LMFDB - Embedded newform 308.2.i.a.177.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [308,2,Mod(177,308)] 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("308.177"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(308, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	308.177
Dual form			308.2.i.a.221.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.59097 - 2.75564i) q^{3} +(1.71053 - 2.96273i) q^{5} +(-0.710533 - 2.54856i) q^{7} +(-3.56238 + 6.17023i) q^{9} +(0.500000 + 0.866025i) q^{11} +3.66019 q^{13} -10.8856 q^{15} +(0.880438 + 1.52496i) q^{17} +(-1.88044 + 3.25701i) q^{19} +(-5.89248 + 6.01266i) q^{21} +(0.619562 - 1.07311i) q^{23} +(-3.35185 - 5.80557i) q^{25} +13.1248 q^{27} -2.89931 q^{29} +(-4.73229 - 8.19656i) q^{31} +(1.59097 - 2.75564i) q^{33} +(-8.76608 - 2.25427i) q^{35} +(-1.42107 + 2.46136i) q^{37} +(-5.82326 - 10.0862i) q^{39} +8.70370 q^{41} +12.0676 q^{43} +(12.1871 + 21.1088i) q^{45} +(-2.11956 + 3.67119i) q^{47} +(-5.99028 + 3.62167i) q^{49} +(2.80150 - 4.85235i) q^{51} +(0.112725 + 0.195246i) q^{53} +3.42107 q^{55} +11.9669 q^{57} +(3.27292 + 5.66886i) q^{59} +(5.12476 - 8.87635i) q^{61} +(18.2564 + 4.69478i) q^{63} +(6.26088 - 10.8442i) q^{65} +(1.70370 + 2.95089i) q^{67} -3.94282 q^{69} -4.23912 q^{71} +(-5.09097 - 8.81782i) q^{73} +(-10.6654 + 18.4730i) q^{75} +(1.85185 - 1.88962i) q^{77} +(3.67511 - 6.36547i) q^{79} +(-10.1940 - 17.6565i) q^{81} -10.4887 q^{83} +6.02408 q^{85} +(4.61273 + 7.98947i) q^{87} +(-3.63160 + 6.29012i) q^{89} +(-2.60069 - 9.32820i) q^{91} +(-15.0579 + 26.0810i) q^{93} +(6.43310 + 11.1425i) q^{95} +11.7472 q^{97} -7.12476 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 2 q^{5} + 4 q^{7} - 4 q^{9} + 3 q^{11} + 6 q^{13} - 30 q^{15} + 5 q^{17} - 11 q^{19} - 10 q^{21} + 4 q^{23} - 11 q^{25} + 44 q^{27} - 2 q^{29} - 19 q^{31} + q^{33} - 17 q^{35} + 8 q^{37}+ \cdots - 8 q^{99}+O(q^{100}) $ 6 * q - q^3 + 2 * q^5 + 4 * q^7 - 4 * q^9 + 3 * q^11 + 6 * q^13 - 30 * q^15 + 5 * q^17 - 11 * q^19 - 10 * q^21 + 4 * q^23 - 11 * q^25 + 44 * q^27 - 2 * q^29 - 19 * q^31 + q^33 - 17 * q^35 + 8 * q^37 - 17 * q^39 + 34 * q^41 + 20 * q^43 + 21 * q^45 - 13 * q^47 - 12 * q^49 - 9 * q^53 + 4 * q^55 + 4 * q^57 - 6 * q^59 - 4 * q^61 + 50 * q^63 + 37 * q^65 - 8 * q^67 - 6 * q^69 - 26 * q^71 - 22 * q^73 - 13 * q^75 + 2 * q^77 - 5 * q^79 - 19 * q^81 + 6 * q^83 - 14 * q^85 + 18 * q^87 + 3 * q^89 - 31 * q^91 - 14 * q^93 - 3 * q^95 + 50 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−1.59097	−	2.75564i	−0.918548	−	1.59097i	−0.801622	−	0.597831i	$-0.796029\pi$
$3$	−1.59097	−	2.75564i	−0.918548	−	1.59097i	−0.116926	−	0.993141i	$-0.537304\pi$
$4$		0			0
$5$	1.71053	−	2.96273i	0.764974	−	1.32497i	−0.175287	−	0.984517i	$-0.556085\pi$
$5$	1.71053	−	2.96273i	0.764974	−	1.32497i	0.940260	−	0.340456i	$-0.110581\pi$
$6$		0			0
$7$	−0.710533	−	2.54856i	−0.268556	−	0.963264i
$7$	−0.710533	−	2.54856i	−0.268556	−	0.963264i
$8$		0			0
$9$	−3.56238	+	6.17023i	−1.18746	+	2.05674i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	3.66019			1.01515			0.507577	−	0.861606i	$-0.330541\pi$
$13$	3.66019			1.01515			0.507577	+	0.861606i	$0.330541\pi$
$14$		0			0
$15$	−10.8856			−2.81066
$16$		0			0
$17$	0.880438	+	1.52496i	0.213538	+	0.369858i	0.952819	−	0.303538i	$-0.0981681\pi$
$17$	0.880438	+	1.52496i	0.213538	+	0.369858i	−0.739282	+	0.673396i	$0.764835\pi$
$18$		0			0
$19$	−1.88044	+	3.25701i	−0.431402	+	0.747210i	−0.996994	−	0.0774746i	$-0.975314\pi$
$19$	−1.88044	+	3.25701i	−0.431402	+	0.747210i	0.565592	+	0.824685i	$0.308648\pi$
$20$		0			0
$21$	−5.89248	+	6.01266i	−1.28584	+	1.31207i
$22$		0			0
$23$	0.619562	−	1.07311i	0.129188	−	0.223759i	−0.794175	−	0.607690i	$-0.792096\pi$
$23$	0.619562	−	1.07311i	0.129188	−	0.223759i	0.923362	+	0.383930i	$0.125430\pi$
$24$		0			0
$25$	−3.35185	−	5.80557i	−0.670370	−	1.16111i
$26$		0			0
$27$	13.1248			2.52586
$28$		0			0
$29$	−2.89931			−0.538389			−0.269194	−	0.963086i	$-0.586757\pi$
$29$	−2.89931			−0.538389			−0.269194	+	0.963086i	$0.586757\pi$
$30$		0			0
$31$	−4.73229	−	8.19656i	−0.849944	−	1.47215i	−0.881258	−	0.472636i	$-0.843302\pi$
$31$	−4.73229	−	8.19656i	−0.849944	−	1.47215i	0.0313138	−	0.999510i	$-0.490031\pi$
$32$		0			0
$33$	1.59097	−	2.75564i	0.276953	−	0.479696i
$34$		0			0
$35$	−8.76608	−	2.25427i	−1.48174	−	0.381042i
$36$		0			0
$37$	−1.42107	+	2.46136i	−0.233622	+	0.404645i	−0.958871	−	0.283841i	$-0.908391\pi$
$37$	−1.42107	+	2.46136i	−0.233622	+	0.404645i	0.725249	+	0.688486i	$0.241724\pi$
$38$		0			0
$39$	−5.82326	−	10.0862i	−0.932468	−	1.61508i
$40$		0			0
$41$	8.70370			1.35929			0.679645	−	0.733542i	$-0.262134\pi$
$41$	8.70370			1.35929			0.679645	+	0.733542i	$0.262134\pi$
$42$		0			0
$43$	12.0676			1.84029			0.920145	−	0.391579i	$-0.128071\pi$
$43$	12.0676			1.84029			0.920145	+	0.391579i	$0.128071\pi$
$44$		0			0
$45$	12.1871	+	21.1088i	1.81675	+	3.14671i
$46$		0			0
$47$	−2.11956	+	3.67119i	−0.309170	+	0.535498i	−0.978181	−	0.207754i	$-0.933384\pi$
$47$	−2.11956	+	3.67119i	−0.309170	+	0.535498i	0.669011	+	0.743252i	$0.266718\pi$
$48$		0			0
$49$	−5.99028	+	3.62167i	−0.855755	+	0.517381i
$50$		0			0
$51$	2.80150	−	4.85235i	0.392289	−	0.679465i
$52$		0			0
$53$	0.112725	+	0.195246i	0.0154840	+	0.0268190i	0.873664	−	0.486531i	$-0.161738\pi$
$53$	0.112725	+	0.195246i	0.0154840	+	0.0268190i	−0.858180	+	0.513350i	$0.828404\pi$
$54$		0			0
$55$	3.42107			0.461297
$56$		0			0
$57$	11.9669			1.58505
$58$		0			0
$59$	3.27292	+	5.66886i	0.426097	+	0.738022i	0.996522	−	0.0833277i	$-0.0265548\pi$
$59$	3.27292	+	5.66886i	0.426097	+	0.738022i	−0.570425	+	0.821350i	$0.693221\pi$
$60$		0			0
$61$	5.12476	−	8.87635i	0.656159	−	1.13650i	−0.325443	−	0.945562i	$-0.605514\pi$
$61$	5.12476	−	8.87635i	0.656159	−	1.13650i	0.981602	−	0.190939i	$-0.0611532\pi$
$62$		0			0
$63$	18.2564	+	4.69478i	2.30009	+	0.591487i
$64$		0			0
$65$	6.26088	−	10.8442i	0.776566	−	1.34505i
$66$		0			0
$67$	1.70370	+	2.95089i	0.208140	+	0.360509i	0.951129	−	0.308795i	$-0.0999258\pi$
$67$	1.70370	+	2.95089i	0.208140	+	0.360509i	−0.742989	+	0.669304i	$0.766592\pi$
$68$		0			0
$69$	−3.94282			−0.474660
$70$		0			0
$71$	−4.23912			−0.503091			−0.251546	−	0.967845i	$-0.580939\pi$
$71$	−4.23912			−0.503091			−0.251546	+	0.967845i	$0.580939\pi$
$72$		0			0
$73$	−5.09097	−	8.81782i	−0.595853	−	1.03205i	−0.993426	−	0.114477i	$-0.963481\pi$
$73$	−5.09097	−	8.81782i	−0.595853	−	1.03205i	0.397573	−	0.917571i	$-0.369853\pi$
$74$		0			0
$75$	−10.6654	+	18.4730i	−1.23153	+	2.13308i
$76$		0			0
$77$	1.85185	−	1.88962i	0.211038	−	0.215342i
$78$		0			0
$79$	3.67511	−	6.36547i	0.413482	−	0.716172i	−0.581786	−	0.813342i	$-0.697646\pi$
$79$	3.67511	−	6.36547i	0.413482	−	0.716172i	0.995268	+	0.0971704i	$0.0309792\pi$
$80$		0			0
$81$	−10.1940	−	17.6565i	−1.13266	−	1.96183i
$82$		0			0
$83$	−10.4887			−1.15128			−0.575639	−	0.817704i	$-0.695247\pi$
$83$	−10.4887			−1.15128			−0.575639	+	0.817704i	$0.695247\pi$
$84$		0			0
$85$	6.02408			0.653403
$86$		0			0
$87$	4.61273	+	7.98947i	0.494536	+	0.856562i
$88$		0			0
$89$	−3.63160	+	6.29012i	−0.384949	+	0.666751i	−0.991762	−	0.128094i	$-0.959114\pi$
$89$	−3.63160	+	6.29012i	−0.384949	+	0.666751i	0.606813	+	0.794844i	$0.292448\pi$
$90$		0			0
$91$	−2.60069	−	9.32820i	−0.272626	−	0.977861i
$92$		0			0
$93$	−15.0579	+	26.0810i	−1.56143	+	2.70447i
$94$		0			0
$95$	6.43310	+	11.1425i	0.660023	+	1.14319i
$96$		0			0
$97$	11.7472			1.19275			0.596374	−	0.802707i	$-0.296608\pi$
$97$	11.7472			1.19275			0.596374	+	0.802707i	$0.296608\pi$
$98$		0			0
$99$	−7.12476			−0.716066
$100$		0			0
$101$	−6.02696	−	10.4390i	−0.599704	−	1.03872i	−0.992864	−	0.119249i	$-0.961951\pi$
$101$	−6.02696	−	10.4390i	−0.599704	−	1.03872i	0.393160	−	0.919470i	$-0.371382\pi$
$102$		0			0
$103$	8.44802	−	14.6324i	0.832408	−	1.44177i	−0.0637149	−	0.997968i	$-0.520295\pi$
$103$	8.44802	−	14.6324i	0.832408	−	1.44177i	0.896123	−	0.443805i	$-0.146372\pi$
$104$		0			0
$105$	7.73461	+	27.7427i	0.754821	+	2.70741i
$106$		0			0
$107$	−0.572097	+	0.990901i	−0.0553067	+	0.0957940i	−0.892353	−	0.451338i	$-0.850947\pi$
$107$	−0.572097	+	0.990901i	−0.0553067	+	0.0957940i	0.837047	+	0.547132i	$0.184280\pi$
$108$		0			0
$109$	1.65335	+	2.86369i	0.158363	+	0.274292i	0.934278	−	0.356545i	$-0.116045\pi$
$109$	1.65335	+	2.86369i	0.158363	+	0.274292i	−0.775916	+	0.630836i	$0.782712\pi$
$110$		0			0
$111$	9.04351			0.858372
$112$		0			0
$113$	−17.5322			−1.64929			−0.824643	−	0.565653i	$-0.808624\pi$
$113$	−17.5322			−1.64929			−0.824643	+	0.565653i	$0.808624\pi$
$114$		0			0
$115$	−2.11956	−	3.67119i	−0.197650	−	0.342340i
$116$		0			0
$117$	−13.0390	+	22.5842i	−1.20546	+	2.08791i
$118$		0			0
$119$	3.26088	−	3.32738i	0.298924	−	0.305021i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−13.8473	−	23.9843i	−1.24857	−	2.16259i
$124$		0			0
$125$	−5.82846			−0.521313
$126$		0			0
$127$	0.660190			0.0585824			0.0292912	−	0.999571i	$-0.490675\pi$
$127$	0.660190			0.0585824			0.0292912	+	0.999571i	$0.490675\pi$
$128$		0			0
$129$	−19.1992	−	33.2540i	−1.69039	−	2.92785i
$130$		0			0
$131$	−9.85705	+	17.0729i	−0.861214	+	1.49167i	0.00954300	+	0.999954i	$0.496962\pi$
$131$	−9.85705	+	17.0729i	−0.861214	+	1.49167i	−0.870757	+	0.491713i	$0.836371\pi$
$132$		0			0
$133$	9.63680	+	2.47819i	0.835617	+	0.214886i
$134$		0			0
$135$	22.4503	−	38.8851i	1.93222	−	3.34670i
$136$		0			0
$137$	−1.38727	−	2.40283i	−0.118523	−	0.205288i	0.800660	−	0.599119i	$-0.204483\pi$
$137$	−1.38727	−	2.40283i	−0.118523	−	0.205288i	−0.919183	+	0.393832i	$0.871149\pi$
$138$		0			0
$139$	11.0000			0.933008			0.466504	−	0.884519i	$-0.345513\pi$
$139$	11.0000			0.933008			0.466504	+	0.884519i	$0.345513\pi$
$140$		0			0
$141$	13.4887			1.13595
$142$		0			0
$143$	1.83009	+	3.16982i	0.153040	+	0.265073i
$144$		0			0
$145$	−4.95937	+	8.58988i	−0.411853	+	0.713351i
$146$		0			0
$147$	19.5104	+	10.7451i	1.60919	+	0.886242i
$148$		0			0
$149$	4.39931	−	7.61983i	0.360406	−	0.624241i	−0.627622	−	0.778518i	$-0.715972\pi$
$149$	4.39931	−	7.61983i	0.360406	−	0.624241i	0.988028	+	0.154277i	$0.0493049\pi$
$150$		0			0
$151$	10.1940	+	17.6565i	0.829574	+	1.43687i	0.898372	+	0.439235i	$0.144750\pi$
$151$	10.1940	+	17.6565i	0.829574	+	1.43687i	−0.0687980	+	0.997631i	$0.521916\pi$
$152$		0			0
$153$	−12.5458			−1.01427
$154$		0			0
$155$	−32.3789			−2.60074
$156$		0			0
$157$	3.79630	+	6.57539i	0.302978	+	0.524773i	0.976809	−	0.214112i	$-0.0686858\pi$
$157$	3.79630	+	6.57539i	0.302978	+	0.524773i	−0.673831	+	0.738885i	$0.735352\pi$
$158$		0			0
$159$	0.358685	−	0.621261i	0.0284456	−	0.0492692i
$160$		0			0
$161$	−3.17511	−	0.816506i	−0.250233	−	0.0643497i
$162$		0			0
$163$	4.02175	−	6.96588i	0.315008	−	0.545610i	−0.664431	−	0.747349i	$-0.731326\pi$
$163$	4.02175	−	6.96588i	0.315008	−	0.545610i	0.979439	+	0.201740i	$0.0646594\pi$
$164$		0			0
$165$	−5.44282	−	9.42724i	−0.423723	−	0.733910i
$166$		0			0
$167$	15.7414			1.21811			0.609055	−	0.793128i	$-0.291549\pi$
$167$	15.7414			1.21811			0.609055	+	0.793128i	$0.291549\pi$
$168$		0			0
$169$	0.396990			0.0305377
$170$		0			0
$171$	−13.3977	−	23.2055i	−1.02455	−	1.77457i
$172$		0			0
$173$	1.87360	−	3.24517i	0.142447	−	0.246726i	−0.785970	−	0.618264i	$-0.787836\pi$
$173$	1.87360	−	3.24517i	0.142447	−	0.246726i	0.928418	+	0.371538i	$0.121170\pi$
$174$		0			0
$175$	−12.4142	+	12.6674i	−0.938428	+	0.957568i
$176$		0			0
$177$	10.4142	−	18.0380i	0.782781	−	1.35582i
$178$		0			0
$179$	5.75116	+	9.96130i	0.429862	+	0.744543i	0.996861	−	0.0791759i	$-0.0252289\pi$
$179$	5.75116	+	9.96130i	0.429862	+	0.744543i	−0.566999	+	0.823719i	$0.691896\pi$
$180$		0			0
$181$	−5.79071			−0.430420			−0.215210	−	0.976568i	$-0.569044\pi$
$181$	−5.79071			−0.430420			−0.215210	+	0.976568i	$0.569044\pi$
$182$		0			0
$183$	−32.6134			−2.41085
$184$		0			0
$185$	4.86156	+	8.42048i	0.357429	+	0.619086i
$186$		0			0
$187$	−0.880438	+	1.52496i	−0.0643840	+	0.111516i
$188$		0			0
$189$	−9.32558	−	33.4492i	−0.678336	−	2.43307i
$190$		0			0
$191$	−9.26088	+	16.0403i	−0.670094	+	1.16064i	0.307784	+	0.951456i	$0.400413\pi$
$191$	−9.26088	+	16.0403i	−0.670094	+	1.16064i	−0.977877	+	0.209180i	$0.932921\pi$
$192$		0			0
$193$	1.88727	+	3.26886i	0.135849	+	0.235297i	0.925921	−	0.377716i	$-0.123290\pi$
$193$	1.88727	+	3.26886i	0.135849	+	0.235297i	−0.790072	+	0.613013i	$0.789957\pi$
$194$		0			0
$195$	−39.8435			−2.85325
$196$		0			0
$197$	10.1683			0.724459			0.362230	−	0.932089i	$-0.382016\pi$
$197$	10.1683			0.724459			0.362230	+	0.932089i	$0.382016\pi$
$198$		0			0
$199$	5.03899	+	8.72779i	0.357205	+	0.618697i	0.987493	−	0.157665i	$-0.0503965\pi$
$199$	5.03899	+	8.72779i	0.357205	+	0.618697i	−0.630288	+	0.776361i	$0.717063\pi$
$200$		0			0
$201$	5.42107	−	9.38956i	0.382373	−	0.662289i
$202$		0			0
$203$	2.06006	+	7.38906i	0.144588	+	0.518611i
$204$		0			0
$205$	14.8880	−	25.7867i	1.03982	−	1.80102i
$206$		0			0
$207$	4.41423	+	7.64567i	0.306810	+	0.531411i
$208$		0			0
$209$	−3.76088			−0.260145
$210$		0			0
$211$	−1.72313			−0.118625			−0.0593125	−	0.998239i	$-0.518891\pi$
$211$	−1.72313			−0.118625			−0.0593125	+	0.998239i	$0.518891\pi$
$212$		0			0
$213$	6.74433	+	11.6815i	0.462114	+	0.800404i
$214$		0			0
$215$	20.6420	−	35.7530i	1.40777	−	2.43833i
$216$		0			0
$217$	−17.5270	+	17.8844i	−1.18981	+	1.21407i
$218$		0			0
$219$	−16.1992	+	28.0578i	−1.09464	+	1.89597i
$220$		0			0
$221$	3.22257	+	5.58166i	0.216774	+	0.375463i
$222$		0			0
$223$	−9.47825			−0.634710			−0.317355	−	0.948307i	$-0.602795\pi$
$223$	−9.47825			−0.634710			−0.317355	+	0.948307i	$0.602795\pi$
$224$		0			0
$225$	47.7623			3.18415
$226$		0			0
$227$	9.72094	+	16.8372i	0.645201	+	1.11752i	0.984255	+	0.176754i	$0.0565598\pi$
$227$	9.72094	+	16.8372i	0.645201	+	1.11752i	−0.339054	+	0.940767i	$0.610107\pi$
$228$		0			0
$229$	5.16019	−	8.93771i	0.340995	−	0.590621i	−0.643623	−	0.765343i	$-0.722569\pi$
$229$	5.16019	−	8.93771i	0.340995	−	0.590621i	0.984618	+	0.174722i	$0.0559028\pi$
$230$		0			0
$231$	−8.15335	−	2.09671i	−0.536451	−	0.137953i
$232$		0			0
$233$	−0.557180	+	0.965064i	−0.0365021	+	0.0632234i	−0.883699	−	0.468055i	$-0.844955\pi$
$233$	−0.557180	+	0.965064i	−0.0365021	+	0.0632234i	0.847197	+	0.531279i	$0.178288\pi$
$234$		0			0
$235$	7.25116	+	12.5594i	0.473014	+	0.819284i
$236$		0			0
$237$	−23.3880			−1.51921
$238$		0			0
$239$	−26.1053			−1.68861			−0.844307	−	0.535860i	$-0.819987\pi$
$239$	−26.1053			−1.68861			−0.844307	+	0.535860i	$0.819987\pi$
$240$		0			0
$241$	−7.39768	−	12.8132i	−0.476526	−	0.825368i	0.523112	−	0.852264i	$-0.324771\pi$
$241$	−7.39768	−	12.8132i	−0.476526	−	0.825368i	−0.999638	+	0.0268962i	$0.991438\pi$
$242$		0			0
$243$	−12.7495	+	22.0828i	−0.817883	+	1.41661i
$244$		0			0
$245$	0.483448	+	23.9426i	0.0308864	+	1.52964i
$246$		0			0
$247$	−6.88276	+	11.9213i	−0.437940	+	0.758534i
$248$		0			0
$249$	16.6871	+	28.9030i	1.05750	+	1.83165i
$250$		0			0
$251$	−1.96225			−0.123856			−0.0619281	−	0.998081i	$-0.519725\pi$
$251$	−1.96225			−0.123856			−0.0619281	+	0.998081i	$0.519725\pi$
$252$		0			0
$253$	1.23912			0.0779030
$254$		0			0
$255$	−9.58414	−	16.6002i	−0.600182	−	1.03955i
$256$		0			0
$257$	−1.25404	+	2.17206i	−0.0782249	+	0.135489i	−0.902484	−	0.430723i	$-0.858259\pi$
$257$	−1.25404	+	2.17206i	−0.0782249	+	0.135489i	0.824259	+	0.566213i	$0.191592\pi$
$258$		0			0
$259$	7.28263	+	1.87279i	0.452521	+	0.116370i
$260$		0			0
$261$	10.3285	−	17.8894i	0.639316	−	1.10733i
$262$		0			0
$263$	2.08414	+	3.60983i	0.128513	+	0.222592i	0.923101	−	0.384558i	$-0.125646\pi$
$263$	2.08414	+	3.60983i	0.128513	+	0.222592i	−0.794587	+	0.607150i	$0.792313\pi$
$264$		0			0
$265$	0.771280			0.0473794
$266$		0			0
$267$	23.1111			1.41438
$268$		0			0
$269$	10.5744	+	18.3154i	0.644734	+	1.11671i	0.984363	+	0.176152i	$0.0563651\pi$
$269$	10.5744	+	18.3154i	0.644734	+	1.11671i	−0.339629	+	0.940559i	$0.610302\pi$
$270$		0			0
$271$	−6.63844	+	11.4981i	−0.403256	+	0.698460i	−0.994117	−	0.108313i	$-0.965455\pi$
$271$	−6.63844	+	11.4981i	−0.403256	+	0.698460i	0.590861	+	0.806774i	$0.298788\pi$
$272$		0			0
$273$	−21.5676	+	22.0075i	−1.30533	+	1.33195i
$274$		0			0
$275$	3.35185	−	5.80557i	0.202124	−	0.350089i
$276$		0			0
$277$	4.75116	+	8.22925i	0.285470	+	0.494448i	0.972723	−	0.231970i	$-0.0745171\pi$
$277$	4.75116	+	8.22925i	0.285470	+	0.494448i	−0.687253	+	0.726418i	$0.741184\pi$
$278$		0			0
$279$	67.4328			4.03710
$280$		0			0
$281$	26.8766			1.60332			0.801662	−	0.597777i	$-0.203949\pi$
$281$	26.8766			1.60332			0.801662	+	0.597777i	$0.203949\pi$
$282$		0			0
$283$	−0.154988	−	0.268447i	−0.00921309	−	0.0159575i	0.861382	−	0.507958i	$-0.169599\pi$
$283$	−0.154988	−	0.268447i	−0.00921309	−	0.0159575i	−0.870595	+	0.492000i	$0.836266\pi$
$284$		0			0
$285$	20.4698	−	35.4547i	1.21252	−	2.10015i
$286$		0			0
$287$	−6.18427	−	22.1819i	−0.365046	−	1.30935i
$288$		0			0
$289$	6.94966	−	12.0372i	0.408803	−	0.708068i
$290$		0			0
$291$	−18.6895	−	32.3711i	−1.09560	−	1.89763i
$292$		0			0
$293$	31.2222			1.82402			0.912010	−	0.410169i	$-0.134530\pi$
$293$	31.2222			1.82402			0.912010	+	0.410169i	$0.134530\pi$
$294$		0			0
$295$	22.3937			1.30381
$296$		0			0
$297$	6.56238	+	11.3664i	0.380788	+	0.659544i
$298$		0			0
$299$	2.26771	−	3.92779i	0.131145	−	0.227150i
$300$		0			0
$301$	−8.57442	−	30.7549i	−0.494221	−	1.77268i
$302$		0			0
$303$	−19.1774	+	33.2163i	−1.10171	+	1.90823i
$304$		0			0
$305$	−17.5322	−	30.3666i	−1.00389	−	1.73879i
$306$		0			0
$307$	7.50808			0.428509			0.214254	−	0.976778i	$-0.431268\pi$
$307$	7.50808			0.428509			0.214254	+	0.976778i	$0.431268\pi$
$308$		0			0
$309$	−53.7623			−3.05843
$310$		0			0
$311$	0.767713	+	1.32972i	0.0435330	+	0.0754014i	0.886971	−	0.461825i	$-0.152805\pi$
$311$	0.767713	+	1.32972i	0.0435330	+	0.0754014i	−0.843438	+	0.537227i	$0.819472\pi$
$312$		0			0
$313$	6.42627	−	11.1306i	0.363234	−	0.629140i	−0.625257	−	0.780419i	$-0.715006\pi$
$313$	6.42627	−	11.1306i	0.363234	−	0.629140i	0.988491	+	0.151279i	$0.0483392\pi$
$314$		0			0
$315$	45.1375	−	46.0581i	2.54321	−	2.59508i
$316$		0			0
$317$	−1.21574	+	2.10571i	−0.0682825	+	0.118269i	−0.898145	−	0.439699i	$-0.855085\pi$
$317$	−1.21574	+	2.10571i	−0.0682825	+	0.118269i	0.829863	+	0.557967i	$0.188419\pi$
$318$		0			0
$319$	−1.44966	−	2.51088i	−0.0811652	−	0.140582i
$320$		0			0
$321$	3.64076			0.203207
$322$		0			0
$323$	−6.62244			−0.368482
$324$		0			0
$325$	−12.2684	−	21.2495i	−0.680528	−	1.17871i
$326$		0			0
$327$	5.26088	−	9.11211i	0.290927	−	0.503901i
$328$		0			0
$329$	10.8623	+	2.79332i	0.598855	+	0.154001i
$330$		0			0
$331$	−5.20370	+	9.01307i	−0.286021	+	0.495403i	−0.972856	−	0.231410i	$-0.925666\pi$
$331$	−5.20370	+	9.01307i	−0.286021	+	0.495403i	0.686835	+	0.726813i	$0.258999\pi$
$332$		0			0
$333$	−10.1248	−	17.5366i	−0.554834	−	0.961000i
$334$		0			0
$335$	11.6569			0.636886
$336$		0			0
$337$	−11.2164			−0.610998			−0.305499	−	0.952192i	$-0.598823\pi$
$337$	−11.2164			−0.610998			−0.305499	+	0.952192i	$0.598823\pi$
$338$		0			0
$339$	27.8932	+	48.3124i	1.51495	+	2.62397i
$340$		0			0
$341$	4.73229	−	8.19656i	0.256268	−	0.443869i
$342$		0			0
$343$	13.4863	+	12.6933i	0.728193	+	0.685372i
$344$		0			0
$345$	−6.74433	+	11.6815i	−0.363102	+	0.628912i
$346$		0			0
$347$	13.3788	+	23.1728i	0.718212	+	1.24398i	0.961708	+	0.274077i	$0.0883724\pi$
$347$	13.3788	+	23.1728i	0.718212	+	1.24398i	−0.243496	+	0.969902i	$0.578294\pi$
$348$		0			0
$349$	−5.11436			−0.273765			−0.136883	−	0.990587i	$-0.543708\pi$
$349$	−5.11436			−0.273765			−0.136883	+	0.990587i	$0.543708\pi$
$350$		0			0
$351$	48.0391			2.56414
$352$		0			0
$353$	10.1505	+	17.5811i	0.540255	+	0.935750i	0.998889	+	0.0471242i	$0.0150057\pi$
$353$	10.1505	+	17.5811i	0.540255	+	0.935750i	−0.458634	+	0.888625i	$0.651661\pi$
$354$		0			0
$355$	−7.25116	+	12.5594i	−0.384852	+	0.666583i
$356$		0			0
$357$	−14.3571	−	3.69204i	−0.759856	−	0.195403i
$358$		0			0
$359$	−4.73392	+	8.19939i	−0.249847	+	0.432747i	−0.963483	−	0.267769i	$-0.913714\pi$
$359$	−4.73392	+	8.19939i	−0.249847	+	0.432747i	0.713636	+	0.700516i	$0.247047\pi$
$360$		0			0
$361$	2.42790	+	4.20525i	0.127784	+	0.221329i
$362$		0			0
$363$	3.18194			0.167009
$364$		0			0
$365$	−34.8331			−1.82325
$366$		0			0
$367$	−10.7323	−	18.5889i	−0.560221	−	0.970331i	−0.997477	−	0.0709938i	$-0.977383\pi$
$367$	−10.7323	−	18.5889i	−0.560221	−	0.970331i	0.437256	−	0.899337i	$-0.355950\pi$
$368$		0			0
$369$	−31.0059	+	53.7038i	−1.61410	+	2.79571i
$370$		0			0
$371$	0.417500	−	0.426015i	0.0216755	−	0.0221176i
$372$		0			0
$373$	−6.66827	+	11.5498i	−0.345270	+	0.598025i	−0.985403	−	0.170239i	$-0.945546\pi$
$373$	−6.66827	+	11.5498i	−0.345270	+	0.598025i	0.640133	+	0.768264i	$0.278879\pi$
$374$		0			0
$375$	9.27292	+	16.0612i	0.478851	+	0.829395i
$376$		0			0
$377$	−10.6120			−0.546548
$378$		0			0
$379$	−5.76088			−0.295916			−0.147958	−	0.988994i	$-0.547270\pi$
$379$	−5.76088			−0.295916			−0.147958	+	0.988994i	$0.547270\pi$
$380$		0			0
$381$	−1.05034	−	1.81925i	−0.0538107	−	0.0932029i
$382$		0			0
$383$	14.6150	−	25.3140i	0.746794	−	1.29349i	−0.202558	−	0.979270i	$-0.564925\pi$
$383$	14.6150	−	25.3140i	0.746794	−	1.29349i	0.949352	−	0.314215i	$-0.101741\pi$
$384$		0			0
$385$	−2.43078	−	8.71878i	−0.123884	−	0.444350i
$386$		0			0
$387$	−42.9893	+	74.4597i	−2.18527	+	3.78500i
$388$		0			0
$389$	10.2540	+	17.7605i	0.519900	+	0.900494i	0.999732	+	0.0231336i	$0.00736431\pi$
$389$	10.2540	+	17.7605i	0.519900	+	0.900494i	−0.479832	+	0.877360i	$0.659302\pi$
$390$		0			0
$391$	2.18194			0.110346
$392$		0			0
$393$	62.7292			3.16427
$394$		0			0
$395$	−12.5728	−	21.7767i	−0.632605	−	1.09570i
$396$		0			0
$397$	−5.78495	+	10.0198i	−0.290338	+	0.502881i	−0.973890	−	0.227022i	$-0.927101\pi$
$397$	−5.78495	+	10.0198i	−0.290338	+	0.502881i	0.683551	+	0.729903i	$0.260435\pi$
$398$		0			0
$399$	−8.50288	−	30.4983i	−0.425676	−	1.52683i
$400$		0			0
$401$	−12.5933	+	21.8122i	−0.628879	+	1.08925i	0.358898	+	0.933377i	$0.383153\pi$
$401$	−12.5933	+	21.8122i	−0.628879	+	1.08925i	−0.987777	+	0.155874i	$0.950181\pi$
$402$		0			0
$403$	−17.3211	−	30.0010i	−0.862824	−	1.49445i
$404$		0			0
$405$	−69.7486			−3.46583
$406$		0			0
$407$	−2.84213			−0.140879
$408$		0			0
$409$	−1.90383	−	3.29752i	−0.0941382	−	0.163052i	0.815110	−	0.579306i	$-0.196676\pi$
$409$	−1.90383	−	3.29752i	−0.0941382	−	0.163052i	−0.909249	+	0.416254i	$0.863343\pi$
$410$		0			0
$411$	−4.41423	+	7.64567i	−0.217738	+	0.377133i
$412$		0			0
$413$	12.1219	−	12.3691i	0.596479	−	0.608645i
$414$		0			0
$415$	−17.9412	+	31.0750i	−0.880698	+	1.52541i
$416$		0			0
$417$	−17.5007	−	30.3121i	−0.857012	−	1.48439i
$418$		0			0
$419$	−5.08701			−0.248517			−0.124258	−	0.992250i	$-0.539655\pi$
$419$	−5.08701			−0.248517			−0.124258	+	0.992250i	$0.539655\pi$
$420$		0			0
$421$	−16.9442			−0.825810			−0.412905	−	0.910774i	$-0.635486\pi$
$421$	−16.9442			−0.825810			−0.412905	+	0.910774i	$0.635486\pi$
$422$		0			0
$423$	−15.1014	−	26.1563i	−0.734254	−	1.27177i
$424$		0			0
$425$	5.90219	−	10.2229i	0.286298	−	0.495883i
$426$		0			0
$427$	−26.2632	−	6.75381i	−1.27097	−	0.326840i
$428$		0			0
$429$	5.82326	−	10.0862i	0.281150	−	0.486965i
$430$		0			0
$431$	−1.22777	−	2.12657i	−0.0591398	−	0.102433i	0.834940	−	0.550341i	$-0.185502\pi$
$431$	−1.22777	−	2.12657i	−0.0591398	−	0.102433i	−0.894079	+	0.447908i	$0.852169\pi$
$432$		0			0
$433$	−32.8629			−1.57929			−0.789646	−	0.613563i	$-0.789736\pi$
$433$	−32.8629			−1.57929			−0.789646	+	0.613563i	$0.789736\pi$
$434$		0			0
$435$	31.5609			1.51323
$436$		0			0
$437$	2.33009	+	4.03584i	0.111464	+	0.193061i
$438$		0			0
$439$	0.0406283	−	0.0703702i	0.00193908	−	0.00335859i	−0.865054	−	0.501678i	$-0.832716\pi$
$439$	0.0406283	−	0.0703702i	0.00193908	−	0.00335859i	0.866993	+	0.498320i	$0.166049\pi$
$440$		0			0
$441$	−1.00684	−	49.8632i	−0.0479446	−	2.37444i
$442$		0			0
$443$	3.86840	−	6.70027i	0.183793	−	0.318339i	−0.759376	−	0.650652i	$-0.774496\pi$
$443$	3.86840	−	6.70027i	0.183793	−	0.318339i	0.943169	+	0.332313i	$0.107829\pi$
$444$		0			0
$445$	12.4239	+	21.5189i	0.588951	+	1.02009i
$446$		0			0
$447$	−27.9967			−1.32420
$448$		0			0
$449$	−21.1078			−0.996140			−0.498070	−	0.867137i	$-0.665958\pi$
$449$	−21.1078			−0.996140			−0.498070	+	0.867137i	$0.665958\pi$
$450$		0			0
$451$	4.35185	+	7.53762i	0.204921	+	0.354933i
$452$		0			0
$453$	32.4367	−	56.1820i	1.52401	−	2.63966i
$454$		0			0
$455$	−32.0855	−	8.25107i	−1.50419	−	0.386816i
$456$		0			0
$457$	8.35868	−	14.4777i	0.391003	−	0.677237i	−0.601579	−	0.798813i	$-0.705462\pi$
$457$	8.35868	−	14.4777i	0.391003	−	0.677237i	0.992582	+	0.121576i	$0.0387949\pi$
$458$		0			0
$459$	11.5555	+	20.0148i	0.539367	+	0.934210i
$460$		0			0
$461$	−5.62571			−0.262015			−0.131008	−	0.991381i	$-0.541821\pi$
$461$	−5.62571			−0.262015			−0.131008	+	0.991381i	$0.541821\pi$
$462$		0			0
$463$	24.3341			1.13090			0.565450	−	0.824783i	$-0.308703\pi$
$463$	24.3341			1.13090			0.565450	+	0.824783i	$0.308703\pi$
$464$		0			0
$465$	51.5140	+	89.2248i	2.38890	+	4.13770i
$466$		0			0
$467$	9.42395	−	16.3228i	0.436088	−	0.755327i	−0.561296	−	0.827615i	$-0.689697\pi$
$467$	9.42395	−	16.3228i	0.436088	−	0.755327i	0.997384	+	0.0722885i	$0.0230302\pi$
$468$		0			0
$469$	6.30998	−	6.43867i	0.291368	−	0.297310i
$470$		0			0
$471$	12.0796	−	20.9225i	0.556600	−	0.964059i
$472$		0			0
$473$	6.03379	+	10.4508i	0.277434	+	0.480530i
$474$		0			0
$475$	25.2118			1.15680
$476$		0			0
$477$	−1.60628			−0.0735465
$478$		0			0
$479$	−14.9383	−	25.8739i	−0.682549	−	1.18221i	−0.974200	−	0.225684i	$-0.927538\pi$
$479$	−14.9383	−	25.8739i	−0.682549	−	1.18221i	0.291652	−	0.956525i	$-0.405795\pi$
$480$		0			0
$481$	−5.20137	+	9.00904i	−0.237162	+	0.410777i
$482$		0			0
$483$	2.80150	+	10.0485i	0.127473	+	0.457223i
$484$		0			0
$485$	20.0940	−	34.8038i	0.912421	−	1.58036i
$486$		0			0
$487$	6.21574	+	10.7660i	0.281662	+	0.487853i	0.971794	−	0.235831i	$-0.0757810\pi$
$487$	6.21574	+	10.7660i	0.281662	+	0.487853i	−0.690132	+	0.723683i	$0.742448\pi$
$488$		0			0
$489$	−25.5940			−1.15740
$490$		0			0
$491$	10.0917			0.455430			0.227715	−	0.973728i	$-0.426875\pi$
$491$	10.0917			0.455430			0.227715	+	0.973728i	$0.426875\pi$
$492$		0			0
$493$	−2.55267	−	4.42135i	−0.114966	−	0.199128i
$494$		0			0
$495$	−12.1871	+	21.1088i	−0.547771	+	0.948768i
$496$		0			0
$497$	3.01204	+	10.8036i	0.135108	+	0.484610i
$498$		0			0
$499$	7.74269	−	13.4107i	0.346610	−	0.600347i	−0.639035	−	0.769178i	$-0.720666\pi$
$499$	7.74269	−	13.4107i	0.346610	−	0.600347i	0.985645	+	0.168831i	$0.0539993\pi$
$500$		0			0
$501$	−25.0442	−	43.3778i	−1.11889	−	1.93798i
$502$		0			0
$503$	−3.99673			−0.178205			−0.0891027	−	0.996022i	$-0.528400\pi$
$503$	−3.99673			−0.178205			−0.0891027	+	0.996022i	$0.528400\pi$
$504$		0			0
$505$	−41.2372			−1.83503
$506$		0			0
$507$	−0.631600	−	1.09396i	−0.0280503	−	0.0485846i
$508$		0			0
$509$	0.891788	−	1.54462i	0.0395278	−	0.0684642i	−0.845585	−	0.533841i	$-0.820748\pi$
$509$	0.891788	−	1.54462i	0.0395278	−	0.0684642i	0.885112	+	0.465377i	$0.154081\pi$
$510$		0			0
$511$	−18.8554	+	19.2400i	−0.834114	+	0.851127i
$512$		0			0
$513$	−24.6803	+	42.7475i	−1.08966	+	1.88735i
$514$		0			0
$515$	−28.9012	−	50.0584i	−1.27354	−	2.20584i
$516$		0			0
$517$	−4.23912			−0.186436
$518$		0			0
$519$	−11.9234			−0.523379
$520$		0			0
$521$	−16.5865	−	28.7286i	−0.726666	−	1.25862i	−0.958285	−	0.285816i	$-0.907735\pi$
$521$	−16.5865	−	28.7286i	−0.726666	−	1.25862i	0.231619	−	0.972807i	$-0.425598\pi$
$522$		0			0
$523$	12.6219	−	21.8617i	0.551916	−	0.955947i	−0.446220	−	0.894923i	$-0.647230\pi$
$523$	12.6219	−	21.8617i	0.551916	−	0.955947i	0.998136	−	0.0610240i	$-0.0194366\pi$
$524$		0			0
$525$	54.6576	+	14.0557i	2.38545	+	0.613440i
$526$		0			0
$527$	8.33297	−	14.4331i	0.362990	−	0.628717i
$528$		0			0
$529$	10.7323	+	18.5889i	0.466621	+	0.808212i
$530$		0			0
$531$	−46.6375			−2.02389
$532$		0			0
$533$	31.8572			1.37989
$534$		0			0
$535$	1.95718	+	3.38994i	0.0846163	+	0.146560i
$536$		0			0
$537$	18.2999	−	31.6963i	0.789698	−	1.36780i
$538$		0			0
$539$	−6.13160	−	3.37690i	−0.264107	−	0.145454i
$540$		0			0
$541$	3.97141	−	6.87868i	0.170744	−	0.295738i	−0.767936	−	0.640527i	$-0.778716\pi$
$541$	3.97141	−	6.87868i	0.170744	−	0.295738i	0.938680	+	0.344789i	$0.112049\pi$
$542$		0			0
$543$	9.21286	+	15.9571i	0.395362	+	0.684786i
$544$		0			0
$545$	11.3125			0.484573
$546$		0			0
$547$	17.2495			0.737537			0.368768	−	0.929521i	$-0.379780\pi$
$547$	17.2495			0.737537			0.368768	+	0.929521i	$0.379780\pi$
$548$		0			0
$549$	36.5127	+	63.2419i	1.55833	+	2.69910i
$550$		0			0
$551$	5.45198	−	9.44311i	0.232262	−	0.402290i
$552$		0			0
$553$	−18.8341	−	4.84334i	−0.800905	−	0.205960i
$554$		0			0
$555$	15.4692	−	26.7935i	0.656632	−	1.13732i
$556$		0			0
$557$	−5.62928	−	9.75019i	−0.238520	−	0.413129i	0.721770	−	0.692133i	$-0.243329\pi$
$557$	−5.62928	−	9.75019i	−0.238520	−	0.413129i	−0.960290	+	0.279004i	$0.909996\pi$
$558$		0			0
$559$	44.1696			1.86818
$560$		0			0
$561$	5.60301			0.236559
$562$		0			0
$563$	5.16143	+	8.93987i	0.217528	+	0.376770i	0.954052	−	0.299642i	$-0.0968672\pi$
$563$	5.16143	+	8.93987i	0.217528	+	0.376770i	−0.736523	+	0.676412i	$0.763534\pi$
$564$		0			0
$565$	−29.9893	+	51.9431i	−1.26166	+	2.18526i
$566$		0			0
$567$	−37.7554	+	38.5255i	−1.58558	+	1.61792i
$568$		0			0
$569$	−5.57605	+	9.65801i	−0.233760	+	0.404885i	−0.958912	−	0.283705i	$-0.908436\pi$
$569$	−5.57605	+	9.65801i	−0.233760	+	0.404885i	0.725151	+	0.688590i	$0.241770\pi$
$570$		0			0
$571$	−4.28783	−	7.42674i	−0.179440	−	0.310800i	0.762249	−	0.647284i	$-0.224095\pi$
$571$	−4.28783	−	7.42674i	−0.179440	−	0.310800i	−0.941689	+	0.336485i	$0.890762\pi$
$572$		0			0
$573$	58.9352			2.46205
$574$		0			0
$575$	−8.30671			−0.346414
$576$		0			0
$577$	−21.7902	−	37.7417i	−0.907136	−	1.57121i	−0.818024	−	0.575184i	$-0.804930\pi$
$577$	−21.7902	−	37.7417i	−0.907136	−	1.57121i	−0.0891120	−	0.996022i	$-0.528403\pi$
$578$		0			0
$579$	6.00520	−	10.4013i	0.249568	−	0.432264i
$580$		0			0
$581$	7.45254	+	26.7309i	0.309183	+	1.10899i
$582$		0			0
$583$	−0.112725	+	0.195246i	−0.00466860	+	0.00808625i
$584$		0			0
$585$	44.6073	+	77.2620i	1.84428	+	3.19439i
$586$		0			0
$587$	−44.4315			−1.83388			−0.916942	−	0.399022i	$-0.869350\pi$
$587$	−44.4315			−1.83388			−0.916942	+	0.399022i	$0.869350\pi$
$588$		0			0
$589$	35.5951			1.46667
$590$		0			0
$591$	−16.1774	−	28.0201i	−0.665451	−	1.15259i
$592$		0			0
$593$	2.51724	−	4.35999i	0.103371	−	0.179043i	−0.809701	−	0.586843i	$-0.800371\pi$
$593$	2.51724	−	4.35999i	0.103371	−	0.179043i	0.913071	+	0.407800i	$0.133704\pi$
$594$		0			0
$595$	−4.28031	−	15.3527i	−0.175475	−	0.629399i
$596$		0			0
$597$	16.0338	−	27.7713i	0.656219	−	1.13661i
$598$		0			0
$599$	3.36784	+	5.83328i	0.137606	+	0.238341i	0.926590	−	0.376073i	$-0.122726\pi$
$599$	3.36784	+	5.83328i	0.137606	+	0.238341i	−0.788984	+	0.614414i	$0.789392\pi$
$600$		0			0
$601$	−30.4854			−1.24352			−0.621762	−	0.783206i	$-0.713583\pi$
$601$	−30.4854			−1.24352			−0.621762	+	0.783206i	$0.713583\pi$
$602$		0			0
$603$	−24.2769			−0.988631
$604$		0			0
$605$	1.71053	+	2.96273i	0.0695431	+	0.120452i
$606$		0			0
$607$	−13.6586	+	23.6573i	−0.554384	+	0.960221i	0.443568	+	0.896241i	$0.353713\pi$
$607$	−13.6586	+	23.6573i	−0.554384	+	0.960221i	−0.997951	+	0.0639797i	$0.979621\pi$
$608$		0			0
$609$	17.0841	−	17.4326i	0.692284	−	0.706404i
$610$		0			0
$611$	−7.75800	+	13.4372i	−0.313855	+	0.543613i
$612$		0			0
$613$	17.1248	+	29.6610i	0.691663	+	1.19799i	0.971293	+	0.237887i	$0.0764548\pi$
$613$	17.1248	+	29.6610i	0.691663	+	1.19799i	−0.279630	+	0.960108i	$0.590212\pi$
$614$		0			0
$615$	−94.7453			−3.82050
$616$		0			0
$617$	9.13052			0.367581			0.183790	−	0.982965i	$-0.441163\pi$
$617$	9.13052			0.367581			0.183790	+	0.982965i	$0.441163\pi$
$618$		0			0
$619$	3.66019	+	6.33963i	0.147115	+	0.254811i	0.930160	−	0.367154i	$-0.119668\pi$
$619$	3.66019	+	6.33963i	0.147115	+	0.254811i	−0.783045	+	0.621965i	$0.786334\pi$
$620$		0			0
$621$	8.13160	−	14.0843i	0.326310	−	0.565185i
$622$		0			0
$623$	18.6111	+	4.78600i	0.745638	+	0.191747i
$624$		0			0
$625$	6.78947	−	11.7597i	0.271579	−	0.470388i
$626$		0			0
$627$	5.98345	+	10.3636i	0.238956	+	0.413884i
$628$		0			0
$629$	−5.00465			−0.199548
$630$		0			0
$631$	12.7199			0.506370			0.253185	−	0.967418i	$-0.418522\pi$
$631$	12.7199			0.506370			0.253185	+	0.967418i	$0.418522\pi$
$632$		0			0
$633$	2.74145	+	4.74832i	0.108963	+	0.188729i
$634$		0			0
$635$	1.12928	−	1.95596i	0.0448140	−	0.0776201i
$636$		0			0
$637$	−21.9256	+	13.2560i	−0.868723	+	0.525222i
$638$		0			0
$639$	15.1014	−	26.1563i	0.597401	−	1.03473i
$640$		0			0
$641$	4.08250	+	7.07110i	0.161249	+	0.279292i	0.935317	−	0.353811i	$-0.115114\pi$
$641$	4.08250	+	7.07110i	0.161249	+	0.279292i	−0.774068	+	0.633103i	$0.781781\pi$
$642$		0			0
$643$	8.39123			0.330918			0.165459	−	0.986217i	$-0.447089\pi$
$643$	8.39123			0.330918			0.165459	+	0.986217i	$0.447089\pi$
$644$		0			0
$645$	−131.363			−5.17243
$646$		0			0
$647$	−20.2599	−	35.0912i	−0.796500	−	1.37958i	−0.921882	−	0.387470i	$-0.873349\pi$
$647$	−20.2599	−	35.0912i	−0.796500	−	1.37958i	0.125382	−	0.992109i	$-0.459984\pi$
$648$		0			0
$649$	−3.27292	+	5.66886i	−0.128473	+	0.222522i
$650$		0			0
$651$	77.1680	+	19.8444i	3.02445	+	0.777764i
$652$		0			0
$653$	−7.35185	+	12.7338i	−0.287700	+	0.498311i	−0.973260	−	0.229705i	$-0.926224\pi$
$653$	−7.35185	+	12.7338i	−0.287700	+	0.498311i	0.685560	+	0.728016i	$0.259557\pi$
$654$		0			0
$655$	33.7216	+	58.4076i	1.31761	+	2.28217i
$656$		0			0
$657$	72.5439			2.83021
$658$		0			0
$659$	19.2873			0.751326			0.375663	−	0.926756i	$-0.377415\pi$
$659$	19.2873			0.751326			0.375663	+	0.926756i	$0.377415\pi$
$660$		0			0
$661$	9.90615	+	17.1580i	0.385305	+	0.667367i	0.991811	−	0.127711i	$-0.0407631\pi$
$661$	9.90615	+	17.1580i	0.385305	+	0.667367i	−0.606507	+	0.795078i	$0.707430\pi$
$662$		0			0
$663$	10.2540	−	17.7605i	0.398234	−	0.689761i
$664$		0			0
$665$	23.8263	−	24.3122i	0.923943	−	0.942788i
$666$		0			0
$667$	−1.79630	+	3.11129i	−0.0695531	+	0.120470i
$668$		0			0
$669$	15.0796	+	26.1187i	0.583012	+	1.00981i
$670$		0			0
$671$	10.2495			0.395679
$672$		0			0
$673$	−1.11901			−0.0431345			−0.0215673	−	0.999767i	$-0.506866\pi$
$673$	−1.11901			−0.0431345			−0.0215673	+	0.999767i	$0.506866\pi$
$674$		0			0
$675$	−43.9922	−	76.1968i	−1.69326	−	2.93281i
$676$		0			0
$677$	−21.7571	+	37.6843i	−0.836191	+	1.44833i	0.0568653	+	0.998382i	$0.481889\pi$
$677$	−21.7571	+	37.6843i	−0.836191	+	1.44833i	−0.893057	+	0.449944i	$0.851444\pi$
$678$		0			0
$679$	−8.34678	−	29.9384i	−0.320320	−	1.14893i
$680$		0			0
$681$	30.9315	−	53.5749i	1.18530	−	2.05299i
$682$		0			0
$683$	7.54746	+	13.0726i	0.288796	+	0.500209i	0.973523	−	0.228591i	$-0.0734118\pi$
$683$	7.54746	+	13.0726i	0.288796	+	0.500209i	−0.684727	+	0.728800i	$0.740078\pi$
$684$		0			0
$685$	−9.49192			−0.362668
$686$		0			0
$687$	−32.8389			−1.25288
$688$		0			0
$689$	0.412595	+	0.714636i	0.0157186	+	0.0272255i
$690$		0			0
$691$	−1.07085	+	1.85477i	−0.0407372	+	0.0705588i	−0.885675	−	0.464306i	$-0.846304\pi$
$691$	−1.07085	+	1.85477i	−0.0407372	+	0.0705588i	0.844938	+	0.534864i	$0.179637\pi$
$692$		0			0
$693$	5.06238	+	18.1579i	0.192304	+	0.689760i
$694$		0			0
$695$	18.8159	−	32.5900i	0.713726	−	1.23621i
$696$		0			0
$697$	7.66307	+	13.2728i	0.290259	+	0.502744i
$698$		0			0
$699$	3.54583			0.134116
$700$		0			0
$701$	−10.1910			−0.384908			−0.192454	−	0.981306i	$-0.561645\pi$
$701$	−10.1910			−0.384908			−0.192454	+	0.981306i	$0.561645\pi$
$702$		0			0
$703$	−5.34446	−	9.25687i	−0.201570	−	0.349129i
$704$		0			0
$705$	23.0728	−	39.9632i	0.868971	−	1.50510i
$706$		0			0
$707$	−22.3220	+	22.7773i	−0.839506	+	0.856628i
$708$		0			0
$709$	−0.172784	+	0.299270i	−0.00648903	+	0.0112393i	−0.869252	−	0.494370i	$-0.835399\pi$
$709$	−0.172784	+	0.299270i	−0.00648903	+	0.0112393i	0.862763	+	0.505609i	$0.168732\pi$
$710$		0			0
$711$	26.1843	+	45.3525i	0.981987	+	1.70085i
$712$		0			0
$713$	−11.7278			−0.439209
$714$		0			0
$715$	12.5218			0.468287
$716$		0			0
$717$	41.5328	+	71.9370i	1.55107	+	2.68654i
$718$		0			0
$719$	13.4383	−	23.2758i	0.501164	−	0.868042i	−0.498835	−	0.866697i	$-0.666239\pi$
$719$	13.4383	−	23.2758i	0.501164	−	0.868042i	0.999999	−	0.00134491i	$-0.000428097\pi$
$720$		0			0
$721$	−43.2941	−	11.1335i	−1.61236	−	0.414632i
$722$		0			0
$723$	−23.5390	+	40.7707i	−0.875425	+	1.51628i
$724$		0			0
$725$	9.71806	+	16.8322i	0.360920	+	0.625131i
$726$		0			0
$727$	−46.1261			−1.71072			−0.855362	−	0.518031i	$-0.826665\pi$
$727$	−46.1261			−1.71072			−0.855362	+	0.518031i	$0.826665\pi$
$728$		0			0
$729$	19.9727			0.739728
$730$		0			0
$731$	10.6248	+	18.4026i	0.392971	+	0.680646i
$732$		0			0
$733$	−15.4698	+	26.7944i	−0.571389	+	0.989675i	0.425034	+	0.905177i	$0.360262\pi$
$733$	−15.4698	+	26.7944i	−0.571389	+	0.989675i	−0.996424	+	0.0844979i	$0.973071\pi$
$734$		0			0
$735$	65.2081	−	39.4242i	2.40524	−	1.45418i
$736$		0			0
$737$	−1.70370	+	2.95089i	−0.0627565	+	0.108697i
$738$		0			0
$739$	−20.1150	−	34.8403i	−0.739944	−	1.28162i	−0.952520	−	0.304476i	$-0.901519\pi$
$739$	−20.1150	−	34.8403i	−0.739944	−	1.28162i	0.212576	−	0.977145i	$-0.431815\pi$
$740$		0			0
$741$	43.8011			1.60907
$742$		0			0
$743$	37.3710			1.37101			0.685505	−	0.728068i	$-0.259582\pi$
$743$	37.3710			1.37101			0.685505	+	0.728068i	$0.259582\pi$
$744$		0			0
$745$	−15.0503	−	26.0680i	−0.551402	−	0.955056i
$746$		0			0
$747$	37.3646	−	64.7173i	1.36710	−	2.36788i
$748$		0			0
$749$	2.93186	+	0.753953i	0.107128	+	0.0275489i
$750$		0			0
$751$	−19.8698	+	34.4155i	−0.725058	+	1.25584i	0.233891	+	0.972263i	$0.424854\pi$
$751$	−19.8698	+	34.4155i	−0.725058	+	1.25584i	−0.958950	+	0.283575i	$0.908479\pi$
$752$		0			0
$753$	3.12188	+	5.40726i	0.113768	+	0.197052i
$754$		0			0
$755$	69.7486			2.53841
$756$		0			0
$757$	6.60628			0.240109			0.120055	−	0.992767i	$-0.461693\pi$
$757$	6.60628			0.240109			0.120055	+	0.992767i	$0.461693\pi$
$758$		0			0
$759$	−1.97141	−	3.41458i	−0.0715577	−	0.123941i
$760$		0			0
$761$	−0.518875	+	0.898718i	−0.0188092	+	0.0325785i	−0.875277	−	0.483622i	$-0.839321\pi$
$761$	−0.518875	+	0.898718i	−0.0188092	+	0.0325785i	0.856468	+	0.516201i	$0.172654\pi$
$762$		0			0
$763$	6.12352	−	6.24841i	0.221686	−	0.226208i
$764$		0			0
$765$	−21.4601	+	37.1699i	−0.775890	+	1.34388i
$766$		0			0
$767$	11.9795	+	20.7491i	0.432554	+	0.749206i
$768$		0			0
$769$	6.03199			0.217519			0.108760	−	0.994068i	$-0.465312\pi$
$769$	6.03199			0.217519			0.108760	+	0.994068i	$0.465312\pi$
$770$		0			0
$771$	7.98057			0.287413
$772$		0			0
$773$	−7.45034	−	12.9044i	−0.267970	−	0.464138i	0.700367	−	0.713783i	$-0.253020\pi$
$773$	−7.45034	−	12.9044i	−0.267970	−	0.464138i	−0.968338	+	0.249645i	$0.919686\pi$
$774$		0			0
$775$	−31.7238	+	54.9473i	−1.13955	+	1.97376i
$776$		0			0
$777$	−6.42571	−	23.0479i	−0.230521	−	0.826839i
$778$		0			0
$779$	−16.3668	+	28.3481i	−0.586400	+	1.01567i
$780$		0			0
$781$	−2.11956	−	3.67119i	−0.0758439	−	0.131365i
$782$		0			0
$783$	−38.0528			−1.35990
$784$		0			0
$785$	25.9748			0.927081
$786$		0			0
$787$	−0.490285	−	0.849198i	−0.0174768	−	0.0302706i	0.857155	−	0.515059i	$-0.172230\pi$
$787$	−0.490285	−	0.849198i	−0.0174768	−	0.0302706i	−0.874632	+	0.484788i	$0.838897\pi$
$788$		0			0
$789$	6.63160	−	11.4863i	0.236091	−	0.408922i
$790$		0			0
$791$	12.4572	+	44.6817i	0.442926	+	1.58870i
$792$		0			0
$793$	18.7576	−	32.4891i	0.666102	−	1.15372i
$794$		0			0
$795$	−1.22708	−	2.12537i	−0.0435202	−	0.0753792i
$796$		0			0
$797$	−37.2873			−1.32078			−0.660392	−	0.750921i	$-0.729610\pi$
$797$	−37.2873			−1.32078			−0.660392	+	0.750921i	$0.729610\pi$
$798$		0			0
$799$	−7.46457			−0.264078
$800$		0			0
$801$	−25.8743	−	44.8156i	−0.914223	−	1.58348i
$802$		0			0
$803$	5.09097	−	8.81782i	0.179656	−	0.311174i
$804$		0			0
$805$	−7.85021	+	8.01033i	−0.276684	+	0.282327i
$806$		0			0
$807$	33.6472	−	58.2787i	1.18444	−	2.05151i
$808$		0			0
$809$	−13.4234	−	23.2500i	−0.471941	−	0.817426i	0.527543	−	0.849528i	$-0.323113\pi$
$809$	−13.4234	−	23.2500i	−0.471941	−	0.817426i	−0.999485	+	0.0321019i	$0.989780\pi$
$810$		0			0
$811$	31.0572			1.09057			0.545283	−	0.838252i	$-0.316422\pi$
$811$	31.0572			1.09057			0.545283	+	0.838252i	$0.316422\pi$
$812$		0			0
$813$	42.2463			1.48164
$814$		0			0
$815$	−13.7587	−	23.8307i	−0.481946	−	0.834755i
$816$		0			0
$817$	−22.6923	+	39.3043i	−0.793905	+	1.37508i
$818$		0			0
$819$	66.8218	+	17.1838i	2.33494	+	0.600450i
$820$		0			0
$821$	9.92231	−	17.1859i	0.346291	−	0.599794i	−0.639296	−	0.768960i	$-0.720774\pi$
$821$	9.92231	−	17.1859i	0.346291	−	0.599794i	0.985587	+	0.169167i	$0.0541076\pi$
$822$		0			0
$823$	−9.29179	−	16.0939i	−0.323891	−	0.560996i	0.657396	−	0.753545i	$-0.271658\pi$
$823$	−9.29179	−	16.0939i	−0.323891	−	0.560996i	−0.981287	+	0.192549i	$0.938325\pi$
$824$		0			0
$825$	−21.3308			−0.742643
$826$		0			0
$827$	7.25744			0.252366			0.126183	−	0.992007i	$-0.459727\pi$
$827$	7.25744			0.252366			0.126183	+	0.992007i	$0.459727\pi$
$828$		0			0
$829$	21.4893	+	37.2206i	0.746356	+	1.29273i	0.949559	+	0.313589i	$0.101531\pi$
$829$	21.4893	+	37.2206i	0.746356	+	1.29273i	−0.203203	+	0.979137i	$0.565135\pi$
$830$		0			0
$831$	15.1179	−	26.1850i	0.524435	−	0.908348i
$832$		0			0
$833$	−10.7970	−	5.94631i	−0.374094	−	0.206028i
$834$		0			0
$835$	26.9263	−	46.6377i	0.931822	−	1.61396i
$836$		0			0
$837$	−62.1101	−	107.578i	−2.14684	−	3.71844i
$838$		0			0
$839$	35.1650			1.21403			0.607015	−	0.794690i	$-0.292367\pi$
$839$	35.1650			1.21403			0.607015	+	0.794690i	$0.292367\pi$
$840$		0			0
$841$	−20.5940			−0.710137
$842$		0			0
$843$	−42.7599	−	74.0624i	−1.47273	−	2.55084i
$844$		0			0
$845$	0.679065	−	1.17617i	0.0233605	−	0.0404616i
$846$		0			0
$847$	2.56238	+	0.658939i	0.0880445	+	0.0226414i
$848$		0			0
$849$	−0.493163	+	0.854184i	−0.0169253	+	0.0293155i
$850$		0			0
$851$	1.76088	+	3.04993i	0.0603621	+	0.104550i
$852$		0			0
$853$	−40.5587			−1.38870			−0.694352	−	0.719635i	$-0.744309\pi$
$853$	−40.5587			−1.38870			−0.694352	+	0.719635i	$0.744309\pi$
$854$		0			0
$855$	−91.6687			−3.13500
$856$		0			0
$857$	21.0978	+	36.5425i	0.720687	+	1.24827i	0.960725	+	0.277504i	$0.0895070\pi$
$857$	21.0978	+	36.5425i	0.720687	+	1.24827i	−0.240037	+	0.970764i	$0.577160\pi$
$858$		0			0
$859$	−26.5715	+	46.0233i	−0.906609	+	1.57029i	−0.0878670	+	0.996132i	$0.528005\pi$
$859$	−26.5715	+	46.0233i	−0.906609	+	1.57029i	−0.818742	+	0.574161i	$0.805328\pi$
$860$		0			0
$861$	−51.2863	+	52.3324i	−1.74783	+	1.78348i
$862$		0			0
$863$	−15.9932	+	27.7010i	−0.544414	+	0.942952i	0.454230	+	0.890884i	$0.349914\pi$
$863$	−15.9932	+	27.7010i	−0.544414	+	0.942952i	−0.998644	+	0.0520676i	$0.983419\pi$
$864$		0			0
$865$	−6.40972	−	11.1020i	−0.217937	−	0.377478i
$866$		0			0
$867$	−44.2268			−1.50202
$868$		0			0
$869$	7.35021			0.249339
$870$		0			0
$871$	6.23585	+	10.8008i	0.211294	+	0.365972i
$872$		0			0
$873$	−41.8480	+	72.4829i	−1.41634	+	2.45317i
$874$		0			0
$875$	4.14132	+	14.8542i	0.140002	+	0.502162i
$876$		0			0
$877$	−9.84609	+	17.0539i	−0.332479	+	0.575870i	−0.982997	−	0.183620i	$-0.941218\pi$
$877$	−9.84609	+	17.0539i	−0.332479	+	0.575870i	0.650518	+	0.759491i	$0.274552\pi$
$878$		0			0
$879$	−49.6736	−	86.0372i	−1.67545	−	2.90196i
$880$		0			0
$881$	−42.3333			−1.42624			−0.713122	−	0.701040i	$-0.752719\pi$
$881$	−42.3333			−1.42624			−0.713122	+	0.701040i	$0.752719\pi$
$882$		0			0
$883$	22.5023			0.757263			0.378632	−	0.925547i	$-0.376395\pi$
$883$	22.5023			0.757263			0.378632	+	0.925547i	$0.376395\pi$
$884$		0			0
$885$	−35.6278	−	61.7091i	−1.19761	−	2.07433i
$886$		0			0
$887$	12.9286	−	22.3930i	0.434100	−	0.751883i	−0.563122	−	0.826374i	$-0.690400\pi$
$887$	12.9286	−	22.3930i	0.434100	−	0.751883i	0.997222	+	0.0744911i	$0.0237333\pi$
$888$		0			0
$889$	−0.469087	−	1.68253i	−0.0157327	−	0.0564303i
$890$		0			0
$891$	10.1940	−	17.6565i	0.341511	−	0.591515i
$892$		0			0
$893$	−7.97141	−	13.8069i	−0.266753	−	0.462030i
$894$		0			0
$895$	39.3502			1.31533
$896$		0			0
$897$	−14.4315			−0.481853
$898$		0			0
$899$	13.7204	+	23.7644i	0.457600	+	0.792587i
$900$		0			0
$901$	−0.198495	+	0.343803i	−0.00661283	+	0.0114538i
$902$		0			0
$903$	−71.1080	+	72.5583i	−2.36632	+	2.41459i
$904$		0			0
$905$	−9.90520	+	17.1563i	−0.329260	+	0.570295i
$906$		0			0
$907$	−7.29071	−	12.6279i	−0.242084	−	0.419302i	0.719224	−	0.694779i	$-0.244498\pi$
$907$	−7.29071	−	12.6279i	−0.242084	−	0.419302i	−0.961308	+	0.275477i	$0.911164\pi$
$908$		0			0
$909$	85.8813			2.84850
$910$		0			0
$911$	−8.63860			−0.286210			−0.143105	−	0.989708i	$-0.545709\pi$
$911$	−8.63860			−0.286210			−0.143105	+	0.989708i	$0.545709\pi$
$912$		0			0
$913$	−5.24433	−	9.08344i	−0.173562	−	0.300618i
$914$		0			0
$915$	−55.7863	+	96.6248i	−1.84424	+	3.19432i
$916$		0			0
$917$	50.5150	+	12.9904i	1.66815	+	0.428980i
$918$		0			0
$919$	15.5241	−	26.8885i	0.512092	−	0.886969i	−0.487810	−	0.872950i	$-0.662204\pi$
$919$	15.5241	−	26.8885i	0.512092	−	0.886969i	0.999902	−	0.0140194i	$-0.00446267\pi$
$920$		0			0
$921$	−11.9451	−	20.6896i	−0.393606	−	0.681745i
$922$		0			0
$923$	−15.5160			−0.510715
$924$		0			0
$925$	19.0528			0.626452
$926$		0			0
$927$	60.1902	+	104.252i	1.97690	+	3.42410i
$928$		0			0
$929$	−3.96333	+	6.86469i	−0.130033	+	0.225223i	−0.923689	−	0.383143i	$-0.874842\pi$
$929$	−3.96333	+	6.86469i	−0.130033	+	0.225223i	0.793656	+	0.608366i	$0.208175\pi$
$930$		0			0
$931$	−0.531469	−	26.3208i	−0.0174182	−	0.862628i
$932$		0			0
$933$	2.44282	−	4.23109i	0.0799743	−	0.138520i
$934$		0			0
$935$	3.01204	+	5.21700i	0.0985042	+	0.170614i
$936$		0			0
$937$	−9.42571			−0.307925			−0.153962	−	0.988077i	$-0.549203\pi$
$937$	−9.42571			−0.307925			−0.153962	+	0.988077i	$0.549203\pi$
$938$		0			0
$939$	−40.8960			−1.33459
$940$		0			0
$941$	23.1826	+	40.1535i	0.755732	+	1.30897i	0.945009	+	0.327043i	$0.106052\pi$
$941$	23.1826	+	40.1535i	0.755732	+	1.30897i	−0.189277	+	0.981924i	$0.560615\pi$
$942$		0			0
$943$	5.39248	−	9.34004i	0.175603	−	0.304154i
$944$		0			0
$945$	−115.053	−	29.5868i	−3.74266	−	0.962459i
$946$		0			0
$947$	−2.06075	+	3.56932i	−0.0669653	+	0.115987i	−0.897564	−	0.440884i	$-0.854665\pi$
$947$	−2.06075	+	3.56932i	−0.0669653	+	0.115987i	0.830599	+	0.556871i	$0.187998\pi$
$948$		0			0
$949$	−18.6339	−	32.2749i	−0.604883	−	1.04769i
$950$		0			0
$951$	7.73680			0.250883
$952$		0			0
$953$	37.6446			1.21943			0.609714	−	0.792621i	$-0.291284\pi$
$953$	37.6446			1.21943			0.609714	+	0.792621i	$0.291284\pi$
$954$		0			0
$955$	31.6821	+	54.8750i	1.02521	+	1.77571i
$956$		0			0
$957$	−4.61273	+	7.98947i	−0.149108	+	0.258263i
$958$		0			0
$959$	−5.13805	+	5.24284i	−0.165916	+	0.169300i
$960$		0			0
$961$	−29.2891	+	50.7302i	−0.944809	+	1.63646i
$962$		0			0
$963$	−4.07605	−	7.05993i	−0.131349	−	0.227503i
$964$		0			0
$965$	12.9130			0.415684
$966$		0			0
$967$	−1.22545			−0.0394078			−0.0197039	−	0.999806i	$-0.506272\pi$
$967$	−1.22545			−0.0394078			−0.0197039	+	0.999806i	$0.506272\pi$
$968$		0			0
$969$	10.5361	+	18.2491i	0.338469	+	0.586245i
$970$		0			0
$971$	16.6814	−	28.8930i	0.535331	−	0.927221i	−0.463816	−	0.885932i	$-0.653520\pi$
$971$	16.6814	−	28.8930i	0.535331	−	0.927221i	0.999147	−	0.0412893i	$-0.0131465\pi$
$972$		0			0
$973$	−7.81587	−	28.0341i	−0.250565	−	0.898733i
$974$		0			0
$975$	−39.0374	+	67.6147i	−1.25020	+	2.16540i
$976$		0			0
$977$	−18.1460	−	31.4297i	−0.580541	−	1.00553i	−0.995415	−	0.0956474i	$-0.969508\pi$
$977$	−18.1460	−	31.4297i	−0.580541	−	1.00553i	0.414875	−	0.909879i	$-0.363825\pi$
$978$		0			0
$979$	−7.26320			−0.232133
$980$		0			0
$981$	−23.5595			−0.752197
$982$		0			0
$983$	0.574975	+	0.995887i	0.0183389	+	0.0317639i	0.875049	−	0.484034i	$-0.160829\pi$
$983$	0.574975	+	0.995887i	0.0183389	+	0.0317639i	−0.856710	+	0.515798i	$0.827496\pi$
$984$		0			0
$985$	17.3932	−	30.1258i	0.554192	−	0.959889i
$986$		0			0
$987$	−9.58414	−	34.3766i	−0.305066	−	1.09422i
$988$		0			0
$989$	7.47661	−	12.9499i	0.237742	−	0.411782i
$990$		0			0
$991$	−12.7603	−	22.1015i	−0.405345	−	0.702078i	0.589017	−	0.808121i	$-0.299515\pi$
$991$	−12.7603	−	22.1015i	−0.405345	−	0.702078i	−0.994362	+	0.106043i	$0.966182\pi$
$992$		0			0
$993$	33.1157			1.05090
$994$		0			0
$995$	34.4775			1.09301
$996$		0			0
$997$	4.27059	+	7.39688i	0.135251	+	0.234262i	0.925693	−	0.378275i	$-0.123483\pi$
$997$	4.27059	+	7.39688i	0.135251	+	0.234262i	−0.790442	+	0.612536i	$0.790149\pi$
$998$		0			0
$999$	−18.6512	+	32.3048i	−0.590097	+	1.02208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.i.a.177.1	✓	6
3.2	odd	2		2772.2.s.f.793.1		6
4.3	odd	2		1232.2.q.l.177.3		6
7.2	even	3		2156.2.a.i.1.3		3
7.3	odd	6		2156.2.i.l.1145.3		6
7.4	even	3	inner	308.2.i.a.221.1	yes	6
7.5	odd	6		2156.2.a.h.1.1		3
7.6	odd	2		2156.2.i.l.177.3		6
21.11	odd	6		2772.2.s.f.2377.1		6
28.11	odd	6		1232.2.q.l.529.3		6
28.19	even	6		8624.2.a.cn.1.3		3
28.23	odd	6		8624.2.a.ci.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.i.a.177.1	✓	6	1.1	even	1	trivial
308.2.i.a.221.1	yes	6	7.4	even	3	inner
1232.2.q.l.177.3		6	4.3	odd	2
1232.2.q.l.529.3		6	28.11	odd	6
2156.2.a.h.1.1		3	7.5	odd	6
2156.2.a.i.1.3		3	7.2	even	3
2156.2.i.l.177.3		6	7.6	odd	2
2156.2.i.l.1145.3		6	7.3	odd	6
2772.2.s.f.793.1		6	3.2	odd	2
2772.2.s.f.2377.1		6	21.11	odd	6
8624.2.a.ci.1.1		3	28.23	odd	6
8624.2.a.cn.1.3		3	28.19	even	6

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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59097 - 2.75564i) q^{3} +(1.71053 - 2.96273i) q^{5} +(-0.710533 - 2.54856i) q^{7} +(-3.56238 + 6.17023i) q^{9} +(0.500000 + 0.866025i) q^{11} +3.66019 q^{13} -10.8856 q^{15} +(0.880438 + 1.52496i) q^{17} +(-1.88044 + 3.25701i) q^{19} +(-5.89248 + 6.01266i) q^{21} +(0.619562 - 1.07311i) q^{23} +(-3.35185 - 5.80557i) q^{25} +13.1248 q^{27} -2.89931 q^{29} +(-4.73229 - 8.19656i) q^{31} +(1.59097 - 2.75564i) q^{33} +(-8.76608 - 2.25427i) q^{35} +(-1.42107 + 2.46136i) q^{37} +(-5.82326 - 10.0862i) q^{39} +8.70370 q^{41} +12.0676 q^{43} +(12.1871 + 21.1088i) q^{45} +(-2.11956 + 3.67119i) q^{47} +(-5.99028 + 3.62167i) q^{49} +(2.80150 - 4.85235i) q^{51} +(0.112725 + 0.195246i) q^{53} +3.42107 q^{55} +11.9669 q^{57} +(3.27292 + 5.66886i) q^{59} +(5.12476 - 8.87635i) q^{61} +(18.2564 + 4.69478i) q^{63} +(6.26088 - 10.8442i) q^{65} +(1.70370 + 2.95089i) q^{67} -3.94282 q^{69} -4.23912 q^{71} +(-5.09097 - 8.81782i) q^{73} +(-10.6654 + 18.4730i) q^{75} +(1.85185 - 1.88962i) q^{77} +(3.67511 - 6.36547i) q^{79} +(-10.1940 - 17.6565i) q^{81} -10.4887 q^{83} +6.02408 q^{85} +(4.61273 + 7.98947i) q^{87} +(-3.63160 + 6.29012i) q^{89} +(-2.60069 - 9.32820i) q^{91} +(-15.0579 + 26.0810i) q^{93} +(6.43310 + 11.1425i) q^{95} +11.7472 q^{97} -7.12476 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 2 q^{5} + 4 q^{7} - 4 q^{9} + 3 q^{11} + 6 q^{13} - 30 q^{15} + 5 q^{17} - 11 q^{19} - 10 q^{21} + 4 q^{23} - 11 q^{25} + 44 q^{27} - 2 q^{29} - 19 q^{31} + q^{33} - 17 q^{35} + 8 q^{37}+ \cdots - 8 q^{99}+O(q^{100}) \) 6 * q - q^3 + 2 * q^5 + 4 * q^7 - 4 * q^9 + 3 * q^11 + 6 * q^13 - 30 * q^15 + 5 * q^17 - 11 * q^19 - 10 * q^21 + 4 * q^23 - 11 * q^25 + 44 * q^27 - 2 * q^29 - 19 * q^31 + q^33 - 17 * q^35 + 8 * q^37 - 17 * q^39 + 34 * q^41 + 20 * q^43 + 21 * q^45 - 13 * q^47 - 12 * q^49 - 9 * q^53 + 4 * q^55 + 4 * q^57 - 6 * q^59 - 4 * q^61 + 50 * q^63 + 37 * q^65 - 8 * q^67 - 6 * q^69 - 26 * q^71 - 22 * q^73 - 13 * q^75 + 2 * q^77 - 5 * q^79 - 19 * q^81 + 6 * q^83 - 14 * q^85 + 18 * q^87 + 3 * q^89 - 31 * q^91 - 14 * q^93 - 3 * q^95 + 50 * q^97 - 8 * q^99

Introduction

L-functions

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Varieties

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Representations

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Database

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