LMFDB - Embedded newform 275.2.h.d.251.2

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 7x^{14} + 25x^{12} + 57x^{10} + 194x^{8} + 303x^{6} + 235x^{4} + 33x^{2} + 121 $ x^16 + 7x^14 + 25x^12 + 57x^10 + 194x^8 + 303x^6 + 235x^4 + 33*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			251.2
Root			$0.649397 - 0.471815i$ of defining polynomial
Character	$\chi$	$=$	275.251
Dual form			275.2.h.d.126.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.248048 + 0.763412i) q^{2} +(1.42447 - 1.03494i) q^{3} +(1.09676 + 0.796845i) q^{4} +(0.436748 + 1.34417i) q^{6} +(0.479022 + 0.348029i) q^{7} +(-2.17917 + 1.58326i) q^{8} +(0.0309674 - 0.0953077i) q^{9} +O(q^{10})$	\(q+(-0.248048 + 0.763412i) q^{2} +(1.42447 - 1.03494i) q^{3} +(1.09676 + 0.796845i) q^{4} +(0.436748 + 1.34417i) q^{6} +(0.479022 + 0.348029i) q^{7} +(-2.17917 + 1.58326i) q^{8} +(0.0309674 - 0.0953077i) q^{9} +(1.96213 + 2.67395i) q^{11} +2.38699 q^{12} +(0.554651 - 1.70704i) q^{13} +(-0.384510 + 0.279363i) q^{14} +(0.169713 + 0.522322i) q^{16} +(-2.18695 - 6.73074i) q^{17} +(0.0650777 + 0.0472817i) q^{18} +(1.85009 - 1.34417i) q^{19} +1.04254 q^{21} +(-2.52803 + 0.834650i) q^{22} -1.49081 q^{23} +(-1.46558 + 4.51060i) q^{24} +(1.16560 + 0.846855i) q^{26} +(1.57777 + 4.85588i) q^{27} +(0.248048 + 0.763412i) q^{28} +(-2.89263 - 2.10162i) q^{29} +(1.90578 - 5.86539i) q^{31} -5.82804 q^{32} +(5.56238 + 1.77828i) q^{33} +5.68079 q^{34} +(0.109909 - 0.0798539i) q^{36} +(5.93610 + 4.31283i) q^{37} +(0.567246 + 1.74580i) q^{38} +(-0.976598 - 3.00566i) q^{39} +(-6.80400 + 4.94339i) q^{41} +(-0.258600 + 0.795888i) q^{42} -9.51936 q^{43} +(0.0212704 + 4.49621i) q^{44} +(0.369792 - 1.13810i) q^{46} +(1.56274 - 1.13540i) q^{47} +(0.782321 + 0.568389i) q^{48} +(-2.05478 - 6.32397i) q^{49} +(-10.0811 - 7.32438i) q^{51} +(1.96857 - 1.43025i) q^{52} +(-0.736359 + 2.26628i) q^{53} -4.09840 q^{54} -1.59489 q^{56} +(1.24427 - 3.82947i) q^{57} +(2.32192 - 1.68697i) q^{58} +(0.0309674 + 0.0224991i) q^{59} +(-1.06351 - 3.27314i) q^{61} +(4.00499 + 2.90979i) q^{62} +(0.0480039 - 0.0348769i) q^{63} +(1.10621 - 3.40455i) q^{64} +(-2.73729 + 3.80529i) q^{66} -6.79162 q^{67} +(2.96479 - 9.12469i) q^{68} +(-2.12361 + 1.54290i) q^{69} +(-3.64439 - 11.2163i) q^{71} +(0.0834136 + 0.256721i) q^{72} +(5.51972 + 4.01031i) q^{73} +(-4.76490 + 3.46191i) q^{74} +3.10021 q^{76} +(0.00929006 + 1.96376i) q^{77} +2.53680 q^{78} +(1.39863 - 4.30453i) q^{79} +(7.51625 + 5.46087i) q^{81} +(-2.08613 - 6.42045i) q^{82} +(-1.83637 - 5.65177i) q^{83} +(1.14342 + 0.830744i) q^{84} +(2.36125 - 7.26720i) q^{86} -6.29552 q^{87} +(-8.50937 - 2.72042i) q^{88} -6.21375 q^{89} +(0.859791 - 0.624675i) q^{91} +(-1.63507 - 1.18795i) q^{92} +(-3.35559 - 10.3274i) q^{93} +(0.479142 + 1.47465i) q^{94} +(-8.30186 + 6.03166i) q^{96} +(1.66119 - 5.11260i) q^{97} +5.33748 q^{98} +(0.315611 - 0.104201i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 18 q^{6} - 2 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 - 18 * q^6 - 2 * q^9	$ 16 q + 4 q^{4} - 18 q^{6} - 2 q^{9} - 6 q^{11} + 12 q^{14} + 16 q^{16} - 6 q^{19} + 8 q^{21} - 6 q^{24} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 16 q^{34} + 10 q^{36} - 30 q^{39} - 52 q^{41} - 4 q^{44} - 62 q^{46} + 10 q^{49} - 42 q^{51} + 40 q^{54} - 20 q^{56} - 2 q^{59} - 40 q^{61} + 8 q^{64} + 58 q^{66} - 26 q^{69} + 36 q^{71} - 48 q^{74} + 56 q^{76} - 38 q^{79} + 68 q^{81} - 12 q^{84} + 22 q^{86} - 24 q^{89} - 20 q^{91} - 14 q^{94} - 86 q^{96} + 72 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 18 * q^6 - 2 * q^9 - 6 * q^11 + 12 * q^14 + 16 * q^16 - 6 * q^19 + 8 * q^21 - 6 * q^24 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 16 * q^34 + 10 * q^36 - 30 * q^39 - 52 * q^41 - 4 * q^44 - 62 * q^46 + 10 * q^49 - 42 * q^51 + 40 * q^54 - 20 * q^56 - 2 * q^59 - 40 * q^61 + 8 * q^64 + 58 * q^66 - 26 * q^69 + 36 * q^71 - 48 * q^74 + 56 * q^76 - 38 * q^79 + 68 * q^81 - 12 * q^84 + 22 * q^86 - 24 * q^89 - 20 * q^91 - 14 * q^94 - 86 * q^96 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−0.248048	+	0.763412i	−0.175396	+	0.539814i	−0.999651	−	0.0264046i	$-0.991594\pi$
$2$	−0.248048	+	0.763412i	−0.175396	+	0.539814i	0.824255	+	0.566219i	$0.191594\pi$
$3$	1.42447	−	1.03494i	0.822418	−	0.597522i	−0.0949859	−	0.995479i	$-0.530281\pi$
$3$	1.42447	−	1.03494i	0.822418	−	0.597522i	0.917404	+	0.397957i	$0.130281\pi$
$4$	1.09676	+	0.796845i	0.548382	+	0.398423i
$5$		0			0
$5$		0			0
$6$	0.436748	+	1.34417i	0.178302	+	0.548756i
$7$	0.479022	+	0.348029i	0.181053	+	0.131543i	0.674620	−	0.738165i	$-0.264307\pi$
$7$	0.479022	+	0.348029i	0.181053	+	0.131543i	−0.493567	+	0.869708i	$0.664307\pi$
$8$	−2.17917	+	1.58326i	−0.770451	+	0.559766i
$9$	0.0309674	−	0.0953077i	0.0103225	−	0.0317692i
$10$		0			0
$11$	1.96213	+	2.67395i	0.591606	+	0.806227i
$11$	1.96213	+	2.67395i	0.591606	+	0.806227i
$12$	2.38699			0.689065
$13$	0.554651	−	1.70704i	0.153833	−	0.473448i	−0.844208	−	0.536016i	$-0.819929\pi$
$13$	0.554651	−	1.70704i	0.153833	−	0.473448i	0.998041	+	0.0625674i	$0.0199288\pi$
$14$	−0.384510	+	0.279363i	−0.102765	+	0.0746629i
$15$		0			0
$16$	0.169713	+	0.522322i	0.0424281	+	0.130580i
$17$	−2.18695	−	6.73074i	−0.530413	−	1.63244i	−0.753357	−	0.657612i	$-0.771567\pi$
$17$	−2.18695	−	6.73074i	−0.530413	−	1.63244i	0.222944	−	0.974831i	$-0.428433\pi$
$18$	0.0650777	+	0.0472817i	0.0153390	+	0.0111444i
$19$	1.85009	−	1.34417i	0.424441	−	0.308374i	−0.354981	−	0.934873i	$-0.615513\pi$
$19$	1.85009	−	1.34417i	0.424441	−	0.308374i	0.779422	+	0.626499i	$0.215513\pi$
$20$		0			0
$21$	1.04254			0.227501
$22$	−2.52803	+	0.834650i	−0.538978	+	0.177948i
$23$	−1.49081			−0.310855			−0.155428	−	0.987847i	$-0.549676\pi$
$23$	−1.49081			−0.310855			−0.155428	+	0.987847i	$0.549676\pi$
$24$	−1.46558	+	4.51060i	−0.299161	+	0.920723i
$25$		0			0
$26$	1.16560	+	0.846855i	0.228592	+	0.166082i
$27$	1.57777	+	4.85588i	0.303642	+	0.934515i
$28$	0.248048	+	0.763412i	0.0468766	+	0.144271i
$29$	−2.89263	−	2.10162i	−0.537149	−	0.390261i	0.285876	−	0.958267i	$-0.407715\pi$
$29$	−2.89263	−	2.10162i	−0.537149	−	0.390261i	−0.823025	+	0.568005i	$0.807715\pi$
$30$		0			0
$31$	1.90578	−	5.86539i	0.342288	−	1.05346i	−0.620731	−	0.784023i	$-0.713164\pi$
$31$	1.90578	−	5.86539i	0.342288	−	1.05346i	0.963020	−	0.269432i	$-0.0868358\pi$
$32$	−5.82804			−1.03026
$33$	5.56238	+	1.77828i	0.968286	+	0.309559i
$34$	5.68079			0.974248
$35$		0			0
$36$	0.109909	−	0.0798539i	0.0183182	−	0.0133090i
$37$	5.93610	+	4.31283i	0.975889	+	0.709025i	0.956786	−	0.290792i	$-0.0939189\pi$
$37$	5.93610	+	4.31283i	0.975889	+	0.709025i	0.0191031	+	0.999818i	$0.493919\pi$
$38$	0.567246	+	1.74580i	0.0920194	+	0.283207i
$39$	−0.976598	−	3.00566i	−0.156381	−	0.481291i
$40$		0			0
$41$	−6.80400	+	4.94339i	−1.06261	+	0.772028i	−0.974569	−	0.224089i	$-0.928059\pi$
$41$	−6.80400	+	4.94339i	−1.06261	+	0.772028i	−0.0880369	+	0.996117i	$0.528059\pi$
$42$	−0.258600	+	0.795888i	−0.0399028	+	0.122808i
$43$	−9.51936			−1.45169			−0.725844	−	0.687859i	$-0.758551\pi$
$43$	−9.51936			−1.45169			−0.725844	+	0.687859i	$0.758551\pi$
$44$	0.0212704	+	4.49621i	0.00320664	+	0.677830i
$45$		0			0
$46$	0.369792	−	1.13810i	0.0545228	−	0.167804i
$47$	1.56274	−	1.13540i	0.227949	−	0.165615i	−0.467948	−	0.883756i	$-0.655007\pi$
$47$	1.56274	−	1.13540i	0.227949	−	0.165615i	0.695898	+	0.718141i	$0.255007\pi$
$48$	0.782321	+	0.568389i	0.112918	+	0.0820400i
$49$	−2.05478	−	6.32397i	−0.293540	−	0.903424i
$50$		0			0
$51$	−10.0811	−	7.32438i	−1.41164	−	1.02562i
$52$	1.96857	−	1.43025i	0.272991	−	0.198340i
$53$	−0.736359	+	2.26628i	−0.101147	+	0.311298i	−0.988807	−	0.149202i	$-0.952330\pi$
$53$	−0.736359	+	2.26628i	−0.101147	+	0.311298i	0.887660	+	0.460499i	$0.152330\pi$
$54$	−4.09840			−0.557722
$55$		0			0
$56$	−1.59489			−0.213126
$57$	1.24427	−	3.82947i	0.164807	−	0.507225i
$58$	2.32192	−	1.68697i	0.304882	−	0.221510i
$59$	0.0309674	+	0.0224991i	0.00403161	+	0.00292913i	0.589799	−	0.807550i	$-0.299207\pi$
$59$	0.0309674	+	0.0224991i	0.00403161	+	0.00292913i	−0.585768	+	0.810479i	$0.699207\pi$
$60$		0			0
$61$	−1.06351	−	3.27314i	−0.136168	−	0.419082i	0.859602	−	0.510965i	$-0.170712\pi$
$61$	−1.06351	−	3.27314i	−0.136168	−	0.419082i	−0.995770	+	0.0918822i	$0.970712\pi$
$62$	4.00499	+	2.90979i	0.508634	+	0.369544i
$63$	0.0480039	−	0.0348769i	0.00604793	−	0.00439408i
$64$	1.10621	−	3.40455i	0.138276	−	0.425569i
$65$		0			0
$66$	−2.73729	+	3.80529i	−0.336938	+	0.468399i
$67$	−6.79162			−0.829728			−0.414864	−	0.909883i	$-0.636171\pi$
$67$	−6.79162			−0.829728			−0.414864	+	0.909883i	$0.636171\pi$
$68$	2.96479	−	9.12469i	0.359534	−	1.10653i
$69$	−2.12361	+	1.54290i	−0.255653	+	0.185743i
$70$		0			0
$71$	−3.64439	−	11.2163i	−0.432510	−	1.33113i	−0.895617	−	0.444826i	$-0.853265\pi$
$71$	−3.64439	−	11.2163i	−0.432510	−	1.33113i	0.463107	−	0.886302i	$-0.346735\pi$
$72$	0.0834136	+	0.256721i	0.00983038	+	0.0302548i
$73$	5.51972	+	4.01031i	0.646035	+	0.469372i	0.861918	−	0.507048i	$-0.169263\pi$
$73$	5.51972	+	4.01031i	0.646035	+	0.469372i	−0.215884	+	0.976419i	$0.569263\pi$
$74$	−4.76490	+	3.46191i	−0.553909	+	0.402438i
$75$		0			0
$76$	3.10021			0.355619
$77$	0.00929006	+	1.96376i	0.00105870	+	0.223791i
$78$	2.53680			0.287236
$79$	1.39863	−	4.30453i	0.157358	−	0.484298i	−0.841034	−	0.540982i	$-0.818053\pi$
$79$	1.39863	−	4.30453i	0.157358	−	0.484298i	0.998392	+	0.0566840i	$0.0180528\pi$
$80$		0			0
$81$	7.51625	+	5.46087i	0.835139	+	0.606764i
$82$	−2.08613	−	6.42045i	−0.230375	−	0.709020i
$83$	−1.83637	−	5.65177i	−0.201568	−	0.620363i	−0.999837	−	0.0180613i	$-0.994251\pi$
$83$	−1.83637	−	5.65177i	−0.201568	−	0.620363i	0.798269	−	0.602301i	$-0.205749\pi$
$84$	1.14342	+	0.830744i	0.124757	+	0.0906416i
$85$		0			0
$86$	2.36125	−	7.26720i	0.254621	−	0.783642i
$87$	−6.29552			−0.674951
$88$	−8.50937	−	2.72042i	−0.907102	−	0.289998i
$89$	−6.21375			−0.658656			−0.329328	−	0.944216i	$-0.606822\pi$
$89$	−6.21375			−0.658656			−0.329328	+	0.944216i	$0.606822\pi$
$90$		0			0
$91$	0.859791	−	0.624675i	0.0901306	−	0.0654837i
$92$	−1.63507	−	1.18795i	−0.170467	−	0.123852i
$93$	−3.35559	−	10.3274i	−0.347958	−	1.07091i
$94$	0.479142	+	1.47465i	0.0494197	+	0.152098i
$95$		0			0
$96$	−8.30186	+	6.03166i	−0.847305	+	0.615603i
$97$	1.66119	−	5.11260i	0.168668	−	0.519106i	−0.830620	−	0.556840i	$-0.812014\pi$
$97$	1.66119	−	5.11260i	0.168668	−	0.519106i	0.999288	+	0.0377334i	$0.0120138\pi$
$98$	5.33748			0.539167
$99$	0.315611	−	0.104201i	0.0317201	−	0.0104726i
$100$		0			0
$101$	−3.06894	+	9.44523i	−0.305371	+	0.939835i	0.674167	+	0.738579i	$0.264503\pi$
$101$	−3.06894	+	9.44523i	−0.305371	+	0.939835i	−0.979538	+	0.201257i	$0.935497\pi$
$102$	8.09212	−	5.87927i	0.801239	−	0.582135i
$103$	10.9390	+	7.94766i	1.07785	+	0.783107i	0.977307	−	0.211826i	$-0.0679410\pi$
$103$	10.9390	+	7.94766i	1.07785	+	0.783107i	0.100546	+	0.994932i	$0.467941\pi$
$104$	1.49401	+	4.59808i	0.146499	+	0.450879i
$105$		0			0
$106$	−1.54745	−	1.12429i	−0.150302	−	0.109201i
$107$	−4.53405	+	3.29418i	−0.438323	+	0.318461i	−0.784968	−	0.619536i	$-0.787321\pi$
$107$	−4.53405	+	3.29418i	−0.438323	+	0.318461i	0.346645	+	0.937996i	$0.387321\pi$
$108$	−2.13895	+	6.58300i	−0.205820	+	0.633449i
$109$	18.6001			1.78157			0.890784	−	0.454428i	$-0.150156\pi$
$109$	18.6001			1.78157			0.890784	+	0.454428i	$0.150156\pi$
$110$		0			0
$111$	12.9193			1.22625
$112$	−0.100487	+	0.309268i	−0.00949516	+	0.0292231i
$113$	−9.54752	+	6.93668i	−0.898155	+	0.652548i	−0.937992	−	0.346658i	$-0.887316\pi$
$113$	−9.54752	+	6.93668i	−0.898155	+	0.652548i	0.0398362	+	0.999206i	$0.487316\pi$
$114$	2.61482	+	1.89978i	0.244901	+	0.177931i
$115$		0			0
$116$	−1.49787	−	4.60997i	−0.139074	−	0.428025i
$117$	−0.145518	−	0.105725i	−0.0134532	−	0.00977429i
$118$	−0.0248575	+	0.0180600i	−0.00228832	+	0.00166256i
$119$	1.29490	−	3.98529i	0.118703	−	0.365331i
$120$		0			0
$121$	−3.30005	+	10.4933i	−0.300005	+	0.953938i
$122$	2.76255			0.250110
$123$	−4.57598	+	14.0834i	−0.412603	+	1.26986i
$124$	6.76400	−	4.91433i	0.607425	−	0.441320i
$125$		0			0
$126$	0.0147182	+	0.0452979i	0.00131120	+	0.00403546i
$127$	4.96177	+	15.2707i	0.440286	+	1.35506i	0.887572	+	0.460669i	$0.152390\pi$
$127$	4.96177	+	15.2707i	0.440286	+	1.35506i	−0.447287	+	0.894391i	$0.647610\pi$
$128$	−7.10528	−	5.16229i	−0.628024	−	0.456286i
$129$	−13.5600	+	9.85195i	−1.19390	+	0.867416i
$130$		0			0
$131$	18.0296			1.57525			0.787625	−	0.616154i	$-0.211310\pi$
$131$	18.0296			1.57525			0.787625	+	0.616154i	$0.211310\pi$
$132$	4.68360	+	6.38271i	0.407655	+	0.555543i
$133$	1.35405			0.117411
$134$	1.68464	−	5.18480i	0.145531	−	0.447899i
$135$		0			0
$136$	15.4222	+	11.2049i	1.32244	+	0.960811i
$137$	1.24598	+	3.83473i	0.106451	+	0.327623i	0.990068	−	0.140587i	$-0.0448990\pi$
$137$	1.24598	+	3.83473i	0.106451	+	0.327623i	−0.883617	+	0.468210i	$0.844899\pi$
$138$	−0.651108	−	2.00390i	−0.0554260	−	0.170584i
$139$	−6.41949	−	4.66403i	−0.544494	−	0.395598i	0.281258	−	0.959632i	$-0.409248\pi$
$139$	−6.41949	−	4.66403i	−0.544494	−	0.395598i	−0.825751	+	0.564035i	$0.809248\pi$
$140$		0			0
$141$	1.05101	−	3.23468i	0.0885111	−	0.272409i
$142$	9.46663			0.794422
$143$	5.65285	−	1.86633i	0.472715	−	0.156071i
$144$	0.0550368			0.00458640
$145$		0			0
$146$	−4.43068	+	3.21907i	−0.366685	+	0.266412i
$147$	−9.47189	−	6.88173i	−0.781228	−	0.567596i
$148$	3.07384	+	9.46031i	0.252668	+	0.777633i
$149$	3.86298	+	11.8890i	0.316468	+	0.973988i	0.975146	+	0.221563i	$0.0711160\pi$
$149$	3.86298	+	11.8890i	0.316468	+	0.973988i	−0.658678	+	0.752425i	$0.728884\pi$
$150$		0			0
$151$	−6.79775	+	4.93885i	−0.553193	+	0.401918i	−0.828961	−	0.559306i	$-0.811068\pi$
$151$	−6.79775	+	4.93885i	−0.553193	+	0.401918i	0.275768	+	0.961224i	$0.411068\pi$
$152$	−1.90349	+	5.85835i	−0.154394	+	0.475175i
$153$	−0.709215			−0.0573367
$154$	−1.50146	−	0.480014i	−0.120991	−	0.0386807i
$155$		0			0
$156$	1.32395	−	4.07470i	0.106001	−	0.326237i
$157$	−11.3229	+	8.22657i	−0.903666	+	0.656552i	−0.939405	−	0.342809i	$-0.888621\pi$
$157$	−11.3229	+	8.22657i	−0.903666	+	0.656552i	0.0357391	+	0.999361i	$0.488621\pi$
$158$	2.93921	+	2.13546i	0.233831	+	0.169888i
$159$	1.29654	+	3.99034i	0.102822	+	0.316454i
$160$		0			0
$161$	−0.714130	−	0.518846i	−0.0562813	−	0.0408908i
$162$	−6.03329	+	4.38344i	−0.474020	+	0.344395i
$163$	3.65922	−	11.2619i	0.286612	−	0.882101i	−0.699299	−	0.714830i	$-0.746504\pi$
$163$	3.65922	−	11.2619i	0.286612	−	0.882101i	0.985911	−	0.167272i	$-0.0534957\pi$
$164$	−11.4015			−0.890307
$165$		0			0
$166$	4.77014			0.370235
$167$	2.69657	−	8.29919i	0.208667	−	0.642210i	−0.790876	−	0.611976i	$-0.790375\pi$
$167$	2.69657	−	8.29919i	0.208667	−	0.642210i	0.999543	−	0.0302340i	$-0.00962526\pi$
$168$	−2.27187	+	1.65061i	−0.175278	+	0.127347i
$169$	7.91087	+	5.74758i	0.608528	+	0.442122i
$170$		0			0
$171$	−0.0708175	−	0.217954i	−0.00541555	−	0.0166673i
$172$	−10.4405	−	7.58546i	−0.796080	−	0.578386i
$173$	7.42565	−	5.39505i	0.564562	−	0.410178i	−0.268564	−	0.963262i	$-0.586549\pi$
$173$	7.42565	−	5.39505i	0.564562	−	0.410178i	0.833126	+	0.553084i	$0.186549\pi$
$174$	1.56159	−	4.80608i	0.118384	−	0.364348i
$175$		0			0
$176$	−1.06366	+	1.47867i	−0.0801767	+	0.111459i
$177$	0.0673973			0.00506589
$178$	1.54130	−	4.74365i	0.115526	−	0.355552i
$179$	−1.17159	+	0.851209i	−0.0875687	+	0.0636224i	−0.630708	−	0.776020i	$-0.717235\pi$
$179$	−1.17159	+	0.851209i	−0.0875687	+	0.0636224i	0.543139	+	0.839642i	$0.317235\pi$
$180$		0			0
$181$	0.245206	+	0.754665i	0.0182260	+	0.0560938i	0.959756	−	0.280836i	$-0.0906116\pi$
$181$	0.245206	+	0.754665i	0.0182260	+	0.0560938i	−0.941530	+	0.336930i	$0.890612\pi$
$182$	0.263615	+	0.811324i	0.0195404	+	0.0601393i
$183$	−4.90243	−	3.56182i	−0.362398	−	0.263298i
$184$	3.24872	−	2.36033i	0.239499	−	0.174006i
$185$		0			0
$186$	8.71644			0.639120
$187$	13.7066	−	19.0544i	1.00233	−	1.39340i
$188$	2.61869			0.190988
$189$	−0.934204	+	2.87518i	−0.0679533	+	0.209139i
$190$		0			0
$191$	6.59373	+	4.79062i	0.477105	+	0.346637i	0.800204	−	0.599728i	$-0.204725\pi$
$191$	6.59373	+	4.79062i	0.477105	+	0.346637i	−0.323099	+	0.946365i	$0.604725\pi$
$192$	−1.94774	−	5.99454i	−0.140566	−	0.432618i
$193$	−1.34990	−	4.15456i	−0.0971678	−	0.299052i	0.890645	−	0.454700i	$-0.150253\pi$
$193$	−1.34990	−	4.15456i	−0.0971678	−	0.299052i	−0.987813	+	0.155648i	$0.950253\pi$
$194$	3.49097	+	2.53634i	0.250637	+	0.182098i
$195$		0			0
$196$	2.78561	−	8.57324i	0.198972	−	0.612374i
$197$	15.6525			1.11520			0.557599	−	0.830111i	$-0.311723\pi$
$197$	15.6525			1.11520			0.557599	+	0.830111i	$0.311723\pi$
$198$	0.00126211	+	0.266788i	8.96940e−5	+	0.0189598i
$199$	1.43830			0.101959			0.0509793	−	0.998700i	$-0.483766\pi$
$199$	1.43830			0.101959			0.0509793	+	0.998700i	$0.483766\pi$
$200$		0			0
$201$	−9.67446	+	7.02890i	−0.682383	+	0.495781i
$202$	−6.44936	−	4.68573i	−0.453775	−	0.329687i
$203$	−0.654208	−	2.01344i	−0.0459164	−	0.141316i
$204$	−5.22023	−	16.0662i	−0.365489	−	1.12486i
$205$		0			0
$206$	−8.78074	+	6.37958i	−0.611783	+	0.444486i
$207$	−0.0461665	+	0.142086i	−0.00320879	+	0.00987564i
$208$	0.985756			0.0683499
$209$	7.22439	+	2.30962i	0.499721	+	0.159760i
$210$		0			0
$211$	2.68267	−	8.25641i	0.184683	−	0.568395i	−0.815260	−	0.579095i	$-0.803406\pi$
$211$	2.68267	−	8.25641i	0.184683	−	0.568395i	0.999943	+	0.0107002i	$0.00340605\pi$
$212$	−2.61349	+	1.89881i	−0.179495	+	0.130411i
$213$	−16.7995	−	12.2055i	−1.15108	−	0.836310i
$214$	−1.39016	−	4.27846i	−0.0950292	−	0.292470i
$215$		0			0
$216$	−11.1263	−	8.08375i	−0.757051	−	0.550030i
$217$	2.95424	−	2.14638i	0.200547	−	0.145706i
$218$	−4.61371	+	14.1995i	−0.312480	+	0.961715i
$219$	12.0131			0.811770
$220$		0			0
$221$	−12.7026			−0.854472
$222$	−3.20461	+	9.86276i	−0.215079	+	0.661945i
$223$	5.10169	−	3.70660i	0.341635	−	0.248212i	−0.403717	−	0.914884i	$-0.632282\pi$
$223$	5.10169	−	3.70660i	0.341635	−	0.248212i	0.745351	+	0.666672i	$0.232282\pi$
$224$	−2.79175	−	2.02833i	−0.186532	−	0.135523i
$225$		0			0
$226$	−2.92731	−	9.00932i	−0.194721	−	0.599291i
$227$	0.903517	+	0.656444i	0.0599686	+	0.0435697i	0.617366	−	0.786676i	$-0.288200\pi$
$227$	0.903517	+	0.656444i	0.0599686	+	0.0435697i	−0.557397	+	0.830246i	$0.688200\pi$
$228$	4.41616	−	3.20853i	0.292467	−	0.212490i
$229$	−1.29669	+	3.99079i	−0.0856874	+	0.263719i	−0.984715	−	0.174173i	$-0.944275\pi$
$229$	−1.29669	+	3.99079i	−0.0856874	+	0.263719i	0.899028	+	0.437892i	$0.144275\pi$
$230$		0			0
$231$	2.04561	+	2.78771i	0.134591	+	0.183418i
$232$	9.63094			0.632302
$233$	−2.09497	+	6.44766i	−0.137246	+	0.422400i	−0.995933	−	0.0901010i	$-0.971281\pi$
$233$	−2.09497	+	6.44766i	−0.137246	+	0.422400i	0.858686	+	0.512501i	$0.171281\pi$
$234$	0.116807	−	0.0848655i	0.00763593	−	0.00554783i
$235$		0			0
$236$	0.0160356	+	0.0493524i	0.00104383	+	0.00321257i
$237$	−2.46262	−	7.57917i	−0.159965	−	0.492320i
$238$	2.72122	+	1.97708i	0.176391	+	0.128155i
$239$	−3.55812	+	2.58513i	−0.230156	+	0.167218i	−0.696886	−	0.717182i	$-0.745432\pi$
$239$	−3.55812	+	2.58513i	−0.230156	+	0.167218i	0.466731	+	0.884400i	$0.345432\pi$
$240$		0			0
$241$	−9.61218			−0.619175			−0.309587	−	0.950871i	$-0.600191\pi$
$241$	−9.61218			−0.619175			−0.309587	+	0.950871i	$0.600191\pi$
$242$	−7.19215	−	5.12214i	−0.462329	−	0.329264i
$243$	1.04101			0.0667807
$244$	1.44177	−	4.43731i	0.0922998	−	0.284070i
$245$		0			0
$246$	−9.61640	−	6.98672i	−0.613119	−	0.445457i
$247$	−1.26840	−	3.90373i	−0.0807064	−	0.248389i
$248$	5.13340	+	15.7990i	0.325971	+	1.00324i
$249$	−8.46509	−	6.15025i	−0.536453	−	0.389756i
$250$		0			0
$251$	4.14719	−	12.7637i	0.261768	−	0.805640i	−0.730652	−	0.682750i	$-0.760784\pi$
$251$	4.14719	−	12.7637i	0.261768	−	0.805640i	0.992420	−	0.122890i	$-0.0392163\pi$
$252$	0.0804405			0.00506727
$253$	−2.92517	−	3.98636i	−0.183904	−	0.250620i
$254$	−12.8886			−0.808704
$255$		0			0
$256$	11.4956	−	8.35202i	0.718473	−	0.522001i
$257$	8.75143	+	6.35829i	0.545899	+	0.396619i	0.826271	−	0.563272i	$-0.190458\pi$
$257$	8.75143	+	6.35829i	0.545899	+	0.396619i	−0.280372	+	0.959891i	$0.590458\pi$
$258$	−4.15756	−	12.7957i	−0.258838	−	0.796623i
$259$	1.34253	+	4.13188i	0.0834207	+	0.256742i
$260$		0			0
$261$	−0.289878	+	0.210609i	−0.0179430	+	0.0130364i
$262$	−4.47219	+	13.7640i	−0.276293	+	0.850342i
$263$	24.6351			1.51906			0.759531	−	0.650471i	$-0.225428\pi$
$263$	24.6351			1.51906			0.759531	+	0.650471i	$0.225428\pi$
$264$	−14.9368	+	4.93151i	−0.919297	+	0.303513i
$265$		0			0
$266$	−0.335868	+	1.03370i	−0.0205934	+	0.0633799i
$267$	−8.85130	+	6.43084i	−0.541691	+	0.393561i
$268$	−7.44880	−	5.41187i	−0.455008	−	0.330582i
$269$	−1.48359	−	4.56603i	−0.0904563	−	0.278396i	0.895587	−	0.444887i	$-0.146756\pi$
$269$	−1.48359	−	4.56603i	−0.0904563	−	0.278396i	−0.986043	+	0.166491i	$0.946756\pi$
$270$		0			0
$271$	−18.8746	−	13.7132i	−1.14655	−	0.833019i	−0.158534	−	0.987353i	$-0.550677\pi$
$271$	−18.8746	−	13.7132i	−1.14655	−	0.833019i	−0.988019	+	0.154334i	$0.950677\pi$
$272$	3.14446	−	2.28458i	0.190661	−	0.138523i
$273$	0.578247	−	1.77966i	0.0349971	−	0.107710i
$274$	−3.23654			−0.195527
$275$		0			0
$276$	−3.55855			−0.214200
$277$	−6.76663	+	20.8256i	−0.406568	+	1.25129i	0.513012	+	0.858382i	$0.328530\pi$
$277$	−6.76663	+	20.8256i	−0.406568	+	1.25129i	−0.919579	+	0.392905i	$0.871470\pi$
$278$	5.15291	−	3.74381i	0.309051	−	0.224539i
$279$	−0.500000	−	0.363271i	−0.0299342	−	0.0217485i
$280$		0			0
$281$	4.87488	+	15.0033i	0.290811	+	0.895024i	0.984596	+	0.174842i	$0.0559416\pi$
$281$	4.87488	+	15.0033i	0.290811	+	0.895024i	−0.693785	+	0.720182i	$0.744058\pi$
$282$	2.20869	+	1.60471i	0.131526	+	0.0955590i
$283$	−18.2912	+	13.2893i	−1.08730	+	0.789968i	−0.978941	−	0.204144i	$-0.934559\pi$
$283$	−18.2912	+	13.2893i	−1.08730	+	0.789968i	−0.108356	+	0.994112i	$0.534559\pi$
$284$	4.94061	−	15.2056i	0.293171	−	0.902288i
$285$		0			0
$286$	0.0226054	+	4.77839i	0.00133668	+	0.282552i
$287$	−4.97971			−0.293943
$288$	−0.180479	+	0.555457i	−0.0106348	+	0.0327306i
$289$	−26.7668	+	19.4472i	−1.57452	+	1.14395i
$290$		0			0
$291$	−2.92492	−	9.00198i	−0.171462	−	0.527705i
$292$	2.85823	+	8.79673i	0.167265	+	0.514790i
$293$	10.7272	+	7.79380i	0.626693	+	0.455319i	0.855253	−	0.518211i	$-0.173402\pi$
$293$	10.7272	+	7.79380i	0.626693	+	0.455319i	−0.228560	+	0.973530i	$0.573402\pi$
$294$	7.60308	−	5.52396i	0.443421	−	0.322164i
$295$		0			0
$296$	−19.7641			−1.14876
$297$	−9.88860	+	13.7468i	−0.573795	+	0.797669i
$298$	−10.0344			−0.581280
$299$	−0.826880	+	2.54487i	−0.0478197	+	0.147174i
$300$		0			0
$301$	−4.55998	−	3.31302i	−0.262833	−	0.190959i
$302$	−2.08421	−	6.41455i	−0.119933	−	0.369116i
$303$	5.40361	+	16.6306i	0.310429	+	0.955404i
$304$	1.01607	+	0.738221i	0.0582758	+	0.0423399i
$305$		0			0
$306$	0.175919	−	0.541424i	0.0100566	−	0.0309511i
$307$	10.0161			0.571650			0.285825	−	0.958282i	$-0.407732\pi$
$307$	10.0161			0.571650			0.285825	+	0.958282i	$0.407732\pi$
$308$	−1.55463	+	2.16119i	−0.0885830	+	0.123145i
$309$	23.8076			1.35437
$310$		0			0
$311$	2.75734	−	2.00332i	0.156354	−	0.113598i	−0.506857	−	0.862030i	$-0.669193\pi$
$311$	2.75734	−	2.00332i	0.156354	−	0.113598i	0.663212	+	0.748432i	$0.269193\pi$
$312$	6.88690	+	5.00362i	0.389894	+	0.283274i
$313$	7.57117	+	23.3017i	0.427948	+	1.31709i	0.900143	+	0.435594i	$0.143462\pi$
$313$	7.57117	+	23.3017i	0.427948	+	1.31709i	−0.472196	+	0.881494i	$0.656538\pi$
$314$	−3.47164	−	10.6846i	−0.195916	−	0.602968i
$315$		0			0
$316$	4.96401	−	3.60657i	0.279247	−	0.202885i
$317$	2.15957	−	6.64646i	0.121293	−	0.373303i	−0.871914	−	0.489659i	$-0.837121\pi$
$317$	2.15957	−	6.64646i	0.121293	−	0.373303i	0.993208	+	0.116356i	$0.0371214\pi$
$318$	−3.36787			−0.188861
$319$	−0.0560993	−	11.8584i	−0.00314096	−	0.663945i
$320$		0			0
$321$	−3.04935	+	9.38493i	−0.170198	+	0.523816i
$322$	0.573232	−	0.416477i	0.0319449	−	0.0232094i
$323$	−13.0933	−	9.51286i	−0.728532	−	0.529310i
$324$	3.89208	+	11.9786i	0.216226	+	0.665476i
$325$		0			0
$326$	7.68982	+	5.58698i	0.425900	+	0.309434i
$327$	26.4953	−	19.2500i	1.46519	−	1.06453i
$328$	7.00037	−	21.5449i	0.386531	−	1.18962i
$329$	1.14374			0.0630563
$330$		0			0
$331$	5.64321			0.310179			0.155089	−	0.987900i	$-0.450433\pi$
$331$	5.64321			0.310179			0.155089	+	0.987900i	$0.450433\pi$
$332$	2.48952	−	7.66196i	0.136630	−	0.420505i
$333$	0.594872	−	0.432200i	0.0325988	−	0.0236844i
$334$	5.66682	+	4.11719i	0.310075	+	0.225282i
$335$		0			0
$336$	0.176932	+	0.544542i	0.00965245	+	0.0297072i
$337$	−18.2970	−	13.2936i	−0.996702	−	0.724146i	−0.0353234	−	0.999376i	$-0.511246\pi$
$337$	−18.2970	−	13.2936i	−0.996702	−	0.724146i	−0.961379	+	0.275230i	$0.911246\pi$
$338$	−6.35005	+	4.61358i	−0.345397	+	0.250946i
$339$	−6.42112	+	19.7622i	−0.348748	+	1.07333i
$340$		0			0
$341$	19.4232	−	6.41272i	1.05182	−	0.347268i
$342$	0.183955			0.00994713
$343$	2.49743	−	7.68631i	0.134849	−	0.415022i
$344$	20.7443	−	15.0716i	1.11846	−	0.812605i
$345$		0			0
$346$	2.27673	+	7.00706i	0.122398	+	0.376702i
$347$	−0.0563630	−	0.173468i	−0.00302573	−	0.00931223i	0.949532	−	0.313669i	$-0.101558\pi$
$347$	−0.0563630	−	0.173468i	−0.00302573	−	0.00931223i	−0.952558	+	0.304357i	$0.901558\pi$
$348$	−6.90470	−	5.01656i	−0.370131	−	0.268916i
$349$	12.4809	−	9.06792i	0.668089	−	0.485395i	−0.201296	−	0.979530i	$-0.564515\pi$
$349$	12.4809	−	9.06792i	0.668089	−	0.485395i	0.869385	+	0.494136i	$0.164515\pi$
$350$		0			0
$351$	9.16431			0.489155
$352$	−11.4354	−	15.5839i	−0.609508	−	0.830625i
$353$	−23.9103			−1.27262			−0.636308	−	0.771435i	$-0.719539\pi$
$353$	−23.9103			−1.27262			−0.636308	+	0.771435i	$0.719539\pi$
$354$	−0.0167177	+	0.0514519i	−0.000888537	+	0.00273464i
$355$		0			0
$356$	−6.81501	−	4.95139i	−0.361195	−	0.262423i
$357$	−2.27998	−	7.01707i	−0.120670	−	0.371383i
$358$	−0.359214	−	1.10555i	−0.0189850	−	0.0584299i
$359$	7.09293	+	5.15332i	0.374351	+	0.271982i	0.759013	−	0.651076i	$-0.225682\pi$
$359$	7.09293	+	5.15332i	0.374351	+	0.271982i	−0.384662	+	0.923057i	$0.625682\pi$
$360$		0			0
$361$	−4.25527	+	13.0964i	−0.223962	+	0.689283i
$362$	−0.636943			−0.0334770
$363$	6.15910	+	18.3628i	0.323269	+	0.963795i
$364$	1.44076			0.0755161
$365$		0			0
$366$	3.93518	−	2.85907i	0.205695	−	0.149446i
$367$	−4.35439	−	3.16365i	−0.227297	−	0.165141i	0.468308	−	0.883565i	$-0.344864\pi$
$367$	−4.35439	−	3.16365i	−0.227297	−	0.165141i	−0.695605	+	0.718424i	$0.744864\pi$
$368$	−0.253009	−	0.778682i	−0.0131890	−	0.0405916i
$369$	0.260442	+	0.801557i	0.0135581	+	0.0417274i
$370$		0			0
$371$	−1.14146	+	0.829322i	−0.0592619	+	0.0430563i
$372$	4.54908	−	14.0006i	0.235859	−	0.725899i
$373$	−3.22450			−0.166958			−0.0834792	−	0.996510i	$-0.526603\pi$
$373$	−3.22450			−0.166958			−0.0834792	+	0.996510i	$0.526603\pi$
$374$	11.1465	+	15.1902i	0.576371	+	0.785465i
$375$		0			0
$376$	−1.60784	+	4.94844i	−0.0829183	+	0.255196i
$377$	−5.19196	+	3.77218i	−0.267400	+	0.194277i
$378$	−1.96322	−	1.42637i	−0.100977	−	0.0733643i
$379$	−6.07632	−	18.7010i	−0.312119	−	0.960605i	−0.976924	−	0.213588i	$-0.931485\pi$
$379$	−6.07632	−	18.7010i	−0.312119	−	0.960605i	0.664804	−	0.747017i	$-0.268515\pi$
$380$		0			0
$381$	22.8722	+	16.6176i	1.17178	+	0.851345i
$382$	−5.29278	+	3.84543i	−0.270802	+	0.196749i
$383$	8.64478	−	26.6059i	0.441728	−	1.35950i	−0.444305	−	0.895876i	$-0.646549\pi$
$383$	8.64478	−	26.6059i	0.441728	−	1.35950i	0.886033	−	0.463623i	$-0.153451\pi$
$384$	−15.4639			−0.789139
$385$		0			0
$386$	3.50648			0.178475
$387$	−0.294789	+	0.907269i	−0.0149850	+	0.0461191i
$388$	5.89588	−	4.28361i	0.299318	−	0.217467i
$389$	−10.5496	−	7.66472i	−0.534885	−	0.388617i	0.287297	−	0.957842i	$-0.407243\pi$
$389$	−10.5496	−	7.66472i	−0.534885	−	0.388617i	−0.822182	+	0.569225i	$0.807243\pi$
$390$		0			0
$391$	3.26033	+	10.0343i	0.164882	+	0.507454i
$392$	14.4902	+	10.5277i	0.731864	+	0.531730i
$393$	25.6826	−	18.6595i	1.29552	−	0.941247i
$394$	−3.88258	+	11.9493i	−0.195601	+	0.601999i
$395$		0			0
$396$	0.429183	+	0.137209i	0.0215672	+	0.00689499i
$397$	−1.82243			−0.0914651			−0.0457325	−	0.998954i	$-0.514562\pi$
$397$	−1.82243			−0.0914651			−0.0457325	+	0.998954i	$0.514562\pi$
$398$	−0.356768	+	1.09802i	−0.0178831	+	0.0550387i
$399$	1.92880	−	1.40135i	0.0965607	−	0.0701555i
$400$		0			0
$401$	1.66277	+	5.11749i	0.0830349	+	0.255555i	0.983951	−	0.178438i	$-0.0571043\pi$
$401$	1.66277	+	5.11749i	0.0830349	+	0.255555i	−0.900916	+	0.433993i	$0.857104\pi$
$402$	−2.96622	−	9.12910i	−0.147942	−	0.455318i
$403$	−8.95542	−	6.50649i	−0.446101	−	0.324111i
$404$	−10.8923	+	7.91371i	−0.541912	+	0.393722i
$405$		0			0
$406$	1.69936			0.0843379
$407$	0.115124	+	24.3352i	0.00570647	+	1.20625i
$408$	33.5648			1.66171
$409$	−11.3354	+	34.8867i	−0.560499	+	1.72504i	0.120462	+	0.992718i	$0.461562\pi$
$409$	−11.3354	+	34.8867i	−0.560499	+	1.72504i	−0.680961	+	0.732320i	$0.738438\pi$
$410$		0			0
$411$	5.74357	+	4.17295i	0.283309	+	0.205836i
$412$	5.66446	+	17.4334i	0.279068	+	0.858883i
$413$	0.00700368	+	0.0215551i	0.000344629	+	0.00106066i
$414$	−0.0970185	−	0.0704881i	−0.00476820	−	0.00346430i
$415$		0			0
$416$	−3.23253	+	9.94870i	−0.158488	+	0.487775i
$417$	−13.9713			−0.684180
$418$	−3.55518	+	4.94229i	−0.173890	+	0.241735i
$419$	2.86630			0.140028			0.0700141	−	0.997546i	$-0.477696\pi$
$419$	2.86630			0.140028			0.0700141	+	0.997546i	$0.477696\pi$
$420$		0			0
$421$	−3.76982	+	2.73893i	−0.183730	+	0.133487i	−0.675848	−	0.737041i	$-0.736223\pi$
$421$	−3.76982	+	2.73893i	−0.183730	+	0.133487i	0.492119	+	0.870528i	$0.336223\pi$
$422$	5.63761	+	4.09597i	0.274435	+	0.199389i
$423$	−0.0598182	−	0.184102i	−0.00290846	−	0.00895132i
$424$	−1.98345	−	6.10445i	−0.0963251	−	0.296458i
$425$		0			0
$426$	13.4849	−	9.79738i	0.653347	−	0.474685i
$427$	0.629706	−	1.93804i	0.0304736	−	0.0937881i
$428$	−7.59774			−0.367250
$429$	6.12078	−	8.50889i	0.295514	−	0.410813i
$430$		0			0
$431$	6.41801	−	19.7526i	0.309145	−	0.951450i	−0.668953	−	0.743304i	$-0.733257\pi$
$431$	6.41801	−	19.7526i	0.309145	−	0.951450i	0.978098	−	0.208145i	$-0.0667426\pi$
$432$	−2.26856	+	1.64821i	−0.109146	+	0.0792995i
$433$	10.3531	+	7.52199i	0.497540	+	0.361484i	0.808076	−	0.589078i	$-0.200509\pi$
$433$	10.3531	+	7.52199i	0.497540	+	0.361484i	−0.310537	+	0.950561i	$0.600509\pi$
$434$	0.905781	+	2.78771i	0.0434789	+	0.133814i
$435$		0			0
$436$	20.3999	+	14.8214i	0.976979	+	0.709817i
$437$	−2.75814	+	2.00390i	−0.131940	+	0.0958598i
$438$	−2.97982	+	9.17095i	−0.142381	+	0.438205i
$439$	−10.6208			−0.506905			−0.253452	−	0.967348i	$-0.581566\pi$
$439$	−10.6208			−0.506905			−0.253452	+	0.967348i	$0.581566\pi$
$440$		0			0
$441$	−0.666354			−0.0317312
$442$	3.15086	−	9.69735i	0.149871	−	0.461256i
$443$	−5.33865	+	3.87876i	−0.253647	+	0.184285i	−0.707342	−	0.706872i	$-0.750106\pi$
$443$	−5.33865	+	3.87876i	−0.253647	+	0.184285i	0.453695	+	0.891157i	$0.350106\pi$
$444$	14.1694	+	10.2947i	0.672452	+	0.488565i
$445$		0			0
$446$	1.56420	+	4.81411i	0.0740669	+	0.227955i
$447$	17.8071	+	12.9376i	0.842248	+	0.611929i
$448$	1.71478	−	1.24586i	0.0810158	−	0.0588614i
$449$	4.21130	−	12.9610i	0.198743	−	0.611670i	−0.801169	−	0.598438i	$-0.795788\pi$
$449$	4.21130	−	12.9610i	0.198743	−	0.611670i	0.999912	−	0.0132314i	$-0.00421180\pi$
$450$		0			0
$451$	−26.5688	−	8.49397i	−1.25107	−	0.399965i
$452$	−15.9988			−0.752522
$453$	−4.57178	+	14.0705i	−0.214801	+	0.661090i
$454$	−0.725253	+	0.526927i	−0.0340378	+	0.0247299i
$455$		0			0
$456$	3.35156	+	10.3150i	0.156951	+	0.483046i
$457$	−4.17169	−	12.8392i	−0.195144	−	0.600590i	−0.999975	−	0.00708664i	$-0.997744\pi$
$457$	−4.17169	−	12.8392i	−0.195144	−	0.600590i	0.804831	−	0.593504i	$-0.202256\pi$
$458$	−2.72498	−	1.97981i	−0.127330	−	0.0925105i
$459$	29.2332	−	21.2391i	1.36449	−	0.991358i
$460$		0			0
$461$	11.3217			0.527303			0.263652	−	0.964618i	$-0.415073\pi$
$461$	11.3217			0.527303			0.263652	+	0.964618i	$0.415073\pi$
$462$	−2.63558	+	0.870156i	−0.122618	+	0.0404833i
$463$	−4.82990			−0.224464			−0.112232	−	0.993682i	$-0.535800\pi$
$463$	−4.82990			−0.224464			−0.112232	+	0.993682i	$0.535800\pi$
$464$	0.606806	−	1.86756i	0.0281703	−	0.0866992i
$465$		0			0
$466$	−4.40257	−	3.19865i	−0.203945	−	0.148175i
$467$	7.42175	+	22.8418i	0.343437	+	1.05699i	0.962415	+	0.271583i	$0.0875472\pi$
$467$	7.42175	+	22.8418i	0.343437	+	1.05699i	−0.618978	+	0.785409i	$0.712453\pi$
$468$	−0.0753524	−	0.231911i	−0.00348317	−	0.0107201i
$469$	−3.25333	−	2.36368i	−0.150225	−	0.109145i
$470$		0			0
$471$	−7.61514	+	23.4370i	−0.350887	+	1.07992i
$472$	−0.103105			−0.00474579
$473$	−18.6783	−	25.4543i	−0.858828	−	1.17039i
$474$	6.39688			0.293818
$475$		0			0
$476$	4.59586	−	3.33909i	0.210651	−	0.153047i
$477$	0.193191	+	0.140361i	0.00884561	+	0.00642671i
$478$	−1.09093	−	3.35755i	−0.0498981	−	0.153571i
$479$	13.3573	+	41.1095i	0.610309	+	1.87834i	0.455052	+	0.890465i	$0.349621\pi$
$479$	13.3573	+	41.1095i	0.610309	+	1.87834i	0.155258	+	0.987874i	$0.450379\pi$
$480$		0			0
$481$	10.6546	−	7.74106i	0.485810	−	0.352962i
$482$	2.38428	−	7.33805i	0.108601	−	0.334239i
$483$	−1.55423			−0.0707199
$484$	−11.9809	+	8.87905i	−0.544588	+	0.403593i
$485$		0			0
$486$	−0.258219	+	0.794718i	−0.0117131	+	0.0360491i
$487$	33.9471	−	24.6640i	1.53829	−	1.11763i	0.586891	−	0.809666i	$-0.300352\pi$
$487$	33.9471	−	24.6640i	1.53829	−	1.11763i	0.951397	−	0.307966i	$-0.0996485\pi$
$488$	7.49977	+	5.44890i	0.339499	+	0.246660i
$489$	−6.44294	−	19.8293i	−0.291360	−	0.896713i
$490$		0			0
$491$	7.32956	+	5.32524i	0.330778	+	0.240325i	0.740761	−	0.671769i	$-0.234465\pi$
$491$	7.32956	+	5.32524i	0.330778	+	0.240325i	−0.409982	+	0.912093i	$0.634465\pi$
$492$	−16.2411	+	11.7998i	−0.732205	+	0.531978i
$493$	−7.81942	+	24.0657i	−0.352169	+	1.08386i
$494$	3.29478			0.148239
$495$		0			0
$496$	3.38705			0.152083
$497$	2.15786	−	6.64120i	0.0967931	−	0.297898i
$498$	6.79492	−	4.93680i	0.304488	−	0.221223i
$499$	−24.4965	−	17.7977i	−1.09661	−	0.796736i	−0.116109	−	0.993236i	$-0.537042\pi$
$499$	−24.4965	−	17.7977i	−1.09661	−	0.796736i	−0.980504	+	0.196501i	$0.937042\pi$
$500$		0			0
$501$	−4.74796	−	14.6127i	−0.212123	−	0.652849i
$502$	8.71530	+	6.33203i	0.388983	+	0.282612i
$503$	−14.6139	+	10.6177i	−0.651604	+	0.473418i	−0.863817	−	0.503806i	$-0.831933\pi$
$503$	−14.6139	+	10.6177i	−0.651604	+	0.473418i	0.212213	+	0.977223i	$0.431933\pi$
$504$	−0.0493894	+	0.152005i	−0.00219998	+	0.00677084i
$505$		0			0
$506$	3.76881	−	1.24430i	0.167544	−	0.0553161i
$507$	17.2172			0.764642
$508$	−6.72654	+	20.7022i	−0.298442	+	0.918510i
$509$	20.1572	−	14.6451i	0.893453	−	0.649132i	−0.0433229	−	0.999061i	$-0.513794\pi$
$509$	20.1572	−	14.6451i	0.893453	−	0.649132i	0.936776	+	0.349929i	$0.113794\pi$
$510$		0			0
$511$	1.24836	+	3.84205i	0.0552241	+	0.169962i
$512$	−1.90337	−	5.85796i	−0.0841177	−	0.258888i
$513$	9.44617	+	6.86304i	0.417058	+	0.303011i
$514$	−7.02477	+	5.10379i	−0.309849	+	0.225119i
$515$		0			0
$516$	−22.7226			−1.00031
$517$	6.10231	+	1.95089i	0.268379	+	0.0858002i
$518$	−3.48734			−0.153225
$519$	4.99407	−	15.3702i	0.219216	−	0.674676i
$520$		0			0
$521$	−29.3537	−	21.3267i	−1.28601	−	0.934339i	−0.286291	−	0.958143i	$-0.592422\pi$
$521$	−29.3537	−	21.3267i	−1.28601	−	0.934339i	−0.999717	+	0.0238032i	$0.992422\pi$
$522$	−0.0888777	−	0.273537i	−0.00389007	−	0.0119724i
$523$	−7.63489	−	23.4978i	−0.333850	−	1.02749i	−0.967286	−	0.253690i	$-0.918356\pi$
$523$	−7.63489	−	23.4978i	−0.333850	−	1.02749i	0.633435	−	0.773796i	$-0.281644\pi$
$524$	19.7742	+	14.3668i	0.863839	+	0.627616i
$525$		0			0
$526$	−6.11067	+	18.8067i	−0.266438	+	0.820011i
$527$	−43.6462			−1.90126
$528$	0.0151722	+	3.20715i	0.000660285	+	0.139573i
$529$	−20.7775			−0.903369
$530$		0			0
$531$	0.00310332	−	0.00225469i	0.000134672	−	9.78453e-5i
$532$	1.48507	+	1.07897i	0.0643859	+	0.0467791i
$533$	4.66473	+	14.3566i	0.202052	+	0.621852i
$534$	−2.71384	−	8.35234i	−0.117439	−	0.361441i
$535$		0			0
$536$	14.8001	−	10.7529i	0.639265	−	0.464453i
$537$	−0.787945	+	2.42504i	−0.0340023	+	0.104648i
$538$	3.85376			0.166148
$539$	12.8782	−	17.9029i	0.554705	−	0.771131i
$540$		0			0
$541$	−3.87568	+	11.9281i	−0.166628	+	0.512829i	−0.999153	−	0.0411593i	$-0.986895\pi$
$541$	−3.87568	+	11.9281i	−0.166628	+	0.512829i	0.832524	+	0.553989i	$0.186895\pi$
$542$	15.1507	−	11.0076i	0.650776	−	0.472817i
$543$	1.13032	+	0.821226i	0.0485067	+	0.0352422i
$544$	12.7456	+	39.2270i	0.546464	+	1.68184i
$545$		0			0
$546$	1.21518	+	0.882881i	0.0520050	+	0.0377838i
$547$	−24.8698	+	18.0689i	−1.06335	+	0.772572i	−0.974706	−	0.223491i	$-0.928255\pi$
$547$	−24.8698	+	18.0689i	−1.06335	+	0.772572i	−0.0886479	+	0.996063i	$0.528255\pi$
$548$	−1.68914	+	5.19865i	−0.0721566	+	0.222075i
$549$	−0.344889			−0.0147195
$550$		0			0
$551$	−8.17659			−0.348334
$552$	2.18491	−	6.72445i	0.0929958	−	0.286212i
$553$	2.16808	−	1.57520i	0.0921960	−	0.0669843i
$554$	−14.2200	−	10.3315i	−0.604151	−	0.438942i
$555$		0			0
$556$	−3.32415	−	10.2307i	−0.140975	−	0.433877i
$557$	−10.8646	−	7.89359i	−0.460347	−	0.334462i	0.333320	−	0.942814i	$-0.391831\pi$
$557$	−10.8646	−	7.89359i	−0.460347	−	0.334462i	−0.793668	+	0.608352i	$0.791831\pi$
$558$	0.401350	−	0.291597i	0.0169905	−	0.0123443i
$559$	−5.27993	+	16.2499i	−0.223317	+	0.687299i
$560$		0			0
$561$	−0.195512	−	41.3279i	−0.00825452	−	1.74487i
$562$	−12.6629			−0.534154
$563$	9.43741	−	29.0454i	0.397740	−	1.22412i	−0.529068	−	0.848580i	$-0.677458\pi$
$563$	9.43741	−	29.0454i	0.397740	−	1.22412i	0.926807	−	0.375537i	$-0.122542\pi$
$564$	3.73025	−	2.71019i	0.157072	−	0.114119i
$565$		0			0
$566$	−5.60814	−	17.2601i	−0.235728	−	0.725495i
$567$	1.69990	+	5.23175i	0.0713891	+	0.219713i
$568$	25.7000	+	18.6721i	1.07835	+	0.783465i
$569$	−20.8082	+	15.1181i	−0.872327	+	0.633783i	−0.931210	−	0.364482i	$-0.881246\pi$
$569$	−20.8082	+	15.1181i	−0.872327	+	0.633783i	0.0588833	+	0.998265i	$0.481246\pi$
$570$		0			0
$571$	−27.1115			−1.13458			−0.567291	−	0.823518i	$-0.692008\pi$
$571$	−27.1115			−1.13458			−0.567291	+	0.823518i	$0.692008\pi$
$572$	7.68702	+	2.45752i	0.321410	+	0.102754i
$573$	14.3506			0.599504
$574$	1.23520	−	3.80157i	0.0515564	−	0.158674i
$575$		0			0
$576$	−0.290224	−	0.210860i	−0.0120927	−	0.00878583i
$577$	0.886926	+	2.72968i	0.0369232	+	0.113638i	0.967819	−	0.251646i	$-0.0809719\pi$
$577$	0.886926	+	2.72968i	0.0369232	+	0.113638i	−0.930896	+	0.365284i	$0.880972\pi$
$578$	−8.20680	−	25.2579i	−0.341358	−	1.05059i
$579$	−6.22260	−	4.52098i	−0.258602	−	0.187886i
$580$		0			0
$581$	1.08732	−	3.34643i	0.0451097	−	0.138833i
$582$	7.59774			0.314936
$583$	−7.50476	+	2.47776i	−0.310816	+	0.102618i
$584$	−18.3777			−0.760476
$585$		0			0
$586$	−8.61075	+	6.25608i	−0.355707	+	0.258436i
$587$	−36.2731	−	26.3539i	−1.49715	−	1.08774i	−0.971499	−	0.237042i	$-0.923822\pi$
$587$	−36.2731	−	26.3539i	−1.49715	−	1.08774i	−0.525651	−	0.850701i	$-0.676178\pi$
$588$	−4.90475	−	15.0953i	−0.202268	−	0.622518i
$589$	−4.35822	−	13.4132i	−0.179577	−	0.552682i
$590$		0			0
$591$	22.2966	−	16.1994i	0.917159	−	0.666355i
$592$	−1.24525	+	3.83250i	−0.0511796	+	0.157515i
$593$	−6.09322			−0.250219			−0.125109	−	0.992143i	$-0.539928\pi$
$593$	−6.09322			−0.250219			−0.125109	+	0.992143i	$0.539928\pi$
$594$	−8.04162	−	10.9589i	−0.329952	−	0.449651i
$595$		0			0
$596$	−5.23695	+	16.1177i	−0.214514	+	0.660206i
$597$	2.04882	−	1.48855i	0.0838526	−	0.0609225i
$598$	−1.73768	−	1.26250i	−0.0710591	−	0.0516275i
$599$	−3.99674	−	12.3007i	−0.163302	−	0.502593i	0.835605	−	0.549331i	$-0.185117\pi$
$599$	−3.99674	−	12.3007i	−0.163302	−	0.502593i	−0.998907	+	0.0467381i	$0.985117\pi$
$600$		0			0
$601$	8.93729	+	6.49332i	0.364560	+	0.264868i	0.754951	−	0.655781i	$-0.227660\pi$
$601$	8.93729	+	6.49332i	0.364560	+	0.264868i	−0.390392	+	0.920649i	$0.627660\pi$
$602$	3.66029	−	2.65936i	0.149182	−	0.108387i
$603$	−0.210318	+	0.647294i	−0.00856483	+	0.0263598i
$604$	−11.3910			−0.463494
$605$		0			0
$606$	−14.0364			−0.570188
$607$	0.0358189	−	0.110239i	0.00145385	−	0.00447448i	−0.950327	−	0.311253i	$-0.899251\pi$
$607$	0.0358189	−	0.110239i	0.00145385	−	0.00447448i	0.951781	+	0.306779i	$0.0992512\pi$
$608$	−10.7824	+	7.83388i	−0.437285	+	0.317706i
$609$	−3.01569	−	2.19103i	−0.122202	−	0.0887849i
$610$		0			0
$611$	−1.07139	−	3.29741i	−0.0433440	−	0.133399i
$612$	−0.777842	−	0.565135i	−0.0314424	−	0.0228442i
$613$	15.4074	−	11.1941i	0.622297	−	0.452125i	−0.231426	−	0.972853i	$-0.574339\pi$
$613$	15.4074	−	11.1941i	0.622297	−	0.452125i	0.853723	+	0.520727i	$0.174339\pi$
$614$	−2.48447	+	7.64643i	−0.100265	+	0.308585i
$615$		0			0
$616$	−3.12938	−	4.26465i	−0.126086	−	0.171828i
$617$	30.8894			1.24356			0.621780	−	0.783192i	$-0.286410\pi$
$617$	30.8894			1.24356			0.621780	+	0.783192i	$0.286410\pi$
$618$	−5.90543	+	18.1750i	−0.237551	+	0.731108i
$619$	−27.1584	+	19.7317i	−1.09159	+	0.793086i	−0.979667	−	0.200631i	$-0.935701\pi$
$619$	−27.1584	+	19.7317i	−1.09159	+	0.793086i	−0.111922	+	0.993717i	$0.535701\pi$
$620$		0			0
$621$	−2.35216	−	7.23920i	−0.0943889	−	0.290499i
$622$	0.845410	+	2.60191i	0.0338979	+	0.104327i
$623$	−2.97652	−	2.16257i	−0.119252	−	0.0866414i
$624$	1.40418	−	1.02020i	0.0562122	−	0.0408405i
$625$		0			0
$626$	−19.6668			−0.786043
$627$	12.6812	−	4.18681i	0.506440	−	0.167205i
$628$	−18.9738			−0.757139
$629$	16.0466	−	49.3863i	0.639819	−	1.96916i
$630$		0			0
$631$	−19.9482	−	14.4932i	−0.794123	−	0.576964i	0.115061	−	0.993358i	$-0.463294\pi$
$631$	−19.9482	−	14.4932i	−0.794123	−	0.576964i	−0.909184	+	0.416394i	$0.863294\pi$
$632$	3.76734	+	11.5947i	0.149857	+	0.461211i
$633$	−4.72349	−	14.5374i	−0.187742	−	0.577810i
$634$	4.53832	+	3.29728i	0.180240	+	0.130952i
$635$		0			0
$636$	−1.75768	+	5.40960i	−0.0696967	+	0.214504i
$637$	−11.9350			−0.472880
$638$	9.06679	+	2.89863i	0.358958	+	0.114758i
$639$	−1.18186			−0.0467535
$640$		0			0
$641$	−5.67644	+	4.12418i	−0.224206	+	0.162895i	−0.694218	−	0.719765i	$-0.744250\pi$
$641$	−5.67644	+	4.12418i	−0.224206	+	0.162895i	0.470012	+	0.882660i	$0.344250\pi$
$642$	−6.40818	−	4.65582i	−0.252911	−	0.183751i
$643$	3.78623	+	11.6528i	0.149315	+	0.459543i	0.997541	−	0.0700915i	$-0.0223291\pi$
$643$	3.78623	+	11.6528i	0.149315	+	0.459543i	−0.848226	+	0.529634i	$0.822329\pi$
$644$	−0.369792	−	1.13810i	−0.0145718	−	0.0448475i
$645$		0			0
$646$	10.5100	−	7.63596i	0.413510	−	0.300433i
$647$	1.89123	−	5.82060i	0.0743519	−	0.228832i	−0.906973	−	0.421188i	$-0.861613\pi$
$647$	1.89123	−	5.82060i	0.0743519	−	0.228832i	0.981325	+	0.192357i	$0.0616131\pi$
$648$	−25.0251			−0.983079
$649$	0.000600576		0.126952i	2.35747e−5		0.00498328i
$650$		0			0
$651$	1.98685	−	6.11491i	0.0778710	−	0.239662i
$652$	12.9873	−	9.43583i	0.508622	−	0.369536i
$653$	30.7682	+	22.3544i	1.20405	+	0.874795i	0.994677	−	0.103041i	$-0.0328572\pi$
$653$	30.7682	+	22.3544i	1.20405	+	0.874795i	0.209375	+	0.977835i	$0.432857\pi$
$654$	8.12356	+	25.0017i	0.317656	+	0.977645i
$655$		0			0
$656$	−3.73676	−	2.71492i	−0.145896	−	0.106000i
$657$	0.553145	−	0.401883i	0.0215802	−	0.0156790i
$658$	−0.283702	+	0.873144i	−0.0110598	+	0.0340387i
$659$	15.7879			0.615011			0.307505	−	0.951546i	$-0.400506\pi$
$659$	15.7879			0.615011			0.307505	+	0.951546i	$0.400506\pi$
$660$		0			0
$661$	−24.5794			−0.956027			−0.478014	−	0.878352i	$-0.658643\pi$
$661$	−24.5794			−0.956027			−0.478014	+	0.878352i	$0.658643\pi$
$662$	−1.39978	+	4.30809i	−0.0544042	+	0.167439i
$663$	−18.0945	+	13.1464i	−0.702733	+	0.510566i
$664$	12.9500	+	9.40870i	0.502556	+	0.365128i
$665$		0			0
$666$	0.182390	+	0.561338i	0.00706746	+	0.0217514i
$667$	4.31237	+	3.13312i	0.166976	+	0.121315i
$668$	9.57067	−	6.95350i	0.370300	−	0.269039i
$669$	3.43111	−	10.5599i	0.132654	−	0.408268i
$670$		0			0
$671$	6.66547	−	9.26611i	0.257318	−	0.357714i
$672$	−6.07597			−0.234385
$673$	9.26226	−	28.5063i	0.357034	−	1.09884i	−0.597787	−	0.801655i	$-0.703953\pi$
$673$	9.26226	−	28.5063i	0.357034	−	1.09884i	0.954821	−	0.297182i	$-0.0960469\pi$
$674$	14.6870	−	10.6707i	0.565722	−	0.411021i
$675$		0			0
$676$	4.09642	+	12.6075i	0.157555	+	0.484903i
$677$	1.16101	+	3.57321i	0.0446211	+	0.137330i	0.970885	−	0.239546i	$-0.0769985\pi$
$677$	1.16101	+	3.57321i	0.0446211	+	0.137330i	−0.926264	+	0.376875i	$0.876999\pi$
$678$	−13.4940	−	9.80393i	−0.518232	−	0.376518i
$679$	2.57508	−	1.87091i	0.0988225	−	0.0717988i
$680$		0			0
$681$	1.96641			0.0753531
$682$	0.0776720	+	16.4185i	0.00297421	+	0.628699i
$683$	21.0157			0.804144			0.402072	−	0.915608i	$-0.368290\pi$
$683$	21.0157			0.804144			0.402072	+	0.915608i	$0.368290\pi$
$684$	0.0960054	−	0.295474i	0.00367086	−	0.0112977i
$685$		0			0
$686$	5.24834	+	3.81314i	0.200382	+	0.145586i
$687$	2.28313	+	7.02675i	0.0871068	+	0.268087i
$688$	−1.61555	−	4.97217i	−0.0615925	−	0.189562i
$689$	3.46021	+	2.51399i	0.131824	+	0.0957754i
$690$		0			0
$691$	−11.8299	+	36.4088i	−0.450032	+	1.38506i	0.426837	+	0.904328i	$0.359628\pi$
$691$	−11.8299	+	36.4088i	−0.450032	+	1.38506i	−0.876870	+	0.480728i	$0.840372\pi$
$692$	12.4432			0.473020
$693$	0.187449	+	0.0599271i	0.00712061	+	0.00227644i
$694$	0.146408			0.00555757
$695$		0			0
$696$	13.7190	−	9.96742i	0.520017	−	0.377814i
$697$	48.1527	+	34.9850i	1.82391	+	1.32515i
$698$	3.82670	+	11.7774i	0.144843	+	0.445780i
$699$	3.68870	+	11.3527i	0.139520	+	0.429397i
$700$		0			0
$701$	27.6963	−	20.1225i	1.04607	−	0.760016i	0.0746112	−	0.997213i	$-0.476228\pi$
$701$	27.6963	−	20.1225i	1.04607	−	0.760016i	0.971462	+	0.237196i	$0.0762284\pi$
$702$	−2.27318	+	6.99614i	−0.0857958	+	0.264052i
$703$	16.7795			0.632852
$704$	11.2741	−	3.72224i	0.424910	−	0.140287i
$705$		0			0
$706$	5.93089	−	18.2534i	0.223212	−	0.686976i
$707$	−4.75731	+	3.45639i	−0.178917	+	0.129991i
$708$	0.0739189	+	0.0537052i	0.00277804	+	0.00201836i
$709$	−1.27462	−	3.92289i	−0.0478695	−	0.147327i	0.924265	−	0.381752i	$-0.124679\pi$
$709$	−1.27462	−	3.92289i	−0.0478695	−	0.147327i	−0.972134	+	0.234425i	$0.924679\pi$
$710$		0			0
$711$	−0.366944	−	0.266600i	−0.0137615	−	0.00999828i
$712$	13.5408	−	9.83795i	0.507462	−	0.368693i
$713$	−2.84116	+	8.74418i	−0.106402	+	0.327472i
$714$	5.92246			0.221642
$715$		0			0
$716$	−1.96324			−0.0733697
$717$	−2.39299	+	7.36487i	−0.0893679	+	0.275046i
$718$	−5.69349	+	4.13656i	−0.212479	+	0.154375i
$719$	−23.7524	−	17.2571i	−0.885814	−	0.643582i	0.0489689	−	0.998800i	$-0.484406\pi$
$719$	−23.7524	−	17.2571i	−0.885814	−	0.643582i	−0.934783	+	0.355218i	$0.884406\pi$
$720$		0			0
$721$	2.47400	+	7.61420i	0.0921367	+	0.283568i
$722$	−8.94243	−	6.49706i	−0.332803	−	0.241795i
$723$	−13.6923	+	9.94801i	−0.509221	+	0.369970i
$724$	−0.332419	+	1.02308i	−0.0123543	+	0.0380225i
$725$		0			0
$726$	−15.5461	+	0.147093i	−0.576970	+	0.00545912i
$727$	−44.0893			−1.63518			−0.817591	−	0.575799i	$-0.804691\pi$
$727$	−44.0893			−1.63518			−0.817591	+	0.575799i	$0.804691\pi$
$728$	−0.884606	+	2.72254i	−0.0327857	+	0.100904i
$729$	−21.0659	+	15.3052i	−0.780217	+	0.566861i
$730$		0			0
$731$	20.8184	+	64.0723i	0.769995	+	2.36980i
$732$	−2.53858	−	7.81296i	−0.0938287	−	0.288775i
$733$	−39.6006	−	28.7715i	−1.46268	−	1.06270i	−0.982654	−	0.185446i	$-0.940627\pi$
$733$	−39.6006	−	28.7715i	−1.46268	−	1.06270i	−0.480026	−	0.877254i	$-0.659373\pi$
$734$	3.49526	−	2.53946i	0.129012	−	0.0937331i
$735$		0			0
$736$	8.68849			0.320262
$737$	−13.3261	−	18.1605i	−0.490872	−	0.668949i
$738$	−0.676520			−0.0249031
$739$	−6.38498	+	19.6509i	−0.234875	+	0.722872i	0.762263	+	0.647268i	$0.224088\pi$
$739$	−6.38498	+	19.6509i	−0.234875	+	0.722872i	−0.997138	+	0.0756039i	$0.975912\pi$
$740$		0			0
$741$	−5.84692	−	4.24804i	−0.214792	−	0.156056i
$742$	−0.349977	−	1.07712i	−0.0128481	−	0.0395423i
$743$	9.32091	+	28.6868i	0.341951	+	1.05242i	0.963196	+	0.268801i	$0.0866272\pi$
$743$	9.32091	+	28.6868i	0.341951	+	1.05242i	−0.621245	+	0.783617i	$0.713373\pi$
$744$	23.6634	+	17.1924i	0.867541	+	0.630305i
$745$		0			0
$746$	0.799830	−	2.46162i	0.0292839	−	0.0901264i
$747$	−0.595525			−0.0217891
$748$	30.2163	−	9.97615i	1.10482	−	0.364764i
$749$	−3.31838			−0.121251
$750$		0			0
$751$	−9.78637	+	7.11021i	−0.357110	+	0.259455i	−0.751846	−	0.659339i	$-0.770836\pi$
$751$	−9.78637	+	7.11021i	−0.357110	+	0.259455i	0.394736	+	0.918795i	$0.370836\pi$
$752$	0.858259	+	0.623562i	0.0312975	+	0.0227390i
$753$	−7.30213	−	22.4737i	−0.266105	−	0.818986i
$754$	−1.59187	−	4.89929i	−0.0579726	−	0.178421i
$755$		0			0
$756$	−3.31568	+	2.40898i	−0.120590	+	0.0876138i
$757$	6.36886	−	19.6013i	0.231480	−	0.712423i	−0.766089	−	0.642735i	$-0.777800\pi$
$757$	6.36886	−	19.6013i	0.231480	−	0.712423i	0.997569	−	0.0696881i	$-0.0222004\pi$
$758$	15.7838			0.573293
$759$	−8.29245	−	2.65108i	−0.300997	−	0.0962280i
$760$		0			0
$761$	6.44146	−	19.8248i	0.233503	−	0.718648i	−0.763814	−	0.645437i	$-0.776675\pi$
$761$	6.44146	−	19.8248i	0.233503	−	0.718648i	0.997316	−	0.0732111i	$-0.0233247\pi$
$762$	−18.3595	+	13.3389i	−0.665093	+	0.483219i
$763$	8.90985	+	6.47339i	0.322558	+	0.234352i
$764$	3.41437	+	10.5084i	0.123528	+	0.380179i
$765$		0			0
$766$	18.1670	+	13.1991i	0.656399	+	0.476902i
$767$	0.0555830	−	0.0403834i	0.00200699	−	0.00145816i
$768$	7.73127	−	23.7944i	0.278978	−	0.858607i
$769$	10.7167			0.386455			0.193228	−	0.981154i	$-0.438104\pi$
$769$	10.7167			0.386455			0.193228	+	0.981154i	$0.438104\pi$
$770$		0			0
$771$	19.0466			0.685946
$772$	1.83002	−	5.63223i	0.0658639	−	0.202708i
$773$	16.4686	−	11.9651i	0.592333	−	0.430355i	−0.250816	−	0.968035i	$-0.580699\pi$
$773$	16.4686	−	11.9651i	0.592333	−	0.430355i	0.843149	+	0.537679i	$0.180699\pi$
$774$	−0.619498	−	0.450092i	−0.0222674	−	0.0161782i
$775$		0			0
$776$	4.47456	+	13.7713i	0.160627	+	0.494361i
$777$	6.18863	+	4.49630i	0.222016	+	0.161304i
$778$	8.46814	−	6.15247i	0.303598	−	0.220577i
$779$	−5.94326	+	18.2915i	−0.212939	+	0.655360i
$780$		0			0
$781$	22.8410	−	31.7528i	0.817317	−	1.13620i
$782$	−8.46898			−0.302850
$783$	5.64131	−	17.3622i	0.201604	−	0.620474i
$784$	2.95442	−	2.14651i	0.105515	−	0.0766612i
$785$		0			0
$786$	7.87438	+	24.2348i	0.280870	+	0.864428i
$787$	4.39491	+	13.5261i	0.156661	+	0.482154i	0.998325	−	0.0578472i	$-0.0184236\pi$
$787$	4.39491	+	13.5261i	0.156661	+	0.482154i	−0.841664	+	0.540002i	$0.818424\pi$
$788$	17.1671	+	12.4727i	0.611554	+	0.444320i
$789$	35.0919	−	25.4958i	1.24930	−	0.907673i
$790$		0			0
$791$	−6.98764			−0.248452
$792$	−0.522790	+	0.726764i	−0.0185765	+	0.0258244i
$793$	−6.17726			−0.219361
$794$	0.452049	−	1.39126i	0.0160426	−	0.0493741i
$795$		0			0
$796$	1.57748	+	1.14610i	0.0559122	+	0.0406226i
$797$	−13.9176	−	42.8341i	−0.492988	−	1.51726i	−0.820069	−	0.572264i	$-0.806065\pi$
$797$	−13.9176	−	42.8341i	−0.492988	−	1.51726i	0.327081	−	0.944996i	$-0.393935\pi$
$798$	0.591377	+	1.82007i	0.0209345	+	0.0644298i
$799$	−11.0597	−	8.03534i	−0.391264	−	0.284270i
$800$		0			0
$801$	−0.192423	+	0.592218i	−0.00679894	+	0.0209250i
$802$	−4.31920			−0.152516
$803$	0.107049	+	22.6283i	0.00377766	+	0.798534i
$804$	−16.2115			−0.571737
$805$		0			0
$806$	7.18851	−	5.22276i	0.253204	−	0.183964i
$807$	−6.83889	−	4.96875i	−0.240740	−	0.174908i
$808$	−8.26649	−	25.4416i	−0.290814	−	0.895034i
$809$	7.34698	+	22.6117i	0.258306	+	0.794984i	0.993160	+	0.116759i	$0.0372506\pi$
$809$	7.34698	+	22.6117i	0.258306	+	0.794984i	−0.734854	+	0.678225i	$0.762749\pi$
$810$		0			0
$811$	6.63288	−	4.81907i	0.232912	−	0.169220i	−0.465208	−	0.885202i	$-0.654020\pi$
$811$	6.63288	−	4.81907i	0.232912	−	0.169220i	0.698120	+	0.715981i	$0.254020\pi$
$812$	0.886893	−	2.72957i	0.0311238	−	0.0957893i
$813$	−41.0787			−1.44069
$814$	−18.6064	−	5.94841i	−0.652152	−	0.208492i
$815$		0			0
$816$	2.11478	−	6.50864i	0.0740322	−	0.227848i
$817$	−17.6117	+	12.7957i	−0.616156	+	0.447663i
$818$	−23.8212	−	17.3071i	−0.832890	−	0.605130i
$819$	−0.0329109	−	0.101289i	−0.00115000	−	0.00353933i
$820$		0			0
$821$	35.1415	+	25.5318i	1.22645	+	0.891066i	0.996619	−	0.0821658i	$-0.0261837\pi$
$821$	35.1415	+	25.5318i	1.22645	+	0.891066i	0.229828	+	0.973231i	$0.426184\pi$
$822$	−4.61036	+	3.34962i	−0.160805	+	0.116831i
$823$	−15.9700	+	49.1507i	−0.556680	+	1.71328i	0.134785	+	0.990875i	$0.456966\pi$
$823$	−15.9700	+	49.1507i	−0.556680	+	1.71328i	−0.691465	+	0.722410i	$0.743034\pi$
$824$	−36.4211			−1.26879
$825$		0			0
$826$	−0.0181927			−0.000633004
$827$	7.82057	−	24.0692i	0.271948	−	0.836970i	−0.718063	−	0.695978i	$-0.754971\pi$
$827$	7.82057	−	24.0692i	0.271948	−	0.836970i	0.990011	−	0.140991i	$-0.0450290\pi$
$828$	−0.163854	+	0.119047i	−0.00569432	+	0.00413717i
$829$	33.8784	+	24.6141i	1.17665	+	0.854883i	0.991789	−	0.127883i	$-0.0408181\pi$
$829$	33.8784	+	24.6141i	1.17665	+	0.854883i	0.184856	+	0.982766i	$0.440818\pi$
$830$		0			0
$831$	11.9143	+	36.6684i	0.413302	+	1.27201i
$832$	−5.19815	−	3.77668i	−0.180213	−	0.130933i
$833$	−38.0713	+	27.6604i	−1.31909	+	0.958376i
$834$	3.46556	−	10.6659i	0.120003	−	0.369330i
$835$		0			0
$836$	6.08303	+	8.28982i	0.210386	+	0.286710i
$837$	31.4885			1.08840
$838$	−0.710980	+	2.18817i	−0.0245604	+	0.0755891i
$839$	11.6376	−	8.45518i	0.401773	−	0.291905i	−0.368490	−	0.929632i	$-0.620125\pi$
$839$	11.6376	−	8.45518i	0.401773	−	0.291905i	0.770263	+	0.637727i	$0.220125\pi$
$840$		0			0
$841$	−5.01097	−	15.4222i	−0.172792	−	0.531800i
$842$	−1.15584	−	3.55731i	−0.0398329	−	0.122593i
$843$	22.4716	+	16.3266i	0.773965	+	0.562318i
$844$	9.52134	−	6.91766i	0.327738	−	0.238116i
$845$		0			0
$846$	0.155383			0.00534218
$847$	−5.23278	+	3.87801i	−0.179800	+	0.133250i
$848$	−1.30870			−0.0449408
$849$	−12.3016	+	37.8605i	−0.422190	+	1.29937i
$850$		0			0
$851$	−8.84960	−	6.42961i	−0.303360	−	0.220404i
$852$	−8.69914	−	26.7732i	−0.298028	−	0.917235i
$853$	13.2882	+	40.8968i	0.454978	+	1.40028i	0.871161	+	0.490998i	$0.163368\pi$
$853$	13.2882	+	40.8968i	0.454978	+	1.40028i	−0.416183	+	0.909281i	$0.636632\pi$
$854$	1.32332	+	0.961450i	0.0452832	+	0.0329001i
$855$		0			0
$856$	4.66492	−	14.3571i	0.159444	−	0.490717i
$857$	54.3052			1.85503			0.927516	−	0.373784i	$-0.121940\pi$
$857$	54.3052			1.85503			0.927516	+	0.373784i	$0.121940\pi$
$858$	4.97754	+	6.78328i	0.169931	+	0.231578i
$859$	24.3361			0.830336			0.415168	−	0.909745i	$-0.363723\pi$
$859$	24.3361			0.830336			0.415168	+	0.909745i	$0.363723\pi$
$860$		0			0
$861$	−7.09344	+	5.15369i	−0.241744	+	0.175637i
$862$	13.4874	+	9.79917i	0.459383	+	0.333761i
$863$	−12.0980	−	37.2339i	−0.411822	−	1.26746i	−0.915063	−	0.403312i	$-0.867859\pi$
$863$	−12.0980	−	37.2339i	−0.411822	−	1.26746i	0.503241	−	0.864146i	$-0.332141\pi$
$864$	−9.19531	−	28.3003i	−0.312831	−	0.962795i
$865$		0			0
$866$	−8.31045	+	6.03789i	−0.282400	+	0.205176i
$867$	−18.0018	+	55.4039i	−0.611374	+	1.88162i
$868$	4.95043			0.168029
$869$	14.2544	−	4.70621i	0.483548	−	0.159647i
$870$		0			0
$871$	−3.76698	+	11.5936i	−0.127639	+	0.392833i
$872$	−40.5327	+	29.4487i	−1.37261	+	0.997260i
$873$	−0.435828	−	0.316648i	−0.0147505	−	0.0107169i
$874$	−0.845656	−	2.60266i	−0.0286047	−	0.0880363i
$875$		0			0
$876$	13.1755	+	9.57259i	0.445160	+	0.323428i
$877$	34.8591	−	25.3266i	1.17711	−	0.855219i	0.185265	−	0.982689i	$-0.440686\pi$
$877$	34.8591	−	25.3266i	1.17711	−	0.855219i	0.991842	+	0.127470i	$0.0406855\pi$
$878$	2.63447	−	8.10808i	0.0889092	−	0.273634i
$879$	23.3468			0.787466
$880$		0			0
$881$	−38.1083			−1.28390			−0.641950	−	0.766746i	$-0.721874\pi$
$881$	−38.1083			−1.28390			−0.641950	+	0.766746i	$0.721874\pi$
$882$	0.165288	−	0.508703i	0.00556552	−	0.0171289i
$883$	23.4826	−	17.0611i	0.790252	−	0.574152i	−0.117786	−	0.993039i	$-0.537580\pi$
$883$	23.4826	−	17.0611i	0.790252	−	0.574152i	0.908038	+	0.418887i	$0.137580\pi$
$884$	−13.9318	−	10.1220i	−0.468577	−	0.340441i
$885$		0			0
$886$	−1.63685	−	5.03771i	−0.0549911	−	0.169245i
$887$	1.78934	+	1.30003i	0.0600801	+	0.0436508i	0.617420	−	0.786634i	$-0.288178\pi$
$887$	1.78934	+	1.30003i	0.0600801	+	0.0436508i	−0.557340	+	0.830284i	$0.688178\pi$
$888$	−28.1533	+	20.4546i	−0.944764	+	0.686411i
$889$	−2.93788	+	9.04186i	−0.0985332	+	0.303254i
$890$		0			0
$891$	0.145769	+	30.8131i	0.00488344	+	1.03228i
$892$	8.54894			0.286240
$893$	1.36505	−	4.20118i	0.0456796	−	0.140587i
$894$	−14.2938	+	10.3850i	−0.478055	+	0.347327i
$895$		0			0
$896$	−1.60695	−	4.94569i	−0.0536845	−	0.165224i
$897$	1.45592	+	4.48087i	0.0486118	+	0.149612i
$898$	8.85002	+	6.42991i	0.295329	+	0.214569i
$899$	−17.8396	+	12.9612i	−0.594983	+	0.432280i
$900$		0			0
$901$	16.8641			0.561825
$902$	13.0747	−	18.1760i	0.435340	−	0.605195i
$903$	−9.92432			−0.330261
$904$	9.82309	−	30.2323i	0.326711	−	1.00551i
$905$		0			0
$906$	−9.60757	−	6.98031i	−0.319190	−	0.231905i
$907$	−8.24653	−	25.3802i	−0.273822	−	0.842736i	−0.989529	−	0.144336i	$-0.953895\pi$
$907$	−8.24653	−	25.3802i	−0.273822	−	0.842736i	0.715707	−	0.698401i	$-0.246105\pi$
$908$	0.467861	+	1.43993i	0.0155265	+	0.0477857i
$909$	0.805166	+	0.584988i	0.0267057	+	0.0194028i
$910$		0			0
$911$	−11.2092	+	34.4983i	−0.371376	+	1.14298i	0.574515	+	0.818494i	$0.305191\pi$
$911$	−11.2092	+	34.4983i	−0.371376	+	1.14298i	−0.945891	+	0.324484i	$0.894809\pi$
$912$	2.21138			0.0732261
$913$	11.5094	−	15.9999i	0.380904	−	0.529520i
$914$	10.8363			0.358434
$915$		0			0
$916$	−4.60220	+	3.34369i	−0.152061	+	0.110479i
$917$	8.63655	+	6.27482i	0.285204	+	0.207213i
$918$	8.96300	+	27.5853i	0.295823	+	0.910450i
$919$	−9.16908	−	28.2195i	−0.302460	−	0.930876i	−0.980613	−	0.195955i	$-0.937219\pi$
$919$	−9.16908	−	28.2195i	−0.302460	−	0.930876i	0.678153	−	0.734921i	$-0.262781\pi$
$920$		0			0
$921$	14.2677	−	10.3661i	0.470135	−	0.341573i
$922$	−2.80832	+	8.64311i	−0.0924870	+	0.284646i
$923$	−21.1680			−0.696754
$924$	0.0221753	+	4.68749i	0.000729514	+	0.154207i
$925$		0			0
$926$	1.19805	−	3.68720i	0.0393702	−	0.121169i
$927$	1.09623	−	0.796455i	0.0360048	−	0.0261590i
$928$	16.8584	+	12.2483i	0.553403	+	0.402071i
$929$	8.58220	+	26.4133i	0.281573	+	0.866592i	0.987405	+	0.158213i	$0.0505733\pi$
$929$	8.58220	+	26.4133i	0.281573	+	0.866592i	−0.705832	+	0.708379i	$0.749427\pi$
$930$		0			0
$931$	−12.3020	−	8.93795i	−0.403183	−	0.292930i
$932$	−7.43548	+	5.40219i	−0.243557	+	0.176955i
$933$	1.85443	−	5.70735i	0.0607113	−	0.186850i
$934$	−19.2786			−0.630817
$935$		0			0
$936$	0.484498			0.0158363
$937$	−9.34532	+	28.7620i	−0.305298	+	0.939612i	0.674267	+	0.738487i	$0.264460\pi$
$937$	−9.34532	+	28.7620i	−0.305298	+	0.939612i	−0.979566	+	0.201125i	$0.935540\pi$
$938$	2.61144	−	1.89733i	0.0852667	−	0.0619499i
$939$	34.9007	+	25.3568i	1.13894	+	0.827489i
$940$		0			0
$941$	−1.85618	−	5.71273i	−0.0605097	−	0.186230i	0.916232	−	0.400647i	$-0.131215\pi$
$941$	−1.85618	−	5.71273i	−0.0605097	−	0.186230i	−0.976742	+	0.214418i	$0.931215\pi$
$942$	−16.0032	−	11.6270i	−0.521412	−	0.378828i
$943$	10.1435	−	7.36966i	0.330317	−	0.239989i
$944$	−0.00649622	+	0.0199933i	−0.000211434	+	0.000650727i
$945$		0			0
$946$	24.0652	−	7.94533i	0.782428	−	0.258325i
$947$	10.0218			0.325665			0.162833	−	0.986654i	$-0.447937\pi$
$947$	10.0218			0.325665			0.162833	+	0.986654i	$0.447937\pi$
$948$	3.33851	−	10.2749i	0.108430	−	0.333713i
$949$	9.90729	−	7.19807i	0.321604	−	0.233659i
$950$		0			0
$951$	−3.80244	−	11.7027i	−0.123303	−	0.379486i
$952$	3.48794	+	10.7348i	0.113045	+	0.347916i
$953$	7.91329	+	5.74934i	0.256336	+	0.186239i	0.708530	−	0.705680i	$-0.249359\pi$
$953$	7.91329	+	5.74934i	0.256336	+	0.186239i	−0.452194	+	0.891920i	$0.649359\pi$
$954$	−0.155074	+	0.112668i	−0.00502071	+	0.00364776i
$955$		0			0
$956$	−5.96237			−0.192837
$957$	−12.3527	−	16.8339i	−0.399305	−	0.544164i
$958$	−34.6967			−1.12100
$959$	−0.737749	+	2.27056i	−0.0238231	+	0.0733201i
$960$		0			0
$961$	−5.69127	−	4.13495i	−0.183589	−	0.133385i
$962$	3.26676	+	10.0540i	0.105324	+	0.324155i
$963$	0.173553	+	0.534142i	0.00559268	+	0.0172125i
$964$	−10.5423	−	7.65942i	−0.339544	−	0.246693i
$965$		0			0
$966$	0.385523	−	1.18652i	0.0124040	−	0.0381756i
$967$	−1.22635			−0.0394367			−0.0197184	−	0.999806i	$-0.506277\pi$
$967$	−1.22635			−0.0394367			−0.0197184	+	0.999806i	$0.506277\pi$
$968$	−9.42224	−	28.0915i	−0.302842	−	0.902895i
$969$	−28.4963			−0.915432
$970$		0			0
$971$	36.1199	−	26.2426i	1.15914	−	0.842167i	0.169473	−	0.985535i	$-0.445793\pi$
$971$	36.1199	−	26.2426i	1.15914	−	0.842167i	0.989669	+	0.143368i	$0.0457933\pi$
$972$	1.14174	+	0.829522i	0.0366213	+	0.0266069i
$973$	−1.45185	−	4.46834i	−0.0465442	−	0.143248i
$974$	10.4083	+	32.0335i	0.333503	+	1.02642i
$975$		0			0
$976$	1.52914	−	1.11099i	0.0489466	−	0.0355618i
$977$	−14.5996	+	44.9328i	−0.467081	+	1.43753i	0.389265	+	0.921126i	$0.372729\pi$
$977$	−14.5996	+	44.9328i	−0.467081	+	1.43753i	−0.856346	+	0.516402i	$0.827271\pi$
$978$	16.7361			0.535162
$979$	−12.1922	−	16.6153i	−0.389665	−	0.531026i
$980$		0			0
$981$	0.575996	−	1.77273i	0.0183901	−	0.0565991i
$982$	−5.88343	+	4.27456i	−0.187748	+	0.136407i
$983$	−11.2737	−	8.19082i	−0.359575	−	0.261247i	0.393300	−	0.919410i	$-0.371333\pi$
$983$	−11.2737	−	8.19082i	−0.359575	−	0.261247i	−0.752875	+	0.658164i	$0.771333\pi$
$984$	−12.3259	−	37.9351i	−0.392934	−	1.20933i
$985$		0			0
$986$	−16.4325	−	11.9389i	−0.523316	−	0.380211i
$987$	1.62922	−	1.18370i	0.0518587	−	0.0376775i
$988$	1.71954	−	5.29219i	0.0547058	−	0.168367i
$989$	14.1916			0.451265
$990$		0			0
$991$	36.5755			1.16186			0.580930	−	0.813953i	$-0.302689\pi$
$991$	36.5755			1.16186			0.580930	+	0.813953i	$0.302689\pi$
$992$	−11.1070	+	34.1837i	−0.352646	+	1.08533i
$993$	8.03858	−	5.84037i	0.255097	−	0.185339i
$994$	4.53472	+	3.29467i	0.143833	+	0.104501i
$995$		0			0
$996$	−4.38341	−	13.4907i	−0.138894	−	0.427470i
$997$	−15.6476	−	11.3687i	−0.495565	−	0.360049i	0.311755	−	0.950162i	$-0.399083\pi$
$997$	−15.6476	−	11.3687i	−0.495565	−	0.360049i	−0.807320	+	0.590113i	$0.799083\pi$
$998$	19.6633	−	14.2862i	0.622431	−	0.452222i
$999$	−11.5768	+	35.6297i	−0.366273	+	1.12727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.h.d.251.2		16
5.2	odd	4		55.2.j.a.9.2	✓	16
5.3	odd	4		55.2.j.a.9.3	yes	16
5.4	even	2	inner	275.2.h.d.251.3		16
11.4	even	5		3025.2.a.bl.1.4		8
11.5	even	5	inner	275.2.h.d.126.2		16
11.7	odd	10		3025.2.a.bk.1.5		8
15.2	even	4		495.2.ba.a.64.3		16
15.8	even	4		495.2.ba.a.64.2		16
20.3	even	4		880.2.cd.c.449.2		16
20.7	even	4		880.2.cd.c.449.3		16
55.2	even	20		605.2.j.g.124.2		16
55.3	odd	20		605.2.j.h.444.3		16
55.4	even	10		3025.2.a.bl.1.5		8
55.7	even	20		605.2.b.f.364.5		8
55.8	even	20		605.2.j.g.444.2		16
55.13	even	20		605.2.j.g.124.3		16
55.17	even	20		605.2.j.d.269.2		16
55.18	even	20		605.2.b.f.364.4		8
55.27	odd	20		55.2.j.a.49.3	yes	16
55.28	even	20		605.2.j.d.269.3		16
55.29	odd	10		3025.2.a.bk.1.4		8
55.32	even	4		605.2.j.d.9.3		16
55.37	odd	20		605.2.b.g.364.4		8
55.38	odd	20		55.2.j.a.49.2	yes	16
55.42	odd	20		605.2.j.h.124.3		16
55.43	even	4		605.2.j.d.9.2		16
55.47	odd	20		605.2.j.h.444.2		16
55.48	odd	20		605.2.b.g.364.5		8
55.49	even	10	inner	275.2.h.d.126.3		16
55.52	even	20		605.2.j.g.444.3		16
55.53	odd	20		605.2.j.h.124.2		16
165.38	even	20		495.2.ba.a.379.3		16
165.137	even	20		495.2.ba.a.379.2		16
220.27	even	20		880.2.cd.c.49.2		16
220.203	even	20		880.2.cd.c.49.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.9.2	✓	16	5.2	odd	4
55.2.j.a.9.3	yes	16	5.3	odd	4
55.2.j.a.49.2	yes	16	55.38	odd	20
55.2.j.a.49.3	yes	16	55.27	odd	20
275.2.h.d.126.2		16	11.5	even	5	inner
275.2.h.d.126.3		16	55.49	even	10	inner
275.2.h.d.251.2		16	1.1	even	1	trivial
275.2.h.d.251.3		16	5.4	even	2	inner
495.2.ba.a.64.2		16	15.8	even	4
495.2.ba.a.64.3		16	15.2	even	4
495.2.ba.a.379.2		16	165.137	even	20
495.2.ba.a.379.3		16	165.38	even	20
605.2.b.f.364.4		8	55.18	even	20
605.2.b.f.364.5		8	55.7	even	20
605.2.b.g.364.4		8	55.37	odd	20
605.2.b.g.364.5		8	55.48	odd	20
605.2.j.d.9.2		16	55.43	even	4
605.2.j.d.9.3		16	55.32	even	4
605.2.j.d.269.2		16	55.17	even	20
605.2.j.d.269.3		16	55.28	even	20
605.2.j.g.124.2		16	55.2	even	20
605.2.j.g.124.3		16	55.13	even	20
605.2.j.g.444.2		16	55.8	even	20
605.2.j.g.444.3		16	55.52	even	20
605.2.j.h.124.2		16	55.53	odd	20
605.2.j.h.124.3		16	55.42	odd	20
605.2.j.h.444.2		16	55.47	odd	20
605.2.j.h.444.3		16	55.3	odd	20
880.2.cd.c.49.2		16	220.27	even	20
880.2.cd.c.49.3		16	220.203	even	20
880.2.cd.c.449.2		16	20.3	even	4
880.2.cd.c.449.3		16	20.7	even	4
3025.2.a.bk.1.4		8	55.29	odd	10
3025.2.a.bk.1.5		8	11.7	odd	10
3025.2.a.bl.1.4		8	11.4	even	5
3025.2.a.bl.1.5		8	55.4	even	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)

\(f(q)\)	\(=\)	\(q+(-0.248048 + 0.763412i) q^{2} +(1.42447 - 1.03494i) q^{3} +(1.09676 + 0.796845i) q^{4} +(0.436748 + 1.34417i) q^{6} +(0.479022 + 0.348029i) q^{7} +(-2.17917 + 1.58326i) q^{8} +(0.0309674 - 0.0953077i) q^{9} +O(q^{10})\)	\(q+(-0.248048 + 0.763412i) q^{2} +(1.42447 - 1.03494i) q^{3} +(1.09676 + 0.796845i) q^{4} +(0.436748 + 1.34417i) q^{6} +(0.479022 + 0.348029i) q^{7} +(-2.17917 + 1.58326i) q^{8} +(0.0309674 - 0.0953077i) q^{9} +(1.96213 + 2.67395i) q^{11} +2.38699 q^{12} +(0.554651 - 1.70704i) q^{13} +(-0.384510 + 0.279363i) q^{14} +(0.169713 + 0.522322i) q^{16} +(-2.18695 - 6.73074i) q^{17} +(0.0650777 + 0.0472817i) q^{18} +(1.85009 - 1.34417i) q^{19} +1.04254 q^{21} +(-2.52803 + 0.834650i) q^{22} -1.49081 q^{23} +(-1.46558 + 4.51060i) q^{24} +(1.16560 + 0.846855i) q^{26} +(1.57777 + 4.85588i) q^{27} +(0.248048 + 0.763412i) q^{28} +(-2.89263 - 2.10162i) q^{29} +(1.90578 - 5.86539i) q^{31} -5.82804 q^{32} +(5.56238 + 1.77828i) q^{33} +5.68079 q^{34} +(0.109909 - 0.0798539i) q^{36} +(5.93610 + 4.31283i) q^{37} +(0.567246 + 1.74580i) q^{38} +(-0.976598 - 3.00566i) q^{39} +(-6.80400 + 4.94339i) q^{41} +(-0.258600 + 0.795888i) q^{42} -9.51936 q^{43} +(0.0212704 + 4.49621i) q^{44} +(0.369792 - 1.13810i) q^{46} +(1.56274 - 1.13540i) q^{47} +(0.782321 + 0.568389i) q^{48} +(-2.05478 - 6.32397i) q^{49} +(-10.0811 - 7.32438i) q^{51} +(1.96857 - 1.43025i) q^{52} +(-0.736359 + 2.26628i) q^{53} -4.09840 q^{54} -1.59489 q^{56} +(1.24427 - 3.82947i) q^{57} +(2.32192 - 1.68697i) q^{58} +(0.0309674 + 0.0224991i) q^{59} +(-1.06351 - 3.27314i) q^{61} +(4.00499 + 2.90979i) q^{62} +(0.0480039 - 0.0348769i) q^{63} +(1.10621 - 3.40455i) q^{64} +(-2.73729 + 3.80529i) q^{66} -6.79162 q^{67} +(2.96479 - 9.12469i) q^{68} +(-2.12361 + 1.54290i) q^{69} +(-3.64439 - 11.2163i) q^{71} +(0.0834136 + 0.256721i) q^{72} +(5.51972 + 4.01031i) q^{73} +(-4.76490 + 3.46191i) q^{74} +3.10021 q^{76} +(0.00929006 + 1.96376i) q^{77} +2.53680 q^{78} +(1.39863 - 4.30453i) q^{79} +(7.51625 + 5.46087i) q^{81} +(-2.08613 - 6.42045i) q^{82} +(-1.83637 - 5.65177i) q^{83} +(1.14342 + 0.830744i) q^{84} +(2.36125 - 7.26720i) q^{86} -6.29552 q^{87} +(-8.50937 - 2.72042i) q^{88} -6.21375 q^{89} +(0.859791 - 0.624675i) q^{91} +(-1.63507 - 1.18795i) q^{92} +(-3.35559 - 10.3274i) q^{93} +(0.479142 + 1.47465i) q^{94} +(-8.30186 + 6.03166i) q^{96} +(1.66119 - 5.11260i) q^{97} +5.33748 q^{98} +(0.315611 - 0.104201i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 18 q^{6} - 2 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 - 18 * q^6 - 2 * q^9	\( 16 q + 4 q^{4} - 18 q^{6} - 2 q^{9} - 6 q^{11} + 12 q^{14} + 16 q^{16} - 6 q^{19} + 8 q^{21} - 6 q^{24} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 16 q^{34} + 10 q^{36} - 30 q^{39} - 52 q^{41} - 4 q^{44} - 62 q^{46} + 10 q^{49} - 42 q^{51} + 40 q^{54} - 20 q^{56} - 2 q^{59} - 40 q^{61} + 8 q^{64} + 58 q^{66} - 26 q^{69} + 36 q^{71} - 48 q^{74} + 56 q^{76} - 38 q^{79} + 68 q^{81} - 12 q^{84} + 22 q^{86} - 24 q^{89} - 20 q^{91} - 14 q^{94} - 86 q^{96} + 72 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 18 * q^6 - 2 * q^9 - 6 * q^11 + 12 * q^14 + 16 * q^16 - 6 * q^19 + 8 * q^21 - 6 * q^24 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 16 * q^34 + 10 * q^36 - 30 * q^39 - 52 * q^41 - 4 * q^44 - 62 * q^46 + 10 * q^49 - 42 * q^51 + 40 * q^54 - 20 * q^56 - 2 * q^59 - 40 * q^61 + 8 * q^64 + 58 * q^66 - 26 * q^69 + 36 * q^71 - 48 * q^74 + 56 * q^76 - 38 * q^79 + 68 * q^81 - 12 * q^84 + 22 * q^86 - 24 * q^89 - 20 * q^91 - 14 * q^94 - 86 * q^96 + 72 * q^99

Introduction

L-functions

Modular forms

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