LMFDB - Embedded newform 828.2.c.f.323.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [828,2,Mod(323,828)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("828.323"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(828, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,4,0,4,0,0,0,4,0,-8,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.61161328736$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 7 x^{10} + 20 x^{9} + 49 x^{8} - 382 x^{7} - 235 x^{6} + 2192 x^{5} + 668 x^{4} + \cdots + 1516 $ x^12 - 6x^11 + 7x^10 + 20x^9 + 49x^8 - 382x^7 - 235x^6 + 2192x^5 + 668x^4 - 5508x^3 - 94x^2 + 3288*x + 1516
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.10
Root			$2.64216 - 2.25841i$ of defining polynomial
Character	$\chi$	$=$	828.323
Dual form			828.2.c.f.323.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.38078 - 0.305697i) q^{2} +(1.81310 - 0.844199i) q^{4} +2.96538i q^{5} -4.88648i q^{7} +(2.24542 - 1.71991i) q^{8} +(0.906508 + 4.09454i) q^{10} -2.48358 q^{11} +6.91053 q^{13} +(-1.49378 - 6.74715i) q^{14} +(2.57466 - 3.06123i) q^{16} -2.39526i q^{17} +1.87079i q^{19} +(2.50337 + 5.37653i) q^{20} +(-3.42928 + 0.759224i) q^{22} +1.00000 q^{23} -3.79349 q^{25} +(9.54191 - 2.11253i) q^{26} +(-4.12516 - 8.85967i) q^{28} +7.93906i q^{29} -4.85376i q^{31} +(2.61922 - 5.01395i) q^{32} +(-0.732224 - 3.30733i) q^{34} +14.4903 q^{35} +1.15415 q^{37} +(0.571894 + 2.58314i) q^{38} +(5.10019 + 6.65853i) q^{40} +0.885578i q^{41} +9.91725i q^{43} +(-4.50298 + 2.09664i) q^{44} +(1.38078 - 0.305697i) q^{46} -0.864641 q^{47} -16.8777 q^{49} +(-5.23797 + 1.15966i) q^{50} +(12.5295 - 5.83386i) q^{52} -4.32369i q^{53} -7.36478i q^{55} +(-8.40431 - 10.9722i) q^{56} +(2.42694 + 10.9621i) q^{58} +2.86425 q^{59} -9.96042 q^{61} +(-1.48378 - 6.70197i) q^{62} +(2.08382 - 7.72384i) q^{64} +20.4924i q^{65} +1.94428i q^{67} +(-2.02208 - 4.34285i) q^{68} +(20.0079 - 4.42963i) q^{70} -6.20578 q^{71} +2.57941 q^{73} +(1.59363 - 0.352821i) q^{74} +(1.57932 + 3.39192i) q^{76} +12.1360i q^{77} +2.73247i q^{79} +(9.07772 + 7.63484i) q^{80} +(0.270718 + 1.22279i) q^{82} -14.4528 q^{83} +7.10287 q^{85} +(3.03167 + 13.6935i) q^{86} +(-5.57669 + 4.27154i) q^{88} +4.01898i q^{89} -33.7682i q^{91} +(1.81310 - 0.844199i) q^{92} +(-1.19388 + 0.264318i) q^{94} -5.54760 q^{95} -12.8218 q^{97} +(-23.3044 + 5.15946i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 4 q^{4} + 4 q^{8} - 8 q^{10} + 12 q^{11} - 4 q^{13} - 12 q^{14} - 12 q^{16} + 20 q^{20} + 4 q^{22} + 12 q^{23} - 40 q^{25} + 8 q^{26} - 24 q^{28} + 44 q^{32} - 28 q^{34} + 40 q^{35} - 32 q^{37}+ \cdots - 20 q^{98}+O(q^{100}) $ 12 * q + 4 * q^2 + 4 * q^4 + 4 * q^8 - 8 * q^10 + 12 * q^11 - 4 * q^13 - 12 * q^14 - 12 * q^16 + 20 * q^20 + 4 * q^22 + 12 * q^23 - 40 * q^25 + 8 * q^26 - 24 * q^28 + 44 * q^32 - 28 * q^34 + 40 * q^35 - 32 * q^37 - 32 * q^38 - 12 * q^40 + 4 * q^44 + 4 * q^46 - 32 * q^49 - 20 * q^50 + 32 * q^52 - 8 * q^56 - 16 * q^58 - 24 * q^59 - 56 * q^61 + 28 * q^64 + 16 * q^68 + 64 * q^70 - 56 * q^71 + 8 * q^73 - 36 * q^74 - 28 * q^76 + 28 * q^80 + 24 * q^82 - 28 * q^83 - 12 * q^85 - 8 * q^86 + 4 * q^88 + 4 * q^92 + 16 * q^94 + 8 * q^95 - 4 * q^97 - 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.38078	−	0.305697i	0.976358	−	0.216160i
$2$	1.38078	−	0.305697i	0.976358	−	0.216160i
$3$		0			0
$3$		0			0
$4$	1.81310	−	0.844199i	0.906550	−	0.422099i
$5$			2.96538i			1.32616i	0.748549	+	0.663080i	$0.230751\pi$
$5$			2.96538i			1.32616i	−0.748549	+	0.663080i	$0.769249\pi$
$6$		0			0
$7$		−	4.88648i		−	1.84692i	−0.383699	−	0.923458i	$-0.625350\pi$
$7$		−	4.88648i		−	1.84692i	0.383699	−	0.923458i	$-0.374650\pi$
$8$	2.24542	−	1.71991i	0.793876	−	0.608080i
$9$		0			0
$10$	0.906508	+	4.09454i	0.286663	+	1.29481i
$11$	−2.48358			−0.748829			−0.374414	−	0.927261i	$-0.622156\pi$
$11$	−2.48358			−0.748829			−0.374414	+	0.927261i	$0.622156\pi$
$12$		0			0
$13$	6.91053			1.91664			0.958318	−	0.285705i	$-0.0922276\pi$
$13$	6.91053			1.91664			0.958318	+	0.285705i	$0.0922276\pi$
$14$	−1.49378	−	6.74715i	−0.399230	−	1.80325i
$15$		0			0
$16$	2.57466	−	3.06123i	0.643664	−	0.765308i
$17$		−	2.39526i		−	0.580937i	−0.956885	−	0.290468i	$-0.906189\pi$
$17$		−	2.39526i		−	0.580937i	0.956885	−	0.290468i	$-0.0938111\pi$
$18$		0			0
$19$			1.87079i			0.429188i	0.976703	+	0.214594i	$0.0688429\pi$
$19$			1.87079i			0.429188i	−0.976703	+	0.214594i	$0.931157\pi$
$20$	2.50337	+	5.37653i	0.559771	+	1.20223i
$21$		0			0
$22$	−3.42928	+	0.759224i	−0.731125	+	0.161867i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$		0			0
$25$	−3.79349			−0.758698
$26$	9.54191	−	2.11253i	1.87132	−	0.414300i
$27$		0			0
$28$	−4.12516	−	8.85967i	−0.779582	−	1.67432i
$29$			7.93906i			1.47425i	0.675759	+	0.737123i	$0.263816\pi$
$29$			7.93906i			1.47425i	−0.675759	+	0.737123i	$0.736184\pi$
$30$		0			0
$31$		−	4.85376i		−	0.871761i	−0.900005	−	0.435880i	$-0.856437\pi$
$31$		−	4.85376i		−	0.871761i	0.900005	−	0.435880i	$-0.143563\pi$
$32$	2.61922	−	5.01395i	0.463017	−	0.886349i
$33$		0			0
$34$	−0.732224	−	3.30733i	−0.125575	−	0.567202i
$35$	14.4903			2.44930
$36$		0			0
$37$	1.15415			0.189742			0.0948708	−	0.995490i	$-0.469756\pi$
$37$	1.15415			0.189742			0.0948708	+	0.995490i	$0.469756\pi$
$38$	0.571894	+	2.58314i	0.0927734	+	0.419041i
$39$		0			0
$40$	5.10019	+	6.65853i	0.806411	+	1.05281i
$41$			0.885578i			0.138304i	0.997606	+	0.0691520i	$0.0220293\pi$
$41$			0.885578i			0.138304i	−0.997606	+	0.0691520i	$0.977971\pi$
$42$		0			0
$43$			9.91725i			1.51237i	0.654360	+	0.756183i	$0.272938\pi$
$43$			9.91725i			1.51237i	−0.654360	+	0.756183i	$0.727062\pi$
$44$	−4.50298	+	2.09664i	−0.678850	+	0.316080i
$45$		0			0
$46$	1.38078	−	0.305697i	0.203585	−	0.0450725i
$47$	−0.864641			−0.126121			−0.0630604	−	0.998010i	$-0.520086\pi$
$47$	−0.864641			−0.126121			−0.0630604	+	0.998010i	$0.520086\pi$
$48$		0			0
$49$	−16.8777			−2.41110
$50$	−5.23797	+	1.15966i	−0.740761	+	0.164000i
$51$		0			0
$52$	12.5295	−	5.83386i	1.73753	−	0.809011i
$53$		−	4.32369i		−	0.593905i	−0.954892	−	0.296952i	$-0.904030\pi$
$53$		−	4.32369i		−	0.593905i	0.954892	−	0.296952i	$-0.0959703\pi$
$54$		0			0
$55$		−	7.36478i		−	0.993066i
$56$	−8.40431	−	10.9722i	−1.12307	−	1.46622i
$57$		0			0
$58$	2.42694	+	10.9621i	0.318673	+	1.43939i
$59$	2.86425			0.372894			0.186447	−	0.982465i	$-0.440303\pi$
$59$	2.86425			0.372894			0.186447	+	0.982465i	$0.440303\pi$
$60$		0			0
$61$	−9.96042			−1.27530			−0.637651	−	0.770326i	$-0.720094\pi$
$61$	−9.96042			−1.27530			−0.637651	+	0.770326i	$0.720094\pi$
$62$	−1.48378	−	6.70197i	−0.188440	−	0.851151i
$63$		0			0
$64$	2.08382	−	7.72384i	0.260477	−	0.965480i
$65$			20.4924i			2.54176i
$66$		0			0
$67$			1.94428i			0.237532i	0.992922	+	0.118766i	$0.0378938\pi$
$67$			1.94428i			0.237532i	−0.992922	+	0.118766i	$0.962106\pi$
$68$	−2.02208	−	4.34285i	−0.245213	−	0.526648i
$69$		0			0
$70$	20.0079	−	4.42963i	2.39140	−	0.529442i
$71$	−6.20578			−0.736490			−0.368245	−	0.929729i	$-0.620041\pi$
$71$	−6.20578			−0.736490			−0.368245	+	0.929729i	$0.620041\pi$
$72$		0			0
$73$	2.57941			0.301897			0.150949	−	0.988542i	$-0.451767\pi$
$73$	2.57941			0.301897			0.150949	+	0.988542i	$0.451767\pi$
$74$	1.59363	−	0.352821i	0.185256	−	0.0410146i
$75$		0			0
$76$	1.57932	+	3.39192i	0.181160	+	0.389080i
$77$			12.1360i			1.38302i
$78$		0			0
$79$			2.73247i			0.307427i	0.988115	+	0.153714i	$0.0491233\pi$
$79$			2.73247i			0.307427i	−0.988115	+	0.153714i	$0.950877\pi$
$80$	9.07772	+	7.63484i	1.01492	+	0.853601i
$81$		0			0
$82$	0.270718	+	1.22279i	0.0298958	+	0.135034i
$83$	−14.4528			−1.58640			−0.793202	−	0.608959i	$-0.791587\pi$
$83$	−14.4528			−1.58640			−0.793202	+	0.608959i	$0.791587\pi$
$84$		0			0
$85$	7.10287			0.770414
$86$	3.03167	+	13.6935i	0.326913	+	1.47661i
$87$		0			0
$88$	−5.57669	+	4.27154i	−0.594477	+	0.455348i
$89$			4.01898i			0.426011i	0.977051	+	0.213005i	$0.0683252\pi$
$89$			4.01898i			0.426011i	−0.977051	+	0.213005i	$0.931675\pi$
$90$		0			0
$91$		−	33.7682i		−	3.53987i
$92$	1.81310	−	0.844199i	0.189029	−	0.0880138i
$93$		0			0
$94$	−1.19388	+	0.264318i	−0.123139	+	0.0272623i
$95$	−5.54760			−0.569172
$96$		0			0
$97$	−12.8218			−1.30186			−0.650928	−	0.759140i	$-0.725620\pi$
$97$	−12.8218			−1.30186			−0.650928	+	0.759140i	$0.725620\pi$
$98$	−23.3044	+	5.15946i	−2.35410	+	0.521184i
$99$		0			0
$100$	−6.87797	+	3.20246i	−0.687797	+	0.320246i
$101$		−	8.08405i		−	0.804393i	−0.915553	−	0.402197i	$-0.868247\pi$
$101$		−	8.08405i		−	0.804393i	0.915553	−	0.402197i	$-0.131753\pi$
$102$		0			0
$103$		−	2.81544i		−	0.277413i	−0.990334	−	0.138707i	$-0.955705\pi$
$103$		−	2.81544i		−	0.277413i	0.990334	−	0.138707i	$-0.0442945\pi$
$104$	15.5170	−	11.8855i	1.52157	−	1.16547i
$105$		0			0
$106$	−1.32174	−	5.97006i	−0.128379	−	0.579864i
$107$	15.3816			1.48700			0.743499	−	0.668737i	$-0.233165\pi$
$107$	15.3816			1.48700			0.743499	+	0.668737i	$0.233165\pi$
$108$		0			0
$109$	−6.03157			−0.577720			−0.288860	−	0.957371i	$-0.593276\pi$
$109$	−6.03157			−0.577720			−0.288860	+	0.957371i	$0.593276\pi$
$110$	−2.25139	−	10.1691i	−0.214661	−	0.969588i
$111$		0			0
$112$	−14.9587	−	12.5810i	−1.41346	−	1.18879i
$113$		−	8.80950i		−	0.828728i	−0.910111	−	0.414364i	$-0.864004\pi$
$113$		−	8.80950i		−	0.828728i	0.910111	−	0.414364i	$-0.135996\pi$
$114$		0			0
$115$			2.96538i			0.276523i
$116$	6.70214	+	14.3943i	0.622278	+	1.33648i
$117$		0			0
$118$	3.95490	−	0.875593i	0.364078	−	0.0806048i
$119$	−11.7044			−1.07294
$120$		0			0
$121$	−4.83181			−0.439255
$122$	−13.7531	+	3.04487i	−1.24515	+	0.275669i
$123$		0			0
$124$	−4.09754	−	8.80035i	−0.367970	−	0.790294i
$125$			3.57776i			0.320005i
$126$		0			0
$127$			3.27672i			0.290762i	0.989376	+	0.145381i	$0.0464408\pi$
$127$			3.27672i			0.290762i	−0.989376	+	0.145381i	$0.953559\pi$
$128$	0.516138	−	11.3019i	0.0456206	−	0.998959i
$129$		0			0
$130$	6.26445	+	28.2954i	0.549428	+	2.48167i
$131$	−20.5175			−1.79262			−0.896311	−	0.443425i	$-0.853763\pi$
$131$	−20.5175			−1.79262			−0.896311	+	0.443425i	$0.853763\pi$
$132$		0			0
$133$	9.14157			0.792675
$134$	0.594360	+	2.68462i	0.0513449	+	0.231916i
$135$		0			0
$136$	−4.11964	−	5.37837i	−0.353256	−	0.461191i
$137$		−	12.0574i		−	1.03013i	−0.857151	−	0.515066i	$-0.827767\pi$
$137$		−	12.0574i		−	1.03013i	0.857151	−	0.515066i	$-0.172233\pi$
$138$		0			0
$139$			8.24742i			0.699537i	0.936836	+	0.349769i	$0.113740\pi$
$139$			8.24742i			0.699537i	−0.936836	+	0.349769i	$0.886260\pi$
$140$	26.2723	−	12.2327i	2.22042	−	1.03385i
$141$		0			0
$142$	−8.56881	+	1.89709i	−0.719078	+	0.159200i
$143$	−17.1629			−1.43523
$144$		0			0
$145$	−23.5423			−1.95508
$146$	3.56160	−	0.788518i	0.294760	−	0.0652582i
$147$		0			0
$148$	2.09259	−	0.974335i	0.172010	−	0.0800898i
$149$			17.4086i			1.42616i	0.701080	+	0.713082i	$0.252701\pi$
$149$			17.4086i			1.42616i	−0.701080	+	0.713082i	$0.747299\pi$
$150$		0			0
$151$			18.3869i			1.49631i	0.663526	+	0.748153i	$0.269059\pi$
$151$			18.3869i			1.49631i	−0.663526	+	0.748153i	$0.730941\pi$
$152$	3.21759	+	4.20070i	0.260981	+	0.340722i
$153$		0			0
$154$	3.70993	+	16.7571i	0.298955	+	1.35033i
$155$	14.3933			1.15609
$156$		0			0
$157$	20.7353			1.65485			0.827427	−	0.561574i	$-0.189804\pi$
$157$	20.7353			1.65485			0.827427	+	0.561574i	$0.189804\pi$
$158$	0.835308	+	3.77294i	0.0664535	+	0.300159i
$159$		0			0
$160$	14.8683	+	7.76699i	1.17544	+	0.614035i
$161$		−	4.88648i		−	0.385109i
$162$		0			0
$163$			15.1100i			1.18350i	0.806120	+	0.591752i	$0.201563\pi$
$163$			15.1100i			1.18350i	−0.806120	+	0.591752i	$0.798437\pi$
$164$	0.747604	+	1.60564i	0.0583781	+	0.125379i
$165$		0			0
$166$	−19.9562	+	4.41818i	−1.54890	+	0.342917i
$167$	18.2976			1.41591			0.707954	−	0.706259i	$-0.249619\pi$
$167$	18.2976			1.41591			0.707954	+	0.706259i	$0.249619\pi$
$168$		0			0
$169$	34.7554			2.67349
$170$	9.80749	−	2.17132i	0.752200	−	0.166533i
$171$		0			0
$172$	8.37213	+	17.9810i	0.638369	+	1.37103i
$173$			15.0892i			1.14721i	0.819132	+	0.573605i	$0.194456\pi$
$173$			15.0892i			1.14721i	−0.819132	+	0.573605i	$0.805544\pi$
$174$		0			0
$175$			18.5368i			1.40125i
$176$	−6.39438	+	7.60283i	−0.481994	+	0.573085i
$177$		0			0
$178$	1.22859	+	5.54932i	0.0920866	+	0.415939i
$179$	0.402653			0.0300957			0.0150478	−	0.999887i	$-0.495210\pi$
$179$	0.402653			0.0300957			0.0150478	+	0.999887i	$0.495210\pi$
$180$		0			0
$181$	−22.2467			−1.65358			−0.826791	−	0.562510i	$-0.809836\pi$
$181$	−22.2467			−1.65358			−0.826791	+	0.562510i	$0.809836\pi$
$182$	−10.3228	−	46.6264i	−0.765178	−	3.45618i
$183$		0			0
$184$	2.24542	−	1.71991i	0.165535	−	0.126793i
$185$			3.42251i			0.251628i
$186$		0			0
$187$			5.94884i			0.435022i
$188$	−1.56768	+	0.729929i	−0.114335	+	0.0532355i
$189$		0			0
$190$	−7.66001	+	1.69588i	−0.555715	+	0.123032i
$191$	−16.5231			−1.19557			−0.597784	−	0.801657i	$-0.703952\pi$
$191$	−16.5231			−1.19557			−0.597784	+	0.801657i	$0.703952\pi$
$192$		0			0
$193$	21.1301			1.52098			0.760489	−	0.649351i	$-0.224959\pi$
$193$	21.1301			1.52098			0.760489	+	0.649351i	$0.224959\pi$
$194$	−17.7040	+	3.91958i	−1.27108	+	0.281409i
$195$		0			0
$196$	−30.6009	+	14.2481i	−2.18578	+	1.01772i
$197$			9.89871i			0.705254i	0.935764	+	0.352627i	$0.114712\pi$
$197$			9.89871i			0.705254i	−0.935764	+	0.352627i	$0.885288\pi$
$198$		0			0
$199$			1.14490i			0.0811601i	0.999176	+	0.0405801i	$0.0129206\pi$
$199$			1.14490i			0.0811601i	−0.999176	+	0.0405801i	$0.987079\pi$
$200$	−8.51798	+	6.52446i	−0.602312	+	0.461349i
$201$		0			0
$202$	−2.47127	−	11.1623i	−0.173878	−	0.785376i
$203$	38.7940			2.72281
$204$		0			0
$205$	−2.62608			−0.183413
$206$	−0.860670	−	3.88750i	−0.0599657	−	0.270855i
$207$		0			0
$208$	17.7922	−	21.1547i	1.23367	−	1.46682i
$209$		−	4.64626i		−	0.321389i
$210$		0			0
$211$		−	11.2048i		−	0.771368i	−0.922631	−	0.385684i	$-0.873966\pi$
$211$		−	11.2048i		−	0.771368i	0.922631	−	0.385684i	$-0.126034\pi$
$212$	−3.65006	−	7.83928i	−0.250687	−	0.538404i
$213$		0			0
$214$	21.2386	−	4.70211i	1.45184	−	0.321430i
$215$	−29.4084			−2.00564
$216$		0			0
$217$	−23.7178			−1.61007
$218$	−8.32827	+	1.84383i	−0.564061	+	0.124880i
$219$		0			0
$220$	−6.21734	−	13.3531i	−0.419173	−	0.900264i
$221$		−	16.5525i		−	1.11344i
$222$		0			0
$223$			16.7818i			1.12379i	0.827207	+	0.561897i	$0.189928\pi$
$223$			16.7818i			1.12379i	−0.827207	+	0.561897i	$0.810072\pi$
$224$	−24.5006	−	12.7988i	−1.63701	−	0.855154i
$225$		0			0
$226$	−2.69304	−	12.1640i	−0.179138	−	0.809135i
$227$	−9.88619			−0.656170			−0.328085	−	0.944648i	$-0.606403\pi$
$227$	−9.88619			−0.656170			−0.328085	+	0.944648i	$0.606403\pi$
$228$		0			0
$229$	−8.92893			−0.590041			−0.295020	−	0.955491i	$-0.595326\pi$
$229$	−8.92893			−0.590041			−0.295020	+	0.955491i	$0.595326\pi$
$230$	0.906508	+	4.09454i	0.0597733	+	0.269986i
$231$		0			0
$232$	13.6545	+	17.8265i	0.896459	+	1.17037i
$233$		−	19.1788i		−	1.25644i	−0.778035	−	0.628221i	$-0.783783\pi$
$233$		−	19.1788i		−	1.25644i	0.778035	−	0.628221i	$-0.216217\pi$
$234$		0			0
$235$		−	2.56399i		−	0.167256i
$236$	5.19317	−	2.41800i	0.338047	−	0.157398i
$237$		0			0
$238$	−16.1612	+	3.57800i	−1.04757	+	0.231927i
$239$	−6.27307			−0.405771			−0.202885	−	0.979202i	$-0.565032\pi$
$239$	−6.27307			−0.405771			−0.202885	+	0.979202i	$0.565032\pi$
$240$		0			0
$241$	14.7427			0.949662			0.474831	−	0.880077i	$-0.342509\pi$
$241$	14.7427			0.949662			0.474831	+	0.880077i	$0.342509\pi$
$242$	−6.67166	+	1.47707i	−0.428870	+	0.0949495i
$243$		0			0
$244$	−18.0592	+	8.40858i	−1.15612	+	0.538304i
$245$		−	50.0488i		−	3.19750i
$246$		0			0
$247$			12.9281i			0.822597i
$248$	−8.34803	−	10.8987i	−0.530100	−	0.692070i
$249$		0			0
$250$	1.09371	+	4.94010i	0.0691723	+	0.312439i
$251$	28.9752			1.82890			0.914449	−	0.404700i	$-0.132624\pi$
$251$	28.9752			1.82890			0.914449	+	0.404700i	$0.132624\pi$
$252$		0			0
$253$	−2.48358			−0.156142
$254$	1.00168	+	4.52443i	0.0628512	+	0.283888i
$255$		0			0
$256$	−2.74229	−	15.7632i	−0.171393	−	0.985203i
$257$		−	4.53342i		−	0.282787i	−0.989953	−	0.141393i	$-0.954842\pi$
$257$		−	4.53342i		−	0.282787i	0.989953	−	0.141393i	$-0.0451583\pi$
$258$		0			0
$259$		−	5.63975i		−	0.350437i
$260$	17.2996	+	37.1547i	1.07288	+	2.30423i
$261$		0			0
$262$	−28.3301	+	6.27213i	−1.75024	+	0.387494i
$263$	14.2268			0.877261			0.438631	−	0.898667i	$-0.355464\pi$
$263$	14.2268			0.877261			0.438631	+	0.898667i	$0.355464\pi$
$264$		0			0
$265$	12.8214			0.787612
$266$	12.6225	−	2.79455i	0.773934	−	0.171345i
$267$		0			0
$268$	1.64136	+	3.52518i	0.100262	+	0.215334i
$269$			2.19869i			0.134056i	0.997751	+	0.0670281i	$0.0213517\pi$
$269$			2.19869i			0.134056i	−0.997751	+	0.0670281i	$0.978648\pi$
$270$		0			0
$271$		−	6.68925i		−	0.406343i	−0.979143	−	0.203171i	$-0.934875\pi$
$271$		−	6.68925i		−	0.406343i	0.979143	−	0.203171i	$-0.0651249\pi$
$272$	−7.33246	−	6.16698i	−0.444596	−	0.373928i
$273$		0			0
$274$	−3.68590	−	16.6486i	−0.222674	−	1.00578i
$275$	9.42145			0.568135
$276$		0			0
$277$	−19.9232			−1.19707			−0.598534	−	0.801097i	$-0.704250\pi$
$277$	−19.9232			−1.19707			−0.598534	+	0.801097i	$0.704250\pi$
$278$	2.52121	+	11.3879i	0.151212	+	0.682999i
$279$		0			0
$280$	32.5368	−	24.9220i	1.94444	−	1.48937i
$281$			12.0779i			0.720507i	0.932854	+	0.360254i	$0.117310\pi$
$281$			12.0779i			0.720507i	−0.932854	+	0.360254i	$0.882690\pi$
$282$		0			0
$283$		−	20.2091i		−	1.20131i	−0.799509	−	0.600654i	$-0.794907\pi$
$283$		−	20.2091i		−	1.20131i	0.799509	−	0.600654i	$-0.205093\pi$
$284$	−11.2517	+	5.23891i	−0.667665	+	0.310872i
$285$		0			0
$286$	−23.6981	+	5.24664i	−1.40130	+	0.310240i
$287$	4.32736			0.255436
$288$		0			0
$289$	11.2627			0.662513
$290$	−32.5068	+	7.19681i	−1.90886	+	0.422611i
$291$		0			0
$292$	4.67673	−	2.17754i	0.273685	−	0.127431i
$293$		−	19.3965i		−	1.13316i	−0.824008	−	0.566578i	$-0.808267\pi$
$293$		−	19.3965i		−	1.13316i	0.824008	−	0.566578i	$-0.191733\pi$
$294$		0			0
$295$			8.49360i			0.494517i
$296$	2.59156	−	1.98504i	0.150631	−	0.115378i
$297$		0			0
$298$	5.32174	+	24.0374i	0.308280	+	1.39245i
$299$	6.91053			0.399646
$300$		0			0
$301$	48.4604			2.79321
$302$	5.62082	+	25.3883i	0.323442	+	1.46093i
$303$		0			0
$304$	5.72692	+	4.81664i	0.328461	+	0.276253i
$305$		−	29.5365i		−	1.69125i
$306$		0			0
$307$			3.90709i			0.222989i	0.993765	+	0.111495i	$0.0355638\pi$
$307$			3.90709i			0.222989i	−0.993765	+	0.111495i	$0.964436\pi$
$308$	10.2452	+	22.0037i	0.583774	+	1.25378i
$309$		0			0
$310$	19.8739	−	4.39997i	1.12876	−	0.249901i
$311$	−14.2299			−0.806905			−0.403453	−	0.915001i	$-0.632190\pi$
$311$	−14.2299			−0.806905			−0.403453	+	0.915001i	$0.632190\pi$
$312$		0			0
$313$	−7.34114			−0.414946			−0.207473	−	0.978241i	$-0.566524\pi$
$313$	−7.34114			−0.414946			−0.207473	+	0.978241i	$0.566524\pi$
$314$	28.6308	−	6.33870i	1.61573	−	0.357713i
$315$		0			0
$316$	2.30675	+	4.95424i	0.129765	+	0.278698i
$317$		−	1.94571i		−	0.109282i	−0.998506	−	0.0546411i	$-0.982599\pi$
$317$		−	1.94571i		−	0.109282i	0.998506	−	0.0546411i	$-0.0174015\pi$
$318$		0			0
$319$		−	19.7173i		−	1.10396i
$320$	22.9041	+	6.17931i	1.28038	+	0.345434i
$321$		0			0
$322$	−1.49378	−	6.74715i	−0.0832452	−	0.376004i
$323$	4.48103			0.249331
$324$		0			0
$325$	−26.2150			−1.45415
$326$	4.61906	+	20.8635i	0.255826	+	1.15552i
$327$		0			0
$328$	1.52311	+	1.98849i	0.0840999	+	0.109796i
$329$			4.22505i			0.232935i
$330$		0			0
$331$		−	33.5035i		−	1.84152i	−0.390134	−	0.920758i	$-0.627571\pi$
$331$		−	33.5035i		−	1.84152i	0.390134	−	0.920758i	$-0.372429\pi$
$332$	−26.2044	+	12.2011i	−1.43815	+	0.669620i
$333$		0			0
$334$	25.2649	−	5.59350i	1.38243	−	0.306063i
$335$	−5.76554			−0.315005
$336$		0			0
$337$	17.3632			0.945835			0.472917	−	0.881107i	$-0.343201\pi$
$337$	17.3632			0.945835			0.472917	+	0.881107i	$0.343201\pi$
$338$	47.9895	−	10.6246i	2.61028	−	0.577903i
$339$		0			0
$340$	12.8782	−	5.99624i	0.698419	−	0.325192i
$341$			12.0547i			0.652800i
$342$		0			0
$343$			48.2672i			2.60618i
$344$	17.0568	+	22.2684i	0.919640	+	1.20063i
$345$		0			0
$346$	4.61272	+	20.8348i	0.247981	+	1.12009i
$347$	−18.0766			−0.970402			−0.485201	−	0.874403i	$-0.661254\pi$
$347$	−18.0766			−0.970402			−0.485201	+	0.874403i	$0.661254\pi$
$348$		0			0
$349$	14.1005			0.754780			0.377390	−	0.926054i	$-0.376822\pi$
$349$	14.1005			0.754780			0.377390	+	0.926054i	$0.376822\pi$
$350$	5.66664	+	25.5952i	0.302895	+	1.36812i
$351$		0			0
$352$	−6.50506	+	12.4526i	−0.346721	+	0.663724i
$353$		−	16.7185i		−	0.889838i	−0.895571	−	0.444919i	$-0.853233\pi$
$353$		−	16.7185i		−	0.889838i	0.895571	−	0.444919i	$-0.146767\pi$
$354$		0			0
$355$		−	18.4025i		−	0.976704i
$356$	3.39282	+	7.28680i	0.179819	+	0.386200i
$357$		0			0
$358$	0.555975	−	0.123090i	0.0293842	−	0.00650549i
$359$	16.6532			0.878923			0.439461	−	0.898262i	$-0.355169\pi$
$359$	16.6532			0.878923			0.439461	+	0.898262i	$0.355169\pi$
$360$		0			0
$361$	15.5002			0.815797
$362$	−30.7177	+	6.80073i	−1.61449	+	0.357438i
$363$		0			0
$364$	−28.5070	−	61.2250i	−1.49418	−	3.20906i
$365$			7.64895i			0.400364i
$366$		0			0
$367$			8.14902i			0.425376i	0.977120	+	0.212688i	$0.0682217\pi$
$367$			8.14902i			0.425376i	−0.977120	+	0.212688i	$0.931778\pi$
$368$	2.57466	−	3.06123i	0.134213	−	0.159578i
$369$		0			0
$370$	1.04625	+	4.72572i	0.0543919	+	0.245679i
$371$	−21.1276			−1.09689
$372$		0			0
$373$	−8.25533			−0.427445			−0.213722	−	0.976894i	$-0.568559\pi$
$373$	−8.25533			−0.427445			−0.213722	+	0.976894i	$0.568559\pi$
$374$	1.81854	+	8.21403i	0.0940345	+	0.424737i
$375$		0			0
$376$	−1.94148	+	1.48710i	−0.100124	+	0.0766916i
$377$			54.8631i			2.82559i
$378$		0			0
$379$		−	16.3808i		−	0.841428i	−0.907193	−	0.420714i	$-0.861780\pi$
$379$		−	16.3808i		−	0.841428i	0.907193	−	0.420714i	$-0.138220\pi$
$380$	−10.0584	+	4.68328i	−0.515983	+	0.240247i
$381$		0			0
$382$	−22.8147	+	5.05105i	−1.16730	+	0.258434i
$383$	−15.7596			−0.805277			−0.402639	−	0.915359i	$-0.631907\pi$
$383$	−15.7596			−0.805277			−0.402639	+	0.915359i	$0.631907\pi$
$384$		0			0
$385$	−35.9878			−1.83411
$386$	29.1760	−	6.45940i	1.48502	−	0.328775i
$387$		0			0
$388$	−23.2472	+	10.8241i	−1.18020	+	0.549512i
$389$		−	22.6408i		−	1.14793i	−0.818879	−	0.573966i	$-0.805404\pi$
$389$		−	22.6408i		−	1.14793i	0.818879	−	0.573966i	$-0.194596\pi$
$390$		0			0
$391$		−	2.39526i		−	0.121134i
$392$	−37.8975	+	29.0281i	−1.91411	+	1.46614i
$393$		0			0
$394$	3.02600	+	13.6679i	0.152448	+	0.688580i
$395$	−8.10282			−0.407697
$396$		0			0
$397$	−9.97581			−0.500671			−0.250336	−	0.968159i	$-0.580541\pi$
$397$	−9.97581			−0.500671			−0.250336	+	0.968159i	$0.580541\pi$
$398$	0.349994	+	1.58086i	0.0175436	+	0.0792414i
$399$		0			0
$400$	−9.76693	+	11.6128i	−0.488347	+	0.580638i
$401$			27.7611i			1.38632i	0.720782	+	0.693162i	$0.243783\pi$
$401$			27.7611i			1.38632i	−0.720782	+	0.693162i	$0.756217\pi$
$402$		0			0
$403$		−	33.5420i		−	1.67085i
$404$	−6.82455	−	14.6572i	−0.339534	−	0.729222i
$405$		0			0
$406$	53.5660	−	11.8592i	2.65844	−	0.588563i
$407$	−2.86644			−0.142084
$408$		0			0
$409$	34.8604			1.72374			0.861868	−	0.507133i	$-0.169295\pi$
$409$	34.8604			1.72374			0.861868	+	0.507133i	$0.169295\pi$
$410$	−3.62603	+	0.802783i	−0.179077	+	0.0396466i
$411$		0			0
$412$	−2.37679	−	5.10467i	−0.117096	−	0.251489i
$413$		−	13.9961i		−	0.688704i
$414$		0			0
$415$		−	42.8581i		−	2.10382i
$416$	18.1002	−	34.6490i	0.887435	−	1.69881i
$417$		0			0
$418$	−1.42035	−	6.41546i	−0.0694714	−	0.313790i
$419$	−1.75706			−0.0858379			−0.0429190	−	0.999079i	$-0.513666\pi$
$419$	−1.75706			−0.0858379			−0.0429190	+	0.999079i	$0.513666\pi$
$420$		0			0
$421$	−7.54441			−0.367692			−0.183846	−	0.982955i	$-0.558855\pi$
$421$	−7.54441			−0.367692			−0.183846	+	0.982955i	$0.558855\pi$
$422$	−3.42526	−	15.4713i	−0.166739	−	0.753131i
$423$		0			0
$424$	−7.43636	−	9.70850i	−0.361142	−	0.471486i
$425$			9.08641i			0.440755i
$426$		0			0
$427$			48.6714i			2.35538i
$428$	27.8884	−	12.9852i	1.34804	−	0.627661i
$429$		0			0
$430$	−40.6065	+	8.99006i	−1.95822	+	0.433539i
$431$	13.7285			0.661279			0.330639	−	0.943757i	$-0.392736\pi$
$431$	13.7285			0.661279			0.330639	+	0.943757i	$0.392736\pi$
$432$		0			0
$433$	7.44507			0.357787			0.178894	−	0.983868i	$-0.442748\pi$
$433$	7.44507			0.357787			0.178894	+	0.983868i	$0.442748\pi$
$434$	−32.7490	+	7.25045i	−1.57200	+	0.348033i
$435$		0			0
$436$	−10.9358	+	5.09185i	−0.523732	+	0.243855i
$437$			1.87079i			0.0894919i
$438$		0			0
$439$		−	36.2933i		−	1.73218i	−0.499885	−	0.866092i	$-0.666624\pi$
$439$		−	36.2933i		−	1.73218i	0.499885	−	0.866092i	$-0.333376\pi$
$440$	−12.6668	−	16.5370i	−0.603864	−	0.788371i
$441$		0			0
$442$	−5.06005	−	22.8554i	−0.240682	−	1.08712i
$443$	11.6126			0.551733			0.275866	−	0.961196i	$-0.411035\pi$
$443$	11.6126			0.551733			0.275866	+	0.961196i	$0.411035\pi$
$444$		0			0
$445$	−11.9178			−0.564958
$446$	5.13015	+	23.1720i	0.242920	+	1.09723i
$447$		0			0
$448$	−37.7424	−	10.1825i	−1.78316	−	0.481079i
$449$		−	32.1871i		−	1.51900i	−0.650506	−	0.759502i	$-0.725443\pi$
$449$		−	32.1871i		−	1.51900i	0.650506	−	0.759502i	$-0.274557\pi$
$450$		0			0
$451$		−	2.19941i		−	0.103566i
$452$	−7.43697	−	15.9725i	−0.349806	−	0.751283i
$453$		0			0
$454$	−13.6506	+	3.02218i	−0.640656	+	0.141838i
$455$	100.135			4.69442
$456$		0			0
$457$	19.6460			0.919000			0.459500	−	0.888178i	$-0.348029\pi$
$457$	19.6460			0.919000			0.459500	+	0.888178i	$0.348029\pi$
$458$	−12.3289	+	2.72955i	−0.576091	+	0.127543i
$459$		0			0
$460$	2.50337	+	5.37653i	0.116720	+	0.250682i
$461$		−	8.04745i		−	0.374807i	−0.982283	−	0.187404i	$-0.939993\pi$
$461$		−	8.04745i		−	0.374807i	0.982283	−	0.187404i	$-0.0600072\pi$
$462$		0			0
$463$			14.2725i			0.663298i	0.943403	+	0.331649i	$0.107605\pi$
$463$			14.2725i			0.663298i	−0.943403	+	0.331649i	$0.892395\pi$
$464$	24.3033	+	20.4403i	1.12825	+	0.948919i
$465$		0			0
$466$	−5.86288	−	26.4816i	−0.271593	−	1.22674i
$467$	−7.86132			−0.363778			−0.181889	−	0.983319i	$-0.558221\pi$
$467$	−7.86132			−0.363778			−0.181889	+	0.983319i	$0.558221\pi$
$468$		0			0
$469$	9.50069			0.438701
$470$	−0.783803	−	3.54030i	−0.0361542	−	0.163302i
$471$		0			0
$472$	6.43145	−	4.92626i	0.296031	−	0.226749i
$473$		−	24.6303i		−	1.13250i
$474$		0			0
$475$		−	7.09682i		−	0.325624i
$476$	−21.2212	+	9.88085i	−0.972674	+	0.452888i
$477$		0			0
$478$	−8.66171	+	1.91766i	−0.396178	+	0.0877115i
$479$	−30.2975			−1.38433			−0.692164	−	0.721740i	$-0.743343\pi$
$479$	−30.2975			−1.38433			−0.692164	+	0.721740i	$0.743343\pi$
$480$		0			0
$481$	7.97581			0.363666
$482$	20.3564	−	4.50680i	0.927210	−	0.205279i
$483$		0			0
$484$	−8.76055	+	4.07901i	−0.398207	+	0.185409i
$485$		−	38.0215i		−	1.72647i
$486$		0			0
$487$			21.4050i			0.969955i	0.874527	+	0.484978i	$0.161172\pi$
$487$			21.4050i			0.969955i	−0.874527	+	0.484978i	$0.838828\pi$
$488$	−22.3653	+	17.1310i	−1.01243	+	0.775486i
$489$		0			0
$490$	−15.2998	−	69.1063i	−0.691173	−	3.12191i
$491$	1.03586			0.0467478			0.0233739	−	0.999727i	$-0.492559\pi$
$491$	1.03586			0.0467478			0.0233739	+	0.999727i	$0.492559\pi$
$492$		0			0
$493$	19.0161			0.856443
$494$	3.95209	+	17.8509i	0.177813	+	0.803149i
$495$		0			0
$496$	−14.8585	−	12.4968i	−0.667166	−	0.561121i
$497$			30.3244i			1.36024i
$498$		0			0
$499$			25.7844i			1.15427i	0.816649	+	0.577135i	$0.195829\pi$
$499$			25.7844i			1.15427i	−0.816649	+	0.577135i	$0.804171\pi$
$500$	3.02034	+	6.48684i	0.135074	+	0.290100i
$501$		0			0
$502$	40.0083	−	8.85763i	1.78566	−	0.395335i
$503$	−15.0341			−0.670336			−0.335168	−	0.942158i	$-0.608793\pi$
$503$	−15.0341			−0.670336			−0.335168	+	0.942158i	$0.608793\pi$
$504$		0			0
$505$	23.9723			1.06675
$506$	−3.42928	+	0.759224i	−0.152450	+	0.0337516i
$507$		0			0
$508$	2.76621	+	5.94102i	0.122731	+	0.263590i
$509$		−	6.52381i		−	0.289163i	−0.989493	−	0.144581i	$-0.953816\pi$
$509$		−	6.52381i		−	0.289163i	0.989493	−	0.144581i	$-0.0461836\pi$
$510$		0			0
$511$		−	12.6043i		−	0.557579i
$512$	−8.60527	−	20.9272i	−0.380303	−	0.924862i
$513$		0			0
$514$	−1.38585	−	6.25965i	−0.0611273	−	0.276101i
$515$	8.34885			0.367894
$516$		0			0
$517$	2.14741			0.0944429
$518$	−1.72405	−	7.78724i	−0.0757505	−	0.342152i
$519$		0			0
$520$	35.2450	+	46.0139i	1.54560	+	2.01784i
$521$			8.26390i			0.362048i	0.983479	+	0.181024i	$0.0579412\pi$
$521$			8.26390i			0.362048i	−0.983479	+	0.181024i	$0.942059\pi$
$522$		0			0
$523$		−	16.0139i		−	0.700239i	−0.936705	−	0.350119i	$-0.886141\pi$
$523$		−	16.0139i		−	0.700239i	0.936705	−	0.350119i	$-0.113859\pi$
$524$	−37.2003	+	17.3209i	−1.62510	+	0.756665i
$525$		0			0
$526$	19.6440	−	4.34908i	0.856521	−	0.189629i
$527$	−11.6260			−0.506438
$528$		0			0
$529$	1.00000			0.0434783
$530$	17.7035	−	3.91946i	0.768991	−	0.170250i
$531$		0			0
$532$	16.5746	−	7.71730i	0.718599	−	0.334588i
$533$			6.11981i			0.265078i
$534$		0			0
$535$			45.6124i			1.97200i
$536$	3.34399	+	4.36573i	0.144438	+	0.188571i
$537$		0			0
$538$	0.672131	+	3.03590i	0.0289776	+	0.130887i
$539$	41.9172			1.80550
$540$		0			0
$541$	5.54076			0.238216			0.119108	−	0.992881i	$-0.461997\pi$
$541$	5.54076			0.238216			0.119108	+	0.992881i	$0.461997\pi$
$542$	−2.04488	−	9.23637i	−0.0878352	−	0.396736i
$543$		0			0
$544$	−12.0097	−	6.27372i	−0.514913	−	0.268984i
$545$		−	17.8859i		−	0.766149i
$546$		0			0
$547$		−	40.0369i		−	1.71185i	−0.517098	−	0.855926i	$-0.672988\pi$
$547$		−	40.0369i		−	1.71185i	0.517098	−	0.855926i	$-0.327012\pi$
$548$	−10.1788	−	21.8612i	−0.434818	−	0.933866i
$549$		0			0
$550$	13.0089	−	2.88011i	0.554703	−	0.122808i
$551$	−14.8523			−0.632729
$552$		0			0
$553$	13.3522			0.567792
$554$	−27.5095	+	6.09046i	−1.16877	+	0.258759i
$555$		0			0
$556$	6.96247	+	14.9534i	0.295274	+	0.634165i
$557$			19.0259i			0.806155i	0.915166	+	0.403077i	$0.132059\pi$
$557$			19.0259i			0.806155i	−0.915166	+	0.403077i	$0.867941\pi$
$558$		0			0
$559$			68.5334i			2.89865i
$560$	37.3075	−	44.3581i	1.57653	−	1.87447i
$561$		0			0
$562$	3.69218	+	16.6769i	0.155745	+	0.703473i
$563$	19.2965			0.813249			0.406624	−	0.913595i	$-0.366706\pi$
$563$	19.2965			0.813249			0.406624	+	0.913595i	$0.366706\pi$
$564$		0			0
$565$	26.1235			1.09903
$566$	−6.17787	−	27.9043i	−0.259675	−	1.17291i
$567$		0			0
$568$	−13.9346	+	10.6734i	−0.584682	+	0.447845i
$569$		−	1.11045i		−	0.0465524i	−0.999729	−	0.0232762i	$-0.992590\pi$
$569$		−	1.11045i		−	0.0465524i	0.999729	−	0.0232762i	$-0.00740971\pi$
$570$		0			0
$571$		−	15.2307i		−	0.637383i	−0.947858	−	0.318692i	$-0.896757\pi$
$571$		−	15.2307i		−	0.637383i	0.947858	−	0.318692i	$-0.103243\pi$
$572$	−31.1180	+	14.4889i	−1.30111	+	0.605811i
$573$		0			0
$574$	5.97512	−	1.32286i	0.249397	−	0.0552151i
$575$	−3.79349			−0.158199
$576$		0			0
$577$	−16.3165			−0.679265			−0.339633	−	0.940558i	$-0.610303\pi$
$577$	−16.3165			−0.679265			−0.339633	+	0.940558i	$0.610303\pi$
$578$	15.5513	−	3.44298i	0.646849	−	0.143209i
$579$		0			0
$580$	−42.6846	+	19.8744i	−1.77238	+	0.825240i
$581$			70.6235i			2.92995i
$582$		0			0
$583$			10.7383i			0.444733i
$584$	5.79186	−	4.43636i	0.239669	−	0.183578i
$585$		0			0
$586$	−5.92945	−	26.7823i	−0.244943	−	1.10637i
$587$	−47.3344			−1.95370			−0.976849	−	0.213930i	$-0.931374\pi$
$587$	−47.3344			−1.95370			−0.976849	+	0.213930i	$0.931374\pi$
$588$		0			0
$589$	9.08036			0.374150
$590$	2.59647	+	11.7278i	0.106895	+	0.482825i
$591$		0			0
$592$	2.97155	−	3.53313i	0.122130	−	0.145211i
$593$			2.02295i			0.0830727i	0.999137	+	0.0415363i	$0.0132252\pi$
$593$			2.02295i			0.0830727i	−0.999137	+	0.0415363i	$0.986775\pi$
$594$		0			0
$595$		−	34.7080i		−	1.42289i
$596$	14.6963	+	31.5634i	0.601983	+	1.29289i
$597$		0			0
$598$	9.54191	−	2.11253i	0.390198	−	0.0863876i
$599$	34.7329			1.41915			0.709574	−	0.704630i	$-0.248887\pi$
$599$	34.7329			1.41915			0.709574	+	0.704630i	$0.248887\pi$
$600$		0			0
$601$	33.6597			1.37301			0.686503	−	0.727127i	$-0.259145\pi$
$601$	33.6597			1.37301			0.686503	+	0.727127i	$0.259145\pi$
$602$	66.9131	−	14.8142i	2.72718	−	0.603782i
$603$		0			0
$604$	15.5222	+	33.3373i	0.631590	+	1.35648i
$605$		−	14.3282i		−	0.582523i
$606$		0			0
$607$		−	9.48505i		−	0.384986i	−0.981298	−	0.192493i	$-0.938343\pi$
$607$		−	9.48505i		−	0.384986i	0.981298	−	0.192493i	$-0.0616573\pi$
$608$	9.38004	+	4.90001i	0.380411	+	0.198722i
$609$		0			0
$610$	−9.02920	−	40.7833i	−0.365582	−	1.65127i
$611$	−5.97512			−0.241728
$612$		0			0
$613$	7.05129			0.284799			0.142400	−	0.989809i	$-0.454518\pi$
$613$	7.05129			0.284799			0.142400	+	0.989809i	$0.454518\pi$
$614$	1.19439	+	5.39483i	0.0482015	+	0.217718i
$615$		0			0
$616$	20.8728	+	27.2504i	0.840989	+	1.09795i
$617$			9.66949i			0.389279i	0.980875	+	0.194640i	$0.0623537\pi$
$617$			9.66949i			0.389279i	−0.980875	+	0.194640i	$0.937646\pi$
$618$		0			0
$619$			40.2173i			1.61647i	0.588861	+	0.808234i	$0.299576\pi$
$619$			40.2173i			1.61647i	−0.588861	+	0.808234i	$0.700424\pi$
$620$	26.0964	−	12.1508i	1.04806	−	0.487987i
$621$		0			0
$622$	−19.6484	+	4.35004i	−0.787828	+	0.174421i
$623$	19.6387			0.786806
$624$		0			0
$625$	−29.5769			−1.18308
$626$	−10.1365	+	2.24416i	−0.405135	+	0.0896947i
$627$		0			0
$628$	37.5951	−	17.5047i	1.50021	−	0.698513i
$629$		−	2.76450i		−	0.110228i
$630$		0			0
$631$			23.4323i			0.932826i	0.884567	+	0.466413i	$0.154454\pi$
$631$			23.4323i			0.932826i	−0.884567	+	0.466413i	$0.845546\pi$
$632$	4.69961	+	6.13555i	0.186940	+	0.244059i
$633$		0			0
$634$	−0.594798	−	2.68660i	−0.0236225	−	0.106699i
$635$	−9.71674			−0.385597
$636$		0			0
$637$	−116.634			−4.62120
$638$	−6.02752	−	27.2252i	−0.238632	−	1.07786i
$639$		0			0
$640$	33.5145	+	1.53055i	1.32478	+	0.0605001i
$641$		−	11.7644i		−	0.464666i	−0.972636	−	0.232333i	$-0.925364\pi$
$641$		−	11.7644i		−	0.464666i	0.972636	−	0.232333i	$-0.0746359\pi$
$642$		0			0
$643$		−	20.6478i		−	0.814271i	−0.913368	−	0.407135i	$-0.866528\pi$
$643$		−	20.6478i		−	0.814271i	0.913368	−	0.407135i	$-0.133472\pi$
$644$	−4.12516	−	8.85967i	−0.162554	−	0.349120i
$645$		0			0
$646$	6.18731	−	1.36984i	0.243436	−	0.0538955i
$647$	−23.6900			−0.931348			−0.465674	−	0.884956i	$-0.654188\pi$
$647$	−23.6900			−0.931348			−0.465674	+	0.884956i	$0.654188\pi$
$648$		0			0
$649$	−7.11361			−0.279234
$650$	−36.1971	+	8.01385i	−1.41977	+	0.314329i
$651$		0			0
$652$	12.7558	+	27.3959i	0.499556	+	1.07290i
$653$			25.4126i			0.994471i	0.867615	+	0.497236i	$0.165652\pi$
$653$			25.4126i			0.994471i	−0.867615	+	0.497236i	$0.834348\pi$
$654$		0			0
$655$		−	60.8422i		−	2.37730i
$656$	2.71096	+	2.28006i	0.105845	+	0.0890213i
$657$		0			0
$658$	1.29158	+	5.83386i	0.0503512	+	0.227428i
$659$	15.2701			0.594840			0.297420	−	0.954747i	$-0.403874\pi$
$659$	15.2701			0.594840			0.297420	+	0.954747i	$0.403874\pi$
$660$		0			0
$661$	0.457019			0.0177760			0.00888799	−	0.999961i	$-0.497171\pi$
$661$	0.457019			0.0177760			0.00888799	+	0.999961i	$0.497171\pi$
$662$	−10.2419	−	46.2609i	−0.398063	−	1.79798i
$663$		0			0
$664$	−32.4527	+	24.8576i	−1.25941	+	0.964660i
$665$			27.1082i			1.05121i
$666$		0			0
$667$			7.93906i			0.307401i
$668$	33.1753	−	15.4468i	1.28359	−	0.597654i
$669$		0			0
$670$	−7.96093	+	1.76251i	−0.307558	+	0.0680915i
$671$	24.7376			0.954983
$672$		0			0
$673$	−21.5969			−0.832500			−0.416250	−	0.909250i	$-0.636656\pi$
$673$	−21.5969			−0.832500			−0.416250	+	0.909250i	$0.636656\pi$
$674$	23.9748	−	5.30788i	0.923473	−	0.204452i
$675$		0			0
$676$	63.0150	−	29.3405i	2.42365	−	1.12848i
$677$		−	25.0650i		−	0.963326i	−0.876357	−	0.481663i	$-0.840033\pi$
$677$		−	25.0650i		−	0.963326i	0.876357	−	0.481663i	$-0.159967\pi$
$678$		0			0
$679$			62.6534i			2.40442i
$680$	15.9489	−	12.2163i	0.611613	−	0.468474i
$681$		0			0
$682$	3.68509	+	16.6449i	0.141109	+	0.637366i
$683$	−2.85457			−0.109227			−0.0546136	−	0.998508i	$-0.517393\pi$
$683$	−2.85457			−0.109227			−0.0546136	+	0.998508i	$0.517393\pi$
$684$		0			0
$685$	35.7547			1.36612
$686$	14.7551	+	66.6463i	0.563353	+	2.54457i
$687$		0			0
$688$	30.3590	+	25.5335i	1.15743	+	0.973456i
$689$		−	29.8790i		−	1.13830i
$690$		0			0
$691$			7.38984i			0.281123i	0.990072	+	0.140561i	$0.0448907\pi$
$691$			7.38984i			0.281123i	−0.990072	+	0.140561i	$0.955109\pi$
$692$	12.7383	+	27.3582i	0.484237	+	1.04000i
$693$		0			0
$694$	−24.9598	+	5.52595i	−0.947459	+	0.209762i
$695$	−24.4568			−0.927698
$696$		0			0
$697$	2.12119			0.0803459
$698$	19.4696	−	4.31046i	0.736936	−	0.163153i
$699$		0			0
$700$	15.6488	+	33.6091i	0.591468	+	1.27030i
$701$			12.0811i			0.456298i	0.973626	+	0.228149i	$0.0732673\pi$
$701$			12.0811i			0.456298i	−0.973626	+	0.228149i	$0.926733\pi$
$702$		0			0
$703$			2.15918i			0.0814349i
$704$	−5.17534	+	19.1828i	−0.195053	+	0.722979i
$705$		0			0
$706$	−5.11080	−	23.0846i	−0.192347	−	0.868800i
$707$	−39.5026			−1.48565
$708$		0			0
$709$	−23.5826			−0.885663			−0.442831	−	0.896605i	$-0.646026\pi$
$709$	−23.5826			−0.885663			−0.442831	+	0.896605i	$0.646026\pi$
$710$	−5.62559	−	25.4098i	−0.211124	−	0.953612i
$711$		0			0
$712$	6.91228	+	9.02429i	0.259049	+	0.338199i
$713$		−	4.85376i		−	0.181775i
$714$		0			0
$715$		−	50.8945i		−	1.90335i
$716$	0.730050	−	0.339919i	0.0272832	−	0.0127034i
$717$		0			0
$718$	22.9944	−	5.09083i	0.858143	−	0.189988i
$719$	−0.889904			−0.0331878			−0.0165939	−	0.999862i	$-0.505282\pi$
$719$	−0.889904			−0.0331878			−0.0165939	+	0.999862i	$0.505282\pi$
$720$		0			0
$721$	−13.7576			−0.512359
$722$	21.4023	−	4.73835i	0.796510	−	0.176343i
$723$		0			0
$724$	−40.3354	+	18.7806i	−1.49905	+	0.697976i
$725$		−	30.1167i		−	1.11851i
$726$		0			0
$727$		−	22.0816i		−	0.818961i	−0.912319	−	0.409480i	$-0.865710\pi$
$727$		−	22.0816i		−	0.818961i	0.912319	−	0.409480i	$-0.134290\pi$
$728$	−58.0782	−	75.8237i	−2.15252	−	2.81021i
$729$		0			0
$730$	2.33826	+	10.5615i	0.0865428	+	0.390899i
$731$	23.7544			0.878589
$732$		0			0
$733$	−9.86197			−0.364260			−0.182130	−	0.983274i	$-0.558299\pi$
$733$	−9.86197			−0.364260			−0.182130	+	0.983274i	$0.558299\pi$
$734$	2.49113	+	11.2520i	0.0919493	+	0.415319i
$735$		0			0
$736$	2.61922	−	5.01395i	0.0965458	−	0.184817i
$737$		−	4.82879i		−	0.177871i
$738$		0			0
$739$		−	24.1781i		−	0.889407i	−0.895678	−	0.444704i	$-0.853309\pi$
$739$		−	24.1781i		−	0.889407i	0.895678	−	0.444704i	$-0.146691\pi$
$740$	2.88928	+	6.20534i	0.106212	+	0.228113i
$741$		0			0
$742$	−29.1726	+	6.45865i	−1.07096	+	0.237104i
$743$	−34.3825			−1.26137			−0.630686	−	0.776038i	$-0.717226\pi$
$743$	−34.3825			−1.26137			−0.630686	+	0.776038i	$0.717226\pi$
$744$		0			0
$745$	−51.6230			−1.89132
$746$	−11.3988	+	2.52363i	−0.417339	+	0.0923966i
$747$		0			0
$748$	5.02200	+	10.7858i	0.183623	+	0.394369i
$749$		−	75.1620i		−	2.74636i
$750$		0			0
$751$		−	21.7090i		−	0.792171i	−0.918214	−	0.396086i	$-0.870368\pi$
$751$		−	21.7090i		−	0.792171i	0.918214	−	0.396086i	$-0.129632\pi$
$752$	−2.22615	+	2.64687i	−0.0811794	+	0.0965213i
$753$		0			0
$754$	16.7715	+	75.7537i	0.610781	+	2.75879i
$755$	−54.5242			−1.98434
$756$		0			0
$757$	10.3678			0.376825			0.188412	−	0.982090i	$-0.439666\pi$
$757$	10.3678			0.376825			0.188412	+	0.982090i	$0.439666\pi$
$758$	−5.00757	−	22.6183i	−0.181883	−	0.821534i
$759$		0			0
$760$	−12.4567	+	9.54138i	−0.451852	+	0.346102i
$761$		−	19.1235i		−	0.693228i	−0.938008	−	0.346614i	$-0.887331\pi$
$761$		−	19.1235i		−	0.693228i	0.938008	−	0.346614i	$-0.112669\pi$
$762$		0			0
$763$			29.4732i			1.06700i
$764$	−29.9580	+	13.9488i	−1.08384	+	0.504648i
$765$		0			0
$766$	−21.7605	+	4.81765i	−0.786239	+	0.174069i
$767$	19.7935			0.714702
$768$		0			0
$769$	6.81042			0.245590			0.122795	−	0.992432i	$-0.460814\pi$
$769$	6.81042			0.245590			0.122795	+	0.992432i	$0.460814\pi$
$770$	−49.6912	+	11.0014i	−1.79075	+	0.396462i
$771$		0			0
$772$	38.3109	−	17.8380i	1.37884	−	0.642004i
$773$		−	19.7958i		−	0.712005i	−0.934485	−	0.356002i	$-0.884139\pi$
$773$		−	19.7958i		−	0.712005i	0.934485	−	0.356002i	$-0.115861\pi$
$774$		0			0
$775$			18.4127i			0.661403i
$776$	−28.7903	+	22.0523i	−1.03351	+	0.791632i
$777$		0			0
$778$	−6.92121	−	31.2619i	−0.248137	−	1.12079i
$779$	−1.65673			−0.0593585
$780$		0			0
$781$	15.4126			0.551505
$782$	−0.732224	−	3.30733i	−0.0261843	−	0.118270i
$783$		0			0
$784$	−43.4543	+	51.6666i	−1.55194	+	1.84523i
$785$			61.4879i			2.19460i
$786$		0			0
$787$			26.7177i			0.952382i	0.879342	+	0.476191i	$0.157983\pi$
$787$			26.7177i			0.952382i	−0.879342	+	0.476191i	$0.842017\pi$
$788$	8.35648	+	17.9473i	0.297687	+	0.639347i
$789$		0			0
$790$	−11.1882	+	2.47701i	−0.398058	+	0.0881279i
$791$	−43.0475			−1.53059
$792$		0			0
$793$	−68.8318			−2.44429
$794$	−13.7744	+	3.04957i	−0.488835	+	0.108225i
$795$		0			0
$796$	0.966527	+	2.07583i	0.0342577	+	0.0735757i
$797$		−	7.91237i		−	0.280270i	−0.990132	−	0.140135i	$-0.955246\pi$
$797$		−	7.91237i		−	0.280270i	0.990132	−	0.140135i	$-0.0447537\pi$
$798$		0			0
$799$			2.07104i			0.0732682i
$800$	−9.93599	+	19.0204i	−0.351290	+	0.672472i
$801$		0			0
$802$	8.48648	+	38.3319i	0.299668	+	1.35355i
$803$	−6.40619			−0.226070
$804$		0			0
$805$	14.4903			0.510715
$806$	−10.2537	−	46.3141i	−0.361171	−	1.63135i
$807$		0			0
$808$	−13.9038	−	18.1521i	−0.489136	−	0.638588i
$809$			39.2974i			1.38162i	0.723035	+	0.690811i	$0.242746\pi$
$809$			39.2974i			1.38162i	−0.723035	+	0.690811i	$0.757254\pi$
$810$		0			0
$811$		−	34.2535i		−	1.20280i	−0.798946	−	0.601402i	$-0.794609\pi$
$811$		−	34.2535i		−	1.20280i	0.798946	−	0.601402i	$-0.205391\pi$
$812$	70.3374	−	32.7499i	2.46836	−	1.14930i
$813$		0			0
$814$	−3.95791	+	0.876260i	−0.138725	+	0.0307129i
$815$	−44.8068			−1.56951
$816$		0			0
$817$	−18.5531			−0.649090
$818$	48.1345	−	10.6567i	1.68298	−	0.372603i
$819$		0			0
$820$	−4.76134	+	2.21693i	−0.166273	+	0.0774186i
$821$			10.5883i			0.369533i	0.982782	+	0.184767i	$0.0591529\pi$
$821$			10.5883i			0.369533i	−0.982782	+	0.184767i	$0.940847\pi$
$822$		0			0
$823$			26.7188i			0.931358i	0.884954	+	0.465679i	$0.154190\pi$
$823$			26.7188i			0.931358i	−0.884954	+	0.465679i	$0.845810\pi$
$824$	−4.84230	−	6.32184i	−0.168690	−	0.220232i
$825$		0			0
$826$	−4.27857	−	19.3255i	−0.148870	−	0.672421i
$827$	28.7417			0.999448			0.499724	−	0.866185i	$-0.333435\pi$
$827$	28.7417			0.999448			0.499724	+	0.866185i	$0.333435\pi$
$828$		0			0
$829$	4.62081			0.160487			0.0802436	−	0.996775i	$-0.474430\pi$
$829$	4.62081			0.160487			0.0802436	+	0.996775i	$0.474430\pi$
$830$	−13.1016	−	59.1776i	−0.454763	−	2.05408i
$831$		0			0
$832$	14.4003	−	53.3758i	0.499240	−	1.85047i
$833$			40.4265i			1.40070i
$834$		0			0
$835$			54.2592i			1.87772i
$836$	−3.92237	−	8.42413i	−0.135658	−	0.291355i
$837$		0			0
$838$	−2.42611	+	0.537127i	−0.0838085	+	0.0185547i
$839$	−27.2451			−0.940605			−0.470302	−	0.882505i	$-0.655855\pi$
$839$	−27.2451			−0.940605			−0.470302	+	0.882505i	$0.655855\pi$
$840$		0			0
$841$	−34.0286			−1.17340
$842$	−10.4172	+	2.30630i	−0.358999	+	0.0794804i
$843$		0			0
$844$	−9.45905	−	20.3153i	−0.325594	−	0.699283i
$845$			103.063i			3.54548i
$846$		0			0
$847$			23.6105i			0.811268i
$848$	−13.2358	−	11.1320i	−0.454520	−	0.382275i
$849$		0			0
$850$	2.77768	+	12.5463i	0.0952738	+	0.430335i
$851$	1.15415			0.0395639
$852$		0			0
$853$	2.66223			0.0911530			0.0455765	−	0.998961i	$-0.485488\pi$
$853$	2.66223			0.0911530			0.0455765	+	0.998961i	$0.485488\pi$
$854$	14.8787	+	67.2045i	0.509138	+	2.29969i
$855$		0			0
$856$	34.5382	−	26.4550i	1.18049	−	0.904214i
$857$		−	30.9690i		−	1.05788i	−0.848659	−	0.528940i	$-0.822590\pi$
$857$		−	30.9690i		−	1.05788i	0.848659	−	0.528940i	$-0.177410\pi$
$858$		0			0
$859$			14.8750i			0.507527i	0.967266	+	0.253764i	$0.0816685\pi$
$859$			14.8750i			0.507527i	−0.967266	+	0.253764i	$0.918331\pi$
$860$	−53.3204	+	24.8266i	−1.81821	+	0.846579i
$861$		0			0
$862$	18.9560	−	4.19676i	0.645645	−	0.142942i
$863$	45.1386			1.53653			0.768267	−	0.640129i	$-0.221119\pi$
$863$	45.1386			1.53653			0.768267	+	0.640129i	$0.221119\pi$
$864$		0			0
$865$	−44.7452			−1.52138
$866$	10.2800	−	2.27593i	0.349329	−	0.0773394i
$867$		0			0
$868$	−43.0027	+	20.0225i	−1.45961	+	0.679609i
$869$		−	6.78632i		−	0.230210i
$870$		0			0
$871$			13.4360i			0.455262i
$872$	−13.5434	+	10.3738i	−0.458638	+	0.351300i
$873$		0			0
$874$	0.571894	+	2.58314i	0.0193446	+	0.0873762i
$875$	17.4827			0.591022
$876$		0			0
$877$	6.41194			0.216516			0.108258	−	0.994123i	$-0.465473\pi$
$877$	6.41194			0.216516			0.108258	+	0.994123i	$0.465473\pi$
$878$	−11.0947	−	50.1130i	−0.374429	−	1.69123i
$879$		0			0
$880$	−22.5453	−	18.9618i	−0.760002	−	0.639201i
$881$			19.8859i			0.669973i	0.942223	+	0.334987i	$0.108732\pi$
$881$			19.8859i			0.669973i	−0.942223	+	0.334987i	$0.891268\pi$
$882$		0			0
$883$		−	26.0266i		−	0.875864i	−0.899008	−	0.437932i	$-0.855711\pi$
$883$		−	26.0266i		−	0.875864i	0.899008	−	0.437932i	$-0.144289\pi$
$884$	−13.9736	−	30.0114i	−0.469984	−	1.00939i
$885$		0			0
$886$	16.0345	−	3.54994i	0.538689	−	0.119263i
$887$	−32.0532			−1.07624			−0.538120	−	0.842868i	$-0.680865\pi$
$887$	−32.0532			−1.07624			−0.538120	+	0.842868i	$0.680865\pi$
$888$		0			0
$889$	16.0116			0.537013
$890$	−16.4558	+	3.64323i	−0.551601	+	0.122121i
$891$		0			0
$892$	14.1672	+	30.4271i	0.474353	+	1.01878i
$893$		−	1.61756i		−	0.0541296i
$894$		0			0
$895$			1.19402i			0.0399117i
$896$	−55.2267	−	2.52210i	−1.84499	−	0.0842573i
$897$		0			0
$898$	−9.83949	−	44.4433i	−0.328348	−	1.48309i
$899$	38.5343			1.28519
$900$		0			0
$901$	−10.3564			−0.345021
$902$	−0.672352	−	3.03689i	−0.0223869	−	0.101118i
$903$		0			0
$904$	−15.1516	−	19.7810i	−0.503933	−	0.657907i
$905$		−	65.9698i		−	2.19291i
$906$		0			0
$907$		−	1.79275i		−	0.0595273i	−0.999557	−	0.0297637i	$-0.990525\pi$
$907$		−	1.79275i		−	0.0595273i	0.999557	−	0.0297637i	$-0.00947547\pi$
$908$	−17.9246	+	8.34591i	−0.594850	+	0.276969i
$909$		0			0
$910$	138.265	−	30.6111i	4.58344	−	1.01475i
$911$	37.0080			1.22613			0.613065	−	0.790032i	$-0.289936\pi$
$911$	37.0080			1.22613			0.613065	+	0.790032i	$0.289936\pi$
$912$		0			0
$913$	35.8948			1.18794
$914$	27.1267	−	6.00571i	0.897273	−	0.198651i
$915$		0			0
$916$	−16.1890	+	7.53780i	−0.534901	+	0.249056i
$917$			100.258i			3.31082i
$918$		0			0
$919$			15.4173i			0.508569i	0.967129	+	0.254285i	$0.0818400\pi$
$919$			15.4173i			0.508569i	−0.967129	+	0.254285i	$0.918160\pi$
$920$	5.10019	+	6.65853i	0.168148	+	0.219525i
$921$		0			0
$922$	−2.46008	−	11.1117i	−0.0810184	−	0.365946i
$923$	−42.8852			−1.41158
$924$		0			0
$925$	−4.37827			−0.143957
$926$	4.36305	+	19.7071i	0.143379	+	0.647616i
$927$		0			0
$928$	39.8060	+	20.7941i	1.30670	+	0.682601i
$929$		−	3.59579i		−	0.117974i	−0.998259	−	0.0589870i	$-0.981213\pi$
$929$		−	3.59579i		−	0.117974i	0.998259	−	0.0589870i	$-0.0187870\pi$
$930$		0			0
$931$		−	31.5746i		−	1.03482i
$932$	−16.1907	−	34.7730i	−0.530344	−	1.13903i
$933$		0			0
$934$	−10.8547	+	2.40318i	−0.355178	+	0.0786344i
$935$	−17.6406			−0.576908
$936$		0			0
$937$	6.74552			0.220366			0.110183	−	0.993911i	$-0.464856\pi$
$937$	6.74552			0.220366			0.110183	+	0.993911i	$0.464856\pi$
$938$	13.1184	−	2.90433i	0.428330	−	0.0948298i
$939$		0			0
$940$	−2.16452	−	4.64877i	−0.0705988	−	0.151626i
$941$			39.3458i			1.28264i	0.767275	+	0.641318i	$0.221612\pi$
$941$			39.3458i			1.28264i	−0.767275	+	0.641318i	$0.778388\pi$
$942$		0			0
$943$			0.885578i			0.0288384i
$944$	7.37447	−	8.76814i	0.240018	−	0.285379i
$945$		0			0
$946$	−7.52941	−	34.0090i	−0.244802	−	1.10573i
$947$	−30.6870			−0.997194			−0.498597	−	0.866834i	$-0.666151\pi$
$947$	−30.6870			−0.997194			−0.498597	+	0.866834i	$0.666151\pi$
$948$		0			0
$949$	17.8251			0.578627
$950$	−2.16947	−	9.79913i	−0.0703870	−	0.317926i
$951$		0			0
$952$	−26.2813	+	20.1305i	−0.851782	+	0.652434i
$953$		−	12.1012i		−	0.391997i	−0.980604	−	0.195998i	$-0.937205\pi$
$953$		−	12.1012i		−	0.391997i	0.980604	−	0.195998i	$-0.0627947\pi$
$954$		0			0
$955$		−	48.9972i		−	1.58551i
$956$	−11.3737	+	5.29572i	−0.367851	+	0.171276i
$957$		0			0
$958$	−41.8342	+	9.26185i	−1.35160	+	0.299237i
$959$	−58.9182			−1.90257
$960$		0			0
$961$	7.44102			0.240033
$962$	11.0128	−	2.43818i	0.355068	−	0.0786100i
$963$		0			0
$964$	26.7300	−	12.4458i	0.860916	−	0.400852i
$965$			62.6588i			2.01706i
$966$		0			0
$967$		−	25.6908i		−	0.826162i	−0.910694	−	0.413081i	$-0.864453\pi$
$967$		−	25.6908i		−	0.826162i	0.910694	−	0.413081i	$-0.135547\pi$
$968$	−10.8494	+	8.31028i	−0.348714	+	0.267102i
$969$		0			0
$970$	−11.6230	−	52.4993i	−0.373193	−	1.68565i
$971$	32.9020			1.05588			0.527938	−	0.849283i	$-0.322965\pi$
$971$	32.9020			1.05588			0.527938	+	0.849283i	$0.322965\pi$
$972$		0			0
$973$	40.3009			1.29199
$974$	6.54345	+	29.5556i	0.209666	+	0.947024i
$975$		0			0
$976$	−25.6447	+	30.4912i	−0.820866	+	0.975999i
$977$			33.5011i			1.07179i	0.844283	+	0.535897i	$0.180026\pi$
$977$			33.5011i			1.07179i	−0.844283	+	0.535897i	$0.819974\pi$
$978$		0			0
$979$		−	9.98147i		−	0.319009i
$980$	−42.2512	−	90.7435i	−1.34966	−	2.89869i
$981$		0			0
$982$	1.43030	−	0.316660i	0.0456426	−	0.0101050i
$983$	8.91513			0.284348			0.142174	−	0.989842i	$-0.454591\pi$
$983$	8.91513			0.284348			0.142174	+	0.989842i	$0.454591\pi$
$984$		0			0
$985$	−29.3535			−0.935279
$986$	26.2571	−	5.81317i	0.836195	−	0.185129i
$987$		0			0
$988$	10.9139	+	23.4400i	0.347218	+	0.745725i
$989$			9.91725i			0.315350i
$990$		0			0
$991$			42.7175i			1.35697i	0.734616	+	0.678483i	$0.237362\pi$
$991$			42.7175i			1.35697i	−0.734616	+	0.678483i	$0.762638\pi$
$992$	−24.3365	−	12.7131i	−0.772685	−	0.403640i
$993$		0			0
$994$	9.27008	+	41.8713i	0.294029	+	1.32808i
$995$	−3.39508			−0.107631
$996$		0			0
$997$	−26.5222			−0.839967			−0.419984	−	0.907532i	$-0.637964\pi$
$997$	−26.5222			−0.839967			−0.419984	+	0.907532i	$0.637964\pi$
$998$	7.88222	+	35.6026i	0.249507	+	1.12698i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	828.2.c.f.323.10	yes	12
3.2	odd	2		828.2.c.e.323.3	yes	12
4.3	odd	2		828.2.c.e.323.2	✓	12
12.11	even	2	inner	828.2.c.f.323.11	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
828.2.c.e.323.2	✓	12	4.3	odd	2
828.2.c.e.323.3	yes	12	3.2	odd	2
828.2.c.f.323.10	yes	12	1.1	even	1	trivial
828.2.c.f.323.11	yes	12	12.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38078 - 0.305697i) q^{2} +(1.81310 - 0.844199i) q^{4} +2.96538i q^{5} -4.88648i q^{7} +(2.24542 - 1.71991i) q^{8} +(0.906508 + 4.09454i) q^{10} -2.48358 q^{11} +6.91053 q^{13} +(-1.49378 - 6.74715i) q^{14} +(2.57466 - 3.06123i) q^{16} -2.39526i q^{17} +1.87079i q^{19} +(2.50337 + 5.37653i) q^{20} +(-3.42928 + 0.759224i) q^{22} +1.00000 q^{23} -3.79349 q^{25} +(9.54191 - 2.11253i) q^{26} +(-4.12516 - 8.85967i) q^{28} +7.93906i q^{29} -4.85376i q^{31} +(2.61922 - 5.01395i) q^{32} +(-0.732224 - 3.30733i) q^{34} +14.4903 q^{35} +1.15415 q^{37} +(0.571894 + 2.58314i) q^{38} +(5.10019 + 6.65853i) q^{40} +0.885578i q^{41} +9.91725i q^{43} +(-4.50298 + 2.09664i) q^{44} +(1.38078 - 0.305697i) q^{46} -0.864641 q^{47} -16.8777 q^{49} +(-5.23797 + 1.15966i) q^{50} +(12.5295 - 5.83386i) q^{52} -4.32369i q^{53} -7.36478i q^{55} +(-8.40431 - 10.9722i) q^{56} +(2.42694 + 10.9621i) q^{58} +2.86425 q^{59} -9.96042 q^{61} +(-1.48378 - 6.70197i) q^{62} +(2.08382 - 7.72384i) q^{64} +20.4924i q^{65} +1.94428i q^{67} +(-2.02208 - 4.34285i) q^{68} +(20.0079 - 4.42963i) q^{70} -6.20578 q^{71} +2.57941 q^{73} +(1.59363 - 0.352821i) q^{74} +(1.57932 + 3.39192i) q^{76} +12.1360i q^{77} +2.73247i q^{79} +(9.07772 + 7.63484i) q^{80} +(0.270718 + 1.22279i) q^{82} -14.4528 q^{83} +7.10287 q^{85} +(3.03167 + 13.6935i) q^{86} +(-5.57669 + 4.27154i) q^{88} +4.01898i q^{89} -33.7682i q^{91} +(1.81310 - 0.844199i) q^{92} +(-1.19388 + 0.264318i) q^{94} -5.54760 q^{95} -12.8218 q^{97} +(-23.3044 + 5.15946i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 4 q^{4} + 4 q^{8} - 8 q^{10} + 12 q^{11} - 4 q^{13} - 12 q^{14} - 12 q^{16} + 20 q^{20} + 4 q^{22} + 12 q^{23} - 40 q^{25} + 8 q^{26} - 24 q^{28} + 44 q^{32} - 28 q^{34} + 40 q^{35} - 32 q^{37}+ \cdots - 20 q^{98}+O(q^{100}) \) 12 * q + 4 * q^2 + 4 * q^4 + 4 * q^8 - 8 * q^10 + 12 * q^11 - 4 * q^13 - 12 * q^14 - 12 * q^16 + 20 * q^20 + 4 * q^22 + 12 * q^23 - 40 * q^25 + 8 * q^26 - 24 * q^28 + 44 * q^32 - 28 * q^34 + 40 * q^35 - 32 * q^37 - 32 * q^38 - 12 * q^40 + 4 * q^44 + 4 * q^46 - 32 * q^49 - 20 * q^50 + 32 * q^52 - 8 * q^56 - 16 * q^58 - 24 * q^59 - 56 * q^61 + 28 * q^64 + 16 * q^68 + 64 * q^70 - 56 * q^71 + 8 * q^73 - 36 * q^74 - 28 * q^76 + 28 * q^80 + 24 * q^82 - 28 * q^83 - 12 * q^85 - 8 * q^86 + 4 * q^88 + 4 * q^92 + 16 * q^94 + 8 * q^95 - 4 * q^97 - 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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