LMFDB - Embedded newform 357.2.p.a.67.3

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			67.3
Character	$\chi$	$=$	357.67
Dual form			357.2.p.a.16.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11091 - 1.92416i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.46826 + 2.54309i) q^{4} +(0.551608 - 0.318471i) q^{5} +2.22183i q^{6} +(1.27391 - 2.31887i) q^{7} +2.08076 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(-1.55173 - 3.81997i) 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} +(-0.566148 + 4.08405i) 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} +(11.9929 + 1.66250i) 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	−0.371560	−	0.928409i	$-0.621177\pi$
$5$	0.551608	−	0.318471i	0.246687	−	0.142425i	0.618246	+	0.785985i	$0.287843\pi$
$6$			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	−0.210384	−	0.977619i	$-0.567471\pi$
$11$	−3.85464	−	2.22548i	−1.16222	−	0.671007i	−0.951835	+	0.306612i	$0.900805\pi$
$12$	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
$17$	−1.55173	−	3.81997i	−0.376349	−	0.926478i
$17$	−1.55173	−	3.81997i	−0.376349	−	0.926478i
$18$	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	−0.607132	−	0.794601i	$-0.707680\pi$
$23$	−1.06733	+	0.616221i	−0.222553	+	0.128491i	0.384579	+	0.923092i	$0.374347\pi$
$24$	−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	$-0.899065\pi$
$29$		−	3.35828i		−	0.623618i	0.950145	−	0.311809i	$-0.100935\pi$
$30$	0.707587	+	1.22558i	0.129187	+	0.223759i
$31$	−3.14993	−	1.81861i	−0.565745	−	0.326633i	0.189703	−	0.981841i	$-0.439247\pi$
$31$	−3.14993	−	1.81861i	−0.565745	−	0.326633i	−0.755448	+	0.655209i	$0.772581\pi$
$32$	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	−0.245283	−	0.969451i	$-0.578881\pi$
$37$	2.86890	−	1.65636i	0.471644	−	0.272304i	0.716928	+	0.697147i	$0.245548\pi$
$38$	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	$0.227903\pi$
$41$			8.40547i			1.31271i	−0.754450	+	0.656357i	$0.772097\pi$
$42$	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
$51$	−0.566148	+	4.08405i	−0.0792766	+	0.571882i
$52$	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	−0.862022	−	0.506872i	$-0.830802\pi$
$61$	−6.67049	+	3.85121i	−0.854069	+	0.493097i	0.00795289	+	0.999968i	$0.497468\pi$
$62$			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	$-0.0155439\pi$
$68$	11.9929	+	1.66250i	1.45435	+	0.201608i
$69$	1.23244			0.148369
$70$	−3.20208	+	1.94055i	−0.382722	+	0.231940i
$71$		−	9.35212i		−	1.10989i	−0.831886	−	0.554946i	$-0.812739\pi$
$71$		−	9.35212i		−	1.10989i	0.831886	−	0.554946i	$-0.187261\pi$
$72$	1.04038	+	1.80199i	0.122610	+	0.212367i
$73$	−7.34831	−	4.24255i	−0.860055	−	0.496553i	0.00397574	−	0.999992i	$-0.498734\pi$
$73$	−7.34831	−	4.24255i	−0.860055	−	0.496553i	−0.864031	+	0.503439i	$0.832068\pi$
$74$	−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	0.419211	−	0.907889i	$-0.362307\pi$
$79$	12.5774	−	7.26158i	1.41507	−	0.816992i	0.995860	+	0.0908965i	$0.0289733\pi$
$80$	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	$-0.771781\pi$
$97$		−	12.9435i		−	1.31421i	0.753800	−	0.657104i	$-0.228219\pi$
$98$	−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	$0.0794027\pi$
$102$	8.48730	−	3.44767i	0.840368	−	0.341370i
$103$	−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	0.101795	−	0.994805i	$-0.467541\pi$
$107$	10.4912	−	6.05708i	1.01422	−	0.585560i	0.912424	+	0.409245i	$0.134208\pi$
$108$	2.54309	+	1.46826i	0.244709	+	0.141283i
$109$	−10.1103	−	5.83720i	−0.968394	−	0.559103i	−0.0696480	−	0.997572i	$-0.522188\pi$
$109$	−10.1103	−	5.83720i	−0.968394	−	0.559103i	−0.898746	+	0.438469i	$0.855521\pi$
$110$	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	$-0.936822\pi$
$113$		−	4.19208i		−	0.394358i	0.980367	−	0.197179i	$-0.0631780\pi$
$114$	−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
$119$	−10.8348	−	1.26806i	−0.993221	−	0.116243i
$120$	−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	−0.890797	−	0.454402i	$-0.849853\pi$
$131$	−10.7894	+	6.22924i	−0.942671	+	0.544251i	−0.0518742	+	0.998654i	$0.516519\pi$
$132$	−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
$136$	−3.22878	−	7.94845i	−0.276865	−	0.681574i
$137$	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	$0.166701\pi$
$139$			11.7920i			1.00019i	−0.865971	+	0.500094i	$0.833299\pi$
$140$	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	−0.312409	−	0.949948i	$-0.601136\pi$
$163$	4.52040	−	2.60985i	0.354065	−	0.204420i	0.666474	+	0.745528i	$0.267803\pi$
$164$	−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	$0.274435\pi$
$167$			19.6234i			1.51850i	−0.650797	+	0.759252i	$0.725565\pi$
$168$	−4.70809	+	2.85323i	−0.363237	+	0.220131i
$169$	11.6168			0.893597
$170$	−0.801198	+	5.77965i	−0.0614491	+	0.443279i
$171$	−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	−0.817718	−	0.575620i	$-0.804761\pi$
$173$	−9.57633	+	5.52890i	−0.728075	+	0.420354i	0.0896424	+	0.995974i	$0.471428\pi$
$174$	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	$-0.857218\pi$
$181$		−	11.6689i		−	0.867343i	0.901071	−	0.433672i	$-0.142782\pi$
$182$	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
$187$	−2.51990	+	18.1779i	−0.184273	+	1.32930i
$188$	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	0.442045	−	0.896993i	$-0.354253\pi$
$193$	−1.58028	−	0.912377i	−0.113751	−	0.0656743i	−0.555796	+	0.831319i	$0.687587\pi$
$194$	−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	$0.214841\pi$
$197$			17.5404i			1.24970i	−0.780743	+	0.624852i	$0.785159\pi$
$198$	−8.56434	+	4.94463i	−0.608641	+	0.351399i
$199$	−10.5663	−	6.10043i	−0.749022	−	0.432448i	0.0763186	−	0.997083i	$-0.475683\pi$
$199$	−10.5663	−	6.10043i	−0.749022	−	0.432448i	−0.825340	+	0.564636i	$0.809017\pi$
$200$	−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	$-0.958818\pi$
$211$		−	3.74811i		−	0.258030i	0.991643	−	0.129015i	$-0.0411816\pi$
$212$	−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
$221$	7.69894	+	18.9529i	0.517887	+	1.27491i
$222$	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	0.778606	−	0.627513i	$-0.215927\pi$
$227$	9.40856	+	5.43203i	0.624468	+	0.360537i	−0.154139	+	0.988049i	$0.549260\pi$
$228$	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	−0.744585	−	0.667528i	$-0.767353\pi$
$233$	−8.22414	+	4.74821i	−0.538782	+	0.311066i	0.205803	+	0.978593i	$0.434019\pi$
$234$	−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
$238$	9.59653	+	22.2565i	0.622051	+	1.44267i
$239$	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	0.821258	−	0.570557i	$-0.193273\pi$
$241$	11.4533	+	6.61255i	0.737771	+	0.425952i	−0.0834876	+	0.996509i	$0.526606\pi$
$242$	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
$255$	0.988360	+	2.43310i	0.0618935	+	0.152366i
$256$	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	0.0111515	−	0.999938i	$-0.496450\pi$
$269$	−13.9286	−	8.04171i	−0.849244	−	0.490311i	−0.860396	+	0.509626i	$0.829784\pi$
$270$	−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	0.174963	−	0.984575i	$-0.444019\pi$
$277$	−9.82327	−	5.67146i	−0.590223	−	0.340765i	−0.765186	+	0.643810i	$0.777353\pi$
$278$	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	0.896238	−	0.443574i	$-0.146290\pi$
$283$	16.1532	+	9.32607i	0.960210	+	0.554377i	0.0639721	+	0.997952i	$0.479623\pi$
$284$	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
$289$	−12.1843	+	11.8551i	−0.716723	+	0.697358i
$290$	−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
$306$	−9.07405	−	1.25788i	−0.518729	−	0.0719083i
$307$	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	0.460029	−	0.887904i	$-0.347839\pi$
$311$	−1.39150	−	0.803381i	−0.0789045	−	0.0455555i	−0.538933	+	0.842349i	$0.681172\pi$
$312$	8.94064	+	5.16188i	0.506164	+	0.292234i
$313$	8.09544	−	4.67390i	0.457581	−	0.264185i	−0.253446	−	0.967350i	$-0.581564\pi$
$313$	8.09544	−	4.67390i	0.457581	−	0.264185i	0.711027	+	0.703165i	$0.248231\pi$
$314$	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	−0.933204	−	0.359346i	$-0.883000\pi$
$317$	−19.3820	+	11.1902i	−1.08860	+	0.628506i	−0.155399	+	0.987852i	$0.549666\pi$
$318$	−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	$-0.895723\pi$
$337$		−	11.8137i		−	0.643535i	0.946819	−	0.321768i	$-0.104277\pi$
$338$	−12.9052	−	22.3525i	−0.701951	−	1.21582i
$339$	−2.09604	+	3.63045i	−0.113841	+	0.197179i
$340$	7.14482	−	2.90233i	0.387482	−	0.157401i
$341$	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	0.0551731	−	0.998477i	$-0.482429\pi$
$347$	−14.5661	−	8.40971i	−0.781947	−	0.451457i	−0.837120	+	0.547020i	$0.815762\pi$
$348$	−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
$357$	8.74915	+	6.51555i	0.463054	+	0.344839i
$358$	−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	−0.280629	−	0.959816i	$-0.590543\pi$
$367$	−23.9881	−	13.8495i	−1.25217	−	0.722940i	−0.971540	+	0.236876i	$0.923876\pi$
$368$	−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	$0.567678\pi$
$374$	37.7766	−	15.3454i	1.95338	−	0.793493i
$375$	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	$0.246748\pi$
$379$			27.2491i			1.39969i	−0.714294	+	0.699845i	$0.753252\pi$
$380$	−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	−0.0870261	−	0.996206i	$-0.527736\pi$
$397$	14.5890	−	8.42296i	0.732201	−	0.422736i	0.819227	+	0.573470i	$0.194403\pi$
$398$			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	0.381257	−	0.924469i	$-0.375491\pi$
$401$	27.4843	−	15.8681i	1.37250	−	0.792413i	0.991242	+	0.132056i	$0.0421579\pi$
$402$	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
$408$	−1.17802	+	8.49795i	−0.0583207	+	0.420711i
$409$	−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	$0.0226485\pi$
$419$			2.91045i			0.142185i	−0.997470	+	0.0710923i	$0.977352\pi$
$420$	−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
$425$	18.7634	+	2.60106i	0.910157	+	0.126170i
$426$	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	0.920097	−	0.391691i	$-0.128110\pi$
$431$	21.6103	+	12.4767i	1.04093	+	0.600981i	0.120834	+	0.992673i	$0.461443\pi$
$432$	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	−0.589197	−	0.807989i	$-0.700556\pi$
$439$	−3.85640	+	2.22649i	−0.184056	+	0.106265i	0.405141	+	0.914254i	$0.367222\pi$
$440$	−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	$-0.689090\pi$
$449$		−	35.1190i		−	1.65737i	0.559716	−	0.828685i	$-0.310910\pi$
$450$	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
$459$	−3.81997	+	1.55173i	−0.178301	+	0.0724284i
$460$	−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
$476$	19.1330	−	25.6920i	0.876959	−	1.17759i
$477$	−12.2832			−0.562411
$478$	−12.7641	−	22.1081i	−0.583816	−	1.01120i
$479$	17.4440	+	10.0713i	0.797037	+	0.460169i	0.842434	−	0.538800i	$-0.181122\pi$
$479$	17.4440	+	10.0713i	0.797037	+	0.460169i	−0.0453972	+	0.998969i	$0.514455\pi$
$480$	−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	0.602148	−	0.798385i	$-0.294312\pi$
$487$	4.67401	+	2.69854i	0.211800	+	0.122283i	−0.390348	+	0.920667i	$0.627645\pi$
$488$	−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
$493$	−12.8285	+	5.21114i	−0.577768	+	0.234698i
$494$	−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	$0.694681\pi$
$499$	−35.0782	+	20.2524i	−1.57031	+	0.906621i	−0.996130	+	0.0878956i	$0.971986\pi$
$500$	−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	$0.00243130\pi$
$503$			0.342609i			0.0152762i	−0.999971	+	0.00763808i	$0.997569\pi$
$504$	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	0.462339	−	0.886703i	$-0.347010\pi$
$521$	−1.69820	−	0.980458i	−0.0743996	−	0.0429546i	−0.536738	+	0.843749i	$0.680344\pi$
$522$	−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
$527$	−2.05921	+	14.8546i	−0.0897006	+	0.647078i
$528$	−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	−0.123121	−	0.992392i	$-0.539290\pi$
$541$	15.6944	−	9.06116i	0.674754	−	0.389570i	0.797876	+	0.602822i	$0.205957\pi$
$542$	−31.3788	+	54.3496i	−1.34783	+	2.33452i
$543$	−5.83446	+	10.1056i	−0.250380	+	0.433672i
$544$	−28.3378	−	3.92830i	−1.21497	−	0.168425i
$545$	−7.43592			−0.318520
$546$	−25.5624	−	14.0432i	−1.09397	−	0.600993i
$547$		−	3.48512i		−	0.149013i	−0.997221	−	0.0745065i	$-0.976262\pi$
$547$		−	3.48512i		−	0.149013i	0.997221	−	0.0745065i	$-0.0237382\pi$
$548$	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	−0.490363	−	0.871518i	$-0.663136\pi$
$571$	−35.6117	−	20.5604i	−1.49030	−	0.860426i	−0.999938	+	0.0110921i	$0.996469\pi$
$572$	−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	$0.329188\pi$
$578$	36.3467	+	10.2745i	1.51183	+	0.427363i
$579$	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
$595$	−6.38038	+	2.75109i	−0.261570	+	0.112784i
$596$	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	$0.302976\pi$
$601$			39.9343i			1.62896i	−0.580195	+	0.814478i	$0.697024\pi$
$602$	−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	−0.333060	−	0.942906i	$-0.608081\pi$
$607$	7.80981	−	4.50900i	0.316990	−	0.183015i	0.650050	+	0.759891i	$0.274748\pi$
$608$	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
$612$	4.55666	+	11.2174i	0.184192	+	0.453435i
$613$	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	$0.355355\pi$
$617$			44.6374i			1.79703i	−0.438938	+	0.898517i	$0.644645\pi$
$618$	21.9562	−	12.6764i	0.883208	−	0.509920i
$619$	29.1522	+	16.8310i	1.17173	+	0.676496i	0.954086	−	0.299533i	$-0.0968310\pi$
$619$	29.1522	+	16.8310i	1.17173	+	0.676496i	0.217639	+	0.976029i	$0.430164\pi$
$620$	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	0.968938	−	0.247304i	$-0.0795446\pi$
$641$	31.3749	+	18.1143i	1.23924	+	0.715473i	0.270298	+	0.962777i	$0.412878\pi$
$642$	13.4578	+	23.3096i	0.531136	+	0.919955i
$643$		−	42.9418i		−	1.69346i	−0.532022	−	0.846731i	$-0.678568\pi$
$643$		−	42.9418i		−	1.69346i	0.532022	−	0.846731i	$-0.321432\pi$
$644$	−8.39217	−	4.61040i	−0.330698	−	0.181675i
$645$	−1.88113			−0.0740694
$646$	−51.7575	−	7.17483i	−2.03637	−	0.282290i
$647$	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	−0.133716	−	0.991020i	$-0.542691\pi$
$653$	16.8061	−	9.70301i	0.657673	−	0.379708i	0.791390	+	0.611312i	$0.209358\pi$
$654$	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
$663$	2.80896	−	20.2631i	0.109091	−	0.786955i
$664$	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	$0.161117\pi$
$673$			25.1549i			0.969650i	−0.874611	+	0.484825i	$0.838883\pi$
$674$	−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	−0.0394489	−	0.999222i	$-0.512560\pi$
$677$	20.9761	−	12.1106i	0.806178	−	0.465447i	0.845627	+	0.533775i	$0.179227\pi$
$678$	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	0.290600	−	0.956845i	$-0.406145\pi$
$683$	−10.2643	−	5.92609i	−0.392752	−	0.226756i	−0.683352	+	0.730089i	$0.739479\pi$
$684$	−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	−0.975038	−	0.222036i	$-0.928730\pi$
$691$	−33.3914	+	19.2785i	−1.27027	+	0.733390i	−0.295230	+	0.955426i	$0.595396\pi$
$692$		−	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
$697$	32.1086	−	13.0430i	1.21620	−	0.494039i
$698$	−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	0.201441	−	0.979501i	$-0.435438\pi$
$709$	30.6327	−	17.6858i	1.15043	−	0.664203i	0.948993	+	0.315297i	$0.102104\pi$
$710$	−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
$714$	2.81740	−	24.0730i	0.105439	−	0.900908i
$715$	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	−0.495259	−	0.868745i	$-0.664927\pi$
$719$	0.253848	−	0.146559i	0.00946693	−	0.00546573i	0.504726	+	0.863280i	$0.331594\pi$
$720$			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
$731$	−4.58284	−	11.2818i	−0.169502	−	0.417273i
$732$	−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	$-0.862864\pi$
$743$		−	22.7670i		−	0.835241i	0.908622	−	0.417620i	$-0.137136\pi$
$744$	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	0.142729	−	0.989762i	$-0.454412\pi$
$751$	29.3570	−	16.9493i	1.07125	−	0.618488i	0.928523	+	0.371274i	$0.121079\pi$
$752$	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
$765$	0.360603	−	2.60130i	0.0130376	−	0.0940504i
$766$	−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
$782$	1.55027	−	11.1832i	0.0554375	−	0.399912i
$783$	−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	$-0.989670\pi$
$787$	−42.8464	−	24.7374i	−1.52731	−	0.881793i	−0.527838	−	0.849345i	$-0.676997\pi$
$788$	−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	0.793092	−	0.609102i	$-0.208470\pi$
$809$	18.8332	+	10.8734i	0.662140	+	0.382287i	−0.130952	+	0.991389i	$0.541803\pi$
$810$	1.22558	−	0.707587i	0.0430624	−	0.0248621i
$811$		−	1.15024i		−	0.0403905i	−0.999796	−	0.0201952i	$-0.993571\pi$
$811$		−	1.15024i		−	0.0403905i	0.999796	−	0.0201952i	$-0.00642878\pi$
$812$	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
$816$	−4.77468	+	1.93955i	−0.167147	+	0.0678977i
$817$	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	−0.999976	−	0.00687127i	$-0.997813\pi$
$821$	−42.8081	+	24.7153i	−1.49401	+	0.862569i	−0.494038	+	0.869441i	$0.664479\pi$
$822$	35.0835	+	20.2554i	1.22368	+	0.706490i
$823$	8.27176	+	4.77570i	0.288335	+	0.166471i	0.637191	−	0.770706i	$-0.280096\pi$
$823$	8.27176	+	4.77570i	0.288335	+	0.166471i	−0.348856	+	0.937177i	$0.613430\pi$
$824$	−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	$-0.547998\pi$
$827$		−	56.8626i		−	1.97731i	0.150219	−	0.988653i	$-0.452002\pi$
$828$	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
$833$	−16.7430	+	23.5090i	−0.580111	+	0.814538i
$834$	−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	$-0.689678\pi$
$839$		−	47.9465i		−	1.65530i	0.561246	−	0.827649i	$-0.310322\pi$
$840$	−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
$850$	−15.8396	−	38.9932i	−0.543295	−	1.33746i
$851$	−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	$0.126412\pi$
$853$			22.5926i			0.773556i	−0.922173	+	0.386778i	$0.873588\pi$
$854$	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	−0.272626	−	0.962120i	$-0.587892\pi$
$857$	−36.3637	−	20.9946i	−1.24216	−	0.717161i	−0.969533	+	0.244959i	$0.921225\pi$
$858$	−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	−0.338819	−	0.940851i	$-0.610028\pi$
$877$	9.07889	−	5.24170i	0.306572	−	0.177000i	0.645392	+	0.763852i	$0.276694\pi$
$878$	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	$-0.786455\pi$
$881$		−	36.9043i		−	1.24334i	0.783280	−	0.621669i	$-0.213545\pi$
$882$	−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	$0.434104\pi$
$884$	−59.5029	−	8.24854i	−2.00130	−	0.277428i
$885$	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	0.00599576	−	0.999982i	$-0.498091\pi$
$887$	26.0598	−	15.0457i	0.875003	−	0.505183i	0.869008	+	0.494799i	$0.164758\pi$
$888$	−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
$901$	50.1654	+	6.95413i	1.67125	+	0.231676i
$902$	−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	0.781961	−	0.623327i	$-0.214219\pi$
$907$	19.0675	+	11.0086i	0.633125	+	0.365535i	−0.148836	+	0.988862i	$0.547553\pi$
$908$	−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	$-0.958158\pi$
$911$		−	7.91228i		−	0.262146i	0.991373	−	0.131073i	$-0.0418422\pi$
$912$	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	−0.418522	−	0.908207i	$-0.637452\pi$
$929$	4.83852	−	2.79352i	0.158747	−	0.0916524i	0.577269	+	0.816554i	$0.304118\pi$
$930$		−	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
$935$	4.39915	+	10.8296i	0.143868	+	0.354166i
$936$	−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	0.483442	−	0.875376i	$-0.339386\pi$
$941$	−1.01029	−	0.583291i	−0.0329345	−	0.0190147i	−0.516377	+	0.856361i	$0.672720\pi$
$942$	−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	−0.998357	−	0.0572964i	$-0.981752\pi$
$947$	−44.5572	+	25.7251i	−1.44792	+	0.835955i	−0.449558	+	0.893251i	$0.648419\pi$
$948$	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
$952$	−22.5446	−	2.63853i	−0.730674	−	0.0855152i
$953$	−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
$969$	−21.7887	+	8.85089i	−0.699954	+	0.284332i
$970$	−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	0.667009	−	0.745050i	$-0.267574\pi$
$983$	11.1391	+	6.43115i	0.355281	+	0.205122i	−0.311728	+	0.950171i	$0.600908\pi$
$984$	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	−0.447998	−	0.894034i	$-0.647863\pi$
$991$	−45.5283	−	26.2858i	−1.44625	−	0.834995i	−0.998256	+	0.0590392i	$0.981196\pi$
$992$	−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	0.429358	−	0.903135i	$-0.358740\pi$
$997$	−4.36058	−	2.51758i	−0.138101	−	0.0797326i	−0.567459	+	0.823402i	$0.692073\pi$
$998$	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.67.3	yes	48
7.2	even	3	inner	357.2.p.a.16.4	yes	48
17.16	even	2	inner	357.2.p.a.67.4	yes	48
119.16	even	6	inner	357.2.p.a.16.3	✓	48

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
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} +(-1.55173 - 3.81997i) 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} +(-0.566148 + 4.08405i) 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} +(11.9929 + 1.66250i) 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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