LMFDB - Embedded newform 231.2.ba.a.19.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(19,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 25, 9]))

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

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

chi := DirichletCharacter("231.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.ba (of order $30$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.13
Character	$\chi$	$=$	231.19
Dual form			231.2.ba.a.73.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80279 - 0.189480i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(1.25784 - 0.267361i) q^{4} +(-1.26266 - 2.83599i) q^{5} +(-1.46652 - 1.06549i) q^{6} +(1.48247 - 2.19141i) q^{7} +(-1.23104 + 0.399989i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(1.80279 - 0.189480i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(1.25784 - 0.267361i) q^{4} +(-1.26266 - 2.83599i) q^{5} +(-1.46652 - 1.06549i) q^{6} +(1.48247 - 2.19141i) q^{7} +(-1.23104 + 0.399989i) q^{8} +(0.104528 + 0.994522i) q^{9} +(-2.81368 - 4.87343i) q^{10} +(2.83565 + 1.72020i) q^{11} +(-1.11365 - 0.642969i) q^{12} +(3.84177 - 2.79121i) q^{13} +(2.25734 - 4.23154i) q^{14} +(-0.959305 + 2.95244i) q^{15} +(-4.49304 + 2.00043i) q^{16} +(-0.673700 + 6.40983i) q^{17} +(0.376885 + 1.77310i) q^{18} +(-0.857214 - 0.182206i) q^{19} +(-2.34646 - 3.22962i) q^{20} +(-2.56803 + 0.636571i) q^{21} +(5.43801 + 2.56385i) q^{22} +(-1.09184 + 1.89111i) q^{23} +(1.18249 + 0.526477i) q^{24} +(-3.10286 + 3.44608i) q^{25} +(6.39700 - 5.75989i) q^{26} +(0.587785 - 0.809017i) q^{27} +(1.27880 - 3.15279i) q^{28} +(6.49150 + 2.10922i) q^{29} +(-1.16999 + 5.50438i) q^{30} +(0.418115 - 0.939102i) q^{31} +(-5.47898 + 3.16329i) q^{32} +(-0.956259 - 3.17578i) q^{33} +11.6832i q^{34} +(-8.08668 - 1.43725i) q^{35} +(0.397376 + 1.22300i) q^{36} +(0.613655 + 0.681533i) q^{37} +(-1.57990 - 0.166054i) q^{38} +(-4.72267 - 0.496373i) q^{39} +(2.68876 + 2.98617i) q^{40} +(-2.43424 - 7.49181i) q^{41} +(-4.50899 + 1.63419i) q^{42} -1.01167i q^{43} +(4.02670 + 1.40559i) q^{44} +(2.68847 - 1.55219i) q^{45} +(-1.61002 + 3.61616i) q^{46} +(-1.57301 + 7.40041i) q^{47} +(4.67752 + 1.51982i) q^{48} +(-2.60457 - 6.49740i) q^{49} +(-4.94083 + 6.80047i) q^{50} +(4.78967 - 4.31264i) q^{51} +(4.08605 - 4.53802i) q^{52} +(-5.13093 - 2.28444i) q^{53} +(0.906358 - 1.56986i) q^{54} +(1.29800 - 10.2139i) q^{55} +(-0.948438 + 3.29069i) q^{56} +(0.515114 + 0.708994i) q^{57} +(12.1024 + 2.57245i) q^{58} +(2.73369 + 12.8610i) q^{59} +(-0.417281 + 3.97017i) q^{60} +(8.08725 - 3.60067i) q^{61} +(0.575831 - 1.77222i) q^{62} +(2.33437 + 1.24528i) q^{63} +(-1.32017 + 0.959157i) q^{64} +(-12.7667 - 7.37086i) q^{65} +(-2.32568 - 5.54405i) q^{66} +(2.64393 + 4.57942i) q^{67} +(0.866336 + 8.24263i) q^{68} +(2.07679 - 0.674792i) q^{69} +(-14.8509 - 1.05879i) q^{70} +(0.0539502 + 0.0391971i) q^{71} +(-0.526477 - 1.18249i) q^{72} +(-12.6460 + 2.68800i) q^{73} +(1.23543 + 1.11238i) q^{74} +(4.61176 - 0.484715i) q^{75} -1.12695 q^{76} +(7.97343 - 3.66393i) q^{77} -8.60802 q^{78} +(15.2287 - 1.60060i) q^{79} +(11.3464 + 10.2163i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-5.80796 - 13.0449i) q^{82} +(-6.26756 - 4.55365i) q^{83} +(-3.05997 + 1.48729i) q^{84} +(19.0289 - 6.18285i) q^{85} +(-0.191691 - 1.82382i) q^{86} +(-3.41278 - 5.91111i) q^{87} +(-4.17886 - 0.983407i) q^{88} +(-0.849198 - 0.490285i) q^{89} +(4.55262 - 3.30767i) q^{90} +(-0.421384 - 12.5568i) q^{91} +(-0.867740 + 2.67063i) q^{92} +(-0.939102 + 0.418115i) q^{93} +(-1.43356 + 13.6394i) q^{94} +(0.565638 + 2.66112i) q^{95} +(6.18833 + 1.31537i) q^{96} +(-1.62607 - 2.23809i) q^{97} +(-5.92661 - 11.2199i) q^{98} +(-1.41437 + 2.99993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9}+O(q^{10}) $ 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9	$ 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9} - 2 q^{11} + 12 q^{14} + 12 q^{15} + 40 q^{16} - 60 q^{17} - 10 q^{18} + 52 q^{22} - 24 q^{23} - 90 q^{24} - 20 q^{25} + 24 q^{26} + 30 q^{28} + 40 q^{29} - 18 q^{31} + 18 q^{33} - 80 q^{35} - 24 q^{36} - 8 q^{37} - 24 q^{38} - 90 q^{40} + 14 q^{42} - 82 q^{44} + 12 q^{45} + 70 q^{46} - 24 q^{47} - 94 q^{49} - 20 q^{51} + 4 q^{53} - 104 q^{56} - 32 q^{58} + 48 q^{59} + 30 q^{61} - 10 q^{63} - 48 q^{64} + 36 q^{66} - 40 q^{67} + 180 q^{68} + 146 q^{70} - 32 q^{71} + 10 q^{72} + 90 q^{73} + 40 q^{74} - 24 q^{75} - 72 q^{78} + 50 q^{79} + 228 q^{80} + 16 q^{81} + 168 q^{82} - 60 q^{84} - 20 q^{85} + 146 q^{86} + 16 q^{88} + 48 q^{91} - 204 q^{92} + 44 q^{93} + 10 q^{95} - 44 q^{99}+O(q^{100}) $ 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9 - 2 * q^11 + 12 * q^14 + 12 * q^15 + 40 * q^16 - 60 * q^17 - 10 * q^18 + 52 * q^22 - 24 * q^23 - 90 * q^24 - 20 * q^25 + 24 * q^26 + 30 * q^28 + 40 * q^29 - 18 * q^31 + 18 * q^33 - 80 * q^35 - 24 * q^36 - 8 * q^37 - 24 * q^38 - 90 * q^40 + 14 * q^42 - 82 * q^44 + 12 * q^45 + 70 * q^46 - 24 * q^47 - 94 * q^49 - 20 * q^51 + 4 * q^53 - 104 * q^56 - 32 * q^58 + 48 * q^59 + 30 * q^61 - 10 * q^63 - 48 * q^64 + 36 * q^66 - 40 * q^67 + 180 * q^68 + 146 * q^70 - 32 * q^71 + 10 * q^72 + 90 * q^73 + 40 * q^74 - 24 * q^75 - 72 * q^78 + 50 * q^79 + 228 * q^80 + 16 * q^81 + 168 * q^82 - 60 * q^84 - 20 * q^85 + 146 * q^86 + 16 * q^88 + 48 * q^91 - 204 * q^92 + 44 * q^93 + 10 * q^95 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	1.80279	−	0.189480i	1.27476	−	0.133983i	0.557141	−	0.830418i	$-0.311898\pi$
$2$	1.80279	−	0.189480i	1.27476	−	0.133983i	0.717620	+	0.696435i	$0.245231\pi$
$3$	−0.743145	−	0.669131i	−0.429055	−	0.386323i
$3$	−0.743145	−	0.669131i	−0.429055	−	0.386323i
$4$	1.25784	−	0.267361i	0.628918	−	0.133681i
$5$	−1.26266	−	2.83599i	−0.564681	−	1.26829i	−0.939929	−	0.341369i	$-0.889109\pi$
$5$	−1.26266	−	2.83599i	−0.564681	−	1.26829i	0.375249	−	0.926924i	$-0.377557\pi$
$6$	−1.46652	−	1.06549i	−0.598703	−	0.434983i
$7$	1.48247	−	2.19141i	0.560321	−	0.828276i
$7$	1.48247	−	2.19141i	0.560321	−	0.828276i
$8$	−1.23104	+	0.399989i	−0.435239	+	0.141418i
$9$	0.104528	+	0.994522i	0.0348428	+	0.331507i
$10$	−2.81368	−	4.87343i	−0.889763	−	1.54111i
$11$	2.83565	+	1.72020i	0.854981	+	0.518660i
$11$	2.83565	+	1.72020i	0.854981	+	0.518660i
$12$	−1.11365	−	0.642969i	−0.321484	−	0.185609i
$13$	3.84177	−	2.79121i	1.06551	−	0.774142i	0.0904142	−	0.995904i	$-0.471181\pi$
$13$	3.84177	−	2.79121i	1.06551	−	0.774142i	0.975101	+	0.221762i	$0.0711809\pi$
$14$	2.25734	−	4.23154i	0.603300	−	1.13093i
$15$	−0.959305	+	2.95244i	−0.247692	+	0.762316i
$16$	−4.49304	+	2.00043i	−1.12326	+	0.500107i
$17$	−0.673700	+	6.40983i	−0.163396	+	1.55461i	0.538681	+	0.842510i	$0.318923\pi$
$17$	−0.673700	+	6.40983i	−0.163396	+	1.55461i	−0.702077	+	0.712101i	$0.747744\pi$
$18$	0.376885	+	1.77310i	0.0888326	+	0.417924i
$19$	−0.857214	−	0.182206i	−0.196658	−	0.0418010i	0.108529	−	0.994093i	$-0.465386\pi$
$19$	−0.857214	−	0.182206i	−0.196658	−	0.0418010i	−0.305188	+	0.952292i	$0.598719\pi$
$20$	−2.34646	−	3.22962i	−0.524684	−	0.722166i
$21$	−2.56803	+	0.636571i	−0.560390	+	0.138911i
$22$	5.43801	+	2.56385i	1.15939	+	0.546615i
$23$	−1.09184	+	1.89111i	−0.227663	+	0.394325i	−0.957115	−	0.289708i	$-0.906442\pi$
$23$	−1.09184	+	1.89111i	−0.227663	+	0.394325i	0.729452	+	0.684032i	$0.239775\pi$
$24$	1.18249	+	0.526477i	0.241374	+	0.107467i
$25$	−3.10286	+	3.44608i	−0.620573	+	0.689216i
$26$	6.39700	−	5.75989i	1.25456	−	1.12961i
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	1.27880	−	3.15279i	0.241671	−	0.595822i
$29$	6.49150	+	2.10922i	1.20544	+	0.391672i	0.841760	−	0.539852i	$-0.181520\pi$
$29$	6.49150	+	2.10922i	1.20544	+	0.391672i	0.363681	+	0.931523i	$0.381520\pi$
$30$	−1.16999	+	5.50438i	−0.213610	+	1.00496i
$31$	0.418115	−	0.939102i	0.0750957	−	0.168668i	−0.872097	−	0.489334i	$-0.837240\pi$
$31$	0.418115	−	0.939102i	0.0750957	−	0.168668i	0.947192	+	0.320666i	$0.103907\pi$
$32$	−5.47898	+	3.16329i	−0.968556	+	0.559196i
$33$	−0.956259	−	3.17578i	−0.166463	−	0.552832i
$34$			11.6832i			2.00365i
$35$	−8.08668	−	1.43725i	−1.36690	−	0.242940i
$36$	0.397376	+	1.22300i	0.0662294	+	0.203833i
$37$	0.613655	+	0.681533i	0.100884	+	0.112043i	0.791472	−	0.611205i	$-0.209315\pi$
$37$	0.613655	+	0.681533i	0.100884	+	0.112043i	−0.690588	+	0.723248i	$0.742648\pi$
$38$	−1.57990	−	0.166054i	−0.256293	−	0.0269375i
$39$	−4.72267	−	0.496373i	−0.756233	−	0.0794833i
$40$	2.68876	+	2.98617i	0.425130	+	0.472154i
$41$	−2.43424	−	7.49181i	−0.380164	−	1.17002i	−0.939928	−	0.341373i	$-0.889108\pi$
$41$	−2.43424	−	7.49181i	−0.380164	−	1.17002i	0.559764	−	0.828652i	$-0.310892\pi$
$42$	−4.50899	+	1.63419i	−0.695752	+	0.252161i
$43$		−	1.01167i		−	0.154278i	−0.997020	−	0.0771388i	$-0.975422\pi$
$43$		−	1.01167i		−	0.154278i	0.997020	−	0.0771388i	$-0.0245785\pi$
$44$	4.02670	+	1.40559i	0.607048	+	0.211900i
$45$	2.68847	−	1.55219i	0.400773	−	0.231387i
$46$	−1.61002	+	3.61616i	−0.237384	+	0.533173i
$47$	−1.57301	+	7.40041i	−0.229447	+	1.07946i	0.701036	+	0.713126i	$0.252721\pi$
$47$	−1.57301	+	7.40041i	−0.229447	+	1.07946i	−0.930483	+	0.366335i	$0.880612\pi$
$48$	4.67752	+	1.51982i	0.675142	+	0.219367i
$49$	−2.60457	−	6.49740i	−0.372082	−	0.928200i
$50$	−4.94083	+	6.80047i	−0.698739	+	0.961732i
$51$	4.78967	−	4.31264i	0.670688	−	0.603890i
$52$	4.08605	−	4.53802i	0.566634	−	0.629311i
$53$	−5.13093	−	2.28444i	−0.704787	−	0.313791i	0.0228643	−	0.999739i	$-0.492721\pi$
$53$	−5.13093	−	2.28444i	−0.704787	−	0.313791i	−0.727651	+	0.685947i	$0.759388\pi$
$54$	0.906358	−	1.56986i	0.123340	−	0.213631i
$55$	1.29800	−	10.2139i	0.175022	−	1.37724i
$56$	−0.948438	+	3.29069i	−0.126740	+	0.439737i
$57$	0.515114	+	0.708994i	0.0682285	+	0.0939085i
$58$	12.1024	+	2.57245i	1.58913	+	0.337780i
$59$	2.73369	+	12.8610i	0.355897	+	1.67436i	0.683814	+	0.729656i	$0.260320\pi$
$59$	2.73369	+	12.8610i	0.355897	+	1.67436i	−0.327917	+	0.944706i	$0.606347\pi$
$60$	−0.417281	+	3.97017i	−0.0538708	+	0.512546i
$61$	8.08725	−	3.60067i	1.03547	−	0.461019i	0.182621	−	0.983183i	$-0.441542\pi$
$61$	8.08725	−	3.60067i	1.03547	−	0.461019i	0.852845	+	0.522164i	$0.174875\pi$
$62$	0.575831	−	1.77222i	0.0731306	−	0.225073i
$63$	2.33437	+	1.24528i	0.294103	+	0.156891i
$64$	−1.32017	+	0.959157i	−0.165021	+	0.119895i
$65$	−12.7667	−	7.37086i	−1.58351	−	0.914242i
$66$	−2.32568	−	5.54405i	−0.286271	−	0.682426i
$67$	2.64393	+	4.57942i	0.323007	+	0.559465i	0.981107	−	0.193466i	$-0.0619728\pi$
$67$	2.64393	+	4.57942i	0.323007	+	0.559465i	−0.658100	+	0.752931i	$0.728639\pi$
$68$	0.866336	+	8.24263i	0.105059	+	0.999566i
$69$	2.07679	−	0.674792i	0.250017	−	0.0812354i
$70$	−14.8509	−	1.05879i	−1.77502	−	0.126549i
$71$	0.0539502	+	0.0391971i	0.00640271	+	0.00465184i	0.590982	−	0.806685i	$-0.298740\pi$
$71$	0.0539502	+	0.0391971i	0.00640271	+	0.00465184i	−0.584579	+	0.811337i	$0.698740\pi$
$72$	−0.526477	−	1.18249i	−0.0620459	−	0.139357i
$73$	−12.6460	+	2.68800i	−1.48011	+	0.314606i	−0.876005	−	0.482302i	$-0.839801\pi$
$73$	−12.6460	+	2.68800i	−1.48011	+	0.314606i	−0.604100	+	0.796908i	$0.706467\pi$
$74$	1.23543	+	1.11238i	0.143615	+	0.129312i
$75$	4.61176	−	0.484715i	0.532520	−	0.0559701i
$76$	−1.12695			−0.129270
$77$	7.97343	−	3.66393i	0.908657	−	0.417544i
$78$	−8.60802			−0.974666
$79$	15.2287	−	1.60060i	1.71336	−	0.180081i	0.803585	−	0.595190i	$-0.202923\pi$
$79$	15.2287	−	1.60060i	1.71336	−	0.180081i	0.909772	+	0.415108i	$0.136256\pi$
$80$	11.3464	+	10.2163i	1.26856	+	1.14222i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	−5.80796	−	13.0449i	−0.641382	−	1.44057i
$83$	−6.26756	−	4.55365i	−0.687954	−	0.499828i	0.188033	−	0.982163i	$-0.439789\pi$
$83$	−6.26756	−	4.55365i	−0.687954	−	0.499828i	−0.875987	+	0.482335i	$0.839789\pi$
$84$	−3.05997	+	1.48729i	−0.333870	+	0.162277i
$85$	19.0289	−	6.18285i	2.06397	−	0.670624i
$86$	−0.191691	−	1.82382i	−0.0206705	−	0.196667i
$87$	−3.41278	−	5.91111i	−0.365889	−	0.633738i
$88$	−4.17886	−	0.983407i	−0.445468	−	0.104832i
$89$	−0.849198	−	0.490285i	−0.0900148	−	0.0519701i	0.454317	−	0.890840i	$-0.349883\pi$
$89$	−0.849198	−	0.490285i	−0.0900148	−	0.0519701i	−0.544332	+	0.838870i	$0.683217\pi$
$90$	4.55262	−	3.30767i	0.479889	−	0.348660i
$91$	−0.421384	−	12.5568i	−0.0441730	−	1.31631i
$92$	−0.867740	+	2.67063i	−0.0904681	+	0.278432i
$93$	−0.939102	+	0.418115i	−0.0973804	+	0.0433565i
$94$	−1.43356	+	13.6394i	−0.147860	+	1.40680i
$95$	0.565638	+	2.66112i	0.0580332	+	0.273025i
$96$	6.18833	+	1.31537i	0.631594	+	0.134249i
$97$	−1.62607	−	2.23809i	−0.165102	−	0.227244i	0.718447	−	0.695581i	$-0.244853\pi$
$97$	−1.62607	−	2.23809i	−0.165102	−	0.227244i	−0.883550	+	0.468337i	$0.844853\pi$
$98$	−5.92661	−	11.2199i	−0.598678	−	1.13338i
$99$	−1.41437	+	2.99993i	−0.142150	+	0.301504i
$100$	−2.98155	+	5.16419i	−0.298155	+	0.516419i
$101$	−14.0192	−	6.24174i	−1.39496	−	0.621076i	−0.434800	−	0.900527i	$-0.643181\pi$
$101$	−14.0192	−	6.24174i	−1.39496	−	0.621076i	−0.960160	+	0.279451i	$0.909847\pi$
$102$	7.81758	−	8.68230i	0.774056	−	0.859676i
$103$	−5.71898	+	5.14939i	−0.563508	+	0.507385i	−0.900928	−	0.433970i	$-0.857113\pi$
$103$	−5.71898	+	5.14939i	−0.563508	+	0.507385i	0.337420	+	0.941354i	$0.390446\pi$
$104$	−3.61292	+	4.97276i	−0.354276	+	0.487619i
$105$	5.04787	+	6.47913i	0.492621	+	0.632298i
$106$	−9.68282	−	3.14614i	−0.940478	−	0.305580i
$107$	−3.50307	+	16.4807i	−0.338655	+	1.59325i	0.398268	+	0.917269i	$0.369611\pi$
$107$	−3.50307	+	16.4807i	−0.338655	+	1.59325i	−0.736923	+	0.675977i	$0.763722\pi$
$108$	0.523038	−	1.17476i	0.0503293	−	0.113042i
$109$	−1.96765	+	1.13602i	−0.188466	+	0.108811i	−0.591264	−	0.806478i	$-0.701371\pi$
$109$	−1.96765	+	1.13602i	−0.188466	+	0.108811i	0.402798	+	0.915289i	$0.368038\pi$
$110$	0.404678	−	18.6594i	0.0385845	−	1.77911i
$111$		−	0.917093i		−	0.0870466i
$112$	−2.27702	+	12.8117i	−0.215159	+	1.21059i
$113$	−4.99757	−	15.3810i	−0.470132	−	1.44692i	−0.852412	−	0.522871i	$-0.824861\pi$
$113$	−4.99757	−	15.3810i	−0.470132	−	1.44692i	0.382279	−	0.924047i	$-0.375139\pi$
$114$	1.06298	+	1.18056i	0.0995573	+	0.110570i
$115$	6.74180	+	0.708592i	0.628676	+	0.0660766i
$116$	8.72917	+	0.917473i	0.810483	+	0.0851852i
$117$	3.17749	+	3.52896i	0.293759	+	0.326253i
$118$	7.36518	+	22.6677i	0.678019	+	2.08673i
$119$	13.0478	+	10.9787i	1.19609	+	1.00642i
$120$		−	4.01828i		−	0.366817i
$121$	5.08182	+	9.75577i	0.461984	+	0.886888i
$122$	13.8973	−	8.02362i	1.25820	−	0.726424i
$123$	−3.20401	+	7.19633i	−0.288896	+	0.648871i
$124$	0.274841	−	1.29303i	0.0246814	−	0.116117i
$125$	−1.07127	−	0.348076i	−0.0958170	−	0.0311328i
$126$	4.44432	+	1.80266i	0.395931	+	0.160594i
$127$	−3.38091	+	4.65342i	−0.300007	+	0.412925i	−0.932232	−	0.361860i	$-0.882142\pi$
$127$	−3.38091	+	4.65342i	−0.300007	+	0.412925i	0.632225	+	0.774785i	$0.282142\pi$
$128$	7.20490	−	6.48732i	0.636829	−	0.573404i
$129$	−0.676936	+	0.751814i	−0.0596009	+	0.0661935i
$130$	−24.4123	−	10.8690i	−2.14110	−	0.953277i
$131$	−0.955159	+	1.65438i	−0.0834526	+	0.144544i	−0.904731	−	0.425984i	$-0.859928\pi$
$131$	−0.955159	+	1.65438i	−0.0834526	+	0.144544i	0.821278	+	0.570528i	$0.193261\pi$
$132$	−2.05190	−	3.73894i	−0.178595	−	0.325433i
$133$	−1.67008	+	1.60839i	−0.144815	+	0.139465i
$134$	5.63415	+	7.75474i	0.486716	+	0.669907i
$135$	−3.03654	−	0.645436i	−0.261344	−	0.0555503i
$136$	−1.73451	−	8.16023i	−0.148733	−	0.699734i
$137$	1.72379	−	16.4007i	0.147273	−	1.40121i	−0.632215	−	0.774793i	$-0.717854\pi$
$137$	1.72379	−	16.4007i	0.147273	−	1.40121i	0.779488	−	0.626417i	$-0.215479\pi$
$138$	3.61616	−	1.61002i	0.307828	−	0.137054i
$139$	−4.11965	+	12.6790i	−0.349424	+	1.07542i	0.609748	+	0.792595i	$0.291271\pi$
$139$	−4.11965	+	12.6790i	−0.349424	+	1.07542i	−0.959172	+	0.282822i	$0.908729\pi$
$140$	−10.5560	+	0.354241i	−0.892144	+	0.0299388i
$141$	6.12081	−	4.44703i	0.515465	−	0.374508i
$142$	0.104688	+	0.0604415i	0.00878520	+	0.00507214i
$143$	15.6953	−	1.30628i	1.31251	−	0.109236i
$144$	−2.45912	−	4.25932i	−0.204927	−	0.354943i
$145$	−2.21487	−	21.0731i	−0.183935	−	1.75002i
$146$	−22.2887	+	7.24205i	−1.84463	+	0.599356i
$147$	−2.41204	+	6.57131i	−0.198941	+	0.541992i
$148$	0.954093	+	0.693189i	0.0784260	+	0.0569798i
$149$	−2.72769	−	6.12649i	−0.223461	−	0.501901i	0.766671	−	0.642040i	$-0.221912\pi$
$149$	−2.72769	−	6.12649i	−0.223461	−	0.501901i	−0.990132	+	0.140139i	$0.955245\pi$
$150$	8.22216	−	1.74767i	0.671337	−	0.142697i
$151$	−14.8258	−	13.3492i	−1.20650	−	1.08634i	−0.994022	−	0.109176i	$-0.965179\pi$
$151$	−14.8258	−	13.3492i	−1.20650	−	1.08634i	−0.212481	−	0.977165i	$-0.568154\pi$
$152$	1.12815	−	0.118573i	0.0915047	−	0.00961753i
$153$	−6.44513			−0.521058
$154$	13.6801	−	8.11609i	1.10238	−	0.654013i
$155$	−3.19122			−0.256325
$156$	−6.07306	+	0.638304i	−0.486234	+	0.0511053i
$157$	2.90951	+	2.61973i	0.232204	+	0.209077i	0.777016	−	0.629481i	$-0.216732\pi$
$157$	2.90951	+	2.61973i	0.232204	+	0.209077i	−0.544812	+	0.838558i	$0.683399\pi$
$158$	27.1507	−	5.77106i	2.15999	−	0.459121i
$159$	2.28444	+	5.13093i	0.181168	+	0.406909i
$160$	15.8892	+	11.5442i	1.25615	+	0.912646i
$161$	2.52560	+	5.19618i	0.199045	+	0.409516i
$162$	−1.72399	+	0.560160i	−0.135450	+	0.0440103i
$163$	−0.480457	−	4.57124i	−0.0376323	−	0.358047i	−0.997092	−	0.0762028i	$-0.975720\pi$
$163$	−0.480457	−	4.57124i	−0.0376323	−	0.358047i	0.959460	−	0.281845i	$-0.0909463\pi$
$164$	−5.06489	−	8.77265i	−0.395502	−	0.685029i
$165$	−7.79904	+	6.72188i	−0.607154	+	0.523298i
$166$	−12.1619	−	7.02167i	−0.943945	−	0.544987i
$167$	1.66678	−	1.21098i	0.128979	−	0.0937088i	−0.521425	−	0.853297i	$-0.674599\pi$
$167$	1.66678	−	1.21098i	0.128979	−	0.0937088i	0.650404	+	0.759588i	$0.274599\pi$
$168$	2.90673	−	1.81083i	0.224259	−	0.139709i
$169$	2.95112	−	9.08262i	0.227009	−	0.698663i
$170$	33.1334	−	14.7519i	2.54122	−	1.13142i
$171$	0.0916050	−	0.871564i	0.00700521	−	0.0666501i
$172$	−0.270480	−	1.27251i	−0.0206239	−	0.0970280i
$173$	7.42382	+	1.57798i	0.564422	+	0.119972i	0.481281	−	0.876566i	$-0.340172\pi$
$173$	7.42382	+	1.57798i	0.564422	+	0.119972i	0.0831408	+	0.996538i	$0.473505\pi$
$174$	−7.27256	−	10.0098i	−0.551331	−	0.758842i
$175$	2.95188	+	11.9084i	0.223141	+	0.900188i
$176$	−16.1818	−	2.05641i	−1.21975	−	0.155008i
$177$	6.57417	−	11.3868i	0.494145	−	0.855884i
$178$	−1.62382	−	0.722972i	−0.121711	−	0.0541890i
$179$	7.40515	−	8.22425i	0.553487	−	0.614710i	−0.399864	−	0.916575i	$-0.630943\pi$
$179$	7.40515	−	8.22425i	0.553487	−	0.614710i	0.953351	+	0.301865i	$0.0976092\pi$
$180$	2.96666	−	2.67119i	0.221122	−	0.199099i
$181$	−6.97751	+	9.60372i	−0.518634	+	0.713839i	−0.985345	−	0.170571i	$-0.945439\pi$
$181$	−6.97751	+	9.60372i	−0.518634	+	0.713839i	0.466711	+	0.884410i	$0.345439\pi$
$182$	−3.13893	−	22.5573i	−0.232673	−	1.67206i
$183$	−8.41932	−	2.73560i	−0.622374	−	0.202222i
$184$	0.587668	−	2.76476i	0.0433235	−	0.203821i
$185$	1.15798	−	2.60087i	0.0851364	−	0.191220i
$186$	−1.61378	+	0.931714i	−0.118328	+	0.0683166i
$187$	−12.9366	+	17.0171i	−0.946015	+	1.24442i
$188$			9.72907i			0.709565i
$189$	−0.901516	−	2.48742i	−0.0655756	−	0.180933i
$190$	1.52395	+	4.69024i	0.110559	+	0.340266i
$191$	8.40284	+	9.33230i	0.608008	+	0.675261i	0.966023	−	0.258454i	$-0.0832131\pi$
$191$	8.40284	+	9.33230i	0.608008	+	0.675261i	−0.358015	+	0.933716i	$0.616546\pi$
$192$	1.62288	+	0.170571i	0.117121	+	0.0123099i
$193$	−6.12102	−	0.643345i	−0.440601	−	0.0463090i	−0.118369	−	0.992970i	$-0.537766\pi$
$193$	−6.12102	−	0.643345i	−0.440601	−	0.0463090i	−0.322232	+	0.946661i	$0.604433\pi$
$194$	−3.35553	−	3.72669i	−0.240913	−	0.267561i
$195$	4.55544	+	14.0202i	0.326222	+	1.00401i
$196$	−5.01328	−	7.47630i	−0.358091	−	0.534022i
$197$			23.0266i			1.64057i	0.571952	+	0.820287i	$0.306186\pi$
$197$			23.0266i			1.64057i	−0.571952	+	0.820287i	$0.693814\pi$
$198$	−1.98138	+	5.67622i	−0.140811	+	0.403391i
$199$	−6.57469	+	3.79590i	−0.466068	+	0.269084i	−0.714592	−	0.699541i	$-0.753388\pi$
$199$	−6.57469	+	3.79590i	−0.466068	+	0.269084i	0.248524	+	0.968626i	$0.420054\pi$
$200$	2.44136	−	5.48338i	0.172630	−	0.387733i
$201$	1.09941	−	5.17231i	0.0775463	−	0.364826i
$202$	−26.4562	−	8.59615i	−1.86145	−	0.604823i
$203$	14.2456	−	11.0987i	0.999846	−	0.778976i
$204$	4.87159	−	6.70516i	0.341079	−	0.469455i
$205$	−18.1731	+	16.3631i	−1.26926	+	1.14285i
$206$	−9.33438	+	10.3669i	−0.650357	+	0.722295i
$207$	−1.99488	−	0.888179i	−0.138654	−	0.0617327i
$208$	−11.6776	+	20.2262i	−0.809695	+	1.40243i
$209$	−2.11733	−	1.99125i	−0.146459	−	0.137738i
$210$	10.3279	+	10.7240i	0.712692	+	0.740027i
$211$	7.58407	+	10.4386i	0.522109	+	0.718621i	0.985902	−	0.167322i	$-0.0535120\pi$
$211$	7.58407	+	10.4386i	0.522109	+	0.718621i	−0.463793	+	0.885943i	$0.653512\pi$
$212$	−7.06464	−	1.50163i	−0.485201	−	0.103133i
$213$	−0.0138648	−	0.0652289i	−0.000950002	−	0.00446941i
$214$	−3.19253	+	30.3749i	−0.218237	+	2.07638i
$215$	−2.86907	+	1.27739i	−0.195669	+	0.0871175i
$216$	−0.399989	+	1.23104i	−0.0272158	+	0.0837617i
$217$	−1.43812	−	2.30845i	−0.0976258	−	0.156708i
$218$	−3.33199	+	2.42083i	−0.225671	+	0.163959i
$219$	11.1964	+	6.46427i	0.756586	+	0.436815i
$220$	−1.09813	−	13.1945i	−0.0740362	−	0.889570i
$221$	15.3030	+	26.5055i	1.02939	+	1.78295i
$222$	−0.173771	−	1.65332i	−0.0116628	−	0.110964i
$223$	10.0401	−	3.26221i	0.672332	−	0.218454i	0.0470966	−	0.998890i	$-0.485003\pi$
$223$	10.0401	−	3.26221i	0.672332	−	0.218454i	0.625235	+	0.780437i	$0.285003\pi$
$224$	−1.19035	+	16.6962i	−0.0795333	+	1.11556i
$225$	−3.75154	−	2.72565i	−0.250103	−	0.181710i
$226$	−11.9239	−	26.7816i	−0.793169	−	1.78149i
$227$	−6.98547	+	1.48481i	−0.463642	+	0.0985501i	−0.433809	−	0.901005i	$-0.642831\pi$
$227$	−6.98547	+	1.48481i	−0.463642	+	0.0985501i	−0.0298328	+	0.999555i	$0.509497\pi$
$228$	0.837487	+	0.754077i	0.0554639	+	0.0499399i
$229$	13.7067	−	1.44063i	0.905762	−	0.0951994i	0.359819	−	0.933022i	$-0.382838\pi$
$229$	13.7067	−	1.44063i	0.905762	−	0.0951994i	0.545943	+	0.837823i	$0.316172\pi$
$230$	12.2883			0.810266
$231$	−8.37706	−	2.61243i	−0.551170	−	0.171886i
$232$	−8.83497			−0.580044
$233$	−5.72449	+	0.601668i	−0.375024	+	0.0394166i	−0.290165	−	0.956976i	$-0.593710\pi$
$233$	−5.72449	+	0.601668i	−0.375024	+	0.0394166i	−0.0848581	+	0.996393i	$0.527044\pi$
$234$	6.39700	+	5.75989i	0.418185	+	0.376536i
$235$	22.9737	−	4.88320i	1.49864	−	0.318545i
$236$	6.87708	+	15.4462i	0.447660	+	1.00546i
$237$	−12.3881	−	9.00048i	−0.804694	−	0.584644i
$238$	25.6027	+	17.3200i	1.65958	+	1.12269i
$239$	−1.05336	+	0.342257i	−0.0681361	+	0.0221388i	−0.342887	−	0.939377i	$-0.611405\pi$
$239$	−1.05336	+	0.342257i	−0.0681361	+	0.0221388i	0.274751	+	0.961516i	$0.411405\pi$
$240$	−1.59595	−	15.1844i	−0.103018	−	0.980151i
$241$	10.9061	+	18.8899i	0.702522	+	1.21680i	0.967578	+	0.252571i	$0.0812760\pi$
$241$	10.9061	+	18.8899i	0.702522	+	1.21680i	−0.265057	+	0.964233i	$0.585391\pi$
$242$	11.0100	+	16.6247i	0.707747	+	1.06867i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	9.20975	−	6.69128i	0.589594	−	0.428365i
$245$	−15.1379	+	15.5906i	−0.967123	+	0.996045i
$246$	−4.41258	+	13.5805i	−0.281336	+	0.865863i
$247$	−3.80179	+	1.69267i	−0.241902	+	0.107702i
$248$	−0.139086	+	1.32331i	−0.00883197	+	0.0840306i
$249$	1.61072	+	7.57783i	0.102075	+	0.480226i
$250$	−1.99722	−	0.424521i	−0.126315	−	0.0268491i
$251$	3.01407	+	4.14851i	0.190246	+	0.261851i	0.893476	−	0.449111i	$-0.148259\pi$
$251$	3.01407	+	4.14851i	0.190246	+	0.261851i	−0.703230	+	0.710963i	$0.748259\pi$
$252$	3.26919	+	0.942243i	0.205940	+	0.0593557i
$253$	−6.34916	+	3.48436i	−0.399168	+	0.219060i
$254$	−5.21332	+	9.02974i	−0.327113	+	0.566576i
$255$	−18.2783	−	8.13804i	−1.14463	−	0.509624i
$256$	13.9435	−	15.4858i	0.871466	−	0.967862i
$257$	2.86449	−	2.57920i	0.178682	−	0.160886i	−0.574937	−	0.818198i	$-0.694973\pi$
$257$	2.86449	−	2.57920i	0.178682	−	0.160886i	0.753619	+	0.657312i	$0.228307\pi$
$258$	−1.07792	+	1.48363i	−0.0671082	+	0.0923665i
$259$	2.40324	−	0.334419i	0.149330	−	0.0207798i
$260$	−18.0291	−	5.85801i	−1.11812	−	0.363298i
$261$	−1.41912	+	6.67641i	−0.0878410	+	0.413260i
$262$	−1.40847	+	3.16348i	−0.0870157	+	0.195441i
$263$	−15.6267	+	9.02210i	−0.963586	+	0.556326i	−0.897275	−	0.441473i	$-0.854456\pi$
$263$	−15.6267	+	9.02210i	−0.963586	+	0.556326i	−0.0663110	+	0.997799i	$0.521123\pi$
$264$	2.44747	+	3.52702i	0.150631	+	0.217073i
$265$			17.4357i			1.07107i
$266$	−2.70604	+	3.21604i	−0.165918	+	0.197188i
$267$	0.303013	+	0.932577i	0.0185441	+	0.0570728i
$268$	4.54999	+	5.05328i	0.277935	+	0.308678i
$269$	3.28992	+	0.345785i	0.200590	+	0.0210829i	0.204291	−	0.978910i	$-0.434511\pi$
$269$	3.28992	+	0.345785i	0.200590	+	0.0210829i	−0.00370048	+	0.999993i	$0.501178\pi$
$270$	−5.59653	−	0.588219i	−0.340594	−	0.0357978i
$271$	−12.3149	−	13.6771i	−0.748077	−	0.830823i	0.242158	−	0.970237i	$-0.422145\pi$
$271$	−12.3149	−	13.6771i	−0.748077	−	0.830823i	−0.990234	+	0.139414i	$0.955478\pi$
$272$	−9.79544	−	30.1473i	−0.593936	−	1.82795i
$273$	−8.08897	+	9.61346i	−0.489567	+	0.581833i
$274$		−	29.8936i		−	1.80594i
$275$	−14.7266	+	4.43433i	−0.888047	+	0.267400i
$276$	2.43185	−	1.40403i	0.146380	−	0.0845128i
$277$	7.14388	−	16.0454i	0.429234	−	0.964075i	−0.561402	−	0.827543i	$-0.689738\pi$
$277$	7.14388	−	16.0454i	0.429234	−	0.964075i	0.990636	−	0.136532i	$-0.0435956\pi$
$278$	−5.02443	+	23.6381i	−0.301345	+	1.41772i
$279$	0.977663	+	0.317662i	0.0585311	+	0.0190179i
$280$	10.5299	−	1.46527i	0.629283	−	0.0875668i
$281$	7.26763	−	10.0030i	0.433550	−	0.596731i	−0.535213	−	0.844717i	$-0.679769\pi$
$281$	7.26763	−	10.0030i	0.433550	−	0.596731i	0.968764	+	0.247986i	$0.0797687\pi$
$282$	10.1919	−	9.17682i	0.606918	−	0.546471i
$283$	−10.1388	+	11.2603i	−0.602692	+	0.669357i	−0.964863	−	0.262755i	$-0.915369\pi$
$283$	−10.1388	+	11.2603i	−0.602692	+	0.669357i	0.362171	+	0.932112i	$0.382036\pi$
$284$	0.0783403	+	0.0348794i	0.00464864	+	0.00206971i
$285$	1.36028	−	2.35608i	0.0805762	−	0.139562i
$286$	28.0478	−	5.32890i	1.65850	−	0.315104i
$287$	−20.0263	−	5.77196i	−1.18212	−	0.340708i
$288$	−3.71867	−	5.11831i	−0.219125	−	0.301600i
$289$	−24.0035	−	5.10210i	−1.41197	−	0.300124i
$290$	−7.98586	−	37.5705i	−0.468946	−	2.20622i
$291$	−0.289171	+	2.75128i	−0.0169515	+	0.161283i
$292$	−15.1880	+	6.76212i	−0.888808	+	0.395723i
$293$	0.321046	−	0.988079i	0.0187557	−	0.0577242i	−0.941241	−	0.337737i	$-0.890339\pi$
$293$	0.321046	−	0.988079i	0.0187557	−	0.0577242i	0.959996	+	0.280013i	$0.0903386\pi$
$294$	−3.10325	+	12.3037i	−0.180985	+	0.717566i
$295$	33.0220	−	23.9919i	1.92261	−	1.39686i
$296$	−1.02804	−	0.593539i	−0.0597536	−	0.0344988i
$297$	3.05842	−	1.28298i	0.177468	−	0.0744461i
$298$	−6.07828	−	10.5279i	−0.352106	−	0.609865i
$299$	1.08392	+	10.3128i	0.0626845	+	0.596403i
$300$	5.67124	−	1.84270i	0.327429	−	0.106388i
$301$	−2.21698	−	1.49976i	−0.127784	−	0.0864449i
$302$	−29.2571	−	21.2565i	−1.68356	−	1.22317i
$303$	6.24174	+	14.0192i	0.358578	+	0.805380i
$304$	4.21598	−	0.896135i	0.241803	−	0.0513969i
$305$	−20.4230	−	18.3889i	−1.16941	−	1.05295i
$306$	−11.6192	+	1.22123i	−0.664225	+	0.0698129i
$307$	16.0421			0.915572			0.457786	−	0.889062i	$-0.348643\pi$
$307$	16.0421			0.915572			0.457786	+	0.889062i	$0.348643\pi$
$308$	9.04968	−	6.74041i	0.515653	−	0.384071i
$309$	7.69565			0.437790
$310$	−5.75309	+	0.604674i	−0.326754	+	0.0343432i
$311$	7.37503	+	6.64050i	0.418199	+	0.376548i	0.851197	−	0.524847i	$-0.175877\pi$
$311$	7.37503	+	6.64050i	0.418199	+	0.376548i	−0.432997	+	0.901395i	$0.642544\pi$
$312$	6.01235	−	1.27796i	0.340382	−	0.0723505i
$313$	4.80045	+	10.7820i	0.271337	+	0.609433i	0.996896	−	0.0787265i	$-0.0250854\pi$
$313$	4.80045	+	10.7820i	0.271337	+	0.609433i	−0.725559	+	0.688160i	$0.758419\pi$
$314$	5.74160	+	4.17152i	0.324017	+	0.235412i
$315$	0.584088	−	8.19262i	0.0329096	−	0.461602i
$316$	18.7272	−	6.08484i	1.05349	−	0.342299i
$317$	−2.96622	−	28.2217i	−0.166600	−	1.58509i	−0.684087	−	0.729400i	$-0.739799\pi$
$317$	−2.96622	−	28.2217i	−0.166600	−	1.58509i	0.517488	−	0.855691i	$-0.326867\pi$
$318$	5.09056	+	8.81710i	0.285464	+	0.494439i
$319$	14.7793	+	17.1477i	0.827485	+	0.960086i
$320$	4.38709	+	2.53289i	0.245246	+	0.141593i
$321$	13.6310	−	9.90350i	0.760808	−	0.552760i
$322$	5.53769	+	8.88905i	0.308603	+	0.495367i
$323$	1.74542	−	5.37184i	0.0971176	−	0.298897i
$324$	−1.17476	+	0.523038i	−0.0652646	+	0.0290577i
$325$	−2.30176	+	21.8998i	−0.127679	+	1.21478i
$326$	−1.73232	−	8.14993i	−0.0959444	−	0.451383i
$327$	2.22239	+	0.472384i	0.122899	+	0.0261229i
$328$	5.99329	+	8.24906i	0.330924	+	0.455478i
$329$	13.8854	+	14.4180i	0.765528	+	0.794889i
$330$	−12.7863	+	13.5959i	−0.703864	+	0.748428i
$331$	17.5054	−	30.3202i	0.962184	−	1.66655i	0.245185	−	0.969476i	$-0.421151\pi$
$331$	17.5054	−	30.3202i	0.962184	−	1.66655i	0.716999	−	0.697074i	$-0.245515\pi$
$332$	−9.10103	−	4.05204i	−0.499484	−	0.222385i
$333$	−0.613655	+	0.681533i	−0.0336281	+	0.0373478i
$334$	2.77538	−	2.49897i	0.151862	−	0.136737i
$335$	9.64880	−	13.2804i	0.527170	−	0.725587i
$336$	10.2648	−	7.99730i	0.559993	−	0.436288i
$337$	−8.30747	−	2.69926i	−0.452537	−	0.147038i	0.0738756	−	0.997267i	$-0.476463\pi$
$337$	−8.30747	−	2.69926i	−0.452537	−	0.147038i	−0.526413	+	0.850229i	$0.676463\pi$
$338$	3.59926	−	16.9332i	0.195774	−	0.921044i
$339$	−6.57794	+	14.7743i	−0.357265	+	0.802430i
$340$	22.2821	−	12.8646i	1.20842	−	0.697681i
$341$	2.80107	−	1.94372i	0.151687	−	0.105259i
$342$		−	1.58860i		−	0.0859016i
$343$	−18.0997	−	3.92451i	−0.977291	−	0.211903i
$344$	0.404655	+	1.24540i	0.0218176	+	0.0671476i
$345$	−4.53600	−	5.03773i	−0.244210	−	0.271222i
$346$	13.6825	+	1.43809i	0.735578	+	0.0773124i
$347$	−7.60496	−	0.799313i	−0.408255	−	0.0429094i	−0.101825	−	0.994802i	$-0.532468\pi$
$347$	−7.60496	−	0.799313i	−0.408255	−	0.0429094i	−0.306431	+	0.951893i	$0.599135\pi$
$348$	−5.87313	−	6.52277i	−0.314833	−	0.349657i
$349$	−5.39096	−	16.5917i	−0.288572	−	0.888132i	−0.985305	−	0.170802i	$-0.945364\pi$
$349$	−5.39096	−	16.5917i	−0.288572	−	0.888132i	0.696734	−	0.717330i	$-0.254636\pi$
$350$	7.57801	+	20.9089i	0.405062	+	1.11763i
$351$		−	4.74869i		−	0.253466i
$352$	−20.9780	−	0.454961i	−1.11813	−	0.0242495i
$353$	28.0874	−	16.2163i	1.49494	−	0.863106i	0.494960	−	0.868916i	$-0.335183\pi$
$353$	28.0874	−	16.2163i	1.49494	−	0.863106i	0.999983	+	0.00581017i	$0.00184944\pi$
$354$	9.69425	−	21.7736i	0.515243	−	1.15726i
$355$	0.0430417	−	0.202495i	0.00228441	−	0.0107473i
$356$	−1.19924	−	0.389655i	−0.0635593	−	0.0206517i
$357$	−2.35023	−	16.8895i	−0.124387	−	0.893886i
$358$	11.7916	−	16.2297i	0.623203	−	0.857766i
$359$	−15.6546	+	14.0955i	−0.826218	+	0.743930i	−0.969326	−	0.245777i	$-0.920957\pi$
$359$	−15.6546	+	14.0955i	−0.826218	+	0.743930i	0.143109	+	0.989707i	$0.454290\pi$
$360$	−2.68876	+	2.98617i	−0.141710	+	0.157385i
$361$	−16.6557	−	7.41562i	−0.876618	−	0.390296i
$362$	−10.7592	+	18.6355i	−0.565493	+	0.979462i
$363$	2.75136	−	10.6504i	0.144409	−	0.558999i
$364$	−3.88723	−	15.6817i	−0.203746	−	0.821945i
$365$	23.5908	+	32.4700i	1.23480	+	1.69956i
$366$	−15.6966	−	3.33641i	−0.820472	−	0.174397i
$367$	−6.11847	−	28.7851i	−0.319381	−	1.50257i	−0.786063	−	0.618146i	$-0.787884\pi$
$367$	−6.11847	−	28.7851i	−0.319381	−	1.50257i	0.466682	−	0.884425i	$-0.345449\pi$
$368$	1.12262	−	10.6810i	0.0585204	−	0.556785i
$369$	7.19633	−	3.20401i	0.374626	−	0.166794i
$370$	1.59478	−	4.90822i	0.0829085	−	0.255166i
$371$	−12.6126	+	7.85737i	−0.654813	+	0.407934i
$372$	−1.06945	+	0.777000i	−0.0554484	+	0.0402856i
$373$	3.70494	+	2.13905i	0.191835	+	0.110756i	0.592841	−	0.805319i	$-0.298006\pi$
$373$	3.70494	+	2.13905i	0.191835	+	0.110756i	−0.401007	+	0.916075i	$0.631340\pi$
$374$	−20.0974	+	33.1294i	−1.03921	+	1.71308i
$375$	0.563198	+	0.975488i	0.0290834	+	0.0503740i
$376$	−1.02365	−	9.73939i	−0.0527908	−	0.502271i
$377$	30.8261	−	10.0160i	1.58763	−	0.515851i
$378$	−2.09656	−	4.31347i	−0.107835	−	0.221861i
$379$	18.1321	+	13.1737i	0.931381	+	0.676688i	0.946331	−	0.323200i	$-0.104759\pi$
$379$	18.1321	+	13.1737i	0.931381	+	0.676688i	−0.0149492	+	0.999888i	$0.504759\pi$
$380$	1.42296	+	3.19602i	0.0729963	+	0.163952i
$381$	5.62625	−	1.19590i	0.288242	−	0.0612677i
$382$	16.9168	+	15.2320i	0.865539	+	0.779335i
$383$	11.8938	−	1.25009i	0.607745	−	0.0638766i	0.204343	−	0.978899i	$-0.434494\pi$
$383$	11.8938	−	1.25009i	0.607745	−	0.0638766i	0.403402	+	0.915023i	$0.367828\pi$
$384$	−9.69515			−0.494754
$385$	−20.4586	−	17.9863i	−1.04267	−	0.916664i
$386$	−11.1568			−0.567866
$387$	1.00612	−	0.105748i	0.0511441	−	0.00537547i
$388$	−2.64371	−	2.38041i	−0.134214	−	0.120847i
$389$	1.72937	−	0.367588i	0.0876823	−	0.0186374i	−0.163862	−	0.986483i	$-0.552395\pi$
$389$	1.72937	−	0.367588i	0.0876823	−	0.0186374i	0.251544	+	0.967846i	$0.419062\pi$
$390$	10.8690	+	24.4123i	0.550375	+	1.23616i
$391$	−11.3861	−	8.27252i	−0.575822	−	0.418359i
$392$	5.80522	+	6.95676i	0.293208	+	0.351370i
$393$	1.81682	−	0.590320i	0.0916464	−	0.0297777i
$394$	4.36308	+	41.5119i	0.219809	+	2.09134i
$395$	−23.7679	−	41.1673i	−1.19590	−	2.07135i
$396$	−0.976983	+	4.15156i	−0.0490953	+	0.208624i
$397$	19.7046	+	11.3764i	0.988945	+	0.570967i	0.904959	−	0.425500i	$-0.139902\pi$
$397$	19.7046	+	11.3764i	0.988945	+	0.570967i	0.0839859	+	0.996467i	$0.473235\pi$
$398$	−11.1335	+	8.08897i	−0.558073	+	0.405463i
$399$	2.31734	−	0.0777659i	0.116012	−	0.00389317i
$400$	7.04765	−	21.6904i	0.352382	−	1.08452i
$401$	−5.87545	+	2.61592i	−0.293406	+	0.130633i	−0.548161	−	0.836373i	$-0.684672\pi$
$401$	−5.87545	+	2.61592i	−0.293406	+	0.130633i	0.254755	+	0.967006i	$0.418005\pi$
$402$	1.00195	−	9.53288i	0.0499725	−	0.475457i
$403$	−1.01493	−	4.77486i	−0.0505572	−	0.237853i
$404$	−19.3026	−	4.10290i	−0.960341	−	0.204127i
$405$	1.82471	+	2.51149i	0.0906704	+	0.124797i
$406$	23.5788	−	22.7078i	1.17020	−	1.12697i
$407$	0.567737	+	2.98820i	0.0281417	+	0.148120i
$408$	−4.17127	+	7.22485i	−0.206509	+	0.357683i
$409$	−13.8921	−	6.18514i	−0.686918	−	0.305836i	0.0334374	−	0.999441i	$-0.489355\pi$
$409$	−13.8921	−	6.18514i	−0.686918	−	0.305836i	−0.720355	+	0.693605i	$0.756021\pi$
$410$	−29.6617	+	32.9426i	−1.46489	+	1.62692i
$411$	−12.2553	+	11.0347i	−0.604507	+	0.544301i
$412$	−5.81679	+	8.00613i	−0.286573	+	0.394434i
$413$	32.2364	+	13.0754i	1.58625	+	0.643399i
$414$	−3.76464	−	1.22321i	−0.185022	−	0.0601172i
$415$	−5.00028	+	23.5244i	−0.245454	+	1.15477i
$416$	−12.2196	+	27.4456i	−0.599114	+	1.34563i
$417$	11.5454	−	6.66573i	0.565380	−	0.326422i
$418$	−4.19439	−	3.18861i	−0.205154	−	0.155960i
$419$		−	22.4641i		−	1.09744i	−0.836005	−	0.548722i	$-0.815115\pi$
$419$		−	22.4641i		−	1.09744i	0.836005	−	0.548722i	$-0.184885\pi$
$420$	8.08166	+	6.80008i	0.394345	+	0.331810i
$421$	−1.79190	−	5.51490i	−0.0873319	−	0.268780i	0.897848	−	0.440306i	$-0.145130\pi$
$421$	−1.79190	−	5.51490i	−0.0873319	−	0.268780i	−0.985180	+	0.171526i	$0.945130\pi$
$422$	15.6504	+	17.3815i	0.761847	+	0.846117i
$423$	−7.52430	−	0.790835i	−0.365844	−	0.0384517i
$424$	7.23013	+	0.759917i	0.351126	+	0.0369048i
$425$	−19.9984	−	22.2104i	−0.970064	−	1.07737i
$426$	−0.0373549	−	0.114967i	−0.00180985	−	0.00557015i
$427$	4.09853	−	23.0604i	0.198342	−	1.11597i
$428$			21.6666i			1.04729i
$429$	−12.5380	−	9.53149i	−0.605340	−	0.460184i
$430$	−4.93028	+	2.84650i	−0.237759	+	0.137270i
$431$	1.37179	−	3.08110i	0.0660769	−	0.148411i	−0.877488	−	0.479598i	$-0.840782\pi$
$431$	1.37179	−	3.08110i	0.0660769	−	0.148411i	0.943565	+	0.331187i	$0.107449\pi$
$432$	−1.02256	+	4.81076i	−0.0491979	+	0.231458i
$433$	−5.50027	−	1.78715i	−0.264326	−	0.0858847i	0.173856	−	0.984771i	$-0.444377\pi$
$433$	−5.50027	−	1.78715i	−0.264326	−	0.0858847i	−0.438182	+	0.898886i	$0.644377\pi$
$434$	−3.03002	−	3.88915i	−0.145446	−	0.186685i
$435$	−12.4547	+	17.1424i	−0.597155	+	0.821914i
$436$	−2.17125	+	1.95500i	−0.103984	+	0.0936276i
$437$	1.28051	−	1.42215i	0.0612551	−	0.0680307i
$438$	21.4096	+	9.53219i	1.02299	+	0.455465i
$439$	−12.7375	+	22.0620i	−0.607929	+	1.05296i	0.383652	+	0.923478i	$0.374666\pi$
$439$	−12.7375	+	22.0620i	−0.607929	+	1.05296i	−0.991581	+	0.129486i	$0.958667\pi$
$440$	2.48757	+	13.0929i	0.118590	+	0.624181i
$441$	6.18955	−	3.26947i	0.294741	−	0.155689i
$442$	32.6102	+	44.8841i	1.55111	+	2.13492i
$443$	−16.9158	−	3.59557i	−0.803695	−	0.170831i	−0.212291	−	0.977206i	$-0.568093\pi$
$443$	−16.9158	−	3.59557i	−0.803695	−	0.170831i	−0.591404	+	0.806376i	$0.701426\pi$
$444$	−0.245195	−	1.15355i	−0.0116365	−	0.0547452i
$445$	−0.318191	+	3.02738i	−0.0150837	+	0.143512i
$446$	17.4819	−	7.78346i	0.827793	−	0.368557i
$447$	−2.07235	+	6.37805i	−0.0980189	+	0.301671i
$448$	0.144802	+	4.31495i	0.00684127	+	0.203862i
$449$	18.7703	−	13.6374i	0.885826	−	0.643590i	−0.0489601	−	0.998801i	$-0.515591\pi$
$449$	18.7703	−	13.6374i	0.885826	−	0.643590i	0.934786	+	0.355210i	$0.115591\pi$
$450$	−7.27968	−	4.20292i	−0.343167	−	0.198128i
$451$	5.98478	−	25.4315i	0.281812	−	1.19752i
$452$	−10.3984	−	18.0106i	−0.489100	−	0.847146i
$453$	2.08535	+	19.8407i	0.0979781	+	0.932200i
$454$	−12.3120	+	4.00040i	−0.577829	+	0.187748i
$455$	−35.0788	+	17.0500i	−1.64452	+	0.799318i
$456$	−0.917716	−	0.666760i	−0.0429760	−	0.0312239i
$457$	−15.9719	−	35.8736i	−0.747136	−	1.67809i	−0.734906	−	0.678169i	$-0.762774\pi$
$457$	−15.9719	−	35.8736i	−0.747136	−	1.67809i	−0.0122294	−	0.999925i	$-0.503893\pi$
$458$	24.4372	−	5.19429i	1.14188	−	0.242713i
$459$	4.78967	+	4.31264i	0.223563	+	0.201297i
$460$	8.66954	−	0.911205i	0.404219	−	0.0424852i
$461$	19.7204			0.918469			0.459235	−	0.888315i	$-0.348124\pi$
$461$	19.7204			0.918469			0.459235	+	0.888315i	$0.348124\pi$
$462$	−15.5971	−	3.12237i	−0.725640	−	0.145266i
$463$	−29.7766			−1.38384			−0.691918	−	0.721976i	$-0.743234\pi$
$463$	−29.7766			−1.38384			−0.691918	+	0.721976i	$0.743234\pi$
$464$	−33.3859	+	3.50900i	−1.54990	+	0.162901i
$465$	2.37154	+	2.13535i	0.109978	+	0.0990243i
$466$	−10.2060	+	2.16936i	−0.472784	+	0.100493i
$467$	−0.154216	−	0.346374i	−0.00713625	−	0.0160283i	0.909942	−	0.414735i	$-0.136126\pi$
$467$	−0.154216	−	0.346374i	−0.00713625	−	0.0160283i	−0.917078	+	0.398707i	$0.869459\pi$
$468$	4.94027	+	3.58932i	0.228364	+	0.165916i
$469$	13.9549	+	0.994910i	0.644379	+	0.0459407i
$470$	40.4913	−	13.1564i	1.86773	−	0.606861i
$471$	−0.409242	−	3.89368i	−0.0188569	−	0.179411i
$472$	−8.50956	−	14.7390i	−0.391684	−	0.678417i
$473$	1.74027	−	2.86873i	0.0800176	−	0.131904i
$474$	−24.0385	−	13.8786i	−1.10412	−	0.637467i
$475$	3.28772	−	2.38867i	0.150851	−	0.109600i
$476$	19.3473	+	10.3210i	0.886783	+	0.473060i
$477$	1.73559	−	5.34161i	0.0794674	−	0.244575i
$478$	−1.83413	+	0.816607i	−0.0838911	+	0.0373507i
$479$	−0.291681	+	2.77516i	−0.0133273	+	0.126800i	−0.999163	−	0.0409156i	$-0.986973\pi$
$479$	−0.291681	+	2.77516i	−0.0133273	+	0.126800i	0.985835	+	0.167716i	$0.0536392\pi$
$480$	−4.08341	−	19.2109i	−0.186381	−	0.876855i
$481$	4.25982	+	0.905453i	0.194231	+	0.0412851i
$482$	23.2406	+	31.9879i	1.05858	+	1.45701i
$483$	1.60004	−	5.55147i	0.0728042	−	0.252601i
$484$	9.00041	+	10.9125i	0.409110	+	0.496022i
$485$	−4.29403	+	7.43748i	−0.194982	+	0.337719i
$486$	1.65600	+	0.737298i	0.0751176	+	0.0334445i
$487$	−1.63898	+	1.82028i	−0.0742694	+	0.0824845i	−0.779134	−	0.626857i	$-0.784341\pi$
$487$	−1.63898	+	1.82028i	−0.0742694	+	0.0824845i	0.704865	+	0.709342i	$0.251008\pi$
$488$	−8.51550	+	7.66739i	−0.385479	+	0.347086i
$489$	−2.70171	+	3.71859i	−0.122176	+	0.168160i
$490$	−24.3362	+	30.9748i	−1.09940	+	1.39930i
$491$	26.1156	+	8.48546i	1.17858	+	0.382943i	0.831838	−	0.555018i	$-0.187289\pi$
$491$	26.1156	+	8.48546i	1.17858	+	0.382943i	0.346740	+	0.937961i	$0.387289\pi$
$492$	−2.10610	+	9.90843i	−0.0949504	+	0.446706i
$493$	−17.8930	+	40.1884i	−0.805862	+	1.81000i
$494$	−6.53309	+	3.77188i	−0.293938	+	0.169705i
$495$	10.2936	+	0.223244i	0.462664	+	0.0100341i
$496$			5.05583i			0.227013i
$497$	0.165877	−	0.0601186i	0.00744058	−	0.00269669i
$498$	4.33963	+	13.3560i	0.194463	+	0.598497i
$499$	0.690486	+	0.766863i	0.0309104	+	0.0343295i	0.758402	−	0.651787i	$-0.225981\pi$
$499$	0.690486	+	0.766863i	0.0309104	+	0.0343295i	−0.727491	+	0.686117i	$0.759314\pi$
$500$	−1.44054	−	0.151407i	−0.0644229	−	0.00677112i
$501$	−2.04896	−	0.215355i	−0.0915409	−	0.00962134i
$502$	6.21977	+	6.90776i	0.277602	+	0.308308i
$503$	−12.9177	−	39.7565i	−0.575971	−	1.77266i	−0.632849	−	0.774275i	$-0.718115\pi$
$503$	−12.9177	−	39.7565i	−0.575971	−	1.77266i	0.0568778	−	0.998381i	$-0.481885\pi$
$504$	−3.37180	−	0.599272i	−0.150192	−	0.0266937i
$505$			47.6394i			2.11993i
$506$	−10.7860	+	7.48460i	−0.479494	+	0.332731i
$507$	−8.27057	+	4.77502i	−0.367309	+	0.212066i
$508$	−3.00849	+	6.75717i	−0.133480	+	0.299801i
$509$	7.03466	−	33.0955i	0.311806	−	1.46693i	−0.491245	−	0.871021i	$-0.663458\pi$
$509$	7.03466	−	33.0955i	0.311806	−	1.46693i	0.803051	−	0.595910i	$-0.203209\pi$
$510$	−34.4939	−	11.2077i	−1.52742	−	0.496288i
$511$	−12.8568	+	31.6975i	−0.568753	+	1.40222i
$512$	10.8055	−	14.8725i	0.477539	−	0.657277i
$513$	−0.651266	+	0.586402i	−0.0287541	+	0.0258903i
$514$	4.67536	−	5.19251i	0.206221	−	0.229032i
$515$	21.8248	+	9.71702i	0.961715	+	0.428183i
$516$	−0.650469	+	1.12665i	−0.0286353	+	0.0495978i
$517$	−17.1907	+	18.2791i	−0.756046	+	0.803913i
$518$	4.26917	−	1.05825i	0.187576	−	0.0464970i
$519$	−4.46109	−	6.14017i	−0.195820	−	0.269524i
$520$	18.6646	+	3.96728i	0.818497	+	0.173977i
$521$	7.41769	+	34.8975i	0.324975	+	1.52889i	0.772733	+	0.634731i	$0.218889\pi$
$521$	7.41769	+	34.8975i	0.324975	+	1.52889i	−0.447758	+	0.894155i	$0.647777\pi$
$522$	−1.29331	+	12.3050i	−0.0566067	+	0.538577i
$523$	12.1935	−	5.42891i	0.533186	−	0.237390i	−0.122439	−	0.992476i	$-0.539072\pi$
$523$	12.1935	−	5.42891i	0.533186	−	0.237390i	0.655626	+	0.755086i	$0.272405\pi$
$524$	−0.759115	+	2.33632i	−0.0331621	+	0.102062i
$525$	5.77457	−	10.8248i	0.252023	−	0.472434i
$526$	−26.4621	+	19.2259i	−1.15380	+	0.838288i
$527$	5.73780	+	3.31272i	0.249942	+	0.144304i
$528$	10.6494	+	12.3560i	0.463457	+	0.537724i
$529$	9.11579	+	15.7890i	0.396339	+	0.686479i
$530$	3.30373	+	31.4329i	0.143505	+	1.36536i
$531$	−12.5048	+	4.06306i	−0.542663	+	0.176322i
$532$	−1.67067	+	2.46961i	−0.0724326	+	0.107071i
$533$	−30.2630	−	21.9873i	−1.31084	−	0.952378i
$534$	0.722972	+	1.62382i	0.0312860	+	0.0702696i
$535$	51.1622	−	10.8749i	2.21193	−	0.470161i
$536$	−5.08651	−	4.57991i	−0.219704	−	0.197822i
$537$	−11.0062	+	1.15680i	−0.474953	+	0.0499195i
$538$	5.99654			0.258529
$539$	3.79118	−	22.9047i	0.163298	−	0.986577i
$540$	−3.99203			−0.171790
$541$	22.0838	−	2.32111i	0.949459	−	0.0997921i	0.382878	−	0.923799i	$-0.374933\pi$
$541$	22.0838	−	2.32111i	0.949459	−	0.0997921i	0.566580	+	0.824007i	$0.308266\pi$
$542$	−24.7926	−	22.3234i	−1.06494	−	0.958872i
$543$	11.6114	−	2.46809i	0.498295	−	0.105916i
$544$	−16.5850	−	37.2504i	−0.711074	−	1.59710i
$545$	5.70622	+	4.14581i	0.244428	+	0.177587i
$546$	−12.7611	+	18.8637i	−0.546126	+	0.807292i
$547$	−3.84507	+	1.24934i	−0.164403	+	0.0534178i	−0.390062	−	0.920789i	$-0.627546\pi$
$547$	−3.84507	+	1.24934i	−0.164403	+	0.0534178i	0.225659	+	0.974206i	$0.427546\pi$
$548$	−2.21668	−	21.0903i	−0.0946919	−	0.900933i
$549$	4.42630	+	7.66657i	0.188910	+	0.327201i
$550$	−25.7087	+	10.7845i	−1.09622	+	0.459854i
$551$	−5.18029	−	2.99084i	−0.220688	−	0.127414i
$552$	−2.28671	+	1.66139i	−0.0973288	+	0.0707135i
$553$	19.0684	−	35.7451i	0.810873	−	1.52004i
$554$	9.83859	−	30.2801i	0.418001	−	1.28648i
$555$	−2.60087	+	1.15798i	−0.110401	+	0.0491535i
$556$	−1.79198	+	17.0495i	−0.0759967	+	0.723061i
$557$	−1.51390	−	7.12234i	−0.0641460	−	0.301783i	0.934366	−	0.356315i	$-0.115967\pi$
$557$	−1.51390	−	7.12234i	−0.0641460	−	0.301783i	−0.998512	+	0.0545313i	$0.982634\pi$
$558$	1.82271	+	0.387428i	0.0771613	+	0.0164011i
$559$	−2.82377	−	3.88659i	−0.119433	−	0.164385i
$560$	39.2089	−	9.71921i	1.65688	−	0.410712i
$561$	21.0004	−	3.98994i	0.886638	−	0.168455i
$562$	11.2066	−	19.4104i	0.472722	−	0.818778i
$563$	−17.1550	−	7.63790i	−0.722998	−	0.321899i	0.0120382	−	0.999928i	$-0.496168\pi$
$563$	−17.1550	−	7.63790i	−0.722998	−	0.321899i	−0.735036	+	0.678028i	$0.762835\pi$
$564$	6.51002	−	7.23011i	0.274121	−	0.304442i
$565$	−37.3100	+	33.5940i	−1.56964	+	1.41331i
$566$	−16.1446	+	22.2211i	−0.678606	+	0.934021i
$567$	−0.994453	+	2.45175i	−0.0417631	+	0.102964i
$568$	−0.0820933	−	0.0266737i	−0.00344456	−	0.00111921i
$569$	−4.16171	+	19.5793i	−0.174468	+	0.820808i	0.800652	+	0.599130i	$0.204487\pi$
$569$	−4.16171	+	19.5793i	−0.174468	+	0.820808i	−0.975120	+	0.221678i	$0.928847\pi$
$570$	2.00587	−	4.50525i	0.0840165	−	0.188704i
$571$	27.2074	−	15.7082i	1.13859	−	0.657367i	0.192512	−	0.981295i	$-0.438337\pi$
$571$	27.2074	−	15.7082i	1.13859	−	0.657367i	0.946082	+	0.323928i	$0.105003\pi$
$572$	19.3929	−	5.83941i	0.810859	−	0.244158i
$573$		−	12.5578i		−	0.524612i
$574$	−37.1968	−	6.61101i	−1.55257	−	0.275938i
$575$	−3.12912	−	9.63043i	−0.130493	−	0.401617i
$576$	−1.09190	−	1.21268i	−0.0454957	−	0.0505281i
$577$	−0.302819	−	0.0318275i	−0.0126065	−	0.00132500i	0.0982231	−	0.995164i	$-0.468684\pi$
$577$	−0.302819	−	0.0318275i	−0.0126065	−	0.00132500i	−0.110830	+	0.993839i	$0.535351\pi$
$578$	−44.2399	−	4.64980i	−1.84014	−	0.193406i
$579$	4.11832	+	4.57386i	0.171152	+	0.190083i
$580$	−8.42006	−	25.9143i	−0.349624	−	1.07603i
$581$	−19.2704	+	6.98416i	−0.799470	+	0.289752i
$582$			5.01476i			0.207869i
$583$	−10.6198	−	15.3041i	−0.439828	−	0.633830i
$584$	14.4926	−	8.36731i	0.599708	−	0.346242i
$585$	5.99600	−	13.4672i	0.247904	−	0.556801i
$586$	0.391556	−	1.84213i	0.0161750	−	0.0760975i
$587$	12.5764	+	4.08633i	0.519084	+	0.168661i	0.556830	−	0.830627i	$-0.312018\pi$
$587$	12.5764	+	4.08633i	0.519084	+	0.168661i	−0.0377454	+	0.999287i	$0.512018\pi$
$588$	−1.27703	+	8.91051i	−0.0526639	+	0.367463i
$589$	−0.529525	+	0.728828i	−0.0218187	+	0.0300308i
$590$	54.9856	−	49.5092i	2.26372	−	2.03826i
$591$	15.4078	−	17.1121i	0.633791	−	0.703897i
$592$	−4.12053	−	1.83458i	−0.169353	−	0.0754007i
$593$	19.9072	−	34.4803i	0.817490	−	1.41593i	−0.0900360	−	0.995939i	$-0.528698\pi$
$593$	19.9072	−	34.4803i	0.817490	−	1.41593i	0.907526	−	0.419996i	$-0.137968\pi$
$594$	5.27058	−	2.89245i	0.216255	−	0.118679i
$595$	14.6605	−	50.8660i	0.601023	−	2.08530i
$596$	−5.06897	−	6.97684i	−0.207633	−	0.285782i
$597$	7.42590	+	1.57842i	0.303922	+	0.0646006i
$598$	3.90813	+	18.3863i	0.159815	+	0.751873i
$599$	−1.73658	+	16.5224i	−0.0709547	+	0.675089i	0.900010	+	0.435868i	$0.143559\pi$
$599$	−1.73658	+	16.5224i	−0.0709547	+	0.675089i	−0.970965	+	0.239221i	$0.923108\pi$
$600$	−5.48338	+	2.44136i	−0.223858	+	0.0996680i
$601$	3.19577	−	9.83556i	0.130358	−	0.401201i	−0.864481	−	0.502665i	$-0.832353\pi$
$601$	3.19577	−	9.83556i	0.130358	−	0.401201i	0.994839	+	0.101464i	$0.0323528\pi$
$602$	−4.28091	−	2.28368i	−0.174477	−	0.0930757i
$603$	−4.27797	+	3.10813i	−0.174212	+	0.126573i
$604$	−22.2174	−	12.8272i	−0.904015	−	0.521933i
$605$	21.2506	−	26.7303i	0.863962	−	1.08674i
$606$	13.9089	+	24.0909i	0.565009	+	0.978625i
$607$	1.54966	+	14.7441i	0.0628989	+	0.598443i	0.979890	+	0.199536i	$0.0639436\pi$
$607$	1.54966	+	14.7441i	0.0628989	+	0.598443i	−0.916992	+	0.398907i	$0.869390\pi$
$608$	5.27303	−	1.71331i	0.213850	−	0.0694840i
$609$	−18.0130	−	1.28423i	−0.729925	−	0.0520396i
$610$	−40.3025	−	29.2815i	−1.63180	−	1.18557i
$611$	14.6130	+	32.8213i	0.591177	+	1.32781i
$612$	−8.10692	+	1.72318i	−0.327703	+	0.0696554i
$613$	16.1774	+	14.5662i	0.653398	+	0.588322i	0.927702	−	0.373321i	$-0.121781\pi$
$613$	16.1774	+	14.5662i	0.653398	+	0.588322i	−0.274305	+	0.961643i	$0.588448\pi$
$614$	28.9205	−	3.03967i	1.16714	−	0.122671i
$615$	24.4543			0.986092
$616$	−8.35008	+	7.69974i	−0.336434	+	0.310231i
$617$	−11.6663			−0.469669			−0.234835	−	0.972035i	$-0.575455\pi$
$617$	−11.6663			−0.469669			−0.234835	+	0.972035i	$0.575455\pi$
$618$	13.8736	−	1.45817i	0.558078	−	0.0586564i
$619$	5.66815	+	5.10362i	0.227822	+	0.205132i	0.775134	−	0.631797i	$-0.217682\pi$
$619$	5.66815	+	5.10362i	0.227822	+	0.205132i	−0.547312	+	0.836929i	$0.684349\pi$
$620$	−4.01404	+	0.853210i	−0.161208	+	0.0342657i
$621$	0.888179	+	1.99488i	0.0356414	+	0.0800519i
$622$	14.5538	+	10.5740i	0.583556	+	0.423978i
$623$	−2.33333	+	1.13411i	−0.0934827	+	0.0454372i
$624$	22.2121	−	7.21715i	0.889196	−	0.288917i
$625$	2.78909	+	26.5364i	0.111563	+	1.06146i
$626$	10.6971	+	18.5280i	0.427544	+	0.740528i
$627$	0.241072	+	2.89656i	0.00962748	+	0.115677i
$628$	4.36010	+	2.51730i	0.173987	+	0.100451i
$629$	−4.78193	+	3.47427i	−0.190668	+	0.138528i
$630$	−0.499354	−	14.8802i	−0.0198947	−	0.592841i
$631$	−13.8240	+	42.5459i	−0.550325	+	1.69373i	0.157656	+	0.987494i	$0.449606\pi$
$631$	−13.8240	+	42.5459i	−0.550325	+	1.69373i	−0.707981	+	0.706231i	$0.750394\pi$
$632$	−18.1069	+	8.06170i	−0.720253	+	0.320677i
$633$	1.34871	−	12.8321i	0.0536064	−	0.510031i
$634$	−10.6949	−	50.3157i	−0.424750	−	1.99829i
$635$	17.4660	+	3.71252i	0.693118	+	0.147327i
$636$	4.24526	+	5.84310i	0.168335	+	0.231694i
$637$	−28.1418	−	17.6916i	−1.11502	−	0.700967i
$638$	29.8931	+	28.1132i	1.18348	+	1.11301i
$639$	−0.0333431	+	0.0577519i	−0.00131903	+	0.00228463i
$640$	−27.4953	−	12.2417i	−1.08685	−	0.483896i
$641$	−32.5989	+	36.2048i	−1.28758	+	1.43000i	−0.441213	+	0.897403i	$0.645452\pi$
$641$	−32.5989	+	36.2048i	−1.28758	+	1.43000i	−0.846367	+	0.532600i	$0.821215\pi$
$642$	22.6973	−	20.4367i	0.895789	−	0.806572i
$643$	−10.9067	+	15.0118i	−0.430119	+	0.592008i	−0.967981	−	0.251025i	$-0.919232\pi$
$643$	−10.9067	+	15.0118i	−0.430119	+	0.592008i	0.537862	+	0.843033i	$0.319232\pi$
$644$	4.56605	+	5.86070i	0.179927	+	0.230944i
$645$	2.98688	+	0.970496i	0.117608	+	0.0382133i
$646$	2.12875	−	10.0150i	0.0837547	−	0.394035i
$647$	8.17243	−	18.3556i	0.321291	−	0.721632i	−0.678626	−	0.734484i	$-0.737424\pi$
$647$	8.17243	−	18.3556i	0.321291	−	0.721632i	0.999917	+	0.0128517i	$0.00409094\pi$
$648$	1.12098	−	0.647196i	0.0440361	−	0.0254243i
$649$	−14.3717	+	41.1719i	−0.564140	+	1.61614i
$650$			39.9167i			1.56566i
$651$	−0.475927	+	2.67780i	−0.0186531	+	0.104951i
$652$	−1.82651	−	5.62142i	−0.0715317	−	0.220152i
$653$	−1.79461	−	1.99312i	−0.0702287	−	0.0779968i	0.707007	−	0.707207i	$-0.250045\pi$
$653$	−1.79461	−	1.99312i	−0.0702287	−	0.0779968i	−0.777235	+	0.629210i	$0.783378\pi$
$654$	4.09600	+	0.430507i	0.160166	+	0.0168342i
$655$	5.89786	+	0.619890i	0.230448	+	0.0242211i
$656$	25.9240	+	28.7915i	1.01216	+	1.12412i
$657$	−3.99514	−	12.2958i	−0.155865	−	0.479704i
$658$	27.7643	+	23.3615i	1.08237	+	0.910727i
$659$		−	22.9520i		−	0.894082i	−0.894513	−	0.447041i	$-0.852478\pi$
$659$		−	22.9520i		−	0.894082i	0.894513	−	0.447041i	$-0.147522\pi$
$660$	−8.01274	+	10.5402i	−0.311896	+	0.410276i
$661$	−4.38323	+	2.53066i	−0.170488	+	0.0984312i	−0.582816	−	0.812604i	$-0.698049\pi$
$661$	−4.38323	+	2.53066i	−0.170488	+	0.0984312i	0.412328	+	0.911035i	$0.364716\pi$
$662$	25.8134	−	57.9778i	1.00327	−	2.25337i
$663$	6.36333	−	29.9371i	0.247131	−	1.16266i
$664$	9.53703	+	3.09877i	0.370108	+	0.120256i
$665$	6.67014	+	2.70548i	0.258657	+	0.104914i
$666$	−0.977151	+	1.34493i	−0.0378638	+	0.0521151i
$667$	−11.0764	+	9.97326i	−0.428881	+	0.386166i
$668$	1.77276	−	1.96885i	0.0685902	−	0.0761771i
$669$	−9.64406	−	4.29381i	−0.372861	−	0.166008i
$670$	14.8783	−	25.7700i	0.574800	−	0.995583i
$671$	29.1265	+	3.70144i	1.12442	+	0.142892i
$672$	12.0565	−	11.6112i	0.465091	−	0.447911i
$673$	−18.6232	−	25.6326i	−0.717871	−	0.988064i	−0.999592	−	0.0285680i	$-0.990905\pi$
$673$	−18.6232	−	25.6326i	−0.717871	−	0.988064i	0.281721	−	0.959496i	$-0.409095\pi$
$674$	−15.4880	−	3.29209i	−0.596577	−	0.126806i
$675$	0.964120	+	4.53583i	0.0371090	+	0.174584i
$676$	1.28369	−	12.2135i	0.0493726	−	0.469749i
$677$	−44.7955	+	19.9442i	−1.72163	+	0.766519i	−0.724628	+	0.689140i	$0.757988\pi$
$677$	−44.7955	+	19.9442i	−1.72163	+	0.766519i	−0.997002	+	0.0773786i	$0.975345\pi$
$678$	−9.05918	+	27.8813i	−0.347916	+	1.07077i
$679$	−7.31518	+	0.245485i	−0.280731	+	0.00942085i
$680$	−20.9522	+	15.2227i	−0.803481	+	0.583763i
$681$	6.18475	+	3.57077i	0.237000	+	0.136832i
$682$	4.68144	−	4.03486i	0.179261	−	0.154503i
$683$	−14.1467	−	24.5027i	−0.541307	−	0.937571i	−0.998829	−	0.0483729i	$-0.984596\pi$
$683$	−14.1467	−	24.5027i	−0.541307	−	0.937571i	0.457523	−	0.889198i	$-0.348737\pi$
$684$	−0.117798	−	1.12078i	−0.00450413	−	0.0428539i
$685$	−48.6889	+	15.8200i	−1.86031	+	0.604450i
$686$	−33.3734	−	3.64551i	−1.27420	−	0.139186i
$687$	−11.1500	−	8.10095i	−0.425399	−	0.309071i
$688$	2.02376	+	4.54545i	0.0771553	+	0.173294i
$689$	−26.0882	+	5.54521i	−0.993880	+	0.211256i
$690$	−9.13198	−	8.22247i	−0.347648	−	0.313024i
$691$	−10.5123	+	1.10489i	−0.399908	+	0.0420320i	−0.302348	−	0.953198i	$-0.597770\pi$
$691$	−10.5123	+	1.10489i	−0.399908	+	0.0420320i	−0.0975600	+	0.995230i	$0.531104\pi$
$692$	9.75984			0.371013
$693$	4.47731	+	7.54677i	0.170079	+	0.286678i
$694$	−13.8616			−0.526177
$695$	41.1592	−	4.32601i	1.56126	−	0.164095i
$696$	6.56566	+	5.91175i	0.248871	+	0.224084i
$697$	49.6612	−	10.5558i	1.88105	−	0.399830i
$698$	−12.8625	−	28.8897i	−0.486854	−	1.09349i
$699$	4.65672	+	3.38330i	0.176133	+	0.127968i
$700$	6.89682	+	14.1896i	0.260675	+	0.536315i
$701$	−34.1877	+	11.1083i	−1.29125	+	0.419553i	−0.872530	−	0.488561i	$-0.837522\pi$
$701$	−34.1877	+	11.1083i	−1.29125	+	0.419553i	−0.418723	+	0.908114i	$0.637522\pi$
$702$	−0.899783	−	8.56086i	−0.0339601	−	0.323109i
$703$	−0.401854	−	0.696031i	−0.0151562	−	0.0262513i
$704$	−5.39347	+	0.448882i	−0.203274	+	0.0169179i
$705$	−20.3403	−	11.7435i	−0.766059	−	0.442284i
$706$	47.5629	−	34.5565i	1.79005	−	1.30055i
$707$	−34.4612	+	21.4686i	−1.29605	+	0.807410i
$708$	5.22484	−	16.0804i	0.196362	−	0.604339i
$709$	3.18722	−	1.41904i	0.119699	−	0.0532933i	−0.346014	−	0.938230i	$-0.612465\pi$
$709$	3.18722	−	1.41904i	0.119699	−	0.0532933i	0.465712	+	0.884936i	$0.345798\pi$
$710$	0.0392260	−	0.373211i	0.00147213	−	0.0140063i
$711$	3.18366	+	14.9779i	0.119396	+	0.561716i
$712$	1.24151	+	0.263890i	0.0465274	+	0.00988970i
$713$	1.31944	+	1.81605i	0.0494133	+	0.0680116i
$714$	−7.43718	−	30.0028i	−0.278330	−	1.12283i
$715$	−23.5225	−	42.8625i	−0.879693	−	1.60297i
$716$	7.11562	−	12.3246i	0.265923	−	0.460593i
$717$	1.01181	+	0.450488i	0.0377868	+	0.0168238i
$718$	−25.5511	+	28.3773i	−0.953557	+	1.05903i
$719$	32.5561	−	29.3136i	1.21414	−	1.09321i	0.221119	−	0.975247i	$-0.429029\pi$
$719$	32.5561	−	29.3136i	1.21414	−	1.09321i	0.993018	−	0.117967i	$-0.0376376\pi$
$720$	−8.97435	+	12.3521i	−0.334454	+	0.460337i
$721$	2.80623	+	20.1665i	0.104509	+	0.751038i
$722$	−31.4318	−	10.2128i	−1.16977	−	0.380082i
$723$	4.53500	−	21.3355i	0.168658	−	0.793476i
$724$	−6.20890	+	13.9454i	−0.230752	+	0.518277i
$725$	−27.4108	+	15.8256i	−1.01801	+	0.587749i
$726$	2.94208	−	19.7216i	0.109191	−	0.731938i
$727$		−	5.89021i		−	0.218456i	−0.994017	−	0.109228i	$-0.965162\pi$
$727$		−	5.89021i		−	0.218456i	0.994017	−	0.109228i	$-0.0348378\pi$
$728$	5.54132	+	15.2894i	0.205375	+	0.566661i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	48.6816	+	54.0664i	1.80179	+	2.00109i
$731$	6.48460	+	0.681559i	0.239842	+	0.0252084i
$732$	−11.3215	−	1.18994i	−0.418455	−	0.0439814i
$733$	−6.52180	−	7.24319i	−0.240888	−	0.267533i	0.610563	−	0.791968i	$-0.290943\pi$
$733$	−6.52180	−	7.24319i	−0.240888	−	0.267533i	−0.851451	+	0.524435i	$0.824277\pi$
$734$	−16.4845	−	50.7341i	−0.608454	−	1.87263i
$735$	21.6818	−	1.45685i	0.799743	−	0.0537366i
$736$		−	13.8152i		−	0.509234i
$737$	−0.380264	+	17.5337i	−0.0140072	+	0.645863i
$738$	12.3663	−	7.13970i	0.455211	−	0.262816i
$739$	−10.1224	+	22.7354i	−0.372360	+	0.836335i	0.626040	+	0.779791i	$0.284675\pi$
$739$	−10.1224	+	22.7354i	−0.372360	+	0.836335i	−0.998400	+	0.0565436i	$0.981992\pi$
$740$	0.761179	−	3.58106i	0.0279815	−	0.131643i
$741$	3.95790	+	1.28600i	0.145397	+	0.0472424i
$742$	−21.2490	+	16.5550i	−0.780074	+	0.607753i
$743$	−9.31265	+	12.8178i	−0.341648	+	0.470238i	−0.944922	−	0.327296i	$-0.893863\pi$
$743$	−9.31265	+	12.8178i	−0.341648	+	0.470238i	0.603274	+	0.797534i	$0.293863\pi$
$744$	0.988832	−	0.890348i	0.0362523	−	0.0326417i
$745$	−13.9305	+	15.4714i	−0.510374	+	0.566828i
$746$	7.08452	+	3.15423i	0.259383	+	0.115485i
$747$	3.87356	−	6.70921i	0.141726	−	0.245477i
$748$	−11.7224	+	24.8635i	−0.428612	+	0.909099i
$749$	30.9227	+	32.1087i	1.12989	+	1.17323i
$750$	1.20016	+	1.65188i	0.0438237	+	0.0603181i
$751$	32.3839	+	6.88342i	1.18171	+	0.251180i	0.756547	−	0.653939i	$-0.226885\pi$
$751$	32.3839	+	6.88342i	1.18171	+	0.251180i	0.425159	+	0.905118i	$0.360218\pi$
$752$	−7.73642	−	36.3970i	−0.282118	−	1.32726i
$753$	0.536005	−	5.09975i	0.0195331	−	0.185845i
$754$	53.6750	−	23.8977i	1.95473	−	0.870301i
$755$	−19.1382	+	58.9013i	−0.696510	+	2.14364i
$756$	−1.79900	−	2.88774i	−0.0654290	−	0.105026i
$757$	8.65274	−	6.28658i	0.314489	−	0.228490i	−0.419331	−	0.907833i	$-0.637735\pi$
$757$	8.65274	−	6.28658i	0.314489	−	0.228490i	0.733820	+	0.679344i	$0.237735\pi$
$758$	35.1844	+	20.3137i	1.27795	+	0.737827i
$759$	7.04984	+	1.65903i	0.255893	+	0.0602190i
$760$	−1.76074	−	3.04969i	−0.0638688	−	0.110624i
$761$	−1.23053	−	11.7077i	−0.0446066	−	0.424403i	−0.993923	−	0.110080i	$-0.964889\pi$
$761$	−1.23053	−	11.7077i	−0.0446066	−	0.424403i	0.949316	−	0.314323i	$-0.101777\pi$
$762$	9.91633	−	3.22201i	0.359231	−	0.116721i
$763$	−0.427484	+	5.99604i	−0.0154760	+	0.217071i
$764$	13.0645	+	9.49191i	0.472657	+	0.343405i
$765$	8.13804	+	18.2783i	0.294231	+	0.660855i
$766$	21.2051	−	4.50729i	0.766172	−	0.162855i
$767$	46.4000	+	41.7788i	1.67541	+	1.50854i
$768$	−20.7240	+	2.17818i	−0.747814	+	0.0785984i
$769$	−10.0363			−0.361918			−0.180959	−	0.983491i	$-0.557920\pi$
$769$	−10.0363			−0.361918			−0.180959	+	0.983491i	$0.557920\pi$
$770$	−40.2906	−	28.5488i	−1.45197	−	1.02883i
$771$	−3.85455			−0.138818
$772$	−7.87125	+	0.827302i	−0.283293	+	0.0297752i
$773$	−17.8179	−	16.0433i	−0.640866	−	0.577038i	0.283299	−	0.959032i	$-0.408571\pi$
$773$	−17.8179	−	16.0433i	−0.640866	−	0.577038i	−0.924165	+	0.381993i	$0.875238\pi$
$774$	1.79379	−	0.381281i	0.0644764	−	0.0137049i
$775$	1.93887	+	4.35477i	0.0696462	+	0.156428i
$776$	2.89697	+	2.10477i	0.103995	+	0.0755570i
$777$	−2.00973	−	1.35956i	−0.0720986	−	0.0487740i
$778$	3.04802	−	0.990363i	0.109277	−	0.0355062i
$779$	0.721606	+	6.86562i	0.0258542	+	0.245986i
$780$	9.47846	+	16.4172i	0.339383	+	0.587829i
$781$	0.0855570	+	0.203955i	0.00306147	+	0.00729807i
$782$	−22.0943	−	12.7561i	−0.790089	−	0.456158i
$783$	5.52200	−	4.01197i	0.197340	−	0.143376i
$784$	24.7000	+	23.9828i	0.882143	+	0.856528i
$785$	3.75580	−	11.5592i	0.134050	−	0.412565i
$786$	3.16348	−	1.40847i	0.112838	−	0.0502386i
$787$	0.236006	−	2.24545i	0.00841270	−	0.0800415i	−0.989510	−	0.144465i	$-0.953854\pi$
$787$	0.236006	−	2.24545i	0.00841270	−	0.0800415i	0.997923	+	0.0644230i	$0.0205207\pi$
$788$	6.15641	+	28.9636i	0.219313	+	1.03179i
$789$	17.6499	+	3.75160i	0.628353	+	0.133560i
$790$	−50.6489	−	69.7122i	−1.80201	−	2.48025i
$791$	−41.1147	−	11.8500i	−1.46187	−	0.421339i
$792$	0.541210	−	4.25876i	0.0192311	−	0.151329i
$793$	21.0191	−	36.4061i	0.746410	−	1.29282i
$794$	37.6787	+	16.7757i	1.33717	+	0.595346i
$795$	11.6668	−	12.9573i	0.413778	−	0.459547i
$796$	−7.25501	+	6.53244i	−0.257147	+	0.231536i
$797$	−5.21396	+	7.17641i	−0.184688	+	0.254201i	−0.891315	−	0.453385i	$-0.850216\pi$
$797$	−5.21396	+	7.17641i	−0.184688	+	0.254201i	0.706627	+	0.707587i	$0.250216\pi$
$798$	4.16293	−	0.579285i	0.147366	−	0.0205065i
$799$	−46.3756	−	15.0684i	−1.64065	−	0.533080i
$800$	6.09958	−	28.6963i	0.215653	−	1.01457i
$801$	0.398833	−	0.895795i	0.0140921	−	0.0316513i
$802$	−10.0965	+	5.82922i	−0.356520	+	0.205837i
$803$	−40.4836	−	14.1315i	−1.42863	−	0.498689i
$804$		−	6.79986i		−	0.239812i
$805$	11.5473	−	13.7236i	0.406990	−	0.483693i
$806$	−2.73444	−	8.41574i	−0.0963165	−	0.296432i
$807$	−2.21351	−	2.45836i	−0.0779194	−	0.0865383i
$808$	19.7548	+	2.07631i	0.694971	+	0.0730444i
$809$	−37.6888	−	3.96125i	−1.32507	−	0.139270i	−0.584578	−	0.811338i	$-0.698740\pi$
$809$	−37.6888	−	3.96125i	−1.32507	−	0.139270i	−0.740490	+	0.672067i	$0.765407\pi$
$810$	3.76543	+	4.18194i	0.132304	+	0.146938i
$811$	−12.7718	−	39.3076i	−0.448479	−	1.38028i	−0.878623	−	0.477516i	$-0.841537\pi$
$811$	−12.7718	−	39.3076i	−0.448479	−	1.38028i	0.430144	−	0.902760i	$-0.358463\pi$
$812$	14.9513	−	17.7691i	0.524687	−	0.623572i
$813$			18.4043i			0.645468i
$814$	1.58971	+	5.27950i	0.0557194	+	0.185047i
$815$	−12.3573	+	7.13452i	−0.432859	+	0.249911i
$816$	−12.8930	+	28.9582i	−0.451346	+	1.01374i
$817$	−0.184332	+	0.867214i	−0.00644896	+	0.0303400i
$818$	−26.2164	−	8.51821i	−0.916633	−	0.297832i
$819$	12.4439	−	1.73162i	0.434827	−	0.0605076i
$820$	−18.4839	+	25.4409i	−0.645486	+	0.888435i
$821$	24.8648	−	22.3884i	0.867788	−	0.781360i	−0.109342	−	0.994004i	$-0.534874\pi$
$821$	24.8648	−	22.3884i	0.867788	−	0.781360i	0.977130	+	0.212645i	$0.0682077\pi$
$822$	−20.0027	+	22.2153i	−0.697676	+	0.774847i
$823$	1.63448	+	0.727717i	0.0569743	+	0.0253666i	0.435026	−	0.900418i	$-0.356739\pi$
$823$	1.63448	+	0.727717i	0.0569743	+	0.0253666i	−0.378052	+	0.925784i	$0.623406\pi$
$824$	4.98060	−	8.62664i	0.173507	−	0.300523i
$825$	13.9111	+	6.55866i	0.484323	+	0.228343i
$826$	60.5929	+	17.4640i	2.10830	+	0.607650i
$827$	12.7414	+	17.5371i	0.443063	+	0.609824i	0.970889	−	0.239528i	$-0.0769928\pi$
$827$	12.7414	+	17.5371i	0.443063	+	0.609824i	−0.527826	+	0.849352i	$0.676993\pi$
$828$	−2.74670	−	0.583829i	−0.0954545	−	0.0202895i
$829$	8.98185	+	42.2563i	0.311953	+	1.46762i	0.802733	+	0.596338i	$0.203378\pi$
$829$	8.98185	+	42.2563i	0.311953	+	1.46762i	−0.490781	+	0.871283i	$0.663288\pi$
$830$	−4.55700	+	43.3570i	−0.158176	+	1.50494i
$831$	−16.0454	+	7.14388i	−0.556609	+	0.247818i
$832$	−2.39457	+	7.36972i	−0.0830167	+	0.255499i
$833$	43.4019	−	12.3176i	1.50379	−	0.426778i
$834$	19.5508	−	14.2045i	0.676990	−	0.491862i
$835$	−5.53892	−	3.19790i	−0.191682	−	0.110668i
$836$	−3.19563	−	1.93858i	−0.110523	−	0.0670472i
$837$	−0.513988	−	0.890253i	−0.0177660	−	0.0307716i
$838$	−4.25651	−	40.4980i	−0.147039	−	1.39898i
$839$	−4.43378	+	1.44062i	−0.153071	+	0.0497358i	−0.384550	−	0.923104i	$-0.625643\pi$
$839$	−4.43378	+	1.44062i	−0.153071	+	0.0497358i	0.231479	+	0.972840i	$0.425643\pi$
$840$	−8.80571	−	5.95698i	−0.303826	−	0.205535i
$841$	14.2293	+	10.3382i	0.490665	+	0.356489i
$842$	−4.27538	−	9.60265i	−0.147339	−	0.330929i
$843$	−12.0942	+	2.57071i	−0.416548	+	0.0885399i
$844$	12.3304	+	11.1023i	0.424430	+	0.382158i
$845$	−29.4845	+	3.09894i	−1.01430	+	0.106607i
$846$	−13.7145			−0.471515
$847$	28.9126	+	3.32627i	0.993447	+	0.114292i
$848$	27.6233			0.948588
$849$	15.0693	−	1.58384i	0.517176	−	0.0543574i
$850$	−40.2612	−	36.2514i	−1.38095	−	1.24341i
$851$	−1.95887	+	0.416370i	−0.0671491	+	0.0142730i
$852$	−0.0348794	−	0.0783403i	−0.00119495	−	0.00268390i
$853$	28.1717	+	20.4679i	0.964580	+	0.700808i	0.954210	−	0.299138i	$-0.0966992\pi$
$853$	28.1717	+	20.4679i	0.964580	+	0.700808i	0.0103697	+	0.999946i	$0.496699\pi$
$854$	3.01929	−	42.3495i	0.103318	−	1.44917i
$855$	−2.58741	+	0.840701i	−0.0884876	+	0.0287514i
$856$	−2.27966	−	21.6896i	−0.0779173	−	0.741334i
$857$	10.0546	+	17.4150i	0.343458	+	0.594886i	0.985072	−	0.172141i	$-0.0550684\pi$
$857$	10.0546	+	17.4150i	0.343458	+	0.594886i	−0.641615	+	0.767027i	$0.721735\pi$
$858$	−24.4093	−	14.8075i	−0.833321	−	0.505520i
$859$	3.52413	+	2.03466i	0.120242	+	0.0694216i	0.558915	−	0.829225i	$-0.311218\pi$
$859$	3.52413	+	2.03466i	0.120242	+	0.0694216i	−0.438673	+	0.898647i	$0.644551\pi$
$860$	−3.26730	+	2.37383i	−0.111414	+	0.0809470i
$861$	11.0203	+	17.6896i	0.375570	+	0.602861i
$862$	1.88924	−	5.81448i	0.0643477	−	0.198042i
$863$	−5.74380	+	2.55730i	−0.195521	+	0.0870516i	−0.502162	−	0.864774i	$-0.667462\pi$
$863$	−5.74380	+	2.55730i	−0.195521	+	0.0870516i	0.306640	+	0.951825i	$0.400795\pi$
$864$	−0.661308	+	6.29193i	−0.0224982	+	0.214056i
$865$	−4.89865	−	23.0463i	−0.166559	−	0.783599i
$866$	−10.2544	−	2.17965i	−0.348460	−	0.0740674i
$867$	14.4241	+	19.8531i	0.489868	+	0.674246i
$868$	−2.42611	−	2.51916i	−0.0823474	−	0.0855058i
$869$	45.9365	+	21.6576i	1.55829	+	0.734684i
$870$	−19.2049	+	33.2639i	−0.651108	+	1.12775i
$871$	22.9395	+	10.2133i	0.777275	+	0.346065i
$872$	1.96786	−	2.18553i	0.0666400	−	0.0740112i
$873$	2.05586	−	1.85111i	0.0695804	−	0.0626505i
$874$	2.03901	−	2.80646i	0.0689707	−	0.0949300i
$875$	−2.35090	+	1.83157i	−0.0794748	+	0.0619185i
$876$	15.8116	+	5.13750i	0.534224	+	0.173580i
$877$	−6.30260	+	29.6514i	−0.212824	+	1.00126i	0.733912	+	0.679245i	$0.237693\pi$
$877$	−6.30260	+	29.6514i	−0.212824	+	1.00126i	−0.946736	+	0.322012i	$0.895641\pi$
$878$	−18.7827	+	42.1866i	−0.633886	+	1.42373i
$879$	−0.899738	+	0.519464i	−0.0303474	+	0.0175211i
$880$	14.6002	+	48.4880i	0.492174	+	1.63453i
$881$			43.6699i			1.47128i	0.677375	+	0.735638i	$0.263118\pi$
$881$			43.6699i			1.47128i	−0.677375	+	0.735638i	$0.736882\pi$
$882$	10.5389	−	7.06694i	0.354864	−	0.237956i
$883$	5.73185	+	17.6408i	0.192892	+	0.593661i	0.999995	+	0.00324990i	$0.00103448\pi$
$883$	5.73185	+	17.6408i	0.192892	+	0.593661i	−0.807102	+	0.590411i	$0.798966\pi$
$884$	26.3352	+	29.2482i	0.885748	+	0.983722i
$885$	−40.5938	−	4.26658i	−1.36455	−	0.143420i
$886$	−31.1769	−	3.27682i	−1.04741	−	0.110087i
$887$	−8.06167	−	8.95339i	−0.270684	−	0.300626i	0.592442	−	0.805613i	$-0.298164\pi$
$887$	−8.06167	−	8.95339i	−0.270684	−	0.300626i	−0.863127	+	0.504987i	$0.831497\pi$
$888$	0.366827	+	1.12898i	0.0123099	+	0.0378860i
$889$	5.18547	+	14.3075i	0.173915	+	0.479859i
$890$			5.51801i			0.184964i
$891$	−3.13133	−	1.09305i	−0.104904	−	0.0366184i
$892$	11.7566	−	6.78765i	0.393638	−	0.227267i
$893$	2.69681	−	6.05712i	0.0902451	−	0.202694i
$894$	−2.52749	+	11.8909i	−0.0845320	+	0.397692i
$895$	−32.6741	−	10.6165i	−1.09218	−	0.354869i
$896$	−3.53535	−	25.4062i	−0.118108	−	0.848760i
$897$	6.09508	−	8.38916i	0.203509	−	0.280106i
$898$	31.2548	−	28.1420i	1.04299	−	0.939110i
$899$	4.69497	−	5.21429i	0.156586	−	0.173906i
$900$	−5.44756	−	2.42541i	−0.181585	−	0.0808470i
$901$	18.0995	−	31.3493i	0.602983	−	1.04440i
$902$	5.97049	−	46.9816i	0.198796	−	1.56432i
$903$	0.643997	+	2.59799i	0.0214309	+	0.0864556i
$904$	12.3044	+	16.9356i	0.409239	+	0.563270i
$905$	36.0463	+	7.66188i	1.19822	+	0.254689i
$906$	7.51886	+	35.3735i	0.249798	+	1.17520i
$907$	4.78977	−	45.5716i	0.159042	−	1.51318i	−0.565960	−	0.824433i	$-0.691494\pi$
$907$	4.78977	−	45.5716i	0.159042	−	1.51318i	0.725001	−	0.688747i	$-0.241839\pi$
$908$	−8.38960	+	3.73529i	−0.278419	+	0.123960i
$909$	4.74214	−	14.5948i	0.157287	−	0.484079i
$910$	−60.0089	+	37.3843i	−1.98928	+	1.23928i
$911$	−3.54994	+	2.57918i	−0.117615	+	0.0854521i	−0.645038	−	0.764151i	$-0.723158\pi$
$911$	−3.54994	+	2.57918i	−0.117615	+	0.0854521i	0.527423	+	0.849603i	$0.323158\pi$
$912$	−3.73272	−	2.15509i	−0.123603	−	0.0713620i
$913$	−9.93941	−	23.6940i	−0.328946	−	0.784157i
$914$	−35.5913	−	61.6459i	−1.17726	−	2.03907i
$915$	2.87263	+	27.3312i	0.0949662	+	0.903543i
$916$	16.8556	−	5.47671i	0.556924	−	0.180956i
$917$	2.20944	+	4.54572i	0.0729622	+	0.150113i
$918$	9.45190	+	6.86721i	0.311959	+	0.226652i
$919$	−19.1877	−	43.0962i	−0.632942	−	1.42161i	−0.890335	−	0.455305i	$-0.849530\pi$
$919$	−19.1877	−	43.0962i	−0.632942	−	1.42161i	0.257393	−	0.966307i	$-0.417136\pi$
$920$	−8.58286	+	1.82434i	−0.282969	+	0.0601468i
$921$	−11.9216	−	10.7343i	−0.392831	−	0.353706i
$922$	35.5516	−	3.73662i	1.17083	−	0.123059i
$923$	0.316672			0.0104234
$924$	−11.2354	−	1.04631i	−0.369619	−	0.0344211i
$925$	−4.25271			−0.139828
$926$	−53.6808	+	5.64208i	−1.76406	+	0.185410i
$927$	−5.71898	−	5.14939i	−0.187836	−	0.169128i
$928$	−42.2389	+	8.97815i	−1.38656	+	0.294722i
$929$	6.25456	+	14.0480i	0.205206	+	0.460899i	0.986604	−	0.163133i	$-0.0521600\pi$
$929$	6.25456	+	14.0480i	0.205206	+	0.460899i	−0.781399	+	0.624032i	$0.785493\pi$
$930$	4.67999	+	3.40021i	0.153463	+	0.111497i
$931$	1.04881	+	6.04423i	0.0343733	+	0.198092i
$932$	−7.03960	+	2.28731i	−0.230590	+	0.0749232i
$933$	−1.03735	−	9.86971i	−0.0339613	−	0.323120i
$934$	−0.343649	−	0.595217i	−0.0112445	−	0.0194761i
$935$	64.5949	+	15.2011i	2.11248	+	0.497128i
$936$	−5.32317	−	3.07333i	−0.173993	−	0.100455i
$937$	−46.4005	+	33.7119i	−1.51584	+	1.10132i	−0.552336	+	0.833622i	$0.686263\pi$
$937$	−46.4005	+	33.7119i	−1.51584	+	1.10132i	−0.963502	+	0.267699i	$0.913737\pi$
$938$	25.3463	−	0.850578i	0.827585	−	0.0277723i
$939$	3.64713	−	11.2247i	0.119019	−	0.366304i
$940$	27.5915	−	12.2845i	0.899937	−	0.400678i
$941$	−0.773773	+	7.36195i	−0.0252243	+	0.239993i	0.974644	+	0.223761i	$0.0718336\pi$
$941$	−0.773773	+	7.36195i	−0.0252243	+	0.239993i	−0.999868	+	0.0162316i	$0.994833\pi$
$942$	−1.47555	−	6.94192i	−0.0480761	−	0.226180i
$943$	16.8257	+	3.57641i	0.547919	+	0.116464i
$944$	−38.0101	−	52.3165i	−1.23712	−	1.70276i
$945$	−5.91599	+	5.69747i	−0.192447	+	0.185339i
$946$	2.59376	−	5.50145i	0.0843305	−	0.178868i
$947$	−12.3644	+	21.4158i	−0.401790	+	0.695921i	−0.993942	−	0.109906i	$-0.964945\pi$
$947$	−12.3644	+	21.4158i	−0.401790	+	0.695921i	0.592152	+	0.805826i	$0.298278\pi$
$948$	−17.9886	−	8.00903i	−0.584242	−	0.260121i
$949$	−41.0803	+	45.6243i	−1.33352	+	1.48103i
$950$	5.47444	−	4.92921i	0.177614	−	0.159925i
$951$	−16.6797	+	22.9576i	−0.540876	+	0.744452i
$952$	−20.4538	−	8.29626i	−0.662911	−	0.268883i
$953$	−54.7371	−	17.7852i	−1.77311	−	0.576118i	−0.774691	−	0.632340i	$-0.782095\pi$
$953$	−54.7371	−	17.7852i	−1.77311	−	0.576118i	−0.998418	+	0.0562219i	$0.982095\pi$
$954$	2.11677	−	9.95863i	0.0685330	−	0.322423i
$955$	15.8563	−	35.6139i	0.513099	−	1.15244i
$956$	−1.23345	+	0.712131i	−0.0398925	+	0.0230320i
$957$	0.490845	−	22.6325i	0.0158668	−	0.731606i
$958$			5.05829i			0.163426i
$959$	−33.3853	−	28.0911i	−1.07807	−	0.907109i
$960$	−1.56541	−	4.81784i	−0.0505234	−	0.155495i
$961$	20.0360	+	22.2522i	0.646321	+	0.717812i
$962$	7.85111	+	0.825185i	0.253130	+	0.0266050i
$963$	−16.7565	−	1.76118i	−0.539972	−	0.0567534i
$964$	18.7685	+	20.8445i	0.604492	+	0.671356i
$965$	5.90427	+	18.1715i	0.190065	+	0.584961i
$966$	1.83263	−	10.3113i	0.0589639	−	0.331760i
$967$			52.4804i			1.68766i	0.536613	+	0.843828i	$0.319703\pi$
$967$			52.4804i			1.68766i	−0.536613	+	0.843828i	$0.680297\pi$
$968$	−10.1581	−	9.97708i	−0.326495	−	0.320676i
$969$	−4.89156	+	2.82414i	−0.157140	+	0.0907246i
$970$	−6.33196	+	14.2218i	−0.203307	+	0.456635i
$971$	1.94731	−	9.16137i	0.0624921	−	0.294002i	−0.935792	−	0.352551i	$-0.885314\pi$
$971$	1.94731	−	9.16137i	0.0624921	−	0.294002i	0.998285	+	0.0585493i	$0.0186475\pi$
$972$	1.22300	+	0.397376i	0.0392277	+	0.0127459i
$973$	21.6776	+	27.8240i	0.694952	+	0.891998i
$974$	−2.60983	+	3.59212i	−0.0836243	+	0.115099i
$975$	16.3644	−	14.7345i	0.524079	−	0.471883i
$976$	−29.1334	+	32.3559i	−0.932537	+	1.03569i
$977$	−12.1860	−	5.42554i	−0.389864	−	0.173579i	0.202437	−	0.979295i	$-0.435114\pi$
$977$	−12.1860	−	5.42554i	−0.389864	−	0.173579i	−0.592301	+	0.805717i	$0.701780\pi$
$978$	−4.16600	+	7.21573i	−0.133214	+	0.230734i
$979$	−1.56464	−	2.85107i	−0.0500061	−	0.0911205i
$980$	−14.8726	+	23.6577i	−0.475089	+	0.755716i
$981$	−1.33547	−	1.83812i	−0.0426384	−	0.0586867i
$982$	48.6886	+	10.3491i	1.55371	+	0.330252i
$983$	−5.97609	−	28.1153i	−0.190608	−	0.896738i	−0.964636	−	0.263587i	$-0.915094\pi$
$983$	−5.97609	−	28.1153i	−0.190608	−	0.896738i	0.774028	−	0.633151i	$-0.218239\pi$
$984$	1.06581	−	10.1405i	0.0339769	−	0.323269i
$985$	65.3031	−	29.0748i	2.08073	−	0.926401i
$986$	−24.6424	+	75.8415i	−0.784773	+	2.41528i
$987$	−0.671361	−	20.0058i	−0.0213696	−	0.636792i
$988$	−4.32948	+	3.14555i	−0.137739	+	0.100073i
$989$	1.91318	+	1.10457i	0.0608355	+	0.0351234i
$990$	18.5995	−	1.54798i	0.591131	−	0.0491981i
$991$	13.6535	+	23.6486i	0.433719	+	0.751224i	0.997190	−	0.0749122i	$-0.0238676\pi$
$991$	13.6535	+	23.6486i	0.433719	+	0.751224i	−0.563471	+	0.826136i	$0.690534\pi$
$992$	0.679809	+	6.46795i	0.0215839	+	0.205358i
$993$	−33.2972	+	10.8189i	−1.05666	+	0.343328i
$994$	0.287649	−	0.139811i	0.00912366	−	0.00443455i
$995$	19.0668	+	13.8528i	0.604457	+	0.439164i
$996$	4.05204	+	9.10103i	0.128394	+	0.288377i
$997$	1.31718	−	0.279976i	0.0417156	−	0.00886692i	−0.187007	−	0.982359i	$-0.559879\pi$
$997$	1.31718	−	0.279976i	0.0417156	−	0.00886692i	0.228722	+	0.973492i	$0.426545\pi$
$998$	1.39010	+	1.25166i	0.0440030	+	0.0396205i
$999$	0.912069	−	0.0958623i	0.0288566	−	0.00303295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.ba.a.19.13	✓	128
3.2	odd	2		693.2.cg.c.19.4		128
7.3	odd	6	inner	231.2.ba.a.52.4	yes	128
11.7	odd	10	inner	231.2.ba.a.40.4	yes	128
21.17	even	6		693.2.cg.c.514.13		128
33.29	even	10		693.2.cg.c.271.13		128
77.73	even	30	inner	231.2.ba.a.73.13	yes	128
231.227	odd	30		693.2.cg.c.73.4		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.ba.a.19.13	✓	128	1.1	even	1	trivial
231.2.ba.a.40.4	yes	128	11.7	odd	10	inner
231.2.ba.a.52.4	yes	128	7.3	odd	6	inner
231.2.ba.a.73.13	yes	128	77.73	even	30	inner
693.2.cg.c.19.4		128	3.2	odd	2
693.2.cg.c.73.4		128	231.227	odd	30
693.2.cg.c.271.13		128	33.29	even	10
693.2.cg.c.514.13		128	21.17	even	6

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80279 - 0.189480i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(1.25784 - 0.267361i) q^{4} +(-1.26266 - 2.83599i) q^{5} +(-1.46652 - 1.06549i) q^{6} +(1.48247 - 2.19141i) q^{7} +(-1.23104 + 0.399989i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(1.80279 - 0.189480i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(1.25784 - 0.267361i) q^{4} +(-1.26266 - 2.83599i) q^{5} +(-1.46652 - 1.06549i) q^{6} +(1.48247 - 2.19141i) q^{7} +(-1.23104 + 0.399989i) q^{8} +(0.104528 + 0.994522i) q^{9} +(-2.81368 - 4.87343i) q^{10} +(2.83565 + 1.72020i) q^{11} +(-1.11365 - 0.642969i) q^{12} +(3.84177 - 2.79121i) q^{13} +(2.25734 - 4.23154i) q^{14} +(-0.959305 + 2.95244i) q^{15} +(-4.49304 + 2.00043i) q^{16} +(-0.673700 + 6.40983i) q^{17} +(0.376885 + 1.77310i) q^{18} +(-0.857214 - 0.182206i) q^{19} +(-2.34646 - 3.22962i) q^{20} +(-2.56803 + 0.636571i) q^{21} +(5.43801 + 2.56385i) q^{22} +(-1.09184 + 1.89111i) q^{23} +(1.18249 + 0.526477i) q^{24} +(-3.10286 + 3.44608i) q^{25} +(6.39700 - 5.75989i) q^{26} +(0.587785 - 0.809017i) q^{27} +(1.27880 - 3.15279i) q^{28} +(6.49150 + 2.10922i) q^{29} +(-1.16999 + 5.50438i) q^{30} +(0.418115 - 0.939102i) q^{31} +(-5.47898 + 3.16329i) q^{32} +(-0.956259 - 3.17578i) q^{33} +11.6832i q^{34} +(-8.08668 - 1.43725i) q^{35} +(0.397376 + 1.22300i) q^{36} +(0.613655 + 0.681533i) q^{37} +(-1.57990 - 0.166054i) q^{38} +(-4.72267 - 0.496373i) q^{39} +(2.68876 + 2.98617i) q^{40} +(-2.43424 - 7.49181i) q^{41} +(-4.50899 + 1.63419i) q^{42} -1.01167i q^{43} +(4.02670 + 1.40559i) q^{44} +(2.68847 - 1.55219i) q^{45} +(-1.61002 + 3.61616i) q^{46} +(-1.57301 + 7.40041i) q^{47} +(4.67752 + 1.51982i) q^{48} +(-2.60457 - 6.49740i) q^{49} +(-4.94083 + 6.80047i) q^{50} +(4.78967 - 4.31264i) q^{51} +(4.08605 - 4.53802i) q^{52} +(-5.13093 - 2.28444i) q^{53} +(0.906358 - 1.56986i) q^{54} +(1.29800 - 10.2139i) q^{55} +(-0.948438 + 3.29069i) q^{56} +(0.515114 + 0.708994i) q^{57} +(12.1024 + 2.57245i) q^{58} +(2.73369 + 12.8610i) q^{59} +(-0.417281 + 3.97017i) q^{60} +(8.08725 - 3.60067i) q^{61} +(0.575831 - 1.77222i) q^{62} +(2.33437 + 1.24528i) q^{63} +(-1.32017 + 0.959157i) q^{64} +(-12.7667 - 7.37086i) q^{65} +(-2.32568 - 5.54405i) q^{66} +(2.64393 + 4.57942i) q^{67} +(0.866336 + 8.24263i) q^{68} +(2.07679 - 0.674792i) q^{69} +(-14.8509 - 1.05879i) q^{70} +(0.0539502 + 0.0391971i) q^{71} +(-0.526477 - 1.18249i) q^{72} +(-12.6460 + 2.68800i) q^{73} +(1.23543 + 1.11238i) q^{74} +(4.61176 - 0.484715i) q^{75} -1.12695 q^{76} +(7.97343 - 3.66393i) q^{77} -8.60802 q^{78} +(15.2287 - 1.60060i) q^{79} +(11.3464 + 10.2163i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-5.80796 - 13.0449i) q^{82} +(-6.26756 - 4.55365i) q^{83} +(-3.05997 + 1.48729i) q^{84} +(19.0289 - 6.18285i) q^{85} +(-0.191691 - 1.82382i) q^{86} +(-3.41278 - 5.91111i) q^{87} +(-4.17886 - 0.983407i) q^{88} +(-0.849198 - 0.490285i) q^{89} +(4.55262 - 3.30767i) q^{90} +(-0.421384 - 12.5568i) q^{91} +(-0.867740 + 2.67063i) q^{92} +(-0.939102 + 0.418115i) q^{93} +(-1.43356 + 13.6394i) q^{94} +(0.565638 + 2.66112i) q^{95} +(6.18833 + 1.31537i) q^{96} +(-1.62607 - 2.23809i) q^{97} +(-5.92661 - 11.2199i) q^{98} +(-1.41437 + 2.99993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9}+O(q^{10}) \) 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9	\( 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9} - 2 q^{11} + 12 q^{14} + 12 q^{15} + 40 q^{16} - 60 q^{17} - 10 q^{18} + 52 q^{22} - 24 q^{23} - 90 q^{24} - 20 q^{25} + 24 q^{26} + 30 q^{28} + 40 q^{29} - 18 q^{31} + 18 q^{33} - 80 q^{35} - 24 q^{36} - 8 q^{37} - 24 q^{38} - 90 q^{40} + 14 q^{42} - 82 q^{44} + 12 q^{45} + 70 q^{46} - 24 q^{47} - 94 q^{49} - 20 q^{51} + 4 q^{53} - 104 q^{56} - 32 q^{58} + 48 q^{59} + 30 q^{61} - 10 q^{63} - 48 q^{64} + 36 q^{66} - 40 q^{67} + 180 q^{68} + 146 q^{70} - 32 q^{71} + 10 q^{72} + 90 q^{73} + 40 q^{74} - 24 q^{75} - 72 q^{78} + 50 q^{79} + 228 q^{80} + 16 q^{81} + 168 q^{82} - 60 q^{84} - 20 q^{85} + 146 q^{86} + 16 q^{88} + 48 q^{91} - 204 q^{92} + 44 q^{93} + 10 q^{95} - 44 q^{99}+O(q^{100}) \) 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9 - 2 * q^11 + 12 * q^14 + 12 * q^15 + 40 * q^16 - 60 * q^17 - 10 * q^18 + 52 * q^22 - 24 * q^23 - 90 * q^24 - 20 * q^25 + 24 * q^26 + 30 * q^28 + 40 * q^29 - 18 * q^31 + 18 * q^33 - 80 * q^35 - 24 * q^36 - 8 * q^37 - 24 * q^38 - 90 * q^40 + 14 * q^42 - 82 * q^44 + 12 * q^45 + 70 * q^46 - 24 * q^47 - 94 * q^49 - 20 * q^51 + 4 * q^53 - 104 * q^56 - 32 * q^58 + 48 * q^59 + 30 * q^61 - 10 * q^63 - 48 * q^64 + 36 * q^66 - 40 * q^67 + 180 * q^68 + 146 * q^70 - 32 * q^71 + 10 * q^72 + 90 * q^73 + 40 * q^74 - 24 * q^75 - 72 * q^78 + 50 * q^79 + 228 * q^80 + 16 * q^81 + 168 * q^82 - 60 * q^84 - 20 * q^85 + 146 * q^86 + 16 * q^88 + 48 * q^91 - 204 * q^92 + 44 * q^93 + 10 * q^95 - 44 * q^99

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