LMFDB - Embedded newform 238.2.e.f.205.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [238,2,Mod(137,238)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(238, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("238.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 238 = 2 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	238.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.90043956811$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 13x^{8} - 4x^{7} + 145x^{6} - 22x^{5} + 316x^{4} + 152x^{3} + 568x^{2} + 96x + 16 $ x^10 + 13x^8 - 4x^7 + 145x^6 - 22x^5 + 316x^4 + 152x^3 + 568x^2 + 96x + 16
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			205.2
Root			$0.861234 + 1.49170i$ of defining polynomial
Character	$\chi$	$=$	238.205
Dual form			238.2.e.f.137.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.861234 - 1.49170i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.21063 + 2.09688i) q^{5} +1.72247 q^{6} +(2.59711 - 0.504977i) q^{7} +1.00000 q^{8} +(0.0165513 - 0.0286678i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.861234 - 1.49170i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.21063 + 2.09688i) q^{5} +1.72247 q^{6} +(2.59711 - 0.504977i) q^{7} +1.00000 q^{8} +(0.0165513 - 0.0286678i) q^{9} +(-1.21063 - 2.09688i) q^{10} +(-1.86123 - 3.22375i) q^{11} +(-0.861234 + 1.49170i) q^{12} +6.58239 q^{13} +(-0.861234 + 2.50165i) q^{14} +4.17056 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{17} +(0.0165513 + 0.0286678i) q^{18} +(2.79120 - 4.83449i) q^{19} +2.42127 q^{20} +(-2.99000 - 3.43921i) q^{21} +3.72247 q^{22} +(2.98528 - 5.17066i) q^{23} +(-0.861234 - 1.49170i) q^{24} +(-0.431272 - 0.746985i) q^{25} +(-3.29120 + 5.70052i) q^{26} -5.22442 q^{27} +(-1.73588 - 1.99668i) q^{28} -0.772958 q^{29} +(-2.08528 + 3.61181i) q^{30} +(4.80775 + 8.32726i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.20592 + 5.55281i) q^{33} -1.00000 q^{34} +(-2.08528 + 6.05718i) q^{35} -0.0331027 q^{36} +(-2.21063 + 3.82893i) q^{37} +(2.79120 + 4.83449i) q^{38} +(-5.66898 - 9.81897i) q^{39} +(-1.21063 + 2.09688i) q^{40} -5.61550 q^{41} +(4.47345 - 0.869806i) q^{42} -6.25437 q^{43} +(-1.86123 + 3.22375i) q^{44} +(0.0400752 + 0.0694124i) q^{45} +(2.98528 + 5.17066i) q^{46} +(0.335989 - 0.581951i) q^{47} +1.72247 q^{48} +(6.49000 - 2.62296i) q^{49} +0.862543 q^{50} +(0.861234 - 1.49170i) q^{51} +(-3.29120 - 5.70052i) q^{52} +(-4.95521 - 8.58267i) q^{53} +(2.61221 - 4.52448i) q^{54} +9.01310 q^{55} +(2.59711 - 0.504977i) q^{56} -9.61550 q^{57} +(0.386479 - 0.669401i) q^{58} +(5.16029 + 8.93788i) q^{59} +(-2.08528 - 3.61181i) q^{60} +(-2.36281 + 4.09251i) q^{61} -9.61550 q^{62} +(0.0285092 - 0.0828115i) q^{63} +1.00000 q^{64} +(-7.96887 + 13.8025i) q^{65} +(-3.20592 - 5.55281i) q^{66} +(-7.21247 - 12.4924i) q^{67} +(0.500000 - 0.866025i) q^{68} -10.2841 q^{69} +(-4.20303 - 4.83449i) q^{70} +9.69303 q^{71} +(0.0165513 - 0.0286678i) q^{72} +(-0.807748 - 1.39906i) q^{73} +(-2.21063 - 3.82893i) q^{74} +(-0.742852 + 1.28666i) q^{75} -5.58239 q^{76} +(-6.46176 - 7.43257i) q^{77} +11.3380 q^{78} +(-2.28250 + 3.95341i) q^{79} +(-1.21063 - 2.09688i) q^{80} +(4.44980 + 7.70728i) q^{81} +(2.80775 - 4.86316i) q^{82} +10.3222 q^{83} +(-1.48345 + 4.30902i) q^{84} -2.42127 q^{85} +(3.12719 - 5.41645i) q^{86} +(0.665698 + 1.15302i) q^{87} +(-1.86123 - 3.22375i) q^{88} +(-2.19711 + 3.80551i) q^{89} -0.0801505 q^{90} +(17.0952 - 3.32395i) q^{91} -5.97056 q^{92} +(8.28119 - 14.3434i) q^{93} +(0.335989 + 0.581951i) q^{94} +(6.75824 + 11.7056i) q^{95} +(-0.861234 + 1.49170i) q^{96} -7.54929 q^{97} +(-0.973446 + 6.93198i) q^{98} -0.123224 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 5 q^{4} + q^{5} - 3 q^{7} + 10 q^{8} - 11 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - 5 * q^4 + q^5 - 3 * q^7 + 10 * q^8 - 11 * q^9	\( 10 q - 5 q^{2} - 5 q^{4} + q^{5} - 3 q^{7} + 10 q^{8} - 11 q^{9} + q^{10} - 10 q^{11} + 4 q^{13} - 8 q^{15} - 5 q^{16} + 5 q^{17} - 11 q^{18} - 3 q^{19} - 2 q^{20} + 10 q^{21} + 20 q^{22} - 3 q^{23} - 18 q^{25} - 2 q^{26} - 12 q^{27} + 3 q^{28} + 24 q^{29} + 4 q^{30} + 6 q^{31} - 5 q^{32} - 26 q^{33} - 10 q^{34} + 4 q^{35} + 22 q^{36} - 9 q^{37} - 3 q^{38} - 6 q^{39} + q^{40} + 28 q^{41} + 16 q^{42} + 2 q^{43} - 10 q^{44} + 37 q^{45} - 3 q^{46} + 2 q^{47} + 25 q^{49} + 36 q^{50} - 2 q^{52} - 20 q^{53} + 6 q^{54} - 12 q^{55} - 3 q^{56} - 12 q^{57} - 12 q^{58} - 3 q^{59} + 4 q^{60} - 16 q^{61} - 12 q^{62} + 6 q^{63} + 10 q^{64} - 2 q^{65} - 26 q^{66} - 15 q^{67} + 5 q^{68} + 8 q^{69} + q^{70} + 14 q^{71} - 11 q^{72} + 34 q^{73} - 9 q^{74} - 46 q^{75} + 6 q^{76} + 16 q^{77} + 12 q^{78} + 12 q^{79} + q^{80} - 53 q^{81} - 14 q^{82} + 32 q^{83} - 26 q^{84} + 2 q^{85} - q^{86} + 20 q^{87} - 10 q^{88} - q^{89} - 74 q^{90} + 42 q^{91} + 6 q^{92} + 12 q^{93} + 2 q^{94} + 3 q^{95} - 36 q^{97} + 19 q^{98} + 32 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 5 * q^4 + q^5 - 3 * q^7 + 10 * q^8 - 11 * q^9 + q^10 - 10 * q^11 + 4 * q^13 - 8 * q^15 - 5 * q^16 + 5 * q^17 - 11 * q^18 - 3 * q^19 - 2 * q^20 + 10 * q^21 + 20 * q^22 - 3 * q^23 - 18 * q^25 - 2 * q^26 - 12 * q^27 + 3 * q^28 + 24 * q^29 + 4 * q^30 + 6 * q^31 - 5 * q^32 - 26 * q^33 - 10 * q^34 + 4 * q^35 + 22 * q^36 - 9 * q^37 - 3 * q^38 - 6 * q^39 + q^40 + 28 * q^41 + 16 * q^42 + 2 * q^43 - 10 * q^44 + 37 * q^45 - 3 * q^46 + 2 * q^47 + 25 * q^49 + 36 * q^50 - 2 * q^52 - 20 * q^53 + 6 * q^54 - 12 * q^55 - 3 * q^56 - 12 * q^57 - 12 * q^58 - 3 * q^59 + 4 * q^60 - 16 * q^61 - 12 * q^62 + 6 * q^63 + 10 * q^64 - 2 * q^65 - 26 * q^66 - 15 * q^67 + 5 * q^68 + 8 * q^69 + q^70 + 14 * q^71 - 11 * q^72 + 34 * q^73 - 9 * q^74 - 46 * q^75 + 6 * q^76 + 16 * q^77 + 12 * q^78 + 12 * q^79 + q^80 - 53 * q^81 - 14 * q^82 + 32 * q^83 - 26 * q^84 + 2 * q^85 - q^86 + 20 * q^87 - 10 * q^88 - q^89 - 74 * q^90 + 42 * q^91 + 6 * q^92 + 12 * q^93 + 2 * q^94 + 3 * q^95 - 36 * q^97 + 19 * q^98 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/238\mathbb{Z}\right)^\times$.

$n$	$71$	$171$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.861234	−	1.49170i	−0.497234	−	0.861234i	0.502761	−	0.864425i	$-0.332318\pi$
$3$	−0.861234	−	1.49170i	−0.497234	−	0.861234i	−0.999995	+	0.00319120i	$0.998984\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.21063	+	2.09688i	−0.541412	+	0.937753i	0.457411	+	0.889255i	$0.348777\pi$
$5$	−1.21063	+	2.09688i	−0.541412	+	0.937753i	−0.998823	+	0.0484981i	$0.984557\pi$
$6$	1.72247			0.703195
$7$	2.59711	−	0.504977i	0.981617	−	0.190863i
$7$	2.59711	−	0.504977i	0.981617	−	0.190863i
$8$	1.00000			0.353553
$9$	0.0165513	−	0.0286678i	0.00551711	−	0.00955592i
$10$	−1.21063	−	2.09688i	−0.382836	−	0.663092i
$11$	−1.86123	−	3.22375i	−0.561183	−	0.971998i	−0.997394	−	0.0721531i	$-0.977013\pi$
$11$	−1.86123	−	3.22375i	−0.561183	−	0.971998i	0.436210	−	0.899845i	$-0.356320\pi$
$12$	−0.861234	+	1.49170i	−0.248617	+	0.430617i
$13$	6.58239			1.82563			0.912814	−	0.408376i	$-0.133905\pi$
$13$	6.58239			1.82563			0.912814	+	0.408376i	$0.133905\pi$
$14$	−0.861234	+	2.50165i	−0.230175	+	0.668595i
$15$	4.17056			1.07683
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$18$	0.0165513	+	0.0286678i	0.00390119	+	0.00675706i
$19$	2.79120	−	4.83449i	0.640344	−	1.10911i	−0.345011	−	0.938598i	$-0.612125\pi$
$19$	2.79120	−	4.83449i	0.640344	−	1.10911i	0.985356	−	0.170511i	$-0.0545417\pi$
$20$	2.42127			0.541412
$21$	−2.99000	−	3.43921i	−0.652471	−	0.750498i
$22$	3.72247			0.793633
$23$	2.98528	−	5.17066i	0.622474	−	1.07816i	−0.366550	−	0.930398i	$-0.619461\pi$
$23$	2.98528	−	5.17066i	0.622474	−	1.07816i	0.989024	−	0.147758i	$-0.0472056\pi$
$24$	−0.861234	−	1.49170i	−0.175799	−	0.304492i
$25$	−0.431272	−	0.746985i	−0.0862543	−	0.149397i
$26$	−3.29120	+	5.70052i	−0.645457	+	1.11796i
$27$	−5.22442			−1.00544
$28$	−1.73588	−	1.99668i	−0.328050	−	0.377337i
$29$	−0.772958			−0.143535			−0.0717674	−	0.997421i	$-0.522864\pi$
$29$	−0.772958			−0.143535			−0.0717674	+	0.997421i	$0.522864\pi$
$30$	−2.08528	+	3.61181i	−0.380718	+	0.659423i
$31$	4.80775	+	8.32726i	0.863497	+	1.49562i	0.868532	+	0.495633i	$0.165064\pi$
$31$	4.80775	+	8.32726i	0.863497	+	1.49562i	−0.00503479	+	0.999987i	$0.501603\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−3.20592	+	5.55281i	−0.558079	+	0.966620i
$34$	−1.00000			−0.171499
$35$	−2.08528	+	6.05718i	−0.352477	+	1.02385i
$36$	−0.0331027			−0.00551711
$37$	−2.21063	+	3.82893i	−0.363426	+	0.629472i	−0.988522	−	0.151075i	$-0.951726\pi$
$37$	−2.21063	+	3.82893i	−0.363426	+	0.629472i	0.625096	+	0.780548i	$0.285060\pi$
$38$	2.79120	+	4.83449i	0.452792	+	0.784259i
$39$	−5.66898	−	9.81897i	−0.907764	−	1.57229i
$40$	−1.21063	+	2.09688i	−0.191418	+	0.331546i
$41$	−5.61550			−0.876993			−0.438497	−	0.898733i	$-0.644489\pi$
$41$	−5.61550			−0.876993			−0.438497	+	0.898733i	$0.644489\pi$
$42$	4.47345	−	0.869806i	0.690268	−	0.134214i
$43$	−6.25437			−0.953783			−0.476891	−	0.878962i	$-0.658237\pi$
$43$	−6.25437			−0.953783			−0.476891	+	0.878962i	$0.658237\pi$
$44$	−1.86123	+	3.22375i	−0.280592	+	0.485999i
$45$	0.0400752	+	0.0694124i	0.00597406	+	0.0103474i
$46$	2.98528	+	5.17066i	0.440155	+	0.762372i
$47$	0.335989	−	0.581951i	0.0490091	−	0.0848862i	−0.840480	−	0.541842i	$-0.817727\pi$
$47$	0.335989	−	0.581951i	0.0490091	−	0.0848862i	0.889489	+	0.456956i	$0.151060\pi$
$48$	1.72247			0.248617
$49$	6.49000	−	2.62296i	0.927142	−	0.374709i
$50$	0.862543			0.121982
$51$	0.861234	−	1.49170i	0.120597	−	0.208880i
$52$	−3.29120	−	5.70052i	−0.456407	−	0.790520i
$53$	−4.95521	−	8.58267i	−0.680650	−	1.17892i	−0.974783	−	0.223156i	$-0.928364\pi$
$53$	−4.95521	−	8.58267i	−0.680650	−	1.17892i	0.294133	−	0.955765i	$-0.404969\pi$
$54$	2.61221	−	4.52448i	0.355477	−	0.615704i
$55$	9.01310			1.21533
$56$	2.59711	−	0.504977i	0.347054	−	0.0674803i
$57$	−9.61550			−1.27360
$58$	0.386479	−	0.669401i	0.0507472	−	0.0878967i
$59$	5.16029	+	8.93788i	0.671812	+	1.16361i	0.977390	+	0.211446i	$0.0678172\pi$
$59$	5.16029	+	8.93788i	0.671812	+	1.16361i	−0.305577	+	0.952167i	$0.598849\pi$
$60$	−2.08528	−	3.61181i	−0.269208	−	0.466283i
$61$	−2.36281	+	4.09251i	−0.302527	+	0.523992i	−0.976708	−	0.214574i	$-0.931164\pi$
$61$	−2.36281	+	4.09251i	−0.302527	+	0.523992i	0.674181	+	0.738566i	$0.264497\pi$
$62$	−9.61550			−1.22117
$63$	0.0285092	−	0.0828115i	0.00359182	−	0.0104333i
$64$	1.00000			0.125000
$65$	−7.96887	+	13.8025i	−0.988417	+	1.71199i
$66$	−3.20592	−	5.55281i	−0.394621	−	0.683504i
$67$	−7.21247	−	12.4924i	−0.881143	−	1.52618i	−0.850072	−	0.526667i	$-0.823441\pi$
$67$	−7.21247	−	12.4924i	−0.881143	−	1.52618i	−0.0310713	−	0.999517i	$-0.509892\pi$
$68$	0.500000	−	0.866025i	0.0606339	−	0.105021i
$69$	−10.2841			−1.23806
$70$	−4.20303	−	4.83449i	−0.502358	−	0.577833i
$71$	9.69303			1.15035			0.575175	−	0.818030i	$-0.304934\pi$
$71$	9.69303			1.15035			0.575175	+	0.818030i	$0.304934\pi$
$72$	0.0165513	−	0.0286678i	0.00195059	−	0.00337853i
$73$	−0.807748	−	1.39906i	−0.0945398	−	0.163748i	0.814877	−	0.579634i	$-0.196805\pi$
$73$	−0.807748	−	1.39906i	−0.0945398	−	0.163748i	−0.909416	+	0.415887i	$0.863471\pi$
$74$	−2.21063	−	3.82893i	−0.256981	−	0.445104i
$75$	−0.742852	+	1.28666i	−0.0857771	+	0.148570i
$76$	−5.58239			−0.640344
$77$	−6.46176	−	7.43257i	−0.736385	−	0.847020i
$78$	11.3380			1.28377
$79$	−2.28250	+	3.95341i	−0.256802	+	0.444794i	−0.965383	−	0.260835i	$-0.916002\pi$
$79$	−2.28250	+	3.95341i	−0.256802	+	0.444794i	0.708582	+	0.705629i	$0.249335\pi$
$80$	−1.21063	−	2.09688i	−0.135353	−	0.234438i
$81$	4.44980	+	7.70728i	0.494422	+	0.856364i
$82$	2.80775	−	4.86316i	0.310064	−	0.537046i
$83$	10.3222			1.13301			0.566507	−	0.824057i	$-0.308294\pi$
$83$	10.3222			1.13301			0.566507	+	0.824057i	$0.308294\pi$
$84$	−1.48345	+	4.30902i	−0.161858	+	0.470153i
$85$	−2.42127			−0.262623
$86$	3.12719	−	5.41645i	0.337213	−	0.584070i
$87$	0.665698	+	1.15302i	0.0713703	+	0.123617i
$88$	−1.86123	−	3.22375i	−0.198408	−	0.343653i
$89$	−2.19711	+	3.80551i	−0.232894	+	0.403383i	−0.958658	−	0.284559i	$-0.908153\pi$
$89$	−2.19711	+	3.80551i	−0.232894	+	0.403383i	0.725765	+	0.687943i	$0.241486\pi$
$90$	−0.0801505			−0.00844860
$91$	17.0952	−	3.32395i	1.79207	−	0.348445i
$92$	−5.97056			−0.622474
$93$	8.28119	−	14.3434i	0.858720	−	1.48735i
$94$	0.335989	+	0.581951i	0.0346547	+	0.0600236i
$95$	6.75824	+	11.7056i	0.693381	+	1.20097i
$96$	−0.861234	+	1.49170i	−0.0878993	+	0.152246i
$97$	−7.54929			−0.766514			−0.383257	−	0.923642i	$-0.625198\pi$
$97$	−7.54929			−0.766514			−0.383257	+	0.923642i	$0.625198\pi$
$98$	−0.973446	+	6.93198i	−0.0983329	+	0.700236i
$99$	−0.123224			−0.0123844
$100$	−0.431272	+	0.746985i	−0.0431272	+	0.0746985i
$101$	6.19423	+	10.7287i	0.616349	+	1.06755i	0.990146	+	0.140037i	$0.0447221\pi$
$101$	6.19423	+	10.7287i	0.616349	+	1.06755i	−0.373798	+	0.927510i	$0.621945\pi$
$102$	0.861234	+	1.49170i	0.0852749	+	0.147700i
$103$	−2.05218	+	3.55447i	−0.202207	+	0.350233i	−0.949239	−	0.314555i	$-0.898145\pi$
$103$	−2.05218	+	3.55447i	−0.202207	+	0.350233i	0.747032	+	0.664788i	$0.231478\pi$
$104$	6.58239			0.645457
$105$	10.8314	−	2.10603i	1.05704	−	0.205528i
$106$	9.91041			0.962585
$107$	−3.24940	+	5.62813i	−0.314131	+	0.544092i	−0.979252	−	0.202644i	$-0.935047\pi$
$107$	−3.24940	+	5.62813i	−0.314131	+	0.544092i	0.665121	+	0.746736i	$0.268380\pi$
$108$	2.61221	+	4.52448i	0.251360	+	0.435369i
$109$	−3.17584	−	5.50072i	−0.304191	−	0.526874i	0.672890	−	0.739742i	$-0.265053\pi$
$109$	−3.17584	−	5.50072i	−0.304191	−	0.526874i	−0.977081	+	0.212869i	$0.931719\pi$
$110$	−4.50655	+	7.80557i	−0.429683	+	0.744232i
$111$	7.61550			0.722831
$112$	−0.861234	+	2.50165i	−0.0813790	+	0.236384i
$113$	4.84254			0.455548			0.227774	−	0.973714i	$-0.426855\pi$
$113$	4.84254			0.455548			0.227774	+	0.973714i	$0.426855\pi$
$114$	4.80775	−	8.32726i	0.450287	−	0.779920i
$115$	7.22817	+	12.5195i	0.674030	+	1.16745i
$116$	0.386479	+	0.669401i	0.0358837	+	0.0621524i
$117$	0.108947	−	0.188702i	0.0100722	−	0.0174455i
$118$	−10.3206			−0.950086
$119$	1.73588	+	1.99668i	0.159128	+	0.183035i
$120$	4.17056			0.380718
$121$	−1.42839	+	2.47404i	−0.129853	+	0.224912i
$122$	−2.36281	−	4.09251i	−0.213919	−	0.370518i
$123$	4.83626	+	8.37664i	0.436071	+	0.755296i
$124$	4.80775	−	8.32726i	0.431749	−	0.747810i
$125$	−10.0179			−0.896028
$126$	0.0574622	+	0.0660954i	0.00511914	+	0.00588824i
$127$	−9.51452			−0.844277			−0.422138	−	0.906531i	$-0.638720\pi$
$127$	−9.51452			−0.844277			−0.422138	+	0.906531i	$0.638720\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	5.38648	+	9.32966i	0.474253	+	0.821430i
$130$	−7.96887	−	13.8025i	−0.698916	−	1.21056i
$131$	2.83310	−	4.90708i	0.247529	−	0.428733i	−0.715310	−	0.698807i	$-0.753715\pi$
$131$	2.83310	−	4.90708i	0.247529	−	0.428733i	0.962840	+	0.270073i	$0.0870480\pi$
$132$	6.41183			0.558079
$133$	4.80775	−	13.9652i	0.416885	−	1.21094i
$134$	14.4249			1.24612
$135$	6.32487	−	10.9550i	0.544358	−	0.942856i
$136$	0.500000	+	0.866025i	0.0428746	+	0.0742611i
$137$	9.08867	+	15.7420i	0.776498	+	1.34493i	0.933949	+	0.357407i	$0.116339\pi$
$137$	9.08867	+	15.7420i	0.776498	+	1.34493i	−0.157451	+	0.987527i	$0.550328\pi$
$138$	5.14205	−	8.90629i	0.437720	−	0.758154i
$139$	−16.1143			−1.36680			−0.683398	−	0.730046i	$-0.739499\pi$
$139$	−16.1143			−1.36680			−0.683398	+	0.730046i	$0.739499\pi$
$140$	6.28831	−	1.22268i	0.531459	−	0.103336i
$141$	−1.15746			−0.0974759
$142$	−4.84651	+	8.39441i	−0.406710	+	0.704443i
$143$	−12.2514	−	21.2200i	−1.02451	−	1.77451i
$144$	0.0165513	+	0.0286678i	0.00137928	+	0.00238898i
$145$	0.935770	−	1.62080i	0.0777114	−	0.134600i
$146$	1.61550			0.133699
$147$	−9.50209	−	7.42215i	−0.783719	−	0.612169i
$148$	4.42127			0.363426
$149$	−0.180562	+	0.312743i	−0.0147922	+	0.0256209i	−0.873327	−	0.487135i	$-0.838042\pi$
$149$	−0.180562	+	0.312743i	−0.0147922	+	0.0256209i	0.858535	+	0.512756i	$0.171375\pi$
$150$	−0.742852	−	1.28666i	−0.0606536	−	0.105055i
$151$	7.14205	+	12.3704i	0.581212	+	1.00669i	0.995336	+	0.0964680i	$0.0307545\pi$
$151$	7.14205	+	12.3704i	0.581212	+	1.00669i	−0.414124	+	0.910220i	$0.635912\pi$
$152$	2.79120	−	4.83449i	0.226396	−	0.392129i
$153$	0.0331027			0.00267619
$154$	9.66767	−	1.87976i	0.779043	−	0.151475i
$155$	−23.2817			−1.87003
$156$	−5.66898	+	9.81897i	−0.453882	+	0.786146i
$157$	−2.56873	−	4.44917i	−0.205007	−	0.355082i	0.745128	−	0.666921i	$-0.232388\pi$
$157$	−2.56873	−	4.44917i	−0.205007	−	0.355082i	−0.950135	+	0.311839i	$0.899055\pi$
$158$	−2.28250	−	3.95341i	−0.181586	−	0.314517i
$159$	−8.53519	+	14.7834i	−0.676884	+	1.17240i
$160$	2.42127			0.191418
$161$	5.14205	−	14.9363i	0.405250	−	1.17714i
$162$	−8.89960			−0.699218
$163$	−0.807748	+	1.39906i	−0.0632677	+	0.109583i	−0.895924	−	0.444207i	$-0.853486\pi$
$163$	−0.807748	+	1.39906i	−0.0632677	+	0.109583i	0.832657	+	0.553790i	$0.186819\pi$
$164$	2.80775	+	4.86316i	0.219248	+	0.379749i
$165$	−7.76239	−	13.4448i	−0.604301	−	1.04668i
$166$	−5.16112	+	8.93933i	−0.400581	+	0.693827i
$167$	−0.477531			−0.0369525			−0.0184762	−	0.999829i	$-0.505882\pi$
$167$	−0.477531			−0.0369525			−0.0184762	+	0.999829i	$0.505882\pi$
$168$	−2.99000	−	3.43921i	−0.230683	−	0.265341i
$169$	30.3279			2.33292
$170$	1.21063	−	2.09688i	0.0928514	−	0.160823i
$171$	−0.0923961	−	0.160035i	−0.00706570	−	0.0122382i
$172$	3.12719	+	5.41645i	0.238446	+	0.413000i
$173$	−3.39711	+	5.88397i	−0.258278	+	0.447350i	−0.965781	−	0.259360i	$-0.916488\pi$
$173$	−3.39711	+	5.88397i	−0.258278	+	0.447350i	0.707503	+	0.706710i	$0.249822\pi$
$174$	−1.33140			−0.100933
$175$	−1.49727	−	1.72222i	−0.113183	−	0.130188i
$176$	3.72247			0.280592
$177$	8.88843	−	15.3952i	0.668096	−	1.15718i
$178$	−2.19711	−	3.80551i	−0.164681	−	0.285235i
$179$	3.74071	+	6.47909i	0.279594	+	0.484270i	0.971284	−	0.237924i	$-0.0764669\pi$
$179$	3.74071	+	6.47909i	0.279594	+	0.484270i	−0.691690	+	0.722194i	$0.743134\pi$
$180$	0.0400752	−	0.0694124i	0.00298703	−	0.00517369i
$181$	−6.91931			−0.514309			−0.257154	−	0.966370i	$-0.582785\pi$
$181$	−6.91931			−0.514309			−0.257154	+	0.966370i	$0.582785\pi$
$182$	−5.66898	+	16.4669i	−0.420213	+	1.22061i
$183$	8.13974			0.601707
$184$	2.98528	−	5.17066i	0.220078	−	0.381186i
$185$	−5.35254	−	9.27087i	−0.393527	−	0.681608i
$186$	8.28119	+	14.3434i	0.607207	+	1.05171i
$187$	1.86123	−	3.22375i	0.136107	−	0.235744i
$188$	−0.671979			−0.0490091
$189$	−13.5684	+	2.63821i	−0.986957	+	0.191902i
$190$	−13.5165			−0.980588
$191$	−2.41015	+	4.17450i	−0.174392	+	0.302056i	−0.939951	−	0.341310i	$-0.889129\pi$
$191$	−2.41015	+	4.17450i	−0.174392	+	0.302056i	0.765559	+	0.643366i	$0.222463\pi$
$192$	−0.861234	−	1.49170i	−0.0621542	−	0.107654i
$193$	−0.588166	−	1.01873i	−0.0423371	−	0.0733300i	0.844080	−	0.536217i	$-0.180147\pi$
$193$	−0.588166	−	1.01873i	−0.0423371	−	0.0733300i	−0.886417	+	0.462887i	$0.846814\pi$
$194$	3.77465	−	6.53788i	0.271004	−	0.469392i
$195$	27.4523			1.96590
$196$	−5.51655	−	4.30902i	−0.394039	−	0.307787i
$197$	4.37393			0.311630			0.155815	−	0.987786i	$-0.450200\pi$
$197$	4.37393			0.311630			0.155815	+	0.987786i	$0.450200\pi$
$198$	0.0616118	−	0.106715i	0.00437856	−	0.00758389i
$199$	−11.9649	−	20.7238i	−0.848169	−	1.46907i	−0.882840	−	0.469673i	$-0.844372\pi$
$199$	−11.9649	−	20.7238i	−0.848169	−	1.46907i	0.0346714	−	0.999399i	$-0.488962\pi$
$200$	−0.431272	−	0.746985i	−0.0304955	−	0.0528198i
$201$	−12.4232	+	21.5177i	−0.876268	+	1.51774i
$202$	−12.3885			−0.871649
$203$	−2.00746	+	0.390326i	−0.140896	+	0.0273955i
$204$	−1.72247			−0.120597
$205$	6.79831	−	11.7750i	0.474815	−	0.822403i
$206$	−2.05218	−	3.55447i	−0.142982	−	0.247652i
$207$	−0.0988207	−	0.171163i	−0.00686852	−	0.0118966i
$208$	−3.29120	+	5.70052i	−0.228203	+	0.395260i
$209$	−20.7803			−1.43740
$210$	−3.59183	+	10.4333i	−0.247860	+	0.719966i
$211$	−9.56479			−0.658467			−0.329234	−	0.944249i	$-0.606790\pi$
$211$	−9.56479			−0.658467			−0.329234	+	0.944249i	$0.606790\pi$
$212$	−4.95521	+	8.58267i	−0.340325	+	0.589460i
$213$	−8.34797	−	14.4591i	−0.571993	−	0.990721i
$214$	−3.24940	−	5.62813i	−0.222124	−	0.384731i
$215$	7.57176	−	13.1147i	0.516390	−	0.894413i
$216$	−5.22442			−0.355477
$217$	16.6913	+	19.1990i	1.13308	+	1.30332i
$218$	6.35169			0.430191
$219$	−1.39132	+	2.40984i	−0.0940167	+	0.162842i
$220$	−4.50655	−	7.80557i	−0.303831	−	0.526251i
$221$	3.29120	+	5.70052i	0.221390	+	0.383458i
$222$	−3.80775	+	6.59521i	−0.255559	+	0.442642i
$223$	12.2338			0.819238			0.409619	−	0.912257i	$-0.365662\pi$
$223$	12.2338			0.819238			0.409619	+	0.912257i	$0.365662\pi$
$224$	−1.73588	−	1.99668i	−0.115983	−	0.133409i
$225$	−0.0285525			−0.00190350
$226$	−2.42127	+	4.19376i	−0.161060	+	0.278965i
$227$	−2.96390	−	5.13363i	−0.196721	−	0.340731i	0.750742	−	0.660595i	$-0.229696\pi$
$227$	−2.96390	−	5.13363i	−0.196721	−	0.340731i	−0.947463	+	0.319864i	$0.896363\pi$
$228$	4.80775	+	8.32726i	0.318401	+	0.551487i
$229$	−9.44662	+	16.3620i	−0.624250	+	1.08123i	0.364435	+	0.931229i	$0.381262\pi$
$229$	−9.44662	+	16.3620i	−0.624250	+	1.08123i	−0.988685	+	0.150005i	$0.952071\pi$
$230$	−14.4563			−0.953222
$231$	−5.52209	+	16.0402i	−0.363327	+	1.05537i
$232$	−0.772958			−0.0507472
$233$	−11.6520	+	20.1818i	−0.763346	+	1.32215i	0.177770	+	0.984072i	$0.443112\pi$
$233$	−11.6520	+	20.1818i	−0.763346	+	1.32215i	−0.941117	+	0.338082i	$0.890222\pi$
$234$	0.108947	+	0.188702i	0.00712212	+	0.0123359i
$235$	0.813521	+	1.40906i	0.0530682	+	0.0919169i
$236$	5.16029	−	8.93788i	0.335906	−	0.581807i
$237$	7.86308			0.510762
$238$	−2.59711	+	0.504977i	−0.168346	+	0.0327328i
$239$	−19.6228			−1.26929			−0.634647	−	0.772802i	$-0.718855\pi$
$239$	−19.6228			−1.26929			−0.634647	+	0.772802i	$0.718855\pi$
$240$	−2.08528	+	3.61181i	−0.134604	+	0.233141i
$241$	3.35169	+	5.80530i	0.215901	+	0.373952i	0.953551	−	0.301232i	$-0.0973977\pi$
$241$	3.35169	+	5.80530i	0.215901	+	0.373952i	−0.737650	+	0.675184i	$0.764064\pi$
$242$	−1.42839	−	2.47404i	−0.0918201	−	0.159037i
$243$	−0.171999	+	0.297910i	−0.0110337	+	0.0191110i
$244$	4.72562			0.302527
$245$	−2.35697	+	16.7842i	−0.150582	+	1.07230i
$246$	−9.67251			−0.616697
$247$	18.3728	−	31.8225i	1.16903	−	2.02482i
$248$	4.80775	+	8.32726i	0.305292	+	0.528782i
$249$	−8.88987	−	15.3977i	−0.563373	−	0.975790i
$250$	5.00895	−	8.67575i	0.316794	−	0.548703i
$251$	0.983528			0.0620798			0.0310399	−	0.999518i	$-0.490118\pi$
$251$	0.983528			0.0620798			0.0310399	+	0.999518i	$0.490118\pi$
$252$	−0.0859714	+	0.0167161i	−0.00541569	+	0.00105301i
$253$	−22.2252			−1.39729
$254$	4.75726	−	8.23981i	0.298497	−	0.517012i
$255$	2.08528	+	3.61181i	0.130585	+	0.226180i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.66741	−	16.7444i	0.603036	−	1.04449i	−0.389322	−	0.921102i	$-0.627291\pi$
$257$	9.66741	−	16.7444i	0.603036	−	1.04449i	0.992359	−	0.123388i	$-0.0393759\pi$
$258$	−10.7730			−0.670695
$259$	−3.80775	+	11.0605i	−0.236602	+	0.687265i
$260$	15.9377			0.988417
$261$	−0.0127935	+	0.0221590i	−0.000791897	+	0.00137161i
$262$	2.83310	+	4.90708i	0.175030	+	0.303160i
$263$	−4.33965	−	7.51650i	−0.267594	−	0.463487i	0.700646	−	0.713509i	$-0.252895\pi$
$263$	−4.33965	−	7.51650i	−0.267594	−	0.463487i	−0.968240	+	0.250022i	$0.919562\pi$
$264$	−3.20592	+	5.55281i	−0.197311	+	0.341752i
$265$	23.9958			1.47405
$266$	9.69036	+	11.1462i	0.594154	+	0.683420i
$267$	7.56892			0.463210
$268$	−7.21247	+	12.4924i	−0.440571	+	0.763092i
$269$	11.2397	+	19.4676i	0.685294	+	1.18696i	0.973344	+	0.229348i	$0.0736595\pi$
$269$	11.2397	+	19.4676i	0.685294	+	1.18696i	−0.288051	+	0.957615i	$0.593007\pi$
$270$	6.32487	+	10.9550i	0.384919	+	0.666700i
$271$	−4.63550	+	8.02892i	−0.281587	+	0.487722i	−0.971776	−	0.235907i	$-0.924194\pi$
$271$	−4.63550	+	8.02892i	−0.281587	+	0.487722i	0.690189	+	0.723629i	$0.257527\pi$
$272$	−1.00000			−0.0606339
$273$	−19.6813	−	22.6383i	−1.19117	−	1.37013i
$274$	−18.1773			−1.09813
$275$	−1.60540	+	2.78063i	−0.0968090	+	0.167678i
$276$	5.14205	+	8.90629i	0.309515	+	0.536096i
$277$	6.19591	+	10.7316i	0.372276	+	0.644802i	0.989915	−	0.141660i	$-0.0452440\pi$
$277$	6.19591	+	10.7316i	0.372276	+	0.644802i	−0.617639	+	0.786462i	$0.711911\pi$
$278$	8.05715	−	13.9554i	0.483236	−	0.836989i
$279$	0.318299			0.0190560
$280$	−2.08528	+	6.05718i	−0.124619	+	0.361986i
$281$	16.0479			0.957336			0.478668	−	0.877996i	$-0.341120\pi$
$281$	16.0479			0.957336			0.478668	+	0.877996i	$0.341120\pi$
$282$	0.578731	−	1.00239i	0.0344629	−	0.0596915i
$283$	3.47476	+	6.01845i	0.206553	+	0.357760i	0.950626	−	0.310338i	$-0.100442\pi$
$283$	3.47476	+	6.01845i	0.206553	+	0.357760i	−0.744074	+	0.668098i	$0.767109\pi$
$284$	−4.84651	−	8.39441i	−0.287588	−	0.498117i
$285$	11.6409	−	20.1625i	0.689545	−	1.19433i
$286$	24.5028			1.44888
$287$	−14.5841	+	2.83569i	−0.860871	+	0.167386i
$288$	−0.0331027			−0.00195059
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	0.935770	+	1.62080i	0.0549503	+	0.0951767i
$291$	6.50171	+	11.2613i	0.381137	+	0.660148i
$292$	−0.807748	+	1.39906i	−0.0472699	+	0.0818738i
$293$	0.0862108			0.00503649			0.00251825	−	0.999997i	$-0.499198\pi$
$293$	0.0862108			0.00503649			0.00251825	+	0.999997i	$0.499198\pi$
$294$	11.1788	−	4.51797i	0.651962	−	0.263493i
$295$	−24.9889			−1.45491
$296$	−2.21063	+	3.82893i	−0.128491	+	0.222552i
$297$	9.72388	+	16.8422i	0.564236	+	0.977286i
$298$	−0.180562	−	0.312743i	−0.0104597	−	0.0181167i
$299$	19.6503	−	34.0353i	1.13641	−	1.96831i
$300$	1.48570			0.0857771
$301$	−16.2433	+	3.15831i	−0.936249	+	0.182042i
$302$	−14.2841			−0.821958
$303$	10.6694	−	18.4799i	0.612939	−	1.06164i
$304$	2.79120	+	4.83449i	0.160086	+	0.277277i
$305$	−5.72100	−	9.90907i	−0.327584	−	0.567391i
$306$	−0.0165513	+	0.0286678i	−0.000946177	+	0.00163883i
$307$	−21.1317			−1.20605			−0.603024	−	0.797723i	$-0.706038\pi$
$307$	−21.1317			−1.20605			−0.603024	+	0.797723i	$0.706038\pi$
$308$	−3.20592	+	9.31233i	−0.182674	+	0.530619i
$309$	7.06962			0.402177
$310$	11.6409	−	20.1625i	0.661156	−	1.14516i
$311$	5.31996	+	9.21444i	0.301667	+	0.522503i	0.976514	−	0.215455i	$-0.0691235\pi$
$311$	5.31996	+	9.21444i	0.301667	+	0.522503i	−0.674846	+	0.737958i	$0.735790\pi$
$312$	−5.66898	−	9.81897i	−0.320943	−	0.555889i
$313$	−10.3317	+	17.8950i	−0.583981	+	1.01149i	0.411020	+	0.911626i	$0.365173\pi$
$313$	−10.3317	+	17.8950i	−0.583981	+	1.01149i	−0.995002	+	0.0998591i	$0.968161\pi$
$314$	5.13746			0.289923
$315$	0.139132	+	0.160035i	0.00783918	+	0.00901693i
$316$	4.56501			0.256802
$317$	4.33697	−	7.51185i	0.243588	−	0.421908i	−0.718145	−	0.695893i	$-0.755009\pi$
$317$	4.33697	−	7.51185i	0.243588	−	0.421908i	0.961734	+	0.273986i	$0.0883421\pi$
$318$	−8.53519	−	14.7834i	−0.478630	−	0.829011i
$319$	1.43866	+	2.49183i	0.0805493	+	0.139515i
$320$	−1.21063	+	2.09688i	−0.0676765	+	0.117219i
$321$	11.1940			0.624787
$322$	10.3642	+	11.9213i	0.577573	+	0.664347i
$323$	5.58239			0.310613
$324$	4.44980	−	7.70728i	0.247211	−	0.428182i
$325$	−2.83880	−	4.91695i	−0.157468	−	0.272743i
$326$	−0.807748	−	1.39906i	−0.0447370	−	0.0774868i
$327$	−5.47029	+	9.47482i	−0.302508	+	0.523959i
$328$	−5.61550			−0.310064
$329$	0.578731	−	1.68106i	0.0319065	−	0.0926798i
$330$	15.5248			0.854611
$331$	−2.84337	+	4.92487i	−0.156286	+	0.270695i	−0.933527	−	0.358508i	$-0.883285\pi$
$331$	−2.84337	+	4.92487i	−0.156286	+	0.270695i	0.777241	+	0.629204i	$0.216619\pi$
$332$	−5.16112	−	8.93933i	−0.283253	−	0.490609i
$333$	0.0731779	+	0.126748i	0.00401013	+	0.00694574i
$334$	0.238766	−	0.413554i	0.0130647	−	0.0226287i
$335$	34.9266			1.90825
$336$	4.47345	−	0.869806i	0.244046	−	0.0474518i
$337$	14.9972			0.816947			0.408474	−	0.912770i	$-0.366061\pi$
$337$	14.9972			0.816947			0.408474	+	0.912770i	$0.366061\pi$
$338$	−15.1640	+	26.2647i	−0.824810	+	1.42861i
$339$	−4.17056	−	7.22362i	−0.226514	−	0.392333i
$340$	1.21063	+	2.09688i	0.0656559	+	0.113719i
$341$	17.8967	−	30.9980i	0.969160	−	1.67863i
$342$	0.184792			0.00999242
$343$	15.5307	−	10.0894i	0.838580	−	0.544778i
$344$	−6.25437			−0.337213
$345$	12.4503	−	21.5645i	0.670301	−	1.16100i
$346$	−3.39711	−	5.88397i	−0.182630	−	0.316324i
$347$	−12.8003	−	22.1707i	−0.687155	−	1.19019i	−0.972754	−	0.231839i	$-0.925526\pi$
$347$	−12.8003	−	22.1707i	−0.687155	−	1.19019i	0.285599	−	0.958349i	$-0.407808\pi$
$348$	0.665698	−	1.15302i	0.0356852	−	0.0618085i
$349$	8.72225			0.466891			0.233446	−	0.972370i	$-0.425000\pi$
$349$	8.72225			0.466891			0.233446	+	0.972370i	$0.425000\pi$
$350$	2.24012	−	0.435564i	0.119740	−	0.0232819i
$351$	−34.3892			−1.83556
$352$	−1.86123	+	3.22375i	−0.0992041	+	0.171827i
$353$	−13.7469	−	23.8104i	−0.731674	−	1.26730i	−0.956167	−	0.292821i	$-0.905406\pi$
$353$	−13.7469	−	23.8104i	−0.731674	−	1.26730i	0.224493	−	0.974476i	$-0.427927\pi$
$354$	8.88843	+	15.3952i	0.472415	+	0.818247i
$355$	−11.7347	+	20.3251i	−0.622814	+	1.07875i
$356$	4.39423			0.232894
$357$	1.48345	−	4.30902i	0.0785124	−	0.228058i
$358$	−7.48141			−0.395405
$359$	7.19789	−	12.4671i	0.379890	−	0.657989i	−0.611156	−	0.791510i	$-0.709295\pi$
$359$	7.19789	−	12.4671i	0.379890	−	0.657989i	0.991046	+	0.133521i	$0.0426285\pi$
$360$	0.0400752	+	0.0694124i	0.00211215	+	0.00365835i
$361$	−6.08156	−	10.5336i	−0.320082	−	0.554398i
$362$	3.45966	−	5.99230i	0.181836	−	0.314948i
$363$	4.92070			0.258270
$364$	−11.4262	−	13.1429i	−0.598898	−	0.688876i
$365$	3.91155			0.204740
$366$	−4.06987	+	7.04922i	−0.212735	+	0.368469i
$367$	6.54194	+	11.3310i	0.341486	+	0.591472i	0.984709	−	0.174207i	$-0.0557363\pi$
$367$	6.54194	+	11.3310i	0.341486	+	0.591472i	−0.643222	+	0.765679i	$0.722403\pi$
$368$	2.98528	+	5.17066i	0.155618	+	0.269539i
$369$	−0.0929440	+	0.160984i	−0.00483847	+	0.00838048i
$370$	10.7051			0.556531
$371$	−17.2033	−	19.7879i	−0.893150	−	1.02734i
$372$	−16.5624			−0.858720
$373$	−14.4101	+	24.9590i	−0.746126	+	1.29233i	0.203541	+	0.979066i	$0.434755\pi$
$373$	−14.4101	+	24.9590i	−0.746126	+	1.29233i	−0.949667	+	0.313262i	$0.898578\pi$
$374$	1.86123	+	3.22375i	0.0962421	+	0.166696i
$375$	8.62775	+	14.9437i	0.445535	+	0.771690i
$376$	0.335989	−	0.581951i	0.0173273	−	0.0300118i
$377$	−5.08791			−0.262041
$378$	4.49945	−	13.0697i	0.231427	−	0.672233i
$379$	−25.8274			−1.32666			−0.663332	−	0.748325i	$-0.730858\pi$
$379$	−25.8274			−1.32666			−0.663332	+	0.748325i	$0.730858\pi$
$380$	6.75824	−	11.7056i	0.346690	−	0.600485i
$381$	8.19423	+	14.1928i	0.419803	+	0.727120i
$382$	−2.41015	−	4.17450i	−0.123314	−	0.213586i
$383$	−0.809435	+	1.40198i	−0.0413602	+	0.0716380i	−0.885964	−	0.463753i	$-0.846502\pi$
$383$	−0.809435	+	1.40198i	−0.0413602	+	0.0716380i	0.844604	+	0.535391i	$0.179836\pi$
$384$	1.72247			0.0878993
$385$	23.4080	−	4.55140i	1.19298	−	0.231961i
$386$	1.17633			0.0598737
$387$	−0.103518	+	0.179299i	−0.00526213	+	0.00911427i
$388$	3.77465	+	6.53788i	0.191629	+	0.331910i
$389$	11.1243	+	19.2679i	0.564024	+	0.976919i	0.997140	+	0.0755804i	$0.0240809\pi$
$389$	11.1243	+	19.2679i	0.564024	+	0.976919i	−0.433115	+	0.901339i	$0.642586\pi$
$390$	−13.7261	+	23.7744i	−0.695050	+	1.20386i
$391$	5.97056			0.301944
$392$	6.49000	−	2.62296i	0.327794	−	0.132480i
$393$	−9.75986			−0.492320
$394$	−2.18697	+	3.78794i	−0.110178	+	0.190834i
$395$	−5.52655	−	9.57227i	−0.278071	−	0.481633i
$396$	0.0616118	+	0.106715i	0.00309611	+	0.00536262i
$397$	12.7913	−	22.1553i	0.641979	−	1.11194i	−0.343011	−	0.939331i	$-0.611447\pi$
$397$	12.7913	−	22.1553i	0.641979	−	1.11194i	0.984990	−	0.172609i	$-0.0552197\pi$
$398$	23.9298			1.19949
$399$	−24.9725	+	4.85560i	−1.25019	+	0.243084i
$400$	0.862543			0.0431272
$401$	−4.03310	+	6.98554i	−0.201404	+	0.348841i	−0.948981	−	0.315334i	$-0.897884\pi$
$401$	−4.03310	+	6.98554i	−0.201404	+	0.348841i	0.747577	+	0.664175i	$0.231217\pi$
$402$	−12.4232	−	21.5177i	−0.619615	−	1.07320i
$403$	31.6465	+	54.8133i	1.57642	+	2.73045i
$404$	6.19423	−	10.7287i	0.308174	−	0.533774i
$405$	−21.5483			−1.07074
$406$	0.665698	−	1.93367i	0.0330380	−	0.0959666i
$407$	16.4580			0.815794
$408$	0.861234	−	1.49170i	0.0426374	−	0.0738502i
$409$	3.57985	+	6.20048i	0.177012	+	0.306594i	0.940856	−	0.338807i	$-0.110023\pi$
$409$	3.57985	+	6.20048i	0.177012	+	0.306594i	−0.763844	+	0.645401i	$0.776690\pi$
$410$	6.79831	+	11.7750i	0.335745	+	0.581527i
$411$	15.6550	−	27.1152i	0.772202	−	1.33749i
$412$	4.10435			0.202207
$413$	17.9153	+	20.6069i	0.881553	+	1.01400i
$414$	0.197641			0.00971355
$415$	−12.4965	+	21.6445i	−0.613428	+	1.06249i
$416$	−3.29120	−	5.70052i	−0.161364	−	0.279491i
$417$	13.8782	+	24.0377i	0.679618	+	1.17713i
$418$	10.3901	−	17.9963i	0.508198	−	0.880225i
$419$	8.56501			0.418428			0.209214	−	0.977870i	$-0.432909\pi$
$419$	8.56501			0.418428			0.209214	+	0.977870i	$0.432909\pi$
$420$	−7.23959	−	8.32726i	−0.353256	−	0.406329i
$421$	9.98508			0.486643			0.243322	−	0.969946i	$-0.421763\pi$
$421$	9.98508			0.486643			0.243322	+	0.969946i	$0.421763\pi$
$422$	4.78239	−	8.28335i	0.232803	−	0.403227i
$423$	−0.0111221	−	0.0192641i	−0.000540777	−	0.000936654i
$424$	−4.95521	−	8.58267i	−0.240646	−	0.416811i
$425$	0.431272	−	0.746985i	0.0209198	−	0.0362341i
$426$	16.6959			0.808921
$427$	−4.06987	+	11.8219i	−0.196955	+	0.572101i
$428$	6.49880			0.314131
$429$	−21.1026	+	36.5508i	−1.01884	+	1.76469i
$430$	7.57176	+	13.1147i	0.365143	+	0.632446i
$431$	−7.11292	−	12.3199i	−0.342617	−	0.593431i	0.642300	−	0.766453i	$-0.277980\pi$
$431$	−7.11292	−	12.3199i	−0.342617	−	0.593431i	−0.984918	+	0.173022i	$0.944647\pi$
$432$	2.61221	−	4.52448i	0.125680	−	0.217684i
$433$	7.58763			0.364638			0.182319	−	0.983239i	$-0.441640\pi$
$433$	7.58763			0.364638			0.182319	+	0.983239i	$0.441640\pi$
$434$	−24.9725	+	4.85560i	−1.19872	+	0.233076i
$435$	−3.22367			−0.154563
$436$	−3.17584	+	5.50072i	−0.152095	+	0.263437i
$437$	−16.6650	−	28.8646i	−0.797195	−	1.38078i
$438$	−1.39132	−	2.40984i	−0.0664799	−	0.115146i
$439$	−6.24412	+	10.8151i	−0.298015	+	0.516178i	−0.975682	−	0.219192i	$-0.929658\pi$
$439$	−6.24412	+	10.8151i	−0.298015	+	0.516178i	0.677666	+	0.735369i	$0.262991\pi$
$440$	9.01310			0.429683
$441$	0.0322237	−	0.229467i	0.00153446	−	0.0109270i
$442$	−6.58239			−0.313093
$443$	−15.6748	+	27.1495i	−0.744732	+	1.28991i	0.205588	+	0.978639i	$0.434089\pi$
$443$	−15.6748	+	27.1495i	−0.744732	+	1.28991i	−0.950320	+	0.311275i	$0.899244\pi$
$444$	−3.80775	−	6.59521i	−0.180708	−	0.312995i
$445$	−5.31980	−	9.21417i	−0.252183	−	0.436793i
$446$	−6.11692	+	10.5948i	−0.289644	+	0.501679i
$447$	0.622025			0.0294208
$448$	2.59711	−	0.504977i	0.122702	−	0.0238579i
$449$	26.3918			1.24551			0.622754	−	0.782418i	$-0.286014\pi$
$449$	26.3918			1.24551			0.622754	+	0.782418i	$0.286014\pi$
$450$	0.0142762	−	0.0247272i	0.000672989	−	0.00116565i
$451$	10.4518	+	18.1030i	0.492154	+	0.852435i
$452$	−2.42127	−	4.19376i	−0.113887	−	0.197258i
$453$	12.3020	−	21.3076i	0.577996	−	1.00112i
$454$	5.92780			0.278206
$455$	−13.7261	+	39.8707i	−0.643491	+	1.86917i
$456$	−9.61550			−0.450287
$457$	12.1089	−	20.9732i	0.566429	−	0.981084i	−0.430486	−	0.902597i	$-0.641658\pi$
$457$	12.1089	−	20.9732i	0.566429	−	0.981084i	0.996915	−	0.0784866i	$-0.0250088\pi$
$458$	−9.44662	−	16.3620i	−0.441412	−	0.764548i
$459$	−2.61221	−	4.52448i	−0.121928	−	0.211185i
$460$	7.22817	−	12.5195i	0.337015	−	0.583727i
$461$	−20.3684			−0.948653			−0.474327	−	0.880349i	$-0.657308\pi$
$461$	−20.3684			−0.948653			−0.474327	+	0.880349i	$0.657308\pi$
$462$	−11.1302	−	12.8024i	−0.517822	−	0.595620i
$463$	−10.7382			−0.499044			−0.249522	−	0.968369i	$-0.580274\pi$
$463$	−10.7382			−0.499044			−0.249522	+	0.968369i	$0.580274\pi$
$464$	0.386479	−	0.669401i	0.0179418	−	0.0310762i
$465$	20.0510	+	34.7293i	0.929843	+	1.61053i
$466$	−11.6520	−	20.1818i	−0.539767	−	0.934904i
$467$	0.653740	−	1.13231i	0.0302515	−	0.0523971i	−0.850503	−	0.525970i	$-0.823703\pi$
$467$	0.653740	−	1.13231i	0.0302515	−	0.0523971i	0.880755	+	0.473573i	$0.157036\pi$
$468$	−0.217895			−0.0100722
$469$	−25.0399	−	28.8019i	−1.15624	−	1.32995i
$470$	−1.62704			−0.0750498
$471$	−4.42455	+	7.66355i	−0.203873	+	0.353118i
$472$	5.16029	+	8.93788i	0.237522	+	0.411399i
$473$	11.6409	+	20.1625i	0.535247	+	0.927075i
$474$	−3.93154	+	6.80963i	−0.180582	+	0.312776i
$475$	−4.81506			−0.220930
$476$	0.861234	−	2.50165i	0.0394746	−	0.114663i
$477$	−0.328061			−0.0150209
$478$	9.81141	−	16.9939i	0.448763	−	0.777281i
$479$	−8.95992	−	15.5190i	−0.409389	−	0.709083i	0.585432	−	0.810722i	$-0.300925\pi$
$479$	−8.95992	−	15.5190i	−0.409389	−	0.709083i	−0.994821	+	0.101638i	$0.967592\pi$
$480$	−2.08528	−	3.61181i	−0.0951796	−	0.164856i
$481$	−14.5513	+	25.2035i	−0.663481	+	1.14918i
$482$	−6.70338			−0.305331
$483$	−26.7090	+	5.19323i	−1.21530	+	0.236300i
$484$	2.85677			0.129853
$485$	9.13943	−	15.8300i	0.415000	−	0.718801i
$486$	−0.171999	−	0.297910i	−0.00780202	−	0.0135135i
$487$	−4.01707	−	6.95777i	−0.182031	−	0.315287i	0.760541	−	0.649290i	$-0.224934\pi$
$487$	−4.01707	−	6.95777i	−0.182031	−	0.315287i	−0.942572	+	0.334003i	$0.891600\pi$
$488$	−2.36281	+	4.09251i	−0.106959	+	0.185259i
$489$	2.78264			0.125835
$490$	−13.3571	−	10.4333i	−0.603410	−	0.471328i
$491$	29.9897			1.35342			0.676708	−	0.736251i	$-0.263406\pi$
$491$	29.9897			1.35342			0.676708	+	0.736251i	$0.263406\pi$
$492$	4.83626	−	8.37664i	0.218035	−	0.377648i
$493$	−0.386479	−	0.669401i	−0.0174061	−	0.0301483i
$494$	18.3728	+	31.8225i	0.826629	+	1.43176i
$495$	0.149179	−	0.258385i	0.00670509	−	0.0116136i
$496$	−9.61550			−0.431749
$497$	25.1739	−	4.89475i	1.12920	−	0.219560i
$498$	17.7797			0.796730
$499$	11.8118	−	20.4586i	0.528768	−	0.915854i	−0.470669	−	0.882310i	$-0.655987\pi$
$499$	11.8118	−	20.4586i	0.528768	−	0.915854i	0.999437	−	0.0335436i	$-0.0106793\pi$
$500$	5.00895	+	8.67575i	0.224007	+	0.387991i
$501$	0.411266	+	0.712334i	0.0183740	+	0.0318247i
$502$	−0.491764	+	0.851760i	−0.0219485	+	0.0380159i
$503$	−18.4187			−0.821247			−0.410624	−	0.911805i	$-0.634689\pi$
$503$	−18.4187			−0.821247			−0.410624	+	0.911805i	$0.634689\pi$
$504$	0.0285092	−	0.0828115i	0.00126990	−	0.00368872i
$505$	−29.9958			−1.33479
$506$	11.1126	−	19.2476i	0.494016	−	0.855660i
$507$	−26.1194	−	45.2402i	−1.16000	−	2.00919i
$508$	4.75726	+	8.23981i	0.211069	+	0.365583i
$509$	−15.1962	+	26.3206i	−0.673560	+	1.16664i	0.303328	+	0.952886i	$0.401902\pi$
$509$	−15.1962	+	26.3206i	−0.673560	+	1.16664i	−0.976888	+	0.213754i	$0.931431\pi$
$510$	−4.17056			−0.184675
$511$	−2.80431	−	3.22563i	−0.124055	−	0.142693i
$512$	1.00000			0.0441942
$513$	−14.5824	+	25.2574i	−0.643828	+	1.11514i
$514$	9.66741	+	16.7444i	0.426411	+	0.738565i
$515$	−4.96887	−	8.60634i	−0.218955	−	0.379241i
$516$	5.38648	−	9.32966i	0.237127	−	0.410715i
$517$	−2.50142			−0.110012
$518$	−7.67479	−	8.82785i	−0.337211	−	0.387873i
$519$	11.7028			0.513698
$520$	−7.96887	+	13.8025i	−0.349458	+	0.605279i
$521$	11.9766	+	20.7441i	0.524705	+	0.908816i	0.999586	+	0.0287661i	$0.00915779\pi$
$521$	11.9766	+	20.7441i	0.524705	+	0.908816i	−0.474881	+	0.880050i	$0.657509\pi$
$522$	−0.0127935	−	0.0221590i	−0.000559956	−	0.000969872i
$523$	10.2179	−	17.6979i	0.446797	−	0.773876i	−0.551378	−	0.834255i	$-0.685898\pi$
$523$	10.2179	−	17.6979i	0.446797	−	0.773876i	0.998175	+	0.0603797i	$0.0192312\pi$
$524$	−5.66621			−0.247529
$525$	−1.27954	+	3.71672i	−0.0558437	+	0.162211i
$526$	8.67930			0.378436
$527$	−4.80775	+	8.32726i	−0.209429	+	0.362741i
$528$	−3.20592	−	5.55281i	−0.139520	−	0.241655i
$529$	−6.32379	−	10.9531i	−0.274947	−	0.476223i
$530$	−11.9979	+	20.7810i	−0.521155	+	0.902667i
$531$	0.341639			0.0148259
$532$	−14.4981	+	2.81898i	−0.628573	+	0.122218i
$533$	−36.9634			−1.60106
$534$	−3.78446	+	6.55487i	−0.163770	+	0.283657i
$535$	−7.86767	−	13.6272i	−0.340149	−	0.589156i
$536$	−7.21247	−	12.4924i	−0.311531	−	0.539588i
$537$	6.44325	−	11.1600i	0.278047	−	0.481591i
$538$	−22.4793			−0.969152
$539$	−20.5352	−	16.0402i	−0.884513	−	0.690900i
$540$	−12.6497			−0.544358
$541$	20.6506	−	35.7678i	0.887838	−	1.53778i	0.0454110	−	0.998968i	$-0.485540\pi$
$541$	20.6506	−	35.7678i	0.887838	−	1.53778i	0.842426	−	0.538811i	$-0.181126\pi$
$542$	−4.63550	−	8.02892i	−0.199112	−	0.344872i
$543$	5.95915	+	10.3216i	0.255732	+	0.442940i
$544$	0.500000	−	0.866025i	0.0214373	−	0.0371305i
$545$	15.3791			0.658770
$546$	29.4460	−	5.72541i	1.26017	−	0.245025i
$547$	41.2956			1.76567			0.882836	−	0.469681i	$-0.155631\pi$
$547$	41.2956			1.76567			0.882836	+	0.469681i	$0.155631\pi$
$548$	9.08867	−	15.7420i	0.388249	−	0.672467i
$549$	0.0782154	+	0.135473i	0.00333815	+	0.00578185i
$550$	−1.60540	−	2.78063i	−0.0684543	−	0.118566i
$551$	−2.15748	+	3.73686i	−0.0919117	+	0.159196i
$552$	−10.2841			−0.437720
$553$	−3.93154	+	11.4201i	−0.167186	+	0.485631i
$554$	−12.3918			−0.526478
$555$	−9.21958	+	15.9688i	−0.391349	+	0.677837i
$556$	8.05715	+	13.9554i	0.341699	+	0.591840i
$557$	−14.3226	−	24.8075i	−0.606869	−	1.05113i	−0.991753	−	0.128162i	$-0.959092\pi$
$557$	−14.3226	−	24.8075i	−0.606869	−	1.05113i	0.384885	−	0.922965i	$-0.374241\pi$
$558$	−0.159149	+	0.275655i	−0.00673733	+	0.0116694i
$559$	−41.1687			−1.74125
$560$	−4.20303	−	4.83449i	−0.177610	−	0.204295i
$561$	−6.41183			−0.270708
$562$	−8.02394	+	13.8979i	−0.338469	+	0.586246i
$563$	3.95379	+	6.84816i	0.166632	+	0.288616i	0.937234	−	0.348702i	$-0.113377\pi$
$563$	3.95379	+	6.84816i	0.166632	+	0.288616i	−0.770601	+	0.637317i	$0.780044\pi$
$564$	0.578731	+	1.00239i	0.0243690	+	0.0422083i
$565$	−5.86254	+	10.1542i	−0.246639	+	0.427191i
$566$	−6.94951			−0.292110
$567$	15.4486	+	17.7696i	0.648781	+	0.746254i
$568$	9.69303			0.406710
$569$	−16.7073	+	28.9379i	−0.700407	+	1.21314i	0.267916	+	0.963442i	$0.413665\pi$
$569$	−16.7073	+	28.9379i	−0.700407	+	1.21314i	−0.968323	+	0.249699i	$0.919668\pi$
$570$	11.6409	+	20.1625i	0.487582	+	0.844516i
$571$	13.7341	+	23.7882i	0.574754	+	0.995503i	0.996068	+	0.0885886i	$0.0282356\pi$
$571$	13.7341	+	23.7882i	0.574754	+	0.995503i	−0.421314	+	0.906915i	$0.638431\pi$
$572$	−12.2514	+	21.2200i	−0.512256	+	0.887253i
$573$	8.30280			0.346855
$574$	4.83626	−	14.0480i	0.201861	−	0.586353i
$575$	−5.14987			−0.214764
$576$	0.0165513	−	0.0286678i	0.000689639	−	0.00119449i
$577$	−9.12839	−	15.8108i	−0.380020	−	0.658213i	0.611045	−	0.791596i	$-0.290749\pi$
$577$	−9.12839	−	15.8108i	−0.380020	−	0.658213i	−0.991065	+	0.133383i	$0.957416\pi$
$578$	−0.500000	−	0.866025i	−0.0207973	−	0.0360219i
$579$	−1.01310	+	1.75474i	−0.0421029	+	0.0729243i
$580$	−1.87154			−0.0777114
$581$	26.8081	−	5.21249i	1.11219	−	0.216251i
$582$	−13.0034			−0.539009
$583$	−18.4456	+	31.9487i	−0.763939	+	1.32318i
$584$	−0.807748	−	1.39906i	−0.0334249	−	0.0578935i
$585$	0.263791	+	0.456899i	0.0109064	+	0.0188905i
$586$	−0.0431054	+	0.0746608i	−0.00178067	+	0.00308421i
$587$	−10.7176			−0.442364			−0.221182	−	0.975232i	$-0.570992\pi$
$587$	−10.7176			−0.442364			−0.221182	+	0.975232i	$0.570992\pi$
$588$	−1.67673	+	11.9401i	−0.0691472	+	0.492402i
$589$	53.6775			2.21174
$590$	12.4944	−	21.6410i	0.514388	−	0.890947i
$591$	−3.76698	−	6.52460i	−0.154953	−	0.268386i
$592$	−2.21063	−	3.82893i	−0.0908565	−	0.157368i
$593$	12.0963	−	20.9515i	0.496737	−	0.860373i	−0.503256	−	0.864137i	$-0.667865\pi$
$593$	12.0963	−	20.9515i	0.496737	−	0.860373i	0.999993	+	0.00376418i	$0.00119818\pi$
$594$	−19.4478			−0.797951
$595$	−6.28831	+	1.22268i	−0.257796	+	0.0501252i
$596$	0.361124			0.0147922
$597$	−20.6092	+	35.6961i	−0.843477	+	1.46094i
$598$	19.6503	+	34.0353i	0.803560	+	1.39181i
$599$	−13.8827	−	24.0455i	−0.567230	−	0.982471i	−0.996838	−	0.0794561i	$-0.974682\pi$
$599$	−13.8827	−	24.0455i	−0.567230	−	0.982471i	0.429608	−	0.903015i	$-0.358652\pi$
$600$	−0.742852	+	1.28666i	−0.0303268	+	0.0525276i
$601$	43.5383			1.77597			0.887983	−	0.459877i	$-0.152107\pi$
$601$	43.5383			1.77597			0.887983	+	0.459877i	$0.152107\pi$
$602$	5.38648	−	15.6463i	0.219536	−	0.637695i
$603$	−0.477504			−0.0194455
$604$	7.14205	−	12.3704i	0.290606	−	0.503344i
$605$	−3.45851	−	5.99031i	−0.140608	−	0.243541i
$606$	10.6694	+	18.4799i	0.433413	+	0.750694i
$607$	−2.45784	+	4.25710i	−0.0997606	+	0.172790i	−0.911586	−	0.411110i	$-0.865141\pi$
$607$	−2.45784	+	4.25710i	−0.0997606	+	0.172790i	0.811825	+	0.583901i	$0.198474\pi$
$608$	−5.58239			−0.226396
$609$	2.31114	+	2.65837i	0.0936522	+	0.107723i
$610$	11.4420			0.463273
$611$	2.21161	−	3.83063i	0.0894723	−	0.154971i
$612$	−0.0165513	−	0.0286678i	−0.000669048	−	0.00115883i
$613$	−24.0210	−	41.6056i	−0.970199	−	1.68043i	−0.694947	−	0.719061i	$-0.744572\pi$
$613$	−24.0210	−	41.6056i	−0.970199	−	1.68043i	−0.275252	−	0.961372i	$-0.588761\pi$
$614$	10.5658	−	18.3006i	0.426403	−	0.738551i
$615$	−23.4198			−0.944376
$616$	−6.46176	−	7.43257i	−0.260352	−	0.299467i
$617$	−8.21941			−0.330901			−0.165450	−	0.986218i	$-0.552908\pi$
$617$	−8.21941			−0.330901			−0.165450	+	0.986218i	$0.552908\pi$
$618$	−3.53481	+	6.12247i	−0.142191	+	0.246282i
$619$	15.8886	+	27.5198i	0.638615	+	1.10611i	0.985737	+	0.168294i	$0.0538258\pi$
$619$	15.8886	+	27.5198i	0.638615	+	1.10611i	−0.347122	+	0.937820i	$0.612841\pi$
$620$	11.6409	+	20.1625i	0.467508	+	0.809747i
$621$	−15.5964	+	27.0137i	−0.625861	+	1.08402i
$622$	−10.6399			−0.426622
$623$	−3.78446	+	10.9928i	−0.151621	+	0.440419i
$624$	11.3380			0.453882
$625$	14.2844	−	24.7413i	0.571375	−	0.989650i
$626$	−10.3317	−	17.8950i	−0.412937	−	0.715228i
$627$	17.8967	+	30.9980i	0.714725	+	1.23794i
$628$	−2.56873	+	4.44917i	−0.102503	+	0.177541i
$629$	−4.42127			−0.176288
$630$	−0.208160	+	0.0404741i	−0.00829329	+	0.00161253i
$631$	−28.2493			−1.12459			−0.562294	−	0.826937i	$-0.690081\pi$
$631$	−28.2493			−1.12459			−0.562294	+	0.826937i	$0.690081\pi$
$632$	−2.28250	+	3.95341i	−0.0907931	+	0.157258i
$633$	8.23752	+	14.2678i	0.327412	+	0.567094i
$634$	4.33697	+	7.51185i	0.172243	+	0.298334i
$635$	11.5186	−	19.9508i	0.457102	−	0.791723i
$636$	17.0704			0.676884
$637$	42.7197	−	17.2654i	1.69262	−	0.684079i
$638$	−2.87731			−0.113914
$639$	0.160433	−	0.277877i	0.00634661	−	0.0109927i
$640$	−1.21063	−	2.09688i	−0.0478545	−	0.0828865i
$641$	−6.54929	−	11.3437i	−0.258681	−	0.448049i	0.707208	−	0.707006i	$-0.249955\pi$
$641$	−6.54929	−	11.3437i	−0.258681	−	0.448049i	−0.965889	+	0.258957i	$0.916621\pi$
$642$	−5.59699	+	9.69427i	−0.220896	+	0.382602i
$643$	−19.3602			−0.763492			−0.381746	−	0.924267i	$-0.624677\pi$
$643$	−19.3602			−0.763492			−0.381746	+	0.924267i	$0.624677\pi$
$644$	−15.5062	+	3.01499i	−0.611031	+	0.118807i
$645$	−26.0842			−1.02707
$646$	−2.79120	+	4.83449i	−0.109818	+	0.190211i
$647$	−16.8131	−	29.1211i	−0.660991	−	1.14487i	−0.980356	−	0.197238i	$-0.936803\pi$
$647$	−16.8131	−	29.1211i	−0.660991	−	1.14487i	0.319365	−	0.947632i	$-0.396531\pi$
$648$	4.44980	+	7.70728i	0.174805	+	0.302770i
$649$	19.2090	−	33.2710i	0.754020	−	1.30600i
$650$	5.67760			0.222694
$651$	14.2641	−	41.4334i	0.559054	−	1.62390i
$652$	1.61550			0.0632677
$653$	11.7802	−	20.4040i	0.460996	−	0.798469i	−0.538015	−	0.842935i	$-0.680826\pi$
$653$	11.7802	−	20.4040i	0.460996	−	0.798469i	0.999011	+	0.0444666i	$0.0141588\pi$
$654$	−5.47029	−	9.47482i	−0.213905	−	0.370495i
$655$	6.85970	+	11.8814i	0.268031	+	0.464243i
$656$	2.80775	−	4.86316i	0.109624	−	0.189875i
$657$	−0.0534772			−0.00208635
$658$	1.16647	+	1.34173i	0.0454739	+	0.0523059i
$659$	−10.7974			−0.420609			−0.210304	−	0.977636i	$-0.567446\pi$
$659$	−10.7974			−0.420609			−0.210304	+	0.977636i	$0.567446\pi$
$660$	−7.76239	+	13.4448i	−0.302151	+	0.523340i
$661$	−5.51450	−	9.55140i	−0.214489	−	0.371506i	0.738625	−	0.674116i	$-0.235475\pi$
$661$	−5.51450	−	9.55140i	−0.214489	−	0.371506i	−0.953114	+	0.302610i	$0.902142\pi$
$662$	−2.84337	−	4.92487i	−0.110511	−	0.191410i
$663$	5.66898	−	9.81897i	0.220165	−	0.381337i
$664$	10.3222			0.400581
$665$	23.4630	+	26.9880i	0.909855	+	1.04655i
$666$	−0.146356			−0.00567117
$667$	−2.30750	+	3.99670i	−0.0893466	+	0.154753i
$668$	0.238766	+	0.413554i	0.00923812	+	0.0160009i
$669$	−10.5362	−	18.2492i	−0.407353	−	0.705556i
$670$	−17.4633	+	30.2474i	−0.674667	+	1.16856i
$671$	17.5910			0.679092
$672$	−1.48345	+	4.30902i	−0.0572253	+	0.166224i
$673$	−46.4316			−1.78981			−0.894903	−	0.446260i	$-0.852756\pi$
$673$	−46.4316			−1.78981			−0.894903	+	0.446260i	$0.852756\pi$
$674$	−7.49858	+	12.9879i	−0.288835	+	0.500276i
$675$	2.25315	+	3.90256i	0.0867236	+	0.150210i
$676$	−15.1640	−	26.2647i	−0.583229	−	1.01018i
$677$	10.8827	−	18.8493i	0.418255	−	0.724438i	−0.577509	−	0.816384i	$-0.695975\pi$
$677$	10.8827	−	18.8493i	0.418255	−	0.724438i	0.995764	+	0.0919457i	$0.0293086\pi$
$678$	8.34112			0.320339
$679$	−19.6064	+	3.81222i	−0.752423	+	0.146299i
$680$	−2.42127			−0.0928514
$681$	−5.10523	+	8.84251i	−0.195633	+	0.338846i
$682$	17.8967	+	30.9980i	0.685300	+	1.18697i
$683$	−9.43879	−	16.3485i	−0.361165	−	0.625556i	0.626988	−	0.779029i	$-0.284288\pi$
$683$	−9.43879	−	16.3485i	−0.361165	−	0.625556i	−0.988153	+	0.153473i	$0.950954\pi$
$684$	−0.0923961	+	0.160035i	−0.00353285	+	0.00611908i
$685$	−44.0122			−1.68162
$686$	0.972340	+	18.4947i	0.0371241	+	0.706132i
$687$	32.5430			1.24159
$688$	3.12719	−	5.41645i	0.119223	−	0.206500i
$689$	−32.6171	−	56.4945i	−1.24261	−	2.15227i
$690$	12.4503	+	21.5645i	0.473974	+	0.820948i
$691$	3.87198	−	6.70646i	0.147297	−	0.255126i	−0.782931	−	0.622109i	$-0.786276\pi$
$691$	3.87198	−	6.70646i	0.147297	−	0.255126i	0.930228	+	0.366983i	$0.119609\pi$
$692$	6.79423			0.258278
$693$	−0.320026	+	0.0622251i	−0.0121568	+	0.00236373i
$694$	25.6006			0.971785
$695$	19.5085	−	33.7898i	0.740000	−	1.28172i
$696$	0.665698	+	1.15302i	0.0252332	+	0.0437052i
$697$	−2.80775	−	4.86316i	−0.106351	−	0.184205i
$698$	−4.36112	+	7.55369i	−0.165071	+	0.285911i
$699$	40.1403			1.51825
$700$	−0.742852	+	2.15779i	−0.0280772	+	0.0815566i
$701$	37.0878			1.40079			0.700393	−	0.713758i	$-0.253008\pi$
$701$	37.0878			1.40079			0.700393	+	0.713758i	$0.253008\pi$
$702$	17.1946	−	29.7819i	0.648969	−	1.12405i
$703$	12.3406	+	21.3746i	0.465436	+	0.806158i
$704$	−1.86123	−	3.22375i	−0.0701479	−	0.121500i
$705$	1.40126	−	2.42706i	0.0527746	−	0.0914084i
$706$	27.4938			1.03474
$707$	21.5049	+	24.7358i	0.808774	+	0.930284i
$708$	−17.7769			−0.668096
$709$	19.4612	−	33.7078i	0.730881	−	1.26592i	−0.225626	−	0.974214i	$-0.572443\pi$
$709$	19.4612	−	33.7078i	0.730881	−	1.26592i	0.956507	−	0.291709i	$-0.0942239\pi$
$710$	−11.7347	−	20.3251i	−0.440396	−	0.762788i
$711$	0.0755570	+	0.130868i	0.00283361	+	0.00490795i
$712$	−2.19711	+	3.80551i	−0.0823403	+	0.142618i
$713$	57.4099			2.15002
$714$	2.99000	+	3.43921i	0.111898	+	0.128709i
$715$	59.3278			2.21873
$716$	3.74071	−	6.47909i	0.139797	−	0.242135i
$717$	16.8998	+	29.2714i	0.631136	+	1.09316i
$718$	7.19789	+	12.4671i	0.268623	+	0.465268i
$719$	8.45306	−	14.6411i	0.315246	−	0.546022i	−0.664244	−	0.747516i	$-0.731246\pi$
$719$	8.45306	−	14.6411i	0.315246	−	0.546022i	0.979490	+	0.201494i	$0.0645796\pi$
$720$	−0.0801505			−0.00298703
$721$	−3.53481	+	10.2677i	−0.131643	+	0.382388i
$722$	12.1631			0.452664
$723$	5.77318	−	9.99944i	0.214707	−	0.371883i
$724$	3.45966	+	5.99230i	0.128577	+	0.222702i
$725$	0.333355	+	0.577388i	0.0123805	+	0.0214436i
$726$	−2.46035	+	4.26145i	−0.0913121	+	0.158157i
$727$	−9.55267			−0.354289			−0.177144	−	0.984185i	$-0.556686\pi$
$727$	−9.55267			−0.354289			−0.177144	+	0.984185i	$0.556686\pi$
$728$	17.0952	−	3.32395i	0.633591	−	0.123194i
$729$	27.2913			1.01079
$730$	−1.95578	+	3.38750i	−0.0723865	+	0.125377i
$731$	−3.12719	−	5.41645i	−0.115663	−	0.200334i
$732$	−4.06987	−	7.04922i	−0.150427	−	0.260547i
$733$	13.1352	−	22.7508i	0.485160	−	0.840321i	−0.514695	−	0.857373i	$-0.672095\pi$
$733$	13.1352	−	22.7508i	0.485160	−	0.840321i	0.999855	+	0.0170521i	$0.00542812\pi$
$734$	−13.0839			−0.482935
$735$	27.0669	−	10.9392i	0.998378	−	0.403499i
$736$	−5.97056			−0.220078
$737$	−26.8482	+	46.5024i	−0.988965	+	1.71294i
$738$	−0.0929440	−	0.160984i	−0.00342131	−	0.00592589i
$739$	−8.15860	−	14.1311i	−0.300119	−	0.519821i	0.676044	−	0.736862i	$-0.263693\pi$
$739$	−8.15860	−	14.1311i	−0.300119	−	0.519821i	−0.976163	+	0.217040i	$0.930360\pi$
$740$	−5.35254	+	9.27087i	−0.196763	+	0.340804i
$741$	−63.2930			−2.32513
$742$	25.7385	−	5.00453i	0.944889	−	0.183722i
$743$	45.3294			1.66297			0.831486	−	0.555545i	$-0.187490\pi$
$743$	45.3294			1.66297			0.831486	+	0.555545i	$0.187490\pi$
$744$	8.28119	−	14.3434i	0.303603	−	0.525856i
$745$	−0.437189	−	0.757234i	−0.0160174	−	0.0277429i
$746$	−14.4101	−	24.9590i	−0.527591	−	0.913814i
$747$	0.170847	−	0.295916i	0.00625097	−	0.0108270i
$748$	−3.72247			−0.136107
$749$	−5.59699	+	16.2578i	−0.204510	+	0.594045i
$750$	−17.2555			−0.630082
$751$	5.28319	−	9.15076i	0.192787	−	0.333916i	−0.753386	−	0.657578i	$-0.771581\pi$
$751$	5.28319	−	9.15076i	0.192787	−	0.333916i	0.946173	+	0.323662i	$0.104914\pi$
$752$	0.335989	+	0.581951i	0.0122523	+	0.0212216i
$753$	−0.847048	−	1.46713i	−0.0308682	−	0.0534652i
$754$	2.54396	−	4.40626i	0.0926454	−	0.160467i
$755$	−34.5856			−1.25870
$756$	9.06897	+	10.4315i	0.329835	+	0.379390i
$757$	36.3965			1.32285			0.661427	−	0.750010i	$-0.269951\pi$
$757$	36.3965			1.32285			0.661427	+	0.750010i	$0.269951\pi$
$758$	12.9137	−	22.3672i	0.469047	−	0.812413i
$759$	19.1411	+	33.1534i	0.694779	+	1.20339i
$760$	6.75824	+	11.7056i	0.245147	+	0.424607i
$761$	−25.3230	+	43.8608i	−0.917960	+	1.58995i	−0.115450	+	0.993313i	$0.536831\pi$
$761$	−25.3230	+	43.8608i	−0.917960	+	1.58995i	−0.802510	+	0.596639i	$0.796502\pi$
$762$	−16.3885			−0.593691
$763$	−11.0258	−	12.6823i	−0.399160	−	0.459129i
$764$	4.82029			0.174392
$765$	−0.0400752	+	0.0694124i	−0.00144892	+	0.00250961i
$766$	−0.809435	−	1.40198i	−0.0292461	−	0.0506557i
$767$	33.9670	+	58.8327i	1.22648	+	2.12432i
$768$	−0.861234	+	1.49170i	−0.0310771	+	0.0538271i
$769$	−17.6097			−0.635023			−0.317511	−	0.948254i	$-0.602847\pi$
$769$	−17.6097			−0.635023			−0.317511	+	0.948254i	$0.602847\pi$
$770$	−7.76239	+	22.5477i	−0.279737	+	0.812561i
$771$	−33.3036			−1.19940
$772$	−0.588166	+	1.01873i	−0.0211686	+	0.0366650i
$773$	−1.65978	−	2.87482i	−0.0596982	−	0.103400i	0.834632	−	0.550808i	$-0.185680\pi$
$773$	−1.65978	−	2.87482i	−0.0596982	−	0.103400i	−0.894330	+	0.447408i	$0.852347\pi$
$774$	−0.103518	−	0.179299i	−0.00372089	−	0.00644476i
$775$	4.14689	−	7.18263i	0.148961	−	0.258008i
$776$	−7.54929			−0.271004
$777$	19.7783	−	3.84565i	0.709543	−	0.137962i
$778$	−22.2486			−0.797651
$779$	−15.6740	+	27.1481i	−0.561578	+	0.972681i
$780$	−13.7261	−	23.7744i	−0.491474	−	0.851258i
$781$	−18.0410	−	31.2479i	−0.645558	−	1.11814i
$782$	−2.98528	+	5.17066i	−0.106753	+	0.184902i
$783$	4.03826			0.144316
$784$	−0.973446	+	6.93198i	−0.0347659	+	0.247571i
$785$	12.4392			0.443973
$786$	4.87993	−	8.45229i	0.174061	−	0.301483i
$787$	−1.61015	−	2.78886i	−0.0573955	−	0.0994120i	0.835900	−	0.548882i	$-0.184946\pi$
$787$	−1.61015	−	2.78886i	−0.0573955	−	0.0994120i	−0.893296	+	0.449470i	$0.851613\pi$
$788$	−2.18697	−	3.78794i	−0.0779075	−	0.134940i
$789$	−7.47491	+	12.9469i	−0.266114	+	0.460923i
$790$	11.0531			0.393252
$791$	12.5766	−	2.44537i	0.447173	−	0.0869473i
$792$	−0.123224			−0.00437856
$793$	−15.5530	+	26.9385i	−0.552302	+	0.956614i
$794$	12.7913	+	22.1553i	0.453948	+	0.786260i
$795$	−20.6660	−	35.7945i	−0.732947	−	1.26950i
$796$	−11.9649	+	20.7238i	−0.424085	+	0.734536i
$797$	1.39748			0.0495013			0.0247507	−	0.999694i	$-0.492121\pi$
$797$	1.39748			0.0495013			0.0247507	+	0.999694i	$0.492121\pi$
$798$	8.28119	−	24.0546i	0.293151	−	0.851525i
$799$	0.671979			0.0237729
$800$	−0.431272	+	0.746985i	−0.0152478	+	0.0264099i
$801$	0.0727303	+	0.125973i	0.00256980	+	0.00445102i
$802$	−4.03310	−	6.98554i	−0.142414	−	0.246668i
$803$	−3.00682	+	5.20796i	−0.106108	+	0.183785i
$804$	24.8465			0.876268
$805$	25.0944	+	28.8646i	0.884463	+	1.01734i
$806$	−63.2930			−2.22940
$807$	19.3599	−	33.5324i	0.681502	−	1.18040i
$808$	6.19423	+	10.7287i	0.217912	+	0.377435i
$809$	−24.2769	−	42.0488i	−0.853530	−	1.47836i	−0.878002	−	0.478657i	$-0.841124\pi$
$809$	−24.2769	−	42.0488i	−0.853530	−	1.47836i	0.0244722	−	0.999701i	$-0.492209\pi$
$810$	10.7742	−	18.6614i	0.378565	−	0.655694i
$811$	56.4439			1.98201			0.991006	−	0.133816i	$-0.0427232\pi$
$811$	56.4439			1.98201			0.991006	+	0.133816i	$0.0427232\pi$
$812$	1.34176	+	1.54335i	0.0470866	+	0.0541609i
$813$	15.9690			0.560058
$814$	−8.22902	+	14.2531i	−0.288427	+	0.499570i
$815$	−1.95578	−	3.38750i	−0.0685078	−	0.118659i
$816$	0.861234	+	1.49170i	0.0301492	+	0.0522200i
$817$	−17.4572	+	30.2367i	−0.610750	+	1.05785i
$818$	−7.15970			−0.250333
$819$	0.187658	−	0.545098i	0.00655732	−	0.0190473i
$820$	−13.5966			−0.474815
$821$	−2.44711	+	4.23852i	−0.0854048	+	0.147925i	−0.905564	−	0.424210i	$-0.860552\pi$
$821$	−2.44711	+	4.23852i	−0.0854048	+	0.147925i	0.820159	+	0.572136i	$0.193885\pi$
$822$	15.6550	+	27.1152i	0.546029	+	0.945750i
$823$	7.85180	+	13.5997i	0.273697	+	0.474056i	0.969805	−	0.243880i	$-0.0784203\pi$
$823$	7.85180	+	13.5997i	0.273697	+	0.474056i	−0.696109	+	0.717936i	$0.745087\pi$
$824$	−2.05218	+	3.55447i	−0.0714910	+	0.123826i
$825$	5.53049			0.192547
$826$	−26.8037	+	5.21165i	−0.932620	+	0.181337i
$827$	0.125810			0.00437485			0.00218743	−	0.999998i	$-0.499304\pi$
$827$	0.125810			0.00437485			0.00218743	+	0.999998i	$0.499304\pi$
$828$	−0.0988207	+	0.171163i	−0.00343426	+	0.00594831i
$829$	18.4514	+	31.9588i	0.640844	+	1.10997i	0.985245	+	0.171151i	$0.0547487\pi$
$829$	18.4514	+	31.9588i	0.640844	+	1.10997i	−0.344401	+	0.938823i	$0.611918\pi$
$830$	−12.4965	−	21.6445i	−0.433759	−	0.751292i
$831$	10.6723	−	18.4849i	0.370217	−	0.641234i
$832$	6.58239			0.228203
$833$	5.51655	+	4.30902i	0.191137	+	0.149299i
$834$	−27.7564			−0.961124
$835$	0.578116	−	1.00133i	0.0200065	−	0.0346523i
$836$	10.3901	+	17.9963i	0.359351	+	0.622413i
$837$	−25.1177	−	43.5052i	−0.868195	−	1.50376i
$838$	−4.28250	+	7.41751i	−0.147937	+	0.256234i
$839$	−19.4435			−0.671265			−0.335632	−	0.941993i	$-0.608950\pi$
$839$	−19.4435			−0.671265			−0.335632	+	0.941993i	$0.608950\pi$
$840$	10.8314	−	2.10603i	0.373719	−	0.0726651i
$841$	−28.4025			−0.979398
$842$	−4.99254	+	8.64733i	−0.172054	+	0.298007i
$843$	−13.8210	−	23.9386i	−0.476020	−	0.824490i
$844$	4.78239	+	8.28335i	0.164617	+	0.285125i
$845$	−36.7160	+	63.5940i	−1.26307	+	2.18770i
$846$	0.0222443			0.000764775
$847$	−2.46035	+	7.14665i	−0.0845386	+	0.245562i
$848$	9.91041			0.340325
$849$	5.98516	−	10.3666i	0.205410	−	0.355781i
$850$	0.431272	+	0.746985i	0.0147925	+	0.0256214i
$851$	13.1987	+	22.8609i	0.452446	+	0.783660i
$852$	−8.34797	+	14.4591i	−0.285997	+	0.495361i
$853$	−6.78450			−0.232297			−0.116148	−	0.993232i	$-0.537055\pi$
$853$	−6.78450			−0.232297			−0.116148	+	0.993232i	$0.537055\pi$
$854$	−8.20311	−	9.43555i	−0.280705	−	0.322878i
$855$	0.447432			0.0153018
$856$	−3.24940	+	5.62813i	−0.111062	+	0.192365i
$857$	−13.3773	−	23.1702i	−0.456961	−	0.791481i	0.541837	−	0.840484i	$-0.317729\pi$
$857$	−13.3773	−	23.1702i	−0.456961	−	0.791481i	−0.998799	+	0.0490030i	$0.984396\pi$
$858$	−21.1026	−	36.5508i	−0.720431	−	1.24782i
$859$	−21.4709	+	37.1887i	−0.732578	+	1.26886i	0.223199	+	0.974773i	$0.428350\pi$
$859$	−21.4709	+	37.1887i	−0.732578	+	1.26886i	−0.955778	+	0.294090i	$0.904983\pi$
$860$	−15.1435			−0.516390
$861$	16.7903	+	19.3129i	0.572212	+	0.658182i
$862$	14.2258			0.484534
$863$	−14.6571	+	25.3868i	−0.498932	+	0.864176i	−0.999999	−	0.00123268i	$-0.999608\pi$
$863$	−14.6571	+	25.3868i	−0.498932	+	0.864176i	0.501067	+	0.865408i	$0.332941\pi$
$864$	2.61221	+	4.52448i	0.0888692	+	0.153926i
$865$	−8.22533	−	14.2467i	−0.279669	−	0.484402i
$866$	−3.79382	+	6.57108i	−0.128919	+	0.223294i
$867$	1.72247			0.0584981
$868$	8.28119	−	24.0546i	0.281082	−	0.816468i
$869$	16.9931			0.576451
$870$	1.61183	−	2.79178i	0.0546463	−	0.0946501i
$871$	−47.4753	−	82.2296i	−1.60864	−	2.78624i
$872$	−3.17584	−	5.50072i	−0.107548	−	0.186278i
$873$	−0.124951	+	0.216421i	−0.00422895	+	0.00732475i
$874$	33.3300			1.12740
$875$	−26.0176	+	5.05880i	−0.879556	+	0.171019i
$876$	2.78264			0.0940167
$877$	17.4121	−	30.1587i	0.587966	−	1.01839i	−0.406532	−	0.913636i	$-0.633262\pi$
$877$	17.4121	−	30.1587i	0.587966	−	1.01839i	0.994499	−	0.104751i	$-0.0334045\pi$
$878$	−6.24412	−	10.8151i	−0.210729	−	0.364993i
$879$	−0.0742477	−	0.128601i	−0.00250431	−	0.00433760i
$880$	−4.50655	+	7.80557i	−0.151916	+	0.263126i
$881$	−33.4518			−1.12702			−0.563510	−	0.826109i	$-0.690549\pi$
$881$	−33.4518			−1.12702			−0.563510	+	0.826109i	$0.690549\pi$
$882$	0.182613	+	0.142640i	0.00614889	+	0.00480294i
$883$	−43.4476			−1.46213			−0.731064	−	0.682309i	$-0.760976\pi$
$883$	−43.4476			−1.46213			−0.731064	+	0.682309i	$0.760976\pi$
$884$	3.29120	−	5.70052i	0.110695	−	0.191729i
$885$	21.5213	+	37.2760i	0.723430	+	1.25302i
$886$	−15.6748	−	27.1495i	−0.526605	−	0.912106i
$887$	−3.34893	+	5.80052i	−0.112446	+	0.194762i	−0.916756	−	0.399448i	$-0.869202\pi$
$887$	−3.34893	+	5.80052i	−0.112446	+	0.194762i	0.804310	+	0.594210i	$0.202535\pi$
$888$	7.61550			0.255559
$889$	−24.7103	+	4.80461i	−0.828756	+	0.161141i
$890$	10.6396			0.356640
$891$	16.5642	−	28.6901i	0.554923	−	0.961154i
$892$	−6.11692	−	10.5948i	−0.204809	−	0.354740i
$893$	−1.87562	−	3.24868i	−0.0627654	−	0.108713i
$894$	−0.311012	+	0.538689i	−0.0104018	+	0.0180165i
$895$	−18.1145			−0.605501
$896$	−0.861234	+	2.50165i	−0.0287718	+	0.0835744i
$897$	−67.6940			−2.26024
$898$	−13.1959	+	22.8560i	−0.440353	+	0.762714i
$899$	−3.71619	−	6.43663i	−0.123942	−	0.214673i
$900$	0.0142762	+	0.0247272i	0.000475875	+	0.000824240i
$901$	4.95521	−	8.58267i	0.165082	−	0.285930i
$902$	−20.9035			−0.696011
$903$	18.7006	+	21.5101i	0.622316	+	0.715812i
$904$	4.84254			0.161060
$905$	8.37676	−	14.5090i	0.278453	−	0.482295i
$906$	12.3020	+	21.3076i	0.408705	+	0.707898i
$907$	−2.05648	−	3.56193i	−0.0682844	−	0.118272i	0.829862	−	0.557969i	$-0.188419\pi$
$907$	−2.05648	−	3.56193i	−0.0682844	−	0.118272i	−0.898146	+	0.439697i	$0.855086\pi$
$908$	−2.96390	+	5.13363i	−0.0983605	+	0.170365i
$909$	0.410091			0.0136019
$910$	−27.6660	−	31.8225i	−0.917119	−	1.05491i
$911$	−24.3957			−0.808264			−0.404132	−	0.914701i	$-0.632426\pi$
$911$	−24.3957			−0.808264			−0.404132	+	0.914701i	$0.632426\pi$
$912$	4.80775	−	8.32726i	0.159200	−	0.275743i
$913$	−19.2121	−	33.2764i	−0.635828	−	1.10129i
$914$	12.1089	+	20.9732i	0.400526	+	0.693731i
$915$	−9.85424	+	17.0681i	−0.325771	+	0.564252i
$916$	18.8932			0.624250
$917$	4.87993	−	14.1749i	0.161150	−	0.468096i
$918$	5.22442			0.172432
$919$	14.2558	−	24.6918i	0.470257	−	0.814509i	−0.529165	−	0.848519i	$-0.677495\pi$
$919$	14.2558	−	24.6918i	0.470257	−	0.814509i	0.999421	+	0.0340106i	$0.0108280\pi$
$920$	7.22817	+	12.5195i	0.238306	+	0.412757i
$921$	18.1993	+	31.5222i	0.599688	+	1.03869i
$922$	10.1842	−	17.6396i	0.335400	−	0.580929i
$923$	63.8033			2.10011
$924$	16.6523	−	3.23783i	0.547819	−	0.106517i
$925$	3.81354			0.125388
$926$	5.36908	−	9.29951i	0.176439	−	0.305601i
$927$	0.0679325	+	0.117663i	0.00223120	+	0.00386455i
$928$	0.386479	+	0.669401i	0.0126868	+	0.0219742i
$929$	−19.0076	+	32.9222i	−0.623620	+	1.08014i	0.365187	+	0.930934i	$0.381005\pi$
$929$	−19.0076	+	32.9222i	−0.623620	+	1.08014i	−0.988806	+	0.149206i	$0.952328\pi$
$930$	−40.1020			−1.31500
$931$	5.43416	−	38.6971i	0.178097	−	1.26824i
$932$	23.3039			0.763346
$933$	9.16346	−	15.8716i	0.299998	−	0.519612i
$934$	0.653740	+	1.13231i	0.0213910	+	0.0370503i
$935$	4.50655	+	7.80557i	0.147380	+	0.255269i
$936$	0.108947	−	0.188702i	0.00356106	−	0.00616793i
$937$	−26.1085			−0.852927			−0.426464	−	0.904505i	$-0.640241\pi$
$937$	−26.1085			−0.852927			−0.426464	+	0.904505i	$0.640241\pi$
$938$	37.4632	−	7.28425i	1.22322	−	0.237839i
$939$	35.5920			1.16150
$940$	0.813521	−	1.40906i	0.0265341	−	0.0459584i
$941$	12.2089	+	21.1465i	0.398000	+	0.689357i	0.993479	−	0.114014i	$-0.0363710\pi$
$941$	12.2089	+	21.1465i	0.398000	+	0.689357i	−0.595479	+	0.803371i	$0.703038\pi$
$942$	−4.42455	−	7.66355i	−0.144160	−	0.249692i
$943$	−16.7638	+	29.0358i	−0.545905	+	0.945536i
$944$	−10.3206			−0.335906
$945$	10.8944	−	31.6453i	0.354394	−	1.02942i
$946$	−23.2817			−0.756953
$947$	−7.82529	+	13.5538i	−0.254288	+	0.440439i	−0.964702	−	0.263345i	$-0.915174\pi$
$947$	−7.82529	+	13.5538i	−0.254288	+	0.440439i	0.710414	+	0.703784i	$0.248508\pi$
$948$	−3.93154	−	6.80963i	−0.127690	−	0.221166i
$949$	−5.31692	−	9.20917i	−0.172594	−	0.298942i
$950$	2.40753	−	4.16996i	0.0781105	−	0.135291i
$951$	−14.9406			−0.484482
$952$	1.73588	+	1.99668i	0.0562602	+	0.0647127i
$953$	49.6977			1.60987			0.804933	−	0.593366i	$-0.202201\pi$
$953$	49.6977			1.60987			0.804933	+	0.593366i	$0.202201\pi$
$954$	0.164031	−	0.284109i	0.00531069	−	0.00919838i
$955$	−5.83561	−	10.1076i	−0.188836	−	0.327074i
$956$	9.81141	+	16.9939i	0.317324	+	0.549621i
$957$	2.47804	−	4.29209i	0.0801036	−	0.138744i
$958$	17.9198			0.578964
$959$	31.5537	+	36.2943i	1.01892	+	1.17200i
$960$	4.17056			0.134604
$961$	−30.7289	+	53.2240i	−0.991254	+	1.71690i
$962$	−14.5513	−	25.2035i	−0.469152	−	0.812594i
$963$	0.107564	+	0.186306i	0.00346620	+	0.00600363i
$964$	3.35169	−	5.80530i	0.107951	−	0.186976i
$965$	2.84822			0.0916873
$966$	8.85702	−	25.7273i	0.284970	−	0.827761i
$967$	−23.2765			−0.748521			−0.374260	−	0.927324i	$-0.622103\pi$
$967$	−23.2765			−0.748521			−0.374260	+	0.927324i	$0.622103\pi$
$968$	−1.42839	+	2.47404i	−0.0459100	+	0.0795185i
$969$	−4.80775	−	8.32726i	−0.154447	−	0.267510i
$970$	9.13943	+	15.8300i	0.293449	+	0.508269i
$971$	21.4746	−	37.1951i	0.689152	−	1.19365i	−0.282960	−	0.959132i	$-0.591316\pi$
$971$	21.4746	−	37.1951i	0.689152	−	1.19365i	0.972112	−	0.234515i	$-0.0753502\pi$
$972$	0.343997			0.0110337
$973$	−41.8507	+	8.13734i	−1.34167	+	0.260871i
$974$	8.03415			0.257431
$975$	−4.88974	+	8.46928i	−0.156597	+	0.271234i
$976$	−2.36281	−	4.09251i	−0.0756317	−	0.130998i
$977$	9.70620	+	16.8116i	0.310529	+	0.537852i	0.978477	−	0.206356i	$-0.0661605\pi$
$977$	9.70620	+	16.8116i	0.310529	+	0.537852i	−0.667948	+	0.744208i	$0.732827\pi$
$978$	−1.39132	+	2.40984i	−0.0444895	+	0.0770581i
$979$	16.3574			0.522784
$980$	15.7140	−	6.35090i	0.501966	−	0.202872i
$981$	−0.210258			−0.00671302
$982$	−14.9949	+	25.9719i	−0.478505	+	0.828795i
$983$	0.876998	+	1.51901i	0.0279719	+	0.0484487i	0.879672	−	0.475580i	$-0.157762\pi$
$983$	0.876998	+	1.51901i	0.0279719	+	0.0484487i	−0.851701	+	0.524029i	$0.824428\pi$
$984$	4.83626	+	8.37664i	0.154174	+	0.267038i
$985$	−5.29523	+	9.17162i	−0.168720	+	0.292232i
$986$	0.772958			0.0246160
$987$	−3.00606	+	0.584491i	−0.0956840	+	0.0186046i
$988$	−36.7455			−1.16903
$989$	−18.6711	+	32.3392i	−0.593705	+	1.02833i
$990$	0.149179	+	0.258385i	0.00474121	+	0.00821202i
$991$	−0.0658757	−	0.114100i	−0.00209261	−	0.00362451i	0.864977	−	0.501811i	$-0.167333\pi$
$991$	−0.0658757	−	0.114100i	−0.00209261	−	0.00362451i	−0.867070	+	0.498187i	$0.833999\pi$
$992$	4.80775	−	8.32726i	0.152646	−	0.264391i
$993$	9.79524			0.310843
$994$	−8.34797	+	24.2486i	−0.264781	+	0.769119i
$995$	57.9405			1.83684
$996$	−8.88987	+	15.3977i	−0.281686	+	0.487895i
$997$	12.0367	+	20.8483i	0.381208	+	0.660271i	0.991235	−	0.132109i	$-0.0421750\pi$
$997$	12.0367	+	20.8483i	0.381208	+	0.660271i	−0.610028	+	0.792380i	$0.708842\pi$
$998$	11.8118	+	20.4586i	0.373896	+	0.647606i
$999$	11.5493	−	20.0040i	0.365403	−	0.632897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	238.2.e.f.205.2	yes	10
7.2	even	3		1666.2.a.z.1.4		5
7.4	even	3	inner	238.2.e.f.137.2	✓	10
7.5	odd	6		1666.2.a.ba.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
238.2.e.f.137.2	✓	10	7.4	even	3	inner
238.2.e.f.205.2	yes	10	1.1	even	1	trivial
1666.2.a.z.1.4		5	7.2	even	3
1666.2.a.ba.1.2		5	7.5	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:	\( N \)	\(=\)	\( 238 = 2 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	238.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.861234 - 1.49170i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.21063 + 2.09688i) q^{5} +1.72247 q^{6} +(2.59711 - 0.504977i) q^{7} +1.00000 q^{8} +(0.0165513 - 0.0286678i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.861234 - 1.49170i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.21063 + 2.09688i) q^{5} +1.72247 q^{6} +(2.59711 - 0.504977i) q^{7} +1.00000 q^{8} +(0.0165513 - 0.0286678i) q^{9} +(-1.21063 - 2.09688i) q^{10} +(-1.86123 - 3.22375i) q^{11} +(-0.861234 + 1.49170i) q^{12} +6.58239 q^{13} +(-0.861234 + 2.50165i) q^{14} +4.17056 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{17} +(0.0165513 + 0.0286678i) q^{18} +(2.79120 - 4.83449i) q^{19} +2.42127 q^{20} +(-2.99000 - 3.43921i) q^{21} +3.72247 q^{22} +(2.98528 - 5.17066i) q^{23} +(-0.861234 - 1.49170i) q^{24} +(-0.431272 - 0.746985i) q^{25} +(-3.29120 + 5.70052i) q^{26} -5.22442 q^{27} +(-1.73588 - 1.99668i) q^{28} -0.772958 q^{29} +(-2.08528 + 3.61181i) q^{30} +(4.80775 + 8.32726i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.20592 + 5.55281i) q^{33} -1.00000 q^{34} +(-2.08528 + 6.05718i) q^{35} -0.0331027 q^{36} +(-2.21063 + 3.82893i) q^{37} +(2.79120 + 4.83449i) q^{38} +(-5.66898 - 9.81897i) q^{39} +(-1.21063 + 2.09688i) q^{40} -5.61550 q^{41} +(4.47345 - 0.869806i) q^{42} -6.25437 q^{43} +(-1.86123 + 3.22375i) q^{44} +(0.0400752 + 0.0694124i) q^{45} +(2.98528 + 5.17066i) q^{46} +(0.335989 - 0.581951i) q^{47} +1.72247 q^{48} +(6.49000 - 2.62296i) q^{49} +0.862543 q^{50} +(0.861234 - 1.49170i) q^{51} +(-3.29120 - 5.70052i) q^{52} +(-4.95521 - 8.58267i) q^{53} +(2.61221 - 4.52448i) q^{54} +9.01310 q^{55} +(2.59711 - 0.504977i) q^{56} -9.61550 q^{57} +(0.386479 - 0.669401i) q^{58} +(5.16029 + 8.93788i) q^{59} +(-2.08528 - 3.61181i) q^{60} +(-2.36281 + 4.09251i) q^{61} -9.61550 q^{62} +(0.0285092 - 0.0828115i) q^{63} +1.00000 q^{64} +(-7.96887 + 13.8025i) q^{65} +(-3.20592 - 5.55281i) q^{66} +(-7.21247 - 12.4924i) q^{67} +(0.500000 - 0.866025i) q^{68} -10.2841 q^{69} +(-4.20303 - 4.83449i) q^{70} +9.69303 q^{71} +(0.0165513 - 0.0286678i) q^{72} +(-0.807748 - 1.39906i) q^{73} +(-2.21063 - 3.82893i) q^{74} +(-0.742852 + 1.28666i) q^{75} -5.58239 q^{76} +(-6.46176 - 7.43257i) q^{77} +11.3380 q^{78} +(-2.28250 + 3.95341i) q^{79} +(-1.21063 - 2.09688i) q^{80} +(4.44980 + 7.70728i) q^{81} +(2.80775 - 4.86316i) q^{82} +10.3222 q^{83} +(-1.48345 + 4.30902i) q^{84} -2.42127 q^{85} +(3.12719 - 5.41645i) q^{86} +(0.665698 + 1.15302i) q^{87} +(-1.86123 - 3.22375i) q^{88} +(-2.19711 + 3.80551i) q^{89} -0.0801505 q^{90} +(17.0952 - 3.32395i) q^{91} -5.97056 q^{92} +(8.28119 - 14.3434i) q^{93} +(0.335989 + 0.581951i) q^{94} +(6.75824 + 11.7056i) q^{95} +(-0.861234 + 1.49170i) q^{96} -7.54929 q^{97} +(-0.973446 + 6.93198i) q^{98} -0.123224 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 5 q^{4} + q^{5} - 3 q^{7} + 10 q^{8} - 11 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - 5 * q^4 + q^5 - 3 * q^7 + 10 * q^8 - 11 * q^9	\( 10 q - 5 q^{2} - 5 q^{4} + q^{5} - 3 q^{7} + 10 q^{8} - 11 q^{9} + q^{10} - 10 q^{11} + 4 q^{13} - 8 q^{15} - 5 q^{16} + 5 q^{17} - 11 q^{18} - 3 q^{19} - 2 q^{20} + 10 q^{21} + 20 q^{22} - 3 q^{23} - 18 q^{25} - 2 q^{26} - 12 q^{27} + 3 q^{28} + 24 q^{29} + 4 q^{30} + 6 q^{31} - 5 q^{32} - 26 q^{33} - 10 q^{34} + 4 q^{35} + 22 q^{36} - 9 q^{37} - 3 q^{38} - 6 q^{39} + q^{40} + 28 q^{41} + 16 q^{42} + 2 q^{43} - 10 q^{44} + 37 q^{45} - 3 q^{46} + 2 q^{47} + 25 q^{49} + 36 q^{50} - 2 q^{52} - 20 q^{53} + 6 q^{54} - 12 q^{55} - 3 q^{56} - 12 q^{57} - 12 q^{58} - 3 q^{59} + 4 q^{60} - 16 q^{61} - 12 q^{62} + 6 q^{63} + 10 q^{64} - 2 q^{65} - 26 q^{66} - 15 q^{67} + 5 q^{68} + 8 q^{69} + q^{70} + 14 q^{71} - 11 q^{72} + 34 q^{73} - 9 q^{74} - 46 q^{75} + 6 q^{76} + 16 q^{77} + 12 q^{78} + 12 q^{79} + q^{80} - 53 q^{81} - 14 q^{82} + 32 q^{83} - 26 q^{84} + 2 q^{85} - q^{86} + 20 q^{87} - 10 q^{88} - q^{89} - 74 q^{90} + 42 q^{91} + 6 q^{92} + 12 q^{93} + 2 q^{94} + 3 q^{95} - 36 q^{97} + 19 q^{98} + 32 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 5 * q^4 + q^5 - 3 * q^7 + 10 * q^8 - 11 * q^9 + q^10 - 10 * q^11 + 4 * q^13 - 8 * q^15 - 5 * q^16 + 5 * q^17 - 11 * q^18 - 3 * q^19 - 2 * q^20 + 10 * q^21 + 20 * q^22 - 3 * q^23 - 18 * q^25 - 2 * q^26 - 12 * q^27 + 3 * q^28 + 24 * q^29 + 4 * q^30 + 6 * q^31 - 5 * q^32 - 26 * q^33 - 10 * q^34 + 4 * q^35 + 22 * q^36 - 9 * q^37 - 3 * q^38 - 6 * q^39 + q^40 + 28 * q^41 + 16 * q^42 + 2 * q^43 - 10 * q^44 + 37 * q^45 - 3 * q^46 + 2 * q^47 + 25 * q^49 + 36 * q^50 - 2 * q^52 - 20 * q^53 + 6 * q^54 - 12 * q^55 - 3 * q^56 - 12 * q^57 - 12 * q^58 - 3 * q^59 + 4 * q^60 - 16 * q^61 - 12 * q^62 + 6 * q^63 + 10 * q^64 - 2 * q^65 - 26 * q^66 - 15 * q^67 + 5 * q^68 + 8 * q^69 + q^70 + 14 * q^71 - 11 * q^72 + 34 * q^73 - 9 * q^74 - 46 * q^75 + 6 * q^76 + 16 * q^77 + 12 * q^78 + 12 * q^79 + q^80 - 53 * q^81 - 14 * q^82 + 32 * q^83 - 26 * q^84 + 2 * q^85 - q^86 + 20 * q^87 - 10 * q^88 - q^89 - 74 * q^90 + 42 * q^91 + 6 * q^92 + 12 * q^93 + 2 * q^94 + 3 * q^95 - 36 * q^97 + 19 * q^98 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more