LMFDB - Embedded newform 152.2.p.a.125.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,2,Mod(45,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("152.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.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:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			125.13
Character	$\chi$	$=$	152.125
Dual form			152.2.p.a.45.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.684248 + 1.23766i) q^{2} +(-1.95927 - 1.13118i) q^{3} +(-1.06361 + 1.69373i) q^{4} +(-3.00559 - 1.73528i) q^{5} +(0.0593980 - 3.19892i) q^{6} -2.66551 q^{7} +(-2.82404 - 0.157456i) q^{8} +(1.05915 + 1.83451i) q^{9} +O(q^{10})$	\(q+(0.684248 + 1.23766i) q^{2} +(-1.95927 - 1.13118i) q^{3} +(-1.06361 + 1.69373i) q^{4} +(-3.00559 - 1.73528i) q^{5} +(0.0593980 - 3.19892i) q^{6} -2.66551 q^{7} +(-2.82404 - 0.157456i) q^{8} +(1.05915 + 1.83451i) q^{9} +(0.0911187 - 4.90726i) q^{10} +5.21404i q^{11} +(3.99982 - 2.11534i) q^{12} +(3.87202 - 2.23551i) q^{13} +(-1.82387 - 3.29900i) q^{14} +(3.92584 + 6.79975i) q^{15} +(-1.73747 - 3.60295i) q^{16} +(-0.0984768 + 0.170567i) q^{17} +(-1.54578 + 2.56613i) q^{18} +(-3.73825 - 2.24177i) q^{19} +(6.13588 - 3.24501i) q^{20} +(5.22245 + 3.01518i) q^{21} +(-6.45321 + 3.56769i) q^{22} +(-2.60934 - 4.51951i) q^{23} +(5.35494 + 3.50301i) q^{24} +(3.52239 + 6.10095i) q^{25} +(5.41623 + 3.26260i) q^{26} +1.99471i q^{27} +(2.83506 - 4.51466i) q^{28} +(-4.51307 + 2.60562i) q^{29} +(-5.72954 + 9.51157i) q^{30} -3.47662 q^{31} +(3.27037 - 4.61570i) q^{32} +(5.89804 - 10.2157i) q^{33} +(-0.278487 - 0.00517097i) q^{34} +(8.01143 + 4.62540i) q^{35} +(-4.23370 - 0.157278i) q^{36} -4.11792i q^{37} +(0.216662 - 6.16061i) q^{38} -10.1151 q^{39} +(8.21468 + 5.37375i) q^{40} +(-1.67461 + 2.90051i) q^{41} +(-0.158326 + 8.52675i) q^{42} +(1.11612 + 0.644390i) q^{43} +(-8.83119 - 5.54571i) q^{44} -7.35171i q^{45} +(3.80819 - 6.32195i) q^{46} +(-0.511521 - 0.885980i) q^{47} +(-0.671432 + 9.02453i) q^{48} +0.104934 q^{49} +(-5.14073 + 8.53408i) q^{50} +(0.385885 - 0.222791i) q^{51} +(-0.331960 + 8.93588i) q^{52} +(-8.19671 + 4.73237i) q^{53} +(-2.46877 + 1.36487i) q^{54} +(9.04781 - 15.6713i) q^{55} +(7.52750 + 0.419701i) q^{56} +(4.78838 + 8.62087i) q^{57} +(-6.31293 - 3.80276i) q^{58} +(-1.43517 - 0.828597i) q^{59} +(-15.6925 - 0.582963i) q^{60} +(1.70425 - 0.983950i) q^{61} +(-2.37887 - 4.30288i) q^{62} +(-2.82319 - 4.88990i) q^{63} +(7.95042 + 0.889326i) q^{64} -15.5169 q^{65} +(16.6793 + 0.309703i) q^{66} +(9.10257 - 5.25537i) q^{67} +(-0.184154 - 0.348210i) q^{68} +11.8066i q^{69} +(-0.242878 + 13.0804i) q^{70} +(-3.35096 + 5.80404i) q^{71} +(-2.70224 - 5.34750i) q^{72} +(6.33977 - 10.9808i) q^{73} +(5.09659 - 2.81768i) q^{74} -15.9379i q^{75} +(7.77299 - 3.94723i) q^{76} -13.8981i q^{77} +(-6.92123 - 12.5191i) q^{78} +(-0.342245 + 0.592786i) q^{79} +(-1.03000 + 13.8440i) q^{80} +(5.43385 - 9.41170i) q^{81} +(-4.73569 - 0.0879329i) q^{82} -2.58839i q^{83} +(-10.6616 + 5.63845i) q^{84} +(0.591962 - 0.341770i) q^{85} +(-0.0338367 + 1.82230i) q^{86} +11.7897 q^{87} +(0.820983 - 14.7247i) q^{88} +(-0.509054 - 0.881708i) q^{89} +(9.09893 - 5.03039i) q^{90} +(-10.3209 + 5.95877i) q^{91} +(10.4302 + 0.387471i) q^{92} +(6.81164 + 3.93270i) q^{93} +(0.746536 - 1.23932i) q^{94} +(7.34555 + 13.2247i) q^{95} +(-11.6287 + 5.34401i) q^{96} +(-8.90520 + 15.4243i) q^{97} +(0.0718010 + 0.129873i) q^{98} +(-9.56521 + 5.52247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} + q^{4} - 3 q^{6} - 8 q^{7} + 2 q^{8} + 12 q^{9}+O(q^{10}) $ 36 * q - q^2 + q^4 - 3 * q^6 - 8 * q^7 + 2 * q^8 + 12 * q^9	$ 36 q - q^{2} + q^{4} - 3 q^{6} - 8 q^{7} + 2 q^{8} + 12 q^{9} - 10 q^{10} - 10 q^{12} - 6 q^{15} - 3 q^{16} - 2 q^{17} - 20 q^{18} + 16 q^{20} - 9 q^{22} - 2 q^{23} + 21 q^{24} + 8 q^{25} - 24 q^{26} + 8 q^{28} - 28 q^{30} - 48 q^{31} + 9 q^{32} + 12 q^{33} + 10 q^{34} + 4 q^{36} - 30 q^{38} - 20 q^{39} - 10 q^{40} + 2 q^{41} - 16 q^{42} + 3 q^{44} + 8 q^{46} + 10 q^{47} + 39 q^{48} - 12 q^{49} - 26 q^{50} - 12 q^{52} - 11 q^{54} + 8 q^{55} - 8 q^{56} - 6 q^{57} + 24 q^{58} + 34 q^{60} + 42 q^{62} - 28 q^{63} + 46 q^{64} - 28 q^{65} + 33 q^{66} + 44 q^{68} + 8 q^{70} - 30 q^{71} - 36 q^{72} - 10 q^{73} + 6 q^{74} + 39 q^{76} - 32 q^{78} + 34 q^{79} + 8 q^{80} - 2 q^{81} + 27 q^{82} - 40 q^{84} + 46 q^{86} + 36 q^{87} + 66 q^{88} - 2 q^{89} + 30 q^{90} + 22 q^{92} - 4 q^{94} + 38 q^{95} - 62 q^{96} - 18 q^{97} + 39 q^{98}+O(q^{100}) $ 36 * q - q^2 + q^4 - 3 * q^6 - 8 * q^7 + 2 * q^8 + 12 * q^9 - 10 * q^10 - 10 * q^12 - 6 * q^15 - 3 * q^16 - 2 * q^17 - 20 * q^18 + 16 * q^20 - 9 * q^22 - 2 * q^23 + 21 * q^24 + 8 * q^25 - 24 * q^26 + 8 * q^28 - 28 * q^30 - 48 * q^31 + 9 * q^32 + 12 * q^33 + 10 * q^34 + 4 * q^36 - 30 * q^38 - 20 * q^39 - 10 * q^40 + 2 * q^41 - 16 * q^42 + 3 * q^44 + 8 * q^46 + 10 * q^47 + 39 * q^48 - 12 * q^49 - 26 * q^50 - 12 * q^52 - 11 * q^54 + 8 * q^55 - 8 * q^56 - 6 * q^57 + 24 * q^58 + 34 * q^60 + 42 * q^62 - 28 * q^63 + 46 * q^64 - 28 * q^65 + 33 * q^66 + 44 * q^68 + 8 * q^70 - 30 * q^71 - 36 * q^72 - 10 * q^73 + 6 * q^74 + 39 * q^76 - 32 * q^78 + 34 * q^79 + 8 * q^80 - 2 * q^81 + 27 * q^82 - 40 * q^84 + 46 * q^86 + 36 * q^87 + 66 * q^88 - 2 * q^89 + 30 * q^90 + 22 * q^92 - 4 * q^94 + 38 * q^95 - 62 * q^96 - 18 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.684248	+	1.23766i	0.483836	+	0.875159i
$2$	0.684248	+	1.23766i	0.483836	+	0.875159i
$3$	−1.95927	−	1.13118i	−1.13118	−	0.653089i	−0.186952	−	0.982369i	$-0.559861\pi$
$3$	−1.95927	−	1.13118i	−1.13118	−	0.653089i	−0.944232	+	0.329280i	$0.893194\pi$
$4$	−1.06361	+	1.69373i	−0.531805	+	0.846867i
$5$	−3.00559	−	1.73528i	−1.34414	−	0.776040i	−0.356729	−	0.934208i	$-0.616108\pi$
$5$	−3.00559	−	1.73528i	−1.34414	−	0.776040i	−0.987412	+	0.158168i	$0.949441\pi$
$6$	0.0593980	−	3.19892i	0.0242491	−	1.30595i
$7$	−2.66551			−1.00747			−0.503734	−	0.863859i	$-0.668041\pi$
$7$	−2.66551			−1.00747			−0.503734	+	0.863859i	$0.668041\pi$
$8$	−2.82404	−	0.157456i	−0.998449	−	0.0556692i
$9$	1.05915	+	1.83451i	0.353052	+	0.611503i
$10$	0.0911187	−	4.90726i	0.0288143	−	1.55181i
$11$			5.21404i			1.57209i	0.618168	+	0.786046i	$0.287875\pi$
$11$			5.21404i			1.57209i	−0.618168	+	0.786046i	$0.712125\pi$
$12$	3.99982	−	2.11534i	1.15465	−	0.610646i
$13$	3.87202	−	2.23551i	1.07390	−	0.620019i	0.144659	−	0.989482i	$-0.453791\pi$
$13$	3.87202	−	2.23551i	1.07390	−	0.620019i	0.929246	+	0.369462i	$0.120458\pi$
$14$	−1.82387	−	3.29900i	−0.487449	−	0.881694i
$15$	3.92584	+	6.79975i	1.01365	+	1.75569i
$16$	−1.73747	−	3.60295i	−0.434366	−	0.900736i
$17$	−0.0984768	+	0.170567i	−0.0238841	+	0.0413685i	−0.877720	−	0.479173i	$-0.840937\pi$
$17$	−0.0984768	+	0.170567i	−0.0238841	+	0.0413685i	0.853836	+	0.520542i	$0.174270\pi$
$18$	−1.54578	+	2.56613i	−0.364343	+	0.604843i
$19$	−3.73825	−	2.24177i	−0.857612	−	0.514297i
$19$	−3.73825	−	2.24177i	−0.857612	−	0.514297i
$20$	6.13588	−	3.24501i	1.37202	−	0.725606i
$21$	5.22245	+	3.01518i	1.13963	+	0.657966i
$22$	−6.45321	+	3.56769i	−1.37583	+	0.760635i
$23$	−2.60934	−	4.51951i	−0.544085	−	0.942383i	−0.998664	−	0.0516767i	$-0.983543\pi$
$23$	−2.60934	−	4.51951i	−0.544085	−	0.942383i	0.454579	−	0.890707i	$-0.349790\pi$
$24$	5.35494	+	3.50301i	1.09307	+	0.715049i
$25$	3.52239	+	6.10095i	0.704477	+	1.22019i
$26$	5.41623	+	3.26260i	1.06221	+	0.639849i
$27$			1.99471i			0.383882i
$28$	2.83506	−	4.51466i	0.535776	−	0.853191i
$29$	−4.51307	+	2.60562i	−0.838056	+	0.483852i	−0.856603	−	0.515976i	$-0.827429\pi$
$29$	−4.51307	+	2.60562i	−0.838056	+	0.483852i	0.0185472	+	0.999828i	$0.494096\pi$
$30$	−5.72954	+	9.51157i	−1.04607	+	1.73657i
$31$	−3.47662			−0.624420			−0.312210	−	0.950013i	$-0.601069\pi$
$31$	−3.47662			−0.624420			−0.312210	+	0.950013i	$0.601069\pi$
$32$	3.27037	−	4.61570i	0.578125	−	0.815948i
$33$	5.89804	−	10.2157i	1.02672	−	1.77833i
$34$	−0.278487	−	0.00517097i	−0.0477600	−	0.000886815i
$35$	8.01143	+	4.62540i	1.35418	+	0.781835i
$36$	−4.23370	−	0.157278i	−0.705616	−	0.0262130i
$37$		−	4.11792i		−	0.676983i	−0.940970	−	0.338491i	$-0.890083\pi$
$37$		−	4.11792i		−	0.676983i	0.940970	−	0.338491i	$-0.109917\pi$
$38$	0.216662	−	6.16061i	0.0351472	−	0.999382i
$39$	−10.1151			−1.61971
$40$	8.21468	+	5.37375i	1.29886	+	0.849664i
$41$	−1.67461	+	2.90051i	−0.261530	+	0.452983i	−0.966649	−	0.256106i	$-0.917560\pi$
$41$	−1.67461	+	2.90051i	−0.261530	+	0.452983i	0.705119	+	0.709089i	$0.250894\pi$
$42$	−0.158326	+	8.52675i	−0.0244302	+	1.31571i
$43$	1.11612	+	0.644390i	0.170206	+	0.0982686i	0.582683	−	0.812699i	$-0.302003\pi$
$43$	1.11612	+	0.644390i	0.170206	+	0.0982686i	−0.412477	+	0.910968i	$0.635336\pi$
$44$	−8.83119	−	5.54571i	−1.33135	−	0.836047i
$45$		−	7.35171i		−	1.09593i
$46$	3.80819	−	6.32195i	0.561487	−	0.932120i
$47$	−0.511521	−	0.885980i	−0.0746129	−	0.129233i	0.826305	−	0.563223i	$-0.190439\pi$
$47$	−0.511521	−	0.885980i	−0.0746129	−	0.129233i	−0.900918	+	0.433990i	$0.857105\pi$
$48$	−0.671432	+	9.02453i	−0.0969129	+	1.30258i
$49$	0.104934			0.0149906
$50$	−5.14073	+	8.53408i	−0.727008	+	1.20690i
$51$	0.385885	−	0.222791i	0.0540347	−	0.0311970i
$52$	−0.331960	+	8.93588i	−0.0460345	+	1.23918i
$53$	−8.19671	+	4.73237i	−1.12590	+	0.650041i	−0.942902	−	0.333071i	$-0.891915\pi$
$53$	−8.19671	+	4.73237i	−1.12590	+	0.650041i	−0.183003	+	0.983112i	$0.558582\pi$
$54$	−2.46877	+	1.36487i	−0.335958	+	0.185736i
$55$	9.04781	−	15.6713i	1.22001	−	2.11311i
$56$	7.52750	+	0.419701i	1.00591	+	0.0560849i
$57$	4.78838	+	8.62087i	0.634236	+	1.14186i
$58$	−6.31293	−	3.80276i	−0.828929	−	0.499327i
$59$	−1.43517	−	0.828597i	−0.186844	−	0.107874i	0.403661	−	0.914909i	$-0.367738\pi$
$59$	−1.43517	−	0.828597i	−0.186844	−	0.107874i	−0.590504	+	0.807035i	$0.701071\pi$
$60$	−15.6925	−	0.582963i	−2.02590	−	0.0752602i
$61$	1.70425	−	0.983950i	0.218207	−	0.125982i	−0.386913	−	0.922116i	$-0.626459\pi$
$61$	1.70425	−	0.983950i	0.218207	−	0.125982i	0.605120	+	0.796134i	$0.293125\pi$
$62$	−2.37887	−	4.30288i	−0.302117	−	0.546467i
$63$	−2.82319	−	4.88990i	−0.355688	−	0.616070i
$64$	7.95042	+	0.889326i	0.993802	+	0.111166i
$65$	−15.5169			−1.92464
$66$	16.6793	+	0.309703i	2.05308	+	0.0381218i
$67$	9.10257	−	5.25537i	1.11206	−	0.642046i	0.172695	−	0.984975i	$-0.444752\pi$
$67$	9.10257	−	5.25537i	1.11206	−	0.642046i	0.939361	+	0.342929i	$0.111419\pi$
$68$	−0.184154	−	0.348210i	−0.0223319	−	0.0422267i
$69$			11.8066i			1.42135i
$70$	−0.242878	+	13.0804i	−0.0290294	+	1.56340i
$71$	−3.35096	+	5.80404i	−0.397686	+	0.688812i	−0.993440	−	0.114355i	$-0.963520\pi$
$71$	−3.35096	+	5.80404i	−0.397686	+	0.688812i	0.595754	+	0.803167i	$0.296853\pi$
$72$	−2.70224	−	5.34750i	−0.318462	−	0.630209i
$73$	6.33977	−	10.9808i	0.742014	−	1.28521i	−0.209563	−	0.977795i	$-0.567204\pi$
$73$	6.33977	−	10.9808i	0.742014	−	1.28521i	0.951577	−	0.307410i	$-0.0994624\pi$
$74$	5.09659	−	2.81768i	0.592467	−	0.327549i
$75$		−	15.9379i		−	1.84035i
$76$	7.77299	−	3.94723i	0.891623	−	0.452778i
$77$		−	13.8981i		−	1.58383i
$78$	−6.92123	−	12.5191i	−0.783675	−	1.41750i
$79$	−0.342245	+	0.592786i	−0.0385056	+	0.0666937i	−0.884636	−	0.466282i	$-0.845593\pi$
$79$	−0.342245	+	0.592786i	−0.0385056	+	0.0666937i	0.846130	+	0.532976i	$0.178926\pi$
$80$	−1.03000	+	13.8440i	−0.115158	+	1.54780i
$81$	5.43385	−	9.41170i	0.603761	−	1.04574i
$82$	−4.73569	−	0.0879329i	−0.522970	−	0.00971057i
$83$		−	2.58839i		−	0.284112i	−0.989859	−	0.142056i	$-0.954629\pi$
$83$		−	2.58839i		−	0.284112i	0.989859	−	0.142056i	$-0.0453714\pi$
$84$	−10.6616	+	5.63845i	−1.16327	+	0.615206i
$85$	0.591962	−	0.341770i	0.0642073	−	0.0370701i
$86$	−0.0338367	+	1.82230i	−0.00364870	+	0.196503i
$87$	11.7897			1.26399
$88$	0.820983	−	14.7247i	0.0875171	−	1.56965i
$89$	−0.509054	−	0.881708i	−0.0539596	−	0.0934609i	0.837784	−	0.546002i	$-0.183851\pi$
$89$	−0.509054	−	0.881708i	−0.0539596	−	0.0934609i	−0.891744	+	0.452541i	$0.850518\pi$
$90$	9.09893	−	5.03039i	0.959112	−	0.530250i
$91$	−10.3209	+	5.95877i	−1.08192	+	0.624649i
$92$	10.4302	+	0.387471i	1.08742	+	0.0403967i
$93$	6.81164	+	3.93270i	0.706334	+	0.407802i
$94$	0.746536	−	1.23932i	0.0769993	−	0.127826i
$95$	7.34555	+	13.2247i	0.753637	+	1.35683i
$96$	−11.6287	+	5.34401i	−1.18685	+	0.545420i
$97$	−8.90520	+	15.4243i	−0.904186	+	1.56610i	−0.0821806	+	0.996617i	$0.526188\pi$
$97$	−8.90520	+	15.4243i	−0.904186	+	1.56610i	−0.822006	+	0.569479i	$0.807145\pi$
$98$	0.0718010	+	0.129873i	0.00725300	+	0.0131192i
$99$	−9.56521	+	5.52247i	−0.961339	+	0.555030i
$100$	−14.0798	−	0.523053i	−1.40798	−	0.0523053i
$101$	−1.83399	+	1.05885i	−0.182489	+	0.105360i	−0.588461	−	0.808525i	$-0.700266\pi$
$101$	−1.83399	+	1.05885i	−0.182489	+	0.105360i	0.405973	+	0.913885i	$0.366933\pi$
$102$	0.539780	+	0.325151i	0.0534462	+	0.0321947i
$103$	−0.333575			−0.0328681			−0.0164341	−	0.999865i	$-0.505231\pi$
$103$	−0.333575			−0.0328681			−0.0164341	+	0.999865i	$0.505231\pi$
$104$	−11.2867	+	5.70350i	−1.10676	+	0.559274i
$105$	−10.4644	−	18.1248i	−1.02122	−	1.76880i
$106$	−11.4657	−	6.90664i	−1.11364	−	0.670832i
$107$			1.88878i			0.182595i	0.995824	+	0.0912977i	$0.0291015\pi$
$107$			1.88878i			0.182595i	−0.995824	+	0.0912977i	$0.970899\pi$
$108$	−3.37850	−	2.12159i	−0.325097	−	0.204150i
$109$	5.01435	+	2.89504i	0.480288	+	0.277294i	0.720536	−	0.693417i	$-0.243896\pi$
$109$	5.01435	+	2.89504i	0.480288	+	0.277294i	−0.240249	+	0.970711i	$0.577229\pi$
$110$	25.5867	+	0.475097i	2.43959	+	0.0452987i
$111$	−4.65813	+	8.06812i	−0.442130	+	0.765792i
$112$	4.63123	+	9.60368i	0.437610	+	0.907462i
$113$	−6.51743			−0.613109			−0.306554	−	0.951853i	$-0.599176\pi$
$113$	−6.51743			−0.613109			−0.306554	+	0.951853i	$0.599176\pi$
$114$	−7.39328	+	11.8252i	−0.692444	+	1.10753i
$115$			18.1117i			1.68893i
$116$	0.386919	−	10.4153i	0.0359245	−	0.967036i
$117$	8.20213	+	4.73550i	0.758288	+	0.437798i
$118$	0.0435093	−	2.34322i	0.00400535	−	0.215711i
$119$	0.262491	−	0.454647i	0.0240625	−	0.0416775i
$120$	−10.0161	−	19.8209i	−0.914338	−	1.80940i
$121$	−16.1862			−1.47147
$122$	2.38393	+	1.43602i	0.215831	+	0.130011i
$123$	6.56201	−	3.78858i	0.591677	−	0.341605i
$124$	3.69777	−	5.88847i	0.332070	−	0.528801i
$125$		−	7.09649i		−	0.634730i
$126$	4.12028	−	6.84005i	0.367064	−	0.609360i
$127$	−1.13140	−	1.95965i	−0.100396	−	0.173891i	0.811452	−	0.584419i	$-0.198678\pi$
$127$	−1.13140	−	1.95965i	−0.100396	−	0.173891i	−0.911848	+	0.410529i	$0.865344\pi$
$128$	4.33937	+	10.4484i	0.383550	+	0.923520i
$129$	−1.45785	−	2.52507i	−0.128356	−	0.222320i
$130$	−10.6174	−	19.2047i	−0.931210	−	1.68436i
$131$	−16.8116	−	9.70621i	−1.46884	−	0.848035i	−0.469450	−	0.882959i	$-0.655548\pi$
$131$	−16.8116	−	9.70621i	−1.46884	−	0.848035i	−0.999390	+	0.0349239i	$0.988881\pi$
$132$	11.0295	+	20.8552i	0.959991	+	1.81521i
$133$	9.96433	+	5.97545i	0.864017	+	0.518137i
$134$	12.7328	+	7.66993i	1.09995	+	0.662581i
$135$	3.46138	−	5.99528i	0.297908	−	0.515991i
$136$	0.304959	−	0.466182i	0.0261501	−	0.0399748i
$137$	6.09173	+	10.5512i	0.520452	+	0.901448i	0.999717	+	0.0237786i	$0.00756968\pi$
$137$	6.09173	+	10.5512i	0.520452	+	0.901448i	−0.479266	+	0.877670i	$0.659097\pi$
$138$	−14.6125	+	8.07863i	−1.24390	+	0.687698i
$139$	5.43079	−	3.13547i	0.460634	−	0.265947i	−0.251677	−	0.967811i	$-0.580982\pi$
$139$	5.43079	−	3.13547i	0.460634	−	0.265947i	0.712311	+	0.701864i	$0.247649\pi$
$140$	−16.3552	+	8.64960i	−1.38227	+	0.731025i
$141$			2.31450i			0.194916i
$142$	−9.47632	−	0.175958i	−0.795235	−	0.0147660i
$143$	11.6560	+	20.1889i	0.974727	+	1.68828i
$144$	4.76939	−	7.00347i	0.397449	−	0.583623i
$145$	18.0859			1.50195
$146$	17.9285	+	0.332898i	1.48377	+	0.0275509i
$147$	−0.205594	−	0.118700i	−0.0169571	−	0.00979021i
$148$	6.97467	+	4.37987i	0.573314	+	0.360023i
$149$	15.6101	+	9.01250i	1.27883	+	0.738333i	0.976633	−	0.214913i	$-0.0689467\pi$
$149$	15.6101	+	9.01250i	1.27883	+	0.738333i	0.302197	+	0.953246i	$0.402280\pi$
$150$	19.7257	−	10.9054i	1.61059	−	0.890426i
$151$	6.91725			0.562918			0.281459	−	0.959573i	$-0.409182\pi$
$151$	6.91725			0.562918			0.281459	+	0.959573i	$0.409182\pi$
$152$	10.2040	+	6.91945i	0.827652	+	0.561242i
$153$	−0.417209			−0.0337293
$154$	17.2011	−	9.50972i	1.38610	−	0.766315i
$155$	10.4493	+	6.03291i	0.839309	+	0.484575i
$156$	10.7585	−	17.1323i	0.861371	−	1.37168i
$157$	−16.4732	−	9.51082i	−1.31471	−	0.759046i	−0.331834	−	0.943338i	$-0.607668\pi$
$157$	−16.4732	−	9.51082i	−1.31471	−	0.759046i	−0.982872	+	0.184292i	$0.941001\pi$
$158$	−0.967849	−	0.0179711i	−0.0769979	−	0.00142971i
$159$	21.4127			1.69814
$160$	−17.8389	+	8.19791i	−1.41029	+	0.648101i
$161$	6.95522	+	12.0468i	0.548148	+	0.949421i
$162$	15.3666	+	0.285329i	1.20731	+	0.0224176i
$163$		−	11.0739i		−	0.867375i	−0.901063	−	0.433688i	$-0.857212\pi$
$163$		−	11.0739i		−	0.867375i	0.901063	−	0.433688i	$-0.142788\pi$
$164$	−3.13155	−	5.92135i	−0.244533	−	0.462380i
$165$	−35.4542	+	20.4695i	−2.76010	+	1.59355i
$166$	3.20355	−	1.77110i	0.248643	−	0.137464i
$167$	−0.136543	−	0.236499i	−0.0105660	−	0.0183008i	0.860694	−	0.509123i	$-0.170030\pi$
$167$	−0.136543	−	0.236499i	−0.0105660	−	0.0183008i	−0.871260	+	0.490822i	$0.836697\pi$
$168$	−14.2736	−	9.33730i	−1.10124	−	0.720388i
$169$	3.49502	−	6.05355i	0.268848	−	0.465658i
$170$	0.828044	+	0.498794i	0.0635080	+	0.0382557i
$171$	0.153162	−	9.23223i	0.0117126	−	0.706006i
$172$	−2.27854	+	1.20502i	−0.173737	+	0.0918822i
$173$	−13.6439	−	7.87732i	−1.03733	−	0.598902i	−0.118253	−	0.992984i	$-0.537729\pi$
$173$	−13.6439	−	7.87732i	−1.03733	−	0.598902i	−0.919075	+	0.394082i	$0.871063\pi$
$174$	8.06711	+	14.5917i	0.611566	+	1.10619i
$175$	−9.38895	−	16.2621i	−0.709738	−	1.22930i
$176$	18.7859	−	9.05921i	1.41604	−	0.682864i
$177$	1.87459	+	3.24689i	0.140903	+	0.244051i
$178$	0.742936	−	1.23334i	0.0556854	−	0.0924430i
$179$		−	19.4516i		−	1.45388i	−0.686701	−	0.726940i	$-0.740942\pi$
$179$		−	19.4516i		−	1.45388i	0.686701	−	0.726940i	$-0.259058\pi$
$180$	12.4518	+	7.81936i	0.928106	+	0.582821i
$181$	−18.1290	+	10.4668i	−1.34752	+	0.777990i	−0.987897	−	0.155109i	$-0.950427\pi$
$181$	−18.1290	+	10.4668i	−1.34752	+	0.777990i	−0.359620	+	0.933099i	$0.617094\pi$
$182$	−14.4370	−	8.69650i	−1.07014	−	0.644627i
$183$	−4.45211			−0.329110
$184$	6.65726	+	13.1741i	0.490780	+	0.971211i
$185$	−7.14575	+	12.3768i	−0.525366	+	0.909960i
$186$	−0.206504	+	11.1214i	−0.0151416	+	0.815464i
$187$	−0.889342	−	0.513462i	−0.0650352	−	0.0375481i
$188$	2.04467	+	0.0759577i	0.149123	+	0.00553978i
$189$		−	5.31691i		−	0.386748i
$190$	−11.3416	+	18.1403i	−0.822804	+	1.31604i
$191$	−12.5169			−0.905694			−0.452847	−	0.891588i	$-0.649592\pi$
$191$	−12.5169			−0.905694			−0.452847	+	0.891588i	$0.649592\pi$
$192$	−14.5710	−	10.7358i	−1.05157	−	0.774790i
$193$	−11.6311	+	20.1457i	−0.837225	+	1.45012i	0.0549812	+	0.998487i	$0.482490\pi$
$193$	−11.6311	+	20.1457i	−0.837225	+	1.45012i	−0.892206	+	0.451629i	$0.850843\pi$
$194$	−25.1834	−	0.467608i	−1.80806	−	0.0335723i
$195$	30.4018	+	17.5525i	2.17712	+	1.25696i
$196$	−0.111609	+	0.177731i	−0.00797208	+	0.0126950i
$197$			2.21331i			0.157692i	0.996887	+	0.0788459i	$0.0251235\pi$
$197$			2.21331i			0.157692i	−0.996887	+	0.0788459i	$0.974876\pi$
$198$	−13.3799	−	8.05974i	−0.950870	−	0.572781i
$199$	5.03045	+	8.71299i	0.356599	+	0.617647i	0.987390	−	0.158305i	$-0.0506030\pi$
$199$	5.03045	+	8.71299i	0.356599	+	0.617647i	−0.630791	+	0.775952i	$0.717270\pi$
$200$	−8.98673	−	17.7840i	−0.635458	−	1.25752i
$201$	−23.7792			−1.67725
$202$	−2.56540	−	1.54534i	−0.180501	−	0.108730i
$203$	12.0296	−	6.94530i	0.844314	−	0.487465i
$204$	−0.0330831	+	0.890549i	−0.00231628	+	0.0623509i
$205$	10.0664	−	5.81182i	0.703066	−	0.405915i
$206$	−0.228248	−	0.412853i	−0.0159028	−	0.0287648i
$207$	5.52739	−	9.57372i	0.384180	−	0.665420i
$208$	−14.7819	−	10.0665i	−1.02494	−	0.697989i
$209$	11.6887	−	19.4914i	0.808521	−	1.34825i
$210$	15.2721	−	25.3532i	1.05388	−	1.74954i
$211$	−3.71224	−	2.14326i	−0.255561	−	0.147548i	0.366747	−	0.930321i	$-0.380472\pi$
$211$	−3.71224	−	2.14326i	−0.255561	−	0.147548i	−0.622308	+	0.782772i	$0.713805\pi$
$212$	0.702728	−	18.9164i	0.0482636	−	1.29919i
$213$	13.1309	−	7.58111i	0.899712	−	0.519449i
$214$	−2.33767	+	1.29239i	−0.159800	+	0.0883463i
$215$	−2.23639	−	3.87355i	−0.152521	−	0.264174i
$216$	0.314079	−	5.63314i	0.0213704	−	0.383287i
$217$	9.26697			0.629083
$218$	−0.152017	+	8.18699i	−0.0102959	+	0.554493i
$219$	−24.8426	+	14.3429i	−1.67871	+	0.969203i
$220$	16.9196	+	31.9927i	1.14072	+	2.15695i
$221$			0.880584i			0.0592345i
$222$	−13.1729	−	0.244596i	−0.884108	−	0.0164162i
$223$	8.76999	−	15.1901i	0.587282	−	1.01720i	−0.407305	−	0.913292i	$-0.633531\pi$
$223$	8.76999	−	15.1901i	0.587282	−	1.01720i	0.994587	−	0.103910i	$-0.0331353\pi$
$224$	−8.71719	+	12.3032i	−0.582442	+	0.822041i
$225$	−7.46150	+	12.9237i	−0.497433	+	0.861580i
$226$	−4.45954	−	8.06637i	−0.296644	−	0.536567i
$227$			3.97290i			0.263691i	0.991270	+	0.131845i	$0.0420902\pi$
$227$			3.97290i			0.263691i	−0.991270	+	0.131845i	$0.957910\pi$
$228$	−19.6944	−	1.05901i	−1.30429	−	0.0701348i
$229$			11.3941i			0.752940i	0.926429	+	0.376470i	$0.122862\pi$
$229$			11.3941i			0.752940i	−0.926429	+	0.376470i	$0.877138\pi$
$230$	−22.4162	+	12.3929i	−1.47808	+	0.817165i
$231$	−15.7213	+	27.2300i	−1.03438	+	1.79160i
$232$	13.1554	−	6.64777i	0.863692	−	0.436447i
$233$	11.2901	−	19.5550i	0.739638	−	1.28109i	−0.213020	−	0.977048i	$-0.568330\pi$
$233$	11.2901	−	19.5550i	0.739638	−	1.28109i	0.952658	−	0.304043i	$-0.0983367\pi$
$234$	−0.248659	+	13.3917i	−0.0162554	+	0.875444i
$235$			3.55052i			0.231611i
$236$	2.92989	−	1.54949i	0.190719	−	0.100864i
$237$	1.34110	−	0.774285i	0.0871138	−	0.0502952i
$238$	0.742308	+	0.0137833i	0.0481167	+	0.000893437i
$239$	−14.7945			−0.956977			−0.478489	−	0.878094i	$-0.658815\pi$
$239$	−14.7945			−0.956977			−0.478489	+	0.878094i	$0.658815\pi$
$240$	17.6781	−	25.9589i	1.14112	−	1.67564i
$241$	−2.20931	−	3.82665i	−0.142314	−	0.246496i	0.786053	−	0.618159i	$-0.212121\pi$
$241$	−2.20931	−	3.82665i	−0.142314	−	0.246496i	−0.928368	+	0.371663i	$0.878788\pi$
$242$	−11.0754	−	20.0330i	−0.711952	−	1.28777i
$243$	−16.1103	+	9.30130i	−1.03348	+	0.596679i
$244$	−0.146110	+	3.93309i	−0.00935377	+	0.251790i
$245$	−0.315389	−	0.182090i	−0.0201495	−	0.0116333i
$246$	9.17902	+	5.52922i	0.585233	+	0.352530i
$247$	−19.4861	−	0.323273i	−1.23987	−	0.0205694i
$248$	9.81813	+	0.547416i	0.623452	+	0.0347610i
$249$	−2.92794	+	5.07135i	−0.185551	+	0.321384i
$250$	8.78305	−	4.85576i	0.555489	−	0.307105i
$251$	19.9778	−	11.5342i	1.26099	−	0.728033i	0.287724	−	0.957713i	$-0.407101\pi$
$251$	19.9778	−	11.5342i	1.26099	−	0.728033i	0.973266	+	0.229680i	$0.0737681\pi$
$252$	11.2850	+	0.419226i	0.710886	+	0.0264087i
$253$	23.5649	−	13.6052i	1.48151	−	0.855352i
$254$	1.65122	−	2.74118i	0.103607	−	0.171997i
$255$	−1.54642			−0.0968404
$256$	−9.96243	+	12.5200i	−0.622652	+	0.782499i
$257$	−7.26634	−	12.5857i	−0.453262	−	0.785072i	0.545325	−	0.838225i	$-0.316406\pi$
$257$	−7.26634	−	12.5857i	−0.453262	−	0.785072i	−0.998586	+	0.0531527i	$0.983073\pi$
$258$	2.12765	−	3.53209i	0.132462	−	0.219899i
$259$			10.9764i			0.682038i
$260$	16.5040	−	26.2816i	1.02353	−	1.62991i
$261$	−9.56007	−	5.51951i	−0.591754	−	0.341649i
$262$	0.509669	−	27.4486i	0.0314874	−	1.69578i
$263$	2.23559	−	3.87216i	0.137852	−	0.238767i	−0.788831	−	0.614610i	$-0.789313\pi$
$263$	2.23559	−	3.87216i	0.137852	−	0.238767i	0.926683	+	0.375843i	$0.122647\pi$
$264$	−18.2648	+	27.9209i	−1.12412	+	1.71841i
$265$	32.8479			2.01783
$266$	−0.577514	+	16.4211i	−0.0354097	+	1.00684i
$267$			2.30334i			0.140962i
$268$	−0.780391	+	21.0070i	−0.0476699	+	1.28321i
$269$	22.5239	+	13.0042i	1.37330	+	0.792877i	0.991343	−	0.131301i	$-0.0419153\pi$
$269$	22.5239	+	13.0042i	1.37330	+	0.792877i	0.381962	+	0.924178i	$0.375249\pi$
$270$	9.78856	+	0.181755i	0.595713	+	0.0110613i
$271$	1.64945	−	2.85693i	0.100197	−	0.173546i	−0.811569	−	0.584257i	$-0.801386\pi$
$271$	1.64945	−	2.85693i	0.100197	−	0.173546i	0.911766	+	0.410711i	$0.134719\pi$
$272$	0.785643	+	0.0584525i	0.0476366	+	0.00354420i
$273$	26.9619			1.63181
$274$	−8.89054	+	14.7591i	−0.537097	+	0.891631i
$275$	−31.8106	+	18.3659i	−1.91825	+	1.10750i
$276$	−19.9972	−	12.5576i	−1.20369	−	0.755879i
$277$		−	23.8677i		−	1.43407i	−0.697035	−	0.717037i	$-0.745498\pi$
$277$		−	23.8677i		−	1.43407i	0.697035	−	0.717037i	$-0.254502\pi$
$278$	7.59665	+	4.57604i	0.455617	+	0.274453i
$279$	−3.68228	−	6.37790i	−0.220453	−	0.381835i
$280$	−21.8963	−	14.3238i	−1.30855	−	0.856009i
$281$	−11.7473	−	20.3469i	−0.700785	−	1.21379i	−0.968191	−	0.250211i	$-0.919500\pi$
$281$	−11.7473	−	20.3469i	−0.700785	−	1.21379i	0.267407	−	0.963584i	$-0.413833\pi$
$282$	−2.86456	+	1.58369i	−0.170582	+	0.0943073i
$283$	−19.9279	−	11.5054i	−1.18459	−	0.683924i	−0.227519	−	0.973774i	$-0.573061\pi$
$283$	−19.9279	−	11.5054i	−1.18459	−	0.683924i	−0.957072	+	0.289849i	$0.906395\pi$
$284$	−6.26637	−	11.8489i	−0.371841	−	0.703101i
$285$	0.567708	−	34.2200i	0.0336281	−	2.02702i
$286$	−17.0113	+	28.2404i	−1.00590	+	1.66989i
$287$	4.46368	−	7.73132i	0.263483	−	0.456366i
$288$	11.9314	+	1.11078i	0.703063	+	0.0654535i
$289$	8.48060	+	14.6888i	0.498859	+	0.864049i
$290$	12.3752	+	22.3842i	0.726699	+	1.31445i
$291$	34.8954	−	20.1468i	2.04560	−	1.18103i
$292$	11.8555	+	22.4172i	0.693791	+	1.31187i
$293$			7.01385i			0.409753i	0.978788	+	0.204877i	$0.0656793\pi$
$293$			7.01385i			0.409753i	−0.978788	+	0.204877i	$0.934321\pi$
$294$	0.00623288	−	0.335676i	0.000363509	−	0.0195770i
$295$	2.87569	+	4.98085i	0.167429	+	0.289996i
$296$	−0.648393	+	11.6292i	−0.0376871	+	0.675933i
$297$	−10.4005			−0.603498
$298$	−0.473242	+	25.4868i	−0.0274142	+	1.47641i
$299$	−20.2068	−	11.6664i	−1.16859	−	0.674687i
$300$	26.9945	+	16.9517i	1.55853	+	0.978706i
$301$	−2.97502	−	1.71763i	−0.171477	−	0.0990024i
$302$	4.73311	+	8.56121i	0.272360	+	0.492642i
$303$	4.79103			0.275238
$304$	−1.58189	+	17.3637i	−0.0907275	+	0.995876i
$305$	−6.82971			−0.391068
$306$	−0.285474	−	0.516363i	−0.0163195	−	0.0295185i
$307$	−9.41068	−	5.43326i	−0.537096	−	0.310092i	0.206805	−	0.978382i	$-0.433693\pi$
$307$	−9.41068	−	5.43326i	−0.537096	−	0.310092i	−0.743901	+	0.668290i	$0.767027\pi$
$308$	23.5396	+	14.7821i	1.34129	+	0.842290i
$309$	0.653563	+	0.377335i	0.0371799	+	0.0214658i
$310$	−0.316786	+	17.0607i	−0.0179922	+	0.968983i
$311$	14.2159			0.806109			0.403054	−	0.915176i	$-0.367949\pi$
$311$	14.2159			0.806109			0.403054	+	0.915176i	$0.367949\pi$
$312$	28.5655	+	1.59269i	1.61720	+	0.0901681i
$313$	−12.0949	−	20.9490i	−0.683646	−	1.18411i	−0.973860	−	0.227148i	$-0.927060\pi$
$313$	−12.0949	−	20.9490i	−0.683646	−	1.18411i	0.290214	−	0.956962i	$-0.406273\pi$
$314$	0.499409	−	26.8960i	0.0281833	−	1.51783i
$315$			19.5961i			1.10411i
$316$	−0.640006	−	1.21017i	−0.0360032	−	0.0680771i
$317$	0.0813466	−	0.0469655i	0.00456888	−	0.00263784i	−0.497714	−	0.867341i	$-0.665827\pi$
$317$	0.0813466	−	0.0469655i	0.00456888	−	0.00263784i	0.502283	+	0.864703i	$0.332494\pi$
$318$	14.6516	+	26.5017i	0.821622	+	1.48614i
$319$	−13.5858	−	23.5313i	−0.760659	−	1.31750i
$320$	−22.3525	−	16.4691i	−1.24954	−	0.920653i
$321$	2.13656	−	3.70063i	0.119251	−	0.206549i
$322$	−10.1508	+	16.8512i	−0.565680	+	0.939081i
$323$	0.750502	−	0.416859i	0.0417590	−	0.0231946i
$324$	10.1614	+	19.2139i	0.564523	+	1.06744i
$325$	27.2775	+	15.7487i	1.51308	+	0.873579i
$326$	13.7057	−	7.57729i	0.759091	−	0.419668i
$327$	−6.54964	−	11.3443i	−0.362196	−	0.627342i
$328$	5.18587	−	7.92747i	0.286342	−	0.437721i
$329$	1.36346	+	2.36159i	0.0751701	+	0.130198i
$330$	−49.5937	−	29.8741i	−2.73004	−	1.64451i
$331$			36.1372i			1.98628i	0.116940	+	0.993139i	$0.462691\pi$
$331$			36.1372i			1.98628i	−0.116940	+	0.993139i	$0.537309\pi$
$332$	4.38404	+	2.75304i	0.240605	+	0.151093i
$333$	7.55437	−	4.36152i	0.413977	−	0.239010i
$334$	0.199277	−	0.330818i	0.0109039	−	0.0181015i
$335$	−36.4782			−1.99301
$336$	1.78971	−	24.0550i	0.0976366	−	1.31231i
$337$	1.23185	−	2.13362i	0.0671029	−	0.116226i	−0.830522	−	0.556986i	$-0.811958\pi$
$337$	1.23185	−	2.13362i	0.0671029	−	0.116226i	0.897625	+	0.440760i	$0.145291\pi$
$338$	9.88371	+	0.183522i	0.537603	+	0.00998228i
$339$	12.7694	+	7.37242i	0.693539	+	0.400415i
$340$	−0.0507507	+	1.36614i	−0.00275234	+	0.0740891i
$341$		−	18.1273i		−	0.981646i
$342$	11.5312	−	6.12757i	0.623534	−	0.331341i
$343$	18.3789			0.992365
$344$	−3.05050	−	1.99552i	−0.164472	−	0.107591i
$345$	20.4877	−	35.4858i	1.10302	−	1.91049i
$346$	0.413635	−	22.2766i	0.0222371	−	1.19760i
$347$	−12.8117	−	7.39683i	−0.687767	−	0.397082i	0.115008	−	0.993365i	$-0.463311\pi$
$347$	−12.8117	−	7.39683i	−0.687767	−	0.397082i	−0.802775	+	0.596282i	$0.796644\pi$
$348$	−12.5397	+	19.9687i	−0.672198	+	1.07043i
$349$		−	9.78087i		−	0.523558i	−0.965128	−	0.261779i	$-0.915691\pi$
$349$		−	9.78087i		−	0.523558i	0.965128	−	0.261779i	$-0.0843091\pi$
$350$	13.7026	−	22.7477i	0.732437	−	1.21591i
$351$	4.45919	+	7.72355i	0.238014	+	0.412253i
$352$	24.0664	+	17.0518i	1.28275	+	0.908866i
$353$	13.7959			0.734283			0.367142	−	0.930165i	$-0.380336\pi$
$353$	13.7959			0.734283			0.367142	+	0.930165i	$0.380336\pi$
$354$	−2.73586	+	4.54179i	−0.145409	+	0.241393i
$355$	20.1432	−	11.6297i	1.06909	−	0.617241i
$356$	2.03481	+	0.0755914i	0.107845	+	0.00400634i
$357$	−1.02858	+	0.593851i	−0.0544382	+	0.0314299i
$358$	24.0745	−	13.3097i	1.27238	−	0.703440i
$359$	−16.1530	+	27.9778i	−0.852523	+	1.47661i	0.0264020	+	0.999651i	$0.491595\pi$
$359$	−16.1530	+	27.9778i	−0.852523	+	1.47661i	−0.878925	+	0.476961i	$0.841738\pi$
$360$	−1.15757	+	20.7615i	−0.0610095	+	1.09423i
$361$	8.94896	+	16.7606i	0.470998	+	0.882134i
$362$	−25.3591	−	15.2757i	−1.33284	−	0.802872i
$363$	31.7131	+	18.3096i	1.66451	+	0.961004i
$364$	0.884841	−	23.8187i	0.0463783	−	1.24844i
$365$	−38.1095	+	22.0025i	−1.99474	+	1.15166i
$366$	−3.04635	−	5.51021i	−0.159235	−	0.288023i
$367$	−2.26422	−	3.92174i	−0.118191	−	0.204713i	0.800860	−	0.598852i	$-0.204376\pi$
$367$	−2.26422	−	3.92174i	−0.118191	−	0.204713i	−0.919051	+	0.394139i	$0.871043\pi$
$368$	−11.7499	+	17.2538i	−0.612506	+	0.899417i
$369$	−7.09468			−0.369334
$370$	−20.2077	−	0.375220i	−1.05055	−	0.0195068i
$371$	21.8484	−	12.6142i	1.13431	−	0.654896i
$372$	−13.9059	+	7.35424i	−0.720986	+	0.381300i
$373$			26.4723i			1.37068i	0.728222	+	0.685341i	$0.240347\pi$
$373$			26.4723i			1.37068i	−0.728222	+	0.685341i	$0.759653\pi$
$374$	0.0269617	−	1.45204i	0.00139415	−	0.0750832i
$375$	−8.02744	+	13.9039i	−0.414535	+	0.717996i
$376$	1.30505	+	2.58258i	0.0673029	+	0.133187i
$377$	−11.6498	+	20.1780i	−0.599995	+	1.03922i
$378$	6.58054	−	3.63808i	0.338466	−	0.187123i
$379$			21.2548i			1.09179i	0.837854	+	0.545894i	$0.183810\pi$
$379$			21.2548i			1.09179i	−0.837854	+	0.545894i	$0.816190\pi$
$380$	−30.2120	−	1.62456i	−1.54984	−	0.0833383i
$381$			5.11930i			0.262270i
$382$	−8.56468	−	15.4917i	−0.438207	−	0.792626i
$383$	0.601501	−	1.04183i	0.0307353	−	0.0532351i	−0.850249	−	0.526381i	$-0.823548\pi$
$383$	0.601501	−	1.04183i	0.0307353	−	0.0532351i	0.880984	+	0.473146i	$0.156882\pi$
$384$	3.31712	−	25.3799i	0.169276	−	1.29516i
$385$	−24.1170	+	41.7719i	−1.22912	+	2.12889i
$386$	−32.8920	−	0.610744i	−1.67416	−	0.0310860i
$387$			2.73004i			0.138776i
$388$	−16.6529	−	31.4884i	−0.845424	−	1.59858i
$389$	7.63203	−	4.40635i	0.386959	−	0.223411i	−0.293883	−	0.955842i	$-0.594947\pi$
$389$	7.63203	−	4.40635i	0.386959	−	0.223411i	0.680842	+	0.732431i	$0.261614\pi$
$390$	−0.921675	+	49.6375i	−0.0466708	+	2.51349i
$391$	1.02784			0.0519800
$392$	−0.296339	−	0.0165226i	−0.0149674	−	0.000834515i
$393$	21.9590	+	38.0341i	1.10769	+	1.91857i
$394$	−2.73933	+	1.51445i	−0.138005	+	0.0762970i
$395$	2.05730	−	1.18778i	0.103514	−	0.0597638i
$396$	0.820054	−	22.0747i	0.0412092	−	1.10929i
$397$	20.6506	+	11.9226i	1.03642	+	0.598378i	0.918818	−	0.394682i	$-0.129145\pi$
$397$	20.6506	+	11.9226i	1.03642	+	0.598378i	0.117604	+	0.993061i	$0.462479\pi$
$398$	−7.34166	+	12.1878i	−0.368004	+	0.610921i
$399$	−12.7635	−	22.9790i	−0.638972	−	1.15039i
$400$	15.8614	−	23.2912i	0.793068	−	1.16456i
$401$	9.50466	−	16.4626i	0.474640	−	0.822101i	−0.524938	−	0.851140i	$-0.675911\pi$
$401$	9.50466	−	16.4626i	0.474640	−	0.822101i	0.999578	+	0.0290394i	$0.00924483\pi$
$402$	−16.2708	−	29.4306i	−0.811516	−	1.46786i
$403$	−13.4616	+	7.77203i	−0.670568	+	0.387153i
$404$	0.157233	−	4.23250i	0.00782265	−	0.210575i
$405$	−32.6638	+	18.8585i	−1.62308	+	0.937085i
$406$	16.8272	+	10.1363i	0.835118	+	0.503055i
$407$	21.4710			1.06428
$408$	−1.12483	+	0.568410i	−0.0556876	+	0.0281405i
$409$	11.5735	+	20.0459i	0.572274	+	0.991208i	0.996332	+	0.0855729i	$0.0272720\pi$
$409$	11.5735	+	20.0459i	0.572274	+	0.991208i	−0.424058	+	0.905635i	$0.639395\pi$
$410$	14.0810	+	8.48204i	0.695409	+	0.418898i
$411$		−	27.5635i		−	1.35961i
$412$	0.354794	−	0.564987i	0.0174794	−	0.0278349i
$413$	3.82546	+	2.20863i	0.188239	+	0.108680i
$414$	15.6311	+	0.290241i	0.768228	+	0.0142646i
$415$	−4.49157	+	7.77964i	−0.220483	+	0.381887i
$416$	2.34448	−	25.1830i	0.114948	−	1.23470i
$417$	−14.1872			−0.694748
$418$	32.1216	+	1.12968i	1.57112	+	0.0552546i
$419$			0.189740i			0.00926943i	0.999989	+	0.00463471i	$0.00147528\pi$
$419$			0.189740i			0.00926943i	−0.999989	+	0.00463471i	$0.998525\pi$
$420$	41.8286	+	1.55389i	2.04103	+	0.0758222i
$421$	−13.9681	−	8.06450i	−0.680765	−	0.393040i	0.119378	−	0.992849i	$-0.461910\pi$
$421$	−13.9681	−	8.06450i	−0.680765	−	0.393040i	−0.800143	+	0.599809i	$0.795243\pi$
$422$	0.112542	−	6.06102i	0.00547845	−	0.295046i
$423$	1.08356	−	1.87678i	0.0526844	−	0.0912521i
$424$	23.8930	−	12.0738i	1.16035	−	0.586355i
$425$	−1.38749			−0.0673033
$426$	18.3676	+	11.0642i	0.889914	+	0.536063i
$427$	−4.54269	+	2.62273i	−0.219836	+	0.126923i
$428$	−3.19909	−	2.00893i	−0.154634	−	0.0971052i
$429$		−	52.7405i		−	2.54634i
$430$	3.26389	−	5.41836i	0.157399	−	0.261297i
$431$	−0.717723	−	1.24313i	−0.0345715	−	0.0598796i	0.848222	−	0.529641i	$-0.177673\pi$
$431$	−0.717723	−	1.24313i	−0.0345715	−	0.0598796i	−0.882793	+	0.469761i	$0.844340\pi$
$432$	7.18683	−	3.46574i	0.345776	−	0.166745i
$433$	−6.72025	−	11.6398i	−0.322955	−	0.559374i	0.658142	−	0.752894i	$-0.271343\pi$
$433$	−6.72025	−	11.6398i	−0.322955	−	0.559374i	−0.981096	+	0.193520i	$0.938009\pi$
$434$	6.34090	+	11.4694i	0.304373	+	0.550547i
$435$	−35.4352	−	20.4585i	−1.69899	−	0.980910i
$436$	−10.2367	+	5.41379i	−0.490251	+	0.259273i
$437$	−0.377332	+	22.7446i	−0.0180502	+	1.08802i
$438$	−34.7501	−	20.9326i	−1.66043	−	1.00020i
$439$	−4.56802	+	7.91204i	−0.218020	+	0.377621i	−0.954202	−	0.299162i	$-0.903293\pi$
$439$	−4.56802	+	7.91204i	−0.218020	+	0.377621i	0.736183	+	0.676783i	$0.236626\pi$
$440$	−28.0189	+	42.8317i	−1.33575	+	2.04192i
$441$	0.111142	+	0.192503i	0.00529246	+	0.00916681i
$442$	−1.08986	+	0.602538i	−0.0518396	+	0.0286598i
$443$	9.11358	−	5.26173i	0.432999	−	0.249992i	−0.267624	−	0.963523i	$-0.586239\pi$
$443$	9.11358	−	5.26173i	0.432999	−	0.249992i	0.700624	+	0.713531i	$0.252905\pi$
$444$	−8.71080	−	16.4710i	−0.413396	−	0.781677i
$445$			3.53340i			0.167499i
$446$	24.8010	+	0.460508i	1.17436	+	0.0218057i
$447$	−20.3896	−	35.3158i	−0.964395	−	1.67038i
$448$	−21.1919	−	2.37051i	−1.00122	−	0.111996i
$449$	24.1747			1.14087			0.570437	−	0.821341i	$-0.306774\pi$
$449$	24.1747			1.14087			0.570437	+	0.821341i	$0.306774\pi$
$450$	−21.1007	−	0.391800i	−0.994695	−	0.0184696i
$451$	−15.1234	−	8.73147i	−0.712131	−	0.411149i
$452$	6.93201	−	11.0388i	0.326054	−	0.519221i
$453$	−13.5527	−	7.82468i	−0.636763	−	0.367636i
$454$	−4.91710	+	2.71845i	−0.230771	+	0.127583i
$455$	41.3605			1.93901
$456$	−12.1652	−	25.0996i	−0.569686	−	1.17540i
$457$	9.03975			0.422862			0.211431	−	0.977393i	$-0.432188\pi$
$457$	9.03975			0.422862			0.211431	+	0.977393i	$0.432188\pi$
$458$	−14.1020	+	7.79636i	−0.658942	+	0.364300i
$459$	−0.340231	−	0.196433i	−0.0158806	−	0.00916869i
$460$	−30.6765	−	19.2638i	−1.43030	−	0.898181i
$461$	−23.8083	−	13.7457i	−1.10886	−	0.640203i	−0.170329	−	0.985387i	$-0.554483\pi$
$461$	−23.8083	−	13.7457i	−1.10886	−	0.640203i	−0.938535	+	0.345184i	$0.887816\pi$
$462$	−44.4588	−	0.825517i	−2.06841	−	0.0384065i
$463$	−17.4960			−0.813109			−0.406554	−	0.913627i	$-0.633270\pi$
$463$	−17.4960			−0.813109			−0.406554	+	0.913627i	$0.633270\pi$
$464$	17.2292	+	11.7332i	0.799846	+	0.544698i
$465$	−13.6487	−	23.6402i	−0.632942	−	1.09629i
$466$	31.9277	+	0.592837i	1.47902	+	0.0274627i
$467$			39.7794i			1.84077i	0.391013	+	0.920385i	$0.372125\pi$
$467$			39.7794i			1.84077i	−0.391013	+	0.920385i	$0.627875\pi$
$468$	−16.7446	+	8.85550i	−0.774017	+	0.409345i
$469$	−24.2630	+	14.0082i	−1.12036	+	0.646840i
$470$	−4.39434	+	2.42944i	−0.202696	+	0.112062i
$471$	21.5170	+	37.2685i	0.991450	+	1.71724i
$472$	3.92252	+	2.56597i	0.180549	+	0.118108i
$473$	−3.35988	+	5.81948i	−0.154487	+	0.267580i
$474$	1.87595	+	1.13003i	0.0861651	+	0.0519038i
$475$	0.509365	−	30.7032i	0.0233713	−	1.40876i
$476$	0.490864	+	0.928157i	0.0224987	+	0.0425420i
$477$	−17.3632	−	10.0246i	−0.795005	−	0.458996i
$478$	−10.1231	−	18.3106i	−0.463020	−	0.837507i
$479$	19.3333	+	33.4863i	0.883361	+	1.53003i	0.847581	+	0.530666i	$0.178058\pi$
$479$	19.3333	+	33.4863i	0.883361	+	1.53003i	0.0357799	+	0.999360i	$0.488608\pi$
$480$	44.2246	+	4.11720i	2.01857	+	0.187924i
$481$	−9.20566	−	15.9447i	−0.419742	−	0.727015i
$482$	3.22437	−	5.35276i	0.146866	−	0.243811i
$483$		−	31.4705i		−	1.43196i
$484$	17.2158	−	27.4151i	0.782537	−	1.24614i
$485$	53.5308	−	30.9060i	2.43071	−	1.40337i
$486$	−22.5353	−	13.5747i	−1.02222	−	0.615762i
$487$	−9.90299			−0.448747			−0.224374	−	0.974503i	$-0.572034\pi$
$487$	−9.90299			−0.448747			−0.224374	+	0.974503i	$0.572034\pi$
$488$	−4.96780	+	2.51037i	−0.224882	+	0.113639i
$489$	−12.5266	+	21.6968i	−0.566474	+	0.981161i
$490$	0.00956148	−	0.514940i	0.000431943	−	0.0232626i
$491$	10.9533	+	6.32390i	0.494317	+	0.285394i	0.726363	−	0.687311i	$-0.241209\pi$
$491$	10.9533	+	6.32390i	0.494317	+	0.285394i	−0.232047	+	0.972705i	$0.574542\pi$
$492$	−0.562581	+	15.1439i	−0.0253631	+	0.682739i
$493$		−	1.02637i		−	0.0462255i
$494$	−12.9332	−	24.3383i	−0.581891	−	1.09503i
$495$	38.3321			1.72290
$496$	6.04052	+	12.5261i	0.271227	+	0.562438i
$497$	8.93202	−	15.4707i	0.400656	−	0.693956i
$498$	−8.28005	−	0.153745i	−0.371038	−	0.00688948i
$499$	−11.7291	−	6.77183i	−0.525069	−	0.303149i	0.213937	−	0.976847i	$-0.431371\pi$
$499$	−11.7291	−	6.77183i	−0.525069	−	0.303149i	−0.739006	+	0.673699i	$0.764704\pi$
$500$	12.0196	+	7.54790i	0.537531	+	0.337553i
$501$			0.617820i			0.0276022i
$502$	27.9452	+	16.8335i	1.24726	+	0.751318i
$503$	−18.3754	−	31.8271i	−0.819317	−	1.41910i	−0.906186	−	0.422879i	$-0.861019\pi$
$503$	−18.3754	−	31.8271i	−0.819317	−	1.41910i	0.0868686	−	0.996220i	$-0.472314\pi$
$504$	7.20285	+	14.2538i	0.320840	+	0.634915i
$505$	7.34963			0.327054
$506$	32.9629	+	19.8560i	1.46538	+	0.882709i
$507$	−13.6954	+	7.90702i	−0.608233	+	0.351163i
$508$	4.52249	+	0.168006i	0.200653	+	0.00745408i
$509$	−0.583539	+	0.336907i	−0.0258649	+	0.0149331i	−0.512877	−	0.858462i	$-0.671420\pi$
$509$	−0.583539	+	0.336907i	−0.0258649	+	0.0149331i	0.487012	+	0.873395i	$0.338087\pi$
$510$	−1.05813	−	1.91394i	−0.0468549	−	0.0847507i
$511$	−16.8987	+	29.2694i	−0.747555	+	1.29480i
$512$	−22.3123	−	3.76334i	−0.986072	−	0.166318i
$513$	4.47167	−	7.45671i	0.197429	−	0.329222i
$514$	10.6048	−	17.6050i	0.467758	−	0.776522i
$515$	1.00259	+	0.578846i	0.0441794	+	0.0255070i
$516$	5.82737	+	0.216482i	0.256536	+	0.00953007i
$517$	4.61953	−	2.66709i	0.203167	−	0.117298i
$518$	−13.5850	+	7.51055i	−0.596891	+	0.329995i
$519$	17.8214	+	30.8676i	0.782273	+	1.35494i
$520$	43.8205	+	2.44324i	1.92166	+	0.107143i
$521$	−16.8110			−0.736504			−0.368252	−	0.929726i	$-0.620044\pi$
$521$	−16.8110			−0.736504			−0.368252	+	0.929726i	$0.620044\pi$
$522$	0.289827	−	15.6088i	0.0126854	−	0.683181i
$523$	−30.6991	+	17.7242i	−1.34238	+	0.775023i	−0.987156	−	0.159758i	$-0.948928\pi$
$523$	−30.6991	+	17.7242i	−1.34238	+	0.775023i	−0.355223	+	0.934782i	$0.615595\pi$
$524$	34.3208	−	18.1508i	1.49931	−	0.792922i
$525$			42.4825i			1.85409i
$526$	6.32212	+	0.117390i	0.275657	+	0.00511844i
$527$	0.342367	−	0.592997i	0.0149137	−	0.0258314i
$528$	−47.0542	−	3.50087i	−2.04777	−	0.152356i
$529$	−2.11732	+	3.66731i	−0.0920576	+	0.159448i
$530$	22.4761	+	40.6546i	0.976301	+	1.76592i
$531$		−	3.51045i		−	0.152341i
$532$	−20.7190	+	10.5214i	−0.898282	+	0.456159i
$533$			14.9744i			0.648614i
$534$	−2.85075	+	1.57605i	−0.123364	+	0.0682025i
$535$	3.27756	−	5.67691i	0.141701	−	0.245434i
$536$	−26.5335	+	13.4081i	−1.14607	+	0.579143i
$537$	−22.0033	+	38.1109i	−0.949514	+	1.64461i
$538$	−0.682843	+	36.7750i	−0.0294394	+	1.58548i
$539$			0.547131i			0.0235666i
$540$	6.47285	+	12.2393i	0.278547	+	0.526695i
$541$	−14.0380	+	8.10482i	−0.603539	+	0.348453i	−0.770433	−	0.637522i	$-0.779960\pi$
$541$	−14.0380	+	8.10482i	−0.603539	+	0.348453i	0.166894	+	0.985975i	$0.446626\pi$
$542$	4.66454	+	0.0866118i	0.200359	+	0.00372029i
$543$	47.3594			2.03239
$544$	0.465230	+	1.01236i	0.0199466	+	0.0434044i
$545$	−10.0474	−	17.4026i	−0.430383	−	0.745446i
$546$	18.4486	+	33.3697i	0.789527	+	1.42809i
$547$	5.54001	−	3.19852i	0.236874	−	0.136759i	−0.376865	−	0.926268i	$-0.622998\pi$
$547$	5.54001	−	3.19852i	0.236874	−	0.136759i	0.613739	+	0.789509i	$0.289665\pi$
$548$	−24.3501	−	0.904584i	−1.04019	−	0.0386419i
$549$	3.61013	+	2.08431i	0.154077	+	0.0889562i
$550$	−44.4970	−	26.8039i	−1.89736	−	1.14292i
$551$	22.7122	+	0.376794i	0.967570	+	0.0160519i
$552$	1.85902	−	33.3423i	0.0791252	−	1.41914i
$553$	0.912258	−	1.58008i	0.0387931	−	0.0671917i
$554$	29.5402	−	16.3315i	1.25504	−	0.693857i
$555$	28.0009	−	16.1663i	1.18857	−	0.686222i
$556$	−0.465598	+	12.5332i	−0.0197457	+	0.531527i
$557$	−23.1445	+	13.3625i	−0.980664	+	0.566187i	−0.902471	−	0.430751i	$-0.858249\pi$
$557$	−23.1445	+	13.3625i	−0.980664	+	0.566187i	−0.0781937	+	0.996938i	$0.524915\pi$
$558$	5.37409	−	8.92148i	0.227503	−	0.377676i
$559$	5.76217			0.243714
$560$	2.74548	−	36.9012i	0.116018	−	1.55936i
$561$	1.16164	+	2.01202i	0.0490445	+	0.0849475i
$562$	17.1445	−	28.4615i	0.723198	−	1.20058i
$563$			26.2880i			1.10791i	0.832547	+	0.553955i	$0.186882\pi$
$563$			26.2880i			1.10791i	−0.832547	+	0.553955i	$0.813118\pi$
$564$	−3.92014	−	2.46172i	−0.165068	−	0.103657i
$565$	19.5887	+	11.3096i	0.824104	+	0.475797i
$566$	0.604143	−	32.5365i	0.0253940	−	1.36761i
$567$	−14.4840	+	25.0870i	−0.608269	+	1.05355i
$568$	10.3771	−	15.8632i	0.435415	−	0.665605i
$569$	1.02599			0.0430118			0.0215059	−	0.999769i	$-0.493154\pi$
$569$	1.02599			0.0430118			0.0215059	+	0.999769i	$0.493154\pi$
$570$	42.7412	−	22.7123i	1.79023	−	0.951314i
$571$		−	11.5119i		−	0.481756i	−0.970555	−	0.240878i	$-0.922565\pi$
$571$		−	11.5119i		−	0.481756i	0.970555	−	0.240878i	$-0.0774354\pi$
$572$	−46.5920	−	1.73085i	−1.94811	−	0.0723705i
$573$	24.5240	+	14.1590i	1.02451	+	0.591499i
$574$	12.6230	+	0.234386i	0.526875	+	0.00978308i
$575$	18.3822	−	31.8389i	0.766591	−	1.32777i
$576$	6.78924	+	15.5270i	0.282885	+	0.646960i
$577$	−32.9606			−1.37217			−0.686085	−	0.727522i	$-0.740672\pi$
$577$	−32.9606			−1.37217			−0.686085	+	0.727522i	$0.740672\pi$
$578$	−12.3770	+	20.5469i	−0.514814	+	0.854639i
$579$	45.5769	−	26.3138i	1.89411	−	1.09357i
$580$	−19.2364	+	30.6327i	−0.798747	+	1.27195i
$581$			6.89937i			0.286234i
$582$	48.8120	+	29.4032i	2.02332	+	1.21880i
$583$	−24.6748	−	42.7380i	−1.02192	−	1.77003i
$584$	−19.6328	+	30.0120i	−0.812409	+	1.24191i
$585$	−16.4348	−	28.4660i	−0.679497	−	1.17692i
$586$	−8.68077	+	4.79921i	−0.358599	+	0.198254i
$587$	17.1848	+	9.92167i	0.709294	+	0.409511i	0.810800	−	0.585324i	$-0.199033\pi$
$587$	17.1848	+	9.92167i	0.709294	+	0.409511i	−0.101505	+	0.994835i	$0.532366\pi$
$588$	0.419718	−	0.221972i	0.0173089	−	0.00915395i
$589$	12.9965	+	7.79378i	0.535510	+	0.321137i
$590$	−4.19692	+	6.96727i	−0.172784	+	0.286838i
$591$	2.50366	−	4.33647i	0.102987	−	0.178378i
$592$	−14.8367	+	7.15475i	−0.609783	+	0.294058i
$593$	−9.13625	−	15.8245i	−0.375181	−	0.649832i	0.615173	−	0.788392i	$-0.289086\pi$
$593$	−9.13625	−	15.8245i	−0.375181	−	0.649832i	−0.990354	+	0.138560i	$0.955753\pi$
$594$	−7.11651	−	12.8723i	−0.291994	−	0.528156i
$595$	−1.57788	+	0.910989i	−0.0646868	+	0.0373469i
$596$	−31.8678	+	16.8536i	−1.30536	+	0.690349i
$597$		−	22.7614i		−	0.931564i
$598$	0.612599	−	32.9919i	0.0250510	−	1.34914i
$599$	−20.2458	−	35.0668i	−0.827223	−	1.43279i	−0.900209	−	0.435459i	$-0.856586\pi$
$599$	−20.2458	−	35.0668i	−0.827223	−	1.43279i	0.0729858	−	0.997333i	$-0.476747\pi$
$600$	−2.50952	+	45.0092i	−0.102451	+	1.83749i
$601$	−14.0685			−0.573867			−0.286933	−	0.957951i	$-0.592636\pi$
$601$	−14.0685			−0.573867			−0.286933	+	0.957951i	$0.592636\pi$
$602$	0.0901919	−	4.85735i	0.00367595	−	0.197971i
$603$	19.2821	+	11.1325i	0.785227	+	0.453351i
$604$	−7.35726	+	11.7160i	−0.299363	+	0.476716i
$605$	48.6491	+	28.0876i	1.97787	+	1.14192i
$606$	3.27825	+	5.92968i	0.133170	+	0.240877i
$607$	−25.6637			−1.04166			−0.520828	−	0.853661i	$-0.674377\pi$
$607$	−25.6637			−1.04166			−0.520828	+	0.853661i	$0.674377\pi$
$608$	−22.5728	+	9.92322i	−0.915446	+	0.402440i
$609$	−31.4257			−1.27343
$610$	−4.67321	−	8.45286i	−0.189213	−	0.342246i
$611$	−3.96123	−	2.28702i	−0.160254	−	0.0925229i
$612$	0.443748	−	0.706640i	0.0179374	−	0.0285642i
$613$	−12.6613	−	7.30998i	−0.511383	−	0.295247i	0.222019	−	0.975042i	$-0.428735\pi$
$613$	−12.6613	−	7.30998i	−0.511383	−	0.295247i	−0.733402	+	0.679795i	$0.762069\pi$
$614$	0.285298	−	15.3649i	0.0115137	−	0.620078i
$615$	−26.2970			−1.06040
$616$	−2.18834	+	39.2487i	−0.0881706	+	1.58138i
$617$	11.2232	+	19.4392i	0.451829	+	0.782591i	0.998500	−	0.0547565i	$-0.0174383\pi$
$617$	11.2232	+	19.4392i	0.451829	+	0.782591i	−0.546670	+	0.837348i	$0.684105\pi$
$618$	−0.0198137	+	1.06708i	−0.000797023	+	0.0429243i
$619$		−	29.1618i		−	1.17211i	−0.810271	−	0.586055i	$-0.800680\pi$
$619$		−	29.1618i		−	1.17211i	0.810271	−	0.586055i	$-0.199320\pi$
$620$	−21.3321	+	11.2817i	−0.856719	+	0.453083i
$621$	9.01511	−	5.20488i	0.361764	−	0.208864i
$622$	9.72718	+	17.5944i	0.390024	+	0.705473i
$623$	1.35689	+	2.35020i	0.0543626	+	0.0941588i
$624$	17.5746	+	36.4441i	0.703549	+	1.45893i
$625$	5.29753	−	9.17559i	0.211901	−	0.367024i
$626$	17.6519	−	29.3038i	0.705511	−	1.17121i
$627$	−44.9495	+	24.9668i	−1.79511	+	0.997077i
$628$	33.6299	−	17.7854i	1.34198	−	0.709716i
$629$	0.702381	+	0.405520i	0.0280058	+	0.0161691i
$630$	−24.2533	+	13.4086i	−0.966274	+	0.534210i
$631$	13.6730	+	23.6824i	0.544315	+	0.942781i	0.998650	+	0.0519501i	$0.0165437\pi$
$631$	13.6730	+	23.6824i	0.544315	+	0.942781i	−0.454335	+	0.890831i	$0.650123\pi$
$632$	1.05985	−	1.62016i	0.0421587	−	0.0644467i
$633$	4.84885	+	8.39846i	0.192725	+	0.333809i
$634$	0.113789	+	0.0685435i	0.00451912	+	0.00272221i
$635$			7.85319i			0.311645i
$636$	−22.7748	+	36.2675i	−0.903080	+	1.43810i
$637$	0.406307	−	0.234582i	0.0160985	−	0.00929447i
$638$	19.8277	−	32.9159i	0.784987	−	1.30315i
$639$	−14.1968			−0.561615
$640$	5.08859	−	38.9337i	0.201144	−	1.53899i
$641$	22.0145	−	38.1302i	0.869520	−	1.50605i	0.00703125	−	0.999975i	$-0.497762\pi$
$641$	22.0145	−	38.1302i	0.869520	−	1.50605i	0.862488	−	0.506077i	$-0.168905\pi$
$642$	6.04206	+	0.112190i	0.238461	+	0.00442778i
$643$	15.4455	+	8.91745i	0.609110	+	0.351670i	0.772617	−	0.634872i	$-0.218947\pi$
$643$	15.4455	+	8.91745i	0.609110	+	0.351670i	−0.163507	+	0.986542i	$0.552281\pi$
$644$	−27.8017	−	1.03281i	−1.09554	−	0.0406983i
$645$			10.1191i			0.398439i
$646$	1.02946	+	0.643632i	0.0405035	+	0.0253234i
$647$	14.3489			0.564113			0.282056	−	0.959398i	$-0.408983\pi$
$647$	14.3489			0.564113			0.282056	+	0.959398i	$0.408983\pi$
$648$	−16.8273	+	25.7234i	−0.661040	+	1.01051i
$649$	4.32034	−	7.48305i	0.169588	−	0.293735i
$650$	−0.826955	+	44.5363i	−0.0324359	+	1.74686i
$651$	−18.1565	−	10.4826i	−0.711609	−	0.410847i
$652$	18.7562	+	11.7783i	0.734551	+	0.461275i
$653$		−	16.5566i		−	0.647909i	−0.946073	−	0.323954i	$-0.894988\pi$
$653$		−	16.5566i		−	0.647909i	0.946073	−	0.323954i	$-0.105012\pi$
$654$	9.55884	−	15.8686i	0.373780	−	0.620510i
$655$	33.6859	+	58.3458i	1.31622	+	2.27976i
$656$	13.3599	+	0.993991i	0.521618	+	0.0388088i
$657$	26.8592			1.04788
$658$	−1.98990	+	3.30341i	−0.0775743	+	0.128780i
$659$	18.9469	−	10.9390i	0.738065	−	0.426122i	−0.0833007	−	0.996524i	$-0.526546\pi$
$659$	18.9469	−	10.9390i	0.738065	−	0.426122i	0.821365	+	0.570403i	$0.193213\pi$
$660$	3.03959	−	81.8215i	0.118316	−	3.18490i
$661$	4.03897	−	2.33190i	0.157098	−	0.0907005i	−0.419390	−	0.907806i	$-0.637756\pi$
$661$	4.03897	−	2.33190i	0.157098	−	0.0907005i	0.576488	+	0.817106i	$0.304423\pi$
$662$	−44.7256	+	24.7268i	−1.73831	+	0.961033i
$663$	0.996103	−	1.72530i	0.0386854	−	0.0670051i
$664$	−0.407558	+	7.30971i	−0.0158163	+	0.283672i
$665$	−19.5796	−	35.2506i	−0.759265	−	1.36696i
$666$	10.5671	+	6.36539i	0.409468	+	0.246654i
$667$	23.5523	+	13.5979i	0.911947	+	0.526513i
$668$	0.545794	+	0.0202758i	0.0211174	+	0.000784493i
$669$	−34.3655	+	19.8409i	−1.32865	+	0.767095i
$670$	−24.9601	−	45.1476i	−0.964292	−	1.74420i
$671$	5.13035	+	8.88603i	0.198055	+	0.343041i
$672$	30.9965	−	14.2445i	1.19572	−	0.549493i
$673$	16.3729			0.631131			0.315565	−	0.948904i	$-0.397806\pi$
$673$	16.3729			0.631131			0.315565	+	0.948904i	$0.397806\pi$
$674$	3.48358	+	0.0646837i	0.134183	+	0.00249152i
$675$	−12.1696	+	7.02613i	−0.468409	+	0.270436i
$676$	6.53576	+	12.3583i	0.251376	+	0.475317i
$677$		−	27.0114i		−	1.03813i	−0.854734	−	0.519066i	$-0.826280\pi$
$677$		−	27.0114i		−	1.03813i	0.854734	−	0.519066i	$-0.173720\pi$
$678$	−0.387122	+	20.8488i	−0.0148673	+	0.800691i
$679$	23.7369	−	41.1135i	0.910938	−	1.57779i
$680$	−1.72554	+	0.871963i	−0.0661714	+	0.0334383i
$681$	4.49408	−	7.78398i	0.172214	−	0.298283i
$682$	22.4354	−	12.4035i	0.859096	−	0.474956i
$683$		−	8.46325i		−	0.323837i	−0.986804	−	0.161919i	$-0.948232\pi$
$683$		−	8.46325i		−	0.323837i	0.986804	−	0.161919i	$-0.0517682\pi$
$684$	15.4740	+	10.0789i	0.591664	+	0.385377i
$685$		−	42.2834i		−	1.61557i
$686$	12.5757	+	22.7468i	0.480142	+	0.868477i
$687$	12.8888	−	22.3240i	0.491737	−	0.851714i
$688$	0.382488	−	5.14091i	0.0145822	−	0.195996i
$689$	−21.1585	+	36.6477i	−0.806076	+	1.39617i
$690$	57.9380	+	1.07580i	2.20566	+	0.0409550i
$691$			8.71559i			0.331557i	0.986163	+	0.165778i	$0.0530136\pi$
$691$			8.71559i			0.331557i	−0.986163	+	0.165778i	$0.946986\pi$
$692$	27.8539	−	14.7308i	1.05885	−	0.559980i
$693$	25.4961	−	14.7202i	0.968518	−	0.559174i
$694$	0.388404	−	20.9178i	0.0147436	−	0.794028i
$695$	−21.7636			−0.825542
$696$	−33.2947	−	1.85637i	−1.26203	−	0.0703655i
$697$	−0.329820	−	0.571265i	−0.0124928	−	0.0216382i
$698$	12.1054	−	6.69254i	0.458196	−	0.253316i
$699$	−44.2406	+	25.5423i	−1.67333	+	0.966100i
$700$	37.5299	+	1.39420i	1.41850	+	0.0526958i
$701$	−18.5405	−	10.7043i	−0.700264	−	0.404298i	0.107182	−	0.994239i	$-0.465817\pi$
$701$	−18.5405	−	10.7043i	−0.700264	−	0.404298i	−0.807446	+	0.589942i	$0.799151\pi$
$702$	−6.50794	+	10.8038i	−0.245627	+	0.407763i
$703$	−9.23142	+	15.3938i	−0.348170	+	0.580589i
$704$	−4.63698	+	41.4538i	−0.174763	+	1.56235i
$705$	4.01630	−	6.95643i	0.151262	−	0.261994i
$706$	9.43983	+	17.0747i	0.355273	+	0.642614i
$707$	4.88851	−	2.82238i	0.183851	−	0.106147i
$708$	−7.49320	−	0.278365i	−0.281612	−	0.0104616i
$709$	14.7102	−	8.49294i	0.552453	−	0.318959i	−0.197658	−	0.980271i	$-0.563333\pi$
$709$	14.7102	−	8.49294i	0.552453	−	0.318959i	0.750111	+	0.661312i	$0.230000\pi$
$710$	28.1766	+	16.9729i	1.05745	+	0.636982i
$711$	−1.44996			−0.0543779
$712$	1.29876	+	2.57013i	0.0486731	+	0.0963198i
$713$	9.07170	+	15.7126i	0.339738	+	0.588443i
$714$	−1.43879	−	0.866692i	−0.0538453	−	0.0324351i
$715$		−	80.9059i		−	3.02571i
$716$	32.9458	+	20.6889i	1.23124	+	0.773181i
$717$	28.9864	+	16.7353i	1.08252	+	0.624992i
$718$	−45.6797	−	0.848187i	−1.70475	−	0.0316540i
$719$	17.8635	−	30.9405i	0.666196	−	1.15388i	−0.312764	−	0.949831i	$-0.601255\pi$
$719$	17.8635	−	30.9405i	0.666196	−	1.15388i	0.978960	−	0.204054i	$-0.0654117\pi$
$720$	−26.4878	+	12.7734i	−0.987143	+	0.476035i
$721$	0.889147			0.0331136
$722$	−14.6206	+	22.5442i	−0.544121	+	0.839006i
$723$			9.99657i			0.371776i
$724$	1.55425	−	41.8383i	0.0577634	−	1.55491i
$725$	−31.7935	−	18.3560i	−1.18078	−	0.681725i
$726$	−0.961428	+	51.7784i	−0.0356819	+	1.92168i
$727$	−7.08583	+	12.2730i	−0.262799	+	0.455181i	−0.966985	−	0.254835i	$-0.917979\pi$
$727$	−7.08583	+	12.2730i	−0.262799	+	0.455181i	0.704186	+	0.710016i	$0.251312\pi$
$728$	30.0849	−	15.2027i	1.11502	−	0.563451i
$729$	9.48284			0.351216
$730$	−53.3080	−	32.1115i	−1.97302	−	1.18850i
$731$	−0.219823	+	0.126915i	−0.00813046	+	0.00469412i
$732$	4.73531	−	7.54069i	0.175022	−	0.278712i
$733$			45.5820i			1.68361i	0.539783	+	0.841804i	$0.318506\pi$
$733$			45.5820i			1.68361i	−0.539783	+	0.841804i	$0.681494\pi$
$734$	3.30450	−	5.48577i	0.121971	−	0.202483i
$735$	0.411955	+	0.713527i	0.0151952	+	0.0263188i
$736$	−29.3942	−	2.73653i	−1.08349	−	0.100870i
$737$	27.4017	+	47.4612i	1.00936	+	1.74825i
$738$	−4.85452	−	8.78081i	−0.178697	−	0.323226i
$739$	28.2953	+	16.3363i	1.04086	+	0.600940i	0.920076	−	0.391739i	$-0.128126\pi$
$739$	28.2953	+	16.3363i	1.04086	+	0.600940i	0.120783	+	0.992679i	$0.461460\pi$
$740$	−13.3627	−	25.2671i	−0.491223	−	0.928836i
$741$	37.8127	+	22.6757i	1.38909	+	0.833012i
$742$	30.5618	+	18.4097i	1.12196	+	0.675841i
$743$	14.2929	−	24.7560i	0.524356	−	0.908211i	−0.475242	−	0.879855i	$-0.657639\pi$
$743$	14.2929	−	24.7560i	0.524356	−	0.908211i	0.999598	−	0.0283561i	$-0.00902724\pi$
$744$	−18.6171	−	12.1786i	−0.682537	−	0.446491i
$745$	−31.2784	−	54.1758i	−1.14595	−	1.98485i
$746$	−32.7637	+	18.1136i	−1.19956	+	0.663185i
$747$	4.74842	−	2.74150i	0.173736	−	0.100306i
$748$	1.81558	−	0.960185i	0.0663842	−	0.0351078i
$749$		−	5.03456i		−	0.183959i
$750$	−22.7011	−	0.421517i	−0.828928	−	0.0153916i
$751$	19.0687	+	33.0280i	0.695828	+	1.20521i	0.969901	+	0.243500i	$0.0782956\pi$
$751$	19.0687	+	33.0280i	0.695828	+	1.20521i	−0.274073	+	0.961709i	$0.588371\pi$
$752$	−2.30339	+	3.38234i	−0.0839959	+	0.123341i
$753$	−52.1893			−1.90188
$754$	−32.9449	−	0.611725i	−1.19978	−	0.0222777i
$755$	−20.7904	−	12.0034i	−0.756641	−	0.436847i
$756$	9.00543	+	5.65512i	0.327524	+	0.205675i
$757$	−39.0576	−	22.5499i	−1.41957	−	0.819592i	−0.423313	−	0.905983i	$-0.639133\pi$
$757$	−39.0576	−	22.5499i	−1.41957	−	0.819592i	−0.996261	+	0.0863918i	$0.972466\pi$
$758$	−26.3063	+	14.5436i	−0.955487	+	0.528246i
$759$	−61.5600			−2.23449
$760$	−18.6618	−	38.5038i	−0.676935	−	1.39668i
$761$	−0.536559			−0.0194502			−0.00972512	−	0.999953i	$-0.503096\pi$
$761$	−0.536559			−0.0194502			−0.00972512	+	0.999953i	$0.503096\pi$
$762$	−6.33596	+	3.50287i	−0.229527	+	0.126895i
$763$	−13.3658	−	7.71675i	−0.483874	−	0.279365i
$764$	13.3131	−	21.2004i	0.481653	−	0.767002i
$765$	1.25396	+	0.723974i	0.0453370	+	0.0261753i
$766$	1.70101	+	0.0315846i	0.0614600	+	0.00114120i
$767$	−7.40935			−0.267536
$768$	33.6815	−	13.2607i	1.21538	−	0.478503i
$769$	−15.3125	−	26.5221i	−0.552184	−	0.956410i	−0.998117	−	0.0613441i	$-0.980461\pi$
$769$	−15.3125	−	26.5221i	−0.552184	−	0.956410i	0.445933	−	0.895066i	$-0.352872\pi$
$770$	−68.2015	−	1.26637i	−2.45781	−	0.0456369i
$771$			32.8783i			1.18408i
$772$	−21.7504	−	41.1271i	−0.782814	−	1.48020i
$773$	−38.8904	+	22.4534i	−1.39879	+	0.807592i	−0.994266	−	0.106936i	$-0.965896\pi$
$773$	−38.8904	+	22.4534i	−1.39879	+	0.807592i	−0.404524	+	0.914527i	$0.632563\pi$
$774$	−3.37886	+	1.86802i	−0.121451	+	0.0671446i
$775$	−12.2460	−	21.2107i	−0.439890	−	0.761911i
$776$	27.5773	−	42.1566i	0.989968	−	1.51333i
$777$	12.4163	−	21.5056i	0.445432	−	0.771510i
$778$	10.6758	+	6.43083i	0.382745	+	0.230556i
$779$	12.7624	−	7.08873i	0.457259	−	0.253980i
$780$	−62.0650	+	32.8236i	−2.22228	+	1.17527i
$781$	−30.2625	−	17.4720i	−1.08288	−	0.625199i
$782$	0.703296	+	1.27212i	0.0251498	+	0.0454908i
$783$	−5.19745	−	9.00225i	−0.185742	−	0.321714i
$784$	−0.182320	−	0.378072i	−0.00651142	−	0.0135026i
$785$	33.0078	+	57.1713i	1.17810	+	2.04053i
$786$	−32.0480	+	53.2026i	−1.14311	+	1.89767i
$787$		−	14.2591i		−	0.508283i	−0.967167	−	0.254141i	$-0.918207\pi$
$787$		−	14.2591i		−	0.508283i	0.967167	−	0.254141i	$-0.0817928\pi$
$788$	−3.74876	−	2.35410i	−0.133544	−	0.0838613i
$789$	−8.76025	+	5.05773i	−0.311873	+	0.180060i
$790$	2.87777	+	1.73350i	0.102387	+	0.0616752i
$791$	17.3723			0.617687
$792$	27.8821	−	14.0896i	0.990747	−	0.500652i
$793$	4.39926	−	7.61974i	0.156222	−	0.270585i
$794$	−0.626051	+	33.7164i	−0.0222177	+	1.19655i
$795$	−64.3579	−	37.1571i	−2.28254	−	1.31783i
$796$	−20.1079	−	0.746990i	−0.712706	−	0.0264764i
$797$			32.4959i			1.15107i	0.817779	+	0.575533i	$0.195205\pi$
$797$			32.4959i			1.15107i	−0.817779	+	0.575533i	$0.804795\pi$
$798$	19.7068	−	31.5202i	0.697615	−	1.11580i
$799$	0.201492			0.00712826
$800$	39.6797	+	3.69408i	1.40289	+	0.130605i
$801$	1.07833	−	1.86773i	0.0381011	−	0.0659930i
$802$	26.8786	+	0.499086i	0.949117	+	0.0176233i
$803$	57.2543	+	33.0558i	2.02046	+	1.16651i
$804$	25.2918	−	40.2756i	0.891972	−	1.42041i
$805$		−	48.2770i		−	1.70154i
$806$	−18.8302	−	11.3428i	−0.663265	−	0.399535i
$807$	−29.4202	−	50.9573i	−1.03564	−	1.79378i
$808$	5.34598	−	2.70147i	0.188071	−	0.0950375i
$809$	−25.8969			−0.910485			−0.455243	−	0.890367i	$-0.650447\pi$
$809$	−25.8969			−0.910485			−0.455243	+	0.890367i	$0.650447\pi$
$810$	−45.6906	−	27.5229i	−1.60540	−	0.967056i
$811$	33.7528	−	19.4872i	1.18522	−	0.684289i	0.228006	−	0.973660i	$-0.426780\pi$
$811$	33.7528	−	19.4872i	1.18522	−	0.684289i	0.957217	+	0.289371i	$0.0934462\pi$
$812$	−1.03133	+	27.7621i	−0.0361928	+	0.974257i
$813$	−6.46342	+	3.73166i	−0.226682	+	0.130875i
$814$	14.6915	+	26.5738i	0.514937	+	0.931413i
$815$	−19.2163	+	33.2836i	−0.673118	+	1.16588i
$816$	−1.47317	−	1.00323i	−0.0515711	−	0.0351201i
$817$	−2.72775	−	4.91096i	−0.0954318	−	0.171813i
$818$	−16.8909	+	28.0405i	−0.590577	+	0.980413i
$819$	−21.8629	−	12.6225i	−0.763950	−	0.441067i
$820$	−0.863020	+	23.2313i	−0.0301380	+	0.811271i
$821$	30.7541	−	17.7559i	1.07332	−	0.619684i	0.144237	−	0.989543i	$-0.453927\pi$
$821$	30.7541	−	17.7559i	1.07332	−	0.619684i	0.929088	+	0.369859i	$0.120594\pi$
$822$	34.1142	−	18.8602i	1.18987	−	0.657826i
$823$	−6.40830	−	11.0995i	−0.223379	−	0.386904i	0.732453	−	0.680818i	$-0.238375\pi$
$823$	−6.40830	−	11.0995i	−0.223379	−	0.386904i	−0.955832	+	0.293914i	$0.905042\pi$
$824$	0.942030	+	0.0525235i	0.0328172	+	0.00182974i
$825$	83.1006			2.89319
$826$	−0.115974	+	6.24588i	−0.00403526	+	0.217322i
$827$	−14.6437	+	8.45456i	−0.509212	+	0.293994i	−0.732510	−	0.680756i	$-0.761651\pi$
$827$	−14.6437	+	8.45456i	−0.509212	+	0.293994i	0.223297	+	0.974750i	$0.428318\pi$
$828$	10.3363	+	19.5446i	0.359213	+	0.679223i
$829$		−	3.08082i		−	0.107001i	−0.998568	−	0.0535006i	$-0.982962\pi$
$829$		−	3.08082i		−	0.107001i	0.998568	−	0.0535006i	$-0.0170379\pi$
$830$	−12.7019	−	0.235851i	−0.440889	−	0.00818649i
$831$	−26.9988	+	46.7633i	−0.936579	+	1.62220i
$832$	32.7723	−	14.3298i	1.13617	−	0.496795i
$833$	−0.0103336	+	0.0178983i	−0.000358038	+	0.000620140i
$834$	−9.70753	−	17.5589i	−0.336144	−	0.608015i
$835$			0.947759i			0.0327985i
$836$	20.5810	+	40.5287i	0.711808	+	1.40171i
$837$		−	6.93485i		−	0.239704i
$838$	−0.234834	+	0.129829i	−0.00811222	+	0.00448488i
$839$	2.40317	−	4.16242i	0.0829667	−	0.143703i	−0.821556	−	0.570127i	$-0.806894\pi$
$839$	2.40317	−	4.16242i	0.0829667	−	0.143703i	0.904523	+	0.426425i	$0.140227\pi$
$840$	26.6979	+	52.8329i	0.921165	+	1.82291i
$841$	−0.921481	+	1.59605i	−0.0317752	+	0.0550363i
$842$	0.423464	−	22.8059i	0.0145935	−	0.785944i
$843$			53.1534i			1.83070i
$844$	7.57850	−	4.00795i	0.260863	−	0.137959i
$845$	−21.0092	+	12.1297i	−0.722739	+	0.417273i
$846$	3.06424	+	0.0568972i	0.105351	+	0.00195617i
$847$	43.1445			1.48246
$848$	31.2920	+	21.3100i	1.07457	+	0.731787i
$849$	26.0294	+	45.0843i	0.893327	+	1.54729i
$850$	−0.949389	−	1.71725i	−0.0325638	−	0.0589011i
$851$	−18.6110	+	10.7451i	−0.637977	+	0.368336i
$852$	−1.12575	+	30.3035i	−0.0385675	+	1.03818i
$853$	−26.3765	−	15.2285i	−0.903116	−	0.521414i	−0.0249060	−	0.999690i	$-0.507929\pi$
$853$	−26.3765	−	15.2285i	−0.903116	−	0.521414i	−0.878210	+	0.478276i	$0.841262\pi$
$854$	−6.35437	−	3.82772i	−0.217442	−	0.130982i
$855$	−16.4808	+	27.4825i	−0.563632	+	0.939882i
$856$	0.297401	−	5.33400i	0.0101649	−	0.182312i
$857$	−2.10945	+	3.65368i	−0.0720575	+	0.124807i	−0.899803	−	0.436297i	$-0.856290\pi$
$857$	−2.10945	+	3.65368i	−0.0720575	+	0.124807i	0.827745	+	0.561104i	$0.189623\pi$
$858$	65.2749	−	36.0876i	2.22845	−	1.23201i
$859$	−5.66461	+	3.27046i	−0.193274	+	0.111587i	−0.593514	−	0.804823i	$-0.702260\pi$
$859$	−5.66461	+	3.27046i	−0.193274	+	0.111587i	0.400240	+	0.916410i	$0.368927\pi$
$860$	8.93941	+	0.332091i	0.304831	+	0.0113242i
$861$	−17.4911	+	10.0985i	−0.596095	+	0.344156i
$862$	1.04748	−	1.73891i	0.0356772	−	0.0592274i
$863$	−7.99022			−0.271990			−0.135995	−	0.990710i	$-0.543423\pi$
$863$	−7.99022			−0.271990			−0.135995	+	0.990710i	$0.543423\pi$
$864$	9.20698	+	6.52343i	0.313228	+	0.221932i
$865$	27.3387	+	47.3520i	0.929544	+	1.61002i
$866$	9.80783	−	16.2819i	0.333284	−	0.553282i
$867$		−	38.3725i		−	1.30320i
$868$	−9.85645	+	15.6958i	−0.334550	+	0.532749i
$869$	−3.09081	−	1.78448i	−0.104849	−	0.0605343i
$870$	1.07427	−	57.8554i	0.0364211	−	1.96148i
$871$	23.4969	−	40.6978i	0.796162	−	1.37899i
$872$	−13.7049	−	8.96525i	−0.464106	−	0.303602i
$873$	−37.7280			−1.27690
$874$	−28.4083	+	15.0959i	−0.960924	+	0.510627i
$875$			18.9158i			0.639469i
$876$	2.12983	−	57.3320i	0.0719603	−	1.93707i
$877$	36.3895	+	21.0095i	1.22878	+	0.709439i	0.966776	−	0.255626i	$-0.0822816\pi$
$877$	36.3895	+	21.0095i	1.22878	+	0.709439i	0.262009	+	0.965065i	$0.415615\pi$
$878$	−12.9181	−	0.239865i	−0.435964	−	0.00809504i
$879$	7.93395	−	13.7420i	0.267606	−	0.463507i
$880$	−72.1830	−	5.37047i	−2.43329	−	0.181039i
$881$	−28.8189			−0.970934			−0.485467	−	0.874255i	$-0.661350\pi$
$881$	−28.8189			−0.970934			−0.485467	+	0.874255i	$0.661350\pi$
$882$	−0.162205	+	0.269275i	−0.00546173	+	0.00906697i
$883$	−18.5190	+	10.6919i	−0.623213	+	0.359812i	−0.778119	−	0.628117i	$-0.783826\pi$
$883$	−18.5190	+	10.6919i	−0.623213	+	0.359812i	0.154906	+	0.987929i	$0.450493\pi$
$884$	−1.49147	−	0.936599i	−0.0501637	−	0.0315012i
$885$		−	13.0118i		−	0.437385i
$886$	12.7482	+	7.67920i	0.428284	+	0.257988i
$887$	−1.26436	−	2.18993i	−0.0424530	−	0.0735307i	0.844018	−	0.536315i	$-0.180184\pi$
$887$	−1.26436	−	2.18993i	−0.0424530	−	0.0735307i	−0.886471	+	0.462784i	$0.846851\pi$
$888$	14.4251	−	22.0512i	0.484076	−	0.739991i
$889$	3.01576	+	5.22345i	0.101145	+	0.175189i
$890$	−4.37316	+	2.41772i	−0.146589	+	0.0810423i
$891$	49.0730	+	28.3323i	1.64401	+	0.949167i
$892$	16.4001	+	31.0103i	0.549115	+	1.03830i
$893$	−0.0739700	+	4.45872i	−0.00247531	+	0.149205i
$894$	29.7575	−	49.4002i	0.995239	−	1.65219i
$895$	−33.7540	+	58.4636i	−1.12827	+	1.95422i
$896$	−11.5666	−	27.8504i	−0.386414	−	0.930417i
$897$	26.3937	+	45.7153i	0.881261	+	1.52639i
$898$	16.5415	+	29.9201i	0.551996	+	0.998446i
$899$	15.6902	−	9.05876i	0.523299	−	0.302127i
$900$	−13.9532	−	26.3836i	−0.465106	−	0.879453i
$901$		−	1.86412i		−	0.0621027i
$902$	0.458486	−	24.6921i	0.0152659	−	0.822156i
$903$	3.88591	+	6.73059i	0.129315	+	0.223980i
$904$	18.4055	+	1.02621i	0.612158	+	0.0341313i
$905$	72.6511			2.41501
$906$	0.410870	−	22.1277i	0.0136503	−	0.735144i
$907$	35.9480	+	20.7546i	1.19363	+	0.689145i	0.959129	−	0.282970i	$-0.0913196\pi$
$907$	35.9480	+	20.7546i	1.19363	+	0.689145i	0.234505	+	0.972115i	$0.424653\pi$
$908$	−6.72903	−	4.22562i	−0.223311	−	0.140232i
$909$	−3.88496	−	2.24298i	−0.128856	−	0.0743950i
$910$	28.3008	+	51.1903i	0.938164	+	1.69694i
$911$	−52.2880			−1.73238			−0.866190	−	0.499715i	$-0.833438\pi$
$911$	−52.2880			−1.73238			−0.866190	+	0.499715i	$0.833438\pi$
$912$	22.7409	−	32.2307i	0.753025	−	1.06727i
$913$	13.4960			0.446651
$914$	6.18543	+	11.1882i	0.204596	+	0.370071i
$915$	13.3812	+	7.72566i	0.442370	+	0.255402i
$916$	−19.2985	−	12.1188i	−0.637640	−	0.400418i
$917$	44.8116	+	25.8720i	1.47981	+	0.854368i
$918$	0.0103146	−	0.555499i	0.000340432	−	0.0183342i
$919$	53.7032			1.77150			0.885752	−	0.464159i	$-0.153643\pi$
$919$	53.7032			1.77150			0.885752	+	0.464159i	$0.153643\pi$
$920$	2.85181	−	51.1483i	0.0940213	−	1.68631i
$921$	12.2920	+	21.2904i	0.405036	+	0.701543i
$922$	0.721783	−	38.8721i	0.0237706	−	1.28018i
$923$			29.9645i			0.986292i
$924$	−29.3991	−	55.5898i	−0.967160	−	1.82877i
$925$	25.1232	−	14.5049i	0.826047	−	0.476919i
$926$	−11.9716	−	21.6541i	−0.393411	−	0.711599i
$927$	−0.353308	−	0.611947i	−0.0116041	−	0.0200990i
$928$	−2.73263	+	29.3523i	−0.0897029	+	0.963537i
$929$	22.6146	−	39.1696i	0.741960	−	1.28511i	−0.209642	−	0.977778i	$-0.567230\pi$
$929$	22.6146	−	39.1696i	0.741960	−	1.28511i	0.951602	−	0.307334i	$-0.0994368\pi$
$930$	19.9195	−	33.0682i	0.653185	−	1.08435i
$931$	−0.392270	−	0.235238i	−0.0128561	−	0.00770962i
$932$	21.1127	+	39.9213i	0.691570	+	1.30767i
$933$	−27.8527	−	16.0808i	−0.911857	−	0.526461i
$934$	−49.2334	+	27.2189i	−1.61097	+	0.890631i
$935$	1.78200	+	3.08651i	0.0582776	+	0.100940i
$936$	−22.4175	−	14.6647i	−0.732740	−	0.479332i
$937$	2.89566	+	5.01542i	0.0945969	+	0.163847i	0.909440	−	0.415834i	$-0.136510\pi$
$937$	2.89566	+	5.01542i	0.0945969	+	0.163847i	−0.814843	+	0.579681i	$0.803177\pi$
$938$	−33.9393	−	20.4442i	−1.10816	−	0.667528i
$939$			54.7264i			1.78593i
$940$	−6.01364	−	3.77637i	−0.196143	−	0.123172i
$941$	−28.2763	+	16.3253i	−0.921782	+	0.532191i	−0.884203	−	0.467103i	$-0.845298\pi$
$941$	−28.2763	+	16.3253i	−0.921782	+	0.532191i	−0.0375786	+	0.999294i	$0.511964\pi$
$942$	−31.4028	+	52.1316i	−1.02316	+	1.69854i
$943$	17.4785			0.569178
$944$	−0.491827	+	6.61051i	−0.0160076	+	0.215154i
$945$	−9.22633	+	15.9805i	−0.300132	+	0.519845i
$946$	−9.50153	−	0.176426i	−0.308921	−	0.00573609i
$947$	−46.9803	−	27.1241i	−1.52665	−	0.881414i	−0.999499	−	0.0316449i	$-0.989925\pi$
$947$	−46.9803	−	27.1241i	−1.52665	−	0.881414i	−0.527155	−	0.849769i	$-0.676741\pi$
$948$	−0.114977	+	3.09500i	−0.00373426	+	0.100521i
$949$		−	56.6905i		−	1.84025i
$950$	38.3487	−	20.3782i	1.24420	−	0.661156i
$951$	−0.212506			−0.00689099
$952$	−0.812872	+	1.24261i	−0.0263453	+	0.0402733i
$953$	−17.6753	+	30.6145i	−0.572559	+	0.991701i	0.423743	+	0.905782i	$0.360716\pi$
$953$	−17.6753	+	30.6145i	−0.572559	+	0.991701i	−0.996302	+	0.0859189i	$0.972617\pi$
$954$	0.526389	−	28.3490i	0.0170425	−	0.917834i
$955$	37.6208	+	21.7204i	1.21738	+	0.702855i
$956$	15.7356	−	25.0580i	0.508925	−	0.810432i
$957$			61.4722i			1.98711i
$958$	−28.2159	+	46.8410i	−0.911613	+	1.51336i
$959$	−16.2376	−	28.1243i	−0.524338	−	0.908180i
$960$	25.1649	+	57.5522i	0.812192	+	1.85749i
$961$	−18.9131			−0.610099
$962$	13.4352	−	22.3036i	0.433167	−	0.719097i
$963$	−3.46499	+	2.00051i	−0.111658	+	0.0644656i
$964$	8.83117	+	0.328070i	0.284433	+	0.0105664i
$965$	69.9167	−	40.3664i	2.25070	−	1.29944i
$966$	38.9499	−	21.5336i	1.25319	−	0.692834i
$967$	−23.9241	+	41.4377i	−0.769346	+	1.33255i	0.168572	+	0.985689i	$0.446084\pi$
$967$	−23.9241	+	41.4377i	−0.769346	+	1.33255i	−0.937918	+	0.346857i	$0.887249\pi$
$968$	45.7105	+	2.54862i	1.46919	+	0.0819157i
$969$	−1.94198	−	0.0322173i	−0.0623853	−	0.00103497i
$970$	74.8795	+	45.1056i	2.40424	+	1.44825i
$971$	−9.26503	−	5.34916i	−0.297329	−	0.171663i	0.343913	−	0.939001i	$-0.388247\pi$
$971$	−9.26503	−	5.34916i	−0.297329	−	0.171663i	−0.641242	+	0.767338i	$0.721581\pi$
$972$	1.38119	−	37.1795i	0.0443016	−	1.19253i
$973$	−14.4758	+	8.35761i	−0.464073	+	0.267933i
$974$	−6.77610	−	12.2565i	−0.217120	−	0.392725i
$975$	−35.6293	−	61.7117i	−1.14105	−	1.97636i
$976$	−6.50619	−	4.43074i	−0.208258	−	0.141825i
$977$	7.04017			0.225235			0.112618	−	0.993638i	$-0.464077\pi$
$977$	7.04017			0.225235			0.112618	+	0.993638i	$0.464077\pi$
$978$	−35.4245	−	0.657768i	−1.13275	−	0.0210331i
$979$	4.59726	−	2.65423i	0.146929	−	0.0848295i
$980$	0.643864	−	0.340513i	0.0205675	−	0.0108773i
$981$			12.2652i			0.391597i
$982$	−0.332065	+	17.8836i	−0.0105966	+	0.570689i
$983$	−24.0902	+	41.7255i	−0.768359	+	1.33084i	0.170093	+	0.985428i	$0.445593\pi$
$983$	−24.0902	+	41.7255i	−0.768359	+	1.33084i	−0.938452	+	0.345409i	$0.887740\pi$
$984$	−19.1279	+	9.66588i	−0.609776	+	0.308137i
$985$	3.84071	−	6.65230i	0.122375	−	0.211960i
$986$	1.27030	−	0.702293i	0.0404547	−	0.0223656i
$987$		−	6.16931i		−	0.196371i
$988$	21.2731	−	32.6603i	0.676788	−	1.03906i
$989$		−	6.72574i		−	0.213866i
$990$	26.2287	+	47.4422i	0.833602	+	1.50781i
$991$	−4.84173	+	8.38612i	−0.153802	+	0.266394i	−0.932622	−	0.360854i	$-0.882485\pi$
$991$	−4.84173	+	8.38612i	−0.153802	+	0.266394i	0.778820	+	0.627248i	$0.215819\pi$
$992$	−11.3698	+	16.0471i	−0.360993	+	0.509495i
$993$	40.8778	−	70.8024i	1.29722	−	2.24685i
$994$	25.2592	+	0.469016i	0.801173	+	0.0148763i
$995$		−	34.9169i		−	1.10694i
$996$	−5.47532	−	10.3531i	−0.173492	−	0.328050i
$997$	−1.84500	+	1.06521i	−0.0584318	+	0.0337356i	−0.528931	−	0.848665i	$-0.677407\pi$
$997$	−1.84500	+	1.06521i	−0.0584318	+	0.0337356i	0.470499	+	0.882400i	$0.344074\pi$
$998$	0.355586	−	19.1503i	0.0112559	−	0.606193i
$999$	8.21406			0.259881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.p.a.125.13	yes	36
4.3	odd	2		608.2.t.a.49.15		36
8.3	odd	2		608.2.t.a.49.4		36
8.5	even	2	inner	152.2.p.a.125.1	yes	36
19.7	even	3	inner	152.2.p.a.45.1	✓	36
76.7	odd	6		608.2.t.a.273.4		36
152.45	even	6	inner	152.2.p.a.45.13	yes	36
152.83	odd	6		608.2.t.a.273.15		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.p.a.45.1	✓	36	19.7	even	3	inner
152.2.p.a.45.13	yes	36	152.45	even	6	inner
152.2.p.a.125.1	yes	36	8.5	even	2	inner
152.2.p.a.125.13	yes	36	1.1	even	1	trivial
608.2.t.a.49.4		36	8.3	odd	2
608.2.t.a.49.15		36	4.3	odd	2
608.2.t.a.273.4		36	76.7	odd	6
608.2.t.a.273.15		36	152.83	odd	6

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.684248 + 1.23766i) q^{2} +(-1.95927 - 1.13118i) q^{3} +(-1.06361 + 1.69373i) q^{4} +(-3.00559 - 1.73528i) q^{5} +(0.0593980 - 3.19892i) q^{6} -2.66551 q^{7} +(-2.82404 - 0.157456i) q^{8} +(1.05915 + 1.83451i) q^{9} +O(q^{10})\)	\(q+(0.684248 + 1.23766i) q^{2} +(-1.95927 - 1.13118i) q^{3} +(-1.06361 + 1.69373i) q^{4} +(-3.00559 - 1.73528i) q^{5} +(0.0593980 - 3.19892i) q^{6} -2.66551 q^{7} +(-2.82404 - 0.157456i) q^{8} +(1.05915 + 1.83451i) q^{9} +(0.0911187 - 4.90726i) q^{10} +5.21404i q^{11} +(3.99982 - 2.11534i) q^{12} +(3.87202 - 2.23551i) q^{13} +(-1.82387 - 3.29900i) q^{14} +(3.92584 + 6.79975i) q^{15} +(-1.73747 - 3.60295i) q^{16} +(-0.0984768 + 0.170567i) q^{17} +(-1.54578 + 2.56613i) q^{18} +(-3.73825 - 2.24177i) q^{19} +(6.13588 - 3.24501i) q^{20} +(5.22245 + 3.01518i) q^{21} +(-6.45321 + 3.56769i) q^{22} +(-2.60934 - 4.51951i) q^{23} +(5.35494 + 3.50301i) q^{24} +(3.52239 + 6.10095i) q^{25} +(5.41623 + 3.26260i) q^{26} +1.99471i q^{27} +(2.83506 - 4.51466i) q^{28} +(-4.51307 + 2.60562i) q^{29} +(-5.72954 + 9.51157i) q^{30} -3.47662 q^{31} +(3.27037 - 4.61570i) q^{32} +(5.89804 - 10.2157i) q^{33} +(-0.278487 - 0.00517097i) q^{34} +(8.01143 + 4.62540i) q^{35} +(-4.23370 - 0.157278i) q^{36} -4.11792i q^{37} +(0.216662 - 6.16061i) q^{38} -10.1151 q^{39} +(8.21468 + 5.37375i) q^{40} +(-1.67461 + 2.90051i) q^{41} +(-0.158326 + 8.52675i) q^{42} +(1.11612 + 0.644390i) q^{43} +(-8.83119 - 5.54571i) q^{44} -7.35171i q^{45} +(3.80819 - 6.32195i) q^{46} +(-0.511521 - 0.885980i) q^{47} +(-0.671432 + 9.02453i) q^{48} +0.104934 q^{49} +(-5.14073 + 8.53408i) q^{50} +(0.385885 - 0.222791i) q^{51} +(-0.331960 + 8.93588i) q^{52} +(-8.19671 + 4.73237i) q^{53} +(-2.46877 + 1.36487i) q^{54} +(9.04781 - 15.6713i) q^{55} +(7.52750 + 0.419701i) q^{56} +(4.78838 + 8.62087i) q^{57} +(-6.31293 - 3.80276i) q^{58} +(-1.43517 - 0.828597i) q^{59} +(-15.6925 - 0.582963i) q^{60} +(1.70425 - 0.983950i) q^{61} +(-2.37887 - 4.30288i) q^{62} +(-2.82319 - 4.88990i) q^{63} +(7.95042 + 0.889326i) q^{64} -15.5169 q^{65} +(16.6793 + 0.309703i) q^{66} +(9.10257 - 5.25537i) q^{67} +(-0.184154 - 0.348210i) q^{68} +11.8066i q^{69} +(-0.242878 + 13.0804i) q^{70} +(-3.35096 + 5.80404i) q^{71} +(-2.70224 - 5.34750i) q^{72} +(6.33977 - 10.9808i) q^{73} +(5.09659 - 2.81768i) q^{74} -15.9379i q^{75} +(7.77299 - 3.94723i) q^{76} -13.8981i q^{77} +(-6.92123 - 12.5191i) q^{78} +(-0.342245 + 0.592786i) q^{79} +(-1.03000 + 13.8440i) q^{80} +(5.43385 - 9.41170i) q^{81} +(-4.73569 - 0.0879329i) q^{82} -2.58839i q^{83} +(-10.6616 + 5.63845i) q^{84} +(0.591962 - 0.341770i) q^{85} +(-0.0338367 + 1.82230i) q^{86} +11.7897 q^{87} +(0.820983 - 14.7247i) q^{88} +(-0.509054 - 0.881708i) q^{89} +(9.09893 - 5.03039i) q^{90} +(-10.3209 + 5.95877i) q^{91} +(10.4302 + 0.387471i) q^{92} +(6.81164 + 3.93270i) q^{93} +(0.746536 - 1.23932i) q^{94} +(7.34555 + 13.2247i) q^{95} +(-11.6287 + 5.34401i) q^{96} +(-8.90520 + 15.4243i) q^{97} +(0.0718010 + 0.129873i) q^{98} +(-9.56521 + 5.52247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} + q^{4} - 3 q^{6} - 8 q^{7} + 2 q^{8} + 12 q^{9}+O(q^{10}) \) 36 * q - q^2 + q^4 - 3 * q^6 - 8 * q^7 + 2 * q^8 + 12 * q^9	\( 36 q - q^{2} + q^{4} - 3 q^{6} - 8 q^{7} + 2 q^{8} + 12 q^{9} - 10 q^{10} - 10 q^{12} - 6 q^{15} - 3 q^{16} - 2 q^{17} - 20 q^{18} + 16 q^{20} - 9 q^{22} - 2 q^{23} + 21 q^{24} + 8 q^{25} - 24 q^{26} + 8 q^{28} - 28 q^{30} - 48 q^{31} + 9 q^{32} + 12 q^{33} + 10 q^{34} + 4 q^{36} - 30 q^{38} - 20 q^{39} - 10 q^{40} + 2 q^{41} - 16 q^{42} + 3 q^{44} + 8 q^{46} + 10 q^{47} + 39 q^{48} - 12 q^{49} - 26 q^{50} - 12 q^{52} - 11 q^{54} + 8 q^{55} - 8 q^{56} - 6 q^{57} + 24 q^{58} + 34 q^{60} + 42 q^{62} - 28 q^{63} + 46 q^{64} - 28 q^{65} + 33 q^{66} + 44 q^{68} + 8 q^{70} - 30 q^{71} - 36 q^{72} - 10 q^{73} + 6 q^{74} + 39 q^{76} - 32 q^{78} + 34 q^{79} + 8 q^{80} - 2 q^{81} + 27 q^{82} - 40 q^{84} + 46 q^{86} + 36 q^{87} + 66 q^{88} - 2 q^{89} + 30 q^{90} + 22 q^{92} - 4 q^{94} + 38 q^{95} - 62 q^{96} - 18 q^{97} + 39 q^{98}+O(q^{100}) \) 36 * q - q^2 + q^4 - 3 * q^6 - 8 * q^7 + 2 * q^8 + 12 * q^9 - 10 * q^10 - 10 * q^12 - 6 * q^15 - 3 * q^16 - 2 * q^17 - 20 * q^18 + 16 * q^20 - 9 * q^22 - 2 * q^23 + 21 * q^24 + 8 * q^25 - 24 * q^26 + 8 * q^28 - 28 * q^30 - 48 * q^31 + 9 * q^32 + 12 * q^33 + 10 * q^34 + 4 * q^36 - 30 * q^38 - 20 * q^39 - 10 * q^40 + 2 * q^41 - 16 * q^42 + 3 * q^44 + 8 * q^46 + 10 * q^47 + 39 * q^48 - 12 * q^49 - 26 * q^50 - 12 * q^52 - 11 * q^54 + 8 * q^55 - 8 * q^56 - 6 * q^57 + 24 * q^58 + 34 * q^60 + 42 * q^62 - 28 * q^63 + 46 * q^64 - 28 * q^65 + 33 * q^66 + 44 * q^68 + 8 * q^70 - 30 * q^71 - 36 * q^72 - 10 * q^73 + 6 * q^74 + 39 * q^76 - 32 * q^78 + 34 * q^79 + 8 * q^80 - 2 * q^81 + 27 * q^82 - 40 * q^84 + 46 * q^86 + 36 * q^87 + 66 * q^88 - 2 * q^89 + 30 * q^90 + 22 * q^92 - 4 * q^94 + 38 * q^95 - 62 * q^96 - 18 * q^97 + 39 * q^98

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