LMFDB - Embedded newform 552.2.j.c.323.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(323,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("552.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.j (of order $2$, degree $1$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.7
Character	$\chi$	$=$	552.323
Dual form			552.2.j.c.323.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28262 - 0.595732i) q^{2} +(-1.03555 - 1.38840i) q^{3} +(1.29021 + 1.52819i) q^{4} +1.31940 q^{5} +(0.501098 + 2.39769i) q^{6} +1.36534i q^{7} +(-0.744447 - 2.72870i) q^{8} +(-0.855283 + 2.87550i) q^{9} +O(q^{10})$	\(q+(-1.28262 - 0.595732i) q^{2} +(-1.03555 - 1.38840i) q^{3} +(1.29021 + 1.52819i) q^{4} +1.31940 q^{5} +(0.501098 + 2.39769i) q^{6} +1.36534i q^{7} +(-0.744447 - 2.72870i) q^{8} +(-0.855283 + 2.87550i) q^{9} +(-1.69228 - 0.786008i) q^{10} -1.33708i q^{11} +(0.785663 - 3.37383i) q^{12} +4.58699i q^{13} +(0.813379 - 1.75121i) q^{14} +(-1.36630 - 1.83185i) q^{15} +(-0.670734 + 3.94336i) q^{16} +4.76435i q^{17} +(2.81003 - 3.17864i) q^{18} -6.45443 q^{19} +(1.70230 + 2.01629i) q^{20} +(1.89564 - 1.41388i) q^{21} +(-0.796543 + 1.71496i) q^{22} -1.00000 q^{23} +(-3.01760 + 3.85928i) q^{24} -3.25919 q^{25} +(2.73261 - 5.88334i) q^{26} +(4.87801 - 1.79024i) q^{27} +(-2.08651 + 1.76158i) q^{28} -4.15227 q^{29} +(0.661147 + 3.16350i) q^{30} +8.95087i q^{31} +(3.20948 - 4.65824i) q^{32} +(-1.85640 + 1.38461i) q^{33} +(2.83828 - 6.11083i) q^{34} +1.80143i q^{35} +(-5.49780 + 2.40295i) q^{36} -2.96579i q^{37} +(8.27855 + 3.84511i) q^{38} +(6.36855 - 4.75004i) q^{39} +(-0.982222 - 3.60024i) q^{40} +6.40374i q^{41} +(-3.27367 + 0.684171i) q^{42} +12.4886 q^{43} +(2.04332 - 1.72511i) q^{44} +(-1.12846 + 3.79393i) q^{45} +(1.28262 + 0.595732i) q^{46} -4.02108 q^{47} +(6.16952 - 3.15230i) q^{48} +5.13584 q^{49} +(4.18029 + 1.94160i) q^{50} +(6.61480 - 4.93371i) q^{51} +(-7.00979 + 5.91816i) q^{52} +9.40100 q^{53} +(-7.32312 - 0.609796i) q^{54} -1.76414i q^{55} +(3.72561 - 1.01643i) q^{56} +(6.68387 + 8.96130i) q^{57} +(5.32577 + 2.47364i) q^{58} -4.77409i q^{59} +(1.03660 - 4.45142i) q^{60} +13.3624i q^{61} +(5.33232 - 11.4805i) q^{62} +(-3.92604 - 1.16776i) q^{63} +(-6.89160 + 4.06274i) q^{64} +6.05206i q^{65} +(3.20590 - 0.670009i) q^{66} +7.21265 q^{67} +(-7.28083 + 6.14699i) q^{68} +(1.03555 + 1.38840i) q^{69} +(1.07317 - 2.31054i) q^{70} -14.4410 q^{71} +(8.48308 + 0.193154i) q^{72} +3.85756 q^{73} +(-1.76681 + 3.80397i) q^{74} +(3.37505 + 4.52504i) q^{75} +(-8.32755 - 9.86360i) q^{76} +1.82558 q^{77} +(-10.9982 + 2.29853i) q^{78} -0.671385i q^{79} +(-0.884965 + 5.20286i) q^{80} +(-7.53698 - 4.91873i) q^{81} +(3.81492 - 8.21354i) q^{82} -6.46804i q^{83} +(4.60644 + 1.07270i) q^{84} +6.28607i q^{85} +(-16.0181 - 7.43988i) q^{86} +(4.29987 + 5.76499i) q^{87} +(-3.64850 + 0.995387i) q^{88} -4.72119i q^{89} +(3.70754 - 4.19389i) q^{90} -6.26281 q^{91} +(-1.29021 - 1.52819i) q^{92} +(12.4273 - 9.26905i) q^{93} +(5.15750 + 2.39549i) q^{94} -8.51596 q^{95} +(-9.79105 + 0.367801i) q^{96} -5.63227 q^{97} +(-6.58730 - 3.05958i) q^{98} +(3.84478 + 1.14358i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9}+O(q^{10}) $ 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9	$ 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{14} + 8 q^{15} - 12 q^{16} + 16 q^{18} + 4 q^{19} + 2 q^{20} - 8 q^{21} + 18 q^{22} - 42 q^{23} - 24 q^{24} + 22 q^{25} - 11 q^{26} - 16 q^{27} + 6 q^{28} - 24 q^{30} + 20 q^{32} + 12 q^{33} + 14 q^{34} + 15 q^{36} + 22 q^{38} - 8 q^{39} + 4 q^{40} + 36 q^{42} + 28 q^{43} - 56 q^{44} + 8 q^{45} - 9 q^{48} - 50 q^{49} - 20 q^{50} + 28 q^{51} - q^{52} - 24 q^{53} - 24 q^{54} + 34 q^{56} - 8 q^{57} - 21 q^{58} + 18 q^{60} + 79 q^{62} + 16 q^{63} + 7 q^{64} + 16 q^{66} - 4 q^{67} - 20 q^{68} - 2 q^{69} - 8 q^{70} - 62 q^{72} + 4 q^{73} - 36 q^{74} - 6 q^{75} + 14 q^{76} - 32 q^{77} - 62 q^{78} + 52 q^{80} + 18 q^{81} + 11 q^{82} + 66 q^{84} + 28 q^{86} + 48 q^{87} - 38 q^{88} - 8 q^{91} - 4 q^{92} + 22 q^{93} + q^{94} + 16 q^{95} - 54 q^{96} + 20 q^{97} - 64 q^{98}+O(q^{100}) $ 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^14 + 8 * q^15 - 12 * q^16 + 16 * q^18 + 4 * q^19 + 2 * q^20 - 8 * q^21 + 18 * q^22 - 42 * q^23 - 24 * q^24 + 22 * q^25 - 11 * q^26 - 16 * q^27 + 6 * q^28 - 24 * q^30 + 20 * q^32 + 12 * q^33 + 14 * q^34 + 15 * q^36 + 22 * q^38 - 8 * q^39 + 4 * q^40 + 36 * q^42 + 28 * q^43 - 56 * q^44 + 8 * q^45 - 9 * q^48 - 50 * q^49 - 20 * q^50 + 28 * q^51 - q^52 - 24 * q^53 - 24 * q^54 + 34 * q^56 - 8 * q^57 - 21 * q^58 + 18 * q^60 + 79 * q^62 + 16 * q^63 + 7 * q^64 + 16 * q^66 - 4 * q^67 - 20 * q^68 - 2 * q^69 - 8 * q^70 - 62 * q^72 + 4 * q^73 - 36 * q^74 - 6 * q^75 + 14 * q^76 - 32 * q^77 - 62 * q^78 + 52 * q^80 + 18 * q^81 + 11 * q^82 + 66 * q^84 + 28 * q^86 + 48 * q^87 - 38 * q^88 - 8 * q^91 - 4 * q^92 + 22 * q^93 + q^94 + 16 * q^95 - 54 * q^96 + 20 * q^97 - 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.28262	−	0.595732i	−0.906946	−	0.421246i
$2$	−1.28262	−	0.595732i	−0.906946	−	0.421246i
$3$	−1.03555	−	1.38840i	−0.597874	−	0.801590i
$3$	−1.03555	−	1.38840i	−0.597874	−	0.801590i
$4$	1.29021	+	1.52819i	0.645103	+	0.764095i
$5$	1.31940			0.590053			0.295026	−	0.955489i	$-0.404672\pi$
$5$	1.31940			0.590053			0.295026	+	0.955489i	$0.404672\pi$
$6$	0.501098	+	2.39769i	0.204572	+	0.978851i
$7$			1.36534i			0.516051i	0.966138	+	0.258026i	$0.0830719\pi$
$7$			1.36534i			0.516051i	−0.966138	+	0.258026i	$0.916928\pi$
$8$	−0.744447	−	2.72870i	−0.263202	−	0.964741i
$9$	−0.855283	+	2.87550i	−0.285094	+	0.958499i
$10$	−1.69228	−	0.786008i	−0.535146	−	0.248557i
$11$		−	1.33708i		−	0.403145i	−0.979474	−	0.201573i	$-0.935395\pi$
$11$		−	1.33708i		−	0.403145i	0.979474	−	0.201573i	$-0.0646052\pi$
$12$	0.785663	−	3.37383i	0.226801	−	0.973941i
$13$			4.58699i			1.27220i	0.771606	+	0.636101i	$0.219454\pi$
$13$			4.58699i			1.27220i	−0.771606	+	0.636101i	$0.780546\pi$
$14$	0.813379	−	1.75121i	0.217385	−	0.468031i
$15$	−1.36630	−	1.83185i	−0.352777	−	0.472981i
$16$	−0.670734	+	3.94336i	−0.167683	+	0.985841i
$17$			4.76435i			1.15552i	0.816205	+	0.577762i	$0.196074\pi$
$17$			4.76435i			1.15552i	−0.816205	+	0.577762i	$0.803926\pi$
$18$	2.81003	−	3.17864i	0.662330	−	0.749213i
$19$	−6.45443			−1.48075			−0.740374	−	0.672195i	$-0.765352\pi$
$19$	−6.45443			−1.48075			−0.740374	+	0.672195i	$0.765352\pi$
$20$	1.70230	+	2.01629i	0.380645	+	0.450856i
$21$	1.89564	−	1.41388i	0.413662	−	0.308534i
$22$	−0.796543	+	1.71496i	−0.169824	+	0.365631i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	−3.01760	+	3.85928i	−0.615966	+	0.787773i
$25$	−3.25919			−0.651838
$26$	2.73261	−	5.88334i	0.535910	−	1.15382i
$27$	4.87801	−	1.79024i	0.938774	−	0.344532i
$28$	−2.08651	+	1.76158i	−0.394313	+	0.332907i
$29$	−4.15227			−0.771057			−0.385529	−	0.922696i	$-0.625981\pi$
$29$	−4.15227			−0.771057			−0.385529	+	0.922696i	$0.625981\pi$
$30$	0.661147	+	3.16350i	0.120708	+	0.577574i
$31$			8.95087i			1.60762i	0.594884	+	0.803812i	$0.297198\pi$
$31$			8.95087i			1.60762i	−0.594884	+	0.803812i	$0.702802\pi$
$32$	3.20948	−	4.65824i	0.567362	−	0.823469i
$33$	−1.85640	+	1.38461i	−0.323158	+	0.241030i
$34$	2.83828	−	6.11083i	0.486760	−	1.04800i
$35$			1.80143i			0.304498i
$36$	−5.49780	+	2.40295i	−0.916300	+	0.400492i
$37$		−	2.96579i		−	0.487573i	−0.969829	−	0.243786i	$-0.921610\pi$
$37$		−	2.96579i		−	0.487573i	0.969829	−	0.243786i	$-0.0783895\pi$
$38$	8.27855	+	3.84511i	1.34296	+	0.623759i
$39$	6.36855	−	4.75004i	1.01978	−	0.760615i
$40$	−0.982222	−	3.60024i	−0.155303	−	0.569248i
$41$			6.40374i			1.00010i	0.865997	+	0.500048i	$0.166684\pi$
$41$			6.40374i			1.00010i	−0.865997	+	0.500048i	$0.833316\pi$
$42$	−3.27367	+	0.684171i	−0.505138	+	0.105570i
$43$	12.4886			1.90450			0.952249	−	0.305322i	$-0.0987639\pi$
$43$	12.4886			1.90450			0.952249	+	0.305322i	$0.0987639\pi$
$44$	2.04332	−	1.72511i	0.308042	−	0.260070i
$45$	−1.12846	+	3.79393i	−0.168221	+	0.565565i
$46$	1.28262	+	0.595732i	0.189111	+	0.0878359i
$47$	−4.02108			−0.586535			−0.293267	−	0.956030i	$-0.594743\pi$
$47$	−4.02108			−0.586535			−0.293267	+	0.956030i	$0.594743\pi$
$48$	6.16952	−	3.15230i	0.890494	−	0.454995i
$49$	5.13584			0.733691
$50$	4.18029	+	1.94160i	0.591182	+	0.274584i
$51$	6.61480	−	4.93371i	0.926257	−	0.690858i
$52$	−7.00979	+	5.91816i	−0.972083	+	0.820701i
$53$	9.40100			1.29133			0.645663	−	0.763622i	$-0.276581\pi$
$53$	9.40100			1.29133			0.645663	+	0.763622i	$0.276581\pi$
$54$	−7.32312	−	0.609796i	−0.996551	−	0.0829827i
$55$		−	1.76414i		−	0.237877i
$56$	3.72561	−	1.01643i	0.497856	−	0.135826i
$57$	6.68387	+	8.96130i	0.885300	+	1.18695i
$58$	5.32577	+	2.47364i	0.699308	+	0.324805i
$59$		−	4.77409i		−	0.621534i	−0.950486	−	0.310767i	$-0.899414\pi$
$59$		−	4.77409i		−	0.621534i	0.950486	−	0.310767i	$-0.100586\pi$
$60$	1.03660	−	4.45142i	0.133825	−	0.574676i
$61$			13.3624i			1.71088i	0.517901	+	0.855441i	$0.326714\pi$
$61$			13.3624i			1.71088i	−0.517901	+	0.855441i	$0.673286\pi$
$62$	5.33232	−	11.4805i	0.677205	−	1.45803i
$63$	−3.92604	−	1.16776i	−0.494635	−	0.147123i
$64$	−6.89160	+	4.06274i	−0.861450	+	0.507843i
$65$			6.05206i			0.750666i
$66$	3.20590	−	0.670009i	0.394620	−	0.0824724i
$67$	7.21265			0.881166			0.440583	−	0.897712i	$-0.354772\pi$
$67$	7.21265			0.881166			0.440583	+	0.897712i	$0.354772\pi$
$68$	−7.28083	+	6.14699i	−0.882931	+	0.745433i
$69$	1.03555	+	1.38840i	0.124665	+	0.167143i
$70$	1.07317	−	2.31054i	0.128268	−	0.276163i
$71$	−14.4410			−1.71383			−0.856915	−	0.515458i	$-0.827622\pi$
$71$	−14.4410			−1.71383			−0.856915	+	0.515458i	$0.827622\pi$
$72$	8.48308	+	0.193154i	0.999741	+	0.0227635i
$73$	3.85756			0.451494			0.225747	−	0.974186i	$-0.427518\pi$
$73$	3.85756			0.451494			0.225747	+	0.974186i	$0.427518\pi$
$74$	−1.76681	+	3.80397i	−0.205388	+	0.442202i
$75$	3.37505	+	4.52504i	0.389717	+	0.522507i
$76$	−8.32755	−	9.86360i	−0.955235	−	1.13143i
$77$	1.82558			0.208044
$78$	−10.9982	+	2.29853i	−1.24530	+	0.260257i
$79$		−	0.671385i		−	0.0755367i	−0.999287	−	0.0377684i	$-0.987975\pi$
$79$		−	0.671385i		−	0.0755367i	0.999287	−	0.0377684i	$-0.0120249\pi$
$80$	−0.884965	+	5.20286i	−0.0989421	+	0.581698i
$81$	−7.53698	−	4.91873i	−0.837442	−	0.546526i
$82$	3.81492	−	8.21354i	0.421287	−	0.907034i
$83$		−	6.46804i		−	0.709959i	−0.934874	−	0.354980i	$-0.884488\pi$
$83$		−	6.46804i		−	0.709959i	0.934874	−	0.354980i	$-0.115512\pi$
$84$	4.60644	+	1.07270i	0.502604	+	0.117041i
$85$			6.28607i			0.681820i
$86$	−16.0181	−	7.43988i	−1.72728	−	0.802263i
$87$	4.29987	+	5.76499i	0.460995	+	0.618072i
$88$	−3.64850	+	0.995387i	−0.388931	+	0.106109i
$89$		−	4.72119i		−	0.500445i	−0.968188	−	0.250222i	$-0.919496\pi$
$89$		−	4.72119i		−	0.500445i	0.968188	−	0.250222i	$-0.0805037\pi$
$90$	3.70754	−	4.19389i	0.390809	−	0.442075i
$91$	−6.26281			−0.656521
$92$	−1.29021	−	1.52819i	−0.134513	−	0.159325i
$93$	12.4273	−	9.26905i	1.28866	−	0.961155i
$94$	5.15750	+	2.39549i	0.531956	+	0.247076i
$95$	−8.51596			−0.873719
$96$	−9.79105	+	0.367801i	−0.999295	+	0.0375385i
$97$	−5.63227			−0.571870			−0.285935	−	0.958249i	$-0.592304\pi$
$97$	−5.63227			−0.571870			−0.285935	+	0.958249i	$0.592304\pi$
$98$	−6.58730	−	3.05958i	−0.665418	−	0.309064i
$99$	3.84478	+	1.14358i	0.386415	+	0.114935i
$100$	−4.20503	−	4.98066i	−0.420503	−	0.498066i
$101$	−7.07707			−0.704195			−0.352097	−	0.935963i	$-0.614531\pi$
$101$	−7.07707			−0.704195			−0.352097	+	0.935963i	$0.614531\pi$
$102$	−11.4234	+	2.38740i	−1.13109	+	0.236388i
$103$		−	5.03050i		−	0.495670i	−0.968802	−	0.247835i	$-0.920281\pi$
$103$		−	5.03050i		−	0.495670i	0.968802	−	0.247835i	$-0.0797191\pi$
$104$	12.5165	−	3.41477i	1.22734	−	0.334846i
$105$	2.50110	−	1.86547i	0.244082	−	0.182051i
$106$	−12.0579	−	5.60048i	−1.17116	−	0.543966i
$107$		−	1.86847i		−	0.180632i	−0.995913	−	0.0903159i	$-0.971212\pi$
$107$		−	1.86847i		−	0.180632i	0.995913	−	0.0903159i	$-0.0287877\pi$
$108$	9.02948	+	5.14475i	0.868862	+	0.495054i
$109$		−	0.891683i		−	0.0854078i	−0.999088	−	0.0427039i	$-0.986403\pi$
$109$		−	0.891683i		−	0.0854078i	0.999088	−	0.0427039i	$-0.0135972\pi$
$110$	−1.05096	+	2.26272i	−0.100205	+	0.215742i
$111$	−4.11769	+	3.07121i	−0.390833	+	0.291507i
$112$	−5.38405	−	0.915783i	−0.508745	−	0.0865333i
$113$			6.29805i			0.592470i	0.955115	+	0.296235i	$0.0957312\pi$
$113$			6.29805i			0.592470i	−0.955115	+	0.296235i	$0.904269\pi$
$114$	−3.23430	−	15.4757i	−0.302920	−	1.44943i
$115$	−1.31940			−0.123034
$116$	−5.35729	−	6.34546i	−0.497412	−	0.589161i
$117$	−13.1899	−	3.92317i	−1.21940	−	0.362697i
$118$	−2.84408	+	6.12332i	−0.261819	+	0.563698i
$119$	−6.50498			−0.596310
$120$	−3.98142	+	5.09193i	−0.363452	+	0.464828i
$121$	9.21221			0.837474
$122$	7.96042	−	17.1388i	0.720702	−	1.55168i
$123$	8.89093	−	6.63138i	0.801668	−	0.597932i
$124$	−13.6786	+	11.5485i	−1.22838	+	1.03708i
$125$	−10.8972			−0.974671
$126$	4.33994	+	3.83665i	0.386632	+	0.341796i
$127$			3.75621i			0.333310i	0.986015	+	0.166655i	$0.0532966\pi$
$127$			3.75621i			0.333310i	−0.986015	+	0.166655i	$0.946703\pi$
$128$	11.2596	−	1.10539i	0.995216	−	0.0977040i
$129$	−12.9326	−	17.3392i	−1.13865	−	1.52663i
$130$	3.60541	−	7.76247i	0.316215	−	0.680813i
$131$			12.3736i			1.08109i	0.841315	+	0.540545i	$0.181782\pi$
$131$			12.3736i			1.08109i	−0.841315	+	0.540545i	$0.818218\pi$
$132$	−4.51109	−	1.05050i	−0.392640	−	0.0914339i
$133$		−	8.81252i		−	0.764142i
$134$	−9.25106	−	4.29681i	−0.799170	−	0.371188i
$135$	6.43604	−	2.36204i	0.553926	−	0.203292i
$136$	13.0005	−	3.54681i	1.11478	−	0.304136i
$137$			16.4005i			1.40119i	0.713559	+	0.700595i	$0.247082\pi$
$137$			16.4005i			1.40119i	−0.713559	+	0.700595i	$0.752918\pi$
$138$	−0.501098	−	2.39769i	−0.0426563	−	0.204105i
$139$	−7.22361			−0.612699			−0.306350	−	0.951919i	$-0.599108\pi$
$139$	−7.22361			−0.612699			−0.306350	+	0.951919i	$0.599108\pi$
$140$	−2.75293	+	2.32422i	−0.232665	+	0.196432i
$141$	4.16402	+	5.58285i	0.350674	+	0.470161i
$142$	18.5222	+	8.60296i	1.55435	+	0.721944i
$143$	6.13318			0.512882
$144$	−10.7655	−	5.30139i	−0.897122	−	0.441782i
$145$	−5.47850			−0.454964
$146$	−4.94777	−	2.29807i	−0.409481	−	0.190190i
$147$	−5.31840	−	7.13057i	−0.438654	−	0.588120i
$148$	4.53229	−	3.82648i	0.372552	−	0.314535i
$149$	−8.95025			−0.733233			−0.366616	−	0.930372i	$-0.619484\pi$
$149$	−8.95025			−0.733233			−0.366616	+	0.930372i	$0.619484\pi$
$150$	−1.63317	−	7.81452i	−0.133348	−	0.638053i
$151$		−	4.23225i		−	0.344415i	−0.985061	−	0.172208i	$-0.944910\pi$
$151$		−	4.23225i		−	0.344415i	0.985061	−	0.172208i	$-0.0550900\pi$
$152$	4.80498	+	17.6122i	0.389735	+	1.42854i
$153$	−13.6999	−	4.07487i	−1.10757	−	0.329434i
$154$	−2.34151	−	1.08755i	−0.188685	−	0.0876377i
$155$			11.8098i			0.948582i
$156$	15.4757	+	3.60382i	1.23905	+	0.288537i
$157$		−	12.6439i		−	1.00909i	−0.863385	−	0.504545i	$-0.831660\pi$
$157$		−	12.6439i		−	1.00909i	0.863385	−	0.504545i	$-0.168340\pi$
$158$	−0.399966	+	0.861129i	−0.0318196	+	0.0685077i
$159$	−9.73518	−	13.0523i	−0.772050	−	1.03512i
$160$	4.23458	−	6.14607i	0.334773	−	0.485890i
$161$		−	1.36534i		−	0.107604i
$162$	6.73680	+	10.7989i	0.529293	+	0.848439i
$163$	−9.44624			−0.739887			−0.369943	−	0.929054i	$-0.620623\pi$
$163$	−9.44624			−0.739887			−0.369943	+	0.929054i	$0.620623\pi$
$164$	−9.78614	+	8.26215i	−0.764169	+	0.645166i
$165$	−2.44933	+	1.82685i	−0.190680	+	0.142220i
$166$	−3.85322	+	8.29601i	−0.299068	+	0.643895i
$167$	16.1151			1.24703			0.623513	−	0.781813i	$-0.285705\pi$
$167$	16.1151			1.24703			0.623513	+	0.781813i	$0.285705\pi$
$168$	−5.26925	−	4.12007i	−0.406531	−	0.317870i
$169$	−8.04044			−0.618496
$170$	3.74481	−	8.06261i	0.287214	−	0.618374i
$171$	5.52037	−	18.5597i	0.422153	−	1.41930i
$172$	16.1129	+	19.0850i	1.22860	+	1.45522i
$173$	19.6294			1.49240			0.746199	−	0.665723i	$-0.231877\pi$
$173$	19.6294			1.49240			0.746199	+	0.665723i	$0.231877\pi$
$174$	−2.08069	−	9.95585i	−0.157737	−	0.754751i
$175$		−	4.44991i		−	0.336382i
$176$	5.27260	+	0.896827i	0.397437	+	0.0676008i
$177$	−6.62833	+	4.94380i	−0.498215	+	0.371599i
$178$	−2.81256	+	6.05547i	−0.210810	+	0.453877i
$179$		−	11.2348i		−	0.839727i	−0.907587	−	0.419864i	$-0.862078\pi$
$179$		−	11.2348i		−	0.839727i	0.907587	−	0.419864i	$-0.137922\pi$
$180$	−7.25379	+	3.17045i	−0.540665	+	0.236311i
$181$		−	15.8349i		−	1.17700i	−0.808497	−	0.588500i	$-0.799719\pi$
$181$		−	15.8349i		−	1.17700i	0.808497	−	0.588500i	$-0.200281\pi$
$182$	8.03278	+	3.73096i	0.595430	+	0.276557i
$183$	18.5523	−	13.8374i	1.37143	−	1.02289i
$184$	0.744447	+	2.72870i	0.0548814	+	0.201162i
$185$		−	3.91305i		−	0.287693i
$186$	−21.4614	+	4.48526i	−1.57362	+	0.328875i
$187$	6.37033			0.465844
$188$	−5.18802	−	6.14498i	−0.378376	−	0.448169i
$189$	2.44430	+	6.66017i	0.177797	+	0.484456i
$190$	10.9227	+	5.07323i	0.792416	+	0.368051i
$191$	−11.4806			−0.830705			−0.415353	−	0.909660i	$-0.636342\pi$
$191$	−11.4806			−0.830705			−0.415353	+	0.909660i	$0.636342\pi$
$192$	12.7773	+	5.36110i	0.922120	+	0.386904i
$193$	−2.22128			−0.159891			−0.0799457	−	0.996799i	$-0.525475\pi$
$193$	−2.22128			−0.159891			−0.0799457	+	0.996799i	$0.525475\pi$
$194$	7.22404	+	3.35532i	0.518656	+	0.240898i
$195$	8.40265	−	6.26719i	0.601726	−	0.448803i
$196$	6.62629	+	7.84854i	0.473306	+	0.560610i
$197$	−4.51543			−0.321711			−0.160856	−	0.986978i	$-0.551425\pi$
$197$	−4.51543			−0.321711			−0.160856	+	0.986978i	$0.551425\pi$
$198$	−4.25010	−	3.75724i	−0.302042	−	0.267015i
$199$			17.5391i			1.24332i	0.783288	+	0.621659i	$0.213541\pi$
$199$			17.5391i			1.24332i	−0.783288	+	0.621659i	$0.786459\pi$
$200$	2.42629	+	8.89335i	0.171565	+	0.628855i
$201$	−7.46904	−	10.0140i	−0.526826	−	0.706334i
$202$	9.07716	+	4.21604i	0.638667	+	0.296639i
$203$		−	5.66928i		−	0.397905i
$204$	16.0741	+	3.74317i	1.12541	+	0.262075i
$205$			8.44909i			0.590110i
$206$	−2.99683	+	6.45220i	−0.208799	+	0.449546i
$207$	0.855283	−	2.87550i	0.0594463	−	0.199861i
$208$	−18.0882	−	3.07665i	−1.25419	−	0.213327i
$209$			8.63010i			0.596957i
$210$	−4.31927	+	0.902693i	−0.298058	+	0.0622918i
$211$	−12.2255			−0.841639			−0.420820	−	0.907144i	$-0.638257\pi$
$211$	−12.2255			−0.841639			−0.420820	+	0.907144i	$0.638257\pi$
$212$	12.1292	+	14.3665i	0.833039	+	0.986697i
$213$	14.9543	+	20.0498i	1.02465	+	1.37379i
$214$	−1.11311	+	2.39653i	−0.0760904	+	0.163823i
$215$	16.4775			1.12375
$216$	−8.51646	−	11.9779i	−0.579472	−	0.814992i
$217$	−12.2210			−0.829616
$218$	−0.531204	+	1.14369i	−0.0359777	+	0.0774603i
$219$	−3.99469	−	5.35582i	−0.269936	−	0.361913i
$220$	2.69595	−	2.27611i	0.181761	−	0.153455i
$221$	−21.8540			−1.47006
$222$	7.11103	−	1.48615i	0.477261	−	0.0997438i
$223$		−	3.16888i		−	0.212204i	−0.994355	−	0.106102i	$-0.966163\pi$
$223$		−	3.16888i		−	0.212204i	0.994355	−	0.106102i	$-0.0338369\pi$
$224$	6.36010	+	4.38205i	0.424952	+	0.292788i
$225$	2.78753	−	9.37179i	0.185835	−	0.624786i
$226$	3.75195	−	8.07797i	0.249576	−	0.537339i
$227$			23.4496i			1.55641i	0.628013	+	0.778203i	$0.283868\pi$
$227$			23.4496i			1.55641i	−0.628013	+	0.778203i	$0.716132\pi$
$228$	−5.07101	+	21.7762i	−0.335836	+	1.44216i
$229$		−	12.8072i		−	0.846325i	−0.906054	−	0.423163i	$-0.860920\pi$
$229$		−	12.8072i		−	0.846325i	0.906054	−	0.423163i	$-0.139080\pi$
$230$	1.69228	+	0.786008i	0.111586	+	0.0518278i
$231$	−1.89047	−	2.53462i	−0.124384	−	0.166766i
$232$	3.09115	+	11.3303i	0.202944	+	0.743871i
$233$		−	15.2951i		−	1.00202i	−0.865443	−	0.501008i	$-0.832963\pi$
$233$		−	15.2951i		−	1.00202i	0.865443	−	0.501008i	$-0.167037\pi$
$234$	14.5804	+	12.8896i	0.953149	+	0.842616i
$235$	−5.30540			−0.346086
$236$	7.29572	−	6.15956i	0.474911	−	0.400953i
$237$	−0.932148	+	0.695251i	−0.0605495	+	0.0451614i
$238$	8.34338	+	3.87522i	0.540821	+	0.251193i
$239$	−1.46620			−0.0948404			−0.0474202	−	0.998875i	$-0.515100\pi$
$239$	−1.46620			−0.0948404			−0.0474202	+	0.998875i	$0.515100\pi$
$240$	8.14006	−	4.15913i	0.525438	−	0.268471i
$241$	27.8093			1.79135			0.895677	−	0.444706i	$-0.146692\pi$
$241$	27.8093			1.79135			0.895677	+	0.444706i	$0.146692\pi$
$242$	−11.8157	−	5.48801i	−0.759544	−	0.352783i
$243$	0.975757	+	15.5579i	0.0625948	+	0.998039i
$244$	−20.4203	+	17.2403i	−1.30728	+	1.10370i
$245$	6.77621			0.432916
$246$	−15.3542	+	3.20890i	−0.978946	+	0.204592i
$247$		−	29.6064i		−	1.88381i
$248$	24.4242	−	6.66345i	1.55094	−	0.423129i
$249$	−8.98019	+	6.69796i	−0.569097	+	0.424466i
$250$	13.9769	+	6.49179i	0.883975	+	0.410577i
$251$			10.3385i			0.652557i	0.945274	+	0.326279i	$0.105795\pi$
$251$			10.3385i			0.652557i	−0.945274	+	0.326279i	$0.894205\pi$
$252$	−3.28085	−	7.50639i	−0.206674	−	0.472858i
$253$			1.33708i			0.0840616i
$254$	2.23770	−	4.81778i	0.140406	−	0.302294i
$255$	8.72755	−	6.50952i	0.546541	−	0.407642i
$256$	−15.1002	−	5.28990i	−0.943764	−	0.330618i
$257$		−	20.6306i		−	1.28690i	−0.765487	−	0.643451i	$-0.777502\pi$
$257$		−	20.6306i		−	1.28690i	0.765487	−	0.643451i	$-0.222498\pi$
$258$	6.25803	+	29.9438i	0.389608	+	1.86422i
$259$	4.04932			0.251613
$260$	−9.24870	+	7.80841i	−0.573580	+	0.484257i
$261$	3.55137	−	11.9398i	0.219824	−	0.739058i
$262$	7.37138	−	15.8706i	0.455405	−	0.980491i
$263$	4.23808			0.261331			0.130666	−	0.991427i	$-0.458289\pi$
$263$	4.23808			0.261331			0.130666	+	0.991427i	$0.458289\pi$
$264$	5.16018	+	4.03478i	0.317587	+	0.248324i
$265$	12.4037			0.761951
$266$	−5.24990	+	11.3031i	−0.321892	+	0.693036i
$267$	−6.55487	+	4.88901i	−0.401152	+	0.299203i
$268$	9.30581	+	11.0223i	0.568443	+	0.673295i
$269$	31.0160			1.89108			0.945539	−	0.325508i	$-0.105535\pi$
$269$	31.0160			1.89108			0.945539	+	0.325508i	$0.105535\pi$
$270$	−9.66211	−	0.804563i	−0.588018	−	0.0489641i
$271$			19.4511i			1.18157i	0.806828	+	0.590786i	$0.201182\pi$
$271$			19.4511i			1.18157i	−0.806828	+	0.590786i	$0.798818\pi$
$272$	−18.7876	−	3.19561i	−1.13916	−	0.193762i
$273$	6.48544	+	8.69526i	0.392517	+	0.526261i
$274$	9.77031	−	21.0356i	0.590246	−	1.27080i
$275$			4.35780i			0.262786i
$276$	−0.785663	+	3.37383i	−0.0472914	+	0.203081i
$277$		−	8.24935i		−	0.495655i	−0.968804	−	0.247828i	$-0.920283\pi$
$277$		−	8.24935i		−	0.495655i	0.968804	−	0.247828i	$-0.0797167\pi$
$278$	9.26512	+	4.30334i	0.555685	+	0.258097i
$279$	−25.7382	−	7.65553i	−1.54091	−	0.458324i
$280$	4.91556	−	1.34107i	0.293761	−	0.0801443i
$281$			10.2587i			0.611982i	0.952034	+	0.305991i	$0.0989877\pi$
$281$			10.2587i			0.611982i	−0.952034	+	0.305991i	$0.901012\pi$
$282$	−2.01495	−	9.64129i	−0.119989	−	0.574130i
$283$	−26.3672			−1.56736			−0.783682	−	0.621162i	$-0.786661\pi$
$283$	−26.3672			−1.56736			−0.783682	+	0.621162i	$0.786661\pi$
$284$	−18.6319	−	22.0686i	−1.10560	−	1.30953i
$285$	8.81868	+	11.8235i	0.522374	+	0.700365i
$286$	−7.86651	−	3.65373i	−0.465157	−	0.216050i
$287$	−8.74331			−0.516102
$288$	10.6498	+	13.2130i	0.627543	+	0.778582i
$289$	−5.69902			−0.335237
$290$	7.02681	+	3.26372i	0.412628	+	0.191652i
$291$	5.83248	+	7.81982i	0.341906	+	0.458406i
$292$	4.97705	+	5.89509i	0.291260	+	0.344984i
$293$	−12.6713			−0.740266			−0.370133	−	0.928979i	$-0.620688\pi$
$293$	−12.6713			−0.740266			−0.370133	+	0.928979i	$0.620688\pi$
$294$	2.57356	+	12.3141i	0.150093	+	0.718174i
$295$		−	6.29893i		−	0.366738i
$296$	−8.09274	+	2.20787i	−0.470381	+	0.128330i
$297$	−2.39370	−	6.52231i	−0.138897	−	0.378463i
$298$	11.4797	+	5.33195i	0.665003	+	0.308872i
$299$		−	4.58699i		−	0.265272i
$300$	−2.56062	+	10.9960i	−0.147838	+	0.634852i
$301$			17.0513i			0.982819i
$302$	−2.52128	+	5.42835i	−0.145084	+	0.312366i
$303$	7.32864	+	9.82577i	0.421019	+	0.564476i
$304$	4.32921	−	25.4522i	0.248297	−	1.45978i
$305$			17.6303i			1.00951i
$306$	15.1442	+	13.3879i	0.865733	+	0.765338i
$307$	18.6406			1.06387			0.531937	−	0.846784i	$-0.321464\pi$
$307$	18.6406			1.06387			0.531937	+	0.846784i	$0.321464\pi$
$308$	2.35537	+	2.78983i	0.134210	+	0.158965i
$309$	−6.98433	+	5.20932i	−0.397324	+	0.296348i
$310$	7.03545	−	15.1474i	0.399587	−	0.860313i
$311$	26.9485			1.52811			0.764056	−	0.645150i	$-0.223205\pi$
$311$	26.9485			1.52811			0.764056	+	0.645150i	$0.223205\pi$
$312$	−17.7025	−	13.8417i	−1.00221	−	0.783632i
$313$	−12.5412			−0.708868			−0.354434	−	0.935081i	$-0.615326\pi$
$313$	−12.5412			−0.708868			−0.354434	+	0.935081i	$0.615326\pi$
$314$	−7.53235	+	16.2172i	−0.425075	+	0.915191i
$315$	−5.18001	−	1.54073i	−0.291861	−	0.0868105i
$316$	1.02600	−	0.866225i	0.0577172	−	0.0487290i
$317$	−19.3938			−1.08926			−0.544631	−	0.838676i	$-0.683330\pi$
$317$	−19.3938			−1.08926			−0.544631	+	0.838676i	$0.683330\pi$
$318$	4.71082	+	22.5407i	0.264170	+	1.26402i
$319$			5.55193i			0.310848i
$320$	−9.09276	+	5.36038i	−0.508301	+	0.299654i
$321$	−2.59417	+	1.93489i	−0.144793	+	0.107995i
$322$	−0.813379	+	1.75121i	−0.0453278	+	0.0975912i
$323$		−	30.7512i		−	1.71104i
$324$	−2.20750	−	17.8641i	−0.122639	−	0.992451i
$325$		−	14.9499i		−	0.829269i
$326$	12.1159	+	5.62743i	0.671038	+	0.311674i
$327$	−1.23801	+	0.923380i	−0.0684620	+	0.0510630i
$328$	17.4739	−	4.76725i	0.964834	−	0.263227i
$329$		−	5.49016i		−	0.302682i
$330$	4.22986	−	0.884008i	0.232846	−	0.0486631i
$331$	−8.77085			−0.482089			−0.241045	−	0.970514i	$-0.577490\pi$
$331$	−8.77085			−0.482089			−0.241045	+	0.970514i	$0.577490\pi$
$332$	9.88439	−	8.34510i	0.542477	−	0.457997i
$333$	8.52812	+	2.53659i	0.467338	+	0.139004i
$334$	−20.6695	−	9.60029i	−1.13098	−	0.525305i
$335$	9.51636			0.519934
$336$	4.30397	+	8.42352i	0.234801	+	0.459541i
$337$	16.7149			0.910520			0.455260	−	0.890359i	$-0.349546\pi$
$337$	16.7149			0.910520			0.455260	+	0.890359i	$0.349546\pi$
$338$	10.3128	+	4.78995i	0.560942	+	0.260539i
$339$	8.74418	−	6.52193i	0.474919	−	0.354222i
$340$	−9.60632	+	8.11033i	−0.520976	+	0.439844i
$341$	11.9680			0.648106
$342$	−18.1371	+	20.5163i	−0.980743	+	1.10939i
$343$			16.5696i			0.894674i
$344$	−9.29713	−	34.0777i	−0.501267	−	1.83735i
$345$	1.36630	+	1.83185i	0.0735591	+	0.0986233i
$346$	−25.1770	−	11.6939i	−1.35352	−	0.628667i
$347$		−	19.4801i		−	1.04575i	−0.852410	−	0.522874i	$-0.824860\pi$
$347$		−	19.4801i		−	1.04575i	0.852410	−	0.522874i	$-0.175140\pi$
$348$	−3.26229	+	14.0091i	−0.174877	+	0.750964i
$349$			9.84324i			0.526896i	0.964674	+	0.263448i	$0.0848598\pi$
$349$			9.84324i			0.526896i	−0.964674	+	0.263448i	$0.915140\pi$
$350$	−2.65096	+	5.70753i	−0.141700	+	0.305080i
$351$	8.21182	+	22.3754i	0.438315	+	1.19431i
$352$	−6.22845	−	4.29134i	−0.331978	−	0.228729i
$353$			22.5931i			1.20251i	0.799058	+	0.601254i	$0.205332\pi$
$353$			22.5931i			1.20251i	−0.799058	+	0.601254i	$0.794668\pi$
$354$	11.4468	−	2.39229i	0.608389	−	0.127149i
$355$	−19.0534			−1.01125
$356$	7.21487	−	6.09131i	0.382388	−	0.322839i
$357$	6.73621	+	9.03148i	0.356518	+	0.477996i
$358$	−6.69292	+	14.4099i	−0.353732	+	0.761587i
$359$	−7.38572			−0.389803			−0.194902	−	0.980823i	$-0.562439\pi$
$359$	−7.38572			−0.389803			−0.194902	+	0.980823i	$0.562439\pi$
$360$	11.1926	+	0.254847i	0.589900	+	0.0134316i
$361$	22.6597			1.19261
$362$	−9.43337	+	20.3101i	−0.495807	+	1.06748i
$363$	−9.53968	−	12.7902i	−0.500703	−	0.671311i
$364$	−8.08032	−	9.57077i	−0.423524	−	0.501645i
$365$	5.08966			0.266405
$366$	−32.0389	+	6.69587i	−1.67470	+	0.349999i
$367$			37.5125i			1.95814i	0.203529	+	0.979069i	$0.434759\pi$
$367$			37.5125i			1.95814i	−0.203529	+	0.979069i	$0.565241\pi$
$368$	0.670734	−	3.94336i	0.0349644	−	0.205562i
$369$	−18.4140	−	5.47702i	−0.958592	−	0.285122i
$370$	−2.33113	+	5.01894i	−0.121190	+	0.260922i
$371$			12.8356i			0.666391i
$372$	30.1987	+	7.03236i	1.56573	+	0.364611i
$373$		−	16.9189i		−	0.876025i	−0.898969	−	0.438013i	$-0.855682\pi$
$373$		−	16.9189i		−	0.876025i	0.898969	−	0.438013i	$-0.144318\pi$
$374$	−8.17068	−	3.79501i	−0.422496	−	0.196235i
$375$	11.2845	+	15.1296i	0.582730	+	0.781287i
$376$	2.99348	+	10.9723i	0.154377	+	0.565854i
$377$		−	19.0464i		−	0.980940i
$378$	0.832581	−	9.99858i	0.0428233	−	0.514272i
$379$	10.0519			0.516332			0.258166	−	0.966101i	$-0.416882\pi$
$379$	10.0519			0.516332			0.258166	+	0.966101i	$0.416882\pi$
$380$	−10.9873	−	13.0140i	−0.563639	−	0.667605i
$381$	5.21511	−	3.88974i	0.267178	−	0.199277i
$382$	14.7252	+	6.83935i	0.753405	+	0.349932i
$383$	−16.7852			−0.857685			−0.428843	−	0.903379i	$-0.641079\pi$
$383$	−16.7852			−0.857685			−0.428843	+	0.903379i	$0.641079\pi$
$384$	−13.1946	−	14.4881i	−0.673332	−	0.739341i
$385$	2.40866			0.122757
$386$	2.84905	+	1.32329i	0.145013	+	0.0673537i
$387$	−10.6813	+	35.9110i	−0.542962	+	1.82546i
$388$	−7.26679	−	8.60718i	−0.368916	−	0.436964i
$389$	11.1008			0.562834			0.281417	−	0.959586i	$-0.409196\pi$
$389$	11.1008			0.562834			0.281417	+	0.959586i	$0.409196\pi$
$390$	−14.5109	+	3.03267i	−0.734790	+	0.153565i
$391$		−	4.76435i		−	0.240944i
$392$	−3.82336	−	14.0142i	−0.193109	−	0.707822i
$393$	17.1795	−	12.8135i	0.866592	−	0.646355i
$394$	5.79157	+	2.68999i	0.291775	+	0.135520i
$395$		−	0.885824i		−	0.0445706i
$396$	3.21294	+	7.35101i	0.161456	+	0.369402i
$397$		−	9.16677i		−	0.460067i	−0.973183	−	0.230034i	$-0.926116\pi$
$397$		−	9.16677i		−	0.460067i	0.973183	−	0.230034i	$-0.0738836\pi$
$398$	10.4486	−	22.4960i	0.523743	−	1.12762i
$399$	−12.2353	+	9.12578i	−0.612529	+	0.456860i
$400$	2.18605	−	12.8522i	0.109302	−	0.642608i
$401$		−	2.17647i		−	0.108688i	−0.998522	−	0.0543438i	$-0.982693\pi$
$401$		−	2.17647i		−	0.108688i	0.998522	−	0.0543438i	$-0.0173067\pi$
$402$	3.61424	+	17.2937i	0.180262	+	0.862531i
$403$	−41.0575			−2.04522
$404$	−9.13088	−	10.8151i	−0.454278	−	0.538072i
$405$	−9.94428	−	6.48976i	−0.494135	−	0.322479i
$406$	−3.37737	+	7.27151i	−0.167616	+	0.360879i
$407$	−3.96550			−0.196563
$408$	−18.3870	−	14.3769i	−0.910291	−	0.711763i
$409$	25.8219			1.27681			0.638405	−	0.769700i	$-0.279594\pi$
$409$	25.8219			1.27681			0.638405	+	0.769700i	$0.279594\pi$
$410$	5.03339	−	10.8369i	0.248582	−	0.535198i
$411$	22.7704	−	16.9835i	1.12318	−	0.837735i
$412$	7.68757	−	6.49039i	0.378739	−	0.319758i
$413$	6.51828			0.320743
$414$	−2.81003	+	3.17864i	−0.138105	+	0.156222i
$415$		−	8.53391i		−	0.418913i
$416$	21.3673	+	14.7219i	1.04762	+	0.721798i
$417$	7.48040	+	10.0292i	0.366317	+	0.491134i
$418$	5.14123	−	11.0691i	0.251466	−	0.541408i
$419$		−	29.2429i		−	1.42861i	−0.699835	−	0.714305i	$-0.746743\pi$
$419$		−	29.2429i		−	1.42861i	0.699835	−	0.714305i	$-0.253257\pi$
$420$	6.07773	+	1.41532i	0.296563	+	0.0690604i
$421$		−	23.3770i		−	1.13933i	−0.821878	−	0.569663i	$-0.807074\pi$
$421$		−	23.3770i		−	1.13933i	0.821878	−	0.569663i	$-0.192926\pi$
$422$	15.6806	+	7.28313i	0.763322	+	0.354537i
$423$	3.43916	−	11.5626i	0.167218	−	0.562193i
$424$	−6.99855	−	25.6525i	−0.339879	−	1.24580i
$425$		−	15.5279i		−	0.753215i
$426$	−7.23635	−	34.6250i	−0.350602	−	1.67758i
$427$	−18.2443			−0.882903
$428$	2.85538	−	2.41071i	0.138020	−	0.116526i
$429$	−6.35120	−	8.51528i	−0.306639	−	0.411121i
$430$	−21.1343	−	9.81616i	−1.01918	−	0.473377i
$431$	32.9383			1.58658			0.793290	−	0.608844i	$-0.208366\pi$
$431$	32.9383			1.58658			0.793290	+	0.608844i	$0.208366\pi$
$432$	3.78773	+	20.4366i	0.182237	+	0.983255i
$433$	3.24715			0.156048			0.0780241	−	0.996951i	$-0.475139\pi$
$433$	3.24715			0.156048			0.0780241	+	0.996951i	$0.475139\pi$
$434$	15.6749	+	7.28045i	0.752417	+	0.349473i
$435$	5.67324	+	7.60632i	0.272011	+	0.364695i
$436$	1.36266	−	1.15046i	0.0652597	−	0.0550968i
$437$	6.45443			0.308757
$438$	1.93302	+	9.24923i	0.0923631	+	0.441945i
$439$		−	37.2668i		−	1.77865i	−0.457280	−	0.889323i	$-0.651176\pi$
$439$		−	37.2668i		−	1.77865i	0.457280	−	0.889323i	$-0.348824\pi$
$440$	−4.81382	+	1.31331i	−0.229490	+	0.0626097i
$441$	−4.39259	+	14.7681i	−0.209171	+	0.703242i
$442$	28.0303	+	13.0191i	1.33327	+	0.619257i
$443$			29.1633i			1.38559i	0.721135	+	0.692795i	$0.243621\pi$
$443$			29.1633i			1.38559i	−0.721135	+	0.692795i	$0.756379\pi$
$444$	−10.0061	−	2.33011i	−0.474867	−	0.110582i
$445$		−	6.22912i		−	0.295289i
$446$	−1.88780	+	4.06445i	−0.0893900	+	0.192457i
$447$	9.26840	+	12.4265i	0.438381	+	0.587752i
$448$	−5.54704	−	9.40940i	−0.262073	−	0.444552i
$449$		−	20.9579i		−	0.989066i	−0.869159	−	0.494533i	$-0.835339\pi$
$449$		−	20.9579i		−	0.989066i	0.869159	−	0.494533i	$-0.164661\pi$
$450$	−9.15841	+	10.3598i	−0.431732	+	0.488365i
$451$	8.56233			0.403185
$452$	−9.62462	+	8.12578i	−0.452704	+	0.382205i
$453$	−5.87603	+	4.38269i	−0.276080	+	0.205917i
$454$	13.9697	−	30.0768i	0.655630	−	1.41158i
$455$	−8.26314			−0.387382
$456$	19.4769	−	24.9095i	0.912090	−	1.16649i
$457$	−6.11443			−0.286021			−0.143010	−	0.989721i	$-0.545678\pi$
$457$	−6.11443			−0.286021			−0.143010	+	0.989721i	$0.545678\pi$
$458$	−7.62968	+	16.4268i	−0.356511	+	0.767572i
$459$	8.52934	+	23.2406i	0.398116	+	1.08478i
$460$	−1.70230	−	2.01629i	−0.0793699	−	0.0940101i
$461$	−13.8440			−0.644781			−0.322391	−	0.946607i	$-0.604486\pi$
$461$	−13.8440			−0.644781			−0.322391	+	0.946607i	$0.604486\pi$
$462$	0.914793	+	4.37716i	0.0425600	+	0.203644i
$463$		−	2.96745i		−	0.137909i	−0.997620	−	0.0689545i	$-0.978034\pi$
$463$		−	2.96745i		−	0.137909i	0.997620	−	0.0689545i	$-0.0219663\pi$
$464$	2.78507	−	16.3739i	0.129294	−	0.760140i
$465$	16.3966	−	12.2296i	0.760374	−	0.567132i
$466$	−9.11179	+	19.6178i	−0.422096	+	0.908775i
$467$			6.01149i			0.278179i	0.990280	+	0.139089i	$0.0444175\pi$
$467$			6.01149i			0.278179i	−0.990280	+	0.139089i	$0.955582\pi$
$468$	−11.0223	−	25.2183i	−0.509506	−	1.16572i
$469$			9.84775i			0.454727i
$470$	6.80479	+	3.16060i	0.313882	+	0.145788i
$471$	−17.5547	+	13.0933i	−0.808877	+	0.603308i
$472$	−13.0271	+	3.55406i	−0.599619	+	0.163589i
$473$		−	16.6983i		−	0.767790i
$474$	1.60977	−	0.336429i	0.0739392	−	0.0154527i
$475$	21.0362			0.965208
$476$	−8.39276	−	9.94084i	−0.384682	−	0.455638i
$477$	−8.04052	+	27.0326i	−0.368150	+	1.23774i
$478$	1.88057	+	0.873460i	0.0860151	+	0.0399511i
$479$	−16.5024			−0.754012			−0.377006	−	0.926211i	$-0.623046\pi$
$479$	−16.5024			−0.754012			−0.377006	+	0.926211i	$0.623046\pi$
$480$	−12.9183	+	0.485276i	−0.589637	+	0.0221497i
$481$	13.6040			0.620290
$482$	−35.6686	−	16.5669i	−1.62466	−	0.754601i
$483$	−1.89564	+	1.41388i	−0.0862545	+	0.0643337i
$484$	11.8857	+	14.0780i	0.540257	+	0.639910i
$485$	−7.43121			−0.337434
$486$	8.01681	−	20.5361i	0.363650	−	0.931536i
$487$		−	20.1595i		−	0.913514i	−0.889591	−	0.456757i	$-0.849011\pi$
$487$		−	20.1595i		−	0.913514i	0.889591	−	0.456757i	$-0.150989\pi$
$488$	36.4620	−	9.94761i	1.65056	−	0.450307i
$489$	9.78203	+	13.1151i	0.442359	+	0.593086i
$490$	−8.69127	−	4.03681i	−0.392632	−	0.182364i
$491$			26.2894i			1.18642i	0.805046	+	0.593212i	$0.202140\pi$
$491$			26.2894i			1.18642i	−0.805046	+	0.593212i	$0.797860\pi$
$492$	21.6052	+	5.03118i	0.974035	+	0.226823i
$493$		−	19.7829i		−	0.890976i
$494$	−17.6375	+	37.9736i	−0.793547	+	1.70851i
$495$	5.07279	+	1.50884i	0.228005	+	0.0678174i
$496$	−35.2965	−	6.00365i	−1.58486	−	0.269572i
$497$		−	19.7169i		−	0.884424i
$498$	15.5083	−	3.24112i	0.694945	−	0.145238i
$499$	0.522855			0.0234062			0.0117031	−	0.999932i	$-0.496275\pi$
$499$	0.522855			0.0234062			0.0117031	+	0.999932i	$0.496275\pi$
$500$	−14.0596	−	16.6529i	−0.628764	−	0.744742i
$501$	−16.6880	−	22.3742i	−0.745563	−	0.999603i
$502$	6.15895	−	13.2603i	0.274887	−	0.591834i
$503$	−8.32652			−0.371261			−0.185631	−	0.982620i	$-0.559433\pi$
$503$	−8.32652			−0.371261			−0.185631	+	0.982620i	$0.559433\pi$
$504$	−0.263722	+	11.5823i	−0.0117471	+	0.515918i
$505$	−9.33747			−0.415512
$506$	0.796543	−	1.71496i	0.0354106	−	0.0762394i
$507$	8.32626	+	11.1633i	0.369782	+	0.495780i
$508$	−5.74021	+	4.84629i	−0.254681	+	0.215019i
$509$	−39.7549			−1.76211			−0.881053	−	0.473017i	$-0.843165\pi$
$509$	−39.7549			−1.76211			−0.881053	+	0.473017i	$0.843165\pi$
$510$	−15.0720	+	3.14994i	−0.667401	+	0.139482i
$511$			5.26690i			0.232994i
$512$	16.2164	+	15.7806i	0.716672	+	0.697410i
$513$	−31.4848	+	11.5550i	−1.39009	+	0.510166i
$514$	−12.2903	+	26.4611i	−0.542102	+	1.16715i
$515$		−	6.63723i		−	0.292471i
$516$	9.81186	−	42.1345i	0.431943	−	1.85487i
$517$			5.37652i			0.236459i
$518$	−5.19372	−	2.41231i	−0.228199	−	0.105991i
$519$	−20.3272	−	27.2534i	−0.892265	−	1.19629i
$520$	16.5142	−	4.50544i	0.724198	−	0.197577i
$521$			8.83118i			0.386901i	0.981110	+	0.193450i	$0.0619679\pi$
$521$			8.83118i			0.386901i	−0.981110	+	0.193450i	$0.938032\pi$
$522$	−11.6680	+	13.1986i	−0.510694	+	0.577686i
$523$	−39.8132			−1.74091			−0.870455	−	0.492249i	$-0.836175\pi$
$523$	−39.8132			−1.74091			−0.870455	+	0.492249i	$0.836175\pi$
$524$	−18.9093	+	15.9646i	−0.826056	+	0.697415i
$525$	−6.17824	+	4.60810i	−0.269641	+	0.201114i
$526$	−5.43583	−	2.52476i	−0.237013	−	0.110085i
$527$	−42.6451			−1.85765
$528$	−4.21488	−	8.24916i	−0.183429	−	0.358999i
$529$	1.00000			0.0434783
$530$	−15.9091	−	7.38926i	−0.691048	−	0.320969i
$531$	13.7279	+	4.08320i	0.595740	+	0.177196i
$532$	13.4672	−	11.3700i	0.583877	−	0.492951i
$533$	−29.3739			−1.27232
$534$	11.3199	−	2.36578i	0.489861	−	0.102377i
$535$		−	2.46525i		−	0.106582i
$536$	−5.36944	−	19.6812i	−0.231924	−	0.850097i
$537$	−15.5983	+	11.6341i	−0.673117	+	0.502051i
$538$	−39.7816	−	18.4772i	−1.71511	−	0.796610i
$539$		−	6.86704i		−	0.295784i
$540$	11.9135	+	6.78798i	0.512674	+	0.292108i
$541$			39.7246i			1.70789i	0.520361	+	0.853946i	$0.325797\pi$
$541$			39.7246i			1.70789i	−0.520361	+	0.853946i	$0.674203\pi$
$542$	11.5877	−	24.9483i	0.497733	−	1.07162i
$543$	−21.9851	+	16.3978i	−0.943472	+	0.703697i
$544$	22.1935	+	15.2911i	0.951538	+	0.655600i
$545$		−	1.17648i		−	0.0503951i
$546$	−3.13828	−	15.0163i	−0.134306	−	0.642637i
$547$	15.1269			0.646779			0.323390	−	0.946266i	$-0.395178\pi$
$547$	15.1269			0.646779			0.323390	+	0.946266i	$0.395178\pi$
$548$	−25.0631	+	21.1600i	−1.07064	+	0.903912i
$549$	−38.4236	−	11.4286i	−1.63988	−	0.487763i
$550$	2.59608	−	5.58939i	0.110697	−	0.238332i
$551$	26.8005			1.14174
$552$	3.01760	−	3.85928i	0.128438	−	0.164262i
$553$	0.916671			0.0389808
$554$	−4.91440	+	10.5807i	−0.208793	+	0.449533i
$555$	−5.43287	+	4.05215i	−0.230612	+	0.172004i
$556$	−9.31996	−	11.0391i	−0.395254	−	0.468160i
$557$	−7.14586			−0.302780			−0.151390	−	0.988474i	$-0.548375\pi$
$557$	−7.14586			−0.302780			−0.151390	+	0.988474i	$0.548375\pi$
$558$	28.4516	+	25.1522i	1.20445	+	1.06478i
$559$			57.2852i			2.42291i
$560$	−7.10370	−	1.20828i	−0.300186	−	0.0510592i
$561$	−6.59678	−	8.84453i	−0.278516	−	0.373416i
$562$	6.11143	−	13.1580i	0.257795	−	0.555035i
$563$			32.7601i			1.38067i	0.723489	+	0.690336i	$0.242537\pi$
$563$			32.7601i			1.38067i	−0.723489	+	0.690336i	$0.757463\pi$
$564$	−3.15921	+	13.5664i	−0.133027	+	0.571250i
$565$			8.30963i			0.349589i
$566$	33.8189	+	15.7078i	1.42152	+	0.660246i
$567$	6.71576	−	10.2906i	0.282035	−	0.432163i
$568$	10.7506	+	39.4051i	0.451083	+	1.65340i
$569$			23.7432i			0.995368i	0.867358	+	0.497684i	$0.165816\pi$
$569$			23.7432i			0.995368i	−0.867358	+	0.497684i	$0.834184\pi$
$570$	−4.26733	−	20.4186i	−0.178739	−	0.855241i
$571$	23.4711			0.982233			0.491117	−	0.871094i	$-0.336589\pi$
$571$	23.4711			0.982233			0.491117	+	0.871094i	$0.336589\pi$
$572$	7.91307	+	9.37267i	0.330862	+	0.391891i
$573$	11.8887	+	15.9396i	0.496657	+	0.665886i
$574$	11.2143	+	5.20867i	0.468076	+	0.217406i
$575$	3.25919			0.135918
$576$	−5.78815	−	23.2916i	−0.241173	−	0.970482i
$577$	43.7823			1.82268			0.911339	−	0.411656i	$-0.135049\pi$
$577$	43.7823			1.82268			0.911339	+	0.411656i	$0.135049\pi$
$578$	7.30966	+	3.39509i	0.304042	+	0.141217i
$579$	2.30024	+	3.08402i	0.0955949	+	0.128167i
$580$	−7.06839	−	8.37219i	−0.293499	−	0.347636i
$581$	8.83110			0.366376
$582$	−2.82232	−	13.5044i	−0.116989	−	0.559776i
$583$		−	12.5699i		−	0.520593i
$584$	−2.87175	−	10.5261i	−0.118834	−	0.435574i
$585$	−17.4027	−	5.17623i	−0.719513	−	0.214011i
$586$	16.2524	+	7.54870i	0.671381	+	0.311834i
$587$			2.79244i			0.115256i	0.998338	+	0.0576281i	$0.0183538\pi$
$587$			2.79244i			0.115256i	−0.998338	+	0.0576281i	$0.981646\pi$
$588$	4.03504	−	17.3274i	0.166402	−	0.714572i
$589$		−	57.7727i		−	2.38048i
$590$	−3.75247	+	8.07910i	−0.154487	+	0.332611i
$591$	4.67595	+	6.26921i	0.192343	+	0.257881i
$592$	11.6952	+	1.98925i	0.480669	+	0.0817579i
$593$		−	32.9094i		−	1.35143i	−0.737164	−	0.675714i	$-0.763836\pi$
$593$		−	32.9094i		−	1.35143i	0.737164	−	0.675714i	$-0.236164\pi$
$594$	−0.815347	+	9.79162i	−0.0334541	+	0.401755i
$595$	−8.58265			−0.351854
$596$	−11.5477	−	13.6777i	−0.473011	−	0.560260i
$597$	24.3513	−	18.1626i	0.996631	−	0.743346i
$598$	−2.73261	+	5.88334i	−0.111745	+	0.240588i
$599$	−17.5271			−0.716136			−0.358068	−	0.933695i	$-0.616564\pi$
$599$	−17.5271			−0.716136			−0.358068	+	0.933695i	$0.616564\pi$
$600$	9.83494	−	12.5781i	0.401510	−	0.513500i
$601$	45.1898			1.84333			0.921664	−	0.387988i	$-0.126830\pi$
$601$	45.1898			1.84333			0.921664	+	0.387988i	$0.126830\pi$
$602$	10.1580	−	21.8702i	0.414009	−	0.891364i
$603$	−6.16886	+	20.7400i	−0.251215	+	0.844597i
$604$	6.46768	−	5.46047i	0.263166	−	0.222183i
$605$	12.1546			0.494154
$606$	−3.54630	−	16.9686i	−0.144059	−	0.689302i
$607$		−	23.5916i		−	0.957553i	−0.877937	−	0.478777i	$-0.841080\pi$
$607$		−	23.5916i		−	0.957553i	0.877937	−	0.478777i	$-0.158920\pi$
$608$	−20.7154	+	30.0663i	−0.840120	+	1.21935i
$609$	−7.87120	+	5.87081i	−0.318957	+	0.237897i
$610$	10.5030	−	22.6129i	0.425252	−	0.915571i
$611$		−	18.4446i		−	0.746190i
$612$	−11.4485	−	26.1934i	−0.462778	−	1.05881i
$613$			0.337356i			0.0136257i	0.999977	+	0.00681283i	$0.00216861\pi$
$613$			0.337356i			0.0136257i	−0.999977	+	0.00681283i	$0.997831\pi$
$614$	−23.9087	−	11.1048i	−0.964877	−	0.448153i
$615$	11.7307	−	8.74943i	0.473026	−	0.352811i
$616$	−1.35905	−	4.98145i	−0.0547575	−	0.200708i
$617$		−	2.54992i		−	0.102656i	−0.998682	−	0.0513279i	$-0.983655\pi$
$617$		−	2.54992i		−	0.102656i	0.998682	−	0.0513279i	$-0.0163454\pi$
$618$	12.0616	−	2.52077i	0.485187	−	0.101400i
$619$	−6.34944			−0.255205			−0.127603	−	0.991825i	$-0.540728\pi$
$619$	−6.34944			−0.255205			−0.127603	+	0.991825i	$0.540728\pi$
$620$	−18.0476	+	15.2370i	−0.724807	+	0.611933i
$621$	−4.87801	+	1.79024i	−0.195748	+	0.0718400i
$622$	−34.5646	−	16.0541i	−1.38591	−	0.643711i
$623$	6.44604			0.258255
$624$	14.4595	+	28.2995i	0.578845	+	1.13289i
$625$	1.91827			0.0767306
$626$	16.0855	+	7.47117i	0.642905	+	0.298608i
$627$	11.9820	−	8.93688i	0.478515	−	0.356905i
$628$	19.3222	−	16.3132i	0.771041	−	0.650967i
$629$	14.1300			0.563402
$630$	5.72610	+	5.06207i	0.228133	+	0.201678i
$631$			5.92767i			0.235977i	0.993015	+	0.117988i	$0.0376446\pi$
$631$			5.92767i			0.235977i	−0.993015	+	0.117988i	$0.962355\pi$
$632$	−1.83201	+	0.499811i	−0.0728733	+	0.0198814i
$633$	12.6601	+	16.9739i	0.503194	+	0.674650i
$634$	24.8748	+	11.5535i	0.987903	+	0.458848i
$635$			4.95594i			0.196670i
$636$	7.38602	−	31.7174i	0.292875	−	1.25768i
$637$			23.5580i			0.933402i
$638$	3.30746	−	7.12099i	0.130944	−	0.281923i
$639$	12.3511	−	41.5250i	0.488603	−	1.64270i
$640$	14.8559	−	1.45845i	0.587230	−	0.0576505i
$641$		−	28.6235i		−	1.13056i	−0.824899	−	0.565280i	$-0.808768\pi$
$641$		−	28.6235i		−	1.13056i	0.824899	−	0.565280i	$-0.191232\pi$
$642$	4.48000	−	0.936286i	0.176812	−	0.0369522i
$643$	3.07769			0.121372			0.0606861	−	0.998157i	$-0.480671\pi$
$643$	3.07769			0.121372			0.0606861	+	0.998157i	$0.480671\pi$
$644$	2.08651	−	1.76158i	0.0822199	−	0.0694158i
$645$	−17.0632	−	22.8772i	−0.671863	−	0.900791i
$646$	−18.3195	+	39.4419i	−0.720769	+	1.55182i
$647$	31.9248			1.25509			0.627546	−	0.778579i	$-0.284059\pi$
$647$	31.9248			1.25509			0.627546	+	0.778579i	$0.284059\pi$
$648$	−7.81085	+	24.2279i	−0.306839	+	0.951761i
$649$	−6.38335			−0.250569
$650$	−8.90611	+	19.1749i	−0.349326	+	0.752102i
$651$	12.6554	+	16.9676i	0.496006	+	0.665012i
$652$	−12.1876	−	14.4357i	−0.477303	−	0.565344i
$653$	−0.756181			−0.0295917			−0.0147958	−	0.999891i	$-0.504710\pi$
$653$	−0.756181			−0.0295917			−0.0147958	+	0.999891i	$0.504710\pi$
$654$	2.13798	−	0.446820i	0.0836015	−	0.0174721i
$655$			16.3258i			0.637900i
$656$	−25.2523	−	4.29521i	−0.985936	−	0.167700i
$657$	−3.29931	+	11.0924i	−0.128718	+	0.432756i
$658$	−3.27066	+	7.04176i	−0.127504	+	0.274516i
$659$			15.7514i			0.613587i	0.951776	+	0.306793i	$0.0992560\pi$
$659$			15.7514i			0.613587i	−0.951776	+	0.306793i	$0.900744\pi$
$660$	−5.95192	−	1.38602i	−0.231678	−	0.0539508i
$661$			38.0513i			1.48002i	0.672593	+	0.740012i	$0.265180\pi$
$661$			38.0513i			1.48002i	−0.672593	+	0.740012i	$0.734820\pi$
$662$	11.2496	+	5.22507i	0.437229	+	0.203078i
$663$	22.6309	+	30.3420i	0.878910	+	1.17839i
$664$	−17.6493	+	4.81511i	−0.684927	+	0.186863i
$665$		−	11.6272i		−	0.450884i
$666$	−9.42717	−	8.33394i	−0.365295	−	0.322934i
$667$	4.15227			0.160777
$668$	20.7918	+	24.6270i	0.804460	+	0.952846i
$669$	−4.39965	+	3.28152i	−0.170100	+	0.126871i
$670$	−12.2058	−	5.66920i	−0.471552	−	0.219020i
$671$	17.8666			0.689734
$672$	−0.502175	−	13.3682i	−0.0193718	−	0.515688i
$673$	35.4773			1.36755			0.683775	−	0.729693i	$-0.260337\pi$
$673$	35.4773			1.36755			0.683775	+	0.729693i	$0.260337\pi$
$674$	−21.4388	−	9.95762i	−0.825793	−	0.383553i
$675$	−15.8984	+	5.83474i	−0.611929	+	0.224579i
$676$	−10.3738	−	12.2873i	−0.398994	−	0.472590i
$677$	12.5695			0.483086			0.241543	−	0.970390i	$-0.422347\pi$
$677$	12.5695			0.483086			0.241543	+	0.970390i	$0.422347\pi$
$678$	−15.1007	+	3.15594i	−0.579940	+	0.121203i
$679$		−	7.68999i		−	0.295115i
$680$	17.1528	−	4.67965i	0.657780	−	0.179456i
$681$	32.5573	−	24.2832i	1.24760	−	0.930534i
$682$	−15.3504	−	7.12975i	−0.587797	−	0.273012i
$683$			10.2599i			0.392585i	0.980545	+	0.196292i	$0.0628902\pi$
$683$			10.2599i			0.392585i	−0.980545	+	0.196292i	$0.937110\pi$
$684$	35.4852	−	15.5097i	1.35681	−	0.593027i
$685$			21.6388i			0.826776i
$686$	9.87104	−	21.2524i	0.376878	−	0.811421i
$687$	−17.7815	+	13.2625i	−0.678406	+	0.505996i
$688$	−8.37655	+	49.2472i	−0.319353	+	1.87753i
$689$			43.1223i			1.64283i
$690$	−0.661147	−	3.16350i	−0.0251694	−	0.120432i
$691$	10.2513			0.389979			0.194990	−	0.980805i	$-0.437533\pi$
$691$	10.2513			0.389979			0.194990	+	0.980805i	$0.437533\pi$
$692$	25.3260	+	29.9975i	0.962751	+	1.14033i
$693$	−1.56139	+	5.24944i	−0.0593121	+	0.199410i
$694$	−11.6049	+	24.9855i	−0.440517	+	0.948437i
$695$	−9.53082			−0.361525
$696$	12.5299	−	16.0248i	0.474945	−	0.607418i
$697$	−30.5097			−1.15564
$698$	5.86393	−	12.6251i	0.221953	−	0.477867i
$699$	−21.2357	+	15.8388i	−0.803207	+	0.599079i
$700$	6.80032	−	5.74131i	0.257028	−	0.217001i
$701$	−11.7178			−0.442577			−0.221289	−	0.975208i	$-0.571026\pi$
$701$	−11.7178			−0.442577			−0.221289	+	0.975208i	$0.571026\pi$
$702$	2.79712	−	33.5911i	0.105571	−	1.26781i
$703$			19.1425i			0.721972i
$704$	5.43222	+	9.21463i	0.204735	+	0.347290i
$705$	5.49400	+	7.36600i	0.206916	+	0.277420i
$706$	13.4594	−	28.9782i	0.506552	−	1.09061i
$707$		−	9.66263i		−	0.363401i
$708$	−16.1070	−	3.75083i	−0.605337	−	0.140965i
$709$			21.3991i			0.803659i	0.915714	+	0.401830i	$0.131626\pi$
$709$			21.3991i			0.803659i	−0.915714	+	0.401830i	$0.868374\pi$
$710$	24.4382	+	11.3507i	0.917149	+	0.425985i
$711$	1.93057	+	0.574224i	0.0724019	+	0.0215351i
$712$	−12.8827	+	3.51467i	−0.482800	+	0.131718i
$713$		−	8.95087i		−	0.335213i
$714$	−3.25963	−	15.5969i	−0.121989	−	0.583699i
$715$	8.09210			0.302627
$716$	17.1689	−	14.4952i	0.641632	−	0.541711i
$717$	1.51832	+	2.03566i	0.0567026	+	0.0760231i
$718$	9.47304	+	4.39991i	0.353531	+	0.164203i
$719$	11.6604			0.434859			0.217429	−	0.976076i	$-0.430233\pi$
$719$	11.6604			0.434859			0.217429	+	0.976076i	$0.430233\pi$
$720$	−14.2039	−	6.99464i	−0.529349	−	0.260675i
$721$	6.86836			0.255791
$722$	−29.0637	−	13.4991i	−1.08164	−	0.502384i
$723$	−28.7978	−	38.6103i	−1.07100	−	1.43593i
$724$	24.1988	−	20.4303i	0.899341	−	0.759287i
$725$	13.5330			0.502604
$726$	4.61622	+	22.0880i	0.171324	+	0.819762i
$727$			28.7017i			1.06449i	0.846591	+	0.532244i	$0.178651\pi$
$727$			28.7017i			1.06449i	−0.846591	+	0.532244i	$0.821349\pi$
$728$	4.66233	+	17.0893i	0.172798	+	0.633373i
$729$	20.5901	−	17.4657i	0.762595	−	0.646877i
$730$	−6.52808	−	3.03207i	−0.241615	−	0.112222i
$731$			59.5002i			2.20069i
$732$	45.0825	+	10.4983i	1.66630	+	0.388030i
$733$		−	26.0758i		−	0.963133i	−0.876410	−	0.481567i	$-0.840068\pi$
$733$		−	26.0758i		−	0.963133i	0.876410	−	0.481567i	$-0.159932\pi$
$734$	22.3474	−	48.1142i	0.824858	−	1.77593i
$735$	−7.01709	−	9.40806i	−0.258829	−	0.347021i
$736$	−3.20948	+	4.65824i	−0.118303	+	0.171705i
$737$		−	9.64391i		−	0.355238i
$738$	20.3552	+	17.9947i	0.749285	+	0.662394i
$739$	−7.38686			−0.271730			−0.135865	−	0.990727i	$-0.543381\pi$
$739$	−7.38686			−0.271730			−0.135865	+	0.990727i	$0.543381\pi$
$740$	5.97989	−	5.04865i	0.219825	−	0.185592i
$741$	−41.1054	+	30.6588i	−1.51004	+	1.12628i
$742$	7.64658	−	16.4631i	0.280715	−	0.604381i
$743$	48.0073			1.76122			0.880609	−	0.473844i	$-0.157134\pi$
$743$	48.0073			1.76122			0.880609	+	0.473844i	$0.157134\pi$
$744$	−34.5439	−	27.0102i	−1.26644	−	0.990241i
$745$	−11.8089			−0.432646
$746$	−10.0791	+	21.7004i	−0.369022	+	0.794508i
$747$	18.5988	+	5.53200i	0.680496	+	0.202405i
$748$	8.21904	+	9.73508i	0.300518	+	0.355950i
$749$	2.55110			0.0932153
$750$	−5.46054	−	26.1280i	−0.199391	−	0.954058i
$751$			32.4882i			1.18551i	0.805383	+	0.592755i	$0.201960\pi$
$751$			32.4882i			1.18551i	−0.805383	+	0.592755i	$0.798040\pi$
$752$	2.69708	−	15.8566i	0.0983522	−	0.578230i
$753$	14.3539	−	10.7060i	0.523084	−	0.390147i
$754$	−11.3466	+	24.4292i	−0.413217	+	0.889660i
$755$		−	5.58402i		−	0.203223i
$756$	−7.02436	+	12.3283i	−0.255473	+	0.448378i
$757$			6.73563i			0.244810i	0.992480	+	0.122405i	$0.0390608\pi$
$757$			6.73563i			0.244810i	−0.992480	+	0.122405i	$0.960939\pi$
$758$	−12.8927	−	5.98825i	−0.468286	−	0.217503i
$759$	1.85640	−	1.38461i	0.0673830	−	0.0502582i
$760$	6.33968	+	23.2375i	0.229964	+	0.842913i
$761$		−	3.01285i		−	0.109216i	−0.998508	−	0.0546079i	$-0.982609\pi$
$761$		−	3.01285i		−	0.109216i	0.998508	−	0.0546079i	$-0.0173909\pi$
$762$	−9.00622	+	1.88223i	−0.326261	+	0.0681860i
$763$	1.21745			0.0440748
$764$	−14.8123	−	17.5445i	−0.535891	−	0.634738i
$765$	−18.0756	−	5.37637i	−0.653524	−	0.194383i
$766$	21.5290	+	9.99950i	0.777875	+	0.361297i
$767$	21.8987			0.790716
$768$	8.29254	+	26.4430i	0.299231	+	0.954181i
$769$	−16.3685			−0.590264			−0.295132	−	0.955457i	$-0.595364\pi$
$769$	−16.3685			−0.590264			−0.295132	+	0.955457i	$0.595364\pi$
$770$	−3.08939	−	1.43492i	−0.111334	−	0.0517108i
$771$	−28.6434	+	21.3640i	−1.03157	+	0.769405i
$772$	−2.86591	−	3.39454i	−0.103146	−	0.122172i
$773$	46.6435			1.67765			0.838825	−	0.544401i	$-0.183243\pi$
$773$	46.6435			1.67765			0.838825	+	0.544401i	$0.183243\pi$
$774$	35.0934	−	39.6969i	1.26141	−	1.42687i
$775$		−	29.1726i		−	1.04791i
$776$	4.19293	+	15.3688i	0.150517	+	0.551707i
$777$	−4.19326	−	5.62206i	−0.150432	−	0.201690i
$778$	−14.2381	−	6.61312i	−0.510461	−	0.237092i
$779$		−	41.3325i		−	1.48089i
$780$	20.4186	+	4.75488i	0.731104	+	0.170252i
$781$			19.3088i			0.690923i
$782$	−2.83828	+	6.11083i	−0.101497	+	0.218523i
$783$	−20.2548	+	7.43358i	−0.723849	+	0.265654i
$784$	−3.44478	+	20.2525i	−0.123028	+	0.723302i
$785$		−	16.6823i		−	0.595416i
$786$	−29.6681	+	6.20040i	−1.05823	+	0.221161i
$787$	39.7932			1.41847			0.709237	−	0.704970i	$-0.249040\pi$
$787$	39.7932			1.41847			0.709237	+	0.704970i	$0.249040\pi$
$788$	−5.82584	−	6.90044i	−0.207537	−	0.245818i
$789$	−4.38873	−	5.88413i	−0.156243	−	0.209481i
$790$	−0.527714	+	1.13617i	−0.0187752	+	0.0404232i
$791$	−8.59900			−0.305745
$792$	0.258263	−	11.3426i	0.00917699	−	0.403041i
$793$	−61.2932			−2.17658
$794$	−5.46094	+	11.7574i	−0.193801	+	0.417256i
$795$	−12.8446	−	17.2212i	−0.455550	−	0.610772i
$796$	−26.8032	+	22.6291i	−0.950013	+	0.802068i
$797$	2.65832			0.0941625			0.0470812	−	0.998891i	$-0.485008\pi$
$797$	2.65832			0.0941625			0.0470812	+	0.998891i	$0.485008\pi$
$798$	21.1297	−	4.41593i	0.747982	−	0.156322i
$799$		−	19.1578i		−	0.677755i
$800$	−10.4603	+	15.1821i	−0.369828	+	0.536768i
$801$	13.5758	+	4.03795i	0.479676	+	0.142674i
$802$	−1.29659	+	2.79157i	−0.0457842	+	0.0985738i
$803$		−	5.15788i		−	0.182018i
$804$	5.66671	−	24.3343i	0.199850	−	0.858204i
$805$		−	1.80143i		−	0.0634921i
$806$	52.6610	+	24.4593i	1.85490	+	0.861541i
$807$	−32.1185	−	43.0625i	−1.13063	−	1.51587i
$808$	5.26850	+	19.3112i	0.185345	+	0.679365i
$809$			13.5359i			0.475898i	0.971278	+	0.237949i	$0.0764751\pi$
$809$			13.5359i			0.475898i	−0.971278	+	0.237949i	$0.923525\pi$
$810$	8.88852	+	14.2480i	0.312311	+	0.500624i
$811$	−1.37725			−0.0483618			−0.0241809	−	0.999708i	$-0.507698\pi$
$811$	−1.37725			−0.0483618			−0.0241809	+	0.999708i	$0.507698\pi$
$812$	8.66374	−	7.31454i	0.304038	−	0.256690i
$813$	27.0059	−	20.1426i	0.947137	−	0.706431i
$814$	5.08622	+	2.36238i	0.178272	+	0.0828013i
$815$	−12.4633			−0.436572
$816$	15.0186	+	29.3938i	0.525758	+	1.02899i
$817$	−80.6070			−2.82008
$818$	−33.1196	−	15.3829i	−1.15800	−	0.537852i
$819$	5.35648	−	18.0087i	0.187171	−	0.629275i
$820$	−12.9118	+	10.9011i	−0.450900	+	0.380682i
$821$	33.3794			1.16495			0.582474	−	0.812849i	$-0.302085\pi$
$821$	33.3794			1.16495			0.582474	+	0.812849i	$0.302085\pi$
$822$	−39.3233	+	8.21826i	−1.37156	+	0.286645i
$823$		−	11.2129i		−	0.390857i	−0.980718	−	0.195428i	$-0.937390\pi$
$823$		−	11.2129i		−	0.390857i	0.980718	−	0.195428i	$-0.0626098\pi$
$824$	−13.7267	+	3.74494i	−0.478193	+	0.130461i
$825$	6.05036	−	4.51271i	0.210646	−	0.157113i
$826$	−8.36044	−	3.88315i	−0.290897	−	0.135112i
$827$			38.6735i			1.34481i	0.740184	+	0.672405i	$0.234739\pi$
$827$			38.6735i			1.34481i	−0.740184	+	0.672405i	$0.765261\pi$
$828$	5.49780	−	2.40295i	0.191062	−	0.0835083i
$829$		−	41.7245i		−	1.44915i	−0.689195	−	0.724576i	$-0.742036\pi$
$829$		−	41.7245i		−	1.44915i	0.689195	−	0.724576i	$-0.257964\pi$
$830$	−5.08393	+	10.9457i	−0.176466	+	0.379932i
$831$	−11.4534	+	8.54259i	−0.397312	+	0.296339i
$832$	−18.6358	−	31.6117i	−0.646078	−	1.09594i
$833$			24.4689i			0.847798i
$834$	−3.61974	−	17.3200i	−0.125341	−	0.599741i
$835$	21.2622			0.735810
$836$	−13.1884	+	11.1346i	−0.456132	+	0.385099i
$837$	16.0242	+	43.6625i	0.553878	+	1.50920i
$838$	−17.4209	+	37.5074i	−0.601797	+	1.29567i
$839$	2.64966			0.0914763			0.0457382	−	0.998953i	$-0.485436\pi$
$839$	2.64966			0.0914763			0.0457382	+	0.998953i	$0.485436\pi$
$840$	−6.95224	−	5.43601i	−0.239875	−	0.187560i
$841$	−11.7586			−0.405470
$842$	−13.9264	+	29.9837i	−0.479937	+	1.03331i
$843$	14.2431	−	10.6234i	0.490559	−	0.365888i
$844$	−15.7734	−	18.6829i	−0.542944	−	0.643093i
$845$	−10.6085			−0.364945
$846$	−11.2993	+	12.7816i	−0.388479	+	0.439439i
$847$			12.5778i			0.432180i
$848$	−6.30557	+	37.0716i	−0.216534	+	1.27304i
$849$	27.3044	+	36.6080i	0.937086	+	1.25638i
$850$	−9.25048	+	19.9164i	−0.317289	+	0.683125i
$851$			2.96579i			0.101666i
$852$	−11.3457	+	48.7214i	−0.388699	+	1.66917i
$853$			35.8481i			1.22741i	0.789534	+	0.613707i	$0.210322\pi$
$853$			35.8481i			1.22741i	−0.789534	+	0.613707i	$0.789678\pi$
$854$	23.4004	+	10.8687i	0.800745	+	0.371919i
$855$	7.28356	−	24.4876i	0.249092	−	0.837459i
$856$	−5.09849	+	1.39098i	−0.174263	+	0.0475426i
$857$			13.4775i			0.460382i	0.973145	+	0.230191i	$0.0739351\pi$
$857$			13.4775i			0.460382i	−0.973145	+	0.230191i	$0.926065\pi$
$858$	3.07332	+	14.7054i	0.104921	+	0.502035i
$859$	10.5134			0.358712			0.179356	−	0.983784i	$-0.442599\pi$
$859$	10.5134			0.358712			0.179356	+	0.983784i	$0.442599\pi$
$860$	21.2593	+	25.1807i	0.724938	+	0.858656i
$861$	9.05412	+	12.1392i	0.308563	+	0.413702i
$862$	−42.2471	−	19.6224i	−1.43894	−	0.668341i
$863$	−30.0153			−1.02173			−0.510866	−	0.859660i	$-0.670675\pi$
$863$	−30.0153			−1.02173			−0.510866	+	0.859660i	$0.670675\pi$
$864$	7.31651	−	28.4687i	0.248913	−	0.968526i
$865$	25.8990			0.880593
$866$	−4.16485	−	1.93443i	−0.141527	−	0.0657347i
$867$	5.90161	+	7.91250i	0.200429	+	0.268723i
$868$	−15.7676	−	18.6760i	−0.535188	−	0.633906i
$869$	−0.897697			−0.0304523
$870$	−2.74526	−	13.1357i	−0.0930731	−	0.445343i
$871$			33.0843i			1.12102i
$872$	−2.43314	+	0.663811i	−0.0823964	+	0.0224795i
$873$	4.81719	−	16.1956i	0.163037	−	0.548138i
$874$	−8.27855	−	3.84511i	−0.280026	−	0.130063i
$875$		−	14.8784i		−	0.502981i
$876$	3.03074	−	13.0148i	0.102399	−	0.439728i
$877$		−	50.7448i		−	1.71353i	−0.515708	−	0.856765i	$-0.672471\pi$
$877$		−	50.7448i		−	1.71353i	0.515708	−	0.856765i	$-0.327529\pi$
$878$	−22.2010	+	47.7989i	−0.749247	+	1.61314i
$879$	13.1217	+	17.5928i	0.442585	+	0.593390i
$880$	6.95666	+	1.18327i	0.234509	+	0.0398881i
$881$		−	49.1117i		−	1.65462i	−0.561748	−	0.827308i	$-0.689871\pi$
$881$		−	49.1117i		−	1.65462i	0.561748	−	0.827308i	$-0.310129\pi$
$882$	14.4318	−	16.3250i	0.485945	−	0.549690i
$883$	−1.27137			−0.0427848			−0.0213924	−	0.999771i	$-0.506810\pi$
$883$	−1.27137			−0.0427848			−0.0213924	+	0.999771i	$0.506810\pi$
$884$	−28.1962	−	33.3971i	−0.948340	−	1.12327i
$885$	−8.74540	+	6.52284i	−0.293973	+	0.219263i
$886$	17.3735	−	37.4053i	0.583674	−	1.25665i
$887$	41.8230			1.40428			0.702140	−	0.712039i	$-0.252228\pi$
$887$	41.8230			1.40428			0.702140	+	0.712039i	$0.252228\pi$
$888$	11.4458	+	8.94957i	0.384096	+	0.300328i
$889$	−5.12852			−0.172005
$890$	−3.71089	+	7.98957i	−0.124389	+	0.267811i
$891$	−6.57675	+	10.0776i	−0.220329	+	0.337611i
$892$	4.84265	−	4.08850i	0.162144	−	0.136893i
$893$	25.9538			0.868510
$894$	−4.48495	−	21.4599i	−0.149999	−	0.717726i
$895$		−	14.8231i		−	0.495483i
$896$	1.50924	+	15.3732i	0.0504203	+	0.513582i
$897$	−6.36855	+	4.75004i	−0.212640	+	0.158599i
$898$	−12.4853	+	26.8810i	−0.416640	+	0.897030i
$899$		−	37.1664i		−	1.23957i
$900$	17.9184	−	7.83167i	0.597279	−	0.261056i
$901$			44.7896i			1.49216i
$902$	−10.9822	−	5.10086i	−0.365667	−	0.169840i
$903$	23.6739	−	17.6574i	0.787819	−	0.587602i
$904$	17.1855	−	4.68856i	0.571580	−	0.155939i
$905$		−	20.8926i		−	0.694492i
$906$	10.1476	−	2.12077i	0.337131	−	0.0704578i
$907$	−6.60707			−0.219384			−0.109692	−	0.993966i	$-0.534986\pi$
$907$	−6.60707			−0.219384			−0.109692	+	0.993966i	$0.534986\pi$
$908$	−35.8355	+	30.2548i	−1.18924	+	1.00404i
$909$	6.05290	−	20.3501i	0.200762	−	0.674970i
$910$	10.5984	+	4.92262i	0.351335	+	0.163183i
$911$	−33.6633			−1.11531			−0.557657	−	0.830071i	$-0.688300\pi$
$911$	−33.6633			−1.11531			−0.557657	+	0.830071i	$0.688300\pi$
$912$	−39.8208	+	20.3463i	−1.31860	+	0.673732i
$913$	−8.64830			−0.286217
$914$	7.84246	+	3.64256i	0.259406	+	0.120485i
$915$	24.4779	−	18.2570i	0.809213	−	0.603559i
$916$	19.5719	−	16.5240i	0.646673	−	0.545967i
$917$	−16.8943			−0.557898
$918$	2.90528	−	34.8899i	0.0958885	−	1.15154i
$919$			25.1074i			0.828217i	0.910228	+	0.414108i	$0.135907\pi$
$919$			25.1074i			0.828217i	−0.910228	+	0.414108i	$0.864093\pi$
$920$	0.982222	+	3.60024i	0.0323829	+	0.118696i
$921$	−19.3032	−	25.8805i	−0.636062	−	0.852791i
$922$	17.7566	+	8.24734i	0.584782	+	0.271612i
$923$		−	66.2406i		−	2.18034i
$924$	1.43429	−	6.15919i	0.0471846	−	0.202622i
$925$			9.66606i			0.317818i
$926$	−1.76780	+	3.80610i	−0.0580937	+	0.125076i
$927$	14.4652	+	4.30250i	0.475099	+	0.141313i
$928$	−13.3266	+	19.3423i	−0.437468	+	0.634942i
$929$		−	0.184520i		−	0.00605391i	−0.999995	−	0.00302695i	$-0.999036\pi$
$929$		−	0.184520i		−	0.00605391i	0.999995	−	0.00302695i	$-0.000963511\pi$
$930$	−28.3161	+	5.91784i	−0.928521	+	0.194054i
$931$	−33.1489			−1.08641
$932$	23.3739	−	19.7339i	0.765636	−	0.646404i
$933$	−27.9065	−	37.4152i	−0.913617	−	1.22492i
$934$	3.58124	−	7.71043i	0.117182	−	0.252293i
$935$	8.40500			0.274873
$936$	−0.885997	+	38.9118i	−0.0289597	+	1.27187i
$937$	48.0815			1.57075			0.785377	−	0.619018i	$-0.212469\pi$
$937$	48.0815			1.57075			0.785377	+	0.619018i	$0.212469\pi$
$938$	5.86662	−	12.6309i	0.191552	−	0.412413i
$939$	12.9870	+	17.4121i	0.423813	+	0.568222i
$940$	−6.84507	−	8.10767i	−0.223261	−	0.264443i
$941$	40.1340			1.30833			0.654165	−	0.756351i	$-0.273020\pi$
$941$	40.1340			1.30833			0.654165	+	0.756351i	$0.273020\pi$
$942$	30.3160	−	6.33581i	0.987749	−	0.206432i
$943$		−	6.40374i		−	0.208535i
$944$	18.8260	+	3.20215i	0.612733	+	0.104221i
$945$	3.22500	+	8.78741i	0.104909	+	0.285854i
$946$	−9.94773	+	21.4175i	−0.323429	+	0.696344i
$947$		−	20.8573i		−	0.677772i	−0.940827	−	0.338886i	$-0.889950\pi$
$947$		−	20.8573i		−	0.677772i	0.940827	−	0.338886i	$-0.110050\pi$
$948$	−2.26514	−	0.527482i	−0.0735683	−	0.0171318i
$949$			17.6946i			0.574391i
$950$	−26.9814	−	12.5319i	−0.875392	−	0.406590i
$951$	20.0832	+	26.9262i	0.651241	+	0.873142i
$952$	4.84261	+	17.7501i	0.156950	+	0.575285i
$953$			29.3926i			0.952119i	0.879413	+	0.476059i	$0.157935\pi$
$953$			29.3926i			0.952119i	−0.879413	+	0.476059i	$0.842065\pi$
$954$	26.4171	−	29.8824i	0.855284	−	0.967478i
$955$	−15.1474			−0.490160
$956$	−1.89170	−	2.24063i	−0.0611818	−	0.0724671i
$957$	7.70827	−	5.74928i	0.249173	−	0.185848i
$958$	21.1662	+	9.83098i	0.683848	+	0.317625i
$959$	−22.3923			−0.723086
$960$	16.8583	+	7.07342i	0.544099	+	0.228294i
$961$	−49.1180			−1.58445
$962$	−17.4487	−	8.10436i	−0.562570	−	0.261295i
$963$	5.37278	+	1.59807i	0.173135	+	0.0514971i
$964$	35.8797	+	42.4979i	1.15561	+	1.36876i
$965$	−2.93076			−0.0943444
$966$	3.27367	−	0.684171i	0.105329	−	0.0220128i
$967$			12.6402i			0.406483i	0.979129	+	0.203241i	$0.0651476\pi$
$967$			12.6402i			0.406483i	−0.979129	+	0.203241i	$0.934852\pi$
$968$	−6.85800	−	25.1374i	−0.220425	−	0.807945i
$969$	−42.6948	+	31.8443i	−1.37155	+	1.02299i
$970$	9.53138	+	4.42701i	0.306034	+	0.142143i
$971$		−	30.5184i		−	0.979382i	−0.871896	−	0.489691i	$-0.837110\pi$
$971$		−	30.5184i		−	0.979382i	0.871896	−	0.489691i	$-0.162890\pi$
$972$	−22.5165	+	21.5640i	−0.722217	+	0.691667i
$973$		−	9.86272i		−	0.316184i
$974$	−12.0097	+	25.8569i	−0.384814	+	0.828509i
$975$	−20.7563	+	15.4813i	−0.664734	+	0.495798i
$976$	−52.6928	−	8.96262i	−1.68666	−	0.286887i
$977$			21.2857i			0.680988i	0.940247	+	0.340494i	$0.110594\pi$
$977$			21.2857i			0.680988i	−0.940247	+	0.340494i	$0.889406\pi$
$978$	−4.73349	−	22.6491i	−0.151360	−	0.724239i
$979$	−6.31262			−0.201752
$980$	8.74271	+	10.3553i	0.279276	+	0.330789i
$981$	2.56403	+	0.762642i	0.0818633	+	0.0243493i
$982$	15.6614	−	33.7192i	0.499776	−	1.07602i
$983$	−7.49983			−0.239208			−0.119604	−	0.992822i	$-0.538162\pi$
$983$	−7.49983			−0.239208			−0.119604	+	0.992822i	$0.538162\pi$
$984$	−24.7139	−	19.3240i	−0.787849	−	0.616025i
$985$	−5.95765			−0.189827
$986$	−11.7853	+	25.3738i	−0.375320	+	0.808067i
$987$	−7.62251	+	5.68532i	−0.242627	+	0.180966i
$988$	45.2442	−	38.1984i	1.43941	−	1.21525i
$989$	−12.4886			−0.397115
$990$	−5.60758	−	4.95729i	−0.178220	−	0.157553i
$991$		−	11.7843i		−	0.374341i	−0.982327	−	0.187170i	$-0.940068\pi$
$991$		−	11.7843i		−	0.374341i	0.982327	−	0.187170i	$-0.0599316\pi$
$992$	41.6953	+	28.7276i	1.32383	+	0.912104i
$993$	9.08263	+	12.1774i	0.288228	+	0.386438i
$994$	−11.7460	+	25.2892i	−0.372560	+	0.802125i
$995$			23.1411i			0.733623i
$996$	−21.8221	−	5.08170i	−0.691459	−	0.161020i
$997$		−	13.9402i		−	0.441490i	−0.975332	−	0.220745i	$-0.929151\pi$
$997$		−	13.9402i		−	0.441490i	0.975332	−	0.220745i	$-0.0708489\pi$
$998$	−0.670622	−	0.311482i	−0.0212282	−	0.00985978i
$999$	−5.30948	−	14.4672i	−0.167985	−	0.457721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.j.c.323.7	✓	42
3.2	odd	2		552.2.j.d.323.36	yes	42
4.3	odd	2		2208.2.j.c.47.30		42
8.3	odd	2		552.2.j.d.323.35	yes	42
8.5	even	2		2208.2.j.d.47.30		42
12.11	even	2		2208.2.j.d.47.29		42
24.5	odd	2		2208.2.j.c.47.29		42
24.11	even	2	inner	552.2.j.c.323.8	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.j.c.323.7	✓	42	1.1	even	1	trivial
552.2.j.c.323.8	yes	42	24.11	even	2	inner
552.2.j.d.323.35	yes	42	8.3	odd	2
552.2.j.d.323.36	yes	42	3.2	odd	2
2208.2.j.c.47.29		42	24.5	odd	2
2208.2.j.c.47.30		42	4.3	odd	2
2208.2.j.d.47.29		42	12.11	even	2
2208.2.j.d.47.30		42	8.5	even	2

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28262 - 0.595732i) q^{2} +(-1.03555 - 1.38840i) q^{3} +(1.29021 + 1.52819i) q^{4} +1.31940 q^{5} +(0.501098 + 2.39769i) q^{6} +1.36534i q^{7} +(-0.744447 - 2.72870i) q^{8} +(-0.855283 + 2.87550i) q^{9} +O(q^{10})\)	\(q+(-1.28262 - 0.595732i) q^{2} +(-1.03555 - 1.38840i) q^{3} +(1.29021 + 1.52819i) q^{4} +1.31940 q^{5} +(0.501098 + 2.39769i) q^{6} +1.36534i q^{7} +(-0.744447 - 2.72870i) q^{8} +(-0.855283 + 2.87550i) q^{9} +(-1.69228 - 0.786008i) q^{10} -1.33708i q^{11} +(0.785663 - 3.37383i) q^{12} +4.58699i q^{13} +(0.813379 - 1.75121i) q^{14} +(-1.36630 - 1.83185i) q^{15} +(-0.670734 + 3.94336i) q^{16} +4.76435i q^{17} +(2.81003 - 3.17864i) q^{18} -6.45443 q^{19} +(1.70230 + 2.01629i) q^{20} +(1.89564 - 1.41388i) q^{21} +(-0.796543 + 1.71496i) q^{22} -1.00000 q^{23} +(-3.01760 + 3.85928i) q^{24} -3.25919 q^{25} +(2.73261 - 5.88334i) q^{26} +(4.87801 - 1.79024i) q^{27} +(-2.08651 + 1.76158i) q^{28} -4.15227 q^{29} +(0.661147 + 3.16350i) q^{30} +8.95087i q^{31} +(3.20948 - 4.65824i) q^{32} +(-1.85640 + 1.38461i) q^{33} +(2.83828 - 6.11083i) q^{34} +1.80143i q^{35} +(-5.49780 + 2.40295i) q^{36} -2.96579i q^{37} +(8.27855 + 3.84511i) q^{38} +(6.36855 - 4.75004i) q^{39} +(-0.982222 - 3.60024i) q^{40} +6.40374i q^{41} +(-3.27367 + 0.684171i) q^{42} +12.4886 q^{43} +(2.04332 - 1.72511i) q^{44} +(-1.12846 + 3.79393i) q^{45} +(1.28262 + 0.595732i) q^{46} -4.02108 q^{47} +(6.16952 - 3.15230i) q^{48} +5.13584 q^{49} +(4.18029 + 1.94160i) q^{50} +(6.61480 - 4.93371i) q^{51} +(-7.00979 + 5.91816i) q^{52} +9.40100 q^{53} +(-7.32312 - 0.609796i) q^{54} -1.76414i q^{55} +(3.72561 - 1.01643i) q^{56} +(6.68387 + 8.96130i) q^{57} +(5.32577 + 2.47364i) q^{58} -4.77409i q^{59} +(1.03660 - 4.45142i) q^{60} +13.3624i q^{61} +(5.33232 - 11.4805i) q^{62} +(-3.92604 - 1.16776i) q^{63} +(-6.89160 + 4.06274i) q^{64} +6.05206i q^{65} +(3.20590 - 0.670009i) q^{66} +7.21265 q^{67} +(-7.28083 + 6.14699i) q^{68} +(1.03555 + 1.38840i) q^{69} +(1.07317 - 2.31054i) q^{70} -14.4410 q^{71} +(8.48308 + 0.193154i) q^{72} +3.85756 q^{73} +(-1.76681 + 3.80397i) q^{74} +(3.37505 + 4.52504i) q^{75} +(-8.32755 - 9.86360i) q^{76} +1.82558 q^{77} +(-10.9982 + 2.29853i) q^{78} -0.671385i q^{79} +(-0.884965 + 5.20286i) q^{80} +(-7.53698 - 4.91873i) q^{81} +(3.81492 - 8.21354i) q^{82} -6.46804i q^{83} +(4.60644 + 1.07270i) q^{84} +6.28607i q^{85} +(-16.0181 - 7.43988i) q^{86} +(4.29987 + 5.76499i) q^{87} +(-3.64850 + 0.995387i) q^{88} -4.72119i q^{89} +(3.70754 - 4.19389i) q^{90} -6.26281 q^{91} +(-1.29021 - 1.52819i) q^{92} +(12.4273 - 9.26905i) q^{93} +(5.15750 + 2.39549i) q^{94} -8.51596 q^{95} +(-9.79105 + 0.367801i) q^{96} -5.63227 q^{97} +(-6.58730 - 3.05958i) q^{98} +(3.84478 + 1.14358i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9}+O(q^{10}) \) 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9	\( 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{14} + 8 q^{15} - 12 q^{16} + 16 q^{18} + 4 q^{19} + 2 q^{20} - 8 q^{21} + 18 q^{22} - 42 q^{23} - 24 q^{24} + 22 q^{25} - 11 q^{26} - 16 q^{27} + 6 q^{28} - 24 q^{30} + 20 q^{32} + 12 q^{33} + 14 q^{34} + 15 q^{36} + 22 q^{38} - 8 q^{39} + 4 q^{40} + 36 q^{42} + 28 q^{43} - 56 q^{44} + 8 q^{45} - 9 q^{48} - 50 q^{49} - 20 q^{50} + 28 q^{51} - q^{52} - 24 q^{53} - 24 q^{54} + 34 q^{56} - 8 q^{57} - 21 q^{58} + 18 q^{60} + 79 q^{62} + 16 q^{63} + 7 q^{64} + 16 q^{66} - 4 q^{67} - 20 q^{68} - 2 q^{69} - 8 q^{70} - 62 q^{72} + 4 q^{73} - 36 q^{74} - 6 q^{75} + 14 q^{76} - 32 q^{77} - 62 q^{78} + 52 q^{80} + 18 q^{81} + 11 q^{82} + 66 q^{84} + 28 q^{86} + 48 q^{87} - 38 q^{88} - 8 q^{91} - 4 q^{92} + 22 q^{93} + q^{94} + 16 q^{95} - 54 q^{96} + 20 q^{97} - 64 q^{98}+O(q^{100}) \) 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^14 + 8 * q^15 - 12 * q^16 + 16 * q^18 + 4 * q^19 + 2 * q^20 - 8 * q^21 + 18 * q^22 - 42 * q^23 - 24 * q^24 + 22 * q^25 - 11 * q^26 - 16 * q^27 + 6 * q^28 - 24 * q^30 + 20 * q^32 + 12 * q^33 + 14 * q^34 + 15 * q^36 + 22 * q^38 - 8 * q^39 + 4 * q^40 + 36 * q^42 + 28 * q^43 - 56 * q^44 + 8 * q^45 - 9 * q^48 - 50 * q^49 - 20 * q^50 + 28 * q^51 - q^52 - 24 * q^53 - 24 * q^54 + 34 * q^56 - 8 * q^57 - 21 * q^58 + 18 * q^60 + 79 * q^62 + 16 * q^63 + 7 * q^64 + 16 * q^66 - 4 * q^67 - 20 * q^68 - 2 * q^69 - 8 * q^70 - 62 * q^72 + 4 * q^73 - 36 * q^74 - 6 * q^75 + 14 * q^76 - 32 * q^77 - 62 * q^78 + 52 * q^80 + 18 * q^81 + 11 * q^82 + 66 * q^84 + 28 * q^86 + 48 * q^87 - 38 * q^88 - 8 * q^91 - 4 * q^92 + 22 * q^93 + q^94 + 16 * q^95 - 54 * q^96 + 20 * q^97 - 64 * q^98

Introduction

L-functions

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