LMFDB - Embedded newform 1071.2.n.a.64.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1071,2,Mod(64,1071)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1071, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("1071.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1071 = 3^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1071.n (of order $4$, degree $2$, 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:	$8.55197805648$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.125772815663104.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 27x^{8} + 107x^{4} + 1 $ x^12 + 27x^8 + 107x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 357)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			64.3
Root			$-1.04736 + 1.04736i$ of defining polynomial
Character	$\chi$	$=$	1071.64
Dual form			1071.2.n.a.820.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.569973i q^{2} +1.67513 q^{4} +(-0.119579 - 0.119579i) q^{5} +(-0.707107 + 0.707107i) q^{7} -2.09473i q^{8} +O(q^{10})$	\(q-0.569973i q^{2} +1.67513 q^{4} +(-0.119579 - 0.119579i) q^{5} +(-0.707107 + 0.707107i) q^{7} -2.09473i q^{8} +(-0.0681566 + 0.0681566i) q^{10} +(2.80282 - 2.80282i) q^{11} +1.71728 q^{13} +(0.403032 + 0.403032i) q^{14} +2.15633 q^{16} +(-3.82883 + 1.52973i) q^{17} -2.80663i q^{19} +(-0.200310 - 0.200310i) q^{20} +(-1.59753 - 1.59753i) q^{22} +(1.19368 - 1.19368i) q^{23} -4.97140i q^{25} -0.978806i q^{26} +(-1.18450 + 1.18450i) q^{28} +(3.57097 + 3.57097i) q^{29} +(6.60249 + 6.60249i) q^{31} -5.41850i q^{32} +(0.871906 + 2.18233i) q^{34} +0.169110 q^{35} +(-3.66289 - 3.66289i) q^{37} -1.59970 q^{38} +(-0.250484 + 0.250484i) q^{40} +(1.15078 - 1.15078i) q^{41} -8.18347i q^{43} +(4.69510 - 4.69510i) q^{44} +(-0.680366 - 0.680366i) q^{46} +2.47379 q^{47} -1.00000i q^{49} -2.83356 q^{50} +2.87668 q^{52} +4.82337i q^{53} -0.670316 q^{55} +(1.48119 + 1.48119i) q^{56} +(2.03535 - 2.03535i) q^{58} -4.45824i q^{59} +(2.83555 - 2.83555i) q^{61} +(3.76324 - 3.76324i) q^{62} +1.22425 q^{64} +(-0.205351 - 0.205351i) q^{65} -7.86892 q^{67} +(-6.41379 + 2.56250i) q^{68} -0.0963880i q^{70} +(8.00718 + 8.00718i) q^{71} +(7.42943 + 7.42943i) q^{73} +(-2.08775 + 2.08775i) q^{74} -4.70147i q^{76} +3.96379i q^{77} +(2.56368 - 2.56368i) q^{79} +(-0.257850 - 0.257850i) q^{80} +(-0.655913 - 0.655913i) q^{82} +17.1221i q^{83} +(0.640769 + 0.274923i) q^{85} -4.66435 q^{86} +(-5.87115 - 5.87115i) q^{88} -4.76283 q^{89} +(-1.21430 + 1.21430i) q^{91} +(1.99957 - 1.99957i) q^{92} -1.40999i q^{94} +(-0.335613 + 0.335613i) q^{95} +(-12.1037 - 12.1037i) q^{97} -0.569973 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{5}+O(q^{10}) $ 12 * q - 8 * q^5	$ 12 q - 8 q^{5} - 16 q^{10} - 4 q^{11} + 4 q^{13} + 4 q^{14} - 16 q^{16} - 20 q^{17} - 12 q^{20} + 32 q^{22} - 4 q^{23} + 32 q^{29} - 8 q^{31} + 20 q^{34} + 12 q^{35} - 16 q^{37} + 16 q^{38} + 12 q^{40} + 20 q^{41} + 8 q^{44} - 12 q^{46} - 32 q^{47} - 48 q^{50} - 16 q^{52} + 76 q^{55} - 4 q^{56} - 28 q^{58} - 20 q^{61} + 28 q^{62} + 8 q^{64} + 44 q^{65} - 56 q^{67} - 12 q^{68} + 16 q^{71} + 8 q^{73} - 8 q^{74} - 24 q^{79} + 8 q^{80} + 12 q^{82} - 24 q^{85} + 32 q^{86} + 12 q^{88} - 64 q^{89} + 4 q^{91} - 24 q^{92} + 36 q^{95} - 52 q^{97}+O(q^{100}) $ 12 * q - 8 * q^5 - 16 * q^10 - 4 * q^11 + 4 * q^13 + 4 * q^14 - 16 * q^16 - 20 * q^17 - 12 * q^20 + 32 * q^22 - 4 * q^23 + 32 * q^29 - 8 * q^31 + 20 * q^34 + 12 * q^35 - 16 * q^37 + 16 * q^38 + 12 * q^40 + 20 * q^41 + 8 * q^44 - 12 * q^46 - 32 * q^47 - 48 * q^50 - 16 * q^52 + 76 * q^55 - 4 * q^56 - 28 * q^58 - 20 * q^61 + 28 * q^62 + 8 * q^64 + 44 * q^65 - 56 * q^67 - 12 * q^68 + 16 * q^71 + 8 * q^73 - 8 * q^74 - 24 * q^79 + 8 * q^80 + 12 * q^82 - 24 * q^85 + 32 * q^86 + 12 * q^88 - 64 * q^89 + 4 * q^91 - 24 * q^92 + 36 * q^95 - 52 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1071\mathbb{Z}\right)^\times$.

$n$	$190$	$596$	$766$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$		−	0.569973i		−	0.403032i	−0.979485	−	0.201516i	$-0.935413\pi$
$2$		−	0.569973i		−	0.403032i	0.979485	−	0.201516i	$-0.0645868\pi$
$3$		0			0
$3$		0			0
$4$	1.67513			0.837565
$5$	−0.119579	−	0.119579i	−0.0534772	−	0.0534772i	0.679862	−	0.733340i	$-0.262039\pi$
$5$	−0.119579	−	0.119579i	−0.0534772	−	0.0534772i	−0.733340	+	0.679862i	$0.762039\pi$
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$		−	2.09473i		−	0.740597i
$9$		0			0
$10$	−0.0681566	+	0.0681566i	−0.0215530	+	0.0215530i
$11$	2.80282	−	2.80282i	0.845083	−	0.845083i	−0.144431	−	0.989515i	$-0.546135\pi$
$11$	2.80282	−	2.80282i	0.845083	−	0.845083i	0.989515	+	0.144431i	$0.0461353\pi$
$12$		0			0
$13$	1.71728			0.476289			0.238145	−	0.971230i	$-0.423461\pi$
$13$	1.71728			0.476289			0.238145	+	0.971230i	$0.423461\pi$
$14$	0.403032	+	0.403032i	0.107715	+	0.107715i
$15$		0			0
$16$	2.15633			0.539081
$17$	−3.82883	+	1.52973i	−0.928627	+	0.371015i
$17$	−3.82883	+	1.52973i	−0.928627	+	0.371015i
$18$		0			0
$19$		−	2.80663i		−	0.643885i	−0.946759	−	0.321942i	$-0.895664\pi$
$19$		−	2.80663i		−	0.643885i	0.946759	−	0.321942i	$-0.104336\pi$
$20$	−0.200310	−	0.200310i	−0.0447907	−	0.0447907i
$21$		0			0
$22$	−1.59753	−	1.59753i	−0.340595	−	0.340595i
$23$	1.19368	−	1.19368i	0.248900	−	0.248900i	−0.571619	−	0.820519i	$-0.693685\pi$
$23$	1.19368	−	1.19368i	0.248900	−	0.248900i	0.820519	+	0.571619i	$0.193685\pi$
$24$		0			0
$25$		−	4.97140i		−	0.994280i
$26$		−	0.978806i		−	0.191960i
$27$		0			0
$28$	−1.18450	+	1.18450i	−0.223849	+	0.223849i
$29$	3.57097	+	3.57097i	0.663112	+	0.663112i	0.956112	−	0.293001i	$-0.0946538\pi$
$29$	3.57097	+	3.57097i	0.663112	+	0.663112i	−0.293001	+	0.956112i	$0.594654\pi$
$30$		0			0
$31$	6.60249	+	6.60249i	1.18584	+	1.18584i	0.978206	+	0.207636i	$0.0665768\pi$
$31$	6.60249	+	6.60249i	1.18584	+	1.18584i	0.207636	+	0.978206i	$0.433423\pi$
$32$		−	5.41850i		−	0.957864i
$33$		0			0
$34$	0.871906	+	2.18233i	0.149531	+	0.374266i
$35$	0.169110			0.0285848
$36$		0			0
$37$	−3.66289	−	3.66289i	−0.602175	−	0.602175i	0.338714	−	0.940889i	$-0.390008\pi$
$37$	−3.66289	−	3.66289i	−0.602175	−	0.602175i	−0.940889	+	0.338714i	$0.890008\pi$
$38$	−1.59970			−0.259506
$39$		0			0
$40$	−0.250484	+	0.250484i	−0.0396051	+	0.0396051i
$41$	1.15078	−	1.15078i	0.179721	−	0.179721i	−0.611513	−	0.791234i	$-0.709439\pi$
$41$	1.15078	−	1.15078i	0.179721	−	0.179721i	0.791234	+	0.611513i	$0.209439\pi$
$42$		0			0
$43$		−	8.18347i		−	1.24797i	−0.781438	−	0.623983i	$-0.785513\pi$
$43$		−	8.18347i		−	1.24797i	0.781438	−	0.623983i	$-0.214487\pi$
$44$	4.69510	−	4.69510i	0.707813	−	0.707813i
$45$		0			0
$46$	−0.680366	−	0.680366i	−0.100315	−	0.100315i
$47$	2.47379			0.360839			0.180420	−	0.983590i	$-0.442254\pi$
$47$	2.47379			0.360839			0.180420	+	0.983590i	$0.442254\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	−2.83356			−0.400727
$51$		0			0
$52$	2.87668			0.398923
$53$			4.82337i			0.662541i	0.943536	+	0.331271i	$0.107477\pi$
$53$			4.82337i			0.662541i	−0.943536	+	0.331271i	$0.892523\pi$
$54$		0			0
$55$	−0.670316			−0.0903854
$56$	1.48119	+	1.48119i	0.197933	+	0.197933i
$57$		0			0
$58$	2.03535	−	2.03535i	0.267255	−	0.267255i
$59$		−	4.45824i		−	0.580413i	−0.956964	−	0.290206i	$-0.906276\pi$
$59$		−	4.45824i		−	0.580413i	0.956964	−	0.290206i	$-0.0937240\pi$
$60$		0			0
$61$	2.83555	−	2.83555i	0.363055	−	0.363055i	−0.501881	−	0.864936i	$-0.667359\pi$
$61$	2.83555	−	2.83555i	0.363055	−	0.363055i	0.864936	+	0.501881i	$0.167359\pi$
$62$	3.76324	−	3.76324i	0.477932	−	0.477932i
$63$		0			0
$64$	1.22425			0.153032
$65$	−0.205351	−	0.205351i	−0.0254706	−	0.0254706i
$66$		0			0
$67$	−7.86892			−0.961341			−0.480671	−	0.876901i	$-0.659607\pi$
$67$	−7.86892			−0.961341			−0.480671	+	0.876901i	$0.659607\pi$
$68$	−6.41379	+	2.56250i	−0.777786	+	0.310749i
$69$		0			0
$70$		−	0.0963880i		−	0.0115206i
$71$	8.00718	+	8.00718i	0.950278	+	0.950278i	0.998821	−	0.0485433i	$-0.0154579\pi$
$71$	8.00718	+	8.00718i	0.950278	+	0.950278i	−0.0485433	+	0.998821i	$0.515458\pi$
$72$		0			0
$73$	7.42943	+	7.42943i	0.869549	+	0.869549i	0.992422	−	0.122873i	$-0.0392108\pi$
$73$	7.42943	+	7.42943i	0.869549	+	0.869549i	−0.122873	+	0.992422i	$0.539211\pi$
$74$	−2.08775	+	2.08775i	−0.242696	+	0.242696i
$75$		0			0
$76$		−	4.70147i		−	0.539296i
$77$			3.96379i			0.451716i
$78$		0			0
$79$	2.56368	−	2.56368i	0.288436	−	0.288436i	−0.548025	−	0.836462i	$-0.684620\pi$
$79$	2.56368	−	2.56368i	0.288436	−	0.288436i	0.836462	+	0.548025i	$0.184620\pi$
$80$	−0.257850	−	0.257850i	−0.0288286	−	0.0288286i
$81$		0			0
$82$	−0.655913	−	0.655913i	−0.0724334	−	0.0724334i
$83$			17.1221i			1.87940i	0.342001	+	0.939700i	$0.388895\pi$
$83$			17.1221i			1.87940i	−0.342001	+	0.939700i	$0.611105\pi$
$84$		0			0
$85$	0.640769	+	0.274923i	0.0695012	+	0.0298195i
$86$	−4.66435			−0.502970
$87$		0			0
$88$	−5.87115	−	5.87115i	−0.625866	−	0.625866i
$89$	−4.76283			−0.504859			−0.252430	−	0.967615i	$-0.581230\pi$
$89$	−4.76283			−0.504859			−0.252430	+	0.967615i	$0.581230\pi$
$90$		0			0
$91$	−1.21430	+	1.21430i	−0.127294	+	0.127294i
$92$	1.99957	−	1.99957i	0.208470	−	0.208470i
$93$		0			0
$94$		−	1.40999i		−	0.145430i
$95$	−0.335613	+	0.335613i	−0.0344332	+	0.0344332i
$96$		0			0
$97$	−12.1037	−	12.1037i	−1.22894	−	1.22894i	−0.964363	−	0.264581i	$-0.914766\pi$
$97$	−12.1037	−	12.1037i	−1.22894	−	1.22894i	−0.264581	−	0.964363i	$-0.585234\pi$
$98$	−0.569973			−0.0575760
$99$		0			0
$100$		−	8.32775i		−	0.832775i
$101$	−5.75753			−0.572895			−0.286448	−	0.958096i	$-0.592474\pi$
$101$	−5.75753			−0.572895			−0.286448	+	0.958096i	$0.592474\pi$
$102$		0			0
$103$	−5.21583			−0.513931			−0.256965	−	0.966421i	$-0.582723\pi$
$103$	−5.21583			−0.513931			−0.256965	+	0.966421i	$0.582723\pi$
$104$		−	3.59724i		−	0.352738i
$105$		0			0
$106$	2.74919			0.267025
$107$	−9.09049	−	9.09049i	−0.878811	−	0.878811i	0.114600	−	0.993412i	$-0.463441\pi$
$107$	−9.09049	−	9.09049i	−0.878811	−	0.878811i	−0.993412	+	0.114600i	$0.963441\pi$
$108$		0			0
$109$	5.23857	−	5.23857i	0.501764	−	0.501764i	−0.410222	−	0.911986i	$-0.634549\pi$
$109$	5.23857	−	5.23857i	0.501764	−	0.501764i	0.911986	+	0.410222i	$0.134549\pi$
$110$			0.382062i			0.0364282i
$111$		0			0
$112$	−1.52475	+	1.52475i	−0.144076	+	0.144076i
$113$	4.75363	−	4.75363i	0.447184	−	0.447184i	−0.447234	−	0.894417i	$-0.647591\pi$
$113$	4.75363	−	4.75363i	0.447184	−	0.447184i	0.894417	+	0.447234i	$0.147591\pi$
$114$		0			0
$115$	−0.285478			−0.0266209
$116$	5.98183	+	5.98183i	0.555399	+	0.555399i
$117$		0			0
$118$	−2.54107			−0.233925
$119$	1.62571	−	3.78907i	0.149028	−	0.347344i
$120$		0			0
$121$		−	4.71165i		−	0.428332i
$122$	−1.61619	−	1.61619i	−0.146323	−	0.146323i
$123$		0			0
$124$	11.0600	+	11.0600i	0.993220	+	0.993220i
$125$	−1.19237	+	1.19237i	−0.106649	+	0.106649i
$126$		0			0
$127$			6.36029i			0.564384i	0.959358	+	0.282192i	$0.0910615\pi$
$127$			6.36029i			0.564384i	−0.959358	+	0.282192i	$0.908938\pi$
$128$		−	11.5348i		−	1.01954i
$129$		0			0
$130$	−0.117044	+	0.117044i	−0.0102655	+	0.0102655i
$131$	−3.38701	−	3.38701i	−0.295924	−	0.295924i	0.543491	−	0.839415i	$-0.317102\pi$
$131$	−3.38701	−	3.38701i	−0.295924	−	0.295924i	−0.839415	+	0.543491i	$0.817102\pi$
$132$		0			0
$133$	1.98459	+	1.98459i	0.172085	+	0.172085i
$134$			4.48507i			0.387451i
$135$		0			0
$136$	3.20437	+	8.02034i	0.274772	+	0.687739i
$137$	18.4595			1.57710			0.788549	−	0.614972i	$-0.210833\pi$
$137$	18.4595			1.57710			0.788549	+	0.614972i	$0.210833\pi$
$138$		0			0
$139$	0.336762	+	0.336762i	0.0285638	+	0.0285638i	0.721244	−	0.692681i	$-0.243570\pi$
$139$	0.336762	+	0.336762i	0.0285638	+	0.0285638i	−0.692681	+	0.721244i	$0.743570\pi$
$140$	0.283281			0.0239416
$141$		0			0
$142$	4.56388	−	4.56388i	0.382992	−	0.382992i
$143$	4.81325	−	4.81325i	0.402504	−	0.402504i
$144$		0			0
$145$		−	0.854023i		−	0.0709227i
$146$	4.23458	−	4.23458i	0.350456	−	0.350456i
$147$		0			0
$148$	−6.13582	−	6.13582i	−0.504361	−	0.504361i
$149$	−22.0065			−1.80285			−0.901423	−	0.432939i	$-0.857477\pi$
$149$	−22.0065			−1.80285			−0.901423	+	0.432939i	$0.857477\pi$
$150$		0			0
$151$			21.2455i			1.72893i	0.502691	+	0.864466i	$0.332344\pi$
$151$			21.2455i			1.72893i	−0.502691	+	0.864466i	$0.667656\pi$
$152$	−5.87912			−0.476859
$153$		0			0
$154$	2.25925			0.182056
$155$		−	1.57903i		−	0.126831i
$156$		0			0
$157$	1.65146			0.131801			0.0659006	−	0.997826i	$-0.479008\pi$
$157$	1.65146			0.131801			0.0659006	+	0.997826i	$0.479008\pi$
$158$	−1.46123	−	1.46123i	−0.116249	−	0.116249i
$159$		0			0
$160$	−0.647937	+	0.647937i	−0.0512239	+	0.0512239i
$161$			1.68812i			0.133043i
$162$		0			0
$163$	−8.52511	+	8.52511i	−0.667738	+	0.667738i	−0.957192	−	0.289454i	$-0.906526\pi$
$163$	−8.52511	+	8.52511i	−0.667738	+	0.667738i	0.289454	+	0.957192i	$0.406526\pi$
$164$	1.92771	−	1.92771i	0.150528	−	0.150528i
$165$		0			0
$166$	9.75916			0.757458
$167$	−5.02678	−	5.02678i	−0.388984	−	0.388984i	0.485341	−	0.874325i	$-0.338695\pi$
$167$	−5.02678	−	5.02678i	−0.388984	−	0.388984i	−0.874325	+	0.485341i	$0.838695\pi$
$168$		0			0
$169$	−10.0509			−0.773149
$170$	0.156698	−	0.365221i	0.0120182	−	0.0280112i
$171$		0			0
$172$		−	13.7084i		−	1.04525i
$173$	8.86351	+	8.86351i	0.673880	+	0.673880i	0.958608	−	0.284728i	$-0.0919033\pi$
$173$	8.86351	+	8.86351i	0.673880	+	0.673880i	−0.284728	+	0.958608i	$0.591903\pi$
$174$		0			0
$175$	3.51531	+	3.51531i	0.265733	+	0.265733i
$176$	6.04380	−	6.04380i	0.455569	−	0.455569i
$177$		0			0
$178$			2.71469i			0.203474i
$179$			7.05053i			0.526982i	0.964662	+	0.263491i	$0.0848738\pi$
$179$			7.05053i			0.526982i	−0.964662	+	0.263491i	$0.915126\pi$
$180$		0			0
$181$	−3.47091	+	3.47091i	−0.257991	+	0.257991i	−0.824236	−	0.566246i	$-0.808395\pi$
$181$	−3.47091	+	3.47091i	−0.257991	+	0.257991i	0.566246	+	0.824236i	$0.308395\pi$
$182$	0.692120	+	0.692120i	0.0513034	+	0.0513034i
$183$		0			0
$184$	−2.50044	−	2.50044i	−0.184335	−	0.184335i
$185$			0.876007i			0.0644053i
$186$		0			0
$187$	−6.44396	+	15.0191i	−0.471229	+	1.09831i
$188$	4.14392			0.302227
$189$		0			0
$190$	0.191290	+	0.191290i	0.0138777	+	0.0138777i
$191$	−11.2040			−0.810692			−0.405346	−	0.914163i	$-0.632849\pi$
$191$	−11.2040			−0.810692			−0.405346	+	0.914163i	$0.632849\pi$
$192$		0			0
$193$	−7.19640	+	7.19640i	−0.518009	+	0.518009i	−0.916968	−	0.398960i	$-0.869371\pi$
$193$	−7.19640	+	7.19640i	−0.518009	+	0.518009i	0.398960	+	0.916968i	$0.369371\pi$
$194$	−6.89878	+	6.89878i	−0.495304	+	0.495304i
$195$		0			0
$196$		−	1.67513i		−	0.119652i
$197$	11.5866	−	11.5866i	0.825511	−	0.825511i	−0.161381	−	0.986892i	$-0.551595\pi$
$197$	11.5866	−	11.5866i	0.825511	−	0.825511i	0.986892	+	0.161381i	$0.0515949\pi$
$198$		0			0
$199$	18.0364	+	18.0364i	1.27856	+	1.27856i	0.941472	+	0.337092i	$0.109443\pi$
$199$	18.0364	+	18.0364i	1.27856	+	1.27856i	0.337092	+	0.941472i	$0.390557\pi$
$200$	−10.4137			−0.736361
$201$		0			0
$202$			3.28163i			0.230895i
$203$	−5.05011			−0.354448
$204$		0			0
$205$	−0.275217			−0.0192220
$206$			2.97288i			0.207130i
$207$		0			0
$208$	3.70302			0.256759
$209$	−7.86649	−	7.86649i	−0.544136	−	0.544136i
$210$		0			0
$211$	−15.5251	+	15.5251i	−1.06879	+	1.06879i	−0.0713412	+	0.997452i	$0.522728\pi$
$211$	−15.5251	+	15.5251i	−1.06879	+	1.06879i	−0.997452	+	0.0713412i	$0.977272\pi$
$212$			8.07978i			0.554922i
$213$		0			0
$214$	−5.18134	+	5.18134i	−0.354189	+	0.354189i
$215$	−0.978568	+	0.978568i	−0.0667378	+	0.0667378i
$216$		0			0
$217$	−9.33733			−0.633859
$218$	−2.98584	−	2.98584i	−0.202227	−	0.202227i
$219$		0			0
$220$	−1.12287			−0.0757037
$221$	−6.57519	+	2.62699i	−0.442295	+	0.176710i
$222$		0			0
$223$			3.23337i			0.216522i	0.994122	+	0.108261i	$0.0345283\pi$
$223$			3.23337i			0.216522i	−0.994122	+	0.108261i	$0.965472\pi$
$224$	3.83146	+	3.83146i	0.256000	+	0.256000i
$225$		0			0
$226$	−2.70944	−	2.70944i	−0.180229	−	0.180229i
$227$	−15.0015	+	15.0015i	−0.995687	+	0.995687i	−0.999991	−	0.00430411i	$-0.998630\pi$
$227$	−15.0015	+	15.0015i	−0.995687	+	0.995687i	0.00430411	+	0.999991i	$0.498630\pi$
$228$		0			0
$229$			23.7619i			1.57023i	0.619350	+	0.785115i	$0.287396\pi$
$229$			23.7619i			1.57023i	−0.619350	+	0.785115i	$0.712604\pi$
$230$			0.162715i			0.0107291i
$231$		0			0
$232$	7.48019	−	7.48019i	0.491099	−	0.491099i
$233$	18.5085	+	18.5085i	1.21253	+	1.21253i	0.970191	+	0.242343i	$0.0779159\pi$
$233$	18.5085	+	18.5085i	1.21253	+	1.21253i	0.242343	+	0.970191i	$0.422084\pi$
$234$		0			0
$235$	−0.295813	−	0.295813i	−0.0192967	−	0.0192967i
$236$		−	7.46813i		−	0.486134i
$237$		0			0
$238$	−2.15967	−	0.926608i	−0.139991	−	0.0600631i
$239$	−5.00483			−0.323735			−0.161868	−	0.986812i	$-0.551752\pi$
$239$	−5.00483			−0.323735			−0.161868	+	0.986812i	$0.551752\pi$
$240$		0			0
$241$	7.33279	+	7.33279i	0.472346	+	0.472346i	0.902673	−	0.430327i	$-0.141602\pi$
$241$	7.33279	+	7.33279i	0.472346	+	0.472346i	−0.430327	+	0.902673i	$0.641602\pi$
$242$	−2.68551			−0.172631
$243$		0			0
$244$	4.74992	−	4.74992i	0.304082	−	0.304082i
$245$	−0.119579	+	0.119579i	−0.00763960	+	0.00763960i
$246$		0			0
$247$		−	4.81978i		−	0.306675i
$248$	13.8304	−	13.8304i	0.878231	−	0.878231i
$249$		0			0
$250$	0.679617	+	0.679617i	0.0429827	+	0.0429827i
$251$	9.67570			0.610725			0.305363	−	0.952236i	$-0.401222\pi$
$251$	9.67570			0.610725			0.305363	+	0.952236i	$0.401222\pi$
$252$		0			0
$253$		−	6.69136i		−	0.420682i
$254$	3.62519			0.227465
$255$		0			0
$256$	−4.12601			−0.257876
$257$			10.1442i			0.632781i	0.948629	+	0.316390i	$0.102471\pi$
$257$			10.1442i			0.632781i	−0.948629	+	0.316390i	$0.897529\pi$
$258$		0			0
$259$	5.18011			0.321876
$260$	−0.343989	−	0.343989i	−0.0213333	−	0.0213333i
$261$		0			0
$262$	−1.93050	+	1.93050i	−0.119267	+	0.119267i
$263$		−	6.93641i		−	0.427717i	−0.976865	−	0.213859i	$-0.931397\pi$
$263$		−	6.93641i		−	0.427717i	0.976865	−	0.213859i	$-0.0686032\pi$
$264$		0			0
$265$	0.576773	−	0.576773i	0.0354309	−	0.0354309i
$266$	1.13116	−	1.13116i	0.0693559	−	0.0693559i
$267$		0			0
$268$	−13.1815			−0.805186
$269$	11.2430	+	11.2430i	0.685496	+	0.685496i	0.961233	−	0.275737i	$-0.0889220\pi$
$269$	11.2430	+	11.2430i	0.685496	+	0.685496i	−0.275737	+	0.961233i	$0.588922\pi$
$270$		0			0
$271$	−30.8491			−1.87395			−0.936975	−	0.349396i	$-0.886387\pi$
$271$	−30.8491			−1.87395			−0.936975	+	0.349396i	$0.886387\pi$
$272$	−8.25620	+	3.29860i	−0.500605	+	0.200007i
$273$		0			0
$274$		−	10.5214i		−	0.635620i
$275$	−13.9340	−	13.9340i	−0.840250	−	0.840250i
$276$		0			0
$277$	11.6717	+	11.6717i	0.701287	+	0.701287i	0.964687	−	0.263400i	$-0.0848438\pi$
$277$	11.6717	+	11.6717i	0.701287	+	0.701287i	−0.263400	+	0.964687i	$0.584844\pi$
$278$	0.191945	−	0.191945i	0.0115121	−	0.0115121i
$279$		0			0
$280$		−	0.354238i		−	0.0211698i
$281$			8.04520i			0.479937i	0.970781	+	0.239968i	$0.0771371\pi$
$281$			8.04520i			0.479937i	−0.970781	+	0.239968i	$0.922863\pi$
$282$		0			0
$283$	−22.4578	+	22.4578i	−1.33498	+	1.33498i	−0.434127	+	0.900851i	$0.642943\pi$
$283$	−22.4578	+	22.4578i	−1.33498	+	1.33498i	−0.900851	+	0.434127i	$0.857057\pi$
$284$	13.4131	+	13.4131i	0.795920	+	0.795920i
$285$		0			0
$286$	−2.74342	−	2.74342i	−0.162222	−	0.162222i
$287$			1.62745i			0.0960652i
$288$		0			0
$289$	12.3198	−	11.7142i	0.724696	−	0.689068i
$290$	−0.486770			−0.0285841
$291$		0			0
$292$	12.4453	+	12.4453i	0.728304	+	0.728304i
$293$	−27.4400			−1.60306			−0.801530	−	0.597954i	$-0.795980\pi$
$293$	−27.4400			−1.60306			−0.801530	+	0.597954i	$0.795980\pi$
$294$		0			0
$295$	−0.533110	+	0.533110i	−0.0310389	+	0.0310389i
$296$	−7.67275	+	7.67275i	−0.445969	+	0.445969i
$297$		0			0
$298$			12.5431i			0.726604i
$299$	2.04989	−	2.04989i	0.118548	−	0.118548i
$300$		0			0
$301$	5.78658	+	5.78658i	0.333533	+	0.333533i
$302$	12.1093			0.696815
$303$		0			0
$304$		−	6.05201i		−	0.347106i
$305$	−0.678142			−0.0388303
$306$		0			0
$307$	−3.00112			−0.171283			−0.0856416	−	0.996326i	$-0.527294\pi$
$307$	−3.00112			−0.171283			−0.0856416	+	0.996326i	$0.527294\pi$
$308$			6.63987i			0.378342i
$309$		0			0
$310$	−0.900006			−0.0511169
$311$	2.94819	+	2.94819i	0.167177	+	0.167177i	0.785737	−	0.618561i	$-0.212284\pi$
$311$	2.94819	+	2.94819i	0.167177	+	0.167177i	−0.618561	+	0.785737i	$0.712284\pi$
$312$		0			0
$313$	2.95301	−	2.95301i	0.166914	−	0.166914i	−0.618708	−	0.785621i	$-0.712343\pi$
$313$	2.95301	−	2.95301i	0.166914	−	0.166914i	0.785621	+	0.618708i	$0.212343\pi$
$314$		−	0.941290i		−	0.0531201i
$315$		0			0
$316$	4.29450	−	4.29450i	0.241584	−	0.241584i
$317$	6.69199	−	6.69199i	0.375859	−	0.375859i	−0.493746	−	0.869606i	$-0.664373\pi$
$317$	6.69199	−	6.69199i	0.375859	−	0.375859i	0.869606	+	0.493746i	$0.164373\pi$
$318$		0			0
$319$	20.0176			1.12077
$320$	−0.146395	−	0.146395i	−0.00818371	−	0.00818371i
$321$		0			0
$322$	0.962183			0.0536204
$323$	4.29339	+	10.7461i	0.238891	+	0.597929i
$324$		0			0
$325$		−	8.53731i		−	0.473565i
$326$	4.85908	+	4.85908i	0.269120	+	0.269120i
$327$		0			0
$328$	−2.41057	−	2.41057i	−0.133101	−	0.133101i
$329$	−1.74923	+	1.74923i	−0.0964384	+	0.0964384i
$330$		0			0
$331$		−	17.6127i		−	0.968084i	−0.875045	−	0.484042i	$-0.839168\pi$
$331$		−	17.6127i		−	0.968084i	0.875045	−	0.484042i	$-0.160832\pi$
$332$			28.6818i			1.57412i
$333$		0			0
$334$	−2.86513	+	2.86513i	−0.156773	+	0.156773i
$335$	0.940955	+	0.940955i	0.0514098	+	0.0514098i
$336$		0			0
$337$	−9.98269	−	9.98269i	−0.543792	−	0.543792i	0.380846	−	0.924638i	$-0.375633\pi$
$337$	−9.98269	−	9.98269i	−0.543792	−	0.543792i	−0.924638	+	0.380846i	$0.875633\pi$
$338$			5.72876i			0.311603i
$339$		0			0
$340$	1.07337	+	0.460531i	0.0582118	+	0.0249758i
$341$	37.0112			2.00427
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−17.1421			−0.924241
$345$		0			0
$346$	5.05196	−	5.05196i	0.271595	−	0.271595i
$347$	−9.60370	+	9.60370i	−0.515554	+	0.515554i	−0.916223	−	0.400669i	$-0.868778\pi$
$347$	−9.60370	+	9.60370i	−0.515554	+	0.515554i	0.400669	+	0.916223i	$0.368778\pi$
$348$		0			0
$349$		−	30.2212i		−	1.61770i	−0.588013	−	0.808851i	$-0.700090\pi$
$349$		−	30.2212i		−	1.61770i	0.588013	−	0.808851i	$-0.299910\pi$
$350$	2.00363	−	2.00363i	0.107099	−	0.107099i
$351$		0			0
$352$	−15.1871	−	15.1871i	−0.809475	−	0.809475i
$353$	−9.56694			−0.509197			−0.254599	−	0.967047i	$-0.581943\pi$
$353$	−9.56694			−0.509197			−0.254599	+	0.967047i	$0.581943\pi$
$354$		0			0
$355$		−	1.91498i		−	0.101636i
$356$	−7.97837			−0.422853
$357$		0			0
$358$	4.01861			0.212390
$359$		−	21.4163i		−	1.13031i	−0.824985	−	0.565155i	$-0.808816\pi$
$359$		−	21.4163i		−	1.13031i	0.824985	−	0.565155i	$-0.191184\pi$
$360$		0			0
$361$	11.1228			0.585412
$362$	1.97833	+	1.97833i	0.103978	+	0.103978i
$363$		0			0
$364$	−2.03412	+	2.03412i	−0.106617	+	0.106617i
$365$		−	1.77680i		−	0.0930021i
$366$		0			0
$367$	−0.630276	+	0.630276i	−0.0329002	+	0.0329002i	−0.723365	−	0.690465i	$-0.757406\pi$
$367$	−0.630276	+	0.630276i	−0.0329002	+	0.0329002i	0.690465	+	0.723365i	$0.257406\pi$
$368$	2.57397	−	2.57397i	0.134177	−	0.134177i
$369$		0			0
$370$	0.499300			0.0259574
$371$	−3.41064	−	3.41064i	−0.177072	−	0.177072i
$372$		0			0
$373$	−21.0868			−1.09183			−0.545917	−	0.837839i	$-0.683819\pi$
$373$	−21.0868			−1.09183			−0.545917	+	0.837839i	$0.683819\pi$
$374$	8.56048	+	3.67288i	0.442652	+	0.189920i
$375$		0			0
$376$		−	5.18191i		−	0.267237i
$377$	6.13237	+	6.13237i	0.315833	+	0.315833i
$378$		0			0
$379$	21.2532	+	21.2532i	1.09170	+	1.09170i	0.995347	+	0.0963580i	$0.0307194\pi$
$379$	21.2532	+	21.2532i	1.09170	+	1.09170i	0.0963580	+	0.995347i	$0.469281\pi$
$380$	−0.562196	+	0.562196i	−0.0288400	+	0.0288400i
$381$		0			0
$382$			6.38597i			0.326735i
$383$		−	15.3752i		−	0.785637i	−0.919616	−	0.392819i	$-0.871500\pi$
$383$		−	15.3752i		−	0.785637i	0.919616	−	0.392819i	$-0.128500\pi$
$384$		0			0
$385$	0.473985	−	0.473985i	0.0241565	−	0.0241565i
$386$	4.10176	+	4.10176i	0.208774	+	0.208774i
$387$		0			0
$388$	−20.2753	−	20.2753i	−1.02932	−	1.02932i
$389$		−	0.413500i		−	0.0209653i	−0.999945	−	0.0104826i	$-0.996663\pi$
$389$		−	0.413500i		−	0.0209653i	0.999945	−	0.0104826i	$-0.00333679\pi$
$390$		0			0
$391$	−2.74439	+	6.39642i	−0.138790	+	0.323481i
$392$	−2.09473			−0.105800
$393$		0			0
$394$	−6.60405	−	6.60405i	−0.332707	−	0.332707i
$395$	−0.613122			−0.0308495
$396$		0			0
$397$	6.61953	−	6.61953i	0.332225	−	0.332225i	−0.521206	−	0.853431i	$-0.674518\pi$
$397$	6.61953	−	6.61953i	0.332225	−	0.332225i	0.853431	+	0.521206i	$0.174518\pi$
$398$	10.2802	−	10.2802i	0.515302	−	0.515302i
$399$		0			0
$400$		−	10.7200i		−	0.535998i
$401$	26.9095	−	26.9095i	1.34380	−	1.34380i	0.451552	−	0.892245i	$-0.350870\pi$
$401$	26.9095	−	26.9095i	1.34380	−	1.34380i	0.892245	−	0.451552i	$-0.149130\pi$
$402$		0			0
$403$	11.3384	+	11.3384i	0.564804	+	0.564804i
$404$	−9.64461			−0.479837
$405$		0			0
$406$			2.87842i			0.142854i
$407$	−20.5329			−1.01778
$408$		0			0
$409$	8.42906			0.416790			0.208395	−	0.978045i	$-0.433176\pi$
$409$	8.42906			0.416790			0.208395	+	0.978045i	$0.433176\pi$
$410$			0.156866i			0.00774708i
$411$		0			0
$412$	−8.73720			−0.430451
$413$	3.15245	+	3.15245i	0.155122	+	0.155122i
$414$		0			0
$415$	2.04744	−	2.04744i	0.100505	−	0.100505i
$416$		−	9.30510i		−	0.456220i
$417$		0			0
$418$	−4.48369	+	4.48369i	−0.219304	+	0.219304i
$419$	−13.1294	+	13.1294i	−0.641414	+	0.641414i	−0.950903	−	0.309489i	$-0.899842\pi$
$419$	−13.1294	+	13.1294i	−0.641414	+	0.641414i	0.309489	+	0.950903i	$0.399842\pi$
$420$		0			0
$421$	0.206598			0.0100689			0.00503447	−	0.999987i	$-0.498397\pi$
$421$	0.206598			0.0100689			0.00503447	+	0.999987i	$0.498397\pi$
$422$	8.84890	+	8.84890i	0.430758	+	0.430758i
$423$		0			0
$424$	10.1036			0.490676
$425$	7.60492	+	19.0346i	0.368893	+	0.923316i
$426$		0			0
$427$			4.01007i			0.194061i
$428$	−15.2278	−	15.2278i	−0.736062	−	0.736062i
$429$		0			0
$430$	0.557757	+	0.557757i	0.0268974	+	0.0268974i
$431$	4.34813	−	4.34813i	0.209442	−	0.209442i	−0.594588	−	0.804030i	$-0.702685\pi$
$431$	4.34813	−	4.34813i	0.209442	−	0.209442i	0.804030	+	0.594588i	$0.202685\pi$
$432$		0			0
$433$		−	16.0573i		−	0.771662i	−0.922569	−	0.385831i	$-0.873915\pi$
$433$		−	16.0573i		−	0.771662i	0.922569	−	0.385831i	$-0.126085\pi$
$434$			5.32202i			0.255465i
$435$		0			0
$436$	8.77528	−	8.77528i	0.420260	−	0.420260i
$437$	−3.35022	−	3.35022i	−0.160263	−	0.160263i
$438$		0			0
$439$	9.96643	+	9.96643i	0.475672	+	0.475672i	0.903744	−	0.428073i	$-0.140807\pi$
$439$	9.96643	+	9.96643i	0.475672	+	0.475672i	−0.428073	+	0.903744i	$0.640807\pi$
$440$			1.40413i			0.0669392i
$441$		0			0
$442$	1.49731	+	3.74768i	0.0712198	+	0.178259i
$443$	13.6714			0.649550			0.324775	−	0.945791i	$-0.394711\pi$
$443$	13.6714			0.649550			0.324775	+	0.945791i	$0.394711\pi$
$444$		0			0
$445$	0.569533	+	0.569533i	0.0269985	+	0.0269985i
$446$	1.84293			0.0872654
$447$		0			0
$448$	−0.865678	+	0.865678i	−0.0408994	+	0.0408994i
$449$	−5.86461	+	5.86461i	−0.276768	+	0.276768i	−0.831817	−	0.555049i	$-0.812699\pi$
$449$	−5.86461	+	5.86461i	−0.276768	+	0.276768i	0.555049	+	0.831817i	$0.312699\pi$
$450$		0			0
$451$		−	6.45086i		−	0.303759i
$452$	7.96295	−	7.96295i	0.374546	−	0.374546i
$453$		0			0
$454$	8.55047	+	8.55047i	0.401293	+	0.401293i
$455$	0.290410			0.0136146
$456$		0			0
$457$		−	17.3463i		−	0.811427i	−0.914000	−	0.405714i	$-0.867023\pi$
$457$		−	17.3463i		−	0.811427i	0.914000	−	0.405714i	$-0.132977\pi$
$458$	13.5436			0.632852
$459$		0			0
$460$	−0.478213			−0.0222968
$461$		−	42.1923i		−	1.96509i	−0.186022	−	0.982546i	$-0.559559\pi$
$461$		−	42.1923i		−	1.96509i	0.186022	−	0.982546i	$-0.440441\pi$
$462$		0			0
$463$	15.6188			0.725865			0.362933	−	0.931815i	$-0.381776\pi$
$463$	15.6188			0.725865			0.362933	+	0.931815i	$0.381776\pi$
$464$	7.70016	+	7.70016i	0.357471	+	0.357471i
$465$		0			0
$466$	10.5494	−	10.5494i	0.488689	−	0.488689i
$467$			18.9739i			0.878007i	0.898485	+	0.439004i	$0.144668\pi$
$467$			18.9739i			0.878007i	−0.898485	+	0.439004i	$0.855332\pi$
$468$		0			0
$469$	5.56417	−	5.56417i	0.256929	−	0.256929i
$470$	−0.168605	+	0.168605i	−0.00777718	+	0.00777718i
$471$		0			0
$472$	−9.33878			−0.429852
$473$	−22.9368	−	22.9368i	−1.05464	−	1.05464i
$474$		0			0
$475$	−13.9529			−0.640202
$476$	2.72327	−	6.34719i	0.124821	−	0.290923i
$477$		0			0
$478$			2.85262i			0.130476i
$479$	−4.13772	−	4.13772i	−0.189057	−	0.189057i	0.606231	−	0.795288i	$-0.292681\pi$
$479$	−4.13772	−	4.13772i	−0.189057	−	0.189057i	−0.795288	+	0.606231i	$0.792681\pi$
$480$		0			0
$481$	−6.29023	−	6.29023i	−0.286810	−	0.286810i
$482$	4.17949	−	4.17949i	0.190371	−	0.190371i
$483$		0			0
$484$		−	7.89263i		−	0.358756i
$485$			2.89469i			0.131441i
$486$		0			0
$487$	−23.2634	+	23.2634i	−1.05417	+	1.05417i	−0.0557206	+	0.998446i	$0.517746\pi$
$487$	−23.2634	+	23.2634i	−1.05417	+	1.05417i	−0.998446	+	0.0557206i	$0.982254\pi$
$488$	−5.93970	−	5.93970i	−0.268877	−	0.268877i
$489$		0			0
$490$	0.0681566	+	0.0681566i	0.00307900	+	0.00307900i
$491$		−	9.29738i		−	0.419585i	−0.977746	−	0.209792i	$-0.932721\pi$
$491$		−	9.29738i		−	0.419585i	0.977746	−	0.209792i	$-0.0672788\pi$
$492$		0			0
$493$	−19.1352	−	8.20999i	−0.861808	−	0.369759i
$494$	−2.74715			−0.123600
$495$		0			0
$496$	14.2371	+	14.2371i	0.639265	+	0.639265i
$497$	−11.3239			−0.507945
$498$		0			0
$499$	21.4950	−	21.4950i	0.962250	−	0.962250i	−0.0370626	−	0.999313i	$-0.511800\pi$
$499$	21.4950	−	21.4950i	0.962250	−	0.962250i	0.999313	+	0.0370626i	$0.0118001\pi$
$500$	−1.99737	+	1.99737i	−0.0893251	+	0.0893251i
$501$		0			0
$502$		−	5.51489i		−	0.246142i
$503$	17.3096	−	17.3096i	0.771795	−	0.771795i	−0.206625	−	0.978420i	$-0.566248\pi$
$503$	17.3096	−	17.3096i	0.771795	−	0.771795i	0.978420	+	0.206625i	$0.0662481\pi$
$504$		0			0
$505$	0.688477	+	0.688477i	0.0306368	+	0.0306368i
$506$	−3.81389			−0.169548
$507$		0			0
$508$			10.6543i			0.472709i
$509$	−25.3122			−1.12194			−0.560971	−	0.827835i	$-0.689572\pi$
$509$	−25.3122			−1.12194			−0.560971	+	0.827835i	$0.689572\pi$
$510$		0			0
$511$	−10.5068			−0.464794
$512$		−	20.7179i		−	0.915609i
$513$		0			0
$514$	5.78194			0.255031
$515$	0.623702	+	0.623702i	0.0274836	+	0.0274836i
$516$		0			0
$517$	6.93360	−	6.93360i	0.304939	−	0.304939i
$518$		−	2.95252i		−	0.129726i
$519$		0			0
$520$	−0.430153	+	0.430153i	−0.0188635	+	0.0188635i
$521$	8.04505	−	8.04505i	0.352460	−	0.352460i	−0.508564	−	0.861024i	$-0.669823\pi$
$521$	8.04505	−	8.04505i	0.352460	−	0.352460i	0.861024	+	0.508564i	$0.169823\pi$
$522$		0			0
$523$	4.39968			0.192385			0.0961924	−	0.995363i	$-0.469334\pi$
$523$	4.39968			0.192385			0.0961924	+	0.995363i	$0.469334\pi$
$524$	−5.67368	−	5.67368i	−0.247856	−	0.247856i
$525$		0			0
$526$	−3.95357			−0.172384
$527$	−35.3798	−	15.1797i	−1.54117	−	0.661240i
$528$		0			0
$529$			20.1502i			0.876098i
$530$	−0.328745	−	0.328745i	−0.0142798	−	0.0142798i
$531$		0			0
$532$	3.32444	+	3.32444i	0.144133	+	0.144133i
$533$	1.97621	−	1.97621i	0.0855994	−	0.0855994i
$534$		0			0
$535$			2.17406i			0.0939927i
$536$			16.4832i			0.711967i
$537$		0			0
$538$	6.40819	−	6.40819i	0.276276	−	0.276276i
$539$	−2.80282	−	2.80282i	−0.120726	−	0.120726i
$540$		0			0
$541$	−16.5237	−	16.5237i	−0.710411	−	0.710411i	0.256210	−	0.966621i	$-0.417526\pi$
$541$	−16.5237	−	16.5237i	−0.710411	−	0.710411i	−0.966621	+	0.256210i	$0.917526\pi$
$542$			17.5832i			0.755261i
$543$		0			0
$544$	8.28885	+	20.7465i	0.355382	+	0.889498i
$545$	−1.25284			−0.0536658
$546$		0			0
$547$	1.59409	+	1.59409i	0.0681584	+	0.0681584i	0.740364	−	0.672206i	$-0.234653\pi$
$547$	1.59409	+	1.59409i	0.0681584	+	0.0681584i	−0.672206	+	0.740364i	$0.734653\pi$
$548$	30.9220			1.32092
$549$		0			0
$550$	−7.94198	+	7.94198i	−0.338647	+	0.338647i
$551$	10.0224	−	10.0224i	0.426968	−	0.426968i
$552$		0			0
$553$			3.62559i			0.154176i
$554$	6.65258	−	6.65258i	0.282641	−	0.282641i
$555$		0			0
$556$	0.564120	+	0.564120i	0.0239240	+	0.0239240i
$557$	−35.4920			−1.50385			−0.751923	−	0.659251i	$-0.770874\pi$
$557$	−35.4920			−1.50385			−0.751923	+	0.659251i	$0.770874\pi$
$558$		0			0
$559$		−	14.0533i		−	0.594393i
$560$	0.364656			0.0154095
$561$		0			0
$562$	4.58555			0.193430
$563$			22.4951i			0.948054i	0.880510	+	0.474027i	$0.157200\pi$
$563$			22.4951i			0.948054i	−0.880510	+	0.474027i	$0.842800\pi$
$564$		0			0
$565$	−1.13686			−0.0478283
$566$	12.8003	+	12.8003i	0.538039	+	0.538039i
$567$		0			0
$568$	16.7728	−	16.7728i	0.703773	−	0.703773i
$569$		−	5.16530i		−	0.216541i	−0.994121	−	0.108270i	$-0.965469\pi$
$569$		−	5.16530i		−	0.216541i	0.994121	−	0.108270i	$-0.0345312\pi$
$570$		0			0
$571$	20.4454	−	20.4454i	0.855615	−	0.855615i	−0.135203	−	0.990818i	$-0.543169\pi$
$571$	20.4454	−	20.4454i	0.855615	−	0.855615i	0.990818	+	0.135203i	$0.0431688\pi$
$572$	8.06282	−	8.06282i	0.337123	−	0.337123i
$573$		0			0
$574$	0.927601			0.0387173
$575$	−5.93427	−	5.93427i	−0.247476	−	0.247476i
$576$		0			0
$577$	−1.62157			−0.0675069			−0.0337534	−	0.999430i	$-0.510746\pi$
$577$	−1.62157			−0.0675069			−0.0337534	+	0.999430i	$0.510746\pi$
$578$	−6.67676	−	7.02197i	−0.277716	−	0.292076i
$579$		0			0
$580$		−	1.43060i		−	0.0594024i
$581$	−12.1072	−	12.1072i	−0.502291	−	0.502291i
$582$		0			0
$583$	13.5191	+	13.5191i	0.559903	+	0.559903i
$584$	15.5626	−	15.5626i	0.643986	−	0.643986i
$585$		0			0
$586$			15.6400i			0.646084i
$587$		−	10.2322i		−	0.422329i	−0.977450	−	0.211165i	$-0.932274\pi$
$587$		−	10.2322i		−	0.422329i	0.977450	−	0.211165i	$-0.0677256\pi$
$588$		0			0
$589$	18.5307	−	18.5307i	0.763546	−	0.763546i
$590$	0.303858	+	0.303858i	0.0125096	+	0.0125096i
$591$		0			0
$592$	−7.89838	−	7.89838i	−0.324621	−	0.324621i
$593$			27.1507i			1.11495i	0.830195	+	0.557473i	$0.188229\pi$
$593$			27.1507i			1.11495i	−0.830195	+	0.557473i	$0.811771\pi$
$594$		0			0
$595$	−0.647492	+	0.258693i	−0.0265446	+	0.0106054i
$596$	−36.8638			−1.51000
$597$		0			0
$598$	−1.16838	−	1.16838i	−0.0477787	−	0.0477787i
$599$	−9.88669			−0.403959			−0.201980	−	0.979390i	$-0.564737\pi$
$599$	−9.88669			−0.403959			−0.201980	+	0.979390i	$0.564737\pi$
$600$		0			0
$601$	12.4756	−	12.4756i	0.508890	−	0.508890i	−0.405296	−	0.914186i	$-0.632831\pi$
$601$	12.4756	−	12.4756i	0.508890	−	0.508890i	0.914186	+	0.405296i	$0.132831\pi$
$602$	3.29820	−	3.29820i	0.134424	−	0.134424i
$603$		0			0
$604$			35.5890i			1.44809i
$605$	−0.563413	+	0.563413i	−0.0229060	+	0.0229060i
$606$		0			0
$607$	−0.699803	−	0.699803i	−0.0284041	−	0.0284041i	0.692762	−	0.721166i	$-0.256394\pi$
$607$	−0.699803	−	0.699803i	−0.0284041	−	0.0284041i	−0.721166	+	0.692762i	$0.756394\pi$
$608$	−15.2077			−0.616754
$609$		0			0
$610$			0.386523i			0.0156499i
$611$	4.24820			0.171864
$612$		0			0
$613$	20.7155			0.836692			0.418346	−	0.908288i	$-0.362610\pi$
$613$	20.7155			0.836692			0.418346	+	0.908288i	$0.362610\pi$
$614$			1.71056i			0.0690325i
$615$		0			0
$616$	8.30306			0.334540
$617$	3.66223	+	3.66223i	0.147436	+	0.147436i	0.776971	−	0.629536i	$-0.216755\pi$
$617$	3.66223	+	3.66223i	0.147436	+	0.147436i	−0.629536	+	0.776971i	$0.716755\pi$
$618$		0			0
$619$	−14.3238	+	14.3238i	−0.575723	+	0.575723i	−0.933722	−	0.357999i	$-0.883459\pi$
$619$	−14.3238	+	14.3238i	−0.575723	+	0.575723i	0.357999	+	0.933722i	$0.383459\pi$
$620$		−	2.64509i		−	0.106229i
$621$		0			0
$622$	1.68039	−	1.68039i	0.0673774	−	0.0673774i
$623$	3.36783	−	3.36783i	0.134929	−	0.134929i
$624$		0			0
$625$	−24.5718			−0.982874
$626$	−1.68313	−	1.68313i	−0.0672716	−	0.0672716i
$627$		0			0
$628$	2.76642			0.110392
$629$	19.6278	+	8.42133i	0.782612	+	0.335780i
$630$		0			0
$631$			30.2440i			1.20399i	0.798498	+	0.601997i	$0.205628\pi$
$631$			30.2440i			1.20399i	−0.798498	+	0.601997i	$0.794372\pi$
$632$	−5.37020	−	5.37020i	−0.213615	−	0.213615i
$633$		0			0
$634$	−3.81425	−	3.81425i	−0.151483	−	0.151483i
$635$	0.760555	−	0.760555i	0.0301817	−	0.0301817i
$636$		0			0
$637$		−	1.71728i		−	0.0680413i
$638$		−	11.4095i		−	0.451706i
$639$		0			0
$640$	−1.37931	+	1.37931i	−0.0545222	+	0.0545222i
$641$	17.2068	+	17.2068i	0.679627	+	0.679627i	0.959916	−	0.280289i	$-0.0904302\pi$
$641$	17.2068	+	17.2068i	0.679627	+	0.679627i	−0.280289	+	0.959916i	$0.590430\pi$
$642$		0			0
$643$	−24.8603	−	24.8603i	−0.980395	−	0.980395i	0.0194169	−	0.999811i	$-0.493819\pi$
$643$	−24.8603	−	24.8603i	−0.980395	−	0.980395i	−0.999811	+	0.0194169i	$0.993819\pi$
$644$			2.82782i			0.111432i
$645$		0			0
$646$	6.12499	−	2.44712i	0.240984	−	0.0962805i
$647$	49.3072			1.93847			0.969233	−	0.246143i	$-0.0791634\pi$
$647$	49.3072			1.93847			0.969233	+	0.246143i	$0.0791634\pi$
$648$		0			0
$649$	−12.4957	−	12.4957i	−0.490497	−	0.490497i
$650$	−4.86604			−0.190862
$651$		0			0
$652$	−14.2807	+	14.2807i	−0.559274	+	0.559274i
$653$	15.9179	−	15.9179i	0.622916	−	0.622916i	−0.323360	−	0.946276i	$-0.604813\pi$
$653$	15.9179	−	15.9179i	0.622916	−	0.622916i	0.946276	+	0.323360i	$0.104813\pi$
$654$		0			0
$655$			0.810028i			0.0316504i
$656$	2.48145	−	2.48145i	0.0968845	−	0.0968845i
$657$		0			0
$658$	0.997016	+	0.997016i	0.0388677	+	0.0388677i
$659$	−39.4858			−1.53815			−0.769074	−	0.639160i	$-0.779282\pi$
$659$	−39.4858			−1.53815			−0.769074	+	0.639160i	$0.779282\pi$
$660$		0			0
$661$		−	12.6197i		−	0.490850i	−0.969416	−	0.245425i	$-0.921073\pi$
$661$		−	12.6197i		−	0.490850i	0.969416	−	0.245425i	$-0.0789275\pi$
$662$	−10.0388			−0.390168
$663$		0			0
$664$	35.8662			1.39188
$665$		−	0.474628i		−	0.0184053i
$666$		0			0
$667$	8.52519			0.330097
$668$	−8.42051	−	8.42051i	−0.325799	−	0.325799i
$669$		0			0
$670$	0.536319	−	0.536319i	0.0207198	−	0.0207198i
$671$		−	15.8951i		−	0.613623i
$672$		0			0
$673$	1.47486	−	1.47486i	0.0568515	−	0.0568515i	−0.678109	−	0.734961i	$-0.737200\pi$
$673$	1.47486	−	1.47486i	0.0568515	−	0.0568515i	0.734961	+	0.678109i	$0.237200\pi$
$674$	−5.68986	+	5.68986i	−0.219165	+	0.219165i
$675$		0			0
$676$	−16.8366			−0.647563
$677$	−11.6586	−	11.6586i	−0.448075	−	0.448075i	0.446639	−	0.894714i	$-0.352621\pi$
$677$	−11.6586	−	11.6586i	−0.448075	−	0.448075i	−0.894714	+	0.446639i	$0.852621\pi$
$678$		0			0
$679$	17.1172			0.656899
$680$	0.575887	−	1.34224i	0.0220843	−	0.0514724i
$681$		0			0
$682$		−	21.0954i		−	0.807785i
$683$	22.1314	+	22.1314i	0.846834	+	0.846834i	0.989737	−	0.142903i	$-0.0456436\pi$
$683$	22.1314	+	22.1314i	0.846834	+	0.846834i	−0.142903	+	0.989737i	$0.545644\pi$
$684$		0			0
$685$	−2.20736	−	2.20736i	−0.0843388	−	0.0843388i
$686$	0.403032	−	0.403032i	0.0153878	−	0.0153878i
$687$		0			0
$688$		−	17.6462i		−	0.672756i
$689$			8.28311i			0.315561i
$690$		0			0
$691$	−2.76135	+	2.76135i	−0.105047	+	0.105047i	−0.757677	−	0.652630i	$-0.773666\pi$
$691$	−2.76135	+	2.76135i	−0.105047	+	0.105047i	0.652630	+	0.757677i	$0.273666\pi$
$692$	14.8475	+	14.8475i	0.564419	+	0.564419i
$693$		0			0
$694$	5.47385	+	5.47385i	0.207784	+	0.207784i
$695$		−	0.0805391i		−	0.00305502i
$696$		0			0
$697$	−2.64575	+	6.16652i	−0.100215	+	0.233573i
$698$	−17.2253			−0.651985
$699$		0			0
$700$	5.88861	+	5.88861i	0.222568	+	0.222568i
$701$	36.3165			1.37166			0.685828	−	0.727763i	$-0.259440\pi$
$701$	36.3165			1.37166			0.685828	+	0.727763i	$0.259440\pi$
$702$		0			0
$703$	−10.2804	+	10.2804i	−0.387732	+	0.387732i
$704$	3.43137	−	3.43137i	0.129325	−	0.129325i
$705$		0			0
$706$			5.45290i			0.205223i
$707$	4.07119	−	4.07119i	0.153113	−	0.153113i
$708$		0			0
$709$	−9.27704	−	9.27704i	−0.348406	−	0.348406i	0.511109	−	0.859516i	$-0.329235\pi$
$709$	−9.27704	−	9.27704i	−0.348406	−	0.348406i	−0.859516	+	0.511109i	$0.829235\pi$
$710$	−1.09148			−0.0409627
$711$		0			0
$712$			9.97683i			0.373897i
$713$	15.7625			0.590312
$714$		0			0
$715$	−1.15112			−0.0430496
$716$			11.8106i			0.441381i
$717$		0			0
$718$	−12.2067			−0.455551
$719$	31.7672	+	31.7672i	1.18472	+	1.18472i	0.978508	+	0.206209i	$0.0661128\pi$
$719$	31.7672	+	31.7672i	1.18472	+	1.18472i	0.206209	+	0.978508i	$0.433887\pi$
$720$		0			0
$721$	3.68815	−	3.68815i	0.137354	−	0.137354i
$722$		−	6.33971i		−	0.235940i
$723$		0			0
$724$	−5.81423	+	5.81423i	−0.216084	+	0.216084i
$725$	17.7527	−	17.7527i	0.659319	−	0.659319i
$726$		0			0
$727$	1.90215			0.0705470			0.0352735	−	0.999378i	$-0.488770\pi$
$727$	1.90215			0.0705470			0.0352735	+	0.999378i	$0.488770\pi$
$728$	2.54363	+	2.54363i	0.0942733	+	0.0942733i
$729$		0			0
$730$	−1.01273			−0.0374828
$731$	12.5185	+	31.3331i	0.463014	+	1.15890i
$732$		0			0
$733$		−	47.0928i		−	1.73941i	−0.493569	−	0.869706i	$-0.664308\pi$
$733$		−	47.0928i		−	1.73941i	0.493569	−	0.869706i	$-0.335692\pi$
$734$	0.359240	+	0.359240i	0.0132598	+	0.0132598i
$735$		0			0
$736$	−6.46796	−	6.46796i	−0.238412	−	0.238412i
$737$	−22.0552	+	22.0552i	−0.812414	+	0.812414i
$738$		0			0
$739$		−	23.6433i		−	0.869732i	−0.900495	−	0.434866i	$-0.856796\pi$
$739$		−	23.6433i		−	0.869732i	0.900495	−	0.434866i	$-0.143204\pi$
$740$			1.46743i			0.0539437i
$741$		0			0
$742$	−1.94397	+	1.94397i	−0.0713655	+	0.0713655i
$743$	22.5544	+	22.5544i	0.827440	+	0.827440i	0.987162	−	0.159722i	$-0.0510598\pi$
$743$	22.5544	+	22.5544i	0.827440	+	0.827440i	−0.159722	+	0.987162i	$0.551060\pi$
$744$		0			0
$745$	2.63151	+	2.63151i	0.0964112	+	0.0964112i
$746$			12.0189i			0.440044i
$747$		0			0
$748$	−10.7945	+	25.1590i	−0.394685	+	0.919903i
$749$	12.8559			0.469744
$750$		0			0
$751$	−28.9462	−	28.9462i	−1.05626	−	1.05626i	−0.998320	−	0.0579400i	$-0.981547\pi$
$751$	−28.9462	−	28.9462i	−1.05626	−	1.05626i	−0.0579400	−	0.998320i	$-0.518453\pi$
$752$	5.33430			0.194522
$753$		0			0
$754$	3.49528	−	3.49528i	0.127291	−	0.127291i
$755$	2.54051	−	2.54051i	0.0924585	−	0.0924585i
$756$		0			0
$757$		−	30.7472i		−	1.11753i	−0.829327	−	0.558763i	$-0.811276\pi$
$757$		−	30.7472i		−	1.11753i	0.829327	−	0.558763i	$-0.188724\pi$
$758$	12.1138	−	12.1138i	0.439992	−	0.439992i
$759$		0			0
$760$	0.703017	+	0.703017i	0.0255011	+	0.0255011i
$761$	−2.98597			−0.108241			−0.0541207	−	0.998534i	$-0.517236\pi$
$761$	−2.98597			−0.108241			−0.0541207	+	0.998534i	$0.517236\pi$
$762$		0			0
$763$			7.40845i			0.268204i
$764$	−18.7681			−0.679008
$765$		0			0
$766$	−8.76346			−0.316637
$767$		−	7.65606i		−	0.276444i
$768$		0			0
$769$	25.6235			0.924007			0.462004	−	0.886878i	$-0.347131\pi$
$769$	25.6235			0.924007			0.462004	+	0.886878i	$0.347131\pi$
$770$	−0.270159	−	0.270159i	−0.00973584	−	0.00973584i
$771$		0			0
$772$	−12.0549	+	12.0549i	−0.433866	+	0.433866i
$773$		−	27.2422i		−	0.979835i	−0.871769	−	0.489918i	$-0.837027\pi$
$773$		−	27.2422i		−	0.979835i	0.871769	−	0.489918i	$-0.162973\pi$
$774$		0			0
$775$	32.8236	−	32.8236i	1.17906	−	1.17906i
$776$	−25.3539	+	25.3539i	−0.910153	+	0.910153i
$777$		0			0
$778$	−0.235684			−0.00844966
$779$	−3.22981	−	3.22981i	−0.115720	−	0.115720i
$780$		0			0
$781$	44.8855			1.60613
$782$	3.64578	+	1.56423i	0.130373	+	0.0559366i
$783$		0			0
$784$		−	2.15633i		−	0.0770116i
$785$	−0.197480	−	0.197480i	−0.00704836	−	0.00704836i
$786$		0			0
$787$	−20.7467	−	20.7467i	−0.739539	−	0.739539i	0.232950	−	0.972489i	$-0.425162\pi$
$787$	−20.7467	−	20.7467i	−0.739539	−	0.739539i	−0.972489	+	0.232950i	$0.925162\pi$
$788$	19.4091	−	19.4091i	0.691419	−	0.691419i
$789$		0			0
$790$			0.349463i			0.0124333i
$791$			6.72264i			0.239030i
$792$		0			0
$793$	4.86945	−	4.86945i	0.172919	−	0.172919i
$794$	−3.77295	−	3.77295i	−0.133897	−	0.133897i
$795$		0			0
$796$	30.2133	+	30.2133i	1.07088	+	1.07088i
$797$		−	4.54196i		−	0.160884i	−0.996759	−	0.0804422i	$-0.974367\pi$
$797$		−	4.54196i		−	0.160884i	0.996759	−	0.0804422i	$-0.0256332\pi$
$798$		0			0
$799$	−9.47172	+	3.78424i	−0.335085	+	0.133877i
$800$	−26.9375			−0.952385
$801$		0			0
$802$	−15.3377	−	15.3377i	−0.541593	−	0.541593i
$803$	41.6468			1.46968
$804$		0			0
$805$	0.201863	−	0.201863i	0.00711474	−	0.00711474i
$806$	6.46255	−	6.46255i	0.227634	−	0.227634i
$807$		0			0
$808$			12.0604i			0.424285i
$809$	−18.3893	+	18.3893i	−0.646535	+	0.646535i	−0.952154	−	0.305619i	$-0.901137\pi$
$809$	−18.3893	+	18.3893i	−0.646535	+	0.646535i	0.305619	+	0.952154i	$0.401137\pi$
$810$		0			0
$811$	−23.7674	−	23.7674i	−0.834588	−	0.834588i	0.153553	−	0.988140i	$-0.450929\pi$
$811$	−23.7674	−	23.7674i	−0.834588	−	0.834588i	−0.988140	+	0.153553i	$0.950929\pi$
$812$	−8.45959			−0.296873
$813$		0			0
$814$			11.7032i			0.410196i
$815$	2.03884			0.0714175
$816$		0			0
$817$	−22.9680			−0.803547
$818$		−	4.80433i		−	0.167980i
$819$		0			0
$820$	−0.461025			−0.0160997
$821$	16.8556	+	16.8556i	0.588266	+	0.588266i	0.937162	−	0.348896i	$-0.113443\pi$
$821$	16.8556	+	16.8556i	0.588266	+	0.588266i	−0.348896	+	0.937162i	$0.613443\pi$
$822$		0			0
$823$	−7.68091	+	7.68091i	−0.267740	+	0.267740i	−0.828189	−	0.560449i	$-0.810629\pi$
$823$	−7.68091	+	7.68091i	−0.267740	+	0.267740i	0.560449	+	0.828189i	$0.310629\pi$
$824$			10.9257i			0.380616i
$825$		0			0
$826$	1.79681	−	1.79681i	0.0625190	−	0.0625190i
$827$	−21.8289	+	21.8289i	−0.759065	+	0.759065i	−0.976152	−	0.217087i	$-0.930344\pi$
$827$	−21.8289	+	21.8289i	−0.759065	+	0.759065i	0.217087	+	0.976152i	$0.430344\pi$
$828$		0			0
$829$	2.11380			0.0734154			0.0367077	−	0.999326i	$-0.488313\pi$
$829$	2.11380			0.0734154			0.0367077	+	0.999326i	$0.488313\pi$
$830$	−1.16699	−	1.16699i	−0.0405067	−	0.0405067i
$831$		0			0
$832$	2.10239			0.0728873
$833$	1.52973	+	3.82883i	0.0530021	+	0.132661i
$834$		0			0
$835$			1.20219i			0.0416035i
$836$	−13.1774	−	13.1774i	−0.455750	−	0.455750i
$837$		0			0
$838$	7.48341	+	7.48341i	0.258510	+	0.258510i
$839$	−26.9183	+	26.9183i	−0.929322	+	0.929322i	−0.997662	−	0.0683400i	$-0.978230\pi$
$839$	−26.9183	+	26.9183i	−0.929322	+	0.929322i	0.0683400	+	0.997662i	$0.478230\pi$
$840$		0			0
$841$		−	3.49641i		−	0.120566i
$842$		−	0.117755i		−	0.00405811i
$843$		0			0
$844$	−26.0066	+	26.0066i	−0.895184	+	0.895184i
$845$	1.20188	+	1.20188i	0.0413458	+	0.0413458i
$846$		0			0
$847$	3.33164	+	3.33164i	0.114477	+	0.114477i
$848$			10.4008i			0.357164i
$849$		0			0
$850$	10.8492	−	4.33460i	0.372125	−	0.148675i
$851$	−8.74465			−0.299763
$852$		0			0
$853$	23.9658	+	23.9658i	0.820574	+	0.820574i	0.986190	−	0.165616i	$-0.0529613\pi$
$853$	23.9658	+	23.9658i	0.820574	+	0.820574i	−0.165616	+	0.986190i	$0.552961\pi$
$854$	2.28563			0.0782127
$855$		0			0
$856$	−19.0421	+	19.0421i	−0.650845	+	0.650845i
$857$	−19.6096	+	19.6096i	−0.669852	+	0.669852i	−0.957682	−	0.287829i	$-0.907066\pi$
$857$	−19.6096	+	19.6096i	−0.669852	+	0.669852i	0.287829	+	0.957682i	$0.407066\pi$
$858$		0			0
$859$		−	25.3104i		−	0.863581i	−0.901974	−	0.431790i	$-0.857882\pi$
$859$		−	25.3104i		−	0.863581i	0.901974	−	0.431790i	$-0.142118\pi$
$860$	−1.63923	+	1.63923i	−0.0558973	+	0.0558973i
$861$		0			0
$862$	−2.47831	−	2.47831i	−0.0844117	−	0.0844117i
$863$	16.6127			0.565504			0.282752	−	0.959193i	$-0.408753\pi$
$863$	16.6127			0.565504			0.282752	+	0.959193i	$0.408753\pi$
$864$		0			0
$865$		−	2.11977i		−	0.0720745i
$866$	−9.15220			−0.311004
$867$		0			0
$868$	−15.6412			−0.530898
$869$		−	14.3711i		−	0.487506i
$870$		0			0
$871$	−13.5132			−0.457876
$872$	−10.9734	−	10.9734i	−0.371605	−	0.371605i
$873$		0			0
$874$	−1.90954	+	1.90954i	−0.0645910	+	0.0645910i
$875$		−	1.68626i		−	0.0570060i
$876$		0			0
$877$	25.5226	−	25.5226i	0.861838	−	0.861838i	−0.129714	−	0.991552i	$-0.541406\pi$
$877$	25.5226	−	25.5226i	0.861838	−	0.861838i	0.991552	+	0.129714i	$0.0414058\pi$
$878$	5.68059	−	5.68059i	0.191711	−	0.191711i
$879$		0			0
$880$	−1.44542			−0.0487251
$881$	−26.8027	−	26.8027i	−0.903006	−	0.903006i	0.0926891	−	0.995695i	$-0.470454\pi$
$881$	−26.8027	−	26.8027i	−0.903006	−	0.903006i	−0.995695	+	0.0926891i	$0.970454\pi$
$882$		0			0
$883$	−30.6151			−1.03028			−0.515140	−	0.857106i	$-0.672260\pi$
$883$	−30.6151			−1.03028			−0.515140	+	0.857106i	$0.672260\pi$
$884$	−11.0143	+	4.40055i	−0.370451	+	0.148006i
$885$		0			0
$886$		−	7.79235i		−	0.261789i
$887$	−35.4188	−	35.4188i	−1.18925	−	1.18925i	−0.977276	−	0.211970i	$-0.932012\pi$
$887$	−35.4188	−	35.4188i	−1.18925	−	1.18925i	−0.211970	−	0.977276i	$-0.567988\pi$
$888$		0			0
$889$	−4.49740	−	4.49740i	−0.150838	−	0.150838i
$890$	0.324619	−	0.324619i	0.0108812	−	0.0108812i
$891$		0			0
$892$			5.41632i			0.181352i
$893$		−	6.94301i		−	0.232339i
$894$		0			0
$895$	0.843093	−	0.843093i	0.0281815	−	0.0281815i
$896$	8.15633	+	8.15633i	0.272484	+	0.272484i
$897$		0			0
$898$	3.34267	+	3.34267i	0.111546	+	0.111546i
$899$			47.1545i			1.57269i
$900$		0			0
$901$	−7.37847	−	18.4679i	−0.245813	−	0.615254i
$902$	−3.67682			−0.122425
$903$		0			0
$904$	−9.95754	−	9.95754i	−0.331183	−	0.331183i
$905$	0.830094			0.0275932
$906$		0			0
$907$	−0.0721880	+	0.0721880i	−0.00239696	+	0.00239696i	−0.708304	−	0.705907i	$-0.750540\pi$
$907$	−0.0721880	+	0.0721880i	−0.00239696	+	0.00239696i	0.705907	+	0.708304i	$0.250540\pi$
$908$	−25.1295	+	25.1295i	−0.833953	+	0.833953i
$909$		0			0
$910$		−	0.165526i		−	0.00548712i
$911$	−7.75030	+	7.75030i	−0.256779	+	0.256779i	−0.823743	−	0.566964i	$-0.808118\pi$
$911$	−7.75030	+	7.75030i	−0.256779	+	0.256779i	0.566964	+	0.823743i	$0.308118\pi$
$912$		0			0
$913$	47.9904	+	47.9904i	1.58825	+	1.58825i
$914$	−9.88694			−0.327031
$915$		0			0
$916$			39.8043i			1.31517i
$917$	4.78995			0.158178
$918$		0			0
$919$	58.8854			1.94245			0.971225	−	0.238165i	$-0.0765460\pi$
$919$	58.8854			1.94245			0.971225	+	0.238165i	$0.0765460\pi$
$920$			0.597997i			0.0197154i
$921$		0			0
$922$	−24.0485			−0.791994
$923$	13.7506	+	13.7506i	0.452607	+	0.452607i
$924$		0			0
$925$	−18.2097	+	18.2097i	−0.598731	+	0.598731i
$926$		−	8.90227i		−	0.292547i
$927$		0			0
$928$	19.3493	−	19.3493i	0.635171	−	0.635171i
$929$	33.2876	−	33.2876i	1.09213	−	1.09213i	0.0968299	−	0.995301i	$-0.469130\pi$
$929$	33.2876	−	33.2876i	1.09213	−	1.09213i	0.995301	−	0.0968299i	$-0.0308703\pi$
$930$		0			0
$931$	−2.80663			−0.0919836
$932$	31.0042	+	31.0042i	1.01558	+	1.01558i
$933$		0			0
$934$	10.8146			0.353865
$935$	2.56652	−	1.02540i	0.0839343	−	0.0335343i
$936$		0			0
$937$			43.9382i			1.43540i	0.696352	+	0.717700i	$0.254805\pi$
$937$			43.9382i			1.43540i	−0.696352	+	0.717700i	$0.745195\pi$
$938$	−3.17142	−	3.17142i	−0.103551	−	0.103551i
$939$		0			0
$940$	−0.495525	−	0.495525i	−0.0161622	−	0.0161622i
$941$	15.1425	−	15.1425i	0.493633	−	0.493633i	−0.415816	−	0.909449i	$-0.636504\pi$
$941$	15.1425	−	15.1425i	0.493633	−	0.493633i	0.909449	+	0.415816i	$0.136504\pi$
$942$		0			0
$943$		−	2.74733i		−	0.0894653i
$944$		−	9.61341i		−	0.312890i
$945$		0			0
$946$	−13.0734	+	13.0734i	−0.425052	+	0.425052i
$947$	30.2053	+	30.2053i	0.981539	+	0.981539i	0.999833	−	0.0182934i	$-0.00582330\pi$
$947$	30.2053	+	30.2053i	0.981539	+	0.981539i	−0.0182934	+	0.999833i	$0.505823\pi$
$948$		0			0
$949$	12.7585	+	12.7585i	0.414157	+	0.414157i
$950$			7.95276i			0.258022i
$951$		0			0
$952$	−7.93707	−	3.40541i	−0.257242	−	0.110370i
$953$	−1.43199			−0.0463866			−0.0231933	−	0.999731i	$-0.507383\pi$
$953$	−1.43199			−0.0463866			−0.0231933	+	0.999731i	$0.507383\pi$
$954$		0			0
$955$	1.33976	+	1.33976i	0.0433535	+	0.0433535i
$956$	−8.38374			−0.271150
$957$		0			0
$958$	−2.35839	+	2.35839i	−0.0761960	+	0.0761960i
$959$	−13.0528	+	13.0528i	−0.421497	+	0.421497i
$960$		0			0
$961$			56.1857i			1.81244i
$962$	−3.58526	+	3.58526i	−0.115593	+	0.115593i
$963$		0			0
$964$	12.2834	+	12.2834i	0.395621	+	0.395621i
$965$	1.72107			0.0554033
$966$		0			0
$967$			50.1315i			1.61212i	0.591834	+	0.806060i	$0.298404\pi$
$967$			50.1315i			1.61212i	−0.591834	+	0.806060i	$0.701596\pi$
$968$	−9.86961			−0.317221
$969$		0			0
$970$	1.64989			0.0529749
$971$		−	31.5488i		−	1.01245i	−0.862402	−	0.506225i	$-0.831041\pi$
$971$		−	31.5488i		−	1.01245i	0.862402	−	0.506225i	$-0.168959\pi$
$972$		0			0
$973$	−0.476253			−0.0152680
$974$	13.2595	+	13.2595i	0.424863	+	0.424863i
$975$		0			0
$976$	6.11437	−	6.11437i	0.195716	−	0.195716i
$977$		−	58.5783i		−	1.87409i	−0.349215	−	0.937043i	$-0.613552\pi$
$977$		−	58.5783i		−	1.87409i	0.349215	−	0.937043i	$-0.386448\pi$
$978$		0			0
$979$	−13.3494	+	13.3494i	−0.426648	+	0.426648i
$980$	−0.200310	+	0.200310i	−0.00639867	+	0.00639867i
$981$		0			0
$982$	−5.29925			−0.169106
$983$	−27.4679	−	27.4679i	−0.876090	−	0.876090i	0.117038	−	0.993127i	$-0.462660\pi$
$983$	−27.4679	−	27.4679i	−0.876090	−	0.876090i	−0.993127	+	0.117038i	$0.962660\pi$
$984$		0			0
$985$	−2.77102			−0.0882920
$986$	−4.67947	+	10.9066i	−0.149025	+	0.347336i
$987$		0			0
$988$		−	8.07377i		−	0.256861i
$989$	−9.76845	−	9.76845i	−0.310619	−	0.310619i
$990$		0			0
$991$	−22.0926	−	22.0926i	−0.701795	−	0.701795i	0.263001	−	0.964796i	$-0.415288\pi$
$991$	−22.0926	−	22.0926i	−0.701795	−	0.701795i	−0.964796	+	0.263001i	$0.915288\pi$
$992$	35.7756	−	35.7756i	1.13588	−	1.13588i
$993$		0			0
$994$			6.45430i			0.204718i
$995$		−	4.31353i		−	0.136748i
$996$		0			0
$997$	8.45732	−	8.45732i	0.267846	−	0.267846i	−0.560386	−	0.828232i	$-0.689347\pi$
$997$	8.45732	−	8.45732i	0.267846	−	0.267846i	0.828232	+	0.560386i	$0.189347\pi$
$998$	−12.2516	−	12.2516i	−0.387817	−	0.387817i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1071.2.n.a.64.3		12
3.2	odd	2		357.2.k.a.64.4	✓	12
17.4	even	4	inner	1071.2.n.a.820.4		12
51.2	odd	8		6069.2.a.y.1.3		6
51.32	odd	8		6069.2.a.x.1.3		6
51.38	odd	4		357.2.k.a.106.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.k.a.64.4	✓	12	3.2	odd	2
357.2.k.a.106.3	yes	12	51.38	odd	4
1071.2.n.a.64.3		12	1.1	even	1	trivial
1071.2.n.a.820.4		12	17.4	even	4	inner
6069.2.a.x.1.3		6	51.32	odd	8
6069.2.a.y.1.3		6	51.2	odd	8

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:	\( N \)	\(=\)	\( 1071 = 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1071.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.569973i q^{2} +1.67513 q^{4} +(-0.119579 - 0.119579i) q^{5} +(-0.707107 + 0.707107i) q^{7} -2.09473i q^{8} +O(q^{10})\)	\(q-0.569973i q^{2} +1.67513 q^{4} +(-0.119579 - 0.119579i) q^{5} +(-0.707107 + 0.707107i) q^{7} -2.09473i q^{8} +(-0.0681566 + 0.0681566i) q^{10} +(2.80282 - 2.80282i) q^{11} +1.71728 q^{13} +(0.403032 + 0.403032i) q^{14} +2.15633 q^{16} +(-3.82883 + 1.52973i) q^{17} -2.80663i q^{19} +(-0.200310 - 0.200310i) q^{20} +(-1.59753 - 1.59753i) q^{22} +(1.19368 - 1.19368i) q^{23} -4.97140i q^{25} -0.978806i q^{26} +(-1.18450 + 1.18450i) q^{28} +(3.57097 + 3.57097i) q^{29} +(6.60249 + 6.60249i) q^{31} -5.41850i q^{32} +(0.871906 + 2.18233i) q^{34} +0.169110 q^{35} +(-3.66289 - 3.66289i) q^{37} -1.59970 q^{38} +(-0.250484 + 0.250484i) q^{40} +(1.15078 - 1.15078i) q^{41} -8.18347i q^{43} +(4.69510 - 4.69510i) q^{44} +(-0.680366 - 0.680366i) q^{46} +2.47379 q^{47} -1.00000i q^{49} -2.83356 q^{50} +2.87668 q^{52} +4.82337i q^{53} -0.670316 q^{55} +(1.48119 + 1.48119i) q^{56} +(2.03535 - 2.03535i) q^{58} -4.45824i q^{59} +(2.83555 - 2.83555i) q^{61} +(3.76324 - 3.76324i) q^{62} +1.22425 q^{64} +(-0.205351 - 0.205351i) q^{65} -7.86892 q^{67} +(-6.41379 + 2.56250i) q^{68} -0.0963880i q^{70} +(8.00718 + 8.00718i) q^{71} +(7.42943 + 7.42943i) q^{73} +(-2.08775 + 2.08775i) q^{74} -4.70147i q^{76} +3.96379i q^{77} +(2.56368 - 2.56368i) q^{79} +(-0.257850 - 0.257850i) q^{80} +(-0.655913 - 0.655913i) q^{82} +17.1221i q^{83} +(0.640769 + 0.274923i) q^{85} -4.66435 q^{86} +(-5.87115 - 5.87115i) q^{88} -4.76283 q^{89} +(-1.21430 + 1.21430i) q^{91} +(1.99957 - 1.99957i) q^{92} -1.40999i q^{94} +(-0.335613 + 0.335613i) q^{95} +(-12.1037 - 12.1037i) q^{97} -0.569973 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{5}+O(q^{10}) \) 12 * q - 8 * q^5	\( 12 q - 8 q^{5} - 16 q^{10} - 4 q^{11} + 4 q^{13} + 4 q^{14} - 16 q^{16} - 20 q^{17} - 12 q^{20} + 32 q^{22} - 4 q^{23} + 32 q^{29} - 8 q^{31} + 20 q^{34} + 12 q^{35} - 16 q^{37} + 16 q^{38} + 12 q^{40} + 20 q^{41} + 8 q^{44} - 12 q^{46} - 32 q^{47} - 48 q^{50} - 16 q^{52} + 76 q^{55} - 4 q^{56} - 28 q^{58} - 20 q^{61} + 28 q^{62} + 8 q^{64} + 44 q^{65} - 56 q^{67} - 12 q^{68} + 16 q^{71} + 8 q^{73} - 8 q^{74} - 24 q^{79} + 8 q^{80} + 12 q^{82} - 24 q^{85} + 32 q^{86} + 12 q^{88} - 64 q^{89} + 4 q^{91} - 24 q^{92} + 36 q^{95} - 52 q^{97}+O(q^{100}) \) 12 * q - 8 * q^5 - 16 * q^10 - 4 * q^11 + 4 * q^13 + 4 * q^14 - 16 * q^16 - 20 * q^17 - 12 * q^20 + 32 * q^22 - 4 * q^23 + 32 * q^29 - 8 * q^31 + 20 * q^34 + 12 * q^35 - 16 * q^37 + 16 * q^38 + 12 * q^40 + 20 * q^41 + 8 * q^44 - 12 * q^46 - 32 * q^47 - 48 * q^50 - 16 * q^52 + 76 * q^55 - 4 * q^56 - 28 * q^58 - 20 * q^61 + 28 * q^62 + 8 * q^64 + 44 * q^65 - 56 * q^67 - 12 * q^68 + 16 * q^71 + 8 * q^73 - 8 * q^74 - 24 * q^79 + 8 * q^80 + 12 * q^82 - 24 * q^85 + 32 * q^86 + 12 * q^88 - 64 * q^89 + 4 * q^91 - 24 * q^92 + 36 * q^95 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more