LMFDB - Embedded newform 440.2.bi.b.141.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [440,2,Mod(141,440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(440, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 0, 6]))

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

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

chi := DirichletCharacter("440.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.bi (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.51341768894$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			141.1
Root			$-0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	440.141
Dual form			440.2.bi.b.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642040 - 1.26007i) q^{2} +(-0.363271 - 0.500000i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(-0.396802 + 0.778768i) q^{6} +(0.618034 + 0.449028i) q^{7} +(2.79360 + 0.442463i) q^{8} +(0.809017 - 2.48990i) q^{9} +O(q^{10})$	\(q+(-0.642040 - 1.26007i) q^{2} +(-0.363271 - 0.500000i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(-0.396802 + 0.778768i) q^{6} +(0.618034 + 0.449028i) q^{7} +(2.79360 + 0.442463i) q^{8} +(0.809017 - 2.48990i) q^{9} +(1.00000 + 1.00000i) q^{10} +(3.21644 - 0.809017i) q^{11} +1.23607 q^{12} +(-0.726543 - 0.236068i) q^{13} +(0.169006 - 1.06706i) q^{14} +(0.500000 + 0.363271i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(-0.118034 - 0.363271i) q^{17} +(-3.65688 + 0.579192i) q^{18} +(-4.75528 - 6.54508i) q^{19} +(0.618034 - 1.90211i) q^{20} -0.472136i q^{21} +(-3.08450 - 3.53353i) q^{22} -3.23607 q^{23} +(-0.793604 - 1.55754i) q^{24} +(0.809017 - 0.587785i) q^{25} +(0.169006 + 1.06706i) q^{26} +(-3.30220 + 1.07295i) q^{27} +(-1.45309 + 0.472136i) q^{28} +(2.35114 - 3.23607i) q^{29} +(0.136729 - 0.863271i) q^{30} +(0.618034 - 1.90211i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-1.57295 - 1.31433i) q^{33} +(-0.381966 + 0.381966i) q^{34} +(-0.726543 - 0.236068i) q^{35} +(3.07768 + 4.23607i) q^{36} +(4.70228 - 6.47214i) q^{37} +(-5.19421 + 10.1942i) q^{38} +(0.145898 + 0.449028i) q^{39} +(-2.79360 + 0.442463i) q^{40} +(5.97214 - 4.33901i) q^{41} +(-0.594926 + 0.303130i) q^{42} +1.85410i q^{43} +(-2.47214 + 6.15537i) q^{44} +2.61803i q^{45} +(2.07768 + 4.07768i) q^{46} +(-8.85410 + 6.43288i) q^{47} +(-1.45309 + 2.00000i) q^{48} +(-1.98278 - 6.10237i) q^{49} +(-1.26007 - 0.642040i) q^{50} +(-0.138757 + 0.190983i) q^{51} +(1.23607 - 0.898056i) q^{52} +(2.62866 + 0.854102i) q^{53} +(3.47214 + 3.47214i) q^{54} +(-2.80902 + 1.76336i) q^{55} +(1.52786 + 1.52786i) q^{56} +(-1.54508 + 4.75528i) q^{57} +(-5.58721 - 0.884927i) q^{58} +(0.951057 - 1.30902i) q^{59} +(-1.17557 + 0.381966i) q^{60} +(4.25325 - 1.38197i) q^{61} +(-2.79360 + 0.442463i) q^{62} +(1.61803 - 1.17557i) q^{63} +(7.60845 + 2.47214i) q^{64} +0.763932 q^{65} +(-0.646254 + 2.82588i) q^{66} -13.3262i q^{67} +(0.726543 + 0.236068i) q^{68} +(1.17557 + 1.61803i) q^{69} +(0.169006 + 1.06706i) q^{70} +(3.38197 + 10.4086i) q^{71} +(3.36176 - 6.59783i) q^{72} +(6.35410 + 4.61653i) q^{73} +(-11.1744 - 1.76985i) q^{74} +(-0.587785 - 0.190983i) q^{75} +16.1803 q^{76} +(2.35114 + 0.944272i) q^{77} +(0.472136 - 0.472136i) q^{78} +(0.708204 - 2.17963i) q^{79} +(2.35114 + 3.23607i) q^{80} +(-4.61803 - 3.35520i) q^{81} +(-9.30182 - 4.73951i) q^{82} +(-4.39201 + 1.42705i) q^{83} +(0.763932 + 0.555029i) q^{84} +(0.224514 + 0.309017i) q^{85} +(2.33630 - 1.19041i) q^{86} -2.47214 q^{87} +(9.34342 - 0.836916i) q^{88} -5.56231 q^{89} +(3.29892 - 1.68088i) q^{90} +(-0.343027 - 0.472136i) q^{91} +(3.80423 - 5.23607i) q^{92} +(-1.17557 + 0.381966i) q^{93} +(13.7906 + 7.02666i) q^{94} +(6.54508 + 4.75528i) q^{95} +(3.45309 + 0.546915i) q^{96} +(-0.899187 + 2.76741i) q^{97} +(-6.41641 + 6.41641i) q^{98} +(0.587785 - 8.66312i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 6 q^{6} - 4 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 6 * q^6 - 4 * q^7 + 4 * q^8 + 2 * q^9	$ 8 q - 2 q^{2} + 6 q^{6} - 4 q^{7} + 4 q^{8} + 2 q^{9} + 8 q^{10} - 8 q^{12} - 4 q^{14} + 4 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} - 4 q^{20} - 22 q^{22} - 8 q^{23} + 12 q^{24} + 2 q^{25} - 4 q^{26} + 4 q^{30} - 4 q^{31} - 32 q^{32} - 26 q^{33} - 12 q^{34} + 20 q^{38} + 28 q^{39} - 4 q^{40} + 12 q^{41} - 28 q^{42} + 16 q^{44} - 8 q^{46} - 44 q^{47} - 74 q^{49} + 2 q^{50} - 8 q^{52} - 8 q^{54} - 18 q^{55} + 48 q^{56} + 10 q^{57} - 8 q^{58} - 4 q^{62} + 4 q^{63} + 24 q^{65} + 4 q^{66} - 4 q^{70} + 36 q^{71} - 4 q^{72} + 24 q^{73} - 16 q^{74} + 40 q^{76} - 32 q^{78} - 48 q^{79} - 28 q^{81} + 22 q^{82} + 24 q^{84} + 18 q^{86} + 16 q^{87} - 4 q^{88} + 36 q^{89} + 2 q^{90} + 36 q^{94} + 30 q^{95} + 16 q^{96} + 42 q^{97} + 56 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 6 * q^6 - 4 * q^7 + 4 * q^8 + 2 * q^9 + 8 * q^10 - 8 * q^12 - 4 * q^14 + 4 * q^15 + 8 * q^16 + 8 * q^17 - 8 * q^18 - 4 * q^20 - 22 * q^22 - 8 * q^23 + 12 * q^24 + 2 * q^25 - 4 * q^26 + 4 * q^30 - 4 * q^31 - 32 * q^32 - 26 * q^33 - 12 * q^34 + 20 * q^38 + 28 * q^39 - 4 * q^40 + 12 * q^41 - 28 * q^42 + 16 * q^44 - 8 * q^46 - 44 * q^47 - 74 * q^49 + 2 * q^50 - 8 * q^52 - 8 * q^54 - 18 * q^55 + 48 * q^56 + 10 * q^57 - 8 * q^58 - 4 * q^62 + 4 * q^63 + 24 * q^65 + 4 * q^66 - 4 * q^70 + 36 * q^71 - 4 * q^72 + 24 * q^73 - 16 * q^74 + 40 * q^76 - 32 * q^78 - 48 * q^79 - 28 * q^81 + 22 * q^82 + 24 * q^84 + 18 * q^86 + 16 * q^87 - 4 * q^88 + 36 * q^89 + 2 * q^90 + 36 * q^94 + 30 * q^95 + 16 * q^96 + 42 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.642040	−	1.26007i	−0.453990	−	0.891007i
$2$	−0.642040	−	1.26007i	−0.453990	−	0.891007i
$3$	−0.363271	−	0.500000i	−0.209735	−	0.288675i	0.691170	−	0.722692i	$-0.257096\pi$
$3$	−0.363271	−	0.500000i	−0.209735	−	0.288675i	−0.900905	+	0.434017i	$0.857096\pi$
$4$	−1.17557	+	1.61803i	−0.587785	+	0.809017i
$5$	−0.951057	+	0.309017i	−0.425325	+	0.138197i
$5$	−0.951057	+	0.309017i	−0.425325	+	0.138197i
$6$	−0.396802	+	0.778768i	−0.161994	+	0.317931i
$7$	0.618034	+	0.449028i	0.233595	+	0.169717i	0.698425	−	0.715683i	$-0.253885\pi$
$7$	0.618034	+	0.449028i	0.233595	+	0.169717i	−0.464830	+	0.885400i	$0.653885\pi$
$8$	2.79360	+	0.442463i	0.987688	+	0.156434i
$9$	0.809017	−	2.48990i	0.269672	−	0.829966i
$10$	1.00000	+	1.00000i	0.316228	+	0.316228i
$11$	3.21644	−	0.809017i	0.969793	−	0.243928i
$11$	3.21644	−	0.809017i	0.969793	−	0.243928i
$12$	1.23607			0.356822
$13$	−0.726543	−	0.236068i	−0.201507	−	0.0654735i	0.206525	−	0.978441i	$-0.433785\pi$
$13$	−0.726543	−	0.236068i	−0.201507	−	0.0654735i	−0.408031	+	0.912968i	$0.633785\pi$
$14$	0.169006	−	1.06706i	0.0451688	−	0.285184i
$15$	0.500000	+	0.363271i	0.129099	+	0.0937962i
$16$	−1.23607	−	3.80423i	−0.309017	−	0.951057i
$17$	−0.118034	−	0.363271i	−0.0286274	−	0.0881062i	0.935722	−	0.352738i	$-0.114749\pi$
$17$	−0.118034	−	0.363271i	−0.0286274	−	0.0881062i	−0.964349	+	0.264632i	$0.914749\pi$
$18$	−3.65688	+	0.579192i	−0.861934	+	0.136517i
$19$	−4.75528	−	6.54508i	−1.09094	−	1.50155i	−0.846880	−	0.531785i	$-0.821522\pi$
$19$	−4.75528	−	6.54508i	−1.09094	−	1.50155i	−0.244057	−	0.969761i	$-0.578478\pi$
$20$	0.618034	−	1.90211i	0.138197	−	0.425325i
$21$		−	0.472136i		−	0.103029i
$22$	−3.08450	−	3.53353i	−0.657618	−	0.753351i
$23$	−3.23607			−0.674767			−0.337383	−	0.941367i	$-0.609542\pi$
$23$	−3.23607			−0.674767			−0.337383	+	0.941367i	$0.609542\pi$
$24$	−0.793604	−	1.55754i	−0.161994	−	0.317931i
$25$	0.809017	−	0.587785i	0.161803	−	0.117557i
$26$	0.169006	+	1.06706i	0.0331448	+	0.209268i
$27$	−3.30220	+	1.07295i	−0.635508	+	0.206489i
$28$	−1.45309	+	0.472136i	−0.274607	+	0.0892253i
$29$	2.35114	−	3.23607i	0.436596	−	0.600923i	−0.532855	−	0.846206i	$-0.678881\pi$
$29$	2.35114	−	3.23607i	0.436596	−	0.600923i	0.969451	+	0.245284i	$0.0788811\pi$
$30$	0.136729	−	0.863271i	0.0249631	−	0.157611i
$31$	0.618034	−	1.90211i	0.111002	−	0.341630i	−0.880090	−	0.474807i	$-0.842518\pi$
$31$	0.618034	−	1.90211i	0.111002	−	0.341630i	0.991092	+	0.133177i	$0.0425179\pi$
$32$	−4.00000	+	4.00000i	−0.707107	+	0.707107i
$33$	−1.57295	−	1.31433i	−0.273815	−	0.228795i
$34$	−0.381966	+	0.381966i	−0.0655066	+	0.0655066i
$35$	−0.726543	−	0.236068i	−0.122808	−	0.0399028i
$36$	3.07768	+	4.23607i	0.512947	+	0.706011i
$37$	4.70228	−	6.47214i	0.773050	−	1.06401i	−0.222965	−	0.974827i	$-0.571573\pi$
$37$	4.70228	−	6.47214i	0.773050	−	1.06401i	0.996015	−	0.0891861i	$-0.0284266\pi$
$38$	−5.19421	+	10.1942i	−0.842612	+	1.65372i
$39$	0.145898	+	0.449028i	0.0233624	+	0.0719020i
$40$	−2.79360	+	0.442463i	−0.441708	+	0.0699596i
$41$	5.97214	−	4.33901i	0.932691	−	0.677640i	−0.0139593	−	0.999903i	$-0.504444\pi$
$41$	5.97214	−	4.33901i	0.932691	−	0.677640i	0.946650	+	0.322263i	$0.104444\pi$
$42$	−0.594926	+	0.303130i	−0.0917991	+	0.0467740i
$43$			1.85410i			0.282748i	0.989956	+	0.141374i	$0.0451520\pi$
$43$			1.85410i			0.282748i	−0.989956	+	0.141374i	$0.954848\pi$
$44$	−2.47214	+	6.15537i	−0.372689	+	0.927957i
$45$			2.61803i			0.390273i
$46$	2.07768	+	4.07768i	0.306338	+	0.601222i
$47$	−8.85410	+	6.43288i	−1.29150	+	0.938332i	−0.999835	−	0.0181871i	$-0.994211\pi$
$47$	−8.85410	+	6.43288i	−1.29150	+	0.938332i	−0.291669	+	0.956519i	$0.594211\pi$
$48$	−1.45309	+	2.00000i	−0.209735	+	0.288675i
$49$	−1.98278	−	6.10237i	−0.283254	−	0.871767i
$50$	−1.26007	−	0.642040i	−0.178201	−	0.0907981i
$51$	−0.138757	+	0.190983i	−0.0194299	+	0.0267430i
$52$	1.23607	−	0.898056i	0.171412	−	0.124538i
$53$	2.62866	+	0.854102i	0.361074	+	0.117320i	0.483935	−	0.875104i	$-0.339207\pi$
$53$	2.62866	+	0.854102i	0.361074	+	0.117320i	−0.122861	+	0.992424i	$0.539207\pi$
$54$	3.47214	+	3.47214i	0.472498	+	0.472498i
$55$	−2.80902	+	1.76336i	−0.378768	+	0.237771i
$56$	1.52786	+	1.52786i	0.204169	+	0.204169i
$57$	−1.54508	+	4.75528i	−0.204652	+	0.629853i
$58$	−5.58721	−	0.884927i	−0.733636	−	0.116197i
$59$	0.951057	−	1.30902i	0.123817	−	0.170419i	−0.742609	−	0.669726i	$-0.766412\pi$
$59$	0.951057	−	1.30902i	0.123817	−	0.170419i	0.866426	+	0.499306i	$0.166412\pi$
$60$	−1.17557	+	0.381966i	−0.151765	+	0.0493116i
$61$	4.25325	−	1.38197i	0.544573	−	0.176943i	−0.0237949	−	0.999717i	$-0.507575\pi$
$61$	4.25325	−	1.38197i	0.544573	−	0.176943i	0.568368	+	0.822774i	$0.307575\pi$
$62$	−2.79360	+	0.442463i	−0.354788	+	0.0561929i
$63$	1.61803	−	1.17557i	0.203853	−	0.148108i
$64$	7.60845	+	2.47214i	0.951057	+	0.309017i
$65$	0.763932			0.0947541
$66$	−0.646254	+	2.82588i	−0.0795484	+	0.347842i
$67$		−	13.3262i		−	1.62806i	−0.580823	−	0.814030i	$-0.697269\pi$
$67$		−	13.3262i		−	1.62806i	0.580823	−	0.814030i	$-0.302731\pi$
$68$	0.726543	+	0.236068i	0.0881062	+	0.0286274i
$69$	1.17557	+	1.61803i	0.141522	+	0.194788i
$70$	0.169006	+	1.06706i	0.0202001	+	0.127538i
$71$	3.38197	+	10.4086i	0.401366	+	1.23528i	0.923892	+	0.382653i	$0.124990\pi$
$71$	3.38197	+	10.4086i	0.401366	+	1.23528i	−0.522527	+	0.852623i	$0.675010\pi$
$72$	3.36176	−	6.59783i	0.396188	−	0.777562i
$73$	6.35410	+	4.61653i	0.743691	+	0.540323i	0.893865	−	0.448336i	$-0.147983\pi$
$73$	6.35410	+	4.61653i	0.743691	+	0.540323i	−0.150174	+	0.988660i	$0.547983\pi$
$74$	−11.1744	−	1.76985i	−1.29900	−	0.205741i
$75$	−0.587785	−	0.190983i	−0.0678716	−	0.0220528i
$76$	16.1803			1.85601
$77$	2.35114	+	0.944272i	0.267937	+	0.107610i
$78$	0.472136	−	0.472136i	0.0534589	−	0.0534589i
$79$	0.708204	−	2.17963i	0.0796792	−	0.245227i	−0.903280	−	0.429052i	$-0.858848\pi$
$79$	0.708204	−	2.17963i	0.0796792	−	0.245227i	0.982959	+	0.183824i	$0.0588478\pi$
$80$	2.35114	+	3.23607i	0.262866	+	0.361803i
$81$	−4.61803	−	3.35520i	−0.513115	−	0.372800i
$82$	−9.30182	−	4.73951i	−1.02721	−	0.523392i
$83$	−4.39201	+	1.42705i	−0.482086	+	0.156639i	−0.539970	−	0.841684i	$-0.681565\pi$
$83$	−4.39201	+	1.42705i	−0.482086	+	0.156639i	0.0578844	+	0.998323i	$0.481565\pi$
$84$	0.763932	+	0.555029i	0.0833518	+	0.0605586i
$85$	0.224514	+	0.309017i	0.0243520	+	0.0335176i
$86$	2.33630	−	1.19041i	0.251930	−	0.128365i
$87$	−2.47214			−0.265041
$88$	9.34342	−	0.836916i	0.996012	−	0.0892155i
$89$	−5.56231			−0.589603			−0.294802	−	0.955558i	$-0.595254\pi$
$89$	−5.56231			−0.589603			−0.294802	+	0.955558i	$0.595254\pi$
$90$	3.29892	−	1.68088i	0.347736	−	0.177180i
$91$	−0.343027	−	0.472136i	−0.0359590	−	0.0494933i
$92$	3.80423	−	5.23607i	0.396618	−	0.545898i
$93$	−1.17557	+	0.381966i	−0.121901	+	0.0396080i
$94$	13.7906	+	7.02666i	1.42239	+	0.724744i
$95$	6.54508	+	4.75528i	0.671512	+	0.487882i
$96$	3.45309	+	0.546915i	0.352429	+	0.0558193i
$97$	−0.899187	+	2.76741i	−0.0912986	+	0.280988i	−0.986271	−	0.165133i	$-0.947195\pi$
$97$	−0.899187	+	2.76741i	−0.0912986	+	0.280988i	0.894973	+	0.446121i	$0.147195\pi$
$98$	−6.41641	+	6.41641i	−0.648155	+	0.648155i
$99$	0.587785	−	8.66312i	0.0590746	−	0.870676i
$100$			2.00000i			0.200000i
$101$	13.4863	+	4.38197i	1.34194	+	0.436022i	0.889973	−	0.456014i	$-0.150723\pi$
$101$	13.4863	+	4.38197i	1.34194	+	0.436022i	0.451965	+	0.892036i	$0.350723\pi$
$102$	0.329740	+	0.0522257i	0.0326492	+	0.00517112i
$103$	−9.47214	−	6.88191i	−0.933317	−	0.678095i	0.0134855	−	0.999909i	$-0.495707\pi$
$103$	−9.47214	−	6.88191i	−0.933317	−	0.678095i	−0.946803	+	0.321814i	$0.895707\pi$
$104$	−1.92522	−	0.980949i	−0.188783	−	0.0961900i
$105$	0.145898	+	0.449028i	0.0142382	+	0.0438206i
$106$	−0.611469	−	3.86067i	−0.0593912	−	0.374981i
$107$	1.26133	+	1.73607i	0.121937	+	0.167832i	0.865622	−	0.500699i	$-0.166924\pi$
$107$	1.26133	+	1.73607i	0.121937	+	0.167832i	−0.743685	+	0.668531i	$0.766924\pi$
$108$	2.14590	−	6.60440i	0.206489	−	0.635508i
$109$			16.4721i			1.57774i	0.614557	+	0.788872i	$0.289335\pi$
$109$			16.4721i			1.57774i	−0.614557	+	0.788872i	$0.710665\pi$
$110$	4.02546	+	2.40742i	0.383812	+	0.229539i
$111$	−4.94427			−0.469290
$112$	0.944272	−	2.90617i	0.0892253	−	0.274607i
$113$	13.3992	−	9.73508i	1.26049	−	0.915799i	0.261708	−	0.965147i	$-0.415714\pi$
$113$	13.3992	−	9.73508i	1.26049	−	0.915799i	0.998782	+	0.0493479i	$0.0157143\pi$
$114$	6.98401	−	1.10616i	0.654113	−	0.103601i
$115$	3.07768	−	1.00000i	0.286995	−	0.0932505i
$116$	2.47214	+	7.60845i	0.229532	+	0.706427i
$117$	−1.17557	+	1.61803i	−0.108682	+	0.149587i
$118$	−2.26007	−	0.357960i	−0.208057	−	0.0329529i
$119$	0.0901699	−	0.277515i	0.00826587	−	0.0254397i
$120$	1.23607	+	1.23607i	0.112837	+	0.112837i
$121$	9.69098	−	5.20431i	0.880998	−	0.473119i
$122$	−4.47214	−	4.47214i	−0.404888	−	0.404888i
$123$	−4.33901	−	1.40983i	−0.391235	−	0.127120i
$124$	2.35114	+	3.23607i	0.211139	+	0.290607i
$125$	−0.587785	+	0.809017i	−0.0525731	+	0.0723607i
$126$	−2.52015	−	1.28408i	−0.224513	−	0.114395i
$127$	5.47214	+	16.8415i	0.485574	+	1.49444i	0.831148	+	0.556051i	$0.187684\pi$
$127$	5.47214	+	16.8415i	0.485574	+	1.49444i	−0.345575	+	0.938391i	$0.612316\pi$
$128$	−1.76985	−	11.1744i	−0.156434	−	0.987688i
$129$	0.927051	−	0.673542i	0.0816223	−	0.0593021i
$130$	−0.490475	−	0.962611i	−0.0430175	−	0.0844265i
$131$			15.3262i			1.33906i	0.742785	+	0.669530i	$0.233504\pi$
$131$			15.3262i			1.33906i	−0.742785	+	0.669530i	$0.766496\pi$
$132$	3.97574	−	1.00000i	0.346044	−	0.0870388i
$133$		−	6.18034i		−	0.535903i
$134$	−16.7920	+	8.55597i	−1.45061	+	0.739123i
$135$	2.80902	−	2.04087i	0.241762	−	0.175650i
$136$	−0.169006	−	1.06706i	−0.0144921	−	0.0914998i
$137$	4.89919	+	15.0781i	0.418566	+	1.28821i	0.909022	+	0.416747i	$0.136830\pi$
$137$	4.89919	+	15.0781i	0.418566	+	1.28821i	−0.490457	+	0.871466i	$0.663170\pi$
$138$	1.28408	−	2.52015i	0.109308	−	0.214529i
$139$	0.898056	−	1.23607i	0.0761721	−	0.104842i	−0.769231	−	0.638971i	$-0.779360\pi$
$139$	0.898056	−	1.23607i	0.0761721	−	0.104842i	0.845403	+	0.534129i	$0.179360\pi$
$140$	1.23607	−	0.898056i	0.104467	−	0.0758996i
$141$	6.43288	+	2.09017i	0.541746	+	0.176024i
$142$	10.9443	−	10.9443i	0.918423	−	0.918423i
$143$	−2.52786	−	0.171513i	−0.211391	−	0.0143427i
$144$	−10.4721			−0.872678
$145$	−1.23607	+	3.80423i	−0.102650	+	0.315924i
$146$	1.73758	−	10.9706i	0.143803	−	0.907936i
$147$	−2.33090	+	3.20820i	−0.192249	+	0.264608i
$148$	4.94427	+	15.2169i	0.406417	+	1.25082i
$149$	−6.43288	+	2.09017i	−0.527002	+	0.171233i	−0.560421	−	0.828208i	$-0.689361\pi$
$149$	−6.43288	+	2.09017i	−0.527002	+	0.171233i	0.0334186	+	0.999441i	$0.489361\pi$
$150$	0.136729	+	0.863271i	0.0111639	+	0.0704858i
$151$	11.2361	−	8.16348i	0.914378	−	0.664335i	−0.0277401	−	0.999615i	$-0.508831\pi$
$151$	11.2361	−	8.16348i	0.914378	−	0.664335i	0.942118	+	0.335280i	$0.108831\pi$
$152$	−10.3884	−	20.3884i	−0.842612	−	1.65372i
$153$	−1.00000			−0.0808452
$154$	−0.319673	−	3.56887i	−0.0257600	−	0.287588i
$155$			2.00000i			0.160644i
$156$	−0.898056	−	0.291796i	−0.0719020	−	0.0233624i
$157$	−5.70634	−	7.85410i	−0.455415	−	0.626826i	0.518135	−	0.855299i	$-0.326627\pi$
$157$	−5.70634	−	7.85410i	−0.455415	−	0.626826i	−0.973550	+	0.228473i	$0.926627\pi$
$158$	−3.20119	+	0.507018i	−0.254673	+	0.0403362i
$159$	−0.527864	−	1.62460i	−0.0418623	−	0.128839i
$160$	2.56816	−	5.04029i	0.203031	−	0.398470i
$161$	−2.00000	−	1.45309i	−0.157622	−	0.114519i
$162$	−1.26284	+	7.97323i	−0.0992178	+	0.626436i
$163$	4.16750	+	1.35410i	0.326424	+	0.106061i	0.467644	−	0.883917i	$-0.345103\pi$
$163$	4.16750	+	1.35410i	0.326424	+	0.106061i	−0.141221	+	0.989978i	$0.545103\pi$
$164$			14.7639i			1.15287i
$165$	1.90211	+	0.763932i	0.148079	+	0.0594720i
$166$	4.61803	+	4.61803i	0.358429	+	0.358429i
$167$	−1.70820	+	5.25731i	−0.132185	+	0.406823i	−0.995142	−	0.0984549i	$-0.968610\pi$
$167$	−1.70820	+	5.25731i	−0.132185	+	0.406823i	0.862957	+	0.505278i	$0.168610\pi$
$168$	0.208903	−	1.31896i	0.0161172	−	0.101760i
$169$	−10.0451	−	7.29818i	−0.772699	−	0.561399i
$170$	0.245237	−	0.481305i	0.0188088	−	0.0369144i
$171$	−20.1437	+	6.54508i	−1.54043	+	0.500515i
$172$	−3.00000	−	2.17963i	−0.228748	−	0.166195i
$173$	5.42882	+	7.47214i	0.412746	+	0.568096i	0.963885	−	0.266317i	$-0.0858068\pi$
$173$	5.42882	+	7.47214i	0.412746	+	0.568096i	−0.551140	+	0.834413i	$0.685807\pi$
$174$	1.58721	+	3.11507i	0.120326	+	0.236153i
$175$	0.763932			0.0577478
$176$	−7.05342	−	11.2361i	−0.531672	−	0.846950i
$177$	−1.00000			−0.0751646
$178$	3.57122	+	7.00891i	0.267674	+	0.525340i
$179$	4.20025	+	5.78115i	0.313942	+	0.432104i	0.936605	−	0.350386i	$-0.113950\pi$
$179$	4.20025	+	5.78115i	0.313942	+	0.432104i	−0.622664	+	0.782490i	$0.713950\pi$
$180$	−4.23607	−	3.07768i	−0.315738	−	0.229397i
$181$	−19.0211	+	6.18034i	−1.41383	+	0.459381i	−0.913636	−	0.406533i	$-0.866738\pi$
$181$	−19.0211	+	6.18034i	−1.41383	+	0.459381i	−0.500193	+	0.865914i	$0.666738\pi$
$182$	−0.374689	+	0.735369i	−0.0277738	+	0.0545092i
$183$	−2.23607	−	1.62460i	−0.165295	−	0.120094i
$184$	−9.04029	−	1.43184i	−0.666459	−	0.105557i
$185$	−2.47214	+	7.60845i	−0.181755	+	0.559385i
$186$	1.23607	+	1.23607i	0.0906329	+	0.0906329i
$187$	−0.673542	−	1.07295i	−0.0492543	−	0.0784618i
$188$		−	21.8885i		−	1.59639i
$189$	−2.52265	−	0.819660i	−0.183496	−	0.0596215i
$190$	1.78980	−	11.3004i	0.129846	−	0.819815i
$191$	−9.85410	−	7.15942i	−0.713018	−	0.518038i	0.171128	−	0.985249i	$-0.445259\pi$
$191$	−9.85410	−	7.15942i	−0.713018	−	0.518038i	−0.884146	+	0.467211i	$0.845259\pi$
$192$	−1.52786	−	4.70228i	−0.110264	−	0.339358i
$193$	−1.85410	−	5.70634i	−0.133461	−	0.410751i	0.861886	−	0.507102i	$-0.169283\pi$
$193$	−1.85410	−	5.70634i	−0.133461	−	0.410751i	−0.995347	+	0.0963503i	$0.969283\pi$
$194$	4.06446	−	0.643747i	0.291811	−	0.0462183i
$195$	−0.277515	−	0.381966i	−0.0198732	−	0.0273532i
$196$	12.2047	+	3.96556i	0.871767	+	0.283254i
$197$			14.9443i			1.06474i	0.846513	+	0.532368i	$0.178698\pi$
$197$			14.9443i			1.06474i	−0.846513	+	0.532368i	$0.821302\pi$
$198$	−11.2935	+	4.82141i	−0.802598	+	0.342643i
$199$	8.65248			0.613358			0.306679	−	0.951813i	$-0.400782\pi$
$199$	8.65248			0.613358			0.306679	+	0.951813i	$0.400782\pi$
$200$	2.52015	−	1.28408i	0.178201	−	0.0907981i
$201$	−6.66312	+	4.84104i	−0.469980	+	0.341461i
$202$	−3.13714	−	19.8071i	−0.220728	−	1.39362i
$203$	2.90617	−	0.944272i	0.203973	−	0.0662749i
$204$	−0.145898	−	0.449028i	−0.0102149	−	0.0314382i
$205$	−4.33901	+	5.97214i	−0.303050	+	0.417112i
$206$	−2.59023	+	16.3540i	−0.180470	+	1.13944i
$207$	−2.61803	+	8.05748i	−0.181966	+	0.560034i
$208$			3.05573i			0.211877i
$209$	−20.5902	−	17.2048i	−1.42425	−	1.19008i
$210$	0.472136	−	0.472136i	0.0325805	−	0.0325805i
$211$	−7.74721	−	2.51722i	−0.533340	−	0.173293i	0.0299509	−	0.999551i	$-0.490465\pi$
$211$	−7.74721	−	2.51722i	−0.533340	−	0.173293i	−0.563291	+	0.826259i	$0.690465\pi$
$212$	−4.47214	+	3.24920i	−0.307148	+	0.223156i
$213$	3.97574	−	5.47214i	0.272413	−	0.374945i
$214$	1.37775	−	2.70399i	0.0941811	−	0.184841i
$215$	−0.572949	−	1.76336i	−0.0390748	−	0.120260i
$216$	−9.69977	+	1.53629i	−0.659986	+	0.104532i
$217$	1.23607	−	0.898056i	0.0839098	−	0.0609640i
$218$	20.7561	−	10.5758i	1.40578	−	0.716281i
$219$		−	4.85410i		−	0.328010i
$220$	0.449028	−	6.61803i	0.0302735	−	0.446188i
$221$			0.291796i			0.0196283i
$222$	3.17442	+	6.23015i	0.213053	+	0.418140i
$223$	2.00000	−	1.45309i	0.133930	−	0.0973058i	−0.518803	−	0.854894i	$-0.673622\pi$
$223$	2.00000	−	1.45309i	0.133930	−	0.0973058i	0.652733	+	0.757588i	$0.273622\pi$
$224$	−4.26825	+	0.676024i	−0.285184	+	0.0451688i
$225$	−0.809017	−	2.48990i	−0.0539345	−	0.165993i
$226$	−20.8697	−	10.6337i	−1.38823	−	0.707340i
$227$	−12.1922	+	16.7812i	−0.809226	+	1.11380i	0.182216	+	0.983259i	$0.441673\pi$
$227$	−12.1922	+	16.7812i	−0.809226	+	1.11380i	−0.991442	+	0.130546i	$0.958327\pi$
$228$	−5.87785	−	8.09017i	−0.389270	−	0.535785i
$229$	−4.42477	−	1.43769i	−0.292397	−	0.0950055i	0.159146	−	0.987255i	$-0.449126\pi$
$229$	−4.42477	−	1.43769i	−0.292397	−	0.0950055i	−0.451542	+	0.892250i	$0.649126\pi$
$230$	−3.23607	−	3.23607i	−0.213380	−	0.213380i
$231$	−0.381966	−	1.51860i	−0.0251315	−	0.0999164i
$232$	8.00000	−	8.00000i	0.525226	−	0.525226i
$233$	0.0450850	−	0.138757i	0.00295361	−	0.00909029i	−0.949569	−	0.313559i	$-0.898479\pi$
$233$	0.0450850	−	0.138757i	0.00295361	−	0.00909029i	0.952522	+	0.304468i	$0.0984788\pi$
$234$	2.79360	+	0.442463i	0.182624	+	0.0289247i
$235$	6.43288	−	8.85410i	0.419635	−	0.577578i
$236$	1.00000	+	3.07768i	0.0650945	+	0.200340i
$237$	−1.34708	+	0.437694i	−0.0875025	+	0.0284313i
$238$	−0.407581	+	0.0645546i	−0.0264196	+	0.00418445i
$239$	21.5623	−	15.6659i	1.39475	−	1.01334i	0.399424	−	0.916766i	$-0.369210\pi$
$239$	21.5623	−	15.6659i	1.39475	−	1.01334i	0.995325	−	0.0965787i	$-0.0307900\pi$
$240$	0.763932	−	2.35114i	0.0493116	−	0.151765i
$241$	21.9787			1.41577			0.707887	−	0.706326i	$-0.249649\pi$
$241$	21.9787			1.41577			0.707887	+	0.706326i	$0.249649\pi$
$242$	−12.7798	−	8.86998i	−0.821517	−	0.570184i
$243$			13.9443i			0.894525i
$244$	−2.76393	+	8.50651i	−0.176943	+	0.544573i
$245$	3.77147	+	5.19098i	0.240950	+	0.331640i
$246$	1.00933	+	6.37264i	0.0643523	+	0.406305i
$247$	1.90983	+	5.87785i	0.121520	+	0.373999i
$248$	2.56816	−	5.04029i	0.163078	−	0.320059i
$249$	2.30902	+	1.67760i	0.146328	+	0.106314i
$250$	1.39680	+	0.221232i	0.0883415	+	0.0139919i
$251$	11.4127	+	3.70820i	0.720362	+	0.234060i	0.646180	−	0.763185i	$-0.276365\pi$
$251$	11.4127	+	3.70820i	0.720362	+	0.234060i	0.0741818	+	0.997245i	$0.476365\pi$
$252$			4.00000i			0.251976i
$253$	−10.4086	+	2.61803i	−0.654384	+	0.164594i
$254$	17.7082	−	17.7082i	1.11111	−	1.11111i
$255$	0.0729490	−	0.224514i	0.00456824	−	0.0140596i
$256$	−12.9443	+	9.40456i	−0.809017	+	0.587785i
$257$	−13.5902	−	9.87384i	−0.847732	−	0.615913i	0.0767881	−	0.997047i	$-0.475533\pi$
$257$	−13.5902	−	9.87384i	−0.847732	−	0.615913i	−0.924520	+	0.381134i	$0.875533\pi$
$258$	−1.44392	−	0.735712i	−0.0898943	−	0.0458034i
$259$	5.81234	−	1.88854i	0.361161	−	0.117348i
$260$	−0.898056	+	1.23607i	−0.0556951	+	0.0766577i
$261$	−6.15537	−	8.47214i	−0.381008	−	0.524412i
$262$	19.3122	−	9.84005i	1.19311	−	0.607920i
$263$	−24.7639			−1.52701			−0.763505	−	0.645802i	$-0.776523\pi$
$263$	−24.7639			−1.52701			−0.763505	+	0.645802i	$0.776523\pi$
$264$	−3.81266	−	4.36768i	−0.234653	−	0.268812i
$265$	−2.76393			−0.169787
$266$	−7.78768	+	3.96802i	−0.477493	+	0.243295i
$267$	2.02063	+	2.78115i	0.123660	+	0.170204i
$268$	21.5623	+	15.6659i	1.31713	+	0.956949i
$269$	−13.2088	+	4.29180i	−0.805354	+	0.261675i	−0.682629	−	0.730765i	$-0.739163\pi$
$269$	−13.2088	+	4.29180i	−0.805354	+	0.261675i	−0.122725	+	0.992441i	$0.539163\pi$
$270$	−4.37515	−	2.22925i	−0.266263	−	0.135668i
$271$	−12.7082	−	9.23305i	−0.771968	−	0.560868i	0.130589	−	0.991437i	$-0.458313\pi$
$271$	−12.7082	−	9.23305i	−0.771968	−	0.560868i	−0.902558	+	0.430569i	$0.858313\pi$
$272$	−1.23607	+	0.898056i	−0.0749476	+	0.0544526i
$273$	−0.111456	+	0.343027i	−0.00674563	+	0.0207609i
$274$	15.8541	−	15.8541i	0.957781	−	0.957781i
$275$	2.12663	−	2.54508i	0.128240	−	0.153474i
$276$	−4.00000			−0.240772
$277$	−12.7598	−	4.14590i	−0.766660	−	0.249103i	−0.100525	−	0.994935i	$-0.532052\pi$
$277$	−12.7598	−	4.14590i	−0.766660	−	0.249103i	−0.666135	+	0.745832i	$0.732052\pi$
$278$	−2.13412	−	0.338012i	−0.127996	−	0.0202726i
$279$	−4.23607	−	3.07768i	−0.253607	−	0.184256i
$280$	−1.92522	−	0.980949i	−0.115054	−	0.0586229i
$281$	3.04508	+	9.37181i	0.181655	+	0.559075i	0.999875	−	0.0158298i	$-0.00503900\pi$
$281$	3.04508	+	9.37181i	0.181655	+	0.559075i	−0.818220	+	0.574905i	$0.805039\pi$
$282$	−1.49640	−	9.44788i	−0.0891091	−	0.562613i
$283$	6.15537	+	8.47214i	0.365899	+	0.503616i	0.951780	−	0.306780i	$-0.0992517\pi$
$283$	6.15537	+	8.47214i	0.365899	+	0.503616i	−0.585882	+	0.810397i	$0.699252\pi$
$284$	−20.8172	−	6.76393i	−1.23528	−	0.401366i
$285$		−	5.00000i		−	0.296174i
$286$	1.40687	+	3.29541i	0.0831899	+	0.194862i
$287$	5.63932			0.332879
$288$	6.72353	+	13.1957i	0.396188	+	0.777562i
$289$	13.6353	−	9.90659i	0.802074	−	0.582741i
$290$	5.58721	−	0.884927i	0.328092	−	0.0519647i
$291$	1.71036	−	0.555728i	0.100263	−	0.0325774i
$292$	−14.9394	+	4.85410i	−0.874262	+	0.284065i
$293$	18.0171	−	24.7984i	1.05257	−	1.44874i	0.166008	−	0.986124i	$-0.446912\pi$
$293$	18.0171	−	24.7984i	1.05257	−	1.44874i	0.886561	−	0.462612i	$-0.153088\pi$
$294$	5.53910	+	0.877307i	0.323047	+	0.0511656i
$295$	−0.500000	+	1.53884i	−0.0291111	+	0.0895948i
$296$	16.0000	−	16.0000i	0.929981	−	0.929981i
$297$	−9.75329	+	6.12261i	−0.565943	+	0.355270i
$298$	6.76393	+	6.76393i	0.391824	+	0.391824i
$299$	2.35114	+	0.763932i	0.135970	+	0.0441793i
$300$	1.00000	−	0.726543i	0.0577350	−	0.0419470i
$301$	−0.832544	+	1.14590i	−0.0479870	+	0.0660485i
$302$	−17.5006	−	8.91699i	−1.00705	−	0.513115i
$303$	−2.70820	−	8.33499i	−0.155582	−	0.478833i
$304$	−19.0211	+	26.1803i	−1.09094	+	1.50155i
$305$	−3.61803	+	2.62866i	−0.207168	+	0.150516i
$306$	0.642040	+	1.26007i	0.0367030	+	0.0720336i
$307$			5.56231i			0.317458i	0.987322	+	0.158729i	$0.0507395\pi$
$307$			5.56231i			0.317458i	−0.987322	+	0.158729i	$0.949260\pi$
$308$	−4.29180	+	2.69417i	−0.244548	+	0.153514i
$309$			7.23607i			0.411646i
$310$	2.52015	−	1.28408i	0.143135	−	0.0729308i
$311$	1.09017	−	0.792055i	0.0618179	−	0.0449133i	−0.556447	−	0.830883i	$-0.687836\pi$
$311$	1.09017	−	0.792055i	0.0618179	−	0.0449133i	0.618265	+	0.785970i	$0.287836\pi$
$312$	0.208903	+	1.31896i	0.0118268	+	0.0746715i
$313$	8.88197	+	27.3359i	0.502038	+	1.54512i	0.805693	+	0.592333i	$0.201793\pi$
$313$	8.88197	+	27.3359i	0.502038	+	1.54512i	−0.303655	+	0.952782i	$0.598207\pi$
$314$	−6.23305	+	12.2331i	−0.351751	+	0.690351i
$315$	−1.17557	+	1.61803i	−0.0662359	+	0.0911659i
$316$	2.69417	+	3.70820i	0.151559	+	0.208603i
$317$	5.60034	+	1.81966i	0.314546	+	0.102202i	0.462036	−	0.886861i	$-0.347119\pi$
$317$	5.60034	+	1.81966i	0.314546	+	0.102202i	−0.147489	+	0.989064i	$0.547119\pi$
$318$	−1.70820	+	1.70820i	−0.0957913	+	0.0957913i
$319$	4.94427	−	12.3107i	0.276826	−	0.689269i
$320$	−8.00000			−0.447214
$321$	0.409830	−	1.26133i	0.0228745	−	0.0704004i
$322$	−0.546915	+	3.45309i	−0.0304784	+	0.192433i
$323$	−1.81636	+	2.50000i	−0.101065	+	0.139104i
$324$	10.8576	−	3.52786i	0.603203	−	0.195992i
$325$	−0.726543	+	0.236068i	−0.0403013	+	0.0130947i
$326$	−0.969430	−	6.12074i	−0.0536918	−	0.338996i
$327$	8.23607	−	5.98385i	0.455456	−	0.330908i
$328$	18.6036	−	9.47903i	1.02721	−	0.523392i
$329$	−8.36068			−0.460939
$330$	−0.258621	−	2.88728i	−0.0142366	−	0.158939i
$331$			10.0344i			0.551543i	0.961223	+	0.275771i	$0.0889333\pi$
$331$			10.0344i			0.551543i	−0.961223	+	0.275771i	$0.911067\pi$
$332$	2.85410	−	8.78402i	0.156639	−	0.482086i
$333$	−12.3107	−	16.9443i	−0.674624	−	0.928540i
$334$	7.72133	−	1.22294i	0.422493	−	0.0669162i
$335$	4.11803	+	12.6740i	0.224992	+	0.692455i
$336$	−1.79611	+	0.583592i	−0.0979859	+	0.0318376i
$337$	27.5795	+	20.0377i	1.50235	+	1.09152i	0.969433	+	0.245357i	$0.0789053\pi$
$337$	27.5795	+	20.0377i	1.50235	+	1.09152i	0.532920	+	0.846166i	$0.321095\pi$
$338$	−2.74690	+	17.3433i	−0.149412	+	0.943349i
$339$	−9.73508	−	3.16312i	−0.528737	−	0.171797i
$340$	−0.763932			−0.0414300
$341$	0.449028	−	6.61803i	0.0243162	−	0.358387i
$342$	21.1803	+	21.1803i	1.14530	+	1.14530i
$343$	3.16718	−	9.74759i	0.171012	−	0.526320i
$344$	−0.820372	+	5.17963i	−0.0442315	+	0.279267i
$345$	−1.61803	−	1.17557i	−0.0871120	−	0.0632906i
$346$	5.92992	−	11.6381i	0.318795	−	0.625669i
$347$	20.4540	−	6.64590i	1.09803	−	0.356770i	0.296684	−	0.954976i	$-0.404119\pi$
$347$	20.4540	−	6.64590i	1.09803	−	0.356770i	0.801343	+	0.598205i	$0.204119\pi$
$348$	2.90617	−	4.00000i	0.155787	−	0.214423i
$349$	9.95959	+	13.7082i	0.533125	+	0.733783i	0.987603	−	0.156975i	$-0.0501741\pi$
$349$	9.95959	+	13.7082i	0.533125	+	0.733783i	−0.454478	+	0.890758i	$0.650174\pi$
$350$	−0.490475	−	0.962611i	−0.0262170	−	0.0514537i
$351$	2.65248			0.141579
$352$	−9.62970	+	16.1018i	−0.513264	+	0.858230i
$353$	10.8541			0.577706			0.288853	−	0.957374i	$-0.406726\pi$
$353$	10.8541			0.577706			0.288853	+	0.957374i	$0.406726\pi$
$354$	0.642040	+	1.26007i	0.0341240	+	0.0669722i
$355$	−6.43288	−	8.85410i	−0.341422	−	0.469927i
$356$	6.53888	−	9.00000i	0.346560	−	0.476999i
$357$	−0.171513	+	0.0557281i	−0.00907745	+	0.00294944i
$358$	4.58795	−	9.00436i	0.242481	−	0.475895i
$359$	16.9443	+	12.3107i	0.894284	+	0.649736i	0.936992	−	0.349352i	$-0.113598\pi$
$359$	16.9443	+	12.3107i	0.894284	+	0.649736i	−0.0427071	+	0.999088i	$0.513598\pi$
$360$	−1.15838	+	7.31375i	−0.0610522	+	0.385469i
$361$	−14.3541	+	44.1774i	−0.755479	+	2.32513i
$362$	20.0000	+	20.0000i	1.05118	+	1.05118i
$363$	−6.12261	−	2.95492i	−0.321354	−	0.155093i
$364$	1.16718			0.0611771
$365$	−7.46969	−	2.42705i	−0.390982	−	0.127038i
$366$	−0.611469	+	3.86067i	−0.0319620	+	0.201800i
$367$	−6.23607	−	4.53077i	−0.325520	−	0.236504i	0.413007	−	0.910728i	$-0.364478\pi$
$367$	−6.23607	−	4.53077i	−0.325520	−	0.236504i	−0.738527	+	0.674224i	$0.764478\pi$
$368$	4.00000	+	12.3107i	0.208514	+	0.641741i
$369$	−5.97214	−	18.3803i	−0.310897	−	0.956843i
$370$	11.1744	−	1.76985i	0.580930	−	0.0920103i
$371$	1.24108	+	1.70820i	0.0644338	+	0.0886855i
$372$	0.763932	−	2.35114i	0.0396080	−	0.121901i
$373$		−	16.4721i		−	0.852895i	−0.904512	−	0.426447i	$-0.859765\pi$
$373$		−	16.4721i		−	0.852895i	0.904512	−	0.426447i	$-0.140235\pi$
$374$	−0.919554	+	1.53759i	−0.0475490	+	0.0795068i
$375$	0.618034			0.0319151
$376$	−27.5812	+	14.0533i	−1.42239	+	0.724744i
$377$	−2.47214	+	1.79611i	−0.127321	+	0.0925045i
$378$	0.586812	+	3.70498i	0.0301823	+	0.190564i
$379$	29.7400	−	9.66312i	1.52764	−	0.496361i	0.579707	−	0.814825i	$-0.303167\pi$
$379$	29.7400	−	9.66312i	1.52764	−	0.496361i	0.947935	+	0.318464i	$0.103167\pi$
$380$	−15.3884	+	5.00000i	−0.789409	+	0.256495i
$381$	6.43288	−	8.85410i	0.329567	−	0.453609i
$382$	−2.69468	+	17.0135i	−0.137872	+	0.870488i
$383$	7.94427	−	24.4500i	0.405933	−	1.24933i	−0.514180	−	0.857682i	$-0.671904\pi$
$383$	7.94427	−	24.4500i	0.405933	−	1.24933i	0.920113	−	0.391652i	$-0.128096\pi$
$384$	−4.94427	+	4.94427i	−0.252311	+	0.252311i
$385$	−2.52786	−	0.171513i	−0.128832	−	0.00874113i
$386$	−6.00000	+	6.00000i	−0.305392	+	0.305392i
$387$	4.61653	+	1.50000i	0.234671	+	0.0762493i
$388$	−3.42071	−	4.70820i	−0.173660	−	0.239023i
$389$	−5.15131	+	7.09017i	−0.261182	+	0.359486i	−0.919388	−	0.393352i	$-0.871315\pi$
$389$	−5.15131	+	7.09017i	−0.261182	+	0.359486i	0.658206	+	0.752838i	$0.271315\pi$
$390$	−0.303130	+	0.594926i	−0.0153496	+	0.0301252i
$391$	0.381966	+	1.17557i	0.0193169	+	0.0594512i
$392$	−2.83903	−	17.9249i	−0.143392	−	0.905344i
$393$	7.66312	−	5.56758i	0.386553	−	0.280847i
$394$	18.8309	−	9.59481i	0.948686	−	0.483380i
$395$			2.29180i			0.115313i
$396$	13.3262	+	11.1352i	0.669669	+	0.559563i
$397$		−	31.4164i		−	1.57674i	−0.615199	−	0.788372i	$-0.710924\pi$
$397$		−	31.4164i		−	1.57674i	0.615199	−	0.788372i	$-0.289076\pi$
$398$	−5.55523	−	10.9028i	−0.278459	−	0.546506i
$399$	−3.09017	+	2.24514i	−0.154702	+	0.112398i
$400$	−3.23607	−	2.35114i	−0.161803	−	0.117557i
$401$	−10.9549	−	33.7158i	−0.547062	−	1.68368i	−0.716035	−	0.698064i	$-0.754045\pi$
$401$	−10.9549	−	33.7158i	−0.547062	−	1.68368i	0.168973	−	0.985621i	$-0.445955\pi$
$402$	10.3781	+	5.28788i	0.517610	+	0.263736i
$403$	−0.898056	+	1.23607i	−0.0447354	+	0.0615729i
$404$	−22.9443	+	16.6700i	−1.14152	+	0.829363i
$405$	5.42882	+	1.76393i	0.269760	+	0.0876505i
$406$	−3.05573	−	3.05573i	−0.151653	−	0.151653i
$407$	9.88854	−	24.6215i	0.490157	−	1.22044i
$408$	−0.472136	+	0.472136i	−0.0233742	+	0.0233742i
$409$	−6.79837	+	20.9232i	−0.336158	+	1.03459i	0.629991	+	0.776603i	$0.283059\pi$
$409$	−6.79837	+	20.9232i	−0.336158	+	1.03459i	−0.966149	+	0.257985i	$0.916941\pi$
$410$	10.3111	+	1.63313i	0.509231	+	0.0806543i
$411$	5.75934	−	7.92705i	0.284087	−	0.391013i
$412$	22.2703	−	7.23607i	1.09718	−	0.356495i
$413$	1.17557	−	0.381966i	0.0578460	−	0.0187953i
$414$	11.8339	−	1.87431i	0.581604	−	0.0921171i
$415$	3.73607	−	2.71441i	0.183396	−	0.133245i
$416$	3.85044	−	1.96190i	0.188783	−	0.0961900i
$417$	−0.944272			−0.0462412
$418$	−8.45958	+	36.9913i	−0.413771	+	1.80930i
$419$		−	6.90983i		−	0.337567i	−0.985653	−	0.168784i	$-0.946016\pi$
$419$		−	6.90983i		−	0.337567i	0.985653	−	0.168784i	$-0.0539839\pi$
$420$	−0.898056	−	0.291796i	−0.0438206	−	0.0142382i
$421$	−13.8293	−	19.0344i	−0.674000	−	0.927682i	0.325842	−	0.945424i	$-0.394352\pi$
$421$	−13.8293	−	19.0344i	−0.674000	−	0.927682i	−0.999843	+	0.0177422i	$0.994352\pi$
$422$	1.80213	+	11.3782i	0.0877264	+	0.553883i
$423$	8.85410	+	27.2501i	0.430501	+	1.32495i
$424$	6.96552	+	3.54911i	0.338275	+	0.172360i
$425$	−0.309017	−	0.224514i	−0.0149895	−	0.0108905i
$426$	−9.44788	−	1.49640i	−0.457751	−	0.0725006i
$427$	3.24920	+	1.05573i	0.157240	+	0.0510903i
$428$	−4.29180			−0.207452
$429$	0.832544	+	1.32624i	0.0401956	+	0.0640314i
$430$	−1.85410	+	1.85410i	−0.0894127	+	0.0894127i
$431$	−3.70820	+	11.4127i	−0.178618	+	0.549729i	−0.999780	−	0.0209654i	$-0.993326\pi$
$431$	−3.70820	+	11.4127i	−0.178618	+	0.549729i	0.821162	+	0.570695i	$0.193326\pi$
$432$	8.16348	+	11.2361i	0.392766	+	0.540596i
$433$	−15.3992	−	11.1882i	−0.740038	−	0.537669i	0.152685	−	0.988275i	$-0.451208\pi$
$433$	−15.3992	−	11.1882i	−0.740038	−	0.537669i	−0.892723	+	0.450606i	$0.851208\pi$
$434$	−1.92522	−	0.980949i	−0.0924136	−	0.0470871i
$435$	2.35114	−	0.763932i	0.112729	−	0.0366277i
$436$	−26.6525	−	19.3642i	−1.27642	−	0.927375i
$437$	15.3884	+	21.1803i	0.736128	+	1.01319i
$438$	−6.11653	+	3.11653i	−0.292259	+	0.148913i
$439$	6.65248			0.317505			0.158753	−	0.987318i	$-0.449253\pi$
$439$	6.65248			0.317505			0.158753	+	0.987318i	$0.449253\pi$
$440$	−8.62750	+	3.68323i	−0.411300	+	0.175591i
$441$	−16.7984			−0.799923
$442$	0.367684	−	0.187345i	0.0174890	−	0.00891107i
$443$	20.6255	+	28.3885i	0.979946	+	1.34878i	0.936858	+	0.349709i	$0.113720\pi$
$443$	20.6255	+	28.3885i	0.979946	+	1.34878i	0.0430880	+	0.999071i	$0.486280\pi$
$444$	5.81234	−	8.00000i	0.275841	−	0.379663i
$445$	5.29007	−	1.71885i	0.250773	−	0.0814812i
$446$	−3.11507	−	1.58721i	−0.147503	−	0.0751565i
$447$	3.38197	+	2.45714i	0.159962	+	0.116219i
$448$	3.59222	+	4.94427i	0.169717	+	0.233595i
$449$	−5.20820	+	16.0292i	−0.245790	+	0.756465i	0.749715	+	0.661761i	$0.230191\pi$
$449$	−5.20820	+	16.0292i	−0.245790	+	0.756465i	−0.995505	+	0.0947042i	$0.969809\pi$
$450$	−2.61803	+	2.61803i	−0.123415	+	0.123415i
$451$	15.6987	−	18.7877i	0.739222	−	0.884680i
$452$			33.1246i			1.55805i
$453$	−8.16348	−	2.65248i	−0.383554	−	0.124624i
$454$	28.9734	+	4.58893i	1.35979	+	0.215369i
$455$	0.472136	+	0.343027i	0.0221341	+	0.0160813i
$456$	−6.42040	+	12.6007i	−0.300663	+	0.590083i
$457$	9.01064	+	27.7319i	0.421500	+	1.29724i	0.906306	+	0.422622i	$0.138890\pi$
$457$	9.01064	+	27.7319i	0.421500	+	1.29724i	−0.484806	+	0.874622i	$0.661110\pi$
$458$	1.02928	+	6.49859i	0.0480949	+	0.303659i
$459$	0.779543	+	1.07295i	0.0363860	+	0.0500810i
$460$	−2.00000	+	6.15537i	−0.0932505	+	0.286995i
$461$		−	39.5967i		−	1.84420i	−0.386946	−	0.922102i	$-0.626470\pi$
$461$		−	39.5967i		−	1.84420i	0.386946	−	0.922102i	$-0.373530\pi$
$462$	−1.66831	+	1.45630i	−0.0776167	+	0.0677534i
$463$	−31.8885			−1.48199			−0.740993	−	0.671513i	$-0.765645\pi$
$463$	−31.8885			−1.48199			−0.740993	+	0.671513i	$0.765645\pi$
$464$	−15.2169	−	4.94427i	−0.706427	−	0.229532i
$465$	1.00000	−	0.726543i	0.0463739	−	0.0336926i
$466$	−0.203791	+	0.0322773i	−0.00944042	+	0.00149522i
$467$	16.6700	−	5.41641i	0.771395	−	0.250641i	0.103233	−	0.994657i	$-0.467081\pi$
$467$	16.6700	−	5.41641i	0.771395	−	0.250641i	0.668162	+	0.744016i	$0.267081\pi$
$468$	−1.23607	−	3.80423i	−0.0571373	−	0.175850i
$469$	5.98385	−	8.23607i	0.276309	−	0.380306i
$470$	−15.2870	−	2.42122i	−0.705136	−	0.111683i
$471$	−1.85410	+	5.70634i	−0.0854325	+	0.262934i
$472$	3.23607	−	3.23607i	0.148952	−	0.148952i
$473$	1.50000	+	5.96361i	0.0689701	+	0.274207i
$474$	1.41641	+	1.41641i	0.0650578	+	0.0650578i
$475$	−7.69421	−	2.50000i	−0.353035	−	0.114708i
$476$	0.343027	+	0.472136i	0.0157226	+	0.0216403i
$477$	4.25325	−	5.85410i	0.194743	−	0.268041i
$478$	−33.5841	−	17.1119i	−1.53610	−	0.782682i
$479$	5.05573	+	15.5599i	0.231002	+	0.710951i	0.997627	+	0.0688557i	$0.0219348\pi$
$479$	5.05573	+	15.5599i	0.231002	+	0.710951i	−0.766625	+	0.642096i	$0.778065\pi$
$480$	−3.45309	+	0.546915i	−0.157611	+	0.0249631i
$481$	−4.94427	+	3.59222i	−0.225439	+	0.163791i
$482$	−14.1112	−	27.6948i	−0.642748	−	1.26146i
$483$			1.52786i			0.0695202i
$484$	−2.97168	+	21.7984i	−0.135076	+	0.990835i
$485$		−	2.90983i		−	0.132129i
$486$	17.5708	−	8.95277i	0.797028	−	0.406106i
$487$	−8.85410	+	6.43288i	−0.401218	+	0.291502i	−0.770037	−	0.637999i	$-0.779762\pi$
$487$	−8.85410	+	6.43288i	−0.401218	+	0.291502i	0.368819	+	0.929501i	$0.379762\pi$
$488$	12.4934	−	1.97876i	0.565549	−	0.0895741i
$489$	−0.836881	−	2.57565i	−0.0378451	−	0.116475i
$490$	4.11959	−	8.08515i	0.186104	−	0.365250i
$491$	−1.15533	+	1.59017i	−0.0521391	+	0.0717634i	−0.834290	−	0.551325i	$-0.814122\pi$
$491$	−1.15533	+	1.59017i	−0.0521391	+	0.0717634i	0.782151	+	0.623089i	$0.214122\pi$
$492$	7.38197	−	5.36331i	0.332805	−	0.241797i
$493$	−1.45309	−	0.472136i	−0.0654437	−	0.0212639i
$494$	6.18034	−	6.18034i	0.278067	−	0.278067i
$495$	2.11803	+	8.42075i	0.0951985	+	0.378485i
$496$	−8.00000			−0.359211
$497$	−2.58359	+	7.95148i	−0.115890	+	0.356673i
$498$	0.631418	−	3.98662i	0.0282945	−	0.178645i
$499$	13.2945	−	18.2984i	0.595146	−	0.819148i	−0.400107	−	0.916468i	$-0.631027\pi$
$499$	13.2945	−	18.2984i	0.595146	−	0.819148i	0.995253	+	0.0973205i	$0.0310272\pi$
$500$	−0.618034	−	1.90211i	−0.0276393	−	0.0850651i
$501$	3.24920	−	1.05573i	0.145163	−	0.0471665i
$502$	−2.65478	−	16.7616i	−0.118489	−	0.748108i
$503$	26.5066	−	19.2582i	1.18187	−	0.858679i	0.189489	−	0.981883i	$-0.439317\pi$
$503$	26.5066	−	19.2582i	1.18187	−	0.858679i	0.992381	+	0.123204i	$0.0393170\pi$
$504$	5.04029	−	2.56816i	0.224513	−	0.114395i
$505$	−14.1803			−0.631017
$506$	9.98166	+	11.4347i	0.443739	+	0.508336i
$507$			7.67376i			0.340804i
$508$	−33.6830	−	10.9443i	−1.49444	−	0.485574i
$509$	19.0866	+	26.2705i	0.846001	+	1.16442i	0.984730	+	0.174090i	$0.0556982\pi$
$509$	19.0866	+	26.2705i	0.846001	+	1.16442i	−0.138729	+	0.990330i	$0.544302\pi$
$510$	−0.329740	+	0.0522257i	−0.0146011	+	0.00231259i
$511$	1.85410	+	5.70634i	0.0820206	+	0.252434i
$512$	20.1612	+	10.2726i	0.891007	+	0.453990i
$513$	22.7254	+	16.5110i	1.00335	+	0.728978i
$514$	−3.71633	+	23.4640i	−0.163920	+	1.03495i
$515$	11.1352	+	3.61803i	0.490674	+	0.159430i
$516$			2.29180i			0.100891i
$517$	−23.2744	+	27.8541i	−1.02361	+	1.22502i
$518$	−6.11146	−	6.11146i	−0.268522	−	0.268522i
$519$	1.76393	−	5.42882i	0.0774280	−	0.238299i
$520$	2.13412	+	0.338012i	0.0935875	+	0.0148228i
$521$	−8.69098	−	6.31437i	−0.380759	−	0.276638i	0.380899	−	0.924617i	$-0.375614\pi$
$521$	−8.69098	−	6.31437i	−0.380759	−	0.276638i	−0.761658	+	0.647979i	$0.775614\pi$
$522$	−6.72353	+	13.1957i	−0.294281	+	0.577558i
$523$	−4.51052	+	1.46556i	−0.197231	+	0.0640844i	−0.405967	−	0.913888i	$-0.633065\pi$
$523$	−4.51052	+	1.46556i	−0.197231	+	0.0640844i	0.208736	+	0.977972i	$0.433065\pi$
$524$	−24.7984	−	18.0171i	−1.08332	−	0.787079i
$525$	−0.277515	−	0.381966i	−0.0121117	−	0.0166704i
$526$	15.8994	+	31.2044i	0.693248	+	1.36058i
$527$	−0.763932			−0.0332774
$528$	−3.05573	+	7.60845i	−0.132983	+	0.331115i
$529$	−12.5279			−0.544690
$530$	1.77455	+	3.48276i	0.0770817	+	0.151281i
$531$	−2.48990	−	3.42705i	−0.108052	−	0.148721i
$532$	10.0000	+	7.26543i	0.433555	+	0.314996i
$533$	−5.36331	+	1.74265i	−0.232311	+	0.0754824i
$534$	2.20714	−	4.33175i	0.0955121	−	0.187453i
$535$	−1.73607	−	1.26133i	−0.0750568	−	0.0545319i
$536$	5.89637	−	37.2282i	0.254685	−	1.60801i
$537$	1.36475	−	4.20025i	0.0588931	−	0.181254i
$538$	13.8885	+	13.8885i	0.598778	+	0.598778i
$539$	−11.3144	−	18.0238i	−0.487346	−	0.776340i
$540$			6.94427i			0.298834i
$541$	−13.9353	−	4.52786i	−0.599127	−	0.194668i	−0.00627582	−	0.999980i	$-0.501998\pi$
$541$	−13.9353	−	4.52786i	−0.599127	−	0.194668i	−0.592851	+	0.805312i	$0.701998\pi$
$542$	−3.47515	+	21.9413i	−0.149271	+	0.942458i
$543$	10.0000	+	7.26543i	0.429141	+	0.311789i
$544$	1.92522	+	0.980949i	0.0825432	+	0.0420578i
$545$	−5.09017	−	15.6659i	−0.218039	−	0.671055i
$546$	0.503798	−	0.0797938i	0.0215606	−	0.00341486i
$547$	−14.8864	−	20.4894i	−0.636496	−	0.876062i	0.361927	−	0.932207i	$-0.382119\pi$
$547$	−14.8864	−	20.4894i	−0.636496	−	0.876062i	−0.998423	+	0.0561450i	$0.982119\pi$
$548$	−30.1563	−	9.79837i	−1.28821	−	0.418566i
$549$		−	11.7082i		−	0.499694i
$550$	−4.57237	−	1.04566i	−0.194967	−	0.0445871i
$551$	−32.3607			−1.37861
$552$	2.56816	+	5.04029i	0.109308	+	0.214529i
$553$	1.41641	−	1.02908i	0.0602318	−	0.0437610i
$554$	2.96814	+	18.7401i	0.126104	+	0.796189i
$555$	4.70228	−	1.52786i	0.199601	−	0.0648542i
$556$	0.944272	+	2.90617i	0.0400460	+	0.123249i
$557$	9.23305	−	12.7082i	0.391217	−	0.538464i	−0.567296	−	0.823514i	$-0.692010\pi$
$557$	9.23305	−	12.7082i	0.391217	−	0.538464i	0.958513	+	0.285050i	$0.0920103\pi$
$558$	−1.15838	+	7.31375i	−0.0490383	+	0.309616i
$559$	0.437694	−	1.34708i	0.0185125	−	0.0569756i
$560$			3.05573i			0.129128i
$561$	−0.291796	+	0.726543i	−0.0123196	+	0.0306746i
$562$	9.85410	−	9.85410i	0.415670	−	0.415670i
$563$	−7.36369	−	2.39261i	−0.310343	−	0.100836i	0.149705	−	0.988731i	$-0.452168\pi$
$563$	−7.36369	−	2.39261i	−0.310343	−	0.100836i	−0.460048	+	0.887894i	$0.652168\pi$
$564$	−10.9443	+	7.95148i	−0.460837	+	0.334818i
$565$	−9.73508	+	13.3992i	−0.409558	+	0.563708i
$566$	6.72353	−	13.1957i	0.282611	−	0.554655i
$567$	−1.34752	−	4.14725i	−0.0565907	−	0.174168i
$568$	4.84244	+	30.5740i	0.203184	+	1.28286i
$569$	−7.16312	+	5.20431i	−0.300294	+	0.218176i	−0.727720	−	0.685874i	$-0.759420\pi$
$569$	−7.16312	+	5.20431i	−0.300294	+	0.218176i	0.427427	+	0.904050i	$0.359420\pi$
$570$	−6.30037	+	3.21020i	−0.263893	+	0.134460i
$571$		−	16.3607i		−	0.684673i	−0.939577	−	0.342337i	$-0.888782\pi$
$571$		−	16.3607i		−	0.684673i	0.939577	−	0.342337i	$-0.111218\pi$
$572$	3.24920	−	3.88854i	0.135856	−	0.162588i
$573$			7.52786i			0.314481i
$574$	−3.62067	−	7.10596i	−0.151124	−	0.296597i
$575$	−2.61803	+	1.90211i	−0.109180	+	0.0793236i
$576$	12.3107	−	16.9443i	0.512947	−	0.706011i
$577$	−13.7016	−	42.1693i	−0.570406	−	1.75553i	−0.651314	−	0.758808i	$-0.725782\pi$
$577$	−13.7016	−	42.1693i	−0.570406	−	1.75553i	0.0809081	−	0.996722i	$-0.474218\pi$
$578$	−21.2374	−	10.8210i	−0.883360	−	0.450094i
$579$	−2.17963	+	3.00000i	−0.0905822	+	0.124676i
$580$	−4.70228	−	6.47214i	−0.195252	−	0.268741i
$581$	−3.35520	−	1.09017i	−0.139197	−	0.0452279i
$582$	−1.79837	−	1.79837i	−0.0745450	−	0.0745450i
$583$	9.14590	+	0.620541i	0.378784	+	0.0257002i
$584$	15.7082	+	15.7082i	0.650010	+	0.650010i
$585$	0.618034	−	1.90211i	0.0255526	−	0.0786427i
$586$	−42.8154	−	6.78130i	−1.76869	−	0.280133i
$587$	−6.82891	+	9.39919i	−0.281859	+	0.387946i	−0.926349	−	0.376667i	$-0.877070\pi$
$587$	−6.82891	+	9.39919i	−0.281859	+	0.387946i	0.644489	+	0.764613i	$0.277070\pi$
$588$	−2.45085	−	7.54294i	−0.101071	−	0.311066i
$589$	−15.3884	+	5.00000i	−0.634069	+	0.206021i
$590$	2.26007	−	0.357960i	0.0930458	−	0.0147370i
$591$	7.47214	−	5.42882i	0.307363	−	0.223312i
$592$	−30.4338	−	9.88854i	−1.25082	−	0.406417i
$593$	−12.5623			−0.515872			−0.257936	−	0.966162i	$-0.583042\pi$
$593$	−12.5623			−0.515872			−0.257936	+	0.966162i	$0.583042\pi$
$594$	13.9769	+	8.35890i	0.573481	+	0.342970i
$595$			0.291796i			0.0119625i
$596$	4.18034	−	12.8658i	0.171233	−	0.527002i
$597$	−3.14320	−	4.32624i	−0.128642	−	0.177061i
$598$	−0.546915	−	3.45309i	−0.0223650	−	0.141207i
$599$	2.03444	+	6.26137i	0.0831250	+	0.255833i	0.983977	−	0.178293i	$-0.0570575\pi$
$599$	2.03444	+	6.26137i	0.0831250	+	0.255833i	−0.900852	+	0.434125i	$0.857057\pi$
$600$	−1.55754	−	0.793604i	−0.0635862	−	0.0323988i
$601$	27.9164	+	20.2825i	1.13873	+	0.827339i	0.986942	−	0.161074i	$-0.0514957\pi$
$601$	27.9164	+	20.2825i	1.13873	+	0.827339i	0.151792	+	0.988413i	$0.451496\pi$
$602$	1.97844	+	0.313354i	0.0806353	+	0.0127714i
$603$	−33.1810	−	10.7812i	−1.35123	−	0.439042i
$604$			27.7771i			1.13023i
$605$	−7.60845	+	7.94427i	−0.309328	+	0.322981i
$606$	−8.76393	+	8.76393i	−0.356010	+	0.356010i
$607$	10.9443	−	33.6830i	0.444214	−	1.36715i	−0.439129	−	0.898424i	$-0.644713\pi$
$607$	10.9443	−	33.6830i	0.444214	−	1.36715i	0.883343	−	0.468727i	$-0.155287\pi$
$608$	45.2015	+	7.15921i	1.83316	+	0.290344i
$609$	−1.52786	−	1.11006i	−0.0619122	−	0.0449818i
$610$	5.63522	+	2.87129i	0.228163	+	0.116255i
$611$	7.95148	−	2.58359i	0.321682	−	0.104521i
$612$	1.17557	−	1.61803i	0.0475196	−	0.0654051i
$613$	4.35926	+	6.00000i	0.176069	+	0.242338i	0.887926	−	0.459986i	$-0.152146\pi$
$613$	4.35926	+	6.00000i	0.176069	+	0.242338i	−0.711857	+	0.702324i	$0.752146\pi$
$614$	7.00891	−	3.57122i	0.282857	−	0.144123i
$615$	4.56231			0.183970
$616$	6.15035	+	3.67822i	0.247805	+	0.148200i
$617$	23.6180			0.950826			0.475413	−	0.879763i	$-0.342299\pi$
$617$	23.6180			0.950826			0.475413	+	0.879763i	$0.342299\pi$
$618$	9.11798	−	4.64584i	0.366779	−	0.186883i
$619$	1.29408	+	1.78115i	0.0520136	+	0.0715906i	0.834232	−	0.551414i	$-0.185912\pi$
$619$	1.29408	+	1.78115i	0.0520136	+	0.0715906i	−0.782218	+	0.623005i	$0.785912\pi$
$620$	−3.23607	−	2.35114i	−0.129964	−	0.0944241i
$621$	10.6861	−	3.47214i	0.428820	−	0.139332i
$622$	−1.69798	−	0.865164i	−0.0680828	−	0.0346899i
$623$	−3.43769	−	2.49763i	−0.137728	−	0.100065i
$624$	1.52786	−	1.11006i	0.0611635	−	0.0444379i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	28.7426	−	28.7426i	1.14879	−	1.14879i
$627$	−1.12257	+	16.5451i	−0.0448311	+	0.660747i
$628$	19.4164			0.774799
$629$	−2.90617	−	0.944272i	−0.115877	−	0.0376506i
$630$	2.79360	+	0.442463i	0.111300	+	0.0176282i
$631$	−26.6525	−	19.3642i	−1.06102	−	0.770875i	−0.0867418	−	0.996231i	$-0.527646\pi$
$631$	−26.6525	−	19.3642i	−1.06102	−	0.770875i	−0.974277	+	0.225356i	$0.927646\pi$
$632$	2.94285	−	5.77566i	0.117060	−	0.229744i
$633$	1.55573	+	4.78804i	0.0618346	+	0.190307i
$634$	−1.30273	−	8.22513i	−0.0517381	−	0.326662i
$635$	−10.4086	−	14.3262i	−0.413054	−	0.568519i
$636$	3.24920	+	1.05573i	0.128839	+	0.0418623i
$637$			4.90170i			0.194212i
$638$	−18.6868	+	1.67383i	−0.739819	+	0.0662676i
$639$	28.6525			1.13347
$640$	5.13632	+	10.0806i	0.203031	+	0.398470i
$641$	15.4443	−	11.2209i	0.610012	−	0.443200i	−0.239407	−	0.970919i	$-0.576953\pi$
$641$	15.4443	−	11.2209i	0.610012	−	0.443200i	0.849419	+	0.527720i	$0.176953\pi$
$642$	−1.85249	+	0.293406i	−0.0731120	+	0.0115798i
$643$	−19.3314	+	6.28115i	−0.762356	+	0.247704i	−0.664290	−	0.747475i	$-0.731266\pi$
$643$	−19.3314	+	6.28115i	−0.762356	+	0.247704i	−0.0980665	+	0.995180i	$0.531266\pi$
$644$	4.70228	−	1.52786i	0.185296	−	0.0602063i
$645$	−0.673542	+	0.927051i	−0.0265207	+	0.0365026i
$646$	4.31636	+	0.683644i	0.169825	+	0.0268976i
$647$	1.52786	−	4.70228i	0.0600665	−	0.184866i	−0.916521	−	0.399987i	$-0.869015\pi$
$647$	1.52786	−	4.70228i	0.0600665	−	0.184866i	0.976587	+	0.215121i	$0.0690146\pi$
$648$	−11.4164	−	11.4164i	−0.448479	−	0.448479i
$649$	2.00000	−	4.97980i	0.0785069	−	0.195474i
$650$	0.763932	+	0.763932i	0.0299639	+	0.0299639i
$651$	−0.898056	−	0.291796i	−0.0351976	−	0.0114364i
$652$	−7.09017	+	5.15131i	−0.277672	+	0.201741i
$653$	13.6578	−	18.7984i	0.534472	−	0.735637i	−0.453332	−	0.891342i	$-0.649765\pi$
$653$	13.6578	−	18.7984i	0.534472	−	0.735637i	0.987804	+	0.155705i	$0.0497648\pi$
$654$	−12.8280	−	6.53618i	−0.501614	−	0.255585i
$655$	−4.73607	−	14.5761i	−0.185053	−	0.569536i
$656$	−23.8885	−	17.3560i	−0.932691	−	0.677640i
$657$	16.6353	−	12.0862i	0.649003	−	0.471528i
$658$	5.36789	+	10.5351i	0.209262	+	0.410700i
$659$			3.14590i			0.122547i	0.998121	+	0.0612734i	$0.0195162\pi$
$659$			3.14590i			0.122547i	−0.998121	+	0.0612734i	$0.980484\pi$
$660$	−3.47214	+	2.17963i	−0.135153	+	0.0848419i
$661$			31.7082i			1.23331i	0.787235	+	0.616653i	$0.211512\pi$
$661$			31.7082i			1.23331i	−0.787235	+	0.616653i	$0.788488\pi$
$662$	12.6441	−	6.44251i	0.491428	−	0.250395i
$663$	0.145898	−	0.106001i	0.00566621	−	0.00411674i
$664$	−12.9010	+	2.04331i	−0.500654	+	0.0792959i
$665$	1.90983	+	5.87785i	0.0740600	+	0.227933i
$666$	−13.4471	+	26.3913i	−0.521063	+	1.02264i
$667$	−7.60845	+	10.4721i	−0.294600	+	0.405483i
$668$	−6.49839	−	8.94427i	−0.251430	−	0.346064i
$669$	−1.45309	−	0.472136i	−0.0561795	−	0.0182538i
$670$	13.3262	−	13.3262i	0.514837	−	0.514837i
$671$	12.5623	−	7.88597i	0.484962	−	0.304434i
$672$	1.88854	+	1.88854i	0.0728522	+	0.0728522i
$673$	8.06231	−	24.8132i	0.310779	−	0.956480i	−0.666678	−	0.745346i	$-0.732284\pi$
$673$	8.06231	−	24.8132i	0.310779	−	0.956480i	0.977457	−	0.211134i	$-0.0677156\pi$
$674$	7.54183	−	47.6172i	0.290500	−	1.83415i
$675$	−2.04087	+	2.80902i	−0.0785531	+	0.108119i
$676$	23.6174	−	7.67376i	0.908362	−	0.295145i
$677$	36.3117	−	11.7984i	1.39557	−	0.453448i	0.487815	−	0.872947i	$-0.337794\pi$
$677$	36.3117	−	11.7984i	1.39557	−	0.453448i	0.907756	+	0.419499i	$0.137794\pi$
$678$	2.26454	+	14.2978i	0.0869693	+	0.549102i
$679$	−1.79837	+	1.30660i	−0.0690153	+	0.0501425i
$680$	0.490475	+	0.962611i	0.0188088	+	0.0369144i
$681$	12.8197			0.491250
$682$	−8.62750	+	3.68323i	−0.330364	+	0.141038i
$683$			27.7771i			1.06286i	0.847102	+	0.531430i	$0.178345\pi$
$683$			27.7771i			1.06286i	−0.847102	+	0.531430i	$0.821655\pi$
$684$	13.0902	−	40.2874i	0.500515	−	1.54043i
$685$	−9.31881	−	12.8262i	−0.356053	−	0.490065i
$686$	−14.3161	+	2.26745i	−0.546593	+	0.0865718i
$687$	0.888544	+	2.73466i	0.0339001	+	0.104334i
$688$	7.05342	−	2.29180i	0.268909	−	0.0873739i
$689$	−1.70820	−	1.24108i	−0.0650774	−	0.0472815i
$690$	−0.442463	+	2.79360i	−0.0168443	+	0.106351i
$691$	9.14729	+	2.97214i	0.347979	+	0.113065i	0.477792	−	0.878473i	$-0.341437\pi$
$691$	9.14729	+	2.97214i	0.347979	+	0.113065i	−0.129812	+	0.991539i	$0.541437\pi$
$692$	−18.4721			−0.702205
$693$	4.25325	−	5.09017i	0.161568	−	0.193360i
$694$	−21.5066	−	21.5066i	−0.816379	−	0.816379i
$695$	−0.472136	+	1.45309i	−0.0179091	+	0.0551187i
$696$	−6.90617	−	1.09383i	−0.261778	−	0.0414615i
$697$	−2.28115	−	1.65735i	−0.0864048	−	0.0627768i
$698$	10.8789	−	21.3510i	0.411772	−	0.808148i
$699$	−0.0857567	+	0.0278640i	−0.00324362	+	0.00105391i
$700$	−0.898056	+	1.23607i	−0.0339433	+	0.0467190i
$701$	6.08985	+	8.38197i	0.230011	+	0.316582i	0.908386	−	0.418133i	$-0.137316\pi$
$701$	6.08985	+	8.38197i	0.230011	+	0.316582i	−0.678375	+	0.734716i	$0.737316\pi$
$702$	−1.70299	−	3.34231i	−0.0642754	−	0.126148i
$703$	−64.7214			−2.44101
$704$	26.4721	+	1.79611i	0.997706	+	0.0676935i
$705$	−6.76393			−0.254744
$706$	−6.96876	−	13.6770i	−0.262273	−	0.514739i
$707$	6.36737	+	8.76393i	0.239470	+	0.329602i
$708$	1.17557	−	1.61803i	0.0441806	−	0.0608094i
$709$	−25.6255	+	8.32624i	−0.962387	+	0.312698i	−0.747739	−	0.663993i	$-0.768860\pi$
$709$	−25.6255	+	8.32624i	−0.962387	+	0.312698i	−0.214648	+	0.976691i	$0.568860\pi$
$710$	−7.02666	+	13.7906i	−0.263706	+	0.517552i
$711$	−4.85410	−	3.52671i	−0.182043	−	0.132262i
$712$	−15.5389	−	2.46112i	−0.582344	−	0.0922343i
$713$	−2.00000	+	6.15537i	−0.0749006	+	0.230520i
$714$	0.180340	+	0.180340i	0.00674905	+	0.00674905i
$715$	2.45714	−	0.618034i	0.0918919	−	0.0231132i
$716$	−14.2918			−0.534109
$717$	−15.6659	−	5.09017i	−0.585055	−	0.190096i
$718$	4.63354	−	29.2550i	0.172922	−	1.09179i
$719$	17.8541	+	12.9718i	0.665846	+	0.483765i	0.868632	−	0.495458i	$-0.165000\pi$
$719$	17.8541	+	12.9718i	0.665846	+	0.483765i	−0.202786	+	0.979223i	$0.565000\pi$
$720$	9.95959	−	3.23607i	0.371172	−	0.120601i
$721$	−2.76393	−	8.50651i	−0.102934	−	0.316799i
$722$	64.8827	−	10.2764i	2.41468	−	0.382448i
$723$	−7.98424	−	10.9894i	−0.296937	−	0.408699i
$724$	12.3607	−	38.0423i	0.459381	−	1.41383i
$725$		−	4.00000i		−	0.148556i
$726$	0.207548	+	9.61211i	0.00770283	+	0.356739i
$727$	−2.76393			−0.102509			−0.0512543	−	0.998686i	$-0.516322\pi$
$727$	−2.76393			−0.102509			−0.0512543	+	0.998686i	$0.516322\pi$
$728$	−0.749378	−	1.47074i	−0.0277738	−	0.0545092i
$729$	−6.88197	+	5.00004i	−0.254888	+	0.185187i
$730$	1.73758	+	10.9706i	0.0643106	+	0.406041i
$731$	0.673542	−	0.218847i	0.0249118	−	0.00809435i
$732$	5.25731	−	1.70820i	0.194316	−	0.0631370i
$733$	−13.2493	+	18.2361i	−0.489373	+	0.673565i	−0.980272	−	0.197652i	$-0.936668\pi$
$733$	−13.2493	+	18.2361i	−0.489373	+	0.673565i	0.490899	+	0.871217i	$0.336668\pi$
$734$	−1.70530	+	10.7668i	−0.0629437	+	0.397411i
$735$	1.22542	−	3.77147i	0.0452005	−	0.139113i
$736$	12.9443	−	12.9443i	0.477132	−	0.477132i
$737$	−10.7812	−	42.8631i	−0.397129	−	1.57888i
$738$	−19.3262	+	19.3262i	−0.711409	+	0.711409i
$739$	22.7396	+	7.38854i	0.836490	+	0.271792i	0.695776	−	0.718258i	$-0.255060\pi$
$739$	22.7396	+	7.38854i	0.836490	+	0.271792i	0.140713	+	0.990050i	$0.455060\pi$
$740$	−9.40456	−	12.9443i	−0.345719	−	0.475841i
$741$	2.24514	−	3.09017i	0.0824773	−	0.113520i
$742$	1.35564	−	2.66059i	0.0497670	−	0.0976733i
$743$	9.32624	+	28.7032i	0.342146	+	1.05302i	0.963094	+	0.269166i	$0.0867481\pi$
$743$	9.32624	+	28.7032i	0.342146	+	1.05302i	−0.620947	+	0.783852i	$0.713252\pi$
$744$	−3.45309	+	0.546915i	−0.126596	+	0.0200509i
$745$	5.47214	−	3.97574i	0.200484	−	0.145660i
$746$	−20.7561	+	10.5758i	−0.759935	+	0.387206i
$747$			12.0902i			0.442356i
$748$	2.52786	+	0.171513i	0.0924279	+	0.00627115i
$749$			1.63932i			0.0598995i
$750$	−0.396802	−	0.778768i	−0.0144892	−	0.0284366i
$751$	−3.09017	+	2.24514i	−0.112762	+	0.0819263i	−0.642737	−	0.766087i	$-0.722201\pi$
$751$	−3.09017	+	2.24514i	−0.112762	+	0.0819263i	0.529975	+	0.848013i	$0.322201\pi$
$752$	35.4164	+	25.7315i	1.29150	+	0.938332i
$753$	−2.29180	−	7.05342i	−0.0835177	−	0.257041i
$754$	3.85044	+	1.96190i	0.140225	+	0.0714481i
$755$	−8.16348	+	11.2361i	−0.297100	+	0.408922i
$756$	4.29180	−	3.11817i	0.156091	−	0.113407i
$757$	29.0462	+	9.43769i	1.05570	+	0.343019i	0.784904	−	0.619617i	$-0.212712\pi$
$757$	29.0462	+	9.43769i	1.05570	+	0.343019i	0.270799	+	0.962636i	$0.412712\pi$
$758$	−31.2705	−	31.2705i	−1.13580	−	1.13580i
$759$	5.09017	+	4.25325i	0.184761	+	0.154383i
$760$	16.1803	+	16.1803i	0.586923	+	0.586923i
$761$	2.73607	−	8.42075i	0.0991824	−	0.305252i	−0.889139	−	0.457638i	$-0.848696\pi$
$761$	2.73607	−	8.42075i	0.0991824	−	0.305252i	0.988321	+	0.152386i	$0.0486956\pi$
$762$	−15.2870	−	2.42122i	−0.553789	−	0.0877116i
$763$	−7.39645	+	10.1803i	−0.267769	+	0.368553i
$764$	23.1684	−	7.52786i	0.838203	−	0.272349i
$765$	0.951057	−	0.309017i	0.0343855	−	0.0111725i
$766$	−35.9093	+	5.68747i	−1.29745	+	0.205497i
$767$	−1.00000	+	0.726543i	−0.0361079	+	0.0262339i
$768$	9.40456	+	3.05573i	0.339358	+	0.110264i
$769$	−4.83282			−0.174276			−0.0871379	−	0.996196i	$-0.527772\pi$
$769$	−4.83282			−0.174276			−0.0871379	+	0.996196i	$0.527772\pi$
$770$	1.40687	+	3.29541i	0.0507000	+	0.118758i
$771$			10.3820i			0.373897i
$772$	11.4127	+	3.70820i	0.410751	+	0.133461i
$773$	4.18774	+	5.76393i	0.150623	+	0.207314i	0.877660	−	0.479283i	$-0.159103\pi$
$773$	4.18774	+	5.76393i	0.150623	+	0.207314i	−0.727038	+	0.686598i	$0.759103\pi$
$774$	−1.07388	−	6.78022i	−0.0385999	−	0.243710i
$775$	−0.618034	−	1.90211i	−0.0222004	−	0.0683259i
$776$	−3.73645	+	7.33320i	−0.134131	+	0.263247i
$777$	−3.05573	−	2.22012i	−0.109624	−	0.0796462i
$778$	12.2415	+	1.93886i	0.438878	+	0.0695115i
$779$	−56.7984	−	18.4549i	−2.03501	−	0.661216i
$780$	0.944272			0.0338104
$781$	19.2986	+	30.7426i	0.690560	+	1.10006i
$782$	1.23607	−	1.23607i	0.0442017	−	0.0442017i
$783$	−4.29180	+	13.2088i	−0.153376	+	0.472044i
$784$	−20.7639	+	15.0859i	−0.741569	+	0.538781i
$785$	7.85410	+	5.70634i	0.280325	+	0.203668i
$786$	−11.9356	−	6.08149i	−0.425728	−	0.216919i
$787$	10.4944	−	3.40983i	0.374084	−	0.121547i	−0.115940	−	0.993256i	$-0.536988\pi$
$787$	10.4944	−	3.40983i	0.374084	−	0.121547i	0.490024	+	0.871709i	$0.336988\pi$
$788$	−24.1803	−	17.5680i	−0.861389	−	0.625836i
$789$	8.99602	+	12.3820i	0.320267	+	0.440810i
$790$	2.88783	−	1.47142i	0.102744	−	0.0523509i
$791$	12.6525			0.449870
$792$	5.47515	−	23.9413i	0.194551	−	0.850715i
$793$	−3.41641			−0.121320
$794$	−39.5870	+	20.1706i	−1.40489	+	0.715827i
$795$	1.00406	+	1.38197i	0.0356102	+	0.0490133i
$796$	−10.1716	+	14.0000i	−0.360523	+	0.496217i
$797$	−21.0948	+	6.85410i	−0.747215	+	0.242785i	−0.657782	−	0.753208i	$-0.728505\pi$
$797$	−21.0948	+	6.85410i	−0.747215	+	0.242785i	−0.0894324	+	0.995993i	$0.528505\pi$
$798$	4.81305	+	2.45237i	0.170380	+	0.0868131i
$799$	3.38197	+	2.45714i	0.119645	+	0.0869274i
$800$	−0.884927	+	5.58721i	−0.0312869	+	0.197538i
$801$	−4.50000	+	13.8496i	−0.159000	+	0.489351i
$802$	−35.4508	+	35.4508i	−1.25181	+	1.25181i
$803$	24.1724	+	9.70820i	0.853027	+	0.342595i
$804$		−	16.4721i		−	0.580927i
$805$	2.35114	+	0.763932i	0.0828668	+	0.0269251i
$806$	2.13412	+	0.338012i	0.0751713	+	0.0119060i
$807$	6.94427	+	5.04531i	0.244450	+	0.177603i
$808$	35.7365	+	18.2087i	1.25721	+	0.640579i
$809$	9.68034	+	29.7930i	0.340343	+	1.04747i	0.964030	+	0.265793i	$0.0856338\pi$
$809$	9.68034	+	29.7930i	0.340343	+	1.04747i	−0.623687	+	0.781674i	$0.714366\pi$
$810$	−1.26284	−	7.97323i	−0.0443715	−	0.280151i
$811$	−14.1926	−	19.5344i	−0.498370	−	0.685947i	0.483535	−	0.875325i	$-0.339353\pi$
$811$	−14.1926	−	19.5344i	−0.498370	−	0.685947i	−0.981904	+	0.189378i	$0.939353\pi$
$812$	−1.88854	+	5.81234i	−0.0662749	+	0.203973i
$813$			9.70820i			0.340482i
$814$	−37.3737	+	3.34766i	−1.30995	+	0.117336i
$815$	−4.38197			−0.153494
$816$	0.898056	+	0.291796i	0.0314382	+	0.0102149i
$817$	12.1353	−	8.81678i	0.424559	−	0.308460i
$818$	30.7296	−	4.86710i	1.07444	−	0.170174i
$819$	−1.45309	+	0.472136i	−0.0507749	+	0.0164978i
$820$	−4.56231	−	14.0413i	−0.159323	−	0.490345i
$821$	−2.41665	+	3.32624i	−0.0843418	+	0.116087i	−0.849103	−	0.528227i	$-0.822857\pi$
$821$	−2.41665	+	3.32624i	−0.0843418	+	0.116087i	0.764761	+	0.644314i	$0.222857\pi$
$822$	−13.6864	−	2.16771i	−0.477368	−	0.0756076i
$823$	−4.65248	+	14.3188i	−0.162175	+	0.499124i	−0.998817	−	0.0486265i	$-0.984516\pi$
$823$	−4.65248	+	14.3188i	−0.162175	+	0.499124i	0.836642	+	0.547750i	$0.184516\pi$
$824$	−23.4164	−	23.4164i	−0.815749	−	0.815749i
$825$	−2.04508	−	0.138757i	−0.0712007	−	0.00483091i
$826$	−1.23607	−	1.23607i	−0.0430083	−	0.0430083i
$827$	−41.6547	−	13.5344i	−1.44848	−	0.470639i	−0.523948	−	0.851750i	$-0.675541\pi$
$827$	−41.6547	−	13.5344i	−1.44848	−	0.470639i	−0.924529	+	0.381112i	$0.875541\pi$
$828$	−9.95959	−	13.7082i	−0.346120	−	0.476393i
$829$	−23.1684	+	31.8885i	−0.804671	+	1.10753i	0.187453	+	0.982274i	$0.439977\pi$
$829$	−23.1684	+	31.8885i	−0.804671	+	1.10753i	−0.992124	+	0.125261i	$0.960023\pi$
$830$	−5.81906	−	2.96496i	−0.201983	−	0.102915i
$831$	2.56231	+	7.88597i	0.0888854	+	0.273561i
$832$	−4.94427	−	3.59222i	−0.171412	−	0.124538i
$833$	−1.98278	+	1.44057i	−0.0686992	+	0.0499129i
$834$	0.606260	+	1.18985i	0.0209931	+	0.0412012i
$835$		−	5.52786i		−	0.191300i
$836$	52.0431	−	13.0902i	1.79995	−	0.452733i
$837$			6.94427i			0.240029i
$838$	−8.70689	+	4.43638i	−0.300775	+	0.153252i
$839$	−39.7426	+	28.8747i	−1.37207	+	0.996866i	−0.374496	+	0.927228i	$0.622184\pi$
$839$	−39.7426	+	28.8747i	−1.37207	+	0.996866i	−0.997572	+	0.0696377i	$0.977816\pi$
$840$	0.208903	+	1.31896i	0.00720784	+	0.0455085i
$841$	4.01722	+	12.3637i	0.138525	+	0.426336i
$842$	−15.1058	+	29.6468i	−0.520581	+	1.02170i
$843$	3.57971	−	4.92705i	0.123292	−	0.169697i
$844$	13.1803	−	9.57608i	0.453686	−	0.329622i
$845$	11.8087	+	3.83688i	0.406232	+	0.131993i
$846$	28.6525	−	28.6525i	0.985092	−	0.985092i
$847$	8.32624	+	1.13508i	0.286093	+	0.0390019i
$848$		−	11.0557i		−	0.379655i
$849$	2.00000	−	6.15537i	0.0686398	−	0.211252i
$850$	−0.0845030	+	0.533531i	−0.00289843	+	0.0183000i
$851$	−15.2169	+	20.9443i	−0.521629	+	0.717960i
$852$	4.18034	+	12.8658i	0.143216	+	0.440774i
$853$	−2.73466	+	0.888544i	−0.0936329	+	0.0304232i	−0.355459	−	0.934692i	$-0.615675\pi$
$853$	−2.73466	+	0.888544i	−0.0936329	+	0.0304232i	0.261826	+	0.965115i	$0.415675\pi$
$854$	−0.755818	−	4.77205i	−0.0258636	−	0.163296i
$855$	17.1353	−	12.4495i	0.586013	−	0.425764i
$856$	2.75550	+	5.40798i	0.0941811	+	0.184841i
$857$	0.798374			0.0272719			0.0136360	−	0.999907i	$-0.495659\pi$
$857$	0.798374			0.0272719			0.0136360	+	0.999907i	$0.495659\pi$
$858$	1.13663	−	1.90056i	0.0388040	−	0.0648842i
$859$			44.6312i			1.52280i	0.648284	+	0.761398i	$0.275487\pi$
$859$			44.6312i			1.52280i	−0.648284	+	0.761398i	$0.724513\pi$
$860$	3.52671	+	1.14590i	0.120260	+	0.0390748i
$861$	−2.04860	−	2.81966i	−0.0698162	−	0.0960938i
$862$	16.7616	−	2.65478i	0.570903	−	0.0904222i
$863$	6.05573	+	18.6376i	0.206139	+	0.634432i	0.999665	+	0.0258945i	$0.00824340\pi$
$863$	6.05573	+	18.6376i	0.206139	+	0.634432i	−0.793525	+	0.608537i	$0.791757\pi$
$864$	8.91699	−	17.5006i	0.303362	−	0.595382i
$865$	−7.47214	−	5.42882i	−0.254060	−	0.184586i
$866$	−4.21102	+	26.5874i	−0.143096	+	0.903475i
$867$	−9.90659	−	3.21885i	−0.336446	−	0.109318i
$868$			3.05573i			0.103718i
$869$	0.514540	−	7.58359i	0.0174546	−	0.257256i
$870$	−2.47214	−	2.47214i	−0.0838133	−	0.0838133i
$871$	−3.14590	+	9.68208i	−0.106595	+	0.328065i
$872$	−7.28832	+	46.0166i	−0.246814	+	1.55832i
$873$	6.16312	+	4.47777i	0.208590	+	0.151549i
$874$	16.8088	−	32.9892i	0.568567	−	1.11587i
$875$	−0.726543	+	0.236068i	−0.0245616	+	0.00798055i
$876$	7.85410	+	5.70634i	0.265366	+	0.192799i
$877$	−9.78808	−	13.4721i	−0.330520	−	0.454922i	0.611123	−	0.791536i	$-0.290718\pi$
$877$	−9.78808	−	13.4721i	−0.330520	−	0.454922i	−0.941643	+	0.336614i	$0.890718\pi$
$878$	−4.27115	−	8.38261i	−0.144144	−	0.282899i
$879$	−18.9443			−0.638974
$880$	10.1803	+	8.50651i	0.343179	+	0.286754i
$881$	−6.43769			−0.216891			−0.108446	−	0.994102i	$-0.534587\pi$
$881$	−6.43769			−0.216891			−0.108446	+	0.994102i	$0.534587\pi$
$882$	10.7852	+	21.1672i	0.363157	+	0.712736i
$883$	9.42481	+	12.9721i	0.317170	+	0.436547i	0.937601	−	0.347714i	$-0.113042\pi$
$883$	9.42481	+	12.9721i	0.317170	+	0.436547i	−0.620430	+	0.784261i	$0.713042\pi$
$884$	−0.472136	−	0.343027i	−0.0158797	−	0.0115372i
$885$	0.951057	−	0.309017i	0.0319694	−	0.0103875i
$886$	22.5293	−	44.2162i	0.756886	−	1.48547i
$887$	−12.2361	−	8.89002i	−0.410847	−	0.298498i	0.363098	−	0.931751i	$-0.381719\pi$
$887$	−12.2361	−	8.89002i	−0.410847	−	0.298498i	−0.773945	+	0.633253i	$0.781719\pi$
$888$	−13.8123	−	2.18766i	−0.463512	−	0.0734131i
$889$	−4.18034	+	12.8658i	−0.140204	+	0.431504i
$890$	−5.56231	−	5.56231i	−0.186449	−	0.186449i
$891$	−17.5680	−	7.05573i	−0.588552	−	0.236376i
$892$			4.94427i			0.165546i
$893$	84.2075	+	27.3607i	2.81790	+	0.915590i
$894$	0.924824	−	5.83911i	0.0309307	−	0.195289i
$895$	−5.78115	−	4.20025i	−0.193243	−	0.140399i
$896$	3.92380	−	7.70088i	0.131085	−	0.257268i
$897$	−0.472136	−	1.45309i	−0.0157642	−	0.0485171i
$898$	23.5418	−	3.72866i	0.785602	−	0.124427i
$899$	−4.70228	−	6.47214i	−0.156830	−	0.215858i
$900$	4.97980	+	1.61803i	0.165993	+	0.0539345i
$901$		−	1.05573i		−	0.0351714i
$902$	−33.7531	−	7.71904i	−1.12386	−	0.257016i
$903$	0.875388			0.0291311
$904$	41.7394	−	21.2673i	1.38823	−	0.707340i
$905$	16.1803	−	11.7557i	0.537853	−	0.390773i
$906$	1.89896	+	11.9896i	0.0630888	+	0.398327i
$907$	42.8958	−	13.9377i	1.42433	−	0.462794i	0.507356	−	0.861736i	$-0.330623\pi$
$907$	42.8958	−	13.9377i	1.42433	−	0.462794i	0.916976	+	0.398943i	$0.130623\pi$
$908$	−12.8197	−	39.4549i	−0.425435	−	1.30936i
$909$	21.8213	−	30.0344i	0.723767	−	0.996180i
$910$	0.129109	−	0.815163i	0.00427993	−	0.0270224i
$911$	−14.0689	+	43.2996i	−0.466123	+	1.43458i	0.391442	+	0.920203i	$0.371976\pi$
$911$	−14.0689	+	43.2996i	−0.466123	+	1.43458i	−0.857565	+	0.514376i	$0.828024\pi$
$912$	20.0000			0.662266
$913$	−12.9721	+	8.14324i	−0.429315	+	0.269502i
$914$	29.1591	−	29.1591i	0.964496	−	0.964496i
$915$	2.62866	+	0.854102i	0.0869007	+	0.0282357i
$916$	7.52786	−	5.46931i	0.248728	−	0.180711i
$917$	−6.88191	+	9.47214i	−0.227261	+	0.312797i
$918$	0.851497	−	1.67116i	0.0281036	−	0.0551564i
$919$	−6.36068	−	19.5762i	−0.209819	−	0.645758i	−0.999481	−	0.0322151i	$-0.989744\pi$
$919$	−6.36068	−	19.5762i	−0.209819	−	0.645758i	0.789661	−	0.613543i	$-0.210256\pi$
$920$	9.04029	−	1.43184i	0.298050	−	0.0472064i
$921$	2.78115	−	2.02063i	0.0916421	−	0.0665819i
$922$	−49.8948	+	25.4227i	−1.64320	+	0.837251i
$923$		−	8.36068i		−	0.275195i
$924$	2.90617	+	1.16718i	0.0956060	+	0.0383975i
$925$		−	8.00000i		−	0.263038i
$926$	20.4737	+	40.1819i	0.672808	+	1.32046i
$927$	−24.7984	+	18.0171i	−0.814485	+	0.591758i
$928$	3.53971	+	22.3488i	0.116197	+	0.733636i
$929$	0.319660	+	0.983813i	0.0104877	+	0.0322778i	0.956163	−	0.292834i	$-0.0945982\pi$
$929$	0.319660	+	0.983813i	0.0104877	+	0.0322778i	−0.945676	+	0.325111i	$0.894598\pi$
$930$	−1.55754	−	0.793604i	−0.0510736	−	0.0260233i
$931$	−30.5118	+	41.9959i	−0.999985	+	1.37636i
$932$	0.171513	+	0.236068i	0.00561811	+	0.00773266i
$933$	−0.792055	−	0.257354i	−0.0259307	−	0.00842540i
$934$	−17.5279	−	17.5279i	−0.573529	−	0.573529i
$935$	0.972136	+	0.812299i	0.0317922	+	0.0265650i
$936$	−4.00000	+	4.00000i	−0.130744	+	0.130744i
$937$	4.93769	−	15.1967i	0.161307	−	0.496453i	−0.837438	−	0.546533i	$-0.815947\pi$
$937$	4.93769	−	15.1967i	0.161307	−	0.496453i	0.998745	+	0.0500794i	$0.0159474\pi$
$938$	−14.2199	−	2.25221i	−0.464297	−	0.0735374i
$939$	10.4414	−	14.3713i	0.340741	−	0.468990i
$940$	6.76393	+	20.8172i	0.220615	+	0.678984i
$941$	−37.2752	+	12.1115i	−1.21514	+	0.394822i	−0.845309	−	0.534278i	$-0.820584\pi$
$941$	−37.2752	+	12.1115i	−1.21514	+	0.394822i	−0.369829	+	0.929100i	$0.620584\pi$
$942$	8.38081	−	1.32739i	0.273062	−	0.0432487i
$943$	−19.3262	+	14.0413i	−0.629349	+	0.457249i
$944$	−6.15537	−	2.00000i	−0.200340	−	0.0650945i
$945$	2.65248			0.0862850
$946$	6.55153	−	5.71898i	0.213009	−	0.185940i
$947$		−	52.3820i		−	1.70219i	−0.525016	−	0.851093i	$-0.675941\pi$
$947$		−	52.3820i		−	1.70219i	0.525016	−	0.851093i	$-0.324059\pi$
$948$	0.875388	−	2.69417i	0.0284313	−	0.0875025i
$949$	−3.52671	−	4.85410i	−0.114482	−	0.157571i
$950$	1.78980	+	11.3004i	0.0580689	+	0.366632i
$951$	−1.12461	−	3.46120i	−0.0364680	−	0.112237i
$952$	0.374689	−	0.735369i	0.0121437	−	0.0238334i
$953$	32.4787	+	23.5972i	1.05209	+	0.764387i	0.972609	−	0.232449i	$-0.0746740\pi$
$953$	32.4787	+	23.5972i	1.05209	+	0.764387i	0.0794802	+	0.996836i	$0.474674\pi$
$954$	−10.1074	−	1.60085i	−0.327238	−	0.0518294i
$955$	11.5842	+	3.76393i	0.374856	+	0.121798i
$956$			53.3050i			1.72401i
$957$	−7.95148	+	2.00000i	−0.257035	+	0.0646508i
$958$	16.3607	−	16.3607i	0.528590	−	0.528590i
$959$	−3.74265	+	11.5187i	−0.120856	+	0.371958i
$960$	2.90617	+	4.00000i	0.0937962	+	0.129099i
$961$	21.8435	+	15.8702i	0.704628	+	0.511942i
$962$	7.70088	+	3.92380i	0.248286	+	0.126508i
$963$	5.34307	−	1.73607i	0.172178	−	0.0559440i
$964$	−25.8375	+	35.5623i	−0.832171	+	1.14538i
$965$	3.52671	+	4.85410i	0.113529	+	0.156259i
$966$	1.92522	−	0.980949i	0.0619430	−	0.0315615i
$967$	−58.7214			−1.88835			−0.944176	−	0.329442i	$-0.893139\pi$
$967$	−58.7214			−1.88835			−0.944176	+	0.329442i	$0.893139\pi$
$968$	29.3755	−	10.2509i	0.944164	−	0.329476i
$969$	1.90983			0.0613526
$970$	−3.66660	+	1.86823i	−0.117727	+	0.0599851i
$971$	26.4176	+	36.3607i	0.847780	+	1.16687i	0.984347	+	0.176239i	$0.0563931\pi$
$971$	26.4176	+	36.3607i	0.847780	+	1.16687i	−0.136567	+	0.990631i	$0.543607\pi$
$972$	−22.5623	−	16.3925i	−0.723686	−	0.525789i
$973$	1.11006	−	0.360680i	0.0355868	−	0.0115629i
$974$	13.7906	+	7.02666i	0.441879	+	0.225149i
$975$	0.381966	+	0.277515i	0.0122327	+	0.00888758i
$976$	−10.5146	−	14.4721i	−0.336565	−	0.463242i
$977$	1.56231	−	4.80828i	0.0499826	−	0.153831i	−0.922950	−	0.384920i	$-0.874229\pi$
$977$	1.56231	−	4.80828i	0.0499826	−	0.153831i	0.972933	+	0.231089i	$0.0742290\pi$
$978$	−2.70820	+	2.70820i	−0.0865988	+	0.0865988i
$979$	−17.8908	+	4.50000i	−0.571793	+	0.143821i
$980$	−12.8328			−0.409929
$981$	41.0139	+	13.3262i	1.30947	+	0.425474i
$982$	2.74550	+	0.434844i	0.0876123	+	0.0138764i
$983$	22.9443	+	16.6700i	0.731809	+	0.531690i	0.890135	−	0.455697i	$-0.150610\pi$
$983$	22.9443	+	16.6700i	0.731809	+	0.531690i	−0.158326	+	0.987387i	$0.550610\pi$
$984$	−11.4977	−	5.85836i	−0.366533	−	0.186758i
$985$	−4.61803	−	14.2128i	−0.147143	−	0.452859i
$986$	0.338012	+	2.13412i	0.0107645	+	0.0679644i
$987$	3.03719	+	4.18034i	0.0966750	+	0.133062i
$988$	−11.7557	−	3.81966i	−0.373999	−	0.121520i
$989$		−	6.00000i		−	0.190789i
$990$	9.25090	−	8.07533i	0.294013	−	0.256651i
$991$	32.0689			1.01870			0.509351	−	0.860559i	$-0.329886\pi$
$991$	32.0689			1.01870			0.509351	+	0.860559i	$0.329886\pi$
$992$	5.13632	+	10.0806i	0.163078	+	0.320059i
$993$	5.01722	−	3.64522i	0.159217	−	0.115678i
$994$	11.6782	−	1.84965i	0.370411	−	0.0586673i
$995$	−8.22899	+	2.67376i	−0.260877	+	0.0847640i
$996$	−5.42882	+	1.76393i	−0.172019	+	0.0558923i
$997$	−27.5276	+	37.8885i	−0.871809	+	1.19994i	0.106814	+	0.994279i	$0.465935\pi$
$997$	−27.5276	+	37.8885i	−0.871809	+	1.19994i	−0.978623	+	0.205663i	$0.934065\pi$
$998$	−31.5929	−	5.00383i	−1.00006	−	0.158393i
$999$	−8.58359	+	26.4176i	−0.271573	+	0.835815i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	440.2.bi.b.141.1	✓	8
8.5	even	2	inner	440.2.bi.b.141.2	yes	8
11.5	even	5	inner	440.2.bi.b.181.2	yes	8
88.5	even	10	inner	440.2.bi.b.181.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.bi.b.141.1	✓	8	1.1	even	1	trivial
440.2.bi.b.141.2	yes	8	8.5	even	2	inner
440.2.bi.b.181.1	yes	8	88.5	even	10	inner
440.2.bi.b.181.2	yes	8	11.5	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642040 - 1.26007i) q^{2} +(-0.363271 - 0.500000i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(-0.396802 + 0.778768i) q^{6} +(0.618034 + 0.449028i) q^{7} +(2.79360 + 0.442463i) q^{8} +(0.809017 - 2.48990i) q^{9} +O(q^{10})\)	\(q+(-0.642040 - 1.26007i) q^{2} +(-0.363271 - 0.500000i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(-0.396802 + 0.778768i) q^{6} +(0.618034 + 0.449028i) q^{7} +(2.79360 + 0.442463i) q^{8} +(0.809017 - 2.48990i) q^{9} +(1.00000 + 1.00000i) q^{10} +(3.21644 - 0.809017i) q^{11} +1.23607 q^{12} +(-0.726543 - 0.236068i) q^{13} +(0.169006 - 1.06706i) q^{14} +(0.500000 + 0.363271i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(-0.118034 - 0.363271i) q^{17} +(-3.65688 + 0.579192i) q^{18} +(-4.75528 - 6.54508i) q^{19} +(0.618034 - 1.90211i) q^{20} -0.472136i q^{21} +(-3.08450 - 3.53353i) q^{22} -3.23607 q^{23} +(-0.793604 - 1.55754i) q^{24} +(0.809017 - 0.587785i) q^{25} +(0.169006 + 1.06706i) q^{26} +(-3.30220 + 1.07295i) q^{27} +(-1.45309 + 0.472136i) q^{28} +(2.35114 - 3.23607i) q^{29} +(0.136729 - 0.863271i) q^{30} +(0.618034 - 1.90211i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-1.57295 - 1.31433i) q^{33} +(-0.381966 + 0.381966i) q^{34} +(-0.726543 - 0.236068i) q^{35} +(3.07768 + 4.23607i) q^{36} +(4.70228 - 6.47214i) q^{37} +(-5.19421 + 10.1942i) q^{38} +(0.145898 + 0.449028i) q^{39} +(-2.79360 + 0.442463i) q^{40} +(5.97214 - 4.33901i) q^{41} +(-0.594926 + 0.303130i) q^{42} +1.85410i q^{43} +(-2.47214 + 6.15537i) q^{44} +2.61803i q^{45} +(2.07768 + 4.07768i) q^{46} +(-8.85410 + 6.43288i) q^{47} +(-1.45309 + 2.00000i) q^{48} +(-1.98278 - 6.10237i) q^{49} +(-1.26007 - 0.642040i) q^{50} +(-0.138757 + 0.190983i) q^{51} +(1.23607 - 0.898056i) q^{52} +(2.62866 + 0.854102i) q^{53} +(3.47214 + 3.47214i) q^{54} +(-2.80902 + 1.76336i) q^{55} +(1.52786 + 1.52786i) q^{56} +(-1.54508 + 4.75528i) q^{57} +(-5.58721 - 0.884927i) q^{58} +(0.951057 - 1.30902i) q^{59} +(-1.17557 + 0.381966i) q^{60} +(4.25325 - 1.38197i) q^{61} +(-2.79360 + 0.442463i) q^{62} +(1.61803 - 1.17557i) q^{63} +(7.60845 + 2.47214i) q^{64} +0.763932 q^{65} +(-0.646254 + 2.82588i) q^{66} -13.3262i q^{67} +(0.726543 + 0.236068i) q^{68} +(1.17557 + 1.61803i) q^{69} +(0.169006 + 1.06706i) q^{70} +(3.38197 + 10.4086i) q^{71} +(3.36176 - 6.59783i) q^{72} +(6.35410 + 4.61653i) q^{73} +(-11.1744 - 1.76985i) q^{74} +(-0.587785 - 0.190983i) q^{75} +16.1803 q^{76} +(2.35114 + 0.944272i) q^{77} +(0.472136 - 0.472136i) q^{78} +(0.708204 - 2.17963i) q^{79} +(2.35114 + 3.23607i) q^{80} +(-4.61803 - 3.35520i) q^{81} +(-9.30182 - 4.73951i) q^{82} +(-4.39201 + 1.42705i) q^{83} +(0.763932 + 0.555029i) q^{84} +(0.224514 + 0.309017i) q^{85} +(2.33630 - 1.19041i) q^{86} -2.47214 q^{87} +(9.34342 - 0.836916i) q^{88} -5.56231 q^{89} +(3.29892 - 1.68088i) q^{90} +(-0.343027 - 0.472136i) q^{91} +(3.80423 - 5.23607i) q^{92} +(-1.17557 + 0.381966i) q^{93} +(13.7906 + 7.02666i) q^{94} +(6.54508 + 4.75528i) q^{95} +(3.45309 + 0.546915i) q^{96} +(-0.899187 + 2.76741i) q^{97} +(-6.41641 + 6.41641i) q^{98} +(0.587785 - 8.66312i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 6 q^{6} - 4 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 6 * q^6 - 4 * q^7 + 4 * q^8 + 2 * q^9	\( 8 q - 2 q^{2} + 6 q^{6} - 4 q^{7} + 4 q^{8} + 2 q^{9} + 8 q^{10} - 8 q^{12} - 4 q^{14} + 4 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} - 4 q^{20} - 22 q^{22} - 8 q^{23} + 12 q^{24} + 2 q^{25} - 4 q^{26} + 4 q^{30} - 4 q^{31} - 32 q^{32} - 26 q^{33} - 12 q^{34} + 20 q^{38} + 28 q^{39} - 4 q^{40} + 12 q^{41} - 28 q^{42} + 16 q^{44} - 8 q^{46} - 44 q^{47} - 74 q^{49} + 2 q^{50} - 8 q^{52} - 8 q^{54} - 18 q^{55} + 48 q^{56} + 10 q^{57} - 8 q^{58} - 4 q^{62} + 4 q^{63} + 24 q^{65} + 4 q^{66} - 4 q^{70} + 36 q^{71} - 4 q^{72} + 24 q^{73} - 16 q^{74} + 40 q^{76} - 32 q^{78} - 48 q^{79} - 28 q^{81} + 22 q^{82} + 24 q^{84} + 18 q^{86} + 16 q^{87} - 4 q^{88} + 36 q^{89} + 2 q^{90} + 36 q^{94} + 30 q^{95} + 16 q^{96} + 42 q^{97} + 56 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 6 * q^6 - 4 * q^7 + 4 * q^8 + 2 * q^9 + 8 * q^10 - 8 * q^12 - 4 * q^14 + 4 * q^15 + 8 * q^16 + 8 * q^17 - 8 * q^18 - 4 * q^20 - 22 * q^22 - 8 * q^23 + 12 * q^24 + 2 * q^25 - 4 * q^26 + 4 * q^30 - 4 * q^31 - 32 * q^32 - 26 * q^33 - 12 * q^34 + 20 * q^38 + 28 * q^39 - 4 * q^40 + 12 * q^41 - 28 * q^42 + 16 * q^44 - 8 * q^46 - 44 * q^47 - 74 * q^49 + 2 * q^50 - 8 * q^52 - 8 * q^54 - 18 * q^55 + 48 * q^56 + 10 * q^57 - 8 * q^58 - 4 * q^62 + 4 * q^63 + 24 * q^65 + 4 * q^66 - 4 * q^70 + 36 * q^71 - 4 * q^72 + 24 * q^73 - 16 * q^74 + 40 * q^76 - 32 * q^78 - 48 * q^79 - 28 * q^81 + 22 * q^82 + 24 * q^84 + 18 * q^86 + 16 * q^87 - 4 * q^88 + 36 * q^89 + 2 * q^90 + 36 * q^94 + 30 * q^95 + 16 * q^96 + 42 * q^97 + 56 * q^98

Introduction

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