LMFDB - Embedded newform 1040.2.dh.a.289.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(289,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("1040.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.dh (of order $6$, degree $2$, not 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:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 8x^{10} + 54x^{8} - 78x^{6} + 92x^{4} - 10x^{2} + 1 $ x^12 - 8x^10 + 54x^8 - 78x^6 + 92x^4 - 10*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.5
Root			$2.20467 + 1.27287i$ of defining polynomial
Character	$\chi$	$=$	1040.289
Dual form			1040.2.dh.a.529.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86449 - 1.07646i) q^{3} +(-0.817544 + 2.08125i) q^{5} +(2.54486 + 1.46928i) q^{7} +(0.817544 - 1.41603i) q^{9} +O(q^{10})$	\(q+(1.86449 - 1.07646i) q^{3} +(-0.817544 + 2.08125i) q^{5} +(2.54486 + 1.46928i) q^{7} +(0.817544 - 1.41603i) q^{9} +(-0.317544 - 0.550003i) q^{11} +(3.60484 + 0.0716710i) q^{13} +(0.716091 + 4.76053i) q^{15} +(-1.05998 - 0.611979i) q^{17} +(-0.682456 + 1.18205i) q^{19} +6.32648 q^{21} +(-1.86449 + 1.07646i) q^{23} +(-3.66324 - 3.40304i) q^{25} +2.93855i q^{27} +(1.50000 + 2.59808i) q^{29} +8.96157 q^{31} +(-1.18412 - 0.683650i) q^{33} +(-5.13847 + 4.09531i) q^{35} +(-1.05998 + 0.611979i) q^{37} +(6.79833 - 3.74685i) q^{39} +(4.98079 + 8.62698i) q^{41} +(-1.18412 - 0.683650i) q^{43} +(2.27874 + 2.85918i) q^{45} -6.16379i q^{47} +(0.817544 + 1.41603i) q^{49} -2.63509 q^{51} +0.642285i q^{53} +(1.40430 - 0.211239i) q^{55} +2.93855i q^{57} +(-3.79833 + 6.57890i) q^{59} +(1.13509 - 1.96603i) q^{61} +(4.16107 - 2.40240i) q^{63} +(-3.09628 + 7.44399i) q^{65} +(6.95421 - 4.01502i) q^{67} +(-2.31754 + 4.01410i) q^{69} +(1.31754 - 2.28205i) q^{71} -10.3263i q^{73} +(-10.4933 - 2.40158i) q^{75} -1.86624i q^{77} +1.03843 q^{79} +(5.61588 + 9.72698i) q^{81} -11.8452i q^{83} +(2.14026 - 1.70576i) q^{85} +(5.59346 + 3.22939i) q^{87} +(-6.27912 - 10.8758i) q^{89} +(9.06851 + 5.47890i) q^{91} +(16.7087 - 9.64680i) q^{93} +(-1.90220 - 2.38674i) q^{95} +(-12.8031 - 7.39190i) q^{97} -1.03843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{5} + 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^5 + 6 * q^9	$ 12 q - 6 q^{5} + 6 q^{9} + 4 q^{15} - 12 q^{19} - 8 q^{21} - 2 q^{25} + 18 q^{29} + 16 q^{31} - 10 q^{35} + 32 q^{39} + 14 q^{41} - 29 q^{45} + 6 q^{49} - 24 q^{51} + 26 q^{55} + 4 q^{59} + 6 q^{61} + 23 q^{65} - 24 q^{69} + 12 q^{71} - 2 q^{75} + 104 q^{79} + 14 q^{81} + 21 q^{85} + 20 q^{89} + 44 q^{91} - 20 q^{95} - 104 q^{99}+O(q^{100}) $ 12 * q - 6 * q^5 + 6 * q^9 + 4 * q^15 - 12 * q^19 - 8 * q^21 - 2 * q^25 + 18 * q^29 + 16 * q^31 - 10 * q^35 + 32 * q^39 + 14 * q^41 - 29 * q^45 + 6 * q^49 - 24 * q^51 + 26 * q^55 + 4 * q^59 + 6 * q^61 + 23 * q^65 - 24 * q^69 + 12 * q^71 - 2 * q^75 + 104 * q^79 + 14 * q^81 + 21 * q^85 + 20 * q^89 + 44 * q^91 - 20 * q^95 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.86449	−	1.07646i	1.07646	−	0.621496i	0.146523	−	0.989207i	$-0.453192\pi$
$3$	1.86449	−	1.07646i	1.07646	−	0.621496i	0.929940	+	0.367711i	$0.119858\pi$
$4$		0			0
$5$	−0.817544	+	2.08125i	−0.365617	+	0.930765i
$5$	−0.817544	+	2.08125i	−0.365617	+	0.930765i
$6$		0			0
$7$	2.54486	+	1.46928i	0.961867	+	0.555334i	0.896747	−	0.442543i	$-0.145924\pi$
$7$	2.54486	+	1.46928i	0.961867	+	0.555334i	0.0651198	+	0.997877i	$0.479257\pi$
$8$		0			0
$9$	0.817544	−	1.41603i	0.272515	−	0.472010i
$10$		0			0
$11$	−0.317544	−	0.550003i	−0.0957433	−	0.165832i	0.814175	−	0.580619i	$-0.197189\pi$
$11$	−0.317544	−	0.550003i	−0.0957433	−	0.165832i	−0.909919	+	0.414787i	$0.863856\pi$
$12$		0			0
$13$	3.60484	+	0.0716710i	0.999802	+	0.0198779i
$13$	3.60484	+	0.0716710i	0.999802	+	0.0198779i
$14$		0			0
$15$	0.716091	+	4.76053i	0.184894	+	1.22916i
$16$		0			0
$17$	−1.05998	−	0.611979i	−0.257082	−	0.148427i	0.365920	−	0.930646i	$-0.380754\pi$
$17$	−1.05998	−	0.611979i	−0.257082	−	0.148427i	−0.623003	+	0.782220i	$0.714088\pi$
$18$		0			0
$19$	−0.682456	+	1.18205i	−0.156566	+	0.271180i	−0.933628	−	0.358244i	$-0.883376\pi$
$19$	−0.682456	+	1.18205i	−0.156566	+	0.271180i	0.777062	+	0.629424i	$0.216709\pi$
$20$		0			0
$21$	6.32648			1.38055
$22$		0			0
$23$	−1.86449	+	1.07646i	−0.388773	+	0.224458i	−0.681628	−	0.731699i	$-0.738728\pi$
$23$	−1.86449	+	1.07646i	−0.388773	+	0.224458i	0.292856	+	0.956157i	$0.405394\pi$
$24$		0			0
$25$	−3.66324	−	3.40304i	−0.732648	−	0.680607i
$26$		0			0
$27$			2.93855i			0.565525i
$28$		0			0
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$		0			0
$31$	8.96157			1.60955			0.804773	−	0.593583i	$-0.202287\pi$
$31$	8.96157			1.60955			0.804773	+	0.593583i	$0.202287\pi$
$32$		0			0
$33$	−1.18412	−	0.683650i	−0.206128	−	0.119008i
$34$		0			0
$35$	−5.13847	+	4.09531i	−0.868561	+	0.692233i
$36$		0			0
$37$	−1.05998	+	0.611979i	−0.174259	+	0.100609i	−0.584593	−	0.811327i	$-0.698746\pi$
$37$	−1.05998	+	0.611979i	−0.174259	+	0.100609i	0.410333	+	0.911936i	$0.365412\pi$
$38$		0			0
$39$	6.79833	−	3.74685i	1.08860	−	0.599975i
$40$		0			0
$41$	4.98079	+	8.62698i	0.777868	+	1.34731i	0.933168	+	0.359440i	$0.117032\pi$
$41$	4.98079	+	8.62698i	0.777868	+	1.34731i	−0.155300	+	0.987867i	$0.549634\pi$
$42$		0			0
$43$	−1.18412	−	0.683650i	−0.180576	−	0.104256i	0.406987	−	0.913434i	$-0.366579\pi$
$43$	−1.18412	−	0.683650i	−0.180576	−	0.104256i	−0.587563	+	0.809178i	$0.699913\pi$
$44$		0			0
$45$	2.27874	+	2.85918i	0.339694	+	0.426222i
$46$		0			0
$47$		−	6.16379i		−	0.899081i	−0.893260	−	0.449540i	$-0.851588\pi$
$47$		−	6.16379i		−	0.899081i	0.893260	−	0.449540i	$-0.148412\pi$
$48$		0			0
$49$	0.817544	+	1.41603i	0.116792	+	0.202290i
$50$		0			0
$51$	−2.63509			−0.368986
$52$		0			0
$53$			0.642285i			0.0882246i	0.999027	+	0.0441123i	$0.0140459\pi$
$53$			0.642285i			0.0882246i	−0.999027	+	0.0441123i	$0.985954\pi$
$54$		0			0
$55$	1.40430	−	0.211239i	0.189356	−	0.0284834i
$56$		0			0
$57$			2.93855i			0.389221i
$58$		0			0
$59$	−3.79833	+	6.57890i	−0.494501	+	0.856500i	−0.999980	−	0.00633858i	$-0.997982\pi$
$59$	−3.79833	+	6.57890i	−0.494501	+	0.856500i	0.505479	+	0.862839i	$0.331316\pi$
$60$		0			0
$61$	1.13509	−	1.96603i	0.145333	−	0.251725i	−0.784164	−	0.620554i	$-0.786908\pi$
$61$	1.13509	−	1.96603i	0.145333	−	0.251725i	0.929497	+	0.368829i	$0.120241\pi$
$62$		0			0
$63$	4.16107	−	2.40240i	0.524246	−	0.302674i
$64$		0			0
$65$	−3.09628	+	7.44399i	−0.384046	+	0.923314i
$66$		0			0
$67$	6.95421	−	4.01502i	0.849592	−	0.490512i	−0.0109212	−	0.999940i	$-0.503476\pi$
$67$	6.95421	−	4.01502i	0.849592	−	0.490512i	0.860513	+	0.509428i	$0.170143\pi$
$68$		0			0
$69$	−2.31754	+	4.01410i	−0.279000	+	0.483241i
$70$		0			0
$71$	1.31754	−	2.28205i	0.156364	−	0.270830i	−0.777191	−	0.629265i	$-0.783356\pi$
$71$	1.31754	−	2.28205i	0.156364	−	0.270830i	0.933555	+	0.358435i	$0.116689\pi$
$72$		0			0
$73$		−	10.3263i		−	1.20860i	−0.796756	−	0.604301i	$-0.793453\pi$
$73$		−	10.3263i		−	1.20860i	0.796756	−	0.604301i	$-0.206547\pi$
$74$		0			0
$75$	−10.4933	−	2.40158i	−1.21166	−	0.277310i
$76$		0			0
$77$		−	1.86624i		−	0.212678i
$78$		0			0
$79$	1.03843			0.116832			0.0584161	−	0.998292i	$-0.481395\pi$
$79$	1.03843			0.116832			0.0584161	+	0.998292i	$0.481395\pi$
$80$		0			0
$81$	5.61588	+	9.72698i	0.623986	+	1.08078i
$82$		0			0
$83$		−	11.8452i		−	1.30018i	−0.759855	−	0.650092i	$-0.774730\pi$
$83$		−	11.8452i		−	1.30018i	0.759855	−	0.650092i	$-0.225270\pi$
$84$		0			0
$85$	2.14026	−	1.70576i	0.232144	−	0.185016i
$86$		0			0
$87$	5.59346	+	3.22939i	0.599682	+	0.346227i
$88$		0			0
$89$	−6.27912	−	10.8758i	−0.665585	−	1.15283i	−0.979126	−	0.203253i	$-0.934849\pi$
$89$	−6.27912	−	10.8758i	−0.665585	−	1.15283i	0.313541	−	0.949575i	$-0.398485\pi$
$90$		0			0
$91$	9.06851	+	5.47890i	0.950638	+	0.574344i
$92$		0			0
$93$	16.7087	−	9.64680i	1.73262	−	1.00033i
$94$		0			0
$95$	−1.90220	−	2.38674i	−0.195162	−	0.244874i
$96$		0			0
$97$	−12.8031	−	7.39190i	−1.29996	−	0.750534i	−0.319565	−	0.947564i	$-0.603537\pi$
$97$	−12.8031	−	7.39190i	−1.29996	−	0.750534i	−0.980397	+	0.197031i	$0.936870\pi$
$98$		0			0
$99$	−1.03843			−0.104366
$100$		0			0
$101$	−6.61588	−	11.4590i	−0.658304	−	1.14022i	−0.981054	−	0.193732i	$-0.937941\pi$
$101$	−6.61588	−	11.4590i	−0.658304	−	1.14022i	0.322750	−	0.946484i	$-0.395393\pi$
$102$		0			0
$103$		−	10.9686i		−	1.08077i	−0.841419	−	0.540383i	$-0.818279\pi$
$103$		−	10.9686i		−	1.08077i	0.841419	−	0.540383i	$-0.181721\pi$
$104$		0			0
$105$	−5.17218	+	13.1670i	−0.504753	+	1.28497i
$106$		0			0
$107$	−9.24360	+	5.33680i	−0.893613	+	0.515928i	−0.875123	−	0.483901i	$-0.839219\pi$
$107$	−9.24360	+	5.33680i	−0.893613	+	0.515928i	−0.0184903	+	0.999829i	$0.505886\pi$
$108$		0			0
$109$	3.27018			0.313226			0.156613	−	0.987660i	$-0.449942\pi$
$109$	3.27018			0.313226			0.156613	+	0.987660i	$0.449942\pi$
$110$		0			0
$111$	−1.31754	+	2.28205i	−0.125056	+	0.216603i
$112$		0			0
$113$	4.78895	+	2.76490i	0.450507	+	0.260100i	0.708044	−	0.706168i	$-0.249578\pi$
$113$	4.78895	+	2.76490i	0.450507	+	0.260100i	−0.257537	+	0.966268i	$0.582911\pi$
$114$		0			0
$115$	−0.716091	−	4.76053i	−0.0667759	−	0.443922i
$116$		0			0
$117$	3.04860	−	5.04596i	0.281844	−	0.466499i
$118$		0			0
$119$	−1.79833	−	3.11480i	−0.164853	−	0.285533i
$120$		0			0
$121$	5.29833	−	9.17698i	0.481666	−	0.834271i
$122$		0			0
$123$	18.5732	+	10.7233i	1.67469	+	0.966884i
$124$		0			0
$125$	10.0774	−	4.84201i	0.901354	−	0.433082i
$126$		0			0
$127$	−14.9231	+	8.61586i	−1.32421	+	0.764534i	−0.984397	−	0.175959i	$-0.943697\pi$
$127$	−14.9231	+	8.61586i	−1.32421	+	0.764534i	−0.339813	+	0.940493i	$0.610364\pi$
$128$		0			0
$129$	−2.94369			−0.259178
$130$		0			0
$131$	−10.0000			−0.873704			−0.436852	−	0.899533i	$-0.643907\pi$
$131$	−10.0000			−0.873704			−0.436852	+	0.899533i	$0.643907\pi$
$132$		0			0
$133$	−3.47351	+	2.00543i	−0.301191	+	0.173893i
$134$		0			0
$135$	−6.11588	−	2.40240i	−0.526371	−	0.206765i
$136$		0			0
$137$	−7.51044	−	4.33616i	−0.641661	−	0.370463i	0.143593	−	0.989637i	$-0.454134\pi$
$137$	−7.51044	−	4.33616i	−0.641661	−	0.370463i	−0.785254	+	0.619174i	$0.787468\pi$
$138$		0			0
$139$	−7.16324	+	12.4071i	−0.607578	+	1.05236i	0.384060	+	0.923308i	$0.374526\pi$
$139$	−7.16324	+	12.4071i	−0.607578	+	1.05236i	−0.991638	+	0.129048i	$0.958808\pi$
$140$		0			0
$141$	−6.63509	−	11.4923i	−0.558775	−	0.967827i
$142$		0			0
$143$	−1.10528	−	2.00543i	−0.0924279	−	0.167703i
$144$		0			0
$145$	−6.63357	+	0.997839i	−0.550888	+	0.0828660i
$146$		0			0
$147$	3.04860	+	1.76011i	0.251445	+	0.145172i
$148$		0			0
$149$	−8.57745	+	14.8566i	−0.702692	+	1.21710i	0.264826	+	0.964296i	$0.414685\pi$
$149$	−8.57745	+	14.8566i	−0.702692	+	1.21710i	−0.967518	+	0.252802i	$0.918648\pi$
$150$		0			0
$151$	21.3828			1.74011			0.870053	−	0.492957i	$-0.164084\pi$
$151$	21.3828			1.74011			0.870053	+	0.492957i	$0.164084\pi$
$152$		0			0
$153$	−1.73316	+	1.00064i	−0.140118	+	0.0808969i
$154$		0			0
$155$	−7.32648	+	18.6513i	−0.588477	+	1.49811i
$156$		0			0
$157$			18.3646i			1.46566i	0.680413	+	0.732829i	$0.261800\pi$
$157$			18.3646i			1.46566i	−0.680413	+	0.732829i	$0.738200\pi$
$158$		0			0
$159$	0.691395	+	1.19753i	0.0548312	+	0.0949705i
$160$		0			0
$161$	−6.32648			−0.498597
$162$		0			0
$163$	−3.47351	−	2.00543i	−0.272066	−	0.157078i	0.357760	−	0.933814i	$-0.383541\pi$
$163$	−3.47351	−	2.00543i	−0.272066	−	0.157078i	−0.629826	+	0.776736i	$0.716874\pi$
$164$		0			0
$165$	2.39092	−	1.90553i	0.186133	−	0.148346i
$166$		0			0
$167$	2.54486	−	1.46928i	0.196927	−	0.113696i	−0.398294	−	0.917258i	$-0.630398\pi$
$167$	2.54486	−	1.46928i	0.196927	−	0.113696i	0.595221	+	0.803562i	$0.297064\pi$
$168$		0			0
$169$	12.9897	+	0.516725i	0.999210	+	0.0397480i
$170$		0			0
$171$	1.11588	+	1.93275i	0.0853331	+	0.147801i
$172$		0			0
$173$	−1.18412	−	0.683650i	−0.0900267	−	0.0519769i	0.454311	−	0.890843i	$-0.349886\pi$
$173$	−1.18412	−	0.683650i	−0.0900267	−	0.0519769i	−0.544337	+	0.838866i	$0.683219\pi$
$174$		0			0
$175$	−4.32244	−	14.0426i	−0.326746	−	1.06152i
$176$		0			0
$177$			16.3550i			1.22932i
$178$		0			0
$179$	−3.89306	−	6.74299i	−0.290981	−	0.503994i	0.683061	−	0.730362i	$-0.260648\pi$
$179$	−3.89306	−	6.74299i	−0.290981	−	0.503994i	−0.974042	+	0.226367i	$0.927315\pi$
$180$		0			0
$181$	−3.86684			−0.287420			−0.143710	−	0.989620i	$-0.545903\pi$
$181$	−3.86684			−0.287420			−0.143710	+	0.989620i	$0.545903\pi$
$182$		0			0
$183$		−	4.88752i		−	0.361296i
$184$		0			0
$185$	−0.407104	−	2.70640i	−0.0299309	−	0.198979i
$186$		0			0
$187$			0.777322i			0.0568434i
$188$		0			0
$189$	−4.31754	+	7.47821i	−0.314055	+	0.543959i
$190$		0			0
$191$	2.47185	−	4.28136i	0.178857	−	0.309789i	−0.762633	−	0.646832i	$-0.776094\pi$
$191$	2.47185	−	4.28136i	0.178857	−	0.309789i	0.941489	+	0.337043i	$0.109427\pi$
$192$		0			0
$193$	4.29240	−	2.47822i	0.308974	−	0.178386i	−0.337493	−	0.941328i	$-0.609579\pi$
$193$	4.29240	−	2.47822i	0.308974	−	0.178386i	0.646467	+	0.762942i	$0.276246\pi$
$194$		0			0
$195$	2.24020	+	17.2123i	0.160424	+	1.23260i
$196$		0			0
$197$	−5.84174	+	3.37273i	−0.416207	+	0.240297i	−0.693453	−	0.720502i	$-0.743912\pi$
$197$	−5.84174	+	3.37273i	−0.416207	+	0.240297i	0.277246	+	0.960799i	$0.410578\pi$
$198$		0			0
$199$	−2.58772	+	4.48207i	−0.183439	+	0.317725i	−0.943049	−	0.332653i	$-0.892056\pi$
$199$	−2.58772	+	4.48207i	−0.183439	+	0.317725i	0.759611	+	0.650378i	$0.225390\pi$
$200$		0			0
$201$	8.64403	−	14.9719i	0.609703	−	1.05604i
$202$		0			0
$203$			8.81566i			0.618738i
$204$		0			0
$205$	−22.0269	+	3.31335i	−1.53843	+	0.231414i
$206$		0			0
$207$			3.52022i			0.244673i
$208$		0			0
$209$	0.866840			0.0599606
$210$		0			0
$211$	−7.00894	−	12.1398i	−0.482515	−	0.835741i	0.517283	−	0.855814i	$-0.326943\pi$
$211$	−7.00894	−	12.1398i	−0.482515	−	0.835741i	−0.999799	+	0.0200732i	$0.993610\pi$
$212$		0			0
$213$		−	5.67315i		−	0.388718i
$214$		0			0
$215$	2.39092	−	1.90553i	0.163059	−	0.129956i
$216$		0			0
$217$	22.8060	+	13.1670i	1.54817	+	0.893836i
$218$		0			0
$219$	−11.1159	−	19.2533i	−0.751141	−	1.30101i
$220$		0			0
$221$	−3.77719	−	2.28205i	−0.254081	−	0.153508i
$222$		0			0
$223$	0.00719226	−	0.00415245i	0.000481629	−	0.000278069i	−0.499759	−	0.866164i	$-0.666578\pi$
$223$	0.00719226	−	0.00415245i	0.000481629	−	0.000278069i	0.500241	+	0.865886i	$0.333245\pi$
$224$		0			0
$225$	−7.81366	+	2.40512i	−0.520911	+	0.160341i
$226$		0			0
$227$	−9.75454	−	5.63179i	−0.647431	−	0.373795i	0.140040	−	0.990146i	$-0.455277\pi$
$227$	−9.75454	−	5.63179i	−0.647431	−	0.373795i	−0.787471	+	0.616351i	$0.788610\pi$
$228$		0			0
$229$	16.5404			1.09302			0.546509	−	0.837453i	$-0.315957\pi$
$229$	16.5404			1.09302			0.546509	+	0.837453i	$0.315957\pi$
$230$		0			0
$231$	−2.00894	−	3.47959i	−0.132179	−	0.228940i
$232$		0			0
$233$			6.94941i			0.455271i	0.973746	+	0.227636i	$0.0730995\pi$
$233$			6.94941i			0.455271i	−0.973746	+	0.227636i	$0.926900\pi$
$234$		0			0
$235$	12.8284	+	5.03917i	0.836833	+	0.328719i
$236$		0			0
$237$	1.93613	−	1.11783i	0.125765	−	0.0726107i
$238$		0			0
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$		0			0
$241$	−9.88605	+	17.1231i	−0.636817	+	1.10300i	0.349310	+	0.937007i	$0.386416\pi$
$241$	−9.88605	+	17.1231i	−0.636817	+	1.10300i	−0.986127	+	0.165992i	$0.946917\pi$
$242$		0			0
$243$	13.3069	+	7.68273i	0.853637	+	0.492848i
$244$		0			0
$245$	−3.61549	+	0.543852i	−0.230985	+	0.0347454i
$246$		0			0
$247$	−2.54486	+	4.21218i	−0.161926	+	0.268015i
$248$		0			0
$249$	−12.7510	−	22.0853i	−0.808060	−	1.39960i
$250$		0			0
$251$	1.83676	−	3.18136i	0.115935	−	0.200806i	−0.802218	−	0.597031i	$-0.796347\pi$
$251$	1.83676	−	3.18136i	0.115935	−	0.200806i	0.918153	+	0.396226i	$0.129680\pi$
$252$		0			0
$253$	1.18412	+	0.683650i	0.0744447	+	0.0429807i
$254$		0			0
$255$	2.15430	−	5.48429i	0.134908	−	0.343440i
$256$		0			0
$257$	11.4877	−	6.63242i	0.716583	−	0.413719i	−0.0969108	−	0.995293i	$-0.530896\pi$
$257$	11.4877	−	6.63242i	0.716583	−	0.413719i	0.813494	+	0.581574i	$0.197563\pi$
$258$		0			0
$259$	−3.59666			−0.223486
$260$		0			0
$261$	4.90527			0.303628
$262$		0			0
$263$	26.2150	−	15.1352i	1.61649	−	0.933279i	0.628667	−	0.777674i	$-0.283601\pi$
$263$	26.2150	−	15.1352i	1.61649	−	0.933279i	0.987819	−	0.155605i	$-0.0497327\pi$
$264$		0			0
$265$	−1.33676	−	0.525096i	−0.0821164	−	0.0322564i
$266$		0			0
$267$	−23.4147	−	13.5185i	−1.43296	−	0.827317i
$268$		0			0
$269$	−11.1248	+	19.2687i	−0.678292	+	1.17484i	0.297203	+	0.954814i	$0.403946\pi$
$269$	−11.1248	+	19.2687i	−0.678292	+	1.17484i	−0.975495	+	0.220022i	$0.929387\pi$
$270$		0			0
$271$	−5.91421	−	10.2437i	−0.359262	−	0.622261i	0.628575	−	0.777749i	$-0.283638\pi$
$271$	−5.91421	−	10.2437i	−0.359262	−	0.622261i	−0.987838	+	0.155488i	$0.950305\pi$
$272$		0			0
$273$	22.8060	+	0.453425i	1.38028	+	0.0274425i
$274$		0			0
$275$	−0.708438	+	3.09541i	−0.0427204	+	0.186660i
$276$		0			0
$277$	−14.5363	−	8.39254i	−0.873402	−	0.504259i	−0.00492452	−	0.999988i	$-0.501568\pi$
$277$	−14.5363	−	8.39254i	−0.873402	−	0.504259i	−0.868477	+	0.495729i	$0.834901\pi$
$278$		0			0
$279$	7.32648	−	12.6898i	0.438625	−	0.759721i
$280$		0			0
$281$	−10.5967			−0.632144			−0.316072	−	0.948735i	$-0.602364\pi$
$281$	−10.5967			−0.632144			−0.316072	+	0.948735i	$0.602364\pi$
$282$		0			0
$283$	−7.63458	+	4.40783i	−0.453829	+	0.262018i	−0.709446	−	0.704760i	$-0.751055\pi$
$283$	−7.63458	+	4.40783i	−0.453829	+	0.262018i	0.255617	+	0.966778i	$0.417721\pi$
$284$		0			0
$285$	−6.11588	−	2.40240i	−0.362273	−	0.142306i
$286$		0			0
$287$			29.2726i			1.72791i
$288$		0			0
$289$	−7.75096	−	13.4251i	−0.455939	−	0.789710i
$290$		0			0
$291$	−31.8284			−1.86581
$292$		0			0
$293$	−24.4675	−	14.1263i	−1.42940	−	0.825267i	−0.432331	−	0.901715i	$-0.642309\pi$
$293$	−24.4675	−	14.1263i	−1.42940	−	0.825267i	−0.997074	+	0.0764476i	$0.975642\pi$
$294$		0			0
$295$	−10.5871	−	13.2838i	−0.616403	−	0.773415i
$296$		0			0
$297$	1.61621	−	0.933121i	0.0937822	−	0.0541452i
$298$		0			0
$299$	−6.79833	+	3.74685i	−0.393158	+	0.216686i
$300$		0			0
$301$	−2.00894	−	3.47959i	−0.115793	−	0.200560i
$302$		0			0
$303$	−24.6704	−	14.2435i	−1.41728	−	0.818267i
$304$		0			0
$305$	3.16383	+	3.96973i	0.181160	+	0.227306i
$306$		0			0
$307$		−	12.7219i		−	0.726077i	−0.931774	−	0.363039i	$-0.881739\pi$
$307$		−	12.7219i		−	0.726077i	0.931774	−	0.363039i	$-0.118261\pi$
$308$		0			0
$309$	−11.8073	−	20.4508i	−0.671692	−	1.16340i
$310$		0			0
$311$	−27.9231			−1.58338			−0.791688	−	0.610925i	$-0.790798\pi$
$311$	−27.9231			−1.58338			−0.791688	+	0.610925i	$0.790798\pi$
$312$		0			0
$313$		−	24.5807i		−	1.38938i	−0.719307	−	0.694692i	$-0.755540\pi$
$313$		−	24.5807i		−	1.38938i	0.719307	−	0.694692i	$-0.244460\pi$
$314$		0			0
$315$	1.59814	+	10.6243i	0.0900448	+	0.598613i
$316$		0			0
$317$		−	0.234377i		−	0.0131639i	−0.999978	−	0.00658196i	$-0.997905\pi$
$317$		−	0.234377i		−	0.0131639i	0.999978	−	0.00658196i	$-0.00209512\pi$
$318$		0			0
$319$	0.952633	−	1.65001i	0.0533372	−	0.0923828i
$320$		0			0
$321$	−11.4897	+	19.9008i	−0.641294	+	1.11075i
$322$		0			0
$323$	1.44678	−	0.835296i	0.0805008	−	0.0464771i
$324$		0			0
$325$	−12.9615	−	12.5299i	−0.718975	−	0.695036i
$326$		0			0
$327$	6.09721	−	3.52022i	0.337176	−	0.194669i
$328$		0			0
$329$	9.05631	−	15.6860i	0.499290	−	0.864796i
$330$		0			0
$331$	−9.16324	+	15.8712i	−0.503657	+	0.872360i	0.496334	+	0.868132i	$0.334679\pi$
$331$	−9.16324	+	15.8712i	−0.503657	+	0.872360i	−0.999991	+	0.00422829i	$0.998654\pi$
$332$		0			0
$333$			2.00128i			0.109669i
$334$		0			0
$335$	2.67089	+	17.7559i	0.145926	+	0.970110i
$336$		0			0
$337$		−	21.2949i		−	1.16001i	−0.814614	−	0.580003i	$-0.803051\pi$
$337$		−	21.2949i		−	1.16001i	0.814614	−	0.580003i	$-0.196949\pi$
$338$		0			0
$339$	11.9053			0.646605
$340$		0			0
$341$	−2.84570	−	4.92889i	−0.154103	−	0.266915i
$342$		0			0
$343$		−	15.7651i		−	0.851234i
$344$		0			0
$345$	−6.45968	−	8.10511i	−0.347777	−	0.436364i
$346$		0			0
$347$	−3.30407	−	1.90761i	−0.177372	−	0.102406i	0.408685	−	0.912675i	$-0.365987\pi$
$347$	−3.30407	−	1.90761i	−0.177372	−	0.102406i	−0.586057	+	0.810270i	$0.699321\pi$
$348$		0			0
$349$	12.1632	+	21.0674i	0.651083	+	1.12771i	0.982860	+	0.184352i	$0.0590185\pi$
$349$	12.1632	+	21.0674i	0.651083	+	1.12771i	−0.331777	+	0.943358i	$0.607648\pi$
$350$		0			0
$351$	−0.210609	+	10.5930i	−0.0112415	+	0.565413i
$352$		0			0
$353$	23.4338	−	13.5295i	1.24726	−	0.720104i	0.276696	−	0.960958i	$-0.410761\pi$
$353$	23.4338	−	13.5295i	1.24726	−	0.720104i	0.970562	+	0.240853i	$0.0774272\pi$
$354$		0			0
$355$	3.67238	+	4.60783i	0.194910	+	0.244558i
$356$		0			0
$357$	−6.70593	−	3.87167i	−0.354916	−	0.204911i
$358$		0			0
$359$	27.0039			1.42521			0.712605	−	0.701566i	$-0.247515\pi$
$359$	27.0039			1.42521			0.712605	+	0.701566i	$0.247515\pi$
$360$		0			0
$361$	8.56851	+	14.8411i	0.450974	+	0.781110i
$362$		0			0
$363$		−	22.8138i		−	1.19742i
$364$		0			0
$365$	21.4917	+	8.44221i	1.12492	+	0.441885i
$366$		0			0
$367$	6.01118	−	3.47055i	0.313781	−	0.181161i	−0.334836	−	0.942276i	$-0.608681\pi$
$367$	6.01118	−	3.47055i	0.313781	−	0.181161i	0.648617	+	0.761115i	$0.275348\pi$
$368$		0			0
$369$	16.2881			0.847922
$370$		0			0
$371$	−0.943693	+	1.63452i	−0.0489941	+	0.0848603i
$372$		0			0
$373$	2.00301	+	1.15644i	0.103712	+	0.0598781i	0.550959	−	0.834532i	$-0.314262\pi$
$373$	2.00301	+	1.15644i	0.103712	+	0.0598781i	−0.447247	+	0.894411i	$0.647595\pi$
$374$		0			0
$375$	13.5770	−	19.8759i	0.701116	−	1.02639i
$376$		0			0
$377$	5.22105	+	9.47315i	0.268898	+	0.487892i
$378$		0			0
$379$	−2.58772	−	4.48207i	−0.132922	−	0.230228i	0.791880	−	0.610677i	$-0.209103\pi$
$379$	−2.58772	−	4.48207i	−0.132922	−	0.230228i	−0.924802	+	0.380449i	$0.875769\pi$
$380$		0			0
$381$	−18.5493	+	32.1283i	−0.950309	+	1.64598i
$382$		0			0
$383$	17.8929	+	10.3305i	0.914283	+	0.527861i	0.881807	−	0.471611i	$-0.156327\pi$
$383$	17.8929	+	10.3305i	0.914283	+	0.527861i	0.0324760	+	0.999473i	$0.489661\pi$
$384$		0			0
$385$	3.88412	+	1.52574i	0.197953	+	0.0777587i
$386$		0			0
$387$	−1.93613	+	1.11783i	−0.0984193	+	0.0568224i
$388$		0			0
$389$	−19.7477			−1.00125			−0.500624	−	0.865665i	$-0.666896\pi$
$389$	−19.7477			−1.00125			−0.500624	+	0.865665i	$0.666896\pi$
$390$		0			0
$391$	2.63509			0.133262
$392$		0			0
$393$	−18.6449	+	10.7646i	−0.940510	+	0.543004i
$394$		0			0
$395$	−0.848960	+	2.16123i	−0.0427158	+	0.108743i
$396$		0			0
$397$	8.13113	+	4.69451i	0.408090	+	0.235611i	0.689969	−	0.723839i	$-0.257624\pi$
$397$	8.13113	+	4.69451i	0.408090	+	0.235611i	−0.281879	+	0.959450i	$0.590958\pi$
$398$		0			0
$399$	−4.31754	+	7.47821i	−0.216148	+	0.374379i
$400$		0			0
$401$	−12.2510	−	21.2193i	−0.611784	−	1.05964i	−0.990940	−	0.134308i	$-0.957119\pi$
$401$	−12.2510	−	21.2193i	−0.611784	−	1.05964i	0.379156	−	0.925333i	$-0.376214\pi$
$402$		0			0
$403$	32.3050	+	0.642285i	1.60923	+	0.0319945i
$404$		0			0
$405$	−24.8356	+	3.73583i	−1.23409	+	0.185635i
$406$		0			0
$407$	0.673180	+	0.388661i	0.0333683	+	0.0192652i
$408$		0			0
$409$	18.0582	−	31.2778i	0.892922	−	1.54659i	0.0565671	−	0.998399i	$-0.481985\pi$
$409$	18.0582	−	31.2778i	0.892922	−	1.54659i	0.836355	−	0.548188i	$-0.184682\pi$
$410$		0			0
$411$	−18.6708			−0.920965
$412$		0			0
$413$	−19.3324	+	11.1616i	−0.951288	+	0.549226i
$414$		0			0
$415$	24.6530	+	9.68401i	1.21017	+	0.475370i
$416$		0			0
$417$			30.8439i			1.51043i
$418$		0			0
$419$	3.43342	+	5.94686i	0.167734	+	0.290523i	0.937623	−	0.347655i	$-0.113022\pi$
$419$	3.43342	+	5.94686i	0.167734	+	0.290523i	−0.769889	+	0.638178i	$0.779689\pi$
$420$		0			0
$421$	33.9795			1.65606			0.828029	−	0.560686i	$-0.189462\pi$
$421$	33.9795			1.65606			0.828029	+	0.560686i	$0.189462\pi$
$422$		0			0
$423$	−8.72810	−	5.03917i	−0.424375	−	0.245013i
$424$		0			0
$425$	1.80037	+	5.84897i	0.0873308	+	0.283717i
$426$		0			0
$427$	5.77729	−	3.33552i	0.279582	−	0.161417i
$428$		0			0
$429$	−4.21955	−	2.54931i	−0.203722	−	0.123082i
$430$		0			0
$431$	−8.12482	−	14.0726i	−0.391359	−	0.677853i	0.601270	−	0.799046i	$-0.294661\pi$
$431$	−8.12482	−	14.0726i	−0.391359	−	0.677853i	−0.992629	+	0.121193i	$0.961328\pi$
$432$		0			0
$433$	0.221929	+	0.128130i	0.0106652	+	0.00615756i	0.505323	−	0.862930i	$-0.331373\pi$
$433$	0.221929	+	0.128130i	0.0106652	+	0.00615756i	−0.494658	+	0.869088i	$0.664707\pi$
$434$		0			0
$435$	−11.2941	+	9.00126i	−0.541510	+	0.431577i
$436$		0			0
$437$		−	2.93855i		−	0.140570i
$438$		0			0
$439$	3.79833	+	6.57890i	0.181284	+	0.313994i	0.942318	−	0.334718i	$-0.108641\pi$
$439$	3.79833	+	6.57890i	0.181284	+	0.313994i	−0.761034	+	0.648712i	$0.775308\pi$
$440$		0			0
$441$	2.67352			0.127310
$442$		0			0
$443$			4.32246i			0.205366i	0.994714	+	0.102683i	$0.0327428\pi$
$443$			4.32246i			0.205366i	−0.994714	+	0.102683i	$0.967257\pi$
$444$		0			0
$445$	27.7687	−	4.17703i	1.31636	−	0.198010i
$446$		0			0
$447$			36.9332i			1.74688i
$448$		0			0
$449$	1.64403	−	2.84754i	0.0775865	−	0.134384i	−0.824622	−	0.565685i	$-0.808612\pi$
$449$	1.64403	−	2.84754i	0.0775865	−	0.134384i	0.902208	+	0.431301i	$0.141945\pi$
$450$		0			0
$451$	3.16324	−	5.47890i	0.148951	−	0.257991i
$452$		0			0
$453$	39.8680	−	23.0178i	1.87316	−	1.08147i
$454$		0			0
$455$	−18.8169	+	14.3946i	−0.882149	+	0.674831i
$456$		0			0
$457$	−13.3594	+	7.71304i	−0.624925	+	0.360801i	−0.778784	−	0.627292i	$-0.784163\pi$
$457$	−13.3594	+	7.71304i	−0.624925	+	0.360801i	0.153859	+	0.988093i	$0.450830\pi$
$458$		0			0
$459$	1.79833	−	3.11480i	0.0839389	−	0.145386i
$460$		0			0
$461$	−12.9424	+	22.4168i	−0.602786	+	1.04406i	0.389611	+	0.920979i	$0.372609\pi$
$461$	−12.9424	+	22.4168i	−0.602786	+	1.04406i	−0.992397	+	0.123076i	$0.960724\pi$
$462$		0			0
$463$			7.04045i			0.327197i	0.986527	+	0.163599i	$0.0523102\pi$
$463$			7.04045i			0.327197i	−0.986527	+	0.163599i	$0.947690\pi$
$464$		0			0
$465$	6.41730	+	42.6618i	0.297595	+	1.97840i
$466$		0			0
$467$		−	18.8113i		−	0.870482i	−0.900314	−	0.435241i	$-0.856663\pi$
$467$		−	18.8113i		−	0.870482i	0.900314	−	0.435241i	$-0.143337\pi$
$468$		0			0
$469$	23.5967			1.08959
$470$		0			0
$471$	19.7688	+	34.2406i	0.910900	+	1.57773i
$472$		0			0
$473$			0.868356i			0.0399271i
$474$		0			0
$475$	6.52255	−	2.00771i	0.299275	−	0.0921199i
$476$		0			0
$477$	0.909493	+	0.525096i	0.0416428	+	0.0240425i
$478$		0			0
$479$	9.73876	+	16.8680i	0.444975	+	0.770720i	0.998051	−	0.0624114i	$-0.0198791\pi$
$479$	9.73876	+	16.8680i	0.444975	+	0.770720i	−0.553075	+	0.833131i	$0.686546\pi$
$480$		0			0
$481$	−3.86491	+	2.13011i	−0.176225	+	0.0971249i
$482$		0			0
$483$	−11.7957	+	6.81023i	−0.536721	+	0.309876i
$484$		0			0
$485$	25.8516	−	20.6034i	1.17386	−	0.935552i
$486$		0			0
$487$	−27.9935	−	16.1620i	−1.26851	−	0.732372i	−0.293800	−	0.955867i	$-0.594920\pi$
$487$	−27.9935	−	16.1620i	−1.26851	−	0.732372i	−0.974705	+	0.223495i	$0.928253\pi$
$488$		0			0
$489$	−8.63509			−0.390492
$490$		0			0
$491$	14.3354	+	24.8297i	0.646949	+	1.12055i	0.983848	+	0.179007i	$0.0572885\pi$
$491$	14.3354	+	24.8297i	0.646949	+	1.12055i	−0.336899	+	0.941541i	$0.609378\pi$
$492$		0			0
$493$		−	3.67187i		−	0.165373i
$494$		0			0
$495$	0.848960	−	2.16123i	0.0381579	−	0.0971401i
$496$		0			0
$497$	6.70593	−	3.87167i	0.300802	−	0.173668i
$498$		0			0
$499$	28.9616			1.29650			0.648249	−	0.761428i	$-0.275502\pi$
$499$	28.9616			1.29650			0.648249	+	0.761428i	$0.275502\pi$
$500$		0			0
$501$	3.16324	−	5.47890i	0.141323	−	0.244779i
$502$		0			0
$503$	24.3433	+	14.0546i	1.08542	+	0.626665i	0.932352	−	0.361551i	$-0.117753\pi$
$503$	24.3433	+	14.0546i	1.08542	+	0.626665i	0.153063	+	0.988216i	$0.451086\pi$
$504$		0			0
$505$	29.2579	−	4.40105i	1.30196	−	0.195844i
$506$		0			0
$507$	24.7754	−	13.0195i	1.10032	−	0.578218i
$508$		0			0
$509$	10.5563	+	18.2841i	0.467900	+	0.810427i	0.999327	−	0.0366773i	$-0.0116774\pi$
$509$	10.5563	+	18.2841i	0.467900	+	0.810427i	−0.531427	+	0.847104i	$0.678344\pi$
$510$		0			0
$511$	15.1722	−	26.2790i	0.671178	−	1.16251i
$512$		0			0
$513$	−3.47351	−	2.00543i	−0.153359	−	0.0885420i
$514$		0			0
$515$	22.8284	+	8.96730i	1.00594	+	0.395147i
$516$		0			0
$517$	−3.39010	+	1.95728i	−0.149097	+	0.0860809i
$518$		0			0
$519$	−2.94369			−0.129214
$520$		0			0
$521$	0.673516			0.0295073			0.0147536	−	0.999891i	$-0.495304\pi$
$521$	0.673516			0.0295073			0.0147536	+	0.999891i	$0.495304\pi$
$522$		0			0
$523$	−25.8618	+	14.9313i	−1.13086	+	0.652900i	−0.944150	−	0.329516i	$-0.893114\pi$
$523$	−25.8618	+	14.9313i	−1.13086	+	0.652900i	−0.186706	+	0.982416i	$0.559781\pi$
$524$		0			0
$525$	−23.1754	−	21.5293i	−1.01146	−	0.939614i
$526$		0			0
$527$	−9.49907	−	5.48429i	−0.413786	−	0.238899i
$528$		0			0
$529$	−9.18246	+	15.9045i	−0.399237	+	0.691499i
$530$		0			0
$531$	6.21061	+	10.7571i	0.269517	+	0.466818i
$532$		0			0
$533$	17.3366	+	31.4558i	0.750933	+	1.36250i
$534$		0			0
$535$	−3.55018	−	23.6014i	−0.153488	−	1.02038i
$536$		0			0
$537$	−14.5171	−	8.38148i	−0.626461	−	0.361687i
$538$		0			0
$539$	0.519213	−	0.899304i	0.0223641	−	0.0387358i
$540$		0			0
$541$	6.28806			0.270345			0.135172	−	0.990822i	$-0.456841\pi$
$541$	6.28806			0.270345			0.135172	+	0.990822i	$0.456841\pi$
$542$		0			0
$543$	−7.20968	+	4.16251i	−0.309397	+	0.178630i
$544$		0			0
$545$	−2.67352	+	6.80607i	−0.114521	+	0.291540i
$546$		0			0
$547$			3.03789i			0.129891i	0.997889	+	0.0649454i	$0.0206873\pi$
$547$			3.03789i			0.129891i	−0.997889	+	0.0649454i	$0.979313\pi$
$548$		0			0
$549$	−1.85597	−	3.21464i	−0.0792109	−	0.137197i
$550$		0			0
$551$	−4.09473			−0.174442
$552$		0			0
$553$	2.64265	+	1.52574i	0.112377	+	0.0648809i
$554$		0			0
$555$	−3.67238	−	4.60783i	−0.155884	−	0.195591i
$556$		0			0
$557$	17.9264	−	10.3498i	0.759566	−	0.438536i	−0.0695738	−	0.997577i	$-0.522164\pi$
$557$	17.9264	−	10.3498i	0.759566	−	0.438536i	0.829140	+	0.559041i	$0.188831\pi$
$558$		0			0
$559$	−4.21955	−	2.54931i	−0.178468	−	0.107824i
$560$		0			0
$561$	0.836758	+	1.44931i	0.0353279	+	0.0611898i
$562$		0			0
$563$	−9.49188	−	5.48014i	−0.400035	−	0.230960i	0.286464	−	0.958091i	$-0.407520\pi$
$563$	−9.49188	−	5.48014i	−0.400035	−	0.230960i	−0.686499	+	0.727131i	$0.740853\pi$
$564$		0			0
$565$	−9.66965	+	7.70660i	−0.406805	+	0.324219i
$566$		0			0
$567$			33.0051i			1.38608i
$568$		0			0
$569$	21.3566	+	36.9907i	0.895314	+	1.55073i	0.833416	+	0.552647i	$0.186382\pi$
$569$	21.3566	+	36.9907i	0.895314	+	1.55073i	0.0618981	+	0.998082i	$0.480285\pi$
$570$		0			0
$571$	23.6145			0.988238			0.494119	−	0.869394i	$-0.335491\pi$
$571$	23.6145			0.988238			0.494119	+	0.869394i	$0.335491\pi$
$572$		0			0
$573$		−	10.6434i		−	0.444635i
$574$		0			0
$575$	10.4933	+	2.40158i	0.437601	+	0.100153i
$576$		0			0
$577$		−	18.3646i		−	0.764530i	−0.924053	−	0.382265i	$-0.875144\pi$
$577$		−	18.3646i		−	0.764530i	0.924053	−	0.382265i	$-0.124856\pi$
$578$		0			0
$579$	5.33542	−	9.24123i	0.221733	−	0.384052i
$580$		0			0
$581$	17.4039	−	30.1445i	0.722037	−	1.25060i
$582$		0			0
$583$	0.353259	−	0.203954i	0.0146305	−	0.00844691i
$584$		0			0
$585$	8.00956	+	10.4702i	0.331155	+	0.432890i
$586$		0			0
$587$	0.608726	−	0.351448i	0.0251248	−	0.0145058i	−0.487385	−	0.873187i	$-0.662049\pi$
$587$	0.608726	−	0.351448i	0.0251248	−	0.0145058i	0.512510	+	0.858681i	$0.328716\pi$
$588$		0			0
$589$	−6.11588	+	10.5930i	−0.252000	+	0.436477i
$590$		0			0
$591$	−7.26124	+	12.5768i	−0.298687	+	0.517342i
$592$		0			0
$593$			37.1593i			1.52595i	0.646428	+	0.762975i	$0.276262\pi$
$593$			37.1593i			1.52595i	−0.646428	+	0.762975i	$0.723738\pi$
$594$		0			0
$595$	7.95291	−	1.19630i	0.326037	−	0.0490434i
$596$		0			0
$597$			11.1423i			0.456026i
$598$		0			0
$599$	−15.6914			−0.641133			−0.320567	−	0.947226i	$-0.603873\pi$
$599$	−15.6914			−0.641133			−0.320567	+	0.947226i	$0.603873\pi$
$600$		0			0
$601$	−6.00193	−	10.3956i	−0.244824	−	0.424047i	0.717258	−	0.696807i	$-0.245397\pi$
$601$	−6.00193	−	10.3956i	−0.244824	−	0.424047i	−0.962082	+	0.272760i	$0.912063\pi$
$602$		0			0
$603$		−	13.1298i		−	0.534687i
$604$		0			0
$605$	14.7680	+	18.5298i	0.600405	+	0.753342i
$606$		0			0
$607$	33.5035	+	19.3433i	1.35987	+	0.785119i	0.989606	−	0.143809i	$-0.0459350\pi$
$607$	33.5035	+	19.3433i	1.35987	+	0.785119i	0.370261	+	0.928928i	$0.379268\pi$
$608$		0			0
$609$	9.48973	+	16.4367i	0.384543	+	0.666048i
$610$		0			0
$611$	0.441765	−	22.2195i	0.0178719	−	0.898903i
$612$		0			0
$613$	14.9684	−	8.64201i	0.604568	−	0.349047i	−0.166269	−	0.986081i	$-0.553172\pi$
$613$	14.9684	−	8.64201i	0.604568	−	0.349047i	0.770836	+	0.637033i	$0.219839\pi$
$614$		0			0
$615$	−37.5023	+	29.8889i	−1.51224	+	1.20524i
$616$		0			0
$617$	−22.9229	−	13.2345i	−0.922841	−	0.532803i	−0.0383009	−	0.999266i	$-0.512195\pi$
$617$	−22.9229	−	13.2345i	−0.922841	−	0.532803i	−0.884540	+	0.466464i	$0.845528\pi$
$618$		0			0
$619$	−31.0039			−1.24615			−0.623075	−	0.782162i	$-0.714117\pi$
$619$	−31.0039			−1.24615			−0.623075	+	0.782162i	$0.714117\pi$
$620$		0			0
$621$	−3.16324	−	5.47890i	−0.126937	−	0.219861i
$622$		0			0
$623$		−	36.9030i		−	1.47849i
$624$		0			0
$625$	1.83869	+	24.9323i	0.0735475	+	0.997292i
$626$		0			0
$627$	1.61621	−	0.933121i	0.0645453	−	0.0372653i
$628$		0			0
$629$	1.49807			0.0597320
$630$		0			0
$631$	−10.3566	+	17.9381i	−0.412288	+	0.714104i	−0.995140	−	0.0984745i	$-0.968604\pi$
$631$	−10.3566	+	17.9381i	−0.412288	+	0.714104i	0.582851	+	0.812579i	$0.301937\pi$
$632$		0			0
$633$	−26.1362	−	15.0897i	−1.03882	−	0.599763i
$634$		0			0
$635$	−5.73149	−	38.1026i	−0.227447	−	1.51206i
$636$		0			0
$637$	2.84563	+	5.16315i	0.112748	+	0.204571i
$638$		0			0
$639$	−2.15430	−	3.73136i	−0.0852229	−	0.147610i
$640$		0			0
$641$	−10.5947	+	18.3506i	−0.418467	+	0.724806i	−0.995785	−	0.0917132i	$-0.970766\pi$
$641$	−10.5947	+	18.3506i	−0.418467	+	0.724806i	0.577319	+	0.816519i	$0.304099\pi$
$642$		0			0
$643$	9.98843	+	5.76682i	0.393905	+	0.227421i	0.683851	−	0.729622i	$-0.260304\pi$
$643$	9.98843	+	5.76682i	0.393905	+	0.227421i	−0.289946	+	0.957043i	$0.593637\pi$
$644$		0			0
$645$	2.40660	−	6.12658i	0.0947598	−	0.241234i
$646$		0			0
$647$	30.1779	−	17.4232i	1.18641	−	0.684977i	0.228925	−	0.973444i	$-0.426479\pi$
$647$	30.1779	−	17.4232i	1.18641	−	0.684977i	0.957490	+	0.288467i	$0.0931456\pi$
$648$		0			0
$649$	4.82456			0.189380
$650$		0			0
$651$	56.6953			2.22206
$652$		0			0
$653$	−19.3324	+	11.1616i	−0.756537	+	0.436787i	−0.828051	−	0.560653i	$-0.810550\pi$
$653$	−19.3324	+	11.1616i	−0.756537	+	0.436787i	0.0715139	+	0.997440i	$0.477217\pi$
$654$		0			0
$655$	8.17544	−	20.8125i	0.319441	−	0.813214i
$656$		0			0
$657$	−14.6223	−	8.44221i	−0.570471	−	0.329362i
$658$		0			0
$659$	0.433420	−	0.750705i	0.0168836	−	0.0292433i	−0.857460	−	0.514550i	$-0.827959\pi$
$659$	0.433420	−	0.750705i	0.0168836	−	0.0292433i	0.874344	+	0.485307i	$0.161292\pi$
$660$		0			0
$661$	−6.65430	−	11.5256i	−0.258822	−	0.448293i	0.707104	−	0.707109i	$-0.250001\pi$
$661$	−6.65430	−	11.5256i	−0.258822	−	0.448293i	−0.965927	+	0.258816i	$0.916668\pi$
$662$		0			0
$663$	−9.49907	−	0.188859i	−0.368913	−	0.00733469i
$664$		0			0
$665$	−1.33407	−	8.86879i	−0.0517328	−	0.343917i
$666$		0			0
$667$	−5.59346	−	3.22939i	−0.216580	−	0.125042i
$668$		0			0
$669$	0.00893993	−	0.0154844i	0.000345637	−	0.000598662i
$670$		0			0
$671$	−1.44176			−0.0556587
$672$		0			0
$673$	4.77457	−	2.75660i	0.184046	−	0.106259i	−0.405146	−	0.914252i	$-0.632779\pi$
$673$	4.77457	−	2.75660i	0.184046	−	0.106259i	0.589192	+	0.807993i	$0.299446\pi$
$674$		0			0
$675$	10.0000	−	10.7646i	0.384900	−	0.414331i
$676$		0			0
$677$		−	4.80479i		−	0.184663i	−0.995728	−	0.0923316i	$-0.970568\pi$
$677$		−	4.80479i		−	0.184663i	0.995728	−	0.0923316i	$-0.0294320\pi$
$678$		0			0
$679$	−21.7215	−	37.6227i	−0.833594	−	1.44383i
$680$		0			0
$681$	−24.2496			−0.929248
$682$		0			0
$683$	−10.1866	−	5.88126i	−0.389781	−	0.225040i	0.292284	−	0.956331i	$-0.405585\pi$
$683$	−10.1866	−	5.88126i	−0.389781	−	0.225040i	−0.682065	+	0.731291i	$0.738918\pi$
$684$		0			0
$685$	15.1648	−	12.0861i	0.579416	−	0.461788i
$686$		0			0
$687$	30.8393	−	17.8051i	1.17659	−	0.679306i
$688$		0			0
$689$	−0.0460332	+	2.31533i	−0.00175372	+	0.0882071i
$690$		0			0
$691$	2.43342	+	4.21481i	0.0925717	+	0.160339i	0.908593	−	0.417684i	$-0.137158\pi$
$691$	2.43342	+	4.21481i	0.0925717	+	0.160339i	−0.816021	+	0.578022i	$0.803825\pi$
$692$		0			0
$693$	−2.64265	−	1.52574i	−0.100386	−	0.0579579i
$694$		0			0
$695$	−19.9661	−	25.0519i	−0.757356	−	0.950272i
$696$		0			0
$697$		−	12.1925i		−	0.461825i
$698$		0			0
$699$	7.48079	+	12.9571i	0.282949	+	0.490083i
$700$		0			0
$701$	21.3828			0.807617			0.403808	−	0.914844i	$-0.367686\pi$
$701$	21.3828			0.807617			0.403808	+	0.914844i	$0.367686\pi$
$702$		0			0
$703$		−	1.67059i		−	0.0630076i
$704$		0			0
$705$	29.3429	−	4.41383i	1.10512	−	0.166235i
$706$		0			0
$707$		−	38.8822i		−	1.46232i
$708$		0			0
$709$	−13.0582	+	22.6175i	−0.490412	+	0.849419i	−0.999939	−	0.0110357i	$-0.996487\pi$
$709$	−13.0582	+	22.6175i	−0.490412	+	0.849419i	0.509527	+	0.860455i	$0.329820\pi$
$710$		0			0
$711$	0.848960	−	1.47044i	0.0318385	−	0.0551459i
$712$		0			0
$713$	−16.7087	+	9.64680i	−0.625748	+	0.361276i
$714$		0			0
$715$	5.07743	−	0.660834i	0.189885	−	0.0247138i
$716$		0			0
$717$	7.45795	−	4.30585i	0.278522	−	0.160805i
$718$		0			0
$719$	−18.3387	+	31.7635i	−0.683918	+	1.18458i	0.289858	+	0.957070i	$0.406392\pi$
$719$	−18.3387	+	31.7635i	−0.683918	+	1.18458i	−0.973776	+	0.227510i	$0.926941\pi$
$720$		0			0
$721$	16.1159	−	27.9135i	0.600187	−	1.03955i
$722$		0			0
$723$			42.5679i			1.58312i
$724$		0			0
$725$	3.34648	−	14.6219i	0.124285	−	0.543045i
$726$		0			0
$727$			26.2596i			0.973916i	0.873425	+	0.486958i	$0.161893\pi$
$727$			26.2596i			0.973916i	−0.873425	+	0.486958i	$0.838107\pi$
$728$		0			0
$729$	−0.614542			−0.0227608
$730$		0			0
$731$	0.836758	+	1.44931i	0.0309486	+	0.0536046i
$732$		0			0
$733$		−	31.7811i		−	1.17386i	−0.809637	−	0.586931i	$-0.800336\pi$
$733$		−	31.7811i		−	1.17386i	0.809637	−	0.586931i	$-0.199664\pi$
$734$		0			0
$735$	−6.15561	+	4.90595i	−0.227053	+	0.180959i
$736$		0			0
$737$	−4.41654	−	2.54989i	−0.162685	−	0.0939265i
$738$		0			0
$739$	17.0685	+	29.5635i	0.627875	+	1.08751i	0.987977	+	0.154599i	$0.0494085\pi$
$739$	17.0685	+	29.5635i	0.627875	+	1.08751i	−0.360102	+	0.932913i	$0.617258\pi$
$740$		0			0
$741$	−0.210609	+	10.5930i	−0.00773691	+	0.389144i
$742$		0			0
$743$	2.70254	−	1.56031i	0.0991465	−	0.0572423i	−0.449607	−	0.893227i	$-0.648436\pi$
$743$	2.70254	−	1.56031i	0.0991465	−	0.0572423i	0.548753	+	0.835984i	$0.315103\pi$
$744$		0			0
$745$	−23.9079	−	29.9978i	−0.875917	−	1.09903i
$746$		0			0
$747$	−16.7732	−	9.68401i	−0.613699	−	0.354320i
$748$		0			0
$749$	−31.3649			−1.14605
$750$		0			0
$751$	0.742024	+	1.28522i	0.0270769	+	0.0468985i	0.879246	−	0.476367i	$-0.158047\pi$
$751$	0.742024	+	1.28522i	0.0270769	+	0.0468985i	−0.852169	+	0.523266i	$0.824713\pi$
$752$		0			0
$753$		−	7.90881i		−	0.288213i
$754$		0			0
$755$	−17.4814	+	44.5030i	−0.636213	+	1.61963i
$756$		0			0
$757$	4.41654	−	2.54989i	0.160522	−	0.0926774i	−0.417587	−	0.908637i	$-0.637124\pi$
$757$	4.41654	−	2.54989i	0.160522	−	0.0926774i	0.578109	+	0.815960i	$0.303791\pi$
$758$		0			0
$759$	2.94369			0.106849
$760$		0			0
$761$	14.8931	−	25.7955i	0.539873	−	0.935088i	−0.459037	−	0.888417i	$-0.651806\pi$
$761$	14.8931	−	25.7955i	0.539873	−	0.935088i	0.998910	−	0.0466707i	$-0.0148611\pi$
$762$		0			0
$763$	8.32215	+	4.80479i	0.301282	+	0.173945i
$764$		0			0
$765$	−0.665652	−	4.42521i	−0.0240667	−	0.159994i
$766$		0			0
$767$	−14.1639	+	23.4437i	−0.511428	+	0.846501i
$768$		0			0
$769$	9.54930	+	16.5399i	0.344356	+	0.596443i	0.985237	−	0.171198i	$-0.0547638\pi$
$769$	9.54930	+	16.5399i	0.344356	+	0.596443i	−0.640880	+	0.767641i	$0.721430\pi$
$770$		0			0
$771$	14.2791	−	24.7322i	0.514250	−	0.890707i
$772$		0			0
$773$	42.6350	+	24.6153i	1.53347	+	0.885351i	0.999198	+	0.0400400i	$0.0127485\pi$
$773$	42.6350	+	24.6153i	1.53347	+	0.885351i	0.534275	+	0.845311i	$0.320585\pi$
$774$		0			0
$775$	−32.8284	−	30.4966i	−1.17923	−	1.09547i
$776$		0			0
$777$	−6.70593	+	3.87167i	−0.240574	+	0.138895i
$778$		0			0
$779$	−13.5967			−0.487151
$780$		0			0
$781$	−1.67352			−0.0598831
$782$		0			0
$783$	−7.63458	+	4.40783i	−0.272838	+	0.157523i
$784$		0			0
$785$	−38.2215	−	15.0139i	−1.36418	−	0.535869i
$786$		0			0
$787$	−8.47263	−	4.89168i	−0.302017	−	0.174369i	0.341332	−	0.939943i	$-0.389122\pi$
$787$	−8.47263	−	4.89168i	−0.302017	−	0.174369i	−0.643349	+	0.765573i	$0.722455\pi$
$788$		0			0
$789$	32.5851	−	56.4390i	1.16006	−	2.00928i
$790$		0			0
$791$	8.12482	+	14.0726i	0.288885	+	0.500364i
$792$		0			0
$793$	4.23272	−	7.00587i	0.150308	−	0.248786i
$794$		0			0
$795$	−3.05762	+	0.459934i	−0.108442	+	0.0163122i
$796$		0			0
$797$	−14.3216	−	8.26856i	−0.507296	−	0.292887i	0.224426	−	0.974491i	$-0.427949\pi$
$797$	−14.3216	−	8.26856i	−0.507296	−	0.292887i	−0.731721	+	0.681604i	$0.761283\pi$
$798$		0			0
$799$	−3.77211	+	6.53348i	−0.133448	+	0.231138i
$800$		0			0
$801$	−20.5338			−0.725527
$802$		0			0
$803$	−5.67950	+	3.27906i	−0.200425	+	0.115715i
$804$		0			0
$805$	5.17218	−	13.1670i	0.182295	−	0.464077i
$806$		0			0
$807$			47.9018i			1.68622i
$808$		0			0
$809$	−15.9212	−	27.5764i	−0.559760	−	0.969533i	−0.997516	−	0.0704392i	$-0.977560\pi$
$809$	−15.9212	−	27.5764i	−0.559760	−	0.969533i	0.437756	−	0.899094i	$-0.355773\pi$
$810$		0			0
$811$	−13.3470			−0.468678			−0.234339	−	0.972155i	$-0.575293\pi$
$811$	−13.3470			−0.468678			−0.234339	+	0.972155i	$0.575293\pi$
$812$		0			0
$813$	−22.0539	−	12.7328i	−0.773465	−	0.446560i
$814$		0			0
$815$	7.01356	−	5.58973i	0.245674	−	0.195800i
$816$		0			0
$817$	1.61621	−	0.933121i	0.0565441	−	0.0326458i
$818$		0			0
$819$	15.1722	−	8.36203i	0.530159	−	0.292193i
$820$		0			0
$821$	−5.83676	−	10.1096i	−0.203704	−	0.352826i	0.746015	−	0.665929i	$-0.231965\pi$
$821$	−5.83676	−	10.1096i	−0.203704	−	0.352826i	−0.949719	+	0.313103i	$0.898631\pi$
$822$		0			0
$823$	−28.0867	−	16.2159i	−0.979041	−	0.565249i	−0.0770602	−	0.997026i	$-0.524553\pi$
$823$	−28.0867	−	16.2159i	−0.979041	−	0.565249i	−0.901980	+	0.431777i	$0.857887\pi$
$824$		0			0
$825$	2.01122	+	6.53396i	0.0700216	+	0.227483i
$826$		0			0
$827$		−	27.3319i		−	0.950425i	−0.879871	−	0.475212i	$-0.842371\pi$
$827$		−	27.3319i		−	0.950425i	0.879871	−	0.475212i	$-0.157629\pi$
$828$		0			0
$829$	1.77018	+	3.06604i	0.0614808	+	0.106488i	0.895128	−	0.445810i	$-0.147084\pi$
$829$	1.77018	+	3.06604i	0.0614808	+	0.106488i	−0.833647	+	0.552298i	$0.813751\pi$
$830$		0			0
$831$	−36.1370			−1.25358
$832$		0			0
$833$		−	2.00128i		−	0.0693402i
$834$		0			0
$835$	0.977401	+	6.49770i	0.0338244	+	0.224862i
$836$		0			0
$837$			26.3341i			0.910238i
$838$		0			0
$839$	−22.3950	+	38.7893i	−0.773161	+	1.33915i	0.162661	+	0.986682i	$0.447992\pi$
$839$	−22.3950	+	38.7893i	−0.773161	+	1.33915i	−0.935822	+	0.352472i	$0.885341\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$		0			0
$843$	−19.7574	+	11.4069i	−0.680479	+	0.392875i
$844$		0			0
$845$	−11.6951	+	26.6125i	−0.402324	+	0.915497i
$846$		0			0
$847$	26.9670	−	15.5694i	0.926598	−	0.534972i
$848$		0			0
$849$	−9.48973	+	16.4367i	−0.325687	+	0.564106i
$850$		0			0
$851$	1.31754	−	2.28205i	0.0451648	−	0.0782278i
$852$		0			0
$853$			31.3732i			1.07420i	0.843519	+	0.537099i	$0.180480\pi$
$853$			31.3732i			1.07420i	−0.843519	+	0.537099i	$0.819520\pi$
$854$		0			0
$855$	−4.93483	+	0.742310i	−0.168768	+	0.0253865i
$856$		0			0
$857$		−	21.2813i		−	0.726955i	−0.931603	−	0.363478i	$-0.881589\pi$
$857$		−	21.2813i		−	0.726955i	0.931603	−	0.363478i	$-0.118411\pi$
$858$		0			0
$859$	56.8502			1.93970			0.969851	−	0.243698i	$-0.0783607\pi$
$859$	56.8502			1.93970			0.969851	+	0.243698i	$0.0783607\pi$
$860$		0			0
$861$	31.5109	+	54.5784i	1.07389	+	1.86003i
$862$		0			0
$863$			32.8011i			1.11656i	0.829651	+	0.558282i	$0.188539\pi$
$863$			32.8011i			1.11656i	−0.829651	+	0.558282i	$0.811461\pi$
$864$		0			0
$865$	2.39092	−	1.90553i	0.0812936	−	0.0647901i
$866$		0			0
$867$	−28.9032	−	16.6873i	−0.981603	−	0.566729i
$868$		0			0
$869$	−0.329747	−	0.571138i	−0.0111859	−	0.0193745i
$870$		0			0
$871$	25.3566	−	13.9751i	0.859174	−	0.473527i
$872$		0			0
$873$	−20.9343	+	12.0864i	−0.708518	+	0.409063i
$874$		0			0
$875$	32.7599	+	2.48432i	1.10749	+	0.0839854i
$876$		0			0
$877$	31.2333	+	18.0325i	1.05467	+	0.608916i	0.923954	−	0.382504i	$-0.124938\pi$
$877$	31.2333	+	18.0325i	1.05467	+	0.608916i	0.130719	+	0.991419i	$0.458271\pi$
$878$		0			0
$879$	−60.8257			−2.05160
$880$		0			0
$881$	23.0198	+	39.8715i	0.775557	+	1.34330i	0.934481	+	0.356013i	$0.115864\pi$
$881$	23.0198	+	39.8715i	0.775557	+	1.34330i	−0.158924	+	0.987291i	$0.550802\pi$
$882$		0			0
$883$			0.802236i			0.0269974i	0.999909	+	0.0134987i	$0.00429690\pi$
$883$			0.802236i			0.0269974i	−0.999909	+	0.0134987i	$0.995703\pi$
$884$		0			0
$885$	−34.0390	−	13.3710i	−1.14421	−	0.449461i
$886$		0			0
$887$	−7.12365	+	4.11284i	−0.239189	+	0.138096i	−0.614804	−	0.788680i	$-0.710765\pi$
$887$	−7.12365	+	4.11284i	−0.239189	+	0.138096i	0.375615	+	0.926776i	$0.377431\pi$
$888$		0			0
$889$	−50.6363			−1.69829
$890$		0			0
$891$	3.56658	−	6.17750i	0.119485	−	0.206954i
$892$		0			0
$893$	7.28589	+	4.20651i	0.243813	+	0.140766i
$894$		0			0
$895$	17.2166	−	2.58977i	0.575488	−	0.0865664i
$896$		0			0
$897$	−8.64207	+	14.3041i	−0.288550	+	0.477600i
$898$		0			0
$899$	13.4424	+	23.2829i	0.448328	+	0.776527i
$900$		0			0
$901$	0.393064	−	0.680808i	0.0130949	−	0.0226810i
$902$		0			0
$903$	−7.49129	−	4.32510i	−0.249295	−	0.143930i
$904$		0			0
$905$	3.16131	−	8.04788i	0.105086	−	0.267521i
$906$		0			0
$907$	26.3583	−	15.2180i	0.875213	−	0.505305i	0.00613601	−	0.999981i	$-0.498047\pi$
$907$	26.3583	−	15.2180i	0.875213	−	0.505305i	0.869077	+	0.494677i	$0.164714\pi$
$908$		0			0
$909$	−21.6351			−0.717591
$910$		0			0
$911$	−43.6145			−1.44501			−0.722507	−	0.691363i	$-0.757010\pi$
$911$	−43.6145			−1.44501			−0.722507	+	0.691363i	$0.757010\pi$
$912$		0			0
$913$	−6.51492	+	3.76139i	−0.215612	+	0.124484i
$914$		0			0
$915$	10.1722	+	3.99577i	0.336282	+	0.132096i
$916$		0			0
$917$	−25.4486	−	14.6928i	−0.840387	−	0.485198i
$918$		0			0
$919$	18.5109	−	32.0618i	0.610617	−	1.05762i	−0.380519	−	0.924773i	$-0.624255\pi$
$919$	18.5109	−	32.0618i	0.610617	−	1.05762i	0.991137	−	0.132847i	$-0.0424119\pi$
$920$		0			0
$921$	−13.6947	−	23.7198i	−0.451254	−	0.781595i
$922$		0			0
$923$	4.91309	−	8.13201i	0.161716	−	0.267668i
$924$		0			0
$925$	5.96554	+	1.36532i	0.196146	+	0.0448914i
$926$		0			0
$927$	−15.5318	−	8.96730i	−0.510132	−	0.294525i
$928$		0			0
$929$	−2.38412	+	4.12942i	−0.0782206	+	0.135482i	−0.902482	−	0.430727i	$-0.858257\pi$
$929$	−2.38412	+	4.12942i	−0.0782206	+	0.135482i	0.824262	+	0.566209i	$0.191591\pi$
$930$		0			0
$931$	−2.23175			−0.0731427
$932$		0			0
$933$	−52.0624	+	30.0582i	−1.70445	+	0.984062i
$934$		0			0
$935$	−1.61780	−	0.635495i	−0.0529079	−	0.0207829i
$936$		0			0
$937$			43.6264i			1.42521i	0.701565	+	0.712606i	$0.252485\pi$
$937$			43.6264i			1.42521i	−0.701565	+	0.712606i	$0.747515\pi$
$938$		0			0
$939$	−26.4602	−	45.8305i	−0.863497	−	1.49562i
$940$		0			0
$941$	18.2675			0.595504			0.297752	−	0.954643i	$-0.403763\pi$
$941$	18.2675			0.595504			0.297752	+	0.954643i	$0.403763\pi$
$942$		0			0
$943$	−18.5732	−	10.7233i	−0.604828	−	0.349197i
$944$		0			0
$945$	−12.0343	−	15.0997i	−0.391475	−	0.491192i
$946$		0			0
$947$	17.3057	−	9.99146i	0.562360	−	0.324679i	−0.191732	−	0.981447i	$-0.561410\pi$
$947$	17.3057	−	9.99146i	0.562360	−	0.324679i	0.754092	+	0.656769i	$0.228077\pi$
$948$		0			0
$949$	0.740096	−	37.2246i	0.0240245	−	1.20836i
$950$		0			0
$951$	−0.252298	−	0.436993i	−0.00818132	−	0.0141705i
$952$		0			0
$953$	−34.5228	−	19.9317i	−1.11830	−	0.645652i	−0.177335	−	0.984150i	$-0.556748\pi$
$953$	−34.5228	−	19.9317i	−1.11830	−	0.645652i	−0.940967	+	0.338498i	$0.890081\pi$
$954$		0			0
$955$	6.88976	+	8.64475i	0.222948	+	0.279737i
$956$		0			0
$957$		−	4.10190i		−	0.132596i
$958$		0			0
$959$	−12.7420	−	22.0698i	−0.411461	−	0.712672i
$960$		0			0
$961$	49.3098			1.59064
$962$		0			0
$963$			17.4523i			0.562392i
$964$		0			0
$965$	1.64858	+	10.9596i	0.0530696	+	0.352803i
$966$		0			0
$967$			43.8607i			1.41047i	0.708975	+	0.705233i	$0.249158\pi$
$967$			43.8607i			1.41047i	−0.708975	+	0.705233i	$0.750842\pi$
$968$		0			0
$969$	1.79833	−	3.11480i	0.0577707	−	0.100062i
$970$		0			0
$971$	30.4897	−	52.8098i	0.978462	−	1.69475i	0.310459	−	0.950587i	$-0.399517\pi$
$971$	30.4897	−	52.8098i	0.978462	−	1.69475i	0.668002	−	0.744159i	$-0.267150\pi$
$972$		0			0
$973$	−36.4589	+	21.0496i	−1.16882	+	0.674818i
$974$		0			0
$975$	−37.6546	−	9.40937i	−1.20591	−	0.301341i
$976$		0			0
$977$	44.4875	−	25.6849i	1.42328	−	0.821731i	0.426703	−	0.904392i	$-0.359675\pi$
$977$	44.4875	−	25.6849i	1.42328	−	0.821731i	0.996578	+	0.0826604i	$0.0263417\pi$
$978$		0			0
$979$	−3.98780	+	6.90707i	−0.127451	+	0.220751i
$980$		0			0
$981$	2.67352	−	4.63066i	0.0853588	−	0.147846i
$982$		0			0
$983$			37.3026i			1.18977i	0.803811	+	0.594885i	$0.202802\pi$
$983$			37.3026i			1.18977i	−0.803811	+	0.594885i	$0.797198\pi$
$984$		0			0
$985$	−2.24363	−	14.9155i	−0.0714880	−	0.475248i
$986$		0			0
$987$		−	38.9951i		−	1.24123i
$988$		0			0
$989$	2.94369			0.0936040
$990$		0			0
$991$	−25.7810	−	44.6541i	−0.818962	−	1.41848i	−0.906448	−	0.422318i	$-0.861217\pi$
$991$	−25.7810	−	44.6541i	−0.818962	−	1.41848i	0.0874859	−	0.996166i	$-0.472117\pi$
$992$		0			0
$993$			39.4556i			1.25208i
$994$		0			0
$995$	−7.21274	−	9.05000i	−0.228659	−	0.286904i
$996$		0			0
$997$	−19.8743	−	11.4744i	−0.629425	−	0.363399i	0.151104	−	0.988518i	$-0.451717\pi$
$997$	−19.8743	−	11.4744i	−0.629425	−	0.363399i	−0.780529	+	0.625119i	$0.785050\pi$
$998$		0			0
$999$	−1.79833	−	3.11480i	−0.0568967	−	0.0985479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.dh.a.289.5		12
4.3	odd	2		65.2.n.a.29.6	yes	12
5.4	even	2	inner	1040.2.dh.a.289.2		12
12.11	even	2		585.2.bs.a.289.1		12
13.9	even	3	inner	1040.2.dh.a.529.2		12
20.3	even	4		325.2.e.e.276.1		12
20.7	even	4		325.2.e.e.276.6		12
20.19	odd	2		65.2.n.a.29.1	yes	12
52.3	odd	6		845.2.b.d.339.6		6
52.7	even	12		845.2.l.f.654.12		24
52.11	even	12		845.2.d.d.844.1		12
52.15	even	12		845.2.d.d.844.11		12
52.19	even	12		845.2.l.f.654.2		24
52.23	odd	6		845.2.b.e.339.1		6
52.31	even	4		845.2.l.f.699.1		24
52.35	odd	6		65.2.n.a.9.1	✓	12
52.43	odd	6		845.2.n.e.529.6		12
52.47	even	4		845.2.l.f.699.11		24
52.51	odd	2		845.2.n.e.484.1		12
60.59	even	2		585.2.bs.a.289.6		12
65.9	even	6	inner	1040.2.dh.a.529.5		12
156.35	even	6		585.2.bs.a.334.6		12
260.3	even	12		4225.2.a.br.1.6		6
260.19	even	12		845.2.l.f.654.11		24
260.23	even	12		4225.2.a.bq.1.1		6
260.59	even	12		845.2.l.f.654.1		24
260.87	even	12		325.2.e.e.126.6		12
260.99	even	4		845.2.l.f.699.2		24
260.107	even	12		4225.2.a.br.1.1		6
260.119	even	12		845.2.d.d.844.2		12
260.127	even	12		4225.2.a.bq.1.6		6
260.139	odd	6		65.2.n.a.9.6	yes	12
260.159	odd	6		845.2.b.d.339.1		6
260.179	odd	6		845.2.b.e.339.6		6
260.199	odd	6		845.2.n.e.529.1		12
260.219	even	12		845.2.d.d.844.12		12
260.239	even	4		845.2.l.f.699.12		24
260.243	even	12		325.2.e.e.126.1		12
260.259	odd	2		845.2.n.e.484.6		12
780.659	even	6		585.2.bs.a.334.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.1	✓	12	52.35	odd	6
65.2.n.a.9.6	yes	12	260.139	odd	6
65.2.n.a.29.1	yes	12	20.19	odd	2
65.2.n.a.29.6	yes	12	4.3	odd	2
325.2.e.e.126.1		12	260.243	even	12
325.2.e.e.126.6		12	260.87	even	12
325.2.e.e.276.1		12	20.3	even	4
325.2.e.e.276.6		12	20.7	even	4
585.2.bs.a.289.1		12	12.11	even	2
585.2.bs.a.289.6		12	60.59	even	2
585.2.bs.a.334.1		12	780.659	even	6
585.2.bs.a.334.6		12	156.35	even	6
845.2.b.d.339.1		6	260.159	odd	6
845.2.b.d.339.6		6	52.3	odd	6
845.2.b.e.339.1		6	52.23	odd	6
845.2.b.e.339.6		6	260.179	odd	6
845.2.d.d.844.1		12	52.11	even	12
845.2.d.d.844.2		12	260.119	even	12
845.2.d.d.844.11		12	52.15	even	12
845.2.d.d.844.12		12	260.219	even	12
845.2.l.f.654.1		24	260.59	even	12
845.2.l.f.654.2		24	52.19	even	12
845.2.l.f.654.11		24	260.19	even	12
845.2.l.f.654.12		24	52.7	even	12
845.2.l.f.699.1		24	52.31	even	4
845.2.l.f.699.2		24	260.99	even	4
845.2.l.f.699.11		24	52.47	even	4
845.2.l.f.699.12		24	260.239	even	4
845.2.n.e.484.1		12	52.51	odd	2
845.2.n.e.484.6		12	260.259	odd	2
845.2.n.e.529.1		12	260.199	odd	6
845.2.n.e.529.6		12	52.43	odd	6
1040.2.dh.a.289.2		12	5.4	even	2	inner
1040.2.dh.a.289.5		12	1.1	even	1	trivial
1040.2.dh.a.529.2		12	13.9	even	3	inner
1040.2.dh.a.529.5		12	65.9	even	6	inner
4225.2.a.bq.1.1		6	260.23	even	12
4225.2.a.bq.1.6		6	260.127	even	12
4225.2.a.br.1.1		6	260.107	even	12
4225.2.a.br.1.6		6	260.3	even	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.dh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.86449 - 1.07646i) q^{3} +(-0.817544 + 2.08125i) q^{5} +(2.54486 + 1.46928i) q^{7} +(0.817544 - 1.41603i) q^{9} +O(q^{10})\)	\(q+(1.86449 - 1.07646i) q^{3} +(-0.817544 + 2.08125i) q^{5} +(2.54486 + 1.46928i) q^{7} +(0.817544 - 1.41603i) q^{9} +(-0.317544 - 0.550003i) q^{11} +(3.60484 + 0.0716710i) q^{13} +(0.716091 + 4.76053i) q^{15} +(-1.05998 - 0.611979i) q^{17} +(-0.682456 + 1.18205i) q^{19} +6.32648 q^{21} +(-1.86449 + 1.07646i) q^{23} +(-3.66324 - 3.40304i) q^{25} +2.93855i q^{27} +(1.50000 + 2.59808i) q^{29} +8.96157 q^{31} +(-1.18412 - 0.683650i) q^{33} +(-5.13847 + 4.09531i) q^{35} +(-1.05998 + 0.611979i) q^{37} +(6.79833 - 3.74685i) q^{39} +(4.98079 + 8.62698i) q^{41} +(-1.18412 - 0.683650i) q^{43} +(2.27874 + 2.85918i) q^{45} -6.16379i q^{47} +(0.817544 + 1.41603i) q^{49} -2.63509 q^{51} +0.642285i q^{53} +(1.40430 - 0.211239i) q^{55} +2.93855i q^{57} +(-3.79833 + 6.57890i) q^{59} +(1.13509 - 1.96603i) q^{61} +(4.16107 - 2.40240i) q^{63} +(-3.09628 + 7.44399i) q^{65} +(6.95421 - 4.01502i) q^{67} +(-2.31754 + 4.01410i) q^{69} +(1.31754 - 2.28205i) q^{71} -10.3263i q^{73} +(-10.4933 - 2.40158i) q^{75} -1.86624i q^{77} +1.03843 q^{79} +(5.61588 + 9.72698i) q^{81} -11.8452i q^{83} +(2.14026 - 1.70576i) q^{85} +(5.59346 + 3.22939i) q^{87} +(-6.27912 - 10.8758i) q^{89} +(9.06851 + 5.47890i) q^{91} +(16.7087 - 9.64680i) q^{93} +(-1.90220 - 2.38674i) q^{95} +(-12.8031 - 7.39190i) q^{97} -1.03843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{5} + 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^5 + 6 * q^9	\( 12 q - 6 q^{5} + 6 q^{9} + 4 q^{15} - 12 q^{19} - 8 q^{21} - 2 q^{25} + 18 q^{29} + 16 q^{31} - 10 q^{35} + 32 q^{39} + 14 q^{41} - 29 q^{45} + 6 q^{49} - 24 q^{51} + 26 q^{55} + 4 q^{59} + 6 q^{61} + 23 q^{65} - 24 q^{69} + 12 q^{71} - 2 q^{75} + 104 q^{79} + 14 q^{81} + 21 q^{85} + 20 q^{89} + 44 q^{91} - 20 q^{95} - 104 q^{99}+O(q^{100}) \) 12 * q - 6 * q^5 + 6 * q^9 + 4 * q^15 - 12 * q^19 - 8 * q^21 - 2 * q^25 + 18 * q^29 + 16 * q^31 - 10 * q^35 + 32 * q^39 + 14 * q^41 - 29 * q^45 + 6 * q^49 - 24 * q^51 + 26 * q^55 + 4 * q^59 + 6 * q^61 + 23 * q^65 - 24 * q^69 + 12 * q^71 - 2 * q^75 + 104 * q^79 + 14 * q^81 + 21 * q^85 + 20 * q^89 + 44 * q^91 - 20 * q^95 - 104 * q^99

Introduction

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