LMFDB - Embedded newform 400.2.be.a.381.51

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(21,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 5, 12]))

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

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

chi := DirichletCharacter("400.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.be (of order $20$, degree $8$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$58$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			381.51
Character	$\chi$	$=$	400.381
Dual form			400.2.be.a.21.51

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31042 - 0.531786i) q^{2} +(1.11563 + 0.176699i) q^{3} +(1.43441 - 1.39373i) q^{4} +(-2.17773 - 0.507439i) q^{5} +(1.55591 - 0.361728i) q^{6} -4.59337i q^{7} +(1.13851 - 2.58917i) q^{8} +(-1.63976 - 0.532790i) q^{9} +O(q^{10})$	\(q+(1.31042 - 0.531786i) q^{2} +(1.11563 + 0.176699i) q^{3} +(1.43441 - 1.39373i) q^{4} +(-2.17773 - 0.507439i) q^{5} +(1.55591 - 0.361728i) q^{6} -4.59337i q^{7} +(1.13851 - 2.58917i) q^{8} +(-1.63976 - 0.532790i) q^{9} +(-3.12359 + 0.493127i) q^{10} +(5.03525 + 2.56559i) q^{11} +(1.84654 - 1.30143i) q^{12} +(-3.07508 + 1.56683i) q^{13} +(-2.44269 - 6.01926i) q^{14} +(-2.33988 - 0.950917i) q^{15} +(0.115048 - 3.99835i) q^{16} +(0.981966 + 0.713440i) q^{17} +(-2.43210 + 0.173822i) q^{18} +(1.06190 + 6.70459i) q^{19} +(-3.83098 + 2.30729i) q^{20} +(0.811643 - 5.12451i) q^{21} +(7.96264 + 0.684325i) q^{22} +(1.41375 - 0.459354i) q^{23} +(1.72766 - 2.68738i) q^{24} +(4.48501 + 2.21013i) q^{25} +(-3.19643 + 3.68849i) q^{26} +(-4.75450 - 2.42254i) q^{27} +(-6.40191 - 6.58877i) q^{28} +(6.83601 + 1.08272i) q^{29} +(-3.57191 - 0.00178616i) q^{30} +(1.40171 + 1.01840i) q^{31} +(-1.97550 - 5.30070i) q^{32} +(5.16415 + 3.75197i) q^{33} +(1.66619 + 0.412711i) q^{34} +(-2.33086 + 10.0031i) q^{35} +(-3.09464 + 1.52114i) q^{36} +(2.06313 + 4.04911i) q^{37} +(4.95695 + 8.22114i) q^{38} +(-3.70751 + 1.20464i) q^{39} +(-3.79322 + 5.06078i) q^{40} +(1.56322 + 0.507919i) q^{41} +(-1.66155 - 7.14689i) q^{42} +(1.39763 - 1.39763i) q^{43} +(10.7983 - 3.33767i) q^{44} +(3.30059 + 1.99235i) q^{45} +(1.60832 - 1.35376i) q^{46} +(-6.49783 + 4.72095i) q^{47} +(0.834853 - 4.44035i) q^{48} -14.0991 q^{49} +(7.05257 + 0.511135i) q^{50} +(0.969449 + 0.969449i) q^{51} +(-2.22718 + 6.53329i) q^{52} +(0.580891 - 3.66760i) q^{53} +(-7.51867 - 0.646169i) q^{54} +(-9.66353 - 8.14224i) q^{55} +(-11.8930 - 5.22961i) q^{56} +7.66749i q^{57} +(9.53383 - 2.21648i) q^{58} +(-6.12515 - 12.0213i) q^{59} +(-4.68166 + 1.89715i) q^{60} +(-0.782928 + 1.53658i) q^{61} +(2.37840 + 0.589125i) q^{62} +(-2.44730 + 7.53202i) q^{63} +(-5.40758 - 5.89560i) q^{64} +(7.49176 - 1.85172i) q^{65} +(8.76245 + 2.17044i) q^{66} +(0.287696 + 1.81644i) q^{67} +(2.40288 - 0.345230i) q^{68} +(1.65839 - 0.262663i) q^{69} +(2.26512 + 14.3478i) q^{70} +(2.40796 + 3.31427i) q^{71} +(-3.24637 + 3.63902i) q^{72} +(-8.13655 + 2.64373i) q^{73} +(4.85682 + 4.20890i) q^{74} +(4.61309 + 3.25819i) q^{75} +(10.8676 + 8.13711i) q^{76} +(11.7847 - 23.1288i) q^{77} +(-4.21779 + 3.55019i) q^{78} +(-9.12238 + 6.62780i) q^{79} +(-2.27946 + 8.64893i) q^{80} +(-0.691625 - 0.502495i) q^{81} +(2.31857 - 0.165708i) q^{82} +(-0.505003 - 3.18846i) q^{83} +(-5.97795 - 8.48185i) q^{84} +(-1.77643 - 2.05197i) q^{85} +(1.08824 - 2.57472i) q^{86} +(7.43515 + 2.41583i) q^{87} +(12.3754 - 10.1162i) q^{88} +(4.23039 - 1.37454i) q^{89} +(5.38467 + 0.855608i) q^{90} +(7.19704 + 14.1250i) q^{91} +(1.38767 - 2.62928i) q^{92} +(1.38384 + 1.38384i) q^{93} +(-6.00436 + 9.64189i) q^{94} +(1.08963 - 15.1396i) q^{95} +(-1.26731 - 6.26269i) q^{96} +(3.31506 - 2.40853i) q^{97} +(-18.4757 + 7.49770i) q^{98} +(-6.88967 - 6.88967i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 12 q^{8}+O(q^{10}) $ 464 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 + 12 * q^8	$ 464 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 12 q^{8} - 14 q^{10} - 6 q^{11} + 10 q^{12} - 6 q^{13} + 6 q^{14} - 16 q^{15} - 6 q^{16} - 12 q^{17} - 24 q^{18} - 6 q^{19} - 22 q^{20} + 12 q^{21} + 10 q^{22} - 16 q^{24} + 4 q^{26} - 18 q^{27} + 18 q^{28} - 6 q^{29} - 6 q^{30} + 12 q^{31} - 36 q^{32} - 12 q^{33} - 30 q^{34} + 44 q^{35} - 82 q^{36} - 6 q^{37} - 76 q^{38} - 52 q^{40} - 10 q^{42} - 48 q^{43} + 36 q^{44} - 12 q^{45} - 14 q^{46} - 12 q^{47} - 116 q^{48} - 400 q^{49} + 10 q^{50} - 4 q^{51} + 32 q^{52} - 6 q^{53} - 30 q^{54} + 36 q^{56} + 26 q^{58} - 6 q^{59} + 48 q^{60} - 6 q^{61} - 34 q^{62} + 72 q^{63} - 24 q^{64} + 16 q^{65} + 92 q^{66} + 30 q^{67} + 28 q^{68} - 18 q^{69} + 60 q^{70} + 22 q^{72} + 28 q^{74} - 26 q^{75} - 76 q^{76} + 36 q^{77} + 14 q^{78} - 52 q^{79} - 34 q^{80} + 72 q^{81} + 56 q^{82} - 46 q^{83} + 112 q^{84} + 2 q^{85} - 46 q^{86} - 136 q^{88} - 42 q^{90} + 36 q^{91} - 4 q^{93} + 50 q^{94} - 40 q^{95} - 66 q^{96} - 12 q^{97} - 8 q^{98} - 40 q^{99}+O(q^{100}) $ 464 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 + 12 * q^8 - 14 * q^10 - 6 * q^11 + 10 * q^12 - 6 * q^13 + 6 * q^14 - 16 * q^15 - 6 * q^16 - 12 * q^17 - 24 * q^18 - 6 * q^19 - 22 * q^20 + 12 * q^21 + 10 * q^22 - 16 * q^24 + 4 * q^26 - 18 * q^27 + 18 * q^28 - 6 * q^29 - 6 * q^30 + 12 * q^31 - 36 * q^32 - 12 * q^33 - 30 * q^34 + 44 * q^35 - 82 * q^36 - 6 * q^37 - 76 * q^38 - 52 * q^40 - 10 * q^42 - 48 * q^43 + 36 * q^44 - 12 * q^45 - 14 * q^46 - 12 * q^47 - 116 * q^48 - 400 * q^49 + 10 * q^50 - 4 * q^51 + 32 * q^52 - 6 * q^53 - 30 * q^54 + 36 * q^56 + 26 * q^58 - 6 * q^59 + 48 * q^60 - 6 * q^61 - 34 * q^62 + 72 * q^63 - 24 * q^64 + 16 * q^65 + 92 * q^66 + 30 * q^67 + 28 * q^68 - 18 * q^69 + 60 * q^70 + 22 * q^72 + 28 * q^74 - 26 * q^75 - 76 * q^76 + 36 * q^77 + 14 * q^78 - 52 * q^79 - 34 * q^80 + 72 * q^81 + 56 * q^82 - 46 * q^83 + 112 * q^84 + 2 * q^85 - 46 * q^86 - 136 * q^88 - 42 * q^90 + 36 * q^91 - 4 * q^93 + 50 * q^94 - 40 * q^95 - 66 * q^96 - 12 * q^97 - 8 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	1.31042	−	0.531786i	0.926608	−	0.376030i
$2$	1.31042	−	0.531786i	0.926608	−	0.376030i
$3$	1.11563	+	0.176699i	0.644110	+	0.102017i	0.469940	−	0.882699i	$-0.344276\pi$
$3$	1.11563	+	0.176699i	0.644110	+	0.102017i	0.174170	+	0.984716i	$0.444276\pi$
$4$	1.43441	−	1.39373i	0.717204	−	0.696864i
$5$	−2.17773	−	0.507439i	−0.973910	−	0.226934i
$5$	−2.17773	−	0.507439i	−0.973910	−	0.226934i
$6$	1.55591	−	0.361728i	0.635199	−	0.147675i
$7$		−	4.59337i		−	1.73613i	−0.496448	−	0.868066i	$-0.665363\pi$
$7$		−	4.59337i		−	1.73613i	0.496448	−	0.868066i	$-0.334637\pi$
$8$	1.13851	−	2.58917i	0.402525	−	0.915409i
$9$	−1.63976	−	0.532790i	−0.546586	−	0.177597i
$10$	−3.12359	+	0.493127i	−0.987766	+	0.155941i
$11$	5.03525	+	2.56559i	1.51818	+	0.773554i	0.996813	−	0.0797758i	$-0.0254205\pi$
$11$	5.03525	+	2.56559i	1.51818	+	0.773554i	0.521372	+	0.853330i	$0.325420\pi$
$12$	1.84654	−	1.30143i	0.533050	−	0.375690i
$13$	−3.07508	+	1.56683i	−0.852873	+	0.434561i	−0.825055	−	0.565052i	$-0.808856\pi$
$13$	−3.07508	+	1.56683i	−0.852873	+	0.434561i	−0.0278181	+	0.999613i	$0.508856\pi$
$14$	−2.44269	−	6.01926i	−0.652837	−	1.60871i
$15$	−2.33988	−	0.950917i	−0.604154	−	0.245526i
$16$	0.115048	−	3.99835i	0.0287619	−	0.999586i
$17$	0.981966	+	0.713440i	0.238162	+	0.173035i	0.700464	−	0.713688i	$-0.252976\pi$
$17$	0.981966	+	0.713440i	0.238162	+	0.173035i	−0.462302	+	0.886722i	$0.652976\pi$
$18$	−2.43210	+	0.173822i	−0.573252	+	0.0409702i
$19$	1.06190	+	6.70459i	0.243617	+	1.53814i	0.741535	+	0.670915i	$0.234098\pi$
$19$	1.06190	+	6.70459i	0.243617	+	1.53814i	−0.497917	+	0.867225i	$0.665902\pi$
$20$	−3.83098	+	2.30729i	−0.856634	+	0.515925i
$21$	0.811643	−	5.12451i	0.177115	−	1.11826i
$22$	7.96264	+	0.684325i	1.69764	+	0.145899i
$23$	1.41375	−	0.459354i	0.294786	−	0.0957819i	−0.157890	−	0.987457i	$-0.550469\pi$
$23$	1.41375	−	0.459354i	0.294786	−	0.0957819i	0.452677	+	0.891675i	$0.350469\pi$
$24$	1.72766	−	2.68738i	0.352658	−	0.548560i
$25$	4.48501	+	2.21013i	0.897002	+	0.442026i
$26$	−3.19643	+	3.68849i	−0.626871	+	0.723373i
$27$	−4.75450	−	2.42254i	−0.915004	−	0.466218i
$28$	−6.40191	−	6.58877i	−1.20985	−	1.24516i
$29$	6.83601	+	1.08272i	1.26942	+	0.201056i	0.754566	−	0.656225i	$-0.227848\pi$
$29$	6.83601	+	1.08272i	1.26942	+	0.201056i	0.514850	+	0.857280i	$0.327848\pi$
$30$	−3.57191	−	0.00178616i	−0.652139	−	0.000326107i
$31$	1.40171	+	1.01840i	0.251754	+	0.182910i	0.706504	−	0.707709i	$-0.250271\pi$
$31$	1.40171	+	1.01840i	0.251754	+	0.182910i	−0.454750	+	0.890619i	$0.650271\pi$
$32$	−1.97550	−	5.30070i	−0.349223	−	0.937040i
$33$	5.16415	+	3.75197i	0.898962	+	0.653134i
$34$	1.66619	+	0.412711i	0.285749	+	0.0707794i
$35$	−2.33086	+	10.0031i	−0.393987	+	1.69084i
$36$	−3.09464	+	1.52114i	−0.515774	+	0.253523i
$37$	2.06313	+	4.04911i	0.339176	+	0.665670i	0.996095	−	0.0882914i	$-0.0281407\pi$
$37$	2.06313	+	4.04911i	0.339176	+	0.665670i	−0.656919	+	0.753961i	$0.728141\pi$
$38$	4.95695	+	8.22114i	0.804123	+	1.33364i
$39$	−3.70751	+	1.20464i	−0.593677	+	0.192897i
$40$	−3.79322	+	5.06078i	−0.599760	+	0.800180i
$41$	1.56322	+	0.507919i	0.244133	+	0.0793237i	0.428528	−	0.903529i	$-0.359032\pi$
$41$	1.56322	+	0.507919i	0.244133	+	0.0793237i	−0.184395	+	0.982852i	$0.559032\pi$
$42$	−1.66155	−	7.14689i	−0.256383	−	1.10279i
$43$	1.39763	−	1.39763i	0.213137	−	0.213137i	−0.592462	−	0.805598i	$-0.701844\pi$
$43$	1.39763	−	1.39763i	0.213137	−	0.213137i	0.805598	+	0.592462i	$0.201844\pi$
$44$	10.7983	−	3.33767i	1.62791	−	0.503172i
$45$	3.30059	+	1.99235i	0.492023	+	0.297002i
$46$	1.60832	−	1.35376i	0.237134	−	0.199601i
$47$	−6.49783	+	4.72095i	−0.947806	+	0.688621i	−0.950287	−	0.311375i	$-0.899210\pi$
$47$	−6.49783	+	4.72095i	−0.947806	+	0.688621i	0.00248086	+	0.999997i	$0.499210\pi$
$48$	0.834853	−	4.44035i	0.120501	−	0.640909i
$49$	−14.0991			−2.01416
$50$	7.05257	+	0.511135i	0.997384	+	0.0722854i
$51$	0.969449	+	0.969449i	0.135750	+	0.135750i
$52$	−2.22718	+	6.53329i	−0.308854	+	0.906005i
$53$	0.580891	−	3.66760i	0.0797915	−	0.503784i	−0.915132	−	0.403153i	$-0.867914\pi$
$53$	0.580891	−	3.66760i	0.0797915	−	0.503784i	0.994924	−	0.100630i	$-0.0320859\pi$
$54$	−7.51867	−	0.646169i	−1.02316	−	0.0879325i
$55$	−9.66353	−	8.14224i	−1.30303	−	1.09790i
$56$	−11.8930	−	5.22961i	−1.58927	−	0.698837i
$57$			7.66749i			1.01558i
$58$	9.53383	−	2.21648i	1.25185	−	0.291038i
$59$	−6.12515	−	12.0213i	−0.797427	−	1.56504i	−0.824808	−	0.565413i	$-0.808717\pi$
$59$	−6.12515	−	12.0213i	−0.797427	−	1.56504i	0.0273809	−	0.999625i	$-0.491283\pi$
$60$	−4.68166	+	1.89715i	−0.604400	+	0.244921i
$61$	−0.782928	+	1.53658i	−0.100244	+	0.196739i	−0.935682	−	0.352846i	$-0.885214\pi$
$61$	−0.782928	+	1.53658i	−0.100244	+	0.196739i	0.835438	+	0.549585i	$0.185214\pi$
$62$	2.37840	+	0.589125i	0.302057	+	0.0748189i
$63$	−2.44730	+	7.53202i	−0.308331	+	0.948946i
$64$	−5.40758	−	5.89560i	−0.675947	−	0.736950i
$65$	7.49176	−	1.85172i	0.929238	−	0.229677i
$66$	8.76245	+	2.17044i	1.07858	+	0.267163i
$67$	0.287696	+	1.81644i	0.0351477	+	0.221914i	0.999010	−	0.0444873i	$-0.0141654\pi$
$67$	0.287696	+	1.81644i	0.0351477	+	0.221914i	−0.963862	+	0.266401i	$0.914165\pi$
$68$	2.40288	−	0.345230i	0.291392	−	0.0418652i
$69$	1.65839	−	0.262663i	0.199646	−	0.0316209i
$70$	2.26512	+	14.3478i	0.270733	+	1.71489i
$71$	2.40796	+	3.31427i	0.285772	+	0.393332i	0.927635	−	0.373488i	$-0.121838\pi$
$71$	2.40796	+	3.31427i	0.285772	+	0.393332i	−0.641863	+	0.766819i	$0.721838\pi$
$72$	−3.24637	+	3.63902i	−0.382588	+	0.428863i
$73$	−8.13655	+	2.64373i	−0.952312	+	0.309425i	−0.743655	−	0.668564i	$-0.766909\pi$
$73$	−8.13655	+	2.64373i	−0.952312	+	0.309425i	−0.208657	+	0.977989i	$0.566909\pi$
$74$	4.85682	+	4.20890i	0.564594	+	0.489275i
$75$	4.61309	+	3.25819i	0.532674	+	0.376223i
$76$	10.8676	+	8.13711i	1.24660	+	0.933391i
$77$	11.7847	−	23.1288i	1.34299	−	2.63577i
$78$	−4.21779	+	3.55019i	−0.477570	+	0.401980i
$79$	−9.12238	+	6.62780i	−1.02635	+	0.745685i	−0.967574	−	0.252586i	$-0.918719\pi$
$79$	−9.12238	+	6.62780i	−1.02635	+	0.745685i	−0.0587734	+	0.998271i	$0.518719\pi$
$80$	−2.27946	+	8.64893i	−0.254851	+	0.966980i
$81$	−0.691625	−	0.502495i	−0.0768472	−	0.0558328i
$82$	2.31857	−	0.165708i	0.256044	−	0.0182994i
$83$	−0.505003	−	3.18846i	−0.0554313	−	0.349979i	−0.999779	−	0.0210299i	$-0.993305\pi$
$83$	−0.505003	−	3.18846i	−0.0554313	−	0.349979i	0.944348	−	0.328949i	$-0.106695\pi$
$84$	−5.97795	−	8.48185i	−0.652248	−	0.925446i
$85$	−1.77643	−	2.05197i	−0.192681	−	0.222567i
$86$	1.08824	−	2.57472i	0.117348	−	0.277640i
$87$	7.43515	+	2.41583i	0.797132	+	0.259004i
$88$	12.3754	−	10.1162i	1.31923	−	1.07839i
$89$	4.23039	−	1.37454i	0.448421	−	0.145701i	−0.0760967	−	0.997100i	$-0.524246\pi$
$89$	4.23039	−	1.37454i	0.448421	−	0.145701i	0.524517	+	0.851400i	$0.324246\pi$
$90$	5.38467	+	0.855608i	0.567594	+	0.0901890i
$91$	7.19704	+	14.1250i	0.754455	+	1.48070i
$92$	1.38767	−	2.62928i	0.144675	−	0.274121i
$93$	1.38384	+	1.38384i	0.143498	+	0.143498i
$94$	−6.00436	+	9.64189i	−0.619302	+	0.994485i
$95$	1.08963	−	15.1396i	0.111794	−	1.55329i
$96$	−1.26731	−	6.26269i	−0.129344	−	0.639183i
$97$	3.31506	−	2.40853i	0.336593	−	0.244549i	−0.406630	−	0.913593i	$-0.633296\pi$
$97$	3.31506	−	2.40853i	0.336593	−	0.244549i	0.743223	+	0.669044i	$0.233296\pi$
$98$	−18.4757	+	7.49770i	−1.86633	+	0.757382i
$99$	−6.88967	−	6.88967i	−0.692438	−	0.692438i
$100$	9.51365	−	3.08066i	0.951365	−	0.308066i
$101$	3.20647	−	3.20647i	0.319055	−	0.319055i	−0.529349	−	0.848404i	$-0.677564\pi$
$101$	3.20647	−	3.20647i	0.319055	−	0.319055i	0.848404	+	0.529349i	$0.177564\pi$
$102$	1.78593	+	0.754847i	0.176833	+	0.0747410i
$103$	−0.801640	−	1.10336i	−0.0789879	−	0.108718i	0.767695	−	0.640816i	$-0.221404\pi$
$103$	−0.801640	−	1.10336i	−0.0789879	−	0.108718i	−0.846683	+	0.532098i	$0.821404\pi$
$104$	0.555772	+	9.74575i	0.0544979	+	0.955649i
$105$	−4.36792	+	10.7479i	−0.426265	+	1.04889i
$106$	−1.18917	−	5.11501i	−0.115502	−	0.496814i
$107$	−10.4805	+	10.4805i	−1.01319	+	1.01319i	−0.0132739	+	0.999912i	$0.504225\pi$
$107$	−10.4805	+	10.4805i	−1.01319	+	1.01319i	−0.999912	+	0.0132739i	$0.995775\pi$
$108$	−10.1962	+	3.15157i	−0.981134	+	0.303260i
$109$	−7.62146	+	3.88333i	−0.730004	+	0.371955i	−0.779151	−	0.626836i	$-0.784350\pi$
$109$	−7.62146	+	3.88333i	−0.730004	+	0.371955i	0.0491475	+	0.998792i	$0.484350\pi$
$110$	−16.9932	−	5.53083i	−1.62024	−	0.527344i
$111$	1.58621	+	4.88187i	0.150557	+	0.463366i
$112$	−18.3659	−	0.528457i	−1.73541	−	0.0499345i
$113$	4.24003	−	13.0495i	0.398868	−	1.22759i	−0.527040	−	0.849840i	$-0.676698\pi$
$113$	4.24003	−	13.0495i	0.398868	−	1.22759i	0.925908	−	0.377749i	$-0.123302\pi$
$114$	4.07747	+	10.0476i	0.381890	+	0.941048i
$115$	−3.31185	+	0.282959i	−0.308832	+	0.0263860i
$116$	11.3146	−	7.97448i	1.05054	−	0.740412i
$117$	5.87718	−	0.930853i	0.543345	−	0.0860574i
$118$	−14.4193	−	12.4957i	−1.32740	−	1.15032i
$119$	3.27710	−	4.51054i	0.300411	−	0.413480i
$120$	−5.12607	+	4.97571i	−0.467944	+	0.454218i
$121$	12.3059	+	16.9376i	1.11871	+	1.53978i
$122$	−0.208832	+	2.42992i	−0.0189068	+	0.219995i
$123$	1.65422	+	0.842869i	0.149156	+	0.0759989i
$124$	3.42999	−	0.492798i	0.308022	−	0.0442546i
$125$	−8.64563	−	7.08894i	−0.773289	−	0.634054i
$126$	0.798428	+	11.1716i	0.0711296	+	0.995242i
$127$	−0.845418	−	2.60193i	−0.0750187	−	0.230884i	0.906515	−	0.422174i	$-0.138733\pi$
$127$	−0.845418	−	2.60193i	−0.0750187	−	0.230884i	−0.981534	+	0.191290i	$0.938733\pi$
$128$	−10.2214	−	4.85004i	−0.903453	−	0.428687i
$129$	1.80620	−	1.31228i	0.159027	−	0.115540i
$130$	8.83264	−	6.41054i	0.774674	−	0.562242i
$131$	2.99314	+	18.8979i	0.261512	+	1.65112i	0.672954	+	0.739685i	$0.265025\pi$
$131$	2.99314	+	18.8979i	0.261512	+	1.65112i	−0.411442	+	0.911436i	$0.634975\pi$
$132$	12.6367	−	1.81556i	1.09988	−	0.158024i
$133$	30.7967	−	4.87772i	2.67041	−	0.422952i
$134$	1.34296	+	2.22731i	0.116014	+	0.192410i
$135$	9.12472	+	7.68825i	0.785331	+	0.661699i
$136$	2.96520	−	1.73021i	0.254264	−	0.148365i
$137$	−7.85978	−	2.55380i	−0.671507	−	0.218186i	−0.0466336	−	0.998912i	$-0.514849\pi$
$137$	−7.85978	−	2.55380i	−0.671507	−	0.218186i	−0.624873	+	0.780726i	$0.714849\pi$
$138$	2.03350	−	1.22611i	0.173103	−	0.104373i
$139$	8.20111	+	4.17867i	0.695609	+	0.354430i	0.765778	−	0.643105i	$-0.222354\pi$
$139$	8.20111	+	4.17867i	0.695609	+	0.354430i	−0.0701693	+	0.997535i	$0.522354\pi$
$140$	10.5982	+	17.5971i	0.895714	+	1.48723i
$141$	−8.08337	+	4.11868i	−0.680743	+	0.346856i
$142$	4.91793	+	3.06257i	0.412703	+	0.257005i
$143$	−19.5036			−1.63097
$144$	−2.31893	+	6.49502i	−0.193244	+	0.541252i
$145$	−14.3376	−	5.82673i	−1.19067	−	0.483883i
$146$	−9.25642	+	7.79130i	−0.766066	+	0.644813i
$147$	−15.7294	−	2.49129i	−1.29734	−	0.205478i
$148$	8.60272	+	2.93264i	0.707139	+	0.241062i
$149$	2.65506	−	2.65506i	0.217511	−	0.217511i	−0.589938	−	0.807449i	$-0.700848\pi$
$149$	2.65506	−	2.65506i	0.217511	−	0.217511i	0.807449	+	0.589938i	$0.200848\pi$
$150$	7.77775	+	1.81642i	0.635051	+	0.148310i
$151$		−	2.12369i		−	0.172823i	−0.996260	−	0.0864116i	$-0.972460\pi$
$151$		−	2.12369i		−	0.172823i	0.996260	−	0.0864116i	$-0.0275400\pi$
$152$	18.5683	+	4.88382i	1.50609	+	0.396130i
$153$	−1.23007	−	1.69305i	−0.0994456	−	0.136875i
$154$	3.14336	−	36.5754i	0.253299	−	2.94733i
$155$	−2.53577	−	2.92908i	−0.203678	−	0.235270i
$156$	−3.63914	+	6.89521i	−0.291364	+	0.552058i
$157$	6.45088	+	6.45088i	0.514837	+	0.514837i	0.916005	−	0.401168i	$-0.131396\pi$
$157$	6.45088	+	6.45088i	0.514837	+	0.514837i	−0.401168	+	0.916005i	$0.631396\pi$
$158$	−8.42959	+	13.5364i	−0.670622	+	1.07689i
$159$	1.29612	−	3.98905i	0.102789	−	0.316352i
$160$	1.61233	+	12.5459i	0.127466	+	0.991843i
$161$	−2.10998	−	6.49386i	−0.166290	−	0.511788i
$162$	−1.17354	−	0.290683i	−0.0922020	−	0.0228382i
$163$	13.0625	−	6.65568i	1.02313	−	0.521313i	0.139861	−	0.990171i	$-0.455335\pi$
$163$	13.0625	−	6.65568i	1.02313	−	0.521313i	0.883273	+	0.468858i	$0.155335\pi$
$164$	2.95019	−	1.45013i	0.230371	−	0.113236i
$165$	−9.34222	−	10.7913i	−0.727291	−	0.840099i
$166$	−2.35735	−	3.90968i	−0.182966	−	0.303450i
$167$	−0.799638	+	1.10061i	−0.0618779	+	0.0851676i	−0.838834	−	0.544387i	$-0.816762\pi$
$167$	−0.799638	+	1.10061i	−0.0618779	+	0.0851676i	0.776957	+	0.629554i	$0.216762\pi$
$168$	−12.3442	−	7.93580i	−0.952373	−	0.612261i
$169$	−0.640062	+	0.880970i	−0.0492355	+	0.0677669i
$170$	−3.41908	−	1.74426i	−0.262231	−	0.133779i
$171$	1.83087	−	11.5597i	0.140010	−	0.883991i
$172$	0.0568552	−	3.95269i	0.00433516	−	0.301390i
$173$	9.89103	−	19.4122i	0.752001	−	1.47589i	−0.123332	−	0.992365i	$-0.539358\pi$
$173$	9.89103	−	19.4122i	0.752001	−	1.47589i	0.875333	−	0.483520i	$-0.160642\pi$
$174$	11.0279	−	0.788159i	0.836022	−	0.0597502i
$175$	10.1520	−	20.6013i	0.767416	−	1.55731i
$176$	10.8374	−	19.8375i	0.816900	−	1.49531i
$177$	−4.70927	−	14.4936i	−0.353970	−	1.08941i
$178$	4.81264	−	4.05089i	0.360722	−	0.303627i
$179$	−7.50302	−	1.18836i	−0.560802	−	0.0888224i	−0.130403	−	0.991461i	$-0.541627\pi$
$179$	−7.50302	−	1.18836i	−0.560802	−	0.0888224i	−0.430399	+	0.902639i	$0.641627\pi$
$180$	7.51118	−	1.74228i	0.559851	−	0.129862i
$181$	−16.3740	+	2.59339i	−1.21707	+	0.192765i	−0.731751	−	0.681572i	$-0.761297\pi$
$181$	−16.3740	+	2.59339i	−1.21707	+	0.192765i	−0.485319	+	0.874337i	$0.661297\pi$
$182$	16.9426	+	14.6824i	1.25587	+	1.08833i
$183$	−1.14497	+	1.57592i	−0.0846387	+	0.116495i
$184$	0.420223	−	4.18340i	0.0309793	−	0.308405i
$185$	−2.43825	−	9.86478i	−0.179264	−	0.725273i
$186$	2.54932	+	1.07751i	0.186925	+	0.0790066i
$187$	3.11405	+	6.11167i	0.227722	+	0.446930i
$188$	−2.74082	+	15.8280i	−0.199895	+	1.15437i
$189$	−11.1276	+	21.8392i	−0.809416	+	1.58857i
$190$	−6.62317	−	20.4188i	−0.480495	−	1.48133i
$191$	−5.14159	+	15.8242i	−0.372033	+	1.14500i	0.573426	+	0.819257i	$0.305614\pi$
$191$	−5.14159	+	15.8242i	−0.372033	+	1.14500i	−0.945459	+	0.325741i	$0.894386\pi$
$192$	−4.99112	−	7.53283i	−0.360203	−	0.543635i
$193$	10.7726			0.775428			0.387714	−	0.921780i	$-0.373265\pi$
$193$	10.7726			0.775428			0.387714	+	0.921780i	$0.373265\pi$
$194$	3.06330	−	4.91909i	0.219932	−	0.353170i
$195$	8.68524	−	0.742051i	0.621963	−	0.0531394i
$196$	−20.2238	+	19.6503i	−1.44456	+	1.40359i
$197$	0.357446	−	2.25683i	0.0254670	−	0.160792i	−0.971677	−	0.236312i	$-0.924061\pi$
$197$	0.357446	−	2.25683i	0.0254670	−	0.160792i	0.997144	+	0.0755192i	$0.0240614\pi$
$198$	−12.6922	−	5.36454i	−0.901996	−	0.381241i
$199$		−	4.42641i		−	0.313780i	−0.987616	−	0.156890i	$-0.949853\pi$
$199$		−	4.42641i		−	0.313780i	0.987616	−	0.156890i	$-0.0501468\pi$
$200$	10.8286	−	9.09618i	0.765700	−	0.643197i
$201$			2.07732i			0.146523i
$202$	2.49667	−	5.90698i	0.175665	−	0.415614i
$203$	4.97333	−	31.4004i	0.349059	−	2.20387i
$204$	2.74173	+	0.0394369i	0.191960	+	0.00276113i
$205$	−3.14652	−	1.89935i	−0.219763	−	0.132656i
$206$	−1.63724	−	1.01957i	−0.114072	−	0.0710367i
$207$	−2.56294			−0.178137
$208$	5.91095	+	12.4755i	0.409851	+	0.865019i
$209$	−11.8543	+	36.4837i	−0.819977	+	2.52363i
$210$	−0.00820452	+	16.4071i	−0.000566166	+	1.13220i
$211$	−0.0937456	+	0.183986i	−0.00645372	+	0.0126661i	−0.894211	−	0.447646i	$-0.852262\pi$
$211$	−0.0937456	+	0.183986i	−0.00645372	+	0.0126661i	0.887757	+	0.460312i	$0.152262\pi$
$212$	−4.27840	−	6.07044i	−0.293842	−	0.416919i
$213$	2.10077	+	4.12299i	0.143942	+	0.282503i
$214$	−8.16047	+	19.3072i	−0.557838	+	1.31981i
$215$	−3.75287	+	2.33445i	−0.255944	+	0.159208i
$216$	−11.6854	+	9.55211i	−0.795092	+	0.649939i
$217$	4.67790	−	6.43857i	0.317556	−	0.437079i
$218$	−7.92222	+	9.14178i	−0.536561	+	0.619160i
$219$	−9.54454	+	1.51171i	−0.644960	+	0.102152i
$220$	−25.2095	+	1.78904i	−1.69962	+	0.120617i
$221$	−4.13746	−	0.655310i	−0.278316	−	0.0440809i
$222$	4.67472	+	5.55378i	0.313747	+	0.372745i
$223$	−1.19353	−	3.67330i	−0.0799245	−	0.245982i	0.903108	−	0.429413i	$-0.141280\pi$
$223$	−1.19353	−	3.67330i	−0.0799245	−	0.245982i	−0.983033	+	0.183431i	$0.941280\pi$
$224$	−24.3481	+	9.07423i	−1.62683	+	0.606297i
$225$	−6.17680	−	6.01365i	−0.411787	−	0.400910i
$226$	−1.38330	−	19.3551i	−0.0920158	−	1.28748i
$227$	9.04448	−	17.7508i	0.600303	−	1.17816i	−0.368337	−	0.929692i	$-0.620073\pi$
$227$	9.04448	−	17.7508i	0.600303	−	1.17816i	0.968640	−	0.248468i	$-0.0799272\pi$
$228$	10.6864	+	10.9983i	0.707724	+	0.728381i
$229$	−4.40261	+	27.7970i	−0.290933	+	1.83688i	0.217849	+	0.975982i	$0.430096\pi$
$229$	−4.40261	+	27.7970i	−0.290933	+	1.83688i	−0.508782	+	0.860895i	$0.669904\pi$
$230$	−4.18944	+	2.13199i	−0.276244	+	0.140579i
$231$	17.2342	−	23.7209i	1.13393	−	1.56072i
$232$	10.5862	−	16.4669i	0.695020	−	1.08110i
$233$	−4.63428	+	6.37854i	−0.303602	+	0.417872i	−0.933373	−	0.358909i	$-0.883149\pi$
$233$	−4.63428	+	6.37854i	−0.303602	+	0.417872i	0.629771	+	0.776781i	$0.283149\pi$
$234$	7.20656	−	4.34521i	0.471108	−	0.284055i
$235$	16.5461	−	6.98370i	1.07935	−	0.455566i
$236$	−25.5404	−	8.70663i	−1.66254	−	0.566753i
$237$	−11.3483	+	5.78227i	−0.737154	+	0.375599i
$238$	1.89574	−	7.65342i	0.122882	−	0.496098i
$239$	−7.20617	−	22.1783i	−0.466128	−	1.43460i	−0.857558	−	0.514387i	$-0.828019\pi$
$239$	−7.20617	−	22.1783i	−0.466128	−	1.43460i	0.391430	−	0.920208i	$-0.371981\pi$
$240$	−4.07129	+	9.24625i	−0.262801	+	0.596843i
$241$	3.87064	−	11.9126i	0.249330	−	0.767358i	−0.745564	−	0.666434i	$-0.767820\pi$
$241$	3.87064	−	11.9126i	0.249330	−	0.767358i	0.994894	−	0.100924i	$-0.0321800\pi$
$242$	25.1330	+	15.6512i	1.61561	+	1.00610i
$243$	10.6368	+	10.6368i	0.682349	+	0.682349i
$244$	1.01854	+	3.29527i	0.0652053	+	0.210958i
$245$	30.7040	+	7.15443i	1.96161	+	0.457080i
$246$	2.61596	+	0.224820i	0.166787	+	0.0143340i
$247$	−13.7704	−	18.9533i	−0.876189	−	1.20597i
$248$	4.23267	−	2.46980i	0.268775	−	0.156832i
$249$		−	3.64638i		−	0.231080i
$250$	−15.0992	−	4.69186i	−0.954958	−	0.296739i
$251$	11.7462	−	11.7462i	0.741411	−	0.741411i	−0.231439	−	0.972850i	$-0.574343\pi$
$251$	11.7462	−	11.7462i	0.741411	−	0.741411i	0.972850	+	0.231439i	$0.0743432\pi$
$252$	6.98716	+	14.2149i	0.440150	+	0.895452i
$253$	8.29707	+	1.31413i	0.521633	+	0.0826185i
$254$	−2.49152	−	2.96004i	−0.156332	−	0.185729i
$255$	−1.61926	−	2.60313i	−0.101402	−	0.163014i
$256$	−15.9735	−	0.920000i	−0.998346	−	0.0575000i
$257$	−8.75293			−0.545993			−0.272996	−	0.962015i	$-0.588015\pi$
$257$	−8.75293			−0.545993			−0.272996	+	0.962015i	$0.588015\pi$
$258$	1.66903	−	2.68015i	0.103909	−	0.166859i
$259$	18.5991	−	9.47671i	1.15569	−	0.588854i
$260$	8.16544	−	13.0976i	0.506399	−	0.812278i
$261$	−10.6325	−	5.41755i	−0.658138	−	0.335338i
$262$	13.9719	+	23.1725i	0.863189	+	1.43160i
$263$	−12.8025	−	4.15978i	−0.789434	−	0.256503i	−0.113571	−	0.993530i	$-0.536229\pi$
$263$	−12.8025	−	4.15978i	−0.789434	−	0.256503i	−0.675863	+	0.737027i	$0.736229\pi$
$264$	15.5939	−	9.09917i	0.959740	−	0.560015i
$265$	−3.12611	+	7.69227i	−0.192035	+	0.472533i
$266$	37.7628	−	22.7691i	2.31538	−	1.39606i
$267$	4.96244	−	0.785973i	0.303696	−	0.0481008i
$268$	2.94430	+	2.20455i	0.179852	+	0.134664i
$269$	−1.67976	−	10.6056i	−0.102417	−	0.646635i	−0.984479	−	0.175502i	$-0.943845\pi$
$269$	−1.67976	−	10.6056i	−0.102417	−	0.646635i	0.882062	−	0.471133i	$-0.156155\pi$
$270$	16.0457	+	5.22245i	0.976512	+	0.317828i
$271$	−23.2370	+	16.8827i	−1.41155	+	1.02555i	−0.418454	+	0.908238i	$0.637428\pi$
$271$	−23.2370	+	16.8827i	−1.41155	+	1.02555i	−0.993095	+	0.117313i	$0.962572\pi$
$272$	2.96555	−	3.84416i	0.179813	−	0.233086i
$273$	5.53338	+	17.0300i	0.334895	+	1.03070i
$274$	−11.6577	+	0.833172i	−0.704268	+	0.0503338i
$275$	16.9129	+	22.6352i	1.01988	+	1.36496i
$276$	2.01272	−	2.68810i	0.121152	−	0.161805i
$277$	−11.1668	−	5.68976i	−0.670947	−	0.341865i	0.0851087	−	0.996372i	$-0.472876\pi$
$277$	−11.1668	−	5.68976i	−0.670947	−	0.341865i	−0.756056	+	0.654507i	$0.772876\pi$
$278$	12.9691	+	1.11459i	0.777833	+	0.0668485i
$279$	−1.75587	−	2.41675i	−0.105121	−	0.144687i
$280$	23.2461	+	17.4237i	1.38922	+	1.04126i
$281$	13.4969	−	18.5769i	0.805157	−	1.10820i	−0.186895	−	0.982380i	$-0.559842\pi$
$281$	13.4969	−	18.5769i	0.805157	−	1.10820i	0.992053	−	0.125824i	$-0.0401575\pi$
$282$	−8.40236	+	9.69583i	−0.500353	+	0.577378i
$283$	−27.7370	+	4.39310i	−1.64879	+	0.261143i	−0.910551	−	0.413396i	$-0.864343\pi$
$283$	−27.7370	+	4.39310i	−1.64879	+	0.261143i	−0.738240	+	0.674539i	$0.764343\pi$
$284$	8.07319	+	1.39798i	0.479056	+	0.0829546i
$285$	3.89079	−	16.6977i	0.230470	−	0.989088i
$286$	−25.5580	+	10.3718i	−1.51127	+	0.613295i
$287$	2.33306	−	7.18043i	0.137716	−	0.423848i
$288$	0.415191	+	9.74439i	0.0244654	+	0.574194i
$289$	−4.79803	−	14.7668i	−0.282237	−	0.868636i
$290$	−21.8868	−	0.0109447i	−1.28524	−	0.000642694i
$291$	4.12397	−	2.10127i	0.241751	−	0.123178i
$292$	−7.98650	+	15.1323i	−0.467374	+	0.885552i
$293$	16.6210	−	16.6210i	0.971009	−	0.971009i	−0.0285825	−	0.999591i	$-0.509099\pi$
$293$	16.6210	−	16.6210i	0.971009	−	0.971009i	0.999591	+	0.0285825i	$0.00909933\pi$
$294$	−21.9370	+	5.10003i	−1.27939	+	0.297440i
$295$	7.23885	+	29.2873i	0.421462	+	1.70517i
$296$	12.8327	−	0.731813i	0.745887	−	0.0425358i
$297$	−17.7249	−	24.3962i	−1.02850	−	1.41561i
$298$	2.06732	−	4.89116i	0.119757	−	0.283338i
$299$	−3.62765	+	3.62765i	−0.209792	+	0.209792i
$300$	11.1581	−	1.75583i	0.644212	−	0.101373i
$301$	−6.41984	−	6.41984i	−0.370033	−	0.370033i
$302$	−1.12935	−	2.78292i	−0.0649866	−	0.160139i
$303$	4.14381	−	3.01066i	0.238056	−	0.172958i
$304$	26.9294	−	3.47451i	1.54451	−	0.199277i
$305$	2.48473	−	2.94897i	0.142275	−	0.168858i
$306$	−2.51226	−	1.56447i	−0.143616	−	0.0894350i
$307$	21.1597	+	21.1597i	1.20765	+	1.20765i	0.971787	+	0.235860i	$0.0757905\pi$
$307$	21.1597	+	21.1597i	1.20765	+	1.20765i	0.235860	+	0.971787i	$0.424209\pi$
$308$	−15.3312	−	49.6008i	−0.873574	−	2.82627i
$309$	−0.699372	−	1.37259i	−0.0397859	−	0.0780842i
$310$	−4.88057	−	2.48985i	−0.277198	−	0.141414i
$311$	−0.893948	+	0.290461i	−0.0506911	+	0.0164705i	−0.334253	−	0.942483i	$-0.608484\pi$
$311$	−0.893948	+	0.290461i	−0.0506911	+	0.0164705i	0.283562	+	0.958954i	$0.408484\pi$
$312$	−1.10202	+	10.9709i	−0.0623898	+	0.621103i
$313$	−1.52495	−	0.495486i	−0.0861953	−	0.0280065i	0.265602	−	0.964083i	$-0.414429\pi$
$313$	−1.52495	−	0.495486i	−0.0861953	−	0.0280065i	−0.351797	+	0.936076i	$0.614429\pi$
$314$	11.8839	+	5.02288i	0.670645	+	0.283458i
$315$	9.15161	−	15.1609i	0.515635	−	0.854217i
$316$	−3.84786	+	22.2211i	−0.216459	+	1.25003i
$317$	4.59779	+	29.0293i	0.258238	+	1.63045i	0.686737	+	0.726906i	$0.259042\pi$
$317$	4.59779	+	29.0293i	0.258238	+	1.63045i	−0.428499	+	0.903542i	$0.640958\pi$
$318$	−0.422857	−	5.91659i	−0.0237126	−	0.331786i
$319$	31.6432	+	22.9901i	1.77168	+	1.28720i
$320$	8.78458	+	15.5830i	0.491073	+	0.871118i
$321$	−13.5442	+	9.84046i	−0.755965	+	0.549241i
$322$	−6.21831	−	7.38764i	−0.346533	−	0.411697i
$323$	−3.74057	+	7.34129i	−0.208131	+	0.408480i
$324$	−1.69241	+	0.243154i	−0.0940229	+	0.0135086i
$325$	−17.2547	+	0.230930i	−0.957116	+	0.0128097i
$326$	13.5780	−	15.6682i	0.752015	−	0.867781i
$327$	−9.18892	+	2.98566i	−0.508149	+	0.165107i
$328$	3.09483	−	3.46915i	0.170883	−	0.191552i
$329$	21.6851	+	29.8470i	1.19554	+	1.64552i
$330$	−17.9809	−	9.17305i	−0.989815	−	0.504960i
$331$	−16.0495	+	2.54199i	−0.882161	+	0.139721i	−0.581050	−	0.813868i	$-0.697358\pi$
$331$	−16.0495	+	2.54199i	−0.882161	+	0.139721i	−0.301112	+	0.953589i	$0.597358\pi$
$332$	−5.16823	−	3.86972i	−0.283643	−	0.212378i
$333$	−1.22570	−	7.73878i	−0.0671680	−	0.424082i
$334$	−0.462575	+	1.86750i	−0.0253110	+	0.102185i
$335$	0.295209	−	4.10171i	0.0161290	−	0.224100i
$336$	−20.3962	−	3.83479i	−1.11270	−	0.209205i
$337$	−0.545359	+	1.67844i	−0.0297076	+	0.0914305i	−0.964811	−	0.262945i	$-0.915306\pi$
$337$	−0.545359	+	1.67844i	−0.0297076	+	0.0914305i	0.935103	+	0.354375i	$0.115306\pi$
$338$	−0.370263	+	1.49482i	−0.0201397	+	0.0813074i
$339$	7.03613	−	13.8092i	0.382150	−	0.750012i
$340$	−5.40801	−	0.467499i	−0.293290	−	0.0253537i
$341$	4.44515	+	8.72411i	0.240719	+	0.472437i
$342$	−3.74806	−	16.1217i	−0.202672	−	0.871761i
$343$			32.6088i			1.76071i
$344$	−2.02748	−	5.20992i	−0.109314	−	0.280900i
$345$	−3.74480	−	0.269522i	−0.201613	−	0.0145106i
$346$	2.63826	−	30.6981i	0.141834	−	1.65034i
$347$	−4.84855	+	30.6126i	−0.260284	+	1.64337i	0.417912	+	0.908487i	$0.362762\pi$
$347$	−4.84855	+	30.6126i	−0.260284	+	1.64337i	−0.678196	+	0.734881i	$0.737238\pi$
$348$	14.0320	−	6.89730i	0.752197	−	0.369734i
$349$	−0.0652599	−	0.0652599i	−0.00349328	−	0.00349328i	0.705358	−	0.708851i	$-0.250786\pi$
$349$	−0.0652599	−	0.0652599i	−0.00349328	−	0.00349328i	−0.708851	+	0.705358i	$0.750786\pi$
$350$	2.34783	−	32.3951i	0.125497	−	1.73159i
$351$	18.4162			0.982982
$352$	3.65225	−	31.7587i	0.194666	−	1.69274i
$353$	−22.5667	+	16.3957i	−1.20111	+	0.872655i	−0.994393	−	0.105746i	$-0.966277\pi$
$353$	−22.5667	+	16.3957i	−1.20111	+	0.872655i	−0.206714	+	0.978401i	$0.566277\pi$
$354$	−13.8786	−	16.4884i	−0.737641	−	0.876351i
$355$	−3.56209	−	8.43948i	−0.189056	−	0.447921i
$356$	4.15237	−	7.86766i	0.220075	−	0.416985i
$357$	4.45304	−	4.45304i	0.235680	−	0.235680i
$358$	−10.4641	+	2.43275i	−0.553044	+	0.128575i
$359$	15.4610	+	5.02357i	0.815998	+	0.265134i	0.687136	−	0.726529i	$-0.258868\pi$
$359$	15.4610	+	5.02357i	0.815998	+	0.265134i	0.128862	+	0.991663i	$0.458868\pi$
$360$	8.91629	−	6.27747i	0.469930	−	0.330852i
$361$	−25.7539	+	8.36794i	−1.35547	+	0.440418i
$362$	−20.0777	+	12.1059i	−1.05526	+	0.636272i
$363$	10.7360	+	21.0705i	0.563492	+	1.10591i
$364$	30.0099	+	10.2303i	1.57294	+	0.536212i
$365$	19.0607	−	1.62852i	0.997685	−	0.0852404i
$366$	−0.662343	+	2.67399i	−0.0346212	+	0.139772i
$367$	−16.4040	−	11.9182i	−0.856280	−	0.622124i	0.0705904	−	0.997505i	$-0.477512\pi$
$367$	−16.4040	−	11.9182i	−0.856280	−	0.622124i	−0.926870	+	0.375382i	$0.877512\pi$
$368$	−1.67401	−	5.70549i	−0.0872637	−	0.297419i
$369$	−2.29268	−	1.66573i	−0.119352	−	0.0867144i
$370$	−8.44109	−	11.6304i	−0.438831	−	0.604635i
$371$	−16.8467	−	2.66825i	−0.874635	−	0.138529i
$372$	3.91369	+	0.0562942i	0.202915	+	0.00291872i
$373$	−5.46962	−	2.78691i	−0.283206	−	0.144301i	0.306617	−	0.951833i	$-0.400803\pi$
$373$	−5.46962	−	2.78691i	−0.283206	−	0.144301i	−0.589824	+	0.807532i	$0.700803\pi$
$374$	7.33082	+	6.35285i	0.379068	+	0.328498i
$375$	−8.39274	−	9.43631i	−0.433399	−	0.487289i
$376$	4.82547	+	22.1988i	0.248855	+	1.14482i
$377$	−22.7177	+	7.38143i	−1.17002	+	0.380163i
$378$	−2.96810	+	34.5361i	−0.152662	+	1.77634i
$379$	−4.69558	+	29.6467i	−0.241196	+	1.52285i	0.508498	+	0.861063i	$0.330201\pi$
$379$	−4.69558	+	29.6467i	−0.241196	+	1.52285i	−0.749693	+	0.661786i	$0.769799\pi$
$380$	−19.5376	−	23.2351i	−1.00226	−	1.19193i
$381$	−0.483417	−	3.05218i	−0.0247662	−	0.156368i
$382$	1.67743	+	23.4706i	0.0858250	+	1.20086i
$383$	−6.11802	−	4.44500i	−0.312616	−	0.227129i	0.420402	−	0.907338i	$-0.361889\pi$
$383$	−6.11802	−	4.44500i	−0.312616	−	0.227129i	−0.733018	+	0.680209i	$0.761889\pi$
$384$	−10.5463	−	7.21697i	−0.538190	−	0.368289i
$385$	−37.4003	+	44.3882i	−1.90610	+	2.26223i
$386$	14.1166	−	5.72872i	0.718518	−	0.291584i
$387$	−3.03642	+	1.54713i	−0.154350	+	0.0786452i
$388$	1.39831	−	8.07510i	0.0709883	−	0.409951i
$389$	10.5423	+	5.37155i	0.534514	+	0.272348i	0.700343	−	0.713806i	$-0.253030\pi$
$389$	10.5423	+	5.37155i	0.534514	+	0.272348i	−0.165830	+	0.986154i	$0.553030\pi$
$390$	10.9867	−	5.59109i	0.556334	−	0.283116i
$391$	1.71597	+	0.557553i	0.0867804	+	0.0281967i
$392$	−16.0520	+	36.5049i	−0.810748	+	1.84378i
$393$			21.6120i			1.09018i
$394$	−0.731744	−	3.14748i	−0.0368647	−	0.158568i
$395$	23.2293	−	9.80450i	1.16879	−	0.493318i
$396$	−19.4849	−	0.280270i	−0.979154	−	0.0140841i
$397$	18.3636	+	2.90851i	0.921642	+	0.145974i	0.599185	−	0.800610i	$-0.295491\pi$
$397$	18.3636	+	2.90851i	0.921642	+	0.145974i	0.322457	+	0.946584i	$0.395491\pi$
$398$	−2.35390	−	5.80046i	−0.117990	−	0.290751i
$399$	35.2197			1.76319
$400$	9.35285	−	17.6784i	0.467643	−	0.883918i
$401$	24.5425			1.22559			0.612797	−	0.790241i	$-0.290044\pi$
$401$	24.5425			1.22559			0.612797	+	0.790241i	$0.290044\pi$
$402$	1.10469	+	2.72216i	0.0550968	+	0.135769i
$403$	−5.90602	−	0.935422i	−0.294200	−	0.0465967i
$404$	0.130438	−	9.06832i	0.00648954	−	0.451166i
$405$	1.25119	+	1.44526i	0.0621720	+	0.0718153i
$406$	−10.1811	−	43.7924i	−0.505281	−	2.17338i
$407$			25.6814i			1.27298i
$408$	3.61379	−	1.40634i	0.178909	−	0.0696240i
$409$	−9.63674	−	3.13117i	−0.476506	−	0.154826i	0.0609103	−	0.998143i	$-0.480600\pi$
$409$	−9.63674	−	3.13117i	−0.476506	−	0.154826i	−0.537416	+	0.843317i	$0.680600\pi$
$410$	−5.13331	−	0.815669i	−0.253516	−	0.0402830i
$411$	−8.31737	−	4.23791i	−0.410266	−	0.209041i
$412$	−2.68766	−	0.465404i	−0.132412	−	0.0229288i
$413$	−55.2183	+	28.1351i	−2.71711	+	1.38444i
$414$	−3.35853	+	1.36294i	−0.165063	+	0.0669847i
$415$	−0.518191	+	7.19987i	−0.0254370	+	0.353428i
$416$	14.3801	+	13.2048i	0.705043	+	0.647417i
$417$	8.41105	+	6.11099i	0.411891	+	0.299256i
$418$	3.86743	+	54.1130i	0.189162	+	2.64675i
$419$	−1.05419	−	6.65591i	−0.0515007	−	0.325162i	−0.999966	−	0.00828067i	$-0.997364\pi$
$419$	−1.05419	−	6.65591i	−0.0515007	−	0.325162i	0.948465	−	0.316882i	$-0.102636\pi$
$420$	8.71433	+	21.5046i	0.425216	+	1.04932i
$421$	2.30454	−	14.5503i	0.112316	−	0.709137i	−0.865693	−	0.500575i	$-0.833122\pi$
$421$	2.30454	−	14.5503i	0.112316	−	0.709137i	0.978009	−	0.208561i	$-0.0668781\pi$
$422$	−0.0250050	+	0.290952i	−0.00121722	+	0.0141633i
$423$	13.1701	−	4.27924i	0.640354	−	0.208064i
$424$	−8.83468	−	5.67963i	−0.429050	−	0.275827i
$425$	2.82733	+	5.37006i	0.137146	+	0.260486i
$426$	4.94544	+	4.28569i	0.239607	+	0.207643i
$427$	7.05810	+	3.59628i	0.341565	+	0.174036i
$428$	−0.426342	+	29.6402i	−0.0206080	+	1.43271i
$429$	−21.7589	−	3.44626i	−1.05053	−	0.166387i
$430$	−3.67642	+	5.05484i	−0.177293	+	0.243766i
$431$	0.0294902	+	0.0214259i	0.00142049	+	0.00103205i	0.588495	−	0.808501i	$-0.299721\pi$
$431$	0.0294902	+	0.0214259i	0.00142049	+	0.00103205i	−0.587075	+	0.809533i	$0.699721\pi$
$432$	−10.2331	+	18.7314i	−0.492342	+	0.901216i
$433$	30.6121	+	22.2410i	1.47112	+	1.06883i	0.980287	+	0.197581i	$0.0633086\pi$
$433$	30.6121	+	22.2410i	1.47112	+	1.06883i	0.490836	+	0.871252i	$0.336691\pi$
$434$	2.70607	−	10.9249i	0.129896	−	0.524411i
$435$	−14.9659	−	9.03391i	−0.717558	−	0.433143i
$436$	−5.51998	+	16.1925i	−0.264359	+	0.775481i
$437$	4.58104	+	8.99080i	0.219141	+	0.430088i
$438$	−11.7035	+	7.05663i	−0.559213	+	0.337179i
$439$	−18.1160	+	5.88624i	−0.864629	+	0.280935i	−0.707561	−	0.706653i	$-0.750204\pi$
$439$	−18.1160	+	5.88624i	−0.864629	+	0.280935i	−0.157069	+	0.987588i	$0.550204\pi$
$440$	−32.0837	+	15.7505i	−1.52953	+	0.750874i
$441$	23.1191	+	7.51185i	1.10091	+	0.357707i
$442$	−5.77030	+	1.34151i	−0.274465	+	0.0638093i
$443$	14.7856	−	14.7856i	0.702487	−	0.702487i	−0.262457	−	0.964944i	$-0.584533\pi$
$443$	14.7856	−	14.7856i	0.702487	−	0.702487i	0.964944	+	0.262457i	$0.0845327\pi$
$444$	9.07927	+	4.79183i	0.430883	+	0.227410i
$445$	−9.91015	+	0.846705i	−0.469786	+	0.0401377i
$446$	−3.51743	−	4.17887i	−0.166555	−	0.197875i
$447$	3.43121	−	2.49292i	0.162291	−	0.117911i
$448$	−27.0807	+	24.8390i	−1.27944	+	1.17353i
$449$	29.5798			1.39596			0.697978	−	0.716119i	$-0.254083\pi$
$449$	29.5798			1.39596			0.697978	+	0.716119i	$0.254083\pi$
$450$	−11.2922	−	4.59567i	−0.532319	−	0.216642i
$451$	6.56807	+	6.56807i	0.309278	+	0.309278i
$452$	−12.1055	−	24.6277i	−0.569393	−	1.15839i
$453$	0.375253	−	2.36925i	0.0176309	−	0.111317i
$454$	2.41245	−	28.0707i	0.113222	−	1.31742i
$455$	−8.50564	−	34.4125i	−0.398750	−	1.61328i
$456$	19.8524	+	8.72954i	0.929675	+	0.408798i
$457$		−	27.2348i		−	1.27399i	−0.770867	−	0.636996i	$-0.780177\pi$
$457$		−	27.2348i		−	1.27399i	0.770867	−	0.636996i	$-0.219823\pi$
$458$	9.01278	+	38.7670i	0.421140	+	1.81146i
$459$	−2.94042	−	5.77090i	−0.137247	−	0.269363i
$460$	−4.35617	+	5.02169i	−0.203108	+	0.234138i
$461$	−16.1284	+	31.6538i	−0.751176	+	1.47427i	0.124940	+	0.992164i	$0.460126\pi$
$461$	−16.1284	+	31.6538i	−0.751176	+	1.47427i	−0.876116	+	0.482101i	$0.839874\pi$
$462$	9.96965	−	40.2492i	0.463830	−	1.87256i
$463$	6.40316	−	19.7069i	0.297580	−	0.915857i	−0.684763	−	0.728766i	$-0.740094\pi$
$463$	6.40316	−	19.7069i	0.297580	−	0.915857i	0.982343	−	0.187091i	$-0.0599059\pi$
$464$	5.11555	−	27.2082i	0.237483	−	1.26311i
$465$	−2.31141	−	3.71584i	−0.107189	−	0.172318i
$466$	−2.68084	+	10.8230i	−0.124188	+	0.501367i
$467$	−2.73493	−	17.2677i	−0.126557	−	0.799052i	−0.966555	−	0.256461i	$-0.917443\pi$
$467$	−2.73493	−	17.2677i	−0.126557	−	0.799052i	0.839997	−	0.542591i	$-0.182557\pi$
$468$	7.13291	−	9.52640i	0.329719	−	0.440358i
$469$	8.34360	−	1.32150i	0.385272	−	0.0610210i
$470$	17.9685	−	17.9506i	0.828827	−	0.827999i
$471$	6.05695	+	8.33667i	0.279089	+	0.384134i
$472$	−38.0987	+	2.17266i	−1.75363	+	0.100005i
$473$	10.6232	−	3.45167i	0.488453	−	0.158708i
$474$	−11.7962	+	13.6121i	−0.541816	+	0.625224i
$475$	−10.0554	+	32.4171i	−0.461372	+	1.48740i
$476$	−1.58577	−	11.0373i	−0.0726836	−	0.505895i
$477$	−2.90658	+	5.70449i	−0.133083	+	0.261190i
$478$	−21.2372	−	25.2308i	−0.971368	−	1.15403i
$479$	20.4306	−	14.8437i	0.933499	−	0.678227i	−0.0133477	−	0.999911i	$-0.504249\pi$
$479$	20.4306	−	14.8437i	0.933499	−	0.678227i	0.946847	+	0.321684i	$0.104249\pi$
$480$	−0.418082	+	14.2815i	−0.0190827	+	0.651860i
$481$	−12.6885	−	9.21876i	−0.578548	−	0.420339i
$482$	−1.26279	−	17.6689i	−0.0575184	−	0.804795i
$483$	−1.20651	−	7.61759i	−0.0548980	−	0.346612i
$484$	41.2579	+	7.14434i	1.87536	+	0.324743i
$485$	−8.44148	+	3.56294i	−0.383308	+	0.161785i
$486$	19.5951	+	8.28216i	0.888853	+	0.375686i
$487$	−8.12154	−	2.63885i	−0.368022	−	0.119578i	0.119167	−	0.992874i	$-0.461978\pi$
$487$	−8.12154	−	2.63885i	−0.368022	−	0.119578i	−0.487189	+	0.873297i	$0.661978\pi$
$488$	3.08709	+	3.77655i	0.139746	+	0.170956i
$489$	15.7490	−	5.11716i	0.712194	−	0.231406i
$490$	44.0398	−	6.95265i	1.98952	−	0.314089i
$491$	−6.85077	−	13.4454i	−0.309171	−	0.606782i	0.683177	−	0.730252i	$-0.260598\pi$
$491$	−6.85077	−	13.4454i	−0.309171	−	0.606782i	−0.992348	+	0.123471i	$0.960598\pi$
$492$	3.54756	−	1.09652i	0.159936	−	0.0494349i
$493$	5.94028	+	5.94028i	0.267537	+	0.267537i
$494$	−28.1241	−	17.5139i	−1.26536	−	0.787989i
$495$	11.5078	+	18.4999i	0.517235	+	0.831510i
$496$	4.23318	−	5.48735i	0.190075	−	0.246389i
$497$	15.2237	−	11.0607i	0.682876	−	0.496139i
$498$	−1.93910	−	4.77830i	−0.0868929	−	0.214121i
$499$	−16.1116	−	16.1116i	−0.721254	−	0.721254i	0.247607	−	0.968861i	$-0.420356\pi$
$499$	−16.1116	−	16.1116i	−0.721254	−	0.721254i	−0.968861	+	0.247607i	$0.920356\pi$
$500$	−22.2814	+	1.88124i	−0.996455	+	0.0841315i
$501$	−1.08658	+	1.08658i	−0.0485447	+	0.0485447i
$502$	9.14597	−	21.6389i	0.408205	−	0.965790i
$503$	0.330658	+	0.455111i	0.0147433	+	0.0202924i	0.816325	−	0.577593i	$-0.196008\pi$
$503$	0.330658	+	0.455111i	0.0147433	+	0.0202924i	−0.801582	+	0.597885i	$0.796008\pi$
$504$	16.7154	+	14.9118i	0.744563	+	0.664224i
$505$	−8.60991	+	5.35573i	−0.383136	+	0.238327i
$506$	11.5715	−	2.69021i	0.514416	−	0.119594i
$507$	−0.869740	+	0.869740i	−0.0386265	+	0.0386265i
$508$	−4.83905	−	2.55394i	−0.214698	−	0.113313i
$509$	1.86717	−	0.951371i	0.0827609	−	0.0421688i	−0.412120	−	0.911129i	$-0.635212\pi$
$509$	1.86717	−	0.951371i	0.0827609	−	0.0421688i	0.494881	+	0.868961i	$0.335212\pi$
$510$	−3.50622	−	2.55010i	−0.155258	−	0.112920i
$511$	12.1436	+	37.3742i	0.537203	+	1.65334i
$512$	−21.4213	+	7.28891i	−0.946696	+	0.322127i
$513$	11.1933	−	34.4495i	0.494197	−	1.52098i
$514$	−11.4700	+	4.65469i	−0.505921	+	0.205309i
$515$	1.18587	+	2.80961i	0.0522555	+	0.123806i
$516$	0.761864	−	4.39970i	0.0335392	−	0.193686i
$517$	−44.8302	+	7.10041i	−1.97163	+	0.312276i
$518$	19.3331	−	22.3092i	0.849446	−	0.980211i
$519$	14.4649	−	19.9092i	0.634937	−	0.873916i
$520$	3.73505	−	21.5056i	0.163793	−	0.943084i
$521$	−20.1684	−	27.7595i	−0.883595	−	1.21616i	−0.975412	−	0.220389i	$-0.929267\pi$
$521$	−20.1684	−	27.7595i	−0.883595	−	1.21616i	0.0918168	−	0.995776i	$-0.470733\pi$
$522$	−16.8141	−	1.44504i	−0.735933	−	0.0632475i
$523$	0.551454	+	0.280980i	0.0241134	+	0.0122864i	0.466006	−	0.884782i	$-0.345693\pi$
$523$	0.551454	+	0.280980i	0.0241134	+	0.0122864i	−0.441892	+	0.897068i	$0.645693\pi$
$524$	30.6320	+	22.9357i	1.33816	+	1.00195i
$525$	14.9661	−	21.1897i	0.653173	−	0.924793i
$526$	−18.9887	+	1.35712i	−0.827949	+	0.0591732i
$527$	0.649862	+	2.00007i	0.0283084	+	0.0871244i
$528$	15.5958	−	20.2164i	0.678720	−	0.879805i
$529$	−16.8197	+	12.2202i	−0.731292	+	0.531315i
$530$	−0.00587195	+	11.7425i	−0.000255061	+	0.510063i
$531$	3.63895	+	22.9754i	0.157917	+	0.997049i
$532$	37.3768	−	49.9189i	1.62049	−	2.16426i
$533$	−5.60283	+	0.887401i	−0.242686	+	0.0384376i
$534$	6.08492	−	3.66891i	0.263320	−	0.158769i
$535$	28.1418	−	17.5054i	1.21668	−	0.756826i
$536$	5.03062	+	1.32315i	0.217290	+	0.0571513i
$537$	−8.16063	−	2.65155i	−0.352157	−	0.114423i
$538$	−7.84111	−	13.0045i	−0.338054	−	0.560665i
$539$	−70.9924	−	36.1725i	−3.05786	−	1.55806i
$540$	23.8039	−	1.68929i	1.02436	−	0.0726956i
$541$	28.8160	−	14.6825i	1.23890	−	0.631250i	0.293124	−	0.956074i	$-0.405305\pi$
$541$	28.8160	−	14.6825i	1.23890	−	0.631250i	0.945774	+	0.324824i	$0.105305\pi$
$542$	−21.4723	+	34.4806i	−0.922315	+	1.48107i
$543$	−18.7256			−0.803592
$544$	1.84185	−	6.61451i	0.0789688	−	0.283595i
$545$	18.5680	−	4.58941i	0.795367	−	0.196589i
$546$	16.3074	+	19.3739i	0.697891	+	0.829126i
$547$	−32.2138	−	5.10217i	−1.37736	−	0.218153i	−0.576547	−	0.817064i	$-0.695600\pi$
$547$	−32.2138	−	5.10217i	−1.37736	−	0.218153i	−0.800816	+	0.598911i	$0.795600\pi$
$548$	−14.8334	+	7.29121i	−0.633653	+	0.311465i
$549$	2.10249	−	2.10249i	0.0897320	−	0.0897320i
$550$	34.2001	+	20.6677i	1.45830	+	0.881273i
$551$			46.9824i			2.00152i
$552$	1.20802	−	4.59289i	0.0514166	−	0.195486i
$553$	30.4440	+	41.9025i	1.29461	+	1.78188i
$554$	−17.6589	−	1.51764i	−0.750256	−	0.0644785i
$555$	−0.977096	−	11.4363i	−0.0414754	−	0.485444i
$556$	17.5877	−	5.43619i	0.745883	−	0.230546i
$557$	21.3956	+	21.3956i	0.906563	+	0.906563i	0.995993	−	0.0894305i	$-0.0285047\pi$
$557$	21.3956	+	21.3956i	0.906563	+	0.906563i	−0.0894305	+	0.995993i	$0.528505\pi$
$558$	−3.58612	−	2.23321i	−0.151813	−	0.0945393i
$559$	−2.10797	+	6.48767i	−0.0891577	+	0.274399i
$560$	39.7278	+	10.4704i	1.67881	+	0.442456i
$561$	2.39421	+	7.36862i	0.101084	+	0.311103i
$562$	7.80769	−	31.5210i	0.329348	−	1.32963i
$563$	5.66590	−	2.88692i	0.238789	−	0.121669i	−0.330502	−	0.943805i	$-0.607218\pi$
$563$	5.66590	−	2.88692i	0.238789	−	0.121669i	0.569291	+	0.822136i	$0.307218\pi$
$564$	−5.85452	+	17.1739i	−0.246520	+	0.723151i
$565$	−15.8554	+	26.2666i	−0.667043	+	1.10505i
$566$	−34.0109	+	20.5069i	−1.42959	+	0.861971i
$567$	−2.30815	+	3.17689i	−0.0969331	+	0.133417i
$568$	11.3227	−	2.46127i	0.475090	−	0.103273i
$569$	17.9787	−	24.7455i	0.753705	−	1.03739i	−0.244006	−	0.969774i	$-0.578462\pi$
$569$	17.9787	−	24.7455i	0.753705	−	1.03739i	0.997712	−	0.0676129i	$-0.0215383\pi$
$570$	−3.78105	−	23.9501i	−0.158371	−	1.00316i
$571$	5.58864	−	35.2853i	0.233877	−	1.47664i	−0.539118	−	0.842231i	$-0.681242\pi$
$571$	5.58864	−	35.2853i	0.233877	−	1.47664i	0.772995	−	0.634412i	$-0.218758\pi$
$572$	−27.9761	+	27.1827i	−1.16974	+	1.13657i
$573$	−8.53224	+	16.7455i	−0.356439	+	0.699551i
$574$	−0.761158	−	10.6501i	−0.0317701	−	0.444526i
$575$	7.35590	+	1.06435i	0.306762	+	0.0443867i
$576$	5.72601	+	12.5485i	0.238584	+	0.522853i
$577$	0.0433591	+	0.133446i	0.00180506	+	0.00555542i	0.951955	−	0.306238i	$-0.0990703\pi$
$577$	0.0433591	+	0.133446i	0.00180506	+	0.00555542i	−0.950150	+	0.311793i	$0.899070\pi$
$578$	−14.1402	−	16.7992i	−0.588156	−	0.698755i
$579$	12.0182	+	1.90350i	0.499461	+	0.0791069i
$580$	−28.6868	+	11.6248i	−1.19115	+	0.482692i
$581$	−14.6458	+	2.31967i	−0.607610	+	0.0962360i
$582$	4.28671	−	4.94661i	0.177690	−	0.205044i
$583$	12.3345	−	16.9770i	0.510842	−	0.703114i
$584$	−2.41852	+	24.0768i	−0.100079	+	0.996306i
$585$	−13.2713	−	0.955162i	−0.548699	−	0.0394911i
$586$	12.9417	−	30.6193i	0.534616	−	1.26487i
$587$	11.4899	+	22.5501i	0.474238	+	0.930744i	0.996936	+	0.0782259i	$0.0249256\pi$
$587$	11.4899	+	22.5501i	0.474238	+	0.930744i	−0.522698	+	0.852518i	$0.675074\pi$
$588$	−26.0345	+	18.3490i	−1.07365	+	0.756698i
$589$	−5.33948	+	10.4793i	−0.220010	+	0.431793i
$590$	25.0605	+	34.5291i	1.03172	+	1.42154i
$591$	0.797557	−	2.45463i	0.0328071	−	0.100970i
$592$	16.4271	−	7.78325i	0.675150	−	0.319889i
$593$	−2.87828			−0.118197			−0.0590985	−	0.998252i	$-0.518823\pi$
$593$	−2.87828			−0.118197			−0.0590985	+	0.998252i	$0.518823\pi$
$594$	−36.2006	−	22.5434i	−1.48533	−	0.924968i
$595$	−9.42546	+	8.15981i	−0.386406	+	0.334519i
$596$	0.108007	−	7.50886i	0.00442413	−	0.307575i
$597$	0.782140	−	4.93824i	0.0320109	−	0.202109i
$598$	−2.82461	+	6.68288i	−0.115507	+	0.273283i
$599$			36.3714i			1.48609i	0.669239	+	0.743047i	$0.266620\pi$
$599$			36.3714i			1.48609i	−0.669239	+	0.743047i	$0.733380\pi$
$600$	13.6881	−	8.23458i	0.558812	−	0.336175i
$601$		−	15.5801i		−	0.635527i	−0.948170	−	0.317764i	$-0.897068\pi$
$601$		−	15.5801i		−	0.635527i	0.948170	−	0.317764i	$-0.102932\pi$
$602$	−11.8267	−	4.99871i	−0.482019	−	0.203732i
$603$	0.496030	−	3.13181i	0.0201999	−	0.127537i
$604$	−2.95984	−	3.04623i	−0.120434	−	0.123949i
$605$	−18.2040	−	43.1299i	−0.740100	−	1.75348i
$606$	3.82912	−	6.14885i	0.155547	−	0.249780i
$607$	−1.33418			−0.0541526			−0.0270763	−	0.999633i	$-0.508620\pi$
$607$	−1.33418			−0.0541526			−0.0270763	+	0.999633i	$0.508620\pi$
$608$	33.4412	−	18.8738i	1.35622	−	0.765433i
$609$	11.0968	−	34.1525i	0.449665	−	1.38393i
$610$	1.68782	−	5.18574i	0.0683377	−	0.209964i
$611$	12.5844	−	24.6983i	0.509111	−	0.999186i
$612$	−4.12408	−	0.714137i	−0.166706	−	0.0288673i
$613$	5.48016	+	10.7554i	0.221341	+	0.434407i	0.974798	−	0.223091i	$-0.0716147\pi$
$613$	5.48016	+	10.7554i	0.221341	+	0.434407i	−0.753456	+	0.657498i	$0.771615\pi$
$614$	38.9805	+	16.4757i	1.57313	+	0.664904i
$615$	−3.17475	−	2.67496i	−0.128018	−	0.107865i
$616$	−46.4673	−	56.8450i	−1.87222	−	2.29035i
$617$	25.9257	−	35.6836i	1.04373	−	1.43657i	0.149606	−	0.988746i	$-0.452199\pi$
$617$	25.9257	−	35.6836i	1.04373	−	1.43657i	0.894122	−	0.447823i	$-0.147801\pi$
$618$	−1.64640	−	1.42676i	−0.0662279	−	0.0573927i
$619$	−6.78331	+	1.07437i	−0.272644	+	0.0431826i	−0.291259	−	0.956644i	$-0.594074\pi$
$619$	−6.78331	+	1.07437i	−0.272644	+	0.0431826i	0.0186151	+	0.999827i	$0.494074\pi$
$620$	−7.71966	−	0.667332i	−0.310029	−	0.0268007i
$621$	−7.83446	−	1.24086i	−0.314386	−	0.0497938i
$622$	−1.01698	+	0.856015i	−0.0407774	+	0.0343231i
$623$	−6.31377	−	19.4318i	−0.252956	−	0.778518i
$624$	4.39004	+	14.9625i	0.175742	+	0.598979i
$625$	15.2306	+	19.8249i	0.609226	+	0.792997i
$626$	−2.26182	+	0.161652i	−0.0904005	+	0.00646089i
$627$	−19.6716	+	38.6077i	−0.785609	+	1.54184i
$628$	18.2440	+	0.262420i	0.728013	+	0.0104717i
$629$	−0.862880	+	5.44801i	−0.0344053	+	0.217226i
$630$	3.93013	−	24.7338i	0.156580	−	0.985418i
$631$	4.46197	−	6.14137i	0.177628	−	0.244484i	−0.710914	−	0.703279i	$-0.751719\pi$
$631$	4.46197	−	6.14137i	0.177628	−	0.244484i	0.888542	+	0.458795i	$0.151719\pi$
$632$	6.77453	+	31.1652i	0.269476	+	1.23969i
$633$	−0.137096	+	0.188696i	−0.00544906	+	0.00749999i
$634$	21.4624	+	35.5956i	0.852382	+	1.41368i
$635$	0.520771	+	6.09529i	0.0206662	+	0.241884i
$636$	−3.70048	−	7.52836i	−0.146734	−	0.298519i
$637$	43.3558	−	22.0909i	1.71782	−	0.875273i
$638$	53.6918	+	13.2993i	2.12568	+	0.526526i
$639$	−2.18266	−	6.71754i	−0.0863448	−	0.265742i
$640$	19.7983	+	15.7488i	0.782598	+	0.622527i
$641$	9.97655	−	30.7047i	0.394050	−	1.21276i	−0.535649	−	0.844441i	$-0.679933\pi$
$641$	9.97655	−	30.7047i	0.394050	−	1.21276i	0.929699	−	0.368320i	$-0.120067\pi$
$642$	−12.5156	+	20.0978i	−0.493953	+	0.793196i
$643$	−5.40446	−	5.40446i	−0.213131	−	0.213131i	0.592465	−	0.805596i	$-0.298155\pi$
$643$	−5.40446	−	5.40446i	−0.213131	−	0.213131i	−0.805596	+	0.592465i	$0.798155\pi$
$644$	−12.0773	−	6.37410i	−0.475910	−	0.251175i
$645$	−4.59932	+	1.94126i	−0.181098	+	0.0764369i
$646$	−0.997731	+	11.6094i	−0.0392552	+	0.456764i
$647$	6.62453	+	9.11788i	0.260437	+	0.358461i	0.919132	−	0.393949i	$-0.128891\pi$
$647$	6.62453	+	9.11788i	0.260437	+	0.358461i	−0.658695	+	0.752410i	$0.728891\pi$
$648$	−2.08847	+	1.21864i	−0.0820427	+	0.0478725i
$649$		−	76.2448i		−	2.99287i
$650$	−22.4881	+	9.47840i	−0.882054	+	0.371774i
$651$	6.35650	−	6.35650i	0.249131	−	0.249131i
$652$	9.46074	−	27.7525i	0.370511	−	1.08687i
$653$	23.7115	+	3.75554i	0.927903	+	0.146965i	0.602053	−	0.798456i	$-0.294349\pi$
$653$	23.7115	+	3.75554i	0.927903	+	0.146965i	0.325850	+	0.945421i	$0.394349\pi$
$654$	−10.4536	+	8.79902i	−0.408769	+	0.344069i
$655$	3.07130	−	42.6734i	0.120006	−	1.66739i
$656$	2.21068	−	6.19184i	0.0863126	−	0.241751i
$657$	14.7505			0.575473
$658$	44.2888	+	27.5803i	1.72656	+	1.07519i
$659$	−7.09464	+	3.61490i	−0.276368	+	0.140816i	−0.586682	−	0.809818i	$-0.699566\pi$
$659$	−7.09464	+	3.61490i	−0.276368	+	0.140816i	0.310314	+	0.950634i	$0.399566\pi$
$660$	−28.4406	−	2.45857i	−1.10705	−	0.0956997i
$661$	−20.4246	−	10.4069i	−0.794425	−	0.404780i	0.00916859	−	0.999958i	$-0.497082\pi$
$661$	−20.4246	−	10.4069i	−0.794425	−	0.404780i	−0.803594	+	0.595178i	$0.797082\pi$
$662$	−19.6798	+	11.8660i	−0.764879	+	0.461185i
$663$	−4.50009	−	1.46217i	−0.174769	−	0.0567859i
$664$	−8.83042	−	2.32257i	−0.342687	−	0.0901331i
$665$	−69.5421	−	5.00510i	−2.69673	−	0.194089i
$666$	−5.72156	−	9.48924i	−0.221706	−	0.367701i
$667$	10.1617	−	1.60946i	0.393464	−	0.0623186i
$668$	0.386940	+	2.69320i	0.0149712	+	0.104203i
$669$	−0.682469	−	4.30894i	−0.0263858	−	0.166593i
$670$	−1.79438	−	5.53195i	−0.0693231	−	0.213718i
$671$	−7.88447	+	5.72840i	−0.304377	+	0.221143i
$672$	−28.7669	+	5.82122i	−1.10971	+	0.224558i
$673$	−0.516000	−	1.58808i	−0.0198903	−	0.0612161i	0.940619	−	0.339465i	$-0.110246\pi$
$673$	−0.516000	−	1.58808i	−0.0198903	−	0.0612161i	−0.960509	+	0.278249i	$0.910246\pi$
$674$	0.177922	+	2.48948i	0.00685331	+	0.0958911i
$675$	−15.9699	−	21.3732i	−0.614680	−	0.822654i
$676$	0.309722	+	2.15574i	0.0119124	+	0.0829131i
$677$	6.69974	+	3.41369i	0.257492	+	0.131199i	0.577972	−	0.816056i	$-0.303844\pi$
$677$	6.69974	+	3.41369i	0.257492	+	0.131199i	−0.320480	+	0.947255i	$0.603844\pi$
$678$	1.87676	−	21.8376i	0.0720766	−	0.838666i
$679$	−11.0633	−	15.2273i	−0.424570	−	0.584370i
$680$	−7.33538	+	2.26328i	−0.281299	+	0.0867929i
$681$	13.2268	−	18.2052i	0.506854	−	0.697624i
$682$	10.4644	+	9.06838i	0.400702	+	0.347246i
$683$	−12.0668	+	1.91119i	−0.461723	+	0.0731297i	−0.382962	−	0.923764i	$-0.625096\pi$
$683$	−12.0668	+	1.91119i	−0.461723	+	0.0731297i	−0.0787601	+	0.996894i	$0.525096\pi$
$684$	−13.4848	−	19.1330i	−0.515605	−	0.731570i
$685$	15.8206	+	9.54985i	0.604474	+	0.364881i
$686$	17.3409	+	42.7313i	0.662079	+	1.63149i
$687$	−9.82339	+	30.2333i	−0.374786	+	1.15347i
$688$	−5.42741	−	5.74900i	−0.206918	−	0.219179i
$689$	3.96022	+	12.1883i	0.150872	+	0.464338i
$690$	−5.05060	+	1.63825i	−0.192273	+	0.0623670i
$691$	28.5578	−	14.5509i	1.08639	−	0.553543i	0.183327	−	0.983052i	$-0.441313\pi$
$691$	28.5578	−	14.5509i	1.08639	−	0.553543i	0.903063	+	0.429509i	$0.141313\pi$
$692$	−12.8676	−	41.6305i	−0.489153	−	1.58255i
$693$	−31.6469	+	31.6469i	−1.20216	+	1.20216i
$694$	9.92569	+	42.6937i	0.376774	+	1.62063i
$695$	−15.7394	−	13.2616i	−0.597029	−	0.503041i
$696$	14.7200	−	16.5004i	0.557960	−	0.625446i
$697$	1.17265	+	1.61402i	0.0444175	+	0.0611354i
$698$	−0.120222	−	0.0508137i	−0.00455048	−	0.00192333i
$699$	−6.29723	+	6.29723i	−0.238183	+	0.238183i
$700$	−14.1506	−	43.6998i	−0.534843	−	1.65170i
$701$	−21.8069	−	21.8069i	−0.823635	−	0.823635i	0.162992	−	0.986627i	$-0.447886\pi$
$701$	−21.8069	−	21.8069i	−0.823635	−	0.823635i	−0.986627	+	0.162992i	$0.947886\pi$
$702$	24.1329	−	9.79346i	0.910839	−	0.369630i
$703$	−24.9568	+	18.1322i	−0.941264	+	0.683868i
$704$	−12.1028	−	43.5594i	−0.456142	−	1.64171i
$705$	19.6934	−	4.86756i	0.741695	−	0.183323i
$706$	−20.8529	+	33.4860i	−0.784811	+	1.26026i
$707$	−14.7285	−	14.7285i	−0.553923	−	0.553923i
$708$	−26.9552	−	14.2263i	−1.01304	−	0.534658i
$709$	−14.6036	−	28.6612i	−0.548450	−	1.07639i	−0.984321	−	0.176385i	$-0.943560\pi$
$709$	−14.6036	−	28.6612i	−0.548450	−	1.07639i	0.435871	−	0.900009i	$-0.356440\pi$
$710$	−9.15584	−	9.16500i	−0.343613	−	0.343956i
$711$	18.4897	−	6.00767i	0.693419	−	0.225305i
$712$	1.25745	−	12.5181i	0.0471248	−	0.469137i
$713$	2.44947	+	0.795880i	0.0917332	+	0.0298059i
$714$	3.46729	−	8.20342i	0.129760	−	0.307005i
$715$	42.4736	+	9.89690i	1.58842	+	0.370123i
$716$	−12.4186	+	8.75257i	−0.464106	+	0.327099i
$717$	−4.12055	−	26.0161i	−0.153885	−	0.971590i
$718$	22.9318	−	1.63893i	0.855808	−	0.0611643i
$719$	16.4640	+	11.9618i	0.614002	+	0.446098i	0.850821	−	0.525455i	$-0.176105\pi$
$719$	16.4640	+	11.9618i	0.614002	+	0.446098i	−0.236819	+	0.971554i	$0.576105\pi$
$720$	8.34583	−	12.9677i	0.311031	−	0.483277i
$721$	−5.06816	+	3.68223i	−0.188748	+	0.137134i
$722$	−29.2985	+	24.6611i	−1.09038	+	0.917790i
$723$	6.42314	−	12.6061i	0.238879	−	0.468827i
$724$	−19.8725	+	26.5409i	−0.738556	+	0.986384i
$725$	28.2666	+	19.9645i	1.04980	+	0.741462i
$726$	25.2736	+	21.9020i	0.937992	+	0.812859i
$727$	25.0902	−	8.15231i	0.930545	−	0.302352i	0.195760	−	0.980652i	$-0.437283\pi$
$727$	25.0902	−	8.15231i	0.930545	−	0.302352i	0.734786	+	0.678299i	$0.237283\pi$
$728$	44.7659	−	2.55287i	1.65913	−	0.0946156i
$729$	11.4947	+	15.8211i	0.425729	+	0.585966i
$730$	24.1116	−	12.2703i	0.892410	−	0.454143i
$731$	2.36955	−	0.375300i	0.0876410	−	0.0138810i
$732$	0.554045	+	3.85628i	0.0204781	+	0.142532i
$733$	−6.69882	−	42.2947i	−0.247426	−	1.56219i	−0.728213	−	0.685351i	$-0.759649\pi$
$733$	−6.69882	−	42.2947i	−0.247426	−	1.56219i	0.480786	−	0.876838i	$-0.340351\pi$
$734$	−27.8340	−	6.89443i	−1.02737	−	0.254478i
$735$	32.9902	+	13.4071i	1.21686	+	0.494527i
$736$	−5.22776	−	6.58638i	−0.192698	−	0.242777i
$737$	−3.21162	+	9.88435i	−0.118302	+	0.364095i
$738$	−3.89019	−	0.963592i	−0.143200	−	0.0354703i
$739$	−5.28378	+	10.3700i	−0.194367	+	0.381467i	−0.967536	−	0.252733i	$-0.918670\pi$
$739$	−5.28378	+	10.3700i	−0.194367	+	0.381467i	0.773169	+	0.634200i	$0.218670\pi$
$740$	−17.2463	−	10.7519i	−0.633985	−	0.395246i
$741$	−12.0137	−	23.5781i	−0.441333	−	0.866164i
$742$	−23.4952	+	5.46229i	−0.862535	+	0.200527i
$743$			20.7713i			0.762025i	0.924570	+	0.381013i	$0.124425\pi$
$743$			20.7713i			0.762025i	−0.924570	+	0.381013i	$0.875575\pi$
$744$	5.15851	−	2.00747i	0.189120	−	0.0735976i
$745$	−7.12927	+	4.43472i	−0.261196	+	0.162475i
$746$	−8.64955	−	0.743359i	−0.316682	−	0.0272163i
$747$	−0.870698	+	5.49737i	−0.0318572	+	0.201138i
$748$	12.9848	+	4.42648i	0.474772	+	0.161848i
$749$	48.1408	+	48.1408i	1.75902	+	1.75902i
$750$	−16.0161	−	7.90240i	−0.584826	−	0.288555i
$751$	−28.6410			−1.04513			−0.522563	−	0.852601i	$-0.675024\pi$
$751$	−28.6410			−1.04513			−0.522563	+	0.852601i	$0.675024\pi$
$752$	18.1284	+	26.5237i	0.661076	+	0.967220i
$753$	15.1799	−	11.0289i	0.553187	−	0.401914i
$754$	−25.8444	+	21.7537i	−0.941198	+	0.792224i
$755$	−1.07764	+	4.62482i	−0.0392194	+	0.168314i
$756$	14.4763	+	46.8352i	0.526500	+	1.70338i
$757$	−19.4633	+	19.4633i	−0.707404	+	0.707404i	−0.965989	−	0.258584i	$-0.916744\pi$
$757$	−19.4633	+	19.4633i	−0.707404	+	0.707404i	0.258584	+	0.965989i	$0.416744\pi$
$758$	9.61252	+	41.3467i	0.349143	+	1.50178i
$759$	9.02427	+	2.93216i	0.327560	+	0.106431i
$760$	−37.9585	−	20.0579i	−1.37690	−	0.727577i
$761$	42.6758	−	13.8662i	1.54699	−	0.502649i	0.593699	−	0.804687i	$-0.297667\pi$
$761$	42.6758	−	13.8662i	1.54699	−	0.502649i	0.953296	+	0.302038i	$0.0976670\pi$
$762$	−2.25659	−	3.74256i	−0.0817475	−	0.135579i
$763$	17.8376	+	35.0082i	0.645764	+	1.26738i
$764$	14.6795	+	29.8643i	0.531085	+	1.08045i
$765$	1.81965	+	4.31120i	0.0657895	+	0.155872i
$766$	−10.3810	−	2.57135i	−0.375080	−	0.0929065i
$767$	37.6706	+	27.3693i	1.36021	+	0.988249i
$768$	−17.6580	−	3.84888i	−0.637178	−	0.138885i
$769$	15.4030	+	11.1909i	0.555446	+	0.403555i	0.829789	−	0.558077i	$-0.188461\pi$
$769$	15.4030	+	11.1909i	0.555446	+	0.403555i	−0.274344	+	0.961632i	$0.588461\pi$
$770$	−25.4052	+	78.0562i	−0.915539	+	2.81295i
$771$	−9.76505	−	1.54663i	−0.351680	−	0.0557006i
$772$	15.4523	−	15.0141i	0.556140	−	0.540368i
$773$	5.92590	+	3.01940i	0.213140	+	0.108600i	0.557301	−	0.830310i	$-0.311837\pi$
$773$	5.92590	+	3.01940i	0.213140	+	0.108600i	−0.344162	+	0.938910i	$0.611837\pi$
$774$	−3.15624	+	3.64212i	−0.113449	+	0.130913i
$775$	4.03588	+	7.66550i	0.144973	+	0.275353i
$776$	−2.46185	−	11.3254i	−0.0883754	−	0.406558i
$777$	22.4242	−	7.28608i	0.804465	−	0.261387i
$778$	16.6713	+	1.43277i	0.597696	+	0.0513671i
$779$	−1.74541	+	11.0201i	−0.0625358	+	0.394835i
$780$	11.4239	−	13.1693i	0.409043	−	0.471535i
$781$	3.62162	+	22.8660i	0.129592	+	0.818211i
$782$	2.54515	−	0.181901i	0.0910142	−	0.00650476i
$783$	−29.8789	−	21.7083i	−1.06778	−	0.775791i
$784$	−1.62207	+	56.3730i	−0.0579310	+	2.01332i
$785$	−10.7748	−	17.3217i	−0.384571	−	0.618238i
$786$	11.4930	+	28.3208i	0.409941	+	1.01017i
$787$	−24.8063	+	12.6395i	−0.884250	+	0.450548i	−0.836281	−	0.548301i	$-0.815275\pi$
$787$	−24.8063	+	12.6395i	−0.884250	+	0.450548i	−0.0479691	+	0.998849i	$0.515275\pi$
$788$	−2.63268	−	3.73539i	−0.0937853	−	0.133068i
$789$	−13.5478	−	6.90296i	−0.482315	−	0.245752i
$790$	25.2262	−	25.2010i	0.897509	−	0.896612i
$791$	−59.9410	−	19.4760i	−2.13126	−	0.692488i
$792$	−25.6825	+	9.99454i	−0.912588	+	0.355140i
$793$		−	5.95182i		−	0.211355i
$794$	25.6107	−	5.95413i	0.908891	−	0.211304i
$795$	−4.84680	+	8.02936i	−0.171898	+	0.284772i
$796$	−6.16921	−	6.34927i	−0.218662	−	0.225044i
$797$	−11.9087	−	1.88615i	−0.421827	−	0.0668109i	−0.0580875	−	0.998311i	$-0.518500\pi$
$797$	−11.9087	−	1.88615i	−0.421827	−	0.0668109i	−0.363740	+	0.931501i	$0.618500\pi$
$798$	46.1526	−	18.7293i	1.63378	−	0.663011i
$799$	−9.74877			−0.344887
$800$	2.85507	−	28.1398i	0.100942	−	0.994892i
$801$	−7.66916			−0.270977
$802$	32.1610	−	13.0514i	1.13564	−	0.460859i
$803$	−47.7523	−	7.56322i	−1.68514	−	0.266900i
$804$	2.89521	+	2.97972i	0.102106	+	0.105087i
$805$	1.29973	+	15.2126i	0.0458096	+	0.536173i
$806$	−8.23682	+	1.91494i	−0.290130	+	0.0674510i
$807$		−	12.1288i		−	0.426952i
$808$	−4.65148	−	11.9527i	−0.163638	−	0.420494i
$809$	3.49981	+	1.13716i	0.123047	+	0.0399804i	0.369893	−	0.929074i	$-0.379394\pi$
$809$	3.49981	+	1.13716i	0.123047	+	0.0399804i	−0.246846	+	0.969055i	$0.579394\pi$
$810$	2.40815	+	1.22853i	0.0846137	+	0.0431661i
$811$	3.61237	+	1.84059i	0.126847	+	0.0646319i	0.516263	−	0.856430i	$-0.327323\pi$
$811$	3.61237	+	1.84059i	0.126847	+	0.0646319i	−0.389415	+	0.921062i	$0.627323\pi$
$812$	−36.6298	−	51.9724i	−1.28545	−	1.82387i
$813$	−28.9071	+	14.7289i	−1.01382	+	0.516565i
$814$	13.6570	+	33.6535i	0.478678	+	1.17955i
$815$	−31.8239	+	7.86584i	−1.11474	+	0.275528i
$816$	3.98772	−	3.76466i	0.139598	−	0.131789i
$817$	10.8547	+	7.88639i	0.379758	+	0.275910i
$818$	−14.2933	+	1.02154i	−0.499753	+	0.0357172i
$819$	−4.27576	−	26.9961i	−0.149407	−	0.943319i
$820$	−7.16057	+	1.66096i	−0.250058	+	0.0580031i
$821$	−3.04515	+	19.2263i	−0.106277	+	0.671004i	0.875822	+	0.482635i	$0.160320\pi$
$821$	−3.04515	+	19.2263i	−0.106277	+	0.671004i	−0.982098	+	0.188369i	$0.939680\pi$
$822$	−13.1529	−	1.13039i	−0.458761	−	0.0394268i
$823$	−49.1835	+	15.9807i	−1.71443	+	0.557052i	−0.991061	−	0.133410i	$-0.957407\pi$
$823$	−49.1835	+	15.9807i	−1.71443	+	0.557052i	−0.723369	+	0.690462i	$0.757407\pi$
$824$	−3.76947	+	0.819388i	−0.131316	+	0.0285447i
$825$	14.8689	+	28.2411i	0.517669	+	0.983228i
$826$	−57.3973	+	66.2332i	−1.99711	+	2.30455i
$827$	−25.4056	−	12.9448i	−0.883440	−	0.450135i	−0.0474463	−	0.998874i	$-0.515108\pi$
$827$	−25.4056	−	12.9448i	−0.883440	−	0.450135i	−0.835994	+	0.548738i	$0.815108\pi$
$828$	−3.67630	+	3.57204i	−0.127760	+	0.124137i
$829$	44.3392	+	7.02264i	1.53997	+	0.243907i	0.867958	−	0.496638i	$-0.165432\pi$
$829$	44.3392	+	7.02264i	1.53997	+	0.243907i	0.672007	+	0.740544i	$0.265432\pi$
$830$	3.14974	+	9.71042i	0.109329	+	0.337054i
$831$	−11.4526	−	8.32084i	−0.397288	−	0.288647i
$832$	25.8661	+	9.65667i	0.896747	+	0.334785i
$833$	−13.8448	−	10.0589i	−0.479695	−	0.348519i
$834$	14.2718	+	3.53509i	0.494190	+	0.122410i
$835$	2.29989	−	1.99106i	0.0795909	−	0.0689034i
$836$	33.8445	+	68.8541i	1.17054	+	2.38137i
$837$	−4.19731	−	8.23768i	−0.145080	−	0.284736i
$838$	−4.92096	−	8.16144i	−0.169992	−	0.281932i
$839$	−7.74935	+	2.51792i	−0.267537	+	0.0869281i	−0.439714	−	0.898138i	$-0.644920\pi$
$839$	−7.74935	+	2.51792i	−0.267537	+	0.0869281i	0.172176	+	0.985066i	$0.444920\pi$
$840$	22.8553	+	23.5459i	0.788583	+	0.812412i
$841$	17.9781	+	5.84145i	0.619935	+	0.201429i
$842$	−4.71772	−	20.2925i	−0.162583	−	0.699326i
$843$	18.3401	−	18.3401i	0.631666	−	0.631666i
$844$	0.121957	+	0.394567i	0.00419794	+	0.0135816i
$845$	1.84092	−	1.59372i	0.0633296	−	0.0548257i
$846$	14.9828	−	12.6113i	0.515119	−	0.433586i
$847$	77.8005	−	56.5254i	2.67326	−	1.94224i
$848$	−14.5975	−	2.74455i	−0.501280	−	0.0942483i
$849$	−31.7205			−1.08864
$850$	6.56072	+	5.53350i	0.225031	+	0.189798i
$851$	4.77671	+	4.77671i	0.163743	+	0.163743i
$852$	8.75968	+	2.98615i	0.300102	+	0.102304i
$853$	−0.416364	+	2.62882i	−0.0142560	+	0.0900091i	−0.993790	−	0.111267i	$-0.964509\pi$
$853$	−0.416364	+	2.62882i	−0.0142560	+	0.0900091i	0.979534	+	0.201277i	$0.0645090\pi$
$854$	11.1615	+	0.959244i	0.381940	+	0.0328246i
$855$	−9.85298	+	24.2448i	−0.336965	+	0.829155i
$856$	15.2036	+	39.0679i	0.519647	+	1.33531i
$857$			9.17805i			0.313516i	0.987637	+	0.156758i	$0.0501043\pi$
$857$			9.17805i			0.313516i	−0.987637	+	0.156758i	$0.949896\pi$
$858$	−30.3459	+	7.05500i	−1.03599	+	0.240854i
$859$	−5.46130	−	10.7184i	−0.186337	−	0.365707i	0.778873	−	0.627181i	$-0.215791\pi$
$859$	−5.46130	−	10.7184i	−0.186337	−	0.365707i	−0.965210	+	0.261474i	$0.915791\pi$
$860$	−2.12956	+	8.57903i	−0.0726175	+	0.292543i
$861$	3.87161	−	7.59847i	0.131944	−	0.258955i
$862$	0.0500386	+	0.0123945i	0.00170432	+	0.000422157i
$863$	−11.3556	+	34.9490i	−0.386549	+	1.18968i	0.548801	+	0.835953i	$0.315085\pi$
$863$	−11.3556	+	34.9490i	−0.386549	+	1.18968i	−0.935350	+	0.353724i	$0.884915\pi$
$864$	−3.44861	+	29.9879i	−0.117324	+	1.02021i
$865$	−31.3905	+	37.2555i	−1.06731	+	1.26673i
$866$	51.9422	+	12.8660i	1.76507	+	0.437203i
$867$	−2.74356	−	17.3221i	−0.0931760	−	0.588290i
$868$	−2.26361	−	15.7552i	−0.0768318	−	0.534768i
$869$	−62.9376	+	9.96834i	−2.13501	+	0.338153i
$870$	−24.4157	−	3.87958i	−0.827770	−	0.131530i
$871$	−3.73075	−	5.13493i	−0.126412	−	0.173991i
$872$	1.37746	+	24.1545i	0.0466467	+	0.817973i
$873$	−6.71914	+	2.18318i	−0.227408	+	0.0738894i
$874$	10.7843	+	9.34560i	0.364784	+	0.316120i
$875$	−32.5621	+	39.7126i	−1.10080	+	1.34253i
$876$	−11.5838	+	15.4709i	−0.391382	+	0.522713i
$877$	3.97620	−	7.80372i	0.134267	−	0.263513i	−0.814078	−	0.580756i	$-0.802757\pi$
$877$	3.97620	−	7.80372i	0.134267	−	0.263513i	0.948344	+	0.317243i	$0.102757\pi$
$878$	−20.6094	+	17.3473i	−0.695532	+	0.585443i
$879$	21.4798	−	15.6060i	0.724496	−	0.526377i
$880$	−33.6672	+	37.7014i	−1.13492	+	1.27091i
$881$	−31.6695	−	23.0092i	−1.06697	−	0.775200i	−0.0916056	−	0.995795i	$-0.529200\pi$
$881$	−31.6695	−	23.0092i	−1.06697	−	0.775200i	−0.975365	+	0.220596i	$0.929200\pi$
$882$	34.2905	−	2.45073i	1.15462	−	0.0825203i
$883$	5.46217	+	34.4868i	0.183817	+	1.16057i	0.891155	+	0.453698i	$0.149896\pi$
$883$	5.46217	+	34.4868i	0.183817	+	1.16057i	−0.707339	+	0.706875i	$0.750104\pi$
$884$	−6.84813	+	4.82651i	−0.230328	+	0.162333i
$885$	2.90087	+	33.9529i	0.0975118	+	1.14131i
$886$	11.5126	−	27.2382i	0.386774	−	0.915086i
$887$	−2.37231	−	0.770809i	−0.0796543	−	0.0258812i	0.268919	−	0.963163i	$-0.413334\pi$
$887$	−2.37231	−	0.770809i	−0.0796543	−	0.0258812i	−0.348573	+	0.937282i	$0.613334\pi$
$888$	14.4459	+	1.45109i	0.484773	+	0.0486954i
$889$	−11.9516	+	3.88332i	−0.400845	+	0.130242i
$890$	−12.5362	+	6.37962i	−0.420214	+	0.213845i
$891$	−2.19331	−	4.30461i	−0.0734786	−	0.144210i
$892$	−6.83158	−	3.60555i	−0.228738	−	0.120723i
$893$	−38.5521	−	38.5521i	−1.29010	−	1.29010i
$894$	3.17063	−	5.09144i	0.106042	−	0.170283i
$895$	15.7365	+	6.39526i	0.526014	+	0.213770i
$896$	−22.2781	+	46.9507i	−0.744258	+	1.56851i
$897$	−4.68812	+	3.40612i	−0.156532	+	0.113727i
$898$	38.7620	−	15.7301i	1.29350	−	0.524921i
$899$	8.47945	+	8.47945i	0.282806	+	0.282806i
$900$	−17.2414	−	0.0172434i	−0.574714	−	0.000574781i
$901$	3.18703	−	3.18703i	0.106175	−	0.106175i
$902$	12.0997	+	5.11413i	0.402877	+	0.170282i
$903$	−6.02780	−	8.29655i	−0.200593	−	0.276092i
$904$	−28.9599	−	25.8351i	−0.963192	−	0.859263i
$905$	36.9741	+	2.66111i	1.22906	+	0.0884584i
$906$	−0.768196	−	3.30427i	−0.0255216	−	0.109777i
$907$	−19.6154	+	19.6154i	−0.651320	+	0.651320i	−0.953311	−	0.301991i	$-0.902349\pi$
$907$	−19.6154	+	19.6154i	−0.651320	+	0.651320i	0.301991	+	0.953311i	$0.402349\pi$
$908$	−11.7663	−	38.0674i	−0.390478	−	1.26331i
$909$	−6.96621	+	3.54946i	−0.231054	+	0.117728i
$910$	−29.4460	−	40.5716i	−0.976126	−	1.34494i
$911$	6.75332	+	20.7846i	0.223747	+	0.688624i	0.998416	+	0.0562568i	$0.0179165\pi$
$911$	6.75332	+	20.7846i	0.223747	+	0.688624i	−0.774669	+	0.632367i	$0.782083\pi$
$912$	30.6573	+	0.882127i	1.01516	+	0.0292101i
$913$	5.63746	−	17.3503i	0.186573	−	0.574212i
$914$	−14.4831	−	35.6891i	−0.479058	−	1.18049i
$915$	3.29312	−	2.85092i	0.108867	−	0.0942484i
$916$	32.4263	+	46.0083i	1.07140	+	1.52016i
$917$	86.8053	−	13.7486i	2.86656	−	0.454019i
$918$	−6.92208	−	5.99864i	−0.228463	−	0.197985i
$919$	14.2442	−	19.6054i	0.469872	−	0.646724i	−0.506647	−	0.862154i	$-0.669115\pi$
$919$	14.2442	−	19.6054i	0.469872	−	0.646724i	0.976519	+	0.215430i	$0.0691153\pi$
$920$	−3.03796	+	8.89709i	−0.100158	+	0.293328i
$921$	19.8675	+	27.3453i	0.654657	+	0.901058i
$922$	−4.30197	+	50.0567i	−0.141678	+	1.64853i
$923$	−12.5976	−	6.41878i	−0.414654	−	0.211277i
$924$	−8.33953	−	58.0452i	−0.274351	−	1.90955i
$925$	0.304077	+	22.7201i	0.00999799	+	0.747032i
$926$	−2.08902	−	29.2294i	−0.0686494	−	0.960539i
$927$	0.726635	+	2.23635i	0.0238658	+	0.0734515i
$928$	−7.76540	−	38.3745i	−0.254912	−	1.25971i
$929$	−7.59886	+	5.52089i	−0.249310	+	0.181135i	−0.705421	−	0.708788i	$-0.749242\pi$
$929$	−7.59886	+	5.52089i	−0.249310	+	0.181135i	0.456111	+	0.889923i	$0.349242\pi$
$930$	−5.00496	−	3.64014i	−0.164119	−	0.119365i
$931$	−14.9719	−	94.5287i	−0.490683	−	3.09805i
$932$	2.24250	+	15.6083i	0.0734556	+	0.511268i
$933$	−1.04864	+	0.166088i	−0.0343309	+	0.00543749i
$934$	−12.7666	−	21.1735i	−0.417736	−	0.692818i
$935$	−3.68026	−	14.8898i	−0.120357	−	0.486947i
$936$	4.28110	−	16.2768i	0.139932	−	0.532023i
$937$	−24.2607	−	7.88276i	−0.792561	−	0.257519i	−0.115367	−	0.993323i	$-0.536804\pi$
$937$	−24.2607	−	7.88276i	−0.792561	−	0.257519i	−0.677194	+	0.735804i	$0.736804\pi$
$938$	10.2309	−	6.16873i	0.334050	−	0.201416i
$939$	−1.61373	−	0.822237i	−0.0526621	−	0.0268327i
$940$	14.0005	−	33.0782i	0.456646	−	1.07889i
$941$	−14.2770	+	7.27450i	−0.465417	+	0.237142i	−0.670942	−	0.741510i	$-0.734110\pi$
$941$	−14.2770	+	7.27450i	−0.465417	+	0.237142i	0.205525	+	0.978652i	$0.434110\pi$
$942$	12.3705	+	7.70355i	0.403052	+	0.250995i
$943$	2.44330			0.0795649
$944$	−48.7699	+	23.1075i	−1.58733	+	0.752083i
$945$	35.3150	−	41.9133i	1.14880	−	1.36344i
$946$	12.0853	−	10.1724i	0.392926	−	0.330733i
$947$	−1.40883	−	0.223137i	−0.0457809	−	0.00725098i	0.133502	−	0.991049i	$-0.457378\pi$
$947$	−1.40883	−	0.223137i	−0.0457809	−	0.00725098i	−0.179283	+	0.983798i	$0.557378\pi$
$948$	−8.21923	+	24.1106i	−0.266948	+	0.783076i
$949$	20.8783	−	20.8783i	0.677737	−	0.677737i
$950$	4.06220	+	47.8274i	0.131795	+	1.55173i
$951$			33.1984i			1.07653i
$952$	−7.94752	−	13.6203i	−0.257581	−	0.441435i
$953$	1.89545	+	2.60886i	0.0613996	+	0.0845092i	0.838613	−	0.544728i	$-0.183367\pi$
$953$	1.89545	+	2.60886i	0.0613996	+	0.0845092i	−0.777213	+	0.629238i	$0.783367\pi$
$954$	−0.775279	+	9.02096i	−0.0251006	+	0.292064i
$955$	19.2268	−	31.8518i	0.622165	−	1.03070i
$956$	−41.2471	−	21.7693i	−1.33403	−	0.704069i
$957$	31.2398	+	31.2398i	1.00984	+	1.00984i
$958$	18.8790	−	30.3163i	0.609954	−	0.979474i
$959$	−11.7306	+	36.1029i	−0.378799	+	1.16582i
$960$	7.04686	+	18.9372i	0.227436	+	0.611194i
$961$	−8.65188	−	26.6278i	−0.279093	−	0.858960i
$962$	−21.5297	−	5.33287i	−0.694147	−	0.171939i
$963$	22.7693	−	11.6016i	0.733732	−	0.373855i
$964$	−11.0508	−	22.4821i	−0.355924	−	0.724101i
$965$	−23.4598	−	5.46644i	−0.755198	−	0.175971i
$966$	−5.63196	−	9.34065i	−0.181205	−	0.300530i
$967$	23.6543	−	32.5573i	0.760670	−	1.04697i	−0.236488	−	0.971635i	$-0.575996\pi$
$967$	23.6543	−	32.5573i	0.760670	−	1.04697i	0.997158	−	0.0753385i	$-0.0240037\pi$
$968$	57.8645	−	12.5783i	1.85984	−	0.404282i
$969$	−5.47030	+	7.52922i	−0.175731	+	0.241873i
$970$	−9.16718	+	9.15801i	−0.294340	+	0.294046i
$971$	−1.89903	+	11.9900i	−0.0609428	+	0.384778i	0.938298	+	0.345827i	$0.112402\pi$
$971$	−1.89903	+	11.9900i	−0.0609428	+	0.384778i	−0.999241	+	0.0389507i	$0.987598\pi$
$972$	30.0822	+	0.432700i	0.964887	+	0.0138789i
$973$	19.1942	−	37.6708i	0.615338	−	1.20767i
$974$	−12.0459	+	0.860920i	−0.385977	+	0.0275856i
$975$	−19.2906	−	2.79124i	−0.617795	−	0.0893913i
$976$	6.05371	+	3.30719i	0.193775	+	0.105861i
$977$	4.04247	+	12.4414i	0.129330	+	0.398037i	0.994665	−	0.103157i	$-0.0328944\pi$
$977$	4.04247	+	12.4414i	0.129330	+	0.398037i	−0.865335	+	0.501194i	$0.832894\pi$
$978$	17.9166	−	15.0807i	0.572909	−	0.482228i
$979$	24.8276	+	3.93230i	0.793493	+	0.125677i
$980$	54.0134	−	32.5307i	1.72539	−	1.03915i
$981$	14.5664	−	2.30708i	0.465068	−	0.0736595i
$982$	−16.1275	−	13.9760i	−0.514648	−	0.445991i
$983$	−1.45763	+	2.00626i	−0.0464912	+	0.0639896i	−0.831630	−	0.555331i	$-0.812592\pi$
$983$	−1.45763	+	2.00626i	−0.0464912	+	0.0639896i	0.785139	+	0.619320i	$0.212592\pi$
$984$	4.06568	−	3.32344i	0.129609	−	0.105948i
$985$	−1.92362	+	4.73338i	−0.0612918	+	0.150818i
$986$	10.9432	+	4.62531i	0.348503	+	0.147300i
$987$	18.9187	+	37.1300i	0.602187	+	1.18186i
$988$	−46.1681	−	7.99460i	−1.46880	−	0.254342i
$989$	1.33389	−	2.61790i	0.0424151	−	0.0832444i
$990$	24.9180	+	18.1230i	0.791946	+	0.575988i
$991$	7.05802	−	21.7224i	0.224205	−	0.690034i	−0.774166	−	0.632983i	$-0.781830\pi$
$991$	7.05802	−	21.7224i	0.224205	−	0.690034i	0.998371	−	0.0570506i	$-0.0181697\pi$
$992$	2.62915	−	9.44188i	0.0834757	−	0.299780i
$993$	−18.3545			−0.582463
$994$	14.0675	−	22.5899i	0.446196	−	0.716507i
$995$	−2.24613	+	9.63952i	−0.0712072	+	0.305593i
$996$	−5.08206	−	5.23040i	−0.161031	−	0.165731i
$997$	3.47346	−	21.9306i	0.110006	−	0.694548i	−0.869621	−	0.493720i	$-0.835637\pi$
$997$	3.47346	−	21.9306i	0.110006	−	0.694548i	0.979626	−	0.200828i	$-0.0643633\pi$
$998$	−29.6809	−	12.5451i	−0.939532	−	0.397107i
$999$		−	24.2495i		−	0.767220i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.be.a.381.51	yes	464
16.5	even	4	inner	400.2.be.a.181.5	yes	464
25.21	even	5	inner	400.2.be.a.221.5	yes	464
400.21	even	20	inner	400.2.be.a.21.51	✓	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.be.a.21.51	✓	464	400.21	even	20	inner
400.2.be.a.181.5	yes	464	16.5	even	4	inner
400.2.be.a.221.5	yes	464	25.21	even	5	inner
400.2.be.a.381.51	yes	464	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.be (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31042 - 0.531786i) q^{2} +(1.11563 + 0.176699i) q^{3} +(1.43441 - 1.39373i) q^{4} +(-2.17773 - 0.507439i) q^{5} +(1.55591 - 0.361728i) q^{6} -4.59337i q^{7} +(1.13851 - 2.58917i) q^{8} +(-1.63976 - 0.532790i) q^{9} +O(q^{10})\)	\(q+(1.31042 - 0.531786i) q^{2} +(1.11563 + 0.176699i) q^{3} +(1.43441 - 1.39373i) q^{4} +(-2.17773 - 0.507439i) q^{5} +(1.55591 - 0.361728i) q^{6} -4.59337i q^{7} +(1.13851 - 2.58917i) q^{8} +(-1.63976 - 0.532790i) q^{9} +(-3.12359 + 0.493127i) q^{10} +(5.03525 + 2.56559i) q^{11} +(1.84654 - 1.30143i) q^{12} +(-3.07508 + 1.56683i) q^{13} +(-2.44269 - 6.01926i) q^{14} +(-2.33988 - 0.950917i) q^{15} +(0.115048 - 3.99835i) q^{16} +(0.981966 + 0.713440i) q^{17} +(-2.43210 + 0.173822i) q^{18} +(1.06190 + 6.70459i) q^{19} +(-3.83098 + 2.30729i) q^{20} +(0.811643 - 5.12451i) q^{21} +(7.96264 + 0.684325i) q^{22} +(1.41375 - 0.459354i) q^{23} +(1.72766 - 2.68738i) q^{24} +(4.48501 + 2.21013i) q^{25} +(-3.19643 + 3.68849i) q^{26} +(-4.75450 - 2.42254i) q^{27} +(-6.40191 - 6.58877i) q^{28} +(6.83601 + 1.08272i) q^{29} +(-3.57191 - 0.00178616i) q^{30} +(1.40171 + 1.01840i) q^{31} +(-1.97550 - 5.30070i) q^{32} +(5.16415 + 3.75197i) q^{33} +(1.66619 + 0.412711i) q^{34} +(-2.33086 + 10.0031i) q^{35} +(-3.09464 + 1.52114i) q^{36} +(2.06313 + 4.04911i) q^{37} +(4.95695 + 8.22114i) q^{38} +(-3.70751 + 1.20464i) q^{39} +(-3.79322 + 5.06078i) q^{40} +(1.56322 + 0.507919i) q^{41} +(-1.66155 - 7.14689i) q^{42} +(1.39763 - 1.39763i) q^{43} +(10.7983 - 3.33767i) q^{44} +(3.30059 + 1.99235i) q^{45} +(1.60832 - 1.35376i) q^{46} +(-6.49783 + 4.72095i) q^{47} +(0.834853 - 4.44035i) q^{48} -14.0991 q^{49} +(7.05257 + 0.511135i) q^{50} +(0.969449 + 0.969449i) q^{51} +(-2.22718 + 6.53329i) q^{52} +(0.580891 - 3.66760i) q^{53} +(-7.51867 - 0.646169i) q^{54} +(-9.66353 - 8.14224i) q^{55} +(-11.8930 - 5.22961i) q^{56} +7.66749i q^{57} +(9.53383 - 2.21648i) q^{58} +(-6.12515 - 12.0213i) q^{59} +(-4.68166 + 1.89715i) q^{60} +(-0.782928 + 1.53658i) q^{61} +(2.37840 + 0.589125i) q^{62} +(-2.44730 + 7.53202i) q^{63} +(-5.40758 - 5.89560i) q^{64} +(7.49176 - 1.85172i) q^{65} +(8.76245 + 2.17044i) q^{66} +(0.287696 + 1.81644i) q^{67} +(2.40288 - 0.345230i) q^{68} +(1.65839 - 0.262663i) q^{69} +(2.26512 + 14.3478i) q^{70} +(2.40796 + 3.31427i) q^{71} +(-3.24637 + 3.63902i) q^{72} +(-8.13655 + 2.64373i) q^{73} +(4.85682 + 4.20890i) q^{74} +(4.61309 + 3.25819i) q^{75} +(10.8676 + 8.13711i) q^{76} +(11.7847 - 23.1288i) q^{77} +(-4.21779 + 3.55019i) q^{78} +(-9.12238 + 6.62780i) q^{79} +(-2.27946 + 8.64893i) q^{80} +(-0.691625 - 0.502495i) q^{81} +(2.31857 - 0.165708i) q^{82} +(-0.505003 - 3.18846i) q^{83} +(-5.97795 - 8.48185i) q^{84} +(-1.77643 - 2.05197i) q^{85} +(1.08824 - 2.57472i) q^{86} +(7.43515 + 2.41583i) q^{87} +(12.3754 - 10.1162i) q^{88} +(4.23039 - 1.37454i) q^{89} +(5.38467 + 0.855608i) q^{90} +(7.19704 + 14.1250i) q^{91} +(1.38767 - 2.62928i) q^{92} +(1.38384 + 1.38384i) q^{93} +(-6.00436 + 9.64189i) q^{94} +(1.08963 - 15.1396i) q^{95} +(-1.26731 - 6.26269i) q^{96} +(3.31506 - 2.40853i) q^{97} +(-18.4757 + 7.49770i) q^{98} +(-6.88967 - 6.88967i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 12 q^{8}+O(q^{10}) \) 464 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 + 12 * q^8	\( 464 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} + 12 q^{8} - 14 q^{10} - 6 q^{11} + 10 q^{12} - 6 q^{13} + 6 q^{14} - 16 q^{15} - 6 q^{16} - 12 q^{17} - 24 q^{18} - 6 q^{19} - 22 q^{20} + 12 q^{21} + 10 q^{22} - 16 q^{24} + 4 q^{26} - 18 q^{27} + 18 q^{28} - 6 q^{29} - 6 q^{30} + 12 q^{31} - 36 q^{32} - 12 q^{33} - 30 q^{34} + 44 q^{35} - 82 q^{36} - 6 q^{37} - 76 q^{38} - 52 q^{40} - 10 q^{42} - 48 q^{43} + 36 q^{44} - 12 q^{45} - 14 q^{46} - 12 q^{47} - 116 q^{48} - 400 q^{49} + 10 q^{50} - 4 q^{51} + 32 q^{52} - 6 q^{53} - 30 q^{54} + 36 q^{56} + 26 q^{58} - 6 q^{59} + 48 q^{60} - 6 q^{61} - 34 q^{62} + 72 q^{63} - 24 q^{64} + 16 q^{65} + 92 q^{66} + 30 q^{67} + 28 q^{68} - 18 q^{69} + 60 q^{70} + 22 q^{72} + 28 q^{74} - 26 q^{75} - 76 q^{76} + 36 q^{77} + 14 q^{78} - 52 q^{79} - 34 q^{80} + 72 q^{81} + 56 q^{82} - 46 q^{83} + 112 q^{84} + 2 q^{85} - 46 q^{86} - 136 q^{88} - 42 q^{90} + 36 q^{91} - 4 q^{93} + 50 q^{94} - 40 q^{95} - 66 q^{96} - 12 q^{97} - 8 q^{98} - 40 q^{99}+O(q^{100}) \) 464 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 + 12 * q^8 - 14 * q^10 - 6 * q^11 + 10 * q^12 - 6 * q^13 + 6 * q^14 - 16 * q^15 - 6 * q^16 - 12 * q^17 - 24 * q^18 - 6 * q^19 - 22 * q^20 + 12 * q^21 + 10 * q^22 - 16 * q^24 + 4 * q^26 - 18 * q^27 + 18 * q^28 - 6 * q^29 - 6 * q^30 + 12 * q^31 - 36 * q^32 - 12 * q^33 - 30 * q^34 + 44 * q^35 - 82 * q^36 - 6 * q^37 - 76 * q^38 - 52 * q^40 - 10 * q^42 - 48 * q^43 + 36 * q^44 - 12 * q^45 - 14 * q^46 - 12 * q^47 - 116 * q^48 - 400 * q^49 + 10 * q^50 - 4 * q^51 + 32 * q^52 - 6 * q^53 - 30 * q^54 + 36 * q^56 + 26 * q^58 - 6 * q^59 + 48 * q^60 - 6 * q^61 - 34 * q^62 + 72 * q^63 - 24 * q^64 + 16 * q^65 + 92 * q^66 + 30 * q^67 + 28 * q^68 - 18 * q^69 + 60 * q^70 + 22 * q^72 + 28 * q^74 - 26 * q^75 - 76 * q^76 + 36 * q^77 + 14 * q^78 - 52 * q^79 - 34 * q^80 + 72 * q^81 + 56 * q^82 - 46 * q^83 + 112 * q^84 + 2 * q^85 - 46 * q^86 - 136 * q^88 - 42 * q^90 + 36 * q^91 - 4 * q^93 + 50 * q^94 - 40 * q^95 - 66 * q^96 - 12 * q^97 - 8 * q^98 - 40 * q^99

Introduction

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