LMFDB - Embedded newform 273.2.l.b.256.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(16,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("273.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.l (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			256.6
Root			$-0.532778 + 0.922798i$ of defining polynomial
Character	$\chi$	$=$	273.256
Dual form			273.2.l.b.16.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.06556 q^{2} +(0.500000 + 0.866025i) q^{3} -0.864591 q^{4} +(1.19023 + 2.06154i) q^{5} +(0.532778 + 0.922798i) q^{6} +(-0.813611 + 2.51755i) q^{7} -3.05238 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.26826 + 2.19668i) q^{10} +(0.333295 + 0.577284i) q^{11} +(-0.432296 - 0.748758i) q^{12} +(2.19926 - 2.85714i) q^{13} +(-0.866948 + 2.68258i) q^{14} +(-1.19023 + 2.06154i) q^{15} -1.52330 q^{16} +1.41579 q^{17} +(-0.532778 + 0.922798i) q^{18} +(1.78135 - 3.08539i) q^{19} +(-1.02906 - 1.78239i) q^{20} +(-2.58706 + 0.554165i) q^{21} +(0.355145 + 0.615128i) q^{22} +5.98253 q^{23} +(-1.52619 - 2.64344i) q^{24} +(-0.333295 + 0.577284i) q^{25} +(2.34343 - 3.04444i) q^{26} -1.00000 q^{27} +(0.703441 - 2.17665i) q^{28} +(0.647747 - 1.12193i) q^{29} +(-1.26826 + 2.19668i) q^{30} +(-3.09078 + 5.35339i) q^{31} +4.48160 q^{32} +(-0.333295 + 0.577284i) q^{33} +1.50861 q^{34} +(-6.15840 + 1.31917i) q^{35} +(0.432296 - 0.748758i) q^{36} -7.89736 q^{37} +(1.89813 - 3.28765i) q^{38} +(3.57399 + 0.476043i) q^{39} +(-3.63304 - 6.29260i) q^{40} +(5.26293 - 9.11566i) q^{41} +(-2.75666 + 0.590493i) q^{42} +(5.22034 + 9.04190i) q^{43} +(-0.288164 - 0.499115i) q^{44} -2.38046 q^{45} +6.37472 q^{46} +(-5.54746 - 9.60848i) q^{47} +(-0.761650 - 1.31922i) q^{48} +(-5.67607 - 4.09661i) q^{49} +(-0.355145 + 0.615128i) q^{50} +(0.707897 + 1.22611i) q^{51} +(-1.90146 + 2.47026i) q^{52} +(3.39224 - 5.87554i) q^{53} -1.06556 q^{54} +(-0.793396 + 1.37420i) q^{55} +(2.48345 - 7.68451i) q^{56} +3.56270 q^{57} +(0.690210 - 1.19548i) q^{58} -5.15282 q^{59} +(1.02906 - 1.78239i) q^{60} +(-2.41878 + 4.18944i) q^{61} +(-3.29340 + 5.70433i) q^{62} +(-1.77345 - 1.96338i) q^{63} +7.82199 q^{64} +(8.50773 + 1.13320i) q^{65} +(-0.355145 + 0.615128i) q^{66} +(-2.78633 - 4.82606i) q^{67} -1.22408 q^{68} +(2.99126 + 5.18102i) q^{69} +(-6.56212 + 1.40565i) q^{70} +(6.01988 + 10.4267i) q^{71} +(1.52619 - 2.64344i) q^{72} +(-4.05962 + 7.03147i) q^{73} -8.41508 q^{74} -0.666590 q^{75} +(-1.54014 + 2.66760i) q^{76} +(-1.72451 + 0.369401i) q^{77} +(3.80828 + 0.507250i) q^{78} +(-2.00333 - 3.46986i) q^{79} +(-1.81308 - 3.14034i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.60794 - 9.71324i) q^{82} +8.44505 q^{83} +(2.23675 - 0.479126i) q^{84} +(1.68512 + 2.91872i) q^{85} +(5.56257 + 9.63465i) q^{86} +1.29549 q^{87} +(-1.01734 - 1.76209i) q^{88} +1.82156 q^{89} -2.53651 q^{90} +(5.40364 + 7.86134i) q^{91} -5.17244 q^{92} -6.18156 q^{93} +(-5.91112 - 10.2384i) q^{94} +8.48087 q^{95} +(2.24080 + 3.88118i) q^{96} +(-7.88484 - 13.6569i) q^{97} +(-6.04817 - 4.36516i) q^{98} -0.666590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9} - 4 q^{10} - 2 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} + 12 q^{16} + 4 q^{17} - 11 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} - 8 q^{23} + 6 q^{24} + 2 q^{25}+ \cdots + 4 q^{99}+O(q^{100}) $ 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9 - 4 * q^10 - 2 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 + 12 * q^16 + 4 * q^17 - 11 * q^19 - 20 * q^20 - q^21 + 7 * q^22 - 8 * q^23 + 6 * q^24 + 2 * q^25 + 33 * q^26 - 16 * q^27 - q^28 + 15 * q^29 + 4 * q^30 + 3 * q^31 - 6 * q^32 + 2 * q^33 - 68 * q^34 - 6 * q^36 - 8 * q^37 + 2 * q^38 + 4 * q^39 - 25 * q^40 + 19 * q^41 - 17 * q^42 + 11 * q^43 - 16 * q^44 - 4 * q^46 + 5 * q^47 + 6 * q^48 + 7 * q^49 - 7 * q^50 + 2 * q^51 - 18 * q^52 + 36 * q^53 - 15 * q^55 - 51 * q^56 - 22 * q^57 + 20 * q^58 + 34 * q^59 + 20 * q^60 - 22 * q^61 - 6 * q^62 - 2 * q^63 - 20 * q^64 - 24 * q^65 - 7 * q^66 + 26 * q^67 - 10 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 - 6 * q^72 - 6 * q^73 - 30 * q^74 + 4 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 - 28 * q^80 - 8 * q^81 - q^82 + 36 * q^83 - 8 * q^84 - 4 * q^85 + 16 * q^86 + 30 * q^87 + 24 * q^88 - 40 * q^89 + 8 * q^90 - 10 * q^91 - 94 * q^92 + 6 * q^93 - 20 * q^94 - 3 * q^96 + 7 * q^97 + 18 * q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.06556			0.753462			0.376731	−	0.926323i	$-0.377048\pi$
$2$	1.06556			0.753462			0.376731	+	0.926323i	$0.377048\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.864591			−0.432296
$5$	1.19023	+	2.06154i	0.532287	+	0.921948i	0.999289	+	0.0376922i	$0.0120006\pi$
$5$	1.19023	+	2.06154i	0.532287	+	0.921948i	−0.467002	+	0.884256i	$0.654666\pi$
$6$	0.532778	+	0.922798i	0.217506	+	0.376731i
$7$	−0.813611	+	2.51755i	−0.307516	+	0.951543i
$7$	−0.813611	+	2.51755i	−0.307516	+	0.951543i
$8$	−3.05238			−1.07918
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.26826	+	2.19668i	0.401058	+	0.694653i
$11$	0.333295	+	0.577284i	0.100492	+	0.174058i	0.911888	−	0.410440i	$-0.134625\pi$
$11$	0.333295	+	0.577284i	0.100492	+	0.174058i	−0.811395	+	0.584498i	$0.801292\pi$
$12$	−0.432296	−	0.748758i	−0.124793	−	0.216148i
$13$	2.19926	−	2.85714i	0.609965	−	0.792429i
$13$	2.19926	−	2.85714i	0.609965	−	0.792429i
$14$	−0.866948	+	2.68258i	−0.231702	+	0.716951i
$15$	−1.19023	+	2.06154i	−0.307316	+	0.532287i
$16$	−1.52330			−0.380825
$17$	1.41579			0.343381			0.171690	−	0.985151i	$-0.445077\pi$
$17$	1.41579			0.343381			0.171690	+	0.985151i	$0.445077\pi$
$18$	−0.532778	+	0.922798i	−0.125577	+	0.217506i
$19$	1.78135	−	3.08539i	0.408670	−	0.707837i	−0.586071	−	0.810260i	$-0.699326\pi$
$19$	1.78135	−	3.08539i	0.408670	−	0.707837i	0.994741	+	0.102423i	$0.0326595\pi$
$20$	−1.02906	−	1.78239i	−0.230105	−	0.398554i
$21$	−2.58706	+	0.554165i	−0.564544	+	0.120929i
$22$	0.355145	+	0.615128i	0.0757171	+	0.131146i
$23$	5.98253			1.24744			0.623722	−	0.781647i	$-0.285620\pi$
$23$	5.98253			1.24744			0.623722	+	0.781647i	$0.285620\pi$
$24$	−1.52619	−	2.64344i	−0.311532	−	0.539590i
$25$	−0.333295	+	0.577284i	−0.0666590	+	0.115457i
$26$	2.34343	−	3.04444i	0.459585	−	0.597065i
$27$	−1.00000			−0.192450
$28$	0.703441	−	2.17665i	0.132938	−	0.411348i
$29$	0.647747	−	1.12193i	0.120284	−	0.208337i	−0.799596	−	0.600538i	$-0.794953\pi$
$29$	0.647747	−	1.12193i	0.120284	−	0.208337i	0.919879	+	0.392201i	$0.128286\pi$
$30$	−1.26826	+	2.19668i	−0.231551	+	0.401058i
$31$	−3.09078	+	5.35339i	−0.555120	+	0.961497i	0.442774	+	0.896633i	$0.353994\pi$
$31$	−3.09078	+	5.35339i	−0.555120	+	0.961497i	−0.997894	+	0.0648633i	$0.979339\pi$
$32$	4.48160			0.792243
$33$	−0.333295	+	0.577284i	−0.0580192	+	0.100492i
$34$	1.50861			0.258724
$35$	−6.15840	+	1.31917i	−1.04096	+	0.222980i
$36$	0.432296	−	0.748758i	0.0720493	−	0.124793i
$37$	−7.89736			−1.29832			−0.649159	−	0.760653i	$-0.724879\pi$
$37$	−7.89736			−1.29832			−0.649159	+	0.760653i	$0.724879\pi$
$38$	1.89813	−	3.28765i	0.307917	−	0.533328i
$39$	3.57399	+	0.476043i	0.572296	+	0.0762278i
$40$	−3.63304	−	6.29260i	−0.574433	−	0.994948i
$41$	5.26293	−	9.11566i	0.821931	−	1.42363i	−0.0823113	−	0.996607i	$-0.526230\pi$
$41$	5.26293	−	9.11566i	0.821931	−	1.42363i	0.904242	−	0.427020i	$-0.140437\pi$
$42$	−2.75666	+	0.590493i	−0.425362	+	0.0911151i
$43$	5.22034	+	9.04190i	0.796095	+	1.37888i	0.922142	+	0.386853i	$0.126438\pi$
$43$	5.22034	+	9.04190i	0.796095	+	1.37888i	−0.126047	+	0.992024i	$0.540229\pi$
$44$	−0.288164	−	0.499115i	−0.0434424	−	0.0752444i
$45$	−2.38046			−0.354858
$46$	6.37472			0.939901
$47$	−5.54746	−	9.60848i	−0.809180	−	1.40154i	−0.913433	−	0.406990i	$-0.866578\pi$
$47$	−5.54746	−	9.60848i	−0.809180	−	1.40154i	0.104253	−	0.994551i	$-0.466755\pi$
$48$	−0.761650	−	1.31922i	−0.109935	−	0.190412i
$49$	−5.67607	−	4.09661i	−0.810868	−	0.585230i
$50$	−0.355145	+	0.615128i	−0.0502250	+	0.0869923i
$51$	0.707897	+	1.22611i	0.0991255	+	0.171690i
$52$	−1.90146	+	2.47026i	−0.263685	+	0.342563i
$53$	3.39224	−	5.87554i	0.465961	−	0.807067i	−0.533284	−	0.845936i	$-0.679042\pi$
$53$	3.39224	−	5.87554i	0.465961	−	0.807067i	0.999244	+	0.0388691i	$0.0123755\pi$
$54$	−1.06556			−0.145004
$55$	−0.793396	+	1.37420i	−0.106981	+	0.185297i
$56$	2.48345	−	7.68451i	0.331865	−	1.02689i
$57$	3.56270			0.471891
$58$	0.690210	−	1.19548i	0.0906291	−	0.156974i
$59$	−5.15282			−0.670840			−0.335420	−	0.942069i	$-0.608878\pi$
$59$	−5.15282			−0.670840			−0.335420	+	0.942069i	$0.608878\pi$
$60$	1.02906	−	1.78239i	0.132851	−	0.230105i
$61$	−2.41878	+	4.18944i	−0.309692	+	0.536403i	−0.978295	−	0.207217i	$-0.933559\pi$
$61$	−2.41878	+	4.18944i	−0.309692	+	0.536403i	0.668603	+	0.743620i	$0.266893\pi$
$62$	−3.29340	+	5.70433i	−0.418262	+	0.724451i
$63$	−1.77345	−	1.96338i	−0.223434	−	0.247363i
$64$	7.82199			0.977749
$65$	8.50773	+	1.13320i	1.05525	+	0.140556i
$66$	−0.355145	+	0.615128i	−0.0437153	+	0.0757171i
$67$	−2.78633	−	4.82606i	−0.340404	−	0.589597i	0.644104	−	0.764938i	$-0.277230\pi$
$67$	−2.78633	−	4.82606i	−0.340404	−	0.589597i	−0.984508	+	0.175341i	$0.943897\pi$
$68$	−1.22408			−0.148442
$69$	2.99126	+	5.18102i	0.360106	+	0.623722i
$70$	−6.56212	+	1.40565i	−0.784323	+	0.168007i
$71$	6.01988	+	10.4267i	0.714428	+	1.23743i	0.963180	+	0.268858i	$0.0866463\pi$
$71$	6.01988	+	10.4267i	0.714428	+	1.23743i	−0.248752	+	0.968567i	$0.580020\pi$
$72$	1.52619	−	2.64344i	0.179863	−	0.311532i
$73$	−4.05962	+	7.03147i	−0.475143	+	0.822971i	−0.999595	−	0.0284689i	$-0.990937\pi$
$73$	−4.05962	+	7.03147i	−0.475143	+	0.822971i	0.524452	+	0.851440i	$0.324270\pi$
$74$	−8.41508			−0.978233
$75$	−0.666590			−0.0769712
$76$	−1.54014	+	2.66760i	−0.176666	+	0.305995i
$77$	−1.72451	+	0.369401i	−0.196526	+	0.0420971i
$78$	3.80828	+	0.507250i	0.431203	+	0.0574348i
$79$	−2.00333	−	3.46986i	−0.225392	−	0.390390i	0.731045	−	0.682329i	$-0.239033\pi$
$79$	−2.00333	−	3.46986i	−0.225392	−	0.390390i	−0.956437	+	0.291939i	$0.905700\pi$
$80$	−1.81308	−	3.14034i	−0.202708	−	0.351101i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.60794	−	9.71324i	0.619293	−	1.07265i
$83$	8.44505			0.926965			0.463483	−	0.886106i	$-0.346600\pi$
$83$	8.44505			0.926965			0.463483	+	0.886106i	$0.346600\pi$
$84$	2.23675	−	0.479126i	0.244050	−	0.0522770i
$85$	1.68512	+	2.91872i	0.182777	+	0.316579i
$86$	5.56257	+	9.63465i	0.599827	+	1.03893i
$87$	1.29549			0.138892
$88$	−1.01734	−	1.76209i	−0.108449	−	0.187840i
$89$	1.82156			0.193085			0.0965423	−	0.995329i	$-0.469222\pi$
$89$	1.82156			0.193085			0.0965423	+	0.995329i	$0.469222\pi$
$90$	−2.53651			−0.267372
$91$	5.40364	+	7.86134i	0.566456	+	0.824092i
$92$	−5.17244			−0.539264
$93$	−6.18156			−0.640998
$94$	−5.91112	−	10.2384i	−0.609686	−	1.05601i
$95$	8.48087			0.870118
$96$	2.24080	+	3.88118i	0.228701	+	0.396121i
$97$	−7.88484	−	13.6569i	−0.800584	−	1.38665i	−0.919232	−	0.393716i	$-0.871189\pi$
$97$	−7.88484	−	13.6569i	−0.800584	−	1.38665i	0.118648	−	0.992936i	$-0.462144\pi$
$98$	−6.04817	−	4.36516i	−0.610958	−	0.440948i
$99$	−0.666590			−0.0669949
$100$	0.288164	−	0.499115i	0.0288164	−	0.0499115i
$101$	−4.48529	−	7.76875i	−0.446303	−	0.773020i	0.551839	−	0.833951i	$-0.313926\pi$
$101$	−4.48529	−	7.76875i	−0.446303	−	0.773020i	−0.998142	+	0.0609311i	$0.980593\pi$
$102$	0.754304	+	1.30649i	0.0746872	+	0.129362i
$103$	−1.58796	−	2.75042i	−0.156466	−	0.271007i	0.777126	−	0.629345i	$-0.216677\pi$
$103$	−1.58796	−	2.75042i	−0.156466	−	0.271007i	−0.933592	+	0.358338i	$0.883344\pi$
$104$	−6.71298	+	8.72109i	−0.658261	+	0.855173i
$105$	−4.22163	−	4.67375i	−0.411989	−	0.456111i
$106$	3.61462	−	6.26071i	0.351083	−	0.608094i
$107$	−5.00535			−0.483886			−0.241943	−	0.970290i	$-0.577785\pi$
$107$	−5.00535			−0.483886			−0.241943	+	0.970290i	$0.577785\pi$
$108$	0.864591			0.0831953
$109$	−8.29305	+	14.3640i	−0.794330	+	1.37582i	0.128934	+	0.991653i	$0.458844\pi$
$109$	−8.29305	+	14.3640i	−0.794330	+	1.37582i	−0.923264	+	0.384167i	$0.874489\pi$
$110$	−0.845407	+	1.46429i	−0.0806064	+	0.139614i
$111$	−3.94868	−	6.83932i	−0.374792	−	0.649159i
$112$	1.23937	−	3.83497i	0.117110	−	0.362371i
$113$	3.57465	+	6.19148i	0.336275	+	0.582446i	0.983729	−	0.179659i	$-0.0574994\pi$
$113$	3.57465	+	6.19148i	0.336275	+	0.582446i	−0.647454	+	0.762105i	$0.724166\pi$
$114$	3.79625			0.355552
$115$	7.12058	+	12.3332i	0.663998	+	1.15008i
$116$	−0.560037	+	0.970012i	−0.0519981	+	0.0900633i
$117$	1.37473	+	3.33318i	0.127094	+	0.308153i
$118$	−5.49062			−0.505453
$119$	−1.15191	+	3.56433i	−0.105595	+	0.326741i
$120$	3.63304	−	6.29260i	0.331649	−	0.574433i
$121$	5.27783	−	9.14147i	0.479803	−	0.831042i
$122$	−2.57734	+	4.46408i	−0.233341	+	0.404159i
$123$	10.5259			0.949084
$124$	2.67226	−	4.62849i	0.239976	−	0.415651i
$125$	10.3155			0.922647
$126$	−1.88971	−	2.09209i	−0.168349	−	0.186378i
$127$	−5.70435	+	9.88023i	−0.506179	+	0.876728i	0.493795	+	0.869578i	$0.335609\pi$
$127$	−5.70435	+	9.88023i	−0.506179	+	0.876728i	−0.999974	+	0.00715012i	$0.997724\pi$
$128$	−0.628436			−0.0555464
$129$	−5.22034	+	9.04190i	−0.459626	+	0.796095i
$130$	9.06546	+	1.20749i	0.795094	+	0.105904i
$131$	−4.30754	−	7.46087i	−0.376351	−	0.651860i	0.614177	−	0.789168i	$-0.289488\pi$
$131$	−4.30754	−	7.46087i	−0.376351	−	0.651860i	−0.990528	+	0.137309i	$0.956155\pi$
$132$	0.288164	−	0.499115i	0.0250815	−	0.0434424i
$133$	6.31828	+	6.99494i	0.547864	+	0.606538i
$134$	−2.96898	−	5.14243i	−0.256481	−	0.444239i
$135$	−1.19023	−	2.06154i	−0.102439	−	0.177429i
$136$	−4.32155			−0.370569
$137$	8.35476			0.713796			0.356898	−	0.934143i	$-0.383834\pi$
$137$	8.35476			0.713796			0.356898	+	0.934143i	$0.383834\pi$
$138$	3.18736	+	5.52067i	0.271326	+	0.469950i
$139$	4.82663	+	8.35996i	0.409389	+	0.709083i	0.994821	−	0.101638i	$-0.0324085\pi$
$139$	4.82663	+	8.35996i	0.409389	+	0.709083i	−0.585432	+	0.810721i	$0.699075\pi$
$140$	5.32450	−	1.14054i	0.450003	−	0.0963933i
$141$	5.54746	−	9.60848i	0.467180	−	0.809180i
$142$	6.41451	+	11.1103i	0.538294	+	0.932352i
$143$	2.38239	+	0.317326i	0.199225	+	0.0265361i
$144$	0.761650	−	1.31922i	0.0634708	−	0.109935i
$145$	3.08387			0.256102
$146$	−4.32575	+	7.49242i	−0.358002	+	0.620077i
$147$	0.709729	−	6.96393i	0.0585375	−	0.574375i
$148$	6.82799			0.561257
$149$	−6.63040	+	11.4842i	−0.543183	+	0.940821i	0.455535	+	0.890218i	$0.349448\pi$
$149$	−6.63040	+	11.4842i	−0.543183	+	0.940821i	−0.998719	+	0.0506036i	$0.983885\pi$
$150$	−0.710289			−0.0579949
$151$	−8.22189	+	14.2407i	−0.669088	+	1.15889i	0.309072	+	0.951039i	$0.399982\pi$
$151$	−8.22189	+	14.2407i	−0.669088	+	1.15889i	−0.978160	+	0.207855i	$0.933352\pi$
$152$	−5.43736	+	9.41778i	−0.441028	+	0.763883i
$153$	−0.707897	+	1.22611i	−0.0572301	+	0.0991255i
$154$	−1.83756	+	0.393617i	−0.148075	+	0.0317186i
$155$	−14.7150			−1.18193
$156$	−3.09004	−	0.411582i	−0.247401	−	0.0329530i
$157$	9.15038	−	15.8489i	0.730279	−	1.26488i	−0.226484	−	0.974015i	$-0.572723\pi$
$157$	9.15038	−	15.8489i	0.730279	−	1.26488i	0.956764	−	0.290866i	$-0.0939435\pi$
$158$	−2.13466	−	3.69733i	−0.169824	−	0.294144i
$159$	6.78449			0.538045
$160$	5.33414	+	9.23900i	0.421701	+	0.730407i
$161$	−4.86745	+	15.0613i	−0.383609	+	1.18700i
$162$	−0.532778	−	0.922798i	−0.0418590	−	0.0725019i
$163$	−3.39411	+	5.87878i	−0.265847	+	0.460461i	−0.967785	−	0.251777i	$-0.918985\pi$
$163$	−3.39411	+	5.87878i	−0.265847	+	0.460461i	0.701938	+	0.712238i	$0.252318\pi$
$164$	−4.55028	+	7.88132i	−0.355317	+	0.615428i
$165$	−1.58679			−0.123532
$166$	8.99868			0.698433
$167$	0.826837	−	1.43212i	0.0639826	−	0.110821i	−0.832260	−	0.554386i	$-0.812953\pi$
$167$	0.826837	−	1.43212i	0.0639826	−	0.110821i	0.896242	+	0.443565i	$0.146286\pi$
$168$	7.89671	−	1.69152i	0.609244	−	0.130504i
$169$	−3.32652	−	12.5672i	−0.255886	−	0.966707i
$170$	1.79559	+	3.11005i	0.137716	+	0.238530i
$171$	1.78135	+	3.08539i	0.136223	+	0.235946i
$172$	−4.51346	−	7.81755i	−0.344148	−	0.596083i
$173$	5.99394	−	10.3818i	0.455711	−	0.789314i	−0.543018	−	0.839721i	$-0.682718\pi$
$173$	5.99394	−	10.3818i	0.455711	−	0.789314i	0.998729	+	0.0504069i	$0.0160518\pi$
$174$	1.38042			0.104649
$175$	−1.18217	−	1.30877i	−0.0893634	−	0.0989338i
$176$	−0.507708	−	0.879376i	−0.0382699	−	0.0662855i
$177$	−2.57641	−	4.46248i	−0.193655	−	0.335420i
$178$	1.94097			0.145482
$179$	1.33508	+	2.31243i	0.0997888	+	0.172839i	0.911597	−	0.411085i	$-0.134850\pi$
$179$	1.33508	+	2.31243i	0.0997888	+	0.172839i	−0.811808	+	0.583924i	$0.801517\pi$
$180$	2.05813			0.153404
$181$	−0.752089			−0.0559024			−0.0279512	−	0.999609i	$-0.508898\pi$
$181$	−0.752089			−0.0559024			−0.0279512	+	0.999609i	$0.508898\pi$
$182$	5.75788	+	8.37669i	0.426803	+	0.620922i
$183$	−4.83755			−0.357602
$184$	−18.2610			−1.34622
$185$	−9.39968	−	16.2807i	−0.691078	−	1.19698i
$186$	−6.58679			−0.482967
$187$	0.471878	+	0.817316i	0.0345071	+	0.0597681i
$188$	4.79628	+	8.30741i	0.349805	+	0.605880i
$189$	0.813611	−	2.51755i	0.0591815	−	0.183125i
$190$	9.03683			0.655601
$191$	−2.57907	+	4.46708i	−0.186615	+	0.323226i	−0.944119	−	0.329603i	$-0.893085\pi$
$191$	−2.57907	+	4.46708i	−0.186615	+	0.323226i	0.757505	+	0.652830i	$0.226418\pi$
$192$	3.91100	+	6.77405i	0.282252	+	0.488875i
$193$	−1.42313	−	2.46494i	−0.102439	−	0.177430i	0.810250	−	0.586085i	$-0.199331\pi$
$193$	−1.42313	−	2.46494i	−0.102439	−	0.177430i	−0.912689	+	0.408655i	$0.865998\pi$
$194$	−8.40173	−	14.5522i	−0.603209	−	1.04479i
$195$	3.27249	+	7.93451i	0.234348	+	0.568202i
$196$	4.90748	+	3.54189i	0.350535	+	0.252992i
$197$	−0.483548	+	0.837530i	−0.0344514	+	0.0596716i	−0.882737	−	0.469867i	$-0.844302\pi$
$197$	−0.483548	+	0.837530i	−0.0344514	+	0.0596716i	0.848286	+	0.529539i	$0.177635\pi$
$198$	−0.710289			−0.0504780
$199$	9.38169			0.665051			0.332525	−	0.943094i	$-0.392099\pi$
$199$	9.38169			0.665051			0.332525	+	0.943094i	$0.392099\pi$
$200$	1.01734	−	1.76209i	0.0719371	−	0.124599i
$201$	2.78633	−	4.82606i	0.196532	−	0.340404i
$202$	−4.77933	−	8.27804i	−0.336272	−	0.582441i
$203$	2.29750	+	2.54355i	0.161253	+	0.178522i
$204$	−0.612042	−	1.06009i	−0.0428515	−	0.0742210i
$205$	25.0564			1.75001
$206$	−1.69206	−	2.93073i	−0.117891	−	0.204194i
$207$	−2.99126	+	5.18102i	−0.207907	+	0.360106i
$208$	−3.35013	+	4.35228i	−0.232290	+	0.301776i
$209$	2.37486			0.164273
$210$	−4.49839	−	4.98014i	−0.310418	−	0.343662i
$211$	10.3756	−	17.9711i	0.714288	−	1.23718i	−0.248945	−	0.968518i	$-0.580084\pi$
$211$	10.3756	−	17.9711i	0.714288	−	1.23718i	0.963233	−	0.268666i	$-0.0865827\pi$
$212$	−2.93290	+	5.07994i	−0.201433	+	0.348892i
$213$	−6.01988	+	10.4267i	−0.412475	+	0.714428i
$214$	−5.33348			−0.364589
$215$	−12.4268	+	21.5239i	−0.847502	+	1.46792i
$216$	3.05238			0.207688
$217$	−10.9627	−	12.1368i	−0.744197	−	0.823897i
$218$	−8.83670	+	15.3056i	−0.598497	+	1.03663i
$219$	−8.11924			−0.548647
$220$	0.685963	−	1.18812i	0.0462476	−	0.0801032i
$221$	3.11370	−	4.04513i	0.209450	−	0.272105i
$222$	−4.20754	−	7.28767i	−0.282392	−	0.489116i
$223$	−4.05504	+	7.02354i	−0.271546	+	0.470331i	−0.969258	−	0.246047i	$-0.920868\pi$
$223$	−4.05504	+	7.02354i	−0.271546	+	0.470331i	0.697712	+	0.716378i	$0.254201\pi$
$224$	−3.64628	+	11.2826i	−0.243627	+	0.753853i
$225$	−0.333295	−	0.577284i	−0.0222197	−	0.0384856i
$226$	3.80899	+	6.59737i	0.253370	+	0.438850i
$227$	2.19729			0.145839			0.0729197	−	0.997338i	$-0.476768\pi$
$227$	2.19729			0.145839			0.0729197	+	0.997338i	$0.476768\pi$
$228$	−3.08028			−0.203997
$229$	−10.1545	−	17.5882i	−0.671030	−	1.16226i	−0.977612	−	0.210414i	$-0.932519\pi$
$229$	−10.1545	−	17.5882i	−0.671030	−	1.16226i	0.306582	−	0.951844i	$-0.400815\pi$
$230$	7.58738	+	13.1417i	0.500297	+	0.866540i
$231$	−1.18217	−	1.30877i	−0.0777809	−	0.0861108i
$232$	−1.97717	+	3.42456i	−0.129808	+	0.224833i
$233$	−10.7709	−	18.6557i	−0.705624	−	1.22218i	−0.966466	−	0.256795i	$-0.917333\pi$
$233$	−10.7709	−	18.6557i	−0.705624	−	1.22218i	0.260842	−	0.965382i	$-0.416000\pi$
$234$	1.46485	+	3.55169i	0.0957602	+	0.232181i
$235$	13.2055	−	22.8726i	0.861432	−	1.49204i
$236$	4.45509			0.290001
$237$	2.00333	−	3.46986i	0.130130	−	0.225392i
$238$	−1.22742	+	3.79799i	−0.0795619	+	0.246187i
$239$	−17.3697			−1.12355			−0.561775	−	0.827290i	$-0.689881\pi$
$239$	−17.3697			−1.12355			−0.561775	+	0.827290i	$0.689881\pi$
$240$	1.81308	−	3.14034i	0.117034	−	0.202708i
$241$	−10.5031			−0.676566			−0.338283	−	0.941044i	$-0.609846\pi$
$241$	−10.5031			−0.676566			−0.338283	+	0.941044i	$0.609846\pi$
$242$	5.62382	−	9.74074i	0.361513	−	0.626159i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	2.09125	−	3.62216i	0.133879	−	0.231885i
$245$	1.68948	−	16.5774i	0.107937	−	1.05909i
$246$	11.2159			0.715098
$247$	−4.89775	−	11.8751i	−0.311636	−	0.755597i
$248$	9.43424	−	16.3406i	0.599075	−	1.03763i
$249$	4.22253	+	7.31363i	0.267592	+	0.463483i
$250$	10.9917			0.695179
$251$	−0.706938	−	1.22445i	−0.0446215	−	0.0772867i	0.842852	−	0.538145i	$-0.180875\pi$
$251$	−0.706938	−	1.22445i	−0.0446215	−	0.0772867i	−0.887474	+	0.460859i	$0.847542\pi$
$252$	1.53331	+	1.69752i	0.0965896	+	0.106934i
$253$	1.99395	+	3.45362i	0.125358	+	0.217127i
$254$	−6.07830	+	10.5279i	−0.381387	+	0.660581i
$255$	−1.68512	+	2.91872i	−0.105526	+	0.182777i
$256$	−16.3136			−1.01960
$257$	−13.7472			−0.857529			−0.428765	−	0.903416i	$-0.641051\pi$
$257$	−13.7472			−0.857529			−0.428765	+	0.903416i	$0.641051\pi$
$258$	−5.56257	+	9.63465i	−0.346310	+	0.599827i
$259$	6.42538	−	19.8820i	0.399254	−	1.23541i
$260$	−7.35571	−	0.979756i	−0.456182	−	0.0607619i
$261$	0.647747	+	1.12193i	0.0400945	+	0.0694458i
$262$	−4.58992	−	7.94998i	−0.283566	−	0.491151i
$263$	−3.98871	−	6.90864i	−0.245954	−	0.426005i	0.716445	−	0.697643i	$-0.245768\pi$
$263$	−3.98871	−	6.90864i	−0.245954	−	0.426005i	−0.962399	+	0.271638i	$0.912435\pi$
$264$	1.01734	−	1.76209i	0.0626132	−	0.108449i
$265$	16.1502			0.992099
$266$	6.73248	+	7.45349i	0.412795	+	0.457003i
$267$	0.910778	+	1.57751i	0.0557387	+	0.0965423i
$268$	2.40903	+	4.17257i	0.147155	+	0.254880i
$269$	27.6383			1.68514			0.842569	−	0.538589i	$-0.181042\pi$
$269$	27.6383			1.68514			0.842569	+	0.538589i	$0.181042\pi$
$270$	−1.26826	−	2.19668i	−0.0771836	−	0.133686i
$271$	10.3191			0.626838			0.313419	−	0.949615i	$-0.398526\pi$
$271$	10.3191			0.626838			0.313419	+	0.949615i	$0.398526\pi$
$272$	−2.15668			−0.130768
$273$	−4.10630	+	8.61036i	−0.248524	+	0.521123i
$274$	8.90247			0.537818
$275$	−0.444343			−0.0267949
$276$	−2.58622	−	4.47947i	−0.155672	−	0.269632i
$277$	−2.15568			−0.129522			−0.0647611	−	0.997901i	$-0.520629\pi$
$277$	−2.15568			−0.129522			−0.0647611	+	0.997901i	$0.520629\pi$
$278$	5.14304	+	8.90801i	0.308459	+	0.534267i
$279$	−3.09078	−	5.35339i	−0.185040	−	0.320499i
$280$	18.7978	−	4.02660i	1.12338	−	0.240635i
$281$	−2.60596			−0.155458			−0.0777292	−	0.996975i	$-0.524767\pi$
$281$	−2.60596			−0.155458			−0.0777292	+	0.996975i	$0.524767\pi$
$282$	5.91112	−	10.2384i	0.352002	−	0.609686i
$283$	−0.866211	−	1.50032i	−0.0514909	−	0.0891849i	0.839131	−	0.543929i	$-0.183064\pi$
$283$	−0.866211	−	1.50032i	−0.0514909	−	0.0891849i	−0.890622	+	0.454744i	$0.849731\pi$
$284$	−5.20473	−	9.01486i	−0.308844	−	0.534934i
$285$	4.24043	+	7.34465i	0.251182	+	0.435059i
$286$	2.53856	+	0.338128i	0.150108	+	0.0199939i
$287$	18.6671	+	20.6663i	1.10188	+	1.21989i
$288$	−2.24080	+	3.88118i	−0.132040	+	0.228701i
$289$	−14.9955			−0.882090
$290$	3.28604			0.192963
$291$	7.88484	−	13.6569i	0.462217	−	0.800584i
$292$	3.50991	−	6.07935i	0.205402	−	0.355767i
$293$	−16.4196	−	28.4396i	−0.959243	−	1.66146i	−0.724345	−	0.689438i	$-0.757858\pi$
$293$	−16.4196	−	28.4396i	−0.959243	−	1.66146i	−0.234898	−	0.972020i	$-0.575476\pi$
$294$	0.756256	−	7.42045i	0.0441057	−	0.432770i
$295$	−6.13305	−	10.6227i	−0.357080	−	0.618480i
$296$	24.1058			1.40112
$297$	−0.333295	−	0.577284i	−0.0193397	−	0.0334974i
$298$	−7.06506	+	12.2370i	−0.409268	+	0.708873i
$299$	13.1571	−	17.0929i	0.760896	−	0.988510i
$300$	0.576328			0.0332743
$301$	−27.0107	+	5.78586i	−1.55687	+	0.333492i
$302$	−8.76088	+	15.1743i	−0.504132	+	0.873182i
$303$	4.48529	−	7.76875i	0.257673	−	0.446303i
$304$	−2.71353	+	4.69997i	−0.155632	+	0.269562i
$305$	−11.5156			−0.659381
$306$	−0.754304	+	1.30649i	−0.0431207	+	0.0746872i
$307$	−29.4618			−1.68147			−0.840737	−	0.541444i	$-0.817878\pi$
$307$	−29.4618			−1.68147			−0.840737	+	0.541444i	$0.817878\pi$
$308$	1.49100	−	0.319381i	0.0849575	−	0.0181984i
$309$	1.58796	−	2.75042i	0.0903358	−	0.156466i
$310$	−15.6796			−0.890541
$311$	−3.53099	+	6.11585i	−0.200224	+	0.346798i	−0.948601	−	0.316476i	$-0.897500\pi$
$311$	−3.53099	+	6.11585i	−0.200224	+	0.346798i	0.748377	+	0.663274i	$0.230834\pi$
$312$	−10.9092	−	1.45306i	−0.617610	−	0.0822635i
$313$	8.17883	+	14.1661i	0.462295	+	0.800718i	0.999075	−	0.0430043i	$-0.0136929\pi$
$313$	8.17883	+	14.1661i	0.462295	+	0.800718i	−0.536780	+	0.843722i	$0.680360\pi$
$314$	9.75023	−	16.8879i	0.550237	−	0.953039i
$315$	1.93677	−	5.99292i	0.109125	−	0.337663i
$316$	1.73206	+	3.00001i	0.0974359	+	0.168764i
$317$	−9.48109	−	16.4217i	−0.532511	−	0.922337i	−0.999279	−	0.0379568i	$-0.987915\pi$
$317$	−9.48109	−	16.4217i	−0.532511	−	0.922337i	0.466768	−	0.884380i	$-0.345418\pi$
$318$	7.22925			0.405396
$319$	0.863564			0.0483503
$320$	9.30997	+	16.1253i	0.520443	+	0.901434i
$321$	−2.50268	−	4.33476i	−0.139686	−	0.241943i
$322$	−5.18654	+	16.0486i	−0.289035	+	0.894356i
$323$	2.52203	−	4.36828i	0.140329	−	0.243057i
$324$	0.432296	+	0.748758i	0.0240164	+	0.0415977i
$325$	0.916381	+	2.22187i	0.0508317	+	0.123247i
$326$	−3.61662	+	6.26416i	−0.200306	+	0.346940i
$327$	−16.5861			−0.917213
$328$	−16.0645	+	27.8245i	−0.887011	+	1.53635i
$329$	28.7033	−	6.14841i	1.58246	−	0.338973i
$330$	−1.69081			−0.0930763
$331$	9.51894	−	16.4873i	0.523208	−	0.906223i	−0.476427	−	0.879214i	$-0.658068\pi$
$331$	9.51894	−	16.4873i	0.523208	−	0.906223i	0.999635	−	0.0270089i	$-0.00859826\pi$
$332$	−7.30152			−0.400723
$333$	3.94868	−	6.83932i	0.216386	−	0.374792i
$334$	0.881041	−	1.52601i	0.0482084	−	0.0834994i
$335$	6.63274	−	11.4882i	0.362385	−	0.627669i
$336$	3.94087	−	0.844159i	0.214992	−	0.0460526i
$337$	1.90388			0.103711			0.0518555	−	0.998655i	$-0.483486\pi$
$337$	1.90388			0.103711			0.0518555	+	0.998655i	$0.483486\pi$
$338$	−3.54460	−	13.3910i	−0.192801	−	0.728376i
$339$	−3.57465	+	6.19148i	−0.194149	+	0.336275i
$340$	−1.45694	−	2.52350i	−0.0790138	−	0.136856i
$341$	−4.12057			−0.223141
$342$	1.89813	+	3.28765i	0.102639	+	0.177776i
$343$	14.9315	−	10.9567i	0.806226	−	0.591608i
$344$	−15.9345	−	27.5993i	−0.859130	−	1.48806i
$345$	−7.12058	+	12.3332i	−0.383359	+	0.663998i
$346$	6.38687	−	11.0624i	0.343360	−	0.594718i
$347$	−20.8805			−1.12092			−0.560462	−	0.828180i	$-0.689376\pi$
$347$	−20.8805			−1.12092			−0.560462	+	0.828180i	$0.689376\pi$
$348$	−1.12007			−0.0600422
$349$	−4.79951	+	8.31300i	−0.256912	+	0.444984i	−0.965413	−	0.260725i	$-0.916038\pi$
$349$	−4.79951	+	8.31300i	−0.256912	+	0.444984i	0.708501	+	0.705710i	$0.249372\pi$
$350$	−1.25966	−	1.39457i	−0.0673319	−	0.0745428i
$351$	−2.19926	+	2.85714i	−0.117388	+	0.152503i
$352$	1.49370	+	2.58716i	0.0796143	+	0.137896i
$353$	−5.40698	−	9.36517i	−0.287785	−	0.498457i	0.685496	−	0.728076i	$-0.259585\pi$
$353$	−5.40698	−	9.36517i	−0.287785	−	0.498457i	−0.973281	+	0.229619i	$0.926252\pi$
$354$	−2.74531	−	4.75502i	−0.145912	−	0.252726i
$355$	−14.3301	+	24.8204i	−0.760561	+	1.31733i
$356$	−1.57490			−0.0834696
$357$	−3.66275	+	0.784584i	−0.193853	+	0.0415246i
$358$	1.42260	+	2.46402i	0.0751870	+	0.130228i
$359$	14.4945	+	25.1052i	0.764990	+	1.32500i	0.940252	+	0.340479i	$0.110589\pi$
$359$	14.4945	+	25.1052i	0.764990	+	1.32500i	−0.175262	+	0.984522i	$0.556077\pi$
$360$	7.26607			0.382956
$361$	3.15358	+	5.46217i	0.165978	+	0.287482i
$362$	−0.801393			−0.0421203
$363$	10.5557			0.554028
$364$	−4.67194	−	6.79684i	−0.244876	−	0.356251i
$365$	−19.3275			−1.01165
$366$	−5.15468			−0.269439
$367$	16.2867	+	28.2093i	0.850156	+	1.47251i	0.881067	+	0.472992i	$0.156826\pi$
$367$	16.2867	+	28.2093i	0.850156	+	1.47251i	−0.0309103	+	0.999522i	$0.509841\pi$
$368$	−9.11318			−0.475057
$369$	5.26293	+	9.11566i	0.273977	+	0.474542i
$370$	−10.0159	−	17.3480i	−0.520701	−	0.901880i
$371$	12.0320	+	13.3205i	0.624669	+	0.691568i
$372$	5.34452			0.277101
$373$	11.9389	−	20.6788i	0.618172	−	1.07071i	−0.371647	−	0.928374i	$-0.621207\pi$
$373$	11.9389	−	20.6788i	0.618172	−	1.07071i	0.989819	−	0.142331i	$-0.0454598\pi$
$374$	0.502812	+	0.870896i	0.0259998	+	0.0450329i
$375$	5.15775	+	8.93349i	0.266345	+	0.461324i
$376$	16.9330	+	29.3287i	0.873250	+	1.51251i
$377$	−1.78095	−	4.31812i	−0.0917237	−	0.222395i
$378$	0.866948	−	2.68258i	0.0445910	−	0.137977i
$379$	−4.89406	+	8.47676i	−0.251391	+	0.435422i	−0.963909	−	0.266232i	$-0.914221\pi$
$379$	−4.89406	+	8.47676i	−0.251391	+	0.435422i	0.712518	+	0.701654i	$0.247555\pi$
$380$	−7.33248			−0.376148
$381$	−11.4087			−0.584486
$382$	−2.74814	+	4.75992i	−0.140607	+	0.243539i
$383$	−7.42839	+	12.8664i	−0.379573	+	0.657440i	−0.991000	−	0.133861i	$-0.957262\pi$
$383$	−7.42839	+	12.8664i	−0.379573	+	0.657440i	0.611427	+	0.791301i	$0.290596\pi$
$384$	−0.314218	−	0.544241i	−0.0160349	−	0.0277732i
$385$	−2.81410	−	3.11548i	−0.143420	−	0.158779i
$386$	−1.51643	−	2.62653i	−0.0771841	−	0.133687i
$387$	−10.4407			−0.530730
$388$	6.81716	+	11.8077i	0.346089	+	0.599444i
$389$	−9.62735	+	16.6751i	−0.488126	+	0.845459i	−0.999907	−	0.0136568i	$-0.995653\pi$
$389$	−9.62735	+	16.6751i	−0.488126	+	0.845459i	0.511781	+	0.859116i	$0.328986\pi$
$390$	3.48702	+	8.45467i	0.176572	+	0.428119i
$391$	8.47003			0.428348
$392$	17.3255	+	12.5044i	0.875072	+	0.631568i
$393$	4.30754	−	7.46087i	0.217287	−	0.376351i
$394$	−0.515248	+	0.892435i	−0.0259578	+	0.0449602i
$395$	4.76884	−	8.25987i	0.239946	−	0.415599i
$396$	0.576328			0.0289616
$397$	−19.1505	+	33.1696i	−0.961136	+	1.66474i	−0.241481	+	0.970406i	$0.577633\pi$
$397$	−19.1505	+	33.1696i	−0.961136	+	1.66474i	−0.719655	+	0.694331i	$0.755700\pi$
$398$	9.99671			0.501090
$399$	−2.89865	+	8.96926i	−0.145114	+	0.449025i
$400$	0.507708	−	0.879376i	0.0253854	−	0.0439688i
$401$	35.6114			1.77835			0.889175	−	0.457566i	$-0.151279\pi$
$401$	35.6114			1.77835			0.889175	+	0.457566i	$0.151279\pi$
$402$	2.96898	−	5.14243i	0.148080	−	0.256481i
$403$	8.49796	+	20.6043i	0.423314	+	1.02637i
$404$	3.87794	+	6.71680i	0.192935	+	0.334173i
$405$	1.19023	−	2.06154i	0.0591430	−	0.102439i
$406$	2.44811	+	2.71029i	0.121498	+	0.134510i
$407$	−2.63215	−	4.55902i	−0.130471	−	0.225982i
$408$	−2.16077	−	3.74257i	−0.106974	−	0.185285i
$409$	−3.16472			−0.156485			−0.0782426	−	0.996934i	$-0.524931\pi$
$409$	−3.16472			−0.156485			−0.0782426	+	0.996934i	$0.524931\pi$
$410$	26.6990			1.31857
$411$	4.17738	+	7.23544i	0.206055	+	0.356898i
$412$	1.37293	+	2.37799i	0.0676396	+	0.117155i
$413$	4.19240	−	12.9725i	0.206294	−	0.638333i
$414$	−3.18736	+	5.52067i	−0.156650	+	0.271326i
$415$	10.0516	+	17.4098i	0.493412	+	0.854614i
$416$	9.85620	−	12.8046i	0.483240	−	0.627796i
$417$	−4.82663	+	8.35996i	−0.236361	+	0.409389i
$418$	2.53055			0.123773
$419$	11.0530	−	19.1444i	0.539975	−	0.935265i	−0.458929	−	0.888473i	$-0.651767\pi$
$419$	11.0530	−	19.1444i	0.539975	−	0.935265i	0.998905	−	0.0467918i	$-0.0148997\pi$
$420$	3.64999	+	4.04088i	0.178101	+	0.197175i
$421$	7.75012			0.377718			0.188859	−	0.982004i	$-0.439521\pi$
$421$	7.75012			0.377718			0.188859	+	0.982004i	$0.439521\pi$
$422$	11.0558	−	19.1492i	0.538189	−	0.932170i
$423$	11.0949			0.539453
$424$	−10.3544	+	17.9344i	−0.502855	+	0.870971i
$425$	−0.471878	+	0.817316i	−0.0228894	+	0.0396456i
$426$	−6.41451	+	11.1103i	−0.310784	+	0.538294i
$427$	−8.57917	−	9.49795i	−0.415175	−	0.459638i
$428$	4.32759			0.209182
$429$	0.916381	+	2.22187i	0.0442433	+	0.107273i
$430$	−13.2415	+	22.9349i	−0.638560	+	1.10602i
$431$	17.2795	+	29.9290i	0.832324	+	1.44163i	0.896191	+	0.443669i	$0.146323\pi$
$431$	17.2795	+	29.9290i	0.832324	+	1.44163i	−0.0638670	+	0.997958i	$0.520343\pi$
$432$	1.52330			0.0732898
$433$	−12.2389	−	21.1985i	−0.588166	−	1.01873i	−0.994473	−	0.104997i	$-0.966517\pi$
$433$	−12.2389	−	21.1985i	−0.588166	−	1.01873i	0.406306	−	0.913737i	$-0.366817\pi$
$434$	−11.6814	−	12.9324i	−0.560724	−	0.620774i
$435$	1.54194	+	2.67071i	0.0739302	+	0.128051i
$436$	7.17010	−	12.4190i	0.343385	−	0.594761i
$437$	10.6570	−	18.4584i	0.509792	−	0.882986i
$438$	−8.65150			−0.413385
$439$	−10.7270			−0.511970			−0.255985	−	0.966681i	$-0.582400\pi$
$439$	−10.7270			−0.511970			−0.255985	+	0.966681i	$0.582400\pi$
$440$	2.42175	−	4.19459i	0.115452	−	0.199969i
$441$	6.38580	−	2.86732i	0.304086	−	0.136539i
$442$	3.31782	−	4.31031i	0.157813	−	0.205020i
$443$	19.9363	+	34.5306i	0.947200	+	1.64060i	0.751284	+	0.659979i	$0.229435\pi$
$443$	19.9363	+	34.5306i	0.947200	+	1.64060i	0.195916	+	0.980621i	$0.437232\pi$
$444$	3.41400	+	5.91321i	0.162021	+	0.280629i
$445$	2.16807	+	3.75521i	0.102776	+	0.178014i
$446$	−4.32087	+	7.48397i	−0.204599	+	0.354376i
$447$	−13.2608			−0.627214
$448$	−6.36406	+	19.6922i	−0.300674	+	0.930370i
$449$	15.2790	+	26.4640i	0.721060	+	1.24891i	0.960575	+	0.278021i	$0.0896783\pi$
$449$	15.2790	+	26.4640i	0.721060	+	1.24891i	−0.239515	+	0.970893i	$0.576988\pi$
$450$	−0.355145	−	0.615128i	−0.0167417	−	0.0289974i
$451$	7.01643			0.330391
$452$	−3.09062	−	5.35310i	−0.145370	−	0.251789i
$453$	−16.4438			−0.772596
$454$	2.34134			0.109884
$455$	−9.77487	+	20.4966i	−0.458253	+	0.960897i
$456$	−10.8747			−0.509255
$457$	−16.0347			−0.750070			−0.375035	−	0.927011i	$-0.622369\pi$
$457$	−16.0347			−0.750070			−0.375035	+	0.927011i	$0.622369\pi$
$458$	−10.8202	−	18.7412i	−0.505596	−	0.875717i
$459$	−1.41579			−0.0660836
$460$	−6.15640	−	10.6632i	−0.287043	−	0.497174i
$461$	19.7152	+	34.1477i	0.918227	+	1.59042i	0.802106	+	0.597181i	$0.203713\pi$
$461$	19.7152	+	34.1477i	0.918227	+	1.59042i	0.116121	+	0.993235i	$0.462954\pi$
$462$	−1.25966	−	1.39457i	−0.0586049	−	0.0648812i
$463$	−25.9972			−1.20819			−0.604096	−	0.796912i	$-0.706466\pi$
$463$	−25.9972			−1.20819			−0.604096	+	0.796912i	$0.706466\pi$
$464$	−0.986712	+	1.70904i	−0.0458070	+	0.0793400i
$465$	−7.35748	−	12.7435i	−0.341195	−	0.590967i
$466$	−11.4770	−	19.8787i	−0.531661	−	0.920863i
$467$	−10.4162	−	18.0413i	−0.482003	−	0.834854i	0.517784	−	0.855512i	$-0.326757\pi$
$467$	−10.4162	−	18.0413i	−0.482003	−	0.834854i	−0.999787	+	0.0206579i	$0.993424\pi$
$468$	−1.18858	−	2.88184i	−0.0549421	−	0.133213i
$469$	14.4168	−	3.08817i	0.665706	−	0.142598i
$470$	14.0712	−	24.3720i	0.649056	−	1.12420i
$471$	18.3008			0.843254
$472$	15.7284			0.723957
$473$	−3.47983	+	6.02724i	−0.160003	+	0.277133i
$474$	2.13466	−	3.69733i	0.0980480	−	0.169824i
$475$	1.18743	+	2.05669i	0.0544831	+	0.0943674i
$476$	0.995929	−	3.08169i	0.0456483	−	0.141249i
$477$	3.39224	+	5.87554i	0.155320	+	0.269022i
$478$	−18.5083			−0.846552
$479$	15.4439	+	26.7496i	0.705650	+	1.22222i	0.966456	+	0.256831i	$0.0826783\pi$
$479$	15.4439	+	26.7496i	0.705650	+	1.22222i	−0.260806	+	0.965391i	$0.583988\pi$
$480$	−5.33414	+	9.23900i	−0.243469	+	0.421701i
$481$	−17.3683	+	22.5639i	−0.791928	+	1.02882i
$482$	−11.1917			−0.509766
$483$	−15.4772	+	3.31531i	−0.704236	+	0.150852i
$484$	−4.56317	+	7.90363i	−0.207417	+	0.359256i
$485$	18.7695	−	32.5098i	0.852281	−	1.47619i
$486$	0.532778	−	0.922798i	0.0241673	−	0.0418590i
$487$	22.4271			1.01627			0.508135	−	0.861278i	$-0.330335\pi$
$487$	22.4271			1.01627			0.508135	+	0.861278i	$0.330335\pi$
$488$	7.38302	−	12.7878i	0.334214	−	0.578875i
$489$	−6.78823			−0.306974
$490$	1.80024	−	17.6641i	0.0813264	−	0.797982i
$491$	−6.66716	+	11.5479i	−0.300885	+	0.521147i	−0.976337	−	0.216257i	$-0.930615\pi$
$491$	−6.66716	+	11.5479i	−0.300885	+	0.521147i	0.675452	+	0.737404i	$0.263949\pi$
$492$	−9.10056			−0.410285
$493$	0.917077	−	1.58842i	0.0413031	−	0.0715390i
$494$	−5.21882	−	12.6536i	−0.234806	−	0.569313i
$495$	−0.793396	−	1.37420i	−0.0356605	−	0.0617658i
$496$	4.70818	−	8.15481i	0.211404	−	0.366162i
$497$	−31.1476	+	6.67201i	−1.39716	+	0.299280i
$498$	4.49934	+	7.79308i	0.201620	+	0.349216i
$499$	−15.2608	−	26.4324i	−0.683165	−	1.18328i	−0.974010	−	0.226507i	$-0.927269\pi$
$499$	−15.2608	−	26.4324i	−0.683165	−	1.18328i	0.290844	−	0.956770i	$-0.406064\pi$
$500$	−8.91870			−0.398856
$501$	1.65367			0.0738807
$502$	−0.753281	−	1.30472i	−0.0336206	−	0.0582326i
$503$	−12.1432	−	21.0327i	−0.541441	−	0.937803i	−0.998822	−	0.0485320i	$-0.984546\pi$
$503$	−12.1432	−	21.0327i	−0.541441	−	0.937803i	0.457381	−	0.889271i	$-0.348788\pi$
$504$	5.41325	+	5.99299i	0.241126	+	0.266949i
$505$	10.6771	−	18.4932i	0.475123	−	0.822937i
$506$	2.12466	+	3.68002i	0.0944528	+	0.163597i
$507$	9.22024	−	9.16445i	0.409485	−	0.407007i
$508$	4.93193	−	8.54236i	0.218819	−	0.379006i
$509$	23.4638			1.04001			0.520007	−	0.854162i	$-0.325929\pi$
$509$	23.4638			1.04001			0.520007	+	0.854162i	$0.325929\pi$
$510$	−1.79559	+	3.11005i	−0.0795101	+	0.137716i
$511$	−14.3991	−	15.9412i	−0.636978	−	0.705195i
$512$	−16.1262			−0.712684
$513$	−1.78135	+	3.08539i	−0.0786485	+	0.136223i
$514$	−14.6484			−0.646115
$515$	3.78007	−	6.54727i	0.166570	−	0.288507i
$516$	4.51346	−	7.81755i	0.198694	−	0.344148i
$517$	3.69788	−	6.40492i	0.162633	−	0.281688i
$518$	6.84660	−	21.1853i	0.300822	−	0.930831i
$519$	11.9879			0.526209
$520$	−25.9688	−	3.45896i	−1.13881	−	0.151685i
$521$	2.93601	−	5.08531i	0.128629	−	0.222791i	−0.794517	−	0.607242i	$-0.792276\pi$
$521$	2.93601	−	5.08531i	0.128629	−	0.222791i	0.923146	+	0.384451i	$0.125609\pi$
$522$	0.690210	+	1.19548i	0.0302097	+	0.0523247i
$523$	10.0697			0.440316			0.220158	−	0.975464i	$-0.429343\pi$
$523$	10.0697			0.440316			0.220158	+	0.975464i	$0.429343\pi$
$524$	3.72426	+	6.45061i	0.162695	+	0.281796i
$525$	0.542345	−	1.67817i	0.0236699	−	0.0732414i
$526$	−4.25019	−	7.36154i	−0.185317	−	0.320978i
$527$	−4.37591	+	7.57930i	−0.190618	+	0.330159i
$528$	0.507708	−	0.879376i	0.0220952	−	0.0382699i
$529$	12.7906			0.556115
$530$	17.2089			0.747509
$531$	2.57641	−	4.46248i	0.111807	−	0.193655i
$532$	−5.46273	−	6.04776i	−0.236839	−	0.262204i
$533$	−14.4702	−	35.0846i	−0.626773	−	1.51968i
$534$	0.970485	+	1.68093i	0.0419970	+	0.0727409i
$535$	−5.95752	−	10.3187i	−0.257566	−	0.446118i
$536$	8.50493	+	14.7310i	0.367357	+	0.636281i
$537$	−1.33508	+	2.31243i	−0.0576131	+	0.0997888i
$538$	29.4502			1.26969
$539$	0.473099	−	4.64209i	0.0203778	−	0.199949i
$540$	1.02906	+	1.78239i	0.0442838	+	0.0767018i
$541$	19.5150	+	33.8010i	0.839015	+	1.45322i	0.890719	+	0.454555i	$0.150202\pi$
$541$	19.5150	+	33.8010i	0.839015	+	1.45322i	−0.0517032	+	0.998662i	$0.516465\pi$
$542$	10.9955			0.472298
$543$	−0.376045	−	0.651328i	−0.0161376	−	0.0279512i
$544$	6.34503			0.272041
$545$	−39.4825			−1.69125
$546$	−4.37549	+	9.17482i	−0.187254	+	0.392646i
$547$	−30.9149			−1.32183			−0.660913	−	0.750462i	$-0.729831\pi$
$547$	−30.9149			−1.32183			−0.660913	+	0.750462i	$0.729831\pi$
$548$	−7.22346			−0.308571
$549$	−2.41878	−	4.18944i	−0.103231	−	0.178801i
$550$	−0.473472			−0.0201889
$551$	−2.30773	−	3.99710i	−0.0983125	−	0.170282i
$552$	−9.13048	−	15.8145i	−0.388619	−	0.673108i
$553$	10.3655	−	2.22035i	0.440784	−	0.0944187i
$554$	−2.29700			−0.0975901
$555$	9.39968	−	16.2807i	0.398994	−	0.691078i
$556$	−4.17306	−	7.22795i	−0.176977	−	0.306533i
$557$	5.41116	+	9.37241i	0.229278	+	0.397122i	0.957594	−	0.288120i	$-0.0930301\pi$
$557$	5.41116	+	9.37241i	0.229278	+	0.397122i	−0.728316	+	0.685241i	$0.759697\pi$
$558$	−3.29340	−	5.70433i	−0.139421	−	0.241484i
$559$	37.3149	+	4.97021i	1.57825	+	0.210218i
$560$	9.38109	−	2.00949i	0.396423	−	0.0849163i
$561$	−0.471878	+	0.817316i	−0.0199227	+	0.0345071i
$562$	−2.77679			−0.117132
$563$	−33.1161			−1.39568			−0.697839	−	0.716254i	$-0.745855\pi$
$563$	−33.1161			−1.39568			−0.697839	+	0.716254i	$0.745855\pi$
$564$	−4.79628	+	8.30741i	−0.201960	+	0.349805i
$565$	−8.50932	+	14.7386i	−0.357990	+	0.620057i
$566$	−0.922996	−	1.59868i	−0.0387964	−	0.0671974i
$567$	2.58706	−	0.554165i	0.108646	−	0.0232727i
$568$	−18.3750	−	31.8264i	−0.770996	−	1.33540i
$569$	−25.4161			−1.06550			−0.532749	−	0.846273i	$-0.678841\pi$
$569$	−25.4161			−1.06550			−0.532749	+	0.846273i	$0.678841\pi$
$570$	4.51842	+	7.82613i	0.189256	+	0.327800i
$571$	19.9266	−	34.5138i	0.833901	−	1.44436i	−0.0610215	−	0.998136i	$-0.519436\pi$
$571$	19.9266	−	34.5138i	0.833901	−	1.44436i	0.894922	−	0.446222i	$-0.147231\pi$
$572$	−2.05979	−	0.274357i	−0.0861241	−	0.0114714i
$573$	−5.15813			−0.215484
$574$	19.8908	+	22.0210i	0.830228	+	0.919141i
$575$	−1.99395	+	3.45362i	−0.0831534	+	0.144026i
$576$	−3.91100	+	6.77405i	−0.162958	+	0.282252i
$577$	−3.99457	+	6.91879i	−0.166296	+	0.288033i	−0.937115	−	0.349021i	$-0.886514\pi$
$577$	−3.99457	+	6.91879i	−0.166296	+	0.288033i	0.770819	+	0.637054i	$0.219847\pi$
$578$	−15.9786			−0.664621
$579$	1.42313	−	2.46494i	0.0591434	−	0.102439i
$580$	−2.66629			−0.110712
$581$	−6.87099	+	21.2608i	−0.285057	+	0.882047i
$582$	8.40173	−	14.5522i	0.348263	−	0.603209i
$583$	4.52247			0.187302
$584$	12.3915	−	21.4627i	0.512764	−	0.888134i
$585$	−5.23525	+	6.80131i	−0.216451	+	0.281200i
$586$	−17.4960	−	30.3039i	−0.722753	−	1.25184i
$587$	7.56713	−	13.1067i	0.312329	−	0.540969i	−0.666537	−	0.745472i	$-0.732224\pi$
$587$	7.56713	−	13.1067i	0.312329	−	0.540969i	0.978866	+	0.204502i	$0.0655576\pi$
$588$	−0.613626	+	6.02095i	−0.0253055	+	0.248300i
$589$	11.0115	+	19.0725i	0.453722	+	0.785869i
$590$	−6.53510	−	11.3191i	−0.269046	−	0.466001i
$591$	−0.967097			−0.0397810
$592$	12.0300			0.494432
$593$	−10.5712	−	18.3099i	−0.434109	−	0.751898i	0.563114	−	0.826379i	$-0.309603\pi$
$593$	−10.5712	−	18.3099i	−0.434109	−	0.751898i	−0.997222	+	0.0744812i	$0.976270\pi$
$594$	−0.355145	−	0.615128i	−0.0145718	−	0.0252390i
$595$	−8.71904	+	1.86767i	−0.357446	+	0.0765670i
$596$	5.73259	−	9.92913i	0.234816	−	0.406713i
$597$	4.69085	+	8.12478i	0.191984	+	0.332525i
$598$	14.0196	−	18.2135i	0.573306	−	0.744804i
$599$	4.21779	−	7.30543i	0.172334	−	0.298492i	−0.766901	−	0.641765i	$-0.778202\pi$
$599$	4.21779	−	7.30543i	0.172334	−	0.298492i	0.939236	+	0.343273i	$0.111536\pi$
$600$	2.03469			0.0830658
$601$	8.61342	−	14.9189i	0.351349	−	0.608554i	−0.635137	−	0.772399i	$-0.719056\pi$
$601$	8.61342	−	14.9189i	0.351349	−	0.608554i	0.986486	+	0.163845i	$0.0523898\pi$
$602$	−28.7814	+	6.16516i	−1.17304	+	0.251273i
$603$	5.57265			0.226936
$604$	7.10857	−	12.3124i	0.289244	−	0.500985i
$605$	25.1273			1.02157
$606$	4.77933	−	8.27804i	0.194147	−	0.336272i
$607$	−8.29269	+	14.3634i	−0.336590	+	0.582991i	−0.983789	−	0.179330i	$-0.942607\pi$
$607$	−8.29269	+	14.3634i	−0.336590	+	0.582991i	0.647199	+	0.762321i	$0.275940\pi$
$608$	7.98330	−	13.8275i	0.323766	−	0.560779i
$609$	−1.05403	+	3.26147i	−0.0427114	+	0.132161i
$610$	−12.2705			−0.496818
$611$	−39.6531	−	5.28165i	−1.60419	−	0.213673i
$612$	0.612042	−	1.06009i	0.0247403	−	0.0428515i
$613$	8.60287	+	14.9006i	0.347467	+	0.601830i	0.985799	−	0.167931i	$-0.0537086\pi$
$613$	8.60287	+	14.9006i	0.347467	+	0.601830i	−0.638332	+	0.769761i	$0.720375\pi$
$614$	−31.3932			−1.26693
$615$	12.5282	+	21.6995i	0.505185	+	0.875007i
$616$	5.26387	−	1.12755i	0.212087	−	0.0454304i
$617$	24.1220	+	41.7805i	0.971115	+	1.68202i	0.692202	+	0.721704i	$0.256641\pi$
$617$	24.1220	+	41.7805i	0.971115	+	1.68202i	0.278913	+	0.960316i	$0.410026\pi$
$618$	1.69206	−	2.93073i	0.0680645	−	0.117891i
$619$	18.8263	−	32.6081i	0.756694	−	1.31063i	−0.187834	−	0.982201i	$-0.560147\pi$
$619$	18.8263	−	32.6081i	0.756694	−	1.31063i	0.944528	−	0.328431i	$-0.106520\pi$
$620$	12.7224			0.510945
$621$	−5.98253			−0.240071
$622$	−3.76246	+	6.51678i	−0.150861	+	0.261299i
$623$	−1.48204	+	4.58585i	−0.0593766	+	0.183728i
$624$	−5.44425	−	0.725155i	−0.217944	−	0.0290295i
$625$	13.9443	+	24.1522i	0.557772	+	0.966090i
$626$	8.71499	+	15.0948i	0.348321	+	0.603310i
$627$	1.18743	+	2.05669i	0.0474214	+	0.0821363i
$628$	−7.91134	+	13.7028i	−0.315697	+	0.546803i
$629$	−11.1810			−0.445817
$630$	2.06374	−	6.38579i	0.0822212	−	0.254416i
$631$	−9.79240	−	16.9609i	−0.389829	−	0.675204i	0.602597	−	0.798046i	$-0.294133\pi$
$631$	−9.79240	−	16.9609i	−0.389829	−	0.675204i	−0.992426	+	0.122841i	$0.960799\pi$
$632$	6.11491	+	10.5913i	0.243238	+	0.421301i
$633$	20.7513			0.824789
$634$	−10.1026	−	17.4983i	−0.401227	−	0.694945i
$635$	−27.1580			−1.07773
$636$	−5.86581			−0.232594
$637$	−24.1877	+	7.20785i	−0.958353	+	0.285585i
$638$	0.920175			0.0364301
$639$	−12.0398			−0.476285
$640$	−0.747983	−	1.29554i	−0.0295666	−	0.0512109i
$641$	−13.9241			−0.549969			−0.274984	−	0.961449i	$-0.588673\pi$
$641$	−13.9241			−0.549969			−0.274984	+	0.961449i	$0.588673\pi$
$642$	−2.66674	−	4.61893i	−0.105248	−	0.182295i
$643$	10.3893	+	17.9948i	0.409714	+	0.709645i	0.994858	−	0.101284i	$-0.0322952\pi$
$643$	10.3893	+	17.9948i	0.409714	+	0.709645i	−0.585144	+	0.810930i	$0.698962\pi$
$644$	4.20836	−	13.0219i	0.165833	−	0.513133i
$645$	−24.8536			−0.978611
$646$	2.68736	−	4.65464i	0.105733	−	0.183134i
$647$	3.96380	+	6.86551i	0.155833	+	0.269911i	0.933362	−	0.358936i	$-0.116860\pi$
$647$	3.96380	+	6.86551i	0.155833	+	0.269911i	−0.777529	+	0.628847i	$0.783527\pi$
$648$	1.52619	+	2.64344i	0.0599544	+	0.103844i
$649$	−1.71741	−	2.97464i	−0.0674143	−	0.116765i
$650$	0.976455	+	2.36752i	0.0382997	+	0.0928620i
$651$	5.02939	−	15.5624i	0.197117	−	0.609937i
$652$	2.93452	−	5.08274i	0.114925	−	0.199055i
$653$	36.2648			1.41915			0.709576	−	0.704629i	$-0.248887\pi$
$653$	36.2648			1.41915			0.709576	+	0.704629i	$0.248887\pi$
$654$	−17.6734			−0.691085
$655$	10.2539	−	17.7603i	0.400654	−	0.693953i
$656$	−8.01701	+	13.8859i	−0.313012	+	0.542152i
$657$	−4.05962	−	7.03147i	−0.158381	−	0.274324i
$658$	30.5849	−	6.55147i	1.19232	−	0.255403i
$659$	11.6108	+	20.1105i	0.452293	+	0.783395i	0.998528	−	0.0542371i	$-0.0172727\pi$
$659$	11.6108	+	20.1105i	0.452293	+	0.783395i	−0.546235	+	0.837632i	$0.683939\pi$
$660$	1.37193			0.0534022
$661$	9.43649	+	16.3445i	0.367037	+	0.635726i	0.989101	−	0.147240i	$-0.0470390\pi$
$661$	9.43649	+	16.3445i	0.367037	+	0.635726i	−0.622064	+	0.782966i	$0.713706\pi$
$662$	10.1430	−	17.5681i	0.394217	−	0.682804i
$663$	5.06003	+	0.673979i	0.196515	+	0.0261752i
$664$	−25.7775			−1.00036
$665$	−6.90013	+	21.3510i	−0.267575	+	0.827955i
$666$	4.20754	−	7.28767i	0.163039	−	0.282392i
$667$	3.87517	−	6.71198i	0.150047	−	0.259889i
$668$	−0.714876	+	1.23820i	−0.0276594	+	0.0479075i
$669$	−8.11008			−0.313554
$670$	7.06755	−	12.2414i	0.273043	−	0.472925i
$671$	−3.22466			−0.124487
$672$	−11.5942	+	2.48355i	−0.447256	+	0.0958049i
$673$	−6.68396	+	11.5770i	−0.257648	+	0.446259i	−0.965611	−	0.259990i	$-0.916281\pi$
$673$	−6.68396	+	11.5770i	−0.257648	+	0.446259i	0.707964	+	0.706249i	$0.249614\pi$
$674$	2.02869			0.0781423
$675$	0.333295	−	0.577284i	0.0128285	−	0.0222197i
$676$	2.87608	+	10.8655i	0.110619	+	0.417903i
$677$	10.5600	+	18.2904i	0.405853	+	0.702958i	0.994420	−	0.105490i	$-0.0336412\pi$
$677$	10.5600	+	18.2904i	0.405853	+	0.702958i	−0.588567	+	0.808448i	$0.700308\pi$
$678$	−3.80899	+	6.59737i	−0.146283	+	0.253370i
$679$	40.7972	−	8.73900i	1.56565	−	0.335372i
$680$	−5.14363	−	8.90903i	−0.197249	−	0.341646i
$681$	1.09865	+	1.90291i	0.0421002	+	0.0729197i
$682$	−4.39069			−0.168128
$683$	−33.8330			−1.29458			−0.647291	−	0.762243i	$-0.724098\pi$
$683$	−33.8330			−1.29458			−0.647291	+	0.762243i	$0.724098\pi$
$684$	−1.54014	−	2.66760i	−0.0588887	−	0.101998i
$685$	9.94409	+	17.2237i	0.379944	+	0.658083i
$686$	15.9104	−	11.6750i	0.607460	−	0.445754i
$687$	10.1545	−	17.5882i	0.387420	−	0.671030i
$688$	−7.95214	−	13.7735i	−0.303173	−	0.525110i
$689$	−9.32683	−	22.6140i	−0.355324	−	0.861523i
$690$	−7.58738	+	13.1417i	−0.288847	+	0.500297i
$691$	26.3523			1.00249			0.501245	−	0.865306i	$-0.332876\pi$
$691$	26.3523			1.00249			0.501245	+	0.865306i	$0.332876\pi$
$692$	−5.18231	+	8.97602i	−0.197002	+	0.341217i
$693$	0.542345	−	1.67817i	0.0206020	−	0.0637485i
$694$	−22.2493			−0.844573
$695$	−11.4896	+	19.9006i	−0.435825	+	0.754871i
$696$	−3.95434			−0.149889
$697$	7.45122	−	12.9059i	0.282235	−	0.488846i
$698$	−5.11414	+	8.85796i	−0.193573	+	0.335279i
$699$	10.7709	−	18.6557i	0.407392	−	0.705624i
$700$	1.02209	+	1.13155i	0.0386314	+	0.0427686i
$701$	11.2115			0.423453			0.211727	−	0.977329i	$-0.432091\pi$
$701$	11.2115			0.423453			0.211727	+	0.977329i	$0.432091\pi$
$702$	−2.34343	+	3.04444i	−0.0884471	+	0.114905i
$703$	−14.0680	+	24.3664i	−0.530583	+	0.918997i
$704$	2.60703	+	4.51551i	0.0982563	+	0.170185i
$705$	26.4110			0.994696
$706$	−5.76144	−	9.97910i	−0.216835	−	0.375569i
$707$	23.2075	−	4.97118i	0.872807	−	0.186961i
$708$	2.22754	+	3.85822i	0.0837162	+	0.145001i
$709$	−5.75056	+	9.96027i	−0.215967	+	0.374066i	−0.953571	−	0.301168i	$-0.902624\pi$
$709$	−5.75056	+	9.96027i	−0.215967	+	0.374066i	0.737604	+	0.675233i	$0.235957\pi$
$710$	−15.2695	+	26.4475i	−0.573054	+	0.992558i
$711$	4.00665			0.150261
$712$	−5.56008			−0.208373
$713$	−18.4907	+	32.0268i	−0.692481	+	1.19941i
$714$	−3.90287	+	0.836018i	−0.146061	+	0.0312872i
$715$	2.18141	+	5.28907i	0.0815800	+	0.197800i
$716$	−1.15430	−	1.99931i	−0.0431383	−	0.0747176i
$717$	−8.68483	−	15.0426i	−0.324341	−	0.561775i
$718$	15.4447	+	26.7510i	0.576390	+	0.998337i
$719$	−12.0552	+	20.8803i	−0.449585	+	0.778704i	−0.998359	−	0.0572668i	$-0.981761\pi$
$719$	−12.0552	+	20.8803i	−0.449585	+	0.778704i	0.548774	+	0.835971i	$0.315095\pi$
$720$	3.62615			0.135139
$721$	8.21630	−	1.75998i	0.305991	−	0.0655451i
$722$	3.36032	+	5.82024i	0.125058	+	0.216607i
$723$	−5.25156	−	9.09597i	−0.195308	−	0.338283i
$724$	0.650250			0.0241663
$725$	0.431782	+	0.747868i	0.0160360	+	0.0277751i
$726$	11.2476			0.417439
$727$	27.2156			1.00937			0.504686	−	0.863303i	$-0.331608\pi$
$727$	27.2156			1.00937			0.504686	+	0.863303i	$0.331608\pi$
$728$	−16.4940	−	23.9958i	−0.611308	−	0.889343i
$729$	1.00000			0.0370370
$730$	−20.5946			−0.762239
$731$	7.39094	+	12.8015i	0.273364	+	0.473480i
$732$	4.18250			0.154590
$733$	−0.965303	−	1.67195i	−0.0356543	−	0.0617550i	0.847648	−	0.530560i	$-0.178018\pi$
$733$	−0.965303	−	1.67195i	−0.0356543	−	0.0617550i	−0.883302	+	0.468805i	$0.844685\pi$
$734$	17.3543	+	30.0586i	0.640560	+	1.10948i
$735$	15.2011	−	6.82554i	0.560703	−	0.251764i
$736$	26.8113			0.988278
$737$	1.85734	−	3.21700i	0.0684159	−	0.118500i
$738$	5.60794	+	9.71324i	0.206431	+	0.357549i
$739$	−11.3609	−	19.6776i	−0.417916	−	0.723851i	0.577814	−	0.816169i	$-0.303906\pi$
$739$	−11.3609	−	19.6776i	−0.417916	−	0.723851i	−0.995730	+	0.0923172i	$0.970573\pi$
$740$	8.12688	+	14.0762i	0.298750	+	0.517450i
$741$	7.83530	−	10.1791i	0.287837	−	0.373940i
$742$	12.8207	+	14.1938i	0.470664	+	0.521070i
$743$	10.9451	−	18.9574i	0.401535	−	0.695480i	−0.592376	−	0.805662i	$-0.701810\pi$
$743$	10.9451	−	18.9574i	0.401535	−	0.695480i	0.993911	+	0.110182i	$0.0351434\pi$
$744$	18.8685			0.691752
$745$	−31.5668			−1.15652
$746$	12.7215	−	22.0344i	0.465769	−	0.806735i
$747$	−4.22253	+	7.31363i	−0.154494	+	0.267592i
$748$	−0.407981	−	0.706644i	−0.0149173	−	0.0258375i
$749$	4.07241	−	12.6012i	0.148803	−	0.460438i
$750$	5.49587	+	9.51913i	0.200681	+	0.347590i
$751$	24.6771			0.900480			0.450240	−	0.892908i	$-0.351338\pi$
$751$	24.6771			0.900480			0.450240	+	0.892908i	$0.351338\pi$
$752$	8.45044	+	14.6366i	0.308156	+	0.533741i
$753$	0.706938	−	1.22445i	0.0257622	−	0.0446215i
$754$	−1.89770	−	4.60120i	−0.0691103	−	0.167566i
$755$	−39.1438			−1.42459
$756$	−0.703441	+	2.17665i	−0.0255839	+	0.0791639i
$757$	1.04346	−	1.80733i	0.0379252	−	0.0656884i	−0.846440	−	0.532484i	$-0.821258\pi$
$757$	1.04346	−	1.80733i	0.0379252	−	0.0656884i	0.884365	+	0.466796i	$0.154592\pi$
$758$	−5.21489	+	9.03246i	−0.189413	+	0.328074i
$759$	−1.99395	+	3.45362i	−0.0723757	+	0.125358i
$760$	−25.8868			−0.939014
$761$	10.7988	−	18.7040i	0.391455	−	0.678020i	−0.601186	−	0.799109i	$-0.705305\pi$
$761$	10.7988	−	18.7040i	0.391455	−	0.678020i	0.992642	+	0.121088i	$0.0386384\pi$
$762$	−12.1566			−0.440387
$763$	−29.4147	−	32.5648i	−1.06488	−	1.17893i
$764$	2.22984	−	3.86219i	0.0806727	−	0.139729i
$765$	−3.37024			−0.121851
$766$	−7.91537	+	13.7098i	−0.285994	+	0.495356i
$767$	−11.3324	+	14.7223i	−0.409189	+	0.531593i
$768$	−8.15681	−	14.1280i	−0.294334	−	0.509801i
$769$	2.39533	−	4.14883i	0.0863777	−	0.149611i	−0.819600	−	0.572937i	$-0.805804\pi$
$769$	2.39533	−	4.14883i	0.0863777	−	0.149611i	0.905977	+	0.423326i	$0.139137\pi$
$770$	−2.99858	−	3.31971i	−0.108061	−	0.119634i
$771$	−6.87362	−	11.9055i	−0.247547	−	0.428765i
$772$	1.23043	+	2.13116i	0.0442841	+	0.0767023i
$773$	10.5896			0.380882			0.190441	−	0.981699i	$-0.439008\pi$
$773$	10.5896			0.380882			0.190441	+	0.981699i	$0.439008\pi$
$774$	−11.1251			−0.399885
$775$	−2.06028	−	3.56852i	−0.0740076	−	0.128185i
$776$	24.0675	+	41.6862i	0.863974	+	1.49645i
$777$	20.4310	−	4.37644i	0.732957	−	0.157004i
$778$	−10.2585	+	17.7682i	−0.367784	+	0.637021i
$779$	−18.7502	−	32.4764i	−0.671797	−	1.16359i
$780$	−2.82936	−	6.86011i	−0.101307	−	0.245631i
$781$	−4.01279	+	6.95036i	−0.143589	+	0.248703i
$782$	9.02529			0.322744
$783$	−0.647747	+	1.12193i	−0.0231486	+	0.0400945i
$784$	8.64636	+	6.24036i	0.308798	+	0.222870i
$785$	43.5642			1.55487
$786$	4.58992	−	7.94998i	0.163717	−	0.283566i
$787$	−30.2310			−1.07762			−0.538810	−	0.842427i	$-0.681126\pi$
$787$	−30.2310			−1.07762			−0.538810	+	0.842427i	$0.681126\pi$
$788$	0.418072	−	0.724121i	0.0148932	−	0.0257958i
$789$	3.98871	−	6.90864i	0.142002	−	0.245954i
$790$	5.08146	−	8.80135i	0.180790	−	0.313138i
$791$	−18.4957	+	3.96190i	−0.657632	+	0.140869i
$792$	2.03469			0.0722995
$793$	6.65032	+	16.1245i	0.236160	+	0.572596i
$794$	−20.4059	+	35.3441i	−0.724179	+	1.25432i
$795$	8.07510	+	13.9865i	0.286394	+	0.496050i
$796$	−8.11133			−0.287498
$797$	−4.57126	−	7.91765i	−0.161922	−	0.280457i	0.773636	−	0.633630i	$-0.218436\pi$
$797$	−4.57126	−	7.91765i	−0.161922	−	0.280457i	−0.935558	+	0.353173i	$0.885103\pi$
$798$	−3.08868	+	9.55725i	−0.109338	+	0.338323i
$799$	−7.85406	−	13.6036i	−0.277857	−	0.481262i
$800$	−1.49370	+	2.58716i	−0.0528102	+	0.0914699i
$801$	−0.910778	+	1.57751i	−0.0321808	+	0.0557387i
$802$	37.9460			1.33992
$803$	−5.41221			−0.190993
$804$	−2.40903	+	4.17257i	−0.0849601	+	0.147155i
$805$	−36.8428	+	7.89196i	−1.29854	+	0.278155i
$806$	9.05505	+	21.9550i	0.318951	+	0.773332i
$807$	13.8192	+	23.9355i	0.486457	+	0.842569i
$808$	13.6908	+	23.7132i	0.481641	+	0.834227i
$809$	17.1951	+	29.7828i	0.604547	+	1.04711i	0.992123	+	0.125269i	$0.0399794\pi$
$809$	17.1951	+	29.7828i	0.604547	+	1.04711i	−0.387575	+	0.921838i	$0.626687\pi$
$810$	1.26826	−	2.19668i	0.0445620	−	0.0771836i
$811$	−11.9106			−0.418237			−0.209119	−	0.977890i	$-0.567060\pi$
$811$	−11.9106			−0.418237			−0.209119	+	0.977890i	$0.567060\pi$
$812$	−1.98640	−	2.19913i	−0.0697089	−	0.0771743i
$813$	5.15953	+	8.93656i	0.180952	+	0.313419i
$814$	−2.80470	−	4.85789i	−0.0983049	−	0.170269i
$815$	−16.1591			−0.566029
$816$	−1.07834	−	1.86774i	−0.0377494	−	0.0653839i
$817$	37.1970			1.30136
$818$	−3.37218			−0.117906
$819$	−9.50994	+	0.749025i	−0.332304	+	0.0261730i
$820$	−21.6635			−0.756523
$821$	2.95276			0.103052			0.0515261	−	0.998672i	$-0.483591\pi$
$821$	2.95276			0.103052			0.0515261	+	0.998672i	$0.483591\pi$
$822$	4.45123	+	7.70976i	0.155255	+	0.268909i
$823$	−42.3055			−1.47468			−0.737338	−	0.675524i	$-0.763917\pi$
$823$	−42.3055			−1.47468			−0.737338	+	0.675524i	$0.763917\pi$
$824$	4.84705	+	8.39534i	0.168855	+	0.292466i
$825$	−0.222171	−	0.384812i	−0.00773501	−	0.0133974i
$826$	4.46723	−	13.8229i	0.155435	−	0.480960i
$827$	−23.0380			−0.801109			−0.400554	−	0.916273i	$-0.631182\pi$
$827$	−23.0380			−0.801109			−0.400554	+	0.916273i	$0.631182\pi$
$828$	2.58622	−	4.47947i	0.0898774	−	0.155672i
$829$	−8.23948	−	14.2712i	−0.286169	−	0.495659i	0.686723	−	0.726919i	$-0.259049\pi$
$829$	−8.23948	−	14.2712i	−0.286169	−	0.495659i	−0.972892	+	0.231260i	$0.925715\pi$
$830$	10.7105	+	18.5511i	0.371767	+	0.643919i
$831$	−1.07784	−	1.86687i	−0.0373899	−	0.0647611i
$832$	17.2026	−	22.3486i	0.596392	−	0.774797i
$833$	−8.03616	−	5.79996i	−0.278436	−	0.200957i
$834$	−5.14304	+	8.90801i	−0.178089	+	0.308459i
$835$	3.93651			0.136228
$836$	−2.05328			−0.0710143
$837$	3.09078	−	5.35339i	0.106833	−	0.185040i
$838$	11.7776	−	20.3994i	0.406851	−	0.704686i
$839$	−8.66147	−	15.0021i	−0.299027	−	0.517930i	0.676887	−	0.736087i	$-0.263329\pi$
$839$	−8.66147	−	15.0021i	−0.299027	−	0.517930i	−0.975914	+	0.218157i	$0.929995\pi$
$840$	12.8860	+	14.2661i	0.444611	+	0.492226i
$841$	13.6608	+	23.6613i	0.471064	+	0.815906i
$842$	8.25818			0.284596
$843$	−1.30298	−	2.25682i	−0.0448770	−	0.0777292i
$844$	−8.97068	+	15.5377i	−0.308784	+	0.534829i
$845$	21.9484	−	21.8156i	0.755049	−	0.750480i
$846$	11.8222			0.406457
$847$	18.7200	+	20.7248i	0.643225	+	0.712112i
$848$	−5.16740	+	8.95020i	−0.177449	+	0.307351i
$849$	0.866211	−	1.50032i	0.0297283	−	0.0514909i
$850$	−0.502812	+	0.870896i	−0.0172463	+	0.0298715i
$851$	−47.2462			−1.61958
$852$	5.20473	−	9.01486i	0.178311	−	0.308844i
$853$	−47.0511			−1.61100			−0.805499	−	0.592597i	$-0.798103\pi$
$853$	−47.0511			−1.61100			−0.805499	+	0.592597i	$0.798103\pi$
$854$	−9.14158	−	10.1206i	−0.312818	−	0.346320i
$855$	−4.24043	+	7.34465i	−0.145020	+	0.251182i
$856$	15.2782			0.522200
$857$	−11.3602	+	19.6764i	−0.388056	+	0.672133i	−0.992188	−	0.124751i	$-0.960187\pi$
$857$	−11.3602	+	19.6764i	−0.388056	+	0.672133i	0.604132	+	0.796884i	$0.293520\pi$
$858$	0.976455	+	2.36752i	0.0333356	+	0.0808260i
$859$	−18.8507	−	32.6504i	−0.643177	−	1.11402i	−0.984719	−	0.174149i	$-0.944282\pi$
$859$	−18.8507	−	32.6504i	−0.643177	−	1.11402i	0.341542	−	0.939867i	$-0.389051\pi$
$860$	10.7441	−	18.6094i	0.366371	−	0.634574i
$861$	−8.56395	+	26.4993i	−0.291859	+	0.903094i
$862$	18.4123	+	31.8910i	0.627124	+	1.08621i
$863$	−19.9474	−	34.5499i	−0.679018	−	1.17609i	−0.975277	−	0.220986i	$-0.929072\pi$
$863$	−19.9474	−	34.5499i	−0.679018	−	1.17609i	0.296259	−	0.955108i	$-0.404261\pi$
$864$	−4.48160			−0.152467
$865$	28.5367			0.970276
$866$	−13.0413	−	22.5882i	−0.443161	−	0.767577i
$867$	−7.49776	−	12.9865i	−0.254637	−	0.441045i
$868$	9.47826	+	10.4933i	0.321713	+	0.356167i
$869$	1.33540	−	2.31298i	0.0453003	−	0.0784624i
$870$	1.64302	+	2.84579i	0.0557035	+	0.0964814i
$871$	−19.9166	−	2.65282i	−0.674848	−	0.0898874i
$872$	25.3135	−	43.8443i	0.857225	−	1.48476i
$873$	15.7697			0.533723
$874$	11.3556	−	19.6685i	0.384109	−	0.665296i
$875$	−8.39281	+	25.9698i	−0.283729	+	0.877938i
$876$	7.01982			0.237178
$877$	7.62722	−	13.2107i	0.257553	−	0.446095i	−0.708033	−	0.706179i	$-0.750417\pi$
$877$	7.62722	−	13.2107i	0.257553	−	0.446095i	0.965586	+	0.260085i	$0.0837505\pi$
$878$	−11.4302			−0.385750
$879$	16.4196	−	28.4396i	0.553819	−	0.959243i
$880$	1.20858	−	2.09332i	0.0407412	−	0.0705658i
$881$	−25.8195	+	44.7207i	−0.869881	+	1.50668i	−0.00776438	+	0.999970i	$0.502472\pi$
$881$	−25.8195	+	44.7207i	−0.869881	+	1.50668i	−0.862117	+	0.506709i	$0.830862\pi$
$882$	6.80443	−	3.05529i	0.229117	−	0.102877i
$883$	27.4588			0.924062			0.462031	−	0.886864i	$-0.347121\pi$
$883$	27.4588			0.924062			0.462031	+	0.886864i	$0.347121\pi$
$884$	−2.69208	+	3.49738i	−0.0905444	+	0.117630i
$885$	6.13305	−	10.6227i	0.206160	−	0.357080i
$886$	21.2432	+	36.7943i	0.713679	+	1.23613i
$887$	32.8632			1.10344			0.551718	−	0.834031i	$-0.313972\pi$
$887$	32.8632			1.10344			0.551718	+	0.834031i	$0.313972\pi$
$888$	12.0529	+	20.8762i	0.404468	+	0.700559i
$889$	−20.2328	−	22.3996i	−0.678586	−	0.751260i
$890$	2.31020	+	4.00138i	0.0774381	+	0.134127i
$891$	0.333295	−	0.577284i	0.0111658	−	0.0193397i
$892$	3.50595	−	6.07249i	0.117388	−	0.203322i
$893$	−39.5279			−1.32275
$894$	−14.1301			−0.472582
$895$	−3.17811	+	5.50465i	−0.106233	+	0.184000i
$896$	0.511302	−	1.58212i	0.0170814	−	0.0528548i
$897$	21.3815	+	2.84794i	0.713907	+	0.0950899i
$898$	16.2806	+	28.1989i	0.543291	+	0.941008i
$899$	4.00409	+	6.93528i	0.133544	+	0.231305i
$900$	0.288164	+	0.499115i	0.00960547	+	0.0166372i
$901$	4.80272	−	8.31856i	0.160002	−	0.277131i
$902$	7.47640			0.248937
$903$	−18.5161	−	20.4990i	−0.616176	−	0.682166i
$904$	−10.9112	−	18.8988i	−0.362901	−	0.628564i
$905$	−0.895159	−	1.55046i	−0.0297561	−	0.0515391i
$906$	−17.5218			−0.582121
$907$	−22.4096	−	38.8145i	−0.744098	−	1.28882i	−0.950615	−	0.310372i	$-0.899546\pi$
$907$	−22.4096	−	38.8145i	−0.744098	−	1.28882i	0.206517	−	0.978443i	$-0.433787\pi$
$908$	−1.89976			−0.0630458
$909$	8.97058			0.297535
$910$	−10.4157	+	21.8403i	−0.345276	+	0.723999i
$911$	31.4169			1.04089			0.520445	−	0.853895i	$-0.325766\pi$
$911$	31.4169			1.04089			0.520445	+	0.853895i	$0.325766\pi$
$912$	−5.42706			−0.179708
$913$	2.81470	+	4.87520i	0.0931528	+	0.161345i
$914$	−17.0858			−0.565149
$915$	−5.75780	−	9.97280i	−0.190347	−	0.329691i
$916$	8.77952	+	15.2066i	0.290084	+	0.502439i
$917$	22.2878	−	4.77417i	0.736006	−	0.157657i
$918$	−1.50861			−0.0497915
$919$	−18.6931	+	32.3774i	−0.616628	+	1.06803i	0.373469	+	0.927643i	$0.378168\pi$
$919$	−18.6931	+	32.3774i	−0.616628	+	1.06803i	−0.990097	+	0.140388i	$0.955165\pi$
$920$	−21.7347	−	37.6457i	−0.716573	−	1.24114i
$921$	−14.7309	−	25.5147i	−0.485400	−	0.840737i
$922$	21.0076	+	36.3863i	0.691849	+	1.19832i
$923$	43.0299	+	5.73144i	1.41635	+	0.188653i
$924$	1.02209	+	1.13155i	0.0336243	+	0.0372253i
$925$	2.63215	−	4.55902i	0.0865446	−	0.149900i
$926$	−27.7014			−0.910326
$927$	3.17592			0.104311
$928$	2.90295	−	5.02805i	0.0952938	−	0.165054i
$929$	11.5787	−	20.0549i	0.379884	−	0.657978i	−0.611161	−	0.791506i	$-0.709297\pi$
$929$	11.5787	−	20.0549i	0.379884	−	0.657978i	0.991045	+	0.133528i	$0.0426306\pi$
$930$	−7.83980	−	13.5789i	−0.257077	−	0.445271i
$931$	−22.7507	+	10.2154i	−0.745624	+	0.334796i
$932$	9.31241	+	16.1296i	0.305038	+	0.528342i
$933$	−7.06198			−0.231199
$934$	−11.0990	−	19.2241i	−0.363171	−	0.629030i
$935$	−1.12329	+	1.94559i	−0.0367354	+	0.0636275i
$936$	−4.19620	−	10.1742i	−0.137157	−	0.332553i
$937$	−20.1142			−0.657103			−0.328552	−	0.944486i	$-0.606560\pi$
$937$	−20.1142			−0.657103			−0.328552	+	0.944486i	$0.606560\pi$
$938$	15.3619	−	3.29061i	0.501584	−	0.107442i
$939$	−8.17883	+	14.1661i	−0.266906	+	0.462295i
$940$	−11.4174	+	19.7755i	−0.372393	+	0.645004i
$941$	9.41116	−	16.3006i	0.306795	−	0.531384i	−0.670864	−	0.741580i	$-0.734077\pi$
$941$	9.41116	−	16.3006i	0.306795	−	0.531384i	0.977659	+	0.210196i	$0.0674101\pi$
$942$	19.5005			0.635360
$943$	31.4856	−	54.5347i	1.02531	−	1.77589i
$944$	7.84929			0.255473
$945$	6.15840	−	1.31917i	0.200333	−	0.0429125i
$946$	−3.70795	+	6.42236i	−0.120556	+	0.208809i
$947$	−25.3469			−0.823663			−0.411832	−	0.911260i	$-0.635111\pi$
$947$	−25.3469			−0.823663			−0.411832	+	0.911260i	$0.635111\pi$
$948$	−1.73206	+	3.00001i	−0.0562546	+	0.0974359i
$949$	11.1617	+	27.0629i	0.362326	+	0.878500i
$950$	1.26527	+	2.19152i	0.0410509	+	0.0711022i
$951$	9.48109	−	16.4217i	0.307446	−	0.532511i
$952$	3.51606	−	10.8797i	0.113956	−	0.352613i
$953$	−0.132751	−	0.229931i	−0.00430021	−	0.00744818i	0.863867	−	0.503719i	$-0.168035\pi$
$953$	−0.132751	−	0.229931i	−0.00430021	−	0.00744818i	−0.868168	+	0.496271i	$0.834702\pi$
$954$	3.61462	+	6.26071i	0.117028	+	0.202698i
$955$	−12.2787			−0.397330
$956$	15.0177			0.485706
$957$	0.431782	+	0.747868i	0.0139575	+	0.0241751i
$958$	16.4563	+	28.5032i	0.531680	+	0.920897i
$959$	−6.79753	+	21.0335i	−0.219504	+	0.679207i
$960$	−9.30997	+	16.1253i	−0.300478	+	0.520443i
$961$	−3.60583	−	6.24549i	−0.116317	−	0.201467i
$962$	−18.5069	+	24.0431i	−0.596687	+	0.775180i
$963$	2.50268	−	4.33476i	0.0806476	−	0.139686i
$964$	9.08091			0.292476
$965$	3.38771	−	5.86769i	0.109054	−	0.188888i
$966$	−16.4918	+	3.53264i	−0.530615	+	0.113661i
$967$	15.3845			0.494732			0.247366	−	0.968922i	$-0.420435\pi$
$967$	15.3845			0.494732			0.247366	+	0.968922i	$0.420435\pi$
$968$	−16.1099	+	27.9032i	−0.517793	+	0.896844i
$969$	5.04405			0.162038
$970$	20.0000	−	34.6410i	0.642161	−	1.11226i
$971$	23.2590	−	40.2858i	0.746418	−	1.29283i	−0.203112	−	0.979156i	$-0.565105\pi$
$971$	23.2590	−	40.2858i	0.746418	−	1.29283i	0.949529	−	0.313678i	$-0.101561\pi$
$972$	−0.432296	+	0.748758i	−0.0138659	+	0.0240164i
$973$	−24.9736	+	5.34949i	−0.800617	+	0.171497i
$974$	23.8973			0.765720
$975$	−1.46600	+	1.90454i	−0.0469497	+	0.0609942i
$976$	3.68452	−	6.38177i	0.117939	−	0.204276i
$977$	−5.27473	−	9.13611i	−0.168754	−	0.292290i	0.769228	−	0.638974i	$-0.220641\pi$
$977$	−5.27473	−	9.13611i	−0.168754	−	0.292290i	−0.937982	+	0.346684i	$0.887308\pi$
$978$	−7.23323			−0.231293
$979$	0.607116	+	1.05156i	0.0194035	+	0.0336079i
$980$	−1.46071	+	14.3326i	−0.0466607	+	0.457839i
$981$	−8.29305	−	14.3640i	−0.264777	−	0.458607i
$982$	−7.10423	+	12.3049i	−0.226705	+	0.392665i
$983$	−16.6152	+	28.7783i	−0.529942	+	0.917887i	0.469448	+	0.882960i	$0.344453\pi$
$983$	−16.6152	+	28.7783i	−0.529942	+	0.917887i	−0.999390	+	0.0349264i	$0.988880\pi$
$984$	−32.1289			−1.02423
$985$	−2.30214			−0.0733521
$986$	0.977196	−	1.69255i	0.0311203	−	0.0539019i
$987$	19.6763	+	21.7835i	0.626304	+	0.693378i
$988$	4.23455	+	10.2671i	0.134719	+	0.326641i
$989$	31.2309	+	54.0934i	0.993083	+	1.72007i
$990$	−0.845407	−	1.46429i	−0.0268688	−	0.0465381i
$991$	−21.8815	−	37.8999i	−0.695089	−	1.20393i	−0.970151	−	0.242503i	$-0.922032\pi$
$991$	−21.8815	−	37.8999i	−0.695089	−	1.20393i	0.275061	−	0.961427i	$-0.411302\pi$
$992$	−13.8516	+	23.9918i	−0.439790	+	0.761739i
$993$	19.0379			0.604149
$994$	−33.1895	+	7.10940i	−1.05271	+	0.225496i
$995$	11.1664	+	19.3407i	0.353998	+	0.613142i
$996$	−3.65076	−	6.32330i	−0.115679	−	0.200362i
$997$	52.0822			1.64946			0.824729	−	0.565528i	$-0.191327\pi$
$997$	52.0822			1.64946			0.824729	+	0.565528i	$0.191327\pi$
$998$	−16.2612	−	28.1652i	−0.514739	−	0.891554i
$999$	7.89736			0.249861

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.l.b.256.6	yes	16
3.2	odd	2		819.2.s.e.802.3		16
7.2	even	3		273.2.j.b.100.3	✓	16
13.3	even	3		273.2.j.b.172.3	yes	16
21.2	odd	6		819.2.n.e.100.6		16
39.29	odd	6		819.2.n.e.172.6		16
91.16	even	3	inner	273.2.l.b.16.6	yes	16
273.107	odd	6		819.2.s.e.289.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.3	✓	16	7.2	even	3
273.2.j.b.172.3	yes	16	13.3	even	3
273.2.l.b.16.6	yes	16	91.16	even	3	inner
273.2.l.b.256.6	yes	16	1.1	even	1	trivial
819.2.n.e.100.6		16	21.2	odd	6
819.2.n.e.172.6		16	39.29	odd	6
819.2.s.e.289.3		16	273.107	odd	6
819.2.s.e.802.3		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.06556 q^{2} +(0.500000 + 0.866025i) q^{3} -0.864591 q^{4} +(1.19023 + 2.06154i) q^{5} +(0.532778 + 0.922798i) q^{6} +(-0.813611 + 2.51755i) q^{7} -3.05238 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.26826 + 2.19668i) q^{10} +(0.333295 + 0.577284i) q^{11} +(-0.432296 - 0.748758i) q^{12} +(2.19926 - 2.85714i) q^{13} +(-0.866948 + 2.68258i) q^{14} +(-1.19023 + 2.06154i) q^{15} -1.52330 q^{16} +1.41579 q^{17} +(-0.532778 + 0.922798i) q^{18} +(1.78135 - 3.08539i) q^{19} +(-1.02906 - 1.78239i) q^{20} +(-2.58706 + 0.554165i) q^{21} +(0.355145 + 0.615128i) q^{22} +5.98253 q^{23} +(-1.52619 - 2.64344i) q^{24} +(-0.333295 + 0.577284i) q^{25} +(2.34343 - 3.04444i) q^{26} -1.00000 q^{27} +(0.703441 - 2.17665i) q^{28} +(0.647747 - 1.12193i) q^{29} +(-1.26826 + 2.19668i) q^{30} +(-3.09078 + 5.35339i) q^{31} +4.48160 q^{32} +(-0.333295 + 0.577284i) q^{33} +1.50861 q^{34} +(-6.15840 + 1.31917i) q^{35} +(0.432296 - 0.748758i) q^{36} -7.89736 q^{37} +(1.89813 - 3.28765i) q^{38} +(3.57399 + 0.476043i) q^{39} +(-3.63304 - 6.29260i) q^{40} +(5.26293 - 9.11566i) q^{41} +(-2.75666 + 0.590493i) q^{42} +(5.22034 + 9.04190i) q^{43} +(-0.288164 - 0.499115i) q^{44} -2.38046 q^{45} +6.37472 q^{46} +(-5.54746 - 9.60848i) q^{47} +(-0.761650 - 1.31922i) q^{48} +(-5.67607 - 4.09661i) q^{49} +(-0.355145 + 0.615128i) q^{50} +(0.707897 + 1.22611i) q^{51} +(-1.90146 + 2.47026i) q^{52} +(3.39224 - 5.87554i) q^{53} -1.06556 q^{54} +(-0.793396 + 1.37420i) q^{55} +(2.48345 - 7.68451i) q^{56} +3.56270 q^{57} +(0.690210 - 1.19548i) q^{58} -5.15282 q^{59} +(1.02906 - 1.78239i) q^{60} +(-2.41878 + 4.18944i) q^{61} +(-3.29340 + 5.70433i) q^{62} +(-1.77345 - 1.96338i) q^{63} +7.82199 q^{64} +(8.50773 + 1.13320i) q^{65} +(-0.355145 + 0.615128i) q^{66} +(-2.78633 - 4.82606i) q^{67} -1.22408 q^{68} +(2.99126 + 5.18102i) q^{69} +(-6.56212 + 1.40565i) q^{70} +(6.01988 + 10.4267i) q^{71} +(1.52619 - 2.64344i) q^{72} +(-4.05962 + 7.03147i) q^{73} -8.41508 q^{74} -0.666590 q^{75} +(-1.54014 + 2.66760i) q^{76} +(-1.72451 + 0.369401i) q^{77} +(3.80828 + 0.507250i) q^{78} +(-2.00333 - 3.46986i) q^{79} +(-1.81308 - 3.14034i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.60794 - 9.71324i) q^{82} +8.44505 q^{83} +(2.23675 - 0.479126i) q^{84} +(1.68512 + 2.91872i) q^{85} +(5.56257 + 9.63465i) q^{86} +1.29549 q^{87} +(-1.01734 - 1.76209i) q^{88} +1.82156 q^{89} -2.53651 q^{90} +(5.40364 + 7.86134i) q^{91} -5.17244 q^{92} -6.18156 q^{93} +(-5.91112 - 10.2384i) q^{94} +8.48087 q^{95} +(2.24080 + 3.88118i) q^{96} +(-7.88484 - 13.6569i) q^{97} +(-6.04817 - 4.36516i) q^{98} -0.666590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9} - 4 q^{10} - 2 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} + 12 q^{16} + 4 q^{17} - 11 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} - 8 q^{23} + 6 q^{24} + 2 q^{25}+ \cdots + 4 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9 - 4 * q^10 - 2 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 + 12 * q^16 + 4 * q^17 - 11 * q^19 - 20 * q^20 - q^21 + 7 * q^22 - 8 * q^23 + 6 * q^24 + 2 * q^25 + 33 * q^26 - 16 * q^27 - q^28 + 15 * q^29 + 4 * q^30 + 3 * q^31 - 6 * q^32 + 2 * q^33 - 68 * q^34 - 6 * q^36 - 8 * q^37 + 2 * q^38 + 4 * q^39 - 25 * q^40 + 19 * q^41 - 17 * q^42 + 11 * q^43 - 16 * q^44 - 4 * q^46 + 5 * q^47 + 6 * q^48 + 7 * q^49 - 7 * q^50 + 2 * q^51 - 18 * q^52 + 36 * q^53 - 15 * q^55 - 51 * q^56 - 22 * q^57 + 20 * q^58 + 34 * q^59 + 20 * q^60 - 22 * q^61 - 6 * q^62 - 2 * q^63 - 20 * q^64 - 24 * q^65 - 7 * q^66 + 26 * q^67 - 10 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 - 6 * q^72 - 6 * q^73 - 30 * q^74 + 4 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 - 28 * q^80 - 8 * q^81 - q^82 + 36 * q^83 - 8 * q^84 - 4 * q^85 + 16 * q^86 + 30 * q^87 + 24 * q^88 - 40 * q^89 + 8 * q^90 - 10 * q^91 - 94 * q^92 + 6 * q^93 - 20 * q^94 - 3 * q^96 + 7 * q^97 + 18 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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