LMFDB - Embedded newform 483.2.r.a.34.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(34,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

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

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

chi := DirichletCharacter("483.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.r (of order $22$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			34.4
Character	$\chi$	$=$	483.34
Dual form			483.2.r.a.412.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.07156 + 1.33131i) q^{2} +(0.989821 + 0.142315i) q^{3} +(1.68815 - 3.69653i) q^{4} +(-3.92324 + 1.15197i) q^{5} +(-2.23994 + 1.02295i) q^{6} +(-2.13872 - 1.55752i) q^{7} +(0.723239 + 5.03024i) q^{8} +(0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(-2.07156 + 1.33131i) q^{2} +(0.989821 + 0.142315i) q^{3} +(1.68815 - 3.69653i) q^{4} +(-3.92324 + 1.15197i) q^{5} +(-2.23994 + 1.02295i) q^{6} +(-2.13872 - 1.55752i) q^{7} +(0.723239 + 5.03024i) q^{8} +(0.959493 + 0.281733i) q^{9} +(6.59362 - 7.60944i) q^{10} +(1.89212 - 2.94419i) q^{11} +(2.19704 - 3.41866i) q^{12} +(-0.793257 - 0.687361i) q^{13} +(6.50404 + 0.379186i) q^{14} +(-4.04725 + 0.581907i) q^{15} +(-2.87265 - 3.31522i) q^{16} +(2.66454 + 5.83452i) q^{17} +(-2.36272 + 0.693758i) q^{18} +(-0.346361 + 0.758424i) q^{19} +(-2.36473 + 16.4471i) q^{20} +(-1.89530 - 1.84604i) q^{21} +8.61807i q^{22} +(4.30464 + 2.11425i) q^{23} +5.08197i q^{24} +(9.85854 - 6.33570i) q^{25} +(2.55837 + 0.367839i) q^{26} +(0.909632 + 0.415415i) q^{27} +(-9.36790 + 5.27654i) q^{28} +(-2.92092 - 6.39592i) q^{29} +(7.60944 - 6.59362i) q^{30} +(8.75171 - 1.25831i) q^{31} +(0.612256 + 0.179774i) q^{32} +(2.29186 - 2.64495i) q^{33} +(-13.2873 - 8.53925i) q^{34} +(10.1849 + 3.64678i) q^{35} +(2.66120 - 3.07119i) q^{36} +(-0.804448 + 2.73970i) q^{37} +(-0.292192 - 2.03224i) q^{38} +(-0.687361 - 0.793257i) q^{39} +(-8.63212 - 18.9017i) q^{40} +(1.15572 + 3.93602i) q^{41} +(6.38388 + 1.30095i) q^{42} +(9.48236 + 1.36336i) q^{43} +(-7.68912 - 11.9645i) q^{44} -4.08887 q^{45} +(-11.7321 + 1.35101i) q^{46} -7.61974i q^{47} +(-2.37161 - 3.69030i) q^{48} +(2.14828 + 6.66220i) q^{49} +(-11.9878 + 26.2496i) q^{50} +(1.80708 + 6.15434i) q^{51} +(-3.87999 + 1.77193i) q^{52} +(-0.894616 + 0.775190i) q^{53} +(-2.43741 + 0.350446i) q^{54} +(-4.03162 + 13.7304i) q^{55} +(6.28788 - 11.8847i) q^{56} +(-0.450770 + 0.701412i) q^{57} +(14.5658 + 9.36089i) q^{58} +(-6.11750 - 5.30085i) q^{59} +(-4.68133 + 15.9431i) q^{60} +(0.390573 + 2.71650i) q^{61} +(-16.4545 + 14.2579i) q^{62} +(-1.61329 - 2.09698i) q^{63} +(6.91028 - 2.02904i) q^{64} +(3.90396 + 1.78288i) q^{65} +(-1.22648 + 8.53035i) q^{66} +(3.02175 + 4.70194i) q^{67} +26.0656 q^{68} +(3.95994 + 2.70535i) q^{69} +(-25.9538 + 6.00481i) q^{70} +(11.9080 - 7.65284i) q^{71} +(-0.723239 + 5.03024i) q^{72} +(-2.76674 - 1.26353i) q^{73} +(-1.98093 - 6.74643i) q^{74} +(10.6599 - 4.86820i) q^{75} +(2.21883 + 2.56067i) q^{76} +(-8.63234 + 3.34980i) q^{77} +(2.47998 + 0.728189i) q^{78} +(-2.98192 - 2.58385i) q^{79} +(15.0891 + 9.69721i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-7.63422 - 6.61509i) q^{82} +(3.67625 + 1.07944i) q^{83} +(-10.0235 + 3.88964i) q^{84} +(-17.1748 - 19.8208i) q^{85} +(-21.4584 + 9.79971i) q^{86} +(-1.98095 - 6.74651i) q^{87} +(16.1784 + 7.38844i) q^{88} +(-0.689807 + 4.79771i) q^{89} +(8.47035 - 5.44357i) q^{90} +(0.625980 + 2.70559i) q^{91} +(15.0823 - 12.3431i) q^{92} +8.84170 q^{93} +(10.1443 + 15.7848i) q^{94} +(0.485177 - 3.37448i) q^{95} +(0.580439 + 0.265078i) q^{96} +(3.41254 - 1.00201i) q^{97} +(-13.3198 - 10.9411i) q^{98} +(2.64495 - 2.29186i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−2.07156	+	1.33131i	−1.46482	+	0.941380i	−0.466432	+	0.884557i	$0.654461\pi$
$2$	−2.07156	+	1.33131i	−1.46482	+	0.941380i	−0.998384	+	0.0568231i	$0.981903\pi$
$3$	0.989821	+	0.142315i	0.571474	+	0.0821655i
$3$	0.989821	+	0.142315i	0.571474	+	0.0821655i
$4$	1.68815	−	3.69653i	0.844075	−	1.84827i
$5$	−3.92324	+	1.15197i	−1.75453	+	0.515176i	−0.991377	−	0.131044i	$-0.958167\pi$
$5$	−3.92324	+	1.15197i	−1.75453	+	0.515176i	−0.763151	+	0.646220i	$0.776349\pi$
$6$	−2.23994	+	1.02295i	−0.914453	+	0.417617i
$7$	−2.13872	−	1.55752i	−0.808362	−	0.588686i
$7$	−2.13872	−	1.55752i	−0.808362	−	0.588686i
$8$	0.723239	+	5.03024i	0.255704	+	1.77846i
$9$	0.959493	+	0.281733i	0.319831	+	0.0939109i
$10$	6.59362	−	7.60944i	2.08508	−	2.40632i
$11$	1.89212	−	2.94419i	0.570494	−	0.887707i	−0.429387	−	0.903121i	$-0.641270\pi$
$11$	1.89212	−	2.94419i	0.570494	−	0.887707i	0.999881	+	0.0154141i	$0.00490665\pi$
$12$	2.19704	−	3.41866i	0.634230	−	0.986881i
$13$	−0.793257	−	0.687361i	−0.220010	−	0.190640i	0.537881	−	0.843021i	$-0.319225\pi$
$13$	−0.793257	−	0.687361i	−0.220010	−	0.190640i	−0.757891	+	0.652381i	$0.773770\pi$
$14$	6.50404	+	0.379186i	1.73828	+	0.101342i
$15$	−4.04725	+	0.581907i	−1.04500	+	0.150248i
$16$	−2.87265	−	3.31522i	−0.718163	−	0.828805i
$17$	2.66454	+	5.83452i	0.646245	+	1.41508i	0.894803	+	0.446462i	$0.147316\pi$
$17$	2.66454	+	5.83452i	0.646245	+	1.41508i	−0.248558	+	0.968617i	$0.579957\pi$
$18$	−2.36272	+	0.693758i	−0.556899	+	0.163520i
$19$	−0.346361	+	0.758424i	−0.0794606	+	0.173994i	−0.945193	−	0.326514i	$-0.894126\pi$
$19$	−0.346361	+	0.758424i	−0.0794606	+	0.173994i	0.865732	+	0.500508i	$0.166853\pi$
$20$	−2.36473	+	16.4471i	−0.528771	+	3.67768i
$21$	−1.89530	−	1.84604i	−0.413588	−	0.402838i
$22$			8.61807i			1.83738i
$23$	4.30464	+	2.11425i	0.897580	+	0.440853i
$23$	4.30464	+	2.11425i	0.897580	+	0.440853i
$24$			5.08197i			1.03735i
$25$	9.85854	−	6.33570i	1.97171	−	1.26714i
$26$	2.55837	+	0.367839i	0.501738	+	0.0721391i
$27$	0.909632	+	0.415415i	0.175059	+	0.0799467i
$28$	−9.36790	+	5.27654i	−1.77037	+	0.997172i
$29$	−2.92092	−	6.39592i	−0.542401	−	1.18769i	−0.960241	−	0.279172i	$-0.909940\pi$
$29$	−2.92092	−	6.39592i	−0.542401	−	1.18769i	0.417841	−	0.908520i	$-0.362787\pi$
$30$	7.60944	−	6.59362i	1.38929	−	1.20382i
$31$	8.75171	−	1.25831i	1.57185	−	0.225998i	0.699412	−	0.714718i	$-0.253445\pi$
$31$	8.75171	−	1.25831i	1.57185	−	0.225998i	0.872441	+	0.488720i	$0.162536\pi$
$32$	0.612256	+	0.179774i	0.108233	+	0.0317799i
$33$	2.29186	−	2.64495i	0.398961	−	0.460426i
$34$	−13.2873	−	8.53925i	−2.27876	−	1.46447i
$35$	10.1849	+	3.64678i	1.72157	+	0.616418i
$36$	2.66120	−	3.07119i	0.443533	−	0.511865i
$37$	−0.804448	+	2.73970i	−0.132251	+	0.450404i	−0.998815	−	0.0486606i	$-0.984505\pi$
$37$	−0.804448	+	2.73970i	−0.132251	+	0.450404i	0.866565	+	0.499064i	$0.166323\pi$
$38$	−0.292192	−	2.03224i	−0.0473998	−	0.329673i
$39$	−0.687361	−	0.793257i	−0.110066	−	0.127023i
$40$	−8.63212	−	18.9017i	−1.36486	−	2.98862i
$41$	1.15572	+	3.93602i	0.180493	+	0.614703i	0.999181	+	0.0404645i	$0.0128838\pi$
$41$	1.15572	+	3.93602i	0.180493	+	0.614703i	−0.818688	+	0.574239i	$0.805298\pi$
$42$	6.38388	+	1.30095i	0.985054	+	0.200741i
$43$	9.48236	+	1.36336i	1.44605	+	0.207910i	0.820218	−	0.572050i	$-0.193852\pi$
$43$	9.48236	+	1.36336i	1.44605	+	0.207910i	0.625829	+	0.779961i	$0.284761\pi$
$44$	−7.68912	−	11.9645i	−1.15918	−	1.80372i
$45$	−4.08887			−0.609533
$46$	−11.7321	+	1.35101i	−1.72980	+	0.199196i
$47$		−	7.61974i		−	1.11145i	−0.831365	−	0.555727i	$-0.812440\pi$
$47$		−	7.61974i		−	1.11145i	0.831365	−	0.555727i	$-0.187560\pi$
$48$	−2.37161	−	3.69030i	−0.342312	−	0.532648i
$49$	2.14828	+	6.66220i	0.306897	+	0.951743i
$50$	−11.9878	+	26.2496i	−1.69533	+	3.71225i
$51$	1.80708	+	6.15434i	0.253041	+	0.861779i
$52$	−3.87999	+	1.77193i	−0.538057	+	0.245723i
$53$	−0.894616	+	0.775190i	−0.122885	+	0.106480i	−0.714135	−	0.700008i	$-0.753180\pi$
$53$	−0.894616	+	0.775190i	−0.122885	+	0.106480i	0.591250	+	0.806488i	$0.298634\pi$
$54$	−2.43741	+	0.350446i	−0.331689	+	0.0476897i
$55$	−4.03162	+	13.7304i	−0.543623	+	1.85141i
$56$	6.28788	−	11.8847i	0.840253	−	1.58817i
$57$	−0.450770	+	0.701412i	−0.0597060	+	0.0929043i
$58$	14.5658	+	9.36089i	1.91259	+	1.22915i
$59$	−6.11750	−	5.30085i	−0.796431	−	0.690111i	0.158363	−	0.987381i	$-0.449379\pi$
$59$	−6.11750	−	5.30085i	−0.796431	−	0.690111i	−0.954794	+	0.297270i	$0.903924\pi$
$60$	−4.68133	+	15.9431i	−0.604357	+	2.05825i
$61$	0.390573	+	2.71650i	0.0500078	+	0.347812i	0.999428	+	0.0338048i	$0.0107625\pi$
$61$	0.390573	+	2.71650i	0.0500078	+	0.347812i	−0.949421	+	0.314007i	$0.898328\pi$
$62$	−16.4545	+	14.2579i	−2.08973	+	1.81076i
$63$	−1.61329	−	2.09698i	−0.203255	−	0.264194i
$64$	6.91028	−	2.02904i	0.863786	−	0.253630i
$65$	3.90396	+	1.78288i	0.484226	+	0.221139i
$66$	−1.22648	+	8.53035i	−0.150969	+	1.05001i
$67$	3.02175	+	4.70194i	0.369166	+	0.574433i	0.975288	−	0.220939i	$-0.0709121\pi$
$67$	3.02175	+	4.70194i	0.369166	+	0.574433i	−0.606122	+	0.795372i	$0.707276\pi$
$68$	26.0656			3.16092
$69$	3.95994	+	2.70535i	0.476720	+	0.325686i
$70$	−25.9538	+	6.00481i	−3.10207	+	0.717712i
$71$	11.9080	−	7.65284i	1.41322	−	0.908225i	0.413228	−	0.910628i	$-0.364401\pi$
$71$	11.9080	−	7.65284i	1.41322	−	0.908225i	0.999997	+	0.00240311i	$0.000764933\pi$
$72$	−0.723239	+	5.03024i	−0.0852346	+	0.592819i
$73$	−2.76674	−	1.26353i	−0.323822	−	0.147885i	0.246870	−	0.969049i	$-0.420598\pi$
$73$	−2.76674	−	1.26353i	−0.323822	−	0.147885i	−0.570692	+	0.821164i	$0.693325\pi$
$74$	−1.98093	−	6.74643i	−0.230279	−	0.784257i
$75$	10.6599	−	4.86820i	1.23089	−	0.562131i
$76$	2.21883	+	2.56067i	0.254517	+	0.293729i
$77$	−8.63234	+	3.34980i	−0.983747	+	0.381746i
$78$	2.47998	+	0.728189i	0.280803	+	0.0824512i
$79$	−2.98192	−	2.58385i	−0.335492	−	0.290705i	0.470780	−	0.882251i	$-0.343973\pi$
$79$	−2.98192	−	2.58385i	−0.335492	−	0.290705i	−0.806272	+	0.591545i	$0.798518\pi$
$80$	15.0891	+	9.69721i	1.68702	+	1.08418i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−7.63422	−	6.61509i	−0.843059	−	0.730515i
$83$	3.67625	+	1.07944i	0.403521	+	0.118484i	0.477194	−	0.878798i	$-0.341654\pi$
$83$	3.67625	+	1.07944i	0.403521	+	0.118484i	−0.0736732	+	0.997282i	$0.523472\pi$
$84$	−10.0235	+	3.88964i	−1.09365	+	0.424394i
$85$	−17.1748	−	19.8208i	−1.86287	−	2.14987i
$86$	−21.4584	+	9.79971i	−2.31392	+	1.05673i
$87$	−1.98095	−	6.74651i	−0.212380	−	0.723301i
$88$	16.1784	+	7.38844i	1.72463	+	0.787610i
$89$	−0.689807	+	4.79771i	−0.0731194	+	0.508556i	0.920043	+	0.391817i	$0.128153\pi$
$89$	−0.689807	+	4.79771i	−0.0731194	+	0.508556i	−0.993163	+	0.116739i	$0.962756\pi$
$90$	8.47035	−	5.44357i	0.892854	−	0.573802i
$91$	0.625980	+	2.70559i	0.0656206	+	0.283623i
$92$	15.0823	−	12.3431i	1.57244	−	1.28685i
$93$	8.84170			0.916842
$94$	10.1443	+	15.7848i	1.04630	+	1.62808i
$95$	0.485177	−	3.37448i	0.0497781	−	0.346214i
$96$	0.580439	+	0.265078i	0.0592408	+	0.0270544i
$97$	3.41254	−	1.00201i	0.346491	−	0.101739i	−0.103857	−	0.994592i	$-0.533118\pi$
$97$	3.41254	−	1.00201i	0.346491	−	0.101739i	0.450347	+	0.892853i	$0.351300\pi$
$98$	−13.3198	−	10.9411i	−1.34550	−	1.10522i
$99$	2.64495	−	2.29186i	0.265827	−	0.230340i
$100$	−6.77742	−	47.1380i	−0.677742	−	4.71380i
$101$	1.65387	−	5.63255i	0.164566	−	0.560460i	−0.835376	−	0.549679i	$-0.814750\pi$
$101$	1.65387	−	5.63255i	0.164566	−	0.560460i	0.999942	−	0.0107808i	$-0.00343170\pi$
$102$	−11.9368	−	10.3433i	−1.18192	−	1.02414i
$103$	0.245688	+	0.157894i	0.0242083	+	0.0155577i	0.552689	−	0.833388i	$-0.313602\pi$
$103$	0.245688	+	0.157894i	0.0242083	+	0.0155577i	−0.528481	+	0.848945i	$0.677238\pi$
$104$	2.88388	−	4.48740i	0.282787	−	0.440025i
$105$	9.56229	+	5.05913i	0.933184	+	0.493720i
$106$	0.821235	−	2.79687i	0.0797654	−	0.271656i
$107$	−0.843377	+	0.121259i	−0.0815323	+	0.0117226i	−0.182960	−	0.983120i	$-0.558568\pi$
$107$	−0.843377	+	0.121259i	−0.0815323	+	0.0117226i	0.101428	+	0.994843i	$0.467659\pi$
$108$	3.07119	−	2.66120i	0.295525	−	0.256074i
$109$	6.76924	−	3.09141i	0.648376	−	0.296103i	−0.0639491	−	0.997953i	$-0.520370\pi$
$109$	6.76924	−	3.09141i	0.648376	−	0.296103i	0.712325	+	0.701850i	$0.247642\pi$
$110$	−9.92775	−	33.8108i	−0.946573	−	3.22373i
$111$	−1.18616	+	2.59733i	−0.112585	+	0.246528i
$112$	0.980300	+	11.5645i	0.0926296	+	1.09275i
$113$	8.07463	+	12.5644i	0.759597	+	1.18196i	0.978507	+	0.206211i	$0.0661135\pi$
$113$	8.07463	+	12.5644i	0.759597	+	1.18196i	−0.218910	+	0.975745i	$0.570250\pi$
$114$		−	2.05314i		−	0.192294i
$115$	−19.3237	−	3.33593i	−1.80194	−	0.311077i
$116$	−28.5737			−2.65300
$117$	−0.567472	−	0.883004i	−0.0524628	−	0.0816338i
$118$	19.7299	+	2.83673i	1.81628	+	0.261142i
$119$	3.38866	−	16.6285i	0.310638	−	1.52433i
$120$	−5.85426	−	19.9378i	−0.534419	−	1.82006i
$121$	−0.518586	−	1.13554i	−0.0471442	−	0.103231i
$122$	−4.42560	−	5.10742i	−0.400675	−	0.462404i
$123$	0.583803	+	4.06044i	0.0526397	+	0.366117i
$124$	10.1228	−	34.4752i	0.909056	−	3.09596i
$125$	−17.9907	+	20.7624i	−1.60914	+	1.85705i
$126$	6.13375	+	2.19623i	0.546438	+	0.195655i
$127$	−4.91575	−	3.15916i	−0.436202	−	0.280330i	0.304054	−	0.952655i	$-0.401660\pi$
$127$	−4.91575	−	3.15916i	−0.436202	−	0.280330i	−0.740257	+	0.672324i	$0.765296\pi$
$128$	−12.4495	+	14.3675i	−1.10039	+	1.26992i
$129$	9.19182	+	2.69896i	0.809295	+	0.237630i
$130$	−10.4609	+	1.50404i	−0.917478	+	0.131913i
$131$	12.9354	−	11.2086i	1.13017	−	0.979298i	0.130245	−	0.991482i	$-0.458424\pi$
$131$	12.9354	−	11.2086i	1.13017	−	0.979298i	0.999926	+	0.0121838i	$0.00387832\pi$
$132$	−5.90813	−	12.9370i	−0.514236	−	1.12602i
$133$	1.92203	−	1.08260i	0.166661	−	0.0938731i
$134$	−12.5195	−	5.71746i	−1.08152	−	0.493913i
$135$	−4.04725	−	0.581907i	−0.348332	−	0.0500826i
$136$	−27.4219	+	17.6230i	−2.35141	+	1.51116i
$137$		−	14.9660i		−	1.27863i	−0.768945	−	0.639315i	$-0.779218\pi$
$137$		−	14.9660i		−	1.27863i	0.768945	−	0.639315i	$-0.220782\pi$
$138$	−11.8049	−	0.332387i	−1.00490	−	0.0282947i
$139$		−	15.7945i		−	1.33967i	−0.742511	−	0.669834i	$-0.766365\pi$
$139$		−	15.7945i		−	1.33967i	0.742511	−	0.669834i	$-0.233635\pi$
$140$	30.6741	−	31.4927i	2.59244	−	2.66162i
$141$	1.08440	−	7.54218i	0.0913232	−	0.635166i
$142$	−14.4799	+	31.7067i	−1.21513	+	2.66076i
$143$	−3.52465	+	1.03493i	−0.294746	+	0.0865454i
$144$	−1.82229	−	3.99025i	−0.151857	−	0.332521i
$145$	18.8274	+	21.7279i	1.56353	+	1.80441i
$146$	7.41362	−	1.06592i	0.613555	−	0.0882159i
$147$	1.17828	+	6.90012i	0.0971830	+	0.569112i
$148$	8.76936	+	7.59869i	0.720837	+	0.624609i
$149$	3.58782	−	5.58275i	0.293925	−	0.457357i	−0.662614	−	0.748961i	$-0.730553\pi$
$149$	3.58782	−	5.58275i	0.293925	−	0.457357i	0.956539	+	0.291605i	$0.0941892\pi$
$150$	−15.6015	+	24.2764i	−1.27386	+	1.98216i
$151$	−8.73356	+	10.0791i	−0.710727	+	0.820223i	−0.990160	−	0.139943i	$-0.955308\pi$
$151$	−8.73356	+	10.0791i	−0.710727	+	0.820223i	0.279433	+	0.960165i	$0.409854\pi$
$152$	−4.06556	−	1.19376i	−0.329760	−	0.0968263i
$153$	0.912829	+	6.34887i	0.0737979	+	0.513276i
$154$	13.4228	−	18.4317i	1.08164	−	1.48527i
$155$	−32.8855	+	15.0183i	−2.64143	+	1.20630i
$156$	−4.09267	+	1.20172i	−0.327676	+	0.0962142i
$157$	0.0986331	−	0.215976i	0.00787177	−	0.0172368i	−0.905655	−	0.424015i	$-0.860620\pi$
$157$	0.0986331	−	0.215976i	0.00787177	−	0.0172368i	0.913527	+	0.406778i	$0.133348\pi$
$158$	9.61714	+	1.38274i	0.765098	+	0.110005i
$159$	−0.995831	+	0.639982i	−0.0789746	+	0.0507539i
$160$	−2.60912			−0.206269
$161$	−5.91345	−	11.2264i	−0.466045	−	0.884761i
$162$	−2.46247			−0.193470
$163$	−3.22195	+	2.07062i	−0.252363	+	0.162184i	−0.660706	−	0.750645i	$-0.729743\pi$
$163$	−3.22195	+	2.07062i	−0.252363	+	0.162184i	0.408343	+	0.912828i	$0.366107\pi$
$164$	16.5007	+	2.37244i	1.28849	+	0.185256i
$165$	−5.94463	+	13.0169i	−0.462789	+	1.01337i
$166$	−9.05266	+	2.65810i	−0.702622	+	0.206309i
$167$	20.4575	−	9.34262i	1.58305	−	0.722954i	0.586819	−	0.809718i	$-0.300380\pi$
$167$	20.4575	−	9.34262i	1.58305	−	0.722954i	0.996229	+	0.0867648i	$0.0276529\pi$
$168$	7.91525	−	10.8689i	0.610675	−	0.838555i
$169$	−1.69330	−	11.7772i	−0.130254	−	0.905936i
$170$	61.9664	+	18.1950i	4.75260	+	1.39549i
$171$	−0.546004	+	0.630122i	−0.0417539	+	0.0481866i
$172$	21.0473	−	32.7503i	1.60485	−	2.49719i
$173$	3.31704	−	5.16142i	0.252190	−	0.392415i	−0.691958	−	0.721938i	$-0.743251\pi$
$173$	3.31704	−	5.16142i	0.252190	−	0.392415i	0.944148	+	0.329523i	$0.106888\pi$
$174$	13.0854	+	11.3385i	0.992000	+	0.859573i
$175$	−30.9527	−	1.80454i	−2.33980	−	0.136411i
$176$	−15.1960	+	2.18486i	−1.14544	+	0.164690i
$177$	−5.30085	−	6.11750i	−0.398436	−	0.459820i
$178$	−4.95828	−	10.8571i	−0.371638	−	0.813775i
$179$	0.260510	−	0.0764925i	0.0194714	−	0.00571732i	−0.271982	−	0.962302i	$-0.587679\pi$
$179$	0.260510	−	0.0764925i	0.0194714	−	0.00571732i	0.291454	+	0.956585i	$0.405861\pi$
$180$	−6.90263	+	15.1146i	−0.514491	+	1.12658i
$181$	1.12148	−	7.80008i	0.0833591	−	0.579775i	−0.904741	−	0.425962i	$-0.859936\pi$
$181$	1.12148	−	7.80008i	0.0833591	−	0.579775i	0.988100	−	0.153813i	$-0.0491553\pi$
$182$	−4.89874	−	4.77142i	−0.363119	−	0.353681i
$183$			2.74443i			0.202874i
$184$	−7.52192	+	23.1825i	−0.554523	+	1.70904i
$185$		−	11.6752i		−	0.858378i
$186$	−18.3161	+	11.7711i	−1.34300	+	0.863097i
$187$	22.2195	+	3.19469i	1.62485	+	0.233619i
$188$	−28.1666	−	12.8633i	−2.05426	−	0.938150i
$189$	−1.29844	−	2.30523i	−0.0944473	−	0.167681i
$190$	3.48741	+	7.63637i	0.253004	+	0.554001i
$191$	0.766696	−	0.664346i	0.0554762	−	0.0480704i	−0.626681	−	0.779276i	$-0.715587\pi$
$191$	0.766696	−	0.664346i	0.0554762	−	0.0480704i	0.682158	+	0.731205i	$0.261042\pi$
$192$	7.12871	−	1.02495i	0.514470	−	0.0739697i
$193$	6.75131	+	1.98236i	0.485970	+	0.142694i	0.515534	−	0.856869i	$-0.327594\pi$
$193$	6.75131	+	1.98236i	0.485970	+	0.142694i	−0.0295640	+	0.999563i	$0.509412\pi$
$194$	−5.73530	+	6.61889i	−0.411770	+	0.475208i
$195$	3.61049	+	2.32032i	0.258553	+	0.166162i
$196$	28.2536	+	3.30561i	2.01812	+	0.236115i
$197$	−12.5038	+	14.4302i	−0.890860	+	1.02811i	0.108562	+	0.994090i	$0.465376\pi$
$197$	−12.5038	+	14.4302i	−0.890860	+	1.02811i	−0.999421	+	0.0340171i	$0.989170\pi$
$198$	−2.42799	+	8.26898i	−0.172550	+	0.587651i
$199$	2.62215	+	18.2375i	0.185880	+	1.29282i	0.842540	+	0.538634i	$0.181059\pi$
$199$	2.62215	+	18.2375i	0.185880	+	1.29282i	−0.656660	+	0.754186i	$0.728031\pi$
$200$	39.0002	+	45.0086i	2.75773	+	3.18259i
$201$	2.32184	+	5.08412i	0.163770	+	0.358606i
$202$	4.07260	+	13.8700i	0.286547	+	0.975889i
$203$	−3.71472	+	18.2285i	−0.260722	+	1.27939i
$204$	25.8003	+	3.70953i	1.80638	+	0.259719i
$205$	−9.06835	−	14.1106i	−0.633361	−	0.985529i
$206$	−0.719163			−0.0501065
$207$	3.53462	+	3.24137i	0.245673	+	0.225291i
$208$			4.60437i			0.319256i
$209$	1.57759	+	2.45478i	0.109124	+	0.169801i
$210$	−26.5442	+	2.25009i	−1.83172	+	0.155271i
$211$	−5.65466	+	12.3820i	−0.389283	+	0.852411i	0.608962	+	0.793199i	$0.291586\pi$
$211$	−5.65466	+	12.3820i	−0.389283	+	0.852411i	−0.998245	+	0.0592120i	$0.981141\pi$
$212$	1.35527	+	4.61561i	0.0930801	+	0.317002i
$213$	12.8760	−	5.88025i	0.882246	−	0.402908i
$214$	1.58567	−	1.37399i	0.108394	−	0.0939243i
$215$	−38.7722	+	5.57460i	−2.64424	+	0.380184i
$216$	−1.43176	+	4.87611i	−0.0974186	+	0.331777i
$217$	−20.6773	−	10.9398i	−1.40367	−	0.742640i
$218$	−9.90728	+	15.4160i	−0.671006	+	1.04411i
$219$	−2.55876	−	1.64441i	−0.172905	−	0.111119i
$220$	43.9490	+	38.0820i	2.96304	+	2.56749i
$221$	1.89676	−	6.45977i	0.127590	−	0.434531i
$222$	−1.00065	−	6.95968i	−0.0671593	−	0.467103i
$223$	−7.56773	+	6.55747i	−0.506773	+	0.439121i	−0.870343	−	0.492446i	$-0.836103\pi$
$223$	−7.56773	+	6.55747i	−0.506773	+	0.439121i	0.363571	+	0.931567i	$0.381558\pi$
$224$	−1.02944	−	1.33809i	−0.0687826	−	0.0894047i
$225$	11.2442	−	3.30159i	0.749612	−	0.220106i
$226$	−33.4542	−	15.2780i	−2.22534	−	1.01628i
$227$	−2.47059	+	17.1833i	−0.163978	+	1.14050i	0.727062	+	0.686572i	$0.240885\pi$
$227$	−2.47059	+	17.1833i	−0.163978	+	1.14050i	−0.891041	+	0.453924i	$0.850024\pi$
$228$	1.83183	+	2.85038i	0.121316	+	0.188771i
$229$	−8.65471			−0.571920			−0.285960	−	0.958242i	$-0.592312\pi$
$229$	−8.65471			−0.571920			−0.285960	+	0.958242i	$0.592312\pi$
$230$	44.4714	−	18.8153i	2.93236	−	1.24065i
$231$	−9.02120	+	2.08720i	−0.593552	+	0.137328i
$232$	30.0605	−	19.3187i	1.97357	−	1.26833i
$233$	−2.80358	+	19.4993i	−0.183668	+	1.27744i	0.664329	+	0.747440i	$0.268717\pi$
$233$	−2.80358	+	19.4993i	−0.183668	+	1.27744i	−0.847997	+	0.530001i	$0.822192\pi$
$234$	2.35111	+	1.07372i	0.153697	+	0.0701910i
$235$	8.77770	+	29.8941i	0.572594	+	1.95008i
$236$	−29.9220	+	13.6649i	−1.94776	+	0.889511i
$237$	−2.58385	−	2.98192i	−0.167839	−	0.193696i
$238$	15.1179	+	38.9583i	0.979947	+	2.52529i
$239$	−11.6601	−	3.42372i	−0.754231	−	0.221462i	−0.118056	−	0.993007i	$-0.537666\pi$
$239$	−11.6601	−	3.42372i	−0.754231	−	0.221462i	−0.636175	+	0.771545i	$0.719484\pi$
$240$	13.5555	+	11.7459i	0.875004	+	0.758195i
$241$	−10.6522	−	6.84576i	−0.686169	−	0.440974i	0.150553	−	0.988602i	$-0.451895\pi$
$241$	−10.6522	−	6.84576i	−0.686169	−	0.440974i	−0.836722	+	0.547628i	$0.815531\pi$
$242$	2.58605	+	1.66195i	0.166237	+	0.106834i
$243$	0.755750	+	0.654861i	0.0484814	+	0.0420093i
$244$	10.7010	+	3.14209i	0.685059	+	0.201151i
$245$	−16.1029	−	23.6627i	−1.02877	−	1.51175i
$246$	−6.61509	−	7.63422i	−0.421763	−	0.486740i
$247$	0.796064	−	0.363550i	0.0506524	−	0.0231322i
$248$	12.6592	+	43.1131i	0.803857	+	2.73769i
$249$	3.48521	+	1.59164i	0.220866	+	0.100866i
$250$	9.62767	−	66.9619i	0.608907	−	4.23504i
$251$	14.4706	−	9.29969i	0.913376	−	0.586991i	0.00264728	−	0.999996i	$-0.499157\pi$
$251$	14.4706	−	9.29969i	0.913376	−	0.586991i	0.910729	+	0.413006i	$0.135521\pi$
$252$	−10.4750	+	2.42356i	−0.659863	+	0.152670i
$253$	14.3696	−	8.67326i	0.903412	−	0.545283i
$254$	14.3891			0.902854
$255$	−14.1792	−	22.0633i	−0.887936	−	1.38166i
$256$	4.61241	−	32.0800i	0.288276	−	2.00500i
$257$	−2.53540	−	1.15788i	−0.158154	−	0.0722264i	0.334765	−	0.942301i	$-0.391343\pi$
$257$	−2.53540	−	1.15788i	−0.158154	−	0.0722264i	−0.492919	+	0.870075i	$0.664070\pi$
$258$	−22.6346	+	6.64612i	−1.40917	+	0.413769i
$259$	5.98762	−	4.60652i	0.372053	−	0.286235i
$260$	13.1809	−	11.4213i	0.817446	−	0.708321i
$261$	−1.00066	−	6.95975i	−0.0619394	−	0.430798i
$262$	−11.8744	+	40.4403i	−0.733600	+	2.49841i
$263$	9.76428	+	8.46080i	0.602091	+	0.521715i	0.901709	−	0.432344i	$-0.142314\pi$
$263$	9.76428	+	8.46080i	0.602091	+	0.521715i	−0.299617	+	0.954059i	$0.596859\pi$
$264$	14.9623	+	9.61567i	0.920864	+	0.591803i
$265$	2.61680	−	4.07183i	0.160749	−	0.250130i
$266$	−2.54033	+	4.80149i	−0.155758	+	0.294398i
$267$	−1.36557	+	4.65071i	−0.0835716	+	0.284619i
$268$	22.4820	−	3.23243i	1.37331	−	0.197452i
$269$	−2.86314	+	2.48093i	−0.174569	+	0.151265i	−0.737763	−	0.675060i	$-0.764118\pi$
$269$	−2.86314	+	2.48093i	−0.174569	+	0.151265i	0.563194	+	0.826325i	$0.309572\pi$
$270$	9.15884	−	4.18270i	0.557389	−	0.254551i
$271$	5.41499	+	18.4418i	0.328937	+	1.12026i	0.943495	+	0.331386i	$0.107516\pi$
$271$	5.41499	+	18.4418i	0.328937	+	1.12026i	−0.614558	+	0.788872i	$0.710666\pi$
$272$	11.6884	−	25.5941i	0.708715	−	1.55187i
$273$	0.234564	+	2.76713i	0.0141964	+	0.167475i
$274$	19.9244	+	31.0030i	1.20368	+	1.87296i
$275$		−	41.0133i		−	2.47319i
$276$	16.6854	−	10.0710i	1.00434	−	0.606203i
$277$	21.9316			1.31774			0.658872	−	0.752255i	$-0.271034\pi$
$277$	21.9316			1.31774			0.658872	+	0.752255i	$0.271034\pi$
$278$	21.0274	+	32.7192i	1.26114	+	1.96237i
$279$	8.75171	+	1.25831i	0.523951	+	0.0753328i
$280$	−10.9780	+	53.8702i	−0.656062	+	3.21936i
$281$	−5.05699	−	17.2225i	−0.301675	−	1.02741i	−0.961229	−	0.275753i	$-0.911073\pi$
$281$	−5.05699	−	17.2225i	−0.301675	−	1.02741i	0.659554	−	0.751657i	$-0.270745\pi$
$282$	7.79460	+	17.0678i	0.464162	+	1.01637i
$283$	−7.57951	−	8.74722i	−0.450555	−	0.519968i	0.484346	−	0.874877i	$-0.339058\pi$
$283$	−7.57951	−	8.74722i	−0.450555	−	0.519968i	−0.934901	+	0.354908i	$0.884512\pi$
$284$	−8.18639	−	56.9376i	−0.485773	−	3.37862i
$285$	0.960477	−	3.27109i	0.0568938	−	0.193762i
$286$	5.92373	−	6.83634i	0.350277	−	0.404241i
$287$	3.65866	−	10.2181i	0.215964	−	0.603157i
$288$	0.536807	+	0.344985i	0.0316316	+	0.0203284i
$289$	−15.8092	+	18.2448i	−0.929955	+	1.07323i
$290$	−67.9287	−	19.9457i	−3.98891	−	1.17125i
$291$	3.52041	−	0.506158i	0.206370	−	0.0296715i
$292$	−9.34133	+	8.09431i	−0.546660	+	0.473684i
$293$	3.58074	+	7.84074i	0.209189	+	0.458061i	0.984922	−	0.173001i	$-0.0553465\pi$
$293$	3.58074	+	7.84074i	0.209189	+	0.458061i	−0.775732	+	0.631062i	$0.782619\pi$
$294$	−11.6271	−	12.7254i	−0.678106	−	0.742159i
$295$	30.1069	+	13.7493i	1.75289	+	0.800518i
$296$	−14.3632	−	2.06511i	−0.834841	−	0.120032i
$297$	2.94419	−	1.89212i	0.170839	−	0.109792i
$298$			16.3415i			0.946639i
$299$	−1.96143	−	4.63599i	−0.113432	−	0.268106i
$300$		−	47.6228i		−	2.74950i
$301$	−18.1567	−	17.6848i	−1.04653	−	1.01933i
$302$	4.67373	−	32.5065i	0.268943	−	1.87054i
$303$	2.43863	−	5.33985i	0.140095	−	0.306766i
$304$	3.50932	−	1.03043i	0.201273	−	0.0590991i
$305$	−4.66163	−	10.2076i	−0.266924	−	0.584483i
$306$	−10.3433	−	11.9368i	−0.591288	−	0.682382i
$307$	5.19678	−	0.747184i	0.296596	−	0.0426441i	0.00758949	−	0.999971i	$-0.497584\pi$
$307$	5.19678	−	0.747184i	0.296596	−	0.0426441i	0.289007	+	0.957327i	$0.406675\pi$
$308$	−2.19002	+	37.5647i	−0.124788	+	2.14045i
$309$	0.220716	+	0.191252i	0.0125561	+	0.0108799i
$310$	48.1304	−	74.8924i	2.73362	−	4.25360i
$311$	8.84474	−	13.7627i	0.501539	−	0.780410i	−0.494514	−	0.869170i	$-0.664654\pi$
$311$	8.84474	−	13.7627i	0.501539	−	0.780410i	0.996053	+	0.0887594i	$0.0282902\pi$
$312$	3.49314	−	4.03130i	0.197760	−	0.228228i
$313$	14.1613	+	4.15813i	0.800444	+	0.235031i	0.656275	−	0.754522i	$-0.272131\pi$
$313$	14.1613	+	4.15813i	0.800444	+	0.235031i	0.144169	+	0.989553i	$0.453949\pi$
$314$	0.0832074	+	0.578720i	0.00469566	+	0.0326591i
$315$	8.74497	+	6.36849i	0.492723	+	0.358824i
$316$	−14.5852	+	6.66083i	−0.820481	+	0.374701i
$317$	−14.0528	+	4.12628i	−0.789285	+	0.231755i	−0.651441	−	0.758699i	$-0.725835\pi$
$317$	−14.0528	+	4.12628i	−0.789285	+	0.231755i	−0.137843	+	0.990454i	$0.544017\pi$
$318$	1.21091	−	2.65153i	0.0679045	−	0.148690i
$319$	−24.3575	−	3.50208i	−1.36376	−	0.196079i
$320$	−24.7733	+	15.9209i	−1.38487	+	0.890003i
$321$	−0.852049			−0.0475568
$322$	27.1959	+	15.3835i	1.51557	+	0.857287i
$323$	−5.34793			−0.297567
$324$	3.41866	−	2.19704i	0.189925	−	0.122058i
$325$	−12.1753	−	1.75054i	−0.675362	−	0.0971024i
$326$	3.91783	−	8.57884i	0.216988	−	0.475138i
$327$	7.14029	−	2.09658i	0.394859	−	0.115941i
$328$	−18.9633	+	8.66024i	−1.04707	+	0.478182i
$329$	−11.8679	+	16.2965i	−0.654298	+	0.898456i
$330$	−5.01492	−	34.8795i	−0.276062	−	1.92005i
$331$	25.1121	+	7.37357i	1.38028	+	0.405288i	0.885868	−	0.463937i	$-0.153564\pi$
$331$	25.1121	+	7.37357i	1.38028	+	0.405288i	0.494416	+	0.869225i	$0.335382\pi$
$332$	10.1963	−	11.7671i	0.559592	−	0.645804i
$333$	−1.54373	+	2.40208i	−0.0845956	+	0.131633i
$334$	−29.9410	+	46.5891i	−1.63830	+	2.54924i
$335$	−17.2715	−	14.9659i	−0.943645	−	0.817673i
$336$	−0.675485	+	11.5863i	−0.0368507	+	0.632087i
$337$	−26.0036	+	3.73875i	−1.41651	+	0.203663i	−0.807671	−	0.589633i	$-0.799272\pi$
$337$	−26.0036	+	3.73875i	−1.41651	+	0.203663i	−0.608836	+	0.793296i	$0.708363\pi$
$338$	19.1869	+	22.1428i	1.04363	+	1.20441i
$339$	6.20435	+	13.5856i	0.336974	+	0.737870i
$340$	−102.262	+	30.0268i	−5.54592	+	1.62843i
$341$	12.8546	−	28.1475i	0.696113	−	1.52427i
$342$	0.292192	−	2.03224i	0.0157999	−	0.109891i
$343$	5.78192	−	17.5946i	0.312194	−	0.950018i
$344$			48.6846i			2.62490i
$345$	−18.6523	−	6.05202i	−1.00420	−	0.325830i
$346$			15.1082i			0.812223i
$347$	−19.7454	+	12.6896i	−1.05999	+	0.681212i	−0.949851	−	0.312704i	$-0.898765\pi$
$347$	−19.7454	+	12.6896i	−1.05999	+	0.681212i	−0.110136	+	0.993916i	$0.535129\pi$
$348$	−28.2828	−	4.06646i	−1.51612	−	0.217985i
$349$	−4.33089	−	1.97785i	−0.231827	−	0.105872i	0.296115	−	0.955152i	$-0.404309\pi$
$349$	−4.33089	−	1.97785i	−0.231827	−	0.105872i	−0.527942	+	0.849280i	$0.677036\pi$
$350$	66.5228	−	37.4694i	3.55579	−	2.00283i
$351$	−0.436032	−	0.954776i	−0.0232737	−	0.0509622i
$352$	1.68775	−	1.46244i	0.0899573	−	0.0779485i
$353$	35.2417	−	5.06700i	1.87573	−	0.269689i	0.892361	−	0.451322i	$-0.149047\pi$
$353$	35.2417	−	5.06700i	1.87573	−	0.269689i	0.983366	+	0.181633i	$0.0581382\pi$
$354$	19.1253	+	5.61571i	1.01650	+	0.298472i
$355$	−37.9023	+	43.7416i	−2.01165	+	2.32156i
$356$	16.5704	+	10.6491i	0.878229	+	0.564404i
$357$	5.72065	−	15.9770i	0.302769	−	0.845591i
$358$	−0.437826	+	0.505279i	−0.0231398	+	0.0267048i
$359$	−9.67814	+	32.9607i	−0.510793	+	1.73960i	0.149664	+	0.988737i	$0.452181\pi$
$359$	−9.67814	+	32.9607i	−0.510793	+	1.73960i	−0.660457	+	0.750864i	$0.729637\pi$
$360$	−2.95723	−	20.5680i	−0.155860	−	1.08403i
$361$	11.9871	+	13.8339i	0.630901	+	0.728098i
$362$	8.06112	+	17.6514i	0.423683	+	0.927737i
$363$	−0.351703	−	1.19779i	−0.0184596	−	0.0628676i
$364$	11.0580	+	2.25348i	0.579598	+	0.118114i
$365$	12.3101	+	1.76993i	0.644341	+	0.0926423i
$366$	−3.65370	−	5.68526i	−0.190982	−	0.297173i
$367$	−21.2662			−1.11009			−0.555043	−	0.831821i	$-0.687298\pi$
$367$	−21.2662			−1.11009			−0.555043	+	0.831821i	$0.687298\pi$
$368$	−5.35653	−	20.3443i	−0.279228	−	1.06052i
$369$			4.10219i			0.213552i
$370$	15.5434	+	24.1859i	0.808060	+	1.25737i
$371$	3.12071	−	0.264535i	0.162019	−	0.0137340i
$372$	14.9261	−	32.6836i	0.773883	−	1.69457i
$373$	−8.92408	−	30.3926i	−0.462071	−	1.57367i	−0.780141	−	0.625603i	$-0.784853\pi$
$373$	−8.92408	−	30.3926i	−0.462071	−	1.57367i	0.318070	−	0.948067i	$-0.396965\pi$
$374$	−50.2823	+	22.9632i	−2.60004	+	1.18740i
$375$	−20.7624	+	17.9907i	−1.07217	+	0.929037i
$376$	38.3291	−	5.51090i	1.97667	−	0.284203i
$377$	−2.07927	+	7.08133i	−0.107088	+	0.364707i
$378$	5.75877	+	3.04680i	0.296199	+	0.156710i
$379$	6.74628	−	10.4974i	0.346533	−	0.539216i	−0.623614	−	0.781732i	$-0.714336\pi$
$379$	6.74628	−	10.4974i	0.346533	−	0.539216i	0.970147	+	0.242516i	$0.0779727\pi$
$380$	−11.6548	−	7.49010i	−0.597880	−	0.384234i
$381$	−4.41612	−	3.82659i	−0.226245	−	0.196042i
$382$	−0.703807	+	2.39695i	−0.0360099	+	0.122638i
$383$	3.13378	+	21.7959i	0.160128	+	1.11372i	0.898388	+	0.439202i	$0.144739\pi$
$383$	3.13378	+	21.7959i	0.160128	+	1.11372i	−0.738260	+	0.674516i	$0.764352\pi$
$384$	−14.3675	+	12.4495i	−0.733190	+	0.635313i
$385$	30.0079	−	23.0863i	1.52934	−	1.17659i
$386$	−16.6249	+	4.88151i	−0.846185	+	0.248462i
$387$	8.71416	+	3.97962i	0.442966	+	0.202296i
$388$	2.05691	−	14.3061i	0.104424	−	0.726282i
$389$	0.0341704	+	0.0531702i	0.00173251	+	0.00269584i	0.842119	−	0.539292i	$-0.181308\pi$
$389$	0.0341704	+	0.0531702i	0.00173251	+	0.00269584i	−0.840386	+	0.541988i	$0.817672\pi$
$390$	−10.5684			−0.535153
$391$	−0.865790	+	30.7490i	−0.0437849	+	1.55504i
$392$	−31.9587	+	15.6247i	−1.61416	+	0.789167i
$393$	14.3989	−	9.25359i	0.726327	−	0.466782i
$394$	6.69137	−	46.5395i	0.337106	−	2.34463i
$395$	14.6753	+	6.70198i	0.738394	+	0.337213i
$396$	−4.00686	−	13.6461i	−0.201353	−	0.685744i
$397$	20.7751	−	9.48766i	1.04267	−	0.476172i	0.180917	−	0.983498i	$-0.442093\pi$
$397$	20.7751	−	9.48766i	1.04267	−	0.476172i	0.861754	+	0.507326i	$0.169366\pi$
$398$	−29.7117	−	34.2892i	−1.48931	−	1.71876i
$399$	2.05654	−	0.798044i	0.102956	−	0.0399522i
$400$	−49.3244	−	14.4830i	−2.46622	−	0.724148i
$401$	0.624798	+	0.541390i	0.0312009	+	0.0270357i	0.670322	−	0.742071i	$-0.266156\pi$
$401$	0.624798	+	0.541390i	0.0312009	+	0.0270357i	−0.639121	+	0.769106i	$0.720702\pi$
$402$	−11.5784	−	7.44098i	−0.577477	−	0.371122i
$403$	−7.80726	−	5.01742i	−0.388907	−	0.249936i
$404$	−18.0289	−	15.6222i	−0.896972	−	0.777231i
$405$	−3.92324	−	1.15197i	−0.194948	−	0.0572418i
$406$	−16.5725	−	42.7069i	−0.822481	−	2.11951i
$407$	6.54409	+	7.55228i	0.324378	+	0.374353i
$408$	−29.6508	+	13.5411i	−1.46793	+	0.670383i
$409$	−3.84709	−	13.1020i	−0.190226	−	0.647852i	−0.998274	−	0.0587340i	$-0.981294\pi$
$409$	−3.84709	−	13.1020i	−0.190226	−	0.647852i	0.808047	−	0.589118i	$-0.200525\pi$
$410$	37.5713	+	17.1582i	1.85551	+	0.847385i
$411$	2.12988	−	14.8136i	0.105059	−	0.730703i
$412$	0.998417	−	0.641643i	0.0491885	−	0.0316115i
$413$	4.82749	+	20.8652i	0.237545	+	1.02671i
$414$	−11.6375	−	2.00902i	−0.571950	−	0.0987379i
$415$	−15.6663			−0.769028
$416$	−0.362106	−	0.563448i	−0.0177537	−	0.0276253i
$417$	2.24778	−	15.6337i	0.110075	−	0.765585i
$418$	−6.53616	−	2.98496i	−0.319694	−	0.145999i
$419$	11.7366	−	3.44617i	0.573369	−	0.168356i	0.0178217	−	0.999841i	$-0.494327\pi$
$419$	11.7366	−	3.44617i	0.573369	−	0.168356i	0.555548	+	0.831485i	$0.312509\pi$
$420$	34.8438	−	26.8067i	1.70020	−	1.30803i
$421$	−3.63748	+	3.15189i	−0.177280	+	0.153614i	−0.738981	−	0.673726i	$-0.764693\pi$
$421$	−3.63748	+	3.15189i	−0.177280	+	0.153614i	0.561701	+	0.827340i	$0.310147\pi$
$422$	−4.77030	−	33.1782i	−0.232215	−	1.61509i
$423$	2.14673	−	7.31109i	0.104378	−	0.355477i
$424$	−4.54641	−	3.93949i	−0.220793	−	0.191318i
$425$	63.2342	+	40.6382i	3.06731	+	1.97124i
$426$	−18.8449	+	29.3232i	−0.913038	+	1.42071i
$427$	3.39566	−	6.41816i	0.164328	−	0.310597i
$428$	−0.975507	+	3.32227i	−0.0471529	+	0.160588i
$429$	−3.63606	+	0.522787i	−0.175551	+	0.0252404i
$430$	72.8975	−	63.1660i	3.51543	−	3.04614i
$431$	−11.5961	+	5.29576i	−0.558564	+	0.255088i	−0.674633	−	0.738153i	$-0.735698\pi$
$431$	−11.5961	+	5.29576i	−0.558564	+	0.255088i	0.116069	+	0.993241i	$0.462971\pi$
$432$	−1.23587	−	4.20897i	−0.0594606	−	0.202504i
$433$	3.90460	−	8.54988i	0.187643	−	0.410881i	−0.792307	−	0.610122i	$-0.791120\pi$
$433$	3.90460	−	8.54988i	0.187643	−	0.410881i	0.979951	+	0.199241i	$0.0638476\pi$
$434$	57.3986	−	4.86555i	2.75522	−	0.233554i
$435$	15.5435	+	24.1862i	0.745255	+	1.15964i
$436$		−	30.2415i		−	1.44830i
$437$	−3.09446	+	2.53245i	−0.148028	+	0.121143i
$438$	7.48985			0.357879
$439$	6.79334	+	10.5706i	0.324229	+	0.504510i	0.964657	−	0.263508i	$-0.0848796\pi$
$439$	6.79334	+	10.5706i	0.324229	+	0.504510i	−0.640429	+	0.768018i	$0.721243\pi$
$440$	−71.9832	−	10.3496i	−3.43166	−	0.493399i
$441$	0.184299	+	6.99757i	0.00877612	+	0.333218i
$442$	4.67072	+	15.9070i	0.222163	+	0.756619i
$443$	−4.81421	−	10.5417i	−0.228730	−	0.500849i	0.760116	−	0.649787i	$-0.225142\pi$
$443$	−4.81421	−	10.5417i	−0.228730	−	0.500849i	−0.988847	+	0.148938i	$0.952415\pi$
$444$	7.59869	+	8.76936i	0.360618	+	0.416175i
$445$	−2.82053	−	19.6172i	−0.133706	−	0.929946i
$446$	6.94698	−	23.6592i	0.328949	−	1.12030i
$447$	4.34580	−	5.01533i	0.205549	−	0.237217i
$448$	−17.9395	−	6.42333i	−0.847560	−	0.303474i
$449$	22.9051	+	14.7202i	1.08096	+	0.694690i	0.954779	−	0.297318i	$-0.0960920\pi$
$449$	22.9051	+	14.7202i	1.08096	+	0.694690i	0.126180	+	0.992007i	$0.459728\pi$
$450$	−18.8976	+	21.8090i	−0.890840	+	1.02808i
$451$	13.7752	+	4.04475i	0.648647	+	0.190460i
$452$	60.0758	−	8.63759i	2.82573	−	0.406278i
$453$	−10.0791	+	8.73356i	−0.473556	+	0.410338i
$454$	−17.7584	−	38.8854i	−0.833441	−	1.82498i
$455$	−5.57262	−	9.89357i	−0.261249	−	0.463817i
$456$	−3.85429	−	1.76019i	−0.180494	−	0.0824286i
$457$	−8.52291	−	1.22541i	−0.398685	−	0.0573223i	−0.0599437	−	0.998202i	$-0.519092\pi$
$457$	−8.52291	−	1.22541i	−0.398685	−	0.0573223i	−0.338741	+	0.940879i	$0.610001\pi$
$458$	17.9288	−	11.5221i	0.837757	−	0.538394i
$459$			6.41415i			0.299387i
$460$	−44.9527	+	65.7992i	−2.09593	+	3.06790i
$461$			30.1359i			1.40357i	0.712390	+	0.701784i	$0.247613\pi$
$461$			30.1359i			1.40357i	−0.712390	+	0.701784i	$0.752387\pi$
$462$	15.9093	−	16.3338i	0.740166	−	0.759917i
$463$	−1.29438	+	9.00265i	−0.0601552	+	0.418388i	0.937385	+	0.348294i	$0.113239\pi$
$463$	−1.29438	+	9.00265i	−0.0601552	+	0.418388i	−0.997540	+	0.0700941i	$0.977670\pi$
$464$	−12.8131	+	28.0567i	−0.594832	+	1.30250i
$465$	−34.6882	+	10.1854i	−1.60862	+	0.472335i
$466$	−20.1519	−	44.1264i	−0.933517	−	2.04412i
$467$	−6.64382	−	7.66738i	−0.307439	−	0.354804i	0.580914	−	0.813965i	$-0.302695\pi$
$467$	−6.64382	−	7.66738i	−0.307439	−	0.354804i	−0.888353	+	0.459161i	$0.848150\pi$
$468$	−4.22203	+	0.607036i	−0.195163	+	0.0280603i
$469$	0.860659	−	14.7626i	0.0397415	−	0.681672i
$470$	−57.9820	−	50.2417i	−2.67451	−	2.31747i
$471$	0.128366	−	0.199741i	0.00591478	−	0.00920358i
$472$	22.2401	−	34.6063i	1.02368	−	1.59288i
$473$	21.9557	−	25.3382i	1.00952	−	1.16505i
$474$	9.32246	+	2.73732i	0.428195	+	0.125729i
$475$	1.39054	+	9.67140i	0.0638022	+	0.443754i
$476$	−55.7472	−	40.5977i	−2.55517	−	1.86079i
$477$	−1.07677	+	0.491746i	−0.0493021	+	0.0225155i
$478$	28.7127	−	8.43082i	1.31329	−	0.385617i
$479$	−8.48472	+	18.5789i	−0.387677	+	0.848894i	0.610696	+	0.791865i	$0.290890\pi$
$479$	−8.48472	+	18.5789i	−0.387677	+	0.848894i	−0.998373	+	0.0570285i	$0.981837\pi$
$480$	−2.58257	−	0.371317i	−0.117877	−	0.0169482i
$481$	2.52130	−	1.62034i	0.114961	−	0.0738811i
$482$	31.1806			1.42024
$483$	−4.25558	−	11.9537i	−0.193636	−	0.543910i
$484$	−5.07303			−0.230592
$485$	−12.2339	+	7.86227i	−0.555514	+	0.357007i
$486$	−2.43741	−	0.350446i	−0.110563	−	0.0158966i
$487$	4.24368	−	9.29236i	0.192299	−	0.421077i	−0.788782	−	0.614673i	$-0.789288\pi$
$487$	4.24368	−	9.29236i	0.192299	−	0.421077i	0.981081	+	0.193596i	$0.0620152\pi$
$488$	−13.3822	+	3.92935i	−0.605782	+	0.177874i
$489$	−3.48383	+	1.59101i	−0.157544	+	0.0719481i
$490$	64.8605	+	27.5808i	2.93010	+	1.24597i
$491$	0.869824	+	6.04976i	0.0392546	+	0.273022i	0.999990	−	0.00444402i	$-0.00141458\pi$
$491$	0.869824	+	6.04976i	0.0392546	+	0.273022i	−0.960736	+	0.277466i	$0.910505\pi$
$492$	15.9951	+	4.69658i	0.721114	+	0.211738i
$493$	29.5342	−	34.0843i	1.33015	−	1.53508i
$494$	−1.16510	+	1.81293i	−0.0524202	+	0.0815675i
$495$	−7.73662	+	12.0384i	−0.347735	+	0.541086i
$496$	−29.3122	−	25.3991i	−1.31616	−	1.14046i
$497$	−37.3874	−	2.17969i	−1.67706	−	0.0977725i
$498$	−9.33880	+	1.34272i	−0.418482	+	0.0601686i
$499$	10.0152	+	11.5582i	0.448343	+	0.517416i	0.934262	−	0.356589i	$-0.116060\pi$
$499$	10.0152	+	11.5582i	0.448343	+	0.517416i	−0.485918	+	0.874004i	$0.661515\pi$
$500$	46.3779	+	101.553i	2.07408	+	4.54160i
$501$	21.5788	−	6.33612i	0.964072	−	0.283077i
$502$	−17.5960	+	38.5298i	−0.785346	+	1.71967i
$503$	−4.88488	+	33.9751i	−0.217806	+	1.51487i	0.528307	+	0.849054i	$0.322827\pi$
$503$	−4.88488	+	33.9751i	−0.217806	+	1.51487i	−0.746113	+	0.665820i	$0.768082\pi$
$504$	9.38149	−	9.63183i	0.417885	−	0.429036i
$505$			24.0031i			1.06812i
$506$	−18.2208	+	37.0977i	−0.810013	+	1.64919i
$507$		−	11.8983i		−	0.528421i
$508$	−19.9765	+	12.8381i	−0.886312	+	0.569598i
$509$	5.46892	+	0.786312i	0.242406	+	0.0348527i	0.262447	−	0.964946i	$-0.415471\pi$
$509$	5.46892	+	0.786312i	0.242406	+	0.0348527i	−0.0200410	+	0.999799i	$0.506380\pi$
$510$	58.7462	+	26.8285i	2.60133	+	1.18799i
$511$	3.94932	+	7.01157i	0.174708	+	0.310174i
$512$	17.3588	+	38.0104i	0.767157	+	1.67984i
$513$	−0.630122	+	0.546004i	−0.0278206	+	0.0241066i
$514$	6.79373	−	0.976791i	0.299659	−	0.0430844i
$515$	−1.14578	−	0.336432i	−0.0504891	−	0.0148249i
$516$	25.4940	−	29.4216i	1.12231	−	1.29521i
$517$	−22.4340	−	14.4174i	−0.986645	−	0.634078i
$518$	−6.27102	+	17.5141i	−0.275533	+	0.769525i
$519$	4.01783	−	4.63682i	0.176363	−	0.203534i
$520$	−6.14481	+	20.9273i	−0.269468	+	0.917722i
$521$	−1.11772	−	7.77390i	−0.0489681	−	0.340581i	−0.999547	−	0.0300976i	$-0.990418\pi$
$521$	−1.11772	−	7.77390i	−0.0489681	−	0.340581i	0.950579	−	0.310483i	$-0.100491\pi$
$522$	11.3385	+	13.0854i	0.496275	+	0.572731i
$523$	−1.85402	−	4.05974i	−0.0810707	−	0.177520i	0.864756	−	0.502193i	$-0.167473\pi$
$523$	−1.85402	−	4.05974i	−0.0810707	−	0.177520i	−0.945826	+	0.324673i	$0.894746\pi$
$524$	−19.5960	−	66.7378i	−0.856055	−	2.91546i
$525$	−30.3808	−	6.19120i	−1.32593	−	0.270206i
$526$	−31.4913	−	4.52776i	−1.37309	−	0.197420i
$527$	30.6608	+	47.7092i	1.33561	+	2.07825i
$528$	−15.3523			−0.668123
$529$	14.0599	+	18.2022i	0.611298	+	0.791400i
$530$			11.9188i			0.517721i
$531$	−4.37628	−	6.80962i	−0.189914	−	0.295513i
$532$	−0.757181	−	8.93243i	−0.0328280	−	0.387270i
$533$	1.78869	−	3.91667i	0.0774765	−	0.169650i
$534$	−3.36268	−	11.4522i	−0.145517	−	0.495587i
$535$	3.16909	−	1.44727i	0.137012	−	0.0625711i
$536$	−21.4664	+	18.6008i	−0.927208	+	0.803430i
$537$	0.268744	−	0.0386395i	0.0115972	−	0.00166742i
$538$	2.62829	−	8.95114i	0.113314	−	0.385911i
$539$	23.6796	+	6.28072i	1.01995	+	0.270530i
$540$	−8.98341	+	13.9785i	−0.386584	+	0.601537i
$541$	4.85765	+	3.12182i	0.208847	+	0.134218i	0.640883	−	0.767639i	$-0.278568\pi$
$541$	4.85765	+	3.12182i	0.208847	+	0.134218i	−0.432036	+	0.901856i	$0.642205\pi$
$542$	−35.7693	−	30.9942i	−1.53642	−	1.33132i
$543$	2.22013	−	7.56108i	0.0952751	−	0.324477i
$544$	0.582479	+	4.05123i	0.0249736	+	0.173695i
$545$	−22.9962	+	19.9263i	−0.985048	+	0.853549i
$546$	−4.16983	−	5.42001i	−0.178452	−	0.231955i
$547$	−38.2630	+	11.2350i	−1.63601	+	0.480375i	−0.965256	−	0.261307i	$-0.915846\pi$
$547$	−38.2630	+	11.2350i	−1.63601	+	0.480375i	−0.670751	+	0.741682i	$0.734028\pi$
$548$	−55.3222	−	25.2648i	−2.36325	−	1.07926i
$549$	−0.390573	+	2.71650i	−0.0166693	+	0.115937i
$550$	54.6015	+	84.9616i	2.32822	+	3.62278i
$551$	5.86251			0.249751
$552$	−10.7446	+	21.8760i	−0.457319	+	0.931106i
$553$	2.35311	+	10.1705i	0.100064	+	0.432495i
$554$	−45.4327	+	29.1979i	−1.93025	+	1.24050i
$555$	1.66156	−	11.5564i	0.0705291	−	0.490541i
$556$	−58.3847	−	26.6634i	−2.47606	−	1.13078i
$557$	−9.75837	−	33.2340i	−0.413475	−	1.40817i	−0.858575	−	0.512687i	$-0.828650\pi$
$557$	−9.75837	−	33.2340i	−0.413475	−	1.40817i	0.445100	−	0.895481i	$-0.353168\pi$
$558$	−19.8049	+	9.04460i	−0.838409	+	0.382888i
$559$	−6.58483	−	7.59930i	−0.278509	−	0.321416i
$560$	−17.1679	−	44.2413i	−0.725478	−	1.86953i
$561$	21.5387	+	6.32434i	0.909366	+	0.267014i
$562$	33.4045	+	28.9451i	1.40908	+	1.22098i
$563$	−12.9198	−	8.30304i	−0.544504	−	0.349931i	0.239294	−	0.970947i	$-0.423084\pi$
$563$	−12.9198	−	8.30304i	−0.544504	−	0.349931i	−0.783798	+	0.621016i	$0.786720\pi$
$564$	−26.0493	−	16.7409i	−1.09687	−	0.704917i
$565$	−46.1525	−	39.9914i	−1.94165	−	1.68245i
$566$	27.3467	+	8.02972i	1.14947	+	0.337514i
$567$	−0.957151	−	2.46655i	−0.0401966	−	0.103585i
$568$	47.1080	+	54.3655i	1.97661	+	2.28112i
$569$	32.2808	−	14.7422i	1.35328	−	0.618023i	0.399006	−	0.916949i	$-0.369355\pi$
$569$	32.2808	−	14.7422i	1.35328	−	0.618023i	0.954277	+	0.298925i	$0.0966282\pi$
$570$	2.36515	+	8.05495i	0.0990651	+	0.337385i
$571$	−41.9278	−	19.1478i	−1.75462	−	0.801310i	−0.987063	−	0.160334i	$-0.948743\pi$
$571$	−41.9278	−	19.1478i	−1.75462	−	0.801310i	−0.767561	−	0.640976i	$-0.778530\pi$
$572$	−2.12449	+	14.7761i	−0.0888292	+	0.617821i
$573$	0.853438	−	0.548472i	0.0356529	−	0.0229127i
$574$	6.02437	+	26.0383i	0.251452	+	1.08682i
$575$	55.8328	−	6.42945i	2.32839	−	0.268126i
$576$	7.20202			0.300084
$577$	−0.312442	−	0.486170i	−0.0130071	−	0.0202395i	0.834689	−	0.550721i	$-0.185647\pi$
$577$	−0.312442	−	0.486170i	−0.0130071	−	0.0202395i	−0.847696	+	0.530482i	$0.822011\pi$
$578$	8.46026	−	58.8424i	0.351900	−	2.44752i
$579$	6.40047	+	2.92300i	0.265994	+	0.121476i
$580$	112.101	−	32.9159i	4.65476	−	1.36676i
$581$	−6.18122	−	8.03445i	−0.256440	−	0.333325i
$582$	−6.61889	+	5.73530i	−0.274362	+	0.237736i
$583$	0.589587	+	4.10067i	0.0244182	+	0.169832i
$584$	4.35483	−	14.8312i	0.180204	−	0.613718i
$585$	3.24353	+	2.81053i	0.134103	+	0.116201i
$586$	−17.8562	−	11.4755i	−0.737633	−	0.474048i
$587$	19.0939	−	29.7107i	0.788090	−	1.22629i	−0.181940	−	0.983310i	$-0.558238\pi$
$587$	19.0939	−	29.7107i	0.788090	−	1.22629i	0.970031	−	0.242983i	$-0.0781258\pi$
$588$	27.4956	+	7.29288i	1.13390	+	0.300753i
$589$	−2.07692	+	7.07334i	−0.0855779	+	0.291452i
$590$	−80.6729	+	11.5990i	−3.32125	+	0.477524i
$591$	−14.4302	+	12.5038i	−0.593578	+	0.514338i
$592$	11.3936	−	5.20329i	0.468274	−	0.213854i
$593$	−11.1968	−	38.1326i	−0.459795	−	1.56592i	−0.784515	−	0.620109i	$-0.787088\pi$
$593$	−11.1968	−	38.1326i	−0.459795	−	1.56592i	0.324720	−	0.945810i	$-0.394730\pi$
$594$	−3.58008	+	7.83927i	−0.146892	+	0.321649i
$595$	5.86094	+	69.1412i	0.240275	+	2.83451i
$596$	−14.5800	−	22.6870i	−0.597222	−	0.929295i
$597$			18.4250i			0.754086i
$598$	10.2352	+	6.99247i	0.418547	+	0.285943i
$599$	21.7945			0.890500			0.445250	−	0.895406i	$-0.353115\pi$
$599$	21.7945			0.890500			0.445250	+	0.895406i	$0.353115\pi$
$600$	32.1978	+	50.1008i	1.31447	+	2.04536i
$601$	−32.7194	−	4.70434i	−1.33465	−	0.191894i	−0.562218	−	0.826989i	$-0.690052\pi$
$601$	−32.7194	−	4.70434i	−1.33465	−	0.191894i	−0.772434	+	0.635095i	$0.780961\pi$
$602$	61.1567	+	12.4629i	2.49256	+	0.507951i
$603$	1.57466	+	5.36280i	0.0641251	+	0.218390i
$604$	22.5140	+	49.2989i	0.916083	+	2.00594i
$605$	3.34265	+	3.85762i	0.135898	+	0.156835i
$606$	2.05724	+	14.3084i	0.0835696	+	0.581239i
$607$	3.23837	−	11.0289i	0.131441	−	0.447648i	−0.867301	−	0.497784i	$-0.834147\pi$
$607$	3.23837	−	11.0289i	0.131441	−	0.447648i	0.998742	+	0.0501361i	$0.0159655\pi$
$608$	−0.348407	+	0.402083i	−0.0141298	+	0.0163066i
$609$	−6.27109	+	17.5143i	−0.254117	+	0.709714i
$610$	23.2463	+	14.9395i	0.941216	+	0.604882i
$611$	−5.23751	+	6.04441i	−0.211887	+	0.244531i
$612$	25.0098	+	7.34354i	1.01096	+	0.296845i
$613$	12.1452	−	1.74621i	0.490539	−	0.0705288i	0.107393	−	0.994217i	$-0.465750\pi$
$613$	12.1452	−	1.74621i	0.490539	−	0.0705288i	0.383146	+	0.923688i	$0.374841\pi$
$614$	−9.77072	+	8.46638i	−0.394314	+	0.341675i
$615$	−6.96789	−	15.2576i	−0.280973	−	0.615244i
$616$	−23.0936	−	41.0000i	−0.930466	−	1.65194i
$617$	35.2783	+	16.1110i	1.42025	+	0.648606i	0.969734	−	0.244162i	$-0.0785130\pi$
$617$	35.2783	+	16.1110i	1.42025	+	0.648606i	0.450515	+	0.892769i	$0.351240\pi$
$618$	−0.711843	−	0.102348i	−0.0286345	−	0.00411702i
$619$	0.160283	−	0.103007i	0.00644230	−	0.00414022i	−0.537416	−	0.843317i	$-0.680599\pi$
$619$	0.160283	−	0.103007i	0.00644230	−	0.00414022i	0.543858	+	0.839177i	$0.316963\pi$
$620$			146.916i			5.90027i
$621$	3.03735	+	3.71141i	0.121884	+	0.148934i
$622$			40.2854i			1.61530i
$623$	8.94783	−	9.18659i	0.358487	−	0.368053i
$624$	−0.655270	+	4.55750i	−0.0262318	+	0.182446i
$625$	22.3234	−	48.8814i	0.892936	−	1.95526i
$626$	−34.8718	+	10.2393i	−1.39376	+	0.409244i
$627$	1.21218	+	2.65431i	0.0484099	+	0.106003i
$628$	−0.631856	−	0.729200i	−0.0252138	−	0.0290983i
$629$	−18.1283	+	2.60646i	−0.722823	+	0.103926i
$630$	−26.5942	−	1.55044i	−1.05954	−	0.0617711i
$631$	−32.8881	−	28.4977i	−1.30925	−	1.13447i	−0.981864	−	0.189584i	$-0.939286\pi$
$631$	−32.8881	−	28.4977i	−1.30925	−	1.13447i	−0.327388	−	0.944890i	$-0.606169\pi$
$632$	10.8407	−	16.8685i	0.431221	−	0.670993i
$633$	−7.35925	+	11.4512i	−0.292504	+	0.455145i
$634$	23.6179	−	27.2565i	0.937987	−	1.08250i
$635$	22.9249	+	6.73137i	0.909749	+	0.267126i
$636$	0.684602	+	4.76151i	0.0271462	+	0.188806i
$637$	2.87520	−	6.76148i	0.113920	−	0.267899i
$638$	55.1205	−	25.1727i	2.18224	−	0.996596i
$639$	13.5817	−	3.98796i	0.537285	−	0.157761i
$640$	32.2916	−	70.7088i	1.27644	−	2.79501i
$641$	−8.58720	−	1.23465i	−0.339174	−	0.0487658i	−0.0293764	−	0.999568i	$-0.509352\pi$
$641$	−8.58720	−	1.23465i	−0.339174	−	0.0487658i	−0.309797	+	0.950803i	$0.600261\pi$
$642$	1.76507	−	1.13434i	0.0696619	−	0.0447690i
$643$	−14.0851			−0.555463			−0.277731	−	0.960659i	$-0.589583\pi$
$643$	−14.0851			−0.555463			−0.277731	+	0.960659i	$0.589583\pi$
$644$	−51.4814	+	2.90747i	−2.02865	+	0.114571i
$645$	−39.1709			−1.54235
$646$	11.0786	−	7.11977i	0.435881	−	0.280124i
$647$	18.1653	+	2.61178i	0.714153	+	0.102680i	0.489808	−	0.871830i	$-0.337067\pi$
$647$	18.1653	+	2.61178i	0.714153	+	0.102680i	0.224345	+	0.974510i	$0.427976\pi$
$648$	−2.11112	+	4.62272i	−0.0829328	+	0.181598i
$649$	−27.1817	+	7.98127i	−1.06698	+	0.313292i
$650$	27.5523	−	12.5827i	1.08069	−	0.493536i
$651$	−18.9100	−	13.7711i	−0.741140	−	0.539732i
$652$	2.21498	+	15.4056i	0.0867455	+	0.603328i
$653$	−19.2402	−	5.64944i	−0.752929	−	0.221080i	−0.117323	−	0.993094i	$-0.537431\pi$
$653$	−19.2402	−	5.64944i	−0.752929	−	0.221080i	−0.635606	+	0.772014i	$0.719250\pi$
$654$	−12.0004	+	13.8492i	−0.469251	+	0.541545i
$655$	−37.8368	+	58.8751i	−1.47840	+	2.30044i
$656$	9.72879	−	15.1383i	0.379846	−	0.591051i
$657$	−2.29869	−	1.99182i	−0.0896804	−	0.0777085i
$658$	2.88930	−	49.5591i	0.112637	−	1.93202i
$659$	−16.7304	+	2.40547i	−0.651724	+	0.0937038i	−0.460244	−	0.887793i	$-0.652238\pi$
$659$	−16.7304	+	2.40547i	−0.651724	+	0.0937038i	−0.191480	+	0.981496i	$0.561329\pi$
$660$	38.0820	+	43.9490i	1.48234	+	1.71071i
$661$	−4.31369	−	9.44566i	−0.167783	−	0.367393i	0.806999	−	0.590553i	$-0.201090\pi$
$661$	−4.31369	−	9.44566i	−0.167783	−	0.367393i	−0.974782	+	0.223159i	$0.928363\pi$
$662$	−61.8378	+	18.1572i	−2.40339	+	0.705700i
$663$	2.79677	−	6.12408i	0.108618	−	0.237840i
$664$	−2.77105	+	19.2731i	−0.107538	+	0.747941i
$665$	−6.29347	+	6.46141i	−0.244050	+	0.250563i
$666$		−	7.03125i		−	0.272455i
$667$	0.949096	−	33.7077i	0.0367492	−	1.30517i
$668$		−	91.3935i		−	3.53612i
$669$	−8.42393	+	5.41373i	−0.325688	+	0.209307i
$670$	55.7034	+	8.00893i	2.15201	+	0.309412i
$671$	8.73689	+	3.99001i	0.337284	+	0.154032i
$672$	−0.828536	−	1.47097i	−0.0319615	−	0.0567440i
$673$	−8.49743	−	18.6068i	−0.327552	−	0.717239i	0.672180	−	0.740388i	$-0.265358\pi$
$673$	−8.49743	−	18.6068i	−0.327552	−	0.717239i	−0.999732	+	0.0231489i	$0.992631\pi$
$674$	48.8907	−	42.3640i	1.88320	−	1.63180i
$675$	11.5996	−	1.66777i	0.446468	−	0.0641925i
$676$	−46.3932	−	13.6223i	−1.78436	−	0.523934i
$677$	21.6679	−	25.0061i	0.832765	−	0.961063i	−0.166924	−	0.985970i	$-0.553384\pi$
$677$	21.6679	−	25.0061i	0.832765	−	0.961063i	0.999690	+	0.0249071i	$0.00792901\pi$
$678$	−30.9394	−	19.8835i	−1.18822	−	0.763623i
$679$	−8.85913	−	3.17206i	−0.339982	−	0.121733i
$680$	87.2818	−	100.729i	3.34710	−	3.86276i
$681$	−4.89088	+	16.6568i	−0.187419	+	0.638290i
$682$	10.8442	+	75.4228i	0.415245	+	2.88809i
$683$	−30.3978	−	35.0810i	−1.16314	−	1.34234i	−0.928977	−	0.370139i	$-0.879310\pi$
$683$	−30.3978	−	35.0810i	−1.16314	−	1.34234i	−0.234164	−	0.972197i	$-0.575235\pi$
$684$	1.40753	+	3.08206i	0.0538182	+	0.117845i
$685$	17.2403	+	58.7152i	0.658719	+	2.24339i
$686$	11.4463	+	44.1458i	0.437021	+	1.68550i
$687$	−8.56662	−	1.23169i	−0.326837	−	0.0469921i
$688$	−22.7197	−	35.3526i	−0.866181	−	1.34780i
$689$	1.24250			0.0473353
$690$	46.6965	−	12.2949i	1.77770	−	0.468057i
$691$		−	13.7105i		−	0.521574i	−0.965396	−	0.260787i	$-0.916018\pi$
$691$		−	13.7105i		−	0.521574i	0.965396	−	0.260787i	$-0.0839820\pi$
$692$	−13.4797	−	20.9748i	−0.512421	−	0.797342i
$693$	−9.22642	+	0.782102i	−0.350483	+	0.0297096i
$694$	24.0100	−	52.5745i	0.911406	−	1.99570i
$695$	18.1947	+	61.9655i	0.690165	+	2.35048i
$696$	32.5038	−	14.8440i	1.23205	−	0.562660i
$697$	−19.8853	+	17.2308i	−0.753211	+	0.652661i
$698$	11.6048	−	1.66852i	0.439250	−	0.0631546i
$699$	−5.55008	+	18.9018i	−0.209923	+	0.714933i
$700$	−58.9233	+	111.371i	−2.22709	+	4.20943i
$701$	17.7961	−	27.6912i	0.672148	−	1.04588i	−0.322895	−	0.946435i	$-0.604656\pi$
$701$	17.7961	−	27.6912i	0.672148	−	1.04588i	0.995043	−	0.0994479i	$-0.0317077\pi$
$702$	2.17437	+	1.39738i	0.0820664	+	0.0527409i
$703$	−1.79923	−	1.55904i	−0.0678591	−	0.0588002i
$704$	7.10117	−	24.1844i	0.267635	−	0.911483i
$705$	4.43398	+	30.8390i	0.166993	+	1.16146i
$706$	−66.2597	+	57.4144i	−2.49372	+	2.16082i
$707$	−12.3100	+	9.47054i	−0.462964	+	0.356176i
$708$	−31.5622	+	9.26749i	−1.18618	+	0.348294i
$709$	5.51109	+	2.51683i	0.206973	+	0.0945215i	0.516204	−	0.856465i	$-0.327344\pi$
$709$	5.51109	+	2.51683i	0.206973	+	0.0945215i	−0.309231	+	0.950987i	$0.600072\pi$
$710$	20.2833	−	141.073i	0.761218	−	5.29439i
$711$	−2.13318	−	3.31929i	−0.0800003	−	0.124483i
$712$	−24.6325			−0.923143
$713$	40.3333	+	13.0868i	1.51049	+	0.490104i
$714$	9.41966	+	40.7133i	0.352522	+	1.52366i
$715$	12.6359	−	8.12058i	0.472555	−	0.303692i
$716$	0.157022	−	1.09211i	0.00586819	−	0.0408142i
$717$	−11.0542	−	5.04828i	−0.412827	−	0.188532i
$718$	−23.8322	−	81.1649i	−0.889408	−	3.02905i
$719$	−39.7983	+	18.1753i	−1.48423	+	0.677824i	−0.982339	−	0.187109i	$-0.940088\pi$
$719$	−39.7983	+	18.1753i	−1.48423	+	0.677824i	−0.501888	+	0.864933i	$0.667361\pi$
$720$	11.7459	+	13.5555i	0.437744	+	0.505184i
$721$	−0.279535	−	0.720354i	−0.0104104	−	0.0268274i
$722$	−43.2493	−	12.6991i	−1.60957	−	0.472613i
$723$	−9.56953	−	8.29204i	−0.355895	−	0.308384i
$724$	−26.9400	−	17.3133i	−1.00122	−	0.643443i
$725$	−69.3186	−	44.5484i	−2.57443	−	1.65448i
$726$	2.32321	+	2.01307i	0.0862222	+	0.0747120i
$727$	−0.824652	−	0.242140i	−0.0305847	−	0.00898047i	0.266404	−	0.963861i	$-0.414164\pi$
$727$	−0.824652	−	0.242140i	−0.0305847	−	0.00898047i	−0.296989	+	0.954881i	$0.595983\pi$
$728$	−13.1570	+	5.10562i	−0.487631	+	0.189227i
$729$	0.654861	+	0.755750i	0.0242541	+	0.0279907i
$730$	−27.8575	+	12.7221i	−1.03105	+	0.470866i
$731$	17.3116	+	58.9578i	0.640291	+	2.18063i
$732$	10.1449	+	4.63301i	0.374965	+	0.171241i
$733$	−2.66335	+	18.5240i	−0.0983732	+	0.684201i	0.879637	+	0.475645i	$0.157785\pi$
$733$	−2.66335	+	18.5240i	−0.0983732	+	0.684201i	−0.978011	+	0.208556i	$0.933124\pi$
$734$	44.0543	−	28.3120i	1.62607	−	1.04501i
$735$	−12.5714	−	25.7135i	−0.463703	−	0.948457i
$736$	2.25545	+	2.06833i	0.0831370	+	0.0762396i
$737$	19.5609			0.720535
$738$	−5.46130	−	8.49795i	−0.201033	−	0.312814i
$739$	0.635306	−	4.41865i	0.0233701	−	0.162543i	−0.974794	−	0.223106i	$-0.928381\pi$
$739$	0.635306	−	4.41865i	0.0233701	−	0.162543i	0.998164	+	0.0605630i	$0.0192896\pi$
$740$	−43.1578	−	19.7095i	−1.58651	−	0.724536i
$741$	0.839700	−	0.246558i	0.0308472	−	0.00905754i
$742$	−6.11257	+	4.70264i	−0.224399	+	0.172639i
$743$	2.86049	−	2.47863i	0.104941	−	0.0909320i	−0.600810	−	0.799392i	$-0.705155\pi$
$743$	2.86049	−	2.47863i	0.104941	−	0.0909320i	0.705751	+	0.708460i	$0.250610\pi$
$744$	6.39467	+	44.4759i	0.234440	+	1.63056i
$745$	−7.64472	+	26.0355i	−0.280081	+	0.953868i
$746$	58.9489	+	51.0795i	2.15827	+	1.87015i
$747$	3.22322	+	2.07144i	0.117931	+	0.0757899i
$748$	49.3192	−	76.7421i	1.80329	−	2.80597i
$749$	1.99261	+	1.05423i	0.0728085	+	0.0385209i
$750$	19.0594	−	64.9102i	0.695949	−	2.37018i
$751$	31.8637	−	4.58131i	1.16272	−	0.167175i	0.466181	−	0.884689i	$-0.345630\pi$
$751$	31.8637	−	4.58131i	1.16272	−	0.167175i	0.696543	+	0.717515i	$0.254720\pi$
$752$	−25.2611	+	21.8889i	−0.921178	+	0.798205i
$753$	15.6468	−	7.14565i	0.570201	−	0.260402i
$754$	−5.12013	−	17.4376i	−0.186464	−	0.635039i
$755$	22.6531	−	49.6034i	0.824431	−	1.80525i
$756$	−10.7133	+	0.908141i	−0.389639	+	0.0330288i
$757$	14.4593	+	22.4991i	0.525533	+	0.817745i	0.997974	−	0.0636172i	$-0.0202637\pi$
$757$	14.4593	+	22.4991i	0.525533	+	0.817745i	−0.472442	+	0.881362i	$0.656627\pi$
$758$			30.7275i			1.11607i
$759$	15.4577	−	6.53997i	0.561080	−	0.237386i
$760$	17.3253			0.628456
$761$	14.5403	+	22.6252i	0.527087	+	0.820163i	0.998078	−	0.0619748i	$-0.0197399\pi$
$761$	14.5403	+	22.6252i	0.527087	+	0.820163i	−0.470991	+	0.882138i	$0.656103\pi$
$762$	14.2427	+	2.04779i	0.515957	+	0.0741834i
$763$	−19.2925	−	3.93154i	−0.698434	−	0.142331i
$764$	−1.16148	−	3.95563i	−0.0420208	−	0.143110i
$765$	−10.8949	−	23.8566i	−0.393908	−	0.862537i
$766$	−35.5090	−	40.9795i	−1.28299	−	1.48065i
$767$	1.20916	+	8.40986i	0.0436601	+	0.303663i
$768$	9.13093	−	31.0971i	0.329484	−	1.12212i
$769$	20.0116	−	23.0946i	0.721636	−	0.832813i	−0.269866	−	0.962898i	$-0.586980\pi$
$769$	20.0116	−	23.0946i	0.721636	−	0.832813i	0.991503	+	0.130085i	$0.0415250\pi$
$770$	−31.4282	+	87.7746i	−1.13259	+	3.16318i
$771$	−2.34481	−	1.50692i	−0.0844462	−	0.0542703i
$772$	18.7251	−	21.6099i	0.673930	−	0.777757i
$773$	26.6922	+	7.83754i	0.960052	+	0.281897i	0.723966	−	0.689835i	$-0.242317\pi$
$773$	26.6922	+	7.83754i	0.960052	+	0.281897i	0.236086	+	0.971732i	$0.424135\pi$
$774$	−23.3501	+	3.35723i	−0.839300	+	0.120673i
$775$	78.3068	−	67.8532i	2.81286	−	2.43736i
$776$	7.50844	+	16.4412i	0.269537	+	0.590204i
$777$	6.58225	−	3.70750i	0.236137	−	0.133006i
$778$	−0.141572	−	0.0646539i	−0.00507561	−	0.00231796i
$779$	−3.38547	−	0.486757i	−0.121297	−	0.0174399i
$780$	14.6722	−	9.42924i	0.525349	−	0.337621i
$781$		−	49.5396i		−	1.77267i
$782$	−39.1430	−	64.8512i	−1.39975	−	2.31907i
$783$		−	7.03132i		−	0.251279i
$784$	15.9154	−	26.2602i	0.568407	−	0.937864i
$785$	−0.138164	+	0.960950i	−0.00493127	+	0.0342978i
$786$	−17.5087	+	38.3388i	−0.624516	+	1.36750i
$787$	−20.3528	+	5.97612i	−0.725499	+	0.213026i	−0.623572	−	0.781766i	$-0.714319\pi$
$787$	−20.3528	+	5.97612i	−0.725499	+	0.213026i	−0.101927	+	0.994792i	$0.532501\pi$
$788$	32.2333	+	70.5810i	1.14826	+	2.51434i
$789$	8.46080	+	9.76428i	0.301212	+	0.347618i
$790$	−39.3232	+	5.65383i	−1.39906	+	0.201154i
$791$	2.29983	−	39.4481i	0.0817724	−	1.40261i
$792$	13.4415	+	11.6471i	0.477624	+	0.413863i
$793$	1.55739	−	2.42334i	0.0553045	−	0.0860555i
$794$	−30.4058	+	47.3124i	−1.07906	+	1.67905i
$795$	3.16965	−	3.65797i	0.112416	−	0.129735i
$796$	71.8420	+	21.0947i	2.54637	+	0.747682i
$797$	−7.04394	−	48.9917i	−0.249509	−	1.73537i	−0.601058	−	0.799205i	$-0.705254\pi$
$797$	−7.04394	−	48.9917i	−0.249509	−	1.73537i	0.351549	−	0.936169i	$-0.385655\pi$
$798$	−3.19780	+	4.39109i	−0.113201	+	0.155443i
$799$	44.4575	−	20.3031i	1.57279	−	0.718271i
$800$	7.17495	−	2.10675i	0.253673	−	0.0744850i
$801$	−2.01354	+	4.40903i	−0.0711448	+	0.155785i
$802$	−2.01507	−	0.289723i	−0.0711545	−	0.0102305i
$803$	−8.95505	+	5.75506i	−0.316017	+	0.203092i
$804$	22.7132			0.801033
$805$	36.1323	+	37.2316i	1.27350	+	1.31224i
$806$	22.8530			0.804962
$807$	−3.18708	+	2.04821i	−0.112190	+	0.0721004i
$808$	29.5292	+	4.24566i	1.03883	+	0.149362i
$809$	17.4801	−	38.2761i	0.614568	−	1.34572i	−0.304837	−	0.952405i	$-0.598602\pi$
$809$	17.4801	−	38.2761i	0.614568	−	1.34572i	0.919405	−	0.393312i	$-0.128671\pi$
$810$	9.66088	−	2.83669i	0.339449	−	0.0996711i
$811$	5.32438	−	2.43156i	0.186964	−	0.0853838i	−0.319733	−	0.947508i	$-0.603593\pi$
$811$	5.32438	−	2.43156i	0.186964	−	0.0853838i	0.506698	+	0.862124i	$0.330866\pi$
$812$	61.1112	+	44.5040i	2.14458	+	1.56178i
$813$	2.73534	+	19.0247i	0.0959325	+	0.667225i
$814$	−23.6109	−	6.93279i	−0.827563	−	0.242994i
$815$	10.2552	−	11.8351i	0.359224	−	0.414567i
$816$	15.2119	−	23.6701i	0.532522	−	0.828620i
$817$	−4.31832	+	6.71944i	−0.151079	+	0.235084i
$818$	25.4123	+	22.0199i	0.888521	+	0.769908i
$819$	−0.161628	+	2.77235i	−0.00564774	+	0.0968738i
$820$	−67.4691	+	9.70059i	−2.35612	+	0.338759i
$821$	−31.4556	−	36.3017i	−1.09781	−	1.26694i	−0.961062	−	0.276331i	$-0.910881\pi$
$821$	−31.4556	−	36.3017i	−1.09781	−	1.26694i	−0.136745	−	0.990606i	$-0.543664\pi$
$822$	15.3094	+	33.5229i	0.533977	+	1.16925i
$823$	33.4762	−	9.82951i	1.16691	−	0.342635i	0.359795	−	0.933031i	$-0.382847\pi$
$823$	33.4762	−	9.82951i	1.16691	−	0.342635i	0.807114	+	0.590396i	$0.201028\pi$
$824$	−0.616553	+	1.35006i	−0.0214786	+	0.0470316i
$825$	5.83680	−	40.5958i	0.203211	−	1.41337i
$826$	−37.7785	−	36.7966i	−1.31448	−	1.28032i
$827$		−	19.1418i		−	0.665626i	−0.942993	−	0.332813i	$-0.892002\pi$
$827$		−	19.1418i		−	0.665626i	0.942993	−	0.332813i	$-0.107998\pi$
$828$	17.9488	−	7.59391i	0.623764	−	0.263907i
$829$			43.6250i			1.51516i	0.652743	+	0.757579i	$0.273618\pi$
$829$			43.6250i			1.51516i	−0.652743	+	0.757579i	$0.726382\pi$
$830$	32.4537	−	20.8567i	1.12649	−	0.723948i
$831$	21.7084	+	3.12120i	0.753056	+	0.108273i
$832$	−6.87631	−	3.14031i	−0.238393	−	0.108871i
$833$	−33.1466	+	30.2858i	−1.14846	+	1.04934i
$834$	16.1569	+	35.3787i	0.559468	+	1.22506i
$835$	−69.4973	+	60.2197i	−2.40505	+	2.08399i
$836$	11.7374	−	1.68758i	0.405946	−	0.0583662i
$837$	8.48355	+	2.49100i	0.293234	+	0.0861014i
$838$	−19.7251	+	22.7640i	−0.681393	+	0.786370i
$839$	−3.23339	−	2.07797i	−0.111629	−	0.0717396i	0.483635	−	0.875270i	$-0.339316\pi$
$839$	−3.23339	−	2.07797i	−0.111629	−	0.0717396i	−0.595264	+	0.803530i	$0.702953\pi$
$840$	−18.5328	+	51.7595i	−0.639443	+	1.78587i
$841$	−13.3850	+	15.4472i	−0.461553	+	0.532660i
$842$	3.33911	−	11.3720i	0.115073	−	0.391904i
$843$	−2.55450	−	17.7669i	−0.0879816	−	0.611925i
$844$	36.2245	+	41.8053i	1.24690	+	1.43900i
$845$	20.2102	+	44.2541i	0.695251	+	1.52239i
$846$	5.28626	+	18.0033i	0.181745	+	0.618968i
$847$	−0.659519	+	3.23632i	−0.0226613	+	0.111201i
$848$	5.13985	+	0.738998i	0.176503	+	0.0253773i
$849$	−6.25750	−	9.73686i	−0.214757	−	0.334168i
$850$	−185.096			−6.34873
$851$	−9.25528	+	10.0926i	−0.317267	+	0.345970i
$852$		−	57.5231i		−	1.97071i
$853$	15.0582	+	23.4311i	0.515584	+	0.802265i	0.997252	−	0.0740894i	$-0.0236050\pi$
$853$	15.0582	+	23.4311i	0.515584	+	0.802265i	−0.481667	+	0.876354i	$0.659969\pi$
$854$	1.51025	+	17.8163i	0.0516796	+	0.609662i
$855$	1.41622	−	3.10110i	0.0484339	−	0.106055i
$856$	−1.21993	−	4.15469i	−0.0416962	−	0.142004i
$857$	−7.95087	+	3.63104i	−0.271597	+	0.124034i	−0.546558	−	0.837421i	$-0.684062\pi$
$857$	−7.95087	+	3.63104i	−0.271597	+	0.124034i	0.274961	+	0.961455i	$0.411335\pi$
$858$	6.83634	−	5.92373i	0.233389	−	0.202233i
$859$	41.4981	−	5.96652i	1.41590	−	0.203575i	0.608485	−	0.793565i	$-0.291777\pi$
$859$	41.4981	−	5.96652i	1.41590	−	0.203575i	0.807410	+	0.589990i	$0.200868\pi$
$860$	−44.8465	+	152.733i	−1.52925	+	5.20816i
$861$	5.07561	−	9.59343i	0.172976	−	0.326943i
$862$	16.9717	−	26.4085i	0.578060	−	0.899478i
$863$	10.8442	+	6.96915i	0.369141	+	0.237232i	0.712039	−	0.702140i	$-0.247772\pi$
$863$	10.8442	+	6.96915i	0.369141	+	0.237232i	−0.342898	+	0.939373i	$0.611408\pi$
$864$	0.482246	+	0.417869i	0.0164064	+	0.0142162i
$865$	−7.06777	+	24.0706i	−0.240312	+	0.818426i
$866$	3.29394	+	22.9099i	0.111933	+	0.778509i
$867$	−18.2448	+	15.8092i	−0.619627	+	0.536910i
$868$	−75.3456	+	57.9664i	−2.55740	+	1.96751i
$869$	−13.2495	+	3.89039i	−0.449457	+	0.131973i
$870$	−64.3988	−	29.4099i	−2.18332	−	0.997090i
$871$	0.834903	−	5.80688i	0.0282896	−	0.196759i
$872$	20.4463	+	31.8151i	0.692399	+	1.07739i
$873$	3.55661			0.120373
$874$	3.03889	−	9.36582i	0.102792	−	0.316804i
$875$	70.8150	−	16.3842i	2.39398	−	0.553886i
$876$	−10.3982	+	6.68251i	−0.351322	+	0.225781i
$877$	−4.71525	+	32.7953i	−0.159223	+	1.10742i	0.740848	+	0.671673i	$0.234424\pi$
$877$	−4.71525	+	32.7953i	−0.159223	+	1.10742i	−0.900070	+	0.435745i	$0.856485\pi$
$878$	−28.1457	−	12.8537i	−0.949871	−	0.433791i
$879$	2.42844	+	8.27052i	0.0819094	+	0.278958i
$880$	57.1008	−	26.0771i	1.92487	−	0.879058i
$881$	4.07663	+	4.70468i	0.137345	+	0.158505i	0.820255	−	0.571998i	$-0.193831\pi$
$881$	4.07663	+	4.70468i	0.137345	+	0.158505i	−0.682910	+	0.730502i	$0.739286\pi$
$882$	−9.69774	−	14.2506i	−0.326540	−	0.479841i
$883$	2.65150	+	0.778551i	0.0892301	+	0.0262003i	0.326043	−	0.945355i	$-0.394285\pi$
$883$	2.65150	+	0.778551i	0.0892301	+	0.0262003i	−0.236813	+	0.971555i	$0.576103\pi$
$884$	−20.6767	−	17.9165i	−0.695434	−	0.602597i
$885$	27.8437	+	17.8940i	0.935955	+	0.601502i
$886$	24.0072	+	15.4285i	0.806537	+	0.518330i
$887$	1.37000	+	1.18712i	0.0460002	+	0.0398594i	0.677558	−	0.735470i	$-0.263038\pi$
$887$	1.37000	+	1.18712i	0.0460002	+	0.0398594i	−0.631557	+	0.775329i	$0.717584\pi$
$888$	−13.9231	−	4.08818i	−0.467227	−	0.137190i
$889$	5.59298	+	14.4129i	0.187583	+	0.483395i
$890$	31.9596	+	36.8833i	1.07129	+	1.23633i
$891$	3.18350	−	1.45385i	0.106651	−	0.0487060i
$892$	11.4645	+	39.0444i	0.383858	+	1.30730i
$893$	5.77900	+	2.63918i	0.193387	+	0.0883168i
$894$	−2.32564	+	16.1752i	−0.0777811	+	0.540979i
$895$	−0.933925	+	0.600197i	−0.0312177	+	0.0200624i
$896$	49.0038	−	11.3378i	1.63710	−	0.378769i
$897$	−1.28169	−	4.86794i	−0.0427945	−	0.162536i
$898$	−67.0466			−2.23737
$899$	−33.6110	−	52.2998i	−1.12099	−	1.74430i
$900$	6.77742	−	47.1380i	0.225914	−	1.57127i
$901$	−6.90660	−	3.15414i	−0.230092	−	0.105080i
$902$	−33.9209	+	9.96008i	−1.12944	+	0.331635i
$903$	−15.4551	−	20.0888i	−0.514313	−	0.668512i
$904$	−57.3619	+	49.7044i	−1.90783	+	1.65314i
$905$	4.58560	+	31.8935i	0.152430	+	1.06018i
$906$	9.25232	−	31.5105i	0.307388	−	1.04687i
$907$	18.4479	+	15.9852i	0.612553	+	0.530780i	0.904951	−	0.425517i	$-0.139908\pi$
$907$	18.4479	+	15.9852i	0.612553	+	0.530780i	−0.292398	+	0.956297i	$0.594453\pi$
$908$	59.3479	+	38.1406i	1.96953	+	1.26574i
$909$	3.17374	−	4.93844i	0.105266	−	0.163798i
$910$	24.7155	+	13.0762i	0.819310	+	0.433473i
$911$	−7.95191	+	27.0817i	−0.263458	+	0.897257i	0.716421	+	0.697668i	$0.245779\pi$
$911$	−7.95191	+	27.0817i	−0.263458	+	0.897257i	−0.979880	+	0.199589i	$0.936039\pi$
$912$	3.62024	−	0.520512i	0.119878	−	0.0172359i
$913$	10.1340	−	8.78114i	0.335386	−	0.290613i
$914$	19.2872	−	8.80815i	0.637962	−	0.291348i
$915$	−3.16150	−	10.7671i	−0.104516	−	0.355948i
$916$	−14.6104	+	31.9924i	−0.482743	+	1.05706i
$917$	−45.1228	+	3.82495i	−1.49009	+	0.126311i
$918$	−8.53925	−	13.2873i	−0.281837	−	0.438547i
$919$			7.69829i			0.253943i	0.991906	+	0.126972i	$0.0405257\pi$
$919$			7.69829i			0.253943i	−0.991906	+	0.126972i	$0.959474\pi$
$920$	2.80484	−	99.6155i	0.0924729	−	3.28423i
$921$	5.25022			0.173001
$922$	−40.1203	−	62.4283i	−1.32129	−	2.05597i
$923$	−14.7064	−	2.11446i	−0.484067	−	0.0695983i
$924$	−7.51375	+	36.8707i	−0.247184	+	1.21296i
$925$	9.42723	+	32.1062i	0.309965	+	1.05565i
$926$	−9.30394	−	20.3728i	−0.305746	−	0.669491i
$927$	0.191252	+	0.220716i	0.00628153	+	0.00724927i
$928$	−0.638526	−	4.44104i	−0.0209606	−	0.145784i
$929$	10.7142	−	36.4891i	0.351520	−	1.19717i	−0.574122	−	0.818770i	$-0.694657\pi$
$929$	10.7142	−	36.4891i	0.351520	−	1.19717i	0.925643	−	0.378399i	$-0.123525\pi$
$930$	58.2988	−	67.2804i	1.91169	−	2.20621i
$931$	−5.79685	−	0.678219i	−0.189984	−	0.0222277i
$932$	67.3469	+	43.2812i	2.20602	+	1.41772i
$933$	10.7134	−	12.3639i	0.350739	−	0.404775i
$934$	23.9708	+	7.03845i	0.784347	+	0.230305i
$935$	−90.8529	+	13.0627i	−2.97121	+	0.427195i
$936$	4.03130	−	3.49314i	0.131767	−	0.114177i
$937$	−23.8632	−	52.2530i	−0.779576	−	1.70703i	−0.704335	−	0.709867i	$-0.748755\pi$
$937$	−23.8632	−	52.2530i	−0.779576	−	1.70703i	−0.0752403	−	0.997165i	$-0.523972\pi$
$938$	17.8707	+	31.7274i	0.583499	+	1.03594i
$939$	13.4254	+	6.13117i	0.438121	+	0.200083i
$940$	125.323	+	18.0187i	4.08757	+	0.587704i
$941$	−28.2816	+	18.1755i	−0.921954	+	0.592504i	−0.913224	−	0.407458i	$-0.866415\pi$
$941$	−28.2816	+	18.1755i	−0.921954	+	0.592504i	−0.00873005	+	0.999962i	$0.502779\pi$
$942$			0.584671i			0.0190496i
$943$	−3.34679	+	19.3867i	−0.108987	+	0.631316i
$944$			35.5084i			1.15570i
$945$	7.74962	+	7.54821i	0.252095	+	0.245543i
$946$	−11.7495	+	81.7197i	−0.382010	+	2.65694i
$947$	−14.0037	+	30.6639i	−0.455060	+	0.996442i	0.533526	+	0.845784i	$0.320867\pi$
$947$	−14.0037	+	30.6639i	−0.455060	+	0.996442i	−0.988586	+	0.150659i	$0.951861\pi$
$948$	−15.3847	+	4.51735i	−0.499671	+	0.146717i
$949$	1.32623	+	2.90405i	0.0430514	+	0.0942694i
$950$	−15.7562	−	18.1837i	−0.511200	−	0.589956i
$951$	−14.4970	+	2.08435i	−0.470098	+	0.0675898i
$952$	86.0961	+	5.01941i	2.79039	+	0.162680i
$953$	−43.5445	−	37.7315i	−1.41054	−	1.22224i	−0.940587	−	0.339553i	$-0.889724\pi$
$953$	−43.5445	−	37.7315i	−1.41054	−	1.22224i	−0.469956	−	0.882690i	$-0.655730\pi$
$954$	1.57594	−	2.45221i	0.0510229	−	0.0793931i
$955$	−2.24263	+	3.48960i	−0.0725698	+	0.112921i
$956$	−32.3399	+	37.3223i	−1.04595	+	1.20709i
$957$	−23.6112	−	6.93287i	−0.763241	−	0.224108i
$958$	−7.15775	−	49.7833i	−0.231257	−	1.60842i
$959$	−23.3098	+	32.0081i	−0.752712	+	1.03359i
$960$	−26.7870	+	12.2332i	−0.864545	+	0.394825i
$961$	45.2647	−	13.2909i	1.46015	−	0.428740i
$962$	−3.06585	+	6.71327i	−0.0988469	+	0.216444i
$963$	−0.843377	−	0.121259i	−0.0271774	−	0.00390753i
$964$	−43.2881	+	27.8196i	−1.39421	+	0.896008i
$965$	−28.7706			−0.926160
$966$	24.7298	+	19.0973i	0.795667	+	0.614444i
$967$	−42.3700			−1.36253			−0.681264	−	0.732038i	$-0.738569\pi$
$967$	−42.3700			−1.36253			−0.681264	+	0.732038i	$0.738569\pi$
$968$	5.33700	−	3.42988i	0.171538	−	0.110241i
$969$	−5.29350	−	0.761090i	−0.170052	−	0.0244497i
$970$	14.8762	−	32.5744i	0.477647	−	1.04590i
$971$	57.3051	−	16.8263i	1.83901	−	0.539981i	0.839016	−	0.544107i	$-0.183132\pi$
$971$	57.3051	−	16.8263i	1.83901	−	0.539981i	0.999991	+	0.00412632i	$0.00131345\pi$
$972$	3.69653	−	1.68815i	0.118566	−	0.0541474i
$973$	−24.6001	+	33.7800i	−0.788644	+	1.08294i
$974$	3.57999	+	24.8994i	0.114710	+	0.797827i
$975$	−11.8022	−	3.46544i	−0.377973	−	0.110983i
$976$	7.88380	−	9.09839i	0.252354	−	0.291232i
$977$	−11.5556	+	17.9808i	−0.369695	+	0.575257i	−0.975403	−	0.220430i	$-0.929254\pi$
$977$	−11.5556	+	17.9808i	−0.369695	+	0.575257i	0.605707	+	0.795688i	$0.292890\pi$
$978$	5.09885	−	7.93396i	0.163043	−	0.253700i
$979$	12.8202	+	11.1087i	0.409735	+	0.355037i
$980$	−114.654	+	19.5786i	−3.66248	+	0.625415i
$981$	7.36599	−	1.05907i	0.235178	−	0.0338135i
$982$	−9.85601	−	11.3744i	−0.314518	−	0.362973i
$983$	−4.50064	−	9.85503i	−0.143548	−	0.314327i	0.824178	−	0.566331i	$-0.191638\pi$
$983$	−4.50064	−	9.85503i	−0.143548	−	0.314327i	−0.967726	+	0.252004i	$0.918910\pi$
$984$	−20.0027	+	5.87333i	−0.637664	+	0.187235i
$985$	32.4324	−	71.0171i	1.03338	−	2.26279i
$986$	−15.8051	+	109.927i	−0.503338	+	3.50079i
$987$	−14.0663	+	14.4417i	−0.447736	+	0.459683i
$988$		−	3.55640i		−	0.113144i
$989$	37.9357	+	25.9169i	1.20628	+	0.824109i
$990$		−	35.2382i		−	1.11994i
$991$	20.5735	−	13.2218i	0.653539	−	0.420004i	−0.171419	−	0.985198i	$-0.554835\pi$
$991$	20.5735	−	13.2218i	0.653539	−	0.420004i	0.824958	+	0.565194i	$0.191199\pi$
$992$	5.58449	+	0.802929i	0.177308	+	0.0254930i
$993$	23.8071	+	10.8723i	0.755495	+	0.345023i
$994$	80.3523	−	45.2590i	2.54862	−	1.43553i
$995$	−31.2963	−	68.5294i	−0.992161	−	2.17253i
$996$	11.7671	−	10.1963i	0.372855	−	0.323081i
$997$	15.9419	−	2.29210i	0.504885	−	0.0725916i	0.114834	−	0.993385i	$-0.463366\pi$
$997$	15.9419	−	2.29210i	0.504885	−	0.0725916i	0.390051	+	0.920793i	$0.372457\pi$
$998$	−36.1347	−	10.6101i	−1.14383	−	0.335857i
$999$	−1.86986	+	2.15794i	−0.0591599	+	0.0682742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.r.a.34.4	yes	320
7.6	odd	2	inner	483.2.r.a.34.3	✓	320
23.21	odd	22	inner	483.2.r.a.412.3	yes	320
161.90	even	22	inner	483.2.r.a.412.4	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.34.3	✓	320	7.6	odd	2	inner
483.2.r.a.34.4	yes	320	1.1	even	1	trivial
483.2.r.a.412.3	yes	320	23.21	odd	22	inner
483.2.r.a.412.4	yes	320	161.90	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.07156 + 1.33131i) q^{2} +(0.989821 + 0.142315i) q^{3} +(1.68815 - 3.69653i) q^{4} +(-3.92324 + 1.15197i) q^{5} +(-2.23994 + 1.02295i) q^{6} +(-2.13872 - 1.55752i) q^{7} +(0.723239 + 5.03024i) q^{8} +(0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(-2.07156 + 1.33131i) q^{2} +(0.989821 + 0.142315i) q^{3} +(1.68815 - 3.69653i) q^{4} +(-3.92324 + 1.15197i) q^{5} +(-2.23994 + 1.02295i) q^{6} +(-2.13872 - 1.55752i) q^{7} +(0.723239 + 5.03024i) q^{8} +(0.959493 + 0.281733i) q^{9} +(6.59362 - 7.60944i) q^{10} +(1.89212 - 2.94419i) q^{11} +(2.19704 - 3.41866i) q^{12} +(-0.793257 - 0.687361i) q^{13} +(6.50404 + 0.379186i) q^{14} +(-4.04725 + 0.581907i) q^{15} +(-2.87265 - 3.31522i) q^{16} +(2.66454 + 5.83452i) q^{17} +(-2.36272 + 0.693758i) q^{18} +(-0.346361 + 0.758424i) q^{19} +(-2.36473 + 16.4471i) q^{20} +(-1.89530 - 1.84604i) q^{21} +8.61807i q^{22} +(4.30464 + 2.11425i) q^{23} +5.08197i q^{24} +(9.85854 - 6.33570i) q^{25} +(2.55837 + 0.367839i) q^{26} +(0.909632 + 0.415415i) q^{27} +(-9.36790 + 5.27654i) q^{28} +(-2.92092 - 6.39592i) q^{29} +(7.60944 - 6.59362i) q^{30} +(8.75171 - 1.25831i) q^{31} +(0.612256 + 0.179774i) q^{32} +(2.29186 - 2.64495i) q^{33} +(-13.2873 - 8.53925i) q^{34} +(10.1849 + 3.64678i) q^{35} +(2.66120 - 3.07119i) q^{36} +(-0.804448 + 2.73970i) q^{37} +(-0.292192 - 2.03224i) q^{38} +(-0.687361 - 0.793257i) q^{39} +(-8.63212 - 18.9017i) q^{40} +(1.15572 + 3.93602i) q^{41} +(6.38388 + 1.30095i) q^{42} +(9.48236 + 1.36336i) q^{43} +(-7.68912 - 11.9645i) q^{44} -4.08887 q^{45} +(-11.7321 + 1.35101i) q^{46} -7.61974i q^{47} +(-2.37161 - 3.69030i) q^{48} +(2.14828 + 6.66220i) q^{49} +(-11.9878 + 26.2496i) q^{50} +(1.80708 + 6.15434i) q^{51} +(-3.87999 + 1.77193i) q^{52} +(-0.894616 + 0.775190i) q^{53} +(-2.43741 + 0.350446i) q^{54} +(-4.03162 + 13.7304i) q^{55} +(6.28788 - 11.8847i) q^{56} +(-0.450770 + 0.701412i) q^{57} +(14.5658 + 9.36089i) q^{58} +(-6.11750 - 5.30085i) q^{59} +(-4.68133 + 15.9431i) q^{60} +(0.390573 + 2.71650i) q^{61} +(-16.4545 + 14.2579i) q^{62} +(-1.61329 - 2.09698i) q^{63} +(6.91028 - 2.02904i) q^{64} +(3.90396 + 1.78288i) q^{65} +(-1.22648 + 8.53035i) q^{66} +(3.02175 + 4.70194i) q^{67} +26.0656 q^{68} +(3.95994 + 2.70535i) q^{69} +(-25.9538 + 6.00481i) q^{70} +(11.9080 - 7.65284i) q^{71} +(-0.723239 + 5.03024i) q^{72} +(-2.76674 - 1.26353i) q^{73} +(-1.98093 - 6.74643i) q^{74} +(10.6599 - 4.86820i) q^{75} +(2.21883 + 2.56067i) q^{76} +(-8.63234 + 3.34980i) q^{77} +(2.47998 + 0.728189i) q^{78} +(-2.98192 - 2.58385i) q^{79} +(15.0891 + 9.69721i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-7.63422 - 6.61509i) q^{82} +(3.67625 + 1.07944i) q^{83} +(-10.0235 + 3.88964i) q^{84} +(-17.1748 - 19.8208i) q^{85} +(-21.4584 + 9.79971i) q^{86} +(-1.98095 - 6.74651i) q^{87} +(16.1784 + 7.38844i) q^{88} +(-0.689807 + 4.79771i) q^{89} +(8.47035 - 5.44357i) q^{90} +(0.625980 + 2.70559i) q^{91} +(15.0823 - 12.3431i) q^{92} +8.84170 q^{93} +(10.1443 + 15.7848i) q^{94} +(0.485177 - 3.37448i) q^{95} +(0.580439 + 0.265078i) q^{96} +(3.41254 - 1.00201i) q^{97} +(-13.3198 - 10.9411i) q^{98} +(2.64495 - 2.29186i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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