LMFDB - Embedded newform 273.2.j.b.172.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(100,273)]

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, 4]))

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

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

chi := DirichletCharacter("273.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.j (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			172.3
Root			$-0.532778 + 0.922798i$ of defining polynomial
Character	$\chi$	$=$	273.172
Dual form			273.2.j.b.100.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.532778 + 0.922798i) q^{2} -1.00000 q^{3} +(0.432296 + 0.748758i) q^{4} +(1.19023 + 2.06154i) q^{5} +(0.532778 - 0.922798i) q^{6} +(2.58706 - 0.554165i) q^{7} -3.05238 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.532778 + 0.922798i) q^{2} -1.00000 q^{3} +(0.432296 + 0.748758i) q^{4} +(1.19023 + 2.06154i) q^{5} +(0.532778 - 0.922798i) q^{6} +(2.58706 - 0.554165i) q^{7} -3.05238 q^{8} +1.00000 q^{9} -2.53651 q^{10} -0.666590 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} +(0.761650 - 1.31922i) q^{16} +(-0.707897 - 1.22611i) q^{17} +(-0.532778 + 0.922798i) q^{18} -3.56270 q^{19} +(-1.02906 + 1.78239i) q^{20} +(-2.58706 + 0.554165i) q^{21} +(0.355145 - 0.615128i) q^{22} +(-2.99126 + 5.18102i) q^{23} +3.05238 q^{24} +(-0.333295 + 0.577284i) q^{25} +(-3.80828 + 0.507250i) q^{26} -1.00000 q^{27} +(1.53331 + 1.69752i) q^{28} +(0.647747 + 1.12193i) q^{29} +2.53651 q^{30} +(-3.09078 + 5.35339i) q^{31} +(-2.24080 - 3.88118i) q^{32} +0.666590 q^{33} +1.50861 q^{34} +(4.22163 + 4.67375i) q^{35} +(0.432296 + 0.748758i) q^{36} +(3.94868 - 6.83932i) q^{37} +(1.89813 - 3.28765i) q^{38} +(-2.19926 - 2.85714i) q^{39} +(-3.63304 - 6.29260i) q^{40} +(5.26293 + 9.11566i) q^{41} +(0.866948 - 2.68258i) q^{42} +(5.22034 - 9.04190i) q^{43} +(-0.288164 - 0.499115i) q^{44} +(1.19023 + 2.06154i) q^{45} +(-3.18736 - 5.52067i) q^{46} +(-5.54746 - 9.60848i) q^{47} +(-0.761650 + 1.31922i) q^{48} +(6.38580 - 2.86732i) q^{49} +(-0.355145 - 0.615128i) q^{50} +(0.707897 + 1.22611i) q^{51} +(-1.18858 + 2.88184i) q^{52} +(3.39224 - 5.87554i) q^{53} +(0.532778 - 0.922798i) q^{54} +(-0.793396 - 1.37420i) q^{55} +(-7.89671 + 1.69152i) q^{56} +3.56270 q^{57} -1.38042 q^{58} +(2.57641 + 4.46248i) q^{59} +(1.02906 - 1.78239i) q^{60} +4.83755 q^{61} +(-3.29340 - 5.70433i) q^{62} +(2.58706 - 0.554165i) q^{63} +7.82199 q^{64} +(-3.27249 + 7.93451i) q^{65} +(-0.355145 + 0.615128i) q^{66} +5.57265 q^{67} +(0.612042 - 1.06009i) q^{68} +(2.99126 - 5.18102i) q^{69} +(-6.56212 + 1.40565i) q^{70} +(6.01988 - 10.4267i) q^{71} -3.05238 q^{72} +(-4.05962 + 7.03147i) q^{73} +(4.20754 + 7.28767i) q^{74} +(0.333295 - 0.577284i) 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} +3.62615 q^{80} +1.00000 q^{81} -11.2159 q^{82} +8.44505 q^{83} +(-1.53331 - 1.69752i) q^{84} +(1.68512 - 2.91872i) q^{85} +(5.56257 + 9.63465i) q^{86} +(-0.647747 - 1.12193i) q^{87} +2.03469 q^{88} +(-0.910778 + 1.57751i) q^{89} -2.53651 q^{90} +(7.27295 + 6.17286i) q^{91} -5.17244 q^{92} +(3.09078 - 5.35339i) q^{93} +11.8222 q^{94} +(-4.24043 - 7.34465i) q^{95} +(2.24080 + 3.88118i) q^{96} +(-7.88484 + 13.6569i) q^{97} +(-0.756256 + 7.42045i) q^{98} -0.666590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9	\( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9} + 8 q^{10} + 4 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} - 6 q^{16} - 2 q^{17} + 22 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} + 4 q^{23} - 12 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{27} - 7 q^{28} + 15 q^{29} - 8 q^{30} + 3 q^{31} + 3 q^{32} - 4 q^{33} - 68 q^{34} - 12 q^{35} - 6 q^{36} + 4 q^{37} + 2 q^{38} - 5 q^{39} - 25 q^{40} + 19 q^{41} + 7 q^{42} + 11 q^{43} - 16 q^{44} + 2 q^{46} + 5 q^{47} + 6 q^{48} + 13 q^{49} - 7 q^{50} + 2 q^{51} + 36 q^{52} + 36 q^{53} - 15 q^{55} + 39 q^{56} - 22 q^{57} - 40 q^{58} - 17 q^{59} + 20 q^{60} + 44 q^{61} - 6 q^{62} + q^{63} - 20 q^{64} - 21 q^{65} - 7 q^{66} - 52 q^{67} + 5 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} + 12 q^{72} - 6 q^{73} + 15 q^{74} - 2 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} + 56 q^{80} + 16 q^{81} + 2 q^{82} + 36 q^{83} + 7 q^{84} - 4 q^{85} + 16 q^{86} - 15 q^{87} - 48 q^{88} + 20 q^{89} + 8 q^{90} - 7 q^{91} - 94 q^{92} - 3 q^{93} + 40 q^{94} - 3 q^{96} + 7 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9 + 8 * q^10 + 4 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 - 6 * q^16 - 2 * q^17 + 22 * q^19 - 20 * q^20 - q^21 + 7 * q^22 + 4 * q^23 - 12 * q^24 + 2 * q^25 - 6 * q^26 - 16 * q^27 - 7 * q^28 + 15 * q^29 - 8 * q^30 + 3 * q^31 + 3 * q^32 - 4 * q^33 - 68 * q^34 - 12 * q^35 - 6 * q^36 + 4 * q^37 + 2 * q^38 - 5 * q^39 - 25 * q^40 + 19 * q^41 + 7 * q^42 + 11 * q^43 - 16 * q^44 + 2 * q^46 + 5 * q^47 + 6 * q^48 + 13 * q^49 - 7 * q^50 + 2 * q^51 + 36 * q^52 + 36 * q^53 - 15 * q^55 + 39 * q^56 - 22 * q^57 - 40 * q^58 - 17 * q^59 + 20 * q^60 + 44 * q^61 - 6 * q^62 + q^63 - 20 * q^64 - 21 * q^65 - 7 * q^66 - 52 * q^67 + 5 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 + 12 * q^72 - 6 * q^73 + 15 * q^74 - 2 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 + 56 * q^80 + 16 * q^81 + 2 * q^82 + 36 * q^83 + 7 * q^84 - 4 * q^85 + 16 * q^86 - 15 * q^87 - 48 * q^88 + 20 * q^89 + 8 * q^90 - 7 * q^91 - 94 * q^92 - 3 * q^93 + 40 * q^94 - 3 * q^96 + 7 * q^97 - 3 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.532778	+	0.922798i	−0.376731	+	0.652517i	−0.990584	−	0.136903i	$-0.956285\pi$
$2$	−0.532778	+	0.922798i	−0.376731	+	0.652517i	0.613854	+	0.789420i	$0.289618\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.432296	+	0.748758i	0.216148	+	0.374379i
$5$	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
$7$	2.58706	−	0.554165i	0.977818	−	0.209455i
$7$	2.58706	−	0.554165i	0.977818	−	0.209455i
$8$	−3.05238			−1.07918
$9$	1.00000			0.333333
$10$	−2.53651			−0.802116
$11$	−0.666590			−0.200985			−0.100492	−	0.994938i	$-0.532042\pi$
$11$	−0.666590			−0.200985			−0.100492	+	0.994938i	$0.532042\pi$
$12$	−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
$16$	0.761650	−	1.31922i	0.190412	−	0.329804i
$17$	−0.707897	−	1.22611i	−0.171690	−	0.297376i	0.767321	−	0.641264i	$-0.221590\pi$
$17$	−0.707897	−	1.22611i	−0.171690	−	0.297376i	−0.939011	+	0.343887i	$0.888256\pi$
$18$	−0.532778	+	0.922798i	−0.125577	+	0.217506i
$19$	−3.56270			−0.817339			−0.408670	−	0.912682i	$-0.634007\pi$
$19$	−3.56270			−0.817339			−0.408670	+	0.912682i	$0.634007\pi$
$20$	−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
$23$	−2.99126	+	5.18102i	−0.623722	+	1.08032i	0.365065	+	0.930982i	$0.381047\pi$
$23$	−2.99126	+	5.18102i	−0.623722	+	1.08032i	−0.988787	+	0.149336i	$0.952287\pi$
$24$	3.05238			0.623065
$25$	−0.333295	+	0.577284i	−0.0666590	+	0.115457i
$26$	−3.80828	+	0.507250i	−0.746865	+	0.0994799i
$27$	−1.00000			−0.192450
$28$	1.53331	+	1.69752i	0.289769	+	0.320802i
$29$	0.647747	+	1.12193i	0.120284	+	0.208337i	0.919879	−	0.392201i	$-0.128286\pi$
$29$	0.647747	+	1.12193i	0.120284	+	0.208337i	−0.799596	+	0.600538i	$0.794953\pi$
$30$	2.53651			0.463102
$31$	−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	$0.979339\pi$
$32$	−2.24080	−	3.88118i	−0.396121	−	0.686102i
$33$	0.666590			0.116038
$34$	1.50861			0.258724
$35$	4.22163	+	4.67375i	0.713586	+	0.790008i
$36$	0.432296	+	0.748758i	0.0720493	+	0.124793i
$37$	3.94868	−	6.83932i	0.649159	−	1.12438i	−0.334165	−	0.942515i	$-0.608454\pi$
$37$	3.94868	−	6.83932i	0.649159	−	1.12438i	0.983324	−	0.181862i	$-0.0582124\pi$
$38$	1.89813	−	3.28765i	0.307917	−	0.533328i
$39$	−2.19926	−	2.85714i	−0.352163	−	0.457509i
$40$	−3.63304	−	6.29260i	−0.574433	−	0.994948i
$41$	5.26293	+	9.11566i	0.821931	+	1.42363i	0.904242	+	0.427020i	$0.140437\pi$
$41$	5.26293	+	9.11566i	0.821931	+	1.42363i	−0.0823113	+	0.996607i	$0.526230\pi$
$42$	0.866948	−	2.68258i	0.133773	−	0.413932i
$43$	5.22034	−	9.04190i	0.796095	−	1.37888i	−0.126047	−	0.992024i	$-0.540229\pi$
$43$	5.22034	−	9.04190i	0.796095	−	1.37888i	0.922142	−	0.386853i	$-0.126438\pi$
$44$	−0.288164	−	0.499115i	−0.0434424	−	0.0752444i
$45$	1.19023	+	2.06154i	0.177429	+	0.307316i
$46$	−3.18736	−	5.52067i	−0.469950	−	0.813978i
$47$	−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
$49$	6.38580	−	2.86732i	0.912258	−	0.409617i
$50$	−0.355145	−	0.615128i	−0.0502250	−	0.0869923i
$51$	0.707897	+	1.22611i	0.0991255	+	0.171690i
$52$	−1.18858	+	2.88184i	−0.164826	+	0.399640i
$53$	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	$0.0123755\pi$
$54$	0.532778	−	0.922798i	0.0725019	−	0.125577i
$55$	−0.793396	−	1.37420i	−0.106981	−	0.185297i
$56$	−7.89671	+	1.69152i	−1.05524	+	0.226039i
$57$	3.56270			0.471891
$58$	−1.38042			−0.181258
$59$	2.57641	+	4.46248i	0.335420	+	0.580965i	0.983565	−	0.180552i	$-0.0577884\pi$
$59$	2.57641	+	4.46248i	0.335420	+	0.580965i	−0.648145	+	0.761517i	$0.724455\pi$
$60$	1.02906	−	1.78239i	0.132851	−	0.230105i
$61$	4.83755			0.619385			0.309692	−	0.950837i	$-0.399774\pi$
$61$	4.83755			0.619385			0.309692	+	0.950837i	$0.399774\pi$
$62$	−3.29340	−	5.70433i	−0.418262	−	0.724451i
$63$	2.58706	−	0.554165i	0.325939	−	0.0698182i
$64$	7.82199			0.977749
$65$	−3.27249	+	7.93451i	−0.405902	+	0.984155i
$66$	−0.355145	+	0.615128i	−0.0437153	+	0.0757171i
$67$	5.57265			0.680808			0.340404	−	0.940279i	$-0.389436\pi$
$67$	5.57265			0.680808			0.340404	+	0.940279i	$0.389436\pi$
$68$	0.612042	−	1.06009i	0.0742210	−	0.128555i
$69$	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	−0.248752	−	0.968567i	$-0.580020\pi$
$71$	6.01988	−	10.4267i	0.714428	−	1.23743i	0.963180	−	0.268858i	$-0.0866463\pi$
$72$	−3.05238			−0.359727
$73$	−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	$0.324270\pi$
$74$	4.20754	+	7.28767i	0.489116	+	0.847175i
$75$	0.333295	−	0.577284i	0.0384856	−	0.0666590i
$76$	−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	$0.905700\pi$
$80$	3.62615			0.405416
$81$	1.00000			0.111111
$82$	−11.2159			−1.23859
$83$	8.44505			0.926965			0.463483	−	0.886106i	$-0.346600\pi$
$83$	8.44505			0.926965			0.463483	+	0.886106i	$0.346600\pi$
$84$	−1.53331	−	1.69752i	−0.167298	−	0.185215i
$85$	1.68512	−	2.91872i	0.182777	−	0.316579i
$86$	5.56257	+	9.63465i	0.599827	+	1.03893i
$87$	−0.647747	−	1.12193i	−0.0694458	−	0.120284i
$88$	2.03469			0.216898
$89$	−0.910778	+	1.57751i	−0.0965423	+	0.167216i	−0.910251	−	0.414056i	$-0.864112\pi$
$89$	−0.910778	+	1.57751i	−0.0965423	+	0.167216i	0.813709	+	0.581273i	$0.197445\pi$
$90$	−2.53651			−0.267372
$91$	7.27295	+	6.17286i	0.762412	+	0.647091i
$92$	−5.17244			−0.539264
$93$	3.09078	−	5.35339i	0.320499	−	0.555120i
$94$	11.8222			1.21937
$95$	−4.24043	−	7.34465i	−0.435059	−	0.753545i
$96$	2.24080	+	3.88118i	0.228701	+	0.396121i
$97$	−7.88484	+	13.6569i	−0.800584	+	1.38665i	0.118648	+	0.992936i	$0.462144\pi$
$97$	−7.88484	+	13.6569i	−0.800584	+	1.38665i	−0.919232	+	0.393716i	$0.871189\pi$
$98$	−0.756256	+	7.42045i	−0.0763934	+	0.749579i
$99$	−0.666590			−0.0669949
$100$	−0.576328			−0.0576328
$101$	8.97058			0.892606			0.446303	−	0.894882i	$-0.352740\pi$
$101$	8.97058			0.892606			0.446303	+	0.894882i	$0.352740\pi$
$102$	−1.50861			−0.149374
$103$	−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
$107$	2.50268	−	4.33476i	0.241943	−	0.419057i	−0.719325	−	0.694674i	$-0.755549\pi$
$107$	2.50268	−	4.33476i	0.241943	−	0.419057i	0.961268	+	0.275617i	$0.0888820\pi$
$108$	−0.432296	−	0.748758i	−0.0415977	−	0.0720493i
$109$	−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	$0.874489\pi$
$110$	1.69081			0.161213
$111$	−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	−0.647454	−	0.762105i	$-0.724166\pi$
$113$	3.57465	−	6.19148i	0.336275	−	0.582446i	0.983729	+	0.179659i	$0.0574994\pi$
$114$	−1.89813	+	3.28765i	−0.177776	+	0.307917i
$115$	−14.2412			−1.32800
$116$	−0.560037	+	0.970012i	−0.0519981	+	0.0900633i
$117$	2.19926	+	2.85714i	0.203322	+	0.264143i
$118$	−5.49062			−0.505453
$119$	−2.51085	−	2.77974i	−0.230169	−	0.254819i
$120$	3.63304	+	6.29260i	0.331649	+	0.574433i
$121$	−10.5557			−0.959605
$122$	−2.57734	+	4.46408i	−0.233341	+	0.404159i
$123$	−5.26293	−	9.11566i	−0.474542	−	0.821931i
$124$	−5.34452			−0.479952
$125$	10.3155			0.922647
$126$	−0.866948	+	2.68258i	−0.0772339	+	0.238984i
$127$	−5.70435	−	9.88023i	−0.506179	−	0.876728i	−0.999974	−	0.00715012i	$-0.997724\pi$
$127$	−5.70435	−	9.88023i	−0.506179	−	0.876728i	0.493795	−	0.869578i	$-0.335609\pi$
$128$	0.314218	−	0.544241i	0.0277732	−	0.0481046i
$129$	−5.22034	+	9.04190i	−0.459626	+	0.796095i
$130$	−5.57845	−	7.24718i	−0.489262	−	0.635619i
$131$	−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
$133$	−9.21693	+	1.97432i	−0.799210	+	0.171196i
$134$	−2.96898	+	5.14243i	−0.256481	+	0.444239i
$135$	−1.19023	−	2.06154i	−0.102439	−	0.177429i
$136$	2.16077	+	3.74257i	0.185285	+	0.320923i
$137$	−4.17738	−	7.23544i	−0.356898	−	0.618165i	0.630543	−	0.776154i	$-0.282832\pi$
$137$	−4.17738	−	7.23544i	−0.356898	−	0.618165i	−0.987441	+	0.157989i	$0.949499\pi$
$138$	3.18736	+	5.52067i	0.271326	+	0.469950i
$139$	4.82663	−	8.35996i	0.409389	−	0.709083i	−0.585432	−	0.810721i	$-0.699075\pi$
$139$	4.82663	−	8.35996i	0.409389	−	0.709083i	0.994821	+	0.101638i	$0.0324085\pi$
$140$	−1.67451	+	5.18142i	−0.141522	+	0.437910i
$141$	5.54746	+	9.60848i	0.467180	+	0.809180i
$142$	6.41451	+	11.1103i	0.538294	+	0.932352i
$143$	−1.46600	−	1.90454i	−0.122593	−	0.159266i
$144$	0.761650	−	1.31922i	0.0634708	−	0.109935i
$145$	−1.54194	+	2.67071i	−0.128051	+	0.221791i
$146$	−4.32575	−	7.49242i	−0.358002	−	0.620077i
$147$	−6.38580	+	2.86732i	−0.526692	+	0.236493i
$148$	6.82799			0.561257
$149$	13.2608			1.08637			0.543183	−	0.839614i	$-0.317219\pi$
$149$	13.2608			1.08637			0.543183	+	0.839614i	$0.317219\pi$
$150$	0.355145	+	0.615128i	0.0289974	+	0.0502250i
$151$	−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	$0.933352\pi$
$152$	10.8747			0.882056
$153$	−0.707897	−	1.22611i	−0.0572301	−	0.0991255i
$154$	0.577899	−	1.78819i	0.0465684	−	0.144096i
$155$	−14.7150			−1.18193
$156$	1.18858	−	2.88184i	0.0951624	−	0.230732i
$157$	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	$-0.0939435\pi$
$158$	4.26931			0.339648
$159$	−3.39224	+	5.87554i	−0.269022	+	0.465961i
$160$	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
$163$	6.78823			0.531695			0.265847	−	0.964015i	$-0.414348\pi$
$163$	6.78823			0.531695			0.265847	+	0.964015i	$0.414348\pi$
$164$	−4.55028	+	7.88132i	−0.355317	+	0.615428i
$165$	0.793396	+	1.37420i	0.0617658	+	0.106981i
$166$	−4.49934	+	7.79308i	−0.349216	+	0.604860i
$167$	0.826837	+	1.43212i	0.0639826	+	0.110821i	0.896242	−	0.443565i	$-0.146286\pi$
$167$	0.826837	+	1.43212i	0.0639826	+	0.110821i	−0.832260	+	0.554386i	$0.812953\pi$
$168$	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
$171$	−3.56270			−0.272446
$172$	9.02693			0.688297
$173$	−11.9879			−0.911421			−0.455711	−	0.890128i	$-0.650615\pi$
$173$	−11.9879			−0.911421			−0.455711	+	0.890128i	$0.650615\pi$
$174$	1.38042			0.104649
$175$	−0.542345	+	1.67817i	−0.0409975	+	0.126858i
$176$	−0.507708	+	0.879376i	−0.0382699	+	0.0662855i
$177$	−2.57641	−	4.46248i	−0.193655	−	0.335420i
$178$	−0.970485	−	1.68093i	−0.0727409	−	0.125991i
$179$	−2.67017			−0.199578			−0.0997888	−	0.995009i	$-0.531817\pi$
$179$	−2.67017			−0.199578			−0.0997888	+	0.995009i	$0.531817\pi$
$180$	−1.02906	+	1.78239i	−0.0767018	+	0.132851i
$181$	−0.752089			−0.0559024			−0.0279512	−	0.999609i	$-0.508898\pi$
$181$	−0.752089			−0.0559024			−0.0279512	+	0.999609i	$0.508898\pi$
$182$	−9.57117	+	3.42270i	−0.709462	+	0.253708i
$183$	−4.83755			−0.357602
$184$	9.13048	−	15.8145i	0.673108	−	1.16586i
$185$	18.7994			1.38216
$186$	3.29340	+	5.70433i	0.241484	+	0.418262i
$187$	0.471878	+	0.817316i	0.0345071	+	0.0597681i
$188$	4.79628	−	8.30741i	0.349805	−	0.605880i
$189$	−2.58706	+	0.554165i	−0.188181	+	0.0403096i
$190$	9.03683			0.655601
$191$	5.15813			0.373229			0.186615	−	0.982433i	$-0.440248\pi$
$191$	5.15813			0.373229			0.186615	+	0.982433i	$0.440248\pi$
$192$	−7.82199			−0.564504
$193$	2.84627			0.204879			0.102439	−	0.994739i	$-0.467335\pi$
$193$	2.84627			0.204879			0.102439	+	0.994739i	$0.467335\pi$
$194$	−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	0.848286	−	0.529539i	$-0.177635\pi$
$197$	−0.483548	−	0.837530i	−0.0344514	−	0.0596716i	−0.882737	+	0.469867i	$0.844302\pi$
$198$	0.355145	−	0.615128i	0.0252390	−	0.0437153i
$199$	−4.69085	−	8.12478i	−0.332525	−	0.575951i	0.650481	−	0.759522i	$-0.274567\pi$
$199$	−4.69085	−	8.12478i	−0.332525	−	0.575951i	−0.983006	+	0.183572i	$0.941234\pi$
$200$	1.01734	−	1.76209i	0.0719371	−	0.124599i
$201$	−5.57265			−0.393065
$202$	−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
$205$	−12.5282	+	21.6995i	−0.875007	+	1.51556i
$206$	3.38411			0.235782
$207$	−2.99126	+	5.18102i	−0.207907	+	0.360106i
$208$	5.44425	−	0.725155i	0.377491	−	0.0502805i
$209$	2.37486			0.164273
$210$	6.56212	−	1.40565i	0.452829	−	0.0969988i
$211$	10.3756	+	17.9711i	0.714288	+	1.23718i	0.963233	+	0.268666i	$0.0865827\pi$
$211$	10.3756	+	17.9711i	0.714288	+	1.23718i	−0.248945	+	0.968518i	$0.580084\pi$
$212$	5.86581			0.402865
$213$	−6.01988	+	10.4267i	−0.412475	+	0.714428i
$214$	2.66674	+	4.61893i	0.182295	+	0.315744i
$215$	24.8536			1.69500
$216$	3.05238			0.207688
$217$	−5.02939	+	15.5624i	−0.341417	+	1.05644i
$218$	−8.83670	−	15.3056i	−0.598497	−	1.03663i
$219$	4.05962	−	7.03147i	0.274324	−	0.475143i
$220$	0.685963	−	1.18812i	0.0462476	−	0.0801032i
$221$	1.94633	−	4.71911i	0.130925	−	0.317441i
$222$	−4.20754	−	7.28767i	−0.282392	−	0.489116i
$223$	−4.05504	−	7.02354i	−0.271546	−	0.470331i	0.697712	−	0.716378i	$-0.254201\pi$
$223$	−4.05504	−	7.02354i	−0.271546	−	0.470331i	−0.969258	+	0.246047i	$0.920868\pi$
$224$	−7.94791	−	8.79909i	−0.531042	−	0.587914i
$225$	−0.333295	+	0.577284i	−0.0222197	+	0.0384856i
$226$	3.80899	+	6.59737i	0.253370	+	0.438850i
$227$	−1.09865	−	1.90291i	−0.0729197	−	0.126301i	0.827260	−	0.561819i	$-0.189898\pi$
$227$	−1.09865	−	1.90291i	−0.0729197	−	0.126301i	−0.900180	+	0.435519i	$0.856565\pi$
$228$	1.54014	+	2.66760i	0.101998	+	0.176666i
$229$	−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
$231$	1.72451	−	0.369401i	0.113465	−	0.0243048i
$232$	−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	$-0.416000\pi$
$234$	−3.80828	+	0.507250i	−0.248955	+	0.0331600i
$235$	13.2055	−	22.8726i	0.861432	−	1.49204i
$236$	−2.22754	+	3.85822i	−0.145001	+	0.251149i
$237$	2.00333	+	3.46986i	0.130130	+	0.225392i
$238$	3.90287	−	0.836018i	0.252985	−	0.0541910i
$239$	−17.3697			−1.12355			−0.561775	−	0.827290i	$-0.689881\pi$
$239$	−17.3697			−1.12355			−0.561775	+	0.827290i	$0.689881\pi$
$240$	−3.62615			−0.234067
$241$	5.25156	+	9.09597i	0.338283	+	0.585923i	0.984110	−	0.177561i	$-0.0568206\pi$
$241$	5.25156	+	9.09597i	0.338283	+	0.585923i	−0.645827	+	0.763484i	$0.723487\pi$
$242$	5.62382	−	9.74074i	0.361513	−	0.626159i
$243$	−1.00000			−0.0641500
$244$	2.09125	+	3.62216i	0.133879	+	0.231885i
$245$	13.5117	+	9.75181i	0.863229	+	0.623020i
$246$	11.2159			0.715098
$247$	−7.83530	−	10.1791i	−0.498548	−	0.647683i
$248$	9.43424	−	16.3406i	0.599075	−	1.03763i
$249$	−8.44505			−0.535184
$250$	−5.49587	+	9.51913i	−0.347590	+	0.602043i
$251$	−0.706938	+	1.22445i	−0.0446215	+	0.0772867i	−0.887474	−	0.460859i	$-0.847542\pi$
$251$	−0.706938	+	1.22445i	−0.0446215	+	0.0772867i	0.842852	+	0.538145i	$0.180875\pi$
$252$	1.53331	+	1.69752i	0.0965896	+	0.106934i
$253$	1.99395	−	3.45362i	0.125358	−	0.217127i
$254$	12.1566			0.762773
$255$	−1.68512	+	2.91872i	−0.105526	+	0.182777i
$256$	8.15681	+	14.1280i	0.509801	+	0.883001i
$257$	6.87362	−	11.9055i	0.428765	−	0.742642i	−0.567999	−	0.823029i	$-0.692282\pi$
$257$	6.87362	−	11.9055i	0.428765	−	0.742642i	0.996764	+	0.0803871i	$0.0256156\pi$
$258$	−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
$262$	9.17984			0.567133
$263$	7.97741			0.491908			0.245954	−	0.969281i	$-0.420899\pi$
$263$	7.97741			0.491908			0.245954	+	0.969281i	$0.420899\pi$
$264$	−2.03469			−0.125226
$265$	16.1502			0.992099
$266$	3.08868	−	9.55725i	0.189379	−	0.585992i
$267$	0.910778	−	1.57751i	0.0557387	−	0.0965423i
$268$	2.40903	+	4.17257i	0.147155	+	0.254880i
$269$	−13.8192	−	23.9355i	−0.842569	−	1.45937i	−0.887716	−	0.460392i	$-0.847709\pi$
$269$	−13.8192	−	23.9355i	−0.842569	−	1.45937i	0.0451470	−	0.998980i	$-0.485624\pi$
$270$	2.53651			0.154367
$271$	−5.15953	+	8.93656i	−0.313419	+	0.542857i	−0.979100	−	0.203379i	$-0.934808\pi$
$271$	−5.15953	+	8.93656i	−0.313419	+	0.542857i	0.665681	+	0.746236i	$0.268141\pi$
$272$	−2.15668			−0.130768
$273$	−7.27295	−	6.17286i	−0.440179	−	0.373598i
$274$	8.90247			0.537818
$275$	0.222171	−	0.384812i	0.0133974	−	0.0232050i
$276$	5.17244			0.311344
$277$	1.07784	+	1.86687i	0.0647611	+	0.112170i	0.896588	−	0.442866i	$-0.146038\pi$
$277$	1.07784	+	1.86687i	0.0647611	+	0.112170i	−0.831827	+	0.555035i	$0.812705\pi$
$278$	5.14304	+	8.90801i	0.308459	+	0.534267i
$279$	−3.09078	+	5.35339i	−0.185040	+	0.320499i
$280$	−12.8860	−	14.2661i	−0.770088	−	0.852561i
$281$	−2.60596			−0.155458			−0.0777292	−	0.996975i	$-0.524767\pi$
$281$	−2.60596			−0.155458			−0.0777292	+	0.996975i	$0.524767\pi$
$282$	−11.8222			−0.704005
$283$	1.73242			0.102982			0.0514909	−	0.998673i	$-0.483603\pi$
$283$	1.73242			0.102982			0.0514909	+	0.998673i	$0.483603\pi$
$284$	10.4095			0.617688
$285$	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
$289$	7.49776	−	12.9865i	0.441045	−	0.763912i
$290$	−1.64302	−	2.84579i	−0.0964814	−	0.167111i
$291$	7.88484	−	13.6569i	0.462217	−	0.800584i
$292$	−7.01982			−0.410804
$293$	−16.4196	+	28.4396i	−0.959243	+	1.66146i	−0.234898	+	0.972020i	$0.575476\pi$
$293$	−16.4196	+	28.4396i	−0.959243	+	1.66146i	−0.724345	+	0.689438i	$0.757858\pi$
$294$	0.756256	−	7.42045i	0.0441057	−	0.432770i
$295$	−6.13305	+	10.6227i	−0.357080	+	0.618480i
$296$	−12.0529	+	20.8762i	−0.700559	+	1.21340i
$297$	0.666590			0.0386795
$298$	−7.06506	+	12.2370i	−0.409268	+	0.708873i
$299$	−21.3815	+	2.84794i	−1.23652	+	0.164701i
$300$	0.576328			0.0332743
$301$	8.49466	−	26.2849i	0.489624	−	1.51504i
$302$	−8.76088	−	15.1743i	−0.504132	−	0.873182i
$303$	−8.97058			−0.515346
$304$	−2.71353	+	4.69997i	−0.155632	+	0.269562i
$305$	5.75780	+	9.97280i	0.329691	+	0.571041i
$306$	1.50861			0.0862414
$307$	−29.4618			−1.68147			−0.840737	−	0.541444i	$-0.817878\pi$
$307$	−29.4618			−1.68147			−0.840737	+	0.541444i	$0.817878\pi$
$308$	−1.02209	−	1.13155i	−0.0582390	−	0.0644762i
$309$	1.58796	+	2.75042i	0.0903358	+	0.156466i
$310$	7.83980	−	13.5789i	0.445271	−	0.771232i
$311$	−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	$0.230834\pi$
$312$	6.71298	+	8.72109i	0.380047	+	0.493734i
$313$	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
$315$	4.22163	+	4.67375i	0.237862	+	0.263336i
$316$	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	$-0.345418\pi$
$318$	−3.61462	−	6.26071i	−0.202698	−	0.351083i
$319$	−0.431782	−	0.747868i	−0.0241751	−	0.0418726i
$320$	9.30997	+	16.1253i	0.520443	+	0.901434i
$321$	−2.50268	+	4.33476i	−0.139686	+	0.241943i
$322$	−11.3053	−	12.5160i	−0.630017	−	0.697489i
$323$	2.52203	+	4.36828i	0.140329	+	0.243057i
$324$	0.432296	+	0.748758i	0.0240164	+	0.0415977i
$325$	−2.38239	+	0.317326i	−0.132151	+	0.0176021i
$326$	−3.61662	+	6.26416i	−0.200306	+	0.346940i
$327$	8.29305	−	14.3640i	0.458607	−	0.794330i
$328$	−16.0645	−	27.8245i	−0.887011	−	1.53635i
$329$	−19.6763	−	21.7835i	−1.08479	−	1.20097i
$330$	−1.69081			−0.0930763
$331$	−19.0379			−1.04642			−0.523208	−	0.852205i	$-0.675265\pi$
$331$	−19.0379			−1.04642			−0.523208	+	0.852205i	$0.675265\pi$
$332$	3.65076	+	6.32330i	0.200362	+	0.347036i
$333$	3.94868	−	6.83932i	0.216386	−	0.374792i
$334$	−1.76208			−0.0964168
$335$	6.63274	+	11.4882i	0.362385	+	0.627669i
$336$	−1.23937	+	3.83497i	−0.0676134	+	0.209215i
$337$	1.90388			0.103711			0.0518555	−	0.998655i	$-0.483486\pi$
$337$	1.90388			0.103711			0.0518555	+	0.998655i	$0.483486\pi$
$338$	−9.82468	−	9.76523i	−0.534392	−	0.531158i
$339$	−3.57465	+	6.19148i	−0.194149	+	0.336275i
$340$	2.91388			0.158028
$341$	2.06028	−	3.56852i	0.111571	−	0.193246i
$342$	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
$345$	14.2412			0.766719
$346$	6.38687	−	11.0624i	0.343360	−	0.594718i
$347$	10.4403	+	18.0831i	0.560462	+	0.970749i	0.997456	+	0.0712845i	$0.0227098\pi$
$347$	10.4403	+	18.0831i	0.560462	+	0.970749i	−0.436994	+	0.899465i	$0.643957\pi$
$348$	0.560037	−	0.970012i	0.0300211	−	0.0519981i
$349$	−4.79951	−	8.31300i	−0.256912	−	0.444984i	0.708501	−	0.705710i	$-0.249372\pi$
$349$	−4.79951	−	8.31300i	−0.256912	−	0.444984i	−0.965413	+	0.260725i	$0.916038\pi$
$350$	−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
$353$	10.8140			0.575569			0.287785	−	0.957695i	$-0.407081\pi$
$353$	10.8140			0.575569			0.287785	+	0.957695i	$0.407081\pi$
$354$	5.49062			0.291823
$355$	28.6602			1.52112
$356$	−1.57490			−0.0834696
$357$	2.51085	+	2.77974i	0.132888	+	0.147120i
$358$	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	$0.556077\pi$
$360$	−3.63304	−	6.29260i	−0.191478	−	0.331649i
$361$	−6.30717			−0.331956
$362$	0.400696	−	0.694027i	0.0210601	−	0.0364772i
$363$	10.5557			0.554028
$364$	−1.47791	+	8.11418i	−0.0774637	+	0.425299i
$365$	−19.3275			−1.01165
$366$	2.57734	−	4.46408i	0.134720	−	0.233341i
$367$	−32.5733			−1.70031			−0.850156	−	0.526530i	$-0.823493\pi$
$367$	−32.5733			−1.70031			−0.850156	+	0.526530i	$0.823493\pi$
$368$	4.55659	+	7.89224i	0.237529	+	0.411412i
$369$	5.26293	+	9.11566i	0.273977	+	0.474542i
$370$	−10.0159	+	17.3480i	−0.520701	+	0.901880i
$371$	5.51994	−	17.0803i	0.286581	−	0.886763i
$372$	5.34452			0.277101
$373$	−23.8778			−1.23634			−0.618172	−	0.786043i	$-0.712126\pi$
$373$	−23.8778			−1.23634			−0.618172	+	0.786043i	$0.712126\pi$
$374$	−1.00562			−0.0519996
$375$	−10.3155			−0.532691
$376$	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	0.712518	−	0.701654i	$-0.247555\pi$
$379$	−4.89406	−	8.47676i	−0.251391	−	0.435422i	−0.963909	+	0.266232i	$0.914221\pi$
$380$	3.66624	−	6.35012i	0.188074	−	0.325754i
$381$	5.70435	+	9.88023i	0.292243	+	0.506179i
$382$	−2.74814	+	4.75992i	−0.140607	+	0.243539i
$383$	14.8568			0.759146			0.379573	−	0.925162i	$-0.376071\pi$
$383$	14.8568			0.759146			0.379573	+	0.925162i	$0.376071\pi$
$384$	−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
$387$	5.22034	−	9.04190i	0.265365	−	0.459626i
$388$	−13.6343			−0.692178
$389$	−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	$0.328986\pi$
$390$	5.57845	+	7.24718i	0.282476	+	0.366975i
$391$	8.47003			0.428348
$392$	−19.4919	+	8.75215i	−0.984490	+	0.442051i
$393$	4.30754	+	7.46087i	0.217287	+	0.376351i
$394$	1.03050			0.0519156
$395$	4.76884	−	8.25987i	0.239946	−	0.415599i
$396$	−0.288164	−	0.499115i	−0.0144808	−	0.0250815i
$397$	38.3010			1.92227			0.961136	−	0.276074i	$-0.0890335\pi$
$397$	38.3010			1.92227			0.961136	+	0.276074i	$0.0890335\pi$
$398$	9.99671			0.501090
$399$	9.21693	−	1.97432i	0.461424	−	0.0988398i
$400$	0.507708	+	0.879376i	0.0253854	+	0.0439688i
$401$	−17.8057	+	30.8404i	−0.889175	+	1.54010i	−0.0483236	+	0.998832i	$0.515388\pi$
$401$	−17.8057	+	30.8404i	−0.889175	+	1.54010i	−0.840852	+	0.541265i	$0.817945\pi$
$402$	2.96898	−	5.14243i	0.148080	−	0.256481i
$403$	−22.0928	+	2.94269i	−1.10052	+	0.146586i
$404$	3.87794	+	6.71680i	0.192935	+	0.334173i
$405$	1.19023	+	2.06154i	0.0591430	+	0.102439i
$406$	−3.57124	+	0.764981i	−0.177238	+	0.0379654i
$407$	−2.63215	+	4.55902i	−0.130471	+	0.225982i
$408$	−2.16077	−	3.74257i	−0.106974	−	0.185285i
$409$	1.58236	+	2.74072i	0.0782426	+	0.135520i	0.902492	−	0.430707i	$-0.141736\pi$
$409$	1.58236	+	2.74072i	0.0782426	+	0.135520i	−0.824249	+	0.566227i	$0.808402\pi$
$410$	−13.3495	−	23.1220i	−0.659284	−	1.14191i
$411$	4.17738	+	7.23544i	0.206055	+	0.356898i
$412$	1.37293	−	2.37799i	0.0676396	−	0.117155i
$413$	9.13829	+	10.1170i	0.449666	+	0.497823i
$414$	−3.18736	−	5.52067i	−0.156650	−	0.271326i
$415$	10.0516	+	17.4098i	0.493412	+	0.854614i
$416$	6.16099	−	14.9380i	0.302067	−	0.732396i
$417$	−4.82663	+	8.35996i	−0.236361	+	0.409389i
$418$	−1.26527	+	2.19152i	−0.0618865	+	0.107191i
$419$	11.0530	+	19.1444i	0.539975	+	0.935265i	0.998905	+	0.0467918i	$0.0148997\pi$
$419$	11.0530	+	19.1444i	0.539975	+	0.935265i	−0.458929	+	0.888473i	$0.651767\pi$
$420$	1.67451	−	5.18142i	0.0817079	−	0.252828i
$421$	7.75012			0.377718			0.188859	−	0.982004i	$-0.439521\pi$
$421$	7.75012			0.377718			0.188859	+	0.982004i	$0.439521\pi$
$422$	−22.1116			−1.07638
$423$	−5.54746	−	9.60848i	−0.269727	−	0.467180i
$424$	−10.3544	+	17.9344i	−0.502855	+	0.870971i
$425$	0.943755			0.0457789
$426$	−6.41451	−	11.1103i	−0.310784	−	0.538294i
$427$	12.5151	−	2.68080i	0.605646	−	0.129733i
$428$	4.32759			0.209182
$429$	1.46600	+	1.90454i	0.0707794	+	0.0919522i
$430$	−13.2415	+	22.9349i	−0.638560	+	1.10602i
$431$	−34.5590			−1.66465			−0.832324	−	0.554290i	$-0.812990\pi$
$431$	−34.5590			−1.66465			−0.832324	+	0.554290i	$0.812990\pi$
$432$	−0.761650	+	1.31922i	−0.0366449	+	0.0634708i
$433$	−12.2389	+	21.1985i	−0.588166	+	1.01873i	0.406306	+	0.913737i	$0.366817\pi$
$433$	−12.2389	+	21.1985i	−0.588166	+	1.01873i	−0.994473	+	0.104997i	$0.966517\pi$
$434$	−11.6814	−	12.9324i	−0.560724	−	0.620774i
$435$	1.54194	−	2.67071i	0.0739302	−	0.128051i
$436$	−14.3402			−0.686771
$437$	10.6570	−	18.4584i	0.509792	−	0.882986i
$438$	4.32575	+	7.49242i	0.206692	+	0.358002i
$439$	5.36348	−	9.28983i	0.255985	−	0.443379i	−0.709177	−	0.705030i	$-0.750934\pi$
$439$	5.36348	−	9.28983i	0.255985	−	0.443379i	0.965163	+	0.261651i	$0.0842669\pi$
$440$	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	$0.437232\pi$
$444$	−6.82799			−0.324042
$445$	−4.33614			−0.205553
$446$	8.64174			0.409198
$447$	−13.2608			−0.627214
$448$	20.2360	−	4.33467i	0.956061	−	0.204794i
$449$	15.2790	−	26.4640i	0.721060	−	1.24891i	−0.239515	−	0.970893i	$-0.576988\pi$
$449$	15.2790	−	26.4640i	0.721060	−	1.24891i	0.960575	−	0.278021i	$-0.0896783\pi$
$450$	−0.355145	−	0.615128i	−0.0167417	−	0.0289974i
$451$	−3.50822	−	6.07641i	−0.165195	−	0.286127i
$452$	6.18123			0.290741
$453$	8.22189	−	14.2407i	0.386298	−	0.669088i
$454$	2.34134			0.109884
$455$	−4.06910	+	22.3406i	−0.190762	+	1.04734i
$456$	−10.8747			−0.509255
$457$	8.01733	−	13.8864i	0.375035	−	0.649579i	−0.615297	−	0.788295i	$-0.710964\pi$
$457$	8.01733	−	13.8864i	0.375035	−	0.649579i	0.990332	+	0.138716i	$0.0442974\pi$
$458$	21.6404			1.01119
$459$	0.707897	+	1.22611i	0.0330418	+	0.0572301i
$460$	−6.15640	−	10.6632i	−0.287043	−	0.497174i
$461$	19.7152	−	34.1477i	0.918227	−	1.59042i	0.116121	−	0.993235i	$-0.462954\pi$
$461$	19.7152	−	34.1477i	0.918227	−	1.59042i	0.802106	−	0.597181i	$-0.203713\pi$
$462$	−0.577899	+	1.78819i	−0.0268863	+	0.0831939i
$463$	−25.9972			−1.20819			−0.604096	−	0.796912i	$-0.706466\pi$
$463$	−25.9972			−1.20819			−0.604096	+	0.796912i	$0.706466\pi$
$464$	1.97342			0.0916140
$465$	14.7150			0.682390
$466$	22.9539			1.06332
$467$	−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
$471$	−9.15038	+	15.8489i	−0.421627	+	0.730279i
$472$	−7.86419	−	13.6212i	−0.361979	−	0.626966i
$473$	−3.47983	+	6.02724i	−0.160003	+	0.277133i
$474$	−4.26931			−0.196096
$475$	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
$478$	9.25417	−	16.0287i	0.423276	−	0.733135i
$479$	−30.8878			−1.41130			−0.705650	−	0.708560i	$-0.749345\pi$
$479$	−30.8878			−1.41130			−0.705650	+	0.708560i	$0.749345\pi$
$480$	−5.33414	+	9.23900i	−0.243469	+	0.421701i
$481$	28.2251	−	3.75948i	1.28695	−	0.171418i
$482$	−11.1917			−0.509766
$483$	4.86745	−	15.0613i	0.221477	−	0.685312i
$484$	−4.56317	−	7.90363i	−0.207417	−	0.359256i
$485$	−37.5391			−1.70456
$486$	0.532778	−	0.922798i	0.0241673	−	0.0418590i
$487$	−11.2136	−	19.4224i	−0.508135	−	0.880115i	−0.999956	−	0.00941874i	$-0.997002\pi$
$487$	−11.2136	−	19.4224i	−0.508135	−	0.880115i	0.491821	−	0.870696i	$-0.336331\pi$
$488$	−14.7660			−0.668428
$489$	−6.78823			−0.306974
$490$	−16.1977	+	7.27299i	−0.731736	+	0.328560i
$491$	−6.66716	−	11.5479i	−0.300885	−	0.521147i	0.675452	−	0.737404i	$-0.263949\pi$
$491$	−6.66716	−	11.5479i	−0.300885	−	0.521147i	−0.976337	+	0.216257i	$0.930615\pi$
$492$	4.55028	−	7.88132i	0.205143	−	0.355317i
$493$	0.917077	−	1.58842i	0.0413031	−	0.0715390i
$494$	13.5678	−	1.80718i	0.610443	−	0.0813089i
$495$	−0.793396	−	1.37420i	−0.0356605	−	0.0617658i
$496$	4.70818	+	8.15481i	0.211404	+	0.366162i
$497$	9.79568	−	30.3106i	0.439396	−	1.35962i
$498$	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	$-0.406064\pi$
$500$	4.45935	+	7.72382i	0.199428	+	0.345420i
$501$	−0.826837	−	1.43212i	−0.0369404	−	0.0639826i
$502$	−0.753281	−	1.30472i	−0.0336206	−	0.0582326i
$503$	−12.1432	+	21.0327i	−0.541441	+	0.937803i	0.457381	+	0.889271i	$0.348788\pi$
$503$	−12.1432	+	21.0327i	−0.541441	+	0.937803i	−0.998822	+	0.0485320i	$0.984546\pi$
$504$	−7.89671	+	1.69152i	−0.351747	+	0.0753464i
$505$	10.6771	+	18.4932i	0.475123	+	0.822937i
$506$	2.12466	+	3.68002i	0.0944528	+	0.163597i
$507$	3.32652	−	12.5672i	0.147736	−	0.558128i
$508$	4.93193	−	8.54236i	0.218819	−	0.379006i
$509$	−11.7319	+	20.3202i	−0.520007	+	0.900678i	0.479723	+	0.877420i	$0.340737\pi$
$509$	−11.7319	+	20.3202i	−0.520007	+	0.900678i	−0.999729	+	0.0232579i	$0.992596\pi$
$510$	−1.79559	−	3.11005i	−0.0795101	−	0.137716i
$511$	−6.60590	+	20.4406i	−0.292228	+	0.904237i
$512$	−16.1262			−0.712684
$513$	3.56270			0.157297
$514$	7.32422	+	12.6859i	0.323058	+	0.559552i
$515$	3.78007	−	6.54727i	0.166570	−	0.288507i
$516$	−9.02693			−0.397388
$517$	3.69788	+	6.40492i	0.162633	+	0.281688i
$518$	14.9237	+	16.5220i	0.655712	+	0.725935i
$519$	11.9879			0.526209
$520$	9.98888	−	24.2192i	0.438041	−	1.06208i
$521$	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	$0.125609\pi$
$522$	−1.38042			−0.0604194
$523$	−5.03484	+	8.72060i	−0.220158	+	0.381325i	−0.954856	−	0.297070i	$-0.903991\pi$
$523$	−5.03484	+	8.72060i	−0.220158	+	0.381325i	0.734698	+	0.678395i	$0.237324\pi$
$524$	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
$527$	8.75182			0.381235
$528$	0.507708	−	0.879376i	0.0220952	−	0.0382699i
$529$	−6.39532	−	11.0770i	−0.278057	−	0.481610i
$530$	−8.60447	+	14.9034i	−0.373754	+	0.647361i
$531$	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
$535$	11.9150			0.515132
$536$	−17.0099			−0.734714
$537$	2.67017			0.115226
$538$	29.4502			1.26969
$539$	−4.25671	+	1.91133i	−0.183350	+	0.0823267i
$540$	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	$0.516465\pi$
$542$	−5.49776	−	9.52240i	−0.236149	−	0.409022i
$543$	0.752089			0.0322752
$544$	−3.17252	+	5.49496i	−0.136020	+	0.235594i
$545$	−39.4825			−1.69125
$546$	9.57117	−	3.42270i	0.409608	−	0.146478i
$547$	−30.9149			−1.32183			−0.660913	−	0.750462i	$-0.729831\pi$
$547$	−30.9149			−1.32183			−0.660913	+	0.750462i	$0.729831\pi$
$548$	3.61173	−	6.25570i	0.154285	−	0.267230i
$549$	4.83755			0.206462
$550$	0.236736	+	0.410039i	0.0100945	+	0.0174841i
$551$	−2.30773	−	3.99710i	−0.0983125	−	0.170282i
$552$	−9.13048	+	15.8145i	−0.388619	+	0.673108i
$553$	−7.10561	−	7.86658i	−0.302161	−	0.334521i
$554$	−2.29700			−0.0975901
$555$	−18.7994			−0.797988
$556$	8.34612			0.353954
$557$	−10.8223			−0.458556			−0.229278	−	0.973361i	$-0.573637\pi$
$557$	−10.8223			−0.458556			−0.229278	+	0.973361i	$0.573637\pi$
$558$	−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
$562$	1.38840	−	2.40477i	0.0585659	−	0.101439i
$563$	16.5581	+	28.6794i	0.697839	+	1.20869i	0.969214	+	0.246219i	$0.0791883\pi$
$563$	16.5581	+	28.6794i	0.697839	+	1.20869i	−0.271375	+	0.962474i	$0.587478\pi$
$564$	−4.79628	+	8.30741i	−0.201960	+	0.349805i
$565$	17.0186			0.715980
$566$	−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
$569$	12.7080	−	22.0110i	0.532749	−	0.922748i	−0.466520	−	0.884511i	$-0.654492\pi$
$569$	12.7080	−	22.0110i	0.532749	−	0.922748i	0.999269	−	0.0382374i	$-0.0121743\pi$
$570$	−9.03683			−0.378511
$571$	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	$-0.147231\pi$
$572$	0.792295	−	1.92101i	0.0331275	−	0.0803214i
$573$	−5.15813			−0.215484
$574$	−29.0162	+	6.21545i	−1.21111	+	0.259428i
$575$	−1.99395	−	3.45362i	−0.0831534	−	0.144026i
$576$	7.82199			0.325916
$577$	−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	$0.219847\pi$
$578$	7.98928	+	13.8378i	0.332310	+	0.575578i
$579$	−2.84627			−0.118287
$580$	−2.66629			−0.110712
$581$	21.8479	−	4.67995i	0.906404	−	0.194157i
$582$	8.40173	+	14.5522i	0.348263	+	0.603209i
$583$	−2.26124	+	3.91658i	−0.0936509	+	0.162208i
$584$	12.3915	−	21.4627i	0.512764	−	0.888134i
$585$	−3.27249	+	7.93451i	−0.135301	+	0.328052i
$586$	−17.4960	−	30.3039i	−0.722753	−	1.25184i
$587$	7.56713	+	13.1067i	0.312329	+	0.540969i	0.978866	−	0.204502i	$-0.0655576\pi$
$587$	7.56713	+	13.1067i	0.312329	+	0.540969i	−0.666537	+	0.745472i	$0.732224\pi$
$588$	−4.90748	−	3.54189i	−0.202381	−	0.146065i
$589$	11.0115	−	19.0725i	0.453722	−	0.785869i
$590$	−6.53510	−	11.3191i	−0.269046	−	0.466001i
$591$	0.483548	+	0.837530i	0.0198905	+	0.0344514i
$592$	−6.01502	−	10.4183i	−0.247216	−	0.428190i
$593$	−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
$595$	2.74207	−	8.48474i	0.112414	−	0.347840i
$596$	5.73259	+	9.92913i	0.234816	+	0.406713i
$597$	4.69085	+	8.12478i	0.191984	+	0.332525i
$598$	8.76350	−	21.2481i	0.358366	−	0.868900i
$599$	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	$0.111536\pi$
$600$	−1.01734	+	1.76209i	−0.0415329	+	0.0719371i
$601$	8.61342	+	14.9189i	0.351349	+	0.608554i	0.986486	−	0.163845i	$-0.0523898\pi$
$601$	8.61342	+	14.9189i	0.351349	+	0.608554i	−0.635137	+	0.772399i	$0.719056\pi$
$602$	19.7299	+	21.8429i	0.804131	+	0.890249i
$603$	5.57265			0.226936
$604$	−14.2171			−0.578488
$605$	−12.5637	−	21.7609i	−0.510785	−	0.884706i
$606$	4.77933	−	8.27804i	0.194147	−	0.336272i
$607$	16.5854			0.673180			0.336590	−	0.941651i	$-0.390726\pi$
$607$	16.5854			0.673180			0.336590	+	0.941651i	$0.390726\pi$
$608$	7.98330	+	13.8275i	0.323766	+	0.560779i
$609$	−2.29750	−	2.54355i	−0.0930993	−	0.103070i
$610$	−12.2705			−0.496818
$611$	15.2525	−	36.9814i	0.617050	−	1.49611i
$612$	0.612042	−	1.06009i	0.0247403	−	0.0428515i
$613$	−17.2057			−0.694934			−0.347467	−	0.937692i	$-0.612958\pi$
$613$	−17.2057			−0.694934			−0.347467	+	0.937692i	$0.612958\pi$
$614$	15.6966	−	27.1873i	0.633463	−	1.09719i
$615$	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	0.278913	−	0.960316i	$-0.410026\pi$
$617$	24.1220	−	41.7805i	0.971115	−	1.68202i	0.692202	−	0.721704i	$-0.256641\pi$
$618$	−3.38411			−0.136129
$619$	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	$-0.106520\pi$
$620$	−6.36121	−	11.0179i	−0.255472	−	0.442491i
$621$	2.99126	−	5.18102i	0.120035	−	0.207907i
$622$	−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
$626$	−17.4300			−0.696642
$627$	−2.37486			−0.0948428
$628$	15.8227			0.631393
$629$	−11.1810			−0.445817
$630$	−6.56212	+	1.40565i	−0.261441	+	0.0560023i
$631$	−9.79240	+	16.9609i	−0.389829	+	0.675204i	−0.992426	−	0.122841i	$-0.960799\pi$
$631$	−9.79240	+	16.9609i	−0.389829	+	0.675204i	0.602597	+	0.798046i	$0.294133\pi$
$632$	6.11491	+	10.5913i	0.243238	+	0.421301i
$633$	−10.3756	−	17.9711i	−0.412394	−	0.714288i
$634$	20.2053			0.802454
$635$	13.5790	−	23.5195i	0.538865	−	0.933342i
$636$	−5.86581			−0.232594
$637$	22.2364	+	11.9392i	0.881037	+	0.473047i
$638$	0.920175			0.0364301
$639$	6.01988	−	10.4267i	0.238143	−	0.412475i
$640$	1.49597			0.0591332
$641$	6.96205	+	12.0586i	0.274984	+	0.476287i	0.970131	−	0.242581i	$-0.0779940\pi$
$641$	6.96205	+	12.0586i	0.274984	+	0.476287i	−0.695147	+	0.718868i	$0.744661\pi$
$642$	−2.66674	−	4.61893i	−0.105248	−	0.182295i
$643$	10.3893	−	17.9948i	0.409714	−	0.709645i	−0.585144	−	0.810930i	$-0.698962\pi$
$643$	10.3893	−	17.9948i	0.409714	−	0.709645i	0.994858	+	0.101284i	$0.0322952\pi$
$644$	−13.3814	+	2.86639i	−0.527303	+	0.112951i
$645$	−24.8536			−0.978611
$646$	−5.37472			−0.211465
$647$	−7.92761			−0.311666			−0.155833	−	0.987783i	$-0.549806\pi$
$647$	−7.92761			−0.311666			−0.155833	+	0.987783i	$0.549806\pi$
$648$	−3.05238			−0.119909
$649$	−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
$653$	−18.1324	+	31.4063i	−0.709576	+	1.22902i	0.255439	+	0.966825i	$0.417780\pi$
$653$	−18.1324	+	31.4063i	−0.709576	+	1.22902i	−0.965015	+	0.262196i	$0.915553\pi$
$654$	8.83670	+	15.3056i	0.345542	+	0.598497i
$655$	10.2539	−	17.7603i	0.400654	−	0.693953i
$656$	16.0340			0.626023
$657$	−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	−0.546235	−	0.837632i	$-0.683939\pi$
$659$	11.6108	−	20.1105i	0.452293	−	0.783395i	0.998528	+	0.0542371i	$0.0172727\pi$
$660$	−0.685963	+	1.18812i	−0.0267011	+	0.0462476i
$661$	−18.8730			−0.734074			−0.367037	−	0.930206i	$-0.619628\pi$
$661$	−18.8730			−0.734074			−0.367037	+	0.930206i	$0.619628\pi$
$662$	10.1430	−	17.5681i	0.394217	−	0.682804i
$663$	−1.94633	+	4.71911i	−0.0755893	+	0.183275i
$664$	−25.7775			−1.00036
$665$	−15.0404	−	16.6512i	−0.583242	−	0.645705i
$666$	4.20754	+	7.28767i	0.163039	+	0.282392i
$667$	−7.75033			−0.300094
$668$	−0.714876	+	1.23820i	−0.0276594	+	0.0479075i
$669$	4.05504	+	7.02354i	0.156777	+	0.271546i
$670$	−14.1351			−0.546087
$671$	−3.22466			−0.124487
$672$	7.94791	+	8.79909i	0.306597	+	0.339432i
$673$	−6.68396	−	11.5770i	−0.257648	−	0.446259i	0.707964	−	0.706249i	$-0.249614\pi$
$673$	−6.68396	−	11.5770i	−0.257648	−	0.446259i	−0.965611	+	0.259990i	$0.916281\pi$
$674$	−1.01435	+	1.75690i	−0.0390711	+	0.0676732i
$675$	0.333295	−	0.577284i	0.0128285	−	0.0222197i
$676$	−10.8478	+	2.94198i	−0.417224	+	0.113153i
$677$	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
$679$	−12.8304	+	39.7009i	−0.492385	+	1.52358i
$680$	−5.14363	+	8.90903i	−0.197249	+	0.341646i
$681$	1.09865	+	1.90291i	0.0421002	+	0.0729197i
$682$	2.19535	+	3.80245i	0.0840642	+	0.145603i
$683$	16.9165	+	29.3002i	0.647291	+	1.12114i	0.983767	+	0.179449i	$0.0574316\pi$
$683$	16.9165	+	29.3002i	0.647291	+	1.12114i	−0.336476	+	0.941692i	$0.609235\pi$
$684$	−1.54014	−	2.66760i	−0.0588887	−	0.101998i
$685$	9.94409	−	17.2237i	0.379944	−	0.658083i
$686$	2.15567	+	19.6163i	0.0823039	+	0.748953i
$687$	10.1545	+	17.5882i	0.387420	+	0.671030i
$688$	−7.95214	−	13.7735i	−0.303173	−	0.525110i
$689$	24.2477	−	3.22971i	0.923763	−	0.123042i
$690$	−7.58738	+	13.1417i	−0.288847	+	0.500297i
$691$	−13.1762	+	22.8218i	−0.501245	+	0.868181i	0.498754	+	0.866743i	$0.333791\pi$
$691$	−13.1762	+	22.8218i	−0.501245	+	0.868181i	−0.999999	+	0.00143773i	$0.999542\pi$
$692$	−5.18231	−	8.97602i	−0.197002	−	0.341217i
$693$	−1.72451	+	0.369401i	−0.0655088	+	0.0140324i
$694$	−22.2493			−0.844573
$695$	22.9792			0.871650
$696$	1.97717	+	3.42456i	0.0749445	+	0.129808i
$697$	7.45122	−	12.9059i	0.282235	−	0.488846i
$698$	10.2283			0.387146
$699$	10.7709	+	18.6557i	0.407392	+	0.705624i
$700$	−1.49100	+	0.319381i	−0.0563544	+	0.0120715i
$701$	11.2115			0.423453			0.211727	−	0.977329i	$-0.432091\pi$
$701$	11.2115			0.423453			0.211727	+	0.977329i	$0.432091\pi$
$702$	3.80828	−	0.507250i	0.143734	−	0.0191449i
$703$	−14.0680	+	24.3664i	−0.530583	+	0.918997i
$704$	−5.21407			−0.196513
$705$	−13.2055	+	22.8726i	−0.497348	+	0.861432i
$706$	−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
$709$	11.5011			0.431934			0.215967	−	0.976401i	$-0.430710\pi$
$709$	11.5011			0.431934			0.215967	+	0.976401i	$0.430710\pi$
$710$	−15.2695	+	26.4475i	−0.573054	+	0.992558i
$711$	−2.00333	−	3.46986i	−0.0751306	−	0.130130i
$712$	2.78004	−	4.81517i	0.104186	−	0.180456i
$713$	−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
$717$	17.3697			0.648682
$718$	−30.8894			−1.15278
$719$	24.1105			0.899170			0.449585	−	0.893238i	$-0.351572\pi$
$719$	24.1105			0.899170			0.449585	+	0.893238i	$0.351572\pi$
$720$	3.62615			0.135139
$721$	−5.63234	−	6.23553i	−0.209759	−	0.232223i
$722$	3.36032	−	5.82024i	0.125058	−	0.216607i
$723$	−5.25156	−	9.09597i	−0.195308	−	0.338283i
$724$	−0.325125	−	0.563133i	−0.0120832	−	0.0209287i
$725$	−0.863564			−0.0320720
$726$	−5.62382	+	9.74074i	−0.208720	+	0.361513i
$727$	27.2156			1.00937			0.504686	−	0.863303i	$-0.331608\pi$
$727$	27.2156			1.00937			0.504686	+	0.863303i	$0.331608\pi$
$728$	−22.1998	−	18.8419i	−0.822780	−	0.698328i
$729$	1.00000			0.0370370
$730$	10.2973	−	17.8354i	0.381119	−	0.660118i
$731$	−14.7819			−0.546727
$732$	−2.09125	−	3.62216i	−0.0772949	−	0.133879i
$733$	−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
$735$	−13.5117	−	9.75181i	−0.498385	−	0.359701i
$736$	26.8113			0.988278
$737$	−3.71468			−0.136832
$738$	−11.2159			−0.412862
$739$	22.7217			0.835832			0.417916	−	0.908486i	$-0.362761\pi$
$739$	22.7217			0.835832			0.417916	+	0.908486i	$0.362761\pi$
$740$	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	0.993911	−	0.110182i	$-0.0351434\pi$
$743$	10.9451	+	18.9574i	0.401535	+	0.695480i	−0.592376	+	0.805662i	$0.701810\pi$
$744$	−9.43424	+	16.3406i	−0.345876	+	0.599075i
$745$	15.7834	+	27.3376i	0.578259	+	1.00157i
$746$	12.7215	−	22.0344i	0.465769	−	0.806735i
$747$	8.44505			0.308988
$748$	−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
$751$	−12.3385	+	21.3710i	−0.450240	+	0.779839i	−0.998401	−	0.0565344i	$-0.981995\pi$
$751$	−12.3385	+	21.3710i	−0.450240	+	0.779839i	0.548161	+	0.836373i	$0.315328\pi$
$752$	−16.9009			−0.616311
$753$	0.706938	−	1.22445i	0.0257622	−	0.0446215i
$754$	−3.03590	−	3.94406i	−0.110561	−	0.143634i
$755$	−39.1438			−1.42459
$756$	−1.53331	−	1.69752i	−0.0557660	−	0.0617383i
$757$	1.04346	+	1.80733i	0.0379252	+	0.0656884i	0.884365	−	0.466796i	$-0.154592\pi$
$757$	1.04346	+	1.80733i	0.0379252	+	0.0656884i	−0.846440	+	0.532484i	$0.821258\pi$
$758$	10.4298			0.378827
$759$	−1.99395	+	3.45362i	−0.0723757	+	0.125358i
$760$	12.9434	+	22.4187i	0.469507	+	0.813210i
$761$	−21.5976			−0.782911			−0.391455	−	0.920197i	$-0.628028\pi$
$761$	−21.5976			−0.782911			−0.391455	+	0.920197i	$0.628028\pi$
$762$	−12.1566			−0.440387
$763$	−13.4946	+	41.7563i	−0.488539	+	1.51168i
$764$	2.22984	+	3.86219i	0.0806727	+	0.139729i
$765$	1.68512	−	2.91872i	0.0609257	−	0.105526i
$766$	−7.91537	+	13.7098i	−0.285994	+	0.495356i
$767$	−7.08373	+	17.1753i	−0.255779	+	0.620165i
$768$	−8.15681	−	14.1280i	−0.294334	−	0.509801i
$769$	2.39533	+	4.14883i	0.0863777	+	0.149611i	0.905977	−	0.423326i	$-0.139137\pi$
$769$	2.39533	+	4.14883i	0.0863777	+	0.149611i	−0.819600	+	0.572937i	$0.805804\pi$
$770$	4.37425	−	0.936990i	0.157637	−	0.0337668i
$771$	−6.87362	+	11.9055i	−0.247547	+	0.428765i
$772$	1.23043	+	2.13116i	0.0442841	+	0.0767023i
$773$	−5.29480	−	9.17087i	−0.190441	−	0.329853i	0.754956	−	0.655776i	$-0.227658\pi$
$773$	−5.29480	−	9.17087i	−0.190441	−	0.329853i	−0.945396	+	0.325923i	$0.894325\pi$
$774$	5.56257	+	9.63465i	0.199942	+	0.346310i
$775$	−2.06028	−	3.56852i	−0.0740076	−	0.128185i
$776$	24.0675	−	41.6862i	0.863974	−	1.49645i
$777$	−6.42538	+	19.8820i	−0.230509	+	0.713262i
$778$	−10.2585	−	17.7682i	−0.367784	−	0.637021i
$779$	−18.7502	−	32.4764i	−0.671797	−	1.16359i
$780$	7.35571	−	0.979756i	0.263377	−	0.0350809i
$781$	−4.01279	+	6.95036i	−0.143589	+	0.248703i
$782$	−4.51265	+	7.81613i	−0.161372	+	0.279504i
$783$	−0.647747	−	1.12193i	−0.0231486	−	0.0400945i
$784$	1.08113	−	10.6081i	0.0386118	−	0.378862i
$785$	43.5642			1.55487
$786$	−9.17984			−0.327434
$787$	15.1155	+	26.1808i	0.538810	+	0.933246i	0.998968	+	0.0454093i	$0.0144592\pi$
$787$	15.1155	+	26.1808i	0.538810	+	0.933246i	−0.460159	+	0.887837i	$0.652207\pi$
$788$	0.418072	−	0.724121i	0.0148932	−	0.0257958i
$789$	−7.97741			−0.284003
$790$	5.08146	+	8.80135i	0.180790	+	0.313138i
$791$	5.81676	−	17.9987i	0.206820	−	0.639960i
$792$	2.03469			0.0722995
$793$	10.6390	+	13.8216i	0.377803	+	0.490818i
$794$	−20.4059	+	35.3441i	−0.724179	+	1.25432i
$795$	−16.1502			−0.572789
$796$	4.05567	−	7.02462i	0.143749	−	0.248981i
$797$	−4.57126	+	7.91765i	−0.161922	+	0.280457i	−0.935558	−	0.353173i	$-0.885103\pi$
$797$	−4.57126	+	7.91765i	−0.161922	+	0.280457i	0.773636	+	0.633630i	$0.218436\pi$
$798$	−3.08868	+	9.55725i	−0.109338	+	0.338323i
$799$	−7.85406	+	13.6036i	−0.277857	+	0.481262i
$800$	2.98739			0.105620
$801$	−0.910778	+	1.57751i	−0.0321808	+	0.0557387i
$802$	−18.9730	−	32.8622i	−0.669960	−	1.16040i
$803$	2.70610	−	4.68711i	0.0954963	−	0.165404i
$804$	−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
$808$	−27.3816			−0.963283
$809$	−34.3902			−1.20909			−0.604547	−	0.796569i	$-0.706646\pi$
$809$	−34.3902			−1.20909			−0.604547	+	0.796569i	$0.706646\pi$
$810$	−2.53651			−0.0891240
$811$	−11.9106			−0.418237			−0.209119	−	0.977890i	$-0.567060\pi$
$811$	−11.9106			−0.418237			−0.209119	+	0.977890i	$0.567060\pi$
$812$	−0.911304	+	2.81984i	−0.0319805	+	0.0989568i
$813$	5.15953	−	8.93656i	0.180952	−	0.313419i
$814$	−2.80470	−	4.85789i	−0.0983049	−	0.170269i
$815$	8.07955	+	13.9942i	0.283014	+	0.490195i
$816$	2.15668			0.0754989
$817$	−18.5985	+	32.2136i	−0.650680	+	1.12701i
$818$	−3.37218			−0.117906
$819$	7.27295	+	6.17286i	0.254137	+	0.215697i
$820$	−21.6635			−0.756523
$821$	−1.47638	+	2.55717i	−0.0515261	+	0.0892458i	−0.890638	−	0.454713i	$-0.849742\pi$
$821$	−1.47638	+	2.55717i	−0.0515261	+	0.0892458i	0.839112	+	0.543959i	$0.183075\pi$
$822$	−8.90247			−0.310509
$823$	21.1527	+	36.6376i	0.737338	+	1.27711i	0.953690	+	0.300791i	$0.0972507\pi$
$823$	21.1527	+	36.6376i	0.737338	+	1.27711i	−0.216352	+	0.976315i	$0.569416\pi$
$824$	4.84705	+	8.39534i	0.168855	+	0.292466i
$825$	−0.222171	+	0.384812i	−0.00773501	+	0.0133974i
$826$	−14.2046	+	3.04271i	−0.494241	+	0.105869i
$827$	−23.0380			−0.801109			−0.400554	−	0.916273i	$-0.631182\pi$
$827$	−23.0380			−0.801109			−0.400554	+	0.916273i	$0.631182\pi$
$828$	−5.17244			−0.179755
$829$	16.4790			0.572338			0.286169	−	0.958179i	$-0.407618\pi$
$829$	16.4790			0.572338			0.286169	+	0.958179i	$0.407618\pi$
$830$	−21.4210			−0.743533
$831$	−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
$835$	−1.96825	+	3.40911i	−0.0681142	+	0.117977i
$836$	1.02664	+	1.77820i	0.0355072	+	0.0615002i
$837$	3.09078	−	5.35339i	0.106833	−	0.185040i
$838$	−23.5552			−0.813701
$839$	−8.66147	+	15.0021i	−0.299027	+	0.517930i	−0.975914	−	0.218157i	$-0.929995\pi$
$839$	−8.66147	+	15.0021i	−0.299027	+	0.517930i	0.676887	+	0.736087i	$0.263329\pi$
$840$	12.8860	+	14.2661i	0.444611	+	0.492226i
$841$	13.6608	−	23.6613i	0.471064	−	0.815906i
$842$	−4.12909	+	7.15179i	−0.142298	+	0.246467i
$843$	2.60596			0.0897539
$844$	−8.97068	+	15.5377i	−0.308784	+	0.534829i
$845$	−29.8671	+	8.10009i	−1.02746	+	0.278652i
$846$	11.8222			0.406457
$847$	−27.3082	+	5.84957i	−0.938320	+	0.200994i
$848$	−5.16740	−	8.95020i	−0.177449	−	0.307351i
$849$	−1.73242			−0.0594566
$850$	−0.502812	+	0.870896i	−0.0172463	+	0.0298715i
$851$	23.6231	+	40.9164i	0.809789	+	1.40260i
$852$	−10.4095			−0.356622
$853$	−47.0511			−1.61100			−0.805499	−	0.592597i	$-0.798103\pi$
$853$	−47.0511			−1.61100			−0.805499	+	0.592597i	$0.798103\pi$
$854$	−4.19390	+	12.9771i	−0.143512	+	0.444069i
$855$	−4.24043	−	7.34465i	−0.145020	−	0.251182i
$856$	−7.63912	+	13.2314i	−0.261100	+	0.452238i
$857$	−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	$0.293520\pi$
$858$	−2.53856	+	0.338128i	−0.0866651	+	0.0115435i
$859$	−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
$861$	−18.6671	−	20.6663i	−0.636173	−	0.704304i
$862$	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	$-0.404261\pi$
$864$	2.24080	+	3.88118i	0.0762336	+	0.132040i
$865$	−14.2683	−	24.7135i	−0.485138	−	0.840283i
$866$	−13.0413	−	22.5882i	−0.443161	−	0.767577i
$867$	−7.49776	+	12.9865i	−0.254637	+	0.441045i
$868$	−13.8266	+	2.96175i	−0.469306	+	0.100528i
$869$	1.33540	+	2.31298i	0.0453003	+	0.0784624i
$870$	1.64302	+	2.84579i	0.0557035	+	0.0964814i
$871$	12.2557	+	15.9219i	0.415269	+	0.539492i
$872$	25.3135	−	43.8443i	0.857225	−	1.48476i
$873$	−7.88484	+	13.6569i	−0.266861	+	0.462217i
$874$	11.3556	+	19.6685i	0.384109	+	0.665296i
$875$	26.6869	−	5.71649i	0.902181	−	0.193253i
$876$	7.01982			0.237178
$877$	−15.2544			−0.515106			−0.257553	−	0.966264i	$-0.582916\pi$
$877$	−15.2544			−0.515106			−0.257553	+	0.966264i	$0.582916\pi$
$878$	5.71509	+	9.89883i	0.192875	+	0.334069i
$879$	16.4196	−	28.4396i	0.553819	−	0.959243i
$880$	−2.41716			−0.0814824
$881$	−25.8195	−	44.7207i	−0.869881	−	1.50668i	−0.862117	−	0.506709i	$-0.830862\pi$
$881$	−25.8195	−	44.7207i	−0.869881	−	1.50668i	−0.00776438	−	0.999970i	$-0.502472\pi$
$882$	−0.756256	+	7.42045i	−0.0254645	+	0.249860i
$883$	27.4588			0.924062			0.462031	−	0.886864i	$-0.347121\pi$
$883$	27.4588			0.924062			0.462031	+	0.886864i	$0.347121\pi$
$884$	4.37486	−	0.582716i	0.147142	−	0.0195989i
$885$	6.13305	−	10.6227i	0.206160	−	0.357080i
$886$	−42.4864			−1.42736
$887$	−16.4316	+	28.4603i	−0.551718	+	0.955604i	0.446432	+	0.894817i	$0.352694\pi$
$887$	−16.4316	+	28.4603i	−0.551718	+	0.955604i	−0.998151	+	0.0607868i	$0.980639\pi$
$888$	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
$891$	−0.666590			−0.0223316
$892$	3.50595	−	6.07249i	0.117388	−	0.203322i
$893$	19.7639	+	34.2321i	0.661375	+	1.14553i
$894$	7.06506	−	12.2370i	0.236291	−	0.409268i
$895$	−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
$899$	−8.00817			−0.267088
$900$	−0.576328			−0.0192109
$901$	−9.60544			−0.320004
$902$	7.47640			0.248937
$903$	−8.49466	+	26.2849i	−0.282685	+	0.874707i
$904$	−10.9112	+	18.8988i	−0.362901	+	0.628564i
$905$	−0.895159	−	1.55046i	−0.0297561	−	0.0515391i
$906$	8.76088	+	15.1743i	0.291061	+	0.504132i
$907$	44.8192			1.48820			0.744098	−	0.668071i	$-0.232880\pi$
$907$	44.8192			1.48820			0.744098	+	0.668071i	$0.232880\pi$
$908$	0.949880	−	1.64524i	0.0315229	−	0.0545992i
$909$	8.97058			0.297535
$910$	−18.4479	−	15.6575i	−0.611543	−	0.519042i
$911$	31.4169			1.04089			0.520445	−	0.853895i	$-0.325766\pi$
$911$	31.4169			1.04089			0.520445	+	0.853895i	$0.325766\pi$
$912$	2.71353	−	4.69997i	0.0898539	−	0.155632i
$913$	−5.62939			−0.186306
$914$	8.54291	+	14.7968i	0.282574	+	0.489433i
$915$	−5.75780	−	9.97280i	−0.190347	−	0.329691i
$916$	8.77952	−	15.2066i	0.290084	−	0.502439i
$917$	−15.2784	−	16.9147i	−0.504538	−	0.558572i
$918$	−1.50861			−0.0497915
$919$	37.3862			1.23326			0.616628	−	0.787255i	$-0.288498\pi$
$919$	37.3862			1.23326			0.616628	+	0.787255i	$0.288498\pi$
$920$	43.4695			1.43315
$921$	29.4618			0.970800
$922$	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
$926$	13.8507	−	23.9902i	0.455163	−	0.788366i
$927$	−1.58796	−	2.75042i	−0.0521554	−	0.0903358i
$928$	2.90295	−	5.02805i	0.0952938	−	0.165054i
$929$	−23.1574			−0.759768			−0.379884	−	0.925034i	$-0.624036\pi$
$929$	−23.1574			−0.759768			−0.379884	+	0.925034i	$0.624036\pi$
$930$	−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
$933$	3.53099	−	6.11585i	0.115599	−	0.200224i
$934$	22.1980			0.726342
$935$	−1.12329	+	1.94559i	−0.0367354	+	0.0636275i
$936$	−6.71298	−	8.72109i	−0.219420	−	0.285058i
$937$	−20.1142			−0.657103			−0.328552	−	0.944486i	$-0.606560\pi$
$937$	−20.1142			−0.657103			−0.328552	+	0.944486i	$0.606560\pi$
$938$	−4.83120	+	14.9491i	−0.157744	+	0.488106i
$939$	−8.17883	−	14.1661i	−0.266906	−	0.462295i
$940$	22.8347			0.744787
$941$	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	$0.0674101\pi$
$942$	−9.75023	−	16.8879i	−0.317680	−	0.550237i
$943$	−62.9712			−2.05062
$944$	7.84929			0.255473
$945$	−4.22163	−	4.67375i	−0.137330	−	0.152037i
$946$	−3.70795	−	6.42236i	−0.120556	−	0.208809i
$947$	12.6734	−	21.9511i	0.411832	−	0.713313i	−0.583258	−	0.812287i	$-0.698223\pi$
$947$	12.6734	−	21.9511i	0.411832	−	0.713313i	0.995090	+	0.0989733i	$0.0315558\pi$
$948$	−1.73206	+	3.00001i	−0.0562546	+	0.0974359i
$949$	−29.0181	+	3.86510i	−0.941966	+	0.125467i
$950$	1.26527	+	2.19152i	0.0410509	+	0.0711022i
$951$	9.48109	+	16.4217i	0.307446	+	0.532511i
$952$	7.66406	+	8.48484i	0.248394	+	0.274995i
$953$	−0.132751	+	0.229931i	−0.00430021	+	0.00744818i	−0.868168	−	0.496271i	$-0.834702\pi$
$953$	−0.132751	+	0.229931i	−0.00430021	+	0.00744818i	0.863867	+	0.503719i	$0.168035\pi$
$954$	3.61462	+	6.26071i	0.117028	+	0.202698i
$955$	6.13937	+	10.6337i	0.198665	+	0.344098i
$956$	−7.50883	−	13.0057i	−0.242853	−	0.420634i
$957$	0.431782	+	0.747868i	0.0139575	+	0.0241751i
$958$	16.4563	−	28.5032i	0.531680	−	0.920897i
$959$	−14.8168	−	16.4036i	−0.478459	−	0.529699i
$960$	−9.30997	−	16.1253i	−0.300478	−	0.520443i
$961$	−3.60583	−	6.24549i	−0.116317	−	0.201467i
$962$	−11.5684	+	28.0490i	−0.372982	+	0.904336i
$963$	2.50268	−	4.33476i	0.0806476	−	0.139686i
$964$	−4.54045	+	7.86430i	−0.146238	+	0.253292i
$965$	3.38771	+	5.86769i	0.109054	+	0.188888i
$966$	11.3053	+	12.5160i	0.363741	+	0.402696i
$967$	15.3845			0.494732			0.247366	−	0.968922i	$-0.420435\pi$
$967$	15.3845			0.494732			0.247366	+	0.968922i	$0.420435\pi$
$968$	32.2199			1.03559
$969$	−2.52203	−	4.36828i	−0.0810192	−	0.140329i
$970$	20.0000	−	34.6410i	0.642161	−	1.11226i
$971$	−46.5181			−1.49284			−0.746418	−	0.665478i	$-0.768228\pi$
$971$	−46.5181			−1.49284			−0.746418	+	0.665478i	$0.768228\pi$
$972$	−0.432296	−	0.748758i	−0.0138659	−	0.0240164i
$973$	7.85400	−	24.3025i	0.251788	−	0.779103i
$974$	23.8973			0.765720
$975$	2.38239	−	0.317326i	0.0762974	−	0.0101625i
$976$	3.68452	−	6.38177i	0.117939	−	0.204276i
$977$	10.5495			0.337507			0.168754	−	0.985658i	$-0.446026\pi$
$977$	10.5495			0.337507			0.168754	+	0.985658i	$0.446026\pi$
$978$	3.61662	−	6.26416i	0.115647	−	0.200306i
$979$	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
$982$	14.2085			0.453410
$983$	−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	$0.988880\pi$
$984$	16.0645	+	27.8245i	0.512116	+	0.887011i
$985$	1.15107	−	1.99371i	0.0366761	−	0.0635248i
$986$	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
$990$	1.69081			0.0537376
$991$	43.7630			1.39018			0.695089	−	0.718923i	$-0.255365\pi$
$991$	43.7630			1.39018			0.695089	+	0.718923i	$0.255365\pi$
$992$	27.7033			0.879580
$993$	19.0379			0.604149
$994$	22.7517	+	25.1883i	0.721639	+	0.798923i
$995$	11.1664	−	19.3407i	0.353998	−	0.613142i
$996$	−3.65076	−	6.32330i	−0.115679	−	0.200362i
$997$	−26.0411	−	45.1045i	−0.824729	−	1.42847i	−0.902126	−	0.431473i	$-0.857994\pi$
$997$	−26.0411	−	45.1045i	−0.824729	−	1.42847i	0.0773967	−	0.997000i	$-0.475339\pi$
$998$	32.5224			1.02948
$999$	−3.94868	+	6.83932i	−0.124931	+	0.216386i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.3	✓	16	91.9	even	3	inner
273.2.j.b.172.3	yes	16	1.1	even	1	trivial
273.2.l.b.16.6	yes	16	7.2	even	3
273.2.l.b.256.6	yes	16	13.9	even	3
819.2.n.e.100.6		16	273.191	odd	6
819.2.n.e.172.6		16	3.2	odd	2
819.2.s.e.289.3		16	21.2	odd	6
819.2.s.e.802.3		16	39.35	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.532778 + 0.922798i) q^{2} -1.00000 q^{3} +(0.432296 + 0.748758i) q^{4} +(1.19023 + 2.06154i) q^{5} +(0.532778 - 0.922798i) q^{6} +(2.58706 - 0.554165i) q^{7} -3.05238 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.532778 + 0.922798i) q^{2} -1.00000 q^{3} +(0.432296 + 0.748758i) q^{4} +(1.19023 + 2.06154i) q^{5} +(0.532778 - 0.922798i) q^{6} +(2.58706 - 0.554165i) q^{7} -3.05238 q^{8} +1.00000 q^{9} -2.53651 q^{10} -0.666590 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} +(0.761650 - 1.31922i) q^{16} +(-0.707897 - 1.22611i) q^{17} +(-0.532778 + 0.922798i) q^{18} -3.56270 q^{19} +(-1.02906 + 1.78239i) q^{20} +(-2.58706 + 0.554165i) q^{21} +(0.355145 - 0.615128i) q^{22} +(-2.99126 + 5.18102i) q^{23} +3.05238 q^{24} +(-0.333295 + 0.577284i) q^{25} +(-3.80828 + 0.507250i) q^{26} -1.00000 q^{27} +(1.53331 + 1.69752i) q^{28} +(0.647747 + 1.12193i) q^{29} +2.53651 q^{30} +(-3.09078 + 5.35339i) q^{31} +(-2.24080 - 3.88118i) q^{32} +0.666590 q^{33} +1.50861 q^{34} +(4.22163 + 4.67375i) q^{35} +(0.432296 + 0.748758i) q^{36} +(3.94868 - 6.83932i) q^{37} +(1.89813 - 3.28765i) q^{38} +(-2.19926 - 2.85714i) q^{39} +(-3.63304 - 6.29260i) q^{40} +(5.26293 + 9.11566i) q^{41} +(0.866948 - 2.68258i) q^{42} +(5.22034 - 9.04190i) q^{43} +(-0.288164 - 0.499115i) q^{44} +(1.19023 + 2.06154i) q^{45} +(-3.18736 - 5.52067i) q^{46} +(-5.54746 - 9.60848i) q^{47} +(-0.761650 + 1.31922i) q^{48} +(6.38580 - 2.86732i) q^{49} +(-0.355145 - 0.615128i) q^{50} +(0.707897 + 1.22611i) q^{51} +(-1.18858 + 2.88184i) q^{52} +(3.39224 - 5.87554i) q^{53} +(0.532778 - 0.922798i) q^{54} +(-0.793396 - 1.37420i) q^{55} +(-7.89671 + 1.69152i) q^{56} +3.56270 q^{57} -1.38042 q^{58} +(2.57641 + 4.46248i) q^{59} +(1.02906 - 1.78239i) q^{60} +4.83755 q^{61} +(-3.29340 - 5.70433i) q^{62} +(2.58706 - 0.554165i) q^{63} +7.82199 q^{64} +(-3.27249 + 7.93451i) q^{65} +(-0.355145 + 0.615128i) q^{66} +5.57265 q^{67} +(0.612042 - 1.06009i) q^{68} +(2.99126 - 5.18102i) q^{69} +(-6.56212 + 1.40565i) q^{70} +(6.01988 - 10.4267i) q^{71} -3.05238 q^{72} +(-4.05962 + 7.03147i) q^{73} +(4.20754 + 7.28767i) q^{74} +(0.333295 - 0.577284i) 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} +3.62615 q^{80} +1.00000 q^{81} -11.2159 q^{82} +8.44505 q^{83} +(-1.53331 - 1.69752i) q^{84} +(1.68512 - 2.91872i) q^{85} +(5.56257 + 9.63465i) q^{86} +(-0.647747 - 1.12193i) q^{87} +2.03469 q^{88} +(-0.910778 + 1.57751i) q^{89} -2.53651 q^{90} +(7.27295 + 6.17286i) q^{91} -5.17244 q^{92} +(3.09078 - 5.35339i) q^{93} +11.8222 q^{94} +(-4.24043 - 7.34465i) q^{95} +(2.24080 + 3.88118i) q^{96} +(-7.88484 + 13.6569i) q^{97} +(-0.756256 + 7.42045i) q^{98} -0.666590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9	\( 16 q - 16 q^{3} - 6 q^{4} + q^{7} + 12 q^{8} + 16 q^{9} + 8 q^{10} + 4 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} - 6 q^{16} - 2 q^{17} + 22 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} + 4 q^{23} - 12 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{27} - 7 q^{28} + 15 q^{29} - 8 q^{30} + 3 q^{31} + 3 q^{32} - 4 q^{33} - 68 q^{34} - 12 q^{35} - 6 q^{36} + 4 q^{37} + 2 q^{38} - 5 q^{39} - 25 q^{40} + 19 q^{41} + 7 q^{42} + 11 q^{43} - 16 q^{44} + 2 q^{46} + 5 q^{47} + 6 q^{48} + 13 q^{49} - 7 q^{50} + 2 q^{51} + 36 q^{52} + 36 q^{53} - 15 q^{55} + 39 q^{56} - 22 q^{57} - 40 q^{58} - 17 q^{59} + 20 q^{60} + 44 q^{61} - 6 q^{62} + q^{63} - 20 q^{64} - 21 q^{65} - 7 q^{66} - 52 q^{67} + 5 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} + 12 q^{72} - 6 q^{73} + 15 q^{74} - 2 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} + 56 q^{80} + 16 q^{81} + 2 q^{82} + 36 q^{83} + 7 q^{84} - 4 q^{85} + 16 q^{86} - 15 q^{87} - 48 q^{88} + 20 q^{89} + 8 q^{90} - 7 q^{91} - 94 q^{92} - 3 q^{93} + 40 q^{94} - 3 q^{96} + 7 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 16 * q^3 - 6 * q^4 + q^7 + 12 * q^8 + 16 * q^9 + 8 * q^10 + 4 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 - 6 * q^16 - 2 * q^17 + 22 * q^19 - 20 * q^20 - q^21 + 7 * q^22 + 4 * q^23 - 12 * q^24 + 2 * q^25 - 6 * q^26 - 16 * q^27 - 7 * q^28 + 15 * q^29 - 8 * q^30 + 3 * q^31 + 3 * q^32 - 4 * q^33 - 68 * q^34 - 12 * q^35 - 6 * q^36 + 4 * q^37 + 2 * q^38 - 5 * q^39 - 25 * q^40 + 19 * q^41 + 7 * q^42 + 11 * q^43 - 16 * q^44 + 2 * q^46 + 5 * q^47 + 6 * q^48 + 13 * q^49 - 7 * q^50 + 2 * q^51 + 36 * q^52 + 36 * q^53 - 15 * q^55 + 39 * q^56 - 22 * q^57 - 40 * q^58 - 17 * q^59 + 20 * q^60 + 44 * q^61 - 6 * q^62 + q^63 - 20 * q^64 - 21 * q^65 - 7 * q^66 - 52 * q^67 + 5 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 + 12 * q^72 - 6 * q^73 + 15 * q^74 - 2 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 + 56 * q^80 + 16 * q^81 + 2 * q^82 + 36 * q^83 + 7 * q^84 - 4 * q^85 + 16 * q^86 - 15 * q^87 - 48 * q^88 + 20 * q^89 + 8 * q^90 - 7 * q^91 - 94 * q^92 - 3 * q^93 + 40 * q^94 - 3 * q^96 + 7 * q^97 - 3 * q^98 + 4 * q^99

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