LMFDB - Embedded newform 275.2.h.a.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(26,275)]

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

lf = mfeigenbasis(mf)

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")

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

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

Self dual:	no
Analytic conductor:	$2.19588605559$
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			26.1
Root			$-0.227943 + 0.701538i$ of defining polynomial
Character	$\chi$	$=$	275.26
Dual form			275.2.h.a.201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.596764 - 0.433574i) q^{2} +(0.868820 - 2.67395i) q^{3} +(-0.449894 - 1.38463i) q^{4} +(-1.67784 + 1.21902i) q^{6} +(-0.318714 - 0.980901i) q^{7} +(-0.787747 + 2.42443i) q^{8} +(-3.96813 - 2.88301i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 8 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.356457	−	0.934312i	$-0.383985\pi$
$2$	−0.596764	−	0.433574i	−0.421976	−	0.306583i	−0.778432	+	0.627729i	$0.783985\pi$
$3$	0.868820	−	2.67395i	0.501614	−	1.54381i	−0.304777	−	0.952424i	$-0.598582\pi$
$3$	0.868820	−	2.67395i	0.501614	−	1.54381i	0.806390	−	0.591384i	$-0.201418\pi$
$4$	−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	0.872585	−	0.488463i	$-0.162442\pi$
$7$	−0.318714	−	0.980901i	−0.120463	−	0.370746i	−0.993047	+	0.117717i	$0.962442\pi$
$8$	−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	0.903138	−	0.429350i	$-0.141257\pi$
$13$	2.79029	+	2.02726i	0.773887	+	0.562262i	−0.129251	+	0.991612i	$0.541257\pi$
$14$	−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	−0.327095	−	0.944991i	$-0.606070\pi$
$17$	1.94020	−	1.40964i	0.470567	−	0.341887i	0.797662	+	0.603105i	$0.206070\pi$
$18$	1.11803	+	3.44095i	0.263523	+	0.811041i
$19$	−2.36979	+	7.29347i	−0.543668	+	1.67324i	0.180470	+	0.983581i	$0.442238\pi$
$19$	−2.36979	+	7.29347i	−0.543668	+	1.67324i	−0.724137	+	0.689656i	$0.757762\pi$
$20$		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	−0.963339	−	0.268287i	$-0.913542\pi$
$29$	−1.83998	−	5.66289i	−0.341677	−	1.05157i	0.621663	−	0.783285i	$-0.286458\pi$
$30$		0			0
$31$	2.98382	+	2.16787i	0.535909	+	0.389361i	0.822564	−	0.568673i	$-0.192543\pi$
$31$	2.98382	+	2.16787i	0.535909	+	0.389361i	−0.286654	+	0.958034i	$0.592543\pi$
$32$	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	−0.980523	−	0.196407i	$-0.937073\pi$
$37$	−1.84130	−	5.66694i	−0.302708	−	0.931640i	0.677814	−	0.735233i	$-0.262927\pi$
$38$	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	−0.810033	−	0.586384i	$-0.800551\pi$
$41$	1.21637	−	3.74360i	0.189965	−	0.584652i	0.999999	+	0.00173135i	$0.000551106\pi$
$42$	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	0.728695	+	0.684838i	$0.240127\pi$
$47$	−1.80557	+	5.55697i	−0.263369	+	0.810567i	−0.992065	+	0.125729i	$0.959873\pi$
$48$	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	−0.999968	−	0.00805607i	$-0.997436\pi$
$53$	−9.58526	−	6.96410i	−1.31664	−	0.956592i	−0.316669	−	0.948536i	$-0.602564\pi$
$54$	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	0.992667	−	0.120880i	$-0.0385715\pi$
$59$	0.910456	+	2.80210i	0.118531	+	0.364802i	−0.874136	+	0.485681i	$0.838572\pi$
$60$		0			0
$61$	−2.00666	+	1.45792i	−0.256927	+	0.186668i	−0.708791	−	0.705419i	$-0.750759\pi$
$61$	−2.00666	+	1.45792i	−0.256927	+	0.186668i	0.451864	+	0.892087i	$0.350759\pi$
$62$	−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	−0.680658	−	0.732601i	$-0.738306\pi$
$71$	−1.63676	+	1.18918i	−0.194248	+	0.141129i	0.486410	+	0.873731i	$0.338306\pi$
$72$	10.1156	−	7.34938i	1.19213	−	0.866133i
$73$	0.255207	+	0.785446i	0.0298697	+	0.0919295i	0.964880	−	0.262691i	$-0.0846100\pi$
$73$	0.255207	+	0.785446i	0.0298697	+	0.0919295i	−0.935010	+	0.354621i	$0.884610\pi$
$74$	−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	0.980958	−	0.194221i	$-0.0622180\pi$
$79$	9.77146	+	7.09938i	1.09937	+	0.798742i	0.118417	+	0.992964i	$0.462218\pi$
$80$		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	−0.514000	−	0.857790i	$-0.671837\pi$
$83$	1.30253	−	0.946345i	0.142971	−	0.103875i	0.656972	+	0.753915i	$0.271837\pi$
$84$	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	0.683577	−	0.729879i	$-0.260423\pi$
$97$	1.97625	+	1.43583i	0.200658	+	0.145787i	−0.482919	+	0.875665i	$0.660423\pi$
$98$	−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	0.847884	−	0.530182i	$-0.177876\pi$
$101$	6.08683	+	4.42234i	0.605662	+	0.440039i	−0.242222	+	0.970221i	$0.577876\pi$
$102$	−1.53696	+	4.73028i	−0.152182	+	0.468367i
$103$	2.93020	+	9.01821i	0.288721	+	0.888591i	0.985259	+	0.171071i	$0.0547228\pi$
$103$	2.93020	+	9.01821i	0.288721	+	0.888591i	−0.696538	+	0.717520i	$0.745277\pi$
$104$	−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	−0.857347	−	0.514739i	$-0.827889\pi$
$107$	1.43593	−	4.41935i	0.138817	−	0.427235i	0.996164	+	0.0875039i	$0.0278890\pi$
$108$	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	−0.955390	−	0.295346i	$-0.904565\pi$
$113$	−0.0942195	+	0.289978i	−0.00886342	+	0.0272788i	0.946527	+	0.322625i	$0.104565\pi$
$114$	−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	−0.926520	−	0.376245i	$-0.877215\pi$
$127$	−9.63536	+	7.00050i	−0.855000	+	0.621194i	0.0715199	+	0.997439i	$0.477215\pi$
$128$	−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	−0.725829	−	0.687875i	$-0.758544\pi$
$137$	−3.46360	+	2.51645i	−0.295915	+	0.214995i	0.429914	+	0.902870i	$0.358544\pi$
$138$	4.12058	−	2.99378i	0.350767	−	0.254847i
$139$	−1.83964	−	5.66183i	−0.156036	−	0.480230i	0.842228	−	0.539121i	$-0.181243\pi$
$139$	−1.83964	−	5.66183i	−0.156036	−	0.480230i	−0.998264	+	0.0588913i	$0.981243\pi$
$140$		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	−0.455269	−	0.890354i	$-0.650457\pi$
$149$	3.06168	−	2.22444i	0.250823	−	0.182233i	0.706091	+	0.708121i	$0.250457\pi$
$150$		0			0
$151$	−7.52661	+	23.1645i	−0.612507	+	1.88510i	−0.179348	+	0.983786i	$0.557399\pi$
$151$	−7.52661	+	23.1645i	−0.612507	+	1.88510i	−0.433159	+	0.901317i	$0.642601\pi$
$152$	−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	−0.999771	−	0.0214015i	$-0.993187\pi$
$157$	−2.23484	+	6.87813i	−0.178360	+	0.548935i	0.821411	+	0.570336i	$0.193187\pi$
$158$	−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	0.992648	−	0.121039i	$-0.0386226\pi$
$163$	15.1198	+	10.9852i	1.18428	+	0.860428i	0.191630	+	0.981467i	$0.438623\pi$
$164$	−5.73074			−0.447496
$165$		0			0
$166$	−1.18761			−0.0921767
$167$	6.35343	+	4.61604i	0.491644	+	0.357200i	0.805816	−	0.592166i	$-0.201727\pi$
$167$	6.35343	+	4.61604i	0.491644	+	0.357200i	−0.314172	+	0.949366i	$0.601727\pi$
$168$	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	0.728848	+	0.684675i	$0.240056\pi$
$173$	−3.46244	+	10.6563i	−0.263244	+	0.810183i	−0.992093	+	0.125508i	$0.959944\pi$
$174$	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	−0.932716	−	0.360611i	$-0.882568\pi$
$179$	0.452595	−	1.39295i	0.0338286	−	0.104114i	0.966545	+	0.256497i	$0.0825684\pi$
$180$		0			0
$181$	−7.51496	+	5.45994i	−0.558583	+	0.405834i	−0.830940	−	0.556362i	$-0.812197\pi$
$181$	−7.51496	+	5.45994i	−0.558583	+	0.405834i	0.272357	+	0.962196i	$0.412197\pi$
$182$	−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	0.888514	−	0.458850i	$-0.151738\pi$
$191$	−1.38222	−	4.25404i	−0.100014	−	0.307811i	−0.988528	+	0.151038i	$0.951738\pi$
$192$	−5.13881	+	3.73357i	−0.370862	+	0.269447i
$193$	−18.3372	+	13.3227i	−1.31994	+	0.958992i	−0.320007	+	0.947415i	$0.603685\pi$
$193$	−18.3372	+	13.3227i	−1.31994	+	0.958992i	−0.999933	+	0.0115772i	$0.996315\pi$
$194$	−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	0.999121	−	0.0419098i	$-0.0133442\pi$
$211$	18.4189	+	13.3821i	1.26801	+	0.921262i	0.268887	+	0.963172i	$0.413344\pi$
$212$	−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	−0.636216	−	0.771511i	$-0.719501\pi$
$223$	4.95746	−	15.2575i	0.331976	−	1.02172i	0.968192	−	0.250207i	$-0.0804985\pi$
$224$	−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	0.816257	+	0.577689i	$0.196045\pi$
$227$	7.46468	+	22.9739i	0.495448	+	1.52483i	−0.320809	+	0.947144i	$0.603955\pi$
$228$	9.70030	−	29.8545i	0.642418	−	1.97716i
$229$	12.1468	+	8.82517i	0.802684	+	0.583184i	0.911700	−	0.410856i	$-0.134770\pi$
$229$	12.1468	+	8.82517i	0.802684	+	0.583184i	−0.109017	+	0.994040i	$0.534770\pi$
$230$		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	0.847855	−	0.530228i	$-0.177894\pi$
$233$	9.24378	+	6.71600i	0.605580	+	0.439980i	−0.242275	+	0.970208i	$0.577894\pi$
$234$	−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	−0.166358	−	0.986065i	$-0.553201\pi$
$239$	8.46914	−	26.0653i	0.547823	−	1.68603i	0.714181	−	0.699961i	$-0.246799\pi$
$240$		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	0.0533238	−	0.998577i	$-0.483018\pi$
$251$	−13.9403	−	10.1282i	−0.879902	−	0.639286i	−0.933225	+	0.359291i	$0.883018\pi$
$252$	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	−0.955125	−	0.296204i	$-0.904279\pi$
$257$	−5.71540	−	17.5902i	−0.356517	−	1.09725i	0.598608	−	0.801042i	$-0.295721\pi$
$258$	−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	−0.314841	−	0.949145i	$-0.601951\pi$
$269$	8.04575	−	5.84558i	0.490558	−	0.356411i	0.805399	+	0.592733i	$0.201951\pi$
$270$		0			0
$271$	0.387400	+	1.19229i	0.0235329	+	0.0724267i	0.962133	−	0.272580i	$-0.0878768\pi$
$271$	0.387400	+	1.19229i	0.0235329	+	0.0724267i	−0.938600	+	0.345006i	$0.887877\pi$
$272$	−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	0.373442	−	0.927654i	$-0.378177\pi$
$277$	−6.54763	−	4.75713i	−0.393409	−	0.285828i	−0.766851	+	0.641825i	$0.778177\pi$
$278$	−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	−0.996459	−	0.0840804i	$-0.973205\pi$
$281$	−20.5250	+	14.9123i	−1.22442	+	0.889591i	−0.227958	+	0.973671i	$0.573205\pi$
$282$	−3.74461	−	11.5247i	−0.222988	−	0.686286i
$283$	6.31705	−	19.4419i	0.375510	−	1.15570i	−0.567624	−	0.823288i	$-0.692137\pi$
$283$	6.31705	−	19.4419i	0.375510	−	1.15570i	0.943134	−	0.332412i	$-0.107863\pi$
$284$	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	0.925407	−	0.378974i	$-0.123723\pi$
$293$	−0.787705	−	2.42431i	−0.0460182	−	0.141630i	−0.971426	+	0.237344i	$0.923723\pi$
$294$	−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	0.604767	+	0.796402i	$0.293266\pi$
$311$	−6.21840	+	19.1383i	−0.352613	+	1.08523i	−0.957380	+	0.288830i	$0.906734\pi$
$312$	7.63881	+	23.5098i	0.432463	+	1.33098i
$313$	5.74792	−	4.17611i	0.324892	−	0.236048i	−0.413368	−	0.910564i	$-0.635648\pi$
$313$	5.74792	−	4.17611i	0.324892	−	0.236048i	0.738260	+	0.674516i	$0.235648\pi$
$314$	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	0.638666	−	0.769484i	$-0.279487\pi$
$317$	1.85526	+	1.34793i	0.104202	+	0.0757071i	−0.534464	+	0.845191i	$0.679487\pi$
$318$	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	0.969978	+	0.243193i	$0.0781949\pi$
$337$	6.02485	+	18.5426i	0.328195	+	1.01008i	−0.641783	+	0.766886i	$0.721805\pi$
$338$	−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	−0.633889	−	0.773424i	$-0.718543\pi$
$347$	−1.75479	+	1.27493i	−0.0942023	+	0.0684420i	0.539687	+	0.841866i	$0.318543\pi$
$348$	7.53163	+	23.1800i	0.403738	+	1.24258i
$349$	−7.74150	+	23.8259i	−0.414393	+	1.27537i	0.498400	+	0.866947i	$0.333921\pi$
$349$	−7.74150	+	23.8259i	−0.414393	+	1.27537i	−0.912793	+	0.408423i	$0.866079\pi$
$350$		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	0.999043	−	0.0437429i	$-0.0139282\pi$
$359$	3.12799	+	9.62695i	0.165089	+	0.508091i	−0.833954	+	0.551834i	$0.813928\pi$
$360$		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	0.916673	−	0.399638i	$-0.130864\pi$
$367$	−1.14622	−	3.52770i	−0.0598322	−	0.184145i	−0.976505	+	0.215493i	$0.930864\pi$
$368$	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	−0.364947	−	0.931028i	$-0.618913\pi$
$379$	7.93783	−	5.76717i	0.407739	−	0.296240i	0.772686	+	0.634789i	$0.218913\pi$
$380$		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	0.148561	−	0.988903i	$-0.452536\pi$
$383$	−14.6002	−	10.6076i	−0.746034	−	0.542025i	−0.894595	+	0.446878i	$0.852536\pi$
$384$	−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	0.826546	+	0.562869i	$0.190302\pi$
$389$	9.63871	+	29.6649i	0.488702	+	1.50407i	−0.337844	+	0.941202i	$0.609698\pi$
$390$		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	0.130503	−	0.991448i	$-0.458341\pi$
$401$	22.3029	−	16.2040i	1.11375	−	0.809190i	0.983251	+	0.182258i	$0.0583407\pi$
$402$	−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	0.262062	−	0.965051i	$-0.415598\pi$
$409$	−11.6241	−	8.44540i	−0.574774	−	0.417598i	−0.836836	+	0.547453i	$0.815598\pi$
$410$		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	−0.524679	−	0.851300i	$-0.675815\pi$
$421$	8.21095	−	25.2707i	0.400177	−	1.23162i	0.924856	−	0.380318i	$-0.124185\pi$
$422$	−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	0.660608	−	0.750731i	$-0.270299\pi$
$431$	3.12984	+	2.27397i	0.150759	+	0.109533i	−0.509849	+	0.860264i	$0.670299\pi$
$432$	1.70693	−	5.25338i	0.0821246	−	0.252754i
$433$	−12.4036	−	38.1743i	−0.596077	−	1.83454i	−0.549288	−	0.835633i	$-0.685101\pi$
$433$	−12.4036	−	38.1743i	−0.596077	−	1.83454i	−0.0467895	−	0.998905i	$-0.514899\pi$
$434$	−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	−0.761011	−	0.648739i	$-0.775297\pi$
$443$	4.96678	−	15.2862i	0.235979	−	0.726268i	0.996990	−	0.0775295i	$-0.0247032\pi$
$444$	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	−0.997857	−	0.0654379i	$-0.979156\pi$
$449$	−28.9969	−	21.0675i	−1.36845	−	0.994235i	−0.370590	−	0.928797i	$-0.620844\pi$
$450$		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	−0.951250	−	0.308422i	$-0.900199\pi$
$457$	−20.3488	+	14.7842i	−0.951875	+	0.691578i	−0.000625413		1.00000i	$0.500199\pi$
$458$	−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	−0.0793559	−	0.996846i	$-0.525286\pi$
$467$	18.2429	−	13.2542i	0.844179	−	0.613332i	0.923535	+	0.383514i	$0.125286\pi$
$468$	−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	−0.557216	−	0.830368i	$-0.688130\pi$
$479$	1.32021	−	0.959186i	0.0603218	−	0.0438263i	0.617538	+	0.786541i	$0.288130\pi$
$480$		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	−0.958141	−	0.286297i	$-0.907575\pi$
$487$	−0.324560	+	0.998894i	−0.0147072	+	0.0452642i	0.943434	+	0.331562i	$0.107575\pi$
$488$	−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	−0.999986	−	0.00520928i	$-0.998342\pi$
$491$	−4.29969	−	13.2331i	−0.194042	−	0.597201i	0.805944	−	0.591992i	$-0.201658\pi$
$492$	−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	0.996381	+	0.0849943i	$0.0270872\pi$
$499$	5.36679	+	16.5173i	0.240250	+	0.739415i	−0.756131	+	0.654420i	$0.772913\pi$
$500$		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	0.324498	+	0.945887i	$0.394805\pi$
$503$	−11.0794	+	34.0988i	−0.494005	+	1.52039i	−0.818502	+	0.574503i	$0.805195\pi$
$504$	−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	−0.935340	−	0.353750i	$-0.884906\pi$
$509$	0.660921	−	2.03410i	0.0292948	−	0.0901601i	0.964635	+	0.263590i	$0.0849065\pi$
$510$		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	0.827093	−	0.562065i	$-0.189993\pi$
$521$	−3.93540	−	12.1119i	−0.172413	−	0.530633i	−0.999506	+	0.0314326i	$0.989993\pi$
$522$	17.4286	−	12.6626i	0.762828	−	0.554227i
$523$	19.3426	−	14.0532i	0.845793	−	0.614504i	−0.0781901	−	0.996938i	$-0.524914\pi$
$523$	19.3426	−	14.0532i	0.845793	−	0.614504i	0.923983	+	0.382434i	$0.124914\pi$
$524$	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	0.564606	−	0.825360i	$-0.309028\pi$
$541$	−1.06726	−	0.775410i	−0.0458851	−	0.0333375i	−0.610491	+	0.792023i	$0.709028\pi$
$542$	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	−0.993561	−	0.113298i	$-0.963859\pi$
$547$	−2.88044	+	8.86507i	−0.123159	+	0.379043i	0.870403	+	0.492341i	$0.163859\pi$
$548$	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	−0.783648	−	0.621205i	$-0.786644\pi$
$557$	−12.1497	−	37.3929i	−0.514798	−	1.58439i	0.268850	−	0.963182i	$-0.413356\pi$
$558$	−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	0.873779	−	0.486323i	$-0.161662\pi$
$563$	16.1649	+	11.7445i	0.681271	+	0.494972i	−0.192508	+	0.981295i	$0.561662\pi$
$564$	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	0.431637	+	0.902047i	$0.357936\pi$
$569$	−10.6811	+	32.8730i	−0.447775	+	1.37811i	−0.879412	+	0.476061i	$0.842064\pi$
$570$		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	−0.0233590	−	0.999727i	$-0.507436\pi$
$577$	22.1044	−	16.0598i	0.920220	−	0.668579i	0.943579	+	0.331148i	$0.107436\pi$
$578$	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	0.583236	+	0.812303i	$0.301786\pi$
$587$	14.2667	+	43.9082i	0.588848	+	1.81229i	0.00561158	+	0.999984i	$0.498214\pi$
$588$	−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	−0.604984	−	0.796238i	$-0.706820\pi$
$599$	−0.848455	+	0.616438i	−0.0346669	+	0.0251870i	0.570317	+	0.821425i	$0.306820\pi$
$600$		0			0
$601$	8.42065	+	25.9161i	0.343485	+	1.05714i	0.962390	+	0.271673i	$0.0875768\pi$
$601$	8.42065	+	25.9161i	0.343485	+	1.05714i	−0.618904	+	0.785466i	$0.712423\pi$
$602$	−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	0.886334	−	0.463047i	$-0.153244\pi$
$607$	17.7350	+	12.8852i	0.719842	+	0.522996i	−0.166492	+	0.986043i	$0.553244\pi$
$608$	−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	−0.995144	−	0.0984293i	$-0.968618\pi$
$613$	−3.27313	+	10.0736i	−0.132200	+	0.406871i	0.862944	+	0.505300i	$0.168618\pi$
$614$	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	−0.406043	−	0.913854i	$-0.633092\pi$
$619$	11.4348	−	35.1926i	0.459603	−	1.41451i	0.865645	−	0.500657i	$-0.166908\pi$
$620$		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	−0.979459	−	0.201644i	$-0.935372\pi$
$631$	−7.67617	−	23.6248i	−0.305583	−	0.940489i	0.673875	−	0.738845i	$-0.264628\pi$
$632$	−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	0.185096	+	0.982720i	$0.440740\pi$
$641$	−13.7294	+	42.2547i	−0.542278	+	1.66896i	−0.727374	+	0.686241i	$0.759260\pi$
$642$	2.97801	+	9.16538i	0.117533	+	0.361729i
$643$	20.9220	−	15.2007i	0.825082	−	0.599457i	−0.0930818	−	0.995658i	$-0.529672\pi$
$643$	20.9220	−	15.2007i	0.825082	−	0.599457i	0.918164	+	0.396201i	$0.129672\pi$
$644$	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	0.852845	−	0.522163i	$-0.174875\pi$
$647$	15.7649	+	11.4539i	0.619782	+	0.450298i	−0.233063	+	0.972462i	$0.574875\pi$
$648$	−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	0.999813	+	0.0193305i	$0.00615349\pi$
$653$	5.16979	+	15.9110i	0.202310	+	0.622645i	−0.797504	+	0.603314i	$0.793847\pi$
$654$	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	−0.208961	−	0.977924i	$-0.567008\pi$
$673$	−31.2239	−	22.6855i	−1.20359	−	0.874462i	−0.994633	+	0.103462i	$0.967008\pi$
$674$	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	−0.994300	−	0.106619i	$-0.965998\pi$
$677$	−31.2271	+	22.6878i	−1.20016	+	0.871964i	−0.205855	+	0.978582i	$0.565998\pi$
$678$	−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	0.504524	−	0.863398i	$-0.331668\pi$
$691$	−4.22456	−	3.06932i	−0.160710	−	0.116763i	−0.665234	+	0.746635i	$0.731668\pi$
$692$	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	−0.999054	−	0.0434831i	$-0.986155\pi$
$701$	−4.37506	+	13.4650i	−0.165244	+	0.508568i	0.833811	+	0.552051i	$0.186155\pi$
$702$	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	−0.294715	−	0.955585i	$-0.595225\pi$
$709$	13.9267	−	10.1183i	0.523028	−	0.380002i	0.817744	+	0.575583i	$0.195225\pi$
$710$		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	−0.979287	−	0.202478i	$-0.935100\pi$
$719$	−8.20624	−	25.2562i	−0.306041	−	0.941897i	0.673246	−	0.739419i	$-0.264900\pi$
$720$		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	−0.986431	−	0.164179i	$-0.947502\pi$
$733$	−7.71320	−	23.7388i	−0.284894	−	0.876812i	0.701537	−	0.712633i	$-0.252498\pi$
$734$	−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	0.225135	−	0.974327i	$-0.427718\pi$
$739$	−17.1789	−	12.4812i	−0.631934	−	0.459127i	−0.857070	+	0.515200i	$0.827718\pi$
$740$		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	−0.940957	−	0.338526i	$-0.890072\pi$
$743$	−24.7986	+	18.0172i	−0.909772	+	0.660988i	0.0311852	+	0.999514i	$0.490072\pi$
$744$	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	0.621549	+	0.783375i	$0.286504\pi$
$751$	−9.36548	+	28.8240i	−0.341751	+	1.05180i	−0.963300	+	0.268427i	$0.913496\pi$
$752$	−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	−0.0579427	−	0.998320i	$-0.518454\pi$
$757$	−28.2099	−	20.4957i	−1.02531	−	0.744929i	−0.967364	+	0.253391i	$0.918454\pi$
$758$	−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	0.626527	−	0.779400i	$-0.284476\pi$
$761$	2.17603	+	1.58098i	0.0788809	+	0.0573104i	−0.547646	+	0.836710i	$0.684476\pi$
$762$	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	0.398314	+	0.917249i	$0.369595\pi$
$773$	−12.8748	+	39.6246i	−0.463074	+	1.42520i	−0.861388	+	0.507947i	$0.830405\pi$
$774$	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	−0.969480	−	0.245170i	$-0.921156\pi$
$787$	−29.0605	+	21.1137i	−1.03589	+	0.752622i	−0.0664148	+	0.997792i	$0.521156\pi$
$788$	−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	−0.940759	−	0.339077i	$-0.889885\pi$
$797$	−25.6618	+	18.6444i	−0.908987	+	0.660418i	0.0317713	+	0.999495i	$0.489885\pi$
$798$	−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	−0.460053	−	0.887891i	$-0.652170\pi$
$809$	6.88936	−	5.00541i	0.242217	−	0.175981i	0.702270	+	0.711910i	$0.252170\pi$
$810$		0			0
$811$	2.79052	−	8.58832i	0.0979882	−	0.301577i	−0.890033	−	0.455897i	$-0.849319\pi$
$811$	2.79052	−	8.58832i	0.0979882	−	0.301577i	0.988021	+	0.154320i	$0.0493186\pi$
$812$	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	−0.595806	−	0.803129i	$-0.703167\pi$
$821$	−16.7866	−	51.6638i	−0.585856	−	1.80308i	0.00994979	−	0.999950i	$-0.496833\pi$
$822$	2.74375	−	8.44439i	0.0956993	−	0.294532i
$823$	14.4486	+	10.4975i	0.503646	+	0.365920i	0.810408	−	0.585866i	$-0.199245\pi$
$823$	14.4486	+	10.4975i	0.503646	+	0.365920i	−0.306762	+	0.951786i	$0.599245\pi$
$824$	−24.1723			−0.842083
$825$		0			0
$826$	−2.24151			−0.0779920
$827$	−42.0280	−	30.5351i	−1.46146	−	1.06181i	−0.982981	−	0.183708i	$-0.941190\pi$
$827$	−42.0280	−	30.5351i	−1.46146	−	1.06181i	−0.478474	−	0.878102i	$-0.658810\pi$
$828$	5.41934	−	16.6790i	0.188335	−	0.579636i
$829$	−6.10185	−	18.7796i	−0.211926	−	0.652241i	−0.999358	−	0.0358392i	$-0.988590\pi$
$829$	−6.10185	−	18.7796i	−0.211926	−	0.652241i	0.787431	−	0.616402i	$-0.211410\pi$
$830$		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	−0.970611	−	0.240655i	$-0.922638\pi$
$839$	−1.27207	+	3.91502i	−0.0439166	+	0.135162i	0.926694	+	0.375817i	$0.122638\pi$
$840$		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	−0.508956	−	0.860792i	$-0.669968\pi$
$853$	4.45190	−	3.23449i	0.152430	−	0.110747i	0.661386	+	0.750046i	$0.269968\pi$
$854$	−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	−0.517368	−	0.855763i	$-0.673088\pi$
$863$	4.01394	−	2.91630i	0.136636	−	0.0992720i	0.654004	+	0.756491i	$0.273088\pi$
$864$	−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	−0.702851	−	0.711338i	$-0.748090\pi$
$877$	8.40691	−	25.8738i	0.283881	−	0.873696i	0.986732	−	0.162359i	$-0.0519102\pi$
$878$	−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	−0.982116	−	0.188276i	$-0.939710\pi$
$883$	−2.28515	+	7.03296i	−0.0769014	+	0.236678i	0.905215	+	0.424954i	$0.139710\pi$
$884$	−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	0.999981	−	0.00612989i	$-0.00195122\pi$
$887$	5.58054	+	17.1752i	0.187376	+	0.576685i	−0.812605	+	0.582815i	$0.801951\pi$
$888$	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	−0.175599	−	0.984462i	$-0.556186\pi$
$907$	21.2748	−	15.4570i	0.706417	−	0.513242i	0.882016	+	0.471220i	$0.156186\pi$
$908$	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	0.133422	−	0.991059i	$-0.457403\pi$
$911$	−23.1774	−	16.8394i	−0.767902	−	0.557913i	−0.901324	+	0.433146i	$0.857403\pi$
$912$	−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	−0.969692	−	0.244330i	$-0.921432\pi$
$919$	−31.4358	+	22.8394i	−1.03697	+	0.753404i	−0.0672794	+	0.997734i	$0.521432\pi$
$920$		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	−0.681905	−	0.731441i	$-0.738848\pi$
$929$	−6.00397	+	4.36214i	−0.196984	+	0.143117i	0.484921	+	0.874558i	$0.338848\pi$
$930$		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	0.372650	−	0.927972i	$-0.378449\pi$
$937$	−12.0834	−	8.77914i	−0.394749	−	0.286802i	−0.767399	+	0.641170i	$0.778449\pi$
$938$	−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	0.383554	−	0.923518i	$-0.374700\pi$
$941$	42.3447	−	30.7652i	1.38040	−	1.00292i	0.996843	−	0.0793986i	$-0.0253000\pi$
$942$	−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	−0.896171	−	0.443709i	$-0.853662\pi$
$953$	−13.3349	−	41.0406i	−0.431959	−	1.32943i	0.464211	−	0.885724i	$-0.346338\pi$
$954$	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	0.730552	+	0.682857i	$0.239263\pi$
$971$	−8.15948	+	25.1123i	−0.261850	+	0.805892i	−0.992402	+	0.123035i	$0.960737\pi$
$972$	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	0.363560	−	0.931571i	$-0.381561\pi$
$977$	−12.8176	−	9.31251i	−0.410070	−	0.297934i	−0.773630	+	0.633637i	$0.781561\pi$
$978$	−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	−0.961053	−	0.276365i	$-0.910870\pi$
$983$	−10.8477	−	33.3858i	−0.345988	−	1.06484i	0.615064	−	0.788477i	$-0.289130\pi$
$984$	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	−0.983249	−	0.182268i	$-0.941656\pi$
$997$	−9.31213	−	28.6598i	−0.294918	−	0.907665i	0.688331	−	0.725397i	$-0.258344\pi$
$998$	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.26.1		8
5.2	odd	4		275.2.z.a.224.3		16
5.3	odd	4		275.2.z.a.224.2		16
5.4	even	2		55.2.g.b.26.2	✓	8
11.3	even	5	inner	275.2.h.a.201.1		8
11.5	even	5		3025.2.a.bd.1.3		4
11.6	odd	10		3025.2.a.w.1.2		4
15.14	odd	2		495.2.n.e.136.1		8
20.19	odd	2		880.2.bo.h.81.2		8
55.3	odd	20		275.2.z.a.124.3		16
55.4	even	10		605.2.g.m.251.1		8
55.9	even	10		605.2.g.m.511.1		8
55.14	even	10		55.2.g.b.36.2	yes	8
55.19	odd	10		605.2.g.k.366.1		8
55.24	odd	10		605.2.g.e.511.2		8
55.29	odd	10		605.2.g.e.251.2		8
55.39	odd	10		605.2.a.k.1.3		4
55.47	odd	20		275.2.z.a.124.2		16
55.49	even	10		605.2.a.j.1.2		4
55.54	odd	2		605.2.g.k.81.1		8
165.14	odd	10		495.2.n.e.91.1		8
165.104	odd	10		5445.2.a.bp.1.3		4
165.149	even	10		5445.2.a.bi.1.2		4
220.39	even	10		9680.2.a.cm.1.4		4
220.159	odd	10		9680.2.a.cn.1.4		4
220.179	odd	10		880.2.bo.h.641.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.26.2	✓	8	5.4	even	2
55.2.g.b.36.2	yes	8	55.14	even	10
275.2.h.a.26.1		8	1.1	even	1	trivial
275.2.h.a.201.1		8	11.3	even	5	inner
275.2.z.a.124.2		16	55.47	odd	20
275.2.z.a.124.3		16	55.3	odd	20
275.2.z.a.224.2		16	5.3	odd	4
275.2.z.a.224.3		16	5.2	odd	4
495.2.n.e.91.1		8	165.14	odd	10
495.2.n.e.136.1		8	15.14	odd	2
605.2.a.j.1.2		4	55.49	even	10
605.2.a.k.1.3		4	55.39	odd	10
605.2.g.e.251.2		8	55.29	odd	10
605.2.g.e.511.2		8	55.24	odd	10
605.2.g.k.81.1		8	55.54	odd	2
605.2.g.k.366.1		8	55.19	odd	10
605.2.g.m.251.1		8	55.4	even	10
605.2.g.m.511.1		8	55.9	even	10
880.2.bo.h.81.2		8	20.19	odd	2
880.2.bo.h.641.2		8	220.179	odd	10
3025.2.a.w.1.2		4	11.6	odd	10
3025.2.a.bd.1.3		4	11.5	even	5
5445.2.a.bi.1.2		4	165.149	even	10
5445.2.a.bp.1.3		4	165.104	odd	10
9680.2.a.cm.1.4		4	220.39	even	10
9680.2.a.cn.1.4		4	220.159	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.596764 - 0.433574i) q^{2} +(0.868820 - 2.67395i) q^{3} +(-0.449894 - 1.38463i) q^{4} +(-1.67784 + 1.21902i) q^{6} +(-0.318714 - 0.980901i) q^{7} +(-0.787747 + 2.42443i) q^{8} +(-3.96813 - 2.88301i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9	\( 8 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9} + 3 q^{11} - 16 q^{12} + 2 q^{13} - 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} - 20 q^{21} + 7 q^{22} - 10 q^{23} + 13 q^{24} + 10 q^{26} - 10 q^{27} + 6 q^{28} - 9 q^{29} - 10 q^{31} - 16 q^{32} - 5 q^{33} + 4 q^{34} - 15 q^{36} - 24 q^{37} + 21 q^{39} + 8 q^{41} - 9 q^{42} + 38 q^{43} - 12 q^{44} + 3 q^{46} - 5 q^{48} + q^{49} + q^{51} + 28 q^{52} - 13 q^{53} + 16 q^{54} + 22 q^{56} + 45 q^{57} - 12 q^{58} - 27 q^{59} + 6 q^{61} + 30 q^{62} - 25 q^{63} - 26 q^{64} + 13 q^{66} + 38 q^{67} - 11 q^{68} - q^{69} - 20 q^{71} + 30 q^{72} - 13 q^{73} + 20 q^{74} - 34 q^{77} + 16 q^{78} + 37 q^{79} + 8 q^{81} - 28 q^{82} - 27 q^{83} + 28 q^{84} - 3 q^{86} - 38 q^{87} + 36 q^{88} - 16 q^{89} + 44 q^{91} - 11 q^{92} + 35 q^{93} + 17 q^{94} - 17 q^{96} - 24 q^{97} - 16 q^{98} - 20 q^{99}+O(q^{100}) \) 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

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