LMFDB - Embedded newform 133.2.g.a.102.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [133,2,Mod(30,133)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(133, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("133.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 133 = 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	133.g (of order $3$, 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:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			102.12
Character	$\chi$	$=$	133.102
Dual form			133.2.g.a.30.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36182 - 2.35875i) q^{2} -2.49127 q^{3} +(-2.70912 - 4.69233i) q^{4} +(-0.614988 + 1.06519i) q^{5} +(-3.39266 + 5.87626i) q^{6} +(2.19933 - 1.47070i) q^{7} -9.31007 q^{8} +3.20641 q^{9} +O(q^{10})$	\(q+(1.36182 - 2.35875i) q^{2} -2.49127 q^{3} +(-2.70912 - 4.69233i) q^{4} +(-0.614988 + 1.06519i) q^{5} +(-3.39266 + 5.87626i) q^{6} +(2.19933 - 1.47070i) q^{7} -9.31007 q^{8} +3.20641 q^{9} +(1.67501 + 2.90120i) q^{10} +(1.11634 - 1.93355i) q^{11} +(6.74914 + 11.6898i) q^{12} +(1.07999 - 1.87060i) q^{13} +(-0.473915 - 7.19049i) q^{14} +(1.53210 - 2.65367i) q^{15} +(-7.26042 + 12.5754i) q^{16} -1.40907 q^{17} +(4.36656 - 7.56310i) q^{18} +(0.945943 - 4.25502i) q^{19} +6.66430 q^{20} +(-5.47911 + 3.66391i) q^{21} +(-3.04051 - 5.26631i) q^{22} +7.60208 q^{23} +23.1939 q^{24} +(1.74358 + 3.01997i) q^{25} +(-2.94151 - 5.09484i) q^{26} -0.514215 q^{27} +(-12.8593 - 6.33567i) q^{28} +(-3.53517 + 6.12309i) q^{29} +(-4.17289 - 7.22766i) q^{30} +(-1.00132 + 1.73434i) q^{31} +(10.4647 + 18.1254i) q^{32} +(-2.78109 + 4.81700i) q^{33} +(-1.91890 + 3.32363i) q^{34} +(0.214016 + 3.24717i) q^{35} +(-8.68654 - 15.0455i) q^{36} +(-1.43395 - 2.48368i) q^{37} +(-8.74830 - 8.02582i) q^{38} +(-2.69054 + 4.66015i) q^{39} +(5.72558 - 9.91700i) q^{40} +(4.18614 + 7.25060i) q^{41} +(1.18065 + 17.9134i) q^{42} +(-1.55531 - 2.69387i) q^{43} -12.0972 q^{44} +(-1.97190 + 3.41543i) q^{45} +(10.3527 - 17.9314i) q^{46} -0.229860 q^{47} +(18.0876 - 31.3287i) q^{48} +(2.67408 - 6.46910i) q^{49} +9.49778 q^{50} +3.51036 q^{51} -11.7033 q^{52} +(0.119005 + 0.206123i) q^{53} +(-0.700269 + 1.21290i) q^{54} +(1.37307 + 2.37822i) q^{55} +(-20.4759 + 13.6923i) q^{56} +(-2.35659 + 10.6004i) q^{57} +(9.62855 + 16.6771i) q^{58} -6.41716 q^{59} -16.6026 q^{60} -2.31664 q^{61} +(2.72724 + 4.72372i) q^{62} +(7.05194 - 4.71566i) q^{63} +27.9627 q^{64} +(1.32836 + 2.30079i) q^{65} +(7.57471 + 13.1198i) q^{66} +(1.17187 + 2.02974i) q^{67} +(3.81733 + 6.61181i) q^{68} -18.9388 q^{69} +(7.95069 + 3.91725i) q^{70} +(1.11072 + 1.92382i) q^{71} -29.8519 q^{72} +11.5781 q^{73} -7.81116 q^{74} +(-4.34372 - 7.52355i) q^{75} +(-22.5286 + 7.08868i) q^{76} +(-0.388486 - 5.89431i) q^{77} +(7.32808 + 12.6926i) q^{78} +(2.72101 - 4.71292i) q^{79} +(-8.93014 - 15.4675i) q^{80} -8.33818 q^{81} +22.8031 q^{82} +3.62035 q^{83} +(32.0358 + 15.7838i) q^{84} +(0.866560 - 1.50093i) q^{85} -8.47221 q^{86} +(8.80705 - 15.2543i) q^{87} +(-10.3932 + 18.0015i) q^{88} -13.2981 q^{89} +(5.37076 + 9.30243i) q^{90} +(-0.375837 - 5.70240i) q^{91} +(-20.5950 - 35.6715i) q^{92} +(2.49456 - 4.32070i) q^{93} +(-0.313028 + 0.542181i) q^{94} +(3.95066 + 3.62439i) q^{95} +(-26.0704 - 45.1553i) q^{96} +(-3.50502 - 6.07088i) q^{97} +(-11.6173 - 15.1172i) q^{98} +(3.57943 - 6.19976i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9}+O(q^{10}) $ 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9} + 16 q^{10} - q^{11} - 2 q^{12} + 6 q^{13} - q^{14} - 9 q^{15} - 9 q^{16} - 16 q^{17} + 5 q^{18} - 4 q^{19} - 21 q^{21} - 2 q^{22} + 18 q^{23} + 16 q^{24} - 14 q^{25} + q^{26} - 18 q^{27} - 14 q^{28} - 2 q^{29} - 9 q^{30} + 11 q^{31} + 24 q^{32} + 3 q^{33} + 6 q^{34} + 38 q^{35} - 7 q^{36} - 14 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 20 q^{41} - 36 q^{42} + 2 q^{43} - 4 q^{44} - 12 q^{45} - 6 q^{46} + 39 q^{48} + 18 q^{49} + 22 q^{50} - 42 q^{51} - 22 q^{52} + 7 q^{53} - 43 q^{54} + 9 q^{55} - 21 q^{56} + 21 q^{57} + 35 q^{58} - 84 q^{59} + 12 q^{60} - 12 q^{61} - 19 q^{62} + 9 q^{63} - 2 q^{64} - 27 q^{65} + 3 q^{66} - 14 q^{67} + 51 q^{68} - 34 q^{69} + 33 q^{70} + q^{71} - 36 q^{72} + 42 q^{73} + 50 q^{74} + 31 q^{75} - 70 q^{76} - 20 q^{77} + 57 q^{78} - 5 q^{79} + 13 q^{80} - 56 q^{81} + 24 q^{82} + 10 q^{83} + 129 q^{84} - 27 q^{85} - 36 q^{86} + 53 q^{87} - 36 q^{88} + 2 q^{89} + 27 q^{90} - 9 q^{91} - 72 q^{92} + 34 q^{93} + 12 q^{94} - 11 q^{95} - 94 q^{96} + 31 q^{97} - 26 q^{98} + 43 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9 + 16 * q^10 - q^11 - 2 * q^12 + 6 * q^13 - q^14 - 9 * q^15 - 9 * q^16 - 16 * q^17 + 5 * q^18 - 4 * q^19 - 21 * q^21 - 2 * q^22 + 18 * q^23 + 16 * q^24 - 14 * q^25 + q^26 - 18 * q^27 - 14 * q^28 - 2 * q^29 - 9 * q^30 + 11 * q^31 + 24 * q^32 + 3 * q^33 + 6 * q^34 + 38 * q^35 - 7 * q^36 - 14 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 20 * q^41 - 36 * q^42 + 2 * q^43 - 4 * q^44 - 12 * q^45 - 6 * q^46 + 39 * q^48 + 18 * q^49 + 22 * q^50 - 42 * q^51 - 22 * q^52 + 7 * q^53 - 43 * q^54 + 9 * q^55 - 21 * q^56 + 21 * q^57 + 35 * q^58 - 84 * q^59 + 12 * q^60 - 12 * q^61 - 19 * q^62 + 9 * q^63 - 2 * q^64 - 27 * q^65 + 3 * q^66 - 14 * q^67 + 51 * q^68 - 34 * q^69 + 33 * q^70 + q^71 - 36 * q^72 + 42 * q^73 + 50 * q^74 + 31 * q^75 - 70 * q^76 - 20 * q^77 + 57 * q^78 - 5 * q^79 + 13 * q^80 - 56 * q^81 + 24 * q^82 + 10 * q^83 + 129 * q^84 - 27 * q^85 - 36 * q^86 + 53 * q^87 - 36 * q^88 + 2 * q^89 + 27 * q^90 - 9 * q^91 - 72 * q^92 + 34 * q^93 + 12 * q^94 - 11 * q^95 - 94 * q^96 + 31 * q^97 - 26 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$.

$n$	$78$	$115$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.36182	−	2.35875i	0.962954	−	1.66788i	0.247939	−	0.968776i	$-0.420247\pi$
$2$	1.36182	−	2.35875i	0.962954	−	1.66788i	0.715015	−	0.699109i	$-0.246420\pi$
$3$	−2.49127			−1.43833			−0.719167	−	0.694838i	$-0.755476\pi$
$3$	−2.49127			−1.43833			−0.719167	+	0.694838i	$0.755476\pi$
$4$	−2.70912	−	4.69233i	−1.35456	−	2.34617i
$5$	−0.614988	+	1.06519i	−0.275031	+	0.476368i	−0.970143	−	0.242534i	$-0.922021\pi$
$5$	−0.614988	+	1.06519i	−0.275031	+	0.476368i	0.695112	+	0.718901i	$0.255355\pi$
$6$	−3.39266	+	5.87626i	−1.38505	+	2.39897i
$7$	2.19933	−	1.47070i	0.831268	−	0.555873i
$7$	2.19933	−	1.47070i	0.831268	−	0.555873i
$8$	−9.31007			−3.29161
$9$	3.20641			1.06880
$10$	1.67501	+	2.90120i	0.529684	+	0.917440i
$11$	1.11634	−	1.93355i	0.336588	−	0.582988i	−0.647200	−	0.762320i	$-0.724060\pi$
$11$	1.11634	−	1.93355i	0.336588	−	0.582988i	0.983789	+	0.179332i	$0.0573936\pi$
$12$	6.74914	+	11.6898i	1.94831	+	3.37457i
$13$	1.07999	−	1.87060i	0.299535	−	0.518810i	−0.676494	−	0.736448i	$-0.736502\pi$
$13$	1.07999	−	1.87060i	0.299535	−	0.518810i	0.976030	+	0.217638i	$0.0698351\pi$
$14$	−0.473915	−	7.19049i	−0.126659	−	1.92174i
$15$	1.53210	−	2.65367i	0.395586	−	0.685175i
$16$	−7.26042	+	12.5754i	−1.81510	+	3.14385i
$17$	−1.40907			−0.341749			−0.170875	−	0.985293i	$-0.554659\pi$
$17$	−1.40907			−0.341749			−0.170875	+	0.985293i	$0.554659\pi$
$18$	4.36656	−	7.56310i	1.02921	−	1.78264i
$19$	0.945943	−	4.25502i	0.217014	−	0.976168i
$19$	0.945943	−	4.25502i	0.217014	−	0.976168i
$20$	6.66430			1.49018
$21$	−5.47911	+	3.66391i	−1.19564	+	0.799530i
$22$	−3.04051	−	5.26631i	−0.648238	−	1.12278i
$23$	7.60208			1.58514			0.792572	−	0.609778i	$-0.208742\pi$
$23$	7.60208			1.58514			0.792572	+	0.609778i	$0.208742\pi$
$24$	23.1939			4.73443
$25$	1.74358	+	3.01997i	0.348716	+	0.603994i
$26$	−2.94151	−	5.09484i	−0.576877	−	0.999180i
$27$	−0.514215			−0.0989606
$28$	−12.8593	−	6.33567i	−2.43017	−	1.19733i
$29$	−3.53517	+	6.12309i	−0.656465	+	1.13703i	0.325060	+	0.945693i	$0.394616\pi$
$29$	−3.53517	+	6.12309i	−0.656465	+	1.13703i	−0.981524	+	0.191337i	$0.938718\pi$
$30$	−4.17289	−	7.22766i	−0.761862	−	1.31958i
$31$	−1.00132	+	1.73434i	−0.179843	+	0.311497i	−0.941827	−	0.336099i	$-0.890892\pi$
$31$	−1.00132	+	1.73434i	−0.179843	+	0.311497i	0.761984	+	0.647596i	$0.224226\pi$
$32$	10.4647	+	18.1254i	1.84992	+	3.20416i
$33$	−2.78109	+	4.81700i	−0.484126	+	0.838531i
$34$	−1.91890	+	3.32363i	−0.329089	+	0.569998i
$35$	0.214016	+	3.24717i	0.0361754	+	0.548871i
$36$	−8.68654	−	15.0455i	−1.44776	−	2.50759i
$37$	−1.43395	−	2.48368i	−0.235741	−	0.408315i	0.723747	−	0.690065i	$-0.242418\pi$
$37$	−1.43395	−	2.48368i	−0.235741	−	0.408315i	−0.959488	+	0.281751i	$0.909085\pi$
$38$	−8.74830	−	8.02582i	−1.41916	−	1.30196i
$39$	−2.69054	+	4.66015i	−0.430831	+	0.746222i
$40$	5.72558	−	9.91700i	0.905294	−	1.56801i
$41$	4.18614	+	7.25060i	0.653765	+	1.13235i	0.982202	+	0.187828i	$0.0601447\pi$
$41$	4.18614	+	7.25060i	0.653765	+	1.13235i	−0.328437	+	0.944526i	$0.606522\pi$
$42$	1.18065	+	17.9134i	0.182178	+	2.76410i
$43$	−1.55531	−	2.69387i	−0.237182	−	0.410812i	0.722722	−	0.691138i	$-0.242891\pi$
$43$	−1.55531	−	2.69387i	−0.237182	−	0.410812i	−0.959905	+	0.280327i	$0.909557\pi$
$44$	−12.0972			−1.82372
$45$	−1.97190	+	3.41543i	−0.293954	+	0.509143i
$46$	10.3527	−	17.9314i	1.52642	−	2.64384i
$47$	−0.229860			−0.0335285			−0.0167642	−	0.999859i	$-0.505336\pi$
$47$	−0.229860			−0.0335285			−0.0167642	+	0.999859i	$0.505336\pi$
$48$	18.0876	−	31.3287i	2.61073	−	4.52191i
$49$	2.67408	−	6.46910i	0.382011	−	0.924158i
$50$	9.49778			1.34319
$51$	3.51036			0.491549
$52$	−11.7033			−1.62295
$53$	0.119005	+	0.206123i	0.0163466	+	0.0283132i	0.874083	−	0.485777i	$-0.161463\pi$
$53$	0.119005	+	0.206123i	0.0163466	+	0.0283132i	−0.857736	+	0.514090i	$0.828130\pi$
$54$	−0.700269	+	1.21290i	−0.0952945	+	0.165055i
$55$	1.37307	+	2.37822i	0.185144	+	0.320680i
$56$	−20.4759	+	13.6923i	−2.73621	+	1.82971i
$57$	−2.35659	+	10.6004i	−0.312139	+	1.40406i
$58$	9.62855	+	16.6771i	1.26429	+	2.18981i
$59$	−6.41716			−0.835443			−0.417722	−	0.908575i	$-0.637171\pi$
$59$	−6.41716			−0.835443			−0.417722	+	0.908575i	$0.637171\pi$
$60$	−16.6026			−2.14338
$61$	−2.31664			−0.296616			−0.148308	−	0.988941i	$-0.547383\pi$
$61$	−2.31664			−0.296616			−0.148308	+	0.988941i	$0.547383\pi$
$62$	2.72724	+	4.72372i	0.346360	+	0.599914i
$63$	7.05194	−	4.71566i	0.888461	−	0.594118i
$64$	27.9627			3.49534
$65$	1.32836	+	2.30079i	0.164763	+	0.285378i
$66$	7.57471	+	13.1198i	0.932382	+	1.61493i
$67$	1.17187	+	2.02974i	0.143167	+	0.247973i	0.928688	−	0.370863i	$-0.120938\pi$
$67$	1.17187	+	2.02974i	0.143167	+	0.247973i	−0.785521	+	0.618836i	$0.787605\pi$
$68$	3.81733	+	6.61181i	0.462920	+	0.801800i
$69$	−18.9388			−2.27997
$70$	7.95069	+	3.91725i	0.950289	+	0.468201i
$71$	1.11072	+	1.92382i	0.131818	+	0.228315i	0.924377	−	0.381480i	$-0.124585\pi$
$71$	1.11072	+	1.92382i	0.131818	+	0.228315i	−0.792560	+	0.609794i	$0.791252\pi$
$72$	−29.8519			−3.51808
$73$	11.5781			1.35512			0.677559	−	0.735468i	$-0.263038\pi$
$73$	11.5781			1.35512			0.677559	+	0.735468i	$0.263038\pi$
$74$	−7.81116			−0.908029
$75$	−4.34372	−	7.52355i	−0.501570	−	0.868744i
$76$	−22.5286	+	7.08868i	−2.58421	+	0.813127i
$77$	−0.388486	−	5.89431i	−0.0442721	−	0.671719i
$78$	7.32808	+	12.6926i	0.829742	+	1.43715i
$79$	2.72101	−	4.71292i	0.306137	−	0.530245i	−0.671377	−	0.741116i	$-0.734297\pi$
$79$	2.72101	−	4.71292i	0.306137	−	0.530245i	0.977514	+	0.210871i	$0.0676300\pi$
$80$	−8.93014	−	15.4675i	−0.998420	−	1.72931i
$81$	−8.33818			−0.926464
$82$	22.8031			2.51818
$83$	3.62035			0.397385			0.198693	−	0.980062i	$-0.436330\pi$
$83$	3.62035			0.397385			0.198693	+	0.980062i	$0.436330\pi$
$84$	32.0358	+	15.7838i	3.49540	+	1.72216i
$85$	0.866560	−	1.50093i	0.0939916	−	0.162798i
$86$	−8.47221			−0.913582
$87$	8.80705	−	15.2543i	0.944215	−	1.63543i
$88$	−10.3932	+	18.0015i	−1.10792	+	1.91897i
$89$	−13.2981			−1.40960			−0.704798	−	0.709408i	$-0.748962\pi$
$89$	−13.2981			−1.40960			−0.704798	+	0.709408i	$0.748962\pi$
$90$	5.37076	+	9.30243i	0.566128	+	0.980562i
$91$	−0.375837	−	5.70240i	−0.0393985	−	0.597774i
$92$	−20.5950	−	35.6715i	−2.14717	−	3.71901i
$93$	2.49456	−	4.32070i	0.258674	−	0.448036i
$94$	−0.313028	+	0.542181i	−0.0322864	+	0.0559217i
$95$	3.95066	+	3.62439i	0.405329	+	0.371855i
$96$	−26.0704	−	45.1553i	−2.66080	−	4.60864i
$97$	−3.50502	−	6.07088i	−0.355881	−	0.616404i	0.631387	−	0.775468i	$-0.282486\pi$
$97$	−3.50502	−	6.07088i	−0.355881	−	0.616404i	−0.987268	+	0.159064i	$0.949153\pi$
$98$	−11.6173	−	15.1172i	−1.17353	−	1.52707i
$99$	3.57943	−	6.19976i	0.359746	−	0.623099i
$100$	9.44713	−	16.3629i	0.944713	−	1.63629i
$101$	6.96133	+	12.0574i	0.692678	+	1.19975i	0.970957	+	0.239253i	$0.0769026\pi$
$101$	6.96133	+	12.0574i	0.692678	+	1.19975i	−0.278279	+	0.960500i	$0.589764\pi$
$102$	4.78049	−	8.28005i	0.473339	−	0.819847i
$103$	−2.46807	−	4.27483i	−0.243187	−	0.421212i	0.718434	−	0.695596i	$-0.244859\pi$
$103$	−2.46807	−	4.27483i	−0.243187	−	0.421212i	−0.961620	+	0.274384i	$0.911526\pi$
$104$	−10.0548	+	17.4154i	−0.985952	+	1.70772i
$105$	−0.533172	−	8.08955i	−0.0520322	−	0.789460i
$106$	0.648256			0.0629642
$107$	0.875789	+	1.51691i	0.0846657	+	0.146645i	0.905249	−	0.424882i	$-0.139684\pi$
$107$	0.875789	+	1.51691i	0.0846657	+	0.146645i	−0.820583	+	0.571527i	$0.806351\pi$
$108$	1.39307	+	2.41287i	0.134048	+	0.232178i
$109$	−13.8940			−1.33080			−0.665401	−	0.746486i	$-0.731739\pi$
$109$	−13.8940			−1.33080			−0.665401	+	0.746486i	$0.731739\pi$
$110$	7.47950			0.713142
$111$	3.57236	+	6.18751i	0.339074	+	0.587293i
$112$	2.52663	+	38.3354i	0.238744	+	3.62235i
$113$	16.7404			1.57480			0.787400	−	0.616442i	$-0.211427\pi$
$113$	16.7404			1.57480			0.787400	+	0.616442i	$0.211427\pi$
$114$	21.7943	+	19.9944i	2.04123	+	1.87265i
$115$	−4.67519	+	8.09767i	−0.435964	+	0.755111i
$116$	38.3088			3.55688
$117$	3.46289	−	5.99789i	0.320144	−	0.554506i
$118$	−8.73903	+	15.1365i	−0.804493	+	1.39342i
$119$	−3.09900	+	2.07232i	−0.284085	+	0.189969i
$120$	−14.2639	+	24.7059i	−1.30211	+	2.25533i
$121$	3.00758	+	5.20928i	0.273417	+	0.473571i
$122$	−3.15486	+	5.46438i	−0.285627	+	0.494721i
$123$	−10.4288	−	18.0632i	−0.940331	−	1.62870i
$124$	10.8508			0.974431
$125$	−10.4390			−0.933693
$126$	−1.51957	−	23.0556i	−0.135374	−	2.05396i
$127$	−1.33773	+	2.31701i	−0.118704	+	0.205601i	−0.919254	−	0.393664i	$-0.871207\pi$
$127$	−1.33773	+	2.31701i	−0.118704	+	0.205601i	0.800550	+	0.599266i	$0.204541\pi$
$128$	17.1508	−	29.7061i	1.51593	−	2.62567i
$129$	3.87469	+	6.71115i	0.341147	+	0.590884i
$130$	7.23597			0.634636
$131$	−0.996482	+	1.72596i	−0.0870630	+	0.150798i	−0.906268	−	0.422703i	$-0.861081\pi$
$131$	−0.996482	+	1.72596i	−0.0870630	+	0.150798i	0.819205	+	0.573500i	$0.194415\pi$
$132$	30.1373			2.62311
$133$	−4.17742	−	10.7494i	−0.362228	−	0.932089i
$134$	6.38353			0.551453
$135$	0.316236	−	0.547736i	0.0272172	−	0.0471416i
$136$	13.1185			1.12490
$137$	−0.163953	−	0.283976i	−0.0140075	−	0.0242617i	0.858937	−	0.512082i	$-0.171126\pi$
$137$	−0.163953	−	0.283976i	−0.0140075	−	0.0242617i	−0.872944	+	0.487820i	$0.837792\pi$
$138$	−25.7913	+	44.6718i	−2.19550	+	3.80272i
$139$	4.95108	−	8.57552i	0.419945	−	0.727366i	−0.575989	−	0.817458i	$-0.695383\pi$
$139$	4.95108	−	8.57552i	0.419945	−	0.727366i	0.995933	+	0.0900919i	$0.0287161\pi$
$140$	14.6570	−	9.80120i	1.23874	−	0.828352i
$141$	0.572642			0.0482251
$142$	6.05039			0.507737
$143$	−2.41127	−	4.17643i	−0.201640	−	0.349251i
$144$	−23.2799	+	40.3219i	−1.93999	+	3.36016i
$145$	−4.34817	−	7.53126i	−0.361096	−	0.625437i
$146$	15.7674	−	27.3099i	1.30492	−	2.26018i
$147$	−6.66184	+	16.1163i	−0.549460	+	1.32925i
$148$	−7.76951	+	13.4572i	−0.638650	+	1.10617i
$149$	−2.75071	+	4.76437i	−0.225347	+	0.390313i	−0.956424	−	0.291983i	$-0.905685\pi$
$149$	−2.75071	+	4.76437i	−0.225347	+	0.390313i	0.731076	+	0.682296i	$0.239018\pi$
$150$	−23.6615			−1.93195
$151$	−3.96251	+	6.86327i	−0.322465	+	0.558525i	−0.980996	−	0.194028i	$-0.937845\pi$
$151$	−3.96251	+	6.86327i	−0.322465	+	0.558525i	0.658531	+	0.752553i	$0.271178\pi$
$152$	−8.80679	+	39.6145i	−0.714325	+	3.21316i
$153$	−4.51804			−0.365262
$154$	−14.4322	−	7.11067i	−1.16298	−	0.572994i
$155$	−1.23160	−	2.13320i	−0.0989246	−	0.171342i
$156$	29.1560			2.33435
$157$	21.4671			1.71326			0.856630	−	0.515932i	$-0.172554\pi$
$157$	21.4671			1.71326			0.856630	+	0.515932i	$0.172554\pi$
$158$	−7.41106	−	12.8363i	−0.589592	−	1.02120i
$159$	−0.296474	−	0.513507i	−0.0235119	−	0.0407238i
$160$	−25.7427			−2.03514
$161$	16.7195	−	11.1804i	1.31768	−	0.881138i
$162$	−11.3551	+	19.6676i	−0.892142	+	1.54524i
$163$	0.265941	+	0.460623i	0.0208301	+	0.0360788i	0.876253	−	0.481852i	$-0.160036\pi$
$163$	0.265941	+	0.460623i	0.0208301	+	0.0360788i	−0.855422	+	0.517931i	$0.826702\pi$
$164$	22.6815	−	39.2855i	1.77113	−	3.06768i
$165$	−3.42068	−	5.92479i	−0.266299	−	0.461244i
$166$	4.93028	−	8.53949i	0.382664	−	0.662793i
$167$	−0.239047	+	0.414042i	−0.0184980	+	0.0320395i	−0.875126	−	0.483895i	$-0.839222\pi$
$167$	−0.239047	+	0.414042i	−0.0184980	+	0.0320395i	0.856628	+	0.515934i	$0.172555\pi$
$168$	51.0109	−	34.1112i	3.93558	−	2.63174i
$169$	4.16724	+	7.21788i	0.320557	+	0.555222i
$170$	−2.36020	−	4.08799i	−0.181019	−	0.313534i
$171$	3.03308	−	13.6433i	0.231945	−	1.04333i
$172$	−8.42703	+	14.5960i	−0.642555	+	1.11294i
$173$	5.25257	−	9.09772i	0.399345	−	0.691687i	−0.594300	−	0.804244i	$-0.702571\pi$
$173$	5.25257	−	9.09772i	0.399345	−	0.691687i	0.993645	+	0.112557i	$0.0359041\pi$
$174$	−23.9873	−	41.5472i	−1.81847	−	3.14968i
$175$	8.27617	+	4.07762i	0.625620	+	0.308239i
$176$	16.2102	+	28.0768i	1.22189	+	2.11637i
$177$	15.9869			1.20165
$178$	−18.1096	+	31.3668i	−1.35738	+	2.35104i
$179$	−7.23771	+	12.5361i	−0.540972	+	0.936991i	0.457877	+	0.889016i	$0.348610\pi$
$179$	−7.23771	+	12.5361i	−0.540972	+	0.936991i	−0.998849	+	0.0479749i	$0.984723\pi$
$180$	21.3685			1.59271
$181$	−1.59130	+	2.75620i	−0.118280	+	0.204867i	−0.919086	−	0.394057i	$-0.871071\pi$
$181$	−1.59130	+	2.75620i	−0.118280	+	0.204867i	0.800806	+	0.598924i	$0.204405\pi$
$182$	−13.9623	−	6.87914i	−1.03496	−	0.509916i
$183$	5.77138			0.426633
$184$	−70.7759			−5.21767
$185$	3.52746			0.259344
$186$	−6.79429	−	11.7681i	−0.498182	−	0.862876i
$187$	−1.57299	+	2.72451i	−0.115029	+	0.199236i
$188$	0.622718	+	1.07858i	0.0454163	+	0.0786634i
$189$	−1.13093	+	0.756256i	−0.0822628	+	0.0550095i
$190$	13.9291	−	4.38283i	1.01052	−	0.317964i
$191$	2.48495	+	4.30406i	0.179805	+	0.311431i	0.941814	−	0.336136i	$-0.109120\pi$
$191$	2.48495	+	4.30406i	0.179805	+	0.311431i	−0.762009	+	0.647567i	$0.775787\pi$
$192$	−69.6626			−5.02747
$193$	22.6631			1.63132			0.815661	−	0.578530i	$-0.196373\pi$
$193$	22.6631			1.63132			0.815661	+	0.578530i	$0.196373\pi$
$194$	−19.0929			−1.37079
$195$	−3.30930	−	5.73188i	−0.236984	−	0.410468i
$196$	−37.5996	+	4.97790i	−2.68568	+	0.355564i
$197$	−14.5534			−1.03689			−0.518445	−	0.855111i	$-0.673489\pi$
$197$	−14.5534			−1.03689			−0.518445	+	0.855111i	$0.673489\pi$
$198$	−9.74910	−	16.8859i	−0.692838	−	1.20003i
$199$	−2.06826	−	3.58233i	−0.146615	−	0.253944i	0.783359	−	0.621569i	$-0.213504\pi$
$199$	−2.06826	−	3.58233i	−0.146615	−	0.253944i	−0.929974	+	0.367625i	$0.880171\pi$
$200$	−16.2328	−	28.1161i	−1.14784	−	1.98811i
$201$	−2.91945	−	5.05663i	−0.205922	−	0.356667i
$202$	37.9204			2.66807
$203$	1.23024	+	18.6659i	0.0863461	+	1.31009i
$204$	−9.50999	−	16.4718i	−0.665833	−	1.15326i
$205$	−10.2977			−0.719222
$206$	−13.4443			−0.936710
$207$	24.3754			1.69421
$208$	15.6824	+	27.1626i	1.08738	+	1.88339i
$209$	−7.17132	−	6.57907i	−0.496050	−	0.455084i
$210$	−19.8073	−	9.75892i	−1.36683	−	0.673429i
$211$	−11.0031	−	19.0580i	−0.757487	−	1.31201i	−0.944128	−	0.329578i	$-0.893093\pi$
$211$	−11.0031	−	19.0580i	−0.757487	−	1.31201i	0.186641	−	0.982428i	$-0.440240\pi$
$212$	0.644799	−	1.11682i	0.0442849	−	0.0767038i
$213$	−2.76709	−	4.79274i	−0.189598	−	0.328393i
$214$	4.77067			0.326117
$215$	3.82598			0.260930
$216$	4.78737			0.325739
$217$	0.348461	+	5.28702i	0.0236551	+	0.358907i
$218$	−18.9211	+	32.7724i	−1.28150	+	2.21962i
$219$	−28.8442			−1.94911
$220$	7.43961	−	12.8858i	0.501579	−	0.868759i
$221$	−1.52178	+	2.63580i	−0.102366	+	0.177303i
$222$	19.4597			1.30605
$223$	6.06047	+	10.4971i	0.405839	+	0.702934i	0.994419	−	0.105505i	$-0.0336459\pi$
$223$	6.06047	+	10.4971i	0.405839	+	0.702934i	−0.588579	+	0.808439i	$0.700313\pi$
$224$	49.6725	+	24.4733i	3.31888	+	1.63519i
$225$	5.59063	+	9.68325i	0.372708	+	0.645550i
$226$	22.7974	−	39.4862i	1.51646	−	2.62659i
$227$	−9.99844	+	17.3178i	−0.663620	+	1.14942i	0.316037	+	0.948747i	$0.397647\pi$
$227$	−9.99844	+	17.3178i	−0.663620	+	1.14942i	−0.979657	+	0.200677i	$0.935686\pi$
$228$	56.1248	−	17.6598i	3.71696	−	1.16955i
$229$	9.22353	+	15.9756i	0.609508	+	1.05570i	0.991322	+	0.131459i	$0.0419663\pi$
$229$	9.22353	+	15.9756i	0.609508	+	1.05570i	−0.381814	+	0.924239i	$0.624700\pi$
$230$	12.7336	+	22.0552i	0.839626	+	1.45427i
$231$	0.967823	+	14.6843i	0.0636781	+	0.966156i
$232$	32.9127	−	57.0064i	2.16082	−	3.74265i
$233$	−4.08148	+	7.06934i	−0.267387	+	0.463128i	−0.968186	−	0.250231i	$-0.919494\pi$
$233$	−4.08148	+	7.06934i	−0.267387	+	0.463128i	0.700799	+	0.713358i	$0.252827\pi$
$234$	−9.43167	−	16.3361i	−0.616568	−	1.06793i
$235$	0.141361	−	0.244844i	0.00922137	−	0.0159719i
$236$	17.3849	+	30.1115i	1.13166	+	1.96009i
$237$	−6.77875	+	11.7411i	−0.440327	+	0.762669i
$238$	0.667779	+	10.1319i	0.0432857	+	0.656752i
$239$	−15.4030			−0.996340			−0.498170	−	0.867079i	$-0.665994\pi$
$239$	−15.4030			−0.996340			−0.498170	+	0.867079i	$0.665994\pi$
$240$	22.2474	+	38.5336i	1.43606	+	2.48733i
$241$	−7.01751	−	12.1547i	−0.452037	−	0.782952i	0.546475	−	0.837475i	$-0.315969\pi$
$241$	−7.01751	−	12.1547i	−0.452037	−	0.782952i	−0.998512	+	0.0545237i	$0.982636\pi$
$242$	16.3832			1.05315
$243$	22.3153			1.43152
$244$	6.27607	+	10.8705i	0.401784	+	0.695910i
$245$	5.24630	+	6.82682i	0.335174	+	0.436150i
$246$	−56.8086			−3.62198
$247$	−6.93782	−	6.36485i	−0.441443	−	0.404986i
$248$	9.32237	−	16.1468i	0.591971	−	1.02532i
$249$	−9.01926			−0.571572
$250$	−14.2161	+	24.6229i	−0.899103	+	1.55729i
$251$	1.06324	−	1.84159i	0.0671114	−	0.116240i	−0.830517	−	0.556993i	$-0.811955\pi$
$251$	1.06324	−	1.84159i	0.0671114	−	0.116240i	0.897629	+	0.440753i	$0.145288\pi$
$252$	−41.2320	−	20.3147i	−2.59737	−	1.27971i
$253$	8.48649	−	14.6990i	0.533541	−	0.924120i
$254$	3.64349	+	6.31071i	0.228613	+	0.395969i
$255$	−2.15883	+	3.73920i	−0.135191	+	0.234158i
$256$	−18.7500	−	32.4759i	−1.17187	−	2.02975i
$257$	−15.1563			−0.945422			−0.472711	−	0.881218i	$-0.656725\pi$
$257$	−15.1563			−0.945422			−0.472711	+	0.881218i	$0.656725\pi$
$258$	21.1065			1.31404
$259$	−6.80649	−	3.35351i	−0.422935	−	0.208377i
$260$	7.19738	−	12.4662i	0.446362	−	0.773123i
$261$	−11.3352	+	19.6331i	−0.701631	+	1.21526i
$262$	2.71406	+	4.70089i	0.167675	+	0.290422i
$263$	−29.2613			−1.80433			−0.902163	−	0.431395i	$-0.858022\pi$
$263$	−29.2613			−1.80433			−0.902163	+	0.431395i	$0.858022\pi$
$264$	25.8922	−	44.8466i	1.59355	−	2.76011i
$265$	−0.292747			−0.0179833
$266$	−31.0440	−	4.78527i	−1.90343	−	0.293404i
$267$	33.1291			2.02747
$268$	6.34949	−	10.9976i	0.387857	−	0.671788i
$269$	10.5188			0.641342			0.320671	−	0.947191i	$-0.396092\pi$
$269$	10.5188			0.641342			0.320671	+	0.947191i	$0.396092\pi$
$270$	−0.861314	−	1.49184i	−0.0524179	−	0.0907904i
$271$	−9.96390	+	17.2580i	−0.605264	+	1.04835i	0.386746	+	0.922186i	$0.373599\pi$
$271$	−9.96390	+	17.2580i	−0.605264	+	1.04835i	−0.992010	+	0.126162i	$0.959734\pi$
$272$	10.2304	−	17.7196i	0.620310	−	1.07441i
$273$	0.936311	+	14.2062i	0.0566681	+	0.859797i
$274$	−0.893102			−0.0539543
$275$	7.78569			0.469495
$276$	51.3075	+	88.8672i	3.08835	+	5.34918i
$277$	−1.42113	+	2.46146i	−0.0853872	+	0.147895i	−0.905556	−	0.424226i	$-0.860546\pi$
$277$	−1.42113	+	2.46146i	−0.0853872	+	0.147895i	0.820169	+	0.572121i	$0.193879\pi$
$278$	−13.4850	−	23.3567i	−0.808775	−	1.40084i
$279$	−3.21064	+	5.56100i	−0.192216	+	0.332928i
$280$	−1.99251	−	30.2313i	−0.119075	−	1.80667i
$281$	0.468612	−	0.811660i	0.0279551	−	0.0484196i	−0.851709	−	0.524014i	$-0.824434\pi$
$281$	0.468612	−	0.811660i	0.0279551	−	0.0484196i	0.879664	+	0.475595i	$0.157767\pi$
$282$	0.779836	−	1.35072i	0.0464386	−	0.0804340i
$283$	−31.4487			−1.86943			−0.934714	−	0.355400i	$-0.884345\pi$
$283$	−31.4487			−1.86943			−0.934714	+	0.355400i	$0.884345\pi$
$284$	6.01812	−	10.4237i	0.357110	−	0.618532i
$285$	−9.84215	−	9.02933i	−0.582999	−	0.534851i
$286$	−13.1349			−0.776681
$287$	19.8701	+	9.78989i	1.17290	+	0.577879i
$288$	33.5542	+	58.1176i	1.97720	+	3.42461i
$289$	−15.0145			−0.883208
$290$	−23.6858			−1.39088
$291$	8.73194	+	15.1242i	0.511876	+	0.886594i
$292$	−31.3666	−	54.3285i	−1.83559	−	3.17933i
$293$	3.20159			0.187039			0.0935194	−	0.995617i	$-0.470188\pi$
$293$	3.20159			0.187039			0.0935194	+	0.995617i	$0.470188\pi$
$294$	28.9419	+	37.6611i	1.68793	+	2.19644i
$295$	3.94648	−	6.83550i	0.229773	−	0.397978i
$296$	13.3502	+	23.1232i	0.775965	+	1.34401i
$297$	−0.574037	+	0.994261i	−0.0333090	+	0.0576929i
$298$	7.49196	+	12.9765i	0.433998	+	0.751706i
$299$	8.21017	−	14.2204i	0.474806	−	0.822389i
$300$	−23.5353	+	40.7644i	−1.35881	+	2.35353i
$301$	−7.38251	−	3.63732i	−0.425521	−	0.209651i
$302$	10.7925	+	18.6931i	0.621037	+	1.07567i
$303$	−17.3425	−	30.0381i	−0.996302	−	1.72565i
$304$	46.6407	+	42.7888i	2.67503	+	2.45411i
$305$	1.42471	−	2.46767i	0.0815786	−	0.141298i
$306$	−6.15277	+	10.6569i	−0.351731	+	0.609215i
$307$	11.4413	+	19.8169i	0.652990	+	1.13101i	0.982394	+	0.186822i	$0.0598188\pi$
$307$	11.4413	+	19.8169i	0.652990	+	1.13101i	−0.329404	+	0.944189i	$0.606848\pi$
$308$	−26.6056	+	17.7913i	−1.51600	+	1.01375i
$309$	6.14863	+	10.6497i	0.349783	+	0.605843i
$310$	−6.70889			−0.381039
$311$	16.2642	−	28.1703i	0.922256	−	1.59739i	0.126339	−	0.991987i	$-0.459677\pi$
$311$	16.2642	−	28.1703i	0.922256	−	1.59739i	0.795916	−	0.605407i	$-0.206989\pi$
$312$	25.0491	−	43.3864i	1.41813	−	2.45627i
$313$	3.45744			0.195426			0.0977129	−	0.995215i	$-0.468847\pi$
$313$	3.45744			0.195426			0.0977129	+	0.995215i	$0.468847\pi$
$314$	29.2343	−	50.6354i	1.64979	−	2.85752i
$315$	0.686224	+	10.4117i	0.0386643	+	0.586635i
$316$	−29.4861			−1.65873
$317$	19.4199			1.09073			0.545366	−	0.838198i	$-0.316391\pi$
$317$	19.4199			1.09073			0.545366	+	0.838198i	$0.316391\pi$
$318$	−1.61498			−0.0905634
$319$	7.89288	+	13.6709i	0.441917	+	0.765422i
$320$	−17.1967	+	29.7856i	−0.961328	+	1.66507i
$321$	−2.18182	−	3.77903i	−0.121777	−	0.210925i
$322$	−3.60274	−	54.6627i	−0.200773	−	3.04623i
$323$	−1.33290	+	5.99561i	−0.0741644	+	0.333605i
$324$	22.5891	+	39.1255i	1.25495	+	2.17364i
$325$	7.53219			0.417811
$326$	1.44866			0.0802336
$327$	34.6136			1.91414
$328$	−38.9732	−	67.5036i	−2.15194	−	3.72726i
$329$	−0.505537	+	0.338055i	−0.0278711	+	0.0186376i
$330$	−18.6334			−1.02574
$331$	−1.24205	−	2.15130i	−0.0682693	−	0.118246i	0.829870	−	0.557956i	$-0.188414\pi$
$331$	−1.24205	−	2.15130i	−0.0682693	−	0.118246i	−0.898140	+	0.439710i	$0.855081\pi$
$332$	−9.80797	−	16.9879i	−0.538282	−	0.932332i
$333$	−4.59784	−	7.96369i	−0.251960	−	0.436408i
$334$	0.651079	+	1.12770i	0.0356255	+	0.0617051i
$335$	−2.88275			−0.157502
$336$	−6.29451	−	95.5036i	−0.343394	−	5.21015i
$337$	−15.1721	−	26.2789i	−0.826479	−	1.43150i	−0.900784	−	0.434268i	$-0.857007\pi$
$337$	−15.1721	−	26.2789i	−0.826479	−	1.43150i	0.0743045	−	0.997236i	$-0.476326\pi$
$338$	22.7002			1.23473
$339$	−41.7047			−2.26509
$340$	−9.39046			−0.509269
$341$	2.23563	+	3.87222i	0.121066	+	0.209692i
$342$	−28.0506	−	25.7340i	−1.51680	−	1.39154i
$343$	−3.63294	−	18.1604i	−0.196160	−	0.980572i
$344$	14.4800	+	25.0801i	0.780711	+	1.35223i
$345$	11.6471	−	20.1734i	0.627061	−	1.08610i
$346$	−14.3061	−	24.7789i	−0.769102	−	1.33212i
$347$	−1.74295			−0.0935666			−0.0467833	−	0.998905i	$-0.514897\pi$
$347$	−1.74295			−0.0935666			−0.0467833	+	0.998905i	$0.514897\pi$
$348$	−95.4374			−5.11598
$349$	25.5744			1.36897			0.684484	−	0.729028i	$-0.260027\pi$
$349$	25.5744			1.36897			0.684484	+	0.729028i	$0.260027\pi$
$350$	20.8887	−	13.9684i	1.11655	−	0.746642i
$351$	−0.555346	+	0.961888i	−0.0296422	+	0.0513418i
$352$	46.7287			2.49065
$353$	−14.8980	+	25.8041i	−0.792941	+	1.37341i	0.131198	+	0.991356i	$0.458118\pi$
$353$	−14.8980	+	25.8041i	−0.792941	+	1.37341i	−0.924139	+	0.382057i	$0.875216\pi$
$354$	21.7713	−	37.7089i	1.15713	−	2.00421i
$355$	−2.73231			−0.145016
$356$	36.0261	+	62.3991i	1.90938	+	3.30715i
$357$	7.72044	−	5.16269i	0.408609	−	0.273239i
$358$	19.7129	+	34.1438i	1.04186	+	1.80456i
$359$	16.8890	−	29.2525i	0.891365	−	1.54389i	0.0531259	−	0.998588i	$-0.483082\pi$
$359$	16.8890	−	29.2525i	0.891365	−	1.54389i	0.838239	−	0.545302i	$-0.183585\pi$
$360$	18.3585	−	31.7979i	0.967580	−	1.67590i
$361$	−17.2104	−	8.05001i	−0.905810	−	0.423685i
$362$	4.33412	+	7.50692i	0.227796	+	0.394555i
$363$	−7.49269	−	12.9777i	−0.393264	−	0.681153i
$364$	−25.7394	+	17.2120i	−1.34911	+	0.902155i
$365$	−7.12041	+	12.3329i	−0.372699	+	0.645534i
$366$	7.85959	−	13.6132i	0.410827	−	0.711574i
$367$	3.23807	+	5.60850i	0.169026	+	0.292762i	0.938078	−	0.346425i	$-0.112604\pi$
$367$	3.23807	+	5.60850i	0.169026	+	0.292762i	−0.769052	+	0.639187i	$0.779271\pi$
$368$	−55.1943	+	95.5994i	−2.87720	+	4.98346i
$369$	13.4225	+	23.2484i	0.698745	+	1.21026i
$370$	4.80377	−	8.32038i	0.249736	−	0.432556i
$371$	0.564877	+	0.278311i	0.0293269	+	0.0144492i
$372$	−27.0322			−1.40156
$373$	13.1933	+	22.8514i	0.683123	+	1.18320i	0.974023	+	0.226450i	$0.0727119\pi$
$373$	13.1933	+	22.8514i	0.683123	+	1.18320i	−0.290900	+	0.956753i	$0.593955\pi$
$374$	4.28428	+	7.42059i	0.221535	+	0.383710i
$375$	26.0063			1.34296
$376$	2.14001			0.110363
$377$	7.63589	+	13.2258i	0.393268	+	0.681161i
$378$	0.243694	+	3.69745i	0.0125343	+	0.190176i
$379$	14.7287			0.756561			0.378281	−	0.925691i	$-0.376515\pi$
$379$	14.7287			0.756561			0.378281	+	0.925691i	$0.376515\pi$
$380$	6.30405	−	28.3567i	0.323391	−	1.45467i
$381$	3.33263	−	5.77229i	0.170736	−	0.295723i
$382$	13.5362			0.692575
$383$	15.9580	−	27.6401i	0.815416	−	1.41234i	−0.0936134	−	0.995609i	$-0.529842\pi$
$383$	15.9580	−	27.6401i	0.815416	−	1.41234i	0.909029	−	0.416733i	$-0.136825\pi$
$384$	−42.7273	+	74.0058i	−2.18042	+	3.77659i
$385$	6.51748	+	3.21112i	0.332162	+	0.163654i
$386$	30.8631	−	53.4564i	1.57089	−	2.72086i
$387$	−4.98695	−	8.63765i	−0.253501	−	0.439077i
$388$	−18.9910	+	32.8935i	−0.964124	+	1.66991i
$389$	−5.49538	−	9.51828i	−0.278627	−	0.482596i	0.692417	−	0.721498i	$-0.256546\pi$
$389$	−5.49538	−	9.51828i	−0.278627	−	0.482596i	−0.971044	+	0.238902i	$0.923213\pi$
$390$	−18.0267			−0.912818
$391$	−10.7119			−0.541722
$392$	−24.8959	+	60.2278i	−1.25743	+	3.04196i
$393$	2.48250	−	4.29982i	0.125226	−	0.216897i
$394$	−19.8192	+	34.3279i	−0.998477	+	1.72941i
$395$	3.34677	+	5.79678i	0.168394	+	0.291668i
$396$	−38.7884			−1.94919
$397$	−2.89548	+	5.01511i	−0.145320	+	0.251701i	−0.929492	−	0.368842i	$-0.879754\pi$
$397$	−2.89548	+	5.01511i	−0.145320	+	0.251701i	0.784172	+	0.620543i	$0.213088\pi$
$398$	−11.2664			−0.564733
$399$	10.4071	+	26.7796i	0.521005	+	1.34066i
$400$	−50.6365			−2.53182
$401$	−7.10732	+	12.3102i	−0.354923	+	0.614744i	−0.987105	−	0.160076i	$-0.948826\pi$
$401$	−7.10732	+	12.3102i	−0.354923	+	0.614744i	0.632182	+	0.774820i	$0.282160\pi$
$402$	−15.9031			−0.793173
$403$	2.16283	+	3.74614i	0.107738	+	0.186608i
$404$	37.7181	−	65.3297i	1.87655	−	3.25028i
$405$	5.12788	−	8.88174i	0.254806	−	0.441337i
$406$	45.7034	+	22.5178i	2.26822	+	1.11754i
$407$	−6.40311			−0.317390
$408$	−32.6817			−1.61799
$409$	−15.8763	−	27.4986i	−0.785034	−	1.35972i	−0.928978	−	0.370134i	$-0.879312\pi$
$409$	−15.8763	−	27.4986i	−0.785034	−	1.35972i	0.143944	−	0.989586i	$-0.454021\pi$
$410$	−14.0236	+	24.2896i	−0.692578	+	1.19958i
$411$	0.408452	+	0.707459i	0.0201474	+	0.0348964i
$412$	−13.3726	+	23.1621i	−0.658822	+	1.14111i
$413$	−14.1134	+	9.43772i	−0.694477	+	0.464400i
$414$	33.1949	−	57.4953i	1.63144	−	2.82574i
$415$	−2.22647	+	3.85636i	−0.109293	+	0.189301i
$416$	45.2072			2.21647
$417$	−12.3345	+	21.3639i	−0.604021	+	1.04619i
$418$	−25.2844	+	7.95579i	−1.23670	+	0.389130i
$419$	5.76864			0.281816			0.140908	−	0.990023i	$-0.454998\pi$
$419$	5.76864			0.281816			0.140908	+	0.990023i	$0.454998\pi$
$420$	−36.5144	+	24.4174i	−1.78172	+	1.19145i
$421$	−3.93410	−	6.81407i	−0.191736	−	0.332097i	0.754089	−	0.656772i	$-0.228079\pi$
$421$	−3.93410	−	6.81407i	−0.191736	−	0.332097i	−0.945826	+	0.324675i	$0.894745\pi$
$422$	−59.9373			−2.91770
$423$	−0.737024			−0.0358353
$424$	−1.10795	−	1.91902i	−0.0538066	−	0.0931958i
$425$	−2.45682	−	4.25534i	−0.119173	−	0.206414i
$426$	−15.0731			−0.730295
$427$	−5.09506	+	3.40709i	−0.246567	+	0.164881i
$428$	4.74523	−	8.21898i	0.229369	−	0.397280i
$429$	6.00710	+	10.4046i	0.290026	+	0.502339i
$430$	5.21031	−	9.02452i	0.251263	−	0.435201i
$431$	10.6893	+	18.5145i	0.514888	+	0.891812i	0.999851	+	0.0172770i	$0.00549970\pi$
$431$	10.6893	+	18.5145i	0.514888	+	0.891812i	−0.484963	+	0.874535i	$0.661167\pi$
$432$	3.73341	−	6.46646i	0.179624	−	0.311118i
$433$	1.95955	−	3.39404i	0.0941700	−	0.163107i	−0.815092	−	0.579332i	$-0.803314\pi$
$433$	1.95955	−	3.39404i	0.0941700	−	0.163107i	0.909262	+	0.416224i	$0.136647\pi$
$434$	12.9453	+	6.37806i	0.621394	+	0.306157i
$435$	10.8325	+	18.7624i	0.519377	+	0.899587i
$436$	37.6404	+	65.1952i	1.80265	+	3.12228i
$437$	7.19113	−	32.3470i	0.343999	−	1.54737i
$438$	−39.2807	+	68.0362i	−1.87690	+	3.25089i
$439$	−11.6736	+	20.2193i	−0.557151	+	0.965015i	0.440581	+	0.897713i	$0.354772\pi$
$439$	−11.6736	+	20.2193i	−0.557151	+	0.965015i	−0.997733	+	0.0673018i	$0.978561\pi$
$440$	−12.7834	−	22.1414i	−0.609423	−	1.05555i
$441$	8.57419	−	20.7426i	0.408295	−	0.987742i
$442$	4.14478	+	7.17898i	0.197147	+	0.341469i
$443$	−20.9040			−0.993181			−0.496591	−	0.867985i	$-0.665415\pi$
$443$	−20.9040			−0.993181			−0.496591	+	0.867985i	$0.665415\pi$
$444$	19.3559	−	33.5254i	0.918591	−	1.59105i
$445$	8.17817	−	14.1650i	0.387682	−	0.671486i
$446$	33.0132			1.56322
$447$	6.85276	−	11.8693i	0.324124	−	0.561400i
$448$	61.4992	−	41.1248i	2.90556	−	1.94297i
$449$	11.8951			0.561367			0.280683	−	0.959800i	$-0.409439\pi$
$449$	11.8951			0.561367			0.280683	+	0.959800i	$0.409439\pi$
$450$	30.4538			1.43560
$451$	18.6926			0.880198
$452$	−45.3516	−	78.5513i	−2.13316	−	3.69474i
$453$	9.87167	−	17.0982i	0.463812	−	0.803345i
$454$	27.2322	+	47.1676i	1.27807	+	2.21368i
$455$	6.30527	+	3.10657i	0.295596	+	0.145638i
$456$	21.9401	−	98.6903i	1.02744	−	4.62160i
$457$	−17.4800	−	30.2762i	−0.817679	−	1.41626i	−0.907388	−	0.420294i	$-0.861927\pi$
$457$	−17.4800	−	30.2762i	−0.817679	−	1.41626i	0.0897088	−	0.995968i	$-0.471406\pi$
$458$	50.2432			2.34771
$459$	0.724563			0.0338197
$460$	50.6626			2.36216
$461$	−4.96234	−	8.59503i	−0.231119	−	0.400310i	0.727019	−	0.686618i	$-0.240905\pi$
$461$	−4.96234	−	8.59503i	−0.231119	−	0.400310i	−0.958138	+	0.286308i	$0.907572\pi$
$462$	35.9545	+	17.7146i	1.67276	+	0.824156i
$463$	−17.4163			−0.809406			−0.404703	−	0.914448i	$-0.632625\pi$
$463$	−17.4163			−0.809406			−0.404703	+	0.914448i	$0.632625\pi$
$464$	−51.3336	−	88.9124i	−2.38310	−	4.12766i
$465$	3.06825	+	5.31436i	0.142287	+	0.246448i
$466$	11.1165	+	19.2544i	0.514962	+	0.891941i
$467$	−10.8072	−	18.7186i	−0.500096	−	0.866192i	−1.00000		0.000110737i	$-0.999965\pi$
$467$	−10.8072	−	18.7186i	−0.500096	−	0.866192i	0.499904	−	0.866081i	$-0.333369\pi$
$468$	−37.5255			−1.73462
$469$	5.56248	+	2.74060i	0.256851	+	0.126549i
$470$	−0.385017	−	0.666869i	−0.0177595	−	0.0307604i
$471$	−53.4802			−2.46424
$472$	59.7442			2.74995
$473$	−6.94500			−0.319331
$474$	18.4629	+	31.9787i	0.848030	+	1.46883i
$475$	14.4994	−	4.56225i	0.665276	−	0.209330i
$476$	18.1196	+	8.92739i	0.830509	+	0.409186i
$477$	0.381579	+	0.660914i	0.0174713	+	0.0302612i
$478$	−20.9762	+	36.3319i	−0.959429	+	1.66178i
$479$	8.02044	+	13.8918i	0.366463	+	0.634733i	0.989010	−	0.147850i	$-0.0472353\pi$
$479$	8.02044	+	13.8918i	0.366463	+	0.634733i	−0.622547	+	0.782583i	$0.713902\pi$
$480$	64.1320			2.92721
$481$	−6.19462			−0.282451
$482$	−38.2264			−1.74116
$483$	−41.6526	+	27.8533i	−1.89526	+	1.26737i
$484$	16.2958	−	28.2251i	0.740718	−	1.28296i
$485$	8.62218			0.391513
$486$	30.3894	−	52.6360i	1.37849	−	2.38762i
$487$	−1.73850	+	3.01117i	−0.0787789	+	0.136449i	−0.902723	−	0.430222i	$-0.858435\pi$
$487$	−1.73850	+	3.01117i	−0.0787789	+	0.136449i	0.823944	+	0.566671i	$0.191769\pi$
$488$	21.5681			0.976343
$489$	−0.662529	−	1.14753i	−0.0299606	−	0.0518933i
$490$	23.2473	−	3.07776i	1.05020	−	0.139039i
$491$	−13.0339	−	22.5753i	−0.588211	−	1.01881i	−0.994467	−	0.105052i	$-0.966499\pi$
$491$	−13.0339	−	22.5753i	−0.588211	−	1.01881i	0.406256	−	0.913759i	$-0.366834\pi$
$492$	−56.5056	+	97.8706i	−2.54747	+	4.41235i
$493$	4.98129	−	8.62785i	0.224346	−	0.388579i
$494$	−24.4611	+	7.69675i	−1.10056	+	0.346293i
$495$	4.40262	+	7.62555i	0.197883	+	0.342743i
$496$	−14.5400	−	25.1841i	−0.652867	−	1.13080i
$497$	5.27218	+	2.59757i	0.236490	+	0.116517i
$498$	−12.2826	+	21.2741i	−0.550398	+	0.953317i
$499$	−14.7368	+	25.5250i	−0.659712	+	1.14265i	0.320978	+	0.947087i	$0.395988\pi$
$499$	−14.7368	+	25.5250i	−0.659712	+	1.14265i	−0.980690	+	0.195568i	$0.937345\pi$
$500$	28.2805	+	48.9833i	1.26474	+	2.19060i
$501$	0.595530	−	1.03149i	0.0266063	−	0.0460835i
$502$	−2.89590	−	5.01585i	−0.129250	−	0.223868i
$503$	20.8586	−	36.1282i	0.930040	−	1.61088i	0.146791	−	0.989167i	$-0.453105\pi$
$503$	20.8586	−	36.1282i	0.930040	−	1.61088i	0.783248	−	0.621709i	$-0.213561\pi$
$504$	−65.6540	+	43.9032i	−2.92446	+	1.95560i
$505$	−17.1245			−0.762032
$506$	−23.1142	−	40.0349i	−1.02755	−	1.77977i
$507$	−10.3817	−	17.9817i	−0.461068	−	0.798594i
$508$	14.4962			0.643167
$509$	−1.58992			−0.0704718			−0.0352359	−	0.999379i	$-0.511218\pi$
$509$	−1.58992			−0.0704718			−0.0352359	+	0.999379i	$0.511218\pi$
$510$	5.87989	+	10.1843i	0.260366	+	0.450967i
$511$	25.4641	−	17.0280i	1.12647	−	0.753273i
$512$	−33.5334			−1.48198
$513$	−0.486417	+	2.18799i	−0.0214759	+	0.0966023i
$514$	−20.6401	+	35.7498i	−0.910398	+	1.57685i
$515$	6.07134			0.267535
$516$	20.9940	−	36.3626i	0.924209	−	1.60078i
$517$	−0.256601	+	0.444446i	−0.0112853	+	0.0195467i
$518$	−17.1793	+	11.4879i	−0.754815	+	0.504749i
$519$	−13.0855	+	22.6648i	−0.574392	+	0.994876i
$520$	−12.3671	−	21.4205i	−0.542335	−	0.939351i
$521$	7.94214	−	13.7562i	0.347951	−	0.602669i	−0.637934	−	0.770091i	$-0.720211\pi$
$521$	7.94214	−	13.7562i	0.347951	−	0.602669i	0.985885	+	0.167422i	$0.0535441\pi$
$522$	30.8730	+	53.4737i	1.35128	+	2.34048i
$523$	−32.0901			−1.40320			−0.701601	−	0.712570i	$-0.747531\pi$
$523$	−32.0901			−1.40320			−0.701601	+	0.712570i	$0.747531\pi$
$524$	10.7984			0.471728
$525$	−20.6181	−	10.1584i	−0.899850	−	0.443350i
$526$	−39.8486	+	69.0199i	−1.73748	+	3.00941i
$527$	1.41093	−	2.44380i	0.0614611	−	0.106454i
$528$	−40.3838	−	69.9468i	−1.75748	−	3.04404i
$529$	34.7917			1.51268
$530$	−0.398669	+	0.690516i	−0.0173171	+	0.0299941i
$531$	−20.5760			−0.892924
$532$	−39.1225	+	48.7232i	−1.69618	+	2.11242i
$533$	18.0839			0.783302
$534$	45.1159	−	78.1431i	1.95236	−	3.38158i
$535$	−2.15440			−0.0931427
$536$	−10.9102	−	18.8971i	−0.471250	−	0.816228i
$537$	18.0311	−	31.2307i	0.778098	−	1.34770i
$538$	14.3247	−	24.8112i	0.617583	−	1.06969i
$539$	−9.52318	−	12.3922i	−0.410192	−	0.533769i
$540$	−3.42688			−0.147470
$541$	22.9331			0.985970			0.492985	−	0.870038i	$-0.335906\pi$
$541$	22.9331			0.985970			0.492985	+	0.870038i	$0.335906\pi$
$542$	27.1381	+	47.0046i	1.16568	+	2.01902i
$543$	3.96434	−	6.86644i	0.170126	−	0.294667i
$544$	−14.7455	−	25.5400i	−0.632209	−	1.09502i
$545$	8.54463	−	14.7997i	0.366012	−	0.633951i
$546$	34.7839	+	17.1378i	1.48861	+	0.733429i
$547$	4.84367	−	8.38949i	0.207101	−	0.358709i	−0.743699	−	0.668514i	$-0.766931\pi$
$547$	4.84367	−	8.38949i	0.207101	−	0.358709i	0.950800	+	0.309805i	$0.100264\pi$
$548$	−0.888339	+	1.53865i	−0.0379480	+	0.0657278i
$549$	−7.42811			−0.317024
$550$	10.6027	−	18.3645i	0.452102	−	0.783063i
$551$	22.7098	+	20.8343i	0.967471	+	0.887572i
$552$	176.322			7.50475
$553$	−0.946913	−	14.3670i	−0.0402668	−	0.610949i
$554$	3.87064	+	6.70415i	0.164448	+	0.284832i
$555$	−8.78784			−0.373023
$556$	−53.6522			−2.27536
$557$	−4.61234	−	7.98881i	−0.195431	−	0.338497i	0.751611	−	0.659607i	$-0.229277\pi$
$557$	−4.61234	−	7.98881i	−0.195431	−	0.338497i	−0.947042	+	0.321110i	$0.895944\pi$
$558$	8.74465	+	15.1462i	0.370191	+	0.641189i
$559$	−6.71887			−0.284178
$560$	−42.3883	−	20.8844i	−1.79123	−	0.882529i
$561$	3.91875	−	6.78747i	0.165450	−	0.286567i
$562$	−1.27633	−	2.21067i	−0.0538388	−	0.0932516i
$563$	−0.577150	+	0.999654i	−0.0243240	+	0.0421304i	−0.877931	−	0.478787i	$-0.841077\pi$
$563$	−0.577150	+	0.999654i	−0.0243240	+	0.0421304i	0.853607	+	0.520917i	$0.174410\pi$
$564$	−1.55136	−	2.68703i	−0.0653238	−	0.113144i
$565$	−10.2951	+	17.8317i	−0.433119	+	0.750184i
$566$	−42.8275	+	74.1794i	−1.80017	+	3.11799i
$567$	−18.3384	+	12.2630i	−0.770139	+	0.514996i
$568$	−10.3408	−	17.9109i	−0.433892	−	0.751523i
$569$	−1.89438	−	3.28116i	−0.0794166	−	0.137554i	0.823582	−	0.567198i	$-0.191972\pi$
$569$	−1.89438	−	3.28116i	−0.0794166	−	0.137554i	−0.902998	+	0.429644i	$0.858639\pi$
$570$	−34.7012	+	10.9188i	−1.45347	+	0.457338i
$571$	−6.30936	+	10.9281i	−0.264038	+	0.457328i	−0.967311	−	0.253592i	$-0.918388\pi$
$571$	−6.30936	+	10.9281i	−0.264038	+	0.457328i	0.703273	+	0.710920i	$0.251721\pi$
$572$	−13.0648	+	22.6289i	−0.546267	+	0.946163i
$573$	−6.19067	−	10.7226i	−0.258619	−	0.447941i
$574$	50.1515	−	33.5365i	2.09328	−	1.39979i
$575$	13.2548	+	22.9581i	0.552765	+	0.957417i
$576$	89.6599			3.73583
$577$	−19.7094	+	34.1376i	−0.820511	+	1.42117i	0.0847910	+	0.996399i	$0.472978\pi$
$577$	−19.7094	+	34.1376i	−0.820511	+	1.42117i	−0.905302	+	0.424768i	$0.860356\pi$
$578$	−20.4471	+	35.4154i	−0.850488	+	1.47309i
$579$	−56.4597			−2.34639
$580$	−23.5594	+	40.8062i	−0.978253	+	1.69438i
$581$	7.96234	−	5.32445i	0.330333	−	0.220896i
$582$	47.5654			1.97165
$583$	0.531400			0.0220083
$584$	−107.793			−4.46052
$585$	4.25927	+	7.37727i	0.176099	+	0.305012i
$586$	4.35999	−	7.55173i	0.180110	−	0.311959i
$587$	−19.1107	−	33.1007i	−0.788783	−	1.36621i	−0.926713	−	0.375771i	$-0.877378\pi$
$587$	−19.1107	−	33.1007i	−0.788783	−	1.36621i	0.137929	−	0.990442i	$-0.455955\pi$
$588$	93.6706	−	12.4013i	3.86291	−	0.511420i
$589$	6.43246	+	5.90123i	0.265045	+	0.243156i
$590$	−10.7488	−	18.6175i	−0.442521	−	0.766469i
$591$	36.2565			1.49139
$592$	41.6444			1.71158
$593$	−17.2853			−0.709822			−0.354911	−	0.934900i	$-0.615489\pi$
$593$	−17.2853			−0.709822			−0.354911	+	0.934900i	$0.615489\pi$
$594$	1.56347	+	2.70801i	0.0641501	+	0.111111i
$595$	−0.301564	−	4.57548i	−0.0123629	−	0.187576i
$596$	29.8080			1.22098
$597$	5.15258	+	8.92453i	0.210881	+	0.365257i
$598$	−22.3616	−	38.7314i	−0.914433	−	1.58385i
$599$	5.93976	+	10.2880i	0.242692	+	0.420355i	0.961480	−	0.274874i	$-0.0886362\pi$
$599$	5.93976	+	10.2880i	0.242692	+	0.420355i	−0.718788	+	0.695229i	$0.755303\pi$
$600$	40.4403	+	70.0447i	1.65097	+	2.85956i
$601$	−38.3519			−1.56441			−0.782204	−	0.623022i	$-0.785905\pi$
$601$	−38.3519			−1.56441			−0.782204	+	0.623022i	$0.785905\pi$
$602$	−18.6332	+	12.4601i	−0.759431	+	0.507835i
$603$	3.75750	+	6.50818i	0.153017	+	0.265034i
$604$	42.9397			1.74719
$605$	−7.39851			−0.300792
$606$	−94.4697			−3.83757
$607$	18.0522	+	31.2673i	0.732715	+	1.26910i	0.955719	+	0.294282i	$0.0950804\pi$
$607$	18.0522	+	31.2673i	0.732715	+	1.26910i	−0.223004	+	0.974818i	$0.571586\pi$
$608$	87.0232	−	27.3820i	3.52926	−	1.11049i
$609$	−3.06486	−	46.5016i	−0.124194	−	1.88434i
$610$	−3.88040	−	6.72105i	−0.157113	−	0.272127i
$611$	−0.248246	+	0.429975i	−0.0100430	+	0.0173949i
$612$	12.2399	+	21.2002i	0.494770	+	0.856966i
$613$	29.0957			1.17516			0.587581	−	0.809165i	$-0.300080\pi$
$613$	29.0957			1.17516			0.587581	+	0.809165i	$0.300080\pi$
$614$	62.3241			2.51520
$615$	25.6543			1.03448
$616$	3.61684	+	54.8765i	0.145726	+	2.21104i
$617$	−17.4069	+	30.1497i	−0.700777	+	1.21378i	0.267418	+	0.963581i	$0.413830\pi$
$617$	−17.4069	+	30.1497i	−0.700777	+	1.21378i	−0.968194	+	0.250200i	$0.919504\pi$
$618$	33.4934			1.34730
$619$	−9.44421	+	16.3578i	−0.379595	+	0.657477i	−0.991003	−	0.133838i	$-0.957270\pi$
$619$	−9.44421	+	16.3578i	−0.379595	+	0.657477i	0.611409	+	0.791315i	$0.290603\pi$
$620$	−6.67311	+	11.5582i	−0.267999	+	0.464187i
$621$	−3.90910			−0.156867
$622$	−44.2978	−	76.7260i	−1.77618	−	3.07643i
$623$	−29.2469	+	19.5575i	−1.17175	+	0.783555i
$624$	−39.0689	−	67.6694i	−1.56401	−	2.70894i
$625$	−2.29804	+	3.98032i	−0.0919215	+	0.159213i
$626$	4.70841	−	8.15521i	0.188186	−	0.325948i
$627$	17.8657	+	16.3902i	0.713486	+	0.654562i
$628$	−58.1569	−	100.731i	−2.32071	−	4.01959i
$629$	2.02054	+	3.49968i	0.0805642	+	0.139541i
$630$	25.4931	+	12.5603i	1.01567	+	0.500414i
$631$	−17.9758	+	31.1350i	−0.715605	+	1.23946i	0.247121	+	0.968985i	$0.420515\pi$
$631$	−17.9758	+	31.1350i	−0.715605	+	1.23946i	−0.962726	+	0.270479i	$0.912818\pi$
$632$	−25.3328	+	43.8776i	−1.00768	+	1.74536i
$633$	27.4117	+	47.4785i	1.08952	+	1.88710i
$634$	26.4465	−	45.8067i	1.05032	−	1.81922i
$635$	−1.64537	−	2.84987i	−0.0652945	−	0.113093i
$636$	−1.60636	+	2.78231i	−0.0636965	+	0.110326i
$637$	−9.21311	−	11.9887i	−0.365037	−	0.475009i
$638$	42.9948			1.70218
$639$	3.56141	+	6.16853i	0.140887	+	0.244023i
$640$	21.0951	+	36.5378i	0.833857	+	1.44428i
$641$	−29.6185			−1.16986			−0.584930	−	0.811083i	$-0.698878\pi$
$641$	−29.6185			−1.16986			−0.584930	+	0.811083i	$0.698878\pi$
$642$	−11.8850			−0.469064
$643$	5.05711	+	8.75918i	0.199433	+	0.345428i	0.948345	−	0.317242i	$-0.102757\pi$
$643$	5.05711	+	8.75918i	0.199433	+	0.345428i	−0.748912	+	0.662670i	$0.769423\pi$
$644$	−97.7571	−	48.1643i	−3.85217	−	1.89794i
$645$	−9.53154			−0.375304
$646$	12.3269	+	11.3089i	0.484997	+	0.444944i
$647$	15.6524	−	27.1108i	0.615361	−	1.06584i	−0.374960	−	0.927041i	$-0.622344\pi$
$647$	15.6524	−	27.1108i	0.615361	−	1.06584i	0.990321	−	0.138796i	$-0.0443231\pi$
$648$	77.6290			3.04955
$649$	−7.16372	+	12.4079i	−0.281201	+	0.487054i
$650$	10.2575	−	17.7665i	0.402332	−	0.696860i
$651$	−0.868109	−	13.1714i	−0.0340239	−	0.516227i
$652$	1.44093	−	2.49577i	0.0564312	−	0.0977417i
$653$	3.58611	+	6.21133i	0.140335	+	0.243068i	0.927623	−	0.373518i	$-0.121849\pi$
$653$	3.58611	+	6.21133i	0.140335	+	0.243068i	−0.787288	+	0.616586i	$0.788515\pi$
$654$	47.1376	−	81.6447i	1.84322	−	3.19256i
$655$	−1.22565	−	2.12289i	−0.0478900	−	0.0829480i
$656$	−121.572			−4.74660
$657$	37.1242			1.44835
$658$	0.108934	+	1.65280i	0.00424669	+	0.0644330i
$659$	−8.24324	+	14.2777i	−0.321111	+	0.556181i	−0.980718	−	0.195430i	$-0.937390\pi$
$659$	−8.24324	+	14.2777i	−0.321111	+	0.556181i	0.659607	+	0.751611i	$0.270723\pi$
$660$	−18.5341	+	32.1019i	−0.721437	+	1.24957i
$661$	22.2362	+	38.5142i	0.864888	+	1.49803i	0.867158	+	0.498033i	$0.165944\pi$
$661$	22.2362	+	38.5142i	0.864888	+	1.49803i	−0.00227017	+	0.999997i	$0.500723\pi$
$662$	−6.76581			−0.262961
$663$	3.79116	−	6.56647i	0.147236	−	0.255021i
$664$	−33.7057			−1.30804
$665$	14.0192	+	2.16099i	0.543641	+	0.0837995i
$666$	−25.0458			−0.970504
$667$	−26.8747	+	46.5483i	−1.04059	+	1.80236i
$668$	2.59043			0.100227
$669$	−15.0983	−	26.1509i	−0.583732	−	1.01105i
$670$	−3.92579	+	6.79968i	−0.151667	+	0.262694i
$671$	−2.58616	+	4.47936i	−0.0998375	+	0.172924i
$672$	−123.747	−	60.9695i	−4.77366	−	2.35195i
$673$	32.8992			1.26817			0.634086	−	0.773263i	$-0.281377\pi$
$673$	32.8992			1.26817			0.634086	+	0.773263i	$0.281377\pi$
$674$	−82.6470			−3.18344
$675$	−0.896574	−	1.55291i	−0.0345092	−	0.0597716i
$676$	22.5791	−	39.1082i	0.868428	−	1.50416i
$677$	15.7166	+	27.2220i	0.604038	+	1.04622i	0.992203	+	0.124635i	$0.0397759\pi$
$677$	15.7166	+	27.2220i	0.604038	+	1.04622i	−0.388165	+	0.921590i	$0.626891\pi$
$678$	−56.7944	+	98.3707i	−2.18117	+	3.77790i
$679$	−16.6371	−	8.19700i	−0.638474	−	0.314572i
$680$	−8.06773	+	13.9737i	−0.309383	+	0.535868i
$681$	24.9088	−	43.1433i	0.954507	−	1.65325i
$682$	12.1781			0.466323
$683$	10.4623	−	18.1212i	0.400327	−	0.693387i	−0.593438	−	0.804880i	$-0.702230\pi$
$683$	10.4623	−	18.1212i	0.400327	−	0.693387i	0.993765	+	0.111493i	$0.0355631\pi$
$684$	−72.2360	+	22.7292i	−2.76201	+	0.869072i
$685$	0.403318			0.0154100
$686$	−47.7833	−	16.1621i	−1.82437	−	0.617073i
$687$	−22.9783	−	39.7995i	−0.876675	−	1.51845i
$688$	45.1688			1.72204
$689$	0.514097			0.0195856
$690$	−31.7227	−	54.9453i	−1.20766	−	2.09173i
$691$	7.22552	+	12.5150i	0.274872	+	0.476091i	0.970103	−	0.242695i	$-0.0780313\pi$
$691$	7.22552	+	12.5150i	0.274872	+	0.476091i	−0.695231	+	0.718786i	$0.744698\pi$
$692$	−56.9194			−2.16375
$693$	−1.24565	−	18.8996i	−0.0473182	−	0.717935i
$694$	−2.37359	+	4.11118i	−0.0901003	+	0.156058i
$695$	6.08971	+	10.5477i	0.230996	+	0.400096i
$696$	−81.9942	+	142.018i	−3.10798	+	5.38318i
$697$	−5.89855	−	10.2166i	−0.223423	−	0.386981i
$698$	34.8279	−	60.3236i	1.31825	−	2.28328i
$699$	10.1681	−	17.6116i	0.384591	−	0.666132i
$700$	−3.28761	−	49.8813i	−0.124260	−	1.88534i
$701$	−5.76137	−	9.97898i	−0.217604	−	0.376901i	0.736471	−	0.676469i	$-0.236491\pi$
$701$	−5.76137	−	9.97898i	−0.217604	−	0.376901i	−0.954075	+	0.299568i	$0.903157\pi$
$702$	1.51257	+	2.61984i	0.0570881	+	0.0988795i
$703$	−11.9246	+	3.75208i	−0.449743	+	0.141513i
$704$	31.2159	−	54.0674i	1.17649	−	2.03774i
$705$	−0.352168	+	0.609973i	−0.0132634	+	0.0229729i
$706$	40.5769	+	70.2812i	1.52713	+	2.64507i
$707$	33.0430	+	16.2801i	1.24271	+	0.612275i
$708$	−43.3103	−	75.0157i	−1.62770	−	2.81926i
$709$	12.6555			0.475288			0.237644	−	0.971352i	$-0.423625\pi$
$709$	12.6555			0.475288			0.237644	+	0.971352i	$0.423625\pi$
$710$	−3.72092	+	6.44481i	−0.139643	+	0.241870i
$711$	8.72466	−	15.1116i	0.327200	−	0.566727i
$712$	123.806			4.63983
$713$	−7.61213	+	13.1846i	−0.285077	+	0.493767i
$714$	−1.66361	−	25.2412i	−0.0622592	−	0.944629i
$715$	5.93160			0.221829
$716$	78.4313			2.93111
$717$	38.3731			1.43307
$718$	−45.9995	−	79.6735i	−1.71669	−	2.97339i
$719$	−6.13185	+	10.6207i	−0.228679	+	0.396084i	−0.957417	−	0.288709i	$-0.906774\pi$
$719$	−6.13185	+	10.6207i	−0.228679	+	0.396084i	0.728738	+	0.684793i	$0.240107\pi$
$720$	−28.6337	−	49.5950i	−1.06711	−	1.84830i
$721$	−11.7151	−	5.77195i	−0.436293	−	0.214959i
$722$	−42.4254	+	29.6322i	−1.57891	+	1.10280i
$723$	17.4825	+	30.2805i	0.650180	+	1.12615i
$724$	17.2440			0.640870
$725$	−24.6554			−0.915679
$726$	−40.8148			−1.51478
$727$	5.78342	+	10.0172i	0.214495	+	0.371517i	0.953116	−	0.302604i	$-0.0978560\pi$
$727$	5.78342	+	10.0172i	0.214495	+	0.371517i	−0.738621	+	0.674121i	$0.764523\pi$
$728$	3.49907	+	53.0897i	0.129684	+	1.96764i
$729$	−30.5787			−1.13255
$730$	19.3935	+	33.5905i	0.717785	+	1.24324i
$731$	2.19153	+	3.79585i	0.0810568	+	0.140395i
$732$	−15.6354	−	27.0812i	−0.577899	−	1.00095i
$733$	−13.1872	−	22.8409i	−0.487081	−	0.843649i	0.512809	−	0.858503i	$-0.328605\pi$
$733$	−13.1872	−	22.8409i	−0.487081	−	0.843649i	−0.999890	+	0.0148539i	$0.995272\pi$
$734$	17.6387			0.651057
$735$	−13.0699	−	17.0074i	−0.482092	−	0.627329i
$736$	79.5538	+	137.791i	2.93239	+	5.07905i
$737$	5.23282			0.192753
$738$	73.1160			2.69144
$739$	−0.0716135			−0.00263434			−0.00131717	−	0.999999i	$-0.500419\pi$
$739$	−0.0716135			−0.00263434			−0.00131717	+	0.999999i	$0.500419\pi$
$740$	−9.55631	−	16.5520i	−0.351297	−	0.608464i
$741$	17.2840	+	15.8565i	0.634942	+	0.582505i
$742$	1.42573	−	0.953390i	0.0523401	−	0.0350000i
$743$	−17.1232	−	29.6582i	−0.628189	−	1.08805i	−0.987915	−	0.154997i	$-0.950463\pi$
$743$	−17.1232	−	29.6582i	−0.628189	−	1.08805i	0.359726	−	0.933058i	$-0.382870\pi$
$744$	−23.2245	+	40.2260i	−0.851452	+	1.47476i
$745$	−3.38331	−	5.86006i	−0.123955	−	0.214696i
$746$	71.8677			2.63126
$747$	11.6083			0.424726
$748$	17.0457			0.623253
$749$	4.15707	+	2.04816i	0.151896	+	0.0748381i
$750$	35.4160	−	61.3423i	1.29321	−	2.23990i
$751$	23.7113			0.865236			0.432618	−	0.901577i	$-0.357590\pi$
$751$	23.7113			0.865236			0.432618	+	0.901577i	$0.357590\pi$
$752$	1.66888	−	2.89058i	0.0608577	−	0.105409i
$753$	−2.64883	+	4.58790i	−0.0965286	+	0.167192i
$754$	41.5949			1.51480
$755$	−4.87380	−	8.44166i	−0.177376	−	0.307224i
$756$	6.61242	+	3.25789i	0.240491	+	0.118488i
$757$	−11.5186	−	19.9509i	−0.418652	−	0.725127i	0.577152	−	0.816637i	$-0.304164\pi$
$757$	−11.5186	−	19.9509i	−0.418652	−	0.725127i	−0.995804	+	0.0915098i	$0.970831\pi$
$758$	20.0578	−	34.7412i	0.728533	−	1.26186i
$759$	−21.1421	+	36.6192i	−0.767410	+	1.32919i
$760$	−36.7809	−	33.7434i	−1.33418	−	1.22400i
$761$	14.9865	+	25.9574i	0.543260	+	0.940954i	0.998714	+	0.0506947i	$0.0161435\pi$
$761$	14.9865	+	25.9574i	0.543260	+	0.940954i	−0.455454	+	0.890259i	$0.650523\pi$
$762$	−9.07690	−	15.7217i	−0.328821	−	0.569536i
$763$	−30.5574	+	20.4339i	−1.10625	+	0.739756i
$764$	13.4641	−	23.3204i	0.487113	−	0.843704i
$765$	2.77854	−	4.81258i	0.100458	−	0.173999i
$766$	−43.4639	−	75.2817i	−1.57042	−	2.72004i
$767$	−6.93047	+	12.0039i	−0.250245	+	0.433437i
$768$	46.7112	+	80.9062i	1.68555	+	2.91945i
$769$	−13.1321	+	22.7454i	−0.473555	+	0.820222i	−0.999542	−	0.0302712i	$-0.990363\pi$
$769$	−13.1321	+	22.7454i	−0.473555	+	0.820222i	0.525986	+	0.850493i	$0.323696\pi$
$770$	16.4499	−	11.0001i	0.592812	−	0.396416i
$771$	37.7583			1.35983
$772$	−61.3969	−	106.343i	−2.20972	−	3.82735i
$773$	−23.5388	−	40.7705i	−0.846633	−	1.46641i	−0.884195	−	0.467118i	$-0.845292\pi$
$773$	−23.5388	−	40.7705i	−0.846633	−	1.46641i	0.0375616	−	0.999294i	$-0.488041\pi$
$774$	−27.1654			−0.976439
$775$	−6.98353			−0.250856
$776$	32.6320	+	56.5203i	1.17142	+	2.02896i
$777$	16.9568	+	8.35449i	0.608321	+	0.299716i
$778$	−29.9349			−1.07322
$779$	34.8113	−	10.9534i	1.24724	−	0.392448i
$780$	−17.9306	+	31.0567i	−0.642018	+	1.11201i
$781$	4.95973			0.177473
$782$	−14.5876	+	25.2665i	−0.521653	+	0.903529i
$783$	1.81784	−	3.14858i	0.0649641	−	0.112521i
$784$	61.9367	+	80.5961i	2.21203	+	2.87843i
$785$	−13.2020	+	22.8665i	−0.471199	+	0.816141i
$786$	−6.76145	−	11.7112i	−0.241173	−	0.417724i
$787$	22.7776	−	39.4519i	0.811932	−	1.40631i	−0.0995772	−	0.995030i	$-0.531749\pi$
$787$	22.7776	−	39.4519i	0.811932	−	1.40631i	0.911510	−	0.411279i	$-0.134918\pi$
$788$	39.4270	+	68.2896i	1.40453	+	2.43272i
$789$	72.8976			2.59522
$790$	18.2308			0.648624
$791$	36.8175	−	24.6200i	1.30908	−	0.875388i
$792$	−33.3248	+	57.7202i	−1.18414	+	2.05100i
$793$	−2.50195	+	4.33351i	−0.0888469	+	0.153887i
$794$	7.88625	+	13.6594i	0.279873	+	0.484754i
$795$	0.729311			0.0258660
$796$	−11.2063	+	19.4099i	−0.397197	+	0.687966i
$797$	−4.23876			−0.150145			−0.0750723	−	0.997178i	$-0.523919\pi$
$797$	−4.23876			−0.150145			−0.0750723	+	0.997178i	$0.523919\pi$
$798$	77.3387	+	11.9214i	2.73776	+	0.422012i
$799$	0.323888			0.0114583
$800$	−36.4922	+	63.2063i	−1.29019	+	2.23468i
$801$	−42.6391			−1.50658
$802$	19.3578	+	33.5287i	0.683548	+	1.18394i
$803$	12.9251	−	22.3869i	0.456117	−	0.790018i
$804$	−15.8183	+	27.3980i	−0.557867	+	0.966254i
$805$	1.62697	+	24.6852i	0.0573432	+	0.870040i
$806$	11.7816			0.414988
$807$	−26.2051			−0.922464
$808$	−64.8104	−	112.255i	−2.28002	−	3.94912i
$809$	24.1716	−	41.8664i	0.849827	−	1.47194i	−0.0315359	−	0.999503i	$-0.510040\pi$
$809$	24.1716	−	41.8664i	0.849827	−	1.47194i	0.881363	−	0.472440i	$-0.156627\pi$
$810$	−13.9665	−	24.1907i	−0.490733	−	0.849975i
$811$	18.9656	−	32.8493i	0.665971	−	1.15350i	−0.313050	−	0.949737i	$-0.601351\pi$
$811$	18.9656	−	32.8493i	0.665971	−	1.15350i	0.979021	−	0.203759i	$-0.0653159\pi$
$812$	84.2536	−	56.3408i	2.95672	−	1.97717i
$813$	24.8227	−	42.9942i	0.870571	−	1.50787i
$814$	−8.71989	+	15.1033i	−0.305632	+	0.529370i
$815$	−0.654201			−0.0229157
$816$	−25.4867	+	44.1443i	−0.892213	+	1.54536i
$817$	−12.9337	+	4.06962i	−0.452493	+	0.142378i
$818$	−86.4830			−3.02381
$819$	−1.20509	−	18.2842i	−0.0421092	−	0.638902i
$820$	27.8977	+	48.3202i	0.974229	+	1.68741i
$821$	5.13590			0.179244			0.0896221	−	0.995976i	$-0.471434\pi$
$821$	5.13590			0.179244			0.0896221	+	0.995976i	$0.471434\pi$
$822$	2.22495			0.0776042
$823$	2.00919	+	3.48001i	0.0700358	+	0.121306i	0.898917	−	0.438119i	$-0.144355\pi$
$823$	2.00919	+	3.48001i	0.0700358	+	0.121306i	−0.828881	+	0.559425i	$0.811022\pi$
$824$	22.9779	+	39.7990i	0.800475	+	1.38646i
$825$	−19.3962			−0.675290
$826$	3.04119	+	46.1425i	0.105817	+	1.60550i
$827$	−6.98917	+	12.1056i	−0.243037	+	0.420953i	−0.961578	−	0.274532i	$-0.911477\pi$
$827$	−6.98917	+	12.1056i	−0.243037	+	0.420953i	0.718541	+	0.695485i	$0.244810\pi$
$828$	−66.0358	−	114.377i	−2.29490	−	3.97489i
$829$	−20.3445	+	35.2378i	−0.706595	+	1.22386i	0.259518	+	0.965738i	$0.416436\pi$
$829$	−20.3445	+	35.2378i	−0.706595	+	1.22386i	−0.966113	+	0.258120i	$0.916897\pi$
$830$	6.06412	+	10.5034i	0.210489	+	0.364577i
$831$	3.54040	−	6.13216i	0.122815	−	0.212722i
$832$	30.1995	−	52.3070i	1.04698	−	1.81342i
$833$	−3.76796	+	9.11540i	−0.130552	+	0.315830i
$834$	33.5947	+	58.1877i	1.16329	+	2.01487i
$835$	−0.294022	−	0.509261i	−0.0101751	−	0.0176237i
$836$	−11.4432	+	51.4737i	−0.395772	+	1.78025i
$837$	0.514894	−	0.891823i	0.0177973	−	0.0308259i
$838$	7.85586	−	13.6067i	0.271376	−	0.470037i
$839$	10.1621	+	17.6013i	0.350836	+	0.607665i	0.986396	−	0.164386i	$-0.0525643\pi$
$839$	10.1621	+	17.6013i	0.350836	+	0.607665i	−0.635561	+	0.772051i	$0.719231\pi$
$840$	4.96387	+	75.3143i	0.171270	+	2.59859i
$841$	−10.4948	−	18.1776i	−0.361891	−	0.626814i
$842$	−21.4302			−0.738534
$843$	−1.16744	+	2.02206i	−0.0402087	+	0.0696435i
$844$	−59.6176	+	103.261i	−2.05212	+	3.55438i
$845$	−10.2512			−0.352653
$846$	−1.00370	+	1.73845i	−0.0345078	+	0.0597692i
$847$	14.2760	+	7.03367i	0.490528	+	0.241680i
$848$	−3.45611			−0.118683
$849$	78.3470			2.68886
$850$	−13.3830			−0.459034
$851$	−10.9010	−	18.8812i	−0.373683	−	0.647238i
$852$	−14.9927	+	25.9682i	−0.513643	+	0.889656i
$853$	27.6362	+	47.8673i	0.946245	+	1.63895i	0.753238	+	0.657748i	$0.228491\pi$
$853$	27.6362	+	47.8673i	0.946245	+	1.63895i	0.193007	+	0.981197i	$0.438176\pi$
$854$	1.09789	+	16.6578i	0.0375691	+	0.570018i
$855$	12.6674	+	11.6213i	0.433217	+	0.397440i
$856$	−8.15365	−	14.1225i	−0.278686	−	0.482698i
$857$	−47.9488			−1.63790			−0.818949	−	0.573866i	$-0.805443\pi$
$857$	−47.9488			−1.63790			−0.818949	+	0.573866i	$0.805443\pi$
$858$	32.7224			1.11713
$859$	−24.3403			−0.830479			−0.415239	−	0.909712i	$-0.636302\pi$
$859$	−24.3403			−0.830479			−0.415239	+	0.909712i	$0.636302\pi$
$860$	−10.3650	−	17.9528i	−0.353445	−	0.612185i
$861$	−49.5018	−	24.3892i	−1.68702	−	0.831182i
$862$	58.2280			1.98325
$863$	9.08328	+	15.7327i	0.309199	+	0.535548i	0.978187	−	0.207725i	$-0.0666059\pi$
$863$	9.08328	+	15.7327i	0.309199	+	0.535548i	−0.668989	+	0.743273i	$0.733273\pi$
$864$	−5.38112	−	9.32037i	−0.183069	−	0.317085i
$865$	6.46053	+	11.1900i	0.219665	+	0.380471i
$866$	−5.33712	−	9.24416i	−0.181363	−	0.314129i
$867$	37.4052			1.27035
$868$	23.8645	−	15.9583i	0.810012	−	0.541659i
$869$	−6.07513	−	10.5224i	−0.206085	−	0.356949i
$870$	59.0075			2.00054
$871$	5.06244			0.171534
$872$	129.354			4.38048
$873$	−11.2385	−	19.4657i	−0.380366	−	0.658814i
$874$	−66.5053	−	61.0129i	−2.24958	−	2.06379i
$875$	−22.9588	+	15.3526i	−0.776148	+	0.519014i
$876$	78.1424	+	135.347i	2.64019	+	4.57294i
$877$	25.7157	−	44.5410i	0.868359	−	1.50404i	0.00468533	−	0.999989i	$-0.498509\pi$
$877$	25.7157	−	44.5410i	0.868359	−	1.50404i	0.863673	−	0.504052i	$-0.168158\pi$
$878$	31.7948	+	55.0702i	1.07302	+	1.85853i
$879$	−7.97601			−0.269024
$880$	−39.8762			−1.34423
$881$	16.1124			0.542840			0.271420	−	0.962461i	$-0.412507\pi$
$881$	16.1124			0.542840			0.271420	+	0.962461i	$0.412507\pi$
$882$	−37.2499	−	48.4720i	−1.25427	−	1.63214i
$883$	13.2973	−	23.0316i	0.447490	−	0.775075i	−0.550732	−	0.834682i	$-0.685651\pi$
$883$	13.2973	−	23.0316i	0.447490	−	0.775075i	0.998222	+	0.0596070i	$0.0189847\pi$
$884$	16.4907			0.554643
$885$	−9.83173	+	17.0290i	−0.330490	+	0.572425i
$886$	−28.4676	+	49.3073i	−0.956388	+	1.65651i
$887$	−35.0178			−1.17578			−0.587891	−	0.808940i	$-0.700042\pi$
$887$	−35.0178			−1.17578			−0.587891	+	0.808940i	$0.700042\pi$
$888$	−33.2589	−	57.6062i	−1.11610	−	1.93314i
$889$	0.465530	+	7.06326i	0.0156134	+	0.236894i
$890$	−22.2744	−	38.5804i	−0.746640	−	1.29322i
$891$	−9.30822	+	16.1223i	−0.311837	+	0.540118i
$892$	32.8371	−	56.8755i	1.09947	−	1.90433i
$893$	−0.217434	+	0.978058i	−0.00727616	+	0.0327295i
$894$	−18.6645	−	32.3278i	−0.624233	−	1.08120i
$895$	−8.90221	−	15.4191i	−0.297568	−	0.515403i
$896$	−5.96850	−	90.5571i	−0.199394	−	3.02530i
$897$	−20.4537	+	35.4269i	−0.682930	+	1.18287i
$898$	16.1991	−	28.0576i	0.540570	−	0.936295i
$899$	−7.07968	−	12.2624i	−0.236121	−	0.408973i
$900$	30.2913	−	52.4662i	1.00971	−	1.74887i
$901$	−0.167686	−	0.290441i	−0.00558644	−	0.00967600i
$902$	25.4559	−	44.0910i	0.847590	−	1.46807i
$903$	18.3918	+	9.06152i	0.612041	+	0.301549i
$904$	−155.854			−5.18362
$905$	−1.95725	−	3.39006i	−0.0650613	−	0.112690i
$906$	−26.8869	−	46.5695i	−0.893258	−	1.54717i
$907$	17.9176			0.594943			0.297471	−	0.954731i	$-0.403857\pi$
$907$	17.9176			0.594943			0.297471	+	0.954731i	$0.403857\pi$
$908$	108.348			3.59565
$909$	22.3208	+	38.6608i	0.740336	+	1.28230i
$910$	15.9143	−	10.6419i	0.527553	−	0.352777i
$911$	2.82805			0.0936973			0.0468487	−	0.998902i	$-0.485082\pi$
$911$	2.82805			0.0936973			0.0468487	+	0.998902i	$0.485082\pi$
$912$	−116.194	−	106.598i	−3.84758	−	3.52983i
$913$	4.04153	−	7.00014i	0.133755	−	0.231671i
$914$	−95.2185			−3.14955
$915$	−3.54933	+	6.14762i	−0.117337	+	0.203234i
$916$	49.9753	−	86.5597i	1.65123	−	2.86001i
$917$	0.346777	+	5.26147i	0.0114516	+	0.173749i
$918$	0.986726	−	1.70906i	0.0325668	−	0.0564074i
$919$	−20.6236	−	35.7212i	−0.680310	−	1.17833i	−0.974886	−	0.222704i	$-0.928512\pi$
$919$	−20.6236	−	35.7212i	−0.680310	−	1.17833i	0.294576	−	0.955628i	$-0.404822\pi$
$920$	43.5263	−	75.3898i	1.43502	−	2.48553i
$921$	−28.5033	−	49.3692i	−0.939217	−	1.62677i
$922$	−27.0313			−0.890228
$923$	4.79824			0.157936
$924$	66.2817	−	44.3229i	2.18051	−	1.45812i
$925$	5.00043	−	8.66099i	0.164413	−	0.284772i
$926$	−23.7180	+	41.0807i	−0.779421	+	1.35000i
$927$	−7.91365	−	13.7068i	−0.259918	−	0.450192i
$928$	−147.978			−4.85763
$929$	−23.6767	+	41.0093i	−0.776808	+	1.34547i	0.156965	+	0.987604i	$0.449829\pi$
$929$	−23.6767	+	41.0093i	−0.776808	+	1.34547i	−0.933773	+	0.357867i	$0.883504\pi$
$930$	16.7136			0.548061
$931$	−24.9966	−	17.4977i	−0.819232	−	0.573463i
$932$	44.2289			1.44877
$933$	−40.5183	+	70.1798i	−1.32651	+	2.29758i
$934$	−58.8697			−1.92628
$935$	−1.93475	−	3.35108i	−0.0632730	−	0.109592i
$936$	−32.2397	+	55.8408i	−1.05379	+	1.82521i
$937$	−21.6557	+	37.5088i	−0.707461	+	1.22536i	0.258335	+	0.966055i	$0.416826\pi$
$937$	−21.6557	+	37.5088i	−0.707461	+	1.22536i	−0.965796	+	0.259303i	$0.916507\pi$
$938$	14.0395	−	9.38826i	0.458405	−	0.306538i
$939$	−8.61339			−0.281087
$940$	−1.53186			−0.0499636
$941$	11.8698	+	20.5591i	0.386945	+	0.670209i	0.992037	−	0.125947i	$-0.0401968\pi$
$941$	11.8698	+	20.5591i	0.386945	+	0.670209i	−0.605092	+	0.796156i	$0.706864\pi$
$942$	−72.8305	+	126.146i	−2.37295	+	4.11006i
$943$	31.8234	+	55.1197i	1.03631	+	1.79494i
$944$	46.5913	−	80.6985i	1.51642	−	2.62651i
$945$	−0.110050	−	1.66974i	−0.00357994	−	0.0543166i
$946$	−9.45785	+	16.3815i	−0.307501	+	0.532608i
$947$	12.0549	−	20.8798i	0.391733	−	0.678502i	−0.600945	−	0.799290i	$-0.705209\pi$
$947$	12.0549	−	20.8798i	0.391733	−	0.678502i	0.992678	+	0.120789i	$0.0385424\pi$
$948$	73.4578			2.38580
$949$	12.5043	−	21.6580i	0.405906	−	0.703049i
$950$	8.98436	−	40.4132i	0.291491	−	1.31118i
$951$	−48.3802			−1.56884
$952$	28.8519	−	19.2934i	0.935096	−	0.625303i
$953$	−0.406411	−	0.703925i	−0.0131649	−	0.0228024i	0.859368	−	0.511358i	$-0.170857\pi$
$953$	−0.406411	−	0.703925i	−0.0131649	−	0.0228024i	−0.872533	+	0.488555i	$0.837524\pi$
$954$	2.07857			0.0672962
$955$	−6.11286			−0.197807
$956$	41.7287	+	72.2762i	1.34960	+	2.33758i
$957$	−19.6633	−	34.0578i	−0.635623	−	1.10093i
$958$	43.6896			1.41155
$959$	−0.778231	−	0.383429i	−0.0251304	−	0.0123816i
$960$	42.8417	−	74.2040i	1.38271	−	2.39492i
$961$	13.4947	+	23.3735i	0.435313	+	0.753985i
$962$	−8.43598	+	14.6115i	−0.271987	+	0.471095i
$963$	2.80813	+	4.86383i	0.0904909	+	0.156735i
$964$	−38.0225	+	65.8570i	−1.22462	+	2.12111i
$965$	−13.9375	+	24.1405i	−0.448664	+	0.777109i
$966$	8.97540	+	136.179i	0.288779	+	4.38150i
$967$	−10.1045	−	17.5016i	−0.324940	−	0.562812i	0.656560	−	0.754274i	$-0.272011\pi$
$967$	−10.1045	−	17.5016i	−0.324940	−	0.562812i	−0.981500	+	0.191461i	$0.938677\pi$
$968$	−28.0008	−	48.4988i	−0.899979	−	1.55881i
$969$	3.32060	−	14.9367i	0.106673	−	0.479835i
$970$	11.7419	−	20.3375i	0.377009	−	0.652999i
$971$	17.1809	−	29.7582i	0.551362	−	0.954987i	−0.446815	−	0.894626i	$-0.647442\pi$
$971$	17.1809	−	29.7582i	0.551362	−	0.954987i	0.998177	−	0.0603601i	$-0.0192249\pi$
$972$	−60.4547	−	104.711i	−1.93909	−	3.35859i
$973$	−1.72298	−	26.1419i	−0.0552362	−	0.838071i
$974$	4.73505	+	8.20135i	0.151721	+	0.262788i
$975$	−18.7647			−0.600951
$976$	16.8198	−	29.1328i	0.538389	−	0.932517i
$977$	10.5308	−	18.2399i	0.336911	−	0.583546i	−0.646939	−	0.762541i	$-0.723951\pi$
$977$	10.5308	−	18.2399i	0.336911	−	0.583546i	0.983850	+	0.178995i	$0.0572847\pi$
$978$	−3.60899			−0.115403
$979$	−14.8452	+	25.7126i	−0.474453	+	0.821777i
$980$	17.8209	−	43.1121i	0.569267	−	1.37716i
$981$	−44.5497			−1.42236
$982$	−70.9993			−2.26568
$983$	38.6759			1.23357			0.616784	−	0.787132i	$-0.288435\pi$
$983$	38.6759			1.23357			0.616784	+	0.787132i	$0.288435\pi$
$984$	97.0926	+	168.169i	3.09520	+	5.36104i
$985$	8.95019	−	15.5022i	0.285177	−	0.493941i
$986$	−13.5673	−	23.4992i	−0.432070	−	0.748367i
$987$	1.25943	−	0.842185i	0.0400880	−	0.0268070i
$988$	−11.0706	+	49.7977i	−0.352204	+	1.58428i
$989$	−11.8236	−	20.4790i	−0.375968	−	0.651196i
$990$	23.9823			0.762208
$991$	40.4907			1.28623			0.643114	−	0.765770i	$-0.277642\pi$
$991$	40.4907			1.28623			0.643114	+	0.765770i	$0.277642\pi$
$992$	−41.9142			−1.33078
$993$	3.09428	+	5.35945i	0.0981941	+	0.170077i
$994$	13.3068	−	8.89831i	0.422065	−	0.282237i
$995$	5.08781			0.161295
$996$	24.4343	+	42.3214i	0.774229	+	1.34100i
$997$	7.64066	+	13.2340i	0.241982	+	0.419126i	0.961279	−	0.275578i	$-0.0888691\pi$
$997$	7.64066	+	13.2340i	0.241982	+	0.419126i	−0.719297	+	0.694703i	$0.755536\pi$
$998$	40.1379	+	69.5209i	1.27054	+	2.20065i
$999$	0.737360	+	1.27715i	0.0233290	+	0.0404071i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.g.a.102.12	yes	24
7.2	even	3		133.2.h.a.121.1	yes	24
7.3	odd	6		931.2.e.e.197.12		24
7.4	even	3		931.2.e.f.197.12		24
7.5	odd	6		931.2.h.h.520.1		24
7.6	odd	2		931.2.g.h.900.12		24
19.11	even	3		133.2.h.a.11.1	yes	24
133.11	even	3		931.2.e.f.638.12		24
133.30	even	3	inner	133.2.g.a.30.12	✓	24
133.68	odd	6		931.2.g.h.30.12		24
133.87	odd	6		931.2.e.e.638.12		24
133.125	odd	6		931.2.h.h.410.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.g.a.30.12	✓	24	133.30	even	3	inner
133.2.g.a.102.12	yes	24	1.1	even	1	trivial
133.2.h.a.11.1	yes	24	19.11	even	3
133.2.h.a.121.1	yes	24	7.2	even	3
931.2.e.e.197.12		24	7.3	odd	6
931.2.e.e.638.12		24	133.87	odd	6
931.2.e.f.197.12		24	7.4	even	3
931.2.e.f.638.12		24	133.11	even	3
931.2.g.h.30.12		24	133.68	odd	6
931.2.g.h.900.12		24	7.6	odd	2
931.2.h.h.410.1		24	133.125	odd	6
931.2.h.h.520.1		24	7.5	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:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36182 - 2.35875i) q^{2} -2.49127 q^{3} +(-2.70912 - 4.69233i) q^{4} +(-0.614988 + 1.06519i) q^{5} +(-3.39266 + 5.87626i) q^{6} +(2.19933 - 1.47070i) q^{7} -9.31007 q^{8} +3.20641 q^{9} +O(q^{10})\)	\(q+(1.36182 - 2.35875i) q^{2} -2.49127 q^{3} +(-2.70912 - 4.69233i) q^{4} +(-0.614988 + 1.06519i) q^{5} +(-3.39266 + 5.87626i) q^{6} +(2.19933 - 1.47070i) q^{7} -9.31007 q^{8} +3.20641 q^{9} +(1.67501 + 2.90120i) q^{10} +(1.11634 - 1.93355i) q^{11} +(6.74914 + 11.6898i) q^{12} +(1.07999 - 1.87060i) q^{13} +(-0.473915 - 7.19049i) q^{14} +(1.53210 - 2.65367i) q^{15} +(-7.26042 + 12.5754i) q^{16} -1.40907 q^{17} +(4.36656 - 7.56310i) q^{18} +(0.945943 - 4.25502i) q^{19} +6.66430 q^{20} +(-5.47911 + 3.66391i) q^{21} +(-3.04051 - 5.26631i) q^{22} +7.60208 q^{23} +23.1939 q^{24} +(1.74358 + 3.01997i) q^{25} +(-2.94151 - 5.09484i) q^{26} -0.514215 q^{27} +(-12.8593 - 6.33567i) q^{28} +(-3.53517 + 6.12309i) q^{29} +(-4.17289 - 7.22766i) q^{30} +(-1.00132 + 1.73434i) q^{31} +(10.4647 + 18.1254i) q^{32} +(-2.78109 + 4.81700i) q^{33} +(-1.91890 + 3.32363i) q^{34} +(0.214016 + 3.24717i) q^{35} +(-8.68654 - 15.0455i) q^{36} +(-1.43395 - 2.48368i) q^{37} +(-8.74830 - 8.02582i) q^{38} +(-2.69054 + 4.66015i) q^{39} +(5.72558 - 9.91700i) q^{40} +(4.18614 + 7.25060i) q^{41} +(1.18065 + 17.9134i) q^{42} +(-1.55531 - 2.69387i) q^{43} -12.0972 q^{44} +(-1.97190 + 3.41543i) q^{45} +(10.3527 - 17.9314i) q^{46} -0.229860 q^{47} +(18.0876 - 31.3287i) q^{48} +(2.67408 - 6.46910i) q^{49} +9.49778 q^{50} +3.51036 q^{51} -11.7033 q^{52} +(0.119005 + 0.206123i) q^{53} +(-0.700269 + 1.21290i) q^{54} +(1.37307 + 2.37822i) q^{55} +(-20.4759 + 13.6923i) q^{56} +(-2.35659 + 10.6004i) q^{57} +(9.62855 + 16.6771i) q^{58} -6.41716 q^{59} -16.6026 q^{60} -2.31664 q^{61} +(2.72724 + 4.72372i) q^{62} +(7.05194 - 4.71566i) q^{63} +27.9627 q^{64} +(1.32836 + 2.30079i) q^{65} +(7.57471 + 13.1198i) q^{66} +(1.17187 + 2.02974i) q^{67} +(3.81733 + 6.61181i) q^{68} -18.9388 q^{69} +(7.95069 + 3.91725i) q^{70} +(1.11072 + 1.92382i) q^{71} -29.8519 q^{72} +11.5781 q^{73} -7.81116 q^{74} +(-4.34372 - 7.52355i) q^{75} +(-22.5286 + 7.08868i) q^{76} +(-0.388486 - 5.89431i) q^{77} +(7.32808 + 12.6926i) q^{78} +(2.72101 - 4.71292i) q^{79} +(-8.93014 - 15.4675i) q^{80} -8.33818 q^{81} +22.8031 q^{82} +3.62035 q^{83} +(32.0358 + 15.7838i) q^{84} +(0.866560 - 1.50093i) q^{85} -8.47221 q^{86} +(8.80705 - 15.2543i) q^{87} +(-10.3932 + 18.0015i) q^{88} -13.2981 q^{89} +(5.37076 + 9.30243i) q^{90} +(-0.375837 - 5.70240i) q^{91} +(-20.5950 - 35.6715i) q^{92} +(2.49456 - 4.32070i) q^{93} +(-0.313028 + 0.542181i) q^{94} +(3.95066 + 3.62439i) q^{95} +(-26.0704 - 45.1553i) q^{96} +(-3.50502 - 6.07088i) q^{97} +(-11.6173 - 15.1172i) q^{98} +(3.57943 - 6.19976i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9}+O(q^{10}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9} + 16 q^{10} - q^{11} - 2 q^{12} + 6 q^{13} - q^{14} - 9 q^{15} - 9 q^{16} - 16 q^{17} + 5 q^{18} - 4 q^{19} - 21 q^{21} - 2 q^{22} + 18 q^{23} + 16 q^{24} - 14 q^{25} + q^{26} - 18 q^{27} - 14 q^{28} - 2 q^{29} - 9 q^{30} + 11 q^{31} + 24 q^{32} + 3 q^{33} + 6 q^{34} + 38 q^{35} - 7 q^{36} - 14 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 20 q^{41} - 36 q^{42} + 2 q^{43} - 4 q^{44} - 12 q^{45} - 6 q^{46} + 39 q^{48} + 18 q^{49} + 22 q^{50} - 42 q^{51} - 22 q^{52} + 7 q^{53} - 43 q^{54} + 9 q^{55} - 21 q^{56} + 21 q^{57} + 35 q^{58} - 84 q^{59} + 12 q^{60} - 12 q^{61} - 19 q^{62} + 9 q^{63} - 2 q^{64} - 27 q^{65} + 3 q^{66} - 14 q^{67} + 51 q^{68} - 34 q^{69} + 33 q^{70} + q^{71} - 36 q^{72} + 42 q^{73} + 50 q^{74} + 31 q^{75} - 70 q^{76} - 20 q^{77} + 57 q^{78} - 5 q^{79} + 13 q^{80} - 56 q^{81} + 24 q^{82} + 10 q^{83} + 129 q^{84} - 27 q^{85} - 36 q^{86} + 53 q^{87} - 36 q^{88} + 2 q^{89} + 27 q^{90} - 9 q^{91} - 72 q^{92} + 34 q^{93} + 12 q^{94} - 11 q^{95} - 94 q^{96} + 31 q^{97} - 26 q^{98} + 43 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9 + 16 * q^10 - q^11 - 2 * q^12 + 6 * q^13 - q^14 - 9 * q^15 - 9 * q^16 - 16 * q^17 + 5 * q^18 - 4 * q^19 - 21 * q^21 - 2 * q^22 + 18 * q^23 + 16 * q^24 - 14 * q^25 + q^26 - 18 * q^27 - 14 * q^28 - 2 * q^29 - 9 * q^30 + 11 * q^31 + 24 * q^32 + 3 * q^33 + 6 * q^34 + 38 * q^35 - 7 * q^36 - 14 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 20 * q^41 - 36 * q^42 + 2 * q^43 - 4 * q^44 - 12 * q^45 - 6 * q^46 + 39 * q^48 + 18 * q^49 + 22 * q^50 - 42 * q^51 - 22 * q^52 + 7 * q^53 - 43 * q^54 + 9 * q^55 - 21 * q^56 + 21 * q^57 + 35 * q^58 - 84 * q^59 + 12 * q^60 - 12 * q^61 - 19 * q^62 + 9 * q^63 - 2 * q^64 - 27 * q^65 + 3 * q^66 - 14 * q^67 + 51 * q^68 - 34 * q^69 + 33 * q^70 + q^71 - 36 * q^72 + 42 * q^73 + 50 * q^74 + 31 * q^75 - 70 * q^76 - 20 * q^77 + 57 * q^78 - 5 * q^79 + 13 * q^80 - 56 * q^81 + 24 * q^82 + 10 * q^83 + 129 * q^84 - 27 * q^85 - 36 * q^86 + 53 * q^87 - 36 * q^88 + 2 * q^89 + 27 * q^90 - 9 * q^91 - 72 * q^92 + 34 * q^93 + 12 * q^94 - 11 * q^95 - 94 * q^96 + 31 * q^97 - 26 * q^98 + 43 * q^99

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