LMFDB - Embedded newform 671.2.e.a.474.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(474,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(6))

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("671.474");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			474.20
Character	$\chi$	$=$	671.474
Dual form			671.2.e.a.562.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.772502 + 1.33801i) q^{2} -0.117047 q^{3} +(-0.193519 + 0.335184i) q^{4} +(-0.0594005 - 0.102885i) q^{5} +(-0.0904189 - 0.156610i) q^{6} +(-2.59858 - 4.50087i) q^{7} +2.49203 q^{8} -2.98630 q^{9} +O(q^{10})$	\(q+(0.772502 + 1.33801i) q^{2} -0.117047 q^{3} +(-0.193519 + 0.335184i) q^{4} +(-0.0594005 - 0.102885i) q^{5} +(-0.0904189 - 0.156610i) q^{6} +(-2.59858 - 4.50087i) q^{7} +2.49203 q^{8} -2.98630 q^{9} +(0.0917739 - 0.158957i) q^{10} +1.00000 q^{11} +(0.0226508 - 0.0392323i) q^{12} +(0.673481 + 1.16650i) q^{13} +(4.01482 - 6.95387i) q^{14} +(0.00695263 + 0.0120423i) q^{15} +(2.31214 + 4.00474i) q^{16} +(2.45809 - 4.25753i) q^{17} +(-2.30692 - 3.99571i) q^{18} +(1.79923 - 3.11637i) q^{19} +0.0459804 q^{20} +(0.304155 + 0.526813i) q^{21} +(0.772502 + 1.33801i) q^{22} +1.79884 q^{23} -0.291684 q^{24} +(2.49294 - 4.31790i) q^{25} +(-1.04053 + 1.80225i) q^{26} +0.700677 q^{27} +2.01150 q^{28} +(2.23005 - 3.86256i) q^{29} +(-0.0107418 + 0.0186054i) q^{30} +(0.891422 - 1.54399i) q^{31} +(-1.08023 + 1.87101i) q^{32} -0.117047 q^{33} +7.59550 q^{34} +(-0.308714 + 0.534708i) q^{35} +(0.577905 - 1.00096i) q^{36} -9.11828 q^{37} +5.55965 q^{38} +(-0.0788288 - 0.136535i) q^{39} +(-0.148028 - 0.256392i) q^{40} -4.41465 q^{41} +(-0.469921 + 0.813927i) q^{42} +(0.633751 + 1.09769i) q^{43} +(-0.193519 + 0.335184i) q^{44} +(0.177388 + 0.307244i) q^{45} +(1.38961 + 2.40688i) q^{46} +(-0.290909 + 0.503869i) q^{47} +(-0.270628 - 0.468742i) q^{48} +(-10.0052 + 17.3296i) q^{49} +7.70321 q^{50} +(-0.287711 + 0.498330i) q^{51} -0.521325 q^{52} +4.04406 q^{53} +(0.541275 + 0.937515i) q^{54} +(-0.0594005 - 0.102885i) q^{55} +(-6.47575 - 11.2163i) q^{56} +(-0.210595 + 0.364761i) q^{57} +6.89088 q^{58} +(4.34699 + 7.52921i) q^{59} -0.00538186 q^{60} +(-3.32924 + 7.06514i) q^{61} +2.75450 q^{62} +(7.76014 + 13.4410i) q^{63} +5.91063 q^{64} +(0.0800102 - 0.138582i) q^{65} +(-0.0904189 - 0.156610i) q^{66} +(-3.25140 - 5.63158i) q^{67} +(0.951372 + 1.64782i) q^{68} -0.210549 q^{69} -0.953928 q^{70} +(0.125281 - 0.216993i) q^{71} -7.44196 q^{72} +(-1.38342 + 2.39616i) q^{73} +(-7.04389 - 12.2004i) q^{74} +(-0.291791 + 0.505397i) q^{75} +(0.696371 + 1.20615i) q^{76} +(-2.59858 - 4.50087i) q^{77} +(0.121791 - 0.210948i) q^{78} +(5.41276 + 9.37517i) q^{79} +(0.274684 - 0.475767i) q^{80} +8.87689 q^{81} +(-3.41032 - 5.90685i) q^{82} +(-0.937378 - 1.62359i) q^{83} -0.235439 q^{84} -0.584046 q^{85} +(-0.979149 + 1.69594i) q^{86} +(-0.261020 + 0.452100i) q^{87} +2.49203 q^{88} -9.27441 q^{89} +(-0.274065 + 0.474694i) q^{90} +(3.50019 - 6.06250i) q^{91} +(-0.348110 + 0.602945i) q^{92} +(-0.104338 + 0.180719i) q^{93} -0.898911 q^{94} -0.427501 q^{95} +(0.126437 - 0.218996i) q^{96} +(-5.71114 + 9.89199i) q^{97} -30.9162 q^{98} -2.98630 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 2 q^{2} + 2 q^{3} - 30 q^{4} - 6 q^{6} - 7 q^{7} + 50 q^{9}+O(q^{10}) $ 52 * q - 2 * q^2 + 2 * q^3 - 30 * q^4 - 6 * q^6 - 7 * q^7 + 50 * q^9	\( 52 q - 2 q^{2} + 2 q^{3} - 30 q^{4} - 6 q^{6} - 7 q^{7} + 50 q^{9} - 2 q^{10} + 52 q^{11} + 11 q^{12} - 3 q^{13} - 3 q^{14} - 12 q^{15} - 34 q^{16} - 8 q^{17} - 12 q^{18} + 5 q^{19} - 22 q^{20} - 2 q^{21} - 2 q^{22} - 2 q^{24} - 16 q^{25} - 37 q^{26} + 8 q^{27} + 104 q^{28} + 10 q^{29} - 20 q^{31} + 8 q^{32} + 2 q^{33} - 12 q^{34} + 18 q^{35} - 60 q^{36} + 4 q^{37} - 20 q^{38} + 23 q^{39} - 38 q^{40} - 6 q^{41} - 56 q^{42} - 22 q^{43} - 30 q^{44} + 25 q^{46} - 26 q^{48} - 45 q^{49} - 16 q^{50} - 38 q^{51} - 18 q^{53} - 46 q^{54} + 16 q^{56} + 36 q^{57} - 56 q^{58} - 13 q^{59} + 40 q^{60} + 14 q^{61} + 26 q^{62} - 39 q^{63} + 164 q^{64} + 15 q^{65} - 6 q^{66} + 7 q^{67} - 39 q^{68} + 20 q^{69} + 162 q^{70} - 8 q^{71} + 6 q^{72} + 27 q^{73} - 13 q^{74} + 16 q^{75} + 20 q^{76} - 7 q^{77} + 20 q^{78} + 5 q^{79} - 8 q^{80} - 68 q^{81} + 6 q^{82} - 22 q^{83} - 28 q^{84} - 36 q^{85} + 13 q^{86} - 25 q^{87} + 36 q^{89} + 41 q^{90} - 42 q^{91} - 17 q^{92} - 26 q^{93} - 14 q^{94} - 40 q^{95} - 3 q^{96} - 47 q^{97} - 2 q^{98} + 50 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 + 2 * q^3 - 30 * q^4 - 6 * q^6 - 7 * q^7 + 50 * q^9 - 2 * q^10 + 52 * q^11 + 11 * q^12 - 3 * q^13 - 3 * q^14 - 12 * q^15 - 34 * q^16 - 8 * q^17 - 12 * q^18 + 5 * q^19 - 22 * q^20 - 2 * q^21 - 2 * q^22 - 2 * q^24 - 16 * q^25 - 37 * q^26 + 8 * q^27 + 104 * q^28 + 10 * q^29 - 20 * q^31 + 8 * q^32 + 2 * q^33 - 12 * q^34 + 18 * q^35 - 60 * q^36 + 4 * q^37 - 20 * q^38 + 23 * q^39 - 38 * q^40 - 6 * q^41 - 56 * q^42 - 22 * q^43 - 30 * q^44 + 25 * q^46 - 26 * q^48 - 45 * q^49 - 16 * q^50 - 38 * q^51 - 18 * q^53 - 46 * q^54 + 16 * q^56 + 36 * q^57 - 56 * q^58 - 13 * q^59 + 40 * q^60 + 14 * q^61 + 26 * q^62 - 39 * q^63 + 164 * q^64 + 15 * q^65 - 6 * q^66 + 7 * q^67 - 39 * q^68 + 20 * q^69 + 162 * q^70 - 8 * q^71 + 6 * q^72 + 27 * q^73 - 13 * q^74 + 16 * q^75 + 20 * q^76 - 7 * q^77 + 20 * q^78 + 5 * q^79 - 8 * q^80 - 68 * q^81 + 6 * q^82 - 22 * q^83 - 28 * q^84 - 36 * q^85 + 13 * q^86 - 25 * q^87 + 36 * q^89 + 41 * q^90 - 42 * q^91 - 17 * q^92 - 26 * q^93 - 14 * q^94 - 40 * q^95 - 3 * q^96 - 47 * q^97 - 2 * q^98 + 50 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/671\mathbb{Z}\right)^\times$.

$n$	$123$	$551$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.772502	+	1.33801i	0.546241	+	0.946118i	0.998528	+	0.0542451i	$0.0172752\pi$
$2$	0.772502	+	1.33801i	0.546241	+	0.946118i	−0.452286	+	0.891873i	$0.649391\pi$
$3$	−0.117047			−0.0675770			−0.0337885	−	0.999429i	$-0.510757\pi$
$3$	−0.117047			−0.0675770			−0.0337885	+	0.999429i	$0.510757\pi$
$4$	−0.193519	+	0.335184i	−0.0967594	+	0.167592i
$5$	−0.0594005	−	0.102885i	−0.0265647	−	0.0460114i	0.852437	−	0.522829i	$-0.175123\pi$
$5$	−0.0594005	−	0.102885i	−0.0265647	−	0.0460114i	−0.879002	+	0.476818i	$0.841790\pi$
$6$	−0.0904189	−	0.156610i	−0.0369134	−	0.0639358i
$7$	−2.59858	−	4.50087i	−0.982171	−	1.70117i	−0.653890	−	0.756589i	$-0.726864\pi$
$7$	−2.59858	−	4.50087i	−0.982171	−	1.70117i	−0.328280	−	0.944580i	$-0.606469\pi$
$8$	2.49203			0.881067
$9$	−2.98630			−0.995433
$10$	0.0917739	−	0.158957i	0.0290215	−	0.0502667i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$	0.0226508	−	0.0392323i	0.00653871	−	0.0113254i
$13$	0.673481	+	1.16650i	0.186790	+	0.323530i	0.944178	−	0.329435i	$-0.106858\pi$
$13$	0.673481	+	1.16650i	0.186790	+	0.323530i	−0.757388	+	0.652965i	$0.773525\pi$
$14$	4.01482	−	6.95387i	1.07300	−	1.85850i
$15$	0.00695263	+	0.0120423i	0.00179516	+	0.00310931i
$16$	2.31214	+	4.00474i	0.578035	+	1.00119i
$17$	2.45809	−	4.25753i	0.596173	−	1.03260i	−0.397207	−	0.917729i	$-0.630020\pi$
$17$	2.45809	−	4.25753i	0.596173	−	1.03260i	0.993380	−	0.114873i	$-0.0366462\pi$
$18$	−2.30692	−	3.99571i	−0.543747	−	0.941797i
$19$	1.79923	−	3.11637i	0.412773	−	0.714943i	−0.582419	−	0.812889i	$-0.697894\pi$
$19$	1.79923	−	3.11637i	0.412773	−	0.714943i	0.995192	+	0.0979454i	$0.0312271\pi$
$20$	0.0459804			0.0102815
$21$	0.304155	+	0.526813i	0.0663721	+	0.114960i
$22$	0.772502	+	1.33801i	0.164698	+	0.285265i
$23$	1.79884			0.375085			0.187542	−	0.982256i	$-0.439948\pi$
$23$	1.79884			0.375085			0.187542	+	0.982256i	$0.439948\pi$
$24$	−0.291684			−0.0595398
$25$	2.49294	−	4.31790i	0.498589	−	0.863581i
$26$	−1.04053	+	1.80225i	−0.204065	+	0.353451i
$27$	0.700677			0.134845
$28$	2.01150			0.380137
$29$	2.23005	−	3.86256i	0.414110	−	0.717260i	−0.581224	−	0.813743i	$-0.697426\pi$
$29$	2.23005	−	3.86256i	0.414110	−	0.717260i	0.995335	+	0.0964835i	$0.0307595\pi$
$30$	−0.0107418	+	0.0186054i	−0.00196118	+	0.00339687i
$31$	0.891422	−	1.54399i	0.160104	−	0.277308i	−0.774802	−	0.632204i	$-0.782150\pi$
$31$	0.891422	−	1.54399i	0.160104	−	0.277308i	0.934906	+	0.354896i	$0.115484\pi$
$32$	−1.08023	+	1.87101i	−0.190960	+	0.330752i
$33$	−0.117047			−0.0203752
$34$	7.59550			1.30262
$35$	−0.308714	+	0.534708i	−0.0521821	+	0.0903821i
$36$	0.577905	−	1.00096i	0.0963176	−	0.166827i
$37$	−9.11828			−1.49904			−0.749518	−	0.661984i	$-0.769715\pi$
$37$	−9.11828			−1.49904			−0.749518	+	0.661984i	$0.769715\pi$
$38$	5.55965			0.901894
$39$	−0.0788288	−	0.136535i	−0.0126227	−	0.0218632i
$40$	−0.148028	−	0.256392i	−0.0234053	−	0.0405391i
$41$	−4.41465			−0.689452			−0.344726	−	0.938703i	$-0.612028\pi$
$41$	−4.41465			−0.689452			−0.344726	+	0.938703i	$0.612028\pi$
$42$	−0.469921	+	0.813927i	−0.0725104	+	0.125592i
$43$	0.633751	+	1.09769i	0.0966462	+	0.167396i	0.910294	−	0.413961i	$-0.135855\pi$
$43$	0.633751	+	1.09769i	0.0966462	+	0.167396i	−0.813648	+	0.581357i	$0.802522\pi$
$44$	−0.193519	+	0.335184i	−0.0291741	+	0.0505310i
$45$	0.177388	+	0.307244i	0.0264434	+	0.0458013i
$46$	1.38961	+	2.40688i	0.204887	+	0.354875i
$47$	−0.290909	+	0.503869i	−0.0424334	+	0.0734969i	−0.886462	−	0.462801i	$-0.846844\pi$
$47$	−0.290909	+	0.503869i	−0.0424334	+	0.0734969i	0.844029	+	0.536298i	$0.180178\pi$
$48$	−0.270628	−	0.468742i	−0.0390618	−	0.0676571i
$49$	−10.0052	+	17.3296i	−1.42932	+	2.47565i
$50$	7.70321			1.08940
$51$	−0.287711	+	0.498330i	−0.0402876	+	0.0697802i
$52$	−0.521325			−0.0722948
$53$	4.04406			0.555495			0.277747	−	0.960654i	$-0.410412\pi$
$53$	4.04406			0.555495			0.277747	+	0.960654i	$0.410412\pi$
$54$	0.541275	+	0.937515i	0.0736581	+	0.127580i
$55$	−0.0594005	−	0.102885i	−0.00800956	−	0.0138730i
$56$	−6.47575	−	11.2163i	−0.865358	−	1.49884i
$57$	−0.210595	+	0.364761i	−0.0278939	+	0.0483137i
$58$	6.89088			0.904816
$59$	4.34699	+	7.52921i	0.565930	+	0.980220i	0.996962	+	0.0778833i	$0.0248162\pi$
$59$	4.34699	+	7.52921i	0.565930	+	0.980220i	−0.431032	+	0.902337i	$0.641851\pi$
$60$	−0.00538186			−0.000694795
$61$	−3.32924	+	7.06514i	−0.426265	+	0.904598i
$61$	−3.32924	+	7.06514i	−0.426265	+	0.904598i
$62$	2.75450			0.349822
$63$	7.76014	+	13.4410i	0.977685	+	1.69340i
$64$	5.91063			0.738829
$65$	0.0800102	−	0.138582i	0.00992404	−	0.0171889i
$66$	−0.0904189	−	0.156610i	−0.0111298	−	0.0192774i
$67$	−3.25140	−	5.63158i	−0.397221	−	0.688007i	0.596161	−	0.802865i	$-0.296692\pi$
$67$	−3.25140	−	5.63158i	−0.397221	−	0.688007i	−0.993382	+	0.114858i	$0.963359\pi$
$68$	0.951372	+	1.64782i	0.115371	+	0.199828i
$69$	−0.210549			−0.0253471
$70$	−0.953928			−0.114016
$71$	0.125281	−	0.216993i	0.0148681	−	0.0257524i	−0.858496	−	0.512821i	$-0.828600\pi$
$71$	0.125281	−	0.216993i	0.0148681	−	0.0257524i	0.873364	+	0.487069i	$0.161934\pi$
$72$	−7.44196			−0.877043
$73$	−1.38342	+	2.39616i	−0.161918	+	0.280449i	−0.935556	−	0.353177i	$-0.885101\pi$
$73$	−1.38342	+	2.39616i	−0.161918	+	0.280449i	0.773639	+	0.633627i	$0.218435\pi$
$74$	−7.04389	−	12.2004i	−0.818835	−	1.41826i
$75$	−0.291791	+	0.505397i	−0.0336931	+	0.0583582i
$76$	0.696371	+	1.20615i	0.0798793	+	0.138355i
$77$	−2.59858	−	4.50087i	−0.296136	−	0.512922i
$78$	0.121791	−	0.210948i	0.0137901	−	0.0238851i
$79$	5.41276	+	9.37517i	0.608983	+	1.05479i	0.991408	+	0.130803i	$0.0417554\pi$
$79$	5.41276	+	9.37517i	0.608983	+	1.05479i	−0.382426	+	0.923986i	$0.624911\pi$
$80$	0.274684	−	0.475767i	0.0307106	−	0.0531924i
$81$	8.87689			0.986321
$82$	−3.41032	−	5.90685i	−0.376607	−	0.652303i
$83$	−0.937378	−	1.62359i	−0.102891	−	0.178212i	0.809984	−	0.586452i	$-0.199476\pi$
$83$	−0.937378	−	1.62359i	−0.102891	−	0.178212i	−0.912874	+	0.408240i	$0.866142\pi$
$84$	−0.235439			−0.0256885
$85$	−0.584046			−0.0633486
$86$	−0.979149	+	1.69594i	−0.105584	+	0.182877i
$87$	−0.261020	+	0.452100i	−0.0279843	+	0.0484703i
$88$	2.49203			0.265652
$89$	−9.27441			−0.983085			−0.491543	−	0.870854i	$-0.663567\pi$
$89$	−9.27441			−0.983085			−0.491543	+	0.870854i	$0.663567\pi$
$90$	−0.274065	+	0.474694i	−0.0288889	+	0.0500371i
$91$	3.50019	−	6.06250i	0.366919	−	0.635523i
$92$	−0.348110	+	0.602945i	−0.0362930	+	0.0628613i
$93$	−0.104338	+	0.180719i	−0.0108193	+	0.0187397i
$94$	−0.898911			−0.0927156
$95$	−0.427501			−0.0438607
$96$	0.126437	−	0.218996i	0.0129045	−	0.0223512i
$97$	−5.71114	+	9.89199i	−0.579879	+	1.00438i	0.415614	+	0.909541i	$0.363567\pi$
$97$	−5.71114	+	9.89199i	−0.579879	+	1.00438i	−0.995493	+	0.0948384i	$0.969767\pi$
$98$	−30.9162			−3.12301
$99$	−2.98630			−0.300134
$100$	0.964863	+	1.67119i	0.0964863	+	0.167119i
$101$	−3.86330	−	6.69142i	−0.384412	−	0.665822i	0.607275	−	0.794492i	$-0.292263\pi$
$101$	−3.86330	−	6.69142i	−0.384412	−	0.665822i	−0.991687	+	0.128670i	$0.958929\pi$
$102$	−0.889029			−0.0880270
$103$	3.25143	−	5.63164i	0.320373	−	0.554902i	−0.660192	−	0.751097i	$-0.729525\pi$
$103$	3.25143	−	5.63164i	0.320373	−	0.554902i	0.980565	+	0.196195i	$0.0628585\pi$
$104$	1.67834	+	2.90697i	0.164575	+	0.285051i
$105$	0.0361339	−	0.0625858i	0.00352631	−	0.00610775i
$106$	3.12405	+	5.41101i	0.303434	+	0.525564i
$107$	−5.44575	−	9.43232i	−0.526461	−	0.911857i	−0.999525	−	0.0308289i	$-0.990185\pi$
$107$	−5.44575	−	9.43232i	−0.526461	−	0.911857i	0.473064	−	0.881028i	$-0.343148\pi$
$108$	−0.135594	+	0.234856i	−0.0130476	+	0.0225990i
$109$	9.57471	+	16.5839i	0.917091	+	1.58845i	0.803810	+	0.594886i	$0.202803\pi$
$109$	9.57471	+	16.5839i	0.917091	+	1.58845i	0.113281	+	0.993563i	$0.463864\pi$
$110$	0.0917739	−	0.158957i	0.00875030	−	0.0151560i
$111$	1.06727			0.101300
$112$	12.0166	−	20.8133i	1.13546	−	1.96667i
$113$	10.9606			1.03109			0.515545	−	0.856862i	$-0.327589\pi$
$113$	10.9606			1.03109			0.515545	+	0.856862i	$0.327589\pi$
$114$	−0.650739			−0.0609473
$115$	−0.106852	−	0.185073i	−0.00996402	−	0.0172582i
$116$	0.863114	+	1.49496i	0.0801381	+	0.138803i
$117$	−2.01122	−	3.48353i	−0.185937	−	0.322052i
$118$	−6.71612	+	11.6327i	−0.618269	+	1.07087i
$119$	−25.5501			−2.34218
$120$	0.0173262	+	0.0300098i	0.00158166	+	0.00273951i
$121$	1.00000			0.0909091
$122$	−12.0251	+	1.00327i	−1.08870	+	0.0908322i
$123$	0.516720			0.0465911
$124$	0.345014	+	0.597581i	0.0309832	+	0.0536644i
$125$	−1.18633			−0.106109
$126$	−11.9894	+	20.7663i	−1.06810	+	1.85001i
$127$	8.59558	+	14.8880i	0.762734	+	1.32109i	0.941436	+	0.337191i	$0.109477\pi$
$127$	8.59558	+	14.8880i	0.762734	+	1.32109i	−0.178702	+	0.983903i	$0.557190\pi$
$128$	6.72644	+	11.6505i	0.594539	+	1.02977i
$129$	−0.0741786	−	0.128481i	−0.00653106	−	0.0113121i
$130$	0.247232			0.0216837
$131$	20.8155			1.81866			0.909328	−	0.416080i	$-0.136596\pi$
$131$	20.8155			1.81866			0.909328	+	0.416080i	$0.136596\pi$
$132$	0.0226508	−	0.0392323i	0.00197150	−	0.00341473i
$133$	−18.7018			−1.62165
$134$	5.02342	−	8.70082i	0.433957	−	0.751636i
$135$	−0.0416205	−	0.0720889i	−0.00358213	−	0.00620442i
$136$	6.12563	−	10.6099i	0.525268	−	0.909792i
$137$	3.00149	+	5.19873i	0.256434	+	0.444158i	0.965284	−	0.261202i	$-0.0841189\pi$
$137$	3.00149	+	5.19873i	0.256434	+	0.444158i	−0.708850	+	0.705360i	$0.750786\pi$
$138$	−0.162649	−	0.281717i	−0.0138456	−	0.0239814i
$139$	6.88986	−	11.9336i	0.584390	−	1.01219i	−0.410561	−	0.911833i	$-0.634667\pi$
$139$	6.88986	−	11.9336i	0.584390	−	1.01219i	0.994951	−	0.100360i	$-0.0319995\pi$
$140$	−0.119484	−	0.206952i	−0.0100982	−	0.0174906i
$141$	0.0340500	−	0.0589763i	0.00286752	−	0.00496670i
$142$	0.387120			0.0324864
$143$	0.673481	+	1.16650i	0.0563193	+	0.0975479i
$144$	−6.90474	−	11.9594i	−0.575395	−	0.996613i
$145$	−0.529864			−0.0440028
$146$	−4.27479			−0.353784
$147$	1.17108	−	2.02837i	0.0965890	−	0.167297i
$148$	1.76456	−	3.05631i	0.145046	−	0.251227i
$149$	−18.1624			−1.48792			−0.743962	−	0.668221i	$-0.767056\pi$
$149$	−18.1624			−1.48792			−0.743962	+	0.668221i	$0.767056\pi$
$150$	−0.901636			−0.0736183
$151$	0.900039	−	1.55891i	0.0732441	−	0.126863i	−0.827077	−	0.562088i	$-0.809998\pi$
$151$	0.900039	−	1.55891i	0.0732441	−	0.126863i	0.900321	+	0.435226i	$0.143331\pi$
$152$	4.48375	−	7.76609i	0.363680	−	0.629913i
$153$	−7.34058	+	12.7143i	−0.593451	+	1.02789i
$154$	4.01482	−	6.95387i	0.323523	−	0.560358i
$155$	−0.211803			−0.0170125
$156$	0.0610194			0.00488546
$157$	1.49787	−	2.59439i	0.119543	−	0.207055i	−0.800044	−	0.599942i	$-0.795190\pi$
$157$	1.49787	−	2.59439i	0.119543	−	0.207055i	0.919587	+	0.392887i	$0.128524\pi$
$158$	−8.36273	+	14.4847i	−0.665303	+	1.15234i
$159$	−0.473345			−0.0375387
$160$	0.256665			0.0202911
$161$	−4.67444	−	8.09637i	−0.368397	−	0.638083i
$162$	6.85741	+	11.8774i	0.538769	+	0.933176i
$163$	10.0460			0.786865			0.393432	−	0.919354i	$-0.371288\pi$
$163$	10.0460			0.786865			0.393432	+	0.919354i	$0.371288\pi$
$164$	0.854317	−	1.47972i	0.0667110	−	0.115547i
$165$	0.00695263	+	0.0120423i	0.000541262	+	0.000937493i
$166$	1.44825	−	2.50845i	0.112406	−	0.194693i
$167$	9.13078	+	15.8150i	0.706561	+	1.22380i	0.966125	+	0.258073i	$0.0830876\pi$
$167$	9.13078	+	15.8150i	0.706561	+	1.22380i	−0.259565	+	0.965726i	$0.583579\pi$
$168$	0.757965	+	1.31283i	0.0584783	+	0.101287i
$169$	5.59285	−	9.68709i	0.430219	−	0.745161i
$170$	−0.451176	−	0.781460i	−0.0346036	−	0.0599353i
$171$	−5.37305	+	9.30640i	−0.410888	+	0.711678i
$172$	−0.490571			−0.0374057
$173$	−2.78094	+	4.81674i	−0.211431	+	0.366210i	−0.952163	−	0.305592i	$-0.901146\pi$
$173$	−2.78094	+	4.81674i	−0.211431	+	0.366210i	0.740731	+	0.671801i	$0.234479\pi$
$174$	−0.806555			−0.0611448
$175$	−25.9124			−1.95880
$176$	2.31214	+	4.00474i	0.174284	+	0.301869i
$177$	−0.508801	−	0.881270i	−0.0382439	−	0.0662403i
$178$	−7.16450	−	12.4093i	−0.537002	−	0.930115i
$179$	−6.16547	+	10.6789i	−0.460829	+	0.798179i	−0.999002	−	0.0446551i	$-0.985781\pi$
$179$	−6.16547	+	10.6789i	−0.460829	+	0.798179i	0.538174	+	0.842834i	$0.319114\pi$
$180$	−0.137311			−0.0102346
$181$	−11.2536	−	19.4919i	−0.836477	−	1.44882i	−0.892822	−	0.450410i	$-0.851278\pi$
$181$	−11.2536	−	19.4919i	−0.836477	−	1.44882i	0.0563450	−	0.998411i	$-0.482055\pi$
$182$	10.8156			0.801706
$183$	0.389676	−	0.826952i	0.0288057	−	0.0611300i
$184$	4.48278			0.330475
$185$	0.541630	+	0.938130i	0.0398214	+	0.0689727i
$186$	−0.322405			−0.0236399
$187$	2.45809	−	4.25753i	0.179753	−	0.311341i
$188$	−0.112593	−	0.195016i	−0.00821167	−	0.0142230i
$189$	−1.82077	−	3.15366i	−0.132441	−	0.229395i
$190$	−0.330246	−	0.572002i	−0.0239585	−	0.0414974i
$191$	0.0785234			0.00568176			0.00284088	−	0.999996i	$-0.499096\pi$
$191$	0.0785234			0.00568176			0.00284088	+	0.999996i	$0.499096\pi$
$192$	−0.691821			−0.0499279
$193$	4.87121	−	8.43719i	0.350638	−	0.607322i	−0.635724	−	0.771917i	$-0.719298\pi$
$193$	4.87121	−	8.43719i	0.350638	−	0.607322i	0.986361	+	0.164595i	$0.0526316\pi$
$194$	−17.6475			−1.26702
$195$	−0.00936493	+	0.0162205i	−0.000670637	+	0.00116158i
$196$	−3.87240	−	6.70720i	−0.276600	−	0.479085i
$197$	11.6809	−	20.2318i	0.832226	−	1.44146i	−0.0640428	−	0.997947i	$-0.520399\pi$
$197$	11.6809	−	20.2318i	0.832226	−	1.44146i	0.896269	−	0.443511i	$-0.146267\pi$
$198$	−2.30692	−	3.99571i	−0.163946	−	0.283963i
$199$	5.36164	+	9.28664i	0.380077	+	0.658312i	0.991073	−	0.133321i	$-0.0425642\pi$
$199$	5.36164	+	9.28664i	0.380077	+	0.658312i	−0.610996	+	0.791634i	$0.709231\pi$
$200$	6.21250	−	10.7604i	0.439290	−	0.760872i
$201$	0.380565	+	0.659159i	0.0268430	+	0.0464935i
$202$	5.96881	−	10.3383i	0.419964	−	0.727399i
$203$	−23.1799			−1.62691
$204$	−0.111355	−	0.192872i	−0.00779641	−	0.0135038i
$205$	0.262232	+	0.454199i	0.0183151	+	0.0317226i
$206$	10.0469			0.700004
$207$	−5.37189			−0.373372
$208$	−3.11436	+	5.39424i	−0.215942	+	0.374023i
$209$	1.79923	−	3.11637i	0.124456	−	0.215563i
$210$	0.111654			0.00770487
$211$	2.52513			0.173837			0.0869187	−	0.996215i	$-0.472298\pi$
$211$	2.52513			0.173837			0.0869187	+	0.996215i	$0.472298\pi$
$212$	−0.782603	+	1.35551i	−0.0537494	+	0.0930966i
$213$	−0.0146638	+	0.0253984i	−0.00100474	+	0.00174027i
$214$	8.41371	−	14.5730i	0.575150	−	0.996188i
$215$	0.0752902	−	0.130407i	0.00513475	−	0.00889365i
$216$	1.74611			0.118808
$217$	−9.26572			−0.628998
$218$	−14.7930	+	25.6222i	−1.00191	+	1.73535i
$219$	0.161925	−	0.280463i	0.0109419	−	0.0189519i
$220$	0.0459804			0.00310000
$221$	6.62190			0.445437
$222$	0.824464	+	1.42801i	0.0553344	+	0.0958420i
$223$	−5.65540	−	9.79544i	−0.378714	−	0.655951i	0.612162	−	0.790733i	$-0.290300\pi$
$223$	−5.65540	−	9.79544i	−0.378714	−	0.655951i	−0.990875	+	0.134781i	$0.956967\pi$
$224$	11.2283			0.750219
$225$	−7.44468	+	12.8946i	−0.496312	+	0.859637i
$226$	8.46712	+	14.6655i	0.563224	+	0.975533i
$227$	9.62160	−	16.6651i	0.638608	−	1.10610i	−0.347130	−	0.937817i	$-0.612844\pi$
$227$	9.62160	−	16.6651i	0.638608	−	1.10610i	0.985738	−	0.168285i	$-0.0538228\pi$
$228$	−0.0815080	−	0.141176i	−0.00539800	−	0.00934961i
$229$	−9.19978	−	15.9345i	−0.607939	−	1.05298i	−0.991580	−	0.129498i	$-0.958663\pi$
$229$	−9.19978	−	15.9345i	−0.607939	−	1.05298i	0.383641	−	0.923482i	$-0.374670\pi$
$230$	0.165087	−	0.285939i	0.0108855	−	0.0188543i
$231$	0.304155	+	0.526813i	0.0200120	+	0.0346617i
$232$	5.55736	−	9.62563i	0.364859	−	0.631954i
$233$	19.3113			1.26513			0.632564	−	0.774508i	$-0.282003\pi$
$233$	19.3113			1.26513			0.632564	+	0.774508i	$0.282003\pi$
$234$	3.10734	−	5.38207i	0.203133	−	0.351837i
$235$	0.0691205			0.00450892
$236$	−3.36490			−0.219036
$237$	−0.633546	−	1.09733i	−0.0411532	−	0.0712795i
$238$	−19.7375	−	34.1864i	−1.27939	−	2.21597i
$239$	12.5933	+	21.8122i	0.814592	+	1.41092i	0.909620	+	0.415441i	$0.136373\pi$
$239$	12.5933	+	21.8122i	0.814592	+	1.41092i	−0.0950279	+	0.995475i	$0.530294\pi$
$240$	−0.0321509	+	0.0556870i	−0.00207533	+	0.00359458i
$241$	4.96197			0.319629			0.159814	−	0.987147i	$-0.448910\pi$
$241$	4.96197			0.319629			0.159814	+	0.987147i	$0.448910\pi$
$242$	0.772502	+	1.33801i	0.0496583	+	0.0860107i
$243$	−3.14104			−0.201498
$244$	−1.72386	−	2.48315i	−0.110359	−	0.158967i
$245$	2.37726			0.151878
$246$	0.399167	+	0.691378i	0.0254500	+	0.0440807i
$247$	4.84700			0.308407
$248$	2.22145	−	3.84767i	0.141062	−	0.244327i
$249$	0.109717	+	0.190036i	0.00695304	+	0.0120430i
$250$	−0.916444	−	1.58733i	−0.0579610	−	0.100391i
$251$	0.391298	+	0.677749i	0.0246985	+	0.0427791i	0.878110	−	0.478458i	$-0.158804\pi$
$251$	0.391298	+	0.677749i	0.0246985	+	0.0427791i	−0.853412	+	0.521237i	$0.825471\pi$
$252$	−6.00693			−0.378401
$253$	1.79884			0.113092
$254$	−13.2802	+	23.0020i	−0.833274	+	1.44327i
$255$	0.0683606			0.00428091
$256$	−4.48174	+	7.76260i	−0.280109	+	0.485163i
$257$	−8.37164	−	14.5001i	−0.522208	−	0.904491i	−0.999666	−	0.0258367i	$-0.991775\pi$
$257$	−8.37164	−	14.5001i	−0.522208	−	0.904491i	0.477458	−	0.878655i	$-0.341558\pi$
$258$	0.114606	−	0.198504i	0.00713507	−	0.0123583i
$259$	23.6946	+	41.0402i	1.47231	+	2.55011i
$260$	0.0309670	+	0.0536363i	0.00192049	+	0.00332638i
$261$	−6.65960	+	11.5348i	−0.412219	+	0.713984i
$262$	16.0800	+	27.8514i	0.993425	+	1.72066i
$263$	−12.2333	+	21.1888i	−0.754340	+	1.30655i	0.191363	+	0.981519i	$0.438709\pi$
$263$	−12.2333	+	21.1888i	−0.754340	+	1.30655i	−0.945702	+	0.325035i	$0.894624\pi$
$264$	−0.291684			−0.0179519
$265$	−0.240219	−	0.416072i	−0.0147566	−	0.0255591i
$266$	−14.4472	−	25.0233i	−0.885814	−	1.53427i
$267$	1.08554			0.0664339
$268$	2.51683			0.153740
$269$	7.01016	−	12.1420i	0.427417	−	0.740308i	−0.569225	−	0.822181i	$-0.692757\pi$
$269$	7.01016	−	12.1420i	0.427417	−	0.740308i	0.996643	+	0.0818730i	$0.0260902\pi$
$270$	0.0643039	−	0.111378i	0.00391341	−	0.00677823i
$271$	19.7831			1.20174			0.600870	−	0.799347i	$-0.294821\pi$
$271$	19.7831			1.20174			0.600870	+	0.799347i	$0.294821\pi$
$272$	22.7337			1.37844
$273$	−0.409686	+	0.709597i	−0.0247953	+	0.0429467i
$274$	−4.63731	+	8.03206i	−0.280150	+	0.485235i
$275$	2.49294	−	4.31790i	0.150330	−	0.260379i
$276$	0.0407452	−	0.0705727i	0.00245257	−	0.00424798i
$277$	20.6333			1.23973			0.619867	−	0.784707i	$-0.287187\pi$
$277$	20.6333			1.23973			0.619867	+	0.784707i	$0.287187\pi$
$278$	21.2897			1.27687
$279$	−2.66205	+	4.61081i	−0.159373	+	0.276042i
$280$	−0.769325	+	1.33251i	−0.0459759	+	0.0796327i
$281$	−22.4858			−1.34139			−0.670695	−	0.741733i	$-0.734004\pi$
$281$	−22.4858			−1.34139			−0.670695	+	0.741733i	$0.734004\pi$
$282$	0.105215			0.00626544
$283$	4.13473	+	7.16156i	0.245784	+	0.425710i	0.962352	−	0.271807i	$-0.0876213\pi$
$283$	4.13473	+	7.16156i	0.245784	+	0.425710i	−0.716568	+	0.697518i	$0.754288\pi$
$284$	0.0484885	+	0.0839846i	0.00287726	+	0.00498357i
$285$	0.0500377			0.00296397
$286$	−1.04053	+	1.80225i	−0.0615279	+	0.106569i
$287$	11.4718	+	19.8698i	0.677159	+	1.17287i
$288$	3.22589	−	5.58741i	0.190087	−	0.329241i
$289$	−3.58437	−	6.20830i	−0.210845	−	0.365194i
$290$	−0.409321	−	0.708965i	−0.0240362	−	0.0416319i
$291$	0.668471	−	1.15783i	0.0391865	−	0.0678729i
$292$	−0.535437	−	0.927404i	−0.0313341	−	0.0542722i
$293$	−11.1731	+	19.3523i	−0.652737	+	1.13057i	0.329719	+	0.944079i	$0.393046\pi$
$293$	−11.1731	+	19.3523i	−0.652737	+	1.13057i	−0.982456	+	0.186495i	$0.940287\pi$
$294$	3.61865			0.211044
$295$	0.516427	−	0.894477i	0.0300675	−	0.0520785i
$296$	−22.7231			−1.32075
$297$	0.700677			0.0406574
$298$	−14.0305	−	24.3016i	−0.812766	−	1.40775i
$299$	1.21149	+	2.09836i	0.0700621	+	0.121351i
$300$	−0.112934	−	0.195608i	−0.00652025	−	0.0112934i
$301$	3.29371	−	5.70487i	0.189846	−	0.328823i
$302$	2.78113			0.160036
$303$	0.452186	+	0.783210i	0.0259774	+	0.0449942i
$304$	16.6403			0.954388
$305$	0.924652	−	0.0771454i	0.0529454	−	0.00441733i
$306$	−22.6825			−1.29667
$307$	9.88175	+	17.1157i	0.563981	+	0.976844i	0.997144	+	0.0755283i	$0.0240643\pi$
$307$	9.88175	+	17.1157i	0.563981	+	0.976844i	−0.433162	+	0.901316i	$0.642602\pi$
$308$	2.01150			0.114616
$309$	−0.380569	+	0.659165i	−0.0216498	+	0.0374986i
$310$	−0.163619	−	0.283396i	−0.00929291	−	0.0160958i
$311$	−6.57750	−	11.3926i	−0.372976	−	0.646013i	0.617046	−	0.786927i	$-0.288329\pi$
$311$	−6.57750	−	11.3926i	−0.372976	−	0.646013i	−0.990022	+	0.140914i	$0.954996\pi$
$312$	−0.196444	−	0.340251i	−0.0111215	−	0.0192629i
$313$	12.6580			0.715475			0.357738	−	0.933822i	$-0.383548\pi$
$313$	12.6580			0.715475			0.357738	+	0.933822i	$0.383548\pi$
$314$	4.62843			0.261198
$315$	0.921911	−	1.59680i	0.0519438	−	0.0899693i
$316$	−4.18988			−0.235699
$317$	−3.33025	+	5.76816i	−0.187046	+	0.323972i	−0.944264	−	0.329189i	$-0.893225\pi$
$317$	−3.33025	+	5.76816i	−0.187046	+	0.323972i	0.757218	+	0.653162i	$0.226558\pi$
$318$	−0.365660	−	0.633341i	−0.0205052	−	0.0355160i
$319$	2.23005	−	3.86256i	0.124859	−	0.216262i
$320$	−0.351094	−	0.608113i	−0.0196268	−	0.0339946i
$321$	0.637408	+	1.10402i	0.0355766	+	0.0616206i
$322$	7.22203	−	12.5089i	0.402468	−	0.697095i
$323$	−8.84534	−	15.3206i	−0.492168	−	0.852460i
$324$	−1.71785	+	2.97539i	−0.0954358	+	0.165300i
$325$	6.71580			0.372526
$326$	7.76057	+	13.4417i	0.429818	+	0.744467i
$327$	−1.12069	−	1.94109i	−0.0619743	−	0.107343i
$328$	−11.0014			−0.607453
$329$	3.02380			0.166708
$330$	−0.0107418	+	0.0186054i	−0.000591319	+	0.00102419i
$331$	−6.22887	+	10.7887i	−0.342369	+	0.593001i	−0.984872	−	0.173282i	$-0.944563\pi$
$331$	−6.22887	+	10.7887i	−0.342369	+	0.593001i	0.642503	+	0.766283i	$0.277896\pi$
$332$	0.725601			0.0398225
$333$	27.2299			1.49219
$334$	−14.1071	+	24.4342i	−0.771905	+	1.33698i
$335$	−0.386269	+	0.669037i	−0.0211041	+	0.0365534i
$336$	−1.40650	+	2.43613i	−0.0767308	+	0.132902i
$337$	−0.290041	+	0.502366i	−0.0157996	+	0.0273656i	−0.873817	−	0.486255i	$-0.838363\pi$
$337$	−0.290041	+	0.502366i	−0.0157996	+	0.0273656i	0.858018	+	0.513620i	$0.171696\pi$
$338$	17.2819			0.940014
$339$	−1.28291			−0.0696780
$340$	0.113024	−	0.195763i	0.00612958	−	0.0106167i
$341$	0.891422	−	1.54399i	0.0482732	−	0.0836116i
$342$	−16.6028			−0.897776
$343$	67.6174			3.65100
$344$	1.57933	+	2.73548i	0.0851518	+	0.147487i
$345$	0.0125067	+	0.0216622i	0.000673338	+	0.00116626i
$346$	−8.59314			−0.461970
$347$	8.61765	−	14.9262i	0.462620	−	0.801281i	−0.536471	−	0.843919i	$-0.680243\pi$
$347$	8.61765	−	14.9262i	0.462620	−	0.801281i	0.999091	+	0.0426378i	$0.0135761\pi$
$348$	−0.101025	−	0.174980i	−0.00541549	−	0.00937991i
$349$	−16.7180	+	28.9565i	−0.894896	+	1.55001i	−0.0609632	+	0.998140i	$0.519417\pi$
$349$	−16.7180	+	28.9565i	−0.894896	+	1.55001i	−0.833933	+	0.551866i	$0.813916\pi$
$350$	−20.0174	−	34.6712i	−1.06998	−	1.85325i
$351$	0.471893	+	0.817342i	0.0251878	+	0.0436265i
$352$	−1.08023	+	1.87101i	−0.0575765	+	0.0997254i
$353$	−3.75003	−	6.49524i	−0.199594	−	0.345707i	0.748803	−	0.662793i	$-0.230629\pi$
$353$	−3.75003	−	6.49524i	−0.199594	−	0.345707i	−0.948397	+	0.317086i	$0.897296\pi$
$354$	0.786100	−	1.36157i	0.0417808	−	0.0723664i
$355$	−0.0297670			−0.00157987
$356$	1.79477	−	3.10864i	0.0951228	−	0.164757i
$357$	2.99056			0.158277
$358$	−19.0514			−1.00690
$359$	5.44377	+	9.42889i	0.287311	+	0.497638i	0.973167	−	0.230100i	$-0.0739052\pi$
$359$	5.44377	+	9.42889i	0.287311	+	0.497638i	−0.685856	+	0.727738i	$0.740572\pi$
$360$	0.442056	+	0.765663i	0.0232984	+	0.0403540i
$361$	3.02551	+	5.24034i	0.159237	+	0.275807i
$362$	17.3869	−	30.1151i	0.913837	−	1.58281i
$363$	−0.117047			−0.00614336
$364$	1.35470	+	2.34642i	0.0710058	+	0.122986i
$365$	0.328704			0.0172052
$366$	1.40750	−	0.117430i	0.0735711	−	0.00613817i
$367$	−22.4844			−1.17368			−0.586838	−	0.809705i	$-0.699627\pi$
$367$	−22.4844			−1.17368			−0.586838	+	0.809705i	$0.699627\pi$
$368$	4.15918	+	7.20391i	0.216812	+	0.375530i
$369$	13.1835			0.686303
$370$	−0.836820	+	1.44942i	−0.0435042	+	0.0753515i
$371$	−10.5088	−	18.2018i	−0.545591	−	0.944991i
$372$	−0.0403827	−	0.0699450i	−0.00209375	−	0.00362648i
$373$	11.4877	+	19.8973i	0.594812	+	1.03025i	0.993573	+	0.113190i	$0.0361070\pi$
$373$	11.4877	+	19.8973i	0.594812	+	1.03025i	−0.398761	+	0.917055i	$0.630560\pi$
$374$	7.59550			0.392754
$375$	0.138856			0.00717051
$376$	−0.724955	+	1.25566i	−0.0373867	+	0.0647557i
$377$	6.00759			0.309407
$378$	2.81309	−	4.87241i	0.144690	−	0.250610i
$379$	−0.823600	−	1.42652i	−0.0423055	−	0.0732752i	0.844097	−	0.536190i	$-0.180137\pi$
$379$	−0.823600	−	1.42652i	−0.0423055	−	0.0732752i	−0.886403	+	0.462915i	$0.846804\pi$
$380$	0.0827296	−	0.143292i	0.00424394	−	0.00735071i
$381$	−1.00608	−	1.74259i	−0.0515433	−	0.0892756i
$382$	0.0606595	+	0.105065i	0.00310361	+	0.00537561i
$383$	−4.65879	+	8.06926i	−0.238053	+	0.412320i	−0.960156	−	0.279466i	$-0.909843\pi$
$383$	−4.65879	+	8.06926i	−0.238053	+	0.412320i	0.722103	+	0.691786i	$0.243176\pi$
$384$	−0.787308	−	1.36366i	−0.0401771	−	0.0695888i
$385$	−0.308714	+	0.534708i	−0.0157335	+	0.0272512i
$386$	15.0521			0.766131
$387$	−1.89257	−	3.27803i	−0.0962048	−	0.166632i
$388$	−2.21043	−	3.82857i	−0.112217	−	0.194366i
$389$	4.59160			0.232804			0.116402	−	0.993202i	$-0.462864\pi$
$389$	4.59160			0.232804			0.116402	+	0.993202i	$0.462864\pi$
$390$	−0.0289377			−0.00146532
$391$	4.42171	−	7.65863i	0.223616	−	0.387314i
$392$	−24.9334	+	43.1859i	−1.25933	+	2.18122i
$393$	−2.43638			−0.122899
$394$	36.0939			1.81839
$395$	0.643040	−	1.11378i	0.0323549	−	0.0560403i
$396$	0.577905	−	1.00096i	0.0290408	−	0.0503002i
$397$	6.86974	−	11.8987i	0.344782	−	0.597180i	−0.640532	−	0.767931i	$-0.721286\pi$
$397$	6.86974	−	11.8987i	0.344782	−	0.597180i	0.985314	+	0.170751i	$0.0546195\pi$
$398$	−8.28376	+	14.3479i	−0.415227	+	0.719195i
$399$	2.18899			0.109586
$400$	23.0561			1.15281
$401$	−4.06550	+	7.04166i	−0.203021	+	0.351644i	−0.949501	−	0.313765i	$-0.898409\pi$
$401$	−4.06550	+	7.04166i	−0.203021	+	0.351644i	0.746479	+	0.665409i	$0.231743\pi$
$402$	−0.587975	+	1.01840i	−0.0293255	+	0.0507933i
$403$	2.40142			0.119623
$404$	2.99048			0.148782
$405$	−0.527291	−	0.913295i	−0.0262013	−	0.0453820i
$406$	−17.9065	−	31.0150i	−0.888684	−	1.53925i
$407$	−9.11828			−0.451976
$408$	−0.716985	+	1.24185i	−0.0354961	+	0.0614810i
$409$	−0.951435	−	1.64793i	−0.0470455	−	0.0814851i	0.841544	−	0.540189i	$-0.181647\pi$
$409$	−0.951435	−	1.64793i	−0.0470455	−	0.0814851i	−0.888589	+	0.458704i	$0.848314\pi$
$410$	−0.405149	+	0.701739i	−0.0200089	+	0.0346564i
$411$	−0.351315	−	0.608495i	−0.0173291	−	0.0300148i
$412$	1.25843	+	2.17966i	0.0619982	+	0.107384i
$413$	22.5920	−	39.1305i	1.11168	−	1.92549i
$414$	−4.14980	−	7.18766i	−0.203951	−	0.353254i
$415$	−0.111361	+	0.192883i	−0.00546651	+	0.00946828i
$416$	−2.91006			−0.142677
$417$	−0.806435	+	1.39679i	−0.0394913	+	0.0684010i
$418$	5.55965			0.271931
$419$	−18.3369			−0.895818			−0.447909	−	0.894079i	$-0.647831\pi$
$419$	−18.3369			−0.895818			−0.447909	+	0.894079i	$0.647831\pi$
$420$	0.0139852	+	0.0242231i	0.000682408	+	0.00118196i
$421$	−6.07646	−	10.5247i	−0.296148	−	0.512944i	0.679103	−	0.734043i	$-0.262369\pi$
$421$	−6.07646	−	10.5247i	−0.296148	−	0.512944i	−0.975251	+	0.221099i	$0.929036\pi$
$422$	1.95067	+	3.37866i	0.0949572	+	0.164471i
$423$	0.868742	−	1.50470i	0.0422397	−	0.0731612i
$424$	10.0779			0.489428
$425$	−12.2557	−	21.2276i	−0.594490	−	1.02969i
$426$	−0.0453111			−0.00219533
$427$	40.4506	−	3.37486i	1.95754	−	0.163321i
$428$	4.21542			0.203760
$429$	−0.0788288	−	0.136535i	−0.00380589	−	0.00659200i
$430$	0.232647			0.0112193
$431$	0.0168578	−	0.0291985i	0.000812010	−	0.00140644i	−0.865619	−	0.500703i	$-0.833075\pi$
$431$	0.0168578	−	0.0291985i	0.000812010	−	0.00140644i	0.866431	+	0.499297i	$0.166408\pi$
$432$	1.62006	+	2.80603i	0.0779453	+	0.135005i
$433$	−9.34644	−	16.1885i	−0.449161	−	0.777970i	0.549170	−	0.835710i	$-0.314944\pi$
$433$	−9.34644	−	16.1885i	−0.449161	−	0.777970i	−0.998332	+	0.0577403i	$0.981610\pi$
$434$	−7.15779	−	12.3977i	−0.343585	−	0.595106i
$435$	0.0620189			0.00297358
$436$	−7.41155			−0.354949
$437$	3.23654	−	5.60586i	0.154825	−	0.268164i
$438$	0.500350			0.0239077
$439$	−16.9212	+	29.3084i	−0.807606	+	1.39882i	0.106911	+	0.994269i	$0.465904\pi$
$439$	−16.9212	+	29.3084i	−0.807606	+	1.39882i	−0.914517	+	0.404547i	$0.867429\pi$
$440$	−0.148028	−	0.256392i	−0.00705695	−	0.0122230i
$441$	29.8786	−	51.7513i	1.42279	−	2.46435i
$442$	5.11543	+	8.86018i	0.243316	+	0.421436i
$443$	−5.55678	−	9.62463i	−0.264011	−	0.457280i	0.703293	−	0.710900i	$-0.251712\pi$
$443$	−5.55678	−	9.62463i	−0.264011	−	0.457280i	−0.967304	+	0.253620i	$0.918379\pi$
$444$	−0.206536	+	0.357731i	−0.00980176	+	0.0169771i
$445$	0.550904	+	0.954194i	0.0261154	+	0.0452331i
$446$	8.73762	−	15.1340i	0.413738	−	0.716616i
$447$	2.12585			0.100549
$448$	−15.3593	−	26.6030i	−0.725656	−	1.25687i
$449$	1.74128	+	3.01598i	0.0821760	+	0.142333i	0.904184	−	0.427142i	$-0.140480\pi$
$449$	1.74128	+	3.01598i	0.0821760	+	0.142333i	−0.822008	+	0.569475i	$0.807146\pi$
$450$	−23.0041			−1.08442
$451$	−4.41465			−0.207878
$452$	−2.12109	+	3.67384i	−0.0997677	+	0.172803i
$453$	−0.105347	+	0.182466i	−0.00494962	+	0.00857299i
$454$	29.7308			1.39534
$455$	−0.831651			−0.0389884
$456$	−0.524809	+	0.908995i	−0.0245764	+	0.0425676i
$457$	−2.97849	+	5.15890i	−0.139328	+	0.241323i	−0.927242	−	0.374461i	$-0.877828\pi$
$457$	−2.97849	+	5.15890i	−0.139328	+	0.241323i	0.787914	+	0.615785i	$0.211161\pi$
$458$	14.2137	−	24.6189i	0.664163	−	1.15036i
$459$	1.72232	−	2.98315i	0.0803912	−	0.139242i
$460$	0.0827116			0.00385645
$461$	−24.5704			−1.14436			−0.572179	−	0.820129i	$-0.693902\pi$
$461$	−24.5704			−1.14436			−0.572179	+	0.820129i	$0.693902\pi$
$462$	−0.469921	+	0.813927i	−0.0218627	+	0.0378673i
$463$	−20.5287	+	35.5568i	−0.954050	+	1.65246i	−0.217523	+	0.976055i	$0.569798\pi$
$463$	−20.5287	+	35.5568i	−0.954050	+	1.65246i	−0.736527	+	0.676408i	$0.763536\pi$
$464$	20.6248			0.957480
$465$	0.0247909			0.00114965
$466$	14.9180	+	25.8388i	0.691065	+	1.19696i
$467$	2.06291	+	3.57306i	0.0954599	+	0.165341i	0.909800	−	0.415046i	$-0.136234\pi$
$467$	2.06291	+	3.57306i	0.0954599	+	0.165341i	−0.814341	+	0.580387i	$0.802901\pi$
$468$	1.55683			0.0719646
$469$	−16.8980	+	29.2682i	−0.780278	+	1.35148i
$470$	0.0533957	+	0.0924841i	0.00246296	+	0.00426597i
$471$	−0.175321	+	0.303665i	−0.00807836	+	0.0139921i
$472$	10.8328	+	18.7630i	0.498622	+	0.863639i
$473$	0.633751	+	1.09769i	0.0291399	+	0.0504718i
$474$	0.978831	−	1.69538i	0.0449592	−	0.0778716i
$475$	−8.97078	−	15.5378i	−0.411608	−	0.712925i
$476$	4.94443	−	8.56400i	0.226628	−	0.392530i
$477$	−12.0768			−0.552958
$478$	−19.4567	+	33.7000i	−0.889928	+	1.54140i
$479$	−15.7372			−0.719050			−0.359525	−	0.933135i	$-0.617061\pi$
$479$	−15.7372			−0.719050			−0.359525	+	0.933135i	$0.617061\pi$
$480$	−0.0300418			−0.00137121
$481$	−6.14099	−	10.6365i	−0.280005	−	0.484983i
$482$	3.83314	+	6.63919i	0.174595	+	0.302407i
$483$	0.547128	+	0.947654i	0.0248952	+	0.0431197i
$484$	−0.193519	+	0.335184i	−0.00879631	+	0.0152357i
$485$	1.35698			0.0616172
$486$	−2.42646	−	4.20276i	−0.110067	−	0.190641i
$487$	24.2081			1.09697			0.548486	−	0.836159i	$-0.315204\pi$
$487$	24.2081			1.09697			0.548486	+	0.836159i	$0.315204\pi$
$488$	−8.29657	+	17.6066i	−0.375568	+	0.797012i
$489$	−1.17585			−0.0531739
$490$	1.83644	+	3.18081i	0.0829619	+	0.143694i
$491$	23.5119			1.06108			0.530538	−	0.847661i	$-0.321990\pi$
$491$	23.5119			1.06108			0.530538	+	0.847661i	$0.321990\pi$
$492$	−0.0999951	+	0.173197i	−0.00450813	+	0.00780830i
$493$	−10.9633	−	18.9890i	−0.493763	−	0.855222i
$494$	3.74432	+	6.48535i	0.168465	+	0.291790i
$495$	0.177388	+	0.307244i	0.00797298	+	0.0138096i
$496$	8.24436			0.370183
$497$	−1.30221			−0.0584122
$498$	−0.169513	+	0.293606i	−0.00759607	+	0.0131568i
$499$	14.9086			0.667403			0.333701	−	0.942679i	$-0.391702\pi$
$499$	14.9086			0.667403			0.333701	+	0.942679i	$0.391702\pi$
$500$	0.229578	−	0.397640i	0.0102670	−	0.0177830i
$501$	−1.06873	−	1.85109i	−0.0477472	−	0.0827006i
$502$	−0.604558	+	1.04712i	−0.0269827	+	0.0467355i
$503$	−15.1812	−	26.2946i	−0.676897	−	1.17242i	−0.975911	−	0.218171i	$-0.929991\pi$
$503$	−15.1812	−	26.2946i	−0.676897	−	1.17242i	0.299014	−	0.954249i	$-0.403342\pi$
$504$	19.3385	+	33.4953i	0.861406	+	1.49200i
$505$	−0.458963	+	0.794947i	−0.0204236	+	0.0353747i
$506$	1.38961	+	2.40688i	0.0617757	+	0.106999i
$507$	−0.654625	+	1.13384i	−0.0290729	+	0.0503557i
$508$	−6.65362			−0.295207
$509$	14.3389	+	24.8358i	0.635563	+	1.10083i	0.986396	+	0.164389i	$0.0525651\pi$
$509$	14.3389	+	24.8358i	0.635563	+	1.10083i	−0.350833	+	0.936438i	$0.614102\pi$
$510$	0.0528087	+	0.0914674i	0.00233841	+	0.00405025i
$511$	14.3797			0.636123
$512$	13.0571			0.577049
$513$	1.26068	−	2.18357i	0.0556605	−	0.0964068i
$514$	12.9342	−	22.4027i	0.570504	−	0.988141i
$515$	−0.772545			−0.0340424
$516$	0.0574198			0.00252777
$517$	−0.290909	+	0.503869i	−0.0127942	+	0.0221601i
$518$	−36.6082	+	63.4073i	−1.60847	+	2.78596i
$519$	0.325501	−	0.563784i	0.0142879	−	0.0247474i
$520$	0.199388	−	0.345350i	0.00874374	−	0.0151446i
$521$	−34.1774			−1.49734			−0.748668	−	0.662945i	$-0.769306\pi$
$521$	−34.1774			−1.49734			−0.748668	+	0.662945i	$0.769306\pi$
$522$	−20.5782			−0.900684
$523$	7.79750	−	13.5057i	0.340961	−	0.590562i	−0.643651	−	0.765320i	$-0.722581\pi$
$523$	7.79750	−	13.5057i	0.340961	−	0.590562i	0.984611	+	0.174758i	$0.0559143\pi$
$524$	−4.02819	+	6.97702i	−0.175972	+	0.304793i
$525$	3.03297			0.132370
$526$	−37.8011			−1.64821
$527$	−4.38238	−	7.59051i	−0.190900	−	0.330648i
$528$	−0.270628	−	0.468742i	−0.0117776	−	0.0203994i
$529$	−19.7642			−0.859311
$530$	0.371140	−	0.642833i	0.0161213	−	0.0279229i
$531$	−12.9814	−	22.4845i	−0.563346	−	0.975744i
$532$	3.61915	−	6.26856i	0.156910	−	0.271776i
$533$	−2.97318	−	5.14970i	−0.128783	−	0.223058i
$534$	0.838582	+	1.45247i	0.0362890	+	0.0628543i
$535$	−0.646961	+	1.12057i	−0.0279705	+	0.0484464i
$536$	−8.10259	−	14.0341i	−0.349978	−	0.606180i
$537$	0.721648	−	1.24993i	0.0311414	−	0.0539385i
$538$	21.6615			0.933892
$539$	−10.0052	+	17.3296i	−0.430956	+	0.746437i
$540$	0.0322174			0.00138642
$541$	−22.7068			−0.976242			−0.488121	−	0.872776i	$-0.662318\pi$
$541$	−22.7068			−0.976242			−0.488121	+	0.872776i	$0.662318\pi$
$542$	15.2825	+	26.4701i	0.656440	+	1.13699i
$543$	1.31720	+	2.28146i	0.0565266	+	0.0979069i
$544$	5.31060	+	9.19822i	0.227690	+	0.394371i
$545$	1.13748	−	1.97018i	0.0487245	−	0.0843933i
$546$	−1.26593			−0.0541769
$547$	−19.6620	−	34.0556i	−0.840686	−	1.45611i	−0.889316	−	0.457294i	$-0.848819\pi$
$547$	−19.6620	−	34.0556i	−0.840686	−	1.45611i	0.0486297	−	0.998817i	$-0.484515\pi$
$548$	−2.32338			−0.0992498
$549$	9.94210	−	21.0986i	0.424318	−	0.900467i
$550$	7.70321			0.328466
$551$	−8.02477	−	13.8993i	−0.341867	−	0.592130i
$552$	−0.524695			−0.0223325
$553$	28.1310	−	48.7242i	1.19625	−	2.07197i
$554$	15.9393	+	27.6076i	0.677194	+	1.17293i
$555$	−0.0633960	−	0.109805i	−0.00269101	−	0.00466097i
$556$	2.66663	+	4.61875i	0.113090	+	0.195878i
$557$	14.4964			0.614231			0.307115	−	0.951672i	$-0.400636\pi$
$557$	14.4964			0.614231			0.307115	+	0.951672i	$0.400636\pi$
$558$	−8.22576			−0.348224
$559$	−0.853639	+	1.47855i	−0.0361051	+	0.0625359i
$560$	−2.85515			−0.120652
$561$	−0.287711	+	0.498330i	−0.0121472	+	0.0210395i
$562$	−17.3703	−	30.0863i	−0.732723	−	1.26911i
$563$	4.65837	−	8.06853i	0.196327	−	0.340048i	−0.751008	−	0.660293i	$-0.770432\pi$
$563$	4.65837	−	8.06853i	0.196327	−	0.340048i	0.947335	+	0.320245i	$0.103765\pi$
$564$	0.0131786	+	0.0228260i	0.000554920	+	0.000961149i
$565$	−0.651067	−	1.12768i	−0.0273906	−	0.0474419i
$566$	−6.38817	+	11.0646i	−0.268515	+	0.465081i
$567$	−23.0673	−	39.9537i	−0.968736	−	1.67790i
$568$	0.312205	−	0.540755i	0.0130998	−	0.0226896i
$569$	−19.6176			−0.822411			−0.411205	−	0.911543i	$-0.634892\pi$
$569$	−19.6176			−0.822411			−0.411205	+	0.911543i	$0.634892\pi$
$570$	0.0386542	+	0.0669510i	0.00161905	+	0.00280427i
$571$	−18.7485	−	32.4733i	−0.784599	−	1.35897i	−0.929238	−	0.369481i	$-0.879535\pi$
$571$	−18.7485	−	32.4733i	−0.784599	−	1.35897i	0.144639	−	0.989484i	$-0.453798\pi$
$572$	−0.521325			−0.0217977
$573$	−0.00919091			−0.000383956
$574$	−17.7240	+	30.6989i	−0.739785	+	1.28135i
$575$	4.48442	−	7.76724i	0.187013	−	0.323916i
$576$	−17.6509			−0.735455
$577$	7.87627			0.327893			0.163947	−	0.986469i	$-0.447578\pi$
$577$	7.87627			0.327893			0.163947	+	0.986469i	$0.447578\pi$
$578$	5.53786	−	9.59186i	0.230345	−	0.398969i
$579$	−0.570160	+	0.987546i	−0.0236950	+	0.0410410i
$580$	0.102539	−	0.177602i	0.00425769	−	0.00737453i
$581$	−4.87170	+	8.43803i	−0.202112	+	0.350069i
$582$	2.06558			0.0856211
$583$	4.04406			0.167488
$584$	−3.44754	+	5.97131i	−0.142660	+	0.247095i
$585$	−0.238934	+	0.413846i	−0.00987872	+	0.0171104i
$586$	−34.5248			−1.42621
$587$	−12.1376			−0.500971			−0.250485	−	0.968120i	$-0.580590\pi$
$587$	−12.1376			−0.500971			−0.250485	+	0.968120i	$0.580590\pi$
$588$	0.453252	+	0.785056i	0.0186918	+	0.0323751i
$589$	−3.20775	−	5.55599i	−0.132173	−	0.228931i
$590$	1.59576			0.0656965
$591$	−1.36721	+	2.36807i	−0.0562393	+	0.0974094i
$592$	−21.0827	−	36.5163i	−0.866495	−	1.50081i
$593$	23.3880	−	40.5091i	0.960428	−	1.66351i	0.239002	−	0.971019i	$-0.423180\pi$
$593$	23.3880	−	40.5091i	0.960428	−	1.66351i	0.721426	−	0.692491i	$-0.243487\pi$
$594$	0.541275	+	0.937515i	0.0222088	+	0.0384667i
$595$	1.51769	+	2.62871i	0.0622192	+	0.107767i
$596$	3.51477	−	6.08777i	0.143971	−	0.249365i
$597$	−0.627563	−	1.08697i	−0.0256845	−	0.0444868i
$598$	−1.87175	+	3.24197i	−0.0765417	+	0.132574i
$599$	−1.84267			−0.0752893			−0.0376447	−	0.999291i	$-0.511986\pi$
$599$	−1.84267			−0.0752893			−0.0376447	+	0.999291i	$0.511986\pi$
$600$	−0.727153	+	1.25947i	−0.0296859	+	0.0514175i
$601$	−36.5668			−1.49159			−0.745795	−	0.666175i	$-0.767930\pi$
$601$	−36.5668			−1.49159			−0.745795	+	0.666175i	$0.767930\pi$
$602$	10.1776			0.414807
$603$	9.70964	+	16.8176i	0.395407	+	0.684865i
$604$	0.348349	+	0.603358i	0.0141741	+	0.0245503i
$605$	−0.0594005	−	0.102885i	−0.00241497	−	0.00418285i
$606$	−0.698630	+	1.21006i	−0.0283799	+	0.0491554i
$607$	17.2418			0.699823			0.349912	−	0.936783i	$-0.386212\pi$
$607$	17.2418			0.699823			0.349912	+	0.936783i	$0.386212\pi$
$608$	3.88717	+	6.73278i	0.157646	+	0.273050i
$609$	2.71313			0.109941
$610$	0.817517	+	1.17760i	0.0331003	+	0.0476797i
$611$	−0.783687			−0.0317046
$612$	−2.84108	−	4.92090i	−0.114844	−	0.198915i
$613$	12.6853			0.512353			0.256176	−	0.966630i	$-0.417537\pi$
$613$	12.6853			0.512353			0.256176	+	0.966630i	$0.417537\pi$
$614$	−15.2673	+	26.4438i	−0.616140	+	1.06719i
$615$	−0.0306934	−	0.0531625i	−0.00123768	−	0.00214372i
$616$	−6.47575	−	11.2163i	−0.260915	−	0.451919i
$617$	8.64002	+	14.9650i	0.347834	+	0.602466i	0.985864	−	0.167545i	$-0.0535839\pi$
$617$	8.64002	+	14.9650i	0.347834	+	0.602466i	−0.638030	+	0.770011i	$0.720251\pi$
$618$	−1.17596			−0.0473041
$619$	15.2121			0.611424			0.305712	−	0.952124i	$-0.401106\pi$
$619$	15.2121			0.611424			0.305712	+	0.952124i	$0.401106\pi$
$620$	0.0409879	−	0.0709932i	0.00164612	−	0.00285116i
$621$	1.26041			0.0505785
$622$	10.1623	−	17.6015i	0.407469	−	0.705758i
$623$	24.1003	+	41.7429i	0.965558	+	1.67239i
$624$	0.364526	−	0.631378i	0.0145927	−	0.0252753i
$625$	−12.3942	−	21.4675i	−0.495770	−	0.858699i
$626$	9.77837	+	16.9366i	0.390822	+	0.676924i
$627$	−0.210595	+	0.364761i	−0.00841034	+	0.0145671i
$628$	0.579732	+	1.00413i	0.0231338	+	0.0400690i
$629$	−22.4135	+	38.8213i	−0.893685	+	1.54791i
$630$	2.84871			0.113495
$631$	6.48376	+	11.2302i	0.258114	+	0.447067i	0.965737	−	0.259524i	$-0.0835655\pi$
$631$	6.48376	+	11.2302i	0.258114	+	0.447067i	−0.707622	+	0.706591i	$0.750232\pi$
$632$	13.4888	+	23.3632i	0.536554	+	0.929339i
$633$	−0.295559			−0.0117474
$634$	−10.2905			−0.408688
$635$	1.02116	−	1.76870i	0.0405236	−	0.0701889i
$636$	0.0916011	−	0.158658i	0.00363222	−	0.00629119i
$637$	−26.9533			−1.06793
$638$	6.89088			0.272812
$639$	−0.374127	+	0.648007i	−0.0148002	+	0.0256348i
$640$	0.799107	−	1.38409i	0.0315875	−	0.0547111i
$641$	−1.35606	+	2.34877i	−0.0535612	+	0.0927707i	−0.891563	−	0.452897i	$-0.850391\pi$
$641$	−1.35606	+	2.34877i	−0.0535612	+	0.0927707i	0.838002	+	0.545668i	$0.183724\pi$
$642$	−0.984798	+	1.70572i	−0.0388669	+	0.0673194i
$643$	−8.55892			−0.337531			−0.168765	−	0.985656i	$-0.553978\pi$
$643$	−8.55892			−0.337531			−0.168765	+	0.985656i	$0.553978\pi$
$644$	3.61837			0.142584
$645$	−0.00881248	+	0.0152637i	−0.000346991	+	0.000601006i
$646$	13.6661	−	23.6704i	0.537685	−	0.931298i
$647$	16.8238			0.661413			0.330707	−	0.943734i	$-0.392713\pi$
$647$	16.8238			0.661413			0.330707	+	0.943734i	$0.392713\pi$
$648$	22.1215			0.869015
$649$	4.34699	+	7.52921i	0.170634	+	0.295547i
$650$	5.18797	+	8.98583i	0.203489	+	0.352453i
$651$	1.08452			0.0425058
$652$	−1.94409	+	3.36727i	−0.0761366	+	0.131872i
$653$	3.64669	+	6.31626i	0.142706	+	0.247174i	0.928515	−	0.371295i	$-0.121086\pi$
$653$	3.64669	+	6.31626i	0.142706	+	0.247174i	−0.785809	+	0.618470i	$0.787753\pi$
$654$	1.73147	−	2.99899i	0.0677058	−	0.117270i
$655$	−1.23645	−	2.14159i	−0.0483120	−	0.0836789i
$656$	−10.2073	−	17.6795i	−0.398527	−	0.690269i
$657$	4.13132	−	7.15565i	0.161178	−	0.279169i
$658$	2.33589	+	4.04588i	0.0910626	+	0.157725i
$659$	−10.2245	+	17.7093i	−0.398289	+	0.689857i	−0.993515	−	0.113701i	$-0.963729\pi$
$659$	−10.2245	+	17.7093i	−0.398289	+	0.689857i	0.595226	+	0.803558i	$0.297063\pi$
$660$	−0.00538186			−0.000209489
$661$	−15.8451	+	27.4445i	−0.616303	+	1.06747i	0.373852	+	0.927488i	$0.378037\pi$
$661$	−15.8451	+	27.4445i	−0.616303	+	1.06747i	−0.990154	+	0.139979i	$0.955297\pi$
$662$	−19.2472			−0.748066
$663$	−0.775072			−0.0301013
$664$	−2.33598	−	4.04603i	−0.0906535	−	0.157016i
$665$	1.11090	+	1.92413i	0.0430787	+	0.0746145i
$666$	21.0352	+	36.4340i	0.815096	+	1.41179i
$667$	4.01152	−	6.94815i	0.155326	−	0.269033i
$668$	−7.06791			−0.273466
$669$	0.661946	+	1.14652i	0.0255923	+	0.0443272i
$670$	−1.19357			−0.0461118
$671$	−3.32924	+	7.06514i	−0.128524	+	0.272747i
$672$	−1.31423			−0.0506976
$673$	18.2621	+	31.6308i	0.703951	+	1.21928i	0.967069	+	0.254515i	$0.0819157\pi$
$673$	18.2621	+	31.6308i	0.703951	+	1.21928i	−0.263118	+	0.964764i	$0.584751\pi$
$674$	−0.896230			−0.0345215
$675$	1.74675	−	3.02546i	0.0672324	−	0.116450i
$676$	2.16464	+	3.74927i	0.0832555	+	0.144203i
$677$	−19.8242	−	34.3366i	−0.761907	−	1.31966i	−0.941866	−	0.335987i	$-0.890930\pi$
$677$	−19.8242	−	34.3366i	−0.761907	−	1.31966i	0.179960	−	0.983674i	$-0.442403\pi$
$678$	−0.991049	−	1.71655i	−0.0380610	−	0.0659236i
$679$	59.3634			2.27816
$680$	−1.45546			−0.0558144
$681$	−1.12618	+	1.95060i	−0.0431552	+	0.0747470i
$682$	2.75450			0.105475
$683$	−14.5235	+	25.1554i	−0.555725	+	0.962544i	0.442122	+	0.896955i	$0.354226\pi$
$683$	−14.5235	+	25.1554i	−0.555725	+	0.962544i	−0.997847	+	0.0655890i	$0.979107\pi$
$684$	−2.07957	−	3.60193i	−0.0795145	−	0.137723i
$685$	0.356580	−	0.617614i	0.0136242	−	0.0235978i
$686$	52.2346	+	90.4730i	1.99433	+	3.45427i
$687$	1.07680	+	1.86508i	0.0410827	+	0.0711573i
$688$	−2.93064	+	5.07602i	−0.111730	+	0.193521i
$689$	2.72360	+	4.71742i	0.103761	+	0.179719i
$690$	−0.0193229	+	0.0334683i	−0.000735610	+	0.00127411i
$691$	−16.9690			−0.645532			−0.322766	−	0.946479i	$-0.604613\pi$
$691$	−16.9690			−0.645532			−0.322766	+	0.946479i	$0.604613\pi$
$692$	−1.07633	−	1.86426i	−0.0409159	−	0.0708685i
$693$	7.76014	+	13.4410i	0.294783	+	0.510580i
$694$	26.6286			1.01081
$695$	−1.63704			−0.0620966
$696$	−0.650471	+	1.12665i	−0.0246561	+	0.0427055i
$697$	−10.8516	+	18.7955i	−0.411033	+	0.711930i
$698$	−51.6589			−1.95532
$699$	−2.26033			−0.0854935
$700$	5.01455	−	8.68545i	0.189532	−	0.328279i
$701$	−14.6298	+	25.3396i	−0.552562	+	0.957065i	0.445527	+	0.895268i	$0.353016\pi$
$701$	−14.6298	+	25.3396i	−0.552562	+	0.957065i	−0.998089	+	0.0617965i	$0.980317\pi$
$702$	−0.729076	+	1.26280i	−0.0275172	+	0.0476612i
$703$	−16.4059	+	28.4159i	−0.618761	+	1.07173i
$704$	5.91063			0.222765
$705$	−0.00809033			−0.000304700
$706$	5.79381	−	10.0352i	0.218053	−	0.377679i
$707$	−20.0782	+	34.7764i	−0.755117	+	1.30790i
$708$	0.393851			0.0148018
$709$	−39.2022			−1.47227			−0.736135	−	0.676835i	$-0.763351\pi$
$709$	−39.2022			−1.47227			−0.736135	+	0.676835i	$0.763351\pi$
$710$	−0.0229951	−	0.0398287i	−0.000862990	−	0.00149474i
$711$	−16.1641	−	27.9971i	−0.606202	−	1.04997i
$712$	−23.1121			−0.866164
$713$	1.60353	−	2.77739i	0.0600526	−	0.104014i
$714$	2.31021	+	4.00141i	0.0864575	+	0.149749i
$715$	0.0800102	−	0.138582i	0.00299221	−	0.00518266i
$716$	−2.38627	−	4.13314i	−0.0891791	−	0.154463i
$717$	−1.47400	−	2.55305i	−0.0550477	−	0.0953454i
$718$	−8.41065	+	14.5677i	−0.313883	+	0.543661i
$719$	−26.6619	−	46.1798i	−0.994322	−	1.72222i	−0.589316	−	0.807903i	$-0.700603\pi$
$719$	−26.6619	−	46.1798i	−0.994322	−	1.72222i	−0.405006	−	0.914314i	$-0.632731\pi$
$720$	−0.820289	+	1.42078i	−0.0305704	+	0.0529494i
$721$	−33.7964			−1.25864
$722$	−4.67443	+	8.09635i	−0.173964	+	0.301315i
$723$	−0.580783			−0.0215996
$724$	8.71117			0.323748
$725$	−11.1188	−	19.2583i	−0.412941	−	0.715235i
$726$	−0.0904189	−	0.156610i	−0.00335576	−	0.00581235i
$727$	14.9775	+	25.9419i	0.555486	+	0.962131i	0.997866	+	0.0653026i	$0.0208013\pi$
$727$	14.9775	+	25.9419i	0.555486	+	0.962131i	−0.442379	+	0.896828i	$0.645865\pi$
$728$	8.72259	−	15.1080i	0.323281	−	0.559938i
$729$	−26.2630			−0.972704
$730$	0.253925	+	0.439810i	0.00939817	+	0.0162781i
$731$	6.23126			0.230471
$732$	0.201772	+	0.290644i	0.00745770	+	0.0107425i
$733$	−24.6076			−0.908904			−0.454452	−	0.890771i	$-0.650165\pi$
$733$	−24.6076			−0.908904			−0.454452	+	0.890771i	$0.650165\pi$
$734$	−17.3692	−	30.0844i	−0.641110	−	1.11044i
$735$	−0.278251			−0.0102634
$736$	−1.94317	+	3.36566i	−0.0716261	+	0.124060i
$737$	−3.25140	−	5.63158i	−0.119767	−	0.207442i
$738$	10.1842	+	17.6396i	0.374887	+	0.649324i
$739$	7.32030	+	12.6791i	0.269281	+	0.466409i	0.968676	−	0.248326i	$-0.0798805\pi$
$739$	7.32030	+	12.6791i	0.269281	+	0.466409i	−0.699395	+	0.714735i	$0.746547\pi$
$740$	−0.419262			−0.0154124
$741$	−0.567326			−0.0208412
$742$	16.2362	−	28.1219i	0.596049	−	1.03239i
$743$	49.5695			1.81853			0.909265	−	0.416218i	$-0.136645\pi$
$743$	49.5695			1.81853			0.909265	+	0.416218i	$0.136645\pi$
$744$	−0.260014	+	0.450357i	−0.00953257	+	0.0165109i
$745$	1.07886	+	1.86864i	0.0395263	+	0.0684615i
$746$	−17.7486	+	30.7415i	−0.649822	+	1.12553i
$747$	2.79929	+	4.84851i	0.102421	+	0.177398i
$748$	0.951372	+	1.64782i	0.0347856	+	0.0602504i
$749$	−28.3025	+	49.0213i	−1.03415	+	1.79120i
$750$	0.107267	+	0.185792i	0.00391683	+	0.00678415i
$751$	−17.0263	+	29.4904i	−0.621297	+	1.07612i	0.367947	+	0.929847i	$0.380061\pi$
$751$	−17.0263	+	29.4904i	−0.621297	+	1.07612i	−0.989244	+	0.146272i	$0.953273\pi$
$752$	−2.69049			−0.0981120
$753$	−0.0458002	−	0.0793283i	−0.00166905	−	0.00289088i
$754$	4.64088	+	8.03823i	0.169011	+	0.292735i
$755$	−0.213851			−0.00778283
$756$	1.40941			0.0512597
$757$	−9.01760	+	15.6189i	−0.327750	+	0.567680i	−0.982065	−	0.188542i	$-0.939624\pi$
$757$	−9.01760	+	15.6189i	−0.327750	+	0.567680i	0.654315	+	0.756222i	$0.272957\pi$
$758$	1.27246	−	2.20397i	0.0462180	−	0.0800519i
$759$	−0.210549			−0.00764244
$760$	−1.06535			−0.0386442
$761$	−4.86541	+	8.42715i	−0.176371	+	0.305484i	−0.940635	−	0.339420i	$-0.889769\pi$
$761$	−4.86541	+	8.42715i	−0.176371	+	0.305484i	0.764264	+	0.644904i	$0.223103\pi$
$762$	1.55440	−	2.69231i	0.0563101	−	0.0975320i
$763$	49.7613	−	86.1891i	1.80148	−	3.12026i
$764$	−0.0151958	+	0.0263198i	−0.000549763	+	0.000952218i
$765$	1.74414			0.0630593
$766$	−14.3957			−0.520138
$767$	−5.85523	+	10.1416i	−0.211420	+	0.366191i
$768$	0.524573	−	0.908587i	0.0189289	−	0.0327858i
$769$	45.6185			1.64505			0.822523	−	0.568731i	$-0.192566\pi$
$769$	45.6185			1.64505			0.822523	+	0.568731i	$0.192566\pi$
$770$	−0.953928			−0.0343772
$771$	0.979873	+	1.69719i	0.0352893	+	0.0611228i
$772$	1.88534	+	3.26551i	0.0678550	+	0.117528i
$773$	19.1162			0.687561			0.343781	−	0.939050i	$-0.388292\pi$
$773$	19.1162			0.687561			0.343781	+	0.939050i	$0.388292\pi$
$774$	2.92403	−	5.06457i	0.105102	−	0.182042i
$775$	−4.44453	−	7.69815i	−0.159652	−	0.276526i
$776$	−14.2324	+	24.6512i	−0.510912	+	0.884926i
$777$	−2.77337	−	4.80362i	−0.0994942	−	0.172329i
$778$	3.54702	+	6.14362i	0.127167	+	0.220260i
$779$	−7.94298	+	13.7576i	−0.284587	+	0.492919i
$780$	−0.00362458	−	0.00627796i	−0.000129781	−	0.000224787i
$781$	0.125281	−	0.216993i	0.00448291	−	0.00776463i
$782$	13.6631			0.488593
$783$	1.56255	−	2.70641i	0.0558408	−	0.0967192i
$784$	−92.5339			−3.30478
$785$	−0.355897			−0.0127025
$786$	−1.88211	−	3.25991i	−0.0671327	−	0.116277i
$787$	−3.69096	−	6.39293i	−0.131569	−	0.227883i	0.792713	−	0.609595i	$-0.208668\pi$
$787$	−3.69096	−	6.39293i	−0.131569	−	0.227883i	−0.924281	+	0.381712i	$0.875335\pi$
$788$	4.52093	+	7.83048i	0.161051	+	0.278949i
$789$	1.43187	−	2.48007i	0.0509760	−	0.0882930i
$790$	1.98700			0.0706943
$791$	−28.4821	−	49.3325i	−1.01271	−	1.75406i
$792$	−7.44196			−0.264439
$793$	−10.4837	+	0.874673i	−0.372287	+	0.0310605i
$794$	21.2275			0.753337
$795$	0.0281169	+	0.0486999i	0.000997203	+	0.00172721i
$796$	−4.15032			−0.147104
$797$	21.4645	−	37.1777i	0.760313	−	1.31690i	−0.182377	−	0.983229i	$-0.558379\pi$
$797$	21.4645	−	37.1777i	0.760313	−	1.31690i	0.942689	−	0.333672i	$-0.108288\pi$
$798$	1.69100	+	2.92889i	0.0598606	+	0.103682i
$799$	1.43016	+	2.47711i	0.0505954	+	0.0876337i
$800$	5.38591	+	9.32866i	0.190420	+	0.329818i
$801$	27.6962			0.978596
$802$	−12.5624			−0.443595
$803$	−1.38342	+	2.39616i	−0.0488200	+	0.0845587i
$804$	−0.294586			−0.0103893
$805$	−0.555328	+	0.961856i	−0.0195727	+	0.0339010i
$806$	1.85510	+	3.21313i	0.0653433	+	0.113178i
$807$	−0.820517	+	1.42118i	−0.0288836	+	0.0500278i
$808$	−9.62746	−	16.6753i	−0.338693	−	0.586633i
$809$	−24.7901	−	42.9378i	−0.871575	−	1.50961i	−0.860367	−	0.509675i	$-0.829766\pi$
$809$	−24.7901	−	42.9378i	−0.871575	−	1.50961i	−0.0112081	−	0.999937i	$-0.503568\pi$
$810$	0.814667	−	1.41104i	0.0286245	−	0.0495791i
$811$	21.9420	+	38.0046i	0.770487	+	1.33452i	0.937296	+	0.348534i	$0.113320\pi$
$811$	21.9420	+	38.0046i	0.770487	+	1.33452i	−0.166809	+	0.985989i	$0.553346\pi$
$812$	4.48574	−	7.76953i	0.157419	−	0.272657i
$813$	−2.31555			−0.0812099
$814$	−7.04389	−	12.2004i	−0.246888	−	0.427623i
$815$	−0.596738	−	1.03358i	−0.0209028	−	0.0362047i
$816$	−2.66091			−0.0931505
$817$	4.56107			0.159572
$818$	1.46997	−	2.54607i	0.0513964	−	0.0890211i
$819$	−10.4526	+	18.1045i	−0.365244	+	0.632621i
$820$	−0.202987			−0.00708862
$821$	−17.8726			−0.623756			−0.311878	−	0.950122i	$-0.600958\pi$
$821$	−17.8726			−0.623756			−0.311878	+	0.950122i	$0.600958\pi$
$822$	0.542782	−	0.940127i	0.0189317	−	0.0327907i
$823$	11.0115	−	19.0726i	0.383838	−	0.664828i	−0.607769	−	0.794114i	$-0.707935\pi$
$823$	11.0115	−	19.0726i	0.383838	−	0.664828i	0.991607	+	0.129286i	$0.0412686\pi$
$824$	8.10267	−	14.0342i	0.282270	−	0.488906i
$825$	−0.291791	+	0.505397i	−0.0101589	+	0.0175957i
$826$	69.8095			2.42898
$827$	−25.2448			−0.877849			−0.438925	−	0.898524i	$-0.644640\pi$
$827$	−25.2448			−0.877849			−0.438925	+	0.898524i	$0.644640\pi$
$828$	1.03956	−	1.80057i	0.0361273	−	0.0625743i
$829$	−19.9011	+	34.4697i	−0.691194	+	1.19718i	0.280253	+	0.959926i	$0.409582\pi$
$829$	−19.9011	+	34.4697i	−0.691194	+	1.19718i	−0.971447	+	0.237256i	$0.923752\pi$
$830$	−0.344107			−0.0119441
$831$	−2.41506			−0.0837775
$832$	3.98070	+	6.89478i	0.138006	+	0.239033i
$833$	49.1874	+	85.1951i	1.70424	+	2.95184i
$834$	−2.49189			−0.0862872
$835$	1.08474	−	1.87883i	0.0375391	−	0.0650197i
$836$	0.696371	+	1.20615i	0.0240845	+	0.0417156i
$837$	0.624599	−	1.08184i	0.0215893	−	0.0373937i
$838$	−14.1653	−	24.5351i	−0.489333	−	0.847549i
$839$	−24.0935	−	41.7312i	−0.831801	−	1.44072i	−0.896608	−	0.442824i	$-0.853977\pi$
$839$	−24.0935	−	41.7312i	−0.831801	−	1.44072i	0.0648073	−	0.997898i	$-0.479357\pi$
$840$	0.0900470	−	0.155966i	0.00310692	−	0.00538134i
$841$	4.55374	+	7.88731i	0.157026	+	0.271976i
$842$	9.38815	−	16.2608i	0.323537	−	0.560383i
$843$	2.63189			0.0906471
$844$	−0.488661	+	0.846385i	−0.0168204	+	0.0291338i
$845$	−1.32887			−0.0457145
$846$	2.68442			0.0922922
$847$	−2.59858	−	4.50087i	−0.0892882	−	0.154652i
$848$	9.35044	+	16.1954i	0.321095	+	0.556153i
$849$	−0.483957	−	0.838237i	−0.0166093	−	0.0287682i
$850$	18.9352	−	32.7967i	0.649471	−	1.12492i
$851$	−16.4024			−0.562266
$852$	−0.00567542	−	0.00983012i	−0.000194437	−	0.000336775i
$853$	−54.8716			−1.87877			−0.939384	−	0.342868i	$-0.888602\pi$
$853$	−54.8716			−1.87877			−0.939384	+	0.342868i	$0.888602\pi$
$854$	35.7638	+	51.5163i	1.22381	+	1.76285i
$855$	1.27665			0.0436604
$856$	−13.5710	−	23.5057i	−0.463847	−	0.803407i
$857$	34.9592			1.19418			0.597092	−	0.802173i	$-0.296323\pi$
$857$	34.9592			1.19418			0.597092	+	0.802173i	$0.296323\pi$
$858$	0.121791	−	0.210948i	0.00415787	−	0.00720164i
$859$	−15.0339	−	26.0396i	−0.512952	−	0.888458i	−0.999887	−	0.0150205i	$-0.995219\pi$
$859$	−15.0339	−	26.0396i	−0.512952	−	0.888458i	0.486935	−	0.873438i	$-0.338115\pi$
$860$	0.0291402	+	0.0504722i	0.000993671	+	0.00172109i
$861$	−1.34274	−	2.32569i	−0.0457604	−	0.0792593i
$862$	0.0520907			0.00177422
$863$	28.7122			0.977375			0.488687	−	0.872459i	$-0.337476\pi$
$863$	28.7122			0.977375			0.488687	+	0.872459i	$0.337476\pi$
$864$	−0.756893	+	1.31098i	−0.0257500	+	0.0446003i
$865$	0.660758			0.0224664
$866$	14.4403	−	25.0113i	0.490701	−	0.849919i
$867$	0.419539	+	0.726662i	0.0142483	+	0.0246787i
$868$	1.79309	−	3.10573i	0.0608615	−	0.105415i
$869$	5.41276	+	9.37517i	0.183615	+	0.318031i
$870$	0.0479097	+	0.0829821i	0.00162429	+	0.00281336i
$871$	4.37951	−	7.58553i	0.148394	−	0.257026i
$872$	23.8605	+	41.3276i	0.808019	+	1.39953i
$873$	17.0552	−	29.5405i	0.577231	−	0.999793i
$874$	10.0009			0.338287
$875$	3.08278	+	5.33953i	0.104217	+	0.180509i
$876$	0.0626712	+	0.108550i	0.00211746	+	0.00366755i
$877$	45.4737			1.53554			0.767768	−	0.640728i	$-0.221367\pi$
$877$	45.4737			1.53554			0.767768	+	0.640728i	$0.221367\pi$
$878$	−52.2867			−1.76459
$879$	1.30777	−	2.26512i	0.0441100	−	0.0764008i
$880$	0.274684	−	0.475767i	0.00925960	−	0.0160381i
$881$	6.13610			0.206730			0.103365	−	0.994643i	$-0.467039\pi$
$881$	6.13610			0.206730			0.103365	+	0.994643i	$0.467039\pi$
$882$	92.3252			3.10875
$883$	−21.9243	+	37.9739i	−0.737810	+	1.27792i	0.215669	+	0.976466i	$0.430807\pi$
$883$	−21.9243	+	37.9739i	−0.737810	+	1.27792i	−0.953479	+	0.301458i	$0.902527\pi$
$884$	−1.28146	+	2.21956i	−0.0431002	+	0.0746518i
$885$	−0.0604461	+	0.104696i	−0.00203187	+	0.00351931i
$886$	8.58526	−	14.8701i	0.288427	−	0.499571i
$887$	37.8379			1.27047			0.635237	−	0.772318i	$-0.280903\pi$
$887$	37.8379			1.27047			0.635237	+	0.772318i	$0.280903\pi$
$888$	2.65966			0.0892524
$889$	44.6726	−	77.3752i	1.49827	−	2.59508i
$890$	−0.851149	+	1.47423i	−0.0285306	+	0.0494164i
$891$	8.87689			0.297387
$892$	4.37771			0.146576
$893$	1.04683	+	1.81316i	0.0350307	+	0.0606750i
$894$	1.64223	+	2.84442i	0.0549243	+	0.0951317i
$895$	1.46493			0.0489671
$896$	34.9584	−	60.5497i	1.16788	−	2.02282i
$897$	−0.141801	−	0.245606i	−0.00473459	−	0.00820055i
$898$	−2.69028	+	4.65970i	−0.0897758	+	0.155496i
$899$	−3.97583	−	6.88634i	−0.132601	−	0.229672i
$900$	−2.88137	−	4.99068i	−0.0960457	−	0.166356i
$901$	9.94066	−	17.2177i	0.331171	−	0.573605i
$902$	−3.41032	−	5.90685i	−0.113551	−	0.196677i
$903$	−0.385518	+	0.667736i	−0.0128292	+	0.0222209i
$904$	27.3143			0.908460
$905$	−1.33694	+	2.31565i	−0.0444415	+	0.0769750i
$906$	−0.325522			−0.0108147
$907$	42.7768			1.42038			0.710190	−	0.704010i	$-0.248609\pi$
$907$	42.7768			1.42038			0.710190	+	0.704010i	$0.248609\pi$
$908$	3.72392	+	6.45002i	0.123583	+	0.214052i
$909$	11.5370	+	19.9826i	0.382657	+	0.662781i
$910$	−0.642452	−	1.11276i	−0.0212971	−	0.0368876i
$911$	19.4528	−	33.6932i	0.644500	−	1.11631i	−0.339917	−	0.940455i	$-0.610399\pi$
$911$	19.4528	−	33.6932i	0.644500	−	1.11631i	0.984417	−	0.175851i	$-0.0562676\pi$
$912$	−1.94770			−0.0644946
$913$	−0.937378	−	1.62359i	−0.0310227	−	0.0537329i
$914$	−9.20357			−0.304427
$915$	−0.108228	+	0.00902962i	−0.00357789	+	0.000298510i
$916$	7.12133			0.235295
$917$	−54.0907	−	93.6878i	−1.78623	−	3.09384i
$918$	5.32200			0.175652
$919$	7.08776	−	12.2764i	0.233804	−	0.404960i	−0.725121	−	0.688622i	$-0.758216\pi$
$919$	7.08776	−	12.2764i	0.233804	−	0.404960i	0.958924	+	0.283662i	$0.0915494\pi$
$920$	−0.266279	−	0.461209i	−0.00877896	−	0.0152056i
$921$	−1.15663	−	2.00334i	−0.0381122	−	0.0660122i
$922$	−18.9807	−	32.8755i	−0.625095	−	1.08270i
$923$	0.337498			0.0111089
$924$	−0.235439			−0.00774538
$925$	−22.7313	+	39.3719i	−0.747402	+	1.29454i
$926$	−63.4339			−2.08457
$927$	−9.70974	+	16.8178i	−0.318910	+	0.552368i
$928$	4.81794	+	8.34491i	0.158157	+	0.273935i
$929$	18.8280	−	32.6111i	0.617727	−	1.06993i	−0.372172	−	0.928164i	$-0.621387\pi$
$929$	18.8280	−	32.6111i	0.617727	−	1.06993i	0.989899	−	0.141771i	$-0.0452797\pi$
$930$	0.0191510	+	0.0331705i	0.000627987	+	0.00108771i
$931$	36.0035	+	62.3599i	1.17997	+	2.04376i
$932$	−3.73711	+	6.47286i	−0.122413	+	0.212026i
$933$	0.769875	+	1.33346i	0.0252046	+	0.0436556i
$934$	−3.18720	+	5.52039i	−0.104288	+	0.180633i
$935$	−0.584046			−0.0191003
$936$	−5.01202	−	8.68107i	−0.163823	−	0.283750i
$937$	−21.0737	−	36.5007i	−0.688447	−	1.19242i	−0.972340	−	0.233569i	$-0.924960\pi$
$937$	−21.0737	−	36.5007i	−0.688447	−	1.19242i	0.283893	−	0.958856i	$-0.408374\pi$
$938$	−52.2150			−1.70488
$939$	−1.48158			−0.0483496
$940$	−0.0133761	+	0.0231681i	−0.000436281	+	0.000755661i
$941$	6.48668	−	11.2353i	0.211460	−	0.366259i	−0.740712	−	0.671823i	$-0.765512\pi$
$941$	6.48668	−	11.2353i	0.211460	−	0.366259i	0.952172	+	0.305564i	$0.0988449\pi$
$942$	−0.541743			−0.0176509
$943$	−7.94126			−0.258603
$944$	−20.1017	+	34.8172i	−0.654255	+	1.13320i
$945$	−0.216309	+	0.374657i	−0.00703652	+	0.0121876i
$946$	−0.979149	+	1.69594i	−0.0318349	+	0.0551396i
$947$	20.6465	−	35.7608i	0.670921	−	1.16207i	−0.306722	−	0.951799i	$-0.599232\pi$
$947$	20.6465	−	35.7608i	0.670921	−	1.16207i	0.977643	−	0.210271i	$-0.0674345\pi$
$948$	0.490412			0.0159278
$949$	−3.72684			−0.120978
$950$	13.8599	−	24.0060i	0.449674	−	0.778859i
$951$	0.389795	−	0.675145i	0.0126400	−	0.0218931i
$952$	−63.6718			−2.06361
$953$	34.5725			1.11991			0.559956	−	0.828522i	$-0.310818\pi$
$953$	34.5725			1.11991			0.559956	+	0.828522i	$0.310818\pi$
$954$	−9.32934	−	16.1589i	−0.302049	−	0.523164i
$955$	−0.00466433	−	0.00807885i	−0.000150934	−	0.000261426i
$956$	−9.74816			−0.315278
$957$	−0.261020	+	0.452100i	−0.00843759	+	0.0146143i
$958$	−12.1570	−	21.0565i	−0.392775	−	0.680306i
$959$	15.5992	−	27.0186i	0.503725	−	0.872477i
$960$	0.0410945	+	0.0711777i	0.00132632	+	0.00229725i
$961$	13.9107	+	24.0941i	0.448733	+	0.777229i
$962$	9.48785	−	16.4334i	0.305901	−	0.529835i
$963$	16.2627	+	28.1677i	0.524057	+	0.907693i
$964$	−0.960236	+	1.66318i	−0.0309271	+	0.0535673i
$965$	−1.15741			−0.0372583
$966$	−0.845315	+	1.46413i	−0.0271976	+	0.0471076i
$967$	26.3879			0.848578			0.424289	−	0.905527i	$-0.360524\pi$
$967$	26.3879			0.848578			0.424289	+	0.905527i	$0.360524\pi$
$968$	2.49203			0.0800970
$969$	1.03532	+	1.79322i	0.0332592	+	0.0576067i
$970$	1.04827	+	1.81565i	0.0336579	+	0.0582971i
$971$	21.7512	+	37.6743i	0.698031	+	1.20902i	0.969148	+	0.246479i	$0.0792735\pi$
$971$	21.7512	+	37.6743i	0.698031	+	1.20902i	−0.271117	+	0.962546i	$0.587393\pi$
$972$	0.607851	−	1.05283i	0.0194968	−	0.0337695i
$973$	−71.6154			−2.29588
$974$	18.7008	+	32.3907i	0.599212	+	1.03787i
$975$	−0.786063			−0.0251742
$976$	−35.9917	+	3.00285i	−1.15207	+	0.0961190i
$977$	34.1299			1.09191			0.545957	−	0.837813i	$-0.316166\pi$
$977$	34.1299			1.09191			0.545957	+	0.837813i	$0.316166\pi$
$978$	−0.908349	−	1.57331i	−0.0290458	−	0.0503088i
$979$	−9.27441			−0.296411
$980$	−0.460045	+	0.796821i	−0.0146956	+	0.0254535i
$981$	−28.5930	−	49.5245i	−0.912903	−	1.58119i
$982$	18.1630	+	31.4592i	0.579604	+	1.00390i
$983$	−26.5388	−	45.9665i	−0.846455	−	1.46610i	−0.884352	−	0.466821i	$-0.845399\pi$
$983$	−26.5388	−	45.9665i	−0.846455	−	1.46610i	0.0378968	−	0.999282i	$-0.487934\pi$
$984$	1.28768			0.0410499
$985$	−2.77539			−0.0884313
$986$	16.9384	−	29.3381i	0.539427	−	0.934316i
$987$	−0.353926			−0.0112656
$988$	−0.937986	+	1.62464i	−0.0298413	+	0.0516867i
$989$	1.14002	+	1.97457i	0.0362505	+	0.0627878i
$990$	−0.274065	+	0.474694i	−0.00871034	+	0.0150868i
$991$	−1.15062	−	1.99293i	−0.0365507	−	0.0633077i	0.847171	−	0.531320i	$-0.178304\pi$
$991$	−1.15062	−	1.99293i	−0.0365507	−	0.0633077i	−0.883722	+	0.468012i	$0.844970\pi$
$992$	1.92588	+	3.33572i	0.0611468	+	0.105909i
$993$	0.729069	−	1.26278i	0.0231363	−	0.0400732i
$994$	−1.00596	−	1.74238i	−0.0319072	−	0.0552648i
$995$	0.636968	−	1.10326i	0.0201932	−	0.0349757i
$996$	−0.0849293			−0.00269109
$997$	1.27165	+	2.20256i	0.0402735	+	0.0697557i	0.885460	−	0.464716i	$-0.153844\pi$
$997$	1.27165	+	2.20256i	0.0402735	+	0.0697557i	−0.845186	+	0.534472i	$0.820510\pi$
$998$	11.5170	+	19.9480i	0.364563	+	0.631442i
$999$	−6.38897			−0.202138

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.e.a.474.20	✓	52
61.13	even	3	inner	671.2.e.a.562.20	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.e.a.474.20	✓	52	1.1	even	1	trivial
671.2.e.a.562.20	yes	52	61.13	even	3	inner

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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.772502 + 1.33801i) q^{2} -0.117047 q^{3} +(-0.193519 + 0.335184i) q^{4} +(-0.0594005 - 0.102885i) q^{5} +(-0.0904189 - 0.156610i) q^{6} +(-2.59858 - 4.50087i) q^{7} +2.49203 q^{8} -2.98630 q^{9} +O(q^{10})\)	\(q+(0.772502 + 1.33801i) q^{2} -0.117047 q^{3} +(-0.193519 + 0.335184i) q^{4} +(-0.0594005 - 0.102885i) q^{5} +(-0.0904189 - 0.156610i) q^{6} +(-2.59858 - 4.50087i) q^{7} +2.49203 q^{8} -2.98630 q^{9} +(0.0917739 - 0.158957i) q^{10} +1.00000 q^{11} +(0.0226508 - 0.0392323i) q^{12} +(0.673481 + 1.16650i) q^{13} +(4.01482 - 6.95387i) q^{14} +(0.00695263 + 0.0120423i) q^{15} +(2.31214 + 4.00474i) q^{16} +(2.45809 - 4.25753i) q^{17} +(-2.30692 - 3.99571i) q^{18} +(1.79923 - 3.11637i) q^{19} +0.0459804 q^{20} +(0.304155 + 0.526813i) q^{21} +(0.772502 + 1.33801i) q^{22} +1.79884 q^{23} -0.291684 q^{24} +(2.49294 - 4.31790i) q^{25} +(-1.04053 + 1.80225i) q^{26} +0.700677 q^{27} +2.01150 q^{28} +(2.23005 - 3.86256i) q^{29} +(-0.0107418 + 0.0186054i) q^{30} +(0.891422 - 1.54399i) q^{31} +(-1.08023 + 1.87101i) q^{32} -0.117047 q^{33} +7.59550 q^{34} +(-0.308714 + 0.534708i) q^{35} +(0.577905 - 1.00096i) q^{36} -9.11828 q^{37} +5.55965 q^{38} +(-0.0788288 - 0.136535i) q^{39} +(-0.148028 - 0.256392i) q^{40} -4.41465 q^{41} +(-0.469921 + 0.813927i) q^{42} +(0.633751 + 1.09769i) q^{43} +(-0.193519 + 0.335184i) q^{44} +(0.177388 + 0.307244i) q^{45} +(1.38961 + 2.40688i) q^{46} +(-0.290909 + 0.503869i) q^{47} +(-0.270628 - 0.468742i) q^{48} +(-10.0052 + 17.3296i) q^{49} +7.70321 q^{50} +(-0.287711 + 0.498330i) q^{51} -0.521325 q^{52} +4.04406 q^{53} +(0.541275 + 0.937515i) q^{54} +(-0.0594005 - 0.102885i) q^{55} +(-6.47575 - 11.2163i) q^{56} +(-0.210595 + 0.364761i) q^{57} +6.89088 q^{58} +(4.34699 + 7.52921i) q^{59} -0.00538186 q^{60} +(-3.32924 + 7.06514i) q^{61} +2.75450 q^{62} +(7.76014 + 13.4410i) q^{63} +5.91063 q^{64} +(0.0800102 - 0.138582i) q^{65} +(-0.0904189 - 0.156610i) q^{66} +(-3.25140 - 5.63158i) q^{67} +(0.951372 + 1.64782i) q^{68} -0.210549 q^{69} -0.953928 q^{70} +(0.125281 - 0.216993i) q^{71} -7.44196 q^{72} +(-1.38342 + 2.39616i) q^{73} +(-7.04389 - 12.2004i) q^{74} +(-0.291791 + 0.505397i) q^{75} +(0.696371 + 1.20615i) q^{76} +(-2.59858 - 4.50087i) q^{77} +(0.121791 - 0.210948i) q^{78} +(5.41276 + 9.37517i) q^{79} +(0.274684 - 0.475767i) q^{80} +8.87689 q^{81} +(-3.41032 - 5.90685i) q^{82} +(-0.937378 - 1.62359i) q^{83} -0.235439 q^{84} -0.584046 q^{85} +(-0.979149 + 1.69594i) q^{86} +(-0.261020 + 0.452100i) q^{87} +2.49203 q^{88} -9.27441 q^{89} +(-0.274065 + 0.474694i) q^{90} +(3.50019 - 6.06250i) q^{91} +(-0.348110 + 0.602945i) q^{92} +(-0.104338 + 0.180719i) q^{93} -0.898911 q^{94} -0.427501 q^{95} +(0.126437 - 0.218996i) q^{96} +(-5.71114 + 9.89199i) q^{97} -30.9162 q^{98} -2.98630 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 2 q^{2} + 2 q^{3} - 30 q^{4} - 6 q^{6} - 7 q^{7} + 50 q^{9}+O(q^{10}) \) 52 * q - 2 * q^2 + 2 * q^3 - 30 * q^4 - 6 * q^6 - 7 * q^7 + 50 * q^9	\( 52 q - 2 q^{2} + 2 q^{3} - 30 q^{4} - 6 q^{6} - 7 q^{7} + 50 q^{9} - 2 q^{10} + 52 q^{11} + 11 q^{12} - 3 q^{13} - 3 q^{14} - 12 q^{15} - 34 q^{16} - 8 q^{17} - 12 q^{18} + 5 q^{19} - 22 q^{20} - 2 q^{21} - 2 q^{22} - 2 q^{24} - 16 q^{25} - 37 q^{26} + 8 q^{27} + 104 q^{28} + 10 q^{29} - 20 q^{31} + 8 q^{32} + 2 q^{33} - 12 q^{34} + 18 q^{35} - 60 q^{36} + 4 q^{37} - 20 q^{38} + 23 q^{39} - 38 q^{40} - 6 q^{41} - 56 q^{42} - 22 q^{43} - 30 q^{44} + 25 q^{46} - 26 q^{48} - 45 q^{49} - 16 q^{50} - 38 q^{51} - 18 q^{53} - 46 q^{54} + 16 q^{56} + 36 q^{57} - 56 q^{58} - 13 q^{59} + 40 q^{60} + 14 q^{61} + 26 q^{62} - 39 q^{63} + 164 q^{64} + 15 q^{65} - 6 q^{66} + 7 q^{67} - 39 q^{68} + 20 q^{69} + 162 q^{70} - 8 q^{71} + 6 q^{72} + 27 q^{73} - 13 q^{74} + 16 q^{75} + 20 q^{76} - 7 q^{77} + 20 q^{78} + 5 q^{79} - 8 q^{80} - 68 q^{81} + 6 q^{82} - 22 q^{83} - 28 q^{84} - 36 q^{85} + 13 q^{86} - 25 q^{87} + 36 q^{89} + 41 q^{90} - 42 q^{91} - 17 q^{92} - 26 q^{93} - 14 q^{94} - 40 q^{95} - 3 q^{96} - 47 q^{97} - 2 q^{98} + 50 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 + 2 * q^3 - 30 * q^4 - 6 * q^6 - 7 * q^7 + 50 * q^9 - 2 * q^10 + 52 * q^11 + 11 * q^12 - 3 * q^13 - 3 * q^14 - 12 * q^15 - 34 * q^16 - 8 * q^17 - 12 * q^18 + 5 * q^19 - 22 * q^20 - 2 * q^21 - 2 * q^22 - 2 * q^24 - 16 * q^25 - 37 * q^26 + 8 * q^27 + 104 * q^28 + 10 * q^29 - 20 * q^31 + 8 * q^32 + 2 * q^33 - 12 * q^34 + 18 * q^35 - 60 * q^36 + 4 * q^37 - 20 * q^38 + 23 * q^39 - 38 * q^40 - 6 * q^41 - 56 * q^42 - 22 * q^43 - 30 * q^44 + 25 * q^46 - 26 * q^48 - 45 * q^49 - 16 * q^50 - 38 * q^51 - 18 * q^53 - 46 * q^54 + 16 * q^56 + 36 * q^57 - 56 * q^58 - 13 * q^59 + 40 * q^60 + 14 * q^61 + 26 * q^62 - 39 * q^63 + 164 * q^64 + 15 * q^65 - 6 * q^66 + 7 * q^67 - 39 * q^68 + 20 * q^69 + 162 * q^70 - 8 * q^71 + 6 * q^72 + 27 * q^73 - 13 * q^74 + 16 * q^75 + 20 * q^76 - 7 * q^77 + 20 * q^78 + 5 * q^79 - 8 * q^80 - 68 * q^81 + 6 * q^82 - 22 * q^83 - 28 * q^84 - 36 * q^85 + 13 * q^86 - 25 * q^87 + 36 * q^89 + 41 * q^90 - 42 * q^91 - 17 * q^92 - 26 * q^93 - 14 * q^94 - 40 * q^95 - 3 * q^96 - 47 * q^97 - 2 * q^98 + 50 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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