LMFDB - Embedded newform 276.2.i.b.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(13,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("276.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 18 x^{18} - 58 x^{17} + 169 x^{16} - 363 x^{15} + 800 x^{14} - 1682 x^{13} + \cdots + 529 $ x^20 - 4x^19 + 18x^18 - 58x^17 + 169x^16 - 363x^15 + 800x^14 - 1682x^13 + 2817x^12 - 3731x^11 + 5829x^10 - 8312x^9 + 7737x^8 + 4348x^7 - 12995x^6 - 2574x^5 + 24401x^4 + 22582x^3 + 9558x^2 + 2829*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.1
Root			$1.79494 - 0.527041i$ of defining polynomial
Character	$\chi$	$=$	276.85
Dual form			276.2.i.b.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 + 0.540641i) q^{3} +(-0.143141 - 0.313435i) q^{5} +(1.55877 - 0.457697i) q^{7} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.841254 + 0.540641i) q^{3} +(-0.143141 - 0.313435i) q^{5} +(1.55877 - 0.457697i) q^{7} +(0.415415 - 0.909632i) q^{9} +(2.18545 + 2.52214i) q^{11} +(5.16264 + 1.51589i) q^{13} +(0.289874 + 0.186291i) q^{15} +(0.127249 - 0.885037i) q^{17} +(0.292667 + 2.03554i) q^{19} +(-1.06387 + 1.22778i) q^{21} +(-2.11562 + 4.30397i) q^{23} +(3.19655 - 3.68902i) q^{25} +(0.142315 + 0.989821i) q^{27} +(0.0845359 - 0.587960i) q^{29} +(2.03655 + 1.30881i) q^{31} +(-3.20209 - 0.940218i) q^{33} +(-0.366583 - 0.423059i) q^{35} +(2.49728 - 5.46827i) q^{37} +(-5.16264 + 1.51589i) q^{39} +(-4.00648 - 8.77296i) q^{41} +(-0.911860 + 0.586017i) q^{43} -0.344574 q^{45} -8.47133 q^{47} +(-3.66849 + 2.35759i) q^{49} +(0.371438 + 0.813336i) q^{51} +(-2.39561 + 0.703414i) q^{53} +(0.477700 - 1.04602i) q^{55} +(-1.34671 - 1.55418i) q^{57} +(-1.10721 - 0.325107i) q^{59} +(-1.26653 - 0.813948i) q^{61} +(0.231202 - 1.60804i) q^{63} +(-0.263853 - 1.83514i) q^{65} +(5.27652 - 6.08943i) q^{67} +(-0.547134 - 4.76452i) q^{69} +(-4.94260 + 5.70407i) q^{71} +(0.296170 + 2.05991i) q^{73} +(-0.694677 + 4.83158i) q^{75} +(4.56099 + 2.93117i) q^{77} +(-10.6720 - 3.13359i) q^{79} +(-0.654861 - 0.755750i) q^{81} +(1.84717 - 4.04473i) q^{83} +(-0.295616 + 0.0868007i) q^{85} +(0.246759 + 0.540327i) q^{87} +(-13.6158 + 8.75033i) q^{89} +8.74121 q^{91} -2.42085 q^{93} +(0.596119 - 0.383102i) q^{95} +(2.68418 + 5.87754i) q^{97} +(3.20209 - 0.940218i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9	$ 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9} + 14 q^{13} - 11 q^{15} + 3 q^{17} + 7 q^{19} + 4 q^{21} + 24 q^{23} + 12 q^{25} + 2 q^{27} - 26 q^{29} + 33 q^{31} - 11 q^{33} - 2 q^{35} - 18 q^{37} - 14 q^{39} + 4 q^{41} - 40 q^{43} - 54 q^{47} + 30 q^{49} - 14 q^{51} - 14 q^{53} + 11 q^{55} - 29 q^{57} + 4 q^{59} + 12 q^{61} - 4 q^{63} - 33 q^{65} + 15 q^{67} - 2 q^{69} - 33 q^{71} + 15 q^{73} + 10 q^{75} + 66 q^{77} - 42 q^{79} - 2 q^{81} - 14 q^{83} - 13 q^{85} + 4 q^{87} - 66 q^{89} - 16 q^{91} - 22 q^{93} - 31 q^{95} - 24 q^{97} + 11 q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9 + 14 * q^13 - 11 * q^15 + 3 * q^17 + 7 * q^19 + 4 * q^21 + 24 * q^23 + 12 * q^25 + 2 * q^27 - 26 * q^29 + 33 * q^31 - 11 * q^33 - 2 * q^35 - 18 * q^37 - 14 * q^39 + 4 * q^41 - 40 * q^43 - 54 * q^47 + 30 * q^49 - 14 * q^51 - 14 * q^53 + 11 * q^55 - 29 * q^57 + 4 * q^59 + 12 * q^61 - 4 * q^63 - 33 * q^65 + 15 * q^67 - 2 * q^69 - 33 * q^71 + 15 * q^73 + 10 * q^75 + 66 * q^77 - 42 * q^79 - 2 * q^81 - 14 * q^83 - 13 * q^85 + 4 * q^87 - 66 * q^89 - 16 * q^91 - 22 * q^93 - 31 * q^95 - 24 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$	$1$

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
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$4$		0			0
$5$	−0.143141	−	0.313435i	−0.0640146	−	0.140172i	0.874921	−	0.484266i	$-0.160913\pi$
$5$	−0.143141	−	0.313435i	−0.0640146	−	0.140172i	−0.938935	+	0.344094i	$0.888186\pi$
$6$		0			0
$7$	1.55877	−	0.457697i	0.589161	−	0.172993i	0.0264543	−	0.999650i	$-0.491578\pi$
$7$	1.55877	−	0.457697i	0.589161	−	0.172993i	0.562706	+	0.826657i	$0.309760\pi$
$8$		0			0
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$		0			0
$11$	2.18545	+	2.52214i	0.658937	+	0.760454i	0.982603	−	0.185717i	$-0.0594608\pi$
$11$	2.18545	+	2.52214i	0.658937	+	0.760454i	−0.323666	+	0.946171i	$0.604915\pi$
$12$		0			0
$13$	5.16264	+	1.51589i	1.43186	+	0.420432i	0.903500	−	0.428588i	$-0.140989\pi$
$13$	5.16264	+	1.51589i	1.43186	+	0.420432i	0.528360	+	0.849020i	$0.322807\pi$
$14$		0			0
$15$	0.289874	+	0.186291i	0.0748451	+	0.0481000i
$16$		0			0
$17$	0.127249	−	0.885037i	0.0308624	−	0.214653i	−0.968554	−	0.248802i	$-0.919963\pi$
$17$	0.127249	−	0.885037i	0.0308624	−	0.214653i	0.999417	+	0.0341493i	$0.0108722\pi$
$18$		0			0
$19$	0.292667	+	2.03554i	0.0671425	+	0.466986i	0.995459	+	0.0951945i	$0.0303473\pi$
$19$	0.292667	+	2.03554i	0.0671425	+	0.466986i	−0.928316	+	0.371792i	$0.878744\pi$
$20$		0			0
$21$	−1.06387	+	1.22778i	−0.232156	+	0.267923i
$22$		0			0
$23$	−2.11562	+	4.30397i	−0.441136	+	0.897440i
$23$	−2.11562	+	4.30397i	−0.441136	+	0.897440i
$24$		0			0
$25$	3.19655	−	3.68902i	0.639310	−	0.737803i
$26$		0			0
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$		0			0
$29$	0.0845359	−	0.587960i	0.0156979	−	0.109181i	−0.980466	−	0.196689i	$-0.936981\pi$
$29$	0.0845359	−	0.587960i	0.0156979	−	0.109181i	0.996164	+	0.0875075i	$0.0278902\pi$
$30$		0			0
$31$	2.03655	+	1.30881i	0.365775	+	0.235070i	0.710598	−	0.703598i	$-0.248425\pi$
$31$	2.03655	+	1.30881i	0.365775	+	0.235070i	−0.344823	+	0.938668i	$0.612061\pi$
$32$		0			0
$33$	−3.20209	−	0.940218i	−0.557412	−	0.163671i
$34$		0			0
$35$	−0.366583	−	0.423059i	−0.0619638	−	0.0715100i
$36$		0			0
$37$	2.49728	−	5.46827i	0.410550	−	0.898979i	−0.585541	−	0.810643i	$-0.699118\pi$
$37$	2.49728	−	5.46827i	0.410550	−	0.898979i	0.996091	−	0.0883358i	$-0.0281549\pi$
$38$		0			0
$39$	−5.16264	+	1.51589i	−0.826685	+	0.242737i
$40$		0			0
$41$	−4.00648	−	8.77296i	−0.625707	−	1.37011i	−0.911295	−	0.411754i	$-0.864916\pi$
$41$	−4.00648	−	8.77296i	−0.625707	−	1.37011i	0.285588	−	0.958352i	$-0.407811\pi$
$42$		0			0
$43$	−0.911860	+	0.586017i	−0.139057	+	0.0893667i	−0.608320	−	0.793692i	$-0.708156\pi$
$43$	−0.911860	+	0.586017i	−0.139057	+	0.0893667i	0.469262	+	0.883059i	$0.344520\pi$
$44$		0			0
$45$	−0.344574			−0.0513660
$46$		0			0
$47$	−8.47133			−1.23567			−0.617835	−	0.786308i	$-0.711990\pi$
$47$	−8.47133			−1.23567			−0.617835	+	0.786308i	$0.711990\pi$
$48$		0			0
$49$	−3.66849	+	2.35759i	−0.524070	+	0.336799i
$50$		0			0
$51$	0.371438	+	0.813336i	0.0520118	+	0.113890i
$52$		0			0
$53$	−2.39561	+	0.703414i	−0.329062	+	0.0966213i	−0.442091	−	0.896970i	$-0.645763\pi$
$53$	−2.39561	+	0.703414i	−0.329062	+	0.0966213i	0.113029	+	0.993592i	$0.463945\pi$
$54$		0			0
$55$	0.477700	−	1.04602i	0.0644131	−	0.141045i
$56$		0			0
$57$	−1.34671	−	1.55418i	−0.178376	−	0.205856i
$58$		0			0
$59$	−1.10721	−	0.325107i	−0.144147	−	0.0423253i	0.208863	−	0.977945i	$-0.433024\pi$
$59$	−1.10721	−	0.325107i	−0.144147	−	0.0423253i	−0.353010	+	0.935620i	$0.614842\pi$
$60$		0			0
$61$	−1.26653	−	0.813948i	−0.162162	−	0.104215i	0.457043	−	0.889445i	$-0.348909\pi$
$61$	−1.26653	−	0.813948i	−0.162162	−	0.104215i	−0.619205	+	0.785229i	$0.712545\pi$
$62$		0			0
$63$	0.231202	−	1.60804i	0.0291287	−	0.202594i
$64$		0			0
$65$	−0.263853	−	1.83514i	−0.0327270	−	0.227621i
$66$		0			0
$67$	5.27652	−	6.08943i	0.644630	−	0.743942i	−0.335557	−	0.942020i	$-0.608924\pi$
$67$	5.27652	−	6.08943i	0.644630	−	0.743942i	0.980186	+	0.198078i	$0.0634698\pi$
$68$		0			0
$69$	−0.547134	−	4.76452i	−0.0658672	−	0.573581i
$70$		0			0
$71$	−4.94260	+	5.70407i	−0.586579	+	0.676949i	−0.969006	−	0.247037i	$-0.920543\pi$
$71$	−4.94260	+	5.70407i	−0.586579	+	0.676949i	0.382427	+	0.923986i	$0.375088\pi$
$72$		0			0
$73$	0.296170	+	2.05991i	0.0346641	+	0.241094i	0.999786	−	0.0207086i	$-0.00659222\pi$
$73$	0.296170	+	2.05991i	0.0346641	+	0.241094i	−0.965122	+	0.261802i	$0.915683\pi$
$74$		0			0
$75$	−0.694677	+	4.83158i	−0.0802144	+	0.557903i
$76$		0			0
$77$	4.56099	+	2.93117i	0.519773	+	0.334038i
$78$		0			0
$79$	−10.6720	−	3.13359i	−1.20070	−	0.352556i	−0.380577	−	0.924749i	$-0.624275\pi$
$79$	−10.6720	−	3.13359i	−1.20070	−	0.352556i	−0.820119	+	0.572193i	$0.806093\pi$
$80$		0			0
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$		0			0
$83$	1.84717	−	4.04473i	0.202753	−	0.443967i	−0.780754	−	0.624839i	$-0.785165\pi$
$83$	1.84717	−	4.04473i	0.202753	−	0.443967i	0.983507	+	0.180872i	$0.0578919\pi$
$84$		0			0
$85$	−0.295616	+	0.0868007i	−0.0320641	+	0.00941486i
$86$		0			0
$87$	0.246759	+	0.540327i	0.0264553	+	0.0579291i
$88$		0			0
$89$	−13.6158	+	8.75033i	−1.44327	+	0.927534i	−0.443763	+	0.896144i	$0.646357\pi$
$89$	−13.6158	+	8.75033i	−1.44327	+	0.927534i	−0.999507	+	0.0313896i	$0.990007\pi$
$90$		0			0
$91$	8.74121			0.916327
$92$		0			0
$93$	−2.42085			−0.251031
$94$		0			0
$95$	0.596119	−	0.383102i	0.0611605	−	0.0393054i
$96$		0			0
$97$	2.68418	+	5.87754i	0.272538	+	0.596774i	0.995568	−	0.0940418i	$-0.0299787\pi$
$97$	2.68418	+	5.87754i	0.272538	+	0.596774i	−0.723031	+	0.690816i	$0.757251\pi$
$98$		0			0
$99$	3.20209	−	0.940218i	0.321822	−	0.0944955i
$100$		0			0
$101$	4.44484	−	9.73285i	0.442278	−	0.968455i	−0.548896	−	0.835891i	$-0.684952\pi$
$101$	4.44484	−	9.73285i	0.442278	−	0.968455i	0.991174	−	0.132564i	$-0.0423210\pi$
$102$		0			0
$103$	−3.05669	−	3.52761i	−0.301185	−	0.347586i	0.584903	−	0.811103i	$-0.301133\pi$
$103$	−3.05669	−	3.52761i	−0.301185	−	0.347586i	−0.886088	+	0.463517i	$0.846587\pi$
$104$		0			0
$105$	0.537112	+	0.157710i	0.0524167	+	0.0153909i
$106$		0			0
$107$	15.2972	+	9.83089i	1.47883	+	0.950388i	0.997260	+	0.0739828i	$0.0235710\pi$
$107$	15.2972	+	9.83089i	1.47883	+	0.950388i	0.481574	+	0.876406i	$0.340065\pi$
$108$		0			0
$109$	−1.94475	+	13.5260i	−0.186273	+	1.29556i	0.655281	+	0.755385i	$0.272550\pi$
$109$	−1.94475	+	13.5260i	−0.186273	+	1.29556i	−0.841554	+	0.540173i	$0.818359\pi$
$110$		0			0
$111$	0.855529	+	5.95033i	0.0812032	+	0.564781i
$112$		0			0
$113$	9.32786	−	10.7649i	0.877492	−	1.01268i	−0.122305	−	0.992493i	$-0.539028\pi$
$113$	9.32786	−	10.7649i	0.877492	−	1.01268i	0.999796	−	0.0201867i	$-0.00642607\pi$
$114$		0			0
$115$	1.65185	+	0.0470333i	0.154036	+	0.00438588i
$116$		0			0
$117$	3.52354	−	4.06638i	0.325751	−	0.375937i
$118$		0			0
$119$	−0.206726	−	1.43781i	−0.0189506	−	0.131804i
$120$		0			0
$121$	−0.0195512	+	0.135981i	−0.00177738	+	0.0123619i
$122$		0			0
$123$	8.11349	+	5.21422i	0.731568	+	0.470150i
$124$		0			0
$125$	−3.26690	−	0.959250i	−0.292201	−	0.0857979i
$126$		0			0
$127$	−9.00585	−	10.3933i	−0.799140	−	0.922257i	0.199194	−	0.979960i	$-0.436168\pi$
$127$	−9.00585	−	10.3933i	−0.799140	−	0.922257i	−0.998334	+	0.0577035i	$0.981622\pi$
$128$		0			0
$129$	0.450281	−	0.985978i	0.0396450	−	0.0868105i
$130$		0			0
$131$	5.34207	−	1.56857i	0.466738	−	0.137047i	−0.0399031	−	0.999204i	$-0.512705\pi$
$131$	5.34207	−	1.56857i	0.466738	−	0.137047i	0.506642	+	0.862157i	$0.330887\pi$
$132$		0			0
$133$	1.38786	+	3.03900i	0.120343	+	0.263515i
$134$		0			0
$135$	0.289874	−	0.186291i	0.0249484	−	0.0160333i
$136$		0			0
$137$	14.3229			1.22369			0.611845	−	0.790978i	$-0.290428\pi$
$137$	14.3229			1.22369			0.611845	+	0.790978i	$0.290428\pi$
$138$		0			0
$139$	−20.4670			−1.73599			−0.867994	−	0.496575i	$-0.834591\pi$
$139$	−20.4670			−1.73599			−0.867994	+	0.496575i	$0.834591\pi$
$140$		0			0
$141$	7.12653	−	4.57995i	0.600162	−	0.385701i
$142$		0			0
$143$	7.45940	+	16.3338i	0.623787	+	1.36590i
$144$		0			0
$145$	−0.196388	+	0.0576647i	−0.0163091	+	0.00478879i
$146$		0			0
$147$	1.81152	−	3.96667i	0.149411	−	0.327165i
$148$		0			0
$149$	−2.50374	−	2.88947i	−0.205115	−	0.236715i	0.643867	−	0.765138i	$-0.277329\pi$
$149$	−2.50374	−	2.88947i	−0.205115	−	0.236715i	−0.848981	+	0.528423i	$0.822784\pi$
$150$		0			0
$151$	3.01277	+	0.884630i	0.245176	+	0.0719902i	0.402012	−	0.915635i	$-0.368311\pi$
$151$	3.01277	+	0.884630i	0.245176	+	0.0719902i	−0.156836	+	0.987625i	$0.550129\pi$
$152$		0			0
$153$	−0.752197	−	0.483407i	−0.0608115	−	0.0390812i
$154$		0			0
$155$	0.118714	−	0.825671i	0.00953530	−	0.0663195i
$156$		0			0
$157$	1.86577	+	12.9767i	0.148904	+	1.03565i	0.918017	+	0.396540i	$0.129789\pi$
$157$	1.86577	+	12.9767i	0.148904	+	1.03565i	−0.769113	+	0.639113i	$0.779302\pi$
$158$		0			0
$159$	1.63502	−	1.88691i	0.129665	−	0.149642i
$160$		0			0
$161$	−1.32785	+	7.67722i	−0.104649	+	0.605050i
$162$		0			0
$163$	2.54467	−	2.93671i	0.199314	−	0.230021i	−0.647290	−	0.762244i	$-0.724098\pi$
$163$	2.54467	−	2.93671i	0.199314	−	0.230021i	0.846604	+	0.532223i	$0.178643\pi$
$164$		0			0
$165$	0.163653	+	1.13823i	0.0127404	+	0.0886111i
$166$		0			0
$167$	1.79840	−	12.5082i	0.139165	−	0.967911i	−0.793860	−	0.608100i	$-0.791932\pi$
$167$	1.79840	−	12.5082i	0.139165	−	0.967911i	0.933025	−	0.359811i	$-0.117159\pi$
$168$		0			0
$169$	13.4187	+	8.62366i	1.03221	+	0.663359i
$170$		0			0
$171$	1.97317	+	0.579376i	0.150892	+	0.0443060i
$172$		0			0
$173$	−1.98016	−	2.28523i	−0.150549	−	0.173743i	0.675466	−	0.737391i	$-0.263943\pi$
$173$	−1.98016	−	2.28523i	−0.150549	−	0.173743i	−0.826015	+	0.563649i	$0.809397\pi$
$174$		0			0
$175$	3.29425	−	7.21339i	0.249022	−	0.545281i
$176$		0			0
$177$	1.10721	−	0.325107i	0.0832231	−	0.0244365i
$178$		0			0
$179$	0.999053	+	2.18762i	0.0746728	+	0.163511i	0.943287	−	0.331979i	$-0.107716\pi$
$179$	0.999053	+	2.18762i	0.0746728	+	0.163511i	−0.868614	+	0.495489i	$0.834989\pi$
$180$		0			0
$181$	−18.0491	+	11.5994i	−1.34158	+	0.862179i	−0.997062	−	0.0766024i	$-0.975593\pi$
$181$	−18.0491	+	11.5994i	−1.34158	+	0.862179i	−0.344514	+	0.938781i	$0.611956\pi$
$182$		0			0
$183$	1.50552			0.111292
$184$		0			0
$185$	−2.07141			−0.152293
$186$		0			0
$187$	2.51028	−	1.61326i	0.183570	−	0.117973i
$188$		0			0
$189$	0.674875	+	1.47777i	0.0490899	+	0.107492i
$190$		0			0
$191$	−3.68826	+	1.08297i	−0.266873	+	0.0783610i	−0.412431	−	0.910989i	$-0.635320\pi$
$191$	−3.68826	+	1.08297i	−0.266873	+	0.0783610i	0.145558	+	0.989350i	$0.453502\pi$
$192$		0			0
$193$	4.92238	−	10.7785i	0.354321	−	0.775854i	−0.645605	−	0.763671i	$-0.723395\pi$
$193$	4.92238	−	10.7785i	0.354321	−	0.775854i	0.999926	−	0.0121826i	$-0.00387794\pi$
$194$		0			0
$195$	1.21412	+	1.40117i	0.0869449	+	0.100340i
$196$		0			0
$197$	18.4104	+	5.40579i	1.31169	+	0.385147i	0.861487	−	0.507780i	$-0.169534\pi$
$197$	18.4104	+	5.40579i	1.31169	+	0.385147i	0.450202	+	0.892927i	$0.351352\pi$
$198$		0			0
$199$	−4.70621	−	3.02450i	−0.333614	−	0.214401i	0.363099	−	0.931751i	$-0.381719\pi$
$199$	−4.70621	−	3.02450i	−0.333614	−	0.214401i	−0.696713	+	0.717350i	$0.745355\pi$
$200$		0			0
$201$	−1.14670	+	7.97546i	−0.0808818	+	0.562545i
$202$		0			0
$203$	−0.137335	−	0.955188i	−0.00963905	−	0.0670410i
$204$		0			0
$205$	−2.17626	+	2.51154i	−0.151997	+	0.175414i
$206$		0			0
$207$	3.03617	+	3.71237i	0.211029	+	0.258027i
$208$		0			0
$209$	−4.49432	+	5.18673i	−0.310879	+	0.358773i
$210$		0			0
$211$	−0.451615	−	3.14105i	−0.0310905	−	0.216239i	0.968353	−	0.249583i	$-0.0802935\pi$
$211$	−0.451615	−	3.14105i	−0.0310905	−	0.216239i	−0.999444	+	0.0333438i	$0.989384\pi$
$212$		0			0
$213$	1.07413	−	7.47074i	0.0735982	−	0.511887i
$214$		0			0
$215$	0.314203	+	0.201926i	0.0214285	+	0.0137712i
$216$		0			0
$217$	3.77356	+	1.10802i	0.256166	+	0.0752171i
$218$		0			0
$219$	−1.36282	−	1.57278i	−0.0920911	−	0.106279i
$220$		0			0
$221$	1.99856	−	4.37623i	0.134438	−	0.294377i
$222$		0			0
$223$	−23.8575	+	7.00520i	−1.59762	+	0.469103i	−0.954882	−	0.296986i	$-0.904019\pi$
$223$	−23.8575	+	7.00520i	−1.59762	+	0.469103i	−0.642735	+	0.766089i	$0.722200\pi$
$224$		0			0
$225$	−2.02775	−	4.44016i	−0.135183	−	0.296011i
$226$		0			0
$227$	12.4300	−	7.98828i	0.825009	−	0.530201i	−0.0586794	−	0.998277i	$-0.518689\pi$
$227$	12.4300	−	7.98828i	0.825009	−	0.530201i	0.883688	+	0.468076i	$0.155053\pi$
$228$		0			0
$229$	−26.3507			−1.74130			−0.870651	−	0.491901i	$-0.836302\pi$
$229$	−26.3507			−1.74130			−0.870651	+	0.491901i	$0.836302\pi$
$230$		0			0
$231$	−5.42166			−0.356719
$232$		0			0
$233$	−21.4586	+	13.7906i	−1.40580	+	0.903451i	−0.999945	−	0.0104884i	$-0.996661\pi$
$233$	−21.4586	+	13.7906i	−1.40580	+	0.903451i	−0.405852	+	0.913939i	$0.633025\pi$
$234$		0			0
$235$	1.21259	+	2.65521i	0.0791009	+	0.173207i
$236$		0			0
$237$	10.6720	−	3.13359i	0.693222	−	0.203548i
$238$		0			0
$239$	10.8729	−	23.8083i	0.703307	−	1.54003i	−0.132607	−	0.991169i	$-0.542335\pi$
$239$	10.8729	−	23.8083i	0.703307	−	1.54003i	0.835914	−	0.548860i	$-0.184938\pi$
$240$		0			0
$241$	−6.92390	−	7.99061i	−0.446008	−	0.514720i	0.487576	−	0.873081i	$-0.337881\pi$
$241$	−6.92390	−	7.99061i	−0.446008	−	0.514720i	−0.933583	+	0.358361i	$0.883336\pi$
$242$		0			0
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$		0			0
$245$	1.26406	+	0.812365i	0.0807581	+	0.0519001i
$246$		0			0
$247$	−1.57472	+	10.9524i	−0.100197	+	0.696887i
$248$		0			0
$249$	0.632811	+	4.40130i	0.0401028	+	0.278921i
$250$		0			0
$251$	−8.95543	+	10.3351i	−0.565262	+	0.652347i	−0.964370	−	0.264557i	$-0.914774\pi$
$251$	−8.95543	+	10.3351i	−0.565262	+	0.652347i	0.399108	+	0.916904i	$0.369320\pi$
$252$		0			0
$253$	−15.4788	+	4.07022i	−0.973143	+	0.255893i
$254$		0			0
$255$	0.201760	−	0.232844i	0.0126347	−	0.0145812i
$256$		0			0
$257$	−4.24244	−	29.5068i	−0.264636	−	1.84059i	−0.496746	−	0.867896i	$-0.665472\pi$
$257$	−4.24244	−	29.5068i	−0.264636	−	1.84059i	0.232110	−	0.972690i	$-0.425437\pi$
$258$		0			0
$259$	1.38987	−	9.66679i	0.0863626	−	0.600665i
$260$		0			0
$261$	−0.499710	−	0.321144i	−0.0309313	−	0.0198783i
$262$		0			0
$263$	−27.0241	−	7.93500i	−1.66638	−	0.489293i	−0.693470	−	0.720485i	$-0.743919\pi$
$263$	−27.0241	−	7.93500i	−1.66638	−	0.489293i	−0.972908	+	0.231192i	$0.925737\pi$
$264$		0			0
$265$	0.563384	+	0.650180i	0.0346084	+	0.0399403i
$266$		0			0
$267$	6.72354	−	14.7225i	0.411474	−	0.901002i
$268$		0			0
$269$	−7.99162	+	2.34655i	−0.487258	+	0.143072i	−0.516128	−	0.856511i	$-0.672627\pi$
$269$	−7.99162	+	2.34655i	−0.487258	+	0.143072i	0.0288704	+	0.999583i	$0.490809\pi$
$270$		0			0
$271$	−11.3513	−	24.8559i	−0.689542	−	1.50989i	−0.852207	−	0.523205i	$-0.824736\pi$
$271$	−11.3513	−	24.8559i	−0.689542	−	1.50989i	0.162665	−	0.986681i	$-0.447991\pi$
$272$		0			0
$273$	−7.35357	+	4.72585i	−0.445058	+	0.286022i
$274$		0			0
$275$	16.2901			0.982331
$276$		0			0
$277$	−20.7921			−1.24928			−0.624638	−	0.780914i	$-0.714754\pi$
$277$	−20.7921			−1.24928			−0.624638	+	0.780914i	$0.714754\pi$
$278$		0			0
$279$	2.03655	−	1.30881i	0.121925	−	0.0783565i
$280$		0			0
$281$	13.2854	+	29.0909i	0.792539	+	1.73542i	0.669237	+	0.743049i	$0.266621\pi$
$281$	13.2854	+	29.0909i	0.792539	+	1.73542i	0.123302	+	0.992369i	$0.460652\pi$
$282$		0			0
$283$	17.6233	−	5.17466i	1.04760	−	0.307602i	0.287750	−	0.957706i	$-0.407093\pi$
$283$	17.6233	−	5.17466i	1.04760	−	0.307602i	0.759846	+	0.650104i	$0.225275\pi$
$284$		0			0
$285$	−0.294366	+	0.644572i	−0.0174367	+	0.0381812i
$286$		0			0
$287$	−10.2605	−	11.8413i	−0.605661	−	0.698970i
$288$		0			0
$289$	15.5443	+	4.56421i	0.914370	+	0.268483i
$290$		0			0
$291$	−5.43572	−	3.49332i	−0.318648	−	0.204782i
$292$		0			0
$293$	−0.273519	+	1.90237i	−0.0159792	+	0.111138i	−0.996250	−	0.0865216i	$-0.972425\pi$
$293$	−0.273519	+	1.90237i	−0.0159792	+	0.111138i	0.980271	+	0.197659i	$0.0633339\pi$
$294$		0			0
$295$	0.0565875	+	0.393575i	0.00329465	+	0.0229148i
$296$		0			0
$297$	−2.18545	+	2.52214i	−0.126813	+	0.146349i
$298$		0			0
$299$	−17.4465	+	19.0128i	−1.00896	+	1.09954i
$300$		0			0
$301$	−1.15316	+	1.33082i	−0.0664673	+	0.0767073i
$302$		0			0
$303$	1.52274	+	10.5909i	0.0874789	+	0.608429i
$304$		0			0
$305$	−0.0738278	+	0.513483i	−0.00422737	+	0.0294020i
$306$		0			0
$307$	7.75753	+	4.98546i	0.442746	+	0.284535i	0.742959	−	0.669337i	$-0.233422\pi$
$307$	7.75753	+	4.98546i	0.442746	+	0.284535i	−0.300214	+	0.953872i	$0.597058\pi$
$308$		0			0
$309$	4.47862	+	1.31504i	0.254780	+	0.0748101i
$310$		0			0
$311$	−5.92547	−	6.83836i	−0.336003	−	0.387768i	0.562455	−	0.826828i	$-0.309857\pi$
$311$	−5.92547	−	6.83836i	−0.336003	−	0.387768i	−0.898458	+	0.439060i	$0.855311\pi$
$312$		0			0
$313$	−0.162302	+	0.355392i	−0.00917386	+	0.0200880i	−0.914163	−	0.405346i	$-0.867151\pi$
$313$	−0.162302	+	0.355392i	−0.00917386	+	0.0200880i	0.904990	+	0.425434i	$0.139878\pi$
$314$		0			0
$315$	−0.537112	+	0.157710i	−0.0302628	+	0.00888597i
$316$		0			0
$317$	−0.707170	−	1.54849i	−0.0397186	−	0.0869717i	0.888733	−	0.458426i	$-0.151587\pi$
$317$	−0.707170	−	1.54849i	−0.0397186	−	0.0869717i	−0.928451	+	0.371454i	$0.878859\pi$
$318$		0			0
$319$	1.66767	−	1.07174i	0.0933714	−	0.0600062i
$320$		0			0
$321$	−18.1838			−1.01492
$322$		0			0
$323$	1.83877			0.102312
$324$		0			0
$325$	22.0948	−	14.1995i	1.22560	−	0.787645i
$326$		0			0
$327$	−5.67669	−	12.4302i	−0.313922	−	0.687393i
$328$		0			0
$329$	−13.2049	+	3.87730i	−0.728008	+	0.213763i
$330$		0			0
$331$	9.59680	−	21.0141i	0.527488	−	1.15504i	−0.439038	−	0.898468i	$-0.644681\pi$
$331$	9.59680	−	21.0141i	0.527488	−	1.15504i	0.966526	−	0.256569i	$-0.0825920\pi$
$332$		0			0
$333$	−3.93671	−	4.54321i	−0.215730	−	0.248966i
$334$		0			0
$335$	−2.66393	−	0.782200i	−0.145546	−	0.0427361i
$336$		0			0
$337$	21.6629	+	13.9219i	1.18006	+	0.758376i	0.975397	−	0.220457i	$-0.0707550\pi$
$337$	21.6629	+	13.9219i	1.18006	+	0.758376i	0.204659	+	0.978833i	$0.434391\pi$
$338$		0			0
$339$	−2.02714	+	14.0991i	−0.110099	+	0.765756i
$340$		0			0
$341$	1.14977	+	7.99681i	0.0622634	+	0.433051i
$342$		0			0
$343$	−12.0864	+	13.9484i	−0.652604	+	0.753145i
$344$		0			0
$345$	−1.41505	+	0.853489i	−0.0761837	+	0.0459503i
$346$		0			0
$347$	22.7018	−	26.1993i	1.21870	−	1.40645i	0.332527	−	0.943094i	$-0.392099\pi$
$347$	22.7018	−	26.1993i	1.21870	−	1.40645i	0.886171	−	0.463359i	$-0.153356\pi$
$348$		0			0
$349$	1.52874	+	10.6326i	0.0818314	+	0.569150i	0.988947	+	0.148269i	$0.0473701\pi$
$349$	1.52874	+	10.6326i	0.0818314	+	0.569150i	−0.907116	+	0.420881i	$0.861721\pi$
$350$		0			0
$351$	−0.765739	+	5.32583i	−0.0408721	+	0.284272i
$352$		0			0
$353$	4.61167	+	2.96374i	0.245454	+	0.157744i	0.657584	−	0.753381i	$-0.271579\pi$
$353$	4.61167	+	2.96374i	0.245454	+	0.157744i	−0.412130	+	0.911125i	$0.635215\pi$
$354$		0			0
$355$	2.49535	+	0.732699i	0.132439	+	0.0388876i
$356$		0			0
$357$	0.951250	+	1.09780i	0.0503455	+	0.0581018i
$358$		0			0
$359$	−6.95208	+	15.2229i	−0.366917	+	0.803436i	0.632662	+	0.774428i	$0.281962\pi$
$359$	−6.95208	+	15.2229i	−0.366917	+	0.803436i	−0.999579	+	0.0290083i	$0.990765\pi$
$360$		0			0
$361$	14.1726	−	4.16144i	0.745925	−	0.219023i
$362$		0			0
$363$	−0.0570696	−	0.124965i	−0.00299538	−	0.00655896i
$364$		0			0
$365$	0.603253	−	0.387687i	0.0315757	−	0.0202925i
$366$		0			0
$367$	26.3585			1.37590			0.687951	−	0.725757i	$-0.258510\pi$
$367$	26.3585			1.37590			0.687951	+	0.725757i	$0.258510\pi$
$368$		0			0
$369$	−9.64452			−0.502074
$370$		0			0
$371$	−3.41226	+	2.19292i	−0.177156	+	0.113851i
$372$		0			0
$373$	3.23877	+	7.09191i	0.167697	+	0.367205i	0.974758	−	0.223262i	$-0.0716706\pi$
$373$	3.23877	+	7.09191i	0.167697	+	0.367205i	−0.807061	+	0.590468i	$0.798943\pi$
$374$		0			0
$375$	3.26690	−	0.959250i	0.168702	−	0.0495354i
$376$		0			0
$377$	1.32771	−	2.90728i	0.0683806	−	0.149733i
$378$		0			0
$379$	5.34449	+	6.16787i	0.274528	+	0.316822i	0.876225	−	0.481902i	$-0.160054\pi$
$379$	5.34449	+	6.16787i	0.274528	+	0.316822i	−0.601697	+	0.798724i	$0.705509\pi$
$380$		0			0
$381$	13.1952	+	3.87447i	0.676013	+	0.198495i
$382$		0			0
$383$	18.5826	+	11.9423i	0.949527	+	0.610224i	0.921081	−	0.389371i	$-0.127308\pi$
$383$	18.5826	+	11.9423i	0.949527	+	0.610224i	0.0284462	+	0.999595i	$0.490944\pi$
$384$		0			0
$385$	0.265867	−	1.84915i	0.0135498	−	0.0942412i
$386$		0			0
$387$	0.154259	+	1.07290i	0.00784144	+	0.0545384i
$388$		0			0
$389$	15.9790	−	18.4408i	0.810168	−	0.934983i	−0.188725	−	0.982030i	$-0.560435\pi$
$389$	15.9790	−	18.4408i	0.810168	−	0.934983i	0.998893	+	0.0470465i	$0.0149809\pi$
$390$		0			0
$391$	3.53996	+	2.42007i	0.179024	+	0.122388i
$392$		0			0
$393$	−3.64600	+	4.20771i	−0.183916	+	0.212251i
$394$		0			0
$395$	0.545428	+	3.79353i	0.0274434	+	0.190873i
$396$		0			0
$397$	−1.25384	+	8.72066i	−0.0629285	+	0.437677i	0.933863	+	0.357632i	$0.116416\pi$
$397$	−1.25384	+	8.72066i	−0.0629285	+	0.437677i	−0.996791	+	0.0800456i	$0.974493\pi$
$398$		0			0
$399$	−2.81055	−	1.80623i	−0.140704	−	0.0904247i
$400$		0			0
$401$	−28.3266	−	8.31745i	−1.41456	−	0.415354i	−0.516905	−	0.856043i	$-0.672916\pi$
$401$	−28.3266	−	8.31745i	−1.41456	−	0.415354i	−0.897660	+	0.440689i	$0.854734\pi$
$402$		0			0
$403$	8.52997	+	9.84411i	0.424908	+	0.490370i
$404$		0			0
$405$	−0.143141	+	0.313435i	−0.00711273	+	0.0155747i
$406$		0			0
$407$	19.2494	−	5.65214i	0.954159	−	0.280166i
$408$		0			0
$409$	5.62057	+	12.3073i	0.277919	+	0.608559i	0.996190	−	0.0872048i	$-0.0277934\pi$
$409$	5.62057	+	12.3073i	0.277919	+	0.608559i	−0.718271	+	0.695764i	$0.755066\pi$
$410$		0			0
$411$	−12.0492	+	7.74356i	−0.594344	+	0.381962i
$412$		0			0
$413$	−1.87469			−0.0922475
$414$		0			0
$415$	−1.53217			−0.0752111
$416$		0			0
$417$	17.2179	−	11.0653i	0.843166	−	0.541870i
$418$		0			0
$419$	8.58795	+	18.8050i	0.419549	+	0.918683i	0.994908	+	0.100783i	$0.0321347\pi$
$419$	8.58795	+	18.8050i	0.419549	+	0.918683i	−0.575360	+	0.817900i	$0.695138\pi$
$420$		0			0
$421$	23.7831	−	6.98334i	1.15912	−	0.340347i	0.355027	−	0.934856i	$-0.384472\pi$
$421$	23.7831	−	6.98334i	1.15912	−	0.340347i	0.804089	+	0.594509i	$0.202654\pi$
$422$		0			0
$423$	−3.51912	+	7.70579i	−0.171105	+	0.374668i
$424$		0			0
$425$	−2.85816	−	3.29849i	−0.138641	−	0.160000i
$426$		0			0
$427$	−2.34677	−	0.689074i	−0.113568	−	0.0333466i
$428$		0			0
$429$	−15.1060	−	9.70802i	−0.729323	−	0.468708i
$430$		0			0
$431$	−4.97314	+	34.5889i	−0.239547	+	1.66609i	0.414813	+	0.909907i	$0.363847\pi$
$431$	−4.97314	+	34.5889i	−0.239547	+	1.66609i	−0.654360	+	0.756183i	$0.727062\pi$
$432$		0			0
$433$	−2.67101	−	18.5773i	−0.128361	−	0.892767i	−0.947633	−	0.319362i	$-0.896531\pi$
$433$	−2.67101	−	18.5773i	−0.128361	−	0.892767i	0.819272	−	0.573405i	$-0.194378\pi$
$434$		0			0
$435$	0.134036	−	0.154686i	0.00642654	−	0.00741662i
$436$		0			0
$437$	−9.38010	−	3.04680i	−0.448711	−	0.145748i
$438$		0			0
$439$	−3.77236	+	4.35354i	−0.180045	+	0.207783i	−0.838597	−	0.544752i	$-0.816624\pi$
$439$	−3.77236	+	4.35354i	−0.180045	+	0.207783i	0.658552	+	0.752535i	$0.271169\pi$
$440$		0			0
$441$	0.620598	+	4.31635i	0.0295523	+	0.205541i
$442$		0			0
$443$	0.469237	−	3.26362i	0.0222941	−	0.155059i	−0.975633	−	0.219407i	$-0.929588\pi$
$443$	0.469237	−	3.26362i	0.0222941	−	0.155059i	0.997928	+	0.0643481i	$0.0204968\pi$
$444$		0			0
$445$	4.69164	+	3.01513i	0.222405	+	0.142931i
$446$		0			0
$447$	3.66845	+	1.07715i	0.173512	+	0.0509476i
$448$		0			0
$449$	11.3348	+	13.0811i	0.534923	+	0.617334i	0.957304	−	0.289085i	$-0.0933509\pi$
$449$	11.3348	+	13.0811i	0.534923	+	0.617334i	−0.422381	+	0.906419i	$0.638805\pi$
$450$		0			0
$451$	13.3707	−	29.2778i	0.629602	−	1.37864i
$452$		0			0
$453$	−3.01277	+	0.884630i	−0.141553	+	0.0415636i
$454$		0			0
$455$	−1.25123	−	2.73980i	−0.0586583	−	0.128444i
$456$		0			0
$457$	4.28250	−	2.75219i	0.200327	−	0.128742i	−0.436632	−	0.899640i	$-0.643829\pi$
$457$	4.28250	−	2.75219i	0.200327	−	0.128742i	0.636958	+	0.770898i	$0.280192\pi$
$458$		0			0
$459$	0.894138			0.0417348
$460$		0			0
$461$	4.25740			0.198287			0.0991435	−	0.995073i	$-0.468390\pi$
$461$	4.25740			0.198287			0.0991435	+	0.995073i	$0.468390\pi$
$462$		0			0
$463$	23.4390	−	15.0633i	1.08930	−	0.700052i	0.132615	−	0.991168i	$-0.457663\pi$
$463$	23.4390	−	15.0633i	1.08930	−	0.700052i	0.956688	+	0.291115i	$0.0940264\pi$
$464$		0			0
$465$	0.346523	+	0.758780i	0.0160696	+	0.0351876i
$466$		0			0
$467$	−18.5955	+	5.46013i	−0.860496	+	0.252665i	−0.682068	−	0.731288i	$-0.738919\pi$
$467$	−18.5955	+	5.46013i	−0.860496	+	0.252665i	−0.178428	+	0.983953i	$0.557101\pi$
$468$		0			0
$469$	5.43778	−	11.9071i	0.251094	−	0.549818i
$470$		0			0
$471$	−8.58531	−	9.90798i	−0.395590	−	0.456536i
$472$		0			0
$473$	−3.47084	−	1.01913i	−0.159589	−	0.0468597i
$474$		0			0
$475$	8.44469	+	5.42707i	0.387469	+	0.249011i
$476$		0			0
$477$	−0.355324	+	2.47133i	−0.0162692	+	0.113154i
$478$		0			0
$479$	−3.45353	−	24.0199i	−0.157796	−	1.09750i	−0.902684	−	0.430305i	$-0.858406\pi$
$479$	−3.45353	−	24.0199i	−0.157796	−	1.09750i	0.744888	−	0.667190i	$-0.232503\pi$
$480$		0			0
$481$	21.1818	−	24.4452i	0.965809	−	1.11460i
$482$		0			0
$483$	−3.03356	−	7.17638i	−0.138032	−	0.326537i
$484$		0			0
$485$	1.45801	−	1.68264i	0.0662049	−	0.0764045i
$486$		0			0
$487$	5.08256	+	35.3500i	0.230313	+	1.60186i	0.696755	+	0.717309i	$0.254626\pi$
$487$	5.08256	+	35.3500i	0.230313	+	1.60186i	−0.466443	+	0.884551i	$0.654465\pi$
$488$		0			0
$489$	−0.553011	+	3.84627i	−0.0250080	+	0.173934i
$490$		0			0
$491$	−19.5620	−	12.5717i	−0.882819	−	0.567354i	0.0188294	−	0.999823i	$-0.494006\pi$
$491$	−19.5620	−	12.5717i	−0.882819	−	0.567354i	−0.901649	+	0.432469i	$0.857642\pi$
$492$		0			0
$493$	−0.509609	−	0.149635i	−0.0229516	−	0.00673921i
$494$		0			0
$495$	−0.753047	−	0.869063i	−0.0338470	−	0.0390615i
$496$		0			0
$497$	−5.09366	+	11.1536i	−0.228482	+	0.500306i
$498$		0			0
$499$	−18.2152	+	5.34847i	−0.815425	+	0.239430i	−0.662745	−	0.748845i	$-0.730609\pi$
$499$	−18.2152	+	5.34847i	−0.815425	+	0.239430i	−0.152680	+	0.988276i	$0.548790\pi$
$500$		0			0
$501$	5.24951	+	11.4948i	0.234531	+	0.513551i
$502$		0			0
$503$	−9.38864	+	6.03371i	−0.418619	+	0.269030i	−0.732949	−	0.680284i	$-0.761856\pi$
$503$	−9.38864	+	6.03371i	−0.418619	+	0.269030i	0.314330	+	0.949314i	$0.398220\pi$
$504$		0			0
$505$	−3.68686			−0.164063
$506$		0			0
$507$	−15.9508			−0.708401
$508$		0			0
$509$	−14.7087	+	9.45271i	−0.651952	+	0.418984i	−0.824379	−	0.566038i	$-0.808476\pi$
$509$	−14.7087	+	9.45271i	−0.651952	+	0.418984i	0.172427	+	0.985022i	$0.444839\pi$
$510$		0			0
$511$	1.40447	+	3.07537i	0.0621303	+	0.136046i
$512$		0			0
$513$	−1.97317	+	0.579376i	−0.0871178	+	0.0255801i
$514$		0			0
$515$	−0.668139	+	1.46302i	−0.0294417	+	0.0644684i
$516$		0			0
$517$	−18.5136	−	21.3659i	−0.814229	−	0.939671i
$518$		0			0
$519$	2.90130	+	0.851900i	0.127353	+	0.0373943i
$520$		0			0
$521$	32.0014	+	20.5661i	1.40201	+	0.901016i	0.999894	−	0.0145736i	$-0.00463909\pi$
$521$	32.0014	+	20.5661i	1.40201	+	0.901016i	0.402114	+	0.915589i	$0.368275\pi$
$522$		0			0
$523$	−5.39632	+	37.5322i	−0.235965	+	1.64117i	0.435539	+	0.900170i	$0.356558\pi$
$523$	−5.39632	+	37.5322i	−0.235965	+	1.64117i	−0.671504	+	0.741001i	$0.734351\pi$
$524$		0			0
$525$	1.12856	+	7.84929i	0.0492543	+	0.342571i
$526$		0			0
$527$	1.41750	−	1.63588i	0.0617471	−	0.0712599i
$528$		0			0
$529$	−14.0483	−	18.2111i	−0.610798	−	0.791787i
$530$		0			0
$531$	−0.755680	+	0.872101i	−0.0327937	+	0.0378460i
$532$		0			0
$533$	−7.38518	−	51.3651i	−0.319888	−	2.22487i
$534$		0			0
$535$	0.891695	−	6.20187i	0.0385513	−	0.268130i
$536$		0			0
$537$	−2.02317	−	1.30022i	−0.0873064	−	0.0561084i
$538$		0			0
$539$	−13.9635	−	4.10005i	−0.601450	−	0.176602i
$540$		0			0
$541$	1.44964	+	1.67297i	0.0623248	+	0.0719267i	0.786056	−	0.618156i	$-0.212120\pi$
$541$	1.44964	+	1.67297i	0.0623248	+	0.0719267i	−0.723731	+	0.690082i	$0.757574\pi$
$542$		0			0
$543$	8.91271	−	19.5161i	0.382481	−	0.837517i
$544$		0			0
$545$	4.51790	−	1.32658i	0.193526	−	0.0568243i
$546$		0			0
$547$	4.04060	+	8.84768i	0.172764	+	0.378299i	0.976130	−	0.217185i	$-0.0696875\pi$
$547$	4.04060	+	8.84768i	0.172764	+	0.378299i	−0.803367	+	0.595484i	$0.796960\pi$
$548$		0			0
$549$	−1.26653	+	0.813948i	−0.0540541	+	0.0347384i
$550$		0			0
$551$	1.22156			0.0520402
$552$		0			0
$553$	−18.0695			−0.768393
$554$		0			0
$555$	1.74258	−	1.11989i	0.0739685	−	0.0475367i
$556$		0			0
$557$	10.7920	+	23.6312i	0.457271	+	1.00128i	0.988101	+	0.153806i	$0.0491531\pi$
$557$	10.7920	+	23.6312i	0.457271	+	1.00128i	−0.530830	+	0.847479i	$0.678120\pi$
$558$		0			0
$559$	−5.59595	+	1.64312i	−0.236683	+	0.0694965i
$560$		0			0
$561$	−1.23959	+	2.71432i	−0.0523355	+	0.114599i
$562$		0			0
$563$	10.4014	+	12.0038i	0.438365	+	0.505900i	0.931344	−	0.364141i	$-0.118637\pi$
$563$	10.4014	+	12.0038i	0.438365	+	0.505900i	−0.492979	+	0.870041i	$0.664092\pi$
$564$		0			0
$565$	−4.70931	−	1.38278i	−0.198122	−	0.0581739i
$566$		0			0
$567$	−1.36668	−	0.878314i	−0.0573953	−	0.0368857i
$568$		0			0
$569$	0.315737	−	2.19600i	0.0132364	−	0.0920612i	−0.982132	−	0.188191i	$-0.939737\pi$
$569$	0.315737	−	2.19600i	0.0132364	−	0.0920612i	0.995369	+	0.0961303i	$0.0306465\pi$
$570$		0			0
$571$	4.33395	+	30.1433i	0.181370	+	1.26146i	0.853527	+	0.521048i	$0.174459\pi$
$571$	4.33395	+	30.1433i	0.181370	+	1.26146i	−0.672157	+	0.740408i	$0.734632\pi$
$572$		0			0
$573$	2.51726	−	2.90508i	0.105160	−	0.121361i
$574$		0			0
$575$	9.11475	+	21.5624i	0.380111	+	0.899215i
$576$		0			0
$577$	13.9136	−	16.0572i	0.579232	−	0.668470i	−0.388207	−	0.921572i	$-0.626906\pi$
$577$	13.9136	−	16.0572i	0.579232	−	0.668470i	0.967439	+	0.253102i	$0.0814510\pi$
$578$		0			0
$579$	1.68633	+	11.7287i	0.0700816	+	0.487428i
$580$		0			0
$581$	1.02805	−	7.15026i	0.0426508	−	0.296643i
$582$		0			0
$583$	−7.00959	−	4.50479i	−0.290307	−	0.186569i
$584$		0			0
$585$	−1.77891	−	0.522335i	−0.0735489	−	0.0215959i
$586$		0			0
$587$	−25.0342	−	28.8910i	−1.03327	−	1.19246i	−0.981036	−	0.193826i	$-0.937910\pi$
$587$	−25.0342	−	28.8910i	−1.03327	−	1.19246i	−0.0522368	−	0.998635i	$-0.516635\pi$
$588$		0			0
$589$	−2.06811	+	4.52854i	−0.0852151	+	0.186595i
$590$		0			0
$591$	−18.4104	+	5.40579i	−0.757304	+	0.222364i
$592$		0			0
$593$	−8.86754	−	19.4172i	−0.364146	−	0.797369i	−0.999680	−	0.0252959i	$-0.991947\pi$
$593$	−8.86754	−	19.4172i	−0.364146	−	0.797369i	0.635534	−	0.772073i	$-0.280780\pi$
$594$		0			0
$595$	−0.421070	+	0.270605i	−0.0172622	+	0.0110937i
$596$		0			0
$597$	5.59428			0.228959
$598$		0			0
$599$	18.9518			0.774349			0.387174	−	0.922006i	$-0.373451\pi$
$599$	18.9518			0.774349			0.387174	+	0.922006i	$0.373451\pi$
$600$		0			0
$601$	16.7787	−	10.7830i	0.684416	−	0.439847i	−0.151681	−	0.988430i	$-0.548469\pi$
$601$	16.7787	−	10.7830i	0.684416	−	0.439847i	0.836097	+	0.548582i	$0.184832\pi$
$602$		0			0
$603$	−3.34719	−	7.32933i	−0.136308	−	0.298474i
$604$		0			0
$605$	0.0454199	−	0.0133365i	0.00184658	−	0.000542206i
$606$		0			0
$607$	−10.9223	+	23.9166i	−0.443324	+	0.970744i	0.547652	+	0.836706i	$0.315522\pi$
$607$	−10.9223	+	23.9166i	−0.443324	+	0.970744i	−0.990976	+	0.134038i	$0.957206\pi$
$608$		0			0
$609$	0.631947	+	0.729306i	0.0256078	+	0.0295530i
$610$		0			0
$611$	−43.7345	−	12.8416i	−1.76931	−	0.519515i
$612$		0			0
$613$	−36.3785	−	23.3790i	−1.46931	−	0.944271i	−0.998059	−	0.0622740i	$-0.980165\pi$
$613$	−36.3785	−	23.3790i	−1.46931	−	0.944271i	−0.471255	−	0.881997i	$-0.656199\pi$
$614$		0			0
$615$	0.472947	−	3.28942i	0.0190711	−	0.132642i
$616$		0			0
$617$	−4.00889	−	27.8824i	−0.161392	−	1.12250i	−0.896013	−	0.444027i	$-0.853549\pi$
$617$	−4.00889	−	27.8824i	−0.161392	−	1.12250i	0.734622	−	0.678477i	$-0.237360\pi$
$618$		0			0
$619$	−12.3488	+	14.2513i	−0.496340	+	0.572807i	−0.947549	−	0.319612i	$-0.896448\pi$
$619$	−12.3488	+	14.2513i	−0.496340	+	0.572807i	0.451209	+	0.892418i	$0.350993\pi$
$620$		0			0
$621$	−4.56125	−	1.48156i	−0.183037	−	0.0594531i
$622$		0			0
$623$	−17.2189	+	19.8717i	−0.689861	+	0.796142i
$624$		0			0
$625$	−3.30642	−	22.9967i	−0.132257	−	0.919866i
$626$		0			0
$627$	0.976710	−	6.79317i	0.0390060	−	0.271293i
$628$		0			0
$629$	−4.52185	−	2.90601i	−0.180298	−	0.115870i
$630$		0			0
$631$	2.66353	+	0.782084i	0.106034	+	0.0311343i	0.334319	−	0.942460i	$-0.391494\pi$
$631$	2.66353	+	0.782084i	0.106034	+	0.0311343i	−0.228285	+	0.973594i	$0.573312\pi$
$632$		0			0
$633$	2.07810	+	2.39826i	0.0825972	+	0.0953223i
$634$		0			0
$635$	−1.96852	+	4.31046i	−0.0781183	+	0.171055i
$636$		0			0
$637$	−22.5130	+	6.61040i	−0.891996	+	0.261914i
$638$		0			0
$639$	3.13537	+	6.86551i	0.124033	+	0.271595i
$640$		0			0
$641$	8.60280	−	5.52869i	0.339790	−	0.218370i	−0.359606	−	0.933104i	$-0.617089\pi$
$641$	8.60280	−	5.52869i	0.339790	−	0.218370i	0.699396	+	0.714734i	$0.253452\pi$
$642$		0			0
$643$	−19.1911			−0.756822			−0.378411	−	0.925638i	$-0.623529\pi$
$643$	−19.1911			−0.756822			−0.378411	+	0.925638i	$0.623529\pi$
$644$		0			0
$645$	−0.373494			−0.0147063
$646$		0			0
$647$	−20.6896	+	13.2964i	−0.813391	+	0.522735i	−0.879960	−	0.475047i	$-0.842431\pi$
$647$	−20.6896	+	13.2964i	−0.813391	+	0.522735i	0.0665693	+	0.997782i	$0.478795\pi$
$648$		0			0
$649$	−1.59979	−	3.50305i	−0.0627972	−	0.137507i
$650$		0			0
$651$	−3.77356	+	1.10802i	−0.147897	+	0.0434266i
$652$		0			0
$653$	−3.74857	+	8.20822i	−0.146693	+	0.321212i	−0.968688	−	0.248282i	$-0.920134\pi$
$653$	−3.74857	+	8.20822i	−0.146693	+	0.321212i	0.821995	+	0.569495i	$0.192861\pi$
$654$		0			0
$655$	−1.25631	−	1.44986i	−0.0490883	−	0.0566509i
$656$		0			0
$657$	1.99679	+	0.586310i	0.0779022	+	0.0228741i
$658$		0			0
$659$	9.16651	+	5.89096i	0.357077	+	0.229479i	0.706863	−	0.707350i	$-0.250110\pi$
$659$	9.16651	+	5.89096i	0.357077	+	0.229479i	−0.349787	+	0.936829i	$0.613746\pi$
$660$		0			0
$661$	6.96229	−	48.4238i	0.270802	−	1.88347i	−0.169368	−	0.985553i	$-0.554173\pi$
$661$	6.96229	−	48.4238i	0.270802	−	1.88347i	0.440170	−	0.897915i	$-0.354918\pi$
$662$		0			0
$663$	0.684676	+	4.76203i	0.0265906	+	0.184942i
$664$		0			0
$665$	0.753869	−	0.870011i	0.0292338	−	0.0337376i
$666$		0			0
$667$	2.35172	+	1.60774i	0.0910589	+	0.0622518i
$668$		0			0
$669$	16.2829	−	18.7915i	0.629534	−	0.726521i
$670$		0			0
$671$	−0.715038	−	4.97320i	−0.0276037	−	0.191988i
$672$		0			0
$673$	0.343177	−	2.38685i	0.0132285	−	0.0920062i	−0.982138	−	0.188164i	$-0.939746\pi$
$673$	0.343177	−	2.38685i	0.0132285	−	0.0920062i	0.995366	+	0.0961579i	$0.0306554\pi$
$674$		0			0
$675$	4.10638	+	2.63901i	0.158055	+	0.101576i
$676$		0			0
$677$	24.0080	+	7.04937i	0.922701	+	0.270929i	0.708378	−	0.705834i	$-0.249427\pi$
$677$	24.0080	+	7.04937i	0.922701	+	0.270929i	0.214323	+	0.976763i	$0.431246\pi$
$678$		0			0
$679$	6.87417	+	7.93321i	0.263806	+	0.304449i
$680$		0			0
$681$	−6.13800	+	13.4403i	−0.235209	+	0.515035i
$682$		0			0
$683$	21.2911	−	6.25164i	0.814683	−	0.239212i	0.152258	−	0.988341i	$-0.451346\pi$
$683$	21.2911	−	6.25164i	0.814683	−	0.239212i	0.662425	+	0.749128i	$0.269527\pi$
$684$		0			0
$685$	−2.05020	−	4.48931i	−0.0783340	−	0.171528i
$686$		0			0
$687$	22.1676	−	14.2463i	0.845747	−	0.543528i
$688$		0			0
$689$	−13.4340			−0.511793
$690$		0			0
$691$	−15.9085			−0.605188			−0.302594	−	0.953120i	$-0.597853\pi$
$691$	−15.9085			−0.605188			−0.302594	+	0.953120i	$0.597853\pi$
$692$		0			0
$693$	4.56099	−	2.93117i	0.173258	−	0.111346i
$694$		0			0
$695$	2.92967	+	6.41507i	0.111129	+	0.243338i
$696$		0			0
$697$	−8.27422	+	2.42953i	−0.313408	+	0.0920250i
$698$		0			0
$699$	10.5963	−	23.2027i	0.400790	−	0.877608i
$700$		0			0
$701$	22.9743	+	26.5138i	0.867728	+	1.00141i	0.999948	+	0.0101906i	$0.00324383\pi$
$701$	22.9743	+	26.5138i	0.867728	+	1.00141i	−0.132221	+	0.991220i	$0.542211\pi$
$702$		0			0
$703$	11.8618	+	3.48293i	0.447376	+	0.131361i
$704$		0			0
$705$	−2.45562	−	1.57813i	−0.0924838	−	0.0594357i
$706$		0			0
$707$	2.47380	−	17.2057i	0.0930370	−	0.647087i
$708$		0			0
$709$	4.13450	+	28.7561i	0.155275	+	1.07996i	0.907197	+	0.420706i	$0.138218\pi$
$709$	4.13450	+	28.7561i	0.155275	+	1.07996i	−0.751922	+	0.659252i	$0.770873\pi$
$710$		0			0
$711$	−7.28373	+	8.40587i	−0.273161	+	0.315245i
$712$		0			0
$713$	−9.94165	+	5.99631i	−0.372318	+	0.224564i
$714$		0			0
$715$	4.05184	−	4.67608i	0.151530	−	0.174875i
$716$		0			0
$717$	3.72488	+	25.9071i	0.139108	+	0.967519i
$718$		0			0
$719$	5.31846	−	36.9907i	0.198345	−	1.37952i	−0.610741	−	0.791830i	$-0.709129\pi$
$719$	5.31846	−	36.9907i	0.198345	−	1.37952i	0.809086	−	0.587690i	$-0.199962\pi$
$720$		0			0
$721$	−6.37926	−	4.09970i	−0.237576	−	0.152681i
$722$		0			0
$723$	10.1448	+	2.97878i	0.377289	+	0.110782i
$724$		0			0
$725$	−1.89877	−	2.19130i	−0.0705186	−	0.0813828i
$726$		0			0
$727$	0.944538	−	2.06825i	0.0350310	−	0.0767071i	−0.891308	−	0.453399i	$-0.850211\pi$
$727$	0.944538	−	2.06825i	0.0350310	−	0.0767071i	0.926339	+	0.376692i	$0.122938\pi$
$728$		0			0
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$		0			0
$731$	0.402613	+	0.881600i	0.0148912	+	0.0326071i
$732$		0			0
$733$	−33.4368	+	21.4885i	−1.23502	+	0.793697i	−0.984665	−	0.174458i	$-0.944183\pi$
$733$	−33.4368	+	21.4885i	−1.23502	+	0.793697i	−0.250352	+	0.968155i	$0.580546\pi$
$734$		0			0
$735$	−1.50260			−0.0554241
$736$		0			0
$737$	26.8900			0.990505
$738$		0			0
$739$	−25.6875	+	16.5083i	−0.944929	+	0.607269i	−0.919788	−	0.392415i	$-0.871640\pi$
$739$	−25.6875	+	16.5083i	−0.944929	+	0.607269i	−0.0251408	+	0.999684i	$0.508003\pi$
$740$		0			0
$741$	−4.59660	−	10.0651i	−0.168860	−	0.369752i
$742$		0			0
$743$	39.9821	−	11.7398i	1.46680	−	0.430692i	0.551744	−	0.834013i	$-0.313962\pi$
$743$	39.9821	−	11.7398i	1.46680	−	0.430692i	0.915058	+	0.403321i	$0.132144\pi$
$744$		0			0
$745$	−0.547274	+	1.19836i	−0.0200506	+	0.0439046i
$746$		0			0
$747$	−2.91188	−	3.36048i	−0.106540	−	0.122954i
$748$		0			0
$749$	28.3444	+	8.32266i	1.03568	+	0.304103i
$750$		0			0
$751$	−21.2285	−	13.6428i	−0.774640	−	0.497831i	0.0926106	−	0.995702i	$-0.470479\pi$
$751$	−21.2285	−	13.6428i	−0.774640	−	0.497831i	−0.867251	+	0.497871i	$0.834115\pi$
$752$		0			0
$753$	1.94620	−	13.5361i	0.0709235	−	0.493284i
$754$		0			0
$755$	−0.153977	−	1.07094i	−0.00560381	−	0.0389754i
$756$		0			0
$757$	−17.6616	+	20.3825i	−0.641920	+	0.740815i	−0.979713	−	0.200405i	$-0.935774\pi$
$757$	−17.6616	+	20.3825i	−0.641920	+	0.740815i	0.337793	+	0.941220i	$0.390320\pi$
$758$		0			0
$759$	10.8211	−	11.7926i	0.392780	−	0.428043i
$760$		0			0
$761$	−30.0547	+	34.6850i	−1.08948	+	1.25733i	−0.125293	+	0.992120i	$0.539987\pi$
$761$	−30.0547	+	34.6850i	−1.08948	+	1.25733i	−0.964190	+	0.265211i	$0.914558\pi$
$762$		0			0
$763$	3.15940	+	21.9741i	0.114378	+	0.795516i
$764$		0			0
$765$	−0.0438467	+	0.304960i	−0.00158528	+	0.0110259i
$766$		0			0
$767$	−5.22331	−	3.35682i	−0.188603	−	0.121208i
$768$		0			0
$769$	11.9463	+	3.50774i	0.430794	+	0.126492i	0.489939	−	0.871757i	$-0.337019\pi$
$769$	11.9463	+	3.50774i	0.430794	+	0.126492i	−0.0591449	+	0.998249i	$0.518837\pi$
$770$		0			0
$771$	19.5216	+	22.5291i	0.703052	+	0.811365i
$772$		0			0
$773$	−6.62308	+	14.5025i	−0.238216	+	0.521619i	−0.990548	−	0.137164i	$-0.956201\pi$
$773$	−6.62308	+	14.5025i	−0.238216	+	0.521619i	0.752333	+	0.658783i	$0.228929\pi$
$774$		0			0
$775$	11.3382	−	3.32919i	0.407279	−	0.119588i
$776$		0			0
$777$	4.05703	+	8.88365i	0.145545	+	0.318699i
$778$		0			0
$779$	16.6852	−	10.7229i	0.597809	−	0.384189i
$780$		0			0
$781$	−25.1883			−0.901307
$782$		0			0
$783$	0.594006			0.0212280
$784$		0			0
$785$	3.80028	−	2.44229i	0.135638	−	0.0871692i
$786$		0			0
$787$	−11.0477	−	24.1911i	−0.393807	−	0.862318i	−0.997861	−	0.0653742i	$-0.979176\pi$
$787$	−11.0477	−	24.1911i	−0.393807	−	0.862318i	0.604053	−	0.796944i	$-0.293551\pi$
$788$		0			0
$789$	27.0241	−	7.93500i	0.962084	−	0.282493i
$790$		0			0
$791$	9.61294	−	21.0494i	0.341797	−	0.748431i
$792$		0			0
$793$	−5.30477	−	6.12204i	−0.188378	−	0.217400i
$794$		0			0
$795$	−0.825463	−	0.242378i	−0.0292762	−	0.00859626i
$796$		0			0
$797$	36.8579	+	23.6871i	1.30557	+	0.839040i	0.993807	−	0.111119i	$-0.0354434\pi$
$797$	36.8579	+	23.6871i	1.30557	+	0.839040i	0.311765	+	0.950159i	$0.399080\pi$
$798$		0			0
$799$	−1.07797	+	7.49744i	−0.0381358	+	0.265240i
$800$		0			0
$801$	2.30338	+	16.0204i	0.0813860	+	0.566052i
$802$		0			0
$803$	−4.54811	+	5.24880i	−0.160499	+	0.185226i
$804$		0			0
$805$	2.59638	−	0.682731i	0.0915104	−	0.0240631i
$806$		0			0
$807$	5.45434	−	6.29464i	0.192002	−	0.221582i
$808$		0			0
$809$	−6.50158	−	45.2195i	−0.228583	−	1.58983i	−0.704084	−	0.710116i	$-0.748642\pi$
$809$	−6.50158	−	45.2195i	−0.228583	−	1.58983i	0.475501	−	0.879715i	$-0.342267\pi$
$810$		0			0
$811$	−1.17918	+	8.20135i	−0.0414065	+	0.287988i	0.958588	+	0.284795i	$0.0919256\pi$
$811$	−1.17918	+	8.20135i	−0.0414065	+	0.287988i	−0.999995	+	0.00319335i	$0.998984\pi$
$812$		0			0
$813$	22.9874	+	14.7731i	0.806204	+	0.518116i
$814$		0			0
$815$	−1.28472	−	0.377227i	−0.0450016	−	0.0132137i
$816$		0			0
$817$	−1.45974	−	1.68462i	−0.0510697	−	0.0589375i
$818$		0			0
$819$	3.63123	−	7.95128i	0.126885	−	0.277840i
$820$		0			0
$821$	16.4045	−	4.81681i	0.572522	−	0.168108i	0.0173594	−	0.999849i	$-0.494474\pi$
$821$	16.4045	−	4.81681i	0.572522	−	0.168108i	0.555163	+	0.831742i	$0.312656\pi$
$822$		0			0
$823$	20.7471	+	45.4298i	0.723198	+	1.58358i	0.809367	+	0.587303i	$0.199810\pi$
$823$	20.7471	+	45.4298i	0.723198	+	1.58358i	−0.0861691	+	0.996281i	$0.527463\pi$
$824$		0			0
$825$	−13.7041	+	8.80710i	−0.477116	+	0.306624i
$826$		0			0
$827$	41.3046			1.43630			0.718151	−	0.695887i	$-0.244989\pi$
$827$	41.3046			1.43630			0.718151	+	0.695887i	$0.244989\pi$
$828$		0			0
$829$	39.0352			1.35575			0.677875	−	0.735177i	$-0.262901\pi$
$829$	39.0352			1.35575			0.677875	+	0.735177i	$0.262901\pi$
$830$		0			0
$831$	17.4914	−	11.2411i	0.606771	−	0.389948i
$832$		0			0
$833$	1.61975	+	3.54675i	0.0561209	+	0.122888i
$834$		0			0
$835$	−4.17792	+	1.22675i	−0.144583	+	0.0424534i
$836$		0			0
$837$	−1.00566	+	2.20208i	−0.0347606	+	0.0761152i
$838$		0			0
$839$	32.0027	+	36.9331i	1.10486	+	1.27507i	0.958267	+	0.285874i	$0.0922838\pi$
$839$	32.0027	+	36.9331i	1.10486	+	1.27507i	0.146588	+	0.989198i	$0.453171\pi$
$840$		0			0
$841$	27.4867	+	8.07084i	0.947819	+	0.278305i
$842$		0			0
$843$	−26.9041	−	17.2902i	−0.926626	−	0.595507i
$844$		0			0
$845$	0.782195	−	5.44028i	0.0269083	−	0.187151i
$846$		0			0
$847$	0.0317624	+	0.220913i	0.00109137	+	0.00759065i
$848$		0			0
$849$	−12.0280	+	13.8811i	−0.412800	+	0.476397i
$850$		0			0
$851$	18.2520	+	22.3170i	0.625671	+	0.765016i
$852$		0			0
$853$	−3.16566	+	3.65337i	−0.108390	+	0.125089i	−0.807352	−	0.590070i	$-0.799100\pi$
$853$	−3.16566	+	3.65337i	−0.108390	+	0.125089i	0.698962	+	0.715159i	$0.253646\pi$
$854$		0			0
$855$	−0.100845	−	0.701395i	−0.00344884	−	0.0239872i
$856$		0			0
$857$	−7.71695	+	53.6726i	−0.263606	+	1.83342i	0.241545	+	0.970390i	$0.422346\pi$
$857$	−7.71695	+	53.6726i	−0.263606	+	1.83342i	−0.505151	+	0.863031i	$0.668563\pi$
$858$		0			0
$859$	2.21625	+	1.42430i	0.0756175	+	0.0485964i	0.577903	−	0.816105i	$-0.303871\pi$
$859$	2.21625	+	1.42430i	0.0756175	+	0.0485964i	−0.502286	+	0.864702i	$0.667507\pi$
$860$		0			0
$861$	15.0336	+	4.41427i	0.512344	+	0.150438i
$862$		0			0
$863$	−5.95760	−	6.87543i	−0.202799	−	0.234042i	0.645235	−	0.763984i	$-0.276759\pi$
$863$	−5.95760	−	6.87543i	−0.202799	−	0.234042i	−0.848034	+	0.529941i	$0.822214\pi$
$864$		0			0
$865$	−0.432828	+	0.947762i	−0.0147166	+	0.0322249i
$866$		0			0
$867$	−15.5443	+	4.56421i	−0.527912	+	0.155009i
$868$		0			0
$869$	−15.4198	−	33.7646i	−0.523081	−	1.14539i
$870$		0			0
$871$	36.4717	−	23.4389i	1.23580	−	0.794198i
$872$		0			0
$873$	6.46145			0.218687
$874$		0			0
$875$	−5.53141			−0.186996
$876$		0			0
$877$	−13.6861	+	8.79554i	−0.462148	+	0.297004i	−0.750920	−	0.660394i	$-0.770389\pi$
$877$	−13.6861	+	8.79554i	−0.462148	+	0.297004i	0.288772	+	0.957398i	$0.406753\pi$
$878$		0			0
$879$	−0.798400	−	1.74825i	−0.0269293	−	0.0589670i
$880$		0			0
$881$	−29.3015	+	8.60369i	−0.987191	+	0.289866i	−0.735190	−	0.677861i	$-0.762907\pi$
$881$	−29.3015	+	8.60369i	−0.987191	+	0.289866i	−0.252002	+	0.967727i	$0.581089\pi$
$882$		0			0
$883$	0.00830960	−	0.0181955i	0.000279640	−	0.000612327i	−0.909492	−	0.415721i	$-0.863529\pi$
$883$	0.00830960	−	0.0181955i	0.000279640	−	0.000612327i	0.909772	+	0.415109i	$0.136256\pi$
$884$		0			0
$885$	−0.260387	−	0.300503i	−0.00875282	−	0.0101013i
$886$		0			0
$887$	−7.15976	−	2.10230i	−0.240401	−	0.0705882i	0.159312	−	0.987228i	$-0.449072\pi$
$887$	−7.15976	−	2.10230i	−0.240401	−	0.0705882i	−0.399714	+	0.916640i	$0.630890\pi$
$888$		0			0
$889$	−18.7951	−	12.0788i	−0.630366	−	0.405112i
$890$		0			0
$891$	0.474943	−	3.30330i	0.0159112	−	0.110665i
$892$		0			0
$893$	−2.47928	−	17.2438i	−0.0829659	−	0.577041i
$894$		0			0
$895$	0.542672	−	0.626277i	0.0181395	−	0.0209341i
$896$		0			0
$897$	4.39783	−	25.4269i	0.146839	−	0.848980i
$898$		0			0
$899$	0.941691	−	1.08677i	0.0314071	−	0.0362458i
$900$		0			0
$901$	0.317708	+	2.20971i	0.0105844	+	0.0736161i
$902$		0			0
$903$	0.250607	−	1.74301i	0.00833967	−	0.0580036i
$904$		0			0
$905$	6.21923	+	3.99686i	0.206734	+	0.132860i
$906$		0			0
$907$	−14.9889	−	4.40114i	−0.497698	−	0.146137i	0.0232432	−	0.999730i	$-0.492601\pi$
$907$	−14.9889	−	4.40114i	−0.497698	−	0.146137i	−0.520941	+	0.853592i	$0.674419\pi$
$908$		0			0
$909$	−7.00686	−	8.08634i	−0.232403	−	0.268207i
$910$		0			0
$911$	−4.76925	+	10.4432i	−0.158012	+	0.345999i	−0.972036	−	0.234834i	$-0.924545\pi$
$911$	−4.76925	+	10.4432i	−0.158012	+	0.345999i	0.814023	+	0.580832i	$0.197273\pi$
$912$		0			0
$913$	14.2383	−	4.18073i	0.471218	−	0.138362i
$914$		0			0
$915$	−0.215502	−	0.471884i	−0.00712428	−	0.0156000i
$916$		0			0
$917$	7.60914	−	4.89009i	0.251276	−	0.161485i
$918$		0			0
$919$	13.9454			0.460017			0.230008	−	0.973189i	$-0.426125\pi$
$919$	13.9454			0.460017			0.230008	+	0.973189i	$0.426125\pi$
$920$		0			0
$921$	−9.22139			−0.303855
$922$		0			0
$923$	−34.1636	+	21.9556i	−1.12451	+	0.722679i
$924$		0			0
$925$	−12.1899	−	26.6921i	−0.400801	−	0.877631i
$926$		0			0
$927$	−4.47862	+	1.31504i	−0.147097	+	0.0431917i
$928$		0			0
$929$	−12.1698	+	26.6481i	−0.399278	+	0.874297i	0.598065	+	0.801448i	$0.295936\pi$
$929$	−12.1698	+	26.6481i	−0.399278	+	0.874297i	−0.997343	+	0.0728493i	$0.976791\pi$
$930$		0			0
$931$	−5.87264	−	6.77738i	−0.192468	−	0.222120i
$932$		0			0
$933$	8.68192	+	2.54924i	0.284233	+	0.0834584i
$934$		0			0
$935$	−0.864977	−	0.555887i	−0.0282878	−	0.0181795i
$936$		0			0
$937$	−1.57780	+	10.9738i	−0.0515445	+	0.358500i	0.947683	+	0.319212i	$0.103418\pi$
$937$	−1.57780	+	10.9738i	−0.0515445	+	0.358500i	−0.999228	+	0.0392880i	$0.987491\pi$
$938$		0			0
$939$	−0.0556022	−	0.386722i	−0.00181451	−	0.0126202i
$940$		0			0
$941$	−2.98399	+	3.44371i	−0.0972753	+	0.112262i	−0.802300	−	0.596921i	$-0.796390\pi$
$941$	−2.98399	+	3.44371i	−0.0972753	+	0.112262i	0.705025	+	0.709183i	$0.250936\pi$
$942$		0			0
$943$	46.2348	+	1.31645i	1.50561	+	0.0428695i
$944$		0			0
$945$	0.366583	−	0.423059i	0.0119249	−	0.0137621i
$946$		0			0
$947$	−2.31050	−	16.0699i	−0.0750813	−	0.522202i	−0.992304	−	0.123827i	$-0.960483\pi$
$947$	−2.31050	−	16.0699i	−0.0750813	−	0.522202i	0.917223	−	0.398375i	$-0.130426\pi$
$948$		0			0
$949$	−1.59357	+	11.0835i	−0.0517295	+	0.359786i
$950$		0			0
$951$	1.43208	+	0.920345i	0.0464385	+	0.0298442i
$952$		0			0
$953$	35.7084	+	10.4849i	1.15671	+	0.339640i	0.803152	−	0.595774i	$-0.203154\pi$
$953$	35.7084	+	10.4849i	1.15671	+	0.339640i	0.353555	+	0.935414i	$0.384973\pi$
$954$		0			0
$955$	0.867383	+	1.00101i	0.0280678	+	0.0323920i
$956$		0			0
$957$	−0.823502	+	1.80322i	−0.0266200	+	0.0582898i
$958$		0			0
$959$	22.3262	−	6.55556i	0.720950	−	0.211690i
$960$		0			0
$961$	−10.4433	−	22.8677i	−0.336881	−	0.737667i
$962$		0			0
$963$	15.2972	−	9.83089i	0.492944	−	0.316796i
$964$		0			0
$965$	−4.08296			−0.131435
$966$		0			0
$967$	−7.52389			−0.241952			−0.120976	−	0.992655i	$-0.538602\pi$
$967$	−7.52389			−0.241952			−0.120976	+	0.992655i	$0.538602\pi$
$968$		0			0
$969$	−1.54687	+	0.994116i	−0.0496928	+	0.0319356i
$970$		0			0
$971$	−23.0919	−	50.5642i	−0.741054	−	1.62268i	−0.781813	−	0.623513i	$-0.785705\pi$
$971$	−23.0919	−	50.5642i	−0.741054	−	1.62268i	0.0407595	−	0.999169i	$-0.487022\pi$
$972$		0			0
$973$	−31.9034	+	9.36768i	−1.02278	+	0.300314i
$974$		0			0
$975$	−10.9105	+	23.8907i	−0.349416	+	0.765115i
$976$		0			0
$977$	−26.9070	−	31.0523i	−0.860830	−	0.993451i	−0.999995	−	0.00318161i	$-0.998987\pi$
$977$	−26.9070	−	31.0523i	−0.860830	−	0.993451i	0.139165	−	0.990269i	$-0.455558\pi$
$978$		0			0
$979$	−51.8262	−	15.2175i	−1.65637	−	0.486355i
$980$		0			0
$981$	11.4958	+	7.38792i	0.367033	+	0.235878i
$982$		0			0
$983$	6.33154	−	44.0369i	0.201945	−	1.40456i	−0.596560	−	0.802569i	$-0.703466\pi$
$983$	6.33154	−	44.0369i	0.201945	−	1.40456i	0.798504	−	0.601989i	$-0.205625\pi$
$984$		0			0
$985$	−0.940923	−	6.54426i	−0.0299803	−	0.208518i
$986$		0			0
$987$	9.01242	−	10.4009i	0.286869	−	0.331064i
$988$		0			0
$989$	−0.593055	−	5.16441i	−0.0188580	−	0.164219i
$990$		0			0
$991$	−1.90225	+	2.19531i	−0.0604269	+	0.0697363i	−0.785158	−	0.619295i	$-0.787418\pi$
$991$	−1.90225	+	2.19531i	−0.0604269	+	0.0697363i	0.724731	+	0.689032i	$0.241964\pi$
$992$		0			0
$993$	3.28772	+	22.8666i	0.104333	+	0.725649i
$994$		0			0
$995$	−0.274332	+	1.90802i	−0.00869691	+	0.0604883i
$996$		0			0
$997$	−1.89501	−	1.21785i	−0.0600155	−	0.0385696i	0.510289	−	0.860003i	$-0.329538\pi$
$997$	−1.89501	−	1.21785i	−0.0600155	−	0.0385696i	−0.570304	+	0.821433i	$0.693175\pi$
$998$		0			0
$999$	5.76801	+	1.69364i	0.182492	+	0.0535845i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.i.b.85.1	yes	20
3.2	odd	2		828.2.q.b.361.2		20
23.6	even	11		6348.2.a.r.1.5		10
23.13	even	11	inner	276.2.i.b.13.1	✓	20
23.17	odd	22		6348.2.a.q.1.6		10
69.59	odd	22		828.2.q.b.289.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.b.13.1	✓	20	23.13	even	11	inner
276.2.i.b.85.1	yes	20	1.1	even	1	trivial
828.2.q.b.289.2		20	69.59	odd	22
828.2.q.b.361.2		20	3.2	odd	2
6348.2.a.q.1.6		10	23.17	odd	22
6348.2.a.r.1.5		10	23.6	even	11

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 + 0.540641i) q^{3} +(-0.143141 - 0.313435i) q^{5} +(1.55877 - 0.457697i) q^{7} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.841254 + 0.540641i) q^{3} +(-0.143141 - 0.313435i) q^{5} +(1.55877 - 0.457697i) q^{7} +(0.415415 - 0.909632i) q^{9} +(2.18545 + 2.52214i) q^{11} +(5.16264 + 1.51589i) q^{13} +(0.289874 + 0.186291i) q^{15} +(0.127249 - 0.885037i) q^{17} +(0.292667 + 2.03554i) q^{19} +(-1.06387 + 1.22778i) q^{21} +(-2.11562 + 4.30397i) q^{23} +(3.19655 - 3.68902i) q^{25} +(0.142315 + 0.989821i) q^{27} +(0.0845359 - 0.587960i) q^{29} +(2.03655 + 1.30881i) q^{31} +(-3.20209 - 0.940218i) q^{33} +(-0.366583 - 0.423059i) q^{35} +(2.49728 - 5.46827i) q^{37} +(-5.16264 + 1.51589i) q^{39} +(-4.00648 - 8.77296i) q^{41} +(-0.911860 + 0.586017i) q^{43} -0.344574 q^{45} -8.47133 q^{47} +(-3.66849 + 2.35759i) q^{49} +(0.371438 + 0.813336i) q^{51} +(-2.39561 + 0.703414i) q^{53} +(0.477700 - 1.04602i) q^{55} +(-1.34671 - 1.55418i) q^{57} +(-1.10721 - 0.325107i) q^{59} +(-1.26653 - 0.813948i) q^{61} +(0.231202 - 1.60804i) q^{63} +(-0.263853 - 1.83514i) q^{65} +(5.27652 - 6.08943i) q^{67} +(-0.547134 - 4.76452i) q^{69} +(-4.94260 + 5.70407i) q^{71} +(0.296170 + 2.05991i) q^{73} +(-0.694677 + 4.83158i) q^{75} +(4.56099 + 2.93117i) q^{77} +(-10.6720 - 3.13359i) q^{79} +(-0.654861 - 0.755750i) q^{81} +(1.84717 - 4.04473i) q^{83} +(-0.295616 + 0.0868007i) q^{85} +(0.246759 + 0.540327i) q^{87} +(-13.6158 + 8.75033i) q^{89} +8.74121 q^{91} -2.42085 q^{93} +(0.596119 - 0.383102i) q^{95} +(2.68418 + 5.87754i) q^{97} +(3.20209 - 0.940218i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9	\( 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9} + 14 q^{13} - 11 q^{15} + 3 q^{17} + 7 q^{19} + 4 q^{21} + 24 q^{23} + 12 q^{25} + 2 q^{27} - 26 q^{29} + 33 q^{31} - 11 q^{33} - 2 q^{35} - 18 q^{37} - 14 q^{39} + 4 q^{41} - 40 q^{43} - 54 q^{47} + 30 q^{49} - 14 q^{51} - 14 q^{53} + 11 q^{55} - 29 q^{57} + 4 q^{59} + 12 q^{61} - 4 q^{63} - 33 q^{65} + 15 q^{67} - 2 q^{69} - 33 q^{71} + 15 q^{73} + 10 q^{75} + 66 q^{77} - 42 q^{79} - 2 q^{81} - 14 q^{83} - 13 q^{85} + 4 q^{87} - 66 q^{89} - 16 q^{91} - 22 q^{93} - 31 q^{95} - 24 q^{97} + 11 q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9 + 14 * q^13 - 11 * q^15 + 3 * q^17 + 7 * q^19 + 4 * q^21 + 24 * q^23 + 12 * q^25 + 2 * q^27 - 26 * q^29 + 33 * q^31 - 11 * q^33 - 2 * q^35 - 18 * q^37 - 14 * q^39 + 4 * q^41 - 40 * q^43 - 54 * q^47 + 30 * q^49 - 14 * q^51 - 14 * q^53 + 11 * q^55 - 29 * q^57 + 4 * q^59 + 12 * q^61 - 4 * q^63 - 33 * q^65 + 15 * q^67 - 2 * q^69 - 33 * q^71 + 15 * q^73 + 10 * q^75 + 66 * q^77 - 42 * q^79 - 2 * q^81 - 14 * q^83 - 13 * q^85 + 4 * q^87 - 66 * q^89 - 16 * q^91 - 22 * q^93 - 31 * q^95 - 24 * q^97 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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