LMFDB - Embedded newform 256.2.m.a.101.4

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			101.4
Character	$\chi$	$=$	256.101
Dual form			256.2.m.a.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31347 + 0.524199i) q^{2} +(-1.57525 + 0.394580i) q^{3} +(1.45043 - 1.37704i) q^{4} +(3.41561 + 1.61546i) q^{5} +(1.86221 - 1.34402i) q^{6} +(-1.44081 - 4.74972i) q^{7} +(-1.18326 + 2.56903i) q^{8} +(-0.320042 + 0.171066i) q^{9} +O(q^{10})$	\(q+(-1.31347 + 0.524199i) q^{2} +(-1.57525 + 0.394580i) q^{3} +(1.45043 - 1.37704i) q^{4} +(3.41561 + 1.61546i) q^{5} +(1.86221 - 1.34402i) q^{6} +(-1.44081 - 4.74972i) q^{7} +(-1.18326 + 2.56903i) q^{8} +(-0.320042 + 0.171066i) q^{9} +(-5.33314 - 0.331411i) q^{10} +(0.632723 - 0.0938556i) q^{11} +(-1.74144 + 2.74150i) q^{12} +(1.67613 - 4.68447i) q^{13} +(4.38227 + 5.48336i) q^{14} +(-6.01787 - 1.19703i) q^{15} +(0.207499 - 3.99461i) q^{16} +(2.48352 - 0.494003i) q^{17} +(0.330694 - 0.392456i) q^{18} +(3.97235 + 3.60033i) q^{19} +(7.17867 - 2.36033i) q^{20} +(4.14378 + 6.91348i) q^{21} +(-0.781866 + 0.454950i) q^{22} +(3.51135 - 0.345838i) q^{23} +(0.850244 - 4.51375i) q^{24} +(5.88470 + 7.17053i) q^{25} +(0.254040 + 7.03156i) q^{26} +(4.04638 - 3.66742i) q^{27} +(-8.63037 - 4.90508i) q^{28} +(-2.46645 - 3.32562i) q^{29} +(8.53180 - 1.58229i) q^{30} +(2.18366 + 0.904500i) q^{31} +(1.82143 + 5.35560i) q^{32} +(-0.959664 + 0.397506i) q^{33} +(-3.00308 + 1.95072i) q^{34} +(2.75175 - 18.5508i) q^{35} +(-0.228633 + 0.688831i) q^{36} +(-0.0957475 + 1.94898i) q^{37} +(-7.10487 - 2.64664i) q^{38} +(-0.791929 + 8.04059i) q^{39} +(-8.19172 + 6.86328i) q^{40} +(0.597257 - 0.727759i) q^{41} +(-9.06679 - 6.90852i) q^{42} +(-0.415342 + 1.65814i) q^{43} +(0.788478 - 1.00742i) q^{44} +(-1.36949 + 0.0672787i) q^{45} +(-4.43078 + 2.29489i) q^{46} +(-3.19742 - 2.13645i) q^{47} +(1.24933 + 6.37439i) q^{48} +(-14.6636 + 9.79790i) q^{49} +(-11.4882 - 6.33356i) q^{50} +(-3.71724 + 1.75812i) q^{51} +(-4.01961 - 9.10261i) q^{52} +(1.82933 - 2.46656i) q^{53} +(-3.39235 + 6.93817i) q^{54} +(2.31275 + 0.701567i) q^{55} +(13.9070 + 1.91866i) q^{56} +(-7.67807 - 4.10401i) q^{57} +(4.98290 + 3.07521i) q^{58} +(3.03405 + 8.47961i) q^{59} +(-10.3769 + 6.55067i) q^{60} +(7.14849 - 11.9265i) q^{61} +(-3.34231 - 0.0433674i) q^{62} +(1.27363 + 1.27363i) q^{63} +(-5.19980 - 6.07965i) q^{64} +(13.2926 - 13.2926i) q^{65} +(1.05212 - 1.02517i) q^{66} +(-10.5739 - 6.33776i) q^{67} +(2.92191 - 4.13643i) q^{68} +(-5.39479 + 1.93029i) q^{69} +(6.10994 + 25.8084i) q^{70} +(-4.30624 + 8.05640i) q^{71} +(-0.0607805 - 1.02461i) q^{72} +(-0.690439 + 2.27607i) q^{73} +(-0.895894 - 2.61013i) q^{74} +(-12.0992 - 8.97340i) q^{75} +(10.7194 - 0.248074i) q^{76} +(-1.35742 - 2.87003i) q^{77} +(-3.17469 - 10.9762i) q^{78} +(1.33348 + 1.99570i) q^{79} +(7.16189 - 13.3088i) q^{80} +(-4.32213 + 6.46853i) q^{81} +(-0.402991 + 1.26897i) q^{82} +(-0.327525 - 6.66693i) q^{83} +(15.5304 + 4.32136i) q^{84} +(9.28078 + 2.32471i) q^{85} +(-0.323653 - 2.39565i) q^{86} +(5.19749 + 4.26547i) q^{87} +(-0.507558 + 1.73654i) q^{88} +(-6.05877 - 0.596737i) q^{89} +(1.76352 - 0.806254i) q^{90} +(-24.6649 - 1.21171i) q^{91} +(4.61674 - 5.33690i) q^{92} +(-3.79670 - 0.563188i) q^{93} +(5.31966 + 1.13009i) q^{94} +(7.75181 + 18.7145i) q^{95} +(-4.98241 - 7.71771i) q^{96} +(1.93933 - 4.68195i) q^{97} +(14.1242 - 20.5559i) q^{98} +(-0.186442 + 0.138275i) 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 $

$2$	−1.31347	+	0.524199i	−0.928767	+	0.370665i
$2$	−1.31347	+	0.524199i	−0.928767	+	0.370665i
$3$	−1.57525	+	0.394580i	−0.909471	+	0.227811i	−0.669363	−	0.742935i	$-0.733433\pi$
$3$	−1.57525	+	0.394580i	−0.909471	+	0.227811i	−0.240108	+	0.970746i	$0.577183\pi$
$4$	1.45043	−	1.37704i	0.725215	−	0.688522i
$5$	3.41561	+	1.61546i	1.52751	+	0.722457i	0.992483	−	0.122380i	$-0.0390526\pi$
$5$	3.41561	+	1.61546i	1.52751	+	0.722457i	0.535024	+	0.844837i	$0.320303\pi$
$6$	1.86221	−	1.34402i	0.760246	−	0.548692i
$7$	−1.44081	−	4.74972i	−0.544575	−	1.79522i	−0.603991	−	0.796991i	$-0.706424\pi$
$7$	−1.44081	−	4.74972i	−0.544575	−	1.79522i	0.0594157	−	0.998233i	$-0.481076\pi$
$8$	−1.18326	+	2.56903i	−0.418345	+	0.908288i
$9$	−0.320042	+	0.171066i	−0.106681	+	0.0570220i
$10$	−5.33314	−	0.331411i	−1.68649	−	0.104801i
$11$	0.632723	−	0.0938556i	0.190773	−	0.0282985i	−0.0506601	−	0.998716i	$-0.516133\pi$
$11$	0.632723	−	0.0938556i	0.190773	−	0.0282985i	0.241433	+	0.970417i	$0.422383\pi$
$12$	−1.74144	+	2.74150i	−0.502710	+	0.791403i
$13$	1.67613	−	4.68447i	0.464875	−	1.29924i	−0.449104	−	0.893479i	$-0.648257\pi$
$13$	1.67613	−	4.68447i	0.464875	−	1.29924i	0.913980	−	0.405760i	$-0.132993\pi$
$14$	4.38227	+	5.48336i	1.17121	+	1.46549i
$15$	−6.01787	−	1.19703i	−1.55381	−	0.309072i
$16$	0.207499	−	3.99461i	0.0518749	−	0.998654i
$17$	2.48352	−	0.494003i	0.602342	−	0.119813i	0.115506	−	0.993307i	$-0.463151\pi$
$17$	2.48352	−	0.494003i	0.602342	−	0.119813i	0.486836	+	0.873494i	$0.338151\pi$
$18$	0.330694	−	0.392456i	0.0779454	−	0.0925029i
$19$	3.97235	+	3.60033i	0.911320	+	0.825973i	0.985220	−	0.171293i	$-0.0547945\pi$
$19$	3.97235	+	3.60033i	0.911320	+	0.825973i	−0.0738998	+	0.997266i	$0.523545\pi$
$20$	7.17867	−	2.36033i	1.60520	−	0.527785i
$21$	4.14378	+	6.91348i	0.904247	+	1.50865i
$22$	−0.781866	+	0.454950i	−0.166694	+	0.0969956i
$23$	3.51135	−	0.345838i	0.732167	−	0.0721121i	0.274939	−	0.961462i	$-0.411342\pi$
$23$	3.51135	−	0.345838i	0.732167	−	0.0721121i	0.457228	+	0.889350i	$0.348842\pi$
$24$	0.850244	−	4.51375i	0.173555	−	0.921366i
$25$	5.88470	+	7.17053i	1.17694	+	1.43411i
$26$	0.254040	+	7.03156i	0.0498214	+	1.37900i
$27$	4.04638	−	3.66742i	0.778726	−	0.705796i
$28$	−8.63037	−	4.90508i	−1.63099	−	0.926972i
$29$	−2.46645	−	3.32562i	−0.458008	−	0.617552i	0.512481	−	0.858699i	$-0.328726\pi$
$29$	−2.46645	−	3.32562i	−0.458008	−	0.617552i	−0.970489	+	0.241147i	$0.922476\pi$
$30$	8.53180	−	1.58229i	1.55769	−	0.288886i
$31$	2.18366	+	0.904500i	0.392196	+	0.162453i	0.570062	−	0.821602i	$-0.306919\pi$
$31$	2.18366	+	0.904500i	0.392196	+	0.162453i	−0.177866	+	0.984055i	$0.556919\pi$
$32$	1.82143	+	5.35560i	0.321986	+	0.946744i
$33$	−0.959664	+	0.397506i	−0.167056	+	0.0691969i
$34$	−3.00308	+	1.95072i	−0.515025	+	0.334545i
$35$	2.75175	−	18.5508i	0.465130	−	3.13565i
$36$	−0.228633	+	0.688831i	−0.0381055	+	0.114805i
$37$	−0.0957475	+	1.94898i	−0.0157408	+	0.320411i	0.977993	+	0.208638i	$0.0669030\pi$
$37$	−0.0957475	+	1.94898i	−0.0157408	+	0.320411i	−0.993734	+	0.111773i	$0.964347\pi$
$38$	−7.10487	−	2.64664i	−1.15256	−	0.429342i
$39$	−0.791929	+	8.04059i	−0.126810	+	1.28752i
$40$	−8.19172	+	6.86328i	−1.29522	+	1.08518i
$41$	0.597257	−	0.727759i	0.0932758	−	0.113657i	−0.724281	−	0.689505i	$-0.757828\pi$
$41$	0.597257	−	0.727759i	0.0932758	−	0.113657i	0.817557	+	0.575848i	$0.195328\pi$
$42$	−9.06679	−	6.90852i	−1.39904	−	1.06601i
$43$	−0.415342	+	1.65814i	−0.0633391	+	0.252864i	−0.993426	−	0.114476i	$-0.963481\pi$
$43$	−0.415342	+	1.65814i	−0.0633391	+	0.252864i	0.930087	+	0.367339i	$0.119731\pi$
$44$	0.788478	−	1.00742i	0.118867	−	0.151874i
$45$	−1.36949	+	0.0672787i	−0.204151	+	0.0100293i
$46$	−4.43078	+	2.29489i	−0.653283	+	0.338364i
$47$	−3.19742	−	2.13645i	−0.466392	−	0.311633i	0.300076	−	0.953915i	$-0.402988\pi$
$47$	−3.19742	−	2.13645i	−0.466392	−	0.311633i	−0.766468	+	0.642282i	$0.777988\pi$
$48$	1.24933	+	6.37439i	0.180325	+	0.920065i
$49$	−14.6636	+	9.79790i	−2.09480	+	1.39970i
$50$	−11.4882	−	6.33356i	−1.62468	−	0.895700i
$51$	−3.71724	+	1.75812i	−0.520518	+	0.246187i
$52$	−4.01961	−	9.10261i	−0.557420	−	1.26231i
$53$	1.82933	−	2.46656i	0.251278	−	0.338808i	−0.659501	−	0.751704i	$-0.729232\pi$
$53$	1.82933	−	2.46656i	0.251278	−	0.338808i	0.910779	+	0.412895i	$0.135482\pi$
$54$	−3.39235	+	6.93817i	−0.461641	+	0.944166i
$55$	2.31275	+	0.701567i	0.311852	+	0.0945992i
$56$	13.9070	+	1.91866i	1.85840	+	0.256392i
$57$	−7.67807	−	4.10401i	−1.01699	−	0.543590i
$58$	4.98290	+	3.07521i	0.654287	+	0.403794i
$59$	3.03405	+	8.47961i	0.395000	+	1.10395i	0.960277	+	0.279049i	$0.0900193\pi$
$59$	3.03405	+	8.47961i	0.395000	+	1.10395i	−0.565277	+	0.824901i	$0.691231\pi$
$60$	−10.3769	+	6.55067i	−1.33965	+	0.845687i
$61$	7.14849	−	11.9265i	0.915271	−	1.52704i	0.0668182	−	0.997765i	$-0.478715\pi$
$61$	7.14849	−	11.9265i	0.915271	−	1.52704i	0.848452	−	0.529272i	$-0.177535\pi$
$62$	−3.34231	−	0.0433674i	−0.424474	−	0.00550767i
$63$	1.27363	+	1.27363i	0.160463	+	0.160463i
$64$	−5.19980	−	6.07965i	−0.649975	−	0.759956i
$65$	13.2926	−	13.2926i	1.64875	−	1.64875i
$66$	1.05212	−	1.02517i	0.129507	−	0.126190i
$67$	−10.5739	−	6.33776i	−1.29181	−	0.774280i	−0.307638	−	0.951504i	$-0.599539\pi$
$67$	−10.5739	−	6.33776i	−1.29181	−	0.774280i	−0.984171	+	0.177223i	$0.943289\pi$
$68$	2.92191	−	4.13643i	0.354334	−	0.501616i
$69$	−5.39479	+	1.93029i	−0.649457	+	0.232379i
$70$	6.10994	+	25.8084i	0.730278	+	3.08470i
$71$	−4.30624	+	8.05640i	−0.511056	+	0.956119i	0.485582	+	0.874191i	$0.338608\pi$
$71$	−4.30624	+	8.05640i	−0.511056	+	0.956119i	−0.996638	+	0.0819281i	$0.973892\pi$
$72$	−0.0607805	−	1.02461i	−0.00716306	−	0.120752i
$73$	−0.690439	+	2.27607i	−0.0808098	+	0.266394i	−0.988030	−	0.154262i	$-0.950700\pi$
$73$	−0.690439	+	2.27607i	−0.0808098	+	0.266394i	0.907220	+	0.420656i	$0.138200\pi$
$74$	−0.895894	−	2.61013i	−0.104146	−	0.303422i
$75$	−12.0992	−	8.97340i	−1.39710	−	1.03616i
$76$	10.7194	−	0.248074i	1.22960	−	0.0284560i
$77$	−1.35742	−	2.87003i	−0.154693	−	0.327070i
$78$	−3.17469	−	10.9762i	−0.359463	−	1.24281i
$79$	1.33348	+	1.99570i	0.150028	+	0.224533i	0.898870	−	0.438216i	$-0.144390\pi$
$79$	1.33348	+	1.99570i	0.150028	+	0.224533i	−0.748841	+	0.662749i	$0.769390\pi$
$80$	7.16189	−	13.3088i	0.800724	−	1.48797i
$81$	−4.32213	+	6.46853i	−0.480237	+	0.718726i
$82$	−0.402991	+	1.26897i	−0.0445029	+	0.140135i
$83$	−0.327525	−	6.66693i	−0.0359506	−	0.731791i	−0.947337	−	0.320239i	$-0.896237\pi$
$83$	−0.327525	−	6.66693i	−0.0359506	−	0.731791i	0.911386	−	0.411552i	$-0.135013\pi$
$84$	15.5304	+	4.32136i	1.69451	+	0.471499i
$85$	9.28078	+	2.32471i	1.00664	+	0.252151i
$86$	−0.323653	−	2.39565i	−0.0349004	−	0.258329i
$87$	5.19749	+	4.26547i	0.557230	+	0.457307i
$88$	−0.507558	+	1.73654i	−0.0541058	+	0.185116i
$89$	−6.05877	−	0.596737i	−0.642228	−	0.0632540i	−0.228340	−	0.973581i	$-0.573330\pi$
$89$	−6.05877	−	0.596737i	−0.642228	−	0.0632540i	−0.413889	+	0.910328i	$0.635830\pi$
$90$	1.76352	−	0.806254i	0.185892	−	0.0849866i
$91$	−24.6649	−	1.21171i	−2.58559	−	0.127022i
$92$	4.61674	−	5.33690i	0.481328	−	0.556410i
$93$	−3.79670	−	0.563188i	−0.393700	−	0.0583998i
$94$	5.31966	+	1.13009i	0.548681	+	0.116559i
$95$	7.75181	+	18.7145i	0.795319	+	1.92007i
$96$	−4.98241	−	7.71771i	−0.508516	−	0.787685i
$97$	1.93933	−	4.68195i	0.196909	−	0.475380i	−0.794326	−	0.607492i	$-0.792176\pi$
$97$	1.93933	−	4.68195i	0.196909	−	0.475380i	0.991235	+	0.132112i	$0.0421757\pi$
$98$	14.1242	−	20.5559i	1.42676	−	2.07646i
$99$	−0.186442	+	0.138275i	−0.0187382	+	0.0138972i
$100$	18.4095	+	2.29687i	1.84095	+	0.229687i
$101$	3.65804	+	4.03603i	0.363989	+	0.401600i	0.895218	−	0.445628i	$-0.147020\pi$
$101$	3.65804	+	4.03603i	0.363989	+	0.401600i	−0.531229	+	0.847228i	$0.678270\pi$
$102$	3.96090	−	4.25783i	0.392187	−	0.421588i
$103$	−3.96553	+	3.25442i	−0.390735	+	0.320668i	−0.809165	−	0.587581i	$-0.800080\pi$
$103$	−3.96553	+	3.25442i	−0.390735	+	0.320668i	0.418430	+	0.908249i	$0.362580\pi$
$104$	10.0512	+	9.84897i	0.985605	+	0.965771i
$105$	2.98507	+	30.3079i	0.291313	+	2.95775i
$106$	−1.10981	+	4.19870i	−0.107794	+	0.407814i
$107$	−8.31622	+	4.98455i	−0.803959	+	0.481875i	−0.856128	−	0.516764i	$-0.827137\pi$
$107$	−8.31622	+	4.98455i	−0.803959	+	0.481875i	0.0521689	+	0.998638i	$0.483387\pi$
$108$	0.818788	−	10.8914i	0.0787879	−	1.04802i
$109$	−0.665914	+	0.734723i	−0.0637830	+	0.0703737i	−0.772007	−	0.635614i	$-0.780747\pi$
$109$	−0.665914	+	0.734723i	−0.0637830	+	0.0703737i	0.708224	+	0.705988i	$0.249497\pi$
$110$	−3.40551	+	0.290854i	−0.324702	+	0.0277318i
$111$	−0.618204	−	3.10792i	−0.0586773	−	0.294991i
$112$	−19.2723	+	4.76992i	−1.82106	+	0.450715i
$113$	−2.39218	+	12.0263i	−0.225037	+	1.13134i	0.688705	+	0.725042i	$0.258180\pi$
$113$	−2.39218	+	12.0263i	−0.225037	+	1.13134i	−0.913742	+	0.406295i	$0.866820\pi$
$114$	12.2363	+	1.36568i	1.14603	+	0.127908i
$115$	12.5521	+	4.49121i	1.17049	+	0.418807i
$116$	−8.15693	−	1.42717i	−0.757352	−	0.132510i
$117$	0.264922	+	1.78596i	0.0244920	+	0.165112i
$118$	−8.43015	−	9.54730i	−0.776058	−	0.878900i
$119$	−5.92465	−	11.0842i	−0.543112	−	1.01609i
$120$	10.1959	−	14.0437i	0.930754	−	1.28201i
$121$	−10.1348	+	3.07436i	−0.921347	+	0.279487i
$122$	−3.13748	+	19.4124i	−0.284054	+	1.75752i
$123$	−0.653670	+	1.38207i	−0.0589394	+	0.124617i
$124$	4.41278	−	1.69508i	0.396279	−	0.152222i
$125$	3.92577	+	15.6726i	0.351132	+	1.40180i
$126$	−2.34052	−	1.00525i	−0.208511	−	0.0895547i
$127$		−	4.34337i		−	0.385412i	−0.981257	−	0.192706i	$-0.938274\pi$
$127$		−	4.34337i		−	0.385412i	0.981257	−	0.192706i	$-0.0617264\pi$
$128$	10.0167	+	5.25974i	0.885364	+	0.464899i
$129$		−	2.77587i		−	0.244402i
$130$	−10.4915	+	24.4275i	−0.920168	+	2.14243i
$131$	1.10000	+	4.39145i	0.0961075	+	0.383682i	0.998926	−	0.0463398i	$-0.0147557\pi$
$131$	1.10000	+	4.39145i	0.0961075	+	0.383682i	−0.902818	+	0.430022i	$0.858506\pi$
$132$	−0.844543	+	1.89805i	−0.0735080	+	0.165204i
$133$	11.3771	−	24.0550i	0.986524	−	2.08583i
$134$	17.2108	+	2.78165i	1.48679	+	0.240298i
$135$	19.7454	−	5.98971i	1.69942	−	0.515512i
$136$	−1.66954	+	6.96476i	−0.143162	+	0.597223i
$137$	−8.73409	−	16.3403i	−0.746204	−	1.39605i	−0.912126	−	0.409910i	$-0.865560\pi$
$137$	−8.73409	−	16.3403i	−0.746204	−	1.39605i	0.165922	−	0.986139i	$-0.446940\pi$
$138$	6.07407	−	5.36333i	0.517059	−	0.456557i
$139$	−0.768145	−	5.17841i	−0.0651532	−	0.439227i	−0.997066	−	0.0765450i	$-0.975611\pi$
$139$	−0.768145	−	5.17841i	−0.0651532	−	0.439227i	0.931913	−	0.362682i	$-0.118139\pi$
$140$	−21.5540	−	30.6959i	−1.82165	−	2.59427i
$141$	5.87974	+	2.10380i	0.495163	+	0.177172i
$142$	1.43297	−	12.8392i	0.120253	−	1.07744i
$143$	0.620863	−	3.12129i	0.0519192	−	0.261015i
$144$	0.616934	+	1.31394i	0.0514112	+	0.109495i
$145$	−3.05201	−	15.3435i	−0.253455	−	1.27421i
$146$	−0.286241	−	3.35149i	−0.0236895	−	0.277372i
$147$	19.2328	−	21.2201i	1.58629	−	1.75020i
$148$	2.54496	+	2.95872i	0.209195	+	0.243205i
$149$	16.4016	−	9.83074i	1.34367	−	0.805365i	0.352229	−	0.935914i	$-0.385424\pi$
$149$	16.4016	−	9.83074i	1.34367	−	0.805365i	0.991442	+	0.130549i	$0.0416738\pi$
$150$	20.5959	+	5.44393i	1.68165	+	0.444495i
$151$	1.29405	+	13.1387i	0.105308	+	1.06921i	0.892053	+	0.451932i	$0.149265\pi$
$151$	1.29405	+	13.1387i	0.105308	+	1.06921i	−0.786744	+	0.617279i	$0.788235\pi$
$152$	−13.9497	+	5.94496i	−1.13147	+	0.482200i
$153$	−0.710323	+	0.582947i	−0.0574262	+	0.0471285i
$154$	3.28740	+	3.05815i	0.264907	+	0.246433i
$155$	5.99733	+	6.61703i	0.481717	+	0.531493i
$156$	9.92361	+	12.7528i	0.794524	+	1.02104i
$157$	−13.7244	+	10.1787i	−1.09532	+	0.812347i	−0.983415	−	0.181371i	$-0.941946\pi$
$157$	−13.7244	+	10.1787i	−1.09532	+	0.812347i	−0.111909	+	0.993719i	$0.535696\pi$
$158$	−2.79764	−	1.92229i	−0.222568	−	0.152929i
$159$	−1.90839	+	4.60727i	−0.151346	+	0.365380i
$160$	−2.43048	+	21.2351i	−0.192146	+	1.67878i
$161$	−6.70182	−	16.1796i	−0.528178	−	1.27513i
$162$	2.28622	−	10.7619i	0.179622	−	0.845535i
$163$	14.2332	+	2.11130i	1.11483	+	0.165370i	0.678631	−	0.734479i	$-0.262573\pi$
$163$	14.2332	+	2.11130i	1.11483	+	0.165370i	0.436202	+	0.899849i	$0.356323\pi$
$164$	−0.135877	−	1.87801i	−0.0106102	−	0.146648i
$165$	−3.91999	−	0.192577i	−0.305171	−	0.0149921i
$166$	3.92500	+	8.58516i	0.304639	+	0.666337i
$167$	−18.8307	−	1.85466i	−1.45716	−	0.143518i	−0.661812	−	0.749670i	$-0.730212\pi$
$167$	−18.8307	−	1.85466i	−1.45716	−	0.143518i	−0.795349	+	0.606152i	$0.792712\pi$
$168$	−22.6641	+	2.46505i	−1.74857	+	0.190182i
$169$	−9.08574	−	7.45648i	−0.698903	−	0.573575i
$170$	−13.4087	+	1.81152i	−1.02840	+	0.138937i
$171$	−1.88721	−	0.472722i	−0.144319	−	0.0361500i
$172$	1.68091	+	2.97696i	0.128168	+	0.226991i
$173$	1.21280	+	24.6872i	0.0922077	+	1.87693i	0.387975	+	0.921670i	$0.373175\pi$
$173$	1.21280	+	24.6872i	0.0922077	+	1.87693i	−0.295767	+	0.955260i	$0.595575\pi$
$174$	−9.06273	−	2.87807i	−0.687044	−	0.218186i
$175$	25.5793	−	38.2821i	1.93361	−	2.89385i
$176$	−0.243627	−	2.54696i	−0.0183641	−	0.191984i
$177$	−8.12527	−	12.1603i	−0.610733	−	0.914026i
$178$	8.27085	−	2.39220i	0.619926	−	0.179303i
$179$	3.33854	+	7.05875i	0.249534	+	0.527596i	0.989410	−	0.145148i	$-0.0463657\pi$
$179$	3.33854	+	7.05875i	0.249534	+	0.527596i	−0.739876	+	0.672744i	$0.765116\pi$
$180$	−1.89370	+	1.98343i	−0.141148	+	0.147836i
$181$	1.98149	+	1.46957i	0.147283	+	0.109232i	0.666832	−	0.745208i	$-0.267650\pi$
$181$	1.98149	+	1.46957i	0.147283	+	0.109232i	−0.519549	+	0.854441i	$0.673900\pi$
$182$	33.0319	−	11.3378i	2.44849	−	0.840412i
$183$	−6.55470	+	21.6079i	−0.484537	+	1.59730i
$184$	−3.26637	+	9.42996i	−0.240800	+	0.695186i
$185$	−3.47555	+	6.50229i	−0.255527	+	0.478058i
$186$	5.28209	−	1.25049i	0.387302	−	0.0916907i
$187$	1.52501	−	0.545659i	0.111520	−	0.0399025i
$188$	−7.57962	+	1.30422i	−0.552801	+	0.0951199i
$189$	−23.2493	−	13.9351i	−1.69114	−	1.01363i
$190$	−19.9919	−	20.5176i	−1.45037	−	1.48850i
$191$	7.99345	−	7.99345i	0.578386	−	0.578386i	−0.356073	−	0.934458i	$-0.615884\pi$
$191$	7.99345	−	7.99345i	0.578386	−	0.578386i	0.934458	+	0.356073i	$0.115884\pi$
$192$	10.5899	+	7.52524i	0.764259	+	0.543087i
$193$	9.61326	+	9.61326i	0.691978	+	0.691978i	0.962667	−	0.270689i	$-0.0872515\pi$
$193$	9.61326	+	9.61326i	0.691978	+	0.691978i	−0.270689	+	0.962667i	$0.587252\pi$
$194$	−0.0929837	+	7.16622i	−0.00667584	+	0.514505i
$195$	−15.6942	+	26.1842i	−1.12388	+	1.87509i
$196$	−7.77639	+	34.4036i	−0.555456	+	2.45740i
$197$	8.57424	+	23.9634i	0.610889	+	1.70732i	0.702646	+	0.711539i	$0.252002\pi$
$197$	8.57424	+	23.9634i	0.610889	+	1.70732i	−0.0917573	+	0.995781i	$0.529248\pi$
$198$	0.172404	−	0.279354i	0.0122522	−	0.0198528i
$199$	10.4443	+	5.58262i	0.740380	+	0.395741i	0.798047	−	0.602595i	$-0.205866\pi$
$199$	10.4443	+	5.58262i	0.740380	+	0.395741i	−0.0576677	+	0.998336i	$0.518366\pi$
$200$	−25.3844	+	6.63336i	−1.79495	+	0.469050i
$201$	19.1573	+	5.81131i	1.35125	+	0.409898i
$202$	−6.92042	−	3.38368i	−0.486919	−	0.238075i
$203$	−12.2421	+	16.5065i	−0.859224	+	1.15853i
$204$	−2.97059	+	7.66884i	−0.207983	+	0.536927i
$205$	3.21566	−	1.52090i	0.224592	−	0.106224i
$206$	3.50265	−	6.35333i	0.244041	−	0.442657i
$207$	−1.06462	+	0.711355i	−0.0739960	+	0.0494426i
$208$	−18.3649	−	7.66753i	−1.27337	−	0.531647i
$209$	2.85131	+	1.90518i	0.197229	+	0.131784i
$210$	−19.8082	−	38.2439i	−1.36689	−	2.63908i
$211$	−0.0504634	+	0.00247911i	−0.00347404	+	0.000170669i	−0.0508046	−	0.998709i	$-0.516179\pi$
$211$	−0.0504634	+	0.00247911i	−0.00347404	+	0.000170669i	0.0473306	+	0.998879i	$0.484929\pi$
$212$	−0.743252	−	6.09664i	−0.0510468	−	0.418719i
$213$	3.60451	−	14.3900i	0.246977	−	0.985987i
$214$	8.31025	−	10.9064i	0.568077	−	0.745548i
$215$	−4.09731	+	4.99259i	−0.279434	+	0.340492i
$216$	4.63379	+	14.7348i	0.315290	+	1.00257i
$217$	1.14988	−	11.6750i	0.0780591	−	0.792548i
$218$	0.489520	−	1.31411i	0.0331545	−	0.0890029i
$219$	0.189523	−	3.85782i	0.0128067	−	0.260687i
$220$	4.32058	−	2.16719i	0.291293	−	0.146112i
$221$	1.84856	−	12.4620i	0.124348	−	0.838284i
$222$	2.44116	+	3.75811i	0.163840	+	0.252228i
$223$	−20.7808	+	8.60770i	−1.39159	+	0.576414i	−0.947554	−	0.319596i	$-0.896453\pi$
$223$	−20.7808	+	8.60770i	−1.39159	+	0.576414i	−0.444034	+	0.896010i	$0.646453\pi$
$224$	22.8132	−	16.3677i	1.52427	−	1.09361i
$225$	−3.10999	−	1.28820i	−0.207332	−	0.0858799i
$226$	−3.16210	−	17.0502i	−0.210340	−	1.13416i
$227$	0.000319048	0	0.000430187i	2.11760e−5	0	2.85525e-5i	0.803218	−	0.595685i	$-0.203119\pi$
$227$	0.000319048	0	0.000430187i	2.11760e−5	0	2.85525e-5i	−0.803197	+	0.595714i	$0.796869\pi$
$228$	−16.7879	+	4.62045i	−1.11181	+	0.305997i
$229$	6.70873	−	6.08043i	0.443325	−	0.401806i	−0.419141	−	0.907921i	$-0.637669\pi$
$229$	6.70873	−	6.08043i	0.443325	−	0.401806i	0.862466	+	0.506115i	$0.168919\pi$
$230$	−18.8411	+	0.680703i	−1.24235	+	0.0448842i
$231$	3.27073	+	3.98540i	0.215198	+	0.262220i
$232$	11.4620	−	2.40130i	0.752520	−	0.157653i
$233$	8.86161	−	0.872793i	0.580544	−	0.0571786i	0.196517	−	0.980500i	$-0.437037\pi$
$233$	8.86161	−	0.872793i	0.580544	−	0.0571786i	0.384027	+	0.923322i	$0.374537\pi$
$234$	−1.28416	−	2.20694i	−0.0839485	−	0.144272i
$235$	−7.46979	−	12.4626i	−0.487275	−	0.812970i
$236$	16.0775	+	8.12106i	1.04655	+	0.528636i
$237$	−2.88803	−	2.61756i	−0.187598	−	0.170029i
$238$	13.5922	+	11.4532i	0.881054	+	0.742400i
$239$	0.300207	−	0.0597150i	0.0194188	−	0.00386264i	−0.185371	−	0.982669i	$-0.559349\pi$
$239$	0.300207	−	0.0597150i	0.0194188	−	0.00386264i	0.204790	+	0.978806i	$0.434349\pi$
$240$	−6.03037	+	23.7907i	−0.389259	+	1.53568i
$241$	−29.0445	−	5.77731i	−1.87092	−	0.372149i	−0.876838	−	0.480787i	$-0.840351\pi$
$241$	−29.0445	−	5.77731i	−1.87092	−	0.372149i	−0.994081	+	0.108638i	$0.965351\pi$
$242$	11.7002	−	9.35076i	0.752120	−	0.601089i
$243$	−1.26323	+	3.53050i	−0.0810364	+	0.226482i
$244$	−6.05497	−	27.1424i	−0.387630	−	1.73761i
$245$	−65.9133	+	9.77731i	−4.21104	+	0.624649i
$246$	0.134100	−	2.15797i	0.00854988	−	0.137587i
$247$	23.5238	−	12.5738i	1.49679	−	0.800049i
$248$	−4.90751	+	4.53961i	−0.311627	+	0.288266i
$249$	3.14657	+	10.3729i	0.199406	+	0.657353i
$250$	−13.3719	−	18.5276i	−0.845716	−	1.17179i
$251$	9.67092	+	4.57400i	0.610423	+	0.288709i	0.707661	−	0.706553i	$-0.249751\pi$
$251$	9.67092	+	4.57400i	0.610423	+	0.288709i	−0.0972374	+	0.995261i	$0.531001\pi$
$252$	3.60117	+	0.0934680i	0.226852	+	0.00588793i
$253$	2.18925	−	0.548379i	0.137637	−	0.0344763i
$254$	2.27679	+	5.70491i	0.142859	+	0.357958i
$255$	−15.5368			−0.972954
$256$	−15.9139	−	1.65776i	−0.994618	−	0.103610i
$257$	1.75894			0.109720			0.0548598	−	0.998494i	$-0.482529\pi$
$257$	1.75894			0.109720			0.0548598	+	0.998494i	$0.482529\pi$
$258$	1.45511	+	3.64604i	0.0905911	+	0.226992i
$259$	9.39508	−	2.35334i	0.583782	−	0.146230i
$260$	0.975503	−	37.5845i	0.0604981	−	2.33089i
$261$	1.35827	+	0.642412i	0.0840746	+	0.0397643i
$262$	−3.74681	−	5.19143i	−0.231479	−	0.320728i
$263$	0.0192798	+	0.0635569i	0.00118884	+	0.00391909i	0.957533	−	0.288325i	$-0.0930982\pi$
$263$	0.0192798	+	0.0635569i	0.00118884	+	0.00391909i	−0.956344	+	0.292244i	$0.905598\pi$
$264$	0.114328	−	2.93575i	0.00703640	−	0.180683i
$265$	10.2329	−	5.46961i	0.628603	−	0.335995i
$266$	−2.33401	+	37.5595i	−0.143107	+	2.30292i
$267$	9.77954	−	1.45066i	0.598498	−	0.0887788i
$268$	−24.0641	+	5.36826i	−1.46995	+	0.327919i
$269$	−1.98683	+	5.55281i	−0.121139	+	0.338561i	−0.986771	−	0.162120i	$-0.948167\pi$
$269$	−1.98683	+	5.55281i	−0.121139	+	0.338561i	0.865632	+	0.500680i	$0.166917\pi$
$270$	−22.7953	+	18.2179i	−1.38728	+	1.10870i
$271$	−0.385042	−	0.0765896i	−0.0233896	−	0.00465249i	0.183382	−	0.983042i	$-0.441296\pi$
$271$	−0.385042	−	0.0765896i	−0.0233896	−	0.00465249i	−0.206771	+	0.978389i	$0.566296\pi$
$272$	−1.45802	−	10.0232i	−0.0884055	−	0.607746i
$273$	39.3315	−	7.82353i	2.38045	−	0.473502i
$274$	20.0376	+	16.8842i	1.21052	+	1.02001i
$275$	4.39638	+	3.98465i	0.265112	+	0.240283i
$276$	−5.16668	+	10.2286i	−0.310998	+	0.615691i
$277$	−9.99527	−	16.6761i	−0.600558	−	1.00197i	−0.996492	−	0.0836910i	$-0.973329\pi$
$277$	−9.99527	−	16.6761i	−0.600558	−	1.00197i	0.395934	−	0.918279i	$-0.370421\pi$
$278$	3.72346	+	6.39905i	0.223318	+	0.383790i
$279$	−0.853590	+	0.0840713i	−0.0511031	+	0.00503322i
$280$	44.4014	+	29.0197i	2.65349	+	1.73426i
$281$	−5.54246	−	6.75351i	−0.330635	−	0.402880i	0.580985	−	0.813915i	$-0.302668\pi$
$281$	−5.54246	−	6.75351i	−0.330635	−	0.402880i	−0.911620	+	0.411034i	$0.865168\pi$
$282$	−8.82570	+	0.318860i	−0.525563	+	0.0189878i
$283$	18.6254	−	16.8811i	1.10717	−	1.00348i	0.107208	−	0.994237i	$-0.465809\pi$
$283$	18.6254	−	16.8811i	1.10717	−	1.00348i	0.999957	−	0.00923945i	$-0.00294105\pi$
$284$	4.84812	+	17.6151i	0.287683	+	1.04527i
$285$	−19.5954	−	26.4214i	−1.16073	−	1.56507i
$286$	0.820688	+	4.42519i	0.0485283	+	0.261667i
$287$	−4.31718	−	1.78824i	−0.254835	−	0.105556i
$288$	−1.49909	−	1.40243i	−0.0883349	−	0.0826390i
$289$	−9.78212	+	4.05189i	−0.575419	+	0.238346i
$290$	12.0518	+	18.5534i	0.707704	+	1.08949i
$291$	−1.20752	+	8.14047i	−0.0707864	+	0.477203i
$292$	2.13282	+	4.25205i	0.124814	+	0.248833i
$293$	−1.60727	+	32.7167i	−0.0938978	+	1.91133i	0.243386	+	0.969930i	$0.421742\pi$
$293$	−1.60727	+	32.7167i	−0.0938978	+	1.91133i	−0.337283	+	0.941403i	$0.609508\pi$
$294$	−14.1382	+	37.9539i	−0.824557	+	2.21351i
$295$	−3.33535	+	33.8644i	−0.194192	+	1.97166i
$296$	−4.89370	−	2.55213i	−0.284440	−	0.148340i
$297$	2.21603	−	2.70024i	0.128587	−	0.156684i
$298$	−16.3898	+	21.5101i	−0.949436	+	1.24605i
$299$	4.26542	−	17.0285i	0.246675	−	0.984783i
$300$	−29.9059	+	3.64588i	−1.72662	+	0.210495i
$301$	8.47412	−	0.416307i	0.488440	−	0.0239955i
$302$	−8.58698	−	16.5790i	−0.494125	−	0.954013i
$303$	−7.35487	−	4.91436i	−0.422526	−	0.282323i
$304$	15.2062	−	15.1210i	0.872135	−	0.867246i
$305$	43.6833	−	29.1883i	2.50130	−	1.67132i
$306$	0.627411	−	1.13804i	0.0358667	−	0.0650572i
$307$	15.0277	−	7.10758i	0.857677	−	0.405651i	0.0524540	−	0.998623i	$-0.483296\pi$
$307$	15.0277	−	7.10758i	0.857677	−	0.405651i	0.805223	+	0.592972i	$0.202046\pi$
$308$	−5.92100	−	2.29355i	−0.337380	−	0.130687i
$309$	4.96257	−	6.69125i	0.282311	−	0.380652i
$310$	−11.3460	−	5.54751i	−0.644408	−	0.315077i
$311$	0.0349415	+	0.0105994i	0.00198135	+	0.000601037i	0.291275	−	0.956639i	$-0.405920\pi$
$311$	0.0349415	+	0.0105994i	0.00198135	+	0.000601037i	−0.289294	+	0.957240i	$0.593420\pi$
$312$	−19.7194	−	11.5486i	−1.11639	−	0.653810i
$313$	7.38463	+	3.94717i	0.417404	+	0.223107i	0.666709	−	0.745318i	$-0.267702\pi$
$313$	7.38463	+	3.94717i	0.417404	+	0.223107i	−0.249305	+	0.968425i	$0.580202\pi$
$314$	12.6909	−	20.5637i	0.716191	−	1.16048i
$315$	2.29273	+	6.40775i	0.129181	+	0.361036i
$316$	4.68228	+	1.05836i	0.263399	+	0.0595372i
$317$	1.25047	−	2.08628i	0.0702333	−	0.117177i	−0.820609	−	0.571491i	$-0.806365\pi$
$317$	1.25047	−	2.08628i	0.0702333	−	0.117177i	0.890842	+	0.454313i	$0.150115\pi$
$318$	0.0915005	−	7.05191i	0.00513109	−	0.395452i
$319$	−1.87270	−	1.87270i	−0.104851	−	0.104851i
$320$	−7.93903	−	29.1658i	−0.443805	−	1.63042i
$321$	11.1333	−	11.1333i	0.621402	−	0.621402i
$322$	17.2840	+	17.7384i	0.963201	+	0.988525i
$323$	11.6440	+	6.97914i	0.647889	+	0.388330i
$324$	2.63849	+	15.3339i	0.146583	+	0.851885i
$325$	43.4537	−	15.5480i	2.41038	−	0.862447i
$326$	−19.8017	+	4.68791i	−1.09672	+	0.259639i
$327$	0.759075	−	1.42013i	0.0419769	−	0.0785333i
$328$	1.16292	+	2.39550i	0.0642117	+	0.132269i
$329$	−5.54065	+	18.2651i	−0.305466	+	1.00699i
$330$	5.24976	−	1.80191i	0.288990	−	0.0991920i
$331$	24.0817	+	17.8602i	1.32365	+	0.981685i	0.999362	+	0.0357258i	$0.0113743\pi$
$331$	24.0817	+	17.8602i	1.32365	+	0.981685i	0.324287	+	0.945959i	$0.394876\pi$
$332$	−9.65571	−	9.21891i	−0.529926	−	0.505953i
$333$	−0.302762	−	0.640136i	−0.0165912	−	0.0350792i
$334$	25.7058	−	7.43497i	1.40656	−	0.406824i
$335$	−25.8779	−	38.7291i	−1.41386	−	2.11599i
$336$	28.4765	−	15.1183i	1.55352	−	0.824769i
$337$	−17.0631	+	25.5368i	−0.929488	+	1.39108i	−0.00914813	+	0.999958i	$0.502912\pi$
$337$	−17.0631	+	25.5368i	−0.929488	+	1.39108i	−0.920340	+	0.391119i	$0.872088\pi$
$338$	15.8426	+	5.03116i	0.861722	+	0.273659i
$339$	−0.977050	−	19.8883i	−0.0530661	−	1.08018i
$340$	16.6624	−	9.40820i	0.903643	−	0.510231i
$341$	1.46654	+	0.367349i	0.0794176	+	0.0198931i
$342$	2.72661	−	0.368367i	0.147438	−	0.0199190i
$343$	40.8072	+	33.4896i	2.20338	+	1.80827i
$344$	−3.76835	−	3.02903i	−0.203176	−	0.163315i
$345$	−21.5448	−	2.12198i	−1.15993	−	0.114244i
$346$	−14.5340	−	31.7902i	−0.781351	−	1.70905i
$347$	−13.9180	−	0.683747i	−0.747157	−	0.0367055i	−0.328072	−	0.944653i	$-0.606399\pi$
$347$	−13.9180	−	0.683747i	−0.747157	−	0.0367055i	−0.419085	+	0.907947i	$0.637649\pi$
$348$	13.4123	−	0.970404i	0.718977	−	0.0520191i
$349$	−7.50514	−	1.11328i	−0.401741	−	0.0595926i	−0.0571971	−	0.998363i	$-0.518216\pi$
$349$	−7.50514	−	1.11328i	−0.401741	−	0.0595926i	−0.344544	+	0.938770i	$0.611966\pi$
$350$	−13.5303	+	63.6911i	−0.723224	+	3.40443i
$351$	−10.3977	−	25.1022i	−0.554987	−	1.33986i
$352$	1.65511	+	3.21766i	0.0882177	+	0.171502i
$353$	−5.71588	+	13.7994i	−0.304226	+	0.734466i	0.695645	+	0.718386i	$0.255119\pi$
$353$	−5.71588	+	13.7994i	−0.304226	+	0.734466i	−0.999871	+	0.0160801i	$0.994881\pi$
$354$	17.0468	+	11.7130i	0.906026	+	0.622540i
$355$	−27.7233	+	20.5610i	−1.47140	+	1.09126i
$356$	−9.60956	+	7.47767i	−0.509306	+	0.396316i
$357$	13.7064	+	15.1227i	0.725422	+	0.800379i
$358$	−8.08528	−	7.52143i	−0.427320	−	0.397520i
$359$	20.1996	−	16.5774i	1.06610	−	0.874922i	0.0736102	−	0.997287i	$-0.476548\pi$
$359$	20.1996	−	16.5774i	1.06610	−	0.874922i	0.992485	+	0.122365i	$0.0390479\pi$
$360$	1.44762	−	3.59786i	0.0762962	−	0.189624i
$361$	0.954880	+	9.69506i	0.0502569	+	0.510266i
$362$	−3.37298	−	0.891550i	−0.177280	−	0.0468588i
$363$	14.7518	−	8.84188i	0.774268	−	0.464079i
$364$	−37.4433	+	32.2072i	−1.96256	+	1.68811i
$365$	−6.03519	+	6.65880i	−0.315896	+	0.348538i
$366$	−2.71743	−	31.8174i	−0.142042	−	1.66312i
$367$	4.53587	+	22.8034i	0.236771	+	1.19033i	0.897950	+	0.440098i	$0.145056\pi$
$367$	4.53587	+	22.8034i	0.236771	+	1.19033i	−0.661179	+	0.750228i	$0.729944\pi$
$368$	−0.652885	−	14.0982i	−0.0340340	−	0.734922i
$369$	−0.0666523	+	0.335084i	−0.00346978	+	0.0174438i
$370$	1.15655	−	10.3625i	0.0601261	−	0.538720i
$371$	−14.3512	−	5.13494i	−0.745077	−	0.266593i
$372$	−6.28239	+	4.41136i	−0.325727	+	0.228718i
$373$	−1.77884	−	11.9920i	−0.0921050	−	0.620921i	−0.985246	−	0.171144i	$-0.945254\pi$
$373$	−1.77884	−	11.9920i	−0.0921050	−	0.620921i	0.893141	−	0.449777i	$-0.148496\pi$
$374$	−1.71703	+	1.51612i	−0.0887857	+	0.0783967i
$375$	−12.3682	−	23.1392i	−0.638689	−	1.19490i
$376$	9.27197	−	5.68629i	0.478165	−	0.293248i
$377$	−19.7129	+	5.97983i	−1.01526	+	0.307977i
$378$	37.8421	+	6.11613i	1.94639	+	0.314580i
$379$	−5.15346	+	10.8961i	−0.264715	+	0.559693i	−0.991940	−	0.126706i	$-0.959560\pi$
$379$	−5.15346	+	10.8961i	−0.264715	+	0.559693i	0.727225	+	0.686399i	$0.240810\pi$
$380$	37.0142	+	16.4695i	1.89879	+	0.844869i
$381$	1.71381	+	6.84190i	0.0878010	+	0.350521i
$382$	−6.30904	+	14.6894i	−0.322798	+	0.751573i
$383$			20.2241i			1.03341i	0.856165	+	0.516703i	$0.172841\pi$
$383$			20.2241i			1.03341i	−0.856165	+	0.516703i	$0.827159\pi$
$384$	−17.8543	−	4.33300i	−0.911122	−	0.221117i
$385$		−	11.9958i		−	0.611360i
$386$	−17.6660	−	7.58751i	−0.899178	−	0.386194i
$387$	−0.150724	−	0.601725i	−0.00766174	−	0.0305874i
$388$	−3.63439	−	9.46139i	−0.184508	−	0.480329i
$389$	10.4056	−	22.0009i	0.527587	−	1.11549i	−0.447627	−	0.894221i	$-0.647731\pi$
$389$	10.4056	−	22.0009i	0.527587	−	1.11549i	0.975213	−	0.221267i	$-0.0710194\pi$
$390$	6.88821	−	42.6191i	0.348798	−	2.15810i
$391$	8.54966	−	2.59351i	0.432375	−	0.131159i
$392$	−7.82024	−	49.2646i	−0.394982	−	2.48824i
$393$	−3.46555	−	6.48359i	−0.174814	−	0.327054i
$394$	−23.8236	−	26.9807i	−1.20022	−	1.35927i
$395$	1.33068	+	8.97071i	0.0669537	+	0.451365i
$396$	−0.0800109	+	0.457298i	−0.00402070	+	0.0229801i
$397$	−6.98003	−	2.49749i	−0.350318	−	0.125346i	0.155850	−	0.987781i	$-0.450188\pi$
$397$	−6.98003	−	2.49749i	−0.350318	−	0.125346i	−0.506168	+	0.862435i	$0.668938\pi$
$398$	−16.6448	−	1.85771i	−0.834327	−	0.0931187i
$399$	−8.43026	+	42.3818i	−0.422041	+	2.12174i
$400$	29.8646	−	22.0192i	1.49323	−	1.10096i
$401$	4.00348	+	20.1268i	0.199924	+	1.00509i	0.942215	+	0.335008i	$0.108739\pi$
$401$	4.00348	+	20.1268i	0.199924	+	1.00509i	−0.742291	+	0.670078i	$0.766261\pi$
$402$	−28.2089	+	2.40924i	−1.40693	+	0.120162i
$403$	7.89720	−	8.71322i	0.393387	−	0.434036i
$404$	10.8635	+	0.816694i	0.540480	+	0.0406320i
$405$	−25.2124	+	15.1117i	−1.25281	+	0.750908i
$406$	7.42694	−	28.0982i	0.368593	−	1.39449i
$407$	0.122341	+	1.24215i	0.00606424	+	0.0615713i
$408$	−0.118209	−	11.6300i	−0.00585220	−	0.575771i
$409$	8.93403	−	7.33197i	0.441759	−	0.362542i	−0.387064	−	0.922053i	$-0.626511\pi$
$409$	8.93403	−	7.33197i	0.441759	−	0.362542i	0.828823	+	0.559510i	$0.189011\pi$
$410$	−3.42644	+	3.68331i	−0.169220	+	0.181905i
$411$	20.2059	+	22.2938i	0.996686	+	1.09967i
$412$	−1.27024	+	10.1810i	−0.0625801	+	0.501583i
$413$	35.9042	−	26.6284i	1.76673	−	1.31030i
$414$	1.02546	−	1.49242i	0.0503985	−	0.0733483i
$415$	9.65149	−	23.3007i	0.473773	−	1.14379i
$416$	28.1411	+	0.444253i	1.37973	+	0.0217813i
$417$	3.25332	+	7.85420i	0.159316	+	0.384622i
$418$	−4.74382	−	1.00776i	−0.232028	−	0.0492910i
$419$	−7.25582	−	1.07630i	−0.354470	−	0.0525807i	−0.0328791	−	0.999459i	$-0.510468\pi$
$419$	−7.25582	−	1.07630i	−0.354470	−	0.0525807i	−0.321591	+	0.946879i	$0.604218\pi$
$420$	46.0649	+	39.8489i	2.24774	+	1.94443i
$421$	−25.7101	−	1.26305i	−1.25303	−	0.0615575i	−0.588302	−	0.808641i	$-0.700203\pi$
$421$	−25.7101	−	1.26305i	−1.25303	−	0.0615575i	−0.664730	+	0.747084i	$0.731453\pi$
$422$	0.0649828	−	0.0297091i	0.00316332	−	0.00144622i
$423$	1.38878	+	0.136783i	0.0675249	+	0.00665062i
$424$	4.17210	+	7.61818i	0.202615	+	0.369971i
$425$	18.1570	+	14.9011i	0.880746	+	0.722809i
$426$	2.80880	+	20.7904i	0.136087	+	1.00730i
$427$	−66.9473	−	16.7694i	−3.23981	−	0.811530i
$428$	−5.19816	+	18.6815i	−0.251262	+	0.903006i
$429$	0.253583	+	5.16179i	0.0122431	+	0.249214i
$430$	2.76460	−	8.70544i	0.133321	−	0.419814i
$431$	9.85118	−	14.7433i	0.474515	−	0.710161i	−0.514580	−	0.857442i	$-0.672052\pi$
$431$	9.85118	−	14.7433i	0.474515	−	0.710161i	0.989095	+	0.147281i	$0.0470521\pi$
$432$	−13.8103	−	16.9247i	−0.664449	−	0.814290i
$433$	2.74806	+	4.11277i	0.132064	+	0.197647i	0.891608	−	0.452809i	$-0.149578\pi$
$433$	2.74806	+	4.11277i	0.132064	+	0.197647i	−0.759544	+	0.650456i	$0.774578\pi$
$434$	4.60966	+	15.9375i	0.221271	+	0.765026i
$435$	10.8619	+	22.9656i	0.520788	+	1.10111i
$436$	0.0458835	+	1.98266i	0.00219742	+	0.0949521i
$437$	15.1934	+	11.2682i	0.726801	+	0.539033i
$438$	1.77333	+	5.16650i	0.0847331	+	0.246865i
$439$	7.51863	−	24.7856i	0.358845	−	1.18295i	−0.572835	−	0.819671i	$-0.694156\pi$
$439$	7.51863	−	24.7856i	0.358845	−	1.18295i	0.931679	−	0.363281i	$-0.118344\pi$
$440$	−4.53893	+	5.11139i	−0.216385	+	0.243676i
$441$	3.01688	−	5.64418i	0.143661	−	0.268770i
$442$	4.10453	+	17.3375i	0.195232	+	0.824662i
$443$	13.7421	−	4.91700i	0.652907	−	0.233614i	0.0104613	−	0.999945i	$-0.496670\pi$
$443$	13.7421	−	4.91700i	0.652907	−	0.233614i	0.642445	+	0.766332i	$0.277920\pi$
$444$	−5.17640	−	3.65653i	−0.245661	−	0.173531i
$445$	−19.7304	−	11.8259i	−0.935310	−	0.560603i
$446$	22.7829	−	22.1993i	1.07880	−	1.05117i
$447$	−21.9576	+	21.9576i	−1.03856	+	1.03856i
$448$	−21.3847	+	33.4572i	−1.01033	+	1.58070i
$449$	−5.03717	−	5.03717i	−0.237719	−	0.237719i	0.578186	−	0.815905i	$-0.303761\pi$
$449$	−5.03717	−	5.03717i	−0.237719	−	0.237719i	−0.815905	+	0.578186i	$0.803761\pi$
$450$	4.76016	+	0.0617644i	0.224396	+	0.00291160i
$451$	0.309594	−	0.516526i	0.0145782	−	0.0243222i
$452$	13.0910	+	20.7374i	0.615750	+	0.975406i
$453$	−7.22271	−	20.1861i	−0.339352	−	0.948426i
$454$	−0.000644565	0	0.000397795i	−3.02510e−5	0	1.86694e-5i
$455$	−82.2883	−	43.9840i	−3.85773	−	2.06200i
$456$	19.6285	−	14.8691i	0.919187	−	0.696307i
$457$	−18.1456	−	5.50441i	−0.848816	−	0.257486i	−0.164234	−	0.986421i	$-0.552515\pi$
$457$	−18.1456	−	5.50441i	−0.848816	−	0.257486i	−0.684582	+	0.728936i	$0.740015\pi$
$458$	−5.62438	+	11.5032i	−0.262810	+	0.537509i
$459$	8.23754	−	11.1070i	0.384495	−	0.518432i
$460$	24.3905	−	10.7706i	1.13721	−	0.502181i
$461$	−18.0905	+	8.55617i	−0.842559	+	0.398501i	−0.799569	−	0.600575i	$-0.794938\pi$
$461$	−18.0905	+	8.55617i	−0.842559	+	0.398501i	−0.0429904	+	0.999075i	$0.513688\pi$
$462$	−6.38517	−	3.52021i	−0.297065	−	0.163775i
$463$	25.0198	−	16.7177i	1.16277	−	0.776937i	0.184206	−	0.982888i	$-0.441029\pi$
$463$	25.0198	−	16.7177i	1.16277	−	0.776937i	0.978562	+	0.205951i	$0.0660287\pi$
$464$	−13.7963	+	9.16244i	−0.640479	+	0.425356i
$465$	−12.0582	−	8.05706i	−0.559188	−	0.373637i
$466$	−11.1820	+	5.79164i	−0.517996	+	0.268293i
$467$	−21.9091	+	1.07632i	−1.01383	+	0.0498063i	−0.549194	−	0.835695i	$-0.685065\pi$
$467$	−21.9091	+	1.07632i	−1.01383	+	0.0498063i	−0.464637	+	0.885501i	$0.653815\pi$
$468$	2.84359	+	2.22560i	0.131445	+	0.102878i
$469$	−14.8675	+	59.3546i	−0.686520	+	2.74074i
$470$	16.3443	+	12.4536i	0.753904	+	0.574444i
$471$	17.6030	−	21.4493i	0.811104	−	0.988333i
$472$	−25.3744	−	2.23901i	−1.16795	−	0.103059i
$473$	−0.107171	+	1.08812i	−0.00492772	+	0.0500320i
$474$	5.16547	+	1.92419i	0.237258	+	0.0883811i
$475$	−2.44017	+	49.6708i	−0.111963	+	2.27905i
$476$	−23.8568	−	7.91843i	−1.09347	−	0.362941i
$477$	−0.163517	+	1.10234i	−0.00748691	+	0.0504726i
$478$	−0.363012	+	0.235802i	−0.0166038	+	0.0107854i
$479$	−24.3901	+	10.1027i	−1.11441	+	0.461605i	−0.862455	−	0.506133i	$-0.831074\pi$
$479$	−24.3901	+	10.1027i	−1.11441	+	0.461605i	−0.251958	+	0.967738i	$0.581074\pi$
$480$	−4.55031	−	34.4096i	−0.207692	−	1.57058i
$481$	8.96948	+	3.71528i	0.408973	+	0.169402i
$482$	41.1776	−	7.63674i	1.87559	−	0.347844i
$483$	16.9412	+	22.8426i	0.770851	+	1.03937i
$484$	−10.4663	+	18.4152i	−0.475742	+	0.837056i
$485$	14.1875	−	12.8588i	0.644222	−	0.583889i
$486$	−0.191460	−	5.29941i	−0.00868480	−	0.240386i
$487$	−2.66889	−	3.25205i	−0.120939	−	0.147365i	0.709021	−	0.705187i	$-0.249137\pi$
$487$	−2.66889	−	3.25205i	−0.120939	−	0.147365i	−0.829960	+	0.557823i	$0.811637\pi$
$488$	22.1811	+	32.4769i	1.00409	+	1.47016i
$489$	−23.2540	+	2.29032i	−1.05158	+	0.103572i
$490$	81.4501	−	47.3939i	3.67954	−	2.14104i
$491$	1.14121	+	1.90399i	0.0515021	+	0.0859260i	0.882403	−	0.470494i	$-0.155924\pi$
$491$	1.14121	+	1.90399i	0.0515021	+	0.0859260i	−0.830901	+	0.556420i	$0.812174\pi$
$492$	0.955067	+	2.90473i	0.0430577	+	0.130955i
$493$	−7.76833	−	7.04081i	−0.349868	−	0.317102i
$494$	−24.3068	+	28.8465i	−1.09362	+	1.29786i
$495$	−0.860193	+	0.171103i	−0.0386628	+	0.00769051i
$496$	4.06623	−	8.53518i	0.182579	−	0.383241i
$497$	44.4701	+	8.84566i	1.99476	+	0.396782i
$498$	−9.57038	−	11.9751i	−0.428859	−	0.536615i
$499$	7.94519	−	22.2053i	0.355676	−	0.994047i	−0.621833	−	0.783150i	$-0.713612\pi$
$499$	7.94519	−	22.2053i	0.355676	−	0.994047i	0.977508	−	0.210897i	$-0.0676384\pi$
$500$	27.2759	+	17.3260i	1.21981	+	0.774843i
$501$	30.3948	−	4.50865i	1.35794	−	0.201432i
$502$	−15.1002	−	0.938352i	−0.673955	−	0.0418807i
$503$	−34.4796	+	18.4297i	−1.53737	+	0.821742i	−0.999770	−	0.0214574i	$-0.993169\pi$
$503$	−34.4796	+	18.4297i	−1.53737	+	0.821742i	−0.537601	+	0.843199i	$0.680669\pi$
$504$	−4.77904	+	1.76496i	−0.212875	+	0.0786177i
$505$	5.97439	+	19.6949i	0.265857	+	0.876412i
$506$	−2.58807	+	1.86789i	−0.115054	+	0.0830376i
$507$	17.2545	+	8.16077i	0.766299	+	0.362433i
$508$	−5.98101	−	6.29976i	−0.265365	−	0.279507i
$509$	37.3458	−	9.35463i	1.65532	−	0.414637i	0.700940	−	0.713221i	$-0.252764\pi$
$509$	37.3458	−	9.35463i	1.65532	−	0.414637i	0.954383	+	0.298584i	$0.0965142\pi$
$510$	20.4072	−	8.14439i	0.903648	−	0.360640i
$511$	11.8055			0.522245
$512$	21.7715	−	6.16462i	0.962173	−	0.272440i
$513$	29.2776			1.29264
$514$	−2.31032	+	0.922034i	−0.101904	+	0.0406692i
$515$	−18.8021	+	4.70968i	−0.828519	+	0.207533i
$516$	−3.82250	−	4.02621i	−0.168276	−	0.177244i
$517$	−2.22360	−	1.05168i	−0.0977938	−	0.0462530i
$518$	−11.1066	+	8.01595i	−0.487995	+	0.352201i
$519$	−11.6515	−	38.4099i	−0.511445	−	1.68601i
$520$	18.4205	+	49.8777i	0.807791	+	2.18728i
$521$	22.0963	−	11.8107i	0.968058	−	0.517438i	0.0899741	−	0.995944i	$-0.471322\pi$
$521$	22.0963	−	11.8107i	0.968058	−	0.517438i	0.878084	+	0.478506i	$0.158822\pi$
$522$	−2.12080	−	0.131790i	−0.0928249	−	0.00576830i
$523$	3.70461	−	0.549527i	0.161991	−	0.0240291i	−0.0652422	−	0.997869i	$-0.520782\pi$
$523$	3.70461	−	0.549527i	0.161991	−	0.0240291i	0.227233	+	0.973840i	$0.427032\pi$
$524$	7.64269	+	4.85474i	0.333872	+	0.212080i
$525$	−25.1884	+	70.3969i	−1.09931	+	3.07237i
$526$	−0.0586400	−	0.0733740i	−0.00255682	−	0.00319926i
$527$	5.86998	+	1.16761i	0.255700	+	0.0508619i
$528$	1.38875	+	3.91597i	0.0604377	+	0.170421i
$529$	−10.3481	+	2.05836i	−0.449917	+	0.0894941i
$530$	−10.5735	+	12.5483i	−0.459284	+	0.545062i
$531$	−2.42160	−	2.19481i	−0.105088	−	0.0952465i
$532$	−16.6230	−	50.5569i	−0.720697	−	2.19192i
$533$	−2.40809	−	4.01765i	−0.104306	−	0.174024i
$534$	−12.0847	+	7.03183i	−0.522958	+	0.304297i
$535$	−36.4573	+	3.59073i	−1.57619	+	0.155241i
$536$	28.7935	−	19.6654i	1.24369	−	0.849418i
$537$	−8.04428	−	9.80198i	−0.347136	−	0.422987i
$538$	−0.301130	−	8.33496i	−0.0129826	−	0.359346i
$539$	−8.35840	+	7.57561i	−0.360022	+	0.326305i
$540$	20.3913	−	35.8780i	0.877502	−	1.54394i
$541$	4.22369	+	5.69499i	0.181591	+	0.244847i	0.884618	−	0.466316i	$-0.154419\pi$
$541$	4.22369	+	5.69499i	0.181591	+	0.244847i	−0.703028	+	0.711163i	$0.748169\pi$
$542$	0.545891	−	0.101240i	0.0234480	−	0.00434863i
$543$	−3.70120	−	1.53309i	−0.158834	−	0.0657911i
$544$	7.16923	+	12.4009i	0.307378	+	0.531686i
$545$	−3.46142	+	1.43377i	−0.148271	+	0.0614159i
$546$	−47.5599	+	30.8936i	−2.03538	+	1.32212i
$547$	3.81577	−	25.7238i	0.163150	−	1.09987i	−0.740642	−	0.671900i	$-0.765478\pi$
$547$	3.81577	−	25.7238i	0.163150	−	1.09987i	0.903792	−	0.427971i	$-0.140772\pi$
$548$	−35.1696	−	11.6733i	−1.50237	−	0.498659i
$549$	−0.247592	+	5.03986i	−0.0105670	+	0.215096i
$550$	−7.86328	−	2.92916i	−0.335292	−	0.124900i
$551$	2.17573	−	22.0906i	0.0926892	−	0.941089i
$552$	1.42448	−	16.1434i	0.0606298	−	0.687109i
$553$	7.55770	−	9.20908i	0.321386	−	0.391610i
$554$	21.8701	+	16.6641i	0.929173	+	0.707991i
$555$	2.90919	−	11.6141i	0.123488	−	0.492992i
$556$	−8.24504	−	6.45316i	−0.349668	−	0.273675i
$557$	5.30225	−	0.260483i	0.224663	−	0.0110370i	0.0635754	−	0.997977i	$-0.479750\pi$
$557$	5.30225	−	0.260483i	0.224663	−	0.0110370i	0.161088	+	0.986940i	$0.448500\pi$
$558$	1.07710	−	0.557877i	0.0455972	−	0.0236168i
$559$	7.07134	+	4.72492i	0.299086	+	0.199843i
$560$	−73.5321	−	14.8414i	−3.10730	−	0.627165i
$561$	−2.18697	+	1.46129i	−0.0923341	+	0.0616957i
$562$	10.8201	+	5.96521i	0.456417	+	0.251627i
$563$	−27.0917	+	12.8134i	−1.14178	+	0.540022i	−0.902398	−	0.430903i	$-0.858195\pi$
$563$	−27.0917	+	12.8134i	−1.14178	+	0.540022i	−0.239383	+	0.970925i	$0.576945\pi$
$564$	11.4252	−	5.04524i	0.481087	−	0.212443i
$565$	−27.5987	+	37.2126i	−1.16109	+	1.56555i
$566$	−15.6149	+	31.9363i	−0.656345	+	1.34238i
$567$	36.9511	+	11.2090i	1.55180	+	0.470733i
$568$	−15.6017	−	20.5957i	−0.654634	−	0.864174i
$569$	−12.2376	−	6.54116i	−0.513029	−	0.274220i	0.194502	−	0.980902i	$-0.437691\pi$
$569$	−12.2376	−	6.54116i	−0.513029	−	0.274220i	−0.707531	+	0.706683i	$0.750191\pi$
$570$	39.5881	+	24.4319i	1.65816	+	1.02334i
$571$	−5.16459	−	14.4341i	−0.216132	−	0.604047i	0.783723	−	0.621111i	$-0.213318\pi$
$571$	−5.16459	−	14.4341i	−0.216132	−	0.604047i	−0.999854	+	0.0170634i	$0.994568\pi$
$572$	−3.39763	−	5.38217i	−0.142062	−	0.225040i
$573$	−9.43764	+	15.7457i	−0.394263	+	0.657788i
$574$	6.60790	+	0.0857393i	0.275809	+	0.00357869i
$575$	23.1431	+	23.1431i	0.965134	+	0.965134i
$576$	2.70417	+	1.05623i	0.112674	+	0.0440097i
$577$	2.62221	−	2.62221i	0.109164	−	0.109164i	−0.650415	−	0.759579i	$-0.725405\pi$
$577$	2.62221	−	2.62221i	0.109164	−	0.109164i	0.759579	+	0.650415i	$0.225405\pi$
$578$	10.7246	−	10.4498i	0.446083	−	0.434656i
$579$	−18.9365	−	11.3501i	−0.786974	−	0.471694i
$580$	−25.5554	−	18.0519i	−1.06113	−	0.749564i
$581$	−31.1941	+	11.1614i	−1.29415	+	0.463055i
$582$	−2.68117	−	11.3253i	−0.111138	−	0.469448i
$583$	0.925957	−	1.73234i	0.0383492	−	0.0717463i
$584$	−5.03033	−	4.46694i	−0.208156	−	0.184843i
$585$	−1.98028	+	6.52810i	−0.0818744	+	0.269904i
$586$	−15.0390	−	43.8151i	−0.621254	−	1.80999i
$587$	−0.318252	−	0.236032i	−0.0131357	−	0.00974206i	0.589112	−	0.808052i	$-0.299478\pi$
$587$	−0.318252	−	0.236032i	−0.0131357	−	0.00974206i	−0.602247	+	0.798310i	$0.705728\pi$
$588$	−1.32520	−	57.2627i	−0.0546502	−	2.36147i
$589$	5.41775	+	11.4549i	0.223235	+	0.471990i
$590$	−13.3708	−	46.2285i	−0.550467	−	1.90320i
$591$	−22.9620	−	34.3651i	−0.944532	−	1.41359i
$592$	7.76557	+	0.786887i	0.319163	+	0.0323409i
$593$	−17.5273	+	26.2315i	−0.719761	+	1.07720i	0.273564	+	0.961854i	$0.411797\pi$
$593$	−17.5273	+	26.2315i	−0.719761	+	1.07720i	−0.993325	+	0.115345i	$0.963203\pi$
$594$	−1.49523	+	4.70833i	−0.0613502	+	0.193185i
$595$	−2.33011	−	47.4305i	−0.0955253	−	1.94446i
$596$	10.2520	−	36.8445i	0.419939	−	1.50921i
$597$	−18.6552	−	4.67290i	−0.763508	−	0.191249i
$598$	3.32380	+	24.6024i	0.135920	+	1.00607i
$599$	−13.9616	−	11.4580i	−0.570455	−	0.468160i	0.304400	−	0.952544i	$-0.401544\pi$
$599$	−13.9616	−	11.4580i	−0.570455	−	0.468160i	−0.874856	+	0.484384i	$0.839044\pi$
$600$	37.3694	−	20.4654i	1.52560	−	0.835496i
$601$	23.3842	+	2.30314i	0.953862	+	0.0939472i	0.562959	−	0.826485i	$-0.309663\pi$
$601$	23.3842	+	2.30314i	0.953862	+	0.0939472i	0.390903	+	0.920432i	$0.372163\pi$
$602$	−10.9123	+	4.98893i	−0.444753	+	0.203334i
$603$	4.46827	+	0.219512i	0.181962	+	0.00893922i
$604$	19.9695	+	17.2748i	0.812546	+	0.702901i
$605$	−39.5831	−	5.87160i	−1.60928	−	0.238714i
$606$	12.2365	+	2.59948i	0.497075	+	0.105597i
$607$	−9.86601	−	23.8186i	−0.400449	−	0.966769i	−0.987557	−	0.157261i	$-0.949734\pi$
$607$	−9.86601	−	23.8186i	−0.400449	−	0.966769i	0.587108	−	0.809508i	$-0.300266\pi$
$608$	−12.0466	+	27.8321i	−0.488553	+	1.12874i
$609$	12.7712	−	30.8324i	0.517514	−	1.24939i
$610$	−42.0765	+	61.2368i	−1.70363	+	2.47941i
$611$	−15.3674	+	11.3973i	−0.621700	+	0.461084i
$612$	−0.227531	+	1.82367i	−0.00919739	+	0.0737175i
$613$	−13.6542	−	15.0651i	−0.551487	−	0.608472i	0.399867	−	0.916573i	$-0.369056\pi$
$613$	−13.6542	−	15.0651i	−0.551487	−	0.608472i	−0.951354	+	0.308101i	$0.900306\pi$
$614$	−16.0127	+	17.2131i	−0.646221	+	0.694666i
$615$	−4.46536	+	3.66463i	−0.180061	+	0.147772i
$616$	8.97936	−	0.0912672i	0.361789	−	0.00367726i
$617$	0.429907	+	4.36492i	0.0173074	+	0.175725i	0.999952	−	0.00977188i	$-0.00311054\pi$
$617$	0.429907	+	4.36492i	0.0173074	+	0.175725i	−0.982645	+	0.185497i	$0.940611\pi$
$618$	−3.01066	+	11.3902i	−0.121107	+	0.458179i
$619$	−21.2150	+	12.7158i	−0.852702	+	0.511090i	−0.872443	−	0.488715i	$-0.837466\pi$
$619$	−21.2150	+	12.7158i	−0.852702	+	0.511090i	0.0197413	+	0.999805i	$0.493716\pi$
$620$	17.8107	+	1.33896i	0.715293	+	0.0537740i
$621$	12.9399	−	14.2770i	0.519261	−	0.572916i
$622$	−0.0514510	+	0.00439427i	−0.00206300	+	0.000176194i
$623$	5.89521	+	29.6372i	0.236187	+	1.18739i
$624$	31.9547	+	4.83187i	1.27921	+	0.193430i
$625$	−2.86114	+	14.3839i	−0.114446	+	0.575357i
$626$	−11.7686	−	1.31349i	−0.470369	−	0.0524976i
$627$	−5.24328	−	1.87607i	−0.209396	−	0.0749232i
$628$	−5.88975	+	33.6625i	−0.235026	+	1.34328i
$629$	0.725013	+	4.88764i	0.0289082	+	0.194883i
$630$	−6.37038	−	7.21457i	−0.253802	−	0.287435i
$631$	5.51755	+	10.3226i	0.219650	+	0.410937i	0.967478	−	0.252957i	$-0.0814030\pi$
$631$	5.51755	+	10.3226i	0.219650	+	0.410937i	−0.747827	+	0.663893i	$0.768903\pi$
$632$	−6.70485	+	1.06432i	−0.266705	+	0.0423365i
$633$	0.0785143	−	0.0238171i	0.00312066	−	0.000946643i
$634$	−0.548832	+	3.39577i	−0.0217969	+	0.134863i
$635$	7.01656	−	14.8353i	0.278444	−	0.588720i
$636$	3.57642	+	9.31047i	0.141814	+	0.369184i
$637$	21.3199	+	85.1138i	0.844725	+	3.37233i
$638$	3.44142	+	1.47808i	0.136247	+	0.0585178i
$639$		−	3.31504i		−	0.131141i
$640$	25.7164	+	34.1469i	1.01653	+	1.34977i
$641$		−	7.70153i		−	0.304192i	−0.988366	−	0.152096i	$-0.951398\pi$
$641$		−	7.70153i		−	0.304192i	0.988366	−	0.152096i	$-0.0486023\pi$
$642$	−8.78726	+	20.4594i	−0.346806	+	0.807469i
$643$	0.582576	+	2.32577i	0.0229746	+	0.0917196i	0.980434	−	0.196849i	$-0.0630708\pi$
$643$	0.582576	+	2.32577i	0.0229746	+	0.0917196i	−0.957459	+	0.288568i	$0.906821\pi$
$644$	−32.0006	−	14.2387i	−1.26100	−	0.561085i
$645$	4.48432	−	9.48129i	0.176570	−	0.373326i
$646$	−18.9525	−	3.06315i	−0.745678	−	0.120518i
$647$	−17.3746	+	5.27053i	−0.683067	+	0.207206i	−0.612701	−	0.790315i	$-0.709917\pi$
$647$	−17.3746	+	5.27053i	−0.683067	+	0.207206i	−0.0703663	+	0.997521i	$0.522417\pi$
$648$	−11.5036	−	18.7576i	−0.451905	−	0.736869i
$649$	2.71557	+	5.08048i	0.106596	+	0.199426i
$650$	−48.9251	+	43.2003i	−1.91900	+	1.69445i
$651$	2.79535	+	18.8447i	0.109558	+	0.738582i
$652$	23.5517	−	16.5375i	0.922355	−	0.647658i
$653$	−0.470995	−	0.168525i	−0.0184315	−	0.00659489i	0.327658	−	0.944796i	$-0.393741\pi$
$653$	−0.470995	−	0.168525i	−0.0184315	−	0.00659489i	−0.346089	+	0.938202i	$0.612491\pi$
$654$	−0.252595	+	2.26321i	−0.00987726	+	0.0884985i
$655$	−3.33705	+	16.7765i	−0.130389	+	0.655511i
$656$	−2.78319	−	2.53682i	−0.108665	−	0.0990462i
$657$	−0.168389	−	0.846550i	−0.00656949	−	0.0330270i
$658$	−2.29703	−	26.8951i	−0.0895475	−	1.04848i
$659$	−10.2566	+	11.3164i	−0.399541	+	0.440826i	−0.907179	−	0.420745i	$-0.861769\pi$
$659$	−10.2566	+	11.3164i	−0.399541	+	0.440826i	0.507638	+	0.861571i	$0.330519\pi$
$660$	−5.95087	+	5.11868i	−0.231637	+	0.199244i
$661$	−14.6477	+	8.77948i	−0.569729	+	0.341482i	−0.769786	−	0.638302i	$-0.779637\pi$
$661$	−14.6477	+	8.77948i	−0.569729	+	0.341482i	0.200057	+	0.979784i	$0.435887\pi$
$662$	−40.9930	−	10.8353i	−1.59324	−	0.421126i
$663$	2.00530	+	20.3602i	0.0778795	+	0.790724i
$664$	17.5151	+	7.04729i	0.679717	+	0.273488i
$665$	77.7198	−	63.7830i	3.01384	−	2.47340i
$666$	0.733228	+	0.682095i	0.0284120	+	0.0264306i
$667$	−9.81068	−	10.8244i	−0.379871	−	0.419123i
$668$	−29.8665	+	23.2406i	−1.15557	+	0.899206i
$669$	29.3386	−	21.7590i	1.13430	−	0.841251i
$670$	54.2917	+	37.3045i	2.09747	+	1.44120i
$671$	3.40364	−	8.21712i	0.131396	−	0.317218i
$672$	−29.4782	+	34.7848i	−1.13715	+	1.34185i
$673$	−18.1382	−	43.7896i	−0.699178	−	1.68796i	−0.725418	−	0.688308i	$-0.758354\pi$
$673$	−18.1382	−	43.7896i	−0.699178	−	1.68796i	0.0262407	−	0.999656i	$-0.491646\pi$
$674$	9.02564	−	42.4864i	0.347655	−	1.63651i
$675$	50.1091	+	7.43299i	1.92870	+	0.286096i
$676$	−23.4461	+	1.69636i	−0.901775	+	0.0652448i
$677$	33.0647	+	1.62436i	1.27078	+	0.0624294i	0.673248	−	0.739416i	$-0.264898\pi$
$677$	33.0647	+	1.62436i	1.27078	+	0.0624294i	0.597531	+	0.801846i	$0.296148\pi$
$678$	11.7088	+	25.6106i	0.449672	+	0.983570i
$679$	−25.0322	−	2.46545i	−0.960646	−	0.0946154i
$680$	−16.9538	+	21.0918i	−0.650149	+	0.808835i
$681$	−0.000672324	0	0.000551762i	−2.57635e−5	0	2.11436e-5i
$682$	−2.11883	+	0.286255i	−0.0811341	+	0.0109613i
$683$	−2.82581	−	0.707829i	−0.108127	−	0.0270843i	0.188539	−	0.982066i	$-0.439625\pi$
$683$	−2.82581	−	0.707829i	−0.108127	−	0.0270843i	−0.296666	+	0.954981i	$0.595875\pi$
$684$	−3.38823	+	1.91312i	−0.129552	+	0.0731502i
$685$	−3.43504	−	69.9218i	−0.131246	−	2.67158i
$686$	−71.1544	−	22.5966i	−2.71669	−	0.862743i
$687$	−8.16871	+	12.2253i	−0.311656	+	0.466426i
$688$	6.53744	+	2.00320i	0.249238	+	0.0763711i
$689$	−8.48836	−	12.7037i	−0.323381	−	0.483973i
$690$	29.4109	−	8.50661i	1.11965	−	0.323841i
$691$	0.753322	+	1.59277i	0.0286577	+	0.0605917i	0.917810	−	0.397019i	$-0.129955\pi$
$691$	0.753322	+	1.59277i	0.0286577	+	0.0605917i	−0.889153	+	0.457611i	$0.848705\pi$
$692$	35.7544	+	34.1369i	1.35918	+	1.29769i
$693$	0.925396	+	0.686320i	0.0351529	+	0.0260711i
$694$	18.6393	−	6.39771i	0.707540	−	0.242854i
$695$	5.74185	−	18.9283i	0.217801	−	0.717993i
$696$	−17.1081	+	8.30534i	−0.648481	+	0.314813i
$697$	1.12378	−	2.10245i	0.0425663	−	0.0796360i
$698$	10.4414	−	2.47192i	0.395212	−	0.0935634i
$699$	−13.6149	+	4.87148i	−0.514962	+	0.184256i
$700$	−15.6151	−	90.7493i	−0.590197	−	3.43000i
$701$	32.2680	+	19.3407i	1.21874	+	0.730487i	0.971172	−	0.238382i	$-0.0766169\pi$
$701$	32.2680	+	19.3407i	1.21874	+	0.730487i	0.247573	+	0.968869i	$0.420367\pi$
$702$	26.8157	+	27.5207i	1.01209	+	1.03870i
$703$	−7.39733	+	7.39733i	−0.278996	+	0.278996i
$704$	−3.86064	−	3.35870i	−0.145503	−	0.126586i
$705$	16.6843	+	16.6843i	0.628366	+	0.628366i
$706$	0.274055	−	21.1214i	0.0103142	−	0.794913i
$707$	13.8994	−	23.1898i	0.522742	−	0.872142i
$708$	−28.5305	−	6.44886i	−1.07224	−	0.242363i
$709$	2.96556	+	8.28819i	0.111374	+	0.311270i	0.984279	−	0.176621i	$-0.0565166\pi$
$709$	2.96556	+	8.28819i	0.111374	+	0.311270i	−0.872905	+	0.487890i	$0.837767\pi$
$710$	25.6358	−	41.5388i	0.962093	−	1.55892i
$711$	−0.768165	−	0.410593i	−0.0288085	−	0.0153984i
$712$	8.70213	−	14.8591i	0.326126	−	0.556866i
$713$	7.98039	+	2.42082i	0.298868	+	0.0906606i
$714$	−25.9304	−	12.6784i	−0.970420	−	0.474478i
$715$	7.16295	−	9.65812i	0.267879	−	0.361193i
$716$	14.5625	+	5.64091i	0.544227	+	0.210811i
$717$	−0.449340	+	0.212522i	−0.0167809	+	0.00793677i
$718$	−17.8418	+	32.3626i	−0.665851	+	1.20776i
$719$	−14.9600	+	9.99594i	−0.557913	+	0.372786i	−0.802326	−	0.596885i	$-0.796405\pi$
$719$	−14.9600	+	9.99594i	−0.557913	+	0.372786i	0.244413	+	0.969671i	$0.421405\pi$
$720$	−0.0154159	+	5.48454i	−0.000574516	+	0.204397i
$721$	21.1712	+	14.1461i	0.788455	+	0.526829i
$722$	−6.33635	−	12.2337i	−0.235815	−	0.455290i
$723$	48.0319	−	2.35966i	1.78633	−	0.0877566i
$724$	4.89767	−	0.597084i	0.182021	−	0.0221904i
$725$	9.33215	−	37.2560i	0.346587	−	1.38365i
$726$	−14.7412	+	19.3465i	−0.547097	+	0.718015i
$727$	12.4323	−	15.1488i	0.461089	−	0.561839i	−0.489615	−	0.871939i	$-0.662863\pi$
$727$	12.4323	−	15.1488i	0.461089	−	0.561839i	0.950704	+	0.310100i	$0.100363\pi$
$728$	32.2979	−	61.9311i	1.19704	−	2.29532i
$729$	2.88446	−	29.2864i	0.106832	−	1.08468i
$730$	4.43653	−	11.9098i	0.164203	−	0.440802i
$731$	−0.212385	+	4.32320i	−0.00785535	+	0.159899i
$732$	20.2479	+	40.3669i	0.748386	+	1.49200i
$733$	4.47433	−	30.1635i	0.165263	−	1.11411i	−0.734778	−	0.678308i	$-0.762714\pi$
$733$	4.47433	−	30.1635i	0.165263	−	1.11411i	0.900041	−	0.435805i	$-0.143536\pi$
$734$	−17.9113	−	27.5739i	−0.661116	−	1.01777i
$735$	99.9720	−	41.4097i	3.68752	−	1.52742i
$736$	8.24783	+	18.1754i	0.304019	+	0.669956i
$737$	−7.28519	−	3.01762i	−0.268353	−	0.111156i
$738$	−0.0881044	−	0.475063i	−0.00324317	−	0.0174873i
$739$	17.3647	+	23.4135i	0.638769	+	0.861281i	0.997390	−	0.0722028i	$-0.0230029\pi$
$739$	17.3647	+	23.4135i	0.638769	+	0.861281i	−0.358621	+	0.933483i	$0.616753\pi$
$740$	3.91290	+	14.2171i	0.143841	+	0.522631i
$741$	−32.0946	+	29.0889i	−1.17902	+	1.06861i
$742$	21.5417	−	0.778269i	0.790819	−	0.0285711i
$743$	12.5929	+	15.3445i	0.461989	+	0.562935i	0.950940	−	0.309376i	$-0.100120\pi$
$743$	12.5929	+	15.3445i	0.461989	+	0.562935i	−0.488951	+	0.872311i	$0.662620\pi$
$744$	5.93933	−	9.08743i	0.217746	−	0.333161i
$745$	71.9026	−	7.08179i	2.63431	−	0.259457i
$746$	8.62265	+	14.8187i	0.315698	+	0.542551i
$747$	1.24531	+	2.07767i	0.0455634	+	0.0760179i
$748$	1.46053	−	2.89145i	0.0534023	−	0.105722i
$749$	35.6573	+	32.3179i	1.30289	+	1.18087i
$750$	28.3748	+	23.9094i	1.03610	+	0.873046i
$751$	0.715135	−	0.142249i	0.0260956	−	0.00519075i	−0.182025	−	0.983294i	$-0.558265\pi$
$751$	0.715135	−	0.142249i	0.0260956	−	0.00519075i	0.208121	+	0.978103i	$0.433265\pi$
$752$	−9.19775	+	12.3292i	−0.335408	+	0.449598i
$753$	−17.0389	−	3.38926i	−0.620933	−	0.123511i
$754$	22.7577	−	18.1878i	0.828787	−	0.662361i
$755$	−16.8051	+	46.9671i	−0.611600	+	1.70931i
$756$	−52.9107	+	11.8034i	−1.92434	+	0.429286i
$757$	5.50357	−	0.816377i	0.200031	−	0.0296717i	−0.0459632	−	0.998943i	$-0.514636\pi$
$757$	5.50357	−	0.816377i	0.200031	−	0.0296717i	0.245994	+	0.969271i	$0.420886\pi$
$758$	1.05723	−	17.0131i	0.0384002	−	0.617945i
$759$	−3.23224	+	1.72767i	−0.117323	+	0.0627104i
$760$	−57.2505	−	2.22952i	−2.07669	−	0.0808733i
$761$	7.79921	+	25.7106i	0.282721	+	0.932007i	0.977169	+	0.212464i	$0.0681488\pi$
$761$	7.79921	+	25.7106i	0.282721	+	0.932007i	−0.694448	+	0.719543i	$0.744351\pi$
$762$	−5.83756	−	8.08829i	−0.211472	−	0.293008i
$763$	4.44918	+	2.10431i	0.161071	+	0.0761810i
$764$	0.586614	−	22.6013i	0.0212230	−	0.817686i
$765$	−3.36792	+	0.843619i	−0.121767	+	0.0305011i
$766$	−10.6015	−	26.5639i	−0.383047	−	0.959792i
$767$	44.8080			1.61792
$768$	25.7225	−	3.66791i	0.928180	−	0.132354i
$769$	−17.8709			−0.644443			−0.322221	−	0.946664i	$-0.604430\pi$
$769$	−17.8709			−0.644443			−0.322221	+	0.946664i	$0.604430\pi$
$770$	6.28816	+	15.7561i	0.226610	+	0.567811i
$771$	−2.77077	+	0.694042i	−0.0997868	+	0.0249953i
$772$	27.1813	+	0.705487i	0.978275	+	0.0253910i
$773$	−27.0597	−	12.7983i	−0.973270	−	0.460322i	−0.126317	−	0.991990i	$-0.540316\pi$
$773$	−27.0597	−	12.7983i	−0.973270	−	0.460322i	−0.846953	+	0.531668i	$0.821566\pi$
$774$	0.513396	+	0.711341i	0.0184536	+	0.0255686i
$775$	6.36442	+	20.9807i	0.228617	+	0.753648i
$776$	9.73334	+	10.5222i	0.349406	+	0.377723i
$777$	−13.8710	+	7.41422i	−0.497620	+	0.265984i
$778$	−2.13470	+	34.3522i	−0.0765329	+	1.23159i
$779$	4.99269	−	0.740595i	0.178882	−	0.0265346i
$780$	13.2934	+	59.5900i	0.475981	+	2.13366i
$781$	−1.96852	+	5.50164i	−0.0704391	+	0.196864i
$782$	−9.87024	+	7.88823i	−0.352959	+	0.282083i
$783$	−22.1766	−	4.41120i	−0.792528	−	0.157644i
$784$	36.0961	+	60.6084i	1.28915	+	2.16459i
$785$	−63.3203	+	12.5952i	−2.26000	+	0.449542i
$786$	7.95061	+	6.69939i	0.283589	+	0.238959i
$787$	35.0926	+	31.8061i	1.25092	+	1.13376i	0.985508	+	0.169627i	$0.0542562\pi$
$787$	35.0926	+	31.8061i	1.25092	+	1.13376i	0.265407	+	0.964137i	$0.414494\pi$
$788$	45.4350	+	22.9501i	1.61855	+	0.817565i
$789$	−0.0554488	−	0.0925107i	−0.00197403	−	0.00329347i
$790$	−6.45025	−	11.0853i	−0.229490	−	0.394396i
$791$	60.5681	−	5.96544i	2.15355	−	0.212107i
$792$	−0.134623	−	0.642591i	−0.00478361	−	0.0228335i
$793$	−43.8877	−	53.4774i	−1.55850	−	1.89904i
$794$	10.4773	−	0.378529i	0.371825	−	0.0134335i
$795$	−13.9612	+	12.6537i	−0.495153	+	0.448781i
$796$	22.8363	−	6.28512i	0.809411	−	0.222770i
$797$	−0.564902	−	0.761682i	−0.0200098	−	0.0269801i	0.793089	−	0.609105i	$-0.208471\pi$
$797$	−0.564902	−	0.761682i	−0.0200098	−	0.0269801i	−0.813099	+	0.582125i	$0.802221\pi$
$798$	−11.1436	−	60.0865i	−0.394477	−	2.12704i
$799$	−8.99627	−	3.72638i	−0.318265	−	0.131830i
$800$	−27.6839	+	44.5767i	−0.978774	+	1.57602i
$801$	2.04114	−	0.845469i	0.0721202	−	0.0298732i
$802$	−15.8089	−	24.3375i	−0.558233	−	0.859386i
$803$	−0.223235	+	1.50493i	−0.00787778	+	0.0531077i
$804$	35.7888	−	17.9516i	1.26217	−	0.633103i
$805$	3.24679	−	66.0898i	0.114434	−	2.32936i
$806$	−5.80531	+	15.5843i	−0.204483	+	0.548933i
$807$	0.938724	−	9.53102i	0.0330446	−	0.335508i
$808$	−14.6971	+	4.62194i	−0.517041	+	0.162599i
$809$	12.5224	−	15.2585i	0.440263	−	0.536462i	−0.504849	−	0.863207i	$-0.668452\pi$
$809$	12.5224	−	15.2585i	0.440263	−	0.536462i	0.945112	+	0.326745i	$0.105952\pi$
$810$	25.1943	−	33.0652i	0.885237	−	1.16179i
$811$	4.08596	−	16.3121i	0.143477	−	0.572794i	−0.855050	−	0.518545i	$-0.826474\pi$
$811$	4.08596	−	16.3121i	0.143477	−	0.572794i	0.998527	−	0.0542483i	$-0.0172763\pi$
$812$	4.97393	+	40.7994i	0.174551	+	1.43178i
$813$	0.636758	−	0.0312819i	0.0223321	−	0.00109710i
$814$	−0.811828	−	1.56741i	−0.0284546	−	0.0549375i
$815$	45.2045	+	30.2046i	1.58344	+	1.05802i
$816$	6.25170	+	15.2138i	0.218853	+	0.532588i
$817$	−7.61974	+	5.09134i	−0.266581	+	0.178124i
$818$	−7.89121	+	14.3136i	−0.275910	+	0.500462i
$819$	8.10109	−	3.83153i	0.283075	−	0.133884i
$820$	2.56976	−	6.63406i	0.0897398	−	0.231672i
$821$	−1.96131	+	2.64452i	−0.0684503	+	0.0922945i	−0.836106	−	0.548568i	$-0.815173\pi$
$821$	−1.96131	+	2.64452i	−0.0684503	+	0.0922945i	0.767656	+	0.640863i	$0.221423\pi$
$822$	−38.2264	−	18.6904i	−1.33330	−	0.651904i
$823$	1.75902	+	0.533592i	0.0613155	+	0.0185999i	0.320793	−	0.947149i	$-0.396050\pi$
$823$	1.75902	+	0.533592i	0.0613155	+	0.0185999i	−0.259478	+	0.965749i	$0.583550\pi$
$824$	−3.66846	−	14.0384i	−0.127797	−	0.489050i
$825$	−8.49767	−	4.54210i	−0.295851	−	0.158136i
$826$	−33.2007	+	53.7967i	−1.15520	+	1.87183i
$827$	−16.5991	−	46.3914i	−0.577208	−	1.61319i	−0.774311	−	0.632805i	$-0.781903\pi$
$827$	−16.5991	−	46.3914i	−0.577208	−	1.61319i	0.197103	−	0.980383i	$-0.436847\pi$
$828$	−0.564587	+	2.49780i	−0.0196208	+	0.0868044i
$829$	0.703109	−	1.17307i	0.0244200	−	0.0407423i	−0.845277	−	0.534329i	$-0.820564\pi$
$829$	0.703109	−	1.17307i	0.0244200	−	0.0407423i	0.869697	+	0.493587i	$0.164314\pi$
$830$	−0.462753	+	35.6642i	−0.0160624	+	1.23792i
$831$	22.3251	+	22.3251i	0.774450	+	0.774450i
$832$	−37.1955	+	14.1680i	−1.28952	+	0.491188i
$833$	−31.5771	+	31.5771i	−1.09408	+	1.09408i
$834$	−8.39031	−	8.61091i	−0.290533	−	0.298171i
$835$	−61.3221	−	36.7551i	−2.12214	−	1.27196i
$836$	6.75915	−	1.16304i	0.233770	−	0.0402246i
$837$	12.1531	−	4.34844i	0.420072	−	0.150304i
$838$	10.0945	−	2.38980i	0.348710	−	0.0825544i
$839$	−3.18614	+	5.96085i	−0.109998	+	0.205791i	−0.930897	−	0.365282i	$-0.880973\pi$
$839$	−3.18614	+	5.96085i	−0.109998	+	0.205791i	0.820899	+	0.571073i	$0.193473\pi$
$840$	−81.3939	−	28.1934i	−2.80836	−	0.972763i
$841$	3.44188	−	11.3464i	0.118685	−	0.391254i
$842$	34.4316	−	11.8182i	1.18659	−	0.407282i
$843$	11.3956	+	8.45152i	0.392484	+	0.291086i
$844$	−0.0697798	+	0.0730861i	−0.00240192	+	0.00251573i
$845$	−18.9877	−	40.1461i	−0.653196	−	1.38107i
$846$	−1.89583	+	0.548337i	−0.0651800	+	0.0188522i
$847$	29.2047	+	43.7079i	1.00349	+	1.50182i
$848$	−9.47338	−	7.81927i	−0.325317	−	0.268515i
$849$	−22.6787	+	33.9411i	−0.778333	+	1.16486i
$850$	−31.6599	−	10.0543i	−1.08593	−	0.344860i
$851$	0.337829	+	6.87668i	0.0115806	+	0.235729i
$852$	−14.5876	−	25.8353i	−0.499762	−	0.885102i
$853$	44.3478	+	11.1085i	1.51844	+	0.380349i	0.910458	−	0.413601i	$-0.135729\pi$
$853$	44.3478	+	11.1085i	1.51844	+	0.380349i	0.607982	+	0.793951i	$0.291979\pi$
$854$	96.7241	−	13.0675i	3.30983	−	0.447160i
$855$	−5.68232	−	4.66336i	−0.194331	−	0.159484i
$856$	−2.96520	−	27.2626i	−0.101348	−	0.931816i
$857$	−37.2272	−	3.66656i	−1.27166	−	0.125247i	−0.560425	−	0.828205i	$-0.689362\pi$
$857$	−37.2272	−	3.66656i	−1.27166	−	0.125247i	−0.711231	+	0.702958i	$0.751862\pi$
$858$	−3.03888	−	6.64695i	−0.103746	−	0.226923i
$859$	−2.10918	−	0.103618i	−0.0719645	−	0.00353539i	0.0130536	−	0.999915i	$-0.495845\pi$
$859$	−2.10918	−	0.103618i	−0.0719645	−	0.00353539i	−0.0850180	+	0.996379i	$0.527095\pi$
$860$	0.932147	+	12.8836i	0.0317859	+	0.439326i
$861$	7.50625	+	1.11345i	0.255812	+	0.0379462i
$862$	−5.21084	+	24.5290i	−0.177482	+	0.835460i
$863$	4.49642	+	10.8553i	0.153060	+	0.369519i	0.981747	−	0.190193i	$-0.0609115\pi$
$863$	4.49642	+	10.8553i	0.153060	+	0.369519i	−0.828687	+	0.559713i	$0.810912\pi$
$864$	27.0114	+	14.9908i	0.918947	+	0.509998i
$865$	−35.7387	+	86.2809i	−1.21515	+	2.93364i
$866$	−5.76542	−	3.96148i	−0.195917	−	0.134617i
$867$	13.8105	−	10.2426i	0.469029	−	0.347856i
$868$	−14.4091	−	18.5172i	−0.489077	−	0.628513i
$869$	1.03103	+	1.13757i	0.0349753	+	0.0385893i
$870$	−26.3053	−	24.4709i	−0.891835	−	0.829640i
$871$	−47.4123	+	38.9103i	−1.60651	+	1.31842i
$872$	−1.09957	−	2.58012i	−0.0372363	−	0.0873739i
$873$	0.180256	+	1.83017i	0.00610076	+	0.0619420i
$874$	−25.8630	−	6.83614i	−0.874829	−	0.231236i
$875$	68.7839	−	41.2275i	2.32532	−	1.39374i
$876$	−5.03750	−	5.85648i	−0.170201	−	0.197872i
$877$	20.9789	−	23.1467i	0.708408	−	0.781608i	−0.275305	−	0.961357i	$-0.588779\pi$
$877$	20.9789	−	23.1467i	0.708408	−	0.781608i	0.983712	+	0.179749i	$0.0575287\pi$
$878$	3.11706	+	36.4965i	0.105196	+	1.23170i
$879$	−10.3775	−	52.1713i	−0.350025	−	1.75969i
$880$	3.28238	−	9.09299i	0.110649	−	0.306525i
$881$	−6.06778	+	30.5048i	−0.204429	+	1.02773i	0.733178	+	0.680036i	$0.238036\pi$
$881$	−6.06778	+	30.5048i	−0.204429	+	1.02773i	−0.937607	+	0.347696i	$0.886964\pi$
$882$	−1.00392	+	8.99493i	−0.0338037	+	0.302875i
$883$	7.32379	+	2.62049i	0.246465	+	0.0881867i	0.457224	−	0.889351i	$-0.348844\pi$
$883$	7.32379	+	2.62049i	0.246465	+	0.0881867i	−0.210759	+	0.977538i	$0.567594\pi$
$884$	−14.4795	−	20.6208i	−0.486998	−	0.693553i
$885$	−8.10820	−	54.6610i	−0.272554	−	1.83741i
$886$	−15.4724	+	13.6619i	−0.519806	+	0.458982i
$887$	−7.90188	−	14.7834i	−0.265319	−	0.496377i	0.713619	−	0.700534i	$-0.247055\pi$
$887$	−7.90188	−	14.7834i	−0.265319	−	0.496377i	−0.978938	+	0.204157i	$0.934555\pi$
$888$	8.71582	+	2.08929i	0.292484	+	0.0701120i
$889$	−20.6298	+	6.25798i	−0.691901	+	0.209886i
$890$	32.1145	+	5.19042i	1.07648	+	0.173983i
$891$	−2.12761	+	4.49844i	−0.0712775	+	0.150704i
$892$	−18.2880	+	41.1010i	−0.612327	+	1.37616i
$893$	−5.00936	−	19.9985i	−0.167632	−	0.669224i
$894$	17.3306	−	40.3509i	0.579622	−	1.34954i
$895$			29.5032i			0.986184i
$896$	10.5500	−	55.1550i	0.352451	−	1.84260i
$897$			28.5072i			0.951827i
$898$	9.25668	+	3.97572i	0.308899	+	0.132671i
$899$	−2.37785	−	9.49290i	−0.0793057	−	0.316606i
$900$	−6.28473	+	2.41414i	−0.209491	+	0.0804715i
$901$	3.32468	−	7.02945i	0.110761	−	0.234185i
$902$	−0.135881	+	0.840732i	−0.00452435	+	0.0279933i
$903$	−13.1846	+	3.99951i	−0.438756	+	0.133095i
$904$	−28.0653	−	20.3758i	−0.933437	−	0.677688i
$905$	4.39395	+	8.22050i	0.146060	+	0.273259i
$906$	20.0684	+	22.7278i	0.666727	+	0.755081i
$907$	−6.13296	−	41.3450i	−0.203642	−	1.37284i	−0.814069	−	0.580768i	$-0.802752\pi$
$907$	−6.13296	−	41.3450i	−0.203642	−	1.37284i	0.610428	−	0.792072i	$-0.290998\pi$
$908$	0.00105514		0.000184613i	3.50162e−5		6.12659e-6i
$909$	−1.86115	−	0.665931i	−0.0617305	−	0.0220875i
$910$	131.140	+	14.6364i	4.34725	+	0.485193i
$911$	7.75462	−	38.9851i	0.256922	−	1.29163i	−0.609685	−	0.792644i	$-0.708704\pi$
$911$	7.75462	−	38.9851i	0.256922	−	1.29163i	0.866607	−	0.498991i	$-0.166296\pi$
$912$	−17.9871	+	29.8193i	−0.595614	+	0.987417i
$913$	−0.832962	−	4.18758i	−0.0275670	−	0.138589i
$914$	26.7192	−	2.28201i	0.883793	−	0.0754821i
$915$	−57.2951	+	63.2154i	−1.89412	+	2.08984i
$916$	1.35752	−	18.0575i	0.0448536	−	0.596635i
$917$	19.2732	−	11.5519i	0.636458	−	0.381478i
$918$	−4.99750	+	18.9069i	−0.164942	+	0.624021i
$919$	−2.73624	−	27.7816i	−0.0902604	−	0.916429i	−0.928551	−	0.371205i	$-0.878945\pi$
$919$	−2.73624	−	27.7816i	−0.0902604	−	0.916429i	0.838290	−	0.545224i	$-0.183555\pi$
$920$	−26.3904	+	26.9324i	−0.870066	+	0.887934i
$921$	−20.8679	+	17.1258i	−0.687621	+	0.564316i
$922$	19.2763	−	20.7213i	0.634831	−	0.682421i
$923$	30.5222	+	33.6761i	1.00465	+	1.10846i
$924$	10.2320	+	1.27660i	0.336610	+	0.0419972i
$925$	−14.5387	+	10.7826i	−0.478030	+	0.354531i
$926$	−24.0995	+	35.0736i	−0.791958	+	1.15259i
$927$	0.712414	−	1.71992i	0.0233987	−	0.0564895i
$928$	13.3182	−	19.2667i	0.437192	−	0.632459i
$929$	−0.0513062	−	0.123864i	−0.00168330	−	0.00406385i	0.923036	−	0.384714i	$-0.125700\pi$
$929$	−0.0513062	−	0.123864i	−0.00168330	−	0.00406385i	−0.924719	+	0.380651i	$0.875700\pi$
$930$	20.0617	+	4.26183i	0.657849	+	0.139751i
$931$	−93.5246	−	13.8731i	−3.06515	−	0.454671i
$932$	11.6513	−	13.4688i	0.381650	−	0.441184i
$933$	−0.0592240	−	0.00290949i	−0.00193891	−	9.52523e-5i
$934$	28.2128	−	12.8984i	0.923151	−	0.422050i
$935$	6.09035	+	0.599847i	0.199176	+	0.0196171i
$936$	−4.90164	−	1.43266i	−0.160215	−	0.0468279i
$937$	26.4584	+	21.7138i	0.864357	+	0.709359i	0.958161	−	0.286231i	$-0.0924026\pi$
$937$	26.4584	+	21.7138i	0.864357	+	0.709359i	−0.0938038	+	0.995591i	$0.529903\pi$
$938$	−11.5855	−	85.7543i	−0.378279	−	2.79998i
$939$	−13.1901	−	3.30395i	−0.430443	−	0.107820i
$940$	−27.9960	−	7.78990i	−0.913127	−	0.254079i
$941$	−1.88179	−	38.3047i	−0.0613446	−	1.24870i	−0.810275	−	0.586050i	$-0.800682\pi$
$941$	−1.88179	−	38.3047i	−0.0613446	−	1.24870i	0.748930	−	0.662649i	$-0.230568\pi$
$942$	−11.8774	+	37.4006i	−0.386986	+	1.21858i
$943$	1.84549	−	2.76197i	0.0600974	−	0.0899421i
$944$	34.5023	−	10.3604i	1.12295	−	0.337201i
$945$	−56.8989	−	85.1552i	−1.85092	−	2.77010i
$946$	−0.429628	−	1.48540i	−0.0139684	−	0.0482946i
$947$	8.82939	+	18.6682i	0.286917	+	0.606634i	0.995042	−	0.0994521i	$-0.0317090\pi$
$947$	8.82939	+	18.6682i	0.286917	+	0.606634i	−0.708126	+	0.706086i	$0.750459\pi$
$948$	−7.79338	+	0.180358i	−0.253117	+	0.00585775i
$949$	9.50494	+	7.04935i	0.308543	+	0.228831i
$950$	−22.8323	−	66.5204i	−0.740777	−	2.15821i
$951$	−1.14660	+	3.77982i	−0.0371810	+	0.122569i
$952$	35.4861	−	2.10506i	1.15011	−	0.0682253i
$953$	19.7474	−	36.9447i	0.639680	−	1.19676i	−0.328024	−	0.944669i	$-0.606383\pi$
$953$	19.7474	−	36.9447i	0.639680	−	1.19676i	0.967704	−	0.252088i	$-0.0811173\pi$
$954$	−0.363070	−	1.53361i	−0.0117548	−	0.0496524i
$955$	40.2156	−	14.3894i	1.30135	−	0.465630i
$956$	0.353200	−	0.500011i	0.0114233	−	0.0161715i
$957$	3.68891	+	2.21105i	0.119246	+	0.0714730i
$958$	26.7400	−	26.0549i	0.863929	−	0.841797i
$959$	−65.0278	+	65.0278i	−2.09986	+	2.09986i
$960$	24.0142	+	42.8108i	0.775055	+	1.38171i
$961$	−17.9701	−	17.9701i	−0.579680	−	0.579680i
$962$	−13.7287	−	0.178134i	−0.442632	−	0.00574327i
$963$	1.80885	−	3.01789i	0.0582894	−	0.0972500i
$964$	−50.0826	+	31.6159i	−1.61305	+	1.01828i
$965$	17.3053	+	48.3650i	0.557077	+	1.55693i
$966$	−34.2259	−	21.1226i	−1.10120	−	0.679608i
$967$	48.8898	+	26.1321i	1.57219	+	0.840353i	0.999792	+	0.0203763i	$0.00648643\pi$
$967$	48.8898	+	26.1321i	1.57219	+	0.840353i	0.572397	+	0.819977i	$0.306014\pi$
$968$	4.09399	−	29.6744i	0.131586	−	0.953771i
$969$	−21.0960	−	6.39941i	−0.677702	−	0.205579i
$970$	−11.8944	+	24.3268i	−0.381905	+	0.781087i
$971$	19.6707	−	26.5229i	0.631264	−	0.851161i	−0.365560	−	0.930788i	$-0.619123\pi$
$971$	19.6707	−	26.5229i	0.631264	−	0.851161i	0.996825	+	0.0796262i	$0.0253727\pi$
$972$	3.02942	+	6.86027i	0.0971687	+	0.220043i
$973$	−23.4892	+	11.1096i	−0.753030	+	0.356157i
$974$	5.21024	+	2.87246i	0.166947	+	0.0920395i
$975$	−62.3156	+	41.6379i	−1.99570	+	1.33348i
$976$	−46.1586	−	31.0302i	−1.47750	−	0.993253i
$977$	6.17881	+	4.12855i	0.197678	+	0.132084i	0.650470	−	0.759532i	$-0.274572\pi$
$977$	6.17881	+	4.12855i	0.197678	+	0.132084i	−0.452792	+	0.891616i	$0.649572\pi$
$978$	29.3429	−	15.1980i	0.938284	−	0.485978i
$979$	−3.88953	+	0.191080i	−0.124310	+	0.00610695i
$980$	−82.1388	+	104.947i	−2.62383	+	3.35240i
$981$	0.0874343	−	0.349057i	0.00279156	−	0.0111445i
$982$	−2.49702	−	1.90263i	−0.0796831	−	0.0607152i
$983$	32.0866	−	39.0977i	1.02340	−	1.24702i	0.0547790	−	0.998499i	$-0.482555\pi$
$983$	32.0866	−	39.0977i	1.02340	−	1.24702i	0.968626	−	0.248524i	$-0.0799454\pi$
$984$	−2.77711	−	3.31464i	−0.0885311	−	0.105667i
$985$	−9.42572	+	95.7010i	−0.300328	+	3.04929i
$986$	13.8943	+	5.17577i	0.442484	+	0.164830i
$987$	1.52088	−	30.9583i	0.0484102	−	0.985413i
$988$	16.8051	−	50.6307i	0.534641	−	1.61078i
$989$	−0.884965	+	5.96595i	−0.0281402	+	0.189706i
$990$	1.04015	−	0.675651i	0.0330581	−	0.0214736i
$991$	−35.4121	+	14.6682i	−1.12490	+	0.465950i	−0.866045	−	0.499966i	$-0.833346\pi$
$991$	−35.4121	+	14.6682i	−1.12490	+	0.465950i	−0.258857	+	0.965916i	$0.583346\pi$
$992$	−0.866764	+	13.3423i	−0.0275198	+	0.423617i
$993$	−44.9819	−	18.6321i	−1.42746	−	0.591273i
$994$	−63.0473	+	11.6926i	−1.99974	+	0.370868i
$995$	26.6553	+	35.9405i	0.845029	+	1.13939i
$996$	18.8478	+	10.7121i	0.597214	+	0.339427i
$997$	−16.8614	+	15.2823i	−0.534006	+	0.483995i	−0.893444	−	0.449174i	$-0.851718\pi$
$997$	−16.8614	+	15.2823i	−0.534006	+	0.483995i	0.359438	+	0.933169i	$0.382968\pi$
$998$	1.20420	+	33.3310i	0.0381183	+	1.05507i
$999$	6.76032	+	8.23747i	0.213887	+	0.260622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.101.4	✓	992
256.109	even	64	inner	256.2.m.a.109.4	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.101.4	✓	992	1.1	even	1	trivial
256.2.m.a.109.4	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)

\(f(q)\)	\(=\)	\(q+(-1.31347 + 0.524199i) q^{2} +(-1.57525 + 0.394580i) q^{3} +(1.45043 - 1.37704i) q^{4} +(3.41561 + 1.61546i) q^{5} +(1.86221 - 1.34402i) q^{6} +(-1.44081 - 4.74972i) q^{7} +(-1.18326 + 2.56903i) q^{8} +(-0.320042 + 0.171066i) q^{9} +O(q^{10})\)	\(q+(-1.31347 + 0.524199i) q^{2} +(-1.57525 + 0.394580i) q^{3} +(1.45043 - 1.37704i) q^{4} +(3.41561 + 1.61546i) q^{5} +(1.86221 - 1.34402i) q^{6} +(-1.44081 - 4.74972i) q^{7} +(-1.18326 + 2.56903i) q^{8} +(-0.320042 + 0.171066i) q^{9} +(-5.33314 - 0.331411i) q^{10} +(0.632723 - 0.0938556i) q^{11} +(-1.74144 + 2.74150i) q^{12} +(1.67613 - 4.68447i) q^{13} +(4.38227 + 5.48336i) q^{14} +(-6.01787 - 1.19703i) q^{15} +(0.207499 - 3.99461i) q^{16} +(2.48352 - 0.494003i) q^{17} +(0.330694 - 0.392456i) q^{18} +(3.97235 + 3.60033i) q^{19} +(7.17867 - 2.36033i) q^{20} +(4.14378 + 6.91348i) q^{21} +(-0.781866 + 0.454950i) q^{22} +(3.51135 - 0.345838i) q^{23} +(0.850244 - 4.51375i) q^{24} +(5.88470 + 7.17053i) q^{25} +(0.254040 + 7.03156i) q^{26} +(4.04638 - 3.66742i) q^{27} +(-8.63037 - 4.90508i) q^{28} +(-2.46645 - 3.32562i) q^{29} +(8.53180 - 1.58229i) q^{30} +(2.18366 + 0.904500i) q^{31} +(1.82143 + 5.35560i) q^{32} +(-0.959664 + 0.397506i) q^{33} +(-3.00308 + 1.95072i) q^{34} +(2.75175 - 18.5508i) q^{35} +(-0.228633 + 0.688831i) q^{36} +(-0.0957475 + 1.94898i) q^{37} +(-7.10487 - 2.64664i) q^{38} +(-0.791929 + 8.04059i) q^{39} +(-8.19172 + 6.86328i) q^{40} +(0.597257 - 0.727759i) q^{41} +(-9.06679 - 6.90852i) q^{42} +(-0.415342 + 1.65814i) q^{43} +(0.788478 - 1.00742i) q^{44} +(-1.36949 + 0.0672787i) q^{45} +(-4.43078 + 2.29489i) q^{46} +(-3.19742 - 2.13645i) q^{47} +(1.24933 + 6.37439i) q^{48} +(-14.6636 + 9.79790i) q^{49} +(-11.4882 - 6.33356i) q^{50} +(-3.71724 + 1.75812i) q^{51} +(-4.01961 - 9.10261i) q^{52} +(1.82933 - 2.46656i) q^{53} +(-3.39235 + 6.93817i) q^{54} +(2.31275 + 0.701567i) q^{55} +(13.9070 + 1.91866i) q^{56} +(-7.67807 - 4.10401i) q^{57} +(4.98290 + 3.07521i) q^{58} +(3.03405 + 8.47961i) q^{59} +(-10.3769 + 6.55067i) q^{60} +(7.14849 - 11.9265i) q^{61} +(-3.34231 - 0.0433674i) q^{62} +(1.27363 + 1.27363i) q^{63} +(-5.19980 - 6.07965i) q^{64} +(13.2926 - 13.2926i) q^{65} +(1.05212 - 1.02517i) q^{66} +(-10.5739 - 6.33776i) q^{67} +(2.92191 - 4.13643i) q^{68} +(-5.39479 + 1.93029i) q^{69} +(6.10994 + 25.8084i) q^{70} +(-4.30624 + 8.05640i) q^{71} +(-0.0607805 - 1.02461i) q^{72} +(-0.690439 + 2.27607i) q^{73} +(-0.895894 - 2.61013i) q^{74} +(-12.0992 - 8.97340i) q^{75} +(10.7194 - 0.248074i) q^{76} +(-1.35742 - 2.87003i) q^{77} +(-3.17469 - 10.9762i) q^{78} +(1.33348 + 1.99570i) q^{79} +(7.16189 - 13.3088i) q^{80} +(-4.32213 + 6.46853i) q^{81} +(-0.402991 + 1.26897i) q^{82} +(-0.327525 - 6.66693i) q^{83} +(15.5304 + 4.32136i) q^{84} +(9.28078 + 2.32471i) q^{85} +(-0.323653 - 2.39565i) q^{86} +(5.19749 + 4.26547i) q^{87} +(-0.507558 + 1.73654i) q^{88} +(-6.05877 - 0.596737i) q^{89} +(1.76352 - 0.806254i) q^{90} +(-24.6649 - 1.21171i) q^{91} +(4.61674 - 5.33690i) q^{92} +(-3.79670 - 0.563188i) q^{93} +(5.31966 + 1.13009i) q^{94} +(7.75181 + 18.7145i) q^{95} +(-4.98241 - 7.71771i) q^{96} +(1.93933 - 4.68195i) q^{97} +(14.1242 - 20.5559i) q^{98} +(-0.186442 + 0.138275i) 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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