LMFDB - Embedded newform 550.2.h.l.401.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,2,Mod(201,550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(550, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("550.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.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:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			401.1
Root			$-0.390899 - 1.20306i$ of defining polynomial
Character	$\chi$	$=$	550.401
Dual form			550.2.h.l.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-0.214371 - 0.155750i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.0818824 - 0.252008i) q^{6} +(-3.48828 + 2.53438i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.905354 - 2.78639i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.214371 - 0.155750i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.0818824 - 0.252008i) q^{6} +(-3.48828 + 2.53438i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.905354 - 2.78639i) q^{9} +(-1.42705 + 2.99391i) q^{11} +0.264977 q^{12} +(-0.374078 - 1.15129i) q^{13} +(-3.48828 - 2.53438i) q^{14} +(0.309017 - 0.951057i) q^{16} +(2.21437 - 6.81513i) q^{17} +(2.37025 - 1.72209i) q^{18} +(-2.19992 - 1.59833i) q^{19} +1.14252 q^{21} +(-3.28837 - 0.432036i) q^{22} -7.01787 q^{23} +(0.0818824 + 0.252008i) q^{24} +(0.979348 - 0.711538i) q^{26} +(-0.485545 + 1.49436i) q^{27} +(1.33240 - 4.10072i) q^{28} +(-8.54782 + 6.21036i) q^{29} +(1.11908 + 3.44417i) q^{31} +1.00000 q^{32} +(0.772220 - 0.419546i) q^{33} +7.16586 q^{34} +(2.37025 + 1.72209i) q^{36} +(1.71437 - 1.24556i) q^{37} +(0.840293 - 2.58616i) q^{38} +(-0.0991220 + 0.305066i) q^{39} +(-2.22713 - 1.61811i) q^{41} +(0.353057 + 1.08660i) q^{42} -6.59251 q^{43} +(-0.605270 - 3.26093i) q^{44} +(-2.16864 - 6.67439i) q^{46} +(4.64416 + 3.37418i) q^{47} +(-0.214371 + 0.155750i) q^{48} +(3.58188 - 11.0239i) q^{49} +(-1.53615 + 1.11608i) q^{51} +(0.979348 + 0.711538i) q^{52} +(1.81558 + 5.58779i) q^{53} -1.57126 q^{54} +4.31175 q^{56} +(0.222659 + 0.685272i) q^{57} +(-8.54782 - 6.21036i) q^{58} +(4.77117 - 3.46646i) q^{59} +(-1.89879 + 5.84387i) q^{61} +(-2.92979 + 2.12861i) q^{62} +(10.2199 + 7.42521i) q^{63} +(0.309017 + 0.951057i) q^{64} +(0.637641 + 0.604778i) q^{66} +1.63381 q^{67} +(2.21437 + 6.81513i) q^{68} +(1.50443 + 1.09303i) q^{69} +(2.29862 - 7.07443i) q^{71} +(-0.905354 + 2.78639i) q^{72} +(-5.98039 + 4.34501i) q^{73} +(1.71437 + 1.24556i) q^{74} +2.71925 q^{76} +(-2.60978 - 14.0603i) q^{77} -0.320766 q^{78} +(2.16376 + 6.65938i) q^{79} +(-6.77391 + 4.92153i) q^{81} +(0.850690 - 2.61815i) q^{82} +(0.492758 - 1.51655i) q^{83} +(-0.924315 + 0.671554i) q^{84} +(-2.03720 - 6.26985i) q^{86} +2.79967 q^{87} +(2.91429 - 1.58333i) q^{88} +1.24711 q^{89} +(4.22271 + 3.06798i) q^{91} +(5.67757 - 4.12500i) q^{92} +(0.296530 - 0.912627i) q^{93} +(-1.77391 + 5.45954i) q^{94} +(-0.214371 - 0.155750i) q^{96} +(2.13632 + 6.57491i) q^{97} +11.5912 q^{98} +(9.63421 + 1.26577i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - q^{6} + q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - q^6 + q^7 - 2 * q^8 - 6 * q^9	$ 8 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - q^{6} + q^{7} - 2 q^{8} - 6 q^{9} + 2 q^{11} - 6 q^{12} - q^{13} + q^{14} - 2 q^{16} + 12 q^{17} - q^{18} - 7 q^{19} + 32 q^{21} - 8 q^{22} - 26 q^{23} - q^{24} - 6 q^{26} + q^{27} - 4 q^{28} - 22 q^{29} - 26 q^{31} + 8 q^{32} - 19 q^{33} + 2 q^{34} - q^{36} + 8 q^{37} + 3 q^{38} - 48 q^{39} - 15 q^{41} + 2 q^{42} - 38 q^{43} + 7 q^{44} - 6 q^{46} - 6 q^{47} + 4 q^{48} + 27 q^{49} - 5 q^{51} - 6 q^{52} + 4 q^{53} - 24 q^{54} + 6 q^{56} - 47 q^{57} - 22 q^{58} + 39 q^{59} - 20 q^{61} + 14 q^{62} + 57 q^{63} - 2 q^{64} + 36 q^{66} + 26 q^{67} + 12 q^{68} - 10 q^{69} + 2 q^{71} - 6 q^{72} - 8 q^{73} + 8 q^{74} + 8 q^{76} - 16 q^{77} + 12 q^{78} + 14 q^{79} - 31 q^{81} + 15 q^{82} + 21 q^{83} - 18 q^{84} + 17 q^{86} - 20 q^{87} + 7 q^{88} + 32 q^{89} + 53 q^{91} + 19 q^{92} + 38 q^{93} + 9 q^{94} + 4 q^{96} + 31 q^{97} + 22 q^{98} + 36 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - q^6 + q^7 - 2 * q^8 - 6 * q^9 + 2 * q^11 - 6 * q^12 - q^13 + q^14 - 2 * q^16 + 12 * q^17 - q^18 - 7 * q^19 + 32 * q^21 - 8 * q^22 - 26 * q^23 - q^24 - 6 * q^26 + q^27 - 4 * q^28 - 22 * q^29 - 26 * q^31 + 8 * q^32 - 19 * q^33 + 2 * q^34 - q^36 + 8 * q^37 + 3 * q^38 - 48 * q^39 - 15 * q^41 + 2 * q^42 - 38 * q^43 + 7 * q^44 - 6 * q^46 - 6 * q^47 + 4 * q^48 + 27 * q^49 - 5 * q^51 - 6 * q^52 + 4 * q^53 - 24 * q^54 + 6 * q^56 - 47 * q^57 - 22 * q^58 + 39 * q^59 - 20 * q^61 + 14 * q^62 + 57 * q^63 - 2 * q^64 + 36 * q^66 + 26 * q^67 + 12 * q^68 - 10 * q^69 + 2 * q^71 - 6 * q^72 - 8 * q^73 + 8 * q^74 + 8 * q^76 - 16 * q^77 + 12 * q^78 + 14 * q^79 - 31 * q^81 + 15 * q^82 + 21 * q^83 - 18 * q^84 + 17 * q^86 - 20 * q^87 + 7 * q^88 + 32 * q^89 + 53 * q^91 + 19 * q^92 + 38 * q^93 + 9 * q^94 + 4 * q^96 + 31 * q^97 + 22 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−0.214371	−	0.155750i	−0.123767	−	0.0899221i	0.524180	−	0.851608i	$-0.324372\pi$
$3$	−0.214371	−	0.155750i	−0.123767	−	0.0899221i	−0.647947	+	0.761686i	$0.724372\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$		0			0
$5$		0			0
$6$	0.0818824	−	0.252008i	0.0334284	−	0.102882i
$7$	−3.48828	+	2.53438i	−1.31845	+	0.957907i	−0.318496	+	0.947924i	$0.603178\pi$
$7$	−3.48828	+	2.53438i	−1.31845	+	0.957907i	−0.999950	+	0.00998336i	$0.996822\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−0.905354	−	2.78639i	−0.301785	−	0.928798i
$10$		0			0
$11$	−1.42705	+	2.99391i	−0.430272	+	0.902699i
$11$	−1.42705	+	2.99391i	−0.430272	+	0.902699i
$12$	0.264977			0.0764923
$13$	−0.374078	−	1.15129i	−0.103750	−	0.319311i	0.885685	−	0.464287i	$-0.153689\pi$
$13$	−0.374078	−	1.15129i	−0.103750	−	0.319311i	−0.989435	+	0.144976i	$0.953689\pi$
$14$	−3.48828	−	2.53438i	−0.932282	−	0.677343i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	2.21437	−	6.81513i	0.537064	−	1.65291i	−0.202083	−	0.979368i	$-0.564771\pi$
$17$	2.21437	−	6.81513i	0.537064	−	1.65291i	0.739147	−	0.673544i	$-0.235229\pi$
$18$	2.37025	−	1.72209i	0.558673	−	0.405899i
$19$	−2.19992	−	1.59833i	−0.504695	−	0.366683i	0.306112	−	0.951995i	$-0.400972\pi$
$19$	−2.19992	−	1.59833i	−0.504695	−	0.366683i	−0.810808	+	0.585313i	$0.800972\pi$
$20$		0			0
$21$	1.14252			0.249317
$22$	−3.28837	−	0.432036i	−0.701082	−	0.0921103i
$23$	−7.01787			−1.46333			−0.731663	−	0.681666i	$-0.761256\pi$
$23$	−7.01787			−1.46333			−0.731663	+	0.681666i	$0.761256\pi$
$24$	0.0818824	+	0.252008i	0.0167142	+	0.0514410i
$25$		0			0
$26$	0.979348	−	0.711538i	0.192066	−	0.139544i
$27$	−0.485545	+	1.49436i	−0.0934433	+	0.287589i
$28$	1.33240	−	4.10072i	0.251801	−	0.774963i
$29$	−8.54782	+	6.21036i	−1.58729	+	1.15323i	−0.679609	+	0.733575i	$0.737850\pi$
$29$	−8.54782	+	6.21036i	−1.58729	+	1.15323i	−0.907682	+	0.419659i	$0.862150\pi$
$30$		0			0
$31$	1.11908	+	3.44417i	0.200993	+	0.618591i	0.999854	+	0.0170766i	$0.00543592\pi$
$31$	1.11908	+	3.44417i	0.200993	+	0.618591i	−0.798862	+	0.601515i	$0.794564\pi$
$32$	1.00000			0.176777
$33$	0.772220	−	0.419546i	0.134426	−	0.0730336i
$34$	7.16586			1.22893
$35$		0			0
$36$	2.37025	+	1.72209i	0.395041	+	0.287014i
$37$	1.71437	−	1.24556i	0.281841	−	0.204769i	−0.437879	−	0.899034i	$-0.644270\pi$
$37$	1.71437	−	1.24556i	0.281841	−	0.204769i	0.719720	+	0.694265i	$0.244270\pi$
$38$	0.840293	−	2.58616i	0.136314	−	0.419530i
$39$	−0.0991220	+	0.305066i	−0.0158722	+	0.0488497i
$40$		0			0
$41$	−2.22713	−	1.61811i	−0.347820	−	0.252706i	0.400134	−	0.916457i	$-0.368964\pi$
$41$	−2.22713	−	1.61811i	−0.347820	−	0.252706i	−0.747954	+	0.663751i	$0.768964\pi$
$42$	0.353057	+	1.08660i	0.0544779	+	0.167666i
$43$	−6.59251			−1.00535			−0.502674	−	0.864476i	$-0.667650\pi$
$43$	−6.59251			−1.00535			−0.502674	+	0.864476i	$0.667650\pi$
$44$	−0.605270	−	3.26093i	−0.0912480	−	0.491603i
$45$		0			0
$46$	−2.16864	−	6.67439i	−0.319749	−	0.984085i
$47$	4.64416	+	3.37418i	0.677420	+	0.492175i	0.872501	−	0.488613i	$-0.162497\pi$
$47$	4.64416	+	3.37418i	0.677420	+	0.492175i	−0.195081	+	0.980787i	$0.562497\pi$
$48$	−0.214371	+	0.155750i	−0.0309418	+	0.0224805i
$49$	3.58188	−	11.0239i	0.511697	−	1.57484i
$50$		0			0
$51$	−1.53615	+	1.11608i	−0.215104	+	0.156282i
$52$	0.979348	+	0.711538i	0.135811	+	0.0986726i
$53$	1.81558	+	5.58779i	0.249390	+	0.767542i	0.994883	+	0.101030i	$0.0322137\pi$
$53$	1.81558	+	5.58779i	0.249390	+	0.767542i	−0.745494	+	0.666512i	$0.767786\pi$
$54$	−1.57126			−0.213821
$55$		0			0
$56$	4.31175			0.576182
$57$	0.222659	+	0.685272i	0.0294918	+	0.0907666i
$58$	−8.54782	−	6.21036i	−1.12238	−	0.815460i
$59$	4.77117	−	3.46646i	0.621154	−	0.451295i	−0.232170	−	0.972675i	$-0.574583\pi$
$59$	4.77117	−	3.46646i	0.621154	−	0.451295i	0.853324	+	0.521380i	$0.174583\pi$
$60$		0			0
$61$	−1.89879	+	5.84387i	−0.243115	+	0.748231i	0.752826	+	0.658220i	$0.228690\pi$
$61$	−1.89879	+	5.84387i	−0.243115	+	0.748231i	−0.995941	+	0.0900109i	$0.971310\pi$
$62$	−2.92979	+	2.12861i	−0.372083	+	0.270334i
$63$	10.2199	+	7.42521i	1.28759	+	0.935488i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$		0			0
$66$	0.637641	+	0.604778i	0.0784881	+	0.0744430i
$67$	1.63381			0.199602			0.0998009	−	0.995007i	$-0.468179\pi$
$67$	1.63381			0.199602			0.0998009	+	0.995007i	$0.468179\pi$
$68$	2.21437	+	6.81513i	0.268532	+	0.826456i
$69$	1.50443	+	1.09303i	0.181112	+	0.131585i
$70$		0			0
$71$	2.29862	−	7.07443i	0.272796	−	0.839580i	−0.716998	−	0.697075i	$-0.754484\pi$
$71$	2.29862	−	7.07443i	0.272796	−	0.839580i	0.989794	−	0.142505i	$-0.0455156\pi$
$72$	−0.905354	+	2.78639i	−0.106697	+	0.328380i
$73$	−5.98039	+	4.34501i	−0.699952	+	0.508545i	−0.879917	−	0.475128i	$-0.842402\pi$
$73$	−5.98039	+	4.34501i	−0.699952	+	0.508545i	0.179965	+	0.983673i	$0.442402\pi$
$74$	1.71437	+	1.24556i	0.199292	+	0.144794i
$75$		0			0
$76$	2.71925			0.311919
$77$	−2.60978	−	14.0603i	−0.297412	−	1.60232i
$78$	−0.320766			−0.0363196
$79$	2.16376	+	6.65938i	0.243443	+	0.749239i	0.995889	+	0.0905854i	$0.0288738\pi$
$79$	2.16376	+	6.65938i	0.243443	+	0.749239i	−0.752446	+	0.658654i	$0.771126\pi$
$80$		0			0
$81$	−6.77391	+	4.92153i	−0.752657	+	0.546837i
$82$	0.850690	−	2.61815i	0.0939430	−	0.289127i
$83$	0.492758	−	1.51655i	0.0540872	−	0.166463i	−0.920364	−	0.391063i	$-0.872107\pi$
$83$	0.492758	−	1.51655i	0.0540872	−	0.166463i	0.974451	+	0.224600i	$0.0721075\pi$
$84$	−0.924315	+	0.671554i	−0.100851	+	0.0732726i
$85$		0			0
$86$	−2.03720	−	6.26985i	−0.219677	−	0.676095i
$87$	2.79967			0.300156
$88$	2.91429	−	1.58333i	0.310664	−	0.168783i
$89$	1.24711			0.132193			0.0660967	−	0.997813i	$-0.478945\pi$
$89$	1.24711			0.132193			0.0660967	+	0.997813i	$0.478945\pi$
$90$		0			0
$91$	4.22271	+	3.06798i	0.442660	+	0.321611i
$92$	5.67757	−	4.12500i	0.591928	−	0.430061i
$93$	0.296530	−	0.912627i	0.0307488	−	0.0946350i
$94$	−1.77391	+	5.45954i	−0.182965	+	0.563108i
$95$		0			0
$96$	−0.214371	−	0.155750i	−0.0218791	−	0.0158961i
$97$	2.13632	+	6.57491i	0.216910	+	0.667581i	0.999012	+	0.0444310i	$0.0141475\pi$
$97$	2.13632	+	6.57491i	0.216910	+	0.667581i	−0.782102	+	0.623150i	$0.785853\pi$
$98$	11.5912			1.17089
$99$	9.63421	+	1.26577i	0.968275	+	0.127215i
$100$		0			0
$101$	1.00000	+	3.07768i	0.0995037	+	0.306241i	0.988401	−	0.151865i	$-0.0485280\pi$
$101$	1.00000	+	3.07768i	0.0995037	+	0.306241i	−0.888897	+	0.458106i	$0.848528\pi$
$102$	−1.53615	−	1.11608i	−0.152102	−	0.110508i
$103$	4.67307	−	3.39518i	0.460451	−	0.334537i	−0.333257	−	0.942836i	$-0.608148\pi$
$103$	4.67307	−	3.39518i	0.460451	−	0.334537i	0.793708	+	0.608299i	$0.208148\pi$
$104$	−0.374078	+	1.15129i	−0.0366813	+	0.112894i
$105$		0			0
$106$	−4.75326	+	3.45344i	−0.461677	+	0.335428i
$107$	0.138686	+	0.100761i	0.0134073	+	0.00974095i	0.594469	−	0.804119i	$-0.297362\pi$
$107$	0.138686	+	0.100761i	0.0134073	+	0.00974095i	−0.581061	+	0.813860i	$0.697362\pi$
$108$	−0.485545	−	1.49436i	−0.0467216	−	0.143794i
$109$	−2.32753			−0.222937			−0.111468	−	0.993768i	$-0.535555\pi$
$109$	−2.32753			−0.222937			−0.111468	+	0.993768i	$0.535555\pi$
$110$		0			0
$111$	−0.561508			−0.0532959
$112$	1.33240	+	4.10072i	0.125900	+	0.387482i
$113$	3.48555	+	2.53240i	0.327893	+	0.238228i	0.739536	−	0.673117i	$-0.235045\pi$
$113$	3.48555	+	2.53240i	0.327893	+	0.238228i	−0.411643	+	0.911345i	$0.635045\pi$
$114$	−0.582928	+	0.423522i	−0.0545962	+	0.0396664i
$115$		0			0
$116$	3.26498	−	10.0486i	0.303146	−	0.932986i
$117$	−2.86928	+	2.08466i	−0.265265	+	0.192726i
$118$	4.77117	+	3.46646i	0.439222	+	0.319114i
$119$	9.54782	+	29.3852i	0.875247	+	2.69373i
$120$		0			0
$121$	−6.92705	−	8.54494i	−0.629732	−	0.776813i
$122$	−6.14461			−0.556307
$123$	0.225413	+	0.693751i	0.0203248	+	0.0625534i
$124$	−2.92979	−	2.12861i	−0.263103	−	0.191155i
$125$		0			0
$126$	−3.90366	+	12.0142i	−0.347766	+	1.07031i
$127$	−3.34855	+	10.3058i	−0.297136	+	0.914490i	0.685360	+	0.728205i	$0.259645\pi$
$127$	−3.34855	+	10.3058i	−0.297136	+	0.914490i	−0.982496	+	0.186285i	$0.940355\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	1.41324	+	1.02678i	0.124429	+	0.0904030i
$130$		0			0
$131$	5.78518			0.505454			0.252727	−	0.967538i	$-0.418673\pi$
$131$	5.78518			0.505454			0.252727	+	0.967538i	$0.418673\pi$
$132$	−0.378136	+	0.793319i	−0.0329125	+	0.0690496i
$133$	11.7247			1.01666
$134$	0.504875	+	1.55385i	0.0436146	+	0.134232i
$135$		0			0
$136$	−5.79730	+	4.21198i	−0.497114	+	0.361175i
$137$	−2.67310	+	8.22695i	−0.228378	+	0.702876i	0.769553	+	0.638583i	$0.220479\pi$
$137$	−2.67310	+	8.22695i	−0.228378	+	0.702876i	−0.997931	+	0.0642926i	$0.979521\pi$
$138$	−0.574640	+	1.76856i	−0.0489166	+	0.150550i
$139$	−10.3135	+	7.49318i	−0.874777	+	0.635563i	−0.931865	−	0.362806i	$-0.881819\pi$
$139$	−10.3135	+	7.49318i	−0.874777	+	0.635563i	0.0570872	+	0.998369i	$0.481819\pi$
$140$		0			0
$141$	−0.470046	−	1.44665i	−0.0395850	−	0.121830i
$142$	7.43849			0.624224
$143$	3.98070	+	0.522997i	0.332883	+	0.0437352i
$144$	−2.92979			−0.244149
$145$		0			0
$146$	−5.98039	−	4.34501i	−0.494941	−	0.359596i
$147$	−2.48482	+	1.80533i	−0.204945	+	0.148901i
$148$	−0.654831	+	2.01536i	−0.0538268	+	0.165662i
$149$	2.04339	−	6.28892i	0.167401	−	0.515208i	−0.831804	−	0.555070i	$-0.812692\pi$
$149$	2.04339	−	6.28892i	0.167401	−	0.515208i	0.999205	+	0.0398613i	$0.0126916\pi$
$150$		0			0
$151$	−16.9064	−	12.2832i	−1.37582	−	0.999591i	−0.997257	−	0.0740153i	$-0.976419\pi$
$151$	−16.9064	−	12.2832i	−1.37582	−	0.999591i	−0.378562	−	0.925576i	$-0.623581\pi$
$152$	0.840293	+	2.58616i	0.0681568	+	0.209765i
$153$	−20.9944			−1.69730
$154$	12.5657	−	6.82692i	1.01257	−	0.550129i
$155$		0			0
$156$	−0.0991220	−	0.305066i	−0.00793611	−	0.0244248i
$157$	−16.3657	−	11.8904i	−1.30613	−	0.948957i	−0.306131	−	0.951989i	$-0.599035\pi$
$157$	−16.3657	−	11.8904i	−1.30613	−	0.948957i	−0.999995	+	0.00303254i	$0.999035\pi$
$158$	−5.66481	+	4.11573i	−0.450668	+	0.327430i
$159$	0.481088	−	1.48064i	0.0381528	−	0.117422i
$160$		0			0
$161$	24.4803	−	17.7860i	1.92932	−	1.40173i
$162$	−6.77391	−	4.92153i	−0.532209	−	0.386672i
$163$	2.49721	+	7.68564i	0.195597	+	0.601986i	0.999969	+	0.00785979i	$0.00250187\pi$
$163$	2.49721	+	7.68564i	0.195597	+	0.601986i	−0.804372	+	0.594126i	$0.797498\pi$
$164$	2.75289			0.214965
$165$		0			0
$166$	1.59460			0.123765
$167$	−5.33751	−	16.4272i	−0.413029	−	1.27117i	−0.914002	−	0.405709i	$-0.867025\pi$
$167$	−5.33751	−	16.4272i	−0.413029	−	1.27117i	0.500973	−	0.865463i	$-0.332975\pi$
$168$	−0.924315	−	0.671554i	−0.0713124	−	0.0518115i
$169$	9.33168	−	6.77986i	0.717822	−	0.521528i
$170$		0			0
$171$	−2.46188	+	7.57689i	−0.188265	+	0.579419i
$172$	5.33345	−	3.87498i	0.406672	−	0.295464i
$173$	11.6286	+	8.44868i	0.884107	+	0.642341i	0.934335	−	0.356397i	$-0.115995\pi$
$173$	11.6286	+	8.44868i	0.884107	+	0.642341i	−0.0502280	+	0.998738i	$0.515995\pi$
$174$	0.865144	+	2.66264i	0.0655864	+	0.201854i
$175$		0			0
$176$	2.40640	+	2.28238i	0.181389	+	0.172041i
$177$	−1.56270			−0.117460
$178$	0.385378	+	1.18607i	0.0288853	+	0.0888999i
$179$	−15.2533	−	11.0822i	−1.14008	−	0.828320i	−0.152953	−	0.988233i	$-0.548878\pi$
$179$	−15.2533	−	11.0822i	−1.14008	−	0.828320i	−0.987131	+	0.159914i	$0.948878\pi$
$180$		0			0
$181$	−4.04887	+	12.4611i	−0.300950	+	0.926228i	0.680208	+	0.733019i	$0.261890\pi$
$181$	−4.04887	+	12.4611i	−0.300950	+	0.926228i	−0.981158	+	0.193209i	$0.938110\pi$
$182$	−1.61293	+	4.96409i	−0.119558	+	0.367963i
$183$	1.31723	−	0.957020i	0.0973721	−	0.0707450i
$184$	5.67757	+	4.12500i	0.418556	+	0.304099i
$185$		0			0
$186$	0.959592			0.0703607
$187$	17.2439	+	16.3552i	1.26100	+	1.19601i
$188$	−5.74050			−0.418669
$189$	−2.09355	−	6.44329i	−0.152283	−	0.468680i
$190$		0			0
$191$	9.11908	−	6.62540i	0.659833	−	0.479397i	−0.206773	−	0.978389i	$-0.566296\pi$
$191$	9.11908	−	6.62540i	0.659833	−	0.479397i	0.866607	+	0.498992i	$0.166296\pi$
$192$	0.0818824	−	0.252008i	0.00590936	−	0.0181871i
$193$	−2.14590	+	6.60440i	−0.154465	+	0.475395i	−0.998106	−	0.0615126i	$-0.980408\pi$
$193$	−2.14590	+	6.60440i	−0.154465	+	0.475395i	0.843641	+	0.536907i	$0.180408\pi$
$194$	−5.59295	+	4.06352i	−0.401551	+	0.291744i
$195$		0			0
$196$	3.58188	+	11.0239i	0.255849	+	0.787421i
$197$	13.4389			0.957485			0.478743	−	0.877955i	$-0.341093\pi$
$197$	13.4389			0.957485			0.478743	+	0.877955i	$0.341093\pi$
$198$	1.77331	+	9.55382i	0.126024	+	0.678961i
$199$	−19.4427			−1.37825			−0.689127	−	0.724640i	$-0.742006\pi$
$199$	−19.4427			−1.37825			−0.689127	+	0.724640i	$0.742006\pi$
$200$		0			0
$201$	−0.350242	−	0.254465i	−0.0247041	−	0.0179486i
$202$	−2.61803	+	1.90211i	−0.184204	+	0.133832i
$203$	14.0778	−	43.3269i	0.988066	−	3.04095i
$204$	0.586758	−	1.80585i	0.0410813	−	0.126435i
$205$		0			0
$206$	4.67307	+	3.39518i	0.325588	+	0.236554i
$207$	6.35365	+	19.5545i	0.441609	+	1.35913i
$208$	−1.21054			−0.0839359
$209$	7.92467	−	4.30546i	0.548161	−	0.297815i
$210$		0			0
$211$	−0.728826	−	2.24309i	−0.0501744	−	0.154421i	0.922830	−	0.385207i	$-0.125870\pi$
$211$	−0.728826	−	2.24309i	−0.0501744	−	0.154421i	−0.973004	+	0.230786i	$0.925870\pi$
$212$	−4.75326	−	3.45344i	−0.326455	−	0.237184i
$213$	−1.59460	+	1.15854i	−0.109260	+	0.0793820i
$214$	−0.0529733	+	0.163035i	−0.00362118	+	0.0111448i
$215$		0			0
$216$	1.27117	−	0.923562i	0.0864925	−	0.0628405i
$217$	−12.6325	−	9.17806i	−0.857551	−	0.623047i
$218$	−0.719246	−	2.21361i	−0.0487135	−	0.149925i
$219$	1.95876			0.132361
$220$		0			0
$221$	−8.67456			−0.583514
$222$	−0.173515	−	0.534025i	−0.0116456	−	0.0358414i
$223$	−11.8090	−	8.57978i	−0.790792	−	0.574544i	0.117406	−	0.993084i	$-0.462542\pi$
$223$	−11.8090	−	8.57978i	−0.790792	−	0.574544i	−0.908198	+	0.418540i	$0.862542\pi$
$224$	−3.48828	+	2.53438i	−0.233071	+	0.169336i
$225$		0			0
$226$	−1.33136	+	4.09750i	−0.0885607	+	0.272562i
$227$	2.41871	−	1.75730i	0.160536	−	0.116636i	−0.504617	−	0.863343i	$-0.668366\pi$
$227$	2.41871	−	1.75730i	0.160536	−	0.116636i	0.665153	+	0.746707i	$0.268366\pi$
$228$	−0.582928	−	0.423522i	−0.0386053	−	0.0280484i
$229$	0.487913	+	1.50164i	0.0322422	+	0.0992312i	0.965883	−	0.258981i	$-0.0833866\pi$
$229$	0.487913	+	1.50164i	0.0322422	+	0.0992312i	−0.933640	+	0.358212i	$0.883387\pi$
$230$		0			0
$231$	−1.63043	+	3.42060i	−0.107274	+	0.225059i
$232$	10.5657			0.693671
$233$	−0.156276	−	0.480967i	−0.0102380	−	0.0315092i	0.945807	−	0.324729i	$-0.105273\pi$
$233$	−0.156276	−	0.480967i	−0.0102380	−	0.0315092i	−0.956045	+	0.293220i	$0.905273\pi$
$234$	−2.86928	−	2.08466i	−0.187571	−	0.136278i
$235$		0			0
$236$	−1.82243	+	5.60885i	−0.118630	+	0.365105i
$237$	0.573348	−	1.76458i	0.0372430	−	0.114622i
$238$	−24.9965	+	18.1610i	−1.62028	+	1.17721i
$239$	13.5444	+	9.84061i	0.876117	+	0.636536i	0.932221	−	0.361889i	$-0.117868\pi$
$239$	13.5444	+	9.84061i	0.876117	+	0.636536i	−0.0561044	+	0.998425i	$0.517868\pi$
$240$		0			0
$241$	−15.2947			−0.985217			−0.492609	−	0.870251i	$-0.663957\pi$
$241$	−15.2947			−0.985217			−0.492609	+	0.870251i	$0.663957\pi$
$242$	5.98614	−	9.22855i	0.384804	−	0.593234i
$243$	6.93243			0.444716
$244$	−1.89879	−	5.84387i	−0.121557	−	0.374115i
$245$		0			0
$246$	−0.590140	+	0.428762i	−0.0376259	+	0.0273368i
$247$	−1.01721	+	3.13065i	−0.0647235	+	0.199198i
$248$	1.11908	−	3.44417i	0.0710616	−	0.218705i
$249$	−0.341835	+	0.248358i	−0.0216629	+	0.0157390i
$250$		0			0
$251$	−0.132071	−	0.406472i	−0.00833623	−	0.0256563i	0.946802	−	0.321817i	$-0.104294\pi$
$251$	−0.132071	−	0.406472i	−0.00833623	−	0.0256563i	−0.955138	+	0.296161i	$0.904294\pi$
$252$	−12.6325			−0.795774
$253$	10.0149	−	21.0109i	0.629628	−	1.32094i
$254$	−10.8361			−0.679920
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	14.4614	−	10.5068i	0.902076	−	0.655397i	−0.0369221	−	0.999318i	$-0.511755\pi$
$257$	14.4614	−	10.5068i	0.902076	−	0.655397i	0.938998	+	0.343921i	$0.111755\pi$
$258$	−0.539811	+	1.66137i	−0.0336071	+	0.103432i
$259$	−2.82347	+	8.68975i	−0.175442	+	0.539955i
$260$		0			0
$261$	25.0433	+	18.1950i	1.55014	+	1.12624i
$262$	1.78772	+	5.50203i	0.110446	+	0.339917i
$263$	−14.4977			−0.893964			−0.446982	−	0.894543i	$-0.647501\pi$
$263$	−14.4977			−0.893964			−0.446982	+	0.894543i	$0.647501\pi$
$264$	−0.871342	−	0.114480i	−0.0536274	−	0.00704573i
$265$		0			0
$266$	3.62314	+	11.1509i	0.222149	+	0.683704i
$267$	−0.267344	−	0.194237i	−0.0163612	−	0.0118871i
$268$	−1.32178	+	0.960330i	−0.0807406	+	0.0586615i
$269$	8.63326	−	26.5704i	0.526379	−	1.62003i	−0.235194	−	0.971948i	$-0.575573\pi$
$269$	8.63326	−	26.5704i	0.526379	−	1.62003i	0.761573	−	0.648079i	$-0.224427\pi$
$270$		0			0
$271$	−8.40531	+	6.10681i	−0.510586	+	0.370962i	−0.813046	−	0.582200i	$-0.802192\pi$
$271$	−8.40531	+	6.10681i	−0.510586	+	0.370962i	0.302460	+	0.953162i	$0.402192\pi$
$272$	−5.79730	−	4.21198i	−0.351513	−	0.255389i
$273$	−0.427390	−	1.31537i	−0.0258668	−	0.0796098i
$274$	−8.65033			−0.522585
$275$		0			0
$276$	−1.85957			−0.111933
$277$	0.194167	+	0.597585i	0.0116664	+	0.0359054i	0.956720	−	0.291009i	$-0.0939910\pi$
$277$	0.194167	+	0.597585i	0.0116664	+	0.0359054i	−0.945054	+	0.326915i	$0.893991\pi$
$278$	−10.3135	−	7.49318i	−0.618561	−	0.449411i
$279$	8.58365	−	6.23639i	0.513890	−	0.373363i
$280$		0			0
$281$	9.30347	−	28.6331i	0.554998	−	1.70811i	−0.140950	−	0.990017i	$-0.545016\pi$
$281$	9.30347	−	28.6331i	0.554998	−	1.70811i	0.695948	−	0.718092i	$-0.254984\pi$
$282$	1.23060	−	0.894080i	0.0732809	−	0.0532417i
$283$	−13.0288	−	9.46599i	−0.774482	−	0.562694i	0.128836	−	0.991666i	$-0.458876\pi$
$283$	−13.0288	−	9.46599i	−0.774482	−	0.562694i	−0.903318	+	0.428972i	$0.858876\pi$
$284$	2.29862	+	7.07443i	0.136398	+	0.419790i
$285$		0			0
$286$	0.732705	+	3.94749i	0.0433257	+	0.233420i
$287$	11.8698			0.700651
$288$	−0.905354	−	2.78639i	−0.0533485	−	0.164190i
$289$	−27.7893	−	20.1901i	−1.63467	−	1.18765i
$290$		0			0
$291$	0.566076	−	1.74220i	0.0331839	−	0.102130i
$292$	2.28431	−	7.03037i	0.133679	−	0.411422i
$293$	−3.21992	+	2.33941i	−0.188110	+	0.136670i	−0.677854	−	0.735196i	$-0.737090\pi$
$293$	−3.21992	+	2.33941i	−0.188110	+	0.136670i	0.489745	+	0.871866i	$0.337090\pi$
$294$	−2.48482	−	1.80533i	−0.144918	−	0.105289i
$295$		0			0
$296$	−2.11908			−0.123169
$297$	−3.78107	−	3.58620i	−0.219400	−	0.208093i
$298$	6.61256			0.383055
$299$	2.62523	+	8.07962i	0.151821	+	0.467256i
$300$		0			0
$301$	22.9965	−	16.7079i	1.32550	−	0.963030i
$302$	6.45765	−	19.8746i	0.371596	−	1.14366i
$303$	0.264977	−	0.815516i	0.0152225	−	0.0468502i
$304$	−2.19992	+	1.59833i	−0.126174	+	0.0916707i
$305$		0			0
$306$	−6.48764	−	19.9669i	−0.370873	−	1.14143i
$307$	−17.6055			−1.00480			−0.502401	−	0.864635i	$-0.667550\pi$
$307$	−17.6055			−1.00480			−0.502401	+	0.864635i	$0.667550\pi$
$308$	10.3758	+	9.84104i	0.591216	+	0.560746i
$309$	−1.53057			−0.0870710
$310$		0			0
$311$	18.3117	+	13.3042i	1.03836	+	0.754412i	0.969964	−	0.243247i	$-0.0782124\pi$
$311$	18.3117	+	13.3042i	1.03836	+	0.754412i	0.0683942	+	0.997658i	$0.478212\pi$
$312$	0.259505	−	0.188541i	0.0146916	−	0.0106741i
$313$	3.89659	−	11.9925i	0.220248	−	0.677855i	−0.778491	−	0.627656i	$-0.784014\pi$
$313$	3.89659	−	11.9925i	0.220248	−	0.677855i	0.998739	−	0.0501989i	$-0.0159855\pi$
$314$	6.25115	−	19.2391i	0.352773	−	1.08572i
$315$		0			0
$316$	−5.66481	−	4.11573i	−0.318670	−	0.231528i
$317$	−8.11722	−	24.9822i	−0.455908	−	1.40314i	−0.870065	−	0.492936i	$-0.835924\pi$
$317$	−8.11722	−	24.9822i	−0.455908	−	1.40314i	0.414157	−	0.910205i	$-0.364076\pi$
$318$	1.55683			0.0873029
$319$	−6.39510	−	34.4539i	−0.358057	−	1.92905i
$320$		0			0
$321$	−0.0140367	−	0.0432005i	−0.000783453	−	0.00241122i
$322$	24.4803	+	17.7860i	1.36423	+	0.991174i
$323$	−15.7643	+	11.4534i	−0.877148	+	0.637285i
$324$	2.58740	−	7.96321i	0.143745	−	0.442401i
$325$		0			0
$326$	−6.53779	+	4.74999i	−0.362095	+	0.263077i
$327$	0.498955	+	0.362512i	0.0275923	+	0.0200470i
$328$	0.850690	+	2.61815i	0.0469715	+	0.144563i
$329$	−24.7516			−1.36460
$330$		0			0
$331$	12.7406			0.700284			0.350142	−	0.936697i	$-0.386133\pi$
$331$	12.7406			0.700284			0.350142	+	0.936697i	$0.386133\pi$
$332$	0.492758	+	1.51655i	0.0270436	+	0.0832316i
$333$	−5.02274	−	3.64924i	−0.275245	−	0.199977i
$334$	13.9738	−	10.1525i	0.764611	−	0.555522i
$335$		0			0
$336$	0.353057	−	1.08660i	0.0192608	−	0.0592787i
$337$	−15.4174	+	11.2014i	−0.839841	+	0.610180i	−0.922326	−	0.386412i	$-0.873714\pi$
$337$	−15.4174	+	11.2014i	−0.839841	+	0.610180i	0.0824856	+	0.996592i	$0.473714\pi$
$338$	9.33168	+	6.77986i	0.507576	+	0.368776i
$339$	−0.352780	−	1.08574i	−0.0191604	−	0.0589696i
$340$		0			0
$341$	−11.9085	−	1.56458i	−0.644884	−	0.0847268i
$342$	−7.96681			−0.430796
$343$	6.11736	+	18.8273i	0.330306	+	1.01658i
$344$	5.33345	+	3.87498i	0.287560	+	0.208925i
$345$		0			0
$346$	−4.44173	+	13.6703i	−0.238789	+	0.734917i
$347$	−5.81663	+	17.9017i	−0.312253	+	0.961016i	0.664617	+	0.747184i	$0.268595\pi$
$347$	−5.81663	+	17.9017i	−0.312253	+	0.961016i	−0.976870	+	0.213832i	$0.931405\pi$
$348$	−2.26498	+	1.64560i	−0.121416	+	0.0882135i
$349$	22.0200	+	15.9984i	1.17870	+	0.856377i	0.992025	−	0.126045i	$-0.0402283\pi$
$349$	22.0200	+	15.9984i	1.17870	+	0.856377i	0.186677	+	0.982421i	$0.440228\pi$
$350$		0			0
$351$	1.90207			0.101525
$352$	−1.42705	+	2.99391i	−0.0760621	+	0.159576i
$353$	−25.6380			−1.36457			−0.682286	−	0.731085i	$-0.739014\pi$
$353$	−25.6380			−1.36457			−0.682286	+	0.731085i	$0.739014\pi$
$354$	−0.482901	−	1.48622i	−0.0256659	−	0.0789916i
$355$		0			0
$356$	−1.00893	+	0.733033i	−0.0534734	+	0.0388507i
$357$	2.52995	−	7.78640i	0.133899	−	0.412100i
$358$	5.82624	−	17.9313i	0.307926	−	0.947700i
$359$	−7.82857	+	5.68779i	−0.413176	+	0.300190i	−0.774886	−	0.632100i	$-0.782193\pi$
$359$	−7.82857	+	5.68779i	−0.413176	+	0.300190i	0.361710	+	0.932291i	$0.382193\pi$
$360$		0			0
$361$	−3.58636	−	11.0377i	−0.188756	−	0.580930i
$362$	−13.1024			−0.688647
$363$	0.154088	+	2.91067i	0.00808751	+	0.152771i
$364$	−5.21955			−0.273579
$365$		0			0
$366$	1.31723	+	0.957020i	0.0688525	+	0.0500243i
$367$	−16.7495	+	12.1692i	−0.874317	+	0.635229i	−0.931742	−	0.363121i	$-0.881711\pi$
$367$	−16.7495	+	12.1692i	−0.874317	+	0.635229i	0.0574247	+	0.998350i	$0.481711\pi$
$368$	−2.16864	+	6.67439i	−0.113048	+	0.347927i
$369$	−2.49234	+	7.67063i	−0.129746	+	0.399317i
$370$		0			0
$371$	−20.4949	−	14.8904i	−1.06404	−	0.773071i
$372$	0.296530	+	0.912627i	0.0153744	+	0.0473175i
$373$	16.1463			0.836021			0.418011	−	0.908442i	$-0.362727\pi$
$373$	16.1463			0.836021			0.418011	+	0.908442i	$0.362727\pi$
$374$	−10.2260	+	21.4540i	−0.528776	+	1.10936i
$375$		0			0
$376$	−1.77391	−	5.45954i	−0.0914825	−	0.281554i
$377$	10.3475	+	7.51789i	0.532923	+	0.387191i
$378$	5.48099	−	3.98217i	0.281912	−	0.204821i
$379$	−0.0709811	+	0.218457i	−0.00364605	+	0.0112214i	−0.952863	−	0.303401i	$-0.901878\pi$
$379$	−0.0709811	+	0.218457i	−0.00364605	+	0.0112214i	0.949217	+	0.314622i	$0.101878\pi$
$380$		0			0
$381$	2.32295	−	1.68772i	0.119009	−	0.0864648i
$382$	9.11908	+	6.62540i	0.466573	+	0.338985i
$383$	−4.02403	−	12.3847i	−0.205619	−	0.632829i	−0.999687	−	0.0250010i	$-0.992041\pi$
$383$	−4.02403	−	12.3847i	−0.205619	−	0.632829i	0.794069	−	0.607828i	$-0.207959\pi$
$384$	0.264977			0.0135221
$385$		0			0
$386$	−6.94427			−0.353454
$387$	5.96855	+	18.3693i	0.303399	+	0.933765i
$388$	−5.59295	−	4.06352i	−0.283939	−	0.206294i
$389$	−23.9676	+	17.4135i	−1.21521	+	0.882899i	−0.995693	−	0.0927106i	$-0.970447\pi$
$389$	−23.9676	+	17.4135i	−1.21521	+	0.882899i	−0.219513	+	0.975610i	$0.570447\pi$
$390$		0			0
$391$	−15.5402	+	47.8277i	−0.785900	+	2.41875i
$392$	−9.37749	+	6.81315i	−0.473635	+	0.344116i
$393$	−1.24018	−	0.901040i	−0.0625586	−	0.0454515i
$394$	4.15286	+	12.7812i	0.209218	+	0.643908i
$395$		0			0
$396$	−8.53824	+	4.63882i	−0.429063	+	0.233109i
$397$	−2.18665			−0.109745			−0.0548724	−	0.998493i	$-0.517475\pi$
$397$	−2.18665			−0.109745			−0.0548724	+	0.998493i	$0.517475\pi$
$398$	−6.00812	−	18.4911i	−0.301160	−	0.926874i
$399$	−2.51344	−	1.82612i	−0.125829	−	0.0914204i
$400$		0			0
$401$	−4.04638	+	12.4535i	−0.202066	+	0.621896i	0.797755	+	0.602982i	$0.206021\pi$
$401$	−4.04638	+	12.4535i	−0.202066	+	0.621896i	−0.999821	+	0.0189143i	$0.993979\pi$
$402$	0.133780	−	0.411734i	0.00667236	−	0.0205354i
$403$	3.54663	−	2.57678i	0.176670	−	0.128358i
$404$	−2.61803	−	1.90211i	−0.130252	−	0.0946337i
$405$		0			0
$406$	45.5566			2.26094
$407$	1.28262	+	6.91016i	0.0635769	+	0.342524i
$408$	1.89879			0.0940040
$409$	9.40299	+	28.9394i	0.464948	+	1.43096i	0.859048	+	0.511895i	$0.171056\pi$
$409$	9.40299	+	28.9394i	0.464948	+	1.43096i	−0.394100	+	0.919067i	$0.628944\pi$
$410$		0			0
$411$	1.85438	−	1.34729i	0.0914698	−	0.0664567i
$412$	−1.78495	+	5.49352i	−0.0879383	+	0.270646i
$413$	−7.85785	+	24.1840i	−0.386660	+	1.19002i
$414$	−16.6341	+	12.0854i	−0.817521	+	0.593963i
$415$		0			0
$416$	−0.374078	−	1.15129i	−0.0183407	−	0.0564468i
$417$	3.37797			0.165420
$418$	6.54359	+	6.20634i	0.320058	+	0.303562i
$419$	26.7473			1.30669			0.653346	−	0.757059i	$-0.273365\pi$
$419$	26.7473			1.30669			0.653346	+	0.757059i	$0.273365\pi$
$420$		0			0
$421$	24.5477	+	17.8350i	1.19638	+	0.869223i	0.993924	−	0.110068i	$-0.0351068\pi$
$421$	24.5477	+	17.8350i	1.19638	+	0.869223i	0.202459	+	0.979291i	$0.435107\pi$
$422$	1.90809	−	1.38631i	0.0928844	−	0.0674844i
$423$	5.19718	−	15.9953i	0.252696	−	0.777717i
$424$	1.81558	−	5.58779i	0.0881725	−	0.271367i
$425$		0			0
$426$	−1.59460	−	1.15854i	−0.0772585	−	0.0561316i
$427$	−8.18710	−	25.1973i	−0.396202	−	1.21938i
$428$	−0.171425			−0.00828615
$429$	−0.771890	−	0.732108i	−0.0372672	−	0.0353465i
$430$		0			0
$431$	−3.65506	−	11.2491i	−0.176058	−	0.541851i	0.823622	−	0.567139i	$-0.191950\pi$
$431$	−3.65506	−	11.2491i	−0.176058	−	0.541851i	−0.999680	+	0.0252880i	$0.991950\pi$
$432$	1.27117	+	0.923562i	0.0611594	+	0.0444349i
$433$	26.3685	−	19.1578i	1.26719	−	0.920665i	0.268100	−	0.963391i	$-0.413604\pi$
$433$	26.3685	−	19.1578i	1.26719	−	0.920665i	0.999087	+	0.0427255i	$0.0136041\pi$
$434$	4.82519	−	14.8504i	0.231617	−	0.712843i
$435$		0			0
$436$	1.88301	−	1.36809i	0.0901799	−	0.0655195i
$437$	15.4387	+	11.2169i	0.738534	+	0.536576i
$438$	0.605289	+	1.86289i	0.0289218	+	0.0890122i
$439$	5.09564			0.243202			0.121601	−	0.992579i	$-0.461197\pi$
$439$	5.09564			0.243202			0.121601	+	0.992579i	$0.461197\pi$
$440$		0			0
$441$	−33.9598			−1.61713
$442$	−2.68059	−	8.25000i	−0.127503	−	0.392412i
$443$	19.9660	+	14.5061i	0.948612	+	0.689207i	0.950478	−	0.310791i	$-0.100594\pi$
$443$	19.9660	+	14.5061i	0.948612	+	0.689207i	−0.00186632	+	0.999998i	$0.500594\pi$
$444$	0.454269	−	0.330046i	0.0215587	−	0.0156633i
$445$		0			0
$446$	4.51065	−	13.8824i	0.213586	−	0.657349i
$447$	−1.41754	+	1.02990i	−0.0670474	+	0.0487128i
$448$	−3.48828	−	2.53438i	−0.164806	−	0.119738i
$449$	−5.86154	−	18.0400i	−0.276623	−	0.851359i	−0.988785	−	0.149344i	$-0.952284\pi$
$449$	−5.86154	−	18.0400i	−0.276623	−	0.851359i	0.712162	−	0.702015i	$-0.247716\pi$
$450$		0			0
$451$	8.02271	−	4.35873i	0.377775	−	0.205245i
$452$	−4.30837			−0.202649
$453$	1.71113	+	5.26632i	0.0803959	+	0.247433i
$454$	2.41871	+	1.75730i	0.113516	+	0.0824741i
$455$		0			0
$456$	0.222659	−	0.685272i	0.0104269	−	0.0320908i
$457$	8.81134	−	27.1185i	0.412177	−	1.26855i	−0.502575	−	0.864534i	$-0.667614\pi$
$457$	8.81134	−	27.1185i	0.412177	−	1.26855i	0.914752	−	0.404016i	$-0.132386\pi$
$458$	−1.27737	+	0.928065i	−0.0596877	+	0.0433656i
$459$	9.10905	+	6.61811i	0.425174	+	0.308907i
$460$		0			0
$461$	−35.3117			−1.64463			−0.822315	−	0.569032i	$-0.807318\pi$
$461$	−35.3117			−1.64463			−0.822315	+	0.569032i	$0.807318\pi$
$462$	−3.75701	−	0.493608i	−0.174792	−	0.0229647i
$463$	−3.89605			−0.181065			−0.0905323	−	0.995894i	$-0.528857\pi$
$463$	−3.89605			−0.181065			−0.0905323	+	0.995894i	$0.528857\pi$
$464$	3.26498	+	10.0486i	0.151573	+	0.466493i
$465$		0			0
$466$	0.409135	−	0.297254i	0.0189528	−	0.0137700i
$467$	3.66272	−	11.2727i	0.169490	−	0.521638i	−0.829849	−	0.557989i	$-0.811573\pi$
$467$	3.66272	−	11.2727i	0.169490	−	0.521638i	0.999339	+	0.0363506i	$0.0115733\pi$
$468$	1.09597	−	3.37304i	0.0506611	−	0.155919i
$469$	−5.69919	+	4.14070i	−0.263164	+	0.191200i
$470$		0			0
$471$	1.65641	+	5.09791i	0.0763234	+	0.234899i
$472$	−5.89750			−0.271454
$473$	9.40784	−	19.7374i	0.432573	−	0.907527i
$474$	1.85539			0.0852211
$475$		0			0
$476$	−24.9965	−	18.1610i	−1.14571	−	0.832410i
$477$	13.9260	−	10.1179i	0.637629	−	0.463265i
$478$	−5.17352	+	15.9224i	−0.236631	+	0.728276i
$479$	3.22158	−	9.91501i	0.147198	−	0.453029i	−0.850089	−	0.526639i	$-0.823452\pi$
$479$	3.22158	−	9.91501i	0.147198	−	0.453029i	0.997287	+	0.0736102i	$0.0234521\pi$
$480$		0			0
$481$	−2.07532	−	1.50781i	−0.0946263	−	0.0687500i
$482$	−4.72632	−	14.5461i	−0.215278	−	0.662557i
$483$	−8.01803			−0.364833
$484$	10.6267	+	2.84138i	0.483031	+	0.129154i
$485$		0			0
$486$	2.14224	+	6.59313i	0.0971739	+	0.299071i
$487$	−19.9030	−	14.4604i	−0.901890	−	0.655261i	0.0370611	−	0.999313i	$-0.488200\pi$
$487$	−19.9030	−	14.4604i	−0.901890	−	0.655261i	−0.938951	+	0.344052i	$0.888200\pi$
$488$	4.97109	−	3.61171i	0.225031	−	0.163494i
$489$	0.661705	−	2.03652i	0.0299233	−	0.0920945i
$490$		0			0
$491$	18.7305	−	13.6085i	0.845296	−	0.614143i	−0.0785493	−	0.996910i	$-0.525029\pi$
$491$	18.7305	−	13.6085i	0.845296	−	0.614143i	0.923845	+	0.382767i	$0.125029\pi$
$492$	−0.590140	−	0.428762i	−0.0266056	−	0.0193301i
$493$	23.3964	+	72.0066i	1.05372	+	3.24301i
$494$	−3.29176			−0.148103
$495$		0			0
$496$	3.62142			0.162606
$497$	9.91108	+	30.5032i	0.444573	+	1.36825i
$498$	−0.341835	−	0.248358i	−0.0153180	−	0.0111292i
$499$	−18.3406	+	13.3253i	−0.821040	+	0.596520i	−0.917010	−	0.398864i	$-0.869405\pi$
$499$	−18.3406	+	13.3253i	−0.821040	+	0.596520i	0.0959702	+	0.995384i	$0.469405\pi$
$500$		0			0
$501$	−1.41432	+	4.35282i	−0.0631871	+	0.194470i
$502$	0.345766	−	0.251213i	0.0154323	−	0.0112122i
$503$	17.5238	+	12.7318i	0.781347	+	0.567682i	0.905383	−	0.424596i	$-0.139584\pi$
$503$	17.5238	+	12.7318i	0.781347	+	0.567682i	−0.124036	+	0.992278i	$0.539584\pi$
$504$	−3.90366	−	12.0142i	−0.173883	−	0.535157i
$505$		0			0
$506$	23.0773	+	3.03197i	1.02591	+	0.134787i
$507$	−3.05640			−0.135740
$508$	−3.34855	−	10.3058i	−0.148568	−	0.457245i
$509$	12.4590	+	9.05200i	0.552236	+	0.401223i	0.828609	−	0.559828i	$-0.189133\pi$
$509$	12.4590	+	9.05200i	0.552236	+	0.401223i	−0.276373	+	0.961050i	$0.589133\pi$
$510$		0			0
$511$	9.84937	−	30.3132i	0.435710	−	1.34098i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	3.45664	−	2.51139i	0.152614	−	0.110881i
$514$	14.4614	+	10.5068i	0.637864	+	0.463436i
$515$		0			0
$516$	−1.74686			−0.0769014
$517$	−16.7295	+	9.08909i	−0.735760	+	0.399738i
$518$	−9.13695			−0.401454
$519$	−1.17696	−	3.62230i	−0.0516627	−	0.159001i
$520$		0			0
$521$	−23.3132	+	16.9380i	−1.02137	+	0.742069i	−0.966563	−	0.256428i	$-0.917454\pi$
$521$	−23.3132	+	16.9380i	−1.02137	+	0.742069i	−0.0548065	+	0.998497i	$0.517454\pi$
$522$	−9.56569	+	29.4402i	−0.418679	+	1.28856i
$523$	−11.0884	+	34.1267i	−0.484863	+	1.49226i	0.347316	+	0.937748i	$0.387093\pi$
$523$	−11.0884	+	34.1267i	−0.484863	+	1.49226i	−0.832179	+	0.554507i	$0.812907\pi$
$524$	−4.68031	+	3.40044i	−0.204460	+	0.148549i
$525$		0			0
$526$	−4.48002	−	13.7881i	−0.195338	−	0.601190i
$527$	25.9505			1.13042
$528$	−0.160383	−	0.864071i	−0.00697977	−	0.0376039i
$529$	26.2505			1.14132
$530$		0			0
$531$	−13.9785	−	10.1560i	−0.606616	−	0.440733i
$532$	−9.48550	+	6.89162i	−0.411248	+	0.298789i
$533$	−1.02979	+	3.16938i	−0.0446054	+	0.137281i
$534$	0.102116	−	0.314282i	0.00441901	−	0.0136003i
$535$		0			0
$536$	−1.32178	−	0.960330i	−0.0570922	−	0.0414799i
$537$	1.54382	+	4.75139i	0.0666207	+	0.205038i
$538$	27.9378			1.20448
$539$	27.8931	+	26.4555i	1.20144	+	1.13952i
$540$		0			0
$541$	2.17819	+	6.70378i	0.0936477	+	0.288218i	0.986899	−	0.161340i	$-0.0515816\pi$
$541$	2.17819	+	6.70378i	0.0936477	+	0.288218i	−0.893251	+	0.449558i	$0.851582\pi$
$542$	−8.40531	−	6.10681i	−0.361039	−	0.262310i
$543$	2.80878	−	2.04070i	0.120536	−	0.0875746i
$544$	2.21437	−	6.81513i	0.0949404	−	0.292196i
$545$		0			0
$546$	1.11892	−	0.812944i	0.0478854	−	0.0347908i
$547$	12.2661	+	8.91181i	0.524459	+	0.381041i	0.818281	−	0.574819i	$-0.194927\pi$
$547$	12.2661	+	8.91181i	0.524459	+	0.381041i	−0.293822	+	0.955860i	$0.594927\pi$
$548$	−2.67310	−	8.22695i	−0.114189	−	0.351438i
$549$	18.0024			0.768323
$550$		0			0
$551$	28.7307			1.22397
$552$	−0.574640	−	1.76856i	−0.0244583	−	0.0752749i
$553$	−24.4253	−	17.7460i	−1.03867	−	0.754636i
$554$	−0.508336	+	0.369328i	−0.0215971	+	0.0156912i
$555$		0			0
$556$	3.93940	−	12.1242i	0.167068	−	0.514181i
$557$	−9.32902	+	6.77793i	−0.395283	+	0.287190i	−0.767617	−	0.640909i	$-0.778558\pi$
$557$	−9.32902	+	6.77793i	−0.395283	+	0.287190i	0.372334	+	0.928099i	$0.378558\pi$
$558$	8.58365	+	6.23639i	0.363375	+	0.264007i
$559$	2.46611	+	7.58991i	0.104305	+	0.321019i
$560$		0			0
$561$	−1.14928	−	6.19181i	−0.0485226	−	0.261418i
$562$	30.1066			1.26997
$563$	10.5443	+	32.4519i	0.444388	+	1.36769i	0.883154	+	0.469084i	$0.155416\pi$
$563$	10.5443	+	32.4519i	0.444388	+	1.36769i	−0.438766	+	0.898601i	$0.644584\pi$
$564$	1.23060	+	0.894080i	0.0518174	+	0.0376476i
$565$		0			0
$566$	4.97656	−	15.3163i	0.209181	−	0.643792i
$567$	11.1562	−	34.3354i	0.468518	−	1.44195i
$568$	−6.01787	+	4.37224i	−0.252504	+	0.183455i
$569$	6.45701	+	4.69129i	0.270692	+	0.196669i	0.714847	−	0.699281i	$-0.246496\pi$
$569$	6.45701	+	4.69129i	0.270692	+	0.196669i	−0.444155	+	0.895950i	$0.646496\pi$
$570$		0			0
$571$	−3.62605			−0.151746			−0.0758728	−	0.997118i	$-0.524174\pi$
$571$	−3.62605			−0.151746			−0.0758728	+	0.997118i	$0.524174\pi$
$572$	−3.52786	+	1.91668i	−0.147507	+	0.0801406i
$573$	−2.98677			−0.124774
$574$	3.66796	+	11.2888i	0.153098	+	0.471187i
$575$		0			0
$576$	2.37025	−	1.72209i	0.0987603	−	0.0717536i
$577$	1.13103	−	3.48094i	0.0470852	−	0.144913i	−0.924750	−	0.380576i	$-0.875726\pi$
$577$	1.13103	−	3.48094i	0.0470852	−	0.144913i	0.971835	+	0.235662i	$0.0757259\pi$
$578$	10.6146	−	32.6683i	0.441508	−	1.35882i
$579$	1.48865	−	1.08157i	0.0618662	−	0.0449484i
$580$		0			0
$581$	2.12465	+	6.53900i	0.0881453	+	0.271283i
$582$	1.83186			0.0759330
$583$	−19.3203	−	2.53836i	−0.800165	−	0.105128i
$584$	7.39217			0.305890
$585$		0			0
$586$	−3.21992	−	2.33941i	−0.133014	−	0.0966402i
$587$	−14.4242	+	10.4798i	−0.595350	+	0.432547i	−0.844225	−	0.535988i	$-0.819939\pi$
$587$	−14.4242	+	10.4798i	−0.595350	+	0.432547i	0.248875	+	0.968536i	$0.419939\pi$
$588$	0.949117	−	2.92108i	0.0391409	−	0.120463i
$589$	3.04305	−	9.36555i	0.125387	−	0.385901i
$590$		0			0
$591$	−2.88092	−	2.09311i	−0.118505	−	0.0860991i
$592$	−0.654831	−	2.01536i	−0.0269134	−	0.0828309i
$593$	−23.0006			−0.944523			−0.472262	−	0.881458i	$-0.656562\pi$
$593$	−23.0006			−0.944523			−0.472262	+	0.881458i	$0.656562\pi$
$594$	2.24227	−	4.70421i	0.0920013	−	0.193016i
$595$		0			0
$596$	2.04339	+	6.28892i	0.0837007	+	0.257604i
$597$	4.16795	+	3.02819i	0.170583	+	0.123936i
$598$	−6.87293	+	4.99348i	−0.281055	+	0.204199i
$599$	1.03235	−	3.17725i	0.0421807	−	0.129819i	−0.927749	−	0.373206i	$-0.878258\pi$
$599$	1.03235	−	3.17725i	0.0421807	−	0.129819i	0.969929	+	0.243387i	$0.0782585\pi$
$600$		0			0
$601$	−28.2605	+	20.5324i	−1.15277	+	0.837535i	−0.988846	−	0.148939i	$-0.952414\pi$
$601$	−28.2605	+	20.5324i	−1.15277	+	0.837535i	−0.163921	+	0.986473i	$0.552414\pi$
$602$	22.9965	+	16.7079i	0.937268	+	0.680965i
$603$	−1.47918	−	4.55244i	−0.0602367	−	0.185390i
$604$	20.8974			0.850303
$605$		0			0
$606$	0.857484			0.0348329
$607$	−3.89620	−	11.9913i	−0.158142	−	0.486711i	0.840324	−	0.542085i	$-0.182365\pi$
$607$	−3.89620	−	11.9913i	−0.158142	−	0.486711i	−0.998466	+	0.0553739i	$0.982365\pi$
$608$	−2.19992	−	1.59833i	−0.0892184	−	0.0648210i
$609$	−9.76602	+	7.09543i	−0.395739	+	0.287521i
$610$		0			0
$611$	2.14739	−	6.60899i	0.0868742	−	0.267371i
$612$	16.9849	−	12.3402i	0.686572	−	0.498824i
$613$	6.92760	+	5.03320i	0.279803	+	0.203289i	0.718832	−	0.695184i	$-0.244677\pi$
$613$	6.92760	+	5.03320i	0.279803	+	0.203289i	−0.439028	+	0.898473i	$0.644677\pi$
$614$	−5.44041	−	16.7439i	−0.219557	−	0.675727i
$615$		0			0
$616$	−6.15309	+	12.9090i	−0.247915	+	0.520119i
$617$	−1.77165			−0.0713241			−0.0356620	−	0.999364i	$-0.511354\pi$
$617$	−1.77165			−0.0713241			−0.0356620	+	0.999364i	$0.511354\pi$
$618$	−0.472972	−	1.45566i	−0.0190257	−	0.0585551i
$619$	15.6706	+	11.3854i	0.629855	+	0.457616i	0.856350	−	0.516396i	$-0.172727\pi$
$619$	15.6706	+	11.3854i	0.629855	+	0.457616i	−0.226495	+	0.974012i	$0.572727\pi$
$620$		0			0
$621$	3.40749	−	10.4872i	0.136738	−	0.420836i
$622$	−6.99443	+	21.5266i	−0.280451	+	0.863140i
$623$	−4.35027	+	3.16066i	−0.174290	+	0.126629i
$624$	0.259505	+	0.188541i	0.0103885	+	0.00754769i
$625$		0			0
$626$	12.6096			0.503982
$627$	−2.36939	−	0.311298i	−0.0946244	−	0.0124320i
$628$	20.2291			0.807231
$629$	−4.69243	−	14.4418i	−0.187099	−	0.575833i
$630$		0			0
$631$	−22.1727	+	16.1094i	−0.882680	+	0.641305i	−0.933959	−	0.357379i	$-0.883670\pi$
$631$	−22.1727	+	16.1094i	−0.882680	+	0.641305i	0.0512788	+	0.998684i	$0.483670\pi$
$632$	2.16376	−	6.65938i	0.0860699	−	0.264896i
$633$	−0.193122	+	0.594369i	−0.00767591	+	0.0236240i
$634$	21.2511	−	15.4399i	0.843991	−	0.613195i
$635$		0			0
$636$	0.481088	+	1.48064i	0.0190764	+	0.0587111i
$637$	−14.0316			−0.555954
$638$	30.7915	−	16.7290i	1.21905	−	0.662306i
$639$	−21.7932			−0.862126
$640$		0			0
$641$	19.3094	+	14.0291i	0.762676	+	0.554117i	0.899730	−	0.436447i	$-0.143763\pi$
$641$	19.3094	+	14.0291i	0.762676	+	0.554117i	−0.137054	+	0.990564i	$0.543763\pi$
$642$	0.0367486	−	0.0266994i	0.00145035	−	0.00105374i
$643$	−3.85766	+	11.8726i	−0.152131	+	0.468211i	−0.997859	−	0.0654032i	$-0.979167\pi$
$643$	−3.85766	+	11.8726i	−0.152131	+	0.468211i	0.845728	+	0.533614i	$0.179167\pi$
$644$	−9.35064	+	28.7783i	−0.368467	+	1.13402i
$645$		0			0
$646$	−15.7643	−	11.4534i	−0.620237	−	0.450629i
$647$	−2.18034	−	6.71040i	−0.0857180	−	0.263813i	0.899006	−	0.437937i	$-0.144291\pi$
$647$	−2.18034	−	6.71040i	−0.0857180	−	0.263813i	−0.984724	+	0.174124i	$0.944291\pi$
$648$	8.37301			0.328923
$649$	3.56958	+	19.2313i	0.140118	+	0.754895i
$650$		0			0
$651$	1.27857	+	3.93502i	0.0501109	+	0.154226i
$652$	−6.53779	−	4.74999i	−0.256040	−	0.186024i
$653$	2.16526	−	1.57315i	0.0847331	−	0.0615622i	−0.544612	−	0.838688i	$-0.683323\pi$
$653$	2.16526	−	1.57315i	0.0847331	−	0.0615622i	0.629345	+	0.777126i	$0.283323\pi$
$654$	−0.190584	+	0.586557i	−0.00745242	+	0.0229362i
$655$		0			0
$656$	−2.22713	+	1.61811i	−0.0869550	+	0.0631765i
$657$	17.5213	+	12.7300i	0.683570	+	0.496643i
$658$	−7.64866	−	23.5402i	−0.298176	−	0.917691i
$659$	−36.5069			−1.42211			−0.711053	−	0.703138i	$-0.751781\pi$
$659$	−36.5069			−1.42211			−0.711053	+	0.703138i	$0.751781\pi$
$660$		0			0
$661$	40.3521			1.56952			0.784758	−	0.619802i	$-0.212787\pi$
$661$	40.3521			1.56952			0.784758	+	0.619802i	$0.212787\pi$
$662$	3.93705	+	12.1170i	0.153018	+	0.470940i
$663$	1.85957	+	1.35106i	0.0722199	+	0.0524708i
$664$	−1.29006	+	0.937281i	−0.0500639	+	0.0363735i
$665$		0			0
$666$	1.91852	−	5.90459i	0.0743410	−	0.228798i
$667$	59.9875	−	43.5834i	2.32272	−	1.68756i
$668$	13.9738	+	10.1525i	0.540662	+	0.392814i
$669$	1.19522	+	3.67851i	0.0462099	+	0.142219i
$670$		0			0
$671$	−14.7864	−	14.0243i	−0.570822	−	0.541402i
$672$	1.14252			0.0440735
$673$	−3.94257	−	12.1340i	−0.151975	−	0.467731i	0.845867	−	0.533394i	$-0.179084\pi$
$673$	−3.94257	−	12.1340i	−0.151975	−	0.467731i	−0.997842	+	0.0656634i	$0.979084\pi$
$674$	−15.4174	−	11.2014i	−0.593857	−	0.431462i
$675$		0			0
$676$	−3.56438	+	10.9700i	−0.137092	+	0.421925i
$677$	3.85703	−	11.8707i	0.148238	−	0.456228i	−0.849175	−	0.528111i	$-0.822901\pi$
$677$	3.85703	−	11.8707i	0.148238	−	0.456228i	0.997413	+	0.0718823i	$0.0229006\pi$
$678$	0.923590	−	0.671027i	0.0354703	−	0.0257706i
$679$	−24.1154	−	17.5209i	−0.925466	−	0.672390i
$680$		0			0
$681$	−0.792201			−0.0303572
$682$	−2.19194	−	11.8092i	−0.0839336	−	0.452197i
$683$	−5.10260			−0.195246			−0.0976228	−	0.995223i	$-0.531124\pi$
$683$	−5.10260			−0.195246			−0.0976228	+	0.995223i	$0.531124\pi$
$684$	−2.46188	−	7.57689i	−0.0941324	−	0.289710i
$685$		0			0
$686$	−16.0155	+	11.6359i	−0.611473	+	0.444261i
$687$	0.129286	−	0.397900i	0.00493256	−	0.0151808i
$688$	−2.03720	+	6.26985i	−0.0776674	+	0.239036i
$689$	5.75401	−	4.18054i	0.219210	−	0.159266i
$690$		0			0
$691$	3.68372	+	11.3373i	0.140135	+	0.431292i	0.996353	−	0.0853223i	$-0.0271920\pi$
$691$	3.68372	+	11.3373i	0.140135	+	0.431292i	−0.856218	+	0.516615i	$0.827192\pi$
$692$	−14.3738			−0.546408
$693$	−36.8148	+	20.0014i	−1.39848	+	0.759791i
$694$	−18.8230			−0.714511
$695$		0			0
$696$	−2.26498	−	1.64560i	−0.0858537	−	0.0623764i
$697$	−15.9593	+	11.5951i	−0.604502	+	0.439197i
$698$	−8.41088	+	25.8860i	−0.318356	+	0.979800i
$699$	−0.0414095	+	0.127445i	−0.00156625	+	0.00482043i
$700$		0			0
$701$	9.19138	+	6.67793i	0.347154	+	0.252222i	0.747674	−	0.664066i	$-0.231171\pi$
$701$	9.19138	+	6.67793i	0.347154	+	0.252222i	−0.400520	+	0.916288i	$0.631171\pi$
$702$	0.587773	+	1.80898i	0.0221840	+	0.0682755i
$703$	−5.76230			−0.217329
$704$	−3.28837	−	0.432036i	−0.123935	−	0.0162830i
$705$		0			0
$706$	−7.92257	−	24.3832i	−0.298170	−	0.917673i
$707$	−11.2883	−	8.20144i	−0.424541	−	0.308447i
$708$	1.26425	−	0.918533i	0.0475135	−	0.0345206i
$709$	3.75791	−	11.5656i	0.141131	−	0.434357i	−0.855362	−	0.518031i	$-0.826665\pi$
$709$	3.75791	−	11.5656i	0.141131	−	0.434357i	0.996493	+	0.0836737i	$0.0266653\pi$
$710$		0			0
$711$	16.5967	−	12.0582i	0.622424	−	0.452218i
$712$	−1.00893	−	0.733033i	−0.0378114	−	0.0274716i
$713$	−7.85355	−	24.1707i	−0.294118	−	0.905201i
$714$	8.18710			0.306395
$715$		0			0
$716$	18.8541			0.704611
$717$	−1.37086	−	4.21908i	−0.0511958	−	0.157565i
$718$	−7.82857	−	5.68779i	−0.292160	−	0.212267i
$719$	27.9662	−	20.3186i	1.04296	−	0.757756i	0.0721003	−	0.997397i	$-0.477030\pi$
$719$	27.9662	−	20.3186i	1.04296	−	0.757756i	0.970862	+	0.239641i	$0.0770298\pi$
$720$		0			0
$721$	−7.69628	+	23.6867i	−0.286624	+	0.882139i
$722$	9.38921	−	6.82166i	0.349430	−	0.253876i
$723$	3.27874	+	2.38214i	0.121938	+	0.0885928i
$724$	−4.04887	−	12.4611i	−0.150475	−	0.463114i
$725$		0			0
$726$	−2.72060	+	1.04599i	−0.100971	+	0.0388205i
$727$	−46.4273			−1.72189			−0.860947	−	0.508695i	$-0.830128\pi$
$727$	−46.4273			−1.72189			−0.860947	+	0.508695i	$0.830128\pi$
$728$	−1.61293	−	4.96409i	−0.0597792	−	0.183981i
$729$	18.8356	+	13.6849i	0.697616	+	0.506847i
$730$		0			0
$731$	−14.5983	+	44.9288i	−0.539936	+	1.66175i
$732$	−0.503135	+	1.54849i	−0.0185964	+	0.0572339i
$733$	11.8252	−	8.59151i	0.436773	−	0.317334i	−0.347578	−	0.937651i	$-0.612996\pi$
$733$	11.8252	−	8.59151i	0.436773	−	0.317334i	0.784352	+	0.620317i	$0.212996\pi$
$734$	−16.7495	−	12.1692i	−0.618236	−	0.449174i
$735$		0			0
$736$	−7.01787			−0.258682
$737$	−2.33153	+	4.89149i	−0.0858830	+	0.180180i
$738$	−8.06538			−0.296891
$739$	−12.8330	−	39.4959i	−0.472070	−	1.45288i	−0.849869	−	0.526994i	$-0.823319\pi$
$739$	−12.8330	−	39.4959i	−0.472070	−	1.45288i	0.377800	−	0.925887i	$-0.376681\pi$
$740$		0			0
$741$	0.705658	−	0.512690i	0.0259230	−	0.0188341i
$742$	7.82835	−	24.0932i	0.287388	−	0.884488i
$743$	12.3655	−	38.0571i	0.453646	−	1.39618i	−0.419071	−	0.907953i	$-0.637644\pi$
$743$	12.3655	−	38.0571i	0.453646	−	1.39618i	0.872717	−	0.488226i	$-0.162356\pi$
$744$	−0.776327	+	0.564034i	−0.0284615	+	0.0206785i
$745$		0			0
$746$	4.98947	+	15.3560i	0.182677	+	0.562223i
$747$	−4.67183			−0.170933
$748$	−23.5639	−	3.09590i	−0.861583	−	0.113197i
$749$	−0.739143			−0.0270077
$750$		0			0
$751$	−11.5210	−	8.37050i	−0.420407	−	0.305444i	0.357394	−	0.933954i	$-0.383665\pi$
$751$	−11.5210	−	8.37050i	−0.420407	−	0.305444i	−0.777802	+	0.628510i	$0.783665\pi$
$752$	4.64416	−	3.37418i	0.169355	−	0.123044i
$753$	−0.0349957	+	0.107706i	−0.00127531	+	0.00392502i
$754$	−3.95239	+	12.1642i	−0.143937	+	0.442994i
$755$		0			0
$756$	5.48099	+	3.98217i	0.199342	+	0.144830i
$757$	9.20948	+	28.3439i	0.334724	+	1.03017i	0.966858	+	0.255316i	$0.0821794\pi$
$757$	9.20948	+	28.3439i	0.334724	+	1.03017i	−0.632134	+	0.774859i	$0.717821\pi$
$758$	−0.229700			−0.00834306
$759$	−5.41933	+	2.94432i	−0.196709	+	0.106872i
$760$		0			0
$761$	−4.10031	−	12.6195i	−0.148636	−	0.457455i	0.848825	−	0.528675i	$-0.177311\pi$
$761$	−4.10031	−	12.6195i	−0.148636	−	0.457455i	−0.997461	+	0.0712199i	$0.977311\pi$
$762$	2.32295	+	1.68772i	0.0841517	+	0.0611398i
$763$	8.11908	−	5.89886i	0.293930	−	0.213553i
$764$	−3.48318	+	10.7201i	−0.126017	+	0.387840i
$765$		0			0
$766$	10.5351	−	7.65417i	0.380647	−	0.276556i
$767$	−5.77570	−	4.19629i	−0.208548	−	0.151519i
$768$	0.0818824	+	0.252008i	0.00295468	+	0.00909356i
$769$	−46.3160			−1.67020			−0.835099	−	0.550099i	$-0.814590\pi$
$769$	−46.3160			−1.67020			−0.835099	+	0.550099i	$0.814590\pi$
$770$		0			0
$771$	−4.73653			−0.170582
$772$	−2.14590	−	6.60440i	−0.0772326	−	0.237697i
$773$	41.3802	+	30.0645i	1.48834	+	1.08134i	0.974747	+	0.223312i	$0.0716868\pi$
$773$	41.3802	+	30.0645i	1.48834	+	1.08134i	0.513596	+	0.858032i	$0.328313\pi$
$774$	−15.6259	+	11.3529i	−0.561660	+	0.408070i
$775$		0			0
$776$	2.13632	−	6.57491i	0.0766894	−	0.236026i
$777$	1.95870	−	1.42308i	0.0702678	−	0.0510526i
$778$	−23.9676	−	17.4135i	−0.859280	−	0.624304i
$779$	2.31323	+	7.11940i	0.0828802	+	0.255079i
$780$		0			0
$781$	17.9000	+	16.9774i	0.640512	+	0.607501i
$782$	−50.2890			−1.79833
$783$	−5.13012	−	15.7889i	−0.183336	−	0.564249i
$784$	−9.37749	−	6.81315i	−0.334910	−	0.243327i
$785$		0			0
$786$	0.473705	−	1.45791i	0.0168965	−	0.0520020i
$787$	−10.7231	+	33.0022i	−0.382236	+	1.17640i	0.556229	+	0.831029i	$0.312248\pi$
$787$	−10.7231	+	33.0022i	−0.382236	+	1.17640i	−0.938465	+	0.345374i	$0.887752\pi$
$788$	−10.8723	+	7.89922i	−0.387311	+	0.281398i
$789$	3.10788	+	2.25801i	0.110643	+	0.0803871i
$790$		0			0
$791$	−18.5766			−0.660509
$792$	−7.05024	−	6.68688i	−0.250519	−	0.237608i
$793$	7.43830			0.264142
$794$	−0.675711	−	2.07963i	−0.0239801	−	0.0738032i
$795$		0			0
$796$	15.7295	−	11.4281i	0.557516	−	0.405059i
$797$	−13.8054	+	42.4885i	−0.489011	+	1.50502i	0.337075	+	0.941478i	$0.390562\pi$
$797$	−13.8054	+	42.4885i	−0.489011	+	1.50502i	−0.826086	+	0.563544i	$0.809438\pi$
$798$	0.960049	−	2.95473i	0.0339853	−	0.104596i
$799$	33.2794	−	24.1789i	1.17734	−	0.855387i
$800$		0			0
$801$	−1.12908	−	3.47494i	−0.0398939	−	0.122781i
$802$	−13.0944			−0.462378
$803$	−4.47426	−	24.1053i	−0.157893	−	0.850659i
$804$	0.432922			0.0152680
$805$		0			0
$806$	3.54663	+	2.57678i	0.124925	+	0.0907630i
$807$	−5.98906	+	4.35130i	−0.210825	+	0.153173i
$808$	1.00000	−	3.07768i	0.0351799	−	0.108273i
$809$	−4.04819	+	12.4590i	−0.142327	+	0.438037i	−0.996658	−	0.0816929i	$-0.973967\pi$
$809$	−4.04819	+	12.4590i	−0.142327	+	0.438037i	0.854331	+	0.519730i	$0.173967\pi$
$810$		0			0
$811$	6.33646	+	4.60371i	0.222503	+	0.161658i	0.693453	−	0.720502i	$-0.256089\pi$
$811$	6.33646	+	4.60371i	0.222503	+	0.161658i	−0.470949	+	0.882160i	$0.656089\pi$
$812$	14.0778	+	43.3269i	0.494033	+	1.52048i
$813$	2.75299			0.0965515
$814$	−6.17561	+	3.35520i	−0.216455	+	0.117600i
$815$		0			0
$816$	0.586758	+	1.80585i	0.0205406	+	0.0632176i
$817$	14.5030	+	10.5370i	0.507394	+	0.368644i
$818$	−24.6173	+	17.8855i	−0.860725	+	0.625353i
$819$	4.72554	−	14.5437i	0.165124	−	0.508199i
$820$		0			0
$821$	19.4432	−	14.1263i	0.678573	−	0.493012i	−0.194311	−	0.980940i	$-0.562247\pi$
$821$	19.4432	−	14.1263i	0.678573	−	0.493012i	0.872884	+	0.487928i	$0.162247\pi$
$822$	1.85438	+	1.34729i	0.0646789	+	0.0469920i
$823$	−3.73052	−	11.4813i	−0.130038	−	0.400215i	0.864748	−	0.502207i	$-0.167478\pi$
$823$	−3.73052	−	11.4813i	−0.130038	−	0.400215i	−0.994785	+	0.101992i	$0.967478\pi$
$824$	−5.77623			−0.201224
$825$		0			0
$826$	−25.4285			−0.884772
$827$	−10.8899	−	33.5158i	−0.378680	−	1.16546i	−0.940962	−	0.338512i	$-0.890076\pi$
$827$	−10.8899	−	33.5158i	−0.378680	−	1.16546i	0.562282	−	0.826946i	$-0.309924\pi$
$828$	−16.6341	−	12.0854i	−0.578074	−	0.419996i
$829$	−19.6457	+	14.2734i	−0.682322	+	0.495736i	−0.874127	−	0.485697i	$-0.838566\pi$
$829$	−19.6457	+	14.2734i	−0.682322	+	0.495736i	0.191805	+	0.981433i	$0.438566\pi$
$830$		0			0
$831$	0.0514499	−	0.158346i	0.00178478	−	0.00549298i
$832$	0.979348	−	0.711538i	0.0339528	−	0.0246681i
$833$	−67.1977	−	48.8220i	−2.32826	−	1.69158i
$834$	1.04385	+	3.21264i	0.0361456	+	0.111245i
$835$		0			0
$836$	−3.88050	+	8.14119i	−0.134210	+	0.281569i
$837$	−5.69018			−0.196681
$838$	8.26538	+	25.4382i	0.285523	+	0.878748i
$839$	−12.3220	−	8.95243i	−0.425401	−	0.309072i	0.354406	−	0.935092i	$-0.384683\pi$
$839$	−12.3220	−	8.95243i	−0.425401	−	0.309072i	−0.779807	+	0.626019i	$0.784683\pi$
$840$		0			0
$841$	25.5352	−	78.5894i	0.880525	−	2.70998i
$842$	−9.37640	+	28.8576i	−0.323132	+	0.994498i
$843$	−6.45399	+	4.68910i	−0.222287	+	0.161501i
$844$	1.90809	+	1.38631i	0.0656792	+	0.0477187i
$845$		0			0
$846$	16.8184			0.578229
$847$	45.8197	+	12.2513i	1.57438	+	0.420961i
$848$	5.87535			0.201760
$849$	1.31868	+	4.05847i	0.0452568	+	0.139286i
$850$		0			0
$851$	−12.0312	+	8.74120i	−0.412425	+	0.299644i
$852$	0.609082	−	1.87456i	0.0208668	−	0.0642214i
$853$	2.13420	−	6.56839i	0.0730736	−	0.224897i	−0.907849	−	0.419298i	$-0.862276\pi$
$853$	2.13420	−	6.56839i	0.0730736	−	0.224897i	0.980922	+	0.194401i	$0.0622762\pi$
$854$	21.4341	−	15.5728i	0.733460	−	0.532890i
$855$		0			0
$856$	−0.0529733	−	0.163035i	−0.00181059	−	0.00557242i
$857$	1.68576			0.0575845			0.0287922	−	0.999585i	$-0.490834\pi$
$857$	1.68576			0.0575845			0.0287922	+	0.999585i	$0.490834\pi$
$858$	0.457749	−	0.960345i	0.0156273	−	0.0327856i
$859$	−52.7330			−1.79923			−0.899613	−	0.436688i	$-0.856151\pi$
$859$	−52.7330			−1.79923			−0.899613	+	0.436688i	$0.856151\pi$
$860$		0			0
$861$	−2.54454	−	1.84871i	−0.0867176	−	0.0630040i
$862$	9.56907	−	6.95234i	0.325924	−	0.236798i
$863$	−9.11412	+	28.0504i	−0.310248	+	0.954846i	0.667418	+	0.744683i	$0.267399\pi$
$863$	−9.11412	+	28.0504i	−0.310248	+	0.954846i	−0.977666	+	0.210163i	$0.932601\pi$
$864$	−0.485545	+	1.49436i	−0.0165186	+	0.0508390i
$865$		0			0
$866$	26.3685	+	19.1578i	0.896037	+	0.651009i
$867$	2.81262	+	8.65635i	0.0955216	+	0.293985i
$868$	15.6147			0.529996
$869$	−23.0254	−	3.02515i	−0.781084	−	0.102621i
$870$		0			0
$871$	−0.611172	−	1.88099i	−0.0207088	−	0.0637351i
$872$	1.88301	+	1.36809i	0.0637668	+	0.0463293i
$873$	16.3862	−	11.9052i	0.554588	−	0.402932i
$874$	−5.89707	+	18.1493i	−0.199471	+	0.613909i
$875$		0			0
$876$	−1.58467	+	1.15133i	−0.0535410	+	0.0388998i
$877$	−22.6710	−	16.4715i	−0.765547	−	0.556202i	0.135060	−	0.990837i	$-0.456877\pi$
$877$	−22.6710	−	16.4715i	−0.765547	−	0.556202i	−0.900607	+	0.434635i	$0.856877\pi$
$878$	1.57464	+	4.84624i	0.0531415	+	0.163553i
$879$	1.05462			0.0355715
$880$		0			0
$881$	−28.1345			−0.947875			−0.473937	−	0.880559i	$-0.657168\pi$
$881$	−28.1345			−0.947875			−0.473937	+	0.880559i	$0.657168\pi$
$882$	−10.4942	−	32.2977i	−0.353357	−	1.08752i
$883$	32.7842	+	23.8191i	1.10328	+	0.801578i	0.981592	−	0.190991i	$-0.0611700\pi$
$883$	32.7842	+	23.8191i	1.10328	+	0.801578i	0.121686	+	0.992569i	$0.461170\pi$
$884$	7.01787	−	5.09878i	0.236036	−	0.171490i
$885$		0			0
$886$	−7.62632	+	23.4714i	−0.256211	+	0.788537i
$887$	11.5317	−	8.37825i	0.387196	−	0.281314i	−0.377110	−	0.926169i	$-0.623082\pi$
$887$	11.5317	−	8.37825i	0.387196	−	0.281314i	0.764305	+	0.644854i	$0.223082\pi$
$888$	0.454269	+	0.330046i	0.0152443	+	0.0110756i
$889$	−14.4381	−	44.4360i	−0.484239	−	1.49033i
$890$		0			0
$891$	−5.06794	−	27.3038i	−0.169782	−	0.914711i
$892$	14.5968			0.488737
$893$	−4.82370	−	14.8458i	−0.161419	−	0.496796i
$894$	−1.41754	−	1.02990i	−0.0474097	−	0.0344451i
$895$		0			0
$896$	1.33240	−	4.10072i	0.0445125	−	0.136995i
$897$	0.695625	−	2.14091i	0.0232263	−	0.0714831i
$898$	15.3457	−	11.1493i	0.512093	−	0.372057i
$899$	−30.9552	−	22.4903i	−1.03241	−	0.750093i
$900$		0			0
$901$	42.1019			1.40262
$902$	6.62455	+	6.28313i	0.220573	+	0.209205i
$903$	−7.53204			−0.250651
$904$	−1.33136	−	4.09750i	−0.0442804	−	0.136281i
$905$		0			0
$906$	−4.47980	+	3.25476i	−0.148831	+	0.108132i
$907$	13.3997	−	41.2401i	0.444931	−	1.36936i	−0.437629	−	0.899156i	$-0.644182\pi$
$907$	13.3997	−	41.2401i	0.444931	−	1.36936i	0.882560	−	0.470200i	$-0.155818\pi$
$908$	−0.923867	+	2.84337i	−0.0306596	+	0.0943605i
$909$	7.67028	−	5.57279i	0.254407	−	0.184838i
$910$		0			0
$911$	7.33435	+	22.5728i	0.242998	+	0.747871i	0.995959	+	0.0898061i	$0.0286247\pi$
$911$	7.33435	+	22.5728i	0.242998	+	0.747871i	−0.752961	+	0.658065i	$0.771375\pi$
$912$	0.720538			0.0238594
$913$	3.83724	+	3.63947i	0.126994	+	0.120449i
$914$	28.5141			0.943162
$915$		0			0
$916$	−1.27737	−	0.928065i	−0.0422055	−	0.0306641i
$917$	−20.1803	+	14.6619i	−0.666414	+	0.484178i
$918$	−3.47935	+	10.7083i	−0.114836	+	0.353428i
$919$	−4.34410	+	13.3698i	−0.143299	+	0.441028i	−0.996788	−	0.0800817i	$-0.974482\pi$
$919$	−4.34410	+	13.3698i	−0.143299	+	0.441028i	0.853490	+	0.521110i	$0.174482\pi$
$920$		0			0
$921$	3.77412	+	2.74206i	0.124361	+	0.0903538i
$922$	−10.9119	−	33.5834i	−0.359365	−	1.10601i
$923$	−9.00460			−0.296390
$924$	−0.691531	−	3.72566i	−0.0227497	−	0.122565i
$925$		0			0
$926$	−1.20394	−	3.70536i	−0.0395641	−	0.121766i
$927$	−13.6911	−	9.94716i	−0.449674	−	0.326708i
$928$	−8.54782	+	6.21036i	−0.280596	+	0.203865i
$929$	−17.2507	+	53.0922i	−0.565977	+	1.74190i	0.0990531	+	0.995082i	$0.468419\pi$
$929$	−17.2507	+	53.0922i	−0.565977	+	1.74190i	−0.665030	+	0.746816i	$0.731581\pi$
$930$		0			0
$931$	−25.4997	+	18.5266i	−0.835719	+	0.607185i
$932$	0.409135	+	0.297254i	0.0134017	+	0.00973688i
$933$	−1.85336	−	5.70407i	−0.0606764	−	0.186743i
$934$	11.8528			0.387836
$935$		0			0
$936$	3.54663			0.115925
$937$	3.84000	+	11.8183i	0.125447	+	0.386088i	0.993982	−	0.109540i	$-0.0349379\pi$
$937$	3.84000	+	11.8183i	0.125447	+	0.386088i	−0.868535	+	0.495628i	$0.834938\pi$
$938$	−5.69919	−	4.14070i	−0.186085	−	0.135199i
$939$	−2.70314	+	1.96395i	−0.0882136	+	0.0640910i
$940$		0			0
$941$	−4.50996	+	13.8802i	−0.147020	+	0.452483i	−0.997265	−	0.0739049i	$-0.976454\pi$
$941$	−4.50996	+	13.8802i	−0.147020	+	0.452483i	0.850245	+	0.526387i	$0.176454\pi$
$942$	−4.33654	+	3.15068i	−0.141292	+	0.102655i
$943$	15.6297	+	11.3557i	0.508974	+	0.369791i
$944$	−1.82243	−	5.60885i	−0.0593149	−	0.182553i
$945$		0			0
$946$	21.6786	+	2.84820i	0.704831	+	0.0926029i
$947$	−38.1184			−1.23868			−0.619340	−	0.785123i	$-0.712600\pi$
$947$	−38.1184			−1.23868			−0.619340	+	0.785123i	$0.712600\pi$
$948$	0.573348	+	1.76458i	0.0186215	+	0.0573110i
$949$	7.23951	+	5.25981i	0.235004	+	0.170741i
$950$		0			0
$951$	−2.15088	+	6.61972i	−0.0697470	+	0.214659i
$952$	9.54782	−	29.3852i	0.309447	−	0.952379i
$953$	0.381518	−	0.277189i	0.0123586	−	0.00897903i	−0.581589	−	0.813483i	$-0.697569\pi$
$953$	0.381518	−	0.277189i	0.0123586	−	0.00897903i	0.593947	+	0.804504i	$0.297569\pi$
$954$	13.9260	+	10.1179i	0.450872	+	0.327578i
$955$		0			0
$956$	−16.7418			−0.541470
$957$	−3.99527	+	8.38196i	−0.129149	+	0.270950i
$958$	10.4253			0.336825
$959$	−11.5257	−	35.4726i	−0.372185	−	1.14547i
$960$		0			0
$961$	14.4695	−	10.5127i	0.466760	−	0.339121i
$962$	0.792700	−	2.43968i	0.0255577	−	0.0786585i
$963$	0.155200	−	0.477658i	0.00500126	−	0.0153923i
$964$	12.3737	−	8.98999i	0.398529	−	0.289548i
$965$		0			0
$966$	−2.47771	−	7.62559i	−0.0797189	−	0.245349i
$967$	29.1678			0.937975			0.468987	−	0.883205i	$-0.344619\pi$
$967$	29.1678			0.937975			0.468987	+	0.883205i	$0.344619\pi$
$968$	0.581513	+	10.9846i	0.0186906	+	0.353059i
$969$	5.16327			0.165868
$970$		0			0
$971$	12.8033	+	9.30216i	0.410878	+	0.298520i	0.773957	−	0.633238i	$-0.218275\pi$
$971$	12.8033	+	9.30216i	0.410878	+	0.298520i	−0.363079	+	0.931758i	$0.618275\pi$
$972$	−5.60845	+	4.07478i	−0.179891	+	0.130699i
$973$	16.9857	−	52.2766i	0.544537	−	1.67591i
$974$	7.60226	−	23.3973i	0.243592	−	0.749699i
$975$		0			0
$976$	4.97109	+	3.61171i	0.159121	+	0.115608i
$977$	−12.9305	−	39.7961i	−0.413684	−	1.27319i	−0.913423	−	0.407013i	$-0.866571\pi$
$977$	−12.9305	−	39.7961i	−0.413684	−	1.27319i	0.499738	−	0.866176i	$-0.333429\pi$
$978$	2.14132			0.0684719
$979$	−1.77969	+	3.73374i	−0.0568791	+	0.119331i
$980$		0			0
$981$	2.10724	+	6.48541i	0.0672789	+	0.207063i
$982$	18.7305	+	13.6085i	0.597714	+	0.434265i
$983$	4.12492	−	2.99693i	0.131565	−	0.0955872i	−0.520057	−	0.854132i	$-0.674089\pi$
$983$	4.12492	−	2.99693i	0.131565	−	0.0955872i	0.651621	+	0.758545i	$0.274089\pi$
$984$	0.225413	−	0.693751i	0.00718591	−	0.0221160i
$985$		0			0
$986$	−61.2524	+	44.5025i	−1.95068	+	1.41725i
$987$	5.30602	+	3.85505i	0.168893	+	0.122708i
$988$	−1.01721	−	3.13065i	−0.0323617	−	0.0995992i
$989$	46.2653			1.47115
$990$		0			0
$991$	−14.8133			−0.470560			−0.235280	−	0.971928i	$-0.575601\pi$
$991$	−14.8133			−0.470560			−0.235280	+	0.971928i	$0.575601\pi$
$992$	1.11908	+	3.44417i	0.0355308	+	0.109353i
$993$	−2.73121	−	1.98434i	−0.0866722	−	0.0629710i
$994$	−25.9476	+	18.8520i	−0.823007	+	0.597949i
$995$		0			0
$996$	0.130569	−	0.401852i	0.00413725	−	0.0127332i
$997$	−46.9861	+	34.1374i	−1.48807	+	1.08114i	−0.513221	+	0.858257i	$0.671548\pi$
$997$	−46.9861	+	34.1374i	−1.48807	+	1.08114i	−0.974844	+	0.222886i	$0.928452\pi$
$998$	−18.3406	−	13.3253i	−0.580563	−	0.421804i
$999$	1.02891	+	3.16666i	0.0325532	+	0.100189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.h.l.401.1		8
5.2	odd	4		550.2.ba.f.49.1		16
5.3	odd	4		550.2.ba.f.49.4		16
5.4	even	2		110.2.g.c.71.2	yes	8
11.3	even	5		6050.2.a.dh.1.3		4
11.8	odd	10		6050.2.a.cy.1.3		4
11.9	even	5	inner	550.2.h.l.251.1		8
15.14	odd	2		990.2.n.j.181.2		8
20.19	odd	2		880.2.bo.g.401.1		8
55.9	even	10		110.2.g.c.31.2	✓	8
55.14	even	10		1210.2.a.u.1.2		4
55.19	odd	10		1210.2.a.v.1.2		4
55.42	odd	20		550.2.ba.f.449.4		16
55.53	odd	20		550.2.ba.f.449.1		16
165.119	odd	10		990.2.n.j.361.2		8
220.19	even	10		9680.2.a.ci.1.3		4
220.119	odd	10		880.2.bo.g.801.1		8
220.179	odd	10		9680.2.a.cj.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.c.31.2	✓	8	55.9	even	10
110.2.g.c.71.2	yes	8	5.4	even	2
550.2.h.l.251.1		8	11.9	even	5	inner
550.2.h.l.401.1		8	1.1	even	1	trivial
550.2.ba.f.49.1		16	5.2	odd	4
550.2.ba.f.49.4		16	5.3	odd	4
550.2.ba.f.449.1		16	55.53	odd	20
550.2.ba.f.449.4		16	55.42	odd	20
880.2.bo.g.401.1		8	20.19	odd	2
880.2.bo.g.801.1		8	220.119	odd	10
990.2.n.j.181.2		8	15.14	odd	2
990.2.n.j.361.2		8	165.119	odd	10
1210.2.a.u.1.2		4	55.14	even	10
1210.2.a.v.1.2		4	55.19	odd	10
6050.2.a.cy.1.3		4	11.8	odd	10
6050.2.a.dh.1.3		4	11.3	even	5
9680.2.a.ci.1.3		4	220.19	even	10
9680.2.a.cj.1.3		4	220.179	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.214371 - 0.155750i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.0818824 - 0.252008i) q^{6} +(-3.48828 + 2.53438i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.905354 - 2.78639i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.214371 - 0.155750i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.0818824 - 0.252008i) q^{6} +(-3.48828 + 2.53438i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.905354 - 2.78639i) q^{9} +(-1.42705 + 2.99391i) q^{11} +0.264977 q^{12} +(-0.374078 - 1.15129i) q^{13} +(-3.48828 - 2.53438i) q^{14} +(0.309017 - 0.951057i) q^{16} +(2.21437 - 6.81513i) q^{17} +(2.37025 - 1.72209i) q^{18} +(-2.19992 - 1.59833i) q^{19} +1.14252 q^{21} +(-3.28837 - 0.432036i) q^{22} -7.01787 q^{23} +(0.0818824 + 0.252008i) q^{24} +(0.979348 - 0.711538i) q^{26} +(-0.485545 + 1.49436i) q^{27} +(1.33240 - 4.10072i) q^{28} +(-8.54782 + 6.21036i) q^{29} +(1.11908 + 3.44417i) q^{31} +1.00000 q^{32} +(0.772220 - 0.419546i) q^{33} +7.16586 q^{34} +(2.37025 + 1.72209i) q^{36} +(1.71437 - 1.24556i) q^{37} +(0.840293 - 2.58616i) q^{38} +(-0.0991220 + 0.305066i) q^{39} +(-2.22713 - 1.61811i) q^{41} +(0.353057 + 1.08660i) q^{42} -6.59251 q^{43} +(-0.605270 - 3.26093i) q^{44} +(-2.16864 - 6.67439i) q^{46} +(4.64416 + 3.37418i) q^{47} +(-0.214371 + 0.155750i) q^{48} +(3.58188 - 11.0239i) q^{49} +(-1.53615 + 1.11608i) q^{51} +(0.979348 + 0.711538i) q^{52} +(1.81558 + 5.58779i) q^{53} -1.57126 q^{54} +4.31175 q^{56} +(0.222659 + 0.685272i) q^{57} +(-8.54782 - 6.21036i) q^{58} +(4.77117 - 3.46646i) q^{59} +(-1.89879 + 5.84387i) q^{61} +(-2.92979 + 2.12861i) q^{62} +(10.2199 + 7.42521i) q^{63} +(0.309017 + 0.951057i) q^{64} +(0.637641 + 0.604778i) q^{66} +1.63381 q^{67} +(2.21437 + 6.81513i) q^{68} +(1.50443 + 1.09303i) q^{69} +(2.29862 - 7.07443i) q^{71} +(-0.905354 + 2.78639i) q^{72} +(-5.98039 + 4.34501i) q^{73} +(1.71437 + 1.24556i) q^{74} +2.71925 q^{76} +(-2.60978 - 14.0603i) q^{77} -0.320766 q^{78} +(2.16376 + 6.65938i) q^{79} +(-6.77391 + 4.92153i) q^{81} +(0.850690 - 2.61815i) q^{82} +(0.492758 - 1.51655i) q^{83} +(-0.924315 + 0.671554i) q^{84} +(-2.03720 - 6.26985i) q^{86} +2.79967 q^{87} +(2.91429 - 1.58333i) q^{88} +1.24711 q^{89} +(4.22271 + 3.06798i) q^{91} +(5.67757 - 4.12500i) q^{92} +(0.296530 - 0.912627i) q^{93} +(-1.77391 + 5.45954i) q^{94} +(-0.214371 - 0.155750i) q^{96} +(2.13632 + 6.57491i) q^{97} +11.5912 q^{98} +(9.63421 + 1.26577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - q^{6} + q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - q^6 + q^7 - 2 * q^8 - 6 * q^9	\( 8 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - q^{6} + q^{7} - 2 q^{8} - 6 q^{9} + 2 q^{11} - 6 q^{12} - q^{13} + q^{14} - 2 q^{16} + 12 q^{17} - q^{18} - 7 q^{19} + 32 q^{21} - 8 q^{22} - 26 q^{23} - q^{24} - 6 q^{26} + q^{27} - 4 q^{28} - 22 q^{29} - 26 q^{31} + 8 q^{32} - 19 q^{33} + 2 q^{34} - q^{36} + 8 q^{37} + 3 q^{38} - 48 q^{39} - 15 q^{41} + 2 q^{42} - 38 q^{43} + 7 q^{44} - 6 q^{46} - 6 q^{47} + 4 q^{48} + 27 q^{49} - 5 q^{51} - 6 q^{52} + 4 q^{53} - 24 q^{54} + 6 q^{56} - 47 q^{57} - 22 q^{58} + 39 q^{59} - 20 q^{61} + 14 q^{62} + 57 q^{63} - 2 q^{64} + 36 q^{66} + 26 q^{67} + 12 q^{68} - 10 q^{69} + 2 q^{71} - 6 q^{72} - 8 q^{73} + 8 q^{74} + 8 q^{76} - 16 q^{77} + 12 q^{78} + 14 q^{79} - 31 q^{81} + 15 q^{82} + 21 q^{83} - 18 q^{84} + 17 q^{86} - 20 q^{87} + 7 q^{88} + 32 q^{89} + 53 q^{91} + 19 q^{92} + 38 q^{93} + 9 q^{94} + 4 q^{96} + 31 q^{97} + 22 q^{98} + 36 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - q^6 + q^7 - 2 * q^8 - 6 * q^9 + 2 * q^11 - 6 * q^12 - q^13 + q^14 - 2 * q^16 + 12 * q^17 - q^18 - 7 * q^19 + 32 * q^21 - 8 * q^22 - 26 * q^23 - q^24 - 6 * q^26 + q^27 - 4 * q^28 - 22 * q^29 - 26 * q^31 + 8 * q^32 - 19 * q^33 + 2 * q^34 - q^36 + 8 * q^37 + 3 * q^38 - 48 * q^39 - 15 * q^41 + 2 * q^42 - 38 * q^43 + 7 * q^44 - 6 * q^46 - 6 * q^47 + 4 * q^48 + 27 * q^49 - 5 * q^51 - 6 * q^52 + 4 * q^53 - 24 * q^54 + 6 * q^56 - 47 * q^57 - 22 * q^58 + 39 * q^59 - 20 * q^61 + 14 * q^62 + 57 * q^63 - 2 * q^64 + 36 * q^66 + 26 * q^67 + 12 * q^68 - 10 * q^69 + 2 * q^71 - 6 * q^72 - 8 * q^73 + 8 * q^74 + 8 * q^76 - 16 * q^77 + 12 * q^78 + 14 * q^79 - 31 * q^81 + 15 * q^82 + 21 * q^83 - 18 * q^84 + 17 * q^86 - 20 * q^87 + 7 * q^88 + 32 * q^89 + 53 * q^91 + 19 * q^92 + 38 * q^93 + 9 * q^94 + 4 * q^96 + 31 * q^97 + 22 * q^98 + 36 * q^99

Introduction

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