LMFDB - Embedded newform 175.2.n.a.169.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(29,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("175.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.n (of order $10$, degree $4$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			169.11
Character	$\chi$	$=$	175.169
Dual form			175.2.n.a.29.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19597 - 0.388594i) q^{2} +(0.374566 + 0.515546i) q^{3} +(-0.338697 + 0.246078i) q^{4} +(1.94508 + 1.10303i) q^{5} +(0.648308 + 0.471023i) q^{6} +1.00000i q^{7} +(-1.78775 + 2.46062i) q^{8} +(0.801563 - 2.46696i) q^{9} +O(q^{10})$	\(q+(1.19597 - 0.388594i) q^{2} +(0.374566 + 0.515546i) q^{3} +(-0.338697 + 0.246078i) q^{4} +(1.94508 + 1.10303i) q^{5} +(0.648308 + 0.471023i) q^{6} +1.00000i q^{7} +(-1.78775 + 2.46062i) q^{8} +(0.801563 - 2.46696i) q^{9} +(2.75488 + 0.563341i) q^{10} +(-0.562815 - 1.73217i) q^{11} +(-0.253729 - 0.0824416i) q^{12} +(-1.90323 - 0.618395i) q^{13} +(0.388594 + 1.19597i) q^{14} +(0.159899 + 1.41594i) q^{15} +(-0.923165 + 2.84121i) q^{16} +(3.99509 - 5.49877i) q^{17} -3.26189i q^{18} +(-1.48059 - 1.07571i) q^{19} +(-0.930223 + 0.105049i) q^{20} +(-0.515546 + 0.374566i) q^{21} +(-1.34622 - 1.85291i) q^{22} +(-4.12974 + 1.34183i) q^{23} -1.93819 q^{24} +(2.56666 + 4.29095i) q^{25} -2.51650 q^{26} +(3.39025 - 1.10156i) q^{27} +(-0.246078 - 0.338697i) q^{28} +(-5.40749 + 3.92877i) q^{29} +(0.741458 + 1.63128i) q^{30} +(-4.00700 - 2.91125i) q^{31} -2.32626i q^{32} +(0.682200 - 0.938968i) q^{33} +(2.64121 - 8.12882i) q^{34} +(-1.10303 + 1.94508i) q^{35} +(0.335576 + 1.03280i) q^{36} +(-2.47507 - 0.804200i) q^{37} +(-2.18876 - 0.711172i) q^{38} +(-0.394073 - 1.21283i) q^{39} +(-6.19144 + 2.81417i) q^{40} +(2.28132 - 7.02118i) q^{41} +(-0.471023 + 0.648308i) q^{42} +7.31612i q^{43} +(0.616871 + 0.448183i) q^{44} +(4.28022 - 3.91428i) q^{45} +(-4.41761 + 3.20958i) q^{46} +(6.15868 + 8.47670i) q^{47} +(-1.81056 + 0.588287i) q^{48} -1.00000 q^{49} +(4.73708 + 4.13446i) q^{50} +4.33130 q^{51} +(0.796790 - 0.258893i) q^{52} +(3.14354 + 4.32670i) q^{53} +(3.62658 - 2.63486i) q^{54} +(0.815908 - 3.99000i) q^{55} +(-2.46062 - 1.78775i) q^{56} -1.16624i q^{57} +(-4.94049 + 6.80001i) q^{58} +(-0.00765237 + 0.0235516i) q^{59} +(-0.402588 - 0.440226i) q^{60} +(-1.22115 - 3.75830i) q^{61} +(-5.92354 - 1.92467i) q^{62} +(2.46696 + 0.801563i) q^{63} +(-2.75030 - 8.46455i) q^{64} +(-3.01982 - 3.30214i) q^{65} +(0.451013 - 1.38808i) q^{66} +(2.72641 - 3.75258i) q^{67} +2.84552i q^{68} +(-2.23864 - 1.62647i) q^{69} +(-0.563341 + 2.75488i) q^{70} +(-9.67307 + 7.02789i) q^{71} +(4.63726 + 6.38263i) q^{72} +(9.04917 - 2.94025i) q^{73} -3.27262 q^{74} +(-1.25080 + 2.93048i) q^{75} +0.766183 q^{76} +(1.73217 - 0.562815i) q^{77} +(-0.942598 - 1.29737i) q^{78} +(4.03120 - 2.92884i) q^{79} +(-4.92956 + 4.50810i) q^{80} +(-4.45778 - 3.23876i) q^{81} -9.28362i q^{82} +(1.56786 - 2.15797i) q^{83} +(0.0824416 - 0.253729i) q^{84} +(13.8361 - 6.28884i) q^{85} +(2.84300 + 8.74985i) q^{86} +(-4.05093 - 1.31623i) q^{87} +(5.26837 + 1.71180i) q^{88} +(4.75121 + 14.6227i) q^{89} +(3.59795 - 6.34462i) q^{90} +(0.618395 - 1.90323i) q^{91} +(1.06854 - 1.47071i) q^{92} -3.15625i q^{93} +(10.6596 + 7.74464i) q^{94} +(-1.69333 - 3.72549i) q^{95} +(1.19929 - 0.871337i) q^{96} +(7.14061 + 9.82821i) q^{97} +(-1.19597 + 0.388594i) q^{98} -4.72431 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9}+O(q^{10}) $ 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9	$ 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9} - 4 q^{10} + 8 q^{11} - 40 q^{12} - 4 q^{14} - 18 q^{15} - 32 q^{16} + 12 q^{19} + 12 q^{20} + 4 q^{21} - 30 q^{22} + 10 q^{23} - 28 q^{24} + 4 q^{25} + 12 q^{26} + 30 q^{27} - 2 q^{29} + 28 q^{30} + 12 q^{31} + 20 q^{33} + 2 q^{35} - 14 q^{36} - 70 q^{37} - 70 q^{38} - 4 q^{39} - 30 q^{40} + 4 q^{41} + 50 q^{42} + 22 q^{44} - 52 q^{45} - 4 q^{46} - 10 q^{47} + 30 q^{48} - 56 q^{49} - 54 q^{50} - 44 q^{51} - 20 q^{53} + 54 q^{54} - 2 q^{55} + 12 q^{56} + 10 q^{58} - 6 q^{59} + 16 q^{60} - 4 q^{61} + 50 q^{62} + 20 q^{63} + 24 q^{64} - 18 q^{65} - 74 q^{66} + 10 q^{67} - 78 q^{69} + 8 q^{70} - 8 q^{71} + 140 q^{72} + 40 q^{73} + 60 q^{74} - 8 q^{75} + 52 q^{76} - 20 q^{77} - 90 q^{78} + 124 q^{80} - 72 q^{81} - 30 q^{83} - 12 q^{84} + 96 q^{85} - 20 q^{86} + 30 q^{87} + 140 q^{88} + 38 q^{89} - 8 q^{90} + 8 q^{91} + 80 q^{92} + 88 q^{94} - 70 q^{95} - 28 q^{96} - 30 q^{97} + 60 q^{99}+O(q^{100}) $ 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9 - 4 * q^10 + 8 * q^11 - 40 * q^12 - 4 * q^14 - 18 * q^15 - 32 * q^16 + 12 * q^19 + 12 * q^20 + 4 * q^21 - 30 * q^22 + 10 * q^23 - 28 * q^24 + 4 * q^25 + 12 * q^26 + 30 * q^27 - 2 * q^29 + 28 * q^30 + 12 * q^31 + 20 * q^33 + 2 * q^35 - 14 * q^36 - 70 * q^37 - 70 * q^38 - 4 * q^39 - 30 * q^40 + 4 * q^41 + 50 * q^42 + 22 * q^44 - 52 * q^45 - 4 * q^46 - 10 * q^47 + 30 * q^48 - 56 * q^49 - 54 * q^50 - 44 * q^51 - 20 * q^53 + 54 * q^54 - 2 * q^55 + 12 * q^56 + 10 * q^58 - 6 * q^59 + 16 * q^60 - 4 * q^61 + 50 * q^62 + 20 * q^63 + 24 * q^64 - 18 * q^65 - 74 * q^66 + 10 * q^67 - 78 * q^69 + 8 * q^70 - 8 * q^71 + 140 * q^72 + 40 * q^73 + 60 * q^74 - 8 * q^75 + 52 * q^76 - 20 * q^77 - 90 * q^78 + 124 * q^80 - 72 * q^81 - 30 * q^83 - 12 * q^84 + 96 * q^85 - 20 * q^86 + 30 * q^87 + 140 * q^88 + 38 * q^89 - 8 * q^90 + 8 * q^91 + 80 * q^92 + 88 * q^94 - 70 * q^95 - 28 * q^96 - 30 * q^97 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	1.19597	−	0.388594i	0.845678	−	0.274777i	0.146043	−	0.989278i	$-0.453346\pi$
$2$	1.19597	−	0.388594i	0.845678	−	0.274777i	0.699635	+	0.714501i	$0.253346\pi$
$3$	0.374566	+	0.515546i	0.216256	+	0.297651i	0.903338	−	0.428929i	$-0.141109\pi$
$3$	0.374566	+	0.515546i	0.216256	+	0.297651i	−0.687082	+	0.726580i	$0.741109\pi$
$4$	−0.338697	+	0.246078i	−0.169349	+	0.123039i
$5$	1.94508	+	1.10303i	0.869866	+	0.493289i
$5$	1.94508	+	1.10303i	0.869866	+	0.493289i
$6$	0.648308	+	0.471023i	0.264671	+	0.192294i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−1.78775	+	2.46062i	−0.632064	+	0.869961i
$9$	0.801563	−	2.46696i	0.267188	−	0.822319i
$10$	2.75488	+	0.563341i	0.871171	+	0.178144i
$11$	−0.562815	−	1.73217i	−0.169695	−	0.522268i	0.829657	−	0.558274i	$-0.188536\pi$
$11$	−0.562815	−	1.73217i	−0.169695	−	0.522268i	−0.999352	+	0.0360066i	$0.988536\pi$
$12$	−0.253729	−	0.0824416i	−0.0732453	−	0.0237988i
$13$	−1.90323	−	0.618395i	−0.527860	−	0.171512i	0.0329496	−	0.999457i	$-0.489510\pi$
$13$	−1.90323	−	0.618395i	−0.527860	−	0.171512i	−0.560809	+	0.827945i	$0.689510\pi$
$14$	0.388594	+	1.19597i	0.103856	+	0.319636i
$15$	0.159899	+	1.41594i	0.0412858	+	0.365593i
$16$	−0.923165	+	2.84121i	−0.230791	+	0.710302i
$17$	3.99509	−	5.49877i	0.968951	−	1.33365i	0.0263765	−	0.999652i	$-0.491603\pi$
$17$	3.99509	−	5.49877i	0.968951	−	1.33365i	0.942575	−	0.333995i	$-0.108397\pi$
$18$		−	3.26189i		−	0.768834i
$19$	−1.48059	−	1.07571i	−0.339672	−	0.246786i	0.404852	−	0.914382i	$-0.367323\pi$
$19$	−1.48059	−	1.07571i	−0.339672	−	0.246786i	−0.744523	+	0.667597i	$0.767323\pi$
$20$	−0.930223	+	0.105049i	−0.208004	+	0.0234896i
$21$	−0.515546	+	0.374566i	−0.112501	+	0.0817371i
$22$	−1.34622	−	1.85291i	−0.287015	−	0.395042i
$23$	−4.12974	+	1.34183i	−0.861110	+	0.279792i	−0.706092	−	0.708120i	$-0.749544\pi$
$23$	−4.12974	+	1.34183i	−0.861110	+	0.279792i	−0.155018	+	0.987912i	$0.549544\pi$
$24$	−1.93819			−0.395632
$25$	2.56666	+	4.29095i	0.513332	+	0.858190i
$26$	−2.51650			−0.493527
$27$	3.39025	−	1.10156i	0.652455	−	0.211995i
$28$	−0.246078	−	0.338697i	−0.0465044	−	0.0640078i
$29$	−5.40749	+	3.92877i	−1.00415	+	0.729554i	−0.962973	−	0.269598i	$-0.913109\pi$
$29$	−5.40749	+	3.92877i	−1.00415	+	0.729554i	−0.0411725	+	0.999152i	$0.513109\pi$
$30$	0.741458	+	1.63128i	0.135371	+	0.297829i
$31$	−4.00700	−	2.91125i	−0.719678	−	0.522876i	0.166603	−	0.986024i	$-0.446720\pi$
$31$	−4.00700	−	2.91125i	−0.719678	−	0.522876i	−0.886281	+	0.463147i	$0.846720\pi$
$32$		−	2.32626i		−	0.411228i
$33$	0.682200	−	0.938968i	0.118756	−	0.163453i
$34$	2.64121	−	8.12882i	0.452965	−	1.39408i
$35$	−1.10303	+	1.94508i	−0.186446	+	0.328778i
$36$	0.335576	+	1.03280i	0.0559294	+	0.172133i
$37$	−2.47507	−	0.804200i	−0.406900	−	0.132210i	0.0984138	−	0.995146i	$-0.468623\pi$
$37$	−2.47507	−	0.804200i	−0.406900	−	0.132210i	−0.505313	+	0.862936i	$0.668623\pi$
$38$	−2.18876	−	0.711172i	−0.355064	−	0.115367i
$39$	−0.394073	−	1.21283i	−0.0631021	−	0.194208i
$40$	−6.19144	+	2.81417i	−0.978953	+	0.444959i
$41$	2.28132	−	7.02118i	0.356282	−	1.09652i	−0.598980	−	0.800764i	$-0.704427\pi$
$41$	2.28132	−	7.02118i	0.356282	−	1.09652i	0.955262	−	0.295760i	$-0.0955728\pi$
$42$	−0.471023	+	0.648308i	−0.0726805	+	0.100036i
$43$			7.31612i			1.11570i	0.829942	+	0.557849i	$0.188373\pi$
$43$			7.31612i			1.11570i	−0.829942	+	0.557849i	$0.811627\pi$
$44$	0.616871	+	0.448183i	0.0929969	+	0.0675662i
$45$	4.28022	−	3.91428i	0.638058	−	0.583506i
$46$	−4.41761	+	3.20958i	−0.651341	+	0.473227i
$47$	6.15868	+	8.47670i	0.898336	+	1.23645i	0.970996	+	0.239097i	$0.0768514\pi$
$47$	6.15868	+	8.47670i	0.898336	+	1.23645i	−0.0726594	+	0.997357i	$0.523149\pi$
$48$	−1.81056	+	0.588287i	−0.261332	+	0.0849120i
$49$	−1.00000			−0.142857
$50$	4.73708	+	4.13446i	0.669925	+	0.584700i
$51$	4.33130			0.606503
$52$	0.796790	−	0.258893i	0.110495	−	0.0359020i
$53$	3.14354	+	4.32670i	0.431798	+	0.594319i	0.968365	−	0.249539i	$-0.0802791\pi$
$53$	3.14354	+	4.32670i	0.431798	+	0.594319i	−0.536567	+	0.843858i	$0.680279\pi$
$54$	3.62658	−	2.63486i	0.493515	−	0.358559i
$55$	0.815908	−	3.99000i	0.110017	−	0.538011i
$56$	−2.46062	−	1.78775i	−0.328814	−	0.238898i
$57$		−	1.16624i		−	0.154472i
$58$	−4.94049	+	6.80001i	−0.648719	+	0.892885i
$59$	−0.00765237	+	0.0235516i	−0.000996254	+	0.00306615i	−0.951553	−	0.307484i	$-0.900513\pi$
$59$	−0.00765237	+	0.0235516i	−0.000996254	+	0.00306615i	0.950557	+	0.310550i	$0.100513\pi$
$60$	−0.402588	−	0.440226i	−0.0519739	−	0.0568329i
$61$	−1.22115	−	3.75830i	−0.156352	−	0.481201i	0.841944	−	0.539565i	$-0.181411\pi$
$61$	−1.22115	−	3.75830i	−0.156352	−	0.481201i	−0.998295	+	0.0583644i	$0.981411\pi$
$62$	−5.92354	−	1.92467i	−0.752290	−	0.244434i
$63$	2.46696	+	0.801563i	0.310807	+	0.100987i
$64$	−2.75030	−	8.46455i	−0.343787	−	1.05807i
$65$	−3.01982	−	3.30214i	−0.374562	−	0.409580i
$66$	0.451013	−	1.38808i	0.0555159	−	0.170860i
$67$	2.72641	−	3.75258i	0.333084	−	0.458450i	−0.609322	−	0.792923i	$-0.708558\pi$
$67$	2.72641	−	3.75258i	0.333084	−	0.458450i	0.942405	+	0.334473i	$0.108558\pi$
$68$			2.84552i			0.345070i
$69$	−2.23864	−	1.62647i	−0.269500	−	0.195804i
$70$	−0.563341	+	2.75488i	−0.0673322	+	0.329272i
$71$	−9.67307	+	7.02789i	−1.14798	+	0.834057i	−0.988211	−	0.153097i	$-0.951075\pi$
$71$	−9.67307	+	7.02789i	−1.14798	+	0.834057i	−0.159770	+	0.987154i	$0.551075\pi$
$72$	4.63726	+	6.38263i	0.546506	+	0.752201i
$73$	9.04917	−	2.94025i	1.05912	−	0.344130i	0.272882	−	0.962048i	$-0.412023\pi$
$73$	9.04917	−	2.94025i	1.05912	−	0.344130i	0.786243	+	0.617917i	$0.212023\pi$
$74$	−3.27262			−0.380434
$75$	−1.25080	+	2.93048i	−0.144430	+	0.338383i
$76$	0.766183			0.0878872
$77$	1.73217	−	0.562815i	0.197399	−	0.0641387i
$78$	−0.942598	−	1.29737i	−0.106728	−	0.146899i
$79$	4.03120	−	2.92884i	0.453546	−	0.329520i	−0.337448	−	0.941344i	$-0.609564\pi$
$79$	4.03120	−	2.92884i	0.453546	−	0.329520i	0.790994	+	0.611824i	$0.209564\pi$
$80$	−4.92956	+	4.50810i	−0.551142	+	0.504021i
$81$	−4.45778	−	3.23876i	−0.495308	−	0.359863i
$82$		−	9.28362i		−	1.02520i
$83$	1.56786	−	2.15797i	0.172095	−	0.236868i	−0.714254	−	0.699887i	$-0.753234\pi$
$83$	1.56786	−	2.15797i	0.172095	−	0.236868i	0.886348	+	0.463019i	$0.153234\pi$
$84$	0.0824416	−	0.253729i	0.00899512	−	0.0276841i
$85$	13.8361	−	6.28884i	1.50073	−	0.682121i
$86$	2.84300	+	8.74985i	0.306569	+	0.943521i
$87$	−4.05093	−	1.31623i	−0.434305	−	0.141114i
$88$	5.26837	+	1.71180i	0.561610	+	0.182478i
$89$	4.75121	+	14.6227i	0.503628	+	1.55001i	0.803066	+	0.595890i	$0.203201\pi$
$89$	4.75121	+	14.6227i	0.503628	+	1.55001i	−0.299438	+	0.954116i	$0.596799\pi$
$90$	3.59795	−	6.34462i	0.379257	−	0.668782i
$91$	0.618395	−	1.90323i	0.0648254	−	0.199512i
$92$	1.06854	−	1.47071i	0.111402	−	0.153332i
$93$		−	3.15625i		−	0.327288i
$94$	10.6596	+	7.74464i	1.09945	+	0.798799i
$95$	−1.69333	−	3.72549i	−0.173732	−	0.382227i
$96$	1.19929	−	0.871337i	0.122402	−	0.0889305i
$97$	7.14061	+	9.82821i	0.725019	+	0.997904i	0.999342	+	0.0362659i	$0.0115463\pi$
$97$	7.14061	+	9.82821i	0.725019	+	0.997904i	−0.274323	+	0.961638i	$0.588454\pi$
$98$	−1.19597	+	0.388594i	−0.120811	+	0.0392539i
$99$	−4.72431			−0.474811
$100$	−1.92523	−	0.821734i	−0.192523	−	0.0821734i
$101$	−13.7082			−1.36402			−0.682008	−	0.731345i	$-0.738893\pi$
$101$	−13.7082			−1.36402			−0.682008	+	0.731345i	$0.738893\pi$
$102$	5.18010	−	1.68312i	0.512906	−	0.166653i
$103$	−3.31220	−	4.55885i	−0.326361	−	0.449197i	0.614035	−	0.789279i	$-0.289545\pi$
$103$	−3.31220	−	4.55885i	−0.326361	−	0.449197i	−0.940396	+	0.340082i	$0.889545\pi$
$104$	4.92412	−	3.57758i	0.482850	−	0.350811i
$105$	−1.41594	+	0.159899i	−0.138181	+	0.0156046i
$106$	5.44090	+	3.95305i	0.528467	+	0.383954i
$107$			17.1093i			1.65402i	0.562186	+	0.827011i	$0.309961\pi$
$107$			17.1093i			1.65402i	−0.562186	+	0.827011i	$0.690039\pi$
$108$	−0.877200	+	1.20736i	−0.0844086	+	0.116178i
$109$	3.94809	−	12.1510i	0.378158	−	1.16385i	−0.563165	−	0.826345i	$-0.690416\pi$
$109$	3.94809	−	12.1510i	0.378158	−	1.16385i	0.941323	−	0.337507i	$-0.109584\pi$
$110$	−0.574689	−	5.08897i	−0.0547944	−	0.485214i
$111$	−0.512477	−	1.57724i	−0.0486422	−	0.149705i
$112$	−2.84121	−	0.923165i	−0.268469	−	0.0872309i
$113$	15.0552	+	4.89173i	1.41627	+	0.460175i	0.914416	−	0.404776i	$-0.132651\pi$
$113$	15.0552	+	4.89173i	1.41627	+	0.460175i	0.501857	+	0.864951i	$0.332651\pi$
$114$	−0.453194	−	1.39479i	−0.0424455	−	0.130634i
$115$	−9.51274	−	1.94524i	−0.887068	−	0.181395i
$116$	0.864718	−	2.66133i	0.0802870	−	0.247098i
$117$	−3.05111	+	4.19949i	−0.282075	+	0.388243i
$118$			0.0311406i			0.00286673i
$119$	5.49877	+	3.99509i	0.504071	+	0.366229i
$120$	−3.76994	−	2.13788i	−0.344147	−	0.195161i
$121$	6.21555	−	4.51586i	0.565050	−	0.410533i
$122$	−2.92091	−	4.02028i	−0.264446	−	0.363979i
$123$	4.47425	−	1.45377i	0.403429	−	0.131082i
$124$	2.07355			0.186211
$125$	0.259319	+	11.1773i	0.0231942	+	0.999731i
$126$	3.26189			0.290592
$127$	−4.79037	+	1.55649i	−0.425077	+	0.138116i	−0.513740	−	0.857946i	$-0.671740\pi$
$127$	−4.79037	+	1.55649i	−0.425077	+	0.138116i	0.0886633	+	0.996062i	$0.471740\pi$
$128$	−3.84387	−	5.29063i	−0.339753	−	0.467630i
$129$	−3.77180	+	2.74037i	−0.332089	+	0.241276i
$130$	−4.89480	−	2.77577i	−0.429302	−	0.243451i
$131$	−3.92779	−	2.85371i	−0.343172	−	0.249329i	0.402827	−	0.915276i	$-0.368028\pi$
$131$	−3.92779	−	2.85371i	−0.343172	−	0.249329i	−0.745999	+	0.665947i	$0.768028\pi$
$132$			0.485900i			0.0422922i
$133$	1.07571	−	1.48059i	0.0932763	−	0.128384i
$134$	1.80247	−	5.54743i	0.155710	−	0.479225i
$135$	7.80936	+	1.59692i	0.672123	+	0.137441i
$136$	6.38818	+	19.6608i	0.547782	+	1.68590i
$137$	−11.1159	−	3.61177i	−0.949693	−	0.308574i	−0.207102	−	0.978319i	$-0.566403\pi$
$137$	−11.1159	−	3.61177i	−0.949693	−	0.308574i	−0.742591	+	0.669745i	$0.766403\pi$
$138$	−3.30938	−	1.07528i	−0.281713	−	0.0915341i
$139$	3.02725	+	9.31691i	0.256768	+	0.790250i	0.993476	+	0.114040i	$0.0363791\pi$
$139$	3.02725	+	9.31691i	0.256768	+	0.790250i	−0.736708	+	0.676211i	$0.763621\pi$
$140$	−0.105049	−	0.930223i	−0.00887822	−	0.0786182i
$141$	−2.06330	+	6.35017i	−0.173761	+	0.534781i
$142$	−8.83769	+	12.1640i	−0.741642	+	1.02078i
$143$			3.64474i			0.304789i
$144$	6.26917	+	4.55482i	0.522431	+	0.379568i
$145$	−14.8515	+	1.67716i	−1.23335	+	0.139280i
$146$	9.67996	−	7.03290i	0.801119	−	0.582047i
$147$	−0.374566	−	0.515546i	−0.0308937	−	0.0425216i
$148$	1.03620	−	0.336681i	0.0851748	−	0.0276750i
$149$	−21.3913			−1.75245			−0.876223	−	0.481907i	$-0.839944\pi$
$149$	−21.3913			−1.75245			−0.876223	+	0.481907i	$0.839944\pi$
$150$	−0.357151	+	3.99081i	−0.0291613	+	0.325849i
$151$	14.2060			1.15607			0.578034	−	0.816013i	$-0.303820\pi$
$151$	14.2060			1.15607			0.578034	+	0.816013i	$0.303820\pi$
$152$	5.29385	−	1.72008i	0.429388	−	0.139517i
$153$	−10.3629	−	14.2633i	−0.837791	−	1.15312i
$154$	1.85291	−	1.34622i	0.149312	−	0.108481i
$155$	−4.58273	−	10.0824i	−0.368094	−	0.809841i
$156$	0.431922	+	0.313810i	0.0345815	+	0.0251249i
$157$		−	11.5228i		−	0.919617i	−0.888018	−	0.459809i	$-0.847918\pi$
$157$		−	11.5228i		−	0.919617i	0.888018	−	0.459809i	$-0.152082\pi$
$158$	3.68306	−	5.06930i	0.293009	−	0.403292i
$159$	−1.05315	+	3.24128i	−0.0835206	+	0.257050i
$160$	2.56592	−	4.52475i	0.202854	−	0.357713i
$161$	−1.34183	−	4.12974i	−0.105751	−	0.325469i
$162$	−6.58993	−	2.14120i	−0.517753	−	0.168228i
$163$	−20.5522	−	6.67782i	−1.60977	−	0.523047i	−0.640276	−	0.768145i	$-0.721180\pi$
$163$	−20.5522	−	6.67782i	−1.60977	−	0.523047i	−0.969498	+	0.245098i	$0.921180\pi$
$164$	0.955080	+	2.93943i	0.0745792	+	0.229531i
$165$	2.36264	−	1.07388i	0.183931	−	0.0836015i
$166$	1.03653	−	3.19012i	0.0804506	−	0.247602i
$167$	−7.98625	+	10.9921i	−0.617995	+	0.850597i	−0.997205	−	0.0747138i	$-0.976196\pi$
$167$	−7.98625	+	10.9921i	−0.617995	+	0.850597i	0.379210	+	0.925311i	$0.376196\pi$
$168$		−	1.93819i		−	0.149535i
$169$	−7.27737	−	5.28732i	−0.559798	−	0.406717i
$170$	14.1037	−	12.8979i	1.08170	−	0.989221i
$171$	−3.84053	+	2.79031i	−0.293693	+	0.213380i
$172$	−1.80034	−	2.47795i	−0.137274	−	0.188942i
$173$	9.93814	−	3.22910i	0.755583	−	0.245504i	0.0942011	−	0.995553i	$-0.469970\pi$
$173$	9.93814	−	3.22910i	0.755583	−	0.245504i	0.661382	+	0.750049i	$0.269970\pi$
$174$	−5.35626			−0.406057
$175$	−4.29095	+	2.56666i	−0.324365	+	0.194021i
$176$	5.44102			0.410132
$177$	−0.0150083	+	0.00487648i	−0.00112809	+	0.000366538i
$178$	11.3646	+	15.6420i	0.851813	+	1.17242i
$179$	−16.4785	+	11.9724i	−1.23166	+	0.894856i	−0.997014	−	0.0772241i	$-0.975394\pi$
$179$	−16.4785	+	11.9724i	−1.23166	+	0.894856i	−0.234650	+	0.972080i	$0.575394\pi$
$180$	−0.486482	+	2.37902i	−0.0362603	+	0.177322i
$181$	8.89809	+	6.46484i	0.661390	+	0.480528i	0.867132	−	0.498079i	$-0.165961\pi$
$181$	8.89809	+	6.46484i	0.661390	+	0.480528i	−0.205742	+	0.978606i	$0.565961\pi$
$182$		−	2.51650i		−	0.186536i
$183$	1.48018	−	2.03729i	0.109418	−	0.150601i
$184$	4.08118	−	12.5606i	0.300869	−	0.925978i
$185$	−3.92716	−	4.29431i	−0.288730	−	0.315724i
$186$	−1.22650	−	3.77478i	−0.0899313	−	0.276780i
$187$	−11.7733	−	3.82537i	−0.860947	−	0.279739i
$188$	−4.17186	−	1.35552i	−0.304264	−	0.0988614i
$189$	1.10156	+	3.39025i	0.0801267	+	0.246605i
$190$	−3.47287	−	3.79755i	−0.251948	−	0.275503i
$191$	3.77265	−	11.6110i	0.272979	−	0.840144i	−0.716768	−	0.697312i	$-0.754379\pi$
$191$	3.77265	−	11.6110i	0.272979	−	0.840144i	0.989747	−	0.142832i	$-0.0456209\pi$
$192$	3.33370	−	4.58844i	0.240589	−	0.331142i
$193$		−	0.109074i		−	0.00785131i	−0.999992	−	0.00392565i	$-0.998750\pi$
$193$		−	0.109074i		−	0.00785131i	0.999992	−	0.00392565i	$-0.00124958\pi$
$194$	12.3591	+	8.97944i	0.887334	+	0.644686i
$195$	0.571284	−	2.79372i	0.0409105	−	0.200063i
$196$	0.338697	−	0.246078i	0.0241927	−	0.0175770i
$197$	5.96758	+	8.21367i	0.425172	+	0.585199i	0.966837	−	0.255395i	$-0.0822056\pi$
$197$	5.96758	+	8.21367i	0.425172	+	0.585199i	−0.541664	+	0.840595i	$0.682206\pi$
$198$	−5.65013	+	1.83584i	−0.401537	+	0.130467i
$199$	−12.7337			−0.902665			−0.451332	−	0.892356i	$-0.649051\pi$
$199$	−12.7337			−0.902665			−0.451332	+	0.892356i	$0.649051\pi$
$200$	−15.1469	−	1.35555i	−1.07105	−	0.0958519i
$201$	2.95585			0.208489
$202$	−16.3946	+	5.32692i	−1.15352	+	0.374801i
$203$	−3.92877	−	5.40749i	−0.275746	−	0.379531i
$204$	−1.46700	+	1.06584i	−0.102710	+	0.0746235i
$205$	12.1819	−	11.1404i	0.850820	−	0.778078i
$206$	−5.73283	−	4.16514i	−0.399425	−	0.290199i
$207$			11.2634i			0.782864i
$208$	3.51398	−	4.83658i	0.243651	−	0.335357i
$209$	−1.03002	+	3.17006i	−0.0712477	+	0.219278i
$210$	−1.63128	+	0.741458i	−0.112569	+	0.0511655i
$211$	−2.42365	−	7.45922i	−0.166851	−	0.513514i	0.832317	−	0.554300i	$-0.187014\pi$
$211$	−2.42365	−	7.45922i	−0.166851	−	0.513514i	−0.999168	+	0.0407858i	$0.987014\pi$
$212$	−2.12941	−	0.691888i	−0.146249	−	0.0475191i
$213$	−7.24641	−	2.35450i	−0.496516	−	0.161328i
$214$	6.64858	+	20.4622i	0.454488	+	1.39877i
$215$	−8.06988	+	14.2304i	−0.550361	+	0.970507i
$216$	−3.35039	+	10.3114i	−0.227965	+	0.701605i
$217$	2.91125	−	4.00700i	0.197629	−	0.272013i
$218$		−	16.0664i		−	1.08815i
$219$	4.90535	+	3.56395i	0.331473	+	0.240829i
$220$	0.705505	+	1.55218i	0.0475651	+	0.104648i
$221$	−11.0040	+	7.99485i	−0.740207	+	0.537792i
$222$	−1.22581	−	1.68719i	−0.0822712	−	0.113237i
$223$	−10.6016	+	3.44466i	−0.709933	+	0.230671i	−0.641653	−	0.766995i	$-0.721751\pi$
$223$	−10.6016	+	3.44466i	−0.709933	+	0.230671i	−0.0682802	+	0.997666i	$0.521751\pi$
$224$	2.32626			0.155429
$225$	12.6429	−	2.89237i	0.842862	−	0.192825i
$226$	19.9064			1.32416
$227$	12.0260	−	3.90749i	0.798195	−	0.259349i	0.118605	−	0.992941i	$-0.462158\pi$
$227$	12.0260	−	3.90749i	0.798195	−	0.259349i	0.679590	+	0.733592i	$0.262158\pi$
$228$	0.286986	+	0.395003i	0.0190061	+	0.0261597i
$229$	7.56712	−	5.49784i	0.500049	−	0.363307i	−0.308986	−	0.951066i	$-0.599990\pi$
$229$	7.56712	−	5.49784i	0.500049	−	0.363307i	0.809036	+	0.587759i	$0.199990\pi$
$230$	−12.1329	+	1.37014i	−0.800017	+	0.0903445i
$231$	0.938968	+	0.682200i	0.0617796	+	0.0448855i
$232$		−	20.3294i		−	1.33469i
$233$	5.17280	−	7.11975i	0.338881	−	0.466430i	−0.605233	−	0.796048i	$-0.706920\pi$
$233$	5.17280	−	7.11975i	0.338881	−	0.466430i	0.944114	+	0.329618i	$0.106920\pi$
$234$	−2.01714	+	6.20810i	−0.131864	+	0.405836i
$235$	2.62909	+	23.2810i	0.171503	+	1.51869i
$236$	−0.00320369	−	0.00985993i	−0.000208542	−	0.000641827i
$237$	3.01991	+	0.981227i	0.196164	+	0.0637375i
$238$	8.12882	+	2.64121i	0.526913	+	0.171205i
$239$	4.40737	+	13.5645i	0.285089	+	0.877413i	0.986372	+	0.164531i	$0.0526109\pi$
$239$	4.40737	+	13.5645i	0.285089	+	0.877413i	−0.701283	+	0.712883i	$0.747389\pi$
$240$	−4.17058	−	0.852835i	−0.269210	−	0.0550503i
$241$	1.48959	−	4.58449i	0.0959531	−	0.295313i	−0.891548	−	0.452927i	$-0.850380\pi$
$241$	1.48959	−	4.58449i	0.0959531	−	0.295313i	0.987501	+	0.157613i	$0.0503800\pi$
$242$	5.67877	−	7.81616i	0.365045	−	0.502442i
$243$		−	14.2055i		−	0.911283i
$244$	1.33843	+	0.972429i	0.0856844	+	0.0622534i
$245$	−1.94508	−	1.10303i	−0.124267	−	0.0704698i
$246$	4.78614	−	3.47733i	0.305153	−	0.221707i
$247$	2.15269	+	2.96292i	0.136972	+	0.188526i
$248$	14.3270	−	4.65512i	0.909764	−	0.295600i
$249$	1.69980			0.107720
$250$	4.65358	+	13.2670i	0.294318	+	0.839077i
$251$	12.7306			0.803549			0.401774	−	0.915739i	$-0.368394\pi$
$251$	12.7306			0.803549			0.401774	+	0.915739i	$0.368394\pi$
$252$	−1.03280	+	0.335576i	−0.0650602	+	0.0211393i
$253$	4.64855	+	6.39819i	0.292252	+	0.402251i
$254$	−5.12430	+	3.72302i	−0.321527	+	0.233603i
$255$	8.42471	+	4.77754i	0.527576	+	0.299181i
$256$	7.74770	+	5.62903i	0.484231	+	0.351815i
$257$		−	24.5321i		−	1.53027i	−0.643869	−	0.765136i	$-0.722672\pi$
$257$		−	24.5321i		−	1.53027i	0.643869	−	0.765136i	$-0.277328\pi$
$258$	−3.44606	+	4.74310i	−0.214543	+	0.295293i
$259$	0.804200	−	2.47507i	0.0499706	−	0.153794i
$260$	1.83539	+	0.375315i	0.113826	+	0.0232760i
$261$	5.35767	+	16.4892i	0.331631	+	1.02066i
$262$	−5.80645	−	1.88663i	−0.358723	−	0.116556i
$263$	14.6782	+	4.76924i	0.905097	+	0.294084i	0.724339	−	0.689444i	$-0.242145\pi$
$263$	14.6782	+	4.76924i	0.905097	+	0.294084i	0.180758	+	0.983528i	$0.442145\pi$
$264$	1.09084	+	3.35727i	0.0671368	+	0.206626i
$265$	1.34195	+	11.8832i	0.0824352	+	0.729978i
$266$	0.711172	−	2.18876i	0.0436047	−	0.134202i
$267$	−5.75905	+	7.92665i	−0.352448	+	0.485103i
$268$			1.94190i			0.118620i
$269$	15.8633	+	11.5254i	0.967201	+	0.702713i	0.954812	−	0.297210i	$-0.0960562\pi$
$269$	15.8633	+	11.5254i	0.967201	+	0.702713i	0.0123894	+	0.999923i	$0.496056\pi$
$270$	9.96031	−	1.12480i	0.606165	−	0.0684532i
$271$	15.4531	−	11.2273i	0.938707	−	0.682010i	−0.00940234	−	0.999956i	$-0.502993\pi$
$271$	15.4531	−	11.2273i	0.938707	−	0.682010i	0.948109	+	0.317945i	$0.102993\pi$
$272$	11.9350	+	16.4272i	0.723667	+	0.996042i
$273$	1.21283	−	0.394073i	0.0734039	−	0.0238504i
$274$	−14.6977			−0.887923
$275$	5.98808	−	6.86089i	0.361095	−	0.413727i
$276$	1.15846			0.0697310
$277$	−2.45108	+	0.796404i	−0.147271	+	0.0478513i	−0.381725	−	0.924276i	$-0.624670\pi$
$277$	−2.45108	+	0.796404i	−0.147271	+	0.0478513i	0.234454	+	0.972127i	$0.424670\pi$
$278$	7.24099	+	9.96637i	0.434286	+	0.597743i
$279$	−10.3938	+	7.55153i	−0.622260	+	0.452098i
$280$	−2.81417	−	6.19144i	−0.168179	−	0.370009i
$281$	11.4849	+	8.34424i	0.685129	+	0.497776i	0.875055	−	0.484023i	$-0.160825\pi$
$281$	11.4849	+	8.34424i	0.685129	+	0.497776i	−0.189926	+	0.981798i	$0.560825\pi$
$282$			8.39640i			0.499998i
$283$	12.0263	−	16.5528i	0.714889	−	0.983961i	−0.284789	−	0.958590i	$-0.591923\pi$
$283$	12.0263	−	16.5528i	0.714889	−	0.983961i	0.999678	−	0.0253705i	$-0.00807656\pi$
$284$	1.54683	−	4.76066i	0.0917875	−	0.282493i
$285$	1.28640	−	2.26843i	0.0761996	−	0.134370i
$286$	1.41632	+	4.35900i	0.0837490	+	0.257753i
$287$	7.02118	+	2.28132i	0.414447	+	0.134662i
$288$	−5.73877	−	1.86464i	−0.338160	−	0.109875i
$289$	−9.02243	−	27.7682i	−0.530731	−	1.63342i
$290$	−17.1102	+	7.77704i	−1.00475	+	0.456684i
$291$	−2.39227	+	7.36264i	−0.140237	+	0.431605i
$292$	−2.34140	+	3.22265i	−0.137020	+	0.188592i
$293$			8.06270i			0.471028i	0.971871	+	0.235514i	$0.0756773\pi$
$293$			8.06270i			0.471028i	−0.971871	+	0.235514i	$0.924323\pi$
$294$	−0.648308	−	0.471023i	−0.0378101	−	0.0274706i
$295$	−0.0408625	+	0.0373689i	−0.00237911	+	0.00217570i
$296$	6.40364	−	4.65251i	0.372204	−	0.270422i
$297$	−3.81617	−	5.25251i	−0.221437	−	0.304781i
$298$	−25.5834	+	8.31254i	−1.48200	+	0.481532i
$299$	8.68961			0.502533
$300$	−0.297484	−	1.30034i	−0.0171752	−	0.0750751i
$301$	−7.31612			−0.421694
$302$	16.9899	−	5.52036i	0.977661	−	0.317661i
$303$	−5.13463	−	7.06721i	−0.294977	−	0.406000i
$304$	4.42316	−	3.21362i	0.253686	−	0.184314i
$305$	1.77028	−	8.65715i	0.101366	−	0.495707i
$306$	−17.9364	−	13.0315i	−1.02535	−	0.744963i
$307$			9.08866i			0.518717i	0.965781	+	0.259359i	$0.0835111\pi$
$307$			9.08866i			0.518717i	−0.965781	+	0.259359i	$0.916489\pi$
$308$	−0.448183	+	0.616871i	−0.0255376	+	0.0351495i
$309$	1.10966	−	3.41518i	0.0631264	−	0.194283i
$310$	−9.39878	−	10.2775i	−0.533815	−	0.583721i
$311$	−8.21191	−	25.2737i	−0.465655	−	1.43314i	−0.858157	−	0.513387i	$-0.828390\pi$
$311$	−8.21191	−	25.2737i	−0.465655	−	1.43314i	0.392502	−	0.919751i	$-0.371610\pi$
$312$	3.68882	+	1.19857i	0.208838	+	0.0678557i
$313$	8.15727	+	2.65046i	0.461076	+	0.149813i	0.530339	−	0.847786i	$-0.322065\pi$
$313$	8.15727	+	2.65046i	0.461076	+	0.149813i	−0.0692627	+	0.997598i	$0.522065\pi$
$314$	−4.47768	−	13.7809i	−0.252690	−	0.777700i
$315$	3.91428	+	4.28022i	0.220545	+	0.241163i
$316$	−0.644634	+	1.98398i	−0.0362635	+	0.111608i
$317$	−3.48825	+	4.80116i	−0.195919	+	0.269660i	−0.895662	−	0.444735i	$-0.853298\pi$
$317$	−3.48825	+	4.80116i	−0.195919	+	0.269660i	0.699743	+	0.714395i	$0.253298\pi$
$318$			4.28572i			0.240331i
$319$	9.84870	+	7.15550i	0.551421	+	0.400631i
$320$	3.98708	−	19.4979i	0.222885	−	1.08996i
$321$	−8.82066	+	6.40858i	−0.492321	+	0.357692i
$322$	−3.20958	−	4.41761i	−0.178863	−	0.246184i
$323$	−11.8302	+	3.84387i	−0.658251	+	0.213879i
$324$	2.30682			0.128157
$325$	−2.23143	−	9.75386i	−0.123777	−	0.541047i
$326$	−27.1748			−1.50507
$327$	7.74321	−	2.51592i	0.428200	−	0.139131i
$328$	13.1980	+	18.1655i	0.728740	+	1.00302i
$329$	−8.47670	+	6.15868i	−0.467336	+	0.339539i
$330$	2.40834	−	2.20244i	0.132575	−	0.121240i
$331$	12.5077	+	9.08737i	0.687485	+	0.499487i	0.875832	−	0.482616i	$-0.160313\pi$
$331$	12.5077	+	9.08737i	0.687485	+	0.499487i	−0.188348	+	0.982102i	$0.560313\pi$
$332$			1.11671i			0.0612876i
$333$	−3.96785	+	5.46128i	−0.217437	+	0.299276i
$334$	−5.27983	+	16.2497i	−0.288900	+	0.889142i
$335$	9.44227	−	4.29175i	0.515886	−	0.234484i
$336$	−0.588287	−	1.81056i	−0.0320937	−	0.0987743i
$337$	−14.1648	−	4.60243i	−0.771608	−	0.250711i	−0.103355	−	0.994645i	$-0.532958\pi$
$337$	−14.1648	−	4.60243i	−0.771608	−	0.250711i	−0.668253	+	0.743934i	$0.732958\pi$
$338$	−10.7581	−	3.49553i	−0.585165	−	0.190132i
$339$	3.11725	+	9.59392i	0.169306	+	0.521070i
$340$	−3.13869	+	5.53476i	−0.170219	+	0.300165i
$341$	−2.78758	+	8.57928i	−0.150956	+	0.464594i
$342$	−3.50886	+	4.82953i	−0.189737	+	0.261151i
$343$		−	1.00000i		−	0.0539949i
$344$	−18.0022	−	13.0794i	−0.970614	−	0.705192i
$345$	−2.56029	−	5.63288i	−0.137841	−	0.303264i
$346$	10.6309	−	7.72380i	0.571521	−	0.415234i
$347$	−8.41195	−	11.5781i	−0.451577	−	0.621543i	0.521158	−	0.853460i	$-0.325500\pi$
$347$	−8.41195	−	11.5781i	−0.451577	−	0.621543i	−0.972736	+	0.231917i	$0.925500\pi$
$348$	1.69593	−	0.551042i	0.0909115	−	0.0295389i
$349$	3.94565			0.211206			0.105603	−	0.994408i	$-0.466323\pi$
$349$	3.94565			0.211206			0.105603	+	0.994408i	$0.466323\pi$
$350$	−4.13446	+	4.73708i	−0.220996	+	0.253208i
$351$	−7.13361			−0.380764
$352$	−4.02946	+	1.30925i	−0.214771	+	0.0697833i
$353$	−5.32143	−	7.32432i	−0.283231	−	0.389834i	0.643570	−	0.765388i	$-0.277453\pi$
$353$	−5.32143	−	7.32432i	−0.283231	−	0.389834i	−0.926801	+	0.375553i	$0.877453\pi$
$354$	−0.0160544	+	0.0116642i	−0.000853284	+	0.000619947i
$355$	−26.5668	+	3.00015i	−1.41002	+	0.159231i
$356$	−5.20755	−	3.78351i	−0.276000	−	0.200526i
$357$			4.33130i			0.229237i
$358$	−15.0554	+	20.7220i	−0.795704	+	1.09519i
$359$	11.3472	−	34.9232i	0.598885	−	1.84318i	0.0645314	−	0.997916i	$-0.479445\pi$
$359$	11.3472	−	34.9232i	0.598885	−	1.84318i	0.534353	−	0.845261i	$-0.320555\pi$
$360$	1.97960	+	17.5297i	0.104334	+	0.923899i
$361$	−4.83633	−	14.8847i	−0.254543	−	0.783404i
$362$	13.1540	+	4.27400i	0.691361	+	0.224637i
$363$	4.65627	+	1.51291i	0.244391	+	0.0794074i
$364$	0.258893	+	0.796790i	0.0135697	+	0.0417632i
$365$	20.8445	+	4.26246i	1.09105	+	0.223107i
$366$	0.978569	−	3.01172i	0.0511506	−	0.157425i
$367$	−9.23299	+	12.7081i	−0.481958	+	0.663358i	−0.978880	−	0.204437i	$-0.934464\pi$
$367$	−9.23299	+	12.7081i	−0.481958	+	0.663358i	0.496922	+	0.867795i	$0.334464\pi$
$368$		−	12.9722i		−	0.676222i
$369$	−15.4923	−	11.2558i	−0.806498	−	0.585955i
$370$	−6.36550	−	3.60979i	−0.330927	−	0.187664i
$371$	−4.32670	+	3.14354i	−0.224631	+	0.163204i
$372$	0.776683	+	1.06901i	0.0402692	+	0.0554257i
$373$	−8.95386	+	2.90928i	−0.463613	+	0.150637i	−0.531504	−	0.847056i	$-0.678373\pi$
$373$	−8.95386	+	2.90928i	−0.463613	+	0.150637i	0.0678910	+	0.997693i	$0.478373\pi$
$374$	−15.5670			−0.804949
$375$	−5.66530	+	4.32034i	−0.292555	+	0.223102i
$376$	−31.8681			−1.64347
$377$	12.7212	−	4.13337i	0.655175	−	0.212879i
$378$	2.63486	+	3.62658i	0.135523	+	0.186531i
$379$	25.3574	−	18.4232i	1.30252	−	0.946339i	0.302546	−	0.953135i	$-0.402163\pi$
$379$	25.3574	−	18.4232i	1.30252	−	0.946339i	0.999977	+	0.00679612i	$0.00216329\pi$
$380$	1.49029	+	0.845121i	0.0764500	+	0.0433538i
$381$	−2.59675	−	1.88665i	−0.133036	−	0.0966561i
$382$		−	15.3525i		−	0.785500i
$383$	10.5691	−	14.5472i	0.540058	−	0.743326i	−0.448564	−	0.893751i	$-0.648064\pi$
$383$	10.5691	−	14.5472i	0.540058	−	0.743326i	0.988621	+	0.150425i	$0.0480642\pi$
$384$	1.28778	−	3.96338i	0.0657168	−	0.202256i
$385$	3.99000	+	0.815908i	0.203349	+	0.0415825i
$386$	−0.0423854	−	0.130449i	−0.00215736	−	0.00663968i
$387$	18.0486	+	5.86433i	0.917460	+	0.298101i
$388$	−4.83701	−	1.57164i	−0.245562	−	0.0797879i
$389$	2.87435	+	8.84634i	0.145735	+	0.448527i	0.997105	−	0.0760391i	$-0.0242274\pi$
$389$	2.87435	+	8.84634i	0.145735	+	0.448527i	−0.851369	+	0.524567i	$0.824227\pi$
$390$	−0.402387	−	3.56321i	−0.0203756	−	0.180430i
$391$	−9.12024	+	28.0692i	−0.461230	+	1.41952i
$392$	1.78775	−	2.46062i	0.0902948	−	0.124280i
$393$		−	3.09386i		−	0.156065i
$394$	10.3288	+	7.50433i	0.520358	+	0.378062i
$395$	11.0716	−	1.25030i	0.557072	−	0.0629092i
$396$	1.60011	−	1.16255i	0.0804086	−	0.0584202i
$397$	−0.852092	−	1.17280i	−0.0427653	−	0.0588613i	0.787099	−	0.616827i	$-0.211582\pi$
$397$	−0.852092	−	1.17280i	−0.0427653	−	0.0588613i	−0.829864	+	0.557966i	$0.811582\pi$
$398$	−15.2291	+	4.94822i	−0.763364	+	0.248032i
$399$	1.16624			0.0583851
$400$	−14.5609	+	3.33116i	−0.728047	+	0.166558i
$401$	−6.92538			−0.345837			−0.172919	−	0.984936i	$-0.555320\pi$
$401$	−6.92538			−0.345837			−0.172919	+	0.984936i	$0.555320\pi$
$402$	3.53510	−	1.14862i	0.176315	−	0.0572882i
$403$	5.82591	+	8.01868i	0.290209	+	0.399439i
$404$	4.64292	−	3.37328i	0.230994	−	0.167827i
$405$	−5.09828	−	11.2167i	−0.253335	−	0.557362i
$406$	−6.80001	−	4.94049i	−0.337479	−	0.245193i
$407$			4.73985i			0.234946i
$408$	−7.74326	+	10.6577i	−0.383348	+	0.527634i
$409$	3.37811	−	10.3967i	0.167037	−	0.514086i	−0.832144	−	0.554560i	$-0.812887\pi$
$409$	3.37811	−	10.3967i	0.167037	−	0.514086i	0.999181	+	0.0404736i	$0.0128867\pi$
$410$	10.2401	−	18.0574i	0.505722	−	0.891790i
$411$	−2.30160	−	7.08359i	−0.113530	−	0.349408i
$412$	2.24366	+	0.729011i	0.110537	+	0.0359158i
$413$	−0.0235516	−	0.00765237i	−0.00115890	−	0.000376548i
$414$	4.37691	+	13.4707i	0.215113	+	0.662051i
$415$	5.42990	−	2.46803i	0.266543	−	0.121151i
$416$	−1.43855	+	4.42739i	−0.0705305	+	0.217071i
$417$	−3.66940	+	5.05049i	−0.179691	+	0.247324i
$418$			4.19155i			0.205016i
$419$	−8.78555	−	6.38307i	−0.429202	−	0.311834i	0.352128	−	0.935952i	$-0.385458\pi$
$419$	−8.78555	−	6.38307i	−0.429202	−	0.311834i	−0.781330	+	0.624118i	$0.785458\pi$
$420$	0.440226	−	0.402588i	0.0214808	−	0.0196443i
$421$	−15.7391	+	11.4351i	−0.767076	+	0.557313i	−0.901073	−	0.433668i	$-0.857219\pi$
$421$	−15.7391	+	11.4351i	−0.767076	+	0.557313i	0.133996	+	0.990982i	$0.457219\pi$
$422$	−5.79722	−	7.97918i	−0.282204	−	0.388421i
$423$	25.8482	−	8.39860i	1.25678	−	0.408354i
$424$	−16.2662			−0.789958
$425$	33.8490	+	3.02926i	1.64192	+	0.146941i
$426$	−9.58143			−0.464222
$427$	3.75830	−	1.22115i	0.181877	−	0.0590954i
$428$	−4.21023	−	5.79488i	−0.203509	−	0.280106i
$429$	−1.87903	+	1.36520i	−0.0907206	+	0.0659124i
$430$	−4.12147	+	20.1551i	−0.198755	+	0.971963i
$431$	−4.14273	−	3.00987i	−0.199548	−	0.144980i	0.483524	−	0.875331i	$-0.339357\pi$
$431$	−4.14273	−	3.00987i	−0.199548	−	0.144980i	−0.683072	+	0.730351i	$0.739357\pi$
$432$			10.6493i			0.512367i
$433$	−8.19091	+	11.2738i	−0.393630	+	0.541785i	−0.959131	−	0.282962i	$-0.908683\pi$
$433$	−8.19091	+	11.2738i	−0.393630	+	0.541785i	0.565501	+	0.824748i	$0.308683\pi$
$434$	1.92467	−	5.92354i	0.0923873	−	0.284339i
$435$	−6.42754	−	7.02845i	−0.308177	−	0.336988i
$436$	1.65288	+	5.08704i	0.0791585	+	0.243625i
$437$	7.55790	+	2.45571i	0.361543	+	0.117473i
$438$	7.25157	+	2.35618i	0.346494	+	0.112583i
$439$	−8.46126	−	26.0411i	−0.403834	−	1.24287i	−0.921865	−	0.387511i	$-0.873335\pi$
$439$	−8.46126	−	26.0411i	−0.403834	−	1.24287i	0.518031	−	0.855362i	$-0.326665\pi$
$440$	8.35924	+	9.14074i	0.398511	+	0.435768i
$441$	−0.801563	+	2.46696i	−0.0381697	+	0.117474i
$442$	−10.0537	+	13.8377i	−0.478204	+	0.658191i
$443$			39.3336i			1.86880i	0.356228	+	0.934399i	$0.384063\pi$
$443$			39.3336i			1.86880i	−0.356228	+	0.934399i	$0.615937\pi$
$444$	0.561699	+	0.408098i	0.0266571	+	0.0193675i
$445$	−6.88779	+	33.6831i	−0.326513	+	1.59673i
$446$	−11.3406	+	8.23941i	−0.536992	+	0.390147i
$447$	−8.01247	−	11.0282i	−0.378977	−	0.521617i
$448$	8.46455	−	2.75030i	0.399912	−	0.129939i
$449$	28.2960			1.33537			0.667685	−	0.744444i	$-0.267285\pi$
$449$	28.2960			1.33537			0.667685	+	0.744444i	$0.267285\pi$
$450$	13.9966	−	8.37215i	0.659806	−	0.394667i
$451$	−13.4458			−0.633138
$452$	−6.30289	+	2.04793i	−0.296463	+	0.0963267i
$453$	5.32109	+	7.32385i	0.250007	+	0.344105i
$454$	12.8643	−	9.34648i	0.603753	−	0.438652i
$455$	3.30214	−	3.01982i	0.154807	−	0.141571i
$456$	2.86968	+	2.08494i	0.134385	+	0.0976365i
$457$		−	7.27936i		−	0.340514i	−0.985400	−	0.170257i	$-0.945540\pi$
$457$		−	7.27936i		−	0.340514i	0.985400	−	0.170257i	$-0.0544598\pi$
$458$	6.91362	−	9.51578i	0.323052	−	0.444643i
$459$	7.48714	−	23.0430i	0.349470	−	1.07556i
$460$	3.70062	−	1.68203i	0.172542	−	0.0784249i
$461$	1.83293	+	5.64118i	0.0853682	+	0.262736i	0.984624	−	0.174687i	$-0.0558913\pi$
$461$	1.83293	+	5.64118i	0.0853682	+	0.262736i	−0.899256	+	0.437423i	$0.855891\pi$
$462$	1.38808	+	0.451013i	0.0645791	+	0.0209830i
$463$	−13.3123	−	4.32543i	−0.618675	−	0.201020i	−0.0171231	−	0.999853i	$-0.505451\pi$
$463$	−13.3123	−	4.32543i	−0.618675	−	0.201020i	−0.601552	+	0.798834i	$0.705451\pi$
$464$	−6.17046	−	18.9907i	−0.286456	−	0.881622i
$465$	3.48143	−	6.13915i	0.161448	−	0.284696i
$466$	3.41982	−	10.5251i	0.158420	−	0.487567i
$467$	−2.73088	+	3.75874i	−0.126370	+	0.173934i	−0.867514	−	0.497413i	$-0.834284\pi$
$467$	−2.73088	+	3.75874i	−0.126370	+	0.173934i	0.741144	+	0.671346i	$0.234284\pi$
$468$		−	2.17317i		−	0.100455i
$469$	3.75258	+	2.72641i	0.173278	+	0.125894i
$470$	12.1912	+	26.8218i	0.562337	+	1.23720i
$471$	5.94052	−	4.31604i	0.273725	−	0.198873i
$472$	−0.0442710	−	0.0609338i	−0.00203774	−	0.00280471i
$473$	12.6727	−	4.11762i	0.582693	−	0.189328i
$474$	3.99301			0.183405
$475$	0.815656	−	9.11415i	0.0374249	−	0.418186i
$476$	−2.84552			−0.130424
$477$	13.1935	−	4.28684i	0.604090	−	0.196281i
$478$	10.5422	+	14.5100i	0.482187	+	0.663673i
$479$	11.1567	−	8.10585i	0.509765	−	0.370366i	−0.302970	−	0.953000i	$-0.597978\pi$
$479$	11.1567	−	8.10585i	0.509765	−	0.370366i	0.812734	+	0.582634i	$0.197978\pi$
$480$	3.29383	−	0.371966i	0.150342	−	0.0169779i
$481$	4.21331	+	3.06115i	0.192110	+	0.139576i
$482$		−	6.06176i		−	0.276106i
$483$	1.62647	−	2.23864i	0.0740068	−	0.101862i
$484$	−0.993936	+	3.05902i	−0.0451789	+	0.139046i
$485$	3.04826	+	26.9929i	0.138415	+	1.22569i
$486$	−5.52017	−	16.9893i	−0.250400	−	0.770652i
$487$	26.3647	+	8.56642i	1.19470	+	0.388182i	0.837808	−	0.545964i	$-0.183837\pi$
$487$	26.3647	+	8.56642i	1.19470	+	0.388182i	0.356891	+	0.934146i	$0.383837\pi$
$488$	11.4309	+	3.71411i	0.517450	+	0.168130i
$489$	−4.25544	−	13.0969i	−0.192438	−	0.592263i
$490$	−2.75488	−	0.563341i	−0.124453	−	0.0254492i
$491$	9.25639	−	28.4882i	0.417735	−	1.28566i	−0.492046	−	0.870569i	$-0.663751\pi$
$491$	9.25639	−	28.4882i	0.417735	−	1.28566i	0.909781	−	0.415088i	$-0.136249\pi$
$492$	−1.15767	+	1.59340i	−0.0521920	+	0.0718361i
$493$			45.4303i			2.04608i
$494$	3.72592	+	2.70704i	0.167637	+	0.121795i
$495$	−9.18915	−	5.21104i	−0.413022	−	0.234219i
$496$	11.9706	−	8.69715i	0.537496	−	0.390513i
$497$	−7.02789	−	9.67307i	−0.315244	−	0.433896i
$498$	2.03291	−	0.660532i	0.0910967	−	0.0295991i
$499$	−13.0499			−0.584196			−0.292098	−	0.956388i	$-0.594353\pi$
$499$	−13.0499			−0.584196			−0.292098	+	0.956388i	$0.594353\pi$
$500$	−2.83833	−	3.72192i	−0.126934	−	0.166449i
$501$	−8.65834			−0.386826
$502$	15.2254	−	4.94704i	0.679543	−	0.220797i
$503$	−22.1517	−	30.4892i	−0.987696	−	1.35945i	−0.932579	−	0.360967i	$-0.882447\pi$
$503$	−22.1517	−	30.4892i	−0.987696	−	1.35945i	−0.0551174	−	0.998480i	$-0.517553\pi$
$504$	−6.38263	+	4.63726i	−0.284305	+	0.206560i
$505$	−26.6635	−	15.1205i	−1.18651	−	0.672854i
$506$	8.04582	+	5.84563i	0.357681	+	0.259870i
$507$		−	5.73227i		−	0.254579i
$508$	1.23947	−	1.70598i	0.0549925	−	0.0756908i
$509$	−13.0535	+	40.1745i	−0.578585	+	1.78070i	0.0450483	+	0.998985i	$0.485656\pi$
$509$	−13.0535	+	40.1745i	−0.578585	+	1.78070i	−0.623633	+	0.781717i	$0.714344\pi$
$510$	11.9322	+	2.44000i	0.528367	+	0.108045i
$511$	2.94025	+	9.04917i	0.130069	+	0.400312i
$512$	23.8924	+	7.76312i	1.05591	+	0.343085i
$513$	−6.20455	−	2.01598i	−0.273938	−	0.0890078i
$514$	−9.53303	−	29.3397i	−0.420484	−	1.29412i
$515$	−1.41395	−	12.5208i	−0.0623060	−	0.551731i
$516$	0.603153	−	1.85631i	0.0265523	−	0.0817196i
$517$	11.2168	−	15.4387i	0.493316	−	0.678992i
$518$		−	3.27262i		−	0.143791i
$519$	5.38724	+	3.91406i	0.236474	+	0.171808i
$520$	13.5240	−	1.52724i	0.593065	−	0.0669738i
$521$	−19.0355	+	13.8301i	−0.833962	+	0.605909i	−0.920678	−	0.390324i	$-0.872363\pi$
$521$	−19.0355	+	13.8301i	−0.833962	+	0.605909i	0.0867152	+	0.996233i	$0.472363\pi$
$522$	12.8152	+	17.6386i	0.560906	+	0.772021i
$523$	−18.6864	+	6.07159i	−0.817100	+	0.265492i	−0.687602	−	0.726088i	$-0.741337\pi$
$523$	−18.6864	+	6.07159i	−0.817100	+	0.265492i	−0.129498	+	0.991580i	$0.541337\pi$
$524$	2.03256			0.0887930
$525$	−2.93048	−	1.25080i	−0.127897	−	0.0545894i
$526$	19.4080			0.846228
$527$	−32.0166	+	10.4028i	−1.39467	+	0.453154i
$528$	2.03802	+	2.80510i	0.0886935	+	0.122076i
$529$	−3.35317	+	2.43622i	−0.145790	+	0.105923i
$530$	6.22266	+	13.6905i	0.270295	+	0.594675i
$531$	0.0519669	+	0.0377561i	0.00225517	+	0.00163848i
$532$			0.766183i			0.0332182i
$533$	−8.68373	+	11.9521i	−0.376134	+	0.517704i
$534$	−3.80740	+	11.7180i	−0.164762	+	0.507086i
$535$	−18.8721	+	33.2790i	−0.815911	+	1.43878i
$536$	4.35955	+	13.4173i	0.188304	+	0.579539i
$537$	−12.3446	−	4.01101i	−0.532709	−	0.173088i
$538$	23.4507	+	7.61959i	1.01103	+	0.328504i
$539$	0.562815	+	1.73217i	0.0242421	+	0.0746096i
$540$	−3.03798	+	1.38084i	−0.130734	+	0.0594218i
$541$	−11.0526	+	34.0164i	−0.475189	+	1.46248i	0.370514	+	0.928827i	$0.379182\pi$
$541$	−11.0526	+	34.0164i	−0.475189	+	1.46248i	−0.845703	+	0.533654i	$0.820818\pi$
$542$	14.1185	−	19.4325i	0.606442	−	0.834696i
$543$			7.00889i			0.300780i
$544$	−12.7915	−	9.29360i	−0.548433	−	0.398460i
$545$	21.0822	−	19.2797i	0.903062	−	0.825853i
$546$	1.29737	−	0.942598i	0.0555225	−	0.0403395i
$547$	11.8094	+	16.2542i	0.504932	+	0.694979i	0.983054	−	0.183314i	$-0.0586826\pi$
$547$	11.8094	+	16.2542i	0.504932	+	0.694979i	−0.478123	+	0.878293i	$0.658683\pi$
$548$	4.65369	−	1.51208i	0.198796	−	0.0645927i
$549$	−10.2504			−0.437476
$550$	4.49546	−	10.5323i	0.191687	−	0.449101i
$551$	12.2325			0.521123
$552$	8.00424	−	2.60073i	0.340683	−	0.110695i
$553$	2.92884	+	4.03120i	0.124547	+	0.171424i
$554$	−2.62194	+	1.90495i	−0.111395	+	0.0809335i
$555$	0.742934	−	3.63314i	0.0315358	−	0.154218i
$556$	−3.31801	−	2.41067i	−0.140715	−	0.102235i
$557$		−	10.2545i		−	0.434498i	−0.976116	−	0.217249i	$-0.930292\pi$
$557$		−	10.2545i		−	0.434498i	0.976116	−	0.217249i	$-0.0697084\pi$
$558$	−9.49618	+	13.0704i	−0.402005	+	0.553313i
$559$	4.52426	−	13.9242i	0.191356	−	0.588932i
$560$	−4.50810	−	4.92956i	−0.190502	−	0.208312i
$561$	−2.43772	−	7.50252i	−0.102921	−	0.316757i
$562$	16.9781	+	5.51651i	0.716176	+	0.232700i
$563$	−35.9613	−	11.6845i	−1.51559	−	0.492445i	−0.571070	−	0.820901i	$-0.693472\pi$
$563$	−35.9613	−	11.6845i	−1.51559	−	0.492445i	−0.944519	+	0.328456i	$0.893472\pi$
$564$	−0.863805	−	2.65852i	−0.0363727	−	0.111944i
$565$	23.8878	+	26.1211i	1.00497	+	1.09892i
$566$	7.95077	−	24.4700i	0.334196	−	1.02855i
$567$	3.23876	−	4.45778i	0.136015	−	0.187209i
$568$		−	36.3658i		−	1.52588i
$569$	−18.6504	−	13.5503i	−0.781866	−	0.568059i	0.123673	−	0.992323i	$-0.460533\pi$
$569$	−18.6504	−	13.5503i	−0.781866	−	0.568059i	−0.905538	+	0.424264i	$0.860533\pi$
$570$	0.656992	−	3.21286i	0.0275184	−	0.134572i
$571$	32.3796	−	23.5252i	1.35505	−	0.984498i	0.356303	−	0.934371i	$-0.384037\pi$
$571$	32.3796	−	23.5252i	1.35505	−	0.984498i	0.998743	−	0.0501274i	$-0.0159627\pi$
$572$	−0.896891	−	1.23446i	−0.0375009	−	0.0516155i
$573$	7.39913	−	2.40412i	0.309103	−	0.100434i
$574$	9.28362			0.387491
$575$	−16.3574	−	14.2765i	−0.682150	−	0.595370i
$576$	−23.0862			−0.961926
$577$	−20.5390	+	6.67353i	−0.855050	+	0.277823i	−0.703560	−	0.710636i	$-0.748407\pi$
$577$	−20.5390	+	6.67353i	−0.855050	+	0.277823i	−0.151490	+	0.988459i	$0.548407\pi$
$578$	−21.5811	−	29.7038i	−0.897655	−	1.23552i
$579$	0.0562327	−	0.0408554i	0.00233695	−	0.00169789i
$580$	4.61746	−	4.22268i	0.191730	−	0.175337i
$581$	2.15797	+	1.56786i	0.0895276	+	0.0650456i
$582$			9.73510i			0.403533i
$583$	5.72534	−	7.88026i	0.237119	−	0.326367i
$584$	−8.94276	+	27.5230i	−0.370054	+	1.13891i
$585$	−10.5668	+	4.80288i	−0.436883	+	0.198575i
$586$	3.13312	+	9.64274i	0.129428	+	0.398338i
$587$	−1.71953	−	0.558710i	−0.0709727	−	0.0230604i	0.273315	−	0.961924i	$-0.411880\pi$
$587$	−1.71953	−	0.558710i	−0.0709727	−	0.0230604i	−0.344288	+	0.938864i	$0.611880\pi$
$588$	0.253729	+	0.0824416i	0.0104636	+	0.00339983i
$589$	2.80106	+	8.62077i	0.115416	+	0.355213i
$590$	−0.0343490	+	0.0605709i	−0.00141412	+	0.00249367i
$591$	−1.99927	+	6.15313i	−0.0822391	+	0.253106i
$592$	4.56980	−	6.28979i	0.187818	−	0.258509i
$593$			38.4929i			1.58071i	0.612648	+	0.790356i	$0.290104\pi$
$593$			38.4929i			1.58071i	−0.612648	+	0.790356i	$0.709896\pi$
$594$	−6.60511	−	4.79889i	−0.271011	−	0.196901i
$595$	6.28884	+	13.8361i	0.257817	+	0.567223i
$596$	7.24518	−	5.26393i	0.296774	−	0.215619i
$597$	−4.76960	−	6.56479i	−0.195207	−	0.268679i
$598$	10.3925	−	3.37673i	0.424981	−	0.138085i
$599$	31.7681			1.29801			0.649005	−	0.760784i	$-0.275185\pi$
$599$	31.7681			1.29801			0.649005	+	0.760784i	$0.275185\pi$
$600$	−4.97469	−	8.31670i	−0.203091	−	0.339528i
$601$	19.1855			0.782592			0.391296	−	0.920265i	$-0.372027\pi$
$601$	19.1855			0.782592			0.391296	+	0.920265i	$0.372027\pi$
$602$	−8.74985	+	2.84300i	−0.356617	+	0.115872i
$603$	−7.07206	−	9.73385i	−0.287996	−	0.396393i
$604$	−4.81153	+	3.49578i	−0.195778	+	0.142241i
$605$	17.0709	−	1.92778i	0.694029	−	0.0783755i
$606$	−8.88713	−	6.45688i	−0.361015	−	0.262293i
$607$		−	35.5410i		−	1.44256i	−0.692641	−	0.721282i	$-0.743553\pi$
$607$		−	35.5410i		−	1.44256i	0.692641	−	0.721282i	$-0.256447\pi$
$608$	−2.50239	+	3.44424i	−0.101485	+	0.139682i
$609$	1.31623	−	4.05093i	0.0533362	−	0.164152i
$610$	−1.24691	−	11.0416i	−0.0504859	−	0.447061i
$611$	−6.47941	−	19.9416i	−0.262129	−	0.806750i
$612$	7.01978	+	2.28086i	0.283758	+	0.0921984i
$613$	3.83439	+	1.24587i	0.154869	+	0.0503201i	0.385426	−	0.922739i	$-0.374055\pi$
$613$	3.83439	+	1.24587i	0.154869	+	0.0503201i	−0.230556	+	0.973059i	$0.574055\pi$
$614$	3.53180	+	10.8698i	0.142532	+	0.438667i
$615$	10.3063	+	2.10752i	0.415591	+	0.0849834i
$616$	−1.71180	+	5.26837i	−0.0689703	+	0.212269i
$617$	−19.2392	+	26.4805i	−0.774542	+	1.06606i	0.221322	+	0.975201i	$0.428963\pi$
$617$	−19.2392	+	26.4805i	−0.774542	+	1.06606i	−0.995863	+	0.0908641i	$0.971037\pi$
$618$		−	4.51566i		−	0.181647i
$619$	38.9974	+	28.3333i	1.56744	+	1.13881i	0.929557	+	0.368678i	$0.120189\pi$
$619$	38.9974	+	28.3333i	1.56744	+	1.13881i	0.637882	+	0.770134i	$0.279811\pi$
$620$	4.03322	+	2.28719i	0.161978	+	0.0918556i
$621$	−12.5227	+	9.09831i	−0.502521	+	0.365103i
$622$	−19.6424	−	27.0354i	−0.787588	−	1.08402i
$623$	−14.6227	+	4.75121i	−0.585847	+	0.190353i
$624$	3.80970			0.152510
$625$	−11.8245	+	22.0268i	−0.472980	+	0.881073i
$626$	10.7858			0.431087
$627$	−2.02012	+	0.656378i	−0.0806760	+	0.0262132i
$628$	2.83550	+	3.90273i	0.113149	+	0.155736i
$629$	−14.3103	+	10.3970i	−0.570587	+	0.414556i
$630$	6.34462	+	3.59795i	0.252776	+	0.143346i
$631$	−11.9008	−	8.64644i	−0.473764	−	0.344209i	0.325143	−	0.945665i	$-0.394588\pi$
$631$	−11.9008	−	8.64644i	−0.473764	−	0.344209i	−0.798906	+	0.601456i	$0.794588\pi$
$632$			15.1553i			0.602845i
$633$	2.93776	−	4.04348i	0.116765	−	0.160714i
$634$	−2.30613	+	7.09755i	−0.0915883	+	0.281880i
$635$	−11.0345	−	2.25643i	−0.437891	−	0.0895435i
$636$	−0.440906	−	1.35697i	−0.0174831	−	0.0538073i
$637$	1.90323	+	0.618395i	0.0754085	+	0.0245017i
$638$	14.5593	+	4.73061i	0.576409	+	0.187287i
$639$	9.58394	+	29.4963i	0.379135	+	1.16686i
$640$	−1.64091	−	14.5306i	−0.0648628	−	0.574372i
$641$	−1.67552	+	5.15671i	−0.0661789	+	0.203678i	−0.978678	−	0.205401i	$-0.934150\pi$
$641$	−1.67552	+	5.15671i	−0.0661789	+	0.203678i	0.912499	+	0.409079i	$0.134150\pi$
$642$	−8.05890	+	11.0921i	−0.318059	+	0.437771i
$643$		−	41.4190i		−	1.63341i	−0.577058	−	0.816703i	$-0.695799\pi$
$643$		−	41.4190i		−	1.63341i	0.577058	−	0.816703i	$-0.304201\pi$
$644$	1.47071	+	1.06854i	0.0579542	+	0.0421062i
$645$	−10.3592	+	1.16984i	−0.407891	+	0.0460625i
$646$	−12.6549	+	9.19430i	−0.497899	+	0.361745i
$647$	3.33796	+	4.59430i	0.131229	+	0.180621i	0.869575	−	0.493801i	$-0.164393\pi$
$647$	3.33796	+	4.59430i	0.131229	+	0.180621i	−0.738346	+	0.674422i	$0.764393\pi$
$648$	15.9387	−	5.17881i	0.626133	−	0.203443i
$649$	0.0451021			0.00177041
$650$	−6.45901	−	10.7982i	−0.253343	−	0.423540i
$651$	3.15625			0.123703
$652$	8.60424	−	2.79569i	0.336968	−	0.109488i
$653$	−0.860358	−	1.18418i	−0.0336684	−	0.0463406i	0.791851	−	0.610714i	$-0.209118\pi$
$653$	−0.860358	−	1.18418i	−0.0336684	−	0.0463406i	−0.825519	+	0.564374i	$0.809118\pi$
$654$	8.28297	−	6.01793i	0.323890	−	0.235320i
$655$	−4.49214	−	9.88314i	−0.175522	−	0.386166i
$656$	17.8426	+	12.9634i	0.696636	+	0.506136i
$657$		−	24.6807i		−	0.962886i
$658$	−7.74464	+	10.6596i	−0.301918	+	0.415554i
$659$	−0.998646	+	3.07352i	−0.0389017	+	0.119727i	−0.968621	−	0.248541i	$-0.920049\pi$
$659$	−0.998646	+	3.07352i	−0.0389017	+	0.119727i	0.929720	+	0.368268i	$0.120049\pi$
$660$	−0.535961	+	0.945114i	−0.0208623	+	0.0367885i
$661$	−5.66903	−	17.4475i	−0.220500	−	0.678628i	−0.998717	−	0.0506336i	$-0.983876\pi$
$661$	−5.66903	−	17.4475i	−0.220500	−	0.678628i	0.778218	−	0.627995i	$-0.216124\pi$
$662$	18.4901	+	6.00780i	0.718638	+	0.233500i
$663$	−8.24343	−	2.67845i	−0.320148	−	0.104023i
$664$	2.50701	+	7.71580i	0.0972910	+	0.299431i
$665$	3.72549	−	1.69333i	0.144468	−	0.0656645i
$666$	−2.62321	+	8.07341i	−0.101647	+	0.312838i
$667$	17.0598	−	23.4807i	0.660557	−	0.909178i
$668$		−	5.68824i		−	0.220085i
$669$	−5.74687	−	4.17535i	−0.222187	−	0.161428i
$670$	9.62491	−	8.80201i	0.371843	−	0.340051i
$671$	−5.82272	+	4.23045i	−0.224784	+	0.163315i
$672$	0.871337	+	1.19929i	0.0336126	+	0.0462637i
$673$	−7.34626	+	2.38694i	−0.283178	+	0.0920100i	−0.447162	−	0.894453i	$-0.647565\pi$
$673$	−7.34626	+	2.38694i	−0.283178	+	0.0920100i	0.163985	+	0.986463i	$0.447565\pi$
$674$	−18.7292			−0.721421
$675$	13.4284	+	11.7201i	0.516858	+	0.451106i
$676$	3.76592			0.144843
$677$	21.9039	−	7.11702i	0.841837	−	0.273529i	0.143814	−	0.989605i	$-0.454063\pi$
$677$	21.9039	−	7.11702i	0.841837	−	0.273529i	0.698023	+	0.716075i	$0.254063\pi$
$678$	7.45628	+	10.2627i	0.286357	+	0.394136i
$679$	−9.82821	+	7.14061i	−0.377172	+	0.274032i
$680$	−9.26089	+	45.2881i	−0.355139	+	1.73672i
$681$	6.51904	+	4.73636i	0.249810	+	0.181498i
$682$			11.3438i			0.434376i
$683$	−20.8236	+	28.6613i	−0.796794	+	1.09669i	0.196435	+	0.980517i	$0.437064\pi$
$683$	−20.8236	+	28.6613i	−0.796794	+	1.09669i	−0.993229	+	0.116176i	$0.962936\pi$
$684$	0.614144	−	1.89014i	0.0234824	−	0.0722713i
$685$	−17.6374	−	19.2863i	−0.673889	−	0.736891i
$686$	−0.388594	−	1.19597i	−0.0148366	−	0.0456623i
$687$	5.66878	+	1.84190i	0.216277	+	0.0702728i
$688$	−20.7866	−	6.75399i	−0.792483	−	0.257493i
$689$	−3.30724	−	10.1786i	−0.125996	−	0.387775i
$690$	−5.25093	−	5.74184i	−0.199900	−	0.218588i
$691$	2.98865	−	9.19813i	0.113694	−	0.349913i	−0.877979	−	0.478700i	$-0.841108\pi$
$691$	2.98865	−	9.19813i	0.113694	−	0.349913i	0.991672	+	0.128786i	$0.0411082\pi$
$692$	−2.57141	+	3.53924i	−0.0977504	+	0.134542i
$693$		−	4.72431i		−	0.179462i
$694$	−14.5596	−	10.5782i	−0.552675	−	0.401542i
$695$	−4.38858	+	21.4613i	−0.166468	+	0.814072i
$696$	10.4808	−	7.61472i	0.397272	−	0.288635i
$697$	−29.4938	−	40.5947i	−1.11716	−	1.53763i
$698$	4.71888	−	1.53326i	0.178612	−	0.0580346i
$699$	5.60812			0.212119
$700$	0.821734	−	1.92523i	0.0310586	−	0.0727668i
$701$	−4.79790			−0.181214			−0.0906071	−	0.995887i	$-0.528881\pi$
$701$	−4.79790			−0.181214			−0.0906071	+	0.995887i	$0.528881\pi$
$702$	−8.53158	+	2.77208i	−0.322004	+	0.104625i
$703$	2.79949	+	3.85317i	0.105585	+	0.145325i
$704$	−13.1141	+	9.52794i	−0.494256	+	0.359098i
$705$	−11.0177	+	10.0757i	−0.414950	+	0.379473i
$706$	−9.21045	−	6.69179i	−0.346640	−	0.251849i
$707$		−	13.7082i		−	0.515549i
$708$	0.00388326	−	0.00534485i	0.000145942	−	0.000200872i
$709$	−13.1070	+	40.3393i	−0.492245	+	1.51497i	0.328962	+	0.944343i	$0.393301\pi$
$709$	−13.1070	+	40.3393i	−0.492245	+	1.51497i	−0.821207	+	0.570631i	$0.806699\pi$
$710$	−30.6073	+	13.9118i	−1.14867	+	0.522100i
$711$	−3.99406	−	12.2924i	−0.149789	−	0.461003i
$712$	−44.4750	−	14.4508i	−1.66677	−	0.541566i
$713$	20.4543	+	6.64599i	0.766018	+	0.248894i
$714$	1.68312	+	5.18010i	0.0629890	+	0.193860i
$715$	−4.02025	+	7.08931i	−0.150349	+	0.265125i
$716$	2.63510	−	8.11001i	0.0984783	−	0.303085i
$717$	−5.34227	+	7.35300i	−0.199511	+	0.274603i
$718$		−	46.1766i		−	1.72329i
$719$	−35.0454	−	25.4620i	−1.30697	−	0.949572i	−0.306976	−	0.951717i	$-0.599317\pi$
$719$	−35.0454	−	25.4620i	−1.30697	−	0.949572i	−0.999998	+	0.00214493i	$0.999317\pi$
$720$	7.16993	+	15.7745i	0.267208	+	0.587882i
$721$	4.55885	−	3.31220i	0.169780	−	0.123353i
$722$	−11.5682	−	15.9223i	−0.430524	−	0.592565i
$723$	2.92147	−	0.949244i	0.108651	−	0.0353027i
$724$	−4.60461			−0.171129
$725$	−30.7374	−	13.1194i	−1.14156	−	0.487244i
$726$	6.15667			0.228495
$727$	−0.236691	+	0.0769054i	−0.00877837	+	0.00285226i	−0.313403	−	0.949620i	$-0.601469\pi$
$727$	−0.236691	+	0.0769054i	−0.00877837	+	0.00285226i	0.304625	+	0.952473i	$0.401469\pi$
$728$	3.57758	+	4.92412i	0.132594	+	0.182500i
$729$	−6.04974	+	4.39539i	−0.224064	+	0.162792i
$730$	26.5858	−	3.00228i	0.983983	−	0.111120i
$731$	40.2297	+	29.2286i	1.48795	+	1.08106i
$732$			1.05426i			0.0389667i
$733$	17.6847	−	24.3409i	0.653200	−	0.899053i	−0.346033	−	0.938222i	$-0.612471\pi$
$733$	17.6847	−	24.3409i	0.653200	−	0.899053i	0.999233	+	0.0391699i	$0.0124713\pi$
$734$	−6.10407	+	18.7864i	−0.225305	+	0.693419i
$735$	−0.159899	−	1.41594i	−0.00589797	−	0.0522276i
$736$	3.12145	+	9.60683i	0.115058	+	0.354112i
$737$	−8.03455	−	2.61058i	−0.295956	−	0.0961620i
$738$	−22.9023	−	7.44140i	−0.843045	−	0.273922i
$739$	−3.10155	−	9.54560i	−0.114092	−	0.351140i	0.877664	−	0.479276i	$-0.159101\pi$
$739$	−3.10155	−	9.54560i	−0.114092	−	0.351140i	−0.991757	+	0.128136i	$0.959101\pi$
$740$	2.38685	+	0.488083i	0.0877424	+	0.0179423i
$741$	−0.721198	+	2.21962i	−0.0264939	+	0.0815398i
$742$	−3.95305	+	5.44090i	−0.145121	+	0.199742i
$743$		−	12.7497i		−	0.467740i	−0.972268	−	0.233870i	$-0.924861\pi$
$743$		−	12.7497i		−	0.467740i	0.972268	−	0.233870i	$-0.0751390\pi$
$744$	7.76634	+	5.64257i	0.284728	+	0.206867i
$745$	−41.6078	−	23.5952i	−1.52439	−	0.864462i
$746$	−9.57800	+	6.95883i	−0.350676	+	0.254781i
$747$	−4.06688	−	5.59758i	−0.148799	−	0.204805i
$748$	4.92891	−	1.60150i	0.180219	−	0.0585567i
$749$	−17.1093			−0.625162
$750$	−5.09667	+	7.36850i	−0.186104	+	0.269060i
$751$	31.5166			1.15006			0.575028	−	0.818133i	$-0.304991\pi$
$751$	31.5166			1.15006			0.575028	+	0.818133i	$0.304991\pi$
$752$	−29.7696	+	9.67272i	−1.08558	+	0.352728i
$753$	4.76846	+	6.56322i	0.173772	+	0.239177i
$754$	13.6080	−	9.88677i	0.495573	−	0.360055i
$755$	27.6318	+	15.6696i	1.00562	+	0.570275i
$756$	−1.20736	−	0.877200i	−0.0439113	−	0.0319034i
$757$			37.1340i			1.34966i	0.737974	+	0.674829i	$0.235783\pi$
$757$			37.1340i			1.34966i	−0.737974	+	0.674829i	$0.764217\pi$
$758$	23.1675	−	31.8874i	0.841483	−	1.15820i
$759$	−1.55737	+	4.79309i	−0.0565289	+	0.173978i
$760$	12.1943	+	2.49358i	0.442332	+	0.0904517i
$761$	10.7244	+	33.0064i	0.388760	+	1.19648i	0.933716	+	0.358015i	$0.116546\pi$
$761$	10.7244	+	33.0064i	0.388760	+	1.19648i	−0.544956	+	0.838464i	$0.683454\pi$
$762$	−3.83878	−	1.24730i	−0.139064	−	0.0451847i
$763$	12.1510	+	3.94809i	0.439895	+	0.142930i
$764$	1.57943	+	4.86099i	0.0571418	+	0.175864i
$765$	−4.42383	−	39.1738i	−0.159944	−	1.41633i
$766$	6.98742	−	21.5051i	0.252466	−	0.777010i
$767$	0.0291284	−	0.0400918i	0.00105176	−	0.00144763i
$768$			6.10275i			0.220214i
$769$	−30.8657	−	22.4252i	−1.11305	−	0.808675i	−0.129905	−	0.991526i	$-0.541467\pi$
$769$	−30.8657	−	22.4252i	−1.11305	−	0.808675i	−0.983141	+	0.182851i	$0.941467\pi$
$770$	5.08897	−	0.574689i	0.183394	−	0.0207103i
$771$	12.6474	−	9.18891i	0.455487	−	0.330931i
$772$	0.0268407	+	0.0369430i	0.000966017	+	0.00132961i
$773$	−23.5914	+	7.66532i	−0.848525	+	0.275703i	−0.700828	−	0.713330i	$-0.747186\pi$
$773$	−23.5914	+	7.66532i	−0.848525	+	0.275703i	−0.147697	+	0.989033i	$0.547186\pi$
$774$	23.8644			0.857787
$775$	2.20744	−	24.6660i	0.0792937	−	0.886030i
$776$	−36.9491			−1.32640
$777$	1.57724	−	0.512477i	0.0565832	−	0.0183850i
$778$	6.87527	+	9.46300i	0.246490	+	0.339265i
$779$	−10.9305	+	7.94147i	−0.391625	+	0.284533i
$780$	0.493982	+	1.08681i	0.0176874	+	0.0389139i
$781$	17.6176	+	12.7999i	0.630408	+	0.458018i
$782$			37.1140i			1.32719i
$783$	−14.0050	+	19.2762i	−0.500497	+	0.688875i
$784$	0.923165	−	2.84121i	0.0329702	−	0.101472i
$785$	12.7099	−	22.4127i	0.453637	−	0.799943i
$786$	−1.20226	−	3.70016i	−0.0428830	−	0.131980i
$787$	25.9207	+	8.42214i	0.923973	+	0.300217i	0.732095	−	0.681202i	$-0.238542\pi$
$787$	25.9207	+	8.42214i	0.923973	+	0.300217i	0.191877	+	0.981419i	$0.438542\pi$
$788$	−4.04240	−	1.31346i	−0.144005	−	0.0467900i
$789$	3.03920	+	9.35369i	0.108198	+	0.333000i
$790$	12.7554	−	5.79767i	0.453818	−	0.206272i
$791$	−4.89173	+	15.0552i	−0.173930	+	0.535301i
$792$	8.44586	−	11.6247i	0.300111	−	0.413067i
$793$			7.90804i			0.280823i
$794$	−1.47482	−	1.07152i	−0.0523394	−	0.0380268i
$795$	−5.62369	+	5.14288i	−0.199452	+	0.182399i
$796$	4.31285	−	3.13347i	0.152865	−	0.111063i
$797$	8.87402	+	12.2140i	0.314334	+	0.432644i	0.936727	−	0.350061i	$-0.113839\pi$
$797$	8.87402	+	12.2140i	0.314334	+	0.432644i	−0.622393	+	0.782705i	$0.713839\pi$
$798$	1.39479	−	0.453194i	0.0493750	−	0.0160429i
$799$	71.2159			2.51944
$800$	9.98185	−	5.97071i	0.352912	−	0.211096i
$801$	39.8820			1.40916
$802$	−8.28255	+	2.69116i	−0.292467	+	0.0950282i
$803$	−10.1860	−	14.0198i	−0.359456	−	0.494749i
$804$	−1.00114	+	0.727369i	−0.0353074	+	0.0256523i
$805$	1.94524	−	9.51274i	0.0685608	−	0.335280i
$806$	10.0836	+	7.32618i	0.355180	+	0.258054i
$807$			12.4953i			0.439854i
$808$	24.5068	−	33.7307i	0.862145	−	1.18664i
$809$	8.59316	−	26.4470i	0.302119	−	0.929828i	−0.678617	−	0.734492i	$-0.737420\pi$
$809$	8.59316	−	26.4470i	0.302119	−	0.929828i	0.980736	−	0.195336i	$-0.0625797\pi$
$810$	−10.4561	−	11.4337i	−0.367391	−	0.401738i
$811$	−7.32802	−	22.5533i	−0.257322	−	0.791954i	−0.993363	−	0.115018i	$-0.963307\pi$
$811$	−7.32802	−	22.5533i	−0.257322	−	0.791954i	0.736042	−	0.676936i	$-0.236693\pi$
$812$	2.66133	+	0.864718i	0.0933943	+	0.0303456i
$813$	11.5764	+	3.76140i	0.406002	+	0.131918i
$814$	1.84188	+	5.66872i	0.0645578	+	0.198688i
$815$	−32.6099	−	35.6585i	−1.14227	−	1.24906i
$816$	−3.99850	+	12.3061i	−0.139976	+	0.430800i
$817$	7.87006	−	10.8322i	0.275338	−	0.378971i
$818$		−	13.7469i		−	0.480649i
$819$	−4.19949	−	3.05111i	−0.146742	−	0.106614i
$820$	−1.38457	+	6.77091i	−0.0483513	+	0.236450i
$821$	−2.85235	+	2.07235i	−0.0995476	+	0.0723256i	−0.636446	−	0.771322i	$-0.719596\pi$
$821$	−2.85235	+	2.07235i	−0.0995476	+	0.0723256i	0.536898	+	0.843647i	$0.319596\pi$
$822$	−5.50528	−	7.57737i	−0.192019	−	0.264291i
$823$	−11.5646	+	3.75757i	−0.403117	+	0.130981i	−0.503556	−	0.863962i	$-0.667975\pi$
$823$	−11.5646	+	3.75757i	−0.403117	+	0.130981i	0.100439	+	0.994943i	$0.467975\pi$
$824$	17.1390			0.597064
$825$	5.78004	+	0.517275i	0.201235	+	0.0180092i
$826$	−0.0311406			−0.00108352
$827$	−42.8452	+	13.9212i	−1.48987	+	0.484089i	−0.937046	−	0.349207i	$-0.886451\pi$
$827$	−42.8452	+	13.9212i	−1.48987	+	0.484089i	−0.552827	+	0.833296i	$0.686451\pi$
$828$	−2.77169	−	3.81490i	−0.0963228	−	0.132577i
$829$	17.1004	−	12.4241i	0.593920	−	0.431508i	−0.249796	−	0.968299i	$-0.580363\pi$
$829$	17.1004	−	12.4241i	0.593920	−	0.431508i	0.843716	+	0.536790i	$0.180363\pi$
$830$	5.53493	−	5.06171i	0.192120	−	0.175695i
$831$	−1.32867	−	0.965339i	−0.0460912	−	0.0334872i
$832$			17.8107i			0.617475i
$833$	−3.99509	+	5.49877i	−0.138422	+	0.190521i
$834$	−2.42589	+	7.46614i	−0.0840019	+	0.258531i
$835$	−27.6585	+	12.5715i	−0.957162	+	0.435055i
$836$	−0.431219	−	1.32716i	−0.0149140	−	0.0459006i
$837$	−16.7917	−	5.45594i	−0.580404	−	0.188585i
$838$	−12.9877	−	4.21995i	−0.448652	−	0.145776i
$839$	8.62838	+	26.5554i	0.297885	+	0.916795i	0.982237	+	0.187643i	$0.0600849\pi$
$839$	8.62838	+	26.5554i	0.297885	+	0.916795i	−0.684353	+	0.729151i	$0.739915\pi$
$840$	2.13788	−	3.76994i	0.0737639	−	0.130075i
$841$	4.84421	−	14.9089i	0.167042	−	0.514101i
$842$	−14.3798	+	19.7922i	−0.495562	+	0.682083i
$843$			9.04645i			0.311576i
$844$	2.65643	+	1.93001i	0.0914382	+	0.0664337i
$845$	−8.32299	−	18.3114i	−0.286320	−	0.629931i
$846$	27.6500	−	20.0889i	0.950628	−	0.690671i
$847$	4.51586	+	6.21555i	0.155167	+	0.213569i
$848$	−15.1951	+	4.93718i	−0.521801	+	0.169543i
$849$	13.0384			0.447476
$850$	41.6595	−	9.53061i	1.42891	−	0.326897i
$851$	11.3005			0.387377
$852$	3.03373	−	0.985719i	0.103934	−	0.0337702i
$853$	16.1335	+	22.2058i	0.552400	+	0.760313i	0.990335	−	0.138693i	$-0.0442902\pi$
$853$	16.1335	+	22.2058i	0.552400	+	0.760313i	−0.437936	+	0.899006i	$0.644290\pi$
$854$	4.02028	−	2.92091i	0.137571	−	0.0999513i
$855$	−10.5479	+	1.19116i	−0.360731	+	0.0407368i
$856$	−42.0996	−	30.5871i	−1.43893	−	1.04545i
$857$			25.1788i			0.860093i	0.902807	+	0.430047i	$0.141503\pi$
$857$			25.1788i			0.860093i	−0.902807	+	0.430047i	$0.858497\pi$
$858$	−1.71676	+	2.36292i	−0.0586092	+	0.0806686i
$859$	−16.5860	+	51.0466i	−0.565908	+	1.74169i	0.0993296	+	0.995055i	$0.468330\pi$
$859$	−16.5860	+	51.0466i	−0.565908	+	1.74169i	−0.665238	+	0.746632i	$0.731670\pi$
$860$	−0.768548	−	6.80563i	−0.0262073	−	0.232070i
$861$	1.45377	+	4.47425i	0.0495444	+	0.152482i
$862$	−6.12420	−	1.98987i	−0.208591	−	0.0677753i
$863$	38.8610	+	12.6267i	1.32284	+	0.429818i	0.883471	−	0.468487i	$-0.155201\pi$
$863$	38.8610	+	12.6267i	1.32284	+	0.429818i	0.439373	+	0.898305i	$0.355201\pi$
$864$	−2.56251	−	7.88660i	−0.0871784	−	0.268307i
$865$	22.8922	+	4.68120i	0.778360	+	0.159165i
$866$	−5.41514	+	16.6661i	−0.184014	+	0.566336i
$867$	10.9363	−	15.0525i	0.371416	−	0.511210i
$868$			2.07355i			0.0703810i
$869$	−7.34205	−	5.33431i	−0.249062	−	0.180954i
$870$	−10.4184	−	5.90811i	−0.353215	−	0.200304i
$871$	−7.50954	+	5.45600i	−0.254451	+	0.184870i
$872$	22.8408	+	31.4376i	0.773485	+	1.06461i
$873$	29.9694	−	9.73765i	1.01431	−	0.329570i
$874$	9.99328			0.338028
$875$	−11.1773	+	0.259319i	−0.377863	+	0.00876659i
$876$	−2.53844			−0.0857658
$877$	31.7629	−	10.3204i	1.07256	−	0.348494i	0.281073	−	0.959686i	$-0.409310\pi$
$877$	31.7629	−	10.3204i	1.07256	−	0.348494i	0.791482	+	0.611192i	$0.209310\pi$
$878$	−20.2388	−	27.8563i	−0.683027	−	0.940106i
$879$	−4.15670	+	3.02002i	−0.140202	+	0.101863i
$880$	10.5832	+	6.00159i	0.356760	+	0.202314i
$881$	13.3680	+	9.71242i	0.450379	+	0.327220i	0.789746	−	0.613435i	$-0.210213\pi$
$881$	13.3680	+	9.71242i	0.450379	+	0.327220i	−0.339366	+	0.940654i	$0.610213\pi$
$882$			3.26189i			0.109833i
$883$	−1.24425	+	1.71256i	−0.0418722	+	0.0576321i	−0.829440	−	0.558596i	$-0.811340\pi$
$883$	−1.24425	+	1.71256i	−0.0418722	+	0.0576321i	0.787568	+	0.616228i	$0.211340\pi$
$884$	1.75966	−	5.41567i	0.0591837	−	0.182149i
$885$	−0.0345711	−	0.00706939i	−0.00116210	−	0.000237635i
$886$	15.2848	+	47.0418i	0.513503	+	1.58040i
$887$	−2.17649	−	0.707185i	−0.0730794	−	0.0237449i	0.272249	−	0.962227i	$-0.412233\pi$
$887$	−2.17649	−	0.707185i	−0.0730794	−	0.0237449i	−0.345329	+	0.938482i	$0.612233\pi$
$888$	4.79717	+	1.55870i	0.160983	+	0.0523064i
$889$	−1.55649	−	4.79037i	−0.0522029	−	0.160664i
$890$	4.85145	+	42.9605i	0.162621	+	1.44004i
$891$	−3.10117	+	9.54443i	−0.103893	+	0.319750i
$892$	2.74307	−	3.77551i	0.0918447	−	0.126413i
$893$		−	19.1755i		−	0.641685i
$894$	−13.8682	−	10.0758i	−0.463821	−	0.336986i
$895$	−45.2579	+	5.11089i	−1.51280	+	0.170838i
$896$	5.29063	−	3.84387i	0.176747	−	0.128415i
$897$	3.25483	+	4.47990i	0.108676	+	0.149579i
$898$	33.8411	−	10.9956i	1.12929	−	0.366929i
$899$	33.1054			1.10413
$900$	−3.57037	+	4.09078i	−0.119012	+	0.136359i
$901$	36.3502			1.21100
$902$	−16.0808	+	5.22496i	−0.535431	+	0.173972i
$903$	−2.74037	−	3.77180i	−0.0911939	−	0.125518i
$904$	−38.9515	+	28.2999i	−1.29551	+	0.941242i
$905$	10.1766	+	22.3895i	0.338281	+	0.744251i
$906$	9.20986	+	6.69136i	0.305977	+	0.222305i
$907$			53.0301i			1.76084i	0.474199	+	0.880418i	$0.342738\pi$
$907$			53.0301i			1.76084i	−0.474199	+	0.880418i	$0.657262\pi$
$908$	−3.11163	+	4.28280i	−0.103263	+	0.142130i
$909$	−10.9880	+	33.8175i	−0.364448	+	1.12166i
$910$	2.77577	−	4.89480i	0.0920160	−	0.162261i
$911$	−0.264200	−	0.813124i	−0.00875334	−	0.0269400i	0.946584	−	0.322456i	$-0.104508\pi$
$911$	−0.264200	−	0.813124i	−0.00875334	−	0.0269400i	−0.955338	+	0.295516i	$0.904508\pi$
$912$	3.31354	+	1.07663i	0.109722	+	0.0356509i
$913$	−4.62037	−	1.50125i	−0.152912	−	0.0496841i
$914$	−2.82871	−	8.70589i	−0.0935655	−	0.287965i
$915$	5.12625	−	2.33001i	0.169469	−	0.0770278i
$916$	−1.21007	+	3.72420i	−0.0399817	+	0.123051i
$917$	2.85371	−	3.92779i	0.0942377	−	0.129707i
$918$		−	30.4682i		−	1.00560i
$919$	39.2405	+	28.5099i	1.29443	+	0.940455i	0.999885	−	0.0151841i	$-0.00483343\pi$
$919$	39.2405	+	28.5099i	1.29443	+	0.940455i	0.294540	+	0.955639i	$0.404833\pi$
$920$	21.7929	−	19.9297i	0.718490	−	0.657061i
$921$	−4.68562	+	3.40431i	−0.154397	+	0.112176i
$922$	4.38426	+	6.03442i	0.144388	+	0.198733i
$923$	22.7560	−	7.39388i	0.749024	−	0.243373i
$924$	−0.485900			−0.0159849
$925$	−2.90189	−	12.6845i	−0.0954136	−	0.417065i
$926$	−17.6019			−0.578436
$927$	−13.9014	+	4.51685i	−0.456583	+	0.148353i
$928$	9.13933	+	12.5792i	0.300013	+	0.412933i
$929$	43.2383	−	31.4145i	1.41860	−	1.03068i	0.426603	−	0.904439i	$-0.359710\pi$
$929$	43.2383	−	31.4145i	1.41860	−	1.03068i	0.992000	−	0.126237i	$-0.0402900\pi$
$930$	1.77805	−	8.69510i	0.0583044	−	0.285124i
$931$	1.48059	+	1.07571i	0.0485245	+	0.0352551i
$932$			3.68435i			0.120685i
$933$	9.95384	−	13.7003i	0.325874	−	0.448527i
$934$	−1.80543	+	5.55653i	−0.0590754	+	0.181815i
$935$	−18.6804	−	20.4269i	−0.610916	−	0.668030i
$936$	−4.87875	−	15.0152i	−0.159467	−	0.490789i
$937$	−8.84897	−	2.87521i	−0.289083	−	0.0939289i	0.160886	−	0.986973i	$-0.448565\pi$
$937$	−8.84897	−	2.87521i	−0.289083	−	0.0939289i	−0.449969	+	0.893044i	$0.648565\pi$
$938$	5.54743	+	1.80247i	0.181130	+	0.0588527i
$939$	1.68901	+	5.19823i	0.0551186	+	0.169638i
$940$	−6.61942	−	7.23826i	−0.215902	−	0.236086i
$941$	−3.37120	+	10.3755i	−0.109898	+	0.338232i	−0.990849	−	0.134977i	$-0.956904\pi$
$941$	−3.37120	+	10.3755i	−0.109898	+	0.338232i	0.880951	+	0.473208i	$0.156904\pi$
$942$	5.42749	−	7.47031i	0.176837	−	0.243396i
$943$			32.0568i			1.04391i
$944$	−0.0598505	−	0.0434840i	−0.00194797	−	0.00141528i
$945$	−1.59692	+	7.80936i	−0.0519479	+	0.254038i
$946$	13.5561	−	9.84909i	0.440747	−	0.320222i
$947$	−19.9601	−	27.4727i	−0.648616	−	0.892743i	0.350422	−	0.936592i	$-0.386038\pi$
$947$	−19.9601	−	27.4727i	−0.648616	−	0.892743i	−0.999038	+	0.0438488i	$0.986038\pi$
$948$	−1.26429	+	0.410793i	−0.0410623	+	0.0133419i
$949$	−19.0408			−0.618092
$950$	−2.56620	−	11.2172i	−0.0832587	−	0.363934i
$951$	−3.78180			−0.122633
$952$	−19.6608	+	6.38818i	−0.637210	+	0.207042i
$953$	−0.671478	−	0.924210i	−0.0217513	−	0.0299381i	0.798003	−	0.602654i	$-0.205890\pi$
$953$	−0.671478	−	0.924210i	−0.0217513	−	0.0299381i	−0.819754	+	0.572716i	$0.805890\pi$
$954$	14.1132	−	10.2539i	0.456932	−	0.331981i
$955$	20.1454	−	18.4230i	0.651889	−	0.596155i
$956$	−4.83068	−	3.50970i	−0.156235	−	0.113512i
$957$			7.75767i			0.250770i
$958$	10.1932	−	14.0298i	0.329329	−	0.453282i
$959$	3.61177	−	11.1159i	0.116630	−	0.358950i
$960$	11.5455	−	5.24772i	0.372629	−	0.169369i
$961$	−1.99890	−	6.15199i	−0.0644808	−	0.198451i
$962$	6.22853	+	2.02377i	0.200816	+	0.0652490i
$963$	42.2080	+	13.7142i	1.36013	+	0.441934i
$964$	0.623622	+	1.91931i	0.0200855	+	0.0618168i
$965$	0.120311	−	0.212157i	0.00387296	−	0.00682958i
$966$	1.07528	−	3.30938i	0.0345966	−	0.106477i
$967$	15.1515	−	20.8543i	0.487241	−	0.670629i	−0.492635	−	0.870236i	$-0.663966\pi$
$967$	15.1515	−	20.8543i	0.487241	−	0.670629i	0.979876	+	0.199606i	$0.0639664\pi$
$968$			23.3673i			0.751054i
$969$	−6.41289	−	4.65924i	−0.206012	−	0.149676i
$970$	14.1349	+	31.0982i	0.453845	+	0.998502i
$971$	−29.5946	+	21.5017i	−0.949735	+	0.690023i	−0.950744	−	0.309977i	$-0.899679\pi$
$971$	−29.5946	+	21.5017i	−0.949735	+	0.690023i	0.00100922	+	0.999999i	$0.499679\pi$
$972$	3.49566	+	4.81136i	0.112123	+	0.154324i
$973$	−9.31691	+	3.02725i	−0.298687	+	0.0970491i
$974$	34.8603			1.11699
$975$	4.19275	−	4.80387i	0.134275	−	0.153847i
$976$	11.8054			0.377883
$977$	−53.8492	+	17.4967i	−1.72279	+	0.559768i	−0.992377	−	0.123240i	$-0.960672\pi$
$977$	−53.8492	+	17.4967i	−1.72279	+	0.559768i	−0.730411	+	0.683007i	$0.760672\pi$
$978$	−10.1788	−	14.0099i	−0.325481	−	0.447986i
$979$	22.6549	−	16.4598i	0.724055	−	0.526057i
$980$	0.930223	−	0.105049i	0.0297149	−	0.00335565i
$981$	−26.8113	−	19.4795i	−0.856018	−	0.621933i
$982$		−	37.6680i		−	1.20204i
$983$	9.03318	−	12.4331i	0.288114	−	0.396555i	−0.640287	−	0.768136i	$-0.721184\pi$
$983$	9.03318	−	12.4331i	0.288114	−	0.396555i	0.928400	+	0.371582i	$0.121184\pi$
$984$	−4.42164	+	13.6084i	−0.140957	+	0.433820i
$985$	2.54751	+	22.5586i	0.0811703	+	0.718778i
$986$	17.6539	+	54.3333i	0.562216	+	1.73032i
$987$	−6.35017	−	2.06330i	−0.202128	−	0.0656755i
$988$	−1.45822	−	0.473804i	−0.0463921	−	0.0150737i
$989$	−9.81702	−	30.2137i	−0.312163	−	0.960739i
$990$	−13.0149	−	2.66140i	−0.413641	−	0.0845848i
$991$	10.3262	−	31.7808i	0.328023	−	1.00955i	−0.642035	−	0.766676i	$-0.721909\pi$
$991$	10.3262	−	31.7808i	0.328023	−	1.00955i	0.970058	−	0.242875i	$-0.0780906\pi$
$992$	−6.77232	+	9.32130i	−0.215021	+	0.295951i
$993$			9.85212i			0.312647i
$994$	−12.1640	−	8.83769i	−0.385820	−	0.280315i
$995$	−24.7680	−	14.0456i	−0.785197	−	0.445275i
$996$	−0.575717	+	0.418283i	−0.0182423	+	0.0132538i
$997$	−3.84182	−	5.28781i	−0.121672	−	0.167466i	0.743836	−	0.668362i	$-0.233004\pi$
$997$	−3.84182	−	5.28781i	−0.121672	−	0.167466i	−0.865508	+	0.500895i	$0.833004\pi$
$998$	−15.6073	+	5.07113i	−0.494041	+	0.160524i
$999$	−9.27700			−0.293511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.n.a.169.11	yes	56
5.2	odd	4		875.2.h.d.526.10		56
5.3	odd	4		875.2.h.e.526.5		56
5.4	even	2		875.2.n.c.99.4		56
25.2	odd	20		4375.2.a.p.1.20		28
25.3	odd	20		875.2.h.e.351.5		56
25.4	even	10	inner	175.2.n.a.29.11	✓	56
25.21	even	5		875.2.n.c.274.4		56
25.22	odd	20		875.2.h.d.351.10		56
25.23	odd	20		4375.2.a.o.1.9		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.29.11	✓	56	25.4	even	10	inner
175.2.n.a.169.11	yes	56	1.1	even	1	trivial
875.2.h.d.351.10		56	25.22	odd	20
875.2.h.d.526.10		56	5.2	odd	4
875.2.h.e.351.5		56	25.3	odd	20
875.2.h.e.526.5		56	5.3	odd	4
875.2.n.c.99.4		56	5.4	even	2
875.2.n.c.274.4		56	25.21	even	5
4375.2.a.o.1.9		28	25.23	odd	20
4375.2.a.p.1.20		28	25.2	odd	20

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19597 - 0.388594i) q^{2} +(0.374566 + 0.515546i) q^{3} +(-0.338697 + 0.246078i) q^{4} +(1.94508 + 1.10303i) q^{5} +(0.648308 + 0.471023i) q^{6} +1.00000i q^{7} +(-1.78775 + 2.46062i) q^{8} +(0.801563 - 2.46696i) q^{9} +O(q^{10})\)	\(q+(1.19597 - 0.388594i) q^{2} +(0.374566 + 0.515546i) q^{3} +(-0.338697 + 0.246078i) q^{4} +(1.94508 + 1.10303i) q^{5} +(0.648308 + 0.471023i) q^{6} +1.00000i q^{7} +(-1.78775 + 2.46062i) q^{8} +(0.801563 - 2.46696i) q^{9} +(2.75488 + 0.563341i) q^{10} +(-0.562815 - 1.73217i) q^{11} +(-0.253729 - 0.0824416i) q^{12} +(-1.90323 - 0.618395i) q^{13} +(0.388594 + 1.19597i) q^{14} +(0.159899 + 1.41594i) q^{15} +(-0.923165 + 2.84121i) q^{16} +(3.99509 - 5.49877i) q^{17} -3.26189i q^{18} +(-1.48059 - 1.07571i) q^{19} +(-0.930223 + 0.105049i) q^{20} +(-0.515546 + 0.374566i) q^{21} +(-1.34622 - 1.85291i) q^{22} +(-4.12974 + 1.34183i) q^{23} -1.93819 q^{24} +(2.56666 + 4.29095i) q^{25} -2.51650 q^{26} +(3.39025 - 1.10156i) q^{27} +(-0.246078 - 0.338697i) q^{28} +(-5.40749 + 3.92877i) q^{29} +(0.741458 + 1.63128i) q^{30} +(-4.00700 - 2.91125i) q^{31} -2.32626i q^{32} +(0.682200 - 0.938968i) q^{33} +(2.64121 - 8.12882i) q^{34} +(-1.10303 + 1.94508i) q^{35} +(0.335576 + 1.03280i) q^{36} +(-2.47507 - 0.804200i) q^{37} +(-2.18876 - 0.711172i) q^{38} +(-0.394073 - 1.21283i) q^{39} +(-6.19144 + 2.81417i) q^{40} +(2.28132 - 7.02118i) q^{41} +(-0.471023 + 0.648308i) q^{42} +7.31612i q^{43} +(0.616871 + 0.448183i) q^{44} +(4.28022 - 3.91428i) q^{45} +(-4.41761 + 3.20958i) q^{46} +(6.15868 + 8.47670i) q^{47} +(-1.81056 + 0.588287i) q^{48} -1.00000 q^{49} +(4.73708 + 4.13446i) q^{50} +4.33130 q^{51} +(0.796790 - 0.258893i) q^{52} +(3.14354 + 4.32670i) q^{53} +(3.62658 - 2.63486i) q^{54} +(0.815908 - 3.99000i) q^{55} +(-2.46062 - 1.78775i) q^{56} -1.16624i q^{57} +(-4.94049 + 6.80001i) q^{58} +(-0.00765237 + 0.0235516i) q^{59} +(-0.402588 - 0.440226i) q^{60} +(-1.22115 - 3.75830i) q^{61} +(-5.92354 - 1.92467i) q^{62} +(2.46696 + 0.801563i) q^{63} +(-2.75030 - 8.46455i) q^{64} +(-3.01982 - 3.30214i) q^{65} +(0.451013 - 1.38808i) q^{66} +(2.72641 - 3.75258i) q^{67} +2.84552i q^{68} +(-2.23864 - 1.62647i) q^{69} +(-0.563341 + 2.75488i) q^{70} +(-9.67307 + 7.02789i) q^{71} +(4.63726 + 6.38263i) q^{72} +(9.04917 - 2.94025i) q^{73} -3.27262 q^{74} +(-1.25080 + 2.93048i) q^{75} +0.766183 q^{76} +(1.73217 - 0.562815i) q^{77} +(-0.942598 - 1.29737i) q^{78} +(4.03120 - 2.92884i) q^{79} +(-4.92956 + 4.50810i) q^{80} +(-4.45778 - 3.23876i) q^{81} -9.28362i q^{82} +(1.56786 - 2.15797i) q^{83} +(0.0824416 - 0.253729i) q^{84} +(13.8361 - 6.28884i) q^{85} +(2.84300 + 8.74985i) q^{86} +(-4.05093 - 1.31623i) q^{87} +(5.26837 + 1.71180i) q^{88} +(4.75121 + 14.6227i) q^{89} +(3.59795 - 6.34462i) q^{90} +(0.618395 - 1.90323i) q^{91} +(1.06854 - 1.47071i) q^{92} -3.15625i q^{93} +(10.6596 + 7.74464i) q^{94} +(-1.69333 - 3.72549i) q^{95} +(1.19929 - 0.871337i) q^{96} +(7.14061 + 9.82821i) q^{97} +(-1.19597 + 0.388594i) q^{98} -4.72431 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9}+O(q^{10}) \) 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9	\( 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9} - 4 q^{10} + 8 q^{11} - 40 q^{12} - 4 q^{14} - 18 q^{15} - 32 q^{16} + 12 q^{19} + 12 q^{20} + 4 q^{21} - 30 q^{22} + 10 q^{23} - 28 q^{24} + 4 q^{25} + 12 q^{26} + 30 q^{27} - 2 q^{29} + 28 q^{30} + 12 q^{31} + 20 q^{33} + 2 q^{35} - 14 q^{36} - 70 q^{37} - 70 q^{38} - 4 q^{39} - 30 q^{40} + 4 q^{41} + 50 q^{42} + 22 q^{44} - 52 q^{45} - 4 q^{46} - 10 q^{47} + 30 q^{48} - 56 q^{49} - 54 q^{50} - 44 q^{51} - 20 q^{53} + 54 q^{54} - 2 q^{55} + 12 q^{56} + 10 q^{58} - 6 q^{59} + 16 q^{60} - 4 q^{61} + 50 q^{62} + 20 q^{63} + 24 q^{64} - 18 q^{65} - 74 q^{66} + 10 q^{67} - 78 q^{69} + 8 q^{70} - 8 q^{71} + 140 q^{72} + 40 q^{73} + 60 q^{74} - 8 q^{75} + 52 q^{76} - 20 q^{77} - 90 q^{78} + 124 q^{80} - 72 q^{81} - 30 q^{83} - 12 q^{84} + 96 q^{85} - 20 q^{86} + 30 q^{87} + 140 q^{88} + 38 q^{89} - 8 q^{90} + 8 q^{91} + 80 q^{92} + 88 q^{94} - 70 q^{95} - 28 q^{96} - 30 q^{97} + 60 q^{99}+O(q^{100}) \) 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9 - 4 * q^10 + 8 * q^11 - 40 * q^12 - 4 * q^14 - 18 * q^15 - 32 * q^16 + 12 * q^19 + 12 * q^20 + 4 * q^21 - 30 * q^22 + 10 * q^23 - 28 * q^24 + 4 * q^25 + 12 * q^26 + 30 * q^27 - 2 * q^29 + 28 * q^30 + 12 * q^31 + 20 * q^33 + 2 * q^35 - 14 * q^36 - 70 * q^37 - 70 * q^38 - 4 * q^39 - 30 * q^40 + 4 * q^41 + 50 * q^42 + 22 * q^44 - 52 * q^45 - 4 * q^46 - 10 * q^47 + 30 * q^48 - 56 * q^49 - 54 * q^50 - 44 * q^51 - 20 * q^53 + 54 * q^54 - 2 * q^55 + 12 * q^56 + 10 * q^58 - 6 * q^59 + 16 * q^60 - 4 * q^61 + 50 * q^62 + 20 * q^63 + 24 * q^64 - 18 * q^65 - 74 * q^66 + 10 * q^67 - 78 * q^69 + 8 * q^70 - 8 * q^71 + 140 * q^72 + 40 * q^73 + 60 * q^74 - 8 * q^75 + 52 * q^76 - 20 * q^77 - 90 * q^78 + 124 * q^80 - 72 * q^81 - 30 * q^83 - 12 * q^84 + 96 * q^85 - 20 * q^86 + 30 * q^87 + 140 * q^88 + 38 * q^89 - 8 * q^90 + 8 * q^91 + 80 * q^92 + 88 * q^94 - 70 * q^95 - 28 * q^96 - 30 * q^97 + 60 * q^99

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