	0.344140i
$624$	−7.25486	−	4.90338i	−0.290427	−	0.196292i
$625$	5.83724	−	29.3458i	0.233490	−	1.17383i
$626$	3.27391	−	14.4895i	0.130852	−	0.579118i
$627$	1.21004	+	0.432960i	0.0483245	+	0.0172908i
$628$	−3.17991	+	7.61978i	−0.126892	+	0.304062i
$629$	−0.552371	−	3.72378i	−0.0220245	−	0.148477i
$630$	4.15359	−	2.91706i	0.165483	−	0.116218i
$631$	20.3165	+	38.0096i	0.808789	+	1.51314i	0.857593	+	0.514329i	$0.171959\pi$
$631$	20.3165	+	38.0096i	0.808789	+	1.51314i	−0.0488041	+	0.998808i	$0.515541\pi$
$632$	6.86101	−	38.6285i	0.272916	−	1.53656i
$633$	24.8952	−	7.55187i	0.989495	−	0.300160i
$634$	−33.6843	−	9.36979i	−1.33778	−	0.372122i
$635$	12.7454	−	26.9480i	0.505788	−	1.06940i
$636$	0.562757	+	3.86435i	0.0223148	+	0.153231i
$637$	−3.09790	−	12.3675i	−0.122743	−	0.490018i
$638$	−30.3629	+	53.4327i	−1.20208	+	2.11542i
$639$			7.67546i			0.303637i
$640$	32.9908	+	4.38015i	1.30408	+	0.173140i
$641$		−	16.7080i		−	0.659928i	−0.943994	−	0.329964i	$-0.892963\pi$
$641$		−	16.7080i		−	0.659928i	0.943994	−	0.329964i	$-0.107037\pi$
$642$	11.3584	+	6.45437i	0.448281	+	0.254734i
$643$	−5.84083	−	23.3179i	−0.230340	−	0.919569i	−0.969312	−	0.245833i	$-0.920939\pi$
$643$	−5.84083	−	23.3179i	−0.230340	−	0.919569i	0.738972	−	0.673736i	$-0.235311\pi$
$644$	4.10878	+	3.06419i	0.161908	+	0.120746i
$645$	−8.91613	+	18.8516i	−0.351072	+	0.742280i
$646$	−0.414747	+	1.49101i	−0.0163180	+	0.0586631i
$647$	29.7038	−	9.01055i	1.16778	−	0.354241i	0.353903	−	0.935282i	$-0.384854\pi$
$647$	29.7038	−	9.01055i	1.16778	−	0.354241i	0.813874	+	0.581041i	$0.197354\pi$
$648$	−1.91271	+	0.421531i	−0.0751383	+	0.0165593i
$649$	−4.75037	−	8.88731i	−0.186468	−	0.348857i
$650$	−5.81165	−	8.27519i	−0.227952	−	0.324580i
$651$	0.451031	+	3.04061i	0.0176773	+	0.119171i
$652$	30.2962	−	12.4551i	1.18649	−	0.487779i
$653$	−1.19103	−	0.426159i	−0.0466088	−	0.0166769i	0.313482	−	0.949594i	$-0.398504\pi$
$653$	−1.19103	−	0.426159i	−0.0466088	−	0.0166769i	−0.360091	+	0.932917i	$0.617254\pi$
$654$	9.07300	+	2.05005i	0.354782	+	0.0801631i
$655$	10.6599	−	53.5909i	0.416516	−	2.09397i
$656$	9.36412	+	22.9504i	0.365608	+	0.896063i
$657$	−5.24671	−	26.3770i	−0.204694	−	1.02906i
$658$	1.25738	+	0.0325346i	0.0490177	+	0.00126833i
$659$	−11.6559	+	12.8603i	−0.454050	+	0.500967i	−0.924353	−	0.381538i	$-0.875395\pi$
$659$	−11.6559	+	12.8603i	−0.454050	+	0.500967i	0.470303	+	0.882505i	$0.344145\pi$
$660$	−35.6389	+	18.9281i	−1.38724	+	0.736774i
$661$	−25.8251	+	15.4789i	−1.00448	+	0.602061i	−0.918991	−	0.394278i	$-0.870995\pi$
$661$	−25.8251	+	15.4789i	−1.00448	+	0.602061i	−0.0854870	+	0.996339i	$0.527245\pi$
$662$	10.3279	−	26.6686i	0.401404	−	1.03651i
$663$	1.25323	+	12.7242i	0.0486714	+	0.494169i
$664$	−8.33753	+	9.58816i	−0.323559	+	0.372093i
$665$	0.297166	−	0.243878i	0.0115236	−	0.00945719i
$666$	−1.20872	+	1.03986i	−0.0468371	+	0.0402938i
$667$	−17.4835	−	19.2901i	−0.676966	−	0.746917i
$668$	0.902822	−	0.424078i	0.0349312	−	0.0164081i
$669$	1.69746	−	1.25892i	0.0656276	−	0.0486727i
$670$	32.2785	−	37.3196i	1.24703	−	1.44178i
$671$	−27.3073	+	65.9258i	−1.05419	+	2.54504i
$672$	1.35638	+	4.19906i	0.0523236	+	0.161982i
$673$	17.3782	+	41.9547i	0.669881	+	1.61724i	0.781808	+	0.623519i	$0.214298\pi$
$673$	17.3782	+	41.9547i	0.669881	+	1.61724i	−0.111927	+	0.993716i	$0.535702\pi$
$674$	7.60914	+	2.52491i	0.293093	+	0.0972560i
$675$	−19.1924	−	2.84692i	−0.738715	−	0.109578i
$676$	−18.1314	−	2.73868i	−0.697362	−	0.105334i
$677$	−33.8798	−	1.66441i	−1.30211	−	0.0639684i	−0.613843	−	0.789428i	$-0.710377\pi$
$677$	−33.8798	−	1.66441i	−1.30211	−	0.0639684i	−0.688264	+	0.725460i	$0.741627\pi$
$678$	5.58418	−	1.83656i	0.214459	−	0.0705325i
$679$	−0.223420	−	0.0220049i	−0.00857406	−	0.000844471i
$680$	−25.8344	−	41.1581i	−0.990704	−	1.57834i
$681$	−3.61012	−	2.96275i	−0.138340	−	0.113533i
$682$	0.793494	+	34.1694i	0.0303845	+	1.30841i
$683$	26.2022	+	6.56332i	1.00260	+	0.251138i	0.709319	−	0.704887i	$-0.249003\pi$
$683$	26.2022	+	6.56332i	1.00260	+	0.251138i	0.293282	+	0.956026i	$0.405253\pi$
$684$	0.627772	−	0.188617i	0.0240035	−	0.00721194i
$685$	1.63375	+	33.2557i	0.0624223	+	1.27064i
$686$	−5.41793	+	12.1791i	−0.206858	+	0.464999i
$687$	9.56154	−	14.3099i	0.364796	−	0.545955i
$688$	18.6967	+	17.1272i	0.712806	+	0.652967i
$689$	−1.89861	−	2.84148i	−0.0723314	−	0.108252i
$690$	−2.90017	−	16.8466i	−0.110408	−	0.641341i
$691$	10.1813	+	21.5265i	0.387314	+	0.818906i	0.999600	+	0.0282699i	$0.00899979\pi$
$691$	10.1813	+	21.5265i	0.387314	+	0.818906i	−0.612287	+	0.790636i	$0.709750\pi$
$692$	−1.52600	−	2.29698i	−0.0580098	−	0.0873180i
$693$	6.01032	+	4.45755i	0.228313	+	0.169328i
$694$	−4.28361	−	19.1948i	−0.162604	−	0.728623i
$695$	5.18032	−	17.0772i	0.196501	−	0.647776i
$696$	−2.65516	−	22.2556i	−0.100644	−	0.843596i
$697$	17.0614	−	31.9195i	0.646245	−	1.20904i
$698$	−3.79301	−	31.0921i	−0.143568	−	1.17685i
$699$	−3.31477	+	1.18604i	−0.125376	+	0.0448603i
$700$	−0.263532	+	5.08900i	−0.00996056	+	0.192346i
$701$	22.4825	+	13.4755i	0.849151	+	0.508961i	0.871276	−	0.490794i	$-0.163293\pi$
$701$	22.4825	+	13.4755i	0.849151	+	0.508961i	−0.0221251	+	0.999755i	$0.507043\pi$
$702$	11.6031	−	9.03043i	0.437931	−	0.340832i
$703$	−0.0853943	+	0.0853943i	−0.00322071	+	0.00322071i
$704$	9.18908	+	48.1967i	0.346326	+	1.81648i
$705$	−2.96627	−	2.96627i	−0.111716	−	0.111716i
$706$	−31.4125	−	3.91664i	−1.18223	−	0.147405i
$707$	−7.07820	+	11.8093i	−0.266203	+	0.444133i
$708$	3.31814	+	1.58014i	0.124703	+	0.0593853i
$709$	−15.6699	−	43.7946i	−0.588497	−	1.64474i	−0.752739	−	0.658319i	$-0.771268\pi$
$709$	−15.6699	−	43.7946i	−0.588497	−	1.64474i	0.164242	−	0.986420i	$-0.447482\pi$
$710$	−14.3754	−	11.2494i	−0.539500	−	0.422182i
$711$	21.3986	+	11.4378i	0.802509	+	0.428950i
$712$	−23.0902	−	26.9842i	−0.865342	−	1.01128i
$713$	−13.8552	−	4.20293i	−0.518882	−	0.157401i
$714$	3.45431	−	5.43899i	0.129274	−	0.203549i
$715$	21.0364	−	28.3643i	0.786717	−	1.06077i
$716$	16.1400	+	10.8464i	0.603178	+	0.405348i
$717$	25.2348	−	11.9352i	0.942413	−	0.445728i
$718$	−29.4155	−	20.7751i	−1.09778	−	0.775321i
$719$	24.8877	−	16.6294i	0.928153	−	0.620172i	0.00309390	−	0.999995i	$-0.499015\pi$
$719$	24.8877	−	16.6294i	0.928153	−	0.620172i	0.925059	+	0.379823i	$0.124015\pi$
$720$	−8.89852	+	18.5591i	−0.331628	+	0.691657i
$721$	−10.2242	−	6.83161i	−0.380770	−	0.254423i
$722$	−25.0360	+	9.61936i	−0.931744	+	0.357995i
$723$	7.41872	−	0.364459i	0.275905	−	0.0135544i
$724$	−11.9014	−	1.20405i	−0.442313	−	0.0447483i
$725$	6.28911	−	25.1076i	0.233572	−	0.932471i
$726$	−30.4486	−	29.0666i	−1.13006	−	1.07876i
$727$	−12.1106	+	14.7568i	−0.449157	+	0.547299i	−0.947531	−	0.319663i	$-0.896430\pi$
$727$	−12.1106	+	14.7568i	−0.449157	+	0.547299i	0.498375	+	0.866962i	$0.333930\pi$
$728$	−2.65159	−	2.80732i	−0.0982744	−	0.104046i
$729$	1.86545	−	18.9402i	0.0690906	−	0.701488i
$730$	57.0914	+	28.8323i	2.11305	+	1.06713i
$731$	1.81664	−	36.9785i	0.0671908	−	1.36770i
$732$	−6.25641	−	25.2609i	−0.231244	−	0.933671i
$733$	−4.64265	+	31.2982i	−0.171480	+	1.15602i	0.716988	+	0.697086i	$0.245520\pi$
$733$	−4.64265	+	31.2982i	−0.171480	+	1.15602i	−0.888468	+	0.458939i	$0.848230\pi$
$734$	38.0798	−	19.1046i	1.40555	−	0.705162i
$735$	19.7970	−	8.20019i	0.730224	−	0.302469i
$736$	−20.6111	−	2.68093i	−0.759737	−	0.0988205i
$737$	67.2075	+	27.8383i	2.47562	+	1.02544i
$738$	−15.2896	+	1.10745i	−0.562817	+	0.0407659i
$739$	−16.5220	−	22.2773i	−0.607770	−	0.819483i	0.386951	−	0.922100i	$-0.373528\pi$
$739$	−16.5220	−	22.2773i	−0.607770	−	0.819483i	−0.994721	+	0.102617i	$0.967278\pi$
$740$	−0.176022	−	3.78788i	−0.00647070	−	0.139245i
$741$	0.303914	−	0.275452i	0.0111646	−	0.0101190i
$742$	−0.128966	+	1.71732i	−0.00473448	+	0.0630446i
$743$	−19.0909	−	23.2623i	−0.700377	−	0.853412i	0.294379	−	0.955689i	$-0.404887\pi$
$743$	−19.0909	−	23.2623i	−0.700377	−	0.853412i	−0.994756	+	0.102277i	$0.967387\pi$
$744$	−7.62970	−	9.85712i	−0.279718	−	0.361380i
$745$	24.2077	−	2.38425i	0.886900	−	0.0873520i
$746$	−8.75685	+	3.86776i	−0.320611	+	0.141609i
$747$	−4.03988	−	6.74013i	−0.147811	−	0.246608i
$748$	45.5960	−	55.2595i	1.66716	−	2.02049i
$749$	4.26883	+	3.86904i	0.155980	+	0.141372i
$750$	−4.54468	+	4.31542i	−0.165948	+	0.157577i
$751$	−12.2706	+	2.44078i	−0.447761	+	0.0890652i	−0.413820	−	0.910359i	$-0.635806\pi$
$751$	−12.2706	+	2.44078i	−0.447761	+	0.0890652i	−0.0339408	+	0.999424i	$0.510806\pi$
$752$	−4.51095	+	2.38049i	−0.164498	+	0.0868076i
$753$	14.8185	+	2.94758i	0.540016	+	0.107416i
$754$	10.4716	+	16.5851i	0.381354	+	0.603993i
$755$	−15.1289	+	42.2825i	−0.550598	+	1.53882i
$756$	−7.40936	−	0.0196418i	−0.269476	−	0.000714367i
$757$	−45.4929	+	6.74824i	−1.65347	+	0.245269i	−0.907299	−	0.420487i	$-0.861859\pi$
$757$	−45.4929	+	6.74824i	−1.65347	+	0.245269i	−0.746170	+	0.665756i	$0.768109\pi$
$758$	25.9444	+	4.53721i	0.942342	+	0.164799i
$759$	22.2264	−	11.8802i	0.806767	−	0.431226i
$760$	−0.566820	+	1.45220i	−0.0205607	+	0.0526769i
$761$	−3.17832	−	10.4775i	−0.115214	−	0.379809i	0.880301	−	0.474416i	$-0.157341\pi$
$761$	−3.17832	−	10.4775i	−0.115214	−	0.379809i	−0.995515	+	0.0946066i	$0.969841\pi$
$762$	−13.9564	+	7.88176i	−0.505585	+	0.285526i
$763$	3.70821	+	1.75385i	0.134246	+	0.0634937i
$764$	7.49957	−	29.6068i	0.271325	−	1.07113i
$765$	29.1524	−	7.30230i	1.05401	−	0.264015i
$766$	−7.65720	+	2.10811i	−0.276666	+	0.0761691i
$767$	−3.21619			−0.116130
$768$	−13.1304	−	12.1568i	−0.473803	−	0.438671i
$769$	6.24623			0.225245			0.112622	−	0.993638i	$-0.464075\pi$
$769$	6.24623			0.225245			0.112622	+	0.993638i	$0.464075\pi$
$770$	−17.1575	+	4.72364i	−0.618313	+	0.170228i
$771$	−1.41119	+	0.353485i	−0.0508228	+	0.0127304i
$772$	−7.13222	−	1.80663i	−0.256694	−	0.0650222i
$773$	−10.5513	−	4.99041i	−0.379505	−	0.179492i	0.228277	−	0.973596i	$-0.426691\pi$
$773$	−10.5513	−	4.99041i	−0.379505	−	0.179492i	−0.607782	+	0.794104i	$0.707941\pi$
$774$	−13.6542	+	7.71111i	−0.490790	+	0.277170i
$775$	−4.17855	−	13.7748i	−0.150098	−	0.494807i
$776$	0.833737	−	0.365611i	0.0299294	−	0.0131247i
$777$	0.443415	−	0.237010i	0.0159074	−	0.00850270i
$778$	39.0560	+	6.83019i	1.40022	+	0.244874i
$779$	−1.14851	+	0.170365i	−0.0411495	+	0.00610396i
$780$	−0.0341415	+	12.8789i	−0.00122246	+	0.461140i
$781$	9.06619	−	25.3383i	0.324414	−	0.906676i
$782$	16.2026	+	25.6619i	0.579405	+	0.917669i
$783$	36.9114	+	7.34213i	1.31911	+	0.262386i
$784$	−2.41623	−	25.9417i	−0.0862941	−	0.926490i
$785$	11.9106	−	2.36916i	0.425106	−	0.0845588i
$786$	−21.3045	+	20.2298i	−0.759907	+	0.721574i
$787$	21.2571	+	19.2663i	0.757734	+	0.686770i	0.955996	−	0.293379i	$-0.0947798\pi$
$787$	21.2571	+	19.2663i	0.757734	+	0.686770i	−0.198262	+	0.980149i	$0.563530\pi$
$788$	−36.6072	−	30.2055i	−1.30408	−	1.07603i
$789$	0.748243	+	1.24837i	0.0266382	+	0.0444431i
$790$	−52.7843	+	23.3140i	−1.87798	+	0.829475i
$791$	2.57990	−	0.254098i	0.0917307	−	0.00903469i
$792$	−30.1009	−	3.83416i	−1.06959	−	0.136241i
$793$	14.4477	+	17.6046i	0.513054	+	0.625158i
$794$	−0.492370	+	6.55643i	−0.0174736	+	0.232679i
$795$	4.25574	−	3.85718i	0.150936	−	0.136800i
$796$	−14.2034	+	0.660028i	−0.503425	+	0.0233941i
$797$	−1.52280	−	2.05326i	−0.0539405	−	0.0727303i	0.775414	−	0.631454i	$-0.217541\pi$
$797$	−1.52280	−	2.05326i	−0.0539405	−	0.0727303i	−0.829354	+	0.558723i	$0.811291\pi$
$798$	−0.206157	+	0.0149324i	−0.00729789	+	0.000528600i
$799$	6.88065	+	2.85006i	0.243420	+	0.100828i
$800$	−9.16833	−	18.5189i	−0.324149	−	0.654743i
$801$	20.2922	−	8.40529i	0.716988	−	0.296986i
$802$	−43.4367	+	21.7921i	−1.53380	+	0.769505i
$803$	−13.8358	+	93.2734i	−0.488255	+	3.29155i
$804$	−25.7521	+	6.37805i	−0.908205	+	0.224937i
$805$	0.369904	−	7.52956i	0.0130374	−	0.265382i
$806$	9.73700	+	4.91738i	0.342971	+	0.173207i
$807$	−0.446417	+	4.53255i	−0.0157146	+	0.159553i
$808$	1.59210	−	55.8086i	0.0560098	−	1.96334i
$809$	18.8986	−	23.0280i	0.664440	−	0.809622i	−0.326319	−	0.945260i	$-0.605808\pi$
$809$	18.8986	−	23.0280i	0.664440	−	0.809622i	0.990759	+	0.135638i	$0.0433083\pi$
$810$	2.08371	+	1.98913i	0.0732141	+	0.0698909i
$811$	0.334810	−	1.33664i	0.0117568	−	0.0469356i	−0.963869	−	0.266377i	$-0.914173\pi$
$811$	0.334810	−	1.33664i	0.0117568	−	0.0469356i	0.975626	+	0.219441i	$0.0704234\pi$
$812$	0.994903	−	9.83410i	0.0349143	−	0.345109i
$813$	−2.36318	+	0.116096i	−0.0828805	+	0.00407166i
$814$	5.21853	−	2.00507i	0.182909	−	0.0702775i
$815$	−40.0586	−	26.7663i	−1.40319	−	0.937583i
$816$	−1.42038	+	26.0894i	−0.0497234	+	0.913311i
$817$	−0.987535	+	0.659850i	−0.0345495	+	0.0230852i
$818$	8.92735	+	6.30507i	0.312137	+	0.220451i
$819$	2.15891	−	1.02109i	0.0754383	−	0.0356797i
$820$	20.3347	−	30.2591i	0.710118	−	1.05669i
$821$	−2.31795	+	3.12540i	−0.0808971	+	0.109077i	−0.841802	−	0.539786i	$-0.818505\pi$
$821$	−2.31795	+	3.12540i	−0.0808971	+	0.109077i	0.760905	+	0.648863i	$0.224755\pi$
$822$	9.59777	−	15.1122i	0.334761	−	0.527098i
$823$	16.8043	+	5.09753i	0.585761	+	0.177689i	0.569235	−	0.822175i	$-0.307239\pi$
$823$	16.8043	+	5.09753i	0.585761	+	0.177689i	0.0165258	+	0.999863i	$0.494739\pi$
$824$	49.7141	+	3.86595i	1.73187	+	0.134677i
$825$	22.0974	+	11.8113i	0.769334	+	0.411218i
$826$	1.27639	+	0.998828i	0.0444112	+	0.0347537i
$827$	−1.81251	−	5.06563i	−0.0630271	−	0.176149i	0.905902	−	0.423487i	$-0.139194\pi$
$827$	−1.81251	−	5.06563i	−0.0630271	−	0.176149i	−0.968929	+	0.247338i	$0.920444\pi$
$828$	5.52671	−	11.6055i	0.192066	−	0.403320i
$829$	10.7772	−	17.9806i	0.374307	−	0.624494i	−0.611721	−	0.791074i	$-0.709522\pi$
$829$	10.7772	−	17.9806i	0.374307	−	0.624494i	0.986028	+	0.166580i	$0.0532724\pi$
$830$	18.5446	+	2.31222i	0.643693	+	0.0802582i
$831$	−7.17267	−	7.17267i	−0.248817	−	0.248817i
$832$	14.9484	+	4.66468i	0.518242	+	0.161719i
$833$	−26.9004	+	26.9004i	−0.932042	+	0.932042i
$834$	−7.57214	+	5.89322i	−0.262202	+	0.204066i
$835$	−1.25834	−	0.754220i	−0.0435467	−	0.0261009i
$836$	−2.29520	−	0.118856i	−0.0793812	−	0.00411072i
$837$	19.7065	−	7.05111i	0.681157	−	0.243722i
$838$	4.50922	+	36.9630i	0.155768	+	1.27687i
$839$	−16.1121	+	30.1437i	−0.556253	+	1.04068i	0.433937	+	0.900943i	$0.357124\pi$
$839$	−16.1121	+	30.1437i	−0.556253	+	1.04068i	−0.990189	+	0.139732i	$0.955376\pi$
$840$	4.01327	−	5.10058i	0.138471	−	0.175987i
$841$	−6.15559	+	20.2923i	−0.212262	+	0.699734i
$842$	−1.29420	−	5.79927i	−0.0446010	−	0.199856i
$843$	−19.2565	−	14.2816i	−0.663227	−	0.491883i
$844$	−38.7513	+	25.7444i	−1.33387	+	0.886161i
$845$	11.5312	+	24.3807i	0.396685	+	0.838721i
$846$	−0.535165	−	3.10869i	−0.0183993	−	0.106879i
$847$	−10.3135	−	15.4353i	−0.354377	−	0.530362i
$848$	−2.95234	−	6.32879i	−0.101384	−	0.217331i
$849$	3.85347	−	5.76713i	0.132251	−	0.197927i
$850$	−12.2639	+	27.5681i	−0.420647	+	0.945579i
$851$	0.116203	+	2.36537i	0.00398339	+	0.0810838i
$852$	2.82413	+	9.39954i	0.0967531	+	0.322023i
$853$	10.8518	+	2.71823i	0.371557	+	0.0930703i	0.424261	−	0.905540i	$-0.360534\pi$
$853$	10.8518	+	2.71823i	0.371557	+	0.0930703i	−0.0527037	+	0.998610i	$0.516784\pi$
$854$	−0.266443	−	11.4735i	−0.00911750	−	0.392617i
$855$	−0.745259	−	0.611618i	−0.0254873	−	0.0209169i
$856$	−22.7745	−	5.20941i	−0.778418	−	0.178054i
$857$	43.3403	+	4.26865i	1.48048	+	0.145814i	0.805751	−	0.592254i	$-0.201762\pi$
$857$	43.3403	+	4.26865i	1.48048	+	0.145814i	0.674726	+	0.738069i	$0.264262\pi$
$858$	−18.0370	+	5.93210i	−0.615771	+	0.202519i
$859$	−2.86228	−	0.140615i	−0.0976599	−	0.00479772i	0.000179051	−	1.00000i	$-0.499943\pi$
$859$	−2.86228	−	0.140615i	−0.0976599	−	0.00479772i	−0.0978390	+	0.995202i	$0.531193\pi$
$860$	5.56978	−	36.8746i	0.189928	−	1.25742i
$861$	4.78157	+	0.709279i	0.162956	+	0.0241722i
$862$	−12.4945	−	4.14599i	−0.425563	−	0.141213i
$863$	−10.3174	−	24.9084i	−0.351209	−	0.847893i	−0.996471	−	0.0839323i	$-0.973252\pi$
$863$	−10.3174	−	24.9084i	−0.351209	−	0.847893i	0.645263	−	0.763961i	$-0.276748\pi$
$864$	26.2402	−	14.6360i	0.892710	−	0.497928i
$865$	−1.55216	+	3.74724i	−0.0527749	+	0.127410i
$866$	25.4341	−	29.4063i	0.864285	−	0.999265i
$867$	15.3722	−	11.4008i	0.522067	−	0.387191i
$868$	−2.33710	−	4.97548i	−0.0793265	−	0.168879i
$869$	−57.1310	−	63.0344i	−1.93804	−	2.13829i
$870$	−24.9903	+	21.4991i	−0.847251	+	0.728887i
$871$	17.9469	−	14.7286i	0.608107	−	0.499060i
$872$	−16.5940	+	1.15772i	−0.561943	+	0.0392054i
$873$	0.0551858	+	0.560311i	0.00186776	+	0.0189636i
$874$	0.351595	−	0.907889i	0.0118929	−	0.0307098i
$875$	−2.37059	+	1.42088i	−0.0801406	+	0.0480344i
$876$	−16.1305	−	30.3714i	−0.544998	−	1.02615i
$877$	6.69874	−	7.39092i	0.226200	−	0.249574i	−0.617267	−	0.786753i	$-0.711760\pi$
$877$	6.69874	−	7.39092i	0.226200	−	0.249574i	0.843468	+	0.537180i	$0.180510\pi$
$878$	−28.2510	−	0.730993i	−0.953425	−	0.0246698i
$879$	6.93373	+	34.8582i	0.233869	+	1.17574i
$880$	51.2977	−	50.7567i	1.72925	−	1.71101i
$881$	−5.61411	+	28.2240i	−0.189144	+	0.950892i	0.763269	+	0.646081i	$0.223593\pi$
$881$	−5.61411	+	28.2240i	−0.189144	+	0.950892i	−0.952413	+	0.304811i	$0.901407\pi$
$882$	15.7168	+	3.55122i	0.529214	+	0.119576i
$883$	4.02898	+	1.44159i	0.135586	+	0.0485134i	0.403808	−	0.914844i	$-0.367686\pi$
$883$	4.02898	+	1.44159i	0.135586	+	0.0485134i	−0.268222	+	0.963357i	$0.586436\pi$
$884$	−8.69401	−	21.1476i	−0.292411	−	0.711270i
$885$	−0.793140	−	5.34692i	−0.0266611	−	0.179735i
$886$	9.67930	+	13.7823i	0.325182	+	0.463026i
$887$	−9.52715	−	17.8240i	−0.319890	−	0.598473i	0.669659	−	0.742669i	$-0.266440\pi$
$887$	−9.52715	−	17.8240i	−0.319890	−	0.598473i	−0.989549	+	0.144196i	$0.953940\pi$
$888$	−1.09762	+	1.71818i	−0.0368337	+	0.0576583i
$889$	−6.76404	+	2.05185i	−0.226859	+	0.0688168i
$890$	−13.9985	+	50.3244i	−0.469230	+	1.68688i
$891$	−1.81583	+	3.83925i	−0.0608326	+	0.128620i
$892$	−2.25938	+	3.02960i	−0.0756496	+	0.101439i
$893$	−0.0580521	−	0.231757i	−0.00194264	−	0.00775546i
$894$	−11.3712	−	6.46163i	−0.380310	−	0.216109i
$895$		−	28.6009i		−	0.956022i
$896$	−4.48379	−	6.49364i	−0.149793	−	0.216937i
$897$		−	8.04341i		−	0.268562i
$898$	12.3153	−	21.6725i	0.410966	−	0.723219i
$899$	6.78428	+	27.0844i	0.226269	+	0.903315i
$900$	12.6463	−	1.84166i	0.421545	−	0.0613886i
$901$	−4.35980	+	9.21801i	−0.145246	+	0.307097i
$902$	51.7822	+	14.4040i	1.72416	+	0.479600i
$903$	4.73181	−	1.43538i	0.157465	−	0.0477665i
$904$	−8.61882	+	6.01893i	−0.286658	+	0.200187i
$905$	8.29372	+	15.5165i	0.275692	+	0.515784i
$906$	19.7596	−	13.8772i	0.656470	−	0.461038i
$907$	7.62747	+	51.4202i	0.253266	+	1.70738i	0.626316	+	0.779570i	$0.284562\pi$
$907$	7.62747	+	51.4202i	0.253266	+	1.70738i	−0.373050	+	0.927811i	$0.621688\pi$
$908$	7.70754	+	3.21653i	0.255784	+	0.106744i
$909$	32.5103	+	11.6324i	1.07830	+	0.385822i
$910$	−1.25176	+	5.53997i	−0.0414953	+	0.183648i
$911$	7.79511	−	39.1887i	0.258264	−	1.29838i	−0.606051	−	0.795426i	$-0.707247\pi$
$911$	7.79511	−	39.1887i	0.258264	−	1.29838i	0.864314	−	0.502952i	$-0.167753\pi$
$912$	0.699384	−	0.461969i	0.0231589	−	0.0152973i
$913$	5.37510	+	27.0225i	0.177890	+	0.894313i
$914$	1.41996	−	54.8779i	0.0469682	−	1.81520i
$915$	−25.7047	+	28.3608i	−0.849772	+	0.937579i
$916$	−9.01223	+	29.4283i	−0.297773	+	0.972338i
$917$	−11.1128	+	6.66078i	−0.366978	+	0.219958i
$918$	−40.9111	−	15.8435i	−1.35027	−	0.522912i
$919$	−2.74094	−	27.8292i	−0.0904152	−	0.918001i	−0.928220	−	0.372032i	$-0.878661\pi$
$919$	−2.74094	−	27.8292i	−0.0904152	−	0.918001i	0.837805	−	0.545970i	$-0.183839\pi$
$920$	13.6360	+	27.3604i	0.449565	+	0.902047i
$921$	4.66496	−	3.82844i	0.153716	−	0.126151i
$922$	−29.2237	−	33.9693i	−0.962430	−	1.11872i
$923$	−5.76796	−	6.36396i	−0.189855	−	0.209472i
$924$	9.00049	+	3.24737i	0.296094	+	0.106831i
$925$	−1.89114	+	1.40256i	−0.0621803	+	0.0461160i
$926$	1.51250	+	1.30819i	0.0497037	+	0.0429897i
$927$	−11.8013	+	28.4910i	−0.387607	+	0.935766i
$928$	15.9997	+	36.7503i	0.525216	+	1.20639i
$929$	9.37683	+	22.6377i	0.307644	+	0.742717i	0.999780	+	0.0209512i	$0.00666946\pi$
$929$	9.37683	+	22.6377i	0.307644	+	0.742717i	−0.692137	+	0.721766i	$0.743331\pi$
$930$	−5.77392	+	17.4004i	−0.189334	+	0.570583i
$931$	1.20720	+	0.179072i	0.0395644	+	0.00586883i
$932$	5.06680	−	3.73702i	0.165969	−	0.122410i
$933$	14.8484	+	0.729457i	0.486116	+	0.0238813i
$934$	6.34940	+	19.3058i	0.207759	+	0.631704i
$935$	−104.864	−	10.3282i	−3.42941	−	0.337767i
$936$	−5.60783	+	7.89562i	−0.183298	+	0.258077i
$937$	−13.0884	−	10.7414i	−0.427579	−	0.350905i	0.395859	−	0.918311i	$-0.370447\pi$
$937$	−13.0884	−	10.7414i	−0.427579	−	0.350905i	−0.823438	+	0.567406i	$0.807947\pi$
$938$	−11.6966	+	0.271623i	−0.381908	+	0.00886882i
$939$	11.3953	+	2.85437i	0.371871	+	0.0931488i
$940$	6.60663	+	3.55387i	0.215485	+	0.115914i
$941$	−1.76991	−	36.0274i	−0.0576976	−	1.17446i	−0.836780	−	0.547539i	$-0.815565\pi$
$941$	−1.76991	−	36.0274i	−0.0576976	−	1.17446i	0.779082	−	0.626922i	$-0.215685\pi$
$942$	−5.96581	−	2.65393i	−0.194376	−	0.0864696i
$943$	−12.6496	+	18.9315i	−0.411929	+	0.616495i
$944$	−6.49600	−	0.998817i	−0.211427	−	0.0325087i
$945$	6.05443	+	9.06109i	0.196951	+	0.294757i
$946$	54.1836	−	9.32779i	1.76166	−	0.303273i
$947$	−8.39786	−	17.7558i	−0.272894	−	0.576986i	0.720273	−	0.693691i	$-0.244017\pi$
$947$	−8.39786	−	17.7558i	−0.272894	−	0.576986i	−0.993167	+	0.116705i	$0.962767\pi$
$948$	30.4136	+	6.13351i	0.987789	+	0.199207i
$949$	24.1720	+	17.9272i	0.784657	+	0.581941i
$950$	0.944705	−	0.210826i	0.0306503	−	0.00684009i
$951$	8.02617	−	26.4587i	0.260266	−	0.857984i
$952$	−3.11731	+	11.0927i	−0.101033	+	0.359518i
$953$	5.38534	−	10.0753i	0.174448	−	0.326370i	−0.779468	−	0.626442i	$-0.784511\pi$
$953$	5.38534	−	10.0753i	0.174448	−	0.326370i	0.953917	+	0.300072i	$0.0970107\pi$
$954$	4.28717	−	0.523004i	0.138802	−	0.0169329i
$955$	−42.2949	+	15.1334i	−1.36863	+	0.489704i
$956$	−37.0774	+	33.4264i	−1.19917	+	1.08109i
$957$	−41.6863	−	24.9858i	−1.34753	−	0.807677i
$958$	16.3308	+	20.9833i	0.527624	+	0.677939i
$959$	5.58256	−	5.58256i	0.180270	−	0.180270i
$960$	−4.06863	+	26.0020i	−0.131315	+	0.839212i
$961$	−10.9403	−	10.9403i	−0.352914	−	0.352914i
$962$	0.220755	−	1.77051i	0.00711742	−	0.0570836i
$963$	7.42809	−	12.3930i	0.239367	−	0.399359i
$964$	−12.5183	+	4.44172i	−0.403188	+	0.143058i
$965$	3.64560	+	10.1888i	0.117356	+	0.327988i
$966$	−2.49798	+	3.19213i	−0.0803712	+	0.102705i
$967$	6.31388	+	3.37484i	0.203041	+	0.108528i	0.569783	−	0.821795i	$-0.307027\pi$
$967$	6.31388	+	3.37484i	0.203041	+	0.108528i	−0.366743	+	0.930322i	$0.619527\pi$
$968$	67.1056	+	34.1133i	2.15686	+	1.09644i
$969$	−1.17118	−	0.355273i	−0.0376237	−	0.0114130i
$970$	−1.13029	−	0.717850i	−0.0362915	−	0.0230488i
$971$	−9.98422	+	13.4622i	−0.320409	+	0.432021i	−0.933820	−	0.357742i	$-0.883547\pi$
$971$	−9.98422	+	13.4622i	−0.320409	+	0.432021i	0.613412	+	0.789763i	$0.289797\pi$
$972$	5.83623	+	29.7527i	0.187197	+	0.954318i
$973$	−3.82520	+	1.80918i	−0.122630	+	0.0579998i
$974$	1.12115	−	1.58744i	0.0359239	−	0.0508647i
$975$	6.64905	−	4.44275i	0.212940	−	0.142282i
$976$	23.7140	+	40.0443i	0.759065	+	1.28179i
$977$	38.5189	+	25.7375i	1.23233	+	0.823416i	0.989199	−	0.146577i	$-0.0468258\pi$
$977$	38.5189	+	25.7375i	1.23233	+	0.823416i	0.243130	+	0.969994i	$0.421826\pi$
$978$	9.29075	+	24.1808i	0.297086	+	0.773216i
$979$	−76.9170	+	3.77869i	−2.45828	+	0.120767i
$980$	−29.6862	+	24.2314i	−0.948290	+	0.774044i
$981$	2.49965	−	9.97916i	0.0798077	−	0.318610i
$982$	17.2631	−	18.0839i	0.550886	−	0.577080i
$983$	10.5625	−	12.8704i	0.336891	−	0.410503i	−0.576817	−	0.816873i	$-0.695706\pi$
$983$	10.5625	−	12.8704i	0.336891	−	0.410503i	0.913709	+	0.406370i	$0.133206\pi$
$984$	−18.3165	+	6.98190i	−0.583908	+	0.222575i
$985$	−6.84198	+	69.4678i	−0.218004	+	2.21343i
$986$	26.3832	−	52.2419i	0.840212	−	1.66372i
$987$	−0.0488067	+	0.993484i	−0.00155354	+	0.0316229i
$988$	−0.378764	+	0.628147i	−0.0120501	+	0.0199840i
$989$	−3.41747	+	23.0387i	−0.108669	+	0.732589i
$990$	20.0133	+	39.8911i	0.636063	+	1.26782i
$991$	6.39766	−	2.65000i	0.203228	−	0.0841799i	−0.278748	−	0.960364i	$-0.589919\pi$
$991$	6.39766	−	2.65000i	0.203228	−	0.0841799i	0.481976	+	0.876184i	$0.339919\pi$
$992$	18.1395	+	12.9559i	0.575929	+	0.411352i
$993$	20.8946	+	8.65481i	0.663069	+	0.274652i
$994$	0.312684	+	4.31694i	0.00991773	+	0.136925i
$995$	12.4577	+	16.7973i	0.394936	+	0.532510i
$996$	−7.42731	−	6.76767i	−0.235343	−	0.214442i
$997$	5.62844	−	5.10132i	0.178254	−	0.161560i	−0.577556	−	0.816351i	$-0.695993\pi$
$997$	5.62844	−	5.10132i	0.178254	−	0.161560i	0.755810	+	0.654791i	$0.227243\pi$
$998$	21.8228	+	1.63883i	0.690790	+	0.0518764i
$999$	−2.17181	−	2.64636i	−0.0687131	−	0.0837271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.101.15	✓	992
256.109	even	64	inner	256.2.m.a.109.15	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.101.15	✓	992	1.1	even	1	trivial
256.2.m.a.109.15	yes	992	256.109	even	64	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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.375382 - 1.36348i) q^{2} +(1.08486 - 0.271743i) q^{3} +(-1.71818 + 1.02365i) q^{4} +(2.65917 + 1.25769i) q^{5} +(-0.777754 - 1.37718i) q^{6} +(-0.202472 - 0.667460i) q^{7} +(2.04071 + 1.95845i) q^{8} +(-1.54269 + 0.824584i) q^{9} +O(q^{10})\)	\(q+(-0.375382 - 1.36348i) q^{2} +(1.08486 - 0.271743i) q^{3} +(-1.71818 + 1.02365i) q^{4} +(2.65917 + 1.25769i) q^{5} +(-0.777754 - 1.37718i) q^{6} +(-0.202472 - 0.667460i) q^{7} +(2.04071 + 1.95845i) q^{8} +(-1.54269 + 0.824584i) q^{9} +(0.716640 - 4.09784i) q^{10} +(6.06673 - 0.899914i) q^{11} +(-1.58581 + 1.57742i) q^{12} +(0.659432 - 1.84299i) q^{13} +(-0.834067 + 0.526620i) q^{14} +(3.22659 + 0.641809i) q^{15} +(1.90426 - 3.51764i) q^{16} +(-5.72839 + 1.13945i) q^{17} +(1.70340 + 1.79390i) q^{18} +(0.138829 + 0.125828i) q^{19} +(-5.85636 + 0.561129i) q^{20} +(-0.401031 - 0.669080i) q^{21} +(-3.50436 - 7.93408i) q^{22} +(3.65657 - 0.360141i) q^{23} +(2.74608 + 1.57009i) q^{24} +(2.31741 + 2.82377i) q^{25} +(-2.76042 - 0.207300i) q^{26} +(-3.93551 + 3.56694i) q^{27} +(1.03113 + 0.939554i) q^{28} +(-4.22087 - 5.69119i) q^{29} +(-0.336108 - 4.64033i) q^{30} +(-3.64060 - 1.50799i) q^{31} +(-5.51107 - 1.27598i) q^{32} +(6.33700 - 2.62487i) q^{33} +(3.70395 + 7.38284i) q^{34} +(0.301053 - 2.02953i) q^{35} +(1.80652 - 2.99596i) q^{36} +(-0.0316262 + 0.643767i) q^{37} +(0.119450 - 0.236525i) q^{38} +(0.214571 - 2.17858i) q^{39} +(2.96346 + 7.77441i) q^{40} +(-3.93122 + 4.79020i) q^{41} +(-0.761741 + 0.797961i) q^{42} +(-1.54023 + 6.14894i) q^{43} +(-9.50251 + 7.75644i) q^{44} +(-5.13933 + 0.252479i) q^{45} +(-1.86366 - 4.85049i) q^{46} +(-1.06023 - 0.708426i) q^{47} +(1.10996 - 4.33362i) q^{48} +(5.41578 - 3.61871i) q^{49} +(2.98025 - 4.21974i) q^{50} +(-5.90486 + 2.79279i) q^{51} +(0.753562 + 3.84161i) q^{52} +(1.04002 - 1.40231i) q^{53} +(6.34078 + 4.02704i) q^{54} +(17.2642 + 5.23705i) q^{55} +(0.893998 - 1.75862i) q^{56} +(0.184803 + 0.0987793i) q^{57} +(-6.17540 + 7.89146i) q^{58} +(-0.553538 - 1.54704i) q^{59} +(-6.20084 + 2.20017i) q^{60} +(-5.98148 + 9.97950i) q^{61} +(-0.689500 + 5.52998i) q^{62} +(0.862728 + 0.862728i) q^{63} +(0.328984 + 7.99323i) q^{64} +(4.07145 - 4.07145i) q^{65} +(-5.95777 - 7.65507i) q^{66} +(10.1735 + 6.09778i) q^{67} +(8.67598 - 7.82166i) q^{68} +(3.86900 - 1.38435i) q^{69} +(-2.88025 + 0.351370i) q^{70} +(2.06844 - 3.86978i) q^{71} +(-4.76308 - 1.33853i) q^{72} +(-4.46300 + 14.7126i) q^{73} +(0.889638 - 0.198537i) q^{74} +(3.28140 + 2.43365i) q^{75} +(-0.367337 - 0.0740808i) q^{76} +(-1.82900 - 3.86709i) q^{77} +(-3.05100 + 0.525235i) q^{78} +(-7.70630 - 11.5333i) q^{79} +(9.48786 - 6.95901i) q^{80} +(-0.384717 + 0.575770i) q^{81} +(8.00707 + 3.56200i) q^{82} +(0.220427 + 4.48690i) q^{83} +(1.37395 + 0.739081i) q^{84} +(-16.6658 - 4.17457i) q^{85} +(8.96215 - 0.208123i) q^{86} +(-6.12560 - 5.02715i) q^{87} +(14.1429 + 10.0449i) q^{88} +(-12.4959 - 1.23074i) q^{89} +(2.27346 + 6.91262i) q^{90} +(-1.36364 - 0.0669912i) q^{91} +(-5.91398 + 4.36185i) q^{92} +(-4.35933 - 0.646646i) q^{93} +(-0.567935 + 1.71154i) q^{94} +(0.210918 + 0.509201i) q^{95} +(-6.32548 + 0.113341i) q^{96} +(0.123173 - 0.297367i) q^{97} +(-6.96704 - 6.02593i) q^{98} +(-8.61701 + 6.39081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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