LMFDB - Embedded newform 231.2.be.a.2.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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([15, 10, 3]))

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

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

chi := DirichletCharacter("231.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.be (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:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			2.20
Character	$\chi$	$=$	231.2
Dual form			231.2.be.a.116.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.830242 + 0.922077i) q^{2} +(-1.55093 + 0.771117i) q^{3} +(0.0481326 - 0.457951i) q^{4} +(0.859357 - 4.04296i) q^{5} +(-1.99867 - 0.789862i) q^{6} +(-0.152025 + 2.64138i) q^{7} +(2.46985 - 1.79445i) q^{8} +(1.81076 - 2.39189i) q^{9} +O(q^{10})$	\(q+(0.830242 + 0.922077i) q^{2} +(-1.55093 + 0.771117i) q^{3} +(0.0481326 - 0.457951i) q^{4} +(0.859357 - 4.04296i) q^{5} +(-1.99867 - 0.789862i) q^{6} +(-0.152025 + 2.64138i) q^{7} +(2.46985 - 1.79445i) q^{8} +(1.81076 - 2.39189i) q^{9} +(4.44139 - 2.56424i) q^{10} +(3.26039 - 0.608160i) q^{11} +(0.278483 + 0.747365i) q^{12} +(-1.08183 - 0.351507i) q^{13} +(-2.56177 + 2.05281i) q^{14} +(1.78479 + 6.93300i) q^{15} +(2.80437 + 0.596086i) q^{16} +(-0.724602 + 0.804752i) q^{17} +(3.70888 - 0.316191i) q^{18} +(-1.51398 + 0.159125i) q^{19} +(-1.81011 - 0.588141i) q^{20} +(-1.80103 - 4.21382i) q^{21} +(3.26768 + 2.50141i) q^{22} +(-1.17103 - 0.676097i) q^{23} +(-2.44683 + 4.68760i) q^{24} +(-11.0393 - 4.91500i) q^{25} +(-0.574062 - 1.28936i) q^{26} +(-0.963929 + 5.10596i) q^{27} +(1.20230 + 0.196756i) q^{28} +(5.37729 + 3.90683i) q^{29} +(-4.91095 + 7.40178i) q^{30} +(4.72526 - 1.00438i) q^{31} +(-1.27423 - 2.20704i) q^{32} +(-4.58767 + 3.45735i) q^{33} -1.34364 q^{34} +(10.5483 + 2.88452i) q^{35} +(-1.00821 - 0.944366i) q^{36} +(-3.02058 + 1.34485i) q^{37} +(-1.40369 - 1.26389i) q^{38} +(1.94889 - 0.289053i) q^{39} +(-5.13240 - 11.5275i) q^{40} +(3.69146 - 2.68200i) q^{41} +(2.39017 - 5.15918i) q^{42} +8.06763i q^{43} +(-0.121577 - 1.52237i) q^{44} +(-8.11423 - 9.37631i) q^{45} +(-0.348828 - 1.64111i) q^{46} +(-10.9787 + 1.15391i) q^{47} +(-4.80902 + 1.23801i) q^{48} +(-6.95378 - 0.803111i) q^{49} +(-4.63325 - 14.2597i) q^{50} +(0.503248 - 1.80687i) q^{51} +(-0.213044 + 0.478505i) q^{52} +(0.815733 + 3.83772i) q^{53} +(-5.50838 + 3.35037i) q^{54} +(0.343073 - 13.7042i) q^{55} +(4.36434 + 6.79660i) q^{56} +(2.22537 - 1.41424i) q^{57} +(0.862053 + 8.20188i) q^{58} +(-2.50803 - 0.263605i) q^{59} +(3.26088 - 0.483642i) q^{60} +(-1.24665 + 5.86504i) q^{61} +(4.84923 + 3.52317i) q^{62} +(6.04262 + 5.14653i) q^{63} +(2.74905 - 8.46071i) q^{64} +(-2.35080 + 4.07171i) q^{65} +(-6.99682 - 1.35974i) q^{66} +(5.62222 + 9.73797i) q^{67} +(0.333660 + 0.370567i) q^{68} +(2.33754 + 0.145574i) q^{69} +(6.09792 + 12.1212i) q^{70} +(1.74957 - 0.568471i) q^{71} +(0.180167 - 9.15692i) q^{72} +(0.873788 + 0.0918389i) q^{73} +(-3.74786 - 1.66866i) q^{74} +(20.9112 - 0.889750i) q^{75} +0.700986i q^{76} +(1.11072 + 8.70438i) q^{77} +(1.88458 + 1.55704i) q^{78} +(-8.24724 + 7.42585i) q^{79} +(4.81990 - 10.8257i) q^{80} +(-2.44231 - 8.66228i) q^{81} +(5.53782 + 1.17710i) q^{82} +(2.66212 + 8.19316i) q^{83} +(-2.01641 + 0.621962i) q^{84} +(2.63089 + 3.62110i) q^{85} +(-7.43897 + 6.69808i) q^{86} +(-11.3524 - 1.91270i) q^{87} +(6.96135 - 7.35266i) q^{88} +(-0.214205 - 0.123671i) q^{89} +(1.90890 - 15.2665i) q^{90} +(1.09293 - 2.80408i) q^{91} +(-0.365984 + 0.503734i) q^{92} +(-6.55404 + 5.20145i) q^{93} +(-10.1789 - 9.16516i) q^{94} +(-0.657709 + 6.25769i) q^{95} +(3.67813 + 2.44037i) q^{96} +(-3.43868 + 10.5832i) q^{97} +(-5.03279 - 7.07869i) q^{98} +(4.44912 - 8.89974i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.830242	+	0.922077i	0.587069	+	0.652007i	0.961357	−	0.275306i	$-0.0887792\pi$
$2$	0.830242	+	0.922077i	0.587069	+	0.652007i	−0.374287	+	0.927313i	$0.622113\pi$
$3$	−1.55093	+	0.771117i	−0.895429	+	0.445204i
$3$	−1.55093	+	0.771117i	−0.895429	+	0.445204i
$4$	0.0481326	−	0.457951i	0.0240663	−	0.228975i
$5$	0.859357	−	4.04296i	0.384316	−	1.80806i	−0.181337	−	0.983421i	$-0.558042\pi$
$5$	0.859357	−	4.04296i	0.384316	−	1.80806i	0.565653	−	0.824644i	$-0.308624\pi$
$6$	−1.99867	−	0.789862i	−0.815955	−	0.322460i
$7$	−0.152025	+	2.64138i	−0.0574600	+	0.998348i
$7$	−0.152025	+	2.64138i	−0.0574600	+	0.998348i
$8$	2.46985	−	1.79445i	0.873223	−	0.634433i
$9$	1.81076	−	2.39189i	0.603586	−	0.797298i
$10$	4.44139	−	2.56424i	1.40449	−	0.810883i
$11$	3.26039	−	0.608160i	0.983044	−	0.183367i
$11$	3.26039	−	0.608160i	0.983044	−	0.183367i
$12$	0.278483	+	0.747365i	0.0803912	+	0.215746i
$13$	−1.08183	−	0.351507i	−0.300045	−	0.0974905i	0.155126	−	0.987895i	$-0.450422\pi$
$13$	−1.08183	−	0.351507i	−0.300045	−	0.0974905i	−0.455171	+	0.890404i	$0.650422\pi$
$14$	−2.56177	+	2.05281i	−0.684662	+	0.548635i
$15$	1.78479	+	6.93300i	0.460831	+	1.79009i
$16$	2.80437	+	0.596086i	0.701092	+	0.149022i
$17$	−0.724602	+	0.804752i	−0.175742	+	0.195181i	−0.824580	−	0.565745i	$-0.808589\pi$
$17$	−0.724602	+	0.804752i	−0.175742	+	0.195181i	0.648838	+	0.760926i	$0.275255\pi$
$18$	3.70888	−	0.316191i	0.874191	−	0.0745269i
$19$	−1.51398	+	0.159125i	−0.347330	+	0.0365059i	−0.276588	−	0.960989i	$-0.589204\pi$
$19$	−1.51398	+	0.159125i	−0.347330	+	0.0365059i	−0.0707426	+	0.997495i	$0.522537\pi$
$20$	−1.81011	−	0.588141i	−0.404753	−	0.131512i
$21$	−1.80103	−	4.21382i	−0.393017	−	0.919531i
$22$	3.26768	+	2.50141i	0.696672	+	0.533302i
$23$	−1.17103	−	0.676097i	−0.244178	−	0.140976i	0.372918	−	0.927864i	$-0.378357\pi$
$23$	−1.17103	−	0.676097i	−0.244178	−	0.140976i	−0.617095	+	0.786888i	$0.711691\pi$
$24$	−2.44683	+	4.68760i	−0.499456	+	0.956852i
$25$	−11.0393	−	4.91500i	−2.20785	−	0.983000i
$26$	−0.574062	−	1.28936i	−0.112583	−	0.252865i
$27$	−0.963929	+	5.10596i	−0.185508	+	0.982643i
$28$	1.20230	+	0.196756i	0.227214	+	0.0371834i
$29$	5.37729	+	3.90683i	0.998537	+	0.725480i	0.961774	−	0.273844i	$-0.0882952\pi$
$29$	5.37729	+	3.90683i	0.998537	+	0.725480i	0.0367633	+	0.999324i	$0.488295\pi$
$30$	−4.91095	+	7.40178i	−0.896613	+	1.35137i
$31$	4.72526	−	1.00438i	0.848681	−	0.180393i	0.237012	−	0.971507i	$-0.423832\pi$
$31$	4.72526	−	1.00438i	0.848681	−	0.180393i	0.611669	+	0.791114i	$0.290498\pi$
$32$	−1.27423	−	2.20704i	−0.225255	−	0.390153i
$33$	−4.58767	+	3.45735i	−0.798611	+	0.601848i
$34$	−1.34364			−0.230432
$35$	10.5483	+	2.88452i	1.78299	+	0.487572i
$36$	−1.00821	−	0.944366i	−0.168035	−	0.157394i
$37$	−3.02058	+	1.34485i	−0.496580	+	0.221092i	−0.639716	−	0.768611i	$-0.720948\pi$
$37$	−3.02058	+	1.34485i	−0.496580	+	0.221092i	0.143136	+	0.989703i	$0.454281\pi$
$38$	−1.40369	−	1.26389i	−0.227709	−	0.205030i
$39$	1.94889	−	0.289053i	0.312072	−	0.0462855i
$40$	−5.13240	−	11.5275i	−0.811503	−	1.82267i
$41$	3.69146	−	2.68200i	0.576510	−	0.418859i	−0.260954	−	0.965351i	$-0.584037\pi$
$41$	3.69146	−	2.68200i	0.576510	−	0.418859i	0.837464	+	0.546492i	$0.184037\pi$
$42$	2.39017	−	5.15918i	0.368812	−	0.796079i
$43$			8.06763i			1.23030i	0.788410	+	0.615151i	$0.210905\pi$
$43$			8.06763i			1.23030i	−0.788410	+	0.615151i	$0.789095\pi$
$44$	−0.121577	−	1.52237i	−0.0183284	−	0.229506i
$45$	−8.11423	−	9.37631i	−1.20960	−	1.39774i
$46$	−0.348828	−	1.64111i	−0.0514319	−	0.241968i
$47$	−10.9787	+	1.15391i	−1.60140	+	0.168314i	−0.862700	−	0.505715i	$-0.831229\pi$
$47$	−10.9787	+	1.15391i	−1.60140	+	0.168314i	−0.738704	+	0.674030i	$0.764562\pi$
$48$	−4.80902	+	1.23801i	−0.694123	+	0.178691i
$49$	−6.95378	−	0.803111i	−0.993397	−	0.114730i
$50$	−4.63325	−	14.2597i	−0.655241	−	2.01662i
$51$	0.503248	−	1.80687i	0.0704689	−	0.253012i
$52$	−0.213044	+	0.478505i	−0.0295439	+	0.0663567i
$53$	0.815733	+	3.83772i	0.112050	+	0.527151i	0.997991	+	0.0633546i	$0.0201799\pi$
$53$	0.815733	+	3.83772i	0.112050	+	0.527151i	−0.885942	+	0.463797i	$0.846487\pi$
$54$	−5.50838	+	3.35037i	−0.749596	+	0.455927i
$55$	0.343073	−	13.7042i	0.0462599	−	1.84788i
$56$	4.36434	+	6.79660i	0.583210	+	0.908234i
$57$	2.22537	−	1.41424i	0.294757	−	0.187321i
$58$	0.862053	+	8.20188i	0.113193	+	1.07696i
$59$	−2.50803	−	0.263605i	−0.326518	−	0.0343184i	−0.0601484	−	0.998189i	$-0.519157\pi$
$59$	−2.50803	−	0.263605i	−0.326518	−	0.0343184i	−0.266369	+	0.963871i	$0.585824\pi$
$60$	3.26088	−	0.483642i	0.420978	−	0.0624380i
$61$	−1.24665	+	5.86504i	−0.159617	+	0.750941i	0.823405	+	0.567455i	$0.192072\pi$
$61$	−1.24665	+	5.86504i	−0.159617	+	0.750941i	−0.983022	+	0.183487i	$0.941262\pi$
$62$	4.84923	+	3.52317i	0.615852	+	0.447443i
$63$	6.04262	+	5.14653i	0.761298	+	0.648402i
$64$	2.74905	−	8.46071i	0.343631	−	1.05759i
$65$	−2.35080	+	4.07171i	−0.291581	+	0.505034i
$66$	−6.99682	−	1.35974i	−0.861249	−	0.167373i
$67$	5.62222	+	9.73797i	0.686864	+	1.18968i	0.972847	+	0.231448i	$0.0743464\pi$
$67$	5.62222	+	9.73797i	0.686864	+	1.18968i	−0.285984	+	0.958235i	$0.592320\pi$
$68$	0.333660	+	0.370567i	0.0404622	+	0.0449378i
$69$	2.33754	+	0.145574i	0.281407	+	0.0175251i
$70$	6.09792	+	12.1212i	0.728841	+	1.44876i
$71$	1.74957	−	0.568471i	0.207636	−	0.0674651i	−0.203352	−	0.979106i	$-0.565184\pi$
$71$	1.74957	−	0.568471i	0.207636	−	0.0674651i	0.410988	+	0.911641i	$0.365184\pi$
$72$	0.180167	−	9.15692i	0.0212329	−	1.07915i
$73$	0.873788	+	0.0918389i	0.102269	+	0.0107489i	0.155525	−	0.987832i	$-0.450293\pi$
$73$	0.873788	+	0.0918389i	0.102269	+	0.0107489i	−0.0532556	+	0.998581i	$0.516960\pi$
$74$	−3.74786	−	1.66866i	−0.435680	−	0.193977i
$75$	20.9112	−	0.889750i	2.41461	−	0.102739i
$76$			0.700986i			0.0804086i
$77$	1.11072	+	8.70438i	0.126579	+	0.991957i
$78$	1.88458	+	1.55704i	0.213386	+	0.176300i
$79$	−8.24724	+	7.42585i	−0.927887	+	0.835473i	−0.986659	−	0.162798i	$-0.947948\pi$
$79$	−8.24724	+	7.42585i	−0.927887	+	0.835473i	0.0587725	+	0.998271i	$0.481281\pi$
$80$	4.81990	−	10.8257i	0.538881	−	1.21035i
$81$	−2.44231	−	8.66228i	−0.271367	−	0.962476i
$82$	5.53782	+	1.17710i	0.611550	+	0.129989i
$83$	2.66212	+	8.19316i	0.292206	+	0.899317i	0.984146	+	0.177362i	$0.0567562\pi$
$83$	2.66212	+	8.19316i	0.292206	+	0.899317i	−0.691940	+	0.721955i	$0.743244\pi$
$84$	−2.01641	+	0.621962i	−0.220008	+	0.0678616i
$85$	2.63089	+	3.62110i	0.285360	+	0.392764i
$86$	−7.43897	+	6.69808i	−0.802165	+	0.722272i
$87$	−11.3524	−	1.91270i	−1.21711	−	0.205063i
$88$	6.96135	−	7.35266i	0.742082	−	0.783797i
$89$	−0.214205	−	0.123671i	−0.0227057	−	0.0131091i	0.488604	−	0.872506i	$-0.337506\pi$
$89$	−0.214205	−	0.123671i	−0.0227057	−	0.0131091i	−0.511310	+	0.859396i	$0.670840\pi$
$90$	1.90890	−	15.2665i	0.201216	−	1.60923i
$91$	1.09293	−	2.80408i	0.114570	−	0.293947i
$92$	−0.365984	+	0.503734i	−0.0381565	+	0.0525179i
$93$	−6.55404	+	5.20145i	−0.679622	+	0.539366i
$94$	−10.1789	−	9.16516i	−1.04988	−	0.945314i
$95$	−0.657709	+	6.25769i	−0.0674796	+	0.642025i
$96$	3.67813	+	2.44037i	0.375397	+	0.249070i
$97$	−3.43868	+	10.5832i	−0.349145	+	1.07456i	0.610183	+	0.792261i	$0.291096\pi$
$97$	−3.43868	+	10.5832i	−0.349145	+	1.07456i	−0.959327	+	0.282296i	$0.908904\pi$
$98$	−5.03279	−	7.07869i	−0.508388	−	0.715056i
$99$	4.44912	−	8.89974i	0.447154	−	0.894457i
$100$	−2.78218	+	4.81887i	−0.278218	+	0.481887i
$101$	11.3949	−	2.42205i	1.13383	−	0.241003i	0.397486	−	0.917608i	$-0.369883\pi$
$101$	11.3949	−	2.42205i	1.13383	−	0.241003i	0.736346	+	0.676605i	$0.236550\pi$
$102$	2.08389	−	1.03610i	0.206336	−	0.102589i
$103$	14.9459	−	6.65434i	1.47266	−	0.655671i	0.495585	−	0.868559i	$-0.334954\pi$
$103$	14.9459	−	6.65434i	1.47266	−	0.655671i	0.977077	+	0.212888i	$0.0682871\pi$
$104$	−3.30271	+	1.07312i	−0.323857	+	0.105228i
$105$	−18.5840	+	3.66032i	−1.81361	+	0.357210i
$106$	−2.86142	+	3.93840i	−0.277925	+	0.382532i
$107$	−1.64338	−	15.6357i	−0.158871	−	1.51156i	−0.725865	−	0.687837i	$-0.758560\pi$
$107$	−1.64338	−	15.6357i	−0.158871	−	1.51156i	0.566994	−	0.823722i	$-0.308106\pi$
$108$	2.29188	+	0.687195i	0.220537	+	0.0661254i
$109$	−2.84264	+	1.64120i	−0.272275	+	0.157198i	−0.629921	−	0.776659i	$-0.716913\pi$
$109$	−2.84264	+	1.64120i	−0.272275	+	0.157198i	0.357646	+	0.933857i	$0.383580\pi$
$110$	12.9212	−	11.0615i	1.23199	−	1.05467i
$111$	3.64767	−	4.41498i	0.346221	−	0.419051i
$112$	−2.00082	+	7.31678i	−0.189060	+	0.691370i
$113$	−4.41665	−	6.07900i	−0.415484	−	0.571864i	0.549062	−	0.835782i	$-0.314985\pi$
$113$	−4.41665	−	6.07900i	−0.415484	−	0.571864i	−0.964545	+	0.263918i	$0.914985\pi$
$114$	3.15163	+	0.877793i	0.295178	+	0.0822129i
$115$	−3.73977	+	4.15343i	−0.348735	+	0.387310i
$116$	2.04796	−	2.27449i	0.190148	−	0.211181i
$117$	−2.79970	+	1.95112i	−0.258832	+	0.180381i
$118$	−1.83921	−	2.53145i	−0.169313	−	0.233039i
$119$	−2.01550	−	2.03629i	−0.184760	−	0.186667i
$120$	16.8491	+	13.9207i	1.53810	+	1.27078i
$121$	10.2603	−	3.96568i	0.932753	−	0.360516i
$122$	−6.44304	+	3.71989i	−0.583325	+	0.336783i
$123$	−3.65706	+	7.00614i	−0.329746	+	0.631723i
$124$	−0.232520	−	2.21228i	−0.0208809	−	0.198669i
$125$	−17.2104	+	23.6881i	−1.53934	+	2.11873i
$126$	0.271339	+	9.84462i	0.0241728	+	0.877029i
$127$	−4.20635	+	1.36673i	−0.373253	+	0.121277i	−0.489636	−	0.871927i	$-0.662870\pi$
$127$	−4.20635	+	1.36673i	−0.373253	+	0.121277i	0.116382	+	0.993204i	$0.462870\pi$
$128$	5.42752	−	2.41649i	0.479729	−	0.213589i
$129$	−6.22108	−	12.5123i	−0.547736	−	1.10165i
$130$	−5.70616	+	1.21288i	−0.500464	+	0.106377i
$131$	−6.15313	+	10.6575i	−0.537601	+	0.931153i	0.461431	+	0.887176i	$0.347336\pi$
$131$	−6.15313	+	10.6575i	−0.537601	+	0.931153i	−0.999033	+	0.0439770i	$0.985997\pi$
$132$	1.36248	+	2.26734i	0.118589	+	0.197346i
$133$	−0.190149	−	4.02318i	−0.0164880	−	0.348854i
$134$	−4.31136	+	13.2690i	−0.372444	+	1.14627i
$135$	19.8148	+	8.28496i	1.70539	+	0.713056i
$136$	−0.345570	+	3.28788i	−0.0296324	+	0.281933i
$137$	−0.219181	−	0.197351i	−0.0187259	−	0.0168608i	0.659715	−	0.751516i	$-0.270677\pi$
$137$	−0.219181	−	0.197351i	−0.0187259	−	0.0168608i	−0.678440	+	0.734655i	$0.737344\pi$
$138$	1.80649	+	2.27625i	0.153779	+	0.193768i
$139$	1.38766	−	1.90995i	0.117700	−	0.162000i	−0.746102	−	0.665832i	$-0.768077\pi$
$139$	1.38766	−	1.90995i	0.117700	−	0.162000i	0.863802	+	0.503832i	$0.168077\pi$
$140$	1.82869	−	4.69178i	0.154552	−	0.396528i
$141$	16.1373	−	10.2555i	1.35901	−	0.863666i
$142$	1.97674	+	1.14127i	0.165884	+	0.0957735i
$143$	−3.74095	−	0.488125i	−0.312834	−	0.0408191i
$144$	6.50381	−	5.62838i	0.541984	−	0.469031i
$145$	20.4161	−	18.3828i	1.69547	−	1.52661i
$146$	0.640773	+	0.881948i	0.0530308	+	0.0729906i
$147$	11.4041	−	4.11661i	0.940595	−	0.339532i
$148$	0.470486	+	1.44801i	0.0386737	+	0.119025i
$149$	−0.0879666	−	0.0186979i	−0.00720651	−	0.00153179i	0.204307	−	0.978907i	$-0.434506\pi$
$149$	−0.0879666	−	0.0186979i	−0.00720651	−	0.00153179i	−0.211514	+	0.977375i	$0.567839\pi$
$150$	18.1817	+	18.5430i	1.48453	+	1.51403i
$151$	4.37028	−	9.81582i	0.355649	−	0.798800i	−0.643787	−	0.765205i	$-0.722638\pi$
$151$	4.37028	−	9.81582i	0.355649	−	0.798800i	0.999436	−	0.0335950i	$-0.0106956\pi$
$152$	−3.45375	+	3.10977i	−0.280136	+	0.252236i
$153$	0.612802	+	3.19038i	0.0495421	+	0.257927i
$154$	−7.10394	+	8.25091i	−0.572452	+	0.664878i
$155$		−	19.9671i		−	1.60380i
$156$	−0.0385668	−	0.906409i	−0.00308782	−	0.0725708i
$157$	14.3538	+	6.39070i	1.14555	+	0.510034i	0.889639	−	0.456665i	$-0.150956\pi$
$157$	14.3538	+	6.39070i	1.14555	+	0.510034i	0.255916	+	0.966699i	$0.417623\pi$
$158$	−13.6944	−	1.43934i	−1.08947	−	0.114508i
$159$	−4.22447	−	5.32301i	−0.335023	−	0.422142i
$160$	−10.0180	+	3.25504i	−0.791990	+	0.257333i
$161$	1.96386	−	2.99036i	0.154774	−	0.235674i
$162$	5.95959	−	9.44378i	0.468229	−	0.741974i
$163$	−11.9326	−	13.2525i	−0.934631	−	1.03801i	−0.999196	−	0.0400994i	$-0.987233\pi$
$163$	−11.9326	−	13.2525i	−0.934631	−	1.03801i	0.0645646	−	0.997914i	$-0.479434\pi$
$164$	−1.05055	−	1.81960i	−0.0820339	−	0.142087i
$165$	10.0355	+	21.5188i	0.781261	+	1.67524i
$166$	−5.34452	+	9.25699i	−0.414815	+	0.718481i
$167$	5.23262	−	16.1043i	0.404912	−	1.24619i	−0.516057	−	0.856554i	$-0.672601\pi$
$167$	5.23262	−	16.1043i	0.404912	−	1.24619i	0.920969	−	0.389637i	$-0.127399\pi$
$168$	−12.0098	−	7.17563i	−0.926573	−	0.553612i
$169$	−9.47043	−	6.88067i	−0.728494	−	0.529282i
$170$	−1.15466	+	5.43227i	−0.0885587	+	0.416636i
$171$	−2.36084	+	3.90941i	−0.180538	+	0.298960i
$172$	3.69458	+	0.388316i	0.281709	+	0.0296088i
$173$	0.0911348	+	0.867090i	0.00692885	+	0.0659236i	0.997440	−	0.0715092i	$-0.0227815\pi$
$173$	0.0911348	+	0.867090i	0.00692885	+	0.0659236i	−0.990511	+	0.137433i	$0.956115\pi$
$174$	−7.66159	−	12.0558i	−0.580824	−	0.913947i
$175$	14.6606	−	28.4117i	1.10824	−	2.14772i
$176$	9.50584	+	0.237970i	0.716530	+	0.0179376i
$177$	4.09305	−	1.52515i	0.307652	−	0.114637i
$178$	−0.0638074	−	0.300190i	−0.00478256	−	0.0225002i
$179$	2.36645	−	5.31513i	0.176877	−	0.397271i	−0.803251	−	0.595641i	$-0.796898\pi$
$179$	2.36645	−	5.31513i	0.176877	−	0.397271i	0.980127	+	0.198370i	$0.0635647\pi$
$180$	−4.68445	+	3.26461i	−0.349158	+	0.243330i
$181$	1.35280	+	4.16348i	0.100553	+	0.309469i	0.988661	−	0.150165i	$-0.0479805\pi$
$181$	1.35280	+	4.16348i	0.100553	+	0.309469i	−0.888108	+	0.459634i	$0.847981\pi$
$182$	3.49297	−	1.32030i	0.258916	−	0.0978671i
$183$	−2.58916	−	10.0576i	−0.191396	−	0.743477i
$184$	−4.10550	+	0.431505i	−0.302661	+	0.0318110i
$185$	2.84141	+	13.3678i	0.208904	+	0.982818i
$186$	−10.2376	−	1.72486i	−0.750655	−	0.126473i
$187$	−1.87307	+	3.06448i	−0.136972	+	0.224097i
$188$			5.08323i			0.370733i
$189$	−13.3402	−	3.32234i	−0.970360	−	0.241664i
$190$	−6.31612	+	4.58893i	−0.458220	+	0.332916i
$191$	6.03464	+	13.5540i	0.436651	+	0.980735i	0.989108	+	0.147193i	$0.0470239\pi$
$191$	6.03464	+	13.5540i	0.436651	+	0.980735i	−0.552456	+	0.833542i	$0.686309\pi$
$192$	2.26061	+	15.2418i	0.163145	+	1.09998i
$193$	1.14632	+	1.03215i	0.0825139	+	0.0742959i	0.709356	−	0.704851i	$-0.248986\pi$
$193$	1.14632	+	1.03215i	0.0825139	+	0.0742959i	−0.626842	+	0.779147i	$0.715653\pi$
$194$	−12.6134	+	5.61585i	−0.905590	+	0.403195i
$195$	0.506165	−	8.12767i	0.0362472	−	0.582035i
$196$	−0.702488	+	3.14583i	−0.0501777	+	0.224702i
$197$	6.55011			0.466676			0.233338	−	0.972396i	$-0.425035\pi$
$197$	6.55011			0.466676			0.233338	+	0.972396i	$0.425035\pi$
$198$	11.9001	−	3.28650i	0.845702	−	0.233561i
$199$	−0.646613	−	1.11997i	−0.0458372	−	0.0793924i	0.842197	−	0.539171i	$-0.181262\pi$
$199$	−0.646613	−	1.11997i	−0.0458372	−	0.0793924i	−0.888034	+	0.459778i	$0.847929\pi$
$200$	−36.0850	+	7.67010i	−2.55160	+	0.542358i
$201$	−16.2288	−	10.7675i	−1.14469	−	0.759482i
$202$	11.6938	+	8.49605i	0.822774	+	0.597780i
$203$	−11.1369	+	13.6095i	−0.781657	+	0.955202i
$204$	−0.803233	−	0.317432i	−0.0562376	−	0.0222247i
$205$	−7.67094	−	17.2292i	−0.535762	−	1.20334i
$206$	18.5445	+	8.25654i	1.29206	+	0.575261i
$207$	−3.73761	+	1.57674i	−0.259782	+	0.109591i
$208$	−2.82431	−	1.63062i	−0.195831	−	0.113063i
$209$	−4.83938	+	1.43955i	−0.334747	+	0.0995759i
$210$	−18.8043	−	14.0969i	−1.29762	−	0.972781i
$211$	−19.6535	−	6.38580i	−1.35300	−	0.439617i	−0.459300	−	0.888281i	$-0.651900\pi$
$211$	−19.6535	−	6.38580i	−1.35300	−	0.439617i	−0.893700	+	0.448664i	$0.851900\pi$
$212$	1.79675	−	0.188846i	0.123401	−	0.0129700i
$213$	−2.27511	+	2.23078i	−0.155888	+	0.152851i
$214$	13.0529	−	14.4967i	0.892278	−	0.990976i
$215$	32.6171	+	6.93297i	2.22446	+	0.472825i
$216$	6.78163	+	14.3407i	0.461431	+	0.975758i
$217$	1.93461	+	12.6339i	0.131330	+	0.857645i
$218$	−3.87339	−	1.25854i	−0.262339	−	0.0852391i
$219$	−1.42600	+	0.531357i	−0.0963603	+	0.0359058i
$220$	−6.25935	−	0.816731i	−0.422006	−	0.0550640i
$221$	1.06677	−	0.615900i	0.0717588	−	0.0414299i
$222$	7.09939	−	0.302073i	0.476480	−	0.0202738i
$223$	−3.22117	+	2.34032i	−0.215706	+	0.156719i	−0.690392	−	0.723436i	$-0.742562\pi$
$223$	−3.22117	+	2.34032i	−0.215706	+	0.156719i	0.474686	+	0.880155i	$0.342562\pi$
$224$	6.02334	−	3.03021i	0.402451	−	0.202464i
$225$	−31.7456	+	17.5049i	−2.11637	+	1.16699i
$226$	1.93842	−	9.11953i	0.128941	−	0.606622i
$227$	2.03444	−	19.3564i	0.135030	−	1.28473i	−0.691723	−	0.722163i	$-0.743148\pi$
$227$	2.03444	−	19.3564i	0.135030	−	1.28473i	0.826753	−	0.562565i	$-0.190185\pi$
$228$	−0.540542	−	1.08718i	−0.0357983	−	0.0720002i
$229$	0.830959	+	0.922874i	0.0549113	+	0.0609852i	0.769975	−	0.638074i	$-0.220269\pi$
$229$	0.830959	+	0.922874i	0.0549113	+	0.0609852i	−0.715063	+	0.699060i	$0.753602\pi$
$230$	−6.93470			−0.457260
$231$	−8.43475	−	12.6434i	−0.554965	−	0.831873i
$232$	20.2917			1.33221
$233$	−11.3050	−	12.5554i	−0.740613	−	0.822534i	0.248664	−	0.968590i	$-0.420009\pi$
$233$	−11.3050	−	12.5554i	−0.740613	−	0.822534i	−0.989276	+	0.146056i	$0.953342\pi$
$234$	−4.12351	−	0.961632i	−0.269562	−	0.0628639i
$235$	−4.76941	+	45.3779i	−0.311122	+	2.96013i
$236$	−0.241436	+	1.13587i	−0.0157161	+	0.0739386i
$237$	7.06468	−	17.8765i	0.458901	−	1.16121i
$238$	0.204266	−	3.54906i	0.0132406	−	0.230051i
$239$	−18.9664	+	13.7799i	−1.22684	+	0.891349i	−0.996649	−	0.0817973i	$-0.973934\pi$
$239$	−18.9664	+	13.7799i	−1.22684	+	0.891349i	−0.230188	+	0.973146i	$0.573934\pi$
$240$	0.872535	+	20.5066i	0.0563219	+	1.32369i
$241$	4.71376	−	2.72149i	0.303640	−	0.175307i	−0.340437	−	0.940267i	$-0.610575\pi$
$241$	4.71376	−	2.72149i	0.303640	−	0.175307i	0.644077	+	0.764961i	$0.277242\pi$
$242$	12.1752	+	6.16830i	0.782650	+	0.396513i
$243$	10.4675	+	11.5513i	0.671489	+	0.741015i
$244$	2.62589	+	0.853205i	0.168106	+	0.0546208i
$245$	−9.22272	+	27.4237i	−0.589218	+	1.75203i
$246$	−9.49644	+	2.44471i	−0.605471	+	0.155869i
$247$	1.69380	+	0.360027i	0.107774	+	0.0229080i
$248$	9.86834	−	10.9599i	0.626641	−	0.695955i
$249$	−10.4466	−	10.6542i	−0.662029	−	0.675183i
$250$	−36.1310	+	3.79752i	−2.28513	+	0.240176i
$251$	−0.772022	−	0.250845i	−0.0487296	−	0.0158332i	0.284551	−	0.958661i	$-0.408156\pi$
$251$	−0.772022	−	0.250845i	−0.0487296	−	0.0158332i	−0.333280	+	0.942828i	$0.608156\pi$
$252$	2.64770	−	2.51951i	0.166790	−	0.158714i
$253$	−4.22921	−	1.49216i	−0.265888	−	0.0938115i
$254$	−4.75251	−	2.74386i	−0.298199	−	0.172165i
$255$	−6.87261	−	3.58735i	−0.430379	−	0.224649i
$256$	−9.51967	−	4.23843i	−0.594980	−	0.264902i
$257$	−3.85174	−	8.65114i	−0.240265	−	0.539643i	0.752657	−	0.658413i	$-0.228772\pi$
$257$	−3.85174	−	8.65114i	−0.240265	−	0.539643i	−0.992922	+	0.118769i	$0.962105\pi$
$258$	6.37231	−	16.1246i	0.396723	−	1.00387i
$259$	−3.09305	−	8.18294i	−0.192193	−	0.508463i
$260$	1.75149	+	1.27253i	0.108623	+	0.0789192i
$261$	19.0817	−	5.78758i	1.18113	−	0.358242i
$262$	−14.9356	+	3.17467i	−0.922728	+	0.196132i
$263$	4.09280	+	7.08893i	0.252373	+	0.437122i	0.964179	−	0.265254i	$-0.0854558\pi$
$263$	4.09280	+	7.08893i	0.252373	+	0.437122i	−0.711806	+	0.702376i	$0.752122\pi$
$264$	−5.12679	+	16.7715i	−0.315532	+	1.03221i
$265$	16.2167			0.996186
$266$	3.55181	−	3.51554i	0.217775	−	0.215552i
$267$	0.427581	+	0.0266283i	0.0261675	+	0.00162963i
$268$	4.73012	−	2.10599i	0.288938	−	0.128644i
$269$	−19.4374	−	17.5015i	−1.18512	−	1.06709i	−0.996376	−	0.0850620i	$-0.972891\pi$
$269$	−19.4374	−	17.5015i	−1.18512	−	1.06709i	−0.188746	−	0.982026i	$-0.560442\pi$
$270$	8.81171	+	25.1493i	0.536264	+	1.53054i
$271$	5.70069	+	12.8040i	0.346292	+	0.777785i	0.999783	+	0.0208500i	$0.00663725\pi$
$271$	5.70069	+	12.8040i	0.346292	+	0.777785i	−0.653491	+	0.756935i	$0.726696\pi$
$272$	−2.51175	+	1.82489i	−0.152297	+	0.110650i
$273$	0.467218	+	5.19170i	0.0282773	+	0.314216i
$274$		−	0.365950i		−	0.0221079i
$275$	−38.9814	−	9.31117i	−2.35067	−	0.561484i
$276$	0.179178	−	1.06347i	0.0107852	−	0.0640135i
$277$	−5.51234	−	25.9335i	−0.331204	−	1.55819i	−0.757025	−	0.653386i	$-0.773348\pi$
$277$	−5.51234	−	25.9335i	−0.331204	−	1.55819i	0.425821	−	0.904807i	$-0.359985\pi$
$278$	2.91322	−	0.306192i	0.174723	−	0.0183642i
$279$	6.15392	−	13.1210i	0.368426	−	0.785534i
$280$	31.2289	−	11.8041i	1.86628	−	0.705432i
$281$	−3.78292	−	11.6426i	−0.225670	−	0.694542i	−0.998223	−	0.0595911i	$-0.981020\pi$
$281$	−3.78292	−	11.6426i	−0.225670	−	0.694542i	0.772552	−	0.634951i	$-0.218980\pi$
$282$	22.8542	+	6.36536i	1.36095	+	0.379052i
$283$	−1.33536	+	2.99927i	−0.0793790	+	0.178288i	−0.948875	−	0.315651i	$-0.897777\pi$
$283$	−1.33536	+	2.99927i	−0.0793790	+	0.178288i	0.869496	+	0.493940i	$0.164444\pi$
$284$	−0.176120	−	0.828580i	−0.0104508	−	0.0491672i
$285$	−3.80535	−	10.2124i	−0.225409	−	0.604930i
$286$	−2.65580	−	3.85471i	−0.157041	−	0.227934i
$287$	6.52300	+	10.1583i	0.385040	+	0.599625i
$288$	−7.58633	−	0.948581i	−0.447029	−	0.0558957i
$289$	1.65441	+	15.7406i	0.0973180	+	0.925919i
$290$	33.9007	+	3.56310i	1.99072	+	0.209233i
$291$	−2.82771	−	19.0653i	−0.165763	−	1.11763i
$292$	0.0841154	−	0.395732i	0.00492248	−	0.0231584i
$293$	5.94373	+	4.31837i	0.347236	+	0.252282i	0.747709	−	0.664027i	$-0.231154\pi$
$293$	5.94373	+	4.31837i	0.347236	+	0.252282i	−0.400472	+	0.916309i	$0.631154\pi$
$294$	13.2640	+	7.09768i	0.773571	+	0.413945i
$295$	−3.22103	+	9.91332i	−0.187536	+	0.577176i
$296$	−5.04710	+	8.74184i	−0.293357	+	0.508109i
$297$	−0.0375409	+	17.2336i	−0.00217835	+	0.999998i
$298$	−0.0557927	−	0.0966357i	−0.00323198	−	0.00559796i
$299$	1.02920	+	1.14305i	0.0595204	+	0.0661042i
$300$	0.599046	−	9.61911i	0.0345859	−	0.555359i
$301$	−21.3097	−	1.22648i	−1.22827	−	0.0706931i
$302$	12.6793	−	4.11976i	0.729613	−	0.237066i
$303$	−15.8049	+	12.5432i	−0.907970	+	0.720588i
$304$	−4.34060	−	0.456215i	−0.248950	−	0.0261657i
$305$	22.6408	+	10.0803i	1.29641	+	0.577197i
$306$	−2.43300	+	3.21384i	−0.139086	+	0.183723i
$307$			29.3466i			1.67490i	0.546516	+	0.837448i	$0.315954\pi$
$307$			29.3466i			1.67490i	−0.546516	+	0.837448i	$0.684046\pi$
$308$	4.03964	−	0.0896919i	0.230180	−	0.00511067i
$309$	−18.0487	+	21.8454i	−1.02676	+	1.24274i
$310$	18.4112	−	16.5775i	1.04569	−	0.941541i
$311$	9.89379	−	22.2218i	0.561026	−	1.26008i	−0.381010	−	0.924571i	$-0.624424\pi$
$311$	9.89379	−	22.2218i	0.561026	−	1.26008i	0.942036	−	0.335513i	$-0.108910\pi$
$312$	4.29477	−	4.21110i	0.243143	−	0.238406i
$313$	−12.5629	−	2.67032i	−0.710096	−	0.150935i	−0.161316	−	0.986903i	$-0.551574\pi$
$313$	−12.5629	−	2.67032i	−0.710096	−	0.150935i	−0.548779	+	0.835967i	$0.684907\pi$
$314$	6.02437	+	18.5411i	0.339975	+	1.04633i
$315$	26.0000	−	20.0073i	1.46493	−	1.12729i
$316$	3.00371	+	4.13426i	0.168972	+	0.232570i
$317$	15.4733	−	13.9322i	0.869065	−	0.782509i	−0.108290	−	0.994119i	$-0.534537\pi$
$317$	15.4733	−	13.9322i	0.869065	−	0.782509i	0.977354	+	0.211610i	$0.0678707\pi$
$318$	1.40089	−	8.31467i	0.0785578	−	0.466263i
$319$	19.9080	+	9.46753i	1.11464	+	0.530080i
$320$	−31.8438	−	18.3851i	−1.78013	−	1.02776i
$321$	14.6057	+	22.9826i	0.815211	+	1.28276i
$322$	4.38782	−	0.671899i	0.244524	−	0.0374435i
$323$	0.968974	−	1.33368i	0.0539152	−	0.0742079i
$324$	−4.08445	+	0.701518i	−0.226914	+	0.0389732i
$325$	10.2149	+	9.19756i	0.566622	+	0.510189i
$326$	2.31287	−	22.0055i	0.128098	−	1.21877i
$327$	3.14317	−	4.73739i	0.173818	−	0.261978i
$328$	4.30463	−	13.2483i	0.237683	−	0.731514i
$329$	−1.37887	−	29.1743i	−0.0760196	−	1.60843i
$330$	−11.5101	+	27.1193i	−0.633613	+	1.49287i
$331$	−11.2781	+	19.5342i	−0.619900	+	1.07370i	0.369604	+	0.929190i	$0.379494\pi$
$331$	−11.2781	+	19.5342i	−0.619900	+	1.07370i	−0.989504	+	0.144509i	$0.953840\pi$
$332$	3.88020	−	0.824762i	0.212954	−	0.0452647i
$333$	−2.25280	+	9.66009i	−0.123453	+	0.529370i
$334$	19.1938	−	8.54562i	1.05024	−	0.467595i
$335$	44.2017	−	14.3620i	2.41500	−	0.784680i
$336$	−2.53895	−	12.8907i	−0.138511	−	0.703244i
$337$	−2.61579	+	3.60032i	−0.142491	+	0.196122i	−0.874298	−	0.485390i	$-0.838677\pi$
$337$	−2.61579	+	3.60032i	−0.142491	+	0.196122i	0.731807	+	0.681512i	$0.238677\pi$
$338$	−1.51824	−	14.4451i	−0.0825813	−	0.785709i
$339$	11.5375	+	6.02234i	0.626632	+	0.327089i
$340$	1.78492	−	1.03052i	0.0968008	−	0.0558880i
$341$	14.7954	−	6.14840i	0.801213	−	0.332955i
$342$	−5.56484	+	1.06888i	−0.300912	+	0.0577985i
$343$	3.17847	−	18.2455i	0.171621	−	0.985163i
$344$	14.4769	+	19.9258i	0.780544	+	1.07433i
$345$	2.59733	−	9.32547i	0.139836	−	0.502067i
$346$	−0.723859	+	0.803927i	−0.0389149	+	0.0432194i
$347$	−16.1731	+	17.9621i	−0.868220	+	0.964256i	−0.999633	−	0.0270719i	$-0.991382\pi$
$347$	−16.1731	+	17.9621i	−0.868220	+	0.964256i	0.131414	+	0.991328i	$0.458048\pi$
$348$	−1.42234	+	5.10678i	−0.0762455	+	0.273752i
$349$	−2.87484	−	3.95687i	−0.153886	−	0.211806i	0.725112	−	0.688631i	$-0.241788\pi$
$349$	−2.87484	−	3.95687i	−0.153886	−	0.211806i	−0.878999	+	0.476824i	$0.841788\pi$
$350$	38.3696	−	10.0704i	2.05094	−	0.538283i
$351$	2.83759	−	5.18494i	0.151459	−	0.276752i
$352$	−5.49673	−	6.42086i	−0.292977	−	0.342233i
$353$	7.91604	−	4.57033i	0.421329	−	0.243254i	−0.274317	−	0.961639i	$-0.588452\pi$
$353$	7.91604	−	4.57033i	0.421329	−	0.243254i	0.695646	+	0.718385i	$0.255118\pi$
$354$	4.80452	+	2.50786i	0.255358	+	0.133291i
$355$	−0.794794	−	7.56196i	−0.0421833	−	0.401347i
$356$	−0.0669455	+	0.0921426i	−0.00354811	+	0.00488355i
$357$	4.69611	+	1.60396i	0.248545	+	0.0848905i
$358$	6.86568	−	2.23079i	0.362862	−	0.117901i
$359$	−22.6959	+	10.1049i	−1.19784	+	0.533314i	−0.906051	−	0.423168i	$-0.860918\pi$
$359$	−22.6959	+	10.1049i	−1.19784	+	0.533314i	−0.291792	+	0.956482i	$0.594252\pi$
$360$	−36.8662	−	8.59747i	−1.94302	−	0.453126i
$361$	−16.3180	+	3.46850i	−0.858842	+	0.182553i
$362$	−2.71590	+	4.70408i	−0.142745	+	0.247241i
$363$	−12.8550	+	14.0624i	−0.674711	+	0.738082i
$364$	−1.23153	−	0.635475i	−0.0645495	−	0.0333079i
$365$	1.12220	−	3.45377i	0.0587384	−	0.180778i
$366$	7.12422	−	10.7376i	0.372389	−	0.561264i
$367$	0.419911	−	3.99519i	0.0219192	−	0.208547i	−0.978081	−	0.208226i	$-0.933231\pi$
$367$	0.419911	−	3.99519i	0.0219192	−	0.208547i	1.00000		0.000321205i	$-0.000102243\pi$
$368$	−2.88100	−	2.59406i	−0.150182	−	0.135225i
$369$	0.269279	−	13.6860i	0.0140181	−	0.712467i
$370$	−9.96705	+	13.7185i	−0.518162	+	0.713189i
$371$	−10.2609	+	1.57123i	−0.532719	+	0.0815743i
$372$	2.06655	+	3.25179i	0.107145	+	0.168597i
$373$	12.9943	+	7.50228i	0.672821	+	0.388453i	0.797145	−	0.603788i	$-0.206343\pi$
$373$	12.9943	+	7.50228i	0.672821	+	0.388453i	−0.124324	+	0.992242i	$0.539676\pi$
$374$	−4.38078	+	0.817147i	−0.226525	+	0.0422537i
$375$	8.42582	−	50.0097i	0.435108	−	2.58249i
$376$	−25.0450	+	22.5506i	−1.29160	+	1.16296i
$377$	−4.44402	−	6.11667i	−0.228879	−	0.315025i
$378$	−8.01218	−	15.0591i	−0.412102	−	0.774555i
$379$	−0.888283	−	2.73385i	−0.0456280	−	0.140429i	0.925647	−	0.378388i	$-0.123521\pi$
$379$	−0.888283	−	2.73385i	−0.0456280	−	0.140429i	−0.971275	+	0.237959i	$0.923521\pi$
$380$	2.83406	+	0.602397i	0.145384	+	0.0309023i
$381$	5.46984	−	5.36328i	0.280228	−	0.274769i
$382$	−7.48764	+	16.8175i	−0.383101	+	0.860459i
$383$	−13.8028	+	12.4281i	−0.705292	+	0.635047i	−0.941640	−	0.336621i	$-0.890716\pi$
$383$	−13.8028	+	12.4281i	−0.705292	+	0.635047i	0.236349	+	0.971668i	$0.424049\pi$
$384$	−6.55430	+	7.93304i	−0.334473	+	0.404831i
$385$	36.1459	+	2.98957i	1.84217	+	0.152363i
$386$			1.91393i			0.0974165i
$387$	19.2969	+	14.6085i	0.980917	+	0.742593i
$388$	4.68105	+	2.08414i	0.237644	+	0.105806i
$389$	35.4401	+	3.72491i	1.79689	+	0.188860i	0.943266	−	0.332038i	$-0.107736\pi$
$389$	35.4401	+	3.72491i	1.79689	+	0.188860i	0.853619	+	0.520898i	$0.174403\pi$
$390$	7.91458	−	6.28121i	0.400770	−	0.318062i
$391$	1.39263	−	0.452491i	0.0704281	−	0.0228835i
$392$	−18.6159	+	10.4946i	−0.940245	+	0.530059i
$393$	1.32486	−	21.2739i	0.0668306	−	1.07312i
$394$	5.43818	+	6.03971i	0.273971	+	0.304276i
$395$	22.9351	+	39.7247i	1.15399	+	1.99877i
$396$	−3.86149	−	2.46585i	−0.194047	−	0.123913i
$397$	−14.9485	+	25.8916i	−0.750246	+	1.29946i	0.197458	+	0.980311i	$0.436731\pi$
$397$	−14.9485	+	25.8916i	−0.750246	+	1.29946i	−0.947704	+	0.319152i	$0.896602\pi$
$398$	0.495850	−	1.52607i	0.0248547	−	0.0764950i
$399$	3.39725	+	6.09304i	0.170075	+	0.305033i
$400$	−28.0284	−	20.3638i	−1.40142	−	1.01819i
$401$	5.63815	−	26.5254i	0.281556	−	1.32462i	−0.579029	−	0.815307i	$-0.696568\pi$
$401$	5.63815	−	26.5254i	0.281556	−	1.32462i	0.860584	−	0.509308i	$-0.170099\pi$
$402$	−3.54533	−	23.9038i	−0.176825	−	1.19221i
$403$	−5.46496	−	0.574391i	−0.272229	−	0.0286124i
$404$	−0.560717	−	5.33487i	−0.0278967	−	0.265420i
$405$	−37.1200	+	2.43014i	−1.84451	+	0.120755i
$406$	−21.7953	+	1.03012i	−1.08168	+	0.0511240i
$407$	−9.03038	+	6.22172i	−0.447619	+	0.308399i
$408$	−1.99938	−	5.36573i	−0.0989841	−	0.265643i
$409$	2.50584	+	11.7891i	0.123906	+	0.582932i	0.995666	+	0.0929992i	$0.0296454\pi$
$409$	2.50584	+	11.7891i	0.123906	+	0.582932i	−0.871760	+	0.489933i	$0.837021\pi$
$410$	9.51793	−	21.3776i	0.470057	−	1.05576i
$411$	0.492114	+	0.137064i	0.0242742	+	0.00676085i
$412$	−2.32797	−	7.16477i	−0.114691	−	0.352983i
$413$	1.07756	−	6.58459i	0.0530234	−	0.324006i
$414$	−4.55700	−	2.13729i	−0.223964	−	0.105042i
$415$	35.4123	−	3.72198i	1.73832	−	0.182705i
$416$	0.602712	+	2.83554i	0.0295504	+	0.139024i
$417$	−0.679369	+	4.03225i	−0.0332688	+	0.197460i
$418$	−5.34523	−	3.26710i	−0.261444	−	0.159799i
$419$		−	6.64114i		−	0.324441i	−0.986755	−	0.162221i	$-0.948134\pi$
$419$		−	6.64114i		−	0.324441i	0.986755	−	0.162221i	$-0.0518656\pi$
$420$	0.781749	+	8.68675i	0.0381454	+	0.423870i
$421$	23.9484	−	17.3995i	1.16717	−	0.848000i	0.176505	−	0.984300i	$-0.443521\pi$
$421$	23.9484	−	17.3995i	1.16717	−	0.848000i	0.990668	+	0.136300i	$0.0435210\pi$
$422$	−10.4289	−	23.4238i	−0.507672	−	1.14025i
$423$	−17.1197	+	28.3493i	−0.832389	+	1.37839i
$424$	8.90133	+	8.01479i	0.432287	+	0.389233i
$425$	11.9544	−	5.32246i	0.579875	−	0.258177i
$426$	−3.94584	−	0.245734i	−0.191177	−	0.0119058i
$427$	−15.3023	−	4.18451i	−0.740529	−	0.202503i
$428$	−7.23948			−0.349933
$429$	6.17835	−	2.12766i	0.298294	−	0.102724i
$430$	20.6873	+	35.8315i	0.997631	+	1.72795i
$431$	−5.36469	+	1.14030i	−0.258408	+	0.0549264i	−0.335294	−	0.942114i	$-0.608836\pi$
$431$	−5.36469	+	1.14030i	−0.258408	+	0.0549264i	0.0768858	+	0.997040i	$0.475502\pi$
$432$	−5.74680	+	13.7444i	−0.276493	+	0.661278i
$433$	−26.8304	−	19.4934i	−1.28939	−	0.936794i	−0.289593	−	0.957150i	$-0.593520\pi$
$433$	−26.8304	−	19.4934i	−1.28939	−	0.936794i	−0.999793	+	0.0203562i	$0.993520\pi$
$434$	−10.0432	+	12.2730i	−0.482090	+	0.589125i
$435$	−17.4887	+	44.2536i	−0.838520	+	2.12180i
$436$	0.614765	+	1.38078i	0.0294419	+	0.0661276i
$437$	1.88050	+	0.837254i	0.0899567	+	0.0400513i
$438$	−1.67388	−	0.873728i	−0.0799810	−	0.0417484i
$439$	24.5448	+	14.1709i	1.17146	+	0.676341i	0.954023	−	0.299734i	$-0.0968978\pi$
$439$	24.5448	+	14.1709i	1.17146	+	0.676341i	0.217434	+	0.976075i	$0.430231\pi$
$440$	−23.7442	−	34.4630i	−1.13196	−	1.64296i
$441$	−14.5126	+	15.1785i	−0.691075	+	0.722783i
$442$	1.45358	+	0.472298i	0.0691400	+	0.0224649i
$443$	2.18452	−	0.229602i	0.103790	−	0.0109087i	−0.0524913	−	0.998621i	$-0.516716\pi$
$443$	2.18452	−	0.229602i	0.103790	−	0.0109087i	0.156281	+	0.987713i	$0.450050\pi$
$444$	−1.84627	−	1.88296i	−0.0876202	−	0.0893611i
$445$	−0.684075	+	0.759742i	−0.0324283	+	0.0360152i
$446$	−4.83231	−	1.02714i	−0.228816	−	0.0486364i
$447$	0.150848	−	0.0388334i	0.00713487	−	0.00183676i
$448$	21.9300	+	8.54752i	1.03610	+	0.403833i
$449$	0.969392	+	0.314975i	0.0457484	+	0.0148646i	0.331802	−	0.943349i	$-0.392343\pi$
$449$	0.969392	+	0.314975i	0.0457484	+	0.0148646i	−0.286053	+	0.958214i	$0.592343\pi$
$450$	−42.4974	−	14.7386i	−2.00334	−	0.694785i
$451$	10.4045	−	10.9894i	0.489930	−	0.517470i
$452$	−2.99647	+	1.73001i	−0.140942	+	0.0813729i
$453$	0.791141	+	18.5936i	0.0371711	+	0.873605i
$454$	19.5371	−	14.1946i	0.916924	−	0.666184i
$455$	−10.3976	−	6.82837i	−0.487445	−	0.320119i
$456$	2.95852	−	7.48627i	0.138545	−	0.350577i
$457$	6.97842	−	32.8309i	0.326437	−	1.53576i	−0.442694	−	0.896673i	$-0.645977\pi$
$457$	6.97842	−	32.8309i	0.326437	−	1.53576i	0.769131	−	0.639092i	$-0.220689\pi$
$458$	−0.161063	+	1.53242i	−0.00752600	+	0.0716051i
$459$	−3.41057	−	4.47551i	−0.159192	−	0.208899i
$460$	1.72206	+	1.91255i	0.0802916	+	0.0891729i
$461$	−3.31197			−0.154254			−0.0771269	−	0.997021i	$-0.524575\pi$
$461$	−3.31197			−0.154254			−0.0771269	+	0.997021i	$0.524575\pi$
$462$	4.65529	−	18.2745i	0.216584	−	0.850209i
$463$	14.1851			0.659237			0.329618	−	0.944114i	$-0.393080\pi$
$463$	14.1851			0.659237			0.329618	+	0.944114i	$0.393080\pi$
$464$	12.7511	+	14.1615i	0.591954	+	0.657432i
$465$	15.3970	+	30.9676i	0.714018	+	1.43609i
$466$	2.19122	−	20.8481i	0.101506	−	0.965769i
$467$	1.11790	−	5.25932i	0.0517304	−	0.243372i	−0.944684	−	0.327983i	$-0.893631\pi$
$467$	1.11790	−	5.25932i	0.0517304	−	0.243372i	0.996414	+	0.0846104i	$0.0269646\pi$
$468$	0.758761	+	1.37604i	0.0350737	+	0.0636073i
$469$	−26.5764	+	13.3700i	−1.22718	+	0.617370i
$470$	−45.8017	+	33.2769i	−2.11267	+	1.53495i
$471$	−27.1896	+	1.15689i	−1.25283	+	0.0533068i
$472$	−6.66747	+	3.84947i	−0.306895	+	0.177186i
$473$	4.90641	+	26.3036i	0.225597	+	1.20944i
$474$	22.3489	−	8.32767i	1.02652	−	0.382502i
$475$	17.4953	+	5.68457i	0.802739	+	0.260826i
$476$	−1.02953	+	0.824987i	−0.0471886	+	0.0378132i
$477$	10.6565	+	4.99804i	0.487928	+	0.228845i
$478$	−28.4529	−	6.04784i	−1.30140	−	0.276622i
$479$	−28.6198	+	31.7855i	−1.30767	+	1.45232i	−0.495859	+	0.868403i	$0.665147\pi$
$479$	−28.6198	+	31.7855i	−1.30767	+	1.45232i	−0.811814	+	0.583916i	$0.801520\pi$
$480$	13.0272	−	12.7734i	0.594605	−	0.583021i
$481$	3.74047	−	0.393139i	0.170551	−	0.0179256i
$482$	6.42299	+	2.08696i	0.292559	+	0.0950582i
$483$	−0.739881	+	6.15220i	−0.0336658	+	0.279935i
$484$	−1.32223	−	4.88958i	−0.0601015	−	0.222254i
$485$	39.8322	+	22.9971i	1.80869	+	1.04425i
$486$	−1.96064	+	19.2422i	−0.0889362	+	0.872842i
$487$	14.4470	+	6.43222i	0.654656	+	0.291472i	0.707059	−	0.707154i	$-0.250021\pi$
$487$	14.4470	+	6.43222i	0.654656	+	0.291472i	−0.0524029	+	0.998626i	$0.516688\pi$
$488$	7.44547	+	16.7228i	0.337041	+	0.757005i
$489$	28.7258	+	11.3522i	1.29902	+	0.513365i
$490$	−32.9438	+	14.2642i	−1.48825	+	0.644391i
$491$	1.61510	+	1.17344i	0.0728883	+	0.0529565i	0.623633	−	0.781717i	$-0.285656\pi$
$491$	1.61510	+	1.17344i	0.0728883	+	0.0529565i	−0.550744	+	0.834674i	$0.685656\pi$
$492$	3.03245	+	2.01198i	0.136713	+	0.0907069i
$493$	−7.04042	+	1.49649i	−0.317085	+	0.0673984i
$494$	1.07429	+	1.86072i	0.0483344	+	0.0837177i
$495$	−32.1578	−	25.6357i	−1.44539	−	1.15224i
$496$	13.8501			0.621886
$497$	1.23557	+	4.70771i	0.0554228	+	0.211170i
$498$	1.15076	−	18.4782i	0.0515667	−	0.828027i
$499$	2.66969	−	1.18862i	0.119512	−	0.0532101i	−0.346110	−	0.938194i	$-0.612497\pi$
$499$	2.66969	−	1.18862i	0.119512	−	0.0532101i	0.465621	+	0.884984i	$0.345831\pi$
$500$	10.0196	+	9.02168i	0.448090	+	0.403462i
$501$	4.30291	+	29.0116i	0.192240	+	1.29614i
$502$	−0.409666	−	0.920126i	−0.0182843	−	0.0410672i
$503$	−10.6228	+	7.71794i	−0.473649	+	0.344126i	−0.798862	−	0.601515i	$-0.794564\pi$
$503$	−10.6228	+	7.71794i	−0.473649	+	0.344126i	0.325213	+	0.945641i	$0.394564\pi$
$504$	24.1595	+	1.86797i	1.07615	+	0.0832059i
$505$		−	48.1504i		−	2.14266i
$506$	−2.13537	−	5.13851i	−0.0949289	−	0.228435i
$507$	19.9938	+	3.36862i	0.887954	+	0.149606i
$508$	0.423431	+	1.99208i	0.0187867	+	0.0883845i
$509$	−7.68853	+	0.808097i	−0.340788	+	0.0358183i	−0.273377	−	0.961907i	$-0.588141\pi$
$509$	−7.68853	+	0.808097i	−0.340788	+	0.0358183i	−0.0674111	+	0.997725i	$0.521474\pi$
$510$	−2.39811	−	9.31544i	−0.106190	−	0.412495i
$511$	−0.375419	+	2.29405i	−0.0166076	+	0.101483i
$512$	−7.66731	−	23.5975i	−0.338850	−	1.04287i
$513$	0.646878	−	7.88369i	0.0285604	−	0.348074i
$514$	4.77914	−	10.7341i	0.210799	−	0.473462i
$515$	−14.0593	−	66.1440i	−0.619528	−	2.91465i
$516$	−6.02946	+	2.24670i	−0.265432	+	0.0989054i
$517$	−35.0930	+	10.4390i	−1.54339	+	0.459106i
$518$	4.97732	−	9.64585i	0.218691	−	0.423814i
$519$	−0.809971	−	1.27452i	−0.0355538	−	0.0559452i
$520$	1.50035	+	14.2749i	0.0657948	+	0.625995i
$521$	−25.6169	−	2.69244i	−1.12230	−	0.117958i	−0.474848	−	0.880068i	$-0.657497\pi$
$521$	−25.6169	−	2.69244i	−1.12230	−	0.117958i	−0.647448	+	0.762109i	$0.724164\pi$
$522$	21.1790	+	12.7897i	0.926980	+	0.559790i
$523$	5.67378	−	26.6930i	0.248097	−	1.16721i	−0.660923	−	0.750454i	$-0.729835\pi$
$523$	5.67378	−	26.6930i	0.248097	−	1.16721i	0.909020	−	0.416752i	$-0.136832\pi$
$524$	4.58446	+	3.33081i	0.200273	+	0.145507i
$525$	−0.828846	+	55.3696i	−0.0361738	+	2.41653i
$526$	−3.13853	+	9.65940i	−0.136846	+	0.421170i
$527$	−2.61565	+	4.53044i	−0.113940	+	0.197349i
$528$	−14.9264	+	6.96104i	−0.649588	+	0.302940i
$529$	−10.5858	−	18.3351i	−0.460252	−	0.797179i
$530$	13.4638	+	14.9531i	0.584831	+	0.649520i
$531$	−5.17195	+	5.52162i	−0.224444	+	0.239618i
$532$	−1.85157	−	0.106567i	−0.0802758	−	0.00462028i
$533$	−4.93627	+	1.60389i	−0.213814	+	0.0694722i
$534$	0.330442	+	0.416370i	0.0142996	+	0.0180181i
$535$	−64.6267	−	6.79254i	−2.79405	−	0.293667i
$536$	31.3603	+	13.9625i	1.35456	+	0.603089i
$537$	0.428392	+	10.0682i	0.0184865	+	0.434474i
$538$		−	32.4533i		−	1.39916i
$539$	−23.1604	+	1.61056i	−0.997591	+	0.0693716i
$540$	4.74784	−	8.67543i	0.204315	−	0.373331i
$541$	−20.6482	+	18.5917i	−0.887734	+	0.799319i	−0.980531	−	0.196366i	$-0.937086\pi$
$541$	−20.6482	+	18.5917i	−0.887734	+	0.799319i	0.0927968	+	0.995685i	$0.470419\pi$
$542$	−7.07328	+	15.8868i	−0.303823	+	0.682398i
$543$	−5.30862	−	5.41410i	−0.227815	−	0.232341i
$544$	2.69943	+	0.573782i	0.115737	+	0.0246007i
$545$	4.19245	+	12.9030i	0.179585	+	0.552705i
$546$	−4.39924	+	4.74118i	−0.188270	+	0.202904i
$547$	−4.47229	−	6.15558i	−0.191221	−	0.263194i	0.702632	−	0.711554i	$-0.252008\pi$
$547$	−4.47229	−	6.15558i	−0.191221	−	0.263194i	−0.893853	+	0.448360i	$0.852008\pi$
$548$	−0.100927	+	0.0908749i	−0.00431138	+	0.00388198i
$549$	11.7712	+	13.6020i	0.502381	+	0.580520i
$550$	−23.7784	−	43.6744i	−1.01391	−	1.86228i
$551$	−8.76277	−	5.05919i	−0.373306	−	0.215529i
$552$	6.03459	−	3.83505i	0.256849	−	0.163231i
$553$	−18.3607	−	22.9130i	−0.780776	−	0.974360i
$554$	19.3361	−	26.6139i	0.821513	−	1.13072i
$555$	−14.7149	−	18.5414i	−0.624614	−	0.787038i
$556$	−0.807874	−	0.727413i	−0.0342615	−	0.0308492i
$557$	−1.50945	+	14.3614i	−0.0639574	+	0.608514i	0.914859	+	0.403774i	$0.132302\pi$
$557$	−1.50945	+	14.3614i	−0.0639574	+	0.608514i	−0.978816	+	0.204740i	$0.934365\pi$
$558$	17.2078	−	5.21922i	0.728465	−	0.220947i
$559$	2.83583	−	8.72778i	0.119943	−	0.369146i
$560$	27.8620	+	14.3770i	1.17738	+	0.607538i
$561$	0.541922	−	6.19714i	0.0228800	−	0.261644i
$562$	7.59467	−	13.1544i	0.320362	−	0.554883i
$563$	19.9042	−	4.23077i	0.838863	−	0.178306i	0.231604	−	0.972810i	$-0.425603\pi$
$563$	19.9042	−	4.23077i	0.838863	−	0.178306i	0.607258	+	0.794504i	$0.292269\pi$
$564$	−3.91977	−	7.88373i	−0.165052	−	0.331965i
$565$	−28.3726	+	12.6323i	−1.19364	+	0.531445i
$566$	−3.87423	+	1.25881i	−0.162846	+	0.0529119i
$567$	23.2517	−	5.13418i	0.976478	−	0.215615i
$568$	3.30108	−	4.54355i	0.138510	−	0.190643i
$569$	−2.62876	−	25.0110i	−0.110203	−	1.04851i	−0.900222	−	0.435431i	$-0.856596\pi$
$569$	−2.62876	−	25.0110i	−0.110203	−	1.04851i	0.790019	−	0.613083i	$-0.210071\pi$
$570$	6.25726	−	11.9876i	0.262088	−	0.502104i
$571$	0.163666	−	0.0944927i	0.00684922	−	0.00395440i	−0.496571	−	0.867996i	$-0.665408\pi$
$571$	0.163666	−	0.0944927i	0.00684922	−	0.00395440i	0.503421	+	0.864041i	$0.332075\pi$
$572$	−0.403599	+	1.68968i	−0.0168753	+	0.0706490i
$573$	−19.8110	−	16.3679i	−0.827618	−	0.683779i
$574$	−3.95105	+	14.4485i	−0.164914	+	0.603070i
$575$	9.60435	+	13.2193i	0.400529	+	0.551281i
$576$	−15.2592	−	21.8957i	−0.635802	−	0.912322i
$577$	23.7183	−	26.3419i	0.987407	−	1.09663i	−0.00791022	−	0.999969i	$-0.502518\pi$
$577$	23.7183	−	26.3419i	0.987407	−	1.09663i	0.995318	−	0.0966583i	$-0.0308154\pi$
$578$	−13.1405	+	14.5940i	−0.546573	+	0.607031i
$579$	−2.57377	−	0.716847i	−0.106962	−	0.0297911i
$580$	−7.43573	−	10.2344i	−0.308752	−	0.424960i
$581$	−22.0460	+	5.78611i	−0.914621	+	0.240048i
$582$	15.2320	−	18.4362i	0.631388	−	0.764205i
$583$	4.99356	+	12.0164i	0.206812	+	0.497667i
$584$	2.32292	−	1.34114i	0.0961232	−	0.0554968i
$585$	5.48236	+	12.9958i	0.226668	+	0.537308i
$586$	0.952861	+	9.06587i	0.0393623	+	0.374508i
$587$	3.96041	−	5.45103i	0.163463	−	0.224988i	−0.719426	−	0.694569i	$-0.755595\pi$
$587$	3.96041	−	5.45103i	0.163463	−	0.224988i	0.882889	+	0.469581i	$0.155595\pi$
$588$	−1.33629	−	5.42066i	−0.0551078	−	0.223544i
$589$	−6.99411	+	2.27252i	−0.288187	+	0.0936377i
$590$	−11.8151	+	5.26041i	−0.486419	+	0.216568i
$591$	−10.1588	+	5.05090i	−0.417875	+	0.207766i
$592$	−9.27245	+	1.97092i	−0.381095	+	0.0810043i
$593$	13.1871	−	22.8406i	0.541527	−	0.937953i	−0.457289	−	0.889318i	$-0.651180\pi$
$593$	13.1871	−	22.8406i	0.541527	−	0.937953i	0.998817	−	0.0486348i	$-0.0154870\pi$
$594$	−15.9219	+	14.2735i	−0.653284	+	0.585648i
$595$	−9.96467	+	6.39867i	−0.408512	+	0.262320i
$596$	−0.0127968	+	0.0393844i	−0.000524176	+	0.00161325i
$597$	1.86648	+	1.23837i	0.0763898	+	0.0506833i
$598$	−0.199489	+	1.89801i	−0.00815771	+	0.0776155i
$599$	7.36593	+	6.63231i	0.300964	+	0.270989i	0.805750	−	0.592255i	$-0.201762\pi$
$599$	7.36593	+	6.63231i	0.300964	+	0.270989i	−0.504787	+	0.863244i	$0.668429\pi$
$600$	50.0507	−	39.7215i	2.04331	−	1.62162i
$601$	12.6752	−	17.4459i	0.517031	−	0.711632i	−0.468054	−	0.883700i	$-0.655045\pi$
$601$	12.6752	−	17.4459i	0.517031	−	0.711632i	0.985085	+	0.172067i	$0.0550447\pi$
$602$	−16.5613	−	20.6674i	−0.674987	−	0.842341i
$603$	33.4727	+	4.18537i	1.36311	+	0.170441i
$604$	−4.28481	−	2.47384i	−0.174346	−	0.100659i
$605$	−7.21582	−	44.8898i	−0.293365	−	1.82503i
$606$	−24.6877	−	4.15948i	−1.00287	−	0.168967i
$607$	12.4082	−	11.1724i	0.503632	−	0.453472i	−0.377729	−	0.925916i	$-0.623295\pi$
$607$	12.4082	−	11.1724i	0.503632	−	0.453472i	0.881361	+	0.472444i	$0.156628\pi$
$608$	2.28036	+	3.13864i	0.0924806	+	0.127289i
$609$	6.77801	−	29.6953i	0.274659	−	1.20331i
$610$	9.50248	+	29.2456i	0.384744	+	1.18412i
$611$	12.2826	+	2.61076i	0.496902	+	0.105620i
$612$	1.49053	−	0.127072i	0.0602513	−	0.00513657i
$613$	−10.5033	+	23.5908i	−0.424224	+	0.952822i	0.567374	+	0.823460i	$0.307960\pi$
$613$	−10.5033	+	23.5908i	−0.424224	+	0.952822i	−0.991597	+	0.129362i	$0.958707\pi$
$614$	−27.0598	+	24.3647i	−1.09204	+	0.983281i
$615$	25.1828	+	20.8061i	1.01547	+	0.838983i
$616$	18.3629	+	19.5054i	0.739862	+	0.785893i
$617$			14.2944i			0.575471i	0.957710	+	0.287735i	$0.0929023\pi$
$617$			14.2944i			0.575471i	−0.957710	+	0.287735i	$0.907098\pi$
$618$	−35.1280	+	1.49466i	−1.41305	+	0.0601241i
$619$	−15.9166	−	7.08653i	−0.639743	−	0.284832i	0.0611173	−	0.998131i	$-0.480534\pi$
$619$	−15.9166	−	7.08653i	−0.639743	−	0.284832i	−0.700860	+	0.713299i	$0.747200\pi$
$620$	−9.14397	−	0.961069i	−0.367230	−	0.0385975i
$621$	4.58092	−	5.32755i	0.183826	−	0.213787i
$622$	28.7045	−	9.32665i	1.15094	−	0.373964i
$623$	0.359227	−	0.546995i	0.0143921	−	0.0219149i
$624$	5.63770	+	0.351097i	0.225689	+	0.0140551i
$625$	40.5511	+	45.0366i	1.62205	+	1.80146i
$626$	−7.96798	−	13.8009i	−0.318465	−	0.551597i
$627$	6.39547	−	5.96437i	0.255411	−	0.238194i
$628$	3.61751	−	6.26571i	0.144354	−	0.250029i
$629$	1.10645	−	3.40530i	0.0441170	−	0.135778i
$630$	40.0345	+	7.36303i	1.59501	+	0.293350i
$631$	21.1898	+	15.3953i	0.843553	+	0.612877i	0.923361	−	0.383933i	$-0.125431\pi$
$631$	21.1898	+	15.3953i	0.843553	+	0.612877i	−0.0798076	+	0.996810i	$0.525431\pi$
$632$	−7.04411	+	33.1399i	−0.280200	+	1.31824i
$633$	35.4053	−	5.25120i	1.40724	−	0.208716i
$634$	25.6931	+	2.70045i	1.02040	+	0.107249i
$635$	1.91086	+	18.1806i	0.0758300	+	0.721474i
$636$	−2.64101	+	1.67839i	−0.104723	+	0.0665525i
$637$	7.24049	+	3.31313i	0.286879	+	0.131271i
$638$	7.79869	+	26.2171i	0.308753	+	1.03794i
$639$	1.80833	−	5.21415i	0.0715366	−	0.206269i
$640$	−5.10557	−	24.0198i	−0.201815	−	0.949467i
$641$	−4.87041	+	10.9391i	−0.192370	+	0.432069i	−0.983819	−	0.179165i	$-0.942660\pi$
$641$	−4.87041	+	10.9391i	−0.192370	+	0.432069i	0.791449	+	0.611235i	$0.209327\pi$
$642$	−9.06547	+	32.5487i	−0.357785	+	1.28459i
$643$	5.78938	+	17.8179i	0.228311	+	0.702668i	0.997939	+	0.0641755i	$0.0204417\pi$
$643$	5.78938	+	17.8179i	0.228311	+	0.702668i	−0.769628	+	0.638493i	$0.779558\pi$
$644$	−1.27491	−	1.04328i	−0.0502387	−	0.0411111i
$645$	−55.9328	+	14.3990i	−2.20235	+	0.566960i
$646$	2.03424	−	0.213807i	0.0800360	−	0.00841212i
$647$	−6.02587	−	28.3495i	−0.236901	−	1.11453i	−0.922333	−	0.386397i	$-0.873720\pi$
$647$	−6.02587	−	28.3495i	−0.236901	−	1.11453i	0.685431	−	0.728137i	$-0.259614\pi$
$648$	−21.5761	−	17.0119i	−0.847591	−	0.668291i
$649$	−8.33747	+	0.665831i	−0.327274	+	0.0261361i
$650$			17.0551i			0.668958i
$651$	−12.7426	−	18.1025i	−0.499423	−	0.709491i
$652$	−6.64332	+	4.82666i	−0.260173	+	0.189026i
$653$	5.44380	+	12.2270i	0.213032	+	0.478478i	0.988179	−	0.153303i	$-0.0489909\pi$
$653$	5.44380	+	12.2270i	0.213032	+	0.478478i	−0.775147	+	0.631781i	$0.782324\pi$
$654$	6.97783	−	1.03493i	0.272855	−	0.0404689i
$655$	37.8002	+	34.0355i	1.47698	+	1.32988i
$656$	11.9509	−	5.32089i	0.466605	−	0.207746i
$657$	1.80189	−	1.92371i	0.0702984	−	0.0750511i
$658$	25.7561	−	25.4931i	1.00408	−	0.993826i
$659$	7.71536			0.300548			0.150274	−	0.988644i	$-0.451984\pi$
$659$	7.71536			0.300548			0.150274	+	0.988644i	$0.451984\pi$
$660$	10.3376	−	3.56000i	0.402391	−	0.138573i
$661$	2.57613	+	4.46199i	0.100200	+	0.173551i	0.911767	−	0.410708i	$-0.134718\pi$
$661$	2.57613	+	4.46199i	0.100200	+	0.173551i	−0.811567	+	0.584259i	$0.801385\pi$
$662$	−27.3756	+	5.81886i	−1.06398	+	0.226157i
$663$	−1.17955	+	1.77782i	−0.0458101	+	0.0690449i
$664$	21.2772	+	15.4588i	0.825717	+	0.599918i
$665$	−16.4289	−	2.68858i	−0.637087	−	0.104259i
$666$	−10.7777	+	5.94295i	−0.417628	+	0.230285i
$667$	−3.65560	−	8.21060i	−0.141545	−	0.317916i
$668$	−7.12314	−	3.17142i	−0.275602	−	0.122706i
$669$	3.19115	−	6.11357i	0.123377	−	0.236364i
$670$	49.9409	+	28.8334i	1.92939	+	1.11393i
$671$	−0.497689	+	19.8805i	−0.0192131	+	0.767477i
$672$	−7.00512	+	9.34434i	−0.270229	+	0.360466i
$673$	40.0374	+	13.0089i	1.54333	+	0.501457i	0.952292	−	0.305188i	$-0.0987195\pi$
$673$	40.0374	+	13.0089i	1.54333	+	0.501457i	0.591035	+	0.806646i	$0.298719\pi$
$674$	−5.49151	+	0.577181i	−0.211525	+	0.0222322i
$675$	35.7369	−	51.6284i	1.37551	−	1.98718i
$676$	−3.60684	+	4.00581i	−0.138725	+	0.154069i
$677$	−8.24672	−	1.75289i	−0.316947	−	0.0673692i	0.0466913	−	0.998909i	$-0.485132\pi$
$677$	−8.24672	−	1.75289i	−0.316947	−	0.0673692i	−0.363638	+	0.931540i	$0.618466\pi$
$678$	4.02588	+	15.6385i	0.154613	+	0.600592i
$679$	−27.4314	−	10.6918i	−1.05272	−	0.410312i
$680$	12.9958	+	4.22258i	0.498365	+	0.161929i
$681$	11.7708	+	31.5892i	0.451056	+	1.21050i
$682$	17.9530	+	8.53780i	0.687457	+	0.326929i
$683$	−22.7773	+	13.1505i	−0.871551	+	0.503190i	−0.867863	−	0.496803i	$-0.834507\pi$
$683$	−22.7773	+	13.1505i	−0.871551	+	0.503190i	−0.00368733	+	0.999993i	$0.501174\pi$
$684$	1.67668	+	1.26932i	0.0641096	+	0.0485335i
$685$	−0.986236	+	0.716542i	−0.0376821	+	0.0273777i
$686$	19.4626	−	12.2174i	0.743086	−	0.466461i
$687$	−2.00040	−	0.790545i	−0.0763201	−	0.0301612i
$688$	−4.80900	+	22.6246i	−0.183342	+	0.862554i
$689$	0.466504	−	4.43849i	0.0177724	−	0.169093i
$690$	10.7552	−	5.34746i	0.409444	−	0.203574i
$691$	−2.09565	−	2.32745i	−0.0797222	−	0.0885405i	0.701964	−	0.712213i	$-0.252307\pi$
$691$	−2.09565	−	2.32745i	−0.0797222	−	0.0885405i	−0.781686	+	0.623672i	$0.785640\pi$
$692$	0.401471			0.0152616
$693$	22.8312	+	13.1048i	0.867286	+	0.497811i
$694$	−29.9900			−1.13841
$695$	−6.52936	−	7.25159i	−0.247673	−	0.275069i
$696$	−31.4709	+	15.6472i	−1.19290	+	0.593107i
$697$	−0.516493	+	4.91410i	−0.0195636	+	0.186135i
$698$	1.26173	−	5.93598i	0.0477572	−	0.224680i
$699$	27.2149	+	10.7551i	1.02936	+	0.406797i
$700$	−12.3055	−	8.08137i	−0.465104	−	0.305447i
$701$	10.6790	−	7.75872i	0.403339	−	0.293043i	−0.367561	−	0.930000i	$-0.619807\pi$
$701$	10.6790	−	7.75872i	0.403339	−	0.293043i	0.770900	+	0.636957i	$0.219807\pi$
$702$	7.13680	−	1.68828i	0.269361	−	0.0637201i
$703$	4.35908	−	2.51672i	0.164406	−	0.0949198i
$704$	3.81751	−	29.2571i	0.143878	−	1.10267i
$705$	−27.5946	−	74.0557i	−1.03927	−	2.78910i
$706$	10.7864	+	3.50472i	0.405952	+	0.131902i
$707$	4.66526	+	30.4664i	0.175455	+	1.14581i
$708$	−0.501436	−	1.94782i	−0.0188451	−	0.0732037i
$709$	−8.04815	−	1.71069i	−0.302255	−	0.0642462i	0.0542878	−	0.998525i	$-0.482711\pi$
$709$	−8.04815	−	1.71069i	−0.302255	−	0.0642462i	−0.356542	+	0.934279i	$0.616044\pi$
$710$	6.31284	−	7.01112i	0.236917	−	0.263123i
$711$	2.82807	+	33.1729i	0.106061	+	1.24408i
$712$	−0.750974	+	0.0789306i	−0.0281439	+	0.00295805i
$713$	−6.21250	−	2.01856i	−0.232660	−	0.0755958i
$714$	2.41994	+	5.66185i	0.0905638	+	0.211889i
$715$	−5.18828	+	14.7050i	−0.194031	+	0.549937i
$716$	−2.32016	−	1.33955i	−0.0867086	−	0.0500612i
$717$	18.7897	−	35.9970i	0.701713	−	1.34433i
$718$	−28.1605	−	12.5379i	−1.05094	−	0.467909i
$719$	−10.4658	−	23.5065i	−0.390308	−	0.876646i	−0.996676	−	0.0814624i	$-0.974041\pi$
$719$	−10.4658	−	23.5065i	−0.390308	−	0.876646i	0.606368	−	0.795184i	$-0.292626\pi$
$720$	−17.1662	−	31.1314i	−0.639746	−	1.16020i
$721$	15.3045	+	40.4894i	0.569969	+	1.50790i
$722$	−16.7461	−	12.1668i	−0.623225	−	0.452800i
$723$	−5.21212	+	7.85570i	−0.193841	+	0.292157i
$724$	1.97178	−	0.419115i	0.0732807	−	0.0155763i
$725$	−40.1593	−	69.5579i	−1.49148	−	2.58332i
$726$	−23.6393	−	0.178108i	−0.877337	−	0.00661019i
$727$	−25.2830			−0.937693			−0.468847	−	0.883280i	$-0.655330\pi$
$727$	−25.2830			−0.937693			−0.468847	+	0.883280i	$0.655330\pi$
$728$	−2.33241	−	8.88685i	−0.0864449	−	0.329369i
$729$	−25.1417	−	9.84357i	−0.931173	−	0.364577i
$730$	4.11633	−	1.83271i	0.152352	−	0.0678316i
$731$	−6.49244	−	5.84582i	−0.240132	−	0.216215i
$732$	−4.73050	+	0.701611i	−0.174844	+	0.0259323i
$733$	18.8562	+	42.3518i	0.696471	+	1.56430i	0.820260	+	0.571991i	$0.193829\pi$
$733$	18.8562	+	42.3518i	0.696471	+	1.56430i	−0.123789	+	0.992309i	$0.539505\pi$
$734$	4.03250	−	2.92978i	0.148842	−	0.108140i
$735$	−6.84306	−	49.6439i	−0.252410	−	1.83114i
$736$			3.44602i			0.127022i
$737$	24.2529	+	28.3304i	0.893366	+	1.04356i
$738$	12.8432	−	11.1144i	0.472763	−	0.409128i
$739$	6.11624	+	28.7747i	0.224990	+	1.05849i	0.935095	+	0.354398i	$0.115314\pi$
$739$	6.11624	+	28.7747i	0.224990	+	1.05849i	−0.710105	+	0.704096i	$0.751353\pi$
$740$	6.25854	−	0.657799i	0.230069	−	0.0241812i
$741$	−2.90458	+	0.747737i	−0.106702	+	0.0274688i
$742$	−9.96781	−	8.15683i	−0.365930	−	0.299447i
$743$	−9.43345	−	29.0332i	−0.346080	−	1.06512i	−0.961003	−	0.276537i	$-0.910813\pi$
$743$	−9.43345	−	29.0332i	−0.346080	−	1.06512i	0.614923	−	0.788587i	$-0.289187\pi$
$744$	−6.85373	+	24.6077i	−0.251270	+	0.902161i
$745$	−0.151189	+	0.339577i	−0.00553915	+	0.0124411i
$746$	3.87076	+	18.2105i	0.141718	+	0.666733i
$747$	24.4176	+	8.46834i	0.893394	+	0.309840i
$748$	1.31323	+	1.00527i	0.0480163	+	0.0367565i
$749$	41.5496	−	1.96377i	1.51819	−	0.0717546i
$750$	53.1083	−	33.7509i	1.93924	−	1.23241i
$751$	−1.41857	−	13.4968i	−0.0517645	−	0.492506i	−0.989435	−	0.144980i	$-0.953688\pi$
$751$	−1.41857	−	13.4968i	−0.0517645	−	0.492506i	0.937670	−	0.347526i	$-0.112978\pi$
$752$	−31.4761	−	3.30827i	−1.14781	−	0.120640i
$753$	1.39078	−	0.206276i	0.0506829	−	0.00751712i
$754$	1.95043	−	9.17604i	0.0710304	−	0.334172i
$755$	−35.9293	−	26.1041i	−1.30760	−	0.950027i
$756$	−2.16357	+	5.94926i	−0.0786882	+	0.216373i
$757$	2.00647	−	6.17527i	0.0729263	−	0.224444i	−0.907949	−	0.419080i	$-0.862353\pi$
$757$	2.00647	−	6.17527i	0.0729263	−	0.224444i	0.980876	+	0.194636i	$0.0623526\pi$
$758$	1.78333	−	3.08883i	0.0647736	−	0.112191i
$759$	7.70983	−	0.946971i	0.279849	−	0.0343729i
$760$	9.60465	+	16.6357i	0.348397	+	0.603442i
$761$	29.5210	+	32.7864i	1.07013	+	1.18850i	0.981305	+	0.192458i	$0.0616459\pi$
$761$	29.5210	+	32.7864i	1.07013	+	1.18850i	0.0888294	+	0.996047i	$0.471687\pi$
$762$	9.48664	+	0.590797i	0.343665	+	0.0214023i
$763$	−3.90288	−	7.75799i	−0.141294	−	0.280858i
$764$	6.49754	−	2.11118i	0.235073	−	0.0763798i
$765$	13.4252	+	0.264147i	0.485389	+	0.00955025i
$766$	−22.9194	−	2.40892i	−0.828110	−	0.0870379i
$767$	2.62060	+	1.16676i	0.0946243	+	0.0421294i
$768$	18.0327	−	0.767273i	0.650698	−	0.0276866i
$769$		−	26.9459i		−	0.971696i	−0.874043	−	0.485848i	$-0.838511\pi$
$769$		−	26.9459i		−	0.971696i	0.874043	−	0.485848i	$-0.161489\pi$
$770$	27.2533	+	35.8114i	0.982139	+	1.29055i
$771$	12.6448	+	10.4472i	0.455391	+	0.376245i
$772$	0.527850	−	0.475278i	0.0189977	−	0.0171056i
$773$	−1.82316	+	4.09488i	−0.0655744	+	0.147283i	−0.943360	−	0.331772i	$-0.892354\pi$
$773$	−1.82316	+	4.09488i	−0.0655744	+	0.147283i	0.877785	+	0.479054i	$0.159020\pi$
$774$	2.55091	+	29.9218i	0.0916906	+	1.07552i
$775$	−57.0999	−	12.1370i	−2.05109	−	0.435973i
$776$	10.4979	+	32.3093i	0.376854	+	1.15984i
$777$	11.1071	+	10.3061i	0.398465	+	0.369728i
$778$	25.9892	+	35.7711i	0.931758	+	1.28246i
$779$	−5.16201	+	4.64790i	−0.184948	+	0.166528i
$780$	−3.69771	−	0.623004i	−0.132399	−	0.0223071i
$781$	5.35857	−	2.91746i	0.191745	−	0.104395i
$782$	1.57345	+	0.908430i	0.0562664	+	0.0324854i
$783$	−25.1314	+	23.6903i	−0.898124	+	0.846623i
$784$	−19.0222	−	6.39727i	−0.679365	−	0.228474i
$785$	38.1723	−	52.5397i	1.36243	−	1.87522i
$786$	20.7161	−	16.4408i	0.738918	−	0.586424i
$787$	−40.1996	−	36.1959i	−1.43296	−	1.29025i	−0.894112	−	0.447844i	$-0.852192\pi$
$787$	−40.1996	−	36.1959i	−1.43296	−	1.29025i	−0.538850	−	0.842401i	$-0.681141\pi$
$788$	0.315274	−	2.99963i	0.0112312	−	0.106857i
$789$	−11.8140	−	7.83841i	−0.420591	−	0.279055i
$790$	−17.5876	+	54.1290i	−0.625737	+	1.92582i
$791$	16.7284	−	10.7419i	0.594793	−	0.381938i
$792$	−4.98146	−	29.9647i	−0.177009	−	1.06475i
$793$	3.41027	−	5.90675i	0.121102	−	0.209755i
$794$	−36.2850	+	7.71261i	−1.28771	+	0.273710i
$795$	−25.1510	+	12.5050i	−0.892014	+	0.443506i
$796$	−0.544013	+	0.242210i	−0.0192820	+	0.00858491i
$797$	−25.8706	+	8.40588i	−0.916385	+	0.297752i	−0.728983	−	0.684532i	$-0.760007\pi$
$797$	−25.8706	+	8.40588i	−0.916385	+	0.297752i	−0.187402	+	0.982283i	$0.560007\pi$
$798$	−2.79771	+	8.19121i	−0.0990379	+	0.289966i
$799$	7.02656	−	9.67124i	0.248582	−	0.342144i
$800$	3.21902	+	30.6269i	0.113810	+	1.08283i
$801$	−0.683681	+	0.288416i	−0.0241567	+	0.0101907i
$802$	29.1395	−	16.8237i	1.02895	−	0.594065i
$803$	2.90474	−	0.231973i	0.102506	−	0.00818615i
$804$	−5.71212	+	6.91371i	−0.201451	+	0.243828i
$805$	−10.4023	−	10.5096i	−0.366631	−	0.370414i
$806$	−4.00761	−	5.51600i	−0.141162	−	0.194293i
$807$	43.6418	+	12.1551i	1.53626	+	0.427880i
$808$	23.7973	−	26.4296i	0.837187	−	0.929790i
$809$	−14.5201	+	16.1262i	−0.510498	+	0.566966i	−0.942200	−	0.335051i	$-0.891247\pi$
$809$	−14.5201	+	16.1262i	−0.510498	+	0.566966i	0.431702	+	0.902016i	$0.357913\pi$
$810$	−33.0594	−	32.2099i	−1.16159	−	1.13174i
$811$	12.1443	+	16.7152i	0.426445	+	0.586952i	0.967133	−	0.254272i	$-0.0818358\pi$
$811$	12.1443	+	16.7152i	0.426445	+	0.586952i	−0.540687	+	0.841224i	$0.681836\pi$
$812$	5.69645	+	5.75521i	0.199906	+	0.201968i
$813$	−18.7147	−	15.4621i	−0.656353	−	0.542280i
$814$	−13.2343	−	3.16117i	−0.463862	−	0.110799i
$815$	−63.8334	+	36.8543i	−2.23599	+	1.29095i
$816$	2.48834	−	4.76713i	0.0871094	−	0.166883i
$817$	−1.28376	−	12.2142i	−0.0449132	−	0.427321i
$818$	−8.78997	+	12.0984i	−0.307334	+	0.423009i
$819$	−4.72803	−	7.69168i	−0.165211	−	0.268769i
$820$	−8.25936	+	2.68363i	−0.288429	+	0.0937163i
$821$	3.23754	−	1.44145i	0.112991	−	0.0503069i	−0.349463	−	0.936950i	$-0.613636\pi$
$821$	3.23754	−	1.44145i	0.112991	−	0.0503069i	0.462454	+	0.886643i	$0.346969\pi$
$822$	0.282190	+	0.567563i	0.00984252	+	0.0197960i
$823$	−29.8431	+	6.34334i	−1.04026	+	0.221115i	−0.696212	−	0.717836i	$-0.745133\pi$
$823$	−29.8431	+	6.34334i	−1.04026	+	0.221115i	−0.344052	+	0.938951i	$0.611800\pi$
$824$	24.9732	−	43.2548i	0.869982	−	1.50685i
$825$	67.6374	−	15.6183i	2.35483	−	0.543758i
$826$	6.96613	−	4.47320i	0.242383	−	0.155643i
$827$	8.09428	−	24.9116i	0.281466	−	0.866262i	−0.705970	−	0.708242i	$-0.749489\pi$
$827$	8.09428	−	24.9116i	0.281466	−	0.866262i	0.987436	−	0.158021i	$-0.0505113\pi$
$828$	0.542169	+	1.78754i	0.0188417	+	0.0621212i
$829$	0.967960	−	9.20953i	0.0336186	−	0.319860i	−0.964769	−	0.263098i	$-0.915256\pi$
$829$	0.967960	−	9.20953i	0.0336186	−	0.319860i	0.998388	−	0.0567620i	$-0.0180776\pi$
$830$	32.8327	+	29.5627i	1.13964	+	1.02614i
$831$	28.5470	+	35.9704i	0.990284	+	1.24780i
$832$	−5.94800	+	8.18671i	−0.206210	+	0.283823i
$833$	5.68503	−	5.01413i	0.196974	−	0.173729i
$834$	−4.28209	+	2.72131i	−0.148277	+	0.0942314i
$835$	−60.6124	−	34.9946i	−2.09758	−	1.21104i
$836$	0.426312	+	2.28549i	0.0147443	+	0.0790452i
$837$	0.573536	+	25.0951i	0.0198243	+	0.867415i
$838$	6.12364	−	5.51375i	0.211538	−	0.190469i
$839$	11.5993	+	15.9651i	0.400453	+	0.551176i	0.960858	−	0.277043i	$-0.0893545\pi$
$839$	11.5993	+	15.9651i	0.400453	+	0.551176i	−0.560405	+	0.828219i	$0.689354\pi$
$840$	−39.3314	+	42.3885i	−1.35706	+	1.46254i
$841$	4.69043	+	14.4357i	0.161739	+	0.497781i
$842$	35.9266	+	7.63644i	1.23811	+	0.263169i
$843$	14.8449	+	15.1398i	0.511285	+	0.521444i
$844$	−3.87035	+	8.69296i	−0.133223	+	0.299224i
$845$	−35.9567	+	32.3756i	−1.23695	+	1.11375i
$846$	−40.3537	+	7.75105i	−1.38739	+	0.266487i
$847$	8.91505	+	27.7042i	0.306325	+	0.951927i
$848$			11.2486i			0.386279i
$849$	−0.241737	−	5.68138i	−0.00829640	−	0.194984i
$850$	14.8328	+	6.60398i	0.508760	+	0.226515i
$851$	4.44645	+	0.467341i	0.152422	+	0.0160202i
$852$	0.912082	+	1.14926i	0.0312474	+	0.0393730i
$853$	2.54811	−	0.827931i	0.0872456	−	0.0283478i	−0.265069	−	0.964229i	$-0.585395\pi$
$853$	2.54811	−	0.827931i	0.0872456	−	0.0283478i	0.352315	+	0.935882i	$0.385395\pi$
$854$	−8.84614	−	17.5840i	−0.302709	−	0.601713i
$855$	13.7768	+	12.9043i	0.471155	+	0.441319i
$856$	−32.1163	−	35.6688i	−1.09771	−	1.21913i
$857$	16.5156	+	28.6058i	0.564161	+	0.977156i	0.997127	+	0.0757455i	$0.0241337\pi$
$857$	16.5156	+	28.6058i	0.564161	+	0.977156i	−0.432966	+	0.901410i	$0.642533\pi$
$858$	7.09139	+	3.93044i	0.242096	+	0.134183i
$859$	10.2092	−	17.6829i	0.348334	−	0.603333i	−0.637619	−	0.770352i	$-0.720081\pi$
$859$	10.2092	−	17.6829i	0.348334	−	0.603333i	0.985954	+	0.167019i	$0.0534141\pi$
$860$	4.74490	−	14.6033i	0.161800	−	0.497969i
$861$	−17.9499	−	10.7248i	−0.611732	−	0.365500i
$862$	−5.50544	−	3.99993i	−0.187516	−	0.136238i
$863$	−8.77491	+	41.2827i	−0.298701	+	1.40528i	0.531142	+	0.847283i	$0.321763\pi$
$863$	−8.77491	+	41.2827i	−0.298701	+	1.40528i	−0.829843	+	0.557996i	$0.811570\pi$
$864$	12.4973	−	4.37876i	0.425167	−	0.148968i
$865$	3.58392	+	0.376685i	0.121857	+	0.0128077i
$866$	−4.30128	−	40.9239i	−0.146163	−	1.39065i
$867$	−14.7037	−	23.1368i	−0.499364	−	0.785768i
$868$	5.87882	−	0.277852i	0.199540	−	0.00943092i
$869$	−22.3731	+	29.2268i	−0.758956	+	0.991451i
$870$	−55.3251	+	20.6152i	−1.87570	+	0.698922i
$871$	−2.65931	−	12.5111i	−0.0901072	−	0.423921i
$872$	−4.07584	+	9.15448i	−0.138025	+	0.310010i
$873$	19.0872	+	27.3885i	0.646003	+	0.926960i
$874$	0.789260	+	2.42909i	0.0266971	+	0.0821653i
$875$	−59.9528	−	49.0604i	−2.02677	−	1.65854i
$876$	0.174698	+	0.678614i	0.00590251	+	0.0229283i
$877$	−34.3269	+	3.60790i	−1.15914	+	0.121830i	−0.664513	−	0.747277i	$-0.731361\pi$
$877$	−34.3269	+	3.60790i	−1.15914	+	0.121830i	−0.494624	+	0.869107i	$0.664694\pi$
$878$	7.31140	+	34.3974i	0.246748	+	1.16086i
$879$	−12.5483	−	2.11418i	−0.423243	−	0.0713095i
$880$	9.13101	−	38.2272i	0.307806	−	1.28864i
$881$		−	57.8553i		−	1.94919i	−0.223964	−	0.974597i	$-0.571900\pi$
$881$		−	57.8553i		−	1.94919i	0.223964	−	0.974597i	$-0.428100\pi$
$882$	−26.0446	−	0.779917i	−0.876968	−	0.0262612i
$883$	16.4125	−	11.9244i	0.552326	−	0.401289i	−0.276316	−	0.961067i	$-0.589114\pi$
$883$	16.4125	−	11.9244i	0.552326	−	0.401289i	0.828642	+	0.559778i	$0.189114\pi$
$884$	−0.230706	−	0.518173i	−0.00775947	−	0.0174281i
$885$	−2.64873	−	17.8586i	−0.0890362	−	0.600312i
$886$	2.02539	+	1.82367i	0.0680442	+	0.0612673i
$887$	29.0712	−	12.9433i	0.976114	−	0.434594i	0.144230	−	0.989544i	$-0.453929\pi$
$887$	29.0712	−	12.9433i	0.976114	−	0.434594i	0.831884	+	0.554950i	$0.187263\pi$
$888$	1.08672	−	17.4499i	0.0364679	−	0.585579i
$889$	−2.97057	−	11.3183i	−0.0996298	−	0.379605i
$890$	−1.26849			−0.0425198
$891$	−13.2309	−	26.7571i	−0.443253	−	0.896397i
$892$	0.916708	+	1.58779i	0.0306937	+	0.0531630i
$893$	16.4378	−	3.49397i	0.550072	−	0.116921i
$894$	0.161048	+	0.106852i	0.00538625	+	0.00357368i
$895$	−19.4552	−	14.1350i	−0.650315	−	0.472482i
$896$	5.55774	+	14.7035i	0.185671	+	0.491209i
$897$	−2.47765	−	0.979148i	−0.0827262	−	0.0326928i
$898$	0.514399	+	1.15536i	0.0171657	+	0.0385548i
$899$	29.3330	+	13.0599i	0.978312	+	0.435572i
$900$	6.48837	+	15.3805i	0.216279	+	0.512683i
$901$	−3.67950	−	2.12436i	−0.122582	−	0.0707726i
$902$	18.7713	+	0.469922i	0.625016	+	0.0156467i
$903$	33.9955	−	14.5301i	1.13130	−	0.483530i
$904$	−21.8169	−	7.08874i	−0.725619	−	0.235768i
$905$	17.9953	−	1.89138i	0.598184	−	0.0628717i
$906$	−16.4879	+	16.1667i	−0.547774	+	0.537102i
$907$	25.5159	−	28.3383i	0.847242	−	0.940958i	−0.151630	−	0.988437i	$-0.548452\pi$
$907$	25.5159	−	28.3383i	0.847242	−	0.940958i	0.998872	+	0.0474794i	$0.0151189\pi$
$908$	−8.76635	−	1.86334i	−0.290922	−	0.0618373i
$909$	14.8401	−	31.6411i	0.492214	−	1.04947i
$910$	−2.33621	−	15.2565i	−0.0774445	−	0.505749i
$911$	−7.48812	−	2.43304i	−0.248093	−	0.0806102i	0.182331	−	0.983237i	$-0.441636\pi$
$911$	−7.48812	−	2.43304i	−0.248093	−	0.0806102i	−0.430424	+	0.902627i	$0.641636\pi$
$912$	7.08375	−	2.63955i	0.234566	−	0.0874042i
$913$	13.6623	+	25.0939i	0.452156	+	0.830487i
$914$	36.0664	−	20.8229i	1.19297	−	0.688761i
$915$	−42.8873	+	1.82482i	−1.41781	+	0.0603265i
$916$	0.462627	−	0.336118i	0.0152856	−	0.0111057i
$917$	−27.2152	−	17.8730i	−0.898724	−	0.590217i
$918$	1.29517	−	6.86056i	0.0427470	−	0.226432i
$919$	3.98345	−	18.7407i	0.131402	−	0.618198i	−0.862324	−	0.506357i	$-0.830992\pi$
$919$	3.98345	−	18.7407i	0.131402	−	0.618198i	0.993726	−	0.111841i	$-0.0356747\pi$
$920$	−1.78353	+	16.9692i	−0.0588013	+	0.559457i
$921$	−22.6296	−	45.5144i	−0.745671	−	1.49975i
$922$	−2.74973	−	3.05389i	−0.0905577	−	0.100574i
$923$	−2.09256			−0.0688774
$924$	−6.19603	+	3.25414i	−0.203835	+	0.107053i
$925$	39.9549			1.31371
$926$	11.7771	+	13.0797i	0.387018	+	0.429827i
$927$	11.1469	−	47.7983i	0.366113	−	1.56990i
$928$	1.77060	−	16.8461i	0.0581226	−	0.553000i
$929$	0.0556416	−	0.261773i	0.00182554	−	0.00858849i	−0.977225	−	0.212204i	$-0.931936\pi$
$929$	0.0556416	−	0.261773i	0.00182554	−	0.00858849i	0.979051	+	0.203615i	$0.0652692\pi$
$930$	−15.7713	+	39.9078i	−0.517161	+	1.30863i
$931$	10.6557	+	0.109368i	0.349225	+	0.00358441i
$932$	−6.29391	+	4.57279i	−0.206164	+	0.149787i
$933$	1.79105	+	42.0937i	0.0586363	+	1.37809i
$934$	5.77762	−	3.33571i	0.189050	−	0.109148i
$935$	10.7799	+	10.2062i	0.352541	+	0.333779i
$936$	−3.41363	+	9.84288i	−0.111578	+	0.321725i
$937$	−26.3131	−	8.54964i	−0.859611	−	0.279304i	−0.154145	−	0.988048i	$-0.549262\pi$
$937$	−26.3131	−	8.54964i	−0.859611	−	0.279304i	−0.705466	+	0.708744i	$0.749262\pi$
$938$	−34.3930	−	13.4051i	−1.12297	−	0.437694i
$939$	21.5433	−	5.54596i	0.703037	−	0.180986i
$940$	20.5513	+	4.36831i	0.670309	+	0.142479i
$941$	17.5944	−	19.5406i	0.573562	−	0.637005i	−0.384651	−	0.923062i	$-0.625678\pi$
$941$	17.5944	−	19.5406i	0.573562	−	0.637005i	0.958213	+	0.286057i	$0.0923447\pi$
$942$	−23.6407	−	24.1104i	−0.770256	−	0.785560i
$943$	−6.13613	+	0.644933i	−0.199820	+	0.0210019i
$944$	−6.87630	−	2.23425i	−0.223805	−	0.0727185i
$945$	−24.8961	+	51.0789i	−0.809870	+	1.66160i
$946$	−20.1804	+	26.3624i	−0.656123	+	0.857117i
$947$	−4.49440	−	2.59484i	−0.146048	−	0.0843211i	0.425195	−	0.905102i	$-0.360205\pi$
$947$	−4.49440	−	2.59484i	−0.146048	−	0.0843211i	−0.571243	+	0.820781i	$0.693539\pi$
$948$	−7.84654	−	4.09572i	−0.254844	−	0.133023i
$949$	−0.913006	−	0.406497i	−0.0296374	−	0.0131954i
$950$	9.28372	+	20.8516i	0.301204	+	0.676514i
$951$	−13.2546	+	33.5395i	−0.429809	+	1.08759i
$952$	−8.63199	−	1.41262i	−0.279765	−	0.0457833i
$953$	47.0764	+	34.2030i	1.52495	+	1.10794i	0.958963	+	0.283531i	$0.0915060\pi$
$953$	47.0764	+	34.2030i	1.52495	+	1.10794i	0.565990	+	0.824412i	$0.308494\pi$
$954$	4.23890	+	13.9757i	0.137240	+	0.452480i
$955$	59.9842	−	12.7500i	1.94104	−	0.412582i
$956$	5.39762	+	9.34896i	0.174572	+	0.302367i
$957$	−38.1765	+	0.667950i	−1.23407	+	0.0215918i
$958$	−53.0701			−1.71462
$959$	0.554600	−	0.548937i	0.0179090	−	0.0177261i
$960$	63.5645	+	3.95859i	2.05154	+	0.127763i
$961$	−7.00063	+	3.11688i	−0.225827	+	0.100545i
$962$	3.46800	+	3.12260i	0.111813	+	0.100677i
$963$	−40.3747	−	24.3817i	−1.30106	−	0.785689i
$964$	−1.01942	−	2.28966i	−0.0328335	−	0.0737451i
$965$	5.15804	−	3.74754i	0.166043	−	0.120637i
$966$	−6.28708	+	4.42559i	−0.202284	+	0.142391i
$967$		−	9.92340i		−	0.319115i	−0.987189	−	0.159557i	$-0.948993\pi$
$967$		−	9.92340i		−	0.319115i	0.987189	−	0.159557i	$-0.0510067\pi$
$968$	18.2251	−	28.2062i	0.585777	−	0.906580i
$969$	−0.474388	+	2.81563i	−0.0152395	+	0.0904512i
$970$	11.8652	+	55.8215i	0.380969	+	1.79232i
$971$	5.14904	−	0.541185i	0.165240	−	0.0173675i	−0.0215469	−	0.999768i	$-0.506859\pi$
$971$	5.14904	−	0.541185i	0.165240	−	0.0173675i	0.186787	+	0.982400i	$0.440192\pi$
$972$	5.79374	−	4.23759i	0.185834	−	0.135921i
$973$	4.83396	+	3.95571i	0.154970	+	0.126814i
$974$	6.06351	+	18.6616i	0.194287	+	0.597955i
$975$	−22.9350	−	6.38786i	−0.734508	−	0.204575i
$976$	−6.99214	+	15.7046i	−0.223813	+	0.502692i
$977$	−6.86164	−	32.2815i	−0.219523	−	1.03278i	−0.940494	−	0.339811i	$-0.889637\pi$
$977$	−6.86164	−	32.2815i	−0.219523	−	1.03278i	0.720970	−	0.692966i	$-0.243696\pi$
$978$	13.3817	+	35.9124i	0.427900	+	1.14835i
$979$	−0.773603	−	0.272945i	−0.0247244	−	0.00872337i
$980$	12.1148	+	5.54352i	0.386992	+	0.177081i
$981$	−1.22176	+	9.77110i	−0.0390079	+	0.311967i
$982$	0.258922	+	2.46348i	0.00826254	+	0.0786128i
$983$	−35.0313	−	3.68193i	−1.11732	−	0.117435i	−0.472184	−	0.881500i	$-0.656534\pi$
$983$	−35.0313	−	3.68193i	−1.11732	−	0.117435i	−0.645140	+	0.764065i	$0.723201\pi$
$984$	3.53980	+	23.8665i	0.112845	+	0.760836i
$985$	5.62888	−	26.4818i	0.179351	−	0.843781i
$986$	−7.22513	−	5.24936i	−0.230095	−	0.167174i
$987$	24.6353	+	44.1840i	0.784150	+	1.40639i
$988$	0.246402	−	0.758346i	0.00783908	−	0.0241262i
$989$	5.45450	−	9.44747i	0.173443	−	0.300412i
$990$	−3.06074	−	50.9358i	−0.0972767	−	1.61885i
$991$	−28.5574	−	49.4629i	−0.907155	−	1.57124i	−0.817997	−	0.575222i	$-0.804916\pi$
$991$	−28.5574	−	49.4629i	−0.907155	−	1.57124i	−0.0891579	−	0.996018i	$-0.528418\pi$
$992$	−8.23780	−	9.14900i	−0.261550	−	0.290481i
$993$	2.42835	−	38.9929i	0.0770613	−	1.23740i
$994$	−3.31505	+	5.04782i	−0.105147	+	0.160107i
$995$	−5.08365	+	1.65178i	−0.161163	+	0.0523649i
$996$	−5.38193	+	4.27123i	−0.170533	+	0.135339i
$997$	31.6252	+	3.32395i	1.00158	+	0.105270i	0.591100	−	0.806599i	$-0.298694\pi$
$997$	31.6252	+	3.32395i	1.00158	+	0.105270i	0.410481	+	0.911869i	$0.365361\pi$
$998$	3.31249	+	1.47482i	0.104855	+	0.0466845i
$999$	−3.95512	−	16.7193i	−0.125134	−	0.528975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.be.a.2.20	yes	224
3.2	odd	2	inner	231.2.be.a.2.9	✓	224
7.4	even	3	inner	231.2.be.a.200.9	yes	224
11.6	odd	10	inner	231.2.be.a.149.20	yes	224
21.11	odd	6	inner	231.2.be.a.200.20	yes	224
33.17	even	10	inner	231.2.be.a.149.9	yes	224
77.39	odd	30	inner	231.2.be.a.116.9	yes	224
231.116	even	30	inner	231.2.be.a.116.20	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.be.a.2.9	✓	224	3.2	odd	2	inner
231.2.be.a.2.20	yes	224	1.1	even	1	trivial
231.2.be.a.116.9	yes	224	77.39	odd	30	inner
231.2.be.a.116.20	yes	224	231.116	even	30	inner
231.2.be.a.149.9	yes	224	33.17	even	10	inner
231.2.be.a.149.20	yes	224	11.6	odd	10	inner
231.2.be.a.200.9	yes	224	7.4	even	3	inner
231.2.be.a.200.20	yes	224	21.11	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.830242 + 0.922077i) q^{2} +(-1.55093 + 0.771117i) q^{3} +(0.0481326 - 0.457951i) q^{4} +(0.859357 - 4.04296i) q^{5} +(-1.99867 - 0.789862i) q^{6} +(-0.152025 + 2.64138i) q^{7} +(2.46985 - 1.79445i) q^{8} +(1.81076 - 2.39189i) q^{9} +O(q^{10})\)	\(q+(0.830242 + 0.922077i) q^{2} +(-1.55093 + 0.771117i) q^{3} +(0.0481326 - 0.457951i) q^{4} +(0.859357 - 4.04296i) q^{5} +(-1.99867 - 0.789862i) q^{6} +(-0.152025 + 2.64138i) q^{7} +(2.46985 - 1.79445i) q^{8} +(1.81076 - 2.39189i) q^{9} +(4.44139 - 2.56424i) q^{10} +(3.26039 - 0.608160i) q^{11} +(0.278483 + 0.747365i) q^{12} +(-1.08183 - 0.351507i) q^{13} +(-2.56177 + 2.05281i) q^{14} +(1.78479 + 6.93300i) q^{15} +(2.80437 + 0.596086i) q^{16} +(-0.724602 + 0.804752i) q^{17} +(3.70888 - 0.316191i) q^{18} +(-1.51398 + 0.159125i) q^{19} +(-1.81011 - 0.588141i) q^{20} +(-1.80103 - 4.21382i) q^{21} +(3.26768 + 2.50141i) q^{22} +(-1.17103 - 0.676097i) q^{23} +(-2.44683 + 4.68760i) q^{24} +(-11.0393 - 4.91500i) q^{25} +(-0.574062 - 1.28936i) q^{26} +(-0.963929 + 5.10596i) q^{27} +(1.20230 + 0.196756i) q^{28} +(5.37729 + 3.90683i) q^{29} +(-4.91095 + 7.40178i) q^{30} +(4.72526 - 1.00438i) q^{31} +(-1.27423 - 2.20704i) q^{32} +(-4.58767 + 3.45735i) q^{33} -1.34364 q^{34} +(10.5483 + 2.88452i) q^{35} +(-1.00821 - 0.944366i) q^{36} +(-3.02058 + 1.34485i) q^{37} +(-1.40369 - 1.26389i) q^{38} +(1.94889 - 0.289053i) q^{39} +(-5.13240 - 11.5275i) q^{40} +(3.69146 - 2.68200i) q^{41} +(2.39017 - 5.15918i) q^{42} +8.06763i q^{43} +(-0.121577 - 1.52237i) q^{44} +(-8.11423 - 9.37631i) q^{45} +(-0.348828 - 1.64111i) q^{46} +(-10.9787 + 1.15391i) q^{47} +(-4.80902 + 1.23801i) q^{48} +(-6.95378 - 0.803111i) q^{49} +(-4.63325 - 14.2597i) q^{50} +(0.503248 - 1.80687i) q^{51} +(-0.213044 + 0.478505i) q^{52} +(0.815733 + 3.83772i) q^{53} +(-5.50838 + 3.35037i) q^{54} +(0.343073 - 13.7042i) q^{55} +(4.36434 + 6.79660i) q^{56} +(2.22537 - 1.41424i) q^{57} +(0.862053 + 8.20188i) q^{58} +(-2.50803 - 0.263605i) q^{59} +(3.26088 - 0.483642i) q^{60} +(-1.24665 + 5.86504i) q^{61} +(4.84923 + 3.52317i) q^{62} +(6.04262 + 5.14653i) q^{63} +(2.74905 - 8.46071i) q^{64} +(-2.35080 + 4.07171i) q^{65} +(-6.99682 - 1.35974i) q^{66} +(5.62222 + 9.73797i) q^{67} +(0.333660 + 0.370567i) q^{68} +(2.33754 + 0.145574i) q^{69} +(6.09792 + 12.1212i) q^{70} +(1.74957 - 0.568471i) q^{71} +(0.180167 - 9.15692i) q^{72} +(0.873788 + 0.0918389i) q^{73} +(-3.74786 - 1.66866i) q^{74} +(20.9112 - 0.889750i) q^{75} +0.700986i q^{76} +(1.11072 + 8.70438i) q^{77} +(1.88458 + 1.55704i) q^{78} +(-8.24724 + 7.42585i) q^{79} +(4.81990 - 10.8257i) q^{80} +(-2.44231 - 8.66228i) q^{81} +(5.53782 + 1.17710i) q^{82} +(2.66212 + 8.19316i) q^{83} +(-2.01641 + 0.621962i) q^{84} +(2.63089 + 3.62110i) q^{85} +(-7.43897 + 6.69808i) q^{86} +(-11.3524 - 1.91270i) q^{87} +(6.96135 - 7.35266i) q^{88} +(-0.214205 - 0.123671i) q^{89} +(1.90890 - 15.2665i) q^{90} +(1.09293 - 2.80408i) q^{91} +(-0.365984 + 0.503734i) q^{92} +(-6.55404 + 5.20145i) q^{93} +(-10.1789 - 9.16516i) q^{94} +(-0.657709 + 6.25769i) q^{95} +(3.67813 + 2.44037i) q^{96} +(-3.43868 + 10.5832i) q^{97} +(-5.03279 - 7.07869i) q^{98} +(4.44912 - 8.89974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Introduction

L-functions

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