LMFDB - Embedded newform 32.3.h.a.3.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,3,Mod(3,32)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("32.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	32.h (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.871936845953$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			3.5
Character	$\chi$	$=$	32.3
Dual form			32.3.h.a.11.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.682385 - 1.87999i) q^{2} +(0.299792 - 0.723762i) q^{3} +(-3.06870 - 2.56575i) q^{4} +(1.34740 + 3.25291i) q^{5} +(-1.15609 - 1.05749i) q^{6} +(0.583225 + 0.583225i) q^{7} +(-6.91761 + 4.01829i) q^{8} +(5.93000 + 5.93000i) q^{9} +O(q^{10})$	\(q+(0.682385 - 1.87999i) q^{2} +(0.299792 - 0.723762i) q^{3} +(-3.06870 - 2.56575i) q^{4} +(1.34740 + 3.25291i) q^{5} +(-1.15609 - 1.05749i) q^{6} +(0.583225 + 0.583225i) q^{7} +(-6.91761 + 4.01829i) q^{8} +(5.93000 + 5.93000i) q^{9} +(7.03487 - 0.313357i) q^{10} +(-3.03620 - 7.33003i) q^{11} +(-2.77696 + 1.45182i) q^{12} +(-6.38385 + 15.4120i) q^{13} +(1.49444 - 0.698471i) q^{14} +2.75827 q^{15} +(2.83386 + 15.7470i) q^{16} -19.0889i q^{17} +(15.1949 - 7.10179i) q^{18} +(-29.6679 - 12.2888i) q^{19} +(4.21138 - 13.4393i) q^{20} +(0.596962 - 0.247270i) q^{21} +(-15.8522 + 0.706111i) q^{22} +(15.2998 - 15.2998i) q^{23} +(0.834442 + 6.21136i) q^{24} +(8.91173 - 8.91173i) q^{25} +(24.6181 + 22.5185i) q^{26} +(12.5835 - 5.21227i) q^{27} +(-0.293334 - 3.28615i) q^{28} +(-20.5148 - 8.49749i) q^{29} +(1.88220 - 5.18552i) q^{30} +53.6582i q^{31} +(31.5380 + 5.41792i) q^{32} -6.21542 q^{33} +(-35.8868 - 13.0260i) q^{34} +(-1.11134 + 2.68301i) q^{35} +(-2.98251 - 33.4123i) q^{36} +(-3.80237 - 9.17973i) q^{37} +(-43.3477 + 47.3895i) q^{38} +(9.24078 + 9.24078i) q^{39} +(-22.3919 - 17.0881i) q^{40} +(14.5108 + 14.5108i) q^{41} +(-0.0575061 - 1.29101i) q^{42} +(20.3685 + 49.1739i) q^{43} +(-9.48983 + 30.2838i) q^{44} +(-11.2997 + 27.2799i) q^{45} +(-18.3230 - 39.2037i) q^{46} +4.73351 q^{47} +(12.2467 + 2.66980i) q^{48} -48.3197i q^{49} +(-10.6727 - 22.8352i) q^{50} +(-13.8158 - 5.72269i) q^{51} +(59.1334 - 30.9154i) q^{52} +(61.4006 - 25.4330i) q^{53} +(-1.21219 - 27.2137i) q^{54} +(19.7530 - 19.7530i) q^{55} +(-6.37809 - 1.69095i) q^{56} +(-17.7884 + 17.7884i) q^{57} +(-29.9741 + 32.7689i) q^{58} +(42.4656 - 17.5898i) q^{59} +(-8.46431 - 7.07703i) q^{60} +(-27.7452 - 11.4924i) q^{61} +(100.877 + 36.6155i) q^{62} +6.91705i q^{63} +(31.7067 - 55.5939i) q^{64} -58.7354 q^{65} +(-4.24131 + 11.6849i) q^{66} +(-9.42323 + 22.7497i) q^{67} +(-48.9772 + 58.5780i) q^{68} +(-6.48665 - 15.6602i) q^{69} +(4.28567 + 3.92015i) q^{70} +(-95.1299 - 95.1299i) q^{71} +(-64.8499 - 17.1930i) q^{72} +(37.1241 + 37.1241i) q^{73} +(-19.8524 + 0.884295i) q^{74} +(-3.77831 - 9.12164i) q^{75} +(59.5118 + 113.831i) q^{76} +(2.50427 - 6.04584i) q^{77} +(23.6783 - 11.0668i) q^{78} -70.3394 q^{79} +(-47.4053 + 30.4358i) q^{80} +64.8066i q^{81} +(37.1821 - 17.3782i) q^{82} +(14.5221 + 6.01526i) q^{83} +(-2.46633 - 0.772858i) q^{84} +(62.0944 - 25.7203i) q^{85} +(106.345 - 4.73698i) q^{86} +(-12.3003 + 12.3003i) q^{87} +(50.4574 + 38.5060i) q^{88} +(-60.8411 + 60.8411i) q^{89} +(43.5750 + 39.8586i) q^{90} +(-12.7119 + 5.26543i) q^{91} +(-86.2059 + 7.69507i) q^{92} +(38.8357 + 16.0863i) q^{93} +(3.23007 - 8.89893i) q^{94} -113.065i q^{95} +(13.3761 - 21.2018i) q^{96} +31.8287 q^{97} +(-90.8404 - 32.9726i) q^{98} +(25.4624 - 61.4718i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 44 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 20 q^{14} - 8 q^{15} + 16 q^{16} + 56 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 144 q^{22} - 68 q^{23} + 208 q^{24} - 4 q^{25} + 96 q^{26} - 100 q^{27} + 56 q^{28} - 4 q^{29} + 20 q^{30} - 24 q^{32} - 8 q^{33} - 48 q^{34} + 92 q^{35} - 336 q^{36} - 4 q^{37} - 396 q^{38} + 188 q^{39} - 408 q^{40} - 4 q^{41} - 424 q^{42} + 92 q^{43} - 188 q^{44} - 40 q^{45} - 36 q^{46} - 8 q^{47} + 48 q^{48} + 308 q^{50} + 224 q^{51} + 420 q^{52} - 164 q^{53} + 592 q^{54} + 252 q^{55} + 552 q^{56} - 4 q^{57} + 528 q^{58} + 124 q^{59} + 440 q^{60} - 68 q^{61} + 216 q^{62} - 232 q^{64} - 8 q^{65} - 580 q^{66} - 164 q^{67} - 368 q^{68} + 188 q^{69} - 664 q^{70} - 260 q^{71} - 748 q^{72} - 4 q^{73} - 532 q^{74} - 488 q^{75} - 516 q^{76} + 220 q^{77} - 236 q^{78} - 520 q^{79} + 312 q^{80} + 636 q^{82} - 484 q^{83} + 992 q^{84} + 96 q^{85} + 688 q^{86} - 452 q^{87} + 672 q^{88} - 4 q^{89} + 872 q^{90} - 196 q^{91} + 616 q^{92} + 32 q^{93} + 40 q^{94} - 128 q^{96} - 8 q^{97} - 328 q^{98} + 216 q^{99}+O(q^{100}) \) 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 44 * q^10 - 4 * q^11 - 52 * q^12 - 4 * q^13 - 20 * q^14 - 8 * q^15 + 16 * q^16 + 56 * q^18 - 4 * q^19 + 76 * q^20 - 4 * q^21 + 144 * q^22 - 68 * q^23 + 208 * q^24 - 4 * q^25 + 96 * q^26 - 100 * q^27 + 56 * q^28 - 4 * q^29 + 20 * q^30 - 24 * q^32 - 8 * q^33 - 48 * q^34 + 92 * q^35 - 336 * q^36 - 4 * q^37 - 396 * q^38 + 188 * q^39 - 408 * q^40 - 4 * q^41 - 424 * q^42 + 92 * q^43 - 188 * q^44 - 40 * q^45 - 36 * q^46 - 8 * q^47 + 48 * q^48 + 308 * q^50 + 224 * q^51 + 420 * q^52 - 164 * q^53 + 592 * q^54 + 252 * q^55 + 552 * q^56 - 4 * q^57 + 528 * q^58 + 124 * q^59 + 440 * q^60 - 68 * q^61 + 216 * q^62 - 232 * q^64 - 8 * q^65 - 580 * q^66 - 164 * q^67 - 368 * q^68 + 188 * q^69 - 664 * q^70 - 260 * q^71 - 748 * q^72 - 4 * q^73 - 532 * q^74 - 488 * q^75 - 516 * q^76 + 220 * q^77 - 236 * q^78 - 520 * q^79 + 312 * q^80 + 636 * q^82 - 484 * q^83 + 992 * q^84 + 96 * q^85 + 688 * q^86 - 452 * q^87 + 672 * q^88 - 4 * q^89 + 872 * q^90 - 196 * q^91 + 616 * q^92 + 32 * q^93 + 40 * q^94 - 128 * q^96 - 8 * q^97 - 328 * q^98 + 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$

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 $

$2$	0.682385	−	1.87999i	0.341192	−	0.939993i
$2$	0.682385	−	1.87999i	0.341192	−	0.939993i
$3$	0.299792	−	0.723762i	0.0999307	−	0.241254i	−0.866005	−	0.500035i	$-0.833321\pi$
$3$	0.299792	−	0.723762i	0.0999307	−	0.241254i	0.965936	+	0.258781i	$0.0833206\pi$
$4$	−3.06870	−	2.56575i	−0.767175	−	0.641437i
$5$	1.34740	+	3.25291i	0.269480	+	0.650582i	0.999459	−	0.0328874i	$-0.0104703\pi$
$5$	1.34740	+	3.25291i	0.269480	+	0.650582i	−0.729979	+	0.683469i	$0.760470\pi$
$6$	−1.15609	−	1.05749i	−0.192682	−	0.176248i
$7$	0.583225	+	0.583225i	0.0833178	+	0.0833178i	0.747537	−	0.664220i	$-0.231236\pi$
$7$	0.583225	+	0.583225i	0.0833178	+	0.0833178i	−0.664220	+	0.747537i	$0.731236\pi$
$8$	−6.91761	+	4.01829i	−0.864701	+	0.502286i
$9$	5.93000	+	5.93000i	0.658889	+	0.658889i
$10$	7.03487	−	0.313357i	0.703487	−	0.0313357i
$11$	−3.03620	−	7.33003i	−0.276018	−	0.666366i	0.723700	−	0.690115i	$-0.242440\pi$
$11$	−3.03620	−	7.33003i	−0.276018	−	0.666366i	−0.999718	+	0.0237484i	$0.992440\pi$
$12$	−2.77696	+	1.45182i	−0.231414	+	0.120985i
$13$	−6.38385	+	15.4120i	−0.491065	+	1.18554i	0.463113	+	0.886299i	$0.346732\pi$
$13$	−6.38385	+	15.4120i	−0.491065	+	1.18554i	−0.954179	+	0.299238i	$0.903268\pi$
$14$	1.49444	−	0.698471i	0.106746	−	0.0498908i
$15$	2.75827			0.183885
$16$	2.83386	+	15.7470i	0.177116	+	0.984190i
$17$		−	19.0889i		−	1.12287i	−0.827519	−	0.561437i	$-0.810249\pi$
$17$		−	19.0889i		−	1.12287i	0.827519	−	0.561437i	$-0.189751\pi$
$18$	15.1949	−	7.10179i	0.844160	−	0.394544i
$19$	−29.6679	−	12.2888i	−1.56147	−	0.646781i	−0.576123	−	0.817363i	$-0.695435\pi$
$19$	−29.6679	−	12.2888i	−1.56147	−	0.646781i	−0.985343	+	0.170582i	$0.945435\pi$
$20$	4.21138	−	13.4393i	0.210569	−	0.671965i
$21$	0.596962	−	0.247270i	0.0284268	−	0.0117748i
$22$	−15.8522	+	0.706111i	−0.720555	+	0.0320959i
$23$	15.2998	−	15.2998i	0.665208	−	0.665208i	−0.291395	−	0.956603i	$-0.594119\pi$
$23$	15.2998	−	15.2998i	0.665208	−	0.665208i	0.956603	+	0.291395i	$0.0941194\pi$
$24$	0.834442	+	6.21136i	0.0347684	+	0.258806i
$25$	8.91173	−	8.91173i	0.356469	−	0.356469i
$26$	24.6181	+	22.5185i	0.946849	+	0.866094i
$27$	12.5835	−	5.21227i	0.466057	−	0.193047i
$28$	−0.293334	−	3.28615i	−0.0104762	−	0.117363i
$29$	−20.5148	−	8.49749i	−0.707405	−	0.293017i	−0.000174983	−	1.00000i	$-0.500056\pi$
$29$	−20.5148	−	8.49749i	−0.707405	−	0.293017i	−0.707231	+	0.706983i	$0.750056\pi$
$30$	1.88220	−	5.18552i	0.0627401	−	0.172851i
$31$			53.6582i			1.73091i	0.500988	+	0.865454i	$0.332970\pi$
$31$			53.6582i			1.73091i	−0.500988	+	0.865454i	$0.667030\pi$
$32$	31.5380	+	5.41792i	0.985563	+	0.169310i
$33$	−6.21542			−0.188346
$34$	−35.8868	−	13.0260i	−1.05549	−	0.383116i
$35$	−1.11134	+	2.68301i	−0.0317526	+	0.0766575i
$36$	−2.98251	−	33.4123i	−0.0828476	−	0.928120i
$37$	−3.80237	−	9.17973i	−0.102767	−	0.248101i	0.864130	−	0.503268i	$-0.167869\pi$
$37$	−3.80237	−	9.17973i	−0.102767	−	0.248101i	−0.966897	+	0.255168i	$0.917869\pi$
$38$	−43.3477	+	47.3895i	−1.14073	+	1.24709i
$39$	9.24078	+	9.24078i	0.236943	+	0.236943i
$40$	−22.3919	−	17.0881i	−0.559798	−	0.427203i
$41$	14.5108	+	14.5108i	0.353922	+	0.353922i	0.861567	−	0.507644i	$-0.169484\pi$
$41$	14.5108	+	14.5108i	0.353922	+	0.353922i	−0.507644	+	0.861567i	$0.669484\pi$
$42$	−0.0575061	−	1.29101i	−0.00136919	−	0.0307384i
$43$	20.3685	+	49.1739i	0.473686	+	1.14358i	0.962522	+	0.271203i	$0.0874214\pi$
$43$	20.3685	+	49.1739i	0.473686	+	1.14358i	−0.488837	+	0.872375i	$0.662579\pi$
$44$	−9.48983	+	30.2838i	−0.215678	+	0.688268i
$45$	−11.2997	+	27.2799i	−0.251104	+	0.606219i
$46$	−18.3230	−	39.2037i	−0.398327	−	0.852255i
$47$	4.73351			0.100713			0.0503565	−	0.998731i	$-0.483964\pi$
$47$	4.73351			0.100713			0.0503565	+	0.998731i	$0.483964\pi$
$48$	12.2467	+	2.66980i	0.255139	+	0.0556207i
$49$		−	48.3197i		−	0.986116i
$50$	−10.6727	−	22.8352i	−0.213454	−	0.456703i
$51$	−13.8158	−	5.72269i	−0.270898	−	0.112210i
$52$	59.1334	−	30.9154i	1.13718	−	0.594527i
$53$	61.4006	−	25.4330i	1.15850	−	0.479867i	0.281126	−	0.959671i	$-0.409292\pi$
$53$	61.4006	−	25.4330i	1.15850	−	0.479867i	0.877376	+	0.479803i	$0.159292\pi$
$54$	−1.21219	−	27.2137i	−0.0224479	−	0.503957i
$55$	19.7530	−	19.7530i	0.359145	−	0.359145i
$56$	−6.37809	−	1.69095i	−0.113894	−	0.0301956i
$57$	−17.7884	+	17.7884i	−0.312077	+	0.312077i
$58$	−29.9741	+	32.7689i	−0.516795	+	0.564981i
$59$	42.4656	−	17.5898i	0.719757	−	0.298133i	0.00742152	−	0.999972i	$-0.497638\pi$
$59$	42.4656	−	17.5898i	0.719757	−	0.298133i	0.712335	+	0.701840i	$0.247638\pi$
$60$	−8.46431	−	7.07703i	−0.141072	−	0.117951i
$61$	−27.7452	−	11.4924i	−0.454839	−	0.188400i	0.143489	−	0.989652i	$-0.454168\pi$
$61$	−27.7452	−	11.4924i	−0.454839	−	0.188400i	−0.598328	+	0.801251i	$0.704168\pi$
$62$	100.877	+	36.6155i	1.62704	+	0.590573i
$63$			6.91705i			0.109794i
$64$	31.7067	−	55.5939i	0.495417	−	0.868655i
$65$	−58.7354			−0.903621
$66$	−4.24131	+	11.6849i	−0.0642623	+	0.177044i
$67$	−9.42323	+	22.7497i	−0.140645	+	0.339548i	−0.978469	−	0.206393i	$-0.933828\pi$
$67$	−9.42323	+	22.7497i	−0.140645	+	0.339548i	0.837824	+	0.545940i	$0.183828\pi$
$68$	−48.9772	+	58.5780i	−0.720254	+	0.861442i
$69$	−6.48665	−	15.6602i	−0.0940094	−	0.226959i
$70$	4.28567	+	3.92015i	0.0612238	+	0.0560022i
$71$	−95.1299	−	95.1299i	−1.33986	−	1.33986i	−0.896193	−	0.443664i	$-0.853678\pi$
$71$	−95.1299	−	95.1299i	−1.33986	−	1.33986i	−0.443664	−	0.896193i	$-0.646322\pi$
$72$	−64.8499	−	17.1930i	−0.900694	−	0.238791i
$73$	37.1241	+	37.1241i	0.508550	+	0.508550i	0.914081	−	0.405531i	$-0.132913\pi$
$73$	37.1241	+	37.1241i	0.508550	+	0.508550i	−0.405531	+	0.914081i	$0.632913\pi$
$74$	−19.8524	+	0.884295i	−0.268276	+	0.0119499i
$75$	−3.77831	−	9.12164i	−0.0503774	−	0.121622i
$76$	59.5118	+	113.831i	0.783050	+	1.49778i
$77$	2.50427	−	6.04584i	0.0325230	−	0.0785174i
$78$	23.6783	−	11.0668i	0.303568	−	0.141882i
$79$	−70.3394			−0.890372			−0.445186	−	0.895438i	$-0.646862\pi$
$79$	−70.3394			−0.890372			−0.445186	+	0.895438i	$0.646862\pi$
$80$	−47.4053	+	30.4358i	−0.592567	+	0.380448i
$81$			64.8066i			0.800081i
$82$	37.1821	−	17.3782i	0.453440	−	0.211929i
$83$	14.5221	+	6.01526i	0.174965	+	0.0724730i	0.468447	−	0.883492i	$-0.344814\pi$
$83$	14.5221	+	6.01526i	0.174965	+	0.0724730i	−0.293481	+	0.955965i	$0.594814\pi$
$84$	−2.46633	−	0.772858i	−0.0293611	−	0.00920069i
$85$	62.0944	−	25.7203i	0.730522	−	0.302592i
$86$	106.345	−	4.73698i	1.23657	−	0.0550812i
$87$	−12.3003	+	12.3003i	−0.141383	+	0.141383i
$88$	50.4574	+	38.5060i	0.573380	+	0.437568i
$89$	−60.8411	+	60.8411i	−0.683608	+	0.683608i	−0.960811	−	0.277204i	$-0.910592\pi$
$89$	−60.8411	+	60.8411i	−0.683608	+	0.683608i	0.277204	+	0.960811i	$0.410592\pi$
$90$	43.5750	+	39.8586i	0.484167	+	0.442874i
$91$	−12.7119	+	5.26543i	−0.139691	+	0.0578618i
$92$	−86.2059	+	7.69507i	−0.937020	+	0.0836420i
$93$	38.8357	+	16.0863i	0.417589	+	0.172971i
$94$	3.23007	−	8.89893i	0.0343625	−	0.0946695i
$95$		−	113.065i		−	1.19016i
$96$	13.3761	−	21.2018i	0.139335	−	0.220852i
$97$	31.8287			0.328131			0.164066	−	0.986449i	$-0.447539\pi$
$97$	31.8287			0.328131			0.164066	+	0.986449i	$0.447539\pi$
$98$	−90.8404	−	32.9726i	−0.926943	−	0.336455i
$99$	25.4624	−	61.4718i	0.257196	−	0.620927i
$100$	−50.2127	+	4.48218i	−0.502127	+	0.0448218i
$101$	11.0397	+	26.6521i	0.109304	+	0.263883i	0.969061	−	0.246820i	$-0.0793855\pi$
$101$	11.0397	+	26.6521i	0.109304	+	0.263883i	−0.859758	+	0.510702i	$0.829385\pi$
$102$	−20.1863	+	22.0684i	−0.197905	+	0.216357i
$103$	56.0862	+	56.0862i	0.544526	+	0.544526i	0.924852	−	0.380326i	$-0.124188\pi$
$103$	56.0862	+	56.0862i	0.544526	+	0.544526i	−0.380326	+	0.924852i	$0.624188\pi$
$104$	−17.7688	−	132.266i	−0.170854	−	1.27179i
$105$	1.60869	+	1.60869i	0.0153209	+	0.0153209i
$106$	−5.91480	−	132.787i	−0.0558000	−	1.25271i
$107$	5.85623	+	14.1382i	0.0547311	+	0.132133i	0.948880	−	0.315637i	$-0.102218\pi$
$107$	5.85623	+	14.1382i	0.0547311	+	0.132133i	−0.894149	+	0.447770i	$0.852218\pi$
$108$	−51.9885	−	16.2913i	−0.481375	−	0.150845i
$109$	37.6258	−	90.8367i	0.345191	−	0.833364i	−0.651983	−	0.758233i	$-0.726063\pi$
$109$	37.6258	−	90.8367i	0.345191	−	0.833364i	0.997174	−	0.0751304i	$-0.0239373\pi$
$110$	−23.6562	−	50.6144i	−0.215056	−	0.460131i
$111$	−7.78386			−0.0701248
$112$	−7.53128	+	10.8368i	−0.0672436	+	0.0967575i
$113$			82.4104i			0.729295i	0.931146	+	0.364648i	$0.118811\pi$
$113$			82.4104i			0.729295i	−0.931146	+	0.364648i	$0.881189\pi$
$114$	21.3034	+	45.5804i	0.186872	+	0.399828i
$115$	70.3837	+	29.1539i	0.612032	+	0.253512i
$116$	41.1512	+	78.7120i	0.354752	+	0.678552i
$117$	−129.249	+	53.5368i	−1.10470	+	0.457580i
$118$	−4.09077	−	91.8379i	−0.0346675	−	0.778287i
$119$	11.1331	−	11.1331i	0.0935555	−	0.0935555i
$120$	−19.0807	+	11.0835i	−0.159005	+	0.0923628i
$121$	41.0491	−	41.0491i	0.339249	−	0.339249i
$122$	−40.5385	+	44.3183i	−0.332283	+	0.363265i
$123$	14.8526	−	6.15215i	0.120753	−	0.0500175i
$124$	137.673	−	164.661i	1.11027	−	1.32791i
$125$	122.319	+	50.6664i	0.978556	+	0.405331i
$126$	13.0040	+	4.72009i	0.103206	+	0.0374610i
$127$			60.4972i			0.476356i	0.971221	+	0.238178i	$0.0765502\pi$
$127$			60.4972i			0.476356i	−0.971221	+	0.238178i	$0.923450\pi$
$128$	−82.8797	−	97.5446i	−0.647498	−	0.762067i
$129$	41.6965			0.323229
$130$	−40.0801	+	110.422i	−0.308309	+	0.849398i
$131$	−56.4124	+	136.192i	−0.430629	+	1.03963i	0.548456	+	0.836179i	$0.315216\pi$
$131$	−56.4124	+	136.192i	−0.430629	+	1.03963i	−0.979085	+	0.203451i	$0.934784\pi$
$132$	19.0733	+	15.9472i	0.144495	+	0.120812i
$133$	−10.1359	−	24.4702i	−0.0762096	−	0.183986i
$134$	36.3389	+	33.2396i	0.271185	+	0.248057i
$135$	33.9101	+	33.9101i	0.251186	+	0.251186i
$136$	76.7046	+	132.049i	0.564005	+	0.970951i
$137$	−139.949	−	139.949i	−1.02152	−	1.02152i	−0.999763	−	0.0217604i	$-0.993073\pi$
$137$	−139.949	−	139.949i	−1.02152	−	1.02152i	−0.0217604	−	0.999763i	$-0.506927\pi$
$138$	−33.8673	+	1.50856i	−0.245415	+	0.0109316i
$139$	−2.63118	−	6.35223i	−0.0189293	−	0.0456995i	0.914132	−	0.405416i	$-0.132873\pi$
$139$	−2.63118	−	6.35223i	−0.0189293	−	0.0456995i	−0.933062	+	0.359717i	$0.882873\pi$
$140$	10.2943	−	5.38195i	0.0735308	−	0.0384425i
$141$	1.41907	−	3.42593i	0.0100643	−	0.0242974i
$142$	−243.758	+	113.928i	−1.71661	+	0.802308i
$143$	132.353			0.925545
$144$	−76.5752	+	110.185i	−0.531772	+	0.765172i
$145$		−	78.1822i		−	0.539187i
$146$	95.1258	−	44.4599i	0.651547	−	0.304520i
$147$	−34.9720	−	14.4859i	−0.237905	−	0.0985433i
$148$	−11.8845	+	37.9258i	−0.0803010	+	0.256255i
$149$	−134.849	+	55.8563i	−0.905027	+	0.374874i	−0.786151	−	0.618035i	$-0.787929\pi$
$149$	−134.849	+	55.8563i	−0.905027	+	0.374874i	−0.118876	+	0.992909i	$0.537929\pi$
$150$	−19.7268	+	0.878699i	−0.131512	+	0.00585799i
$151$	−131.423	+	131.423i	−0.870353	+	0.870353i	−0.992511	−	0.122158i	$-0.961019\pi$
$151$	−131.423	+	131.423i	−0.870353	+	0.870353i	0.122158	+	0.992511i	$0.461019\pi$
$152$	254.611	−	34.2048i	1.67507	−	0.225031i
$153$	113.197	−	113.197i	0.739850	−	0.739850i
$154$	−9.65723	−	8.83358i	−0.0627093	−	0.0573609i
$155$	−174.545	+	72.2990i	−1.12610	+	0.466445i
$156$	−4.64767	−	52.0667i	−0.0297928	−	0.333761i
$157$	−151.775	−	62.8673i	−0.966720	−	0.400429i	−0.157230	−	0.987562i	$-0.550256\pi$
$157$	−151.775	−	62.8673i	−0.966720	−	0.400429i	−0.809490	+	0.587133i	$0.800256\pi$
$158$	−47.9985	+	132.237i	−0.303788	+	0.836944i
$159$		−	52.0640i		−	0.327447i
$160$	24.8703	+	109.890i	0.155439	+	0.686815i
$161$	17.8464			0.110847
$162$	121.835	+	44.2230i	0.752071	+	0.272982i
$163$	75.6492	−	182.633i	0.464106	−	1.12045i	−0.502591	−	0.864524i	$-0.667620\pi$
$163$	75.6492	−	182.633i	0.464106	−	1.12045i	0.966696	−	0.255926i	$-0.0823802\pi$
$164$	−7.29825	−	81.7605i	−0.0445015	−	0.498540i
$165$	−8.37466	−	20.2182i	−0.0507555	−	0.122535i
$166$	21.2183	−	23.1967i	0.127821	−	0.139739i
$167$	148.515	+	148.515i	0.889310	+	0.889310i	0.994457	−	0.105147i	$-0.0335313\pi$
$167$	148.515	+	148.515i	0.889310	+	0.889310i	−0.105147	+	0.994457i	$0.533531\pi$
$168$	−3.13595	+	4.10928i	−0.0186664	+	0.0244600i
$169$	−77.2745	−	77.2745i	−0.457246	−	0.457246i
$170$	−5.98163	−	134.288i	−0.0351860	−	0.789928i
$171$	−103.058	−	248.803i	−0.602677	−	1.45499i
$172$	63.6630	−	203.160i	0.370134	−	1.18116i
$173$	14.9093	−	35.9942i	0.0861808	−	0.208059i	−0.874914	−	0.484279i	$-0.839082\pi$
$173$	14.9093	−	35.9942i	0.0861808	−	0.208059i	0.961094	+	0.276220i	$0.0890819\pi$
$174$	14.7309	+	31.5180i	0.0846603	+	0.181138i
$175$	10.3951			0.0594005
$176$	106.822	−	68.5834i	0.606944	−	0.389678i
$177$		−	36.0083i		−	0.203437i
$178$	72.8634	+	155.897i	0.409345	+	0.875829i
$179$	276.876	+	114.686i	1.54679	+	0.640703i	0.982733	−	0.185029i	$-0.0592379\pi$
$179$	276.876	+	114.686i	1.54679	+	0.640703i	0.564062	+	0.825733i	$0.309238\pi$
$180$	104.669	−	54.7216i	0.581492	−	0.304009i
$181$	−82.1686	+	34.0354i	−0.453970	+	0.188041i	−0.597939	−	0.801542i	$-0.704014\pi$
$181$	−82.1686	+	34.0354i	−0.453970	+	0.188041i	0.143969	+	0.989582i	$0.454014\pi$
$182$	1.22455	+	27.4912i	0.00672830	+	0.151051i
$183$	−16.6356	+	16.6356i	−0.0909047	+	0.0909047i
$184$	−44.3590	+	167.317i	−0.241081	+	0.909331i
$185$	24.7375	−	24.7375i	0.133716	−	0.133716i
$186$	56.7429	−	62.0336i	0.305070	−	0.333514i
$187$	−139.922	+	57.9576i	−0.748246	+	0.309933i
$188$	−14.5257	−	12.1450i	−0.0772645	−	0.0646010i
$189$	10.3790	+	4.29911i	0.0549151	+	0.0227466i
$190$	−212.560	−	77.1537i	−1.11874	−	0.406072i
$191$		−	178.857i		−	0.936426i	−0.883616	−	0.468213i	$-0.844898\pi$
$191$		−	178.857i		−	0.936426i	0.883616	−	0.468213i	$-0.155102\pi$
$192$	−30.7314	−	39.6147i	−0.160059	−	0.206327i
$193$	197.034			1.02090			0.510450	−	0.859908i	$-0.329479\pi$
$193$	197.034			1.02090			0.510450	+	0.859908i	$0.329479\pi$
$194$	21.7194	−	59.8376i	0.111956	−	0.308441i
$195$	−17.6084	+	42.5104i	−0.0902995	+	0.218002i
$196$	−123.976	+	148.279i	−0.632532	+	0.756524i
$197$	62.3398	+	150.502i	0.316446	+	0.763968i	0.999437	+	0.0335413i	$0.0106785\pi$
$197$	62.3398	+	150.502i	0.316446	+	0.763968i	−0.682992	+	0.730426i	$0.739321\pi$
$198$	−98.1909	−	89.8165i	−0.495914	−	0.453618i
$199$	22.3835	+	22.3835i	0.112480	+	0.112480i	0.761107	−	0.648627i	$-0.224656\pi$
$199$	22.3835	+	22.3835i	0.112480	+	0.112480i	−0.648627	+	0.761107i	$0.724656\pi$
$200$	−25.8380	+	97.4578i	−0.129190	+	0.487289i
$201$	13.6404	+	13.6404i	0.0678625	+	0.0678625i
$202$	57.6390	−	2.56744i	0.285342	−	0.0127101i
$203$	−7.00877	−	16.9207i	−0.0345260	−	0.0833530i
$204$	27.7136	+	53.0091i	0.135851	+	0.259849i
$205$	−27.6505	+	66.7542i	−0.134881	+	0.325630i
$206$	143.714	−	67.1690i	0.697640	−	0.326063i
$207$	181.456			0.876597
$208$	−260.784	−	56.8513i	−1.25377	−	0.273324i
$209$			254.778i			1.21903i
$210$	4.12207	−	1.92657i	0.0196289	−	0.00917416i
$211$	−315.926	−	130.861i	−1.49728	−	0.620194i	−0.524394	−	0.851476i	$-0.675708\pi$
$211$	−315.926	−	130.861i	−1.49728	−	0.620194i	−0.972887	+	0.231282i	$0.925708\pi$
$212$	−253.675	−	79.4924i	−1.19658	−	0.374964i
$213$	−97.3706	+	40.3322i	−0.457139	+	0.189353i
$214$	30.5758	−	1.36195i	0.142878	−	0.00636425i
$215$	−132.514	+	132.514i	−0.616343	+	0.616343i
$216$	−66.1036	+	86.6208i	−0.306035	+	0.401022i
$217$	−31.2948	+	31.2948i	−0.144216	+	0.144216i
$218$	−145.096	−	132.722i	−0.665580	−	0.608814i
$219$	37.9986	−	15.7395i	0.173509	−	0.0718699i
$220$	−111.297	+	9.93480i	−0.505896	+	0.0451582i
$221$	294.197	+	121.860i	1.33121	+	0.551405i
$222$	−5.31159	+	14.6336i	−0.0239261	+	0.0659169i
$223$			103.995i			0.466346i	0.972435	+	0.233173i	$0.0749109\pi$
$223$			103.995i			0.466346i	−0.972435	+	0.233173i	$0.925089\pi$
$224$	15.2339	+	21.5536i	0.0680084	+	0.0962215i
$225$	105.693			0.469748
$226$	154.930	+	56.2356i	0.685533	+	0.248830i
$227$	19.9655	−	48.2010i	0.0879538	−	0.212339i	−0.873782	−	0.486318i	$-0.838340\pi$
$227$	19.9655	−	48.2010i	0.0879538	−	0.212339i	0.961736	+	0.273979i	$0.0883397\pi$
$228$	100.228	−	8.94671i	0.439595	−	0.0392400i
$229$	52.0405	+	125.637i	0.227251	+	0.548633i	0.995841	−	0.0911090i	$-0.0290412\pi$
$229$	52.0405	+	125.637i	0.227251	+	0.548633i	−0.768590	+	0.639742i	$0.779041\pi$
$230$	102.838	−	112.426i	0.447120	−	0.488810i
$231$	−3.62499	−	3.62499i	−0.0156926	−	0.0156926i
$232$	176.059	−	23.6519i	0.758873	−	0.101948i
$233$	−0.497550	−	0.497550i	−0.00213541	−	0.00213541i	0.706038	−	0.708174i	$-0.250481\pi$
$233$	−0.497550	−	0.497550i	−0.00213541	−	0.00213541i	−0.708174	+	0.706038i	$0.750481\pi$
$234$	12.4508	+	279.520i	0.0532084	+	1.19453i
$235$	6.37793	+	15.3977i	0.0271401	+	0.0655220i
$236$	−175.446	−	54.9782i	−0.743413	−	0.232958i
$237$	−21.0872	+	50.9090i	−0.0889755	+	0.214806i
$238$	−13.3330	−	28.5271i	−0.0560211	−	0.119862i
$239$	−80.2602			−0.335817			−0.167908	−	0.985803i	$-0.553701\pi$
$239$	−80.2602			−0.335817			−0.167908	+	0.985803i	$0.553701\pi$
$240$	7.81656	+	43.4346i	0.0325690	+	0.180978i
$241$		−	9.94799i		−	0.0412780i	−0.999787	−	0.0206390i	$-0.993430\pi$
$241$		−	9.94799i		−	0.0412780i	0.999787	−	0.0206390i	$-0.00657006\pi$
$242$	−49.1605	−	105.183i	−0.203142	−	0.434641i
$243$	160.156	+	66.3389i	0.659080	+	0.273000i
$244$	55.6550	+	106.454i	0.228094	+	0.436287i
$245$	157.180	−	65.1059i	0.641549	−	0.265738i
$246$	−1.43077	−	32.1208i	−0.00581614	−	0.130573i
$247$	378.790	−	378.790i	1.53356	−	1.53356i
$248$	−215.614	−	371.186i	−0.869412	−	1.49672i
$249$	8.70723	−	8.70723i	0.0349688	−	0.0349688i
$250$	178.721	−	195.385i	0.714884	−	0.781540i
$251$	−37.4569	+	15.5152i	−0.149231	+	0.0618134i	−0.456049	−	0.889955i	$-0.650736\pi$
$251$	−37.4569	+	15.5152i	−0.149231	+	0.0618134i	0.306818	+	0.951768i	$0.400736\pi$
$252$	17.7474	−	21.2264i	0.0704263	−	0.0842316i
$253$	−158.601	−	65.6947i	−0.626881	−	0.259663i
$254$	113.734	+	41.2824i	0.447772	+	0.162529i
$255$		−	52.6523i		−	0.206480i
$256$	−239.938	+	89.2499i	−0.937260	+	0.348632i
$257$	−351.412			−1.36736			−0.683680	−	0.729782i	$-0.739622\pi$
$257$	−351.412			−1.36736			−0.683680	+	0.729782i	$0.739622\pi$
$258$	28.4530	−	78.3888i	0.110283	−	0.303833i
$259$	3.13621	−	7.57148i	0.0121089	−	0.0292335i
$260$	180.241	+	150.700i	0.693236	+	0.579616i
$261$	−71.2625	−	172.043i	−0.273036	−	0.659168i
$262$	217.543	+	198.990i	0.830318	+	0.759502i
$263$	−347.609	−	347.609i	−1.32171	−	1.32171i	−0.912393	−	0.409316i	$-0.865767\pi$
$263$	−347.609	−	347.609i	−1.32171	−	1.32171i	−0.409316	−	0.912393i	$-0.634233\pi$
$264$	42.9959	−	24.9754i	0.162863	−	0.0946037i
$265$	165.462	+	165.462i	0.624386	+	0.624386i
$266$	−52.9202	+	2.35724i	−0.198948	+	0.00886182i
$267$	25.7948	+	62.2741i	0.0966097	+	0.233236i
$268$	87.2871	−	45.6344i	0.325698	−	0.170278i
$269$	77.8419	−	187.927i	0.289375	−	0.698613i	−0.710613	−	0.703584i	$-0.751582\pi$
$269$	77.8419	−	187.927i	0.289375	−	0.698613i	0.999988	+	0.00497024i	$0.00158208\pi$
$270$	86.8903	−	40.6108i	0.321816	−	0.150410i
$271$	−380.417			−1.40375			−0.701876	−	0.712299i	$-0.747654\pi$
$271$	−380.417			−1.40375			−0.701876	+	0.712299i	$0.747654\pi$
$272$	300.593	−	54.0952i	1.10512	−	0.198879i
$273$			10.7789i			0.0394832i
$274$	−358.601	+	167.603i	−1.30876	+	0.611689i
$275$	−92.3810	−	38.2655i	−0.335931	−	0.139147i
$276$	−20.2744	+	64.6995i	−0.0734581	+	0.234418i
$277$	130.082	−	53.8819i	0.469612	−	0.194519i	−0.135312	−	0.990803i	$-0.543204\pi$
$277$	130.082	−	53.8819i	0.469612	−	0.194519i	0.604924	+	0.796284i	$0.293204\pi$
$278$	−13.7376	+	0.611918i	−0.0494158	+	0.00220114i
$279$	−318.193	+	318.193i	−1.14048	+	1.14048i
$280$	−3.09331	−	23.0257i	−0.0110475	−	0.0822348i
$281$	−40.5881	+	40.5881i	−0.144442	+	0.144442i	−0.775630	−	0.631188i	$-0.782568\pi$
$281$	−40.5881	+	40.5881i	−0.144442	+	0.144442i	0.631188	+	0.775630i	$0.282568\pi$
$282$	−5.47236	−	5.00563i	−0.0194055	−	0.0177505i
$283$	442.450	−	183.269i	1.56343	−	0.647593i	0.577748	−	0.816215i	$-0.303932\pi$
$283$	442.450	−	183.269i	1.56343	−	0.647593i	0.985681	+	0.168622i	$0.0539316\pi$
$284$	47.8458	+	536.005i	0.168471	+	1.88734i
$285$	−81.8320	−	33.8959i	−0.287130	−	0.118933i
$286$	90.3156	−	248.822i	0.315789	−	0.870006i
$287$			16.9261i			0.0589761i
$288$	154.892	+	219.149i	0.537820	+	0.760933i
$289$	−75.3848			−0.260847
$290$	−146.981	−	53.3503i	−0.506833	−	0.183967i
$291$	9.54200	−	23.0364i	0.0327904	−	0.0791629i
$292$	−18.6717	−	209.174i	−0.0639441	−	0.716350i
$293$	−141.261	−	341.035i	−0.482120	−	1.16394i	−0.958600	−	0.284756i	$-0.908087\pi$
$293$	−141.261	−	341.035i	−0.482120	−	1.16394i	0.476479	−	0.879186i	$-0.341913\pi$
$294$	−51.0976	+	55.8619i	−0.173801	+	0.190006i
$295$	114.436	+	114.436i	0.387920	+	0.387920i
$296$	63.1901	+	48.2228i	0.213480	+	0.162915i
$297$	−76.4122	−	76.4122i	−0.257280	−	0.257280i
$298$	12.9902	+	291.630i	0.0435912	+	0.978623i
$299$	138.128	+	333.471i	0.461968	+	1.11529i
$300$	−11.8093	+	37.6858i	−0.0393645	+	0.125619i
$301$	−16.8000	+	40.5588i	−0.0558140	+	0.134747i
$302$	157.393	+	336.755i	0.521168	+	1.11508i
$303$	22.5994			0.0745856
$304$	109.438	−	502.006i	0.359994	−	1.65134i
$305$		−	105.737i		−	0.346680i
$306$	−135.565	−	290.053i	−0.443023	−	0.947885i
$307$	27.5569	+	11.4145i	0.0897620	+	0.0371807i	0.427113	−	0.904198i	$-0.359531\pi$
$307$	27.5569	+	11.4145i	0.0897620	+	0.0371807i	−0.337351	+	0.941379i	$0.609531\pi$
$308$	−23.1970	+	12.1276i	−0.0753148	+	0.0393752i
$309$	57.4073	−	23.7789i	0.185784	−	0.0769543i
$310$	16.8142	+	377.478i	0.0542392	+	1.21767i
$311$	262.516	−	262.516i	0.844102	−	0.844102i	−0.145288	−	0.989389i	$-0.546411\pi$
$311$	262.516	−	262.516i	0.844102	−	0.844102i	0.989389	+	0.145288i	$0.0464108\pi$
$312$	−101.056	−	26.7920i	−0.323898	−	0.0858717i
$313$	−346.338	+	346.338i	−1.10651	+	1.10651i	−0.112907	+	0.993606i	$0.536016\pi$
$313$	−346.338	+	346.338i	−1.10651	+	1.10651i	−0.993606	+	0.112907i	$0.963984\pi$
$314$	−221.759	+	242.435i	−0.706238	+	0.772087i
$315$	−22.5005	+	9.32003i	−0.0714303	+	0.0295874i
$316$	215.851	+	180.473i	0.683071	+	0.571118i
$317$	37.8371	+	15.6726i	0.119360	+	0.0494405i	0.441564	−	0.897230i	$-0.354424\pi$
$317$	37.8371	+	15.6726i	0.119360	+	0.0494405i	−0.322204	+	0.946670i	$0.604424\pi$
$318$	−97.8797	−	35.5277i	−0.307798	−	0.111722i
$319$			176.174i			0.552269i
$320$	223.564	+	28.2317i	0.698636	+	0.0882241i
$321$	11.9883			0.0373469
$322$	12.1781	−	33.5510i	0.0378203	−	0.104196i
$323$	−234.580	+	566.326i	−0.726253	+	1.75333i
$324$	166.277	−	198.872i	0.513202	−	0.613802i
$325$	80.4563	+	194.239i	0.247558	+	0.597657i
$326$	−291.726	−	266.846i	−0.894866	−	0.818545i
$327$	−54.4642	−	54.4642i	−0.166557	−	0.166557i
$328$	−158.689	−	42.0715i	−0.483807	−	0.128267i
$329$	2.76070	+	2.76070i	0.00839118	+	0.00839118i
$330$	−43.7247	+	1.94765i	−0.132499	+	0.00590196i
$331$	123.850	+	298.999i	0.374168	+	0.903321i	0.993034	+	0.117825i	$0.0375921\pi$
$331$	123.850	+	298.999i	0.374168	+	0.903321i	−0.618867	+	0.785496i	$0.712408\pi$
$332$	−29.1304	−	55.7192i	−0.0877422	−	0.167829i
$333$	31.8878	−	76.9839i	0.0957591	−	0.231183i
$334$	380.550	−	177.862i	1.13937	−	0.532520i
$335$	−86.6995			−0.258805
$336$	5.58548	+	8.69966i	0.0166234	+	0.0258918i
$337$		−	553.901i		−	1.64362i	−0.569759	−	0.821812i	$-0.692963\pi$
$337$		−	553.901i		−	1.64362i	0.569759	−	0.821812i	$-0.307037\pi$
$338$	−198.006	+	92.5441i	−0.585817	+	0.273799i
$339$	59.6455	+	24.7060i	0.175945	+	0.0728790i
$340$	−256.541	−	80.3905i	−0.754532	−	0.236443i
$341$	393.316	−	162.917i	1.15342	−	0.477762i
$342$	−538.072	+	23.9675i	−1.57331	+	0.0700805i
$343$	56.7593	−	56.7593i	0.165479	−	0.165479i
$344$	−338.496	−	258.319i	−0.984000	−	0.750928i
$345$	42.2010	−	42.2010i	0.122322	−	0.122322i
$346$	−57.4947	−	52.5912i	−0.166170	−	0.151998i
$347$	149.596	−	61.9645i	0.431111	−	0.178572i	−0.156566	−	0.987667i	$-0.550042\pi$
$347$	149.596	−	61.9645i	0.431111	−	0.178572i	0.587677	+	0.809095i	$0.300042\pi$
$348$	69.3056	−	6.18648i	0.199154	−	0.0177772i
$349$	−354.488	−	146.834i	−1.01572	−	0.420727i	−0.188184	−	0.982134i	$-0.560260\pi$
$349$	−354.488	−	146.834i	−1.01572	−	0.420727i	−0.827540	+	0.561407i	$0.810260\pi$
$350$	7.09345	−	19.5426i	0.0202670	−	0.0558361i
$351$			227.212i			0.647327i
$352$	−56.0421	−	247.624i	−0.159211	−	0.703478i
$353$	−360.254			−1.02055			−0.510275	−	0.860011i	$-0.670456\pi$
$353$	−360.254			−1.02055			−0.510275	+	0.860011i	$0.670456\pi$
$354$	−67.6952	−	24.5715i	−0.191229	−	0.0694111i
$355$	181.271	−	437.627i	0.510622	−	1.23275i
$356$	342.806	−	30.6002i	0.962939	−	0.0859556i
$357$	−4.72010	−	11.3953i	−0.0132216	−	0.0319197i
$358$	404.544	−	442.264i	1.13001	−	1.23537i
$359$	92.0047	+	92.0047i	0.256280	+	0.256280i	0.823539	−	0.567259i	$-0.191996\pi$
$359$	92.0047	+	92.0047i	0.256280	+	0.256280i	−0.567259	+	0.823539i	$0.691996\pi$
$360$	−31.4516	−	234.117i	−0.0873655	−	0.650325i
$361$	473.901	+	473.901i	1.31275	+	1.31275i
$362$	7.91541	+	177.701i	0.0218658	+	0.490887i
$363$	−17.4036	−	42.0160i	−0.0479438	−	0.115746i
$364$	52.5187	+	16.4574i	0.144282	+	0.0452127i
$365$	−70.7404	+	170.782i	−0.193809	+	0.467897i
$366$	19.9228	+	42.6265i	0.0544339	+	0.116466i
$367$	254.513			0.693496			0.346748	−	0.937958i	$-0.387286\pi$
$367$	254.513			0.693496			0.346748	+	0.937958i	$0.387286\pi$
$368$	284.284	+	197.569i	0.772510	+	0.536872i
$369$			172.098i			0.466391i
$370$	−29.6257	−	63.3867i	−0.0800695	−	0.171315i
$371$	50.6435	+	20.9772i	0.136505	+	0.0565424i
$372$	−77.9019	−	149.007i	−0.209414	−	0.400556i
$373$	440.477	−	182.452i	1.18090	−	0.489147i	0.296122	−	0.955150i	$-0.404307\pi$
$373$	440.477	−	182.452i	1.18090	−	0.489147i	0.884783	+	0.466004i	$0.154307\pi$
$374$	13.4789	+	302.601i	0.0360397	+	0.809093i
$375$	73.3408	−	73.3408i	0.195575	−	0.195575i
$376$	−32.7446	+	19.0206i	−0.0870866	+	0.0505867i
$377$	261.926	−	261.926i	0.694765	−	0.694765i
$378$	15.1647	−	16.5787i	0.0401183	−	0.0438589i
$379$	124.964	−	51.7618i	0.329720	−	0.136575i	−0.211681	−	0.977339i	$-0.567894\pi$
$379$	124.964	−	51.7618i	0.329720	−	0.136575i	0.541402	+	0.840764i	$0.317894\pi$
$380$	−290.096	+	346.962i	−0.763411	+	0.913059i
$381$	43.7856	+	18.1366i	0.114923	+	0.0476026i
$382$	−336.250	−	122.050i	−0.880235	−	0.319502i
$383$			182.483i			0.476458i	0.971209	+	0.238229i	$0.0765669\pi$
$383$			182.483i			0.476458i	−0.971209	+	0.238229i	$0.923433\pi$
$384$	−95.4458	+	30.7421i	−0.248557	+	0.0800576i
$385$	23.0408			0.0598463
$386$	134.453	−	370.421i	0.348323	−	0.959639i
$387$	−170.816	+	412.386i	−0.441385	+	1.06560i
$388$	−97.6728	−	81.6645i	−0.251734	−	0.210476i
$389$	−134.979	−	325.868i	−0.346990	−	0.837708i	−0.996972	−	0.0777583i	$-0.975224\pi$
$389$	−134.979	−	325.868i	−0.346990	−	0.837708i	0.649982	−	0.759949i	$-0.274776\pi$
$390$	67.9034	+	62.1120i	0.174111	+	0.159262i
$391$	−292.055	−	292.055i	−0.746945	−	0.746945i
$392$	194.163	+	334.257i	0.495313	+	0.852696i
$393$	81.6583	+	81.6583i	0.207782	+	0.207782i
$394$	325.481	−	14.4980i	0.826093	−	0.0367970i
$395$	−94.7752	−	228.808i	−0.239937	−	0.579260i
$396$	−235.858	+	123.308i	−0.595600	+	0.311385i
$397$	−272.283	+	657.350i	−0.685852	+	1.65579i	0.0671236	+	0.997745i	$0.478618\pi$
$397$	−272.283	+	657.350i	−0.685852	+	1.65579i	−0.752976	+	0.658048i	$0.771382\pi$
$398$	57.3549	−	26.8066i	0.144108	−	0.0673532i
$399$	−20.7492			−0.0520031
$400$	165.588	+	115.079i	0.413970	+	0.287697i
$401$		−	74.4996i		−	0.185785i	−0.995676	−	0.0928923i	$-0.970389\pi$
$401$		−	74.4996i		−	0.185785i	0.995676	−	0.0928923i	$-0.0296112\pi$
$402$	34.9517	−	16.3357i	0.0869444	−	0.0406361i
$403$	−826.978	−	342.546i	−2.05206	−	0.849989i
$404$	34.5052	−	110.113i	0.0854090	−	0.272556i
$405$	−210.810	+	87.3203i	−0.520518	+	0.215606i
$406$	−36.5933	+	1.62999i	−0.0901313	+	0.00401475i
$407$	−55.7429	+	55.7429i	−0.136961	+	0.136961i
$408$	118.568	−	15.9285i	0.290607	−	0.0390406i
$409$	−289.633	+	289.633i	−0.708149	+	0.708149i	−0.966146	−	0.257997i	$-0.916938\pi$
$409$	−289.633	+	289.633i	−0.708149	+	0.708149i	0.257997	+	0.966146i	$0.416938\pi$
$410$	106.629	+	97.5347i	0.260070	+	0.237889i
$411$	−143.245	+	59.3341i	−0.348528	+	0.144365i
$412$	−28.2087	−	316.015i	−0.0684678	−	0.767027i
$413$	35.0258	+	14.5082i	0.0848083	+	0.0351288i
$414$	123.823	−	341.134i	0.299088	−	0.823995i
$415$			55.3441i			0.133359i
$416$	−284.835	+	451.476i	−0.684699	+	1.08528i
$417$	−5.38631			−0.0129168
$418$	478.979	+	173.856i	1.14588	+	0.415924i
$419$	234.290	−	565.626i	0.559165	−	1.34994i	−0.351264	−	0.936277i	$-0.614248\pi$
$419$	234.290	−	565.626i	0.559165	−	1.34994i	0.910428	−	0.413667i	$-0.135752\pi$
$420$	−0.809096	−	9.06410i	−0.00192642	−	0.0215812i
$421$	205.463	+	496.031i	0.488035	+	1.17822i	0.955707	+	0.294319i	$0.0950929\pi$
$421$	205.463	+	496.031i	0.488035	+	1.17822i	−0.467672	+	0.883902i	$0.654907\pi$
$422$	−461.600	+	504.640i	−1.09384	+	1.19583i
$423$	28.0697	+	28.0697i	0.0663587	+	0.0663587i
$424$	−322.549	+	422.661i	−0.760728	+	0.996842i
$425$	−170.115	−	170.115i	−0.400270	−	0.400270i
$426$	9.37983	+	210.577i	0.0220184	+	0.494313i
$427$	−9.47901	−	22.8843i	−0.0221991	−	0.0535933i
$428$	18.3040	−	58.4115i	0.0427664	−	0.136476i
$429$	39.6783	−	95.7920i	0.0924903	−	0.223291i
$430$	158.699	+	339.549i	0.369067	+	0.789649i
$431$	−94.1706			−0.218493			−0.109247	−	0.994015i	$-0.534844\pi$
$431$	−94.1706			−0.218493			−0.109247	+	0.994015i	$0.534844\pi$
$432$	117.738	+	183.383i	0.272541	+	0.424497i
$433$		−	66.2703i		−	0.153049i	−0.997068	−	0.0765246i	$-0.975618\pi$
$433$		−	66.2703i		−	0.153049i	0.997068	−	0.0765246i	$-0.0243824\pi$
$434$	37.4787	+	80.1888i	0.0863564	+	0.184767i
$435$	−56.5853	−	23.4384i	−0.130081	−	0.0538814i
$436$	−348.526	+	182.212i	−0.799372	+	0.417918i
$437$	−641.928	+	265.895i	−1.46894	+	0.608456i
$438$	−3.66045	−	82.1772i	−0.00835719	−	0.187619i
$439$	393.404	−	393.404i	0.896137	−	0.896137i	−0.0989551	−	0.995092i	$-0.531550\pi$
$439$	393.404	−	393.404i	0.896137	−	0.896137i	0.995092	+	0.0989551i	$0.0315500\pi$
$440$	−57.2701	+	216.016i	−0.130159	+	0.490946i
$441$	286.536	−	286.536i	0.649742	−	0.649742i
$442$	429.852	−	469.931i	0.972515	−	1.06319i
$443$	124.298	−	51.4859i	0.280583	−	0.116221i	−0.237954	−	0.971276i	$-0.576477\pi$
$443$	124.298	−	51.4859i	0.280583	−	0.116221i	0.518537	+	0.855055i	$0.326477\pi$
$444$	23.8863	+	19.9714i	0.0537981	+	0.0449807i
$445$	−279.888	−	115.933i	−0.628961	−	0.260524i
$446$	195.510	+	70.9647i	0.438362	+	0.159114i
$447$			114.344i			0.255803i
$448$	50.9159	−	13.9317i	0.113652	−	0.0310974i
$449$	621.505			1.38420			0.692099	−	0.721802i	$-0.256686\pi$
$449$	621.505			1.38420			0.692099	+	0.721802i	$0.256686\pi$
$450$	72.1235	−	198.702i	0.160274	−	0.441560i
$451$	62.3070	−	150.422i	0.138153	−	0.333531i
$452$	211.444	−	252.893i	0.467797	−	0.559498i
$453$	55.7195	+	134.519i	0.123001	+	0.296951i
$454$	−76.9931	−	70.4265i	−0.169588	−	0.155124i
$455$	−34.2559	−	34.2559i	−0.0752877	−	0.0752877i
$456$	51.5742	−	194.532i	0.113101	−	0.426605i
$457$	−121.890	−	121.890i	−0.266718	−	0.266718i	0.561058	−	0.827776i	$-0.310394\pi$
$457$	−121.890	−	121.890i	−0.266718	−	0.266718i	−0.827776	+	0.561058i	$0.810394\pi$
$458$	271.708	−	12.1028i	0.593248	−	0.0264253i
$459$	−99.4964	−	240.205i	−0.216768	−	0.523323i
$460$	−141.185	−	270.052i	−0.306924	−	0.587069i
$461$	92.0148	−	222.143i	0.199598	−	0.481873i	−0.792111	−	0.610378i	$-0.791018\pi$
$461$	92.0148	−	222.143i	0.199598	−	0.481873i	0.991709	+	0.128505i	$0.0410177\pi$
$462$	−9.28857	+	4.34130i	−0.0201051	+	0.00939674i
$463$	−133.158			−0.287598			−0.143799	−	0.989607i	$-0.545932\pi$
$463$	−133.158			−0.287598			−0.143799	+	0.989607i	$0.545932\pi$
$464$	75.6743	−	347.127i	0.163091	−	0.748119i
$465$			148.004i			0.318288i
$466$	−1.27491	+	0.595867i	−0.00273586	+	0.00127869i
$467$	−414.267	−	171.595i	−0.887082	−	0.367441i	−0.107843	−	0.994168i	$-0.534394\pi$
$467$	−414.267	−	171.595i	−0.887082	−	0.367441i	−0.779239	+	0.626727i	$0.784394\pi$
$468$	533.990	+	167.333i	1.14100	+	0.357549i
$469$	−18.7640	+	7.77232i	−0.0400086	+	0.0165721i
$470$	33.2996	−	1.48328i	0.0708503	−	0.00315591i
$471$	−91.0019	+	91.0019i	−0.193210	+	0.193210i
$472$	−223.080	+	292.319i	−0.472626	+	0.619320i
$473$	298.603	−	298.603i	0.631296	−	0.631296i
$474$	81.3186	+	74.3831i	0.171558	+	0.156926i
$475$	−373.907	+	154.877i	−0.787172	+	0.326058i
$476$	−62.7289	+	5.59942i	−0.131783	+	0.0117635i
$477$	514.924	+	213.288i	1.07950	+	0.447145i
$478$	−54.7683	+	150.888i	−0.114578	+	0.315665i
$479$		−	293.655i		−	0.613059i	−0.951861	−	0.306530i	$-0.900832\pi$
$479$		−	293.655i		−	0.613059i	0.951861	−	0.306530i	$-0.0991679\pi$
$480$	86.9904	+	14.9441i	0.181230	+	0.0311335i
$481$	165.752			0.344598
$482$	−18.7021	−	6.78836i	−0.0388010	−	0.0140837i
$483$	5.35022	−	12.9166i	0.0110771	−	0.0267424i
$484$	−231.289	+	20.6458i	−0.477870	+	0.0426565i
$485$	42.8860	+	103.536i	0.0884247	+	0.213476i
$486$	234.005	−	255.823i	0.481491	−	0.526385i
$487$	468.368	+	468.368i	0.961741	+	0.961741i	0.999295	−	0.0375532i	$-0.0119564\pi$
$487$	468.368	+	468.368i	0.961741	+	0.961741i	−0.0375532	+	0.999295i	$0.511956\pi$
$488$	238.110	−	31.9881i	0.487931	−	0.0655493i
$489$	−109.504	−	109.504i	−0.223935	−	0.223935i
$490$	−15.1413	−	339.923i	−0.0309006	−	0.693720i
$491$	−120.443	−	290.775i	−0.245301	−	0.592210i	0.752492	−	0.658601i	$-0.228851\pi$
$491$	−120.443	−	290.775i	−0.245301	−	0.592210i	−0.997794	+	0.0663911i	$0.978851\pi$
$492$	−61.3631	−	19.2289i	−0.124722	−	0.0390832i
$493$	−162.207	+	391.603i	−0.329021	+	0.794328i
$494$	−453.640	−	970.602i	−0.918300	−	1.96478i
$495$	234.270			0.473273
$496$	−844.957	+	152.060i	−1.70354	+	0.306572i
$497$		−	110.964i		−	0.223268i
$498$	−10.4278	−	22.3112i	−0.0209394	−	0.0448015i
$499$	572.626	+	237.190i	1.14755	+	0.475330i	0.873711	−	0.486446i	$-0.161707\pi$
$499$	572.626	+	237.190i	1.14755	+	0.475330i	0.273837	+	0.961776i	$0.411707\pi$
$500$	−245.365	−	469.321i	−0.490729	−	0.938642i
$501$	152.013	−	62.9658i	0.303419	−	0.125680i
$502$	3.60827	+	81.0058i	0.00718779	+	0.161366i
$503$	−397.129	+	397.129i	−0.789520	+	0.789520i	−0.981415	−	0.191895i	$-0.938537\pi$
$503$	−397.129	+	397.129i	−0.789520	+	0.789520i	0.191895	+	0.981415i	$0.438537\pi$
$504$	−27.7947	−	47.8495i	−0.0551483	−	0.0949394i
$505$	−71.8222	+	71.8222i	−0.142222	+	0.142222i
$506$	−231.732	+	253.339i	−0.457968	+	0.500669i
$507$	−79.0946	+	32.7621i	−0.156005	+	0.0646195i
$508$	155.221	−	185.648i	0.305553	−	0.365449i
$509$	−16.5014	−	6.83509i	−0.0324192	−	0.0134285i	0.366415	−	0.930452i	$-0.380585\pi$
$509$	−16.5014	−	6.83509i	−0.0324192	−	0.0134285i	−0.398834	+	0.917023i	$0.630585\pi$
$510$	−98.9856	−	35.9291i	−0.194089	−	0.0704493i
$511$			43.3034i			0.0847425i
$512$	4.05825	+	511.984i	0.00792626	+	0.999969i
$513$	−437.380			−0.852592
$514$	−239.798	+	660.649i	−0.466533	+	1.28531i
$515$	−106.873	+	258.014i	−0.207520	+	0.500998i
$516$	−127.954	−	106.983i	−0.247973	−	0.207331i
$517$	−14.3719	−	34.6968i	−0.0277986	−	0.0671117i
$518$	−12.0942	−	11.0627i	−0.0233478	−	0.0213566i
$519$	−21.5815	−	21.5815i	−0.0415829	−	0.0415829i
$520$	406.308	−	236.016i	0.781362	−	0.453877i
$521$	−11.8175	−	11.8175i	−0.0226824	−	0.0226824i	0.695675	−	0.718357i	$-0.255106\pi$
$521$	−11.8175	−	11.8175i	−0.0226824	−	0.0226824i	−0.718357	+	0.695675i	$0.755106\pi$
$522$	−372.067	+	16.5731i	−0.712771	+	0.0317492i
$523$	141.420	+	341.417i	0.270401	+	0.652806i	0.999501	−	0.0316019i	$-0.0100609\pi$
$523$	141.420	+	341.417i	0.270401	+	0.652806i	−0.729100	+	0.684408i	$0.760061\pi$
$524$	522.546	−	273.191i	0.997225	−	0.521357i
$525$	3.11636	−	7.52357i	0.00593593	−	0.0143306i
$526$	−890.705	+	416.298i	−1.69335	+	0.791441i
$527$	1024.27			1.94359
$528$	−17.6137	−	97.8745i	−0.0333592	−	0.185368i
$529$			60.8334i			0.114997i
$530$	423.976	−	198.158i	0.799955	−	0.373883i
$531$	356.129	+	147.514i	0.670677	+	0.277803i
$532$	−31.6804	+	101.098i	−0.0595495	+	0.190034i
$533$	−316.275	+	131.006i	−0.593387	+	0.245789i
$534$	134.677	−	5.99895i	0.252203	−	0.0112340i
$535$	−38.0996	+	38.0996i	−0.0712142	+	0.0712142i
$536$	−26.2286	−	195.239i	−0.0489340	−	0.364251i
$537$	166.011	−	166.011i	0.309145	−	0.309145i
$538$	−300.182	−	274.580i	−0.557959	−	0.510372i
$539$	−354.185	+	146.708i	−0.657115	+	0.272186i
$540$	−17.0552	−	191.065i	−0.0315837	−	0.353824i
$541$	−117.048	−	48.4829i	−0.216355	−	0.0896172i	0.271874	−	0.962333i	$-0.412357\pi$
$541$	−117.048	−	48.4829i	−0.216355	−	0.0896172i	−0.488229	+	0.872716i	$0.662357\pi$
$542$	−259.591	+	715.178i	−0.478949	+	1.31952i
$543$			69.6741i			0.128313i
$544$	103.422	−	602.025i	0.190114	−	1.10666i
$545$	346.180			0.635193
$546$	20.2642	+	7.35536i	0.0371139	+	0.0134714i
$547$	−113.911	+	275.005i	−0.208247	+	0.502752i	−0.993147	−	0.116870i	$-0.962714\pi$
$547$	−113.911	+	275.005i	−0.208247	+	0.502752i	0.784901	+	0.619622i	$0.212714\pi$
$548$	70.3876	+	788.534i	0.128445	+	1.43893i
$549$	−96.3789	−	232.679i	−0.175553	−	0.423824i
$550$	−134.978	+	147.563i	−0.245415	+	0.268297i
$551$	504.205	+	504.205i	0.915072	+	0.915072i
$552$	107.799	+	82.2656i	0.195288	+	0.149032i
$553$	−41.0237	−	41.0237i	−0.0741838	−	0.0741838i
$554$	−12.5310	−	281.321i	−0.0226191	−	0.507800i
$555$	−10.4880	−	25.3202i	−0.0188972	−	0.0456220i
$556$	−8.22392	+	26.2440i	−0.0147912	+	0.0472015i
$557$	87.2197	−	210.567i	0.156588	−	0.378037i	−0.826043	−	0.563607i	$-0.809413\pi$
$557$	87.2197	−	210.567i	0.156588	−	0.378037i	0.982631	+	0.185570i	$0.0594131\pi$
$558$	381.069	+	815.329i	0.682919	+	1.46116i
$559$	−887.896			−1.58836
$560$	−45.3989	−	9.89703i	−0.0810695	−	0.0176733i
$561$			118.645i			0.211489i
$562$	48.6084	+	104.002i	0.0864918	+	0.185057i
$563$	697.221	+	288.798i	1.23840	+	0.512963i	0.903215	−	0.429188i	$-0.141200\pi$
$563$	697.221	+	288.798i	1.23840	+	0.512963i	0.335188	+	0.942151i	$0.391200\pi$
$564$	−13.1448	+	6.87220i	−0.0233064	+	0.0121847i
$565$	−268.074	+	111.040i	−0.474466	+	0.196530i
$566$	−42.6218	−	956.861i	−0.0753035	−	1.69057i
$567$	−37.7968	+	37.7968i	−0.0666610	+	0.0666610i
$568$	1040.33	+	275.812i	1.83157	+	0.485584i
$569$	−252.850	+	252.850i	−0.444376	+	0.444376i	−0.893480	−	0.449104i	$-0.851743\pi$
$569$	−252.850	+	252.850i	−0.444376	+	0.444376i	0.449104	+	0.893480i	$0.351743\pi$
$570$	−119.565	+	130.713i	−0.209763	+	0.229321i
$571$	352.993	−	146.215i	0.618202	−	0.256068i	−0.0515290	−	0.998672i	$-0.516409\pi$
$571$	352.993	−	146.215i	0.618202	−	0.256068i	0.669731	+	0.742604i	$0.266409\pi$
$572$	−406.152	−	339.584i	−0.710055	−	0.593679i
$573$	−129.450	−	53.6200i	−0.225917	−	0.0935777i
$574$	31.8209	+	11.5501i	0.0554371	+	0.0201222i
$575$		−	272.695i		−	0.474252i
$576$	517.693	−	141.652i	0.898773	−	0.245923i
$577$	−197.099			−0.341593			−0.170797	−	0.985306i	$-0.554634\pi$
$577$	−197.099			−0.341593			−0.170797	+	0.985306i	$0.554634\pi$
$578$	−51.4414	+	141.722i	−0.0889990	+	0.245194i
$579$	59.0691	−	142.605i	0.102019	−	0.246296i
$580$	−200.596	+	239.918i	−0.345855	+	0.413651i
$581$	4.96141	+	11.9779i	0.00853944	+	0.0206160i
$582$	−36.7968	−	33.6585i	−0.0632248	−	0.0578325i
$583$	−372.849	−	372.849i	−0.639535	−	0.639535i
$584$	−405.986	−	107.635i	−0.695181	−	0.184306i
$585$	−348.301	−	348.301i	−0.595386	−	0.595386i
$586$	−737.536	+	32.8523i	−1.25859	+	0.0560620i
$587$	−238.745	−	576.382i	−0.406721	−	0.981912i	−0.985994	−	0.166778i	$-0.946664\pi$
$587$	−238.745	−	576.382i	−0.406721	−	0.981912i	0.579273	−	0.815134i	$-0.303336\pi$
$588$	70.1514	+	134.182i	0.119305	+	0.228201i
$589$	659.396	−	1591.92i	1.11952	−	2.70276i
$590$	293.228	−	137.049i	0.496997	−	0.232287i
$591$	127.616			0.215933
$592$	133.778	−	85.8901i	0.225977	−	0.145085i
$593$			276.598i			0.466438i	0.972424	+	0.233219i	$0.0749260\pi$
$593$			276.598i			0.466438i	−0.972424	+	0.233219i	$0.925074\pi$
$594$	−195.797	+	91.5114i	−0.329624	+	0.154060i
$595$	51.2157	+	21.2142i	0.0860768	+	0.0356542i
$596$	557.124	+	174.582i	0.934772	+	0.292923i
$597$	22.9108	−	9.48995i	0.0383765	−	0.0158961i
$598$	721.179	−	32.1237i	1.20598	−	0.0537186i
$599$	−710.727	+	710.727i	−1.18652	+	1.18652i	−0.208501	+	0.978022i	$0.566859\pi$
$599$	−710.727	+	710.727i	−1.18652	+	1.18652i	−0.978022	+	0.208501i	$0.933141\pi$
$600$	62.7903	+	47.9176i	0.104650	+	0.0798627i
$601$	−215.219	+	215.219i	−0.358102	+	0.358102i	−0.863113	−	0.505011i	$-0.831488\pi$
$601$	−215.219	+	215.219i	−0.358102	+	0.358102i	0.505011	+	0.863113i	$0.331488\pi$
$602$	64.7860	+	59.2605i	0.107618	+	0.0984394i
$603$	−190.786	+	79.0260i	−0.316394	+	0.131055i
$604$	740.498	−	66.0997i	1.22599	−	0.109437i
$605$	188.839	+	78.2195i	0.312130	+	0.129288i
$606$	15.4215	−	42.4866i	0.0254480	−	0.0701099i
$607$		−	683.779i		−	1.12649i	−0.826290	−	0.563245i	$-0.809553\pi$
$607$		−	683.779i		−	1.12649i	0.826290	−	0.563245i	$-0.190447\pi$
$608$	−869.086	−	548.303i	−1.42942	−	0.901815i
$609$	−14.3477			−0.0235595
$610$	−198.785	−	72.1536i	−0.325877	−	0.118285i
$611$	−30.2180	+	72.9527i	−0.0494566	+	0.119399i
$612$	−637.803	+	56.9328i	−1.04216	+	0.0930274i
$613$	−296.111	−	714.875i	−0.483052	−	1.16619i	−0.958152	−	0.286259i	$-0.907588\pi$
$613$	−296.111	−	714.875i	−0.483052	−	1.16619i	0.475100	−	0.879932i	$-0.342412\pi$
$614$	40.2635	−	44.0176i	0.0655757	−	0.0716900i
$615$	40.0248	+	40.0248i	0.0650809	+	0.0650809i
$616$	6.97039	+	51.8856i	0.0113156	+	0.0842299i
$617$	−275.822	−	275.822i	−0.447037	−	0.447037i	0.447331	−	0.894368i	$-0.352374\pi$
$617$	−275.822	−	275.822i	−0.447037	−	0.447037i	−0.894368	+	0.447331i	$0.852374\pi$
$618$	−5.53012	−	124.151i	−0.00894841	−	0.200892i
$619$	201.130	+	485.570i	0.324927	+	0.784443i	0.998954	+	0.0457357i	$0.0145632\pi$
$619$	201.130	+	485.570i	0.324927	+	0.784443i	−0.674027	+	0.738707i	$0.735437\pi$
$620$	721.128	+	225.975i	1.16311	+	0.364476i
$621$	112.779	−	272.272i	0.181608	−	0.438441i
$622$	−314.389	−	672.663i	−0.505449	−	1.08145i
$623$	−70.9681			−0.113913
$624$	−119.328	+	171.702i	−0.191230	+	0.275163i
$625$			151.085i			0.241735i
$626$	414.775	+	887.448i	0.662581	+	1.41765i
$627$	184.398	+	76.3803i	0.294096	+	0.121819i
$628$	304.451	+	582.338i	0.484794	+	0.927289i
$629$	−175.231	+	72.5829i	−0.278586	+	0.115394i
$630$	2.16751	+	48.6606i	0.00344048	+	0.0772390i
$631$	48.9545	−	48.9545i	0.0775823	−	0.0775823i	−0.667251	−	0.744833i	$-0.732529\pi$
$631$	48.9545	−	48.9545i	0.0775823	−	0.0775823i	0.744833	+	0.667251i	$0.232529\pi$
$632$	486.580	−	282.644i	0.769906	−	0.447222i
$633$	−189.424	+	189.424i	−0.299249	+	0.299249i
$634$	55.2838	−	60.4385i	0.0871984	−	0.0953288i
$635$	−196.792	+	81.5139i	−0.309909	+	0.128368i
$636$	−133.583	+	159.769i	−0.210037	+	0.251209i
$637$	744.702	+	308.466i	1.16908	+	0.484248i
$638$	331.205	+	120.218i	0.519129	+	0.188430i
$639$		−	1128.24i		−	1.76564i
$640$	205.632	−	401.032i	0.321299	−	0.626612i
$641$	320.295			0.499680			0.249840	−	0.968287i	$-0.419622\pi$
$641$	320.295			0.499680			0.249840	+	0.968287i	$0.419622\pi$
$642$	8.18066	−	22.5379i	0.0127425	−	0.0351058i
$643$	39.8184	−	96.1302i	0.0619260	−	0.149503i	−0.889887	−	0.456180i	$-0.849217\pi$
$643$	39.8184	−	96.1302i	0.0619260	−	0.149503i	0.951813	+	0.306677i	$0.0992173\pi$
$644$	−54.7653	−	45.7894i	−0.0850394	−	0.0711016i
$645$	56.1818	+	135.635i	0.0871036	+	0.210287i
$646$	904.612	+	827.459i	1.40033	+	1.28090i
$647$	−134.372	−	134.372i	−0.207684	−	0.207684i	0.595598	−	0.803282i	$-0.296915\pi$
$647$	−134.372	−	134.372i	−0.207684	−	0.207684i	−0.803282	+	0.595598i	$0.796915\pi$
$648$	−260.412	−	448.306i	−0.401870	−	0.691831i
$649$	−257.868	−	257.868i	−0.397331	−	0.397331i
$650$	420.068	−	18.7113i	0.646259	−	0.0287865i
$651$	13.2680	+	32.0319i	0.0203810	+	0.0492041i
$652$	−700.736	+	366.350i	−1.07475	+	0.561887i
$653$	−358.760	+	866.123i	−0.549403	+	1.32638i	0.368521	+	0.929619i	$0.379864\pi$
$653$	−358.760	+	866.123i	−0.549403	+	1.32638i	−0.917924	+	0.396756i	$0.870136\pi$
$654$	−139.558	+	65.2265i	−0.213391	+	0.0997347i
$655$	−519.029			−0.792410
$656$	−187.381	+	269.624i	−0.285641	+	0.411012i
$657$			440.293i			0.670156i
$658$	7.07394	−	3.30622i	0.0107507	−	0.00502465i
$659$	596.224	+	246.964i	0.904741	+	0.374756i	0.786041	−	0.618174i	$-0.212127\pi$
$659$	596.224	+	246.964i	0.904741	+	0.374756i	0.118700	+	0.992930i	$0.462127\pi$
$660$	−26.1755	+	83.5309i	−0.0396599	+	0.126562i
$661$	16.3196	−	6.75978i	0.0246892	−	0.0102266i	−0.370305	−	0.928910i	$-0.620747\pi$
$661$	16.3196	−	6.75978i	0.0246892	−	0.0102266i	0.394994	+	0.918684i	$0.370747\pi$
$662$	646.628	−	28.8030i	0.976779	−	0.0435090i
$663$	176.396	−	176.396i	0.266057	−	0.266057i
$664$	−124.629	+	16.7429i	−0.187695	+	0.0252152i
$665$	65.9422	−	65.9422i	0.0991612	−	0.0991612i
$666$	−122.969	−	112.481i	−0.184638	−	0.168891i
$667$	−443.881	+	183.862i	−0.665489	+	0.275655i
$668$	−74.6959	−	836.799i	−0.111820	−	1.25269i
$669$	75.2678	+	31.1769i	0.112508	+	0.0466023i
$670$	−59.1625	+	162.994i	−0.0883022	+	0.243275i
$671$			238.266i			0.355091i
$672$	20.1667	−	4.56411i	0.0300099	−	0.00679183i
$673$	−334.752			−0.497403			−0.248701	−	0.968580i	$-0.580004\pi$
$673$	−334.752			−0.497403			−0.248701	+	0.968580i	$0.580004\pi$
$674$	−1041.33	−	377.974i	−1.54500	−	0.560792i
$675$	65.6908	−	158.592i	0.0973197	−	0.234950i
$676$	38.8654	+	435.399i	0.0574932	+	0.644082i
$677$	294.364	+	710.658i	0.434807	+	1.04972i	0.977717	+	0.209926i	$0.0673222\pi$
$677$	294.364	+	710.658i	0.434807	+	1.04972i	−0.542911	+	0.839790i	$0.682678\pi$
$678$	87.1481	−	95.2738i	0.128537	−	0.140522i
$679$	18.5633	+	18.5633i	0.0273392	+	0.0273392i
$680$	−326.193	+	427.436i	−0.479695	+	0.628583i
$681$	−28.9006	−	28.9006i	−0.0424384	−	0.0424384i
$682$	−37.8886	−	850.601i	−0.0555551	−	1.24721i
$683$	−118.311	−	285.628i	−0.173223	−	0.418196i	0.813295	−	0.581851i	$-0.197672\pi$
$683$	−118.311	−	285.628i	−0.173223	−	0.418196i	−0.986518	+	0.163655i	$0.947672\pi$
$684$	−322.114	+	1027.92i	−0.470926	+	1.50281i
$685$	266.674	−	643.807i	0.389305	−	0.939865i
$686$	−67.9750	−	145.438i	−0.0990889	−	0.212009i
$687$	106.533			0.155069
$688$	−716.621	+	460.095i	−1.04160	+	0.668743i
$689$			1108.67i			1.60909i
$690$	−50.5400	−	108.135i	−0.0732463	−	0.156717i
$691$	−13.1275	−	5.43758i	−0.0189978	−	0.00786914i	0.373164	−	0.927765i	$-0.378273\pi$
$691$	−13.1275	−	5.43758i	−0.0189978	−	0.00786914i	−0.392162	+	0.919896i	$0.628273\pi$
$692$	−138.104	+	72.2020i	−0.199573	+	0.104338i
$693$	50.7022	−	21.0015i	0.0731633	−	0.0303052i
$694$	−14.4107	−	323.522i	−0.0207647	−	0.466169i
$695$	17.1180	−	17.1180i	0.0246302	−	0.0246302i
$696$	35.6626	−	134.515i	0.0512393	−	0.193269i
$697$	276.995	−	276.995i	0.397410	−	0.397410i
$698$	−517.942	+	566.235i	−0.742038	+	0.811225i
$699$	−0.509270	+	0.210946i	−0.000728569	+	0.000301783i
$700$	−31.8994	−	26.6712i	−0.0455706	−	0.0381017i
$701$	−100.100	−	41.4627i	−0.142796	−	0.0591480i	0.310141	−	0.950691i	$-0.399624\pi$
$701$	−100.100	−	41.4627i	−0.142796	−	0.0591480i	−0.452937	+	0.891543i	$0.649624\pi$
$702$	427.155	+	155.046i	0.608483	+	0.220863i
$703$			319.070i			0.453869i
$704$	−503.773	−	63.6166i	−0.715587	−	0.0903645i
$705$	13.0563			0.0185196
$706$	−245.832	+	677.273i	−0.348204	+	0.959310i
$707$	−9.10558	+	21.9828i	−0.0128792	+	0.0310931i
$708$	−92.3883	+	110.499i	−0.130492	+	0.156072i
$709$	273.663	+	660.681i	0.385985	+	0.931849i	0.990781	+	0.135470i	$0.0432543\pi$
$709$	273.663	+	660.681i	0.385985	+	0.931849i	−0.604797	+	0.796380i	$0.706746\pi$
$710$	−699.036	−	639.417i	−0.984558	−	0.900587i
$711$	−417.113	−	417.113i	−0.586657	−	0.586657i
$712$	176.398	−	665.352i	0.247750	−	0.934483i
$713$	820.958	+	820.958i	1.15141	+	1.15141i
$714$	−24.6440	+	1.09773i	−0.0345154	+	0.00153743i
$715$	178.332	+	430.532i	0.249416	+	0.602143i
$716$	−555.395	−	1062.33i	−0.775692	−	1.48370i
$717$	−24.0614	+	58.0893i	−0.0335584	+	0.0810171i
$718$	235.750	−	110.185i	0.328343	−	0.153461i
$719$	−532.079			−0.740026			−0.370013	−	0.929026i	$-0.620647\pi$
$719$	−532.079			−0.740026			−0.370013	+	0.929026i	$0.620647\pi$
$720$	−461.599	−	100.629i	−0.641109	−	0.139763i
$721$			65.4218i			0.0907375i
$722$	1214.31	−	567.545i	1.68187	−	0.786074i
$723$	−7.19998	−	2.98233i	−0.00995848	−	0.00412494i
$724$	339.477	+	106.380i	0.468891	+	0.146933i
$725$	−258.549	+	107.095i	−0.356620	+	0.147717i
$726$	−90.8654	+	4.04745i	−0.125159	+	0.00557500i
$727$	305.054	−	305.054i	0.419606	−	0.419606i	−0.465462	−	0.885068i	$-0.654112\pi$
$727$	305.054	−	305.054i	0.419606	−	0.419606i	0.885068	+	0.465462i	$0.154112\pi$
$728$	66.7777	−	87.5042i	0.0917276	−	0.120198i
$729$	−316.399	+	316.399i	−0.434018	+	0.434018i
$730$	272.797	+	249.530i	0.373694	+	0.341823i
$731$	938.673	−	388.811i	1.28409	−	0.531889i
$732$	93.7323	−	8.36690i	0.128050	−	0.0114302i
$733$	344.710	+	142.783i	0.470272	+	0.194793i	0.605218	−	0.796060i	$-0.293086\pi$
$733$	344.710	+	142.783i	0.470272	+	0.194793i	−0.134946	+	0.990853i	$0.543086\pi$
$734$	173.676	−	478.481i	0.236616	−	0.651882i
$735$		−	133.279i		−	0.181332i
$736$	565.418	−	399.632i	0.768230	−	0.542978i
$737$	195.367			0.265084
$738$	323.543	+	117.437i	0.438405	+	0.159129i
$739$	107.676	−	259.954i	0.145706	−	0.351765i	−0.834131	−	0.551567i	$-0.814030\pi$
$739$	107.676	−	259.954i	0.145706	−	0.351765i	0.979836	+	0.199803i	$0.0640301\pi$
$740$	−139.382	+	12.4418i	−0.188354	+	0.0168132i
$741$	−160.596	−	387.713i	−0.216728	−	0.523229i
$742$	73.9953	−	80.8946i	0.0997241	−	0.109022i
$743$	−470.112	−	470.112i	−0.632721	−	0.632721i	0.316029	−	0.948750i	$-0.397650\pi$
$743$	−470.112	−	470.112i	−0.632721	−	0.632721i	−0.948750	+	0.316029i	$0.897650\pi$
$744$	−333.290	+	44.7746i	−0.447970	+	0.0601809i
$745$	−363.391	−	363.391i	−0.487773	−	0.487773i
$746$	−42.4317	−	952.594i	−0.0568790	−	1.27694i
$747$	50.4457	+	121.787i	0.0675311	+	0.163034i
$748$	578.083	+	181.150i	0.772839	+	0.242179i
$749$	−4.83025	+	11.6612i	−0.00644893	+	0.0155691i
$750$	−87.8331	−	187.926i	−0.117111	−	0.250569i
$751$	844.801			1.12490			0.562451	−	0.826831i	$-0.309859\pi$
$751$	844.801			1.12490			0.562451	+	0.826831i	$0.309859\pi$
$752$	13.4141	+	74.5387i	0.0178379	+	0.0991207i
$753$			31.7612i			0.0421796i
$754$	−313.684	−	671.153i	−0.416026	−	0.890123i
$755$	−604.588	−	250.428i	−0.800778	−	0.331693i
$756$	−20.8195	−	39.8225i	−0.0275390	−	0.0526752i
$757$	1050.78	−	435.247i	1.38808	−	0.574962i	0.441452	−	0.897285i	$-0.354464\pi$
$757$	1050.78	−	435.247i	1.38808	−	0.574962i	0.946630	+	0.322322i	$0.104464\pi$
$758$	−12.0379	−	270.252i	−0.0158812	−	0.356533i
$759$	−95.0946	+	95.0946i	−0.125289	+	0.125289i
$760$	454.327	+	782.139i	0.597799	+	1.02913i
$761$	−44.1359	+	44.1359i	−0.0579972	+	0.0579972i	−0.735511	−	0.677513i	$-0.763058\pi$
$761$	−44.1359	+	44.1359i	−0.0579972	+	0.0579972i	0.677513	+	0.735511i	$0.263058\pi$
$762$	63.9752	−	69.9402i	0.0839569	−	0.0917851i
$763$	74.9225	−	31.0339i	0.0981946	−	0.0406735i
$764$	−458.903	+	548.860i	−0.600659	+	0.718403i
$765$	520.741	+	215.698i	0.680708	+	0.281958i
$766$	343.066	+	124.524i	0.447867	+	0.162564i
$767$			766.771i			0.999701i
$768$	−7.33597	+	200.415i	−0.00955204	+	0.260957i
$769$	794.025			1.03254			0.516271	−	0.856425i	$-0.327320\pi$
$769$	794.025			1.03254			0.516271	+	0.856425i	$0.327320\pi$
$770$	15.7227	−	43.3164i	0.0204191	−	0.0562551i
$771$	−105.350	+	254.338i	−0.136641	+	0.329881i
$772$	−604.637	−	505.539i	−0.783209	−	0.654843i
$773$	−395.664	−	955.218i	−0.511856	−	1.23573i	−0.942803	−	0.333351i	$-0.891820\pi$
$773$	−395.664	−	955.218i	−0.511856	−	1.23573i	0.430947	−	0.902377i	$-0.358180\pi$
$774$	658.719	+	602.538i	0.851058	+	0.778473i
$775$	478.187	+	478.187i	0.617016	+	0.617016i
$776$	−220.179	+	127.897i	−0.283735	+	0.164816i
$777$	−4.53974	−	4.53974i	−0.00584265	−	0.00584265i
$778$	−704.736	+	31.3913i	−0.905830	+	0.0403487i
$779$	−252.184	−	608.826i	−0.323728	−	0.781548i
$780$	163.106	−	85.2731i	0.209110	−	0.109324i
$781$	−408.472	+	986.138i	−0.523011	+	1.26266i
$782$	−748.355	+	349.766i	−0.956975	+	0.447271i
$783$	−302.440			−0.386257
$784$	760.892	−	136.931i	0.970526	−	0.174657i
$785$		−	578.418i		−	0.736838i
$786$	209.239	−	97.7941i	0.266207	−	0.124420i
$787$	−445.085	−	184.360i	−0.565547	−	0.234257i	0.0815444	−	0.996670i	$-0.474015\pi$
$787$	−445.085	−	184.360i	−0.565547	−	0.234257i	−0.647091	+	0.762413i	$0.724015\pi$
$788$	194.847	−	621.793i	0.247268	−	0.789077i
$789$	−355.797	+	147.376i	−0.450947	+	0.186788i
$790$	−494.828	+	22.0413i	−0.626365	+	0.0279004i
$791$	−48.0638	+	48.0638i	−0.0607633	+	0.0607633i
$792$	70.8722	+	527.553i	0.0894851	+	0.666103i
$793$	354.242	−	354.242i	0.446711	−	0.446711i
$794$	1050.01	+	960.455i	1.32243	+	1.20964i
$795$	169.360	−	70.1511i	0.213031	−	0.0882403i
$796$	−11.2579	−	126.119i	−0.0141430	−	0.158441i
$797$	−1384.22	−	573.363i	−1.73679	−	0.719402i	−0.999016	−	0.0443527i	$-0.985877\pi$
$797$	−1384.22	−	573.363i	−1.73679	−	0.719402i	−0.737773	−	0.675049i	$-0.764123\pi$
$798$	−14.1590	+	39.0083i	−0.0177431	+	0.0488826i
$799$		−	90.3573i		−	0.113088i
$800$	329.341	−	232.775i	0.411677	−	0.290969i
$801$	−721.576			−0.900844
$802$	−140.058	−	50.8374i	−0.174636	−	0.0633883i
$803$	159.405	−	384.837i	0.198512	−	0.479249i
$804$	−6.86045	−	76.8559i	−0.00853290	−	0.0955919i
$805$	24.0463	+	58.0528i	0.0298711	+	0.0721153i
$806$	−1208.30	+	1320.96i	−1.49913	+	1.63891i
$807$	−112.678	−	112.678i	−0.139626	−	0.139626i
$808$	−183.464	−	140.009i	−0.227060	−	0.173278i
$809$	462.148	+	462.148i	0.571258	+	0.571258i	0.932480	−	0.361222i	$-0.117640\pi$
$809$	462.148	+	462.148i	0.571258	+	0.571258i	−0.361222	+	0.932480i	$0.617640\pi$
$810$	20.3076	+	455.906i	0.0250711	+	0.562847i
$811$	32.9003	+	79.4282i	0.0405675	+	0.0979386i	0.942865	−	0.333176i	$-0.108120\pi$
$811$	32.9003	+	79.4282i	0.0405675	+	0.0979386i	−0.902297	+	0.431115i	$0.858120\pi$
$812$	−21.9064	+	69.9072i	−0.0269783	+	0.0860926i
$813$	−114.046	+	275.331i	−0.140278	+	0.338661i
$814$	66.7578	+	142.834i	0.0820121	+	0.175472i
$815$	696.019			0.854012
$816$	50.9634	−	233.775i	0.0624551	−	0.286489i
$817$		−	1709.19i		−	2.09203i
$818$	346.865	+	742.147i	0.424040	+	0.907270i
$819$	−106.605	−	44.1574i	−0.130165	−	0.0539163i
$820$	256.126	−	133.905i	0.312349	−	0.163298i
$821$	−724.768	+	300.209i	−0.882787	+	0.365662i	−0.777577	−	0.628788i	$-0.783551\pi$
$821$	−724.768	+	300.209i	−0.882787	+	0.365662i	−0.105210	+	0.994450i	$0.533551\pi$
$822$	13.7990	+	309.788i	0.0167871	+	0.376871i
$823$	−378.179	+	378.179i	−0.459513	+	0.459513i	−0.898496	−	0.438982i	$-0.855339\pi$
$823$	−378.179	+	378.179i	−0.459513	+	0.459513i	0.438982	+	0.898496i	$0.355339\pi$
$824$	−613.353	−	162.612i	−0.744361	−	0.197345i
$825$	−55.3902	+	55.3902i	−0.0671396	+	0.0671396i
$826$	51.1763	−	55.9480i	0.0619568	−	0.0677336i
$827$	−1071.43	+	443.801i	−1.29556	+	0.536639i	−0.920638	−	0.390416i	$-0.872331\pi$
$827$	−1071.43	+	443.801i	−1.29556	+	0.536639i	−0.374924	+	0.927056i	$0.622331\pi$
$828$	−556.833	−	465.569i	−0.672504	−	0.562282i
$829$	−1023.61	−	423.991i	−1.23475	−	0.511449i	−0.332678	−	0.943041i	$-0.607952\pi$
$829$	−1023.61	−	423.991i	−1.23475	−	0.511449i	−0.902069	+	0.431592i	$0.857952\pi$
$830$	104.046	+	37.7660i	0.125357	+	0.0455012i
$831$		−	110.302i		−	0.132734i
$832$	654.402	+	843.566i	0.786541	+	1.01390i
$833$	−922.368			−1.10728
$834$	−3.67553	+	10.1262i	−0.00440712	+	0.0121417i
$835$	−282.996	+	683.214i	−0.338918	+	0.818220i
$836$	653.696	−	781.837i	0.781932	−	0.935211i
$837$	279.681	+	675.210i	0.334147	+	0.806702i
$838$	−903.494	−	826.437i	−1.07815	−	0.986202i
$839$	1157.38	+	1157.38i	1.37947	+	1.37947i	0.845506	+	0.533966i	$0.179299\pi$
$839$	1157.38	+	1157.38i	1.37947	+	1.37947i	0.533966	+	0.845506i	$0.320701\pi$
$840$	−17.5925	−	4.66411i	−0.0209435	−	0.00555252i
$841$	−246.029	−	246.029i	−0.292543	−	0.292543i
$842$	1072.74	−	47.7833i	1.27403	−	0.0567498i
$843$	17.2081	+	41.5441i	0.0204130	+	0.0492813i
$844$	633.727	+	1212.16i	0.750862	+	1.43621i
$845$	147.247	−	355.487i	0.174257	−	0.420694i
$846$	71.9251	−	33.6164i	0.0850178	−	0.0397357i
$847$	47.8817			0.0565309
$848$	574.495	+	894.805i	0.677470	+	1.05519i
$849$		−	375.171i		−	0.441898i
$850$	−435.898	+	203.730i	−0.512821	+	0.239682i
$851$	−198.623	−	82.2724i	−0.233400	−	0.0966773i
$852$	402.284	+	126.061i	0.472164	+	0.147959i
$853$	1189.88	−	492.862i	1.39493	−	0.577799i	0.446499	−	0.894784i	$-0.352671\pi$
$853$	1189.88	−	492.862i	1.39493	−	0.577799i	0.948431	+	0.316985i	$0.102671\pi$
$854$	−49.4906	+	2.20448i	−0.0579515	+	0.00258136i
$855$	670.475	−	670.475i	0.784181	−	0.784181i
$856$	−97.3225	−	74.2705i	−0.113695	−	0.0867646i
$857$	240.773	−	240.773i	0.280948	−	0.280948i	−0.552539	−	0.833487i	$-0.686341\pi$
$857$	240.773	−	240.773i	0.280948	−	0.280948i	0.833487	+	0.552539i	$0.186341\pi$
$858$	−153.012	−	139.962i	−0.178335	−	0.163126i
$859$	−577.833	+	239.346i	−0.672682	+	0.278634i	−0.692764	−	0.721164i	$-0.743607\pi$
$859$	−577.833	+	239.346i	−0.672682	+	0.278634i	0.0200823	+	0.999798i	$0.493607\pi$
$860$	746.642	−	66.6481i	0.868188	−	0.0774978i
$861$	12.2505	+	5.07432i	0.0142282	+	0.00589352i
$862$	−64.2606	+	177.040i	−0.0745483	+	0.205382i
$863$			1084.57i			1.25675i	0.777912	+	0.628373i	$0.216279\pi$
$863$			1084.57i			1.25675i	−0.777912	+	0.628373i	$0.783721\pi$
$864$	425.099	−	96.2082i	0.492013	−	0.111352i
$865$	137.175			0.158583
$866$	−124.587	−	45.2218i	−0.143865	−	0.0522192i
$867$	−22.5998	+	54.5606i	−0.0260666	+	0.0629304i
$868$	176.329	−	15.7398i	0.203144	−	0.0181334i
$869$	213.564	+	515.590i	0.245759	+	0.593314i
$870$	−82.6768	+	90.3856i	−0.0950308	+	0.103891i
$871$	−290.461	−	290.461i	−0.333480	−	0.333480i
$872$	104.728	+	779.564i	0.120101	+	0.893995i
$873$	188.744	+	188.744i	0.216202	+	0.216202i
$874$	61.8378	+	1388.26i	0.0707526	+	1.58840i
$875$	41.7899	+	100.890i	0.0477598	+	0.115302i
$876$	−156.990	−	49.1949i	−0.179212	−	0.0561585i
$877$	−331.246	+	799.700i	−0.377704	+	0.911858i	0.614691	+	0.788768i	$0.289281\pi$
$877$	−331.246	+	799.700i	−0.377704	+	0.911858i	−0.992395	+	0.123090i	$0.960719\pi$
$878$	−471.142	−	1008.05i	−0.536608	−	1.14812i
$879$	−289.177			−0.328984
$880$	367.028	+	255.073i	0.417077	+	0.289856i
$881$		−	995.281i		−	1.12972i	−0.825188	−	0.564859i	$-0.808931\pi$
$881$		−	995.281i		−	1.12972i	0.825188	−	0.564859i	$-0.191069\pi$
$882$	−343.156	−	734.212i	−0.389066	−	0.832440i
$883$	−587.282	−	243.260i	−0.665098	−	0.275493i	0.0244838	−	0.999700i	$-0.492206\pi$
$883$	−587.282	−	243.260i	−0.665098	−	0.275493i	−0.689582	+	0.724207i	$0.742206\pi$
$884$	−590.140	−	1128.79i	−0.667579	−	1.27691i
$885$	117.132	−	48.5176i	0.132352	−	0.0548221i
$886$	−11.9738	−	268.812i	−0.0135144	−	0.303400i
$887$	679.194	−	679.194i	0.765720	−	0.765720i	−0.211630	−	0.977350i	$-0.567877\pi$
$887$	679.194	−	679.194i	0.765720	−	0.765720i	0.977350	+	0.211630i	$0.0678772\pi$
$888$	53.8457	−	31.2778i	0.0606370	−	0.0352228i
$889$	−35.2835	+	35.2835i	−0.0396890	+	0.0396890i
$890$	−408.944	+	447.074i	−0.459488	+	0.502331i
$891$	475.034	−	196.765i	0.533147	−	0.220837i
$892$	266.826	−	319.130i	0.299132	−	0.357769i
$893$	−140.433	−	58.1693i	−0.157260	−	0.0651392i
$894$	214.965	+	78.0265i	0.240453	+	0.0872779i
$895$			1055.18i			1.17897i
$896$	8.55291	−	105.228i	0.00954566	−	0.117442i
$897$	282.764			0.315233
$898$	424.106	−	1168.42i	0.472278	−	1.30114i
$899$	455.960	−	1100.78i	0.507185	−	1.22445i
$900$	−324.341	−	271.182i	−0.360379	−	0.301314i
$901$	−485.487	−	1172.07i	−0.538831	−	1.30085i
$902$	−240.275	−	219.782i	−0.266380	−	0.243661i
$903$	24.3184	+	24.3184i	0.0269307	+	0.0269307i
$904$	−331.149	−	570.083i	−0.366315	−	0.630623i
$905$	−221.428	−	221.428i	−0.244672	−	0.244672i
$906$	290.916	−	12.9584i	0.321099	−	0.0143028i
$907$	77.7483	+	187.701i	0.0857203	+	0.206947i	0.960927	−	0.276802i	$-0.0892746\pi$
$907$	77.7483	+	187.701i	0.0857203	+	0.206947i	−0.875207	+	0.483749i	$0.839275\pi$
$908$	−184.940	+	96.6880i	−0.203678	+	0.106485i
$909$	−92.5820	+	223.513i	−0.101850	+	0.245889i
$910$	−87.7764	+	41.0250i	−0.0964576	+	0.0450824i
$911$	300.365			0.329710			0.164855	−	0.986318i	$-0.447284\pi$
$911$	300.365			0.329710			0.164855	+	0.986318i	$0.447284\pi$
$912$	−330.524	−	229.705i	−0.362417	−	0.251869i
$913$		−	124.711i		−	0.136595i
$914$	−312.328	+	145.976i	−0.341716	+	0.159711i
$915$	−76.5287	−	31.6992i	−0.0836380	−	0.0346440i
$916$	162.656	−	519.065i	0.177572	−	0.566665i
$917$	−112.331	+	46.5292i	−0.122499	+	0.0507407i
$918$	−519.478	+	23.1393i	−0.565880	+	0.0252062i
$919$	−149.768	+	149.768i	−0.162968	+	0.162968i	−0.783880	−	0.620912i	$-0.786762\pi$
$919$	−149.768	+	149.768i	−0.162968	+	0.162968i	0.620912	+	0.783880i	$0.286762\pi$
$920$	−604.036	+	81.1470i	−0.656561	+	0.0882033i
$921$	16.5227	−	16.5227i	0.0179400	−	0.0179400i
$922$	−354.837	−	324.574i	−0.384856	−	0.352032i
$923$	2073.43	−	858.845i	2.24641	−	0.930493i
$924$	1.82320	+	20.4248i	0.00197316	+	0.0221048i
$925$	−115.693	−	47.9216i	−0.125073	−	0.0518071i
$926$	−90.8649	+	250.335i	−0.0981262	+	0.270340i
$927$			665.183i			0.717565i
$928$	−600.956	−	379.141i	−0.647582	−	0.408557i
$929$	1235.73			1.33017			0.665086	−	0.746767i	$-0.268395\pi$
$929$	1235.73			1.33017			0.665086	+	0.746767i	$0.268395\pi$
$930$	278.245	+	100.996i	0.299188	+	0.108597i
$931$	−593.793	+	1433.54i	−0.637801	+	1.53979i
$932$	0.250244	+	2.80342i	0.000268502	+	0.00300796i
$933$	−111.299	−	268.699i	−0.119291	−	0.287995i
$934$	−605.286	+	661.723i	−0.648058	+	0.708483i
$935$	−377.061	−	377.061i	−0.403274	−	0.403274i
$936$	678.970	−	889.709i	0.725396	−	0.950543i
$937$	955.999	+	955.999i	1.02028	+	1.02028i	0.999790	+	0.0204864i	$0.00652149\pi$
$937$	955.999	+	955.999i	1.02028	+	1.02028i	0.0204864	+	0.999790i	$0.493479\pi$
$938$	1.80756	+	40.5799i	0.00192704	+	0.0432621i
$939$	146.837	+	354.496i	0.156376	+	0.377525i
$940$	19.9346	−	63.6150i	0.0212070	−	0.0676756i
$941$	−337.224	+	814.132i	−0.358368	+	0.865177i	0.637162	+	0.770730i	$0.280108\pi$
$941$	−337.224	+	814.132i	−0.358368	+	0.865177i	−0.995530	+	0.0944471i	$0.969892\pi$
$942$	108.984	+	233.181i	0.115694	+	0.247538i
$943$	444.025			0.470864
$944$	397.330	+	618.861i	0.420900	+	0.655573i
$945$			39.5544i			0.0418565i
$946$	−357.608	−	765.132i	−0.378021	−	0.808808i
$947$	−1611.78	−	667.619i	−1.70198	−	0.704983i	−0.702007	−	0.712171i	$-0.747712\pi$
$947$	−1611.78	−	667.619i	−1.70198	−	0.704983i	−0.999974	+	0.00718706i	$0.997712\pi$
$948$	195.330	−	102.120i	0.206044	−	0.107722i
$949$	−809.151	+	335.161i	−0.852636	+	0.353173i
$950$	36.0189	+	808.626i	0.0379147	+	0.851185i
$951$	22.6865	−	22.6865i	0.0238554	−	0.0238554i
$952$	−32.2784	+	121.750i	−0.0339059	+	0.127889i
$953$	661.490	−	661.490i	0.694114	−	0.694114i	−0.269021	−	0.963134i	$-0.586700\pi$
$953$	661.490	−	661.490i	0.694114	−	0.694114i	0.963134	+	0.269021i	$0.0867000\pi$
$954$	752.355	−	822.505i	0.788633	−	0.862165i
$955$	581.807	−	240.992i	0.609222	−	0.252348i
$956$	246.295	+	205.927i	0.257630	+	0.215405i
$957$	127.508	+	52.8155i	0.133237	+	0.0551886i
$958$	−552.068	−	200.386i	−0.576272	−	0.209171i
$959$		−	163.243i		−	0.170222i
$960$	87.4556	−	153.343i	0.0910996	−	0.159733i
$961$	−1918.20			−1.99604
$962$	113.106	−	311.611i	0.117574	−	0.323920i
$963$	−49.1121	+	118.567i	−0.0509990	+	0.123123i
$964$	−25.5241	+	30.5274i	−0.0264772	+	0.0316674i
$965$	265.483	+	640.932i	0.275112	+	0.664179i
$966$	−20.6321	−	18.8724i	−0.0213582	−	0.0195366i
$967$	38.7070	+	38.7070i	0.0400279	+	0.0400279i	0.726837	−	0.686810i	$-0.240989\pi$
$967$	38.7070	+	38.7070i	0.0400279	+	0.0400279i	−0.686810	+	0.726837i	$0.740989\pi$
$968$	−119.014	+	448.909i	−0.122949	+	0.463749i
$969$	339.560	+	339.560i	0.350423	+	0.350423i
$970$	223.911	−	9.97375i	0.230836	−	0.0102822i
$971$	253.057	+	610.934i	0.260615	+	0.629180i	0.998977	−	0.0452246i	$-0.0144003\pi$
$971$	253.057	+	610.934i	0.260615	+	0.629180i	−0.738362	+	0.674405i	$0.764400\pi$
$972$	−321.263	−	614.496i	−0.330518	−	0.632197i
$973$	2.17021	−	5.23934i	0.00223043	−	0.00538473i
$974$	1200.13	−	560.919i	1.23217	−	0.575892i
$975$	164.703			0.168926
$976$	102.346	−	469.472i	0.104862	−	0.481017i
$977$			122.372i			0.125253i	0.998037	+	0.0626263i	$0.0199476\pi$
$977$			122.372i			0.125253i	−0.998037	+	0.0626263i	$0.980052\pi$
$978$	−280.590	+	131.142i	−0.286902	+	0.134092i
$979$	630.692	+	261.241i	0.644221	+	0.266845i
$980$	−649.383	−	203.493i	−0.662636	−	0.207646i
$981$	761.783	−	315.541i	0.776537	−	0.321652i
$982$	−628.842	+	28.0107i	−0.640368	+	0.0285242i
$983$	696.783	−	696.783i	0.708833	−	0.708833i	−0.257457	−	0.966290i	$-0.582884\pi$
$983$	696.783	−	696.783i	0.708833	−	0.708833i	0.966290	+	0.257457i	$0.0828845\pi$
$984$	−78.0234	+	102.240i	−0.0792921	+	0.103903i
$985$	−405.572	+	405.572i	−0.411748	+	0.411748i
$986$	625.521	+	572.172i	0.634403	+	0.580296i
$987$	2.82573	−	1.17045i	0.00286294	−	0.00118587i
$988$	−2134.28	+	190.514i	−2.16020	+	0.192828i
$989$	1063.98	+	440.716i	1.07582	+	0.445618i
$990$	159.862	−	440.425i	0.161477	−	0.444874i
$991$			536.777i			0.541652i	0.962628	+	0.270826i	$0.0872968\pi$
$991$			536.777i			0.541652i	−0.962628	+	0.270826i	$0.912703\pi$
$992$	−290.715	+	1692.27i	−0.293060	+	1.70592i
$993$	253.533			0.255321
$994$	−208.611	−	75.7203i	−0.209870	−	0.0761773i
$995$	−42.6521	+	102.971i	−0.0428664	+	0.103489i
$996$	−49.0605	+	4.37933i	−0.0492575	+	0.00439691i
$997$	250.176	+	603.979i	0.250929	+	0.605796i	0.998280	−	0.0586337i	$-0.0186744\pi$
$997$	250.176	+	603.979i	0.250929	+	0.605796i	−0.747351	+	0.664430i	$0.768674\pi$
$998$	836.665	−	914.676i	0.838342	−	0.916509i
$999$	−95.6945	−	95.6945i	−0.0957903	−	0.0957903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.3.h.a.3.5	✓	28
3.2	odd	2		288.3.u.a.163.3		28
4.3	odd	2		128.3.h.a.47.4		28
8.3	odd	2		256.3.h.a.95.4		28
8.5	even	2		256.3.h.b.95.4		28
32.5	even	8		256.3.h.a.159.4		28
32.11	odd	8	inner	32.3.h.a.11.5	yes	28
32.21	even	8		128.3.h.a.79.4		28
32.27	odd	8		256.3.h.b.159.4		28
96.11	even	8		288.3.u.a.235.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.5	✓	28	1.1	even	1	trivial
32.3.h.a.11.5	yes	28	32.11	odd	8	inner
128.3.h.a.47.4		28	4.3	odd	2
128.3.h.a.79.4		28	32.21	even	8
256.3.h.a.95.4		28	8.3	odd	2
256.3.h.a.159.4		28	32.5	even	8
256.3.h.b.95.4		28	8.5	even	2
256.3.h.b.159.4		28	32.27	odd	8
288.3.u.a.163.3		28	3.2	odd	2
288.3.u.a.235.3		28	96.11	even	8

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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	32.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.682385 - 1.87999i) q^{2} +(0.299792 - 0.723762i) q^{3} +(-3.06870 - 2.56575i) q^{4} +(1.34740 + 3.25291i) q^{5} +(-1.15609 - 1.05749i) q^{6} +(0.583225 + 0.583225i) q^{7} +(-6.91761 + 4.01829i) q^{8} +(5.93000 + 5.93000i) q^{9} +O(q^{10})\)	\(q+(0.682385 - 1.87999i) q^{2} +(0.299792 - 0.723762i) q^{3} +(-3.06870 - 2.56575i) q^{4} +(1.34740 + 3.25291i) q^{5} +(-1.15609 - 1.05749i) q^{6} +(0.583225 + 0.583225i) q^{7} +(-6.91761 + 4.01829i) q^{8} +(5.93000 + 5.93000i) q^{9} +(7.03487 - 0.313357i) q^{10} +(-3.03620 - 7.33003i) q^{11} +(-2.77696 + 1.45182i) q^{12} +(-6.38385 + 15.4120i) q^{13} +(1.49444 - 0.698471i) q^{14} +2.75827 q^{15} +(2.83386 + 15.7470i) q^{16} -19.0889i q^{17} +(15.1949 - 7.10179i) q^{18} +(-29.6679 - 12.2888i) q^{19} +(4.21138 - 13.4393i) q^{20} +(0.596962 - 0.247270i) q^{21} +(-15.8522 + 0.706111i) q^{22} +(15.2998 - 15.2998i) q^{23} +(0.834442 + 6.21136i) q^{24} +(8.91173 - 8.91173i) q^{25} +(24.6181 + 22.5185i) q^{26} +(12.5835 - 5.21227i) q^{27} +(-0.293334 - 3.28615i) q^{28} +(-20.5148 - 8.49749i) q^{29} +(1.88220 - 5.18552i) q^{30} +53.6582i q^{31} +(31.5380 + 5.41792i) q^{32} -6.21542 q^{33} +(-35.8868 - 13.0260i) q^{34} +(-1.11134 + 2.68301i) q^{35} +(-2.98251 - 33.4123i) q^{36} +(-3.80237 - 9.17973i) q^{37} +(-43.3477 + 47.3895i) q^{38} +(9.24078 + 9.24078i) q^{39} +(-22.3919 - 17.0881i) q^{40} +(14.5108 + 14.5108i) q^{41} +(-0.0575061 - 1.29101i) q^{42} +(20.3685 + 49.1739i) q^{43} +(-9.48983 + 30.2838i) q^{44} +(-11.2997 + 27.2799i) q^{45} +(-18.3230 - 39.2037i) q^{46} +4.73351 q^{47} +(12.2467 + 2.66980i) q^{48} -48.3197i q^{49} +(-10.6727 - 22.8352i) q^{50} +(-13.8158 - 5.72269i) q^{51} +(59.1334 - 30.9154i) q^{52} +(61.4006 - 25.4330i) q^{53} +(-1.21219 - 27.2137i) q^{54} +(19.7530 - 19.7530i) q^{55} +(-6.37809 - 1.69095i) q^{56} +(-17.7884 + 17.7884i) q^{57} +(-29.9741 + 32.7689i) q^{58} +(42.4656 - 17.5898i) q^{59} +(-8.46431 - 7.07703i) q^{60} +(-27.7452 - 11.4924i) q^{61} +(100.877 + 36.6155i) q^{62} +6.91705i q^{63} +(31.7067 - 55.5939i) q^{64} -58.7354 q^{65} +(-4.24131 + 11.6849i) q^{66} +(-9.42323 + 22.7497i) q^{67} +(-48.9772 + 58.5780i) q^{68} +(-6.48665 - 15.6602i) q^{69} +(4.28567 + 3.92015i) q^{70} +(-95.1299 - 95.1299i) q^{71} +(-64.8499 - 17.1930i) q^{72} +(37.1241 + 37.1241i) q^{73} +(-19.8524 + 0.884295i) q^{74} +(-3.77831 - 9.12164i) q^{75} +(59.5118 + 113.831i) q^{76} +(2.50427 - 6.04584i) q^{77} +(23.6783 - 11.0668i) q^{78} -70.3394 q^{79} +(-47.4053 + 30.4358i) q^{80} +64.8066i q^{81} +(37.1821 - 17.3782i) q^{82} +(14.5221 + 6.01526i) q^{83} +(-2.46633 - 0.772858i) q^{84} +(62.0944 - 25.7203i) q^{85} +(106.345 - 4.73698i) q^{86} +(-12.3003 + 12.3003i) q^{87} +(50.4574 + 38.5060i) q^{88} +(-60.8411 + 60.8411i) q^{89} +(43.5750 + 39.8586i) q^{90} +(-12.7119 + 5.26543i) q^{91} +(-86.2059 + 7.69507i) q^{92} +(38.8357 + 16.0863i) q^{93} +(3.23007 - 8.89893i) q^{94} -113.065i q^{95} +(13.3761 - 21.2018i) q^{96} +31.8287 q^{97} +(-90.8404 - 32.9726i) q^{98} +(25.4624 - 61.4718i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 44 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 20 q^{14} - 8 q^{15} + 16 q^{16} + 56 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 144 q^{22} - 68 q^{23} + 208 q^{24} - 4 q^{25} + 96 q^{26} - 100 q^{27} + 56 q^{28} - 4 q^{29} + 20 q^{30} - 24 q^{32} - 8 q^{33} - 48 q^{34} + 92 q^{35} - 336 q^{36} - 4 q^{37} - 396 q^{38} + 188 q^{39} - 408 q^{40} - 4 q^{41} - 424 q^{42} + 92 q^{43} - 188 q^{44} - 40 q^{45} - 36 q^{46} - 8 q^{47} + 48 q^{48} + 308 q^{50} + 224 q^{51} + 420 q^{52} - 164 q^{53} + 592 q^{54} + 252 q^{55} + 552 q^{56} - 4 q^{57} + 528 q^{58} + 124 q^{59} + 440 q^{60} - 68 q^{61} + 216 q^{62} - 232 q^{64} - 8 q^{65} - 580 q^{66} - 164 q^{67} - 368 q^{68} + 188 q^{69} - 664 q^{70} - 260 q^{71} - 748 q^{72} - 4 q^{73} - 532 q^{74} - 488 q^{75} - 516 q^{76} + 220 q^{77} - 236 q^{78} - 520 q^{79} + 312 q^{80} + 636 q^{82} - 484 q^{83} + 992 q^{84} + 96 q^{85} + 688 q^{86} - 452 q^{87} + 672 q^{88} - 4 q^{89} + 872 q^{90} - 196 q^{91} + 616 q^{92} + 32 q^{93} + 40 q^{94} - 128 q^{96} - 8 q^{97} - 328 q^{98} + 216 q^{99}+O(q^{100}) \) 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 44 * q^10 - 4 * q^11 - 52 * q^12 - 4 * q^13 - 20 * q^14 - 8 * q^15 + 16 * q^16 + 56 * q^18 - 4 * q^19 + 76 * q^20 - 4 * q^21 + 144 * q^22 - 68 * q^23 + 208 * q^24 - 4 * q^25 + 96 * q^26 - 100 * q^27 + 56 * q^28 - 4 * q^29 + 20 * q^30 - 24 * q^32 - 8 * q^33 - 48 * q^34 + 92 * q^35 - 336 * q^36 - 4 * q^37 - 396 * q^38 + 188 * q^39 - 408 * q^40 - 4 * q^41 - 424 * q^42 + 92 * q^43 - 188 * q^44 - 40 * q^45 - 36 * q^46 - 8 * q^47 + 48 * q^48 + 308 * q^50 + 224 * q^51 + 420 * q^52 - 164 * q^53 + 592 * q^54 + 252 * q^55 + 552 * q^56 - 4 * q^57 + 528 * q^58 + 124 * q^59 + 440 * q^60 - 68 * q^61 + 216 * q^62 - 232 * q^64 - 8 * q^65 - 580 * q^66 - 164 * q^67 - 368 * q^68 + 188 * q^69 - 664 * q^70 - 260 * q^71 - 748 * q^72 - 4 * q^73 - 532 * q^74 - 488 * q^75 - 516 * q^76 + 220 * q^77 - 236 * q^78 - 520 * q^79 + 312 * q^80 + 636 * q^82 - 484 * q^83 + 992 * q^84 + 96 * q^85 + 688 * q^86 - 452 * q^87 + 672 * q^88 - 4 * q^89 + 872 * q^90 - 196 * q^91 + 616 * q^92 + 32 * q^93 + 40 * q^94 - 128 * q^96 - 8 * q^97 - 328 * q^98 + 216 * q^99

Introduction

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