LMFDB - Embedded newform 112.3.l.b.13.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,3,Mod(13,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("112.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	112.l (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:	$3.05177896084$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.25
Character	$\chi$	$=$	112.13
Dual form			112.3.l.b.69.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.89147 + 0.649887i) q^{2} +(-1.75534 + 1.75534i) q^{3} +(3.15529 + 2.45848i) q^{4} +(3.25602 + 3.25602i) q^{5} +(-4.46095 + 2.17940i) q^{6} +(-4.90539 - 4.99371i) q^{7} +(4.37040 + 6.70072i) q^{8} +2.83754i q^{9} +O(q^{10})$	\(q+(1.89147 + 0.649887i) q^{2} +(-1.75534 + 1.75534i) q^{3} +(3.15529 + 2.45848i) q^{4} +(3.25602 + 3.25602i) q^{5} +(-4.46095 + 2.17940i) q^{6} +(-4.90539 - 4.99371i) q^{7} +(4.37040 + 6.70072i) q^{8} +2.83754i q^{9} +(4.04260 + 8.27469i) q^{10} +(-2.01178 + 2.01178i) q^{11} +(-9.85410 + 1.22314i) q^{12} +(6.07310 - 6.07310i) q^{13} +(-6.03303 - 12.6334i) q^{14} -11.4309 q^{15} +(3.91175 + 15.5145i) q^{16} +9.55815i q^{17} +(-1.84408 + 5.36712i) q^{18} +(25.2086 - 25.2086i) q^{19} +(2.26883 + 18.2785i) q^{20} +(17.3763 + 0.155043i) q^{21} +(-5.11264 + 2.49778i) q^{22} -14.0394i q^{23} +(-19.4336 - 4.09052i) q^{24} -3.79671i q^{25} +(15.4339 - 7.54024i) q^{26} +(-20.7789 - 20.7789i) q^{27} +(-3.20099 - 27.8164i) q^{28} +(-11.2161 - 11.2161i) q^{29} +(-21.6211 - 7.42876i) q^{30} -16.5180i q^{31} +(-2.68371 + 31.8873i) q^{32} -7.06271i q^{33} +(-6.21172 + 18.0789i) q^{34} +(0.287592 - 32.2316i) q^{35} +(-6.97605 + 8.95328i) q^{36} +(27.6654 - 27.6654i) q^{37} +(64.0639 - 31.2985i) q^{38} +21.3208i q^{39} +(-7.58757 + 36.0477i) q^{40} +12.9650 q^{41} +(32.7660 + 11.5859i) q^{42} +(-50.9760 + 50.9760i) q^{43} +(-11.2937 + 1.40183i) q^{44} +(-9.23909 + 9.23909i) q^{45} +(9.12403 - 26.5550i) q^{46} +66.5020i q^{47} +(-34.0996 - 20.3667i) q^{48} +(-0.874351 + 48.9922i) q^{49} +(2.46744 - 7.18136i) q^{50} +(-16.7778 - 16.7778i) q^{51} +(34.0930 - 4.23181i) q^{52} +(39.3660 - 39.3660i) q^{53} +(-25.7987 - 52.8067i) q^{54} -13.1008 q^{55} +(12.0230 - 54.6941i) q^{56} +88.4994i q^{57} +(-13.9257 - 28.5042i) q^{58} +(-30.4313 - 30.4313i) q^{59} +(-36.0677 - 28.1025i) q^{60} +(11.9950 - 11.9950i) q^{61} +(10.7348 - 31.2432i) q^{62} +(14.1699 - 13.9192i) q^{63} +(-25.7993 + 58.5696i) q^{64} +39.5482 q^{65} +(4.58997 - 13.3589i) q^{66} +(-19.5294 - 19.5294i) q^{67} +(-23.4985 + 30.1587i) q^{68} +(24.6440 + 24.6440i) q^{69} +(21.4909 - 60.7782i) q^{70} +69.7628i q^{71} +(-19.0136 + 12.4012i) q^{72} -143.326 q^{73} +(70.3076 - 34.3488i) q^{74} +(6.66453 + 6.66453i) q^{75} +(141.515 - 17.5657i) q^{76} +(19.9148 + 0.177693i) q^{77} +(-13.8561 + 40.3275i) q^{78} +66.7548 q^{79} +(-37.7786 + 63.2520i) q^{80} +47.4105 q^{81} +(24.5229 + 8.42578i) q^{82} +(-60.7490 + 60.7490i) q^{83} +(54.4462 + 43.2085i) q^{84} +(-31.1215 + 31.1215i) q^{85} +(-129.548 + 63.2908i) q^{86} +39.3763 q^{87} +(-22.2726 - 4.68809i) q^{88} -78.9394 q^{89} +(-23.4798 + 11.4711i) q^{90} +(-60.1182 - 0.536415i) q^{91} +(34.5156 - 44.2984i) q^{92} +(28.9947 + 28.9947i) q^{93} +(-43.2188 + 125.786i) q^{94} +164.159 q^{95} +(-51.2623 - 60.6839i) q^{96} -35.4878i q^{97} +(-33.4932 + 92.0989i) q^{98} +(-5.70850 - 5.70850i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{2} - 8 q^{4} - 16 q^{8}+O(q^{10}) $ 56 * q - 4 * q^2 - 8 * q^4 - 16 * q^8	$ 56 q - 4 q^{2} - 8 q^{4} - 16 q^{8} + 40 q^{14} - 8 q^{15} + 48 q^{16} + 196 q^{18} - 20 q^{21} - 120 q^{22} - 96 q^{29} - 40 q^{30} - 184 q^{32} - 100 q^{35} + 160 q^{36} - 128 q^{37} - 144 q^{42} - 72 q^{43} - 448 q^{44} - 168 q^{46} + 192 q^{49} - 364 q^{50} - 128 q^{51} + 88 q^{53} + 56 q^{56} + 408 q^{58} + 504 q^{60} + 444 q^{63} + 256 q^{64} - 8 q^{65} + 440 q^{67} - 112 q^{70} + 592 q^{72} - 408 q^{74} + 12 q^{77} + 664 q^{78} - 8 q^{79} + 64 q^{81} - 576 q^{84} + 96 q^{85} + 256 q^{86} + 448 q^{88} - 388 q^{91} - 1192 q^{92} + 32 q^{93} - 776 q^{95} + 540 q^{98} + 8 q^{99}+O(q^{100}) $ 56 * q - 4 * q^2 - 8 * q^4 - 16 * q^8 + 40 * q^14 - 8 * q^15 + 48 * q^16 + 196 * q^18 - 20 * q^21 - 120 * q^22 - 96 * q^29 - 40 * q^30 - 184 * q^32 - 100 * q^35 + 160 * q^36 - 128 * q^37 - 144 * q^42 - 72 * q^43 - 448 * q^44 - 168 * q^46 + 192 * q^49 - 364 * q^50 - 128 * q^51 + 88 * q^53 + 56 * q^56 + 408 * q^58 + 504 * q^60 + 444 * q^63 + 256 * q^64 - 8 * q^65 + 440 * q^67 - 112 * q^70 + 592 * q^72 - 408 * q^74 + 12 * q^77 + 664 * q^78 - 8 * q^79 + 64 * q^81 - 576 * q^84 + 96 * q^85 + 256 * q^86 + 448 * q^88 - 388 * q^91 - 1192 * q^92 + 32 * q^93 - 776 * q^95 + 540 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.89147	+	0.649887i	0.945733	+	0.324944i
$2$	1.89147	+	0.649887i	0.945733	+	0.324944i
$3$	−1.75534	+	1.75534i	−0.585114	+	0.585114i	−0.936304	−	0.351190i	$-0.885777\pi$
$3$	−1.75534	+	1.75534i	−0.585114	+	0.585114i	0.351190	+	0.936304i	$0.385777\pi$
$4$	3.15529	+	2.45848i	0.788823	+	0.614620i
$5$	3.25602	+	3.25602i	0.651203	+	0.651203i	0.953283	−	0.302079i	$-0.0976808\pi$
$5$	3.25602	+	3.25602i	0.651203	+	0.651203i	−0.302079	+	0.953283i	$0.597681\pi$
$6$	−4.46095	+	2.17940i	−0.743491	+	0.363233i
$7$	−4.90539	−	4.99371i	−0.700770	−	0.713388i
$7$	−4.90539	−	4.99371i	−0.700770	−	0.713388i
$8$	4.37040	+	6.70072i	0.546300	+	0.837590i
$9$			2.83754i			0.315283i
$10$	4.04260	+	8.27469i	0.404260	+	0.827469i
$11$	−2.01178	+	2.01178i	−0.182889	+	0.182889i	−0.792613	−	0.609725i	$-0.791280\pi$
$11$	−2.01178	+	2.01178i	−0.182889	+	0.182889i	0.609725	+	0.792613i	$0.291280\pi$
$12$	−9.85410	+	1.22314i	−0.821175	+	0.101929i
$13$	6.07310	−	6.07310i	0.467162	−	0.467162i	−0.433832	−	0.900994i	$-0.642839\pi$
$13$	6.07310	−	6.07310i	0.467162	−	0.467162i	0.900994	+	0.433832i	$0.142839\pi$
$14$	−6.03303	−	12.6334i	−0.430930	−	0.902385i
$15$	−11.4309			−0.762057
$16$	3.91175	+	15.5145i	0.244484	+	0.969653i
$17$			9.55815i			0.562244i	0.959672	+	0.281122i	$0.0907065\pi$
$17$			9.55815i			0.562244i	−0.959672	+	0.281122i	$0.909293\pi$
$18$	−1.84408	+	5.36712i	−0.102449	+	0.298173i
$19$	25.2086	−	25.2086i	1.32677	−	1.32677i	0.418595	−	0.908173i	$-0.362523\pi$
$19$	25.2086	−	25.2086i	1.32677	−	1.32677i	0.908173	−	0.418595i	$-0.137477\pi$
$20$	2.26883	+	18.2785i	0.113442	+	0.913927i
$21$	17.3763	+	0.155043i	0.827444	+	0.00738300i
$22$	−5.11264	+	2.49778i	−0.232393	+	0.113535i
$23$		−	14.0394i		−	0.610408i	−0.952287	−	0.305204i	$-0.901275\pi$
$23$		−	14.0394i		−	0.610408i	0.952287	−	0.305204i	$-0.0987247\pi$
$24$	−19.4336	−	4.09052i	−0.809733	−	0.170438i
$25$		−	3.79671i		−	0.151869i
$26$	15.4339	−	7.54024i	0.593612	−	0.290009i
$27$	−20.7789	−	20.7789i	−0.769591	−	0.769591i
$28$	−3.20099	−	27.8164i	−0.114321	−	0.993444i
$29$	−11.2161	−	11.2161i	−0.386764	−	0.386764i	0.486768	−	0.873531i	$-0.338176\pi$
$29$	−11.2161	−	11.2161i	−0.386764	−	0.386764i	−0.873531	+	0.486768i	$0.838176\pi$
$30$	−21.6211	−	7.42876i	−0.720702	−	0.247625i
$31$		−	16.5180i		−	0.532837i	−0.963857	−	0.266419i	$-0.914160\pi$
$31$		−	16.5180i		−	0.532837i	0.963857	−	0.266419i	$-0.0858404\pi$
$32$	−2.68371	+	31.8873i	−0.0838659	+	0.996477i
$33$		−	7.06271i		−	0.214022i
$34$	−6.21172	+	18.0789i	−0.182698	+	0.531733i
$35$	0.287592	−	32.2316i	0.00821691	−	0.920904i
$36$	−6.97605	+	8.95328i	−0.193779	+	0.248702i
$37$	27.6654	−	27.6654i	0.747714	−	0.747714i	−0.226335	−	0.974049i	$-0.572675\pi$
$37$	27.6654	−	27.6654i	0.747714	−	0.747714i	0.974049	+	0.226335i	$0.0726746\pi$
$38$	64.0639	−	31.2985i	1.68589	−	0.823644i
$39$			21.3208i			0.546686i
$40$	−7.58757	+	36.0477i	−0.189689	+	0.901193i
$41$	12.9650			0.316219			0.158110	−	0.987422i	$-0.449460\pi$
$41$	12.9650			0.316219			0.158110	+	0.987422i	$0.449460\pi$
$42$	32.7660	+	11.5859i	0.780142	+	0.275855i
$43$	−50.9760	+	50.9760i	−1.18549	+	1.18549i	−0.207187	+	0.978301i	$0.566431\pi$
$43$	−50.9760	+	50.9760i	−1.18549	+	1.18549i	−0.978301	+	0.207187i	$0.933569\pi$
$44$	−11.2937	+	1.40183i	−0.256674	+	0.0318598i
$45$	−9.23909	+	9.23909i	−0.205313	+	0.205313i
$46$	9.12403	−	26.5550i	0.198348	−	0.577284i
$47$			66.5020i			1.41494i	0.706745	+	0.707468i	$0.250163\pi$
$47$			66.5020i			1.41494i	−0.706745	+	0.707468i	$0.749837\pi$
$48$	−34.0996	−	20.3667i	−0.710409	−	0.424307i
$49$	−0.874351	+	48.9922i	−0.0178439	+	0.999841i
$50$	2.46744	−	7.18136i	0.0493487	−	0.143627i
$51$	−16.7778	−	16.7778i	−0.328977	−	0.328977i
$52$	34.0930	−	4.23181i	0.655635	−	0.0813810i
$53$	39.3660	−	39.3660i	0.742755	−	0.742755i	−0.230353	−	0.973107i	$-0.573988\pi$
$53$	39.3660	−	39.3660i	0.742755	−	0.742755i	0.973107	+	0.230353i	$0.0739880\pi$
$54$	−25.7987	−	52.8067i	−0.477754	−	0.977901i
$55$	−13.1008			−0.238196
$56$	12.0230	−	54.6941i	0.214696	−	0.976681i
$57$			88.4994i			1.55262i
$58$	−13.9257	−	28.5042i	−0.240099	−	0.491452i
$59$	−30.4313	−	30.4313i	−0.515785	−	0.515785i	0.400508	−	0.916293i	$-0.368834\pi$
$59$	−30.4313	−	30.4313i	−0.515785	−	0.515785i	−0.916293	+	0.400508i	$0.868834\pi$
$60$	−36.0677	−	28.1025i	−0.601128	−	0.468375i
$61$	11.9950	−	11.9950i	0.196639	−	0.196639i	−0.601918	−	0.798558i	$-0.705597\pi$
$61$	11.9950	−	11.9950i	0.196639	−	0.196639i	0.798558	+	0.601918i	$0.205597\pi$
$62$	10.7348	−	31.2432i	0.173142	−	0.503922i
$63$	14.1699	−	13.9192i	0.224919	−	0.220940i
$64$	−25.7993	+	58.5696i	−0.403114	+	0.915150i
$65$	39.5482			0.608434
$66$	4.58997	−	13.3589i	0.0695450	−	0.202407i
$67$	−19.5294	−	19.5294i	−0.291483	−	0.291483i	0.546183	−	0.837666i	$-0.316080\pi$
$67$	−19.5294	−	19.5294i	−0.291483	−	0.291483i	−0.837666	+	0.546183i	$0.816080\pi$
$68$	−23.4985	+	30.1587i	−0.345566	+	0.443511i
$69$	24.6440	+	24.6440i	0.357159	+	0.357159i
$70$	21.4909	−	60.7782i	0.307013	−	0.868260i
$71$			69.7628i			0.982574i	0.870998	+	0.491287i	$0.163473\pi$
$71$			69.7628i			0.982574i	−0.870998	+	0.491287i	$0.836527\pi$
$72$	−19.0136	+	12.4012i	−0.264078	+	0.172239i
$73$	−143.326			−1.96337			−0.981686	−	0.190507i	$-0.938987\pi$
$73$	−143.326			−1.96337			−0.981686	+	0.190507i	$0.938987\pi$
$74$	70.3076	−	34.3488i	0.950103	−	0.464173i
$75$	6.66453	+	6.66453i	0.0888604	+	0.0888604i
$76$	141.515	−	17.5657i	1.86204	−	0.231127i
$77$	19.9148	+	0.177693i	0.258633	+	0.00230770i
$78$	−13.8561	+	40.3275i	−0.177642	+	0.517019i
$79$	66.7548			0.844998			0.422499	−	0.906363i	$-0.361153\pi$
$79$	66.7548			0.844998			0.422499	+	0.906363i	$0.361153\pi$
$80$	−37.7786	+	63.2520i	−0.472233	+	0.790650i
$81$	47.4105			0.585314
$82$	24.5229	+	8.42578i	0.299059	+	0.102753i
$83$	−60.7490	+	60.7490i	−0.731916	+	0.731916i	−0.970999	−	0.239083i	$-0.923153\pi$
$83$	−60.7490	+	60.7490i	−0.731916	+	0.731916i	0.239083	+	0.970999i	$0.423153\pi$
$84$	54.4462	+	43.2085i	0.648169	+	0.514387i
$85$	−31.1215	+	31.1215i	−0.366135	+	0.366135i
$86$	−129.548	+	63.2908i	−1.50637	+	0.735939i
$87$	39.3763			0.452602
$88$	−22.2726	−	4.68809i	−0.253098	−	0.0532737i
$89$	−78.9394			−0.886960			−0.443480	−	0.896284i	$-0.646256\pi$
$89$	−78.9394			−0.886960			−0.443480	+	0.896284i	$0.646256\pi$
$90$	−23.4798	+	11.4711i	−0.260887	+	0.127456i
$91$	−60.1182	−	0.536415i	−0.660640	−	0.00589467i
$92$	34.5156	−	44.2984i	0.375169	−	0.481504i
$93$	28.9947	+	28.9947i	0.311771	+	0.311771i
$94$	−43.2188	+	125.786i	−0.459775	+	1.33815i
$95$	164.159			1.72799
$96$	−51.2623	−	60.6839i	−0.533982	−	0.632124i
$97$		−	35.4878i		−	0.365854i	−0.983126	−	0.182927i	$-0.941443\pi$
$97$		−	35.4878i		−	0.365854i	0.983126	−	0.182927i	$-0.0585572\pi$
$98$	−33.4932	+	92.0989i	−0.341768	+	0.939785i
$99$	−5.70850	−	5.70850i	−0.0576616	−	0.0576616i
$100$	9.33414	−	11.9797i	0.0933414	−	0.119797i
$101$	135.312	+	135.312i	1.33972	+	1.33972i	0.896324	+	0.443400i	$0.146228\pi$
$101$	135.312	+	135.312i	1.33972	+	1.33972i	0.443400	+	0.896324i	$0.353772\pi$
$102$	−20.8310	−	42.6384i	−0.204225	−	0.418023i
$103$	−76.3602			−0.741361			−0.370680	−	0.928760i	$-0.620875\pi$
$103$	−76.3602			−0.741361			−0.370680	+	0.928760i	$0.620875\pi$
$104$	67.2360	+	14.1523i	0.646500	+	0.136080i
$105$	56.0727	+	57.0824i	0.534026	+	0.543642i
$106$	100.043	−	48.8760i	0.943801	−	0.461094i
$107$	61.8636	−	61.8636i	0.578164	−	0.578164i	−0.356233	−	0.934397i	$-0.615939\pi$
$107$	61.8636	−	61.8636i	0.578164	−	0.578164i	0.934397	+	0.356233i	$0.115939\pi$
$108$	−14.4790	−	116.648i	−0.134065	−	1.08008i
$109$	−95.4954	−	95.4954i	−0.876105	−	0.876105i	0.117024	−	0.993129i	$-0.462664\pi$
$109$	−95.4954	−	95.4954i	−0.876105	−	0.876105i	−0.993129	+	0.117024i	$0.962664\pi$
$110$	−24.7796	−	8.51401i	−0.225269	−	0.0774001i
$111$			97.1246i			0.874996i
$112$	58.2861	−	95.6385i	0.520412	−	0.853916i
$113$	−141.353			−1.25091			−0.625456	−	0.780260i	$-0.715087\pi$
$113$	−141.353			−1.25091			−0.625456	+	0.780260i	$0.715087\pi$
$114$	−57.5147	+	167.394i	−0.504515	+	1.46837i
$115$	45.7125	−	45.7125i	0.397500	−	0.397500i
$116$	−7.81555	−	62.9649i	−0.0673754	−	0.542801i
$117$	17.2327	+	17.2327i	0.147288	+	0.147288i
$118$	−37.7829	−	77.3367i	−0.320194	−	0.655396i
$119$	47.7306	−	46.8864i	0.401098	−	0.394003i
$120$	−49.9573	−	76.5949i	−0.416311	−	0.638291i
$121$			112.906i			0.933103i
$122$	30.4835	−	14.8927i	0.249865	−	0.122072i
$123$	−22.7580	+	22.7580i	−0.185024	+	0.185024i
$124$	40.6091	−	52.1190i	0.327493	−	0.420315i
$125$	93.7626	−	93.7626i	0.750101	−	0.750101i
$126$	35.8478	−	17.1190i	0.284506	−	0.135865i
$127$	−80.1444			−0.631058			−0.315529	−	0.948916i	$-0.602182\pi$
$127$	−80.1444			−0.631058			−0.315529	+	0.948916i	$0.602182\pi$
$128$	−86.8621	+	94.0158i	−0.678610	+	0.734499i
$129$		−	178.961i		−	1.38729i
$130$	74.8042	+	25.7019i	0.575417	+	0.197707i
$131$	90.0359	−	90.0359i	0.687297	−	0.687297i	−0.274337	−	0.961634i	$-0.588458\pi$
$131$	90.0359	−	90.0359i	0.687297	−	0.687297i	0.961634	+	0.274337i	$0.0884582\pi$
$132$	17.3635	−	22.2849i	0.131542	−	0.168825i
$133$	−249.542	−	2.22658i	−1.87626	−	0.0167412i
$134$	−24.2472	−	49.6310i	−0.180950	−	0.370381i
$135$		−	135.313i		−	1.00232i
$136$	−64.0465	+	41.7729i	−0.470930	+	0.307154i
$137$		−	253.079i		−	1.84729i	−0.383247	−	0.923646i	$-0.625194\pi$
$137$		−	253.079i		−	1.84729i	0.383247	−	0.923646i	$-0.374806\pi$
$138$	30.5974	+	62.6290i	0.221720	+	0.453833i
$139$	49.2592	+	49.2592i	0.354382	+	0.354382i	0.861737	−	0.507355i	$-0.169377\pi$
$139$	49.2592	+	49.2592i	0.354382	+	0.354382i	−0.507355	+	0.861737i	$0.669377\pi$
$140$	80.1483	−	100.993i	0.572488	−	0.721380i
$141$	−116.734	−	116.734i	−0.827899	−	0.827899i
$142$	−45.3379	+	131.954i	−0.319281	+	0.929253i
$143$			24.4354i			0.170877i
$144$	−44.0229	+	11.0997i	−0.305715	+	0.0770816i
$145$		−	73.0399i		−	0.503723i
$146$	−271.097	−	93.1458i	−1.85683	−	0.637985i
$147$	−84.4633	−	87.5329i	−0.574580	−	0.595462i
$148$	155.307	−	19.2776i	1.04937	−	0.130254i
$149$	40.4528	−	40.4528i	0.271495	−	0.271495i	−0.558207	−	0.829702i	$-0.688510\pi$
$149$	40.4528	−	40.4528i	0.271495	−	0.271495i	0.829702	+	0.558207i	$0.188510\pi$
$150$	8.27455	+	16.9369i	0.0551636	+	0.112913i
$151$			34.5523i			0.228823i	0.993433	+	0.114412i	$0.0364983\pi$
$151$			34.5523i			0.228823i	−0.993433	+	0.114412i	$0.963502\pi$
$152$	279.087	+	58.7442i	1.83610	+	0.386475i
$153$	−27.1217			−0.177266
$154$	37.5527	+	13.2785i	0.243848	+	0.0862238i
$155$	53.7828	−	53.7828i	0.346986	−	0.346986i
$156$	−52.4167	+	67.2732i	−0.336004	+	0.431239i
$157$	17.2009	−	17.2009i	0.109560	−	0.109560i	−0.650202	−	0.759762i	$-0.725316\pi$
$157$	17.2009	−	17.2009i	0.109560	−	0.109560i	0.759762	+	0.650202i	$0.225316\pi$
$158$	126.265	+	43.3831i	0.799143	+	0.274577i
$159$			138.202i			0.869193i
$160$	−112.564	+	95.0873i	−0.703523	+	0.594295i
$161$	−70.1087	+	68.8687i	−0.435458	+	0.427756i
$162$	89.6753	+	30.8115i	0.553551	+	0.190194i
$163$	−38.9774	−	38.9774i	−0.239125	−	0.239125i	0.577363	−	0.816488i	$-0.304082\pi$
$163$	−38.9774	−	38.9774i	−0.239125	−	0.239125i	−0.816488	+	0.577363i	$0.804082\pi$
$164$	40.9083	+	31.8742i	0.249441	+	0.194355i
$165$	22.9963	−	22.9963i	0.139372	−	0.139372i
$166$	−154.385	+	75.4248i	−0.930029	+	0.454366i
$167$	137.053			0.820679			0.410339	−	0.911933i	$-0.365410\pi$
$167$	137.053			0.820679			0.410339	+	0.911933i	$0.365410\pi$
$168$	74.9025	+	117.111i	0.445848	+	0.697092i
$169$			95.2349i			0.563520i
$170$	−79.0907	+	38.6398i	−0.465239	+	0.227293i
$171$	71.5305	+	71.5305i	0.418307	+	0.418307i
$172$	−286.168	+	35.5207i	−1.66377	+	0.206516i
$173$	59.0992	−	59.0992i	0.341614	−	0.341614i	−0.515360	−	0.856974i	$-0.672342\pi$
$173$	59.0992	−	59.0992i	0.341614	−	0.341614i	0.856974	+	0.515360i	$0.172342\pi$
$174$	74.4791	+	25.5902i	0.428041	+	0.147070i
$175$	−18.9597	+	18.6243i	−0.108341	+	0.106425i
$176$	−39.0812	−	23.3420i	−0.222052	−	0.132625i
$177$	106.835			0.603586
$178$	−149.311	−	51.3017i	−0.838827	−	0.288212i
$179$	150.604	+	150.604i	0.841364	+	0.841364i	0.989036	−	0.147673i	$-0.0471782\pi$
$179$	150.604	+	150.604i	0.841364	+	0.841364i	−0.147673	+	0.989036i	$0.547178\pi$
$180$	−51.8661	+	6.43791i	−0.288145	+	0.0357662i
$181$	−195.403	−	195.403i	−1.07958	−	1.07958i	−0.996547	−	0.0830294i	$-0.973540\pi$
$181$	−195.403	−	195.403i	−1.07958	−	1.07958i	−0.0830294	−	0.996547i	$-0.526460\pi$
$182$	−113.363	−	40.0847i	−0.622874	−	0.220246i
$183$			42.1106i			0.230113i
$184$	94.0740	−	61.3577i	0.511272	−	0.333466i
$185$	180.158			0.973828
$186$	35.9992	+	73.6858i	0.193544	+	0.396160i
$187$	−19.2288	−	19.2288i	−0.102828	−	0.102828i
$188$	−163.494	+	209.833i	−0.869648	+	1.11613i
$189$	−1.83533	+	205.693i	−0.00971073	+	1.08832i
$190$	310.502	+	106.685i	1.63422	+	0.561500i
$191$	59.1682			0.309781			0.154891	−	0.987932i	$-0.450497\pi$
$191$	59.1682			0.309781			0.154891	+	0.987932i	$0.450497\pi$
$192$	−57.5231	−	148.096i	−0.299600	−	0.771335i
$193$	−190.929			−0.989269			−0.494634	−	0.869101i	$-0.664698\pi$
$193$	−190.929			−0.989269			−0.494634	+	0.869101i	$0.664698\pi$
$194$	23.0631	−	67.1241i	0.118882	−	0.346000i
$195$	−69.4207	+	69.4207i	−0.356004	+	0.356004i
$196$	−123.205	+	152.435i	−0.628598	+	0.777730i
$197$	142.902	−	142.902i	0.725390	−	0.725390i	−0.244308	−	0.969698i	$-0.578561\pi$
$197$	142.902	−	142.902i	0.725390	−	0.725390i	0.969698	+	0.244308i	$0.0785608\pi$
$198$	−7.08756	−	14.5073i	−0.0357958	−	0.0732693i
$199$	138.990			0.698440			0.349220	−	0.937041i	$-0.386447\pi$
$199$	138.990			0.698440			0.349220	+	0.937041i	$0.386447\pi$
$200$	25.4407	−	16.5931i	0.127204	−	0.0829657i
$201$	68.5614			0.341102
$202$	168.001	+	343.876i	0.831687	+	1.70236i
$203$	−0.990681	+	111.030i	−0.00488020	+	0.546944i
$204$	−11.6910	−	94.1869i	−0.0573088	−	0.461700i
$205$	42.2142	+	42.2142i	0.205923	+	0.205923i
$206$	−144.433	−	49.6255i	−0.701130	−	0.240901i
$207$	39.8374			0.192451
$208$	117.977	+	70.4644i	0.567198	+	0.338771i
$209$			101.428i			0.485302i
$210$	68.9626	+	144.410i	0.328393	+	0.687669i
$211$	212.666	+	212.666i	1.00789	+	1.00789i	0.999969	+	0.00792508i	$0.00252266\pi$
$211$	212.666	+	212.666i	1.00789	+	1.00789i	0.00792508	+	0.999969i	$0.497477\pi$
$212$	220.992	−	27.4307i	1.04241	−	0.129390i
$213$	−122.458	−	122.458i	−0.574918	−	0.574918i
$214$	157.217	−	76.8085i	0.734660	−	0.358918i
$215$	−331.957			−1.54399
$216$	48.4217	−	230.046i	0.224174	−	1.06503i
$217$	−82.4860	+	81.0270i	−0.380120	+	0.373396i
$218$	−118.565	−	242.688i	−0.543877	−	1.11325i
$219$	251.586	−	251.586i	1.14880	−	1.14880i
$220$	−41.3367	−	32.2079i	−0.187894	−	0.146400i
$221$	58.0476	+	58.0476i	0.262659	+	0.262659i
$222$	−63.1200	+	183.708i	−0.284324	+	0.827513i
$223$		−	346.003i		−	1.55158i	−0.630988	−	0.775792i	$-0.717350\pi$
$223$		−	346.003i		−	1.55158i	0.630988	−	0.775792i	$-0.282650\pi$
$224$	172.401	−	143.018i	0.769645	−	0.638472i
$225$	10.7733			0.0478815
$226$	−267.364	−	91.8635i	−1.18303	−	0.406476i
$227$	−189.005	+	189.005i	−0.832622	+	0.832622i	−0.987875	−	0.155252i	$-0.950381\pi$
$227$	−189.005	+	189.005i	−0.832622	+	0.832622i	0.155252	+	0.987875i	$0.450381\pi$
$228$	−217.574	+	279.242i	−0.954272	+	1.22474i
$229$	151.137	+	151.137i	0.659987	+	0.659987i	0.955377	−	0.295390i	$-0.0954496\pi$
$229$	151.137	+	151.137i	0.659987	+	0.659987i	−0.295390	+	0.955377i	$0.595450\pi$
$230$	116.172	−	56.7557i	0.505094	−	0.246764i
$231$	−35.2692	+	34.6453i	−0.152680	+	0.149980i
$232$	26.1372	−	124.175i	0.112661	−	0.535238i
$233$		−	10.5086i		−	0.0451015i	−0.999746	−	0.0225507i	$-0.992821\pi$
$233$		−	10.5086i		−	0.0451015i	0.999746	−	0.0225507i	$-0.00717873\pi$
$234$	21.3958	+	43.7944i	0.0914348	+	0.187155i
$235$	−216.532	+	216.532i	−0.921411	+	0.921411i
$236$	−21.2049	−	170.834i	−0.0898513	−	0.723875i
$237$	−117.178	+	117.178i	−0.494420	+	0.494420i
$238$	120.752	−	57.6645i	0.507361	−	0.242288i
$239$	−362.334			−1.51604			−0.758021	−	0.652230i	$-0.773834\pi$
$239$	−362.334			−1.51604			−0.758021	+	0.652230i	$0.773834\pi$
$240$	−44.7146	−	177.343i	−0.186311	−	0.738931i
$241$			363.356i			1.50770i	0.657046	+	0.753851i	$0.271806\pi$
$241$			363.356i			1.50770i	−0.657046	+	0.753851i	$0.728194\pi$
$242$	−73.3759	+	213.557i	−0.303206	+	0.882467i
$243$	103.789	−	103.789i	0.427115	−	0.427115i
$244$	67.3371	−	8.35825i	0.275972	−	0.0342551i
$245$	−162.366	+	156.673i	−0.662720	+	0.639480i
$246$	−57.8362	+	28.2559i	−0.235106	+	0.114861i
$247$		−	306.189i		−	1.23963i
$248$	110.682	−	72.1900i	0.446299	−	0.291089i
$249$		−	213.271i		−	0.856509i
$250$	238.284	−	116.414i	0.953136	−	0.465655i
$251$	54.1542	+	54.1542i	0.215754	+	0.215754i	0.806706	−	0.590952i	$-0.201248\pi$
$251$	54.1542	+	54.1542i	0.215754	+	0.215754i	−0.590952	+	0.806706i	$0.701248\pi$
$252$	78.9303	−	9.08294i	0.313216	−	0.0360434i
$253$	28.2441	+	28.2441i	0.111637	+	0.111637i
$254$	−151.590	−	52.0848i	−0.596813	−	0.205058i
$255$		−	109.258i		−	0.428462i
$256$	−225.396	+	121.377i	−0.880455	+	0.474130i
$257$		−	45.3701i		−	0.176537i	−0.996097	−	0.0882687i	$-0.971867\pi$
$257$		−	45.3701i		−	0.176537i	0.996097	−	0.0882687i	$-0.0281334\pi$
$258$	116.304	−	338.498i	0.450792	−	1.31201i
$259$	−273.863	−	2.44358i	−1.05739	−	0.00943469i
$260$	124.786	+	97.2286i	0.479947	+	0.373956i
$261$	31.8263	−	31.8263i	0.121940	−	0.121940i
$262$	228.813	−	111.787i	0.873333	−	0.426667i
$263$			502.464i			1.91051i	0.295787	+	0.955254i	$0.404418\pi$
$263$			502.464i			1.91051i	−0.295787	+	0.955254i	$0.595582\pi$
$264$	47.3253	−	30.8669i	0.179262	−	0.116920i
$265$	256.353			0.967368
$266$	−470.554	−	166.386i	−1.76900	−	0.625511i
$267$	138.566	−	138.566i	0.518973	−	0.518973i
$268$	−13.6083	−	109.633i	−0.0507772	−	0.409080i
$269$	−81.3588	+	81.3588i	−0.302449	+	0.302449i	−0.841971	−	0.539522i	$-0.818605\pi$
$269$	−81.3588	+	81.3588i	−0.302449	+	0.302449i	0.539522	+	0.841971i	$0.318605\pi$
$270$	87.9383	−	255.940i	0.325698	−	0.947927i
$271$		−	192.959i		−	0.712026i	−0.934481	−	0.356013i	$-0.884136\pi$
$271$		−	192.959i		−	0.712026i	0.934481	−	0.356013i	$-0.115864\pi$
$272$	−148.289	+	37.3890i	−0.545182	+	0.137460i
$273$	106.470	−	104.587i	0.389999	−	0.383101i
$274$	164.473	−	478.691i	0.600266	−	1.74705i
$275$	7.63814	+	7.63814i	0.0277750	+	0.0277750i
$276$	17.1722	+	138.346i	0.0622181	+	0.501252i
$277$	−211.837	+	211.837i	−0.764756	+	0.764756i	−0.977178	−	0.212422i	$-0.931865\pi$
$277$	−211.837	+	211.837i	−0.764756	+	0.764756i	0.212422	+	0.977178i	$0.431865\pi$
$278$	61.1591	+	125.185i	0.219997	+	0.450306i
$279$	46.8704			0.167994
$280$	217.232	−	138.938i	0.775829	−	0.496207i
$281$		−	85.3556i		−	0.303756i	−0.988399	−	0.151878i	$-0.951468\pi$
$281$		−	85.3556i		−	0.303756i	0.988399	−	0.151878i	$-0.0485322\pi$
$282$	−144.934	−	296.662i	−0.513951	−	1.05199i
$283$	−87.4756	−	87.4756i	−0.309101	−	0.309101i	0.535460	−	0.844561i	$-0.320138\pi$
$283$	−87.4756	−	87.4756i	−0.309101	−	0.309101i	−0.844561	+	0.535460i	$0.820138\pi$
$284$	−171.510	+	220.122i	−0.603910	+	0.775077i
$285$	−288.156	+	288.156i	−1.01107	+	1.01107i
$286$	−15.8803	+	46.2188i	−0.0555255	+	0.161604i
$287$	−63.5983	−	64.7435i	−0.221597	−	0.225587i
$288$	−90.4815	−	7.61514i	−0.314172	−	0.0264415i
$289$	197.642			0.683882
$290$	47.4677	−	138.153i	0.163682	−	0.476388i
$291$	62.2933	+	62.2933i	0.214066	+	0.214066i
$292$	−452.236	−	352.365i	−1.54875	−	1.20673i
$293$	30.7055	+	30.7055i	0.104797	+	0.104797i	0.757561	−	0.652764i	$-0.226391\pi$
$293$	30.7055	+	30.7055i	0.104797	+	0.104797i	−0.652764	+	0.757561i	$0.726391\pi$
$294$	−102.873	−	220.457i	−0.349908	−	0.749854i
$295$		−	198.170i		−	0.671762i
$296$	306.287	+	64.4694i	1.03475	+	0.217802i
$297$	83.6052			0.281499
$298$	102.805	−	50.2253i	0.344983	−	0.168541i
$299$	−85.2627	−	85.2627i	−0.285159	−	0.285159i
$300$	4.64393	+	37.4132i	0.0154798	+	0.124711i
$301$	504.617	+	4.50252i	1.67647	+	0.0149585i
$302$	−22.4551	+	65.3546i	−0.0743547	+	0.216406i
$303$	−475.038			−1.56778
$304$	489.707	+	292.488i	1.61088	+	0.962131i
$305$	78.1117			0.256104
$306$	−51.2997	−	17.6260i	−0.167646	−	0.0576014i
$307$	31.6433	−	31.6433i	0.103073	−	0.103073i	−0.653690	−	0.756763i	$-0.726780\pi$
$307$	31.6433	−	31.6433i	0.103073	−	0.103073i	0.756763	+	0.653690i	$0.226780\pi$
$308$	62.4001	+	49.5208i	0.202598	+	0.160782i
$309$	134.038	−	134.038i	0.433781	−	0.433781i
$310$	136.681	−	66.7756i	0.440907	−	0.215405i
$311$	−499.800			−1.60708			−0.803538	−	0.595254i	$-0.797052\pi$
$311$	−499.800			−1.60708			−0.803538	+	0.595254i	$0.797052\pi$
$312$	−142.864	+	93.1801i	−0.457899	+	0.298654i
$313$	−52.7521			−0.168537			−0.0842685	−	0.996443i	$-0.526855\pi$
$313$	−52.7521			−0.168537			−0.0842685	+	0.996443i	$0.526855\pi$
$314$	43.7136	−	21.3563i	0.139215	−	0.0680137i
$315$	91.4587	+	0.816055i	0.290345	+	0.00259065i
$316$	210.631	+	164.115i	0.666554	+	0.519353i
$317$	218.091	+	218.091i	0.687983	+	0.687983i	0.961786	−	0.273803i	$-0.0882816\pi$
$317$	218.091	+	218.091i	0.687983	+	0.687983i	−0.273803	+	0.961786i	$0.588282\pi$
$318$	−89.8155	+	261.404i	−0.282439	+	0.822024i
$319$	45.1287			0.141469
$320$	−274.706	+	106.701i	−0.858458	+	0.333440i
$321$			217.184i			0.676584i
$322$	−177.365	+	84.7000i	−0.550824	+	0.263044i
$323$	240.947	+	240.947i	0.745967	+	0.745967i
$324$	149.594	+	116.558i	0.461709	+	0.359746i
$325$	−23.0578	−	23.0578i	−0.0709471	−	0.0709471i
$326$	−48.3935	−	99.0553i	−0.148446	−	0.303851i
$327$	335.254			1.02524
$328$	56.6622	+	86.8748i	0.172750	+	0.264862i
$329$	332.092	−	326.218i	1.00940	−	0.991544i
$330$	58.4418	−	28.5517i	0.177096	−	0.0865204i
$331$	−20.4515	+	20.4515i	−0.0617871	+	0.0617871i	−0.737325	−	0.675538i	$-0.763911\pi$
$331$	−20.4515	+	20.4515i	−0.0617871	+	0.0617871i	0.675538	+	0.737325i	$0.263911\pi$
$332$	−341.031	+	42.3307i	−1.02720	+	0.127502i
$333$	78.5018	+	78.5018i	0.235741	+	0.235741i
$334$	259.232	+	89.0692i	0.776143	+	0.266674i
$335$		−	127.176i		−	0.379629i
$336$	65.5663	+	270.191i	0.195138	+	0.804138i
$337$	451.093			1.33855			0.669277	−	0.743013i	$-0.266604\pi$
$337$	451.093			1.33855			0.669277	+	0.743013i	$0.266604\pi$
$338$	−61.8919	+	180.134i	−0.183112	+	0.532940i
$339$	248.123	−	248.123i	0.731926	−	0.731926i
$340$	−174.709	+	21.6858i	−0.513850	+	0.0637818i
$341$	33.2304	+	33.2304i	0.0974500	+	0.0974500i
$342$	88.8107	+	181.784i	0.259681	+	0.531533i
$343$	248.942	−	235.959i	0.725779	−	0.687928i
$344$	−564.361	−	118.791i	−1.64058	−	0.345321i
$345$			160.482i			0.465166i
$346$	150.192	−	73.3763i	0.434081	−	0.212070i
$347$	−313.926	+	313.926i	−0.904687	+	0.904687i	−0.995837	−	0.0911505i	$-0.970946\pi$
$347$	−313.926	+	313.926i	−0.904687	+	0.904687i	0.0911505	+	0.995837i	$0.470946\pi$
$348$	124.244	+	96.8060i	0.357023	+	0.278178i
$349$	−400.540	+	400.540i	−1.14768	+	1.14768i	−0.160670	+	0.987008i	$0.551366\pi$
$349$	−400.540	+	400.540i	−1.14768	+	1.14768i	−0.987008	+	0.160670i	$0.948634\pi$
$350$	−47.9654	+	22.9057i	−0.137044	+	0.0654448i
$351$	−252.385			−0.719046
$352$	−58.7510	−	69.5491i	−0.166906	−	0.197583i
$353$		−	464.090i		−	1.31470i	−0.753584	−	0.657352i	$-0.771677\pi$
$353$		−	464.090i		−	1.31470i	0.753584	−	0.657352i	$-0.228323\pi$
$354$	202.074	+	69.4306i	0.570832	+	0.196132i
$355$	−227.149	+	227.149i	−0.639855	+	0.639855i
$356$	−249.077	−	194.071i	−0.699654	−	0.545143i
$357$	−1.48192	+	166.085i	−0.00415105	+	0.465225i
$358$	186.987	+	382.738i	0.522310	+	1.06910i
$359$			126.355i			0.351963i	0.984393	+	0.175982i	$0.0563099\pi$
$359$			126.355i			0.351963i	−0.984393	+	0.175982i	$0.943690\pi$
$360$	−102.287	−	21.5301i	−0.284131	−	0.0598057i
$361$		−	909.946i		−	2.52063i
$362$	−242.609	−	496.589i	−0.670190	−	1.37179i
$363$	−198.188	−	198.188i	−0.545972	−	0.545972i
$364$	−188.372	−	149.492i	−0.517505	−	0.410693i
$365$	−466.672	−	466.672i	−1.27855	−	1.27855i
$366$	−27.3672	+	79.6508i	−0.0747737	+	0.217625i
$367$			90.0661i			0.245412i	0.992443	+	0.122706i	$0.0391572\pi$
$367$			90.0661i			0.245412i	−0.992443	+	0.122706i	$0.960843\pi$
$368$	217.814	−	54.9186i	0.591885	−	0.149235i
$369$			36.7887i			0.0996985i
$370$	340.763	+	117.082i	0.920981	+	0.316439i
$371$	−389.688	−	3.47705i	−1.05037	−	0.00937211i
$372$	20.2039	+	162.770i	0.0543114	+	0.437553i
$373$	−363.710	+	363.710i	−0.975094	+	0.975094i	−0.999697	−	0.0246037i	$-0.992168\pi$
$373$	−363.710	+	363.710i	−0.975094	+	0.975094i	0.0246037	+	0.999697i	$0.492168\pi$
$374$	−23.8741	−	48.8673i	−0.0638346	−	0.130661i
$375$			329.171i			0.877789i
$376$	−445.611	+	290.640i	−1.18514	+	0.772979i
$377$	−136.234			−0.361362
$378$	−137.149	+	387.868i	−0.362827	+	1.02611i
$379$	290.869	−	290.869i	0.767465	−	0.767465i	−0.210194	−	0.977660i	$-0.567410\pi$
$379$	290.869	−	290.869i	0.767465	−	0.767465i	0.977660	+	0.210194i	$0.0674096\pi$
$380$	517.970	+	403.582i	1.36308	+	1.06206i
$381$	140.681	−	140.681i	0.369241	−	0.369241i
$382$	111.915	+	38.4527i	0.292970	+	0.100661i
$383$		−	234.051i		−	0.611099i	−0.952176	−	0.305550i	$-0.901160\pi$
$383$		−	234.051i		−	0.611099i	0.952176	−	0.305550i	$-0.0988402\pi$
$384$	−12.5572	−	317.503i	−0.0327011	−	0.826830i
$385$	64.2643	+	65.4214i	0.166920	+	0.169926i
$386$	−361.136	−	124.082i	−0.935584	−	0.321457i
$387$	−144.647	−	144.647i	−0.373764	−	0.373764i
$388$	87.2462	−	111.975i	0.224861	−	0.288594i
$389$	83.4977	−	83.4977i	0.214647	−	0.214647i	−0.591591	−	0.806238i	$-0.701500\pi$
$389$	83.4977	−	83.4977i	0.214647	−	0.214647i	0.806238	+	0.591591i	$0.201500\pi$
$390$	−176.423	+	86.1913i	−0.452366	+	0.221003i
$391$	134.191			0.343198
$392$	−332.104	+	208.257i	−0.847205	+	0.531267i
$393$			316.088i			0.804295i
$394$	363.164	−	177.424i	0.921736	−	0.450314i
$395$	217.355	+	217.355i	0.550265	+	0.550265i
$396$	−3.97775	−	32.0462i	−0.0100448	−	0.0809248i
$397$	174.436	−	174.436i	0.439386	−	0.439386i	−0.452419	−	0.891805i	$-0.649439\pi$
$397$	174.436	−	174.436i	0.439386	−	0.439386i	0.891805	+	0.452419i	$0.149439\pi$
$398$	262.894	+	90.3275i	0.660538	+	0.226954i
$399$	441.941	−	434.124i	1.10762	−	1.08803i
$400$	58.9039	−	14.8518i	0.147260	−	0.0371294i
$401$	−187.735			−0.468168			−0.234084	−	0.972216i	$-0.575209\pi$
$401$	−187.735			−0.468168			−0.234084	+	0.972216i	$0.575209\pi$
$402$	129.682	+	44.5572i	0.322591	+	0.110839i
$403$	−100.315	−	100.315i	−0.248921	−	0.248921i
$404$	94.2871	+	759.612i	0.233384	+	1.88023i
$405$	154.369	+	154.369i	0.381159	+	0.381159i
$406$	−74.0307	+	209.365i	−0.182342	+	0.515678i
$407$			111.313i			0.273497i
$408$	39.0977	−	185.749i	0.0958278	−	0.455268i
$409$	−144.940			−0.354377			−0.177188	−	0.984177i	$-0.556700\pi$
$409$	−144.940			−0.354377			−0.177188	+	0.984177i	$0.556700\pi$
$410$	52.4123	+	107.281i	0.127835	+	0.261662i
$411$	444.240	+	444.240i	1.08088	+	1.08088i
$412$	−240.939	−	187.730i	−0.584803	−	0.455655i
$413$	−2.68789	+	301.243i	−0.00650820	+	0.729401i
$414$	75.3511	+	25.8898i	0.182008	+	0.0625358i
$415$	−395.600			−0.953253
$416$	177.356	+	209.953i	0.426337	+	0.504695i
$417$	−172.933			−0.414708
$418$	−65.9168	+	191.848i	−0.157696	+	0.458966i
$419$	177.168	−	177.168i	0.422835	−	0.422835i	−0.463344	−	0.886179i	$-0.653350\pi$
$419$	177.168	−	177.168i	0.422835	−	0.422835i	0.886179	+	0.463344i	$0.153350\pi$
$420$	36.5900	+	317.965i	0.0871190	+	0.757061i
$421$	468.234	−	468.234i	1.11220	−	1.11220i	0.119342	−	0.992853i	$-0.461922\pi$
$421$	468.234	−	468.234i	1.11220	−	1.11220i	0.992853	−	0.119342i	$-0.0380784\pi$
$422$	264.041	+	540.459i	0.625690	+	1.28071i
$423$	−188.702			−0.446105
$424$	435.825	+	91.7355i	1.02789	+	0.216357i
$425$	36.2895			0.0853871
$426$	−152.041	−	311.208i	−0.356903	−	0.730535i
$427$	−118.740	−	1.05947i	−0.278079	−	0.00248120i
$428$	347.288	−	43.1073i	0.811421	−	0.100718i
$429$	−42.8926	−	42.8926i	−0.0999827	−	0.0999827i
$430$	−627.886	−	215.735i	−1.46020	−	0.501709i
$431$	497.233			1.15367			0.576836	−	0.816860i	$-0.304287\pi$
$431$	497.233			1.15367			0.576836	+	0.816860i	$0.304287\pi$
$432$	241.092	−	403.656i	0.558083	−	0.934389i
$433$			210.739i			0.486696i	0.969939	+	0.243348i	$0.0782457\pi$
$433$			210.739i			0.486696i	−0.969939	+	0.243348i	$0.921754\pi$
$434$	−208.678	+	99.6533i	−0.480825	+	0.229616i
$435$	128.210	+	128.210i	0.294736	+	0.294736i
$436$	−66.5424	−	536.090i	−0.152620	−	1.22956i
$437$	−353.913	−	353.913i	−0.809870	−	0.809870i
$438$	639.370	−	312.365i	1.45975	−	0.713161i
$439$	762.892			1.73779			0.868897	−	0.494993i	$-0.164829\pi$
$439$	762.892			1.73779			0.868897	+	0.494993i	$0.164829\pi$
$440$	−57.2555	−	87.7845i	−0.130126	−	0.199510i
$441$	−139.017	−	2.48101i	−0.315232	−	0.00562587i
$442$	72.0707	+	147.519i	0.163056	+	0.333754i
$443$	−140.252	+	140.252i	−0.316596	+	0.316596i	−0.847458	−	0.530862i	$-0.821868\pi$
$443$	−140.252	+	140.252i	−0.316596	+	0.316596i	0.530862	+	0.847458i	$0.321868\pi$
$444$	−238.779	+	306.456i	−0.537790	+	0.690217i
$445$	−257.028	−	257.028i	−0.577591	−	0.577591i
$446$	224.863	−	654.454i	0.504178	−	1.46739i
$447$			142.017i			0.317711i
$448$	419.035	−	158.472i	0.935346	−	0.353733i
$449$	−599.904			−1.33609			−0.668044	−	0.744122i	$-0.732868\pi$
$449$	−599.904			−1.33609			−0.668044	+	0.744122i	$0.732868\pi$
$450$	20.3774	+	7.00146i	0.0452831	+	0.0155588i
$451$	−26.0827	+	26.0827i	−0.0578330	+	0.0578330i
$452$	−446.010	−	347.514i	−0.986748	−	0.768835i
$453$	−60.6512	−	60.6512i	−0.133888	−	0.133888i
$454$	−480.329	+	234.665i	−1.05799	+	0.516883i
$455$	−193.999	−	197.493i	−0.426372	−	0.434050i
$456$	−593.010	+	386.778i	−1.30046	+	0.848196i
$457$			557.580i			1.22009i	0.792368	+	0.610044i	$0.208848\pi$
$457$			557.580i			1.22009i	−0.792368	+	0.610044i	$0.791152\pi$
$458$	187.648	+	384.092i	0.409713	+	0.838630i
$459$	198.608	−	198.608i	0.432698	−	0.432698i
$460$	256.620	−	31.8530i	0.557869	−	0.0692457i
$461$	482.593	−	482.593i	1.04684	−	1.04684i	0.0479917	−	0.998848i	$-0.484718\pi$
$461$	482.593	−	482.593i	1.04684	−	1.04684i	0.998848	−	0.0479917i	$-0.0152821\pi$
$462$	−89.2260	+	42.6095i	−0.193130	+	0.0922284i
$463$	−326.635			−0.705475			−0.352737	−	0.935722i	$-0.614749\pi$
$463$	−326.635			−0.705475			−0.352737	+	0.935722i	$0.614749\pi$
$464$	130.138	−	217.887i	0.280469	−	0.469584i
$465$			188.814i			0.406052i
$466$	6.82944	−	19.8768i	0.0146554	−	0.0426540i
$467$	−213.948	+	213.948i	−0.458132	+	0.458132i	−0.898042	−	0.439910i	$-0.855010\pi$
$467$	−213.948	+	213.948i	−0.458132	+	0.458132i	0.439910	+	0.898042i	$0.355010\pi$
$468$	12.0079	+	96.7404i	0.0256580	+	0.206710i
$469$	−1.72496	+	193.323i	−0.00367794	+	0.412203i
$470$	−550.284	+	268.841i	−1.17082	+	0.572003i
$471$			60.3870i			0.128210i
$472$	70.9148	−	336.909i	0.150243	−	0.713789i
$473$		−	205.105i		−	0.433625i
$474$	−297.790	+	145.485i	−0.628249	+	0.306931i
$475$	−95.7098	−	95.7098i	−0.201494	−	0.201494i
$476$	265.873	−	30.5955i	0.558558	−	0.0642762i
$477$	111.703	+	111.703i	0.234178	+	0.234178i
$478$	−685.343	−	235.476i	−1.43377	−	0.492629i
$479$			437.605i			0.913581i	0.889574	+	0.456790i	$0.151001\pi$
$479$			437.605i			0.913581i	−0.889574	+	0.456790i	$0.848999\pi$
$480$	30.6771	−	364.499i	0.0639106	−	0.759372i
$481$		−	336.030i		−	0.698607i
$482$	−236.140	+	687.276i	−0.489918	+	1.42588i
$483$	2.17671	−	243.953i	0.00450665	−	0.505079i
$484$	−277.576	+	356.250i	−0.573504	+	0.736054i
$485$	115.549	−	115.549i	0.238245	−	0.238245i
$486$	263.764	−	128.862i	0.542725	−	0.265149i
$487$		−	681.542i		−	1.39947i	−0.714402	−	0.699735i	$-0.753301\pi$
$487$		−	681.542i		−	1.39947i	0.714402	−	0.699735i	$-0.246699\pi$
$488$	132.798	+	27.9522i	0.272127	+	0.0572791i
$489$	136.837			0.279831
$490$	−408.930	+	190.821i	−0.834551	+	0.389431i
$491$	324.611	−	324.611i	0.661122	−	0.661122i	−0.294523	−	0.955644i	$-0.595161\pi$
$491$	324.611	−	324.611i	0.661122	−	0.661122i	0.955644	+	0.294523i	$0.0951607\pi$
$492$	−127.758	+	15.8581i	−0.259671	+	0.0322318i
$493$	107.206	−	107.206i	0.217455	−	0.217455i
$494$	198.988	−	579.146i	0.402810	−	1.17236i
$495$		−	37.1740i		−	0.0750989i
$496$	256.267	−	64.6141i	0.516668	−	0.130270i
$497$	348.375	−	342.213i	0.700956	−	0.688558i
$498$	138.602	−	403.395i	0.278317	−	0.810029i
$499$	23.3782	+	23.3782i	0.0468501	+	0.0468501i	0.730144	−	0.683294i	$-0.239453\pi$
$499$	23.3782	+	23.3782i	0.0468501	+	0.0468501i	−0.683294	+	0.730144i	$0.739453\pi$
$500$	526.362	−	65.3349i	1.05272	−	0.130670i
$501$	−240.576	+	240.576i	−0.480191	+	0.480191i
$502$	67.2368	+	137.625i	0.133938	+	0.274154i
$503$	−693.554			−1.37884			−0.689418	−	0.724364i	$-0.742133\pi$
$503$	−693.554			−1.37884			−0.689418	+	0.724364i	$0.742133\pi$
$504$	155.197	+	34.1157i	0.307930	+	0.0676900i
$505$			881.157i			1.74487i
$506$	35.0673	+	71.7783i	0.0693030	+	0.141854i
$507$	−167.170	−	167.170i	−0.329724	−	0.329724i
$508$	−252.879	−	197.033i	−0.497793	−	0.387861i
$509$	175.357	−	175.357i	0.344512	−	0.344512i	−0.513548	−	0.858061i	$-0.671669\pi$
$509$	175.357	−	175.357i	0.344512	−	0.344512i	0.858061	+	0.513548i	$0.171669\pi$
$510$	71.0052	−	206.657i	0.139226	−	0.405211i
$511$	703.070	+	715.730i	1.37587	+	1.40065i
$512$	−505.211	+	83.0986i	−0.986741	+	0.162302i
$513$	−1047.62			−2.04214
$514$	29.4855	−	85.8160i	0.0573647	−	0.166957i
$515$	−248.630	−	248.630i	−0.482777	−	0.482777i
$516$	439.971	−	564.673i	0.852658	−	1.09433i
$517$	−133.787	−	133.787i	−0.258776	−	0.258776i
$518$	−516.414	−	182.602i	−0.996939	−	0.352513i
$519$			207.479i			0.399766i
$520$	172.841	+	265.002i	0.332387	+	0.509619i
$521$	602.394			1.15623			0.578113	−	0.815957i	$-0.303789\pi$
$521$	602.394			1.15623			0.578113	+	0.815957i	$0.303789\pi$
$522$	80.8819	−	39.5149i	0.154946	−	0.0756990i
$523$	−296.480	−	296.480i	−0.566883	−	0.566883i	0.364371	−	0.931254i	$-0.381284\pi$
$523$	−296.480	−	296.480i	−0.566883	−	0.566883i	−0.931254	+	0.364371i	$0.881284\pi$
$524$	505.441	−	62.7381i	0.964583	−	0.119729i
$525$	0.588654	−	65.9729i	0.00112125	−	0.125663i
$526$	−326.545	+	950.393i	−0.620808	+	1.80683i
$527$	157.881			0.299585
$528$	109.574	−	27.6275i	0.207527	−	0.0523249i
$529$	331.895			0.627401
$530$	484.883	+	166.600i	0.914873	+	0.314340i
$531$	86.3502	−	86.3502i	0.162618	−	0.162618i
$532$	−781.905	−	620.521i	−1.46975	−	1.16639i
$533$	78.7377	−	78.7377i	0.147726	−	0.147726i
$534$	352.145	−	172.040i	0.659447	−	0.322173i
$535$	402.858			0.753005
$536$	45.5097	−	216.212i	0.0849062	−	0.403380i
$537$	−528.724			−0.984588
$538$	−206.762	+	101.013i	−0.384315	+	0.187757i
$539$	−96.8023	−	100.320i	−0.179596	−	0.186123i
$540$	332.665	−	426.953i	0.616046	−	0.790653i
$541$	−221.579	−	221.579i	−0.409573	−	0.409573i	0.472017	−	0.881590i	$-0.343526\pi$
$541$	−221.579	−	221.579i	−0.409573	−	0.409573i	−0.881590	+	0.472017i	$0.843526\pi$
$542$	125.402	−	364.976i	0.231368	−	0.673387i
$543$	686.000			1.26335
$544$	−304.783	−	25.6513i	−0.560263	−	0.0471531i
$545$		−	621.869i		−	1.14104i
$546$	269.353	−	128.629i	0.493321	−	0.235584i
$547$	545.973	+	545.973i	0.998123	+	0.998123i	0.999998	−	0.00187545i	$-0.000596974\pi$
$547$	545.973	+	545.973i	0.998123	+	0.998123i	−0.00187545	+	0.999998i	$0.500597\pi$
$548$	622.190	−	798.538i	1.13538	−	1.45719i
$549$	34.0363	+	34.0363i	0.0619969	+	0.0619969i
$550$	9.48335	+	19.4112i	0.0172425	+	0.0352931i
$551$	−565.486			−1.02629
$552$	−57.4284	+	272.836i	−0.104037	+	0.494268i
$553$	−327.458	−	333.355i	−0.592149	−	0.602811i
$554$	−538.354	+	263.013i	−0.971758	+	0.474753i
$555$	−316.239	+	316.239i	−0.569800	+	0.569800i
$556$	34.3244	+	276.530i	0.0617345	+	0.497356i
$557$	87.7052	+	87.7052i	0.157460	+	0.157460i	0.781440	−	0.623980i	$-0.214485\pi$
$557$	87.7052	+	87.7052i	0.157460	+	0.157460i	−0.623980	+	0.781440i	$0.714485\pi$
$558$	88.6539	+	30.4605i	0.158878	+	0.0545887i
$559$			619.165i			1.10763i
$560$	501.181	−	121.620i	0.894966	−	0.217179i
$561$	67.5064			0.120332
$562$	55.4715	−	161.447i	0.0987037	−	0.287273i
$563$	125.548	−	125.548i	0.222997	−	0.222997i	−0.586762	−	0.809759i	$-0.699598\pi$
$563$	125.548	−	125.548i	0.222997	−	0.222997i	0.809759	+	0.586762i	$0.199598\pi$
$564$	−81.3415	−	655.317i	−0.144223	−	1.16191i
$565$	−460.248	−	460.248i	−0.814598	−	0.814598i
$566$	−108.608	−	222.307i	−0.191887	−	0.392768i
$567$	−232.567	−	236.754i	−0.410170	−	0.417556i
$568$	−467.461	+	304.891i	−0.822994	+	0.536780i
$569$			963.505i			1.69333i	0.532126	+	0.846665i	$0.321393\pi$
$569$			963.505i			1.69333i	−0.532126	+	0.846665i	$0.678607\pi$
$570$	−732.305	+	357.768i	−1.28475	+	0.627663i
$571$	−254.297	+	254.297i	−0.445355	+	0.445355i	−0.893807	−	0.448452i	$-0.851975\pi$
$571$	−254.297	+	254.297i	−0.445355	+	0.445355i	0.448452	+	0.893807i	$0.351975\pi$
$572$	−60.0741	+	77.1010i	−0.105025	+	0.134792i
$573$	−103.860	+	103.860i	−0.181257	+	0.181257i
$574$	−78.2181	−	163.792i	−0.136269	−	0.285352i
$575$	−53.3036			−0.0927018
$576$	−166.194	−	73.2066i	−0.288531	−	0.127095i
$577$			792.088i			1.37277i	0.727239	+	0.686384i	$0.240803\pi$
$577$			792.088i			1.37277i	−0.727239	+	0.686384i	$0.759197\pi$
$578$	373.833	+	128.445i	0.646770	+	0.222223i
$579$	335.146	−	335.146i	0.578835	−	0.578835i
$580$	179.567	−	230.462i	0.309599	−	0.397349i
$581$	601.361	+	5.36574i	1.03504	+	0.00923535i
$582$	77.3421	+	158.309i	0.132890	+	0.272009i
$583$			158.391i			0.271683i
$584$	−626.392	−	960.388i	−1.07259	−	1.64450i
$585$			112.220i			0.191829i
$586$	38.1233	+	78.0336i	0.0650569	+	0.133163i
$587$	436.848	+	436.848i	0.744204	+	0.744204i	0.973384	−	0.229180i	$-0.0736044\pi$
$587$	436.848	+	436.848i	0.744204	+	0.744204i	−0.229180	+	0.973384i	$0.573604\pi$
$588$	−51.3086	−	483.843i	−0.0872595	−	0.822863i
$589$	−416.394	−	416.394i	−0.706952	−	0.706952i
$590$	128.788	−	374.831i	0.218285	−	0.635307i
$591$			501.683i			0.848872i
$592$	537.434	+	320.994i	0.907828	+	0.542219i
$593$			668.916i			1.12802i	0.825768	+	0.564010i	$0.190742\pi$
$593$			668.916i			1.12802i	−0.825768	+	0.564010i	$0.809258\pi$
$594$	158.136	+	54.3339i	0.266223	+	0.0914713i
$595$	308.075	+	2.74885i	0.517773	+	0.00461991i
$596$	227.093	−	28.1880i	0.381028	−	0.0472953i
$597$	−243.974	+	243.974i	−0.408667	+	0.408667i
$598$	−105.860	−	216.683i	−0.177024	−	0.362346i
$599$			411.756i			0.687405i	0.939079	+	0.343703i	$0.111681\pi$
$599$			411.756i			0.687405i	−0.939079	+	0.343703i	$0.888319\pi$
$600$	−15.5305	+	73.7838i	−0.0258842	+	0.122973i
$601$	−688.982			−1.14639			−0.573196	−	0.819418i	$-0.694297\pi$
$601$	−688.982			−1.14639			−0.573196	+	0.819418i	$0.694297\pi$
$602$	951.539	+	336.460i	1.58063	+	0.558904i
$603$	55.4154	−	55.4154i	0.0918995	−	0.0918995i
$604$	−84.9463	+	109.023i	−0.140639	+	0.180501i
$605$	−367.622	+	367.622i	−0.607640	+	0.607640i
$606$	−898.519	−	308.721i	−1.48270	−	0.509441i
$607$			768.094i			1.26539i	0.774400	+	0.632697i	$0.218052\pi$
$607$			768.094i			1.26539i	−0.774400	+	0.632697i	$0.781948\pi$
$608$	736.180	+	871.485i	1.21082	+	1.43336i
$609$	−193.156	−	196.634i	−0.317170	−	0.322880i
$610$	147.746	+	50.7638i	0.242206	+	0.0832194i
$611$	403.873	+	403.873i	0.661004	+	0.661004i
$612$	−85.5768	−	66.6781i	−0.139831	−	0.108951i
$613$	−163.362	+	163.362i	−0.266495	+	0.266495i	−0.827686	−	0.561191i	$-0.810343\pi$
$613$	−163.362	+	163.362i	−0.266495	+	0.266495i	0.561191	+	0.827686i	$0.310343\pi$
$614$	80.4168	−	39.2877i	0.130972	−	0.0639864i
$615$	−148.201			−0.240977
$616$	85.8448	+	134.220i	0.139358	+	0.217889i
$617$			652.431i			1.05742i	0.848801	+	0.528712i	$0.177325\pi$
$617$			652.431i			1.05742i	−0.848801	+	0.528712i	$0.822675\pi$
$618$	340.639	−	166.419i	0.551195	−	0.269287i
$619$	78.1751	+	78.1751i	0.126293	+	0.126293i	0.767428	−	0.641135i	$-0.221536\pi$
$619$	78.1751	+	78.1751i	0.126293	+	0.126293i	−0.641135	+	0.767428i	$0.721536\pi$
$620$	301.924	−	37.4765i	0.486975	−	0.0604459i
$621$	−291.724	+	291.724i	−0.469765	+	0.469765i
$622$	−945.356	−	324.814i	−1.51986	−	0.522209i
$623$	387.228	+	394.201i	0.621554	+	0.632746i
$624$	−330.780	+	83.4014i	−0.530096	+	0.133656i
$625$	515.667			0.825067
$626$	−99.7788	−	34.2829i	−0.159391	−	0.0547650i
$627$	−178.041	−	178.041i	−0.283957	−	0.283957i
$628$	96.5620	−	11.9858i	0.153761	−	0.0190857i
$629$	264.430	+	264.430i	0.420398	+	0.420398i
$630$	172.461	+	60.9814i	0.273747	+	0.0967958i
$631$		−	219.948i		−	0.348570i	−0.984695	−	0.174285i	$-0.944239\pi$
$631$		−	219.948i		−	0.348570i	0.984695	−	0.174285i	$-0.0557614\pi$
$632$	291.745	+	447.305i	0.461622	+	0.707762i
$633$	−746.602			−1.17947
$634$	270.777	+	554.245i	0.427093	+	0.874204i
$635$	−260.951	−	260.951i	−0.410947	−	0.410947i
$636$	−339.766	+	436.067i	−0.534223	+	0.685639i
$637$	292.225	+	302.845i	0.458751	+	0.475423i
$638$	85.3595	+	29.3286i	0.133792	+	0.0459696i
$639$	−197.955			−0.309789
$640$	−588.942	+	23.2926i	−0.920221	+	0.0363947i
$641$	−186.577			−0.291072			−0.145536	−	0.989353i	$-0.546491\pi$
$641$	−186.577			−0.291072			−0.145536	+	0.989353i	$0.546491\pi$
$642$	−141.145	+	410.795i	−0.219852	+	0.639868i
$643$	215.904	−	215.904i	0.335776	−	0.335776i	−0.518999	−	0.854775i	$-0.673695\pi$
$643$	215.904	−	215.904i	0.335776	−	0.335776i	0.854775	+	0.518999i	$0.173695\pi$
$644$	−390.526	+	44.9399i	−0.606407	+	0.0697825i
$645$	582.699	−	582.699i	0.903409	−	0.903409i
$646$	299.155	+	612.333i	0.463089	+	0.947883i
$647$	663.677			1.02578			0.512888	−	0.858456i	$-0.328576\pi$
$647$	663.677			1.02578			0.512888	+	0.858456i	$0.328576\pi$
$648$	207.202	+	317.684i	0.319757	+	0.490253i
$649$	122.442			0.188663
$650$	−28.6281	−	58.5981i	−0.0440433	−	0.0901509i
$651$	2.56099	−	287.021i	0.00393394	−	0.440893i
$652$	−27.1599	−	218.810i	−0.0416563	−	0.335598i
$653$	−411.703	−	411.703i	−0.630479	−	0.630479i	0.317709	−	0.948188i	$-0.397086\pi$
$653$	−411.703	−	411.703i	−0.630479	−	0.630479i	−0.948188	+	0.317709i	$0.897086\pi$
$654$	634.123	+	217.878i	0.969606	+	0.333146i
$655$	586.317			0.895140
$656$	50.7158	+	201.145i	0.0773106	+	0.306623i
$657$		−	406.694i		−	0.619017i
$658$	840.146	−	401.208i	1.27682	−	0.609739i
$659$	−149.906	−	149.906i	−0.227475	−	0.227475i	0.584162	−	0.811637i	$-0.301423\pi$
$659$	−149.906	−	149.906i	−0.227475	−	0.227475i	−0.811637	+	0.584162i	$0.801423\pi$
$660$	129.096	−	16.0241i	0.195600	−	0.0242790i
$661$	166.233	+	166.233i	0.251487	+	0.251487i	0.821580	−	0.570093i	$-0.193093\pi$
$661$	166.233	+	166.233i	0.251487	+	0.251487i	−0.570093	+	0.821580i	$0.693093\pi$
$662$	−51.9746	+	25.3922i	−0.0785115	+	0.0383568i
$663$	−203.787			−0.307371
$664$	−672.560	−	141.565i	−1.01289	−	0.213200i
$665$	−805.264	−	819.764i	−1.21092	−	1.23273i
$666$	97.4662	+	199.501i	0.146346	+	0.299551i
$667$	−157.468	+	157.468i	−0.236084	+	0.236084i
$668$	432.443	+	336.943i	0.647370	+	0.504406i
$669$	607.355	+	607.355i	0.907854	+	0.907854i
$670$	82.6499	−	240.549i	0.123358	−	0.359028i
$671$			48.2625i			0.0719262i
$672$	−51.5769	+	553.667i	−0.0767513	+	0.823909i
$673$	315.076			0.468167			0.234083	−	0.972217i	$-0.424791\pi$
$673$	315.076			0.468167			0.234083	+	0.972217i	$0.424791\pi$
$674$	853.227	+	293.160i	1.26592	+	0.434955i
$675$	−78.8917	+	78.8917i	−0.116877	+	0.116877i
$676$	−234.133	+	300.494i	−0.346351	+	0.444518i
$677$	496.264	+	496.264i	0.733034	+	0.733034i	0.971220	−	0.238186i	$-0.0765528\pi$
$677$	496.264	+	496.264i	0.733034	+	0.733034i	−0.238186	+	0.971220i	$0.576553\pi$
$678$	630.568	−	308.064i	0.930042	−	0.454372i
$679$	−177.216	+	174.082i	−0.260996	+	0.256379i
$680$	−344.549	−	72.5231i	−0.506690	−	0.106652i
$681$		−	663.538i		−	0.974359i
$682$	41.2582	+	84.4503i	0.0604959	+	0.123827i
$683$	−387.884	+	387.884i	−0.567913	+	0.567913i	−0.931543	−	0.363631i	$-0.881537\pi$
$683$	−387.884	+	387.884i	−0.567913	+	0.567913i	0.363631	+	0.931543i	$0.381537\pi$
$684$	49.8433	+	401.556i	0.0728703	+	0.587070i
$685$	824.029	−	824.029i	1.20296	−	1.20296i
$686$	624.213	−	284.525i	0.909931	−	0.414760i
$687$	−530.594			−0.772335
$688$	−990.270	−	591.460i	−1.43935	−	0.859680i
$689$		−	478.147i		−	0.693973i
$690$	−104.295	+	303.547i	−0.151153	+	0.439923i
$691$	−776.671	+	776.671i	−1.12398	+	1.12398i	−0.132844	+	0.991137i	$0.542411\pi$
$691$	−776.671	+	776.671i	−1.12398	+	1.12398i	−0.991137	+	0.132844i	$0.957589\pi$
$692$	331.769	−	41.1810i	0.479436	−	0.0595102i
$693$	−0.504211	+	56.5090i	−0.000727577	+	0.0815426i
$694$	−797.798	+	389.764i	−1.14956	+	0.561620i
$695$			320.777i			0.461550i
$696$	172.090	+	263.850i	0.247256	+	0.379095i
$697$			123.921i			0.177792i
$698$	−1017.91	+	497.302i	−1.45833	+	0.712467i
$699$	18.4463	+	18.4463i	0.0263895	+	0.0263895i
$700$	−105.611	+	12.1532i	−0.150873	+	0.0173617i
$701$	−504.506	−	504.506i	−0.719695	−	0.719695i	0.248848	−	0.968543i	$-0.419948\pi$
$701$	−504.506	−	504.506i	−0.719695	−	0.719695i	−0.968543	+	0.248848i	$0.919948\pi$
$702$	−477.378	−	164.022i	−0.680026	−	0.233650i
$703$		−	1394.81i		−	1.98409i
$704$	−65.9265	−	169.731i	−0.0936457	−	0.241096i
$705$		−	760.174i		−	1.07826i
$706$	301.606	−	877.812i	0.427205	−	1.24336i
$707$	11.9516	−	1339.47i	0.0169047	−	1.89458i
$708$	337.095	+	262.651i	0.476123	+	0.370976i
$709$	329.265	−	329.265i	0.464408	−	0.464408i	−0.435689	−	0.900097i	$-0.643495\pi$
$709$	329.265	−	329.265i	0.464408	−	0.464408i	0.900097	+	0.435689i	$0.143495\pi$
$710$	−577.265	+	282.023i	−0.813050	+	0.397216i
$711$			189.420i			0.266413i
$712$	−344.997	−	528.951i	−0.484546	−	0.742909i
$713$	−231.902			−0.325249
$714$	−110.740	+	313.182i	−0.155098	+	0.438630i
$715$	−79.5622	+	79.5622i	−0.111276	+	0.111276i
$716$	104.943	+	845.457i	0.146568	+	1.18081i
$717$	636.021	−	636.021i	0.887058	−	0.887058i
$718$	−82.1164	+	238.996i	−0.114368	+	0.332863i
$719$		−	612.721i		−	0.852185i	−0.904680	−	0.426093i	$-0.859890\pi$
$719$		−	612.721i		−	0.852185i	0.904680	−	0.426093i	$-0.140110\pi$
$720$	−179.480	−	107.198i	−0.249278	−	0.148887i
$721$	374.576	+	381.321i	0.519523	+	0.528878i
$722$	591.362	−	1721.13i	0.819061	−	2.38384i
$723$	−637.814	−	637.814i	−0.882177	−	0.882177i
$724$	−136.159	−	1096.95i	−0.188066	−	1.51512i
$725$	−42.5845	+	42.5845i	−0.0587372	+	0.0587372i
$726$	−246.066	−	503.666i	−0.338934	−	0.693754i
$727$	884.961			1.21728			0.608639	−	0.793447i	$-0.291716\pi$
$727$	884.961			1.21728			0.608639	+	0.793447i	$0.291716\pi$
$728$	−259.146	−	405.180i	−0.355970	−	0.556566i
$729$			791.064i			1.08514i
$730$	−579.411	−	1185.98i	−0.793713	−	1.62463i
$731$	−487.236	−	487.236i	−0.666534	−	0.666534i
$732$	−103.528	+	132.871i	−0.141432	+	0.181518i
$733$	630.619	−	630.619i	0.860327	−	0.860327i	−0.131049	−	0.991376i	$-0.541835\pi$
$733$	630.619	−	630.619i	0.860327	−	0.860327i	0.991376	+	0.131049i	$0.0418346\pi$
$734$	−58.5328	+	170.357i	−0.0797450	+	0.232094i
$735$	9.99458	−	560.022i	0.0135981	−	0.761935i
$736$	447.678	+	37.6776i	0.608258	+	0.0511925i
$737$	78.5774			0.106618
$738$	−23.9085	+	69.5847i	−0.0323964	+	0.0942882i
$739$	−885.422	−	885.422i	−1.19813	−	1.19813i	−0.974725	−	0.223410i	$-0.928281\pi$
$739$	−885.422	−	885.422i	−1.19813	−	1.19813i	−0.223410	−	0.974725i	$-0.571719\pi$
$740$	568.452	+	442.915i	0.768178	+	0.598534i
$741$	537.466	+	537.466i	0.725325	+	0.725325i
$742$	−734.822	−	259.830i	−0.990326	−	0.350175i
$743$		−	454.580i		−	0.611817i	−0.952061	−	0.305909i	$-0.901040\pi$
$743$		−	454.580i		−	0.611817i	0.952061	−	0.305909i	$-0.0989602\pi$
$744$	−67.5670	+	321.003i	−0.0908158	+	0.431456i
$745$	263.430			0.353597
$746$	−924.316	+	451.575i	−1.23903	+	0.605328i
$747$	−172.378	−	172.378i	−0.230760	−	0.230760i
$748$	−13.3989	−	107.946i	−0.0179130	−	0.144313i
$749$	−612.394	−	5.46418i	−0.817615	−	0.00729530i
$750$	−213.924	+	622.616i	−0.285232	+	0.830154i
$751$	220.761			0.293956			0.146978	−	0.989140i	$-0.453045\pi$
$751$	220.761			0.293956			0.146978	+	0.989140i	$0.453045\pi$
$752$	−1031.74	+	260.139i	−1.37200	+	0.345929i
$753$	−190.119			−0.252481
$754$	−257.681	−	88.5365i	−0.341752	−	0.117422i
$755$	−112.503	+	112.503i	−0.149011	+	0.149011i
$756$	−511.483	+	644.509i	−0.676565	+	0.852525i
$757$	195.831	−	195.831i	0.258693	−	0.258693i	−0.565829	−	0.824522i	$-0.691444\pi$
$757$	195.831	−	195.831i	0.258693	−	0.258693i	0.824522	+	0.565829i	$0.191444\pi$
$758$	739.202	−	361.137i	0.975201	−	0.476435i
$759$	−99.1562			−0.130641
$760$	717.441	+	1099.98i	0.944001	+	1.44735i
$761$	1450.33			1.90583			0.952913	−	0.303244i	$-0.0980698\pi$
$761$	1450.33			1.90583			0.952913	+	0.303244i	$0.0980698\pi$
$762$	357.520	−	174.666i	0.469186	−	0.229221i
$763$	−8.43476	+	945.319i	−0.0110547	+	1.23895i
$764$	186.693	+	145.464i	0.244363	+	0.190398i
$765$	−88.3086	−	88.3086i	−0.115436	−	0.115436i
$766$	152.107	−	442.700i	0.198573	−	0.577937i
$767$	−369.625			−0.481910
$768$	182.589	−	608.707i	0.237747	−	0.792587i
$769$		−	95.3790i		−	0.124030i	−0.998075	−	0.0620150i	$-0.980247\pi$
$769$		−	95.3790i		−	0.124030i	0.998075	−	0.0620150i	$-0.0197527\pi$
$770$	79.0372	+	165.507i	0.102646	+	0.214944i
$771$	79.6401	+	79.6401i	0.103295	+	0.103295i
$772$	−602.436	−	469.395i	−0.780358	−	0.608024i
$773$	811.244	+	811.244i	1.04948	+	1.04948i	0.998711	+	0.0507646i	$0.0161658\pi$
$773$	811.244	+	811.244i	1.04948	+	1.04948i	0.0507646	+	0.998711i	$0.483834\pi$
$774$	−179.590	−	367.598i	−0.232029	−	0.474933i
$775$	−62.7140			−0.0809212
$776$	237.794	−	155.096i	0.306436	−	0.199866i
$777$	485.012	−	476.434i	0.624211	−	0.613171i
$778$	212.197	−	103.669i	0.272747	−	0.133251i
$779$	326.829	−	326.829i	0.419550	−	0.419550i
$780$	−389.712	+	48.3732i	−0.499631	+	0.0620169i
$781$	−140.347	−	140.347i	−0.179702	−	0.179702i
$782$	253.817	+	87.2088i	0.324574	+	0.111520i
$783$			466.119i			0.595299i
$784$	−763.507	+	178.080i	−0.973861	+	0.227143i
$785$	112.013			0.142692
$786$	−205.422	+	597.870i	−0.261351	+	0.760648i
$787$	96.6979	−	96.6979i	0.122869	−	0.122869i	−0.642998	−	0.765867i	$-0.722310\pi$
$787$	96.6979	−	96.6979i	0.122869	−	0.122869i	0.765867	+	0.642998i	$0.222310\pi$
$788$	802.218	−	99.5757i	1.01804	−	0.126365i
$789$	−881.996	−	881.996i	−1.11787	−	1.11787i
$790$	269.863	+	552.376i	0.341599	+	0.699210i
$791$	693.391	+	705.876i	0.876601	+	0.892385i
$792$	13.3027	−	63.1995i	0.0167963	−	0.0797973i
$793$		−	145.694i		−	0.183725i
$794$	443.304	−	216.576i	0.558318	−	0.272766i
$795$	−449.987	+	449.987i	−0.566021	+	0.566021i
$796$	438.553	+	341.703i	0.550946	+	0.429275i
$797$	−581.633	+	581.633i	−0.729778	+	0.729778i	−0.970575	−	0.240798i	$-0.922591\pi$
$797$	−581.633	+	581.633i	−0.729778	+	0.729778i	0.240798	+	0.970575i	$0.422591\pi$
$798$	1118.05	−	533.919i	1.40106	−	0.669072i
$799$	−635.636			−0.795539
$800$	121.067	+	10.1893i	0.151333	+	0.0127366i
$801$		−	223.994i		−	0.279643i
$802$	−355.095	−	122.007i	−0.442762	−	0.152128i
$803$	288.340	−	288.340i	0.359079	−	0.359079i
$804$	216.331	+	168.557i	0.269069	+	0.209648i
$805$	−452.513	−	4.03762i	−0.562128	−	0.00501567i
$806$	−124.549	−	254.937i	−0.154528	−	0.316299i
$807$		−	285.625i		−	0.353935i
$808$	−315.321	+	1498.06i	−0.390249	+	1.85403i
$809$			296.533i			0.366543i	0.983062	+	0.183272i	$0.0586688\pi$
$809$			296.533i			0.366543i	−0.983062	+	0.183272i	$0.941331\pi$
$810$	191.662	+	392.307i	0.236619	+	0.484329i
$811$	−605.219	−	605.219i	−0.746262	−	0.746262i	0.227513	−	0.973775i	$-0.426941\pi$
$811$	−605.219	−	605.219i	−0.746262	−	0.746262i	−0.973775	+	0.227513i	$0.926941\pi$
$812$	−276.090	+	347.896i	−0.340013	+	0.428443i
$813$	338.709	+	338.709i	0.416617	+	0.416617i
$814$	−72.3411	+	210.545i	−0.0888711	+	0.258655i
$815$		−	253.822i		−	0.311438i
$816$	194.668	−	325.929i	0.238564	−	0.399423i
$817$			2570.07i			3.14574i
$818$	−274.149	−	94.1947i	−0.335146	−	0.115152i
$819$	1.52210	−	170.588i	0.00185849	−	0.208288i
$820$	29.4154	+	236.981i	0.0358724	+	0.289001i
$821$	460.505	−	460.505i	0.560907	−	0.560907i	−0.368658	−	0.929565i	$-0.620183\pi$
$821$	460.505	−	460.505i	0.560907	−	0.560907i	0.929565	+	0.368658i	$0.120183\pi$
$822$	551.560	+	1128.97i	0.670997	+	1.37345i
$823$		−	1126.18i		−	1.36839i	−0.729300	−	0.684194i	$-0.760154\pi$
$823$		−	1126.18i		−	1.36839i	0.729300	−	0.684194i	$-0.239846\pi$
$824$	−333.724	−	511.668i	−0.405005	−	0.620956i
$825$	−26.8151			−0.0325031
$826$	−200.858	+	568.044i	−0.243169	+	0.687704i
$827$	686.896	−	686.896i	0.830587	−	0.830587i	−0.157010	−	0.987597i	$-0.550185\pi$
$827$	686.896	−	686.896i	0.830587	−	0.830587i	0.987597	+	0.157010i	$0.0501855\pi$
$828$	125.699	+	97.9395i	0.151810	+	0.118284i
$829$	−732.088	+	732.088i	−0.883098	+	0.883098i	−0.993848	−	0.110750i	$-0.964675\pi$
$829$	−732.088	+	732.088i	−0.883098	+	0.883098i	0.110750	+	0.993848i	$0.464675\pi$
$830$	−748.264	−	257.095i	−0.901523	−	0.309753i
$831$		−	743.694i		−	0.894939i
$832$	199.017	+	512.381i	0.239204	+	0.615842i
$833$	−468.275	−	8.35718i	−0.562154	−	0.0100326i
$834$	−327.098	−	112.387i	−0.392204	−	0.134757i
$835$	446.248	+	446.248i	0.534429	+	0.534429i
$836$	−249.359	+	320.035i	−0.298276	+	0.382817i
$837$	−343.226	+	343.226i	−0.410067	+	0.410067i
$838$	450.247	−	219.968i	0.537287	−	0.262492i
$839$	−903.003			−1.07628			−0.538142	−	0.842854i	$-0.680874\pi$
$839$	−903.003			−1.07628			−0.538142	+	0.842854i	$0.680874\pi$
$840$	−137.433	+	625.200i	−0.163611	+	0.744286i
$841$		−	589.396i		−	0.700828i
$842$	1189.95	−	581.350i	1.41324	−	0.690439i
$843$	149.828	+	149.828i	0.177732	+	0.177732i
$844$	148.188	+	1193.86i	0.175578	+	1.41452i
$845$	−310.086	+	310.086i	−0.366966	+	0.366966i
$846$	−356.924	−	122.635i	−0.421896	−	0.144959i
$847$	563.818	−	553.845i	0.665664	−	0.653891i
$848$	764.732	+	456.752i	0.901806	+	0.538623i
$849$	307.099			0.361719
$850$	68.6404	+	23.5841i	0.0807535	+	0.0277460i
$851$	−388.406	−	388.406i	−0.456411	−	0.456411i
$852$	−85.3299	−	687.449i	−0.100152	−	0.806865i
$853$	38.7225	+	38.7225i	0.0453957	+	0.0453957i	0.729440	−	0.684045i	$-0.239781\pi$
$853$	38.7225	+	38.7225i	0.0453957	+	0.0453957i	−0.684045	+	0.729440i	$0.739781\pi$
$854$	−223.903	−	79.1713i	−0.262182	−	0.0927064i
$855$			465.809i			0.544806i
$856$	684.899	+	144.162i	0.800115	+	0.168414i
$857$	−653.919			−0.763032			−0.381516	−	0.924362i	$-0.624598\pi$
$857$	−653.919			−0.763032			−0.381516	+	0.924362i	$0.624598\pi$
$858$	−53.2545	−	109.005i	−0.0620682	−	0.127046i
$859$	−340.187	−	340.187i	−0.396026	−	0.396026i	0.480802	−	0.876829i	$-0.340345\pi$
$859$	−340.187	−	340.187i	−0.396026	−	0.396026i	−0.876829	+	0.480802i	$0.840345\pi$
$860$	−1047.42	−	816.111i	−1.21793	−	0.948966i
$861$	225.284	+	2.01013i	0.261654	+	0.00233465i
$862$	940.499	+	323.145i	1.09107	+	0.374879i
$863$	−106.239			−0.123104			−0.0615519	−	0.998104i	$-0.519605\pi$
$863$	−106.239			−0.123104			−0.0615519	+	0.998104i	$0.519605\pi$
$864$	718.348	−	606.819i	0.831422	−	0.702337i
$865$	384.856			0.444920
$866$	−136.957	+	398.606i	−0.158149	+	0.460284i
$867$	−346.929	+	346.929i	−0.400149	+	0.400149i
$868$	−459.471	+	52.8738i	−0.529344	+	0.0609145i
$869$	−134.296	+	134.296i	−0.154541	+	0.154541i
$870$	159.183	+	325.827i	0.182969	+	0.374514i
$871$	−237.207			−0.272339
$872$	222.535	−	1057.24i	0.255201	−	1.21243i
$873$	100.698			0.115347
$874$	−439.411	−	899.419i	−0.502759	−	1.02908i
$875$	−928.165	−	8.28170i	−1.06076	−	0.00946480i
$876$	1412.35	−	175.309i	1.61227	−	0.200124i
$877$	−535.021	−	535.021i	−0.610059	−	0.610059i	0.332903	−	0.942961i	$-0.391972\pi$
$877$	−535.021	−	535.021i	−0.610059	−	0.610059i	−0.942961	+	0.332903i	$0.891972\pi$
$878$	1442.98	+	495.794i	1.64349	+	0.564685i
$879$	−107.797			−0.122636
$880$	−51.2468	−	203.251i	−0.0582350	−	0.230967i
$881$		−	370.517i		−	0.420564i	−0.977641	−	0.210282i	$-0.932562\pi$
$881$		−	370.517i		−	0.420564i	0.977641	−	0.210282i	$-0.0674382\pi$
$882$	−261.335	−	95.0385i	−0.296298	−	0.107753i
$883$	109.056	+	109.056i	0.123507	+	0.123507i	0.766158	−	0.642652i	$-0.222166\pi$
$883$	109.056	+	109.056i	0.123507	+	0.123507i	−0.642652	+	0.766158i	$0.722166\pi$
$884$	40.4483	+	325.866i	0.0457560	+	0.368627i
$885$	347.856	+	347.856i	0.393057	+	0.393057i
$886$	−356.430	+	174.134i	−0.402291	+	0.196539i
$887$	1435.92			1.61884			0.809422	−	0.587227i	$-0.199780\pi$
$887$	1435.92			1.61884			0.809422	+	0.587227i	$0.199780\pi$
$888$	−650.805	+	424.473i	−0.732888	+	0.478010i
$889$	393.139	+	400.218i	0.442226	+	0.450189i
$890$	−319.121	−	653.199i	−0.358563	−	0.733932i
$891$	−95.3792	+	95.3792i	−0.107047	+	0.107047i
$892$	850.643	−	1091.74i	0.953635	−	1.22393i
$893$	1676.42	+	1676.42i	1.87729	+	1.87729i
$894$	−92.2950	+	268.620i	−0.103238	+	0.300470i
$895$			980.739i			1.09580i
$896$	895.580	−	27.4195i	0.999532	−	0.0306021i
$897$	299.330			0.333702
$898$	−1134.70	−	389.870i	−1.26358	−	0.434153i
$899$	−185.268	+	185.268i	−0.206082	+	0.206082i
$900$	33.9930	+	26.4860i	0.0377700	+	0.0294289i
$901$	376.266	+	376.266i	0.417609	+	0.417609i
$902$	−66.2853	+	32.3837i	−0.0734870	+	0.0359021i
$903$	−893.679	+	877.872i	−0.989677	+	0.972172i
$904$	−617.768	−	947.167i	−0.683372	−	1.04775i
$905$		−	1272.47i		−	1.40605i
$906$	−75.3033	−	154.136i	−0.0831162	−	0.170128i
$907$	726.879	−	726.879i	0.801410	−	0.801410i	−0.181906	−	0.983316i	$-0.558227\pi$
$907$	726.879	−	726.879i	0.801410	−	0.801410i	0.983316	+	0.181906i	$0.0582265\pi$
$908$	−1061.03	+	131.701i	−1.16854	+	0.145045i
$909$	−383.954	+	383.954i	−0.422392	+	0.422392i
$910$	−238.596	−	499.628i	−0.262193	−	0.549042i
$911$	−474.695			−0.521070			−0.260535	−	0.965464i	$-0.583899\pi$
$911$	−474.695			−0.521070			−0.260535	+	0.965464i	$0.583899\pi$
$912$	−1373.02	+	346.187i	−1.50550	+	0.379591i
$913$		−	244.427i		−	0.267718i
$914$	−362.364	+	1054.64i	−0.396460	+	1.15388i
$915$	−137.113	+	137.113i	−0.149850	+	0.149850i
$916$	105.314	+	848.448i	0.114972	+	0.926254i
$917$	−891.275	−	7.95254i	−0.971946	−	0.00867235i
$918$	504.734	−	246.588i	0.549819	−	0.268614i
$919$			947.682i			1.03121i	0.856827	+	0.515605i	$0.172433\pi$
$919$			947.682i			1.03121i	−0.856827	+	0.515605i	$0.827567\pi$
$920$	506.088	+	106.525i	0.550096	+	0.115788i
$921$			111.090i			0.120619i
$922$	1226.44	−	599.178i	1.33019	−	0.649867i
$923$	423.676	+	423.676i	0.459021	+	0.459021i
$924$	−196.459	+	22.6076i	−0.212618	+	0.0244671i
$925$	−105.038	−	105.038i	−0.113554	−	0.113554i
$926$	−617.819	−	212.276i	−0.667191	−	0.229240i
$927$		−	216.675i		−	0.233738i
$928$	387.753	−	327.551i	0.417837	−	0.352965i
$929$		−	448.957i		−	0.483269i	−0.970367	−	0.241634i	$-0.922317\pi$
$929$		−	448.957i		−	0.483269i	0.970367	−	0.241634i	$-0.0776834\pi$
$930$	−122.708	+	357.136i	−0.131944	+	0.384017i
$931$	1212.98	+	1257.07i	1.30288	+	1.35023i
$932$	25.8353	−	33.1579i	0.0277203	−	0.0355771i
$933$	877.321	−	877.321i	0.940323	−	0.940323i
$934$	−543.716	+	265.633i	−0.582138	+	0.284404i
$935$		−	125.219i		−	0.133924i
$936$	−40.1577	+	190.785i	−0.0429036	+	0.203830i
$937$	857.680			0.915347			0.457674	−	0.889120i	$-0.348683\pi$
$937$	857.680			0.915347			0.457674	+	0.889120i	$0.348683\pi$
$938$	−128.901	+	364.543i	−0.137421	+	0.388639i
$939$	92.5980	−	92.5980i	0.0986134	−	0.0986134i
$940$	−1215.56	+	150.882i	−1.29315	+	0.160513i
$941$	−151.657	+	151.657i	−0.161166	+	0.161166i	−0.783083	−	0.621917i	$-0.786354\pi$
$941$	−151.657	+	151.657i	−0.161166	+	0.161166i	0.621917	+	0.783083i	$0.286354\pi$
$942$	−39.2447	+	114.220i	−0.0416611	+	0.121253i
$943$		−	182.021i		−	0.193023i
$944$	353.086	−	591.165i	0.374031	−	0.626234i
$945$	−675.715	+	663.764i	−0.715043	+	0.702395i
$946$	133.295	−	387.949i	0.140904	−	0.410094i
$947$	908.719	+	908.719i	0.959577	+	0.959577i	0.999214	−	0.0396372i	$-0.0126202\pi$
$947$	908.719	+	908.719i	0.959577	+	0.959577i	−0.0396372	+	0.999214i	$0.512620\pi$
$948$	−657.809	+	81.6508i	−0.693891	+	0.0861295i
$949$	−870.434	+	870.434i	−0.917212	+	0.917212i
$950$	−118.831	−	243.232i	−0.125086	−	0.256034i
$951$	−765.648			−0.805097
$952$	522.774	+	114.917i	0.549133	+	0.120712i
$953$			844.182i			0.885815i	0.896567	+	0.442908i	$0.146053\pi$
$953$			844.182i			0.885815i	−0.896567	+	0.442908i	$0.853947\pi$
$954$	138.688	+	283.876i	0.145375	+	0.297564i
$955$	192.653	+	192.653i	0.201731	+	0.201731i
$956$	−1143.27	−	890.792i	−1.19589	−	0.931790i
$957$	−79.2164	+	79.2164i	−0.0827758	+	0.0827758i
$958$	−284.394	+	827.716i	−0.296862	+	0.864004i
$959$	−1263.80	+	1241.45i	−1.31784	+	1.29453i
$960$	294.908	−	669.500i	0.307195	−	0.697396i
$961$	688.157			0.716084
$962$	218.382	−	635.589i	0.227008	−	0.660696i
$963$	175.541	+	175.541i	0.182285	+	0.182285i
$964$	−893.304	+	1146.49i	−0.926663	+	1.18931i
$965$	−621.668	−	621.668i	−0.644215	−	0.644215i
$966$	162.659	−	460.014i	0.168384	−	0.476205i
$967$		−	1481.66i		−	1.53223i	−0.642705	−	0.766114i	$-0.722188\pi$
$967$		−	1481.66i		−	1.53223i	0.642705	−	0.766114i	$-0.277812\pi$
$968$	−756.548	+	493.442i	−0.781558	+	0.509754i
$969$	−845.890			−0.872952
$970$	293.651	−	143.463i	0.302733	−	0.147900i
$971$	736.360	+	736.360i	0.758352	+	0.758352i	0.976022	−	0.217671i	$-0.0698458\pi$
$971$	736.360	+	736.360i	0.758352	+	0.758352i	−0.217671	+	0.976022i	$0.569846\pi$
$972$	582.647	−	72.3214i	0.599432	−	0.0744047i
$973$	4.35088	−	487.621i	0.00447161	−	0.501152i
$974$	442.926	−	1289.11i	0.454749	−	1.32353i
$975$	80.9488			0.0830244
$976$	233.017	+	139.174i	0.238747	+	0.142597i
$977$	736.267			0.753600			0.376800	−	0.926295i	$-0.377024\pi$
$977$	736.267			0.753600			0.376800	+	0.926295i	$0.377024\pi$
$978$	258.823	+	88.9288i	0.264645	+	0.0909293i
$979$	158.808	−	158.808i	0.162215	−	0.162215i
$980$	−897.490	+	95.1732i	−0.915806	+	0.0971155i
$981$	270.972	−	270.972i	0.276221	−	0.276221i
$982$	824.951	−	403.030i	0.840072	−	0.410417i
$983$	−564.432			−0.574194			−0.287097	−	0.957902i	$-0.592690\pi$
$983$	−564.432			−0.574194			−0.287097	+	0.957902i	$0.592690\pi$
$984$	−251.957	−	53.0335i	−0.256053	−	0.0538958i
$985$	930.581			0.944752
$986$	272.447	−	133.104i	0.276316	−	0.134994i
$987$	−10.3107	+	1155.56i	−0.0104465	+	1.17078i
$988$	752.759	−	966.115i	0.761902	−	0.977849i
$989$	715.672	+	715.672i	0.723632	+	0.723632i
$990$	24.1589	−	70.3133i	0.0244029	−	0.0710235i
$991$	−715.833			−0.722334			−0.361167	−	0.932501i	$-0.617622\pi$
$991$	−715.833			−0.722334			−0.361167	+	0.932501i	$0.617622\pi$
$992$	526.713	+	44.3294i	0.530960	+	0.0446869i
$993$		−	71.7989i		−	0.0723051i
$994$	881.340	−	420.880i	0.886660	−	0.423421i
$995$	452.552	+	452.552i	0.454826	+	0.454826i
$996$	524.322	−	672.932i	0.526428	−	0.675634i
$997$	−892.876	−	892.876i	−0.895562	−	0.895562i	0.0994775	−	0.995040i	$-0.468283\pi$
$997$	−892.876	−	892.876i	−0.895562	−	0.895562i	−0.995040	+	0.0994775i	$0.968283\pi$
$998$	29.0259	+	59.4123i	0.0290841	+	0.0595314i
$999$	−1149.72			−1.15087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.3.l.b.13.25	✓	56
4.3	odd	2		448.3.l.b.209.19		56
7.6	odd	2	inner	112.3.l.b.13.26	yes	56
16.5	even	4	inner	112.3.l.b.69.26	yes	56
16.11	odd	4		448.3.l.b.433.10		56
28.27	even	2		448.3.l.b.209.10		56
112.27	even	4		448.3.l.b.433.19		56
112.69	odd	4	inner	112.3.l.b.69.25	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.3.l.b.13.25	✓	56	1.1	even	1	trivial
112.3.l.b.13.26	yes	56	7.6	odd	2	inner
112.3.l.b.69.25	yes	56	112.69	odd	4	inner
112.3.l.b.69.26	yes	56	16.5	even	4	inner
448.3.l.b.209.10		56	28.27	even	2
448.3.l.b.209.19		56	4.3	odd	2
448.3.l.b.433.10		56	16.11	odd	4
448.3.l.b.433.19		56	112.27	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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	112.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.89147 + 0.649887i) q^{2} +(-1.75534 + 1.75534i) q^{3} +(3.15529 + 2.45848i) q^{4} +(3.25602 + 3.25602i) q^{5} +(-4.46095 + 2.17940i) q^{6} +(-4.90539 - 4.99371i) q^{7} +(4.37040 + 6.70072i) q^{8} +2.83754i q^{9} +O(q^{10})\)	\(q+(1.89147 + 0.649887i) q^{2} +(-1.75534 + 1.75534i) q^{3} +(3.15529 + 2.45848i) q^{4} +(3.25602 + 3.25602i) q^{5} +(-4.46095 + 2.17940i) q^{6} +(-4.90539 - 4.99371i) q^{7} +(4.37040 + 6.70072i) q^{8} +2.83754i q^{9} +(4.04260 + 8.27469i) q^{10} +(-2.01178 + 2.01178i) q^{11} +(-9.85410 + 1.22314i) q^{12} +(6.07310 - 6.07310i) q^{13} +(-6.03303 - 12.6334i) q^{14} -11.4309 q^{15} +(3.91175 + 15.5145i) q^{16} +9.55815i q^{17} +(-1.84408 + 5.36712i) q^{18} +(25.2086 - 25.2086i) q^{19} +(2.26883 + 18.2785i) q^{20} +(17.3763 + 0.155043i) q^{21} +(-5.11264 + 2.49778i) q^{22} -14.0394i q^{23} +(-19.4336 - 4.09052i) q^{24} -3.79671i q^{25} +(15.4339 - 7.54024i) q^{26} +(-20.7789 - 20.7789i) q^{27} +(-3.20099 - 27.8164i) q^{28} +(-11.2161 - 11.2161i) q^{29} +(-21.6211 - 7.42876i) q^{30} -16.5180i q^{31} +(-2.68371 + 31.8873i) q^{32} -7.06271i q^{33} +(-6.21172 + 18.0789i) q^{34} +(0.287592 - 32.2316i) q^{35} +(-6.97605 + 8.95328i) q^{36} +(27.6654 - 27.6654i) q^{37} +(64.0639 - 31.2985i) q^{38} +21.3208i q^{39} +(-7.58757 + 36.0477i) q^{40} +12.9650 q^{41} +(32.7660 + 11.5859i) q^{42} +(-50.9760 + 50.9760i) q^{43} +(-11.2937 + 1.40183i) q^{44} +(-9.23909 + 9.23909i) q^{45} +(9.12403 - 26.5550i) q^{46} +66.5020i q^{47} +(-34.0996 - 20.3667i) q^{48} +(-0.874351 + 48.9922i) q^{49} +(2.46744 - 7.18136i) q^{50} +(-16.7778 - 16.7778i) q^{51} +(34.0930 - 4.23181i) q^{52} +(39.3660 - 39.3660i) q^{53} +(-25.7987 - 52.8067i) q^{54} -13.1008 q^{55} +(12.0230 - 54.6941i) q^{56} +88.4994i q^{57} +(-13.9257 - 28.5042i) q^{58} +(-30.4313 - 30.4313i) q^{59} +(-36.0677 - 28.1025i) q^{60} +(11.9950 - 11.9950i) q^{61} +(10.7348 - 31.2432i) q^{62} +(14.1699 - 13.9192i) q^{63} +(-25.7993 + 58.5696i) q^{64} +39.5482 q^{65} +(4.58997 - 13.3589i) q^{66} +(-19.5294 - 19.5294i) q^{67} +(-23.4985 + 30.1587i) q^{68} +(24.6440 + 24.6440i) q^{69} +(21.4909 - 60.7782i) q^{70} +69.7628i q^{71} +(-19.0136 + 12.4012i) q^{72} -143.326 q^{73} +(70.3076 - 34.3488i) q^{74} +(6.66453 + 6.66453i) q^{75} +(141.515 - 17.5657i) q^{76} +(19.9148 + 0.177693i) q^{77} +(-13.8561 + 40.3275i) q^{78} +66.7548 q^{79} +(-37.7786 + 63.2520i) q^{80} +47.4105 q^{81} +(24.5229 + 8.42578i) q^{82} +(-60.7490 + 60.7490i) q^{83} +(54.4462 + 43.2085i) q^{84} +(-31.1215 + 31.1215i) q^{85} +(-129.548 + 63.2908i) q^{86} +39.3763 q^{87} +(-22.2726 - 4.68809i) q^{88} -78.9394 q^{89} +(-23.4798 + 11.4711i) q^{90} +(-60.1182 - 0.536415i) q^{91} +(34.5156 - 44.2984i) q^{92} +(28.9947 + 28.9947i) q^{93} +(-43.2188 + 125.786i) q^{94} +164.159 q^{95} +(-51.2623 - 60.6839i) q^{96} -35.4878i q^{97} +(-33.4932 + 92.0989i) q^{98} +(-5.70850 - 5.70850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{2} - 8 q^{4} - 16 q^{8}+O(q^{10}) \) 56 * q - 4 * q^2 - 8 * q^4 - 16 * q^8	\( 56 q - 4 q^{2} - 8 q^{4} - 16 q^{8} + 40 q^{14} - 8 q^{15} + 48 q^{16} + 196 q^{18} - 20 q^{21} - 120 q^{22} - 96 q^{29} - 40 q^{30} - 184 q^{32} - 100 q^{35} + 160 q^{36} - 128 q^{37} - 144 q^{42} - 72 q^{43} - 448 q^{44} - 168 q^{46} + 192 q^{49} - 364 q^{50} - 128 q^{51} + 88 q^{53} + 56 q^{56} + 408 q^{58} + 504 q^{60} + 444 q^{63} + 256 q^{64} - 8 q^{65} + 440 q^{67} - 112 q^{70} + 592 q^{72} - 408 q^{74} + 12 q^{77} + 664 q^{78} - 8 q^{79} + 64 q^{81} - 576 q^{84} + 96 q^{85} + 256 q^{86} + 448 q^{88} - 388 q^{91} - 1192 q^{92} + 32 q^{93} - 776 q^{95} + 540 q^{98} + 8 q^{99}+O(q^{100}) \) 56 * q - 4 * q^2 - 8 * q^4 - 16 * q^8 + 40 * q^14 - 8 * q^15 + 48 * q^16 + 196 * q^18 - 20 * q^21 - 120 * q^22 - 96 * q^29 - 40 * q^30 - 184 * q^32 - 100 * q^35 + 160 * q^36 - 128 * q^37 - 144 * q^42 - 72 * q^43 - 448 * q^44 - 168 * q^46 + 192 * q^49 - 364 * q^50 - 128 * q^51 + 88 * q^53 + 56 * q^56 + 408 * q^58 + 504 * q^60 + 444 * q^63 + 256 * q^64 - 8 * q^65 + 440 * q^67 - 112 * q^70 + 592 * q^72 - 408 * q^74 + 12 * q^77 + 664 * q^78 - 8 * q^79 + 64 * q^81 - 576 * q^84 + 96 * q^85 + 256 * q^86 + 448 * q^88 - 388 * q^91 - 1192 * q^92 + 32 * q^93 - 776 * q^95 + 540 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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