LMFDB - Embedded newform 483.2.e.a.344.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(344,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("483.344");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.e (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			344.11
Character	$\chi$	$=$	483.344
Dual form			483.2.e.a.344.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.67931i q^{2} +(1.72585 + 0.146449i) q^{3} -0.820088 q^{4} -1.07520 q^{5} +(0.245933 - 2.89824i) q^{6} +1.00000i q^{7} -1.98144i q^{8} +(2.95711 + 0.505497i) q^{9} +O(q^{10})$	\(q-1.67931i q^{2} +(1.72585 + 0.146449i) q^{3} -0.820088 q^{4} -1.07520 q^{5} +(0.245933 - 2.89824i) q^{6} +1.00000i q^{7} -1.98144i q^{8} +(2.95711 + 0.505497i) q^{9} +1.80559i q^{10} +4.88809 q^{11} +(-1.41535 - 0.120101i) q^{12} +2.70154 q^{13} +1.67931 q^{14} +(-1.85563 - 0.157462i) q^{15} -4.96763 q^{16} -1.92396 q^{17} +(0.848887 - 4.96590i) q^{18} -2.60918i q^{19} +0.881757 q^{20} +(-0.146449 + 1.72585i) q^{21} -8.20863i q^{22} +(-4.77519 + 0.444455i) q^{23} +(0.290180 - 3.41967i) q^{24} -3.84395 q^{25} -4.53672i q^{26} +(5.02949 + 1.30548i) q^{27} -0.820088i q^{28} -3.02873i q^{29} +(-0.264427 + 3.11618i) q^{30} -0.579419 q^{31} +4.37932i q^{32} +(8.43610 + 0.715855i) q^{33} +3.23092i q^{34} -1.07520i q^{35} +(-2.42509 - 0.414552i) q^{36} +4.14067i q^{37} -4.38162 q^{38} +(4.66244 + 0.395637i) q^{39} +2.13044i q^{40} +1.46700i q^{41} +(2.89824 + 0.245933i) q^{42} -8.37391i q^{43} -4.00866 q^{44} +(-3.17947 - 0.543510i) q^{45} +(0.746378 + 8.01904i) q^{46} +11.2649i q^{47} +(-8.57338 - 0.727504i) q^{48} -1.00000 q^{49} +6.45519i q^{50} +(-3.32046 - 0.281761i) q^{51} -2.21550 q^{52} +7.56270 q^{53} +(2.19230 - 8.44607i) q^{54} -5.25567 q^{55} +1.98144 q^{56} +(0.382111 - 4.50304i) q^{57} -5.08618 q^{58} +2.98924i q^{59} +(1.52178 + 0.129132i) q^{60} +10.5340i q^{61} +0.973024i q^{62} +(-0.505497 + 2.95711i) q^{63} -2.58102 q^{64} -2.90469 q^{65} +(1.20214 - 14.1668i) q^{66} -13.1635i q^{67} +1.57781 q^{68} +(-8.30635 + 0.0677403i) q^{69} -1.80559 q^{70} +8.36199i q^{71} +(1.00161 - 5.85933i) q^{72} -12.6126 q^{73} +6.95348 q^{74} +(-6.63407 - 0.562942i) q^{75} +2.13975i q^{76} +4.88809i q^{77} +(0.664398 - 7.82969i) q^{78} +9.65575i q^{79} +5.34119 q^{80} +(8.48895 + 2.98962i) q^{81} +2.46356 q^{82} -6.30550 q^{83} +(0.120101 - 1.41535i) q^{84} +2.06863 q^{85} -14.0624 q^{86} +(0.443554 - 5.22713i) q^{87} -9.68546i q^{88} +2.72509 q^{89} +(-0.912722 + 5.33933i) q^{90} +2.70154i q^{91} +(3.91608 - 0.364492i) q^{92} +(-0.999989 - 0.0848552i) q^{93} +18.9172 q^{94} +2.80538i q^{95} +(-0.641346 + 7.55804i) q^{96} +13.9861i q^{97} +1.67931i q^{98} +(14.4546 + 2.47092i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9	$ 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9} + 22 q^{12} - 8 q^{13} + 24 q^{16} - 14 q^{18} - 12 q^{24} + 88 q^{25} - 16 q^{27} - 8 q^{31} - 10 q^{36} + 8 q^{46} - 98 q^{48} - 48 q^{49} + 28 q^{52} - 28 q^{54} - 92 q^{58} + 92 q^{64} + 8 q^{69} + 8 q^{70} + 60 q^{72} + 40 q^{73} - 80 q^{75} + 114 q^{78} - 28 q^{81} - 20 q^{82} - 40 q^{85} - 28 q^{87} - 76 q^{93} - 12 q^{94} - 6 q^{96}+O(q^{100}) $ 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9 + 22 * q^12 - 8 * q^13 + 24 * q^16 - 14 * q^18 - 12 * q^24 + 88 * q^25 - 16 * q^27 - 8 * q^31 - 10 * q^36 + 8 * q^46 - 98 * q^48 - 48 * q^49 + 28 * q^52 - 28 * q^54 - 92 * q^58 + 92 * q^64 + 8 * q^69 + 8 * q^70 + 60 * q^72 + 40 * q^73 - 80 * q^75 + 114 * q^78 - 28 * q^81 - 20 * q^82 - 40 * q^85 - 28 * q^87 - 76 * q^93 - 12 * q^94 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	1.67931i		−	1.18745i	−0.804667	−	0.593726i	$-0.797656\pi$
$2$		−	1.67931i		−	1.18745i	0.804667	−	0.593726i	$-0.202344\pi$
$3$	1.72585	+	0.146449i	0.996419	+	0.0845523i
$3$	1.72585	+	0.146449i	0.996419	+	0.0845523i
$4$	−0.820088			−0.410044
$5$	−1.07520			−0.480843			−0.240422	−	0.970669i	$-0.577286\pi$
$5$	−1.07520			−0.480843			−0.240422	+	0.970669i	$0.577286\pi$
$6$	0.245933	−	2.89824i	0.100402	−	1.18320i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		−	1.98144i		−	0.700545i
$9$	2.95711	+	0.505497i	0.985702	+	0.168499i
$10$			1.80559i			0.570979i
$11$	4.88809			1.47381			0.736907	−	0.675994i	$-0.236285\pi$
$11$	4.88809			1.47381			0.736907	+	0.675994i	$0.236285\pi$
$12$	−1.41535	−	0.120101i	−0.408575	−	0.0346701i
$13$	2.70154			0.749271			0.374636	−	0.927172i	$-0.377768\pi$
$13$	2.70154			0.749271			0.374636	+	0.927172i	$0.377768\pi$
$14$	1.67931			0.448815
$15$	−1.85563	−	0.157462i	−0.479121	−	0.0406564i
$16$	−4.96763			−1.24191
$17$	−1.92396			−0.466628			−0.233314	−	0.972401i	$-0.574957\pi$
$17$	−1.92396			−0.466628			−0.233314	+	0.972401i	$0.574957\pi$
$18$	0.848887	−	4.96590i	0.200085	−	1.17047i
$19$		−	2.60918i		−	0.598586i	−0.954161	−	0.299293i	$-0.903249\pi$
$19$		−	2.60918i		−	0.598586i	0.954161	−	0.299293i	$-0.0967508\pi$
$20$	0.881757			0.197167
$21$	−0.146449	+	1.72585i	−0.0319578	+	0.376611i
$22$		−	8.20863i		−	1.75009i
$23$	−4.77519	+	0.444455i	−0.995696	+	0.0926752i
$23$	−4.77519	+	0.444455i	−0.995696	+	0.0926752i
$24$	0.290180	−	3.41967i	0.0592327	−	0.698036i
$25$	−3.84395			−0.768790
$26$		−	4.53672i		−	0.889724i
$27$	5.02949	+	1.30548i	0.967925	+	0.251239i
$28$		−	0.820088i		−	0.154982i
$29$		−	3.02873i		−	0.562421i	−0.959646	−	0.281211i	$-0.909264\pi$
$29$		−	3.02873i		−	0.562421i	0.959646	−	0.281211i	$-0.0907360\pi$
$30$	−0.264427	+	3.11618i	−0.0482775	+	0.568934i
$31$	−0.579419			−0.104067			−0.0520333	−	0.998645i	$-0.516570\pi$
$31$	−0.579419			−0.104067			−0.0520333	+	0.998645i	$0.516570\pi$
$32$			4.37932i			0.774162i
$33$	8.43610	+	0.715855i	1.46854	+	0.124614i
$34$			3.23092i			0.554099i
$35$		−	1.07520i		−	0.181742i
$36$	−2.42509	−	0.414552i	−0.404181	−	0.0690920i
$37$			4.14067i			0.680723i	0.940295	+	0.340361i	$0.110549\pi$
$37$			4.14067i			0.680723i	−0.940295	+	0.340361i	$0.889451\pi$
$38$	−4.38162			−0.710792
$39$	4.66244	+	0.395637i	0.746588	+	0.0633526i
$40$			2.13044i			0.336852i
$41$			1.46700i			0.229108i	0.993417	+	0.114554i	$0.0365438\pi$
$41$			1.46700i			0.229108i	−0.993417	+	0.114554i	$0.963456\pi$
$42$	2.89824	+	0.245933i	0.447208	+	0.0379483i
$43$		−	8.37391i		−	1.27701i	−0.769618	−	0.638504i	$-0.779553\pi$
$43$		−	8.37391i		−	1.27701i	0.769618	−	0.638504i	$-0.220447\pi$
$44$	−4.00866			−0.604329
$45$	−3.17947	−	0.543510i	−0.473968	−	0.0810216i
$46$	0.746378	+	8.01904i	0.110047	+	1.18234i
$47$			11.2649i			1.64315i	0.570101	+	0.821575i	$0.306904\pi$
$47$			11.2649i			1.64315i	−0.570101	+	0.821575i	$0.693096\pi$
$48$	−8.57338	−	0.727504i	−1.23746	−	0.105006i
$49$	−1.00000			−0.142857
$50$			6.45519i			0.912901i
$51$	−3.32046	−	0.281761i	−0.464957	−	0.0394545i
$52$	−2.21550			−0.307234
$53$	7.56270			1.03882			0.519408	−	0.854526i	$-0.326152\pi$
$53$	7.56270			1.03882			0.519408	+	0.854526i	$0.326152\pi$
$54$	2.19230	−	8.44607i	0.298334	−	1.14937i
$55$	−5.25567			−0.708674
$56$	1.98144			0.264781
$57$	0.382111	−	4.50304i	0.0506118	−	0.596442i
$58$	−5.08618			−0.667849
$59$			2.98924i			0.389166i	0.980886	+	0.194583i	$0.0623354\pi$
$59$			2.98924i			0.389166i	−0.980886	+	0.194583i	$0.937665\pi$
$60$	1.52178	+	0.129132i	0.196461	+	0.0166709i
$61$			10.5340i			1.34874i	0.738396	+	0.674368i	$0.235584\pi$
$61$			10.5340i			1.34874i	−0.738396	+	0.674368i	$0.764416\pi$
$62$			0.973024i			0.123574i
$63$	−0.505497	+	2.95711i	−0.0636866	+	0.372560i
$64$	−2.58102			−0.322627
$65$	−2.90469			−0.360282
$66$	1.20214	−	14.1668i	0.147974	−	1.74382i
$67$		−	13.1635i		−	1.60818i	−0.594506	−	0.804091i	$-0.702652\pi$
$67$		−	13.1635i		−	1.60818i	0.594506	−	0.804091i	$-0.297348\pi$
$68$	1.57781			0.191338
$69$	−8.30635	+	0.0677403i	−0.999967	+	0.00815497i
$70$	−1.80559			−0.215810
$71$			8.36199i			0.992385i	0.868213	+	0.496193i	$0.165269\pi$
$71$			8.36199i			0.992385i	−0.868213	+	0.496193i	$0.834731\pi$
$72$	1.00161	−	5.85933i	0.118041	−	0.690529i
$73$	−12.6126			−1.47619			−0.738097	−	0.674695i	$-0.764275\pi$
$73$	−12.6126			−1.47619			−0.738097	+	0.674695i	$0.764275\pi$
$74$	6.95348			0.808326
$75$	−6.63407	−	0.562942i	−0.766037	−	0.0650029i
$76$			2.13975i			0.245446i
$77$			4.88809i			0.557050i
$78$	0.664398	−	7.82969i	0.0752282	−	0.886538i
$79$			9.65575i			1.08636i	0.839617	+	0.543178i	$0.182779\pi$
$79$			9.65575i			1.08636i	−0.839617	+	0.543178i	$0.817221\pi$
$80$	5.34119			0.597163
$81$	8.48895	+	2.98962i	0.943216	+	0.332180i
$82$	2.46356			0.272055
$83$	−6.30550			−0.692119			−0.346059	−	0.938213i	$-0.612480\pi$
$83$	−6.30550			−0.692119			−0.346059	+	0.938213i	$0.612480\pi$
$84$	0.120101	−	1.41535i	0.0131041	−	0.154427i
$85$	2.06863			0.224375
$86$	−14.0624			−1.51639
$87$	0.443554	−	5.22713i	0.0475540	−	0.560407i
$88$		−	9.68546i		−	1.03247i
$89$	2.72509			0.288859			0.144430	−	0.989515i	$-0.453865\pi$
$89$	2.72509			0.288859			0.144430	+	0.989515i	$0.453865\pi$
$90$	−0.912722	+	5.33933i	−0.0962093	+	0.562815i
$91$			2.70154i			0.283198i
$92$	3.91608	−	0.364492i	0.408279	−	0.0380009i
$93$	−0.999989	−	0.0848552i	−0.103694	−	0.00879907i
$94$	18.9172			1.95116
$95$			2.80538i			0.287826i
$96$	−0.641346	+	7.55804i	−0.0654571	+	0.771390i
$97$			13.9861i			1.42007i	0.704167	+	0.710035i	$0.251321\pi$
$97$			13.9861i			1.42007i	−0.704167	+	0.710035i	$0.748679\pi$
$98$			1.67931i			0.169636i
$99$	14.4546	+	2.47092i	1.45274	+	0.248336i
$100$	3.15237			0.315237
$101$			8.92520i			0.888091i	0.896004	+	0.444046i	$0.146457\pi$
$101$			8.92520i			0.888091i	−0.896004	+	0.444046i	$0.853543\pi$
$102$	−0.473165	+	5.57608i	−0.0468503	+	0.552114i
$103$			4.81546i			0.474481i	0.971451	+	0.237241i	$0.0762430\pi$
$103$			4.81546i			0.474481i	−0.971451	+	0.237241i	$0.923757\pi$
$104$		−	5.35293i		−	0.524898i
$105$	0.157462	−	1.85563i	0.0153667	−	0.181091i
$106$		−	12.7001i		−	1.23354i
$107$	−12.3881			−1.19760			−0.598802	−	0.800897i	$-0.704357\pi$
$107$	−12.3881			−1.19760			−0.598802	+	0.800897i	$0.704357\pi$
$108$	−4.12462	−	1.07060i	−0.396892	−	0.103019i
$109$		−	16.8016i		−	1.60930i	−0.593746	−	0.804652i	$-0.702352\pi$
$109$		−	16.8016i		−	1.60930i	0.593746	−	0.804652i	$-0.297648\pi$
$110$			8.82590i			0.841517i
$111$	−0.606397	+	7.14618i	−0.0575567	+	0.678285i
$112$		−	4.96763i		−	0.469397i
$113$	0.927688			0.0872696			0.0436348	−	0.999048i	$-0.486106\pi$
$113$	0.927688			0.0872696			0.0436348	+	0.999048i	$0.486106\pi$
$114$	−7.56201	−	0.641683i	−0.708247	−	0.0600991i
$115$	5.13428	−	0.477877i	0.478774	−	0.0445623i
$116$			2.48383i			0.230617i
$117$	7.98873	+	1.36562i	0.738558	+	0.126251i
$118$	5.01987			0.462116
$119$		−	1.92396i		−	0.176369i
$120$	−0.312001	+	3.67682i	−0.0284816	+	0.335646i
$121$	12.8934			1.17213
$122$	17.6898			1.60156
$123$	−0.214841	+	2.53183i	−0.0193716	+	0.228287i
$124$	0.475174			0.0426719
$125$	9.50900			0.850511
$126$	4.96590	+	0.848887i	0.442398	+	0.0756249i
$127$	12.6466			1.12220			0.561101	−	0.827747i	$-0.310378\pi$
$127$	12.6466			1.12220			0.561101	+	0.827747i	$0.310378\pi$
$128$			13.0930i			1.15727i
$129$	1.22635	−	14.4521i	0.107974	−	1.27244i
$130$			4.87787i			0.427818i
$131$		−	12.4935i		−	1.09156i	−0.837927	−	0.545782i	$-0.816233\pi$
$131$		−	12.4935i		−	1.09156i	0.837927	−	0.545782i	$-0.183767\pi$
$132$	−6.91834	−	0.587064i	−0.602165	−	0.0510974i
$133$	2.60918			0.226244
$134$	−22.1057			−1.90964
$135$	−5.40769	−	1.40365i	−0.465420	−	0.120807i
$136$			3.81220i			0.326894i
$137$	−12.5629			−1.07332			−0.536660	−	0.843799i	$-0.680314\pi$
$137$	−12.5629			−1.07332			−0.536660	+	0.843799i	$0.680314\pi$
$138$	0.113757	+	13.9489i	0.00968364	+	1.18741i
$139$	4.97835			0.422259			0.211129	−	0.977458i	$-0.432286\pi$
$139$	4.97835			0.422259			0.211129	+	0.977458i	$0.432286\pi$
$140$			0.881757i			0.0745220i
$141$	−1.64973	+	19.4415i	−0.138932	+	1.63727i
$142$	14.0424			1.17841
$143$	13.2054			1.10429
$144$	−14.6898	−	2.51112i	−1.22415	−	0.209260i
$145$			3.25649i			0.270436i
$146$			21.1805i			1.75291i
$147$	−1.72585	−	0.146449i	−0.142346	−	0.0120789i
$148$		−	3.39572i		−	0.279126i
$149$	3.25098			0.266330			0.133165	−	0.991094i	$-0.457486\pi$
$149$	3.25098			0.266330			0.133165	+	0.991094i	$0.457486\pi$
$150$	−0.945355	+	11.1407i	−0.0771879	+	0.909632i
$151$	−1.82643			−0.148633			−0.0743163	−	0.997235i	$-0.523677\pi$
$151$	−1.82643			−0.148633			−0.0743163	+	0.997235i	$0.523677\pi$
$152$	−5.16993			−0.419336
$153$	−5.68934	−	0.972554i	−0.459956	−	0.0786263i
$154$	8.20863			0.661470
$155$	0.622990			0.0500397
$156$	−3.82361	−	0.324457i	−0.306134	−	0.0259773i
$157$			10.6834i			0.852624i	0.904576	+	0.426312i	$0.140188\pi$
$157$			10.6834i			0.852624i	−0.904576	+	0.426312i	$0.859812\pi$
$158$	16.2150			1.29000
$159$	13.0521	+	1.10755i	1.03510	+	0.0878343i
$160$		−	4.70864i		−	0.372250i
$161$	−0.444455	−	4.77519i	−0.0350279	−	0.376338i
$162$	5.02050	−	14.2556i	0.394448	−	1.12002i
$163$	−15.3817			−1.20479			−0.602394	−	0.798199i	$-0.705786\pi$
$163$	−15.3817			−1.20479			−0.602394	+	0.798199i	$0.705786\pi$
$164$		−	1.20307i		−	0.0939442i
$165$	−9.07048	−	0.769686i	−0.706136	−	0.0599200i
$166$			10.5889i			0.821858i
$167$			3.91077i			0.302624i	0.988486	+	0.151312i	$0.0483499\pi$
$167$			3.91077i			0.302624i	−0.988486	+	0.151312i	$0.951650\pi$
$168$	3.41967	+	0.290180i	0.263833	+	0.0223879i
$169$	−5.70171			−0.438593
$170$		−	3.47388i		−	0.266435i
$171$	1.31893	−	7.71561i	0.100861	−	0.590027i
$172$			6.86734i			0.523629i
$173$			2.02837i			0.154214i	0.997023	+	0.0771072i	$0.0245684\pi$
$173$			2.02837i			0.154214i	−0.997023	+	0.0771072i	$0.975432\pi$
$174$	−8.77798	−	0.744866i	−0.665457	−	0.0564681i
$175$		−	3.84395i		−	0.290575i
$176$	−24.2822			−1.83034
$177$	−0.437771	+	5.15898i	−0.0329049	+	0.387773i
$178$		−	4.57628i		−	0.343007i
$179$		−	8.76297i		−	0.654975i	−0.944856	−	0.327487i	$-0.893798\pi$
$179$		−	8.76297i		−	0.654975i	0.944856	−	0.327487i	$-0.106202\pi$
$180$	2.60745	+	0.445725i	0.194348	+	0.0332224i
$181$		−	20.5703i		−	1.52898i	−0.644635	−	0.764490i	$-0.722991\pi$
$181$		−	20.5703i		−	1.52898i	0.644635	−	0.764490i	$-0.277009\pi$
$182$	4.53672			0.336284
$183$	−1.54269	+	18.1800i	−0.114039	+	1.34391i
$184$	0.880661	+	9.46176i	0.0649232	+	0.697530i
$185$		−	4.45205i		−	0.327321i
$186$	−0.142498	+	1.67929i	−0.0104485	+	0.123132i
$187$	−9.40447			−0.687723
$188$		−	9.23818i		−	0.673763i
$189$	−1.30548	+	5.02949i	−0.0949594	+	0.365841i
$190$	4.71111			0.341780
$191$	−10.7445			−0.777443			−0.388721	−	0.921355i	$-0.627083\pi$
$191$	−10.7445			−0.777443			−0.388721	+	0.921355i	$0.627083\pi$
$192$	−4.45445	−	0.377987i	−0.321472	−	0.0272789i
$193$	2.53155			0.182225			0.0911124	−	0.995841i	$-0.470958\pi$
$193$	2.53155			0.182225			0.0911124	+	0.995841i	$0.470958\pi$
$194$	23.4870			1.68627
$195$	−5.01305	−	0.425388i	−0.358992	−	0.0304627i
$196$	0.820088			0.0585777
$197$		−	14.5537i		−	1.03691i	−0.855104	−	0.518456i	$-0.826507\pi$
$197$		−	14.5537i		−	1.03691i	0.855104	−	0.518456i	$-0.173493\pi$
$198$	4.14944	−	24.2738i	0.294888	−	1.72506i
$199$		−	0.453169i		−	0.0321243i	−0.999871	−	0.0160622i	$-0.994887\pi$
$199$		−	0.453169i		−	0.0321243i	0.999871	−	0.0160622i	$-0.00511296\pi$
$200$			7.61656i			0.538572i
$201$	1.92779	−	22.7183i	0.135976	−	1.60242i
$202$	14.9882			1.05457
$203$	3.02873			0.212575
$204$	2.72307	+	0.231069i	0.190653	+	0.0161781i
$205$		−	1.57732i		−	0.110165i
$206$	8.08666			0.563424
$207$	−14.3454	−	1.09955i	−0.997075	−	0.0764237i
$208$	−13.4202			−0.930526
$209$		−	12.7539i		−	0.882205i
$210$	−3.11618	−	0.264427i	−0.215037	−	0.0182472i
$211$	10.0506			0.691909			0.345955	−	0.938251i	$-0.387555\pi$
$211$	10.0506			0.691909			0.345955	+	0.938251i	$0.387555\pi$
$212$	−6.20207			−0.425960
$213$	−1.22460	+	14.4315i	−0.0839084	+	0.988831i
$214$			20.8035i			1.42210i
$215$			9.00361i			0.614041i
$216$	2.58672	−	9.96563i	0.176004	−	0.678075i
$217$		−	0.579419i		−	0.0393335i
$218$	−28.2152			−1.91097
$219$	−21.7674	−	1.84710i	−1.47091	−	0.124816i
$220$	4.31011			0.290587
$221$	−5.19764			−0.349631
$222$	12.0007	+	1.01833i	0.805431	+	0.0683458i
$223$	−25.3175			−1.69539			−0.847693	−	0.530487i	$-0.822009\pi$
$223$	−25.3175			−1.69539			−0.847693	+	0.530487i	$0.822009\pi$
$224$	−4.37932			−0.292606
$225$	−11.3670	−	1.94310i	−0.757797	−	0.129540i
$226$		−	1.55788i		−	0.103628i
$227$	21.6370			1.43610			0.718049	−	0.695993i	$-0.245036\pi$
$227$	21.6370			1.43610			0.718049	+	0.695993i	$0.245036\pi$
$228$	−0.313364	+	3.69289i	−0.0207531	+	0.244567i
$229$		−	10.1579i		−	0.671250i	−0.941996	−	0.335625i	$-0.891052\pi$
$229$		−	10.1579i		−	0.671250i	0.941996	−	0.335625i	$-0.108948\pi$
$230$	−0.802504	−	8.62205i	−0.0529156	−	0.568521i
$231$	−0.715855	+	8.43610i	−0.0470998	+	0.555055i
$232$	−6.00125			−0.394001
$233$		−	19.0312i		−	1.24678i	−0.781912	−	0.623389i	$-0.785755\pi$
$233$		−	19.0312i		−	1.24678i	0.781912	−	0.623389i	$-0.214245\pi$
$234$	2.29330	−	13.4156i	0.149918	−	0.877003i
$235$		−	12.1120i		−	0.790097i
$236$		−	2.45144i		−	0.159575i
$237$	−1.41407	+	16.6644i	−0.0918539	+	1.08247i
$238$	−3.23092			−0.209430
$239$		−	17.6488i		−	1.14161i	−0.821087	−	0.570803i	$-0.806632\pi$
$239$		−	17.6488i		−	1.14161i	0.821087	−	0.570803i	$-0.193368\pi$
$240$	9.21808	+	0.782211i	0.595025	+	0.0504915i
$241$			19.6791i			1.26764i	0.773480	+	0.633821i	$0.218515\pi$
$241$			19.6791i			1.26764i	−0.773480	+	0.633821i	$0.781485\pi$
$242$		−	21.6521i		−	1.39185i
$243$	14.2128	+	6.40282i	0.911752	+	0.410741i
$244$		−	8.63877i		−	0.553041i
$245$	1.07520			0.0686919
$246$	4.25173	+	0.360785i	0.271080	+	0.0230028i
$247$		−	7.04878i		−	0.448503i
$248$			1.14808i			0.0729034i
$249$	−10.8823	−	0.923433i	−0.689640	−	0.0585202i
$250$		−	15.9686i		−	1.00994i
$251$	19.4953			1.23053			0.615267	−	0.788319i	$-0.289048\pi$
$251$	19.4953			1.23053			0.615267	+	0.788319i	$0.289048\pi$
$252$	0.414552	−	2.42509i	0.0261143	−	0.152766i
$253$	−23.3416	+	2.17254i	−1.46747	+	0.136586i
$254$		−	21.2375i		−	1.33256i
$255$	3.57015	+	0.302949i	0.223571	+	0.0189714i
$256$	16.8251			1.05157
$257$		−	26.8998i		−	1.67796i	−0.544160	−	0.838982i	$-0.683152\pi$
$257$		−	26.8998i		−	1.67796i	0.544160	−	0.838982i	$-0.316848\pi$
$258$	−24.2696	−	2.05942i	−1.51096	−	0.128214i
$259$	−4.14067			−0.257289
$260$	2.38210			0.147731
$261$	1.53101	−	8.95628i	0.0947674	−	0.554380i
$262$	−20.9805			−1.29618
$263$	4.27009			0.263305			0.131653	−	0.991296i	$-0.457972\pi$
$263$	4.27009			0.263305			0.131653	+	0.991296i	$0.457972\pi$
$264$	1.41842	−	16.7156i	0.0872980	−	1.02878i
$265$	−8.13140			−0.499508
$266$		−	4.38162i		−	0.268654i
$267$	4.70310	+	0.399087i	0.287825	+	0.0244237i
$268$			10.7953i			0.659425i
$269$		−	27.8135i		−	1.69582i	−0.530142	−	0.847909i	$-0.677861\pi$
$269$		−	27.8135i		−	1.69582i	0.530142	−	0.847909i	$-0.322139\pi$
$270$	−2.35716	+	9.08120i	−0.143452	+	0.552664i
$271$	−0.549375			−0.0333722			−0.0166861	−	0.999861i	$-0.505312\pi$
$271$	−0.549375			−0.0333722			−0.0166861	+	0.999861i	$0.505312\pi$
$272$	9.55750			0.579509
$273$	−0.395637	+	4.66244i	−0.0239450	+	0.282184i
$274$			21.0970i			1.27452i
$275$	−18.7896			−1.13305
$276$	6.81193	−	0.0555529i	0.410030	−	0.00334389i
$277$	0.719606			0.0432369			0.0216185	−	0.999766i	$-0.493118\pi$
$277$	0.719606			0.0432369			0.0216185	+	0.999766i	$0.493118\pi$
$278$		−	8.36021i		−	0.501412i
$279$	−1.71340	−	0.292894i	−0.102579	−	0.0175351i
$280$	−2.13044			−0.127318
$281$	33.3787			1.99121			0.995603	−	0.0936751i	$-0.0298615\pi$
$281$	33.3787			1.99121			0.995603	+	0.0936751i	$0.0298615\pi$
$282$	32.6483	+	2.77041i	1.94418	+	0.164975i
$283$			20.6634i			1.22831i	0.789184	+	0.614157i	$0.210504\pi$
$283$			20.6634i			1.22831i	−0.789184	+	0.614157i	$0.789496\pi$
$284$		−	6.85756i		−	0.406921i
$285$	−0.410845	+	4.84166i	−0.0243363	+	0.286795i
$286$		−	22.1759i		−	1.31129i
$287$	−1.46700			−0.0865946
$288$	−2.21373	+	12.9501i	−0.130445	+	0.763093i
$289$	−13.2984			−0.782258
$290$	5.46866			0.321131
$291$	−2.04824	+	24.1378i	−0.120070	+	1.41498i
$292$	10.3434			0.605304
$293$	−29.0066			−1.69458			−0.847292	−	0.531127i	$-0.821769\pi$
$293$	−29.0066			−1.69458			−0.847292	+	0.531127i	$0.821769\pi$
$294$	−0.245933	+	2.89824i	−0.0143431	+	0.169029i
$295$		−	3.21403i		−	0.187128i
$296$	8.20450			0.476877
$297$	24.5846	+	6.38128i	1.42654	+	0.370280i
$298$		−	5.45940i		−	0.316255i
$299$	−12.9004	+	1.20071i	−0.746047	+	0.0694389i
$300$	5.44052	+	0.461662i	0.314109	+	0.0266541i
$301$	8.37391			0.482664
$302$			3.06714i			0.176494i
$303$	−1.30709	+	15.4036i	−0.0750901	+	0.884911i
$304$			12.9614i			0.743389i
$305$		−	11.3261i		−	0.648530i
$306$	−1.63322	+	9.55418i	−0.0933651	+	0.546176i
$307$	−0.654401			−0.0373487			−0.0186743	−	0.999826i	$-0.505945\pi$
$307$	−0.654401			−0.0373487			−0.0186743	+	0.999826i	$0.505945\pi$
$308$		−	4.00866i		−	0.228415i
$309$	−0.705218	+	8.31075i	−0.0401185	+	0.472782i
$310$		−	1.04619i		−	0.0594198i
$311$			24.3340i			1.37985i	0.723879	+	0.689927i	$0.242358\pi$
$311$			24.3340i			1.37985i	−0.723879	+	0.689927i	$0.757642\pi$
$312$	0.783931	−	9.23835i	0.0443813	−	0.523019i
$313$		−	14.7735i		−	0.835050i	−0.908665	−	0.417525i	$-0.862898\pi$
$313$		−	14.7735i		−	0.835050i	0.908665	−	0.417525i	$-0.137102\pi$
$314$	17.9407			1.01245
$315$	0.543510	−	3.17947i	0.0306233	−	0.179143i
$316$		−	7.91856i		−	0.445454i
$317$			22.3131i			1.25323i	0.779329	+	0.626616i	$0.215560\pi$
$317$			22.3131i			1.25323i	−0.779329	+	0.626616i	$0.784440\pi$
$318$	1.85992	−	21.9185i	0.104299	−	1.22913i
$319$		−	14.8047i		−	0.828905i
$320$	2.77511			0.155133
$321$	−21.3800	−	1.81423i	−1.19332	−	0.101260i
$322$	−8.01904	+	0.746378i	−0.446883	+	0.0415940i
$323$			5.01994i			0.279317i
$324$	−6.96168	−	2.45175i	−0.386760	−	0.136208i
$325$	−10.3846			−0.576032
$326$			25.8307i			1.43063i
$327$	2.46058	−	28.9971i	0.136070	−	1.60354i
$328$	2.90678			0.160500
$329$	−11.2649			−0.621052
$330$	−1.29254	+	15.2322i	−0.0711522	+	0.838503i
$331$	14.7288			0.809566			0.404783	−	0.914413i	$-0.367347\pi$
$331$	14.7288			0.809566			0.404783	+	0.914413i	$0.367347\pi$
$332$	5.17106			0.283799
$333$	−2.09310	+	12.2444i	−0.114701	+	0.670990i
$334$	6.56740			0.359352
$335$			14.1534i			0.773284i
$336$	0.727504	−	8.57338i	0.0396886	−	0.467716i
$337$			6.41722i			0.349568i	0.984607	+	0.174784i	$0.0559228\pi$
$337$			6.41722i			0.349568i	−0.984607	+	0.174784i	$0.944077\pi$
$338$			9.57494i			0.520808i
$339$	1.60105	+	0.135859i	0.0869571	+	0.00737884i
$340$	−1.69646			−0.0920035
$341$	−2.83225			−0.153375
$342$	−12.9569	−	2.21490i	−0.700629	−	0.119768i
$343$		−	1.00000i		−	0.0539949i
$344$	−16.5924			−0.894602
$345$	8.93097	−	0.0728342i	0.480827	−	0.00392126i
$346$	3.40627			0.183122
$347$			20.8158i			1.11745i	0.829352	+	0.558726i	$0.188710\pi$
$347$			20.8158i			1.11745i	−0.829352	+	0.558726i	$0.811290\pi$
$348$	−0.363753	+	4.28671i	−0.0194992	+	0.229792i
$349$	17.8466			0.955309			0.477655	−	0.878548i	$-0.341487\pi$
$349$	17.8466			0.955309			0.477655	+	0.878548i	$0.341487\pi$
$350$	−6.45519			−0.345044
$351$	13.5873	+	3.52679i	0.725238	+	0.188246i
$352$			21.4065i			1.14097i
$353$		−	33.9622i		−	1.80763i	−0.427928	−	0.903813i	$-0.640756\pi$
$353$		−	33.9622i		−	1.80763i	0.427928	−	0.903813i	$-0.359244\pi$
$354$	8.66353	+	0.735154i	0.460462	+	0.0390730i
$355$		−	8.99079i		−	0.477182i
$356$	−2.23481			−0.118445
$357$	0.281761	−	3.32046i	0.0149124	−	0.175737i
$358$	−14.7158			−0.777752
$359$	−31.1074			−1.64179			−0.820894	−	0.571081i	$-0.806524\pi$
$359$	−31.1074			−1.64179			−0.820894	+	0.571081i	$0.806524\pi$
$360$	−1.07693	+	6.29994i	−0.0567593	+	0.332036i
$361$	12.1922			0.641695
$362$	−34.5440			−1.81559
$363$	22.2521	+	1.88823i	1.16793	+	0.0991063i
$364$		−	2.21550i		−	0.116124i
$365$	13.5610			0.709818
$366$	30.5299	+	2.59065i	1.59582	+	0.135416i
$367$			7.84977i			0.409755i	0.978788	+	0.204877i	$0.0656795\pi$
$367$			7.84977i			0.409755i	−0.978788	+	0.204877i	$0.934320\pi$
$368$	23.7214	−	2.20789i	1.23656	−	0.115094i
$369$	−0.741567	+	4.33809i	−0.0386044	+	0.225832i
$370$	−7.47637			−0.388678
$371$			7.56270i			0.392636i
$372$	0.820078	+	0.0695887i	0.0425191	+	0.00360801i
$373$		−	9.13114i		−	0.472792i	−0.971657	−	0.236396i	$-0.924034\pi$
$373$		−	9.13114i		−	0.472792i	0.971657	−	0.236396i	$-0.0759663\pi$
$374$			15.7930i			0.816639i
$375$	16.4111	+	1.39258i	0.847465	+	0.0719126i
$376$	22.3207			1.15110
$377$		−	8.18223i		−	0.421406i
$378$	8.44607	+	2.19230i	0.434419	+	0.112760i
$379$			27.8480i			1.43045i	0.698892	+	0.715227i	$0.253677\pi$
$379$			27.8480i			1.43045i	−0.698892	+	0.715227i	$0.746323\pi$
$380$		−	2.30066i		−	0.118021i
$381$	21.8261	+	1.85208i	1.11818	+	0.0948847i
$382$			18.0433i			0.923176i
$383$	7.42040			0.379165			0.189582	−	0.981865i	$-0.439287\pi$
$383$	7.42040			0.379165			0.189582	+	0.981865i	$0.439287\pi$
$384$	−1.91745	+	22.5965i	−0.0978495	+	1.15312i
$385$		−	5.25567i		−	0.267854i
$386$		−	4.25126i		−	0.216383i
$387$	4.23298	−	24.7625i	0.215175	−	1.25875i
$388$		−	11.4698i		−	0.582291i
$389$	25.3397			1.28477			0.642386	−	0.766381i	$-0.277945\pi$
$389$	25.3397			1.28477			0.642386	+	0.766381i	$0.277945\pi$
$390$	−0.714359	+	8.41847i	−0.0361730	+	0.426286i
$391$	9.18726	−	0.855112i	0.464620	−	0.0432449i
$392$			1.98144i			0.100078i
$393$	1.82966	−	21.5619i	0.0922942	−	1.08765i
$394$	−24.4403			−1.23128
$395$		−	10.3818i		−	0.522367i
$396$	−11.8540	−	2.02637i	−0.595688	−	0.101829i
$397$	−13.8009			−0.692648			−0.346324	−	0.938115i	$-0.612570\pi$
$397$	−13.8009			−0.692648			−0.346324	+	0.938115i	$0.612570\pi$
$398$	−0.761012			−0.0381461
$399$	4.50304	+	0.382111i	0.225434	+	0.0191295i
$400$	19.0953			0.954766
$401$	8.39623			0.419288			0.209644	−	0.977778i	$-0.432770\pi$
$401$	8.39623			0.419288			0.209644	+	0.977778i	$0.432770\pi$
$402$	−38.1511	−	3.23735i	−1.90280	−	0.161464i
$403$	−1.56532			−0.0779741
$404$		−	7.31945i		−	0.364156i
$405$	−9.12730	−	3.21443i	−0.453539	−	0.159726i
$406$		−	5.08618i		−	0.252423i
$407$			20.2400i			1.00326i
$408$	−0.558293	+	6.57929i	−0.0276396	+	0.325723i
$409$	6.99074			0.345670			0.172835	−	0.984951i	$-0.444707\pi$
$409$	6.99074			0.345670			0.172835	+	0.984951i	$0.444707\pi$
$410$	−2.64881			−0.130816
$411$	−21.6816	−	1.83982i	−1.06948	−	0.0907517i
$412$		−	3.94910i		−	0.194558i
$413$	−2.98924			−0.147091
$414$	−1.84648	+	24.0904i	−0.0907495	+	1.18398i
$415$	6.77966			0.332801
$416$			11.8309i			0.580057i
$417$	8.59188	+	0.729074i	0.420746	+	0.0357029i
$418$	−21.4177			−1.04758
$419$	23.9809			1.17155			0.585773	−	0.810475i	$-0.300791\pi$
$419$	23.9809			1.17155			0.585773	+	0.810475i	$0.300791\pi$
$420$	−0.129132	+	1.52178i	−0.00630101	+	0.0742552i
$421$			5.74652i			0.280068i	0.990147	+	0.140034i	$0.0447212\pi$
$421$			5.74652i			0.280068i	−0.990147	+	0.140034i	$0.955279\pi$
$422$		−	16.8780i		−	0.821610i
$423$	−5.69436	+	33.3114i	−0.276869	+	1.61966i
$424$		−	14.9850i		−	0.727738i
$425$	7.39559			0.358739
$426$	24.2350	+	2.05649i	1.17419	+	0.0996373i
$427$	−10.5340			−0.509774
$428$	10.1593			0.491070
$429$	22.7904	+	1.93391i	1.10033	+	0.0933700i
$430$	15.1199			0.729145
$431$	2.21365			0.106628			0.0533140	−	0.998578i	$-0.483022\pi$
$431$	2.21365			0.106628			0.0533140	+	0.998578i	$0.483022\pi$
$432$	−24.9846	−	6.48512i	−1.20207	−	0.312016i
$433$		−	4.37317i		−	0.210161i	−0.994464	−	0.105081i	$-0.966490\pi$
$433$		−	4.37317i		−	0.210161i	0.994464	−	0.105081i	$-0.0335100\pi$
$434$	−0.973024			−0.0467067
$435$	−0.476909	+	5.62020i	−0.0228660	+	0.269468i
$436$			13.7788i			0.659885i
$437$	1.15966	+	12.4593i	0.0554741	+	0.596010i
$438$	−3.10186	+	36.5543i	−0.148213	+	1.74663i
$439$	28.0817			1.34027			0.670134	−	0.742240i	$-0.266237\pi$
$439$	28.0817			1.34027			0.670134	+	0.742240i	$0.266237\pi$
$440$			10.4138i			0.496458i
$441$	−2.95711	−	0.505497i	−0.140815	−	0.0240713i
$442$			8.72845i			0.415170i
$443$		−	21.0413i		−	0.999704i	−0.866111	−	0.499852i	$-0.833388\pi$
$443$		−	21.0413i		−	0.999704i	0.866111	−	0.499852i	$-0.166612\pi$
$444$	0.497299	−	5.86049i	0.0236008	−	0.278127i
$445$	−2.93001			−0.138896
$446$			42.5160i			2.01319i
$447$	5.61069	+	0.476102i	0.265377	+	0.0225188i
$448$		−	2.58102i		−	0.121942i
$449$		−	18.5228i		−	0.874146i	−0.899426	−	0.437073i	$-0.856015\pi$
$449$		−	18.5228i		−	0.874146i	0.899426	−	0.437073i	$-0.143985\pi$
$450$	−3.26308	+	19.0887i	−0.153823	+	0.899849i
$451$			7.17085i			0.337662i
$452$	−0.760786			−0.0357843
$453$	−3.15214	−	0.267478i	−0.148100	−	0.0125672i
$454$		−	36.3352i		−	1.70530i
$455$		−	2.90469i		−	0.136174i
$456$	−8.92251	−	0.757130i	−0.417835	−	0.0354559i
$457$		−	32.5292i		−	1.52165i	−0.648956	−	0.760826i	$-0.724794\pi$
$457$		−	32.5292i		−	1.52165i	0.648956	−	0.760826i	$-0.275206\pi$
$458$	−17.0582			−0.797078
$459$	−9.67651	−	2.51168i	−0.451661	−	0.117235i
$460$	−4.21056	+	0.391901i	−0.196318	+	0.0182725i
$461$		−	30.5246i		−	1.42167i	−0.703357	−	0.710837i	$-0.748316\pi$
$461$		−	30.5246i		−	1.42167i	0.703357	−	0.710837i	$-0.251684\pi$
$462$	14.1668	+	1.20214i	0.659101	+	0.0559288i
$463$	−2.17485			−0.101074			−0.0505368	−	0.998722i	$-0.516093\pi$
$463$	−2.17485			−0.101074			−0.0505368	+	0.998722i	$0.516093\pi$
$464$			15.0456i			0.698475i
$465$	1.07519	+	0.0912362i	0.0498606	+	0.00423098i
$466$	−31.9594			−1.48049
$467$	−19.3900			−0.897263			−0.448631	−	0.893717i	$-0.648088\pi$
$467$	−19.3900			−0.897263			−0.448631	+	0.893717i	$0.648088\pi$
$468$	−6.55145	−	1.11993i	−0.302841	−	0.0517686i
$469$	13.1635			0.607836
$470$	−20.3398			−0.938203
$471$	−1.56457	+	18.4378i	−0.0720914	+	0.849571i
$472$	5.92301			0.272628
$473$		−	40.9324i		−	1.88207i
$474$	27.9846	+	2.37467i	1.28538	+	0.109072i
$475$			10.0295i			0.460187i
$476$			1.57781i			0.0723189i
$477$	22.3637	+	3.82292i	1.02396	+	0.175040i
$478$	−29.6378			−1.35560
$479$	−28.6271			−1.30801			−0.654003	−	0.756492i	$-0.726912\pi$
$479$	−28.6271			−1.30801			−0.654003	+	0.756492i	$0.726912\pi$
$480$	0.689575	−	8.12639i	0.0314746	−	0.370917i
$481$			11.1862i			0.510046i
$482$	33.0473			1.50527
$483$	−0.0677403	−	8.30635i	−0.00308229	−	0.377952i
$484$	−10.5737			−0.480625
$485$		−	15.0378i		−	0.682831i
$486$	10.7523	−	23.8677i	0.487736	−	1.08266i
$487$	−25.9249			−1.17477			−0.587384	−	0.809309i	$-0.699842\pi$
$487$	−25.9249			−1.17477			−0.587384	+	0.809309i	$0.699842\pi$
$488$	20.8724			0.944850
$489$	−26.5465	−	2.25263i	−1.20047	−	0.101868i
$490$		−	1.80559i		−	0.0815684i
$491$			20.1676i			0.910149i	0.890453	+	0.455075i	$0.150387\pi$
$491$			20.1676i			0.910149i	−0.890453	+	0.455075i	$0.849613\pi$
$492$	0.176189	−	2.07632i	0.00794320	−	0.0936078i
$493$			5.82715i			0.262441i
$494$	−11.8371			−0.532576
$495$	−15.5416	−	2.65672i	−0.698541	−	0.119411i
$496$	2.87834			0.129241
$497$	−8.36199			−0.375086
$498$	−1.55073	+	18.2748i	−0.0694900	+	0.818915i
$499$	2.04380			0.0914932			0.0457466	−	0.998953i	$-0.485433\pi$
$499$	2.04380			0.0914932			0.0457466	+	0.998953i	$0.485433\pi$
$500$	−7.79821			−0.348747
$501$	−0.572728	+	6.74939i	−0.0255876	+	0.301541i
$502$		−	32.7387i		−	1.46120i
$503$	19.1474			0.853741			0.426870	−	0.904313i	$-0.359616\pi$
$503$	19.1474			0.853741			0.426870	+	0.904313i	$0.359616\pi$
$504$	5.85933	+	1.00161i	0.260995	+	0.0446154i
$505$		−	9.59636i		−	0.427033i
$506$	3.64836	+	39.1978i	0.162190	+	1.74255i
$507$	−9.84028	−	0.835008i	−0.437022	−	0.0370840i
$508$	−10.3713			−0.460152
$509$			1.57505i			0.0698129i	0.999391	+	0.0349065i	$0.0111133\pi$
$509$			1.57505i			0.0698129i	−0.999391	+	0.0349065i	$0.988887\pi$
$510$	0.508746	−	5.99539i	0.0225276	−	0.265480i
$511$		−	12.6126i		−	0.557949i
$512$		−	2.06871i		−	0.0914251i
$513$	3.40622	−	13.1228i	0.150388	−	0.579386i
$514$	−45.1731			−1.99250
$515$		−	5.17757i		−	0.228151i
$516$	−1.00571	+	11.8520i	−0.0442741	+	0.521754i
$517$			55.0637i			2.42170i
$518$			6.95348i			0.305518i
$519$	−0.297053	+	3.50067i	−0.0130392	+	0.153662i
$520$			5.75546i			0.252394i
$521$	−38.7907			−1.69945			−0.849725	−	0.527225i	$-0.823232\pi$
$521$	−38.7907			−1.69945			−0.849725	+	0.527225i	$0.823232\pi$
$522$	−15.0404	−	2.57105i	−0.658300	−	0.112532i
$523$			26.5139i			1.15937i	0.814840	+	0.579686i	$0.196825\pi$
$523$			26.5139i			1.15937i	−0.814840	+	0.579686i	$0.803175\pi$
$524$			10.2458i			0.447589i
$525$	0.562942	−	6.63407i	0.0245688	−	0.289535i
$526$		−	7.17082i		−	0.312663i
$527$	1.11478			0.0485604
$528$	−41.9075	−	3.55611i	−1.82379	−	0.154760i
$529$	22.6049	−	4.24471i	0.982823	−	0.184553i
$530$			13.6551i			0.593142i
$531$	−1.51105	+	8.83950i	−0.0655741	+	0.383602i
$532$	−2.13975			−0.0927700
$533$			3.96317i			0.171664i
$534$	0.670191	−	7.89796i	0.0290020	−	0.341778i
$535$	13.3197			0.575860
$536$	−26.0828			−1.12660
$537$	1.28333	−	15.1236i	0.0553796	−	0.652629i
$538$	−46.7075			−2.01370
$539$	−4.88809			−0.210545
$540$	4.43478	+	1.15111i	0.190843	+	0.0495360i
$541$	6.56150			0.282101			0.141050	−	0.990002i	$-0.454952\pi$
$541$	6.56150			0.282101			0.141050	+	0.990002i	$0.454952\pi$
$542$			0.922572i			0.0396279i
$543$	3.01250	−	35.5013i	0.129279	−	1.52351i
$544$		−	8.42562i		−	0.361245i
$545$			18.0651i			0.773823i
$546$	7.82969	+	0.664398i	0.335080	+	0.0284336i
$547$	−1.29095			−0.0551971			−0.0275985	−	0.999619i	$-0.508786\pi$
$547$	−1.29095			−0.0551971			−0.0275985	+	0.999619i	$0.508786\pi$
$548$	10.3027			0.440108
$549$	−5.32489	+	31.1500i	−0.227261	+	1.32945i
$550$			31.5535i			1.34545i
$551$	−7.90249			−0.336657
$552$	0.134223	+	16.4585i	0.00571292	+	0.700522i
$553$	−9.65575			−0.410604
$554$		−	1.20844i		−	0.0513418i
$555$	0.651997	−	7.68356i	0.0276757	−	0.326149i
$556$	−4.08269			−0.173144
$557$	12.0971			0.512570			0.256285	−	0.966601i	$-0.417501\pi$
$557$	12.0971			0.512570			0.256285	+	0.966601i	$0.417501\pi$
$558$	−0.491861	+	2.87734i	−0.0208221	+	0.121807i
$559$		−	22.6224i		−	0.956826i
$560$			5.34119i			0.225706i
$561$	−16.2307	−	1.37727i	−0.685260	−	0.0581486i
$562$		−	56.0532i		−	2.36446i
$563$	24.4911			1.03218			0.516089	−	0.856535i	$-0.327387\pi$
$563$	24.4911			1.03218			0.516089	+	0.856535i	$0.327387\pi$
$564$	1.35292	−	15.9437i	0.0569682	−	0.671351i
$565$	−0.997449			−0.0419630
$566$	34.7003			1.45856
$567$	−2.98962	+	8.48895i	−0.125552	+	0.356502i
$568$	16.5688			0.695210
$569$	7.52684			0.315542			0.157771	−	0.987476i	$-0.449569\pi$
$569$	7.52684			0.315542			0.157771	+	0.987476i	$0.449569\pi$
$570$	8.13066	+	0.689936i	0.340556	+	0.0288983i
$571$			13.9532i			0.583922i	0.956430	+	0.291961i	$0.0943077\pi$
$571$			13.9532i			0.583922i	−0.956430	+	0.291961i	$0.905692\pi$
$572$	−10.8295			−0.452806
$573$	−18.5433	−	1.57352i	−0.774659	−	0.0657346i
$574$			2.46356i			0.102827i
$575$	18.3556	−	1.70846i	0.765481	−	0.0712478i
$576$	−7.63235	−	1.30470i	−0.318014	−	0.0543624i
$577$	−16.5737			−0.689974			−0.344987	−	0.938607i	$-0.612117\pi$
$577$	−16.5737			−0.689974			−0.344987	+	0.938607i	$0.612117\pi$
$578$			22.3321i			0.928895i
$579$	4.36907	+	0.370742i	0.181572	+	0.0154075i
$580$		−	2.67060i		−	0.110891i
$581$		−	6.30550i		−	0.261596i
$582$	40.5349	+	3.43964i	1.68023	+	0.142578i
$583$	36.9671			1.53102
$584$			24.9911i			1.03414i
$585$	−8.58946	−	1.46831i	−0.355131	−	0.0607072i
$586$			48.7112i			2.01224i
$587$		−	18.1820i		−	0.750451i	−0.926934	−	0.375225i	$-0.877565\pi$
$587$		−	18.1820i		−	0.750451i	0.926934	−	0.375225i	$-0.122435\pi$
$588$	1.41535	+	0.120101i	0.0583679	+	0.00495288i
$589$			1.51180i			0.0622928i
$590$	−5.39735			−0.222206
$591$	2.13138	−	25.1176i	0.0876732	−	1.03320i
$592$		−	20.5693i		−	0.845395i
$593$		−	31.7560i		−	1.30406i	−0.758192	−	0.652031i	$-0.773917\pi$
$593$		−	31.7560i		−	1.30406i	0.758192	−	0.652031i	$-0.226083\pi$
$594$	10.7162	−	41.2852i	0.439690	−	1.69395i
$595$			2.06863i			0.0848057i
$596$	−2.66609			−0.109207
$597$	0.0663661	−	0.782101i	0.00271618	−	0.0320093i
$598$	2.01637	+	21.6637i	0.0824554	+	0.885895i
$599$			36.9274i			1.50881i	0.656408	+	0.754406i	$0.272075\pi$
$599$			36.9274i			1.50881i	−0.656408	+	0.754406i	$0.727925\pi$
$600$	−1.11544	+	13.1450i	−0.0455375	+	0.536643i
$601$	16.2603			0.663270			0.331635	−	0.943408i	$-0.392400\pi$
$601$	16.2603			0.663270			0.331635	+	0.943408i	$0.392400\pi$
$602$		−	14.0624i		−	0.573141i
$603$	6.65413	−	38.9260i	0.270977	−	1.58519i
$604$	1.49783			0.0609459
$605$	−13.8630			−0.563611
$606$	25.8674	+	2.19500i	1.05079	+	0.0891660i
$607$	28.9295			1.17421			0.587107	−	0.809509i	$-0.300267\pi$
$607$	28.9295			1.17421			0.587107	+	0.809509i	$0.300267\pi$
$608$	11.4264			0.463402
$609$	5.22713	+	0.443554i	0.211814	+	0.0179737i
$610$	−19.0200			−0.770099
$611$			30.4324i			1.23116i
$612$	4.66576	+	0.797580i	0.188602	+	0.0322402i
$613$		−	47.1711i		−	1.90522i	−0.304192	−	0.952611i	$-0.598386\pi$
$613$		−	47.1711i		−	1.90522i	0.304192	−	0.952611i	$-0.401614\pi$
$614$			1.09894i			0.0443498i
$615$	0.230997	−	2.72222i	0.00931469	−	0.109770i
$616$	9.68546			0.390238
$617$	−4.82717			−0.194335			−0.0971673	−	0.995268i	$-0.530978\pi$
$617$	−4.82717			−0.194335			−0.0971673	+	0.995268i	$0.530978\pi$
$618$	13.9563	+	1.18428i	0.561406	+	0.0476388i
$619$			1.36572i			0.0548929i	0.999623	+	0.0274465i	$0.00873758\pi$
$619$			1.36572i			0.0548929i	−0.999623	+	0.0274465i	$0.991262\pi$
$620$	−0.510906			−0.0205185
$621$	−24.5970	−	3.99852i	−0.987043	−	0.160455i
$622$	40.8644			1.63851
$623$			2.72509i			0.109178i
$624$	−23.1613	−	1.96538i	−0.927194	−	0.0786781i
$625$	8.99569			0.359828
$626$	−24.8094			−0.991583
$627$	1.86779	−	22.0113i	0.0745924	−	0.879046i
$628$		−	8.76129i		−	0.349613i
$629$		−	7.96648i		−	0.317644i
$630$	−5.33933	−	0.912722i	−0.212724	−	0.0363637i
$631$			13.7416i			0.547043i	0.961866	+	0.273521i	$0.0881884\pi$
$631$			13.7416i			0.547043i	−0.961866	+	0.273521i	$0.911812\pi$
$632$	19.1323			0.761042
$633$	17.3458	+	1.47189i	0.689432	+	0.0585025i
$634$	37.4707			1.48815
$635$	−13.5976			−0.539603
$636$	−10.7038	−	0.908287i	−0.424435	−	0.0360159i
$637$	−2.70154			−0.107039
$638$	−24.8617			−0.984285
$639$	−4.22696	+	24.7273i	−0.167216	+	0.978196i
$640$		−	14.0775i		−	0.556464i
$641$	12.0264			0.475013			0.237507	−	0.971386i	$-0.423670\pi$
$641$	12.0264			0.475013			0.237507	+	0.971386i	$0.423670\pi$
$642$	−3.04665	+	35.9037i	−0.120242	+	1.41701i
$643$			8.11099i			0.319866i	0.987128	+	0.159933i	$0.0511279\pi$
$643$			8.11099i			0.319866i	−0.987128	+	0.159933i	$0.948872\pi$
$644$	0.364492	+	3.91608i	0.0143630	+	0.154315i
$645$	−1.31857	+	15.5389i	−0.0519186	+	0.611842i
$646$	8.43004			0.331676
$647$		−	9.63151i		−	0.378654i	−0.981914	−	0.189327i	$-0.939369\pi$
$647$		−	9.63151i		−	0.378654i	0.981914	−	0.189327i	$-0.0606306\pi$
$648$	5.92375	−	16.8203i	0.232707	−	0.660765i
$649$			14.6117i			0.573559i
$650$			17.4389i			0.684011i
$651$	0.0848552	−	0.999989i	0.00332574	−	0.0391926i
$652$	12.6143			0.494016
$653$		−	34.9353i		−	1.36712i	−0.729892	−	0.683562i	$-0.760430\pi$
$653$		−	34.9353i		−	1.36712i	0.729892	−	0.683562i	$-0.239570\pi$
$654$	−48.6951	−	4.13208i	−1.90413	−	0.161577i
$655$			13.4330i			0.524871i
$656$		−	7.28754i		−	0.284531i
$657$	−37.2968	−	6.37563i	−1.45509	−	0.248737i
$658$			18.9172i			0.737470i
$659$	22.4382			0.874068			0.437034	−	0.899445i	$-0.356029\pi$
$659$	22.4382			0.874068			0.437034	+	0.899445i	$0.356029\pi$
$660$	7.43859	+	0.631210i	0.289547	+	0.0245698i
$661$		−	48.2563i		−	1.87695i	−0.345344	−	0.938476i	$-0.612238\pi$
$661$		−	48.2563i		−	1.87695i	0.345344	−	0.938476i	$-0.387762\pi$
$662$		−	24.7342i		−	0.961322i
$663$	−8.97033	−	0.761188i	−0.348379	−	0.0295621i
$664$			12.4940i			0.484860i
$665$	−2.80538			−0.108788
$666$	20.5622	+	3.51497i	0.796768	+	0.136202i
$667$	1.34613	+	14.4628i	0.0521225	+	0.560001i
$668$		−	3.20717i		−	0.124089i
$669$	−43.6942	−	3.70772i	−1.68931	−	0.143349i
$670$	23.7680			0.918238
$671$			51.4910i			1.98779i
$672$	−7.55804	−	0.641346i	−0.291558	−	0.0247405i
$673$	23.1417			0.892045			0.446023	−	0.895022i	$-0.352840\pi$
$673$	23.1417			0.892045			0.446023	+	0.895022i	$0.352840\pi$
$674$	10.7765			0.415096
$675$	−19.3331	−	5.01818i	−0.744131	−	0.193150i
$676$	4.67590			0.179842
$677$	−18.0139			−0.692331			−0.346165	−	0.938173i	$-0.612516\pi$
$677$	−18.0139			−0.692331			−0.346165	+	0.938173i	$0.612516\pi$
$678$	0.228149	−	2.68866i	0.00876202	−	0.103257i
$679$	−13.9861			−0.536736
$680$		−	4.09888i		−	0.157185i
$681$	37.3422	+	3.16871i	1.43095	+	0.121425i
$682$			4.75623i			0.182126i
$683$			11.3161i			0.432999i	0.976283	+	0.216500i	$0.0694640\pi$
$683$			11.3161i			0.432999i	−0.976283	+	0.216500i	$0.930536\pi$
$684$	−1.08164	+	6.32747i	−0.0413575	+	0.241937i
$685$	13.5076			0.516099
$686$	−1.67931			−0.0641164
$687$	1.48761	−	17.5309i	0.0567557	−	0.668847i
$688$			41.5985i			1.58593i
$689$	20.4309			0.778355
$690$	−0.122311	−	14.9979i	−0.00465631	−	0.570960i
$691$	−21.0922			−0.802386			−0.401193	−	0.915994i	$-0.631404\pi$
$691$	−21.0922			−0.802386			−0.401193	+	0.915994i	$0.631404\pi$
$692$		−	1.66344i		−	0.0632347i
$693$	−2.47092	+	14.4546i	−0.0938623	+	0.549085i
$694$	34.9563			1.32692
$695$	−5.35272			−0.203040
$696$	−10.3573	−	0.878877i	−0.392591	−	0.0333137i
$697$		−	2.82245i		−	0.106908i
$698$		−	29.9701i		−	1.13438i
$699$	2.78710	−	32.8450i	0.105418	−	1.24231i
$700$			3.15237i			0.119149i
$701$	27.2019			1.02740			0.513700	−	0.857970i	$-0.328274\pi$
$701$	27.2019			1.02740			0.513700	+	0.857970i	$0.328274\pi$
$702$	5.92258	−	22.8174i	0.223533	−	0.861186i
$703$	10.8037			0.407471
$704$	−12.6163			−0.475493
$705$	1.77378	−	20.9034i	0.0668045	−	0.787268i
$706$	−57.0331			−2.14647
$707$	−8.92520			−0.335667
$708$	0.359011	−	4.23081i	0.0134924	−	0.159004i
$709$		−	5.59276i		−	0.210041i	−0.994470	−	0.105020i	$-0.966509\pi$
$709$		−	5.59276i		−	0.210041i	0.994470	−	0.105020i	$-0.0334907\pi$
$710$	−15.0983			−0.566631
$711$	−4.88095	+	28.5531i	−0.183050	+	1.07082i
$712$		−	5.39961i		−	0.202359i
$713$	2.76684	−	0.257525i	0.103619	−	0.00964440i
$714$	−5.57608	−	0.473165i	−0.208680	−	0.0177077i
$715$	−14.1984			−0.530989
$716$			7.18640i			0.268568i
$717$	2.58464	−	30.4591i	0.0965253	−	1.13752i
$718$			52.2391i			1.94954i
$719$		−	1.87625i		−	0.0699723i	−0.999388	−	0.0349862i	$-0.988861\pi$
$719$		−	1.87625i		−	0.0699723i	0.999388	−	0.0349862i	$-0.0111387\pi$
$720$	15.7945	+	2.69996i	0.588625	+	0.100621i
$721$	−4.81546			−0.179337
$722$		−	20.4745i		−	0.761982i
$723$	−2.88198	+	33.9631i	−0.107182	+	1.26310i
$724$			16.8695i			0.626949i
$725$			11.6423i			0.432384i
$726$	3.17092	−	37.3682i	0.117684	−	1.38686i
$727$			32.0550i			1.18885i	0.804150	+	0.594427i	$0.202621\pi$
$727$			32.0550i			1.18885i	−0.804150	+	0.594427i	$0.797379\pi$
$728$	5.35293			0.198393
$729$	23.5915	+	13.1317i	0.873758	+	0.486361i
$730$		−	22.7732i		−	0.842875i
$731$			16.1110i			0.595888i
$732$	1.26514	−	14.9092i	0.0467608	−	0.551060i
$733$			9.68354i			0.357670i	0.983879	+	0.178835i	$0.0572328\pi$
$733$			9.68354i			0.357670i	−0.983879	+	0.178835i	$0.942767\pi$
$734$	13.1822			0.486564
$735$	1.85563	+	0.157462i	0.0684459	+	0.00580806i
$736$	−1.94641	−	20.9121i	−0.0717456	−	0.770830i
$737$		−	64.3446i		−	2.37016i
$738$	7.28500	+	1.24532i	0.268165	+	0.0458409i
$739$	47.0860			1.73209			0.866044	−	0.499968i	$-0.166655\pi$
$739$	47.0860			1.73209			0.866044	+	0.499968i	$0.166655\pi$
$740$			3.65107i			0.134216i
$741$	1.03229	−	12.1651i	0.0379220	−	0.446897i
$742$	12.7001			0.466236
$743$	−26.9763			−0.989666			−0.494833	−	0.868988i	$-0.664771\pi$
$743$	−26.9763			−0.989666			−0.494833	+	0.868988i	$0.664771\pi$
$744$	−0.168136	+	1.98142i	−0.00616415	+	0.0726423i
$745$	−3.49544			−0.128063
$746$	−15.3340			−0.561418
$747$	−18.6460	−	3.18741i	−0.682223	−	0.116621i
$748$	7.71249			0.281997
$749$		−	12.3881i		−	0.452652i
$750$	2.33858	−	27.5593i	0.0853928	−	1.00632i
$751$		−	27.1488i		−	0.990672i	−0.868701	−	0.495336i	$-0.835045\pi$
$751$		−	27.1488i		−	0.990672i	0.868701	−	0.495336i	$-0.164955\pi$
$752$		−	55.9597i		−	2.04064i
$753$	33.6460	+	2.85507i	1.22613	+	0.104044i
$754$	−13.7405			−0.500400
$755$	1.96377			0.0714690
$756$	1.07060	−	4.12462i	0.0389375	−	0.150011i
$757$		−	20.0515i		−	0.728784i	−0.931246	−	0.364392i	$-0.881277\pi$
$757$		−	20.0515i		−	0.728784i	0.931246	−	0.364392i	$-0.118723\pi$
$758$	46.7654			1.69860
$759$	−40.6022	+	0.331121i	−1.47377	+	0.0120189i
$760$	5.55869			0.201635
$761$			51.4825i			1.86624i	0.359565	+	0.933120i	$0.382925\pi$
$761$			51.4825i			1.86624i	−0.359565	+	0.933120i	$0.617075\pi$
$762$	3.11021	−	36.6528i	0.112671	−	1.32779i
$763$	16.8016			0.608260
$764$	8.81141			0.318786
$765$	6.11717	+	1.04569i	0.221167	+	0.0378069i
$766$		−	12.4612i		−	0.450240i
$767$			8.07554i			0.291591i
$768$	29.0377	+	2.46402i	1.04781	+	0.0889128i
$769$			4.11260i			0.148304i	0.997247	+	0.0741521i	$0.0236250\pi$
$769$			4.11260i			0.148304i	−0.997247	+	0.0741521i	$0.976375\pi$
$770$	−8.82590			−0.318063
$771$	3.93944	−	46.4250i	0.141876	−	1.67195i
$772$	−2.07609			−0.0747201
$773$	−42.4283			−1.52604			−0.763020	−	0.646375i	$-0.776284\pi$
$773$	−42.4283			−1.52604			−0.763020	+	0.646375i	$0.776284\pi$
$774$	−41.5840	−	7.10850i	−1.49471	−	0.255510i
$775$	2.22726			0.0800054
$776$	27.7125			0.994823
$777$	−7.14618	−	0.606397i	−0.256368	−	0.0217544i
$778$		−	42.5532i		−	1.52561i
$779$	3.82767			0.137141
$780$	4.11114	+	0.348855i	0.147202	+	0.0124910i
$781$			40.8741i			1.46259i
$782$	−1.43600	−	15.4283i	−0.0513512	−	0.551714i
$783$	3.95394	−	15.2330i	0.141302	−	0.544382i
$784$	4.96763			0.177415
$785$		−	11.4867i		−	0.409979i
$786$	−36.2092	−	3.07257i	−1.29154	−	0.109595i
$787$		−	38.4191i		−	1.36949i	−0.728782	−	0.684746i	$-0.759913\pi$
$787$		−	38.4191i		−	1.36949i	0.728782	−	0.684746i	$-0.240087\pi$
$788$			11.9353i			0.425179i
$789$	7.36953	+	0.625350i	0.262362	+	0.0222631i
$790$	−17.4343			−0.620286
$791$			0.927688i			0.0329848i
$792$	4.89597	−	28.6409i	0.173971	−	1.01771i
$793$			28.4579i			1.01057i
$794$			23.1760i			0.822486i
$795$	−14.0336	−	1.19083i	−0.497719	−	0.0422345i
$796$			0.371638i			0.0131724i
$797$	15.2067			0.538649			0.269324	−	0.963050i	$-0.413200\pi$
$797$	15.2067			0.538649			0.269324	+	0.963050i	$0.413200\pi$
$798$	0.641683	−	7.56201i	0.0227153	−	0.267692i
$799$		−	21.6731i		−	0.766739i
$800$		−	16.8339i		−	0.595168i
$801$	8.05838	+	1.37753i	0.284729	+	0.0486725i
$802$		−	14.0999i		−	0.497884i
$803$	−61.6515			−2.17564
$804$	−1.58095	+	18.6310i	−0.0557559	+	0.657064i
$805$	0.477877	+	5.13428i	0.0168430	+	0.180960i
$806$			2.62866i			0.0925906i
$807$	4.07325	−	48.0019i	0.143385	−	1.68975i
$808$	17.6848			0.622148
$809$		−	9.25231i		−	0.325294i	−0.986684	−	0.162647i	$-0.947997\pi$
$809$		−	9.25231i		−	0.325294i	0.986684	−	0.162647i	$-0.0520032\pi$
$810$	−5.39803	+	15.3276i	−0.189667	+	0.538556i
$811$	−12.5829			−0.441844			−0.220922	−	0.975291i	$-0.570907\pi$
$811$	−12.5829			−0.441844			−0.220922	+	0.975291i	$0.570907\pi$
$812$	−2.48383			−0.0871652
$813$	−0.948138	−	0.0804554i	−0.0332527	−	0.00282169i
$814$	33.9893			1.19132
$815$	16.5384			0.579314
$816$	16.4948	+	1.39969i	0.577434	+	0.0489988i
$817$	−21.8490			−0.764399
$818$		−	11.7396i		−	0.410467i
$819$	−1.36562	+	7.98873i	−0.0477186	+	0.279149i
$820$			1.29354i			0.0451724i
$821$			36.6127i			1.27779i	0.769293	+	0.638897i	$0.220609\pi$
$821$			36.6127i			1.27779i	−0.769293	+	0.638897i	$0.779391\pi$
$822$	−3.08963	+	36.4102i	−0.107763	+	1.26995i
$823$	−17.1788			−0.598816			−0.299408	−	0.954125i	$-0.596789\pi$
$823$	−17.1788			−0.598816			−0.299408	+	0.954125i	$0.596789\pi$
$824$	9.54155			0.332395
$825$	−32.4279	−	2.75171i	−1.12900	−	0.0958023i
$826$			5.01987i			0.174664i
$827$	23.4508			0.815462			0.407731	−	0.913102i	$-0.366320\pi$
$827$	23.4508			0.815462			0.407731	+	0.913102i	$0.366320\pi$
$828$	11.7645	+	0.901724i	0.408845	+	0.0313371i
$829$	48.5061			1.68469			0.842343	−	0.538942i	$-0.181176\pi$
$829$	48.5061			1.68469			0.842343	+	0.538942i	$0.181176\pi$
$830$		−	11.3852i		−	0.395185i
$831$	1.24193	+	0.105385i	0.0430821	+	0.00365578i
$832$	−6.97272			−0.241735
$833$	1.92396			0.0666611
$834$	1.22434	−	14.4285i	0.0423955	−	0.499616i
$835$		−	4.20485i		−	0.145515i
$836$			10.4593i			0.361743i
$837$	−2.91418	−	0.756417i	−0.100729	−	0.0261456i
$838$		−	40.2715i		−	1.39115i
$839$	48.7224			1.68208			0.841042	−	0.540970i	$-0.181943\pi$
$839$	48.7224			1.68208			0.841042	+	0.540970i	$0.181943\pi$
$840$	−3.67682	−	0.312001i	−0.126862	−	0.0107650i
$841$	19.8268			0.683682
$842$	9.65020			0.332568
$843$	57.6066	+	4.88827i	1.98408	+	0.168361i
$844$	−8.24234			−0.283713
$845$	6.13046			0.210894
$846$	55.9402	+	9.56260i	1.92326	+	0.328769i
$847$			12.8934i			0.443023i
$848$	−37.5687			−1.29011
$849$	−3.02614	+	35.6620i	−0.103857	+	1.22392i
$850$		−	12.4195i		−	0.425985i
$851$	−1.84034	−	19.7725i	−0.0630861	−	0.677793i
$852$	1.00428	−	11.8351i	0.0344061	−	0.405464i
$853$	42.1733			1.44399			0.721993	−	0.691901i	$-0.243226\pi$
$853$	42.1733			1.44399			0.721993	+	0.691901i	$0.243226\pi$
$854$			17.6898i			0.605333i
$855$	−1.41811	+	8.29581i	−0.0484984	+	0.283711i
$856$			24.5463i			0.838976i
$857$			30.7553i			1.05058i	0.850923	+	0.525291i	$0.176044\pi$
$857$			30.7553i			1.05058i	−0.850923	+	0.525291i	$0.823956\pi$
$858$	3.24764	−	38.2722i	0.110872	−	1.30659i
$859$	−14.4862			−0.494263			−0.247131	−	0.968982i	$-0.579488\pi$
$859$	−14.4862			−0.494263			−0.247131	+	0.968982i	$0.579488\pi$
$860$		−	7.38375i		−	0.251784i
$861$	−2.53183	−	0.214841i	−0.0862845	−	0.00732177i
$862$		−	3.71742i		−	0.126616i
$863$			42.0798i			1.43241i	0.697889	+	0.716206i	$0.254123\pi$
$863$			42.0798i			1.43241i	−0.697889	+	0.716206i	$0.745877\pi$
$864$	−5.71710	+	22.0257i	−0.194500	+	0.749331i
$865$		−	2.18090i		−	0.0741530i
$866$	−7.34392			−0.249556
$867$	−22.9510	−	1.94753i	−0.779457	−	0.0661417i
$868$			0.475174i			0.0161285i
$869$			47.1982i			1.60109i
$870$	9.43807	+	0.800878i	0.319981	+	0.0271523i
$871$		−	35.5618i		−	1.20496i
$872$	−33.2914			−1.12739
$873$	−7.06991	+	41.3583i	−0.239280	+	1.39976i
$874$	20.9231	−	1.94743i	0.707733	−	0.0658729i
$875$			9.50900i			0.321463i
$876$	17.8512	+	1.51479i	0.603136	+	0.0511798i
$877$	−50.1451			−1.69328			−0.846640	−	0.532166i	$-0.821378\pi$
$877$	−50.1451			−1.69328			−0.846640	+	0.532166i	$0.821378\pi$
$878$		−	47.1580i		−	1.59150i
$879$	−50.0610	−	4.24799i	−1.68852	−	0.143281i
$880$	26.1082			0.880108
$881$	−36.6083			−1.23336			−0.616682	−	0.787213i	$-0.711523\pi$
$881$	−36.6083			−1.23336			−0.616682	+	0.787213i	$0.711523\pi$
$882$	−0.848887	+	4.96590i	−0.0285835	+	0.167211i
$883$	−41.6882			−1.40292			−0.701460	−	0.712709i	$-0.747468\pi$
$883$	−41.6882			−1.40292			−0.701460	+	0.712709i	$0.747468\pi$
$884$	4.26252			0.143364
$885$	0.470691	−	5.54692i	0.0158221	−	0.186458i
$886$	−35.3350			−1.18710
$887$			8.00329i			0.268724i	0.990932	+	0.134362i	$0.0428985\pi$
$887$			8.00329i			0.268724i	−0.990932	+	0.134362i	$0.957101\pi$
$888$	14.1597	+	1.20154i	0.475169	+	0.0403210i
$889$			12.6466i			0.424152i
$890$			4.92041i			0.164932i
$891$	41.4947	+	14.6135i	1.39013	+	0.489571i
$892$	20.7626			0.695183
$893$	29.3920			0.983566
$894$	0.799523	−	9.42210i	0.0267401	−	0.315122i
$895$			9.42193i			0.314940i
$896$	−13.0930			−0.437406
$897$	−22.4399	+	0.183003i	−0.749246	+	0.00611028i
$898$	−31.1056			−1.03801
$899$			1.75490i			0.0585293i
$900$	9.32190	+	1.59352i	0.310730	+	0.0531172i
$901$	−14.5503			−0.484741
$902$	12.0421			0.400958
$903$	14.4521	+	1.22635i	0.480935	+	0.0408103i
$904$		−	1.83816i		−	0.0611363i
$905$			22.1172i			0.735200i
$906$	−0.449179	+	5.29342i	−0.0149230	+	0.175862i
$907$		−	40.0047i		−	1.32833i	−0.747584	−	0.664167i	$-0.768786\pi$
$907$		−	40.0047i		−	1.32833i	0.747584	−	0.664167i	$-0.231214\pi$
$908$	−17.7442			−0.588863
$909$	−4.51166	+	26.3928i	−0.149642	+	0.875393i
$910$	−4.87787			−0.161700
$911$	−6.84870			−0.226908			−0.113454	−	0.993543i	$-0.536191\pi$
$911$	−6.84870			−0.226908			−0.113454	+	0.993543i	$0.536191\pi$
$912$	−1.89819	+	22.3694i	−0.0628552	+	0.740726i
$913$	−30.8219			−1.02005
$914$	−54.6267			−1.80689
$915$	1.65869	−	19.5471i	0.0548347	−	0.646208i
$916$			8.33033i			0.275242i
$917$	12.4935			0.412572
$918$	−4.21789	+	16.2499i	−0.139211	+	0.536326i
$919$			2.03085i			0.0669916i	0.999439	+	0.0334958i	$0.0106640\pi$
$919$			2.03085i			0.0669916i	−0.999439	+	0.0334958i	$0.989336\pi$
$920$	−0.946885	−	10.1733i	−0.0312179	−	0.335403i
$921$	−1.12940	−	0.0958364i	−0.0372149	−	0.00315792i
$922$	−51.2604			−1.68817
$923$			22.5902i			0.743566i
$924$	0.587064	−	6.91834i	0.0193130	−	0.227597i
$925$		−	15.9165i		−	0.523333i
$926$			3.65224i			0.120020i
$927$	−2.43420	+	14.2398i	−0.0799496	+	0.467697i
$928$	13.2638			0.435405
$929$		−	6.38599i		−	0.209518i	−0.994498	−	0.104759i	$-0.966593\pi$
$929$		−	6.38599i		−	0.209518i	0.994498	−	0.104759i	$-0.0334071\pi$
$930$	0.153214	−	1.80557i	0.00502408	−	0.0592071i
$931$			2.60918i			0.0855123i
$932$			15.6073i			0.511233i
$933$	−3.56369	+	41.9968i	−0.116670	+	1.37491i
$934$			32.5619i			1.06546i
$935$	10.1117			0.330687
$936$	2.70589	−	15.8292i	0.0884448	−	0.517393i
$937$			13.7613i			0.449562i	0.974409	+	0.224781i	$0.0721666\pi$
$937$			13.7613i			0.449562i	−0.974409	+	0.224781i	$0.927833\pi$
$938$		−	22.1057i		−	0.721776i
$939$	2.16357	−	25.4969i	0.0706054	−	0.832060i
$940$			9.93287i			0.323975i
$941$	−31.9570			−1.04177			−0.520885	−	0.853627i	$-0.674398\pi$
$941$	−31.9570			−1.04177			−0.520885	+	0.853627i	$0.674398\pi$
$942$	30.9629	+	2.62739i	1.00883	+	0.0856051i
$943$	−0.652017	−	7.00523i	−0.0212326	−	0.228122i
$944$		−	14.8495i		−	0.483309i
$945$	1.40365	−	5.40769i	0.0456606	−	0.175912i
$946$	−68.7383			−2.23487
$947$			57.2708i			1.86105i	0.366228	+	0.930525i	$0.380649\pi$
$947$			57.2708i			1.86105i	−0.366228	+	0.930525i	$0.619351\pi$
$948$	1.15966	−	13.6662i	0.0376641	−	0.443859i
$949$	−34.0734			−1.10607
$950$	16.8427			0.546450
$951$	−3.26773	+	38.5091i	−0.105964	+	1.24874i
$952$	−3.81220			−0.123554
$953$	14.7695			0.478432			0.239216	−	0.970966i	$-0.423110\pi$
$953$	14.7695			0.478432			0.239216	+	0.970966i	$0.423110\pi$
$954$	6.41987	−	37.5556i	0.207851	−	1.21591i
$955$	11.5524			0.373828
$956$			14.4736i			0.468108i
$957$	2.16813	−	25.5507i	0.0700858	−	0.825937i
$958$			48.0738i			1.55319i
$959$		−	12.5629i		−	0.405677i
$960$	4.78942	+	0.406411i	0.154578	+	0.0131169i
$961$	−30.6643			−0.989170
$962$	18.7851			0.605655
$963$	−36.6330	−	6.26216i	−1.18048	−	0.201795i
$964$		−	16.1386i		−	0.519789i
$965$	−2.72192			−0.0876216
$966$	−13.9489	+	0.113757i	−0.448800	+	0.00366007i
$967$	−11.7072			−0.376479			−0.188239	−	0.982123i	$-0.560278\pi$
$967$	−11.7072			−0.376479			−0.188239	+	0.982123i	$0.560278\pi$
$968$		−	25.5476i		−	0.821130i
$969$	−0.735164	+	8.66365i	−0.0236169	+	0.278317i
$970$	−25.2531			−0.810829
$971$	−28.4473			−0.912916			−0.456458	−	0.889745i	$-0.650882\pi$
$971$	−28.4473			−0.912916			−0.456458	+	0.889745i	$0.650882\pi$
$972$	−11.6557	−	5.25087i	−0.373858	−	0.168422i
$973$			4.97835i			0.159599i
$974$			43.5359i			1.39498i
$975$	−17.9222	−	1.52081i	−0.573969	−	0.0487048i
$976$		−	52.3288i		−	1.67501i
$977$	24.8874			0.796217			0.398108	−	0.917338i	$-0.369667\pi$
$977$	24.8874			0.796217			0.398108	+	0.917338i	$0.369667\pi$
$978$	−3.78287	+	44.5798i	−0.120963	+	1.42551i
$979$	13.3205			0.425725
$980$	−0.881757			−0.0281667
$981$	8.49318	−	49.6842i	0.271166	−	1.58629i
$982$	33.8676			1.08076
$983$	32.9439			1.05075			0.525373	−	0.850872i	$-0.323926\pi$
$983$	32.9439			1.05075			0.525373	+	0.850872i	$0.323926\pi$
$984$	5.01667	+	0.425695i	0.159926	+	0.0135707i
$985$			15.6482i			0.498592i
$986$	9.78560			0.311637
$987$	−19.4415	−	1.64973i	−0.618828	−	0.0525114i
$988$			5.78062i			0.183906i
$989$	3.72182	+	39.9870i	0.118347	+	1.27151i
$990$	−4.46147	+	26.0991i	−0.141795	+	0.829484i
$991$	−34.5681			−1.09809			−0.549046	−	0.835792i	$-0.685009\pi$
$991$	−34.5681			−1.09809			−0.549046	+	0.835792i	$0.685009\pi$
$992$		−	2.53746i		−	0.0805644i
$993$	25.4196	+	2.15701i	0.806667	+	0.0684507i
$994$			14.0424i			0.445397i
$995$			0.487247i			0.0154468i
$996$	8.92447	+	0.757296i	0.282783	+	0.0239959i
$997$	−8.97502			−0.284242			−0.142121	−	0.989849i	$-0.545392\pi$
$997$	−8.97502			−0.284242			−0.142121	+	0.989849i	$0.545392\pi$
$998$		−	3.43218i		−	0.108644i
$999$	−5.40555	+	20.8255i	−0.171024	+	0.658889i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.e.a.344.11	✓	48
3.2	odd	2	inner	483.2.e.a.344.38	yes	48
23.22	odd	2	inner	483.2.e.a.344.12	yes	48
69.68	even	2	inner	483.2.e.a.344.37	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.e.a.344.11	✓	48	1.1	even	1	trivial
483.2.e.a.344.12	yes	48	23.22	odd	2	inner
483.2.e.a.344.37	yes	48	69.68	even	2	inner
483.2.e.a.344.38	yes	48	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.67931i q^{2} +(1.72585 + 0.146449i) q^{3} -0.820088 q^{4} -1.07520 q^{5} +(0.245933 - 2.89824i) q^{6} +1.00000i q^{7} -1.98144i q^{8} +(2.95711 + 0.505497i) q^{9} +O(q^{10})\)	\(q-1.67931i q^{2} +(1.72585 + 0.146449i) q^{3} -0.820088 q^{4} -1.07520 q^{5} +(0.245933 - 2.89824i) q^{6} +1.00000i q^{7} -1.98144i q^{8} +(2.95711 + 0.505497i) q^{9} +1.80559i q^{10} +4.88809 q^{11} +(-1.41535 - 0.120101i) q^{12} +2.70154 q^{13} +1.67931 q^{14} +(-1.85563 - 0.157462i) q^{15} -4.96763 q^{16} -1.92396 q^{17} +(0.848887 - 4.96590i) q^{18} -2.60918i q^{19} +0.881757 q^{20} +(-0.146449 + 1.72585i) q^{21} -8.20863i q^{22} +(-4.77519 + 0.444455i) q^{23} +(0.290180 - 3.41967i) q^{24} -3.84395 q^{25} -4.53672i q^{26} +(5.02949 + 1.30548i) q^{27} -0.820088i q^{28} -3.02873i q^{29} +(-0.264427 + 3.11618i) q^{30} -0.579419 q^{31} +4.37932i q^{32} +(8.43610 + 0.715855i) q^{33} +3.23092i q^{34} -1.07520i q^{35} +(-2.42509 - 0.414552i) q^{36} +4.14067i q^{37} -4.38162 q^{38} +(4.66244 + 0.395637i) q^{39} +2.13044i q^{40} +1.46700i q^{41} +(2.89824 + 0.245933i) q^{42} -8.37391i q^{43} -4.00866 q^{44} +(-3.17947 - 0.543510i) q^{45} +(0.746378 + 8.01904i) q^{46} +11.2649i q^{47} +(-8.57338 - 0.727504i) q^{48} -1.00000 q^{49} +6.45519i q^{50} +(-3.32046 - 0.281761i) q^{51} -2.21550 q^{52} +7.56270 q^{53} +(2.19230 - 8.44607i) q^{54} -5.25567 q^{55} +1.98144 q^{56} +(0.382111 - 4.50304i) q^{57} -5.08618 q^{58} +2.98924i q^{59} +(1.52178 + 0.129132i) q^{60} +10.5340i q^{61} +0.973024i q^{62} +(-0.505497 + 2.95711i) q^{63} -2.58102 q^{64} -2.90469 q^{65} +(1.20214 - 14.1668i) q^{66} -13.1635i q^{67} +1.57781 q^{68} +(-8.30635 + 0.0677403i) q^{69} -1.80559 q^{70} +8.36199i q^{71} +(1.00161 - 5.85933i) q^{72} -12.6126 q^{73} +6.95348 q^{74} +(-6.63407 - 0.562942i) q^{75} +2.13975i q^{76} +4.88809i q^{77} +(0.664398 - 7.82969i) q^{78} +9.65575i q^{79} +5.34119 q^{80} +(8.48895 + 2.98962i) q^{81} +2.46356 q^{82} -6.30550 q^{83} +(0.120101 - 1.41535i) q^{84} +2.06863 q^{85} -14.0624 q^{86} +(0.443554 - 5.22713i) q^{87} -9.68546i q^{88} +2.72509 q^{89} +(-0.912722 + 5.33933i) q^{90} +2.70154i q^{91} +(3.91608 - 0.364492i) q^{92} +(-0.999989 - 0.0848552i) q^{93} +18.9172 q^{94} +2.80538i q^{95} +(-0.641346 + 7.55804i) q^{96} +13.9861i q^{97} +1.67931i q^{98} +(14.4546 + 2.47092i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9	\( 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9} + 22 q^{12} - 8 q^{13} + 24 q^{16} - 14 q^{18} - 12 q^{24} + 88 q^{25} - 16 q^{27} - 8 q^{31} - 10 q^{36} + 8 q^{46} - 98 q^{48} - 48 q^{49} + 28 q^{52} - 28 q^{54} - 92 q^{58} + 92 q^{64} + 8 q^{69} + 8 q^{70} + 60 q^{72} + 40 q^{73} - 80 q^{75} + 114 q^{78} - 28 q^{81} - 20 q^{82} - 40 q^{85} - 28 q^{87} - 76 q^{93} - 12 q^{94} - 6 q^{96}+O(q^{100}) \) 48 * q - 4 * q^3 - 40 * q^4 + 6 * q^6 + 4 * q^9 + 22 * q^12 - 8 * q^13 + 24 * q^16 - 14 * q^18 - 12 * q^24 + 88 * q^25 - 16 * q^27 - 8 * q^31 - 10 * q^36 + 8 * q^46 - 98 * q^48 - 48 * q^49 + 28 * q^52 - 28 * q^54 - 92 * q^58 + 92 * q^64 + 8 * q^69 + 8 * q^70 + 60 * q^72 + 40 * q^73 - 80 * q^75 + 114 * q^78 - 28 * q^81 - 20 * q^82 - 40 * q^85 - 28 * q^87 - 76 * q^93 - 12 * q^94 - 6 * q^96

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