LMFDB - Embedded newform 690.2.h.a.689.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(689,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("690.689");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.h (of order $2$, degree $1$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			689.15
Character	$\chi$	$=$	690.689
Dual form			690.2.h.a.689.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.571841 + 1.63493i) q^{3} +1.00000 q^{4} +(-2.12720 - 0.689226i) q^{5} +(-0.571841 - 1.63493i) q^{6} +1.28874 q^{7} -1.00000 q^{8} +(-2.34600 + 1.86984i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.571841 + 1.63493i) q^{3} +1.00000 q^{4} +(-2.12720 - 0.689226i) q^{5} +(-0.571841 - 1.63493i) q^{6} +1.28874 q^{7} -1.00000 q^{8} +(-2.34600 + 1.86984i) q^{9} +(2.12720 + 0.689226i) q^{10} -4.52819 q^{11} +(0.571841 + 1.63493i) q^{12} -3.04015i q^{13} -1.28874 q^{14} +(-0.0895807 - 3.87195i) q^{15} +1.00000 q^{16} -5.73191i q^{17} +(2.34600 - 1.86984i) q^{18} -3.52988i q^{19} +(-2.12720 - 0.689226i) q^{20} +(0.736956 + 2.10701i) q^{21} +4.52819 q^{22} +(4.79401 - 0.132152i) q^{23} +(-0.571841 - 1.63493i) q^{24} +(4.04993 + 2.93224i) q^{25} +3.04015i q^{26} +(-4.39860 - 2.76629i) q^{27} +1.28874 q^{28} +3.03143i q^{29} +(0.0895807 + 3.87195i) q^{30} -7.30904 q^{31} -1.00000 q^{32} +(-2.58940 - 7.40327i) q^{33} +5.73191i q^{34} +(-2.74141 - 0.888236i) q^{35} +(-2.34600 + 1.86984i) q^{36} -8.69205 q^{37} +3.52988i q^{38} +(4.97044 - 1.73848i) q^{39} +(2.12720 + 0.689226i) q^{40} -12.7037i q^{41} +(-0.736956 - 2.10701i) q^{42} +8.85037 q^{43} -4.52819 q^{44} +(6.27914 - 2.36060i) q^{45} +(-4.79401 + 0.132152i) q^{46} +3.48815 q^{47} +(0.571841 + 1.63493i) q^{48} -5.33914 q^{49} +(-4.04993 - 2.93224i) q^{50} +(9.37127 - 3.27774i) q^{51} -3.04015i q^{52} -4.54605i q^{53} +(4.39860 + 2.76629i) q^{54} +(9.63235 + 3.12095i) q^{55} -1.28874 q^{56} +(5.77111 - 2.01853i) q^{57} -3.03143i q^{58} +12.7816i q^{59} +(-0.0895807 - 3.87195i) q^{60} -3.04124i q^{61} +7.30904 q^{62} +(-3.02339 + 2.40974i) q^{63} +1.00000 q^{64} +(-2.09535 + 6.46700i) q^{65} +(2.58940 + 7.40327i) q^{66} +3.98470 q^{67} -5.73191i q^{68} +(2.95747 + 7.76230i) q^{69} +(2.74141 + 0.888236i) q^{70} -5.30287i q^{71} +(2.34600 - 1.86984i) q^{72} -9.43385i q^{73} +8.69205 q^{74} +(-2.47809 + 8.29814i) q^{75} -3.52988i q^{76} -5.83567 q^{77} +(-4.97044 + 1.73848i) q^{78} -16.0456i q^{79} +(-2.12720 - 0.689226i) q^{80} +(2.00739 - 8.77328i) q^{81} +12.7037i q^{82} -8.09448i q^{83} +(0.736956 + 2.10701i) q^{84} +(-3.95058 + 12.1929i) q^{85} -8.85037 q^{86} +(-4.95619 + 1.73350i) q^{87} +4.52819 q^{88} -6.63721 q^{89} +(-6.27914 + 2.36060i) q^{90} -3.91797i q^{91} +(4.79401 - 0.132152i) q^{92} +(-4.17961 - 11.9498i) q^{93} -3.48815 q^{94} +(-2.43289 + 7.50876i) q^{95} +(-0.571841 - 1.63493i) q^{96} +0.0268467 q^{97} +5.33914 q^{98} +(10.6231 - 8.46699i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 2 q^{3} + 24 q^{4} - 2 q^{6} - 24 q^{8} + 6 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 2 * q^3 + 24 * q^4 - 2 * q^6 - 24 * q^8 + 6 * q^9	$ 24 q - 24 q^{2} + 2 q^{3} + 24 q^{4} - 2 q^{6} - 24 q^{8} + 6 q^{9} + 2 q^{12} + 24 q^{16} - 6 q^{18} - 4 q^{23} - 2 q^{24} + 12 q^{25} + 2 q^{27} - 28 q^{31} - 24 q^{32} + 8 q^{35} + 6 q^{36} + 4 q^{46} + 16 q^{47} + 2 q^{48} - 4 q^{49} - 12 q^{50} - 2 q^{54} + 4 q^{55} + 28 q^{62} + 24 q^{64} - 8 q^{69} - 8 q^{70} - 6 q^{72} + 14 q^{75} + 8 q^{77} + 14 q^{81} - 44 q^{85} + 28 q^{87} - 4 q^{92} - 4 q^{93} - 16 q^{94} + 4 q^{95} - 2 q^{96} + 4 q^{98}+O(q^{100}) $ 24 * q - 24 * q^2 + 2 * q^3 + 24 * q^4 - 2 * q^6 - 24 * q^8 + 6 * q^9 + 2 * q^12 + 24 * q^16 - 6 * q^18 - 4 * q^23 - 2 * q^24 + 12 * q^25 + 2 * q^27 - 28 * q^31 - 24 * q^32 + 8 * q^35 + 6 * q^36 + 4 * q^46 + 16 * q^47 + 2 * q^48 - 4 * q^49 - 12 * q^50 - 2 * q^54 + 4 * q^55 + 28 * q^62 + 24 * q^64 - 8 * q^69 - 8 * q^70 - 6 * q^72 + 14 * q^75 + 8 * q^77 + 14 * q^81 - 44 * q^85 + 28 * q^87 - 4 * q^92 - 4 * q^93 - 16 * q^94 + 4 * q^95 - 2 * q^96 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.571841	+	1.63493i	0.330152	+	0.943928i
$3$	0.571841	+	1.63493i	0.330152	+	0.943928i
$4$	1.00000			0.500000
$5$	−2.12720	−	0.689226i	−0.951311	−	0.308231i
$5$	−2.12720	−	0.689226i	−0.951311	−	0.308231i
$6$	−0.571841	−	1.63493i	−0.233453	−	0.667458i
$7$	1.28874			0.487099			0.243550	−	0.969888i	$-0.421688\pi$
$7$	1.28874			0.487099			0.243550	+	0.969888i	$0.421688\pi$
$8$	−1.00000			−0.353553
$9$	−2.34600	+	1.86984i	−0.781999	+	0.623280i
$10$	2.12720	+	0.689226i	0.672679	+	0.217953i
$11$	−4.52819			−1.36530			−0.682650	−	0.730745i	$-0.739173\pi$
$11$	−4.52819			−1.36530			−0.682650	+	0.730745i	$0.739173\pi$
$12$	0.571841	+	1.63493i	0.165076	+	0.471964i
$13$		−	3.04015i		−	0.843186i	−0.906785	−	0.421593i	$-0.861471\pi$
$13$		−	3.04015i		−	0.843186i	0.906785	−	0.421593i	$-0.138529\pi$
$14$	−1.28874			−0.344431
$15$	−0.0895807	−	3.87195i	−0.0231296	−	0.999732i
$16$	1.00000			0.250000
$17$		−	5.73191i		−	1.39019i	−0.718917	−	0.695096i	$-0.755362\pi$
$17$		−	5.73191i		−	1.39019i	0.718917	−	0.695096i	$-0.244638\pi$
$18$	2.34600	−	1.86984i	0.552957	−	0.440726i
$19$		−	3.52988i		−	0.809811i	−0.914359	−	0.404905i	$-0.867304\pi$
$19$		−	3.52988i		−	0.809811i	0.914359	−	0.404905i	$-0.132696\pi$
$20$	−2.12720	−	0.689226i	−0.475656	−	0.154116i
$21$	0.736956	+	2.10701i	0.160817	+	0.459786i
$22$	4.52819			0.965413
$23$	4.79401	−	0.132152i	0.999620	−	0.0275555i
$23$	4.79401	−	0.132152i	0.999620	−	0.0275555i
$24$	−0.571841	−	1.63493i	−0.116727	−	0.333729i
$25$	4.04993	+	2.93224i	0.809987	+	0.586448i
$26$			3.04015i			0.596223i
$27$	−4.39860	−	2.76629i	−0.846510	−	0.532373i
$28$	1.28874			0.243550
$29$			3.03143i			0.562923i	0.959572	+	0.281462i	$0.0908192\pi$
$29$			3.03143i			0.562923i	−0.959572	+	0.281462i	$0.909181\pi$
$30$	0.0895807	+	3.87195i	0.0163551	+	0.706918i
$31$	−7.30904			−1.31274			−0.656371	−	0.754438i	$-0.727909\pi$
$31$	−7.30904			−1.31274			−0.656371	+	0.754438i	$0.727909\pi$
$32$	−1.00000			−0.176777
$33$	−2.58940	−	7.40327i	−0.450757	−	1.28874i
$34$			5.73191i			0.983014i
$35$	−2.74141	−	0.888236i	−0.463383	−	0.150139i
$36$	−2.34600	+	1.86984i	−0.390999	+	0.311640i
$37$	−8.69205			−1.42896			−0.714482	−	0.699654i	$-0.753338\pi$
$37$	−8.69205			−1.42896			−0.714482	+	0.699654i	$0.753338\pi$
$38$			3.52988i			0.572623i
$39$	4.97044	−	1.73848i	0.795907	−	0.278380i
$40$	2.12720	+	0.689226i	0.336339	+	0.108976i
$41$		−	12.7037i		−	1.98399i	−0.126290	−	0.991993i	$-0.540307\pi$
$41$		−	12.7037i		−	1.98399i	0.126290	−	0.991993i	$-0.459693\pi$
$42$	−0.736956	−	2.10701i	−0.113715	−	0.325118i
$43$	8.85037			1.34967			0.674834	−	0.737969i	$-0.264215\pi$
$43$	8.85037			1.34967			0.674834	+	0.737969i	$0.264215\pi$
$44$	−4.52819			−0.682650
$45$	6.27914	−	2.36060i	0.936039	−	0.351897i
$46$	−4.79401	+	0.132152i	−0.706838	+	0.0194847i
$47$	3.48815			0.508799			0.254400	−	0.967099i	$-0.418122\pi$
$47$	3.48815			0.508799			0.254400	+	0.967099i	$0.418122\pi$
$48$	0.571841	+	1.63493i	0.0825381	+	0.235982i
$49$	−5.33914			−0.762734
$50$	−4.04993	−	2.93224i	−0.572747	−	0.414681i
$51$	9.37127	−	3.27774i	1.31224	−	0.458975i
$52$		−	3.04015i		−	0.421593i
$53$		−	4.54605i		−	0.624448i	−0.950008	−	0.312224i	$-0.898926\pi$
$53$		−	4.54605i		−	0.624448i	0.950008	−	0.312224i	$-0.101074\pi$
$54$	4.39860	+	2.76629i	0.598573	+	0.376444i
$55$	9.63235	+	3.12095i	1.29883	+	0.420829i
$56$	−1.28874			−0.172216
$57$	5.77111	−	2.01853i	0.764403	−	0.267361i
$58$		−	3.03143i		−	0.398047i
$59$			12.7816i			1.66402i	0.554757	+	0.832012i	$0.312811\pi$
$59$			12.7816i			1.66402i	−0.554757	+	0.832012i	$0.687189\pi$
$60$	−0.0895807	−	3.87195i	−0.0115648	−	0.499866i
$61$		−	3.04124i		−	0.389391i	−0.980864	−	0.194696i	$-0.937628\pi$
$61$		−	3.04124i		−	0.389391i	0.980864	−	0.194696i	$-0.0623719\pi$
$62$	7.30904			0.928249
$63$	−3.02339	+	2.40974i	−0.380911	+	0.303599i
$64$	1.00000			0.125000
$65$	−2.09535	+	6.46700i	−0.259897	+	0.802133i
$66$	2.58940	+	7.40327i	0.318734	+	0.911280i
$67$	3.98470			0.486808			0.243404	−	0.969925i	$-0.421736\pi$
$67$	3.98470			0.486808			0.243404	+	0.969925i	$0.421736\pi$
$68$		−	5.73191i		−	0.695096i
$69$	2.95747	+	7.76230i	0.356038	+	0.934472i
$70$	2.74141	+	0.888236i	0.327661	+	0.106165i
$71$		−	5.30287i		−	0.629335i	−0.949202	−	0.314667i	$-0.898107\pi$
$71$		−	5.30287i		−	0.629335i	0.949202	−	0.314667i	$-0.101893\pi$
$72$	2.34600	−	1.86984i	0.276478	−	0.220363i
$73$		−	9.43385i		−	1.10415i	−0.833795	−	0.552074i	$-0.813836\pi$
$73$		−	9.43385i		−	1.10415i	0.833795	−	0.552074i	$-0.186164\pi$
$74$	8.69205			1.01043
$75$	−2.47809	+	8.29814i	−0.286146	+	0.958186i
$76$		−	3.52988i		−	0.404905i
$77$	−5.83567			−0.665037
$78$	−4.97044	+	1.73848i	−0.562791	+	0.196844i
$79$		−	16.0456i		−	1.80527i	−0.430410	−	0.902633i	$-0.641631\pi$
$79$		−	16.0456i		−	1.80527i	0.430410	−	0.902633i	$-0.358369\pi$
$80$	−2.12720	−	0.689226i	−0.237828	−	0.0770579i
$81$	2.00739	−	8.77328i	0.223044	−	0.974808i
$82$			12.7037i			1.40289i
$83$		−	8.09448i		−	0.888484i	−0.895907	−	0.444242i	$-0.853473\pi$
$83$		−	8.09448i		−	0.888484i	0.895907	−	0.444242i	$-0.146527\pi$
$84$	0.736956	+	2.10701i	0.0804085	+	0.229893i
$85$	−3.95058	+	12.1929i	−0.428501	+	1.32250i
$86$	−8.85037			−0.954360
$87$	−4.95619	+	1.73350i	−0.531359	+	0.185851i
$88$	4.52819			0.482707
$89$	−6.63721			−0.703543			−0.351772	−	0.936086i	$-0.614421\pi$
$89$	−6.63721			−0.703543			−0.351772	+	0.936086i	$0.614421\pi$
$90$	−6.27914	+	2.36060i	−0.661879	+	0.248829i
$91$		−	3.91797i		−	0.410715i
$92$	4.79401	−	0.132152i	0.499810	−	0.0137778i
$93$	−4.17961	−	11.9498i	−0.433405	−	1.23913i
$94$	−3.48815			−0.359776
$95$	−2.43289	+	7.50876i	−0.249609	+	0.770382i
$96$	−0.571841	−	1.63493i	−0.0583633	−	0.166864i
$97$	0.0268467			0.00272587			0.00136294	−	0.999999i	$-0.499566\pi$
$97$	0.0268467			0.00272587			0.00136294	+	0.999999i	$0.499566\pi$
$98$	5.33914			0.539335
$99$	10.6231	−	8.46699i	1.06766	−	0.850965i
$100$	4.04993	+	2.93224i	0.404993	+	0.293224i
$101$		−	1.23854i		−	0.123239i	−0.998100	−	0.0616195i	$-0.980373\pi$
$101$		−	1.23854i		−	0.123239i	0.998100	−	0.0616195i	$-0.0196265\pi$
$102$	−9.37127	+	3.27774i	−0.927894	+	0.324544i
$103$	−15.0918			−1.48704			−0.743520	−	0.668714i	$-0.766845\pi$
$103$	−15.0918			−1.48704			−0.743520	+	0.668714i	$0.766845\pi$
$104$			3.04015i			0.298111i
$105$	−0.115447	−	4.98995i	−0.0112664	−	0.486969i
$106$			4.54605i			0.441552i
$107$			16.5225i			1.59729i	0.601802	+	0.798645i	$0.294450\pi$
$107$			16.5225i			1.59729i	−0.601802	+	0.798645i	$0.705550\pi$
$108$	−4.39860	−	2.76629i	−0.423255	−	0.266186i
$109$			17.0974i			1.63764i	0.574053	+	0.818818i	$0.305370\pi$
$109$			17.0974i			1.63764i	−0.574053	+	0.818818i	$0.694630\pi$
$110$	−9.63235	−	3.12095i	−0.918409	−	0.297571i
$111$	−4.97047	−	14.2109i	−0.471776	−	1.34884i
$112$	1.28874			0.121775
$113$			17.3017i			1.62761i	0.581139	+	0.813804i	$0.302607\pi$
$113$			17.3017i			1.62761i	−0.581139	+	0.813804i	$0.697393\pi$
$114$	−5.77111	+	2.01853i	−0.540514	+	0.189053i
$115$	−10.2889	−	3.02305i	−0.959444	−	0.281901i
$116$			3.03143i			0.281462i
$117$	5.68460	+	7.13218i	0.525541	+	0.659371i
$118$		−	12.7816i		−	1.17664i
$119$		−	7.38696i		−	0.677161i
$120$	0.0895807	+	3.87195i	0.00817756	+	0.353459i
$121$	9.50450			0.864045
$122$			3.04124i			0.275341i
$123$	20.7697	−	7.26450i	1.87274	−	0.655018i
$124$	−7.30904			−0.656371
$125$	−6.59403	−	9.02878i	−0.589788	−	0.807558i
$126$	3.02339	−	2.40974i	0.269345	−	0.214677i
$127$		−	6.86184i		−	0.608890i	−0.952530	−	0.304445i	$-0.901529\pi$
$127$		−	6.86184i		−	0.608890i	0.952530	−	0.304445i	$-0.0984709\pi$
$128$	−1.00000			−0.0883883
$129$	5.06100	+	14.4697i	0.445596	+	1.27399i
$130$	2.09535	−	6.46700i	0.183775	−	0.567193i
$131$			0.675240i			0.0589960i	0.999565	+	0.0294980i	$0.00939087\pi$
$131$			0.675240i			0.0589960i	−0.999565	+	0.0294980i	$0.990609\pi$
$132$	−2.58940	−	7.40327i	−0.225379	−	0.644372i
$133$		−	4.54911i		−	0.394458i
$134$	−3.98470			−0.344225
$135$	7.45008	+	8.91607i	0.641201	+	0.767373i
$136$			5.73191i			0.491507i
$137$			6.14111i			0.524670i	0.964977	+	0.262335i	$0.0844926\pi$
$137$			6.14111i			0.524670i	−0.964977	+	0.262335i	$0.915507\pi$
$138$	−2.95747	−	7.76230i	−0.251757	−	0.660771i
$139$	−13.8754			−1.17689			−0.588447	−	0.808536i	$-0.700261\pi$
$139$	−13.8754			−1.17689			−0.588447	+	0.808536i	$0.700261\pi$
$140$	−2.74141	−	0.888236i	−0.231692	−	0.0750697i
$141$	1.99467	+	5.70289i	0.167981	+	0.480270i
$142$			5.30287i			0.445007i
$143$			13.7664i			1.15120i
$144$	−2.34600	+	1.86984i	−0.195500	+	0.155820i
$145$	2.08935	−	6.44846i	0.173511	−	0.535515i
$146$			9.43385i			0.780751i
$147$	−3.05314	−	8.72912i	−0.251819	−	0.719966i
$148$	−8.69205			−0.714482
$149$	−12.8749			−1.05475			−0.527377	−	0.849631i	$-0.676825\pi$
$149$	−12.8749			−1.05475			−0.527377	+	0.849631i	$0.676825\pi$
$150$	2.47809	−	8.29814i	0.202335	−	0.677540i
$151$	−4.34447			−0.353548			−0.176774	−	0.984251i	$-0.556566\pi$
$151$	−4.34447			−0.353548			−0.176774	+	0.984251i	$0.556566\pi$
$152$			3.52988i			0.286311i
$153$	10.7177	+	13.4470i	0.866479	+	1.08713i
$154$	5.83567			0.470252
$155$	15.5478	+	5.03758i	1.24883	+	0.404628i
$156$	4.97044	−	1.73848i	0.397953	−	0.139190i
$157$	−11.9565			−0.954234			−0.477117	−	0.878840i	$-0.658318\pi$
$157$	−11.9565			−0.954234			−0.477117	+	0.878840i	$0.658318\pi$
$158$			16.0456i			1.27652i
$159$	7.43248	−	2.59962i	0.589434	−	0.206163i
$160$	2.12720	+	0.689226i	0.168170	+	0.0544881i
$161$	6.17825	−	0.170309i	0.486914	−	0.0134223i
$162$	−2.00739	+	8.77328i	−0.157716	+	0.689294i
$163$		−	4.08030i		−	0.319594i	−0.987150	−	0.159797i	$-0.948916\pi$
$163$		−	4.08030i		−	0.319594i	0.987150	−	0.159797i	$-0.0510839\pi$
$164$		−	12.7037i		−	0.991993i
$165$	0.405638	+	17.5329i	0.0315789	+	1.36494i
$166$			8.09448i			0.628253i
$167$	−5.57148			−0.431134			−0.215567	−	0.976489i	$-0.569160\pi$
$167$	−5.57148			−0.431134			−0.215567	+	0.976489i	$0.569160\pi$
$168$	−0.736956	−	2.10701i	−0.0568574	−	0.162559i
$169$	3.75748			0.289037
$170$	3.95058	−	12.1929i	0.302996	−	0.935152i
$171$	6.60032	+	8.28109i	0.504739	+	0.633271i
$172$	8.85037			0.674834
$173$	−11.6414			−0.885082			−0.442541	−	0.896748i	$-0.645923\pi$
$173$	−11.6414			−0.885082			−0.442541	+	0.896748i	$0.645923\pi$
$174$	4.95619	−	1.73350i	0.375727	−	0.131416i
$175$	5.21933	+	3.77891i	0.394544	+	0.285658i
$176$	−4.52819			−0.341325
$177$	−20.8971	+	7.30905i	−1.57072	+	0.549382i
$178$	6.63721			0.497480
$179$			6.37813i			0.476724i	0.971176	+	0.238362i	$0.0766104\pi$
$179$			6.37813i			0.476724i	−0.971176	+	0.238362i	$0.923390\pi$
$180$	6.27914	−	2.36060i	0.468019	−	0.175948i
$181$			7.84733i			0.583287i	0.956527	+	0.291644i	$0.0942022\pi$
$181$			7.84733i			0.583287i	−0.956527	+	0.291644i	$0.905798\pi$
$182$			3.91797i			0.290420i
$183$	4.97222	−	1.73911i	0.367557	−	0.128559i
$184$	−4.79401	+	0.132152i	−0.353419	+	0.00974234i
$185$	18.4897	+	5.99079i	1.35939	+	0.440452i
$186$	4.17961	+	11.9498i	0.306464	+	0.876200i
$187$			25.9552i			1.89803i
$188$	3.48815			0.254400
$189$	−5.66866	−	3.56504i	−0.412334	−	0.259318i
$190$	2.43289	−	7.50876i	0.176500	−	0.544742i
$191$	6.06089			0.438550			0.219275	−	0.975663i	$-0.429631\pi$
$191$	6.06089			0.438550			0.219275	+	0.975663i	$0.429631\pi$
$192$	0.571841	+	1.63493i	0.0412691	+	0.117991i
$193$		−	4.83220i		−	0.347829i	−0.984761	−	0.173915i	$-0.944358\pi$
$193$		−	4.83220i		−	0.347829i	0.984761	−	0.173915i	$-0.0556417\pi$
$194$	−0.0268467			−0.00192748
$195$	−11.7713	+	0.272339i	−0.842961	+	0.0195026i
$196$	−5.33914			−0.381367
$197$	12.3455			0.879581			0.439790	−	0.898101i	$-0.355053\pi$
$197$	12.3455			0.879581			0.439790	+	0.898101i	$0.355053\pi$
$198$	−10.6231	+	8.46699i	−0.754952	+	0.601723i
$199$			4.31745i			0.306056i	0.988222	+	0.153028i	$0.0489024\pi$
$199$			4.31745i			0.306056i	−0.988222	+	0.153028i	$0.951098\pi$
$200$	−4.04993	−	2.93224i	−0.286374	−	0.207341i
$201$	2.27861	+	6.51470i	0.160721	+	0.459512i
$202$			1.23854i			0.0871431i
$203$			3.90674i			0.274200i
$204$	9.37127	−	3.27774i	0.656120	−	0.229488i
$205$	−8.75574	+	27.0233i	−0.611527	+	1.88739i
$206$	15.0918			1.05150
$207$	−10.9996	+	9.27406i	−0.764527	+	0.644592i
$208$		−	3.04015i		−	0.210797i
$209$			15.9840i			1.10563i
$210$	0.115447	+	4.98995i	0.00796657	+	0.344339i
$211$	21.0772			1.45101			0.725507	−	0.688214i	$-0.241605\pi$
$211$	21.0772			1.45101			0.725507	+	0.688214i	$0.241605\pi$
$212$		−	4.54605i		−	0.312224i
$213$	8.66982	−	3.03240i	0.594047	−	0.207776i
$214$		−	16.5225i		−	1.12945i
$215$	−18.8265	−	6.09991i	−1.28396	−	0.416010i
$216$	4.39860	+	2.76629i	0.299287	+	0.188222i
$217$	−9.41947			−0.639436
$218$		−	17.0974i		−	1.15798i
$219$	15.4237	−	5.39466i	1.04224	−	0.364538i
$220$	9.63235	+	3.12095i	0.649413	+	0.210414i
$221$	−17.4259			−1.17219
$222$	4.97047	+	14.2109i	0.333596	+	0.953773i
$223$		−	20.9973i		−	1.40608i	−0.711149	−	0.703042i	$-0.751825\pi$
$223$		−	20.9973i		−	1.40608i	0.711149	−	0.703042i	$-0.248175\pi$
$224$	−1.28874			−0.0861078
$225$	−14.9840	+	0.693703i	−0.998930	+	0.0462469i
$226$		−	17.3017i		−	1.15089i
$227$		−	5.88743i		−	0.390762i	−0.980727	−	0.195381i	$-0.937406\pi$
$227$		−	5.88743i		−	0.390762i	0.980727	−	0.195381i	$-0.0625944\pi$
$228$	5.77111	−	2.01853i	0.382201	−	0.133680i
$229$			22.8454i			1.50967i	0.655916	+	0.754834i	$0.272282\pi$
$229$			22.8454i			1.50967i	−0.655916	+	0.754834i	$0.727718\pi$
$230$	10.2889	+	3.02305i	0.678429	+	0.199334i
$231$	−3.33708	−	9.54092i	−0.219564	−	0.627747i
$232$		−	3.03143i		−	0.199023i
$233$	1.99467			0.130675			0.0653375	−	0.997863i	$-0.479188\pi$
$233$	1.99467			0.130675			0.0653375	+	0.997863i	$0.479188\pi$
$234$	−5.68460	−	7.13218i	−0.371614	−	0.466245i
$235$	−7.41999	−	2.40413i	−0.484027	−	0.156828i
$236$			12.7816i			0.832012i
$237$	26.2334	−	9.17551i	1.70404	−	0.596013i
$238$			7.38696i			0.478825i
$239$		−	16.2137i		−	1.04878i	−0.851479	−	0.524388i	$-0.824294\pi$
$239$		−	16.2137i		−	1.04878i	0.851479	−	0.524388i	$-0.175706\pi$
$240$	−0.0895807	−	3.87195i	−0.00578241	−	0.249933i
$241$			19.7040i			1.26924i	0.772823	+	0.634622i	$0.218844\pi$
$241$			19.7040i			1.26924i	−0.772823	+	0.634622i	$0.781156\pi$
$242$	−9.50450			−0.610972
$243$	15.4916	−	1.73497i	0.993787	−	0.111298i
$244$		−	3.04124i		−	0.194696i
$245$	11.3574	+	3.67988i	0.725598	+	0.235099i
$246$	−20.7697	+	7.26450i	−1.32423	+	0.463168i
$247$	−10.7314			−0.682821
$248$	7.30904			0.464124
$249$	13.2339	−	4.62875i	0.838665	−	0.293335i
$250$	6.59403	+	9.02878i	0.417043	+	0.571030i
$251$	−5.44250			−0.343527			−0.171764	−	0.985138i	$-0.554947\pi$
$251$	−5.44250			−0.343527			−0.171764	+	0.985138i	$0.554947\pi$
$252$	−3.02339	+	2.40974i	−0.190455	+	0.151800i
$253$	−21.7082	+	0.598407i	−1.36478	+	0.0376215i
$254$			6.86184i			0.430550i
$255$	−22.1936	+	0.513468i	−1.38982	+	0.0321546i
$256$	1.00000			0.0625000
$257$	10.2937			0.642105			0.321052	−	0.947061i	$-0.395963\pi$
$257$	10.2937			0.642105			0.321052	+	0.947061i	$0.395963\pi$
$258$	−5.06100	−	14.4697i	−0.315084	−	0.900847i
$259$	−11.2018			−0.696047
$260$	−2.09535	+	6.46700i	−0.129948	+	0.401066i
$261$	−5.66830	−	7.11173i	−0.350859	−	0.440205i
$262$		−	0.675240i		−	0.0417165i
$263$		−	18.0484i		−	1.11291i	−0.830877	−	0.556457i	$-0.812161\pi$
$263$		−	18.0484i		−	1.11291i	0.830877	−	0.556457i	$-0.187839\pi$
$264$	2.58940	+	7.40327i	0.159367	+	0.455640i
$265$	−3.13326	+	9.67035i	−0.192475	+	0.594045i
$266$			4.54911i			0.278924i
$267$	−3.79543	−	10.8514i	−0.232277	−	0.664094i
$268$	3.98470			0.243404
$269$		−	5.62437i		−	0.342924i	−0.985191	−	0.171462i	$-0.945151\pi$
$269$		−	5.62437i		−	0.342924i	0.985191	−	0.171462i	$-0.0548491\pi$
$270$	−7.45008	−	8.91607i	−0.453397	−	0.542615i
$271$	19.4771			1.18315			0.591575	−	0.806250i	$-0.298506\pi$
$271$	19.4771			1.18315			0.591575	+	0.806250i	$0.298506\pi$
$272$		−	5.73191i		−	0.347548i
$273$	6.40562	−	2.24046i	0.387686	−	0.135599i
$274$		−	6.14111i		−	0.370998i
$275$	−18.3389	−	13.2777i	−1.10588	−	0.800678i
$276$	2.95747	+	7.76230i	0.178019	+	0.467236i
$277$			1.53636i			0.0923111i	0.998934	+	0.0461555i	$0.0146970\pi$
$277$			1.53636i			0.0923111i	−0.998934	+	0.0461555i	$0.985303\pi$
$278$	13.8754			0.832190
$279$	17.1470	−	13.6667i	1.02656	−	0.818206i
$280$	2.74141	+	0.888236i	0.163831	+	0.0530823i
$281$	−6.23953			−0.372219			−0.186110	−	0.982529i	$-0.559588\pi$
$281$	−6.23953			−0.372219			−0.186110	+	0.982529i	$0.559588\pi$
$282$	−1.99467	−	5.70289i	−0.118781	−	0.339602i
$283$	7.82642			0.465232			0.232616	−	0.972569i	$-0.425271\pi$
$283$	7.82642			0.465232			0.232616	+	0.972569i	$0.425271\pi$
$284$		−	5.30287i		−	0.314667i
$285$	−13.6675	+	0.316209i	−0.809594	+	0.0187306i
$286$		−	13.7664i		−	0.814023i
$287$		−	16.3718i		−	0.966398i
$288$	2.34600	−	1.86984i	0.138239	−	0.110181i
$289$	−15.8547			−0.932632
$290$	−2.08935	+	6.44846i	−0.122691	+	0.378667i
$291$	0.0153521	+	0.0438925i	0.000899953	+	0.00257303i
$292$		−	9.43385i		−	0.552074i
$293$		−	17.3337i		−	1.01264i	−0.862345	−	0.506322i	$-0.831005\pi$
$293$		−	17.3337i		−	1.01264i	0.862345	−	0.506322i	$-0.168995\pi$
$294$	3.05314	+	8.72912i	0.178063	+	0.509093i
$295$	8.80943	−	27.1890i	0.512905	−	1.58301i
$296$	8.69205			0.505215
$297$	19.9177	+	12.5263i	1.15574	+	0.726849i
$298$	12.8749			0.745824
$299$	−0.401761	−	14.5745i	−0.0232344	−	0.842866i
$300$	−2.47809	+	8.29814i	−0.143073	+	0.479093i
$301$	11.4059			0.657423
$302$	4.34447			0.249996
$303$	2.02492	−	0.708246i	0.116329	−	0.0406876i
$304$		−	3.52988i		−	0.202453i
$305$	−2.09611	+	6.46933i	−0.120023	+	0.370432i
$306$	−10.7177	−	13.4470i	−0.612693	−	0.768715i
$307$		−	14.6960i		−	0.838745i	−0.907814	−	0.419373i	$-0.862250\pi$
$307$		−	14.6960i		−	0.838745i	0.907814	−	0.419373i	$-0.137750\pi$
$308$	−5.83567			−0.332518
$309$	−8.63011	−	24.6741i	−0.490950	−	1.40366i
$310$	−15.5478	−	5.03758i	−0.883054	−	0.286115i
$311$			5.16495i			0.292878i	0.989220	+	0.146439i	$0.0467811\pi$
$311$			5.16495i			0.292878i	−0.989220	+	0.146439i	$0.953219\pi$
$312$	−4.97044	+	1.73848i	−0.281396	+	0.0984222i
$313$	14.4632			0.817509			0.408754	−	0.912644i	$-0.365963\pi$
$313$	14.4632			0.817509			0.408754	+	0.912644i	$0.365963\pi$
$314$	11.9565			0.674745
$315$	8.09220	−	3.04220i	0.455944	−	0.171409i
$316$		−	16.0456i		−	0.902633i
$317$	5.68991			0.319577			0.159789	−	0.987151i	$-0.448919\pi$
$317$	5.68991			0.319577			0.159789	+	0.987151i	$0.448919\pi$
$318$	−7.43248	+	2.59962i	−0.416793	+	0.145779i
$319$		−	13.7269i		−	0.768559i
$320$	−2.12720	−	0.689226i	−0.118914	−	0.0385289i
$321$	−27.0131	+	9.44824i	−1.50773	+	0.527349i
$322$	−6.17825	+	0.170309i	−0.344300	+	0.00949098i
$323$	−20.2330			−1.12579
$324$	2.00739	−	8.77328i	0.111522	−	0.487404i
$325$	8.91446	−	12.3124i	0.494485	−	0.682970i
$326$			4.08030i			0.225987i
$327$	−27.9531	+	9.77700i	−1.54581	+	0.540670i
$328$			12.7037i			0.701445i
$329$	4.49533			0.247836
$330$	−0.405638	−	17.5329i	−0.0223297	−	0.965155i
$331$	−12.3989			−0.681506			−0.340753	−	0.940153i	$-0.610682\pi$
$331$	−12.3989			−0.681506			−0.340753	+	0.940153i	$0.610682\pi$
$332$		−	8.09448i		−	0.444242i
$333$	20.3915	−	16.2527i	1.11745	−	0.890645i
$334$	5.57148			0.304858
$335$	−8.47624	−	2.74636i	−0.463106	−	0.150050i
$336$	0.736956	+	2.10701i	0.0402043	+	0.114947i
$337$	13.5952			0.740575			0.370288	−	0.928917i	$-0.379259\pi$
$337$	13.5952			0.740575			0.370288	+	0.928917i	$0.379259\pi$
$338$	−3.75748			−0.204380
$339$	−28.2871	+	9.89383i	−1.53634	+	0.537359i
$340$	−3.95058	+	12.1929i	−0.214250	+	0.661252i
$341$	33.0967			1.79229
$342$	−6.60032	−	8.28109i	−0.356904	−	0.447790i
$343$	−15.9020			−0.858627
$344$	−8.85037			−0.477180
$345$	−0.941135	−	18.5503i	−0.0506690	−	0.998716i
$346$	11.6414			0.625848
$347$	−6.55994			−0.352156			−0.176078	−	0.984376i	$-0.556341\pi$
$347$	−6.55994			−0.352156			−0.176078	+	0.984376i	$0.556341\pi$
$348$	−4.95619	+	1.73350i	−0.265679	+	0.0929253i
$349$	−28.1738			−1.50811			−0.754055	−	0.656811i	$-0.771905\pi$
$349$	−28.1738			−1.50811			−0.754055	+	0.656811i	$0.771905\pi$
$350$	−5.21933	−	3.77891i	−0.278985	−	0.201991i
$351$	−8.40994	+	13.3724i	−0.448889	+	0.713766i
$352$	4.52819			0.241353
$353$	5.76001			0.306574			0.153287	−	0.988182i	$-0.451014\pi$
$353$	5.76001			0.306574			0.153287	+	0.988182i	$0.451014\pi$
$354$	20.8971	−	7.30905i	1.11067	−	0.388472i
$355$	−3.65488	+	11.2802i	−0.193981	+	0.598693i
$356$	−6.63721			−0.351772
$357$	12.0772	−	4.22416i	0.639191	−	0.223566i
$358$		−	6.37813i		−	0.337095i
$359$	6.40987			0.338300			0.169150	−	0.985590i	$-0.445898\pi$
$359$	6.40987			0.338300			0.169150	+	0.985590i	$0.445898\pi$
$360$	−6.27914	+	2.36060i	−0.330940	+	0.124414i
$361$	6.53993			0.344207
$362$		−	7.84733i		−	0.412447i
$363$	5.43506	+	15.5392i	0.285267	+	0.815596i
$364$		−	3.91797i		−	0.205358i
$365$	−6.50206	+	20.0677i	−0.340333	+	1.05039i
$366$	−4.97222	+	1.73911i	−0.259902	+	0.0909046i
$367$	26.8268			1.40035			0.700174	−	0.713972i	$-0.253106\pi$
$367$	26.8268			1.40035			0.700174	+	0.713972i	$0.253106\pi$
$368$	4.79401	−	0.132152i	0.249905	−	0.00688888i
$369$	23.7539	+	29.8029i	1.23658	+	1.55148i
$370$	−18.4897	−	5.99079i	−0.961234	−	0.311446i
$371$		−	5.85870i		−	0.304168i
$372$	−4.17961	−	11.9498i	−0.216702	−	0.619567i
$373$	−8.96103			−0.463984			−0.231992	−	0.972718i	$-0.574524\pi$
$373$	−8.96103			−0.463984			−0.231992	+	0.972718i	$0.574524\pi$
$374$		−	25.9552i		−	1.34211i
$375$	10.9907	−	15.9438i	0.567557	−	0.823334i
$376$	−3.48815			−0.179888
$377$	9.21602			0.474649
$378$	5.66866	+	3.56504i	0.291564	+	0.183366i
$379$			4.30108i			0.220931i	0.993880	+	0.110466i	$0.0352342\pi$
$379$			4.30108i			0.220931i	−0.993880	+	0.110466i	$0.964766\pi$
$380$	−2.43289	+	7.50876i	−0.124805	+	0.385191i
$381$	11.2186	−	3.92388i	0.574748	−	0.201026i
$382$	−6.06089			−0.310102
$383$		−	10.2019i		−	0.521291i	−0.965435	−	0.260646i	$-0.916065\pi$
$383$		−	10.2019i		−	0.521291i	0.965435	−	0.260646i	$-0.0839354\pi$
$384$	−0.571841	−	1.63493i	−0.0291816	−	0.0834322i
$385$	12.4136	+	4.02210i	0.632657	+	0.204985i
$386$			4.83220i			0.245952i
$387$	−20.7629	+	16.5488i	−1.05544	+	0.841222i
$388$	0.0268467			0.00136294
$389$	10.3677			0.525664			0.262832	−	0.964842i	$-0.415343\pi$
$389$	10.3677			0.525664			0.262832	+	0.964842i	$0.415343\pi$
$390$	11.7713	−	0.272339i	0.596063	−	0.0137904i
$391$	−0.757480	−	27.4788i	−0.0383074	−	1.38966i
$392$	5.33914			0.269667
$393$	−1.10397	+	0.386130i	−0.0556880	+	0.0194777i
$394$	−12.3455			−0.621957
$395$	−11.0590	+	34.1321i	−0.556440	+	1.71737i
$396$	10.6231	−	8.46699i	0.533832	−	0.425482i
$397$			15.6662i			0.786264i	0.919482	+	0.393132i	$0.128608\pi$
$397$			15.6662i			0.786264i	−0.919482	+	0.393132i	$0.871392\pi$
$398$		−	4.31745i		−	0.216414i
$399$	7.43748	−	2.60137i	0.372340	−	0.130231i
$400$	4.04993	+	2.93224i	0.202497	+	0.146612i
$401$	−21.5559			−1.07645			−0.538224	−	0.842802i	$-0.680905\pi$
$401$	−21.5559			−1.07645			−0.538224	+	0.842802i	$0.680905\pi$
$402$	−2.27861	−	6.51470i	−0.113647	−	0.324924i
$403$			22.2206i			1.10689i
$404$		−	1.23854i		−	0.0616195i
$405$	−10.3169	+	17.2789i	−0.512651	+	0.858597i
$406$		−	3.90674i		−	0.193888i
$407$	39.3592			1.95096
$408$	−9.37127	+	3.27774i	−0.463947	+	0.162272i
$409$	−32.7301			−1.61840			−0.809200	−	0.587533i	$-0.800099\pi$
$409$	−32.7301			−1.61840			−0.809200	+	0.587533i	$0.800099\pi$
$410$	8.75574	−	27.0233i	0.432415	−	1.33459i
$411$	−10.0403	+	3.51174i	−0.495251	+	0.173221i
$412$	−15.0918			−0.743520
$413$			16.4722i			0.810545i
$414$	10.9996	−	9.27406i	0.540602	−	0.455795i
$415$	−5.57893	+	17.2185i	−0.273859	+	0.845225i
$416$			3.04015i			0.149056i
$417$	−7.93451	−	22.6853i	−0.388555	−	1.11090i
$418$		−	15.9840i		−	0.781802i
$419$	−3.77943			−0.184637			−0.0923186	−	0.995730i	$-0.529428\pi$
$419$	−3.77943			−0.184637			−0.0923186	+	0.995730i	$0.529428\pi$
$420$	−0.115447	−	4.98995i	−0.00563321	−	0.243484i
$421$		−	21.2423i		−	1.03529i	−0.855597	−	0.517643i	$-0.826810\pi$
$421$		−	21.2423i		−	1.03529i	0.855597	−	0.517643i	$-0.173190\pi$
$422$	−21.0772			−1.02602
$423$	−8.18319	+	6.52229i	−0.397881	+	0.317125i
$424$			4.54605i			0.220776i
$425$	16.8073	−	23.2138i	0.815275	−	1.12604i
$426$	−8.66982	+	3.03240i	−0.420054	+	0.146920i
$427$		−	3.91938i		−	0.189672i
$428$			16.5225i			0.798645i
$429$	−22.5071	+	7.87218i	−1.08665	+	0.380072i
$430$	18.8265	+	6.09991i	0.907893	+	0.294164i
$431$	15.0460			0.724742			0.362371	−	0.932034i	$-0.381967\pi$
$431$	15.0460			0.724742			0.362371	+	0.932034i	$0.381967\pi$
$432$	−4.39860	−	2.76629i	−0.211628	−	0.133093i
$433$	−1.05773			−0.0508313			−0.0254157	−	0.999677i	$-0.508091\pi$
$433$	−1.05773			−0.0508313			−0.0254157	+	0.999677i	$0.508091\pi$
$434$	9.41947			0.452149
$435$	11.7376	−	0.271558i	0.562773	−	0.0130202i
$436$			17.0974i			0.818818i
$437$	−0.466480	−	16.9223i	−0.0223147	−	0.809503i
$438$	−15.4237	+	5.39466i	−0.736973	+	0.257767i
$439$	15.4166			0.735795			0.367897	−	0.929866i	$-0.380078\pi$
$439$	15.4166			0.735795			0.367897	+	0.929866i	$0.380078\pi$
$440$	−9.63235	−	3.12095i	−0.459204	−	0.148785i
$441$	12.5256	−	9.98334i	0.596457	−	0.475397i
$442$	17.4259			0.828864
$443$	19.2882			0.916410			0.458205	−	0.888847i	$-0.348493\pi$
$443$	19.2882			0.916410			0.458205	+	0.888847i	$0.348493\pi$
$444$	−4.97047	−	14.2109i	−0.235888	−	0.674419i
$445$	14.1187	+	4.57454i	0.669289	+	0.216854i
$446$			20.9973i			0.994251i
$447$	−7.36241	−	21.0496i	−0.348230	−	0.995612i
$448$	1.28874			0.0608874
$449$		−	2.45364i		−	0.115794i	−0.998323	−	0.0578972i	$-0.981560\pi$
$449$		−	2.45364i		−	0.115794i	0.998323	−	0.0578972i	$-0.0184395\pi$
$450$	14.9840	−	0.693703i	0.706350	−	0.0327015i
$451$			57.5248i			2.70874i
$452$			17.3017i			0.813804i
$453$	−2.48435	−	7.10291i	−0.116725	−	0.333724i
$454$			5.88743i			0.276311i
$455$	−2.70037	+	8.33430i	−0.126595	+	0.390718i
$456$	−5.77111	+	2.01853i	−0.270257	+	0.0945264i
$457$	31.5879			1.47762			0.738809	−	0.673915i	$-0.235389\pi$
$457$	31.5879			1.47762			0.738809	+	0.673915i	$0.235389\pi$
$458$		−	22.8454i		−	1.06750i
$459$	−15.8561	+	25.2123i	−0.740100	+	1.17681i
$460$	−10.2889	−	3.02305i	−0.479722	−	0.140950i
$461$		−	30.5064i		−	1.42082i	−0.703786	−	0.710412i	$-0.748509\pi$
$461$		−	30.5064i		−	1.42082i	0.703786	−	0.710412i	$-0.251491\pi$
$462$	3.33708	+	9.54092i	0.155255	+	0.443884i
$463$			14.9598i			0.695241i	0.937635	+	0.347620i	$0.113010\pi$
$463$			14.9598i			0.695241i	−0.937635	+	0.347620i	$0.886990\pi$
$464$			3.03143i			0.140731i
$465$	0.654749	+	28.3002i	0.0303632	+	1.31239i
$466$	−1.99467			−0.0924012
$467$		−	31.8778i		−	1.47513i	−0.675277	−	0.737564i	$-0.735976\pi$
$467$		−	31.8778i		−	1.47513i	0.675277	−	0.737564i	$-0.264024\pi$
$468$	5.68460	+	7.13218i	0.262771	+	0.329685i
$469$	5.13525			0.237124
$470$	7.41999	+	2.40413i	0.342259	+	0.110894i
$471$	−6.83722	−	19.5481i	−0.315043	−	0.900728i
$472$		−	12.7816i		−	0.588322i
$473$	−40.0761			−1.84270
$474$	−26.2334	+	9.17551i	−1.20494	+	0.421445i
$475$	10.3505	−	14.2958i	0.474912	−	0.655936i
$476$		−	7.38696i		−	0.338581i
$477$	8.50039	+	10.6650i	0.389206	+	0.488318i
$478$			16.2137i			0.741597i
$479$	16.8162			0.768351			0.384175	−	0.923260i	$-0.374486\pi$
$479$	16.8162			0.768351			0.384175	+	0.923260i	$0.374486\pi$
$480$	0.0895807	+	3.87195i	0.00408878	+	0.176729i
$481$			26.4251i			1.20488i
$482$		−	19.7040i		−	0.897491i
$483$	3.81142	+	10.0036i	0.173426	+	0.455180i
$484$	9.50450			0.432023
$485$	−0.0571083	−	0.0185035i	−0.00259315	−	0.000840199i
$486$	−15.4916	+	1.73497i	−0.702714	+	0.0786997i
$487$			8.87949i			0.402368i	0.979553	+	0.201184i	$0.0644789\pi$
$487$			8.87949i			0.402368i	−0.979553	+	0.201184i	$0.935521\pi$
$488$			3.04124i			0.137671i
$489$	6.67101	−	2.33328i	0.301673	−	0.105515i
$490$	−11.3574	−	3.67988i	−0.513075	−	0.166240i
$491$			2.36576i			0.106765i	0.998574	+	0.0533827i	$0.0170003\pi$
$491$			2.36576i			0.106765i	−0.998574	+	0.0533827i	$0.983000\pi$
$492$	20.7697	−	7.26450i	0.936370	−	0.327509i
$493$	17.3759			0.782571
$494$	10.7314			0.482827
$495$	−28.4331	+	10.6892i	−1.27797	+	0.480445i
$496$	−7.30904			−0.328185
$497$		−	6.83404i		−	0.306548i
$498$	−13.2339	+	4.62875i	−0.593026	+	0.207419i
$499$	−15.7984			−0.707234			−0.353617	−	0.935390i	$-0.615048\pi$
$499$	−15.7984			−0.707234			−0.353617	+	0.935390i	$0.615048\pi$
$500$	−6.59403	−	9.02878i	−0.294894	−	0.403779i
$501$	−3.18600	−	9.10898i	−0.142340	−	0.406959i
$502$	5.44250			0.242910
$503$		−	14.9574i		−	0.666916i	−0.942765	−	0.333458i	$-0.891784\pi$
$503$		−	14.9574i		−	0.666916i	0.942765	−	0.333458i	$-0.108216\pi$
$504$	3.02339	−	2.40974i	0.134672	−	0.107339i
$505$	−0.853632	+	2.63461i	−0.0379861	+	0.117239i
$506$	21.7082	−	0.598407i	0.965047	−	0.0266025i
$507$	2.14868	+	6.14322i	0.0954263	+	0.272830i
$508$		−	6.86184i		−	0.304445i
$509$		−	5.36677i		−	0.237878i	−0.992902	−	0.118939i	$-0.962051\pi$
$509$		−	5.36677i		−	0.237878i	0.992902	−	0.118939i	$-0.0379492\pi$
$510$	22.1936	−	0.513468i	0.982751	−	0.0227367i
$511$		−	12.1578i		−	0.537830i
$512$	−1.00000			−0.0441942
$513$	−9.76468	+	15.5265i	−0.431121	+	0.685513i
$514$	−10.2937			−0.454037
$515$	32.1033	+	10.4017i	1.41464	+	0.458353i
$516$	5.06100	+	14.4697i	0.222798	+	0.636995i
$517$	−15.7950			−0.694664
$518$	11.2018			0.492180
$519$	−6.65705	−	19.0330i	−0.292212	−	0.835454i
$520$	2.09535	−	6.46700i	0.0918873	−	0.283597i
$521$	32.7112			1.43310			0.716551	−	0.697535i	$-0.245720\pi$
$521$	32.7112			1.43310			0.716551	+	0.697535i	$0.245720\pi$
$522$	5.66830	+	7.11173i	0.248095	+	0.311272i
$523$	13.9174			0.608567			0.304284	−	0.952582i	$-0.401583\pi$
$523$	13.9174			0.608567			0.304284	+	0.952582i	$0.401583\pi$
$524$			0.675240i			0.0294980i
$525$	−3.19363	+	10.6942i	−0.139381	+	0.466732i
$526$			18.0484i			0.786948i
$527$			41.8947i			1.82496i
$528$	−2.58940	−	7.40327i	−0.112689	−	0.322186i
$529$	22.9651	−	1.26707i	0.998481	−	0.0550901i
$530$	3.13326	−	9.67035i	0.136100	−	0.420053i
$531$	−23.8996	−	29.9856i	−1.03715	−	1.30127i
$532$		−	4.54911i		−	0.197229i
$533$	−38.6212			−1.67287
$534$	3.79543	+	10.8514i	0.164244	+	0.469585i
$535$	11.3877	−	35.1466i	0.492335	−	1.51952i
$536$	−3.98470			−0.172113
$537$	−10.4278	+	3.64727i	−0.449993	+	0.157392i
$538$			5.62437i			0.242484i
$539$	24.1766			1.04136
$540$	7.45008	+	8.91607i	0.320600	+	0.383687i
$541$	13.3952			0.575904			0.287952	−	0.957645i	$-0.407026\pi$
$541$	13.3952			0.575904			0.287952	+	0.957645i	$0.407026\pi$
$542$	−19.4771			−0.836614
$543$	−12.8298	+	4.48742i	−0.550581	+	0.192574i
$544$			5.73191i			0.245753i
$545$	11.7840	−	36.3696i	0.504771	−	1.55790i
$546$	−6.40562	+	2.24046i	−0.274135	+	0.0958828i
$547$		−	39.1904i		−	1.67566i	−0.545931	−	0.837830i	$-0.683824\pi$
$547$		−	39.1904i		−	1.67566i	0.545931	−	0.837830i	$-0.316176\pi$
$548$			6.14111i			0.262335i
$549$	5.68664	+	7.13475i	0.242700	+	0.304504i
$550$	18.3389	+	13.2777i	0.781972	+	0.566165i
$551$	10.7006			0.455861
$552$	−2.95747	−	7.76230i	−0.125878	−	0.330386i
$553$		−	20.6786i		−	0.879344i
$554$		−	1.53636i		−	0.0652738i
$555$	0.778640	+	33.6552i	0.0330514	+	1.42858i
$556$	−13.8754			−0.588447
$557$			17.4131i			0.737816i	0.929466	+	0.368908i	$0.120268\pi$
$557$			17.4131i			0.737816i	−0.929466	+	0.368908i	$0.879732\pi$
$558$	−17.1470	+	13.6667i	−0.725889	+	0.578559i
$559$		−	26.9065i		−	1.13802i
$560$	−2.74141	−	0.888236i	−0.115846	−	0.0375348i
$561$	−42.4349	+	14.8422i	−1.79160	+	0.626639i
$562$	6.23953			0.263199
$563$			14.0445i			0.591904i	0.955203	+	0.295952i	$0.0956369\pi$
$563$			14.0445i			0.591904i	−0.955203	+	0.295952i	$0.904363\pi$
$564$	1.99467	+	5.70289i	0.0839907	+	0.240135i
$565$	11.9248	−	36.8042i	0.501680	−	1.54836i
$566$	−7.82642			−0.328969
$567$	2.58702	−	11.3065i	0.108645	−	0.474828i
$568$			5.30287i			0.222503i
$569$	26.6443			1.11699			0.558493	−	0.829509i	$-0.311380\pi$
$569$	26.6443			1.11699			0.558493	+	0.829509i	$0.311380\pi$
$570$	13.6675	−	0.316209i	0.572469	−	0.0132445i
$571$		−	25.3537i		−	1.06102i	−0.847679	−	0.530509i	$-0.822001\pi$
$571$		−	25.3537i		−	1.06102i	0.847679	−	0.530509i	$-0.177999\pi$
$572$			13.7664i			0.575601i
$573$	3.46586	+	9.90913i	0.144788	+	0.413960i
$574$			16.3718i			0.683347i
$575$	19.8029	+	13.5220i	0.825839	+	0.563906i
$576$	−2.34600	+	1.86984i	−0.0977498	+	0.0779100i
$577$			13.6359i			0.567669i	0.958873	+	0.283835i	$0.0916067\pi$
$577$			13.6359i			0.567669i	−0.958873	+	0.283835i	$0.908393\pi$
$578$	15.8547			0.659470
$579$	7.90030	−	2.76325i	0.328325	−	0.114837i
$580$	2.08935	−	6.44846i	0.0867553	−	0.267758i
$581$		−	10.4317i		−	0.432780i
$582$	−0.0153521	−	0.0438925i	−0.000636363	−	0.00181940i
$583$			20.5854i			0.852560i
$584$			9.43385i			0.390376i
$585$	−7.17657	−	19.0895i	−0.296715	−	0.789255i
$586$			17.3337i			0.716047i
$587$	2.20981			0.0912086			0.0456043	−	0.998960i	$-0.485479\pi$
$587$	2.20981			0.0912086			0.0456043	+	0.998960i	$0.485479\pi$
$588$	−3.05314	−	8.72912i	−0.125909	−	0.359983i
$589$			25.8000i			1.06307i
$590$	−8.80943	+	27.1890i	−0.362678	+	1.11935i
$591$	7.05966	+	20.1840i	0.290396	+	0.830260i
$592$	−8.69205			−0.357241
$593$	38.0686			1.56329			0.781646	−	0.623723i	$-0.214381\pi$
$593$	38.0686			1.56329			0.781646	+	0.623723i	$0.214381\pi$
$594$	−19.9177	−	12.5263i	−0.817232	−	0.513960i
$595$	−5.09129	+	15.7135i	−0.208722	+	0.644191i
$596$	−12.8749			−0.527377
$597$	−7.05873	+	2.46889i	−0.288895	+	0.101045i
$598$	0.401761	+	14.5745i	0.0164292	+	0.595996i
$599$			11.0815i			0.452780i	0.974037	+	0.226390i	$0.0726923\pi$
$599$			11.0815i			0.452780i	−0.974037	+	0.226390i	$0.927308\pi$
$600$	2.47809	−	8.29814i	0.101168	−	0.338770i
$601$	−17.3266			−0.706767			−0.353384	−	0.935479i	$-0.614969\pi$
$601$	−17.3266			−0.706767			−0.353384	+	0.935479i	$0.614969\pi$
$602$	−11.4059			−0.464868
$603$	−9.34808	+	7.45075i	−0.380683	+	0.303418i
$604$	−4.34447			−0.176774
$605$	−20.2179	−	6.55075i	−0.821976	−	0.266326i
$606$	−2.02492	+	0.708246i	−0.0822568	+	0.0287705i
$607$		−	19.9355i		−	0.809157i	−0.914503	−	0.404578i	$-0.867418\pi$
$607$		−	19.9355i		−	0.809157i	0.914503	−	0.404578i	$-0.132582\pi$
$608$			3.52988i			0.143156i
$609$	−6.38725	+	2.23403i	−0.258824	+	0.0905277i
$610$	2.09611	−	6.46933i	0.0848689	−	0.261935i
$611$		−	10.6045i		−	0.429013i
$612$	10.7177	+	13.4470i	0.433239	+	0.543564i
$613$	−21.9438			−0.886301			−0.443151	−	0.896447i	$-0.646139\pi$
$613$	−21.9438			−0.886301			−0.443151	+	0.896447i	$0.646139\pi$
$614$			14.6960i			0.593083i
$615$	−49.1881	+	1.13801i	−1.98346	+	0.0458889i
$616$	5.83567			0.235126
$617$			32.9610i			1.32696i	0.748194	+	0.663480i	$0.230921\pi$
$617$			32.9610i			1.32696i	−0.748194	+	0.663480i	$0.769079\pi$
$618$	8.63011	+	24.6741i	0.347154	+	0.992536i
$619$			41.3766i			1.66307i	0.555475	+	0.831533i	$0.312537\pi$
$619$			41.3766i			1.66307i	−0.555475	+	0.831533i	$0.687463\pi$
$620$	15.5478	+	5.03758i	0.624413	+	0.202314i
$621$	−21.4525	−	12.6803i	−0.860858	−	0.508845i
$622$		−	5.16495i		−	0.207096i
$623$	−8.55367			−0.342695
$624$	4.97044	−	1.73848i	0.198977	−	0.0695950i
$625$	7.80393	+	23.7508i	0.312157	+	0.950031i
$626$	−14.4632			−0.578066
$627$	−26.1327	+	9.14029i	−1.04364	+	0.365028i
$628$	−11.9565			−0.477117
$629$			49.8220i			1.98653i
$630$	−8.09220	+	3.04220i	−0.322401	+	0.121204i
$631$		−	41.5867i		−	1.65554i	−0.561068	−	0.827770i	$-0.689609\pi$
$631$		−	41.5867i		−	1.65554i	0.561068	−	0.827770i	$-0.310391\pi$
$632$			16.0456i			0.638258i
$633$	12.0528	+	34.4598i	0.479056	+	1.36965i
$634$	−5.68991			−0.225975
$635$	−4.72936	+	14.5965i	−0.187679	+	0.579244i
$636$	7.43248	−	2.59962i	0.294717	−	0.103082i
$637$			16.2318i			0.643127i
$638$			13.7269i			0.543454i
$639$	9.91552	+	12.4405i	0.392252	+	0.492139i
$640$	2.12720	+	0.689226i	0.0840848	+	0.0272441i
$641$	−30.3693			−1.19951			−0.599757	−	0.800182i	$-0.704736\pi$
$641$	−30.3693			−1.19951			−0.599757	+	0.800182i	$0.704736\pi$
$642$	27.0131	−	9.44824i	1.06612	−	0.372892i
$643$	24.8143			0.978582			0.489291	−	0.872121i	$-0.337256\pi$
$643$	24.8143			0.978582			0.489291	+	0.872121i	$0.337256\pi$
$644$	6.17825	−	0.170309i	0.243457	−	0.00671113i
$645$	−0.792822	−	34.2682i	−0.0312173	−	1.34931i
$646$	20.2330			0.796055
$647$	4.31799			0.169758			0.0848788	−	0.996391i	$-0.472950\pi$
$647$	4.31799			0.169758			0.0848788	+	0.996391i	$0.472950\pi$
$648$	−2.00739	+	8.77328i	−0.0788579	+	0.344647i
$649$		−	57.8776i		−	2.27189i
$650$	−8.91446	+	12.3124i	−0.349654	+	0.482932i
$651$	−5.38644	−	15.4002i	−0.211111	−	0.603581i
$652$		−	4.08030i		−	0.159797i
$653$	−19.7040			−0.771076			−0.385538	−	0.922692i	$-0.625984\pi$
$653$	−19.7040			−0.771076			−0.385538	+	0.922692i	$0.625984\pi$
$654$	27.9531	−	9.77700i	1.09305	−	0.382311i
$655$	0.465394	−	1.43637i	0.0181844	−	0.0561236i
$656$		−	12.7037i		−	0.495997i
$657$	17.6398	+	22.1318i	0.688194	+	0.863443i
$658$	−4.49533			−0.175246
$659$	12.5928			0.490548			0.245274	−	0.969454i	$-0.421122\pi$
$659$	12.5928			0.490548			0.245274	+	0.969454i	$0.421122\pi$
$660$	0.405638	+	17.5329i	0.0157894	+	0.682468i
$661$		−	25.4148i		−	0.988520i	−0.869314	−	0.494260i	$-0.835439\pi$
$661$		−	25.4148i		−	0.988520i	0.869314	−	0.494260i	$-0.164561\pi$
$662$	12.3989			0.481898
$663$	−9.96482	−	28.4901i	−0.387001	−	1.10646i
$664$			8.09448i			0.314127i
$665$	−3.13537	+	9.67686i	−0.121584	+	0.375252i
$666$	−20.3915	+	16.2527i	−0.790155	+	0.629781i
$667$	0.400609	+	14.5327i	0.0155116	+	0.562710i
$668$	−5.57148			−0.215567
$669$	34.3291	−	12.0071i	1.32724	−	0.464222i
$670$	8.47624	+	2.74636i	0.327466	+	0.106101i
$671$			13.7713i			0.531636i
$672$	−0.736956	−	2.10701i	−0.0284287	−	0.0812795i
$673$			9.43823i			0.363817i	0.983315	+	0.181908i	$0.0582274\pi$
$673$			9.43823i			0.363817i	−0.983315	+	0.181908i	$0.941773\pi$
$674$	−13.5952			−0.523666
$675$	−9.70259	−	24.1010i	−0.373453	−	0.927649i
$676$	3.75748			0.144518
$677$			12.7665i			0.490656i	0.969440	+	0.245328i	$0.0788957\pi$
$677$			12.7665i			0.490656i	−0.969440	+	0.245328i	$0.921104\pi$
$678$	28.2871	−	9.89383i	1.08636	−	0.379970i
$679$	0.0345985			0.00132777
$680$	3.95058	−	12.1929i	0.151498	−	0.467576i
$681$	9.62554	−	3.36667i	0.368851	−	0.129011i
$682$	−33.0967			−1.26734
$683$	−33.2408			−1.27192			−0.635962	−	0.771720i	$-0.719397\pi$
$683$	−33.2408			−1.27192			−0.635962	+	0.771720i	$0.719397\pi$
$684$	6.60032	+	8.28109i	0.252369	+	0.316635i
$685$	4.23261	−	13.0633i	0.161720	−	0.499125i
$686$	15.9020			0.607141
$687$	−37.3507	+	13.0639i	−1.42502	+	0.498420i
$688$	8.85037			0.337417
$689$	−13.8207			−0.526526
$690$	0.941135	+	18.5503i	0.0358284	+	0.706199i
$691$	16.1409			0.614028			0.307014	−	0.951705i	$-0.400670\pi$
$691$	16.1409			0.614028			0.307014	+	0.951705i	$0.400670\pi$
$692$	−11.6414			−0.442541
$693$	13.6905	−	10.9118i	0.520058	−	0.414504i
$694$	6.55994			0.249012
$695$	29.5157	+	9.56328i	1.11959	+	0.362756i
$696$	4.95619	−	1.73350i	0.187864	−	0.0657081i
$697$	−72.8165			−2.75812
$698$	28.1738			1.06639
$699$	1.14063	+	3.26114i	0.0431427	+	0.123348i
$700$	5.21933	+	3.77891i	0.197272	+	0.142829i
$701$	11.0988			0.419195			0.209598	−	0.977788i	$-0.432785\pi$
$701$	11.0988			0.419195			0.209598	+	0.977788i	$0.432785\pi$
$702$	8.40994	−	13.3724i	0.317413	−	0.504709i
$703$			30.6819i			1.15719i
$704$	−4.52819			−0.170663
$705$	−0.312471	−	13.5059i	−0.0117683	−	0.508663i
$706$	−5.76001			−0.216781
$707$		−	1.59616i		−	0.0600296i
$708$	−20.8971	+	7.30905i	−0.785360	+	0.274691i
$709$		−	27.1166i		−	1.01839i	−0.860652	−	0.509193i	$-0.829944\pi$
$709$		−	27.1166i		−	1.01839i	0.860652	−	0.509193i	$-0.170056\pi$
$710$	3.65488	−	11.2802i	0.137165	−	0.423340i
$711$	30.0026	+	37.6428i	1.12519	+	1.41172i
$712$	6.63721			0.248740
$713$	−35.0396	+	0.965901i	−1.31224	+	0.0361733i
$714$	−12.0772	+	4.22416i	−0.451976	+	0.158085i
$715$	9.48815	−	29.2838i	0.354837	−	1.09515i
$716$			6.37813i			0.238362i
$717$	26.5082	−	9.27165i	0.989969	−	0.346256i
$718$	−6.40987			−0.239214
$719$		−	48.4417i		−	1.80657i	−0.429039	−	0.903286i	$-0.641148\pi$
$719$		−	48.4417i		−	1.80657i	0.429039	−	0.903286i	$-0.358852\pi$
$720$	6.27914	−	2.36060i	0.234010	−	0.0879742i
$721$	−19.4495			−0.724336
$722$	−6.53993			−0.243391
$723$	−32.2146	+	11.2675i	−1.19807	+	0.419044i
$724$			7.84733i			0.291644i
$725$	−8.88890	+	12.2771i	−0.330125	+	0.455960i
$726$	−5.43506	−	15.5392i	−0.201714	−	0.576713i
$727$	34.0855			1.26416			0.632080	−	0.774903i	$-0.282201\pi$
$727$	34.0855			1.26416			0.632080	+	0.774903i	$0.282201\pi$
$728$			3.91797i			0.145210i
$729$	11.6953	+	24.3356i	0.433159	+	0.901318i
$730$	6.50206	−	20.0677i	0.240652	−	0.742738i
$731$		−	50.7295i		−	1.87630i
$732$	4.97222	−	1.73911i	0.183779	−	0.0642793i
$733$	4.78843			0.176865			0.0884324	−	0.996082i	$-0.471814\pi$
$733$	4.78843			0.176865			0.0884324	+	0.996082i	$0.471814\pi$
$734$	−26.8268			−0.990196
$735$	0.478284	+	20.6729i	0.0176418	+	0.762530i
$736$	−4.79401	+	0.132152i	−0.176710	+	0.00487117i
$737$	−18.0435			−0.664640
$738$	−23.7539	−	29.8029i	−0.874394	−	1.09706i
$739$	−24.0111			−0.883262			−0.441631	−	0.897197i	$-0.645600\pi$
$739$	−24.0111			−0.883262			−0.441631	+	0.897197i	$0.645600\pi$
$740$	18.4897	+	5.99079i	0.679695	+	0.220226i
$741$	−6.13664	−	17.5451i	−0.225435	−	0.644534i
$742$			5.85870i			0.215080i
$743$		−	5.51270i		−	0.202242i	−0.994874	−	0.101121i	$-0.967757\pi$
$743$		−	5.51270i		−	0.202242i	0.994874	−	0.101121i	$-0.0322428\pi$
$744$	4.17961	+	11.9498i	0.153232	+	0.438100i
$745$	27.3875	+	8.87374i	1.00340	+	0.325109i
$746$	8.96103			0.328086
$747$	15.1354	+	18.9896i	0.553775	+	0.694794i
$748$			25.9552i			0.949014i
$749$			21.2933i			0.778039i
$750$	−10.9907	+	15.9438i	−0.401323	+	0.582185i
$751$			8.57209i			0.312800i	0.987694	+	0.156400i	$0.0499889\pi$
$751$			8.57209i			0.312800i	−0.987694	+	0.156400i	$0.950011\pi$
$752$	3.48815			0.127200
$753$	−3.11224	−	8.89810i	−0.113416	−	0.324265i
$754$	−9.21602			−0.335628
$755$	9.24155	+	2.99432i	0.336334	+	0.108975i
$756$	−5.66866	−	3.56504i	−0.206167	−	0.129659i
$757$	−48.2632			−1.75416			−0.877078	−	0.480349i	$-0.840510\pi$
$757$	−48.2632			−1.75416			−0.877078	+	0.480349i	$0.840510\pi$
$758$		−	4.30108i		−	0.156222i
$759$	−13.3920	−	35.1492i	−0.486098	−	1.27583i
$760$	2.43289	−	7.50876i	0.0882501	−	0.272371i
$761$			0.0297036i			0.00107675i	1.00000		0.000538377i	$0.000171371\pi$
$761$			0.0297036i			0.00107675i	−1.00000		0.000538377i	$0.999829\pi$
$762$	−11.2186	+	3.92388i	−0.406408	+	0.142147i
$763$			22.0342i			0.797691i
$764$	6.06089			0.219275
$765$	−13.5307	−	35.9914i	−0.489204	−	1.30127i
$766$			10.2019i			0.368609i
$767$	38.8581			1.40308
$768$	0.571841	+	1.63493i	0.0206345	+	0.0589955i
$769$		−	32.7603i		−	1.18137i	−0.806903	−	0.590684i	$-0.798858\pi$
$769$		−	32.7603i		−	1.18137i	0.806903	−	0.590684i	$-0.201142\pi$
$770$	−12.4136	−	4.02210i	−0.447356	−	0.144946i
$771$	5.88637	+	16.8295i	0.211993	+	0.606101i
$772$		−	4.83220i		−	0.173915i
$773$		−	32.8434i		−	1.18130i	−0.806929	−	0.590648i	$-0.798872\pi$
$773$		−	32.8434i		−	1.18130i	0.806929	−	0.590648i	$-0.201128\pi$
$774$	20.7629	−	16.5488i	0.746308	−	0.594834i
$775$	−29.6011	−	21.4319i	−1.06330	−	0.769855i
$776$	−0.0268467			−0.000963741
$777$	−6.40566	−	18.3142i	−0.229802	−	0.657018i
$778$	−10.3677			−0.371701
$779$	−44.8426			−1.60665
$780$	−11.7713	+	0.272339i	−0.421480	+	0.00975129i
$781$			24.0124i			0.859231i
$782$	0.757480	+	27.4788i	0.0270874	+	0.982640i
$783$	8.38583	−	13.3341i	0.299685	−	0.476520i
$784$	−5.33914			−0.190684
$785$	25.4339	+	8.24075i	0.907774	+	0.294125i
$786$	1.10397	−	0.386130i	0.0393774	−	0.0137728i
$787$	28.7301			1.02412			0.512058	−	0.858951i	$-0.328883\pi$
$787$	28.7301			1.02412			0.512058	+	0.858951i	$0.328883\pi$
$788$	12.3455			0.439790
$789$	29.5079	−	10.3208i	1.05051	−	0.367431i
$790$	11.0590	−	34.1321i	0.393463	−	1.21436i
$791$			22.2975i			0.792807i
$792$	−10.6231	+	8.46699i	−0.377476	+	0.300861i
$793$	−9.24584			−0.328329
$794$		−	15.6662i		−	0.555973i
$795$	−17.6021	+	0.407239i	−0.624281	+	0.0144433i
$796$			4.31745i			0.153028i
$797$		−	45.7409i		−	1.62022i	−0.586275	−	0.810112i	$-0.699406\pi$
$797$		−	45.7409i		−	1.62022i	0.586275	−	0.810112i	$-0.300594\pi$
$798$	−7.43748	+	2.60137i	−0.263284	+	0.0920874i
$799$		−	19.9938i		−	0.707329i
$800$	−4.04993	−	2.93224i	−0.143187	−	0.103670i
$801$	15.5709	−	12.4105i	0.550170	−	0.438504i
$802$	21.5559			0.761164
$803$			42.7183i			1.50749i
$804$	2.27861	+	6.51470i	0.0803605	+	0.229756i
$805$	−13.2597	−	3.89593i	−0.467344	−	0.137314i
$806$		−	22.2206i		−	0.782687i
$807$	9.19546	−	3.21625i	0.323695	−	0.113217i
$808$			1.23854i			0.0435715i
$809$		−	35.8505i		−	1.26044i	−0.776419	−	0.630218i	$-0.782966\pi$
$809$		−	35.8505i		−	1.26044i	0.776419	−	0.630218i	$-0.217034\pi$
$810$	10.3169	−	17.2789i	0.362499	−	0.607120i
$811$	34.8564			1.22397			0.611987	−	0.790868i	$-0.290370\pi$
$811$	34.8564			1.22397			0.611987	+	0.790868i	$0.290370\pi$
$812$			3.90674i			0.137100i
$813$	11.1378	+	31.8437i	0.390620	+	1.11681i
$814$	−39.3592			−1.37954
$815$	−2.81225	+	8.67960i	−0.0985088	+	0.304033i
$816$	9.37127	−	3.27774i	0.328060	−	0.114744i
$817$		−	31.2408i		−	1.09298i
$818$	32.7301			1.14438
$819$	7.32599	+	9.19155i	0.255991	+	0.321179i
$820$	−8.75574	+	27.0233i	−0.305764	+	0.943695i
$821$			31.9229i			1.11412i	0.830474	+	0.557058i	$0.188070\pi$
$821$			31.9229i			1.11412i	−0.830474	+	0.557058i	$0.811930\pi$
$822$	10.0403	−	3.51174i	0.350195	−	0.122486i
$823$			46.3311i			1.61500i	0.589866	+	0.807501i	$0.299180\pi$
$823$			46.3311i			1.61500i	−0.589866	+	0.807501i	$0.700820\pi$
$824$	15.0918			0.525748
$825$	11.2213	−	37.5755i	0.390675	−	1.30821i
$826$		−	16.4722i		−	0.573142i
$827$		−	19.0668i		−	0.663016i	−0.943452	−	0.331508i	$-0.892443\pi$
$827$		−	19.0668i		−	0.663016i	0.943452	−	0.331508i	$-0.107557\pi$
$828$	−10.9996	+	9.27406i	−0.382263	+	0.322296i
$829$	−52.5034			−1.82352			−0.911759	−	0.410727i	$-0.865275\pi$
$829$	−52.5034			−1.82352			−0.911759	+	0.410727i	$0.865275\pi$
$830$	5.57893	−	17.2185i	0.193647	−	0.597665i
$831$	−2.51185	+	0.878555i	−0.0871350	+	0.0304767i
$832$		−	3.04015i		−	0.105398i
$833$			30.6034i			1.06035i
$834$	7.93451	+	22.6853i	0.274750	+	0.785527i
$835$	11.8516	+	3.84001i	0.410143	+	0.132889i
$836$			15.9840i			0.552817i
$837$	32.1495	+	20.2189i	1.11125	+	0.698868i
$838$	3.77943			0.130558
$839$	−15.3959			−0.531525			−0.265762	−	0.964039i	$-0.585624\pi$
$839$	−15.3959			−0.531525			−0.265762	+	0.964039i	$0.585624\pi$
$840$	0.115447	+	4.98995i	0.00398328	+	0.172170i
$841$	19.8104			0.683117
$842$			21.2423i			0.732058i
$843$	−3.56802	−	10.2012i	−0.122889	−	0.351348i
$844$	21.0772			0.725507
$845$	−7.99290	−	2.58975i	−0.274964	−	0.0890903i
$846$	8.18319	−	6.52229i	0.281344	−	0.224241i
$847$	12.2489			0.420876
$848$		−	4.54605i		−	0.156112i
$849$	4.47547	+	12.7957i	0.153598	+	0.439146i
$850$	−16.8073	+	23.2138i	−0.576487	+	0.796228i
$851$	−41.6698	+	1.14867i	−1.42842	+	0.0393758i
$852$	8.66982	−	3.03240i	0.297023	−	0.103888i
$853$			22.8095i			0.780982i	0.920607	+	0.390491i	$0.127695\pi$
$853$			22.8095i			0.780982i	−0.920607	+	0.390491i	$0.872305\pi$
$854$			3.91938i			0.134119i
$855$	−8.33263	−	22.1646i	−0.284970	−	0.758014i
$856$		−	16.5225i		−	0.564727i
$857$	−37.3502			−1.27586			−0.637930	−	0.770095i	$-0.720209\pi$
$857$	−37.3502			−1.27586			−0.637930	+	0.770095i	$0.720209\pi$
$858$	22.5071	−	7.87218i	0.768379	−	0.268752i
$859$	−2.26159			−0.0771643			−0.0385822	−	0.999255i	$-0.512284\pi$
$859$	−2.26159			−0.0771643			−0.0385822	+	0.999255i	$0.512284\pi$
$860$	−18.8265	−	6.09991i	−0.641978	−	0.208005i
$861$	26.7668	−	9.36208i	0.912210	−	0.319059i
$862$	−15.0460			−0.512470
$863$	44.0444			1.49929			0.749644	−	0.661842i	$-0.230225\pi$
$863$	44.0444			1.49929			0.749644	+	0.661842i	$0.230225\pi$
$864$	4.39860	+	2.76629i	0.149643	+	0.0941111i
$865$	24.7636	+	8.02359i	0.841989	+	0.272810i
$866$	1.05773			0.0359432
$867$	−9.06639	−	25.9214i	−0.307911	−	0.880337i
$868$	−9.41947			−0.319718
$869$			72.6573i			2.46473i
$870$	−11.7376	+	0.271558i	−0.397940	+	0.00920668i
$871$		−	12.1141i		−	0.410470i
$872$		−	17.0974i		−	0.578992i
$873$	−0.0629823	+	0.0501991i	−0.00213163	+	0.00169898i
$874$	0.466480	+	16.9223i	0.0157789	+	0.572405i
$875$	−8.49801	−	11.6358i	−0.287285	−	0.393361i
$876$	15.4237	−	5.39466i	0.521118	−	0.182269i
$877$		−	40.4451i		−	1.36573i	−0.730542	−	0.682867i	$-0.760733\pi$
$877$		−	40.4451i		−	1.36573i	0.730542	−	0.682867i	$-0.239267\pi$
$878$	−15.4166			−0.520285
$879$	28.3393	−	9.91210i	0.955862	−	0.334327i
$880$	9.63235	+	3.12095i	0.324706	+	0.105207i
$881$	36.5778			1.23234			0.616168	−	0.787615i	$-0.288684\pi$
$881$	36.5778			1.23234			0.616168	+	0.787615i	$0.288684\pi$
$882$	−12.5256	+	9.98334i	−0.421759	+	0.336157i
$883$			7.52943i			0.253386i	0.991942	+	0.126693i	$0.0404362\pi$
$883$			7.52943i			0.253386i	−0.991942	+	0.126693i	$0.959564\pi$
$884$	−17.4259			−0.586095
$885$	49.4898	−	1.14499i	1.66358	−	0.0384883i
$886$	−19.2882			−0.648000
$887$	−37.3052			−1.25259			−0.626293	−	0.779587i	$-0.715429\pi$
$887$	−37.3052			−1.25259			−0.626293	+	0.779587i	$0.715429\pi$
$888$	4.97047	+	14.2109i	0.166798	+	0.476886i
$889$		−	8.84315i		−	0.296590i
$890$	−14.1187	−	4.57454i	−0.473259	−	0.153339i
$891$	−9.08986	+	39.7271i	−0.304522	+	1.33091i
$892$		−	20.9973i		−	0.703042i
$893$		−	12.3128i		−	0.412031i
$894$	7.36241	+	21.0496i	0.246236	+	0.704004i
$895$	4.39598	−	13.5675i	0.146941	−	0.453513i
$896$	−1.28874			−0.0430539
$897$	23.5986	−	8.99116i	0.787934	−	0.300206i
$898$			2.45364i			0.0818789i
$899$		−	22.1569i		−	0.738973i
$900$	−14.9840	+	0.693703i	−0.499465	+	0.0231234i
$901$	−26.0575			−0.868103
$902$		−	57.5248i		−	1.91537i
$903$	6.52233	+	18.6478i	0.217050	+	0.620559i
$904$		−	17.3017i		−	0.575447i
$905$	5.40859	−	16.6928i	0.179788	−	0.554888i
$906$	2.48435	+	7.10291i	0.0825369	+	0.235978i
$907$	38.8447			1.28982			0.644909	−	0.764259i	$-0.276895\pi$
$907$	38.8447			1.28982			0.644909	+	0.764259i	$0.276895\pi$
$908$		−	5.88743i		−	0.195381i
$909$	2.31586	+	2.90560i	0.0768124	+	0.0963727i
$910$	2.70037	−	8.33430i	0.0895165	−	0.276279i
$911$	2.59781			0.0860693			0.0430346	−	0.999074i	$-0.486297\pi$
$911$	2.59781			0.0860693			0.0430346	+	0.999074i	$0.486297\pi$
$912$	5.77111	−	2.01853i	0.191101	−	0.0668402i
$913$			36.6533i			1.21305i
$914$	−31.5879			−1.04483
$915$	−11.7755	+	0.272437i	−0.389287	+	0.00900648i
$916$			22.8454i			0.754834i
$917$			0.870212i			0.0287369i
$918$	15.8561	−	25.2123i	0.523330	−	0.832131i
$919$			46.9542i			1.54888i	0.632650	+	0.774438i	$0.281967\pi$
$919$			46.9542i			1.54888i	−0.632650	+	0.774438i	$0.718033\pi$
$920$	10.2889	+	3.02305i	0.339215	+	0.0996669i
$921$	24.0270	−	8.40378i	0.791715	−	0.276914i
$922$			30.5064i			1.00467i
$923$	−16.1215			−0.530646
$924$	−3.33708	−	9.54092i	−0.109782	−	0.313873i
$925$	−35.2022	−	25.4872i	−1.15744	−	0.838013i
$926$		−	14.9598i		−	0.491609i
$927$	35.4053	−	28.2193i	1.16286	−	0.926843i
$928$		−	3.03143i		−	0.0995117i
$929$			37.5448i			1.23181i	0.787822	+	0.615903i	$0.211209\pi$
$929$			37.5448i			1.23181i	−0.787822	+	0.615903i	$0.788791\pi$
$930$	−0.654749	−	28.3002i	−0.0214700	−	0.928000i
$931$			18.8465i			0.617670i
$932$	1.99467			0.0653375
$933$	−8.44434	+	2.95353i	−0.276455	+	0.0966943i
$934$			31.8778i			1.04307i
$935$	17.8890	−	55.2117i	0.585032	−	1.80562i
$936$	−5.68460	−	7.13218i	−0.185807	−	0.233123i
$937$	37.5203			1.22574			0.612868	−	0.790186i	$-0.290016\pi$
$937$	37.5203			1.22574			0.612868	+	0.790186i	$0.290016\pi$
$938$	−5.13525			−0.167672
$939$	8.27065	+	23.6463i	0.269902	+	0.771669i
$940$	−7.41999	−	2.40413i	−0.242013	−	0.0784140i
$941$	−35.7322			−1.16484			−0.582418	−	0.812889i	$-0.697893\pi$
$941$	−35.7322			−1.16484			−0.582418	+	0.812889i	$0.697893\pi$
$942$	6.83722	+	19.5481i	0.222769	+	0.636911i
$943$	−1.67882	−	60.9017i	−0.0546698	−	1.98323i
$944$			12.7816i			0.416006i
$945$	9.60124	+	11.4905i	0.312328	+	0.373787i
$946$	40.0761			1.30299
$947$	34.6296			1.12531			0.562656	−	0.826691i	$-0.309780\pi$
$947$	34.6296			1.12531			0.562656	+	0.826691i	$0.309780\pi$
$948$	26.2334	−	9.17551i	0.852021	−	0.298007i
$949$	−28.6803			−0.931003
$950$	−10.3505	+	14.2958i	−0.335813	+	0.463817i
$951$	3.25372	+	9.30260i	0.105509	+	0.301658i
$952$			7.38696i			0.239413i
$953$		−	16.1851i		−	0.524287i	−0.965029	−	0.262144i	$-0.915571\pi$
$953$		−	16.1851i		−	0.524287i	0.965029	−	0.262144i	$-0.0844294\pi$
$954$	−8.50039	−	10.6650i	−0.275210	−	0.345293i
$955$	−12.8927	−	4.17732i	−0.417198	−	0.135175i
$956$		−	16.2137i		−	0.524388i
$957$	22.4425	−	7.84961i	0.725464	−	0.253742i
$958$	−16.8162			−0.543306
$959$			7.91431i			0.255566i
$960$	−0.0895807	−	3.87195i	−0.00289120	−	0.124967i
$961$	22.4220			0.723291
$962$		−	26.4251i		−	0.851981i
$963$	−30.8944	−	38.7617i	−0.995559	−	1.24908i
$964$			19.7040i			0.634622i
$965$	−3.33048	+	10.2790i	−0.107212	+	0.330894i
$966$	−3.81142	−	10.0036i	−0.122630	−	0.321861i
$967$			37.6064i			1.20934i	0.796476	+	0.604670i	$0.206695\pi$
$967$			37.6064i			1.20934i	−0.796476	+	0.604670i	$0.793305\pi$
$968$	−9.50450			−0.305486
$969$	−11.5700	−	33.0795i	−0.371683	−	1.06267i
$970$	0.0571083	+	0.0185035i	0.00183364	+	0.000594111i
$971$	12.0962			0.388187			0.194093	−	0.980983i	$-0.437824\pi$
$971$	12.0962			0.388187			0.194093	+	0.980983i	$0.437824\pi$
$972$	15.4916	−	1.73497i	0.496894	−	0.0556491i
$973$	−17.8818			−0.573265
$974$		−	8.87949i		−	0.284517i
$975$	25.2276	+	7.53378i	0.807929	+	0.241274i
$976$		−	3.04124i		−	0.0973479i
$977$		−	1.12241i		−	0.0359092i	−0.999839	−	0.0179546i	$-0.994285\pi$
$977$		−	1.12241i		−	0.0359092i	0.999839	−	0.0179546i	$-0.00571543\pi$
$978$	−6.67101	+	2.33328i	−0.213315	+	0.0746101i
$979$	30.0546			0.960548
$980$	11.3574	+	3.67988i	0.362799	+	0.117549i
$981$	−31.9694	−	40.1105i	−1.02071	−	1.28063i
$982$		−	2.36576i		−	0.0754946i
$983$			33.1802i			1.05828i	0.848534	+	0.529141i	$0.177486\pi$
$983$			33.1802i			1.05828i	−0.848534	+	0.529141i	$0.822514\pi$
$984$	−20.7697	+	7.26450i	−0.662114	+	0.231584i
$985$	−26.2613	−	8.50885i	−0.836755	−	0.271114i
$986$	−17.3759			−0.553361
$987$	2.57062	+	7.34956i	0.0818236	+	0.233939i
$988$	−10.7314			−0.341411
$989$	42.4288	−	1.16959i	1.34916	−	0.0371908i
$990$	28.4331	−	10.6892i	0.903664	−	0.339726i
$991$	−38.6528			−1.22785			−0.613924	−	0.789366i	$-0.710410\pi$
$991$	−38.6528			−1.22785			−0.613924	+	0.789366i	$0.710410\pi$
$992$	7.30904			0.232062
$993$	−7.09021	−	20.2714i	−0.225001	−	0.643293i
$994$			6.83404i			0.216763i
$995$	2.97570	−	9.18406i	0.0943360	−	0.291154i
$996$	13.2339	−	4.62875i	0.419332	−	0.146668i
$997$			10.0084i			0.316968i	0.987362	+	0.158484i	$0.0506606\pi$
$997$			10.0084i			0.316968i	−0.987362	+	0.158484i	$0.949339\pi$
$998$	15.7984			0.500090
$999$	38.2328	+	24.0447i	1.20963	+	0.760741i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.h.a.689.15	yes	24
3.2	odd	2		690.2.h.b.689.12	yes	24
5.4	even	2		690.2.h.b.689.9	yes	24
15.14	odd	2	inner	690.2.h.a.689.14	yes	24
23.22	odd	2	inner	690.2.h.a.689.16	yes	24
69.68	even	2		690.2.h.b.689.11	yes	24
115.114	odd	2		690.2.h.b.689.10	yes	24
345.344	even	2	inner	690.2.h.a.689.13	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.h.a.689.13	✓	24	345.344	even	2	inner
690.2.h.a.689.14	yes	24	15.14	odd	2	inner
690.2.h.a.689.15	yes	24	1.1	even	1	trivial
690.2.h.a.689.16	yes	24	23.22	odd	2	inner
690.2.h.b.689.9	yes	24	5.4	even	2
690.2.h.b.689.10	yes	24	115.114	odd	2
690.2.h.b.689.11	yes	24	69.68	even	2
690.2.h.b.689.12	yes	24	3.2	odd	2

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.571841 + 1.63493i) q^{3} +1.00000 q^{4} +(-2.12720 - 0.689226i) q^{5} +(-0.571841 - 1.63493i) q^{6} +1.28874 q^{7} -1.00000 q^{8} +(-2.34600 + 1.86984i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.571841 + 1.63493i) q^{3} +1.00000 q^{4} +(-2.12720 - 0.689226i) q^{5} +(-0.571841 - 1.63493i) q^{6} +1.28874 q^{7} -1.00000 q^{8} +(-2.34600 + 1.86984i) q^{9} +(2.12720 + 0.689226i) q^{10} -4.52819 q^{11} +(0.571841 + 1.63493i) q^{12} -3.04015i q^{13} -1.28874 q^{14} +(-0.0895807 - 3.87195i) q^{15} +1.00000 q^{16} -5.73191i q^{17} +(2.34600 - 1.86984i) q^{18} -3.52988i q^{19} +(-2.12720 - 0.689226i) q^{20} +(0.736956 + 2.10701i) q^{21} +4.52819 q^{22} +(4.79401 - 0.132152i) q^{23} +(-0.571841 - 1.63493i) q^{24} +(4.04993 + 2.93224i) q^{25} +3.04015i q^{26} +(-4.39860 - 2.76629i) q^{27} +1.28874 q^{28} +3.03143i q^{29} +(0.0895807 + 3.87195i) q^{30} -7.30904 q^{31} -1.00000 q^{32} +(-2.58940 - 7.40327i) q^{33} +5.73191i q^{34} +(-2.74141 - 0.888236i) q^{35} +(-2.34600 + 1.86984i) q^{36} -8.69205 q^{37} +3.52988i q^{38} +(4.97044 - 1.73848i) q^{39} +(2.12720 + 0.689226i) q^{40} -12.7037i q^{41} +(-0.736956 - 2.10701i) q^{42} +8.85037 q^{43} -4.52819 q^{44} +(6.27914 - 2.36060i) q^{45} +(-4.79401 + 0.132152i) q^{46} +3.48815 q^{47} +(0.571841 + 1.63493i) q^{48} -5.33914 q^{49} +(-4.04993 - 2.93224i) q^{50} +(9.37127 - 3.27774i) q^{51} -3.04015i q^{52} -4.54605i q^{53} +(4.39860 + 2.76629i) q^{54} +(9.63235 + 3.12095i) q^{55} -1.28874 q^{56} +(5.77111 - 2.01853i) q^{57} -3.03143i q^{58} +12.7816i q^{59} +(-0.0895807 - 3.87195i) q^{60} -3.04124i q^{61} +7.30904 q^{62} +(-3.02339 + 2.40974i) q^{63} +1.00000 q^{64} +(-2.09535 + 6.46700i) q^{65} +(2.58940 + 7.40327i) q^{66} +3.98470 q^{67} -5.73191i q^{68} +(2.95747 + 7.76230i) q^{69} +(2.74141 + 0.888236i) q^{70} -5.30287i q^{71} +(2.34600 - 1.86984i) q^{72} -9.43385i q^{73} +8.69205 q^{74} +(-2.47809 + 8.29814i) q^{75} -3.52988i q^{76} -5.83567 q^{77} +(-4.97044 + 1.73848i) q^{78} -16.0456i q^{79} +(-2.12720 - 0.689226i) q^{80} +(2.00739 - 8.77328i) q^{81} +12.7037i q^{82} -8.09448i q^{83} +(0.736956 + 2.10701i) q^{84} +(-3.95058 + 12.1929i) q^{85} -8.85037 q^{86} +(-4.95619 + 1.73350i) q^{87} +4.52819 q^{88} -6.63721 q^{89} +(-6.27914 + 2.36060i) q^{90} -3.91797i q^{91} +(4.79401 - 0.132152i) q^{92} +(-4.17961 - 11.9498i) q^{93} -3.48815 q^{94} +(-2.43289 + 7.50876i) q^{95} +(-0.571841 - 1.63493i) q^{96} +0.0268467 q^{97} +5.33914 q^{98} +(10.6231 - 8.46699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 2 q^{3} + 24 q^{4} - 2 q^{6} - 24 q^{8} + 6 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 2 * q^3 + 24 * q^4 - 2 * q^6 - 24 * q^8 + 6 * q^9	\( 24 q - 24 q^{2} + 2 q^{3} + 24 q^{4} - 2 q^{6} - 24 q^{8} + 6 q^{9} + 2 q^{12} + 24 q^{16} - 6 q^{18} - 4 q^{23} - 2 q^{24} + 12 q^{25} + 2 q^{27} - 28 q^{31} - 24 q^{32} + 8 q^{35} + 6 q^{36} + 4 q^{46} + 16 q^{47} + 2 q^{48} - 4 q^{49} - 12 q^{50} - 2 q^{54} + 4 q^{55} + 28 q^{62} + 24 q^{64} - 8 q^{69} - 8 q^{70} - 6 q^{72} + 14 q^{75} + 8 q^{77} + 14 q^{81} - 44 q^{85} + 28 q^{87} - 4 q^{92} - 4 q^{93} - 16 q^{94} + 4 q^{95} - 2 q^{96} + 4 q^{98}+O(q^{100}) \) 24 * q - 24 * q^2 + 2 * q^3 + 24 * q^4 - 2 * q^6 - 24 * q^8 + 6 * q^9 + 2 * q^12 + 24 * q^16 - 6 * q^18 - 4 * q^23 - 2 * q^24 + 12 * q^25 + 2 * q^27 - 28 * q^31 - 24 * q^32 + 8 * q^35 + 6 * q^36 + 4 * q^46 + 16 * q^47 + 2 * q^48 - 4 * q^49 - 12 * q^50 - 2 * q^54 + 4 * q^55 + 28 * q^62 + 24 * q^64 - 8 * q^69 - 8 * q^70 - 6 * q^72 + 14 * q^75 + 8 * q^77 + 14 * q^81 - 44 * q^85 + 28 * q^87 - 4 * q^92 - 4 * q^93 - 16 * q^94 + 4 * q^95 - 2 * q^96 + 4 * q^98

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