LMFDB - Embedded newform 357.2.p.a.67.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(16,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("357.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.p (of order $6$, degree $2$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			67.4
Character	$\chi$	$=$	357.67
Dual form			357.2.p.a.16.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11091 - 1.92416i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.46826 + 2.54309i) q^{4} +(-0.551608 + 0.318471i) q^{5} -2.22183i q^{6} +(-1.27391 + 2.31887i) q^{7} +2.08076 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.11091 - 1.92416i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.46826 + 2.54309i) q^{4} +(-0.551608 + 0.318471i) q^{5} -2.22183i q^{6} +(-1.27391 + 2.31887i) q^{7} +2.08076 q^{8} +(0.500000 + 0.866025i) q^{9} +(1.22558 + 0.707587i) q^{10} +(3.85464 + 2.22548i) q^{11} +(-2.54309 + 1.46826i) q^{12} -4.96153 q^{13} +(5.87707 - 0.124849i) q^{14} -0.636942 q^{15} +(0.624963 + 1.08247i) q^{16} +(4.08405 - 0.566148i) q^{17} +(1.11091 - 1.92416i) q^{18} +(2.85195 + 4.93972i) q^{19} -1.87039i q^{20} +(-2.26267 + 1.37124i) q^{21} -9.88925i q^{22} +(1.06733 - 0.616221i) q^{23} +(1.80199 + 1.04038i) q^{24} +(-2.29715 + 3.97878i) q^{25} +(5.51183 + 9.54676i) q^{26} +1.00000i q^{27} +(-4.02666 - 6.64437i) q^{28} +3.35828i q^{29} +(0.707587 + 1.22558i) q^{30} +(3.14993 + 1.81861i) q^{31} +(3.46932 - 6.00904i) q^{32} +(2.22548 + 3.85464i) q^{33} +(-5.62638 - 7.22942i) q^{34} +(-0.0357911 - 1.68481i) q^{35} -2.93651 q^{36} +(-2.86890 + 1.65636i) q^{37} +(6.33653 - 10.9752i) q^{38} +(-4.29681 - 2.48076i) q^{39} +(-1.14777 + 0.662663i) q^{40} -8.40547i q^{41} +(5.15212 + 2.83041i) q^{42} +2.95338 q^{43} +(-11.3192 + 6.53514i) q^{44} +(-0.551608 - 0.318471i) q^{45} +(-2.37141 - 1.36914i) q^{46} +(-5.19336 - 8.99516i) q^{47} +1.24993i q^{48} +(-3.75429 - 5.90807i) q^{49} +10.2077 q^{50} +(3.81997 + 1.55173i) q^{51} +(7.28479 - 12.6176i) q^{52} +(-6.14162 + 10.6376i) q^{53} +(1.92416 - 1.11091i) q^{54} -2.83500 q^{55} +(-2.65071 + 4.82501i) q^{56} +5.70390i q^{57} +(6.46187 - 3.73076i) q^{58} +(-0.809436 + 1.40198i) q^{59} +(0.935194 - 1.61980i) q^{60} +(6.67049 - 3.85121i) q^{61} -8.08129i q^{62} +(-2.64515 + 0.0561921i) q^{63} -12.9166 q^{64} +(2.73682 - 1.58010i) q^{65} +(4.94463 - 8.56434i) q^{66} +(4.43382 - 7.67960i) q^{67} +(-4.55666 + 11.2174i) q^{68} +1.23244 q^{69} +(-3.20208 + 1.94055i) q^{70} +9.35212i q^{71} +(1.04038 + 1.80199i) q^{72} +(7.34831 + 4.24255i) q^{73} +(6.37420 + 3.68015i) q^{74} +(-3.97878 + 2.29715i) q^{75} -16.7496 q^{76} +(-10.0711 + 6.10333i) q^{77} +11.0237i q^{78} +(-12.5774 + 7.26158i) q^{79} +(-0.689470 - 0.398066i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-16.1735 + 9.33775i) q^{82} +1.17614 q^{83} +(-0.165009 - 7.76752i) q^{84} +(-2.07249 + 1.61294i) q^{85} +(-3.28095 - 5.68276i) q^{86} +(-1.67914 + 2.90836i) q^{87} +(8.02060 + 4.63069i) q^{88} +(-1.92963 - 3.34222i) q^{89} +1.41517i q^{90} +(6.32056 - 11.5051i) q^{91} +3.61908i q^{92} +(1.81861 + 3.14993i) q^{93} +(-11.5387 + 19.9857i) q^{94} +(-3.14632 - 1.81653i) q^{95} +(6.00904 - 3.46932i) q^{96} +12.9435i q^{97} +(-7.19737 + 13.7872i) q^{98} +4.45096i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{4} + 24 q^{9}+O(q^{10}) $ 48 * q - 24 * q^4 + 24 * q^9	$ 48 q - 24 q^{4} + 24 q^{9} + 16 q^{13} - 40 q^{16} + 8 q^{17} + 16 q^{19} + 36 q^{25} - 52 q^{26} + 24 q^{30} + 20 q^{32} - 8 q^{33} - 32 q^{34} - 36 q^{35} - 48 q^{36} + 40 q^{38} + 4 q^{42} + 40 q^{43} - 80 q^{50} - 12 q^{52} - 60 q^{53} - 24 q^{59} + 112 q^{64} + 4 q^{66} - 4 q^{67} + 88 q^{68} + 64 q^{69} - 24 q^{70} - 184 q^{76} - 72 q^{77} - 24 q^{81} - 88 q^{83} - 20 q^{84} + 16 q^{85} + 60 q^{86} + 36 q^{87} + 12 q^{89} - 24 q^{93} - 32 q^{94} + 48 q^{98}+O(q^{100}) $ 48 * q - 24 * q^4 + 24 * q^9 + 16 * q^13 - 40 * q^16 + 8 * q^17 + 16 * q^19 + 36 * q^25 - 52 * q^26 + 24 * q^30 + 20 * q^32 - 8 * q^33 - 32 * q^34 - 36 * q^35 - 48 * q^36 + 40 * q^38 + 4 * q^42 + 40 * q^43 - 80 * q^50 - 12 * q^52 - 60 * q^53 - 24 * q^59 + 112 * q^64 + 4 * q^66 - 4 * q^67 + 88 * q^68 + 64 * q^69 - 24 * q^70 - 184 * q^76 - 72 * q^77 - 24 * q^81 - 88 * q^83 - 20 * q^84 + 16 * q^85 + 60 * q^86 + 36 * q^87 + 12 * q^89 - 24 * q^93 - 32 * q^94 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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 $

$2$	−1.11091	−	1.92416i	−0.785534	−	1.36058i	−0.928679	−	0.370883i	$-0.879055\pi$
$2$	−1.11091	−	1.92416i	−0.785534	−	1.36058i	0.143145	−	0.989702i	$-0.454278\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−1.46826	+	2.54309i	−0.734128	+	1.27155i
$5$	−0.551608	+	0.318471i	−0.246687	+	0.142425i	−0.618246	−	0.785985i	$-0.712157\pi$
$5$	−0.551608	+	0.318471i	−0.246687	+	0.142425i	0.371560	+	0.928409i	$0.378823\pi$
$6$		−	2.22183i		−	0.907057i
$7$	−1.27391	+	2.31887i	−0.481494	+	0.876449i
$7$	−1.27391	+	2.31887i	−0.481494	+	0.876449i
$8$	2.08076			0.735661
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.22558	+	0.707587i	0.387561	+	0.223759i
$11$	3.85464	+	2.22548i	1.16222	+	0.671007i	0.951835	−	0.306612i	$-0.0991954\pi$
$11$	3.85464	+	2.22548i	1.16222	+	0.671007i	0.210384	+	0.977619i	$0.432529\pi$
$12$	−2.54309	+	1.46826i	−0.734128	+	0.423849i
$13$	−4.96153			−1.37608			−0.688040	−	0.725673i	$-0.741529\pi$
$13$	−4.96153			−1.37608			−0.688040	+	0.725673i	$0.741529\pi$
$14$	5.87707	−	0.124849i	1.57071	−	0.0333673i
$15$	−0.636942			−0.164458
$16$	0.624963	+	1.08247i	0.156241	+	0.270617i
$17$	4.08405	−	0.566148i	0.990528	−	0.137311i
$17$	4.08405	−	0.566148i	0.990528	−	0.137311i
$18$	1.11091	−	1.92416i	0.261845	−	0.453528i
$19$	2.85195	+	4.93972i	0.654282	+	1.13325i	0.982073	+	0.188500i	$0.0603624\pi$
$19$	2.85195	+	4.93972i	0.654282	+	1.13325i	−0.327791	+	0.944750i	$0.606304\pi$
$20$		−	1.87039i		−	0.418231i
$21$	−2.26267	+	1.37124i	−0.493756	+	0.299229i
$22$		−	9.88925i		−	2.10840i
$23$	1.06733	−	0.616221i	0.222553	−	0.128491i	−0.384579	−	0.923092i	$-0.625653\pi$
$23$	1.06733	−	0.616221i	0.222553	−	0.128491i	0.607132	+	0.794601i	$0.292320\pi$
$24$	1.80199	+	1.04038i	0.367830	+	0.212367i
$25$	−2.29715	+	3.97878i	−0.459430	+	0.795757i
$26$	5.51183	+	9.54676i	1.08096	+	1.87227i
$27$			1.00000i			0.192450i
$28$	−4.02666	−	6.64437i	−0.760968	−	1.25567i
$29$			3.35828i			0.623618i	0.950145	+	0.311809i	$0.100935\pi$
$29$			3.35828i			0.623618i	−0.950145	+	0.311809i	$0.899065\pi$
$30$	0.707587	+	1.22558i	0.129187	+	0.223759i
$31$	3.14993	+	1.81861i	0.565745	+	0.326633i	0.755448	−	0.655209i	$-0.227419\pi$
$31$	3.14993	+	1.81861i	0.565745	+	0.326633i	−0.189703	+	0.981841i	$0.560753\pi$
$32$	3.46932	−	6.00904i	0.613296	−	1.06226i
$33$	2.22548	+	3.85464i	0.387406	+	0.671007i
$34$	−5.62638	−	7.22942i	−0.964917	−	1.23983i
$35$	−0.0357911	−	1.68481i	−0.00604980	−	0.284785i
$36$	−2.93651			−0.489418
$37$	−2.86890	+	1.65636i	−0.471644	+	0.272304i	−0.716928	−	0.697147i	$-0.754452\pi$
$37$	−2.86890	+	1.65636i	−0.471644	+	0.272304i	0.245283	+	0.969451i	$0.421119\pi$
$38$	6.33653	−	10.9752i	1.02792	−	1.78041i
$39$	−4.29681	−	2.48076i	−0.688040	−	0.397240i
$40$	−1.14777	+	0.662663i	−0.181478	+	0.104776i
$41$		−	8.40547i		−	1.31271i	−0.754450	−	0.656357i	$-0.772097\pi$
$41$		−	8.40547i		−	1.31271i	0.754450	−	0.656357i	$-0.227903\pi$
$42$	5.15212	+	2.83041i	0.794989	+	0.436742i
$43$	2.95338			0.450386			0.225193	−	0.974314i	$-0.427699\pi$
$43$	2.95338			0.450386			0.225193	+	0.974314i	$0.427699\pi$
$44$	−11.3192	+	6.53514i	−1.70643	+	0.985210i
$45$	−0.551608	−	0.318471i	−0.0822289	−	0.0474749i
$46$	−2.37141	−	1.36914i	−0.349646	−	0.201868i
$47$	−5.19336	−	8.99516i	−0.757529	−	1.31208i	−0.944107	−	0.329639i	$-0.893073\pi$
$47$	−5.19336	−	8.99516i	−0.757529	−	1.31208i	0.186578	−	0.982440i	$-0.440260\pi$
$48$			1.24993i			0.180411i
$49$	−3.75429	−	5.90807i	−0.536327	−	0.844010i
$50$	10.2077			1.44359
$51$	3.81997	+	1.55173i	0.534902	+	0.217285i
$52$	7.28479	−	12.6176i	1.01022	−	1.74975i
$53$	−6.14162	+	10.6376i	−0.843616	+	1.46119i	0.0432018	+	0.999066i	$0.486244\pi$
$53$	−6.14162	+	10.6376i	−0.843616	+	1.46119i	−0.886818	+	0.462119i	$0.847089\pi$
$54$	1.92416	−	1.11091i	0.261845	−	0.151176i
$55$	−2.83500			−0.382272
$56$	−2.65071	+	4.82501i	−0.354216	+	0.644770i
$57$			5.70390i			0.755500i
$58$	6.46187	−	3.73076i	0.848485	−	0.489873i
$59$	−0.809436	+	1.40198i	−0.105380	+	0.182523i	−0.913893	−	0.405955i	$-0.866939\pi$
$59$	−0.809436	+	1.40198i	−0.105380	+	0.182523i	0.808514	+	0.588477i	$0.200272\pi$
$60$	0.935194	−	1.61980i	0.120733	−	0.209116i
$61$	6.67049	−	3.85121i	0.854069	−	0.493097i	−0.00795289	−	0.999968i	$-0.502532\pi$
$61$	6.67049	−	3.85121i	0.854069	−	0.493097i	0.862022	+	0.506872i	$0.169198\pi$
$62$		−	8.08129i		−	1.02632i
$63$	−2.64515	+	0.0561921i	−0.333258	+	0.00707954i
$64$	−12.9166			−1.61458
$65$	2.73682	−	1.58010i	0.339461	−	0.195988i
$66$	4.94463	−	8.56434i	0.608641	−	1.05420i
$67$	4.43382	−	7.67960i	0.541677	−	0.938213i	−0.457130	−	0.889400i	$-0.651123\pi$
$67$	4.43382	−	7.67960i	0.541677	−	0.938213i	0.998808	−	0.0488132i	$-0.0155439\pi$
$68$	−4.55666	+	11.2174i	−0.552577	+	1.36031i
$69$	1.23244			0.148369
$70$	−3.20208	+	1.94055i	−0.382722	+	0.231940i
$71$			9.35212i			1.10989i	0.831886	+	0.554946i	$0.187261\pi$
$71$			9.35212i			1.10989i	−0.831886	+	0.554946i	$0.812739\pi$
$72$	1.04038	+	1.80199i	0.122610	+	0.212367i
$73$	7.34831	+	4.24255i	0.860055	+	0.496553i	0.864031	−	0.503439i	$-0.167932\pi$
$73$	7.34831	+	4.24255i	0.860055	+	0.496553i	−0.00397574	+	0.999992i	$0.501266\pi$
$74$	6.37420	+	3.68015i	0.740986	+	0.427808i
$75$	−3.97878	+	2.29715i	−0.459430	+	0.265252i
$76$	−16.7496			−1.92131
$77$	−10.0711	+	6.10333i	−1.14770	+	0.695540i
$78$			11.0237i			1.24818i
$79$	−12.5774	+	7.26158i	−1.41507	+	0.816992i	−0.995860	−	0.0908965i	$-0.971027\pi$
$79$	−12.5774	+	7.26158i	−1.41507	+	0.816992i	−0.419211	+	0.907889i	$0.637693\pi$
$80$	−0.689470	−	0.398066i	−0.0770851	−	0.0445051i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−16.1735	+	9.33775i	−1.78606	+	1.03118i
$83$	1.17614			0.129098			0.0645491	−	0.997915i	$-0.479439\pi$
$83$	1.17614			0.129098			0.0645491	+	0.997915i	$0.479439\pi$
$84$	−0.165009	−	7.76752i	−0.0180039	−	0.847506i
$85$	−2.07249	+	1.61294i	−0.224794	+	0.174948i
$86$	−3.28095	−	5.68276i	−0.353793	−	0.612788i
$87$	−1.67914	+	2.90836i	−0.180023	+	0.311809i
$88$	8.02060	+	4.63069i	0.854999	+	0.493634i
$89$	−1.92963	−	3.34222i	−0.204541	−	0.354275i	0.745446	−	0.666566i	$-0.232237\pi$
$89$	−1.92963	−	3.34222i	−0.204541	−	0.354275i	−0.949986	+	0.312292i	$0.898903\pi$
$90$			1.41517i			0.149172i
$91$	6.32056	−	11.5051i	0.662575	−	1.20606i
$92$			3.61908i			0.377315i
$93$	1.81861	+	3.14993i	0.188582	+	0.326633i
$94$	−11.5387	+	19.9857i	−1.19013	+	2.06137i
$95$	−3.14632	−	1.81653i	−0.322805	−	0.186372i
$96$	6.00904	−	3.46932i	0.613296	−	0.354086i
$97$			12.9435i			1.31421i	0.753800	+	0.657104i	$0.228219\pi$
$97$			12.9435i			1.31421i	−0.753800	+	0.657104i	$0.771781\pi$
$98$	−7.19737	+	13.7872i	−0.727045	+	1.39272i
$99$			4.45096i			0.447338i
$100$	−6.74561	−	11.6837i	−0.674561	−	1.16837i
$101$	2.72077	−	4.71251i	0.270727	−	0.468912i	−0.698321	−	0.715784i	$-0.746069\pi$
$101$	2.72077	−	4.71251i	0.270727	−	0.468912i	0.969048	+	0.246872i	$0.0794027\pi$
$102$	−1.25788	−	9.07405i	−0.124549	−	0.898465i
$103$	−5.70540	−	9.88205i	−0.562170	−	0.973707i	−0.997307	−	0.0733429i	$-0.976633\pi$
$103$	−5.70540	−	9.88205i	−0.562170	−	0.973707i	0.435137	−	0.900364i	$-0.356700\pi$
$104$	−10.3238			−1.01233
$105$	0.811409	−	1.47698i	0.0791854	−	0.144139i
$106$	27.2912			2.65076
$107$	−10.4912	+	6.05708i	−1.01422	+	0.585560i	−0.912424	−	0.409245i	$-0.865792\pi$
$107$	−10.4912	+	6.05708i	−1.01422	+	0.585560i	−0.101795	+	0.994805i	$0.532459\pi$
$108$	−2.54309	−	1.46826i	−0.244709	−	0.141283i
$109$	10.1103	+	5.83720i	0.968394	+	0.559103i	0.898746	−	0.438469i	$-0.144479\pi$
$109$	10.1103	+	5.83720i	0.968394	+	0.559103i	0.0696480	+	0.997572i	$0.477812\pi$
$110$	3.14944	+	5.45499i	0.300287	+	0.520113i
$111$	−3.31272			−0.314430
$112$	−3.30625	+	0.0702360i	−0.312411	+	0.00663668i
$113$			4.19208i			0.394358i	0.980367	+	0.197179i	$0.0631780\pi$
$113$			4.19208i			0.394358i	−0.980367	+	0.197179i	$0.936822\pi$
$114$	10.9752	−	6.33653i	1.02792	−	0.593471i
$115$	−0.392497	+	0.679825i	−0.0366006	+	0.0633940i
$116$	−8.54043	−	4.93082i	−0.792959	−	0.457815i
$117$	−2.48076	−	4.29681i	−0.229347	−	0.397240i
$118$	3.59685			0.331117
$119$	−3.88991	+	10.1916i	−0.356587	+	0.934262i
$120$	−1.32533			−0.120985
$121$	4.40551	+	7.63056i	0.400501	+	0.693688i
$122$	−14.8207	−	8.55672i	−1.34180	−	0.774689i
$123$	4.20274	−	7.27935i	0.378948	−	0.656357i
$124$	−9.24981	+	5.34038i	−0.830658	+	0.479580i
$125$		−	6.11102i		−	0.546586i
$126$	3.04666	+	5.02727i	0.271418	+	0.447865i
$127$	17.6363			1.56497			0.782485	−	0.622669i	$-0.213952\pi$
$127$	17.6363			1.56497			0.782485	+	0.622669i	$0.213952\pi$
$128$	7.41058	+	12.8355i	0.655009	+	1.13451i
$129$	2.55770	+	1.47669i	0.225193	+	0.130015i
$130$	−6.08074	−	3.51071i	−0.533316	−	0.307910i
$131$	10.7894	−	6.22924i	0.942671	−	0.544251i	0.0518742	−	0.998654i	$-0.483481\pi$
$131$	10.7894	−	6.22924i	0.942671	−	0.544251i	0.890797	+	0.454402i	$0.150147\pi$
$132$	−13.0703			−1.13762
$133$	−15.0877	+	0.320514i	−1.30827	+	0.0277921i
$134$	−19.7024			−1.70202
$135$	−0.318471	−	0.551608i	−0.0274096	−	0.0474749i
$136$	8.49795	−	1.17802i	0.728693	−	0.101014i
$137$	9.11657	−	15.7904i	0.778882	−	1.34906i	−0.153705	−	0.988117i	$-0.549121\pi$
$137$	9.11657	−	15.7904i	0.778882	−	1.34906i	0.932587	−	0.360946i	$-0.117546\pi$
$138$	−1.36914	−	2.37141i	−0.116549	−	0.201868i
$139$		−	11.7920i		−	1.00019i	−0.865971	−	0.500094i	$-0.833299\pi$
$139$		−	11.7920i		−	1.00019i	0.865971	−	0.500094i	$-0.166701\pi$
$140$	4.33718	+	2.38271i	0.366559	+	0.201376i
$141$		−	10.3867i		−	0.874720i
$142$	17.9950	−	10.3894i	1.51010	−	0.871858i
$143$	−19.1249	−	11.0418i	−1.59931	−	0.923360i
$144$	−0.624963	+	1.08247i	−0.0520803	+	0.0902057i
$145$	−1.06952	−	1.85246i	−0.0888185	−	0.153838i
$146$		−	18.8524i		−	1.56024i
$147$	−0.297274	−	6.99368i	−0.0245187	−	0.576829i
$148$		−	9.72784i		−	0.799624i
$149$	−5.60174	−	9.70250i	−0.458912	−	0.794860i	0.539991	−	0.841671i	$-0.318428\pi$
$149$	−5.60174	−	9.70250i	−0.458912	−	0.794860i	−0.998904	+	0.0468109i	$0.985094\pi$
$150$	8.84017	+	5.10387i	0.721797	+	0.416729i
$151$	6.82085	−	11.8141i	0.555073	−	0.961414i	−0.442825	−	0.896608i	$-0.646024\pi$
$151$	6.82085	−	11.8141i	0.555073	−	0.961414i	0.997898	−	0.0648064i	$-0.0206430\pi$
$152$	5.93423	+	10.2784i	0.481330	+	0.833688i
$153$	2.53232	+	3.25382i	0.204726	+	0.263056i
$154$	22.9319	+	12.5981i	1.84790	+	1.01518i
$155$	−2.31670			−0.186082
$156$	12.6176	−	7.28479i	1.01022	−	0.583250i
$157$	−0.168499	+	0.291848i	−0.0134476	+	0.0232920i	−0.872671	−	0.488309i	$-0.837614\pi$
$157$	−0.168499	+	0.291848i	−0.0134476	+	0.0232920i	0.859223	+	0.511601i	$0.170947\pi$
$158$	27.9449	+	16.1340i	2.22317	+	1.28355i
$159$	−10.6376	+	6.14162i	−0.843616	+	0.487062i
$160$			4.41952i			0.349393i
$161$	0.0692535	+	3.26000i	0.00545794	+	0.256924i
$162$	2.22183			0.174563
$163$	−4.52040	+	2.60985i	−0.354065	+	0.204420i	−0.666474	−	0.745528i	$-0.732197\pi$
$163$	−4.52040	+	2.60985i	−0.354065	+	0.204420i	0.312409	+	0.949948i	$0.398864\pi$
$164$	21.3759	+	12.3414i	1.66918	+	0.963700i
$165$	−2.45518	−	1.41750i	−0.191136	−	0.110352i
$166$	−1.30659	−	2.26308i	−0.101411	−	0.175649i
$167$		−	19.6234i		−	1.51850i	−0.650797	−	0.759252i	$-0.725565\pi$
$167$		−	19.6234i		−	1.51850i	0.650797	−	0.759252i	$-0.274435\pi$
$168$	−4.70809	+	2.85323i	−0.363237	+	0.220131i
$169$	11.6168			0.893597
$170$	5.40592	+	2.19596i	0.414615	+	0.168423i
$171$	−2.85195	+	4.93972i	−0.218094	+	0.377750i
$172$	−4.33631	+	7.51071i	−0.330641	+	0.572687i
$173$	9.57633	−	5.52890i	0.728075	−	0.420354i	−0.0896424	−	0.995974i	$-0.528572\pi$
$173$	9.57633	−	5.52890i	0.728075	−	0.420354i	0.817718	+	0.575620i	$0.195239\pi$
$174$	7.46152			0.565657
$175$	−6.29990	−	10.3954i	−0.476228	−	0.785820i
$176$			5.56337i			0.419355i
$177$	−1.40198	+	0.809436i	−0.105380	+	0.0608409i
$178$	−4.28731	+	7.42584i	−0.321347	+	0.556590i
$179$	2.93488	−	5.08337i	0.219364	−	0.379949i	−0.735250	−	0.677796i	$-0.762935\pi$
$179$	2.93488	−	5.08337i	0.219364	−	0.379949i	0.954614	+	0.297847i	$0.0962686\pi$
$180$	1.61980	−	0.935194i	0.120733	−	0.0697052i
$181$			11.6689i			0.867343i	0.901071	+	0.433672i	$0.142782\pi$
$181$			11.6689i			0.867343i	−0.901071	+	0.433672i	$0.857218\pi$
$182$	−29.1593	+	0.619442i	−2.16143	+	0.0459161i
$183$	7.70242			0.569379
$184$	2.22085	−	1.28221i	0.163724	−	0.0945258i
$185$	1.05501	−	1.82732i	0.0775656	−	0.134348i
$186$	4.04065	−	6.99860i	0.296274	−	0.513162i
$187$	17.0025	+	6.90667i	1.24335	+	0.505066i
$188$	30.5007			2.22449
$189$	−2.31887	−	1.27391i	−0.168673	−	0.0926636i
$190$			8.07201i			0.585605i
$191$	7.88271	+	13.6533i	0.570373	+	0.987915i	0.996527	+	0.0832649i	$0.0265348\pi$
$191$	7.88271	+	13.6533i	0.570373	+	0.987915i	−0.426154	+	0.904651i	$0.640132\pi$
$192$	−11.1861	−	6.45831i	−0.807288	−	0.466088i
$193$	1.58028	+	0.912377i	0.113751	+	0.0656743i	0.555796	−	0.831319i	$-0.312413\pi$
$193$	1.58028	+	0.912377i	0.113751	+	0.0656743i	−0.442045	+	0.896993i	$0.645747\pi$
$194$	24.9052	−	14.3791i	1.78809	−	1.03236i
$195$	3.16021			0.226307
$196$	20.5370	−	0.872947i	1.46693	−	0.0623534i
$197$		−	17.5404i		−	1.24970i	−0.780743	−	0.624852i	$-0.785159\pi$
$197$		−	17.5404i		−	1.24970i	0.780743	−	0.624852i	$-0.214841\pi$
$198$	8.56434	−	4.94463i	0.608641	−	0.351399i
$199$	10.5663	+	6.10043i	0.749022	+	0.432448i	0.825340	−	0.564636i	$-0.190983\pi$
$199$	10.5663	+	6.10043i	0.749022	+	0.432448i	−0.0763186	+	0.997083i	$0.524317\pi$
$200$	−4.77983	+	8.27891i	−0.337985	+	0.585407i
$201$	7.67960	−	4.43382i	0.541677	−	0.312738i
$202$	−12.0902			−0.850660
$203$	−7.78741	−	4.27816i	−0.546569	−	0.300268i
$204$	−9.55487	+	7.43620i	−0.668975	+	0.520638i
$205$	2.67690	+	4.63653i	0.186963	+	0.323829i
$206$	−12.6764	+	21.9562i	−0.883208	+	1.52976i
$207$	1.06733	+	0.616221i	0.0741843	+	0.0428303i
$208$	−3.10077	−	5.37070i	−0.215000	−	0.372391i
$209$			25.3878i			1.75611i
$210$	−3.74336	+	0.0795216i	−0.258316	+	0.00548751i
$211$			3.74811i			0.258030i	0.991643	+	0.129015i	$0.0411816\pi$
$211$			3.74811i			0.258030i	−0.991643	+	0.129015i	$0.958818\pi$
$212$	−18.0349	−	31.2374i	−1.23864	−	2.14539i
$213$	−4.67606	+	8.09917i	−0.320398	+	0.554946i
$214$	23.3096	+	13.4578i	1.59341	+	0.919955i
$215$	−1.62911	+	0.940565i	−0.111104	+	0.0641460i
$216$			2.08076i			0.141578i
$217$	−8.22987	+	4.98752i	−0.558680	+	0.338575i
$218$		−	25.9385i		−	1.75678i
$219$	4.24255	+	7.34831i	0.286685	+	0.496553i
$220$	4.16251	−	7.20967i	0.280636	−	0.486076i
$221$	−20.2631	+	2.80896i	−1.36305	+	0.188951i
$222$	3.68015	+	6.37420i	0.246995	+	0.427808i
$223$	−10.9773			−0.735097			−0.367548	−	0.930004i	$-0.619803\pi$
$223$	−10.9773			−0.735097			−0.367548	+	0.930004i	$0.619803\pi$
$224$	9.51456	+	15.6999i	0.635718	+	1.04899i
$225$	−4.59430			−0.306287
$226$	8.06623	−	4.65704i	0.536558	−	0.309782i
$227$	−9.40856	−	5.43203i	−0.624468	−	0.360537i	0.154139	−	0.988049i	$-0.450740\pi$
$227$	−9.40856	−	5.43203i	−0.624468	−	0.360537i	−0.778606	+	0.627513i	$0.784073\pi$
$228$	−14.5055	−	8.37478i	−0.960653	−	0.554633i
$229$	4.77603	+	8.27234i	0.315609	+	0.546651i	0.979567	−	0.201119i	$-0.0644578\pi$
$229$	4.77603	+	8.27234i	0.315609	+	0.546651i	−0.663958	+	0.747770i	$0.731124\pi$
$230$	1.74412			0.115004
$231$	−11.7735	+	0.250109i	−0.774637	+	0.0164559i
$232$			6.98779i			0.458771i
$233$	8.22414	−	4.74821i	0.538782	−	0.311066i	−0.205803	−	0.978593i	$-0.565981\pi$
$233$	8.22414	−	4.74821i	0.538782	−	0.311066i	0.744585	+	0.667528i	$0.232647\pi$
$234$	−5.51183	+	9.54676i	−0.360319	+	0.624091i
$235$	5.72940	+	3.30787i	0.373745	+	0.215782i
$236$	−2.37692	−	4.11694i	−0.154724	−	0.267990i
$237$	−14.5232			−0.943381
$238$	23.9316	−	3.83718i	1.55125	−	0.248728i
$239$	11.4897			0.743209			0.371605	−	0.928391i	$-0.378808\pi$
$239$	11.4897			0.743209			0.371605	+	0.928391i	$0.378808\pi$
$240$	−0.398066	−	0.689470i	−0.0256950	−	0.0445051i
$241$	−11.4533	−	6.61255i	−0.737771	−	0.425952i	0.0834876	−	0.996509i	$-0.473394\pi$
$241$	−11.4533	−	6.61255i	−0.737771	−	0.425952i	−0.821258	+	0.570557i	$0.806727\pi$
$242$	9.78827	−	16.9538i	0.629214	−	1.08983i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$			22.6182i			1.44798i
$245$	3.95245	+	2.06331i	0.252512	+	0.131820i
$246$	−18.6755			−1.19071
$247$	−14.1500	−	24.5086i	−0.900345	−	1.55944i
$248$	6.55427	+	3.78411i	0.416196	+	0.240291i
$249$	1.01857	+	0.588071i	0.0645491	+	0.0372675i
$250$	−11.7586	+	6.78881i	−0.743677	+	0.429362i
$251$	1.84848			0.116675			0.0583376	−	0.998297i	$-0.481420\pi$
$251$	1.84848			0.116675			0.0583376	+	0.998297i	$0.481420\pi$
$252$	3.74086	−	6.80938i	0.235652	−	0.428950i
$253$	5.48555			0.344873
$254$	−19.5924	−	33.9351i	−1.22934	−	2.12927i
$255$	−2.60130	+	0.360603i	−0.162900	+	0.0225819i
$256$	3.54842	−	6.14604i	0.221776	−	0.384128i
$257$	3.50196	+	6.06558i	0.218446	+	0.378360i	0.954333	−	0.298744i	$-0.0965678\pi$
$257$	3.50196	+	6.06558i	0.218446	+	0.378360i	−0.735887	+	0.677105i	$0.763234\pi$
$258$		−	6.56189i		−	0.408526i
$259$	−0.186149	−	8.76266i	−0.0115667	−	0.544485i
$260$			9.27998i			0.575520i
$261$	−2.90836	+	1.67914i	−0.180023	+	0.103936i
$262$	−23.9721	−	13.8403i	−1.48100	−	0.855056i
$263$	2.41099	−	4.17595i	0.148668	−	0.257500i	−0.782068	−	0.623194i	$-0.785835\pi$
$263$	2.41099	−	4.17595i	0.148668	−	0.257500i	0.930735	+	0.365694i	$0.119168\pi$
$264$	4.63069	+	8.02060i	0.285000	+	0.493634i
$265$		−	7.82371i		−	0.480607i
$266$	17.3778	+	28.6750i	1.06550	+	1.75818i
$267$		−	3.85927i		−	0.236183i
$268$	13.0200	+	22.5512i	0.795321	+	1.37754i
$269$	13.9286	+	8.04171i	0.849244	+	0.490311i	0.860396	−	0.509626i	$-0.170216\pi$
$269$	13.9286	+	8.04171i	0.849244	+	0.490311i	−0.0111515	+	0.999938i	$0.503550\pi$
$270$	−0.707587	+	1.22558i	−0.0430624	+	0.0745862i
$271$	−14.1230	−	24.4617i	−0.857909	−	1.48594i	−0.873919	−	0.486071i	$-0.838430\pi$
$271$	−14.1230	−	24.4617i	−0.857909	−	1.48594i	0.0160101	−	0.999872i	$-0.494904\pi$
$272$	3.16522	+	4.06703i	0.191920	+	0.246600i
$273$	11.2263	−	6.80345i	0.679448	−	0.411764i
$274$	−40.5109			−2.44735
$275$	−17.7094	+	10.2245i	−1.06792	+	0.616562i
$276$	−1.80954	+	3.13422i	−0.108922	+	0.188658i
$277$	9.82327	+	5.67146i	0.590223	+	0.340765i	0.765186	−	0.643810i	$-0.222647\pi$
$277$	9.82327	+	5.67146i	0.590223	+	0.340765i	−0.174963	+	0.984575i	$0.555981\pi$
$278$	−22.6898	+	13.0999i	−1.36084	+	0.785682i
$279$			3.63723i			0.217755i
$280$	−0.0744728	−	3.50569i	−0.00445060	−	0.209505i
$281$	0.839507			0.0500808			0.0250404	−	0.999686i	$-0.492029\pi$
$281$	0.839507			0.0500808			0.0250404	+	0.999686i	$0.492029\pi$
$282$	−19.9857	+	11.5387i	−1.19013	+	0.687122i
$283$	−16.1532	−	9.32607i	−0.960210	−	0.554377i	−0.0639721	−	0.997952i	$-0.520377\pi$
$283$	−16.1532	−	9.32607i	−0.960210	−	0.554377i	−0.896238	+	0.443574i	$0.853710\pi$
$284$	−23.7833	−	13.7313i	−1.41128	−	0.814803i
$285$	−1.81653	−	3.14632i	−0.107602	−	0.186372i
$286$			49.0658i			2.90132i
$287$	19.4912	+	10.7078i	1.15053	+	0.632064i
$288$	6.93865			0.408864
$289$	16.3590	−	4.62436i	0.962291	−	0.272021i
$290$	−2.37628	+	4.11584i	−0.139540	+	0.241690i
$291$	−6.47173	+	11.2094i	−0.379379	+	0.657104i
$292$	−21.5784	+	12.4583i	−1.26278	+	0.729066i
$293$	−2.99309			−0.174858			−0.0874292	−	0.996171i	$-0.527865\pi$
$293$	−2.99309			−0.174858			−0.0874292	+	0.996171i	$0.527865\pi$
$294$	−13.1267	+	8.34138i	−0.765565	+	0.486479i
$295$		−	1.03113i		−	0.0600346i
$296$	−5.96950	+	3.44649i	−0.346970	+	0.200323i
$297$	−2.22548	+	3.85464i	−0.129135	+	0.223669i
$298$	−12.4461	+	21.5573i	−0.720983	+	1.24878i
$299$	−5.29557	+	3.05740i	−0.306251	+	0.176814i
$300$		−	13.4912i		−	0.778916i
$301$	−3.76235	+	6.84849i	−0.216858	+	0.394740i
$302$	−30.3095			−1.74411
$303$	4.71251	−	2.72077i	0.270727	−	0.156304i
$304$	−3.56473	+	6.17429i	−0.204451	+	0.354120i
$305$	−2.45300	+	4.24872i	−0.140458	+	0.243281i
$306$	3.44767	−	8.48730i	0.197090	−	0.485187i
$307$	25.0511			1.42974			0.714871	−	0.699256i	$-0.246485\pi$
$307$	25.0511			1.42974			0.714871	+	0.699256i	$0.246485\pi$
$308$	−0.734447	−	34.5729i	−0.0418490	−	1.96997i
$309$		−	11.4108i		−	0.649138i
$310$	2.57366	+	4.45770i	0.146174	+	0.253181i
$311$	1.39150	+	0.803381i	0.0789045	+	0.0455555i	0.538933	−	0.842349i	$-0.318828\pi$
$311$	1.39150	+	0.803381i	0.0789045	+	0.0455555i	−0.460029	+	0.887904i	$0.652161\pi$
$312$	−8.94064	−	5.16188i	−0.506164	−	0.292234i
$313$	−8.09544	+	4.67390i	−0.457581	+	0.264185i	−0.711027	−	0.703165i	$-0.751769\pi$
$313$	−8.09544	+	4.67390i	−0.457581	+	0.264185i	0.253446	+	0.967350i	$0.418436\pi$
$314$	0.748749			0.0422543
$315$	1.44119	−	0.873401i	0.0812020	−	0.0492106i
$316$		−	42.6474i		−	2.39911i
$317$	19.3820	−	11.1902i	1.08860	−	0.628506i	0.155399	−	0.987852i	$-0.450334\pi$
$317$	19.3820	−	11.1902i	1.08860	−	0.628506i	0.933204	+	0.359346i	$0.117000\pi$
$318$	23.6349	+	13.6456i	1.32538	+	0.765207i
$319$	−7.47379	+	12.9450i	−0.418452	+	0.724780i
$320$	7.12491	−	4.11357i	0.398294	−	0.229955i
$321$	−12.1142			−0.676146
$322$	6.19582	−	3.75483i	0.345280	−	0.209249i
$323$	14.4441	+	18.5594i	0.803692	+	1.03268i
$324$	−1.46826	−	2.54309i	−0.0815697	−	0.141283i
$325$	11.3974	−	19.7409i	0.632213	−	1.09503i
$326$	10.0435	+	5.79864i	0.556260	+	0.321157i
$327$	5.83720	+	10.1103i	0.322798	+	0.559103i
$328$		−	17.4898i		−	0.965712i
$329$	27.4745	−	0.583652i	1.51472	−	0.0321778i
$330$			6.29888i			0.346742i
$331$	−9.19545	−	15.9270i	−0.505427	−	0.875426i	−0.999980	−	0.00627837i	$-0.998002\pi$
$331$	−9.19545	−	15.9270i	−0.505427	−	0.875426i	0.494553	−	0.869148i	$-0.335332\pi$
$332$	−1.72688	+	2.99104i	−0.0947746	+	0.164154i
$333$	−2.86890	−	1.65636i	−0.157215	−	0.0907680i
$334$	−37.7585	+	21.7999i	−2.06605	+	1.19284i
$335$			5.64817i			0.308593i
$336$	−2.89841	−	1.59230i	−0.158121	−	0.0868670i
$337$			11.8137i			0.643535i	0.946819	+	0.321768i	$0.104277\pi$
$337$			11.8137i			0.643535i	−0.946819	+	0.321768i	$0.895723\pi$
$338$	−12.9052	−	22.3525i	−0.701951	−	1.21582i
$339$	−2.09604	+	3.63045i	−0.113841	+	0.197179i
$340$	−1.05892	−	7.63876i	−0.0574278	−	0.414270i
$341$	8.09458	+	14.0202i	0.438346	+	0.759237i
$342$	12.6731			0.685281
$343$	18.4827	−	1.17932i	0.997971	−	0.0636775i
$344$	6.14528			0.331331
$345$	−0.679825	+	0.392497i	−0.0366006	+	0.0211313i
$346$	−21.2769	−	12.2843i	−1.14386	−	0.660405i
$347$	14.5661	+	8.40971i	0.781947	+	0.451457i	0.837120	−	0.547020i	$-0.184238\pi$
$347$	14.5661	+	8.40971i	0.781947	+	0.451457i	−0.0551731	+	0.998477i	$0.517571\pi$
$348$	−4.93082	−	8.54043i	−0.264320	−	0.457815i
$349$	26.7376			1.43123			0.715616	−	0.698494i	$-0.246146\pi$
$349$	26.7376			1.43123			0.715616	+	0.698494i	$0.246146\pi$
$350$	−13.0038	+	23.6704i	−0.695082	+	1.26524i
$351$		−	4.96153i		−	0.264827i
$352$	26.7460	−	15.4418i	1.42557	−	0.823051i
$353$	−5.56692	+	9.64219i	−0.296297	+	0.513202i	−0.975286	−	0.220947i	$-0.929085\pi$
$353$	−5.56692	+	9.64219i	−0.296297	+	0.513202i	0.678989	+	0.734149i	$0.262419\pi$
$354$	3.11496	+	1.79843i	0.165558	+	0.0955852i
$355$	−2.97838	−	5.15870i	−0.158076	−	0.273796i
$356$	11.3328			0.600636
$357$	−8.46456	+	6.88123i	−0.447992	+	0.364193i
$358$	−13.0416			−0.689270
$359$	3.39000	+	5.87165i	0.178917	+	0.309894i	0.941510	−	0.336985i	$-0.109407\pi$
$359$	3.39000	+	5.87165i	0.178917	+	0.309894i	−0.762593	+	0.646879i	$0.776074\pi$
$360$	−1.14777	−	0.662663i	−0.0604926	−	0.0349254i
$361$	−6.76723	+	11.7212i	−0.356170	+	0.616904i
$362$	22.4528	−	12.9631i	1.18009	−	0.681328i
$363$			8.81102i			0.462458i
$364$	19.9784	+	32.9662i	1.04715	+	1.72790i
$365$	−5.40452			−0.282885
$366$	−8.55672	−	14.8207i	−0.447267	−	0.774689i
$367$	23.9881	+	13.8495i	1.25217	+	0.722940i	0.971540	−	0.236876i	$-0.0761236\pi$
$367$	23.9881	+	13.8495i	1.25217	+	0.722940i	0.280629	+	0.959816i	$0.409457\pi$
$368$	1.33408	+	0.770232i	0.0695437	+	0.0401511i
$369$	7.27935	−	4.20274i	0.378948	−	0.218786i
$370$	−4.68808			−0.243722
$371$	−16.8433	−	27.7930i	−0.874459	−	1.44294i
$372$	−10.6808			−0.553772
$373$	14.3114	+	24.7881i	0.741016	+	1.28348i	0.952033	+	0.305994i	$0.0989889\pi$
$373$	14.3114	+	24.7881i	0.741016	+	1.28348i	−0.211018	+	0.977482i	$0.567678\pi$
$374$	−5.59878	−	40.3882i	−0.289506	−	2.08842i
$375$	3.05551	−	5.29230i	0.157786	−	0.273293i
$376$	−10.8062	−	18.7168i	−0.557285	−	0.965246i
$377$		−	16.6622i		−	0.858148i
$378$	0.124849	+	5.87707i	0.00642154	+	0.302284i
$379$		−	27.2491i		−	1.39969i	−0.714294	−	0.699845i	$-0.753252\pi$
$379$		−	27.2491i		−	1.39969i	0.714294	−	0.699845i	$-0.246748\pi$
$380$	9.23919	−	5.33425i	0.473960	−	0.273641i
$381$	15.2735	+	8.81816i	0.782485	+	0.451768i
$382$	17.5140	−	30.3352i	0.896095	−	1.55208i
$383$	−17.7384	−	30.7238i	−0.906391	−	1.56991i	−0.819039	−	0.573737i	$-0.805493\pi$
$383$	−17.7384	−	30.7238i	−0.906391	−	1.56991i	−0.0873512	−	0.996178i	$-0.527840\pi$
$384$			14.8212i			0.756340i
$385$	3.61155	−	6.57399i	0.184061	−	0.335042i
$386$		−	4.05428i		−	0.206358i
$387$	1.47669	+	2.55770i	0.0750643	+	0.130015i
$388$	−32.9164	−	19.0043i	−1.67108	−	0.964797i
$389$	−8.97450	+	15.5443i	−0.455025	+	0.788126i	−0.998690	−	0.0511761i	$-0.983703\pi$
$389$	−8.97450	+	15.5443i	−0.455025	+	0.788126i	0.543665	+	0.839303i	$0.317036\pi$
$390$	−3.51071	−	6.08074i	−0.177772	−	0.307910i
$391$	4.01014	−	3.12094i	0.202802	−	0.157833i
$392$	−7.81179	−	12.2933i	−0.394555	−	0.620905i
$393$	12.4585			0.628447
$394$	−33.7506	+	19.4859i	−1.70033	+	0.981686i
$395$	4.62521	−	8.01110i	0.232720	−	0.403082i
$396$	−11.3192	−	6.53514i	−0.568811	−	0.328403i
$397$	−14.5890	+	8.42296i	−0.732201	+	0.422736i	−0.819227	−	0.573470i	$-0.805597\pi$
$397$	−14.5890	+	8.42296i	−0.732201	+	0.422736i	0.0870261	+	0.996206i	$0.472264\pi$
$398$		−	27.1082i		−	1.35881i
$399$	−13.2266	−	7.26627i	−0.662157	−	0.363769i
$400$	−5.74255			−0.287127
$401$	−27.4843	+	15.8681i	−1.37250	+	0.792413i	−0.991242	−	0.132056i	$-0.957842\pi$
$401$	−27.4843	+	15.8681i	−1.37250	+	0.792413i	−0.381257	+	0.924469i	$0.624509\pi$
$402$	−17.0627	−	9.85118i	−0.851012	−	0.491332i
$403$	−15.6285	−	9.02311i	−0.778510	−	0.449473i
$404$	7.98957	+	13.8383i	0.397496	+	0.688483i
$405$		−	0.636942i		−	0.0316499i
$406$	0.419279	+	19.7369i	0.0208084	+	0.979525i
$407$	−14.7448			−0.730872
$408$	7.94845	+	3.22878i	0.393507	+	0.159848i
$409$	−7.11957	+	12.3315i	−0.352040	+	0.609751i	−0.986607	−	0.163117i	$-0.947845\pi$
$409$	−7.11957	+	12.3315i	−0.352040	+	0.609751i	0.634567	+	0.772868i	$0.281179\pi$
$410$	5.94760	−	10.3016i	0.293731	−	0.508757i
$411$	15.7904	−	9.11657i	0.778882	−	0.449687i
$412$	33.5080			1.65082
$413$	−2.21986	−	3.66298i	−0.109232	−	0.180243i
$414$		−	2.73827i		−	0.134579i
$415$	−0.648769	+	0.374567i	−0.0318468	+	0.0183868i
$416$	−17.2131	+	29.8140i	−0.843944	+	1.46175i
$417$	5.89602	−	10.2122i	0.288729	−	0.500094i
$418$	48.8501	−	28.2036i	2.38934	−	1.37949i
$419$		−	2.91045i		−	0.142185i	−0.997470	−	0.0710923i	$-0.977352\pi$
$419$		−	2.91045i		−	0.142185i	0.997470	−	0.0710923i	$-0.0226485\pi$
$420$	2.56475	+	4.23208i	0.125147	+	0.206504i
$421$	0.521247			0.0254040			0.0127020	−	0.999919i	$-0.495957\pi$
$421$	0.521247			0.0254040			0.0127020	+	0.999919i	$0.495957\pi$
$422$	7.21195	−	4.16382i	0.351072	−	0.202692i
$423$	5.19336	−	8.99516i	0.252510	−	0.437360i
$424$	−12.7793	+	22.1343i	−0.620615	+	1.07494i
$425$	−7.12911	+	17.5501i	−0.345813	+	0.851304i
$426$	20.7788			1.00674
$427$	0.432815	+	20.3741i	0.0209454	+	0.985971i
$428$		−	35.5734i		−	1.71950i
$429$	−11.0418	−	19.1249i	−0.533102	−	0.923360i
$430$	3.61959	+	2.08977i	0.174552	+	0.100778i
$431$	−21.6103	−	12.4767i	−1.04093	−	0.600981i	−0.120834	−	0.992673i	$-0.538557\pi$
$431$	−21.6103	−	12.4767i	−1.04093	−	0.600981i	−0.920097	+	0.391691i	$0.871890\pi$
$432$	−1.08247	+	0.624963i	−0.0520803	+	0.0300686i
$433$	−8.79699			−0.422756			−0.211378	−	0.977404i	$-0.567795\pi$
$433$	−8.79699			−0.422756			−0.211378	+	0.977404i	$0.567795\pi$
$434$	18.7394	+	10.2949i	0.899522	+	0.494169i
$435$		−	2.13903i		−	0.102559i
$436$	−29.6891	+	17.1410i	−1.42185	+	0.820906i
$437$	6.08792	+	3.51486i	0.291225	+	0.168139i
$438$	9.42621	−	16.3267i	0.450402	−	0.780119i
$439$	3.85640	−	2.22649i	0.184056	−	0.106265i	−0.405141	−	0.914254i	$-0.632778\pi$
$439$	3.85640	−	2.22649i	0.184056	−	0.106265i	0.589197	+	0.807989i	$0.299444\pi$
$440$	−5.89897			−0.281222
$441$	3.23940	−	6.20535i	0.154257	−	0.295493i
$442$	27.9155	+	35.8690i	1.32780	+	1.70611i
$443$	15.5992	+	27.0186i	0.741141	+	1.28369i	0.951976	+	0.306173i	$0.0990485\pi$
$443$	15.5992	+	27.0186i	0.741141	+	1.28369i	−0.210835	+	0.977522i	$0.567618\pi$
$444$	4.86392	−	8.42456i	0.230831	−	0.399812i
$445$	2.12880	+	1.22906i	0.100915	+	0.0582632i
$446$	12.1949	+	21.1221i	0.577444	+	1.00016i
$447$		−	11.2035i		−	0.529906i
$448$	16.4546	−	29.9519i	0.777409	−	1.41509i
$449$			35.1190i			1.65737i	0.559716	+	0.828685i	$0.310910\pi$
$449$			35.1190i			1.65737i	−0.559716	+	0.828685i	$0.689090\pi$
$450$	5.10387	+	8.84017i	0.240599	+	0.416729i
$451$	18.7062	−	32.4001i	0.880840	−	1.52566i
$452$	−10.6609	−	6.15505i	−0.501445	−	0.289509i
$453$	11.8141	−	6.82085i	0.555073	−	0.320471i
$454$			24.1381i			1.13286i
$455$	0.177579	+	8.35923i	0.00832501	+	0.391887i
$456$			11.8685i			0.555792i
$457$	4.26769	+	7.39186i	0.199634	+	0.345777i	0.948410	−	0.317047i	$-0.102691\pi$
$457$	4.26769	+	7.39186i	0.199634	+	0.345777i	−0.748776	+	0.662824i	$0.769358\pi$
$458$	10.6115	−	18.3797i	0.495844	−	0.858826i
$459$	0.566148	+	4.08405i	0.0264255	+	0.190627i
$460$	−1.15257	−	1.99631i	−0.0537390	−	0.0930786i
$461$	16.5716			0.771819			0.385909	−	0.922537i	$-0.373888\pi$
$461$	16.5716			0.771819			0.385909	+	0.922537i	$0.373888\pi$
$462$	13.5605	+	22.3762i	0.630894	+	1.04103i
$463$	−9.46742			−0.439989			−0.219994	−	0.975501i	$-0.570604\pi$
$463$	−9.46742			−0.439989			−0.219994	+	0.975501i	$0.570604\pi$
$464$	−3.63524	+	2.09880i	−0.168762	+	0.0974346i
$465$	−2.00632	−	1.15835i	−0.0930411	−	0.0537173i
$466$	−18.2726	−	10.5497i	−0.846463	−	0.488705i
$467$	−4.59009	−	7.95027i	−0.212404	−	0.367895i	0.740062	−	0.672538i	$-0.234796\pi$
$467$	−4.59009	−	7.95027i	−0.212404	−	0.367895i	−0.952466	+	0.304644i	$0.901463\pi$
$468$	14.5696			0.673479
$469$	12.1597	+	20.0646i	0.561482	+	0.926497i
$470$		−	14.6990i		−	0.678015i
$471$	−0.291848	+	0.168499i	−0.0134476	+	0.00776400i
$472$	−1.68424	+	2.91720i	−0.0775236	+	0.134275i
$473$	11.3842	+	6.57268i	0.523447	+	0.302212i
$474$	16.1340	+	27.9449i	0.741058	+	1.28355i
$475$	−26.2054			−1.20239
$476$	−20.2068	−	24.8563i	−0.926177	−	1.13928i
$477$	−12.2832			−0.562411
$478$	−12.7641	−	22.1081i	−0.583816	−	1.01120i
$479$	−17.4440	−	10.0713i	−0.797037	−	0.460169i	0.0453972	−	0.998969i	$-0.485545\pi$
$479$	−17.4440	−	10.0713i	−0.797037	−	0.460169i	−0.842434	+	0.538800i	$0.818878\pi$
$480$	−2.20976	+	3.82741i	−0.100861	+	0.174697i
$481$	14.2341	−	8.21808i	0.649021	−	0.374712i
$482$			29.3839i			1.33840i
$483$	−1.57003	+	2.85787i	−0.0714386	+	0.130038i
$484$	−25.8736			−1.17607
$485$	−4.12212	−	7.13971i	−0.187176	−	0.324198i
$486$	1.92416	+	1.11091i	0.0872816	+	0.0503920i
$487$	−4.67401	−	2.69854i	−0.211800	−	0.122283i	0.390348	−	0.920667i	$-0.372355\pi$
$487$	−4.67401	−	2.69854i	−0.211800	−	0.122283i	−0.602148	+	0.798385i	$0.705688\pi$
$488$	13.8797	−	8.01345i	0.628305	−	0.362752i
$489$	−5.21971			−0.236043
$490$	−0.420694	−	9.89728i	−0.0190050	−	0.447114i
$491$	−4.61469			−0.208258			−0.104129	−	0.994564i	$-0.533206\pi$
$491$	−4.61469			−0.208258			−0.104129	+	0.994564i	$0.533206\pi$
$492$	12.3414	+	21.3759i	0.556392	+	0.963700i
$493$	1.90129	+	13.7154i	0.0856296	+	0.617711i
$494$	−31.4389	+	54.4538i	−1.41450	+	2.44999i
$495$	−1.41750	−	2.45518i	−0.0637119	−	0.110352i
$496$			4.54627i			0.204134i
$497$	−21.6863	−	11.9138i	−0.972765	−	0.534407i
$498$		−	2.61318i		−	0.117099i
$499$	35.0782	−	20.2524i	1.57031	−	0.906621i	0.574185	−	0.818726i	$-0.305319\pi$
$499$	35.0782	−	20.2524i	1.57031	−	0.906621i	0.996130	−	0.0878956i	$-0.0280142\pi$
$500$	15.5409	+	8.97253i	0.695009	+	0.401264i
$501$	9.81170	−	16.9944i	0.438354	−	0.759252i
$502$	−2.05350	−	3.55677i	−0.0916523	−	0.158746i
$503$		−	0.342609i		−	0.0152762i	−0.999971	−	0.00763808i	$-0.997569\pi$
$503$		−	0.342609i		−	0.0152762i	0.999971	−	0.00763808i	$-0.00243130\pi$
$504$	−5.50394	+	0.116922i	−0.245165	+	0.00520814i
$505$			3.46595i			0.154233i
$506$	−6.09397	−	10.5551i	−0.270910	−	0.469230i
$507$	10.0604	+	5.80838i	0.446799	+	0.257959i
$508$	−25.8946	+	44.8508i	−1.14889	+	1.98993i
$509$	9.05619	+	15.6858i	0.401409	+	0.695260i	0.993896	−	0.110320i	$-0.0351874\pi$
$509$	9.05619	+	15.6858i	0.401409	+	0.695260i	−0.592488	+	0.805580i	$0.701854\pi$
$510$	3.58368	+	4.60472i	0.158688	+	0.203900i
$511$	−19.1990	+	11.6351i	−0.849315	+	0.514707i
$512$	13.8744			0.613168
$513$	−4.93972	+	2.85195i	−0.218094	+	0.125917i
$514$	7.78075	−	13.4767i	0.343194	−	0.594430i
$515$	6.29429	+	3.63401i	0.277360	+	0.160134i
$516$	−7.51071	+	4.33631i	−0.330641	+	0.190896i
$517$		−	46.2308i		−	2.03323i
$518$	−16.6539	+	10.0927i	−0.731732	+	0.443449i
$519$	11.0578			0.485383
$520$	5.69467	−	3.28782i	0.249728	−	0.144180i
$521$	1.69820	+	0.980458i	0.0743996	+	0.0429546i	0.536738	−	0.843749i	$-0.319656\pi$
$521$	1.69820	+	0.980458i	0.0743996	+	0.0429546i	−0.462339	+	0.886703i	$0.652990\pi$
$522$	6.46187	+	3.73076i	0.282828	+	0.163291i
$523$	−17.6024	−	30.4883i	−0.769700	−	1.33316i	−0.937726	−	0.347377i	$-0.887073\pi$
$523$	−17.6024	−	30.4883i	−0.769700	−	1.33316i	0.168026	−	0.985783i	$-0.446261\pi$
$524$			36.5845i			1.59820i
$525$	−0.258164	−	12.1526i	−0.0112672	−	0.530385i
$526$	−10.7136			−0.467134
$527$	13.8941	+	5.64399i	0.605236	+	0.245856i
$528$	−2.78169	+	4.81802i	−0.121057	+	0.209677i
$529$	−10.7405	+	18.6032i	−0.466980	+	0.808833i
$530$	−15.0540	+	8.69146i	−0.653906	+	0.377533i
$531$	−1.61887			−0.0702530
$532$	21.3375	−	38.8400i	0.925097	−	1.68393i
$533$			41.7040i			1.80640i
$534$	−7.42584	+	4.28731i	−0.321347	+	0.185530i
$535$	3.85801	−	6.68227i	0.166796	−	0.288900i
$536$	9.22573	−	15.9794i	0.398491	−	0.690207i
$537$	5.08337	−	2.93488i	0.219364	−	0.126650i
$538$		−	35.7345i		−	1.54063i
$539$	−1.32315	−	31.1286i	−0.0569922	−	1.34080i
$540$	1.87039			0.0804886
$541$	−15.6944	+	9.06116i	−0.674754	+	0.389570i	−0.797876	−	0.602822i	$-0.794043\pi$
$541$	−15.6944	+	9.06116i	−0.674754	+	0.389570i	0.123121	+	0.992392i	$0.460710\pi$
$542$	−31.3788	+	54.3496i	−1.34783	+	2.33452i
$543$	−5.83446	+	10.1056i	−0.250380	+	0.433672i
$544$	10.7669	−	26.5054i	0.461626	−	1.13641i
$545$	−7.43592			−0.318520
$546$	−25.5624	−	14.0432i	−1.09397	−	0.600993i
$547$			3.48512i			0.149013i	0.997221	+	0.0745065i	$0.0237382\pi$
$547$			3.48512i			0.149013i	−0.997221	+	0.0745065i	$0.976262\pi$
$548$	26.7709	+	46.3686i	1.14360	+	1.98077i
$549$	6.67049	+	3.85121i	0.284690	+	0.164366i
$550$	39.3472	+	22.7171i	1.67777	+	0.968661i
$551$	−16.5890	+	9.57766i	−0.706715	+	0.408022i
$552$	2.56442			0.109149
$553$	−0.816087	−	38.4160i	−0.0347036	−	1.63362i
$554$		−	25.2020i		−	1.07073i
$555$	1.82732	−	1.05501i	0.0775656	−	0.0447825i
$556$	29.9883	+	17.3137i	1.27179	+	0.734266i
$557$	11.3343	−	19.6315i	0.480249	−	0.831815i	−0.519494	−	0.854474i	$-0.673880\pi$
$557$	11.3343	−	19.6315i	0.480249	−	0.831815i	0.999743	+	0.0226584i	$0.00721302\pi$
$558$	6.99860	−	4.04065i	0.296274	−	0.171054i
$559$	−14.6533			−0.619767
$560$	1.80139	−	1.09169i	0.0761224	−	0.0461322i
$561$	11.2713	+	14.4826i	0.475873	+	0.611456i
$562$	−0.932619	−	1.61534i	−0.0393402	−	0.0681392i
$563$	−4.36066	+	7.55289i	−0.183780	+	0.318316i	−0.943165	−	0.332326i	$-0.892167\pi$
$563$	−4.36066	+	7.55289i	−0.183780	+	0.318316i	0.759385	+	0.650642i	$0.225500\pi$
$564$	26.4144	+	15.2504i	1.11225	+	0.642156i
$565$	−1.33506	−	2.31239i	−0.0561663	−	0.0972829i
$566$			41.4418i			1.74193i
$567$	−1.37124	−	2.26267i	−0.0575867	−	0.0950234i
$568$			19.4595i			0.816505i
$569$	18.9894	+	32.8906i	0.796078	+	1.37885i	0.922152	+	0.386827i	$0.126429\pi$
$569$	18.9894	+	32.8906i	0.796078	+	1.37885i	−0.126074	+	0.992021i	$0.540238\pi$
$570$	−4.03601	+	6.99057i	−0.169050	+	0.292803i
$571$	35.6117	+	20.5604i	1.49030	+	0.860426i	0.999938	−	0.0110921i	$-0.00353079\pi$
$571$	35.6117	+	20.5604i	1.49030	+	0.860426i	0.490363	+	0.871518i	$0.336864\pi$
$572$	56.1605	−	32.4243i	2.34819	−	1.35573i
$573$			15.7654i			0.658610i
$574$	−1.04942	−	49.3996i	−0.0438017	−	2.06190i
$575$			5.66222i			0.236131i
$576$	−6.45831	−	11.1861i	−0.269096	−	0.466088i
$577$	−11.7385	+	20.3316i	−0.488679	+	0.846417i	−0.999915	−	0.0130235i	$-0.995854\pi$
$577$	−11.7385	+	20.3316i	−0.488679	+	0.846417i	0.511236	+	0.859440i	$0.329188\pi$
$578$	−27.0714	−	26.3399i	−1.12602	−	1.09560i
$579$	0.912377	+	1.58028i	0.0379171	+	0.0656743i
$580$	6.28129			0.260816
$581$	−1.49830	+	2.72732i	−0.0621600	+	0.113148i
$582$	28.7581			1.19206
$583$	−47.3475	+	27.3361i	−1.96093	+	1.13214i
$584$	15.2901	+	8.82774i	0.632709	+	0.365295i
$585$	2.73682	+	1.58010i	0.113154	+	0.0653292i
$586$	3.32507	+	5.75918i	0.137357	+	0.237910i
$587$	−23.3181			−0.962443			−0.481221	−	0.876599i	$-0.659807\pi$
$587$	−23.3181			−0.962443			−0.481221	+	0.876599i	$0.659807\pi$
$588$	18.2221	+	9.51252i	0.751465	+	0.392290i
$589$			20.7464i			0.854840i
$590$	−1.98405	+	1.14549i	−0.0816821	+	0.0471592i
$591$	8.77022	−	15.1905i	0.360759	−	0.624852i
$592$	−3.58592	−	2.07033i	−0.147380	−	0.0850900i
$593$	−7.23725	−	12.5353i	−0.297198	−	0.514763i	0.678295	−	0.734789i	$-0.262719\pi$
$593$	−7.23725	−	12.5353i	−0.297198	−	0.514763i	−0.975494	+	0.220026i	$0.929386\pi$
$594$	9.88925			0.405761
$595$	−1.10002	−	6.86059i	−0.0450966	−	0.281257i
$596$	32.8991			1.34760
$597$	6.10043	+	10.5663i	0.249674	+	0.432448i
$598$	11.7658	+	6.79301i	0.481141	+	0.277787i
$599$	0.156806	−	0.271596i	0.00640692	−	0.0110971i	−0.862804	−	0.505538i	$-0.831294\pi$
$599$	0.156806	−	0.271596i	0.00640692	−	0.0110971i	0.869211	+	0.494441i	$0.164627\pi$
$600$	−8.27891	+	4.77983i	−0.337985	+	0.195136i
$601$		−	39.9343i		−	1.62896i	−0.580195	−	0.814478i	$-0.697024\pi$
$601$		−	39.9343i		−	1.62896i	0.580195	−	0.814478i	$-0.302976\pi$
$602$	17.3572	−	0.368726i	0.707427	−	0.0150282i
$603$	8.86764			0.361118
$604$	20.0295	+	34.6921i	0.814989	+	1.41160i
$605$	−4.86023	−	2.80605i	−0.197596	−	0.114082i
$606$	−10.4704	−	6.04508i	−0.425330	−	0.245564i
$607$	−7.80981	+	4.50900i	−0.316990	+	0.183015i	−0.650050	−	0.759891i	$-0.725252\pi$
$607$	−7.80981	+	4.50900i	−0.316990	+	0.183015i	0.333060	+	0.942906i	$0.391919\pi$
$608$	39.5773			1.60507
$609$	−4.60502	−	7.59871i	−0.186605	−	0.307915i
$610$	10.9003			0.441339
$611$	25.7670	+	44.6298i	1.04242	+	1.80553i
$612$	−11.9929	+	1.66250i	−0.484783	+	0.0672026i
$613$	9.03406	−	15.6475i	0.364882	−	0.631995i	−0.623875	−	0.781524i	$-0.714443\pi$
$613$	9.03406	−	15.6475i	0.364882	−	0.631995i	0.988757	+	0.149529i	$0.0477759\pi$
$614$	−27.8296	−	48.2023i	−1.12311	−	1.94529i
$615$			5.35380i			0.215886i
$616$	−20.9555	+	12.6996i	−0.844322	+	0.511681i
$617$		−	44.6374i		−	1.79703i	−0.438938	−	0.898517i	$-0.644645\pi$
$617$		−	44.6374i		−	1.79703i	0.438938	−	0.898517i	$-0.355355\pi$
$618$	−21.9562	+	12.6764i	−0.883208	+	0.509920i
$619$	−29.1522	−	16.8310i	−1.17173	−	0.676496i	−0.217639	−	0.976029i	$-0.569836\pi$
$619$	−29.1522	−	16.8310i	−1.17173	−	0.676496i	−0.954086	+	0.299533i	$0.903169\pi$
$620$	3.40151	−	5.89159i	0.136608	−	0.236612i
$621$	0.616221	+	1.06733i	0.0247281	+	0.0428303i
$622$		−	3.56994i		−	0.143142i
$623$	10.2084	−	0.216860i	0.408989	−	0.00868832i
$624$		−	6.20155i		−	0.248261i
$625$	−9.53958	−	16.5230i	−0.381583	−	0.660922i
$626$	17.9867	+	10.3846i	0.718891	+	0.415052i
$627$	−12.6939	+	21.9865i	−0.506946	+	0.878056i
$628$	−0.494798	−	0.857015i	−0.0197446	−	0.0341986i
$629$	−10.7790	+	8.38888i	−0.429787	+	0.334487i
$630$	−3.28160	−	1.80281i	−0.130742	−	0.0718257i
$631$	46.1081			1.83553			0.917767	−	0.397120i	$-0.129990\pi$
$631$	46.1081			1.83553			0.917767	+	0.397120i	$0.129990\pi$
$632$	−26.1707	+	15.1096i	−1.04101	+	0.601029i
$633$	−1.87405	+	3.24596i	−0.0744869	+	0.129015i
$634$	−43.0635	−	24.8627i	−1.71027	−	0.987425i
$635$	−9.72833	+	5.61666i	−0.386057	+	0.222890i
$636$		−	36.0698i		−	1.43026i
$637$	18.6270	+	29.3131i	0.738029	+	1.16143i
$638$	33.2109			1.31483
$639$	−8.09917	+	4.67606i	−0.320398	+	0.184982i
$640$	−8.17548	−	4.72011i	−0.323164	−	0.186579i
$641$	−31.3749	−	18.1143i	−1.23924	−	0.715473i	−0.270298	−	0.962777i	$-0.587122\pi$
$641$	−31.3749	−	18.1143i	−1.23924	−	0.715473i	−0.968938	+	0.247304i	$0.920455\pi$
$642$	13.4578	+	23.3096i	0.531136	+	0.919955i
$643$			42.9418i			1.69346i	0.532022	+	0.846731i	$0.321432\pi$
$643$			42.9418i			1.69346i	−0.532022	+	0.846731i	$0.678568\pi$
$644$	−8.39217	−	4.61040i	−0.330698	−	0.181675i
$645$	−1.88113			−0.0740694
$646$	19.6651	−	48.4107i	0.773715	−	1.90469i
$647$	11.9012	−	20.6134i	0.467884	−	0.810398i	−0.531443	−	0.847094i	$-0.678350\pi$
$647$	11.9012	−	20.6134i	0.467884	−	0.810398i	0.999326	+	0.0366959i	$0.0116833\pi$
$648$	−1.04038	+	1.80199i	−0.0408701	+	0.0707890i
$649$	−6.24017	+	3.60276i	−0.244948	+	0.141421i
$650$	−50.6460			−1.98650
$651$	−9.62103	+	0.204384i	−0.377078	+	0.00801042i
$652$		−	15.3277i		−	0.600280i
$653$	−16.8061	+	9.70301i	−0.657673	+	0.379708i	−0.791390	−	0.611312i	$-0.790642\pi$
$653$	−16.8061	+	9.70301i	−0.657673	+	0.379708i	0.133716	+	0.991020i	$0.457309\pi$
$654$	12.9693	−	22.4634i	0.507138	−	0.878389i
$655$	−3.96766	+	6.87220i	−0.155029	+	0.268519i
$656$	9.09866	−	5.25311i	0.355243	−	0.205100i
$657$			8.48510i			0.331035i
$658$	−31.6448	−	52.2168i	−1.23364	−	2.03562i
$659$	−5.28871			−0.206019			−0.103009	−	0.994680i	$-0.532847\pi$
$659$	−5.28871			−0.206019			−0.103009	+	0.994680i	$0.532847\pi$
$660$	7.20967	−	4.16251i	0.280636	−	0.162025i
$661$	4.45043	−	7.70836i	0.173102	−	0.299821i	−0.766401	−	0.642362i	$-0.777954\pi$
$661$	4.45043	−	7.70836i	0.173102	−	0.299821i	0.939503	+	0.342542i	$0.111288\pi$
$662$	−20.4307	+	35.3870i	−0.794061	+	1.37535i
$663$	−18.9529	−	7.69894i	−0.736069	−	0.299002i
$664$	2.44727			0.0949726
$665$	8.22042	−	4.98179i	0.318774	−	0.193186i
$666$			7.36029i			0.285205i
$667$	2.06945	+	3.58439i	0.0801293	+	0.138788i
$668$	49.9041	+	28.8122i	1.93085	+	1.11478i
$669$	−9.50665	−	5.48867i	−0.367548	−	0.212204i
$670$	10.8680	−	6.27463i	0.419867	−	0.242410i
$671$	34.2831			1.32349
$672$	0.389897	+	18.3538i	0.0150406	+	0.708013i
$673$		−	25.1549i		−	0.969650i	−0.874611	−	0.484825i	$-0.838883\pi$
$673$		−	25.1549i		−	0.969650i	0.874611	−	0.484825i	$-0.161117\pi$
$674$	22.7315	−	13.1240i	0.875584	−	0.505519i
$675$	−3.97878	−	2.29715i	−0.153143	−	0.0884174i
$676$	−17.0564	+	29.5425i	−0.656015	+	1.13625i
$677$	−20.9761	+	12.1106i	−0.806178	+	0.465447i	−0.845627	−	0.533775i	$-0.820773\pi$
$677$	−20.9761	+	12.1106i	−0.806178	+	0.465447i	0.0394489	+	0.999222i	$0.487440\pi$
$678$	9.31408			0.357705
$679$	−30.0142	−	16.4888i	−1.15184	−	0.632784i
$680$	−4.31237	+	3.35615i	−0.165372	+	0.128703i
$681$	−5.43203	−	9.40856i	−0.208156	−	0.360537i
$682$	17.9847	−	31.1505i	0.688671	−	1.19281i
$683$	10.2643	+	5.92609i	0.392752	+	0.226756i	0.683352	−	0.730089i	$-0.260521\pi$
$683$	10.2643	+	5.92609i	0.392752	+	0.226756i	−0.290600	+	0.956845i	$0.593855\pi$
$684$	−8.37478	−	14.5055i	−0.320218	−	0.554633i
$685$			11.6135i			0.443727i
$686$	−22.8018	−	34.2535i	−0.870579	−	1.30780i
$687$			9.55207i			0.364434i
$688$	1.84575	+	3.19694i	0.0703687	+	0.121882i
$689$	30.4718	−	52.7787i	1.16088	−	2.01071i
$690$	1.51045	+	0.872061i	0.0575020	+	0.0331988i
$691$	33.3914	−	19.2785i	1.27027	−	0.733390i	0.295230	−	0.955426i	$-0.404604\pi$
$691$	33.3914	−	19.2785i	1.27027	−	0.733390i	0.975038	+	0.222036i	$0.0712704\pi$
$692$			32.4713i			1.23438i
$693$	−10.3212	−	5.67013i	−0.392069	−	0.215391i
$694$		−	37.3698i		−	1.41854i
$695$	3.75542	+	6.50459i	0.142451	+	0.246733i
$696$	−3.49390	+	6.05161i	−0.132436	+	0.229386i
$697$	−4.75874	−	34.3284i	−0.180250	−	1.30028i
$698$	−29.7032	−	51.4474i	−1.12428	−	1.94731i
$699$	9.49642			0.359188
$700$	35.6864	−	0.758100i	1.34882	−	0.0286535i
$701$	−25.5314			−0.964308			−0.482154	−	0.876087i	$-0.660145\pi$
$701$	−25.5314			−0.964308			−0.482154	+	0.876087i	$0.660145\pi$
$702$	−9.54676	+	5.51183i	−0.360319	+	0.208030i
$703$	−16.3639	−	9.44771i	−0.617177	−	0.356327i
$704$	−49.7889	−	28.7456i	−1.87649	−	1.08339i
$705$	3.30787	+	5.72940i	0.124582	+	0.215782i
$706$	24.7375			0.931007
$707$	7.46166	+	12.3124i	0.280625	+	0.463057i
$708$		−	4.75383i		−	0.178660i
$709$	−30.6327	+	17.6858i	−1.15043	+	0.664203i	−0.948993	−	0.315297i	$-0.897896\pi$
$709$	−30.6327	+	17.6858i	−1.15043	+	0.664203i	−0.201441	+	0.979501i	$0.564562\pi$
$710$	−6.61744	+	11.4617i	−0.248348	+	0.430152i
$711$	−12.5774	−	7.26158i	−0.471691	−	0.272331i
$712$	−4.01511	−	6.95438i	−0.150473	−	0.260626i
$713$	4.48268			0.167878
$714$	22.6440	+	8.64269i	0.847429	+	0.323445i
$715$	14.0659			0.526036
$716$	8.61832	+	14.9274i	0.322082	+	0.557862i
$717$	9.95040	+	5.74487i	0.371605	+	0.214546i
$718$	7.53199	−	13.0458i	0.281091	−	0.486864i
$719$	−0.253848	+	0.146559i	−0.00946693	+	0.00546573i	−0.504726	−	0.863280i	$-0.668406\pi$
$719$	−0.253848	+	0.146559i	−0.00946693	+	0.00546573i	0.495259	+	0.868745i	$0.335073\pi$
$720$		−	0.796131i		−	0.0296701i
$721$	30.1834	−	0.641197i	1.12409	−	0.0238794i
$722$	30.0712			1.11913
$723$	−6.61255	−	11.4533i	−0.245924	−	0.425952i
$724$	−29.6751	−	17.1329i	−1.10287	−	0.636741i
$725$	−13.3619	−	7.71449i	−0.496248	−	0.286509i
$726$	16.9538	−	9.78827i	0.629214	−	0.363277i
$727$	−8.78145			−0.325686			−0.162843	−	0.986652i	$-0.552066\pi$
$727$	−8.78145			−0.325686			−0.162843	+	0.986652i	$0.552066\pi$
$728$	13.1516	−	23.9394i	0.487430	−	0.887255i
$729$	−1.00000			−0.0370370
$730$	6.00395	+	10.3991i	0.222216	+	0.384890i
$731$	12.0617	−	1.67205i	0.446120	−	0.0618430i
$732$	−11.3091	+	19.5880i	−0.417997	+	0.723992i
$733$	17.9304	+	31.0564i	0.662275	+	1.14709i	0.980016	+	0.198917i	$0.0637423\pi$
$733$	17.9304	+	31.0564i	0.662275	+	1.14709i	−0.317741	+	0.948177i	$0.602924\pi$
$734$		−	61.5425i		−	2.27158i
$735$	2.39126	+	3.76310i	0.0882031	+	0.138804i
$736$		−	8.55148i		−	0.315212i
$737$	34.1816	−	19.7347i	1.25909	−	0.726939i
$738$	−16.1735	−	9.33775i	−0.595353	−	0.343727i
$739$	−11.0541	+	19.1462i	−0.406631	+	0.704306i	−0.994510	−	0.104643i	$-0.966630\pi$
$739$	−11.0541	+	19.1462i	−0.406631	+	0.704306i	0.587879	+	0.808949i	$0.299963\pi$
$740$	3.09804	+	5.36596i	0.113886	+	0.197256i
$741$		−	28.3001i		−	1.03963i
$742$	−34.7666	+	63.2847i	−1.27632	+	2.32325i
$743$			22.7670i			0.835241i	0.908622	+	0.417620i	$0.137136\pi$
$743$			22.7670i			0.835241i	−0.908622	+	0.417620i	$0.862864\pi$
$744$	3.78411	+	6.55427i	0.138732	+	0.240291i
$745$	6.17993	+	3.56798i	0.226415	+	0.130721i
$746$	31.7974	−	55.0747i	1.16419	−	2.01643i
$747$	0.588071	+	1.01857i	0.0215164	+	0.0372675i
$748$	−42.5283	+	33.0982i	−1.55499	+	1.21019i
$749$	−0.680720	−	32.0438i	−0.0248730	−	1.17086i
$750$	−13.5776			−0.495784
$751$	−29.3570	+	16.9493i	−1.07125	+	0.618488i	−0.928523	−	0.371274i	$-0.878921\pi$
$751$	−29.3570	+	16.9493i	−1.07125	+	0.618488i	−0.142729	+	0.989762i	$0.545588\pi$
$752$	6.49132	−	11.2433i	0.236714	−	0.410001i
$753$	1.60083	+	0.924241i	0.0583376	+	0.0336812i
$754$	−32.0607	+	18.5103i	−1.16758	+	0.674105i
$755$			8.68897i			0.316224i
$756$	6.64437	−	4.02666i	0.241653	−	0.146448i
$757$	−47.8187			−1.73800			−0.869000	−	0.494813i	$-0.835237\pi$
$757$	−47.8187			−1.73800			−0.869000	+	0.494813i	$0.835237\pi$
$758$	−52.4315	+	30.2713i	−1.90440	+	1.09950i
$759$	4.75062	+	2.74277i	0.172437	+	0.0995564i
$760$	−6.54674	−	3.77976i	−0.237475	−	0.137106i
$761$	−8.17259	−	14.1553i	−0.296256	−	0.513131i	0.679020	−	0.734120i	$-0.262405\pi$
$761$	−8.17259	−	14.1553i	−0.296256	−	0.513131i	−0.975276	+	0.220989i	$0.929072\pi$
$762$		−	39.1848i		−	1.41952i
$763$	−26.4154	+	16.0084i	−0.956301	+	0.579544i
$764$	−46.2954			−1.67491
$765$	−2.43310	−	0.988360i	−0.0879688	−	0.0357342i
$766$	−39.4117	+	68.2630i	−1.42400	+	2.46644i
$767$	4.01604	−	6.95598i	0.145011	−	0.251166i
$768$	6.14604	−	3.54842i	0.221776	−	0.128043i
$769$	4.74962			0.171276			0.0856378	−	0.996326i	$-0.472707\pi$
$769$	4.74962			0.171276			0.0856378	+	0.996326i	$0.472707\pi$
$770$	−16.6615	+	0.353947i	−0.600439	+	0.0127554i
$771$			7.00393i			0.252240i
$772$	−4.64052	+	2.67920i	−0.167016	+	0.0964267i
$773$	6.84878	−	11.8624i	0.246333	−	0.426662i	−0.716172	−	0.697924i	$-0.754108\pi$
$773$	6.84878	−	11.8624i	0.246333	−	0.426662i	0.962506	+	0.271262i	$0.0874408\pi$
$774$	3.28095	−	5.68276i	0.117931	−	0.204263i
$775$	−14.4718	+	8.35527i	−0.519841	+	0.300130i
$776$			26.9323i			0.966812i
$777$	4.22012	−	7.68176i	0.151396	−	0.275582i
$778$	39.8795			1.42975
$779$	41.5207	−	23.9720i	1.48763	−	0.858885i
$780$	−4.63999	+	8.03670i	−0.166138	+	0.287760i
$781$	−20.8129	+	36.0491i	−0.744746	+	1.28994i
$782$	−10.4601	−	4.24905i	−0.374053	−	0.151946i
$783$	−3.35828			−0.120015
$784$	4.04901	−	7.75623i	0.144607	−	0.277008i
$785$		−	0.214648i		−	0.00766110i
$786$	−13.8403	−	23.9721i	−0.493667	−	0.855056i
$787$	42.8464	+	24.7374i	1.52731	+	0.881793i	0.999473	+	0.0324481i	$0.0103304\pi$
$787$	42.8464	+	24.7374i	1.52731	+	0.881793i	0.527838	+	0.849345i	$0.323003\pi$
$788$	44.6070	+	25.7538i	1.58906	+	0.917443i
$789$	4.17595	−	2.41099i	0.148668	−	0.0858333i
$790$	−20.5528			−0.731236
$791$	−9.72089	−	5.34035i	−0.345635	−	0.189881i
$792$			9.26139i			0.329089i
$793$	−33.0958	+	19.1079i	−1.17527	+	0.678541i
$794$	32.4142	+	18.7143i	1.15034	+	0.664147i
$795$	3.91185	−	6.77553i	0.138739	−	0.240303i
$796$	−31.0279	+	17.9140i	−1.09976	+	0.634944i
$797$	−19.8771			−0.704082			−0.352041	−	0.935985i	$-0.614512\pi$
$797$	−19.8771			−0.704082			−0.352041	+	0.935985i	$0.614512\pi$
$798$	0.712126	+	33.5222i	0.0252090	+	1.18667i
$799$	−26.3025	−	33.7965i	−0.930517	−	1.19563i
$800$	15.9391	+	27.6074i	0.563533	+	0.976068i
$801$	1.92963	−	3.34222i	0.0681802	−	0.118092i
$802$	61.0653	+	35.2561i	2.15629	+	1.24493i
$803$	18.8834	+	32.7070i	0.666381	+	1.15421i
$804$			26.0399i			0.918357i
$805$	−1.07642	−	1.77619i	−0.0379387	−	0.0626024i
$806$			40.0956i			1.41231i
$807$	8.04171	+	13.9286i	0.283081	+	0.490311i
$808$	5.66128	−	9.80562i	0.199163	−	0.344961i
$809$	−18.8332	−	10.8734i	−0.662140	−	0.382287i	0.130952	−	0.991389i	$-0.458197\pi$
$809$	−18.8332	−	10.8734i	−0.662140	−	0.382287i	−0.793092	+	0.609102i	$0.791530\pi$
$810$	−1.22558	+	0.707587i	−0.0430624	+	0.0248621i
$811$			1.15024i			0.0403905i	0.999796	+	0.0201952i	$0.00642878\pi$
$811$			1.15024i			0.0403905i	−0.999796	+	0.0201952i	$0.993571\pi$
$812$	22.3137	−	13.5227i	0.783057	−	0.474553i
$813$		−	28.2459i		−	0.990628i
$814$	16.3802	+	28.3713i	0.574125	+	0.994413i
$815$	1.66233	−	2.87923i	0.0582287	−	0.100855i
$816$	0.707644	+	5.10477i	0.0247725	+	0.178703i
$817$	8.42288	+	14.5889i	0.294679	+	0.510400i
$818$	31.6369			1.10616
$819$	13.1240	−	0.278799i	0.458590	−	0.00974201i
$820$	−15.7215			−0.549018
$821$	42.8081	−	24.7153i	1.49401	−	0.862569i	0.494038	−	0.869441i	$-0.335521\pi$
$821$	42.8081	−	24.7153i	1.49401	−	0.862569i	0.999976	+	0.00687127i	$0.00218721\pi$
$822$	−35.0835	−	20.2554i	−1.22368	−	0.706490i
$823$	−8.27176	−	4.77570i	−0.288335	−	0.166471i	0.348856	−	0.937177i	$-0.386570\pi$
$823$	−8.27176	−	4.77570i	−0.288335	−	0.166471i	−0.637191	+	0.770706i	$0.719904\pi$
$824$	−11.8716	−	20.5622i	−0.413567	−	0.716318i
$825$	−20.4491			−0.711945
$826$	−4.58208	+	8.34062i	−0.159431	+	0.290207i
$827$			56.8626i			1.97731i	0.150219	+	0.988653i	$0.452002\pi$
$827$			56.8626i			1.97731i	−0.150219	+	0.988653i	$0.547998\pi$
$828$	−3.13422	+	1.80954i	−0.108922	+	0.0628859i
$829$	21.4785	−	37.2019i	0.745981	−	1.29208i	−0.203754	−	0.979022i	$-0.565314\pi$
$829$	21.4785	−	37.2019i	0.745981	−	1.29208i	0.949735	−	0.313055i	$-0.101352\pi$
$830$	1.44145	+	0.832223i	0.0500335	+	0.0288869i
$831$	5.67146	+	9.82327i	0.196741	+	0.340765i
$832$	64.0861			2.22179
$833$	−18.6776	−	22.0034i	−0.647139	−	0.762372i
$834$	−26.1999			−0.907227
$835$	6.24948	+	10.8244i	0.216272	+	0.374595i
$836$	−64.5635	−	37.2758i	−2.23298	−	1.28921i
$837$	−1.81861	+	3.14993i	−0.0628605	+	0.108878i
$838$	−5.60016	+	3.23325i	−0.193454	+	0.111691i
$839$			47.9465i			1.65530i	0.561246	+	0.827649i	$0.310322\pi$
$839$			47.9465i			1.65530i	−0.561246	+	0.827649i	$0.689678\pi$
$840$	1.68835	−	3.07325i	0.0582536	−	0.106037i
$841$	17.7219			0.611101
$842$	−0.579061	−	1.00296i	−0.0199557	−	0.0345644i
$843$	0.727034	+	0.419754i	0.0250404	+	0.0144571i
$844$	−9.53178	−	5.50318i	−0.328097	−	0.189427i
$845$	−6.40790	+	3.69960i	−0.220438	+	0.127270i
$846$	−23.0775			−0.793420
$847$	−23.3065	+	0.495110i	−0.800821	+	0.0170122i
$848$	−15.3531			−0.527229
$849$	−9.32607	−	16.1532i	−0.320070	−	0.554377i
$850$	41.6890	−	5.77909i	1.42992	−	0.198221i
$851$	−2.04137	+	3.53576i	−0.0699772	+	0.121204i
$852$	−13.7313	−	23.7833i	−0.470427	−	0.814803i
$853$		−	22.5926i		−	0.773556i	−0.922173	−	0.386778i	$-0.873588\pi$
$853$		−	22.5926i		−	0.773556i	0.922173	−	0.386778i	$-0.126412\pi$
$854$	38.7221	−	23.4666i	1.32504	−	0.803012i
$855$		−	3.63305i		−	0.124248i
$856$	−21.8296	+	12.6034i	−0.746122	+	0.430774i
$857$	36.3637	+	20.9946i	1.24216	+	0.717161i	0.969533	−	0.244959i	$-0.0787746\pi$
$857$	36.3637	+	20.9946i	1.24216	+	0.717161i	0.272626	+	0.962120i	$0.412108\pi$
$858$	−24.5329	+	42.4922i	−0.837539	+	1.45066i
$859$	27.1729	+	47.0649i	0.927128	+	1.60583i	0.788103	+	0.615543i	$0.211063\pi$
$859$	27.1729	+	47.0649i	0.927128	+	1.60583i	0.139024	+	0.990289i	$0.455603\pi$
$860$		−	5.52396i		−	0.188365i
$861$	11.5259	+	19.0188i	0.392803	+	0.648161i
$862$			55.4421i			1.88837i
$863$	−27.7443	−	48.0545i	−0.944426	−	1.63579i	−0.756896	−	0.653535i	$-0.773285\pi$
$863$	−27.7443	−	48.0545i	−0.944426	−	1.63579i	−0.187530	−	0.982259i	$-0.560048\pi$
$864$	6.00904	+	3.46932i	0.204432	+	0.118029i
$865$	−3.52159	+	6.09957i	−0.119738	+	0.207392i
$866$	9.77269	+	16.9268i	0.332089	+	0.575196i
$867$	16.4794	+	4.17467i	0.559671	+	0.141779i
$868$	−0.600174	−	28.2523i	−0.0203712	−	0.958944i
$869$	−64.6420			−2.19283
$870$	−4.11584	+	2.37628i	−0.139540	+	0.0805634i
$871$	−21.9985	+	38.1026i	−0.745392	+	1.29106i
$872$	21.0372	+	12.1458i	0.712410	+	0.411310i
$873$	−11.2094	+	6.47173i	−0.379379	+	0.219035i
$874$		−	15.6188i		−	0.528315i
$875$	14.1706	+	7.78491i	0.479055	+	0.263178i
$876$	−24.9166			−0.841853
$877$	−9.07889	+	5.24170i	−0.306572	+	0.177000i	−0.645392	−	0.763852i	$-0.723306\pi$
$877$	−9.07889	+	5.24170i	−0.306572	+	0.177000i	0.338819	+	0.940851i	$0.389972\pi$
$878$	−8.56825	−	4.94688i	−0.289165	−	0.166949i
$879$	−2.59209	−	1.49655i	−0.0874292	−	0.0504772i
$880$	−1.77177	−	3.06880i	−0.0597264	−	0.103449i
$881$			36.9043i			1.24334i	0.783280	+	0.621669i	$0.213545\pi$
$881$			36.9043i			1.24334i	−0.783280	+	0.621669i	$0.786455\pi$
$882$	−15.5388	+	0.660490i	−0.523217	+	0.0222399i
$883$	12.2155			0.411086			0.205543	−	0.978648i	$-0.434104\pi$
$883$	12.2155			0.411086			0.205543	+	0.978648i	$0.434104\pi$
$884$	22.6080	−	55.6553i	0.760390	−	1.87189i
$885$	0.515564	−	0.892983i	0.0173305	−	0.0300173i
$886$	34.6587	−	60.0307i	1.16438	−	2.01677i
$887$	−26.0598	+	15.0457i	−0.875003	+	0.505183i	−0.869008	−	0.494799i	$-0.835242\pi$
$887$	−26.0598	+	15.0457i	−0.875003	+	0.505183i	−0.00599576	+	0.999982i	$0.501909\pi$
$888$	−6.89299			−0.231314
$889$	−22.4671	+	40.8963i	−0.753524	+	1.37162i
$890$		−	5.46154i		−	0.183071i
$891$	−3.85464	+	2.22548i	−0.129135	+	0.0745563i
$892$	16.1175	−	27.9164i	0.539655	−	0.934710i
$893$	29.6224	−	51.3075i	0.991276	−	1.71694i
$894$	−21.5573	+	12.4461i	−0.720983	+	0.416260i
$895$			3.73870i			0.124971i
$896$	−39.2043	+	0.832833i	−1.30972	+	0.0278230i
$897$	−6.11480			−0.204167
$898$	67.5745	−	39.0142i	2.25499	−	1.30192i
$899$	−6.10742	+	10.5784i	−0.203694	+	0.352808i
$900$	6.74561	−	11.6837i	0.224854	−	0.389458i
$901$	−19.0602	+	46.9215i	−0.634988	+	1.56318i
$902$	−83.1238			−2.76772
$903$	−6.68253	+	4.04979i	−0.222381	+	0.134769i
$904$			8.72273i			0.290114i
$905$	−3.71621	−	6.43666i	−0.123531	−	0.213962i
$906$	−26.2488	−	15.1547i	−0.872057	−	0.503483i
$907$	−19.0675	−	11.0086i	−0.633125	−	0.365535i	0.148836	−	0.988862i	$-0.452447\pi$
$907$	−19.0675	−	11.0086i	−0.633125	−	0.365535i	−0.781961	+	0.623327i	$0.785781\pi$
$908$	27.6283	−	15.9512i	0.916878	−	0.529360i
$909$	5.44154			0.180484
$910$	15.8872	−	9.62807i	0.526656	−	0.319167i
$911$			7.91228i			0.262146i	0.991373	+	0.131073i	$0.0418422\pi$
$911$			7.91228i			0.262146i	−0.991373	+	0.131073i	$0.958158\pi$
$912$	−6.17429	+	3.56473i	−0.204451	+	0.118040i
$913$	4.53360	+	2.61748i	0.150040	+	0.0866258i
$914$	9.48207	−	16.4234i	0.313639	−	0.543239i
$915$	−4.24872	+	2.45300i	−0.140458	+	0.0810936i
$916$	−28.0498			−0.926790
$917$	0.700068	+	32.9546i	0.0231183	+	1.08826i
$918$	7.22942	−	5.62638i	0.238606	−	0.185698i
$919$	−27.6410	−	47.8756i	−0.911792	−	1.57927i	−0.811531	−	0.584309i	$-0.801366\pi$
$919$	−27.6410	−	47.8756i	−0.911792	−	1.57927i	−0.100261	−	0.994961i	$-0.531968\pi$
$920$	−0.816694	+	1.41456i	−0.0269256	+	0.0466365i
$921$	21.6949	+	12.5256i	0.714871	+	0.412731i
$922$	−18.4097	−	31.8865i	−0.606290	−	1.05012i
$923$		−	46.4008i		−	1.52730i
$924$	16.6504	−	30.3082i	0.547758	−	0.997068i
$925$		−	15.2197i		−	0.500419i
$926$	10.5175	+	18.2168i	0.345626	+	0.598642i
$927$	5.70540	−	9.88205i	0.187390	−	0.324569i
$928$	20.1801	+	11.6510i	0.662444	+	0.382462i
$929$	−4.83852	+	2.79352i	−0.158747	+	0.0916524i	−0.577269	−	0.816554i	$-0.695882\pi$
$929$	−4.83852	+	2.79352i	−0.158747	+	0.0916524i	0.418522	+	0.908207i	$0.362548\pi$
$930$			5.14731i			0.168787i
$931$	18.4772	−	35.3947i	0.605565	−	1.16001i
$932$			27.8863i			0.913448i
$933$	0.803381	+	1.39150i	0.0263015	+	0.0455555i
$934$	−10.1984	+	17.6641i	−0.333701	+	0.577988i
$935$	−11.5783	+	1.60503i	−0.378651	+	0.0524901i
$936$	−5.16188	−	8.94064i	−0.168721	−	0.292234i
$937$	−35.3405			−1.15452			−0.577262	−	0.816559i	$-0.695879\pi$
$937$	−35.3405			−1.15452			−0.577262	+	0.816559i	$0.695879\pi$
$938$	25.0991	−	45.6871i	0.819515	−	1.49174i
$939$	−9.34780			−0.305054
$940$	−16.8244	+	9.71359i	−0.548753	+	0.316823i
$941$	1.01029	+	0.583291i	0.0329345	+	0.0190147i	0.516377	−	0.856361i	$-0.327280\pi$
$941$	1.01029	+	0.583291i	0.0329345	+	0.0190147i	−0.483442	+	0.875376i	$0.660614\pi$
$942$	0.648436	+	0.374374i	0.0211272	+	0.0121978i
$943$	−5.17963	−	8.97138i	−0.168672	−	0.292148i
$944$	−2.02347			−0.0658584
$945$	1.68481	−	0.0357911i	0.0548069	−	0.00116428i
$946$		−	29.2067i		−	0.949592i
$947$	44.5572	−	25.7251i	1.44792	−	0.835955i	0.449558	−	0.893251i	$-0.351581\pi$
$947$	44.5572	−	25.7251i	1.44792	−	0.835955i	0.998357	+	0.0572964i	$0.0182480\pi$
$948$	21.3237	−	36.9338i	0.692562	−	1.19955i
$949$	−36.4589	−	21.0495i	−1.18350	−	0.683297i
$950$	29.1120	+	50.4234i	0.944517	+	1.63595i
$951$	22.3804			0.725736
$952$	−8.09397	+	21.2063i	−0.262327	+	0.687300i
$953$	−36.9788			−1.19786			−0.598930	−	0.800801i	$-0.704407\pi$
$953$	−36.9788			−1.19786			−0.598930	+	0.800801i	$0.704407\pi$
$954$	13.6456	+	23.6349i	0.441793	+	0.765207i
$955$	−8.69634	−	5.02083i	−0.281407	−	0.162470i
$956$	−16.8699	+	29.2195i	−0.545610	+	0.945025i
$957$	−12.9450	+	7.47379i	−0.418452	+	0.241593i
$958$			44.7533i			1.44591i
$959$	25.0020	+	41.2557i	0.807358	+	1.33222i
$960$	8.22713			0.265530
$961$	−8.88528	−	15.3898i	−0.286622	−	0.496444i
$962$	−31.6258	−	18.2591i	−1.01966	−	0.588698i
$963$	−10.4912	−	6.05708i	−0.338073	−	0.195187i
$964$	33.6327	−	19.4178i	1.08324	−	0.625406i
$965$	−1.16226			−0.0374145
$966$	7.24315	−	0.153869i	0.233045	−	0.00495066i
$967$	11.5339			0.370905			0.185453	−	0.982653i	$-0.440625\pi$
$967$	11.5339			0.370905			0.185453	+	0.982653i	$0.440625\pi$
$968$	9.16682	+	15.8774i	0.294633	+	0.510319i
$969$	3.22925	+	23.2950i	0.103738	+	0.748344i
$970$	−9.15862	+	15.8632i	−0.294066	+	0.509337i
$971$	4.18925	+	7.25599i	0.134439	+	0.232856i	0.925383	−	0.379033i	$-0.123743\pi$
$971$	4.18925	+	7.25599i	0.134439	+	0.232856i	−0.790944	+	0.611889i	$0.790410\pi$
$972$		−	2.93651i		−	0.0941886i
$973$	27.3442	+	15.0220i	0.876614	+	0.481585i
$974$			11.9914i			0.384229i
$975$	19.7409	−	11.3974i	0.632213	−	0.365009i
$976$	8.33762	+	4.81373i	0.266881	+	0.154084i
$977$	−3.37704	+	5.84921i	−0.108041	+	0.187133i	−0.914977	−	0.403507i	$-0.867791\pi$
$977$	−3.37704	+	5.84921i	−0.108041	+	0.187133i	0.806935	+	0.590640i	$0.201124\pi$
$978$	5.79864	+	10.0435i	0.185420	+	0.321157i
$979$		−	17.1774i		−	0.548993i
$980$	−11.0504	+	7.02197i	−0.352991	+	0.224309i
$981$			11.6744i			0.372735i
$982$	5.12652	+	8.87940i	0.163594	+	0.283353i
$983$	−11.1391	−	6.43115i	−0.355281	−	0.205122i	0.311728	−	0.950171i	$-0.399092\pi$
$983$	−11.1391	−	6.43115i	−0.355281	−	0.205122i	−0.667009	+	0.745050i	$0.732426\pi$
$984$	8.74490	−	15.1466i	0.278777	−	0.482856i
$985$	5.58612	+	9.67545i	0.177989	+	0.308285i
$986$	24.2784	−	18.8950i	0.773183	−	0.601739i
$987$	24.0854	+	13.2318i	0.766647	+	0.421172i
$988$	83.1034			2.64387
$989$	3.15222	−	1.81993i	0.100235	−	0.0578705i
$990$	−3.14944	+	5.45499i	−0.100096	+	0.173371i
$991$	45.5283	+	26.2858i	1.44625	+	0.834995i	0.998256	−	0.0590392i	$-0.0188037\pi$
$991$	45.5283	+	26.2858i	1.44625	+	0.834995i	0.447998	+	0.894034i	$0.352137\pi$
$992$	21.8563	−	12.6187i	0.693937	−	0.400645i
$993$		−	18.3909i		−	0.583617i
$994$	1.16760	+	54.9631i	0.0370341	+	1.74332i
$995$	−7.77124			−0.246365
$996$	−2.99104	+	1.72688i	−0.0947746	+	0.0547181i
$997$	4.36058	+	2.51758i	0.138101	+	0.0797326i	0.567459	−	0.823402i	$-0.307927\pi$
$997$	4.36058	+	2.51758i	0.138101	+	0.0797326i	−0.429358	+	0.903135i	$0.641260\pi$
$998$	−77.9376	−	44.9973i	−2.46707	−	1.42436i
$999$	−1.65636	−	2.86890i	−0.0524049	−	0.0907680i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.p.a.67.4	yes	48
7.2	even	3	inner	357.2.p.a.16.3	✓	48
17.16	even	2	inner	357.2.p.a.67.3	yes	48
119.16	even	6	inner	357.2.p.a.16.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.p.a.16.3	✓	48	7.2	even	3	inner
357.2.p.a.16.4	yes	48	119.16	even	6	inner
357.2.p.a.67.3	yes	48	17.16	even	2	inner
357.2.p.a.67.4	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11091 - 1.92416i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.46826 + 2.54309i) q^{4} +(-0.551608 + 0.318471i) q^{5} -2.22183i q^{6} +(-1.27391 + 2.31887i) q^{7} +2.08076 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.11091 - 1.92416i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.46826 + 2.54309i) q^{4} +(-0.551608 + 0.318471i) q^{5} -2.22183i q^{6} +(-1.27391 + 2.31887i) q^{7} +2.08076 q^{8} +(0.500000 + 0.866025i) q^{9} +(1.22558 + 0.707587i) q^{10} +(3.85464 + 2.22548i) q^{11} +(-2.54309 + 1.46826i) q^{12} -4.96153 q^{13} +(5.87707 - 0.124849i) q^{14} -0.636942 q^{15} +(0.624963 + 1.08247i) q^{16} +(4.08405 - 0.566148i) q^{17} +(1.11091 - 1.92416i) q^{18} +(2.85195 + 4.93972i) q^{19} -1.87039i q^{20} +(-2.26267 + 1.37124i) q^{21} -9.88925i q^{22} +(1.06733 - 0.616221i) q^{23} +(1.80199 + 1.04038i) q^{24} +(-2.29715 + 3.97878i) q^{25} +(5.51183 + 9.54676i) q^{26} +1.00000i q^{27} +(-4.02666 - 6.64437i) q^{28} +3.35828i q^{29} +(0.707587 + 1.22558i) q^{30} +(3.14993 + 1.81861i) q^{31} +(3.46932 - 6.00904i) q^{32} +(2.22548 + 3.85464i) q^{33} +(-5.62638 - 7.22942i) q^{34} +(-0.0357911 - 1.68481i) q^{35} -2.93651 q^{36} +(-2.86890 + 1.65636i) q^{37} +(6.33653 - 10.9752i) q^{38} +(-4.29681 - 2.48076i) q^{39} +(-1.14777 + 0.662663i) q^{40} -8.40547i q^{41} +(5.15212 + 2.83041i) q^{42} +2.95338 q^{43} +(-11.3192 + 6.53514i) q^{44} +(-0.551608 - 0.318471i) q^{45} +(-2.37141 - 1.36914i) q^{46} +(-5.19336 - 8.99516i) q^{47} +1.24993i q^{48} +(-3.75429 - 5.90807i) q^{49} +10.2077 q^{50} +(3.81997 + 1.55173i) q^{51} +(7.28479 - 12.6176i) q^{52} +(-6.14162 + 10.6376i) q^{53} +(1.92416 - 1.11091i) q^{54} -2.83500 q^{55} +(-2.65071 + 4.82501i) q^{56} +5.70390i q^{57} +(6.46187 - 3.73076i) q^{58} +(-0.809436 + 1.40198i) q^{59} +(0.935194 - 1.61980i) q^{60} +(6.67049 - 3.85121i) q^{61} -8.08129i q^{62} +(-2.64515 + 0.0561921i) q^{63} -12.9166 q^{64} +(2.73682 - 1.58010i) q^{65} +(4.94463 - 8.56434i) q^{66} +(4.43382 - 7.67960i) q^{67} +(-4.55666 + 11.2174i) q^{68} +1.23244 q^{69} +(-3.20208 + 1.94055i) q^{70} +9.35212i q^{71} +(1.04038 + 1.80199i) q^{72} +(7.34831 + 4.24255i) q^{73} +(6.37420 + 3.68015i) q^{74} +(-3.97878 + 2.29715i) q^{75} -16.7496 q^{76} +(-10.0711 + 6.10333i) q^{77} +11.0237i q^{78} +(-12.5774 + 7.26158i) q^{79} +(-0.689470 - 0.398066i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-16.1735 + 9.33775i) q^{82} +1.17614 q^{83} +(-0.165009 - 7.76752i) q^{84} +(-2.07249 + 1.61294i) q^{85} +(-3.28095 - 5.68276i) q^{86} +(-1.67914 + 2.90836i) q^{87} +(8.02060 + 4.63069i) q^{88} +(-1.92963 - 3.34222i) q^{89} +1.41517i q^{90} +(6.32056 - 11.5051i) q^{91} +3.61908i q^{92} +(1.81861 + 3.14993i) q^{93} +(-11.5387 + 19.9857i) q^{94} +(-3.14632 - 1.81653i) q^{95} +(6.00904 - 3.46932i) q^{96} +12.9435i q^{97} +(-7.19737 + 13.7872i) q^{98} +4.45096i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{4} + 24 q^{9}+O(q^{10}) \) 48 * q - 24 * q^4 + 24 * q^9	\( 48 q - 24 q^{4} + 24 q^{9} + 16 q^{13} - 40 q^{16} + 8 q^{17} + 16 q^{19} + 36 q^{25} - 52 q^{26} + 24 q^{30} + 20 q^{32} - 8 q^{33} - 32 q^{34} - 36 q^{35} - 48 q^{36} + 40 q^{38} + 4 q^{42} + 40 q^{43} - 80 q^{50} - 12 q^{52} - 60 q^{53} - 24 q^{59} + 112 q^{64} + 4 q^{66} - 4 q^{67} + 88 q^{68} + 64 q^{69} - 24 q^{70} - 184 q^{76} - 72 q^{77} - 24 q^{81} - 88 q^{83} - 20 q^{84} + 16 q^{85} + 60 q^{86} + 36 q^{87} + 12 q^{89} - 24 q^{93} - 32 q^{94} + 48 q^{98}+O(q^{100}) \) 48 * q - 24 * q^4 + 24 * q^9 + 16 * q^13 - 40 * q^16 + 8 * q^17 + 16 * q^19 + 36 * q^25 - 52 * q^26 + 24 * q^30 + 20 * q^32 - 8 * q^33 - 32 * q^34 - 36 * q^35 - 48 * q^36 + 40 * q^38 + 4 * q^42 + 40 * q^43 - 80 * q^50 - 12 * q^52 - 60 * q^53 - 24 * q^59 + 112 * q^64 + 4 * q^66 - 4 * q^67 + 88 * q^68 + 64 * q^69 - 24 * q^70 - 184 * q^76 - 72 * q^77 - 24 * q^81 - 88 * q^83 - 20 * q^84 + 16 * q^85 + 60 * q^86 + 36 * q^87 + 12 * q^89 - 24 * q^93 - 32 * q^94 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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