LMFDB - Embedded newform 552.2.j.d.323.18

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			323.18
Character	$\chi$	$=$	552.323
Dual form			552.2.j.d.323.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.242573 + 1.39325i) q^{2} +(1.04780 - 1.37917i) q^{3} +(-1.88232 - 0.675933i) q^{4} -2.15601 q^{5} +(1.66736 + 1.79441i) q^{6} +2.22228i q^{7} +(1.39835 - 2.45858i) q^{8} +(-0.804216 - 2.89020i) q^{9} +O(q^{10})$	\(q+(-0.242573 + 1.39325i) q^{2} +(1.04780 - 1.37917i) q^{3} +(-1.88232 - 0.675933i) q^{4} -2.15601 q^{5} +(1.66736 + 1.79441i) q^{6} +2.22228i q^{7} +(1.39835 - 2.45858i) q^{8} +(-0.804216 - 2.89020i) q^{9} +(0.522991 - 3.00387i) q^{10} +0.626490i q^{11} +(-2.90452 + 1.88779i) q^{12} +6.39606i q^{13} +(-3.09620 - 0.539065i) q^{14} +(-2.25908 + 2.97350i) q^{15} +(3.08623 + 2.54464i) q^{16} +6.37058i q^{17} +(4.22186 - 0.419393i) q^{18} +5.79186 q^{19} +(4.05830 + 1.45732i) q^{20} +(3.06490 + 2.32851i) q^{21} +(-0.872860 - 0.151970i) q^{22} +1.00000 q^{23} +(-1.92561 - 4.50467i) q^{24} -0.351614 q^{25} +(-8.91134 - 1.55151i) q^{26} +(-4.82873 - 1.91921i) q^{27} +(1.50211 - 4.18303i) q^{28} +2.65071 q^{29} +(-3.59486 - 3.86876i) q^{30} +8.01146i q^{31} +(-4.29397 + 3.68264i) q^{32} +(0.864036 + 0.656438i) q^{33} +(-8.87583 - 1.54533i) q^{34} -4.79125i q^{35} +(-0.439790 + 5.98386i) q^{36} -10.2039i q^{37} +(-1.40495 + 8.06954i) q^{38} +(8.82125 + 6.70181i) q^{39} +(-3.01485 + 5.30073i) q^{40} +7.00850i q^{41} +(-3.98767 + 3.70535i) q^{42} +3.82323 q^{43} +(0.423465 - 1.17925i) q^{44} +(1.73390 + 6.23130i) q^{45} +(-0.242573 + 1.39325i) q^{46} -11.0290 q^{47} +(6.74325 - 1.59015i) q^{48} +2.06149 q^{49} +(0.0852922 - 0.489888i) q^{50} +(8.78610 + 6.67511i) q^{51} +(4.32331 - 12.0394i) q^{52} -2.62158 q^{53} +(3.84527 - 6.26210i) q^{54} -1.35072i q^{55} +(5.46365 + 3.10751i) q^{56} +(6.06873 - 7.98796i) q^{57} +(-0.642993 + 3.69312i) q^{58} +6.88102i q^{59} +(6.26219 - 4.07009i) q^{60} -11.0044i q^{61} +(-11.1620 - 1.94337i) q^{62} +(6.42282 - 1.78719i) q^{63} +(-4.08926 - 6.87590i) q^{64} -13.7900i q^{65} +(-1.12418 + 1.04459i) q^{66} -6.97288 q^{67} +(4.30608 - 11.9914i) q^{68} +(1.04780 - 1.37917i) q^{69} +(6.67544 + 1.16223i) q^{70} +5.08761 q^{71} +(-8.23036 - 2.06426i) q^{72} -10.1166 q^{73} +(14.2166 + 2.47519i) q^{74} +(-0.368422 + 0.484935i) q^{75} +(-10.9021 - 3.91491i) q^{76} -1.39223 q^{77} +(-11.4771 + 10.6646i) q^{78} +9.79878i q^{79} +(-6.65395 - 5.48627i) q^{80} +(-7.70647 + 4.64868i) q^{81} +(-9.76463 - 1.70008i) q^{82} +0.202439i q^{83} +(-4.19519 - 6.45465i) q^{84} -13.7350i q^{85} +(-0.927413 + 5.32673i) q^{86} +(2.77743 - 3.65578i) q^{87} +(1.54028 + 0.876050i) q^{88} +0.147764i q^{89} +(-9.10238 + 0.904216i) q^{90} -14.2138 q^{91} +(-1.88232 - 0.675933i) q^{92} +(11.0492 + 8.39443i) q^{93} +(2.67534 - 15.3662i) q^{94} -12.4873 q^{95} +(0.579754 + 9.78079i) q^{96} +5.73742 q^{97} +(-0.500062 + 2.87218i) q^{98} +(1.81068 - 0.503833i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) $ 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9	$ 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) $ 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * 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 $

$2$	−0.242573	+	1.39325i	−0.171525	+	0.985180i
$2$	−0.242573	+	1.39325i	−0.171525	+	0.985180i
$3$	1.04780	−	1.37917i	0.604950	−	0.796264i
$3$	1.04780	−	1.37917i	0.604950	−	0.796264i
$4$	−1.88232	−	0.675933i	−0.941158	−	0.337966i
$5$	−2.15601			−0.964198			−0.482099	−	0.876117i	$-0.660125\pi$
$5$	−2.15601			−0.964198			−0.482099	+	0.876117i	$0.660125\pi$
$6$	1.66736	+	1.79441i	0.680699	+	0.732563i
$7$			2.22228i			0.839942i	0.907538	+	0.419971i	$0.137960\pi$
$7$			2.22228i			0.839942i	−0.907538	+	0.419971i	$0.862040\pi$
$8$	1.39835	−	2.45858i	0.494390	−	0.869240i
$9$	−0.804216	−	2.89020i	−0.268072	−	0.963399i
$10$	0.522991	−	3.00387i	0.165384	−	0.949908i
$11$			0.626490i			0.188894i	0.995530	+	0.0944469i	$0.0301083\pi$
$11$			0.626490i			0.188894i	−0.995530	+	0.0944469i	$0.969892\pi$
$12$	−2.90452	+	1.88779i	−0.838464	+	0.544958i
$13$			6.39606i			1.77395i	0.461820	+	0.886974i	$0.347197\pi$
$13$			6.39606i			1.77395i	−0.461820	+	0.886974i	$0.652803\pi$
$14$	−3.09620	−	0.539065i	−0.827493	−	0.144071i
$15$	−2.25908	+	2.97350i	−0.583291	+	0.767756i
$16$	3.08623	+	2.54464i	0.771557	+	0.636160i
$17$			6.37058i			1.54509i	0.634959	+	0.772546i	$0.281017\pi$
$17$			6.37058i			1.54509i	−0.634959	+	0.772546i	$0.718983\pi$
$18$	4.22186	−	0.419393i	0.995102	−	0.0988518i
$19$	5.79186			1.32874			0.664372	−	0.747402i	$-0.268699\pi$
$19$	5.79186			1.32874			0.664372	+	0.747402i	$0.268699\pi$
$20$	4.05830	+	1.45732i	0.907463	+	0.325866i
$21$	3.06490	+	2.32851i	0.668815	+	0.508122i
$22$	−0.872860	−	0.151970i	−0.186094	−	0.0324001i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	−1.92561	−	4.50467i	−0.393063	−	0.919511i
$25$	−0.351614			−0.0703228
$26$	−8.91134	−	1.55151i	−1.74766	−	0.304277i
$27$	−4.82873	−	1.91921i	−0.929290	−	0.369352i
$28$	1.50211	−	4.18303i	0.283872	−	0.790518i
$29$	2.65071			0.492225			0.246113	−	0.969241i	$-0.420847\pi$
$29$	2.65071			0.492225			0.246113	+	0.969241i	$0.420847\pi$
$30$	−3.59486	−	3.86876i	−0.656328	−	0.706336i
$31$			8.01146i			1.43890i	0.694544	+	0.719450i	$0.255606\pi$
$31$			8.01146i			1.43890i	−0.694544	+	0.719450i	$0.744394\pi$
$32$	−4.29397	+	3.68264i	−0.759073	+	0.651005i
$33$	0.864036	+	0.656438i	0.150409	+	0.114271i
$34$	−8.87583	−	1.54533i	−1.52219	−	0.265022i
$35$		−	4.79125i		−	0.809870i
$36$	−0.439790	+	5.98386i	−0.0732983	+	0.997310i
$37$		−	10.2039i		−	1.67751i	−0.544509	−	0.838755i	$-0.683284\pi$
$37$		−	10.2039i		−	1.67751i	0.544509	−	0.838755i	$-0.316716\pi$
$38$	−1.40495	+	8.06954i	−0.227913	+	1.30905i
$39$	8.82125	+	6.70181i	1.41253	+	1.07315i
$40$	−3.01485	+	5.30073i	−0.476690	+	0.838119i
$41$			7.00850i			1.09454i	0.836955	+	0.547272i	$0.184334\pi$
$41$			7.00850i			1.09454i	−0.836955	+	0.547272i	$0.815666\pi$
$42$	−3.98767	+	3.70535i	−0.615310	+	0.571747i
$43$	3.82323			0.583036			0.291518	−	0.956565i	$-0.405840\pi$
$43$	3.82323			0.583036			0.291518	+	0.956565i	$0.405840\pi$
$44$	0.423465	−	1.17925i	0.0638398	−	0.177779i
$45$	1.73390	+	6.23130i	0.258474	+	0.928907i
$46$	−0.242573	+	1.39325i	−0.0357655	+	0.205424i
$47$	−11.0290			−1.60874			−0.804371	−	0.594127i	$-0.797497\pi$
$47$	−11.0290			−1.60874			−0.804371	+	0.594127i	$0.797497\pi$
$48$	6.74325	−	1.59015i	0.973304	−	0.229519i
$49$	2.06149			0.294498
$50$	0.0852922	−	0.489888i	0.0120621	−	0.0692806i
$51$	8.78610	+	6.67511i	1.23030	+	0.934703i
$52$	4.32331	−	12.0394i	0.599535	−	1.66956i
$53$	−2.62158			−0.360101			−0.180051	−	0.983657i	$-0.557626\pi$
$53$	−2.62158			−0.360101			−0.180051	+	0.983657i	$0.557626\pi$
$54$	3.84527	−	6.26210i	0.523275	−	0.852164i
$55$		−	1.35072i		−	0.182131i
$56$	5.46365	+	3.10751i	0.730111	+	0.415259i
$57$	6.06873	−	7.98796i	0.803823	−	1.05803i
$58$	−0.642993	+	3.69312i	−0.0844291	+	0.484930i
$59$			6.88102i			0.895832i	0.894076	+	0.447916i	$0.147834\pi$
$59$			6.88102i			0.895832i	−0.894076	+	0.447916i	$0.852166\pi$
$60$	6.26219	−	4.07009i	0.808445	−	0.525447i
$61$		−	11.0044i		−	1.40897i	−0.709717	−	0.704487i	$-0.751177\pi$
$61$		−	11.0044i		−	1.40897i	0.709717	−	0.704487i	$-0.248823\pi$
$62$	−11.1620	−	1.94337i	−1.41758	−	0.246808i
$63$	6.42282	−	1.78719i	0.809199	−	0.225165i
$64$	−4.08926	−	6.87590i	−0.511157	−	0.859487i
$65$		−	13.7900i		−	1.71044i
$66$	−1.12418	+	1.04459i	−0.138377	+	0.128580i
$67$	−6.97288			−0.851872			−0.425936	−	0.904753i	$-0.640055\pi$
$67$	−6.97288			−0.851872			−0.425936	+	0.904753i	$0.640055\pi$
$68$	4.30608	−	11.9914i	0.522189	−	1.45418i
$69$	1.04780	−	1.37917i	0.126141	−	0.166032i
$70$	6.67544	+	1.16223i	0.797867	+	0.138913i
$71$	5.08761			0.603788			0.301894	−	0.953341i	$-0.402381\pi$
$71$	5.08761			0.603788			0.301894	+	0.953341i	$0.402381\pi$
$72$	−8.23036	−	2.06426i	−0.969957	−	0.243276i
$73$	−10.1166			−1.18406			−0.592031	−	0.805915i	$-0.701674\pi$
$73$	−10.1166			−1.18406			−0.592031	+	0.805915i	$0.701674\pi$
$74$	14.2166	+	2.47519i	1.65265	+	0.287735i
$75$	−0.368422	+	0.484935i	−0.0425418	+	0.0559955i
$76$	−10.9021	−	3.91491i	−1.25056	−	0.449071i
$77$	−1.39223			−0.158660
$78$	−11.4771	+	10.6646i	−1.29953	+	1.20752i
$79$			9.79878i			1.10245i	0.834357	+	0.551225i	$0.185839\pi$
$79$			9.79878i			1.10245i	−0.834357	+	0.551225i	$0.814161\pi$
$80$	−6.65395	−	5.48627i	−0.743934	−	0.613384i
$81$	−7.70647	+	4.64868i	−0.856275	+	0.516520i
$82$	−9.76463	−	1.70008i	−1.07832	−	0.187742i
$83$			0.202439i			0.0222206i	0.999938	+	0.0111103i	$0.00353659\pi$
$83$			0.202439i			0.0222206i	−0.999938	+	0.0111103i	$0.996463\pi$
$84$	−4.19519	−	6.45465i	−0.457732	−	0.704260i
$85$		−	13.7350i		−	1.48977i
$86$	−0.927413	+	5.32673i	−0.100005	+	0.574396i
$87$	2.77743	−	3.65578i	0.297771	−	0.391941i
$88$	1.54028	+	0.876050i	0.164194	+	0.0933872i
$89$			0.147764i			0.0156629i	0.999969	+	0.00783145i	$0.00249285\pi$
$89$			0.147764i			0.0156629i	−0.999969	+	0.00783145i	$0.997507\pi$
$90$	−9.10238	+	0.904216i	−0.959475	+	0.0953127i
$91$	−14.2138			−1.49001
$92$	−1.88232	−	0.675933i	−0.196245	−	0.0704709i
$93$	11.0492	+	8.39443i	1.14574	+	0.870462i
$94$	2.67534	−	15.3662i	0.275940	−	1.58490i
$95$	−12.4873			−1.28117
$96$	0.579754	+	9.78079i	0.0591709	+	0.998248i
$97$	5.73742			0.582546			0.291273	−	0.956640i	$-0.405921\pi$
$97$	5.73742			0.582546			0.291273	+	0.956640i	$0.405921\pi$
$98$	−0.500062	+	2.87218i	−0.0505139	+	0.290134i
$99$	1.81068	−	0.503833i	0.181980	−	0.0506371i
$100$	0.661849	+	0.237668i	0.0661849	+	0.0237668i
$101$	12.7129			1.26498			0.632490	−	0.774568i	$-0.282033\pi$
$101$	12.7129			1.26498			0.632490	+	0.774568i	$0.282033\pi$
$102$	−11.4314	+	10.6221i	−1.13188	+	1.05174i
$103$		−	1.36466i		−	0.134464i	−0.997737	−	0.0672320i	$-0.978583\pi$
$103$		−	1.36466i		−	0.134464i	0.997737	−	0.0672320i	$-0.0214168\pi$
$104$	15.7252	+	8.94390i	1.54199	+	0.877022i
$105$	−6.60795	−	5.02029i	−0.644870	−	0.489930i
$106$	0.635925	−	3.65253i	0.0617665	−	0.354765i
$107$		−	9.41344i		−	0.910032i	−0.890483	−	0.455016i	$-0.849634\pi$
$107$		−	9.41344i		−	0.910032i	0.890483	−	0.455016i	$-0.150366\pi$
$108$	7.79194	+	6.87645i	0.749780	+	0.661687i
$109$		−	9.73860i		−	0.932788i	−0.884577	−	0.466394i	$-0.845553\pi$
$109$		−	9.73860i		−	0.932788i	0.884577	−	0.466394i	$-0.154447\pi$
$110$	1.88190	+	0.327649i	0.179432	+	0.0312401i
$111$	−14.0729	−	10.6917i	−1.33574	−	1.01481i
$112$	−5.65489	+	6.85846i	−0.534337	+	0.648063i
$113$		−	14.5036i		−	1.36439i	−0.731172	−	0.682193i	$-0.761026\pi$
$113$		−	14.5036i		−	1.36439i	0.731172	−	0.682193i	$-0.238974\pi$
$114$	9.65715	+	10.3930i	0.904475	+	0.973390i
$115$	−2.15601			−0.201049
$116$	−4.98948	−	1.79170i	−0.463262	−	0.166356i
$117$	18.4859	−	5.14381i	1.70902	−	0.475545i
$118$	−9.58701	−	1.66915i	−0.882555	−	0.153658i
$119$	−14.1572			−1.29779
$120$	4.15164	+	9.71212i	0.378991	+	0.886591i
$121$	10.6075			0.964319
$122$	15.3320	+	2.66938i	1.38809	+	0.241674i
$123$	9.66591	+	7.34354i	0.871546	+	0.662144i
$124$	5.41521	−	15.0801i	0.486300	−	1.35423i
$125$	11.5381			1.03200
$126$	0.932007	+	9.38214i	0.0830298	+	0.835828i
$127$		−	6.38137i		−	0.566255i	−0.959082	−	0.283128i	$-0.908628\pi$
$127$		−	6.38137i		−	0.566255i	0.959082	−	0.283128i	$-0.0913720\pi$
$128$	10.5718	−	4.02946i	0.934426	−	0.356158i
$129$	4.00599	−	5.27288i	0.352708	−	0.464251i
$130$	19.2129	+	3.34508i	1.68509	+	0.293383i
$131$			14.2966i			1.24910i	0.780984	+	0.624551i	$0.214718\pi$
$131$			14.2966i			1.24910i	−0.780984	+	0.624551i	$0.785282\pi$
$132$	−1.18268	−	1.81965i	−0.102939	−	0.158381i
$133$			12.8711i			1.11607i
$134$	1.69143	−	9.71499i	0.146118	−	0.839247i
$135$	10.4108	+	4.13784i	0.896019	+	0.356128i
$136$	15.6626	+	8.90827i	1.34306	+	0.763878i
$137$			10.3639i			0.885444i	0.896659	+	0.442722i	$0.145987\pi$
$137$			10.3639i			0.885444i	−0.896659	+	0.442722i	$0.854013\pi$
$138$	1.66736	+	1.79441i	0.141936	+	0.152750i
$139$	−7.41605			−0.629021			−0.314511	−	0.949254i	$-0.601840\pi$
$139$	−7.41605			−0.629021			−0.314511	+	0.949254i	$0.601840\pi$
$140$	−3.23857	+	9.01866i	−0.273709	+	0.762216i
$141$	−11.5562	+	15.2108i	−0.973208	+	1.28098i
$142$	−1.23412	+	7.08834i	−0.103565	+	0.594840i
$143$	−4.00707			−0.335088
$144$	4.87251	−	10.9662i	0.406043	−	0.913854i
$145$	−5.71497			−0.474602
$146$	2.45403	−	14.0950i	0.203097	−	1.16651i
$147$	2.16003	−	2.84314i	0.178157	−	0.234498i
$148$	−6.89715	+	19.2070i	−0.566942	+	1.57880i
$149$	9.03410			0.740103			0.370051	−	0.929011i	$-0.379340\pi$
$149$	9.03410			0.740103			0.370051	+	0.929011i	$0.379340\pi$
$150$	−0.586269	−	0.630939i	−0.0478687	−	0.0515159i
$151$			17.1563i			1.39616i	0.716021	+	0.698078i	$0.245961\pi$
$151$			17.1563i			1.39616i	−0.716021	+	0.698078i	$0.754039\pi$
$152$	8.09903	−	14.2398i	0.656918	−	1.15500i
$153$	18.4122	−	5.12332i	1.48854	−	0.414196i
$154$	0.337719	−	1.93974i	0.0272142	−	0.156308i
$155$		−	17.2728i		−	1.38738i
$156$	−12.0744	−	18.5775i	−0.966726	−	1.48739i
$157$			1.54672i			0.123442i	0.998093	+	0.0617210i	$0.0196589\pi$
$157$			1.54672i			0.123442i	−0.998093	+	0.0617210i	$0.980341\pi$
$158$	−13.6522	−	2.37692i	−1.08611	−	0.189098i
$159$	−2.74690	+	3.61560i	−0.217843	+	0.286736i
$160$	9.25784	−	7.93982i	0.731897	−	0.627698i
$161$			2.22228i			0.175140i
$162$	−4.60742	−	11.8647i	−0.361993	−	0.932181i
$163$	9.28880			0.727555			0.363777	−	0.931486i	$-0.381487\pi$
$163$	9.28880			0.727555			0.363777	+	0.931486i	$0.381487\pi$
$164$	4.73728	−	13.1922i	0.369919	−	1.03014i
$165$	−1.86287	−	1.41529i	−0.145024	−	0.110180i
$166$	−0.282050	−	0.0491064i	−0.0218913	−	0.00381140i
$167$	−4.33580			−0.335514			−0.167757	−	0.985828i	$-0.553652\pi$
$167$	−4.33580			−0.335514			−0.167757	+	0.985828i	$0.553652\pi$
$168$	10.0106	−	4.27924i	0.772336	−	0.330150i
$169$	−27.9095			−2.14689
$170$	19.1364	+	3.33175i	1.46770	+	0.255534i
$171$	−4.65791	−	16.7396i	−0.356199	−	1.28011i
$172$	−7.19652	−	2.58424i	−0.548730	−	0.197047i
$173$	5.37208			0.408432			0.204216	−	0.978926i	$-0.434536\pi$
$173$	5.37208			0.408432			0.204216	+	0.978926i	$0.434536\pi$
$174$	4.41971	+	4.75646i	0.335057	+	0.360586i
$175$		−	0.781384i		−	0.0590671i
$176$	−1.59419	+	1.93349i	−0.120167	+	0.145742i
$177$	9.49009	+	7.20995i	0.713319	+	0.541933i
$178$	−0.205872	−	0.0358435i	−0.0154308	−	0.00268658i
$179$			6.85584i			0.512429i	0.966620	+	0.256215i	$0.0824754\pi$
$179$			6.85584i			0.512429i	−0.966620	+	0.256215i	$0.917525\pi$
$180$	0.948193	−	12.9013i	0.0706741	−	0.961604i
$181$		−	7.39246i		−	0.549477i	−0.961519	−	0.274739i	$-0.911409\pi$
$181$		−	7.39246i		−	0.549477i	0.961519	−	0.274739i	$-0.0885913\pi$
$182$	3.44789	−	19.8035i	0.255575	−	1.46793i
$183$	−15.1770	−	11.5305i	−1.12191	−	0.852358i
$184$	1.39835	−	2.45858i	0.103087	−	0.181249i
$185$			21.9997i			1.61745i
$186$	−14.3758	+	13.3580i	−1.05409	+	0.979458i
$187$	−3.99110			−0.291858
$188$	20.7600	+	7.45485i	1.51408	+	0.543701i
$189$	4.26501	−	10.7308i	0.310234	−	0.780549i
$190$	3.02909	−	17.3980i	0.219753	−	1.26218i
$191$	13.1125			0.948787			0.474394	−	0.880313i	$-0.342667\pi$
$191$	13.1125			0.948787			0.474394	+	0.880313i	$0.342667\pi$
$192$	−13.7678	−	1.56482i	−0.993603	−	0.112931i
$193$	16.2789			1.17178			0.585890	−	0.810391i	$-0.300745\pi$
$193$	16.2789			1.17178			0.585890	+	0.810391i	$0.300745\pi$
$194$	−1.39174	+	7.99368i	−0.0999214	+	0.573913i
$195$	−19.0187	−	14.4492i	−1.36196	−	1.03473i
$196$	−3.88037	−	1.39343i	−0.277169	−	0.0995305i
$197$	−1.43188			−0.102017			−0.0510086	−	0.998698i	$-0.516244\pi$
$197$	−1.43188			−0.102017			−0.0510086	+	0.998698i	$0.516244\pi$
$198$	0.262745	+	2.64495i	0.0186725	+	0.187969i
$199$			6.33548i			0.449110i	0.974461	+	0.224555i	$0.0720928\pi$
$199$			6.33548i			0.449110i	−0.974461	+	0.224555i	$0.927907\pi$
$200$	−0.491678	+	0.864472i	−0.0347669	+	0.0611274i
$201$	−7.30620	+	9.61678i	−0.515340	+	0.678315i
$202$	−3.08381	+	17.7123i	−0.216976	+	1.24623i
$203$			5.89062i			0.413440i
$204$	−12.0263	−	18.5035i	−0.842009	−	1.29550i
$205$		−	15.1104i		−	1.05536i
$206$	1.90132	+	0.331030i	0.132471	+	0.0230640i
$207$	−0.804216	−	2.89020i	−0.0558969	−	0.200883i
$208$	−16.2757	+	19.7397i	−1.12851	+	1.36870i
$209$			3.62854i			0.250992i
$210$	8.59746	−	7.98877i	0.593281	−	0.551277i
$211$	17.5582			1.20876			0.604379	−	0.796697i	$-0.293421\pi$
$211$	17.5582			1.20876			0.604379	+	0.796697i	$0.293421\pi$
$212$	4.93464	+	1.77201i	0.338912	+	0.121702i
$213$	5.33082	−	7.01668i	0.365262	−	0.480775i
$214$	13.1153	+	2.28345i	0.896545	+	0.156093i
$215$	−8.24292			−0.562162
$216$	−11.4708	+	9.18812i	−0.780487	+	0.625172i
$217$	−17.8037			−1.20859
$218$	13.5683	+	2.36232i	0.918964	+	0.159997i
$219$	−10.6002	+	13.9525i	−0.716298	+	0.942826i
$220$	−0.912996	+	2.54248i	−0.0615542	+	0.171414i
$221$	−40.7466			−2.74091
$222$	18.3099	−	17.0136i	1.22888	−	1.14188i
$223$		−	14.8118i		−	0.991875i	−0.868358	−	0.495937i	$-0.834825\pi$
$223$		−	14.8118i		−	0.991875i	0.868358	−	0.495937i	$-0.165175\pi$
$224$	−8.18385	−	9.54238i	−0.546806	−	0.637577i
$225$	0.282774	+	1.01623i	0.0188516	+	0.0677489i
$226$	20.2072	+	3.51819i	1.34417	+	0.234027i
$227$			16.5925i			1.10129i	0.834741	+	0.550643i	$0.185617\pi$
$227$			16.5925i			1.10129i	−0.834741	+	0.550643i	$0.814383\pi$
$228$	−16.8226	+	10.9338i	−1.11410	+	0.724109i
$229$		−	4.40321i		−	0.290972i	−0.989360	−	0.145486i	$-0.953525\pi$
$229$		−	4.40321i		−	0.290972i	0.989360	−	0.145486i	$-0.0464746\pi$
$230$	0.522991	−	3.00387i	0.0344850	−	0.198070i
$231$	−1.45879	+	1.92013i	−0.0959812	+	0.126335i
$232$	3.70662	−	6.51700i	0.243351	−	0.427862i
$233$		−	20.0423i		−	1.31302i	−0.754319	−	0.656508i	$-0.772033\pi$
$233$		−	20.0423i		−	1.31302i	0.754319	−	0.656508i	$-0.227967\pi$
$234$	2.68246	+	27.0033i	0.175358	+	1.76526i
$235$	23.7786			1.55115
$236$	4.65110	−	12.9522i	0.302761	−	0.843120i
$237$	13.5142	+	10.2672i	0.877840	+	0.666926i
$238$	3.43416	−	19.7246i	0.222603	−	1.27855i
$239$	−4.44567			−0.287567			−0.143783	−	0.989609i	$-0.545927\pi$
$239$	−4.44567			−0.287567			−0.143783	+	0.989609i	$0.545927\pi$
$240$	−14.5385	+	3.42839i	−0.938458	+	0.221301i
$241$	5.30058			0.341440			0.170720	−	0.985320i	$-0.445391\pi$
$241$	5.30058			0.341440			0.170720	+	0.985320i	$0.445391\pi$
$242$	−2.57310	+	14.7790i	−0.165405	+	0.950028i
$243$	−1.66355	+	15.4994i	−0.106717	+	0.994289i
$244$	−7.43826	+	20.7138i	−0.476186	+	1.32607i
$245$	−4.44459			−0.283954
$246$	−12.5761	+	11.6857i	−0.801823	+	0.745055i
$247$			37.0451i			2.35712i
$248$	19.6968	+	11.2028i	1.25075	+	0.711378i
$249$	0.279198	+	0.212117i	0.0176935	+	0.0134423i
$250$	−2.79885	+	16.0756i	−0.177015	+	1.01671i
$251$		−	7.23597i		−	0.456730i	−0.973576	−	0.228365i	$-0.926662\pi$
$251$		−	7.23597i		−	0.456730i	0.973576	−	0.228365i	$-0.0733380\pi$
$252$	−13.2978	−	0.977335i	−0.837682	−	0.0615663i
$253$			0.626490i			0.0393871i
$254$	8.89088	+	1.54795i	0.557863	+	0.0971271i
$255$	−18.9429	−	14.3916i	−1.18625	−	0.901238i
$256$	3.04963	+	15.7067i	0.190602	+	0.981667i
$257$		−	18.0970i		−	1.12886i	−0.825482	−	0.564429i	$-0.809096\pi$
$257$		−	18.0970i		−	1.12886i	0.825482	−	0.564429i	$-0.190904\pi$
$258$	6.37471	+	6.86042i	0.396872	+	0.427111i
$259$	22.6759			1.40901
$260$	−9.32110	+	25.9571i	−0.578070	+	1.60979i
$261$	−2.13175	−	7.66109i	−0.131952	−	0.474209i
$262$	−19.9188	−	3.46798i	−1.23059	−	0.214253i
$263$	−22.2853			−1.37417			−0.687086	−	0.726576i	$-0.741110\pi$
$263$	−22.2853			−1.37417			−0.687086	+	0.726576i	$0.741110\pi$
$264$	2.82213	−	1.20637i	0.173690	−	0.0742472i
$265$	5.65215			0.347209
$266$	−17.9327	−	3.12219i	−1.09953	−	0.191434i
$267$	0.203791	+	0.154827i	0.0124718	+	0.00947527i
$268$	13.1252	+	4.71320i	0.801747	+	0.287904i
$269$	−6.26665			−0.382085			−0.191042	−	0.981582i	$-0.561187\pi$
$269$	−6.26665			−0.382085			−0.191042	+	0.981582i	$0.561187\pi$
$270$	−8.29044	+	13.5012i	−0.504540	+	0.821655i
$271$		−	18.0131i		−	1.09422i	−0.837061	−	0.547110i	$-0.815728\pi$
$271$		−	18.0131i		−	1.09422i	0.837061	−	0.547110i	$-0.184272\pi$
$272$	−16.2108	+	19.6611i	−0.982925	+	1.19213i
$273$	−14.8933	+	19.6032i	−0.901382	+	1.18644i
$274$	−14.4395	−	2.51399i	−0.872321	−	0.151876i
$275$		−	0.220283i		−	0.0132835i
$276$	−2.90452	+	1.88779i	−0.174832	+	0.113631i
$277$		−	9.79710i		−	0.588651i	−0.955705	−	0.294325i	$-0.904905\pi$
$277$		−	9.79710i		−	0.588651i	0.955705	−	0.294325i	$-0.0950949\pi$
$278$	1.79894	−	10.3324i	0.107893	−	0.619699i
$279$	23.1547	−	6.44294i	1.38624	−	0.385729i
$280$	−11.7797	−	6.69983i	−0.703971	−	0.400392i
$281$			14.5377i			0.867247i	0.901094	+	0.433623i	$0.142765\pi$
$281$			14.5377i			0.867247i	−0.901094	+	0.433623i	$0.857235\pi$
$282$	−18.3893	−	19.7905i	−1.09507	−	1.17851i
$283$	6.32621			0.376054			0.188027	−	0.982164i	$-0.439791\pi$
$283$	6.32621			0.376054			0.188027	+	0.982164i	$0.439791\pi$
$284$	−9.57649	−	3.43888i	−0.568260	−	0.204060i
$285$	−13.0843	+	17.2221i	−0.775045	+	1.02015i
$286$	0.972007	−	5.58286i	0.0574760	−	0.330122i
$287$	−15.5748			−0.919353
$288$	14.0968	+	9.44877i	0.830664	+	0.556774i
$289$	−23.5842			−1.38731
$290$	1.38630	−	7.96241i	0.0814063	−	0.467569i
$291$	6.01169	−	7.91287i	0.352411	−	0.463861i
$292$	19.0427	+	6.83816i	1.11439	+	0.400173i
$293$	−31.1865			−1.82194			−0.910968	−	0.412477i	$-0.864664\pi$
$293$	−31.1865			−1.82194			−0.910968	+	0.412477i	$0.864664\pi$
$294$	3.43725	+	3.69915i	0.200465	+	0.215739i
$295$		−	14.8355i		−	0.863759i
$296$	−25.0871	−	14.2686i	−1.45816	−	0.829344i
$297$	1.20236	−	3.02515i	0.0697683	−	0.175537i
$298$	−2.19143	+	12.5868i	−0.126946	+	0.729134i
$299$			6.39606i			0.369894i
$300$	1.02127	−	0.663773i	0.0589631	−	0.0383229i
$301$			8.49626i			0.489717i
$302$	−23.9030	−	4.16165i	−1.37547	−	0.239476i
$303$	13.3206	−	17.5332i	0.765249	−	1.00726i
$304$	17.8750	+	14.7382i	1.02520	+	0.845294i
$305$			23.7257i			1.35853i
$306$	2.67177	+	26.8957i	0.152735	+	1.53752i
$307$	−9.38172			−0.535443			−0.267721	−	0.963496i	$-0.586271\pi$
$307$	−9.38172			−0.535443			−0.267721	+	0.963496i	$0.586271\pi$
$308$	2.62062	+	0.941057i	0.149324	+	0.0536217i
$309$	−1.88210	−	1.42990i	−0.107069	−	0.0813439i
$310$	24.0654	+	4.18992i	1.36682	+	0.237971i
$311$	9.41509			0.533881			0.266940	−	0.963713i	$-0.413987\pi$
$311$	9.41509			0.533881			0.266940	+	0.963713i	$0.413987\pi$
$312$	28.8121	−	12.3163i	1.63116	−	0.697274i
$313$	1.96540			0.111091			0.0555455	−	0.998456i	$-0.482310\pi$
$313$	1.96540			0.111091			0.0555455	+	0.998456i	$0.482310\pi$
$314$	−2.15498	−	0.375194i	−0.121613	−	0.0211734i
$315$	−13.8477	+	3.85320i	−0.780228	+	0.217103i
$316$	6.62332	−	18.4444i	0.372591	−	1.03758i
$317$	3.81424			0.214229			0.107115	−	0.994247i	$-0.465839\pi$
$317$	3.81424			0.214229			0.107115	+	0.994247i	$0.465839\pi$
$318$	−4.37113	−	4.70418i	−0.245121	−	0.263797i
$319$			1.66065i			0.0929783i
$320$	8.81648	+	14.8245i	0.492856	+	0.828716i
$321$	−12.9827	−	9.86344i	−0.724626	−	0.550524i
$322$	−3.09620	−	0.539065i	−0.172544	−	0.0300409i
$323$			36.8975i			2.05303i
$324$	17.6482	−	3.54124i	0.980457	−	0.196735i
$325$		−	2.24894i		−	0.124749i
$326$	−2.25321	+	12.9417i	−0.124794	+	0.716772i
$327$	−13.4312	−	10.2041i	−0.742746	−	0.564290i
$328$	17.2310	+	9.80032i	0.951422	+	0.541132i
$329$		−	24.5094i		−	1.35125i
$330$	2.42374	−	2.25214i	0.133423	−	0.123976i
$331$	−26.7603			−1.47088			−0.735440	−	0.677590i	$-0.763024\pi$
$331$	−26.7603			−1.47088			−0.735440	+	0.677590i	$0.763024\pi$
$332$	0.136835	−	0.381055i	0.00750982	−	0.0209131i
$333$	−29.4913	+	8.20613i	−1.61611	+	0.449693i
$334$	1.05175	−	6.04088i	0.0575492	−	0.330542i
$335$	15.0336			0.821373
$336$	3.53376	+	14.9854i	0.192782	+	0.817519i
$337$	−1.54971			−0.0844182			−0.0422091	−	0.999109i	$-0.513440\pi$
$337$	−1.54971			−0.0844182			−0.0422091	+	0.999109i	$0.513440\pi$
$338$	6.77011	−	38.8851i	0.368246	−	2.11507i
$339$	−20.0030	−	15.1970i	−1.08641	−	0.825385i
$340$	−9.28396	+	25.8537i	−0.503494	+	1.40211i
$341$	−5.01910			−0.271799
$342$	24.4524	−	2.42907i	1.32224	−	0.131349i
$343$			20.1371i			1.08730i
$344$	5.34619	−	9.39972i	0.288247	−	0.506799i
$345$	−2.25908	+	2.97350i	−0.121625	+	0.160088i
$346$	−1.30312	+	7.48468i	−0.0700564	+	0.402379i
$347$		−	7.68702i		−	0.412661i	−0.978482	−	0.206330i	$-0.933848\pi$
$347$		−	7.68702i		−	0.412661i	0.978482	−	0.206330i	$-0.0661522\pi$
$348$	−7.69906	+	5.00399i	−0.412713	+	0.268242i
$349$			1.00258i			0.0536671i	0.999640	+	0.0268335i	$0.00854241\pi$
$349$			1.00258i			0.0536671i	−0.999640	+	0.0268335i	$0.991458\pi$
$350$	1.08867	+	0.189543i	0.0581917	+	0.0101315i
$351$	12.2754	−	30.8848i	0.655211	−	1.64851i
$352$	−2.30714	−	2.69013i	−0.122971	−	0.143384i
$353$		−	8.45137i		−	0.449821i	−0.974379	−	0.224911i	$-0.927791\pi$
$353$		−	8.45137i		−	0.449821i	0.974379	−	0.224911i	$-0.0722090\pi$
$354$	−12.3473	+	11.4732i	−0.656254	+	0.609792i
$355$	−10.9689			−0.582171
$356$	0.0998782	−	0.278138i	0.00529354	−	0.0147413i
$357$	−14.8339	+	19.5252i	−0.785096	+	1.03338i
$358$	−9.55193	−	1.66304i	−0.504835	−	0.0878946i
$359$	32.7862			1.73039			0.865194	−	0.501437i	$-0.167195\pi$
$359$	32.7862			1.73039			0.865194	+	0.501437i	$0.167195\pi$
$360$	17.7447	+	4.45058i	0.935230	+	0.234566i
$361$	14.5457			0.765562
$362$	10.2996	+	1.79321i	0.541334	+	0.0942492i
$363$	11.1146	−	14.6296i	0.583364	−	0.767852i
$364$	26.7549	+	9.60758i	1.40234	+	0.503574i
$365$	21.8116			1.14167
$366$	19.7464	−	18.3484i	1.03216	−	0.959086i
$367$			11.3864i			0.594365i	0.954821	+	0.297182i	$0.0960469\pi$
$367$			11.3864i			0.594365i	−0.954821	+	0.297182i	$0.903953\pi$
$368$	3.08623	+	2.54464i	0.160881	+	0.132648i
$369$	20.2560	−	5.63635i	1.05448	−	0.293417i
$370$	−30.6512	−	5.33654i	−1.59348	−	0.277434i
$371$		−	5.82587i		−	0.302464i
$372$	−15.1239	−	23.2695i	−0.784140	−	1.20647i
$373$		−	24.8585i		−	1.28713i	−0.765393	−	0.643563i	$-0.777455\pi$
$373$		−	24.8585i		−	1.28713i	0.765393	−	0.643563i	$-0.222545\pi$
$374$	0.968135	−	5.56062i	0.0500611	−	0.287533i
$375$	12.0897	−	15.9131i	0.624310	−	0.821746i
$376$	−15.4223	+	27.1157i	−0.795346	+	1.39838i
$377$			16.9541i			0.873182i
$378$	13.9161	+	8.54525i	0.715768	+	0.439520i
$379$	29.0547			1.49244			0.746219	−	0.665701i	$-0.231867\pi$
$379$	29.0547			1.49244			0.746219	+	0.665701i	$0.231867\pi$
$380$	23.5051	+	8.44059i	1.20579	+	0.432993i
$381$	−8.80099	−	6.68643i	−0.450889	−	0.342556i
$382$	−3.18074	+	18.2690i	−0.162741	+	0.934726i
$383$	−0.803954			−0.0410802			−0.0205401	−	0.999789i	$-0.506539\pi$
$383$	−0.803954			−0.0410802			−0.0205401	+	0.999789i	$0.506539\pi$
$384$	5.51988	−	18.8024i	0.281685	−	0.959507i
$385$	3.00167			0.152979
$386$	−3.94882	+	22.6806i	−0.200990	+	1.15441i
$387$	−3.07470	−	11.0499i	−0.156296	−	0.561697i
$388$	−10.7996	−	3.87811i	−0.548268	−	0.196881i
$389$	−19.7855			−1.00316			−0.501582	−	0.865110i	$-0.667248\pi$
$389$	−19.7855			−1.00316			−0.501582	+	0.865110i	$0.667248\pi$
$390$	24.7448	−	22.9929i	1.25300	−	1.16429i
$391$			6.37058i			0.322174i
$392$	2.88267	−	5.06834i	0.145597	−	0.255990i
$393$	19.7175	+	14.9801i	0.994615	+	0.755644i
$394$	0.347336	−	1.99497i	0.0174985	−	0.100505i
$395$		−	21.1263i		−	1.06298i
$396$	−3.74883	−	0.275524i	−0.188386	−	0.0138456i
$397$			25.0551i			1.25748i	0.777616	+	0.628740i	$0.216429\pi$
$397$			25.0551i			1.25748i	−0.777616	+	0.628740i	$0.783571\pi$
$398$	−8.82693	−	1.53682i	−0.442454	−	0.0770337i
$399$	17.7515	+	13.4864i	0.888684	+	0.675165i
$400$	−1.08516	−	0.894731i	−0.0542581	−	0.0447365i
$401$		−	17.0861i		−	0.853242i	−0.904431	−	0.426621i	$-0.859704\pi$
$401$		−	17.0861i		−	0.853242i	0.904431	−	0.426621i	$-0.140296\pi$
$402$	−11.6263	−	12.5122i	−0.579868	−	0.624050i
$403$	−51.2417			−2.55253
$404$	−23.9297	−	8.59306i	−1.19055	−	0.427521i
$405$	16.6152	−	10.0226i	0.825618	−	0.498028i
$406$	−8.20713	−	1.42891i	−0.407313	−	0.0709155i
$407$	6.39264			0.316871
$408$	28.6973	−	12.2672i	1.42073	−	0.607319i
$409$	26.7946			1.32491			0.662454	−	0.749102i	$-0.269515\pi$
$409$	26.7946			1.32491			0.662454	+	0.749102i	$0.269515\pi$
$410$	21.0527	+	3.66538i	1.03972	+	0.181020i
$411$	14.2935	+	10.8593i	0.705047	+	0.535649i
$412$	−0.922418	+	2.56872i	−0.0454443	+	0.126552i
$413$	−15.2915			−0.752446
$414$	4.22186	−	0.419393i	0.207493	−	0.0206120i
$415$		−	0.436462i		−	0.0214251i
$416$	−23.5544	−	27.4645i	−1.15485	−	1.34656i
$417$	−7.77056	+	10.2280i	−0.380526	+	0.500867i
$418$	−5.05549	−	0.880188i	−0.247272	−	0.0430514i
$419$		−	14.2583i		−	0.696563i	−0.937390	−	0.348282i	$-0.886765\pi$
$419$		−	14.2583i		−	0.696563i	0.937390	−	0.348282i	$-0.113235\pi$
$420$	9.04487	+	13.9163i	0.441345	+	0.679046i
$421$			6.84504i			0.333607i	0.985990	+	0.166803i	$0.0533446\pi$
$421$			6.84504i			0.333607i	−0.985990	+	0.166803i	$0.946655\pi$
$422$	−4.25916	+	24.4631i	−0.207333	+	1.19084i
$423$	8.86968	+	31.8759i	0.431259	+	1.54986i
$424$	−3.66587	+	6.44537i	−0.178031	+	0.313015i
$425$		−	2.23998i		−	0.108655i
$426$	8.48290	+	9.12924i	0.410998	+	0.442313i
$427$	24.4549			1.18346
$428$	−6.36286	+	17.7191i	−0.307560	+	0.856484i
$429$	−4.19862	+	5.52642i	−0.202711	+	0.266818i
$430$	1.99951	−	11.4845i	0.0964251	−	0.553831i
$431$	5.25636			0.253190			0.126595	−	0.991954i	$-0.459595\pi$
$431$	5.25636			0.253190			0.126595	+	0.991954i	$0.459595\pi$
$432$	−10.0189	−	18.2105i	−0.482034	−	0.876153i
$433$	−13.3257			−0.640390			−0.320195	−	0.947352i	$-0.603748\pi$
$433$	−13.3257			−0.640390			−0.320195	+	0.947352i	$0.603748\pi$
$434$	4.31870	−	24.8051i	0.207304	−	1.19068i
$435$	−5.98817	+	7.88191i	−0.287111	+	0.377909i
$436$	−6.58264	+	18.3311i	−0.315251	+	0.877901i
$437$	5.79186			0.277062
$438$	−16.8681	−	18.1534i	−0.805990	−	0.867401i
$439$			2.97239i			0.141864i	0.997481	+	0.0709322i	$0.0225974\pi$
$439$			2.97239i			0.141864i	−0.997481	+	0.0709322i	$0.977403\pi$
$440$	−3.32086	−	1.88877i	−0.158316	−	0.0900438i
$441$	−1.65788	−	5.95810i	−0.0789467	−	0.283719i
$442$	9.88403	−	56.7703i	0.470135	−	2.70029i
$443$		−	15.3236i		−	0.728047i	−0.931390	−	0.364024i	$-0.881403\pi$
$443$		−	15.3236i		−	0.728047i	0.931390	−	0.364024i	$-0.118597\pi$
$444$	19.2628	+	29.6374i	0.914172	+	1.40653i
$445$		−	0.318580i		−	0.0151021i
$446$	20.6367	+	3.59296i	0.977175	+	0.170132i
$447$	9.46597	−	12.4596i	0.447725	−	0.589317i
$448$	15.2801	−	9.08746i	0.721919	−	0.429342i
$449$			12.2537i			0.578289i	0.957285	+	0.289145i	$0.0933709\pi$
$449$			12.2537i			0.578289i	−0.957285	+	0.289145i	$0.906629\pi$
$450$	−1.48447	+	0.147464i	−0.0699784	+	0.00695154i
$451$	−4.39076			−0.206753
$452$	−9.80348	+	27.3004i	−0.461117	+	1.28410i
$453$	23.6614	+	17.9764i	1.11171	+	0.844604i
$454$	−23.1176	−	4.02491i	−1.08496	−	0.188898i
$455$	30.6451			1.43667
$456$	−11.1529	−	26.0904i	−0.522281	−	1.22180i
$457$	21.4455			1.00318			0.501590	−	0.865106i	$-0.332749\pi$
$457$	21.4455			1.00318			0.501590	+	0.865106i	$0.332749\pi$
$458$	6.13480	+	1.06810i	0.286660	+	0.0499091i
$459$	12.2265	−	30.7618i	0.570682	−	1.43584i
$460$	4.05830	+	1.45732i	0.189219	+	0.0679478i
$461$	25.7082			1.19735			0.598675	−	0.800992i	$-0.295694\pi$
$461$	25.7082			1.19735			0.598675	+	0.800992i	$0.295694\pi$
$462$	−2.32136	−	2.49823i	−0.108000	−	0.116228i
$463$		−	9.09256i		−	0.422567i	−0.977425	−	0.211284i	$-0.932236\pi$
$463$		−	9.09256i		−	0.422567i	0.977425	−	0.211284i	$-0.0677643\pi$
$464$	8.18071	+	6.74511i	0.379780	+	0.313134i
$465$	−23.8221	−	18.0985i	−1.10472	−	0.839298i
$466$	27.9240	+	4.86173i	1.29356	+	0.225215i
$467$			15.2765i			0.706914i	0.935451	+	0.353457i	$0.114994\pi$
$467$			15.2765i			0.706914i	−0.935451	+	0.353457i	$0.885006\pi$
$468$	−38.2731	−	2.81292i	−1.76918	−	0.130027i
$469$		−	15.4957i		−	0.715523i
$470$	−5.76806	+	33.1297i	−0.266061	+	1.52816i
$471$	2.13319	+	1.62066i	0.0982924	+	0.0746762i
$472$	16.9175	+	9.62204i	0.778693	+	0.442890i
$473$			2.39521i			0.110132i
$474$	−17.5830	+	16.3381i	−0.807614	+	0.750436i
$475$	−2.03650			−0.0934411
$476$	26.6483	+	9.56930i	1.22142	+	0.438608i
$477$	2.10831	+	7.57688i	0.0965331	+	0.346921i
$478$	1.07840	−	6.19395i	0.0493250	−	0.283305i
$479$	32.6191			1.49040			0.745201	−	0.666840i	$-0.232353\pi$
$479$	32.6191			1.49040			0.745201	+	0.666840i	$0.232353\pi$
$480$	−1.24996	−	21.0875i	−0.0570524	−	0.962508i
$481$	65.2647			2.97581
$482$	−1.28578	+	7.38506i	−0.0585657	+	0.336380i
$483$	3.06490	+	2.32851i	0.139458	+	0.105951i
$484$	−19.9667	−	7.16996i	−0.907577	−	0.325907i
$485$	−12.3699			−0.561690
$486$	−21.1911	−	6.07750i	−0.961249	−	0.275681i
$487$		−	3.50484i		−	0.158820i	−0.996842	−	0.0794098i	$-0.974696\pi$
$487$		−	3.50484i		−	0.158820i	0.996842	−	0.0794098i	$-0.0253036\pi$
$488$	−27.0553	−	15.3880i	−1.22474	−	0.696582i
$489$	9.73283	−	12.8108i	0.440134	−	0.579325i
$490$	1.07814	−	6.19245i	0.0487054	−	0.279746i
$491$			16.7658i			0.756632i	0.925676	+	0.378316i	$0.123497\pi$
$491$			16.7658i			0.756632i	−0.925676	+	0.378316i	$0.876503\pi$
$492$	−13.2306	−	20.3564i	−0.596480	−	0.917736i
$493$			16.8866i			0.760533i
$494$	−51.6132	−	8.98615i	−2.32219	−	0.404306i
$495$	−3.90385	+	1.08627i	−0.175465	+	0.0488242i
$496$	−20.3863	+	24.7252i	−0.915370	+	1.11019i
$497$			11.3061i			0.507147i
$498$	−0.363259	+	0.337540i	−0.0162780	+	0.0151255i
$499$	−8.69917			−0.389428			−0.194714	−	0.980860i	$-0.562378\pi$
$499$	−8.69917			−0.389428			−0.194714	+	0.980860i	$0.562378\pi$
$500$	−21.7184	−	7.79901i	−0.971278	−	0.348782i
$501$	−4.54307	+	5.97981i	−0.202969	+	0.267158i
$502$	10.0816	+	1.75525i	0.449962	+	0.0783408i
$503$	33.2633			1.48314			0.741568	−	0.670877i	$-0.234082\pi$
$503$	33.2633			1.48314			0.741568	+	0.670877i	$0.234082\pi$
$504$	4.58737	−	18.2901i	0.204338	−	0.814707i
$505$	−27.4091			−1.21969
$506$	−0.872860	−	0.151970i	−0.0388034	−	0.00675588i
$507$	−29.2437	+	38.4920i	−1.29876	+	1.70949i
$508$	−4.31338	+	12.0118i	−0.191375	+	0.532936i
$509$	11.2110			0.496917			0.248459	−	0.968642i	$-0.420076\pi$
$509$	11.2110			0.496917			0.248459	+	0.968642i	$0.420076\pi$
$510$	24.6462	−	22.9013i	1.09135	−	1.01409i
$511$		−	22.4820i		−	0.994543i
$512$	−22.6232	+	0.438884i	−0.999812	+	0.0193961i
$513$	−27.9673	−	11.1158i	−1.23479	−	0.490774i
$514$	25.2137	+	4.38984i	1.11213	+	0.193628i
$515$			2.94222i			0.129650i
$516$	−11.1046	+	7.21744i	−0.488855	+	0.317730i
$517$		−	6.90954i		−	0.303881i
$518$	−5.50056	+	31.5933i	−0.241681	+	1.38813i
$519$	5.62889	−	7.40901i	0.247081	−	0.325220i
$520$	−33.9038	−	19.2832i	−1.48678	−	0.845622i
$521$		−	34.9909i		−	1.53298i	−0.642258	−	0.766489i	$-0.722002\pi$
$521$		−	34.9909i		−	1.53298i	0.642258	−	0.766489i	$-0.277998\pi$
$522$	11.1909	−	1.11169i	0.489814	−	0.0486574i
$523$	7.73434			0.338199			0.169100	−	0.985599i	$-0.445914\pi$
$523$	7.73434			0.338199			0.169100	+	0.985599i	$0.445914\pi$
$524$	9.66356	−	26.9108i	0.422155	−	1.17560i
$525$	−1.07766	−	0.818737i	−0.0470330	−	0.0357326i
$526$	5.40583	−	31.0491i	0.235705	−	1.35381i
$527$	−51.0376			−2.22323
$528$	0.996214	+	4.22458i	0.0433547	+	0.183851i
$529$	1.00000			0.0434783
$530$	−1.37106	+	7.87489i	−0.0595551	+	0.342063i
$531$	19.8875	−	5.53382i	0.863044	−	0.240147i
$532$	8.70001	−	24.2275i	0.377193	−	1.05040i
$533$	−44.8268			−1.94166
$534$	−0.265148	+	0.246376i	−0.0114741	+	0.0106617i
$535$			20.2955i			0.877451i
$536$	−9.75049	+	17.1434i	−0.421157	+	0.740482i
$537$	9.45536	+	7.18357i	0.408029	+	0.309994i
$538$	1.52012	−	8.73104i	0.0655372	−	0.376422i
$539$			1.29150i			0.0556289i
$540$	−16.7995	−	14.8257i	−0.722936	−	0.637997i
$541$			15.9208i			0.684489i	0.939611	+	0.342245i	$0.111187\pi$
$541$			15.9208i			0.684489i	−0.939611	+	0.342245i	$0.888813\pi$
$542$	25.0969	+	4.36951i	1.07800	+	0.187686i
$543$	−10.1955	−	7.74584i	−0.437529	−	0.332406i
$544$	−23.4606	−	27.3550i	−1.00586	−	1.17284i
$545$			20.9965i			0.899392i
$546$	−23.6996	−	25.5054i	−1.01425	−	1.09153i
$547$	6.19649			0.264943			0.132471	−	0.991187i	$-0.457709\pi$
$547$	6.19649			0.264943			0.132471	+	0.991187i	$0.457709\pi$
$548$	7.00527	−	19.5081i	0.299250	−	0.833343i
$549$	−31.8050	+	8.84994i	−1.35740	+	0.377706i
$550$	0.306910	+	0.0534347i	0.0130867	+	0.00227846i
$551$	15.3526			0.654042
$552$	−1.92561	−	4.50467i	−0.0819594	−	0.191731i
$553$	−21.7756			−0.925993
$554$	13.6499	+	2.37652i	0.579927	+	0.100968i
$555$	30.3413	+	23.0514i	1.28792	+	0.978476i
$556$	13.9594	+	5.01275i	0.592008	+	0.212588i
$557$	10.2135			0.432761			0.216380	−	0.976309i	$-0.430575\pi$
$557$	10.2135			0.432761			0.216380	+	0.976309i	$0.430575\pi$
$558$	3.35995	+	33.8233i	0.142238	+	1.43185i
$559$			24.4536i			1.03428i
$560$	12.1920	−	14.7869i	0.515206	−	0.624861i
$561$	−4.18189	+	5.50441i	−0.176560	+	0.232396i
$562$	−20.2547	−	3.52646i	−0.854394	−	0.148755i
$563$		−	14.7172i		−	0.620255i	−0.950695	−	0.310127i	$-0.899628\pi$
$563$		−	14.7172i		−	0.620255i	0.950695	−	0.310127i	$-0.100372\pi$
$564$	32.0339	−	20.8204i	1.34887	−	0.876696i
$565$			31.2700i			1.31554i
$566$	−1.53457	+	8.81402i	−0.0645028	+	0.370481i
$567$	−10.3307	−	17.1259i	−0.433847	−	0.719221i
$568$	7.11424	−	12.5083i	0.298507	−	0.524837i
$569$			1.16166i			0.0486994i	0.999704	+	0.0243497i	$0.00775152\pi$
$569$			1.16166i			0.0486994i	−0.999704	+	0.0243497i	$0.992248\pi$
$570$	−20.8209	−	22.4073i	−0.872092	−	0.938540i
$571$	−27.1053			−1.13432			−0.567160	−	0.823608i	$-0.691958\pi$
$571$	−27.1053			−1.13432			−0.567160	+	0.823608i	$0.691958\pi$
$572$	7.54257	+	2.70851i	0.315370	+	0.113248i
$573$	13.7393	−	18.0844i	0.573968	−	0.755485i
$574$	3.77804	−	21.6997i	0.157692	−	0.905728i
$575$	−0.351614			−0.0146633
$576$	−16.5841	+	17.3485i	−0.691002	+	0.722853i
$577$	25.7002			1.06991			0.534956	−	0.844880i	$-0.320328\pi$
$577$	25.7002			1.06991			0.534956	+	0.844880i	$0.320328\pi$
$578$	5.72091	−	32.8589i	0.237958	−	1.36675i
$579$	17.0571	−	22.4513i	0.708867	−	0.933045i
$580$	10.7574	+	3.86294i	0.446676	+	0.160400i
$581$	−0.449876			−0.0186640
$582$	9.56637	+	10.2953i	0.396539	+	0.426752i
$583$		−	1.64239i		−	0.0680209i
$584$	−14.1466	+	24.8726i	−0.585389	+	1.02923i
$585$	−39.8557	+	11.0901i	−1.64783	+	0.458520i
$586$	7.56502	−	43.4508i	0.312508	−	1.79493i
$587$		−	9.46184i		−	0.390532i	−0.980750	−	0.195266i	$-0.937443\pi$
$587$		−	9.46184i		−	0.390532i	0.980750	−	0.195266i	$-0.0625570\pi$
$588$	−5.98764	+	3.89165i	−0.246926	+	0.160489i
$589$			46.4013i			1.91193i
$590$	20.6697	+	3.59871i	0.850958	+	0.148157i
$591$	−1.50033	+	1.97480i	−0.0617152	+	0.0812326i
$592$	25.9652	−	31.4916i	1.06716	−	1.29430i
$593$			40.9966i			1.68353i	0.539845	+	0.841764i	$0.318483\pi$
$593$			40.9966i			1.68353i	−0.539845	+	0.841764i	$0.681517\pi$
$594$	3.92314	+	2.40902i	0.160969	+	0.0988433i
$595$	30.5230			1.25132
$596$	−17.0050	−	6.10645i	−0.696554	−	0.250130i
$597$	8.73769	+	6.63833i	0.357610	+	0.271689i
$598$	−8.91134	−	1.55151i	−0.364412	−	0.0634461i
$599$	48.6949			1.98962			0.994810	−	0.101752i	$-0.0324448\pi$
$599$	48.6949			1.98962			0.994810	+	0.101752i	$0.0324448\pi$
$600$	0.677071	+	1.58390i	0.0276413	+	0.0646626i
$601$	9.88424			0.403187			0.201593	−	0.979469i	$-0.435388\pi$
$601$	9.88424			0.403187			0.201593	+	0.979469i	$0.435388\pi$
$602$	−11.8375	−	2.06097i	−0.482459	−	0.0839988i
$603$	5.60770	+	20.1530i	0.228363	+	0.820693i
$604$	11.5965	−	32.2935i	0.471854	−	1.31400i
$605$	−22.8699			−0.929794
$606$	21.1970	+	22.8121i	0.861070	+	0.926678i
$607$			26.4395i			1.07315i	0.843854	+	0.536573i	$0.180282\pi$
$607$			26.4395i			1.07315i	−0.843854	+	0.536573i	$0.819718\pi$
$608$	−24.8701	+	21.3294i	−1.00861	+	0.865020i
$609$	8.12416	+	6.17221i	0.329208	+	0.250111i
$610$	−33.0559	−	5.75522i	−1.33839	−	0.233022i
$611$		−	70.5420i		−	2.85382i
$612$	−38.1206	−	2.80172i	−1.54094	−	0.113253i
$613$		−	42.2095i		−	1.70483i	−0.522869	−	0.852413i	$-0.675138\pi$
$613$		−	42.2095i		−	1.70483i	0.522869	−	0.852413i	$-0.324862\pi$
$614$	2.27575	−	13.0711i	0.0918420	−	0.527507i
$615$	−20.8398	−	15.8327i	−0.840343	−	0.638438i
$616$	−1.94683	+	3.42292i	−0.0784398	+	0.137913i
$617$		−	22.6489i		−	0.911811i	−0.890028	−	0.455905i	$-0.849316\pi$
$617$		−	22.6489i		−	0.911811i	0.890028	−	0.455905i	$-0.150684\pi$
$618$	2.44875	−	2.27539i	0.0985033	−	0.0915294i
$619$	−43.8760			−1.76353			−0.881763	−	0.471692i	$-0.843643\pi$
$619$	−43.8760			−1.76353			−0.881763	+	0.471692i	$0.843643\pi$
$620$	−11.6753	+	32.5129i	−0.468889	+	1.30575i
$621$	−4.82873	−	1.91921i	−0.193770	−	0.0770152i
$622$	−2.28385	+	13.1176i	−0.0915741	+	0.525969i
$623$	−0.328371			−0.0131559
$624$	10.1707	+	43.1302i	0.407154	+	1.72659i
$625$	−23.1183			−0.924732
$626$	−0.476754	+	2.73830i	−0.0190549	+	0.109445i
$627$	5.00438	+	3.80200i	0.199856	+	0.151837i
$628$	1.04548	−	2.91142i	0.0417192	−	0.116178i
$629$	65.0047			2.59191
$630$	−2.00942	−	20.2280i	−0.0800571	−	0.805903i
$631$			14.8205i			0.589997i	0.955498	+	0.294998i	$0.0953191\pi$
$631$			14.8205i			0.589997i	−0.955498	+	0.294998i	$0.904681\pi$
$632$	24.0911	+	13.7021i	0.958293	+	0.545040i
$633$	18.3976	−	24.2158i	0.731238	−	0.962491i
$634$	−0.925234	+	5.31421i	−0.0367457	+	0.211054i
$635$			13.7583i			0.545982i
$636$	7.61444	−	4.94898i	0.301932	−	0.196240i
$637$			13.1854i			0.522424i
$638$	−2.31370	−	0.402828i	−0.0916003	−	0.0159481i
$639$	−4.09154	−	14.7042i	−0.161859	−	0.581689i
$640$	−22.7930	+	8.68757i	−0.900971	+	0.343406i
$641$			3.96034i			0.156424i	0.996937	+	0.0782120i	$0.0249211\pi$
$641$			3.96034i			0.156424i	−0.996937	+	0.0782120i	$0.975079\pi$
$642$	16.8915	−	15.6956i	0.666656	−	0.619458i
$643$	10.9712			0.432660			0.216330	−	0.976320i	$-0.430591\pi$
$643$	10.9712			0.432660			0.216330	+	0.976320i	$0.430591\pi$
$644$	1.50211	−	4.18303i	0.0591914	−	0.164834i
$645$	−8.63696	+	11.3684i	−0.340080	+	0.447630i
$646$	−51.4076	−	8.95035i	−2.02261	−	0.352147i
$647$	1.68607			0.0662864			0.0331432	−	0.999451i	$-0.489448\pi$
$647$	1.68607			0.0662864			0.0331432	+	0.999451i	$0.489448\pi$
$648$	0.652855	+	25.4475i	0.0256466	+	0.999671i
$649$	−4.31089			−0.169217
$650$	3.13335	+	0.545534i	0.122900	+	0.0213976i
$651$	−18.6548	+	24.5543i	−0.731137	+	0.962358i
$652$	−17.4845	−	6.27860i	−0.684744	−	0.245889i
$653$	−4.90522			−0.191956			−0.0959781	−	0.995383i	$-0.530598\pi$
$653$	−4.90522			−0.191956			−0.0959781	+	0.995383i	$0.530598\pi$
$654$	17.4750	−	16.2378i	0.683327	−	0.634948i
$655$		−	30.8237i		−	1.20438i
$656$	−17.8341	+	21.6299i	−0.696305	+	0.844504i
$657$	8.13596	+	29.2391i	0.317414	+	1.14072i
$658$	34.1479	+	5.94534i	1.33122	+	0.231773i
$659$		−	21.0553i		−	0.820197i	−0.912041	−	0.410098i	$-0.865494\pi$
$659$		−	21.0553i		−	0.820197i	0.912041	−	0.410098i	$-0.134506\pi$
$660$	2.54987	+	3.92320i	0.0992537	+	0.152710i
$661$			27.9046i			1.08536i	0.839939	+	0.542681i	$0.182591\pi$
$661$			27.9046i			1.08536i	−0.839939	+	0.542681i	$0.817409\pi$
$662$	6.49134	−	37.2839i	0.252293	−	1.44908i
$663$	−42.6944	+	56.1964i	−1.65811	+	2.18249i
$664$	0.497714	+	0.283080i	0.0193150	+	0.0109856i
$665$		−	27.7503i		−	1.07611i
$666$	−4.27944	−	43.0794i	−0.165825	−	1.66929i
$667$	2.65071			0.102636
$668$	8.16135	+	2.93071i	0.315772	+	0.113393i
$669$	−20.4280	−	15.5199i	−0.789794	−	0.600034i
$670$	−3.64675	+	20.9456i	−0.140886	+	0.809200i
$671$	6.89417			0.266146
$672$	−21.7356	+	1.28837i	−0.838470	+	0.0497001i
$673$	−51.0437			−1.96759			−0.983796	−	0.179294i	$-0.942619\pi$
$673$	−51.0437			−1.96759			−0.983796	+	0.179294i	$0.942619\pi$
$674$	0.375919	−	2.15914i	0.0144799	−	0.0831671i
$675$	1.69785	+	0.674821i	0.0653503	+	0.0259739i
$676$	52.5346	+	18.8650i	2.02056	+	0.725576i
$677$	33.4606			1.28599			0.642997	−	0.765868i	$-0.277691\pi$
$677$	33.4606			1.28599			0.642997	+	0.765868i	$0.277691\pi$
$678$	26.0254	−	24.1828i	0.999500	−	0.928736i
$679$			12.7501i			0.489305i
$680$	−33.7687	−	19.2063i	−1.29497	−	0.736529i
$681$	22.8839	+	17.3857i	0.876914	+	0.666222i
$682$	1.21750	−	6.99288i	0.0466205	−	0.267771i
$683$		−	16.3618i		−	0.626069i	−0.949742	−	0.313034i	$-0.898655\pi$
$683$		−	16.3618i		−	0.626069i	0.949742	−	0.313034i	$-0.101345\pi$
$684$	−2.54720	+	34.6577i	−0.0973948	+	1.32517i
$685$		−	22.3446i		−	0.853743i
$686$	−28.0561	−	4.88473i	−1.07119	−	0.186500i
$687$	−6.07278	−	4.61370i	−0.231691	−	0.176024i
$688$	11.7994	+	9.72873i	0.449846	+	0.370904i
$689$		−	16.7678i		−	0.638801i
$690$	−3.59486	−	3.86876i	−0.136854	−	0.147281i
$691$	13.4058			0.509981			0.254991	−	0.966944i	$-0.417928\pi$
$691$	13.4058			0.509981			0.254991	+	0.966944i	$0.417928\pi$
$692$	−10.1120	−	3.63117i	−0.384399	−	0.138036i
$693$	1.11966	+	4.02383i	0.0425322	+	0.152853i
$694$	10.7100	+	1.86467i	0.406545	+	0.0707817i
$695$	15.9891			0.606501
$696$	−5.10424	−	11.9406i	−0.193476	−	0.452607i
$697$	−44.6482			−1.69117
$698$	−1.39685	−	0.243200i	−0.0528717	−	0.00920526i
$699$	−27.6417	−	21.0004i	−1.04551	−	0.794308i
$700$	−0.528163	+	1.47081i	−0.0199627	+	0.0555914i
$701$	32.0325			1.20985			0.604926	−	0.796282i	$-0.293203\pi$
$701$	32.0325			1.20985			0.604926	+	0.796282i	$0.293203\pi$
$702$	40.0528	+	24.5945i	1.51169	+	0.928261i
$703$		−	59.0996i		−	2.22898i
$704$	4.30768	−	2.56188i	0.162352	−	0.0965544i
$705$	24.9153	−	32.7947i	0.938365	−	1.23512i
$706$	11.7749	+	2.05008i	0.443155	+	0.0771557i
$707$			28.2516i			1.06251i
$708$	−12.9899	−	19.9861i	−0.488190	−	0.751123i
$709$			14.0521i			0.527737i	0.964559	+	0.263869i	$0.0849986\pi$
$709$			14.0521i			0.527737i	−0.964559	+	0.263869i	$0.915001\pi$
$710$	2.66077	−	15.2825i	0.0998571	−	0.573543i
$711$	28.3204	−	7.88034i	1.06210	−	0.295536i
$712$	0.363289	+	0.206625i	0.0136148	+	0.00774359i
$713$			8.01146i			0.300031i
$714$	−23.6052	−	25.4037i	−0.883402	−	0.950711i
$715$	8.63928			0.323091
$716$	4.63409	−	12.9049i	0.173184	−	0.482277i
$717$	−4.65819	+	6.13134i	−0.173963	+	0.228979i
$718$	−7.95306	+	45.6795i	−0.296805	+	1.70474i
$719$	5.15631			0.192298			0.0961489	−	0.995367i	$-0.469347\pi$
$719$	5.15631			0.192298			0.0961489	+	0.995367i	$0.469347\pi$
$720$	−10.5052	+	23.6434i	−0.391505	+	0.881136i
$721$	3.03265			0.112942
$722$	−3.52839	+	20.2658i	−0.131313	+	0.754216i
$723$	5.55397	−	7.31040i	0.206554	−	0.271877i
$724$	−4.99681	+	13.9149i	−0.185705	+	0.517145i
$725$	−0.932028			−0.0346147
$726$	17.6866	+	19.0342i	0.656411	+	0.706425i
$727$			6.93284i			0.257125i	0.991701	+	0.128562i	$0.0410363\pi$
$727$			6.93284i			0.257125i	−0.991701	+	0.128562i	$0.958964\pi$
$728$	−19.8758	+	34.9458i	−0.736647	+	1.29518i
$729$	19.6333	+	18.5347i	0.727159	+	0.686470i
$730$	−5.29091	+	30.3891i	−0.195825	+	1.12475i
$731$			24.3562i			0.900845i
$732$	20.7740	+	31.9626i	0.767830	+	1.18137i
$733$		−	30.5749i		−	1.12931i	−0.825327	−	0.564655i	$-0.809009\pi$
$733$		−	30.5749i		−	1.12931i	0.825327	−	0.564655i	$-0.190991\pi$
$734$	−15.8641	−	2.76204i	−0.585556	−	0.101949i
$735$	−4.65706	+	6.12984i	−0.171778	+	0.226103i
$736$	−4.29397	+	3.68264i	−0.158278	+	0.135744i
$737$		−	4.36844i		−	0.160913i
$738$	2.93932	+	29.5889i	0.108198	+	1.08918i
$739$	−21.3391			−0.784972			−0.392486	−	0.919758i	$-0.628385\pi$
$739$	−21.3391			−0.784972			−0.392486	+	0.919758i	$0.628385\pi$
$740$	14.8703	−	41.4104i	0.546644	−	1.52228i
$741$	51.0914	+	38.8160i	1.87689	+	1.42594i
$742$	8.11692	+	1.41320i	0.297982	+	0.0518803i
$743$	−38.0022			−1.39417			−0.697083	−	0.716990i	$-0.745519\pi$
$743$	−38.0022			−1.39417			−0.697083	+	0.716990i	$0.745519\pi$
$744$	36.0890	−	15.4269i	1.32309	−	0.565579i
$745$	−19.4776			−0.713605
$746$	34.6343	+	6.03002i	1.26805	+	0.220775i
$747$	0.585090	−	0.162805i	0.0214073	−	0.00595672i
$748$	7.51252	+	2.69772i	0.274685	+	0.0986383i
$749$	20.9193			0.764374
$750$	19.2383	+	20.7041i	0.702483	+	0.756007i
$751$			18.4320i			0.672594i	0.941756	+	0.336297i	$0.109175\pi$
$751$			18.4320i			0.672594i	−0.941756	+	0.336297i	$0.890825\pi$
$752$	−34.0380	−	28.0648i	−1.24124	−	1.02342i
$753$	−9.97963	−	7.58188i	−0.363678	−	0.276299i
$754$	−23.6214	−	4.11262i	−0.860241	−	0.149773i
$755$		−	36.9891i		−	1.34617i
$756$	−15.2814	+	17.3159i	−0.555779	+	0.629771i
$757$			11.9248i			0.433416i	0.976236	+	0.216708i	$0.0695319\pi$
$757$			11.9248i			0.433416i	−0.976236	+	0.216708i	$0.930468\pi$
$758$	−7.04789	+	40.4805i	−0.255991	+	1.47032i
$759$	0.864036	+	0.656438i	0.0313625	+	0.0238272i
$760$	−17.4616	+	30.7011i	−0.633399	+	1.11365i
$761$			21.9664i			0.796281i	0.917324	+	0.398140i	$0.130344\pi$
$761$			21.9664i			0.796281i	−0.917324	+	0.398140i	$0.869656\pi$
$762$	11.4508	−	10.6401i	0.414818	−	0.385449i
$763$	21.6419			0.783488
$764$	−24.6819	−	8.86317i	−0.892959	−	0.320658i
$765$	−39.6970	+	11.0459i	−1.43525	+	0.399367i
$766$	0.195018	−	1.12011i	0.00704628	−	0.0404713i
$767$	−44.0114			−1.58916
$768$	24.8576	+	12.2516i	0.896971	+	0.442090i
$769$	−15.0271			−0.541893			−0.270946	−	0.962594i	$-0.587337\pi$
$769$	−15.0271			−0.541893			−0.270946	+	0.962594i	$0.587337\pi$
$770$	−0.728126	+	4.18209i	−0.0262398	+	0.150712i
$771$	−24.9588	−	18.9621i	−0.898869	−	0.682902i
$772$	−30.6420	−	11.0034i	−1.10283	−	0.396022i
$773$	33.8157			1.21626			0.608132	−	0.793836i	$-0.291919\pi$
$773$	33.8157			1.21626			0.608132	+	0.793836i	$0.291919\pi$
$774$	16.1411	−	1.60343i	0.580181	−	0.0576342i
$775$		−	2.81694i		−	0.101188i
$776$	8.02290	−	14.1059i	0.288005	−	0.506373i
$777$	23.7599	−	31.2739i	0.852380	−	1.12194i
$778$	4.79943	−	27.5662i	0.172068	−	0.988296i
$779$			40.5923i			1.45437i
$780$	26.0325	+	40.0533i	0.932115	+	1.43414i
$781$			3.18734i			0.114052i
$782$	−8.87583	−	1.54533i	−0.317399	−	0.0552610i
$783$	−12.7996	−	5.08727i	−0.457420	−	0.181804i
$784$	6.36222	+	5.24574i	0.227222	+	0.187348i
$785$		−	3.33475i		−	0.119022i
$786$	−25.6540	+	23.8377i	−0.915047	+	0.850262i
$787$	46.0168			1.64032			0.820162	−	0.572132i	$-0.193883\pi$
$787$	46.0168			1.64032			0.820162	+	0.572132i	$0.193883\pi$
$788$	2.69525	+	0.967854i	0.0960143	+	0.0344784i
$789$	−23.3506	+	30.7352i	−0.831305	+	1.09420i
$790$	29.4343	+	5.12467i	1.04723	+	0.182328i
$791$	32.2311			1.14601
$792$	1.29324	−	5.15624i	0.0459533	−	0.183219i
$793$	70.3850			2.49944
$794$	−34.9081	−	6.07770i	−1.23884	−	0.215689i
$795$	5.92235	−	7.79528i	0.210044	−	0.276470i
$796$	4.28236	−	11.9254i	0.151784	−	0.422684i
$797$	9.91816			0.351319			0.175660	−	0.984451i	$-0.443794\pi$
$797$	9.91816			0.351319			0.175660	+	0.984451i	$0.443794\pi$
$798$	−23.0960	+	21.4609i	−0.817590	+	0.759706i
$799$		−	70.2610i		−	2.48565i
$800$	1.50982	−	1.29487i	0.0533802	−	0.0457805i
$801$	0.427066	−	0.118834i	0.0150896	−	0.00419879i
$802$	23.8054	+	4.14464i	0.840596	+	0.146352i
$803$		−	6.33797i		−	0.223662i
$804$	20.2529	−	13.1633i	0.714264	−	0.464234i
$805$		−	4.79125i		−	0.168870i
$806$	12.4299	−	71.3928i	0.437824	−	2.51470i
$807$	−6.56622	+	8.64277i	−0.231142	+	0.304240i
$808$	17.7770	−	31.2557i	0.625394	−	1.09957i
$809$			4.31171i			0.151592i	0.997123	+	0.0757958i	$0.0241497\pi$
$809$			4.31171i			0.151592i	−0.997123	+	0.0757958i	$0.975850\pi$
$810$	9.93364	+	25.5805i	0.349033	+	0.898807i
$811$	−3.17486			−0.111484			−0.0557422	−	0.998445i	$-0.517753\pi$
$811$	−3.17486			−0.111484			−0.0557422	+	0.998445i	$0.517753\pi$
$812$	3.98166	−	11.0880i	0.139729	−	0.389113i
$813$	−24.8432	−	18.8742i	−0.871288	−	0.661948i
$814$	−1.55068	+	8.90657i	−0.0543514	+	0.312175i
$815$	−20.0268			−0.701507
$816$	10.1302	+	42.9584i	0.354627	+	1.50384i
$817$	22.1436			0.774706
$818$	−6.49966	+	37.3317i	−0.227255	+	1.30527i
$819$	11.4310	+	41.0807i	0.399430	+	1.43548i
$820$	−10.2136	+	28.4426i	−0.356675	+	0.993258i
$821$	−19.7380			−0.688861			−0.344431	−	0.938812i	$-0.611928\pi$
$821$	−19.7380			−0.688861			−0.344431	+	0.938812i	$0.611928\pi$
$822$	−18.5970	+	17.2803i	−0.648644	+	0.602721i
$823$			13.9106i			0.484892i	0.970165	+	0.242446i	$0.0779497\pi$
$823$			13.9106i			0.484892i	−0.970165	+	0.242446i	$0.922050\pi$
$824$	−3.35513	−	1.90827i	−0.116881	−	0.0664776i
$825$	−0.303807	−	0.230813i	−0.0105772	−	0.00803588i
$826$	3.70932	−	21.3050i	0.129064	−	0.741295i
$827$		−	0.00176927i		−	6.15235e-5i	−1.00000		3.07617e-5i	$-0.999990\pi$
$827$		−	0.00176927i		−	6.15235e-5i	1.00000		3.07617e-5i	$-9.79177e-6\pi$
$828$	−0.439790	+	5.98386i	−0.0152838	+	0.207954i
$829$		−	29.1986i		−	1.01411i	−0.861914	−	0.507054i	$-0.830734\pi$
$829$		−	29.1986i		−	1.01411i	0.861914	−	0.507054i	$-0.169266\pi$
$830$	0.608102	+	0.105874i	0.0211075	+	0.00367494i
$831$	−13.5119	−	10.2654i	−0.468721	−	0.356104i
$832$	43.9786	−	26.1551i	1.52469	−	0.906765i
$833$			13.1329i			0.455027i
$834$	−12.3653	−	13.3074i	−0.428174	−	0.460798i
$835$	9.34804			0.323502
$836$	2.45265	−	6.83007i	0.0848267	−	0.236223i
$837$	15.3757	−	38.6852i	0.531460	−	1.33716i
$838$	19.8654	+	3.45868i	0.686240	+	0.119478i
$839$	−3.13499			−0.108232			−0.0541159	−	0.998535i	$-0.517234\pi$
$839$	−3.13499			−0.108232			−0.0541159	+	0.998535i	$0.517234\pi$
$840$	−21.5830	+	9.22608i	−0.744684	+	0.318330i
$841$	−21.9737			−0.757714
$842$	−9.53689	−	1.66043i	−0.328663	−	0.0572220i
$843$	20.0500	+	15.2327i	0.690557	+	0.524641i
$844$	−33.0502	−	11.8682i	−1.13763	−	0.408520i
$845$	60.1733			2.07002
$846$	−46.5628	+	4.62547i	−1.60086	+	0.159027i
$847$			23.5728i			0.809972i
$848$	−8.09079	−	6.67097i	−0.277839	−	0.229082i
$849$	6.62862	−	8.72491i	0.227494	−	0.299438i
$850$	3.12087	+	0.543361i	0.107045	+	0.0186371i
$851$		−	10.2039i		−	0.349785i
$852$	−14.7771	+	9.60433i	−0.506255	+	0.329039i
$853$			9.78652i			0.335084i	0.985865	+	0.167542i	$0.0535830\pi$
$853$			9.78652i			0.335084i	−0.985865	+	0.167542i	$0.946417\pi$
$854$	−5.93210	+	34.0719i	−0.202992	+	1.16592i
$855$	10.0425	+	36.0908i	0.343446	+	1.23428i
$856$	−23.1437	−	13.1633i	−0.791036	−	0.449911i
$857$		−	8.17070i		−	0.279106i	−0.990215	−	0.139553i	$-0.955433\pi$
$857$		−	8.17070i		−	0.279106i	0.990215	−	0.139553i	$-0.0445665\pi$
$858$	−6.68124	−	7.19030i	−0.228094	−	0.245473i
$859$	14.1409			0.482480			0.241240	−	0.970465i	$-0.422446\pi$
$859$	14.1409			0.482480			0.241240	+	0.970465i	$0.422446\pi$
$860$	15.5158	+	5.57166i	0.529084	+	0.189992i
$861$	−16.3194	+	21.4803i	−0.556163	+	0.732048i
$862$	−1.27505	+	7.32345i	−0.0434285	+	0.249438i
$863$	20.3267			0.691928			0.345964	−	0.938248i	$-0.387552\pi$
$863$	20.3267			0.691928			0.345964	+	0.938248i	$0.387552\pi$
$864$	27.8022	−	9.54147i	0.945849	−	0.324607i
$865$	−11.5823			−0.393809
$866$	3.23245	−	18.5660i	0.109843	−	0.630900i
$867$	−24.7117	+	32.5267i	−0.839252	+	1.10466i
$868$	33.5121	+	12.0341i	1.13748	+	0.408464i
$869$	−6.13884			−0.208246
$870$	−9.52894	−	10.2550i	−0.323061	−	0.347676i
$871$		−	44.5989i		−	1.51118i
$872$	−23.9431	−	13.6179i	−0.810817	−	0.461161i
$873$	−4.61412	−	16.5823i	−0.156164	−	0.561225i
$874$	−1.40495	+	8.06954i	−0.0475232	+	0.272956i
$875$			25.6409i			0.866822i
$876$	29.3840	−	19.0981i	0.992793	−	0.645264i
$877$		−	5.92738i		−	0.200153i	−0.994980	−	0.100077i	$-0.968091\pi$
$877$		−	5.92738i		−	0.200153i	0.994980	−	0.100077i	$-0.0319088\pi$
$878$	−4.14130	−	0.721023i	−0.139762	−	0.0243333i
$879$	−32.6773	+	43.0115i	−1.10218	+	1.45074i
$880$	3.43709	−	4.16863i	0.115864	−	0.140525i
$881$		−	33.5127i		−	1.12907i	−0.825409	−	0.564536i	$-0.809055\pi$
$881$		−	33.5127i		−	1.12907i	0.825409	−	0.564536i	$-0.190945\pi$
$882$	8.70331	−	0.864573i	0.293056	−	0.0291117i
$883$	−45.8263			−1.54218			−0.771088	−	0.636728i	$-0.780287\pi$
$883$	−45.8263			−1.54218			−0.771088	+	0.636728i	$0.780287\pi$
$884$	76.6979	+	27.5419i	2.57963	+	0.926336i
$885$	−20.4607	−	15.5447i	−0.687780	−	0.522531i
$886$	21.3497	+	3.71710i	0.717258	+	0.124879i
$887$	−39.2872			−1.31914			−0.659568	−	0.751645i	$-0.729261\pi$
$887$	−39.2872			−1.31914			−0.659568	+	0.751645i	$0.729261\pi$
$888$	−45.9651	+	19.6487i	−1.54249	+	0.659368i
$889$	14.1812			0.475621
$890$	0.443863	+	0.0772790i	0.0148783	+	0.00259040i
$891$	−2.91235	−	4.82803i	−0.0975675	−	0.161745i
$892$	−10.0118	+	27.8806i	−0.335220	+	0.933511i
$893$	−63.8783			−2.13761
$894$	15.0631	+	16.2109i	0.503787	+	0.542172i
$895$		−	14.7813i		−	0.494083i
$896$	8.95458	+	23.4935i	0.299152	+	0.784863i
$897$	8.82125	+	6.70181i	0.294533	+	0.223767i
$898$	−17.0726	−	2.97243i	−0.569719	−	0.0991912i
$899$			21.2361i			0.708263i
$900$	0.154636	−	2.10401i	0.00515455	−	0.0701337i
$901$		−	16.7010i		−	0.556390i
$902$	1.06508	−	6.11744i	0.0354633	−	0.203689i
$903$	11.7178	+	8.90242i	0.389944	+	0.296254i
$904$	−35.6584	−	20.2811i	−1.18598	−	0.674539i
$905$			15.9382i			0.529805i
$906$	−30.7853	+	28.6057i	−1.02277	+	0.950362i
$907$	47.7076			1.58411			0.792053	−	0.610452i	$-0.209012\pi$
$907$	47.7076			1.58411			0.792053	+	0.610452i	$0.209012\pi$
$908$	11.2154	−	31.2324i	0.372198	−	1.03648i
$909$	−10.2239	−	36.7428i	−0.339106	−	1.21868i
$910$	−7.43369	+	42.6965i	−0.246425	+	1.41537i
$911$	−4.11601			−0.136370			−0.0681848	−	0.997673i	$-0.521721\pi$
$911$	−4.11601			−0.136370			−0.0681848	+	0.997673i	$0.521721\pi$
$912$	39.0560	−	9.20994i	1.29327	−	0.304972i
$913$	−0.126826			−0.00419734
$914$	−5.20211	+	29.8791i	−0.172071	+	0.988312i
$915$	32.7217	+	24.8599i	1.08175	+	0.821841i
$916$	−2.97628	+	8.28824i	−0.0983389	+	0.273851i
$917$	−31.7711			−1.04917
$918$	39.8932	+	24.4966i	1.31667	+	0.808507i
$919$		−	10.0809i		−	0.332539i	−0.986080	−	0.166269i	$-0.946828\pi$
$919$		−	10.0809i		−	0.332539i	0.986080	−	0.166269i	$-0.0531722\pi$
$920$	−3.01485	+	5.30073i	−0.0993967	+	0.174760i
$921$	−9.83019	+	12.9390i	−0.323916	+	0.426354i
$922$	−6.23613	+	35.8181i	−0.205376	+	1.17961i
$923$			32.5407i			1.07109i
$924$	4.04378	−	2.62824i	0.133030	−	0.0864628i
$925$			3.58783i			0.117967i
$926$	12.6682	+	2.20561i	0.416304	+	0.0724809i
$927$	−3.94413	+	1.09748i	−0.129542	+	0.0360460i
$928$	−11.3821	+	9.76163i	−0.373635	+	0.320441i
$929$			21.1046i			0.692420i	0.938157	+	0.346210i	$0.112532\pi$
$929$			21.1046i			0.692420i	−0.938157	+	0.346210i	$0.887468\pi$
$930$	30.9944	−	28.8001i	1.01635	−	0.944391i
$931$	11.9399			0.391313
$932$	−13.5473	+	37.7260i	−0.443755	+	1.23575i
$933$	9.86517	−	12.9850i	0.322971	−	0.425110i
$934$	−21.2841	−	3.70568i	−0.696437	−	0.121254i
$935$	8.60486			0.281409
$936$	13.2032	−	52.6418i	0.431559	−	1.72065i
$937$	−36.7370			−1.20014			−0.600072	−	0.799946i	$-0.704862\pi$
$937$	−36.7370			−1.20014			−0.600072	+	0.799946i	$0.704862\pi$
$938$	21.5894	+	3.75883i	0.704919	+	0.122730i
$939$	2.05935	−	2.71062i	0.0672045	−	0.0884578i
$940$	−44.7589	−	16.0727i	−1.45987	−	0.524235i
$941$	19.2814			0.628555			0.314277	−	0.949331i	$-0.398238\pi$
$941$	19.2814			0.628555			0.314277	+	0.949331i	$0.398238\pi$
$942$	−2.77545	+	2.57895i	−0.0904291	+	0.0840268i
$943$			7.00850i			0.228228i
$944$	−17.5097	+	21.2364i	−0.569892	+	0.691186i
$945$	−9.19541	+	23.1357i	−0.299127	+	0.752604i
$946$	−3.33714	−	0.581015i	−0.108500	−	0.0188904i
$947$		−	25.6254i		−	0.832715i	−0.909201	−	0.416357i	$-0.863306\pi$
$947$		−	25.6254i		−	0.832715i	0.909201	−	0.416357i	$-0.136694\pi$
$948$	−18.4980	−	28.4608i	−0.600788	−	0.924363i
$949$		−	64.7066i		−	2.10046i
$950$	0.494001	−	2.83736i	0.0160275	−	0.0920562i
$951$	3.99658	−	5.26049i	0.129598	−	0.170583i
$952$	−19.7966	+	34.8066i	−0.641613	+	1.12809i
$953$			44.1193i			1.42916i	0.699552	+	0.714582i	$0.253383\pi$
$953$			44.1193i			1.42916i	−0.699552	+	0.714582i	$0.746617\pi$
$954$	−11.0679	+	1.09947i	−0.358338	+	0.0355967i
$955$	−28.2707			−0.914818
$956$	8.36816	+	3.00498i	0.270646	+	0.0971879i
$957$	2.29031	+	1.74003i	0.0740353	+	0.0562472i
$958$	−7.91251	+	45.4466i	−0.255642	+	1.46831i
$959$	−23.0313			−0.743721
$960$	29.6835	+	3.37376i	0.958030	+	0.108888i
$961$	−33.1835			−1.07043
$962$	−15.8315	+	90.9303i	−0.510427	+	2.93171i
$963$	−27.2067	+	7.57044i	−0.876724	+	0.243954i
$964$	−9.97737	−	3.58284i	−0.321349	−	0.115395i
$965$	−35.0974			−1.12983
$966$	−3.98767	+	3.70535i	−0.128301	+	0.119218i
$967$			55.2798i			1.77768i	0.458219	+	0.888839i	$0.348488\pi$
$967$			55.2798i			1.77768i	−0.458219	+	0.888839i	$0.651512\pi$
$968$	14.8330	−	26.0794i	0.476750	−	0.838225i
$969$	50.8879	+	38.6613i	1.63476	+	1.24198i
$970$	3.00062	−	17.2345i	0.0963440	−	0.553366i
$971$		−	39.8403i		−	1.27854i	−0.768984	−	0.639268i	$-0.779237\pi$
$971$		−	39.8403i		−	1.27854i	0.768984	−	0.639268i	$-0.220763\pi$
$972$	13.6079	−	28.0504i	0.436474	−	0.899717i
$973$		−	16.4805i		−	0.528341i
$974$	4.88314	+	0.850181i	0.156466	+	0.0272416i
$975$	−3.10167	−	2.35645i	−0.0993331	−	0.0754668i
$976$	28.0023	−	33.9622i	0.896332	−	1.08710i
$977$		−	24.2542i		−	0.775961i	−0.921668	−	0.387980i	$-0.873173\pi$
$977$		−	24.2542i		−	0.775961i	0.921668	−	0.387980i	$-0.126827\pi$
$978$	15.4878	+	16.6679i	0.495246	+	0.532980i
$979$	−0.0925724			−0.00295863
$980$	8.36612	+	3.00424i	0.267246	+	0.0959671i
$981$	−28.1465	+	7.83193i	−0.898647	+	0.250054i
$982$	−23.3591	−	4.06695i	−0.745419	−	0.129782i
$983$	4.71528			0.150394			0.0751970	−	0.997169i	$-0.476041\pi$
$983$	4.71528			0.150394			0.0751970	+	0.997169i	$0.476041\pi$
$984$	31.5710	−	13.4956i	1.00645	−	0.430225i
$985$	3.08715			0.0983647
$986$	−23.5273	−	4.09623i	−0.749262	−	0.130451i
$987$	−33.8027	−	25.6811i	−1.07595	−	0.817438i
$988$	25.0400	−	69.7306i	0.796628	−	2.21842i
$989$	3.82323			0.121572
$990$	−0.566482	−	5.70255i	−0.0180040	−	0.181239i
$991$			7.45074i			0.236680i	0.992973	+	0.118340i	$0.0377573\pi$
$991$			7.45074i			0.236680i	−0.992973	+	0.118340i	$0.962243\pi$
$992$	−29.5033	−	34.4009i	−0.936732	−	1.09223i
$993$	−28.0395	+	36.9070i	−0.889808	+	1.17121i
$994$	−15.7522	−	2.74255i	−0.499631	−	0.0869885i
$995$		−	13.6594i		−	0.433031i
$996$	−0.382163	−	0.587990i	−0.0121093	−	0.0186312i
$997$			46.6922i			1.47876i	0.673290	+	0.739378i	$0.264880\pi$
$997$			46.6922i			1.47876i	−0.673290	+	0.739378i	$0.735120\pi$
$998$	2.11019	−	12.1202i	0.0667968	−	0.383657i
$999$	−19.5834	+	49.2719i	−0.619591	+	1.55889i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.j.d.323.18	yes	42
3.2	odd	2		552.2.j.c.323.25	✓	42
4.3	odd	2		2208.2.j.d.47.14		42
8.3	odd	2		552.2.j.c.323.26	yes	42
8.5	even	2		2208.2.j.c.47.14		42
12.11	even	2		2208.2.j.c.47.13		42
24.5	odd	2		2208.2.j.d.47.13		42
24.11	even	2	inner	552.2.j.d.323.17	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.j.c.323.25	✓	42	3.2	odd	2
552.2.j.c.323.26	yes	42	8.3	odd	2
552.2.j.d.323.17	yes	42	24.11	even	2	inner
552.2.j.d.323.18	yes	42	1.1	even	1	trivial
2208.2.j.c.47.13		42	12.11	even	2
2208.2.j.c.47.14		42	8.5	even	2
2208.2.j.d.47.13		42	24.5	odd	2
2208.2.j.d.47.14		42	4.3	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.242573 + 1.39325i) q^{2} +(1.04780 - 1.37917i) q^{3} +(-1.88232 - 0.675933i) q^{4} -2.15601 q^{5} +(1.66736 + 1.79441i) q^{6} +2.22228i q^{7} +(1.39835 - 2.45858i) q^{8} +(-0.804216 - 2.89020i) q^{9} +O(q^{10})\)	\(q+(-0.242573 + 1.39325i) q^{2} +(1.04780 - 1.37917i) q^{3} +(-1.88232 - 0.675933i) q^{4} -2.15601 q^{5} +(1.66736 + 1.79441i) q^{6} +2.22228i q^{7} +(1.39835 - 2.45858i) q^{8} +(-0.804216 - 2.89020i) q^{9} +(0.522991 - 3.00387i) q^{10} +0.626490i q^{11} +(-2.90452 + 1.88779i) q^{12} +6.39606i q^{13} +(-3.09620 - 0.539065i) q^{14} +(-2.25908 + 2.97350i) q^{15} +(3.08623 + 2.54464i) q^{16} +6.37058i q^{17} +(4.22186 - 0.419393i) q^{18} +5.79186 q^{19} +(4.05830 + 1.45732i) q^{20} +(3.06490 + 2.32851i) q^{21} +(-0.872860 - 0.151970i) q^{22} +1.00000 q^{23} +(-1.92561 - 4.50467i) q^{24} -0.351614 q^{25} +(-8.91134 - 1.55151i) q^{26} +(-4.82873 - 1.91921i) q^{27} +(1.50211 - 4.18303i) q^{28} +2.65071 q^{29} +(-3.59486 - 3.86876i) q^{30} +8.01146i q^{31} +(-4.29397 + 3.68264i) q^{32} +(0.864036 + 0.656438i) q^{33} +(-8.87583 - 1.54533i) q^{34} -4.79125i q^{35} +(-0.439790 + 5.98386i) q^{36} -10.2039i q^{37} +(-1.40495 + 8.06954i) q^{38} +(8.82125 + 6.70181i) q^{39} +(-3.01485 + 5.30073i) q^{40} +7.00850i q^{41} +(-3.98767 + 3.70535i) q^{42} +3.82323 q^{43} +(0.423465 - 1.17925i) q^{44} +(1.73390 + 6.23130i) q^{45} +(-0.242573 + 1.39325i) q^{46} -11.0290 q^{47} +(6.74325 - 1.59015i) q^{48} +2.06149 q^{49} +(0.0852922 - 0.489888i) q^{50} +(8.78610 + 6.67511i) q^{51} +(4.32331 - 12.0394i) q^{52} -2.62158 q^{53} +(3.84527 - 6.26210i) q^{54} -1.35072i q^{55} +(5.46365 + 3.10751i) q^{56} +(6.06873 - 7.98796i) q^{57} +(-0.642993 + 3.69312i) q^{58} +6.88102i q^{59} +(6.26219 - 4.07009i) q^{60} -11.0044i q^{61} +(-11.1620 - 1.94337i) q^{62} +(6.42282 - 1.78719i) q^{63} +(-4.08926 - 6.87590i) q^{64} -13.7900i q^{65} +(-1.12418 + 1.04459i) q^{66} -6.97288 q^{67} +(4.30608 - 11.9914i) q^{68} +(1.04780 - 1.37917i) q^{69} +(6.67544 + 1.16223i) q^{70} +5.08761 q^{71} +(-8.23036 - 2.06426i) q^{72} -10.1166 q^{73} +(14.2166 + 2.47519i) q^{74} +(-0.368422 + 0.484935i) q^{75} +(-10.9021 - 3.91491i) q^{76} -1.39223 q^{77} +(-11.4771 + 10.6646i) q^{78} +9.79878i q^{79} +(-6.65395 - 5.48627i) q^{80} +(-7.70647 + 4.64868i) q^{81} +(-9.76463 - 1.70008i) q^{82} +0.202439i q^{83} +(-4.19519 - 6.45465i) q^{84} -13.7350i q^{85} +(-0.927413 + 5.32673i) q^{86} +(2.77743 - 3.65578i) q^{87} +(1.54028 + 0.876050i) q^{88} +0.147764i q^{89} +(-9.10238 + 0.904216i) q^{90} -14.2138 q^{91} +(-1.88232 - 0.675933i) q^{92} +(11.0492 + 8.39443i) q^{93} +(2.67534 - 15.3662i) q^{94} -12.4873 q^{95} +(0.579754 + 9.78079i) q^{96} +5.73742 q^{97} +(-0.500062 + 2.87218i) q^{98} +(1.81068 - 0.503833i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9	\( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) \) 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

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