LMFDB - Embedded newform 275.2.h.a.201.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(26,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.26"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,2,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.1
Root			$-0.227943 - 0.701538i$ of defining polynomial
Character	$\chi$	$=$	275.201
Dual form			275.2.h.a.26.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.596764 + 0.433574i) q^{2} +(0.868820 + 2.67395i) q^{3} +(-0.449894 + 1.38463i) q^{4} +(-1.67784 - 1.21902i) q^{6} +(-0.318714 + 0.980901i) q^{7} +(-0.787747 - 2.42443i) q^{8} +(-3.96813 + 2.88301i) q^{9} +(1.93675 + 2.69240i) q^{11} -4.09331 q^{12} +(2.79029 - 2.02726i) q^{13} +(-0.235096 - 0.723552i) q^{14} +(-0.834404 - 0.606230i) q^{16} +(1.94020 + 1.40964i) q^{17} +(1.11803 - 3.44095i) q^{18} +(-2.36979 - 7.29347i) q^{19} -2.89979 q^{21} +(-2.32313 - 0.767001i) q^{22} -2.45589 q^{23} +(5.79842 - 4.21280i) q^{24} +(-0.786174 + 2.41960i) q^{26} +(-4.33283 - 3.14799i) q^{27} +(-1.21480 - 0.882602i) q^{28} +(-1.83998 + 5.66289i) q^{29} +(2.98382 - 2.16787i) q^{31} +5.85919 q^{32} +(-5.51666 + 7.51798i) q^{33} -1.76902 q^{34} +(-2.20667 - 6.79144i) q^{36} +(-1.84130 + 5.66694i) q^{37} +(4.57646 + 3.32500i) q^{38} +(7.84507 + 5.69978i) q^{39} +(1.21637 + 3.74360i) q^{41} +(1.73049 - 1.25727i) q^{42} +7.64941 q^{43} +(-4.59931 + 1.47039i) q^{44} +(1.46558 - 1.06481i) q^{46} +(-1.80557 - 5.55697i) q^{47} +(0.896084 - 2.75786i) q^{48} +(4.80253 + 3.48924i) q^{49} +(-2.08362 + 6.41272i) q^{51} +(1.55168 + 4.77558i) q^{52} +(-9.58526 + 6.96410i) q^{53} +3.95056 q^{54} +2.62920 q^{56} +(17.4435 - 12.6734i) q^{57} +(-1.35725 - 4.17718i) q^{58} +(0.910456 - 2.80210i) q^{59} +(-2.00666 - 1.45792i) q^{61} +(-0.840701 + 2.58741i) q^{62} +(-1.56325 - 4.81120i) q^{63} +(-1.82774 + 1.32793i) q^{64} +(0.0325397 - 6.87834i) q^{66} +6.14702 q^{67} +(-2.82471 + 2.05227i) q^{68} +(-2.13372 - 6.56693i) q^{69} +(-1.63676 - 1.18918i) q^{71} +(10.1156 + 7.34938i) q^{72} +(0.255207 - 0.785446i) q^{73} +(-1.35822 - 4.18017i) q^{74} +11.1649 q^{76} +(-3.25824 + 1.04165i) q^{77} -7.15293 q^{78} +(9.77146 - 7.09938i) q^{79} +(0.106048 - 0.326382i) q^{81} +(-2.34901 - 1.70666i) q^{82} +(1.30253 + 0.946345i) q^{83} +(1.30460 - 4.01513i) q^{84} +(-4.56489 + 3.31659i) q^{86} -16.7409 q^{87} +(5.00188 - 6.81645i) q^{88} +8.16116 q^{89} +(1.09924 + 3.38312i) q^{91} +(1.10489 - 3.40050i) q^{92} +(8.38919 + 6.09510i) q^{93} +(3.48685 + 2.53335i) q^{94} +(5.09058 + 15.6672i) q^{96} +(1.97625 - 1.43583i) q^{97} -4.37882 q^{98} +(-15.4475 - 5.10011i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9} + 3 q^{11} - 16 q^{12} + 2 q^{13} - 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} - 20 q^{21} + 7 q^{22} - 10 q^{23} + 13 q^{24} + 10 q^{26}+ \cdots - 20 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9 + 3 * q^11 - 16 * q^12 + 2 * q^13 - 16 * q^14 + 4 * q^16 + 13 * q^17 + 15 * q^19 - 20 * q^21 + 7 * q^22 - 10 * q^23 + 13 * q^24 + 10 * q^26 - 10 * q^27 + 6 * q^28 - 9 * q^29 - 10 * q^31 - 16 * q^32 - 5 * q^33 + 4 * q^34 - 15 * q^36 - 24 * q^37 + 21 * q^39 + 8 * q^41 - 9 * q^42 + 38 * q^43 - 12 * q^44 + 3 * q^46 - 5 * q^48 + q^49 + q^51 + 28 * q^52 - 13 * q^53 + 16 * q^54 + 22 * q^56 + 45 * q^57 - 12 * q^58 - 27 * q^59 + 6 * q^61 + 30 * q^62 - 25 * q^63 - 26 * q^64 + 13 * q^66 + 38 * q^67 - 11 * q^68 - q^69 - 20 * q^71 + 30 * q^72 - 13 * q^73 + 20 * q^74 - 34 * q^77 + 16 * q^78 + 37 * q^79 + 8 * q^81 - 28 * q^82 - 27 * q^83 + 28 * q^84 - 3 * q^86 - 38 * q^87 + 36 * q^88 - 16 * q^89 + 44 * q^91 - 11 * q^92 + 35 * q^93 + 17 * q^94 - 17 * q^96 - 24 * q^97 - 16 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.596764	+	0.433574i	−0.421976	+	0.306583i	−0.778432	−	0.627729i	$-0.783985\pi$
$2$	−0.596764	+	0.433574i	−0.421976	+	0.306583i	0.356457	+	0.934312i	$0.383985\pi$
$3$	0.868820	+	2.67395i	0.501614	+	1.54381i	0.806390	+	0.591384i	$0.201418\pi$
$3$	0.868820	+	2.67395i	0.501614	+	1.54381i	−0.304777	+	0.952424i	$0.598582\pi$
$4$	−0.449894	+	1.38463i	−0.224947	+	0.692315i
$5$		0			0
$5$		0			0
$6$	−1.67784	−	1.21902i	−0.684974	−	0.497663i
$7$	−0.318714	+	0.980901i	−0.120463	+	0.370746i	−0.993047	−	0.117717i	$-0.962442\pi$
$7$	−0.318714	+	0.980901i	−0.120463	+	0.370746i	0.872585	+	0.488463i	$0.162442\pi$
$8$	−0.787747	−	2.42443i	−0.278510	−	0.857167i
$9$	−3.96813	+	2.88301i	−1.32271	+	0.961005i
$10$		0			0
$11$	1.93675	+	2.69240i	0.583951	+	0.811789i
$11$	1.93675	+	2.69240i	0.583951	+	0.811789i
$12$	−4.09331			−1.18164
$13$	2.79029	−	2.02726i	0.773887	−	0.562262i	−0.129251	−	0.991612i	$-0.541257\pi$
$13$	2.79029	−	2.02726i	0.773887	−	0.562262i	0.903138	+	0.429350i	$0.141257\pi$
$14$	−0.235096	−	0.723552i	−0.0628321	−	0.193377i
$15$		0			0
$16$	−0.834404	−	0.606230i	−0.208601	−	0.151557i
$17$	1.94020	+	1.40964i	0.470567	+	0.341887i	0.797662	−	0.603105i	$-0.206070\pi$
$17$	1.94020	+	1.40964i	0.470567	+	0.341887i	−0.327095	+	0.944991i	$0.606070\pi$
$18$	1.11803	−	3.44095i	0.263523	−	0.811041i
$19$	−2.36979	−	7.29347i	−0.543668	−	1.67324i	−0.724137	−	0.689656i	$-0.757762\pi$
$19$	−2.36979	−	7.29347i	−0.543668	−	1.67324i	0.180470	−	0.983581i	$-0.442238\pi$
$20$		0			0
$21$	−2.89979			−0.632786
$22$	−2.32313	−	0.767001i	−0.495294	−	0.163525i
$23$	−2.45589			−0.512088			−0.256044	−	0.966665i	$-0.582419\pi$
$23$	−2.45589			−0.512088			−0.256044	+	0.966665i	$0.582419\pi$
$24$	5.79842	−	4.21280i	1.18360	−	0.859933i
$25$		0			0
$26$	−0.786174	+	2.41960i	−0.154181	+	0.474522i
$27$	−4.33283	−	3.14799i	−0.833854	−	0.605830i
$28$	−1.21480	−	0.882602i	−0.229575	−	0.166796i
$29$	−1.83998	+	5.66289i	−0.341677	+	1.05157i	0.621663	+	0.783285i	$0.286458\pi$
$29$	−1.83998	+	5.66289i	−0.341677	+	1.05157i	−0.963339	+	0.268287i	$0.913542\pi$
$30$		0			0
$31$	2.98382	−	2.16787i	0.535909	−	0.389361i	−0.286654	−	0.958034i	$-0.592543\pi$
$31$	2.98382	−	2.16787i	0.535909	−	0.389361i	0.822564	+	0.568673i	$0.192543\pi$
$32$	5.85919			1.03577
$33$	−5.51666	+	7.51798i	−0.960328	+	1.30871i
$34$	−1.76902			−0.303384
$35$		0			0
$36$	−2.20667	−	6.79144i	−0.367779	−	1.13191i
$37$	−1.84130	+	5.66694i	−0.302708	+	0.931640i	0.677814	+	0.735233i	$0.262927\pi$
$37$	−1.84130	+	5.66694i	−0.302708	+	0.931640i	−0.980523	+	0.196407i	$0.937073\pi$
$38$	4.57646	+	3.32500i	0.742401	+	0.539386i
$39$	7.84507	+	5.69978i	1.25622	+	0.912695i
$40$		0			0
$41$	1.21637	+	3.74360i	0.189965	+	0.584652i	0.999999	−	0.00173135i	$-0.000551106\pi$
$41$	1.21637	+	3.74360i	0.189965	+	0.584652i	−0.810033	+	0.586384i	$0.800551\pi$
$42$	1.73049	−	1.25727i	0.267020	−	0.194001i
$43$	7.64941			1.16652			0.583262	−	0.812284i	$-0.301776\pi$
$43$	7.64941			1.16652			0.583262	+	0.812284i	$0.301776\pi$
$44$	−4.59931	+	1.47039i	−0.693372	+	0.221669i
$45$		0			0
$46$	1.46558	−	1.06481i	0.216089	−	0.156998i
$47$	−1.80557	−	5.55697i	−0.263369	−	0.810567i	−0.992065	−	0.125729i	$-0.959873\pi$
$47$	−1.80557	−	5.55697i	−0.263369	−	0.810567i	0.728695	−	0.684838i	$-0.240127\pi$
$48$	0.896084	−	2.75786i	0.129339	−	0.398063i
$49$	4.80253	+	3.48924i	0.686076	+	0.498463i
$50$		0			0
$51$	−2.08362	+	6.41272i	−0.291765	+	0.897960i
$52$	1.55168	+	4.77558i	0.215179	+	0.662253i
$53$	−9.58526	+	6.96410i	−1.31664	+	0.956592i	−0.316669	+	0.948536i	$0.602564\pi$
$53$	−9.58526	+	6.96410i	−1.31664	+	0.956592i	−0.999968	+	0.00805607i	$0.997436\pi$
$54$	3.95056			0.537603
$55$		0			0
$56$	2.62920			0.351341
$57$	17.4435	−	12.6734i	2.31044	−	1.67864i
$58$	−1.35725	−	4.17718i	−0.178215	−	0.548490i
$59$	0.910456	−	2.80210i	0.118531	−	0.364802i	−0.874136	−	0.485681i	$-0.838572\pi$
$59$	0.910456	−	2.80210i	0.118531	−	0.364802i	0.992667	+	0.120880i	$0.0385715\pi$
$60$		0			0
$61$	−2.00666	−	1.45792i	−0.256927	−	0.186668i	0.451864	−	0.892087i	$-0.350759\pi$
$61$	−2.00666	−	1.45792i	−0.256927	−	0.186668i	−0.708791	+	0.705419i	$0.750759\pi$
$62$	−0.840701	+	2.58741i	−0.106769	+	0.328602i
$63$	−1.56325	−	4.81120i	−0.196951	−	0.606154i
$64$	−1.82774	+	1.32793i	−0.228468	+	0.165992i
$65$		0			0
$66$	0.0325397	−	6.87834i	0.00400536	−	0.846665i
$67$	6.14702			0.750978			0.375489	−	0.926827i	$-0.377475\pi$
$67$	6.14702			0.750978			0.375489	+	0.926827i	$0.377475\pi$
$68$	−2.82471	+	2.05227i	−0.342546	+	0.248874i
$69$	−2.13372	−	6.56693i	−0.256870	−	0.790565i
$70$		0			0
$71$	−1.63676	−	1.18918i	−0.194248	−	0.141129i	0.486410	−	0.873731i	$-0.338306\pi$
$71$	−1.63676	−	1.18918i	−0.194248	−	0.141129i	−0.680658	+	0.732601i	$0.738306\pi$
$72$	10.1156	+	7.34938i	1.19213	+	0.866133i
$73$	0.255207	−	0.785446i	0.0298697	−	0.0919295i	−0.935010	−	0.354621i	$-0.884610\pi$
$73$	0.255207	−	0.785446i	0.0298697	−	0.0919295i	0.964880	+	0.262691i	$0.0846100\pi$
$74$	−1.35822	−	4.18017i	−0.157890	−	0.485934i
$75$		0			0
$76$	11.1649			1.28070
$77$	−3.25824	+	1.04165i	−0.371311	+	0.118707i
$78$	−7.15293			−0.809910
$79$	9.77146	−	7.09938i	1.09937	−	0.798742i	0.118417	−	0.992964i	$-0.462218\pi$
$79$	9.77146	−	7.09938i	1.09937	−	0.798742i	0.980958	+	0.194221i	$0.0622180\pi$
$80$		0			0
$81$	0.106048	−	0.326382i	0.0117831	−	0.0362647i
$82$	−2.34901	−	1.70666i	−0.259405	−	0.188469i
$83$	1.30253	+	0.946345i	0.142971	+	0.103875i	0.656972	−	0.753915i	$-0.271837\pi$
$83$	1.30253	+	0.946345i	0.142971	+	0.103875i	−0.514000	+	0.857790i	$0.671837\pi$
$84$	1.30460	−	4.01513i	0.142343	−	0.438087i
$85$		0			0
$86$	−4.56489	+	3.31659i	−0.492245	+	0.357637i
$87$	−16.7409			−1.79481
$88$	5.00188	−	6.81645i	0.533202	−	0.726636i
$89$	8.16116			0.865081			0.432541	−	0.901614i	$-0.357617\pi$
$89$	8.16116			0.865081			0.432541	+	0.901614i	$0.357617\pi$
$90$		0			0
$91$	1.09924	+	3.38312i	0.115232	+	0.354647i
$92$	1.10489	−	3.40050i	0.115193	−	0.354526i
$93$	8.38919	+	6.09510i	0.869918	+	0.632032i
$94$	3.48685	+	2.53335i	0.359642	+	0.261295i
$95$		0			0
$96$	5.09058	+	15.6672i	0.519555	+	1.59903i
$97$	1.97625	−	1.43583i	0.200658	−	0.145787i	−0.482919	−	0.875665i	$-0.660423\pi$
$97$	1.97625	−	1.43583i	0.200658	−	0.145787i	0.683577	+	0.729879i	$0.260423\pi$
$98$	−4.37882			−0.442328
$99$	−15.4475	−	5.10011i	−1.55253	−	0.512580i
$100$		0			0
$101$	6.08683	−	4.42234i	0.605662	−	0.440039i	−0.242222	−	0.970221i	$-0.577876\pi$
$101$	6.08683	−	4.42234i	0.605662	−	0.440039i	0.847884	+	0.530182i	$0.177876\pi$
$102$	−1.53696	−	4.73028i	−0.152182	−	0.468367i
$103$	2.93020	−	9.01821i	0.288721	−	0.888591i	−0.696538	−	0.717520i	$-0.745277\pi$
$103$	2.93020	−	9.01821i	0.288721	−	0.888591i	0.985259	−	0.171071i	$-0.0547228\pi$
$104$	−7.11301	−	5.16791i	−0.697488	−	0.506755i
$105$		0			0
$106$	2.70068	−	8.31184i	0.262313	−	0.807317i
$107$	1.43593	+	4.41935i	0.138817	+	0.427235i	0.996164	−	0.0875039i	$-0.0278890\pi$
$107$	1.43593	+	4.41935i	0.138817	+	0.427235i	−0.857347	+	0.514739i	$0.827889\pi$
$108$	6.30811	−	4.58311i	0.606998	−	0.441010i
$109$	−5.32826			−0.510355			−0.255178	−	0.966894i	$-0.582134\pi$
$109$	−5.32826			−0.510355			−0.255178	+	0.966894i	$0.582134\pi$
$110$		0			0
$111$	−16.7529			−1.59012
$112$	0.860587	−	0.625253i	0.0813179	−	0.0590809i
$113$	−0.0942195	−	0.289978i	−0.00886342	−	0.0272788i	0.946527	−	0.322625i	$-0.104565\pi$
$113$	−0.0942195	−	0.289978i	−0.00886342	−	0.0272788i	−0.955390	+	0.295346i	$0.904565\pi$
$114$	−4.91476	+	15.1261i	−0.460310	+	1.41669i
$115$		0			0
$116$	−7.01321	−	5.09540i	−0.651160	−	0.473096i
$117$	−5.22760	+	16.0889i	−0.483292	+	1.48742i
$118$	0.671589	+	2.06694i	0.0618248	+	0.190277i
$119$	−2.00108	+	1.45387i	−0.183439	+	0.133276i
$120$		0			0
$121$	−3.49802	+	10.4290i	−0.318001	+	0.948090i
$122$	1.82962			0.165646
$123$	−8.95341	+	6.50503i	−0.807302	+	0.586539i
$124$	1.65930	+	5.10680i	0.149009	+	0.458604i
$125$		0			0
$126$	3.01890	+	2.19336i	0.268945	+	0.195400i
$127$	−9.63536	−	7.00050i	−0.855000	−	0.621194i	0.0715199	−	0.997439i	$-0.477215\pi$
$127$	−9.63536	−	7.00050i	−0.855000	−	0.621194i	−0.926520	+	0.376245i	$0.877215\pi$
$128$	−3.10621	+	9.55992i	−0.274552	+	0.844985i
$129$	6.64596	+	20.4542i	0.585145	+	1.80089i
$130$		0			0
$131$	−11.1875			−0.977452			−0.488726	−	0.872437i	$-0.662538\pi$
$131$	−11.1875			−0.977452			−0.488726	+	0.872437i	$0.662538\pi$
$132$	−7.92772	−	11.0208i	−0.690019	−	0.959240i
$133$	7.90945			0.685837
$134$	−3.66832	+	2.66519i	−0.316894	+	0.230237i
$135$		0			0
$136$	1.88919	−	5.81432i	0.161996	−	0.498573i
$137$	−3.46360	−	2.51645i	−0.295915	−	0.214995i	0.429914	−	0.902870i	$-0.358544\pi$
$137$	−3.46360	−	2.51645i	−0.295915	−	0.214995i	−0.725829	+	0.687875i	$0.758544\pi$
$138$	4.12058	+	2.99378i	0.350767	+	0.254847i
$139$	−1.83964	+	5.66183i	−0.156036	+	0.480230i	−0.998264	−	0.0588913i	$-0.981243\pi$
$139$	−1.83964	+	5.66183i	−0.156036	+	0.480230i	0.842228	+	0.539121i	$0.181243\pi$
$140$		0			0
$141$	13.2904	−	9.65601i	1.11925	−	0.813183i
$142$	1.49235			0.125236
$143$	10.8623	+	3.58627i	0.908351	+	0.299899i
$144$	5.05879			0.421566
$145$		0			0
$146$	0.188251	+	0.579377i	0.0155798	+	0.0479495i
$147$	−5.15754	+	15.8733i	−0.425387	+	1.30921i
$148$	−7.01823	−	5.09905i	−0.576895	−	0.419139i
$149$	3.06168	+	2.22444i	0.250823	+	0.182233i	0.706091	−	0.708121i	$-0.250457\pi$
$149$	3.06168	+	2.22444i	0.250823	+	0.182233i	−0.455269	+	0.890354i	$0.650457\pi$
$150$		0			0
$151$	−7.52661	−	23.1645i	−0.612507	−	1.88510i	−0.433159	−	0.901317i	$-0.642601\pi$
$151$	−7.52661	−	23.1645i	−0.612507	−	1.88510i	−0.179348	−	0.983786i	$-0.557399\pi$
$152$	−15.8157	+	11.4908i	−1.28283	+	0.932028i
$153$	−11.7629			−0.950978
$154$	1.49277	−	2.03431i	0.120291	−	0.163929i
$155$		0			0
$156$	−11.4215	+	8.29823i	−0.914455	+	0.664390i
$157$	−2.23484	−	6.87813i	−0.178360	−	0.548935i	0.821411	−	0.570336i	$-0.193187\pi$
$157$	−2.23484	−	6.87813i	−0.178360	−	0.548935i	−0.999771	+	0.0214015i	$0.993187\pi$
$158$	−2.75314	+	8.47330i	−0.219028	+	0.674100i
$159$	−26.9495	−	19.5800i	−2.13724	−	1.55279i
$160$		0			0
$161$	0.782725	−	2.40898i	0.0616874	−	0.189854i
$162$	0.0782252	+	0.240753i	0.00614596	+	0.0189153i
$163$	15.1198	−	10.9852i	1.18428	−	0.860428i	0.191630	−	0.981467i	$-0.438623\pi$
$163$	15.1198	−	10.9852i	1.18428	−	0.860428i	0.992648	+	0.121039i	$0.0386226\pi$
$164$	−5.73074			−0.447496
$165$		0			0
$166$	−1.18761			−0.0921767
$167$	6.35343	−	4.61604i	0.491644	−	0.357200i	−0.314172	−	0.949366i	$-0.601727\pi$
$167$	6.35343	−	4.61604i	0.491644	−	0.357200i	0.805816	+	0.592166i	$0.201727\pi$
$168$	2.28430	+	7.03035i	0.176237	+	0.542403i
$169$	−0.341302	+	1.05042i	−0.0262540	+	0.0808014i
$170$		0			0
$171$	30.4308	+	22.1093i	2.32710	+	1.69074i
$172$	−3.44142	+	10.5916i	−0.262406	+	0.807603i
$173$	−3.46244	−	10.6563i	−0.263244	−	0.810183i	−0.992093	−	0.125508i	$-0.959944\pi$
$173$	−3.46244	−	10.6563i	−0.263244	−	0.810183i	0.728848	−	0.684675i	$-0.240056\pi$
$174$	9.99037	−	7.25843i	0.757368	−	0.550260i
$175$		0			0
$176$	0.0161823	−	3.42066i	0.00121979	−	0.257842i
$177$	8.28370			0.622641
$178$	−4.87028	+	3.53847i	−0.365043	+	0.265219i
$179$	0.452595	+	1.39295i	0.0338286	+	0.104114i	0.966545	−	0.256497i	$-0.0825684\pi$
$179$	0.452595	+	1.39295i	0.0338286	+	0.104114i	−0.932716	+	0.360611i	$0.882568\pi$
$180$		0			0
$181$	−7.51496	−	5.45994i	−0.558583	−	0.405834i	0.272357	−	0.962196i	$-0.412197\pi$
$181$	−7.51496	−	5.45994i	−0.558583	−	0.405834i	−0.830940	+	0.556362i	$0.812197\pi$
$182$	−2.12282	−	1.54232i	−0.157354	−	0.114324i
$183$	2.15499	−	6.63239i	0.159302	−	0.490280i
$184$	1.93462	+	5.95414i	0.142622	+	0.438945i
$185$		0			0
$186$	−7.64904			−0.560855
$187$	−0.0376278	+	7.95389i	−0.00275162	+	0.581646i
$188$	8.50666			0.620412
$189$	4.46880	−	3.24677i	0.325057	−	0.236168i
$190$		0			0
$191$	−1.38222	+	4.25404i	−0.100014	+	0.307811i	−0.988528	−	0.151038i	$-0.951738\pi$
$191$	−1.38222	+	4.25404i	−0.100014	+	0.307811i	0.888514	+	0.458850i	$0.151738\pi$
$192$	−5.13881	−	3.73357i	−0.370862	−	0.269447i
$193$	−18.3372	−	13.3227i	−1.31994	−	0.958992i	−0.999933	−	0.0115772i	$-0.996315\pi$
$193$	−18.3372	−	13.3227i	−1.31994	−	0.958992i	−0.320007	−	0.947415i	$-0.603685\pi$
$194$	−0.556816	+	1.71370i	−0.0399771	+	0.123037i
$195$		0			0
$196$	−6.99194	+	5.07994i	−0.499424	+	0.362853i
$197$	11.2080			0.798535			0.399267	−	0.916835i	$-0.369265\pi$
$197$	11.2080			0.798535			0.399267	+	0.916835i	$0.369265\pi$
$198$	11.4298	−	3.65407i	0.812278	−	0.259683i
$199$	−7.81979			−0.554330			−0.277165	−	0.960822i	$-0.589395\pi$
$199$	−7.81979			−0.554330			−0.277165	+	0.960822i	$0.589395\pi$
$200$		0			0
$201$	5.34065	+	16.4368i	0.376701	+	1.15937i
$202$	−1.71499	+	5.27818i	−0.120666	+	0.371372i
$203$	−4.96830	−	3.60968i	−0.348707	−	0.253350i
$204$	−7.94184	−	5.77008i	−0.556040	−	0.403987i
$205$		0			0
$206$	2.16143	+	6.65220i	0.150594	+	0.463481i
$207$	9.74527	−	7.08035i	0.677343	−	0.492119i
$208$	−3.55722			−0.246649
$209$	15.0472	−	20.5060i	1.04084	−	1.41843i
$210$		0			0
$211$	18.4189	−	13.3821i	1.26801	−	0.921262i	0.268887	−	0.963172i	$-0.413344\pi$
$211$	18.4189	−	13.3821i	1.26801	−	0.921262i	0.999121	+	0.0419098i	$0.0133442\pi$
$212$	−5.33035	−	16.4051i	−0.366090	−	1.12671i
$213$	1.75775	−	5.40980i	0.120439	−	0.370673i
$214$	−2.77303	−	2.01472i	−0.189560	−	0.137724i
$215$		0			0
$216$	−4.21891	+	12.9845i	−0.287061	+	0.883482i
$217$	1.17548	+	3.61776i	0.0797969	+	0.245589i
$218$	3.17971	−	2.31020i	0.215357	−	0.156466i
$219$	2.32197			0.156905
$220$		0			0
$221$	8.27142			0.556396
$222$	9.99752	−	7.26363i	0.670990	−	0.487503i
$223$	4.95746	+	15.2575i	0.331976	+	1.02172i	0.968192	+	0.250207i	$0.0804985\pi$
$223$	4.95746	+	15.2575i	0.331976	+	1.02172i	−0.636216	+	0.771511i	$0.719501\pi$
$224$	−1.86741	+	5.74728i	−0.124771	+	0.384006i
$225$		0			0
$226$	0.181954	+	0.132197i	0.0121034	+	0.00879361i
$227$	7.46468	−	22.9739i	0.495448	−	1.52483i	−0.320809	−	0.947144i	$-0.603955\pi$
$227$	7.46468	−	22.9739i	0.495448	−	1.52483i	0.816257	−	0.577689i	$-0.196045\pi$
$228$	9.70030	+	29.8545i	0.642418	+	1.97716i
$229$	12.1468	−	8.82517i	0.802684	−	0.583184i	−0.109017	−	0.994040i	$-0.534770\pi$
$229$	12.1468	−	8.82517i	0.802684	−	0.583184i	0.911700	+	0.410856i	$0.134770\pi$
$230$		0			0
$231$	−5.61616	−	7.80738i	−0.369516	−	0.513688i
$232$	15.1787			0.996534
$233$	9.24378	−	6.71600i	0.605580	−	0.439980i	−0.242275	−	0.970208i	$-0.577894\pi$
$233$	9.24378	−	6.71600i	0.605580	−	0.439980i	0.847855	+	0.530228i	$0.177894\pi$
$234$	−3.85609	−	11.8678i	−0.252080	−	0.775823i
$235$		0			0
$236$	3.47026	+	2.52129i	0.225895	+	0.164122i
$237$	27.4730	+	19.9603i	1.78457	+	1.29656i
$238$	0.563811	−	1.73523i	0.0365465	−	0.112478i
$239$	8.46914	+	26.0653i	0.547823	+	1.68603i	0.714181	+	0.699961i	$0.246799\pi$
$239$	8.46914	+	26.0653i	0.547823	+	1.68603i	−0.166358	+	0.986065i	$0.553201\pi$
$240$		0			0
$241$	10.9387			0.704624			0.352312	−	0.935883i	$-0.385396\pi$
$241$	10.9387			0.704624			0.352312	+	0.935883i	$0.385396\pi$
$242$	−2.43425	−	7.74029i	−0.156480	−	0.497565i
$243$	−15.1022			−0.968804
$244$	2.92147	−	2.12257i	0.187028	−	0.135884i
$245$		0			0
$246$	2.52265	−	7.76393i	0.160839	−	0.495010i
$247$	−21.3982	−	15.5467i	−1.36154	−	0.989213i
$248$	−7.60635	−	5.52634i	−0.483004	−	0.350923i
$249$	−1.39882	+	4.30511i	−0.0886463	+	0.272825i
$250$		0			0
$251$	−13.9403	+	10.1282i	−0.879902	+	0.639286i	−0.933225	−	0.359291i	$-0.883018\pi$
$251$	−13.9403	+	10.1282i	−0.879902	+	0.639286i	0.0533238	+	0.998577i	$0.483018\pi$
$252$	7.36503			0.463953
$253$	−4.75643	−	6.61222i	−0.299034	−	0.415707i
$254$	8.78527			0.551237
$255$		0			0
$256$	−3.68753	−	11.3491i	−0.230471	−	0.709316i
$257$	−5.71540	+	17.5902i	−0.356517	+	1.09725i	0.598608	+	0.801042i	$0.295721\pi$
$257$	−5.71540	+	17.5902i	−0.356517	+	1.09725i	−0.955125	+	0.296204i	$0.904279\pi$
$258$	−12.8345	−	9.32479i	−0.799039	−	0.580536i
$259$	−4.97186	−	3.61227i	−0.308936	−	0.224455i
$260$		0			0
$261$	−9.02489	−	27.7758i	−0.558627	−	1.71928i
$262$	6.67626	−	4.85059i	0.412461	−	0.299670i
$263$	−3.69135			−0.227618			−0.113809	−	0.993503i	$-0.536305\pi$
$263$	−3.69135			−0.227618			−0.113809	+	0.993503i	$0.536305\pi$
$264$	22.5726	+	7.45252i	1.38925	+	0.458671i
$265$		0			0
$266$	−4.72007	+	3.42933i	−0.289406	+	0.210266i
$267$	7.09058	+	21.8226i	0.433937	+	1.33552i
$268$	−2.76550	+	8.51135i	−0.168930	+	0.519913i
$269$	8.04575	+	5.84558i	0.490558	+	0.356411i	0.805399	−	0.592733i	$-0.201951\pi$
$269$	8.04575	+	5.84558i	0.490558	+	0.356411i	−0.314841	+	0.949145i	$0.601951\pi$
$270$		0			0
$271$	0.387400	−	1.19229i	0.0235329	−	0.0724267i	−0.938600	−	0.345006i	$-0.887877\pi$
$271$	0.387400	−	1.19229i	0.0235329	−	0.0724267i	0.962133	+	0.272580i	$0.0878768\pi$
$272$	−0.764345	−	2.35241i	−0.0463452	−	0.142636i
$273$	−8.09125	+	5.87864i	−0.489705	+	0.355791i
$274$	3.15802			0.190783
$275$		0			0
$276$	10.0527			0.605102
$277$	−6.54763	+	4.75713i	−0.393409	+	0.285828i	−0.766851	−	0.641825i	$-0.778177\pi$
$277$	−6.54763	+	4.75713i	−0.393409	+	0.285828i	0.373442	+	0.927654i	$0.378177\pi$
$278$	−1.35699	−	4.17639i	−0.0813870	−	0.250483i
$279$	−5.59017	+	17.2048i	−0.334675	+	1.03002i
$280$		0			0
$281$	−20.5250	−	14.9123i	−1.22442	−	0.889591i	−0.227958	−	0.973671i	$-0.573205\pi$
$281$	−20.5250	−	14.9123i	−1.22442	−	0.889591i	−0.996459	+	0.0840804i	$0.973205\pi$
$282$	−3.74461	+	11.5247i	−0.222988	+	0.686286i
$283$	6.31705	+	19.4419i	0.375510	+	1.15570i	0.943134	+	0.332412i	$0.107863\pi$
$283$	6.31705	+	19.4419i	0.375510	+	1.15570i	−0.567624	+	0.823288i	$0.692137\pi$
$284$	2.38294	−	1.73131i	0.141401	−	0.102734i
$285$		0			0
$286$	−8.03714	+	2.56945i	−0.475246	+	0.151935i
$287$	−4.05977			−0.239641
$288$	−23.2500	+	16.8921i	−1.37002	+	0.995378i
$289$	−3.47600	−	10.6980i	−0.204470	−	0.629295i
$290$		0			0
$291$	5.55635	+	4.03693i	0.325719	+	0.236649i
$292$	0.972737	+	0.706734i	0.0569251	+	0.0413585i
$293$	−0.787705	+	2.42431i	−0.0460182	+	0.141630i	−0.971426	−	0.237344i	$-0.923723\pi$
$293$	−0.787705	+	2.42431i	−0.0460182	+	0.141630i	0.925407	+	0.378974i	$0.123723\pi$
$294$	−3.80441	−	11.7088i	−0.221878	−	0.682869i
$295$		0			0
$296$	15.1896			0.882878
$297$	0.0840302	−	17.7626i	0.00487593	−	1.03069i
$298$	−2.79156			−0.161711
$299$	−6.85264	+	4.97873i	−0.396298	+	0.287928i
$300$		0			0
$301$	−2.43797	+	7.50331i	−0.140523	+	0.432484i
$302$	14.5352	+	10.5604i	0.836404	+	0.607683i
$303$	17.1135	+	12.4337i	0.983144	+	0.714296i
$304$	−2.44416	+	7.52234i	−0.140182	+	0.431436i
$305$		0			0
$306$	7.01970	−	5.10011i	0.401289	−	0.291554i
$307$	−8.99273			−0.513242			−0.256621	−	0.966512i	$-0.582609\pi$
$307$	−8.99273			−0.513242			−0.256621	+	0.966512i	$0.582609\pi$
$308$	0.0235596	−	4.98010i	0.00134243	−	0.283767i
$309$	26.6601			1.51664
$310$		0			0
$311$	−6.21840	−	19.1383i	−0.352613	−	1.08523i	−0.957380	−	0.288830i	$-0.906734\pi$
$311$	−6.21840	−	19.1383i	−0.352613	−	1.08523i	0.604767	−	0.796402i	$-0.293266\pi$
$312$	7.63881	−	23.5098i	0.432463	−	1.33098i
$313$	5.74792	+	4.17611i	0.324892	+	0.236048i	0.738260	−	0.674516i	$-0.235648\pi$
$313$	5.74792	+	4.17611i	0.324892	+	0.236048i	−0.413368	+	0.910564i	$0.635648\pi$
$314$	4.31585	+	3.13565i	0.243558	+	0.176955i
$315$		0			0
$316$	5.43390	+	16.7238i	0.305681	+	0.940789i
$317$	1.85526	−	1.34793i	0.104202	−	0.0757071i	−0.534464	−	0.845191i	$-0.679487\pi$
$317$	1.85526	−	1.34793i	0.104202	−	0.0757071i	0.638666	+	0.769484i	$0.279487\pi$
$318$	24.5719			1.37792
$319$	−18.8103	+	6.01362i	−1.05318	+	0.336698i
$320$		0			0
$321$	−10.5696	+	7.67924i	−0.589936	+	0.428613i
$322$	0.577370	+	1.77696i	0.0321756	+	0.0990262i
$323$	5.68327	−	17.4913i	0.316226	−	0.973242i
$324$	0.404208	+	0.293674i	0.0224560	+	0.0163152i
$325$		0			0
$326$	−4.26007	+	13.1111i	−0.235943	+	0.726159i
$327$	−4.62930	−	14.2475i	−0.256001	−	0.787890i
$328$	8.11793	−	5.89802i	0.448237	−	0.325664i
$329$	6.02629			0.332240
$330$		0			0
$331$	15.3951			0.846192			0.423096	−	0.906085i	$-0.360943\pi$
$331$	15.3951			0.846192			0.423096	+	0.906085i	$0.360943\pi$
$332$	−1.89634	+	1.37777i	−0.104075	+	0.0756150i
$333$	−9.03136	−	27.7957i	−0.494915	−	1.52319i
$334$	−1.79010	+	5.50937i	−0.0979501	+	0.301459i
$335$		0			0
$336$	2.41959	+	1.75794i	0.132000	+	0.0959034i
$337$	6.02485	−	18.5426i	0.328195	−	1.01008i	−0.641783	−	0.766886i	$-0.721805\pi$
$337$	6.02485	−	18.5426i	0.328195	−	1.01008i	0.969978	−	0.243193i	$-0.0781949\pi$
$338$	−0.251758	−	0.774831i	−0.0136938	−	0.0421453i
$339$	0.693527	−	0.503877i	0.0376672	−	0.0273668i
$340$		0			0
$341$	11.6157	+	3.83501i	0.629024	+	0.207677i
$342$	−27.7460			−1.50033
$343$	−10.7941	+	7.84234i	−0.582825	+	0.423447i
$344$	−6.02580	−	18.5455i	−0.324889	−	0.999907i
$345$		0			0
$346$	6.68655	+	4.85806i	0.359471	+	0.261171i
$347$	−1.75479	−	1.27493i	−0.0942023	−	0.0684420i	0.539687	−	0.841866i	$-0.318543\pi$
$347$	−1.75479	−	1.27493i	−0.0942023	−	0.0684420i	−0.633889	+	0.773424i	$0.718543\pi$
$348$	7.53163	−	23.1800i	0.403738	−	1.24258i
$349$	−7.74150	−	23.8259i	−0.414393	−	1.27537i	−0.912793	−	0.408423i	$-0.866079\pi$
$349$	−7.74150	−	23.8259i	−0.414393	−	1.27537i	0.498400	−	0.866947i	$-0.333921\pi$
$350$		0			0
$351$	−18.4717			−0.985944
$352$	11.3478	+	15.7753i	0.604838	+	0.840825i
$353$	23.2532			1.23764			0.618821	−	0.785532i	$-0.287611\pi$
$353$	23.2532			1.23764			0.618821	+	0.785532i	$0.287611\pi$
$354$	−4.94341	+	3.59160i	−0.262739	+	0.190891i
$355$		0			0
$356$	−3.67166	+	11.3002i	−0.194597	+	0.598909i
$357$	−5.62616	−	4.08764i	−0.297768	−	0.216341i
$358$	−0.874037	−	0.635025i	−0.0461943	−	0.0335621i
$359$	3.12799	−	9.62695i	0.165089	−	0.508091i	−0.833954	−	0.551834i	$-0.813928\pi$
$359$	3.12799	−	9.62695i	0.165089	−	0.508091i	0.999043	+	0.0437429i	$0.0139282\pi$
$360$		0			0
$361$	−32.2075	+	23.4001i	−1.69513	+	1.23158i
$362$	6.85194			0.360130
$363$	−30.9258	−	0.292611i	−1.62318	−	0.0153581i
$364$	−5.17891			−0.271448
$365$		0			0
$366$	1.58961	+	4.89232i	0.0830903	+	0.255726i
$367$	−1.14622	+	3.52770i	−0.0598322	+	0.184145i	−0.976505	−	0.215493i	$-0.930864\pi$
$367$	−1.14622	+	3.52770i	−0.0598322	+	0.184145i	0.916673	+	0.399638i	$0.130864\pi$
$368$	2.04920	+	1.48883i	0.106822	+	0.0776107i
$369$	−15.6196	−	11.3483i	−0.813122	−	0.590768i
$370$		0			0
$371$	−3.77613	−	11.6217i	−0.196047	−	0.603371i
$372$	−12.2137	+	8.87378i	−0.633251	+	0.460084i
$373$	9.34017			0.483616			0.241808	−	0.970324i	$-0.422260\pi$
$373$	9.34017			0.483616			0.241808	+	0.970324i	$0.422260\pi$
$374$	−3.42615	−	4.76291i	−0.177162	−	0.246284i
$375$		0			0
$376$	−12.0502	+	8.75496i	−0.621440	+	0.451503i
$377$	6.34609	+	19.5312i	0.326840	+	1.00591i
$378$	−1.25910	+	3.87511i	−0.0647611	+	0.199314i
$379$	7.93783	+	5.76717i	0.407739	+	0.296240i	0.772686	−	0.634789i	$-0.218913\pi$
$379$	7.93783	+	5.76717i	0.407739	+	0.296240i	−0.364947	+	0.931028i	$0.618913\pi$
$380$		0			0
$381$	10.3476	−	31.8467i	0.530124	−	1.63156i
$382$	−1.01958	−	3.13795i	−0.0521663	−	0.160552i
$383$	−14.6002	+	10.6076i	−0.746034	+	0.542025i	−0.894595	−	0.446878i	$-0.852536\pi$
$383$	−14.6002	+	10.6076i	−0.746034	+	0.542025i	0.148561	+	0.988903i	$0.452536\pi$
$384$	−28.2615			−1.44221
$385$		0			0
$386$	16.7194			0.850993
$387$	−30.3539	+	22.0534i	−1.54297	+	1.12104i
$388$	1.09899	+	3.38235i	0.0557929	+	0.171713i
$389$	9.63871	−	29.6649i	0.488702	−	1.50407i	−0.337844	−	0.941202i	$-0.609698\pi$
$389$	9.63871	−	29.6649i	0.488702	−	1.50407i	0.826546	−	0.562869i	$-0.190302\pi$
$390$		0			0
$391$	−4.76490	−	3.46191i	−0.240972	−	0.175076i
$392$	4.67626	−	14.3921i	0.236187	−	0.726909i
$393$	−9.71989	−	29.9147i	−0.490303	−	1.50900i
$394$	−6.68851	+	4.85948i	−0.336962	+	0.244817i
$395$		0			0
$396$	14.0115	−	19.0946i	0.704104	−	0.959537i
$397$	10.6212			0.533062			0.266531	−	0.963826i	$-0.414123\pi$
$397$	10.6212			0.533062			0.266531	+	0.963826i	$0.414123\pi$
$398$	4.66657	−	3.39046i	0.233914	−	0.169948i
$399$	6.87189	+	21.1495i	0.344025	+	1.05880i
$400$		0			0
$401$	22.3029	+	16.2040i	1.11375	+	0.809190i	0.983251	−	0.182258i	$-0.0583407\pi$
$401$	22.3029	+	16.2040i	1.11375	+	0.809190i	0.130503	+	0.991448i	$0.458341\pi$
$402$	−10.3137	−	7.49334i	−0.514400	−	0.373734i
$403$	3.93087	−	12.0980i	0.195811	−	0.602643i
$404$	3.38488	+	10.4176i	0.168404	+	0.518295i
$405$		0			0
$406$	4.52997			0.224818
$407$	−18.8238	+	6.01792i	−0.933061	+	0.298297i
$408$	17.1886			0.850961
$409$	−11.6241	+	8.44540i	−0.574774	+	0.417598i	−0.836836	−	0.547453i	$-0.815598\pi$
$409$	−11.6241	+	8.44540i	−0.574774	+	0.417598i	0.262062	+	0.965051i	$0.415598\pi$
$410$		0			0
$411$	3.71963	−	11.4478i	0.183476	−	0.564681i
$412$	11.1686	+	8.11448i	0.550238	+	0.399772i
$413$	2.45840	+	1.78613i	0.120970	+	0.0878899i
$414$	−2.74576	+	8.45060i	−0.134947	+	0.415324i
$415$		0			0
$416$	16.3488	−	11.8781i	0.801568	−	0.582373i
$417$	−16.7378			−0.819652
$418$	−0.0887552	+	18.7613i	−0.00434116	+	0.917647i
$419$	−31.4707			−1.53744			−0.768722	−	0.639584i	$-0.779107\pi$
$419$	−31.4707			−1.53744			−0.768722	+	0.639584i	$0.779107\pi$
$420$		0			0
$421$	8.21095	+	25.2707i	0.400177	+	1.23162i	0.924856	+	0.380318i	$0.124185\pi$
$421$	8.21095	+	25.2707i	0.400177	+	1.23162i	−0.524679	+	0.851300i	$0.675815\pi$
$422$	−5.18959	+	15.9719i	−0.252625	+	0.777500i
$423$	23.1855	+	16.8453i	1.12732	+	0.819045i
$424$	24.4348	+	17.7529i	1.18666	+	0.862156i
$425$		0			0
$426$	1.29659	+	3.99049i	0.0628199	+	0.193340i
$427$	2.06963	−	1.50367i	0.100156	−	0.0727679i
$428$	−6.76518			−0.327008
$429$	−0.152146	+	32.1611i	−0.00734568	+	1.55275i
$430$		0			0
$431$	3.12984	−	2.27397i	0.150759	−	0.109533i	−0.509849	−	0.860264i	$-0.670299\pi$
$431$	3.12984	−	2.27397i	0.150759	−	0.109533i	0.660608	+	0.750731i	$0.270299\pi$
$432$	1.70693	+	5.25338i	0.0821246	+	0.252754i
$433$	−12.4036	+	38.1743i	−0.596077	+	1.83454i	−0.0467895	+	0.998905i	$0.514899\pi$
$433$	−12.4036	+	38.1743i	−0.596077	+	1.83454i	−0.549288	+	0.835633i	$0.685101\pi$
$434$	−2.27005	−	1.64929i	−0.108966	−	0.0791684i
$435$		0			0
$436$	2.39715	−	7.37768i	0.114803	−	0.353327i
$437$	5.81994	+	17.9119i	0.278406	+	0.856844i
$438$	−1.38567	+	1.00675i	−0.0662099	+	0.0481043i
$439$	1.02336			0.0488425			0.0244212	−	0.999702i	$-0.492226\pi$
$439$	1.02336			0.0488425			0.0244212	+	0.999702i	$0.492226\pi$
$440$		0			0
$441$	−29.1166			−1.38650
$442$	−4.93608	+	3.58627i	−0.234785	+	0.170582i
$443$	4.96678	+	15.2862i	0.235979	+	0.726268i	0.996990	+	0.0775295i	$0.0247032\pi$
$443$	4.96678	+	15.2862i	0.235979	+	0.726268i	−0.761011	+	0.648739i	$0.775297\pi$
$444$	7.53703	−	23.1966i	0.357691	−	1.10086i
$445$		0			0
$446$	−9.57368	−	6.95569i	−0.453327	−	0.329361i
$447$	−3.28800	+	10.1194i	−0.155517	+	0.478633i
$448$	−0.720043	−	2.21607i	−0.0340188	−	0.104699i
$449$	−28.9969	+	21.0675i	−1.36845	+	0.994235i	−0.370590	+	0.928797i	$0.620844\pi$
$449$	−28.9969	+	21.0675i	−1.36845	+	0.994235i	−0.997857	+	0.0654379i	$0.979156\pi$
$450$		0			0
$451$	−7.72346	+	10.5254i	−0.363684	+	0.495620i
$452$	0.443901			0.0208793
$453$	55.4016	−	40.2516i	2.60299	−	1.89119i
$454$	5.50625	+	16.9465i	0.258421	+	0.795338i
$455$		0			0
$456$	−44.4669	−	32.3071i	−2.08235	−	1.51292i
$457$	−20.3488	−	14.7842i	−0.951875	−	0.691578i	−0.000625413	−	1.00000i	$-0.500199\pi$
$457$	−20.3488	−	14.7842i	−0.951875	−	0.691578i	−0.951250	+	0.308422i	$0.900199\pi$
$458$	−3.42241	+	10.5331i	−0.159919	+	0.492179i
$459$	−3.96903	−	12.2154i	−0.185259	−	0.570167i
$460$		0			0
$461$	6.65631			0.310015			0.155008	−	0.987913i	$-0.450460\pi$
$461$	6.65631			0.310015			0.155008	+	0.987913i	$0.450460\pi$
$462$	6.73660	+	2.22414i	0.313415	+	0.103476i
$463$	−38.7730			−1.80194			−0.900968	−	0.433886i	$-0.857142\pi$
$463$	−38.7730			−1.80194			−0.900968	+	0.433886i	$0.857142\pi$
$464$	4.96830	−	3.60968i	0.230648	−	0.167575i
$465$		0			0
$466$	−2.60447	+	8.01573i	−0.120650	+	0.371321i
$467$	18.2429	+	13.2542i	0.844179	+	0.613332i	0.923535	−	0.383514i	$-0.125286\pi$
$467$	18.2429	+	13.2542i	0.844179	+	0.613332i	−0.0793559	+	0.996846i	$0.525286\pi$
$468$	−19.9253	−	14.4766i	−0.921048	−	0.669180i
$469$	−1.95914	+	6.02961i	−0.0904647	+	0.278422i
$470$		0			0
$471$	16.4501	−	11.9517i	0.757982	−	0.550706i
$472$	−7.51071			−0.345708
$473$	14.8150	+	20.5953i	0.681194	+	0.946971i
$474$	−25.0492			−1.15055
$475$		0			0
$476$	−1.11280	−	3.42484i	−0.0510051	−	0.156977i
$477$	17.9579	−	55.2689i	0.822238	−	2.53059i
$478$	−16.3553	−	11.8828i	−0.748075	−	0.543509i
$479$	1.32021	+	0.959186i	0.0603218	+	0.0438263i	0.617538	−	0.786541i	$-0.288130\pi$
$479$	1.32021	+	0.959186i	0.0603218	+	0.0438263i	−0.557216	+	0.830368i	$0.688130\pi$
$480$		0			0
$481$	6.35063	+	19.5452i	0.289564	+	0.891186i
$482$	−6.52782	+	4.74274i	−0.297334	+	0.216026i
$483$	7.12155			0.324042
$484$	−12.8666	−	9.53540i	−0.584844	−	0.433427i
$485$		0			0
$486$	9.01242	−	6.54790i	0.408811	−	0.297019i
$487$	−0.324560	−	0.998894i	−0.0147072	−	0.0452642i	0.943434	−	0.331562i	$-0.107575\pi$
$487$	−0.324560	−	0.998894i	−0.0147072	−	0.0452642i	−0.958141	+	0.286297i	$0.907575\pi$
$488$	−1.95390	+	6.01349i	−0.0884490	+	0.272218i
$489$	42.5104	+	30.8856i	1.92239	+	1.39669i
$490$		0			0
$491$	−4.29969	+	13.2331i	−0.194042	+	0.597201i	0.805944	+	0.591992i	$0.201658\pi$
$491$	−4.29969	+	13.2331i	−0.194042	+	0.597201i	−0.999986	+	0.00520928i	$0.998342\pi$
$492$	−4.97898	−	15.3237i	−0.224470	−	0.690847i
$493$	−11.5525	+	8.39341i	−0.520300	+	0.378020i
$494$	19.5103			0.877811
$495$		0			0
$496$	−3.80394			−0.170802
$497$	1.68812	−	1.22649i	0.0757226	−	0.0550157i
$498$	−1.03182	−	3.17562i	−0.0462371	−	0.142303i
$499$	5.36679	−	16.5173i	0.240250	−	0.739415i	−0.756131	−	0.654420i	$-0.772913\pi$
$499$	5.36679	−	16.5173i	0.240250	−	0.739415i	0.996381	−	0.0849943i	$-0.0270872\pi$
$500$		0			0
$501$	17.8631	+	12.9783i	0.798063	+	0.579827i
$502$	3.92772	−	12.0883i	0.175303	−	0.539526i
$503$	−11.0794	−	34.0988i	−0.494005	−	1.52039i	−0.818502	−	0.574503i	$-0.805195\pi$
$503$	−11.0794	−	34.0988i	−0.494005	−	1.52039i	0.324498	−	0.945887i	$-0.394805\pi$
$504$	−10.4330	+	7.58000i	−0.464722	+	0.337640i
$505$		0			0
$506$	5.70536	+	1.88367i	0.253634	+	0.0837393i
$507$	−3.10530			−0.137911
$508$	14.0280	−	10.1919i	0.622392	−	0.452194i
$509$	0.660921	+	2.03410i	0.0292948	+	0.0901601i	0.964635	−	0.263590i	$-0.0849065\pi$
$509$	0.660921	+	2.03410i	0.0292948	+	0.0901601i	−0.935340	+	0.353750i	$0.884906\pi$
$510$		0			0
$511$	0.689106	+	0.500665i	0.0304843	+	0.0221481i
$512$	−9.14306	−	6.64282i	−0.404070	−	0.293574i
$513$	−12.6918	+	39.0614i	−0.560358	+	1.72461i
$514$	−4.21591	−	12.9752i	−0.185956	−	0.572313i
$515$		0			0
$516$	−31.3115			−1.37841
$517$	11.4646	−	15.6238i	0.504214	−	0.687132i
$518$	4.53321			0.199178
$519$	25.4862	−	18.5168i	1.11872	−	0.812797i
$520$		0			0
$521$	−3.93540	+	12.1119i	−0.172413	+	0.530633i	−0.999506	−	0.0314326i	$-0.989993\pi$
$521$	−3.93540	+	12.1119i	−0.172413	+	0.530633i	0.827093	+	0.562065i	$0.189993\pi$
$522$	17.4286	+	12.6626i	0.762828	+	0.554227i
$523$	19.3426	+	14.0532i	0.845793	+	0.614504i	0.923983	−	0.382434i	$-0.124914\pi$
$523$	19.3426	+	14.0532i	0.845793	+	0.614504i	−0.0781901	+	0.996938i	$0.524914\pi$
$524$	5.03317	−	15.4905i	0.219875	−	0.676705i
$525$		0			0
$526$	2.20286	−	1.60047i	0.0960493	−	0.0697839i
$527$	8.84510			0.385299
$528$	9.16075	−	2.92867i	0.398670	−	0.127454i
$529$	−16.9686			−0.737766
$530$		0			0
$531$	4.46567	+	13.7439i	0.193794	+	0.596436i
$532$	−3.55841	+	10.9517i	−0.154277	+	0.474815i
$533$	10.9833	+	7.97983i	0.475739	+	0.345645i
$534$	−13.6931	−	9.94862i	−0.592558	−	0.430519i
$535$		0			0
$536$	−4.84229	−	14.9030i	−0.209155	−	0.643713i
$537$	−3.33145	+	2.42044i	−0.143763	+	0.104450i
$538$	−7.33590			−0.316273
$539$	−0.0931395	+	19.6881i	−0.00401180	+	0.848027i
$540$		0			0
$541$	−1.06726	+	0.775410i	−0.0458851	+	0.0333375i	−0.610491	−	0.792023i	$-0.709028\pi$
$541$	−1.06726	+	0.775410i	−0.0458851	+	0.0333375i	0.564606	+	0.825360i	$0.309028\pi$
$542$	0.285762	+	0.879484i	0.0122745	+	0.0377771i
$543$	8.07047	−	24.8384i	0.346337	−	1.06592i
$544$	11.3680	+	8.25932i	0.487398	+	0.354116i
$545$		0			0
$546$	2.27974	−	7.01631i	0.0975638	−	0.300270i
$547$	−2.88044	−	8.86507i	−0.123159	−	0.379043i	0.870403	−	0.492341i	$-0.163859\pi$
$547$	−2.88044	−	8.86507i	−0.123159	−	0.379043i	−0.993561	+	0.113298i	$0.963859\pi$
$548$	5.04261	−	3.66367i	0.215410	−	0.156504i
$549$	12.1659			0.519228
$550$		0			0
$551$	45.6625			1.94529
$552$	−14.2403	+	10.3461i	−0.606105	+	0.440361i
$553$	3.84949	+	11.8475i	0.163697	+	0.503807i
$554$	1.84482	−	5.67776i	0.0783788	−	0.241225i
$555$		0			0
$556$	−7.01190	−	5.09444i	−0.297371	−	0.216052i
$557$	−12.1497	+	37.3929i	−0.514798	+	1.58439i	0.268850	+	0.963182i	$0.413356\pi$
$557$	−12.1497	+	37.3929i	−0.514798	+	1.58439i	−0.783648	+	0.621205i	$0.786644\pi$
$558$	−4.12353	−	12.6909i	−0.174563	−	0.537250i
$559$	21.3441	−	15.5074i	0.902759	−	0.655893i
$560$		0			0
$561$	−21.3010	+	6.80989i	−0.899330	+	0.287514i
$562$	18.7141			0.789407
$563$	16.1649	−	11.7445i	0.681271	−	0.494972i	−0.192508	−	0.981295i	$-0.561662\pi$
$563$	16.1649	−	11.7445i	0.681271	−	0.494972i	0.873779	+	0.486323i	$0.161662\pi$
$564$	7.39076	+	22.7464i	0.311207	+	0.957797i
$565$		0			0
$566$	−12.1993	−	8.86330i	−0.512774	−	0.372552i
$567$	0.286349	+	0.208045i	0.0120255	+	0.00873707i
$568$	−1.59373	+	4.90499i	−0.0668713	+	0.205809i
$569$	−10.6811	−	32.8730i	−0.447775	−	1.37811i	−0.879412	−	0.476061i	$-0.842064\pi$
$569$	−10.6811	−	32.8730i	−0.447775	−	1.37811i	0.431637	−	0.902047i	$-0.357936\pi$
$570$		0			0
$571$	3.15090			0.131861			0.0659306	−	0.997824i	$-0.478998\pi$
$571$	3.15090			0.131861			0.0659306	+	0.997824i	$0.478998\pi$
$572$	−9.85254	+	13.4268i	−0.411955	+	0.561404i
$573$	−12.5760			−0.525370
$574$	2.42273	−	1.76021i	0.101123	−	0.0734699i
$575$		0			0
$576$	3.42427	−	10.5388i	0.142678	−	0.439117i
$577$	22.1044	+	16.0598i	0.920220	+	0.668579i	0.943579	−	0.331148i	$-0.107436\pi$
$577$	22.1044	+	16.0598i	0.920220	+	0.668579i	−0.0233590	+	0.999727i	$0.507436\pi$
$578$	6.71273	+	4.87709i	0.279213	+	0.202860i
$579$	19.6927	−	60.6079i	0.818400	−	2.51878i
$580$		0			0
$581$	−1.34340	+	0.976041i	−0.0557338	+	0.0404930i
$582$	−5.06614			−0.209998
$583$	−37.3143	−	12.3196i	−1.54540	−	0.510227i
$584$	−2.10530			−0.0871180
$585$		0			0
$586$	−0.581043	−	1.78827i	−0.0240027	−	0.0738726i
$587$	14.2667	−	43.9082i	0.588848	−	1.81229i	0.00561158	−	0.999984i	$-0.498214\pi$
$587$	14.2667	−	43.9082i	0.588848	−	1.81229i	0.583236	−	0.812303i	$-0.301786\pi$
$588$	−19.6583	−	14.2826i	−0.810694	−	0.589003i
$589$	−22.8823	−	16.6250i	−0.942850	−	0.685020i
$590$		0			0
$591$	9.73771	+	29.9696i	0.400556	+	1.23278i
$592$	4.97186	−	3.61227i	0.204342	−	0.148463i
$593$	−39.4265			−1.61905			−0.809525	−	0.587085i	$-0.800275\pi$
$593$	−39.4265			−1.61905			−0.809525	+	0.587085i	$0.800275\pi$
$594$	7.65124	+	10.6365i	0.313934	+	0.436420i
$595$		0			0
$596$	−4.45746	+	3.23853i	−0.182585	+	0.132656i
$597$	−6.79399	−	20.9098i	−0.278060	−	0.855780i
$598$	1.93075	−	5.94225i	0.0789544	−	0.242997i
$599$	−0.848455	−	0.616438i	−0.0346669	−	0.0251870i	0.570317	−	0.821425i	$-0.306820\pi$
$599$	−0.848455	−	0.616438i	−0.0346669	−	0.0251870i	−0.604984	+	0.796238i	$0.706820\pi$
$600$		0			0
$601$	8.42065	−	25.9161i	0.343485	−	1.05714i	−0.618904	−	0.785466i	$-0.712423\pi$
$601$	8.42065	−	25.9161i	0.343485	−	1.05714i	0.962390	−	0.271673i	$-0.0875768\pi$
$602$	−1.79835	−	5.53475i	−0.0732952	−	0.225579i
$603$	−24.3921	+	17.7219i	−0.993325	+	0.721693i
$604$	35.4605			1.44287
$605$		0			0
$606$	−15.6036			−0.633854
$607$	17.7350	−	12.8852i	0.719842	−	0.522996i	−0.166492	−	0.986043i	$-0.553244\pi$
$607$	17.7350	−	12.8852i	0.719842	−	0.522996i	0.886334	+	0.463047i	$0.153244\pi$
$608$	−13.8851	−	42.7338i	−0.563114	−	1.73309i
$609$	5.33556	−	16.4212i	0.216208	−	0.665420i
$610$		0			0
$611$	−16.3035	−	11.8452i	−0.659569	−	0.479205i
$612$	5.29208	−	16.2873i	0.213920	−	0.658377i
$613$	−3.27313	−	10.0736i	−0.132200	−	0.406871i	0.862944	−	0.505300i	$-0.168618\pi$
$613$	−3.27313	−	10.0736i	−0.132200	−	0.406871i	−0.995144	+	0.0984293i	$0.968618\pi$
$614$	5.36653	−	3.89901i	0.216576	−	0.157351i
$615$		0			0
$616$	5.09209	+	7.07884i	0.205166	+	0.285215i
$617$	−4.60402			−0.185351			−0.0926755	−	0.995696i	$-0.529542\pi$
$617$	−4.60402			−0.185351			−0.0926755	+	0.995696i	$0.529542\pi$
$618$	−15.9098	+	11.5591i	−0.639985	+	0.464976i
$619$	11.4348	+	35.1926i	0.459603	+	1.41451i	0.865645	+	0.500657i	$0.166908\pi$
$619$	11.4348	+	35.1926i	0.459603	+	1.41451i	−0.406043	+	0.913854i	$0.633092\pi$
$620$		0			0
$621$	10.6409	+	7.73110i	0.427006	+	0.310238i
$622$	12.0088	+	8.72489i	0.481508	+	0.349836i
$623$	−2.60108	+	8.00529i	−0.104210	+	0.320725i
$624$	−3.09058	−	9.51183i	−0.123722	−	0.380778i
$625$		0			0
$626$	−5.24081			−0.209465
$627$	67.9055	+	22.4195i	2.71189	+	0.895350i
$628$	10.5291			0.420157
$629$	−11.5608	+	8.39942i	−0.460960	+	0.334907i
$630$		0			0
$631$	−7.67617	+	23.6248i	−0.305583	+	0.940489i	0.673875	+	0.738845i	$0.264628\pi$
$631$	−7.67617	+	23.6248i	−0.305583	+	0.940489i	−0.979459	+	0.201644i	$0.935372\pi$
$632$	−24.9094	−	18.0977i	−0.990843	−	0.719890i
$633$	51.7858	+	37.6246i	2.05830	+	1.49544i
$634$	−0.522727	+	1.60879i	−0.0207601	+	0.0638931i
$635$		0			0
$636$	39.2355	−	28.5062i	1.55579	−	1.13035i
$637$	20.4741			0.811213
$638$	8.61798	−	11.7444i	0.341189	−	0.464965i
$639$	9.92328			0.392559
$640$		0			0
$641$	−13.7294	−	42.2547i	−0.542278	−	1.66896i	−0.727374	−	0.686241i	$-0.759260\pi$
$641$	−13.7294	−	42.2547i	−0.542278	−	1.66896i	0.185096	−	0.982720i	$-0.440740\pi$
$642$	2.97801	−	9.16538i	0.117533	−	0.361729i
$643$	20.9220	+	15.2007i	0.825082	+	0.599457i	0.918164	−	0.396201i	$-0.129672\pi$
$643$	20.9220	+	15.2007i	0.825082	+	0.599457i	−0.0930818	+	0.995658i	$0.529672\pi$
$644$	2.98341	+	2.16757i	0.117563	+	0.0854143i
$645$		0			0
$646$	4.19221	+	12.9023i	0.164940	+	0.507634i
$647$	15.7649	−	11.4539i	0.619782	−	0.450298i	−0.233063	−	0.972462i	$-0.574875\pi$
$647$	15.7649	−	11.4539i	0.619782	−	0.450298i	0.852845	+	0.522163i	$0.174875\pi$
$648$	−0.874831			−0.0343666
$649$	9.30768	−	2.97564i	0.365358	−	0.116804i
$650$		0			0
$651$	−8.65244	+	6.28636i	−0.339116	+	0.246382i
$652$	8.40814	+	25.8776i	0.329288	+	1.01344i
$653$	5.16979	−	15.9110i	0.202310	−	0.622645i	−0.797504	−	0.603314i	$-0.793847\pi$
$653$	5.16979	−	15.9110i	0.202310	−	0.622645i	0.999813	−	0.0193305i	$-0.00615349\pi$
$654$	8.93996	+	6.49526i	0.349580	+	0.253985i
$655$		0			0
$656$	1.25454	−	3.86108i	0.0489815	−	0.150750i
$657$	1.25176	+	3.85251i	0.0488357	+	0.150301i
$658$	−3.59627	+	2.61284i	−0.140197	+	0.101859i
$659$	−1.66127			−0.0647137			−0.0323569	−	0.999476i	$-0.510301\pi$
$659$	−1.66127			−0.0647137			−0.0323569	+	0.999476i	$0.510301\pi$
$660$		0			0
$661$	−44.0130			−1.71191			−0.855953	−	0.517053i	$-0.827029\pi$
$661$	−44.0130			−1.71191			−0.855953	+	0.517053i	$0.827029\pi$
$662$	−9.18724	+	6.67492i	−0.357072	+	0.259428i
$663$	7.18637	+	22.1174i	0.279096	+	0.858968i
$664$	1.26829	−	3.90338i	0.0492190	−	0.151481i
$665$		0			0
$666$	17.4411	+	12.6717i	0.675827	+	0.491017i
$667$	4.51879	−	13.9074i	0.174968	−	0.538497i
$668$	3.53314	+	10.8739i	0.136701	+	0.420723i
$669$	−36.4907	+	26.5120i	−1.41081	+	1.02501i
$670$		0			0
$671$	0.0389168	−	8.22636i	0.00150237	−	0.317575i
$672$	−16.9904			−0.655419
$673$	−31.2239	+	22.6855i	−1.20359	+	0.874462i	−0.994633	−	0.103462i	$-0.967008\pi$
$673$	−31.2239	+	22.6855i	−1.20359	+	0.874462i	−0.208961	+	0.977924i	$0.567008\pi$
$674$	4.44417	+	13.6778i	0.171183	+	0.526848i
$675$		0			0
$676$	−1.30089	−	0.945154i	−0.0500343	−	0.0363521i
$677$	−31.2271	−	22.6878i	−1.20016	−	0.871964i	−0.205855	−	0.978582i	$-0.565998\pi$
$677$	−31.2271	−	22.6878i	−1.20016	−	0.871964i	−0.994300	+	0.106619i	$0.965998\pi$
$678$	−0.195404	+	0.601391i	−0.00750443	+	0.0230963i
$679$	0.778549	+	2.39613i	0.0298780	+	0.0919549i
$680$		0			0
$681$	67.9167			2.60257
$682$	−8.59457	+	2.74766i	−0.329103	+	0.105213i
$683$	0.748158			0.0286275			0.0143137	−	0.999898i	$-0.495444\pi$
$683$	0.748158			0.0286275			0.0143137	+	0.999898i	$0.495444\pi$
$684$	−44.3038	+	32.1886i	−1.69400	+	1.23076i
$685$		0			0
$686$	3.04126	−	9.36005i	0.116116	−	0.357368i
$687$	34.1515	+	24.8125i	1.30296	+	0.946656i
$688$	−6.38270	−	4.63730i	−0.243338	−	0.176796i
$689$	−12.6276	+	38.8637i	−0.481073	+	1.48059i
$690$		0			0
$691$	−4.22456	+	3.06932i	−0.160710	+	0.116763i	−0.665234	−	0.746635i	$-0.731668\pi$
$691$	−4.22456	+	3.06932i	−0.160710	+	0.116763i	0.504524	+	0.863398i	$0.331668\pi$
$692$	16.3128			0.620118
$693$	9.92603	−	13.5270i	0.377059	−	0.513847i
$694$	1.59998			0.0607342
$695$		0			0
$696$	13.1876	+	40.5873i	0.499875	+	1.53846i
$697$	−2.91712	+	8.97796i	−0.110494	+	0.340065i
$698$	14.9501	+	10.8619i	0.565871	+	0.411129i
$699$	25.9895	+	18.8824i	0.983011	+	0.714200i
$700$		0			0
$701$	−4.37506	−	13.4650i	−0.165244	−	0.508568i	0.833811	−	0.552051i	$-0.186155\pi$
$701$	−4.37506	−	13.4650i	−0.165244	−	0.508568i	−0.999054	+	0.0434831i	$0.986155\pi$
$702$	11.0232	−	8.00883i	0.416044	−	0.302274i
$703$	45.6952			1.72343
$704$	−7.11520	−	2.34914i	−0.268164	−	0.0885366i
$705$		0			0
$706$	−13.8766	+	10.0820i	−0.522255	+	0.379440i
$707$	2.39792	+	7.38004i	0.0901830	+	0.277555i
$708$	−3.72678	+	11.4699i	−0.140061	+	0.431064i
$709$	13.9267	+	10.1183i	0.523028	+	0.380002i	0.817744	−	0.575583i	$-0.195225\pi$
$709$	13.9267	+	10.1183i	0.523028	+	0.380002i	−0.294715	+	0.955585i	$0.595225\pi$
$710$		0			0
$711$	−18.3068	+	56.3425i	−0.686558	+	2.11301i
$712$	−6.42893	−	19.7862i	−0.240934	−	0.741519i
$713$	−7.32792	+	5.32404i	−0.274433	+	0.199387i
$714$	5.12978			0.191977
$715$		0			0
$716$	−2.13233			−0.0796891
$717$	−62.3393	+	45.2922i	−2.32811	+	1.69147i
$718$	2.30733	+	7.10123i	0.0861087	+	0.265015i
$719$	−8.20624	+	25.2562i	−0.306041	+	0.941897i	0.673246	+	0.739419i	$0.264900\pi$
$719$	−8.20624	+	25.2562i	−0.306041	+	0.941897i	−0.979287	+	0.202478i	$0.935100\pi$
$720$		0			0
$721$	7.91208	+	5.74846i	0.294661	+	0.214084i
$722$	9.07457	−	27.9286i	0.337720	−	1.03940i
$723$	9.50377	+	29.2496i	0.353449	+	1.08780i
$724$	10.9409	−	7.94905i	0.406617	−	0.295424i
$725$		0			0
$726$	18.5823	−	13.2340i	0.689652	−	0.491160i
$727$	−44.1917			−1.63898			−0.819490	−	0.573094i	$-0.805743\pi$
$727$	−44.1917			−1.63898			−0.819490	+	0.573094i	$0.805743\pi$
$728$	7.33622	−	5.33007i	0.271898	−	0.197546i
$729$	−13.4392	−	41.3616i	−0.497748	−	1.53191i
$730$		0			0
$731$	14.8414	+	10.7829i	0.548928	+	0.398819i
$732$	8.21389	+	5.96774i	0.303594	+	0.220574i
$733$	−7.71320	+	23.7388i	−0.284894	+	0.876812i	0.701537	+	0.712633i	$0.252498\pi$
$733$	−7.71320	+	23.7388i	−0.284894	+	0.876812i	−0.986431	+	0.164179i	$0.947502\pi$
$734$	−0.845498	−	2.60218i	−0.0312079	−	0.0960480i
$735$		0			0
$736$	−14.3895			−0.530404
$737$	11.9052	+	16.5502i	0.438534	+	0.609635i
$738$	14.2415			0.524237
$739$	−17.1789	+	12.4812i	−0.631934	+	0.459127i	−0.857070	−	0.515200i	$-0.827718\pi$
$739$	−17.1789	+	12.4812i	−0.631934	+	0.459127i	0.225135	+	0.974327i	$0.427718\pi$
$740$		0			0
$741$	22.9800	−	70.7251i	0.844190	−	2.59815i
$742$	7.29234	+	5.29820i	0.267710	+	0.194503i
$743$	−24.7986	−	18.0172i	−0.909772	−	0.660988i	0.0311852	−	0.999514i	$-0.490072\pi$
$743$	−24.7986	−	18.0172i	−0.909772	−	0.660988i	−0.940957	+	0.338526i	$0.890072\pi$
$744$	8.16862	−	25.1404i	0.299476	−	0.921693i
$745$		0			0
$746$	−5.57387	+	4.04965i	−0.204074	+	0.148268i
$747$	−7.89694			−0.288934
$748$	−10.9963	−	3.63051i	−0.402064	−	0.132744i
$749$	−4.79259			−0.175118
$750$		0			0
$751$	−9.36548	−	28.8240i	−0.341751	−	1.05180i	−0.963300	−	0.268427i	$-0.913496\pi$
$751$	−9.36548	−	28.8240i	−0.341751	−	1.05180i	0.621549	−	0.783375i	$-0.286504\pi$
$752$	−1.86223	+	5.73134i	−0.0679084	+	0.209001i
$753$	−39.1939	−	28.4760i	−1.42831	−	1.03772i
$754$	−12.2554	−	8.90404i	−0.446314	−	0.324266i
$755$		0			0
$756$	2.48509	+	7.64833i	0.0903820	+	0.278167i
$757$	−28.2099	+	20.4957i	−1.02531	+	0.744929i	−0.967364	−	0.253391i	$-0.918454\pi$
$757$	−28.2099	+	20.4957i	−1.02531	+	0.744929i	−0.0579427	+	0.998320i	$0.518454\pi$
$758$	−7.23750			−0.262878
$759$	13.5483	−	18.4633i	0.491772	−	0.670176i
$760$		0			0
$761$	2.17603	−	1.58098i	0.0788809	−	0.0573104i	−0.547646	−	0.836710i	$-0.684476\pi$
$761$	2.17603	−	1.58098i	0.0788809	−	0.0573104i	0.626527	+	0.779400i	$0.284476\pi$
$762$	7.63282	+	23.4914i	0.276508	+	0.851004i
$763$	1.69819	−	5.22650i	0.0614787	−	0.189212i
$764$	−5.26842	−	3.82773i	−0.190605	−	0.138482i
$765$		0			0
$766$	4.11365	−	12.6605i	0.148632	−	0.457443i
$767$	−3.14015	−	9.66440i	−0.113384	−	0.348961i
$768$	27.1431	−	19.7206i	0.979441	−	0.711605i
$769$	−32.5735			−1.17463			−0.587315	−	0.809359i	$-0.699815\pi$
$769$	−32.5735			−1.17463			−0.587315	+	0.809359i	$0.699815\pi$
$770$		0			0
$771$	−52.0010			−1.87277
$772$	26.6969	−	19.3964i	0.960841	−	0.698092i
$773$	−12.8748	−	39.6246i	−0.463074	−	1.42520i	−0.861388	−	0.507947i	$-0.830405\pi$
$773$	−12.8748	−	39.6246i	−0.463074	−	1.42520i	0.398314	−	0.917249i	$-0.369595\pi$
$774$	8.55230	−	26.3213i	0.307406	−	0.946099i
$775$		0			0
$776$	−5.03787	−	3.66022i	−0.180849	−	0.131394i
$777$	5.33938	−	16.4329i	0.191549	−	0.589528i
$778$	7.10990	+	21.8820i	0.254902	+	0.784509i
$779$	24.4213	−	17.7431i	0.874984	−	0.635713i
$780$		0			0
$781$	0.0317431	−	6.70994i	0.00113586	−	0.240101i
$782$	4.34451			0.155359
$783$	25.7990	−	18.7441i	0.921983	−	0.669860i
$784$	−1.89197	−	5.82288i	−0.0675703	−	0.207960i
$785$		0			0
$786$	18.7707	+	13.6377i	0.669530	+	0.486442i
$787$	−29.0605	−	21.1137i	−1.03589	−	0.752622i	−0.0664148	−	0.997792i	$-0.521156\pi$
$787$	−29.0605	−	21.1137i	−1.03589	−	0.752622i	−0.969480	+	0.245170i	$0.921156\pi$
$788$	−5.04239	+	15.5189i	−0.179628	+	0.552838i
$789$	−3.20712	−	9.87049i	−0.114176	−	0.351399i
$790$		0			0
$791$	0.314468			0.0111812
$792$	−0.196179	+	41.4690i	−0.00697093	+	1.47354i
$793$	−8.55476			−0.303789
$794$	−6.33833	+	4.60507i	−0.224939	+	0.163428i
$795$		0			0
$796$	3.51808	−	10.8275i	0.124695	−	0.383771i
$797$	−25.6618	−	18.6444i	−0.908987	−	0.660418i	0.0317713	−	0.999495i	$-0.489885\pi$
$797$	−25.6618	−	18.6444i	−0.908987	−	0.660418i	−0.940759	+	0.339077i	$0.889885\pi$
$798$	−13.2708	−	9.64178i	−0.469780	−	0.341315i
$799$	4.33014	−	13.3268i	0.153189	−	0.471468i
$800$		0			0
$801$	−32.3845	+	23.5287i	−1.14425	+	0.831347i
$802$	−20.3352			−0.718061
$803$	2.60900	−	0.834092i	0.0920698	−	0.0294345i
$804$	−25.1617			−0.887384
$805$		0			0
$806$	2.89957	+	8.92396i	0.102133	+	0.314333i
$807$	−8.64050	+	26.5927i	−0.304160	+	0.936108i
$808$	−15.5166	−	11.2734i	−0.545870	−	0.396598i
$809$	6.88936	+	5.00541i	0.242217	+	0.175981i	0.702270	−	0.711910i	$-0.252170\pi$
$809$	6.88936	+	5.00541i	0.242217	+	0.175981i	−0.460053	+	0.887891i	$0.652170\pi$
$810$		0			0
$811$	2.79052	+	8.58832i	0.0979882	+	0.301577i	0.988021	−	0.154320i	$-0.0493186\pi$
$811$	2.79052	+	8.58832i	0.0979882	+	0.301577i	−0.890033	+	0.455897i	$0.849319\pi$
$812$	7.23329	−	5.25529i	0.253839	−	0.184425i
$813$	3.52472			0.123617
$814$	8.62415	−	11.7528i	0.302276	−	0.411935i
$815$		0			0
$816$	5.62616	−	4.08764i	0.196955	−	0.143096i
$817$	−18.1275	−	55.7908i	−0.634202	−	1.95187i
$818$	3.27513	−	10.0798i	0.114512	−	0.352432i
$819$	−14.1155	−	10.2555i	−0.493235	−	0.358356i
$820$		0			0
$821$	−16.7866	+	51.6638i	−0.585856	+	1.80308i	0.00994979	+	0.999950i	$0.496833\pi$
$821$	−16.7866	+	51.6638i	−0.585856	+	1.80308i	−0.595806	+	0.803129i	$0.703167\pi$
$822$	2.74375	+	8.44439i	0.0956993	+	0.294532i
$823$	14.4486	−	10.4975i	0.503646	−	0.365920i	−0.306762	−	0.951786i	$-0.599245\pi$
$823$	14.4486	−	10.4975i	0.503646	−	0.365920i	0.810408	+	0.585866i	$0.199245\pi$
$824$	−24.1723			−0.842083
$825$		0			0
$826$	−2.24151			−0.0779920
$827$	−42.0280	+	30.5351i	−1.46146	+	1.06181i	−0.478474	+	0.878102i	$0.658810\pi$
$827$	−42.0280	+	30.5351i	−1.46146	+	1.06181i	−0.982981	+	0.183708i	$0.941190\pi$
$828$	5.41934	+	16.6790i	0.188335	+	0.579636i
$829$	−6.10185	+	18.7796i	−0.211926	+	0.652241i	0.787431	+	0.616402i	$0.211410\pi$
$829$	−6.10185	+	18.7796i	−0.211926	+	0.652241i	−0.999358	+	0.0358392i	$0.988590\pi$
$830$		0			0
$831$	−18.4091	−	13.3750i	−0.638603	−	0.463972i
$832$	−2.40786	+	7.41064i	−0.0834776	+	0.256918i
$833$	4.39930	+	13.5396i	0.152427	+	0.469121i
$834$	9.98849	−	7.25707i	0.345873	−	0.251292i
$835$		0			0
$836$	21.6236	+	30.0604i	0.747869	+	1.03966i
$837$	−19.7528			−0.682757
$838$	18.7806	−	13.6449i	0.648763	−	0.471354i
$839$	−1.27207	−	3.91502i	−0.0439166	−	0.135162i	0.926694	−	0.375817i	$-0.122638\pi$
$839$	−1.27207	−	3.91502i	−0.0439166	−	0.135162i	−0.970611	+	0.240655i	$0.922638\pi$
$840$		0			0
$841$	−5.22128	−	3.79348i	−0.180044	−	0.130810i
$842$	−15.8567	−	11.5206i	−0.546458	−	0.397025i
$843$	22.0422	−	67.8389i	0.759173	−	2.33649i
$844$	10.2427	+	31.5239i	0.352569	+	1.08510i
$845$		0			0
$846$	−21.1400			−0.726807
$847$	−9.11494	−	6.75507i	−0.313193	−	0.232107i
$848$	12.2198			0.419630
$849$	−46.4983	+	33.7830i	−1.59582	+	1.15943i
$850$		0			0
$851$	4.52203	−	13.9174i	0.155013	−	0.477081i
$852$	6.69978	+	4.86767i	0.229531	+	0.166764i
$853$	4.45190	+	3.23449i	0.152430	+	0.110747i	0.661386	−	0.750046i	$-0.269968\pi$
$853$	4.45190	+	3.23449i	0.152430	+	0.110747i	−0.508956	+	0.860792i	$0.669968\pi$
$854$	−0.583125	+	1.79468i	−0.0199541	+	0.0614125i
$855$		0			0
$856$	9.58327	−	6.96265i	0.327549	−	0.237979i
$857$	26.9281			0.919847			0.459924	−	0.887959i	$-0.347877\pi$
$857$	26.9281			0.919847			0.459924	+	0.887959i	$0.347877\pi$
$858$	−13.8534	−	19.2585i	−0.472948	−	0.657476i
$859$	19.1519			0.653456			0.326728	−	0.945118i	$-0.394054\pi$
$859$	19.1519			0.653456			0.326728	+	0.945118i	$0.394054\pi$
$860$		0			0
$861$	−3.52721	−	10.8556i	−0.120207	−	0.369960i
$862$	−0.881845	+	2.71404i	−0.0300358	+	0.0924405i
$863$	4.01394	+	2.91630i	0.136636	+	0.0992720i	0.654004	−	0.756491i	$-0.273088\pi$
$863$	4.01394	+	2.91630i	0.136636	+	0.0992720i	−0.517368	+	0.855763i	$0.673088\pi$
$864$	−25.3869	−	18.4447i	−0.863679	−	0.627500i
$865$		0			0
$866$	−9.14937	−	28.1589i	−0.310908	−	0.956877i
$867$	25.5860	−	18.5893i	0.868946	−	0.631326i
$868$	−5.53810			−0.187975
$869$	38.0392	+	12.5589i	1.29039	+	0.426033i
$870$		0			0
$871$	17.1520	−	12.4616i	0.581172	−	0.422246i
$872$	4.19732	+	12.9180i	0.142139	+	0.437460i
$873$	−3.70250	+	11.3951i	−0.125311	+	0.385667i
$874$	−11.2393	−	8.16581i	−0.380174	−	0.276213i
$875$		0			0
$876$	−1.04464	+	3.21508i	−0.0352952	+	0.108627i
$877$	8.40691	+	25.8738i	0.283881	+	0.873696i	0.986732	+	0.162359i	$0.0519102\pi$
$877$	8.40691	+	25.8738i	0.283881	+	0.873696i	−0.702851	+	0.711338i	$0.748090\pi$
$878$	−0.610706	+	0.443704i	−0.0206103	+	0.0149743i
$879$	−7.16686			−0.241732
$880$		0			0
$881$	10.3570			0.348935			0.174467	−	0.984663i	$-0.444180\pi$
$881$	10.3570			0.348935			0.174467	+	0.984663i	$0.444180\pi$
$882$	17.3757	−	12.6242i	0.585071	−	0.425079i
$883$	−2.28515	−	7.03296i	−0.0769014	−	0.236678i	0.905215	−	0.424954i	$-0.139710\pi$
$883$	−2.28515	−	7.03296i	−0.0769014	−	0.236678i	−0.982116	+	0.188276i	$0.939710\pi$
$884$	−3.72126	+	11.4529i	−0.125159	+	0.385201i
$885$		0			0
$886$	−9.59168	−	6.96877i	−0.322239	−	0.234120i
$887$	5.58054	−	17.1752i	0.187376	−	0.576685i	−0.812605	−	0.582815i	$-0.801951\pi$
$887$	5.58054	−	17.1752i	0.187376	−	0.576685i	0.999981	+	0.00612989i	$0.00195122\pi$
$888$	13.1970	+	40.6163i	0.442864	+	1.36299i
$889$	9.93772	−	7.22018i	0.333300	−	0.242157i
$890$		0			0
$891$	1.08414	−	0.346596i	0.0363200	−	0.0116114i
$892$	−23.3563			−0.782027
$893$	−36.2507	+	26.3377i	−1.21309	+	0.881358i
$894$	−2.42536	−	7.46450i	−0.0811163	−	0.249650i
$895$		0			0
$896$	−8.38734	−	6.09376i	−0.280201	−	0.203578i
$897$	−19.2666	−	13.9980i	−0.643293	−	0.467380i
$898$	8.16997	−	25.1446i	0.272635	−	0.839085i
$899$	6.78623	+	20.8859i	0.226334	+	0.696583i
$900$		0			0
$901$	−28.4141			−0.946612
$902$	0.0455564	−	9.62985i	0.00151686	−	0.320639i
$903$	−22.1817			−0.738160
$904$	−0.628811	+	0.456858i	−0.0209139	+	0.0151949i
$905$		0			0
$906$	−15.6096	+	48.0414i	−0.518594	+	1.59607i
$907$	21.2748	+	15.4570i	0.706417	+	0.513242i	0.882016	−	0.471220i	$-0.156186\pi$
$907$	21.2748	+	15.4570i	0.706417	+	0.513242i	−0.175599	+	0.984462i	$0.556186\pi$
$908$	28.4521	+	20.6716i	0.944215	+	0.686013i
$909$	−11.4036	+	35.0968i	−0.378235	+	1.16409i
$910$		0			0
$911$	−23.1774	+	16.8394i	−0.767902	+	0.557913i	−0.901324	−	0.433146i	$-0.857403\pi$
$911$	−23.1774	+	16.8394i	−0.767902	+	0.557913i	0.133422	+	0.991059i	$0.457403\pi$
$912$	−22.2379			−0.736371
$913$	−0.0252611	+	5.33976i	−0.000836020	+	0.176720i
$914$	18.5535			0.613694
$915$		0			0
$916$	6.75483	+	20.7892i	0.223186	+	0.686896i
$917$	3.56560	−	10.9738i	0.117746	−	0.362386i
$918$	7.66487	+	5.56885i	0.252978	+	0.183799i
$919$	−31.4358	−	22.8394i	−1.03697	−	0.753404i	−0.0672794	−	0.997734i	$-0.521432\pi$
$919$	−31.4358	−	22.8394i	−1.03697	−	0.753404i	−0.969692	+	0.244330i	$0.921432\pi$
$920$		0			0
$921$	−7.81306	−	24.0461i	−0.257449	−	0.792347i
$922$	−3.97224	+	2.88600i	−0.130819	+	0.0950455i
$923$	−6.97781			−0.229677
$924$	13.3370	−	4.26381i	0.438756	−	0.140269i
$925$		0			0
$926$	23.1383	−	16.8110i	0.760373	−	0.552443i
$927$	14.3722	+	44.2332i	0.472046	+	1.45281i
$928$	−10.7808	+	33.1799i	−0.353898	+	1.08919i
$929$	−6.00397	−	4.36214i	−0.196984	−	0.143117i	0.484921	−	0.874558i	$-0.338848\pi$
$929$	−6.00397	−	4.36214i	−0.196984	−	0.143117i	−0.681905	+	0.731441i	$0.738848\pi$
$930$		0			0
$931$	14.0677	−	43.2959i	0.461050	−	1.41897i
$932$	5.14046	+	15.8207i	0.168381	+	0.518224i
$933$	45.7722	−	33.2554i	1.49851	−	1.08873i
$934$	−16.6334			−0.544260
$935$		0			0
$936$	43.1245			1.40957
$937$	−12.0834	+	8.77914i	−0.394749	+	0.286802i	−0.767399	−	0.641170i	$-0.778449\pi$
$937$	−12.0834	+	8.77914i	−0.394749	+	0.286802i	0.372650	+	0.927972i	$0.378449\pi$
$938$	−1.44514	−	4.44768i	−0.0471855	−	0.145222i
$939$	−6.17282	+	18.9980i	−0.201442	+	0.619975i
$940$		0			0
$941$	42.3447	+	30.7652i	1.38040	+	1.00292i	0.996843	+	0.0793986i	$0.0253000\pi$
$941$	42.3447	+	30.7652i	1.38040	+	1.00292i	0.383554	+	0.923518i	$0.374700\pi$
$942$	−4.63488	+	14.2647i	−0.151013	+	0.464769i
$943$	−2.98727	−	9.19386i	−0.0972788	−	0.299393i
$944$	−2.45840	+	1.78613i	−0.0800142	+	0.0581337i
$945$		0			0
$946$	−17.7706	−	5.86711i	−0.577773	−	0.190756i
$947$	3.69553			0.120088			0.0600442	−	0.998196i	$-0.480876\pi$
$947$	3.69553			0.120088			0.0600442	+	0.998196i	$0.480876\pi$
$948$	−39.9976	+	29.0600i	−1.29906	+	0.943825i
$949$	−0.880206	−	2.70899i	−0.0285727	−	0.0879377i
$950$		0			0
$951$	5.21618	+	3.78978i	0.169146	+	0.122892i
$952$	5.10116	+	3.70621i	0.165329	+	0.120119i
$953$	−13.3349	+	41.0406i	−0.431959	+	1.32943i	0.464211	+	0.885724i	$0.346338\pi$
$953$	−13.3349	+	41.0406i	−0.431959	+	1.32943i	−0.896171	+	0.443709i	$0.853662\pi$
$954$	13.2465	+	40.7685i	0.428871	+	1.31993i
$955$		0			0
$956$	−39.9011			−1.29049
$957$	−32.4229	−	45.0732i	−1.04808	−	1.45701i
$958$	−1.20373			−0.0388907
$959$	3.57229	−	2.59542i	0.115355	−	0.0838104i
$960$		0			0
$961$	−5.37602	+	16.5457i	−0.173420	+	0.533732i
$962$	−12.2641	−	8.91041i	−0.395411	−	0.287283i
$963$	−18.4390	−	13.3967i	−0.594189	−	0.431704i
$964$	−4.92126	+	15.1461i	−0.158503	+	0.487822i
$965$		0			0
$966$	−4.24988	+	3.08772i	−0.136738	+	0.0993457i
$967$	29.2144			0.939471			0.469736	−	0.882807i	$-0.344349\pi$
$967$	29.2144			0.939471			0.469736	+	0.882807i	$0.344349\pi$
$968$	28.0400	+	0.265306i	0.901238	+	0.00852725i
$969$	51.7087			1.66112
$970$		0			0
$971$	−8.15948	−	25.1123i	−0.261850	−	0.805892i	−0.992402	−	0.123035i	$-0.960737\pi$
$971$	−8.15948	−	25.1123i	−0.261850	−	0.805892i	0.730552	−	0.682857i	$-0.239263\pi$
$972$	6.79437	−	20.9109i	0.217929	−	0.670718i
$973$	−4.96737	−	3.60901i	−0.159247	−	0.115699i
$974$	0.626780	+	0.455382i	0.0200833	+	0.0145914i
$975$		0			0
$976$	0.790528	+	2.43300i	0.0253042	+	0.0778783i
$977$	−12.8176	+	9.31251i	−0.410070	+	0.297934i	−0.773630	−	0.633637i	$-0.781561\pi$
$977$	−12.8176	+	9.31251i	−0.410070	+	0.297934i	0.363560	+	0.931571i	$0.381561\pi$
$978$	−38.7598			−1.23940
$979$	15.8061	+	21.9731i	0.505166	+	0.702263i
$980$		0			0
$981$	21.1432	−	15.3615i	0.675051	−	0.490454i
$982$	−3.17163	−	9.76126i	−0.101211	−	0.311494i
$983$	−10.8477	+	33.3858i	−0.345988	+	1.06484i	0.615064	+	0.788477i	$0.289130\pi$
$983$	−10.8477	+	33.3858i	−0.345988	+	1.06484i	−0.961053	+	0.276365i	$0.910870\pi$
$984$	22.8240	+	16.5826i	0.727604	+	0.528635i
$985$		0			0
$986$	3.25497	−	10.0178i	0.103659	−	0.319031i
$987$	5.23576	+	16.1140i	0.166656	+	0.512915i
$988$	31.1534	−	22.6342i	0.991120	−	0.720091i
$989$	−18.7861			−0.597363
$990$		0			0
$991$	18.9700			0.602600			0.301300	−	0.953529i	$-0.402579\pi$
$991$	18.9700			0.602600			0.301300	+	0.953529i	$0.402579\pi$
$992$	17.4828	−	12.7020i	0.555078	−	0.403288i
$993$	13.3756	+	41.1658i	0.424461	+	1.30636i
$994$	−0.475634	+	1.46385i	−0.0150862	+	0.0464306i
$995$		0			0
$996$	−5.33167	−	3.87369i	−0.168940	−	0.122742i
$997$	−9.31213	+	28.6598i	−0.294918	+	0.907665i	0.688331	+	0.725397i	$0.258344\pi$
$997$	−9.31213	+	28.6598i	−0.294918	+	0.907665i	−0.983249	+	0.182268i	$0.941656\pi$
$998$	3.95876	+	12.1838i	0.125312	+	0.385672i
$999$	25.8175	−	18.7575i	0.816830	−	0.593462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.h.a.201.1		8
5.2	odd	4		275.2.z.a.124.2		16
5.3	odd	4		275.2.z.a.124.3		16
5.4	even	2		55.2.g.b.36.2	yes	8
11.2	odd	10		3025.2.a.w.1.2		4
11.4	even	5	inner	275.2.h.a.26.1		8
11.9	even	5		3025.2.a.bd.1.3		4
15.14	odd	2		495.2.n.e.91.1		8
20.19	odd	2		880.2.bo.h.641.2		8
55.4	even	10		55.2.g.b.26.2	✓	8
55.9	even	10		605.2.a.j.1.2		4
55.14	even	10		605.2.g.m.511.1		8
55.19	odd	10		605.2.g.e.511.2		8
55.24	odd	10		605.2.a.k.1.3		4
55.29	odd	10		605.2.g.k.81.1		8
55.37	odd	20		275.2.z.a.224.3		16
55.39	odd	10		605.2.g.e.251.2		8
55.48	odd	20		275.2.z.a.224.2		16
55.49	even	10		605.2.g.m.251.1		8
55.54	odd	2		605.2.g.k.366.1		8
165.59	odd	10		495.2.n.e.136.1		8
165.119	odd	10		5445.2.a.bp.1.3		4
165.134	even	10		5445.2.a.bi.1.2		4
220.59	odd	10		880.2.bo.h.81.2		8
220.79	even	10		9680.2.a.cm.1.4		4
220.119	odd	10		9680.2.a.cn.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.26.2	✓	8	55.4	even	10
55.2.g.b.36.2	yes	8	5.4	even	2
275.2.h.a.26.1		8	11.4	even	5	inner
275.2.h.a.201.1		8	1.1	even	1	trivial
275.2.z.a.124.2		16	5.2	odd	4
275.2.z.a.124.3		16	5.3	odd	4
275.2.z.a.224.2		16	55.48	odd	20
275.2.z.a.224.3		16	55.37	odd	20
495.2.n.e.91.1		8	15.14	odd	2
495.2.n.e.136.1		8	165.59	odd	10
605.2.a.j.1.2		4	55.9	even	10
605.2.a.k.1.3		4	55.24	odd	10
605.2.g.e.251.2		8	55.39	odd	10
605.2.g.e.511.2		8	55.19	odd	10
605.2.g.k.81.1		8	55.29	odd	10
605.2.g.k.366.1		8	55.54	odd	2
605.2.g.m.251.1		8	55.49	even	10
605.2.g.m.511.1		8	55.14	even	10
880.2.bo.h.81.2		8	220.59	odd	10
880.2.bo.h.641.2		8	20.19	odd	2
3025.2.a.w.1.2		4	11.2	odd	10
3025.2.a.bd.1.3		4	11.9	even	5
5445.2.a.bi.1.2		4	165.134	even	10
5445.2.a.bp.1.3		4	165.119	odd	10
9680.2.a.cm.1.4		4	220.79	even	10
9680.2.a.cn.1.4		4	220.119	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.596764 + 0.433574i) q^{2} +(0.868820 + 2.67395i) q^{3} +(-0.449894 + 1.38463i) q^{4} +(-1.67784 - 1.21902i) q^{6} +(-0.318714 + 0.980901i) q^{7} +(-0.787747 - 2.42443i) q^{8} +(-3.96813 + 2.88301i) q^{9} +(1.93675 + 2.69240i) q^{11} -4.09331 q^{12} +(2.79029 - 2.02726i) q^{13} +(-0.235096 - 0.723552i) q^{14} +(-0.834404 - 0.606230i) q^{16} +(1.94020 + 1.40964i) q^{17} +(1.11803 - 3.44095i) q^{18} +(-2.36979 - 7.29347i) q^{19} -2.89979 q^{21} +(-2.32313 - 0.767001i) q^{22} -2.45589 q^{23} +(5.79842 - 4.21280i) q^{24} +(-0.786174 + 2.41960i) q^{26} +(-4.33283 - 3.14799i) q^{27} +(-1.21480 - 0.882602i) q^{28} +(-1.83998 + 5.66289i) q^{29} +(2.98382 - 2.16787i) q^{31} +5.85919 q^{32} +(-5.51666 + 7.51798i) q^{33} -1.76902 q^{34} +(-2.20667 - 6.79144i) q^{36} +(-1.84130 + 5.66694i) q^{37} +(4.57646 + 3.32500i) q^{38} +(7.84507 + 5.69978i) q^{39} +(1.21637 + 3.74360i) q^{41} +(1.73049 - 1.25727i) q^{42} +7.64941 q^{43} +(-4.59931 + 1.47039i) q^{44} +(1.46558 - 1.06481i) q^{46} +(-1.80557 - 5.55697i) q^{47} +(0.896084 - 2.75786i) q^{48} +(4.80253 + 3.48924i) q^{49} +(-2.08362 + 6.41272i) q^{51} +(1.55168 + 4.77558i) q^{52} +(-9.58526 + 6.96410i) q^{53} +3.95056 q^{54} +2.62920 q^{56} +(17.4435 - 12.6734i) q^{57} +(-1.35725 - 4.17718i) q^{58} +(0.910456 - 2.80210i) q^{59} +(-2.00666 - 1.45792i) q^{61} +(-0.840701 + 2.58741i) q^{62} +(-1.56325 - 4.81120i) q^{63} +(-1.82774 + 1.32793i) q^{64} +(0.0325397 - 6.87834i) q^{66} +6.14702 q^{67} +(-2.82471 + 2.05227i) q^{68} +(-2.13372 - 6.56693i) q^{69} +(-1.63676 - 1.18918i) q^{71} +(10.1156 + 7.34938i) q^{72} +(0.255207 - 0.785446i) q^{73} +(-1.35822 - 4.18017i) q^{74} +11.1649 q^{76} +(-3.25824 + 1.04165i) q^{77} -7.15293 q^{78} +(9.77146 - 7.09938i) q^{79} +(0.106048 - 0.326382i) q^{81} +(-2.34901 - 1.70666i) q^{82} +(1.30253 + 0.946345i) q^{83} +(1.30460 - 4.01513i) q^{84} +(-4.56489 + 3.31659i) q^{86} -16.7409 q^{87} +(5.00188 - 6.81645i) q^{88} +8.16116 q^{89} +(1.09924 + 3.38312i) q^{91} +(1.10489 - 3.40050i) q^{92} +(8.38919 + 6.09510i) q^{93} +(3.48685 + 2.53335i) q^{94} +(5.09058 + 15.6672i) q^{96} +(1.97625 - 1.43583i) q^{97} -4.37882 q^{98} +(-15.4475 - 5.10011i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9} + 3 q^{11} - 16 q^{12} + 2 q^{13} - 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} - 20 q^{21} + 7 q^{22} - 10 q^{23} + 13 q^{24} + 10 q^{26}+ \cdots - 20 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9 + 3 * q^11 - 16 * q^12 + 2 * q^13 - 16 * q^14 + 4 * q^16 + 13 * q^17 + 15 * q^19 - 20 * q^21 + 7 * q^22 - 10 * q^23 + 13 * q^24 + 10 * q^26 - 10 * q^27 + 6 * q^28 - 9 * q^29 - 10 * q^31 - 16 * q^32 - 5 * q^33 + 4 * q^34 - 15 * q^36 - 24 * q^37 + 21 * q^39 + 8 * q^41 - 9 * q^42 + 38 * q^43 - 12 * q^44 + 3 * q^46 - 5 * q^48 + q^49 + q^51 + 28 * q^52 - 13 * q^53 + 16 * q^54 + 22 * q^56 + 45 * q^57 - 12 * q^58 - 27 * q^59 + 6 * q^61 + 30 * q^62 - 25 * q^63 - 26 * q^64 + 13 * q^66 + 38 * q^67 - 11 * q^68 - q^69 - 20 * q^71 + 30 * q^72 - 13 * q^73 + 20 * q^74 - 34 * q^77 + 16 * q^78 + 37 * q^79 + 8 * q^81 - 28 * q^82 - 27 * q^83 + 28 * q^84 - 3 * q^86 - 38 * q^87 + 36 * q^88 - 16 * q^89 + 44 * q^91 - 11 * q^92 + 35 * q^93 + 17 * q^94 - 17 * q^96 - 24 * q^97 - 16 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more