LMFDB - Embedded newform 2340.2.g.b.1691.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2340,2,Mod(1691,2340)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2340, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2340.1691"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2340.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,-4,0,0,0,0,0,-4,0,0,48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$18.6849940730$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1691.19
Character	$\chi$	$=$	2340.1691
Dual form			2340.2.g.b.1691.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.405974 - 1.35469i) q^{2} +(-1.67037 + 1.09994i) q^{4} +1.00000i q^{5} +1.05331i q^{7} +(2.16820 + 1.81629i) q^{8} +(1.35469 - 0.405974i) q^{10} -2.94047 q^{11} +1.00000 q^{13} +(1.42691 - 0.427617i) q^{14} +(1.58028 - 3.67461i) q^{16} +2.82145i q^{17} -4.64725i q^{19} +(-1.09994 - 1.67037i) q^{20} +(1.19375 + 3.98343i) q^{22} +6.54399 q^{23} -1.00000 q^{25} +(-0.405974 - 1.35469i) q^{26} +(-1.15858 - 1.75942i) q^{28} +0.0387991i q^{29} -0.836825i q^{31} +(-5.61950 - 0.648991i) q^{32} +(3.82219 - 1.14544i) q^{34} -1.05331 q^{35} -3.57653 q^{37} +(-6.29559 + 1.88666i) q^{38} +(-1.81629 + 2.16820i) q^{40} +10.2580i q^{41} -5.05107i q^{43} +(4.91167 - 3.23433i) q^{44} +(-2.65669 - 8.86508i) q^{46} -1.00144 q^{47} +5.89053 q^{49} +(0.405974 + 1.35469i) q^{50} +(-1.67037 + 1.09994i) q^{52} +13.7903i q^{53} -2.94047i q^{55} +(-1.91312 + 2.28379i) q^{56} +(0.0525607 - 0.0157514i) q^{58} -5.31956 q^{59} -2.98720 q^{61} +(-1.13364 + 0.339729i) q^{62} +(1.40219 + 7.87616i) q^{64} +1.00000i q^{65} +15.1114i q^{67} +(-3.10342 - 4.71287i) q^{68} +(0.427617 + 1.42691i) q^{70} -9.53560 q^{71} -5.77827 q^{73} +(1.45198 + 4.84509i) q^{74} +(5.11169 + 7.76264i) q^{76} -3.09723i q^{77} +5.96259i q^{79} +(3.67461 + 1.58028i) q^{80} +(13.8964 - 4.16448i) q^{82} -15.8285 q^{83} -2.82145 q^{85} +(-6.84263 + 2.05060i) q^{86} +(-6.37553 - 5.34074i) q^{88} -2.96256i q^{89} +1.05331i q^{91} +(-10.9309 + 7.19798i) q^{92} +(0.406560 + 1.35665i) q^{94} +4.64725 q^{95} +6.69353 q^{97} +(-2.39140 - 7.97985i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4} - 4 q^{10} + 48 q^{13} - 36 q^{16} - 8 q^{22} - 48 q^{25} + 8 q^{28} + 8 q^{34} + 16 q^{37} + 4 q^{40} + 32 q^{46} - 64 q^{49} - 4 q^{52} + 72 q^{58} - 32 q^{61} - 28 q^{64} - 24 q^{70} - 48 q^{73}+ \cdots - 32 q^{97}+O(q^{100}) $ 48 * q - 4 * q^4 - 4 * q^10 + 48 * q^13 - 36 * q^16 - 8 * q^22 - 48 * q^25 + 8 * q^28 + 8 * q^34 + 16 * q^37 + 4 * q^40 + 32 * q^46 - 64 * q^49 - 4 * q^52 + 72 * q^58 - 32 * q^61 - 28 * q^64 - 24 * q^70 - 48 * q^73 - 72 * q^76 + 48 * q^82 + 32 * q^85 - 24 * q^88 - 56 * q^94 - 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2340\mathbb{Z}\right)^\times$.

$n$	$937$	$1081$	$1171$	$2081$
$\chi(n)$	$1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.405974	−	1.35469i	−0.287067	−	0.957911i
$2$	−0.405974	−	1.35469i	−0.287067	−	0.957911i
$3$		0			0
$3$		0			0
$4$	−1.67037	+	1.09994i	−0.835185	+	0.549969i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$			1.05331i			0.398115i	0.979988	+	0.199057i	$0.0637880\pi$
$7$			1.05331i			0.398115i	−0.979988	+	0.199057i	$0.936212\pi$
$8$	2.16820	+	1.81629i	0.766575	+	0.642155i
$9$		0			0
$10$	1.35469	−	0.405974i	0.428391	−	0.128380i
$11$	−2.94047			−0.886585			−0.443292	−	0.896377i	$-0.646190\pi$
$11$	−2.94047			−0.886585			−0.443292	+	0.896377i	$0.646190\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	1.42691	−	0.427617i	0.381358	−	0.114285i
$15$		0			0
$16$	1.58028	−	3.67461i	0.395069	−	0.918651i
$17$			2.82145i			0.684303i	0.939645	+	0.342151i	$0.111156\pi$
$17$			2.82145i			0.684303i	−0.939645	+	0.342151i	$0.888844\pi$
$18$		0			0
$19$		−	4.64725i		−	1.06615i	−0.846067	−	0.533077i	$-0.821036\pi$
$19$		−	4.64725i		−	1.06615i	0.846067	−	0.533077i	$-0.178964\pi$
$20$	−1.09994	−	1.67037i	−0.245953	−	0.373506i
$21$		0			0
$22$	1.19375	+	3.98343i	0.254509	+	0.849269i
$23$	6.54399			1.36452			0.682258	−	0.731111i	$-0.260998\pi$
$23$	6.54399			1.36452			0.682258	+	0.731111i	$0.260998\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−0.405974	−	1.35469i	−0.0796180	−	0.265677i
$27$		0			0
$28$	−1.15858	−	1.75942i	−0.218950	−	0.332499i
$29$			0.0387991i			0.00720481i	0.999994	+	0.00360240i	$0.00114668\pi$
$29$			0.0387991i			0.00720481i	−0.999994	+	0.00360240i	$0.998853\pi$
$30$		0			0
$31$		−	0.836825i		−	0.150298i	−0.997172	−	0.0751491i	$-0.976057\pi$
$31$		−	0.836825i		−	0.150298i	0.997172	−	0.0751491i	$-0.0239433\pi$
$32$	−5.61950	−	0.648991i	−0.993397	−	0.114727i
$33$		0			0
$34$	3.82219	−	1.14544i	0.655501	−	0.196441i
$35$	−1.05331			−0.178042
$36$		0			0
$37$	−3.57653			−0.587978			−0.293989	−	0.955809i	$-0.594983\pi$
$37$	−3.57653			−0.587978			−0.293989	+	0.955809i	$0.594983\pi$
$38$	−6.29559	+	1.88666i	−1.02128	+	0.306057i
$39$		0			0
$40$	−1.81629	+	2.16820i	−0.287181	+	0.342823i
$41$			10.2580i			1.60203i	0.598642	+	0.801016i	$0.295707\pi$
$41$			10.2580i			1.60203i	−0.598642	+	0.801016i	$0.704293\pi$
$42$		0			0
$43$		−	5.05107i		−	0.770280i	−0.922858	−	0.385140i	$-0.874153\pi$
$43$		−	5.05107i		−	0.770280i	0.922858	−	0.385140i	$-0.125847\pi$
$44$	4.91167	−	3.23433i	0.740463	−	0.487594i
$45$		0			0
$46$	−2.65669	−	8.86508i	−0.391707	−	1.30708i
$47$	−1.00144			−0.146076			−0.0730379	−	0.997329i	$-0.523269\pi$
$47$	−1.00144			−0.146076			−0.0730379	+	0.997329i	$0.523269\pi$
$48$		0			0
$49$	5.89053			0.841505
$50$	0.405974	+	1.35469i	0.0574134	+	0.191582i
$51$		0			0
$52$	−1.67037	+	1.09994i	−0.231639	+	0.152534i
$53$			13.7903i			1.89424i	0.320872	+	0.947122i	$0.396024\pi$
$53$			13.7903i			1.89424i	−0.320872	+	0.947122i	$0.603976\pi$
$54$		0			0
$55$		−	2.94047i		−	0.396493i
$56$	−1.91312	+	2.28379i	−0.255651	+	0.305185i
$57$		0			0
$58$	0.0525607	−	0.0157514i	0.00690156	−	0.00206826i
$59$	−5.31956			−0.692547			−0.346274	−	0.938134i	$-0.612553\pi$
$59$	−5.31956			−0.692547			−0.346274	+	0.938134i	$0.612553\pi$
$60$		0			0
$61$	−2.98720			−0.382472			−0.191236	−	0.981544i	$-0.561250\pi$
$61$	−2.98720			−0.382472			−0.191236	+	0.981544i	$0.561250\pi$
$62$	−1.13364	+	0.339729i	−0.143972	+	0.0431456i
$63$		0			0
$64$	1.40219	+	7.87616i	0.175274	+	0.984520i
$65$			1.00000i			0.124035i
$66$		0			0
$67$			15.1114i			1.84615i	0.384614	+	0.923077i	$0.374334\pi$
$67$			15.1114i			1.84615i	−0.384614	+	0.923077i	$0.625666\pi$
$68$	−3.10342	−	4.71287i	−0.376345	−	0.571519i
$69$		0			0
$70$	0.427617	+	1.42691i	0.0511100	+	0.170549i
$71$	−9.53560			−1.13167			−0.565834	−	0.824519i	$-0.691446\pi$
$71$	−9.53560			−1.13167			−0.565834	+	0.824519i	$0.691446\pi$
$72$		0			0
$73$	−5.77827			−0.676295			−0.338148	−	0.941093i	$-0.609800\pi$
$73$	−5.77827			−0.676295			−0.338148	+	0.941093i	$0.609800\pi$
$74$	1.45198	+	4.84509i	0.168789	+	0.563231i
$75$		0			0
$76$	5.11169	+	7.76264i	0.586351	+	0.890435i
$77$		−	3.09723i		−	0.352962i
$78$		0			0
$79$			5.96259i			0.670844i	0.942068	+	0.335422i	$0.108879\pi$
$79$			5.96259i			0.670844i	−0.942068	+	0.335422i	$0.891121\pi$
$80$	3.67461	+	1.58028i	0.410833	+	0.176680i
$81$		0			0
$82$	13.8964	−	4.16448i	1.53460	−	0.459890i
$83$	−15.8285			−1.73740			−0.868702	−	0.495335i	$-0.835045\pi$
$83$	−15.8285			−1.73740			−0.868702	+	0.495335i	$0.835045\pi$
$84$		0			0
$85$	−2.82145			−0.306029
$86$	−6.84263	+	2.05060i	−0.737860	+	0.221122i
$87$		0			0
$88$	−6.37553	−	5.34074i	−0.679634	−	0.569325i
$89$		−	2.96256i		−	0.314031i	−0.987596	−	0.157015i	$-0.949813\pi$
$89$		−	2.96256i		−	0.314031i	0.987596	−	0.157015i	$-0.0501872\pi$
$90$		0			0
$91$			1.05331i			0.110417i
$92$	−10.9309	+	7.19798i	−1.13962	+	0.750441i
$93$		0			0
$94$	0.406560	+	1.35665i	0.0419335	+	0.139927i
$95$	4.64725			0.476798
$96$		0			0
$97$	6.69353			0.679625			0.339813	−	0.940493i	$-0.389636\pi$
$97$	6.69353			0.679625			0.339813	+	0.940493i	$0.389636\pi$
$98$	−2.39140	−	7.97985i	−0.241568	−	0.806086i
$99$		0			0
$100$	1.67037	−	1.09994i	0.167037	−	0.109994i
$101$			17.9036i			1.78148i	0.454515	+	0.890739i	$0.349812\pi$
$101$			17.9036i			1.78148i	−0.454515	+	0.890739i	$0.650188\pi$
$102$		0			0
$103$		−	3.96918i		−	0.391095i	−0.980694	−	0.195547i	$-0.937352\pi$
$103$		−	3.96918i		−	0.391095i	0.980694	−	0.195547i	$-0.0626484\pi$
$104$	2.16820	+	1.81629i	0.212610	+	0.178102i
$105$		0			0
$106$	18.6816	−	5.59850i	1.81452	−	0.543775i
$107$	−10.0977			−0.976179			−0.488090	−	0.872793i	$-0.662306\pi$
$107$	−10.0977			−0.976179			−0.488090	+	0.872793i	$0.662306\pi$
$108$		0			0
$109$	1.00633			0.0963889			0.0481944	−	0.998838i	$-0.484653\pi$
$109$	1.00633			0.0963889			0.0481944	+	0.998838i	$0.484653\pi$
$110$	−3.98343	+	1.19375i	−0.379805	+	0.113820i
$111$		0			0
$112$	3.87051	+	1.66452i	0.365728	+	0.157283i
$113$			0.938566i			0.0882929i	0.999025	+	0.0441464i	$0.0140568\pi$
$113$			0.938566i			0.0882929i	−0.999025	+	0.0441464i	$0.985943\pi$
$114$		0			0
$115$			6.54399i			0.610230i
$116$	−0.0426765	−	0.0648088i	−0.00396242	−	0.00601735i
$117$		0			0
$118$	2.15960	+	7.20635i	0.198807	+	0.663398i
$119$	−2.97187			−0.272431
$120$		0			0
$121$	−2.35364			−0.213967
$122$	1.21273	+	4.04674i	0.109795	+	0.366374i
$123$		0			0
$124$	0.920455	+	1.39781i	0.0826593	+	0.125527i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$		−	5.55523i		−	0.492947i	−0.969149	−	0.246474i	$-0.920728\pi$
$127$		−	5.55523i		−	0.492947i	0.969149	−	0.246474i	$-0.0792719\pi$
$128$	10.1005	−	5.09704i	0.892767	−	0.450519i
$129$		0			0
$130$	1.35469	−	0.405974i	0.118814	−	0.0356063i
$131$	−21.2161			−1.85366			−0.926830	−	0.375481i	$-0.877478\pi$
$131$	−21.2161			−1.85366			−0.926830	+	0.375481i	$0.877478\pi$
$132$		0			0
$133$	4.89501			0.424451
$134$	20.4713	−	6.13484i	1.76845	−	0.529970i
$135$		0			0
$136$	−5.12457	+	6.11747i	−0.439428	+	0.524569i
$137$			17.8350i			1.52375i	0.647723	+	0.761876i	$0.275721\pi$
$137$			17.8350i			1.52375i	−0.647723	+	0.761876i	$0.724279\pi$
$138$		0			0
$139$			10.7470i			0.911553i	0.890094	+	0.455776i	$0.150638\pi$
$139$			10.7470i			0.911553i	−0.890094	+	0.455776i	$0.849362\pi$
$140$	1.75942	−	1.15858i	0.148698	−	0.0979176i
$141$		0			0
$142$	3.87120	+	12.9178i	0.324864	+	1.08404i
$143$	−2.94047			−0.245894
$144$		0			0
$145$	−0.0387991			−0.00322209
$146$	2.34583	+	7.82776i	0.194142	+	0.647830i
$147$		0			0
$148$	5.97414	−	3.93396i	0.491071	−	0.323370i
$149$			19.7279i			1.61617i	0.589065	+	0.808086i	$0.299496\pi$
$149$			19.7279i			1.61617i	−0.589065	+	0.808086i	$0.700504\pi$
$150$		0			0
$151$			13.3532i			1.08667i	0.839516	+	0.543335i	$0.182839\pi$
$151$			13.3532i			1.08667i	−0.839516	+	0.543335i	$0.817161\pi$
$152$	8.44076	−	10.0762i	0.684636	−	0.817286i
$153$		0			0
$154$	−4.19579	+	1.25739i	−0.338106	+	0.101324i
$155$	0.836825			0.0672154
$156$		0			0
$157$	2.73873			0.218574			0.109287	−	0.994010i	$-0.465143\pi$
$157$	2.73873			0.218574			0.109287	+	0.994010i	$0.465143\pi$
$158$	8.07746	−	2.42065i	0.642608	−	0.192577i
$159$		0			0
$160$	0.648991	−	5.61950i	0.0513073	−	0.444261i
$161$			6.89286i			0.543234i
$162$		0			0
$163$		−	22.1496i		−	1.73489i	−0.497535	−	0.867444i	$-0.665761\pi$
$163$		−	22.1496i		−	1.73489i	0.497535	−	0.867444i	$-0.334239\pi$
$164$	−11.2832	−	17.1347i	−0.881068	−	1.33799i
$165$		0			0
$166$	6.42596	+	21.4427i	0.498751	+	1.66428i
$167$	21.8513			1.69090			0.845451	−	0.534053i	$-0.179332\pi$
$167$	21.8513			1.69090			0.845451	+	0.534053i	$0.179332\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	1.14544	+	3.82219i	0.0878509	+	0.293149i
$171$		0			0
$172$	5.55586	+	8.43715i	0.423630	+	0.643327i
$173$		−	4.32498i		−	0.328822i	−0.986392	−	0.164411i	$-0.947428\pi$
$173$		−	4.32498i		−	0.328822i	0.986392	−	0.164411i	$-0.0525724\pi$
$174$		0			0
$175$		−	1.05331i		−	0.0796229i
$176$	−4.64675	+	10.8051i	−0.350262	+	0.814463i
$177$		0			0
$178$	−4.01335	+	1.20272i	−0.300813	+	0.0901478i
$179$	18.5968			1.38999			0.694996	−	0.719013i	$-0.255406\pi$
$179$	18.5968			1.38999			0.694996	+	0.719013i	$0.255406\pi$
$180$		0			0
$181$	3.24660			0.241318			0.120659	−	0.992694i	$-0.461499\pi$
$181$	3.24660			0.241318			0.120659	+	0.992694i	$0.461499\pi$
$182$	1.42691	−	0.427617i	0.105770	−	0.0316971i
$183$		0			0
$184$	14.1887	+	11.8858i	1.04600	+	0.876231i
$185$		−	3.57653i		−	0.262952i
$186$		0			0
$187$		−	8.29639i		−	0.606692i
$188$	1.67278	−	1.10153i	0.122000	−	0.0803371i
$189$		0			0
$190$	−1.88666	−	6.29559i	−0.136873	−	0.456730i
$191$	−4.83744			−0.350025			−0.175012	−	0.984566i	$-0.555997\pi$
$191$	−4.83744			−0.350025			−0.175012	+	0.984566i	$0.555997\pi$
$192$		0			0
$193$	−8.94915			−0.644174			−0.322087	−	0.946710i	$-0.604384\pi$
$193$	−8.94915			−0.644174			−0.322087	+	0.946710i	$0.604384\pi$
$194$	−2.71740	−	9.06766i	−0.195098	−	0.651020i
$195$		0			0
$196$	−9.83937	+	6.47922i	−0.702812	+	0.462801i
$197$		−	25.3567i		−	1.80659i	−0.429017	−	0.903296i	$-0.641140\pi$
$197$		−	25.3567i		−	1.80659i	0.429017	−	0.903296i	$-0.358860\pi$
$198$		0			0
$199$			0.0844252i			0.00598474i	0.999996	+	0.00299237i	$0.000952503\pi$
$199$			0.0844252i			0.00598474i	−0.999996	+	0.00299237i	$0.999047\pi$
$200$	−2.16820	−	1.81629i	−0.153315	−	0.128431i
$201$		0			0
$202$	24.2539	−	7.26840i	1.70650	−	0.511403i
$203$	−0.0408675			−0.00286834
$204$		0			0
$205$	−10.2580			−0.716451
$206$	−5.37701	+	1.61138i	−0.374634	+	0.112270i
$207$		0			0
$208$	1.58028	−	3.67461i	0.109572	−	0.254788i
$209$			13.6651i			0.945235i
$210$		0			0
$211$			7.27338i			0.500720i	0.968153	+	0.250360i	$0.0805490\pi$
$211$			7.27338i			0.500720i	−0.968153	+	0.250360i	$0.919451\pi$
$212$	−15.1685	−	23.0349i	−1.04178	−	1.58205i
$213$		0			0
$214$	4.09939	+	13.6792i	0.280229	+	0.935093i
$215$	5.05107			0.344480
$216$		0			0
$217$	0.881438			0.0598359
$218$	−0.408543	−	1.36326i	−0.0276700	−	0.0923319i
$219$		0			0
$220$	3.23433	+	4.91167i	0.218059	+	0.331145i
$221$			2.82145i			0.189791i
$222$		0			0
$223$			11.9534i			0.800461i	0.916414	+	0.400231i	$0.131070\pi$
$223$			11.9534i			0.800461i	−0.916414	+	0.400231i	$0.868930\pi$
$224$	0.683590	−	5.91909i	0.0456743	−	0.395486i
$225$		0			0
$226$	1.27147	−	0.381033i	0.0845767	−	0.0253460i
$227$	10.6394			0.706164			0.353082	−	0.935592i	$-0.385134\pi$
$227$	10.6394			0.706164			0.353082	+	0.935592i	$0.385134\pi$
$228$		0			0
$229$	14.9630			0.988783			0.494392	−	0.869239i	$-0.335391\pi$
$229$	14.9630			0.988783			0.494392	+	0.869239i	$0.335391\pi$
$230$	8.86508	−	2.65669i	0.584546	−	0.175177i
$231$		0			0
$232$	−0.0704703	+	0.0841242i	−0.00462660	+	0.00552302i
$233$			2.57732i			0.168846i	0.996430	+	0.0844229i	$0.0269047\pi$
$233$			2.57732i			0.168846i	−0.996430	+	0.0844229i	$0.973095\pi$
$234$		0			0
$235$		−	1.00144i		−	0.0653271i
$236$	8.88563	−	5.85118i	0.578405	−	0.380879i
$237$		0			0
$238$	1.20650	+	4.02596i	0.0782058	+	0.260964i
$239$	2.36787			0.153165			0.0765825	−	0.997063i	$-0.475599\pi$
$239$	2.36787			0.153165			0.0765825	+	0.997063i	$0.475599\pi$
$240$		0			0
$241$	−12.0291			−0.774861			−0.387430	−	0.921899i	$-0.626637\pi$
$241$	−12.0291			−0.774861			−0.387430	+	0.921899i	$0.626637\pi$
$242$	0.955516	+	3.18845i	0.0614229	+	0.204961i
$243$		0			0
$244$	4.98974	−	3.28574i	0.319435	−	0.210348i
$245$			5.89053i			0.376332i
$246$		0			0
$247$		−	4.64725i		−	0.295698i
$248$	1.51992	−	1.81440i	0.0965148	−	0.115215i
$249$		0			0
$250$	−1.35469	+	0.405974i	−0.0856781	+	0.0256760i
$251$	2.25731			0.142480			0.0712401	−	0.997459i	$-0.477304\pi$
$251$	2.25731			0.142480			0.0712401	+	0.997459i	$0.477304\pi$
$252$		0			0
$253$	−19.2424			−1.20976
$254$	−7.52562	+	2.25528i	−0.472199	+	0.141509i
$255$		0			0
$256$	−11.0055	−	11.6138i	−0.687841	−	0.725862i
$257$		−	1.83970i		−	0.114757i	−0.998352	−	0.0573785i	$-0.981726\pi$
$257$		−	1.83970i		−	0.114757i	0.998352	−	0.0573785i	$-0.0182742\pi$
$258$		0			0
$259$		−	3.76720i		−	0.234083i
$260$	−1.09994	−	1.67037i	−0.0682152	−	0.103592i
$261$		0			0
$262$	8.61318	+	28.7413i	0.532124	+	1.77564i
$263$	7.46623			0.460388			0.230194	−	0.973145i	$-0.426064\pi$
$263$	7.46623			0.460388			0.230194	+	0.973145i	$0.426064\pi$
$264$		0			0
$265$	−13.7903			−0.847132
$266$	−1.98724	−	6.63122i	−0.121846	−	0.406586i
$267$		0			0
$268$	−16.6216	−	25.2417i	−1.01533	−	1.54188i
$269$		−	5.35185i		−	0.326308i	−0.986601	−	0.163154i	$-0.947833\pi$
$269$		−	5.35185i		−	0.326308i	0.986601	−	0.163154i	$-0.0521668\pi$
$270$		0			0
$271$		−	20.8262i		−	1.26510i	−0.774519	−	0.632550i	$-0.782008\pi$
$271$		−	20.8262i		−	1.26510i	0.774519	−	0.632550i	$-0.217992\pi$
$272$	10.3677	+	4.45867i	0.628636	+	0.270347i
$273$		0			0
$274$	24.1610	−	7.24056i	1.45962	−	0.437418i
$275$	2.94047			0.177317
$276$		0			0
$277$	−21.6153			−1.29873			−0.649367	−	0.760475i	$-0.724966\pi$
$277$	−21.6153			−1.29873			−0.649367	+	0.760475i	$0.724966\pi$
$278$	14.5589	−	4.36302i	0.873186	−	0.261677i
$279$		0			0
$280$	−2.28379	−	1.91312i	−0.136483	−	0.114331i
$281$			12.2235i			0.729196i	0.931165	+	0.364598i	$0.118794\pi$
$281$			12.2235i			0.729196i	−0.931165	+	0.364598i	$0.881206\pi$
$282$		0			0
$283$		−	3.84030i		−	0.228282i	−0.993465	−	0.114141i	$-0.963588\pi$
$283$		−	3.84030i		−	0.228282i	0.993465	−	0.114141i	$-0.0364116\pi$
$284$	15.9280	−	10.4886i	0.945152	−	0.622382i
$285$		0			0
$286$	1.19375	+	3.98343i	0.0705881	+	0.235545i
$287$	−10.8049			−0.637793
$288$		0			0
$289$	9.03941			0.531730
$290$	0.0157514	+	0.0525607i	0.000924954	+	0.00308647i
$291$		0			0
$292$	9.65185	−	6.35573i	0.564832	−	0.371941i
$293$		−	13.3925i		−	0.782399i	−0.920306	−	0.391199i	$-0.872060\pi$
$293$		−	13.3925i		−	0.782399i	0.920306	−	0.391199i	$-0.127940\pi$
$294$		0			0
$295$		−	5.31956i		−	0.309717i
$296$	−7.75464	−	6.49602i	−0.450729	−	0.377573i
$297$		0			0
$298$	26.7252	−	8.00900i	1.54815	−	0.463949i
$299$	6.54399			0.378449
$300$		0			0
$301$	5.32035			0.306660
$302$	18.0895	−	5.42106i	1.04093	−	0.311947i
$303$		0			0
$304$	−17.0768	−	7.34394i	−0.979423	−	0.421204i
$305$		−	2.98720i		−	0.171047i
$306$		0			0
$307$			8.99995i			0.513654i	0.966457	+	0.256827i	$0.0826771\pi$
$307$			8.99995i			0.513654i	−0.966457	+	0.256827i	$0.917323\pi$
$308$	3.40676	+	5.17353i	0.194118	+	0.294789i
$309$		0			0
$310$	−0.339729	−	1.13364i	−0.0192953	−	0.0643864i
$311$	−0.931498			−0.0528204			−0.0264102	−	0.999651i	$-0.508408\pi$
$311$	−0.931498			−0.0528204			−0.0264102	+	0.999651i	$0.508408\pi$
$312$		0			0
$313$	8.95381			0.506099			0.253050	−	0.967453i	$-0.418566\pi$
$313$	8.95381			0.506099			0.253050	+	0.967453i	$0.418566\pi$
$314$	−1.11185	−	3.71013i	−0.0627454	−	0.209375i
$315$		0			0
$316$	−6.55847	−	9.95973i	−0.368943	−	0.560279i
$317$		−	3.58090i		−	0.201124i	−0.994931	−	0.100562i	$-0.967936\pi$
$317$		−	3.58090i		−	0.201124i	0.994931	−	0.100562i	$-0.0320640\pi$
$318$		0			0
$319$		−	0.114087i		−	0.00638767i
$320$	−7.87616	+	1.40219i	−0.440291	+	0.0783847i
$321$		0			0
$322$	9.33769	−	2.79832i	0.520369	−	0.155944i
$323$	13.1120			0.729571
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	−30.0058	+	8.99214i	−1.66187	+	0.498029i
$327$		0			0
$328$	−18.6315	+	22.2414i	−1.02875	+	1.22808i
$329$		−	1.05483i		−	0.0581549i
$330$		0			0
$331$		−	1.76396i		−	0.0969559i	−0.998824	−	0.0484780i	$-0.984563\pi$
$331$		−	1.76396i		−	0.0969559i	0.998824	−	0.0484780i	$-0.0154371\pi$
$332$	26.4395	−	17.4104i	1.45105	−	0.955518i
$333$		0			0
$334$	−8.87104	−	29.6017i	−0.485402	−	1.61973i
$335$	−15.1114			−0.825625
$336$		0			0
$337$	−10.5875			−0.576740			−0.288370	−	0.957519i	$-0.593113\pi$
$337$	−10.5875			−0.576740			−0.288370	+	0.957519i	$0.593113\pi$
$338$	−0.405974	−	1.35469i	−0.0220821	−	0.0736854i
$339$		0			0
$340$	4.71287	−	3.10342i	0.255591	−	0.168307i
$341$			2.46066i			0.133252i
$342$		0			0
$343$			13.5778i			0.733130i
$344$	9.17420	−	10.9517i	0.494639	−	0.590477i
$345$		0			0
$346$	−5.85901	+	1.75583i	−0.314982	+	0.0943939i
$347$	4.16045			0.223345			0.111672	−	0.993745i	$-0.464379\pi$
$347$	4.16045			0.223345			0.111672	+	0.993745i	$0.464379\pi$
$348$		0			0
$349$	5.85211			0.313256			0.156628	−	0.987658i	$-0.449938\pi$
$349$	5.85211			0.313256			0.156628	+	0.987658i	$0.449938\pi$
$350$	−1.42691	+	0.427617i	−0.0762716	+	0.0228571i
$351$		0			0
$352$	16.5240	+	1.90834i	0.880731	+	0.101715i
$353$			10.2397i			0.545004i	0.962155	+	0.272502i	$0.0878512\pi$
$353$			10.2397i			0.545004i	−0.962155	+	0.272502i	$0.912149\pi$
$354$		0			0
$355$		−	9.53560i		−	0.506097i
$356$	3.25863	+	4.94857i	0.172707	+	0.262274i
$357$		0			0
$358$	−7.54982	−	25.1929i	−0.399021	−	1.33149i
$359$	−3.35259			−0.176943			−0.0884715	−	0.996079i	$-0.528198\pi$
$359$	−3.35259			−0.176943			−0.0884715	+	0.996079i	$0.528198\pi$
$360$		0			0
$361$	−2.59697			−0.136683
$362$	−1.31803	−	4.39813i	−0.0692743	−	0.231161i
$363$		0			0
$364$	−1.15858	−	1.75942i	−0.0607259	−	0.0922187i
$365$		−	5.77827i		−	0.302448i
$366$		0			0
$367$		−	29.0091i		−	1.51426i	−0.653262	−	0.757132i	$-0.726600\pi$
$367$		−	29.0091i		−	1.51426i	0.653262	−	0.757132i	$-0.273400\pi$
$368$	10.3413	−	24.0466i	0.539078	−	1.25351i
$369$		0			0
$370$	−4.84509	+	1.45198i	−0.251884	+	0.0754848i
$371$	−14.5255			−0.754126
$372$		0			0
$373$	−2.98117			−0.154359			−0.0771795	−	0.997017i	$-0.524591\pi$
$373$	−2.98117			−0.154359			−0.0771795	+	0.997017i	$0.524591\pi$
$374$	−11.2390	+	3.36812i	−0.581157	+	0.174161i
$375$		0			0
$376$	−2.17133	−	1.81891i	−0.111978	−	0.0938033i
$377$			0.0387991i			0.00199825i
$378$		0			0
$379$			27.7780i			1.42686i	0.700728	+	0.713429i	$0.252859\pi$
$379$			27.7780i			1.42686i	−0.700728	+	0.713429i	$0.747141\pi$
$380$	−7.76264	+	5.11169i	−0.398215	+	0.262224i
$381$		0			0
$382$	1.96387	+	6.55323i	0.100481	+	0.335293i
$383$	−23.2824			−1.18968			−0.594838	−	0.803846i	$-0.702784\pi$
$383$	−23.2824			−1.18968			−0.594838	+	0.803846i	$0.702784\pi$
$384$		0			0
$385$	3.09723			0.157850
$386$	3.63312	+	12.1233i	0.184921	+	0.617061i
$387$		0			0
$388$	−11.1807	+	7.36246i	−0.567613	+	0.373772i
$389$		−	20.6880i		−	1.04892i	−0.851434	−	0.524462i	$-0.824266\pi$
$389$		−	20.6880i		−	1.04892i	0.851434	−	0.524462i	$-0.175734\pi$
$390$		0			0
$391$			18.4636i			0.933742i
$392$	12.7719	+	10.6989i	0.645076	+	0.540377i
$393$		0			0
$394$	−34.3505	+	10.2942i	−1.73055	+	0.518613i
$395$	−5.96259			−0.300010
$396$		0			0
$397$	−30.6375			−1.53765			−0.768826	−	0.639458i	$-0.779159\pi$
$397$	−30.6375			−1.53765			−0.768826	+	0.639458i	$0.779159\pi$
$398$	0.114370	−	0.0342744i	0.00573285	−	0.00171802i
$399$		0			0
$400$	−1.58028	+	3.67461i	−0.0790138	+	0.183730i
$401$			9.17964i			0.458409i	0.973378	+	0.229205i	$0.0736125\pi$
$401$			9.17964i			0.458409i	−0.973378	+	0.229205i	$0.926388\pi$
$402$		0			0
$403$		−	0.836825i		−	0.0416852i
$404$	−19.6929	−	29.9057i	−0.979757	−	1.48786i
$405$		0			0
$406$	0.0165911	+	0.0553628i	0.000823405	+	0.00274761i
$407$	10.5167			0.521293
$408$		0			0
$409$	6.98980			0.345623			0.172812	−	0.984955i	$-0.444715\pi$
$409$	6.98980			0.345623			0.172812	+	0.984955i	$0.444715\pi$
$410$	4.16448	+	13.8964i	0.205669	+	0.686296i
$411$		0			0
$412$	4.36585	+	6.63000i	0.215090	+	0.326637i
$413$		−	5.60315i		−	0.275713i
$414$		0			0
$415$		−	15.8285i		−	0.776991i
$416$	−5.61950	−	0.648991i	−0.275519	−	0.0318194i
$417$		0			0
$418$	18.5120	−	5.54768i	0.905451	−	0.271346i
$419$	11.2283			0.548538			0.274269	−	0.961653i	$-0.411564\pi$
$419$	11.2283			0.548538			0.274269	+	0.961653i	$0.411564\pi$
$420$		0			0
$421$	−9.79629			−0.477442			−0.238721	−	0.971088i	$-0.576728\pi$
$421$	−9.79629			−0.477442			−0.238721	+	0.971088i	$0.576728\pi$
$422$	9.85318	−	2.95280i	0.479645	−	0.143740i
$423$		0			0
$424$	−25.0472	+	29.9002i	−1.21640	+	1.45208i
$425$		−	2.82145i		−	0.136861i
$426$		0			0
$427$		−	3.14646i		−	0.152268i
$428$	16.8669	−	11.1068i	0.815291	−	0.536868i
$429$		0			0
$430$	−2.05060	−	6.84263i	−0.0988887	−	0.329981i
$431$	24.2060			1.16596			0.582982	−	0.812485i	$-0.301886\pi$
$431$	24.2060			1.16596			0.582982	+	0.812485i	$0.301886\pi$
$432$		0			0
$433$	0.782969			0.0376271			0.0188136	−	0.999823i	$-0.494011\pi$
$433$	0.782969			0.0376271			0.0188136	+	0.999823i	$0.494011\pi$
$434$	−0.357841	−	1.19408i	−0.0171769	−	0.0573174i
$435$		0			0
$436$	−1.68094	+	1.10690i	−0.0805026	+	0.0530109i
$437$		−	30.4116i		−	1.45478i
$438$		0			0
$439$			24.4364i			1.16628i	0.812370	+	0.583142i	$0.198177\pi$
$439$			24.4364i			1.16628i	−0.812370	+	0.583142i	$0.801823\pi$
$440$	5.34074	−	6.37553i	0.254610	−	0.303941i
$441$		0			0
$442$	3.82219	−	1.14544i	0.181803	−	0.0544828i
$443$	15.4804			0.735495			0.367748	−	0.929926i	$-0.380129\pi$
$443$	15.4804			0.735495			0.367748	+	0.929926i	$0.380129\pi$
$444$		0			0
$445$	2.96256			0.140439
$446$	16.1932	−	4.85278i	0.766770	−	0.229786i
$447$		0			0
$448$	−8.29605	+	1.47694i	−0.391952	+	0.0697790i
$449$			26.3821i			1.24505i	0.782601	+	0.622523i	$0.213892\pi$
$449$			26.3821i			1.24505i	−0.782601	+	0.622523i	$0.786108\pi$
$450$		0			0
$451$		−	30.1634i		−	1.42034i
$452$	−1.03236	−	1.56775i	−0.0485583	−	0.0737409i
$453$		0			0
$454$	−4.31933	−	14.4131i	−0.202716	−	0.676442i
$455$	−1.05331			−0.0493800
$456$		0			0
$457$	10.8114			0.505737			0.252868	−	0.967501i	$-0.418626\pi$
$457$	10.8114			0.505737			0.252868	+	0.967501i	$0.418626\pi$
$458$	−6.07459	−	20.2702i	−0.283847	−	0.947166i
$459$		0			0
$460$	−7.19798	−	10.9309i	−0.335607	−	0.509655i
$461$			31.4194i			1.46335i	0.681656	+	0.731673i	$0.261260\pi$
$461$			31.4194i			1.46335i	−0.681656	+	0.731673i	$0.738740\pi$
$462$		0			0
$463$		−	14.1971i		−	0.659795i	−0.944017	−	0.329897i	$-0.892986\pi$
$463$		−	14.1971i		−	0.659795i	0.944017	−	0.329897i	$-0.107014\pi$
$464$	0.142571	+	0.0613132i	0.00661871	+	0.00284640i
$465$		0			0
$466$	3.49147	−	1.04632i	0.161739	−	0.0484700i
$467$	41.0005			1.89727			0.948637	−	0.316366i	$-0.102463\pi$
$467$	41.0005			1.89727			0.948637	+	0.316366i	$0.102463\pi$
$468$		0			0
$469$	−15.9170			−0.734981
$470$	−1.35665	+	0.406560i	−0.0625775	+	0.0187532i
$471$		0			0
$472$	−11.5339	−	9.66185i	−0.530889	−	0.444723i
$473$			14.8525i			0.682919i
$474$		0			0
$475$			4.64725i			0.213231i
$476$	4.96412	−	3.26887i	0.227530	−	0.149828i
$477$		0			0
$478$	−0.961294	−	3.20773i	−0.0439686	−	0.146718i
$479$	−35.5508			−1.62436			−0.812179	−	0.583408i	$-0.801719\pi$
$479$	−35.5508			−1.62436			−0.812179	+	0.583408i	$0.801719\pi$
$480$		0			0
$481$	−3.57653			−0.163076
$482$	4.88349	+	16.2957i	0.222437	+	0.742247i
$483$		0			0
$484$	3.93145	−	2.58885i	0.178702	−	0.117675i
$485$			6.69353i			0.303938i
$486$		0			0
$487$			18.8833i			0.855684i	0.903853	+	0.427842i	$0.140726\pi$
$487$			18.8833i			0.855684i	−0.903853	+	0.427842i	$0.859274\pi$
$488$	−6.47686	−	5.42563i	−0.293194	−	0.245607i
$489$		0			0
$490$	7.97985	−	2.39140i	0.360493	−	0.108033i
$491$	−30.8985			−1.39443			−0.697214	−	0.716863i	$-0.745577\pi$
$491$	−30.8985			−1.39443			−0.697214	+	0.716863i	$0.745577\pi$
$492$		0			0
$493$	−0.109470			−0.00493027
$494$	−6.29559	+	1.88666i	−0.283252	+	0.0848850i
$495$		0			0
$496$	−3.07500	−	1.32241i	−0.138072	−	0.0593782i
$497$		−	10.0440i		−	0.450533i
$498$		0			0
$499$		−	14.8595i		−	0.665201i	−0.943068	−	0.332601i	$-0.892074\pi$
$499$		−	14.8595i		−	0.665201i	0.943068	−	0.332601i	$-0.107926\pi$
$500$	1.09994	+	1.67037i	0.0491907	+	0.0747012i
$501$		0			0
$502$	−0.916409	−	3.05796i	−0.0409013	−	0.136483i
$503$	22.2041			0.990032			0.495016	−	0.868884i	$-0.335162\pi$
$503$	22.2041			0.990032			0.495016	+	0.868884i	$0.335162\pi$
$504$		0			0
$505$	−17.9036			−0.796701
$506$	7.81191	+	26.0675i	0.347282	+	1.15884i
$507$		0			0
$508$	6.11041	+	9.27930i	0.271106	+	0.411702i
$509$			14.2922i			0.633490i	0.948511	+	0.316745i	$0.102590\pi$
$509$			14.2922i			0.633490i	−0.948511	+	0.316745i	$0.897410\pi$
$510$		0			0
$511$		−	6.08632i		−	0.269243i
$512$	−11.2652	+	19.6239i	−0.497854	+	0.867261i
$513$		0			0
$514$	−2.49222	+	0.746868i	−0.109927	+	0.0329429i
$515$	3.96918			0.174903
$516$		0			0
$517$	2.94472			0.129509
$518$	−5.10340	+	1.52939i	−0.224230	+	0.0671974i
$519$		0			0
$520$	−1.81629	+	2.16820i	−0.0796495	+	0.0950819i
$521$			24.6719i			1.08090i	0.841377	+	0.540449i	$0.181745\pi$
$521$			24.6719i			1.08090i	−0.841377	+	0.540449i	$0.818255\pi$
$522$		0			0
$523$			23.2536i			1.01681i	0.861119	+	0.508403i	$0.169764\pi$
$523$			23.2536i			1.01681i	−0.861119	+	0.508403i	$0.830236\pi$
$524$	35.4388	−	23.3364i	1.54815	−	1.01945i
$525$		0			0
$526$	−3.03109	−	10.1144i	−0.132162	−	0.441010i
$527$	2.36106			0.102849
$528$		0			0
$529$	19.8238			0.861905
$530$	5.59850	+	18.6816i	0.243183	+	0.811477i
$531$		0			0
$532$	−8.17648	+	5.38420i	−0.354495	+	0.233435i
$533$			10.2580i			0.444324i
$534$		0			0
$535$		−	10.0977i		−	0.436561i
$536$	−27.4467	+	32.7646i	−1.18552	+	1.41522i
$537$		0			0
$538$	−7.25010	+	2.17271i	−0.312574	+	0.0936723i
$539$	−17.3209			−0.746065
$540$		0			0
$541$	−41.4505			−1.78210			−0.891049	−	0.453908i	$-0.850030\pi$
$541$	−41.4505			−1.78210			−0.891049	+	0.453908i	$0.850030\pi$
$542$	−28.2130	+	8.45488i	−1.21185	+	0.363168i
$543$		0			0
$544$	1.83110	−	15.8552i	0.0785077	−	0.679784i
$545$			1.00633i			0.0431064i
$546$		0			0
$547$		−	25.6656i		−	1.09738i	−0.836025	−	0.548691i	$-0.815126\pi$
$547$		−	25.6656i		−	1.09738i	0.836025	−	0.548691i	$-0.184874\pi$
$548$	−19.6174	−	29.7911i	−0.838015	−	1.27261i
$549$		0			0
$550$	−1.19375	−	3.98343i	−0.0509018	−	0.169854i
$551$	0.180309			0.00768143
$552$		0			0
$553$	−6.28047			−0.267073
$554$	8.77523	+	29.2820i	0.372824	+	1.24407i
$555$		0			0
$556$	−11.8211	−	17.9516i	−0.501325	−	0.761316i
$557$		−	44.5000i		−	1.88553i	−0.333463	−	0.942763i	$-0.608217\pi$
$557$		−	44.5000i		−	1.88553i	0.333463	−	0.942763i	$-0.391783\pi$
$558$		0			0
$559$		−	5.05107i		−	0.213637i
$560$	−1.66452	+	3.87051i	−0.0703390	+	0.163559i
$561$		0			0
$562$	16.5591	−	4.96244i	0.698504	−	0.209328i
$563$	27.5301			1.16026			0.580129	−	0.814525i	$-0.303002\pi$
$563$	27.5301			1.16026			0.580129	+	0.814525i	$0.303002\pi$
$564$		0			0
$565$	−0.938566			−0.0394858
$566$	−5.20241	+	1.55906i	−0.218674	+	0.0655322i
$567$		0			0
$568$	−20.6751	−	17.3194i	−0.867508	−	0.726706i
$569$			16.1417i			0.676694i	0.941021	+	0.338347i	$0.109868\pi$
$569$			16.1417i			0.676694i	−0.941021	+	0.338347i	$0.890132\pi$
$570$		0			0
$571$			39.9657i			1.67251i	0.548337	+	0.836257i	$0.315261\pi$
$571$			39.9657i			1.67251i	−0.548337	+	0.836257i	$0.684739\pi$
$572$	4.91167	−	3.23433i	0.205367	−	0.135234i
$573$		0			0
$574$	4.38650	+	14.6373i	0.183089	+	0.610948i
$575$	−6.54399			−0.272903
$576$		0			0
$577$	−6.58765			−0.274247			−0.137124	−	0.990554i	$-0.543786\pi$
$577$	−6.58765			−0.274247			−0.137124	+	0.990554i	$0.543786\pi$
$578$	−3.66976	−	12.2456i	−0.152642	−	0.509350i
$579$		0			0
$580$	0.0648088	−	0.0426765i	0.00269104	−	0.00177205i
$581$		−	16.6724i		−	0.691686i
$582$		0			0
$583$		−	40.5500i		−	1.67941i
$584$	−12.5284	−	10.4950i	−0.518431	−	0.434286i
$585$		0			0
$586$	−18.1427	+	5.43701i	−0.749468	+	0.224601i
$587$	−42.2691			−1.74463			−0.872316	−	0.488943i	$-0.837382\pi$
$587$	−42.2691			−1.74463			−0.872316	+	0.488943i	$0.837382\pi$
$588$		0			0
$589$	−3.88894			−0.160241
$590$	−7.20635	+	2.15960i	−0.296681	+	0.0889093i
$591$		0			0
$592$	−5.65191	+	13.1423i	−0.232292	+	0.540147i
$593$		−	28.8146i		−	1.18327i	−0.806205	−	0.591636i	$-0.798482\pi$
$593$		−	28.8146i		−	1.18327i	0.806205	−	0.591636i	$-0.201518\pi$
$594$		0			0
$595$		−	2.97187i		−	0.121835i
$596$	−21.6994	−	32.9529i	−0.888843	−	1.34980i
$597$		0			0
$598$	−2.65669	−	8.86508i	−0.108640	−	0.362520i
$599$	−22.4024			−0.915338			−0.457669	−	0.889123i	$-0.651316\pi$
$599$	−22.4024			−0.915338			−0.457669	+	0.889123i	$0.651316\pi$
$600$		0			0
$601$	34.1054			1.39119			0.695594	−	0.718435i	$-0.255141\pi$
$601$	34.1054			1.39119			0.695594	+	0.718435i	$0.255141\pi$
$602$	−2.15992	−	7.20742i	−0.0880318	−	0.293753i
$603$		0			0
$604$	−14.6877	−	22.3048i	−0.597635	−	0.907571i
$605$		−	2.35364i		−	0.0956890i
$606$		0			0
$607$			32.7256i			1.32829i	0.747603	+	0.664146i	$0.231205\pi$
$607$			32.7256i			1.32829i	−0.747603	+	0.664146i	$0.768795\pi$
$608$	−3.01603	+	26.1153i	−0.122316	+	1.05911i
$609$		0			0
$610$	−4.04674	+	1.21273i	−0.163848	+	0.0491019i
$611$	−1.00144			−0.0405141
$612$		0			0
$613$	25.9015			1.04615			0.523076	−	0.852286i	$-0.324785\pi$
$613$	25.9015			1.04615			0.523076	+	0.852286i	$0.324785\pi$
$614$	12.1921	−	3.65374i	0.492035	−	0.147453i
$615$		0			0
$616$	5.62547	−	6.71542i	0.226657	−	0.270572i
$617$		−	22.9070i		−	0.922201i	−0.887348	−	0.461100i	$-0.847455\pi$
$617$		−	22.9070i		−	0.922201i	0.887348	−	0.461100i	$-0.152545\pi$
$618$		0			0
$619$		−	34.2080i		−	1.37494i	−0.726214	−	0.687468i	$-0.758722\pi$
$619$		−	34.2080i		−	1.37494i	0.726214	−	0.687468i	$-0.241278\pi$
$620$	−1.39781	+	0.920455i	−0.0561373	+	0.0369664i
$621$		0			0
$622$	0.378164	+	1.26189i	0.0151630	+	0.0505972i
$623$	3.12050			0.125020
$624$		0			0
$625$	1.00000			0.0400000
$626$	−3.63501	−	12.1296i	−0.145284	−	0.484798i
$627$		0			0
$628$	−4.57469	+	3.01243i	−0.182550	+	0.120209i
$629$		−	10.0910i		−	0.402355i
$630$		0			0
$631$		−	41.3100i		−	1.64453i	−0.569108	−	0.822263i	$-0.692711\pi$
$631$		−	41.3100i		−	1.64453i	0.569108	−	0.822263i	$-0.307289\pi$
$632$	−10.8298	+	12.9281i	−0.430786	+	0.514252i
$633$		0			0
$634$	−4.85102	+	1.45375i	−0.192658	+	0.0577359i
$635$	5.55523			0.220453
$636$		0			0
$637$	5.89053			0.233391
$638$	−0.154553	+	0.0463165i	−0.00611882	+	0.00183369i
$639$		0			0
$640$	5.09704	+	10.1005i	0.201478	+	0.399257i
$641$		−	2.36666i		−	0.0934776i	−0.998907	−	0.0467388i	$-0.985117\pi$
$641$		−	2.36666i		−	0.0934776i	0.998907	−	0.0467388i	$-0.0148828\pi$
$642$		0			0
$643$			8.39957i			0.331247i	0.986189	+	0.165623i	$0.0529636\pi$
$643$			8.39957i			0.331247i	−0.986189	+	0.165623i	$0.947036\pi$
$644$	−7.58172	−	11.5136i	−0.298762	−	0.453701i
$645$		0			0
$646$	−5.32313	−	17.7627i	−0.209436	−	0.698864i
$647$	−28.4889			−1.12001			−0.560007	−	0.828488i	$-0.689202\pi$
$647$	−28.4889			−1.12001			−0.560007	+	0.828488i	$0.689202\pi$
$648$		0			0
$649$	15.6420			0.614002
$650$	0.405974	+	1.35469i	0.0159236	+	0.0531353i
$651$		0			0
$652$	24.3631	+	36.9980i	0.954134	+	1.44895i
$653$		−	15.1822i		−	0.594124i	−0.954858	−	0.297062i	$-0.903993\pi$
$653$		−	15.1822i		−	0.594124i	0.954858	−	0.297062i	$-0.0960068\pi$
$654$		0			0
$655$		−	21.2161i		−	0.828982i
$656$	37.6942	+	16.2105i	1.47171	+	0.632914i
$657$		0			0
$658$	−1.42897	+	0.428235i	−0.0557072	+	0.0166943i
$659$	−19.3682			−0.754480			−0.377240	−	0.926116i	$-0.623127\pi$
$659$	−19.3682			−0.754480			−0.377240	+	0.926116i	$0.623127\pi$
$660$		0			0
$661$	−33.7323			−1.31203			−0.656017	−	0.754746i	$-0.727760\pi$
$661$	−33.7323			−1.31203			−0.656017	+	0.754746i	$0.727760\pi$
$662$	−2.38962	+	0.716121i	−0.0928751	+	0.0278328i
$663$		0			0
$664$	−34.3194	−	28.7491i	−1.33185	−	1.11568i
$665$			4.89501i			0.189820i
$666$		0			0
$667$			0.253901i			0.00983107i
$668$	−36.4997	+	24.0350i	−1.41222	+	0.929943i
$669$		0			0
$670$	6.13484	+	20.4713i	0.237010	+	0.790875i
$671$	8.78378			0.339094
$672$		0			0
$673$	26.5860			1.02482			0.512408	−	0.858742i	$-0.328754\pi$
$673$	26.5860			1.02482			0.512408	+	0.858742i	$0.328754\pi$
$674$	4.29826	+	14.3428i	0.165563	+	0.552465i
$675$		0			0
$676$	−1.67037	+	1.09994i	−0.0642450	+	0.0423053i
$677$			1.21310i			0.0466232i	0.999728	+	0.0233116i	$0.00742098\pi$
$677$			1.21310i			0.0466232i	−0.999728	+	0.0233116i	$0.992579\pi$
$678$		0			0
$679$			7.05038i			0.270569i
$680$	−6.11747	−	5.12457i	−0.234594	−	0.196518i
$681$		0			0
$682$	3.33343	−	0.998963i	0.127644	−	0.0382523i
$683$	−9.78586			−0.374446			−0.187223	−	0.982317i	$-0.559949\pi$
$683$	−9.78586			−0.374446			−0.187223	+	0.982317i	$0.559949\pi$
$684$		0			0
$685$	−17.8350			−0.681442
$686$	18.3936	−	5.51221i	0.702273	−	0.210457i
$687$		0			0
$688$	−18.5607	−	7.98208i	−0.707619	−	0.304314i
$689$			13.7903i			0.525369i
$690$		0			0
$691$			13.8480i			0.526801i	0.964687	+	0.263401i	$0.0848441\pi$
$691$			13.8480i			0.526801i	−0.964687	+	0.263401i	$0.915156\pi$
$692$	4.75721	+	7.22432i	0.180842	+	0.274627i
$693$		0			0
$694$	−1.68903	−	5.63612i	−0.0641149	−	0.213944i
$695$	−10.7470			−0.407659
$696$		0			0
$697$	−28.9425			−1.09628
$698$	−2.37580	−	7.92780i	−0.0899255	−	0.300072i
$699$		0			0
$700$	1.15858	+	1.75942i	0.0437901	+	0.0664999i
$701$		−	15.4379i		−	0.583082i	−0.956558	−	0.291541i	$-0.905832\pi$
$701$		−	15.4379i		−	0.583082i	0.956558	−	0.291541i	$-0.0941680\pi$
$702$		0			0
$703$			16.6211i			0.626875i
$704$	−4.12309	−	23.1596i	−0.155395	−	0.872860i
$705$		0			0
$706$	13.8716	−	4.15705i	0.522066	−	0.156453i
$707$	−18.8581			−0.709232
$708$		0			0
$709$	−8.23882			−0.309416			−0.154708	−	0.987960i	$-0.549444\pi$
$709$	−8.23882			−0.309416			−0.154708	+	0.987960i	$0.549444\pi$
$710$	−12.9178	+	3.87120i	−0.484796	+	0.145284i
$711$		0			0
$712$	5.38086	−	6.42342i	0.201656	−	0.240728i
$713$		−	5.47618i		−	0.205084i
$714$		0			0
$715$		−	2.94047i		−	0.109967i
$716$	−31.0636	+	20.4553i	−1.16090	+	0.764452i
$717$		0			0
$718$	1.36106	+	4.54172i	0.0507945	+	0.169496i
$719$	37.1091			1.38394			0.691969	−	0.721927i	$-0.256744\pi$
$719$	37.1091			1.38394			0.691969	+	0.721927i	$0.256744\pi$
$720$		0			0
$721$	4.18078			0.155701
$722$	1.05430	+	3.51809i	0.0392370	+	0.130930i
$723$		0			0
$724$	−5.42302	+	3.57105i	−0.201545	+	0.132717i
$725$		−	0.0387991i		−	0.00144096i
$726$		0			0
$727$			41.8540i			1.55228i	0.630561	+	0.776140i	$0.282825\pi$
$727$			41.8540i			1.55228i	−0.630561	+	0.776140i	$0.717175\pi$
$728$	−1.91312	+	2.28379i	−0.0709049	+	0.0846430i
$729$		0			0
$730$	−7.82776	+	2.34583i	−0.289719	+	0.0868229i
$731$	14.2513			0.527105
$732$		0			0
$733$	−17.6558			−0.652131			−0.326066	−	0.945347i	$-0.605723\pi$
$733$	−17.6558			−0.652131			−0.326066	+	0.945347i	$0.605723\pi$
$734$	−39.2984	+	11.7769i	−1.45053	+	0.434695i
$735$		0			0
$736$	−36.7740	−	4.24699i	−1.35551	−	0.156546i
$737$		−	44.4347i		−	1.63677i
$738$		0			0
$739$		−	26.6870i		−	0.981697i	−0.871245	−	0.490848i	$-0.836687\pi$
$739$		−	26.6870i		−	0.981697i	0.871245	−	0.490848i	$-0.163313\pi$
$740$	3.93396	+	5.97414i	0.144615	+	0.219614i
$741$		0			0
$742$	5.89697	+	19.6776i	0.216485	+	0.722386i
$743$	22.2196			0.815158			0.407579	−	0.913170i	$-0.366373\pi$
$743$	22.2196			0.815158			0.407579	+	0.913170i	$0.366373\pi$
$744$		0			0
$745$	−19.7279			−0.722774
$746$	1.21028	+	4.03856i	0.0443114	+	0.147862i
$747$		0			0
$748$	9.12551	+	13.8581i	0.333662	+	0.506701i
$749$		−	10.6360i		−	0.388631i
$750$		0			0
$751$		−	26.1685i		−	0.954902i	−0.878658	−	0.477451i	$-0.841561\pi$
$751$		−	26.1685i		−	0.954902i	0.878658	−	0.477451i	$-0.158439\pi$
$752$	−1.58256	+	3.67991i	−0.0577100	+	0.134193i
$753$		0			0
$754$	0.0525607	−	0.0157514i	0.00191415	−	0.000573632i
$755$	−13.3532			−0.485974
$756$		0			0
$757$	26.3551			0.957892			0.478946	−	0.877844i	$-0.341019\pi$
$757$	26.3551			0.957892			0.478946	+	0.877844i	$0.341019\pi$
$758$	37.6305	−	11.2771i	1.36680	−	0.409604i
$759$		0			0
$760$	10.0762	+	8.44076i	0.365501	+	0.306178i
$761$			20.7186i			0.751048i	0.926813	+	0.375524i	$0.122537\pi$
$761$			20.7186i			0.751048i	−0.926813	+	0.375524i	$0.877463\pi$
$762$		0			0
$763$			1.05998i			0.0383738i
$764$	8.08032	−	5.32088i	0.292336	−	0.192503i
$765$		0			0
$766$	9.45205	+	31.5405i	0.341517	+	1.13960i
$767$	−5.31956			−0.192078
$768$		0			0
$769$	43.2023			1.55791			0.778957	−	0.627077i	$-0.215749\pi$
$769$	43.2023			1.55791			0.778957	+	0.627077i	$0.215749\pi$
$770$	−1.25739	−	4.19579i	−0.0453134	−	0.151206i
$771$		0			0
$772$	14.9484	−	9.84351i	0.538005	−	0.354276i
$773$			2.06517i			0.0742791i	0.999310	+	0.0371395i	$0.0118246\pi$
$773$			2.06517i			0.0742791i	−0.999310	+	0.0371395i	$0.988175\pi$
$774$		0			0
$775$			0.836825i			0.0300596i
$776$	14.5129	+	12.1574i	0.520983	+	0.436425i
$777$		0			0
$778$	−28.0259	+	8.39880i	−1.00478	+	0.301112i
$779$	47.6716			1.70801
$780$		0			0
$781$	28.0391			1.00332
$782$	25.0124	−	7.49572i	0.894441	−	0.268046i
$783$		0			0
$784$	9.30867	−	21.6454i	0.332453	−	0.773050i
$785$			2.73873i			0.0977494i
$786$		0			0
$787$		−	21.5366i		−	0.767697i	−0.923396	−	0.383848i	$-0.874599\pi$
$787$		−	21.5366i		−	0.767697i	0.923396	−	0.383848i	$-0.125401\pi$
$788$	27.8908	+	42.3552i	0.993569	+	1.50884i
$789$		0			0
$790$	2.42065	+	8.07746i	0.0861230	+	0.287383i
$791$	−0.988603			−0.0351507
$792$		0			0
$793$	−2.98720			−0.106079
$794$	12.4380	+	41.5043i	0.441409	+	1.47293i
$795$		0			0
$796$	−0.0928624	−	0.141021i	−0.00329142	−	0.00499837i
$797$		−	23.8557i		−	0.845014i	−0.906360	−	0.422507i	$-0.861150\pi$
$797$		−	23.8557i		−	0.845014i	0.906360	−	0.422507i	$-0.138850\pi$
$798$		0			0
$799$		−	2.82553i		−	0.0999600i
$800$	5.61950	+	0.648991i	0.198679	+	0.0229453i
$801$		0			0
$802$	12.4356	−	3.72669i	0.439115	−	0.131594i
$803$	16.9908			0.599593
$804$		0			0
$805$	−6.89286			−0.242942
$806$	−1.13364	+	0.339729i	−0.0399307	+	0.0119664i
$807$		0			0
$808$	−32.5182	+	38.8187i	−1.14399	+	1.36564i
$809$		−	6.23599i		−	0.219246i	−0.993973	−	0.109623i	$-0.965036\pi$
$809$		−	6.23599i		−	0.219246i	0.993973	−	0.109623i	$-0.0349643\pi$
$810$		0			0
$811$		−	32.1270i		−	1.12813i	−0.825730	−	0.564066i	$-0.809236\pi$
$811$		−	32.1270i		−	1.12813i	0.825730	−	0.564066i	$-0.190764\pi$
$812$	0.0682639	−	0.0449517i	0.00239559	−	0.00157750i
$813$		0			0
$814$	−4.26950	−	14.2468i	−0.149646	−	0.499352i
$815$	22.1496			0.775866
$816$		0			0
$817$	−23.4736			−0.821237
$818$	−2.83767	−	9.46901i	−0.0992169	−	0.331076i
$819$		0			0
$820$	17.1347	−	11.2832i	0.598369	−	0.394025i
$821$			16.6273i			0.580297i	0.956982	+	0.290148i	$0.0937046\pi$
$821$			16.6273i			0.580297i	−0.956982	+	0.290148i	$0.906295\pi$
$822$		0			0
$823$		−	14.7242i		−	0.513254i	−0.966510	−	0.256627i	$-0.917389\pi$
$823$		−	14.7242i		−	0.513254i	0.966510	−	0.256627i	$-0.0826112\pi$
$824$	7.20918	−	8.60598i	0.251144	−	0.299803i
$825$		0			0
$826$	−7.59054	+	2.27473i	−0.264109	+	0.0791481i
$827$	53.5217			1.86113			0.930566	−	0.366125i	$-0.119316\pi$
$827$	53.5217			1.86113			0.930566	+	0.366125i	$0.119316\pi$
$828$		0			0
$829$	42.9301			1.49102			0.745511	−	0.666493i	$-0.232205\pi$
$829$	42.9301			1.49102			0.745511	+	0.666493i	$0.232205\pi$
$830$	−21.4427	+	6.42596i	−0.744288	+	0.223048i
$831$		0			0
$832$	1.40219	+	7.87616i	0.0486121	+	0.273057i
$833$			16.6199i			0.575844i
$834$		0			0
$835$			21.8513i			0.756195i
$836$	−15.0308	−	22.8258i	−0.519850	−	0.789447i
$837$		0			0
$838$	−4.55840	−	15.2109i	−0.157467	−	0.525451i
$839$	−16.1309			−0.556900			−0.278450	−	0.960451i	$-0.589821\pi$
$839$	−16.1309			−0.556900			−0.278450	+	0.960451i	$0.589821\pi$
$840$		0			0
$841$	28.9985			0.999948
$842$	3.97704	+	13.2709i	0.137058	+	0.457347i
$843$		0			0
$844$	−8.00027	−	12.1492i	−0.275381	−	0.418194i
$845$			1.00000i			0.0344010i
$846$		0			0
$847$		−	2.47912i		−	0.0851834i
$848$	50.6740	+	21.7925i	1.74015	+	0.748358i
$849$		0			0
$850$	−3.82219	+	1.14544i	−0.131100	+	0.0392881i
$851$	−23.4048			−0.802306
$852$		0			0
$853$	39.9874			1.36914			0.684572	−	0.728945i	$-0.259989\pi$
$853$	39.9874			1.36914			0.684572	+	0.728945i	$0.259989\pi$
$854$	−4.26248	+	1.27738i	−0.145859	+	0.0437110i
$855$		0			0
$856$	−21.8938	−	18.3403i	−0.748314	−	0.626859i
$857$		−	39.7421i		−	1.35756i	−0.734340	−	0.678782i	$-0.762508\pi$
$857$		−	39.7421i		−	1.35756i	0.734340	−	0.678782i	$-0.237492\pi$
$858$		0			0
$859$			31.8271i			1.08593i	0.839757	+	0.542963i	$0.182698\pi$
$859$			31.8271i			1.08593i	−0.839757	+	0.542963i	$0.817302\pi$
$860$	−8.43715	+	5.55586i	−0.287705	+	0.189453i
$861$		0			0
$862$	−9.82701	−	32.7917i	−0.334709	−	1.11689i
$863$	−36.4117			−1.23947			−0.619734	−	0.784812i	$-0.712759\pi$
$863$	−36.4117			−1.23947			−0.619734	+	0.784812i	$0.712759\pi$
$864$		0			0
$865$	4.32498			0.147054
$866$	−0.317865	−	1.06068i	−0.0108015	−	0.0360434i
$867$		0			0
$868$	−1.47233	+	0.969526i	−0.0499741	+	0.0329079i
$869$		−	17.5328i		−	0.594760i
$870$		0			0
$871$			15.1114i			0.512031i
$872$	2.18192	+	1.82779i	0.0738893	+	0.0618966i
$873$		0			0
$874$	−41.1983	+	12.3463i	−1.39355	+	0.417620i
$875$	1.05331			0.0356084
$876$		0			0
$877$	−55.9168			−1.88817			−0.944087	−	0.329695i	$-0.893054\pi$
$877$	−55.9168			−1.88817			−0.944087	+	0.329695i	$0.893054\pi$
$878$	33.1037	−	9.92052i	1.11720	−	0.334801i
$879$		0			0
$880$	−10.8051	−	4.64675i	−0.364239	−	0.156642i
$881$		−	26.8470i		−	0.904498i	−0.891892	−	0.452249i	$-0.850622\pi$
$881$		−	26.8470i		−	0.904498i	0.891892	−	0.452249i	$-0.149378\pi$
$882$		0			0
$883$			35.7176i			1.20199i	0.799252	+	0.600996i	$0.205229\pi$
$883$			35.7176i			1.20199i	−0.799252	+	0.600996i	$0.794771\pi$
$884$	−3.10342	−	4.71287i	−0.104379	−	0.158511i
$885$		0			0
$886$	−6.28463	−	20.9711i	−0.211136	−	0.704539i
$887$	24.9974			0.839329			0.419665	−	0.907679i	$-0.362148\pi$
$887$	24.9974			0.839329			0.419665	+	0.907679i	$0.362148\pi$
$888$		0			0
$889$	5.85139			0.196249
$890$	−1.20272	−	4.01335i	−0.0403153	−	0.134528i
$891$		0			0
$892$	−13.1480	−	19.9667i	−0.440229	−	0.668534i
$893$			4.65397i			0.155739i
$894$		0			0
$895$			18.5968i			0.621623i
$896$	5.36878	+	10.6390i	0.179358	+	0.355423i
$897$		0			0
$898$	35.7395	−	10.7104i	1.19264	−	0.357412i
$899$	0.0324680			0.00108287
$900$		0			0
$901$	−38.9087			−1.29624
$902$	−40.8620	+	12.2455i	−1.36056	+	0.407732i
$903$		0			0
$904$	−1.70471	+	2.03500i	−0.0566977	+	0.0676831i
$905$			3.24660i			0.107921i
$906$		0			0
$907$		−	2.80328i		−	0.0930813i	−0.998916	−	0.0465407i	$-0.985180\pi$
$907$		−	2.80328i		−	0.0930813i	0.998916	−	0.0465407i	$-0.0148197\pi$
$908$	−17.7718	+	11.7027i	−0.589778	+	0.388368i
$909$		0			0
$910$	0.427617	+	1.42691i	0.0141754	+	0.0473017i
$911$	10.8021			0.357889			0.178944	−	0.983859i	$-0.442732\pi$
$911$	10.8021			0.357889			0.178944	+	0.983859i	$0.442732\pi$
$912$		0			0
$913$	46.5432			1.54036
$914$	−4.38915	−	14.6461i	−0.145180	−	0.484451i
$915$		0			0
$916$	−24.9938	+	16.4584i	−0.825817	+	0.543800i
$917$		−	22.3472i		−	0.737969i
$918$		0			0
$919$			8.18284i			0.269927i	0.990851	+	0.134964i	$0.0430917\pi$
$919$			8.18284i			0.269927i	−0.990851	+	0.134964i	$0.956908\pi$
$920$	−11.8858	+	14.1887i	−0.391862	+	0.467787i
$921$		0			0
$922$	42.5635	−	12.7554i	1.40175	−	0.420078i
$923$	−9.53560			−0.313868
$924$		0			0
$925$	3.57653			0.117596
$926$	−19.2327	+	5.76365i	−0.632024	+	0.189405i
$927$		0			0
$928$	0.0251803	−	0.218031i	0.000826582	−	0.00715723i
$929$		−	2.05904i		−	0.0675550i	−0.999429	−	0.0337775i	$-0.989246\pi$
$929$		−	2.05904i		−	0.0675550i	0.999429	−	0.0337775i	$-0.0107538\pi$
$930$		0			0
$931$		−	27.3748i		−	0.897173i
$932$	−2.83489	−	4.30508i	−0.0928599	−	0.141018i
$933$		0			0
$934$	−16.6451	−	55.5429i	−0.544645	−	1.81742i
$935$	8.29639			0.271321
$936$		0			0
$937$	−30.9393			−1.01074			−0.505372	−	0.862902i	$-0.668645\pi$
$937$	−30.9393			−1.01074			−0.505372	+	0.862902i	$0.668645\pi$
$938$	6.46190	+	21.5627i	0.210989	+	0.704046i
$939$		0			0
$940$	1.10153	+	1.67278i	0.0359278	+	0.0545602i
$941$		−	0.795560i		−	0.0259345i	−0.999916	−	0.0129673i	$-0.995872\pi$
$941$		−	0.795560i		−	0.0259345i	0.999916	−	0.0129673i	$-0.00412772\pi$
$942$		0			0
$943$			67.1283i			2.18600i
$944$	−8.40637	+	19.5473i	−0.273604	+	0.636210i
$945$		0			0
$946$	20.1205	−	6.02973i	0.654175	−	0.196043i
$947$	34.2536			1.11309			0.556547	−	0.830816i	$-0.312126\pi$
$947$	34.2536			1.11309			0.556547	+	0.830816i	$0.312126\pi$
$948$		0			0
$949$	−5.77827			−0.187571
$950$	6.29559	−	1.88666i	0.204256	−	0.0612114i
$951$		0			0
$952$	−6.44361	−	5.39777i	−0.208839	−	0.174943i
$953$			5.88066i			0.190493i	0.995454	+	0.0952467i	$0.0303640\pi$
$953$			5.88066i			0.190493i	−0.995454	+	0.0952467i	$0.969636\pi$
$954$		0			0
$955$		−	4.83744i		−	0.156536i
$956$	−3.95523	+	2.60451i	−0.127921	+	0.0842359i
$957$		0			0
$958$	14.4327	+	48.1603i	0.466299	+	1.55599i
$959$	−18.7859			−0.606627
$960$		0			0
$961$	30.2997			0.977410
$962$	1.45198	+	4.84509i	0.0468137	+	0.156212i
$963$		0			0
$964$	20.0930	−	13.2312i	0.647152	−	0.426149i
$965$		−	8.94915i		−	0.288083i
$966$		0			0
$967$			0.248778i			0.00800015i	0.999992	+	0.00400007i	$0.00127327\pi$
$967$			0.248778i			0.00800015i	−0.999992	+	0.00400007i	$0.998727\pi$
$968$	−5.10316	−	4.27489i	−0.164022	−	0.137400i
$969$		0			0
$970$	9.06766	−	2.71740i	0.291145	−	0.0872504i
$971$	26.8071			0.860280			0.430140	−	0.902762i	$-0.358464\pi$
$971$	26.8071			0.860280			0.430140	+	0.902762i	$0.358464\pi$
$972$		0			0
$973$	−11.3200			−0.362902
$974$	25.5810	−	7.66613i	0.819669	−	0.245639i
$975$		0			0
$976$	−4.72061	+	10.9768i	−0.151103	+	0.351359i
$977$			20.6746i			0.661439i	0.943729	+	0.330720i	$0.107291\pi$
$977$			20.6746i			0.661439i	−0.943729	+	0.330720i	$0.892709\pi$
$978$		0			0
$979$			8.71132i			0.278415i
$980$	−6.47922	−	9.83937i	−0.206971	−	0.314307i
$981$		0			0
$982$	12.5440	+	41.8578i	0.400294	+	1.33574i
$983$	−5.06227			−0.161461			−0.0807306	−	0.996736i	$-0.525725\pi$
$983$	−5.06227			−0.161461			−0.0807306	+	0.996736i	$0.525725\pi$
$984$		0			0
$985$	25.3567			0.807933
$986$	0.0444418	+	0.148298i	0.00141532	+	0.00472276i
$987$		0			0
$988$	5.11169	+	7.76264i	0.162624	+	0.246962i
$989$		−	33.0541i		−	1.05106i
$990$		0			0
$991$			39.5125i			1.25516i	0.778554	+	0.627578i	$0.215953\pi$
$991$			39.5125i			1.25516i	−0.778554	+	0.627578i	$0.784047\pi$
$992$	−0.543092	+	4.70254i	−0.0172432	+	0.149306i
$993$		0			0
$994$	−13.6065	+	4.07759i	−0.431571	+	0.129333i
$995$	−0.0844252			−0.00267646
$996$		0			0
$997$	49.8485			1.57872			0.789360	−	0.613931i	$-0.210413\pi$
$997$	49.8485			1.57872			0.789360	+	0.613931i	$0.210413\pi$
$998$	−20.1300	+	6.03256i	−0.637204	+	0.190957i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2340.2.g.b.1691.19	✓	48
3.2	odd	2	inner	2340.2.g.b.1691.30	yes	48
4.3	odd	2	inner	2340.2.g.b.1691.29	yes	48
12.11	even	2	inner	2340.2.g.b.1691.20	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2340.2.g.b.1691.19	✓	48	1.1	even	1	trivial
2340.2.g.b.1691.20	yes	48	12.11	even	2	inner
2340.2.g.b.1691.29	yes	48	4.3	odd	2	inner
2340.2.g.b.1691.30	yes	48	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.405974 - 1.35469i) q^{2} +(-1.67037 + 1.09994i) q^{4} +1.00000i q^{5} +1.05331i q^{7} +(2.16820 + 1.81629i) q^{8} +(1.35469 - 0.405974i) q^{10} -2.94047 q^{11} +1.00000 q^{13} +(1.42691 - 0.427617i) q^{14} +(1.58028 - 3.67461i) q^{16} +2.82145i q^{17} -4.64725i q^{19} +(-1.09994 - 1.67037i) q^{20} +(1.19375 + 3.98343i) q^{22} +6.54399 q^{23} -1.00000 q^{25} +(-0.405974 - 1.35469i) q^{26} +(-1.15858 - 1.75942i) q^{28} +0.0387991i q^{29} -0.836825i q^{31} +(-5.61950 - 0.648991i) q^{32} +(3.82219 - 1.14544i) q^{34} -1.05331 q^{35} -3.57653 q^{37} +(-6.29559 + 1.88666i) q^{38} +(-1.81629 + 2.16820i) q^{40} +10.2580i q^{41} -5.05107i q^{43} +(4.91167 - 3.23433i) q^{44} +(-2.65669 - 8.86508i) q^{46} -1.00144 q^{47} +5.89053 q^{49} +(0.405974 + 1.35469i) q^{50} +(-1.67037 + 1.09994i) q^{52} +13.7903i q^{53} -2.94047i q^{55} +(-1.91312 + 2.28379i) q^{56} +(0.0525607 - 0.0157514i) q^{58} -5.31956 q^{59} -2.98720 q^{61} +(-1.13364 + 0.339729i) q^{62} +(1.40219 + 7.87616i) q^{64} +1.00000i q^{65} +15.1114i q^{67} +(-3.10342 - 4.71287i) q^{68} +(0.427617 + 1.42691i) q^{70} -9.53560 q^{71} -5.77827 q^{73} +(1.45198 + 4.84509i) q^{74} +(5.11169 + 7.76264i) q^{76} -3.09723i q^{77} +5.96259i q^{79} +(3.67461 + 1.58028i) q^{80} +(13.8964 - 4.16448i) q^{82} -15.8285 q^{83} -2.82145 q^{85} +(-6.84263 + 2.05060i) q^{86} +(-6.37553 - 5.34074i) q^{88} -2.96256i q^{89} +1.05331i q^{91} +(-10.9309 + 7.19798i) q^{92} +(0.406560 + 1.35665i) q^{94} +4.64725 q^{95} +6.69353 q^{97} +(-2.39140 - 7.97985i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4} - 4 q^{10} + 48 q^{13} - 36 q^{16} - 8 q^{22} - 48 q^{25} + 8 q^{28} + 8 q^{34} + 16 q^{37} + 4 q^{40} + 32 q^{46} - 64 q^{49} - 4 q^{52} + 72 q^{58} - 32 q^{61} - 28 q^{64} - 24 q^{70} - 48 q^{73}+ \cdots - 32 q^{97}+O(q^{100}) \) 48 * q - 4 * q^4 - 4 * q^10 + 48 * q^13 - 36 * q^16 - 8 * q^22 - 48 * q^25 + 8 * q^28 + 8 * q^34 + 16 * q^37 + 4 * q^40 + 32 * q^46 - 64 * q^49 - 4 * q^52 + 72 * q^58 - 32 * q^61 - 28 * q^64 - 24 * q^70 - 48 * q^73 - 72 * q^76 + 48 * q^82 + 32 * q^85 - 24 * q^88 - 56 * q^94 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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