LMFDB - Embedded newform 261.2.x.a.2.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(2,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(84))

chi = DirichletCharacter(H, H._module([14, 3]))

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

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

chi := DirichletCharacter("261.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.x (of order $84$, degree $24$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			2.3
Character	$\chi$	$=$	261.2
Dual form			261.2.x.a.131.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87887 - 1.38667i) q^{2} +(-1.39195 + 1.03077i) q^{3} +(1.01780 + 3.29961i) q^{4} +(-0.932500 + 2.37597i) q^{5} +(4.04463 - 0.00651310i) q^{6} +(0.824688 + 0.254382i) q^{7} +(1.12065 - 3.20264i) q^{8} +(0.875028 - 2.86955i) q^{9} +O(q^{10})$	\(q+(-1.87887 - 1.38667i) q^{2} +(-1.39195 + 1.03077i) q^{3} +(1.01780 + 3.29961i) q^{4} +(-0.932500 + 2.37597i) q^{5} +(4.04463 - 0.00651310i) q^{6} +(0.824688 + 0.254382i) q^{7} +(1.12065 - 3.20264i) q^{8} +(0.875028 - 2.86955i) q^{9} +(5.04674 - 3.17108i) q^{10} +(-1.65515 - 0.313171i) q^{11} +(-4.81786 - 3.54377i) q^{12} +(-2.39958 + 0.179824i) q^{13} +(-1.19674 - 1.62152i) q^{14} +(-1.15109 - 4.26842i) q^{15} +(-0.840543 + 0.573072i) q^{16} +(-3.98857 - 3.98857i) q^{17} +(-5.62319 + 4.17815i) q^{18} +(1.05371 + 1.67697i) q^{19} +(-8.78888 - 0.658636i) q^{20} +(-1.41013 + 0.495976i) q^{21} +(2.67555 + 2.88355i) q^{22} +(0.235741 - 1.56404i) q^{23} +(1.74130 + 5.61305i) q^{24} +(-1.11043 - 1.03032i) q^{25} +(4.75787 + 2.98957i) q^{26} +(1.73985 + 4.89621i) q^{27} +2.98006i q^{28} +(-5.33566 + 0.728525i) q^{29} +(-3.75614 + 9.61600i) q^{30} +(-3.20326 - 7.34196i) q^{31} +(-4.40742 - 0.164914i) q^{32} +(2.62668 - 1.27016i) q^{33} +(1.96318 + 13.0248i) q^{34} +(-1.37343 + 1.72222i) q^{35} +(10.3590 - 0.0333625i) q^{36} +(-6.85094 - 2.39725i) q^{37} +(0.345618 - 4.61196i) q^{38} +(3.15474 - 2.72372i) q^{39} +(6.56438 + 5.64911i) q^{40} +(9.31633 + 2.49630i) q^{41} +(3.33721 + 1.02351i) q^{42} +(-5.70727 - 2.49005i) q^{43} +(-0.651260 - 5.78009i) q^{44} +(6.00201 + 4.75490i) q^{45} +(-2.61173 + 2.61173i) q^{46} +(2.00066 - 10.5738i) q^{47} +(0.579285 - 1.66409i) q^{48} +(-5.16827 - 3.52367i) q^{49} +(0.657627 + 3.47564i) q^{50} +(9.66316 + 1.44058i) q^{51} +(-3.03564 - 7.73468i) q^{52} +(-6.52641 + 5.20463i) q^{53} +(3.52048 - 11.6120i) q^{54} +(2.28751 - 3.64055i) q^{55} +(1.73889 - 2.35611i) q^{56} +(-3.19527 - 1.24812i) q^{57} +(11.0352 + 6.03000i) q^{58} +(6.77990 - 3.91438i) q^{59} +(12.9126 - 8.14253i) q^{60} +(0.866962 - 0.458203i) q^{61} +(-4.16236 + 18.2365i) q^{62} +(1.45159 - 2.14389i) q^{63} +(9.64304 + 7.69007i) q^{64} +(1.81036 - 5.86903i) q^{65} +(-6.69650 - 1.25588i) q^{66} +(0.723739 - 1.06153i) q^{67} +(9.10118 - 17.2203i) q^{68} +(1.28402 + 2.42005i) q^{69} +(4.96865 - 1.33135i) q^{70} +(7.20334 + 3.46895i) q^{71} +(-8.20955 - 6.01818i) q^{72} +(-9.86170 + 1.11115i) q^{73} +(9.54785 + 14.0041i) q^{74} +(2.60768 + 0.289563i) q^{75} +(-4.46088 + 5.18364i) q^{76} +(-1.28531 - 0.679309i) q^{77} +(-9.70426 + 0.742950i) q^{78} +(1.14271 + 1.32785i) q^{79} +(-0.577797 - 2.53150i) q^{80} +(-7.46865 - 5.02188i) q^{81} +(-14.0427 - 17.6089i) q^{82} +(-3.12707 + 3.37018i) q^{83} +(-3.07175 - 4.14808i) q^{84} +(13.1961 - 5.75738i) q^{85} +(7.27034 + 12.5926i) q^{86} +(6.67601 - 6.51390i) q^{87} +(-2.85782 + 4.94989i) q^{88} +(-0.810687 + 7.19504i) q^{89} +(-4.68353 - 17.2567i) q^{90} +(-2.02465 - 0.462114i) q^{91} +(5.40066 - 0.814018i) q^{92} +(12.0266 + 6.91779i) q^{93} +(-18.4213 + 17.0925i) q^{94} +(-4.96701 + 0.939809i) q^{95} +(6.30488 - 4.31348i) q^{96} +(0.0849716 + 2.27091i) q^{97} +(4.82436 + 13.7872i) q^{98} +(-2.34696 + 4.47550i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.87887	−	1.38667i	−1.32856	−	0.980525i	−0.999342	−	0.0362721i	$-0.988452\pi$
$2$	−1.87887	−	1.38667i	−1.32856	−	0.980525i	−0.329222	−	0.944253i	$-0.606786\pi$
$3$	−1.39195	+	1.03077i	−0.803641	+	0.595115i
$3$	−1.39195	+	1.03077i	−0.803641	+	0.595115i
$4$	1.01780	+	3.29961i	0.508898	+	1.64981i
$5$	−0.932500	+	2.37597i	−0.417027	+	1.06257i	0.555858	+	0.831277i	$0.312390\pi$
$5$	−0.932500	+	2.37597i	−0.417027	+	1.06257i	−0.972885	+	0.231290i	$0.925705\pi$
$6$	4.04463	−	0.00651310i	1.65121	−	0.00265896i
$7$	0.824688	+	0.254382i	0.311703	+	0.0961475i	0.446660	−	0.894704i	$-0.352613\pi$
$7$	0.824688	+	0.254382i	0.311703	+	0.0961475i	−0.134957	+	0.990851i	$0.543090\pi$
$8$	1.12065	−	3.20264i	0.396211	−	1.13231i
$9$	0.875028	−	2.86955i	0.291676	−	0.956517i
$10$	5.04674	−	3.17108i	1.59592	−	1.00278i
$11$	−1.65515	−	0.313171i	−0.499046	−	0.0944245i	−0.0697059	−	0.997568i	$-0.522206\pi$
$11$	−1.65515	−	0.313171i	−0.499046	−	0.0944245i	−0.429340	+	0.903143i	$0.641254\pi$
$12$	−4.81786	−	3.54377i	−1.39080	−	1.02300i
$13$	−2.39958	+	0.179824i	−0.665525	+	0.0498742i	−0.403209	−	0.915108i	$-0.632105\pi$
$13$	−2.39958	+	0.179824i	−0.665525	+	0.0498742i	−0.262316	+	0.964982i	$0.584486\pi$
$14$	−1.19674	−	1.62152i	−0.319842	−	0.433370i
$15$	−1.15109	−	4.26842i	−0.297210	−	1.10210i
$16$	−0.840543	+	0.573072i	−0.210136	+	0.143268i
$17$	−3.98857	−	3.98857i	−0.967369	−	0.967369i	0.0321147	−	0.999484i	$-0.489776\pi$
$17$	−3.98857	−	3.98857i	−0.967369	−	0.967369i	−0.999484	+	0.0321147i	$0.989776\pi$
$18$	−5.62319	+	4.17815i	−1.32540	+	0.984798i
$19$	1.05371	+	1.67697i	0.241737	+	0.384723i	0.945453	−	0.325759i	$-0.105620\pi$
$19$	1.05371	+	1.67697i	0.241737	+	0.384723i	−0.703716	+	0.710482i	$0.748477\pi$
$20$	−8.78888	−	0.658636i	−1.96525	−	0.147275i
$21$	−1.41013	+	0.495976i	−0.307716	+	0.108231i
$22$	2.67555	+	2.88355i	0.570428	+	0.614776i
$23$	0.235741	−	1.56404i	0.0491554	−	0.326125i	−0.950716	−	0.310064i	$-0.899649\pi$
$23$	0.235741	−	1.56404i	0.0491554	−	0.326125i	0.999871	−	0.0160605i	$-0.00511242\pi$
$24$	1.74130	+	5.61305i	0.355441	+	1.14576i
$25$	−1.11043	−	1.03032i	−0.222085	−	0.206065i
$26$	4.75787	+	2.98957i	0.933095	+	0.586303i
$27$	1.73985	+	4.89621i	0.334835	+	0.942277i
$28$			2.98006i			0.563178i
$29$	−5.33566	+	0.728525i	−0.990807	+	0.135284i
$29$	−5.33566	+	0.728525i	−0.990807	+	0.135284i
$30$	−3.75614	+	9.61600i	−0.685775	+	1.75563i
$31$	−3.20326	−	7.34196i	−0.575323	−	1.31866i	−0.924351	−	0.381543i	$-0.875393\pi$
$31$	−3.20326	−	7.34196i	−0.575323	−	1.31866i	0.349028	−	0.937112i	$-0.386512\pi$
$32$	−4.40742	−	0.164914i	−0.779130	−	0.0291530i
$33$	2.62668	−	1.27016i	0.457247	−	0.221106i
$34$	1.96318	+	13.0248i	0.336682	+	2.23374i
$35$	−1.37343	+	1.72222i	−0.232152	+	0.291109i
$36$	10.3590	−	0.0333625i	1.72650	−	0.00556042i
$37$	−6.85094	−	2.39725i	−1.12629	−	0.394105i	−0.298088	−	0.954539i	$-0.596349\pi$
$37$	−6.85094	−	2.39725i	−1.12629	−	0.394105i	−0.828199	+	0.560434i	$0.810634\pi$
$38$	0.345618	−	4.61196i	0.0560667	−	0.748158i
$39$	3.15474	−	2.72372i	0.505162	−	0.436145i
$40$	6.56438	+	5.64911i	1.03792	+	0.893203i
$41$	9.31633	+	2.49630i	1.45497	+	0.389857i	0.897748	−	0.440509i	$-0.145202\pi$
$41$	9.31633	+	2.49630i	1.45497	+	0.389857i	0.557219	+	0.830366i	$0.311869\pi$
$42$	3.33721	+	1.02351i	0.514943	+	0.157931i
$43$	−5.70727	−	2.49005i	−0.870350	−	0.379730i	−0.0832305	−	0.996530i	$-0.526524\pi$
$43$	−5.70727	−	2.49005i	−0.870350	−	0.379730i	−0.787120	+	0.616801i	$0.788429\pi$
$44$	−0.651260	−	5.78009i	−0.0981811	−	0.871381i
$45$	6.00201	+	4.75490i	0.894727	+	0.708819i
$46$	−2.61173	+	2.61173i	−0.385079	+	0.385079i
$47$	2.00066	−	10.5738i	0.291827	−	1.54234i	−0.462965	−	0.886376i	$-0.653214\pi$
$47$	2.00066	−	10.5738i	0.291827	−	1.54234i	0.754792	−	0.655964i	$-0.227738\pi$
$48$	0.579285	−	1.66409i	0.0836125	−	0.240191i
$49$	−5.16827	−	3.52367i	−0.738325	−	0.503381i
$50$	0.657627	+	3.47564i	0.0930025	+	0.491530i
$51$	9.66316	+	1.44058i	1.35311	+	0.201721i
$52$	−3.03564	−	7.73468i	−0.420967	−	1.07261i
$53$	−6.52641	+	5.20463i	−0.896471	+	0.714912i	−0.959083	−	0.283126i	$-0.908628\pi$
$53$	−6.52641	+	5.20463i	−0.896471	+	0.714912i	0.0626119	+	0.998038i	$0.480057\pi$
$54$	3.52048	−	11.6120i	0.479076	−	1.58019i
$55$	2.28751	−	3.64055i	0.308448	−	0.490892i
$56$	1.73889	−	2.35611i	0.232368	−	0.314848i
$57$	−3.19527	−	1.24812i	−0.423224	−	0.165317i
$58$	11.0352	+	6.03000i	1.44900	+	0.791778i
$59$	6.77990	−	3.91438i	0.882667	−	0.509608i	0.0111304	−	0.999938i	$-0.496457\pi$
$59$	6.77990	−	3.91438i	0.882667	−	0.509608i	0.871537	+	0.490330i	$0.163124\pi$
$60$	12.9126	−	8.14253i	1.66700	−	1.05120i
$61$	0.866962	−	0.458203i	0.111003	−	0.0586669i	−0.410845	−	0.911705i	$-0.634766\pi$
$61$	0.866962	−	0.458203i	0.111003	−	0.0586669i	0.521849	+	0.853038i	$0.325243\pi$
$62$	−4.16236	+	18.2365i	−0.528620	+	2.31604i
$63$	1.45159	−	2.14389i	0.182883	−	0.270105i
$64$	9.64304	+	7.69007i	1.20538	+	0.961258i
$65$	1.81036	−	5.86903i	0.224547	−	0.727964i
$66$	−6.69650	−	1.25588i	−0.824282	−	0.154588i
$67$	0.723739	−	1.06153i	0.0884188	−	0.129687i	−0.779481	−	0.626426i	$-0.784517\pi$
$67$	0.723739	−	1.06153i	0.0884188	−	0.129687i	0.867900	+	0.496739i	$0.165469\pi$
$68$	9.10118	−	17.2203i	1.10368	−	2.08826i
$69$	1.28402	+	2.42005i	0.154578	+	0.291340i
$70$	4.96865	−	1.33135i	0.593868	−	0.159126i
$71$	7.20334	+	3.46895i	0.854880	+	0.411688i	0.809386	−	0.587276i	$-0.199800\pi$
$71$	7.20334	+	3.46895i	0.854880	+	0.411688i	0.0454931	+	0.998965i	$0.485514\pi$
$72$	−8.20955	−	6.01818i	−0.967505	−	0.709249i
$73$	−9.86170	+	1.11115i	−1.15422	+	0.130050i	−0.668259	−	0.743928i	$-0.732960\pi$
$73$	−9.86170	+	1.11115i	−1.15422	+	0.130050i	−0.485965	+	0.873978i	$0.661532\pi$
$74$	9.54785	+	14.0041i	1.10991	+	1.62795i
$75$	2.60768	+	0.289563i	0.301109	+	0.0334359i
$76$	−4.46088	+	5.18364i	−0.511698	+	0.594604i
$77$	−1.28531	−	0.679309i	−0.146475	−	0.0774144i
$78$	−9.70426	+	0.742950i	−1.09879	+	0.0841225i
$79$	1.14271	+	1.32785i	0.128565	+	0.149395i	0.818565	−	0.574415i	$-0.194770\pi$
$79$	1.14271	+	1.32785i	0.128565	+	0.149395i	−0.689999	+	0.723810i	$0.742389\pi$
$80$	−0.577797	−	2.53150i	−0.0645997	−	0.283030i
$81$	−7.46865	−	5.02188i	−0.829850	−	0.557986i
$82$	−14.0427	−	17.6089i	−1.55075	−	1.94458i
$83$	−3.12707	+	3.37018i	−0.343240	+	0.369925i	−0.880954	−	0.473203i	$-0.843098\pi$
$83$	−3.12707	+	3.37018i	−0.343240	+	0.369925i	0.537713	+	0.843128i	$0.319288\pi$
$84$	−3.07175	−	4.14808i	−0.335156	−	0.452593i
$85$	13.1961	−	5.75738i	1.43131	−	0.624476i
$86$	7.27034	+	12.5926i	0.783981	+	1.35789i
$87$	6.67601	−	6.51390i	0.715743	−	0.698364i
$88$	−2.85782	+	4.94989i	−0.304645	+	0.527660i
$89$	−0.810687	+	7.19504i	−0.0859326	+	0.762673i	0.874665	+	0.484729i	$0.161082\pi$
$89$	−0.810687	+	7.19504i	−0.0859326	+	0.762673i	−0.960597	+	0.277944i	$0.910347\pi$
$90$	−4.68353	−	17.2567i	−0.493687	−	1.81901i
$91$	−2.02465	−	0.462114i	−0.212241	−	0.0484427i
$92$	5.40066	−	0.814018i	0.563057	−	0.0848673i
$93$	12.0266	+	6.91779i	1.24710	+	0.717341i
$94$	−18.4213	+	17.0925i	−1.90001	+	1.76296i
$95$	−4.96701	+	0.939809i	−0.509604	+	0.0964224i
$96$	6.30488	−	4.31348i	0.643489	−	0.440243i
$97$	0.0849716	+	2.27091i	0.00862756	+	0.230576i	0.996942	+	0.0781466i	$0.0249002\pi$
$97$	0.0849716	+	2.27091i	0.00862756	+	0.230576i	−0.988314	+	0.152430i	$0.951290\pi$
$98$	4.82436	+	13.7872i	0.487334	+	1.39272i
$99$	−2.34696	+	4.47550i	−0.235878	+	0.449804i
$100$	2.26948	−	4.71263i	0.226948	−	0.471263i
$101$	4.54964	−	10.4279i	0.452707	−	1.03761i	−0.529243	−	0.848470i	$-0.677524\pi$
$101$	4.54964	−	10.4279i	0.452707	−	1.03761i	0.981949	−	0.189144i	$-0.0605713\pi$
$102$	−16.1582	−	16.1063i	−1.59990	−	1.59476i
$103$	1.36210	+	18.1760i	0.134212	+	1.79093i	0.505915	+	0.862583i	$0.331155\pi$
$103$	1.36210	+	18.1760i	0.134212	+	1.79093i	−0.371703	+	0.928352i	$0.621226\pi$
$104$	−2.11319	+	7.88654i	−0.207215	+	0.773339i
$105$	0.136521	−	3.81293i	0.0133231	−	0.372104i
$106$	19.4794	−	0.728868i	1.89201	−	0.0707939i
$107$	0.0334487	+	0.0694569i	0.00323361	+	0.00671465i	0.902579	−	0.430523i	$-0.141671\pi$
$107$	0.0334487	+	0.0694569i	0.00323361	+	0.00671465i	−0.899346	+	0.437238i	$0.855957\pi$
$108$	−14.3848	+	10.7242i	−1.38418	+	1.03194i
$109$	−13.9478	+	3.18351i	−1.33596	+	0.304924i	−0.830064	−	0.557669i	$-0.811696\pi$
$109$	−13.9478	+	3.18351i	−1.33596	+	0.304924i	−0.505898	+	0.862593i	$0.668839\pi$
$110$	−9.34619	+	3.66811i	−0.891124	+	0.349740i
$111$	12.0071	−	3.72490i	1.13967	−	0.353552i
$112$	−0.838965	+	0.258786i	−0.0792747	+	0.0244530i
$113$	−0.528830	+	14.1333i	−0.0497481	+	1.32955i	0.721235	+	0.692691i	$0.243575\pi$
$113$	−0.528830	+	14.1333i	−0.0497481	+	1.32955i	−0.770983	+	0.636856i	$0.780235\pi$
$114$	4.27278	+	6.77585i	0.400183	+	0.634616i
$115$	3.49628	+	2.01858i	0.326030	+	0.188234i
$116$	−7.83446	−	16.8641i	−0.727412	−	1.56579i
$117$	−1.58369	+	7.04308i	−0.146412	+	0.651133i
$118$	−18.1665	−	2.04687i	−1.67236	−	0.188430i
$119$	−2.27470	−	4.30394i	−0.208521	−	0.394542i
$120$	−14.9602	−	1.09689i	−1.36567	−	0.100132i
$121$	−7.59817	−	2.98206i	−0.690743	−	0.271097i
$122$	−2.26429	−	0.341287i	−0.204999	−	0.0308986i
$123$	−15.5410	+	6.12827i	−1.40128	+	0.552568i
$124$	20.9654	−	18.0422i	1.88274	−	1.62023i
$125$	−8.01472	+	3.85968i	−0.716858	+	0.345221i
$126$	−5.70022	+	2.01522i	−0.507816	+	0.179530i
$127$	7.50792	−	2.62714i	0.666220	−	0.233121i	0.0240827	−	0.999710i	$-0.492334\pi$
$127$	7.50792	−	2.62714i	0.666220	−	0.233121i	0.642138	+	0.766589i	$0.278048\pi$
$128$	−5.17140	−	19.2999i	−0.457092	−	1.70589i
$129$	10.5109	−	2.41685i	0.925431	−	0.212792i
$130$	−11.5398	+	8.51679i	−1.01211	+	0.746972i
$131$	−4.17900	+	3.08424i	−0.365121	+	0.269471i	−0.760893	−	0.648877i	$-0.775239\pi$
$131$	−4.17900	+	3.08424i	−0.365121	+	0.269471i	0.395772	+	0.918349i	$0.370477\pi$
$132$	6.86446	+	7.37428i	0.597474	+	0.641848i
$133$	0.442389	+	1.65102i	0.0383600	+	0.143162i
$134$	−2.83181	+	0.990892i	−0.244631	+	0.0856001i
$135$	−13.2557	−	0.431877i	−1.14087	−	0.0371700i
$136$	−17.2438	+	8.30416i	−1.47864	+	0.712076i
$137$	−16.9132	+	14.5550i	−1.44499	+	1.24351i	−0.525272	+	0.850934i	$0.676036\pi$
$137$	−16.9132	+	14.5550i	−1.44499	+	1.24351i	−0.919718	+	0.392580i	$0.871583\pi$
$138$	0.943297	−	6.32749i	0.0802988	−	0.538632i
$139$	−2.12825	−	0.320782i	−0.180516	−	0.0272083i	0.0581623	−	0.998307i	$-0.481476\pi$
$139$	−2.12825	−	0.320782i	−0.180516	−	0.0272083i	−0.238678	+	0.971099i	$0.576714\pi$
$140$	−7.08054	−	2.77891i	−0.598415	−	0.234860i
$141$	8.11429	+	16.7803i	0.683347	+	1.41316i
$142$	−8.72388	−	16.5064i	−0.732092	−	1.38518i
$143$	4.02798	+	0.453845i	0.336837	+	0.0379524i
$144$	0.908962	+	2.91343i	0.0757468	+	0.242786i
$145$	3.24455	−	13.3567i	0.269445	−	1.10922i
$146$	20.0697	+	11.5872i	1.66098	+	0.958966i
$147$	10.8260	−	0.422541i	0.892917	−	0.0348506i
$148$	0.937131	−	25.0453i	0.0770317	−	2.05871i
$149$	−6.94985	+	2.14374i	−0.569354	+	0.175622i	−0.566048	−	0.824372i	$-0.691528\pi$
$149$	−6.94985	+	2.14374i	−0.569354	+	0.175622i	−0.00330545	+	0.999995i	$0.501052\pi$
$150$	−4.49797	−	4.16005i	−0.367258	−	0.339666i
$151$	8.23328	−	3.23133i	0.670015	−	0.262962i	−0.00585438	−	0.999983i	$-0.501864\pi$
$151$	8.23328	−	3.23133i	0.670015	−	0.262962i	0.675870	+	0.737021i	$0.263768\pi$
$152$	6.55157	−	1.49535i	0.531403	−	0.121289i
$153$	−14.9355	+	7.95529i	−1.20746	+	0.643147i
$154$	1.47297	+	3.05864i	0.118695	+	0.246473i
$155$	20.4313	−	0.764487i	1.64108	−	0.0614050i
$156$	12.1981	+	7.63721i	0.976630	+	0.611466i
$157$	2.53666	−	9.46694i	0.202447	−	0.755544i	−0.787765	−	0.615976i	$-0.788762\pi$
$157$	2.53666	−	9.46694i	0.202447	−	0.755544i	0.990212	−	0.139568i	$-0.0445715\pi$
$158$	−0.305711	−	4.07944i	−0.0243211	−	0.324543i
$159$	3.71963	−	13.9718i	0.294986	−	1.10804i
$160$	4.50175	−	10.3181i	0.355895	−	0.815720i
$161$	0.592277	−	1.22987i	0.0466779	−	0.0969277i
$162$	7.06895	+	19.7920i	0.555389	+	1.55501i
$163$	3.29986	+	9.43045i	0.258465	+	0.738650i	0.997861	+	0.0653787i	$0.0208255\pi$
$163$	3.29986	+	9.43045i	0.258465	+	0.738650i	−0.739396	+	0.673271i	$0.764889\pi$
$164$	1.24529	+	33.2810i	0.0972407	+	2.59881i
$165$	0.568479	+	7.42535i	0.0442560	+	0.578063i
$166$	10.5487	−	1.99592i	0.818738	−	0.154914i
$167$	14.9454	−	13.8673i	1.15651	−	1.07309i	0.160216	−	0.987082i	$-0.448781\pi$
$167$	14.9454	−	13.8673i	1.15651	−	1.07309i	0.996295	−	0.0860035i	$-0.0274096\pi$
$168$	0.00816743	+	5.07197i	0.000630131	+	0.391311i
$169$	−7.12913	+	1.07454i	−0.548395	+	0.0826572i
$170$	−32.7773	−	7.48121i	−2.51391	−	0.573783i
$171$	5.73417	−	1.55628i	0.438503	−	0.119011i
$172$	2.40739	−	21.3661i	0.183561	−	1.62915i
$173$	9.91642	−	17.1757i	0.753931	−	1.30585i	−0.191973	−	0.981400i	$-0.561488\pi$
$173$	9.91642	−	17.1757i	0.753931	−	1.30585i	0.945904	−	0.324447i	$-0.105178\pi$
$174$	−21.5760	+	2.98137i	−1.63567	+	0.226017i
$175$	−0.653658	−	1.13217i	−0.0494119	−	0.0855839i
$176$	1.57069	−	0.685286i	0.118395	−	0.0516554i
$177$	−5.40243	+	12.4371i	−0.406072	+	0.934831i
$178$	11.5003	−	12.3944i	0.861987	−	0.929001i
$179$	0.388639	+	0.487338i	0.0290483	+	0.0364254i	0.796143	−	0.605108i	$-0.206870\pi$
$179$	0.388639	+	0.487338i	0.0290483	+	0.0364254i	−0.767095	+	0.641533i	$0.778299\pi$
$180$	−9.58051	+	24.6438i	−0.714089	+	1.83684i
$181$	1.81487	+	7.95147i	0.134898	+	0.591028i	0.996511	+	0.0834618i	$0.0265977\pi$
$181$	1.81487	+	7.95147i	0.134898	+	0.591028i	−0.861613	+	0.507566i	$0.830545\pi$
$182$	3.16326	+	3.67578i	0.234477	+	0.272467i
$183$	−0.734463	+	1.53143i	−0.0542931	+	0.113207i
$184$	−4.74488	−	2.50774i	−0.349797	−	0.184873i
$185$	12.0843	−	14.0422i	0.888454	−	1.03240i
$186$	−13.0038	−	29.6746i	−0.953487	−	2.17585i
$187$	5.35256	+	7.85077i	0.391418	+	0.574105i
$188$	36.9256	−	4.16051i	2.69307	−	0.303437i
$189$	0.189325	+	4.48044i	0.0137714	+	0.325904i
$190$	10.6356	+	5.12183i	0.771586	+	0.371576i
$191$	−24.2044	+	6.48555i	−1.75137	+	0.469278i	−0.984917	−	0.173025i	$-0.944646\pi$
$191$	−24.2044	+	6.48555i	−1.75137	+	0.469278i	−0.766451	+	0.642303i	$0.777979\pi$
$192$	−21.3493	−	0.764409i	−1.54075	−	0.0551664i
$193$	5.31626	−	10.0589i	0.382673	−	0.724052i	−0.615260	−	0.788324i	$-0.710949\pi$
$193$	5.31626	−	10.0589i	0.382673	−	0.724052i	0.997932	+	0.0642725i	$0.0204727\pi$
$194$	2.98936	−	4.38459i	0.214624	−	0.314795i
$195$	3.52970	+	10.0354i	0.252767	+	0.718652i
$196$	6.36650	−	20.6397i	0.454750	−	1.47426i
$197$	−10.3031	−	8.21644i	−0.734065	−	0.585397i	0.183483	−	0.983023i	$-0.441263\pi$
$197$	−10.3031	−	8.21644i	−0.734065	−	0.585397i	−0.917548	+	0.397626i	$0.869834\pi$
$198$	10.6157	−	5.15443i	0.754424	−	0.366309i
$199$	−3.04261	+	13.3306i	−0.215685	+	0.944978i	0.744940	+	0.667131i	$0.232478\pi$
$199$	−3.04261	+	13.3306i	−0.215685	+	0.944978i	−0.960625	+	0.277847i	$0.910379\pi$
$200$	−4.54416	+	2.40166i	−0.321321	+	0.169823i
$201$	0.0867872	+	2.22360i	0.00612150	+	0.156841i
$202$	−23.0083	+	13.2838i	−1.61886	+	0.934647i
$203$	−4.58558	−	0.756492i	−0.321844	−	0.0530953i
$204$	5.08178	+	33.3509i	0.355796	+	2.33503i
$205$	−14.6186	+	19.8075i	−1.02101	+	1.38342i
$206$	22.6449	−	36.0392i	1.57775	−	2.51097i
$207$	−4.28181	−	2.04505i	−0.297606	−	0.142141i
$208$	1.91390	−	1.52628i	0.132705	−	0.105829i
$209$	−1.21887	−	3.10562i	−0.0843107	−	0.214820i
$210$	−5.54379	+	6.97470i	−0.382558	+	0.481300i
$211$	2.37441	+	12.5490i	0.163461	+	0.863911i	0.964256	+	0.264973i	$0.0853630\pi$
$211$	2.37441	+	12.5490i	0.163461	+	0.863911i	−0.800795	+	0.598938i	$0.795589\pi$
$212$	−23.8158	−	16.2374i	−1.63568	−	1.11519i
$213$	−13.6024	+	2.59640i	−0.932018	+	0.177902i
$214$	0.0334681	−	0.176883i	0.00228783	−	0.0120915i
$215$	11.2383	−	11.2383i	0.766448	−	0.766448i
$216$	17.6306	−	0.0851728i	1.19961	−	0.00579527i
$217$	−0.774027	−	6.86968i	−0.0525444	−	0.466344i
$218$	30.6207	+	13.3597i	2.07390	+	0.904832i
$219$	12.5816	−	11.7118i	0.850187	−	0.791410i
$220$	14.3406	+	3.84256i	0.966845	+	0.259065i
$221$	10.2881	+	8.85366i	0.692055	+	0.595562i
$222$	−27.7251	−	9.65135i	−1.86079	−	0.647756i
$223$	1.69574	−	22.6280i	0.113555	−	1.51528i	−0.591600	−	0.806231i	$-0.701504\pi$
$223$	1.69574	−	22.6280i	0.113555	−	1.51528i	0.705155	−	0.709053i	$-0.250877\pi$
$224$	−3.59280	−	1.25717i	−0.240054	−	0.0839984i
$225$	−3.92822	+	2.28486i	−0.261881	+	0.152324i
$226$	20.5918	−	25.8213i	1.36975	−	1.71761i
$227$	0.554036	+	3.67579i	0.0367727	+	0.243971i	0.999664	−	0.0259184i	$-0.00825102\pi$
$227$	0.554036	+	3.67579i	0.0367727	+	0.243971i	−0.962891	+	0.269889i	$0.913013\pi$
$228$	0.866171	−	11.8135i	0.0573636	−	0.782367i
$229$	15.7412	+	0.588994i	1.04021	+	0.0389218i	0.552031	−	0.833823i	$-0.313853\pi$
$229$	15.7412	+	0.588994i	1.04021	+	0.0389218i	0.488176	+	0.872745i	$0.337662\pi$
$230$	−3.76996	−	8.64085i	−0.248584	−	0.569761i
$231$	2.48930	−	0.379302i	0.163784	−	0.0249562i
$232$	−3.64622	+	17.9046i	−0.239386	+	1.17550i
$233$		−	13.1293i		−	0.860131i	−0.902798	−	0.430065i	$-0.858491\pi$
$233$		−	13.1293i		−	0.860131i	0.902798	−	0.430065i	$-0.141509\pi$
$234$	12.7420	−	11.0370i	0.832970	−	0.721511i
$235$	23.2573	+	14.6135i	1.51714	+	0.953283i
$236$	19.8165	+	18.3870i	1.28994	+	1.19689i
$237$	−2.95931	−	0.670430i	−0.192228	−	0.0435491i
$238$	−1.69428	+	11.2408i	−0.109824	+	0.728634i
$239$	−9.93501	−	10.7074i	−0.642642	−	0.692604i	0.324775	−	0.945791i	$-0.394711\pi$
$239$	−9.93501	−	10.7074i	−0.642642	−	0.692604i	−0.967417	+	0.253188i	$0.918521\pi$
$240$	3.41365	+	2.92813i	0.220350	+	0.189010i
$241$	−27.0900	−	2.03012i	−1.74502	−	0.130771i	−0.836326	−	0.548232i	$-0.815301\pi$
$241$	−27.0900	−	2.03012i	−1.74502	−	0.130771i	−0.908695	+	0.417461i	$0.862920\pi$
$242$	10.1409	+	16.1391i	0.651879	+	1.03746i
$243$	15.5724	−	0.708274i	0.998967	−	0.0454358i
$244$	2.39428	+	2.39428i	0.153278	+	0.153278i
$245$	13.1915	−	8.99385i	0.842777	−	0.574596i
$246$	37.6974	+	10.0359i	2.40350	+	0.639869i
$247$	−2.83002	−	3.83454i	−0.180070	−	0.243986i
$248$	−27.1034	+	2.03112i	−1.72107	+	0.128976i
$249$	0.878834	−	7.91440i	0.0556939	−	0.501554i
$250$	20.4108	+	3.86192i	1.29089	+	0.244249i
$251$	−12.2081	+	7.67085i	−0.770567	+	0.484180i	−0.859046	−	0.511898i	$-0.828942\pi$
$251$	−12.2081	+	7.67085i	−0.770567	+	0.484180i	0.0884785	+	0.996078i	$0.471800\pi$
$252$	8.55144	+	2.60764i	0.538690	+	0.164266i
$253$	−0.879997	+	2.51489i	−0.0553249	+	0.158110i
$254$	−17.7494	−	5.47497i	−1.11370	−	0.343530i
$255$	−12.4337	+	21.6161i	−0.778627	+	1.35365i
$256$	−8.03410	+	20.4705i	−0.502131	+	1.27941i
$257$	8.38995	+	27.1995i	0.523351	+	1.69666i	0.701510	+	0.712659i	$0.252509\pi$
$257$	8.38995	+	27.1995i	0.523351	+	1.69666i	−0.178160	+	0.984002i	$0.557014\pi$
$258$	−23.1000	−	10.0342i	−1.43814	−	0.624700i
$259$	−5.04007	−	3.71974i	−0.313174	−	0.231133i
$260$	21.2081			1.31527
$261$	−2.57831	+	15.9484i	−0.159593	+	0.987183i
$262$	12.1286			0.749310
$263$	−19.0855	−	14.0858i	−1.17686	−	0.868566i	−0.183438	−	0.983031i	$-0.558723\pi$
$263$	−19.0855	−	14.0858i	−1.17686	−	0.868566i	−0.993427	+	0.114466i	$0.963484\pi$
$264$	−1.12426	−	9.83574i	−0.0691937	−	0.605348i
$265$	−6.28019	−	20.3599i	−0.385789	−	1.25070i
$266$	1.45823	−	3.71550i	0.0894097	−	0.227812i
$267$	−6.28800	−	10.8507i	−0.384819	−	0.664055i
$268$	4.23926	+	1.30764i	0.258954	+	0.0798767i
$269$	2.53525	−	7.24532i	0.154577	−	0.441755i	−0.840387	−	0.541986i	$-0.817673\pi$
$269$	2.53525	−	7.24532i	0.154577	−	0.441755i	0.994964	+	0.100231i	$0.0319583\pi$
$270$	24.3069	+	19.1927i	1.47927	+	1.16803i
$271$	−9.47187	+	5.95157i	−0.575375	+	0.361532i	−0.788069	−	0.615587i	$-0.788919\pi$
$271$	−9.47187	+	5.95157i	−0.575375	+	0.361532i	0.212694	+	0.977119i	$0.431776\pi$
$272$	5.63830	+	1.06682i	0.341872	+	0.0646857i
$273$	3.29454	−	1.44371i	0.199395	−	0.0873774i
$274$	51.9607	−	3.89391i	3.13906	−	0.235240i
$275$	1.51525	+	2.05309i	0.0913730	+	0.123806i
$276$	−6.67836	+	6.69990i	−0.401990	+	0.403287i
$277$	−24.2253	+	16.5165i	−1.45555	+	0.992380i	−0.461085	+	0.887356i	$0.652540\pi$
$277$	−24.2253	+	16.5165i	−1.45555	+	0.992380i	−0.994470	+	0.105024i	$0.966508\pi$
$278$	3.55389	+	3.55389i	0.213148	+	0.213148i
$279$	−23.8711	+	2.76751i	−1.42912	+	0.165686i
$280$	3.97653	+	6.32862i	0.237643	+	0.378207i
$281$	0.614262	+	0.0460326i	0.0366438	+	0.00274607i	0.0930394	−	0.995662i	$-0.470342\pi$
$281$	0.614262	+	0.0460326i	0.0366438	+	0.00274607i	−0.0563956	+	0.998409i	$0.517961\pi$
$282$	8.02307	−	42.7799i	0.477767	−	2.54751i
$283$	7.51624	+	8.10058i	0.446794	+	0.481530i	0.915782	−	0.401675i	$-0.131572\pi$
$283$	7.51624	+	8.10058i	0.446794	+	0.481530i	−0.468988	+	0.883204i	$0.655381\pi$
$284$	−4.11465	+	27.2989i	−0.244160	+	1.61989i
$285$	5.94508	−	6.42801i	0.352156	−	0.380762i
$286$	−6.93873	−	6.43820i	−0.410296	−	0.380699i
$287$	7.04805	+	4.42858i	0.416033	+	0.261411i
$288$	−4.32985	+	12.5030i	−0.255139	+	0.736748i
$289$			14.8173i			0.871607i
$290$	−24.6175	+	20.5965i	−1.44559	+	1.20947i
$291$	−2.45906	−	3.07340i	−0.144153	−	0.180166i
$292$	−13.7035	−	31.4089i	−0.801939	−	1.83806i
$293$	9.08390	+	0.339895i	0.530687	+	0.0198569i	0.301392	−	0.953500i	$-0.402549\pi$
$293$	9.08390	+	0.339895i	0.530687	+	0.0198569i	0.229294	+	0.973357i	$0.426358\pi$
$294$	−20.9267	−	14.2183i	−1.22047	−	0.829226i
$295$	2.97819	+	19.7590i	0.173397	+	1.15041i
$296$	−15.3551	+	19.2546i	−0.892495	+	1.11915i
$297$	−1.34636	−	8.64883i	−0.0781239	−	0.501856i
$298$	16.0305	+	5.60933i	0.928624	+	0.324940i
$299$	−0.284428	+	3.79543i	−0.0164489	+	0.219496i
$300$	1.69864	+	8.89905i	0.0980709	+	0.513787i
$301$	−4.07329	−	3.50535i	−0.234780	−	0.202045i
$302$	−19.9501	−	5.34561i	−1.14800	−	0.307605i
$303$	4.41590	+	19.2047i	0.253687	+	1.10328i
$304$	−1.84671	−	0.805711i	−0.105916	−	0.0462107i
$305$	0.280235	+	2.48715i	0.0160462	+	0.142414i
$306$	39.0933	+	5.76366i	2.23481	+	0.329487i
$307$	22.1094	−	22.1094i	1.26185	−	1.26185i	0.311657	−	0.950195i	$-0.399116\pi$
$307$	22.1094	−	22.1094i	1.26185	−	1.26185i	0.950195	−	0.311657i	$-0.100884\pi$
$308$	0.933268	−	4.93244i	0.0531779	−	0.281052i
$309$	−20.6312	−	23.8960i	−1.17367	−	1.35940i
$310$	−39.4480	−	26.8952i	−2.24049	−	1.52754i
$311$	1.86813	+	9.87329i	0.105932	+	0.559863i	0.994813	+	0.101724i	$0.0324360\pi$
$311$	1.86813	+	9.87329i	0.105932	+	0.559863i	−0.888881	+	0.458138i	$0.848516\pi$
$312$	−5.18775	−	13.1558i	−0.293699	−	0.744803i
$313$	3.33364	+	8.49398i	0.188429	+	0.480108i	0.993603	−	0.112930i	$-0.0360236\pi$
$313$	3.33364	+	8.49398i	0.188429	+	0.480108i	−0.805174	+	0.593038i	$0.797928\pi$
$314$	−17.8936	+	14.2697i	−1.00979	+	0.805284i
$315$	3.74022	+	5.44811i	0.210738	+	0.306966i
$316$	−3.21836	+	5.12199i	−0.181047	+	0.288135i
$317$	−12.2216	+	16.5597i	−0.686434	+	0.930085i	−0.999809	−	0.0195447i	$-0.993778\pi$
$317$	−12.2216	+	16.5597i	−0.686434	+	0.930085i	0.313375	+	0.949629i	$0.398540\pi$
$318$	−26.3630	+	21.0933i	−1.47836	+	1.18285i
$319$	9.05945	+	0.465156i	0.507232	+	0.0260437i
$320$	−27.2635	+	15.7406i	−1.52408	+	0.879926i
$321$	−0.118153	−	0.0622024i	−0.00659465	−	0.00347180i
$322$	−2.81824	+	1.48949i	−0.157055	+	0.0830058i
$323$	2.48591	−	10.8915i	0.138320	−	0.606018i
$324$	8.96869	−	29.7549i	0.498261	−	1.65305i
$325$	2.84984	+	2.27267i	0.158080	+	0.126065i
$326$	6.87692	−	22.2944i	0.380877	−	1.23477i
$327$	16.1332	−	18.8083i	0.892168	−	1.04010i
$328$	18.4352	−	27.0394i	1.01791	−	1.49300i
$329$	4.33970	−	8.21111i	0.239255	−	0.452693i
$330$	9.22842	−	14.7396i	0.508008	−	0.811387i
$331$	−25.5432	+	6.84428i	−1.40398	+	0.376196i	−0.879773	−	0.475394i	$-0.842306\pi$
$331$	−25.5432	+	6.84428i	−1.40398	+	0.376196i	−0.524209	+	0.851590i	$0.675639\pi$
$332$	−14.3030	−	6.88796i	−0.784979	−	0.378026i
$333$	−12.8738	+	17.5615i	−0.705479	+	0.962362i
$334$	−47.3100	+	5.33055i	−2.58869	+	0.291675i
$335$	1.84728	+	2.70946i	0.100928	+	0.148034i
$336$	0.901045	−	1.22500i	0.0491560	−	0.0668290i
$337$	−10.8407	+	12.5971i	−0.590529	+	0.686207i	−0.971135	−	0.238530i	$-0.923334\pi$
$337$	−10.8407	+	12.5971i	−0.590529	+	0.686207i	0.380606	+	0.924737i	$0.375715\pi$
$338$	14.8848	+	7.86683i	0.809625	+	0.427899i
$339$	−13.8320	−	20.2179i	−0.751253	−	1.09808i
$340$	32.4280	+	37.6821i	1.75866	+	2.04360i
$341$	3.00259	+	13.1552i	0.162599	+	0.712394i
$342$	−12.9318	−	5.02736i	−0.699273	−	0.271849i
$343$	−7.13248	−	8.94385i	−0.385118	−	0.482923i
$344$	−14.3706	+	15.4879i	−0.774813	+	0.835049i
$345$	−6.94733	+	0.794107i	−0.374032	+	0.0427533i
$346$	−42.4488	+	18.5202i	−2.28206	+	0.995653i
$347$	−4.03455	−	6.98805i	−0.216586	−	0.375138i	0.737176	−	0.675701i	$-0.236159\pi$
$347$	−4.03455	−	6.98805i	−0.216586	−	0.375138i	−0.953762	+	0.300563i	$0.902826\pi$
$348$	28.2882	+	15.3984i	1.51641	+	0.825442i
$349$	5.62167	−	9.73702i	0.300921	−	0.521211i	−0.675424	−	0.737430i	$-0.736039\pi$
$349$	5.62167	−	9.73702i	0.300921	−	0.521211i	0.976345	+	0.216219i	$0.0693726\pi$
$350$	−0.341806	+	3.03361i	−0.0182703	+	0.162153i
$351$	−5.05538	−	11.4360i	−0.269836	−	0.610409i
$352$	7.24329	+	1.65323i	0.386069	+	0.0881176i
$353$	29.0222	−	4.37439i	1.54470	−	0.232825i	0.679280	−	0.733879i	$-0.262292\pi$
$353$	29.0222	−	4.37439i	1.54470	−	0.232825i	0.865416	+	0.501054i	$0.167054\pi$
$354$	27.3967	−	15.8764i	1.45612	−	0.843819i
$355$	−14.9592	+	13.8801i	−0.793954	+	0.736682i
$356$	−24.5660	+	4.64813i	−1.30199	+	0.246351i
$357$	7.60263	+	3.64617i	0.402374	+	0.192976i
$358$	−0.0544259	−	1.45456i	−0.00287650	−	0.0768760i
$359$	−4.63488	−	13.2457i	−0.244620	−	0.699083i	−0.999086	−	0.0427442i	$-0.986390\pi$
$359$	−4.63488	−	13.2457i	−0.244620	−	0.699083i	0.754466	−	0.656339i	$-0.227896\pi$
$360$	21.9544	−	13.8937i	1.15710	−	0.732263i
$361$	6.54187	−	13.5843i	0.344309	−	0.714965i
$362$	7.61617	−	17.4564i	0.400297	−	0.917490i
$363$	13.6501	−	3.68109i	0.716443	−	0.193207i
$364$	−0.535886	−	7.15090i	−0.0280881	−	0.374809i
$365$	6.55598	−	24.4673i	0.343156	−	1.28067i
$366$	3.50356	−	1.85891i	0.183134	−	0.0971666i
$367$	−4.84877	+	0.181428i	−0.253104	+	0.00947048i	−0.163642	−	0.986520i	$-0.552324\pi$
$367$	−4.84877	+	0.181428i	−0.253104	+	0.00947048i	−0.0894618	+	0.995990i	$0.528515\pi$
$368$	0.698157	+	1.44974i	0.0363939	+	0.0755728i
$369$	15.3153	−	24.5494i	0.797284	−	1.27799i
$370$	−42.1768	+	9.62657i	−2.19266	+	0.500461i
$371$	−6.70621	+	2.63200i	−0.348169	+	0.136646i
$372$	−10.5854	+	46.7242i	−0.548825	+	2.42253i
$373$	20.7407	−	6.39764i	1.07391	−	0.331257i	0.293136	−	0.956071i	$-0.405301\pi$
$373$	20.7407	−	6.39764i	1.07391	−	0.331257i	0.780774	+	0.624813i	$0.214825\pi$
$374$	0.829649	−	22.1728i	0.0429001	−	1.14653i
$375$	7.17761	−	13.6338i	0.370650	−	0.704046i
$376$	−31.6219	−	18.2569i	−1.63078	−	0.941529i
$377$	12.6724	−	2.70764i	0.652660	−	0.139450i
$378$	5.85717	−	8.68070i	0.301261	−	0.446487i
$379$	−2.62370	−	0.295620i	−0.134771	−	0.0151850i	0.0443214	−	0.999017i	$-0.485887\pi$
$379$	−2.62370	−	0.295620i	−0.134771	−	0.0151850i	−0.179092	+	0.983832i	$0.557316\pi$
$380$	−8.15641	−	15.4327i	−0.418415	−	0.791680i
$381$	−7.74265	+	11.3958i	−0.396668	+	0.583823i
$382$	54.4703	+	21.3780i	2.78694	+	1.09379i
$383$	−10.7587	−	1.62162i	−0.549745	−	0.0828607i	−0.131704	−	0.991289i	$-0.542045\pi$
$383$	−10.7587	−	1.62162i	−0.549745	−	0.0828607i	−0.418041	+	0.908428i	$0.637283\pi$
$384$	27.0921	+	21.5339i	1.38254	+	1.09890i
$385$	2.81257	−	2.42042i	0.143342	−	0.123356i
$386$	−23.9369	+	11.5274i	−1.21836	+	0.586729i
$387$	−12.1394	+	14.1984i	−0.617078	+	0.721747i
$388$	−7.40665	+	2.59170i	−0.376016	+	0.131574i
$389$	0.457919	+	1.70898i	0.0232174	+	0.0866485i	0.976562	−	0.215234i	$-0.0690515\pi$
$389$	0.457919	+	1.70898i	0.0232174	+	0.0866485i	−0.953345	+	0.301883i	$0.902385\pi$
$390$	7.28399	−	23.7498i	0.368839	−	1.20262i
$391$	−7.17854	+	5.29800i	−0.363034	+	0.267932i
$392$	−17.0769	+	12.6033i	−0.862514	+	0.636564i
$393$	2.63780	−	8.60068i	0.133059	−	0.433847i
$394$	7.96469	+	29.7246i	0.401256	+	1.49751i
$395$	−4.22052	+	1.47683i	−0.212358	+	0.0743071i
$396$	−17.1561	−	3.18892i	−0.862128	−	0.160249i
$397$	9.18733	−	4.42438i	0.461099	−	0.222053i	−0.188889	−	0.981999i	$-0.560488\pi$
$397$	9.18733	−	4.42438i	0.461099	−	0.222053i	0.649987	+	0.759945i	$0.274774\pi$
$398$	24.2018	−	20.8273i	1.21313	−	1.04398i
$399$	−2.31760	−	1.84213i	−0.116025	−	0.0922218i
$400$	1.52381	+	0.229677i	0.0761905	+	0.0114839i
$401$	20.5440	+	8.06293i	1.02592	+	0.402644i	0.817826	−	0.575465i	$-0.195179\pi$
$401$	20.5440	+	8.06293i	1.02592	+	0.402644i	0.208093	+	0.978109i	$0.433274\pi$
$402$	2.92034	−	4.29821i	0.145653	−	0.214375i
$403$	9.00676	+	17.0416i	0.448659	+	0.848904i
$404$	39.0386	+	4.39860i	1.94224	+	0.218838i
$405$	18.8964	−	13.0624i	0.938968	−	0.649076i
$406$	7.56671	+	7.78004i	0.375529	+	0.386117i
$407$	10.5886	+	6.11331i	0.524856	+	0.303025i
$408$	15.4427	−	29.3333i	0.764528	−	1.45221i
$409$	−0.0384664	+	1.02804i	−0.00190204	+	0.0508331i	−0.999928	−	0.0119626i	$-0.996192\pi$
$409$	−0.0384664	+	1.02804i	−0.00190204	+	0.0508331i	0.998026	+	0.0627956i	$0.0200016\pi$
$410$	54.9331	−	16.9446i	2.71295	−	0.836835i
$411$	8.53942	−	37.6933i	0.421218	−	1.85927i
$412$	−58.5874	+	22.9939i	−2.88640	+	1.13283i
$413$	6.58705	−	1.50345i	0.324127	−	0.0739800i
$414$	5.20916	+	9.77985i	0.256016	+	0.480653i
$415$	−5.09146	−	10.5725i	−0.249930	−	0.518985i
$416$	10.6056	−	0.396835i	0.519984	−	0.0194564i
$417$	3.29306	−	1.74722i	0.161262	−	0.0855618i
$418$	−2.01638	+	7.52523i	−0.0986243	+	0.368071i
$419$	−1.16311	−	15.5206i	−0.0568214	−	0.758229i	−0.950738	−	0.309996i	$-0.899672\pi$
$419$	−1.16311	−	15.5206i	−0.0568214	−	0.758229i	0.893916	−	0.448234i	$-0.147947\pi$
$420$	12.7201	−	3.43031i	0.620679	−	0.167382i
$421$	6.51433	−	14.9310i	0.317489	−	0.727692i	−0.682506	−	0.730880i	$-0.739110\pi$
$421$	6.51433	−	14.9310i	0.317489	−	0.727692i	0.999995	+	0.00318757i	$0.00101464\pi$
$422$	12.9402	−	26.8706i	0.629918	−	1.30804i
$423$	−28.5913	−	14.9933i	−1.39016	−	0.729001i
$424$	9.35475	+	26.7344i	0.454307	+	1.29833i
$425$	0.319489	+	8.53852i	0.0154975	+	0.414179i
$426$	29.1574	+	13.9837i	1.41268	+	0.677512i
$427$	0.831532	−	0.157334i	0.0402407	−	0.00761394i
$428$	−0.195137	+	0.181061i	−0.00943230	+	0.00875190i
$429$	−6.07454	+	3.52019i	−0.293282	+	0.169957i
$430$	−36.6993	+	5.53152i	−1.76980	+	0.266754i
$431$	−34.1132	−	7.78611i	−1.64317	−	0.375044i	−0.701790	−	0.712384i	$-0.747616\pi$
$431$	−34.1132	−	7.78611i	−1.64317	−	0.375044i	−0.941383	+	0.337340i	$0.890473\pi$
$432$	−4.26831	−	3.11841i	−0.205359	−	0.150035i
$433$	−3.67706	+	32.6348i	−0.176708	+	1.56833i	0.522015	+	0.852937i	$0.325181\pi$
$433$	−3.67706	+	32.6348i	−0.176708	+	1.56833i	−0.698723	+	0.715393i	$0.746248\pi$
$434$	−8.07169	+	13.9806i	−0.387453	+	0.671089i
$435$	9.25147	+	21.9362i	0.443574	+	1.05176i
$436$	−24.7004	−	42.7823i	−1.18293	−	2.04890i
$437$	2.87124	−	1.25271i	0.137350	−	0.0599253i
$438$	−39.8797	+	4.55840i	−1.90552	+	0.217809i
$439$	11.4240	−	12.3122i	0.545240	−	0.587629i	−0.398974	−	0.916962i	$-0.630634\pi$
$439$	11.4240	−	12.3122i	0.545240	−	0.587629i	0.944214	+	0.329334i	$0.106824\pi$
$440$	−9.09589	−	11.4059i	−0.433629	−	0.543754i
$441$	−14.6337	+	11.7473i	−0.696844	+	0.559396i
$442$	−7.05299	−	30.9012i	−0.335477	−	1.46982i
$443$	16.2138	+	18.8408i	0.770340	+	0.895151i	0.996887	−	0.0788491i	$-0.0251245\pi$
$443$	16.2138	+	18.8408i	0.770340	+	0.895151i	−0.226547	+	0.974000i	$0.572744\pi$
$444$	24.5115	+	35.8277i	1.16327	+	1.70031i
$445$	−16.3393	−	8.63555i	−0.774555	−	0.409364i
$446$	−34.5637	+	40.1638i	−1.63664	+	1.90181i
$447$	7.46411	−	10.1477i	0.353040	−	0.479968i
$448$	5.99628	+	8.79492i	0.283297	+	0.415521i
$449$	27.8890	−	3.14234i	1.31616	−	0.148296i	0.574189	−	0.818723i	$-0.305317\pi$
$449$	27.8890	−	3.14234i	1.31616	−	0.148296i	0.741976	+	0.670427i	$0.233889\pi$
$450$	10.5490	+	1.15419i	0.497284	+	0.0544091i
$451$	−14.6381	−	7.04936i	−0.689283	−	0.331941i
$452$	−47.1726	+	12.6399i	−2.21881	+	0.594529i
$453$	−8.12954	+	12.9844i	−0.381959	+	0.610063i
$454$	4.05615	−	7.67461i	0.190365	−	0.360187i
$455$	2.98596	−	4.37959i	0.139984	−	0.205319i
$456$	−7.57807	+	8.83461i	−0.354876	+	0.413719i
$457$	3.68175	−	11.9359i	0.172225	−	0.558340i	−0.827771	−	0.561066i	$-0.810391\pi$
$457$	3.68175	−	11.9359i	0.172225	−	0.558340i	0.999996	+	0.00272585i	$0.000867668\pi$
$458$	−28.7590	−	22.9345i	−1.34382	−	1.07166i
$459$	12.5894	−	26.4684i	0.587621	−	1.23544i
$460$	−3.10203	+	13.5909i	−0.144633	+	0.633678i
$461$	−5.70685	+	3.01616i	−0.265795	+	0.140477i	−0.594857	−	0.803832i	$-0.702791\pi$
$461$	−5.70685	+	3.01616i	−0.265795	+	0.140477i	0.329062	+	0.944308i	$0.393267\pi$
$462$	−5.20304	−	2.73918i	−0.242068	−	0.127438i
$463$	14.6908	−	8.48172i	0.682738	−	0.394179i	−0.118148	−	0.992996i	$-0.537696\pi$
$463$	14.6908	−	8.48172i	0.682738	−	0.394179i	0.800886	+	0.598817i	$0.204362\pi$
$464$	4.06735	−	3.67007i	0.188822	−	0.170379i
$465$	−27.6513	+	22.1241i	−1.28230	+	1.02598i
$466$	−18.2061	+	24.6683i	−0.843379	+	1.14274i
$467$	−8.67183	+	13.8011i	−0.401285	+	0.638641i	−0.984847	−	0.173428i	$-0.944516\pi$
$467$	−8.67183	+	13.8011i	−0.401285	+	0.638641i	0.583562	+	0.812069i	$0.301658\pi$
$468$	−24.8513	+	1.94285i	−1.14875	+	0.0898085i
$469$	0.866893	−	0.691324i	0.0400294	−	0.0319224i
$470$	−23.4334	−	59.7073i	−1.08090	−	2.75409i
$471$	6.22734	+	15.7922i	0.286941	+	0.727665i
$472$	−4.93844	−	26.1003i	−0.227310	−	1.20136i
$473$	8.66655	+	5.90876i	0.398489	+	0.271685i
$474$	4.63049	+	5.36324i	0.212686	+	0.246342i
$475$	0.557755	−	2.94781i	0.0255916	−	0.135255i
$476$	11.8862	−	11.8862i	0.544802	−	0.544802i
$477$	9.22418	+	23.2821i	0.422346	+	1.06601i
$478$	3.81899	+	33.8944i	0.174676	+	1.55030i
$479$	7.85883	+	3.42877i	0.359079	+	0.156665i	0.571684	−	0.820474i	$-0.306290\pi$
$479$	7.85883	+	3.42877i	0.359079	+	0.156665i	−0.212606	+	0.977138i	$0.568195\pi$
$480$	4.36941	+	19.0025i	0.199436	+	0.867344i
$481$	16.8705	+	4.52043i	0.769228	+	0.206114i
$482$	48.0836	+	41.3793i	2.19015	+	1.88477i
$483$	0.443301	+	2.32242i	0.0201709	+	0.105674i
$484$	2.10627	−	28.1062i	0.0957394	−	1.27755i
$485$	−5.47486	−	1.91574i	−0.248601	−	0.0869891i
$486$	−30.2406	−	20.2630i	−1.37174	−	0.919148i
$487$	−3.37899	+	4.23711i	−0.153116	+	0.192002i	−0.852473	−	0.522771i	$-0.824898\pi$
$487$	−3.37899	+	4.23711i	−0.153116	+	0.192002i	0.699357	+	0.714773i	$0.253470\pi$
$488$	−0.495897	−	3.29006i	−0.0224482	−	0.148934i
$489$	−14.3138	−	9.72528i	−0.647294	−	0.439793i
$490$	−37.2568	−	1.39405i	−1.68309	−	0.0629767i
$491$	−1.37330	−	3.14764i	−0.0619763	−	0.142051i	0.882818	−	0.469715i	$-0.155643\pi$
$491$	−1.37330	−	3.14764i	−0.0619763	−	0.142051i	−0.944794	+	0.327664i	$0.893739\pi$
$492$	−36.0384	−	45.0418i	−1.62474	−	2.03064i
$493$	24.1874	+	18.3759i	1.08935	+	0.827607i
$494$			11.1289i			0.500714i
$495$	−8.44511	−	9.74971i	−0.379580	−	0.438217i
$496$	6.89995	+	4.33553i	0.309817	+	0.194671i
$497$	5.05807	+	4.69320i	0.226885	+	0.210519i
$498$	−12.6259	+	13.6515i	−0.565779	+	0.611738i
$499$	0.120980	−	0.802647i	0.00541579	−	0.0359314i	−0.985960	−	0.166983i	$-0.946597\pi$
$499$	0.120980	−	0.802647i	0.00541579	−	0.0359314i	0.991376	+	0.131052i	$0.0418355\pi$
$500$	−20.8928	−	22.5171i	−0.934355	−	1.00700i
$501$	−6.50920	+	34.7078i	−0.290810	+	1.55063i
$502$	33.5744	+	2.51605i	1.49850	+	0.112297i
$503$	21.5931	+	34.3652i	0.962789	+	1.53227i	0.841920	+	0.539602i	$0.181425\pi$
$503$	21.5931	+	34.3652i	0.962789	+	1.53227i	0.120869	+	0.992668i	$0.461432\pi$
$504$	−5.23940	−	7.05148i	−0.233381	−	0.314098i
$505$	20.5338	+	20.5338i	0.913744	+	0.913744i
$506$	5.14072	−	3.50489i	0.228533	−	0.155811i
$507$	8.81576	−	8.84420i	0.391522	−	0.392785i
$508$	16.3101	+	22.0993i	0.723642	+	0.980500i
$509$	−28.0499	+	2.10205i	−1.24329	+	0.0931717i	−0.680077	−	0.733140i	$-0.738054\pi$
$509$	−28.0499	+	2.10205i	−1.24329	+	0.0931717i	−0.563212	+	0.826312i	$0.690435\pi$
$510$	53.3357	−	23.3724i	2.36174	−	1.03495i
$511$	−8.41548	−	1.59229i	−0.372279	−	0.0704389i
$512$	9.64457	−	6.06008i	0.426234	−	0.267820i
$513$	−6.37749	+	8.07686i	−0.281573	+	0.356602i
$514$	21.9532	−	62.7386i	0.968313	−	2.76728i
$515$	−44.4558	−	13.7128i	−1.95896	−	0.604259i
$516$	18.6726	+	32.2220i	0.822016	+	1.41849i
$517$	−6.62278	+	16.8746i	−0.291270	+	0.742143i
$518$	4.31159	+	13.9778i	0.189440	+	0.614151i
$519$	3.90111	+	34.1292i	0.171240	+	1.49811i
$520$	−16.7676	−	12.3751i	−0.735310	−	0.542683i
$521$	−11.1683			−0.489294			−0.244647	−	0.969612i	$-0.578672\pi$
$521$	−11.1683			−0.489294			−0.244647	+	0.969612i	$0.578672\pi$
$522$	26.9595	−	26.3898i	1.17999	−	1.15505i
$523$	30.3212			1.32586			0.662928	−	0.748683i	$-0.269314\pi$
$523$	30.3212			1.32586			0.662928	+	0.748683i	$0.269314\pi$
$524$	−14.4302	−	10.6499i	−0.630385	−	0.465245i
$525$	2.07686	+	0.902147i	0.0906416	+	0.0393729i
$526$	16.3270	+	52.9307i	0.711890	+	2.30789i
$527$	−16.5075	+	42.0603i	−0.719076	+	1.83218i
$528$	−1.47995	+	2.57290i	−0.0644064	+	0.111971i
$529$	19.5875	+	6.04195i	0.851632	+	0.262694i
$530$	−16.4328	+	46.9622i	−0.713794	+	2.03991i
$531$	−5.29990	−	22.8805i	−0.229996	−	0.992927i
$532$	−4.99746	+	3.14011i	−0.216667	+	0.136141i
$533$	−22.8042	−	4.31479i	−0.987761	−	0.186894i
$534$	−3.23207	+	29.1066i	−0.139865	+	1.25956i
$535$	−0.196219	+	0.0147045i	−0.00848327	+	0.000635733i
$536$	−2.58864	−	3.50749i	−0.111812	−	0.151500i
$537$	−1.04330	−	0.277751i	−0.0450216	−	0.0119858i
$538$	−14.8103	+	10.0975i	−0.638516	+	0.435333i
$539$	7.45074	+	7.45074i	0.320926	+	0.320926i
$540$	−12.0665	−	44.1782i	−0.519262	−	1.90113i
$541$	14.3296	+	22.8055i	0.616078	+	0.980483i	0.998405	+	0.0564557i	$0.0179800\pi$
$541$	14.3296	+	22.8055i	0.616078	+	0.980483i	−0.382327	+	0.924027i	$0.624877\pi$
$542$	26.0493	+	1.95213i	1.11891	+	0.0838510i
$543$	−10.7223	−	9.19731i	−0.460140	−	0.394694i
$544$	16.9215	+	18.2371i	0.725504	+	0.781908i
$545$	5.44245	−	36.1083i	0.233129	−	1.54671i
$546$	−8.19197	−	1.85589i	−0.350584	−	0.0794248i
$547$	−0.494198	−	0.458549i	−0.0211304	−	0.0196061i	0.669537	−	0.742779i	$-0.266493\pi$
$547$	−0.494198	−	0.458549i	−0.0211304	−	0.0196061i	−0.690667	+	0.723173i	$0.742683\pi$
$548$	−65.2399	−	40.9929i	−2.78691	−	1.75113i
$549$	−0.556220	−	2.88873i	−0.0237389	−	0.123288i
$550$		−	5.95865i		−	0.254078i
$551$	−6.84394	−	8.18007i	−0.291562	−	0.348483i
$552$	9.18951	−	1.40023i	0.391132	−	0.0595979i
$553$	0.604597	+	1.38575i	0.0257101	+	0.0589281i
$554$	68.4191	+	2.56006i	2.90685	+	0.108767i
$555$	−2.34641	+	32.0021i	−0.0995995	+	1.35841i
$556$	−1.10767	−	7.34888i	−0.0469755	−	0.311662i
$557$	21.6002	−	27.0858i	0.915230	−	1.14766i	−0.0734016	−	0.997302i	$-0.523385\pi$
$557$	21.6002	−	27.0858i	0.915230	−	1.14766i	0.988631	−	0.150359i	$-0.0480431\pi$
$558$	48.6884	+	27.9015i	2.06114	+	1.18117i
$559$	14.1428	+	4.94879i	0.598178	+	0.209312i
$560$	0.167466	−	2.23467i	0.00707672	−	0.0944322i
$561$	−15.5428	−	5.41059i	−0.656218	−	0.228435i
$562$	−1.09029	−	0.938269i	−0.0459910	−	0.0395785i
$563$	−13.7643	−	3.68814i	−0.580097	−	0.155436i	−0.0431735	−	0.999068i	$-0.513747\pi$
$563$	−13.7643	−	3.68814i	−0.580097	−	0.155436i	−0.536923	+	0.843631i	$0.680413\pi$
$564$	−47.1099	+	43.8530i	−1.98368	+	1.84654i
$565$	−33.0871	−	14.4358i	−1.39199	−	0.607317i
$566$	−2.88922	−	25.6425i	−0.121443	−	1.07784i
$567$	−4.88183	−	6.04138i	−0.205017	−	0.253714i
$568$	19.1823	−	19.1823i	0.804870	−	0.804870i
$569$	0.179366	−	0.947971i	0.00751940	−	0.0397410i	−0.978606	−	0.205744i	$-0.934039\pi$
$569$	0.179366	−	0.947971i	0.00751940	−	0.0397410i	0.986125	+	0.166003i	$0.0530862\pi$
$570$	−20.0836	+	3.83353i	−0.841209	+	0.160569i
$571$	9.55420	+	6.51395i	0.399831	+	0.272600i	0.746497	−	0.665388i	$-0.231734\pi$
$571$	9.55420	+	6.51395i	0.399831	+	0.272600i	−0.346666	+	0.937988i	$0.612686\pi$
$572$	2.60215	+	13.7527i	0.108801	+	0.575029i
$573$	27.0061	−	33.9767i	1.12820	−	1.41940i
$574$	−7.10140	−	18.0941i	−0.296407	−	0.755232i
$575$	−1.87324	+	1.49386i	−0.0781195	+	0.0622982i
$576$	30.5050	−	20.9422i	1.27104	−	0.872590i
$577$	10.8054	−	17.1966i	0.449833	−	0.715906i	−0.542424	−	0.840105i	$-0.682493\pi$
$577$	10.8054	−	17.1966i	0.449833	−	0.715906i	0.992257	+	0.124199i	$0.0396362\pi$
$578$	20.5468	−	27.8399i	0.854633	−	1.15799i
$579$	2.96841	+	19.4812i	0.123363	+	0.809612i
$580$	47.3743	−	2.88867i	1.96711	−	0.119945i
$581$	−3.43617	+	1.98387i	−0.142556	+	0.0823050i
$582$	0.358469	+	9.18445i	0.0148590	+	0.380708i
$583$	12.4321	−	6.57056i	0.514885	−	0.272125i
$584$	−7.49294	+	32.8287i	−0.310060	+	1.35846i
$585$	−15.2574	−	10.3305i	−0.630815	−	0.427113i
$586$	−16.5962	−	13.2350i	−0.685581	−	0.546733i
$587$	9.71226	−	31.4864i	0.400868	−	1.29958i	−0.500202	−	0.865909i	$-0.666741\pi$
$587$	9.71226	−	31.4864i	0.400868	−	1.29958i	0.901070	−	0.433673i	$-0.142783\pi$
$588$	12.4129	+	35.2917i	0.511900	+	1.45541i
$589$	8.93692	−	13.1081i	0.368239	−	0.540108i
$590$	21.8036	−	41.2544i	0.897640	−	1.69842i
$591$	22.8106	+	0.816731i	0.938303	+	0.0335958i
$592$	7.13230	−	1.91109i	0.293136	−	0.0785455i
$593$	−19.3989	−	9.34200i	−0.796616	−	0.383630i	−0.00912663	−	0.999958i	$-0.502905\pi$
$593$	−19.3989	−	9.34200i	−0.796616	−	0.383630i	−0.787489	+	0.616328i	$0.788619\pi$
$594$	−9.46343	+	18.1170i	−0.388289	+	0.743350i
$595$	12.3472	−	1.39120i	0.506186	−	0.0570335i
$596$	−14.1470	−	20.7499i	−0.579486	−	0.849949i
$597$	−9.50558	−	21.6917i	−0.389037	−	0.887780i
$598$	5.79742	−	6.73673i	0.237074	−	0.275485i
$599$	−13.7290	−	7.25599i	−0.560952	−	0.296472i	0.162656	−	0.986683i	$-0.447994\pi$
$599$	−13.7290	−	7.25599i	−0.560952	−	0.296472i	−0.723608	+	0.690211i	$0.757518\pi$
$600$	3.84967	−	8.02697i	0.157162	−	0.327700i
$601$	0.721957	+	0.838929i	0.0294492	+	0.0342206i	0.772503	−	0.635011i	$-0.219004\pi$
$601$	0.721957	+	0.838929i	0.0294492	+	0.0342206i	−0.743054	+	0.669232i	$0.766623\pi$
$602$	2.79242	+	12.2344i	0.113811	+	0.498637i
$603$	−2.41282	−	3.00568i	−0.0982578	−	0.122401i
$604$	19.0419	+	23.8778i	0.774805	+	0.971575i
$605$	14.1706	−	15.2723i	0.576117	−	0.620906i
$606$	18.3337	−	42.2066i	0.744756	−	1.71453i
$607$	−19.1693	+	8.36348i	−0.778057	+	0.339463i	−0.751113	−	0.660174i	$-0.770483\pi$
$607$	−19.1693	+	8.36348i	−0.778057	+	0.339463i	−0.0269447	+	0.999637i	$0.508578\pi$
$608$	−4.36758	−	7.56487i	−0.177129	−	0.306796i
$609$	7.16264	−	3.67368i	0.290245	−	0.148865i
$610$	2.92234	−	5.06164i	0.118322	−	0.204940i
$611$	−2.89934	+	25.7324i	−0.117295	+	1.04102i
$612$	−41.4507	−	41.1845i	−1.67554	−	1.66479i
$613$	−13.7851	−	3.14635i	−0.556774	−	0.127080i	−0.0651308	−	0.997877i	$-0.520746\pi$
$613$	−13.7851	−	3.14635i	−0.556774	−	0.127080i	−0.491643	+	0.870797i	$0.663604\pi$
$614$	−72.1993	+	10.8823i	−2.91373	+	0.439174i
$615$	−0.0686627	−	42.6395i	−0.00276875	−	1.71939i
$616$	−3.61598	+	3.35514i	−0.145692	+	0.135182i
$617$	1.06002	−	0.200566i	0.0426747	−	0.00807448i	−0.164530	−	0.986372i	$-0.552611\pi$
$617$	1.06002	−	0.200566i	0.0426747	−	0.00807448i	0.207205	+	0.978298i	$0.433563\pi$
$618$	5.62758	+	73.5063i	0.226375	+	2.95686i
$619$	−1.09505	−	29.2658i	−0.0440138	−	1.17629i	−0.829896	−	0.557918i	$-0.811600\pi$
$619$	−1.09505	−	29.2658i	−0.0440138	−	1.17629i	0.785882	−	0.618376i	$-0.212209\pi$
$620$	23.3174	+	66.6374i	0.936451	+	2.67622i
$621$	8.06802	−	1.56696i	0.323759	−	0.0628800i
$622$	10.1810	−	21.1411i	0.408222	−	0.847682i
$623$	−2.49886	+	5.72744i	−0.100115	+	0.229465i
$624$	−1.09080	+	4.09730i	−0.0436669	+	0.164023i
$625$	−2.26278	−	30.1947i	−0.0905112	−	1.20779i
$626$	5.51487	−	20.5818i	0.220419	−	0.822613i
$627$	4.89777	+	3.06648i	0.195598	+	0.122464i
$628$	33.8190	−	1.26542i	1.34953	−	0.0504957i
$629$	17.7638	+	36.8870i	0.708291	+	1.47078i
$630$	0.527345	−	15.4228i	0.0210099	−	0.614458i
$631$	2.68421	−	0.612654i	0.106857	−	0.0243894i	−0.168758	−	0.985657i	$-0.553976\pi$
$631$	2.68421	−	0.612654i	0.106857	−	0.0243894i	0.275615	+	0.961268i	$0.411119\pi$
$632$	5.53323	−	2.17163i	0.220100	−	0.0863829i
$633$	−16.2402	−	15.0201i	−0.645490	−	0.596996i
$634$	45.9257	−	14.1662i	1.82394	−	0.562612i
$635$	−0.759139	+	20.2884i	−0.0301255	+	0.805121i
$636$	49.8873	−	1.94710i	1.97816	−	0.0772077i
$637$	13.0353	+	7.52596i	0.516479	+	0.298189i
$638$	−16.3765	−	13.4365i	−0.648354	−	0.531954i
$639$	16.2575	−	17.6349i	0.643135	−	0.697627i
$640$	50.6784	+	5.71009i	2.00324	+	0.225711i
$641$	6.64808	+	12.5788i	0.262583	+	0.496832i	0.979790	−	0.200029i	$-0.0641035\pi$
$641$	6.64808	+	12.5788i	0.262583	+	0.496832i	−0.717207	+	0.696860i	$0.754580\pi$
$642$	0.135740	+	0.280709i	0.00535722	+	0.0110787i
$643$	41.8166	+	16.4118i	1.64908	+	0.647218i	0.994104	−	0.108428i	$-0.0345816\pi$
$643$	41.8166	+	16.4118i	1.64908	+	0.647218i	0.654980	+	0.755646i	$0.272677\pi$
$644$	4.66093	+	0.702522i	0.183666	+	0.0276832i
$645$	−4.05902	+	27.2273i	−0.159824	+	1.07207i
$646$	−19.7736	+	17.0166i	−0.777982	+	0.669508i
$647$	−22.8344	+	10.9965i	−0.897712	+	0.432315i	−0.825062	−	0.565042i	$-0.808860\pi$
$647$	−22.8344	+	10.9965i	−0.897712	+	0.432315i	−0.0726497	+	0.997358i	$0.523146\pi$
$648$	−24.4531	+	18.2916i	−0.960607	+	0.718564i
$649$	−12.4476	+	4.35560i	−0.488611	+	0.170972i
$650$	−2.20304	−	8.22184i	−0.0864102	−	0.322487i
$651$	8.15846	+	8.76438i	0.319755	+	0.343503i
$652$	−27.7582	+	20.4865i	−1.08710	+	0.802314i
$653$	4.43797	−	3.27537i	0.173671	−	0.128175i	−0.503516	−	0.863986i	$-0.667961\pi$
$653$	4.43797	−	3.27537i	0.173671	−	0.128175i	0.677187	+	0.735811i	$0.263199\pi$
$654$	−56.3931	+	12.9669i	−2.20515	+	0.507047i
$655$	−3.43115	−	12.8052i	−0.134066	−	0.500342i
$656$	−9.26134	+	3.24068i	−0.361595	+	0.126527i
$657$	−5.44077	+	29.2709i	−0.212265	+	1.14197i
$658$	−19.5399	+	9.40990i	−0.761743	+	0.366836i
$659$	4.69039	−	4.03641i	0.182712	−	0.157236i	−0.556176	−	0.831064i	$-0.687732\pi$
$659$	4.69039	−	4.03641i	0.182712	−	0.157236i	0.738888	+	0.673828i	$0.235351\pi$
$660$	−23.9222	+	9.43325i	−0.931170	+	0.367189i
$661$	−25.6732	−	3.86962i	−0.998574	−	0.150511i	−0.370639	−	0.928777i	$-0.620861\pi$
$661$	−25.6732	−	3.86962i	−0.998574	−	0.150511i	−0.627934	+	0.778266i	$0.716099\pi$
$662$	57.4832	+	22.5605i	2.23415	+	0.876839i
$663$	−23.4466	−	1.71912i	−0.910591	−	0.0667650i
$664$	7.28913	+	13.7917i	0.282873	+	0.535222i
$665$	−4.33530	−	0.488471i	−0.168116	−	0.0189421i
$666$	48.5402	−	15.1440i	1.88089	−	0.586819i
$667$	−0.118391	+	8.51692i	−0.00458412	+	0.329776i
$668$	60.9682	+	35.2000i	2.35893	+	1.36193i
$669$	20.9639	+	33.2449i	0.810511	+	1.28532i
$670$	0.286329	−	7.65230i	0.0110619	−	0.295634i
$671$	−1.57845	+	0.486886i	−0.0609352	+	0.0187960i
$672$	6.29683	−	1.95343i	0.242906	−	0.0753551i
$673$	31.3511	−	12.3044i	1.20850	−	0.474300i	0.326338	−	0.945253i	$-0.394185\pi$
$673$	31.3511	−	12.3044i	1.20850	−	0.474300i	0.882158	+	0.470953i	$0.156090\pi$
$674$	37.8363	−	8.63588i	1.45740	−	0.332642i
$675$	3.11271	−	7.22949i	0.119808	−	0.278263i
$676$	−10.8016	−	22.4297i	−0.415445	−	0.862681i
$677$	−18.1436	+	0.678885i	−0.697315	+	0.0260917i	−0.383699	−	0.923458i	$-0.625350\pi$
$677$	−18.1436	+	0.678885i	−0.697315	+	0.0260917i	−0.313616	+	0.949550i	$0.601540\pi$
$678$	−2.04687	+	57.1673i	−0.0786095	+	2.19550i
$679$	−0.507606	+	1.89441i	−0.0194801	+	0.0727008i
$680$	−3.65063	−	48.7143i	−0.139995	−	1.86811i
$681$	−4.56008	−	4.54542i	−0.174743	−	0.174181i
$682$	12.6005	−	28.8805i	0.482496	−	1.10589i
$683$	4.83121	−	10.0321i	0.184861	−	0.383868i	−0.787857	−	0.615858i	$-0.788809\pi$
$683$	4.83121	−	10.0321i	0.184861	−	0.383868i	0.972718	+	0.231990i	$0.0745237\pi$
$684$	10.9713	+	17.3366i	0.419499	+	0.662880i
$685$	−18.8106	−	53.7577i	−0.718718	−	2.05398i
$686$	0.998848	+	26.6948i	0.0381362	+	1.01921i
$687$	−22.5180	+	15.4057i	−0.859116	+	0.587764i
$688$	6.22418	−	1.17768i	0.237295	−	0.0448986i
$689$	14.7247	−	13.6626i	0.560968	−	0.520502i
$690$	14.1543	+	8.14163i	0.538845	+	0.309947i
$691$	23.2042	−	3.49747i	0.882730	−	0.133050i	0.307993	−	0.951389i	$-0.400343\pi$
$691$	23.2042	−	3.49747i	0.882730	−	0.133050i	0.574737	+	0.818338i	$0.305104\pi$
$692$	66.7662	+	15.2389i	2.53807	+	0.579298i
$693$	−3.07400	+	3.09386i	−0.116772	+	0.117526i
$694$	−2.10972	+	18.7243i	−0.0800838	+	0.710763i
$695$	2.74676	−	4.75753i	0.104191	−	0.180463i
$696$	−13.3802	−	28.6807i	−0.507176	−	1.08714i
$697$	−27.2021	−	47.1155i	−1.03035	−	1.78463i
$698$	−24.0644	+	10.4992i	−0.910853	+	0.397401i
$699$	13.5333	+	18.2753i	0.511877	+	0.691236i
$700$	3.07043	−	3.30913i	0.116051	−	0.125073i
$701$	−22.5161	−	28.2343i	−0.850421	−	1.06639i	−0.997016	−	0.0771971i	$-0.975403\pi$
$701$	−22.5161	−	28.2343i	−0.850421	−	1.06639i	0.146595	−	0.989197i	$-0.453168\pi$
$702$	−6.35957	+	28.4970i	−0.240026	+	1.07555i
$703$	−3.19878	−	14.0148i	−0.120644	−	0.528578i
$704$	−13.5523	−	15.7481i	−0.510773	−	0.593529i
$705$	−47.4361	+	3.63167i	−1.78655	+	0.136777i
$706$	−60.5949	−	32.0253i	−2.28052	−	1.20529i
$707$	6.40471	−	7.44241i	0.240874	−	0.279901i
$708$	−46.5362	−	5.16750i	−1.74894	−	0.194206i
$709$	−13.3464	−	19.5756i	−0.501236	−	0.735178i	0.489348	−	0.872089i	$-0.337235\pi$
$709$	−13.3464	−	19.5756i	−0.501236	−	0.735178i	−0.990583	+	0.136911i	$0.956283\pi$
$710$	47.3537	−	5.33548i	1.77715	−	0.200237i
$711$	4.81025	−	2.11716i	0.180399	−	0.0793997i
$712$	22.1347	+	10.6595i	0.829532	+	0.399482i
$713$	−12.2382	+	3.27923i	−0.458326	+	0.122808i
$714$	−9.22835	−	17.3930i	−0.345362	−	0.650918i
$715$	−4.83441	+	9.14716i	−0.180797	+	0.342084i
$716$	−1.21247	+	1.77837i	−0.0453122	+	0.0664608i
$717$	24.8659	+	4.66341i	0.928632	+	0.174158i
$718$	−9.65912	+	31.3141i	−0.360475	+	1.16863i
$719$	2.69688	+	2.15069i	0.100577	+	0.0802071i	0.672487	−	0.740109i	$-0.265226\pi$
$719$	2.69688	+	2.15069i	0.100577	+	0.0802071i	−0.571910	+	0.820316i	$0.693798\pi$
$720$	−7.76985	−	0.557111i	−0.289565	−	0.0207623i
$721$	−3.50035	+	15.3360i	−0.130360	+	0.571143i
$722$	−31.1284	+	16.4518i	−1.15848	+	0.612273i
$723$	39.8004	−	25.0978i	1.48019	−	0.933395i
$724$	−24.3896	+	14.0813i	−0.906433	+	0.523329i
$725$	6.67547	+	4.68848i	0.247921	+	0.174126i
$726$	−30.7512	−	12.0119i	−1.14128	−	0.445802i
$727$	6.31645	−	8.55848i	0.234264	−	0.317417i	−0.671658	−	0.740862i	$-0.734417\pi$
$727$	6.31645	−	8.55848i	0.234264	−	0.317417i	0.905922	+	0.423445i	$0.139179\pi$
$728$	−3.74892	+	5.96637i	−0.138944	+	0.221128i
$729$	−20.9458	+	17.0374i	−0.775771	+	0.631015i
$730$	−46.2459	+	36.8799i	−1.71164	+	1.36499i
$731$	12.8321	+	32.6956i	0.474611	+	1.20929i
$732$	−5.80067	−	0.864759i	−0.214399	−	0.0319624i
$733$	−3.25124	−	17.1832i	−0.120087	−	0.634677i	−0.989954	−	0.141390i	$-0.954843\pi$
$733$	−3.25124	−	17.1832i	−0.120087	−	0.634677i	0.869866	−	0.493287i	$-0.164205\pi$
$734$	9.36181	+	6.38277i	0.345551	+	0.235592i
$735$	−9.09134	+	26.1164i	−0.335339	+	0.963318i
$736$	−1.29694	+	6.85450i	−0.0478059	+	0.252660i
$737$	−1.53034	+	1.53034i	−0.0563706	+	0.0563706i
$738$	−62.8175	+	24.8878i	−2.31234	+	0.916133i
$739$	−0.934111	−	8.29047i	−0.0343618	−	0.304970i	−0.999124	−	0.0418465i	$-0.986676\pi$
$739$	−0.934111	−	8.29047i	−0.0343618	−	0.304970i	0.964762	−	0.263123i	$-0.0847526\pi$
$740$	58.6332	+	25.5814i	2.15540	+	0.940390i
$741$	7.89177	+	2.42038i	0.289911	+	0.0889148i
$742$	16.2498	+	4.35413i	0.596550	+	0.159845i
$743$	−10.9981	−	9.46460i	−0.403480	−	0.347222i	0.427019	−	0.904243i	$-0.359564\pi$
$743$	−10.9981	−	9.46460i	−0.403480	−	0.347222i	−0.830499	+	0.557020i	$0.811945\pi$
$744$	35.6329	−	30.7646i	1.30637	−	1.12789i
$745$	1.38726	−	18.5117i	0.0508252	−	0.678215i
$746$	−47.8405	−	16.7401i	−1.75156	−	0.612899i
$747$	6.93463	+	11.9223i	0.253725	+	0.436214i
$748$	−20.4567	+	25.6519i	−0.747970	+	0.937925i
$749$	0.00991610	+	0.0657890i	0.000362326	+	0.00240388i
$750$	−32.3914	+	15.6632i	−1.18277	+	0.571939i
$751$	−17.1957	−	0.643419i	−0.627481	−	0.0234787i	−0.278240	−	0.960512i	$-0.589751\pi$
$751$	−17.1957	−	0.643419i	−0.627481	−	0.0234787i	−0.349241	+	0.937033i	$0.613561\pi$
$752$	4.37788	+	10.0342i	0.159645	+	0.365910i
$753$	9.08612	−	23.2611i	0.331117	−	0.847683i
$754$	−27.5643	−	12.4851i	−1.00383	−	0.454680i
$755$			22.5753i			0.821598i
$756$	−14.5910	+	5.18487i	−0.530670	+	0.188572i
$757$	−12.3896	−	7.78493i	−0.450309	−	0.282948i	0.287723	−	0.957714i	$-0.407102\pi$
$757$	−12.3896	−	7.78493i	−0.450309	−	0.282948i	−0.738032	+	0.674766i	$0.764245\pi$
$758$	4.51968	+	4.19365i	0.164162	+	0.152320i
$759$	−1.36736	−	4.40766i	−0.0496320	−	0.159988i
$760$	−2.55642	+	16.9608i	−0.0927313	+	0.615232i
$761$	−14.2131	−	15.3180i	−0.515223	−	0.555278i	0.420829	−	0.907140i	$-0.361739\pi$
$761$	−14.2131	−	15.3180i	−0.515223	−	0.555278i	−0.936052	+	0.351862i	$0.885549\pi$
$762$	30.3496	−	10.6747i	1.09945	−	0.386703i
$763$	−12.3124	−	0.922690i	−0.445740	−	0.0334036i
$764$	−46.0349	−	73.2642i	−1.66548	−	2.65060i
$765$	−4.97418	−	42.9046i	−0.179842	−	1.55122i
$766$	17.9656	+	17.9656i	0.649124	+	0.649124i
$767$	−15.5650	+	10.6121i	−0.562021	+	0.383179i
$768$	−9.91738	−	36.7752i	−0.357863	−	1.32701i
$769$	−18.5023	−	25.0698i	−0.667211	−	0.904039i	0.332019	−	0.943273i	$-0.392270\pi$
$769$	−18.5023	−	25.0698i	−0.667211	−	0.904039i	−0.999230	+	0.0392337i	$0.987508\pi$
$770$	−8.64079	+	0.647538i	−0.311392	+	0.0233356i
$771$	−39.7148	−	29.2122i	−1.43029	−	1.05205i
$772$	38.6012	+	7.30374i	1.38929	+	0.262867i
$773$	−30.4834	+	19.1540i	−1.09641	+	0.688922i	−0.953675	−	0.300838i	$-0.902734\pi$
$773$	−30.4834	+	19.1540i	−1.09641	+	0.688922i	−0.142738	+	0.989760i	$0.545591\pi$
$774$	42.4969	−	9.84374i	1.52752	−	0.353826i
$775$	−4.00761	+	11.4531i	−0.143958	+	0.411407i
$776$	7.36815	+	2.27277i	0.264501	+	0.0815878i
$777$	10.8497	−	0.0174714i	0.389231	−	0.000626781i
$778$	1.50942	−	3.84593i	0.0541152	−	0.137883i
$779$	5.63048	+	18.2536i	0.201733	+	0.654002i
$780$	−29.5205	+	21.8607i	−1.05700	+	0.782737i
$781$	−10.8362	−	7.99750i	−0.387751	−	0.286173i
$782$	20.8342			0.745028
$783$	−12.8503	−	24.8570i	−0.459232	−	0.888317i
$784$	6.36347			0.227267
$785$	20.1277	+	14.8550i	0.718390	+	0.530196i
$786$	−16.8824	+	12.5018i	−0.602175	+	0.445925i
$787$	−8.69058	−	28.1742i	−0.309786	−	1.00430i	−0.967890	−	0.251374i	$-0.919118\pi$
$787$	−8.69058	−	28.1742i	−0.309786	−	1.00430i	0.658104	−	0.752927i	$-0.271359\pi$
$788$	16.6246	−	42.3589i	0.592228	−	1.50897i
$789$	41.0852	−	0.0661599i	1.46267	−	0.00235536i
$790$	9.97770	+	3.07771i	0.354991	+	0.109500i
$791$	−4.03138	+	11.5210i	−0.143339	+	0.409640i
$792$	11.7033	+	12.5320i	0.415859	+	0.445304i
$793$	−1.99795	+	1.25540i	−0.0709494	+	0.0445805i
$794$	−23.3970	−	4.42695i	−0.830328	−	0.157107i
$795$	29.7280	+	21.8664i	1.05434	+	0.775522i
$796$	−47.0824	+	3.52834i	−1.66879	+	0.125059i
$797$	−3.82547	−	5.18332i	−0.135505	−	0.183603i	0.731591	−	0.681744i	$-0.238778\pi$
$797$	−3.82547	−	5.18332i	−0.135505	−	0.183603i	−0.867096	+	0.498141i	$0.834016\pi$
$798$	1.80005	+	6.67488i	0.0637212	+	0.236288i
$799$	−50.1539	+	34.1944i	−1.77432	+	1.20971i
$800$	4.72420	+	4.72420i	0.167026	+	0.167026i
$801$	19.9372	+	8.62218i	0.704446	+	0.304650i
$802$	−27.4190	−	43.6370i	−0.968197	−	1.54088i
$803$	16.6705	+	1.24928i	0.588291	+	0.0440863i
$804$	−7.24869	+	2.54954i	−0.255642	+	0.0899152i
$805$	2.36985	+	2.55409i	0.0835262	+	0.0900199i
$806$	6.70857	−	44.5085i	0.236299	−	1.56774i
$807$	3.93933	+	12.6983i	0.138671	+	0.447003i
$808$	−28.2983	−	26.2570i	−0.995530	−	0.923717i
$809$	30.9958	+	19.4759i	1.08975	+	0.684738i	0.952114	−	0.305744i	$-0.0989053\pi$
$809$	30.9958	+	19.4759i	1.08975	+	0.684738i	0.137640	+	0.990482i	$0.456048\pi$
$810$	−53.6171	−	1.66045i	−1.88391	−	0.0583421i
$811$			45.7489i			1.60646i	0.595669	+	0.803230i	$0.296887\pi$
$811$			45.7489i			1.60646i	−0.595669	+	0.803230i	$0.703113\pi$
$812$	−2.17105	−	15.9006i	−0.0761889	−	0.558001i
$813$	7.04964	−	18.0476i	0.247242	−	0.632957i
$814$	−11.4174	−	26.1690i	−0.400180	−	0.917222i
$815$	−25.4836	−	0.953529i	−0.892651	−	0.0334007i
$816$	−8.94786	+	4.32682i	−0.313238	+	0.151469i
$817$	−1.83805	−	12.1947i	−0.0643054	−	0.426638i
$818$	1.49782	−	1.87821i	0.0523701	−	0.0656700i
$819$	−3.09769	+	5.40548i	−0.108242	+	0.188883i
$820$	−80.2360	−	28.0758i	−2.80196	−	0.980449i
$821$	−0.356916	+	4.76271i	−0.0124564	+	0.166220i	0.987506	+	0.157580i	$0.0503692\pi$
$821$	−0.356916	+	4.76271i	−0.0124564	+	0.166220i	−0.999963	+	0.00863974i	$0.997250\pi$
$822$	−68.3127	+	58.9796i	−2.38268	+	2.05715i
$823$	−15.1874	−	13.0698i	−0.529399	−	0.455585i	0.346520	−	0.938043i	$-0.387363\pi$
$823$	−15.1874	−	13.0698i	−0.529399	−	0.455585i	−0.875919	+	0.482458i	$0.839744\pi$
$824$	59.7377	+	16.0067i	2.08106	+	0.557619i
$825$	−4.22541	−	1.29592i	−0.147110	−	0.0451181i
$826$	−14.4610	−	6.30928i	−0.503163	−	0.219528i
$827$	−2.42917	−	21.5595i	−0.0844706	−	0.749698i	−0.962535	−	0.271156i	$-0.912594\pi$
$827$	−2.42917	−	21.5595i	−0.0844706	−	0.749698i	0.878065	−	0.478542i	$-0.158834\pi$
$828$	2.38986	−	16.2098i	0.0830534	−	0.563328i
$829$	−5.18697	+	5.18697i	−0.180151	+	0.180151i	−0.791422	−	0.611271i	$-0.790659\pi$
$829$	−5.18697	+	5.18697i	−0.180151	+	0.180151i	0.611271	+	0.791422i	$0.290659\pi$
$830$	−5.09441	+	26.9246i	−0.176830	+	0.934567i
$831$	16.6955	−	47.9607i	0.579162	−	1.66374i
$832$	−24.5221	−	16.7189i	−0.850152	−	0.579624i
$833$	6.55961	+	34.6684i	0.227277	+	1.20119i
$834$	−8.61006	−	1.28358i	−0.298142	−	0.0444468i
$835$	19.0118	+	48.4412i	0.657929	+	1.67638i
$836$	9.00678	−	7.18267i	0.311506	−	0.248418i
$837$	30.3746	−	28.4578i	1.04990	−	0.983646i
$838$	−19.3366	+	30.7740i	−0.667972	+	1.06307i
$839$	29.2243	−	39.5975i	1.00893	−	1.36706i	0.0800073	−	0.996794i	$-0.474506\pi$
$839$	29.2243	−	39.5975i	1.00893	−	1.36706i	0.928927	−	0.370263i	$-0.120732\pi$
$840$	−12.0585	−	4.71020i	−0.416056	−	0.162517i
$841$	27.9385	−	7.77432i	0.963397	−	0.268080i
$842$	−32.9440	+	19.0202i	−1.13532	+	0.655480i
$843$	−0.902469	+	0.569088i	−0.0310827	+	0.0196004i
$844$	−38.9903	+	20.6070i	−1.34210	+	0.709321i
$845$	4.09483	−	17.9406i	0.140866	−	0.617176i
$846$	32.9286	+	67.8173i	1.13211	+	2.33161i
$847$	−5.50754	−	4.39211i	−0.189241	−	0.150915i
$848$	2.50309	−	8.11482i	0.0859565	−	0.278664i
$849$	−18.8120	−	3.52806i	−0.645627	−	0.121083i
$850$	11.2398	−	16.4858i	0.385523	−	0.565459i
$851$	−5.36443	+	10.1500i	−0.183890	+	0.347937i
$852$	−22.4115	−	42.2399i	−0.767806	−	1.44711i
$853$	−18.3804	+	4.92500i	−0.629331	+	0.168629i	−0.559366	−	0.828921i	$-0.688955\pi$
$853$	−18.3804	+	4.92500i	−0.629331	+	0.168629i	−0.0699651	+	0.997549i	$0.522289\pi$
$854$	−1.78051	−	0.857450i	−0.0609279	−	0.0293413i
$855$	−1.64944	+	15.0754i	−0.0564098	+	0.515569i
$856$	0.259930	−	0.0292871i	0.00888423	−	0.00100101i
$857$	4.87587	+	7.15160i	0.166557	+	0.244294i	0.900438	−	0.434983i	$-0.143246\pi$
$857$	4.87587	+	7.15160i	0.166557	+	0.244294i	−0.733882	+	0.679277i	$0.762293\pi$
$858$	16.2946	+	1.80940i	0.556290	+	0.0617718i
$859$	−5.34462	+	6.21056i	−0.182356	+	0.211902i	−0.841708	−	0.539933i	$-0.818450\pi$
$859$	−5.34462	+	6.21056i	−0.182356	+	0.211902i	0.659352	+	0.751834i	$0.270831\pi$
$860$	48.5204	+	25.6438i	1.65453	+	0.874447i
$861$	−14.3754	+	1.10057i	−0.489911	+	0.0375072i
$862$	53.2975	+	61.9328i	1.81532	+	2.10944i
$863$	−0.140523	−	0.615672i	−0.00478346	−	0.0209577i	0.972480	−	0.232987i	$-0.0748499\pi$
$863$	−0.140523	−	0.615672i	−0.00478346	−	0.0209577i	−0.977263	+	0.212029i	$0.931993\pi$
$864$	−6.86082	−	21.8666i	−0.233410	−	0.743917i
$865$	31.5620	+	39.5775i	1.07314	+	1.34568i
$866$	52.1625	−	56.2178i	1.77255	−	1.91036i
$867$	−15.2732	−	20.6249i	−0.518707	−	0.700459i
$868$	21.8795	−	9.54592i	0.742638	−	0.324010i
$869$	−1.47551	−	2.55566i	−0.0500533	−	0.0866948i
$870$	13.0360	−	54.0441i	0.441962	−	1.83227i
$871$	−1.54578	+	2.67738i	−0.0523769	+	0.0907195i
$872$	−5.43507	+	48.2376i	−0.184055	+	1.63353i
$873$	6.59086	+	1.74328i	0.223067	+	0.0590012i
$874$	−7.13180	−	1.62779i	−0.241237	−	0.0550607i
$875$	−7.59148	+	1.14423i	−0.256639	+	0.0386821i
$876$	51.4499	+	29.5942i	1.73833	+	0.999897i
$877$	0.800913	−	0.743138i	0.0270449	−	0.0250940i	−0.666535	−	0.745474i	$-0.732223\pi$
$877$	0.800913	−	0.743138i	0.0270449	−	0.0250940i	0.693579	+	0.720380i	$0.256033\pi$
$878$	−38.5373	+	7.29165i	−1.30057	+	0.246081i
$879$	−12.9946	+	8.89029i	−0.438299	+	0.299862i
$880$	0.163549	+	4.37095i	0.00551325	+	0.147345i
$881$	−3.38456	−	9.67252i	−0.114029	−	0.325875i	0.872699	−	0.488258i	$-0.162368\pi$
$881$	−3.38456	−	9.67252i	−0.114029	−	0.325875i	−0.986728	+	0.162383i	$0.948082\pi$
$882$	43.7846	−	1.77953i	1.47430	−	0.0599200i
$883$	−18.4472	+	38.3060i	−0.620798	+	1.28910i	0.319124	+	0.947713i	$0.396611\pi$
$883$	−18.4472	+	38.3060i	−0.620798	+	1.28910i	−0.939922	+	0.341388i	$0.889103\pi$
$884$	−18.7424	+	42.9581i	−0.630376	+	1.44484i
$885$	−24.5125	−	24.4336i	−0.823977	−	0.821328i
$886$	−4.33770	−	57.8826i	−0.145728	−	1.94460i
$887$	−7.20728	+	26.8979i	−0.241997	+	0.903144i	0.732872	+	0.680366i	$0.238179\pi$
$887$	−7.20728	+	26.8979i	−0.241997	+	0.903144i	−0.974869	+	0.222778i	$0.928487\pi$
$888$	1.52632	−	42.6289i	0.0512201	−	1.43053i
$889$	6.85999	−	0.256683i	0.230077	−	0.00860886i
$890$	18.7247	+	38.8823i	0.627654	+	1.30334i
$891$	10.7890	+	10.6509i	0.361446	+	0.356819i
$892$	76.3896	−	17.4354i	2.55771	−	0.583782i
$893$	19.8400	−	7.78661i	0.663919	−	0.260569i
$894$	−28.0956	+	8.71591i	−0.939657	+	0.291504i
$895$	−1.52031	+	0.468953i	−0.0508183	+	0.0156754i
$896$	0.644774	−	17.2319i	0.0215404	−	0.575679i
$897$	−3.51631	−	5.57622i	−0.117406	−	0.186185i
$898$	−56.7573	−	32.7689i	−1.89402	−	1.09351i
$899$	22.4403	+	36.8405i	0.748427	+	1.22870i
$900$	−11.5373	−	10.6361i	−0.384576	−	0.354536i
$901$	46.7900	+	5.27197i	1.55880	+	0.175635i
$902$	17.7281	+	33.5431i	0.590280	+	1.11686i
$903$	9.28300	+	0.680634i	0.308919	+	0.0226501i
$904$	44.6712	+	17.5322i	1.48574	+	0.583111i
$905$	−20.5848	−	3.10267i	−0.684263	−	0.103136i
$906$	33.2795	−	13.1231i	1.10564	−	0.435987i
$907$	16.3055	−	14.0320i	0.541414	−	0.465924i	−0.338561	−	0.940944i	$-0.609940\pi$
$907$	16.3055	−	14.0320i	0.541414	−	0.465924i	0.879975	+	0.475020i	$0.157559\pi$
$908$	−11.5648	+	5.56931i	−0.383791	+	0.184824i
$909$	−25.9423	−	22.1801i	−0.860452	−	0.735669i
$910$	−11.6833	+	4.08816i	−0.387297	+	0.135521i
$911$	6.42326	+	23.9719i	0.212812	+	0.794226i	0.986925	+	0.161179i	$0.0515295\pi$
$911$	6.42326	+	23.9719i	0.212812	+	0.794226i	−0.774113	+	0.633047i	$0.781804\pi$
$912$	3.40102	−	0.782026i	0.112619	−	0.0258955i
$913$	6.23120	−	4.59884i	0.206223	−	0.152199i
$914$	−23.4688	+	17.3207i	−0.776278	+	0.572919i
$915$	−2.95375	−	3.17312i	−0.0976480	−	0.104900i
$916$	14.0779	+	52.5393i	0.465146	+	1.73595i
$917$	−4.23095	+	1.48047i	−0.139718	+	0.0488895i
$918$	−60.3568	+	32.2735i	−1.99207	+	1.06518i
$919$	−18.5613	+	8.93866i	−0.612282	+	0.294859i	−0.714209	−	0.699933i	$-0.753213\pi$
$919$	−18.5613	+	8.93866i	−0.612282	+	0.294859i	0.101927	+	0.994792i	$0.467499\pi$
$920$	10.3829	−	8.93522i	0.342315	−	0.294586i
$921$	−7.98541	+	53.5648i	−0.263128	+	1.76502i
$922$	14.9049	+	2.24655i	0.490866	+	0.0739861i
$923$	−17.9088	−	7.02870i	−0.589476	−	0.231352i
$924$	3.78515	+	7.82767i	0.124522	+	0.257512i
$925$	5.13751	+	9.72065i	0.168920	+	0.319613i
$926$	−39.3635	−	4.43520i	−1.29356	−	0.145750i
$927$	53.3489	+	11.9959i	1.75221	+	0.393997i
$928$	23.6366	−	2.33099i	0.775911	−	0.0765186i
$929$	19.5003	+	11.2585i	0.639783	+	0.369379i	0.784531	−	0.620090i	$-0.212904\pi$
$929$	19.5003	+	11.2585i	0.639783	+	0.369379i	−0.144748	+	0.989469i	$0.546237\pi$
$930$	82.6322	−	3.22514i	2.70962	−	0.105756i
$931$	0.463225	−	12.3799i	0.0151816	−	0.405736i
$932$	43.3217	−	13.3630i	1.41905	−	0.437719i
$933$	−12.7774	−	11.8175i	−0.418314	−	0.386887i
$934$	35.4309	−	13.9056i	1.15934	−	0.455005i
$935$	−23.6445	+	5.39670i	−0.773257	+	0.176491i
$936$	20.7817	+	12.9649i	0.679272	+	0.423770i
$937$	1.32329	+	2.74785i	0.0432301	+	0.0897683i	0.921465	−	0.388461i	$-0.126993\pi$
$937$	1.32329	+	2.74785i	0.0432301	+	0.0897683i	−0.878235	+	0.478229i	$0.841279\pi$
$938$	−2.58742	+	0.0968145i	−0.0844823	+	0.00316111i
$939$	−13.3956	−	8.38695i	−0.437148	−	0.273698i
$940$	−24.5478	+	91.6138i	−0.800662	+	2.98811i
$941$	2.27848	+	30.4042i	0.0742762	+	0.991147i	0.902483	+	0.430725i	$0.141742\pi$
$941$	2.27848	+	30.4042i	0.0742762	+	0.991147i	−0.828207	+	0.560422i	$0.810639\pi$
$942$	10.1982	−	38.3068i	0.332275	−	1.24810i
$943$	6.10056	−	13.9826i	0.198661	−	0.455337i
$944$	−3.45557	+	7.17557i	−0.112469	+	0.233545i
$945$	−10.8219	−	3.72818i	−0.352038	−	0.121278i
$946$	−8.08985	−	23.1195i	−0.263024	−	0.751679i
$947$	1.71174	+	45.7473i	0.0556242	+	1.48659i	0.695731	+	0.718303i	$0.255081\pi$
$947$	1.71174	+	45.7473i	0.0556242	+	1.48659i	−0.640106	+	0.768286i	$0.721110\pi$
$948$	−0.799808	−	10.4469i	−0.0259766	−	0.339300i
$949$	23.4642	−	4.43966i	0.761679	−	0.144117i
$950$	−5.13559	+	4.76513i	−0.166621	+	0.154601i
$951$	−0.0574041	−	35.6479i	−0.00186145	−	1.15596i
$952$	−16.3332	+	2.46183i	−0.529361	+	0.0797883i
$953$	24.8016	+	5.66080i	0.803402	+	0.183371i	0.604455	−	0.796639i	$-0.293391\pi$
$953$	24.8016	+	5.66080i	0.803402	+	0.183371i	0.198947	+	0.980010i	$0.436248\pi$
$954$	14.9535	−	56.5349i	0.484138	−	1.83039i
$955$	7.16112	−	63.5567i	0.231728	−	2.05665i
$956$	25.2184	−	43.6796i	0.815623	−	1.41270i
$957$	−13.0897	+	8.69074i	−0.423131	+	0.280932i
$958$	−10.0112	−	17.3398i	−0.323446	−	0.560225i
$959$	−17.6506	+	7.70088i	−0.569968	+	0.248675i
$960$	21.7244	−	50.0125i	0.701152	−	1.61415i
$961$	−22.5581	+	24.3119i	−0.727681	+	0.784254i
$962$	−25.4291	−	31.8871i	−0.819868	−	1.02808i
$963$	0.228579	−	0.0352059i	0.00736584	−	0.00113450i
$964$	−20.8735	−	91.4528i	−0.672290	−	2.94550i
$965$	18.9421	+	22.0112i	0.609769	+	0.708564i
$966$	2.38753	−	4.97824i	0.0768175	−	0.160172i
$967$	43.0065	+	22.7296i	1.38300	+	0.730935i	0.982657	−	0.185433i	$-0.0593687\pi$
$967$	43.0065	+	22.7296i	1.38300	+	0.730935i	0.400339	+	0.916367i	$0.368892\pi$
$968$	−18.0654	+	20.9924i	−0.580644	+	0.674721i
$969$	7.76635	+	17.7228i	0.249491	+	0.569337i
$970$	7.63007	+	11.1913i	0.244987	+	0.359330i
$971$	21.6000	−	2.43373i	0.693176	−	0.0781022i	0.241654	−	0.970362i	$-0.422310\pi$
$971$	21.6000	−	2.43373i	0.693176	−	0.0781022i	0.451522	+	0.892260i	$0.350881\pi$
$972$	18.1865	+	50.6619i	0.583333	+	1.62498i
$973$	−1.67354	−	0.805934i	−0.0536512	−	0.0258370i
$974$	12.2242	−	3.27546i	0.391688	−	0.104952i
$975$	−6.30942	−	0.225908i	−0.202063	−	0.00723484i
$976$	−0.466135	+	0.881971i	−0.0149206	+	0.0282312i
$977$	−17.7471	+	26.0301i	−0.567779	+	0.832778i	−0.997535	−	0.0701665i	$-0.977647\pi$
$977$	−17.7471	+	26.0301i	−0.567779	+	0.832778i	0.429757	+	0.902945i	$0.358599\pi$
$978$	13.4081	+	38.1212i	0.428744	+	1.21898i
$979$	3.59508	−	11.6550i	0.114899	−	0.372495i
$980$	43.1025	+	34.3731i	1.37686	+	1.09801i
$981$	−3.06953	+	42.8097i	−0.0980026	+	1.36681i
$982$	−1.78449	+	7.81834i	−0.0569452	+	0.249493i
$983$	12.2540	−	6.47642i	0.390842	−	0.206566i	−0.260290	−	0.965530i	$-0.583818\pi$
$983$	12.2540	−	6.47642i	0.390842	−	0.206566i	0.651132	+	0.758965i	$0.274294\pi$
$984$	2.21065	+	56.6398i	0.0704731	+	1.80561i
$985$	29.1297	−	16.8180i	0.928148	−	0.535867i
$986$	−19.9638	−	68.0659i	−0.635776	−	2.16766i
$987$	2.42314	+	15.9027i	0.0771293	+	0.506187i
$988$	9.77212	−	13.2408i	0.310893	−	0.421244i
$989$	−5.23998	+	8.33938i	−0.166622	+	0.265177i
$990$	2.34765	+	30.0291i	0.0746131	+	0.954387i
$991$	14.0792	−	11.2278i	0.447241	−	0.356663i	−0.373822	−	0.927501i	$-0.621953\pi$
$991$	14.0792	−	11.2278i	0.447241	−	0.356663i	0.821063	+	0.570837i	$0.193381\pi$
$992$	12.9073	+	32.8874i	0.409809	+	1.04418i
$993$	28.4999	−	35.8560i	0.904417	−	1.13786i
$994$	−2.99554	−	15.8318i	−0.0950128	−	0.502155i
$995$	−28.8358	−	19.6599i	−0.914156	−	0.623261i
$996$	27.0089	−	5.15543i	0.855810	−	0.163356i
$997$	−1.87236	+	9.89569i	−0.0592984	+	0.313400i	−0.999640	−	0.0268324i	$-0.991458\pi$
$997$	−1.87236	+	9.89569i	−0.0592984	+	0.313400i	0.940342	+	0.340232i	$0.110506\pi$
$998$	−1.34031	+	1.34031i	−0.0424269	+	0.0424269i
$999$	−0.182197	−	37.7145i	−0.00576447	−	1.19323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.2.3	✓	672
3.2	odd	2		783.2.be.a.89.26		672
9.4	even	3		783.2.be.a.611.26		672
9.5	odd	6	inner	261.2.x.a.176.3	yes	672
29.15	odd	28	inner	261.2.x.a.218.3	yes	672
87.44	even	28		783.2.be.a.305.26		672
261.131	even	84	inner	261.2.x.a.131.3	yes	672
261.247	odd	84		783.2.be.a.44.26		672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.2.3	✓	672	1.1	even	1	trivial
261.2.x.a.131.3	yes	672	261.131	even	84	inner
261.2.x.a.176.3	yes	672	9.5	odd	6	inner
261.2.x.a.218.3	yes	672	29.15	odd	28	inner
783.2.be.a.44.26		672	261.247	odd	84
783.2.be.a.89.26		672	3.2	odd	2
783.2.be.a.305.26		672	87.44	even	28
783.2.be.a.611.26		672	9.4	even	3

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87887 - 1.38667i) q^{2} +(-1.39195 + 1.03077i) q^{3} +(1.01780 + 3.29961i) q^{4} +(-0.932500 + 2.37597i) q^{5} +(4.04463 - 0.00651310i) q^{6} +(0.824688 + 0.254382i) q^{7} +(1.12065 - 3.20264i) q^{8} +(0.875028 - 2.86955i) q^{9} +O(q^{10})\)	\(q+(-1.87887 - 1.38667i) q^{2} +(-1.39195 + 1.03077i) q^{3} +(1.01780 + 3.29961i) q^{4} +(-0.932500 + 2.37597i) q^{5} +(4.04463 - 0.00651310i) q^{6} +(0.824688 + 0.254382i) q^{7} +(1.12065 - 3.20264i) q^{8} +(0.875028 - 2.86955i) q^{9} +(5.04674 - 3.17108i) q^{10} +(-1.65515 - 0.313171i) q^{11} +(-4.81786 - 3.54377i) q^{12} +(-2.39958 + 0.179824i) q^{13} +(-1.19674 - 1.62152i) q^{14} +(-1.15109 - 4.26842i) q^{15} +(-0.840543 + 0.573072i) q^{16} +(-3.98857 - 3.98857i) q^{17} +(-5.62319 + 4.17815i) q^{18} +(1.05371 + 1.67697i) q^{19} +(-8.78888 - 0.658636i) q^{20} +(-1.41013 + 0.495976i) q^{21} +(2.67555 + 2.88355i) q^{22} +(0.235741 - 1.56404i) q^{23} +(1.74130 + 5.61305i) q^{24} +(-1.11043 - 1.03032i) q^{25} +(4.75787 + 2.98957i) q^{26} +(1.73985 + 4.89621i) q^{27} +2.98006i q^{28} +(-5.33566 + 0.728525i) q^{29} +(-3.75614 + 9.61600i) q^{30} +(-3.20326 - 7.34196i) q^{31} +(-4.40742 - 0.164914i) q^{32} +(2.62668 - 1.27016i) q^{33} +(1.96318 + 13.0248i) q^{34} +(-1.37343 + 1.72222i) q^{35} +(10.3590 - 0.0333625i) q^{36} +(-6.85094 - 2.39725i) q^{37} +(0.345618 - 4.61196i) q^{38} +(3.15474 - 2.72372i) q^{39} +(6.56438 + 5.64911i) q^{40} +(9.31633 + 2.49630i) q^{41} +(3.33721 + 1.02351i) q^{42} +(-5.70727 - 2.49005i) q^{43} +(-0.651260 - 5.78009i) q^{44} +(6.00201 + 4.75490i) q^{45} +(-2.61173 + 2.61173i) q^{46} +(2.00066 - 10.5738i) q^{47} +(0.579285 - 1.66409i) q^{48} +(-5.16827 - 3.52367i) q^{49} +(0.657627 + 3.47564i) q^{50} +(9.66316 + 1.44058i) q^{51} +(-3.03564 - 7.73468i) q^{52} +(-6.52641 + 5.20463i) q^{53} +(3.52048 - 11.6120i) q^{54} +(2.28751 - 3.64055i) q^{55} +(1.73889 - 2.35611i) q^{56} +(-3.19527 - 1.24812i) q^{57} +(11.0352 + 6.03000i) q^{58} +(6.77990 - 3.91438i) q^{59} +(12.9126 - 8.14253i) q^{60} +(0.866962 - 0.458203i) q^{61} +(-4.16236 + 18.2365i) q^{62} +(1.45159 - 2.14389i) q^{63} +(9.64304 + 7.69007i) q^{64} +(1.81036 - 5.86903i) q^{65} +(-6.69650 - 1.25588i) q^{66} +(0.723739 - 1.06153i) q^{67} +(9.10118 - 17.2203i) q^{68} +(1.28402 + 2.42005i) q^{69} +(4.96865 - 1.33135i) q^{70} +(7.20334 + 3.46895i) q^{71} +(-8.20955 - 6.01818i) q^{72} +(-9.86170 + 1.11115i) q^{73} +(9.54785 + 14.0041i) q^{74} +(2.60768 + 0.289563i) q^{75} +(-4.46088 + 5.18364i) q^{76} +(-1.28531 - 0.679309i) q^{77} +(-9.70426 + 0.742950i) q^{78} +(1.14271 + 1.32785i) q^{79} +(-0.577797 - 2.53150i) q^{80} +(-7.46865 - 5.02188i) q^{81} +(-14.0427 - 17.6089i) q^{82} +(-3.12707 + 3.37018i) q^{83} +(-3.07175 - 4.14808i) q^{84} +(13.1961 - 5.75738i) q^{85} +(7.27034 + 12.5926i) q^{86} +(6.67601 - 6.51390i) q^{87} +(-2.85782 + 4.94989i) q^{88} +(-0.810687 + 7.19504i) q^{89} +(-4.68353 - 17.2567i) q^{90} +(-2.02465 - 0.462114i) q^{91} +(5.40066 - 0.814018i) q^{92} +(12.0266 + 6.91779i) q^{93} +(-18.4213 + 17.0925i) q^{94} +(-4.96701 + 0.939809i) q^{95} +(6.30488 - 4.31348i) q^{96} +(0.0849716 + 2.27091i) q^{97} +(4.82436 + 13.7872i) q^{98} +(-2.34696 + 4.47550i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

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