LMFDB - Embedded newform 875.2.n.c.99.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(99,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([9, 0]))

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

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

chi := DirichletCharacter("875.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.n (of order $10$, degree $4$, not 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:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			99.4
Character	$\chi$	$=$	875.99
Dual form			875.2.n.c.274.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19597 + 0.388594i) q^{2} +(-0.374566 - 0.515546i) q^{3} +(-0.338697 + 0.246078i) q^{4} +(0.648308 + 0.471023i) q^{6} -1.00000i q^{7} +(1.78775 - 2.46062i) q^{8} +(0.801563 - 2.46696i) q^{9} +O(q^{10})$	\(q+(-1.19597 + 0.388594i) q^{2} +(-0.374566 - 0.515546i) q^{3} +(-0.338697 + 0.246078i) q^{4} +(0.648308 + 0.471023i) q^{6} -1.00000i q^{7} +(1.78775 - 2.46062i) q^{8} +(0.801563 - 2.46696i) q^{9} +(-0.562815 - 1.73217i) q^{11} +(0.253729 + 0.0824416i) q^{12} +(1.90323 + 0.618395i) q^{13} +(0.388594 + 1.19597i) q^{14} +(-0.923165 + 2.84121i) q^{16} +(-3.99509 + 5.49877i) q^{17} +3.26189i q^{18} +(-1.48059 - 1.07571i) q^{19} +(-0.515546 + 0.374566i) q^{21} +(1.34622 + 1.85291i) q^{22} +(4.12974 - 1.34183i) q^{23} -1.93819 q^{24} -2.51650 q^{26} +(-3.39025 + 1.10156i) q^{27} +(0.246078 + 0.338697i) q^{28} +(-5.40749 + 3.92877i) q^{29} +(-4.00700 - 2.91125i) q^{31} +2.32626i q^{32} +(-0.682200 + 0.938968i) q^{33} +(2.64121 - 8.12882i) q^{34} +(0.335576 + 1.03280i) q^{36} +(2.47507 + 0.804200i) q^{37} +(2.18876 + 0.711172i) q^{38} +(-0.394073 - 1.21283i) q^{39} +(2.28132 - 7.02118i) q^{41} +(0.471023 - 0.648308i) q^{42} -7.31612i q^{43} +(0.616871 + 0.448183i) q^{44} +(-4.41761 + 3.20958i) q^{46} +(-6.15868 - 8.47670i) q^{47} +(1.81056 - 0.588287i) q^{48} -1.00000 q^{49} +4.33130 q^{51} +(-0.796790 + 0.258893i) q^{52} +(-3.14354 - 4.32670i) q^{53} +(3.62658 - 2.63486i) q^{54} +(-2.46062 - 1.78775i) q^{56} +1.16624i q^{57} +(4.94049 - 6.80001i) q^{58} +(-0.00765237 + 0.0235516i) q^{59} +(-1.22115 - 3.75830i) q^{61} +(5.92354 + 1.92467i) q^{62} +(-2.46696 - 0.801563i) q^{63} +(-2.75030 - 8.46455i) q^{64} +(0.451013 - 1.38808i) q^{66} +(-2.72641 + 3.75258i) q^{67} -2.84552i q^{68} +(-2.23864 - 1.62647i) q^{69} +(-9.67307 + 7.02789i) q^{71} +(-4.63726 - 6.38263i) q^{72} +(-9.04917 + 2.94025i) q^{73} -3.27262 q^{74} +0.766183 q^{76} +(-1.73217 + 0.562815i) q^{77} +(0.942598 + 1.29737i) q^{78} +(4.03120 - 2.92884i) q^{79} +(-4.45778 - 3.23876i) q^{81} +9.28362i q^{82} +(-1.56786 + 2.15797i) q^{83} +(0.0824416 - 0.253729i) q^{84} +(2.84300 + 8.74985i) q^{86} +(4.05093 + 1.31623i) q^{87} +(-5.26837 - 1.71180i) q^{88} +(4.75121 + 14.6227i) q^{89} +(0.618395 - 1.90323i) q^{91} +(-1.06854 + 1.47071i) q^{92} +3.15625i q^{93} +(10.6596 + 7.74464i) q^{94} +(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^{9}+O(q^{10}) $ 56 * q + 12 * q^4 + 6 * q^9	$ 56 q + 12 q^{4} + 6 q^{9} + 8 q^{11} + 40 q^{12} - 4 q^{14} - 32 q^{16} + 12 q^{19} + 4 q^{21} + 30 q^{22} - 10 q^{23} - 28 q^{24} + 12 q^{26} - 30 q^{27} - 2 q^{29} + 12 q^{31} - 20 q^{33} - 14 q^{36} + 70 q^{37} + 70 q^{38} - 4 q^{39} + 4 q^{41} - 50 q^{42} + 22 q^{44} - 4 q^{46} + 10 q^{47} - 30 q^{48} - 56 q^{49} - 44 q^{51} + 20 q^{53} + 54 q^{54} + 12 q^{56} - 10 q^{58} - 6 q^{59} - 4 q^{61} - 50 q^{62} - 20 q^{63} + 24 q^{64} - 74 q^{66} - 10 q^{67} - 78 q^{69} - 8 q^{71} - 140 q^{72} - 40 q^{73} + 60 q^{74} + 52 q^{76} + 20 q^{77} + 90 q^{78} - 72 q^{81} + 30 q^{83} - 12 q^{84} - 20 q^{86} - 30 q^{87} - 140 q^{88} + 38 q^{89} + 8 q^{91} - 80 q^{92} + 88 q^{94} - 28 q^{96} + 30 q^{97} + 60 q^{99}+O(q^{100}) $ 56 * q + 12 * q^4 + 6 * q^9 + 8 * q^11 + 40 * q^12 - 4 * q^14 - 32 * q^16 + 12 * q^19 + 4 * q^21 + 30 * q^22 - 10 * q^23 - 28 * q^24 + 12 * q^26 - 30 * q^27 - 2 * q^29 + 12 * q^31 - 20 * q^33 - 14 * q^36 + 70 * q^37 + 70 * q^38 - 4 * q^39 + 4 * q^41 - 50 * q^42 + 22 * q^44 - 4 * q^46 + 10 * q^47 - 30 * q^48 - 56 * q^49 - 44 * q^51 + 20 * q^53 + 54 * q^54 + 12 * q^56 - 10 * q^58 - 6 * q^59 - 4 * q^61 - 50 * q^62 - 20 * q^63 + 24 * q^64 - 74 * q^66 - 10 * q^67 - 78 * q^69 - 8 * q^71 - 140 * q^72 - 40 * q^73 + 60 * q^74 + 52 * q^76 + 20 * q^77 + 90 * q^78 - 72 * q^81 + 30 * q^83 - 12 * q^84 - 20 * q^86 - 30 * q^87 - 140 * q^88 + 38 * q^89 + 8 * q^91 - 80 * q^92 + 88 * q^94 - 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 $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.19597	+	0.388594i	−0.845678	+	0.274777i	−0.699635	−	0.714501i	$-0.746654\pi$
$2$	−1.19597	+	0.388594i	−0.845678	+	0.274777i	−0.146043	+	0.989278i	$0.546654\pi$
$3$	−0.374566	−	0.515546i	−0.216256	−	0.297651i	0.687082	−	0.726580i	$-0.258891\pi$
$3$	−0.374566	−	0.515546i	−0.216256	−	0.297651i	−0.903338	+	0.428929i	$0.858891\pi$
$4$	−0.338697	+	0.246078i	−0.169349	+	0.123039i
$5$		0			0
$5$		0			0
$6$	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
$10$		0			0
$11$	−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	0.560809	−	0.827945i	$-0.310490\pi$
$13$	1.90323	+	0.618395i	0.527860	+	0.171512i	−0.0329496	+	0.999457i	$0.510490\pi$
$14$	0.388594	+	1.19597i	0.103856	+	0.319636i
$15$		0			0
$16$	−0.923165	+	2.84121i	−0.230791	+	0.710302i
$17$	−3.99509	+	5.49877i	−0.968951	+	1.33365i	−0.0263765	+	0.999652i	$0.508397\pi$
$17$	−3.99509	+	5.49877i	−0.968951	+	1.33365i	−0.942575	+	0.333995i	$0.891603\pi$
$18$			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			0
$21$	−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	0.155018	−	0.987912i	$-0.450456\pi$
$23$	4.12974	−	1.34183i	0.861110	−	0.279792i	0.706092	+	0.708120i	$0.250456\pi$
$24$	−1.93819			−0.395632
$25$		0			0
$26$	−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			0
$31$	−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
$35$		0			0
$36$	0.335576	+	1.03280i	0.0559294	+	0.172133i
$37$	2.47507	+	0.804200i	0.406900	+	0.132210i	0.505313	−	0.862936i	$-0.331377\pi$
$37$	2.47507	+	0.804200i	0.406900	+	0.132210i	−0.0984138	+	0.995146i	$0.531377\pi$
$38$	2.18876	+	0.711172i	0.355064	+	0.115367i
$39$	−0.394073	−	1.21283i	−0.0631021	−	0.194208i
$40$		0			0
$41$	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	$-0.811627\pi$
$43$		−	7.31612i		−	1.11570i	0.829942	−	0.557849i	$-0.188373\pi$
$44$	0.616871	+	0.448183i	0.0929969	+	0.0675662i
$45$		0			0
$46$	−4.41761	+	3.20958i	−0.651341	+	0.473227i
$47$	−6.15868	−	8.47670i	−0.898336	−	1.23645i	−0.970996	−	0.239097i	$-0.923149\pi$
$47$	−6.15868	−	8.47670i	−0.898336	−	1.23645i	0.0726594	−	0.997357i	$-0.476851\pi$
$48$	1.81056	−	0.588287i	0.261332	−	0.0849120i
$49$	−1.00000			−0.142857
$50$		0			0
$51$	4.33130			0.606503
$52$	−0.796790	+	0.258893i	−0.110495	+	0.0359020i
$53$	−3.14354	−	4.32670i	−0.431798	−	0.594319i	0.536567	−	0.843858i	$-0.319721\pi$
$53$	−3.14354	−	4.32670i	−0.431798	−	0.594319i	−0.968365	+	0.249539i	$0.919721\pi$
$54$	3.62658	−	2.63486i	0.493515	−	0.358559i
$55$		0			0
$56$	−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			0
$61$	−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
$65$		0			0
$66$	0.451013	−	1.38808i	0.0555159	−	0.170860i
$67$	−2.72641	+	3.75258i	−0.333084	+	0.458450i	−0.942405	−	0.334473i	$-0.891442\pi$
$67$	−2.72641	+	3.75258i	−0.333084	+	0.458450i	0.609322	+	0.792923i	$0.291442\pi$
$68$		−	2.84552i		−	0.345070i
$69$	−2.23864	−	1.62647i	−0.269500	−	0.195804i
$70$		0			0
$71$	−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	−0.786243	−	0.617917i	$-0.787977\pi$
$73$	−9.04917	+	2.94025i	−1.05912	+	0.344130i	−0.272882	+	0.962048i	$0.587977\pi$
$74$	−3.27262			−0.380434
$75$		0			0
$76$	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	$0.209564\pi$
$80$		0			0
$81$	−4.45778	−	3.23876i	−0.495308	−	0.359863i
$82$			9.28362i			1.02520i
$83$	−1.56786	+	2.15797i	−0.172095	+	0.236868i	−0.886348	−	0.463019i	$-0.846766\pi$
$83$	−1.56786	+	2.15797i	−0.172095	+	0.236868i	0.714254	+	0.699887i	$0.246766\pi$
$84$	0.0824416	−	0.253729i	0.00899512	−	0.0276841i
$85$		0			0
$86$	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	$0.596799\pi$
$90$		0			0
$91$	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
$95$		0			0
$96$	1.19929	−	0.871337i	0.122402	−	0.0889305i
$97$	−7.14061	−	9.82821i	−0.725019	−	0.997904i	−0.999342	−	0.0362659i	$-0.988454\pi$
$97$	−7.14061	−	9.82821i	−0.725019	−	0.997904i	0.274323	−	0.961638i	$-0.411546\pi$
$98$	1.19597	−	0.388594i	0.120811	−	0.0392539i
$99$	−4.72431			−0.474811
$100$		0			0
$101$	−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	0.940396	−	0.340082i	$-0.110455\pi$
$103$	3.31220	+	4.55885i	0.326361	+	0.449197i	−0.614035	+	0.789279i	$0.710455\pi$
$104$	4.92412	−	3.57758i	0.482850	−	0.350811i
$105$		0			0
$106$	5.44090	+	3.95305i	0.528467	+	0.383954i
$107$		−	17.1093i		−	1.65402i	−0.562186	−	0.827011i	$-0.690039\pi$
$107$		−	17.1093i		−	1.65402i	0.562186	−	0.827011i	$-0.309961\pi$
$108$	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			0
$111$	−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	−0.501857	−	0.864951i	$-0.667349\pi$
$113$	−15.0552	−	4.89173i	−1.41627	−	0.460175i	−0.914416	+	0.404776i	$0.867349\pi$
$114$	−0.453194	−	1.39479i	−0.0424455	−	0.130634i
$115$		0			0
$116$	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
$120$		0			0
$121$	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			0
$126$	3.26189			0.290592
$127$	4.79037	−	1.55649i	0.425077	−	0.138116i	−0.0886633	−	0.996062i	$-0.528260\pi$
$127$	4.79037	−	1.55649i	0.425077	−	0.138116i	0.513740	+	0.857946i	$0.328260\pi$
$128$	3.84387	+	5.29063i	0.339753	+	0.467630i
$129$	−3.77180	+	2.74037i	−0.332089	+	0.241276i
$130$		0			0
$131$	−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
$135$		0			0
$136$	6.38818	+	19.6608i	0.547782	+	1.68590i
$137$	11.1159	+	3.61177i	0.949693	+	0.308574i	0.742591	−	0.669745i	$-0.233597\pi$
$137$	11.1159	+	3.61177i	0.949693	+	0.308574i	0.207102	+	0.978319i	$0.433597\pi$
$138$	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			0
$141$	−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
$145$		0			0
$146$	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			0
$151$	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
$155$		0			0
$156$	0.431922	+	0.313810i	0.0345815	+	0.0251249i
$157$			11.5228i			0.919617i	0.888018	+	0.459809i	$0.152082\pi$
$157$			11.5228i			0.919617i	−0.888018	+	0.459809i	$0.847918\pi$
$158$	−3.68306	+	5.06930i	−0.293009	+	0.403292i
$159$	−1.05315	+	3.24128i	−0.0835206	+	0.257050i
$160$		0			0
$161$	−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	0.969498	−	0.245098i	$-0.0788202\pi$
$163$	20.5522	+	6.67782i	1.60977	+	0.523047i	0.640276	+	0.768145i	$0.278820\pi$
$164$	0.955080	+	2.93943i	0.0745792	+	0.229531i
$165$		0			0
$166$	1.03653	−	3.19012i	0.0804506	−	0.247602i
$167$	7.98625	−	10.9921i	0.617995	−	0.850597i	−0.379210	−	0.925311i	$-0.623804\pi$
$167$	7.98625	−	10.9921i	0.617995	−	0.850597i	0.997205	+	0.0747138i	$0.0238043\pi$
$168$			1.93819i			0.149535i
$169$	−7.27737	−	5.28732i	−0.559798	−	0.406717i
$170$		0			0
$171$	−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	−0.661382	−	0.750049i	$-0.730030\pi$
$173$	−9.93814	+	3.22910i	−0.755583	+	0.245504i	−0.0942011	+	0.995553i	$0.530030\pi$
$174$	−5.35626			−0.406057
$175$		0			0
$176$	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			0
$181$	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
$185$		0			0
$186$	−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
$190$		0			0
$191$	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	$0.00124958\pi$
$193$			0.109074i			0.00785131i	−0.999992	+	0.00392565i	$0.998750\pi$
$194$	12.3591	+	8.97944i	0.887334	+	0.644686i
$195$		0			0
$196$	0.338697	−	0.246078i	0.0241927	−	0.0175770i
$197$	−5.96758	−	8.21367i	−0.425172	−	0.585199i	0.541664	−	0.840595i	$-0.317794\pi$
$197$	−5.96758	−	8.21367i	−0.425172	−	0.585199i	−0.966837	+	0.255395i	$0.917794\pi$
$198$	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	$0.649051\pi$
$200$		0			0
$201$	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
$205$		0			0
$206$	−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
$210$		0			0
$211$	−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
$215$		0			0
$216$	−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			0
$221$	−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	0.0682802	−	0.997666i	$-0.478249\pi$
$223$	10.6016	−	3.44466i	0.709933	−	0.230671i	0.641653	+	0.766995i	$0.278249\pi$
$224$	2.32626			0.155429
$225$		0			0
$226$	19.9064			1.32416
$227$	−12.0260	+	3.90749i	−0.798195	+	0.259349i	−0.679590	−	0.733592i	$-0.737842\pi$
$227$	−12.0260	+	3.90749i	−0.798195	+	0.259349i	−0.118605	+	0.992941i	$0.537842\pi$
$228$	−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	$0.199990\pi$
$230$		0			0
$231$	0.938968	+	0.682200i	0.0617796	+	0.0448855i
$232$			20.3294i			1.33469i
$233$	−5.17280	+	7.11975i	−0.338881	+	0.466430i	−0.944114	−	0.329618i	$-0.893080\pi$
$233$	−5.17280	+	7.11975i	−0.338881	+	0.466430i	0.605233	+	0.796048i	$0.293080\pi$
$234$	−2.01714	+	6.20810i	−0.131864	+	0.405836i
$235$		0			0
$236$	−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	$0.747389\pi$
$240$		0			0
$241$	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
$245$		0			0
$246$	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
$250$		0			0
$251$	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
$255$		0			0
$256$	7.74770	+	5.62903i	0.484231	+	0.351815i
$257$			24.5321i			1.53027i	0.643869	+	0.765136i	$0.277328\pi$
$257$			24.5321i			1.53027i	−0.643869	+	0.765136i	$0.722672\pi$
$258$	3.44606	−	4.74310i	0.214543	−	0.295293i
$259$	0.804200	−	2.47507i	0.0499706	−	0.153794i
$260$		0			0
$261$	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	−0.180758	−	0.983528i	$-0.557855\pi$
$263$	−14.6782	−	4.76924i	−0.905097	−	0.294084i	−0.724339	+	0.689444i	$0.757855\pi$
$264$	1.09084	+	3.35727i	0.0671368	+	0.206626i
$265$		0			0
$266$	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	$0.496056\pi$
$270$		0			0
$271$	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
$275$		0			0
$276$	1.15846			0.0697310
$277$	2.45108	−	0.796404i	0.147271	−	0.0478513i	−0.234454	−	0.972127i	$-0.575330\pi$
$277$	2.45108	−	0.796404i	0.147271	−	0.0478513i	0.381725	+	0.924276i	$0.375330\pi$
$278$	−7.24099	−	9.96637i	−0.434286	−	0.597743i
$279$	−10.3938	+	7.55153i	−0.622260	+	0.452098i
$280$		0			0
$281$	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	$0.408077\pi$
$283$	−12.0263	+	16.5528i	−0.714889	+	0.983961i	−0.999678	+	0.0253705i	$0.991923\pi$
$284$	1.54683	−	4.76066i	0.0917875	−	0.282493i
$285$		0			0
$286$	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
$290$		0			0
$291$	−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	$-0.924323\pi$
$293$		−	8.06270i		−	0.471028i	0.971871	−	0.235514i	$-0.0756773\pi$
$294$	−0.648308	−	0.471023i	−0.0378101	−	0.0274706i
$295$		0			0
$296$	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			0
$301$	−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
$305$		0			0
$306$	−17.9364	−	13.0315i	−1.02535	−	0.744963i
$307$		−	9.08866i		−	0.518717i	−0.965781	−	0.259359i	$-0.916489\pi$
$307$		−	9.08866i		−	0.518717i	0.965781	−	0.259359i	$-0.0835111\pi$
$308$	0.448183	−	0.616871i	0.0255376	−	0.0351495i
$309$	1.10966	−	3.41518i	0.0631264	−	0.194283i
$310$		0			0
$311$	−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	0.0692627	−	0.997598i	$-0.477935\pi$
$313$	−8.15727	−	2.65046i	−0.461076	−	0.149813i	−0.530339	+	0.847786i	$0.677935\pi$
$314$	−4.47768	−	13.7809i	−0.252690	−	0.777700i
$315$		0			0
$316$	−0.644634	+	1.98398i	−0.0362635	+	0.111608i
$317$	3.48825	−	4.80116i	0.195919	−	0.269660i	−0.699743	−	0.714395i	$-0.746702\pi$
$317$	3.48825	−	4.80116i	0.195919	−	0.269660i	0.895662	+	0.444735i	$0.146702\pi$
$318$		−	4.28572i		−	0.240331i
$319$	9.84870	+	7.15550i	0.551421	+	0.400631i
$320$		0			0
$321$	−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
$325$		0			0
$326$	−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
$330$		0			0
$331$	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
$335$		0			0
$336$	−0.588287	−	1.81056i	−0.0320937	−	0.0987743i
$337$	14.1648	+	4.60243i	0.771608	+	0.250711i	0.668253	−	0.743934i	$-0.267042\pi$
$337$	14.1648	+	4.60243i	0.771608	+	0.250711i	0.103355	+	0.994645i	$0.467042\pi$
$338$	10.7581	+	3.49553i	0.585165	+	0.190132i
$339$	3.11725	+	9.59392i	0.169306	+	0.521070i
$340$		0			0
$341$	−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
$345$		0			0
$346$	10.6309	−	7.72380i	0.571521	−	0.415234i
$347$	8.41195	+	11.5781i	0.451577	+	0.621543i	0.972736	−	0.231917i	$-0.0744999\pi$
$347$	8.41195	+	11.5781i	0.451577	+	0.621543i	−0.521158	+	0.853460i	$0.674500\pi$
$348$	−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	$0.466323\pi$
$350$		0			0
$351$	−7.13361			−0.380764
$352$	4.02946	−	1.30925i	0.214771	−	0.0697833i
$353$	5.32143	+	7.32432i	0.283231	+	0.389834i	0.926801	−	0.375553i	$-0.122547\pi$
$353$	5.32143	+	7.32432i	0.283231	+	0.389834i	−0.643570	+	0.765388i	$0.722547\pi$
$354$	−0.0160544	+	0.0116642i	−0.000853284	+	0.000619947i
$355$		0			0
$356$	−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	$-0.320555\pi$
$360$		0			0
$361$	−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
$365$		0			0
$366$	0.978569	−	3.01172i	0.0511506	−	0.157425i
$367$	9.23299	−	12.7081i	0.481958	−	0.663358i	−0.496922	−	0.867795i	$-0.665536\pi$
$367$	9.23299	−	12.7081i	0.481958	−	0.663358i	0.978880	+	0.204437i	$0.0655364\pi$
$368$			12.9722i			0.676222i
$369$	−15.4923	−	11.2558i	−0.806498	−	0.585955i
$370$		0			0
$371$	−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	−0.0678910	−	0.997693i	$-0.521627\pi$
$373$	8.95386	−	2.90928i	0.463613	−	0.150637i	0.531504	+	0.847056i	$0.321627\pi$
$374$	−15.5670			−0.804949
$375$		0			0
$376$	−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	$0.00216329\pi$
$380$		0			0
$381$	−2.59675	−	1.88665i	−0.133036	−	0.0966561i
$382$			15.3525i			0.785500i
$383$	−10.5691	+	14.5472i	−0.540058	+	0.743326i	−0.988621	−	0.150425i	$-0.951936\pi$
$383$	−10.5691	+	14.5472i	−0.540058	+	0.743326i	0.448564	+	0.893751i	$0.351936\pi$
$384$	1.28778	−	3.96338i	0.0657168	−	0.202256i
$385$		0			0
$386$	−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			0
$391$	−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
$395$		0			0
$396$	1.60011	−	1.16255i	0.0804086	−	0.0584202i
$397$	0.852092	+	1.17280i	0.0427653	+	0.0588613i	0.829864	−	0.557966i	$-0.188418\pi$
$397$	0.852092	+	1.17280i	0.0427653	+	0.0588613i	−0.787099	+	0.616827i	$0.788418\pi$
$398$	15.2291	−	4.94822i	0.763364	−	0.248032i
$399$	1.16624			0.0583851
$400$		0			0
$401$	−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
$405$		0			0
$406$	−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	$0.0128867\pi$
$410$		0			0
$411$	−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
$415$		0			0
$416$	−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			0
$421$	−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
$425$		0			0
$426$	−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
$430$		0			0
$431$	−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	−0.565501	−	0.824748i	$-0.691317\pi$
$433$	8.19091	−	11.2738i	0.393630	−	0.541785i	0.959131	+	0.282962i	$0.0913172\pi$
$434$	1.92467	−	5.92354i	0.0923873	−	0.284339i
$435$		0			0
$436$	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	$-0.326665\pi$
$440$		0			0
$441$	−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	$-0.615937\pi$
$443$		−	39.3336i		−	1.86880i	0.356228	−	0.934399i	$-0.384063\pi$
$444$	0.561699	+	0.408098i	0.0266571	+	0.0193675i
$445$		0			0
$446$	−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	$0.267285\pi$
$450$		0			0
$451$	−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
$455$		0			0
$456$	2.86968	+	2.08494i	0.134385	+	0.0976365i
$457$			7.27936i			0.340514i	0.985400	+	0.170257i	$0.0544598\pi$
$457$			7.27936i			0.340514i	−0.985400	+	0.170257i	$0.945540\pi$
$458$	−6.91362	+	9.51578i	−0.323052	+	0.444643i
$459$	7.48714	−	23.0430i	0.349470	−	1.07556i
$460$		0			0
$461$	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	0.601552	−	0.798834i	$-0.294549\pi$
$463$	13.3123	+	4.32543i	0.618675	+	0.201020i	0.0171231	+	0.999853i	$0.494549\pi$
$464$	−6.17046	−	18.9907i	−0.286456	−	0.881622i
$465$		0			0
$466$	3.41982	−	10.5251i	0.158420	−	0.487567i
$467$	2.73088	−	3.75874i	0.126370	−	0.173934i	−0.741144	−	0.671346i	$-0.765716\pi$
$467$	2.73088	−	3.75874i	0.126370	−	0.173934i	0.867514	+	0.497413i	$0.165716\pi$
$468$			2.17317i			0.100455i
$469$	3.75258	+	2.72641i	0.173278	+	0.125894i
$470$		0			0
$471$	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			0
$476$	−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	$0.197978\pi$
$480$		0			0
$481$	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
$485$		0			0
$486$	−5.52017	−	16.9893i	−0.250400	−	0.770652i
$487$	−26.3647	−	8.56642i	−1.19470	−	0.388182i	−0.356891	−	0.934146i	$-0.616163\pi$
$487$	−26.3647	−	8.56642i	−1.19470	−	0.388182i	−0.837808	+	0.545964i	$0.816163\pi$
$488$	−11.4309	−	3.71411i	−0.517450	−	0.168130i
$489$	−4.25544	−	13.0969i	−0.192438	−	0.592263i
$490$		0			0
$491$	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
$495$		0			0
$496$	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	$0.594353\pi$
$500$		0			0
$501$	−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	$0.117553\pi$
$503$	22.1517	+	30.4892i	0.987696	+	1.35945i	0.0551174	+	0.998480i	$0.482447\pi$
$504$	−6.38263	+	4.63726i	−0.284305	+	0.206560i
$505$		0			0
$506$	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	$0.714344\pi$
$510$		0			0
$511$	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
$515$		0			0
$516$	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
$520$		0			0
$521$	−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	0.129498	−	0.991580i	$-0.458663\pi$
$523$	18.6864	−	6.07159i	0.817100	−	0.265492i	0.687602	+	0.726088i	$0.258663\pi$
$524$	2.03256			0.0887930
$525$		0			0
$526$	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
$530$		0			0
$531$	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
$535$		0			0
$536$	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
$540$		0			0
$541$	−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
$545$		0			0
$546$	1.29737	−	0.942598i	0.0555225	−	0.0403395i
$547$	−11.8094	−	16.2542i	−0.504932	−	0.694979i	0.478123	−	0.878293i	$-0.341317\pi$
$547$	−11.8094	−	16.2542i	−0.504932	−	0.694979i	−0.983054	+	0.183314i	$0.941317\pi$
$548$	−4.65369	+	1.51208i	−0.198796	+	0.0645927i
$549$	−10.2504			−0.437476
$550$		0			0
$551$	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			0
$556$	−3.31801	−	2.41067i	−0.140715	−	0.102235i
$557$			10.2545i			0.434498i	0.976116	+	0.217249i	$0.0697084\pi$
$557$			10.2545i			0.434498i	−0.976116	+	0.217249i	$0.930292\pi$
$558$	9.49618	−	13.0704i	0.402005	−	0.553313i
$559$	4.52426	−	13.9242i	0.191356	−	0.588932i
$560$		0			0
$561$	−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	0.944519	−	0.328456i	$-0.106528\pi$
$563$	35.9613	+	11.6845i	1.51559	+	0.492445i	0.571070	+	0.820901i	$0.306528\pi$
$564$	−0.863805	−	2.65852i	−0.0363727	−	0.111944i
$565$		0			0
$566$	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			0
$571$	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
$575$		0			0
$576$	−23.0862			−0.961926
$577$	20.5390	−	6.67353i	0.855050	−	0.277823i	0.151490	−	0.988459i	$-0.451593\pi$
$577$	20.5390	−	6.67353i	0.855050	−	0.277823i	0.703560	+	0.710636i	$0.251593\pi$
$578$	21.5811	+	29.7038i	0.897655	+	1.23552i
$579$	0.0562327	−	0.0408554i	0.00233695	−	0.00169789i
$580$		0			0
$581$	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
$585$		0			0
$586$	3.13312	+	9.64274i	0.129428	+	0.398338i
$587$	1.71953	+	0.558710i	0.0709727	+	0.0230604i	0.344288	−	0.938864i	$-0.388120\pi$
$587$	1.71953	+	0.558710i	0.0709727	+	0.0230604i	−0.273315	+	0.961924i	$0.588120\pi$
$588$	−0.253729	−	0.0824416i	−0.0104636	−	0.00339983i
$589$	2.80106	+	8.62077i	0.115416	+	0.355213i
$590$		0			0
$591$	−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	$-0.709896\pi$
$593$		−	38.4929i		−	1.58071i	0.612648	−	0.790356i	$-0.290104\pi$
$594$	−6.60511	−	4.79889i	−0.271011	−	0.196901i
$595$		0			0
$596$	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	$0.275185\pi$
$600$		0			0
$601$	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
$605$		0			0
$606$	−8.88713	−	6.45688i	−0.361015	−	0.262293i
$607$			35.5410i			1.44256i	0.692641	+	0.721282i	$0.256447\pi$
$607$			35.5410i			1.44256i	−0.692641	+	0.721282i	$0.743553\pi$
$608$	2.50239	−	3.44424i	0.101485	−	0.139682i
$609$	1.31623	−	4.05093i	0.0533362	−	0.164152i
$610$		0			0
$611$	−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	0.230556	−	0.973059i	$-0.425945\pi$
$613$	−3.83439	−	1.24587i	−0.154869	−	0.0503201i	−0.385426	+	0.922739i	$0.625945\pi$
$614$	3.53180	+	10.8698i	0.142532	+	0.438667i
$615$		0			0
$616$	−1.71180	+	5.26837i	−0.0689703	+	0.212269i
$617$	19.2392	−	26.4805i	0.774542	−	1.06606i	−0.221322	−	0.975201i	$-0.571037\pi$
$617$	19.2392	−	26.4805i	0.774542	−	1.06606i	0.995863	−	0.0908641i	$-0.0289629\pi$
$618$			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	$0.279811\pi$
$620$		0			0
$621$	−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
$625$		0			0
$626$	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
$630$		0			0
$631$	−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
$635$		0			0
$636$	−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
$640$		0			0
$641$	−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	$0.304201\pi$
$643$			41.4190i			1.63341i	−0.577058	+	0.816703i	$0.695799\pi$
$644$	1.47071	+	1.06854i	0.0579542	+	0.0421062i
$645$		0			0
$646$	−12.6549	+	9.19430i	−0.497899	+	0.361745i
$647$	−3.33796	−	4.59430i	−0.131229	−	0.180621i	0.738346	−	0.674422i	$-0.235607\pi$
$647$	−3.33796	−	4.59430i	−0.131229	−	0.180621i	−0.869575	+	0.493801i	$0.835607\pi$
$648$	−15.9387	+	5.17881i	−0.626133	+	0.203443i
$649$	0.0451021			0.00177041
$650$		0			0
$651$	3.15625			0.123703
$652$	−8.60424	+	2.79569i	−0.336968	+	0.109488i
$653$	0.860358	+	1.18418i	0.0336684	+	0.0463406i	0.825519	−	0.564374i	$-0.190882\pi$
$653$	0.860358	+	1.18418i	0.0336684	+	0.0463406i	−0.791851	+	0.610714i	$0.790882\pi$
$654$	8.28297	−	6.01793i	0.323890	−	0.235320i
$655$		0			0
$656$	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			0
$661$	−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
$665$		0			0
$666$	−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
$670$		0			0
$671$	−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	−0.163985	−	0.986463i	$-0.552435\pi$
$673$	7.34626	−	2.38694i	0.283178	−	0.0920100i	0.447162	+	0.894453i	$0.352435\pi$
$674$	−18.7292			−0.721421
$675$		0			0
$676$	3.76592			0.144843
$677$	−21.9039	+	7.11702i	−0.841837	+	0.273529i	−0.698023	−	0.716075i	$-0.745937\pi$
$677$	−21.9039	+	7.11702i	−0.841837	+	0.273529i	−0.143814	+	0.989605i	$0.545937\pi$
$678$	−7.45628	−	10.2627i	−0.286357	−	0.394136i
$679$	−9.82821	+	7.14061i	−0.377172	+	0.274032i
$680$		0			0
$681$	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	$-0.562936\pi$
$683$	20.8236	−	28.6613i	0.796794	−	1.09669i	0.993229	−	0.116176i	$-0.0370635\pi$
$684$	0.614144	−	1.89014i	0.0234824	−	0.0722713i
$685$		0			0
$686$	−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
$690$		0			0
$691$	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
$695$		0			0
$696$	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			0
$701$	−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
$705$		0			0
$706$	−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	$0.806699\pi$
$710$		0			0
$711$	−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
$715$		0			0
$716$	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	$0.999317\pi$
$720$		0			0
$721$	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
$725$		0			0
$726$	6.15667			0.228495
$727$	0.236691	−	0.0769054i	0.00877837	−	0.00285226i	−0.304625	−	0.952473i	$-0.598531\pi$
$727$	0.236691	−	0.0769054i	0.00877837	−	0.00285226i	0.313403	+	0.949620i	$0.398531\pi$
$728$	−3.57758	−	4.92412i	−0.132594	−	0.182500i
$729$	−6.04974	+	4.39539i	−0.224064	+	0.162792i
$730$		0			0
$731$	40.2297	+	29.2286i	1.48795	+	1.08106i
$732$		−	1.05426i		−	0.0389667i
$733$	−17.6847	+	24.3409i	−0.653200	+	0.899053i	−0.999233	−	0.0391699i	$-0.987529\pi$
$733$	−17.6847	+	24.3409i	−0.653200	+	0.899053i	0.346033	+	0.938222i	$0.387529\pi$
$734$	−6.10407	+	18.7864i	−0.225305	+	0.693419i
$735$		0			0
$736$	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	$0.959101\pi$
$740$		0			0
$741$	−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	$0.0751390\pi$
$743$			12.7497i			0.467740i	−0.972268	+	0.233870i	$0.924861\pi$
$744$	7.76634	+	5.64257i	0.284728	+	0.206867i
$745$		0			0
$746$	−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
$750$		0			0
$751$	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
$755$		0			0
$756$	−1.20736	−	0.877200i	−0.0439113	−	0.0319034i
$757$		−	37.1340i		−	1.34966i	−0.737974	−	0.674829i	$-0.764217\pi$
$757$		−	37.1340i		−	1.34966i	0.737974	−	0.674829i	$-0.235783\pi$
$758$	−23.1675	+	31.8874i	−0.841483	+	1.15820i
$759$	−1.55737	+	4.79309i	−0.0565289	+	0.173978i
$760$		0			0
$761$	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
$765$		0			0
$766$	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	$0.941467\pi$
$770$		0			0
$771$	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	0.147697	−	0.989033i	$-0.452814\pi$
$773$	23.5914	−	7.66532i	0.848525	−	0.275703i	0.700828	+	0.713330i	$0.252814\pi$
$774$	23.8644			0.857787
$775$		0			0
$776$	−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			0
$781$	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
$785$		0			0
$786$	−1.20226	−	3.70016i	−0.0428830	−	0.131980i
$787$	−25.9207	−	8.42214i	−0.923973	−	0.300217i	−0.191877	−	0.981419i	$-0.561458\pi$
$787$	−25.9207	−	8.42214i	−0.923973	−	0.300217i	−0.732095	+	0.681202i	$0.761458\pi$
$788$	4.04240	+	1.31346i	0.144005	+	0.0467900i
$789$	3.03920	+	9.35369i	0.108198	+	0.333000i
$790$		0			0
$791$	−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
$795$		0			0
$796$	4.31285	−	3.13347i	0.152865	−	0.111063i
$797$	−8.87402	−	12.2140i	−0.314334	−	0.432644i	0.622393	−	0.782705i	$-0.286161\pi$
$797$	−8.87402	−	12.2140i	−0.314334	−	0.432644i	−0.936727	+	0.350061i	$0.886161\pi$
$798$	−1.39479	+	0.453194i	−0.0493750	+	0.0160429i
$799$	71.2159			2.51944
$800$		0			0
$801$	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
$805$		0			0
$806$	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	$-0.0625797\pi$
$810$		0			0
$811$	−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
$815$		0			0
$816$	−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
$820$		0			0
$821$	−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	−0.100439	−	0.994943i	$-0.532025\pi$
$823$	11.5646	−	3.75757i	0.403117	−	0.130981i	0.503556	+	0.863962i	$0.332025\pi$
$824$	17.1390			0.597064
$825$		0			0
$826$	−0.0311406			−0.00108352
$827$	42.8452	−	13.9212i	1.48987	−	0.484089i	0.552827	−	0.833296i	$-0.313549\pi$
$827$	42.8452	−	13.9212i	1.48987	−	0.484089i	0.937046	+	0.349207i	$0.113549\pi$
$828$	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	$0.180363\pi$
$830$		0			0
$831$	−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
$835$		0			0
$836$	−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	$0.739915\pi$
$840$		0			0
$841$	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
$845$		0			0
$846$	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
$850$		0			0
$851$	11.3005			0.387377
$852$	−3.03373	+	0.985719i	−0.103934	+	0.0337702i
$853$	−16.1335	−	22.2058i	−0.552400	−	0.760313i	0.437936	−	0.899006i	$-0.355710\pi$
$853$	−16.1335	−	22.2058i	−0.552400	−	0.760313i	−0.990335	+	0.138693i	$0.955710\pi$
$854$	4.02028	−	2.92091i	0.137571	−	0.0999513i
$855$		0			0
$856$	−42.0996	−	30.5871i	−1.43893	−	1.04545i
$857$		−	25.1788i		−	0.860093i	−0.902807	−	0.430047i	$-0.858497\pi$
$857$		−	25.1788i		−	0.860093i	0.902807	−	0.430047i	$-0.141503\pi$
$858$	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			0
$861$	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	−0.439373	−	0.898305i	$-0.644799\pi$
$863$	−38.8610	−	12.6267i	−1.32284	−	0.429818i	−0.883471	+	0.468487i	$0.844799\pi$
$864$	−2.56251	−	7.88660i	−0.0871784	−	0.268307i
$865$		0			0
$866$	−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
$870$		0			0
$871$	−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
$875$		0			0
$876$	−2.53844			−0.0857658
$877$	−31.7629	+	10.3204i	−1.07256	+	0.348494i	−0.791482	−	0.611192i	$-0.790690\pi$
$877$	−31.7629	+	10.3204i	−1.07256	+	0.348494i	−0.281073	+	0.959686i	$0.590690\pi$
$878$	20.2388	+	27.8563i	0.683027	+	0.940106i
$879$	−4.15670	+	3.02002i	−0.140202	+	0.101863i
$880$		0			0
$881$	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	−0.787568	−	0.616228i	$-0.788660\pi$
$883$	1.24425	−	1.71256i	0.0418722	−	0.0576321i	0.829440	+	0.558596i	$0.188660\pi$
$884$	1.75966	−	5.41567i	0.0591837	−	0.182149i
$885$		0			0
$886$	15.2848	+	47.0418i	0.513503	+	1.58040i
$887$	2.17649	+	0.707185i	0.0730794	+	0.0237449i	0.345329	−	0.938482i	$-0.387767\pi$
$887$	2.17649	+	0.707185i	0.0730794	+	0.0237449i	−0.272249	+	0.962227i	$0.587767\pi$
$888$	−4.79717	−	1.55870i	−0.160983	−	0.0523064i
$889$	−1.55649	−	4.79037i	−0.0522029	−	0.160664i
$890$		0			0
$891$	−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
$895$		0			0
$896$	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
$900$		0			0
$901$	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
$905$		0			0
$906$	9.20986	+	6.69136i	0.305977	+	0.222305i
$907$		−	53.0301i		−	1.76084i	−0.474199	−	0.880418i	$-0.657262\pi$
$907$		−	53.0301i		−	1.76084i	0.474199	−	0.880418i	$-0.342738\pi$
$908$	3.11163	−	4.28280i	0.103263	−	0.142130i
$909$	−10.9880	+	33.8175i	−0.364448	+	1.12166i
$910$		0			0
$911$	−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
$915$		0			0
$916$	−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	$0.404833\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$	−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	$-0.0402900\pi$
$930$		0			0
$931$	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
$935$		0			0
$936$	−4.87875	−	15.0152i	−0.159467	−	0.490789i
$937$	8.84897	+	2.87521i	0.289083	+	0.0939289i	0.449969	−	0.893044i	$-0.351435\pi$
$937$	8.84897	+	2.87521i	0.289083	+	0.0939289i	−0.160886	+	0.986973i	$0.551435\pi$
$938$	−5.54743	−	1.80247i	−0.181130	−	0.0588527i
$939$	1.68901	+	5.19823i	0.0551186	+	0.169638i
$940$		0			0
$941$	−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
$945$		0			0
$946$	13.5561	−	9.84909i	0.440747	−	0.320222i
$947$	19.9601	+	27.4727i	0.648616	+	0.892743i	0.999038	−	0.0438488i	$-0.0139620\pi$
$947$	19.9601	+	27.4727i	0.648616	+	0.892743i	−0.350422	+	0.936592i	$0.613962\pi$
$948$	1.26429	−	0.410793i	0.0410623	−	0.0133419i
$949$	−19.0408			−0.618092
$950$		0			0
$951$	−3.78180			−0.122633
$952$	19.6608	−	6.38818i	0.637210	−	0.207042i
$953$	0.671478	+	0.924210i	0.0217513	+	0.0299381i	0.819754	−	0.572716i	$-0.194110\pi$
$953$	0.671478	+	0.924210i	0.0217513	+	0.0299381i	−0.798003	+	0.602654i	$0.794110\pi$
$954$	14.1132	−	10.2539i	0.456932	−	0.331981i
$955$		0			0
$956$	−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
$960$		0			0
$961$	−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			0
$966$	1.07528	−	3.30938i	0.0345966	−	0.106477i
$967$	−15.1515	+	20.8543i	−0.487241	+	0.670629i	−0.979876	−	0.199606i	$-0.936034\pi$
$967$	−15.1515	+	20.8543i	−0.487241	+	0.670629i	0.492635	+	0.870236i	$0.336034\pi$
$968$		−	23.3673i		−	0.751054i
$969$	−6.41289	−	4.65924i	−0.206012	−	0.149676i
$970$		0			0
$971$	−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
$975$		0			0
$976$	11.8054			0.377883
$977$	53.8492	−	17.4967i	1.72279	−	0.559768i	0.730411	−	0.683007i	$-0.239328\pi$
$977$	53.8492	−	17.4967i	1.72279	−	0.559768i	0.992377	+	0.123240i	$0.0393284\pi$
$978$	10.1788	+	14.0099i	0.325481	+	0.447986i
$979$	22.6549	−	16.4598i	0.724055	−	0.526057i
$980$		0			0
$981$	−26.8113	−	19.4795i	−0.856018	−	0.621933i
$982$			37.6680i			1.20204i
$983$	−9.03318	+	12.4331i	−0.288114	+	0.396555i	−0.928400	−	0.371582i	$-0.878816\pi$
$983$	−9.03318	+	12.4331i	−0.288114	+	0.396555i	0.640287	+	0.768136i	$0.278816\pi$
$984$	−4.42164	+	13.6084i	−0.140957	+	0.433820i
$985$		0			0
$986$	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
$990$		0			0
$991$	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
$995$		0			0
$996$	−0.575717	+	0.418283i	−0.0182423	+	0.0132538i
$997$	3.84182	+	5.28781i	0.121672	+	0.167466i	0.865508	−	0.500895i	$-0.166996\pi$
$997$	3.84182	+	5.28781i	0.121672	+	0.167466i	−0.743836	+	0.668362i	$0.766996\pi$
$998$	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	875.2.n.c.99.4		56
5.2	odd	4		875.2.h.e.526.5		56
5.3	odd	4		875.2.h.d.526.10		56
5.4	even	2		175.2.n.a.169.11	yes	56
25.2	odd	20		4375.2.a.o.1.9		28
25.3	odd	20		875.2.h.d.351.10		56
25.4	even	10	inner	875.2.n.c.274.4		56
25.21	even	5		175.2.n.a.29.11	✓	56
25.22	odd	20		875.2.h.e.351.5		56
25.23	odd	20		4375.2.a.p.1.20		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.29.11	✓	56	25.21	even	5
175.2.n.a.169.11	yes	56	5.4	even	2
875.2.h.d.351.10		56	25.3	odd	20
875.2.h.d.526.10		56	5.3	odd	4
875.2.h.e.351.5		56	25.22	odd	20
875.2.h.e.526.5		56	5.2	odd	4
875.2.n.c.99.4		56	1.1	even	1	trivial
875.2.n.c.274.4		56	25.4	even	10	inner
4375.2.a.o.1.9		28	25.2	odd	20
4375.2.a.p.1.20		28	25.23	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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.n (of order \(10\), degree \(4\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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