LMFDB - Embedded newform 230.2.e.a.183.1

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			183.1
Root			$0.360409i$ of defining polynomial
Character	$\chi$	$=$	230.183
Dual form			230.2.e.a.137.1

$q$-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} +(-1.84214 - 4.42793i) 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} +(-4.42793 + 1.84214i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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	−0.989721	−	0.143014i	$-0.954320\pi$
$3$	−1.96195	−	1.96195i	−1.13274	−	1.13274i	−0.143014	−	0.989721i	$-0.545680\pi$
$4$		−	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	$-0.241018\pi$
$7$	0.105561	+	0.105561i	0.0398985	+	0.0398985i	−0.686876	+	0.726775i	$0.741018\pi$
$8$	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	0.198443	−	0.980112i	$-0.436411\pi$
$13$	−2.81835	−	2.81835i	−0.781669	−	0.781669i	−0.980112	+	0.198443i	$0.936411\pi$
$14$	−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	$-0.476855\pi$
$17$	−3.81267	−	3.81267i	−0.924708	−	0.924708i	−0.997358	+	0.0726497i	$0.976855\pi$
$18$	−3.32236	−	3.32236i	−0.783089	−	0.783089i
$19$	3.56350			0.817523			0.408761	−	0.912641i	$-0.365961\pi$
$19$	3.56350			0.817523			0.408761	+	0.912641i	$0.365961\pi$
$20$	1.36041	−	1.77462i	0.304197	−	0.396818i
$21$		−	0.414214i		−	0.0903888i
$22$	4.37617	+	4.37617i	0.933002	+	0.933002i
$23$	−1.84214	−	4.42793i	−0.384113	−	0.923286i
$23$	−1.84214	−	4.42793i	−0.384113	−	0.923286i
$24$		−	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	$-0.979493\pi$
$29$		−	0.693395i		−	0.128760i	0.997925	−	0.0643801i	$-0.0205070\pi$
$30$	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	$-0.132915\pi$
$37$	3.09335	+	3.09335i	0.508544	+	0.508544i	−0.405535	+	0.914079i	$0.632915\pi$
$38$	−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	0.171132	−	0.985248i	$-0.445258\pi$
$43$	7.58289	−	7.58289i	1.15638	−	1.15638i	0.985248	−	0.171132i	$-0.0547425\pi$
$44$	−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	−0.915121	−	0.403179i	$-0.867905\pi$
$47$	−3.50970	+	3.50970i	−0.511942	+	0.511942i	0.403179	+	0.915121i	$0.367905\pi$
$48$	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	$-0.693550\pi$
$53$	1.81630	−	1.81630i	0.249488	−	0.249488i	0.820761	+	0.571272i	$0.193550\pi$
$54$			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	$0.0585170\pi$
$59$			2.80827i			0.365605i	−0.983150	+	0.182803i	$0.941483\pi$
$60$	−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	$-0.0538446\pi$
$67$	6.69050	+	6.69050i	0.817375	+	0.817375i	−0.168352	+	0.985727i	$0.553845\pi$
$68$	−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	0.994599	−	0.103789i	$-0.0330968\pi$
$73$	7.61108	+	7.61108i	0.890810	+	0.890810i	−0.103789	+	0.994599i	$0.533097\pi$
$74$	−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	$-0.668376\pi$
$79$	−8.97072			−1.00929			−0.504643	+	0.863328i	$0.668376\pi$
$80$	−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	$-0.748951\pi$
$83$	0.0424449	−	0.0424449i	0.00465894	−	0.00465894i	0.709432	+	0.704773i	$0.248951\pi$
$84$	−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	$-0.268403\pi$
$89$	12.5485			1.33014			0.665068	+	0.746783i	$0.268403\pi$
$90$	−1.37617	−	10.4157i	−0.145061	−	1.09791i
$91$		−	0.595018i		−	0.0623748i
$92$	−4.42793	+	1.84214i	−0.461643	+	0.192056i
$93$	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	0.990292	+	0.139005i	$0.0443904\pi$
$97$	11.1223	+	11.1223i	1.12930	+	1.12930i	0.139005	+	0.990292i	$0.455610\pi$
$98$	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	$-0.834280\pi$
$103$	−3.75597	+	3.75597i	−0.370087	+	0.370087i	0.497422	+	0.867509i	$0.334280\pi$
$104$		−	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	$-0.227427\pi$
$107$	1.03654	+	1.03654i	0.100206	+	0.100206i	−0.655226	+	0.755433i	$0.727427\pi$
$108$	−3.33244	−	3.33244i	−0.320665	−	0.320665i
$109$	8.14094			0.779760			0.389880	−	0.920866i	$-0.372516\pi$
$109$	8.14094			0.779760			0.389880	+	0.920866i	$0.372516\pi$
$110$	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	$-0.544348\pi$
$113$	9.05091	−	9.05091i	0.851438	−	0.851438i	0.990310	+	0.138872i	$0.0443478\pi$
$114$	9.88737			0.926037
$115$	2.75469	−	10.3640i	0.256876	−	0.966444i
$116$	−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	−0.889879	−	0.456196i	$-0.849212\pi$
$127$	−4.88737	+	4.88737i	−0.433684	+	0.433684i	0.456196	+	0.889879i	$0.349212\pi$
$128$	−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	$-0.376406\pi$
$137$	−6.40201	−	6.40201i	−0.546960	−	0.546960i	−0.925560	+	0.378600i	$0.876406\pi$
$138$	−5.11124	−	12.2858i	−0.435098	−	1.04584i
$139$		−	4.51696i		−	0.383124i	−0.981481	−	0.191562i	$-0.938645\pi$
$139$		−	4.51696i		−	0.383124i	0.981481	−	0.191562i	$-0.0613552\pi$
$140$	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	$-0.601452\pi$
$149$	−7.64987			−0.626701			−0.313351	+	0.949637i	$0.601452\pi$
$150$	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	−0.997169	−	0.0751893i	$-0.976044\pi$
$157$	−13.4366	−	13.4366i	−1.07236	−	1.07236i	−0.0751893	−	0.997169i	$-0.523956\pi$
$158$	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	0.983413	+	0.181379i	$0.0580559\pi$
$163$	14.8711	+	14.8711i	1.16479	+	1.16479i	0.181379	+	0.983413i	$0.441944\pi$
$164$		−	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	−0.434906	−	0.900476i	$-0.643218\pi$
$167$	6.01650	−	6.01650i	0.465570	−	0.465570i	0.900476	+	0.434906i	$0.143218\pi$
$168$	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	0.776502	−	0.630115i	$-0.216992\pi$
$173$	1.92541	+	1.92541i	0.146387	+	0.146387i	−0.630115	+	0.776502i	$0.716992\pi$
$174$		−	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	$-0.754040\pi$
$179$		−	18.6793i		−	1.39615i	0.716023	−	0.698077i	$-0.245960\pi$
$180$	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	0.905689	−	0.423943i	$-0.139354\pi$
$193$	6.69263	+	6.69263i	0.481746	+	0.481746i	−0.423943	+	0.905689i	$0.639354\pi$
$194$	−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	−0.812500	−	0.582961i	$-0.801894\pi$
$197$	−3.22174	+	3.22174i	−0.229540	+	0.229540i	0.582961	+	0.812500i	$0.301894\pi$
$198$	−20.5616	+	20.5616i	−1.46125	+	1.46125i
$199$	−10.7052			−0.758872			−0.379436	−	0.925218i	$-0.623882\pi$
$199$	−10.7052			−0.758872			−0.379436	+	0.925218i	$0.623882\pi$
$200$	−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
$207$	20.8048	−	8.65535i	1.44603	−	0.601588i
$208$	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	0.556847	−	0.830615i	$-0.312011\pi$
$223$	−4.08822	−	4.08822i	−0.273767	−	0.273767i	−0.830615	+	0.556847i	$0.812011\pi$
$224$	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	0.989722	+	0.143001i	$0.0456754\pi$
$227$	17.0662	+	17.0662i	1.13272	+	1.13272i	0.143001	+	0.989722i	$0.454325\pi$
$228$	−6.99143	+	6.99143i	−0.463018	+	0.463018i
$229$	9.95968			0.658154			0.329077	−	0.944303i	$-0.393262\pi$
$229$	9.95968			0.658154			0.329077	+	0.944303i	$0.393262\pi$
$230$	5.38057	+	9.27629i	0.354784	+	0.611660i
$231$	−2.56350			−0.168666
$232$	0.490304	−	0.490304i	0.0321900	−	0.0321900i
$233$	−6.85886	−	6.85886i	−0.449339	−	0.449339i	0.445796	−	0.895135i	$-0.352921\pi$
$233$	−6.85886	−	6.85886i	−0.449339	−	0.449339i	−0.895135	+	0.445796i	$0.852921\pi$
$234$			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	$0.0789403\pi$
$239$			7.58956i			0.490928i	−0.969406	+	0.245464i	$0.921060\pi$
$240$	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
$253$	−27.4037	+	11.4007i	−1.72286	+	0.716756i
$254$		−	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	−0.598805	−	0.800895i	$-0.704358\pi$
$257$	3.23975	−	3.23975i	0.202090	−	0.202090i	0.800895	+	0.598805i	$0.204358\pi$
$258$	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	$-0.753250\pi$
$263$	−0.234147	+	0.234147i	−0.0144381	+	0.0144381i	0.699851	+	0.714289i	$0.253250\pi$
$264$	−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	$0.261050\pi$
$269$			23.9859i			1.46244i	−0.682140	+	0.731222i	$0.738950\pi$
$270$	−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	0.0262258	−	0.999656i	$-0.491651\pi$
$277$	17.0741	−	17.0741i	1.02588	−	1.02588i	0.999656	−	0.0262258i	$-0.00834890\pi$
$278$	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	$-0.556580\pi$
$283$	13.5830	−	13.5830i	0.807426	−	0.807426i	0.984244	+	0.176818i	$0.0565803\pi$
$284$			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	$-0.553376\pi$
$293$	14.0203	−	14.0203i	0.819073	−	0.819073i	0.985974	+	0.166901i	$0.0533759\pi$
$294$		−	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	−0.997312	−	0.0732738i	$-0.976655\pi$
$307$	−16.1905	+	16.1905i	−0.924038	+	0.924038i	0.0732738	+	0.997312i	$0.476655\pi$
$308$	−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	$-0.778366\pi$
$313$	−2.22666	+	2.22666i	−0.125858	+	0.125858i	0.641372	+	0.767230i	$0.278366\pi$
$314$	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	−0.0927548	−	0.995689i	$-0.529567\pi$
$317$	16.0763	−	16.0763i	0.902934	−	0.902934i	0.995689	+	0.0927548i	$0.0295673\pi$
$318$	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
$322$	0.275006	+	0.661029i	0.0153255	+	0.0368377i
$323$	−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	$-0.193047\pi$
$337$	4.62039	+	4.62039i	0.251689	+	0.251689i	−0.569974	+	0.821663i	$0.693047\pi$
$338$	−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
$345$	−25.7382	+	14.9290i	−1.38570	+	0.803753i
$346$	−2.72295			−0.146387
$347$	16.5306	−	16.5306i	0.887409	−	0.887409i	−0.106865	−	0.994274i	$-0.534081\pi$
$347$	16.5306	−	16.5306i	0.887409	−	0.887409i	0.994274	+	0.106865i	$0.0340812\pi$
$348$	1.36041	+	1.36041i	0.0729256	+	0.0729256i
$349$		−	4.22674i		−	0.226252i	−0.993581	−	0.113126i	$-0.963914\pi$
$349$		−	4.22674i		−	0.226252i	0.993581	−	0.113126i	$-0.0360864\pi$
$350$	−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	0.0227275	−	0.999742i	$-0.492765\pi$
$353$	−18.3564	−	18.3564i	−0.977014	−	0.977014i	−0.999742	+	0.0227275i	$0.992765\pi$
$354$			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	$-0.190570\pi$
$359$	31.3037			1.65214			0.826072	+	0.563564i	$0.190570\pi$
$360$	−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	$-0.269850\pi$
$367$	−1.68837	−	1.68837i	−0.0881323	−	0.0881323i	−0.749799	+	0.661666i	$0.769850\pi$
$368$	1.84214	+	4.42793i	0.0960281	+	0.230822i
$369$			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	0.244621	−	0.969619i	$-0.421336\pi$
$373$	23.4509	−	23.4509i	1.21424	−	1.21424i	0.969619	−	0.244621i	$-0.0786636\pi$
$374$		−	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	$-0.656189\pi$
$379$	−18.3477			−0.942457			−0.471228	+	0.882011i	$0.656189\pi$
$380$	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	$-0.788036\pi$
$383$	−3.29934	+	3.29934i	−0.168588	+	0.168588i	0.617770	+	0.786359i	$0.288036\pi$
$384$			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	$-0.387929\pi$
$389$	13.6031			0.689702			0.344851	+	0.938657i	$0.387929\pi$
$390$	−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	−0.542981	−	0.839745i	$-0.682705\pi$
$397$	5.91297	−	5.91297i	0.296763	−	0.296763i	0.839745	+	0.542981i	$0.182705\pi$
$398$	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	$-0.977607\pi$
$409$		−	2.84313i		−	0.140584i	0.997526	−	0.0702919i	$-0.0223931\pi$
$410$	−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	$-0.575148\pi$
$419$	−9.57558			−0.467798			−0.233899	+	0.972261i	$0.575148\pi$
$420$	−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	$-0.975995\pi$
$433$	−19.1818	+	19.1818i	−0.921817	+	0.921817i	0.0753410	+	0.997158i	$0.475995\pi$
$434$	0.220354			0.0105773
$435$	−4.26493	+	0.563500i	−0.204488	+	0.0270178i
$436$		−	8.14094i		−	0.389880i
$437$	−6.56446	−	15.7789i	−0.314021	−	0.754808i
$438$	21.1179	+	21.1179i	1.00905	+	1.00905i
$439$		−	27.6042i		−	1.31748i	−0.752372	−	0.658738i	$-0.771090\pi$
$439$		−	27.6042i		−	1.31748i	0.752372	−	0.658738i	$-0.228910\pi$
$440$	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	0.876491	−	0.481418i	$-0.159878\pi$
$443$	8.31532	+	8.31532i	0.395073	+	0.395073i	−0.481418	+	0.876491i	$0.659878\pi$
$444$	−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	$0.174841\pi$
$449$			22.1250i			1.04414i	−0.852901	+	0.522072i	$0.825159\pi$
$450$	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	$-0.311655\pi$
$457$	−5.81931	−	5.81931i	−0.272216	−	0.272216i	−0.829992	+	0.557776i	$0.811655\pi$
$458$	−7.04256	+	7.04256i	−0.329077	+	0.329077i
$459$	−25.4110			−1.18608
$460$	−10.3640	−	2.75469i	−0.483222	−	0.128438i
$461$	−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	0.740305	−	0.672271i	$-0.234681\pi$
$463$	1.46392	+	1.46392i	0.0680343	+	0.0680343i	−0.672271	+	0.740305i	$0.734681\pi$
$464$			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	$-0.450131\pi$
$467$	−17.9737	−	17.9737i	−0.831725	−	0.831725i	−0.987753	+	0.156027i	$0.950131\pi$
$468$	−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	$-0.258299\pi$
$479$	30.1342			1.37687			0.688433	+	0.725300i	$0.258299\pi$
$480$	−4.92391	−	3.77462i	−0.224745	−	0.172287i
$481$		−	17.4363i		−	0.795027i
$482$	−8.78779	−	8.78779i	−0.400273	−	0.400273i
$483$	−1.83411	+	0.763039i	−0.0834547	+	0.0347195i
$484$			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	−0.847466	−	0.530850i	$-0.821873\pi$
$487$	−6.98711	+	6.98711i	−0.316616	+	0.316616i	0.530850	+	0.847466i	$0.321873\pi$
$488$	−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	$-0.993028\pi$
$499$		−	0.978439i		−	0.0438010i	0.999760	−	0.0219005i	$-0.00697170\pi$
$500$	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	−0.230653	+	0.973036i	$0.574086\pi$
$503$	−26.9959	+	26.9959i	−1.20369	+	1.20369i	−0.973036	+	0.230653i	$0.925914\pi$
$504$	−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	$0.268733\pi$
$509$			33.7275i			1.49495i	−0.664292	+	0.747474i	$0.731267\pi$
$510$	−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	$-0.997914\pi$
$523$	−22.7188	+	22.7188i	−0.993424	+	0.993424i	0.00655453	+	0.999979i	$0.497914\pi$
$524$		−	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	−0.828807	−	0.559535i	$-0.810980\pi$
$547$	−6.29772	+	6.29772i	−0.269271	+	0.269271i	0.559535	+	0.828807i	$0.310980\pi$
$548$	−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
$552$	−12.2858	+	5.11124i	−0.522919	+	0.217549i
$553$	−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	$-0.138994\pi$
$557$	11.4051	+	11.4051i	0.483249	+	0.483249i	−0.422918	+	0.906168i	$0.638994\pi$
$558$	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	$-0.753226\pi$
$563$	−0.340089	+	0.340089i	−0.0143330	+	0.0143330i	0.699904	+	0.714237i	$0.253226\pi$
$564$		−	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	$-0.342323\pi$
$569$	22.6776			0.950693			0.475346	+	0.879799i	$0.342323\pi$
$570$	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
$575$	18.9878	−	14.6446i	0.791844	−	0.610723i
$576$	−4.69853			−0.195772
$577$	−12.2581	+	12.2581i	−0.510309	+	0.510309i	−0.914621	−	0.404312i	$-0.867511\pi$
$577$	−12.2581	+	12.2581i	−0.510309	+	0.510309i	0.404312	+	0.914621i	$0.367511\pi$
$578$	−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	−0.117889	+	0.993027i	$0.537613\pi$
$587$	−26.9154	+	26.9154i	−1.11092	+	1.11092i	−0.993027	+	0.117889i	$0.962387\pi$
$588$	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	0.997909	−	0.0646344i	$-0.0205881\pi$
$593$	22.7267	+	22.7267i	0.933275	+	0.933275i	−0.0646344	+	0.997909i	$0.520588\pi$
$594$	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
$598$	−7.34230	−	17.6486i	−0.300249	−	0.721704i
$599$			33.3373i			1.36213i	0.732225	+	0.681063i	$0.238482\pi$
$599$			33.3373i			1.36213i	−0.732225	+	0.681063i	$0.761518\pi$
$600$	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	−0.830985	−	0.556295i	$-0.812222\pi$
$607$	−6.76763	+	6.76763i	−0.274690	+	0.274690i	0.556295	+	0.830985i	$0.312222\pi$
$608$	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	$-0.726195\pi$
$613$	2.61611	−	2.61611i	0.105663	−	0.105663i	0.757962	+	0.652299i	$0.226195\pi$
$614$		−	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	$-0.267203\pi$
$617$	−1.89756	−	1.89756i	−0.0763928	−	0.0763928i	−0.744271	+	0.667878i	$0.767203\pi$
$618$	−10.4214	+	10.4214i	−0.419210	+	0.419210i
$619$	35.4461			1.42470			0.712349	−	0.701825i	$-0.247631\pi$
$619$	35.4461			1.42470			0.712349	+	0.701825i	$0.247631\pi$
$620$	−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	$-0.702933\pi$
$643$	5.28328	−	5.28328i	0.208352	−	0.208352i	0.803567	+	0.595215i	$0.202933\pi$
$644$	−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	−0.401716	−	0.915764i	$-0.631586\pi$
$647$	13.0754	−	13.0754i	0.514049	−	0.514049i	0.915764	+	0.401716i	$0.131586\pi$
$648$	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	−0.988550	−	0.150892i	$-0.951785\pi$
$653$	−29.1171	−	29.1171i	−1.13944	−	1.13944i	−0.150892	−	0.988550i	$-0.548215\pi$
$654$	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	$-0.591675\pi$
$659$	−14.5832			−0.568080			−0.284040	+	0.958812i	$0.591675\pi$
$660$	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
$667$	−3.07030	+	1.27733i	−0.118883	+	0.0494584i
$668$	−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	0.804384	−	0.594110i	$-0.202496\pi$
$673$	5.45496	+	5.45496i	0.210273	+	0.210273i	−0.594110	+	0.804384i	$0.702496\pi$
$674$	−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	$-0.393640\pi$
$677$	−16.0470	−	16.0470i	−0.616735	−	0.616735i	−0.944693	+	0.327957i	$0.893640\pi$
$678$	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	0.845560	−	0.533880i	$-0.179267\pi$
$683$	8.14554	+	8.14554i	0.311681	+	0.311681i	−0.533880	+	0.845560i	$0.679267\pi$
$684$	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
$690$	7.64322	−	28.7561i	0.290973	−	1.09473i
$691$	−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	$-0.786203\pi$
$709$	−41.6866			−1.56557			−0.782787	+	0.622289i	$0.786203\pi$
$710$	34.4810	−	4.55577i	1.29405	−	0.170975i
$711$		−	42.1492i		−	1.58072i
$712$	8.87311	+	8.87311i	0.332534	+	0.332534i
$713$	2.71909	+	6.53584i	0.101831	+	0.244769i
$714$		−	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	$0.0383982\pi$
$719$			6.45359i			0.240678i	−0.992733	+	0.120339i	$0.961602\pi$
$720$	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	$-0.0403501\pi$
$727$	23.3378	+	23.3378i	0.865552	+	0.865552i	−0.126424	+	0.991976i	$0.540350\pi$
$728$	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	$-0.583842\pi$
$733$	19.0912	−	19.0912i	0.705151	−	0.705151i	0.965511	+	0.260361i	$0.0838415\pi$
$734$	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	$-0.851578\pi$
$739$		−	24.4426i		−	0.899137i	0.893246	−	0.449568i	$-0.148422\pi$
$740$	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	$-0.847480\pi$
$743$	−11.6216	+	11.6216i	−0.426355	+	0.426355i	0.461030	+	0.887385i	$0.347480\pi$
$744$			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	$-0.195853\pi$
$757$	6.58699	+	6.58699i	0.239408	+	0.239408i	−0.577197	+	0.816605i	$0.695853\pi$
$758$	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	$-0.319220\pi$
$769$	29.8326			1.07579			0.537895	+	0.843012i	$0.319220\pi$
$770$	−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	$-0.920609\pi$
$773$	−20.0799	+	20.0799i	−0.722223	+	0.722223i	0.246835	+	0.969058i	$0.420609\pi$
$774$	−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
$782$	−9.93268	−	23.8751i	−0.355192	−	0.853770i
$783$	−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	$-0.449910\pi$
$787$	−23.3105	−	23.3105i	−0.830929	−	0.830929i	−0.987644	+	0.156715i	$0.949910\pi$
$788$	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	−0.998591	−	0.0530737i	$-0.983098\pi$
$797$	−29.6897	−	29.6897i	−1.05166	−	1.05166i	−0.0530737	−	0.998591i	$-0.516902\pi$
$798$	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
$805$	1.38482	−	0.803246i	0.0488086	−	0.0283107i
$806$	−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	$0.0482113\pi$
$809$			8.58305i			0.301764i	−0.988552	+	0.150882i	$0.951789\pi$
$810$	−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	0.941388	−	0.337326i	$-0.109522\pi$
$823$	17.3293	+	17.3293i	0.604062	+	0.604062i	−0.337326	+	0.941388i	$0.609522\pi$
$824$	−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	0.948775	+	0.315952i	$0.102324\pi$
$827$	36.3705	+	36.3705i	1.26473	+	1.26473i	0.315952	+	0.948775i	$0.397676\pi$
$828$	−8.65535	−	20.8048i	−0.300794	−	0.723015i
$829$			36.2528i			1.25911i	0.776956	+	0.629555i	$0.216763\pi$
$829$			36.2528i			1.25911i	−0.776956	+	0.629555i	$0.783237\pi$
$830$	−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	$-0.478265\pi$
$839$	3.95258			0.136458			0.0682291	+	0.997670i	$0.478265\pi$
$840$	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	0.664324	−	0.747444i	$-0.268719\pi$
$853$	−2.42762	−	2.42762i	−0.0831201	−	0.0831201i	−0.747444	+	0.664324i	$0.768719\pi$
$854$		−	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	−0.973081	−	0.230465i	$-0.925975\pi$
$857$	−21.7397	+	21.7397i	−0.742615	+	0.742615i	0.230465	+	0.973081i	$0.425975\pi$
$858$	−48.3958	+	48.3958i	−1.65220	+	1.65220i
$859$		−	39.4154i		−	1.34483i	−0.740172	−	0.672417i	$-0.765256\pi$
$859$		−	39.4154i		−	1.34483i	0.740172	−	0.672417i	$-0.234744\pi$
$860$	−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	0.246289	−	0.969196i	$-0.420789\pi$
$863$	−21.2367	−	21.2367i	−0.722907	−	0.722907i	−0.969196	+	0.246289i	$0.920789\pi$
$864$		−	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	−0.0322740	+	0.999479i	$0.510275\pi$
$877$	−30.5545	+	30.5545i	−1.03175	+	1.03175i	−0.999479	+	0.0322740i	$0.989725\pi$
$878$	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	0.742652	−	0.669677i	$-0.233568\pi$
$883$	2.16848	+	2.16848i	0.0729752	+	0.0729752i	−0.669677	+	0.742652i	$0.733568\pi$
$884$	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	−0.890720	−	0.454553i	$-0.849799\pi$
$887$	−12.9902	+	12.9902i	−0.436167	+	0.436167i	0.454553	+	0.890720i	$0.349799\pi$
$888$	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
$897$	48.9682	−	20.3721i	1.63500	−	0.680205i
$898$	−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	$-0.444126\pi$
$907$	−24.3943	−	24.3943i	−0.809999	−	0.809999i	−0.984633	+	0.174634i	$0.944126\pi$
$908$	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	$-0.362206\pi$
$919$	25.4342			0.838997			0.419499	+	0.907756i	$0.362206\pi$
$920$	9.27629	−	5.38057i	0.305830	−	0.177392i
$921$	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	$0.247611\pi$
$929$			42.7798i			1.40356i	−0.712393	+	0.701780i	$0.752389\pi$
$930$	−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	$-0.0362775\pi$
$937$	26.9308	+	26.9308i	0.879790	+	0.879790i	−0.113722	+	0.993513i	$0.536277\pi$
$938$	−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
$943$	−7.12927	−	17.1365i	−0.232161	−	0.558042i
$944$		−	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	−0.949842	−	0.312731i	$-0.898756\pi$
$947$	−19.6060	+	19.6060i	−0.637110	+	0.637110i	0.312731	+	0.949842i	$0.398756\pi$
$948$	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	$-0.833360\pi$
$953$	−11.3030	+	11.3030i	−0.366139	+	0.366139i	0.499928	+	0.866067i	$0.333360\pi$
$954$	−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	−0.838657	−	0.544660i	$-0.816659\pi$
$967$	−9.14230	+	9.14230i	−0.293996	+	0.293996i	0.544660	+	0.838657i	$0.316659\pi$
$968$	−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	$-0.436114\pi$
$977$	−24.3981	−	24.3981i	−0.780566	−	0.780566i	−0.979926	+	0.199361i	$0.936114\pi$
$978$	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	$-0.531590\pi$
$983$	28.0921	−	28.0921i	0.895998	−	0.895998i	0.995079	+	0.0990812i	$0.0315904\pi$
$984$		−	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	−0.0681047	−	0.997678i	$-0.521695\pi$
$997$	29.3516	−	29.3516i	0.929574	−	0.929574i	0.997678	+	0.0681047i	$0.0216952\pi$
$998$	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.a.183.1	yes	8
5.2	odd	4		230.2.e.b.137.1	yes	8
5.3	odd	4		1150.2.e.b.1057.4		8
5.4	even	2		1150.2.e.c.643.4		8
23.22	odd	2		230.2.e.b.183.1	yes	8
115.22	even	4	inner	230.2.e.a.137.1	✓	8
115.68	even	4		1150.2.e.c.1057.4		8
115.114	odd	2		1150.2.e.b.643.4		8

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

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} +(-1.84214 - 4.42793i) 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} +(-4.42793 + 1.84214i) 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

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Database

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