LMFDB - Embedded newform 1380.2.p.b.91.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(91,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 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("1380.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.p (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:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.15
Character	$\chi$	$=$	1380.91
Dual form			1380.2.p.b.91.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.952347 - 1.04548i) q^{2} -1.00000i q^{3} +(-0.186069 + 1.99133i) q^{4} +1.00000i q^{5} +(-1.04548 + 0.952347i) q^{6} -3.49678 q^{7} +(2.25910 - 1.70190i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.952347 - 1.04548i) q^{2} -1.00000i q^{3} +(-0.186069 + 1.99133i) q^{4} +1.00000i q^{5} +(-1.04548 + 0.952347i) q^{6} -3.49678 q^{7} +(2.25910 - 1.70190i) q^{8} -1.00000 q^{9} +(1.04548 - 0.952347i) q^{10} -1.36625 q^{11} +(1.99133 + 0.186069i) q^{12} +3.35306 q^{13} +(3.33015 + 3.65582i) q^{14} +1.00000 q^{15} +(-3.93076 - 0.741046i) q^{16} -0.0719348i q^{17} +(0.952347 + 1.04548i) q^{18} +5.04791 q^{19} +(-1.99133 - 0.186069i) q^{20} +3.49678i q^{21} +(1.30115 + 1.42839i) q^{22} +(-4.76200 - 0.568640i) q^{23} +(-1.70190 - 2.25910i) q^{24} -1.00000 q^{25} +(-3.19327 - 3.50556i) q^{26} +1.00000i q^{27} +(0.650640 - 6.96322i) q^{28} +9.80417 q^{29} +(-0.952347 - 1.04548i) q^{30} +8.07183i q^{31} +(2.96870 + 4.81527i) q^{32} +1.36625i q^{33} +(-0.0752066 + 0.0685069i) q^{34} -3.49678i q^{35} +(0.186069 - 1.99133i) q^{36} -3.32625i q^{37} +(-4.80737 - 5.27750i) q^{38} -3.35306i q^{39} +(1.70190 + 2.25910i) q^{40} +1.37906 q^{41} +(3.65582 - 3.33015i) q^{42} -8.91103 q^{43} +(0.254216 - 2.72065i) q^{44} -1.00000i q^{45} +(3.94058 + 5.52013i) q^{46} -12.6923i q^{47} +(-0.741046 + 3.93076i) q^{48} +5.22746 q^{49} +(0.952347 + 1.04548i) q^{50} -0.0719348 q^{51} +(-0.623898 + 6.67703i) q^{52} -10.9669i q^{53} +(1.04548 - 0.952347i) q^{54} -1.36625i q^{55} +(-7.89957 + 5.95118i) q^{56} -5.04791i q^{57} +(-9.33697 - 10.2501i) q^{58} -4.71711i q^{59} +(-0.186069 + 1.99133i) q^{60} -6.38461i q^{61} +(8.43896 - 7.68719i) q^{62} +3.49678 q^{63} +(2.20705 - 7.68953i) q^{64} +3.35306i q^{65} +(1.42839 - 1.30115i) q^{66} +15.2636 q^{67} +(0.143246 + 0.0133848i) q^{68} +(-0.568640 + 4.76200i) q^{69} +(-3.65582 + 3.33015i) q^{70} -15.7028i q^{71} +(-2.25910 + 1.70190i) q^{72} +5.24792 q^{73} +(-3.47754 + 3.16775i) q^{74} +1.00000i q^{75} +(-0.939258 + 10.0520i) q^{76} +4.77748 q^{77} +(-3.50556 + 3.19327i) q^{78} -4.20591 q^{79} +(0.741046 - 3.93076i) q^{80} +1.00000 q^{81} +(-1.31334 - 1.44178i) q^{82} +13.4916 q^{83} +(-6.96322 - 0.650640i) q^{84} +0.0719348 q^{85} +(8.48639 + 9.31632i) q^{86} -9.80417i q^{87} +(-3.08650 + 2.32523i) q^{88} +11.5228i q^{89} +(-1.04548 + 0.952347i) q^{90} -11.7249 q^{91} +(2.01841 - 9.37689i) q^{92} +8.07183 q^{93} +(-13.2696 + 12.0875i) q^{94} +5.04791i q^{95} +(4.81527 - 2.96870i) q^{96} -4.72490i q^{97} +(-4.97835 - 5.46522i) q^{98} +1.36625 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} + 2 q^{10} - 20 q^{14} + 48 q^{15} - 6 q^{16} + 4 q^{18} - 16 q^{19} - 28 q^{22} - 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} - 4 q^{30} + 16 q^{32} + 28 q^{34} + 2 q^{36} - 2 q^{40} - 8 q^{41} + 26 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 16 q^{51} - 16 q^{52} + 2 q^{54} - 40 q^{56} - 8 q^{58} - 2 q^{60} + 24 q^{62} - 26 q^{64} + 48 q^{67} + 44 q^{68} - 8 q^{69} + 4 q^{72} - 20 q^{74} + 64 q^{76} + 32 q^{77} + 64 q^{79} - 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} + 40 q^{86} - 2 q^{90} - 28 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 + 2 * q^10 - 20 * q^14 + 48 * q^15 - 6 * q^16 + 4 * q^18 - 16 * q^19 - 28 * q^22 - 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 - 4 * q^30 + 16 * q^32 + 28 * q^34 + 2 * q^36 - 2 * q^40 - 8 * q^41 + 26 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 - 16 * q^51 - 16 * q^52 + 2 * q^54 - 40 * q^56 - 8 * q^58 - 2 * q^60 + 24 * q^62 - 26 * q^64 + 48 * q^67 + 44 * q^68 - 8 * q^69 + 4 * q^72 - 20 * q^74 + 64 * q^76 + 32 * q^77 + 64 * q^79 - 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 + 40 * q^86 - 2 * q^90 - 28 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$1$	$1$	$-1$	$-1$

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 $

$2$	−0.952347	−	1.04548i	−0.673411	−	0.739268i
$2$	−0.952347	−	1.04548i	−0.673411	−	0.739268i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−0.186069	+	1.99133i	−0.0930343	+	0.995663i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−1.04548	+	0.952347i	−0.426817	+	0.388794i
$7$	−3.49678			−1.32166			−0.660829	−	0.750537i	$-0.729795\pi$
$7$	−3.49678			−1.32166			−0.660829	+	0.750537i	$0.729795\pi$
$8$	2.25910	−	1.70190i	0.798712	−	0.601713i
$9$	−1.00000			−0.333333
$10$	1.04548	−	0.952347i	0.330611	−	0.301159i
$11$	−1.36625			−0.411940			−0.205970	−	0.978558i	$-0.566035\pi$
$11$	−1.36625			−0.411940			−0.205970	+	0.978558i	$0.566035\pi$
$12$	1.99133	+	0.186069i	0.574846	+	0.0537134i
$13$	3.35306			0.929970			0.464985	−	0.885318i	$-0.346060\pi$
$13$	3.35306			0.929970			0.464985	+	0.885318i	$0.346060\pi$
$14$	3.33015	+	3.65582i	0.890019	+	0.977059i
$15$	1.00000			0.258199
$16$	−3.93076	−	0.741046i	−0.982689	−	0.185262i
$17$		−	0.0719348i		−	0.0174468i	−0.999962	−	0.00872338i	$-0.997223\pi$
$17$		−	0.0719348i		−	0.0174468i	0.999962	−	0.00872338i	$-0.00277677\pi$
$18$	0.952347	+	1.04548i	0.224470	+	0.246423i
$19$	5.04791			1.15807			0.579035	−	0.815303i	$-0.303429\pi$
$19$	5.04791			1.15807			0.579035	+	0.815303i	$0.303429\pi$
$20$	−1.99133	−	0.186069i	−0.445274	−	0.0416062i
$21$			3.49678i			0.763060i
$22$	1.30115	+	1.42839i	0.277405	+	0.304534i
$23$	−4.76200	−	0.568640i	−0.992946	−	0.118570i
$23$	−4.76200	−	0.568640i	−0.992946	−	0.118570i
$24$	−1.70190	−	2.25910i	−0.347399	−	0.461137i
$25$	−1.00000			−0.200000
$26$	−3.19327	−	3.50556i	−0.626253	−	0.687497i
$27$			1.00000i			0.192450i
$28$	0.650640	−	6.96322i	0.122959	−	1.31593i
$29$	9.80417			1.82059			0.910294	−	0.413962i	$-0.135855\pi$
$29$	9.80417			1.82059			0.910294	+	0.413962i	$0.135855\pi$
$30$	−0.952347	−	1.04548i	−0.173874	−	0.190878i
$31$			8.07183i			1.44974i	0.688884	+	0.724872i	$0.258101\pi$
$31$			8.07183i			1.44974i	−0.688884	+	0.724872i	$0.741899\pi$
$32$	2.96870	+	4.81527i	0.524796	+	0.851228i
$33$			1.36625i			0.237834i
$34$	−0.0752066	+	0.0685069i	−0.0128978	+	0.0117488i
$35$		−	3.49678i		−	0.591063i
$36$	0.186069	−	1.99133i	0.0310114	−	0.331888i
$37$		−	3.32625i		−	0.546833i	−0.961896	−	0.273416i	$-0.911846\pi$
$37$		−	3.32625i		−	0.546833i	0.961896	−	0.273416i	$-0.0881537\pi$
$38$	−4.80737	−	5.27750i	−0.779858	−	0.856124i
$39$		−	3.35306i		−	0.536919i
$40$	1.70190	+	2.25910i	0.269094	+	0.357195i
$41$	1.37906			0.215373			0.107686	−	0.994185i	$-0.465656\pi$
$41$	1.37906			0.215373			0.107686	+	0.994185i	$0.465656\pi$
$42$	3.65582	−	3.33015i	0.564105	−	0.513853i
$43$	−8.91103			−1.35892			−0.679459	−	0.733713i	$-0.737786\pi$
$43$	−8.91103			−1.35892			−0.679459	+	0.733713i	$0.737786\pi$
$44$	0.254216	−	2.72065i	0.0383246	−	0.410154i
$45$		−	1.00000i		−	0.149071i
$46$	3.94058	+	5.52013i	0.581006	+	0.813899i
$47$		−	12.6923i		−	1.85137i	−0.378296	−	0.925684i	$-0.623490\pi$
$47$		−	12.6923i		−	1.85137i	0.378296	−	0.925684i	$-0.376510\pi$
$48$	−0.741046	+	3.93076i	−0.106961	+	0.567356i
$49$	5.22746			0.746779
$50$	0.952347	+	1.04548i	0.134682	+	0.147854i
$51$	−0.0719348			−0.0100729
$52$	−0.623898	+	6.67703i	−0.0865191	+	0.925937i
$53$		−	10.9669i		−	1.50642i	−0.657780	−	0.753210i	$-0.728504\pi$
$53$		−	10.9669i		−	1.50642i	0.657780	−	0.753210i	$-0.271496\pi$
$54$	1.04548	−	0.952347i	0.142272	−	0.129598i
$55$		−	1.36625i		−	0.184225i
$56$	−7.89957	+	5.95118i	−1.05562	+	0.795259i
$57$		−	5.04791i		−	0.668612i
$58$	−9.33697	−	10.2501i	−1.22600	−	1.34590i
$59$		−	4.71711i		−	0.614116i	−0.951691	−	0.307058i	$-0.900655\pi$
$59$		−	4.71711i		−	0.614116i	0.951691	−	0.307058i	$-0.0993445\pi$
$60$	−0.186069	+	1.99133i	−0.0240213	+	0.257079i
$61$		−	6.38461i		−	0.817465i	−0.912654	−	0.408733i	$-0.865971\pi$
$61$		−	6.38461i		−	0.817465i	0.912654	−	0.408733i	$-0.134029\pi$
$62$	8.43896	−	7.68719i	1.07175	−	0.976274i
$63$	3.49678			0.440553
$64$	2.20705	−	7.68953i	0.275882	−	0.961192i
$65$			3.35306i			0.415895i
$66$	1.42839	−	1.30115i	0.175823	−	0.160160i
$67$	15.2636			1.86475			0.932374	−	0.361496i	$-0.117734\pi$
$67$	15.2636			1.86475			0.932374	+	0.361496i	$0.117734\pi$
$68$	0.143246	+	0.0133848i	0.0173711	+	0.00162315i
$69$	−0.568640	+	4.76200i	−0.0684562	+	0.573277i
$70$	−3.65582	+	3.33015i	−0.436954	+	0.398029i
$71$		−	15.7028i		−	1.86358i	−0.362995	−	0.931791i	$-0.618246\pi$
$71$		−	15.7028i		−	1.86358i	0.362995	−	0.931791i	$-0.381754\pi$
$72$	−2.25910	+	1.70190i	−0.266237	+	0.200571i
$73$	5.24792			0.614222			0.307111	−	0.951674i	$-0.400638\pi$
$73$	5.24792			0.614222			0.307111	+	0.951674i	$0.400638\pi$
$74$	−3.47754	+	3.16775i	−0.404256	+	0.368243i
$75$			1.00000i			0.115470i
$76$	−0.939258	+	10.0520i	−0.107740	+	1.15305i
$77$	4.77748			0.544444
$78$	−3.50556	+	3.19327i	−0.396927	+	0.361567i
$79$	−4.20591			−0.473202			−0.236601	−	0.971607i	$-0.576033\pi$
$79$	−4.20591			−0.473202			−0.236601	+	0.971607i	$0.576033\pi$
$80$	0.741046	−	3.93076i	0.0828515	−	0.439472i
$81$	1.00000			0.111111
$82$	−1.31334	−	1.44178i	−0.145034	−	0.159218i
$83$	13.4916			1.48089			0.740447	−	0.672115i	$-0.234614\pi$
$83$	13.4916			1.48089			0.740447	+	0.672115i	$0.234614\pi$
$84$	−6.96322	−	0.650640i	−0.759750	−	0.0709907i
$85$	0.0719348			0.00780242
$86$	8.48639	+	9.31632i	0.915111	+	1.00461i
$87$		−	9.80417i		−	1.05112i
$88$	−3.08650	+	2.32523i	−0.329022	+	0.247870i
$89$			11.5228i			1.22141i	0.791857	+	0.610706i	$0.209114\pi$
$89$			11.5228i			1.22141i	−0.791857	+	0.610706i	$0.790886\pi$
$90$	−1.04548	+	0.952347i	−0.110204	+	0.100386i
$91$	−11.7249			−1.22910
$92$	2.01841	−	9.37689i	0.210433	−	0.977608i
$93$	8.07183			0.837010
$94$	−13.2696	+	12.0875i	−1.36866	+	1.24673i
$95$			5.04791i			0.517905i
$96$	4.81527	−	2.96870i	0.491457	−	0.302991i
$97$		−	4.72490i		−	0.479741i	−0.970805	−	0.239871i	$-0.922895\pi$
$97$		−	4.72490i		−	0.479741i	0.970805	−	0.239871i	$-0.0771050\pi$
$98$	−4.97835	−	5.46522i	−0.502890	−	0.552070i
$99$	1.36625			0.137313
$100$	0.186069	−	1.99133i	0.0186069	−	0.199133i
$101$	10.7894			1.07358			0.536791	−	0.843715i	$-0.319636\pi$
$101$	10.7894			1.07358			0.536791	+	0.843715i	$0.319636\pi$
$102$	0.0685069	+	0.0752066i	0.00678320	+	0.00744656i
$103$	−8.71856			−0.859065			−0.429533	−	0.903051i	$-0.641322\pi$
$103$	−8.71856			−0.859065			−0.429533	+	0.903051i	$0.641322\pi$
$104$	7.57488	−	5.70657i	0.742779	−	0.559576i
$105$	−3.49678			−0.341251
$106$	−11.4657	+	10.4443i	−1.11365	+	1.01444i
$107$	15.4237			1.49106			0.745530	−	0.666472i	$-0.232196\pi$
$107$	15.4237			1.49106			0.745530	+	0.666472i	$0.232196\pi$
$108$	−1.99133	−	0.186069i	−0.191615	−	0.0179045i
$109$			2.16171i			0.207054i	0.994627	+	0.103527i	$0.0330129\pi$
$109$			2.16171i			0.207054i	−0.994627	+	0.103527i	$0.966987\pi$
$110$	−1.42839	+	1.30115i	−0.136192	+	0.124059i
$111$	−3.32625			−0.315714
$112$	13.7450	+	2.59127i	1.29878	+	0.244852i
$113$		−	8.97756i		−	0.844538i	−0.906471	−	0.422269i	$-0.861234\pi$
$113$		−	8.97756i		−	0.844538i	0.906471	−	0.422269i	$-0.138766\pi$
$114$	−5.27750	+	4.80737i	−0.494284	+	0.450251i
$115$	0.568640	−	4.76200i	0.0530260	−	0.444059i
$116$	−1.82425	+	19.5233i	−0.169377	+	1.81269i
$117$	−3.35306			−0.309990
$118$	−4.93166	+	4.49233i	−0.453996	+	0.413552i
$119$			0.251540i			0.0230586i
$120$	2.25910	−	1.70190i	0.206227	−	0.155362i
$121$	−9.13336			−0.830305
$122$	−6.67500	+	6.08036i	−0.604326	+	0.550490i
$123$		−	1.37906i		−	0.124345i
$124$	−16.0737	−	1.50191i	−1.44346	−	0.134876i
$125$		−	1.00000i		−	0.0894427i
$126$	−3.33015	−	3.65582i	−0.296673	−	0.325686i
$127$		−	12.7171i		−	1.12846i	−0.825618	−	0.564230i	$-0.809173\pi$
$127$		−	12.7171i		−	1.12846i	0.825618	−	0.564230i	$-0.190827\pi$
$128$	−10.1412	+	5.01567i	−0.896360	+	0.443327i
$129$			8.91103i			0.784572i
$130$	3.50556	−	3.19327i	0.307458	−	0.280069i
$131$		−	21.4821i		−	1.87690i	−0.345417	−	0.938449i	$-0.612262\pi$
$131$		−	21.4821i		−	1.87690i	0.345417	−	0.938449i	$-0.387738\pi$
$132$	−2.72065	−	0.254216i	−0.236802	−	0.0221267i
$133$	−17.6514			−1.53057
$134$	−14.5363	−	15.9578i	−1.25574	−	1.37855i
$135$	−1.00000			−0.0860663
$136$	−0.122426	−	0.162508i	−0.0104979	−	0.0139349i
$137$			8.83193i			0.754562i	0.926099	+	0.377281i	$0.123141\pi$
$137$			8.83193i			0.754562i	−0.926099	+	0.377281i	$0.876859\pi$
$138$	5.52013	−	3.94058i	0.469905	−	0.335444i
$139$			1.47914i			0.125459i	0.998031	+	0.0627295i	$0.0199805\pi$
$139$			1.47914i			0.125459i	−0.998031	+	0.0627295i	$0.980019\pi$
$140$	6.96322	+	0.650640i	0.588500	+	0.0549892i
$141$	−12.6923			−1.06889
$142$	−16.4170	+	14.9545i	−1.37769	+	1.25496i
$143$	−4.58112			−0.383092
$144$	3.93076	+	0.741046i	0.327563	+	0.0617539i
$145$			9.80417i			0.814192i
$146$	−4.99784	−	5.48661i	−0.413624	−	0.454075i
$147$		−	5.22746i		−	0.431153i
$148$	6.62366	+	0.618911i	0.544461	+	0.0508742i
$149$		−	12.9154i		−	1.05807i	−0.848600	−	0.529034i	$-0.822554\pi$
$149$		−	12.9154i		−	1.05807i	0.848600	−	0.529034i	$-0.177446\pi$
$150$	1.04548	−	0.952347i	0.0853633	−	0.0777588i
$151$			1.48821i			0.121109i	0.998165	+	0.0605546i	$0.0192869\pi$
$151$			1.48821i			0.121109i	−0.998165	+	0.0605546i	$0.980713\pi$
$152$	11.4037	−	8.59105i	0.924965	−	0.696827i
$153$			0.0719348i			0.00581558i
$154$	−4.54982	−	4.99477i	−0.366635	−	0.402490i
$155$	−8.07183			−0.648345
$156$	6.67703	+	0.623898i	0.534590	+	0.0499518i
$157$			0.789022i			0.0629708i	0.999504	+	0.0314854i	$0.0100238\pi$
$157$			0.789022i			0.0629708i	−0.999504	+	0.0314854i	$0.989976\pi$
$158$	4.00549	+	4.39721i	0.318659	+	0.349823i
$159$	−10.9669			−0.869733
$160$	−4.81527	+	2.96870i	−0.380681	+	0.234696i
$161$	16.6517	+	1.98841i	1.31233	+	0.156708i
$162$	−0.952347	−	1.04548i	−0.0748235	−	0.0821409i
$163$		−	10.0679i		−	0.788576i	−0.918987	−	0.394288i	$-0.870991\pi$
$163$		−	10.0679i		−	0.788576i	0.918987	−	0.394288i	$-0.129009\pi$
$164$	−0.256599	+	2.74615i	−0.0200370	+	0.214439i
$165$	−1.36625			−0.106363
$166$	−12.8487	−	14.1052i	−0.997251	−	1.09478i
$167$			12.3125i			0.952769i	0.879237	+	0.476384i	$0.158053\pi$
$167$			12.3125i			0.952769i	−0.879237	+	0.476384i	$0.841947\pi$
$168$	5.95118	+	7.89957i	0.459143	+	0.609465i
$169$	−1.75702			−0.135155
$170$	−0.0685069	−	0.0752066i	−0.00525424	−	0.00576808i
$171$	−5.04791			−0.386023
$172$	1.65806	−	17.7448i	0.126426	−	1.35303i
$173$	3.04079			0.231187			0.115593	−	0.993297i	$-0.463123\pi$
$173$	3.04079			0.231187			0.115593	+	0.993297i	$0.463123\pi$
$174$	−10.2501	+	9.33697i	−0.777057	+	0.707834i
$175$	3.49678			0.264332
$176$	5.37040	+	1.01246i	0.404809	+	0.0763167i
$177$	−4.71711			−0.354560
$178$	12.0469	−	10.9737i	0.902951	−	0.822513i
$179$			9.66616i			0.722483i	0.932472	+	0.361242i	$0.117647\pi$
$179$			9.66616i			0.722483i	−0.932472	+	0.361242i	$0.882353\pi$
$180$	1.99133	+	0.186069i	0.148425	+	0.0138687i
$181$			26.0047i			1.93291i	0.256827	+	0.966457i	$0.417323\pi$
$181$			26.0047i			1.93291i	−0.256827	+	0.966457i	$0.582677\pi$
$182$	11.1662	+	12.2582i	0.827692	+	0.908636i
$183$	−6.38461			−0.471964
$184$	−11.7256	+	6.81985i	−0.864423	+	0.502766i
$185$	3.32625			0.244551
$186$	−7.68719	−	8.43896i	−0.563652	−	0.618775i
$187$			0.0982810i			0.00718702i
$188$	25.2746	+	2.36165i	1.84334	+	0.172241i
$189$		−	3.49678i		−	0.254353i
$190$	5.27750	−	4.80737i	0.382870	−	0.348763i
$191$	−1.45243			−0.105094			−0.0525469	−	0.998618i	$-0.516734\pi$
$191$	−1.45243			−0.105094			−0.0525469	+	0.998618i	$0.516734\pi$
$192$	−7.68953	−	2.20705i	−0.554944	−	0.159280i
$193$	12.6263			0.908861			0.454431	−	0.890782i	$-0.349843\pi$
$193$	12.6263			0.908861			0.454431	+	0.890782i	$0.349843\pi$
$194$	−4.93981	+	4.49975i	−0.354657	+	0.323063i
$195$	3.35306			0.240117
$196$	−0.972665	+	10.4096i	−0.0694761	+	0.743541i
$197$	−23.9878			−1.70906			−0.854530	−	0.519401i	$-0.826155\pi$
$197$	−23.9878			−1.70906			−0.854530	+	0.519401i	$0.826155\pi$
$198$	−1.30115	−	1.42839i	−0.0924684	−	0.101511i
$199$	16.8297			1.19303			0.596513	−	0.802603i	$-0.296552\pi$
$199$	16.8297			1.19303			0.596513	+	0.802603i	$0.296552\pi$
$200$	−2.25910	+	1.70190i	−0.159742	+	0.120343i
$201$		−	15.2636i		−	1.07661i
$202$	−10.2752	−	11.2801i	−0.722962	−	0.793665i
$203$	−34.2830			−2.40619
$204$	0.0133848	−	0.143246i	0.000937124	−	0.0100292i
$205$			1.37906i			0.0963176i
$206$	8.30310	+	9.11510i	0.578504	+	0.635079i
$207$	4.76200	+	0.568640i	0.330982	+	0.0395232i
$208$	−13.1800	−	2.48477i	−0.913872	−	0.172288i
$209$	−6.89672			−0.477056
$210$	3.33015	+	3.65582i	0.229802	+	0.252276i
$211$			20.6790i			1.42360i	0.702382	+	0.711800i	$0.252120\pi$
$211$			20.6790i			1.42360i	−0.702382	+	0.711800i	$0.747880\pi$
$212$	21.8387	+	2.04060i	1.49989	+	0.140149i
$213$	−15.7028			−1.07594
$214$	−14.6887	−	16.1252i	−1.00410	−	1.10229i
$215$		−	8.91103i		−	0.607727i
$216$	1.70190	+	2.25910i	0.115800	+	0.153712i
$217$		−	28.2254i		−	1.91607i
$218$	2.26003	−	2.05870i	0.153069	−	0.139433i
$219$		−	5.24792i		−	0.354621i
$220$	2.72065	+	0.254216i	0.183426	+	0.0171393i
$221$		−	0.241201i		−	0.0162250i
$222$	3.16775	+	3.47754i	0.212605	+	0.233397i
$223$			10.0263i			0.671409i	0.941967	+	0.335704i	$0.108974\pi$
$223$			10.0263i			0.671409i	−0.941967	+	0.335704i	$0.891026\pi$
$224$	−10.3809	−	16.8379i	−0.693601	−	1.12503i
$225$	1.00000			0.0666667
$226$	−9.38588	+	8.54976i	−0.624340	+	0.568721i
$227$	5.76617			0.382714			0.191357	−	0.981520i	$-0.438711\pi$
$227$	5.76617			0.382714			0.191357	+	0.981520i	$0.438711\pi$
$228$	10.0520	+	0.939258i	0.665712	+	0.0622039i
$229$			2.46613i			0.162966i	0.996675	+	0.0814831i	$0.0259657\pi$
$229$			2.46613i			0.162966i	−0.996675	+	0.0814831i	$0.974034\pi$
$230$	−5.52013	+	3.94058i	−0.363987	+	0.259834i
$231$		−	4.77748i		−	0.314335i
$232$	22.1486	−	16.6857i	1.45413	−	1.09547i
$233$	17.1486			1.12344			0.561722	−	0.827326i	$-0.310139\pi$
$233$	17.1486			1.12344			0.561722	+	0.827326i	$0.310139\pi$
$234$	3.19327	+	3.50556i	0.208751	+	0.229166i
$235$	12.6923			0.827957
$236$	9.39331	+	0.877706i	0.611452	+	0.0571338i
$237$			4.20591i			0.273203i
$238$	0.262981	−	0.239554i	0.0170465	−	0.0155279i
$239$		−	7.88125i		−	0.509796i	−0.966968	−	0.254898i	$-0.917958\pi$
$239$		−	7.88125i		−	0.509796i	0.966968	−	0.254898i	$-0.0820419\pi$
$240$	−3.93076	−	0.741046i	−0.253729	−	0.0478343i
$241$			13.3123i			0.857523i	0.903418	+	0.428762i	$0.141050\pi$
$241$			13.3123i			0.857523i	−0.903418	+	0.428762i	$0.858950\pi$
$242$	8.69813	+	9.54877i	0.559137	+	0.613818i
$243$		−	1.00000i		−	0.0641500i
$244$	12.7138	+	1.18797i	0.813920	+	0.0760523i
$245$			5.22746i			0.333970i
$246$	−1.44178	+	1.31334i	−0.0919246	+	0.0837356i
$247$	16.9259			1.07697
$248$	13.7375	+	18.2351i	0.872330	+	1.15793i
$249$		−	13.4916i		−	0.854994i
$250$	−1.04548	+	0.952347i	−0.0661221	+	0.0602317i
$251$	16.9160			1.06773			0.533865	−	0.845570i	$-0.320739\pi$
$251$	16.9160			1.06773			0.533865	+	0.845570i	$0.320739\pi$
$252$	−0.650640	+	6.96322i	−0.0409865	+	0.438642i
$253$	6.50609	+	0.776905i	0.409034	+	0.0488436i
$254$	−13.2955	+	12.1111i	−0.834234	+	0.759918i
$255$		−	0.0719348i		−	0.00450473i
$256$	14.9017	+	5.82575i	0.931356	+	0.364109i
$257$	19.6697			1.22696			0.613482	−	0.789709i	$-0.289768\pi$
$257$	19.6697			1.22696			0.613482	+	0.789709i	$0.289768\pi$
$258$	9.31632	−	8.48639i	0.580009	−	0.528340i
$259$			11.6312i			0.722726i
$260$	−6.67703	−	0.623898i	−0.414092	−	0.0386925i
$261$	−9.80417			−0.606863
$262$	−22.4592	+	20.4584i	−1.38753	+	1.26392i
$263$	−3.46611			−0.213730			−0.106865	−	0.994274i	$-0.534081\pi$
$263$	−3.46611			−0.213730			−0.106865	+	0.994274i	$0.534081\pi$
$264$	2.32523	+	3.08650i	0.143108	+	0.189961i
$265$	10.9669			0.673692
$266$	16.8103	+	18.4543i	1.03071	+	1.13150i
$267$	11.5228			0.705183
$268$	−2.84008	+	30.3948i	−0.173485	+	1.85666i
$269$	−0.230066			−0.0140274			−0.00701369	−	0.999975i	$-0.502233\pi$
$269$	−0.230066			−0.0140274			−0.00701369	+	0.999975i	$0.502233\pi$
$270$	0.952347	+	1.04548i	0.0579580	+	0.0636261i
$271$			6.04603i			0.367270i	0.982994	+	0.183635i	$0.0587865\pi$
$271$			6.04603i			0.367270i	−0.982994	+	0.183635i	$0.941214\pi$
$272$	−0.0533070	+	0.282758i	−0.00323221	+	0.0171447i
$273$			11.7249i			0.709623i
$274$	9.23363	−	8.41106i	0.557824	−	0.508131i
$275$	1.36625			0.0823881
$276$	−9.37689	−	2.01841i	−0.564422	−	0.121494i
$277$	14.3524			0.862355			0.431177	−	0.902267i	$-0.358098\pi$
$277$	14.3524			0.862355			0.431177	+	0.902267i	$0.358098\pi$
$278$	1.54642	−	1.40866i	0.0927479	−	0.0844855i
$279$		−	8.07183i		−	0.483248i
$280$	−5.95118	−	7.89957i	−0.355651	−	0.472089i
$281$		−	9.58403i		−	0.571735i	−0.958269	−	0.285868i	$-0.907718\pi$
$281$		−	9.58403i		−	0.571735i	0.958269	−	0.285868i	$-0.0922818\pi$
$282$	12.0875	+	13.2696i	0.719802	+	0.790195i
$283$	−29.7360			−1.76762			−0.883812	−	0.467842i	$-0.845031\pi$
$283$	−29.7360			−1.76762			−0.883812	+	0.467842i	$0.845031\pi$
$284$	31.2694	+	2.92180i	1.85550	+	0.173377i
$285$	5.04791			0.299012
$286$	4.36282	+	4.78948i	0.257979	+	0.283208i
$287$	−4.82226			−0.284649
$288$	−2.96870	−	4.81527i	−0.174932	−	0.283743i
$289$	16.9948			0.999696
$290$	10.2501	−	9.33697i	0.601906	−	0.548286i
$291$	−4.72490			−0.276979
$292$	−0.976473	+	10.4503i	−0.0571437	+	0.611558i
$293$		−	19.4305i		−	1.13514i	−0.823324	−	0.567572i	$-0.807883\pi$
$293$		−	19.4305i		−	1.13514i	0.823324	−	0.567572i	$-0.192117\pi$
$294$	−5.46522	+	4.97835i	−0.318738	+	0.290344i
$295$	4.71711			0.274641
$296$	−5.66096	−	7.51434i	−0.329037	−	0.436762i
$297$		−	1.36625i		−	0.0792779i
$298$	−13.5028	+	12.2999i	−0.782196	+	0.712516i
$299$	−15.9673	−	1.90668i	−0.923410	−	0.110266i
$300$	−1.99133	−	0.186069i	−0.114969	−	0.0107427i
$301$	31.1599			1.79603
$302$	1.55590	−	1.41730i	0.0895321	−	0.0815562i
$303$		−	10.7894i		−	0.619833i
$304$	−19.8421	−	3.74074i	−1.13802	−	0.214546i
$305$	6.38461			0.365581
$306$	0.0752066	−	0.0685069i	0.00429928	−	0.00391628i
$307$			24.3915i			1.39209i	0.717996	+	0.696047i	$0.245059\pi$
$307$			24.3915i			1.39209i	−0.717996	+	0.696047i	$0.754941\pi$
$308$	−0.888938	+	9.51351i	−0.0506520	+	0.542083i
$309$			8.71856i			0.495981i
$310$	7.68719	+	8.43896i	0.436603	+	0.479301i
$311$			3.30836i			0.187600i	0.995591	+	0.0937999i	$0.0299014\pi$
$311$			3.30836i			0.187600i	−0.995591	+	0.0937999i	$0.970099\pi$
$312$	−5.70657	−	7.57488i	−0.323071	−	0.428843i
$313$			16.4380i			0.929130i	0.885539	+	0.464565i	$0.153789\pi$
$313$			16.4380i			0.929130i	−0.885539	+	0.464565i	$0.846211\pi$
$314$	0.824909	−	0.751424i	0.0465523	−	0.0424053i
$315$			3.49678i			0.197021i
$316$	0.782588	−	8.37534i	0.0440240	−	0.471149i
$317$	−21.1799			−1.18958			−0.594791	−	0.803880i	$-0.702765\pi$
$317$	−21.1799			−1.18958			−0.594791	+	0.803880i	$0.702765\pi$
$318$	10.4443	+	11.4657i	0.585688	+	0.642965i
$319$	−13.3950			−0.749974
$320$	7.68953	+	2.20705i	0.429858	+	0.123378i
$321$		−	15.4237i		−	0.860864i
$322$	−13.7793	−	19.3027i	−0.767891	−	1.07570i
$323$		−	0.363121i		−	0.0202046i
$324$	−0.186069	+	1.99133i	−0.0103371	+	0.110629i
$325$	−3.35306			−0.185994
$326$	−10.5258	+	9.58810i	−0.582969	+	0.531036i
$327$	2.16171			0.119543
$328$	3.11543	−	2.34702i	0.172021	−	0.129593i
$329$			44.3823i			2.44688i
$330$	1.30115	+	1.42839i	0.0716257	+	0.0786304i
$331$		−	7.56275i		−	0.415687i	−0.978162	−	0.207843i	$-0.933356\pi$
$331$		−	7.56275i		−	0.415687i	0.978162	−	0.207843i	$-0.0666444\pi$
$332$	−2.51036	+	26.8661i	−0.137774	+	1.47447i
$333$			3.32625i			0.182278i
$334$	12.8725	−	11.7258i	0.704351	−	0.641605i
$335$			15.2636i			0.833940i
$336$	2.59127	−	13.7450i	0.141366	−	0.749850i
$337$		−	16.3852i		−	0.892556i	−0.894894	−	0.446278i	$-0.852749\pi$
$337$		−	16.3852i		−	0.892556i	0.894894	−	0.446278i	$-0.147251\pi$
$338$	1.67329	+	1.83693i	0.0910150	+	0.0999159i
$339$	−8.97756			−0.487594
$340$	−0.0133848	+	0.143246i	−0.000725893	+	0.00776859i
$341$		−	11.0282i		−	0.597208i
$342$	4.80737	+	5.27750i	0.259953	+	0.285375i
$343$	6.19819			0.334671
$344$	−20.1309	+	15.1657i	−1.08538	+	0.817680i
$345$	−4.76200	−	0.568640i	−0.256377	−	0.0306145i
$346$	−2.89589	−	3.17909i	−0.155684	−	0.170909i
$347$			10.3602i			0.556166i	0.960557	+	0.278083i	$0.0896991\pi$
$347$			10.3602i			0.556166i	−0.960557	+	0.278083i	$0.910301\pi$
$348$	19.5233	+	1.82425i	1.04656	+	0.0977899i
$349$	0.414108			0.0221667			0.0110833	−	0.999939i	$-0.496472\pi$
$349$	0.414108			0.0221667			0.0110833	+	0.999939i	$0.496472\pi$
$350$	−3.33015	−	3.65582i	−0.178004	−	0.195412i
$351$			3.35306i			0.178973i
$352$	−4.05598	−	6.57887i	−0.216185	−	0.350655i
$353$	−33.5214			−1.78416			−0.892082	−	0.451874i	$-0.850756\pi$
$353$	−33.5214			−1.78416			−0.892082	+	0.451874i	$0.850756\pi$
$354$	4.49233	+	4.93166i	0.238765	+	0.262115i
$355$	15.7028			0.833419
$356$	−22.9456	−	2.14403i	−1.21611	−	0.113633i
$357$	0.251540			0.0133129
$358$	10.1058	−	9.20555i	0.534109	−	0.486528i
$359$	15.7877			0.833240			0.416620	−	0.909081i	$-0.363214\pi$
$359$	15.7877			0.833240			0.416620	+	0.909081i	$0.363214\pi$
$360$	−1.70190	−	2.25910i	−0.0896981	−	0.119065i
$361$	6.48141			0.341127
$362$	27.1875	−	24.7655i	1.42894	−	1.30165i
$363$			9.13336i			0.479377i
$364$	2.18163	−	23.3481i	0.114349	−	1.22377i
$365$			5.24792i			0.274689i
$366$	6.08036	+	6.67500i	0.317826	+	0.348908i
$367$	10.8732			0.567578			0.283789	−	0.958887i	$-0.408408\pi$
$367$	10.8732			0.567578			0.283789	+	0.958887i	$0.408408\pi$
$368$	18.2969	+	5.76405i	0.953791	+	0.300472i
$369$	−1.37906			−0.0717909
$370$	−3.16775	−	3.47754i	−0.164683	−	0.180789i
$371$			38.3488i			1.99097i
$372$	−1.50191	+	16.0737i	−0.0778706	+	0.833380i
$373$		−	11.5032i		−	0.595614i	−0.954626	−	0.297807i	$-0.903745\pi$
$373$		−	11.5032i		−	0.595614i	0.954626	−	0.297807i	$-0.0962551\pi$
$374$	0.102751	−	0.0935977i	0.00531313	−	0.00483982i
$375$	−1.00000			−0.0516398
$376$	−21.6011	−	28.6733i	−1.11399	−	1.47871i
$377$	32.8739			1.69309
$378$	−3.65582	+	3.33015i	−0.188035	+	0.171284i
$379$	22.3509			1.14809			0.574044	−	0.818825i	$-0.305374\pi$
$379$	22.3509			1.14809			0.574044	+	0.818825i	$0.305374\pi$
$380$	−10.0520	−	0.939258i	−0.515659	−	0.0481829i
$381$	−12.7171			−0.651517
$382$	1.38321	+	1.51849i	0.0707714	+	0.0776925i
$383$	−11.2864			−0.576709			−0.288354	−	0.957524i	$-0.593108\pi$
$383$	−11.2864			−0.576709			−0.288354	+	0.957524i	$0.593108\pi$
$384$	5.01567	+	10.1412i	0.255955	+	0.517514i
$385$			4.77748i			0.243483i
$386$	−12.0246	−	13.2006i	−0.612038	−	0.671892i
$387$	8.91103			0.452973
$388$	9.40882	+	0.879156i	0.477661	+	0.0446324i
$389$		−	19.9787i		−	1.01296i	−0.862252	−	0.506480i	$-0.830946\pi$
$389$		−	19.9787i		−	1.01296i	0.862252	−	0.506480i	$-0.169054\pi$
$390$	−3.19327	−	3.50556i	−0.161698	−	0.177511i
$391$	−0.0409050	+	0.342554i	−0.00206866	+	0.0173237i
$392$	11.8093	−	8.89662i	0.596462	−	0.449347i
$393$	−21.4821			−1.08363
$394$	22.8447	+	25.0788i	1.15090	+	1.26345i
$395$		−	4.20591i		−	0.211622i
$396$	−0.254216	+	2.72065i	−0.0127749	+	0.136718i
$397$	17.1842			0.862452			0.431226	−	0.902244i	$-0.358081\pi$
$397$	17.1842			0.862452			0.431226	+	0.902244i	$0.358081\pi$
$398$	−16.0277	−	17.5952i	−0.803397	−	0.881966i
$399$			17.6514i			0.883677i
$400$	3.93076	+	0.741046i	0.196538	+	0.0370523i
$401$		−	21.5671i		−	1.07701i	−0.842622	−	0.538505i	$-0.818989\pi$
$401$		−	21.5671i		−	1.07701i	0.842622	−	0.538505i	$-0.181011\pi$
$402$	−15.9578	+	14.5363i	−0.795905	+	0.725003i
$403$			27.0653i			1.34822i
$404$	−2.00756	+	21.4851i	−0.0998799	+	1.06893i
$405$			1.00000i			0.0496904i
$406$	32.6493	+	35.8423i	1.62036	+	1.77882i
$407$			4.54450i			0.225262i
$408$	−0.162508	+	0.122426i	−0.00804534	+	0.00606099i
$409$	20.5077			1.01404			0.507021	−	0.861934i	$-0.330747\pi$
$409$	20.5077			1.01404			0.507021	+	0.861934i	$0.330747\pi$
$410$	1.44178	−	1.31334i	0.0712045	−	0.0648613i
$411$	8.83193			0.435647
$412$	1.62225	−	17.3615i	0.0799225	−	0.855339i
$413$			16.4947i			0.811651i
$414$	−3.94058	−	5.52013i	−0.193669	−	0.271300i
$415$			13.4916i			0.662276i
$416$	9.95420	+	16.1459i	0.488045	+	0.791617i
$417$	1.47914			0.0724338
$418$	6.56807	+	7.21040i	0.321255	+	0.352672i
$419$	6.48385			0.316757			0.158378	−	0.987378i	$-0.449373\pi$
$419$	6.48385			0.316757			0.158378	+	0.987378i	$0.449373\pi$
$420$	0.650640	−	6.96322i	0.0317480	−	0.339771i
$421$		−	16.5039i		−	0.804351i	−0.915563	−	0.402175i	$-0.868254\pi$
$421$		−	16.5039i		−	0.804351i	0.915563	−	0.402175i	$-0.131746\pi$
$422$	21.6195	−	19.6936i	1.05242	−	0.958668i
$423$			12.6923i			0.617123i
$424$	−18.6646	−	24.7753i	−0.906434	−	1.20320i
$425$			0.0719348i			0.00348935i
$426$	14.9545	+	16.4170i	0.724550	+	0.795408i
$427$			22.3256i			1.08041i
$428$	−2.86986	+	30.7135i	−0.138720	+	1.48459i
$429$			4.58112i			0.221178i
$430$	−9.31632	+	8.48639i	−0.449273	+	0.409250i
$431$	−31.4733			−1.51602			−0.758009	−	0.652244i	$-0.773828\pi$
$431$	−31.4733			−1.51602			−0.758009	+	0.652244i	$0.773828\pi$
$432$	0.741046	−	3.93076i	0.0356536	−	0.189119i
$433$		−	18.7432i		−	0.900741i	−0.892842	−	0.450370i	$-0.851292\pi$
$433$		−	18.7432i		−	0.900741i	0.892842	−	0.450370i	$-0.148708\pi$
$434$	−29.5092	+	26.8804i	−1.41649	+	1.29030i
$435$	9.80417			0.470074
$436$	−4.30467	−	0.402227i	−0.206156	−	0.0192632i
$437$	−24.0382	−	2.87044i	−1.14990	−	0.137312i
$438$	−5.48661	+	4.99784i	−0.262160	+	0.238806i
$439$			9.37553i			0.447470i	0.974650	+	0.223735i	$0.0718250\pi$
$439$			9.37553i			0.447470i	−0.974650	+	0.223735i	$0.928175\pi$
$440$	−2.32523	−	3.08650i	−0.110851	−	0.147143i
$441$	−5.22746			−0.248926
$442$	−0.252172	+	0.229708i	−0.0119946	+	0.0109261i
$443$			21.6166i			1.02704i	0.858079	+	0.513518i	$0.171658\pi$
$443$			21.6166i			1.02704i	−0.858079	+	0.513518i	$0.828342\pi$
$444$	0.618911	−	6.62366i	0.0293722	−	0.314345i
$445$	−11.5228			−0.546232
$446$	10.4823	−	9.54849i	0.496351	−	0.452134i
$447$	−12.9154			−0.610876
$448$	−7.71758	+	26.8886i	−0.364621	+	1.27037i
$449$	−11.7632			−0.555141			−0.277571	−	0.960705i	$-0.589529\pi$
$449$	−11.7632			−0.555141			−0.277571	+	0.960705i	$0.589529\pi$
$450$	−0.952347	−	1.04548i	−0.0448941	−	0.0492845i
$451$	−1.88414			−0.0887207
$452$	17.8772	+	1.67044i	0.840875	+	0.0785710i
$453$	1.48821			0.0699224
$454$	−5.49140	−	6.02843i	−0.257724	−	0.282928i
$455$		−	11.7249i		−	0.549671i
$456$	−8.59105	−	11.4037i	−0.402313	−	0.534029i
$457$		−	35.4431i		−	1.65796i	−0.559279	−	0.828980i	$-0.688922\pi$
$457$		−	35.4431i		−	1.65796i	0.559279	−	0.828980i	$-0.311078\pi$
$458$	2.57829	−	2.34861i	0.120476	−	0.109743i
$459$	0.0719348			0.00335763
$460$	9.37689	+	2.01841i	0.437200	+	0.0941087i
$461$	−14.2189			−0.662240			−0.331120	−	0.943589i	$-0.607427\pi$
$461$	−14.2189			−0.662240			−0.331120	+	0.943589i	$0.607427\pi$
$462$	−4.99477	+	4.54982i	−0.232378	+	0.211677i
$463$		−	1.35225i		−	0.0628444i	−0.999506	−	0.0314222i	$-0.989996\pi$
$463$		−	1.35225i		−	0.0628444i	0.999506	−	0.0314222i	$-0.0100036\pi$
$464$	−38.5378	−	7.26534i	−1.78907	−	0.337285i
$465$			8.07183i			0.374322i
$466$	−16.3314	−	17.9286i	−0.756539	−	0.830525i
$467$	19.9740			0.924289			0.462144	−	0.886805i	$-0.347080\pi$
$467$	19.9740			0.924289			0.462144	+	0.886805i	$0.347080\pi$
$468$	0.623898	−	6.67703i	0.0288397	−	0.308646i
$469$	−53.3735			−2.46456
$470$	−12.0875	−	13.2696i	−0.557556	−	0.612082i
$471$	0.789022			0.0363562
$472$	−8.02807	−	10.6564i	−0.369522	−	0.490502i
$473$	12.1747			0.559793
$474$	4.39721	−	4.00549i	0.201970	−	0.183978i
$475$	−5.04791			−0.231614
$476$	−0.500898	−	0.0468037i	−0.0229586	−	0.00214524i
$477$			10.9669i			0.502140i
$478$	−8.23971	+	7.50569i	−0.376876	+	0.343302i
$479$	27.9827			1.27856			0.639282	−	0.768972i	$-0.279232\pi$
$479$	27.9827			1.27856			0.639282	+	0.768972i	$0.279232\pi$
$480$	2.96870	+	4.81527i	0.135502	+	0.219786i
$481$		−	11.1531i		−	0.508538i
$482$	13.9178	−	12.6780i	0.633939	−	0.577466i
$483$	1.98841	−	16.6517i	0.0904757	−	0.757677i
$484$	1.69943	−	18.1875i	0.0772468	−	0.826704i
$485$	4.72490			0.214547
$486$	−1.04548	+	0.952347i	−0.0474241	+	0.0431994i
$487$		−	30.1729i		−	1.36727i	−0.729826	−	0.683633i	$-0.760399\pi$
$487$		−	30.1729i		−	1.36727i	0.729826	−	0.683633i	$-0.239601\pi$
$488$	−10.8660	−	14.4235i	−0.491880	−	0.652919i
$489$	−10.0679			−0.455284
$490$	5.46522	−	4.97835i	0.246893	−	0.224899i
$491$		−	7.08265i		−	0.319635i	−0.987147	−	0.159818i	$-0.948909\pi$
$491$		−	7.08265i		−	0.319635i	0.987147	−	0.159818i	$-0.0510906\pi$
$492$	2.74615	+	0.256599i	0.123806	+	0.0115684i
$493$		−	0.705261i		−	0.0317633i
$494$	−16.1194	−	17.6958i	−0.725245	−	0.796170i
$495$			1.36625i			0.0614084i
$496$	5.98160	−	31.7284i	0.268582	−	1.42465i
$497$			54.9093i			2.46302i
$498$	−14.1052	+	12.8487i	−0.632070	+	0.575763i
$499$		−	17.2498i		−	0.772207i	−0.922455	−	0.386104i	$-0.873821\pi$
$499$		−	17.2498i		−	0.772207i	0.922455	−	0.386104i	$-0.126179\pi$
$500$	1.99133	+	0.186069i	0.0890548	+	0.00832124i
$501$	12.3125			0.550081
$502$	−16.1099	−	17.6854i	−0.719022	−	0.789339i
$503$	−34.6103			−1.54320			−0.771598	−	0.636111i	$-0.780542\pi$
$503$	−34.6103			−1.54320			−0.771598	+	0.636111i	$0.780542\pi$
$504$	7.89957	−	5.95118i	0.351875	−	0.265086i
$505$			10.7894i			0.480120i
$506$	−5.38382	−	7.54189i	−0.239340	−	0.335278i
$507$			1.75702i			0.0780318i
$508$	25.3239	+	2.36625i	1.12357	+	0.104985i
$509$	−15.0316			−0.666266			−0.333133	−	0.942880i	$-0.608106\pi$
$509$	−15.0316			−0.666266			−0.333133	+	0.942880i	$0.608106\pi$
$510$	−0.0752066	+	0.0685069i	−0.00333020	+	0.00303354i
$511$	−18.3508			−0.811792
$512$	−8.10088	−	21.1276i	−0.358012	−	0.933717i
$513$			5.04791i			0.222871i
$514$	−18.7324	−	20.5644i	−0.826251	−	0.907055i
$515$		−	8.71856i		−	0.384186i
$516$	−17.7448	−	1.65806i	−0.781169	−	0.0729921i
$517$			17.3409i			0.762653i
$518$	12.1602	−	11.0769i	0.534288	−	0.486692i
$519$		−	3.04079i		−	0.133476i
$520$	5.70657	+	7.57488i	0.250250	+	0.332181i
$521$		−	2.09374i		−	0.0917284i	−0.998948	−	0.0458642i	$-0.985396\pi$
$521$		−	2.09374i		−	0.0917284i	0.998948	−	0.0458642i	$-0.0146041\pi$
$522$	9.33697	+	10.2501i	0.408668	+	0.448634i
$523$	4.78053			0.209038			0.104519	−	0.994523i	$-0.466670\pi$
$523$	4.78053			0.209038			0.104519	+	0.994523i	$0.466670\pi$
$524$	42.7778	+	3.99714i	1.86876	+	0.174616i
$525$		−	3.49678i		−	0.152612i
$526$	3.30094	+	3.62376i	0.143928	+	0.158003i
$527$	0.580646			0.0252933
$528$	1.01246	−	5.37040i	0.0440615	−	0.233717i
$529$	22.3533	+	5.41573i	0.971882	+	0.235466i
$530$	−10.4443	−	11.4657i	−0.453672	−	0.498039i
$531$			4.71711i			0.204705i
$532$	3.28438	−	35.1497i	0.142396	−	1.52393i
$533$	4.62406			0.200290
$534$	−10.9737	−	12.0469i	−0.474878	−	0.521319i
$535$			15.4237i			0.666823i
$536$	34.4820	−	25.9772i	1.48940	−	1.12204i
$537$	9.66616			0.417126
$538$	0.219103	+	0.240530i	0.00944620	+	0.0103700i
$539$	−7.14202			−0.307629
$540$	0.186069	−	1.99133i	0.00800712	−	0.0856930i
$541$	−32.7776			−1.40922			−0.704610	−	0.709594i	$-0.748878\pi$
$541$	−32.7776			−1.40922			−0.704610	+	0.709594i	$0.748878\pi$
$542$	6.32102	−	5.75792i	0.271511	−	0.247324i
$543$	26.0047			1.11597
$544$	0.346386	−	0.213553i	0.0148512	−	0.00915599i
$545$	−2.16171			−0.0925976
$546$	12.2582	−	11.1662i	0.524601	−	0.477868i
$547$			15.0838i			0.644936i	0.946580	+	0.322468i	$0.104513\pi$
$547$			15.0838i			0.644936i	−0.946580	+	0.322468i	$0.895487\pi$
$548$	−17.5872	−	1.64334i	−0.751290	−	0.0702002i
$549$			6.38461i			0.272488i
$550$	−1.30115	−	1.42839i	−0.0554811	−	0.0609069i
$551$	49.4906			2.10837
$552$	6.81985	+	11.7256i	0.290272	+	0.499075i
$553$	14.7071			0.625411
$554$	−13.6685	−	15.0052i	−0.580720	−	0.637511i
$555$		−	3.32625i		−	0.141192i
$556$	−2.94545	−	0.275222i	−0.124915	−	0.0116720i
$557$		−	18.7166i		−	0.793048i	−0.918024	−	0.396524i	$-0.870216\pi$
$557$		−	18.7166i		−	0.793048i	0.918024	−	0.396524i	$-0.129784\pi$
$558$	−8.43896	+	7.68719i	−0.357250	+	0.325425i
$559$	−29.8792			−1.26375
$560$	−2.59127	+	13.7450i	−0.109501	+	0.580832i
$561$	0.0982810			0.00414943
$562$	−10.0199	+	9.12733i	−0.422666	+	0.385013i
$563$	1.60093			0.0674712			0.0337356	−	0.999431i	$-0.489260\pi$
$563$	1.60093			0.0674712			0.0337356	+	0.999431i	$0.489260\pi$
$564$	2.36165	−	25.2746i	0.0994433	−	1.06425i
$565$	8.97756			0.377689
$566$	28.3190	+	31.0885i	1.19034	+	1.30675i
$567$	−3.49678			−0.146851
$568$	−26.7247	−	35.4742i	−1.12134	−	1.48847i
$569$			25.5371i			1.07057i	0.844672	+	0.535285i	$0.179796\pi$
$569$			25.5371i			1.07057i	−0.844672	+	0.535285i	$0.820204\pi$
$570$	−4.80737	−	5.27750i	−0.201358	−	0.221050i
$571$	−14.4267			−0.603738			−0.301869	−	0.953349i	$-0.597610\pi$
$571$	−14.4267			−0.603738			−0.301869	+	0.953349i	$0.597610\pi$
$572$	0.852402	−	9.12250i	0.0356407	−	0.381431i
$573$			1.45243i			0.0606759i
$574$	4.59247	+	5.04159i	0.191686	+	0.210432i
$575$	4.76200	+	0.568640i	0.198589	+	0.0237139i
$576$	−2.20705	+	7.68953i	−0.0919606	+	0.320397i
$577$	2.17614			0.0905938			0.0452969	−	0.998974i	$-0.485577\pi$
$577$	2.17614			0.0905938			0.0452969	+	0.998974i	$0.485577\pi$
$578$	−16.1850	−	17.7678i	−0.673206	−	0.739043i
$579$		−	12.6263i		−	0.524731i
$580$	−19.5233	−	1.82425i	−0.810660	−	0.0757477i
$581$	−47.1771			−1.95723
$582$	4.49975	+	4.93981i	0.186521	+	0.204762i
$583$			14.9836i			0.620555i
$584$	11.8556	−	8.93145i	0.490587	−	0.369586i
$585$		−	3.35306i		−	0.138632i
$586$	−20.3143	+	18.5046i	−0.839176	+	0.764419i
$587$			30.9114i			1.27585i	0.770099	+	0.637925i	$0.220207\pi$
$587$			30.9114i			1.27585i	−0.770099	+	0.637925i	$0.779793\pi$
$588$	10.4096	+	0.972665i	0.429283	+	0.0401120i
$589$			40.7459i			1.67891i
$590$	−4.49233	−	4.93166i	−0.184946	−	0.203033i
$591$			23.9878i			0.986727i
$592$	−2.46491	+	13.0747i	−0.101307	+	0.537367i
$593$	−18.1730			−0.746276			−0.373138	−	0.927776i	$-0.621718\pi$
$593$	−18.1730			−0.746276			−0.373138	+	0.927776i	$0.621718\pi$
$594$	−1.42839	+	1.30115i	−0.0586076	+	0.0533867i
$595$	−0.251540			−0.0103121
$596$	25.7187	+	2.40315i	1.05348	+	0.0984367i
$597$		−	16.8297i		−	0.688794i
$598$	13.2130	+	18.5093i	0.540319	+	0.756902i
$599$		−	13.0346i		−	0.532581i	−0.963893	−	0.266291i	$-0.914202\pi$
$599$		−	13.0346i		−	0.532581i	0.963893	−	0.266291i	$-0.0857981\pi$
$600$	1.70190	+	2.25910i	0.0694799	+	0.0922273i
$601$	−28.6319			−1.16792			−0.583959	−	0.811783i	$-0.698497\pi$
$601$	−28.6319			−1.16792			−0.583959	+	0.811783i	$0.698497\pi$
$602$	−29.6750	−	32.5771i	−1.20946	−	1.32774i
$603$	−15.2636			−0.621582
$604$	−2.96352	−	0.276910i	−0.120584	−	0.0112673i
$605$		−	9.13336i		−	0.371324i
$606$	−11.2801	+	10.2752i	−0.458222	+	0.417402i
$607$		−	8.85705i		−	0.359496i	−0.983713	−	0.179748i	$-0.942472\pi$
$607$		−	8.85705i		−	0.359496i	0.983713	−	0.179748i	$-0.0575283\pi$
$608$	14.9857	+	24.3071i	0.607751	+	0.985782i
$609$			34.2830i			1.38922i
$610$	−6.08036	−	6.67500i	−0.246187	−	0.270263i
$611$		−	42.5581i		−	1.72172i
$612$	−0.143246	−	0.0133848i	−0.00579036	−	0.000541049i
$613$			34.3412i			1.38703i	0.720443	+	0.693514i	$0.243939\pi$
$613$			34.3412i			1.38703i	−0.720443	+	0.693514i	$0.756061\pi$
$614$	25.5008	−	23.2291i	1.02913	−	0.937452i
$615$	1.37906			0.0556090
$616$	10.7928	−	8.13080i	0.434854	−	0.327599i
$617$		−	7.75901i		−	0.312366i	−0.987728	−	0.156183i	$-0.950081\pi$
$617$		−	7.75901i		−	0.312366i	0.987728	−	0.156183i	$-0.0499190\pi$
$618$	9.11510	−	8.30310i	0.366663	−	0.334000i
$619$	22.8208			0.917244			0.458622	−	0.888631i	$-0.348343\pi$
$619$	22.8208			0.917244			0.458622	+	0.888631i	$0.348343\pi$
$620$	1.50191	−	16.0737i	0.0603183	−	0.645533i
$621$	0.568640	−	4.76200i	0.0228187	−	0.191092i
$622$	3.45883	−	3.15071i	0.138686	−	0.126332i
$623$		−	40.2926i		−	1.61429i
$624$	−2.48477	+	13.1800i	−0.0994704	+	0.527624i
$625$	1.00000			0.0400000
$626$	17.1856	−	15.6547i	0.686876	−	0.625687i
$627$			6.89672i			0.275428i
$628$	−1.57120	−	0.146812i	−0.0626977	−	0.00585845i
$629$	−0.239273			−0.00954046
$630$	3.65582	−	3.33015i	0.145651	−	0.132676i
$631$	−42.6051			−1.69608			−0.848041	−	0.529931i	$-0.822218\pi$
$631$	−42.6051			−1.69608			−0.848041	+	0.529931i	$0.822218\pi$
$632$	−9.50157	+	7.15805i	−0.377952	+	0.284732i
$633$	20.6790			0.821916
$634$	20.1706	+	22.1432i	0.801078	+	0.879420i
$635$	12.7171			0.504663
$636$	2.04060	−	21.8387i	0.0809149	−	0.865960i
$637$	17.5280			0.694483
$638$	12.7567	+	14.0042i	0.505041	+	0.554431i
$639$			15.7028i			0.621194i
$640$	−5.01567	−	10.1412i	−0.198262	−	0.400864i
$641$			34.2171i			1.35149i	0.737134	+	0.675746i	$0.236179\pi$
$641$			34.2171i			1.35149i	−0.737134	+	0.675746i	$0.763821\pi$
$642$	−16.1252	+	14.6887i	−0.636409	+	0.579716i
$643$	−10.3253			−0.407189			−0.203595	−	0.979055i	$-0.565262\pi$
$643$	−10.3253			−0.407189			−0.203595	+	0.979055i	$0.565262\pi$
$644$	−7.05792	+	32.7889i	−0.278121	+	1.29206i
$645$	−8.91103			−0.350871
$646$	−0.379636	+	0.345817i	−0.0149366	+	0.0136060i
$647$		−	4.42046i		−	0.173786i	−0.996218	−	0.0868930i	$-0.972306\pi$
$647$		−	4.42046i		−	0.173786i	0.996218	−	0.0868930i	$-0.0276938\pi$
$648$	2.25910	−	1.70190i	0.0887458	−	0.0668570i
$649$			6.44476i			0.252979i
$650$	3.19327	+	3.50556i	0.125251	+	0.137499i
$651$	−28.2254			−1.10624
$652$	20.0484	+	1.87331i	0.785155	+	0.0733646i
$653$	−33.8914			−1.32627			−0.663137	−	0.748498i	$-0.730775\pi$
$653$	−33.8914			−1.32627			−0.663137	+	0.748498i	$0.730775\pi$
$654$	−2.05870	−	2.26003i	−0.0805016	−	0.0883743i
$655$	21.4821			0.839375
$656$	−5.42074	−	1.02195i	−0.211644	−	0.0399003i
$657$	−5.24792			−0.204741
$658$	46.4009	−	42.2674i	1.80890	−	1.64775i
$659$	35.4900			1.38250			0.691248	−	0.722618i	$-0.257061\pi$
$659$	35.4900			1.38250			0.691248	+	0.722618i	$0.257061\pi$
$660$	0.254216	−	2.72065i	0.00989536	−	0.105901i
$661$		−	6.67221i		−	0.259519i	−0.991546	−	0.129759i	$-0.958579\pi$
$661$		−	6.67221i		−	0.259519i	0.991546	−	0.129759i	$-0.0414205\pi$
$662$	−7.90673	+	7.20237i	−0.307304	+	0.279928i
$663$	−0.241201			−0.00936749
$664$	30.4788	−	22.9614i	1.18281	−	0.891074i
$665$		−	17.6514i		−	0.684493i
$666$	3.47754	−	3.16775i	0.134752	−	0.122748i
$667$	−46.6874	−	5.57504i	−1.80775	−	0.215866i
$668$	−24.5182	−	2.29097i	−0.948637	−	0.0886402i
$669$	10.0263			0.387638
$670$	15.9578	−	14.5363i	0.616505	−	0.561585i
$671$			8.72298i			0.336747i
$672$	−16.8379	+	10.3809i	−0.649538	+	0.400451i
$673$	19.0840			0.735634			0.367817	−	0.929898i	$-0.380105\pi$
$673$	19.0840			0.735634			0.367817	+	0.929898i	$0.380105\pi$
$674$	−17.1304	+	15.6044i	−0.659838	+	0.601058i
$675$		−	1.00000i		−	0.0384900i
$676$	0.326926	−	3.49879i	0.0125741	−	0.134569i
$677$			31.0941i			1.19505i	0.801852	+	0.597523i	$0.203848\pi$
$677$			31.0941i			1.19505i	−0.801852	+	0.597523i	$0.796152\pi$
$678$	8.54976	+	9.38588i	0.328351	+	0.360463i
$679$			16.5219i			0.634054i
$680$	0.162508	−	0.122426i	0.00623189	−	0.00469482i
$681$		−	5.76617i		−	0.220960i
$682$	−11.5297	+	10.5026i	−0.441497	+	0.402167i
$683$			0.183753i			0.00703110i	0.999994	+	0.00351555i	$0.00111904\pi$
$683$			0.183753i			0.00703110i	−0.999994	+	0.00351555i	$0.998881\pi$
$684$	0.939258	−	10.0520i	0.0359134	−	0.384349i
$685$	−8.83193			−0.337451
$686$	−5.90283	−	6.48010i	−0.225371	−	0.247411i
$687$	2.46613			0.0940886
$688$	35.0271	+	6.60348i	1.33539	+	0.251755i
$689$		−	36.7727i		−	1.40093i
$690$	3.94058	+	5.52013i	0.150015	+	0.210148i
$691$		−	19.4942i		−	0.741593i	−0.928714	−	0.370796i	$-0.879085\pi$
$691$		−	19.4942i		−	0.741593i	0.928714	−	0.370796i	$-0.120915\pi$
$692$	−0.565795	+	6.05520i	−0.0215083	+	0.230184i
$693$	−4.77748			−0.181481
$694$	10.8314	−	9.86654i	0.411156	−	0.374529i
$695$	−1.47914			−0.0561070
$696$	−16.6857	−	22.1486i	−0.632471	−	0.839540i
$697$		−	0.0992022i		−	0.00375755i
$698$	−0.394374	−	0.432942i	−0.0149273	−	0.0163871i
$699$		−	17.1486i		−	0.648620i
$700$	−0.650640	+	6.96322i	−0.0245919	+	0.263185i
$701$			8.26187i			0.312047i	0.987753	+	0.156023i	$0.0498675\pi$
$701$			8.26187i			0.312047i	−0.987753	+	0.156023i	$0.950132\pi$
$702$	3.50556	−	3.19327i	0.132309	−	0.120522i
$703$		−	16.7906i		−	0.633271i
$704$	−3.01539	+	10.5058i	−0.113647	+	0.395954i
$705$		−	12.6923i		−	0.478021i
$706$	31.9240	+	35.0460i	1.20148	+	1.31898i
$707$	−37.7280			−1.41891
$708$	0.877706	−	9.39331i	0.0329862	−	0.353022i
$709$		−	18.7338i		−	0.703564i	−0.936082	−	0.351782i	$-0.885576\pi$
$709$		−	18.7338i		−	0.703564i	0.936082	−	0.351782i	$-0.114424\pi$
$710$	−14.9545	−	16.4170i	−0.561234	−	0.616120i
$711$	4.20591			0.157734
$712$	19.6106	+	26.0311i	0.734940	+	0.975556i
$713$	4.58997	−	38.4381i	0.171896	−	1.43952i
$714$	−0.239554	−	0.262981i	−0.00896507	−	0.00984181i
$715$		−	4.58112i		−	0.171324i
$716$	−19.2485	−	1.79857i	−0.719350	−	0.0672157i
$717$	−7.88125			−0.294331
$718$	−15.0353	−	16.5057i	−0.561114	−	0.615988i
$719$		−	15.0358i		−	0.560741i	−0.959892	−	0.280370i	$-0.909543\pi$
$719$		−	15.0358i		−	0.560741i	0.959892	−	0.280370i	$-0.0904573\pi$
$720$	−0.741046	+	3.93076i	−0.0276172	+	0.146491i
$721$	30.4869			1.13539
$722$	−6.17256	−	6.77621i	−0.229719	−	0.252184i
$723$	13.3123			0.495091
$724$	−51.7838	−	4.83866i	−1.92453	−	0.179827i
$725$	−9.80417			−0.364118
$726$	9.54877	−	8.69813i	0.354388	−	0.322818i
$727$	35.8931			1.33120			0.665601	−	0.746308i	$-0.268175\pi$
$727$	35.8931			1.33120			0.665601	+	0.746308i	$0.268175\pi$
$728$	−26.4877	+	19.9546i	−0.981699	+	0.739568i
$729$	−1.00000			−0.0370370
$730$	5.48661	−	4.99784i	0.203068	−	0.184978i
$731$			0.641013i			0.0237087i
$732$	1.18797	−	12.7138i	0.0439088	−	0.469917i
$733$		−	31.3376i		−	1.15748i	−0.815512	−	0.578740i	$-0.803545\pi$
$733$		−	31.3376i		−	1.15748i	0.815512	−	0.578740i	$-0.196455\pi$
$734$	−10.3551	−	11.3678i	−0.382213	−	0.419592i
$735$	5.22746			0.192818
$736$	−11.3988	−	24.6184i	−0.420164	−	0.907448i
$737$	−20.8539			−0.768165
$738$	1.31334	+	1.44178i	0.0483448	+	0.0530727i
$739$			18.0131i			0.662622i	0.943522	+	0.331311i	$0.107491\pi$
$739$			18.0131i			0.662622i	−0.943522	+	0.331311i	$0.892509\pi$
$740$	−0.618911	+	6.62366i	−0.0227516	+	0.243490i
$741$		−	16.9259i		−	0.621790i
$742$	40.0931	−	36.5214i	1.47186	−	1.34074i
$743$	−5.74188			−0.210649			−0.105325	−	0.994438i	$-0.533588\pi$
$743$	−5.74188			−0.210649			−0.105325	+	0.994438i	$0.533588\pi$
$744$	18.2351	−	13.7375i	0.668530	−	0.503640i
$745$	12.9154			0.473183
$746$	−12.0264	+	10.9551i	−0.440318	+	0.401093i
$747$	−13.4916			−0.493631
$748$	−0.195710	−	0.0182870i	−0.00715585	−	0.000668639i
$749$	−53.9331			−1.97067
$750$	0.952347	+	1.04548i	0.0347748	+	0.0381756i
$751$	47.7051			1.74078			0.870391	−	0.492361i	$-0.163866\pi$
$751$	47.7051			1.74078			0.870391	+	0.492361i	$0.163866\pi$
$752$	−9.40562	+	49.8905i	−0.342988	+	1.81932i
$753$		−	16.9160i		−	0.616454i
$754$	−31.3074	−	34.3691i	−1.14015	−	1.25165i
$755$	−1.48821			−0.0541616
$756$	6.96322	+	0.650640i	0.253250	+	0.0236636i
$757$		−	33.3125i		−	1.21076i	−0.795935	−	0.605382i	$-0.793020\pi$
$757$		−	33.3125i		−	1.21076i	0.795935	−	0.605382i	$-0.206980\pi$
$758$	−21.2858	−	23.3675i	−0.773135	−	0.848744i
$759$	0.776905	−	6.50609i	0.0281999	−	0.236156i
$760$	8.59105	+	11.4037i	0.311630	+	0.413657i
$761$	−13.8151			−0.500797			−0.250399	−	0.968143i	$-0.580562\pi$
$761$	−13.8151			−0.500797			−0.250399	+	0.968143i	$0.580562\pi$
$762$	12.1111	+	13.2955i	0.438739	+	0.481646i
$763$		−	7.55903i		−	0.273655i
$764$	0.270251	−	2.89225i	0.00977733	−	0.104638i
$765$	−0.0719348			−0.00260081
$766$	10.7486	+	11.7997i	0.388362	+	0.426342i
$767$		−	15.8167i		−	0.571109i
$768$	5.82575	−	14.9017i	0.210218	−	0.537719i
$769$		−	32.1778i		−	1.16036i	−0.814487	−	0.580181i	$-0.802982\pi$
$769$		−	32.1778i		−	1.16036i	0.814487	−	0.580181i	$-0.197018\pi$
$770$	4.99477	−	4.54982i	0.179999	−	0.163964i
$771$		−	19.6697i		−	0.708388i
$772$	−2.34936	+	25.1431i	−0.0845553	+	0.904919i
$773$			9.57568i			0.344413i	0.985061	+	0.172207i	$0.0550897\pi$
$773$			9.57568i			0.344413i	−0.985061	+	0.172207i	$0.944910\pi$
$774$	−8.48639	−	9.31632i	−0.305037	−	0.334868i
$775$		−	8.07183i		−	0.289949i
$776$	−8.04133	−	10.6740i	−0.288667	−	0.383175i
$777$	11.6312			0.417266
$778$	−20.8874	+	19.0267i	−0.748849	+	0.682139i
$779$	6.96136			0.249417
$780$	−0.623898	+	6.67703i	−0.0223391	+	0.239076i
$781$			21.4540i			0.767684i
$782$	0.397090	−	0.283465i	0.0141999	−	0.0101367i
$783$			9.80417i			0.350372i
$784$	−20.5479	−	3.87379i	−0.733852	−	0.138350i
$785$	−0.789022			−0.0281614
$786$	20.4584	+	22.4592i	0.729727	+	0.801092i
$787$	−48.0736			−1.71364			−0.856819	−	0.515617i	$-0.827563\pi$
$787$	−48.0736			−1.71364			−0.856819	+	0.515617i	$0.827563\pi$
$788$	4.46338	−	47.7675i	0.159001	−	1.70165i
$789$			3.46611i			0.123397i
$790$	−4.39721	+	4.00549i	−0.156446	+	0.142509i
$791$			31.3925i			1.11619i
$792$	3.08650	−	2.32523i	0.109674	−	0.0826233i
$793$		−	21.4079i		−	0.760218i
$794$	−16.3654	−	17.9658i	−0.580785	−	0.637583i
$795$		−	10.9669i		−	0.388956i
$796$	−3.13148	+	33.5134i	−0.110992	+	1.18785i
$797$			47.3644i			1.67773i	0.544338	+	0.838866i	$0.316781\pi$
$797$			47.3644i			1.67773i	−0.544338	+	0.838866i	$0.683219\pi$
$798$	18.4543	−	16.8103i	0.653274	−	0.595078i
$799$	−0.913021			−0.0323004
$800$	−2.96870	−	4.81527i	−0.104959	−	0.170246i
$801$		−	11.5228i		−	0.407137i
$802$	−22.5480	+	20.5394i	−0.796199	+	0.725271i
$803$	−7.16998			−0.253023
$804$	30.3948	+	2.84008i	1.07194	+	0.100162i
$805$	−1.98841	+	16.6517i	−0.0700822	+	0.586894i
$806$	28.2963	−	25.7756i	0.996695	−	0.907906i
$807$			0.230066i			0.00809871i
$808$	24.3742	−	18.3624i	0.857483	−	0.645989i
$809$	32.6507			1.14794			0.573970	−	0.818877i	$-0.305403\pi$
$809$	32.6507			1.14794			0.573970	+	0.818877i	$0.305403\pi$
$810$	1.04548	−	0.952347i	0.0367345	−	0.0334621i
$811$		−	32.8029i		−	1.15187i	−0.817497	−	0.575934i	$-0.804639\pi$
$811$		−	32.8029i		−	1.15187i	0.817497	−	0.575934i	$-0.195361\pi$
$812$	6.37899	−	68.2686i	0.223859	−	2.39576i
$813$	6.04603			0.212044
$814$	4.75120	−	4.32794i	0.166529	−	0.151694i
$815$	10.0679			0.352662
$816$	0.282758	+	0.0533070i	0.00989852	+	0.00186612i
$817$	−44.9821			−1.57372
$818$	−19.5305	−	21.4405i	−0.682867	−	0.749648i
$819$	11.7249			0.409701
$820$	−2.74615	−	0.256599i	−0.0958998	−	0.00896084i
$821$	−12.6775			−0.442446			−0.221223	−	0.975223i	$-0.571005\pi$
$821$	−12.6775			−0.442446			−0.221223	+	0.975223i	$0.571005\pi$
$822$	−8.41106	−	9.23363i	−0.293369	−	0.322060i
$823$			34.7717i			1.21207i	0.795439	+	0.606033i	$0.207240\pi$
$823$			34.7717i			1.21207i	−0.795439	+	0.606033i	$0.792760\pi$
$824$	−19.6961	+	14.8381i	−0.686146	+	0.516911i
$825$		−	1.36625i		−	0.0475668i
$826$	17.2449	−	15.7087i	0.600027	−	0.546575i
$827$	−37.9777			−1.32062			−0.660308	−	0.750995i	$-0.729574\pi$
$827$	−37.9777			−1.32062			−0.660308	+	0.750995i	$0.729574\pi$
$828$	−2.01841	+	9.37689i	−0.0701445	+	0.325869i
$829$	17.5863			0.610796			0.305398	−	0.952225i	$-0.401210\pi$
$829$	17.5863			0.610796			0.305398	+	0.952225i	$0.401210\pi$
$830$	14.1052	−	12.8487i	0.489599	−	0.445984i
$831$		−	14.3524i		−	0.497881i
$832$	7.40038	−	25.7834i	0.256562	−	0.893880i
$833$		−	0.376036i		−	0.0130289i
$834$	−1.40866	−	1.54642i	−0.0487778	−	0.0535480i
$835$	−12.3125			−0.426091
$836$	1.28326	−	13.7336i	0.0443825	−	0.474987i
$837$	−8.07183			−0.279003
$838$	−6.17488	−	6.77875i	−0.213308	−	0.234168i
$839$	22.3742			0.772444			0.386222	−	0.922406i	$-0.373780\pi$
$839$	22.3742			0.772444			0.386222	+	0.922406i	$0.373780\pi$
$840$	−7.89957	+	5.95118i	−0.272561	+	0.205335i
$841$	67.1217			2.31454
$842$	−17.2545	+	15.7174i	−0.594631	+	0.541659i
$843$	−9.58403			−0.330092
$844$	−41.1786	−	3.84771i	−1.41743	−	0.132444i
$845$		−	1.75702i		−	0.0604432i
$846$	13.2696	−	12.0875i	0.456219	−	0.415578i
$847$	31.9373			1.09738
$848$	−8.12699	+	43.1083i	−0.279082	+	1.48034i
$849$			29.7360i			1.02054i
$850$	0.0752066	−	0.0685069i	0.00257957	−	0.00234977i
$851$	−1.89144	+	15.8396i	−0.0648378	+	0.542975i
$852$	2.92180	−	31.2694i	0.100099	−	1.07127i
$853$	−42.0149			−1.43856			−0.719281	−	0.694719i	$-0.755529\pi$
$853$	−42.0149			−1.43856			−0.719281	+	0.694719i	$0.755529\pi$
$854$	23.3410	−	21.2617i	0.798712	−	0.727560i
$855$		−	5.04791i		−	0.172635i
$856$	34.8436	−	26.2496i	1.19093	−	0.897191i
$857$	6.03951			0.206306			0.103153	−	0.994666i	$-0.467107\pi$
$857$	6.03951			0.206306			0.103153	+	0.994666i	$0.467107\pi$
$858$	4.78948	−	4.36282i	0.163510	−	0.148944i
$859$		−	27.5246i		−	0.939128i	−0.882899	−	0.469564i	$-0.844411\pi$
$859$		−	27.5246i		−	0.939128i	0.882899	−	0.469564i	$-0.155589\pi$
$860$	17.7448	+	1.65806i	0.605091	+	0.0565394i
$861$			4.82226i			0.164342i
$862$	29.9736	+	32.9048i	1.02090	+	1.12074i
$863$			16.4378i			0.559551i	0.960066	+	0.279775i	$0.0902600\pi$
$863$			16.4378i			0.559551i	−0.960066	+	0.279775i	$0.909740\pi$
$864$	−4.81527	+	2.96870i	−0.163819	+	0.100997i
$865$			3.04079i			0.103390i
$866$	−19.5957	+	17.8500i	−0.665889	+	0.606569i
$867$		−	16.9948i		−	0.577175i
$868$	56.2060	+	5.25186i	1.90776	+	0.178260i
$869$	5.74633			0.194931
$870$	−9.33697	−	10.2501i	−0.316553	−	0.347511i
$871$	51.1798			1.73416
$872$	3.67902	+	4.88352i	0.124587	+	0.165377i
$873$			4.72490i			0.159914i
$874$	19.8917	+	27.8651i	0.672846	+	0.942552i
$875$			3.49678i			0.118213i
$876$	10.4503	+	0.976473i	0.353083	+	0.0329920i
$877$	−22.5117			−0.760165			−0.380083	−	0.924953i	$-0.624104\pi$
$877$	−22.5117			−0.760165			−0.380083	+	0.924953i	$0.624104\pi$
$878$	9.80196	−	8.92877i	0.330800	−	0.301331i
$879$	−19.4305			−0.655376
$880$	−1.01246	+	5.37040i	−0.0341299	+	0.181036i
$881$		−	16.5757i		−	0.558448i	−0.960226	−	0.279224i	$-0.909923\pi$
$881$		−	16.5757i		−	0.558448i	0.960226	−	0.279224i	$-0.0900772\pi$
$882$	4.97835	+	5.46522i	0.167630	+	0.184023i
$883$			23.5714i			0.793239i	0.917983	+	0.396620i	$0.129817\pi$
$883$			23.5714i			0.793239i	−0.917983	+	0.396620i	$0.870183\pi$
$884$	0.480311	+	0.0448800i	0.0161546	+	0.00150948i
$885$		−	4.71711i		−	0.158564i
$886$	22.5998	−	20.5865i	0.759255	−	0.691618i
$887$		−	31.4813i		−	1.05704i	−0.848921	−	0.528519i	$-0.822747\pi$
$887$		−	31.4813i		−	1.05704i	0.848921	−	0.528519i	$-0.177253\pi$
$888$	−7.51434	+	5.66096i	−0.252165	+	0.189969i
$889$			44.4689i			1.49144i
$890$	10.9737	+	12.0469i	0.367839	+	0.403812i
$891$	−1.36625			−0.0457711
$892$	−19.9656	−	1.86557i	−0.668497	−	0.0624640i
$893$		−	64.0698i		−	2.14402i
$894$	12.2999	+	13.5028i	0.411371	+	0.451601i
$895$	−9.66616			−0.323104
$896$	35.4614	−	17.5387i	1.18468	−	0.585926i
$897$	−1.90668	+	15.9673i	−0.0636622	+	0.533131i
$898$	11.2027	+	12.2983i	0.373839	+	0.410398i
$899$			79.1376i			2.63939i
$900$	−0.186069	+	1.99133i	−0.00620229	+	0.0663775i
$901$	−0.788903			−0.0262822
$902$	1.79436	+	1.96984i	0.0597455	+	0.0655883i
$903$		−	31.1599i		−	1.03694i
$904$	−15.2789	−	20.2812i	−0.508170	−	0.674542i
$905$	−26.0047			−0.864426
$906$	−1.41730	−	1.55590i	−0.0470865	−	0.0516914i
$907$	3.62895			0.120497			0.0602486	−	0.998183i	$-0.480811\pi$
$907$	3.62895			0.120497			0.0602486	+	0.998183i	$0.480811\pi$
$908$	−1.07290	+	11.4823i	−0.0356056	+	0.381054i
$909$	−10.7894			−0.357861
$910$	−12.2582	+	11.1662i	−0.406354	+	0.370155i
$911$	−37.6483			−1.24735			−0.623673	−	0.781686i	$-0.714360\pi$
$911$	−37.6483			−1.24735			−0.623673	+	0.781686i	$0.714360\pi$
$912$	−3.74074	+	19.8421i	−0.123868	+	0.657038i
$913$	−18.4329			−0.610040
$914$	−37.0552	+	33.7542i	−1.22568	+	1.11649i
$915$		−	6.38461i		−	0.211069i
$916$	−4.91086	−	0.458868i	−0.162259	−	0.0151614i
$917$			75.1181i			2.48062i
$918$	−0.0685069	−	0.0752066i	−0.00226107	−	0.00248219i
$919$	−39.4637			−1.30179			−0.650893	−	0.759169i	$-0.725605\pi$
$919$	−39.4637			−1.30179			−0.650893	+	0.759169i	$0.725605\pi$
$920$	−6.81985	−	11.7256i	−0.224844	−	0.386582i
$921$	24.3915			0.803726
$922$	13.5413	+	14.8656i	0.445960	+	0.489573i
$923$		−	52.6524i		−	1.73308i
$924$	9.51351	+	0.888938i	0.312972	+	0.0292439i
$925$			3.32625i			0.109367i
$926$	−1.41375	+	1.28781i	−0.0464588	+	0.0423201i
$927$	8.71856			0.286355
$928$	29.1056	+	47.2097i	0.955438	+	1.54974i
$929$	−18.7511			−0.615204			−0.307602	−	0.951515i	$-0.599527\pi$
$929$	−18.7511			−0.615204			−0.307602	+	0.951515i	$0.599527\pi$
$930$	8.43896	−	7.68719i	0.276724	−	0.252073i
$931$	26.3877			0.864823
$932$	−3.19082	+	34.1485i	−0.104519	+	1.11857i
$933$	3.30836			0.108311
$934$	−19.0222	−	20.8825i	−0.622426	−	0.683297i
$935$	−0.0982810			−0.00321413
$936$	−7.57488	+	5.70657i	−0.247593	+	0.186525i
$937$		−	2.65735i		−	0.0868117i	−0.999058	−	0.0434059i	$-0.986179\pi$
$937$		−	2.65735i		−	0.0868117i	0.999058	−	0.0434059i	$-0.0138209\pi$
$938$	50.8301	+	55.8010i	1.65966	+	1.82197i
$939$	16.4380			0.536434
$940$	−2.36165	+	25.2746i	−0.0770284	+	0.824366i
$941$		−	53.1284i		−	1.73194i	−0.500100	−	0.865968i	$-0.666704\pi$
$941$		−	53.1284i		−	1.73194i	0.500100	−	0.865968i	$-0.333296\pi$
$942$	−0.751424	−	0.824909i	−0.0244827	−	0.0268770i
$943$	−6.56707	−	0.784187i	−0.213853	−	0.0255367i
$944$	−3.49560	+	18.5418i	−0.113772	+	0.603485i
$945$	3.49678			0.113750
$946$	−11.5945	−	12.7284i	−0.376971	−	0.413837i
$947$			22.2269i			0.722278i	0.932512	+	0.361139i	$0.117612\pi$
$947$			22.2269i			0.722278i	−0.932512	+	0.361139i	$0.882388\pi$
$948$	−8.37534	−	0.782588i	−0.272018	−	0.0254173i
$949$	17.5966			0.571209
$950$	4.80737	+	5.27750i	0.155972	+	0.171225i
$951$			21.1799i			0.686806i
$952$	0.428097	+	0.568254i	0.0138747	+	0.0184172i
$953$		−	26.2415i		−	0.850046i	−0.905183	−	0.425023i	$-0.860266\pi$
$953$		−	26.2415i		−	0.850046i	0.905183	−	0.425023i	$-0.139734\pi$
$954$	11.4657	−	10.4443i	0.371216	−	0.338147i
$955$		−	1.45243i		−	0.0469994i
$956$	15.6941	+	1.46645i	0.507585	+	0.0474285i
$957$			13.3950i			0.432997i
$958$	−26.6493	−	29.2555i	−0.860999	−	0.945201i
$959$		−	30.8833i		−	0.997273i
$960$	2.20705	−	7.68953i	0.0712324	−	0.248179i
$961$	−34.1545			−1.10176
$962$	−11.6604	+	10.6216i	−0.375946	+	0.342456i
$963$	−15.4237			−0.497020
$964$	−26.5092	−	2.47701i	−0.853804	−	0.0797791i
$965$			12.6263i			0.406455i
$966$	−19.3027	+	13.7793i	−0.621053	+	0.443342i
$967$			7.54606i			0.242665i	0.992612	+	0.121333i	$0.0387167\pi$
$967$			7.54606i			0.242665i	−0.992612	+	0.121333i	$0.961283\pi$
$968$	−20.6332	+	15.5441i	−0.663175	+	0.499606i
$969$	−0.363121			−0.0116651
$970$	−4.49975	−	4.93981i	−0.144478	−	0.158608i
$971$	−11.9488			−0.383456			−0.191728	−	0.981448i	$-0.561409\pi$
$971$	−11.9488			−0.383456			−0.191728	+	0.981448i	$0.561409\pi$
$972$	1.99133	+	0.186069i	0.0638718	+	0.00596815i
$973$		−	5.17223i		−	0.165814i
$974$	−31.5453	+	28.7351i	−1.01078	+	0.920732i
$975$			3.35306i			0.107384i
$976$	−4.73129	+	25.0963i	−0.151445	+	0.803314i
$977$		−	19.3143i		−	0.617919i	−0.951075	−	0.308960i	$-0.900019\pi$
$977$		−	19.3143i		−	0.617919i	0.951075	−	0.308960i	$-0.0999808\pi$
$978$	9.58810	+	10.5258i	0.306594	+	0.336577i
$979$		−	15.7430i		−	0.503149i
$980$	−10.4096	−	0.972665i	−0.332521	−	0.0310707i
$981$		−	2.16171i		−	0.0690181i
$982$	−7.40479	+	6.74514i	−0.236296	+	0.215246i
$983$	−5.59462			−0.178441			−0.0892204	−	0.996012i	$-0.528438\pi$
$983$	−5.59462			−0.178441			−0.0892204	+	0.996012i	$0.528438\pi$
$984$	−2.34702	−	3.11543i	−0.0748203	−	0.0993162i
$985$		−	23.9878i		−	0.764315i
$986$	−0.737338	+	0.671653i	−0.0234816	+	0.0213898i
$987$	44.3823			1.41270
$988$	−3.14938	+	33.7050i	−0.100195	+	1.07230i
$989$	42.4343	+	5.06717i	1.34933	+	0.161126i
$990$	1.42839	−	1.30115i	0.0453973	−	0.0413531i
$991$			46.6872i			1.48307i	0.670916	+	0.741533i	$0.265901\pi$
$991$			46.6872i			1.48307i	−0.670916	+	0.741533i	$0.734099\pi$
$992$	−38.8681	+	23.9628i	−1.23406	+	0.760820i
$993$	−7.56275			−0.239997
$994$	57.4067	−	52.2927i	1.82083	−	1.65862i
$995$			16.8297i			0.533537i
$996$	26.8661	+	2.51036i	0.851286	+	0.0795438i
$997$	−2.45370			−0.0777095			−0.0388547	−	0.999245i	$-0.512371\pi$
$997$	−2.45370			−0.0777095			−0.0388547	+	0.999245i	$0.512371\pi$
$998$	−18.0344	+	16.4278i	−0.570868	+	0.520013i
$999$	3.32625			0.105238

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.p.b.91.15	yes	48
4.3	odd	2		1380.2.p.a.91.16	yes	48
23.22	odd	2		1380.2.p.a.91.15	✓	48
92.91	even	2	inner	1380.2.p.b.91.16	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.p.a.91.15	✓	48	23.22	odd	2
1380.2.p.a.91.16	yes	48	4.3	odd	2
1380.2.p.b.91.15	yes	48	1.1	even	1	trivial
1380.2.p.b.91.16	yes	48	92.91	even	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:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.952347 - 1.04548i) q^{2} -1.00000i q^{3} +(-0.186069 + 1.99133i) q^{4} +1.00000i q^{5} +(-1.04548 + 0.952347i) q^{6} -3.49678 q^{7} +(2.25910 - 1.70190i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.952347 - 1.04548i) q^{2} -1.00000i q^{3} +(-0.186069 + 1.99133i) q^{4} +1.00000i q^{5} +(-1.04548 + 0.952347i) q^{6} -3.49678 q^{7} +(2.25910 - 1.70190i) q^{8} -1.00000 q^{9} +(1.04548 - 0.952347i) q^{10} -1.36625 q^{11} +(1.99133 + 0.186069i) q^{12} +3.35306 q^{13} +(3.33015 + 3.65582i) q^{14} +1.00000 q^{15} +(-3.93076 - 0.741046i) q^{16} -0.0719348i q^{17} +(0.952347 + 1.04548i) q^{18} +5.04791 q^{19} +(-1.99133 - 0.186069i) q^{20} +3.49678i q^{21} +(1.30115 + 1.42839i) q^{22} +(-4.76200 - 0.568640i) q^{23} +(-1.70190 - 2.25910i) q^{24} -1.00000 q^{25} +(-3.19327 - 3.50556i) q^{26} +1.00000i q^{27} +(0.650640 - 6.96322i) q^{28} +9.80417 q^{29} +(-0.952347 - 1.04548i) q^{30} +8.07183i q^{31} +(2.96870 + 4.81527i) q^{32} +1.36625i q^{33} +(-0.0752066 + 0.0685069i) q^{34} -3.49678i q^{35} +(0.186069 - 1.99133i) q^{36} -3.32625i q^{37} +(-4.80737 - 5.27750i) q^{38} -3.35306i q^{39} +(1.70190 + 2.25910i) q^{40} +1.37906 q^{41} +(3.65582 - 3.33015i) q^{42} -8.91103 q^{43} +(0.254216 - 2.72065i) q^{44} -1.00000i q^{45} +(3.94058 + 5.52013i) q^{46} -12.6923i q^{47} +(-0.741046 + 3.93076i) q^{48} +5.22746 q^{49} +(0.952347 + 1.04548i) q^{50} -0.0719348 q^{51} +(-0.623898 + 6.67703i) q^{52} -10.9669i q^{53} +(1.04548 - 0.952347i) q^{54} -1.36625i q^{55} +(-7.89957 + 5.95118i) q^{56} -5.04791i q^{57} +(-9.33697 - 10.2501i) q^{58} -4.71711i q^{59} +(-0.186069 + 1.99133i) q^{60} -6.38461i q^{61} +(8.43896 - 7.68719i) q^{62} +3.49678 q^{63} +(2.20705 - 7.68953i) q^{64} +3.35306i q^{65} +(1.42839 - 1.30115i) q^{66} +15.2636 q^{67} +(0.143246 + 0.0133848i) q^{68} +(-0.568640 + 4.76200i) q^{69} +(-3.65582 + 3.33015i) q^{70} -15.7028i q^{71} +(-2.25910 + 1.70190i) q^{72} +5.24792 q^{73} +(-3.47754 + 3.16775i) q^{74} +1.00000i q^{75} +(-0.939258 + 10.0520i) q^{76} +4.77748 q^{77} +(-3.50556 + 3.19327i) q^{78} -4.20591 q^{79} +(0.741046 - 3.93076i) q^{80} +1.00000 q^{81} +(-1.31334 - 1.44178i) q^{82} +13.4916 q^{83} +(-6.96322 - 0.650640i) q^{84} +0.0719348 q^{85} +(8.48639 + 9.31632i) q^{86} -9.80417i q^{87} +(-3.08650 + 2.32523i) q^{88} +11.5228i q^{89} +(-1.04548 + 0.952347i) q^{90} -11.7249 q^{91} +(2.01841 - 9.37689i) q^{92} +8.07183 q^{93} +(-13.2696 + 12.0875i) q^{94} +5.04791i q^{95} +(4.81527 - 2.96870i) q^{96} -4.72490i q^{97} +(-4.97835 - 5.46522i) q^{98} +1.36625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} + 2 q^{10} - 20 q^{14} + 48 q^{15} - 6 q^{16} + 4 q^{18} - 16 q^{19} - 28 q^{22} - 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} - 4 q^{30} + 16 q^{32} + 28 q^{34} + 2 q^{36} - 2 q^{40} - 8 q^{41} + 26 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 16 q^{51} - 16 q^{52} + 2 q^{54} - 40 q^{56} - 8 q^{58} - 2 q^{60} + 24 q^{62} - 26 q^{64} + 48 q^{67} + 44 q^{68} - 8 q^{69} + 4 q^{72} - 20 q^{74} + 64 q^{76} + 32 q^{77} + 64 q^{79} - 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} + 40 q^{86} - 2 q^{90} - 28 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 + 2 * q^10 - 20 * q^14 + 48 * q^15 - 6 * q^16 + 4 * q^18 - 16 * q^19 - 28 * q^22 - 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 - 4 * q^30 + 16 * q^32 + 28 * q^34 + 2 * q^36 - 2 * q^40 - 8 * q^41 + 26 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 - 16 * q^51 - 16 * q^52 + 2 * q^54 - 40 * q^56 - 8 * q^58 - 2 * q^60 + 24 * q^62 - 26 * q^64 + 48 * q^67 + 44 * q^68 - 8 * q^69 + 4 * q^72 - 20 * q^74 + 64 * q^76 + 32 * q^77 + 64 * q^79 - 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 + 40 * q^86 - 2 * q^90 - 28 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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