LMFDB - Embedded newform 483.2.r.a.412.3

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			412.3
Character	$\chi$	$=$	483.412
Dual form			483.2.r.a.34.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.07156 - 1.33131i) q^{2} +(-0.989821 + 0.142315i) q^{3} +(1.68815 + 3.69653i) q^{4} +(3.92324 + 1.15197i) q^{5} +(2.23994 + 1.02295i) q^{6} +(1.23729 - 2.33861i) q^{7} +(0.723239 - 5.03024i) q^{8} +(0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(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} +(1.23729 - 2.33861i) 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} +(-5.67655 + 3.19736i) 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} +(-0.891879 + 2.49089i) 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} +(10.7335 + 0.625763i) 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} +(7.54821 - 7.74962i) 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} +(5.16374 - 3.97267i) 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} +(-3.93822 - 5.78709i) 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} +(-10.8689 - 7.91525i) 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} +(0.528310 - 2.59247i) 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} +(9.22642 - 0.782102i) 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} +(-10.7133 + 0.908141i) 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} +(0.453830 + 17.2313i) 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 $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{22}\right)$

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	−0.998384	−	0.0568231i	$-0.981903\pi$
$2$	−2.07156	−	1.33131i	−1.46482	−	0.941380i	−0.466432	−	0.884557i	$-0.654461\pi$
$3$	−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	$-0.0418329\pi$
$5$	3.92324	+	1.15197i	1.75453	+	0.515176i	0.763151	+	0.646220i	$0.223651\pi$
$6$	2.23994	+	1.02295i	0.914453	+	0.417617i
$7$	1.23729	−	2.33861i	0.467653	−	0.883912i
$7$	1.23729	−	2.33861i	0.467653	−	0.883912i
$8$	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	0.999881	−	0.0154141i	$-0.00490665\pi$
$11$	1.89212	+	2.94419i	0.570494	+	0.887707i	−0.429387	+	0.903121i	$0.641270\pi$
$12$	−2.19704	−	3.41866i	−0.634230	−	0.986881i
$13$	0.793257	−	0.687361i	0.220010	−	0.190640i	−0.537881	−	0.843021i	$-0.680775\pi$
$13$	0.793257	−	0.687361i	0.220010	−	0.190640i	0.757891	+	0.652381i	$0.226230\pi$
$14$	−5.67655	+	3.19736i	−1.51712	+	0.854530i
$15$	−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	0.248558	+	0.968617i	$0.420043\pi$
$17$	−2.66454	+	5.83452i	−0.646245	+	1.41508i	−0.894803	+	0.446462i	$0.852684\pi$
$18$	−2.36272	−	0.693758i	−0.556899	−	0.163520i
$19$	0.346361	+	0.758424i	0.0794606	+	0.173994i	0.945193	−	0.326514i	$-0.105874\pi$
$19$	0.346361	+	0.758424i	0.0794606	+	0.173994i	−0.865732	+	0.500508i	$0.833147\pi$
$20$	2.36473	+	16.4471i	0.528771	+	3.67768i
$21$	−0.891879	+	2.49089i	−0.194624	+	0.543558i
$22$		−	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
$28$	10.7335	+	0.625763i	2.02844	+	0.118258i
$29$	−2.92092	+	6.39592i	−0.542401	+	1.18769i	0.417841	+	0.908520i	$0.362787\pi$
$29$	−2.92092	+	6.39592i	−0.542401	+	1.18769i	−0.960241	+	0.279172i	$0.909940\pi$
$30$	7.60944	+	6.59362i	1.38929	+	1.20382i
$31$	−8.75171	−	1.25831i	−1.57185	−	0.225998i	−0.699412	−	0.714718i	$-0.746555\pi$
$31$	−8.75171	−	1.25831i	−1.57185	−	0.225998i	−0.872441	+	0.488720i	$0.837464\pi$
$32$	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
$35$	7.54821	−	7.74962i	1.27588	−	1.30993i
$36$	2.66120	+	3.07119i	0.443533	+	0.511865i
$37$	−0.804448	−	2.73970i	−0.132251	−	0.450404i	0.866565	−	0.499064i	$-0.166323\pi$
$37$	−0.804448	−	2.73970i	−0.132251	−	0.450404i	−0.998815	+	0.0486606i	$0.984505\pi$
$38$	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	0.818688	+	0.574239i	$0.194702\pi$
$41$	−1.15572	+	3.93602i	−0.180493	+	0.614703i	−0.999181	+	0.0404645i	$0.987116\pi$
$42$	5.16374	−	3.97267i	0.796783	−	0.612997i
$43$	9.48236	−	1.36336i	1.44605	−	0.207910i	0.625829	−	0.779961i	$-0.284761\pi$
$43$	9.48236	−	1.36336i	1.44605	−	0.207910i	0.820218	+	0.572050i	$0.193852\pi$
$44$	−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
$49$	−3.93822	−	5.78709i	−0.562602	−	0.826728i
$50$	−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	0.591250	−	0.806488i	$-0.298634\pi$
$53$	−0.894616	−	0.775190i	−0.122885	−	0.106480i	−0.714135	+	0.700008i	$0.753180\pi$
$54$	2.43741	+	0.350446i	0.331689	+	0.0476897i
$55$	4.03162	+	13.7304i	0.543623	+	1.85141i
$56$	−10.8689	−	7.91525i	−1.45242	−	1.05772i
$57$	−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	$-0.550621\pi$
$59$	6.11750	−	5.30085i	0.796431	−	0.690111i	0.954794	+	0.297270i	$0.0960760\pi$
$60$	−4.68133	−	15.9431i	−0.604357	−	2.05825i
$61$	−0.390573	+	2.71650i	−0.0500078	+	0.347812i	0.949421	+	0.314007i	$0.101672\pi$
$61$	−0.390573	+	2.71650i	−0.0500078	+	0.347812i	−0.999428	+	0.0338048i	$0.989238\pi$
$62$	16.4545	+	14.2579i	2.08973	+	1.81076i
$63$	0.528310	−	2.59247i	0.0665608	−	0.326620i
$64$	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	−0.606122	−	0.795372i	$-0.707276\pi$
$67$	3.02175	−	4.70194i	0.369166	−	0.574433i	0.975288	+	0.220939i	$0.0709121\pi$
$68$	−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	0.999997	−	0.00240311i	$-0.000764933\pi$
$71$	11.9080	+	7.65284i	1.41322	+	0.908225i	0.413228	+	0.910628i	$0.364401\pi$
$72$	−0.723239	−	5.03024i	−0.0852346	−	0.592819i
$73$	2.76674	−	1.26353i	0.323822	−	0.147885i	−0.246870	−	0.969049i	$-0.579402\pi$
$73$	2.76674	−	1.26353i	0.323822	−	0.147885i	0.570692	+	0.821164i	$0.306675\pi$
$74$	−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
$77$	9.22642	−	0.782102i	1.05145	−	0.0891288i
$78$	2.47998	−	0.728189i	0.280803	−	0.0824512i
$79$	−2.98192	+	2.58385i	−0.335492	+	0.290705i	−0.806272	−	0.591545i	$-0.798518\pi$
$79$	−2.98192	+	2.58385i	−0.335492	+	0.290705i	0.470780	+	0.882251i	$0.343973\pi$
$80$	−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	$-0.658346\pi$
$83$	−3.67625	+	1.07944i	−0.403521	+	0.118484i	0.0736732	+	0.997282i	$0.476528\pi$
$84$	−10.7133	+	0.908141i	−1.16892	+	0.0990863i
$85$	−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	0.993163	+	0.116739i	$0.0372442\pi$
$89$	0.689807	+	4.79771i	0.0731194	+	0.508556i	−0.920043	+	0.391817i	$0.871847\pi$
$90$	−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	$-0.466882\pi$
$97$	−3.41254	−	1.00201i	−0.346491	−	0.101739i	−0.450347	+	0.892853i	$0.648700\pi$
$98$	0.453830	+	17.2313i	0.0458437	+	1.74063i
$99$	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	−0.999942	−	0.0107808i	$-0.996568\pi$
$101$	−1.65387	−	5.63255i	−0.164566	−	0.560460i	0.835376	−	0.549679i	$-0.185250\pi$
$102$	−11.9368	+	10.3433i	−1.18192	+	1.02414i
$103$	−0.245688	+	0.157894i	−0.0242083	+	0.0155577i	−0.552689	−	0.833388i	$-0.686398\pi$
$103$	−0.245688	+	0.157894i	−0.0242083	+	0.0155577i	0.528481	+	0.848945i	$0.322762\pi$
$104$	−2.88388	−	4.48740i	−0.282787	−	0.440025i
$105$	−6.36849	+	8.74497i	−0.621501	+	0.853421i
$106$	0.821235	+	2.79687i	0.0797654	+	0.271656i
$107$	−0.843377	−	0.121259i	−0.0815323	−	0.0117226i	0.101428	−	0.994843i	$-0.467659\pi$
$107$	−0.843377	−	0.121259i	−0.0815323	−	0.0117226i	−0.182960	+	0.983120i	$0.558568\pi$
$108$	−3.07119	−	2.66120i	−0.295525	−	0.256074i
$109$	6.76924	+	3.09141i	0.648376	+	0.296103i	0.712325	−	0.701850i	$-0.247642\pi$
$109$	6.76924	+	3.09141i	0.648376	+	0.296103i	−0.0639491	+	0.997953i	$0.520370\pi$
$110$	9.92775	−	33.8108i	0.946573	−	3.22373i
$111$	1.18616	+	2.59733i	0.112585	+	0.246528i
$112$	4.19870	+	10.8199i	0.396740	+	1.02239i
$113$	8.07463	−	12.5644i	0.759597	−	1.18196i	−0.218910	−	0.975745i	$-0.570250\pi$
$113$	8.07463	−	12.5644i	0.759597	−	1.18196i	0.978507	−	0.206211i	$-0.0661135\pi$
$114$			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
$119$	10.3479	+	13.4503i	0.948588	+	1.23299i
$120$	−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
$126$	−4.54581	+	4.66711i	−0.404973	+	0.415780i
$127$	−4.91575	+	3.15916i	−0.436202	+	0.280330i	−0.740257	−	0.672324i	$-0.765296\pi$
$127$	−4.91575	+	3.15916i	−0.436202	+	0.280330i	0.304054	+	0.952655i	$0.401660\pi$
$128$	−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	$-0.541576\pi$
$131$	−12.9354	−	11.2086i	−1.13017	−	0.979298i	−0.999926	+	0.0121838i	$0.996122\pi$
$132$	5.90813	−	12.9370i	0.514236	−	1.12602i
$133$	2.20221	+	0.128389i	0.190956	+	0.0111327i
$134$	−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	$0.220782\pi$
$137$			14.9660i			1.27863i	−0.768945	+	0.639315i	$0.779218\pi$
$138$	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	$-0.233635\pi$
$140$	41.3892	+	14.8197i	3.49803	+	1.25249i
$141$	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
$147$	4.72172	+	5.16772i	0.389441	+	0.426227i
$148$	8.76936	−	7.59869i	0.720837	−	0.624609i
$149$	3.58782	+	5.58275i	0.293925	+	0.457357i	0.956539	−	0.291605i	$-0.0941892\pi$
$149$	3.58782	+	5.58275i	0.293925	+	0.457357i	−0.662614	+	0.748961i	$0.730553\pi$
$150$	15.6015	+	24.2764i	1.27386	+	1.98216i
$151$	−8.73356	−	10.0791i	−0.710727	−	0.820223i	0.279433	−	0.960165i	$-0.409854\pi$
$151$	−8.73356	−	10.0791i	−0.710727	−	0.820223i	−0.990160	+	0.139943i	$0.955308\pi$
$152$	4.06556	−	1.19376i	0.329760	−	0.0968263i
$153$	−0.912829	+	6.34887i	−0.0737979	+	0.513276i
$154$	−20.1543	−	10.6631i	−1.62408	−	0.859255i
$155$	−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	$-0.139380\pi$
$157$	−0.0986331	−	0.215976i	−0.00787177	−	0.0172368i	−0.913527	+	0.406778i	$0.866652\pi$
$158$	9.61714	−	1.38274i	0.765098	−	0.110005i
$159$	0.995831	+	0.639982i	0.0789746	+	0.0507539i
$160$	2.60912			0.206269
$161$	0.381677	−	12.6828i	0.0300804	−	0.999547i
$162$	−2.46247			−0.193470
$163$	−3.22195	−	2.07062i	−0.252363	−	0.162184i	0.408343	−	0.912828i	$-0.366107\pi$
$163$	−3.22195	−	2.07062i	−0.252363	−	0.162184i	−0.660706	+	0.750645i	$0.729743\pi$
$164$	−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	$-0.699620\pi$
$167$	−20.4575	−	9.34262i	−1.58305	−	0.722954i	−0.996229	+	0.0867648i	$0.972347\pi$
$168$	11.8847	+	6.28788i	0.916928	+	0.485120i
$169$	−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	$-0.256749\pi$
$173$	−3.31704	−	5.16142i	−0.252190	−	0.392415i	−0.944148	+	0.329523i	$0.893112\pi$
$174$	−13.0854	+	11.3385i	−0.992000	+	0.859573i
$175$	27.0146	−	15.2162i	2.04212	−	1.15024i
$176$	−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	0.291454	−	0.956585i	$-0.405861\pi$
$179$	0.260510	+	0.0764925i	0.0194714	+	0.00571732i	−0.271982	+	0.962302i	$0.587679\pi$
$180$	6.90263	+	15.1146i	0.514491	+	1.12658i
$181$	−1.12148	−	7.80008i	−0.0833591	−	0.579775i	−0.988100	−	0.153813i	$-0.950845\pi$
$181$	−1.12148	−	7.80008i	−0.0833591	−	0.579775i	0.904741	−	0.425962i	$-0.140064\pi$
$182$	−2.30522	+	6.43817i	−0.170875	+	0.477229i
$183$		−	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
$189$	−0.153986	+	2.64127i	−0.0112008	+	0.192124i
$190$	3.48741	−	7.63637i	0.253004	−	0.554001i
$191$	0.766696	+	0.664346i	0.0554762	+	0.0480704i	0.682158	−	0.731205i	$-0.261042\pi$
$191$	0.766696	+	0.664346i	0.0554762	+	0.0480704i	−0.626681	+	0.779276i	$0.715587\pi$
$192$	−7.12871	−	1.02495i	−0.514470	−	0.0739697i
$193$	6.75131	−	1.98236i	0.485970	−	0.142694i	−0.0295640	−	0.999563i	$-0.509412\pi$
$193$	6.75131	−	1.98236i	0.485970	−	0.142694i	0.515534	+	0.856869i	$0.327594\pi$
$194$	5.73530	+	6.61889i	0.411770	+	0.475208i
$195$	−3.61049	+	2.32032i	−0.258553	+	0.166162i
$196$	14.7439	−	24.3272i	1.05313	−	1.73766i
$197$	−12.5038	−	14.4302i	−0.890860	−	1.02811i	−0.999421	−	0.0340171i	$-0.989170\pi$
$197$	−12.5038	−	14.4302i	−0.890860	−	1.02811i	0.108562	−	0.994090i	$-0.465376\pi$
$198$	−2.42799	−	8.26898i	−0.172550	−	0.587651i
$199$	−2.62215	+	18.2375i	−0.185880	+	1.29282i	0.656660	+	0.754186i	$0.271969\pi$
$199$	−2.62215	+	18.2375i	−0.185880	+	1.29282i	−0.842540	+	0.538634i	$0.818941\pi$
$200$	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
$203$	11.3435	+	14.7445i	0.796161	+	1.03486i
$204$	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
$210$	24.8350	−	9.63730i	1.71378	−	0.665037i
$211$	−5.65466	−	12.3820i	−0.389283	−	0.852411i	−0.998245	−	0.0592120i	$-0.981141\pi$
$211$	−5.65466	−	12.3820i	−0.389283	−	0.852411i	0.608962	−	0.793199i	$-0.291586\pi$
$212$	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
$217$	−13.7711	+	18.9100i	−0.934844	+	1.28369i
$218$	−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	$-0.163897\pi$
$223$	7.56773	+	6.55747i	0.506773	+	0.439121i	−0.363571	+	0.931567i	$0.618442\pi$
$224$	0.337116	−	1.65426i	0.0225245	−	0.110530i
$225$	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	0.891041	+	0.453924i	$0.149976\pi$
$227$	2.47059	+	17.1833i	0.163978	+	1.14050i	−0.727062	+	0.686572i	$0.759115\pi$
$228$	1.83183	−	2.85038i	0.121316	−	0.188771i
$229$	8.65471			0.571920			0.285960	−	0.958242i	$-0.407688\pi$
$229$	8.65471			0.571920			0.285960	+	0.958242i	$0.407688\pi$
$230$	−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	−0.847997	−	0.530001i	$-0.822192\pi$
$233$	−2.80358	−	19.4993i	−0.183668	−	1.27744i	0.664329	−	0.747440i	$-0.268717\pi$
$234$	−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
$238$	−3.52968	−	41.6394i	−0.228795	−	2.69908i
$239$	−11.6601	+	3.42372i	−0.754231	+	0.221462i	−0.636175	−	0.771545i	$-0.719484\pi$
$239$	−11.6601	+	3.42372i	−0.754231	+	0.221462i	−0.118056	+	0.993007i	$0.537666\pi$
$240$	13.5555	−	11.7459i	0.875004	−	0.758195i
$241$	10.6522	−	6.84576i	0.686169	−	0.440974i	−0.150553	−	0.988602i	$-0.548105\pi$
$241$	10.6522	−	6.84576i	0.686169	−	0.440974i	0.836722	+	0.547628i	$0.184469\pi$
$242$	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
$245$	−8.78403	−	27.2409i	−0.561191	−	1.74036i
$246$	−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	$-0.500843\pi$
$251$	−14.4706	−	9.29969i	−0.913376	−	0.586991i	−0.910729	+	0.413006i	$0.864479\pi$
$252$	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	$-0.608657\pi$
$257$	2.53540	−	1.15788i	0.158154	−	0.0722264i	0.492919	+	0.870075i	$0.335930\pi$
$258$	22.6346	+	6.64612i	1.40917	+	0.413769i
$259$	−7.40243	−	1.50852i	−0.459965	−	0.0937346i
$260$	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	−0.299617	−	0.954059i	$-0.596859\pi$
$263$	9.76428	−	8.46080i	0.602091	−	0.521715i	0.901709	+	0.432344i	$0.142314\pi$
$264$	−14.9623	+	9.61567i	−0.920864	+	0.591803i
$265$	−2.61680	−	4.07183i	−0.160749	−	0.250130i
$266$	−4.39109	−	3.19780i	−0.269235	−	0.196069i
$267$	−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	$-0.235882\pi$
$269$	2.86314	+	2.48093i	0.174569	+	0.151265i	−0.563194	+	0.826325i	$0.690428\pi$
$270$	9.15884	+	4.18270i	0.557389	+	0.254551i
$271$	−5.41499	+	18.4418i	−0.328937	+	1.12026i	0.614558	+	0.788872i	$0.289334\pi$
$271$	−5.41499	+	18.4418i	−0.328937	+	1.12026i	−0.943495	+	0.331386i	$0.892484\pi$
$272$	−11.6884	−	25.5941i	−0.708715	−	1.55187i
$273$	1.00465	+	2.58896i	0.0608044	+	0.156691i
$274$	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
$280$	−33.5233	−	43.5741i	−2.00340	−	2.60405i
$281$	−5.05699	+	17.2225i	−0.301675	+	1.02741i	0.659554	+	0.751657i	$0.270745\pi$
$281$	−5.05699	+	17.2225i	−0.301675	+	1.02741i	−0.961229	+	0.275753i	$0.911073\pi$
$282$	7.79460	−	17.0678i	0.464162	−	1.01637i
$283$	7.57951	−	8.74722i	0.450555	−	0.519968i	−0.484346	−	0.874877i	$-0.660942\pi$
$283$	7.57951	−	8.74722i	0.450555	−	0.519968i	0.934901	+	0.354908i	$0.115488\pi$
$284$	−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
$287$	7.77487	+	7.57279i	0.458936	+	0.447008i
$288$	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	$-0.944653\pi$
$293$	−3.58074	+	7.84074i	−0.209189	+	0.458061i	0.775732	+	0.631062i	$0.217381\pi$
$294$	−2.90148	−	16.9913i	−0.169218	−	0.990956i
$295$	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
$301$	8.54409	−	23.8624i	0.492473	−	1.37541i
$302$	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	$-0.502416\pi$
$307$	−5.19678	−	0.747184i	−0.296596	−	0.0426441i	−0.289007	+	0.957327i	$0.593325\pi$
$308$	18.4666	+	32.7854i	1.05223	+	1.86812i
$309$	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	$-0.335346\pi$
$311$	−8.84474	−	13.7627i	−0.501539	−	0.780410i	−0.996053	+	0.0887594i	$0.971710\pi$
$312$	3.49314	+	4.03130i	0.197760	+	0.228228i
$313$	−14.1613	+	4.15813i	−0.800444	+	0.235031i	−0.656275	−	0.754522i	$-0.727869\pi$
$313$	−14.1613	+	4.15813i	−0.800444	+	0.235031i	−0.144169	+	0.989553i	$0.546051\pi$
$314$	−0.0832074	+	0.578720i	−0.00469566	+	0.0326591i
$315$	5.05913	−	9.56229i	0.285050	−	0.538774i
$316$	−14.5852	−	6.66083i	−0.820481	−	0.374701i
$317$	−14.0528	−	4.12628i	−0.789285	−	0.231755i	−0.137843	−	0.990454i	$-0.544017\pi$
$317$	−14.0528	−	4.12628i	−0.789285	−	0.231755i	−0.651441	+	0.758699i	$0.725835\pi$
$318$	−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
$322$	−17.6755	+	25.7652i	−0.985016	+	1.43584i
$323$	−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
$329$	−17.8196	−	9.42785i	−0.982428	−	0.519774i
$330$	−5.01492	+	34.8795i	−0.276062	+	1.92005i
$331$	25.1121	−	7.37357i	1.38028	−	0.405288i	0.494416	−	0.869225i	$-0.335382\pi$
$331$	25.1121	−	7.37357i	1.38028	−	0.405288i	0.885868	+	0.463937i	$0.153564\pi$
$332$	−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
$336$	−5.69580	−	10.1123i	−0.310731	−	0.551668i
$337$	−26.0036	−	3.73875i	−1.41651	−	0.203663i	−0.608836	−	0.793296i	$-0.708363\pi$
$337$	−26.0036	−	3.73875i	−1.41651	−	0.203663i	−0.807671	+	0.589633i	$0.799272\pi$
$338$	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
$343$	−18.4065	+	2.04963i	−0.993857	+	0.110670i
$344$		−	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	−0.110136	−	0.993916i	$-0.535129\pi$
$347$	−19.7454	−	12.6896i	−1.05999	−	0.681212i	−0.949851	+	0.312704i	$0.898765\pi$
$348$	28.2828	−	4.06646i	1.51612	−	0.217985i
$349$	4.33089	−	1.97785i	0.231827	−	0.105872i	−0.296115	−	0.955152i	$-0.595691\pi$
$349$	4.33089	−	1.97785i	0.231827	−	0.105872i	0.527942	+	0.849280i	$0.322964\pi$
$350$	−76.2201	−	4.44363i	−4.07413	−	0.237522i
$351$	−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	$-0.850953\pi$
$353$	−35.2417	−	5.06700i	−1.87573	−	0.269689i	−0.983366	+	0.181633i	$0.941862\pi$
$354$	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
$357$	−12.1567	−	11.8408i	−0.643402	−	0.626680i
$358$	−0.437826	−	0.505279i	−0.0231398	−	0.0267048i
$359$	−9.67814	−	32.9607i	−0.510793	−	1.73960i	−0.660457	−	0.750864i	$-0.729637\pi$
$359$	−9.67814	−	32.9607i	−0.510793	−	1.73960i	0.149664	−	0.988737i	$-0.452181\pi$
$360$	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
$364$	8.94454	−	6.88139i	0.468821	−	0.360683i
$365$	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	$-0.312702\pi$
$367$	21.2662			1.11009			0.555043	+	0.831821i	$0.312702\pi$
$368$	−5.35653	+	20.3443i	−0.279228	+	1.06052i
$369$			4.10219i			0.213552i
$370$	−15.5434	+	24.1859i	−0.808060	+	1.25737i
$371$	−2.91977	+	1.13302i	−0.151587	+	0.0588237i
$372$	14.9261	+	32.6836i	0.773883	+	1.69457i
$373$	−8.92408	+	30.3926i	−0.462071	+	1.57367i	0.318070	+	0.948067i	$0.396965\pi$
$373$	−8.92408	+	30.3926i	−0.462071	+	1.57367i	−0.780141	+	0.625603i	$0.784853\pi$
$374$	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
$378$	3.83534	−	5.26655i	0.197269	−	0.270882i
$379$	6.74628	+	10.4974i	0.346533	+	0.539216i	0.970147	−	0.242516i	$-0.0779727\pi$
$379$	6.74628	+	10.4974i	0.346533	+	0.539216i	−0.623614	+	0.781732i	$0.714336\pi$
$380$	−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	0.738260	+	0.674516i	$0.235648\pi$
$383$	−3.13378	+	21.7959i	−0.160128	+	1.11372i	−0.898388	+	0.439202i	$0.855261\pi$
$384$	14.3675	+	12.4495i	0.733190	+	0.635313i
$385$	37.0984	+	7.56016i	1.89071	+	0.385302i
$386$	−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	−0.840386	−	0.541988i	$-0.817672\pi$
$389$	0.0341704	−	0.0531702i	0.00173251	−	0.00269584i	0.842119	+	0.539292i	$0.181308\pi$
$390$	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	$-0.557907\pi$
$397$	−20.7751	−	9.48766i	−1.04267	−	0.476172i	−0.861754	+	0.507326i	$0.830634\pi$
$398$	29.7117	−	34.2892i	1.48931	−	1.71876i
$399$	−2.19807	+	0.186325i	−0.110041	+	0.00932792i
$400$	−49.3244	+	14.4830i	−2.46622	+	0.724148i
$401$	0.624798	−	0.541390i	0.0312009	−	0.0270357i	−0.639121	−	0.769106i	$-0.720702\pi$
$401$	0.624798	−	0.541390i	0.0312009	−	0.0270357i	0.670322	+	0.742071i	$0.266156\pi$
$402$	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
$406$	−3.86930	−	45.6460i	−0.192030	−	2.26537i
$407$	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	−0.808047	−	0.589118i	$-0.799475\pi$
$409$	3.84709	−	13.1020i	0.190226	−	0.647852i	0.998274	−	0.0587340i	$-0.0187064\pi$
$410$	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	$-0.505673\pi$
$419$	−11.7366	−	3.44617i	−0.573369	−	0.168356i	−0.555548	+	0.831485i	$0.687491\pi$
$420$	−43.0770	−	8.77851i	−2.10194	−	0.428348i
$421$	−3.63748	−	3.15189i	−0.177280	−	0.153614i	0.561701	−	0.827340i	$-0.310147\pi$
$421$	−3.63748	−	3.15189i	−0.177280	−	0.153614i	−0.738981	+	0.673726i	$0.764693\pi$
$422$	−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
$427$	5.86958	+	4.27450i	0.284049	+	0.206858i
$428$	−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	0.116069	−	0.993241i	$-0.462971\pi$
$431$	−11.5961	−	5.29576i	−0.558564	−	0.255088i	−0.674633	+	0.738153i	$0.735698\pi$
$432$	1.23587	−	4.20897i	0.0594606	−	0.202504i
$433$	−3.90460	−	8.54988i	−0.187643	−	0.410881i	0.792307	−	0.610122i	$-0.208880\pi$
$433$	−3.90460	−	8.54988i	−0.187643	−	0.410881i	−0.979951	+	0.199241i	$0.936152\pi$
$434$	53.7028	−	20.8395i	2.57782	−	1.00033i
$435$	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	$-0.915120\pi$
$439$	−6.79334	+	10.5706i	−0.324229	+	0.504510i	0.640429	+	0.768018i	$0.278757\pi$
$440$	71.9832	−	10.3496i	3.43166	−	0.493399i
$441$	−5.40910	−	4.44315i	−0.257576	−	0.211579i
$442$	4.67072	−	15.9070i	0.222163	−	0.756619i
$443$	−4.81421	+	10.5417i	−0.228730	+	0.500849i	−0.988847	−	0.148938i	$-0.952415\pi$
$443$	−4.81421	+	10.5417i	−0.228730	+	0.500849i	0.760116	+	0.649787i	$0.225142\pi$
$444$	−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
$448$	13.2952	−	13.6500i	0.628138	−	0.644900i
$449$	22.9051	−	14.7202i	1.08096	−	0.694690i	0.126180	−	0.992007i	$-0.459728\pi$
$449$	22.9051	−	14.7202i	1.08096	−	0.694690i	0.954779	+	0.297318i	$0.0960920\pi$
$450$	−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
$455$	0.660877	−	11.3358i	0.0309824	−	0.531430i
$456$	−3.85429	+	1.76019i	−0.180494	+	0.0824286i
$457$	−8.52291	+	1.22541i	−0.398685	+	0.0573223i	−0.338741	−	0.940879i	$-0.610001\pi$
$457$	−8.52291	+	1.22541i	−0.398685	+	0.0573223i	−0.0599437	+	0.998202i	$0.519092\pi$
$458$	−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	$0.752387\pi$
$462$	21.4667	+	7.68628i	0.998721	+	0.357598i
$463$	−1.29438	−	9.00265i	−0.0601552	−	0.418388i	−0.997540	−	0.0700941i	$-0.977670\pi$
$463$	−1.29438	−	9.00265i	−0.0601552	−	0.418388i	0.937385	−	0.348294i	$-0.113239\pi$
$464$	−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	$-0.697305\pi$
$467$	6.64382	−	7.66738i	0.307439	−	0.354804i	0.888353	+	0.459161i	$0.151850\pi$
$468$	4.22203	+	0.607036i	0.195163	+	0.0280603i
$469$	−7.25722	−	12.8844i	−0.335107	−	0.594945i
$470$	−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
$476$	−32.2508	+	60.9574i	−1.47821	+	2.79398i
$477$	−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	0.998373	+	0.0570285i	$0.0181626\pi$
$479$	8.48472	+	18.5789i	0.387677	+	0.848894i	−0.610696	+	0.791865i	$0.709110\pi$
$480$	−2.58257	+	0.371317i	−0.117877	+	0.0169482i
$481$	−2.52130	−	1.62034i	−0.114961	−	0.0738811i
$482$	−31.1806			−1.42024
$483$	1.42716	+	12.6081i	0.0649382	+	0.573687i
$484$	−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	0.981081	−	0.193596i	$-0.0620152\pi$
$487$	4.24368	+	9.29236i	0.192299	+	0.421077i	−0.788782	+	0.614673i	$0.789288\pi$
$488$	13.3822	+	3.92935i	0.605782	+	0.177874i
$489$	3.48383	+	1.59101i	0.157544	+	0.0719481i
$490$	−18.0695	+	68.1255i	−0.816295	+	3.07760i
$491$	0.869824	−	6.04976i	0.0392546	−	0.273022i	−0.960736	−	0.277466i	$-0.910505\pi$
$491$	0.869824	−	6.04976i	0.0392546	−	0.273022i	0.999990	+	0.00444402i	$0.00141458\pi$
$492$	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
$497$	32.6307	−	18.3795i	1.46369	−	0.824434i
$498$	−9.33880	−	1.34272i	−0.418482	−	0.0601686i
$499$	10.0152	−	11.5582i	0.448343	−	0.517416i	−0.485918	−	0.874004i	$-0.661515\pi$
$499$	10.0152	−	11.5582i	0.448343	−	0.517416i	0.934262	+	0.356589i	$0.116060\pi$
$500$	−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	0.746113	+	0.665820i	$0.231918\pi$
$503$	4.88488	+	33.9751i	0.217806	+	1.51487i	−0.528307	+	0.849054i	$0.677173\pi$
$504$	−12.6586	−	4.53250i	−0.563860	−	0.201894i
$505$		−	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	$-0.584529\pi$
$509$	−5.46892	+	0.786312i	−0.242406	+	0.0348527i	0.0200410	+	0.999799i	$0.493620\pi$
$510$	−58.7462	+	26.8285i	−2.60133	+	1.18799i
$511$	0.468364	−	8.03368i	0.0207192	−	0.355389i
$512$	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
$518$	13.3263	+	12.9799i	0.585524	+	0.570306i
$519$	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	−0.950579	−	0.310483i	$-0.899509\pi$
$521$	1.11772	−	7.77390i	0.0489681	−	0.340581i	0.999547	−	0.0300976i	$-0.00958180\pi$
$522$	11.3385	−	13.0854i	0.496275	−	0.572731i
$523$	1.85402	−	4.05974i	0.0810707	−	0.177520i	−0.864756	−	0.502193i	$-0.832527\pi$
$523$	1.85402	−	4.05974i	0.0810707	−	0.177520i	0.945826	+	0.324673i	$0.105254\pi$
$524$	19.5960	−	66.7378i	0.856055	−	2.91546i
$525$	−24.5742	+	18.9059i	−1.07251	+	0.825121i
$526$	−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
$532$	3.24307	+	8.35728i	0.140605	+	0.362334i
$533$	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
$539$	9.58674	−	22.5447i	0.412930	−	0.971069i
$540$	−8.98341	−	13.9785i	−0.386584	−	0.601537i
$541$	4.85765	−	3.12182i	0.208847	−	0.134218i	−0.432036	−	0.901856i	$-0.642205\pi$
$541$	4.85765	−	3.12182i	0.208847	−	0.134218i	0.640883	+	0.767639i	$0.278568\pi$
$542$	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
$546$	1.36551	−	6.70070i	0.0584386	−	0.286764i
$547$	−38.2630	−	11.2350i	−1.63601	−	0.480375i	−0.670751	−	0.741682i	$-0.734028\pi$
$547$	−38.2630	−	11.2350i	−1.63601	−	0.480375i	−0.965256	+	0.261307i	$0.915846\pi$
$548$	−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	0.445100	+	0.895481i	$0.353168\pi$
$557$	−9.75837	+	33.2340i	−0.413475	+	1.40817i	−0.858575	+	0.512687i	$0.828650\pi$
$558$	19.8049	+	9.04460i	0.838409	+	0.382888i
$559$	6.58483	−	7.59930i	0.278509	−	0.321416i
$560$	4.00832	+	47.2859i	0.169382	+	1.99820i
$561$	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	$-0.576916\pi$
$563$	12.9198	−	8.30304i	0.544504	−	0.349931i	0.783798	+	0.621016i	$0.213280\pi$
$564$	−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
$567$	−0.223473	−	2.63630i	−0.00938498	−	0.110714i
$568$	47.1080	−	54.3655i	1.97661	−	2.28112i
$569$	32.2808	+	14.7422i	1.35328	+	0.618023i	0.954277	−	0.298925i	$-0.0966282\pi$
$569$	32.2808	+	14.7422i	1.35328	+	0.618023i	0.399006	+	0.916949i	$0.369355\pi$
$570$	−2.36515	+	8.05495i	−0.0990651	+	0.337385i
$571$	−41.9278	+	19.1478i	−1.75462	+	0.801310i	−0.767561	+	0.640976i	$0.778530\pi$
$571$	−41.9278	+	19.1478i	−1.75462	+	0.801310i	−0.987063	+	0.160334i	$0.948743\pi$
$572$	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	$-0.814353\pi$
$577$	0.312442	−	0.486170i	0.0130071	−	0.0202395i	0.847696	+	0.530482i	$0.177989\pi$
$578$	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
$581$	−2.02419	+	9.93291i	−0.0839777	+	0.412086i
$582$	−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	−0.970031	−	0.242983i	$-0.921874\pi$
$587$	−19.0939	−	29.7107i	−0.788090	−	1.22629i	0.181940	−	0.983310i	$-0.441762\pi$
$588$	−11.1317	+	26.1779i	−0.459063	+	1.07956i
$589$	−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	−0.324720	−	0.945810i	$-0.605270\pi$
$593$	11.1968	−	38.1326i	0.459795	−	1.56592i	0.784515	−	0.620109i	$-0.212912\pi$
$594$	3.58008	+	7.83927i	0.146892	+	0.321649i
$595$	25.1029	+	64.6893i	1.02912	+	2.65200i
$596$	−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	$-0.309948\pi$
$601$	32.7194	−	4.70434i	1.33465	−	0.191894i	0.772434	+	0.635095i	$0.219039\pi$
$602$	−49.4680	+	38.0577i	−2.01617	+	1.55112i
$603$	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	$-0.165853\pi$
$607$	−3.23837	−	11.0289i	−0.131441	−	0.447648i	−0.998742	+	0.0501361i	$0.984034\pi$
$608$	0.348407	+	0.402083i	0.0141298	+	0.0163066i
$609$	−13.3264	−	12.9801i	−0.540015	−	0.525979i
$610$	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	0.383146	−	0.923688i	$-0.374841\pi$
$613$	12.1452	+	1.74621i	0.490539	+	0.0705288i	0.107393	+	0.994217i	$0.465750\pi$
$614$	9.77072	+	8.46638i	0.394314	+	0.341675i
$615$	6.96789	−	15.2576i	0.280973	−	0.615244i
$616$	2.73875	−	46.9767i	0.110347	−	1.89275i
$617$	35.2783	−	16.1110i	1.42025	−	0.648606i	0.450515	−	0.892769i	$-0.351240\pi$
$617$	35.2783	−	16.1110i	1.42025	−	0.648606i	0.969734	+	0.244162i	$0.0785130\pi$
$618$	−0.711843	+	0.102348i	−0.0286345	+	0.00411702i
$619$	−0.160283	−	0.103007i	−0.00644230	−	0.00414022i	0.537416	−	0.843317i	$-0.319401\pi$
$619$	−0.160283	−	0.103007i	−0.00644230	−	0.00414022i	−0.543858	+	0.839177i	$0.683037\pi$
$620$		−	146.916i		−	5.90027i
$621$	−3.03735	+	3.71141i	−0.121884	+	0.148934i
$622$			40.2854i			1.61530i
$623$	12.0735	+	4.32298i	0.483714	+	0.173197i
$624$	−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
$630$	−23.2107	+	13.0736i	−0.924736	+	0.520864i
$631$	−32.8881	+	28.4977i	−1.30925	+	1.13447i	−0.327388	+	0.944890i	$0.606169\pi$
$631$	−32.8881	+	28.4977i	−1.30925	+	1.13447i	−0.981864	+	0.189584i	$0.939286\pi$
$632$	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
$637$	−7.10184	−	1.88368i	−0.281385	−	0.0746340i
$638$	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	−0.309797	−	0.950803i	$-0.600261\pi$
$641$	−8.58720	+	1.23465i	−0.339174	+	0.0487658i	−0.0293764	+	0.999568i	$0.509352\pi$
$642$	−1.76507	−	1.13434i	−0.0696619	−	0.0447690i
$643$	14.0851			0.555463			0.277731	−	0.960659i	$-0.410417\pi$
$643$	14.0851			0.555463			0.277731	+	0.960659i	$0.410417\pi$
$644$	47.5268	−	19.9996i	1.87282	−	0.788096i
$645$	−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	$-0.662933\pi$
$647$	−18.1653	+	2.61178i	−0.714153	+	0.102680i	−0.224345	+	0.974510i	$0.572024\pi$
$648$	−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
$651$	10.9398	−	20.6773i	0.428763	−	0.810408i
$652$	2.21498	−	15.4056i	0.0867455	−	0.603328i
$653$	−19.2402	+	5.64944i	−0.752929	+	0.221080i	−0.635606	−	0.772014i	$-0.719250\pi$
$653$	−19.2402	+	5.64944i	−0.752929	+	0.221080i	−0.117323	+	0.993094i	$0.537431\pi$
$654$	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
$658$	24.3631	+	43.2539i	0.949771	+	1.68621i
$659$	−16.7304	−	2.40547i	−0.651724	−	0.0937038i	−0.191480	−	0.981496i	$-0.561329\pi$
$659$	−16.7304	−	2.40547i	−0.651724	−	0.0937038i	−0.460244	+	0.887793i	$0.652238\pi$
$660$	38.0820	−	43.9490i	1.48234	−	1.71071i
$661$	4.31369	−	9.44566i	0.167783	−	0.367393i	−0.806999	−	0.590553i	$-0.798910\pi$
$661$	4.31369	−	9.44566i	0.167783	−	0.367393i	0.974782	+	0.223159i	$0.0716370\pi$
$662$	−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
$665$	8.49191	+	3.04058i	0.329302	+	0.117909i
$666$			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
$672$	−0.0982590	+	1.68540i	−0.00379042	+	0.0650158i
$673$	−8.49743	+	18.6068i	−0.327552	+	0.717239i	−0.999732	−	0.0231489i	$-0.992631\pi$
$673$	−8.49743	+	18.6068i	−0.327552	+	0.717239i	0.672180	+	0.740388i	$0.265358\pi$
$674$	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	$-0.446616\pi$
$677$	−21.6679	−	25.0061i	−0.832765	−	0.961063i	−0.999690	+	0.0249071i	$0.992071\pi$
$678$	30.9394	−	19.8835i	1.18822	−	0.763623i
$679$	−6.56563	+	6.74082i	−0.251966	+	0.258689i
$680$	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	−0.234164	+	0.972197i	$0.575235\pi$
$683$	−30.3978	+	35.0810i	−1.16314	+	1.34234i	−0.928977	+	0.370139i	$0.879310\pi$
$684$	−1.40753	+	3.08206i	−0.0538182	+	0.117845i
$685$	−17.2403	+	58.7152i	−0.658719	+	2.24339i
$686$	40.8589	+	20.2589i	1.56000	+	0.773487i
$687$	−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
$693$	8.63234	−	3.34980i	0.327916	−	0.127249i
$694$	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
$700$	101.852	+	74.1733i	3.84964	+	2.80349i
$701$	17.7961	+	27.6912i	0.672148	+	1.04588i	0.995043	+	0.0994479i	$0.0317077\pi$
$701$	17.7961	+	27.6912i	0.672148	+	1.04588i	−0.322895	+	0.946435i	$0.604656\pi$
$702$	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
$707$	−15.2187	−	3.10136i	−0.572357	−	0.116639i
$708$	−31.5622	−	9.26749i	−1.18618	−	0.348294i
$709$	5.51109	−	2.51683i	0.206973	−	0.0945215i	−0.309231	−	0.950987i	$-0.600072\pi$
$709$	5.51109	−	2.51683i	0.206973	−	0.0945215i	0.516204	+	0.856465i	$0.327344\pi$
$710$	−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	$-0.0599117\pi$
$719$	39.7983	+	18.1753i	1.48423	+	0.677824i	0.501888	+	0.864933i	$0.332639\pi$
$720$	−11.7459	+	13.5555i	−0.437744	+	0.505184i
$721$	0.0652651	+	0.769929i	0.00243060	+	0.0286736i
$722$	−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	$-0.585836\pi$
$727$	0.824652	−	0.242140i	0.0305847	−	0.00898047i	0.296989	+	0.954881i	$0.404017\pi$
$728$	−14.0625	+	1.19204i	−0.521190	+	0.0441801i
$729$	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	0.978011	+	0.208556i	$0.0668762\pi$
$733$	2.66335	+	18.5240i	0.0983732	+	0.684201i	−0.879637	+	0.475645i	$0.842215\pi$
$734$	−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	0.998164	−	0.0605630i	$-0.0192896\pi$
$739$	0.635306	+	4.41865i	0.0233701	+	0.162543i	−0.974794	+	0.223106i	$0.928381\pi$
$740$	43.1578	−	19.7095i	1.58651	−	0.724536i
$741$	−0.839700	−	0.246558i	−0.0308472	−	0.00905754i
$742$	7.55690	+	1.53999i	0.277422	+	0.0565350i
$743$	2.86049	+	2.47863i	0.104941	+	0.0909320i	0.705751	−	0.708460i	$-0.250610\pi$
$743$	2.86049	+	2.47863i	0.104941	+	0.0909320i	−0.600810	+	0.799392i	$0.705155\pi$
$744$	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
$749$	−1.32708	+	1.82230i	−0.0484905	+	0.0665853i
$750$	19.0594	+	64.9102i	0.695949	+	2.37018i
$751$	31.8637	+	4.58131i	1.16272	+	0.167175i	0.696543	−	0.717515i	$-0.254720\pi$
$751$	31.8637	+	4.58131i	1.16272	+	0.167175i	0.466181	+	0.884689i	$0.345630\pi$
$752$	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
$756$	−10.0235	+	3.88964i	−0.364550	+	0.141465i
$757$	14.4593	−	22.4991i	0.525533	−	0.817745i	−0.472442	−	0.881362i	$-0.656627\pi$
$757$	14.4593	−	22.4991i	0.525533	−	0.817745i	0.997974	+	0.0636172i	$0.0202637\pi$
$758$		−	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	$-0.980260\pi$
$761$	−14.5403	+	22.6252i	−0.527087	+	0.820163i	0.470991	+	0.882138i	$0.343897\pi$
$762$	−14.2427	+	2.04779i	−0.515957	+	0.0741834i
$763$	15.6051	−	12.0057i	0.564944	−	0.434634i
$764$	−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	$-0.413020\pi$
$769$	−20.0116	−	23.0946i	−0.721636	−	0.832813i	−0.991503	+	0.130085i	$0.958475\pi$
$770$	−66.7868	−	65.0510i	−2.40683	−	2.34427i
$771$	−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	$-0.757683\pi$
$773$	−26.6922	+	7.83754i	−0.960052	+	0.281897i	−0.236086	+	0.971732i	$0.575865\pi$
$774$	−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
$777$	7.54177	+	0.439686i	0.270560	+	0.0157736i
$778$	−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
$784$	30.4986	+	3.56827i	1.08924	+	0.127438i
$785$	−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	$-0.285681\pi$
$787$	20.3528	+	5.97612i	0.725499	+	0.213026i	0.101927	+	0.994792i	$0.467499\pi$
$788$	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
$791$	−19.3925	−	34.4292i	−0.689518	−	1.22416i
$792$	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	−0.351549	−	0.936169i	$-0.614345\pi$
$797$	7.04394	−	48.9917i	0.249509	−	1.73537i	0.601058	−	0.799205i	$-0.294746\pi$
$798$	4.80149	+	2.54033i	0.169971	+	0.0899267i
$799$	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
$805$	16.1076	−	49.3182i	0.567720	−	1.73824i
$806$	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	0.919405	+	0.393312i	$0.128671\pi$
$809$	17.4801	+	38.2761i	0.614568	+	1.34572i	−0.304837	+	0.952405i	$0.598602\pi$
$810$	−9.66088	−	2.83669i	−0.339449	−	0.0996711i
$811$	−5.32438	−	2.43156i	−0.186964	−	0.0853838i	0.319733	−	0.947508i	$-0.396407\pi$
$811$	−5.32438	−	2.43156i	−0.186964	−	0.0853838i	−0.506698	+	0.862124i	$0.669134\pi$
$812$	−35.3540	+	66.8227i	−1.24068	+	2.34502i
$813$	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
$819$	−1.36288	−	2.41963i	−0.0476227	−	0.0845488i
$820$	−67.4691	−	9.70059i	−2.35612	−	0.338759i
$821$	−31.4556	+	36.3017i	−1.09781	+	1.26694i	−0.136745	+	0.990606i	$0.543664\pi$
$821$	−31.4556	+	36.3017i	−1.09781	+	1.26694i	−0.961062	+	0.276331i	$0.910881\pi$
$822$	−15.3094	+	33.5229i	−0.533977	+	1.16925i
$823$	33.4762	+	9.82951i	1.16691	+	0.342635i	0.807114	−	0.590396i	$-0.201028\pi$
$823$	33.4762	+	9.82951i	1.16691	+	0.342635i	0.359795	+	0.933031i	$0.382847\pi$
$824$	0.616553	+	1.35006i	0.0214786	+	0.0470316i
$825$	−5.83680	−	40.5958i	−0.203211	−	1.41337i
$826$	−17.7776	+	49.6504i	−0.618562	+	1.72756i
$827$			19.1418i			0.665626i	0.942993	+	0.332813i	$0.107998\pi$
$827$			19.1418i			0.665626i	−0.942993	+	0.332813i	$0.892002\pi$
$828$	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
$833$	44.2584	−	7.55768i	1.53346	−	0.261858i
$834$	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	$-0.660684\pi$
$839$	3.23339	−	2.07797i	0.111629	−	0.0717396i	0.595264	+	0.803530i	$0.297047\pi$
$840$	39.3833	+	38.3597i	1.35885	+	1.32354i
$841$	−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
$847$	2.01396	+	2.61777i	0.0692004	+	0.0899477i
$848$	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	$-0.976395\pi$
$853$	−15.0582	+	23.4311i	−0.515584	+	0.802265i	0.481667	+	0.876354i	$0.340031\pi$
$854$	−6.46851	−	16.6691i	−0.221348	−	0.570406i
$855$	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	$-0.315938\pi$
$857$	7.95087	+	3.63104i	0.271597	+	0.124034i	−0.274961	+	0.961455i	$0.588665\pi$
$858$	6.83634	+	5.92373i	0.233389	+	0.202233i
$859$	−41.4981	−	5.96652i	−1.41590	−	0.203575i	−0.608485	−	0.793565i	$-0.708223\pi$
$859$	−41.4981	−	5.96652i	−1.41590	−	0.203575i	−0.807410	+	0.589990i	$0.799132\pi$
$860$	44.8465	+	152.733i	1.52925	+	5.20816i
$861$	−8.77345	−	6.38923i	−0.298998	−	0.217745i
$862$	16.9717	+	26.4085i	0.578060	+	0.899478i
$863$	10.8442	−	6.96915i	0.369141	−	0.237232i	−0.342898	−	0.939373i	$-0.611408\pi$
$863$	10.8442	−	6.96915i	0.369141	−	0.237232i	0.712039	+	0.702140i	$0.247772\pi$
$864$	−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
$868$	−93.1489	−	18.9825i	−3.16168	−	0.644308i
$869$	−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	−0.900070	−	0.435745i	$-0.856485\pi$
$877$	−4.71525	−	32.7953i	−0.159223	−	1.10742i	0.740848	−	0.671673i	$-0.234424\pi$
$878$	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	$-0.806169\pi$
$881$	−4.07663	+	4.70468i	−0.137345	+	0.158505i	0.682910	+	0.730502i	$0.260714\pi$
$882$	5.29007	+	16.4055i	0.178126	+	0.552401i
$883$	2.65150	−	0.778551i	0.0892301	−	0.0262003i	−0.236813	−	0.971555i	$-0.576103\pi$
$883$	2.65150	−	0.778551i	0.0892301	−	0.0262003i	0.326043	+	0.945355i	$0.394285\pi$
$884$	−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	$-0.736962\pi$
$887$	−1.37000	+	1.18712i	−0.0460002	+	0.0398594i	0.631557	+	0.775329i	$0.282416\pi$
$888$	13.9231	−	4.08818i	0.467227	−	0.137190i
$889$	1.30583	+	15.4048i	0.0437962	+	0.516662i
$890$	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
$903$	−5.06114	+	24.8355i	−0.168424	+	0.826474i
$904$	−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	−0.292398	−	0.956297i	$-0.594453\pi$
$907$	18.4479	−	15.9852i	0.612553	−	0.530780i	0.904951	+	0.425517i	$0.139908\pi$
$908$	−59.3479	+	38.1406i	−1.96953	+	1.26574i
$909$	−3.17374	−	4.93844i	−0.105266	−	0.163798i
$910$	−16.4605	+	22.6030i	−0.545661	+	0.749281i
$911$	−7.95191	−	27.0817i	−0.263458	−	0.897257i	−0.979880	−	0.199589i	$-0.936039\pi$
$911$	−7.95191	−	27.0817i	−0.263458	−	0.897257i	0.716421	−	0.697668i	$-0.245779\pi$
$912$	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
$917$	−42.2174	+	16.3826i	−1.39414	+	0.541000i
$918$	−8.53925	+	13.2873i	−0.281837	+	0.438547i
$919$		−	7.69829i		−	0.253943i	−0.991906	−	0.126972i	$-0.959474\pi$
$919$		−	7.69829i		−	0.253943i	0.991906	−	0.126972i	$-0.0405257\pi$
$920$	−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
$924$	−22.9445	−	29.8237i	−0.754820	−	0.981126i
$925$	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	−0.925643	−	0.378399i	$-0.876475\pi$
$929$	−10.7142	−	36.4891i	−0.351520	−	1.19717i	0.574122	−	0.818770i	$-0.305343\pi$
$930$	−58.2988	−	67.2804i	−1.91169	−	2.20621i
$931$	3.02503	−	4.99126i	0.0991413	−	0.163582i
$932$	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	0.0752403	−	0.997165i	$-0.476028\pi$
$937$	23.8632	−	52.2530i	0.779576	−	1.70703i	0.704335	−	0.709867i	$-0.251245\pi$
$938$	−2.11935	+	36.3524i	−0.0691992	+	1.18695i
$939$	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	$-0.133585\pi$
$941$	28.2816	+	18.1755i	0.921954	+	0.592504i	0.00873005	+	0.999962i	$0.497221\pi$
$942$		−	0.584671i		−	0.0190496i
$943$	3.34679	+	19.3867i	0.108987	+	0.631316i
$944$			35.5084i			1.15570i
$945$	−3.64678	+	10.1849i	−0.118630	+	0.331316i
$946$	−11.7495	−	81.7197i	−0.382010	−	2.65694i
$947$	−14.0037	−	30.6639i	−0.455060	−	0.996442i	−0.988586	−	0.150659i	$-0.951861\pi$
$947$	−14.0037	−	30.6639i	−0.455060	−	0.996442i	0.533526	−	0.845784i	$-0.320867\pi$
$948$	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
$952$	75.1423	−	42.3245i	2.43538	−	1.37174i
$953$	−43.5445	+	37.7315i	−1.41054	+	1.22224i	−0.469956	+	0.882690i	$0.655730\pi$
$953$	−43.5445	+	37.7315i	−1.41054	+	1.22224i	−0.940587	+	0.339553i	$0.889724\pi$
$954$	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
$959$	34.9996	+	18.5173i	1.13020	+	0.597954i
$960$	−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
$966$	13.8288	−	28.0184i	0.444935	−	0.901477i
$967$	−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	$-0.816868\pi$
$971$	−57.3051	−	16.8263i	−1.83901	−	0.539981i	−0.999991	+	0.00412632i	$0.998687\pi$
$972$	−3.69653	−	1.68815i	−0.118566	−	0.0541474i
$973$	−36.9371	−	19.5424i	−1.18415	−	0.626499i
$974$	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	0.605707	−	0.795688i	$-0.292890\pi$
$977$	−11.5556	−	17.9808i	−0.369695	−	0.575257i	−0.975403	+	0.220430i	$0.929254\pi$
$978$	−5.09885	−	7.93396i	−0.163043	−	0.253700i
$979$	−12.8202	+	11.1087i	−0.409735	+	0.355037i
$980$	85.8680	−	78.4571i	2.74295	−	2.50622i
$981$	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	$-0.808362\pi$
$983$	4.50064	−	9.85503i	0.143548	−	0.314327i	0.967726	+	0.252004i	$0.0810897\pi$
$984$	−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
$987$	18.9800	+	6.79589i	0.604139	+	0.216316i
$988$			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	0.824958	−	0.565194i	$-0.191199\pi$
$991$	20.5735	+	13.2218i	0.653539	+	0.420004i	−0.171419	+	0.985198i	$0.554835\pi$
$992$	−5.58449	+	0.802929i	−0.177308	+	0.0254930i
$993$	−23.8071	+	10.8723i	−0.755495	+	0.345023i
$994$	−92.0655	−	5.36742i	−2.92014	−	0.170244i
$995$	−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	$-0.536634\pi$
$997$	−15.9419	−	2.29210i	−0.504885	−	0.0725916i	−0.390051	+	0.920793i	$0.627543\pi$
$998$	−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.412.3	yes	320
7.6	odd	2	inner	483.2.r.a.412.4	yes	320
23.11	odd	22	inner	483.2.r.a.34.4	yes	320
161.34	even	22	inner	483.2.r.a.34.3	✓	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.34.3	✓	320	161.34	even	22	inner
483.2.r.a.34.4	yes	320	23.11	odd	22	inner
483.2.r.a.412.3	yes	320	1.1	even	1	trivial
483.2.r.a.412.4	yes	320	7.6	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-2.07156 - 1.33131i) q^{2} +(-0.989821 + 0.142315i) q^{3} +(1.68815 + 3.69653i) q^{4} +(3.92324 + 1.15197i) q^{5} +(2.23994 + 1.02295i) q^{6} +(1.23729 - 2.33861i) q^{7} +(0.723239 - 5.03024i) q^{8} +(0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(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} +(1.23729 - 2.33861i) 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} +(-5.67655 + 3.19736i) 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} +(-0.891879 + 2.49089i) 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} +(10.7335 + 0.625763i) 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} +(7.54821 - 7.74962i) 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} +(5.16374 - 3.97267i) 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} +(-3.93822 - 5.78709i) 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} +(-10.8689 - 7.91525i) 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} +(0.528310 - 2.59247i) 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} +(9.22642 - 0.782102i) 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} +(-10.7133 + 0.908141i) 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} +(0.453830 + 17.2313i) 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

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