LMFDB - Embedded newform 230.2.e.b.137.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(137,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("230.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.e (of order $4$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.110166016.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 10x^{6} + 19x^{4} + 10x^{2} + 1 $ x^8 + 10x^6 + 19x^4 + 10*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.1
Root			$-0.360409i$ of defining polynomial
Character	$\chi$	$=$	230.137
Dual form			230.2.e.b.183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.96195 + 1.96195i) q^{3} +1.00000i q^{4} +(-1.77462 + 1.36041i) q^{5} +2.77462 q^{6} +(-0.105561 + 0.105561i) q^{7} +(0.707107 - 0.707107i) q^{8} -4.69853i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.96195 + 1.96195i) q^{3} +1.00000i q^{4} +(-1.77462 + 1.36041i) q^{5} +2.77462 q^{6} +(-0.105561 + 0.105561i) q^{7} +(0.707107 - 0.707107i) q^{8} -4.69853i q^{9} +(2.21680 + 0.292893i) q^{10} -6.18884i q^{11} +(-1.96195 - 1.96195i) q^{12} +(-2.81835 + 2.81835i) q^{13} +0.149286 q^{14} +(0.812668 - 6.15079i) q^{15} -1.00000 q^{16} +(3.81267 - 3.81267i) q^{17} +(-3.32236 + 3.32236i) q^{18} -3.56350 q^{19} +(-1.36041 - 1.77462i) q^{20} -0.414214i q^{21} +(-4.37617 + 4.37617i) q^{22} +(-4.42793 + 1.84214i) q^{23} +2.77462i q^{24} +(1.29857 - 4.82843i) q^{25} +3.98575 q^{26} +(3.33244 + 3.33244i) q^{27} +(-0.105561 - 0.105561i) q^{28} +0.693395i q^{29} +(-4.92391 + 3.77462i) q^{30} -1.47605 q^{31} +(0.707107 + 0.707107i) q^{32} +(12.1422 + 12.1422i) q^{33} -5.39193 q^{34} +(0.0437250 - 0.330939i) q^{35} +4.69853 q^{36} +(-3.09335 + 3.09335i) q^{37} +(2.51978 + 2.51978i) q^{38} -11.0589i q^{39} +(-0.292893 + 2.21680i) q^{40} +3.87011 q^{41} +(-0.292893 + 0.292893i) q^{42} +(-7.58289 - 7.58289i) q^{43} +6.18884 q^{44} +(6.39193 + 8.33812i) q^{45} +(4.43361 + 1.82843i) q^{46} +(-3.50970 - 3.50970i) q^{47} +(1.96195 - 1.96195i) q^{48} +6.97771i q^{49} +(-4.33244 + 2.49598i) q^{50} +14.9606i q^{51} +(-2.81835 - 2.81835i) q^{52} +(-1.81630 - 1.81630i) q^{53} -4.71279i q^{54} +(8.41935 + 10.9829i) q^{55} +0.149286i q^{56} +(6.99143 - 6.99143i) q^{57} +(0.490304 - 0.490304i) q^{58} -2.80827i q^{59} +(6.15079 + 0.812668i) q^{60} +4.92680i q^{61} +(1.04372 + 1.04372i) q^{62} +(0.495984 + 0.495984i) q^{63} -1.00000i q^{64} +(1.16740 - 8.83561i) q^{65} -17.1717i q^{66} +(-6.69050 + 6.69050i) q^{67} +(3.81267 + 3.81267i) q^{68} +(5.07320 - 12.3016i) q^{69} +(-0.264927 + 0.203091i) q^{70} -15.5544 q^{71} +(-3.32236 - 3.32236i) q^{72} +(7.61108 - 7.61108i) q^{73} +4.37466 q^{74} +(6.92541 + 12.0209i) q^{75} -3.56350i q^{76} +(0.653303 + 0.653303i) q^{77} +(-7.81985 + 7.81985i) q^{78} +8.97072 q^{79} +(1.77462 - 1.36041i) q^{80} +1.01939 q^{81} +(-2.73658 - 2.73658i) q^{82} +(-0.0424449 - 0.0424449i) q^{83} +0.414214 q^{84} +(-1.57926 + 11.9528i) q^{85} +10.7238i q^{86} +(-1.36041 - 1.36041i) q^{87} +(-4.37617 - 4.37617i) q^{88} -12.5485 q^{89} +(1.37617 - 10.4157i) q^{90} -0.595018i q^{91} +(-1.84214 - 4.42793i) q^{92} +(2.89594 - 2.89594i) q^{93} +4.96346i q^{94} +(6.32387 - 4.84782i) q^{95} -2.77462 q^{96} +(-11.1223 + 11.1223i) q^{97} +(4.93399 - 4.93399i) q^{98} -29.0784 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{5} + 4 q^{6}+O(q^{10}) $ 8 * q - 4 * q^3 + 4 * q^5 + 4 * q^6	$ 8 q - 4 q^{3} + 4 q^{5} + 4 q^{6} - 4 q^{12} - 4 q^{14} - 8 q^{16} + 24 q^{17} - 8 q^{18} - 12 q^{19} - 4 q^{20} - 12 q^{22} - 16 q^{23} + 12 q^{26} + 8 q^{27} - 16 q^{30} - 4 q^{31} + 20 q^{33} - 4 q^{34} - 4 q^{35} - 4 q^{36} + 4 q^{37} + 8 q^{38} - 8 q^{40} + 12 q^{41} - 8 q^{42} - 20 q^{43} + 20 q^{44} + 12 q^{45} - 16 q^{47} + 4 q^{48} - 16 q^{50} + 12 q^{55} + 20 q^{57} + 16 q^{58} + 8 q^{60} + 4 q^{62} + 12 q^{65} - 4 q^{67} + 24 q^{68} + 12 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 28 q^{73} + 48 q^{74} - 4 q^{75} + 4 q^{77} - 4 q^{78} + 8 q^{79} - 4 q^{80} - 16 q^{81} + 8 q^{82} - 28 q^{83} - 8 q^{84} + 20 q^{85} - 4 q^{87} - 12 q^{88} - 40 q^{89} - 12 q^{90} + 16 q^{92} - 12 q^{93} - 4 q^{95} - 4 q^{96} - 8 q^{97} + 16 q^{98} - 36 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^5 + 4 * q^6 - 4 * q^12 - 4 * q^14 - 8 * q^16 + 24 * q^17 - 8 * q^18 - 12 * q^19 - 4 * q^20 - 12 * q^22 - 16 * q^23 + 12 * q^26 + 8 * q^27 - 16 * q^30 - 4 * q^31 + 20 * q^33 - 4 * q^34 - 4 * q^35 - 4 * q^36 + 4 * q^37 + 8 * q^38 - 8 * q^40 + 12 * q^41 - 8 * q^42 - 20 * q^43 + 20 * q^44 + 12 * q^45 - 16 * q^47 + 4 * q^48 - 16 * q^50 + 12 * q^55 + 20 * q^57 + 16 * q^58 + 8 * q^60 + 4 * q^62 + 12 * q^65 - 4 * q^67 + 24 * q^68 + 12 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 28 * q^73 + 48 * q^74 - 4 * q^75 + 4 * q^77 - 4 * q^78 + 8 * q^79 - 4 * q^80 - 16 * q^81 + 8 * q^82 - 28 * q^83 - 8 * q^84 + 20 * q^85 - 4 * q^87 - 12 * q^88 - 40 * q^89 - 12 * q^90 + 16 * q^92 - 12 * q^93 - 4 * q^95 - 4 * q^96 - 8 * q^97 + 16 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−1.96195	+	1.96195i	−1.13274	+	1.13274i	−0.143014	+	0.989721i	$0.545680\pi$
$3$	−1.96195	+	1.96195i	−1.13274	+	1.13274i	−0.989721	+	0.143014i	$0.954320\pi$
$4$			1.00000i			0.500000i
$5$	−1.77462	+	1.36041i	−0.793635	+	0.608394i
$5$	−1.77462	+	1.36041i	−0.793635	+	0.608394i
$6$	2.77462			1.13274
$7$	−0.105561	+	0.105561i	−0.0398985	+	0.0398985i	−0.726775	−	0.686876i	$-0.758982\pi$
$7$	−0.105561	+	0.105561i	−0.0398985	+	0.0398985i	0.686876	+	0.726775i	$0.258982\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		−	4.69853i		−	1.56618i
$10$	2.21680	+	0.292893i	0.701015	+	0.0926210i
$11$		−	6.18884i		−	1.86600i	−0.359871	−	0.933002i	$-0.617179\pi$
$11$		−	6.18884i		−	1.86600i	0.359871	−	0.933002i	$-0.382821\pi$
$12$	−1.96195	−	1.96195i	−0.566368	−	0.566368i
$13$	−2.81835	+	2.81835i	−0.781669	+	0.781669i	−0.980112	−	0.198443i	$-0.936411\pi$
$13$	−2.81835	+	2.81835i	−0.781669	+	0.781669i	0.198443	+	0.980112i	$0.436411\pi$
$14$	0.149286			0.0398985
$15$	0.812668	−	6.15079i	0.209830	−	1.58813i
$16$	−1.00000			−0.250000
$17$	3.81267	−	3.81267i	0.924708	−	0.924708i	−0.0726497	−	0.997358i	$-0.523145\pi$
$17$	3.81267	−	3.81267i	0.924708	−	0.924708i	0.997358	+	0.0726497i	$0.0231455\pi$
$18$	−3.32236	+	3.32236i	−0.783089	+	0.783089i
$19$	−3.56350			−0.817523			−0.408761	−	0.912641i	$-0.634039\pi$
$19$	−3.56350			−0.817523			−0.408761	+	0.912641i	$0.634039\pi$
$20$	−1.36041	−	1.77462i	−0.304197	−	0.396818i
$21$		−	0.414214i		−	0.0903888i
$22$	−4.37617	+	4.37617i	−0.933002	+	0.933002i
$23$	−4.42793	+	1.84214i	−0.923286	+	0.384113i
$23$	−4.42793	+	1.84214i	−0.923286	+	0.384113i
$24$			2.77462i			0.566368i
$25$	1.29857	−	4.82843i	0.259715	−	0.965685i
$26$	3.98575			0.781669
$27$	3.33244	+	3.33244i	0.641329	+	0.641329i
$28$	−0.105561	−	0.105561i	−0.0199492	−	0.0199492i
$29$			0.693395i			0.128760i	0.997925	+	0.0643801i	$0.0205070\pi$
$29$			0.693395i			0.128760i	−0.997925	+	0.0643801i	$0.979493\pi$
$30$	−4.92391	+	3.77462i	−0.898979	+	0.689149i
$31$	−1.47605			−0.265106			−0.132553	−	0.991176i	$-0.542318\pi$
$31$	−1.47605			−0.265106			−0.132553	+	0.991176i	$0.542318\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	12.1422	+	12.1422i	2.11369	+	2.11369i
$34$	−5.39193			−0.924708
$35$	0.0437250	−	0.330939i	0.00739087	−	0.0559388i
$36$	4.69853			0.783089
$37$	−3.09335	+	3.09335i	−0.508544	+	0.508544i	−0.914079	−	0.405535i	$-0.867085\pi$
$37$	−3.09335	+	3.09335i	−0.508544	+	0.508544i	0.405535	+	0.914079i	$0.367085\pi$
$38$	2.51978	+	2.51978i	0.408761	+	0.408761i
$39$		−	11.0589i		−	1.77085i
$40$	−0.292893	+	2.21680i	−0.0463105	+	0.350507i
$41$	3.87011			0.604409			0.302204	−	0.953243i	$-0.402277\pi$
$41$	3.87011			0.604409			0.302204	+	0.953243i	$0.402277\pi$
$42$	−0.292893	+	0.292893i	−0.0451944	+	0.0451944i
$43$	−7.58289	−	7.58289i	−1.15638	−	1.15638i	−0.985248	−	0.171132i	$-0.945258\pi$
$43$	−7.58289	−	7.58289i	−1.15638	−	1.15638i	−0.171132	−	0.985248i	$-0.554742\pi$
$44$	6.18884			0.933002
$45$	6.39193	+	8.33812i	0.952852	+	1.24297i
$46$	4.43361	+	1.82843i	0.653699	+	0.269587i
$47$	−3.50970	−	3.50970i	−0.511942	−	0.511942i	0.403179	−	0.915121i	$-0.367905\pi$
$47$	−3.50970	−	3.50970i	−0.511942	−	0.511942i	−0.915121	+	0.403179i	$0.867905\pi$
$48$	1.96195	−	1.96195i	0.283184	−	0.283184i
$49$			6.97771i			0.996816i
$50$	−4.33244	+	2.49598i	−0.612700	+	0.352985i
$51$			14.9606i			2.09490i
$52$	−2.81835	−	2.81835i	−0.390835	−	0.390835i
$53$	−1.81630	−	1.81630i	−0.249488	−	0.249488i	0.571272	−	0.820761i	$-0.306450\pi$
$53$	−1.81630	−	1.81630i	−0.249488	−	0.249488i	−0.820761	+	0.571272i	$0.806450\pi$
$54$		−	4.71279i		−	0.641329i
$55$	8.41935	+	10.9829i	1.13527	+	1.48093i
$56$			0.149286i			0.0199492i
$57$	6.99143	−	6.99143i	0.926037	−	0.926037i
$58$	0.490304	−	0.490304i	0.0643801	−	0.0643801i
$59$		−	2.80827i		−	0.365605i	−0.983150	−	0.182803i	$-0.941483\pi$
$59$		−	2.80827i		−	0.365605i	0.983150	−	0.182803i	$-0.0585170\pi$
$60$	6.15079	+	0.812668i	0.794064	+	0.104915i
$61$			4.92680i			0.630813i	0.948957	+	0.315406i	$0.102141\pi$
$61$			4.92680i			0.630813i	−0.948957	+	0.315406i	$0.897859\pi$
$62$	1.04372	+	1.04372i	0.132553	+	0.132553i
$63$	0.495984	+	0.495984i	0.0624881	+	0.0624881i
$64$		−	1.00000i		−	0.125000i
$65$	1.16740	−	8.83561i	0.144798	−	1.09592i
$66$		−	17.1717i		−	2.11369i
$67$	−6.69050	+	6.69050i	−0.817375	+	0.817375i	−0.985727	−	0.168352i	$-0.946155\pi$
$67$	−6.69050	+	6.69050i	−0.817375	+	0.817375i	0.168352	+	0.985727i	$0.446155\pi$
$68$	3.81267	+	3.81267i	0.462354	+	0.462354i
$69$	5.07320	−	12.3016i	0.610741	−	1.48094i
$70$	−0.264927	+	0.203091i	−0.0316648	+	0.0242740i
$71$	−15.5544			−1.84597			−0.922983	−	0.384841i	$-0.874256\pi$
$71$	−15.5544			−1.84597			−0.922983	+	0.384841i	$0.874256\pi$
$72$	−3.32236	−	3.32236i	−0.391544	−	0.391544i
$73$	7.61108	−	7.61108i	0.890810	−	0.890810i	−0.103789	−	0.994599i	$-0.533097\pi$
$73$	7.61108	−	7.61108i	0.890810	−	0.890810i	0.994599	+	0.103789i	$0.0330968\pi$
$74$	4.37466			0.508544
$75$	6.92541	+	12.0209i	0.799678	+	1.38805i
$76$		−	3.56350i		−	0.408761i
$77$	0.653303	+	0.653303i	0.0744507	+	0.0744507i
$78$	−7.81985	+	7.81985i	−0.885424	+	0.885424i
$79$	8.97072			1.00929			0.504643	−	0.863328i	$-0.331624\pi$
$79$	8.97072			1.00929			0.504643	+	0.863328i	$0.331624\pi$
$80$	1.77462	−	1.36041i	0.198409	−	0.152098i
$81$	1.01939			0.113266
$82$	−2.73658	−	2.73658i	−0.302204	−	0.302204i
$83$	−0.0424449	−	0.0424449i	−0.00465894	−	0.00465894i	0.704773	−	0.709432i	$-0.251049\pi$
$83$	−0.0424449	−	0.0424449i	−0.00465894	−	0.00465894i	−0.709432	+	0.704773i	$0.751049\pi$
$84$	0.414214			0.0451944
$85$	−1.57926	+	11.9528i	−0.171295	+	1.29647i
$86$			10.7238i			1.15638i
$87$	−1.36041	−	1.36041i	−0.145851	−	0.145851i
$88$	−4.37617	−	4.37617i	−0.466501	−	0.466501i
$89$	−12.5485			−1.33014			−0.665068	−	0.746783i	$-0.731597\pi$
$89$	−12.5485			−1.33014			−0.665068	+	0.746783i	$0.731597\pi$
$90$	1.37617	−	10.4157i	0.145061	−	1.09791i
$91$		−	0.595018i		−	0.0623748i
$92$	−1.84214	−	4.42793i	−0.192056	−	0.461643i
$93$	2.89594	−	2.89594i	0.300295	−	0.300295i
$94$			4.96346i			0.511942i
$95$	6.32387	−	4.84782i	0.648815	−	0.497376i
$96$	−2.77462			−0.283184
$97$	−11.1223	+	11.1223i	−1.12930	+	1.12930i	−0.139005	+	0.990292i	$0.544390\pi$
$97$	−11.1223	+	11.1223i	−1.12930	+	1.12930i	−0.990292	+	0.139005i	$0.955610\pi$
$98$	4.93399	−	4.93399i	0.498408	−	0.498408i
$99$	−29.0784			−2.92249
$100$	4.82843	+	1.29857i	0.482843	+	0.129857i
$101$	−2.70066			−0.268726			−0.134363	−	0.990932i	$-0.542899\pi$
$101$	−2.70066			−0.268726			−0.134363	+	0.990932i	$0.542899\pi$
$102$	10.5787	−	10.5787i	1.04745	−	1.04745i
$103$	3.75597	+	3.75597i	0.370087	+	0.370087i	0.867509	−	0.497422i	$-0.165720\pi$
$103$	3.75597	+	3.75597i	0.370087	+	0.370087i	−0.497422	+	0.867509i	$0.665720\pi$
$104$			3.98575i			0.390835i
$105$	0.563500	+	0.735073i	0.0549920	+	0.0717358i
$106$			2.56864i			0.249488i
$107$	−1.03654	+	1.03654i	−0.100206	+	0.100206i	−0.755433	−	0.655226i	$-0.772573\pi$
$107$	−1.03654	+	1.03654i	−0.100206	+	0.100206i	0.655226	+	0.755433i	$0.272573\pi$
$108$	−3.33244	+	3.33244i	−0.320665	+	0.320665i
$109$	−8.14094			−0.779760			−0.389880	−	0.920866i	$-0.627484\pi$
$109$	−8.14094			−0.779760			−0.389880	+	0.920866i	$0.627484\pi$
$110$	1.81267	−	13.7194i	0.172831	−	1.30810i
$111$		−	12.1380i		−	1.15209i
$112$	0.105561	−	0.105561i	0.00997462	−	0.00997462i
$113$	−9.05091	−	9.05091i	−0.851438	−	0.851438i	0.138872	−	0.990310i	$-0.455652\pi$
$113$	−9.05091	−	9.05091i	−0.851438	−	0.851438i	−0.990310	+	0.138872i	$0.955652\pi$
$114$	−9.88737			−0.926037
$115$	5.35183	−	9.29289i	0.499061	−	0.866567i
$116$	−0.693395			−0.0643801
$117$	13.2421	+	13.2421i	1.22423	+	1.22423i
$118$	−1.98575	+	1.98575i	−0.182803	+	0.182803i
$119$			0.804942i			0.0737889i
$120$	−3.77462	−	4.92391i	−0.344574	−	0.449489i
$121$	−27.3017			−2.48197
$122$	3.48378	−	3.48378i	0.315406	−	0.315406i
$123$	−7.59297	+	7.59297i	−0.684635	+	0.684635i
$124$		−	1.47605i		−	0.132553i
$125$	4.26416	+	10.3352i	0.381398	+	0.924411i
$126$		−	0.701427i		−	0.0624881i
$127$	−4.88737	−	4.88737i	−0.433684	−	0.433684i	0.456196	−	0.889879i	$-0.349212\pi$
$127$	−4.88737	−	4.88737i	−0.433684	−	0.433684i	−0.889879	+	0.456196i	$0.849212\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	29.7546			2.61974
$130$	−7.07320	+	5.42225i	−0.620360	+	0.475562i
$131$	1.84055			0.160810			0.0804049	−	0.996762i	$-0.474379\pi$
$131$	1.84055			0.160810			0.0804049	+	0.996762i	$0.474379\pi$
$132$	−12.1422	+	12.1422i	−1.05684	+	1.05684i
$133$	0.376168	−	0.376168i	0.0326179	−	0.0326179i
$134$	9.46180			0.817375
$135$	−10.4473	−	1.38034i	−0.899162	−	0.118801i
$136$		−	5.39193i		−	0.462354i
$137$	6.40201	−	6.40201i	0.546960	−	0.546960i	−0.378600	−	0.925560i	$-0.623594\pi$
$137$	6.40201	−	6.40201i	0.546960	−	0.546960i	0.925560	+	0.378600i	$0.123594\pi$
$138$	−12.2858	+	5.11124i	−1.04584	+	0.435098i
$139$			4.51696i			0.383124i	0.981481	+	0.191562i	$0.0613552\pi$
$139$			4.51696i			0.383124i	−0.981481	+	0.191562i	$0.938645\pi$
$140$	0.330939	+	0.0437250i	0.0279694	+	0.00369544i
$141$	13.7717			1.15979
$142$	10.9986	+	10.9986i	0.922983	+	0.922983i
$143$	17.4423	+	17.4423i	1.45860	+	1.45860i
$144$			4.69853i			0.391544i
$145$	−0.943301	−	1.23051i	−0.0783369	−	0.102189i
$146$	−10.7637			−0.890810
$147$	−13.6900	−	13.6900i	−1.12913	−	1.12913i
$148$	−3.09335	−	3.09335i	−0.254272	−	0.254272i
$149$	7.64987			0.626701			0.313351	−	0.949637i	$-0.398548\pi$
$149$	7.64987			0.626701			0.313351	+	0.949637i	$0.398548\pi$
$150$	3.60305	−	13.3971i	0.294188	−	1.09387i
$151$	13.3919			1.08982			0.544910	−	0.838495i	$-0.316564\pi$
$151$	13.3919			1.08982			0.544910	+	0.838495i	$0.316564\pi$
$152$	−2.51978	+	2.51978i	−0.204381	+	0.204381i
$153$	−17.9139	−	17.9139i	−1.44826	−	1.44826i
$154$		−	0.923909i		−	0.0744507i
$155$	2.61943	−	2.00803i	0.210398	−	0.161289i
$156$	11.0589			0.885424
$157$	13.4366	−	13.4366i	1.07236	−	1.07236i	0.0751893	−	0.997169i	$-0.476044\pi$
$157$	13.4366	−	13.4366i	1.07236	−	1.07236i	0.997169	−	0.0751893i	$-0.0239561\pi$
$158$	−6.34326	−	6.34326i	−0.504643	−	0.504643i
$159$	7.12700			0.565208
$160$	−2.21680	−	0.292893i	−0.175254	−	0.0231552i
$161$	0.272959	−	0.661877i	0.0215122	−	0.0521632i
$162$	−0.720819	−	0.720819i	−0.0566329	−	0.0566329i
$163$	14.8711	−	14.8711i	1.16479	−	1.16479i	0.181379	−	0.983413i	$-0.441944\pi$
$163$	14.8711	−	14.8711i	1.16479	−	1.16479i	0.983413	−	0.181379i	$-0.0580559\pi$
$164$			3.87011i			0.302204i
$165$	−38.0662	−	5.02947i	−2.96345	−	0.391544i
$166$			0.0600262i			0.00465894i
$167$	6.01650	+	6.01650i	0.465570	+	0.465570i	0.900476	−	0.434906i	$-0.143218\pi$
$167$	6.01650	+	6.01650i	0.465570	+	0.465570i	−0.434906	+	0.900476i	$0.643218\pi$
$168$	−0.292893	−	0.292893i	−0.0225972	−	0.0225972i
$169$		−	2.88617i		−	0.222013i
$170$	9.56864	−	7.33523i	0.733881	−	0.562586i
$171$			16.7432i			1.28039i
$172$	7.58289	−	7.58289i	0.578190	−	0.578190i
$173$	1.92541	−	1.92541i	0.146387	−	0.146387i	−0.630115	−	0.776502i	$-0.716992\pi$
$173$	1.92541	−	1.92541i	0.146387	−	0.146387i	0.776502	+	0.630115i	$0.216992\pi$
$174$			1.92391i			0.145851i
$175$	0.372617	+	0.646775i	0.0281672	+	0.0488916i
$176$			6.18884i			0.466501i
$177$	5.50970	+	5.50970i	0.414134	+	0.414134i
$178$	8.87311	+	8.87311i	0.665068	+	0.665068i
$179$			18.6793i			1.39615i	0.716023	+	0.698077i	$0.245960\pi$
$179$			18.6793i			1.39615i	−0.716023	+	0.698077i	$0.754040\pi$
$180$	−8.33812	+	6.39193i	−0.621487	+	0.476426i
$181$			9.76326i			0.725698i	0.931848	+	0.362849i	$0.118196\pi$
$181$			9.76326i			0.725698i	−0.931848	+	0.362849i	$0.881804\pi$
$182$	−0.420741	+	0.420741i	−0.0311874	+	0.0311874i
$183$	−9.66617	−	9.66617i	−0.714544	−	0.714544i
$184$	−1.82843	+	4.43361i	−0.134793	+	0.326850i
$185$	1.28131	−	9.69777i	0.0942037	−	0.712994i
$186$	−4.09548			−0.300295
$187$	−23.5960	−	23.5960i	−1.72551	−	1.72551i
$188$	3.50970	−	3.50970i	0.255971	−	0.255971i
$189$	−0.703555			−0.0511761
$190$	−7.89958	−	1.04372i	−0.573095	−	0.0757198i
$191$		−	12.9262i		−	0.935304i	−0.883913	−	0.467652i	$-0.845100\pi$
$191$		−	12.9262i		−	0.935304i	0.883913	−	0.467652i	$-0.154900\pi$
$192$	1.96195	+	1.96195i	0.141592	+	0.141592i
$193$	6.69263	−	6.69263i	0.481746	−	0.481746i	−0.423943	−	0.905689i	$-0.639354\pi$
$193$	6.69263	−	6.69263i	0.481746	−	0.481746i	0.905689	+	0.423943i	$0.139354\pi$
$194$	15.7293			1.12930
$195$	15.0447	+	19.6255i	1.07737	+	1.40541i
$196$	−6.97771			−0.498408
$197$	−3.22174	−	3.22174i	−0.229540	−	0.229540i	0.582961	−	0.812500i	$-0.301894\pi$
$197$	−3.22174	−	3.22174i	−0.229540	−	0.229540i	−0.812500	+	0.582961i	$0.801894\pi$
$198$	20.5616	+	20.5616i	1.46125	+	1.46125i
$199$	10.7052			0.758872			0.379436	−	0.925218i	$-0.376118\pi$
$199$	10.7052			0.758872			0.379436	+	0.925218i	$0.376118\pi$
$200$	−2.49598	−	4.33244i	−0.176493	−	0.306350i
$201$		−	26.2529i		−	1.85174i
$202$	1.90966	+	1.90966i	0.134363	+	0.134363i
$203$	−0.0731958	−	0.0731958i	−0.00513734	−	0.00513734i
$204$	−14.9606			−1.04745
$205$	−6.86798	+	5.26493i	−0.479680	+	0.367718i
$206$		−	5.31174i		−	0.370087i
$207$	8.65535	+	20.8048i	0.601588	+	1.44603i
$208$	2.81835	−	2.81835i	0.195417	−	0.195417i
$209$			22.0539i			1.52550i
$210$	0.121320	−	0.918230i	0.00837190	−	0.0633639i
$211$	19.7557			1.36004			0.680018	−	0.733195i	$-0.261972\pi$
$211$	19.7557			1.36004			0.680018	+	0.733195i	$0.261972\pi$
$212$	1.81630	−	1.81630i	0.124744	−	0.124744i
$213$	30.5170	−	30.5170i	2.09099	−	2.09099i
$214$	1.46589			0.100206
$215$	23.7726	+	3.14094i	1.62128	+	0.214210i
$216$	4.71279			0.320665
$217$	0.155814	−	0.155814i	0.0105773	−	0.0105773i
$218$	5.75651	+	5.75651i	0.389880	+	0.389880i
$219$			29.8652i			2.01810i
$220$	−10.9829	+	8.41935i	−0.740464	+	0.567633i
$221$			21.4909i			1.44563i
$222$	−8.58289	+	8.58289i	−0.576046	+	0.576046i
$223$	−4.08822	+	4.08822i	−0.273767	+	0.273767i	−0.830615	−	0.556847i	$-0.812011\pi$
$223$	−4.08822	+	4.08822i	−0.273767	+	0.273767i	0.556847	+	0.830615i	$0.312011\pi$
$224$	−0.149286			−0.00997462
$225$	−22.6865	−	6.10139i	−1.51243	−	0.406759i
$226$			12.7999i			0.851438i
$227$	−17.0662	+	17.0662i	−1.13272	+	1.13272i	−0.143001	+	0.989722i	$0.545675\pi$
$227$	−17.0662	+	17.0662i	−1.13272	+	1.13272i	−0.989722	+	0.143001i	$0.954325\pi$
$228$	6.99143	+	6.99143i	0.463018	+	0.463018i
$229$	−9.95968			−0.658154			−0.329077	−	0.944303i	$-0.606738\pi$
$229$	−9.95968			−0.658154			−0.329077	+	0.944303i	$0.606738\pi$
$230$	−10.3554	+	2.78675i	−0.682814	+	0.183753i
$231$	−2.56350			−0.168666
$232$	0.490304	+	0.490304i	0.0321900	+	0.0321900i
$233$	−6.85886	+	6.85886i	−0.449339	+	0.449339i	−0.895135	−	0.445796i	$-0.852921\pi$
$233$	−6.85886	+	6.85886i	−0.449339	+	0.449339i	0.445796	+	0.895135i	$0.352921\pi$
$234$		−	18.7272i		−	1.22423i
$235$	11.0030	+	1.45376i	0.717757	+	0.0948331i
$236$	2.80827			0.182803
$237$	−17.6002	+	17.6002i	−1.14325	+	1.14325i
$238$	0.569180	−	0.569180i	0.0368944	−	0.0368944i
$239$		−	7.58956i		−	0.490928i	−0.969406	−	0.245464i	$-0.921060\pi$
$239$		−	7.58956i		−	0.490928i	0.969406	−	0.245464i	$-0.0789403\pi$
$240$	−0.812668	+	6.15079i	−0.0524575	+	0.397032i
$241$			12.4278i			0.800546i	0.916396	+	0.400273i	$0.131085\pi$
$241$			12.4278i			0.800546i	−0.916396	+	0.400273i	$0.868915\pi$
$242$	19.3052	+	19.3052i	1.24099	+	1.24099i
$243$	−11.9973	+	11.9973i	−0.769629	+	0.769629i
$244$	−4.92680			−0.315406
$245$	−9.49255	−	12.3828i	−0.606457	−	0.791109i
$246$	10.7381			0.684635
$247$	10.0432	−	10.0432i	0.639032	−	0.639032i
$248$	−1.04372	+	1.04372i	−0.0662766	+	0.0662766i
$249$	0.166550			0.0105547
$250$	4.29289	−	10.3233i	0.271506	−	0.652904i
$251$			11.5592i			0.729613i	0.931083	+	0.364807i	$0.118865\pi$
$251$			11.5592i			0.729613i	−0.931083	+	0.364807i	$0.881135\pi$
$252$	−0.495984	+	0.495984i	−0.0312440	+	0.0312440i
$253$	11.4007	+	27.4037i	0.716756	+	1.72286i
$254$			6.91178i			0.433684i
$255$	−20.3525	−	26.5494i	−1.27452	−	1.66259i
$256$	1.00000			0.0625000
$257$	3.23975	+	3.23975i	0.202090	+	0.202090i	0.800895	−	0.598805i	$-0.204358\pi$
$257$	3.23975	+	3.23975i	0.202090	+	0.202090i	−0.598805	+	0.800895i	$0.704358\pi$
$258$	−21.0397	−	21.0397i	−1.30987	−	1.30987i
$259$		−	0.653078i		−	0.0405803i
$260$	8.83561	+	1.16740i	0.547961	+	0.0723989i
$261$	3.25794			0.201661
$262$	−1.30147	−	1.30147i	−0.0804049	−	0.0804049i
$263$	0.234147	+	0.234147i	0.0144381	+	0.0144381i	0.714289	−	0.699851i	$-0.246750\pi$
$263$	0.234147	+	0.234147i	0.0144381	+	0.0144381i	−0.699851	+	0.714289i	$0.746750\pi$
$264$	17.1717			1.05684
$265$	5.69416	+	0.752336i	0.349790	+	0.0462157i
$266$	−0.531982			−0.0326179
$267$	24.6195	−	24.6195i	1.50669	−	1.50669i
$268$	−6.69050	−	6.69050i	−0.408687	−	0.408687i
$269$		−	23.9859i		−	1.46244i	−0.682140	−	0.731222i	$-0.738950\pi$
$269$		−	23.9859i		−	1.46244i	0.682140	−	0.731222i	$-0.261050\pi$
$270$	6.41132	+	8.36342i	0.390180	+	0.508981i
$271$	−20.0001			−1.21492			−0.607460	−	0.794350i	$-0.707812\pi$
$271$	−20.0001			−1.21492			−0.607460	+	0.794350i	$0.707812\pi$
$272$	−3.81267	+	3.81267i	−0.231177	+	0.231177i
$273$	1.16740	+	1.16740i	0.0706541	+	0.0706541i
$274$	−9.05380			−0.546960
$275$	−29.8823	−	8.03666i	−1.80197	−	0.484629i
$276$	12.3016	+	5.07320i	0.740468	+	0.305371i
$277$	17.0741	+	17.0741i	1.02588	+	1.02588i	0.999656	+	0.0262258i	$0.00834890\pi$
$277$	17.0741	+	17.0741i	1.02588	+	1.02588i	0.0262258	+	0.999656i	$0.491651\pi$
$278$	3.19397	−	3.19397i	0.191562	−	0.191562i
$279$			6.93527i			0.415204i
$280$	−0.203091	−	0.264927i	−0.0121370	−	0.0158324i
$281$		−	15.8489i		−	0.945466i	−0.881206	−	0.472733i	$-0.843267\pi$
$281$		−	15.8489i		−	0.945466i	0.881206	−	0.472733i	$-0.156733\pi$
$282$	−9.73808	−	9.73808i	−0.579894	−	0.579894i
$283$	−13.5830	−	13.5830i	−0.807426	−	0.807426i	0.176818	−	0.984244i	$-0.443420\pi$
$283$	−13.5830	−	13.5830i	−0.807426	−	0.807426i	−0.984244	+	0.176818i	$0.943420\pi$
$284$		−	15.5544i		−	0.922983i
$285$	−2.89594	+	21.9183i	−0.171541	+	1.29833i
$286$		−	24.6671i		−	1.45860i
$287$	−0.408534	+	0.408534i	−0.0241150	+	0.0241150i
$288$	3.32236	−	3.32236i	0.195772	−	0.195772i
$289$		−	12.0729i		−	0.710169i
$290$	−0.203091	+	1.53712i	−0.0119259	+	0.0902628i
$291$		−	43.6428i		−	2.55839i
$292$	7.61108	+	7.61108i	0.445405	+	0.445405i
$293$	−14.0203	−	14.0203i	−0.819073	−	0.819073i	0.166901	−	0.985974i	$-0.446624\pi$
$293$	−14.0203	−	14.0203i	−0.819073	−	0.819073i	−0.985974	+	0.166901i	$0.946624\pi$
$294$			19.3605i			1.12913i
$295$	3.82039	+	4.98362i	0.222432	+	0.290157i
$296$			4.37466i			0.254272i
$297$	20.6239	−	20.6239i	1.19672	−	1.19672i
$298$	−5.40927	−	5.40927i	−0.313351	−	0.313351i
$299$	7.28765	−	17.6712i	0.421455	−	1.02195i
$300$	−12.0209	+	6.92541i	−0.694027	+	0.399839i
$301$	1.60092			0.0922756
$302$	−9.46952	−	9.46952i	−0.544910	−	0.544910i
$303$	5.29857	−	5.29857i	0.304395	−	0.304395i
$304$	3.56350			0.204381
$305$	−6.70247	−	8.74322i	−0.383782	−	0.500635i
$306$			25.3341i			1.44826i
$307$	−16.1905	−	16.1905i	−0.924038	−	0.924038i	0.0732738	−	0.997312i	$-0.476655\pi$
$307$	−16.1905	−	16.1905i	−0.924038	−	0.924038i	−0.997312	+	0.0732738i	$0.976655\pi$
$308$	−0.653303	+	0.653303i	−0.0372254	+	0.0372254i
$309$	−14.7381			−0.838420
$310$	−3.27211	−	0.432325i	−0.185843	−	0.0245544i
$311$	−14.6602			−0.831303			−0.415651	−	0.909524i	$-0.636446\pi$
$311$	−14.6602			−0.831303			−0.415651	+	0.909524i	$0.636446\pi$
$312$	−7.81985	−	7.81985i	−0.442712	−	0.442712i
$313$	2.22666	+	2.22666i	0.125858	+	0.125858i	0.767230	−	0.641372i	$-0.221634\pi$
$313$	2.22666	+	2.22666i	0.125858	+	0.125858i	−0.641372	+	0.767230i	$0.721634\pi$
$314$	−19.0022			−1.07236
$315$	−1.55493	−	0.205443i	−0.0876101	−	0.0115754i
$316$			8.97072i			0.504643i
$317$	16.0763	+	16.0763i	0.902934	+	0.902934i	0.995689	−	0.0927548i	$-0.0295673\pi$
$317$	16.0763	+	16.0763i	0.902934	+	0.902934i	−0.0927548	+	0.995689i	$0.529567\pi$
$318$	−5.03955	−	5.03955i	−0.282604	−	0.282604i
$319$	4.29131			0.240267
$320$	1.36041	+	1.77462i	0.0760492	+	0.0992044i
$321$		−	4.06729i		−	0.227014i
$322$	−0.661029	+	0.275006i	−0.0368377	+	0.0153255i
$323$	−13.5864	+	13.5864i	−0.755970	+	0.755970i
$324$			1.01939i			0.0566329i
$325$	9.94836	+	17.2680i	0.551836	+	0.957857i
$326$	−21.0309			−1.16479
$327$	15.9721	−	15.9721i	0.883262	−	0.883262i
$328$	2.73658	−	2.73658i	0.151102	−	0.151102i
$329$	0.740977			0.0408514
$330$	23.3605	+	30.4733i	1.28595	+	1.67750i
$331$	0.123673			0.00679768			0.00339884	−	0.999994i	$-0.498918\pi$
$331$	0.123673			0.00679768			0.00339884	+	0.999994i	$0.498918\pi$
$332$	0.0424449	−	0.0424449i	0.00232947	−	0.00232947i
$333$	14.5342	+	14.5342i	0.796471	+	0.796471i
$334$		−	8.50861i		−	0.465570i
$335$	2.77130	−	20.9749i	0.151412	−	1.14598i
$336$			0.414214i			0.0225972i
$337$	−4.62039	+	4.62039i	−0.251689	+	0.251689i	−0.821663	−	0.569974i	$-0.806953\pi$
$337$	−4.62039	+	4.62039i	−0.251689	+	0.251689i	0.569974	+	0.821663i	$0.306953\pi$
$338$	−2.04083	+	2.04083i	−0.111007	+	0.111007i
$339$	35.5149			1.92891
$340$	−11.9528	−	1.57926i	−0.648234	−	0.0856473i
$341$			9.13503i			0.494690i
$342$	11.8392	−	11.8392i	0.640193	−	0.640193i
$343$	−1.47551	−	1.47551i	−0.0796699	−	0.0796699i
$344$	−10.7238			−0.578190
$345$	7.73218	+	28.7323i	0.416286	+	1.54689i
$346$	−2.72295			−0.146387
$347$	16.5306	+	16.5306i	0.887409	+	0.887409i	0.994274	−	0.106865i	$-0.0340812\pi$
$347$	16.5306	+	16.5306i	0.887409	+	0.887409i	−0.106865	+	0.994274i	$0.534081\pi$
$348$	1.36041	−	1.36041i	0.0729256	−	0.0729256i
$349$			4.22674i			0.226252i	0.993581	+	0.113126i	$0.0360864\pi$
$349$			4.22674i			0.226252i	−0.993581	+	0.113126i	$0.963914\pi$
$350$	0.193859	−	0.720819i	0.0103622	−	0.0385294i
$351$	−18.7840			−1.00261
$352$	4.37617	−	4.37617i	0.233251	−	0.233251i
$353$	−18.3564	+	18.3564i	−0.977014	+	0.977014i	−0.999742	−	0.0227275i	$-0.992765\pi$
$353$	−18.3564	+	18.3564i	−0.977014	+	0.977014i	0.0227275	+	0.999742i	$0.492765\pi$
$354$		−	7.79189i		−	0.414134i
$355$	27.6032	−	21.1603i	1.46502	−	1.12307i
$356$		−	12.5485i		−	0.665068i
$357$	−1.57926	−	1.57926i	−0.0835832	−	0.0835832i
$358$	13.2082	−	13.2082i	0.698077	−	0.698077i
$359$	−31.3037			−1.65214			−0.826072	−	0.563564i	$-0.809430\pi$
$359$	−31.3037			−1.65214			−0.826072	+	0.563564i	$0.809430\pi$
$360$	10.4157	+	1.37617i	0.548957	+	0.0725304i
$361$	−6.30147			−0.331656
$362$	6.90367	−	6.90367i	0.362849	−	0.362849i
$363$	53.5647	−	53.5647i	2.81142	−	2.81142i
$364$	0.595018			0.0311874
$365$	−3.15261	+	23.8610i	−0.165015	+	1.24894i
$366$			13.6700i			0.714544i
$367$	1.68837	−	1.68837i	0.0881323	−	0.0881323i	−0.661666	−	0.749799i	$-0.730150\pi$
$367$	1.68837	−	1.68837i	0.0881323	−	0.0881323i	0.749799	+	0.661666i	$0.230150\pi$
$368$	4.42793	−	1.84214i	0.230822	−	0.0960281i
$369$		−	18.1838i		−	0.946612i
$370$	−7.76338	+	5.95133i	−0.403599	+	0.309395i
$371$	0.383463			0.0199084
$372$	2.89594	+	2.89594i	0.150148	+	0.150148i
$373$	−23.4509	−	23.4509i	−1.21424	−	1.21424i	−0.969619	−	0.244621i	$-0.921336\pi$
$373$	−23.4509	−	23.4509i	−1.21424	−	1.21424i	−0.244621	−	0.969619i	$-0.578664\pi$
$374$			33.3698i			1.72551i
$375$	−28.6433	−	11.9112i	−1.47914	−	0.615090i
$376$	−4.96346			−0.255971
$377$	−1.95423	−	1.95423i	−0.100648	−	0.100648i
$378$	0.497489	+	0.497489i	0.0255881	+	0.0255881i
$379$	18.3477			0.942457			0.471228	−	0.882011i	$-0.343811\pi$
$379$	18.3477			0.942457			0.471228	+	0.882011i	$0.343811\pi$
$380$	4.84782	+	6.32387i	0.248688	+	0.324408i
$381$	19.1776			0.982498
$382$	−9.14017	+	9.14017i	−0.467652	+	0.467652i
$383$	3.29934	+	3.29934i	0.168588	+	0.168588i	0.786359	−	0.617770i	$-0.211964\pi$
$383$	3.29934	+	3.29934i	0.168588	+	0.168588i	−0.617770	+	0.786359i	$0.711964\pi$
$384$		−	2.77462i		−	0.141592i
$385$	−2.04812	−	0.270607i	−0.104382	−	0.0137914i
$386$	−9.46481			−0.481746
$387$	−35.6285	+	35.6285i	−1.81110	+	1.81110i
$388$	−11.1223	−	11.1223i	−0.564648	−	0.564648i
$389$	−13.6031			−0.689702			−0.344851	−	0.938657i	$-0.612071\pi$
$389$	−13.6031			−0.689702			−0.344851	+	0.938657i	$0.612071\pi$
$390$	3.23909	−	24.5155i	0.164018	−	1.24139i
$391$	−9.85875	+	23.9057i	−0.498578	+	1.20896i
$392$	4.93399	+	4.93399i	0.249204	+	0.249204i
$393$	−3.61108	+	3.61108i	−0.182155	+	0.182155i
$394$			4.55623i			0.229540i
$395$	−15.9197	+	12.2039i	−0.801005	+	0.614043i
$396$		−	29.0784i		−	1.46125i
$397$	5.91297	+	5.91297i	0.296763	+	0.296763i	0.839745	−	0.542981i	$-0.182705\pi$
$397$	5.91297	+	5.91297i	0.296763	+	0.296763i	−0.542981	+	0.839745i	$0.682705\pi$
$398$	−7.56972	−	7.56972i	−0.379436	−	0.379436i
$399$			1.47605i			0.0738949i
$400$	−1.29857	+	4.82843i	−0.0649286	+	0.241421i
$401$		−	0.599926i		−	0.0299589i	−0.999888	−	0.0149794i	$-0.995232\pi$
$401$		−	0.599926i		−	0.0299589i	0.999888	−	0.0149794i	$-0.00476828\pi$
$402$	−18.5636	+	18.5636i	−0.925869	+	0.925869i
$403$	4.16002	−	4.16002i	0.207225	−	0.207225i
$404$		−	2.70066i		−	0.134363i
$405$	−1.80904	+	1.38679i	−0.0898917	+	0.0689101i
$406$			0.103514i			0.00513734i
$407$	19.1443	+	19.1443i	0.948946	+	0.948946i
$408$	10.5787	+	10.5787i	0.523725	+	0.523725i
$409$			2.84313i			0.140584i	0.997526	+	0.0702919i	$0.0223931\pi$
$409$			2.84313i			0.140584i	−0.997526	+	0.0702919i	$0.977607\pi$
$410$	8.57926	+	1.13353i	0.423699	+	0.0559809i
$411$			25.1209i			1.23912i
$412$	−3.75597	+	3.75597i	−0.185043	+	0.185043i
$413$	0.296445	+	0.296445i	0.0145871	+	0.0145871i
$414$	8.59092	−	20.8314i	0.422221	−	1.02381i
$415$	0.133066	+	0.0175813i	0.00653196	+	0.000863030i
$416$	−3.98575			−0.195417
$417$	−8.86207	−	8.86207i	−0.433978	−	0.433978i
$418$	15.5945	−	15.5945i	0.762751	−	0.762751i
$419$	9.57558			0.467798			0.233899	−	0.972261i	$-0.424852\pi$
$419$	9.57558			0.467798			0.233899	+	0.972261i	$0.424852\pi$
$420$	−0.735073	+	0.563500i	−0.0358679	+	0.0274960i
$421$		−	26.0781i		−	1.27097i	−0.772113	−	0.635485i	$-0.780800\pi$
$421$		−	26.0781i		−	1.27097i	0.772113	−	0.635485i	$-0.219200\pi$
$422$	−13.9694	−	13.9694i	−0.680018	−	0.680018i
$423$	−16.4904	+	16.4904i	−0.801792	+	0.801792i
$424$	−2.56864			−0.124744
$425$	−13.4582	−	23.3602i	−0.652817	−	1.13314i
$426$	−43.1575			−2.09099
$427$	−0.520081	−	0.520081i	−0.0251685	−	0.0251685i
$428$	−1.03654	−	1.03654i	−0.0501031	−	0.0501031i
$429$	−68.4420			−3.30441
$430$	−14.5888	−	19.0308i	−0.703534	−	0.917744i
$431$			31.5000i			1.51730i	0.651498	+	0.758650i	$0.274141\pi$
$431$			31.5000i			1.51730i	−0.651498	+	0.758650i	$0.725859\pi$
$432$	−3.33244	−	3.33244i	−0.160332	−	0.160332i
$433$	19.1818	+	19.1818i	0.921817	+	0.921817i	0.997158	−	0.0753410i	$-0.0240045\pi$
$433$	19.1818	+	19.1818i	0.921817	+	0.921817i	−0.0753410	+	0.997158i	$0.524005\pi$
$434$	−0.220354			−0.0105773
$435$	4.26493	+	0.563500i	0.204488	+	0.0270178i
$436$		−	8.14094i		−	0.389880i
$437$	15.7789	−	6.56446i	0.754808	−	0.314021i
$438$	21.1179	−	21.1179i	1.00905	−	1.00905i
$439$			27.6042i			1.31748i	0.752372	+	0.658738i	$0.228910\pi$
$439$			27.6042i			1.31748i	−0.752372	+	0.658738i	$0.771090\pi$
$440$	13.7194	+	1.81267i	0.654048	+	0.0864156i
$441$	32.7850			1.56119
$442$	15.1963	−	15.1963i	0.722816	−	0.722816i
$443$	8.31532	−	8.31532i	0.395073	−	0.395073i	−0.481418	−	0.876491i	$-0.659878\pi$
$443$	8.31532	−	8.31532i	0.395073	−	0.395073i	0.876491	+	0.481418i	$0.159878\pi$
$444$	12.1380			0.576046
$445$	22.2688	−	17.0711i	1.05564	−	0.809246i
$446$	5.78161			0.273767
$447$	−15.0087	+	15.0087i	−0.709887	+	0.709887i
$448$	0.105561	+	0.105561i	0.00498731	+	0.00498731i
$449$		−	22.1250i		−	1.04414i	−0.852901	−	0.522072i	$-0.825159\pi$
$449$		−	22.1250i		−	1.04414i	0.852901	−	0.522072i	$-0.174841\pi$
$450$	11.7275	+	20.3561i	0.552838	+	0.959597i
$451$		−	23.9514i		−	1.12783i
$452$	9.05091	−	9.05091i	0.425719	−	0.425719i
$453$	−26.2744	+	26.2744i	−1.23448	+	1.23448i
$454$	24.1353			1.13272
$455$	0.809468	+	1.05593i	0.0379484	+	0.0495029i
$456$		−	9.88737i		−	0.463018i
$457$	5.81931	−	5.81931i	0.272216	−	0.272216i	−0.557776	−	0.829992i	$-0.688345\pi$
$457$	5.81931	−	5.81931i	0.272216	−	0.272216i	0.829992	+	0.557776i	$0.188345\pi$
$458$	7.04256	+	7.04256i	0.329077	+	0.329077i
$459$	25.4110			1.18608
$460$	9.29289	+	5.35183i	0.433283	+	0.249531i
$461$	−4.95937			−0.230981			−0.115490	−	0.993309i	$-0.536844\pi$
$461$	−4.95937			−0.230981			−0.115490	+	0.993309i	$0.536844\pi$
$462$	1.81267	+	1.81267i	0.0843330	+	0.0843330i
$463$	1.46392	−	1.46392i	0.0680343	−	0.0680343i	−0.672271	−	0.740305i	$-0.734681\pi$
$463$	1.46392	−	1.46392i	0.0680343	−	0.0680343i	0.740305	+	0.672271i	$0.234681\pi$
$464$		−	0.693395i		−	0.0321900i
$465$	−1.19954	+	9.07888i	−0.0556273	+	0.421023i
$466$	9.69989			0.449339
$467$	17.9737	−	17.9737i	0.831725	−	0.831725i	−0.156027	−	0.987753i	$-0.549869\pi$
$467$	17.9737	−	17.9737i	0.831725	−	0.831725i	0.987753	+	0.156027i	$0.0498688\pi$
$468$	−13.2421	+	13.2421i	−0.612116	+	0.612116i
$469$		−	1.41252i		−	0.0652240i
$470$	−6.75234	−	8.80827i	−0.311462	−	0.406295i
$471$			52.7241i			2.42940i
$472$	−1.98575	−	1.98575i	−0.0914014	−	0.0914014i
$473$	−46.9293	+	46.9293i	−2.15781	+	2.15781i
$474$	24.8904			1.14325
$475$	−4.62746	+	17.2061i	−0.212323	+	0.789470i
$476$	−0.804942			−0.0368944
$477$	−8.53395	+	8.53395i	−0.390743	+	0.390743i
$478$	−5.36663	+	5.36663i	−0.245464	+	0.245464i
$479$	−30.1342			−1.37687			−0.688433	−	0.725300i	$-0.741701\pi$
$479$	−30.1342			−1.37687			−0.688433	+	0.725300i	$0.741701\pi$
$480$	4.92391	−	3.77462i	0.224745	−	0.172287i
$481$		−	17.4363i		−	0.795027i
$482$	8.78779	−	8.78779i	0.400273	−	0.400273i
$483$	0.763039	+	1.83411i	0.0347195	+	0.0834547i
$484$		−	27.3017i		−	1.24099i
$485$	4.60700	−	34.8687i	0.209193	−	1.58331i
$486$	16.9668			0.769629
$487$	−6.98711	−	6.98711i	−0.316616	−	0.316616i	0.530850	−	0.847466i	$-0.321873\pi$
$487$	−6.98711	−	6.98711i	−0.316616	−	0.316616i	−0.847466	+	0.530850i	$0.821873\pi$
$488$	3.48378	+	3.48378i	0.157703	+	0.157703i
$489$			58.3527i			2.63880i
$490$	−2.04372	+	15.4682i	−0.0923261	+	0.698783i
$491$	21.2796			0.960334			0.480167	−	0.877177i	$-0.340576\pi$
$491$	21.2796			0.960334			0.480167	+	0.877177i	$0.340576\pi$
$492$	−7.59297	−	7.59297i	−0.342318	−	0.342318i
$493$	2.64368	+	2.64368i	0.119066	+	0.119066i
$494$	−14.2032			−0.639032
$495$	51.6033	−	39.5586i	2.31939	−	1.77803i
$496$	1.47605			0.0662766
$497$	1.64194	−	1.64194i	0.0736512	−	0.0736512i
$498$	−0.117769	−	0.117769i	−0.00527734	−	0.00527734i
$499$			0.978439i			0.0438010i	0.999760	+	0.0219005i	$0.00697170\pi$
$499$			0.978439i			0.0438010i	−0.999760	+	0.0219005i	$0.993028\pi$
$500$	−10.3352	+	4.26416i	−0.462205	+	0.190699i
$501$	−23.6082			−1.05474
$502$	8.17362	−	8.17362i	0.364807	−	0.364807i
$503$	26.9959	+	26.9959i	1.20369	+	1.20369i	0.973036	+	0.230653i	$0.0740864\pi$
$503$	26.9959	+	26.9959i	1.20369	+	1.20369i	0.230653	+	0.973036i	$0.425914\pi$
$504$	0.701427			0.0312440
$505$	4.79265	−	3.67400i	0.213270	−	0.163491i
$506$	11.3158	−	27.4389i	0.503050	−	1.21981i
$507$	5.66253	+	5.66253i	0.251482	+	0.251482i
$508$	4.88737	−	4.88737i	0.216842	−	0.216842i
$509$		−	33.7275i		−	1.49495i	−0.664292	−	0.747474i	$-0.731267\pi$
$509$		−	33.7275i		−	1.49495i	0.664292	−	0.747474i	$-0.268733\pi$
$510$	−4.38185	+	33.1646i	−0.194031	+	1.46855i
$511$			1.60687i			0.0710839i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−11.8752	−	11.8752i	−0.524301	−	0.524301i
$514$		−	4.58169i		−	0.202090i
$515$	−11.7751	−	1.55577i	−0.518872	−	0.0685556i
$516$			29.7546i			1.30987i
$517$	−21.7209	+	21.7209i	−0.955286	+	0.955286i
$518$	−0.461796	+	0.461796i	−0.0202901	+	0.0202901i
$519$			7.55515i			0.331634i
$520$	−5.42225	−	7.07320i	−0.237781	−	0.310180i
$521$			0.314475i			0.0137774i	0.999976	+	0.00688871i	$0.00219276\pi$
$521$			0.314475i			0.0137774i	−0.999976	+	0.00688871i	$0.997807\pi$
$522$	−2.30371	−	2.30371i	−0.100831	−	0.100831i
$523$	22.7188	+	22.7188i	0.993424	+	0.993424i	0.999979	−	0.00655453i	$-0.00208639\pi$
$523$	22.7188	+	22.7188i	0.993424	+	0.993424i	−0.00655453	+	0.999979i	$0.502086\pi$
$524$			1.84055i			0.0804049i
$525$	−2.00000	−	0.537886i	−0.0872872	−	0.0234753i
$526$		−	0.331134i		−	0.0144381i
$527$	−5.62769	+	5.62769i	−0.245146	+	0.245146i
$528$	−12.1422	−	12.1422i	−0.528422	−	0.528422i
$529$	16.2130	−	16.3137i	0.704915	−	0.709292i
$530$	−3.49440	−	4.55836i	−0.151787	−	0.198003i
$531$	−13.1947			−0.572603
$532$	0.376168	+	0.376168i	0.0163090	+	0.0163090i
$533$	−10.9073	+	10.9073i	−0.472448	+	0.472448i
$534$	−34.8173			−1.50669
$535$	0.429349	−	3.24959i	0.0185624	−	0.140492i
$536$			9.46180i			0.408687i
$537$	−36.6479	−	36.6479i	−1.58147	−	1.58147i
$538$	−16.9606	+	16.9606i	−0.731222	+	0.731222i
$539$	43.1839			1.86006
$540$	1.38034	−	10.4473i	0.0594005	−	0.449581i
$541$	8.40465			0.361344			0.180672	−	0.983543i	$-0.442173\pi$
$541$	8.40465			0.361344			0.180672	+	0.983543i	$0.442173\pi$
$542$	14.1422	+	14.1422i	0.607460	+	0.607460i
$543$	−19.1551	−	19.1551i	−0.822023	−	0.822023i
$544$	5.39193			0.231177
$545$	14.4471	−	11.0750i	0.618845	−	0.474401i
$546$		−	1.65095i		−	0.0706541i
$547$	−6.29772	−	6.29772i	−0.269271	−	0.269271i	0.559535	−	0.828807i	$-0.310980\pi$
$547$	−6.29772	−	6.29772i	−0.269271	−	0.269271i	−0.828807	+	0.559535i	$0.810980\pi$
$548$	6.40201	+	6.40201i	0.273480	+	0.273480i
$549$	23.1487			0.987965
$550$	15.4472	+	26.8128i	0.658672	+	1.14330i
$551$		−	2.47091i		−	0.105264i
$552$	−5.11124	−	12.2858i	−0.217549	−	0.522919i
$553$	−0.946963	+	0.946963i	−0.0402690	+	0.0402690i
$554$		−	24.1464i		−	1.02588i
$555$	16.5127	+	21.5404i	0.700925	+	0.914341i
$556$	−4.51696			−0.191562
$557$	−11.4051	+	11.4051i	−0.483249	+	0.483249i	−0.906168	−	0.422918i	$-0.861006\pi$
$557$	−11.4051	+	11.4051i	−0.483249	+	0.483249i	0.422918	+	0.906168i	$0.361006\pi$
$558$	4.90398	−	4.90398i	0.207602	−	0.207602i
$559$	42.7425			1.80781
$560$	−0.0437250	+	0.330939i	−0.00184772	+	0.0139847i
$561$	92.5885			3.90909
$562$	−11.2069	+	11.2069i	−0.472733	+	0.472733i
$563$	0.340089	+	0.340089i	0.0143330	+	0.0143330i	0.714237	−	0.699904i	$-0.246774\pi$
$563$	0.340089	+	0.340089i	0.0143330	+	0.0143330i	−0.699904	+	0.714237i	$0.746774\pi$
$564$			13.7717i			0.579894i
$565$	28.3749	+	3.74901i	1.19374	+	0.157722i
$566$			19.2093i			0.807426i
$567$	−0.107608	+	0.107608i	−0.00451913	+	0.00451913i
$568$	−10.9986	+	10.9986i	−0.461491	+	0.461491i
$569$	−22.6776			−0.950693			−0.475346	−	0.879799i	$-0.657677\pi$
$569$	−22.6776			−0.950693			−0.475346	+	0.879799i	$0.657677\pi$
$570$	17.5464	−	13.4509i	0.734936	−	0.563395i
$571$		−	21.9576i		−	0.918895i	−0.888205	−	0.459448i	$-0.848047\pi$
$571$		−	21.9576i		−	0.918895i	0.888205	−	0.459448i	$-0.151953\pi$
$572$	−17.4423	+	17.4423i	−0.729299	+	0.729299i
$573$	25.3605	+	25.3605i	1.05945	+	1.05945i
$574$	0.577754			0.0241150
$575$	3.14465	+	23.7721i	0.131141	+	0.991364i
$576$	−4.69853			−0.195772
$577$	−12.2581	−	12.2581i	−0.510309	−	0.510309i	0.404312	−	0.914621i	$-0.367511\pi$
$577$	−12.2581	−	12.2581i	−0.510309	−	0.510309i	−0.914621	+	0.404312i	$0.867511\pi$
$578$	−8.53681	+	8.53681i	−0.355085	+	0.355085i
$579$			26.2613i			1.09138i
$580$	1.23051	−	0.943301i	0.0510943	−	0.0391684i
$581$	0.00896109			0.000371769
$582$	−30.8601	+	30.8601i	−1.27919	+	1.27919i
$583$	−11.2408	+	11.2408i	−0.465546	+	0.465546i
$584$		−	10.7637i		−	0.445405i
$585$	−41.5144	−	5.48506i	−1.71641	−	0.226779i
$586$			19.8277i			0.819073i
$587$	−26.9154	−	26.9154i	−1.11092	−	1.11092i	−0.993027	−	0.117889i	$-0.962387\pi$
$587$	−26.9154	−	26.9154i	−1.11092	−	1.11092i	−0.117889	−	0.993027i	$-0.537613\pi$
$588$	13.6900	−	13.6900i	0.564564	−	0.564564i
$589$	5.25990			0.216731
$590$	0.822523	−	6.22538i	0.0338627	−	0.256295i
$591$	12.6418			0.520016
$592$	3.09335	−	3.09335i	0.127136	−	0.127136i
$593$	22.7267	−	22.7267i	0.933275	−	0.933275i	−0.0646344	−	0.997909i	$-0.520588\pi$
$593$	22.7267	−	22.7267i	0.933275	−	0.933275i	0.997909	+	0.0646344i	$0.0205881\pi$
$594$	−29.1667			−1.19672
$595$	−1.09505	−	1.42847i	−0.0448927	−	0.0585615i
$596$			7.64987i			0.313351i
$597$	−21.0031	+	21.0031i	−0.859601	+	0.859601i
$598$	−17.6486	+	7.34230i	−0.721704	+	0.300249i
$599$		−	33.3373i		−	1.36213i	−0.732225	−	0.681063i	$-0.761518\pi$
$599$		−	33.3373i		−	1.36213i	0.732225	−	0.681063i	$-0.238482\pi$
$600$	13.3971	+	3.60305i	0.546933	+	0.147094i
$601$	16.0535			0.654835			0.327418	−	0.944880i	$-0.393822\pi$
$601$	16.0535			0.654835			0.327418	+	0.944880i	$0.393822\pi$
$602$	−1.13202	−	1.13202i	−0.0461378	−	0.0461378i
$603$	31.4355	+	31.4355i	1.28015	+	1.28015i
$604$			13.3919i			0.544910i
$605$	48.4502	−	37.1415i	1.96978	−	1.51002i
$606$	−7.49331			−0.304395
$607$	−6.76763	−	6.76763i	−0.274690	−	0.274690i	0.556295	−	0.830985i	$-0.312222\pi$
$607$	−6.76763	−	6.76763i	−0.274690	−	0.274690i	−0.830985	+	0.556295i	$0.812222\pi$
$608$	−2.51978	−	2.51978i	−0.102190	−	0.102190i
$609$	0.287214			0.0116385
$610$	−1.44303	+	10.9218i	−0.0584265	+	0.442209i
$611$	19.7831			0.800338
$612$	17.9139	−	17.9139i	0.724128	−	0.724128i
$613$	−2.61611	−	2.61611i	−0.105663	−	0.105663i	0.652299	−	0.757962i	$-0.273805\pi$
$613$	−2.61611	−	2.61611i	−0.105663	−	0.105663i	−0.757962	+	0.652299i	$0.773805\pi$
$614$			22.8968i			0.924038i
$615$	3.14511	−	23.8042i	0.126823	−	0.959878i
$616$	0.923909			0.0372254
$617$	1.89756	−	1.89756i	0.0763928	−	0.0763928i	−0.667878	−	0.744271i	$-0.732797\pi$
$617$	1.89756	−	1.89756i	0.0763928	−	0.0763928i	0.744271	+	0.667878i	$0.232797\pi$
$618$	10.4214	+	10.4214i	0.419210	+	0.419210i
$619$	−35.4461			−1.42470			−0.712349	−	0.701825i	$-0.752369\pi$
$619$	−35.4461			−1.42470			−0.712349	+	0.701825i	$0.752369\pi$
$620$	2.00803	+	2.61943i	0.0806445	+	0.105199i
$621$	−20.8946	−	8.61699i	−0.838473	−	0.345788i
$622$	10.3663	+	10.3663i	0.415651	+	0.415651i
$623$	1.32464	−	1.32464i	0.0530704	−	0.0530704i
$624$			11.0589i			0.442712i
$625$	−21.6274	−	12.5401i	−0.865097	−	0.501605i
$626$		−	3.14897i		−	0.125858i
$627$	−43.2688	−	43.2688i	−1.72799	−	1.72799i
$628$	13.4366	+	13.4366i	0.536179	+	0.536179i
$629$			23.5879i			0.940510i
$630$	0.954228	+	1.24477i	0.0380174	+	0.0495928i
$631$		−	27.9402i		−	1.11228i	−0.831088	−	0.556141i	$-0.812281\pi$
$631$		−	27.9402i		−	1.11228i	0.831088	−	0.556141i	$-0.187719\pi$
$632$	6.34326	−	6.34326i	0.252321	−	0.252321i
$633$	−38.7597	+	38.7597i	−1.54056	+	1.54056i
$634$		−	22.7353i		−	0.902934i
$635$	15.3221	+	2.02441i	0.608037	+	0.0803364i
$636$			7.12700i			0.282604i
$637$	−19.6656	−	19.6656i	−0.779180	−	0.779180i
$638$	−3.03441	−	3.03441i	−0.120134	−	0.120134i
$639$			73.0828i			2.89111i
$640$	0.292893	−	2.21680i	0.0115776	−	0.0876268i
$641$		−	30.3329i		−	1.19808i	−0.800719	−	0.599040i	$-0.795549\pi$
$641$		−	30.3329i		−	1.19808i	0.800719	−	0.599040i	$-0.204451\pi$
$642$	−2.87601	+	2.87601i	−0.113507	+	0.113507i
$643$	−5.28328	−	5.28328i	−0.208352	−	0.208352i	0.595215	−	0.803567i	$-0.297067\pi$
$643$	−5.28328	−	5.28328i	−0.208352	−	0.208352i	−0.803567	+	0.595215i	$0.797067\pi$
$644$	0.661877	+	0.272959i	0.0260816	+	0.0107561i
$645$	−52.8032	+	40.4784i	−2.07912	+	1.59384i
$646$	19.2141			0.755970
$647$	13.0754	+	13.0754i	0.514049	+	0.514049i	0.915764	−	0.401716i	$-0.131586\pi$
$647$	13.0754	+	13.0754i	0.514049	+	0.514049i	−0.401716	+	0.915764i	$0.631586\pi$
$648$	0.720819	−	0.720819i	0.0283164	−	0.0283164i
$649$	−17.3799			−0.682221
$650$	5.17578	−	19.2449i	0.203011	−	0.754846i
$651$			0.611400i			0.0239627i
$652$	14.8711	+	14.8711i	0.582396	+	0.582396i
$653$	−29.1171	+	29.1171i	−1.13944	+	1.13944i	−0.150892	+	0.988550i	$0.548215\pi$
$653$	−29.1171	+	29.1171i	−1.13944	+	1.13944i	−0.988550	+	0.150892i	$0.951785\pi$
$654$	−22.5880			−0.883262
$655$	−3.26629	+	2.50391i	−0.127624	+	0.0978357i
$656$	−3.87011			−0.151102
$657$	−35.7609	−	35.7609i	−1.39517	−	1.39517i
$658$	−0.523950	−	0.523950i	−0.0204257	−	0.0204257i
$659$	14.5832			0.568080			0.284040	−	0.958812i	$-0.408325\pi$
$659$	14.5832			0.568080			0.284040	+	0.958812i	$0.408325\pi$
$660$	5.02947	−	38.0662i	0.195772	−	1.48173i
$661$		−	22.9841i		−	0.893976i	−0.894540	−	0.446988i	$-0.852497\pi$
$661$		−	22.9841i		−	0.893976i	0.894540	−	0.446988i	$-0.147503\pi$
$662$	−0.0874500	−	0.0874500i	−0.00339884	−	0.00339884i
$663$	−42.1641	−	42.1641i	−1.63752	−	1.63752i
$664$	−0.0600262			−0.00232947
$665$	−0.155814	+	1.17930i	−0.00604221	+	0.0457313i
$666$		−	20.5545i		−	0.796471i
$667$	−1.27733	−	3.07030i	−0.0494584	−	0.118883i
$668$	−6.01650	+	6.01650i	−0.232785	+	0.232785i
$669$		−	16.0418i		−	0.620212i
$670$	−16.7911	+	12.8719i	−0.648698	+	0.497285i
$671$	30.4912			1.17710
$672$	0.292893	−	0.292893i	0.0112986	−	0.0112986i
$673$	5.45496	−	5.45496i	0.210273	−	0.210273i	−0.594110	−	0.804384i	$-0.702496\pi$
$673$	5.45496	−	5.45496i	0.210273	−	0.210273i	0.804384	+	0.594110i	$0.202496\pi$
$674$	6.53422			0.251689
$675$	20.4179	−	11.7630i	0.785885	−	0.452760i
$676$	2.88617			0.111007
$677$	16.0470	−	16.0470i	0.616735	−	0.616735i	−0.327957	−	0.944693i	$-0.606360\pi$
$677$	16.0470	−	16.0470i	0.616735	−	0.616735i	0.944693	+	0.327957i	$0.106360\pi$
$678$	−25.1129	−	25.1129i	−0.964454	−	0.964454i
$679$		−	2.34817i		−	0.0901144i
$680$	7.33523	+	9.56864i	0.281293	+	0.366940i
$681$		−	66.9662i		−	2.56615i
$682$	6.45944	−	6.45944i	0.247345	−	0.247345i
$683$	8.14554	−	8.14554i	0.311681	−	0.311681i	−0.533880	−	0.845560i	$-0.679267\pi$
$683$	8.14554	−	8.14554i	0.311681	−	0.311681i	0.845560	+	0.533880i	$0.179267\pi$
$684$	−16.7432			−0.640193
$685$	−2.65180	+	20.0705i	−0.101320	+	0.766854i
$686$			2.08668i			0.0796699i
$687$	19.5404	−	19.5404i	0.745515	−	0.745515i
$688$	7.58289	+	7.58289i	0.289095	+	0.289095i
$689$	10.2379			0.390034
$690$	14.8493	−	25.7843i	0.565304	−	0.981591i
$691$	−4.68521			−0.178234			−0.0891168	−	0.996021i	$-0.528404\pi$
$691$	−4.68521			−0.178234			−0.0891168	+	0.996021i	$0.528404\pi$
$692$	1.92541	+	1.92541i	0.0731933	+	0.0731933i
$693$	3.06956	−	3.06956i	0.116603	−	0.116603i
$694$		−	23.3778i		−	0.887409i
$695$	−6.14492	−	8.01590i	−0.233090	−	0.304061i
$696$	−1.92391			−0.0729256
$697$	14.7554	−	14.7554i	0.558902	−	0.558902i
$698$	2.98876	−	2.98876i	0.113126	−	0.113126i
$699$		−	26.9135i		−	1.01796i
$700$	−0.646775	+	0.372617i	−0.0244458	+	0.0140836i
$701$		−	36.0445i		−	1.36138i	−0.732571	−	0.680690i	$-0.761680\pi$
$701$		−	36.0445i		−	1.36138i	0.732571	−	0.680690i	$-0.238320\pi$
$702$	13.2823	+	13.2823i	0.501307	+	0.501307i
$703$	11.0232	−	11.0232i	0.415747	−	0.415747i
$704$	−6.18884			−0.233251
$705$	−24.4396	+	18.7352i	−0.920449	+	0.705608i
$706$	25.9599			0.977014
$707$	0.285086	−	0.285086i	0.0107217	−	0.0107217i
$708$	−5.50970	+	5.50970i	−0.207067	+	0.207067i
$709$	41.6866			1.56557			0.782787	−	0.622289i	$-0.213797\pi$
$709$	41.6866			1.56557			0.782787	+	0.622289i	$0.213797\pi$
$710$	−34.4810	−	4.55577i	−1.29405	−	0.170975i
$711$		−	42.1492i		−	1.58072i
$712$	−8.87311	+	8.87311i	−0.332534	+	0.332534i
$713$	6.53584	−	2.71909i	0.244769	−	0.101831i
$714$			2.23341i			0.0835832i
$715$	−54.6822	−	7.22483i	−2.04500	−	0.270194i
$716$	−18.6793			−0.698077
$717$	14.8904	+	14.8904i	0.556091	+	0.556091i
$718$	22.1350	+	22.1350i	0.826072	+	0.826072i
$719$		−	6.45359i		−	0.240678i	−0.992733	−	0.120339i	$-0.961602\pi$
$719$		−	6.45359i		−	0.240678i	0.992733	−	0.120339i	$-0.0383982\pi$
$720$	−6.39193	−	8.33812i	−0.238213	−	0.310743i
$721$	−0.792971			−0.0295318
$722$	4.45581	+	4.45581i	0.165828	+	0.165828i
$723$	−24.3828	−	24.3828i	−0.906806	−	0.906806i
$724$	−9.76326			−0.362849
$725$	3.34801	+	0.900424i	0.124342	+	0.0334409i
$726$	−75.7519			−2.81142
$727$	−23.3378	+	23.3378i	−0.865552	+	0.865552i	−0.991976	−	0.126424i	$-0.959650\pi$
$727$	−23.3378	+	23.3378i	−0.865552	+	0.865552i	0.126424	+	0.991976i	$0.459650\pi$
$728$	−0.420741	−	0.420741i	−0.0155937	−	0.0155937i
$729$		−	44.0183i		−	1.63031i
$730$	19.1015	−	14.6430i	0.706978	−	0.541963i
$731$	−57.8221			−2.13863
$732$	9.66617	−	9.66617i	0.357272	−	0.357272i
$733$	−19.0912	−	19.0912i	−0.705151	−	0.705151i	0.260361	−	0.965511i	$-0.416158\pi$
$733$	−19.0912	−	19.0912i	−0.705151	−	0.705151i	−0.965511	+	0.260361i	$0.916158\pi$
$734$	−2.38772			−0.0881323
$735$	42.9185	+	5.67057i	1.58307	+	0.209162i
$736$	−4.43361	−	1.82843i	−0.163425	−	0.0673967i
$737$	41.4064	+	41.4064i	1.52522	+	1.52522i
$738$	−12.8579	+	12.8579i	−0.473306	+	0.473306i
$739$			24.4426i			0.899137i	0.893246	+	0.449568i	$0.148422\pi$
$739$			24.4426i			0.899137i	−0.893246	+	0.449568i	$0.851578\pi$
$740$	9.69777	+	1.28131i	0.356497	+	0.0471019i
$741$			39.4085i			1.44771i
$742$	−0.271149	−	0.271149i	−0.00995420	−	0.00995420i
$743$	11.6216	+	11.6216i	0.426355	+	0.426355i	0.887385	−	0.461030i	$-0.152520\pi$
$743$	11.6216	+	11.6216i	0.426355	+	0.426355i	−0.461030	+	0.887385i	$0.652520\pi$
$744$		−	4.09548i		−	0.150148i
$745$	−13.5756	+	10.4069i	−0.497372	+	0.381281i
$746$			33.1645i			1.21424i
$747$	−0.199429	+	0.199429i	−0.00729672	+	0.00729672i
$748$	23.5960	−	23.5960i	0.862754	−	0.862754i
$749$		−	0.218837i		−	0.00799615i
$750$	11.8314	+	28.6764i	0.432023	+	1.04711i
$751$			47.8024i			1.74433i	0.489208	+	0.872167i	$0.337286\pi$
$751$			47.8024i			1.74433i	−0.489208	+	0.872167i	$0.662714\pi$
$752$	3.50970	+	3.50970i	0.127985	+	0.127985i
$753$	−22.6787	−	22.6787i	−0.826458	−	0.826458i
$754$			2.76370i			0.100648i
$755$	−23.7656	+	18.2185i	−0.864919	+	0.663039i
$756$		−	0.703555i		−	0.0255881i
$757$	−6.58699	+	6.58699i	−0.239408	+	0.239408i	−0.816605	−	0.577197i	$-0.804147\pi$
$757$	−6.58699	+	6.58699i	−0.239408	+	0.239408i	0.577197	+	0.816605i	$0.304147\pi$
$758$	−12.9738	−	12.9738i	−0.471228	−	0.471228i
$759$	−76.1325	−	31.3972i	−2.76343	−	1.13965i
$760$	1.04372	−	7.89958i	0.0378599	−	0.286548i
$761$	11.1059			0.402588			0.201294	−	0.979531i	$-0.435485\pi$
$761$	11.1059			0.402588			0.201294	+	0.979531i	$0.435485\pi$
$762$	−13.5606	−	13.5606i	−0.491249	−	0.491249i
$763$	0.859369	−	0.859369i	0.0311112	−	0.0311112i
$764$	12.9262			0.467652
$765$	56.1608	+	7.42020i	2.03050	+	0.268278i
$766$		−	4.66597i		−	0.168588i
$767$	7.91468	+	7.91468i	0.285782	+	0.285782i
$768$	−1.96195	+	1.96195i	−0.0707959	+	0.0707959i
$769$	−29.8326			−1.07579			−0.537895	−	0.843012i	$-0.680780\pi$
$769$	−29.8326			−1.07579			−0.537895	+	0.843012i	$0.680780\pi$
$770$	1.25689	+	1.63959i	0.0452953	+	0.0590867i
$771$	−12.7125			−0.457828
$772$	6.69263	+	6.69263i	0.240873	+	0.240873i
$773$	20.0799	+	20.0799i	0.722223	+	0.722223i	0.969058	−	0.246835i	$-0.0793905\pi$
$773$	20.0799	+	20.0799i	0.722223	+	0.722223i	−0.246835	+	0.969058i	$0.579391\pi$
$774$	50.3863			1.81110
$775$	−1.91676	+	7.12700i	−0.0688520	+	0.256009i
$776$			15.7293i			0.564648i
$777$	1.28131	+	1.28131i	0.0459667	+	0.0459667i
$778$	9.61881	+	9.61881i	0.344851	+	0.344851i
$779$	−13.7911			−0.494118
$780$	−19.6255	+	15.0447i	−0.702704	+	0.538686i
$781$			96.2635i			3.44458i
$782$	23.8751	−	9.93268i	0.853770	−	0.355192i
$783$	−2.31070	+	2.31070i	−0.0825776	+	0.0825776i
$784$		−	6.97771i		−	0.249204i
$785$	−5.56563	+	42.1242i	−0.198646	+	1.50348i
$786$	5.10684			0.182155
$787$	23.3105	−	23.3105i	0.830929	−	0.830929i	−0.156715	−	0.987644i	$-0.550090\pi$
$787$	23.3105	−	23.3105i	0.830929	−	0.830929i	0.987644	+	0.156715i	$0.0500903\pi$
$788$	3.22174	−	3.22174i	0.114770	−	0.114770i
$789$	−0.918772			−0.0327091
$790$	19.8863	+	2.62746i	0.707524	+	0.0934810i
$791$	1.91085			0.0679422
$792$	−20.5616	+	20.5616i	−0.730623	+	0.730623i
$793$	−13.8854	−	13.8854i	−0.493087	−	0.493087i
$794$		−	8.36220i		−	0.296763i
$795$	−12.6477	+	9.69564i	−0.448569	+	0.343869i
$796$			10.7052i			0.379436i
$797$	29.6897	−	29.6897i	1.05166	−	1.05166i	0.0530737	−	0.998591i	$-0.483098\pi$
$797$	29.6897	−	29.6897i	1.05166	−	1.05166i	0.998591	−	0.0530737i	$-0.0169018\pi$
$798$	1.04372	−	1.04372i	0.0369475	−	0.0369475i
$799$	−26.7626			−0.946793
$800$	4.33244	−	2.49598i	0.153175	−	0.0882464i
$801$			58.9594i			2.08323i
$802$	−0.424212	+	0.424212i	−0.0149794	+	0.0149794i
$803$	−47.1037	−	47.1037i	−1.66226	−	1.66226i
$804$	26.2529			0.925869
$805$	0.416024	+	1.54592i	0.0146629	+	0.0544865i
$806$	−5.88316			−0.207225
$807$	47.0592	+	47.0592i	1.65656	+	1.65656i
$808$	−1.90966	+	1.90966i	−0.0671814	+	0.0671814i
$809$		−	8.58305i		−	0.301764i	−0.988552	−	0.150882i	$-0.951789\pi$
$809$		−	8.58305i		−	0.301764i	0.988552	−	0.150882i	$-0.0482113\pi$
$810$	2.25979	+	0.298573i	0.0794009	+	0.0104908i
$811$	38.3978			1.34833			0.674164	−	0.738582i	$-0.264504\pi$
$811$	38.3978			1.34833			0.674164	+	0.738582i	$0.264504\pi$
$812$	0.0731958	−	0.0731958i	0.00256867	−	0.00256867i
$813$	39.2393	−	39.2393i	1.37618	−	1.37618i
$814$		−	27.0741i		−	0.948946i
$815$	−6.15980	+	46.6213i	−0.215768	+	1.63307i
$816$		−	14.9606i		−	0.523725i
$817$	27.0216	+	27.0216i	0.945367	+	0.945367i
$818$	2.01040	−	2.01040i	0.0702919	−	0.0702919i
$819$	−2.79571			−0.0976900
$820$	−5.26493	−	6.86798i	−0.183859	−	0.239840i
$821$	−28.8841			−1.00806			−0.504032	−	0.863685i	$-0.668151\pi$
$821$	−28.8841			−1.00806			−0.504032	+	0.863685i	$0.668151\pi$
$822$	17.7632	−	17.7632i	0.619561	−	0.619561i
$823$	17.3293	−	17.3293i	0.604062	−	0.604062i	−0.337326	−	0.941388i	$-0.609522\pi$
$823$	17.3293	−	17.3293i	0.604062	−	0.604062i	0.941388	+	0.337326i	$0.109522\pi$
$824$	5.31174			0.185043
$825$	74.3954	−	42.8603i	2.59011	−	1.49220i
$826$		−	0.419236i		−	0.0145871i
$827$	−36.3705	+	36.3705i	−1.26473	+	1.26473i	−0.315952	+	0.948775i	$0.602324\pi$
$827$	−36.3705	+	36.3705i	−1.26473	+	1.26473i	−0.948775	+	0.315952i	$0.897676\pi$
$828$	−20.8048	+	8.65535i	−0.723015	+	0.300794i
$829$		−	36.2528i		−	1.25911i	−0.776956	−	0.629555i	$-0.783237\pi$
$829$		−	36.2528i		−	1.25911i	0.776956	−	0.629555i	$-0.216763\pi$
$830$	−0.0816602	−	0.106524i	−0.00283447	−	0.00369750i
$831$	−66.9971			−2.32410
$832$	2.81835	+	2.81835i	0.0977086	+	0.0977086i
$833$	26.6037	+	26.6037i	0.921764	+	0.921764i
$834$			12.5329i			0.433978i
$835$	−18.8619	−	2.49211i	−0.652743	−	0.0862432i
$836$	−22.0539			−0.762751
$837$	−4.91885	−	4.91885i	−0.170020	−	0.170020i
$838$	−6.77096	−	6.77096i	−0.233899	−	0.233899i
$839$	−3.95258			−0.136458			−0.0682291	−	0.997670i	$-0.521735\pi$
$839$	−3.95258			−0.136458			−0.0682291	+	0.997670i	$0.521735\pi$
$840$	0.918230	+	0.121320i	0.0316819	+	0.00418595i
$841$	28.5192			0.983421
$842$	−18.4400	+	18.4400i	−0.635485	+	0.635485i
$843$	31.0948	+	31.0948i	1.07096	+	1.07096i
$844$			19.7557i			0.680018i
$845$	3.92637	+	5.12186i	0.135071	+	0.176197i
$846$	23.3210			0.801792
$847$	2.88201	−	2.88201i	0.0990269	−	0.0990269i
$848$	1.81630	+	1.81630i	0.0623720	+	0.0623720i
$849$	53.2985			1.82920
$850$	−7.00181	+	26.0345i	−0.240160	+	0.892977i
$851$	7.99875	−	19.3955i	0.274194	−	0.664870i
$852$	30.5170	+	30.5170i	1.04550	+	1.04550i
$853$	−2.42762	+	2.42762i	−0.0831201	+	0.0831201i	−0.747444	−	0.664324i	$-0.768719\pi$
$853$	−2.42762	+	2.42762i	−0.0831201	+	0.0831201i	0.664324	+	0.747444i	$0.268719\pi$
$854$			0.735505i			0.0251685i
$855$	−22.7776	−	29.7129i	−0.778979	−	1.01616i
$856$			1.46589i			0.0501031i
$857$	−21.7397	−	21.7397i	−0.742615	−	0.742615i	0.230465	−	0.973081i	$-0.425975\pi$
$857$	−21.7397	−	21.7397i	−0.742615	−	0.742615i	−0.973081	+	0.230465i	$0.925975\pi$
$858$	48.3958	+	48.3958i	1.65220	+	1.65220i
$859$			39.4154i			1.34483i	0.740172	+	0.672417i	$0.234744\pi$
$859$			39.4154i			1.34483i	−0.740172	+	0.672417i	$0.765256\pi$
$860$	−3.14094	+	23.7726i	−0.107105	+	0.810639i
$861$		−	1.60305i		−	0.0546318i
$862$	22.2738	−	22.2738i	0.758650	−	0.758650i
$863$	−21.2367	+	21.2367i	−0.722907	+	0.722907i	−0.969196	−	0.246289i	$-0.920789\pi$
$863$	−21.2367	+	21.2367i	−0.722907	+	0.722907i	0.246289	+	0.969196i	$0.420789\pi$
$864$			4.71279i			0.160332i
$865$	−0.797533	+	6.03624i	−0.0271169	+	0.205238i
$866$		−	27.1271i		−	0.921817i
$867$	23.6864	+	23.6864i	0.804434	+	0.804434i
$868$	0.155814	+	0.155814i	0.00528867	+	0.00528867i
$869$		−	55.5183i		−	1.88333i
$870$	−2.61730	−	3.41421i	−0.0887349	−	0.115753i
$871$		−	37.7123i		−	1.27783i
$872$	−5.75651	+	5.75651i	−0.194940	+	0.194940i
$873$	52.2584	+	52.2584i	1.76868	+	1.76868i
$874$	−15.7992	−	6.51560i	−0.534414	−	0.220393i
$875$	−1.54113	−	0.640871i	−0.0520998	−	0.0216654i
$876$	−29.8652			−1.00905
$877$	−30.5545	−	30.5545i	−1.03175	−	1.03175i	−0.999479	−	0.0322740i	$-0.989725\pi$
$877$	−30.5545	−	30.5545i	−1.03175	−	1.03175i	−0.0322740	−	0.999479i	$-0.510275\pi$
$878$	19.5191	−	19.5191i	0.658738	−	0.658738i
$879$	55.0143			1.85559
$880$	−8.41935	−	10.9829i	−0.283816	−	0.370232i
$881$			27.9370i			0.941223i	0.882341	+	0.470611i	$0.155967\pi$
$881$			27.9370i			0.941223i	−0.882341	+	0.470611i	$0.844033\pi$
$882$	−23.1825	−	23.1825i	−0.780596	−	0.780596i
$883$	2.16848	−	2.16848i	0.0729752	−	0.0729752i	−0.669677	−	0.742652i	$-0.733568\pi$
$883$	2.16848	−	2.16848i	0.0729752	−	0.0729752i	0.742652	+	0.669677i	$0.233568\pi$
$884$	−21.4909			−0.722816
$885$	−17.2731	−	2.28219i	−0.580628	−	0.0767150i
$886$	−11.7596			−0.395073
$887$	−12.9902	−	12.9902i	−0.436167	−	0.436167i	0.454553	−	0.890720i	$-0.349799\pi$
$887$	−12.9902	−	12.9902i	−0.436167	−	0.436167i	−0.890720	+	0.454553i	$0.849799\pi$
$888$	−8.58289	−	8.58289i	−0.288023	−	0.288023i
$889$	1.03184			0.0346067
$890$	−27.8175	−	3.67536i	−0.932445	−	0.123198i
$891$		−	6.30885i		−	0.211354i
$892$	−4.08822	−	4.08822i	−0.136884	−	0.136884i
$893$	12.5068	+	12.5068i	0.418524	+	0.418524i
$894$	21.2255			0.709887
$895$	−25.4114	−	33.1486i	−0.849411	−	1.10804i
$896$		−	0.149286i		−	0.00498731i
$897$	20.3721	+	48.9682i	0.680205	+	1.63500i
$898$	−15.6448	+	15.6448i	−0.522072	+	0.522072i
$899$		−	1.02349i		−	0.0341352i
$900$	6.10139	−	22.6865i	0.203380	−	0.756217i
$901$	−13.8499			−0.461407
$902$	−16.9362	+	16.9362i	−0.563915	+	0.563915i
$903$	−3.14094	+	3.14094i	−0.104524	+	0.104524i
$904$	−12.7999			−0.425719
$905$	−13.2820	−	17.3261i	−0.441510	−	0.575939i
$906$	37.1575			1.23448
$907$	24.3943	−	24.3943i	0.809999	−	0.809999i	−0.174634	−	0.984633i	$-0.555874\pi$
$907$	24.3943	−	24.3943i	0.809999	−	0.809999i	0.984633	+	0.174634i	$0.0558744\pi$
$908$	−17.0662	−	17.0662i	−0.566362	−	0.566362i
$909$			12.6891i			0.420872i
$910$	0.174277	−	1.31904i	0.00577722	−	0.0437256i
$911$			28.8254i			0.955029i	0.878624	+	0.477514i	$0.158462\pi$
$911$			28.8254i			0.955029i	−0.878624	+	0.477514i	$0.841538\pi$
$912$	−6.99143	+	6.99143i	−0.231509	+	0.231509i
$913$	−0.262685	+	0.262685i	−0.00869359	+	0.00869359i
$914$	−8.22975			−0.272216
$915$	30.3037	+	4.00386i	1.00181	+	0.132363i
$916$		−	9.95968i		−	0.329077i
$917$	−0.194291	+	0.194291i	−0.00641607	+	0.00641607i
$918$	−17.9683	−	17.9683i	−0.593042	−	0.593042i
$919$	−25.4342			−0.838997			−0.419499	−	0.907756i	$-0.637794\pi$
$919$	−25.4342			−0.838997			−0.419499	+	0.907756i	$0.637794\pi$
$920$	−2.78675	−	10.3554i	−0.0918764	−	0.341407i
$921$	63.5299			2.09338
$922$	3.50680	+	3.50680i	0.115490	+	0.115490i
$923$	43.8377	−	43.8377i	1.44293	−	1.44293i
$924$		−	2.56350i		−	0.0843330i
$925$	10.9191	+	18.9530i	0.359017	+	0.623170i
$926$	−2.07030			−0.0680343
$927$	17.6475	−	17.6475i	0.579621	−	0.579621i
$928$	−0.490304	+	0.490304i	−0.0160950	+	0.0160950i
$929$		−	42.7798i		−	1.40356i	−0.712393	−	0.701780i	$-0.752389\pi$
$929$		−	42.7798i		−	1.40356i	0.712393	−	0.701780i	$-0.247611\pi$
$930$	7.26794	−	5.57153i	0.238325	−	0.182698i
$931$		−	24.8651i		−	0.814920i
$932$	−6.85886	−	6.85886i	−0.224669	−	0.224669i
$933$	28.7626	−	28.7626i	0.941646	−	0.941646i
$934$	−25.4187			−0.831725
$935$	73.9742	+	9.77378i	2.41921	+	0.319637i
$936$	18.7272			0.612116
$937$	−26.9308	+	26.9308i	−0.879790	+	0.879790i	−0.993513	−	0.113722i	$-0.963723\pi$
$937$	−26.9308	+	26.9308i	−0.879790	+	0.879790i	0.113722	+	0.993513i	$0.463723\pi$
$938$	−0.998801	+	0.998801i	−0.0326120	+	0.0326120i
$939$	−8.73720			−0.285128
$940$	−1.45376	+	11.0030i	−0.0474165	+	0.358879i
$941$			1.80799i			0.0589389i	0.999566	+	0.0294694i	$0.00938177\pi$
$941$			1.80799i			0.0589389i	−0.999566	+	0.0294694i	$0.990618\pi$
$942$	37.2815	−	37.2815i	1.21470	−	1.21470i
$943$	−17.1365	+	7.12927i	−0.558042	+	0.232161i
$944$			2.80827i			0.0914014i
$945$	1.24854	−	0.957123i	0.0406152	−	0.0311352i
$946$	66.3680			2.15781
$947$	−19.6060	−	19.6060i	−0.637110	−	0.637110i	0.312731	−	0.949842i	$-0.398756\pi$
$947$	−19.6060	−	19.6060i	−0.637110	−	0.637110i	−0.949842	+	0.312731i	$0.898756\pi$
$948$	−17.6002	−	17.6002i	−0.571626	−	0.571626i
$949$			42.9014i			1.39264i
$950$	15.4387	−	8.89444i	0.500896	−	0.288574i
$951$	−63.0819			−2.04557
$952$	0.569180	+	0.569180i	0.0184472	+	0.0184472i
$953$	11.3030	+	11.3030i	0.366139	+	0.366139i	0.866067	−	0.499928i	$-0.166640\pi$
$953$	11.3030	+	11.3030i	0.366139	+	0.366139i	−0.499928	+	0.866067i	$0.666640\pi$
$954$	12.0688			0.390743
$955$	17.5849	+	22.9390i	0.569033	+	0.742290i
$956$	7.58956			0.245464
$957$	−8.41935	+	8.41935i	−0.272159	+	0.272159i
$958$	21.3081	+	21.3081i	0.688433	+	0.688433i
$959$			1.35161i			0.0436458i
$960$	−6.15079	−	0.812668i	−0.198516	−	0.0262288i
$961$	−28.8213			−0.929719
$962$	−12.3293	+	12.3293i	−0.397513	+	0.397513i
$963$	4.87022	+	4.87022i	0.156941	+	0.156941i
$964$	−12.4278			−0.400273
$965$	−2.77218	+	20.9816i	−0.0892395	+	0.675422i
$966$	0.757359	−	1.83646i	0.0243676	−	0.0590871i
$967$	−9.14230	−	9.14230i	−0.293996	−	0.293996i	0.544660	−	0.838657i	$-0.316659\pi$
$967$	−9.14230	−	9.14230i	−0.293996	−	0.293996i	−0.838657	+	0.544660i	$0.816659\pi$
$968$	−19.3052	+	19.3052i	−0.620493	+	0.620493i
$969$		−	53.3120i		−	1.71263i
$970$	−27.9135	+	21.3983i	−0.896250	+	0.687057i
$971$		−	0.0205906i		−	0.000660785i	−1.00000		0.000330393i	$-0.999895\pi$
$971$		−	0.0205906i		−	0.000660785i	1.00000		0.000330393i	$-0.000105167\pi$
$972$	−11.9973	−	11.9973i	−0.384815	−	0.384815i
$973$	−0.476817	−	0.476817i	−0.0152861	−	0.0152861i
$974$			9.88126i			0.316616i
$975$	−53.3973	−	14.3608i	−1.71008	−	0.459915i
$976$		−	4.92680i		−	0.157703i
$977$	24.3981	−	24.3981i	0.780566	−	0.780566i	−0.199361	−	0.979926i	$-0.563886\pi$
$977$	24.3981	−	24.3981i	0.780566	−	0.780566i	0.979926	+	0.199361i	$0.0638865\pi$
$978$	41.2616	−	41.2616i	1.31940	−	1.31940i
$979$			77.6605i			2.48204i
$980$	12.3828	−	9.49255i	0.395554	−	0.303228i
$981$			38.2505i			1.22124i
$982$	−15.0469	−	15.0469i	−0.480167	−	0.480167i
$983$	−28.0921	−	28.0921i	−0.895998	−	0.895998i	0.0990812	−	0.995079i	$-0.468410\pi$
$983$	−28.0921	−	28.0921i	−0.895998	−	0.895998i	−0.995079	+	0.0990812i	$0.968410\pi$
$984$			10.7381i			0.342318i
$985$	10.1003	+	1.33449i	0.321821	+	0.0425204i
$986$		−	3.73873i		−	0.119066i
$987$	−1.45376	+	1.45376i	−0.0462738	+	0.0462738i
$988$	10.0432	+	10.0432i	0.319516	+	0.319516i
$989$	47.5452	+	19.6077i	1.51185	+	0.623490i
$990$	−64.4612	−	8.51688i	−2.04871	−	0.270684i
$991$	58.8565			1.86964			0.934819	−	0.355124i	$-0.115561\pi$
$991$	58.8565			1.86964			0.934819	+	0.355124i	$0.115561\pi$
$992$	−1.04372	−	1.04372i	−0.0331383	−	0.0331383i
$993$	−0.242641	+	0.242641i	−0.00769997	+	0.00769997i
$994$	−2.32206			−0.0736512
$995$	−18.9977	+	14.5635i	−0.602268	+	0.461693i
$996$			0.166550i			0.00527734i
$997$	29.3516	+	29.3516i	0.929574	+	0.929574i	0.997678	−	0.0681047i	$-0.0216952\pi$
$997$	29.3516	+	29.3516i	0.929574	+	0.929574i	−0.0681047	+	0.997678i	$0.521695\pi$
$998$	0.691861	−	0.691861i	0.0219005	−	0.0219005i
$999$	−20.6169			−0.652288

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.e.b.137.1	yes	8
5.2	odd	4		1150.2.e.c.643.4		8
5.3	odd	4		230.2.e.a.183.1	yes	8
5.4	even	2		1150.2.e.b.1057.4		8
23.22	odd	2		230.2.e.a.137.1	✓	8
115.22	even	4		1150.2.e.b.643.4		8
115.68	even	4	inner	230.2.e.b.183.1	yes	8
115.114	odd	2		1150.2.e.c.1057.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.e.a.137.1	✓	8	23.22	odd	2
230.2.e.a.183.1	yes	8	5.3	odd	4
230.2.e.b.137.1	yes	8	1.1	even	1	trivial
230.2.e.b.183.1	yes	8	115.68	even	4	inner
1150.2.e.b.643.4		8	115.22	even	4
1150.2.e.b.1057.4		8	5.4	even	2
1150.2.e.c.643.4		8	5.2	odd	4
1150.2.e.c.1057.4		8	115.114	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.96195 + 1.96195i) q^{3} +1.00000i q^{4} +(-1.77462 + 1.36041i) q^{5} +2.77462 q^{6} +(-0.105561 + 0.105561i) q^{7} +(0.707107 - 0.707107i) q^{8} -4.69853i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.96195 + 1.96195i) q^{3} +1.00000i q^{4} +(-1.77462 + 1.36041i) q^{5} +2.77462 q^{6} +(-0.105561 + 0.105561i) q^{7} +(0.707107 - 0.707107i) q^{8} -4.69853i q^{9} +(2.21680 + 0.292893i) q^{10} -6.18884i q^{11} +(-1.96195 - 1.96195i) q^{12} +(-2.81835 + 2.81835i) q^{13} +0.149286 q^{14} +(0.812668 - 6.15079i) q^{15} -1.00000 q^{16} +(3.81267 - 3.81267i) q^{17} +(-3.32236 + 3.32236i) q^{18} -3.56350 q^{19} +(-1.36041 - 1.77462i) q^{20} -0.414214i q^{21} +(-4.37617 + 4.37617i) q^{22} +(-4.42793 + 1.84214i) q^{23} +2.77462i q^{24} +(1.29857 - 4.82843i) q^{25} +3.98575 q^{26} +(3.33244 + 3.33244i) q^{27} +(-0.105561 - 0.105561i) q^{28} +0.693395i q^{29} +(-4.92391 + 3.77462i) q^{30} -1.47605 q^{31} +(0.707107 + 0.707107i) q^{32} +(12.1422 + 12.1422i) q^{33} -5.39193 q^{34} +(0.0437250 - 0.330939i) q^{35} +4.69853 q^{36} +(-3.09335 + 3.09335i) q^{37} +(2.51978 + 2.51978i) q^{38} -11.0589i q^{39} +(-0.292893 + 2.21680i) q^{40} +3.87011 q^{41} +(-0.292893 + 0.292893i) q^{42} +(-7.58289 - 7.58289i) q^{43} +6.18884 q^{44} +(6.39193 + 8.33812i) q^{45} +(4.43361 + 1.82843i) q^{46} +(-3.50970 - 3.50970i) q^{47} +(1.96195 - 1.96195i) q^{48} +6.97771i q^{49} +(-4.33244 + 2.49598i) q^{50} +14.9606i q^{51} +(-2.81835 - 2.81835i) q^{52} +(-1.81630 - 1.81630i) q^{53} -4.71279i q^{54} +(8.41935 + 10.9829i) q^{55} +0.149286i q^{56} +(6.99143 - 6.99143i) q^{57} +(0.490304 - 0.490304i) q^{58} -2.80827i q^{59} +(6.15079 + 0.812668i) q^{60} +4.92680i q^{61} +(1.04372 + 1.04372i) q^{62} +(0.495984 + 0.495984i) q^{63} -1.00000i q^{64} +(1.16740 - 8.83561i) q^{65} -17.1717i q^{66} +(-6.69050 + 6.69050i) q^{67} +(3.81267 + 3.81267i) q^{68} +(5.07320 - 12.3016i) q^{69} +(-0.264927 + 0.203091i) q^{70} -15.5544 q^{71} +(-3.32236 - 3.32236i) q^{72} +(7.61108 - 7.61108i) q^{73} +4.37466 q^{74} +(6.92541 + 12.0209i) q^{75} -3.56350i q^{76} +(0.653303 + 0.653303i) q^{77} +(-7.81985 + 7.81985i) q^{78} +8.97072 q^{79} +(1.77462 - 1.36041i) q^{80} +1.01939 q^{81} +(-2.73658 - 2.73658i) q^{82} +(-0.0424449 - 0.0424449i) q^{83} +0.414214 q^{84} +(-1.57926 + 11.9528i) q^{85} +10.7238i q^{86} +(-1.36041 - 1.36041i) q^{87} +(-4.37617 - 4.37617i) q^{88} -12.5485 q^{89} +(1.37617 - 10.4157i) q^{90} -0.595018i q^{91} +(-1.84214 - 4.42793i) q^{92} +(2.89594 - 2.89594i) q^{93} +4.96346i q^{94} +(6.32387 - 4.84782i) q^{95} -2.77462 q^{96} +(-11.1223 + 11.1223i) q^{97} +(4.93399 - 4.93399i) q^{98} -29.0784 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{5} + 4 q^{6}+O(q^{10}) \) 8 * q - 4 * q^3 + 4 * q^5 + 4 * q^6	\( 8 q - 4 q^{3} + 4 q^{5} + 4 q^{6} - 4 q^{12} - 4 q^{14} - 8 q^{16} + 24 q^{17} - 8 q^{18} - 12 q^{19} - 4 q^{20} - 12 q^{22} - 16 q^{23} + 12 q^{26} + 8 q^{27} - 16 q^{30} - 4 q^{31} + 20 q^{33} - 4 q^{34} - 4 q^{35} - 4 q^{36} + 4 q^{37} + 8 q^{38} - 8 q^{40} + 12 q^{41} - 8 q^{42} - 20 q^{43} + 20 q^{44} + 12 q^{45} - 16 q^{47} + 4 q^{48} - 16 q^{50} + 12 q^{55} + 20 q^{57} + 16 q^{58} + 8 q^{60} + 4 q^{62} + 12 q^{65} - 4 q^{67} + 24 q^{68} + 12 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 28 q^{73} + 48 q^{74} - 4 q^{75} + 4 q^{77} - 4 q^{78} + 8 q^{79} - 4 q^{80} - 16 q^{81} + 8 q^{82} - 28 q^{83} - 8 q^{84} + 20 q^{85} - 4 q^{87} - 12 q^{88} - 40 q^{89} - 12 q^{90} + 16 q^{92} - 12 q^{93} - 4 q^{95} - 4 q^{96} - 8 q^{97} + 16 q^{98} - 36 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^5 + 4 * q^6 - 4 * q^12 - 4 * q^14 - 8 * q^16 + 24 * q^17 - 8 * q^18 - 12 * q^19 - 4 * q^20 - 12 * q^22 - 16 * q^23 + 12 * q^26 + 8 * q^27 - 16 * q^30 - 4 * q^31 + 20 * q^33 - 4 * q^34 - 4 * q^35 - 4 * q^36 + 4 * q^37 + 8 * q^38 - 8 * q^40 + 12 * q^41 - 8 * q^42 - 20 * q^43 + 20 * q^44 + 12 * q^45 - 16 * q^47 + 4 * q^48 - 16 * q^50 + 12 * q^55 + 20 * q^57 + 16 * q^58 + 8 * q^60 + 4 * q^62 + 12 * q^65 - 4 * q^67 + 24 * q^68 + 12 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 28 * q^73 + 48 * q^74 - 4 * q^75 + 4 * q^77 - 4 * q^78 + 8 * q^79 - 4 * q^80 - 16 * q^81 + 8 * q^82 - 28 * q^83 - 8 * q^84 + 20 * q^85 - 4 * q^87 - 12 * q^88 - 40 * q^89 - 12 * q^90 + 16 * q^92 - 12 * q^93 - 4 * q^95 - 4 * q^96 - 8 * q^97 + 16 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more