LMFDB - Embedded newform 464.2.k.c.447.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,2,Mod(191,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("464.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.k (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:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{17} - 6 x^{16} - 2 x^{15} + 18 x^{14} + 42 x^{13} + 9 x^{12} - 30 x^{11} - 142 x^{10} + \cdots + 1024 $ x^20 - 6x^17 - 6x^16 - 2x^15 + 18x^14 + 42x^13 + 9x^12 - 30x^11 - 142x^10 - 60x^9 + 36x^8 + 336x^7 + 288x^6 - 64x^5 - 384x^4 - 768*x^3 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{17} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			447.10
Root			$-0.702175 - 1.22758i$ of defining polynomial
Character	$\chi$	$=$	464.447
Dual form			464.2.k.c.191.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.92975 - 1.92975i) q^{3} -2.39709i q^{5} -1.01973i q^{7} -4.44790i q^{9} +O(q^{10})$	\(q+(1.92975 - 1.92975i) q^{3} -2.39709i q^{5} -1.01973i q^{7} -4.44790i q^{9} +(-2.07012 + 2.07012i) q^{11} -1.30477i q^{13} +(-4.62579 - 4.62579i) q^{15} +(3.78485 + 3.78485i) q^{17} +(-3.70412 + 3.70412i) q^{19} +(-1.96782 - 1.96782i) q^{21} -4.28773i q^{23} -0.746041 q^{25} +(-2.79409 - 2.79409i) q^{27} +(3.15397 + 4.36491i) q^{29} +(2.93783 - 2.93783i) q^{31} +7.98963i q^{33} -2.44438 q^{35} +(-1.63087 + 1.63087i) q^{37} +(-2.51788 - 2.51788i) q^{39} +(8.28356 - 8.28356i) q^{41} +(-8.05370 + 8.05370i) q^{43} -10.6620 q^{45} +(-4.09792 - 4.09792i) q^{47} +5.96016 q^{49} +14.6076 q^{51} +6.32929 q^{53} +(4.96226 + 4.96226i) q^{55} +14.2961i q^{57} -4.26443i q^{59} +(-8.36809 - 8.36809i) q^{61} -4.53564 q^{63} -3.12765 q^{65} +9.62370 q^{67} +(-8.27426 - 8.27426i) q^{69} +11.5718 q^{71} +(-2.47075 + 2.47075i) q^{73} +(-1.43968 + 1.43968i) q^{75} +(2.11095 + 2.11095i) q^{77} +(-10.5493 + 10.5493i) q^{79} +2.55989 q^{81} +0.320297i q^{83} +(9.07262 - 9.07262i) q^{85} +(14.5096 + 2.33681i) q^{87} +(-8.21575 - 8.21575i) q^{89} -1.33051 q^{91} -11.3386i q^{93} +(8.87910 + 8.87910i) q^{95} +(1.53089 - 1.53089i) q^{97} +(9.20767 + 9.20767i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q+O(q^{10}) $ 20 * q	$ 20 q - 4 q^{17} - 16 q^{21} - 28 q^{25} - 4 q^{29} - 20 q^{37} - 4 q^{41} - 40 q^{45} + 28 q^{49} + 48 q^{53} + 4 q^{61} + 40 q^{65} - 24 q^{69} - 20 q^{73} - 16 q^{77} + 108 q^{81} + 16 q^{85} + 36 q^{89} - 36 q^{97}+O(q^{100}) $ 20 * q - 4 * q^17 - 16 * q^21 - 28 * q^25 - 4 * q^29 - 20 * q^37 - 4 * q^41 - 40 * q^45 + 28 * q^49 + 48 * q^53 + 4 * q^61 + 40 * q^65 - 24 * q^69 - 20 * q^73 - 16 * q^77 + 108 * q^81 + 16 * q^85 + 36 * q^89 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	1.92975	−	1.92975i	1.11414	−	1.11414i	0.121560	−	0.992584i	$-0.461210\pi$
$3$	1.92975	−	1.92975i	1.11414	−	1.11414i	0.992584	−	0.121560i	$-0.0387896\pi$
$4$		0			0
$5$		−	2.39709i		−	1.07201i	−0.844214	−	0.536006i	$-0.819933\pi$
$5$		−	2.39709i		−	1.07201i	0.844214	−	0.536006i	$-0.180067\pi$
$6$		0			0
$7$		−	1.01973i		−	0.385420i	−0.981256	−	0.192710i	$-0.938272\pi$
$7$		−	1.01973i		−	0.385420i	0.981256	−	0.192710i	$-0.0617277\pi$
$8$		0			0
$9$		−	4.44790i		−	1.48263i
$10$		0			0
$11$	−2.07012	+	2.07012i	−0.624164	+	0.624164i	−0.946593	−	0.322430i	$-0.895500\pi$
$11$	−2.07012	+	2.07012i	−0.624164	+	0.624164i	0.322430	+	0.946593i	$0.395500\pi$
$12$		0			0
$13$		−	1.30477i		−	0.361878i	−0.983494	−	0.180939i	$-0.942086\pi$
$13$		−	1.30477i		−	0.361878i	0.983494	−	0.180939i	$-0.0579136\pi$
$14$		0			0
$15$	−4.62579	−	4.62579i	−1.19437	−	1.19437i
$16$		0			0
$17$	3.78485	+	3.78485i	0.917960	+	0.917960i	0.996881	−	0.0789206i	$-0.0251474\pi$
$17$	3.78485	+	3.78485i	0.917960	+	0.917960i	−0.0789206	+	0.996881i	$0.525147\pi$
$18$		0			0
$19$	−3.70412	+	3.70412i	−0.849783	+	0.849783i	−0.990106	−	0.140323i	$-0.955186\pi$
$19$	−3.70412	+	3.70412i	−0.849783	+	0.849783i	0.140323	+	0.990106i	$0.455186\pi$
$20$		0			0
$21$	−1.96782	−	1.96782i	−0.429414	−	0.429414i
$22$		0			0
$23$		−	4.28773i		−	0.894053i	−0.894521	−	0.447027i	$-0.852483\pi$
$23$		−	4.28773i		−	0.894053i	0.894521	−	0.447027i	$-0.147517\pi$
$24$		0			0
$25$	−0.746041			−0.149208
$26$		0			0
$27$	−2.79409	−	2.79409i	−0.537723	−	0.537723i
$28$		0			0
$29$	3.15397	+	4.36491i	0.585678	+	0.810544i
$29$	3.15397	+	4.36491i	0.585678	+	0.810544i
$30$		0			0
$31$	2.93783	−	2.93783i	0.527650	−	0.527650i	−0.392221	−	0.919871i	$-0.628293\pi$
$31$	2.93783	−	2.93783i	0.527650	−	0.527650i	0.919871	+	0.392221i	$0.128293\pi$
$32$		0			0
$33$			7.98963i			1.39082i
$34$		0			0
$35$	−2.44438			−0.413175
$36$		0			0
$37$	−1.63087	+	1.63087i	−0.268114	+	0.268114i	−0.828340	−	0.560226i	$-0.810714\pi$
$37$	−1.63087	+	1.63087i	−0.268114	+	0.268114i	0.560226	+	0.828340i	$0.310714\pi$
$38$		0			0
$39$	−2.51788	−	2.51788i	−0.403184	−	0.403184i
$40$		0			0
$41$	8.28356	−	8.28356i	1.29367	−	1.29367i	0.361177	−	0.932497i	$-0.382375\pi$
$41$	8.28356	−	8.28356i	1.29367	−	1.29367i	0.932497	−	0.361177i	$-0.117625\pi$
$42$		0			0
$43$	−8.05370	+	8.05370i	−1.22818	+	1.22818i	−0.263526	+	0.964652i	$0.584885\pi$
$43$	−8.05370	+	8.05370i	−1.22818	+	1.22818i	−0.964652	+	0.263526i	$0.915115\pi$
$44$		0			0
$45$	−10.6620			−1.58940
$46$		0			0
$47$	−4.09792	−	4.09792i	−0.597743	−	0.597743i	0.341968	−	0.939711i	$-0.388906\pi$
$47$	−4.09792	−	4.09792i	−0.597743	−	0.597743i	−0.939711	+	0.341968i	$0.888906\pi$
$48$		0			0
$49$	5.96016			0.851451
$50$		0			0
$51$	14.6076			2.04548
$52$		0			0
$53$	6.32929			0.869394			0.434697	−	0.900577i	$-0.356855\pi$
$53$	6.32929			0.869394			0.434697	+	0.900577i	$0.356855\pi$
$54$		0			0
$55$	4.96226	+	4.96226i	0.669111	+	0.669111i
$56$		0			0
$57$			14.2961i			1.89356i
$58$		0			0
$59$		−	4.26443i		−	0.555182i	−0.960699	−	0.277591i	$-0.910464\pi$
$59$		−	4.26443i		−	0.555182i	0.960699	−	0.277591i	$-0.0895359\pi$
$60$		0			0
$61$	−8.36809	−	8.36809i	−1.07142	−	1.07142i	−0.997245	−	0.0741794i	$-0.976366\pi$
$61$	−8.36809	−	8.36809i	−1.07142	−	1.07142i	−0.0741794	−	0.997245i	$-0.523634\pi$
$62$		0			0
$63$	−4.53564			−0.571437
$64$		0			0
$65$	−3.12765			−0.387937
$66$		0			0
$67$	9.62370			1.17572			0.587861	−	0.808962i	$-0.299970\pi$
$67$	9.62370			1.17572			0.587861	+	0.808962i	$0.299970\pi$
$68$		0			0
$69$	−8.27426	−	8.27426i	−0.996104	−	0.996104i
$70$		0			0
$71$	11.5718			1.37332			0.686658	−	0.726981i	$-0.259077\pi$
$71$	11.5718			1.37332			0.686658	+	0.726981i	$0.259077\pi$
$72$		0			0
$73$	−2.47075	+	2.47075i	−0.289179	+	0.289179i	−0.836756	−	0.547577i	$-0.815550\pi$
$73$	−2.47075	+	2.47075i	−0.289179	+	0.289179i	0.547577	+	0.836756i	$0.315550\pi$
$74$		0			0
$75$	−1.43968	+	1.43968i	−0.166240	+	0.166240i
$76$		0			0
$77$	2.11095	+	2.11095i	0.240565	+	0.240565i
$78$		0			0
$79$	−10.5493	+	10.5493i	−1.18689	+	1.18689i	−0.208966	+	0.977923i	$0.567010\pi$
$79$	−10.5493	+	10.5493i	−1.18689	+	1.18689i	−0.977923	+	0.208966i	$0.932990\pi$
$80$		0			0
$81$	2.55989			0.284432
$82$		0			0
$83$			0.320297i			0.0351572i	0.999845	+	0.0175786i	$0.00559573\pi$
$83$			0.320297i			0.0351572i	−0.999845	+	0.0175786i	$0.994404\pi$
$84$		0			0
$85$	9.07262	−	9.07262i	0.984064	−	0.984064i
$86$		0			0
$87$	14.5096	+	2.33681i	1.55559	+	0.250532i
$88$		0			0
$89$	−8.21575	−	8.21575i	−0.870868	−	0.870868i	0.121699	−	0.992567i	$-0.461166\pi$
$89$	−8.21575	−	8.21575i	−0.870868	−	0.870868i	−0.992567	+	0.121699i	$0.961166\pi$
$90$		0			0
$91$	−1.33051			−0.139475
$92$		0			0
$93$		−	11.3386i		−	1.17576i
$94$		0			0
$95$	8.87910	+	8.87910i	0.910977	+	0.910977i
$96$		0			0
$97$	1.53089	−	1.53089i	0.155438	−	0.155438i	−0.625104	−	0.780542i	$-0.714943\pi$
$97$	1.53089	−	1.53089i	0.155438	−	0.155438i	0.780542	+	0.625104i	$0.214943\pi$
$98$		0			0
$99$	9.20767	+	9.20767i	0.925406	+	0.925406i
$100$		0			0
$101$	1.65372	+	1.65372i	0.164551	+	0.164551i	0.784579	−	0.620028i	$-0.212879\pi$
$101$	1.65372	+	1.65372i	0.164551	+	0.164551i	−0.620028	+	0.784579i	$0.712879\pi$
$102$		0			0
$103$			7.31685i			0.720951i	0.932769	+	0.360475i	$0.117386\pi$
$103$			7.31685i			0.720951i	−0.932769	+	0.360475i	$0.882614\pi$
$104$		0			0
$105$	−4.71704	+	4.71704i	−0.460336	+	0.460336i
$106$		0			0
$107$			2.77845i			0.268603i	0.990941	+	0.134302i	$0.0428791\pi$
$107$			2.77845i			0.268603i	−0.990941	+	0.134302i	$0.957121\pi$
$108$		0			0
$109$			7.65884i			0.733583i	0.930303	+	0.366792i	$0.119544\pi$
$109$			7.65884i			0.733583i	−0.930303	+	0.366792i	$0.880456\pi$
$110$		0			0
$111$			6.29437i			0.597435i
$112$		0			0
$113$	−13.6620	+	13.6620i	−1.28521	+	1.28521i	−0.347555	+	0.937660i	$0.612988\pi$
$113$	−13.6620	+	13.6620i	−1.28521	+	1.28521i	−0.937660	+	0.347555i	$0.887012\pi$
$114$		0			0
$115$	−10.2781			−0.958435
$116$		0			0
$117$	−5.80348			−0.536532
$118$		0			0
$119$	3.85951	−	3.85951i	0.353800	−	0.353800i
$120$		0			0
$121$			2.42923i			0.220839i
$122$		0			0
$123$		−	31.9704i		−	2.88268i
$124$		0			0
$125$		−	10.1971i		−	0.912058i
$126$		0			0
$127$	−11.7272	+	11.7272i	−1.04062	+	1.04062i	−0.0414774	+	0.999139i	$0.513206\pi$
$127$	−11.7272	+	11.7272i	−1.04062	+	1.04062i	−0.999139	+	0.0414774i	$0.986794\pi$
$128$		0			0
$129$			31.0833i			2.73673i
$130$		0			0
$131$	3.45621	+	3.45621i	0.301970	+	0.301970i	0.841784	−	0.539814i	$-0.181505\pi$
$131$	3.45621	+	3.45621i	0.301970	+	0.301970i	−0.539814	+	0.841784i	$0.681505\pi$
$132$		0			0
$133$	3.77719	+	3.77719i	0.327524	+	0.327524i
$134$		0			0
$135$	−6.69769	+	6.69769i	−0.576445	+	0.576445i
$136$		0			0
$137$	10.6008	+	10.6008i	0.905691	+	0.905691i	0.995921	−	0.0902302i	$-0.0287603\pi$
$137$	10.6008	+	10.6008i	0.905691	+	0.905691i	−0.0902302	+	0.995921i	$0.528760\pi$
$138$		0			0
$139$			7.28724i			0.618096i	0.951046	+	0.309048i	$0.100010\pi$
$139$			7.28724i			0.618096i	−0.951046	+	0.309048i	$0.899990\pi$
$140$		0			0
$141$	−15.8160			−1.33194
$142$		0			0
$143$	2.70102	+	2.70102i	0.225871	+	0.225871i
$144$		0			0
$145$	10.4631	−	7.56036i	0.868912	−	0.627854i
$146$		0			0
$147$	11.5016	−	11.5016i	0.948639	−	0.948639i
$148$		0			0
$149$			19.0251i			1.55860i	0.626652	+	0.779299i	$0.284425\pi$
$149$			19.0251i			1.55860i	−0.626652	+	0.779299i	$0.715575\pi$
$150$		0			0
$151$	2.57130			0.209249			0.104625	−	0.994512i	$-0.466636\pi$
$151$	2.57130			0.209249			0.104625	+	0.994512i	$0.466636\pi$
$152$		0			0
$153$	16.8346	−	16.8346i	1.36100	−	1.36100i
$154$		0			0
$155$	−7.04225	−	7.04225i	−0.565647	−	0.565647i
$156$		0			0
$157$	−12.2269	+	12.2269i	−0.975812	+	0.975812i	−0.999714	−	0.0239018i	$-0.992391\pi$
$157$	−12.2269	+	12.2269i	−0.975812	+	0.975812i	0.0239018	+	0.999714i	$0.492391\pi$
$158$		0			0
$159$	12.2140	−	12.2140i	0.968630	−	0.968630i
$160$		0			0
$161$	−4.37231			−0.344586
$162$		0			0
$163$	−10.5052	−	10.5052i	−0.822832	−	0.822832i	0.163682	−	0.986513i	$-0.447663\pi$
$163$	−10.5052	−	10.5052i	−0.822832	−	0.822832i	−0.986513	+	0.163682i	$0.947663\pi$
$164$		0			0
$165$	19.1519			1.49097
$166$		0			0
$167$	0.0200904			0.00155464			0.000777320	−	1.00000i	$-0.499753\pi$
$167$	0.0200904			0.00155464			0.000777320		1.00000i	$0.499753\pi$
$168$		0			0
$169$	11.2976			0.869045
$170$		0			0
$171$	16.4755	+	16.4755i	1.25992	+	1.25992i
$172$		0			0
$173$			5.67975i			0.431823i	0.976413	+	0.215912i	$0.0692723\pi$
$173$			5.67975i			0.431823i	−0.976413	+	0.215912i	$0.930728\pi$
$174$		0			0
$175$			0.760758i			0.0575079i
$176$		0			0
$177$	−8.22930	−	8.22930i	−0.618552	−	0.618552i
$178$		0			0
$179$	3.66020			0.273576			0.136788	−	0.990600i	$-0.456322\pi$
$179$	3.66020			0.273576			0.136788	+	0.990600i	$0.456322\pi$
$180$		0			0
$181$	−24.3983			−1.81351			−0.906755	−	0.421657i	$-0.861449\pi$
$181$	−24.3983			−1.81351			−0.906755	+	0.421657i	$0.861449\pi$
$182$		0			0
$183$	−32.2967			−2.38744
$184$		0			0
$185$	3.90935	+	3.90935i	0.287421	+	0.287421i
$186$		0			0
$187$	−15.6702			−1.14591
$188$		0			0
$189$	−2.84921	+	2.84921i	−0.207249	+	0.207249i
$190$		0			0
$191$	−5.04414	+	5.04414i	−0.364981	+	0.364981i	−0.865643	−	0.500662i	$-0.833090\pi$
$191$	−5.04414	+	5.04414i	−0.364981	+	0.364981i	0.500662	+	0.865643i	$0.333090\pi$
$192$		0			0
$193$	−13.3530	−	13.3530i	−0.961172	−	0.961172i	0.0381016	−	0.999274i	$-0.487869\pi$
$193$	−13.3530	−	13.3530i	−0.961172	−	0.961172i	−0.999274	+	0.0381016i	$0.987869\pi$
$194$		0			0
$195$	−6.03559	+	6.03559i	−0.432217	+	0.432217i
$196$		0			0
$197$	8.14197			0.580091			0.290046	−	0.957013i	$-0.406329\pi$
$197$	8.14197			0.580091			0.290046	+	0.957013i	$0.406329\pi$
$198$		0			0
$199$		−	17.8100i		−	1.26252i	−0.775572	−	0.631259i	$-0.782538\pi$
$199$		−	17.8100i		−	1.26252i	0.775572	−	0.631259i	$-0.217462\pi$
$200$		0			0
$201$	18.5714	−	18.5714i	1.30992	−	1.30992i
$202$		0			0
$203$	4.45101	−	3.21619i	0.312400	−	0.225732i
$204$		0			0
$205$	−19.8564	−	19.8564i	−1.38683	−	1.38683i
$206$		0			0
$207$	−19.0714			−1.32555
$208$		0			0
$209$		−	15.3359i		−	1.06081i
$210$		0			0
$211$	−11.9689	−	11.9689i	−0.823976	−	0.823976i	0.162699	−	0.986676i	$-0.447980\pi$
$211$	−11.9689	−	11.9689i	−0.823976	−	0.823976i	−0.986676	+	0.162699i	$0.947980\pi$
$212$		0			0
$213$	22.3307	−	22.3307i	1.53007	−	1.53007i
$214$		0			0
$215$	19.3055	+	19.3055i	1.31662	+	1.31662i
$216$		0			0
$217$	−2.99578	−	2.99578i	−0.203367	−	0.203367i
$218$		0			0
$219$			9.53586i			0.644374i
$220$		0			0
$221$	4.93835	−	4.93835i	0.332189	−	0.332189i
$222$		0			0
$223$		−	1.58592i		−	0.106201i	−0.998589	−	0.0531007i	$-0.983090\pi$
$223$		−	1.58592i		−	0.106201i	0.998589	−	0.0531007i	$-0.0169104\pi$
$224$		0			0
$225$			3.31832i			0.221221i
$226$		0			0
$227$			0.875438i			0.0581049i	0.999578	+	0.0290524i	$0.00924898\pi$
$227$			0.875438i			0.0581049i	−0.999578	+	0.0290524i	$0.990751\pi$
$228$		0			0
$229$	7.50804	−	7.50804i	0.496145	−	0.496145i	−0.414090	−	0.910236i	$-0.635900\pi$
$229$	7.50804	−	7.50804i	0.496145	−	0.496145i	0.910236	+	0.414090i	$0.135900\pi$
$230$		0			0
$231$	8.14724			0.536049
$232$		0			0
$233$	8.17093			0.535296			0.267648	−	0.963517i	$-0.413754\pi$
$233$	8.17093			0.535296			0.267648	+	0.963517i	$0.413754\pi$
$234$		0			0
$235$	−9.82308	+	9.82308i	−0.640787	+	0.640787i
$236$		0			0
$237$			40.7151i			2.64473i
$238$		0			0
$239$		−	27.7911i		−	1.79766i	−0.438299	−	0.898829i	$-0.644419\pi$
$239$		−	27.7911i		−	1.79766i	0.438299	−	0.898829i	$-0.355581\pi$
$240$		0			0
$241$		−	17.5034i		−	1.12749i	−0.825948	−	0.563747i	$-0.809359\pi$
$241$		−	17.5034i		−	1.12749i	0.825948	−	0.563747i	$-0.190641\pi$
$242$		0			0
$243$	13.3222	−	13.3222i	0.854621	−	0.854621i
$244$		0			0
$245$		−	14.2870i		−	0.912765i
$246$		0			0
$247$	4.83301	+	4.83301i	0.307517	+	0.307517i
$248$		0			0
$249$	0.618095	+	0.618095i	0.0391702	+	0.0391702i
$250$		0			0
$251$	15.4849	−	15.4849i	0.977396	−	0.977396i	−0.0223544	−	0.999750i	$-0.507116\pi$
$251$	15.4849	−	15.4849i	0.977396	−	0.977396i	0.999750	+	0.0223544i	$0.00711621\pi$
$252$		0			0
$253$	8.87610	+	8.87610i	0.558035	+	0.558035i
$254$		0			0
$255$		−	35.0158i		−	2.19278i
$256$		0			0
$257$	−4.86005			−0.303162			−0.151581	−	0.988445i	$-0.548436\pi$
$257$	−4.86005			−0.303162			−0.151581	+	0.988445i	$0.548436\pi$
$258$		0			0
$259$	1.66304	+	1.66304i	0.103336	+	0.103336i
$260$		0			0
$261$	19.4147	−	14.0286i	1.20174	−	0.868346i
$262$		0			0
$263$	11.3440	−	11.3440i	0.699503	−	0.699503i	−0.264800	−	0.964303i	$-0.585306\pi$
$263$	11.3440	−	11.3440i	0.699503	−	0.699503i	0.964303	+	0.264800i	$0.0853060\pi$
$264$		0			0
$265$		−	15.1719i		−	0.932001i
$266$		0			0
$267$	−31.7088			−1.94054
$268$		0			0
$269$	−6.29276	+	6.29276i	−0.383677	+	0.383677i	−0.872425	−	0.488748i	$-0.837454\pi$
$269$	−6.29276	+	6.29276i	−0.383677	+	0.383677i	0.488748	+	0.872425i	$0.337454\pi$
$270$		0			0
$271$	18.2544	+	18.2544i	1.10888	+	1.10888i	0.993298	+	0.115579i	$0.0368724\pi$
$271$	18.2544	+	18.2544i	1.10888	+	1.10888i	0.115579	+	0.993298i	$0.463128\pi$
$272$		0			0
$273$	−2.56755	+	2.56755i	−0.155395	+	0.155395i
$274$		0			0
$275$	1.54439	−	1.54439i	0.0931304	−	0.0931304i
$276$		0			0
$277$	−21.9576			−1.31930			−0.659651	−	0.751572i	$-0.729296\pi$
$277$	−21.9576			−1.31930			−0.659651	+	0.751572i	$0.729296\pi$
$278$		0			0
$279$	−13.0672	−	13.0672i	−0.782312	−	0.782312i
$280$		0			0
$281$	−14.5131			−0.865780			−0.432890	−	0.901447i	$-0.642506\pi$
$281$	−14.5131			−0.865780			−0.432890	+	0.901447i	$0.642506\pi$
$282$		0			0
$283$	8.00022			0.475564			0.237782	−	0.971319i	$-0.423580\pi$
$283$	8.00022			0.475564			0.237782	+	0.971319i	$0.423580\pi$
$284$		0			0
$285$	34.2690			2.02992
$286$		0			0
$287$	−8.44696	−	8.44696i	−0.498608	−	0.498608i
$288$		0			0
$289$			11.6501i			0.685302i
$290$		0			0
$291$		−	5.90848i		−	0.346361i
$292$		0			0
$293$	−11.2820	−	11.2820i	−0.659102	−	0.659102i	0.296066	−	0.955168i	$-0.404325\pi$
$293$	−11.2820	−	11.2820i	−0.659102	−	0.659102i	−0.955168	+	0.296066i	$0.904325\pi$
$294$		0			0
$295$	−10.2222			−0.595161
$296$		0			0
$297$	11.5682			0.671254
$298$		0			0
$299$	−5.59449			−0.323538
$300$		0			0
$301$	8.21257	+	8.21257i	0.473365	+	0.473365i
$302$		0			0
$303$	6.38254			0.366667
$304$		0			0
$305$	−20.0591	+	20.0591i	−1.14858	+	1.14858i
$306$		0			0
$307$	−11.8614	+	11.8614i	−0.676966	+	0.676966i	−0.959312	−	0.282347i	$-0.908887\pi$
$307$	−11.8614	+	11.8614i	−0.676966	+	0.676966i	0.282347	+	0.959312i	$0.408887\pi$
$308$		0			0
$309$	14.1197	+	14.1197i	0.803243	+	0.803243i
$310$		0			0
$311$	−12.8979	+	12.8979i	−0.731374	+	0.731374i	−0.970892	−	0.239518i	$-0.923011\pi$
$311$	−12.8979	+	12.8979i	−0.731374	+	0.731374i	0.239518	+	0.970892i	$0.423011\pi$
$312$		0			0
$313$	−2.84860			−0.161012			−0.0805061	−	0.996754i	$-0.525654\pi$
$313$	−2.84860			−0.161012			−0.0805061	+	0.996754i	$0.525654\pi$
$314$		0			0
$315$			10.8723i			0.612587i
$316$		0			0
$317$	8.05244	−	8.05244i	0.452270	−	0.452270i	−0.443837	−	0.896107i	$-0.646383\pi$
$317$	8.05244	−	8.05244i	0.452270	−	0.452270i	0.896107	+	0.443837i	$0.146383\pi$
$318$		0			0
$319$	−15.5650	−	2.50678i	−0.871471	−	0.140353i
$320$		0			0
$321$	5.36173	+	5.36173i	0.299263	+	0.299263i
$322$		0			0
$323$	−28.0390			−1.56013
$324$		0			0
$325$			0.973411i			0.0539951i
$326$		0			0
$327$	14.7797	+	14.7797i	0.817317	+	0.817317i
$328$		0			0
$329$	−4.17876	+	4.17876i	−0.230382	+	0.230382i
$330$		0			0
$331$	17.1099	+	17.1099i	0.940446	+	0.940446i	0.998324	−	0.0578780i	$-0.0184334\pi$
$331$	17.1099	+	17.1099i	0.940446	+	0.940446i	−0.0578780	+	0.998324i	$0.518433\pi$
$332$		0			0
$333$	7.25396	+	7.25396i	0.397514	+	0.397514i
$334$		0			0
$335$		−	23.0689i		−	1.26039i
$336$		0			0
$337$	−19.0347	+	19.0347i	−1.03689	+	1.03689i	−0.0375939	+	0.999293i	$0.511969\pi$
$337$	−19.0347	+	19.0347i	−1.03689	+	1.03689i	−0.999293	+	0.0375939i	$0.988031\pi$
$338$		0			0
$339$			52.7287i			2.86383i
$340$		0			0
$341$			12.1633i			0.658680i
$342$		0			0
$343$		−	13.2158i		−	0.713587i
$344$		0			0
$345$	−19.8341	+	19.8341i	−1.06783	+	1.06783i
$346$		0			0
$347$	−5.24183			−0.281396			−0.140698	−	0.990053i	$-0.544935\pi$
$347$	−5.24183			−0.281396			−0.140698	+	0.990053i	$0.544935\pi$
$348$		0			0
$349$	3.74531			0.200482			0.100241	−	0.994963i	$-0.468039\pi$
$349$	3.74531			0.200482			0.100241	+	0.994963i	$0.468039\pi$
$350$		0			0
$351$	−3.64564	+	3.64564i	−0.194590	+	0.194590i
$352$		0			0
$353$			3.55110i			0.189006i	0.995525	+	0.0945030i	$0.0301262\pi$
$353$			3.55110i			0.189006i	−0.995525	+	0.0945030i	$0.969874\pi$
$354$		0			0
$355$		−	27.7386i		−	1.47221i
$356$		0			0
$357$		−	14.8958i		−	0.788369i
$358$		0			0
$359$	4.54790	−	4.54790i	0.240029	−	0.240029i	−0.576833	−	0.816862i	$-0.695712\pi$
$359$	4.54790	−	4.54790i	0.240029	−	0.240029i	0.816862	+	0.576833i	$0.195712\pi$
$360$		0			0
$361$		−	8.44098i		−	0.444262i
$362$		0			0
$363$	4.68782	+	4.68782i	0.246047	+	0.246047i
$364$		0			0
$365$	5.92260	+	5.92260i	0.310003	+	0.310003i
$366$		0			0
$367$	−16.0417	+	16.0417i	−0.837372	+	0.837372i	−0.988512	−	0.151141i	$-0.951705\pi$
$367$	−16.0417	+	16.0417i	−0.837372	+	0.837372i	0.151141	+	0.988512i	$0.451705\pi$
$368$		0			0
$369$	−36.8444	−	36.8444i	−1.91804	−	1.91804i
$370$		0			0
$371$		−	6.45414i		−	0.335082i
$372$		0			0
$373$	13.3301			0.690209			0.345104	−	0.938564i	$-0.387843\pi$
$373$	13.3301			0.690209			0.345104	+	0.938564i	$0.387843\pi$
$374$		0			0
$375$	−19.6779	−	19.6779i	−1.01616	−	1.01616i
$376$		0			0
$377$	5.69520	−	4.11521i	0.293317	−	0.211944i
$378$		0			0
$379$	−1.77935	+	1.77935i	−0.0913989	+	0.0913989i	−0.751328	−	0.659929i	$-0.770586\pi$
$379$	−1.77935	+	1.77935i	−0.0913989	+	0.0913989i	0.659929	+	0.751328i	$0.270586\pi$
$380$		0			0
$381$			45.2610i			2.31879i
$382$		0			0
$383$	3.05809			0.156261			0.0781304	−	0.996943i	$-0.475105\pi$
$383$	3.05809			0.156261			0.0781304	+	0.996943i	$0.475105\pi$
$384$		0			0
$385$	5.06014	−	5.06014i	0.257889	−	0.257889i
$386$		0			0
$387$	35.8221	+	35.8221i	1.82094	+	1.82094i
$388$		0			0
$389$	7.57632	−	7.57632i	0.384135	−	0.384135i	−0.488455	−	0.872589i	$-0.662439\pi$
$389$	7.57632	−	7.57632i	0.384135	−	0.384135i	0.872589	+	0.488455i	$0.162439\pi$
$390$		0			0
$391$	16.2284	−	16.2284i	0.820705	−	0.820705i
$392$		0			0
$393$	13.3393			0.672876
$394$		0			0
$395$	25.2876	+	25.2876i	1.27236	+	1.27236i
$396$		0			0
$397$	−29.7428			−1.49275			−0.746374	−	0.665526i	$-0.768207\pi$
$397$	−29.7428			−1.49275			−0.746374	+	0.665526i	$0.768207\pi$
$398$		0			0
$399$	14.5781			0.729817
$400$		0			0
$401$	−30.4125			−1.51873			−0.759365	−	0.650665i	$-0.774490\pi$
$401$	−30.4125			−1.51873			−0.759365	+	0.650665i	$0.774490\pi$
$402$		0			0
$403$	−3.83319	−	3.83319i	−0.190945	−	0.190945i
$404$		0			0
$405$		−	6.13628i		−	0.304914i
$406$		0			0
$407$		−	6.75219i		−	0.334694i
$408$		0			0
$409$	1.35062	+	1.35062i	0.0667840	+	0.0667840i	0.739710	−	0.672926i	$-0.234963\pi$
$409$	1.35062	+	1.35062i	0.0667840	+	0.0667840i	−0.672926	+	0.739710i	$0.734963\pi$
$410$		0			0
$411$	40.9140			2.01814
$412$		0			0
$413$	−4.34855			−0.213978
$414$		0			0
$415$	0.767781			0.0376889
$416$		0			0
$417$	14.0626	+	14.0626i	0.688648	+	0.688648i
$418$		0			0
$419$	−10.2511			−0.500798			−0.250399	−	0.968143i	$-0.580562\pi$
$419$	−10.2511			−0.500798			−0.250399	+	0.968143i	$0.580562\pi$
$420$		0			0
$421$	−15.2038	+	15.2038i	−0.740987	+	0.740987i	−0.972768	−	0.231781i	$-0.925545\pi$
$421$	−15.2038	+	15.2038i	−0.740987	+	0.740987i	0.231781	+	0.972768i	$0.425545\pi$
$422$		0			0
$423$	−18.2271	+	18.2271i	−0.886234	+	0.886234i
$424$		0			0
$425$	−2.82365	−	2.82365i	−0.136967	−	0.136967i
$426$		0			0
$427$	−8.53316	+	8.53316i	−0.412949	+	0.412949i
$428$		0			0
$429$	10.4246			0.503305
$430$		0			0
$431$			30.8075i			1.48395i	0.670430	+	0.741973i	$0.266110\pi$
$431$			30.8075i			1.48395i	−0.670430	+	0.741973i	$0.733890\pi$
$432$		0			0
$433$	19.4713	−	19.4713i	0.935729	−	0.935729i	−0.0623269	−	0.998056i	$-0.519852\pi$
$433$	19.4713	−	19.4713i	0.935729	−	0.935729i	0.998056	+	0.0623269i	$0.0198521\pi$
$434$		0			0
$435$	5.60154	−	34.7808i	0.268573	−	1.66761i
$436$		0			0
$437$	15.8822	+	15.8822i	0.759751	+	0.759751i
$438$		0			0
$439$	18.0950			0.863629			0.431815	−	0.901962i	$-0.357873\pi$
$439$	18.0950			0.863629			0.431815	+	0.901962i	$0.357873\pi$
$440$		0			0
$441$		−	26.5102i		−	1.26239i
$442$		0			0
$443$	−25.8647	−	25.8647i	−1.22887	−	1.22887i	−0.964391	−	0.264479i	$-0.914800\pi$
$443$	−25.8647	−	25.8647i	−1.22887	−	1.22887i	−0.264479	−	0.964391i	$-0.585200\pi$
$444$		0			0
$445$	−19.6939	+	19.6939i	−0.933580	+	0.933580i
$446$		0			0
$447$	36.7138	+	36.7138i	1.73650	+	1.73650i
$448$		0			0
$449$	9.87295	+	9.87295i	0.465933	+	0.465933i	0.900594	−	0.434661i	$-0.143132\pi$
$449$	9.87295	+	9.87295i	0.465933	+	0.465933i	−0.434661	+	0.900594i	$0.643132\pi$
$450$		0			0
$451$			34.2959i			1.61493i
$452$		0			0
$453$	4.96197	−	4.96197i	0.233134	−	0.233134i
$454$		0			0
$455$			3.18934i			0.149519i
$456$		0			0
$457$		−	15.9119i		−	0.744327i	−0.928167	−	0.372163i	$-0.878616\pi$
$457$		−	15.9119i		−	0.744327i	0.928167	−	0.372163i	$-0.121384\pi$
$458$		0			0
$459$		−	21.1504i		−	0.987217i
$460$		0			0
$461$	3.12029	−	3.12029i	0.145326	−	0.145326i	−0.630700	−	0.776026i	$-0.717232\pi$
$461$	3.12029	−	3.12029i	0.145326	−	0.145326i	0.776026	+	0.630700i	$0.217232\pi$
$462$		0			0
$463$	30.3565			1.41078			0.705392	−	0.708817i	$-0.250771\pi$
$463$	30.3565			1.41078			0.705392	+	0.708817i	$0.250771\pi$
$464$		0			0
$465$	−27.1796			−1.26042
$466$		0			0
$467$	15.6312	−	15.6312i	0.723325	−	0.723325i	−0.245956	−	0.969281i	$-0.579102\pi$
$467$	15.6312	−	15.6312i	0.723325	−	0.723325i	0.969281	+	0.245956i	$0.0791018\pi$
$468$		0			0
$469$		−	9.81354i		−	0.453147i
$470$		0			0
$471$			47.1898i			2.17439i
$472$		0			0
$473$		−	33.3442i		−	1.53317i
$474$		0			0
$475$	2.76343	−	2.76343i	0.126795	−	0.126795i
$476$		0			0
$477$		−	28.1520i		−	1.28899i
$478$		0			0
$479$	10.3990	+	10.3990i	0.475141	+	0.475141i	0.903574	−	0.428433i	$-0.140934\pi$
$479$	10.3990	+	10.3990i	0.475141	+	0.475141i	−0.428433	+	0.903574i	$0.640934\pi$
$480$		0			0
$481$	2.12791	+	2.12791i	0.0970244	+	0.0970244i
$482$		0			0
$483$	−8.43748	+	8.43748i	−0.383919	+	0.383919i
$484$		0			0
$485$	−3.66968	−	3.66968i	−0.166632	−	0.166632i
$486$		0			0
$487$		−	21.1081i		−	0.956500i	−0.878224	−	0.478250i	$-0.841271\pi$
$487$		−	21.1081i		−	0.956500i	0.878224	−	0.478250i	$-0.158729\pi$
$488$		0			0
$489$	−40.5449			−1.83351
$490$		0			0
$491$	4.39350	+	4.39350i	0.198276	+	0.198276i	0.799261	−	0.600985i	$-0.205225\pi$
$491$	4.39350	+	4.39350i	0.198276	+	0.198276i	−0.600985	+	0.799261i	$0.705225\pi$
$492$		0			0
$493$	−4.58321	+	28.4578i	−0.206417	+	1.28168i
$494$		0			0
$495$	22.0716	−	22.0716i	0.992046	−	0.992046i
$496$		0			0
$497$		−	11.8000i		−	0.529304i
$498$		0			0
$499$	−4.86379			−0.217733			−0.108866	−	0.994056i	$-0.534722\pi$
$499$	−4.86379			−0.217733			−0.108866	+	0.994056i	$0.534722\pi$
$500$		0			0
$501$	0.0387695	−	0.0387695i	0.00173209	−	0.00173209i
$502$		0			0
$503$	−22.7249	−	22.7249i	−1.01325	−	1.01325i	−0.999911	−	0.0133431i	$-0.995753\pi$
$503$	−22.7249	−	22.7249i	−1.01325	−	1.01325i	−0.0133431	−	0.999911i	$-0.504247\pi$
$504$		0			0
$505$	3.96411	−	3.96411i	0.176401	−	0.176401i
$506$		0			0
$507$	21.8015	−	21.8015i	0.968241	−	0.968241i
$508$		0			0
$509$	11.3980			0.505205			0.252603	−	0.967570i	$-0.418713\pi$
$509$	11.3980			0.505205			0.252603	+	0.967570i	$0.418713\pi$
$510$		0			0
$511$	2.51948	+	2.51948i	0.111455	+	0.111455i
$512$		0			0
$513$	20.6993			0.913895
$514$		0			0
$515$	17.5392			0.772868
$516$		0			0
$517$	16.9663			0.746179
$518$		0			0
$519$	10.9605	+	10.9605i	0.481113	+	0.481113i
$520$		0			0
$521$			20.6772i			0.905885i	0.891540	+	0.452942i	$0.149626\pi$
$521$			20.6772i			0.905885i	−0.891540	+	0.452942i	$0.850374\pi$
$522$		0			0
$523$		−	10.4479i		−	0.456856i	−0.973561	−	0.228428i	$-0.926641\pi$
$523$		−	10.4479i		−	0.456856i	0.973561	−	0.228428i	$-0.0733586\pi$
$524$		0			0
$525$	1.46808	+	1.46808i	0.0640721	+	0.0640721i
$526$		0			0
$527$	22.2385			0.968724
$528$		0			0
$529$	4.61539			0.200669
$530$		0			0
$531$	−18.9678			−0.823131
$532$		0			0
$533$	−10.8081	−	10.8081i	−0.468152	−	0.468152i
$534$		0			0
$535$	6.66020			0.287946
$536$		0			0
$537$	7.06329	−	7.06329i	0.304803	−	0.304803i
$538$		0			0
$539$	−12.3382	+	12.3382i	−0.531445	+	0.531445i
$540$		0			0
$541$	−8.11668	−	8.11668i	−0.348963	−	0.348963i	0.510760	−	0.859723i	$-0.329364\pi$
$541$	−8.11668	−	8.11668i	−0.348963	−	0.348963i	−0.859723	+	0.510760i	$0.829364\pi$
$542$		0			0
$543$	−47.0827	+	47.0827i	−2.02051	+	2.02051i
$544$		0			0
$545$	18.3589			0.786410
$546$		0			0
$547$			25.6172i			1.09531i	0.836703	+	0.547656i	$0.184480\pi$
$547$			25.6172i			1.09531i	−0.836703	+	0.547656i	$0.815520\pi$
$548$		0			0
$549$	−37.2204	+	37.2204i	−1.58853	+	1.58853i
$550$		0			0
$551$	−27.8508	−	4.48545i	−1.18649	−	0.191087i
$552$		0			0
$553$	10.7574	+	10.7574i	0.457451	+	0.457451i
$554$		0			0
$555$	15.0882			0.640457
$556$		0			0
$557$		−	5.26149i		−	0.222937i	−0.993768	−	0.111468i	$-0.964445\pi$
$557$		−	5.26149i		−	0.222937i	0.993768	−	0.111468i	$-0.0355554\pi$
$558$		0			0
$559$	10.5082	+	10.5082i	0.444450	+	0.444450i
$560$		0			0
$561$	−30.2395	+	30.2395i	−1.27671	+	1.27671i
$562$		0			0
$563$	−18.2037	−	18.2037i	−0.767192	−	0.767192i	0.210419	−	0.977611i	$-0.432517\pi$
$563$	−18.2037	−	18.2037i	−0.767192	−	0.767192i	−0.977611	+	0.210419i	$0.932517\pi$
$564$		0			0
$565$	32.7491	+	32.7491i	1.37776	+	1.37776i
$566$		0			0
$567$		−	2.61038i		−	0.109626i
$568$		0			0
$569$	32.9411	−	32.9411i	1.38096	−	1.38096i	0.538049	−	0.842914i	$-0.319162\pi$
$569$	32.9411	−	32.9411i	1.38096	−	1.38096i	0.842914	−	0.538049i	$-0.180838\pi$
$570$		0			0
$571$		−	41.7994i		−	1.74925i	−0.484799	−	0.874626i	$-0.661107\pi$
$571$		−	41.7994i		−	1.74925i	0.484799	−	0.874626i	$-0.338893\pi$
$572$		0			0
$573$			19.4679i			0.813283i
$574$		0			0
$575$			3.19882i			0.133400i
$576$		0			0
$577$	1.98390	−	1.98390i	0.0825910	−	0.0825910i	−0.664604	−	0.747195i	$-0.731400\pi$
$577$	1.98390	−	1.98390i	0.0825910	−	0.0825910i	0.747195	+	0.664604i	$0.231400\pi$
$578$		0			0
$579$	−51.5361			−2.14177
$580$		0			0
$581$	0.326615			0.0135503
$582$		0			0
$583$	−13.1024	+	13.1024i	−0.542644	+	0.542644i
$584$		0			0
$585$			13.9115i			0.575168i
$586$		0			0
$587$			1.01770i			0.0420051i	0.999779	+	0.0210025i	$0.00668581\pi$
$587$			1.01770i			0.0420051i	−0.999779	+	0.0210025i	$0.993314\pi$
$588$		0			0
$589$			21.7641i			0.896776i
$590$		0			0
$591$	15.7120	−	15.7120i	0.646305	−	0.646305i
$592$		0			0
$593$			17.2975i			0.710323i	0.934805	+	0.355162i	$0.115574\pi$
$593$			17.2975i			0.710323i	−0.934805	+	0.355162i	$0.884426\pi$
$594$		0			0
$595$	−9.25159	−	9.25159i	−0.379278	−	0.379278i
$596$		0			0
$597$	−34.3690	−	34.3690i	−1.40663	−	1.40663i
$598$		0			0
$599$	−18.4376	+	18.4376i	−0.753339	+	0.753339i	−0.975101	−	0.221762i	$-0.928819\pi$
$599$	−18.4376	+	18.4376i	−0.753339	+	0.753339i	0.221762	+	0.975101i	$0.428819\pi$
$600$		0			0
$601$	−4.48215	−	4.48215i	−0.182831	−	0.182831i	0.609757	−	0.792588i	$-0.291267\pi$
$601$	−4.48215	−	4.48215i	−0.182831	−	0.182831i	−0.792588	+	0.609757i	$0.791267\pi$
$602$		0			0
$603$		−	42.8052i		−	1.74316i
$604$		0			0
$605$	5.82309			0.236742
$606$		0			0
$607$	3.31696	+	3.31696i	0.134631	+	0.134631i	0.771211	−	0.636580i	$-0.219651\pi$
$607$	3.31696	+	3.31696i	0.134631	+	0.134631i	−0.636580	+	0.771211i	$0.719651\pi$
$608$		0			0
$609$	2.38290	−	14.7958i	0.0965602	−	0.599557i
$610$		0			0
$611$	−5.34684	+	5.34684i	−0.216310	+	0.216310i
$612$		0			0
$613$		−	25.9090i		−	1.04646i	−0.852193	−	0.523228i	$-0.824728\pi$
$613$		−	25.9090i		−	1.04646i	0.852193	−	0.523228i	$-0.175272\pi$
$614$		0			0
$615$	−76.6361			−3.09026
$616$		0			0
$617$	−15.0531	+	15.0531i	−0.606014	+	0.606014i	−0.941902	−	0.335888i	$-0.890964\pi$
$617$	−15.0531	+	15.0531i	−0.606014	+	0.606014i	0.335888	+	0.941902i	$0.390964\pi$
$618$		0			0
$619$	29.7437	+	29.7437i	1.19550	+	1.19550i	0.975500	+	0.220000i	$0.0706058\pi$
$619$	29.7437	+	29.7437i	1.19550	+	1.19550i	0.220000	+	0.975500i	$0.429394\pi$
$620$		0			0
$621$	−11.9803	+	11.9803i	−0.480753	+	0.480753i
$622$		0			0
$623$	−8.37782	+	8.37782i	−0.335650	+	0.335650i
$624$		0			0
$625$	−28.1736			−1.12695
$626$		0			0
$627$	−29.5945	−	29.5945i	−1.18189	−	1.18189i
$628$		0			0
$629$	−12.3452			−0.492236
$630$		0			0
$631$	−46.8743			−1.86604			−0.933018	−	0.359831i	$-0.882834\pi$
$631$	−46.8743			−1.86604			−0.933018	+	0.359831i	$0.882834\pi$
$632$		0			0
$633$	−46.1942			−1.83606
$634$		0			0
$635$	28.1111	+	28.1111i	1.11555	+	1.11555i
$636$		0			0
$637$		−	7.77662i		−	0.308121i
$638$		0			0
$639$		−	51.4701i		−	2.03612i
$640$		0			0
$641$	22.5210	+	22.5210i	0.889527	+	0.889527i	0.994477	−	0.104950i	$-0.0334683\pi$
$641$	22.5210	+	22.5210i	0.889527	+	0.889527i	−0.104950	+	0.994477i	$0.533468\pi$
$642$		0			0
$643$	−3.60602			−0.142208			−0.0711038	−	0.997469i	$-0.522652\pi$
$643$	−3.60602			−0.142208			−0.0711038	+	0.997469i	$0.522652\pi$
$644$		0			0
$645$	74.5095			2.93381
$646$		0			0
$647$	8.60945			0.338473			0.169236	−	0.985576i	$-0.445870\pi$
$647$	8.60945			0.338473			0.169236	+	0.985576i	$0.445870\pi$
$648$		0			0
$649$	8.82787	+	8.82787i	0.346524	+	0.346524i
$650$		0			0
$651$	−11.5622			−0.453160
$652$		0			0
$653$	9.68383	−	9.68383i	0.378957	−	0.378957i	−0.491769	−	0.870726i	$-0.663649\pi$
$653$	9.68383	−	9.68383i	0.378957	−	0.378957i	0.870726	+	0.491769i	$0.163649\pi$
$654$		0			0
$655$	8.28484	−	8.28484i	0.323715	−	0.323715i
$656$		0			0
$657$	10.9896	+	10.9896i	0.428746	+	0.428746i
$658$		0			0
$659$	−1.84113	+	1.84113i	−0.0717203	+	0.0717203i	−0.742057	−	0.670337i	$-0.766150\pi$
$659$	−1.84113	+	1.84113i	−0.0717203	+	0.0717203i	0.670337	+	0.742057i	$0.266150\pi$
$660$		0			0
$661$	23.7086			0.922157			0.461078	−	0.887359i	$-0.347463\pi$
$661$	23.7086			0.922157			0.461078	+	0.887359i	$0.347463\pi$
$662$		0			0
$663$		−	19.0596i		−	0.740213i
$664$		0			0
$665$	9.05425	−	9.05425i	0.351109	−	0.351109i
$666$		0			0
$667$	18.7155	−	13.5234i	0.724669	−	0.523628i
$668$		0			0
$669$	−3.06044	−	3.06044i	−0.118324	−	0.118324i
$670$		0			0
$671$	34.6459			1.33749
$672$		0			0
$673$		−	15.8919i		−	0.612587i	−0.951937	−	0.306294i	$-0.900911\pi$
$673$		−	15.8919i		−	0.612587i	0.951937	−	0.306294i	$-0.0990889\pi$
$674$		0			0
$675$	2.08451	+	2.08451i	0.0802327	+	0.0802327i
$676$		0			0
$677$	3.48507	−	3.48507i	0.133942	−	0.133942i	−0.636957	−	0.770899i	$-0.719807\pi$
$677$	3.48507	−	3.48507i	0.133942	−	0.133942i	0.770899	+	0.636957i	$0.219807\pi$
$678$		0			0
$679$	−1.56109	−	1.56109i	−0.0599090	−	0.0599090i
$680$		0			0
$681$	1.68938	+	1.68938i	0.0647372	+	0.0647372i
$682$		0			0
$683$			16.1199i			0.616809i	0.951255	+	0.308405i	$0.0997951\pi$
$683$			16.1199i			0.616809i	−0.951255	+	0.308405i	$0.900205\pi$
$684$		0			0
$685$	25.4112	−	25.4112i	0.970911	−	0.970911i
$686$		0			0
$687$		−	28.9773i		−	1.10555i
$688$		0			0
$689$		−	8.25825i		−	0.314614i
$690$		0			0
$691$		−	35.7904i		−	1.36153i	−0.732502	−	0.680765i	$-0.761647\pi$
$691$		−	35.7904i		−	1.36153i	0.732502	−	0.680765i	$-0.238353\pi$
$692$		0			0
$693$	9.38930	−	9.38930i	0.356670	−	0.356670i
$694$		0			0
$695$	17.4682			0.662606
$696$		0			0
$697$	62.7040			2.37508
$698$		0			0
$699$	15.7679	−	15.7679i	0.596396	−	0.596396i
$700$		0			0
$701$		−	2.21227i		−	0.0835563i	−0.999127	−	0.0417782i	$-0.986698\pi$
$701$		−	2.21227i		−	0.0835563i	0.999127	−	0.0417782i	$-0.0133023\pi$
$702$		0			0
$703$		−	12.0819i		−	0.455677i
$704$		0			0
$705$			37.9123i			1.42786i
$706$		0			0
$707$	1.68634	−	1.68634i	0.0634214	−	0.0634214i
$708$		0			0
$709$			31.0570i			1.16637i	0.812340	+	0.583184i	$0.198193\pi$
$709$			31.0570i			1.16637i	−0.812340	+	0.583184i	$0.801807\pi$
$710$		0			0
$711$	46.9222	+	46.9222i	1.75972	+	1.75972i
$712$		0			0
$713$	−12.5966	−	12.5966i	−0.471747	−	0.471747i
$714$		0			0
$715$	6.47459	−	6.47459i	0.242136	−	0.242136i
$716$		0			0
$717$	−53.6300	−	53.6300i	−2.00285	−	2.00285i
$718$		0			0
$719$			36.2112i			1.35045i	0.737611	+	0.675226i	$0.235954\pi$
$719$			36.2112i			1.35045i	−0.737611	+	0.675226i	$0.764046\pi$
$720$		0			0
$721$	7.46119			0.277869
$722$		0			0
$723$	−33.7773	−	33.7773i	−1.25619	−	1.25619i
$724$		0			0
$725$	−2.35300	−	3.25640i	−0.0873881	−	0.120940i
$726$		0			0
$727$	20.7794	−	20.7794i	0.770667	−	0.770667i	−0.207556	−	0.978223i	$-0.566551\pi$
$727$	20.7794	−	20.7794i	0.770667	−	0.770667i	0.978223	+	0.207556i	$0.0665510\pi$
$728$		0			0
$729$		−	43.7376i		−	1.61991i
$730$		0			0
$731$	−60.9641			−2.25484
$732$		0			0
$733$	−8.22927	+	8.22927i	−0.303955	+	0.303955i	−0.842559	−	0.538604i	$-0.818952\pi$
$733$	−8.22927	+	8.22927i	−0.303955	+	0.303955i	0.538604	+	0.842559i	$0.318952\pi$
$734$		0			0
$735$	−27.5705	−	27.5705i	−1.01695	−	1.01695i
$736$		0			0
$737$	−19.9222	+	19.9222i	−0.733843	+	0.733843i
$738$		0			0
$739$	14.6530	−	14.6530i	0.539017	−	0.539017i	−0.384223	−	0.923240i	$-0.625531\pi$
$739$	14.6530	−	14.6530i	0.539017	−	0.539017i	0.923240	+	0.384223i	$0.125531\pi$
$740$		0			0
$741$	18.6531			0.685237
$742$		0			0
$743$	−24.0803	−	24.0803i	−0.883419	−	0.883419i	0.110462	−	0.993880i	$-0.464767\pi$
$743$	−24.0803	−	24.0803i	−0.883419	−	0.883419i	−0.993880	+	0.110462i	$0.964767\pi$
$744$		0			0
$745$	45.6049			1.67084
$746$		0			0
$747$	1.42465			0.0521252
$748$		0			0
$749$	2.83326			0.103525
$750$		0			0
$751$	3.36482	+	3.36482i	0.122784	+	0.122784i	0.765829	−	0.643045i	$-0.222329\pi$
$751$	3.36482	+	3.36482i	0.122784	+	0.122784i	−0.643045	+	0.765829i	$0.722329\pi$
$752$		0			0
$753$		−	59.7639i		−	2.17792i
$754$		0			0
$755$		−	6.16363i		−	0.224317i
$756$		0			0
$757$	22.8533	+	22.8533i	0.830619	+	0.830619i	0.987601	−	0.156983i	$-0.0501767\pi$
$757$	22.8533	+	22.8533i	0.830619	+	0.830619i	−0.156983	+	0.987601i	$0.550177\pi$
$758$		0			0
$759$	34.2574			1.24346
$760$		0			0
$761$	−24.7027			−0.895473			−0.447736	−	0.894166i	$-0.647770\pi$
$761$	−24.7027			−0.895473			−0.447736	+	0.894166i	$0.647770\pi$
$762$		0			0
$763$	7.80991			0.282738
$764$		0			0
$765$	−40.3541	−	40.3541i	−1.45901	−	1.45901i
$766$		0			0
$767$	−5.56409			−0.200908
$768$		0			0
$769$	25.9480	−	25.9480i	0.935710	−	0.935710i	−0.0623451	−	0.998055i	$-0.519858\pi$
$769$	25.9480	−	25.9480i	0.935710	−	0.935710i	0.998055	+	0.0623451i	$0.0198580\pi$
$770$		0			0
$771$	−9.37870	+	9.37870i	−0.337766	+	0.337766i
$772$		0			0
$773$	−34.1840	−	34.1840i	−1.22951	−	1.22951i	−0.964147	−	0.265367i	$-0.914507\pi$
$773$	−34.1840	−	34.1840i	−1.22951	−	1.22951i	−0.265367	−	0.964147i	$-0.585493\pi$
$774$		0			0
$775$	−2.19174	+	2.19174i	−0.0787298	+	0.0787298i
$776$		0			0
$777$	6.41853			0.230263
$778$		0			0
$779$			61.3665i			2.19868i
$780$		0			0
$781$	−23.9549	+	23.9549i	−0.857174	+	0.857174i
$782$		0			0
$783$	3.38346	−	21.0084i	0.120915	−	0.750780i
$784$		0			0
$785$	29.3090	+	29.3090i	1.04608	+	1.04608i
$786$		0			0
$787$	28.0749			1.00076			0.500381	−	0.865805i	$-0.333193\pi$
$787$	28.0749			1.00076			0.500381	+	0.865805i	$0.333193\pi$
$788$		0			0
$789$		−	43.7824i		−	1.55869i
$790$		0			0
$791$	13.9315	+	13.9315i	0.495348	+	0.495348i
$792$		0			0
$793$	−10.9184	+	10.9184i	−0.387724	+	0.387724i
$794$		0			0
$795$	−29.2780	−	29.2780i	−1.03838	−	1.03838i
$796$		0			0
$797$	−10.3597	−	10.3597i	−0.366958	−	0.366958i	0.499409	−	0.866367i	$-0.333551\pi$
$797$	−10.3597	−	10.3597i	−0.366958	−	0.366958i	−0.866367	+	0.499409i	$0.833551\pi$
$798$		0			0
$799$		−	31.0200i		−	1.09741i
$800$		0			0
$801$	−36.5428	+	36.5428i	−1.29118	+	1.29118i
$802$		0			0
$803$		−	10.2295i		−	0.360990i
$804$		0			0
$805$			10.4808i			0.369400i
$806$		0			0
$807$			24.2870i			0.854942i
$808$		0			0
$809$	−16.1015	+	16.1015i	−0.566100	+	0.566100i	−0.931033	−	0.364934i	$-0.881092\pi$
$809$	−16.1015	+	16.1015i	−0.566100	+	0.566100i	0.364934	+	0.931033i	$0.381092\pi$
$810$		0			0
$811$	4.16152			0.146131			0.0730654	−	0.997327i	$-0.476722\pi$
$811$	4.16152			0.146131			0.0730654	+	0.997327i	$0.476722\pi$
$812$		0			0
$813$	70.4531			2.47090
$814$		0			0
$815$	−25.1819	+	25.1819i	−0.882085	+	0.882085i
$816$		0			0
$817$		−	59.6637i		−	2.08737i
$818$		0			0
$819$			5.91796i			0.206790i
$820$		0			0
$821$			7.38797i			0.257842i	0.991655	+	0.128921i	$0.0411514\pi$
$821$			7.38797i			0.257842i	−0.991655	+	0.128921i	$0.958849\pi$
$822$		0			0
$823$	−30.7910	+	30.7910i	−1.07331	+	1.07331i	−0.0762167	+	0.997091i	$0.524284\pi$
$823$	−30.7910	+	30.7910i	−1.07331	+	1.07331i	−0.997091	+	0.0762167i	$0.975716\pi$
$824$		0			0
$825$		−	5.96060i		−	0.207521i
$826$		0			0
$827$	30.1364	+	30.1364i	1.04794	+	1.04794i	0.998791	+	0.0491533i	$0.0156523\pi$
$827$	30.1364	+	30.1364i	1.04794	+	1.04794i	0.0491533	+	0.998791i	$0.484348\pi$
$828$		0			0
$829$	−28.4455	−	28.4455i	−0.987954	−	0.987954i	0.0119743	−	0.999928i	$-0.496188\pi$
$829$	−28.4455	−	28.4455i	−0.987954	−	0.987954i	−0.999928	+	0.0119743i	$0.996188\pi$
$830$		0			0
$831$	−42.3727	+	42.3727i	−1.46989	+	1.46989i
$832$		0			0
$833$	22.5583	+	22.5583i	0.781598	+	0.781598i
$834$		0			0
$835$		−	0.0481585i		−	0.00166659i
$836$		0			0
$837$	−16.4171			−0.567459
$838$		0			0
$839$	−35.9098	−	35.9098i	−1.23975	−	1.23975i	−0.960105	−	0.279640i	$-0.909785\pi$
$839$	−35.9098	−	35.9098i	−1.23975	−	1.23975i	−0.279640	−	0.960105i	$-0.590215\pi$
$840$		0			0
$841$	−9.10489	+	27.5336i	−0.313962	+	0.949436i
$842$		0			0
$843$	−28.0068	+	28.0068i	−0.964604	+	0.964604i
$844$		0			0
$845$		−	27.0813i		−	0.931626i
$846$		0			0
$847$	2.47715			0.0851160
$848$		0			0
$849$	15.4385	−	15.4385i	0.529847	−	0.529847i
$850$		0			0
$851$	6.99274	+	6.99274i	0.239708	+	0.239708i
$852$		0			0
$853$	−29.1924	+	29.1924i	−0.999528	+	0.999528i	−1.00000		0.000471811i	$-0.999850\pi$
$853$	−29.1924	+	29.1924i	−0.999528	+	0.999528i	0.000471811		1.00000i	$0.499850\pi$
$854$		0			0
$855$	39.4934	−	39.4934i	1.35064	−	1.35064i
$856$		0			0
$857$	14.8618			0.507669			0.253834	−	0.967248i	$-0.418308\pi$
$857$	14.8618			0.507669			0.253834	+	0.967248i	$0.418308\pi$
$858$		0			0
$859$	19.8098	+	19.8098i	0.675901	+	0.675901i	0.959070	−	0.283169i	$-0.0913858\pi$
$859$	19.8098	+	19.8098i	0.675901	+	0.675901i	−0.283169	+	0.959070i	$0.591386\pi$
$860$		0			0
$861$	−32.6011			−1.11104
$862$		0			0
$863$	52.8614			1.79942			0.899712	−	0.436484i	$-0.143776\pi$
$863$	52.8614			1.79942			0.899712	+	0.436484i	$0.143776\pi$
$864$		0			0
$865$	13.6149			0.462919
$866$		0			0
$867$	22.4819	+	22.4819i	0.763525	+	0.763525i
$868$		0			0
$869$		−	43.6766i		−	1.48163i
$870$		0			0
$871$		−	12.5567i		−	0.425467i
$872$		0			0
$873$	−6.80924	−	6.80924i	−0.230458	−	0.230458i
$874$		0			0
$875$	−10.3983			−0.351526
$876$		0			0
$877$	−2.66279			−0.0899161			−0.0449580	−	0.998989i	$-0.514315\pi$
$877$	−2.66279			−0.0899161			−0.0449580	+	0.998989i	$0.514315\pi$
$878$		0			0
$879$	−43.5430			−1.46867
$880$		0			0
$881$	13.4842	+	13.4842i	0.454293	+	0.454293i	0.896777	−	0.442484i	$-0.145903\pi$
$881$	13.4842	+	13.4842i	0.454293	+	0.454293i	−0.442484	+	0.896777i	$0.645903\pi$
$882$		0			0
$883$	36.1788			1.21751			0.608756	−	0.793357i	$-0.291669\pi$
$883$	36.1788			1.21751			0.608756	+	0.793357i	$0.291669\pi$
$884$		0			0
$885$	−19.7264	+	19.7264i	−0.663095	+	0.663095i
$886$		0			0
$887$	0.606597	−	0.606597i	0.0203675	−	0.0203675i	−0.696850	−	0.717217i	$-0.745416\pi$
$887$	0.606597	−	0.606597i	0.0203675	−	0.0203675i	0.717217	+	0.696850i	$0.245416\pi$
$888$		0			0
$889$	11.9585	+	11.9585i	0.401075	+	0.401075i
$890$		0			0
$891$	−5.29927	+	5.29927i	−0.177532	+	0.177532i
$892$		0			0
$893$	30.3584			1.01590
$894$		0			0
$895$		−	8.77383i		−	0.293277i
$896$		0			0
$897$	−10.7960	+	10.7960i	−0.360468	+	0.360468i
$898$		0			0
$899$	22.0892	+	3.55753i	0.736717	+	0.118650i
$900$		0			0
$901$	23.9554	+	23.9554i	0.798069	+	0.798069i
$902$		0			0
$903$	31.6965			1.05479
$904$		0			0
$905$			58.4849i			1.94410i
$906$		0			0
$907$	−40.2170	−	40.2170i	−1.33538	−	1.33538i	−0.900475	−	0.434907i	$-0.856781\pi$
$907$	−40.2170	−	40.2170i	−1.33538	−	1.33538i	−0.434907	−	0.900475i	$-0.643219\pi$
$908$		0			0
$909$	7.35558	−	7.35558i	0.243969	−	0.243969i
$910$		0			0
$911$	−23.3002	−	23.3002i	−0.771968	−	0.771968i	0.206482	−	0.978450i	$-0.433799\pi$
$911$	−23.3002	−	23.3002i	−0.771968	−	0.771968i	−0.978450	+	0.206482i	$0.933799\pi$
$912$		0			0
$913$	−0.663052	−	0.663052i	−0.0219438	−	0.0219438i
$914$		0			0
$915$			77.4181i			2.55936i
$916$		0			0
$917$	3.52438	−	3.52438i	0.116385	−	0.116385i
$918$		0			0
$919$		−	27.0113i		−	0.891021i	−0.895277	−	0.445511i	$-0.853022\pi$
$919$		−	27.0113i		−	0.891021i	0.895277	−	0.445511i	$-0.146978\pi$
$920$		0			0
$921$			45.7792i			1.50847i
$922$		0			0
$923$		−	15.0985i		−	0.496972i
$924$		0			0
$925$	1.21670	−	1.21670i	0.0400048	−	0.0400048i
$926$		0			0
$927$	32.5446			1.06891
$928$		0			0
$929$	−35.3035			−1.15827			−0.579136	−	0.815231i	$-0.696610\pi$
$929$	−35.3035			−1.15827			−0.579136	+	0.815231i	$0.696610\pi$
$930$		0			0
$931$	−22.0771	+	22.0771i	−0.723549	+	0.723549i
$932$		0			0
$933$			49.7796i			1.62971i
$934$		0			0
$935$			37.5628i			1.22843i
$936$		0			0
$937$			32.2106i			1.05228i	0.850399	+	0.526138i	$0.176360\pi$
$937$			32.2106i			1.05228i	−0.850399	+	0.526138i	$0.823640\pi$
$938$		0			0
$939$	−5.49709	+	5.49709i	−0.179391	+	0.179391i
$940$		0			0
$941$		−	16.7561i		−	0.546235i	−0.961981	−	0.273117i	$-0.911945\pi$
$941$		−	16.7561i		−	0.546235i	0.961981	−	0.273117i	$-0.0880547\pi$
$942$		0			0
$943$	−35.5176	−	35.5176i	−1.15661	−	1.15661i
$944$		0			0
$945$	6.82981	+	6.82981i	0.222174	+	0.222174i
$946$		0			0
$947$	19.1359	−	19.1359i	0.621834	−	0.621834i	−0.324166	−	0.946000i	$-0.605084\pi$
$947$	19.1359	−	19.1359i	0.621834	−	0.621834i	0.946000	+	0.324166i	$0.105084\pi$
$948$		0			0
$949$	3.22375	+	3.22375i	0.104647	+	0.104647i
$950$		0			0
$951$		−	31.0785i		−	1.00779i
$952$		0			0
$953$	−10.6671			−0.345543			−0.172771	−	0.984962i	$-0.555272\pi$
$953$	−10.6671			−0.345543			−0.172771	+	0.984962i	$0.555272\pi$
$954$		0			0
$955$	12.0913	+	12.0913i	0.391264	+	0.391264i
$956$		0			0
$957$	−34.8740	+	25.1991i	−1.12732	+	0.814571i
$958$		0			0
$959$	10.8100	−	10.8100i	0.349072	−	0.349072i
$960$		0			0
$961$			13.7383i			0.443171i
$962$		0			0
$963$	12.3583			0.398240
$964$		0			0
$965$	−32.0084	+	32.0084i	−1.03039	+	1.03039i
$966$		0			0
$967$	18.6237	+	18.6237i	0.598898	+	0.598898i	0.940019	−	0.341121i	$-0.110807\pi$
$967$	18.6237	+	18.6237i	0.598898	+	0.598898i	−0.341121	+	0.940019i	$0.610807\pi$
$968$		0			0
$969$	−54.1084	+	54.1084i	−1.73821	+	1.73821i
$970$		0			0
$971$	14.0949	−	14.0949i	0.452326	−	0.452326i	−0.443800	−	0.896126i	$-0.646370\pi$
$971$	14.0949	−	14.0949i	0.452326	−	0.452326i	0.896126	+	0.443800i	$0.146370\pi$
$972$		0			0
$973$	7.43099			0.238227
$974$		0			0
$975$	1.87844	+	1.87844i	0.0601583	+	0.0601583i
$976$		0			0
$977$	−12.0214			−0.384598			−0.192299	−	0.981336i	$-0.561594\pi$
$977$	−12.0214			−0.384598			−0.192299	+	0.981336i	$0.561594\pi$
$978$		0			0
$979$	34.0151			1.08713
$980$		0			0
$981$	34.0657			1.08764
$982$		0			0
$983$	18.0750	+	18.0750i	0.576502	+	0.576502i	0.933938	−	0.357436i	$-0.116349\pi$
$983$	18.0750	+	18.0750i	0.576502	+	0.576502i	−0.357436	+	0.933938i	$0.616349\pi$
$984$		0			0
$985$		−	19.5170i		−	0.621865i
$986$		0			0
$987$			16.1279i			0.513358i
$988$		0			0
$989$	34.5321	+	34.5321i	1.09806	+	1.09806i
$990$		0			0
$991$	48.5529			1.54233			0.771167	−	0.636633i	$-0.219674\pi$
$991$	48.5529			1.54233			0.771167	+	0.636633i	$0.219674\pi$
$992$		0			0
$993$	66.0358			2.09558
$994$		0			0
$995$	−42.6922			−1.35343
$996$		0			0
$997$	4.56165	+	4.56165i	0.144469	+	0.144469i	0.775642	−	0.631173i	$-0.217426\pi$
$997$	4.56165	+	4.56165i	0.144469	+	0.144469i	−0.631173	+	0.775642i	$0.717426\pi$
$998$		0			0
$999$	9.11361			0.288342

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.2.k.c.447.10	yes	20
4.3	odd	2	inner	464.2.k.c.447.1	yes	20
29.17	odd	4	inner	464.2.k.c.191.1	✓	20
116.75	even	4	inner	464.2.k.c.191.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
464.2.k.c.191.1	✓	20	29.17	odd	4	inner
464.2.k.c.191.10	yes	20	116.75	even	4	inner
464.2.k.c.447.1	yes	20	4.3	odd	2	inner
464.2.k.c.447.10	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.92975 - 1.92975i) q^{3} -2.39709i q^{5} -1.01973i q^{7} -4.44790i q^{9} +O(q^{10})\)	\(q+(1.92975 - 1.92975i) q^{3} -2.39709i q^{5} -1.01973i q^{7} -4.44790i q^{9} +(-2.07012 + 2.07012i) q^{11} -1.30477i q^{13} +(-4.62579 - 4.62579i) q^{15} +(3.78485 + 3.78485i) q^{17} +(-3.70412 + 3.70412i) q^{19} +(-1.96782 - 1.96782i) q^{21} -4.28773i q^{23} -0.746041 q^{25} +(-2.79409 - 2.79409i) q^{27} +(3.15397 + 4.36491i) q^{29} +(2.93783 - 2.93783i) q^{31} +7.98963i q^{33} -2.44438 q^{35} +(-1.63087 + 1.63087i) q^{37} +(-2.51788 - 2.51788i) q^{39} +(8.28356 - 8.28356i) q^{41} +(-8.05370 + 8.05370i) q^{43} -10.6620 q^{45} +(-4.09792 - 4.09792i) q^{47} +5.96016 q^{49} +14.6076 q^{51} +6.32929 q^{53} +(4.96226 + 4.96226i) q^{55} +14.2961i q^{57} -4.26443i q^{59} +(-8.36809 - 8.36809i) q^{61} -4.53564 q^{63} -3.12765 q^{65} +9.62370 q^{67} +(-8.27426 - 8.27426i) q^{69} +11.5718 q^{71} +(-2.47075 + 2.47075i) q^{73} +(-1.43968 + 1.43968i) q^{75} +(2.11095 + 2.11095i) q^{77} +(-10.5493 + 10.5493i) q^{79} +2.55989 q^{81} +0.320297i q^{83} +(9.07262 - 9.07262i) q^{85} +(14.5096 + 2.33681i) q^{87} +(-8.21575 - 8.21575i) q^{89} -1.33051 q^{91} -11.3386i q^{93} +(8.87910 + 8.87910i) q^{95} +(1.53089 - 1.53089i) q^{97} +(9.20767 + 9.20767i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q+O(q^{10}) \) 20 * q	\( 20 q - 4 q^{17} - 16 q^{21} - 28 q^{25} - 4 q^{29} - 20 q^{37} - 4 q^{41} - 40 q^{45} + 28 q^{49} + 48 q^{53} + 4 q^{61} + 40 q^{65} - 24 q^{69} - 20 q^{73} - 16 q^{77} + 108 q^{81} + 16 q^{85} + 36 q^{89} - 36 q^{97}+O(q^{100}) \) 20 * q - 4 * q^17 - 16 * q^21 - 28 * q^25 - 4 * q^29 - 20 * q^37 - 4 * q^41 - 40 * q^45 + 28 * q^49 + 48 * q^53 + 4 * q^61 + 40 * q^65 - 24 * q^69 - 20 * q^73 - 16 * q^77 + 108 * q^81 + 16 * q^85 + 36 * q^89 - 36 * q^97

Introduction

L-functions

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