LMFDB - Embedded newform 924.2.n.c.923.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [924,2,Mod(923,924)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(924, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("924.923");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 924 = 2^{2} \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	924.n (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:	$7.37817714677$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.3317760000.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 8x^{6} + 13x^{4} - 12x^{2} + 36 $ x^8 + 8x^6 + 13x^4 - 12*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			923.6
Root			$0.965926 + 0.578737i$ of defining polynomial
Character	$\chi$	$=$	924.923
Dual form			924.2.n.c.923.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 1.11803i) q^{2} +1.73205 q^{3} +(-0.500000 - 1.93649i) q^{4} +1.41421 q^{5} +(1.50000 - 1.93649i) q^{6} +(2.12132 + 1.58114i) q^{7} +(-2.59808 - 1.11803i) q^{8} +3.00000 q^{9} +(1.22474 - 1.58114i) q^{10} +(2.44949 - 2.23607i) q^{11} +(-0.866025 - 3.35410i) q^{12} -2.44949 q^{13} +(3.60488 - 1.00240i) q^{14} +2.44949 q^{15} +(-3.50000 + 1.93649i) q^{16} +(2.59808 - 3.35410i) q^{18} +6.32456i q^{19} +(-0.707107 - 2.73861i) q^{20} +(3.67423 + 2.73861i) q^{21} +(-0.378680 - 4.67510i) q^{22} -2.44949 q^{23} +(-4.50000 - 1.93649i) q^{24} -3.00000 q^{25} +(-2.12132 + 2.73861i) q^{26} +5.19615 q^{27} +(2.00120 - 4.89849i) q^{28} -6.92820 q^{29} +(2.12132 - 2.73861i) q^{30} +3.46410 q^{31} +(-0.866025 + 5.59017i) q^{32} +(4.24264 - 3.87298i) q^{33} +(3.00000 + 2.23607i) q^{35} +(-1.50000 - 5.80948i) q^{36} +2.00000 q^{37} +(7.07107 + 5.47723i) q^{38} -4.24264 q^{39} +(-3.67423 - 1.58114i) q^{40} -7.74597i q^{41} +(6.24384 - 1.73621i) q^{42} +(-5.55487 - 3.62538i) q^{44} +4.24264 q^{45} +(-2.12132 + 2.73861i) q^{46} -5.47723i q^{47} +(-6.06218 + 3.35410i) q^{48} +(2.00000 + 6.70820i) q^{49} +(-2.59808 + 3.35410i) q^{50} +(1.22474 + 4.74342i) q^{52} -9.48683i q^{53} +(4.50000 - 5.80948i) q^{54} +(3.46410 - 3.16228i) q^{55} +(-3.74358 - 6.47963i) q^{56} +10.9545i q^{57} +(-6.00000 + 7.74597i) q^{58} +10.9545i q^{59} +(-1.22474 - 4.74342i) q^{60} -7.34847 q^{61} +(3.00000 - 3.87298i) q^{62} +(6.36396 + 4.74342i) q^{63} +(5.50000 + 5.80948i) q^{64} -3.46410 q^{65} +(-0.655892 - 8.09752i) q^{66} -7.74597i q^{67} -4.24264 q^{69} +(5.09808 - 1.41761i) q^{70} -12.2474 q^{71} +(-7.79423 - 3.35410i) q^{72} -9.79796 q^{73} +(1.73205 - 2.23607i) q^{74} -5.19615 q^{75} +(12.2474 - 3.16228i) q^{76} +(8.73169 - 0.870433i) q^{77} +(-3.67423 + 4.74342i) q^{78} -4.24264 q^{79} +(-4.94975 + 2.73861i) q^{80} +9.00000 q^{81} +(-8.66025 - 6.70820i) q^{82} +6.00000 q^{83} +(3.46618 - 8.48443i) q^{84} -12.0000 q^{87} +(-8.86396 + 3.07086i) q^{88} -2.82843 q^{89} +(3.67423 - 4.74342i) q^{90} +(-5.19615 - 3.87298i) q^{91} +(1.22474 + 4.74342i) q^{92} +6.00000 q^{93} +(-6.12372 - 4.74342i) q^{94} +8.94427i q^{95} +(-1.50000 + 9.68246i) q^{96} +13.4164i q^{97} +(9.23205 + 3.57341i) q^{98} +(7.34847 - 6.70820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} + 12 q^{6} + 24 q^{9} - 28 q^{16} - 20 q^{22} - 36 q^{24} - 24 q^{25} + 24 q^{35} - 12 q^{36} + 16 q^{37} + 16 q^{49} + 36 q^{54} - 48 q^{58} + 24 q^{62} + 44 q^{64} + 20 q^{70} + 72 q^{81}+ \cdots + 60 q^{98}+O(q^{100}) $ 8 * q - 4 * q^4 + 12 * q^6 + 24 * q^9 - 28 * q^16 - 20 * q^22 - 36 * q^24 - 24 * q^25 + 24 * q^35 - 12 * q^36 + 16 * q^37 + 16 * q^49 + 36 * q^54 - 48 * q^58 + 24 * q^62 + 44 * q^64 + 20 * q^70 + 72 * q^81 + 48 * q^83 - 96 * q^87 - 20 * q^88 + 48 * q^93 - 12 * q^96 + 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/924\mathbb{Z}\right)^\times$.

$n$	$463$	$617$	$661$	$673$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	0.866025	−	1.11803i	0.612372	−	0.790569i
$2$	0.866025	−	1.11803i	0.612372	−	0.790569i
$3$	1.73205			1.00000
$3$	1.73205			1.00000
$4$	−0.500000	−	1.93649i	−0.250000	−	0.968246i
$5$	1.41421			0.632456			0.316228	−	0.948683i	$-0.397584\pi$
$5$	1.41421			0.632456			0.316228	+	0.948683i	$0.397584\pi$
$6$	1.50000	−	1.93649i	0.612372	−	0.790569i
$7$	2.12132	+	1.58114i	0.801784	+	0.597614i
$7$	2.12132	+	1.58114i	0.801784	+	0.597614i
$8$	−2.59808	−	1.11803i	−0.918559	−	0.395285i
$9$	3.00000			1.00000
$10$	1.22474	−	1.58114i	0.387298	−	0.500000i
$11$	2.44949	−	2.23607i	0.738549	−	0.674200i
$11$	2.44949	−	2.23607i	0.738549	−	0.674200i
$12$	−0.866025	−	3.35410i	−0.250000	−	0.968246i
$13$	−2.44949			−0.679366			−0.339683	−	0.940540i	$-0.610320\pi$
$13$	−2.44949			−0.679366			−0.339683	+	0.940540i	$0.610320\pi$
$14$	3.60488	−	1.00240i	0.963446	−	0.267903i
$15$	2.44949			0.632456
$16$	−3.50000	+	1.93649i	−0.875000	+	0.484123i
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	2.59808	−	3.35410i	0.612372	−	0.790569i
$19$			6.32456i			1.45095i	0.688247	+	0.725476i	$0.258380\pi$
$19$			6.32456i			1.45095i	−0.688247	+	0.725476i	$0.741620\pi$
$20$	−0.707107	−	2.73861i	−0.158114	−	0.612372i
$21$	3.67423	+	2.73861i	0.801784	+	0.597614i
$22$	−0.378680	−	4.67510i	−0.0807348	−	0.996736i
$23$	−2.44949			−0.510754			−0.255377	−	0.966842i	$-0.582200\pi$
$23$	−2.44949			−0.510754			−0.255377	+	0.966842i	$0.582200\pi$
$24$	−4.50000	−	1.93649i	−0.918559	−	0.395285i
$25$	−3.00000			−0.600000
$26$	−2.12132	+	2.73861i	−0.416025	+	0.537086i
$27$	5.19615			1.00000
$28$	2.00120	−	4.89849i	0.378192	−	0.925727i
$29$	−6.92820			−1.28654			−0.643268	−	0.765641i	$-0.722422\pi$
$29$	−6.92820			−1.28654			−0.643268	+	0.765641i	$0.722422\pi$
$30$	2.12132	−	2.73861i	0.387298	−	0.500000i
$31$	3.46410			0.622171			0.311086	−	0.950382i	$-0.399307\pi$
$31$	3.46410			0.622171			0.311086	+	0.950382i	$0.399307\pi$
$32$	−0.866025	+	5.59017i	−0.153093	+	0.988212i
$33$	4.24264	−	3.87298i	0.738549	−	0.674200i
$34$		0			0
$35$	3.00000	+	2.23607i	0.507093	+	0.377964i
$36$	−1.50000	−	5.80948i	−0.250000	−	0.968246i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	7.07107	+	5.47723i	1.14708	+	0.888523i
$39$	−4.24264			−0.679366
$40$	−3.67423	−	1.58114i	−0.580948	−	0.250000i
$41$		−	7.74597i		−	1.20972i	−0.796333	−	0.604858i	$-0.793230\pi$
$41$		−	7.74597i		−	1.20972i	0.796333	−	0.604858i	$-0.206770\pi$
$42$	6.24384	−	1.73621i	0.963446	−	0.267903i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	−5.55487	−	3.62538i	−0.837428	−	0.546547i
$45$	4.24264			0.632456
$46$	−2.12132	+	2.73861i	−0.312772	+	0.403786i
$47$		−	5.47723i		−	0.798935i	−0.916747	−	0.399468i	$-0.869195\pi$
$47$		−	5.47723i		−	0.798935i	0.916747	−	0.399468i	$-0.130805\pi$
$48$	−6.06218	+	3.35410i	−0.875000	+	0.484123i
$49$	2.00000	+	6.70820i	0.285714	+	0.958315i
$50$	−2.59808	+	3.35410i	−0.367423	+	0.474342i
$51$		0			0
$52$	1.22474	+	4.74342i	0.169842	+	0.657794i
$53$		−	9.48683i		−	1.30312i	−0.758599	−	0.651558i	$-0.774116\pi$
$53$		−	9.48683i		−	1.30312i	0.758599	−	0.651558i	$-0.225884\pi$
$54$	4.50000	−	5.80948i	0.612372	−	0.790569i
$55$	3.46410	−	3.16228i	0.467099	−	0.426401i
$56$	−3.74358	−	6.47963i	−0.500258	−	0.865877i
$57$			10.9545i			1.45095i
$58$	−6.00000	+	7.74597i	−0.787839	+	1.01710i
$59$			10.9545i			1.42615i	0.701089	+	0.713074i	$0.252698\pi$
$59$			10.9545i			1.42615i	−0.701089	+	0.713074i	$0.747302\pi$
$60$	−1.22474	−	4.74342i	−0.158114	−	0.612372i
$61$	−7.34847			−0.940875			−0.470438	−	0.882433i	$-0.655904\pi$
$61$	−7.34847			−0.940875			−0.470438	+	0.882433i	$0.655904\pi$
$62$	3.00000	−	3.87298i	0.381000	−	0.491869i
$63$	6.36396	+	4.74342i	0.801784	+	0.597614i
$64$	5.50000	+	5.80948i	0.687500	+	0.726184i
$65$	−3.46410			−0.429669
$66$	−0.655892	−	8.09752i	−0.0807348	−	0.996736i
$67$		−	7.74597i		−	0.946320i	−0.880976	−	0.473160i	$-0.843113\pi$
$67$		−	7.74597i		−	0.946320i	0.880976	−	0.473160i	$-0.156887\pi$
$68$		0			0
$69$	−4.24264			−0.510754
$70$	5.09808	−	1.41761i	0.609337	−	0.169437i
$71$	−12.2474			−1.45350			−0.726752	−	0.686900i	$-0.758971\pi$
$71$	−12.2474			−1.45350			−0.726752	+	0.686900i	$0.758971\pi$
$72$	−7.79423	−	3.35410i	−0.918559	−	0.395285i
$73$	−9.79796			−1.14676			−0.573382	−	0.819288i	$-0.694369\pi$
$73$	−9.79796			−1.14676			−0.573382	+	0.819288i	$0.694369\pi$
$74$	1.73205	−	2.23607i	0.201347	−	0.259938i
$75$	−5.19615			−0.600000
$76$	12.2474	−	3.16228i	1.40488	−	0.362738i
$77$	8.73169	−	0.870433i	0.995068	−	0.0991951i
$78$	−3.67423	+	4.74342i	−0.416025	+	0.537086i
$79$	−4.24264			−0.477334			−0.238667	−	0.971101i	$-0.576710\pi$
$79$	−4.24264			−0.477334			−0.238667	+	0.971101i	$0.576710\pi$
$80$	−4.94975	+	2.73861i	−0.553399	+	0.306186i
$81$	9.00000			1.00000
$82$	−8.66025	−	6.70820i	−0.956365	−	0.740797i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	3.46618	−	8.48443i	0.378192	−	0.925727i
$85$		0			0
$86$		0			0
$87$	−12.0000			−1.28654
$88$	−8.86396	+	3.07086i	−0.944901	+	0.327355i
$89$	−2.82843			−0.299813			−0.149906	−	0.988700i	$-0.547897\pi$
$89$	−2.82843			−0.299813			−0.149906	+	0.988700i	$0.547897\pi$
$90$	3.67423	−	4.74342i	0.387298	−	0.500000i
$91$	−5.19615	−	3.87298i	−0.544705	−	0.405999i
$92$	1.22474	+	4.74342i	0.127688	+	0.494535i
$93$	6.00000			0.622171
$94$	−6.12372	−	4.74342i	−0.631614	−	0.489246i
$95$			8.94427i			0.917663i
$96$	−1.50000	+	9.68246i	−0.153093	+	0.988212i
$97$			13.4164i			1.36223i	0.732177	+	0.681115i	$0.238505\pi$
$97$			13.4164i			1.36223i	−0.732177	+	0.681115i	$0.761495\pi$
$98$	9.23205	+	3.57341i	0.932578	+	0.360969i
$99$	7.34847	−	6.70820i	0.738549	−	0.674200i
$100$	1.50000	+	5.80948i	0.150000	+	0.580948i
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$		0			0
$103$	3.46410			0.341328			0.170664	−	0.985329i	$-0.445409\pi$
$103$	3.46410			0.341328			0.170664	+	0.985329i	$0.445409\pi$
$104$	6.36396	+	2.73861i	0.624038	+	0.268543i
$105$	5.19615	+	3.87298i	0.507093	+	0.377964i
$106$	−10.6066	−	8.21584i	−1.03020	−	0.797993i
$107$			4.47214i			0.432338i	0.976356	+	0.216169i	$0.0693562\pi$
$107$			4.47214i			0.432338i	−0.976356	+	0.216169i	$0.930644\pi$
$108$	−2.59808	−	10.0623i	−0.250000	−	0.968246i
$109$			5.47723i			0.524623i	0.964983	+	0.262312i	$0.0844848\pi$
$109$			5.47723i			0.524623i	−0.964983	+	0.262312i	$0.915515\pi$
$110$	−0.535534	−	6.61160i	−0.0510612	−	0.630391i
$111$	3.46410			0.328798
$112$	−10.4865	−	1.42607i	−0.990880	−	0.134751i
$113$			18.9737i			1.78489i	0.451154	+	0.892446i	$0.351013\pi$
$113$			18.9737i			1.78489i	−0.451154	+	0.892446i	$0.648987\pi$
$114$	12.2474	+	9.48683i	1.14708	+	0.888523i
$115$	−3.46410			−0.323029
$116$	3.46410	+	13.4164i	0.321634	+	1.24568i
$117$	−7.34847			−0.679366
$118$	12.2474	+	9.48683i	1.12747	+	0.873334i
$119$		0			0
$120$	−6.36396	−	2.73861i	−0.580948	−	0.250000i
$121$	1.00000	−	10.9545i	0.0909091	−	0.995859i
$122$	−6.36396	+	8.21584i	−0.576166	+	0.743827i
$123$		−	13.4164i		−	1.20972i
$124$	−1.73205	−	6.70820i	−0.155543	−	0.602414i
$125$	−11.3137			−1.01193
$126$	10.8147	−	3.00721i	0.963446	−	0.267903i
$127$	21.2132			1.88237			0.941184	−	0.337895i	$-0.109715\pi$
$127$	21.2132			1.88237			0.941184	+	0.337895i	$0.109715\pi$
$128$	11.2583	−	1.11803i	0.995105	−	0.0988212i
$129$		0			0
$130$	−3.00000	+	3.87298i	−0.263117	+	0.339683i
$131$	18.0000			1.57267			0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000			1.57267			0.786334	+	0.617802i	$0.211977\pi$
$132$	−9.62132	−	6.27935i	−0.837428	−	0.546547i
$133$	−10.0000	+	13.4164i	−0.867110	+	1.16335i
$134$	−8.66025	−	6.70820i	−0.748132	−	0.579501i
$135$	7.34847			0.632456
$136$		0			0
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$	−3.67423	+	4.74342i	−0.312772	+	0.403786i
$139$		−	12.6491i		−	1.07288i	−0.843937	−	0.536442i	$-0.819768\pi$
$139$		−	12.6491i		−	1.07288i	0.843937	−	0.536442i	$-0.180232\pi$
$140$	2.83013	−	6.92751i	0.239189	−	0.585481i
$141$		−	9.48683i		−	0.798935i
$142$	−10.6066	+	13.6931i	−0.890086	+	1.14910i
$143$	−6.00000	+	5.47723i	−0.501745	+	0.458029i
$144$	−10.5000	+	5.80948i	−0.875000	+	0.484123i
$145$	−9.79796			−0.813676
$146$	−8.48528	+	10.9545i	−0.702247	+	0.906597i
$147$	3.46410	+	11.6190i	0.285714	+	0.958315i
$148$	−1.00000	−	3.87298i	−0.0821995	−	0.318357i
$149$	6.92820			0.567581			0.283790	−	0.958886i	$-0.408408\pi$
$149$	6.92820			0.567581			0.283790	+	0.958886i	$0.408408\pi$
$150$	−4.50000	+	5.80948i	−0.367423	+	0.474342i
$151$	12.7279			1.03578			0.517892	−	0.855446i	$-0.326717\pi$
$151$	12.7279			1.03578			0.517892	+	0.855446i	$0.326717\pi$
$152$	7.07107	−	16.4317i	0.573539	−	1.33278i
$153$		0			0
$154$	6.58869	−	10.5161i	0.530932	−	0.847415i
$155$	4.89898			0.393496
$156$	2.12132	+	8.21584i	0.169842	+	0.657794i
$157$			13.4164i			1.07075i	0.844616	+	0.535373i	$0.179829\pi$
$157$			13.4164i			1.07075i	−0.844616	+	0.535373i	$0.820171\pi$
$158$	−3.67423	+	4.74342i	−0.292306	+	0.377366i
$159$		−	16.4317i		−	1.30312i
$160$	−1.22474	+	7.90569i	−0.0968246	+	0.625000i
$161$	−5.19615	−	3.87298i	−0.409514	−	0.305234i
$162$	7.79423	−	10.0623i	0.612372	−	0.790569i
$163$		−	15.4919i		−	1.21342i	−0.794923	−	0.606711i	$-0.792489\pi$
$163$		−	15.4919i		−	1.21342i	0.794923	−	0.606711i	$-0.207511\pi$
$164$	−15.0000	+	3.87298i	−1.17130	+	0.302429i
$165$	6.00000	−	5.47723i	0.467099	−	0.426401i
$166$	5.19615	−	6.70820i	0.403300	−	0.520658i
$167$	−12.0000			−0.928588			−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$	−6.48408	−	11.2230i	−0.500258	−	0.865877i
$169$	−7.00000			−0.538462
$170$		0			0
$171$			18.9737i			1.45095i
$172$		0			0
$173$			15.4919i			1.17783i	0.808195	+	0.588915i	$0.200445\pi$
$173$			15.4919i			1.17783i	−0.808195	+	0.588915i	$0.799555\pi$
$174$	−10.3923	+	13.4164i	−0.787839	+	1.01710i
$175$	−6.36396	−	4.74342i	−0.481070	−	0.358569i
$176$	−4.24309	+	12.5697i	−0.319835	+	0.947473i
$177$			18.9737i			1.42615i
$178$	−2.44949	+	3.16228i	−0.183597	+	0.237023i
$179$	14.6969			1.09850			0.549250	−	0.835658i	$-0.314913\pi$
$179$	14.6969			1.09850			0.549250	+	0.835658i	$0.314913\pi$
$180$	−2.12132	−	8.21584i	−0.158114	−	0.612372i
$181$		−	13.4164i		−	0.997234i	−0.866822	−	0.498617i	$-0.833841\pi$
$181$		−	13.4164i		−	0.997234i	0.866822	−	0.498617i	$-0.166159\pi$
$182$	−8.83013	+	2.45537i	−0.654533	+	0.182004i
$183$	−12.7279			−0.940875
$184$	6.36396	+	2.73861i	0.469157	+	0.201893i
$185$	2.82843			0.207950
$186$	5.19615	−	6.70820i	0.381000	−	0.491869i
$187$		0			0
$188$	−10.6066	+	2.73861i	−0.773566	+	0.199734i
$189$	11.0227	+	8.21584i	0.801784	+	0.597614i
$190$	10.0000	+	7.74597i	0.725476	+	0.561951i
$191$	−12.2474			−0.886194			−0.443097	−	0.896474i	$-0.646120\pi$
$191$	−12.2474			−0.886194			−0.443097	+	0.896474i	$0.646120\pi$
$192$	9.52628	+	10.0623i	0.687500	+	0.726184i
$193$		0			0		1.00000			$0$
$193$		0			0		−1.00000			$\pi$
$194$	15.0000	+	11.6190i	1.07694	+	0.834192i
$195$	−6.00000			−0.429669
$196$	11.9904	−	7.22709i	0.856456	−	0.516220i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	−1.13604	−	14.0253i	−0.0807348	−	0.996736i
$199$	−24.2487			−1.71895			−0.859473	−	0.511182i	$-0.829208\pi$
$199$	−24.2487			−1.71895			−0.859473	+	0.511182i	$0.829208\pi$
$200$	7.79423	+	3.35410i	0.551135	+	0.237171i
$201$		−	13.4164i		−	0.946320i
$202$		0			0
$203$	−14.6969	−	10.9545i	−1.03152	−	0.768852i
$204$		0			0
$205$		−	10.9545i		−	0.765092i
$206$	3.00000	−	3.87298i	0.209020	−	0.269844i
$207$	−7.34847			−0.510754
$208$	8.57321	−	4.74342i	0.594445	−	0.328897i
$209$	14.1421	+	15.4919i	0.978232	+	1.07160i
$210$	8.83013	−	2.45537i	0.609337	−	0.169437i
$211$	8.48528			0.584151			0.292075	−	0.956395i	$-0.405654\pi$
$211$	8.48528			0.584151			0.292075	+	0.956395i	$0.405654\pi$
$212$	−18.3712	+	4.74342i	−1.26174	+	0.325779i
$213$	−21.2132			−1.45350
$214$	5.00000	+	3.87298i	0.341793	+	0.264752i
$215$		0			0
$216$	−13.5000	−	5.80948i	−0.918559	−	0.395285i
$217$	7.34847	+	5.47723i	0.498847	+	0.371818i
$218$	6.12372	+	4.74342i	0.414751	+	0.321265i
$219$	−16.9706			−1.14676
$220$	−7.85578	−	5.12707i	−0.529636	−	0.345667i
$221$		0			0
$222$	3.00000	−	3.87298i	0.201347	−	0.259938i
$223$	17.3205			1.15987			0.579934	−	0.814664i	$-0.303079\pi$
$223$	17.3205			1.15987			0.579934	+	0.814664i	$0.303079\pi$
$224$	−10.6760	+	10.4892i	−0.713317	+	0.700841i
$225$	−9.00000			−0.600000
$226$	21.2132	+	16.4317i	1.41108	+	1.09302i
$227$	−12.0000			−0.796468			−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000			−0.796468			−0.398234	+	0.917284i	$0.630377\pi$
$228$	21.2132	−	5.47723i	1.40488	−	0.362738i
$229$		−	13.4164i		−	0.886581i	−0.896378	−	0.443291i	$-0.853811\pi$
$229$		−	13.4164i		−	0.886581i	0.896378	−	0.443291i	$-0.146189\pi$
$230$	−3.00000	+	3.87298i	−0.197814	+	0.255377i
$231$	15.1237	−	1.50763i	0.995068	−	0.0991951i
$232$	18.0000	+	7.74597i	1.18176	+	0.508548i
$233$	20.7846			1.36165			0.680823	−	0.732448i	$-0.261622\pi$
$233$	20.7846			1.36165			0.680823	+	0.732448i	$0.261622\pi$
$234$	−6.36396	+	8.21584i	−0.416025	+	0.537086i
$235$		−	7.74597i		−	0.505291i
$236$	21.2132	−	5.47723i	1.38086	−	0.356537i
$237$	−7.34847			−0.477334
$238$		0			0
$239$			8.94427i			0.578557i	0.957245	+	0.289278i	$0.0934153\pi$
$239$			8.94427i			0.578557i	−0.957245	+	0.289278i	$0.906585\pi$
$240$	−8.57321	+	4.74342i	−0.553399	+	0.306186i
$241$	24.4949			1.57786			0.788928	−	0.614486i	$-0.210637\pi$
$241$	24.4949			1.57786			0.788928	+	0.614486i	$0.210637\pi$
$242$	−11.3814	−	10.6049i	−0.731626	−	0.681707i
$243$	15.5885			1.00000
$244$	3.67423	+	14.2302i	0.235219	+	0.910998i
$245$	2.82843	+	9.48683i	0.180702	+	0.606092i
$246$	−15.0000	−	11.6190i	−0.956365	−	0.740797i
$247$		−	15.4919i		−	0.985728i
$248$	−9.00000	−	3.87298i	−0.571501	−	0.245935i
$249$	10.3923			0.658586
$250$	−9.79796	+	12.6491i	−0.619677	+	0.800000i
$251$			21.9089i			1.38288i	0.722435	+	0.691439i	$0.243023\pi$
$251$			21.9089i			1.38288i	−0.722435	+	0.691439i	$0.756977\pi$
$252$	6.00361	−	14.6955i	0.378192	−	0.925727i
$253$	−6.00000	+	5.47723i	−0.377217	+	0.344350i
$254$	18.3712	−	23.7171i	1.15271	−	1.48814i
$255$		0			0
$256$	8.50000	−	13.5554i	0.531250	−	0.847215i
$257$	−14.1421			−0.882162			−0.441081	−	0.897467i	$-0.645405\pi$
$257$	−14.1421			−0.882162			−0.441081	+	0.897467i	$0.645405\pi$
$258$		0			0
$259$	4.24264	+	3.16228i	0.263625	+	0.196494i
$260$	1.73205	+	6.70820i	0.107417	+	0.416025i
$261$	−20.7846			−1.28654
$262$	15.5885	−	20.1246i	0.963058	−	1.24330i
$263$			8.94427i			0.551527i	0.961225	+	0.275764i	$0.0889307\pi$
$263$			8.94427i			0.551527i	−0.961225	+	0.275764i	$0.911069\pi$
$264$	−15.3528	+	5.31889i	−0.944901	+	0.327355i
$265$		−	13.4164i		−	0.824163i
$266$	6.33975	+	22.7993i	0.388715	+	1.39791i
$267$	−4.89898			−0.299813
$268$	−15.0000	+	3.87298i	−0.916271	+	0.236580i
$269$	−9.89949			−0.603583			−0.301791	−	0.953374i	$-0.597585\pi$
$269$	−9.89949			−0.603583			−0.301791	+	0.953374i	$0.597585\pi$
$270$	6.36396	−	8.21584i	0.387298	−	0.500000i
$271$		−	15.8114i		−	0.960473i	−0.877139	−	0.480237i	$-0.840551\pi$
$271$		−	15.8114i		−	0.960473i	0.877139	−	0.480237i	$-0.159449\pi$
$272$		0			0
$273$	−9.00000	−	6.70820i	−0.544705	−	0.405999i
$274$		0			0
$275$	−7.34847	+	6.70820i	−0.443129	+	0.404520i
$276$	2.12132	+	8.21584i	0.127688	+	0.494535i
$277$		−	5.47723i		−	0.329095i	−0.986369	−	0.164547i	$-0.947384\pi$
$277$		−	5.47723i		−	0.329095i	0.986369	−	0.164547i	$-0.0526163\pi$
$278$	−14.1421	−	10.9545i	−0.848189	−	0.657004i
$279$	10.3923			0.622171
$280$	−5.29423	−	9.16358i	−0.316391	−	0.547628i
$281$	3.46410			0.206651			0.103325	−	0.994648i	$-0.467052\pi$
$281$	3.46410			0.206651			0.103325	+	0.994648i	$0.467052\pi$
$282$	−10.6066	−	8.21584i	−0.631614	−	0.489246i
$283$			25.2982i			1.50382i	0.659264	+	0.751912i	$0.270868\pi$
$283$			25.2982i			1.50382i	−0.659264	+	0.751912i	$0.729132\pi$
$284$	6.12372	+	23.7171i	0.363376	+	1.40735i
$285$			15.4919i			0.917663i
$286$	0.927572	+	11.4516i	0.0548485	+	0.677149i
$287$	12.2474	−	16.4317i	0.722944	−	0.969931i
$288$	−2.59808	+	16.7705i	−0.153093	+	0.988212i
$289$	17.0000			1.00000
$290$	−8.48528	+	10.9545i	−0.498273	+	0.643268i
$291$			23.2379i			1.36223i
$292$	4.89898	+	18.9737i	0.286691	+	1.11035i
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	15.9904	+	6.18932i	0.932578	+	0.360969i
$295$			15.4919i			0.901975i
$296$	−5.19615	−	2.23607i	−0.302020	−	0.129969i
$297$	12.7279	−	11.6190i	0.738549	−	0.674200i
$298$	6.00000	−	7.74597i	0.347571	−	0.448712i
$299$	6.00000			0.346989
$300$	2.59808	+	10.0623i	0.150000	+	0.580948i
$301$		0			0
$302$	11.0227	−	14.2302i	0.634285	−	0.818859i
$303$		0			0
$304$	−12.2474	−	22.1359i	−0.702439	−	1.26958i
$305$	−10.3923			−0.595062
$306$		0			0
$307$		−	25.2982i		−	1.44385i	−0.691974	−	0.721923i	$-0.743259\pi$
$307$		−	25.2982i		−	1.44385i	0.691974	−	0.721923i	$-0.256741\pi$
$308$	−6.05143	−	16.4736i	−0.344812	−	0.938672i
$309$	6.00000			0.341328
$310$	4.24264	−	5.47723i	0.240966	−	0.311086i
$311$			16.4317i			0.931755i	0.884849	+	0.465877i	$0.154261\pi$
$311$			16.4317i			0.931755i	−0.884849	+	0.465877i	$0.845739\pi$
$312$	11.0227	+	4.74342i	0.624038	+	0.268543i
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	15.0000	+	11.6190i	0.846499	+	0.655695i
$315$	9.00000	+	6.70820i	0.507093	+	0.377964i
$316$	2.12132	+	8.21584i	0.119334	+	0.462177i
$317$		−	28.4605i		−	1.59850i	−0.600998	−	0.799250i	$-0.705230\pi$
$317$		−	28.4605i		−	1.59850i	0.600998	−	0.799250i	$-0.294770\pi$
$318$	−18.3712	−	14.2302i	−1.03020	−	0.797993i
$319$	−16.9706	+	15.4919i	−0.950169	+	0.867382i
$320$	7.77817	+	8.21584i	0.434813	+	0.459279i
$321$			7.74597i			0.432338i
$322$	−8.83013	+	2.45537i	−0.492084	+	0.136833i
$323$		0			0
$324$	−4.50000	−	17.4284i	−0.250000	−	0.968246i
$325$	7.34847			0.407620
$326$	−17.3205	−	13.4164i	−0.959294	−	0.743066i
$327$			9.48683i			0.524623i
$328$	−8.66025	+	20.1246i	−0.478183	+	1.11120i
$329$	8.66025	−	11.6190i	0.477455	−	0.640573i
$330$	−0.927572	−	11.4516i	−0.0510612	−	0.630391i
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	−3.00000	−	11.6190i	−0.164646	−	0.637673i
$333$	6.00000			0.328798
$334$	−10.3923	+	13.4164i	−0.568642	+	0.734113i
$335$		−	10.9545i		−	0.598506i
$336$	−18.1631	−	2.47002i	−0.990880	−	0.134751i
$337$		−	10.9545i		−	0.596727i	−0.954452	−	0.298363i	$-0.903559\pi$
$337$		−	10.9545i		−	0.596727i	0.954452	−	0.298363i	$-0.0964408\pi$
$338$	−6.06218	+	7.82624i	−0.329739	+	0.425691i
$339$			32.8634i			1.78489i
$340$		0			0
$341$	8.48528	−	7.74597i	0.459504	−	0.419468i
$342$	21.2132	+	16.4317i	1.14708	+	0.888523i
$343$	−6.36396	+	17.3925i	−0.343622	+	0.939108i
$344$		0			0
$345$	−6.00000			−0.323029
$346$	17.3205	+	13.4164i	0.931156	+	0.721271i
$347$		−	17.8885i		−	0.960307i	−0.877184	−	0.480154i	$-0.840581\pi$
$347$		−	17.8885i		−	0.960307i	0.877184	−	0.480154i	$-0.159419\pi$
$348$	6.00000	+	23.2379i	0.321634	+	1.24568i
$349$	−12.2474			−0.655591			−0.327795	−	0.944749i	$-0.606306\pi$
$349$	−12.2474			−0.655591			−0.327795	+	0.944749i	$0.606306\pi$
$350$	−10.8147	+	3.00721i	−0.578068	+	0.160742i
$351$	−12.7279			−0.679366
$352$	10.3787	+	15.6296i	0.553185	+	0.833058i
$353$	−22.6274			−1.20434			−0.602168	−	0.798369i	$-0.705696\pi$
$353$	−22.6274			−1.20434			−0.602168	+	0.798369i	$0.705696\pi$
$354$	21.2132	+	16.4317i	1.12747	+	0.873334i
$355$	−17.3205			−0.919277
$356$	1.41421	+	5.47723i	0.0749532	+	0.290292i
$357$		0			0
$358$	12.7279	−	16.4317i	0.672692	−	0.868441i
$359$		−	17.8885i		−	0.944121i	−0.881566	−	0.472061i	$-0.843510\pi$
$359$		−	17.8885i		−	0.944121i	0.881566	−	0.472061i	$-0.156490\pi$
$360$	−11.0227	−	4.74342i	−0.580948	−	0.250000i
$361$	−21.0000			−1.10526
$362$	−15.0000	−	11.6190i	−0.788382	−	0.610678i
$363$	1.73205	−	18.9737i	0.0909091	−	0.995859i
$364$	−4.90192	+	11.9988i	−0.256931	+	0.628908i
$365$	−13.8564			−0.725277
$366$	−11.0227	+	14.2302i	−0.576166	+	0.743827i
$367$	−17.3205			−0.904123			−0.452062	−	0.891987i	$-0.649311\pi$
$367$	−17.3205			−0.904123			−0.452062	+	0.891987i	$0.649311\pi$
$368$	8.57321	−	4.74342i	0.446910	−	0.247268i
$369$		−	23.2379i		−	1.20972i
$370$	2.44949	−	3.16228i	0.127343	−	0.164399i
$371$	15.0000	−	20.1246i	0.778761	−	1.04482i
$372$	−3.00000	−	11.6190i	−0.155543	−	0.602414i
$373$			5.47723i			0.283600i	0.989895	+	0.141800i	$0.0452890\pi$
$373$			5.47723i			0.283600i	−0.989895	+	0.141800i	$0.954711\pi$
$374$		0			0
$375$	−19.5959			−1.01193
$376$	−6.12372	+	14.2302i	−0.315807	+	0.733869i
$377$	16.9706			0.874028
$378$	18.7315	−	5.20863i	0.963446	−	0.267903i
$379$			15.4919i			0.795767i	0.917436	+	0.397884i	$0.130255\pi$
$379$			15.4919i			0.795767i	−0.917436	+	0.397884i	$0.869745\pi$
$380$	17.3205	−	4.47214i	0.888523	−	0.229416i
$381$	36.7423			1.88237
$382$	−10.6066	+	13.6931i	−0.542681	+	0.700598i
$383$			16.4317i			0.839619i	0.907612	+	0.419810i	$0.137903\pi$
$383$			16.4317i			0.839619i	−0.907612	+	0.419810i	$0.862097\pi$
$384$	19.5000	−	1.93649i	0.995105	−	0.0988212i
$385$	12.3485	−	1.23098i	0.629336	−	0.0627365i
$386$		0			0
$387$		0			0
$388$	25.9808	−	6.70820i	1.31897	−	0.340557i
$389$			28.4605i			1.44300i	0.692412	+	0.721502i	$0.256548\pi$
$389$			28.4605i			1.44300i	−0.692412	+	0.721502i	$0.743452\pi$
$390$	−5.19615	+	6.70820i	−0.263117	+	0.339683i
$391$		0			0
$392$	2.30385	−	19.6645i	0.116362	−	0.993207i
$393$	31.1769			1.57267
$394$		0			0
$395$	−6.00000			−0.301893
$396$	−16.6646	−	10.8761i	−0.837428	−	0.546547i
$397$		−	13.4164i		−	0.673350i	−0.941621	−	0.336675i	$-0.890698\pi$
$397$		−	13.4164i		−	0.673350i	0.941621	−	0.336675i	$-0.109302\pi$
$398$	−21.0000	+	27.1109i	−1.05263	+	1.35895i
$399$	−17.3205	+	23.2379i	−0.867110	+	1.16335i
$400$	10.5000	−	5.80948i	0.525000	−	0.290474i
$401$		−	18.9737i		−	0.947500i	−0.880659	−	0.473750i	$-0.842900\pi$
$401$		−	18.9737i		−	0.947500i	0.880659	−	0.473750i	$-0.157100\pi$
$402$	−15.0000	−	11.6190i	−0.748132	−	0.579501i
$403$	−8.48528			−0.422682
$404$		0			0
$405$	12.7279			0.632456
$406$	−24.9754	+	6.94484i	−1.23951	+	0.344667i
$407$	4.89898	−	4.47214i	0.242833	−	0.221676i
$408$		0			0
$409$		0			0			−	1.00000i	$-0.5\pi$
$409$		0			0				1.00000i	$0.5\pi$
$410$	−12.2474	−	9.48683i	−0.604858	−	0.468521i
$411$		0			0
$412$	−1.73205	−	6.70820i	−0.0853320	−	0.330489i
$413$	−17.3205	+	23.2379i	−0.852286	+	1.14346i
$414$	−6.36396	+	8.21584i	−0.312772	+	0.403786i
$415$	8.48528			0.416526
$416$	2.12132	−	13.6931i	0.104006	−	0.671358i
$417$		−	21.9089i		−	1.07288i
$418$	29.5680	−	2.39498i	1.44622	−	0.117142i
$419$		−	21.9089i		−	1.07032i	−0.844751	−	0.535160i	$-0.820251\pi$
$419$		−	21.9089i		−	1.07032i	0.844751	−	0.535160i	$-0.179749\pi$
$420$	4.90192	−	11.9988i	0.239189	−	0.585481i
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	7.34847	−	9.48683i	0.357718	−	0.461812i
$423$		−	16.4317i		−	0.798935i
$424$	−10.6066	+	24.6475i	−0.515102	+	1.19699i
$425$		0			0
$426$	−18.3712	+	23.7171i	−0.890086	+	1.14910i
$427$	−15.5885	−	11.6190i	−0.754378	−	0.562280i
$428$	8.66025	−	2.23607i	0.418609	−	0.108084i
$429$	−10.3923	+	9.48683i	−0.501745	+	0.458029i
$430$		0			0
$431$			17.8885i			0.861661i	0.902433	+	0.430830i	$0.141779\pi$
$431$			17.8885i			0.861661i	−0.902433	+	0.430830i	$0.858221\pi$
$432$	−18.1865	+	10.0623i	−0.875000	+	0.484123i
$433$		−	26.8328i		−	1.28950i	−0.764392	−	0.644751i	$-0.776961\pi$
$433$		−	26.8328i		−	1.28950i	0.764392	−	0.644751i	$-0.223039\pi$
$434$	12.4877	−	3.47242i	0.599428	−	0.166682i
$435$	−16.9706			−0.813676
$436$	10.6066	−	2.73861i	0.507964	−	0.131156i
$437$		−	15.4919i		−	0.741080i
$438$	−14.6969	+	18.9737i	−0.702247	+	0.906597i
$439$		−	34.7851i		−	1.66020i	−0.557615	−	0.830100i	$-0.688283\pi$
$439$		−	34.7851i		−	1.66020i	0.557615	−	0.830100i	$-0.311717\pi$
$440$	−12.5355	+	4.34286i	−0.597608	+	0.207037i
$441$	6.00000	+	20.1246i	0.285714	+	0.958315i
$442$		0			0
$443$	39.1918			1.86206			0.931030	−	0.364942i	$-0.118911\pi$
$443$	39.1918			1.86206			0.931030	+	0.364942i	$0.118911\pi$
$444$	−1.73205	−	6.70820i	−0.0821995	−	0.318357i
$445$	−4.00000			−0.189618
$446$	15.0000	−	19.3649i	0.710271	−	0.916955i
$447$	12.0000			0.567581
$448$	2.48168	+	21.0200i	0.117248	+	0.993103i
$449$		−	37.9473i		−	1.79085i	−0.445217	−	0.895423i	$-0.646873\pi$
$449$		−	37.9473i		−	1.79085i	0.445217	−	0.895423i	$-0.353127\pi$
$450$	−7.79423	+	10.0623i	−0.367423	+	0.474342i
$451$	−17.3205	−	18.9737i	−0.815591	−	0.893435i
$452$	36.7423	−	9.48683i	1.72821	−	0.446223i
$453$	22.0454			1.03578
$454$	−10.3923	+	13.4164i	−0.487735	+	0.629663i
$455$	−7.34847	−	5.47723i	−0.344502	−	0.256776i
$456$	12.2474	−	28.4605i	0.573539	−	1.33278i
$457$		−	10.9545i		−	0.512428i	−0.966620	−	0.256214i	$-0.917525\pi$
$457$		−	10.9545i		−	0.512428i	0.966620	−	0.256214i	$-0.0824751\pi$
$458$	−15.0000	−	11.6190i	−0.700904	−	0.542918i
$459$		0			0
$460$	1.73205	+	6.70820i	0.0807573	+	0.312772i
$461$		−	30.9839i		−	1.44306i	−0.692382	−	0.721531i	$-0.743439\pi$
$461$		−	30.9839i		−	1.44306i	0.692382	−	0.721531i	$-0.256561\pi$
$462$	11.4119	−	18.2145i	0.530932	−	0.847415i
$463$			7.74597i			0.359986i	0.983668	+	0.179993i	$0.0576074\pi$
$463$			7.74597i			0.359986i	−0.983668	+	0.179993i	$0.942393\pi$
$464$	24.2487	−	13.4164i	1.12572	−	0.622841i
$465$	8.48528			0.393496
$466$	18.0000	−	23.2379i	0.833834	−	1.07647i
$467$		−	10.9545i		−	0.506912i	−0.967347	−	0.253456i	$-0.918433\pi$
$467$		−	10.9545i		−	0.506912i	0.967347	−	0.253456i	$-0.0815672\pi$
$468$	3.67423	+	14.2302i	0.169842	+	0.657794i
$469$	12.2474	−	16.4317i	0.565535	−	0.758744i
$470$	−8.66025	−	6.70820i	−0.399468	−	0.309426i
$471$			23.2379i			1.07075i
$472$	12.2474	−	28.4605i	0.563735	−	1.31000i
$473$		0			0
$474$	−6.36396	+	8.21584i	−0.292306	+	0.377366i
$475$		−	18.9737i		−	0.870572i
$476$		0			0
$477$		−	28.4605i		−	1.30312i
$478$	10.0000	+	7.74597i	0.457389	+	0.354292i
$479$	−36.0000			−1.64488			−0.822441	−	0.568850i	$-0.807388\pi$
$479$	−36.0000			−1.64488			−0.822441	+	0.568850i	$0.807388\pi$
$480$	−2.12132	+	13.6931i	−0.0968246	+	0.625000i
$481$	−4.89898			−0.223374
$482$	21.2132	−	27.3861i	0.966235	−	1.24740i
$483$	−9.00000	−	6.70820i	−0.409514	−	0.305234i
$484$	−21.7132	+	3.54073i	−0.986964	+	0.160942i
$485$			18.9737i			0.861550i
$486$	13.5000	−	17.4284i	0.612372	−	0.790569i
$487$		−	23.2379i		−	1.05301i	−0.850172	−	0.526505i	$-0.823502\pi$
$487$		−	23.2379i		−	1.05301i	0.850172	−	0.526505i	$-0.176498\pi$
$488$	19.0919	+	8.21584i	0.864249	+	0.371914i
$489$		−	26.8328i		−	1.21342i
$490$	13.0561	+	5.05356i	0.589814	+	0.228297i
$491$		−	4.47214i		−	0.201825i	−0.994895	−	0.100912i	$-0.967824\pi$
$491$		−	4.47214i		−	0.201825i	0.994895	−	0.100912i	$-0.0321762\pi$
$492$	−25.9808	+	6.70820i	−1.17130	+	0.302429i
$493$		0			0
$494$	−17.3205	−	13.4164i	−0.779287	−	0.603633i
$495$	10.3923	−	9.48683i	0.467099	−	0.426401i
$496$	−12.1244	+	6.70820i	−0.544400	+	0.301207i
$497$	−25.9808	−	19.3649i	−1.16540	−	0.868635i
$498$	9.00000	−	11.6190i	0.403300	−	0.520658i
$499$			30.9839i			1.38703i	0.720443	+	0.693514i	$0.243939\pi$
$499$			30.9839i			1.38703i	−0.720443	+	0.693514i	$0.756061\pi$
$500$	5.65685	+	21.9089i	0.252982	+	0.979796i
$501$	−20.7846			−0.928588
$502$	24.4949	+	18.9737i	1.09326	+	0.846836i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$	−11.2308	−	19.4389i	−0.500258	−	0.865877i
$505$		0			0
$506$	0.927572	+	11.4516i	0.0412356	+	0.509087i
$507$	−12.1244			−0.538462
$508$	−10.6066	−	41.0792i	−0.470592	−	1.82259i
$509$	24.0416			1.06563			0.532813	−	0.846233i	$-0.321135\pi$
$509$	24.0416			1.06563			0.532813	+	0.846233i	$0.321135\pi$
$510$		0			0
$511$	−20.7846	−	15.4919i	−0.919457	−	0.685323i
$512$	−7.79423	−	21.2426i	−0.344459	−	0.938801i
$513$			32.8634i			1.45095i
$514$	−12.2474	+	15.8114i	−0.540212	+	0.697410i
$515$	4.89898			0.215875
$516$		0			0
$517$	−12.2474	−	13.4164i	−0.538642	−	0.590053i
$518$	7.20977	−	2.00480i	0.316779	−	0.0880860i
$519$			26.8328i			1.17783i
$520$	9.00000	+	3.87298i	0.394676	+	0.169842i
$521$	19.7990			0.867409			0.433705	−	0.901055i	$-0.357206\pi$
$521$	19.7990			0.867409			0.433705	+	0.901055i	$0.357206\pi$
$522$	−18.0000	+	23.2379i	−0.787839	+	1.01710i
$523$			6.32456i			0.276553i	0.990394	+	0.138277i	$0.0441563\pi$
$523$			6.32456i			0.276553i	−0.990394	+	0.138277i	$0.955844\pi$
$524$	−9.00000	−	34.8569i	−0.393167	−	1.52273i
$525$	−11.0227	−	8.21584i	−0.481070	−	0.358569i
$526$	10.0000	+	7.74597i	0.436021	+	0.337740i
$527$		0			0
$528$	−7.34924	+	21.7713i	−0.319835	+	0.947473i
$529$	−17.0000			−0.739130
$530$	−15.0000	−	11.6190i	−0.651558	−	0.504695i
$531$			32.8634i			1.42615i
$532$	30.9808	+	12.6567i	1.34319	+	0.548738i
$533$			18.9737i			0.821841i
$534$	−4.24264	+	5.47723i	−0.183597	+	0.237023i
$535$			6.32456i			0.273434i
$536$	−8.66025	+	20.1246i	−0.374066	+	0.869251i
$537$	25.4558			1.09850
$538$	−8.57321	+	11.0680i	−0.369618	+	0.477174i
$539$	19.8990	+	11.9595i	0.857110	+	0.515134i
$540$	−3.67423	−	14.2302i	−0.158114	−	0.612372i
$541$		−	38.3406i		−	1.64839i	−0.566306	−	0.824195i	$-0.691628\pi$
$541$		−	38.3406i		−	1.64839i	0.566306	−	0.824195i	$-0.308372\pi$
$542$	−17.6777	−	13.6931i	−0.759321	−	0.588167i
$543$		−	23.2379i		−	0.997234i
$544$		0			0
$545$			7.74597i			0.331801i
$546$	−15.2942	+	4.25283i	−0.654533	+	0.182004i
$547$	16.9706			0.725609			0.362804	−	0.931865i	$-0.381819\pi$
$547$	16.9706			0.725609			0.362804	+	0.931865i	$0.381819\pi$
$548$		0			0
$549$	−22.0454			−0.940875
$550$	1.13604	+	14.0253i	0.0484409	+	0.598041i
$551$		−	43.8178i		−	1.86670i
$552$	11.0227	+	4.74342i	0.469157	+	0.201893i
$553$	−9.00000	−	6.70820i	−0.382719	−	0.285262i
$554$	−6.12372	−	4.74342i	−0.260172	−	0.201528i
$555$	4.89898			0.207950
$556$	−24.4949	+	6.32456i	−1.03882	+	0.268221i
$557$	6.92820			0.293557			0.146779	−	0.989169i	$-0.453109\pi$
$557$	6.92820			0.293557			0.146779	+	0.989169i	$0.453109\pi$
$558$	9.00000	−	11.6190i	0.381000	−	0.491869i
$559$		0			0
$560$	−14.8301	−	2.01676i	−0.626687	−	0.0852238i
$561$		0			0
$562$	3.00000	−	3.87298i	0.126547	−	0.163372i
$563$	36.0000			1.51722			0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000			1.51722			0.758610	+	0.651546i	$0.225879\pi$
$564$	−18.3712	+	4.74342i	−0.773566	+	0.199734i
$565$			26.8328i			1.12887i
$566$	28.2843	+	21.9089i	1.18888	+	0.920900i
$567$	19.0919	+	14.2302i	0.801784	+	0.597614i
$568$	31.8198	+	13.6931i	1.33513	+	0.574548i
$569$	10.3923			0.435668			0.217834	−	0.975986i	$-0.430101\pi$
$569$	10.3923			0.435668			0.217834	+	0.975986i	$0.430101\pi$
$570$	17.3205	+	13.4164i	0.725476	+	0.561951i
$571$	−8.48528			−0.355098			−0.177549	−	0.984112i	$-0.556817\pi$
$571$	−8.48528			−0.355098			−0.177549	+	0.984112i	$0.556817\pi$
$572$	13.6066	+	8.88034i	0.568921	+	0.371306i
$573$	−21.2132			−0.886194
$574$	−7.76457	−	27.9233i	−0.324087	−	1.16550i
$575$	7.34847			0.306452
$576$	16.5000	+	17.4284i	0.687500	+	0.726184i
$577$			40.2492i			1.67560i	0.545979	+	0.837799i	$0.316158\pi$
$577$			40.2492i			1.67560i	−0.545979	+	0.837799i	$0.683842\pi$
$578$	14.7224	−	19.0066i	0.612372	−	0.790569i
$579$		0			0
$580$	4.89898	+	18.9737i	0.203419	+	0.787839i
$581$	12.7279	+	9.48683i	0.528043	+	0.393580i
$582$	25.9808	+	20.1246i	1.07694	+	0.834192i
$583$	−21.2132	−	23.2379i	−0.878561	−	0.962415i
$584$	25.4558	+	10.9545i	1.05337	+	0.453298i
$585$	−10.3923			−0.429669
$586$		0			0
$587$			10.9545i			0.452139i	0.974111	+	0.226069i	$0.0725876\pi$
$587$			10.9545i			0.452139i	−0.974111	+	0.226069i	$0.927412\pi$
$588$	20.7679	−	12.5177i	0.856456	−	0.516220i
$589$			21.9089i			0.902741i
$590$	17.3205	+	13.4164i	0.713074	+	0.552345i
$591$		0			0
$592$	−7.00000	+	3.87298i	−0.287698	+	0.159179i
$593$			30.9839i			1.27235i	0.771543	+	0.636177i	$0.219485\pi$
$593$			30.9839i			1.27235i	−0.771543	+	0.636177i	$0.780515\pi$
$594$	−1.96768	−	24.2926i	−0.0807348	−	0.996736i
$595$		0			0
$596$	−3.46410	−	13.4164i	−0.141895	−	0.549557i
$597$	−42.0000			−1.71895
$598$	5.19615	−	6.70820i	0.212486	−	0.274319i
$599$	−26.9444			−1.10092			−0.550459	−	0.834862i	$-0.685547\pi$
$599$	−26.9444			−1.10092			−0.550459	+	0.834862i	$0.685547\pi$
$600$	13.5000	+	5.80948i	0.551135	+	0.237171i
$601$	−19.5959			−0.799334			−0.399667	−	0.916660i	$-0.630874\pi$
$601$	−19.5959			−0.799334			−0.399667	+	0.916660i	$0.630874\pi$
$602$		0			0
$603$		−	23.2379i		−	0.946320i
$604$	−6.36396	−	24.6475i	−0.258946	−	1.00289i
$605$	1.41421	−	15.4919i	0.0574960	−	0.629837i
$606$		0			0
$607$			3.16228i			0.128353i	0.997939	+	0.0641764i	$0.0204420\pi$
$607$			3.16228i			0.128353i	−0.997939	+	0.0641764i	$0.979558\pi$
$608$	−35.3553	−	5.47723i	−1.43385	−	0.222131i
$609$	−25.4558	−	18.9737i	−1.03152	−	0.768852i
$610$	−9.00000	+	11.6190i	−0.364399	+	0.470438i
$611$			13.4164i			0.542770i
$612$		0			0
$613$			27.3861i			1.10612i	0.833143	+	0.553058i	$0.186539\pi$
$613$			27.3861i			1.10612i	−0.833143	+	0.553058i	$0.813461\pi$
$614$	−28.2843	−	21.9089i	−1.14146	−	0.884171i
$615$		−	18.9737i		−	0.765092i
$616$	−23.6588	−	7.50087i	−0.953239	−	0.302219i
$617$			18.9737i			0.763851i	0.924193	+	0.381926i	$0.124739\pi$
$617$			18.9737i			0.763851i	−0.924193	+	0.381926i	$0.875261\pi$
$618$	5.19615	−	6.70820i	0.209020	−	0.269844i
$619$	27.7128			1.11387			0.556936	−	0.830555i	$-0.311977\pi$
$619$	27.7128			1.11387			0.556936	+	0.830555i	$0.311977\pi$
$620$	−2.44949	−	9.48683i	−0.0983739	−	0.381000i
$621$	−12.7279			−0.510754
$622$	18.3712	+	14.2302i	0.736617	+	0.570581i
$623$	−6.00000	−	4.47214i	−0.240385	−	0.179172i
$624$	14.8492	−	8.21584i	0.594445	−	0.328897i
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	24.4949	+	26.8328i	0.978232	+	1.07160i
$628$	25.9808	−	6.70820i	1.03675	−	0.267686i
$629$		0			0
$630$	15.2942	−	4.25283i	0.609337	−	0.169437i
$631$		−	23.2379i		−	0.925086i	−0.886597	−	0.462543i	$-0.846937\pi$
$631$		−	23.2379i		−	0.925086i	0.886597	−	0.462543i	$-0.153063\pi$
$632$	11.0227	+	4.74342i	0.438460	+	0.188683i
$633$	14.6969			0.584151
$634$	−31.8198	−	24.6475i	−1.26373	−	0.978878i
$635$	30.0000			1.19051
$636$	−31.8198	+	8.21584i	−1.26174	+	0.325779i
$637$	−4.89898	−	16.4317i	−0.194105	−	0.651047i
$638$	2.62357	+	32.3901i	0.103868	+	1.28234i
$639$	−36.7423			−1.45350
$640$	15.9217	−	1.58114i	0.629360	−	0.0625000i
$641$		−	18.9737i		−	0.749415i	−0.927143	−	0.374707i	$-0.877743\pi$
$641$		−	18.9737i		−	0.749415i	0.927143	−	0.374707i	$-0.122257\pi$
$642$	8.66025	+	6.70820i	0.341793	+	0.264752i
$643$	34.6410			1.36611			0.683054	−	0.730368i	$-0.260651\pi$
$643$	34.6410			1.36611			0.683054	+	0.730368i	$0.260651\pi$
$644$	−4.90192	+	11.9988i	−0.193163	+	0.472819i
$645$		0			0
$646$		0			0
$647$			5.47723i			0.215332i	0.994187	+	0.107666i	$0.0343377\pi$
$647$			5.47723i			0.215332i	−0.994187	+	0.107666i	$0.965662\pi$
$648$	−23.3827	−	10.0623i	−0.918559	−	0.395285i
$649$	24.4949	+	26.8328i	0.961509	+	1.05328i
$650$	6.36396	−	8.21584i	0.249615	−	0.322252i
$651$	12.7279	+	9.48683i	0.498847	+	0.371818i
$652$	−30.0000	+	7.74597i	−1.17489	+	0.303355i
$653$		−	9.48683i		−	0.371248i	−0.982621	−	0.185624i	$-0.940569\pi$
$653$		−	9.48683i		−	0.371248i	0.982621	−	0.185624i	$-0.0594307\pi$
$654$	10.6066	+	8.21584i	0.414751	+	0.321265i
$655$	25.4558			0.994642
$656$	15.0000	+	27.1109i	0.585652	+	1.05850i
$657$	−29.3939			−1.14676
$658$	−5.49038	−	19.7448i	−0.214037	−	0.769731i
$659$		−	49.1935i		−	1.91631i	−0.286256	−	0.958153i	$-0.592411\pi$
$659$		−	49.1935i		−	1.91631i	0.286256	−	0.958153i	$-0.407589\pi$
$660$	−13.6066	−	8.88034i	−0.529636	−	0.345667i
$661$		−	13.4164i		−	0.521838i	−0.965361	−	0.260919i	$-0.915974\pi$
$661$		−	13.4164i		−	0.521838i	0.965361	−	0.260919i	$-0.0840255\pi$
$662$		0			0
$663$		0			0
$664$	−15.5885	−	6.70820i	−0.604949	−	0.260329i
$665$	−14.1421	+	18.9737i	−0.548408	+	0.735767i
$666$	5.19615	−	6.70820i	0.201347	−	0.259938i
$667$	16.9706			0.657103
$668$	6.00000	+	23.2379i	0.232147	+	0.899101i
$669$	30.0000			1.15987
$670$	−12.2474	−	9.48683i	−0.473160	−	0.366508i
$671$	−18.0000	+	16.4317i	−0.694882	+	0.634338i
$672$	−18.4913	+	18.1679i	−0.713317	+	0.700841i
$673$		−	32.8634i		−	1.26679i	−0.773829	−	0.633395i	$-0.781661\pi$
$673$		−	32.8634i		−	1.26679i	0.773829	−	0.633395i	$-0.218339\pi$
$674$	−12.2474	−	9.48683i	−0.471754	−	0.365419i
$675$	−15.5885			−0.600000
$676$	3.50000	+	13.5554i	0.134615	+	0.521363i
$677$		−	30.9839i		−	1.19081i	−0.803427	−	0.595403i	$-0.796992\pi$
$677$		−	30.9839i		−	1.19081i	0.803427	−	0.595403i	$-0.203008\pi$
$678$	36.7423	+	28.4605i	1.41108	+	1.09302i
$679$	−21.2132	+	28.4605i	−0.814088	+	1.09221i
$680$		0			0
$681$	−20.7846			−0.796468
$682$	−1.31178	−	16.1950i	−0.0502308	−	0.620140i
$683$	−9.79796			−0.374908			−0.187454	−	0.982273i	$-0.560024\pi$
$683$	−9.79796			−0.374908			−0.187454	+	0.982273i	$0.560024\pi$
$684$	36.7423	−	9.48683i	1.40488	−	0.362738i
$685$		0			0
$686$	13.9341	+	22.1775i	0.532006	+	0.846741i
$687$		−	23.2379i		−	0.886581i
$688$		0			0
$689$			23.2379i			0.885293i
$690$	−5.19615	+	6.70820i	−0.197814	+	0.255377i
$691$	20.7846			0.790684			0.395342	−	0.918534i	$-0.370626\pi$
$691$	20.7846			0.790684			0.395342	+	0.918534i	$0.370626\pi$
$692$	30.0000	−	7.74597i	1.14043	−	0.294457i
$693$	26.1951	−	2.61130i	0.995068	−	0.0991951i
$694$	−20.0000	−	15.4919i	−0.759190	−	0.588066i
$695$		−	17.8885i		−	0.678551i
$696$	31.1769	+	13.4164i	1.18176	+	0.508548i
$697$		0			0
$698$	−10.6066	+	13.6931i	−0.401466	+	0.518290i
$699$	36.0000			1.36165
$700$	−6.00361	+	14.6955i	−0.226915	+	0.555436i
$701$	20.7846			0.785024			0.392512	−	0.919747i	$-0.371606\pi$
$701$	20.7846			0.785024			0.392512	+	0.919747i	$0.371606\pi$
$702$	−11.0227	+	14.2302i	−0.416025	+	0.537086i
$703$			12.6491i			0.477070i
$704$	26.4626	+	1.93188i	0.997346	+	0.0728103i
$705$		−	13.4164i		−	0.505291i
$706$	−19.5959	+	25.2982i	−0.737502	+	0.952111i
$707$		0			0
$708$	36.7423	−	9.48683i	1.38086	−	0.356537i
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$	−15.0000	+	19.3649i	−0.562940	+	0.726752i
$711$	−12.7279			−0.477334
$712$	7.34847	+	3.16228i	0.275396	+	0.118511i
$713$	−8.48528			−0.317776
$714$		0			0
$715$	−8.48528	+	7.74597i	−0.317332	+	0.289683i
$716$	−7.34847	−	28.4605i	−0.274625	−	1.06362i
$717$			15.4919i			0.578557i
$718$	−20.0000	−	15.4919i	−0.746393	−	0.578154i
$719$		−	5.47723i		−	0.204266i	−0.994771	−	0.102133i	$-0.967433\pi$
$719$		−	5.47723i		−	0.204266i	0.994771	−	0.102133i	$-0.0325667\pi$
$720$	−14.8492	+	8.21584i	−0.553399	+	0.306186i
$721$	7.34847	+	5.47723i	0.273671	+	0.203983i
$722$	−18.1865	+	23.4787i	−0.676833	+	0.873787i
$723$	42.4264			1.57786
$724$	−25.9808	+	6.70820i	−0.965567	+	0.249308i
$725$	20.7846			0.771921
$726$	−19.7132	−	18.3682i	−0.731626	−	0.681707i
$727$	10.3923			0.385429			0.192715	−	0.981255i	$-0.438271\pi$
$727$	10.3923			0.385429			0.192715	+	0.981255i	$0.438271\pi$
$728$	9.16987	+	15.8718i	0.339858	+	0.588247i
$729$	27.0000			1.00000
$730$	−12.0000	+	15.4919i	−0.444140	+	0.573382i
$731$		0			0
$732$	6.36396	+	24.6475i	0.235219	+	0.910998i
$733$	22.0454			0.814266			0.407133	−	0.913369i	$-0.366529\pi$
$733$	22.0454			0.814266			0.407133	+	0.913369i	$0.366529\pi$
$734$	−15.0000	+	19.3649i	−0.553660	+	0.714772i
$735$	4.89898	+	16.4317i	0.180702	+	0.606092i
$736$	2.12132	−	13.6931i	0.0781929	−	0.504733i
$737$	−17.3205	−	18.9737i	−0.638009	−	0.698904i
$738$	−25.9808	−	20.1246i	−0.956365	−	0.740797i
$739$	25.4558			0.936408			0.468204	−	0.883620i	$-0.344901\pi$
$739$	25.4558			0.936408			0.468204	+	0.883620i	$0.344901\pi$
$740$	−1.41421	−	5.47723i	−0.0519875	−	0.201347i
$741$		−	26.8328i		−	0.985728i
$742$	−9.50962	−	34.1989i	−0.349109	−	1.25548i
$743$			44.7214i			1.64067i	0.571885	+	0.820334i	$0.306212\pi$
$743$			44.7214i			1.64067i	−0.571885	+	0.820334i	$0.693788\pi$
$744$	−15.5885	−	6.70820i	−0.571501	−	0.245935i
$745$	9.79796			0.358969
$746$	6.12372	+	4.74342i	0.224205	+	0.173669i
$747$	18.0000			0.658586
$748$		0			0
$749$	−7.07107	+	9.48683i	−0.258371	+	0.346641i
$750$	−16.9706	+	21.9089i	−0.619677	+	0.800000i
$751$			38.7298i			1.41327i	0.707577	+	0.706636i	$0.249788\pi$
$751$			38.7298i			1.41327i	−0.707577	+	0.706636i	$0.750212\pi$
$752$	10.6066	+	19.1703i	0.386783	+	0.699069i
$753$			37.9473i			1.38288i
$754$	14.6969	−	18.9737i	0.535231	−	0.690980i
$755$	18.0000			0.655087
$756$	10.3986	−	25.4533i	0.378192	−	0.925727i
$757$	22.0000			0.799604			0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000			0.799604			0.399802	+	0.916602i	$0.369079\pi$
$758$	17.3205	+	13.4164i	0.629109	+	0.487306i
$759$	−10.3923	+	9.48683i	−0.377217	+	0.344350i
$760$	10.0000	−	23.2379i	0.362738	−	0.842927i
$761$		0			0		1.00000			$0$
$761$		0			0		−1.00000			$\pi$
$762$	31.8198	−	41.0792i	1.15271	−	1.48814i
$763$	−8.66025	+	11.6190i	−0.313522	+	0.420634i
$764$	6.12372	+	23.7171i	0.221549	+	0.858054i
$765$		0			0
$766$	18.3712	+	14.2302i	0.663777	+	0.514160i
$767$		−	26.8328i		−	0.968877i
$768$	14.7224	−	23.4787i	0.531250	−	0.847215i
$769$	−24.4949			−0.883309			−0.441654	−	0.897185i	$-0.645608\pi$
$769$	−24.4949			−0.883309			−0.441654	+	0.897185i	$0.645608\pi$
$770$	9.31781	−	14.8721i	0.335791	−	0.535952i
$771$	−24.4949			−0.882162
$772$		0			0
$773$	7.07107			0.254329			0.127164	−	0.991882i	$-0.459412\pi$
$773$	7.07107			0.254329			0.127164	+	0.991882i	$0.459412\pi$
$774$		0			0
$775$	−10.3923			−0.373303
$776$	15.0000	−	34.8569i	0.538469	−	1.25129i
$777$	7.34847	+	5.47723i	0.263625	+	0.196494i
$778$	31.8198	+	24.6475i	1.14080	+	0.883656i
$779$	48.9898			1.75524
$780$	3.00000	+	11.6190i	0.107417	+	0.416025i
$781$	−30.0000	+	27.3861i	−1.07348	+	0.979953i
$782$		0			0
$783$	−36.0000			−1.28654
$784$	−19.9904	−	19.6057i	−0.713942	−	0.700205i
$785$			18.9737i			0.677199i
$786$	27.0000	−	34.8569i	0.963058	−	1.24330i
$787$			31.6228i			1.12723i	0.826038	+	0.563615i	$0.190590\pi$
$787$			31.6228i			1.12723i	−0.826038	+	0.563615i	$0.809410\pi$
$788$		0			0
$789$			15.4919i			0.551527i
$790$	−5.19615	+	6.70820i	−0.184871	+	0.238667i
$791$	−30.0000	+	40.2492i	−1.06668	+	1.43110i
$792$	−26.5919	+	9.21259i	−0.944901	+	0.327355i
$793$	18.0000			0.639199
$794$	−15.0000	−	11.6190i	−0.532330	−	0.412341i
$795$		−	23.2379i		−	0.824163i
$796$	12.1244	+	46.9574i	0.429736	+	1.66436i
$797$	−49.4975			−1.75329			−0.876645	−	0.481137i	$-0.840224\pi$
$797$	−49.4975			−1.75329			−0.876645	+	0.481137i	$0.840224\pi$
$798$	10.9808	+	39.4895i	0.388715	+	1.39791i
$799$		0			0
$800$	2.59808	−	16.7705i	0.0918559	−	0.592927i
$801$	−8.48528			−0.299813
$802$	−21.2132	−	16.4317i	−0.749064	−	0.580223i
$803$	−24.0000	+	21.9089i	−0.846942	+	0.773148i
$804$	−25.9808	+	6.70820i	−0.916271	+	0.236580i
$805$	−7.34847	−	5.47723i	−0.259000	−	0.193047i
$806$	−7.34847	+	9.48683i	−0.258839	+	0.334159i
$807$	−17.1464			−0.603583
$808$		0			0
$809$	6.92820			0.243583			0.121791	−	0.992556i	$-0.461136\pi$
$809$	6.92820			0.243583			0.121791	+	0.992556i	$0.461136\pi$
$810$	11.0227	−	14.2302i	0.387298	−	0.500000i
$811$		−	6.32456i		−	0.222085i	−0.993816	−	0.111043i	$-0.964581\pi$
$811$		−	6.32456i		−	0.222085i	0.993816	−	0.111043i	$-0.0354190\pi$
$812$	−13.8647	+	33.9377i	−0.486557	+	1.19098i
$813$		−	27.3861i		−	0.960473i
$814$	−0.757359	−	9.35021i	−0.0265454	−	0.327725i
$815$		−	21.9089i		−	0.767435i
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−15.5885	−	11.6190i	−0.544705	−	0.405999i
$820$	−21.2132	+	5.47723i	−0.740797	+	0.191273i
$821$	48.4974			1.69257			0.846286	−	0.532729i	$-0.178834\pi$
$821$	48.4974			1.69257			0.846286	+	0.532729i	$0.178834\pi$
$822$		0			0
$823$			38.7298i			1.35004i	0.737801	+	0.675019i	$0.235864\pi$
$823$			38.7298i			1.35004i	−0.737801	+	0.675019i	$0.764136\pi$
$824$	−9.00000	−	3.87298i	−0.313530	−	0.134922i
$825$	−12.7279	+	11.6190i	−0.443129	+	0.404520i
$826$	10.9808	+	39.4895i	0.382070	+	1.37402i
$827$		−	17.8885i		−	0.622046i	−0.950402	−	0.311023i	$-0.899328\pi$
$827$		−	17.8885i		−	0.622046i	0.950402	−	0.311023i	$-0.100672\pi$
$828$	3.67423	+	14.2302i	0.127688	+	0.494535i
$829$			13.4164i			0.465971i	0.972480	+	0.232986i	$0.0748495\pi$
$829$			13.4164i			0.465971i	−0.972480	+	0.232986i	$0.925151\pi$
$830$	7.34847	−	9.48683i	0.255069	−	0.329293i
$831$		−	9.48683i		−	0.329095i
$832$	−13.4722	−	14.2302i	−0.467064	−	0.493345i
$833$		0			0
$834$	−24.4949	−	18.9737i	−0.848189	−	0.657004i
$835$	−16.9706			−0.587291
$836$	22.9289	−	35.1321i	0.793014	−	1.21507i
$837$	18.0000			0.622171
$838$	−24.4949	−	18.9737i	−0.846162	−	0.655434i
$839$		−	38.3406i		−	1.32366i	−0.749652	−	0.661832i	$-0.769779\pi$
$839$		−	38.3406i		−	1.32366i	0.749652	−	0.661832i	$-0.230221\pi$
$840$	−9.16987	−	15.8718i	−0.316391	−	0.547628i
$841$	19.0000			0.655172
$842$	−8.66025	+	11.1803i	−0.298452	+	0.385300i
$843$	6.00000			0.206651
$844$	−4.24264	−	16.4317i	−0.146038	−	0.565602i
$845$	−9.89949			−0.340553
$846$	−18.3712	−	14.2302i	−0.631614	−	0.489246i
$847$	19.4418	−	21.6568i	0.668029	−	0.744135i
$848$	18.3712	+	33.2039i	0.630869	+	1.14023i
$849$			43.8178i			1.50382i
$850$		0			0
$851$	−4.89898			−0.167935
$852$	10.6066	+	41.0792i	0.363376	+	1.40735i
$853$	−22.0454			−0.754820			−0.377410	−	0.926046i	$-0.623185\pi$
$853$	−22.0454			−0.754820			−0.377410	+	0.926046i	$0.623185\pi$
$854$	−26.4904	+	7.36612i	−0.906482	+	0.252063i
$855$			26.8328i			0.917663i
$856$	5.00000	−	11.6190i	0.170896	−	0.397128i
$857$			7.74597i			0.264597i	0.991210	+	0.132299i	$0.0422358\pi$
$857$			7.74597i			0.264597i	−0.991210	+	0.132299i	$0.957764\pi$
$858$	1.60660	+	19.8348i	0.0548485	+	0.677149i
$859$	45.0333			1.53652			0.768259	−	0.640140i	$-0.221124\pi$
$859$	45.0333			1.53652			0.768259	+	0.640140i	$0.221124\pi$
$860$		0			0
$861$	21.2132	−	28.4605i	0.722944	−	0.969931i
$862$	20.0000	+	15.4919i	0.681203	+	0.527657i
$863$	−51.4393			−1.75101			−0.875507	−	0.483206i	$-0.839472\pi$
$863$	−51.4393			−1.75101			−0.875507	+	0.483206i	$0.839472\pi$
$864$	−4.50000	+	29.0474i	−0.153093	+	0.988212i
$865$			21.9089i			0.744925i
$866$	−30.0000	−	23.2379i	−1.01944	−	0.789656i
$867$	29.4449			1.00000
$868$	6.93237	−	16.9689i	0.235300	−	0.575961i
$869$	−10.3923	+	9.48683i	−0.352535	+	0.321819i
$870$	−14.6969	+	18.9737i	−0.498273	+	0.643268i
$871$			18.9737i			0.642898i
$872$	6.12372	−	14.2302i	0.207375	−	0.481897i
$873$			40.2492i			1.36223i
$874$	−17.3205	−	13.4164i	−0.585875	−	0.453817i
$875$	−24.0000	−	17.8885i	−0.811348	−	0.604743i
$876$	8.48528	+	32.8634i	0.286691	+	1.11035i
$877$			49.2950i			1.66457i	0.554344	+	0.832287i	$0.312969\pi$
$877$			49.2950i			1.66457i	−0.554344	+	0.832287i	$0.687031\pi$
$878$	−38.8909	−	30.1247i	−1.31250	−	1.01666i
$879$		0			0
$880$	−6.00063	+	17.7762i	−0.202281	+	0.599235i
$881$	5.65685			0.190584			0.0952921	−	0.995449i	$-0.469621\pi$
$881$	5.65685			0.190584			0.0952921	+	0.995449i	$0.469621\pi$
$882$	27.6962	+	10.7202i	0.932578	+	0.360969i
$883$		−	7.74597i		−	0.260673i	−0.991470	−	0.130336i	$-0.958394\pi$
$883$		−	7.74597i		−	0.260673i	0.991470	−	0.130336i	$-0.0416057\pi$
$884$		0			0
$885$			26.8328i			0.901975i
$886$	33.9411	−	43.8178i	1.14027	−	1.47209i
$887$	−48.0000			−1.61168			−0.805841	−	0.592132i	$-0.798286\pi$
$887$	−48.0000			−1.61168			−0.805841	+	0.592132i	$0.798286\pi$
$888$	−9.00000	−	3.87298i	−0.302020	−	0.129969i
$889$	45.0000	+	33.5410i	1.50925	+	1.12493i
$890$	−3.46410	+	4.47214i	−0.116117	+	0.149906i
$891$	22.0454	−	20.1246i	0.738549	−	0.674200i
$892$	−8.66025	−	33.5410i	−0.289967	−	1.12304i
$893$	34.6410			1.15922
$894$	10.3923	−	13.4164i	0.347571	−	0.448712i
$895$	20.7846			0.694753
$896$	25.6503	+	15.4293i	0.856916	+	0.515456i
$897$	10.3923			0.346989
$898$	−42.4264	−	32.8634i	−1.41579	−	1.09666i
$899$	−24.0000			−0.800445
$900$	4.50000	+	17.4284i	0.150000	+	0.580948i
$901$		0			0
$902$	−36.2132	+	2.93324i	−1.20577	+	0.0976662i
$903$		0			0
$904$	21.2132	−	49.2950i	0.705541	−	1.63953i
$905$		−	18.9737i		−	0.630706i
$906$	19.0919	−	24.6475i	0.634285	−	0.818859i
$907$			23.2379i			0.771602i	0.922582	+	0.385801i	$0.126075\pi$
$907$			23.2379i			0.771602i	−0.922582	+	0.385801i	$0.873925\pi$
$908$	6.00000	+	23.2379i	0.199117	+	0.771177i
$909$		0			0
$910$	−12.4877	+	3.47242i	−0.413963	+	0.115110i
$911$	36.7423			1.21733			0.608664	−	0.793428i	$-0.291706\pi$
$911$	36.7423			1.21733			0.608664	+	0.793428i	$0.291706\pi$
$912$	−21.2132	−	38.3406i	−0.702439	−	1.26958i
$913$	14.6969	−	13.4164i	0.486398	−	0.444018i
$914$	−12.2474	−	9.48683i	−0.405110	−	0.313797i
$915$	−18.0000			−0.595062
$916$	−25.9808	+	6.70820i	−0.858429	+	0.221645i
$917$	38.1838	+	28.4605i	1.26094	+	0.939848i
$918$		0			0
$919$	−4.24264			−0.139952			−0.0699759	−	0.997549i	$-0.522292\pi$
$919$	−4.24264			−0.139952			−0.0699759	+	0.997549i	$0.522292\pi$
$920$	9.00000	+	3.87298i	0.296721	+	0.127688i
$921$		−	43.8178i		−	1.44385i
$922$	−34.6410	−	26.8328i	−1.14084	−	0.883692i
$923$	30.0000			0.987462
$924$	−10.4814	−	28.5331i	−0.344812	−	0.938672i
$925$	−6.00000			−0.197279
$926$	8.66025	+	6.70820i	0.284594	+	0.220445i
$927$	10.3923			0.341328
$928$	6.00000	−	38.7298i	0.196960	−	1.27137i
$929$	−45.2548			−1.48476			−0.742381	−	0.669977i	$-0.766304\pi$
$929$	−45.2548			−1.48476			−0.742381	+	0.669977i	$0.766304\pi$
$930$	7.34847	−	9.48683i	0.240966	−	0.311086i
$931$	−42.4264	+	12.6491i	−1.39047	+	0.414558i
$932$	−10.3923	−	40.2492i	−0.340411	−	1.31841i
$933$			28.4605i			0.931755i
$934$	−12.2474	−	9.48683i	−0.400749	−	0.310419i
$935$		0			0
$936$	19.0919	+	8.21584i	0.624038	+	0.268543i
$937$	−44.0908			−1.44038			−0.720192	−	0.693775i	$-0.755946\pi$
$937$	−44.0908			−1.44038			−0.720192	+	0.693775i	$0.755946\pi$
$938$	−7.76457	−	27.9233i	−0.253522	−	0.911729i
$939$		0			0
$940$	−15.0000	+	3.87298i	−0.489246	+	0.126323i
$941$			15.4919i			0.505023i	0.967594	+	0.252511i	$0.0812565\pi$
$941$			15.4919i			0.505023i	−0.967594	+	0.252511i	$0.918744\pi$
$942$	25.9808	+	20.1246i	0.846499	+	0.655695i
$943$			18.9737i			0.617868i
$944$	−21.2132	−	38.3406i	−0.690431	−	1.24788i
$945$	15.5885	+	11.6190i	0.507093	+	0.377964i
$946$		0			0
$947$	19.5959			0.636782			0.318391	−	0.947960i	$-0.396858\pi$
$947$	19.5959			0.636782			0.318391	+	0.947960i	$0.396858\pi$
$948$	3.67423	+	14.2302i	0.119334	+	0.462177i
$949$	24.0000			0.779073
$950$	−21.2132	−	16.4317i	−0.688247	−	0.533114i
$951$		−	49.2950i		−	1.59850i
$952$		0			0
$953$	−34.6410			−1.12213			−0.561066	−	0.827771i	$-0.689609\pi$
$953$	−34.6410			−1.12213			−0.561066	+	0.827771i	$0.689609\pi$
$954$	−31.8198	−	24.6475i	−1.03020	−	0.797993i
$955$	−17.3205			−0.560478
$956$	17.3205	−	4.47214i	0.560185	−	0.144639i
$957$	−29.3939	+	26.8328i	−0.950169	+	0.867382i
$958$	−31.1769	+	40.2492i	−1.00728	+	1.30039i
$959$		0			0
$960$	13.4722	+	14.2302i	0.434813	+	0.459279i
$961$	−19.0000			−0.612903
$962$	−4.24264	+	5.47723i	−0.136788	+	0.176593i
$963$			13.4164i			0.432338i
$964$	−12.2474	−	47.4342i	−0.394464	−	1.52775i
$965$		0			0
$966$	−15.2942	+	4.25283i	−0.492084	+	0.136833i
$967$	4.24264			0.136434			0.0682171	−	0.997671i	$-0.478269\pi$
$967$	4.24264			0.136434			0.0682171	+	0.997671i	$0.478269\pi$
$968$	−14.8455	+	27.3425i	−0.477153	+	0.878820i
$969$		0			0
$970$	21.2132	+	16.4317i	0.681115	+	0.527589i
$971$			43.8178i			1.40618i	0.711101	+	0.703090i	$0.248197\pi$
$971$			43.8178i			1.40618i	−0.711101	+	0.703090i	$0.751803\pi$
$972$	−7.79423	−	30.1869i	−0.250000	−	0.968246i
$973$	20.0000	−	26.8328i	0.641171	−	0.860221i
$974$	−25.9808	−	20.1246i	−0.832477	−	0.644834i
$975$	12.7279			0.407620
$976$	25.7196	−	14.2302i	0.823266	−	0.455499i
$977$		−	18.9737i		−	0.607021i	−0.952828	−	0.303511i	$-0.901841\pi$
$977$		−	18.9737i		−	0.607021i	0.952828	−	0.303511i	$-0.0981588\pi$
$978$	−30.0000	−	23.2379i	−0.959294	−	0.743066i
$979$	−6.92820	+	6.32456i	−0.221426	+	0.202134i
$980$	16.9570	−	10.2206i	0.541670	−	0.326486i
$981$			16.4317i			0.524623i
$982$	−5.00000	−	3.87298i	−0.159556	−	0.123592i
$983$		−	49.2950i		−	1.57227i	−0.618057	−	0.786134i	$-0.712080\pi$
$983$		−	49.2950i		−	1.57227i	0.618057	−	0.786134i	$-0.287920\pi$
$984$	−15.0000	+	34.8569i	−0.478183	+	1.11120i
$985$		0			0
$986$		0			0
$987$	15.0000	−	20.1246i	0.477455	−	0.640573i
$988$	−30.0000	+	7.74597i	−0.954427	+	0.246432i
$989$		0			0
$990$	−1.60660	−	19.8348i	−0.0510612	−	0.630391i
$991$			38.7298i			1.23029i	0.788413	+	0.615147i	$0.210903\pi$
$991$			38.7298i			1.23029i	−0.788413	+	0.615147i	$0.789097\pi$
$992$	−3.00000	+	19.3649i	−0.0952501	+	0.614837i
$993$		0			0
$994$	−44.1506	+	12.2769i	−1.40037	+	0.389399i
$995$	−34.2929			−1.08716
$996$	−5.19615	−	20.1246i	−0.164646	−	0.637673i
$997$	−7.34847			−0.232728			−0.116364	−	0.993207i	$-0.537124\pi$
$997$	−7.34847			−0.232728			−0.116364	+	0.993207i	$0.537124\pi$
$998$	34.6410	+	26.8328i	1.09654	+	0.849378i
$999$	10.3923			0.328798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	924.2.n.c.923.6	yes	8
3.2	odd	2		924.2.n.b.923.3	yes	8
4.3	odd	2		924.2.n.b.923.8	yes	8
7.6	odd	2		924.2.n.b.923.5	yes	8
11.10	odd	2		924.2.n.b.923.4	yes	8
12.11	even	2	inner	924.2.n.c.923.1	yes	8
21.20	even	2	inner	924.2.n.c.923.4	yes	8
28.27	even	2	inner	924.2.n.c.923.7	yes	8
33.32	even	2	inner	924.2.n.c.923.5	yes	8
44.43	even	2	inner	924.2.n.c.923.2	yes	8
77.76	even	2	inner	924.2.n.c.923.3	yes	8
84.83	odd	2		924.2.n.b.923.2	yes	8
132.131	odd	2		924.2.n.b.923.7	yes	8
231.230	odd	2		924.2.n.b.923.6	yes	8
308.307	odd	2		924.2.n.b.923.1	✓	8
924.923	even	2	inner	924.2.n.c.923.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
924.2.n.b.923.1	✓	8	308.307	odd	2
924.2.n.b.923.2	yes	8	84.83	odd	2
924.2.n.b.923.3	yes	8	3.2	odd	2
924.2.n.b.923.4	yes	8	11.10	odd	2
924.2.n.b.923.5	yes	8	7.6	odd	2
924.2.n.b.923.6	yes	8	231.230	odd	2
924.2.n.b.923.7	yes	8	132.131	odd	2
924.2.n.b.923.8	yes	8	4.3	odd	2
924.2.n.c.923.1	yes	8	12.11	even	2	inner
924.2.n.c.923.2	yes	8	44.43	even	2	inner
924.2.n.c.923.3	yes	8	77.76	even	2	inner
924.2.n.c.923.4	yes	8	21.20	even	2	inner
924.2.n.c.923.5	yes	8	33.32	even	2	inner
924.2.n.c.923.6	yes	8	1.1	even	1	trivial
924.2.n.c.923.7	yes	8	28.27	even	2	inner
924.2.n.c.923.8	yes	8	924.923	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:	\( N \)	\(=\)	\( 924 = 2^{2} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	924.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 1.11803i) q^{2} +1.73205 q^{3} +(-0.500000 - 1.93649i) q^{4} +1.41421 q^{5} +(1.50000 - 1.93649i) q^{6} +(2.12132 + 1.58114i) q^{7} +(-2.59808 - 1.11803i) q^{8} +3.00000 q^{9} +(1.22474 - 1.58114i) q^{10} +(2.44949 - 2.23607i) q^{11} +(-0.866025 - 3.35410i) q^{12} -2.44949 q^{13} +(3.60488 - 1.00240i) q^{14} +2.44949 q^{15} +(-3.50000 + 1.93649i) q^{16} +(2.59808 - 3.35410i) q^{18} +6.32456i q^{19} +(-0.707107 - 2.73861i) q^{20} +(3.67423 + 2.73861i) q^{21} +(-0.378680 - 4.67510i) q^{22} -2.44949 q^{23} +(-4.50000 - 1.93649i) q^{24} -3.00000 q^{25} +(-2.12132 + 2.73861i) q^{26} +5.19615 q^{27} +(2.00120 - 4.89849i) q^{28} -6.92820 q^{29} +(2.12132 - 2.73861i) q^{30} +3.46410 q^{31} +(-0.866025 + 5.59017i) q^{32} +(4.24264 - 3.87298i) q^{33} +(3.00000 + 2.23607i) q^{35} +(-1.50000 - 5.80948i) q^{36} +2.00000 q^{37} +(7.07107 + 5.47723i) q^{38} -4.24264 q^{39} +(-3.67423 - 1.58114i) q^{40} -7.74597i q^{41} +(6.24384 - 1.73621i) q^{42} +(-5.55487 - 3.62538i) q^{44} +4.24264 q^{45} +(-2.12132 + 2.73861i) q^{46} -5.47723i q^{47} +(-6.06218 + 3.35410i) q^{48} +(2.00000 + 6.70820i) q^{49} +(-2.59808 + 3.35410i) q^{50} +(1.22474 + 4.74342i) q^{52} -9.48683i q^{53} +(4.50000 - 5.80948i) q^{54} +(3.46410 - 3.16228i) q^{55} +(-3.74358 - 6.47963i) q^{56} +10.9545i q^{57} +(-6.00000 + 7.74597i) q^{58} +10.9545i q^{59} +(-1.22474 - 4.74342i) q^{60} -7.34847 q^{61} +(3.00000 - 3.87298i) q^{62} +(6.36396 + 4.74342i) q^{63} +(5.50000 + 5.80948i) q^{64} -3.46410 q^{65} +(-0.655892 - 8.09752i) q^{66} -7.74597i q^{67} -4.24264 q^{69} +(5.09808 - 1.41761i) q^{70} -12.2474 q^{71} +(-7.79423 - 3.35410i) q^{72} -9.79796 q^{73} +(1.73205 - 2.23607i) q^{74} -5.19615 q^{75} +(12.2474 - 3.16228i) q^{76} +(8.73169 - 0.870433i) q^{77} +(-3.67423 + 4.74342i) q^{78} -4.24264 q^{79} +(-4.94975 + 2.73861i) q^{80} +9.00000 q^{81} +(-8.66025 - 6.70820i) q^{82} +6.00000 q^{83} +(3.46618 - 8.48443i) q^{84} -12.0000 q^{87} +(-8.86396 + 3.07086i) q^{88} -2.82843 q^{89} +(3.67423 - 4.74342i) q^{90} +(-5.19615 - 3.87298i) q^{91} +(1.22474 + 4.74342i) q^{92} +6.00000 q^{93} +(-6.12372 - 4.74342i) q^{94} +8.94427i q^{95} +(-1.50000 + 9.68246i) q^{96} +13.4164i q^{97} +(9.23205 + 3.57341i) q^{98} +(7.34847 - 6.70820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 12 q^{6} + 24 q^{9} - 28 q^{16} - 20 q^{22} - 36 q^{24} - 24 q^{25} + 24 q^{35} - 12 q^{36} + 16 q^{37} + 16 q^{49} + 36 q^{54} - 48 q^{58} + 24 q^{62} + 44 q^{64} + 20 q^{70} + 72 q^{81}+ \cdots + 60 q^{98}+O(q^{100}) \) 8 * q - 4 * q^4 + 12 * q^6 + 24 * q^9 - 28 * q^16 - 20 * q^22 - 36 * q^24 - 24 * q^25 + 24 * q^35 - 12 * q^36 + 16 * q^37 + 16 * q^49 + 36 * q^54 - 48 * q^58 + 24 * q^62 + 44 * q^64 + 20 * q^70 + 72 * q^81 + 48 * q^83 - 96 * q^87 - 20 * q^88 + 48 * q^93 - 12 * q^96 + 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more