LMFDB - Embedded newform 875.2.h.e.351.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(176,875)]

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([8, 0]))

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

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

chi := DirichletCharacter("875.176");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.h (of order $5$, 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 $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			351.5
Character	$\chi$	$=$	875.351
Dual form			875.2.h.e.526.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.388594 + 1.19597i) q^{2} +(-0.515546 - 0.374566i) q^{3} +(0.338697 + 0.246078i) q^{4} +(0.648308 - 0.471023i) q^{6} +1.00000 q^{7} +(-2.46062 + 1.78775i) q^{8} +(-0.801563 - 2.46696i) q^{9} +O(q^{10})$	\(q+(-0.388594 + 1.19597i) q^{2} +(-0.515546 - 0.374566i) q^{3} +(0.338697 + 0.246078i) q^{4} +(0.648308 - 0.471023i) q^{6} +1.00000 q^{7} +(-2.46062 + 1.78775i) q^{8} +(-0.801563 - 2.46696i) q^{9} +(-0.562815 + 1.73217i) q^{11} +(-0.0824416 - 0.253729i) q^{12} +(0.618395 + 1.90323i) q^{13} +(-0.388594 + 1.19597i) q^{14} +(-0.923165 - 2.84121i) q^{16} +(-5.49877 + 3.99509i) q^{17} +3.26189 q^{18} +(1.48059 - 1.07571i) q^{19} +(-0.515546 - 0.374566i) q^{21} +(-1.85291 - 1.34622i) q^{22} +(-1.34183 + 4.12974i) q^{23} +1.93819 q^{24} -2.51650 q^{26} +(-1.10156 + 3.39025i) q^{27} +(0.338697 + 0.246078i) q^{28} +(5.40749 + 3.92877i) q^{29} +(-4.00700 + 2.91125i) q^{31} -2.32626 q^{32} +(0.938968 - 0.682200i) q^{33} +(-2.64121 - 8.12882i) q^{34} +(0.335576 - 1.03280i) q^{36} +(-0.804200 - 2.47507i) q^{37} +(0.711172 + 2.18876i) q^{38} +(0.394073 - 1.21283i) q^{39} +(2.28132 + 7.02118i) q^{41} +(0.648308 - 0.471023i) q^{42} -7.31612 q^{43} +(-0.616871 + 0.448183i) q^{44} +(-4.41761 - 3.20958i) q^{46} +(8.47670 + 6.15868i) q^{47} +(-0.588287 + 1.81056i) q^{48} +1.00000 q^{49} +4.33130 q^{51} +(-0.258893 + 0.796790i) q^{52} +(-4.32670 - 3.14354i) q^{53} +(-3.62658 - 2.63486i) q^{54} +(-2.46062 + 1.78775i) q^{56} -1.16624 q^{57} +(-6.80001 + 4.94049i) q^{58} +(0.00765237 + 0.0235516i) q^{59} +(-1.22115 + 3.75830i) q^{61} +(-1.92467 - 5.92354i) q^{62} +(-0.801563 - 2.46696i) q^{63} +(2.75030 - 8.46455i) q^{64} +(0.451013 + 1.38808i) q^{66} +(-3.75258 + 2.72641i) q^{67} -2.84552 q^{68} +(2.23864 - 1.62647i) q^{69} +(-9.67307 - 7.02789i) q^{71} +(6.38263 + 4.63726i) q^{72} +(2.94025 - 9.04917i) q^{73} +3.27262 q^{74} +0.766183 q^{76} +(-0.562815 + 1.73217i) q^{77} +(1.29737 + 0.942598i) q^{78} +(-4.03120 - 2.92884i) q^{79} +(-4.45778 + 3.23876i) q^{81} -9.28362 q^{82} +(2.15797 - 1.56786i) q^{83} +(-0.0824416 - 0.253729i) q^{84} +(2.84300 - 8.74985i) q^{86} +(-1.31623 - 4.05093i) q^{87} +(-1.71180 - 5.26837i) q^{88} +(-4.75121 + 14.6227i) q^{89} +(0.618395 + 1.90323i) q^{91} +(-1.47071 + 1.06854i) q^{92} +3.15625 q^{93} +(-10.6596 + 7.74464i) q^{94} +(1.19929 + 0.871337i) q^{96} +(9.82821 + 7.14061i) q^{97} +(-0.388594 + 1.19597i) q^{98} +4.72431 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{2} + 4 q^{3} - 12 q^{4} + 56 q^{7} + 12 q^{8} - 6 q^{9}+O(q^{10}) $ 56 * q + 4 * q^2 + 4 * q^3 - 12 * q^4 + 56 * q^7 + 12 * q^8 - 6 * q^9	$ 56 q + 4 q^{2} + 4 q^{3} - 12 q^{4} + 56 q^{7} + 12 q^{8} - 6 q^{9} + 8 q^{11} + 12 q^{12} + 8 q^{13} + 4 q^{14} - 32 q^{16} + 20 q^{17} - 48 q^{18} - 12 q^{19} + 4 q^{21} + 8 q^{22} + 16 q^{23} + 28 q^{24} + 12 q^{26} + 16 q^{27} - 12 q^{28} + 2 q^{29} + 12 q^{31} - 112 q^{32} + 14 q^{33} - 14 q^{36} + 16 q^{37} + 20 q^{38} + 4 q^{39} + 4 q^{41} - 32 q^{43} - 22 q^{44} - 4 q^{46} + 18 q^{47} + 48 q^{48} + 56 q^{49} - 44 q^{51} - 16 q^{52} + 20 q^{53} - 54 q^{54} + 12 q^{56} - 152 q^{57} - 32 q^{58} + 6 q^{59} - 4 q^{61} - 18 q^{62} - 6 q^{63} - 24 q^{64} - 74 q^{66} + 32 q^{67} - 124 q^{68} + 78 q^{69} - 8 q^{71} + 100 q^{72} + 48 q^{73} - 60 q^{74} + 52 q^{76} + 8 q^{77} - 124 q^{78} - 72 q^{81} - 44 q^{82} - 10 q^{83} + 12 q^{84} - 20 q^{86} - 26 q^{87} + 88 q^{88} - 38 q^{89} + 8 q^{91} + 96 q^{92} - 96 q^{93} - 88 q^{94} - 28 q^{96} + 90 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) $ 56 * q + 4 * q^2 + 4 * q^3 - 12 * q^4 + 56 * q^7 + 12 * q^8 - 6 * q^9 + 8 * q^11 + 12 * q^12 + 8 * q^13 + 4 * q^14 - 32 * q^16 + 20 * q^17 - 48 * q^18 - 12 * q^19 + 4 * q^21 + 8 * q^22 + 16 * q^23 + 28 * q^24 + 12 * q^26 + 16 * q^27 - 12 * q^28 + 2 * q^29 + 12 * q^31 - 112 * q^32 + 14 * q^33 - 14 * q^36 + 16 * q^37 + 20 * q^38 + 4 * q^39 + 4 * q^41 - 32 * q^43 - 22 * q^44 - 4 * q^46 + 18 * q^47 + 48 * q^48 + 56 * q^49 - 44 * q^51 - 16 * q^52 + 20 * q^53 - 54 * q^54 + 12 * q^56 - 152 * q^57 - 32 * q^58 + 6 * q^59 - 4 * q^61 - 18 * q^62 - 6 * q^63 - 24 * q^64 - 74 * q^66 + 32 * q^67 - 124 * q^68 + 78 * q^69 - 8 * q^71 + 100 * q^72 + 48 * q^73 - 60 * q^74 + 52 * q^76 + 8 * q^77 - 124 * q^78 - 72 * q^81 - 44 * q^82 - 10 * q^83 + 12 * q^84 - 20 * q^86 - 26 * q^87 + 88 * q^88 - 38 * q^89 + 8 * q^91 + 96 * q^92 - 96 * q^93 - 88 * q^94 - 28 * q^96 + 90 * q^97 + 4 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−0.388594	+	1.19597i	−0.274777	+	0.845678i	0.714501	+	0.699635i	$0.246654\pi$
$2$	−0.388594	+	1.19597i	−0.274777	+	0.845678i	−0.989278	+	0.146043i	$0.953346\pi$
$3$	−0.515546	−	0.374566i	−0.297651	−	0.216256i	0.428929	−	0.903338i	$-0.358891\pi$
$3$	−0.515546	−	0.374566i	−0.297651	−	0.216256i	−0.726580	+	0.687082i	$0.758891\pi$
$4$	0.338697	+	0.246078i	0.169349	+	0.123039i
$5$		0			0
$5$		0			0
$6$	0.648308	−	0.471023i	0.264671	−	0.192294i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.46062	+	1.78775i	−0.869961	+	0.632064i
$9$	−0.801563	−	2.46696i	−0.267188	−	0.822319i
$10$		0			0
$11$	−0.562815	+	1.73217i	−0.169695	+	0.522268i	−0.999352	−	0.0360066i	$-0.988536\pi$
$11$	−0.562815	+	1.73217i	−0.169695	+	0.522268i	0.829657	+	0.558274i	$0.188536\pi$
$12$	−0.0824416	−	0.253729i	−0.0237988	−	0.0732453i
$13$	0.618395	+	1.90323i	0.171512	+	0.527860i	0.999457	−	0.0329496i	$-0.0104901\pi$
$13$	0.618395	+	1.90323i	0.171512	+	0.527860i	−0.827945	+	0.560809i	$0.810490\pi$
$14$	−0.388594	+	1.19597i	−0.103856	+	0.319636i
$15$		0			0
$16$	−0.923165	−	2.84121i	−0.230791	−	0.710302i
$17$	−5.49877	+	3.99509i	−1.33365	+	0.968951i	−0.333995	+	0.942575i	$0.608397\pi$
$17$	−5.49877	+	3.99509i	−1.33365	+	0.968951i	−0.999652	+	0.0263765i	$0.991603\pi$
$18$	3.26189			0.768834
$19$	1.48059	−	1.07571i	0.339672	−	0.246786i	−0.404852	−	0.914382i	$-0.632677\pi$
$19$	1.48059	−	1.07571i	0.339672	−	0.246786i	0.744523	+	0.667597i	$0.232677\pi$
$20$		0			0
$21$	−0.515546	−	0.374566i	−0.112501	−	0.0817371i
$22$	−1.85291	−	1.34622i	−0.395042	−	0.287015i
$23$	−1.34183	+	4.12974i	−0.279792	+	0.861110i	0.708120	+	0.706092i	$0.249544\pi$
$23$	−1.34183	+	4.12974i	−0.279792	+	0.861110i	−0.987912	+	0.155018i	$0.950456\pi$
$24$	1.93819			0.395632
$25$		0			0
$26$	−2.51650			−0.493527
$27$	−1.10156	+	3.39025i	−0.211995	+	0.652455i
$28$	0.338697	+	0.246078i	0.0640078	+	0.0465044i
$29$	5.40749	+	3.92877i	1.00415	+	0.729554i	0.962973	−	0.269598i	$-0.0868907\pi$
$29$	5.40749	+	3.92877i	1.00415	+	0.729554i	0.0411725	+	0.999152i	$0.486891\pi$
$30$		0			0
$31$	−4.00700	+	2.91125i	−0.719678	+	0.522876i	−0.886281	−	0.463147i	$-0.846720\pi$
$31$	−4.00700	+	2.91125i	−0.719678	+	0.522876i	0.166603	+	0.986024i	$0.446720\pi$
$32$	−2.32626			−0.411228
$33$	0.938968	−	0.682200i	0.163453	−	0.118756i
$34$	−2.64121	−	8.12882i	−0.452965	−	1.39408i
$35$		0			0
$36$	0.335576	−	1.03280i	0.0559294	−	0.172133i
$37$	−0.804200	−	2.47507i	−0.132210	−	0.406900i	0.862936	−	0.505313i	$-0.168623\pi$
$37$	−0.804200	−	2.47507i	−0.132210	−	0.406900i	−0.995146	+	0.0984138i	$0.968623\pi$
$38$	0.711172	+	2.18876i	0.115367	+	0.355064i
$39$	0.394073	−	1.21283i	0.0631021	−	0.194208i
$40$		0			0
$41$	2.28132	+	7.02118i	0.356282	+	1.09652i	0.955262	+	0.295760i	$0.0955728\pi$
$41$	2.28132	+	7.02118i	0.356282	+	1.09652i	−0.598980	+	0.800764i	$0.704427\pi$
$42$	0.648308	−	0.471023i	0.100036	−	0.0726805i
$43$	−7.31612			−1.11570			−0.557849	−	0.829942i	$-0.688373\pi$
$43$	−7.31612			−1.11570			−0.557849	+	0.829942i	$0.688373\pi$
$44$	−0.616871	+	0.448183i	−0.0929969	+	0.0675662i
$45$		0			0
$46$	−4.41761	−	3.20958i	−0.651341	−	0.473227i
$47$	8.47670	+	6.15868i	1.23645	+	0.898336i	0.997357	−	0.0726594i	$-0.0231486\pi$
$47$	8.47670	+	6.15868i	1.23645	+	0.898336i	0.239097	+	0.970996i	$0.423149\pi$
$48$	−0.588287	+	1.81056i	−0.0849120	+	0.261332i
$49$	1.00000			0.142857
$50$		0			0
$51$	4.33130			0.606503
$52$	−0.258893	+	0.796790i	−0.0359020	+	0.110495i
$53$	−4.32670	−	3.14354i	−0.594319	−	0.431798i	0.249539	−	0.968365i	$-0.419721\pi$
$53$	−4.32670	−	3.14354i	−0.594319	−	0.431798i	−0.843858	+	0.536567i	$0.819721\pi$
$54$	−3.62658	−	2.63486i	−0.493515	−	0.358559i
$55$		0			0
$56$	−2.46062	+	1.78775i	−0.328814	+	0.238898i
$57$	−1.16624			−0.154472
$58$	−6.80001	+	4.94049i	−0.892885	+	0.648719i
$59$	0.00765237	+	0.0235516i	0.000996254	+	0.00306615i	0.951553	−	0.307484i	$-0.0994869\pi$
$59$	0.00765237	+	0.0235516i	0.000996254	+	0.00306615i	−0.950557	+	0.310550i	$0.899487\pi$
$60$		0			0
$61$	−1.22115	+	3.75830i	−0.156352	+	0.481201i	−0.998295	−	0.0583644i	$-0.981411\pi$
$61$	−1.22115	+	3.75830i	−0.156352	+	0.481201i	0.841944	+	0.539565i	$0.181411\pi$
$62$	−1.92467	−	5.92354i	−0.244434	−	0.752290i
$63$	−0.801563	−	2.46696i	−0.100987	−	0.310807i
$64$	2.75030	−	8.46455i	0.343787	−	1.05807i
$65$		0			0
$66$	0.451013	+	1.38808i	0.0555159	+	0.170860i
$67$	−3.75258	+	2.72641i	−0.458450	+	0.333084i	−0.792923	−	0.609322i	$-0.791442\pi$
$67$	−3.75258	+	2.72641i	−0.458450	+	0.333084i	0.334473	+	0.942405i	$0.391442\pi$
$68$	−2.84552			−0.345070
$69$	2.23864	−	1.62647i	0.269500	−	0.195804i
$70$		0			0
$71$	−9.67307	−	7.02789i	−1.14798	−	0.834057i	−0.159770	−	0.987154i	$-0.551075\pi$
$71$	−9.67307	−	7.02789i	−1.14798	−	0.834057i	−0.988211	+	0.153097i	$0.951075\pi$
$72$	6.38263	+	4.63726i	0.752201	+	0.546506i
$73$	2.94025	−	9.04917i	0.344130	−	1.05912i	−0.617917	−	0.786243i	$-0.712023\pi$
$73$	2.94025	−	9.04917i	0.344130	−	1.05912i	0.962048	−	0.272882i	$-0.0879767\pi$
$74$	3.27262			0.380434
$75$		0			0
$76$	0.766183			0.0878872
$77$	−0.562815	+	1.73217i	−0.0641387	+	0.197399i
$78$	1.29737	+	0.942598i	0.146899	+	0.106728i
$79$	−4.03120	−	2.92884i	−0.453546	−	0.329520i	0.337448	−	0.941344i	$-0.390436\pi$
$79$	−4.03120	−	2.92884i	−0.453546	−	0.329520i	−0.790994	+	0.611824i	$0.790436\pi$
$80$		0			0
$81$	−4.45778	+	3.23876i	−0.495308	+	0.359863i
$82$	−9.28362			−1.02520
$83$	2.15797	−	1.56786i	0.236868	−	0.172095i	−0.463019	−	0.886348i	$-0.653234\pi$
$83$	2.15797	−	1.56786i	0.236868	−	0.172095i	0.699887	+	0.714254i	$0.253234\pi$
$84$	−0.0824416	−	0.253729i	−0.00899512	−	0.0276841i
$85$		0			0
$86$	2.84300	−	8.74985i	0.306569	−	0.943521i
$87$	−1.31623	−	4.05093i	−0.141114	−	0.434305i
$88$	−1.71180	−	5.26837i	−0.182478	−	0.561610i
$89$	−4.75121	+	14.6227i	−0.503628	+	1.55001i	0.299438	+	0.954116i	$0.403201\pi$
$89$	−4.75121	+	14.6227i	−0.503628	+	1.55001i	−0.803066	+	0.595890i	$0.796799\pi$
$90$		0			0
$91$	0.618395	+	1.90323i	0.0648254	+	0.199512i
$92$	−1.47071	+	1.06854i	−0.153332	+	0.111402i
$93$	3.15625			0.327288
$94$	−10.6596	+	7.74464i	−1.09945	+	0.798799i
$95$		0			0
$96$	1.19929	+	0.871337i	0.122402	+	0.0889305i
$97$	9.82821	+	7.14061i	0.997904	+	0.725019i	0.961638	−	0.274323i	$-0.0884537\pi$
$97$	9.82821	+	7.14061i	0.997904	+	0.725019i	0.0362659	+	0.999342i	$0.488454\pi$
$98$	−0.388594	+	1.19597i	−0.0392539	+	0.120811i
$99$	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	$0.738893\pi$
$102$	−1.68312	+	5.18010i	−0.166653	+	0.512906i
$103$	4.55885	+	3.31220i	0.449197	+	0.326361i	0.789279	−	0.614035i	$-0.210455\pi$
$103$	4.55885	+	3.31220i	0.449197	+	0.326361i	−0.340082	+	0.940396i	$0.610455\pi$
$104$	−4.92412	−	3.57758i	−0.482850	−	0.350811i
$105$		0			0
$106$	5.44090	−	3.95305i	0.528467	−	0.383954i
$107$	17.1093			1.65402			0.827011	−	0.562186i	$-0.190039\pi$
$107$	17.1093			1.65402			0.827011	+	0.562186i	$0.190039\pi$
$108$	−1.20736	+	0.877200i	−0.116178	+	0.0844086i
$109$	−3.94809	−	12.1510i	−0.378158	−	1.16385i	−0.941323	−	0.337507i	$-0.890416\pi$
$109$	−3.94809	−	12.1510i	−0.378158	−	1.16385i	0.563165	−	0.826345i	$-0.309584\pi$
$110$		0			0
$111$	−0.512477	+	1.57724i	−0.0486422	+	0.149705i
$112$	−0.923165	−	2.84121i	−0.0872309	−	0.268469i
$113$	−4.89173	−	15.0552i	−0.460175	−	1.41627i	−0.864951	−	0.501857i	$-0.832651\pi$
$113$	−4.89173	−	15.0552i	−0.460175	−	1.41627i	0.404776	−	0.914416i	$-0.367349\pi$
$114$	0.453194	−	1.39479i	0.0424455	−	0.130634i
$115$		0			0
$116$	0.864718	+	2.66133i	0.0802870	+	0.247098i
$117$	4.19949	−	3.05111i	0.388243	−	0.282075i
$118$	−0.0311406			−0.00286673
$119$	−5.49877	+	3.99509i	−0.504071	+	0.366229i
$120$		0			0
$121$	6.21555	+	4.51586i	0.565050	+	0.410533i
$122$	−4.02028	−	2.92091i	−0.363979	−	0.264446i
$123$	1.45377	−	4.47425i	0.131082	−	0.403429i
$124$	−2.07355			−0.186211
$125$		0			0
$126$	3.26189			0.290592
$127$	1.55649	−	4.79037i	0.138116	−	0.425077i	−0.857946	−	0.513740i	$-0.828260\pi$
$127$	1.55649	−	4.79037i	0.138116	−	0.425077i	0.996062	+	0.0886633i	$0.0282595\pi$
$128$	5.29063	+	3.84387i	0.467630	+	0.339753i
$129$	3.77180	+	2.74037i	0.332089	+	0.241276i
$130$		0			0
$131$	−3.92779	+	2.85371i	−0.343172	+	0.249329i	−0.745999	−	0.665947i	$-0.768028\pi$
$131$	−3.92779	+	2.85371i	−0.343172	+	0.249329i	0.402827	+	0.915276i	$0.368028\pi$
$132$	0.485900			0.0422922
$133$	1.48059	−	1.07571i	0.128384	−	0.0932763i
$134$	−1.80247	−	5.54743i	−0.155710	−	0.479225i
$135$		0			0
$136$	6.38818	−	19.6608i	0.547782	−	1.68590i
$137$	−3.61177	−	11.1159i	−0.308574	−	0.949693i	−0.978319	−	0.207102i	$-0.933597\pi$
$137$	−3.61177	−	11.1159i	−0.308574	−	0.949693i	0.669745	−	0.742591i	$-0.266403\pi$
$138$	1.07528	+	3.30938i	0.0915341	+	0.281713i
$139$	−3.02725	+	9.31691i	−0.256768	+	0.790250i	0.736708	+	0.676211i	$0.236379\pi$
$139$	−3.02725	+	9.31691i	−0.256768	+	0.790250i	−0.993476	+	0.114040i	$0.963621\pi$
$140$		0			0
$141$	−2.06330	−	6.35017i	−0.173761	−	0.534781i
$142$	12.1640	−	8.83769i	1.02078	−	0.741642i
$143$	−3.64474			−0.304789
$144$	−6.26917	+	4.55482i	−0.522431	+	0.379568i
$145$		0			0
$146$	9.67996	+	7.03290i	0.801119	+	0.582047i
$147$	−0.515546	−	0.374566i	−0.0425216	−	0.0308937i
$148$	0.336681	−	1.03620i	0.0276750	−	0.0851748i
$149$	21.3913			1.75245			0.876223	−	0.481907i	$-0.160056\pi$
$149$	21.3913			1.75245			0.876223	+	0.481907i	$0.160056\pi$
$150$		0			0
$151$	14.2060			1.15607			0.578034	−	0.816013i	$-0.303820\pi$
$151$	14.2060			1.15607			0.578034	+	0.816013i	$0.303820\pi$
$152$	−1.72008	+	5.29385i	−0.139517	+	0.429388i
$153$	14.2633	+	10.3629i	1.15312	+	0.837791i
$154$	−1.85291	−	1.34622i	−0.149312	−	0.108481i
$155$		0			0
$156$	0.431922	−	0.313810i	0.0345815	−	0.0251249i
$157$	−11.5228			−0.919617			−0.459809	−	0.888018i	$-0.652082\pi$
$157$	−11.5228			−0.919617			−0.459809	+	0.888018i	$0.652082\pi$
$158$	5.06930	−	3.68306i	0.403292	−	0.293009i
$159$	1.05315	+	3.24128i	0.0835206	+	0.257050i
$160$		0			0
$161$	−1.34183	+	4.12974i	−0.105751	+	0.325469i
$162$	−2.14120	−	6.58993i	−0.168228	−	0.517753i
$163$	6.67782	+	20.5522i	0.523047	+	1.60977i	0.768145	+	0.640276i	$0.221180\pi$
$163$	6.67782	+	20.5522i	0.523047	+	1.60977i	−0.245098	+	0.969498i	$0.578820\pi$
$164$	−0.955080	+	2.93943i	−0.0745792	+	0.229531i
$165$		0			0
$166$	1.03653	+	3.19012i	0.0804506	+	0.247602i
$167$	10.9921	−	7.98625i	0.850597	−	0.617995i	−0.0747138	−	0.997205i	$-0.523804\pi$
$167$	10.9921	−	7.98625i	0.850597	−	0.617995i	0.925311	+	0.379210i	$0.123804\pi$
$168$	1.93819			0.149535
$169$	7.27737	−	5.28732i	0.559798	−	0.406717i
$170$		0			0
$171$	−3.84053	−	2.79031i	−0.293693	−	0.213380i
$172$	−2.47795	−	1.80034i	−0.188942	−	0.137274i
$173$	3.22910	−	9.93814i	0.245504	−	0.755583i	−0.750049	−	0.661382i	$-0.769970\pi$
$173$	3.22910	−	9.93814i	0.245504	−	0.755583i	0.995553	−	0.0942011i	$-0.0300297\pi$
$174$	5.35626			0.406057
$175$		0			0
$176$	5.44102			0.410132
$177$	0.00487648	−	0.0150083i	0.000366538	−	0.00112809i
$178$	−15.6420	−	11.3646i	−1.17242	−	0.851813i
$179$	16.4785	+	11.9724i	1.23166	+	0.894856i	0.997014	−	0.0772241i	$-0.0246057\pi$
$179$	16.4785	+	11.9724i	1.23166	+	0.894856i	0.234650	+	0.972080i	$0.424606\pi$
$180$		0			0
$181$	8.89809	−	6.46484i	0.661390	−	0.480528i	−0.205742	−	0.978606i	$-0.565961\pi$
$181$	8.89809	−	6.46484i	0.661390	−	0.480528i	0.867132	+	0.498079i	$0.165961\pi$
$182$	−2.51650			−0.186536
$183$	2.03729	−	1.48018i	0.150601	−	0.109418i
$184$	−4.08118	−	12.5606i	−0.300869	−	0.925978i
$185$		0			0
$186$	−1.22650	+	3.77478i	−0.0899313	+	0.276780i
$187$	−3.82537	−	11.7733i	−0.279739	−	0.860947i
$188$	1.35552	+	4.17186i	0.0988614	+	0.304264i
$189$	−1.10156	+	3.39025i	−0.0801267	+	0.246605i
$190$		0			0
$191$	3.77265	+	11.6110i	0.272979	+	0.840144i	0.989747	+	0.142832i	$0.0456209\pi$
$191$	3.77265	+	11.6110i	0.272979	+	0.840144i	−0.716768	+	0.697312i	$0.754379\pi$
$192$	−4.58844	+	3.33370i	−0.331142	+	0.240589i
$193$	0.109074			0.00785131			0.00392565	−	0.999992i	$-0.498750\pi$
$193$	0.109074			0.00785131			0.00392565	+	0.999992i	$0.498750\pi$
$194$	−12.3591	+	8.97944i	−0.887334	+	0.644686i
$195$		0			0
$196$	0.338697	+	0.246078i	0.0241927	+	0.0175770i
$197$	8.21367	+	5.96758i	0.585199	+	0.425172i	0.840595	−	0.541664i	$-0.182206\pi$
$197$	8.21367	+	5.96758i	0.585199	+	0.425172i	−0.255395	+	0.966837i	$0.582206\pi$
$198$	−1.83584	+	5.65013i	−0.130467	+	0.401537i
$199$	12.7337			0.902665			0.451332	−	0.892356i	$-0.350949\pi$
$199$	12.7337			0.902665			0.451332	+	0.892356i	$0.350949\pi$
$200$		0			0
$201$	2.95585			0.208489
$202$	5.32692	−	16.3946i	0.374801	−	1.15352i
$203$	5.40749	+	3.92877i	0.379531	+	0.275746i
$204$	1.46700	+	1.06584i	0.102710	+	0.0746235i
$205$		0			0
$206$	−5.73283	+	4.16514i	−0.399425	+	0.290199i
$207$	11.2634			0.782864
$208$	4.83658	−	3.51398i	0.335357	−	0.243651i
$209$	1.03002	+	3.17006i	0.0712477	+	0.219278i
$210$		0			0
$211$	−2.42365	+	7.45922i	−0.166851	+	0.513514i	−0.999168	−	0.0407858i	$-0.987014\pi$
$211$	−2.42365	+	7.45922i	−0.166851	+	0.513514i	0.832317	+	0.554300i	$0.187014\pi$
$212$	−0.691888	−	2.12941i	−0.0475191	−	0.146249i
$213$	2.35450	+	7.24641i	0.161328	+	0.496516i
$214$	−6.64858	+	20.4622i	−0.454488	+	1.39877i
$215$		0			0
$216$	−3.35039	−	10.3114i	−0.227965	−	0.701605i
$217$	−4.00700	+	2.91125i	−0.272013	+	0.197629i
$218$	16.0664			1.08815
$219$	−4.90535	+	3.56395i	−0.331473	+	0.240829i
$220$		0			0
$221$	−11.0040	−	7.99485i	−0.740207	−	0.537792i
$222$	−1.68719	−	1.22581i	−0.113237	−	0.0822712i
$223$	−3.44466	+	10.6016i	−0.230671	+	0.709933i	0.766995	+	0.641653i	$0.221751\pi$
$223$	−3.44466	+	10.6016i	−0.230671	+	0.709933i	−0.997666	+	0.0682802i	$0.978249\pi$
$224$	−2.32626			−0.155429
$225$		0			0
$226$	19.9064			1.32416
$227$	−3.90749	+	12.0260i	−0.259349	+	0.798195i	0.733592	+	0.679590i	$0.237842\pi$
$227$	−3.90749	+	12.0260i	−0.259349	+	0.798195i	−0.992941	+	0.118605i	$0.962158\pi$
$228$	−0.395003	−	0.286986i	−0.0261597	−	0.0190061i
$229$	−7.56712	−	5.49784i	−0.500049	−	0.363307i	0.308986	−	0.951066i	$-0.400010\pi$
$229$	−7.56712	−	5.49784i	−0.500049	−	0.363307i	−0.809036	+	0.587759i	$0.800010\pi$
$230$		0			0
$231$	0.938968	−	0.682200i	0.0617796	−	0.0448855i
$232$	−20.3294			−1.33469
$233$	7.11975	−	5.17280i	0.466430	−	0.338881i	−0.329618	−	0.944114i	$-0.606920\pi$
$233$	7.11975	−	5.17280i	0.466430	−	0.338881i	0.796048	+	0.605233i	$0.206920\pi$
$234$	2.01714	+	6.20810i	0.131864	+	0.405836i
$235$		0			0
$236$	−0.00320369	+	0.00985993i	−0.000208542	+	0.000641827i
$237$	0.981227	+	3.01991i	0.0637375	+	0.196164i
$238$	−2.64121	−	8.12882i	−0.171205	−	0.526913i
$239$	−4.40737	+	13.5645i	−0.285089	+	0.877413i	0.701283	+	0.712883i	$0.252611\pi$
$239$	−4.40737	+	13.5645i	−0.285089	+	0.877413i	−0.986372	+	0.164531i	$0.947389\pi$
$240$		0			0
$241$	1.48959	+	4.58449i	0.0959531	+	0.295313i	0.987501	−	0.157613i	$-0.0503800\pi$
$241$	1.48959	+	4.58449i	0.0959531	+	0.295313i	−0.891548	+	0.452927i	$0.850380\pi$
$242$	−7.81616	+	5.67877i	−0.502442	+	0.365045i
$243$	14.2055			0.911283
$244$	−1.33843	+	0.972429i	−0.0856844	+	0.0622534i
$245$		0			0
$246$	4.78614	+	3.47733i	0.305153	+	0.221707i
$247$	2.96292	+	2.15269i	0.188526	+	0.136972i
$248$	4.65512	−	14.3270i	0.295600	−	0.909764i
$249$	−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	$0.368394\pi$
$252$	0.335576	−	1.03280i	0.0211393	−	0.0650602i
$253$	−6.39819	−	4.64855i	−0.402251	−	0.292252i
$254$	5.12430	+	3.72302i	0.321527	+	0.233603i
$255$		0			0
$256$	7.74770	−	5.62903i	0.484231	−	0.351815i
$257$	−24.5321			−1.53027			−0.765136	−	0.643869i	$-0.777328\pi$
$257$	−24.5321			−1.53027			−0.765136	+	0.643869i	$0.777328\pi$
$258$	−4.74310	+	3.44606i	−0.295293	+	0.214543i
$259$	−0.804200	−	2.47507i	−0.0499706	−	0.153794i
$260$		0			0
$261$	5.35767	−	16.4892i	0.331631	−	1.02066i
$262$	−1.88663	−	5.80645i	−0.116556	−	0.358723i
$263$	−4.76924	−	14.6782i	−0.294084	−	0.905097i	−0.983528	−	0.180758i	$-0.942145\pi$
$263$	−4.76924	−	14.6782i	−0.294084	−	0.905097i	0.689444	−	0.724339i	$-0.257855\pi$
$264$	−1.09084	+	3.35727i	−0.0671368	+	0.206626i
$265$		0			0
$266$	0.711172	+	2.18876i	0.0436047	+	0.134202i
$267$	7.92665	−	5.75905i	0.485103	−	0.352448i
$268$	−1.94190			−0.118620
$269$	−15.8633	+	11.5254i	−0.967201	+	0.702713i	−0.954812	−	0.297210i	$-0.903944\pi$
$269$	−15.8633	+	11.5254i	−0.967201	+	0.702713i	−0.0123894	+	0.999923i	$0.503944\pi$
$270$		0			0
$271$	15.4531	+	11.2273i	0.938707	+	0.682010i	0.948109	−	0.317945i	$-0.102993\pi$
$271$	15.4531	+	11.2273i	0.938707	+	0.682010i	−0.00940234	+	0.999956i	$0.502993\pi$
$272$	16.4272	+	11.9350i	0.996042	+	0.723667i
$273$	0.394073	−	1.21283i	0.0238504	−	0.0734039i
$274$	14.6977			0.887923
$275$		0			0
$276$	1.15846			0.0697310
$277$	0.796404	−	2.45108i	0.0478513	−	0.147271i	−0.924276	−	0.381725i	$-0.875330\pi$
$277$	0.796404	−	2.45108i	0.0478513	−	0.147271i	0.972127	+	0.234454i	$0.0753302\pi$
$278$	−9.96637	−	7.24099i	−0.597743	−	0.434286i
$279$	10.3938	+	7.55153i	0.622260	+	0.452098i
$280$		0			0
$281$	11.4849	−	8.34424i	0.685129	−	0.497776i	−0.189926	−	0.981798i	$-0.560825\pi$
$281$	11.4849	−	8.34424i	0.685129	−	0.497776i	0.875055	+	0.484023i	$0.160825\pi$
$282$	8.39640			0.499998
$283$	16.5528	−	12.0263i	0.983961	−	0.714889i	0.0253705	−	0.999678i	$-0.491923\pi$
$283$	16.5528	−	12.0263i	0.983961	−	0.714889i	0.958590	+	0.284789i	$0.0919234\pi$
$284$	−1.54683	−	4.76066i	−0.0917875	−	0.282493i
$285$		0			0
$286$	1.41632	−	4.35900i	0.0837490	−	0.257753i
$287$	2.28132	+	7.02118i	0.134662	+	0.414447i
$288$	1.86464	+	5.73877i	0.109875	+	0.338160i
$289$	9.02243	−	27.7682i	0.530731	−	1.63342i
$290$		0			0
$291$	−2.39227	−	7.36264i	−0.140237	−	0.431605i
$292$	3.22265	−	2.34140i	0.188592	−	0.137020i
$293$	−8.06270			−0.471028			−0.235514	−	0.971871i	$-0.575677\pi$
$293$	−8.06270			−0.471028			−0.235514	+	0.971871i	$0.575677\pi$
$294$	0.648308	−	0.471023i	0.0378101	−	0.0274706i
$295$		0			0
$296$	6.40364	+	4.65251i	0.372204	+	0.270422i
$297$	−5.25251	−	3.81617i	−0.304781	−	0.221437i
$298$	−8.31254	+	25.5834i	−0.481532	+	1.48200i
$299$	−8.68961			−0.502533
$300$		0			0
$301$	−7.31612			−0.421694
$302$	−5.52036	+	16.9899i	−0.317661	+	0.977661i
$303$	7.06721	+	5.13463i	0.406000	+	0.294977i
$304$	−4.42316	−	3.21362i	−0.253686	−	0.184314i
$305$		0			0
$306$	−17.9364	+	13.0315i	−1.02535	+	0.744963i
$307$	9.08866			0.518717			0.259359	−	0.965781i	$-0.416489\pi$
$307$	9.08866			0.518717			0.259359	+	0.965781i	$0.416489\pi$
$308$	−0.616871	+	0.448183i	−0.0351495	+	0.0255376i
$309$	−1.10966	−	3.41518i	−0.0631264	−	0.194283i
$310$		0			0
$311$	−8.21191	+	25.2737i	−0.465655	+	1.43314i	0.392502	+	0.919751i	$0.371610\pi$
$311$	−8.21191	+	25.2737i	−0.465655	+	1.43314i	−0.858157	+	0.513387i	$0.828390\pi$
$312$	1.19857	+	3.68882i	0.0678557	+	0.208838i
$313$	−2.65046	−	8.15727i	−0.149813	−	0.461076i	0.847786	−	0.530339i	$-0.177935\pi$
$313$	−2.65046	−	8.15727i	−0.149813	−	0.461076i	−0.997598	+	0.0692627i	$0.977935\pi$
$314$	4.47768	−	13.7809i	0.252690	−	0.777700i
$315$		0			0
$316$	−0.644634	−	1.98398i	−0.0362635	−	0.111608i
$317$	4.80116	−	3.48825i	0.269660	−	0.195919i	−0.444735	−	0.895662i	$-0.646702\pi$
$317$	4.80116	−	3.48825i	0.269660	−	0.195919i	0.714395	+	0.699743i	$0.246702\pi$
$318$	−4.28572			−0.240331
$319$	−9.84870	+	7.15550i	−0.551421	+	0.400631i
$320$		0			0
$321$	−8.82066	−	6.40858i	−0.492321	−	0.357692i
$322$	−4.41761	−	3.20958i	−0.246184	−	0.178863i
$323$	−3.84387	+	11.8302i	−0.213879	+	0.658251i
$324$	−2.30682			−0.128157
$325$		0			0
$326$	−27.1748			−1.50507
$327$	−2.51592	+	7.74321i	−0.139131	+	0.428200i
$328$	−18.1655	−	13.1980i	−1.00302	−	0.728740i
$329$	8.47670	+	6.15868i	0.467336	+	0.339539i
$330$		0			0
$331$	12.5077	−	9.08737i	0.687485	−	0.499487i	−0.188348	−	0.982102i	$-0.560313\pi$
$331$	12.5077	−	9.08737i	0.687485	−	0.499487i	0.875832	+	0.482616i	$0.160313\pi$
$332$	1.11671			0.0612876
$333$	−5.46128	+	3.96785i	−0.299276	+	0.217437i
$334$	5.27983	+	16.2497i	0.288900	+	0.889142i
$335$		0			0
$336$	−0.588287	+	1.81056i	−0.0320937	+	0.0987743i
$337$	−4.60243	−	14.1648i	−0.250711	−	0.771608i	−0.994645	−	0.103355i	$-0.967042\pi$
$337$	−4.60243	−	14.1648i	−0.250711	−	0.771608i	0.743934	−	0.668253i	$-0.232958\pi$
$338$	3.49553	+	10.7581i	0.190132	+	0.585165i
$339$	−3.11725	+	9.59392i	−0.169306	+	0.521070i
$340$		0			0
$341$	−2.78758	−	8.57928i	−0.150956	−	0.464594i
$342$	4.82953	−	3.50886i	0.261151	−	0.189737i
$343$	1.00000			0.0539949
$344$	18.0022	−	13.0794i	0.970614	−	0.705192i
$345$		0			0
$346$	10.6309	+	7.72380i	0.571521	+	0.415234i
$347$	−11.5781	−	8.41195i	−0.621543	−	0.451577i	0.231917	−	0.972736i	$-0.425500\pi$
$347$	−11.5781	−	8.41195i	−0.621543	−	0.451577i	−0.853460	+	0.521158i	$0.825500\pi$
$348$	0.551042	−	1.69593i	0.0295389	−	0.0909115i
$349$	−3.94565			−0.211206			−0.105603	−	0.994408i	$-0.533677\pi$
$349$	−3.94565			−0.211206			−0.105603	+	0.994408i	$0.533677\pi$
$350$		0			0
$351$	−7.13361			−0.380764
$352$	1.30925	−	4.02946i	0.0697833	−	0.214771i
$353$	7.32432	+	5.32143i	0.389834	+	0.283231i	0.765388	−	0.643570i	$-0.222547\pi$
$353$	7.32432	+	5.32143i	0.389834	+	0.283231i	−0.375553	+	0.926801i	$0.622547\pi$
$354$	0.0160544	+	0.0116642i	0.000853284	+	0.000619947i
$355$		0			0
$356$	−5.20755	+	3.78351i	−0.276000	+	0.200526i
$357$	4.33130			0.229237
$358$	−20.7220	+	15.0554i	−1.09519	+	0.795704i
$359$	−11.3472	−	34.9232i	−0.598885	−	1.84318i	−0.534353	−	0.845261i	$-0.679445\pi$
$359$	−11.3472	−	34.9232i	−0.598885	−	1.84318i	−0.0645314	−	0.997916i	$-0.520555\pi$
$360$		0			0
$361$	−4.83633	+	14.8847i	−0.254543	+	0.783404i
$362$	4.27400	+	13.1540i	0.224637	+	0.691361i
$363$	−1.51291	−	4.65627i	−0.0794074	−	0.244391i
$364$	−0.258893	+	0.796790i	−0.0135697	+	0.0417632i
$365$		0			0
$366$	0.978569	+	3.01172i	0.0511506	+	0.157425i
$367$	12.7081	−	9.23299i	0.663358	−	0.481958i	−0.204437	−	0.978880i	$-0.565536\pi$
$367$	12.7081	−	9.23299i	0.663358	−	0.481958i	0.867795	+	0.496922i	$0.165536\pi$
$368$	12.9722			0.676222
$369$	15.4923	−	11.2558i	0.806498	−	0.585955i
$370$		0			0
$371$	−4.32670	−	3.14354i	−0.224631	−	0.163204i
$372$	1.06901	+	0.776683i	0.0554257	+	0.0402692i
$373$	−2.90928	+	8.95386i	−0.150637	+	0.463613i	−0.997693	−	0.0678910i	$-0.978373\pi$
$373$	−2.90928	+	8.95386i	−0.150637	+	0.463613i	0.847056	+	0.531504i	$0.178373\pi$
$374$	15.5670			0.804949
$375$		0			0
$376$	−31.8681			−1.64347
$377$	−4.13337	+	12.7212i	−0.212879	+	0.655175i
$378$	−3.62658	−	2.63486i	−0.186531	−	0.135523i
$379$	−25.3574	−	18.4232i	−1.30252	−	0.946339i	−0.302546	−	0.953135i	$-0.597837\pi$
$379$	−25.3574	−	18.4232i	−1.30252	−	0.946339i	−0.999977	+	0.00679612i	$0.997837\pi$
$380$		0			0
$381$	−2.59675	+	1.88665i	−0.133036	+	0.0966561i
$382$	−15.3525			−0.785500
$383$	14.5472	−	10.5691i	0.743326	−	0.540058i	−0.150425	−	0.988621i	$-0.548064\pi$
$383$	14.5472	−	10.5691i	0.743326	−	0.540058i	0.893751	+	0.448564i	$0.148064\pi$
$384$	−1.28778	−	3.96338i	−0.0657168	−	0.202256i
$385$		0			0
$386$	−0.0423854	+	0.130449i	−0.00215736	+	0.00663968i
$387$	5.86433	+	18.0486i	0.298101	+	0.917460i
$388$	1.57164	+	4.83701i	0.0797879	+	0.245562i
$389$	−2.87435	+	8.84634i	−0.145735	+	0.448527i	−0.997105	−	0.0760391i	$-0.975773\pi$
$389$	−2.87435	+	8.84634i	−0.145735	+	0.448527i	0.851369	+	0.524567i	$0.175773\pi$
$390$		0			0
$391$	−9.12024	−	28.0692i	−0.461230	−	1.41952i
$392$	−2.46062	+	1.78775i	−0.124280	+	0.0902948i
$393$	3.09386			0.156065
$394$	−10.3288	+	7.50433i	−0.520358	+	0.378062i
$395$		0			0
$396$	1.60011	+	1.16255i	0.0804086	+	0.0584202i
$397$	−1.17280	−	0.852092i	−0.0588613	−	0.0427653i	0.557966	−	0.829864i	$-0.311582\pi$
$397$	−1.17280	−	0.852092i	−0.0588613	−	0.0427653i	−0.616827	+	0.787099i	$0.711582\pi$
$398$	−4.94822	+	15.2291i	−0.248032	+	0.763364i
$399$	−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	$0.555320\pi$
$402$	−1.14862	+	3.53510i	−0.0572882	+	0.176315i
$403$	−8.01868	−	5.82591i	−0.399439	−	0.290209i
$404$	−4.64292	−	3.37328i	−0.230994	−	0.167827i
$405$		0			0
$406$	−6.80001	+	4.94049i	−0.337479	+	0.245193i
$407$	4.73985			0.234946
$408$	−10.6577	+	7.74326i	−0.527634	+	0.383348i
$409$	−3.37811	−	10.3967i	−0.167037	−	0.514086i	0.832144	−	0.554560i	$-0.187113\pi$
$409$	−3.37811	−	10.3967i	−0.167037	−	0.514086i	−0.999181	+	0.0404736i	$0.987113\pi$
$410$		0			0
$411$	−2.30160	+	7.08359i	−0.113530	+	0.349408i
$412$	0.729011	+	2.24366i	0.0359158	+	0.110537i
$413$	0.00765237	+	0.0235516i	0.000376548	+	0.00115890i
$414$	−4.37691	+	13.4707i	−0.215113	+	0.662051i
$415$		0			0
$416$	−1.43855	−	4.42739i	−0.0705305	−	0.217071i
$417$	5.05049	−	3.66940i	0.247324	−	0.179691i
$418$	−4.19155			−0.205016
$419$	8.78555	−	6.38307i	0.429202	−	0.311834i	−0.352128	−	0.935952i	$-0.614542\pi$
$419$	8.78555	−	6.38307i	0.429202	−	0.311834i	0.781330	+	0.624118i	$0.214542\pi$
$420$		0			0
$421$	−15.7391	−	11.4351i	−0.767076	−	0.557313i	0.133996	−	0.990982i	$-0.457219\pi$
$421$	−15.7391	−	11.4351i	−0.767076	−	0.557313i	−0.901073	+	0.433668i	$0.857219\pi$
$422$	−7.97918	−	5.79722i	−0.388421	−	0.282204i
$423$	8.39860	−	25.8482i	0.408354	−	1.25678i
$424$	16.2662			0.789958
$425$		0			0
$426$	−9.58143			−0.464222
$427$	−1.22115	+	3.75830i	−0.0590954	+	0.181877i
$428$	5.79488	+	4.21023i	0.280106	+	0.203509i
$429$	1.87903	+	1.36520i	0.0907206	+	0.0659124i
$430$		0			0
$431$	−4.14273	+	3.00987i	−0.199548	+	0.144980i	−0.683072	−	0.730351i	$-0.739357\pi$
$431$	−4.14273	+	3.00987i	−0.199548	+	0.144980i	0.483524	+	0.875331i	$0.339357\pi$
$432$	10.6493			0.512367
$433$	−11.2738	+	8.19091i	−0.541785	+	0.393630i	−0.824748	−	0.565501i	$-0.808683\pi$
$433$	−11.2738	+	8.19091i	−0.541785	+	0.393630i	0.282962	+	0.959131i	$0.408683\pi$
$434$	−1.92467	−	5.92354i	−0.0923873	−	0.284339i
$435$		0			0
$436$	1.65288	−	5.08704i	0.0791585	−	0.243625i
$437$	2.45571	+	7.55790i	0.117473	+	0.361543i
$438$	−2.35618	−	7.25157i	−0.112583	−	0.346494i
$439$	8.46126	−	26.0411i	0.403834	−	1.24287i	−0.518031	−	0.855362i	$-0.673335\pi$
$439$	8.46126	−	26.0411i	0.403834	−	1.24287i	0.921865	−	0.387511i	$-0.126665\pi$
$440$		0			0
$441$	−0.801563	−	2.46696i	−0.0381697	−	0.117474i
$442$	13.8377	−	10.0537i	0.658191	−	0.478204i
$443$	−39.3336			−1.86880			−0.934399	−	0.356228i	$-0.884063\pi$
$443$	−39.3336			−1.86880			−0.934399	+	0.356228i	$0.884063\pi$
$444$	−0.561699	+	0.408098i	−0.0266571	+	0.0193675i
$445$		0			0
$446$	−11.3406	−	8.23941i	−0.536992	−	0.390147i
$447$	−11.0282	−	8.01247i	−0.521617	−	0.378977i
$448$	2.75030	−	8.46455i	0.129939	−	0.399912i
$449$	−28.2960			−1.33537			−0.667685	−	0.744444i	$-0.732715\pi$
$449$	−28.2960			−1.33537			−0.667685	+	0.744444i	$0.732715\pi$
$450$		0			0
$451$	−13.4458			−0.633138
$452$	2.04793	−	6.30289i	0.0963267	−	0.296463i
$453$	−7.32385	−	5.32109i	−0.344105	−	0.250007i
$454$	−12.8643	−	9.34648i	−0.603753	−	0.438652i
$455$		0			0
$456$	2.86968	−	2.08494i	0.134385	−	0.0976365i
$457$	−7.27936			−0.340514			−0.170257	−	0.985400i	$-0.554460\pi$
$457$	−7.27936			−0.340514			−0.170257	+	0.985400i	$0.554460\pi$
$458$	9.51578	−	6.91362i	0.444643	−	0.323052i
$459$	−7.48714	−	23.0430i	−0.349470	−	1.07556i
$460$		0			0
$461$	1.83293	−	5.64118i	0.0853682	−	0.262736i	−0.899256	−	0.437423i	$-0.855891\pi$
$461$	1.83293	−	5.64118i	0.0853682	−	0.262736i	0.984624	+	0.174687i	$0.0558913\pi$
$462$	0.451013	+	1.38808i	0.0209830	+	0.0645791i
$463$	4.32543	+	13.3123i	0.201020	+	0.618675i	0.999853	+	0.0171231i	$0.00545073\pi$
$463$	4.32543	+	13.3123i	0.201020	+	0.618675i	−0.798834	+	0.601552i	$0.794549\pi$
$464$	6.17046	−	18.9907i	0.286456	−	0.881622i
$465$		0			0
$466$	3.41982	+	10.5251i	0.158420	+	0.487567i
$467$	3.75874	−	2.73088i	0.173934	−	0.126370i	−0.497413	−	0.867514i	$-0.665716\pi$
$467$	3.75874	−	2.73088i	0.173934	−	0.126370i	0.671346	+	0.741144i	$0.265716\pi$
$468$	2.17317			0.100455
$469$	−3.75258	+	2.72641i	−0.173278	+	0.125894i
$470$		0			0
$471$	5.94052	+	4.31604i	0.273725	+	0.198873i
$472$	−0.0609338	−	0.0442710i	−0.00280471	−	0.00203774i
$473$	4.11762	−	12.6727i	0.189328	−	0.582693i
$474$	−3.99301			−0.183405
$475$		0			0
$476$	−2.84552			−0.130424
$477$	−4.28684	+	13.1935i	−0.196281	+	0.604090i
$478$	−14.5100	−	10.5422i	−0.663673	−	0.482187i
$479$	−11.1567	−	8.10585i	−0.509765	−	0.370366i	0.302970	−	0.953000i	$-0.402022\pi$
$479$	−11.1567	−	8.10585i	−0.509765	−	0.370366i	−0.812734	+	0.582634i	$0.802022\pi$
$480$		0			0
$481$	4.21331	−	3.06115i	0.192110	−	0.139576i
$482$	−6.06176			−0.276106
$483$	2.23864	−	1.62647i	0.101862	−	0.0740068i
$484$	0.993936	+	3.05902i	0.0451789	+	0.139046i
$485$		0			0
$486$	−5.52017	+	16.9893i	−0.250400	+	0.770652i
$487$	8.56642	+	26.3647i	0.388182	+	1.19470i	0.934146	+	0.356891i	$0.116163\pi$
$487$	8.56642	+	26.3647i	0.388182	+	1.19470i	−0.545964	+	0.837808i	$0.683837\pi$
$488$	−3.71411	−	11.4309i	−0.168130	−	0.517450i
$489$	4.25544	−	13.0969i	0.192438	−	0.592263i
$490$		0			0
$491$	9.25639	+	28.4882i	0.417735	+	1.28566i	0.909781	+	0.415088i	$0.136249\pi$
$491$	9.25639	+	28.4882i	0.417735	+	1.28566i	−0.492046	+	0.870569i	$0.663751\pi$
$492$	1.59340	−	1.15767i	0.0718361	−	0.0521920i
$493$	−45.4303			−2.04608
$494$	−3.72592	+	2.70704i	−0.167637	+	0.121795i
$495$		0			0
$496$	11.9706	+	8.69715i	0.537496	+	0.390513i
$497$	−9.67307	−	7.02789i	−0.433896	−	0.315244i
$498$	0.660532	−	2.03291i	0.0295991	−	0.0910967i
$499$	13.0499			0.584196			0.292098	−	0.956388i	$-0.405647\pi$
$499$	13.0499			0.584196			0.292098	+	0.956388i	$0.405647\pi$
$500$		0			0
$501$	−8.65834			−0.386826
$502$	−4.94704	+	15.2254i	−0.220797	+	0.679543i
$503$	30.4892	+	22.1517i	1.35945	+	0.987696i	0.998480	+	0.0551174i	$0.0175533\pi$
$503$	30.4892	+	22.1517i	1.35945	+	0.987696i	0.360967	+	0.932579i	$0.382447\pi$
$504$	6.38263	+	4.63726i	0.284305	+	0.206560i
$505$		0			0
$506$	8.04582	−	5.84563i	0.357681	−	0.259870i
$507$	−5.73227			−0.254579
$508$	1.70598	−	1.23947i	0.0756908	−	0.0549925i
$509$	13.0535	+	40.1745i	0.578585	+	1.78070i	0.623633	+	0.781717i	$0.285656\pi$
$509$	13.0535	+	40.1745i	0.578585	+	1.78070i	−0.0450483	+	0.998985i	$0.514344\pi$
$510$		0			0
$511$	2.94025	−	9.04917i	0.130069	−	0.400312i
$512$	7.76312	+	23.8924i	0.343085	+	1.05591i
$513$	2.01598	+	6.20455i	0.0890078	+	0.273938i
$514$	9.53303	−	29.3397i	0.420484	−	1.29412i
$515$		0			0
$516$	0.603153	+	1.85631i	0.0265523	+	0.0817196i
$517$	−15.4387	+	11.2168i	−0.678992	+	0.493316i
$518$	3.27262			0.143791
$519$	−5.38724	+	3.91406i	−0.236474	+	0.171808i
$520$		0			0
$521$	−19.0355	−	13.8301i	−0.833962	−	0.605909i	0.0867152	−	0.996233i	$-0.472363\pi$
$521$	−19.0355	−	13.8301i	−0.833962	−	0.605909i	−0.920678	+	0.390324i	$0.872363\pi$
$522$	17.6386	+	12.8152i	0.772021	+	0.560906i
$523$	−6.07159	+	18.6864i	−0.265492	+	0.817100i	0.726088	+	0.687602i	$0.241337\pi$
$523$	−6.07159	+	18.6864i	−0.265492	+	0.817100i	−0.991580	+	0.129498i	$0.958663\pi$
$524$	−2.03256			−0.0887930
$525$		0			0
$526$	19.4080			0.846228
$527$	10.4028	−	32.0166i	0.453154	−	1.39467i
$528$	−2.80510	−	2.03802i	−0.122076	−	0.0886935i
$529$	3.35317	+	2.43622i	0.145790	+	0.105923i
$530$		0			0
$531$	0.0519669	−	0.0377561i	0.00225517	−	0.00163848i
$532$	0.766183			0.0332182
$533$	−11.9521	+	8.68373i	−0.517704	+	0.376134i
$534$	3.80740	+	11.7180i	0.164762	+	0.507086i
$535$		0			0
$536$	4.35955	−	13.4173i	0.188304	−	0.579539i
$537$	−4.01101	−	12.3446i	−0.173088	−	0.532709i
$538$	−7.61959	−	23.4507i	−0.328504	−	1.01103i
$539$	−0.562815	+	1.73217i	−0.0242421	+	0.0746096i
$540$		0			0
$541$	−11.0526	−	34.0164i	−0.475189	−	1.46248i	−0.845703	−	0.533654i	$-0.820818\pi$
$541$	−11.0526	−	34.0164i	−0.475189	−	1.46248i	0.370514	−	0.928827i	$-0.379182\pi$
$542$	−19.4325	+	14.1185i	−0.834696	+	0.606442i
$543$	−7.00889			−0.300780
$544$	12.7915	−	9.29360i	0.548433	−	0.398460i
$545$		0			0
$546$	1.29737	+	0.942598i	0.0555225	+	0.0403395i
$547$	16.2542	+	11.8094i	0.694979	+	0.504932i	0.878293	−	0.478123i	$-0.158683\pi$
$547$	16.2542	+	11.8094i	0.694979	+	0.504932i	−0.183314	+	0.983054i	$0.558683\pi$
$548$	1.51208	−	4.65369i	0.0645927	−	0.198796i
$549$	10.2504			0.437476
$550$		0			0
$551$	12.2325			0.521123
$552$	−2.60073	+	8.00424i	−0.110695	+	0.340683i
$553$	−4.03120	−	2.92884i	−0.171424	−	0.124547i
$554$	2.62194	+	1.90495i	0.111395	+	0.0809335i
$555$		0			0
$556$	−3.31801	+	2.41067i	−0.140715	+	0.102235i
$557$	−10.2545			−0.434498			−0.217249	−	0.976116i	$-0.569708\pi$
$557$	−10.2545			−0.434498			−0.217249	+	0.976116i	$0.569708\pi$
$558$	−13.0704	+	9.49618i	−0.553313	+	0.402005i
$559$	−4.52426	−	13.9242i	−0.191356	−	0.588932i
$560$		0			0
$561$	−2.43772	+	7.50252i	−0.102921	+	0.316757i
$562$	5.51651	+	16.9781i	0.232700	+	0.716176i
$563$	11.6845	+	35.9613i	0.492445	+	1.51559i	0.820901	+	0.571070i	$0.193472\pi$
$563$	11.6845	+	35.9613i	0.492445	+	1.51559i	−0.328456	+	0.944519i	$0.606528\pi$
$564$	0.863805	−	2.65852i	0.0363727	−	0.111944i
$565$		0			0
$566$	7.95077	+	24.4700i	0.334196	+	1.02855i
$567$	−4.45778	+	3.23876i	−0.187209	+	0.136015i
$568$	36.3658			1.52588
$569$	18.6504	−	13.5503i	0.781866	−	0.568059i	−0.123673	−	0.992323i	$-0.539467\pi$
$569$	18.6504	−	13.5503i	0.781866	−	0.568059i	0.905538	+	0.424264i	$0.139467\pi$
$570$		0			0
$571$	32.3796	+	23.5252i	1.35505	+	0.984498i	0.998743	+	0.0501274i	$0.0159627\pi$
$571$	32.3796	+	23.5252i	1.35505	+	0.984498i	0.356303	+	0.934371i	$0.384037\pi$
$572$	−1.23446	−	0.896891i	−0.0516155	−	0.0375009i
$573$	2.40412	−	7.39913i	0.100434	−	0.309103i
$574$	−9.28362			−0.387491
$575$		0			0
$576$	−23.0862			−0.961926
$577$	6.67353	−	20.5390i	0.277823	−	0.855050i	−0.710636	−	0.703560i	$-0.751593\pi$
$577$	6.67353	−	20.5390i	0.277823	−	0.855050i	0.988459	−	0.151490i	$-0.0484072\pi$
$578$	29.7038	+	21.5811i	1.23552	+	0.897655i
$579$	−0.0562327	−	0.0408554i	−0.00233695	−	0.00169789i
$580$		0			0
$581$	2.15797	−	1.56786i	0.0895276	−	0.0650456i
$582$	9.73510			0.403533
$583$	7.88026	−	5.72534i	0.326367	−	0.237119i
$584$	8.94276	+	27.5230i	0.370054	+	1.13891i
$585$		0			0
$586$	3.13312	−	9.64274i	0.129428	−	0.398338i
$587$	−0.558710	−	1.71953i	−0.0230604	−	0.0709727i	0.938864	−	0.344288i	$-0.111880\pi$
$587$	−0.558710	−	1.71953i	−0.0230604	−	0.0709727i	−0.961924	+	0.273315i	$0.911880\pi$
$588$	−0.0824416	−	0.253729i	−0.00339983	−	0.0104636i
$589$	−2.80106	+	8.62077i	−0.115416	+	0.355213i
$590$		0			0
$591$	−1.99927	−	6.15313i	−0.0822391	−	0.253106i
$592$	−6.28979	+	4.56980i	−0.258509	+	0.187818i
$593$	−38.4929			−1.58071			−0.790356	−	0.612648i	$-0.790104\pi$
$593$	−38.4929			−1.58071			−0.790356	+	0.612648i	$0.790104\pi$
$594$	6.60511	−	4.79889i	0.271011	−	0.196901i
$595$		0			0
$596$	7.24518	+	5.26393i	0.296774	+	0.215619i
$597$	−6.56479	−	4.76960i	−0.268679	−	0.195207i
$598$	3.37673	−	10.3925i	0.138085	−	0.424981i
$599$	−31.7681			−1.29801			−0.649005	−	0.760784i	$-0.724815\pi$
$599$	−31.7681			−1.29801			−0.649005	+	0.760784i	$0.724815\pi$
$600$		0			0
$601$	19.1855			0.782592			0.391296	−	0.920265i	$-0.372027\pi$
$601$	19.1855			0.782592			0.391296	+	0.920265i	$0.372027\pi$
$602$	2.84300	−	8.74985i	0.115872	−	0.356617i
$603$	9.73385	+	7.07206i	0.396393	+	0.287996i
$604$	4.81153	+	3.49578i	0.195778	+	0.142241i
$605$		0			0
$606$	−8.88713	+	6.45688i	−0.361015	+	0.262293i
$607$	−35.5410			−1.44256			−0.721282	−	0.692641i	$-0.756447\pi$
$607$	−35.5410			−1.44256			−0.721282	+	0.692641i	$0.756447\pi$
$608$	−3.44424	+	2.50239i	−0.139682	+	0.101485i
$609$	−1.31623	−	4.05093i	−0.0533362	−	0.164152i
$610$		0			0
$611$	−6.47941	+	19.9416i	−0.262129	+	0.806750i
$612$	2.28086	+	7.01978i	0.0921984	+	0.283758i
$613$	−1.24587	−	3.83439i	−0.0503201	−	0.154869i	0.922739	−	0.385426i	$-0.125945\pi$
$613$	−1.24587	−	3.83439i	−0.0503201	−	0.154869i	−0.973059	+	0.230556i	$0.925945\pi$
$614$	−3.53180	+	10.8698i	−0.142532	+	0.438667i
$615$		0			0
$616$	−1.71180	−	5.26837i	−0.0689703	−	0.212269i
$617$	26.4805	−	19.2392i	1.06606	−	0.774542i	0.0908641	−	0.995863i	$-0.471037\pi$
$617$	26.4805	−	19.2392i	1.06606	−	0.774542i	0.975201	+	0.221322i	$0.0710371\pi$
$618$	4.51566			0.181647
$619$	−38.9974	+	28.3333i	−1.56744	+	1.13881i	−0.637882	+	0.770134i	$0.720189\pi$
$619$	−38.9974	+	28.3333i	−1.56744	+	1.13881i	−0.929557	+	0.368678i	$0.879811\pi$
$620$		0			0
$621$	−12.5227	−	9.09831i	−0.502521	−	0.365103i
$622$	−27.0354	−	19.6424i	−1.08402	−	0.787588i
$623$	−4.75121	+	14.6227i	−0.190353	+	0.585847i
$624$	−3.80970			−0.152510
$625$		0			0
$626$	10.7858			0.431087
$627$	0.656378	−	2.02012i	0.0262132	−	0.0806760i
$628$	−3.90273	−	2.83550i	−0.155736	−	0.113149i
$629$	14.3103	+	10.3970i	0.570587	+	0.414556i
$630$		0			0
$631$	−11.9008	+	8.64644i	−0.473764	+	0.344209i	−0.798906	−	0.601456i	$-0.794588\pi$
$631$	−11.9008	+	8.64644i	−0.473764	+	0.344209i	0.325143	+	0.945665i	$0.394588\pi$
$632$	15.1553			0.602845
$633$	4.04348	−	2.93776i	0.160714	−	0.116765i
$634$	2.30613	+	7.09755i	0.0915883	+	0.281880i
$635$		0			0
$636$	−0.440906	+	1.35697i	−0.0174831	+	0.0538073i
$637$	0.618395	+	1.90323i	0.0245017	+	0.0754085i
$638$	−4.73061	−	14.5593i	−0.187287	−	0.576409i
$639$	−9.58394	+	29.4963i	−0.379135	+	1.16686i
$640$		0			0
$641$	−1.67552	−	5.15671i	−0.0661789	−	0.203678i	0.912499	−	0.409079i	$-0.134150\pi$
$641$	−1.67552	−	5.15671i	−0.0661789	−	0.203678i	−0.978678	+	0.205401i	$0.934150\pi$
$642$	11.0921	−	8.05890i	0.437771	−	0.318059i
$643$	41.4190			1.63341			0.816703	−	0.577058i	$-0.195799\pi$
$643$	41.4190			1.63341			0.816703	+	0.577058i	$0.195799\pi$
$644$	−1.47071	+	1.06854i	−0.0579542	+	0.0421062i
$645$		0			0
$646$	−12.6549	−	9.19430i	−0.497899	−	0.361745i
$647$	4.59430	+	3.33796i	0.180621	+	0.131229i	0.674422	−	0.738346i	$-0.264393\pi$
$647$	4.59430	+	3.33796i	0.180621	+	0.131229i	−0.493801	+	0.869575i	$0.664393\pi$
$648$	5.17881	−	15.9387i	0.203443	−	0.626133i
$649$	−0.0451021			−0.00177041
$650$		0			0
$651$	3.15625			0.123703
$652$	−2.79569	+	8.60424i	−0.109488	+	0.336968i
$653$	1.18418	+	0.860358i	0.0463406	+	0.0336684i	0.610714	−	0.791851i	$-0.290882\pi$
$653$	1.18418	+	0.860358i	0.0463406	+	0.0336684i	−0.564374	+	0.825519i	$0.690882\pi$
$654$	−8.28297	−	6.01793i	−0.323890	−	0.235320i
$655$		0			0
$656$	17.8426	−	12.9634i	0.696636	−	0.506136i
$657$	−24.6807			−0.962886
$658$	−10.6596	+	7.74464i	−0.415554	+	0.301918i
$659$	0.998646	+	3.07352i	0.0389017	+	0.119727i	0.968621	−	0.248541i	$-0.0799509\pi$
$659$	0.998646	+	3.07352i	0.0389017	+	0.119727i	−0.929720	+	0.368268i	$0.879951\pi$
$660$		0			0
$661$	−5.66903	+	17.4475i	−0.220500	+	0.678628i	0.778218	+	0.627995i	$0.216124\pi$
$661$	−5.66903	+	17.4475i	−0.220500	+	0.678628i	−0.998717	+	0.0506336i	$0.983876\pi$
$662$	6.00780	+	18.4901i	0.233500	+	0.718638i
$663$	2.67845	+	8.24343i	0.104023	+	0.320148i
$664$	−2.50701	+	7.71580i	−0.0972910	+	0.299431i
$665$		0			0
$666$	−2.62321	−	8.07341i	−0.101647	−	0.312838i
$667$	−23.4807	+	17.0598i	−0.909178	+	0.660557i
$668$	5.68824			0.220085
$669$	5.74687	−	4.17535i	0.222187	−	0.161428i
$670$		0			0
$671$	−5.82272	−	4.23045i	−0.224784	−	0.163315i
$672$	1.19929	+	0.871337i	0.0462637	+	0.0336126i
$673$	−2.38694	+	7.34626i	−0.0920100	+	0.283178i	−0.986463	−	0.163985i	$-0.947565\pi$
$673$	−2.38694	+	7.34626i	−0.0920100	+	0.283178i	0.894453	+	0.447162i	$0.147565\pi$
$674$	18.7292			0.721421
$675$		0			0
$676$	3.76592			0.144843
$677$	−7.11702	+	21.9039i	−0.273529	+	0.841837i	0.716075	+	0.698023i	$0.245937\pi$
$677$	−7.11702	+	21.9039i	−0.273529	+	0.841837i	−0.989605	+	0.143814i	$0.954063\pi$
$678$	−10.2627	−	7.45628i	−0.394136	−	0.286357i
$679$	9.82821	+	7.14061i	0.377172	+	0.274032i
$680$		0			0
$681$	6.51904	−	4.73636i	0.249810	−	0.181498i
$682$	11.3438			0.434376
$683$	−28.6613	+	20.8236i	−1.09669	+	0.796794i	−0.980517	−	0.196435i	$-0.937064\pi$
$683$	−28.6613	+	20.8236i	−1.09669	+	0.796794i	−0.116176	+	0.993229i	$0.537064\pi$
$684$	−0.614144	−	1.89014i	−0.0234824	−	0.0722713i
$685$		0			0
$686$	−0.388594	+	1.19597i	−0.0148366	+	0.0456623i
$687$	1.84190	+	5.66878i	0.0702728	+	0.216277i
$688$	6.75399	+	20.7866i	0.257493	+	0.792483i
$689$	3.30724	−	10.1786i	0.125996	−	0.387775i
$690$		0			0
$691$	2.98865	+	9.19813i	0.113694	+	0.349913i	0.991672	−	0.128786i	$-0.0411082\pi$
$691$	2.98865	+	9.19813i	0.113694	+	0.349913i	−0.877979	+	0.478700i	$0.841108\pi$
$692$	3.53924	−	2.57141i	0.134542	−	0.0977504i
$693$	4.72431			0.179462
$694$	14.5596	−	10.5782i	0.552675	−	0.401542i
$695$		0			0
$696$	10.4808	+	7.61472i	0.397272	+	0.288635i
$697$	−40.5947	−	29.4938i	−1.53763	−	1.11716i
$698$	1.53326	−	4.71888i	0.0580346	−	0.178612i
$699$	−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	$0.528881\pi$
$702$	2.77208	−	8.53158i	0.104625	−	0.322004i
$703$	−3.85317	−	2.79949i	−0.145325	−	0.105585i
$704$	13.1141	+	9.52794i	0.494256	+	0.359098i
$705$		0			0
$706$	−9.21045	+	6.69179i	−0.346640	+	0.251849i
$707$	−13.7082			−0.515549
$708$	0.00534485	−	0.00388326i	0.000200872	−	0.000145942i
$709$	13.1070	+	40.3393i	0.492245	+	1.51497i	0.821207	+	0.570631i	$0.193301\pi$
$709$	13.1070	+	40.3393i	0.492245	+	1.51497i	−0.328962	+	0.944343i	$0.606699\pi$
$710$		0			0
$711$	−3.99406	+	12.2924i	−0.149789	+	0.461003i
$712$	−14.4508	−	44.4750i	−0.541566	−	1.66677i
$713$	−6.64599	−	20.4543i	−0.248894	−	0.766018i
$714$	−1.68312	+	5.18010i	−0.0629890	+	0.193860i
$715$		0			0
$716$	2.63510	+	8.11001i	0.0984783	+	0.303085i
$717$	7.35300	−	5.34227i	0.274603	−	0.199511i
$718$	46.1766			1.72329
$719$	35.0454	−	25.4620i	1.30697	−	0.949572i	0.306976	−	0.951717i	$-0.400683\pi$
$719$	35.0454	−	25.4620i	1.30697	−	0.949572i	0.999998	+	0.00214493i	$0.000682754\pi$
$720$		0			0
$721$	4.55885	+	3.31220i	0.169780	+	0.123353i
$722$	−15.9223	−	11.5682i	−0.592565	−	0.430524i
$723$	0.949244	−	2.92147i	0.0353027	−	0.108651i
$724$	4.60461			0.171129
$725$		0			0
$726$	6.15667			0.228495
$727$	0.0769054	−	0.236691i	0.00285226	−	0.00877837i	−0.949620	−	0.313403i	$-0.898531\pi$
$727$	0.0769054	−	0.236691i	0.00285226	−	0.00877837i	0.952473	+	0.304625i	$0.0985310\pi$
$728$	−4.92412	−	3.57758i	−0.182500	−	0.132594i
$729$	6.04974	+	4.39539i	0.224064	+	0.162792i
$730$		0			0
$731$	40.2297	−	29.2286i	1.48795	−	1.08106i
$732$	1.05426			0.0389667
$733$	24.3409	−	17.6847i	0.899053	−	0.653200i	−0.0391699	−	0.999233i	$-0.512471\pi$
$733$	24.3409	−	17.6847i	0.899053	−	0.653200i	0.938222	+	0.346033i	$0.112471\pi$
$734$	6.10407	+	18.7864i	0.225305	+	0.693419i
$735$		0			0
$736$	3.12145	−	9.60683i	0.115058	−	0.354112i
$737$	−2.61058	−	8.03455i	−0.0961620	−	0.295956i
$738$	7.44140	+	22.9023i	0.273922	+	0.843045i
$739$	3.10155	−	9.54560i	0.114092	−	0.351140i	−0.877664	−	0.479276i	$-0.840899\pi$
$739$	3.10155	−	9.54560i	0.114092	−	0.351140i	0.991757	+	0.128136i	$0.0408993\pi$
$740$		0			0
$741$	−0.721198	−	2.21962i	−0.0264939	−	0.0815398i
$742$	5.44090	−	3.95305i	0.199742	−	0.145121i
$743$	12.7497			0.467740			0.233870	−	0.972268i	$-0.424861\pi$
$743$	12.7497			0.467740			0.233870	+	0.972268i	$0.424861\pi$
$744$	−7.76634	+	5.64257i	−0.284728	+	0.206867i
$745$		0			0
$746$	−9.57800	−	6.95883i	−0.350676	−	0.254781i
$747$	−5.59758	−	4.06688i	−0.204805	−	0.148799i
$748$	1.60150	−	4.92891i	0.0585567	−	0.180219i
$749$	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	$0.304991\pi$
$752$	9.67272	−	29.7696i	0.352728	−	1.08558i
$753$	−6.56322	−	4.76846i	−0.239177	−	0.173772i
$754$	−13.6080	−	9.88677i	−0.495573	−	0.360055i
$755$		0			0
$756$	−1.20736	+	0.877200i	−0.0439113	+	0.0319034i
$757$	37.1340			1.34966			0.674829	−	0.737974i	$-0.264217\pi$
$757$	37.1340			1.34966			0.674829	+	0.737974i	$0.264217\pi$
$758$	31.8874	−	23.1675i	1.15820	−	0.841483i
$759$	1.55737	+	4.79309i	0.0565289	+	0.173978i
$760$		0			0
$761$	10.7244	−	33.0064i	0.388760	−	1.19648i	−0.544956	−	0.838464i	$-0.683454\pi$
$761$	10.7244	−	33.0064i	0.388760	−	1.19648i	0.933716	−	0.358015i	$-0.116546\pi$
$762$	−1.24730	−	3.83878i	−0.0451847	−	0.139064i
$763$	−3.94809	−	12.1510i	−0.142930	−	0.439895i
$764$	−1.57943	+	4.86099i	−0.0571418	+	0.175864i
$765$		0			0
$766$	6.98742	+	21.5051i	0.252466	+	0.777010i
$767$	−0.0400918	+	0.0291284i	−0.00144763	+	0.00105176i
$768$	−6.10275			−0.220214
$769$	30.8657	−	22.4252i	1.11305	−	0.808675i	0.129905	−	0.991526i	$-0.458533\pi$
$769$	30.8657	−	22.4252i	1.11305	−	0.808675i	0.983141	+	0.182851i	$0.0585327\pi$
$770$		0			0
$771$	12.6474	+	9.18891i	0.455487	+	0.330931i
$772$	0.0369430	+	0.0268407i	0.00132961	+	0.000966017i
$773$	−7.66532	+	23.5914i	−0.275703	+	0.848525i	0.713330	+	0.700828i	$0.247186\pi$
$773$	−7.66532	+	23.5914i	−0.275703	+	0.848525i	−0.989033	+	0.147697i	$0.952814\pi$
$774$	−23.8644			−0.857787
$775$		0			0
$776$	−36.9491			−1.32640
$777$	−0.512477	+	1.57724i	−0.0183850	+	0.0565832i
$778$	−9.46300	−	6.87527i	−0.339265	−	0.246490i
$779$	10.9305	+	7.94147i	0.391625	+	0.284533i
$780$		0			0
$781$	17.6176	−	12.7999i	0.630408	−	0.458018i
$782$	37.1140			1.32719
$783$	−19.2762	+	14.0050i	−0.688875	+	0.500497i
$784$	−0.923165	−	2.84121i	−0.0329702	−	0.101472i
$785$		0			0
$786$	−1.20226	+	3.70016i	−0.0428830	+	0.131980i
$787$	8.42214	+	25.9207i	0.300217	+	0.923973i	0.981419	+	0.191877i	$0.0614575\pi$
$787$	8.42214	+	25.9207i	0.300217	+	0.923973i	−0.681202	+	0.732095i	$0.738542\pi$
$788$	1.31346	+	4.04240i	0.0467900	+	0.144005i
$789$	−3.03920	+	9.35369i	−0.108198	+	0.333000i
$790$		0			0
$791$	−4.89173	−	15.0552i	−0.173930	−	0.535301i
$792$	−11.6247	+	8.44586i	−0.413067	+	0.300111i
$793$	−7.90804			−0.280823
$794$	1.47482	−	1.07152i	0.0523394	−	0.0380268i
$795$		0			0
$796$	4.31285	+	3.13347i	0.152865	+	0.111063i
$797$	12.2140	+	8.87402i	0.432644	+	0.314334i	0.782705	−	0.622393i	$-0.213839\pi$
$797$	12.2140	+	8.87402i	0.432644	+	0.314334i	−0.350061	+	0.936727i	$0.613839\pi$
$798$	0.453194	−	1.39479i	0.0160429	−	0.0493750i
$799$	−71.2159			−2.51944
$800$		0			0
$801$	39.8820			1.40916
$802$	2.69116	−	8.28255i	0.0950282	−	0.292467i
$803$	14.0198	+	10.1860i	0.494749	+	0.359456i
$804$	1.00114	+	0.727369i	0.0353074	+	0.0256523i
$805$		0			0
$806$	10.0836	−	7.32618i	0.355180	−	0.258054i
$807$	12.4953			0.439854
$808$	33.7307	−	24.5068i	1.18664	−	0.862145i
$809$	−8.59316	−	26.4470i	−0.302119	−	0.929828i	−0.980736	−	0.195336i	$-0.937420\pi$
$809$	−8.59316	−	26.4470i	−0.302119	−	0.929828i	0.678617	−	0.734492i	$-0.262580\pi$
$810$		0			0
$811$	−7.32802	+	22.5533i	−0.257322	+	0.791954i	0.736042	+	0.676936i	$0.236693\pi$
$811$	−7.32802	+	22.5533i	−0.257322	+	0.791954i	−0.993363	+	0.115018i	$0.963307\pi$
$812$	0.864718	+	2.66133i	0.0303456	+	0.0933943i
$813$	−3.76140	−	11.5764i	−0.131918	−	0.406002i
$814$	−1.84188	+	5.66872i	−0.0645578	+	0.198688i
$815$		0			0
$816$	−3.99850	−	12.3061i	−0.139976	−	0.430800i
$817$	−10.8322	+	7.87006i	−0.378971	+	0.275338i
$818$	13.7469			0.480649
$819$	4.19949	−	3.05111i	0.146742	−	0.106614i
$820$		0			0
$821$	−2.85235	−	2.07235i	−0.0995476	−	0.0723256i	0.536898	−	0.843647i	$-0.319596\pi$
$821$	−2.85235	−	2.07235i	−0.0995476	−	0.0723256i	−0.636446	+	0.771322i	$0.719596\pi$
$822$	−7.57737	−	5.50528i	−0.264291	−	0.192019i
$823$	−3.75757	+	11.5646i	−0.130981	+	0.403117i	−0.994943	−	0.100439i	$-0.967975\pi$
$823$	−3.75757	+	11.5646i	−0.130981	+	0.403117i	0.863962	+	0.503556i	$0.167975\pi$
$824$	−17.1390			−0.597064
$825$		0			0
$826$	−0.0311406			−0.00108352
$827$	13.9212	−	42.8452i	0.484089	−	1.48987i	−0.349207	−	0.937046i	$-0.613549\pi$
$827$	13.9212	−	42.8452i	0.484089	−	1.48987i	0.833296	−	0.552827i	$-0.186451\pi$
$828$	3.81490	+	2.77169i	0.132577	+	0.0963228i
$829$	−17.1004	−	12.4241i	−0.593920	−	0.431508i	0.249796	−	0.968299i	$-0.419637\pi$
$829$	−17.1004	−	12.4241i	−0.593920	−	0.431508i	−0.843716	+	0.536790i	$0.819637\pi$
$830$		0			0
$831$	−1.32867	+	0.965339i	−0.0460912	+	0.0334872i
$832$	17.8107			0.617475
$833$	−5.49877	+	3.99509i	−0.190521	+	0.138422i
$834$	2.42589	+	7.46614i	0.0840019	+	0.258531i
$835$		0			0
$836$	−0.431219	+	1.32716i	−0.0149140	+	0.0459006i
$837$	−5.45594	−	16.7917i	−0.188585	−	0.580404i
$838$	4.21995	+	12.9877i	0.145776	+	0.448652i
$839$	−8.62838	+	26.5554i	−0.297885	+	0.916795i	0.684353	+	0.729151i	$0.260085\pi$
$839$	−8.62838	+	26.5554i	−0.297885	+	0.916795i	−0.982237	+	0.187643i	$0.939915\pi$
$840$		0			0
$841$	4.84421	+	14.9089i	0.167042	+	0.514101i
$842$	19.7922	−	14.3798i	0.682083	−	0.495562i
$843$	−9.04645			−0.311576
$844$	−2.65643	+	1.93001i	−0.0914382	+	0.0664337i
$845$		0			0
$846$	27.6500	+	20.0889i	0.950628	+	0.690671i
$847$	6.21555	+	4.51586i	0.213569	+	0.155167i
$848$	−4.93718	+	15.1951i	−0.169543	+	0.521801i
$849$	−13.0384			−0.447476
$850$		0			0
$851$	11.3005			0.387377
$852$	−0.985719	+	3.03373i	−0.0337702	+	0.103934i
$853$	−22.2058	−	16.1335i	−0.760313	−	0.552400i	0.138693	−	0.990335i	$-0.455710\pi$
$853$	−22.2058	−	16.1335i	−0.760313	−	0.552400i	−0.899006	+	0.437936i	$0.855710\pi$
$854$	−4.02028	−	2.92091i	−0.137571	−	0.0999513i
$855$		0			0
$856$	−42.0996	+	30.5871i	−1.43893	+	1.04545i
$857$	25.1788			0.860093			0.430047	−	0.902807i	$-0.358497\pi$
$857$	25.1788			0.860093			0.430047	+	0.902807i	$0.358497\pi$
$858$	−2.36292	+	1.71676i	−0.0806686	+	0.0586092i
$859$	16.5860	+	51.0466i	0.565908	+	1.74169i	0.665238	+	0.746632i	$0.268330\pi$
$859$	16.5860	+	51.0466i	0.565908	+	1.74169i	−0.0993296	+	0.995055i	$0.531670\pi$
$860$		0			0
$861$	1.45377	−	4.47425i	0.0495444	−	0.152482i
$862$	−1.98987	−	6.12420i	−0.0677753	−	0.208591i
$863$	−12.6267	−	38.8610i	−0.429818	−	1.32284i	−0.898305	−	0.439373i	$-0.855201\pi$
$863$	−12.6267	−	38.8610i	−0.429818	−	1.32284i	0.468487	−	0.883471i	$-0.344799\pi$
$864$	2.56251	−	7.88660i	0.0871784	−	0.268307i
$865$		0			0
$866$	−5.41514	−	16.6661i	−0.184014	−	0.566336i
$867$	−15.0525	+	10.9363i	−0.511210	+	0.371416i
$868$	−2.07355			−0.0703810
$869$	7.34205	−	5.33431i	0.249062	−	0.180954i
$870$		0			0
$871$	−7.50954	−	5.45600i	−0.254451	−	0.184870i
$872$	31.4376	+	22.8408i	1.06461	+	0.773485i
$873$	9.73765	−	29.9694i	0.329570	−	1.01431i
$874$	−9.99328			−0.338028
$875$		0			0
$876$	−2.53844			−0.0857658
$877$	−10.3204	+	31.7629i	−0.348494	+	1.07256i	0.611192	+	0.791482i	$0.290690\pi$
$877$	−10.3204	+	31.7629i	−0.348494	+	1.07256i	−0.959686	+	0.281073i	$0.909310\pi$
$878$	27.8563	+	20.2388i	0.940106	+	0.683027i
$879$	4.15670	+	3.02002i	0.140202	+	0.101863i
$880$		0			0
$881$	13.3680	−	9.71242i	0.450379	−	0.327220i	−0.339366	−	0.940654i	$-0.610213\pi$
$881$	13.3680	−	9.71242i	0.450379	−	0.327220i	0.789746	+	0.613435i	$0.210213\pi$
$882$	3.26189			0.109833
$883$	−1.71256	+	1.24425i	−0.0576321	+	0.0418722i	−0.616228	−	0.787568i	$-0.711340\pi$
$883$	−1.71256	+	1.24425i	−0.0576321	+	0.0418722i	0.558596	+	0.829440i	$0.311340\pi$
$884$	−1.75966	−	5.41567i	−0.0591837	−	0.182149i
$885$		0			0
$886$	15.2848	−	47.0418i	0.513503	−	1.58040i
$887$	−0.707185	−	2.17649i	−0.0237449	−	0.0730794i	0.938482	−	0.345329i	$-0.112233\pi$
$887$	−0.707185	−	2.17649i	−0.0237449	−	0.0730794i	−0.962227	+	0.272249i	$0.912233\pi$
$888$	−1.55870	−	4.79717i	−0.0523064	−	0.160983i
$889$	1.55649	−	4.79037i	0.0522029	−	0.160664i
$890$		0			0
$891$	−3.10117	−	9.54443i	−0.103893	−	0.319750i
$892$	−3.77551	+	2.74307i	−0.126413	+	0.0918447i
$893$	19.1755			0.641685
$894$	13.8682	−	10.0758i	0.463821	−	0.336986i
$895$		0			0
$896$	5.29063	+	3.84387i	0.176747	+	0.128415i
$897$	4.47990	+	3.25483i	0.149579	+	0.108676i
$898$	10.9956	−	33.8411i	0.366929	−	1.12929i
$899$	−33.1054			−1.10413
$900$		0			0
$901$	36.3502			1.21100
$902$	5.22496	−	16.0808i	0.173972	−	0.535431i
$903$	3.77180	+	2.74037i	0.125518	+	0.0911939i
$904$	38.9515	+	28.2999i	1.29551	+	0.941242i
$905$		0			0
$906$	9.20986	−	6.69136i	0.305977	−	0.222305i
$907$	53.0301			1.76084			0.880418	−	0.474199i	$-0.157262\pi$
$907$	53.0301			1.76084			0.880418	+	0.474199i	$0.157262\pi$
$908$	−4.28280	+	3.11163i	−0.142130	+	0.103263i
$909$	10.9880	+	33.8175i	0.364448	+	1.12166i
$910$		0			0
$911$	−0.264200	+	0.813124i	−0.00875334	+	0.0269400i	−0.955338	−	0.295516i	$-0.904508\pi$
$911$	−0.264200	+	0.813124i	−0.00875334	+	0.0269400i	0.946584	+	0.322456i	$0.104508\pi$
$912$	1.07663	+	3.31354i	0.0356509	+	0.109722i
$913$	1.50125	+	4.62037i	0.0496841	+	0.152912i
$914$	2.82871	−	8.70589i	0.0935655	−	0.287965i
$915$		0			0
$916$	−1.21007	−	3.72420i	−0.0399817	−	0.123051i
$917$	−3.92779	+	2.85371i	−0.129707	+	0.0942377i
$918$	30.4682			1.00560
$919$	−39.2405	+	28.5099i	−1.29443	+	0.940455i	−0.999885	−	0.0151841i	$-0.995167\pi$
$919$	−39.2405	+	28.5099i	−1.29443	+	0.940455i	−0.294540	+	0.955639i	$0.595167\pi$
$920$		0			0
$921$	−4.68562	−	3.40431i	−0.154397	−	0.112176i
$922$	6.03442	+	4.38426i	0.198733	+	0.144388i
$923$	7.39388	−	22.7560i	0.243373	−	0.749024i
$924$	0.485900			0.0159849
$925$		0			0
$926$	−17.6019			−0.578436
$927$	4.51685	−	13.9014i	0.148353	−	0.456583i
$928$	−12.5792	−	9.13933i	−0.412933	−	0.300013i
$929$	−43.2383	−	31.4145i	−1.41860	−	1.03068i	−0.992000	−	0.126237i	$-0.959710\pi$
$929$	−43.2383	−	31.4145i	−1.41860	−	1.03068i	−0.426603	−	0.904439i	$-0.640290\pi$
$930$		0			0
$931$	1.48059	−	1.07571i	0.0485245	−	0.0352551i
$932$	3.68435			0.120685
$933$	13.7003	−	9.95384i	0.448527	−	0.325874i
$934$	1.80543	+	5.55653i	0.0590754	+	0.181815i
$935$		0			0
$936$	−4.87875	+	15.0152i	−0.159467	+	0.490789i
$937$	−2.87521	−	8.84897i	−0.0939289	−	0.289083i	0.893044	−	0.449969i	$-0.148565\pi$
$937$	−2.87521	−	8.84897i	−0.0939289	−	0.289083i	−0.986973	+	0.160886i	$0.948565\pi$
$938$	−1.80247	−	5.54743i	−0.0588527	−	0.181130i
$939$	−1.68901	+	5.19823i	−0.0551186	+	0.169638i
$940$		0			0
$941$	−3.37120	−	10.3755i	−0.109898	−	0.338232i	0.880951	−	0.473208i	$-0.156904\pi$
$941$	−3.37120	−	10.3755i	−0.109898	−	0.338232i	−0.990849	+	0.134977i	$0.956904\pi$
$942$	−7.47031	+	5.42749i	−0.243396	+	0.176837i
$943$	−32.0568			−1.04391
$944$	0.0598505	−	0.0434840i	0.00194797	−	0.00141528i
$945$		0			0
$946$	13.5561	+	9.84909i	0.440747	+	0.320222i
$947$	−27.4727	−	19.9601i	−0.892743	−	0.648616i	0.0438488	−	0.999038i	$-0.486038\pi$
$947$	−27.4727	−	19.9601i	−0.892743	−	0.648616i	−0.936592	+	0.350422i	$0.886038\pi$
$948$	−0.410793	+	1.26429i	−0.0133419	+	0.0410623i
$949$	19.0408			0.618092
$950$		0			0
$951$	−3.78180			−0.122633
$952$	6.38818	−	19.6608i	0.207042	−	0.637210i
$953$	0.924210	+	0.671478i	0.0299381	+	0.0217513i	0.602654	−	0.798003i	$-0.294110\pi$
$953$	0.924210	+	0.671478i	0.0299381	+	0.0217513i	−0.572716	+	0.819754i	$0.694110\pi$
$954$	−14.1132	−	10.2539i	−0.456932	−	0.331981i
$955$		0			0
$956$	−4.83068	+	3.50970i	−0.156235	+	0.113512i
$957$	7.75767			0.250770
$958$	14.0298	−	10.1932i	0.453282	−	0.329329i
$959$	−3.61177	−	11.1159i	−0.116630	−	0.358950i
$960$		0			0
$961$	−1.99890	+	6.15199i	−0.0644808	+	0.198451i
$962$	2.02377	+	6.22853i	0.0652490	+	0.200816i
$963$	−13.7142	−	42.2080i	−0.441934	−	1.36013i
$964$	−0.623622	+	1.91931i	−0.0200855	+	0.0618168i
$965$		0			0
$966$	1.07528	+	3.30938i	0.0345966	+	0.106477i
$967$	−20.8543	+	15.1515i	−0.670629	+	0.487241i	−0.870236	−	0.492635i	$-0.836034\pi$
$967$	−20.8543	+	15.1515i	−0.670629	+	0.487241i	0.199606	+	0.979876i	$0.436034\pi$
$968$	−23.3673			−0.751054
$969$	6.41289	−	4.65924i	0.206012	−	0.149676i
$970$		0			0
$971$	−29.5946	−	21.5017i	−0.949735	−	0.690023i	0.00100922	−	0.999999i	$-0.499679\pi$
$971$	−29.5946	−	21.5017i	−0.949735	−	0.690023i	−0.950744	+	0.309977i	$0.899679\pi$
$972$	4.81136	+	3.49566i	0.154324	+	0.112123i
$973$	−3.02725	+	9.31691i	−0.0970491	+	0.298687i
$974$	−34.8603			−1.11699
$975$		0			0
$976$	11.8054			0.377883
$977$	17.4967	−	53.8492i	0.559768	−	1.72279i	−0.123240	−	0.992377i	$-0.539328\pi$
$977$	17.4967	−	53.8492i	0.559768	−	1.72279i	0.683007	−	0.730411i	$-0.260672\pi$
$978$	14.0099	+	10.1788i	0.447986	+	0.325481i
$979$	−22.6549	−	16.4598i	−0.724055	−	0.526057i
$980$		0			0
$981$	−26.8113	+	19.4795i	−0.856018	+	0.621933i
$982$	−37.6680			−1.20204
$983$	12.4331	−	9.03318i	0.396555	−	0.288114i	−0.371582	−	0.928400i	$-0.621184\pi$
$983$	12.4331	−	9.03318i	0.396555	−	0.288114i	0.768136	+	0.640287i	$0.221184\pi$
$984$	4.42164	+	13.6084i	0.140957	+	0.433820i
$985$		0			0
$986$	17.6539	−	54.3333i	0.562216	−	1.73032i
$987$	−2.06330	−	6.35017i	−0.0656755	−	0.202128i
$988$	0.473804	+	1.45822i	0.0150737	+	0.0463921i
$989$	9.81702	−	30.2137i	0.312163	−	0.960739i
$990$		0			0
$991$	10.3262	+	31.7808i	0.328023	+	1.00955i	0.970058	+	0.242875i	$0.0780906\pi$
$991$	10.3262	+	31.7808i	0.328023	+	1.00955i	−0.642035	+	0.766676i	$0.721909\pi$
$992$	9.32130	−	6.77232i	0.295951	−	0.215021i
$993$	−9.85212			−0.312647
$994$	12.1640	−	8.83769i	0.385820	−	0.280315i
$995$		0			0
$996$	−0.575717	−	0.418283i	−0.0182423	−	0.0132538i
$997$	−5.28781	−	3.84182i	−0.167466	−	0.121672i	0.500895	−	0.865508i	$-0.333004\pi$
$997$	−5.28781	−	3.84182i	−0.167466	−	0.121672i	−0.668362	+	0.743836i	$0.733004\pi$
$998$	−5.07113	+	15.6073i	−0.160524	+	0.494041i
$999$	9.27700			0.293511

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.29.11	✓	56	5.3	odd	4
175.2.n.a.169.11	yes	56	25.17	odd	20
875.2.h.d.351.10		56	5.4	even	2
875.2.h.d.526.10		56	25.19	even	10
875.2.h.e.351.5		56	1.1	even	1	trivial
875.2.h.e.526.5		56	25.6	even	5	inner
875.2.n.c.99.4		56	25.8	odd	20
875.2.n.c.274.4		56	5.2	odd	4
4375.2.a.o.1.9		28	25.16	even	5
4375.2.a.p.1.20		28	25.9	even	10

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.h (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.388594 + 1.19597i) q^{2} +(-0.515546 - 0.374566i) q^{3} +(0.338697 + 0.246078i) q^{4} +(0.648308 - 0.471023i) q^{6} +1.00000 q^{7} +(-2.46062 + 1.78775i) q^{8} +(-0.801563 - 2.46696i) q^{9} +O(q^{10})\)	\(q+(-0.388594 + 1.19597i) q^{2} +(-0.515546 - 0.374566i) q^{3} +(0.338697 + 0.246078i) q^{4} +(0.648308 - 0.471023i) q^{6} +1.00000 q^{7} +(-2.46062 + 1.78775i) q^{8} +(-0.801563 - 2.46696i) q^{9} +(-0.562815 + 1.73217i) q^{11} +(-0.0824416 - 0.253729i) q^{12} +(0.618395 + 1.90323i) q^{13} +(-0.388594 + 1.19597i) q^{14} +(-0.923165 - 2.84121i) q^{16} +(-5.49877 + 3.99509i) q^{17} +3.26189 q^{18} +(1.48059 - 1.07571i) q^{19} +(-0.515546 - 0.374566i) q^{21} +(-1.85291 - 1.34622i) q^{22} +(-1.34183 + 4.12974i) q^{23} +1.93819 q^{24} -2.51650 q^{26} +(-1.10156 + 3.39025i) q^{27} +(0.338697 + 0.246078i) q^{28} +(5.40749 + 3.92877i) q^{29} +(-4.00700 + 2.91125i) q^{31} -2.32626 q^{32} +(0.938968 - 0.682200i) q^{33} +(-2.64121 - 8.12882i) q^{34} +(0.335576 - 1.03280i) q^{36} +(-0.804200 - 2.47507i) q^{37} +(0.711172 + 2.18876i) q^{38} +(0.394073 - 1.21283i) q^{39} +(2.28132 + 7.02118i) q^{41} +(0.648308 - 0.471023i) q^{42} -7.31612 q^{43} +(-0.616871 + 0.448183i) q^{44} +(-4.41761 - 3.20958i) q^{46} +(8.47670 + 6.15868i) q^{47} +(-0.588287 + 1.81056i) q^{48} +1.00000 q^{49} +4.33130 q^{51} +(-0.258893 + 0.796790i) q^{52} +(-4.32670 - 3.14354i) q^{53} +(-3.62658 - 2.63486i) q^{54} +(-2.46062 + 1.78775i) q^{56} -1.16624 q^{57} +(-6.80001 + 4.94049i) q^{58} +(0.00765237 + 0.0235516i) q^{59} +(-1.22115 + 3.75830i) q^{61} +(-1.92467 - 5.92354i) q^{62} +(-0.801563 - 2.46696i) q^{63} +(2.75030 - 8.46455i) q^{64} +(0.451013 + 1.38808i) q^{66} +(-3.75258 + 2.72641i) q^{67} -2.84552 q^{68} +(2.23864 - 1.62647i) q^{69} +(-9.67307 - 7.02789i) q^{71} +(6.38263 + 4.63726i) q^{72} +(2.94025 - 9.04917i) q^{73} +3.27262 q^{74} +0.766183 q^{76} +(-0.562815 + 1.73217i) q^{77} +(1.29737 + 0.942598i) q^{78} +(-4.03120 - 2.92884i) q^{79} +(-4.45778 + 3.23876i) q^{81} -9.28362 q^{82} +(2.15797 - 1.56786i) q^{83} +(-0.0824416 - 0.253729i) q^{84} +(2.84300 - 8.74985i) q^{86} +(-1.31623 - 4.05093i) q^{87} +(-1.71180 - 5.26837i) q^{88} +(-4.75121 + 14.6227i) q^{89} +(0.618395 + 1.90323i) q^{91} +(-1.47071 + 1.06854i) q^{92} +3.15625 q^{93} +(-10.6596 + 7.74464i) q^{94} +(1.19929 + 0.871337i) q^{96} +(9.82821 + 7.14061i) q^{97} +(-0.388594 + 1.19597i) q^{98} +4.72431 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{2} + 4 q^{3} - 12 q^{4} + 56 q^{7} + 12 q^{8} - 6 q^{9}+O(q^{10}) \) 56 * q + 4 * q^2 + 4 * q^3 - 12 * q^4 + 56 * q^7 + 12 * q^8 - 6 * q^9	\( 56 q + 4 q^{2} + 4 q^{3} - 12 q^{4} + 56 q^{7} + 12 q^{8} - 6 q^{9} + 8 q^{11} + 12 q^{12} + 8 q^{13} + 4 q^{14} - 32 q^{16} + 20 q^{17} - 48 q^{18} - 12 q^{19} + 4 q^{21} + 8 q^{22} + 16 q^{23} + 28 q^{24} + 12 q^{26} + 16 q^{27} - 12 q^{28} + 2 q^{29} + 12 q^{31} - 112 q^{32} + 14 q^{33} - 14 q^{36} + 16 q^{37} + 20 q^{38} + 4 q^{39} + 4 q^{41} - 32 q^{43} - 22 q^{44} - 4 q^{46} + 18 q^{47} + 48 q^{48} + 56 q^{49} - 44 q^{51} - 16 q^{52} + 20 q^{53} - 54 q^{54} + 12 q^{56} - 152 q^{57} - 32 q^{58} + 6 q^{59} - 4 q^{61} - 18 q^{62} - 6 q^{63} - 24 q^{64} - 74 q^{66} + 32 q^{67} - 124 q^{68} + 78 q^{69} - 8 q^{71} + 100 q^{72} + 48 q^{73} - 60 q^{74} + 52 q^{76} + 8 q^{77} - 124 q^{78} - 72 q^{81} - 44 q^{82} - 10 q^{83} + 12 q^{84} - 20 q^{86} - 26 q^{87} + 88 q^{88} - 38 q^{89} + 8 q^{91} + 96 q^{92} - 96 q^{93} - 88 q^{94} - 28 q^{96} + 90 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) 56 * q + 4 * q^2 + 4 * q^3 - 12 * q^4 + 56 * q^7 + 12 * q^8 - 6 * q^9 + 8 * q^11 + 12 * q^12 + 8 * q^13 + 4 * q^14 - 32 * q^16 + 20 * q^17 - 48 * q^18 - 12 * q^19 + 4 * q^21 + 8 * q^22 + 16 * q^23 + 28 * q^24 + 12 * q^26 + 16 * q^27 - 12 * q^28 + 2 * q^29 + 12 * q^31 - 112 * q^32 + 14 * q^33 - 14 * q^36 + 16 * q^37 + 20 * q^38 + 4 * q^39 + 4 * q^41 - 32 * q^43 - 22 * q^44 - 4 * q^46 + 18 * q^47 + 48 * q^48 + 56 * q^49 - 44 * q^51 - 16 * q^52 + 20 * q^53 - 54 * q^54 + 12 * q^56 - 152 * q^57 - 32 * q^58 + 6 * q^59 - 4 * q^61 - 18 * q^62 - 6 * q^63 - 24 * q^64 - 74 * q^66 + 32 * q^67 - 124 * q^68 + 78 * q^69 - 8 * q^71 + 100 * q^72 + 48 * q^73 - 60 * q^74 + 52 * q^76 + 8 * q^77 - 124 * q^78 - 72 * q^81 - 44 * q^82 - 10 * q^83 + 12 * q^84 - 20 * q^86 - 26 * q^87 + 88 * q^88 - 38 * q^89 + 8 * q^91 + 96 * q^92 - 96 * q^93 - 88 * q^94 - 28 * q^96 + 90 * q^97 + 4 * q^98 - 60 * q^99

Introduction

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