LMFDB - Embedded newform 231.2.ba.a.19.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("231.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.10
Character	$\chi$	$=$	231.19
Dual form			231.2.ba.a.73.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0732542 + 0.00769933i) q^{2} +(0.743145 + 0.669131i) q^{3} +(-1.95099 + 0.414695i) q^{4} +(-1.46180 - 3.28325i) q^{5} +(-0.0595904 - 0.0432949i) q^{6} +(0.114944 - 2.64325i) q^{7} +(0.279831 - 0.0909225i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.0732542 + 0.00769933i) q^{2} +(0.743145 + 0.669131i) q^{3} +(-1.95099 + 0.414695i) q^{4} +(-1.46180 - 3.28325i) q^{5} +(-0.0595904 - 0.0432949i) q^{6} +(0.114944 - 2.64325i) q^{7} +(0.279831 - 0.0909225i) q^{8} +(0.104528 + 0.994522i) q^{9} +(0.132362 + 0.229257i) q^{10} +(-0.420635 - 3.28984i) q^{11} +(-1.72735 - 0.997287i) q^{12} +(-1.90184 + 1.38177i) q^{13} +(0.0119312 + 0.194514i) q^{14} +(1.11060 - 3.41806i) q^{15} +(3.62447 - 1.61372i) q^{16} +(0.117194 - 1.11502i) q^{17} +(-0.0153143 - 0.0720481i) q^{18} +(-0.654706 - 0.139162i) q^{19} +(4.21350 + 5.79938i) q^{20} +(1.85410 - 1.88741i) q^{21} +(0.0561429 + 0.237756i) q^{22} +(2.18056 - 3.77684i) q^{23} +(0.268794 + 0.119675i) q^{24} +(-5.29723 + 5.88317i) q^{25} +(0.128679 - 0.115863i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(0.871891 + 5.20462i) q^{28} +(6.36199 + 2.06713i) q^{29} +(-0.0550391 + 0.258938i) q^{30} +(-2.35061 + 5.27956i) q^{31} +(-0.762707 + 0.440349i) q^{32} +(1.88874 - 2.72629i) q^{33} +0.0825825i q^{34} +(-8.84649 + 3.48651i) q^{35} +(-0.616357 - 1.89695i) q^{36} +(-4.31193 - 4.78888i) q^{37} +(0.0490314 + 0.00515341i) q^{38} +(-2.33793 - 0.245726i) q^{39} +(-0.707577 - 0.785844i) q^{40} +(-2.39158 - 7.36053i) q^{41} +(-0.121289 + 0.152536i) q^{42} +6.65108i q^{43} +(2.18494 + 6.24401i) q^{44} +(3.11246 - 1.79698i) q^{45} +(-0.130656 + 0.293459i) q^{46} +(0.140758 - 0.662214i) q^{47} +(3.77329 + 1.22602i) q^{48} +(-6.97358 - 0.607651i) q^{49} +(0.342748 - 0.471752i) q^{50} +(0.833188 - 0.750206i) q^{51} +(3.13746 - 3.48450i) q^{52} +(9.94892 + 4.42954i) q^{53} +(0.0368289 - 0.0637895i) q^{54} +(-10.1865 + 6.19013i) q^{55} +(-0.208166 - 0.750114i) q^{56} +(-0.393424 - 0.541501i) q^{57} +(-0.481958 - 0.102443i) q^{58} +(-0.786182 - 3.69870i) q^{59} +(-0.749305 + 7.12916i) q^{60} +(9.33840 - 4.15772i) q^{61} +(0.131543 - 0.404848i) q^{62} +(2.64079 - 0.161981i) q^{63} +(-6.36703 + 4.62592i) q^{64} +(7.31680 + 4.22436i) q^{65} +(-0.117368 + 0.214254i) q^{66} +(5.63993 + 9.76865i) q^{67} +(0.233751 + 2.22400i) q^{68} +(4.14768 - 1.34766i) q^{69} +(0.621199 - 0.323514i) q^{70} +(-2.58782 - 1.88016i) q^{71} +(0.119675 + 0.268794i) q^{72} +(8.17571 - 1.73780i) q^{73} +(0.352738 + 0.317607i) q^{74} +(-7.87322 + 0.827508i) q^{75} +1.33503 q^{76} +(-8.74424 + 0.733698i) q^{77} +0.173155 q^{78} +(15.2985 - 1.60793i) q^{79} +(-10.5965 - 9.54111i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(0.231864 + 0.520776i) q^{82} +(1.02509 + 0.744769i) q^{83} +(-2.83463 + 4.45120i) q^{84} +(-3.83221 + 1.24516i) q^{85} +(-0.0512088 - 0.487219i) q^{86} +(3.34469 + 5.79318i) q^{87} +(-0.416827 - 0.882354i) q^{88} +(-12.6678 - 7.31375i) q^{89} +(-0.214166 + 0.155600i) q^{90} +(3.43376 + 5.18588i) q^{91} +(-2.68801 + 8.27285i) q^{92} +(-5.27956 + 2.35061i) q^{93} +(-0.00521251 + 0.0495937i) q^{94} +(0.500143 + 2.35299i) q^{95} +(-0.861453 - 0.183107i) q^{96} +(-8.52486 - 11.7335i) q^{97} +(0.515522 - 0.00917883i) q^{98} +(3.22785 - 0.762213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9}+O(q^{10}) $ 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9	$ 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9} - 2 q^{11} + 12 q^{14} + 12 q^{15} + 40 q^{16} - 60 q^{17} - 10 q^{18} + 52 q^{22} - 24 q^{23} - 90 q^{24} - 20 q^{25} + 24 q^{26} + 30 q^{28} + 40 q^{29} - 18 q^{31} + 18 q^{33} - 80 q^{35} - 24 q^{36} - 8 q^{37} - 24 q^{38} - 90 q^{40} + 14 q^{42} - 82 q^{44} + 12 q^{45} + 70 q^{46} - 24 q^{47} - 94 q^{49} - 20 q^{51} + 4 q^{53} - 104 q^{56} - 32 q^{58} + 48 q^{59} + 30 q^{61} - 10 q^{63} - 48 q^{64} + 36 q^{66} - 40 q^{67} + 180 q^{68} + 146 q^{70} - 32 q^{71} + 10 q^{72} + 90 q^{73} + 40 q^{74} - 24 q^{75} - 72 q^{78} + 50 q^{79} + 228 q^{80} + 16 q^{81} + 168 q^{82} - 60 q^{84} - 20 q^{85} + 146 q^{86} + 16 q^{88} + 48 q^{91} - 204 q^{92} + 44 q^{93} + 10 q^{95} - 44 q^{99}+O(q^{100}) $ 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9 - 2 * q^11 + 12 * q^14 + 12 * q^15 + 40 * q^16 - 60 * q^17 - 10 * q^18 + 52 * q^22 - 24 * q^23 - 90 * q^24 - 20 * q^25 + 24 * q^26 + 30 * q^28 + 40 * q^29 - 18 * q^31 + 18 * q^33 - 80 * q^35 - 24 * q^36 - 8 * q^37 - 24 * q^38 - 90 * q^40 + 14 * q^42 - 82 * q^44 + 12 * q^45 + 70 * q^46 - 24 * q^47 - 94 * q^49 - 20 * q^51 + 4 * q^53 - 104 * q^56 - 32 * q^58 + 48 * q^59 + 30 * q^61 - 10 * q^63 - 48 * q^64 + 36 * q^66 - 40 * q^67 + 180 * q^68 + 146 * q^70 - 32 * q^71 + 10 * q^72 + 90 * q^73 + 40 * q^74 - 24 * q^75 - 72 * q^78 + 50 * q^79 + 228 * q^80 + 16 * q^81 + 168 * q^82 - 60 * q^84 - 20 * q^85 + 146 * q^86 + 16 * q^88 + 48 * q^91 - 204 * q^92 + 44 * q^93 + 10 * q^95 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.0732542	+	0.00769933i	−0.0517986	+	0.00544425i	−0.130392	−	0.991462i	$-0.541624\pi$
$2$	−0.0732542	+	0.00769933i	−0.0517986	+	0.00544425i	0.0785937	+	0.996907i	$0.474957\pi$
$3$	0.743145	+	0.669131i	0.429055	+	0.386323i
$3$	0.743145	+	0.669131i	0.429055	+	0.386323i
$4$	−1.95099	+	0.414695i	−0.975494	+	0.207348i
$5$	−1.46180	−	3.28325i	−0.653736	−	1.46831i	−0.870539	−	0.492099i	$-0.836230\pi$
$5$	−1.46180	−	3.28325i	−0.653736	−	1.46831i	0.216804	−	0.976215i	$-0.430437\pi$
$6$	−0.0595904	−	0.0432949i	−0.0243277	−	0.0176751i
$7$	0.114944	−	2.64325i	0.0434447	−	0.999056i
$7$	0.114944	−	2.64325i	0.0434447	−	0.999056i
$8$	0.279831	−	0.0909225i	0.0989351	−	0.0321460i
$9$	0.104528	+	0.994522i	0.0348428	+	0.331507i
$10$	0.132362	+	0.229257i	0.0418564	+	0.0724975i
$11$	−0.420635	−	3.28984i	−0.126826	−	0.991925i
$11$	−0.420635	−	3.28984i	−0.126826	−	0.991925i
$12$	−1.72735	−	0.997287i	−0.498644	−	0.287892i
$13$	−1.90184	+	1.38177i	−0.527476	+	0.383234i	−0.819413	−	0.573204i	$-0.805700\pi$
$13$	−1.90184	+	1.38177i	−0.527476	+	0.383234i	0.291937	+	0.956438i	$0.405700\pi$
$14$	0.0119312	+	0.194514i	0.00318874	+	0.0519862i
$15$	1.11060	−	3.41806i	0.286755	−	0.882540i
$16$	3.62447	−	1.61372i	0.906118	−	0.403430i
$17$	0.117194	−	1.11502i	0.0284236	−	0.270433i	−0.971075	−	0.238774i	$-0.923254\pi$
$17$	0.117194	−	1.11502i	0.0284236	−	0.270433i	0.999499	−	0.0316586i	$-0.0100789\pi$
$18$	−0.0153143	−	0.0720481i	−0.00360962	−	0.0169819i
$19$	−0.654706	−	0.139162i	−0.150200	−	0.0319259i	0.132198	−	0.991223i	$-0.457796\pi$
$19$	−0.654706	−	0.139162i	−0.150200	−	0.0319259i	−0.282398	+	0.959297i	$0.591130\pi$
$20$	4.21350	+	5.79938i	0.942167	+	1.29678i
$21$	1.85410	−	1.88741i	0.404598	−	0.411866i
$22$	0.0561429	+	0.237756i	0.0119697	+	0.0506898i
$23$	2.18056	−	3.77684i	0.454679	−	0.787527i	−0.543991	−	0.839091i	$-0.683087\pi$
$23$	2.18056	−	3.77684i	0.454679	−	0.787527i	0.998670	+	0.0515645i	$0.0164208\pi$
$24$	0.268794	+	0.119675i	0.0548673	+	0.0244285i
$25$	−5.29723	+	5.88317i	−1.05945	+	1.17663i
$26$	0.128679	−	0.115863i	0.0252361	−	0.0227227i
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	0.871891	+	5.20462i	0.164772	+	0.983581i
$29$	6.36199	+	2.06713i	1.18139	+	0.383857i	0.832883	−	0.553449i	$-0.186689\pi$
$29$	6.36199	+	2.06713i	1.18139	+	0.383857i	0.348508	+	0.937306i	$0.386689\pi$
$30$	−0.0550391	+	0.258938i	−0.0100487	+	0.0472755i
$31$	−2.35061	+	5.27956i	−0.422182	+	0.948237i	0.569791	+	0.821789i	$0.307024\pi$
$31$	−2.35061	+	5.27956i	−0.422182	+	0.948237i	−0.991973	+	0.126447i	$0.959643\pi$
$32$	−0.762707	+	0.440349i	−0.134829	+	0.0778434i
$33$	1.88874	−	2.72629i	0.328788	−	0.474586i
$34$			0.0825825i			0.0141628i
$35$	−8.84649	+	3.48651i	−1.49533	+	0.589328i
$36$	−0.616357	−	1.89695i	−0.102726	−	0.316159i
$37$	−4.31193	−	4.78888i	−0.708877	−	0.787288i	0.275886	−	0.961190i	$-0.411029\pi$
$37$	−4.31193	−	4.78888i	−0.708877	−	0.787288i	−0.984763	+	0.173903i	$0.944362\pi$
$38$	0.0490314	+	0.00515341i	0.00795394	+	0.000835993i
$39$	−2.33793	−	0.245726i	−0.374368	−	0.0393477i
$40$	−0.707577	−	0.785844i	−0.111878	−	0.124253i
$41$	−2.39158	−	7.36053i	−0.373502	−	1.14952i	−0.944484	−	0.328558i	$-0.893437\pi$
$41$	−2.39158	−	7.36053i	−0.373502	−	1.14952i	0.570982	−	0.820963i	$-0.306563\pi$
$42$	−0.121289	+	0.152536i	−0.0187153	+	0.0235368i
$43$			6.65108i			1.01428i	0.861864	+	0.507140i	$0.169297\pi$
$43$			6.65108i			1.01428i	−0.861864	+	0.507140i	$0.830703\pi$
$44$	2.18494	+	6.24401i	0.329392	+	0.941320i
$45$	3.11246	−	1.79698i	0.463979	−	0.267878i
$46$	−0.130656	+	0.293459i	−0.0192642	+	0.0432681i
$47$	0.140758	−	0.662214i	0.0205316	−	0.0965938i	−0.966689	−	0.255955i	$-0.917610\pi$
$47$	0.140758	−	0.662214i	0.0205316	−	0.0965938i	0.987220	+	0.159361i	$0.0509434\pi$
$48$	3.77329	+	1.22602i	0.544628	+	0.176960i
$49$	−6.97358	−	0.607651i	−0.996225	−	0.0868073i
$50$	0.342748	−	0.471752i	0.0484719	−	0.0667158i
$51$	0.833188	−	0.750206i	0.116670	−	0.105050i
$52$	3.13746	−	3.48450i	0.435087	−	0.483213i
$53$	9.94892	+	4.42954i	1.36659	+	0.608445i	0.953264	−	0.302139i	$-0.0977006\pi$
$53$	9.94892	+	4.42954i	1.36659	+	0.608445i	0.413325	+	0.910583i	$0.364367\pi$
$54$	0.0368289	−	0.0637895i	0.00501177	−	0.00868065i
$55$	−10.1865	+	6.19013i	−1.37355	+	0.834677i
$56$	−0.208166	−	0.750114i	−0.0278174	−	0.100238i
$57$	−0.393424	−	0.541501i	−0.0521102	−	0.0717236i
$58$	−0.481958	−	0.102443i	−0.0632842	−	0.0134515i
$59$	−0.786182	−	3.69870i	−0.102352	−	0.481529i	−0.999229	−	0.0392496i	$-0.987503\pi$
$59$	−0.786182	−	3.69870i	−0.102352	−	0.481529i	0.896877	−	0.442280i	$-0.145830\pi$
$60$	−0.749305	+	7.12916i	−0.0967349	+	0.920371i
$61$	9.33840	−	4.15772i	1.19566	−	0.532342i	0.290279	−	0.956942i	$-0.406252\pi$
$61$	9.33840	−	4.15772i	1.19566	−	0.532342i	0.905381	+	0.424600i	$0.139585\pi$
$62$	0.131543	−	0.404848i	0.0167060	−	0.0514158i
$63$	2.64079	−	0.161981i	0.332708	−	0.0204077i
$64$	−6.36703	+	4.62592i	−0.795879	+	0.578240i
$65$	7.31680	+	4.22436i	0.907537	+	0.523967i
$66$	−0.117368	+	0.214254i	−0.0144470	+	0.0263729i
$67$	5.63993	+	9.76865i	0.689027	+	1.19343i	0.972153	+	0.234347i	$0.0752953\pi$
$67$	5.63993	+	9.76865i	0.689027	+	1.19343i	−0.283126	+	0.959083i	$0.591371\pi$
$68$	0.233751	+	2.22400i	0.0283465	+	0.269699i
$69$	4.14768	−	1.34766i	0.499322	−	0.162239i
$70$	0.621199	−	0.323514i	0.0742475	−	0.0386673i
$71$	−2.58782	−	1.88016i	−0.307117	−	0.223134i	0.423541	−	0.905877i	$-0.360787\pi$
$71$	−2.58782	−	1.88016i	−0.307117	−	0.223134i	−0.730659	+	0.682743i	$0.760787\pi$
$72$	0.119675	+	0.268794i	0.0141038	+	0.0316776i
$73$	8.17571	−	1.73780i	0.956894	−	0.203394i	0.297105	−	0.954845i	$-0.403979\pi$
$73$	8.17571	−	1.73780i	0.956894	−	0.203394i	0.659789	+	0.751451i	$0.270646\pi$
$74$	0.352738	+	0.317607i	0.0410050	+	0.0369211i
$75$	−7.87322	+	0.827508i	−0.909121	+	0.0955524i
$76$	1.33503			0.153139
$77$	−8.74424	+	0.733698i	−0.996498	+	0.0836127i
$78$	0.173155			0.0196059
$79$	15.2985	−	1.60793i	1.72121	−	0.180907i	0.808220	−	0.588881i	$-0.200431\pi$
$79$	15.2985	−	1.60793i	1.72121	−	0.180907i	0.912993	+	0.407974i	$0.133765\pi$
$80$	−10.5965	−	9.54111i	−1.18472	−	1.06673i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	0.231864	+	0.520776i	0.0256051	+	0.0575101i
$83$	1.02509	+	0.744769i	0.112518	+	0.0817490i	0.642621	−	0.766184i	$-0.277847\pi$
$83$	1.02509	+	0.744769i	0.112518	+	0.0817490i	−0.530103	+	0.847933i	$0.677847\pi$
$84$	−2.83463	+	4.45120i	−0.309284	+	0.485665i
$85$	−3.83221	+	1.24516i	−0.415662	+	0.135057i
$86$	−0.0512088	−	0.487219i	−0.00552199	−	0.0525382i
$87$	3.34469	+	5.79318i	0.358589	+	0.621094i
$88$	−0.416827	−	0.882354i	−0.0444339	−	0.0940592i
$89$	−12.6678	−	7.31375i	−1.34278	−	0.775256i	−0.355567	−	0.934651i	$-0.615712\pi$
$89$	−12.6678	−	7.31375i	−1.34278	−	0.775256i	−0.987215	+	0.159395i	$0.949046\pi$
$90$	−0.214166	+	0.155600i	−0.0225750	+	0.0164017i
$91$	3.43376	+	5.18588i	0.359956	+	0.543627i
$92$	−2.68801	+	8.27285i	−0.280245	+	0.862504i
$93$	−5.27956	+	2.35061i	−0.547465	+	0.243747i
$94$	−0.00521251	+	0.0495937i	−0.000537629	+	0.00511520i
$95$	0.500143	+	2.35299i	0.0513136	+	0.241412i
$96$	−0.861453	−	0.183107i	−0.0879216	−	0.0186883i
$97$	−8.52486	−	11.7335i	−0.865568	−	1.19135i	−0.980213	−	0.197946i	$-0.936573\pi$
$97$	−8.52486	−	11.7335i	−0.865568	−	1.19135i	0.114645	−	0.993407i	$-0.463427\pi$
$98$	0.515522	−	0.00917883i	0.0520756	−	0.000927202i
$99$	3.22785	−	0.762213i	0.324411	−	0.0766053i
$100$	7.89511	−	13.6747i	0.789511	−	1.36747i
$101$	12.7394	+	5.67197i	1.26762	+	0.564382i	0.926733	−	0.375721i	$-0.122605\pi$
$101$	12.7394	+	5.67197i	1.26762	+	0.564382i	0.340890	+	0.940103i	$0.389272\pi$
$102$	−0.0552585	+	0.0613707i	−0.00547140	+	0.00607661i
$103$	2.48785	−	2.24007i	0.245135	−	0.220721i	−0.537399	−	0.843328i	$-0.680593\pi$
$103$	2.48785	−	2.24007i	0.245135	−	0.220721i	0.782535	+	0.622607i	$0.213927\pi$
$104$	−0.406560	+	0.559581i	−0.0398665	+	0.0548715i
$105$	−8.90715	−	3.32847i	−0.869249	−	0.324826i
$106$	−0.762905	−	0.247883i	−0.0740999	−	0.0240765i
$107$	2.51976	−	11.8545i	0.243594	−	1.14602i	−0.670940	−	0.741511i	$-0.734109\pi$
$107$	2.51976	−	11.8545i	0.243594	−	1.14602i	0.914534	−	0.404508i	$-0.132557\pi$
$108$	0.811267	−	1.82213i	0.0780642	−	0.175335i
$109$	17.4986	−	10.1028i	1.67606	−	0.967672i	0.711923	−	0.702258i	$-0.247825\pi$
$109$	17.4986	−	10.1028i	1.67606	−	0.967672i	0.964134	−	0.265414i	$-0.0855087\pi$
$110$	0.698544	−	0.531883i	0.0666036	−	0.0507130i
$111$		−	6.44408i		−	0.611645i
$112$	−3.84886	−	9.76588i	−0.363683	−	0.922789i
$113$	−0.960179	−	2.95513i	−0.0903260	−	0.277995i	0.895681	−	0.444696i	$-0.146688\pi$
$113$	−0.960179	−	2.95513i	−0.0903260	−	0.277995i	−0.986007	+	0.166701i	$0.946688\pi$
$114$	0.0329891	+	0.0366381i	0.00308972	+	0.00343148i
$115$	−15.5879	−	1.63835i	−1.45358	−	0.152777i
$116$	−13.2694	−	1.39467i	−1.23203	−	0.129492i
$117$	−1.57300	−	1.74699i	−0.145424	−	0.161509i
$118$	0.0860686	+	0.264892i	0.00792326	+	0.0243853i
$119$	−2.93382	−	0.437937i	−0.268943	−	0.0401457i
$120$		−	1.05746i		−	0.0965322i
$121$	−10.6461	+	2.76765i	−0.967830	+	0.251604i
$122$	−0.652066	+	0.376470i	−0.0590352	+	0.0340840i
$123$	3.14786	−	7.07022i	0.283833	−	0.637500i
$124$	2.39661	−	11.2751i	0.215222	−	1.01254i
$125$	9.96907	+	3.23915i	0.891660	+	0.289718i
$126$	−0.192202	+	0.0321981i	−0.0171227	+	0.00286843i
$127$	1.09519	−	1.50741i	0.0971828	−	0.133761i	−0.757656	−	0.652654i	$-0.773656\pi$
$127$	1.09519	−	1.50741i	0.0971828	−	0.133761i	0.854839	+	0.518893i	$0.173656\pi$
$128$	1.73977	−	1.56649i	0.153775	−	0.138460i
$129$	−4.45044	+	4.94271i	−0.391839	+	0.435182i
$130$	−0.568511	−	0.253118i	−0.0498617	−	0.0221999i
$131$	−7.71707	+	13.3663i	−0.674243	+	1.16782i	0.302446	+	0.953166i	$0.402197\pi$
$131$	−7.71707	+	13.3663i	−0.674243	+	1.16782i	−0.976690	+	0.214657i	$0.931137\pi$
$132$	−2.55433	+	6.10221i	−0.222326	+	0.531129i
$133$	−0.443095	+	1.71456i	−0.0384212	+	0.148671i
$134$	−0.488361	−	0.672171i	−0.0421879	−	0.0580667i
$135$	3.51543	+	0.747227i	0.302560	+	0.0643111i
$136$	−0.0685863	−	0.322673i	−0.00588123	−	0.0276690i
$137$	−0.236803	+	2.25303i	−0.0202315	+	0.192490i	−0.999970	−	0.00779305i	$-0.997519\pi$
$137$	−0.236803	+	2.25303i	−0.0202315	+	0.192490i	0.979738	+	0.200283i	$0.0641860\pi$
$138$	−0.293459	+	0.130656i	−0.0249809	+	0.0111222i
$139$	2.36809	−	7.28824i	0.200859	−	0.618181i	−0.798999	−	0.601332i	$-0.794637\pi$
$139$	2.36809	−	7.28824i	0.200859	−	0.618181i	0.999858	−	0.0168483i	$-0.00536324\pi$
$140$	15.8136	−	10.4707i	1.33649	−	0.884939i
$141$	0.547711	−	0.397935i	0.0461256	−	0.0335122i
$142$	0.204044	+	0.117805i	0.0171230	+	0.00988599i
$143$	5.34578	+	5.67554i	0.447037	+	0.474613i
$144$	1.98374	+	3.43594i	0.165312	+	0.286328i
$145$	−2.51301	−	23.9097i	−0.208694	−	1.98559i
$146$	−0.585525	+	0.190249i	−0.0484584	+	0.0157451i
$147$	−4.77578	−	5.11781i	−0.393900	−	0.422110i
$148$	10.3985	+	7.55492i	0.854748	+	0.621011i
$149$	3.33880	+	7.49907i	0.273525	+	0.614348i	0.997117	−	0.0758804i	$-0.0241767\pi$
$149$	3.33880	+	7.49907i	0.273525	+	0.614348i	−0.723592	+	0.690228i	$0.757510\pi$
$150$	0.570375	−	0.121237i	0.0465709	−	0.00989896i
$151$	7.39883	+	6.66193i	0.602108	+	0.542140i	0.912819	−	0.408364i	$-0.133901\pi$
$151$	7.39883	+	6.66193i	0.602108	+	0.542140i	−0.310711	+	0.950504i	$0.600567\pi$
$152$	−0.195860	+	0.0205857i	−0.0158863	+	0.00166972i
$153$	1.12116			0.0906408
$154$	0.634903	−	0.121071i	0.0511620	−	0.00975620i
$155$	20.7702			1.66830
$156$	4.66317	−	0.490119i	0.373353	−	0.0392409i
$157$	−11.4334	−	10.2947i	−0.912484	−	0.821604i	0.0719413	−	0.997409i	$-0.477081\pi$
$157$	−11.4334	−	10.2947i	−0.912484	−	0.821604i	−0.984425	+	0.175805i	$0.943747\pi$
$158$	−1.10830	+	0.235576i	−0.0881715	+	0.0187414i
$159$	4.42954	+	9.94892i	0.351286	+	0.789001i
$160$	2.56070	+	1.86046i	0.202441	+	0.147082i
$161$	−9.73252	−	6.19790i	−0.767030	−	0.488463i
$162$	0.0700527	−	0.0227615i	0.00550386	−	0.00178831i
$163$	1.15847	+	11.0221i	0.0907382	+	0.863316i	0.941330	+	0.337489i	$0.109578\pi$
$163$	1.15847	+	11.0221i	0.0907382	+	0.863316i	−0.850591	+	0.525827i	$0.823756\pi$
$164$	7.71832	+	13.3685i	0.602700	+	1.04391i
$165$	−11.7120	−	2.21593i	−0.911782	−	0.172510i
$166$	−0.0808261	−	0.0466650i	−0.00627332	−	0.00362191i
$167$	−10.6028	+	7.70342i	−0.820473	+	0.596108i	−0.916848	−	0.399237i	$-0.869275\pi$
$167$	−10.6028	+	7.70342i	−0.820473	+	0.596108i	0.0963752	+	0.995345i	$0.469275\pi$
$168$	0.347227	−	0.696734i	0.0267891	−	0.0537542i
$169$	−2.30950	+	7.10792i	−0.177654	+	0.546763i
$170$	0.271139	−	0.120719i	0.0207954	−	0.00925871i
$171$	0.0699643	−	0.665665i	0.00535030	−	0.0509047i
$172$	−2.75817	−	12.9762i	−0.210309	−	0.989424i
$173$	−8.21125	−	1.74535i	−0.624290	−	0.132697i	−0.115104	−	0.993353i	$-0.536720\pi$
$173$	−8.21125	−	1.74535i	−0.624290	−	0.132697i	−0.509186	+	0.860657i	$0.670053\pi$
$174$	−0.289617	−	0.398623i	−0.0219558	−	0.0302195i
$175$	14.9418	+	14.6781i	1.12950	+	1.10956i
$176$	−6.83346	−	11.2452i	−0.515091	−	0.847635i
$177$	1.89066	−	3.27472i	0.142111	−	0.246143i
$178$	0.984279	+	0.438229i	0.0737749	+	0.0328467i
$179$	−10.4174	+	11.5697i	−0.778631	+	0.864758i	−0.993727	−	0.111835i	$-0.964327\pi$
$179$	−10.4174	+	11.5697i	−0.778631	+	0.864758i	0.215095	+	0.976593i	$0.430994\pi$
$180$	−5.32718	+	4.79662i	−0.397065	+	0.357519i
$181$	−7.41574	+	10.2069i	−0.551208	+	0.758672i	−0.990175	−	0.139830i	$-0.955344\pi$
$181$	−7.41574	+	10.2069i	−0.551208	+	0.758672i	0.438968	+	0.898503i	$0.355344\pi$
$182$	−0.291465	−	0.353450i	−0.0216048	−	0.0261994i
$183$	9.72184	+	3.15882i	0.718659	+	0.233507i
$184$	0.266788	−	1.25514i	0.0196679	−	0.0925301i
$185$	−9.41994	+	21.1575i	−0.692568	+	1.55553i
$186$	0.368652	−	0.212841i	0.0270309	−	0.0156063i
$187$	−3.71755	+	0.0834692i	−0.271854	+	0.00610387i
$188$			1.35034i			0.0984839i
$189$	2.07087	+	1.64666i	0.150634	+	0.119777i
$190$	−0.0547540	−	0.168516i	−0.00397228	−	0.0122254i
$191$	−4.07996	−	4.53126i	−0.295216	−	0.327870i	0.577230	−	0.816582i	$-0.304134\pi$
$191$	−4.07996	−	4.53126i	−0.295216	−	0.327870i	−0.872445	+	0.488711i	$0.837467\pi$
$192$	−7.82697	−	0.822648i	−0.564863	−	0.0593695i
$193$	−8.51017	−	0.894455i	−0.612576	−	0.0643843i	−0.206840	−	0.978375i	$-0.566318\pi$
$193$	−8.51017	−	0.894455i	−0.612576	−	0.0643843i	−0.405736	+	0.913990i	$0.632985\pi$
$194$	0.714822	+	0.793890i	0.0513212	+	0.0569980i
$195$	2.61080	+	8.03520i	0.186963	+	0.575413i
$196$	13.8574	−	1.70639i	0.989811	−	0.121885i
$197$		−	27.2493i		−	1.94143i	−0.240236	−	0.970715i	$-0.577225\pi$
$197$		−	27.2493i		−	1.94143i	0.240236	−	0.970715i	$-0.422775\pi$
$198$	−0.230585	+	0.0806876i	−0.0163870	+	0.00573422i
$199$	1.40776	−	0.812768i	0.0997931	−	0.0576156i	−0.449273	−	0.893395i	$-0.648317\pi$
$199$	1.40776	−	0.812768i	0.0997931	−	0.0576156i	0.549066	+	0.835779i	$0.314984\pi$
$200$	−0.947414	+	2.12793i	−0.0669923	+	0.150467i
$201$	−2.34521	+	11.0334i	−0.165419	+	0.778234i
$202$	−0.976889	−	0.317410i	−0.0687337	−	0.0223329i
$203$	6.19523	−	16.5787i	0.434820	−	1.16360i
$204$	−1.31443	+	1.80916i	−0.0920287	+	0.126667i
$205$	−20.6704	+	18.6118i	−1.44369	+	1.29990i
$206$	−0.164999	+	0.183250i	−0.0114960	+	0.0127676i
$207$	3.98409	+	1.77383i	0.276913	+	0.123290i
$208$	−4.66338	+	8.07722i	−0.323347	+	0.560054i
$209$	−0.182429	+	2.21241i	−0.0126189	+	0.153036i
$210$	0.678114	+	0.175246i	0.0467943	+	0.0120931i
$211$	10.3303	+	14.2185i	0.711170	+	0.978842i	0.999771	+	0.0213921i	$0.00680984\pi$
$211$	10.3303	+	14.2185i	0.711170	+	0.978842i	−0.288601	+	0.957449i	$0.593190\pi$
$212$	−21.2471	−	4.51622i	−1.45926	−	0.310175i
$213$	−0.665051	−	3.12882i	−0.0455685	−	0.214383i
$214$	−0.0933109	+	0.887794i	−0.00637860	+	0.0606884i
$215$	21.8371	−	9.72252i	1.48928	−	0.663071i
$216$	−0.0909225	+	0.279831i	−0.00618649	+	0.0190401i
$217$	13.6850	+	6.82011i	0.929000	+	0.462979i
$218$	−1.20406	+	0.874799i	−0.0815491	+	0.0592489i
$219$	7.23855	+	4.17918i	0.489136	+	0.282403i
$220$	17.3067	−	16.3012i	1.16682	−	1.09902i
$221$	1.31782	+	2.28253i	0.0886462	+	0.153540i
$222$	0.0496151	+	0.472056i	0.00332995	+	0.0316823i
$223$	7.31557	−	2.37697i	0.489887	−	0.159174i	−0.0536488	−	0.998560i	$-0.517085\pi$
$223$	7.31557	−	2.37697i	0.489887	−	0.159174i	0.543536	+	0.839386i	$0.317085\pi$
$224$	1.07629	+	2.06664i	0.0719123	+	0.138083i
$225$	−6.40465	−	4.65325i	−0.426977	−	0.310217i
$226$	0.0930897	+	0.209083i	0.00619223	+	0.0139080i
$227$	8.31664	−	1.76776i	0.551995	−	0.117330i	0.0765339	−	0.997067i	$-0.475615\pi$
$227$	8.31664	−	1.76776i	0.551995	−	0.117330i	0.475461	+	0.879737i	$0.342281\pi$
$228$	0.992123	+	0.893311i	0.0657049	+	0.0591610i
$229$	21.6495	−	2.27546i	1.43064	−	0.150366i	0.642700	−	0.766118i	$-0.277814\pi$
$229$	21.6495	−	2.27546i	1.43064	−	0.150366i	0.787940	+	0.615751i	$0.211147\pi$
$230$	1.15449			0.0761249
$231$	−6.98917	−	5.30579i	−0.459854	−	0.349096i
$232$	1.96823			0.129220
$233$	−20.6972	+	2.17536i	−1.35592	+	0.142513i	−0.754436	−	0.656373i	$-0.772090\pi$
$233$	−20.6972	+	2.17536i	−1.35592	+	0.142513i	−0.601482	+	0.798886i	$0.705423\pi$
$234$	0.128679	+	0.115863i	0.00841203	+	0.00757422i
$235$	−2.37997	+	0.505879i	−0.155252	+	0.0329999i
$236$	3.06766	+	6.89009i	0.199688	+	0.448506i
$237$	12.4449	+	9.04175i	0.808383	+	0.587325i
$238$	0.218286	+	0.00949234i	0.0141494	+	0.000615297i
$239$	1.93606	−	0.629065i	0.125233	−	0.0406908i	−0.245730	−	0.969338i	$-0.579028\pi$
$239$	1.93606	−	0.629065i	0.125233	−	0.0406908i	0.370963	+	0.928648i	$0.379028\pi$
$240$	−1.49047	−	14.1809i	−0.0962093	−	0.915371i
$241$	−1.05310	−	1.82403i	−0.0678364	−	0.117496i	0.830112	−	0.557596i	$-0.188276\pi$
$241$	−1.05310	−	1.82403i	−0.0678364	−	0.117496i	−0.897949	+	0.440100i	$0.854943\pi$
$242$	0.758565	−	0.284710i	0.0487624	−	0.0183018i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−16.4949	+	11.9843i	−1.05598	+	0.767214i
$245$	8.19888	+	23.7843i	0.523807	+	1.51952i
$246$	−0.176158	+	0.542160i	−0.0112314	+	0.0345668i
$247$	1.43744	−	0.639988i	0.0914619	−	0.0407215i
$248$	−0.177742	+	1.69111i	−0.0112866	+	0.107385i
$249$	0.263440	+	1.23939i	0.0166948	+	0.0785430i
$250$	−0.755216	−	0.160526i	−0.0477640	−	0.0101526i
$251$	8.25692	+	11.3647i	0.521172	+	0.717332i	0.985753	−	0.168199i	$-0.0537950\pi$
$251$	8.25692	+	11.3647i	0.521172	+	0.717332i	−0.464581	+	0.885531i	$0.653795\pi$
$252$	−5.08497	+	1.41115i	−0.320323	+	0.0888938i
$253$	−13.3424	−	5.58503i	−0.838832	−	0.351128i
$254$	−0.0686216	+	0.118856i	−0.00430570	+	0.00745770i
$255$	−3.68106	−	1.63892i	−0.230517	−	0.102633i
$256$	10.4168	−	11.5691i	0.651053	−	0.723067i
$257$	−1.92468	+	1.73299i	−0.120058	+	0.108101i	−0.726973	−	0.686666i	$-0.759074\pi$
$257$	−1.92468	+	1.73299i	−0.120058	+	0.108101i	0.606915	+	0.794767i	$0.292407\pi$
$258$	0.287958	−	0.396340i	0.0179275	−	0.0246751i
$259$	−13.1539	+	10.8471i	−0.817341	+	0.674004i
$260$	−16.0268	−	5.20743i	−0.993941	−	0.322951i
$261$	−1.39080	+	6.54321i	−0.0860885	+	0.405014i
$262$	0.462396	−	1.03856i	0.0285669	−	0.0641623i
$263$	−6.73948	+	3.89104i	−0.415574	+	0.239932i	−0.693182	−	0.720763i	$-0.743792\pi$
$263$	−6.73948	+	3.89104i	−0.415574	+	0.239932i	0.277608	+	0.960695i	$0.410458\pi$
$264$	0.280647	−	0.934628i	0.0172726	−	0.0575224i
$265$		−	39.1399i		−	2.40434i
$266$	0.0192576	−	0.129010i	0.00118076	−	0.00791012i
$267$	−4.52014	−	13.9116i	−0.276628	−	0.851374i
$268$	−15.0544	−	16.7197i	−0.919597	−	1.02132i
$269$	16.9795	+	1.78461i	1.03526	+	0.108810i	0.606882	−	0.794792i	$-0.292420\pi$
$269$	16.9795	+	1.78461i	1.03526	+	0.108810i	0.428374	+	0.903602i	$0.359087\pi$
$270$	−0.263273	−	0.0276711i	−0.0160223	−	0.00168401i
$271$	19.4686	+	21.6221i	1.18263	+	1.31345i	0.939135	+	0.343548i	$0.111629\pi$
$271$	19.4686	+	21.6221i	1.18263	+	1.31345i	0.243500	+	0.969901i	$0.421704\pi$
$272$	−1.37457	−	4.23048i	−0.0833454	−	0.256511i
$273$	−0.918247	+	6.15149i	−0.0555748	+	0.372305i
$274$		−	0.166867i		−	0.0100808i
$275$	21.5829	+	14.9524i	1.30150	+	0.901663i
$276$	−7.53320	+	4.34929i	−0.453445	+	0.261797i
$277$	−2.68784	+	6.03698i	−0.161497	+	0.362727i	−0.976110	−	0.217277i	$-0.930282\pi$
$277$	−2.68784	+	6.03698i	−0.161497	+	0.362727i	0.814613	+	0.580004i	$0.196949\pi$
$278$	−0.117358	+	0.552127i	−0.00703868	+	0.0331144i
$279$	−5.49634	−	1.78587i	−0.329057	−	0.106917i
$280$	−2.15852	+	1.77998i	−0.128996	+	0.106374i
$281$	−2.44359	+	3.36331i	−0.145772	+	0.200638i	−0.875659	−	0.482930i	$-0.839573\pi$
$281$	−2.44359	+	3.36331i	−0.145772	+	0.200638i	0.729887	+	0.683568i	$0.239573\pi$
$282$	−0.0370583	+	0.0333675i	−0.00220679	+	0.00198700i
$283$	−5.27358	+	5.85690i	−0.313482	+	0.348157i	−0.879209	−	0.476435i	$-0.841929\pi$
$283$	−5.27358	+	5.85690i	−0.313482	+	0.348157i	0.565728	+	0.824592i	$0.308595\pi$
$284$	5.82849	+	2.59501i	0.345857	+	0.153986i
$285$	−1.20278	+	2.08327i	−0.0712464	+	0.123402i
$286$	−0.435299	−	0.374598i	−0.0257398	−	0.0221505i
$287$	−19.7306	+	5.47550i	−1.16466	+	0.323209i
$288$	−0.517661	−	0.712500i	−0.0305035	−	0.0419844i
$289$	15.3990	+	3.27315i	0.905822	+	0.192538i
$290$	0.368178	+	1.73214i	0.0216201	+	0.101715i
$291$	1.51601	−	14.4239i	0.0888703	−	0.845544i
$292$	−15.2301	+	6.78086i	−0.891272	+	0.396820i
$293$	4.28631	−	13.1919i	0.250409	−	0.770679i	−0.744291	−	0.667856i	$-0.767212\pi$
$293$	4.28631	−	13.1919i	0.250409	−	0.770679i	0.994700	−	0.102823i	$-0.0327876\pi$
$294$	0.389250	+	0.338131i	0.0227015	+	0.0197202i
$295$	−10.9945	+	7.98797i	−0.640125	+	0.465078i
$296$	−1.64203	−	0.948025i	−0.0954409	−	0.0551028i
$297$	2.90878	+	1.59342i	0.168785	+	0.0924596i
$298$	−0.302319	−	0.523632i	−0.0175129	−	0.0303332i
$299$	1.07164	+	10.1960i	0.0619747	+	0.589650i
$300$	15.0174	−	4.87944i	0.867029	−	0.281715i
$301$	17.5805	+	0.764500i	1.01332	+	0.0440651i
$302$	−0.593288	−	0.431049i	−0.0341399	−	0.0248041i
$303$	5.67197	+	12.7394i	0.325846	+	0.731862i
$304$	−2.59753	+	0.552122i	−0.148979	+	0.0316664i
$305$	−27.3017	−	24.5826i	−1.56329	−	1.40759i
$306$	−0.0821301	+	0.00863222i	−0.00469506	+	0.000493471i
$307$	−24.9100			−1.42169			−0.710844	−	0.703350i	$-0.751687\pi$
$307$	−24.9100			−1.42169			−0.710844	+	0.703350i	$0.751687\pi$
$308$	16.7556	−	5.05763i	0.954741	−	0.288185i
$309$	3.34773			0.190446
$310$	−1.52151	+	0.159917i	−0.0864158	+	0.00908267i
$311$	−13.4303	−	12.0927i	−0.761565	−	0.685716i	0.193834	−	0.981034i	$-0.437908\pi$
$311$	−13.4303	−	12.0927i	−0.761565	−	0.685716i	−0.955399	+	0.295318i	$0.904574\pi$
$312$	−0.676566	+	0.143809i	−0.0383030	+	0.00814155i
$313$	−0.618991	−	1.39028i	−0.0349875	−	0.0785831i	0.895206	−	0.445652i	$-0.147028\pi$
$313$	−0.618991	−	1.39028i	−0.0349875	−	0.0785831i	−0.930194	+	0.367069i	$0.880361\pi$
$314$	0.916806	+	0.666099i	0.0517384	+	0.0375901i
$315$	−4.39212	−	8.43358i	−0.247468	−	0.475179i
$316$	−29.1803	+	9.48127i	−1.64152	+	0.533363i
$317$	−0.745744	−	7.09528i	−0.0418851	−	0.398511i	−0.995299	−	0.0968463i	$-0.969124\pi$
$317$	−0.745744	−	7.09528i	−0.0418851	−	0.398511i	0.953414	−	0.301664i	$-0.0975422\pi$
$318$	−0.401083	−	0.694696i	−0.0224916	−	0.0389566i
$319$	4.12447	−	21.7994i	0.230926	−	1.22053i
$320$	24.4954	+	14.1424i	1.36933	+	0.790584i
$321$	9.80476	−	7.12358i	0.547249	−	0.397599i
$322$	0.760668	+	0.379089i	0.0423904	+	0.0211258i
$323$	−0.231896	+	0.713703i	−0.0129030	+	0.0397115i
$324$	1.82213	−	0.811267i	0.101230	−	0.0450704i
$325$	1.94531	−	18.5084i	0.107906	−	1.02666i
$326$	−0.169725	−	0.798495i	−0.00940022	−	0.0442245i
$327$	19.7640	+	4.20098i	1.09295	+	0.232315i
$328$	−1.33847	−	1.84225i	−0.0739049	−	0.101721i
$329$	−1.73422	−	0.448176i	−0.0956106	−	0.0247087i
$330$	0.875018	+	0.0721513i	0.0481682	+	0.00397180i
$331$	−12.8936	+	22.3324i	−0.708696	+	1.22750i	0.256644	+	0.966506i	$0.417383\pi$
$331$	−12.8936	+	22.3324i	−0.708696	+	1.22750i	−0.965341	+	0.260992i	$0.915950\pi$
$332$	−2.30878	−	1.02794i	−0.126711	−	0.0564154i
$333$	4.31193	−	4.78888i	0.236292	−	0.262429i
$334$	0.717392	−	0.645943i	0.0392539	−	0.0353444i
$335$	23.8285	−	32.7971i	1.30189	−	1.79190i
$336$	3.67439	−	9.83285i	0.200455	−	0.536426i
$337$	21.3764	+	6.94561i	1.16445	+	0.378351i	0.826567	−	0.562838i	$-0.190291\pi$
$337$	21.3764	+	6.94561i	1.16445	+	0.378351i	0.337879	+	0.941190i	$0.390291\pi$
$338$	0.114455	−	0.538467i	0.00622551	−	0.0292887i
$339$	1.26381	−	2.83857i	0.0686409	−	0.154170i
$340$	6.96024	−	4.01850i	0.377472	−	0.217934i
$341$	18.3577	+	5.51237i	0.994123	+	0.298512i
$342$			0.0493015i			0.00266592i
$343$	−2.40775	+	18.3631i	−0.130006	+	0.991513i
$344$	0.604732	+	1.86117i	0.0326050	+	0.100348i
$345$	−10.4878	−	11.6479i	−0.564643	−	0.627099i
$346$	0.614947	+	0.0646335i	0.0330597	+	0.00347472i
$347$	18.9764	+	1.99450i	1.01871	+	0.107070i	0.599132	−	0.800650i	$-0.295512\pi$
$347$	18.9764	+	1.99450i	1.01871	+	0.107070i	0.419575	+	0.907721i	$0.362179\pi$
$348$	−8.92786	−	9.91540i	−0.478584	−	0.531521i
$349$	−1.73271	−	5.33272i	−0.0927496	−	0.285454i	0.893911	−	0.448244i	$-0.147951\pi$
$349$	−1.73271	−	5.33272i	−0.0927496	−	0.285454i	−0.986661	+	0.162790i	$0.947951\pi$
$350$	−1.20756	−	0.960195i	−0.0645470	−	0.0513246i
$351$		−	2.35081i		−	0.125477i
$352$	1.76950	+	2.32396i	0.0943147	+	0.123867i
$353$	−2.70427	+	1.56131i	−0.143934	+	0.0831003i	−0.570238	−	0.821480i	$-0.693149\pi$
$353$	−2.70427	+	1.56131i	−0.143934	+	0.0831003i	0.426304	+	0.904580i	$0.359816\pi$
$354$	−0.113286	+	0.254444i	−0.00602108	+	0.0135236i
$355$	−2.39017	+	11.2449i	−0.126857	+	0.596815i
$356$	27.7477	+	9.01576i	1.47062	+	0.477834i
$357$	−1.88721	−	2.28856i	−0.0998819	−	0.121123i
$358$	0.674038	−	0.927734i	0.0356240	−	0.0490323i
$359$	−6.51616	+	5.86718i	−0.343910	+	0.309658i	−0.822926	−	0.568148i	$-0.807660\pi$
$359$	−6.51616	+	5.86718i	−0.343910	+	0.309658i	0.479017	+	0.877806i	$0.340993\pi$
$360$	0.707577	−	0.785844i	0.0372926	−	0.0414176i
$361$	−16.9481	−	7.54578i	−0.892005	−	0.397146i
$362$	0.464648	−	0.804794i	0.0244214	−	0.0422991i
$363$	−9.76354	−	5.06689i	−0.512453	−	0.265943i
$364$	−8.84979	−	8.69362i	−0.463855	−	0.455669i
$365$	−17.6569	−	24.3026i	−0.924202	−	1.27206i
$366$	−0.736487	−	0.156545i	−0.0384968	−	0.00818274i
$367$	−2.47087	−	11.6245i	−0.128979	−	0.606796i	−0.994394	−	0.105741i	$-0.966279\pi$
$367$	−2.47087	−	11.6245i	−0.128979	−	0.606796i	0.865415	−	0.501055i	$-0.167055\pi$
$368$	1.80862	−	17.2079i	0.0942809	−	0.897022i
$369$	7.07022	−	3.14786i	0.368061	−	0.163871i
$370$	0.527152	−	1.62241i	0.0274053	−	0.0843449i
$371$	12.8520	−	25.7884i	0.667241	−	1.33887i
$372$	9.32557	−	6.77542i	0.483508	−	0.351289i
$373$	−7.34486	−	4.24056i	−0.380302	−	0.219568i	0.297647	−	0.954676i	$-0.403798\pi$
$373$	−7.34486	−	4.24056i	−0.380302	−	0.219568i	−0.677950	+	0.735108i	$0.737131\pi$
$374$	0.271683	−	0.0347371i	0.0140484	−	0.00179621i
$375$	5.24105	+	9.07776i	0.270647	+	0.468774i
$376$	−0.0208218	−	0.198106i	−0.00107380	−	0.0102165i
$377$	−14.9558	+	4.85943i	−0.770262	+	0.250273i
$378$	−0.164378	−	0.104680i	−0.00845472	−	0.00538417i
$379$	−6.36219	−	4.62240i	−0.326804	−	0.237437i	0.412269	−	0.911062i	$-0.364736\pi$
$379$	−6.36219	−	4.62240i	−0.326804	−	0.237437i	−0.739073	+	0.673625i	$0.764736\pi$
$380$	−1.95155	−	4.38325i	−0.100112	−	0.224856i
$381$	1.82254	−	0.387393i	0.0933716	−	0.0198467i
$382$	0.333762	+	0.300521i	0.0170768	+	0.0153760i
$383$	−33.4156	+	3.51213i	−1.70746	+	0.179461i	−0.907345	−	0.420387i	$-0.861894\pi$
$383$	−33.4156	+	3.51213i	−1.70746	+	0.179461i	−0.800114	+	0.599848i	$0.795228\pi$
$384$	2.34109			0.119468
$385$	15.1912	+	27.6370i	0.774216	+	1.40851i
$386$	0.630293			0.0320811
$387$	−6.61464	+	0.695227i	−0.336241	+	0.0353404i
$388$	21.4977	+	19.3566i	1.09138	+	0.982684i
$389$	19.6592	−	4.17868i	0.996759	−	0.211868i	0.319479	−	0.947593i	$-0.396492\pi$
$389$	19.6592	−	4.17868i	0.996759	−	0.211868i	0.677280	+	0.735725i	$0.263159\pi$
$390$	−0.253118	−	0.568511i	−0.0128171	−	0.0287877i
$391$	−3.95572	−	2.87400i	−0.200049	−	0.145344i
$392$	−2.00667	+	0.464015i	−0.101352	+	0.0234363i
$393$	−14.6787	+	4.76941i	−0.740444	+	0.240585i
$394$	0.209801	+	1.99612i	0.0105696	+	0.100563i
$395$	−27.6425	−	47.8783i	−1.39085	−	2.40902i
$396$	−5.98142	+	2.82564i	−0.300577	+	0.141994i
$397$	−19.9376	−	11.5110i	−1.00064	−	0.577719i	−0.0922018	−	0.995740i	$-0.529390\pi$
$397$	−19.9376	−	11.5110i	−1.00064	−	0.577719i	−0.908437	+	0.418021i	$0.862724\pi$
$398$	−0.0968663	+	0.0703775i	−0.00485547	+	0.00352770i
$399$	−1.47655	+	0.977676i	−0.0739198	+	0.0489450i
$400$	−9.70587	+	29.8716i	−0.485294	+	1.49358i
$401$	6.26311	−	2.78852i	0.312765	−	0.139252i	−0.244351	−	0.969687i	$-0.578575\pi$
$401$	6.26311	−	2.78852i	0.312765	−	0.139252i	0.557115	+	0.830435i	$0.311908\pi$
$402$	0.0868474	−	0.826297i	0.00433155	−	0.0412120i
$403$	−2.82464	−	13.2889i	−0.140705	−	0.661967i
$404$	−27.2067	−	5.78295i	−1.35358	−	0.287713i
$405$	2.11248	+	2.90758i	0.104970	+	0.144479i
$406$	−0.326182	+	1.26216i	−0.0161881	+	0.0626400i
$407$	−13.9409	+	16.1999i	−0.691026	+	0.803002i
$408$	0.164941	−	0.285686i	0.00816579	−	0.0141436i
$409$	12.0633	+	5.37092i	0.596491	+	0.265575i	0.682696	−	0.730703i	$-0.260807\pi$
$409$	12.0633	+	5.37092i	0.596491	+	0.265575i	−0.0862050	+	0.996277i	$0.527474\pi$
$410$	1.37090	−	1.52254i	0.0677039	−	0.0751928i
$411$	−1.68355	+	1.51588i	−0.0830435	+	0.0747727i
$412$	−3.92482	+	5.40205i	−0.193362	+	0.266140i
$413$	−9.86696	+	1.65294i	−0.485521	+	0.0813357i
$414$	−0.305508	−	0.0992657i	−0.0150149	−	0.00487864i
$415$	0.946794	−	4.45432i	0.0464763	−	0.218654i
$416$	0.842087	−	1.89136i	0.0412867	−	0.0927315i
$417$	6.63662	−	3.83166i	0.324997	−	0.187637i
$418$	−0.00367043	−	0.163473i	−0.000179527	−	0.00799574i
$419$			23.9458i			1.16983i	0.811096	+	0.584914i	$0.198872\pi$
$419$			23.9458i			1.16983i	−0.811096	+	0.584914i	$0.801128\pi$
$420$	18.7581	+	2.80006i	0.915299	+	0.136629i
$421$	1.57107	+	4.83525i	0.0765692	+	0.235656i	0.982014	−	0.188808i	$-0.0604625\pi$
$421$	1.57107	+	4.83525i	0.0765692	+	0.235656i	−0.905445	+	0.424464i	$0.860463\pi$
$422$	−0.866214	−	0.962028i	−0.0421666	−	0.0468308i
$423$	0.673299	+	0.0707666i	0.0327369	+	0.00344079i
$424$	3.18676	+	0.334942i	0.154763	+	0.0162662i
$425$	5.93907	+	6.59600i	0.288087	+	0.319953i
$426$	0.0728076	+	0.224079i	0.00352754	+	0.0108566i
$427$	−9.91652	−	25.1617i	−0.479894	−	1.21766i
$428$			24.1730i			1.16844i
$429$	0.175014	+	7.79478i	0.00844977	+	0.376335i
$430$	−1.52481	+	0.880347i	−0.0735327	+	0.0424541i
$431$	11.8759	−	26.6736i	0.572040	−	1.28482i	−0.363497	−	0.931595i	$-0.618417\pi$
$431$	11.8759	−	26.6736i	0.572040	−	1.28482i	0.935537	−	0.353228i	$-0.114916\pi$
$432$	−0.824885	+	3.88078i	−0.0396873	+	0.186714i
$433$	15.5551	+	5.05415i	0.747530	+	0.242887i	0.657918	−	0.753090i	$-0.271437\pi$
$433$	15.5551	+	5.05415i	0.747530	+	0.242887i	0.0896118	+	0.995977i	$0.471437\pi$
$434$	−1.05500	−	0.394237i	−0.0506414	−	0.0189240i
$435$	14.1312	−	19.4499i	0.677539	−	0.932552i
$436$	−29.9499	+	26.9670i	−1.43434	+	1.29149i
$437$	−1.95322	+	2.16927i	−0.0934352	+	0.103770i
$438$	−0.562431	−	0.250411i	−0.0268740	−	0.0119651i
$439$	−6.68012	+	11.5703i	−0.318825	+	0.552221i	−0.980243	−	0.197797i	$-0.936621\pi$
$439$	−6.68012	+	11.5703i	−0.318825	+	0.552221i	0.661418	+	0.750017i	$0.269955\pi$
$440$	−2.28767	+	2.65837i	−0.109060	+	0.126733i
$441$	−0.124615	−	6.99889i	−0.00593403	−	0.333281i
$442$	−0.114110	−	0.157059i	−0.00542765	−	0.00747052i
$443$	−4.41381	−	0.938184i	−0.209706	−	0.0445745i	0.101860	−	0.994799i	$-0.467520\pi$
$443$	−4.41381	−	0.938184i	−0.209706	−	0.0445745i	−0.311567	+	0.950224i	$0.600854\pi$
$444$	2.67233	+	12.5723i	0.126823	+	0.596656i
$445$	−5.49513	+	52.2827i	−0.260494	+	2.47844i
$446$	−0.517596	+	0.230448i	−0.0245089	+	0.0109121i
$447$	−2.53665	+	7.80699i	−0.119979	+	0.369258i
$448$	11.4956	+	17.3614i	0.543117	+	0.820249i
$449$	28.3820	−	20.6207i	1.33943	−	0.973152i	0.339964	−	0.940438i	$-0.389585\pi$
$449$	28.3820	−	20.6207i	1.33943	−	0.973152i	0.999465	−	0.0327134i	$-0.0104149\pi$
$450$	0.504995	+	0.291559i	0.0238057	+	0.0137442i
$451$	−23.2090	+	10.9640i	−1.09287	+	0.516275i
$452$	3.09878	+	5.36724i	0.145754	+	0.252454i
$453$	1.04070	+	9.90156i	0.0488962	+	0.465216i
$454$	−0.595619	+	0.193528i	−0.0279538	+	0.00908273i
$455$	12.0071	−	18.8546i	0.562900	−	0.883917i
$456$	−0.159327	−	0.115758i	−0.00746115	−	0.00542084i
$457$	−11.1775	−	25.1051i	−0.522862	−	1.17437i	−0.961274	−	0.275594i	$-0.911126\pi$
$457$	−11.1775	−	25.1051i	−0.522862	−	1.17437i	0.438412	−	0.898774i	$-0.355541\pi$
$458$	−1.56840	+	0.333374i	−0.0732865	+	0.0155775i
$459$	0.833188	+	0.750206i	0.0388899	+	0.0350166i
$460$	31.0912	−	3.26781i	1.44963	−	0.152363i
$461$	−22.8953			−1.06634			−0.533171	−	0.846008i	$-0.679000\pi$
$461$	−22.8953			−1.06634			−0.533171	+	0.846008i	$0.679000\pi$
$462$	0.552838	+	0.334860i	0.0257203	+	0.0155791i
$463$	−1.14900			−0.0533985			−0.0266993	−	0.999644i	$-0.508500\pi$
$463$	−1.14900			−0.0533985			−0.0266993	+	0.999644i	$0.508500\pi$
$464$	26.3946	−	2.77418i	1.22534	−	0.128788i
$465$	15.4353	+	13.8980i	0.715794	+	0.644504i
$466$	1.49941	−	0.318709i	0.0694588	−	0.0147639i
$467$	9.82355	+	22.0641i	0.454580	+	1.02100i	0.984887	+	0.173197i	$0.0554099\pi$
$467$	9.82355	+	22.0641i	0.454580	+	1.02100i	−0.530307	+	0.847806i	$0.677923\pi$
$468$	3.79337	+	2.75604i	0.175348	+	0.127398i
$469$	26.4693	−	13.7849i	1.22224	−	0.636528i
$470$	0.170448	−	0.0553820i	0.00786219	−	0.00255458i
$471$	−1.60819	−	15.3009i	−0.0741013	−	0.705026i
$472$	−0.556292	−	0.963527i	−0.0256054	−	0.0443499i
$473$	21.8810	−	2.79768i	1.00609	−	0.128637i
$474$	−0.981257	−	0.566529i	−0.0450706	−	0.0260215i
$475$	4.28684	−	3.11457i	0.196694	−	0.142906i
$476$	5.90545	−	0.362230i	0.270676	−	0.0166028i
$477$	−3.36533	+	10.3574i	−0.154088	+	0.474234i
$478$	−0.136981	+	0.0609880i	−0.00626538	+	0.00278953i
$479$	−2.76794	+	26.3352i	−0.126470	+	1.20328i	0.728662	+	0.684874i	$0.240143\pi$
$479$	−2.76794	+	26.3352i	−0.126470	+	1.20328i	−0.855132	+	0.518410i	$0.826524\pi$
$480$	0.658082	+	3.09603i	0.0300372	+	0.141314i
$481$	14.8177	+	3.14961i	0.675631	+	0.143610i
$482$	0.0911882	+	0.125510i	0.00415351	+	0.00571681i
$483$	−3.08546	−	11.1183i	−0.140393	−	0.505899i
$484$	19.6227	−	9.81455i	0.891943	−	0.446116i
$485$	−26.0623	+	45.1412i	−1.18343	+	2.04976i
$486$	0.0672897	+	0.0299593i	0.00305232	+	0.00135898i
$487$	0.894112	−	0.993012i	0.0405161	−	0.0449977i	−0.722546	−	0.691323i	$-0.757028\pi$
$487$	0.894112	−	0.993012i	0.0405161	−	0.0449977i	0.763062	+	0.646325i	$0.223695\pi$
$488$	2.23514	−	2.01253i	0.101180	−	0.0911029i
$489$	−6.51430	+	8.96617i	−0.294587	+	0.405464i
$490$	−0.783726	−	1.67917i	−0.0354051	−	0.0758572i
$491$	26.4348	+	8.58918i	1.19298	+	0.387624i	0.837175	−	0.546935i	$-0.184205\pi$
$491$	26.4348	+	8.58918i	1.19298	+	0.387624i	0.355809	+	0.934559i	$0.384205\pi$
$492$	−3.20946	+	15.0993i	−0.144694	+	0.680730i
$493$	3.05049	−	6.85150i	0.137387	−	0.308576i
$494$	−0.100371	+	0.0579491i	−0.00451590	+	0.00260725i
$495$	−7.22100	−	9.48365i	−0.324560	−	0.426258i
$496$			22.9288i			1.02953i
$497$	−5.26719	+	6.62414i	−0.236266	+	0.297133i
$498$	−0.0288406	−	0.0887621i	−0.00129238	−	0.00397752i
$499$	−3.02948	−	3.36458i	−0.135618	−	0.150619i	0.671510	−	0.740995i	$-0.265646\pi$
$499$	−3.02948	−	3.36458i	−0.135618	−	0.150619i	−0.807128	+	0.590376i	$0.798979\pi$
$500$	−20.7928	−	2.18541i	−0.929882	−	0.0977345i
$501$	−13.0340	−	1.36993i	−0.582318	−	0.0612041i
$502$	−0.692355	−	0.768938i	−0.0309013	−	0.0343194i
$503$	12.2743	+	37.7763i	0.547283	+	1.68436i	0.715500	+	0.698613i	$0.246199\pi$
$503$	12.2743	+	37.7763i	0.547283	+	1.68436i	−0.168217	+	0.985750i	$0.553801\pi$
$504$	0.724246	−	0.285434i	0.0322605	−	0.0127143i
$505$		−	50.1181i		−	2.23022i
$506$	1.02039	+	0.306399i	0.0453619	+	0.0136211i
$507$	−6.47242	+	3.73686i	−0.287450	+	0.165960i
$508$	−1.51160	+	3.39510i	−0.0670663	+	0.150633i
$509$	−2.88099	+	13.5540i	−0.127698	+	0.600770i	0.867033	+	0.498250i	$0.166024\pi$
$509$	−2.88099	+	13.5540i	−0.127698	+	0.600770i	−0.994731	+	0.102520i	$0.967309\pi$
$510$	0.282272	+	0.0917158i	0.0124992	+	0.00406124i
$511$	−3.65370	−	21.8102i	−0.161630	−	0.964827i
$512$	−3.42612	+	4.71565i	−0.151414	+	0.208404i
$513$	0.497411	−	0.447871i	0.0219612	−	0.0197740i
$514$	0.127648	−	0.141768i	0.00563032	−	0.00625310i
$515$	−10.9915	−	4.89371i	−0.484341	−	0.215643i
$516$	6.63303	−	11.4888i	0.292003	−	0.505764i
$517$	−2.23779	−	0.184521i	−0.0984177	−	0.00811522i
$518$	0.880061	−	0.895870i	0.0386677	−	0.0393623i
$519$	−4.93428	−	6.79145i	−0.216591	−	0.298112i
$520$	2.43155	+	0.516843i	0.106631	+	0.0226651i
$521$	1.27618	+	6.00395i	0.0559104	+	0.263038i	0.997221	−	0.0745048i	$-0.0237376\pi$
$521$	1.27618	+	6.00395i	0.0559104	+	0.263038i	−0.941310	+	0.337543i	$0.890404\pi$
$522$	0.0515038	−	0.490026i	0.00225426	−	0.0214479i
$523$	1.94158	−	0.864447i	0.0848993	−	0.0377996i	−0.363848	−	0.931458i	$-0.618537\pi$
$523$	1.94158	−	0.864447i	0.0848993	−	0.0377996i	0.448747	+	0.893659i	$0.351870\pi$
$524$	9.51294	−	29.2778i	0.415575	−	1.27901i
$525$	1.28234	+	20.9060i	0.0559657	+	0.912413i
$526$	0.463737	−	0.336925i	0.0202199	−	0.0146906i
$527$	5.61135	+	3.23972i	0.244434	+	0.141124i
$528$	2.44623	−	12.9293i	0.106458	−	0.562673i
$529$	1.99030	+	3.44729i	0.0865346	+	0.149882i
$530$	0.301351	+	2.86716i	0.0130898	+	0.124542i
$531$	3.59626	−	1.16849i	0.156064	−	0.0507083i
$532$	0.153454	−	3.52883i	0.00665307	−	0.152994i
$533$	14.7190	+	10.6939i	0.637549	+	0.463206i
$534$	0.438229	+	0.984279i	0.0189640	+	0.0425939i
$535$	−42.6047	+	9.05591i	−1.84196	+	0.391521i
$536$	2.46641	+	2.22077i	0.106533	+	0.0959226i
$537$	−15.4832	+	1.62735i	−0.668151	+	0.0702255i
$538$	−1.25756			−0.0542171
$539$	0.934254	+	23.1976i	0.0402412	+	0.999190i
$540$	−7.16843			−0.308480
$541$	40.2514	−	4.23060i	1.73054	−	0.181888i	0.813741	−	0.581227i	$-0.197427\pi$
$541$	40.2514	−	4.23060i	1.73054	−	0.181888i	0.916803	+	0.399340i	$0.130761\pi$
$542$	−1.59264	−	1.43402i	−0.0684095	−	0.0615962i
$543$	−12.3407	+	2.62310i	−0.529591	+	0.112568i
$544$	0.401615	+	0.902042i	0.0172191	+	0.0386747i
$545$	−58.7493	−	42.6839i	−2.51654	−	1.82838i
$546$	0.0199031	−	0.457693i	0.000851774	−	0.0195874i
$547$	2.97155	−	0.965514i	0.127054	−	0.0412824i	−0.244800	−	0.969574i	$-0.578722\pi$
$547$	2.97155	−	0.965514i	0.127054	−	0.0412824i	0.371854	+	0.928291i	$0.378722\pi$
$548$	−0.472322	−	4.49384i	−0.0201766	−	0.191967i
$549$	5.11107	+	8.85264i	0.218135	+	0.377822i
$550$	−1.69616	−	0.929151i	−0.0723246	−	0.0396191i
$551$	−3.87756	−	2.23871i	−0.165190	−	0.0953723i
$552$	1.03811	−	0.754234i	0.0441851	−	0.0321023i
$553$	−2.49171	−	40.6226i	−0.105958	−	1.72745i
$554$	0.150415	−	0.462929i	0.00639051	−	0.0196680i
$555$	−21.1575	+	9.41994i	−0.898087	+	0.399854i
$556$	−1.59772	+	15.2013i	−0.0677585	+	0.644679i
$557$	6.65766	+	31.3218i	0.282094	+	1.32715i	0.859686	+	0.510823i	$0.170659\pi$
$557$	6.65766	+	31.3218i	0.282094	+	1.32715i	−0.577591	+	0.816326i	$0.696007\pi$
$558$	0.416380	+	0.0885044i	0.0176268	+	0.00374669i
$559$	−9.19025	−	12.6493i	−0.388706	−	0.535008i
$560$	−26.4376	+	26.9125i	−1.11719	+	1.13726i
$561$	−2.81853	−	2.42549i	−0.118998	−	0.102404i
$562$	0.153108	−	0.265190i	0.00645846	−	0.0111864i
$563$	−5.72128	−	2.54728i	−0.241123	−	0.107355i	0.282617	−	0.959233i	$-0.408797\pi$
$563$	−5.72128	−	2.54728i	−0.241123	−	0.107355i	−0.523741	+	0.851878i	$0.675464\pi$
$564$	−0.903556	+	1.00350i	−0.0380466	+	0.0422550i
$565$	−8.29883	+	7.47230i	−0.349135	+	0.314362i
$566$	0.341218	−	0.469646i	0.0143424	−	0.0197407i
$567$	0.437131	+	2.60939i	0.0183578	+	0.109584i
$568$	−0.895099	−	0.290835i	−0.0375575	−	0.0122032i
$569$	2.38702	−	11.2300i	0.100069	−	0.470787i	−0.899367	−	0.437195i	$-0.855972\pi$
$569$	2.38702	−	11.2300i	0.100069	−	0.470787i	0.999436	−	0.0335923i	$-0.0106948\pi$
$570$	0.0720688	−	0.161869i	0.00301863	−	0.00677995i
$571$	2.12520	−	1.22698i	0.0889367	−	0.0513476i	−0.454872	−	0.890557i	$-0.650315\pi$
$571$	2.12520	−	1.22698i	0.0889367	−	0.0513476i	0.543809	+	0.839209i	$0.316982\pi$
$572$	−12.7832	−	8.85604i	−0.534492	−	0.370290i
$573$		−	6.09741i		−	0.254723i
$574$	1.40319	−	0.553017i	0.0585682	−	0.0230825i
$575$	10.6689	+	32.8354i	0.444923	+	1.36933i
$576$	−5.26611	−	5.84861i	−0.219421	−	0.243692i
$577$	19.7384	+	2.07459i	0.821719	+	0.0863662i	0.506051	−	0.862503i	$-0.331105\pi$
$577$	19.7384	+	2.07459i	0.821719	+	0.0863662i	0.315668	+	0.948870i	$0.397771\pi$
$578$	−1.15324	−	0.121210i	−0.0479685	−	0.00504169i
$579$	−5.72578	−	6.35913i	−0.237955	−	0.264276i
$580$	14.8181	+	45.6055i	0.615288	+	1.89366i
$581$	2.08644	−	2.62396i	0.0865601	−	0.108860i
$582$			1.06828i			0.0442818i
$583$	10.3876	−	34.5936i	0.430212	−	1.43272i
$584$	2.12981	−	1.22965i	0.0881321	−	0.0508831i
$585$	−3.43640	+	7.71828i	−0.142078	+	0.319112i
$586$	−0.212421	+	0.999364i	−0.00877505	+	0.0412833i
$587$	38.3017	+	12.4450i	1.58088	+	0.513659i	0.962284	−	0.272048i	$-0.0877011\pi$
$587$	38.3017	+	12.4450i	1.58088	+	0.513659i	0.618598	+	0.785708i	$0.287701\pi$
$588$	11.4398	+	8.00429i	0.471770	+	0.330091i
$589$	2.27367	−	3.12944i	0.0936850	−	0.128946i
$590$	0.743892	−	0.669803i	0.0306255	−	0.0275754i
$591$	18.2333	−	20.2501i	0.750018	−	0.832980i
$592$	−23.3564	−	10.3989i	−0.959941	−	0.427393i
$593$	17.5699	−	30.4319i	0.721508	−	1.24969i	−0.238887	−	0.971047i	$-0.576782\pi$
$593$	17.5699	−	30.4319i	0.721508	−	1.24969i	0.960395	−	0.278642i	$-0.0898842\pi$
$594$	−0.225349	−	0.0943291i	−0.00924618	−	0.00387037i
$595$	2.85079	+	10.2726i	0.116871	+	0.421137i
$596$	−9.62379	−	13.2460i	−0.394206	−	0.542578i
$597$	1.59001	+	0.337968i	0.0650749	+	0.0138321i
$598$	−0.157005	−	0.738649i	−0.00642040	−	0.0302056i
$599$	1.94285	−	18.4850i	0.0793828	−	0.755277i	−0.880343	−	0.474338i	$-0.842687\pi$
$599$	1.94285	−	18.4850i	0.0793828	−	0.755277i	0.959726	−	0.280939i	$-0.0906459\pi$
$600$	−2.12793	+	0.947414i	−0.0868723	+	0.0386780i
$601$	2.56249	−	7.88654i	0.104526	−	0.321699i	−0.885093	−	0.465415i	$-0.845905\pi$
$601$	2.56249	−	7.88654i	0.104526	−	0.321699i	0.989619	+	0.143716i	$0.0459052\pi$
$602$	−1.29373	+	0.0793550i	−0.0527285	+	0.00323427i
$603$	−9.12560	+	6.63014i	−0.371623	+	0.270000i
$604$	−17.1977	−	9.92909i	−0.699764	−	0.404009i
$605$	24.6494	+	30.9082i	1.00214	+	1.25660i
$606$	−0.513581	−	0.889548i	−0.0208628	−	0.0361354i
$607$	−3.85056	−	36.6356i	−0.156289	−	1.48699i	−0.738665	−	0.674073i	$-0.764543\pi$
$607$	−3.85056	−	36.6356i	−0.156289	−	1.48699i	0.582375	−	0.812920i	$-0.302123\pi$
$608$	0.560628	−	0.182159i	0.0227365	−	0.00738753i
$609$	15.6973	−	8.17498i	0.636086	−	0.331267i
$610$	2.18923	+	1.59057i	0.0886395	+	0.0644003i
$611$	0.647327	+	1.45392i	0.0261881	+	0.0588193i
$612$	−2.18738	+	0.464942i	−0.0884196	+	0.0187942i
$613$	0.360988	+	0.325035i	0.0145802	+	0.0131280i	0.676388	−	0.736545i	$-0.263544\pi$
$613$	0.360988	+	0.325035i	0.0145802	+	0.0131280i	−0.661808	+	0.749673i	$0.730211\pi$
$614$	1.82476	−	0.191790i	0.0736414	−	0.00774002i
$615$	−27.8148			−1.12160
$616$	−2.38020	+	1.00036i	−0.0959008	+	0.0403056i
$617$	−10.5763			−0.425786			−0.212893	−	0.977076i	$-0.568289\pi$
$617$	−10.5763			−0.425786			−0.212893	+	0.977076i	$0.568289\pi$
$618$	−0.245236	+	0.0257753i	−0.00986483	+	0.00103684i
$619$	29.2623	+	26.3479i	1.17615	+	1.05901i	0.997172	+	0.0751566i	$0.0239457\pi$
$619$	29.2623	+	26.3479i	1.17615	+	1.05901i	0.178978	+	0.983853i	$0.442721\pi$
$620$	−40.5225	+	8.61332i	−1.62742	+	0.345919i
$621$	1.77383	+	3.98409i	0.0711813	+	0.159876i
$622$	1.07694	+	0.782440i	0.0431812	+	0.0313730i
$623$	−20.7882	+	32.6435i	−0.832860	+	1.30783i
$624$	−8.87028	+	2.88213i	−0.355096	+	0.115378i
$625$	0.199715	+	1.90016i	0.00798859	+	0.0760064i
$626$	0.0560479	+	0.0970779i	0.00224013	+	0.00388001i
$627$	−1.61597	+	1.52208i	−0.0645354	+	0.0607859i
$628$	26.5756	+	15.3434i	1.06048	+	0.612269i
$629$	−5.84505	+	4.24668i	−0.233057	+	0.169326i
$630$	0.386674	+	0.583979i	0.0154055	+	0.0232663i
$631$	−5.14474	+	15.8339i	−0.204809	+	0.630337i	0.794912	+	0.606725i	$0.207517\pi$
$631$	−5.14474	+	15.8339i	−0.204809	+	0.630337i	−0.999721	+	0.0236129i	$0.992483\pi$
$632$	4.13479	−	1.84092i	0.164473	−	0.0732281i
$633$	−1.83709	+	17.4787i	−0.0730178	+	0.694718i
$634$	0.109258	+	0.514018i	0.00433918	+	0.0204142i
$635$	−6.55014	−	1.39228i	−0.259935	−	0.0552508i
$636$	−12.7678	−	17.5733i	−0.506275	−	0.696827i
$637$	14.1023	−	8.48021i	0.558752	−	0.335998i
$638$	−0.134294	+	1.62866i	−0.00531675	+	0.0644791i
$639$	1.59936	−	2.77017i	0.0632696	−	0.109586i
$640$	−7.68638	−	3.42220i	−0.303831	−	0.135274i
$641$	4.38159	−	4.86625i	0.173063	−	0.192205i	−0.650373	−	0.759615i	$-0.725388\pi$
$641$	4.38159	−	4.86625i	0.173063	−	0.192205i	0.823436	+	0.567409i	$0.192054\pi$
$642$	−0.663394	+	0.597322i	−0.0261821	+	0.0235744i
$643$	17.9951	−	24.7681i	0.709657	−	0.976760i	−0.290147	−	0.956982i	$-0.593704\pi$
$643$	17.9951	−	24.7681i	0.709657	−	0.976760i	0.999804	−	0.0197776i	$-0.00629582\pi$
$644$	21.5583	+	8.05601i	0.849515	+	0.317451i
$645$	22.7338	+	7.38666i	0.895142	+	0.290849i
$646$	0.0114923	−	0.0540672i	0.000452160	−	0.00212725i
$647$	15.3840	−	34.5531i	0.604809	−	1.35842i	−0.308527	−	0.951216i	$-0.599836\pi$
$647$	15.3840	−	34.5531i	0.604809	−	1.35842i	0.913336	−	0.407208i	$-0.133497\pi$
$648$	−0.254812	+	0.147116i	−0.0100100	+	0.00577925i
$649$	−11.8374	+	4.14222i	−0.464660	+	0.162596i
$650$			1.37080i			0.0537671i
$651$	5.60641	+	14.2254i	0.219732	+	0.557537i
$652$	−6.83096	−	21.0235i	−0.267521	−	0.823346i
$653$	−4.62940	−	5.14147i	−0.181162	−	0.201201i	0.645723	−	0.763572i	$-0.276556\pi$
$653$	−4.62940	−	5.14147i	−0.181162	−	0.201201i	−0.826885	+	0.562371i	$0.809889\pi$
$654$	−1.48014	−	0.155569i	−0.0578782	−	0.00608325i
$655$	55.1659	+	5.79816i	2.15551	+	0.226553i
$656$	−20.5460	−	22.8187i	−0.802188	−	0.890920i
$657$	2.58288	+	7.94927i	0.100768	+	0.310131i
$658$	0.130490	+	0.0194785i	0.00508701	+	0.000759350i
$659$		−	37.2276i		−	1.45018i	−0.688654	−	0.725090i	$-0.741798\pi$
$659$		−	37.2276i		−	1.45018i	0.688654	−	0.725090i	$-0.258202\pi$
$660$	23.7690	−	0.533680i	0.925207	−	0.0207735i
$661$	−23.2430	+	13.4194i	−0.904048	+	0.521952i	−0.878511	−	0.477722i	$-0.841463\pi$
$661$	−23.2430	+	13.4194i	−0.904048	+	0.521952i	−0.0255366	+	0.999674i	$0.508129\pi$
$662$	0.772567	−	1.73521i	0.0300267	−	0.0674410i
$663$	−0.547981	+	2.57805i	−0.0212818	+	0.100123i
$664$	0.354567	+	0.115206i	0.0137599	+	0.00447085i
$665$	6.27703	−	1.05154i	0.243413	−	0.0407771i
$666$	−0.278996	+	0.384005i	−0.0108109	+	0.0148799i
$667$	21.6800	−	19.5207i	0.839451	−	0.755845i
$668$	17.4915	−	19.4262i	0.676765	−	0.751623i
$669$	7.02704	+	3.12864i	0.271681	+	0.120960i
$670$	−1.49302	+	2.58599i	−0.0576804	+	0.0999054i
$671$	−17.6063	−	28.9730i	−0.679684	−	1.11849i
$672$	−0.583018	+	2.25599i	−0.0224904	+	0.0870267i
$673$	−16.5459	−	22.7735i	−0.637797	−	0.877852i	0.360699	−	0.932682i	$-0.382538\pi$
$673$	−16.5459	−	22.7735i	−0.637797	−	0.877852i	−0.998496	+	0.0548302i	$0.982538\pi$
$674$	−1.61939	−	0.344211i	−0.0623764	−	0.0132585i
$675$	−1.64595	−	7.74359i	−0.0633527	−	0.298051i
$676$	1.55819	−	14.8252i	0.0599305	−	0.570201i
$677$	3.53617	−	1.57440i	0.135906	−	0.0605092i	−0.337657	−	0.941269i	$-0.609634\pi$
$677$	3.53617	−	1.57440i	0.135906	−	0.0605092i	0.473563	+	0.880760i	$0.342968\pi$
$678$	−0.0707246	+	0.217668i	−0.00271616	+	0.00835949i
$679$	−31.9944	+	21.1847i	−1.22783	+	0.812993i
$680$	−0.959157	+	0.696869i	−0.0367820	+	0.0267237i
$681$	7.36333	+	4.25122i	0.282163	+	0.162907i
$682$	−1.38722	−	0.262463i	−0.0531193	−	0.0100502i
$683$	−17.8247	−	30.8733i	−0.682043	−	1.18133i	−0.974356	−	0.225010i	$-0.927758\pi$
$683$	−17.8247	−	30.8733i	−0.682043	−	1.18133i	0.292314	−	0.956323i	$-0.405575\pi$
$684$	0.139549	+	1.32772i	0.00533579	+	0.0507666i
$685$	7.74343	−	2.51599i	0.295861	−	0.0961311i
$686$	0.0349942	−	1.36371i	0.00133608	−	0.0520667i
$687$	17.6113	+	12.7954i	0.671913	+	0.488174i
$688$	10.7330	+	24.1066i	0.409190	+	0.919056i
$689$	−25.0419	+	5.32282i	−0.954020	+	0.202783i
$690$	0.857954	+	0.772506i	0.0326618	+	0.0294088i
$691$	6.76460	−	0.710989i	0.257338	−	0.0270473i	0.0250189	−	0.999687i	$-0.492035\pi$
$691$	6.76460	−	0.710989i	0.257338	−	0.0270473i	0.232319	+	0.972640i	$0.425369\pi$
$692$	16.7438			0.636505
$693$	−1.64370	−	8.61964i	−0.0624390	−	0.327433i
$694$	−1.40546			−0.0533505
$695$	−27.3908	+	2.87889i	−1.03899	+	0.109202i
$696$	1.46268	+	1.31700i	0.0554427	+	0.0499208i
$697$	−8.48743	+	1.80406i	−0.321484	+	0.0683336i
$698$	0.167986	+	0.377304i	0.00635838	+	0.0142812i
$699$	−16.8366	−	12.2325i	−0.636820	−	0.462676i
$700$	−35.2383	−	22.4406i	−1.33188	−	0.848175i
$701$	−32.6788	+	10.6180i	−1.23426	+	0.401035i	−0.852256	−	0.523125i	$-0.824766\pi$
$701$	−32.6788	+	10.6180i	−1.23426	+	0.401035i	−0.382004	+	0.924161i	$0.624766\pi$
$702$	0.0180996	+	0.172206i	0.000683127	+	0.00649951i
$703$	2.15661	+	3.73537i	0.0813383	+	0.140882i
$704$	17.8967	+	19.0007i	0.674509	+	0.716116i
$705$	−2.10716	−	1.21657i	−0.0793604	−	0.0458187i
$706$	0.186078	−	0.135194i	0.00700315	−	0.00508809i
$707$	16.4568	−	33.0216i	0.618920	−	1.24191i
$708$	−2.33065	+	7.17300i	−0.0875911	+	0.269578i
$709$	9.67610	−	4.30808i	0.363393	−	0.161793i	−0.216914	−	0.976191i	$-0.569599\pi$
$709$	9.67610	−	4.30808i	0.363393	−	0.161793i	0.580307	+	0.814398i	$0.302932\pi$
$710$	0.0885121	−	0.842136i	0.00332180	−	0.0316048i
$711$	3.19825	+	15.0466i	0.119944	+	0.564291i
$712$	−4.20982	−	0.894824i	−0.157770	−	0.0335350i
$713$	14.8144	+	20.3903i	0.554804	+	0.763623i
$714$	0.155867	+	0.153116i	0.00583317	+	0.00573023i
$715$	10.8198	−	25.8480i	0.404636	−	0.966662i
$716$	15.5263	−	26.8923i	0.580245	−	1.00501i
$717$	1.85970	+	0.827992i	0.0694518	+	0.0309219i
$718$	0.432163	−	0.479966i	0.0161282	−	0.0179122i
$719$	2.05726	−	1.85237i	0.0767229	−	0.0690816i	−0.629877	−	0.776695i	$-0.716895\pi$
$719$	2.05726	−	1.85237i	0.0767229	−	0.0690816i	0.706600	+	0.707613i	$0.250228\pi$
$720$	8.38121	−	11.5358i	0.312349	−	0.429912i
$721$	−5.63511	−	6.83350i	−0.209863	−	0.254493i
$722$	1.29962	+	0.422271i	0.0483667	+	0.0157153i
$723$	0.437905	−	2.06018i	0.0162859	−	0.0766190i
$724$	10.2353	−	22.9888i	0.380391	−	0.854372i
$725$	−45.8622	+	26.4785i	−1.70328	+	0.983388i
$726$	0.754232	+	0.295998i	0.0279922	+	0.0109855i
$727$		−	20.9741i		−	0.777885i	−0.921262	−	0.388942i	$-0.872841\pi$
$727$		−	20.9741i		−	0.777885i	0.921262	−	0.388942i	$-0.127159\pi$
$728$	1.43238	+	1.13896i	0.0530877	+	0.0422127i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	1.48055	+	1.64432i	0.0547978	+	0.0608591i
$731$	7.41610	+	0.779464i	0.274294	+	0.0288295i
$732$	−20.2771	−	2.13121i	−0.749465	−	0.0787719i
$733$	3.77784	+	4.19572i	0.139538	+	0.154972i	0.808863	−	0.587997i	$-0.200083\pi$
$733$	3.77784	+	4.19572i	0.139538	+	0.154972i	−0.669325	+	0.742970i	$0.733417\pi$
$734$	0.270503	+	0.832523i	0.00998445	+	0.0307290i
$735$	−9.82182	+	23.1613i	−0.362283	+	0.854316i
$736$			3.84083i			0.141575i
$737$	29.7650	−	22.6635i	1.09641	−	0.834821i
$738$	−0.493687	+	0.285030i	−0.0181729	+	0.0104921i
$739$	−6.93491	+	15.5761i	−0.255105	+	0.572974i	−0.995014	−	0.0997318i	$-0.968202\pi$
$739$	−6.93491	+	15.5761i	−0.255105	+	0.572974i	0.739910	+	0.672706i	$0.234868\pi$
$740$	9.60426	−	45.1845i	0.353060	−	1.66101i
$741$	1.49646	+	0.486229i	0.0549738	+	0.0178621i
$742$	−0.742908	+	1.98806i	−0.0272730	+	0.0729839i
$743$	−16.0233	+	22.0542i	−0.587838	+	0.809089i	−0.994527	−	0.104477i	$-0.966683\pi$
$743$	−16.0233	+	22.0542i	−0.587838	+	0.809089i	0.406690	+	0.913566i	$0.366683\pi$
$744$	−1.26366	+	1.13780i	−0.0463280	+	0.0417139i
$745$	19.7407	−	21.9242i	0.723243	−	0.803242i
$746$	0.570691	+	0.254088i	0.0208945	+	0.00930283i
$747$	−0.633538	+	1.09732i	−0.0231800	+	0.0401489i
$748$	7.21827	−	1.70450i	0.263926	−	0.0623226i
$749$	−31.0449	−	8.02296i	−1.13435	−	0.293152i
$750$	−0.453822	−	0.624632i	−0.0165712	−	0.0228083i
$751$	9.73931	+	2.07015i	0.355393	+	0.0755410i	0.382148	−	0.924101i	$-0.375184\pi$
$751$	9.73931	+	2.07015i	0.355393	+	0.0755410i	−0.0267558	+	0.999642i	$0.508518\pi$
$752$	−0.558454	−	2.62732i	−0.0203647	−	0.0958084i
$753$	−1.46836	+	13.9706i	−0.0535102	+	0.509115i
$754$	1.05816	−	0.471124i	0.0385359	−	0.0171573i
$755$	11.0572	−	34.0306i	0.402413	−	1.23850i
$756$	−4.72311	−	2.35383i	−0.171778	−	0.0856078i
$757$	−14.4315	+	10.4851i	−0.524522	+	0.381087i	−0.818305	−	0.574785i	$-0.805086\pi$
$757$	−14.4315	+	10.4851i	−0.524522	+	0.381087i	0.293783	+	0.955872i	$0.405086\pi$
$758$	0.501647	+	0.289626i	0.0182206	+	0.0105197i
$759$	−6.17825	−	13.0783i	−0.224256	−	0.474713i
$760$	0.353895	+	0.612964i	0.0128371	+	0.0222345i
$761$	4.63434	+	44.0928i	0.167995	+	1.59836i	0.675928	+	0.736968i	$0.263743\pi$
$761$	4.63434	+	44.0928i	0.167995	+	1.59836i	−0.507933	+	0.861396i	$0.669590\pi$
$762$	−0.130526	+	0.0424105i	−0.00472846	+	0.00153637i
$763$	−24.6929	−	47.4144i	−0.893943	−	1.71651i
$764$	9.83905	+	7.14849i	0.355965	+	0.258623i
$765$	−1.63892	−	3.68106i	−0.0592551	−	0.133089i
$766$	2.42080	−	0.514556i	0.0874669	−	0.0185917i
$767$	6.60594	+	5.94801i	0.238527	+	0.214770i
$768$	15.4824	−	1.62727i	0.558675	−	0.0587191i
$769$	−13.4507			−0.485044			−0.242522	−	0.970146i	$-0.577975\pi$
$769$	−13.4507			−0.485044			−0.242522	+	0.970146i	$0.577975\pi$
$770$	−1.32561	−	1.90757i	−0.0477716	−	0.0687439i
$771$	−2.58991			−0.0932734
$772$	16.9742	−	1.78406i	0.610914	−	0.0642096i
$773$	17.0132	+	15.3187i	0.611921	+	0.550976i	0.915749	−	0.401751i	$-0.131598\pi$
$773$	17.0132	+	15.3187i	0.611921	+	0.550976i	−0.303828	+	0.952727i	$0.598265\pi$
$774$	0.479198	−	0.101857i	0.0172244	−	0.00366116i
$775$	−18.6088	−	41.7961i	−0.668448	−	1.50136i
$776$	−3.45235	−	2.50828i	−0.123932	−	0.0900420i
$777$	−17.0333	−	0.740707i	−0.611068	−	0.0265727i
$778$	−1.40794	+	0.457469i	−0.0504772	+	0.0164011i
$779$	0.541475	+	5.15179i	0.0194004	+	0.184582i
$780$	−8.42579	−	14.5939i	−0.301692	−	0.522546i
$781$	−5.09690	+	9.30437i	−0.182381	+	0.332937i
$782$	0.311901	+	0.180076i	0.0111536	+	0.00643951i
$783$	−5.41183	+	3.93192i	−0.193403	+	0.140515i
$784$	−26.2561	+	9.05097i	−0.937718	+	0.323249i
$785$	−17.0867	+	52.5874i	−0.609850	+	1.87692i
$786$	1.03856	−	0.462396i	0.0370441	−	0.0164931i
$787$	−2.23029	+	21.2198i	−0.0795013	+	0.756404i	0.880052	+	0.474877i	$0.157508\pi$
$787$	−2.23029	+	21.2198i	−0.0795013	+	0.756404i	−0.959553	+	0.281527i	$0.909159\pi$
$788$	11.3001	+	53.1630i	0.402551	+	1.89385i
$789$	−7.61203	−	1.61799i	−0.270995	−	0.0576018i
$790$	2.39356	+	3.29446i	0.0851591	+	0.117211i
$791$	−7.92151	+	2.19832i	−0.281657	+	0.0781633i
$792$	0.833950	−	0.506775i	0.0296331	−	0.0180075i
$793$	−12.0151	+	20.8108i	−0.426670	+	0.739015i
$794$	1.54914	+	0.689722i	0.0549769	+	0.0244773i
$795$	26.1897	−	29.0866i	0.928853	−	1.03160i
$796$	−2.40946	+	2.16949i	−0.0854012	+	0.0768956i
$797$	−12.3189	+	16.9555i	−0.436357	+	0.600594i	−0.969398	−	0.245495i	$-0.921049\pi$
$797$	−12.3189	+	16.9555i	−0.436357	+	0.600594i	0.533040	+	0.846090i	$0.321049\pi$
$798$	0.100636	−	0.0829873i	0.00356247	−	0.00293772i
$799$	−0.721888	−	0.234555i	−0.0255385	−	0.00829798i
$800$	1.44959	−	6.81976i	0.0512506	−	0.241115i
$801$	5.94954	−	13.3629i	0.210217	−	0.472154i
$802$	−0.437330	+	0.252492i	−0.0154426	+	0.00891581i
$803$	−9.15608	−	26.1658i	−0.323111	−	0.923372i
$804$		−	22.4985i		−	0.793462i
$805$	−6.12231	+	41.0144i	−0.215783	+	1.44557i
$806$	0.309232	+	0.951719i	0.0108922	+	0.0335229i
$807$	11.4241	+	12.6877i	0.402146	+	0.446628i
$808$	4.08060	+	0.428888i	0.143555	+	0.0150882i
$809$	38.8451	+	4.08279i	1.36572	+	0.143543i	0.758855	−	0.651260i	$-0.225759\pi$
$809$	38.8451	+	4.08279i	1.36572	+	0.143543i	0.606867	+	0.794803i	$0.292426\pi$
$810$	−0.177134	−	0.196728i	−0.00622387	−	0.00691231i
$811$	14.5187	+	44.6841i	0.509822	+	1.56907i	0.792510	+	0.609858i	$0.208774\pi$
$811$	14.5187	+	44.6841i	0.509822	+	1.56907i	−0.282689	+	0.959212i	$0.591226\pi$
$812$	−5.21170	+	34.9140i	−0.182895	+	1.22524i
$813$			29.0954i			1.02042i
$814$	0.896503	−	1.29405i	0.0314224	−	0.0453565i
$815$	34.4948	−	19.9156i	1.20830	−	0.697613i
$816$	1.80924	−	4.06363i	0.0633362	−	0.142255i
$817$	0.925577	−	4.35450i	0.0323818	−	0.152345i
$818$	−0.925039	−	0.300563i	−0.0323432	−	0.0105090i
$819$	−4.79854	+	3.95702i	−0.167675	+	0.138270i
$820$	32.6096	−	44.8832i	1.13878	−	1.56739i
$821$	−7.02979	+	6.32965i	−0.245341	+	0.220906i	−0.782622	−	0.622497i	$-0.786118\pi$
$821$	−7.02979	+	6.32965i	−0.245341	+	0.220906i	0.537281	+	0.843404i	$0.319452\pi$
$822$	0.111656	−	0.124007i	0.00389445	−	0.00432523i
$823$	−1.82984	−	0.814697i	−0.0637842	−	0.0283986i	0.374597	−	0.927188i	$-0.377781\pi$
$823$	−1.82984	−	0.814697i	−0.0637842	−	0.0283986i	−0.438381	+	0.898789i	$0.644448\pi$
$824$	0.492504	−	0.853042i	0.0171572	−	0.0297171i
$825$	6.03412	+	25.5536i	0.210081	+	0.889661i
$826$	0.710070	−	0.197053i	0.0247065	−	0.00685637i
$827$	5.68747	+	7.82812i	0.197773	+	0.272211i	0.896372	−	0.443302i	$-0.146193\pi$
$827$	5.68747	+	7.82812i	0.197773	+	0.272211i	−0.698600	+	0.715513i	$0.746193\pi$
$828$	−8.50850	−	1.80854i	−0.295691	−	0.0628510i
$829$	−6.18788	−	29.1117i	−0.214914	−	1.01109i	−0.944832	−	0.327556i	$-0.893775\pi$
$829$	−6.18788	−	29.1117i	−0.214914	−	1.01109i	0.729918	−	0.683535i	$-0.239558\pi$
$830$	−0.0350614	+	0.333587i	−0.00121700	+	0.0115790i
$831$	−6.03698	+	2.68784i	−0.209421	+	0.0932401i
$832$	5.71714	−	17.5955i	0.198206	−	0.610015i
$833$	−1.49480	+	7.70448i	−0.0517919	+	0.266945i
$834$	−0.456660	+	0.331783i	−0.0158128	+	0.0114887i
$835$	40.7914	+	23.5510i	1.41165	+	0.815014i
$836$	−0.561562	−	4.39205i	−0.0194220	−	0.151902i
$837$	−2.88960	−	5.00493i	−0.0998791	−	0.172996i
$838$	−0.184366	−	1.75413i	−0.00636883	−	0.0605954i
$839$	−52.7919	+	17.1531i	−1.82258	+	0.592192i	−0.822865	+	0.568236i	$0.807626\pi$
$839$	−52.7919	+	17.1531i	−1.82258	+	0.592192i	−0.999713	+	0.0239551i	$0.992374\pi$
$840$	−2.79513	−	0.121548i	−0.0964410	−	0.00419381i
$841$	12.7403	+	9.25638i	0.439321	+	0.319186i
$842$	−0.152316	−	0.342106i	−0.00524914	−	0.0117898i
$843$	−4.06643	+	0.864346i	−0.140055	+	0.0297697i
$844$	−26.0507	−	23.4562i	−0.896703	−	0.807395i
$845$	26.7131	−	2.80766i	0.918959	−	0.0965865i
$846$	−0.0498669			−0.00171446
$847$	6.09188	+	28.4585i	0.209320	+	0.977847i
$848$	43.2076			1.48376
$849$	−7.83806	+	0.823814i	−0.269002	+	0.0282732i
$850$	−0.485846	−	0.437458i	−0.0166644	−	0.0150047i
$851$	−27.4893	+	5.84303i	−0.942321	+	0.200297i
$852$	2.59501	+	5.82849i	0.0889037	+	0.199681i
$853$	41.4149	+	30.0897i	1.41802	+	1.03025i	0.992094	+	0.125493i	$0.0400514\pi$
$853$	41.4149	+	30.0897i	1.41802	+	1.03025i	0.425925	+	0.904758i	$0.359949\pi$
$854$	0.920155	+	1.76685i	0.0314871	+	0.0604603i
$855$	−2.28782	+	0.743358i	−0.0782418	+	0.0254223i
$856$	−0.372737	−	3.54636i	−0.0127399	−	0.121212i
$857$	11.5818	+	20.0604i	0.395628	+	0.685249i	0.993181	−	0.116581i	$-0.0371935\pi$
$857$	11.5818	+	20.0604i	0.395628	+	0.685249i	−0.597553	+	0.801830i	$0.703860\pi$
$858$	−0.0728351	−	0.569653i	−0.00248655	−	0.0194476i
$859$	9.09336	+	5.25005i	0.310261	+	0.179129i	0.647043	−	0.762453i	$-0.276005\pi$
$859$	9.09336	+	5.25005i	0.310261	+	0.179129i	−0.336782	+	0.941583i	$0.609339\pi$
$860$	−38.5721	+	28.0243i	−1.31530	+	0.955620i
$861$	−18.3265	−	9.13328i	−0.624567	−	0.311261i
$862$	−0.664588	+	2.04539i	−0.0226360	+	0.0696663i
$863$	−4.17175	+	1.85738i	−0.142008	+	0.0632261i	−0.476510	−	0.879169i	$-0.658098\pi$
$863$	−4.17175	+	1.85738i	−0.142008	+	0.0632261i	0.334502	+	0.942395i	$0.391432\pi$
$864$	0.0920580	−	0.875873i	0.00313188	−	0.0297978i
$865$	6.27274	+	29.5109i	0.213280	+	1.00340i
$866$	−1.17839	−	0.250474i	−0.0400433	−	0.00851147i
$867$	9.25350	+	12.7363i	0.314265	+	0.432549i
$868$	−29.5276	−	7.63084i	−1.00223	−	0.259008i
$869$	−11.7249	−	49.6532i	−0.397741	−	1.68437i
$870$	−0.885418	+	1.53359i	−0.0300185	+	0.0519936i
$871$	−24.2243	−	10.7853i	−0.820808	−	0.365447i
$872$	3.97806	−	4.41808i	0.134714	−	0.149615i
$873$	10.7781	−	9.70464i	0.364783	−	0.328452i
$874$	0.126380	−	0.173947i	0.00427486	−	0.00588383i
$875$	9.70777	−	25.9785i	0.328182	−	0.878232i
$876$	−15.8554	−	5.15174i	−0.535705	−	0.174061i
$877$	9.24978	−	43.5168i	0.312343	−	1.46946i	−0.489542	−	0.871980i	$-0.662836\pi$
$877$	9.24978	−	43.5168i	0.312343	−	1.46946i	0.801885	−	0.597478i	$-0.203831\pi$
$878$	0.400263	−	0.899006i	0.0135082	−	0.0303400i
$879$	12.0124	−	6.93539i	0.405170	−	0.233925i
$880$	−26.9315	+	38.8741i	−0.907861	+	1.31045i
$881$			7.93967i			0.267494i	0.991015	+	0.133747i	$0.0427010\pi$
$881$			7.93967i			0.267494i	−0.991015	+	0.133747i	$0.957299\pi$
$882$	0.0630153	+	0.511739i	0.00212184	+	0.0172311i
$883$	10.1302	+	31.1777i	0.340910	+	1.04921i	0.963737	+	0.266853i	$0.0859840\pi$
$883$	10.1302	+	31.1777i	0.340910	+	1.04921i	−0.622827	+	0.782359i	$0.714016\pi$
$884$	−3.51761	−	3.90670i	−0.118310	−	0.131397i
$885$	−13.5155	−	1.42054i	−0.454319	−	0.0477508i
$886$	0.330554	+	0.0347426i	0.0111052	+	0.00116720i
$887$	−7.41982	−	8.24054i	−0.249133	−	0.276690i	0.605587	−	0.795779i	$-0.292938\pi$
$887$	−7.41982	−	8.24054i	−0.249133	−	0.276690i	−0.854721	+	0.519088i	$0.826272\pi$
$888$	−0.585912	−	1.80325i	−0.0196619	−	0.0605131i
$889$	−3.85857	−	3.06814i	−0.129412	−	0.102902i
$890$		−	3.87224i		−	0.129798i
$891$	1.09544	+	3.13050i	0.0366986	+	0.104876i
$892$	−13.2869	+	7.67118i	−0.444878	+	0.256850i
$893$	−0.184310	+	0.413967i	−0.00616770	+	0.0138529i
$894$	0.125711	−	0.591426i	0.00420442	−	0.0197802i
$895$	53.2142	+	17.2903i	1.77876	+	0.577953i
$896$	−3.94066	−	4.77871i	−0.131648	−	0.159645i
$897$	−6.02607	+	8.29417i	−0.201205	+	0.276934i
$898$	−1.92033	+	1.72908i	−0.0640824	+	0.0577001i
$899$	−25.8681	+	28.7294i	−0.862750	+	0.958180i
$900$	14.4251	+	6.42246i	0.480836	+	0.214082i
$901$	6.10499	−	10.5742i	0.203387	−	0.352276i
$902$	1.61574	−	0.981854i	0.0537983	−	0.0326922i
$903$	12.5533	+	12.3318i	0.417747	+	0.410376i
$904$	−0.537375	−	0.739633i	−0.0178728	−	0.0245998i
$905$	44.3521	+	9.42733i	1.47431	+	0.313375i
$906$	−0.152471	−	0.717319i	−0.00506550	−	0.0238313i
$907$	0.593130	−	5.64325i	0.0196946	−	0.187381i	−0.980252	−	0.197754i	$-0.936635\pi$
$907$	0.593130	−	5.64325i	0.0196946	−	0.187381i	0.999946	+	0.0103730i	$0.00330189\pi$
$908$	−15.4926	+	6.89774i	−0.514140	+	0.228910i
$909$	−4.30926	+	13.2625i	−0.142929	+	0.439891i
$910$	−0.734401	+	1.47363i	−0.0243451	+	0.0488502i
$911$	−2.03150	+	1.47597i	−0.0673064	+	0.0489010i	−0.620930	−	0.783866i	$-0.713245\pi$
$911$	−2.03150	+	1.47597i	−0.0673064	+	0.0489010i	0.553623	+	0.832767i	$0.313245\pi$
$912$	−2.29978	−	1.32778i	−0.0761534	−	0.0439672i
$913$	2.01899	−	3.68565i	0.0668187	−	0.121977i
$914$	1.01209	+	1.75300i	0.0334771	+	0.0579840i
$915$	−3.84017	−	36.5368i	−0.126952	−	1.20787i
$916$	−41.2943	+	13.4173i	−1.36440	+	0.443322i
$917$	34.4436	+	21.9345i	1.13743	+	0.724342i
$918$	−0.0668106	−	0.0485408i	−0.00220508	−	0.00160208i
$919$	1.89233	+	4.25024i	0.0624222	+	0.140202i	0.942063	−	0.335436i	$-0.108884\pi$
$919$	1.89233	+	4.25024i	0.0624222	+	0.140202i	−0.879641	+	0.475639i	$0.842217\pi$
$920$	−4.51093	+	0.958827i	−0.148721	+	0.0316116i
$921$	−18.5117	−	16.6680i	−0.609982	−	0.549230i
$922$	1.67718	−	0.176279i	0.0552350	−	0.00580543i
$923$	7.51956			0.247509
$924$	15.8361	+	7.45316i	0.520969	+	0.245191i
$925$	51.0151			1.67737
$926$	0.0841690	−	0.00884652i	0.00276597	−	0.000290715i
$927$	2.48785	+	2.24007i	0.0817118	+	0.0735736i
$928$	−5.76259	+	1.22488i	−0.189166	+	0.0402085i
$929$	−13.3847	−	30.0626i	−0.439138	−	0.986321i	−0.988567	−	0.150780i	$-0.951821\pi$
$929$	−13.3847	−	30.0626i	−0.439138	−	0.986321i	0.549429	−	0.835540i	$-0.314845\pi$
$930$	−1.23771	−	0.899245i	−0.0405860	−	0.0294874i
$931$	4.48108	+	1.36829i	0.146861	+	0.0448439i
$932$	39.4779	−	12.8271i	1.29314	−	0.420167i
$933$	−1.88907	−	17.9733i	−0.0618454	−	0.588420i
$934$	−0.889495	−	1.54065i	−0.0291052	−	0.0504116i
$935$	5.70835	+	12.0836i	0.186683	+	0.395177i
$936$	−0.599013	−	0.345840i	−0.0195794	−	0.0113041i
$937$	4.58065	−	3.32804i	0.149643	−	0.108722i	−0.510444	−	0.859911i	$-0.670519\pi$
$937$	4.58065	−	3.32804i	0.149643	−	0.108722i	0.660088	+	0.751189i	$0.270519\pi$
$938$	−1.83285	+	1.21360i	−0.0598447	+	0.0396254i
$939$	0.470277	−	1.44736i	0.0153469	−	0.0472329i
$940$	4.43351	−	1.97393i	0.144605	−	0.0643824i
$941$	0.432867	−	4.11846i	0.0141111	−	0.134258i	−0.985198	−	0.171419i	$-0.945165\pi$
$941$	0.432867	−	4.11846i	0.0141111	−	0.134258i	0.999309	+	0.0371611i	$0.0118315\pi$
$942$	0.235613	+	1.10847i	0.00767668	+	0.0361159i
$943$	−33.0146	−	7.01746i	−1.07510	−	0.228520i
$944$	−8.81814	−	12.1371i	−0.287006	−	0.395030i
$945$	2.37919	−	9.20628i	0.0773950	−	0.299480i
$946$	−1.58134	+	0.373411i	−0.0514136	+	0.0121406i
$947$	−30.1498	+	52.2209i	−0.979736	+	1.69695i	−0.316408	+	0.948623i	$0.602477\pi$
$947$	−30.1498	+	52.2209i	−0.979736	+	1.69695i	−0.663328	+	0.748329i	$0.730856\pi$
$948$	−28.0294	−	12.4795i	−0.910354	−	0.405316i
$949$	−13.1477	+	14.6020i	−0.426791	+	0.474000i
$950$	−0.290049	+	0.261161i	−0.00941043	+	0.00847319i
$951$	4.19347	−	5.77182i	0.135983	−	0.187164i
$952$	−0.860790	+	0.144202i	−0.0278984	+	0.00467360i
$953$	11.0841	+	3.60143i	0.359048	+	0.116662i	0.482986	−	0.875628i	$-0.339552\pi$
$953$	11.0841	+	3.60143i	0.359048	+	0.116662i	−0.123938	+	0.992290i	$0.539552\pi$
$954$	0.166780	−	0.784637i	0.00539969	−	0.0254035i
$955$	−8.91318	+	20.0193i	−0.288424	+	0.647810i
$956$	−3.51636	+	2.03017i	−0.113727	+	0.0656605i
$957$	17.6518	−	13.4403i	0.570600	−	0.434464i
$958$		−	1.95047i		−	0.0630169i
$959$	5.92812	+	0.884903i	0.191429	+	0.0285750i
$960$	8.74048	+	26.9004i	0.282098	+	0.868208i
$961$	−1.60531	−	1.78288i	−0.0517842	−	0.0575122i
$962$	−1.10971	−	0.116635i	−0.0357786	−	0.00376048i
$963$	12.0530	+	1.26682i	0.388401	+	0.0408226i
$964$	2.81101	+	3.12194i	0.0905366	+	0.100551i
$965$	9.50343	+	29.2485i	0.305926	+	0.941544i
$966$	0.311626	+	0.790704i	0.0100264	+	0.0254405i
$967$			14.9771i			0.481631i	0.970571	+	0.240815i	$0.0774148\pi$
$967$			14.9771i			0.481631i	−0.970571	+	0.240815i	$0.922585\pi$
$968$	−2.72747	+	1.74245i	−0.0876643	+	0.0560043i
$969$	−0.649893	+	0.375216i	−0.0208776	+	0.0120537i
$970$	1.56162	−	3.50745i	0.0501404	−	0.112617i
$971$	1.30012	−	6.11660i	0.0417230	−	0.196291i	−0.952350	−	0.305008i	$-0.901341\pi$
$971$	1.30012	−	6.11660i	0.0417230	−	0.196291i	0.994073	+	0.108717i	$0.0346742\pi$
$972$	1.89695	+	0.616357i	0.0608448	+	0.0197697i
$973$	−18.9925	−	7.09721i	−0.608871	−	0.227526i
$974$	−0.0578520	+	0.0796264i	−0.00185370	+	0.00255139i
$975$	13.8302	−	12.4528i	0.442920	−	0.398807i
$976$	27.1374	−	30.1391i	0.868646	−	0.964729i
$977$	−7.90136	−	3.51791i	−0.252787	−	0.112548i	0.276431	−	0.961034i	$-0.410848\pi$
$977$	−7.90136	−	3.51791i	−0.252787	−	0.112548i	−0.529218	+	0.848486i	$0.677515\pi$
$978$	0.408167	−	0.706966i	0.0130517	−	0.0226063i
$979$	−18.7326	+	44.7514i	−0.598695	+	1.43026i
$980$	−25.8591	−	43.0028i	−0.826040	−	1.37367i
$981$	11.8765	+	16.3467i	0.379189	+	0.521909i
$982$	−2.00259	−	0.425663i	−0.0639052	−	0.0135835i
$983$	−10.4815	−	49.3116i	−0.334308	−	1.57280i	−0.748833	−	0.662759i	$-0.769385\pi$
$983$	−10.4815	−	49.3116i	−0.334308	−	1.57280i	0.414524	−	0.910038i	$-0.363948\pi$
$984$	0.238027	−	2.26467i	0.00758802	−	0.0721952i
$985$	−89.4661	+	39.8329i	−2.85063	+	1.26918i
$986$	−0.170709	+	0.525388i	−0.00543648	+	0.0167318i
$987$	−0.988888	−	1.49348i	−0.0314766	−	0.0475380i
$988$	−2.53902	+	1.84471i	−0.0807770	+	0.0586879i
$989$	25.1201	+	14.5031i	0.798772	+	0.461171i
$990$	0.601987	+	0.639120i	0.0191324	+	0.0203126i
$991$	16.4738	+	28.5335i	0.523308	+	0.906396i	0.999632	+	0.0271261i	$0.00863556\pi$
$991$	16.4738	+	28.5335i	0.523308	+	0.906396i	−0.476324	+	0.879270i	$0.658031\pi$
$992$	−0.532021	−	5.06184i	−0.0168917	−	0.160714i
$993$	−24.5251	+	7.96868i	−0.778280	+	0.252879i
$994$	0.334842	−	0.525800i	0.0106206	−	0.0166774i
$995$	−4.72637	−	3.43391i	−0.149836	−	0.108862i
$996$	−1.02794	−	2.30878i	−0.0325714	−	0.0731566i
$997$	−8.00358	+	1.70121i	−0.253476	+	0.0538780i	−0.332897	−	0.942963i	$-0.608026\pi$
$997$	−8.00358	+	1.70121i	−0.253476	+	0.0538780i	0.0794211	+	0.996841i	$0.474693\pi$
$998$	0.247827	+	0.223144i	0.00784483	+	0.00706352i
$999$	6.40878	−	0.673590i	0.202765	−	0.0213114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.ba.a.19.10	✓	128
3.2	odd	2		693.2.cg.c.19.7		128
7.3	odd	6	inner	231.2.ba.a.52.7	yes	128
11.7	odd	10	inner	231.2.ba.a.40.7	yes	128
21.17	even	6		693.2.cg.c.514.10		128
33.29	even	10		693.2.cg.c.271.10		128
77.73	even	30	inner	231.2.ba.a.73.10	yes	128
231.227	odd	30		693.2.cg.c.73.7		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.ba.a.19.10	✓	128	1.1	even	1	trivial
231.2.ba.a.40.7	yes	128	11.7	odd	10	inner
231.2.ba.a.52.7	yes	128	7.3	odd	6	inner
231.2.ba.a.73.10	yes	128	77.73	even	30	inner
693.2.cg.c.19.7		128	3.2	odd	2
693.2.cg.c.73.7		128	231.227	odd	30
693.2.cg.c.271.10		128	33.29	even	10
693.2.cg.c.514.10		128	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.0732542 + 0.00769933i) q^{2} +(0.743145 + 0.669131i) q^{3} +(-1.95099 + 0.414695i) q^{4} +(-1.46180 - 3.28325i) q^{5} +(-0.0595904 - 0.0432949i) q^{6} +(0.114944 - 2.64325i) q^{7} +(0.279831 - 0.0909225i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.0732542 + 0.00769933i) q^{2} +(0.743145 + 0.669131i) q^{3} +(-1.95099 + 0.414695i) q^{4} +(-1.46180 - 3.28325i) q^{5} +(-0.0595904 - 0.0432949i) q^{6} +(0.114944 - 2.64325i) q^{7} +(0.279831 - 0.0909225i) q^{8} +(0.104528 + 0.994522i) q^{9} +(0.132362 + 0.229257i) q^{10} +(-0.420635 - 3.28984i) q^{11} +(-1.72735 - 0.997287i) q^{12} +(-1.90184 + 1.38177i) q^{13} +(0.0119312 + 0.194514i) q^{14} +(1.11060 - 3.41806i) q^{15} +(3.62447 - 1.61372i) q^{16} +(0.117194 - 1.11502i) q^{17} +(-0.0153143 - 0.0720481i) q^{18} +(-0.654706 - 0.139162i) q^{19} +(4.21350 + 5.79938i) q^{20} +(1.85410 - 1.88741i) q^{21} +(0.0561429 + 0.237756i) q^{22} +(2.18056 - 3.77684i) q^{23} +(0.268794 + 0.119675i) q^{24} +(-5.29723 + 5.88317i) q^{25} +(0.128679 - 0.115863i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(0.871891 + 5.20462i) q^{28} +(6.36199 + 2.06713i) q^{29} +(-0.0550391 + 0.258938i) q^{30} +(-2.35061 + 5.27956i) q^{31} +(-0.762707 + 0.440349i) q^{32} +(1.88874 - 2.72629i) q^{33} +0.0825825i q^{34} +(-8.84649 + 3.48651i) q^{35} +(-0.616357 - 1.89695i) q^{36} +(-4.31193 - 4.78888i) q^{37} +(0.0490314 + 0.00515341i) q^{38} +(-2.33793 - 0.245726i) q^{39} +(-0.707577 - 0.785844i) q^{40} +(-2.39158 - 7.36053i) q^{41} +(-0.121289 + 0.152536i) q^{42} +6.65108i q^{43} +(2.18494 + 6.24401i) q^{44} +(3.11246 - 1.79698i) q^{45} +(-0.130656 + 0.293459i) q^{46} +(0.140758 - 0.662214i) q^{47} +(3.77329 + 1.22602i) q^{48} +(-6.97358 - 0.607651i) q^{49} +(0.342748 - 0.471752i) q^{50} +(0.833188 - 0.750206i) q^{51} +(3.13746 - 3.48450i) q^{52} +(9.94892 + 4.42954i) q^{53} +(0.0368289 - 0.0637895i) q^{54} +(-10.1865 + 6.19013i) q^{55} +(-0.208166 - 0.750114i) q^{56} +(-0.393424 - 0.541501i) q^{57} +(-0.481958 - 0.102443i) q^{58} +(-0.786182 - 3.69870i) q^{59} +(-0.749305 + 7.12916i) q^{60} +(9.33840 - 4.15772i) q^{61} +(0.131543 - 0.404848i) q^{62} +(2.64079 - 0.161981i) q^{63} +(-6.36703 + 4.62592i) q^{64} +(7.31680 + 4.22436i) q^{65} +(-0.117368 + 0.214254i) q^{66} +(5.63993 + 9.76865i) q^{67} +(0.233751 + 2.22400i) q^{68} +(4.14768 - 1.34766i) q^{69} +(0.621199 - 0.323514i) q^{70} +(-2.58782 - 1.88016i) q^{71} +(0.119675 + 0.268794i) q^{72} +(8.17571 - 1.73780i) q^{73} +(0.352738 + 0.317607i) q^{74} +(-7.87322 + 0.827508i) q^{75} +1.33503 q^{76} +(-8.74424 + 0.733698i) q^{77} +0.173155 q^{78} +(15.2985 - 1.60793i) q^{79} +(-10.5965 - 9.54111i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(0.231864 + 0.520776i) q^{82} +(1.02509 + 0.744769i) q^{83} +(-2.83463 + 4.45120i) q^{84} +(-3.83221 + 1.24516i) q^{85} +(-0.0512088 - 0.487219i) q^{86} +(3.34469 + 5.79318i) q^{87} +(-0.416827 - 0.882354i) q^{88} +(-12.6678 - 7.31375i) q^{89} +(-0.214166 + 0.155600i) q^{90} +(3.43376 + 5.18588i) q^{91} +(-2.68801 + 8.27285i) q^{92} +(-5.27956 + 2.35061i) q^{93} +(-0.00521251 + 0.0495937i) q^{94} +(0.500143 + 2.35299i) q^{95} +(-0.861453 - 0.183107i) q^{96} +(-8.52486 - 11.7335i) q^{97} +(0.515522 - 0.00917883i) q^{98} +(3.22785 - 0.762213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9}+O(q^{10}) \) 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9	\( 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9} - 2 q^{11} + 12 q^{14} + 12 q^{15} + 40 q^{16} - 60 q^{17} - 10 q^{18} + 52 q^{22} - 24 q^{23} - 90 q^{24} - 20 q^{25} + 24 q^{26} + 30 q^{28} + 40 q^{29} - 18 q^{31} + 18 q^{33} - 80 q^{35} - 24 q^{36} - 8 q^{37} - 24 q^{38} - 90 q^{40} + 14 q^{42} - 82 q^{44} + 12 q^{45} + 70 q^{46} - 24 q^{47} - 94 q^{49} - 20 q^{51} + 4 q^{53} - 104 q^{56} - 32 q^{58} + 48 q^{59} + 30 q^{61} - 10 q^{63} - 48 q^{64} + 36 q^{66} - 40 q^{67} + 180 q^{68} + 146 q^{70} - 32 q^{71} + 10 q^{72} + 90 q^{73} + 40 q^{74} - 24 q^{75} - 72 q^{78} + 50 q^{79} + 228 q^{80} + 16 q^{81} + 168 q^{82} - 60 q^{84} - 20 q^{85} + 146 q^{86} + 16 q^{88} + 48 q^{91} - 204 q^{92} + 44 q^{93} + 10 q^{95} - 44 q^{99}+O(q^{100}) \) 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9 - 2 * q^11 + 12 * q^14 + 12 * q^15 + 40 * q^16 - 60 * q^17 - 10 * q^18 + 52 * q^22 - 24 * q^23 - 90 * q^24 - 20 * q^25 + 24 * q^26 + 30 * q^28 + 40 * q^29 - 18 * q^31 + 18 * q^33 - 80 * q^35 - 24 * q^36 - 8 * q^37 - 24 * q^38 - 90 * q^40 + 14 * q^42 - 82 * q^44 + 12 * q^45 + 70 * q^46 - 24 * q^47 - 94 * q^49 - 20 * q^51 + 4 * q^53 - 104 * q^56 - 32 * q^58 + 48 * q^59 + 30 * q^61 - 10 * q^63 - 48 * q^64 + 36 * q^66 - 40 * q^67 + 180 * q^68 + 146 * q^70 - 32 * q^71 + 10 * q^72 + 90 * q^73 + 40 * q^74 - 24 * q^75 - 72 * q^78 + 50 * q^79 + 228 * q^80 + 16 * q^81 + 168 * q^82 - 60 * q^84 - 20 * q^85 + 146 * q^86 + 16 * q^88 + 48 * q^91 - 204 * q^92 + 44 * q^93 + 10 * q^95 - 44 * q^99

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