LMFDB - Embedded newform 525.2.t.h.26.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(26,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("525.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 8 x^{18} - 15 x^{17} + 18 x^{16} - 45 x^{15} + 59 x^{14} - 147 x^{13} + 271 x^{12} + \cdots + 59049 $ x^20 - 3x^19 + 8x^18 - 15x^17 + 18x^16 - 45x^15 + 59x^14 - 147x^13 + 271x^12 - 330x^11 + 879x^10 - 990x^9 + 2439x^8 - 3969x^7 + 4779x^6 - 10935x^5 + 13122x^4 - 32805x^3 + 52488x^2 - 59049*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.6
Root			$0.189492 + 1.72165i$ of defining polynomial
Character	$\chi$	$=$	525.26
Dual form			525.2.t.h.101.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766266 + 0.442404i) q^{2} +(-0.189492 - 1.72165i) q^{3} +(-0.608557 - 1.05405i) q^{4} +(0.616465 - 1.40308i) q^{6} +(-2.63771 - 0.206062i) q^{7} -2.84653i q^{8} +(-2.92819 + 0.652481i) q^{9} +O(q^{10})$	\(q+(0.766266 + 0.442404i) q^{2} +(-0.189492 - 1.72165i) q^{3} +(-0.608557 - 1.05405i) q^{4} +(0.616465 - 1.40308i) q^{6} +(-2.63771 - 0.206062i) q^{7} -2.84653i q^{8} +(-2.92819 + 0.652481i) q^{9} +(1.25362 - 0.723775i) q^{11} +(-1.69940 + 1.24746i) q^{12} +4.04326i q^{13} +(-1.93003 - 1.32483i) q^{14} +(0.0422021 - 0.0730962i) q^{16} +(-2.87862 - 4.98592i) q^{17} +(-2.53243 - 0.795467i) q^{18} +(-0.356910 - 0.206062i) q^{19} +(0.145060 + 4.58028i) q^{21} +1.28081 q^{22} +(-6.33444 - 3.65719i) q^{23} +(-4.90074 + 0.539396i) q^{24} +(-1.78875 + 3.09821i) q^{26} +(1.67821 + 4.91768i) q^{27} +(1.38800 + 2.90569i) q^{28} +1.82121i q^{29} +(2.30936 - 1.33331i) q^{31} +(-4.86566 + 2.80919i) q^{32} +(-1.48364 - 2.02114i) q^{33} -5.09406i q^{34} +(2.46972 + 2.68939i) q^{36} +(2.92387 - 5.06429i) q^{37} +(-0.182325 - 0.315797i) q^{38} +(6.96109 - 0.766166i) q^{39} +6.46287 q^{41} +(-1.91518 + 3.57389i) q^{42} -10.3583 q^{43} +(-1.52579 - 0.880917i) q^{44} +(-3.23592 - 5.60477i) q^{46} +(5.43364 - 9.41134i) q^{47} +(-0.133843 - 0.0588063i) q^{48} +(6.91508 + 1.08706i) q^{49} +(-8.03855 + 5.90078i) q^{51} +(4.26180 - 2.46055i) q^{52} +(1.20893 - 0.697977i) q^{53} +(-0.889643 + 4.51070i) q^{54} +(-0.586561 + 7.50833i) q^{56} +(-0.287136 + 0.653522i) q^{57} +(-0.805713 + 1.39554i) q^{58} +(-0.583941 - 1.01142i) q^{59} +(3.58903 + 2.07213i) q^{61} +2.35944 q^{62} +(7.85817 - 1.11767i) q^{63} -5.14000 q^{64} +(-0.242703 - 2.20510i) q^{66} +(-3.46011 - 5.99309i) q^{67} +(-3.50361 + 6.06843i) q^{68} +(-5.09609 + 11.5987i) q^{69} -13.3217i q^{71} +(1.85731 + 8.33517i) q^{72} +(2.72344 - 1.57238i) q^{73} +(4.48093 - 2.58707i) q^{74} +0.501602i q^{76} +(-3.45582 + 1.65079i) q^{77} +(5.67300 + 2.49253i) q^{78} +(6.42216 - 11.1235i) q^{79} +(8.14854 - 3.82117i) q^{81} +(4.95228 + 2.85920i) q^{82} +11.5010 q^{83} +(4.73957 - 2.94026i) q^{84} +(-7.93724 - 4.58257i) q^{86} +(3.13550 - 0.345106i) q^{87} +(-2.06025 - 3.56845i) q^{88} +(-3.90111 + 6.75692i) q^{89} +(0.833161 - 10.6650i) q^{91} +8.90244i q^{92} +(-2.73310 - 3.72326i) q^{93} +(8.32723 - 4.80773i) q^{94} +(5.75846 + 7.84466i) q^{96} +3.86099i q^{97} +(4.81787 + 3.89224i) q^{98} +(-3.19857 + 2.93731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{3} + 14 q^{4} - 7 q^{9}+O(q^{10}) $ 20 * q - 3 * q^3 + 14 * q^4 - 7 * q^9	$ 20 q - 3 q^{3} + 14 q^{4} - 7 q^{9} + 21 q^{12} - 18 q^{16} - 14 q^{18} - 9 q^{21} - 20 q^{22} + 18 q^{24} + 10 q^{28} + 42 q^{31} - 12 q^{33} - 36 q^{36} - 24 q^{37} - 33 q^{42} - 36 q^{43} - 8 q^{46} - 4 q^{49} + 21 q^{51} + 84 q^{52} - 75 q^{54} - 6 q^{57} + 4 q^{58} - 90 q^{61} + 5 q^{63} - 120 q^{64} + 6 q^{66} - 20 q^{67} + 35 q^{72} + 48 q^{73} + 108 q^{78} + 46 q^{79} + 29 q^{81} - 36 q^{82} + 75 q^{84} - 69 q^{87} - 4 q^{88} - 30 q^{91} + 30 q^{93} + 6 q^{94} + 135 q^{96} + 94 q^{99}+O(q^{100}) $ 20 * q - 3 * q^3 + 14 * q^4 - 7 * q^9 + 21 * q^12 - 18 * q^16 - 14 * q^18 - 9 * q^21 - 20 * q^22 + 18 * q^24 + 10 * q^28 + 42 * q^31 - 12 * q^33 - 36 * q^36 - 24 * q^37 - 33 * q^42 - 36 * q^43 - 8 * q^46 - 4 * q^49 + 21 * q^51 + 84 * q^52 - 75 * q^54 - 6 * q^57 + 4 * q^58 - 90 * q^61 + 5 * q^63 - 120 * q^64 + 6 * q^66 - 20 * q^67 + 35 * q^72 + 48 * q^73 + 108 * q^78 + 46 * q^79 + 29 * q^81 - 36 * q^82 + 75 * q^84 - 69 * q^87 - 4 * q^88 - 30 * q^91 + 30 * q^93 + 6 * q^94 + 135 * q^96 + 94 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.766266	+	0.442404i	0.541832	+	0.312827i	0.745821	−	0.666146i	$-0.232057\pi$
$2$	0.766266	+	0.442404i	0.541832	+	0.312827i	−0.203989	+	0.978973i	$0.565391\pi$
$3$	−0.189492	−	1.72165i	−0.109403	−	0.993997i
$3$	−0.189492	−	1.72165i	−0.109403	−	0.993997i
$4$	−0.608557	−	1.05405i	−0.304279	−	0.527026i
$5$		0			0
$5$		0			0
$6$	0.616465	−	1.40308i	0.251671	−	0.572804i
$7$	−2.63771	−	0.206062i	−0.996962	−	0.0778841i
$7$	−2.63771	−	0.206062i	−0.996962	−	0.0778841i
$8$		−	2.84653i		−	1.00640i
$9$	−2.92819	+	0.652481i	−0.976062	+	0.217494i
$10$		0			0
$11$	1.25362	−	0.723775i	0.377979	−	0.218227i	−0.298959	−	0.954266i	$-0.596640\pi$
$11$	1.25362	−	0.723775i	0.377979	−	0.218227i	0.676939	+	0.736039i	$0.263306\pi$
$12$	−1.69940	+	1.24746i	−0.490573	+	0.360111i
$13$			4.04326i			1.12140i	0.828020	+	0.560699i	$0.189467\pi$
$13$			4.04326i			1.12140i	−0.828020	+	0.560699i	$0.810533\pi$
$14$	−1.93003	−	1.32483i	−0.515822	−	0.354077i
$15$		0			0
$16$	0.0422021	−	0.0730962i	0.0105505	−	0.0182741i
$17$	−2.87862	−	4.98592i	−0.698168	−	1.20926i	−0.969101	−	0.246665i	$-0.920665\pi$
$17$	−2.87862	−	4.98592i	−0.698168	−	1.20926i	0.270933	−	0.962598i	$-0.412668\pi$
$18$	−2.53243	−	0.795467i	−0.596900	−	0.187493i
$19$	−0.356910	−	0.206062i	−0.0818807	−	0.0472738i	0.458501	−	0.888694i	$-0.348387\pi$
$19$	−0.356910	−	0.206062i	−0.0818807	−	0.0472738i	−0.540381	+	0.841420i	$0.681720\pi$
$20$		0			0
$21$	0.145060	+	4.58028i	0.0316546	+	0.999499i
$22$	1.28081			0.273069
$23$	−6.33444	−	3.65719i	−1.32082	−	0.762578i	−0.336963	−	0.941518i	$-0.609400\pi$
$23$	−6.33444	−	3.65719i	−1.32082	−	0.762578i	−0.983860	+	0.178940i	$0.942733\pi$
$24$	−4.90074	+	0.539396i	−1.00036	+	0.110104i
$25$		0			0
$26$	−1.78875	+	3.09821i	−0.350803	+	0.607609i
$27$	1.67821	+	4.91768i	0.322973	+	0.946408i
$28$	1.38800	+	2.90569i	0.262307	+	0.549124i
$29$			1.82121i			0.338191i	0.985600	+	0.169095i	$0.0540846\pi$
$29$			1.82121i			0.338191i	−0.985600	+	0.169095i	$0.945915\pi$
$30$		0			0
$31$	2.30936	−	1.33331i	0.414772	−	0.239469i	−0.278066	−	0.960562i	$-0.589693\pi$
$31$	2.30936	−	1.33331i	0.414772	−	0.239469i	0.692838	+	0.721093i	$0.256360\pi$
$32$	−4.86566	+	2.80919i	−0.860135	+	0.496599i
$33$	−1.48364	−	2.02114i	−0.258269	−	0.351836i
$34$		−	5.09406i		−	0.873623i
$35$		0			0
$36$	2.46972	+	2.68939i	0.411619	+	0.448231i
$37$	2.92387	−	5.06429i	0.480682	−	0.832565i	−0.519073	−	0.854730i	$-0.673723\pi$
$37$	2.92387	−	5.06429i	0.480682	−	0.832565i	0.999754	+	0.0221652i	$0.00705597\pi$
$38$	−0.182325	−	0.315797i	−0.0295771	−	0.0512290i
$39$	6.96109	−	0.766166i	1.11467	−	0.122685i
$40$		0			0
$41$	6.46287			1.00933			0.504665	−	0.863315i	$-0.331616\pi$
$41$	6.46287			1.00933			0.504665	+	0.863315i	$0.331616\pi$
$42$	−1.91518	+	3.57389i	−0.295519	+	0.551463i
$43$	−10.3583			−1.57963			−0.789815	−	0.613345i	$-0.789823\pi$
$43$	−10.3583			−1.57963			−0.789815	+	0.613345i	$0.789823\pi$
$44$	−1.52579	−	0.880917i	−0.230022	−	0.132803i
$45$		0			0
$46$	−3.23592	−	5.60477i	−0.477110	−	0.826378i
$47$	5.43364	−	9.41134i	0.792578	−	1.37279i	−0.131788	−	0.991278i	$-0.542072\pi$
$47$	5.43364	−	9.41134i	0.792578	−	1.37279i	0.924366	−	0.381507i	$-0.124595\pi$
$48$	−0.133843	−	0.0588063i	−0.0193186	−	0.00848796i
$49$	6.91508	+	1.08706i	0.987868	+	0.155295i
$50$		0			0
$51$	−8.03855	+	5.90078i	−1.12562	+	0.826275i
$52$	4.26180	−	2.46055i	0.591005	−	0.341217i
$53$	1.20893	−	0.697977i	0.166059	−	0.0958745i	−0.414667	−	0.909973i	$-0.636102\pi$
$53$	1.20893	−	0.697977i	0.166059	−	0.0958745i	0.580726	+	0.814099i	$0.302769\pi$
$54$	−0.889643	+	4.51070i	−0.121065	+	0.613829i
$55$		0			0
$56$	−0.586561	+	7.50833i	−0.0783825	+	1.00334i
$57$	−0.287136	+	0.653522i	−0.0380320	+	0.0865611i
$58$	−0.805713	+	1.39554i	−0.105795	+	0.183243i
$59$	−0.583941	−	1.01142i	−0.0760227	−	0.131675i	0.825508	−	0.564391i	$-0.190889\pi$
$59$	−0.583941	−	1.01142i	−0.0760227	−	0.131675i	−0.901531	+	0.432715i	$0.857555\pi$
$60$		0			0
$61$	3.58903	+	2.07213i	0.459529	+	0.265309i	0.711846	−	0.702335i	$-0.247859\pi$
$61$	3.58903	+	2.07213i	0.459529	+	0.265309i	−0.252317	+	0.967645i	$0.581193\pi$
$62$	2.35944			0.299649
$63$	7.85817	−	1.11767i	0.990036	−	0.140813i
$64$	−5.14000			−0.642499
$65$		0			0
$66$	−0.242703	−	2.20510i	−0.0298747	−	0.271429i
$67$	−3.46011	−	5.99309i	−0.422720	−	0.732173i	0.573484	−	0.819217i	$-0.305591\pi$
$67$	−3.46011	−	5.99309i	−0.422720	−	0.732173i	−0.996205	+	0.0870436i	$0.972258\pi$
$68$	−3.50361	+	6.06843i	−0.424875	+	0.735906i
$69$	−5.09609	+	11.5987i	−0.613497	+	1.39632i
$70$		0			0
$71$		−	13.3217i		−	1.58100i	−0.612463	−	0.790499i	$-0.709821\pi$
$71$		−	13.3217i		−	1.58100i	0.612463	−	0.790499i	$-0.290179\pi$
$72$	1.85731	+	8.33517i	0.218886	+	0.982309i
$73$	2.72344	−	1.57238i	0.318755	−	0.184033i	−0.332082	−	0.943250i	$-0.607751\pi$
$73$	2.72344	−	1.57238i	0.318755	−	0.184033i	0.650838	+	0.759217i	$0.274418\pi$
$74$	4.48093	−	2.58707i	0.520898	−	0.300740i
$75$		0			0
$76$			0.501602i			0.0575377i
$77$	−3.45582	+	1.65079i	−0.393828	+	0.188125i
$78$	5.67300	+	2.49253i	0.642341	+	0.282223i
$79$	6.42216	−	11.1235i	0.722550	−	1.25149i	−0.237425	−	0.971406i	$-0.576303\pi$
$79$	6.42216	−	11.1235i	0.722550	−	1.25149i	0.959975	−	0.280087i	$-0.0903633\pi$
$80$		0			0
$81$	8.14854	−	3.82117i	0.905393	−	0.424574i
$82$	4.95228	+	2.85920i	0.546888	+	0.315746i
$83$	11.5010			1.26240			0.631200	−	0.775620i	$-0.282563\pi$
$83$	11.5010			1.26240			0.631200	+	0.775620i	$0.282563\pi$
$84$	4.73957	−	2.94026i	0.517130	−	0.320809i
$85$		0			0
$86$	−7.93724	−	4.58257i	−0.855894	−	0.494151i
$87$	3.13550	−	0.345106i	0.336161	−	0.0369993i
$88$	−2.06025	−	3.56845i	−0.219623	−	0.380399i
$89$	−3.90111	+	6.75692i	−0.413517	+	0.716232i	−0.995271	−	0.0971324i	$-0.969033\pi$
$89$	−3.90111	+	6.75692i	−0.413517	+	0.716232i	0.581755	+	0.813364i	$0.302366\pi$
$90$		0			0
$91$	0.833161	−	10.6650i	0.0873390	−	1.11799i
$92$			8.90244i			0.928144i
$93$	−2.73310	−	3.72326i	−0.283409	−	0.386084i
$94$	8.32723	−	4.80773i	0.858889	−	0.495880i
$95$		0			0
$96$	5.75846	+	7.84466i	0.587720	+	0.800642i
$97$			3.86099i			0.392024i	0.980601	+	0.196012i	$0.0627992\pi$
$97$			3.86099i			0.392024i	−0.980601	+	0.196012i	$0.937201\pi$
$98$	4.81787	+	3.89224i	0.486678	+	0.393176i
$99$	−3.19857	+	2.93731i	−0.321468	+	0.295211i
$100$		0			0
$101$	−6.61336	−	11.4547i	−0.658054	−	1.13978i	−0.981119	−	0.193406i	$-0.938046\pi$
$101$	−6.61336	−	11.4547i	−0.658054	−	1.13978i	0.323065	−	0.946377i	$-0.395287\pi$
$102$	−8.77020	+	0.965285i	−0.868379	+	0.0955774i
$103$	14.7144	+	8.49538i	1.44986	+	0.837075i	0.998472	−	0.0552547i	$-0.0175971\pi$
$103$	14.7144	+	8.49538i	1.44986	+	0.837075i	0.451384	+	0.892330i	$0.350930\pi$
$104$	11.5092			1.12857
$105$		0			0
$106$	1.23515			0.119968
$107$	11.2134	+	6.47403i	1.08404	+	0.625868i	0.931982	−	0.362504i	$-0.118078\pi$
$107$	11.2134	+	6.47403i	1.08404	+	0.625868i	0.152054	+	0.988372i	$0.451411\pi$
$108$	4.16220	−	4.76162i	0.400508	−	0.458187i
$109$	−3.63427	−	6.29474i	−0.348100	−	0.602927i	0.637812	−	0.770192i	$-0.279840\pi$
$109$	−3.63427	−	6.29474i	−0.348100	−	0.602927i	−0.985912	+	0.167265i	$0.946506\pi$
$110$		0			0
$111$	−9.27301	−	4.07425i	−0.880156	−	0.386711i
$112$	−0.126380	+	0.184111i	−0.0119417	+	0.0173968i
$113$			4.78517i			0.450151i	0.974341	+	0.225075i	$0.0722628\pi$
$113$			4.78517i			0.450151i	−0.974341	+	0.225075i	$0.927737\pi$
$114$	−0.509143	+	0.373742i	−0.0476856	+	0.0350041i
$115$		0			0
$116$	1.91965	−	1.10831i	0.178235	−	0.102904i
$117$	−2.63815	−	11.8394i	−0.243897	−	1.09455i
$118$		−	1.03335i		−	0.0951278i
$119$	6.56557	+	13.7446i	0.601865	+	1.25997i
$120$		0			0
$121$	−4.45230	+	7.71161i	−0.404754	+	0.701055i
$122$	1.83344	+	3.17561i	0.165992	+	0.287506i
$123$	−1.22466	−	11.1268i	−0.110424	−	1.00327i
$124$	−2.81075	−	1.62279i	−0.252413	−	0.145731i
$125$		0			0
$126$	6.51591	+	2.62005i	0.580484	+	0.233413i
$127$	−9.16192			−0.812989			−0.406495	−	0.913653i	$-0.633249\pi$
$127$	−9.16192			−0.812989			−0.406495	+	0.913653i	$0.633249\pi$
$128$	5.79271	+	3.34442i	0.512008	+	0.295608i
$129$	1.96282	+	17.8335i	0.172817	+	1.57015i
$130$		0			0
$131$	−10.4220	+	18.0514i	−0.910574	+	1.57716i	−0.0973191	+	0.995253i	$0.531027\pi$
$131$	−10.4220	+	18.0514i	−0.910574	+	1.57716i	−0.813255	+	0.581907i	$0.802307\pi$
$132$	−1.22751	+	2.79382i	−0.106841	+	0.243170i
$133$	0.898964	+	0.617078i	0.0779501	+	0.0535074i
$134$		−	6.12308i		−	0.528953i
$135$		0			0
$136$	−14.1926	+	8.19408i	−1.21700	+	0.702637i
$137$	−8.20795	+	4.73886i	−0.701253	+	0.404868i	−0.807814	−	0.589438i	$-0.799349\pi$
$137$	−8.20795	+	4.73886i	−0.701253	+	0.404868i	0.106561	+	0.994306i	$0.466016\pi$
$138$	−9.03629	+	6.63319i	−0.769220	+	0.564654i
$139$		−	5.75447i		−	0.488088i	−0.969764	−	0.244044i	$-0.921526\pi$
$139$		−	5.75447i		−	0.488088i	0.969764	−	0.244044i	$-0.0784741\pi$
$140$		0			0
$141$	−17.2327	−	7.57147i	−1.45126	−	0.637633i
$142$	5.89359	−	10.2080i	0.494579	−	0.856636i
$143$	2.92641	+	5.06869i	0.244719	+	0.423865i
$144$	−0.0758818	+	0.241575i	−0.00632348	+	0.0201313i
$145$		0			0
$146$	2.78251			0.230282
$147$	0.561195	−	12.1114i	0.0462866	−	0.998928i
$148$	−7.11737			−0.585044
$149$	−5.57080	−	3.21630i	−0.456378	−	0.263490i	0.254142	−	0.967167i	$-0.418207\pi$
$149$	−5.57080	−	3.21630i	−0.456378	−	0.263490i	−0.710520	+	0.703677i	$0.751540\pi$
$150$		0			0
$151$	−2.06002	−	3.56807i	−0.167642	−	0.290365i	0.769948	−	0.638107i	$-0.220282\pi$
$151$	−2.06002	−	3.56807i	−0.167642	−	0.290365i	−0.937591	+	0.347741i	$0.886949\pi$
$152$	−0.586561	+	1.01595i	−0.0475764	+	0.0824047i
$153$	11.6824	+	12.7214i	0.944462	+	1.02847i
$154$	−3.37840	−	0.263925i	−0.272239	−	0.0212677i
$155$		0			0
$156$	−5.04380	−	6.87109i	−0.403827	−	0.550128i
$157$	1.07366	−	0.619880i	0.0856877	−	0.0494718i	−0.456544	−	0.889701i	$-0.650913\pi$
$157$	1.07366	−	0.619880i	0.0856877	−	0.0494718i	0.542232	+	0.840229i	$0.317580\pi$
$158$	9.84218	−	5.68238i	0.783001	−	0.452066i
$159$	−1.43076	−	1.94910i	−0.113466	−	0.154574i
$160$		0			0
$161$	15.9548	+	10.9519i	1.25742	+	0.863132i
$162$	7.93445	+	0.676913i	0.623389	+	0.0531833i
$163$	3.72151	−	6.44585i	0.291491	−	0.504878i	−0.682671	−	0.730726i	$-0.739182\pi$
$163$	3.72151	−	6.44585i	0.291491	−	0.504878i	0.974163	+	0.225848i	$0.0725152\pi$
$164$	−3.93302	−	6.81220i	−0.307118	−	0.531943i
$165$		0			0
$166$	8.81284	+	5.08809i	0.684009	+	0.394913i
$167$	−2.50723			−0.194015			−0.0970077	−	0.995284i	$-0.530927\pi$
$167$	−2.50723			−0.194015			−0.0970077	+	0.995284i	$0.530927\pi$
$168$	13.0379	−	0.412917i	1.00590	−	0.0318572i
$169$	−3.34791			−0.257532
$170$		0			0
$171$	1.17955	+	0.370511i	0.0902023	+	0.0283337i
$172$	6.30363	+	10.9182i	0.480647	+	0.832506i
$173$	−8.52481	+	14.7654i	−0.648130	+	1.12259i	0.335440	+	0.942062i	$0.391115\pi$
$173$	−8.52481	+	14.7654i	−0.648130	+	1.12259i	−0.983569	+	0.180532i	$0.942218\pi$
$174$	2.55531	+	1.12272i	0.193717	+	0.0851128i
$175$		0			0
$176$		−	0.122179i		−	0.00920962i
$177$	−1.63066	+	1.19700i	−0.122568	+	0.0899721i
$178$	−5.97858	+	3.45173i	−0.448113	+	0.258718i
$179$	−10.1751	+	5.87462i	−0.760525	+	0.439090i	−0.829484	−	0.558530i	$-0.811366\pi$
$179$	−10.1751	+	5.87462i	−0.760525	+	0.439090i	0.0689590	+	0.997619i	$0.478032\pi$
$180$		0			0
$181$		−	2.41221i		−	0.179298i	−0.995973	−	0.0896490i	$-0.971425\pi$
$181$		−	2.41221i		−	0.179298i	0.995973	−	0.0896490i	$-0.0285745\pi$
$182$	5.35664	−	7.80360i	0.397061	−	0.578442i
$183$	2.88740	−	6.57173i	0.213442	−	0.485796i
$184$	−10.4103	+	18.0312i	−0.767458	+	1.32928i
$185$		0			0
$186$	−0.447096	−	4.06214i	−0.0327827	−	0.297851i
$187$	−7.21737	−	4.16695i	−0.527786	−	0.304718i
$188$	−13.2267			−0.964658
$189$	−3.41331	−	13.3173i	−0.248281	−	0.968688i
$190$		0			0
$191$	−11.9159	−	6.87963i	−0.862202	−	0.497793i	0.00254675	−	0.999997i	$-0.499189\pi$
$191$	−11.9159	−	6.87963i	−0.862202	−	0.497793i	−0.864749	+	0.502204i	$0.832523\pi$
$192$	0.973990	+	8.84929i	0.0702917	+	0.638643i
$193$	4.60685	+	7.97929i	0.331608	+	0.574362i	0.982827	−	0.184528i	$-0.0590755\pi$
$193$	4.60685	+	7.97929i	0.331608	+	0.574362i	−0.651219	+	0.758890i	$0.725742\pi$
$194$	−1.70812	+	2.95855i	−0.122636	+	0.212411i
$195$		0			0
$196$	−3.06240	−	7.95039i	−0.218743	−	0.567885i
$197$		−	4.11728i		−	0.293344i	−0.989185	−	0.146672i	$-0.953144\pi$
$197$		−	4.11728i		−	0.293344i	0.989185	−	0.146672i	$-0.0468562\pi$
$198$	−3.75043	+	0.835701i	−0.266532	+	0.0593907i
$199$	0.0694265	−	0.0400834i	0.00492151	−	0.00284144i	−0.497537	−	0.867443i	$-0.665762\pi$
$199$	0.0694265	−	0.0400834i	0.00492151	−	0.00284144i	0.502459	+	0.864601i	$0.332429\pi$
$200$		0			0
$201$	−9.66237	+	7.09277i	−0.681531	+	0.500285i
$202$		−	11.7031i		−	0.823428i
$203$	0.375283	−	4.80384i	0.0263397	−	0.337164i
$204$	11.1116	+	4.88208i	0.777971	+	0.341814i
$205$		0			0
$206$	7.51679	+	13.0195i	0.523719	+	0.907108i
$207$	20.9347	+	6.57584i	1.45506	+	0.457052i
$208$	0.295547	+	0.170634i	0.0204925	+	0.0118313i
$209$	−0.596570			−0.0412656
$210$		0			0
$211$	17.5804			1.21028			0.605141	−	0.796118i	$-0.293117\pi$
$211$	17.5804			1.21028			0.605141	+	0.796118i	$0.293117\pi$
$212$	−1.47141	−	0.849517i	−0.101057	−	0.0583451i
$213$	−22.9354	+	2.52437i	−1.57151	+	0.172967i
$214$	5.72828	+	9.92167i	0.391577	+	0.678231i
$215$		0			0
$216$	13.9983	−	4.77709i	0.952465	−	0.325040i
$217$	−6.36616	+	3.04101i	−0.432163	+	0.206437i
$218$		−	6.43127i		−	0.435580i
$219$	−3.22317	−	4.39088i	−0.217802	−	0.296708i
$220$		0			0
$221$	20.1593	−	11.6390i	1.35606	−	0.782924i
$222$	−5.30313	−	7.22438i	−0.355923	−	0.484869i
$223$		−	27.4965i		−	1.84130i	−0.390387	−	0.920651i	$-0.627659\pi$
$223$		−	27.4965i		−	1.84130i	0.390387	−	0.920651i	$-0.372341\pi$
$224$	13.4131	−	6.40721i	0.896199	−	0.428100i
$225$		0			0
$226$	−2.11698	+	3.66671i	−0.140819	+	0.243906i
$227$	6.20253	+	10.7431i	0.411676	+	0.713044i	0.995073	−	0.0991431i	$-0.0316101\pi$
$227$	6.20253	+	10.7431i	0.411676	+	0.713044i	−0.583397	+	0.812187i	$0.698277\pi$
$228$	0.863584	−	0.0950497i	0.0571923	−	0.00629482i
$229$	23.5513	+	13.5973i	1.55631	+	0.898538i	0.997605	+	0.0691740i	$0.0220364\pi$
$229$	23.5513	+	13.5973i	1.55631	+	0.898538i	0.558709	+	0.829364i	$0.311297\pi$
$230$		0			0
$231$	3.49694	+	5.63692i	0.230082	+	0.370882i
$232$	5.18414			0.340355
$233$	−25.0585	−	14.4675i	−1.64163	−	0.947798i	−0.980253	−	0.197749i	$-0.936637\pi$
$233$	−25.0585	−	14.4675i	−1.64163	−	0.947798i	−0.661382	−	0.750049i	$-0.730030\pi$
$234$	3.21628	−	10.2393i	0.210255	−	0.669362i
$235$		0			0
$236$	−0.710723	+	1.23101i	−0.0462641	+	0.0801318i
$237$	−20.3678	−	8.94892i	−1.32303	−	0.581295i
$238$	−1.04969	+	13.4367i	−0.0680413	+	0.870970i
$239$		−	19.2419i		−	1.24465i	−0.782757	−	0.622327i	$-0.786187\pi$
$239$		−	19.2419i		−	1.24465i	0.782757	−	0.622327i	$-0.213813\pi$
$240$		0			0
$241$	4.90603	−	2.83250i	0.316025	−	0.182457i	−0.333594	−	0.942717i	$-0.608262\pi$
$241$	4.90603	−	2.83250i	0.316025	−	0.182457i	0.649619	+	0.760260i	$0.274928\pi$
$242$	−6.82329	+	3.93943i	−0.438618	+	0.253236i
$243$	−8.12282	−	13.3049i	−0.521079	−	0.853508i
$244$		−	5.04404i		−	0.322911i
$245$		0			0
$246$	3.98413	−	9.06791i	0.254019	−	0.578149i
$247$	0.833161	−	1.44308i	0.0530127	−	0.0918208i
$248$	−3.79530	−	6.57365i	−0.241002	−	0.417427i
$249$	−2.17935	−	19.8008i	−0.138111	−	1.25482i
$250$		0			0
$251$	−6.55844			−0.413965			−0.206983	−	0.978345i	$-0.566364\pi$
$251$	−6.55844			−0.413965			−0.206983	+	0.978345i	$0.566364\pi$
$252$	−5.96023	−	7.60275i	−0.375459	−	0.478928i
$253$	−10.5879			−0.665659
$254$	−7.02047	−	4.05327i	−0.440504	−	0.254325i
$255$		0			0
$256$	8.09917	+	14.0282i	0.506198	+	0.876761i
$257$	4.36647	−	7.56295i	0.272373	−	0.471764i	−0.697096	−	0.716978i	$-0.745525\pi$
$257$	4.36647	−	7.56295i	0.272373	−	0.471764i	0.969469	+	0.245214i	$0.0788582\pi$
$258$	−6.38555	+	14.5335i	−0.397547	+	0.904818i
$259$	−8.75590	+	12.7557i	−0.544065	+	0.792598i
$260$		0			0
$261$	−1.18831	−	5.33285i	−0.0735544	−	0.330095i
$262$	−15.9721	+	9.22147i	−0.986757	+	0.569704i
$263$	19.5217	−	11.2709i	1.20376	−	0.694992i	0.242372	−	0.970183i	$-0.422075\pi$
$263$	19.5217	−	11.2709i	1.20376	−	0.694992i	0.961389	+	0.275192i	$0.0887413\pi$
$264$	−5.75324	+	4.22323i	−0.354088	+	0.259922i
$265$		0			0
$266$	0.415848	+	0.870551i	0.0254973	+	0.0533769i
$267$	12.3723	+	5.43597i	0.757173	+	0.332676i
$268$	−4.21135	+	7.29428i	−0.257249	+	0.445569i
$269$	−7.09460	−	12.2882i	−0.432565	−	0.749225i	0.564528	−	0.825414i	$-0.309058\pi$
$269$	−7.09460	−	12.2882i	−0.432565	−	0.749225i	−0.997093	+	0.0761890i	$0.975725\pi$
$270$		0			0
$271$	−11.0247	−	6.36513i	−0.669705	−	0.386654i	0.126260	−	0.991997i	$-0.459703\pi$
$271$	−11.0247	−	6.36513i	−0.669705	−	0.386654i	−0.795965	+	0.605343i	$0.793036\pi$
$272$	−0.485936			−0.0294642
$273$	−18.5192	+	0.586513i	−1.12084	+	0.0354974i
$274$	−8.38597			−0.506615
$275$		0			0
$276$	15.3269	−	1.68695i	0.922573	−	0.101542i
$277$	14.4086	+	24.9564i	0.865727	+	1.49948i	0.866323	+	0.499484i	$0.166477\pi$
$277$	14.4086	+	24.9564i	0.865727	+	1.49948i	−0.000595725		1.00000i	$0.500190\pi$
$278$	2.54580	−	4.40946i	0.152687	−	0.264462i
$279$	−5.89226	+	5.41098i	−0.352761	+	0.323947i
$280$		0			0
$281$			13.4500i			0.802357i	0.916000	+	0.401179i	$0.131399\pi$
$281$			13.4500i			0.802357i	−0.916000	+	0.401179i	$0.868601\pi$
$282$	−9.85520	−	13.4256i	−0.586868	−	0.799482i
$283$	12.1908	−	7.03838i	0.724670	−	0.418388i	−0.0917992	−	0.995778i	$-0.529262\pi$
$283$	12.1908	−	7.03838i	0.724670	−	0.418388i	0.816469	+	0.577389i	$0.195928\pi$
$284$	−14.0418	+	8.10703i	−0.833227	+	0.481064i
$285$		0			0
$286$			5.17862i			0.306218i
$287$	−17.0472	−	1.33175i	−1.00626	−	0.0786107i
$288$	12.4146	−	11.4006i	0.731538	−	0.671785i
$289$	−8.07292	+	13.9827i	−0.474878	+	0.822512i
$290$		0			0
$291$	6.64729	−	0.731629i	0.389671	−	0.0428888i
$292$	−3.31474	−	1.91377i	−0.193981	−	0.111995i
$293$	−16.7139			−0.976436			−0.488218	−	0.872722i	$-0.662353\pi$
$293$	−16.7139			−0.976436			−0.488218	+	0.872722i	$0.662353\pi$
$294$	5.78814	−	9.03225i	0.337571	−	0.526772i
$295$		0			0
$296$	−14.4157	−	8.32289i	−0.837893	−	0.483758i
$297$	5.66313	+	4.95023i	0.328608	+	0.287242i
$298$	−2.84581	−	4.92909i	−0.164853	−	0.285534i
$299$	14.7870	−	25.6118i	0.855152	−	1.48117i
$300$		0			0
$301$	27.3223	+	2.13446i	1.57483	+	0.123028i
$302$		−	3.64545i		−	0.209772i
$303$	−18.4678	+	13.5565i	−1.06095	+	0.778800i
$304$	−0.0301247	+	0.0173925i	−0.00172777	+	0.000997528i
$305$		0			0
$306$	3.32377	+	14.9163i	0.190007	+	0.852710i
$307$			9.72258i			0.554897i	0.960741	+	0.277449i	$0.0894888\pi$
$307$			9.72258i			0.554897i	−0.960741	+	0.277449i	$0.910511\pi$
$308$	3.84309	+	2.63802i	0.218980	+	0.150315i
$309$	11.8378	−	26.9430i	0.673431	−	1.53273i
$310$		0			0
$311$	2.50723	+	4.34265i	0.142172	+	0.246249i	0.928314	−	0.371796i	$-0.121258\pi$
$311$	2.50723	+	4.34265i	0.142172	+	0.246249i	−0.786142	+	0.618046i	$0.787925\pi$
$312$	−2.18091	−	19.8149i	−0.123470	−	1.12180i
$313$	15.3536	+	8.86441i	0.867837	+	0.501046i	0.866629	−	0.498953i	$-0.166282\pi$
$313$	15.3536	+	8.86441i	0.867837	+	0.501046i	0.00120811	+	0.999999i	$0.499615\pi$
$314$	1.09695			0.0619045
$315$		0			0
$316$	−15.6330			−0.879426
$317$	3.63917	+	2.10107i	0.204396	+	0.118008i	0.598704	−	0.800970i	$-0.295682\pi$
$317$	3.63917	+	2.10107i	0.204396	+	0.118008i	−0.394308	+	0.918978i	$0.629016\pi$
$318$	−0.234052	−	2.12650i	−0.0131250	−	0.119248i
$319$	1.31815	+	2.28310i	0.0738022	+	0.127829i
$320$		0			0
$321$	9.02120	−	20.5323i	0.503514	−	1.14600i
$322$	7.38049	+	15.4506i	0.411299	+	0.861027i
$323$			2.37270i			0.132020i
$324$	−8.98656	−	6.26358i	−0.499253	−	0.347977i
$325$		0			0
$326$	5.70334	−	3.29282i	0.315879	−	0.182373i
$327$	−10.1487	+	7.44977i	−0.561225	+	0.411973i
$328$		−	18.3967i		−	1.01579i
$329$	−16.2717	+	23.7048i	−0.897089	+	1.30689i
$330$		0			0
$331$	0.680140	−	1.17804i	0.0373839	−	0.0647508i	−0.846728	−	0.532026i	$-0.821431\pi$
$331$	0.680140	−	1.17804i	0.0373839	−	0.0647508i	0.884112	+	0.467275i	$0.154764\pi$
$332$	−6.99902	−	12.1227i	−0.384121	−	0.665317i
$333$	−5.25728	+	16.7370i	−0.288097	+	0.917180i
$334$	−1.92121	−	1.10921i	−0.105124	−	0.0606933i
$335$		0			0
$336$	0.340923	+	0.182694i	0.0185989	+	0.00996679i
$337$	−26.2620			−1.43058			−0.715292	−	0.698826i	$-0.753706\pi$
$337$	−26.2620			−1.43058			−0.715292	+	0.698826i	$0.753706\pi$
$338$	−2.56539	−	1.48113i	−0.139539	−	0.0805629i
$339$	8.23840	−	0.906753i	0.447449	−	0.0492480i
$340$		0			0
$341$	1.93003	−	3.34291i	0.104517	−	0.181029i
$342$	0.739933	+	0.805747i	0.0400110	+	0.0435698i
$343$	−18.0160	−	4.29230i	−0.972772	−	0.231762i
$344$			29.4853i			1.58974i
$345$		0			0
$346$	−13.0646	+	7.54283i	−0.702355	+	0.405505i
$347$	5.43714	−	3.13913i	0.291881	−	0.168517i	−0.346909	−	0.937899i	$-0.612769\pi$
$347$	5.43714	−	3.13913i	0.291881	−	0.168517i	0.638790	+	0.769381i	$0.279435\pi$
$348$	−2.27189	−	3.09496i	−0.121786	−	0.165907i
$349$			4.99426i			0.267336i	0.991026	+	0.133668i	$0.0426756\pi$
$349$			4.99426i			0.267336i	−0.991026	+	0.133668i	$0.957324\pi$
$350$		0			0
$351$	−19.8834	+	6.78545i	−1.06130	+	0.362181i
$352$	−4.06644	+	7.04329i	−0.216742	+	0.375408i
$353$	−0.393860	−	0.682186i	−0.0209631	−	0.0363091i	0.855354	−	0.518045i	$-0.173340\pi$
$353$	−0.393860	−	0.682186i	−0.0209631	−	0.0363091i	−0.876317	+	0.481736i	$0.840007\pi$
$354$	−1.77907	+	0.195812i	−0.0945568	+	0.0104073i
$355$		0			0
$356$	9.49619			0.503297
$357$	22.4193	−	13.9081i	1.18656	−	0.736097i
$358$	−10.3958			−0.549436
$359$	21.9487	+	12.6721i	1.15841	+	0.668808i	0.950922	−	0.309430i	$-0.100138\pi$
$359$	21.9487	+	12.6721i	1.15841	+	0.668808i	0.207487	+	0.978238i	$0.433472\pi$
$360$		0			0
$361$	−9.41508	−	16.3074i	−0.495530	−	0.858284i
$362$	1.06717	−	1.84840i	0.0560893	−	0.0971495i
$363$	14.1204	+	6.20403i	0.741129	+	0.325627i
$364$	−11.7484	+	5.61204i	−0.615786	+	0.294151i
$365$		0			0
$366$	5.11987	−	3.75830i	0.267620	−	0.196449i
$367$	1.58130	−	0.912964i	0.0825432	−	0.0476563i	−0.458160	−	0.888870i	$-0.651491\pi$
$367$	1.58130	−	0.912964i	0.0825432	−	0.0476563i	0.540703	+	0.841213i	$0.318158\pi$
$368$	−0.534654	+	0.308683i	−0.0278708	+	0.0160912i
$369$	−18.9245	+	4.21690i	−0.985169	+	0.219523i
$370$		0			0
$371$	−3.33264	+	1.59195i	−0.173022	+	0.0826499i
$372$	−2.26126	+	5.14664i	−0.117241	+	0.266841i
$373$	−1.05009	+	1.81882i	−0.0543718	+	0.0941748i	−0.891930	−	0.452173i	$-0.850649\pi$
$373$	−1.05009	+	1.81882i	−0.0543718	+	0.0941748i	0.837558	+	0.546348i	$0.183982\pi$
$374$	−3.68695	−	6.38599i	−0.190648	−	0.330212i
$375$		0			0
$376$	−26.7897	−	15.4670i	−1.38157	−	0.797651i
$377$	−7.36363			−0.379246
$378$	3.27611	−	11.7146i	0.168505	−	0.602535i
$379$	−19.2106			−0.986782			−0.493391	−	0.869808i	$-0.664243\pi$
$379$	−19.2106			−0.986782			−0.493391	+	0.869808i	$0.664243\pi$
$380$		0			0
$381$	1.73611	+	15.7737i	0.0889439	+	0.808109i
$382$	−6.08716	−	10.5433i	−0.311446	−	0.539440i
$383$	−1.58032	+	2.73720i	−0.0807506	+	0.139864i	−0.903573	−	0.428435i	$-0.859065\pi$
$383$	−1.58032	+	2.73720i	−0.0807506	+	0.139864i	0.822822	+	0.568299i	$0.192398\pi$
$384$	4.66026	−	10.6068i	0.237818	−	0.541275i
$385$		0			0
$386$			8.15235i			0.414944i
$387$	30.3311	−	6.75861i	1.54182	−	0.343559i
$388$	4.06969	−	2.34963i	0.206607	−	0.119285i
$389$	9.77019	−	5.64082i	0.495368	−	0.286001i	−0.231430	−	0.972851i	$-0.574341\pi$
$389$	9.77019	−	5.64082i	0.495368	−	0.286001i	0.726799	+	0.686850i	$0.241007\pi$
$390$		0			0
$391$			42.1107i			2.12963i
$392$	3.09436	−	19.6840i	0.156289	−	0.994191i
$393$	33.0532	+	14.5225i	1.66731	+	0.732561i
$394$	1.82150	−	3.15493i	0.0917659	−	0.158943i
$395$		0			0
$396$	5.04259	+	1.58394i	0.253400	+	0.0795959i
$397$	26.5154	+	15.3087i	1.33077	+	0.768319i	0.985417	−	0.170154i	$-0.0544266\pi$
$397$	26.5154	+	15.3087i	1.33077	+	0.768319i	0.345351	+	0.938474i	$0.387760\pi$
$398$	0.0709323			0.00355551
$399$	0.892048	−	1.66464i	0.0446582	−	0.0833361i
$400$		0			0
$401$	20.4532	+	11.8087i	1.02139	+	0.589697i	0.914505	−	0.404574i	$-0.132580\pi$
$401$	20.4532	+	11.8087i	1.02139	+	0.589697i	0.106881	+	0.994272i	$0.465914\pi$
$402$	−10.5418	+	1.16028i	−0.525778	+	0.0578693i
$403$	5.39090	+	9.33731i	0.268540	+	0.465125i
$404$	−8.04922	+	13.9417i	−0.400464	+	0.693623i
$405$		0			0
$406$	2.41281	−	3.51500i	0.119746	−	0.174446i
$407$		−	8.46491i		−	0.419590i
$408$	16.7968	+	22.8820i	0.831563	+	1.13283i
$409$	−11.1411	+	6.43231i	−0.550891	+	0.318057i	−0.749481	−	0.662025i	$-0.769697\pi$
$409$	−11.1411	+	6.43231i	−0.550891	+	0.318057i	0.198590	+	0.980083i	$0.436364\pi$
$410$		0			0
$411$	9.71403	+	13.2333i	0.479158	+	0.652749i
$412$		−	20.6797i		−	1.01882i
$413$	1.33186	+	2.78815i	0.0655364	+	0.137196i
$414$	13.1324	+	14.3004i	0.645420	+	0.702828i
$415$		0			0
$416$	−11.3583	−	19.6731i	−0.556885	−	0.964553i
$417$	−9.90720	+	1.09043i	−0.485158	+	0.0533985i
$418$	−0.457132	−	0.263925i	−0.0223590	−	0.0129090i
$419$	−3.78089			−0.184708			−0.0923542	−	0.995726i	$-0.529439\pi$
$419$	−3.78089			−0.184708			−0.0923542	+	0.995726i	$0.529439\pi$
$420$		0			0
$421$	−2.43659			−0.118752			−0.0593759	−	0.998236i	$-0.518911\pi$
$421$	−2.43659			−0.118752			−0.0593759	+	0.998236i	$0.518911\pi$
$422$	13.4712	+	7.77763i	0.655770	+	0.378609i
$423$	−9.76999	+	31.1035i	−0.475033	+	1.51230i
$424$	−1.98681	−	3.44126i	−0.0964881	−	0.167122i
$425$		0			0
$426$	−18.6914	−	8.21238i	−0.905603	−	0.397891i
$427$	−9.03986	−	6.20525i	−0.437470	−	0.300293i
$428$		−	15.7593i		−	0.761753i
$429$	8.17200	−	5.99874i	0.394548	−	0.289622i
$430$		0			0
$431$	−26.4558	+	15.2743i	−1.27433	+	0.735737i	−0.975800	−	0.218663i	$-0.929830\pi$
$431$	−26.4558	+	15.2743i	−1.27433	+	0.735737i	−0.298533	+	0.954399i	$0.596497\pi$
$432$	0.430288	+	0.0848655i	0.0207023	+	0.00408309i
$433$		−	37.7749i		−	1.81534i	−0.419680	−	0.907672i	$-0.637858\pi$
$433$		−	37.7749i		−	1.81534i	0.419680	−	0.907672i	$-0.362142\pi$
$434$	−6.22353	−	0.486191i	−0.298739	−	0.0233379i
$435$		0			0
$436$	−4.42332	+	7.66142i	−0.211839	+	0.366916i
$437$	1.50722	+	2.61057i	0.0720999	+	0.124881i
$438$	−0.527265	−	4.79052i	−0.0251937	−	0.228900i
$439$	−3.55267	−	2.05113i	−0.169560	−	0.0978953i	0.412819	−	0.910813i	$-0.364544\pi$
$439$	−3.55267	−	2.05113i	−0.169560	−	0.0978953i	−0.582378	+	0.812918i	$0.697878\pi$
$440$		0			0
$441$	−20.9579	+	1.32883i	−0.997996	+	0.0632775i
$442$	20.5966			0.979679
$443$	22.7315	+	13.1240i	1.08001	+	0.623541i	0.930898	−	0.365280i	$-0.119027\pi$
$443$	22.7315	+	13.1240i	1.08001	+	0.623541i	0.149107	+	0.988821i	$0.452360\pi$
$444$	1.34869	+	12.2537i	0.0640059	+	0.581533i
$445$		0			0
$446$	12.1646	−	21.0696i	0.576009	−	0.997677i
$447$	−4.48174	+	10.2005i	−0.211979	+	0.482465i
$448$	13.5578	+	1.05916i	0.640548	+	0.0500405i
$449$		−	14.6382i		−	0.690821i	−0.938452	−	0.345411i	$-0.887740\pi$
$449$		−	14.6382i		−	0.690821i	0.938452	−	0.345411i	$-0.112260\pi$
$450$		0			0
$451$	8.10195	−	4.67766i	0.381506	−	0.220263i
$452$	5.04381	−	2.91205i	0.237241	−	0.136971i
$453$	−5.75262	+	4.22277i	−0.270282	+	0.198403i
$454$			10.9761i			0.515134i
$455$		0			0
$456$	1.86027	+	0.817340i	0.0871151	+	0.0382754i
$457$	−14.5940	+	25.2776i	−0.682679	+	1.18244i	0.291481	+	0.956577i	$0.405852\pi$
$457$	−14.5940	+	25.2776i	−0.682679	+	1.18244i	−0.974160	+	0.225858i	$0.927481\pi$
$458$	12.0310	+	20.8384i	0.562174	+	0.973714i
$459$	19.6882	−	22.5236i	0.918967	−	1.05131i
$460$		0			0
$461$	−15.8295			−0.737255			−0.368627	−	0.929577i	$-0.620172\pi$
$461$	−15.8295			−0.737255			−0.368627	+	0.929577i	$0.620172\pi$
$462$	0.185793	+	5.86644i	0.00864388	+	0.272932i
$463$	19.1466			0.889816			0.444908	−	0.895576i	$-0.353236\pi$
$463$	19.1466			0.889816			0.444908	+	0.895576i	$0.353236\pi$
$464$	0.133124	+	0.0768591i	0.00618012	+	0.00356809i
$465$		0			0
$466$	−12.8010	−	22.1719i	−0.592994	−	1.02710i
$467$	−7.45251	+	12.9081i	−0.344861	+	0.597317i	−0.985328	−	0.170669i	$-0.945407\pi$
$467$	−7.45251	+	12.9081i	−0.344861	+	0.597317i	0.640468	+	0.767985i	$0.278741\pi$
$468$	−10.8739	+	9.98570i	−0.502645	+	0.461589i
$469$	7.89185	+	16.5211i	0.364412	+	0.762872i
$470$		0			0
$471$	−1.27067	−	1.73102i	−0.0585494	−	0.0797610i
$472$	−2.87903	+	1.66221i	−0.132518	+	0.0765092i
$473$	−12.9854	+	7.49710i	−0.597067	+	0.344717i
$474$	−11.6481	−	15.8681i	−0.535016	−	0.728844i
$475$		0			0
$476$	10.4920	−	15.2848i	0.480900	−	0.700579i
$477$	−3.08456	+	2.83261i	−0.141232	+	0.129696i
$478$	8.51269	−	14.7444i	0.389362	−	0.674394i
$479$	10.9530	+	18.9712i	0.500456	+	0.866815i	1.00000		0.000526656i	$0.000167640\pi$
$479$	10.9530	+	18.9712i	0.500456	+	0.866815i	−0.499544	+	0.866289i	$0.666499\pi$
$480$		0			0
$481$	20.4762	+	11.8220i	0.933636	+	0.539035i
$482$	5.01243			0.228310
$483$	15.8321	−	29.5440i	0.720385	−	1.34430i
$484$	10.8379			0.492632
$485$		0			0
$486$	−0.338108	−	13.7887i	−0.0153369	−	0.625466i
$487$	−6.21983	−	10.7731i	−0.281848	−	0.488174i	0.689992	−	0.723817i	$-0.257614\pi$
$487$	−6.21983	−	10.7731i	−0.281848	−	0.488174i	−0.971840	+	0.235642i	$0.924281\pi$
$488$	5.89838	−	10.2163i	0.267007	−	0.462470i
$489$	−11.8027	−	5.18572i	−0.533737	−	0.234506i
$490$		0			0
$491$		−	23.2765i		−	1.05045i	−0.850962	−	0.525227i	$-0.823980\pi$
$491$		−	23.2765i		−	1.05045i	0.850962	−	0.525227i	$-0.176020\pi$
$492$	−10.9830	+	8.06217i	−0.495150	+	0.363470i
$493$	9.08043	−	5.24259i	0.408962	−	0.236114i
$494$	1.27685	−	0.737187i	0.0574480	−	0.0331676i
$495$		0			0
$496$		−	0.225074i		−	0.0101061i
$497$	−2.74510	+	35.1389i	−0.123135	+	1.57620i
$498$	7.08997	−	16.1368i	0.317709	−	0.723108i
$499$	13.2171	−	22.8927i	0.591680	−	1.02482i	−0.402327	−	0.915496i	$-0.631798\pi$
$499$	13.2171	−	22.8927i	0.591680	−	1.02482i	0.994006	−	0.109323i	$-0.0348683\pi$
$500$		0			0
$501$	0.475101	+	4.31659i	0.0212260	+	0.192851i
$502$	−5.02551	−	2.90148i	−0.224300	−	0.129499i
$503$	17.4645			0.778702			0.389351	−	0.921090i	$-0.372699\pi$
$503$	17.4645			0.778702			0.389351	+	0.921090i	$0.372699\pi$
$504$	−3.18148	−	22.3685i	−0.141714	−	0.996373i
$505$		0			0
$506$	−8.11319	−	4.68415i	−0.360675	−	0.208236i
$507$	0.634404	+	5.76395i	0.0281749	+	0.255986i
$508$	5.57555	+	9.65714i	0.247375	+	0.428466i
$509$	−1.20504	+	2.08719i	−0.0534124	+	0.0925129i	−0.891495	−	0.453030i	$-0.850343\pi$
$509$	−1.20504	+	2.08719i	−0.0534124	+	0.0925129i	0.838083	+	0.545543i	$0.183676\pi$
$510$		0			0
$511$	−7.50768	+	3.58630i	−0.332120	+	0.158648i
$512$			0.954733i			0.0421937i
$513$	0.414376	−	2.10098i	0.0182951	−	0.0927607i
$514$	6.69176	−	3.86349i	0.295161	−	0.170411i
$515$		0			0
$516$	17.6029	−	12.9216i	0.774924	−	0.568841i
$517$		−	15.7309i		−	0.691846i
$518$	−12.3525	+	5.90059i	−0.542738	+	0.259257i
$519$	27.0363	+	11.8788i	1.18676	+	0.521424i
$520$		0			0
$521$	−15.7340	−	27.2520i	−0.689317	−	1.19393i	−0.972059	−	0.234736i	$-0.924577\pi$
$521$	−15.7340	−	27.2520i	−0.689317	−	1.19393i	0.282742	−	0.959196i	$-0.408756\pi$
$522$	1.44872	−	4.61210i	0.0634086	−	0.201866i
$523$	14.8061	+	8.54828i	0.647424	+	0.373790i	0.787469	−	0.616355i	$-0.211391\pi$
$523$	14.8061	+	8.54828i	0.647424	+	0.373790i	−0.140045	+	0.990145i	$0.544725\pi$
$524$	25.3695			1.10827
$525$		0			0
$526$	19.9451			0.869649
$527$	−13.2955	−	7.67617i	−0.579162	−	0.334379i
$528$	−0.210351	+	0.0231521i	−0.00915434	+	0.00100756i
$529$	15.2501	+	26.4140i	0.663049	+	1.14843i
$530$		0			0
$531$	2.36982	+	2.58060i	0.102841	+	0.111989i
$532$	0.103361	−	1.32308i	0.00448127	−	0.0573629i
$533$			26.1310i			1.13186i
$534$	7.07558	+	9.63896i	0.306190	+	0.417119i
$535$		0			0
$536$	−17.0595	+	9.84932i	−0.736859	+	0.425426i
$537$	12.0422	+	16.4049i	0.519658	+	0.707922i
$538$		−	12.5547i		−	0.541272i
$539$	9.45564	−	3.64220i	0.407283	−	0.156881i
$540$		0			0
$541$	10.8422	−	18.7792i	0.466142	−	0.807382i	−0.533110	−	0.846046i	$-0.678977\pi$
$541$	10.8422	−	18.7792i	0.466142	−	0.807382i	0.999252	+	0.0386641i	$0.0123102\pi$
$542$	−5.63192	−	9.75478i	−0.241912	−	0.419004i
$543$	−4.15299	+	0.457095i	−0.178222	+	0.0196158i
$544$	28.0128	+	16.1732i	1.20104	+	0.693419i
$545$		0			0
$546$	−14.4501	−	7.74356i	−0.618409	−	0.331394i
$547$	9.42694			0.403067			0.201533	−	0.979482i	$-0.435408\pi$
$547$	9.42694			0.403067			0.201533	+	0.979482i	$0.435408\pi$
$548$	9.99001	+	5.76774i	0.426752	+	0.246386i
$549$	−11.8614	−	3.72580i	−0.506231	−	0.159013i
$550$		0			0
$551$	0.375283	−	0.650009i	0.0159876	−	0.0276913i
$552$	33.0161	+	14.5062i	1.40526	+	0.617424i
$553$	−19.2320	+	28.0173i	−0.817826	+	1.19142i
$554$			25.4977i			1.08329i
$555$		0			0
$556$	−6.06551	+	3.50192i	−0.257235	+	0.148515i
$557$	4.89952	−	2.82874i	0.207599	−	0.119858i	−0.392596	−	0.919711i	$-0.628423\pi$
$557$	4.89952	−	2.82874i	0.207599	−	0.119858i	0.600195	+	0.799854i	$0.295090\pi$
$558$	−6.90888	+	1.53949i	−0.292476	+	0.0651718i
$559$		−	41.8814i		−	1.77139i
$560$		0			0
$561$	−5.80641	+	13.2154i	−0.245147	+	0.557956i
$562$	−5.95032	+	10.3063i	−0.250999	+	0.434743i
$563$	3.65140	+	6.32441i	0.153888	+	0.266542i	0.932654	−	0.360773i	$-0.117487\pi$
$563$	3.65140	+	6.32441i	0.153888	+	0.266542i	−0.778765	+	0.627315i	$0.784154\pi$
$564$	2.50636	+	22.7718i	0.105537	+	0.958868i
$565$		0			0
$566$	12.4552			0.523533
$567$	−22.2809	+	8.40005i	−0.935710	+	0.352769i
$568$	−37.9207			−1.59112
$569$	12.6704	+	7.31525i	0.531170	+	0.306671i	0.741493	−	0.670961i	$-0.234118\pi$
$569$	12.6704	+	7.31525i	0.531170	+	0.306671i	−0.210323	+	0.977632i	$0.567451\pi$
$570$		0			0
$571$	15.0693	+	26.1009i	0.630632	+	1.09229i	0.987423	+	0.158103i	$0.0505377\pi$
$571$	15.0693	+	26.1009i	0.630632	+	1.09229i	−0.356790	+	0.934184i	$0.616129\pi$
$572$	3.56177	−	6.16917i	0.148925	−	0.257946i
$573$	−9.58638	+	21.8187i	−0.400477	+	0.911487i
$574$	−12.4735	−	8.56223i	−0.520635	−	0.357380i
$575$		0			0
$576$	15.0509	−	3.35375i	0.627119	−	0.139739i
$577$	39.2538	−	22.6632i	1.63416	−	0.943482i	0.651367	−	0.758762i	$-0.274196\pi$
$577$	39.2538	−	22.6632i	1.63416	−	0.943482i	0.982791	−	0.184720i	$-0.0591377\pi$
$578$	−12.3720	+	7.14299i	−0.514608	+	0.297109i
$579$	12.8646	−	9.44341i	0.534635	−	0.392455i
$580$		0			0
$581$	−30.3364	−	2.36992i	−1.25856	−	0.0983208i
$582$	5.41727	+	2.38017i	0.224553	+	0.0986611i
$583$	1.01036	−	1.74999i	0.0418447	−	0.0724771i
$584$	−4.47583	−	7.75237i	−0.185211	−	0.320795i
$585$		0			0
$586$	−12.8073	−	7.39430i	−0.529065	−	0.305456i
$587$	27.9328			1.15291			0.576455	−	0.817129i	$-0.304436\pi$
$587$	27.9328			1.15291			0.576455	+	0.817129i	$0.304436\pi$
$588$	−13.1075	+	6.77893i	−0.540545	+	0.279558i
$589$	−1.09897			−0.0452825
$590$		0			0
$591$	−7.08853	+	0.780193i	−0.291583	+	0.0320928i
$592$	−0.246787	−	0.427448i	−0.0101429	−	0.0175680i
$593$	14.7273	−	25.5085i	0.604779	−	1.04751i	−0.387307	−	0.921951i	$-0.626595\pi$
$593$	14.7273	−	25.5085i	0.604779	−	1.04751i	0.992086	−	0.125558i	$-0.0400721\pi$
$594$	2.14947	+	6.29859i	0.0881937	+	0.258434i
$595$		0			0
$596$			7.82921i			0.320697i
$597$	−0.0821656	−	0.111933i	−0.00336281	−	0.00458111i
$598$	22.6615	−	13.0836i	0.926698	−	0.535029i
$599$	13.1940	−	7.61757i	0.539093	−	0.311245i	−0.205618	−	0.978632i	$-0.565921\pi$
$599$	13.1940	−	7.61757i	0.539093	−	0.311245i	0.744711	+	0.667387i	$0.232587\pi$
$600$		0			0
$601$			18.6064i			0.758970i	0.925198	+	0.379485i	$0.123899\pi$
$601$			18.6064i			0.758970i	−0.925198	+	0.379485i	$0.876101\pi$
$602$	19.9919	+	13.7231i	0.814808	+	0.559310i
$603$	14.0422	+	15.2912i	0.571844	+	0.622707i
$604$	−2.50729	+	4.34275i	−0.102020	+	0.176704i
$605$		0			0
$606$	−20.1487	+	2.21765i	−0.818486	+	0.0900859i
$607$	−16.5452	−	9.55240i	−0.671550	−	0.387720i	0.125113	−	0.992142i	$-0.460071\pi$
$607$	−16.5452	−	9.55240i	−0.671550	−	0.387720i	−0.796664	+	0.604423i	$0.793404\pi$
$608$	2.31547			0.0939046
$609$	−8.34167	+	0.264185i	−0.338022	+	0.0107053i
$610$		0			0
$611$	38.0525	+	21.9696i	1.53944	+	0.888795i
$612$	6.29969	−	20.0555i	0.254650	−	0.810697i
$613$	−6.23054	−	10.7916i	−0.251649	−	0.435869i	0.712331	−	0.701844i	$-0.247640\pi$
$613$	−6.23054	−	10.7916i	−0.251649	−	0.435869i	−0.963980	+	0.265975i	$0.914306\pi$
$614$	−4.30131	+	7.45009i	−0.173587	+	0.300661i
$615$		0			0
$616$	4.69902	+	9.83710i	0.189329	+	0.396348i
$617$			19.4451i			0.782829i	0.920214	+	0.391414i	$0.128014\pi$
$617$			19.4451i			0.782829i	−0.920214	+	0.391414i	$0.871986\pi$
$618$	20.9906	−	15.4084i	0.844367	−	0.619816i
$619$	−9.61812	+	5.55302i	−0.386585	+	0.223195i	−0.680679	−	0.732582i	$-0.738315\pi$
$619$	−9.61812	+	5.55302i	−0.386585	+	0.223195i	0.294095	+	0.955776i	$0.404982\pi$
$620$		0			0
$621$	7.35435	−	37.2883i	0.295120	−	1.49633i
$622$			4.43684i			0.177901i
$623$	11.6824	−	17.0189i	0.468044	−	0.681850i
$624$	0.237769	−	0.541163i	0.00951837	−	0.0216639i
$625$		0			0
$626$	7.84330	+	13.5850i	0.313481	+	0.542966i
$627$	0.113045	+	1.02709i	0.00451460	+	0.0410179i
$628$	−1.30677	−	0.754465i	−0.0521459	−	0.0301064i
$629$	−33.6669			−1.34239
$630$		0			0
$631$	9.89504			0.393915			0.196958	−	0.980412i	$-0.436894\pi$
$631$	9.89504			0.393915			0.196958	+	0.980412i	$0.436894\pi$
$632$	−31.6634	−	18.2809i	−1.25950	−	0.727174i
$633$	−3.33135	−	30.2673i	−0.132409	−	1.20302i
$634$	1.85905	+	3.21996i	0.0738322	+	0.127881i
$635$		0			0
$636$	−1.18375	+	2.69423i	−0.0469389	+	0.106833i
$637$	−4.39528	+	27.9594i	−0.174147	+	1.10779i
$638$			2.33262i			0.0923493i
$639$	8.69217	+	39.0085i	0.343857	+	1.54315i
$640$		0			0
$641$	−2.40816	+	1.39035i	−0.0951166	+	0.0549156i	−0.546804	−	0.837261i	$-0.684156\pi$
$641$	−2.40816	+	1.39035i	−0.0951166	+	0.0549156i	0.451687	+	0.892176i	$0.350822\pi$
$642$	15.9962	−	11.7422i	0.631320	−	0.463427i
$643$			37.8005i			1.49071i	0.666669	+	0.745354i	$0.267719\pi$
$643$			37.8005i			1.49071i	−0.666669	+	0.745354i	$0.732281\pi$
$644$	1.83445	−	23.4821i	0.0722876	−	0.925325i
$645$		0			0
$646$	−1.04969	+	1.81812i	−0.0412995	+	0.0715329i
$647$	−10.1708	−	17.6163i	−0.399855	−	0.692569i	0.593853	−	0.804574i	$-0.297606\pi$
$647$	−10.1708	−	17.6163i	−0.399855	−	0.692569i	−0.993708	+	0.112005i	$0.964273\pi$
$648$	−10.8771	−	23.1951i	−0.427292	−	0.911188i
$649$	−1.46408	−	0.845285i	−0.0574700	−	0.0331803i
$650$		0			0
$651$	6.44191	+	10.3841i	0.252478	+	0.406984i
$652$	−9.05901			−0.354778
$653$	21.5592	+	12.4472i	0.843677	+	0.487097i	0.858512	−	0.512793i	$-0.171389\pi$
$653$	21.5592	+	12.4472i	0.843677	+	0.487097i	−0.0148355	+	0.999890i	$0.504722\pi$
$654$	−11.0724	+	1.21868i	−0.432966	+	0.0476540i
$655$		0			0
$656$	0.272747	−	0.472411i	0.0106490	−	0.0184446i
$657$	−6.94880	+	6.38122i	−0.271099	+	0.248955i
$658$	−22.9556	+	10.9655i	−0.894901	+	0.427480i
$659$		−	29.3981i		−	1.14519i	−0.819840	−	0.572593i	$-0.805938\pi$
$659$		−	29.3981i		−	1.14519i	0.819840	−	0.572593i	$-0.194062\pi$
$660$		0			0
$661$	17.1948	−	9.92744i	0.668801	−	0.386133i	−0.126821	−	0.991926i	$-0.540477\pi$
$661$	17.1948	−	9.92744i	0.668801	−	0.386133i	0.795622	+	0.605793i	$0.207144\pi$
$662$	1.04234	−	0.601794i	0.0405116	−	0.0233894i
$663$	−23.8584	−	32.5019i	−0.926583	−	1.26227i
$664$		−	32.7380i		−	1.27048i
$665$		0			0
$666$	−11.4330	+	10.4991i	−0.443019	+	0.406833i
$667$	6.66053	−	11.5364i	0.257897	−	0.446690i
$668$	1.52579	+	2.64275i	0.0590347	+	0.102251i
$669$	−47.3395	+	5.21038i	−1.83025	+	0.201445i
$670$		0			0
$671$	5.99903			0.231590
$672$	−13.5727	−	21.8786i	−0.523577	−	0.843984i
$673$	−17.4983			−0.674509			−0.337255	−	0.941414i	$-0.609498\pi$
$673$	−17.4983			−0.674509			−0.337255	+	0.941414i	$0.609498\pi$
$674$	−20.1237	−	11.6184i	−0.775136	−	0.447525i
$675$		0			0
$676$	2.03740	+	3.52888i	0.0783614	+	0.135726i
$677$	−2.18727	+	3.78846i	−0.0840635	+	0.145602i	−0.904992	−	0.425429i	$-0.860123\pi$
$677$	−2.18727	+	3.78846i	−0.0840635	+	0.145602i	0.820928	+	0.571031i	$0.193457\pi$
$678$	6.71396	+	2.94989i	0.257848	+	0.113290i
$679$	0.795603	−	10.1842i	0.0305324	−	0.390834i
$680$		0			0
$681$	17.3206	−	12.7143i	0.663725	−	0.487215i
$682$	2.95783	−	1.70771i	0.113261	−	0.0653915i
$683$	−25.4692	+	14.7046i	−0.974550	+	0.562657i	−0.900620	−	0.434606i	$-0.856887\pi$
$683$	−25.4692	+	14.7046i	−0.974550	+	0.562657i	−0.0739300	+	0.997263i	$0.523554\pi$
$684$	−0.327285	−	1.46878i	−0.0125141	−	0.0561603i
$685$		0			0
$686$	−11.9061	−	11.2594i	−0.454578	−	0.429886i
$687$	18.9471	−	43.1238i	0.722878	−	1.64527i
$688$	−0.437143	+	0.757154i	−0.0166659	+	0.0288662i
$689$	2.82210	+	4.88802i	0.107513	+	0.186219i
$690$		0			0
$691$	−43.6753	−	25.2160i	−1.66149	−	0.959260i	−0.972006	−	0.234956i	$-0.924505\pi$
$691$	−43.6753	−	25.2160i	−1.66149	−	0.959260i	−0.689481	−	0.724304i	$-0.742161\pi$
$692$	20.7513			0.788848
$693$	9.04218	−	7.08868i	0.343484	−	0.269277i
$694$	5.55506			0.210867
$695$		0			0
$696$	−0.982355	−	8.92530i	−0.0372361	−	0.338312i
$697$	−18.6041	−	32.2233i	−0.704682	−	1.22055i
$698$	−2.20948	+	3.82693i	−0.0836301	+	0.144852i
$699$	−20.1597	+	45.8835i	−0.762509	+	1.73547i
$700$		0			0
$701$			19.8266i			0.748842i	0.927259	+	0.374421i	$0.122159\pi$
$701$			19.8266i			0.748842i	−0.927259	+	0.374421i	$0.877841\pi$
$702$	−18.2379	−	3.59705i	−0.688346	−	0.135762i
$703$	−2.08712	+	1.20500i	−0.0787171	+	0.0454473i
$704$	−6.44358	+	3.72020i	−0.242852	+	0.140210i
$705$		0			0
$706$		−	0.696982i		−	0.0262313i
$707$	15.0838	+	31.5769i	0.567284	+	1.18757i
$708$	2.25405	+	0.990353i	0.0847123	+	0.0372197i
$709$	13.2605	−	22.9678i	0.498008	−	0.862575i	−0.501990	−	0.864874i	$-0.667398\pi$
$709$	13.2605	−	22.9678i	0.498008	−	0.862575i	0.999997	+	0.00229888i	$0.000731757\pi$
$710$		0			0
$711$	−11.5474	+	36.7620i	−0.433062	+	1.37868i
$712$	19.2338	+	11.1046i	0.720816	+	0.416163i
$713$	−19.5046			−0.730455
$714$	23.3322	−	0.738942i	0.873186	−	0.0276542i
$715$		0			0
$716$	12.3843	+	7.15008i	0.462823	+	0.267211i
$717$	−33.1279	+	3.64619i	−1.23718	+	0.136170i
$718$	11.2124	+	19.4204i	0.418442	+	0.724763i
$719$	1.12519	−	1.94889i	0.0419627	−	0.0726815i	−0.844281	−	0.535900i	$-0.819972\pi$
$719$	1.12519	−	1.94889i	0.0419627	−	0.0726815i	0.886244	+	0.463219i	$0.153306\pi$
$720$		0			0
$721$	−37.0619	−	25.4405i	−1.38026	−	0.947453i
$722$		−	16.6611i		−	0.620061i
$723$	−5.80623	−	7.90974i	−0.215936	−	0.294167i
$724$	−2.54259	+	1.46797i	−0.0944947	+	0.0545566i
$725$		0			0
$726$	8.07530	+	11.0009i	0.299702	+	0.408280i
$727$			6.85964i			0.254410i	0.991876	+	0.127205i	$0.0406006\pi$
$727$			6.85964i			0.254410i	−0.991876	+	0.127205i	$0.959399\pi$
$728$	−30.3581	−	2.37162i	−1.12515	−	0.0878980i
$729$	−21.3672	+	16.5059i	−0.791377	+	0.611328i
$730$		0			0
$731$	29.8177	+	51.6458i	1.10285	+	1.91019i
$732$	−8.68409	+	0.955807i	−0.320973	+	0.0353276i
$733$	4.77925	+	2.75930i	0.176526	+	0.101917i	0.585659	−	0.810557i	$-0.300836\pi$
$733$	4.77925	+	2.75930i	0.176526	+	0.101917i	−0.409134	+	0.912474i	$0.634169\pi$
$734$	1.61560			0.0596327
$735$		0			0
$736$	41.0950			1.51478
$737$	−8.67531	−	5.00869i	−0.319559	−	0.184498i
$738$	−16.3668	−	5.14100i	−0.602469	−	0.189243i
$739$	−5.01222	−	8.68142i	−0.184378	−	0.319351i	0.758989	−	0.651103i	$-0.225694\pi$
$739$	−5.01222	−	8.68142i	−0.184378	−	0.319351i	−0.943367	+	0.331752i	$0.892360\pi$
$740$		0			0
$741$	−2.64236	−	1.16096i	−0.0970694	−	0.0426490i
$742$	−3.25798	−	0.254518i	−0.119604	−	0.00934363i
$743$		−	26.2588i		−	0.963342i	−0.876352	−	0.481671i	$-0.840030\pi$
$743$		−	26.2588i		−	0.963342i	0.876352	−	0.481671i	$-0.159970\pi$
$744$	−10.5984	+	7.77985i	−0.388555	+	0.285223i
$745$		0			0
$746$	−1.60930	+	0.929132i	−0.0589208	+	0.0340180i
$747$	−33.6771	+	7.50419i	−1.23218	+	0.274564i
$748$			10.1433i			0.370876i
$749$	−28.2436	−	19.3873i	−1.03200	−	0.708396i
$750$		0			0
$751$	−5.68833	+	9.85247i	−0.207570	+	0.359522i	−0.950949	−	0.309349i	$-0.899889\pi$
$751$	−5.68833	+	9.85247i	−0.207570	+	0.359522i	0.743378	+	0.668871i	$0.233222\pi$
$752$	−0.458622	−	0.794357i	−0.0167242	−	0.0289672i
$753$	1.24277	+	11.2914i	0.0452892	+	0.411480i
$754$	−5.64251	−	3.25770i	−0.205488	−	0.118639i
$755$		0			0
$756$	−11.9599	+	11.7021i	−0.434977	+	0.425602i
$757$	−20.1866			−0.733693			−0.366847	−	0.930281i	$-0.619563\pi$
$757$	−20.1866			−0.733693			−0.366847	+	0.930281i	$0.619563\pi$
$758$	−14.7204	−	8.49884i	−0.534670	−	0.308692i
$759$	2.00634	+	18.2288i	0.0728254	+	0.661663i
$760$		0			0
$761$	2.04697	−	3.54546i	0.0742026	−	0.128523i	−0.826537	−	0.562883i	$-0.809692\pi$
$761$	2.04697	−	3.54546i	0.0742026	−	0.128523i	0.900739	+	0.434360i	$0.143026\pi$
$762$	−5.64801	+	12.8549i	−0.204606	+	0.465684i
$763$	8.28907	+	17.3526i	0.300084	+	0.628207i
$764$			16.7466i			0.605871i
$765$		0			0
$766$	−2.42189	+	1.39828i	−0.0875066	+	0.0505219i
$767$	4.08941	−	2.36102i	0.147660	−	0.0852516i
$768$	22.6169	−	16.6022i	0.816118	−	0.599080i
$769$			8.66796i			0.312575i	0.987712	+	0.156287i	$0.0499526\pi$
$769$			8.66796i			0.312575i	−0.987712	+	0.156287i	$0.950047\pi$
$770$		0			0
$771$	−13.8482	−	6.08443i	−0.498730	−	0.219125i
$772$	5.60706	−	9.71171i	0.201803	−	0.349532i
$773$	−22.1640	−	38.3891i	−0.797183	−	1.38076i	−0.921444	−	0.388512i	$-0.872989\pi$
$773$	−22.1640	−	38.3891i	−0.797183	−	1.38076i	0.124261	−	0.992250i	$-0.460344\pi$
$774$	26.2317	+	8.23971i	0.942880	+	0.296170i
$775$		0			0
$776$	10.9904			0.394533
$777$	23.6200	+	12.6575i	0.847363	+	0.454086i
$778$	9.98209			0.357875
$779$	−2.30666	−	1.33175i	−0.0826446	−	0.0477149i
$780$		0			0
$781$	−9.64194	−	16.7003i	−0.345016	−	0.597585i
$782$	−18.6299	+	32.2680i	−0.666206	+	1.15390i
$783$	−8.95615	+	3.05639i	−0.320067	+	0.109226i
$784$	0.371291	−	0.459590i	0.0132604	−	0.0164139i
$785$		0			0
$786$	18.9028	+	25.7510i	0.674239	+	0.918506i
$787$	21.8059	−	12.5896i	0.777296	−	0.448772i	−0.0581753	−	0.998306i	$-0.518528\pi$
$787$	21.8059	−	12.5896i	0.777296	−	0.448772i	0.835471	+	0.549535i	$0.185195\pi$
$788$	−4.33982	+	2.50560i	−0.154600	+	0.0892583i
$789$	−23.1038	−	31.4739i	−0.822516	−	1.12050i
$790$		0			0
$791$	0.986040	−	12.6219i	0.0350596	−	0.448783i
$792$	8.36114	+	9.10482i	0.297100	+	0.323526i
$793$	−8.37815	+	14.5114i	−0.297517	+	0.515314i
$794$	13.5452	+	23.4610i	0.480702	+	0.832600i
$795$		0			0
$796$	−0.0845000	−	0.0487861i	−0.00299502	−	0.00172918i
$797$	−48.5237			−1.71880			−0.859400	−	0.511305i	$-0.829162\pi$
$797$	−48.5237			−1.71880			−0.859400	+	0.511305i	$0.829162\pi$
$798$	1.41999	−	0.880910i	0.0502670	−	0.0311839i
$799$	−62.5656			−2.21341
$800$		0			0
$801$	7.01441	−	22.3309i	0.247842	−	0.789024i
$802$	10.4484	+	18.0972i	0.368947	+	0.639034i
$803$	2.27610	−	3.94232i	0.0803219	−	0.139122i
$804$	13.3562	+	5.86829i	0.471039	+	0.206958i
$805$		0			0
$806$			9.53983i			0.336026i
$807$	−19.8117	+	14.5430i	−0.697403	+	0.511936i
$808$	−32.6061	+	18.8251i	−1.14708	+	0.662266i
$809$	0.751275	−	0.433749i	0.0264134	−	0.0152498i	−0.486735	−	0.873550i	$-0.661812\pi$
$809$	0.751275	−	0.433749i	0.0264134	−	0.0152498i	0.513149	+	0.858300i	$0.328479\pi$
$810$		0			0
$811$		−	19.2304i		−	0.675271i	−0.941277	−	0.337636i	$-0.890373\pi$
$811$		−	19.2304i		−	0.675271i	0.941277	−	0.337636i	$-0.109627\pi$
$812$	−5.29188	+	2.52785i	−0.185709	+	0.0887100i
$813$	−8.86946	+	20.1869i	−0.311065	+	0.707986i
$814$	3.74491	−	6.48637i	0.131259	−	0.227347i
$815$		0			0
$816$	0.0920811	+	0.836613i	0.00322348	+	0.0292873i
$817$	3.69699	+	2.13446i	0.129341	+	0.0746751i
$818$	−11.3827			−0.397987
$819$	4.51903	+	31.7726i	0.157908	+	1.11022i
$820$		0			0
$821$	32.0917	+	18.5281i	1.12001	+	0.646636i	0.941403	−	0.337285i	$-0.109509\pi$
$821$	32.0917	+	18.5281i	1.12001	+	0.646636i	0.178604	+	0.983921i	$0.442842\pi$
$822$	1.58908	+	14.4377i	0.0554254	+	0.503574i
$823$	12.2789	+	21.2677i	0.428016	+	0.741345i	0.996697	−	0.0812133i	$-0.0258795\pi$
$823$	12.2789	+	21.2677i	0.428016	+	0.741345i	−0.568681	+	0.822558i	$0.692546\pi$
$824$	24.1824	−	41.8851i	0.842432	−	1.45914i
$825$		0			0
$826$	−0.212934	+	2.72569i	−0.00740894	+	0.0948388i
$827$		−	28.2836i		−	0.983518i	−0.870731	−	0.491759i	$-0.836354\pi$
$827$		−	28.2836i		−	0.983518i	0.870731	−	0.491759i	$-0.163646\pi$
$828$	−5.80867	−	26.0680i	−0.201865	−	0.905926i
$829$	41.6000	−	24.0178i	1.44483	−	0.834171i	0.446660	−	0.894704i	$-0.352613\pi$
$829$	41.6000	−	24.0178i	1.44483	−	0.834171i	0.998166	+	0.0605325i	$0.0192799\pi$
$830$		0			0
$831$	40.2359	−	29.5356i	1.39577	−	1.02458i
$832$		−	20.7823i		−	0.720497i
$833$	−14.4859	−	37.6073i	−0.501906	−	1.30301i
$834$	−8.07397	−	3.54743i	−0.279579	−	0.122837i
$835$		0			0
$836$	0.363047	+	0.628816i	0.0125562	+	0.0217480i
$837$	10.4324	+	9.11910i	0.360596	+	0.315202i
$838$	−2.89717	−	1.67268i	−0.100081	−	0.0577818i
$839$	−26.6446			−0.919874			−0.459937	−	0.887952i	$-0.652128\pi$
$839$	−26.6446			−0.919874			−0.459937	+	0.887952i	$0.652128\pi$
$840$		0			0
$841$	25.6832			0.885627
$842$	−1.86707	−	1.07796i	−0.0643436	−	0.0371488i
$843$	23.1562	−	2.54867i	0.797541	−	0.0877807i
$844$	−10.6987	−	18.5306i	−0.368263	−	0.637850i
$845$		0			0
$846$	−21.2467	+	19.5113i	−0.730478	+	0.670812i
$847$	13.3330	−	19.4236i	0.458126	−	0.667402i
$848$		−	0.117824i		−	0.00404611i
$849$	−14.4277	−	19.6547i	−0.495158	−	0.674547i
$850$		0			0
$851$	−37.0422	+	21.3863i	−1.26979	+	0.733114i
$852$	16.6183	+	22.6389i	0.569334	+	0.775596i
$853$		−	35.4466i		−	1.21367i	−0.794829	−	0.606834i	$-0.792439\pi$
$853$		−	35.4466i		−	1.21367i	0.794829	−	0.606834i	$-0.207561\pi$
$854$	−4.18171	−	8.75415i	−0.143095	−	0.299561i
$855$		0			0
$856$	18.4285	−	31.9191i	0.629874	−	1.09097i
$857$	5.70072	+	9.87394i	0.194733	+	0.337287i	0.946813	−	0.321785i	$-0.104283\pi$
$857$	5.70072	+	9.87394i	0.194733	+	0.337287i	−0.752080	+	0.659072i	$0.770949\pi$
$858$	8.91580	−	0.981310i	0.304380	−	0.0335014i
$859$	−18.3838	−	10.6139i	−0.627248	−	0.362142i	0.152438	−	0.988313i	$-0.451288\pi$
$859$	−18.3838	−	10.6139i	−0.627248	−	0.362142i	−0.779686	+	0.626171i	$0.784621\pi$
$860$		0			0
$861$	0.937501	+	29.6017i	0.0319500	+	1.00882i
$862$	−27.0296			−0.920633
$863$	1.21717	+	0.702733i	0.0414329	+	0.0239213i	0.520573	−	0.853817i	$-0.325718\pi$
$863$	1.21717	+	0.702733i	0.0414329	+	0.0239213i	−0.479140	+	0.877738i	$0.659052\pi$
$864$	−21.9803	−	19.2133i	−0.747785	−	0.653651i
$865$		0			0
$866$	16.7118	−	28.9456i	0.567889	−	0.983612i
$867$	25.6031	+	11.2492i	0.869528	+	0.382042i
$868$	7.07956	+	4.85964i	0.240296	+	0.164947i
$869$		−	18.5928i		−	0.630718i
$870$		0			0
$871$	24.2316	−	13.9901i	0.821057	−	0.474037i
$872$	−17.9182	+	10.3451i	−0.606786	+	0.350328i
$873$	−2.51922	−	11.3057i	−0.0852628	−	0.382640i
$874$			2.66719i			0.0902192i
$875$		0			0
$876$	−2.66673	+	6.06949i	−0.0901004	+	0.205069i
$877$	1.05597	−	1.82900i	0.0356577	−	0.0617610i	−0.847646	−	0.530563i	$-0.821981\pi$
$877$	1.05597	−	1.82900i	0.0356577	−	0.0617610i	0.883304	+	0.468802i	$0.155314\pi$
$878$	−1.81486	−	3.14343i	−0.0612486	−	0.106086i
$879$	3.16716	+	28.7755i	0.106826	+	0.970575i
$880$		0			0
$881$	−35.9949			−1.21270			−0.606349	−	0.795199i	$-0.707366\pi$
$881$	−35.9949			−1.21270			−0.606349	+	0.795199i	$0.707366\pi$
$882$	−16.6472	−	8.25363i	−0.560541	−	0.277914i
$883$	−17.2298			−0.579828			−0.289914	−	0.957053i	$-0.593627\pi$
$883$	−17.2298			−0.579828			−0.289914	+	0.957053i	$0.593627\pi$
$884$	−24.5362	−	14.1660i	−0.825242	−	0.476454i
$885$		0			0
$886$	11.6122	+	20.1130i	0.390121	+	0.675709i
$887$	−3.12159	+	5.40675i	−0.104813	+	0.181541i	−0.913662	−	0.406476i	$-0.866758\pi$
$887$	−3.12159	+	5.40675i	−0.104813	+	0.181541i	0.808849	+	0.588016i	$0.200091\pi$
$888$	−11.5975	+	26.3959i	−0.389186	+	0.885789i
$889$	24.1665	+	1.88792i	0.810520	+	0.0633189i
$890$		0			0
$891$	7.44947	−	10.6880i	0.249567	−	0.358061i
$892$	−28.9827	+	16.7332i	−0.970414	+	0.560269i
$893$	−3.87864	+	2.23933i	−0.129794	+	0.0749364i
$894$	−7.94693	+	5.83353i	−0.265785	+	0.195102i
$895$		0			0
$896$	−14.5904	−	10.0153i	−0.487430	−	0.334587i
$897$	−46.8966	−	20.6048i	−1.56583	−	0.687974i
$898$	6.47602	−	11.2168i	0.216108	−	0.374309i
$899$	2.42824	+	4.20583i	0.0809863	+	0.140272i
$900$		0			0
$901$	−6.96011	−	4.01842i	−0.231875	−	0.133873i
$902$	8.27767			0.275616
$903$	−1.50257	−	47.4440i	−0.0500026	−	1.57884i
$904$	13.6211			0.453032
$905$		0			0
$906$	−6.27621	+	0.690786i	−0.208513	+	0.0229498i
$907$	−19.7880	−	34.2738i	−0.657049	−	1.13804i	−0.981376	−	0.192097i	$-0.938471\pi$
$907$	−19.7880	−	34.2738i	−0.657049	−	1.13804i	0.324327	−	0.945945i	$-0.394862\pi$
$908$	7.54918	−	13.0756i	0.250528	−	0.433928i
$909$	26.8391	+	29.2263i	0.890197	+	0.969376i
$910$		0			0
$911$		−	24.4007i		−	0.808431i	−0.914664	−	0.404215i	$-0.867545\pi$
$911$		−	24.4007i		−	0.808431i	0.914664	−	0.404215i	$-0.132455\pi$
$912$	0.0356523	+	0.0485685i	0.00118056	+	0.00160827i
$913$	14.4178	−	8.32415i	0.477161	−	0.275489i
$914$	−22.3658	+	12.9129i	−0.739795	+	0.427121i
$915$		0			0
$916$		−	33.0990i		−	1.09362i
$917$	31.2100	−	45.4669i	1.03064	−	1.50145i
$918$	25.0509	−	8.54892i	0.826804	−	0.282156i
$919$	10.5155	−	18.2133i	0.346873	−	0.600802i	−0.638819	−	0.769357i	$-0.720577\pi$
$919$	10.5155	−	18.2133i	0.346873	−	0.600802i	0.985692	+	0.168555i	$0.0539100\pi$
$920$		0			0
$921$	16.7389	−	1.84236i	0.551566	−	0.0607077i
$922$	−12.1296	−	7.00305i	−0.399468	−	0.230633i
$923$	53.8632			1.77293
$924$	3.81352	−	7.11635i	0.125455	−	0.234111i
$925$		0			0
$926$	14.6714	+	8.47052i	0.482131	+	0.278358i
$927$	−48.6297	−	15.2752i	−1.59721	−	0.501702i
$928$	−5.11613	−	8.86140i	−0.167945	−	0.290890i
$929$	−6.50741	+	11.2712i	−0.213501	+	0.369795i	−0.952808	−	0.303574i	$-0.901820\pi$
$929$	−6.50741	+	11.2712i	−0.213501	+	0.369795i	0.739307	+	0.673369i	$0.235153\pi$
$930$		0			0
$931$	−2.24405	−	1.81292i	−0.0735459	−	0.0594160i
$932$			35.2172i			1.15358i
$933$	7.00144	−	5.13949i	0.229217	−	0.168259i
$934$	−11.4212	+	6.59404i	−0.373713	+	0.215764i
$935$		0			0
$936$	−33.7012	+	7.50956i	−1.10156	+	0.245458i
$937$			29.9338i			0.977896i	0.872313	+	0.488948i	$0.162619\pi$
$937$			29.9338i			0.977896i	−0.872313	+	0.488948i	$0.837381\pi$
$938$	−1.26173	+	16.1509i	−0.0411970	+	0.527346i
$939$	12.3521	−	28.1133i	0.403094	−	0.917444i
$940$		0			0
$941$	3.58035	+	6.20135i	0.116716	+	0.202158i	0.918464	−	0.395504i	$-0.129430\pi$
$941$	3.58035	+	6.20135i	0.116716	+	0.202158i	−0.801748	+	0.597662i	$0.796097\pi$
$942$	−0.207864	−	1.88857i	−0.00677257	−	0.0615329i
$943$	−40.9387	−	23.6360i	−1.33315	−	0.769693i
$944$	−0.0985743			−0.00320832
$945$		0			0
$946$	−13.2670			−0.431347
$947$	20.0088	+	11.5521i	0.650200	+	0.375393i	0.788533	−	0.614993i	$-0.210841\pi$
$947$	20.0088	+	11.5521i	0.650200	+	0.375393i	−0.138333	+	0.990386i	$0.544174\pi$
$948$	2.96234	+	26.9146i	0.0962122	+	0.874147i
$949$	6.35754	+	11.0116i	0.206374	+	0.357451i
$950$		0			0
$951$	2.92773	−	6.66352i	0.0949380	−	0.216079i
$952$	39.1244	−	18.6891i	1.26803	−	0.605717i
$953$			42.4806i			1.37608i	0.725672	+	0.688040i	$0.241529\pi$
$953$			42.4806i			1.37608i	−0.725672	+	0.688040i	$0.758471\pi$
$954$	−3.61675	+	0.805912i	−0.117097	+	0.0260924i
$955$		0			0
$956$	−20.2820	+	11.7098i	−0.655965	+	0.378722i
$957$	3.68093	−	2.70203i	0.118988	−	0.0873442i
$958$			19.3826i			0.626225i
$959$	22.6267	−	10.8084i	0.730655	−	0.349022i
$960$		0			0
$961$	−11.9446	+	20.6886i	−0.385309	+	0.667375i
$962$	10.4602	+	18.1175i	0.337249	+	0.584133i
$963$	−37.0590	−	11.6407i	−1.19421	−	0.375115i
$964$	−5.97119	−	3.44747i	−0.192319	−	0.111036i
$965$		0			0
$966$	25.2020	−	15.6344i	0.810861	−	0.503029i
$967$	2.04795			0.0658575			0.0329288	−	0.999458i	$-0.489517\pi$
$967$	2.04795			0.0658575			0.0329288	+	0.999458i	$0.489517\pi$
$968$	21.9513	+	12.6736i	0.705542	+	0.407345i
$969$	4.08496	−	0.449608i	0.131228	−	0.0144435i
$970$		0			0
$971$	29.0027	−	50.2341i	0.930740	−	1.61209i	0.148679	−	0.988885i	$-0.452498\pi$
$971$	29.0027	−	50.2341i	0.930740	−	1.61209i	0.782060	−	0.623203i	$-0.214169\pi$
$972$	−9.08084	+	16.6587i	−0.291268	+	0.534326i
$973$	−1.18578	+	15.1786i	−0.0380142	+	0.486605i
$974$		−	11.0067i		−	0.352678i
$975$		0			0
$976$	0.302930	−	0.174897i	0.00969655	−	0.00559830i
$977$	43.0694	−	24.8661i	1.37791	−	0.795538i	0.386004	−	0.922497i	$-0.373855\pi$
$977$	43.0694	−	24.8661i	1.37791	−	0.795538i	0.991908	+	0.126960i	$0.0405219\pi$
$978$	−6.74984	−	9.19521i	−0.215836	−	0.294030i
$979$			11.2941i			0.360961i
$980$		0			0
$981$	14.7490	+	16.0609i	0.470900	+	0.512785i
$982$	10.2976	−	17.8360i	0.328610	−	0.569170i
$983$	−6.95123	−	12.0399i	−0.221710	−	0.384013i	0.733617	−	0.679563i	$-0.237830\pi$
$983$	−6.95123	−	12.0399i	−0.221710	−	0.384013i	−0.955327	+	0.295550i	$0.904497\pi$
$984$	−31.6728	+	3.48604i	−1.00969	+	0.111131i
$985$		0			0
$986$	9.27737			0.295452
$987$	43.8948	+	23.5224i	1.39719	+	0.748726i
$988$	−2.02810			−0.0645226
$989$	65.6142	+	37.8824i	2.08641	+	1.20459i
$990$		0			0
$991$	−4.79414	−	8.30370i	−0.152291	−	0.263776i	0.779778	−	0.626056i	$-0.215332\pi$
$991$	−4.79414	−	8.30370i	−0.152291	−	0.263776i	−0.932069	+	0.362280i	$0.881998\pi$
$992$	−7.49102	+	12.9748i	−0.237840	+	0.411951i
$993$	−2.15705	−	0.947737i	−0.0684521	−	0.0300755i
$994$	−17.6491	+	25.7113i	−0.559795	+	0.815514i
$995$		0			0
$996$	−19.5448	+	14.3470i	−0.619299	+	0.454603i
$997$	20.5651	−	11.8733i	0.651303	−	0.376030i	−0.137652	−	0.990481i	$-0.543956\pi$
$997$	20.5651	−	11.8733i	0.651303	−	0.376030i	0.788955	+	0.614451i	$0.210622\pi$
$998$	20.2557	−	11.6946i	0.641182	−	0.370187i
$999$	29.8115	+	5.87970i	0.943193	+	0.186025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.t.h.26.6	yes	20
3.2	odd	2	inner	525.2.t.h.26.5	✓	20
5.2	odd	4		525.2.q.g.299.9		40
5.3	odd	4		525.2.q.g.299.12		40
5.4	even	2		525.2.t.i.26.5	yes	20
7.3	odd	6	inner	525.2.t.h.101.5	yes	20
15.2	even	4		525.2.q.g.299.11		40
15.8	even	4		525.2.q.g.299.10		40
15.14	odd	2		525.2.t.i.26.6	yes	20
21.17	even	6	inner	525.2.t.h.101.6	yes	20
35.3	even	12		525.2.q.g.374.11		40
35.17	even	12		525.2.q.g.374.10		40
35.24	odd	6		525.2.t.i.101.6	yes	20
105.17	odd	12		525.2.q.g.374.12		40
105.38	odd	12		525.2.q.g.374.9		40
105.59	even	6		525.2.t.i.101.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.q.g.299.9		40	5.2	odd	4
525.2.q.g.299.10		40	15.8	even	4
525.2.q.g.299.11		40	15.2	even	4
525.2.q.g.299.12		40	5.3	odd	4
525.2.q.g.374.9		40	105.38	odd	12
525.2.q.g.374.10		40	35.17	even	12
525.2.q.g.374.11		40	35.3	even	12
525.2.q.g.374.12		40	105.17	odd	12
525.2.t.h.26.5	✓	20	3.2	odd	2	inner
525.2.t.h.26.6	yes	20	1.1	even	1	trivial
525.2.t.h.101.5	yes	20	7.3	odd	6	inner
525.2.t.h.101.6	yes	20	21.17	even	6	inner
525.2.t.i.26.5	yes	20	5.4	even	2
525.2.t.i.26.6	yes	20	15.14	odd	2
525.2.t.i.101.5	yes	20	105.59	even	6
525.2.t.i.101.6	yes	20	35.24	odd	6

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766266 + 0.442404i) q^{2} +(-0.189492 - 1.72165i) q^{3} +(-0.608557 - 1.05405i) q^{4} +(0.616465 - 1.40308i) q^{6} +(-2.63771 - 0.206062i) q^{7} -2.84653i q^{8} +(-2.92819 + 0.652481i) q^{9} +O(q^{10})\)	\(q+(0.766266 + 0.442404i) q^{2} +(-0.189492 - 1.72165i) q^{3} +(-0.608557 - 1.05405i) q^{4} +(0.616465 - 1.40308i) q^{6} +(-2.63771 - 0.206062i) q^{7} -2.84653i q^{8} +(-2.92819 + 0.652481i) q^{9} +(1.25362 - 0.723775i) q^{11} +(-1.69940 + 1.24746i) q^{12} +4.04326i q^{13} +(-1.93003 - 1.32483i) q^{14} +(0.0422021 - 0.0730962i) q^{16} +(-2.87862 - 4.98592i) q^{17} +(-2.53243 - 0.795467i) q^{18} +(-0.356910 - 0.206062i) q^{19} +(0.145060 + 4.58028i) q^{21} +1.28081 q^{22} +(-6.33444 - 3.65719i) q^{23} +(-4.90074 + 0.539396i) q^{24} +(-1.78875 + 3.09821i) q^{26} +(1.67821 + 4.91768i) q^{27} +(1.38800 + 2.90569i) q^{28} +1.82121i q^{29} +(2.30936 - 1.33331i) q^{31} +(-4.86566 + 2.80919i) q^{32} +(-1.48364 - 2.02114i) q^{33} -5.09406i q^{34} +(2.46972 + 2.68939i) q^{36} +(2.92387 - 5.06429i) q^{37} +(-0.182325 - 0.315797i) q^{38} +(6.96109 - 0.766166i) q^{39} +6.46287 q^{41} +(-1.91518 + 3.57389i) q^{42} -10.3583 q^{43} +(-1.52579 - 0.880917i) q^{44} +(-3.23592 - 5.60477i) q^{46} +(5.43364 - 9.41134i) q^{47} +(-0.133843 - 0.0588063i) q^{48} +(6.91508 + 1.08706i) q^{49} +(-8.03855 + 5.90078i) q^{51} +(4.26180 - 2.46055i) q^{52} +(1.20893 - 0.697977i) q^{53} +(-0.889643 + 4.51070i) q^{54} +(-0.586561 + 7.50833i) q^{56} +(-0.287136 + 0.653522i) q^{57} +(-0.805713 + 1.39554i) q^{58} +(-0.583941 - 1.01142i) q^{59} +(3.58903 + 2.07213i) q^{61} +2.35944 q^{62} +(7.85817 - 1.11767i) q^{63} -5.14000 q^{64} +(-0.242703 - 2.20510i) q^{66} +(-3.46011 - 5.99309i) q^{67} +(-3.50361 + 6.06843i) q^{68} +(-5.09609 + 11.5987i) q^{69} -13.3217i q^{71} +(1.85731 + 8.33517i) q^{72} +(2.72344 - 1.57238i) q^{73} +(4.48093 - 2.58707i) q^{74} +0.501602i q^{76} +(-3.45582 + 1.65079i) q^{77} +(5.67300 + 2.49253i) q^{78} +(6.42216 - 11.1235i) q^{79} +(8.14854 - 3.82117i) q^{81} +(4.95228 + 2.85920i) q^{82} +11.5010 q^{83} +(4.73957 - 2.94026i) q^{84} +(-7.93724 - 4.58257i) q^{86} +(3.13550 - 0.345106i) q^{87} +(-2.06025 - 3.56845i) q^{88} +(-3.90111 + 6.75692i) q^{89} +(0.833161 - 10.6650i) q^{91} +8.90244i q^{92} +(-2.73310 - 3.72326i) q^{93} +(8.32723 - 4.80773i) q^{94} +(5.75846 + 7.84466i) q^{96} +3.86099i q^{97} +(4.81787 + 3.89224i) q^{98} +(-3.19857 + 2.93731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{3} + 14 q^{4} - 7 q^{9}+O(q^{10}) \) 20 * q - 3 * q^3 + 14 * q^4 - 7 * q^9	\( 20 q - 3 q^{3} + 14 q^{4} - 7 q^{9} + 21 q^{12} - 18 q^{16} - 14 q^{18} - 9 q^{21} - 20 q^{22} + 18 q^{24} + 10 q^{28} + 42 q^{31} - 12 q^{33} - 36 q^{36} - 24 q^{37} - 33 q^{42} - 36 q^{43} - 8 q^{46} - 4 q^{49} + 21 q^{51} + 84 q^{52} - 75 q^{54} - 6 q^{57} + 4 q^{58} - 90 q^{61} + 5 q^{63} - 120 q^{64} + 6 q^{66} - 20 q^{67} + 35 q^{72} + 48 q^{73} + 108 q^{78} + 46 q^{79} + 29 q^{81} - 36 q^{82} + 75 q^{84} - 69 q^{87} - 4 q^{88} - 30 q^{91} + 30 q^{93} + 6 q^{94} + 135 q^{96} + 94 q^{99}+O(q^{100}) \) 20 * q - 3 * q^3 + 14 * q^4 - 7 * q^9 + 21 * q^12 - 18 * q^16 - 14 * q^18 - 9 * q^21 - 20 * q^22 + 18 * q^24 + 10 * q^28 + 42 * q^31 - 12 * q^33 - 36 * q^36 - 24 * q^37 - 33 * q^42 - 36 * q^43 - 8 * q^46 - 4 * q^49 + 21 * q^51 + 84 * q^52 - 75 * q^54 - 6 * q^57 + 4 * q^58 - 90 * q^61 + 5 * q^63 - 120 * q^64 + 6 * q^66 - 20 * q^67 + 35 * q^72 + 48 * q^73 + 108 * q^78 + 46 * q^79 + 29 * q^81 - 36 * q^82 + 75 * q^84 - 69 * q^87 - 4 * q^88 - 30 * q^91 + 30 * q^93 + 6 * q^94 + 135 * q^96 + 94 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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