LMFDB - Embedded newform 1110.2.l.a.43.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.8
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.a.697.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.05054 - 0.891783i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.56460 + 1.56460i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.05054 - 0.891783i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.56460 + 1.56460i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(0.891783 + 2.05054i) q^{10} +3.92190i q^{11} +(0.707107 - 0.707107i) q^{12} -0.319413i q^{13} +(-1.56460 - 1.56460i) q^{14} +(-0.819367 + 2.08054i) q^{15} +1.00000 q^{16} +1.25497 q^{17} +1.00000 q^{18} +(-2.17875 + 2.17875i) q^{19} +(-2.05054 + 0.891783i) q^{20} -2.21268i q^{21} -3.92190 q^{22} -1.15203i q^{23} +(0.707107 + 0.707107i) q^{24} +(3.40945 - 3.65728i) q^{25} +0.319413 q^{26} +(0.707107 + 0.707107i) q^{27} +(1.56460 - 1.56460i) q^{28} +(1.22361 + 1.22361i) q^{29} +(-2.08054 - 0.819367i) q^{30} +(-6.78274 + 6.78274i) q^{31} +1.00000i q^{32} +(-2.77320 - 2.77320i) q^{33} +1.25497i q^{34} +(-1.81300 + 4.60357i) q^{35} +1.00000i q^{36} +(0.0100817 + 6.08275i) q^{37} +(-2.17875 - 2.17875i) q^{38} +(0.225859 + 0.225859i) q^{39} +(-0.891783 - 2.05054i) q^{40} +3.92813i q^{41} +2.21268 q^{42} -1.87330i q^{43} -3.92190i q^{44} +(-0.891783 - 2.05054i) q^{45} +1.15203 q^{46} +(-4.88442 + 4.88442i) q^{47} +(-0.707107 + 0.707107i) q^{48} +2.10403i q^{49} +(3.65728 + 3.40945i) q^{50} +(-0.887401 + 0.887401i) q^{51} +0.319413i q^{52} +(-3.03226 - 3.03226i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(3.49748 + 8.04202i) q^{55} +(1.56460 + 1.56460i) q^{56} -3.08122i q^{57} +(-1.22361 + 1.22361i) q^{58} +(-4.70399 + 4.70399i) q^{59} +(0.819367 - 2.08054i) q^{60} +(-5.56135 + 5.56135i) q^{61} +(-6.78274 - 6.78274i) q^{62} +(1.56460 + 1.56460i) q^{63} -1.00000 q^{64} +(-0.284847 - 0.654970i) q^{65} +(2.77320 - 2.77320i) q^{66} +(-6.88391 - 6.88391i) q^{67} -1.25497 q^{68} +(0.814607 + 0.814607i) q^{69} +(-4.60357 - 1.81300i) q^{70} -3.29012 q^{71} -1.00000 q^{72} +(8.53399 - 8.53399i) q^{73} +(-6.08275 + 0.0100817i) q^{74} +(0.175243 + 4.99693i) q^{75} +(2.17875 - 2.17875i) q^{76} +(-6.13622 - 6.13622i) q^{77} +(-0.225859 + 0.225859i) q^{78} +(3.59077 - 3.59077i) q^{79} +(2.05054 - 0.891783i) q^{80} -1.00000 q^{81} -3.92813 q^{82} +(-1.13008 - 1.13008i) q^{83} +2.21268i q^{84} +(2.57338 - 1.11916i) q^{85} +1.87330 q^{86} -1.73044 q^{87} +3.92190 q^{88} +(-1.33809 - 1.33809i) q^{89} +(2.05054 - 0.891783i) q^{90} +(0.499755 + 0.499755i) q^{91} +1.15203i q^{92} -9.59224i q^{93} +(-4.88442 - 4.88442i) q^{94} +(-2.52465 + 6.41059i) q^{95} +(-0.707107 - 0.707107i) q^{96} +4.01884 q^{97} -2.10403 q^{98} +3.92190 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) $ 36 * q - 36 * q^4 + 4 * q^7	$ 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	2.05054	−	0.891783i	0.917030	−	0.398817i
$5$	2.05054	−	0.891783i	0.917030	−	0.398817i
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	−1.56460	+	1.56460i	−0.591365	+	0.591365i	−0.938000	−	0.346635i	$-0.887324\pi$
$7$	−1.56460	+	1.56460i	−0.591365	+	0.591365i	0.346635	+	0.938000i	$0.387324\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	0.891783	+	2.05054i	0.282007	+	0.648438i
$11$			3.92190i			1.18250i	0.806489	+	0.591249i	$0.201365\pi$
$11$			3.92190i			1.18250i	−0.806489	+	0.591249i	$0.798635\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$		−	0.319413i		−	0.0885893i	−0.999019	−	0.0442946i	$-0.985896\pi$
$13$		−	0.319413i		−	0.0885893i	0.999019	−	0.0442946i	$-0.0141040\pi$
$14$	−1.56460	−	1.56460i	−0.418158	−	0.418158i
$15$	−0.819367	+	2.08054i	−0.211560	+	0.537193i
$16$	1.00000			0.250000
$17$	1.25497			0.304376			0.152188	−	0.988352i	$-0.451368\pi$
$17$	1.25497			0.304376			0.152188	+	0.988352i	$0.451368\pi$
$18$	1.00000			0.235702
$19$	−2.17875	+	2.17875i	−0.499839	+	0.499839i	−0.911388	−	0.411549i	$-0.864988\pi$
$19$	−2.17875	+	2.17875i	−0.499839	+	0.499839i	0.411549	+	0.911388i	$0.364988\pi$
$20$	−2.05054	+	0.891783i	−0.458515	+	0.199409i
$21$		−	2.21268i		−	0.482847i
$22$	−3.92190			−0.836152
$23$		−	1.15203i		−	0.240215i	−0.992761	−	0.120107i	$-0.961676\pi$
$23$		−	1.15203i		−	0.240215i	0.992761	−	0.120107i	$-0.0383239\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	3.40945	−	3.65728i	0.681889	−	0.731455i
$26$	0.319413			0.0626421
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	1.56460	−	1.56460i	0.295682	−	0.295682i
$29$	1.22361	+	1.22361i	0.227218	+	0.227218i	0.811529	−	0.584312i	$-0.198635\pi$
$29$	1.22361	+	1.22361i	0.227218	+	0.227218i	−0.584312	+	0.811529i	$0.698635\pi$
$30$	−2.08054	−	0.819367i	−0.379853	−	0.149595i
$31$	−6.78274	+	6.78274i	−1.21822	+	1.21822i	−0.249959	+	0.968256i	$0.580417\pi$
$31$	−6.78274	+	6.78274i	−1.21822	+	1.21822i	−0.968256	+	0.249959i	$0.919583\pi$
$32$			1.00000i			0.176777i
$33$	−2.77320	−	2.77320i	−0.482753	−	0.482753i
$34$			1.25497i			0.215226i
$35$	−1.81300	+	4.60357i	−0.306453	+	0.778146i
$36$			1.00000i			0.166667i
$37$	0.0100817	+	6.08275i	0.00165742	+	0.999999i
$37$	0.0100817	+	6.08275i	0.00165742	+	0.999999i
$38$	−2.17875	−	2.17875i	−0.353440	−	0.353440i
$39$	0.225859	+	0.225859i	0.0361664	+	0.0361664i
$40$	−0.891783	−	2.05054i	−0.141003	−	0.324219i
$41$			3.92813i			0.613470i	0.951795	+	0.306735i	$0.0992366\pi$
$41$			3.92813i			0.613470i	−0.951795	+	0.306735i	$0.900763\pi$
$42$	2.21268			0.341425
$43$		−	1.87330i		−	0.285675i	−0.989746	−	0.142838i	$-0.954377\pi$
$43$		−	1.87330i		−	0.285675i	0.989746	−	0.142838i	$-0.0456227\pi$
$44$		−	3.92190i		−	0.591249i
$45$	−0.891783	−	2.05054i	−0.132939	−	0.305677i
$46$	1.15203			0.169857
$47$	−4.88442	+	4.88442i	−0.712466	+	0.712466i	−0.967051	−	0.254585i	$-0.918061\pi$
$47$	−4.88442	+	4.88442i	−0.712466	+	0.712466i	0.254585	+	0.967051i	$0.418061\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$			2.10403i			0.300576i
$50$	3.65728	+	3.40945i	0.517217	+	0.482169i
$51$	−0.887401	+	0.887401i	−0.124261	+	0.124261i
$52$			0.319413i			0.0442946i
$53$	−3.03226	−	3.03226i	−0.416513	−	0.416513i	0.467487	−	0.884000i	$-0.345160\pi$
$53$	−3.03226	−	3.03226i	−0.416513	−	0.416513i	−0.884000	+	0.467487i	$0.845160\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	3.49748	+	8.04202i	0.471601	+	1.08439i
$56$	1.56460	+	1.56460i	0.209079	+	0.209079i
$57$		−	3.08122i		−	0.408117i
$58$	−1.22361	+	1.22361i	−0.160667	+	0.160667i
$59$	−4.70399	+	4.70399i	−0.612407	+	0.612407i	−0.943573	−	0.331165i	$-0.892558\pi$
$59$	−4.70399	+	4.70399i	−0.612407	+	0.612407i	0.331165	+	0.943573i	$0.392558\pi$
$60$	0.819367	−	2.08054i	0.105780	−	0.268596i
$61$	−5.56135	+	5.56135i	−0.712058	+	0.712058i	−0.966965	−	0.254908i	$-0.917955\pi$
$61$	−5.56135	+	5.56135i	−0.712058	+	0.712058i	0.254908	+	0.966965i	$0.417955\pi$
$62$	−6.78274	−	6.78274i	−0.861408	−	0.861408i
$63$	1.56460	+	1.56460i	0.197122	+	0.197122i
$64$	−1.00000			−0.125000
$65$	−0.284847	−	0.654970i	−0.0353309	−	0.0812390i
$66$	2.77320	−	2.77320i	0.341358	−	0.341358i
$67$	−6.88391	−	6.88391i	−0.841003	−	0.841003i	0.147986	−	0.988989i	$-0.452721\pi$
$67$	−6.88391	−	6.88391i	−0.841003	−	0.841003i	−0.988989	+	0.147986i	$0.952721\pi$
$68$	−1.25497			−0.152188
$69$	0.814607	+	0.814607i	0.0980672	+	0.0980672i
$70$	−4.60357	−	1.81300i	−0.550232	−	0.216695i
$71$	−3.29012			−0.390466			−0.195233	−	0.980757i	$-0.562546\pi$
$71$	−3.29012			−0.390466			−0.195233	+	0.980757i	$0.562546\pi$
$72$	−1.00000			−0.117851
$73$	8.53399	−	8.53399i	0.998828	−	0.998828i	−0.00117124	−	0.999999i	$-0.500373\pi$
$73$	8.53399	−	8.53399i	0.998828	−	0.998828i	0.999999	+	0.00117124i	$0.000372817\pi$
$74$	−6.08275	+	0.0100817i	−0.707106	+	0.00117198i
$75$	0.175243	+	4.99693i	0.0202353	+	0.576996i
$76$	2.17875	−	2.17875i	0.249920	−	0.249920i
$77$	−6.13622	−	6.13622i	−0.699287	−	0.699287i
$78$	−0.225859	+	0.225859i	−0.0255735	+	0.0255735i
$79$	3.59077	−	3.59077i	0.403993	−	0.403993i	−0.475645	−	0.879638i	$-0.657785\pi$
$79$	3.59077	−	3.59077i	0.403993	−	0.403993i	0.879638	+	0.475645i	$0.157785\pi$
$80$	2.05054	−	0.891783i	0.229258	−	0.0997044i
$81$	−1.00000			−0.111111
$82$	−3.92813			−0.433789
$83$	−1.13008	−	1.13008i	−0.124042	−	0.124042i	0.642360	−	0.766403i	$-0.277955\pi$
$83$	−1.13008	−	1.13008i	−0.124042	−	0.124042i	−0.766403	+	0.642360i	$0.777955\pi$
$84$			2.21268i			0.241424i
$85$	2.57338	−	1.11916i	0.279122	−	0.121390i
$86$	1.87330			0.202003
$87$	−1.73044			−0.185523
$88$	3.92190			0.418076
$89$	−1.33809	−	1.33809i	−0.141837	−	0.141837i	0.632623	−	0.774460i	$-0.281978\pi$
$89$	−1.33809	−	1.33809i	−0.141837	−	0.141837i	−0.774460	+	0.632623i	$0.781978\pi$
$90$	2.05054	−	0.891783i	0.216146	−	0.0940022i
$91$	0.499755	+	0.499755i	0.0523886	+	0.0523886i
$92$			1.15203i			0.120107i
$93$		−	9.59224i		−	0.994669i
$94$	−4.88442	−	4.88442i	−0.503790	−	0.503790i
$95$	−2.52465	+	6.41059i	−0.259023	+	0.657712i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	4.01884			0.408051			0.204025	−	0.978966i	$-0.434597\pi$
$97$	4.01884			0.408051			0.204025	+	0.978966i	$0.434597\pi$
$98$	−2.10403			−0.212539
$99$	3.92190			0.394166
$100$	−3.40945	+	3.65728i	−0.340945	+	0.365728i
$101$			11.0673i			1.10124i	0.834757	+	0.550618i	$0.185608\pi$
$101$			11.0673i			1.10124i	−0.834757	+	0.550618i	$0.814392\pi$
$102$	−0.887401	−	0.887401i	−0.0878658	−	0.0878658i
$103$	13.8134			1.36107			0.680536	−	0.732715i	$-0.261747\pi$
$103$	13.8134			1.36107			0.680536	+	0.732715i	$0.261747\pi$
$104$	−0.319413			−0.0313210
$105$	−1.97323	−	4.53720i	−0.192568	−	0.442785i
$106$	3.03226	−	3.03226i	0.294520	−	0.294520i
$107$	1.55870	−	1.55870i	0.150685	−	0.150685i	−0.627739	−	0.778424i	$-0.716019\pi$
$107$	1.55870	−	1.55870i	0.150685	−	0.150685i	0.778424	+	0.627739i	$0.216019\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	4.24101	−	4.24101i	0.406215	−	0.406215i	−0.474201	−	0.880416i	$-0.657263\pi$
$109$	4.24101	−	4.24101i	0.406215	−	0.406215i	0.880416	+	0.474201i	$0.157263\pi$
$110$	−8.04202	+	3.49748i	−0.766777	+	0.333472i
$111$	−4.30829	−	4.29403i	−0.408924	−	0.407571i
$112$	−1.56460	+	1.56460i	−0.147841	+	0.147841i
$113$	−16.5384			−1.55580			−0.777899	−	0.628390i	$-0.783714\pi$
$113$	−16.5384			−1.55580			−0.777899	+	0.628390i	$0.783714\pi$
$114$	3.08122			0.288582
$115$	−1.02736	−	2.36228i	−0.0958018	−	0.220284i
$116$	−1.22361	−	1.22361i	−0.113609	−	0.113609i
$117$	−0.319413			−0.0295298
$118$	−4.70399	−	4.70399i	−0.433037	−	0.433037i
$119$	−1.96354	+	1.96354i	−0.179997	+	0.179997i
$120$	2.08054	+	0.819367i	0.189926	+	0.0747976i
$121$	−4.38131			−0.398301
$122$	−5.56135	−	5.56135i	−0.503501	−	0.503501i
$123$	−2.77761	−	2.77761i	−0.250448	−	0.250448i
$124$	6.78274	−	6.78274i	0.609108	−	0.609108i
$125$	3.72972	−	10.5399i	0.333596	−	0.942716i
$126$	−1.56460	+	1.56460i	−0.139386	+	0.139386i
$127$	7.06209	−	7.06209i	0.626659	−	0.626659i	−0.320567	−	0.947226i	$-0.603873\pi$
$127$	7.06209	−	7.06209i	0.626659	−	0.626659i	0.947226	+	0.320567i	$0.103873\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	1.32462	+	1.32462i	0.116626	+	0.116626i
$130$	0.654970	−	0.284847i	0.0574447	−	0.0249828i
$131$	−9.32171	+	9.32171i	−0.814442	+	0.814442i	−0.985296	−	0.170855i	$-0.945347\pi$
$131$	−9.32171	+	9.32171i	−0.814442	+	0.814442i	0.170855	+	0.985296i	$0.445347\pi$
$132$	2.77320	+	2.77320i	0.241376	+	0.241376i
$133$		−	6.81776i		−	0.591174i
$134$	6.88391	−	6.88391i	0.594679	−	0.594679i
$135$	2.08054	+	0.819367i	0.179064	+	0.0705198i
$136$		−	1.25497i		−	0.107613i
$137$	−14.5752	+	14.5752i	−1.24525	+	1.24525i	−0.287450	+	0.957796i	$0.592807\pi$
$137$	−14.5752	+	14.5752i	−1.24525	+	1.24525i	−0.957796	+	0.287450i	$0.907193\pi$
$138$	−0.814607	+	0.814607i	−0.0693440	+	0.0693440i
$139$	1.20629			0.102316			0.0511582	−	0.998691i	$-0.483709\pi$
$139$	1.20629			0.102316			0.0511582	+	0.998691i	$0.483709\pi$
$140$	1.81300	−	4.60357i	0.153226	−	0.389073i
$141$		−	6.90761i		−	0.581726i
$142$		−	3.29012i		−	0.276101i
$143$	1.25271			0.104757
$144$		−	1.00000i		−	0.0833333i
$145$	3.60025	+	1.41786i	0.298984	+	0.117747i
$146$	8.53399	+	8.53399i	0.706278	+	0.706278i
$147$	−1.48777	−	1.48777i	−0.122710	−	0.122710i
$148$	−0.0100817	−	6.08275i	−0.000828712	−	0.499999i
$149$			0.425764i			0.0348800i	0.999848	+	0.0174400i	$0.00555160\pi$
$149$			0.425764i			0.0348800i	−0.999848	+	0.0174400i	$0.994448\pi$
$150$	−4.99693	+	0.175243i	−0.407997	+	0.0143085i
$151$			18.6559i			1.51820i	0.650976	+	0.759098i	$0.274360\pi$
$151$			18.6559i			1.51820i	−0.650976	+	0.759098i	$0.725640\pi$
$152$	2.17875	+	2.17875i	0.176720	+	0.176720i
$153$		−	1.25497i		−	0.101459i
$154$	6.13622	−	6.13622i	0.494471	−	0.494471i
$155$	−7.85956	+	19.9570i	−0.631295	+	1.60299i
$156$	−0.225859	−	0.225859i	−0.0180832	−	0.0180832i
$157$	6.23375	−	6.23375i	0.497507	−	0.497507i	−0.413154	−	0.910661i	$-0.635573\pi$
$157$	6.23375	−	6.23375i	0.497507	−	0.497507i	0.910661	+	0.413154i	$0.135573\pi$
$158$	3.59077	+	3.59077i	0.285666	+	0.285666i
$159$	4.28827			0.340082
$160$	0.891783	+	2.05054i	0.0705016	+	0.162110i
$161$	1.80247	+	1.80247i	0.142054	+	0.142054i
$162$		−	1.00000i		−	0.0785674i
$163$	15.4091			1.20693			0.603466	−	0.797389i	$-0.293786\pi$
$163$	15.4091			1.20693			0.603466	+	0.797389i	$0.293786\pi$
$164$		−	3.92813i		−	0.306735i
$165$	−8.15967	−	3.21347i	−0.635229	−	0.250169i
$166$	1.13008	−	1.13008i	0.0877111	−	0.0877111i
$167$	16.8371			1.30289			0.651447	−	0.758694i	$-0.274162\pi$
$167$	16.8371			1.30289			0.651447	+	0.758694i	$0.274162\pi$
$168$	−2.21268			−0.170712
$169$	12.8980			0.992152
$170$	1.11916	+	2.57338i	0.0858360	+	0.197369i
$171$	2.17875	+	2.17875i	0.166613	+	0.166613i
$172$			1.87330i			0.142838i
$173$	5.18404	−	5.18404i	0.394136	−	0.394136i	−0.482023	−	0.876159i	$-0.660098\pi$
$173$	5.18404	−	5.18404i	0.394136	−	0.394136i	0.876159	+	0.482023i	$0.160098\pi$
$174$		−	1.73044i		−	0.131184i
$175$	0.387756	+	11.0566i	0.0293116	+	0.835802i
$176$			3.92190i			0.295624i
$177$		−	6.65245i		−	0.500029i
$178$	1.33809	−	1.33809i	0.100294	−	0.100294i
$179$	−1.70251	−	1.70251i	−0.127252	−	0.127252i	0.640613	−	0.767864i	$-0.278680\pi$
$179$	−1.70251	−	1.70251i	−0.127252	−	0.127252i	−0.767864	+	0.640613i	$0.778680\pi$
$180$	0.891783	+	2.05054i	0.0664696	+	0.152838i
$181$	8.75170			0.650509			0.325254	−	0.945627i	$-0.394550\pi$
$181$	8.75170			0.650509			0.325254	+	0.945627i	$0.394550\pi$
$182$	−0.499755	+	0.499755i	−0.0370443	+	0.0370443i
$183$		−	7.86494i		−	0.581393i
$184$	−1.15203			−0.0849287
$185$	5.44517	+	12.4640i	0.400337	+	0.916368i
$186$	9.59224			0.703337
$187$			4.92188i			0.359924i
$188$	4.88442	−	4.88442i	0.356233	−	0.356233i
$189$	−2.21268			−0.160949
$190$	−6.41059	−	2.52465i	−0.465073	−	0.183157i
$191$	4.56780	+	4.56780i	0.330514	+	0.330514i	0.852782	−	0.522268i	$-0.174914\pi$
$191$	4.56780	+	4.56780i	0.330514	+	0.330514i	−0.522268	+	0.852782i	$0.674914\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$		−	5.51547i		−	0.397012i	−0.980100	−	0.198506i	$-0.936391\pi$
$193$		−	5.51547i		−	0.397012i	0.980100	−	0.198506i	$-0.0636090\pi$
$194$			4.01884i			0.288536i
$195$	0.664551	+	0.261716i	0.0475895	+	0.0187419i
$196$		−	2.10403i		−	0.150288i
$197$	−3.48510	+	3.48510i	−0.248303	+	0.248303i	−0.820274	−	0.571971i	$-0.806179\pi$
$197$	−3.48510	+	3.48510i	−0.248303	+	0.248303i	0.571971	+	0.820274i	$0.306179\pi$
$198$			3.92190i			0.278717i
$199$	−11.0862	−	11.0862i	−0.785883	−	0.785883i	0.194933	−	0.980817i	$-0.437551\pi$
$199$	−11.0862	−	11.0862i	−0.785883	−	0.785883i	−0.980817	+	0.194933i	$0.937551\pi$
$200$	−3.65728	−	3.40945i	−0.258609	−	0.241084i
$201$	9.73532			0.686676
$202$	−11.0673			−0.778692
$203$	−3.82892			−0.268737
$204$	0.887401	−	0.887401i	0.0621305	−	0.0621305i
$205$	3.50304	+	8.05479i	0.244663	+	0.562571i
$206$			13.8134i			0.962423i
$207$	−1.15203			−0.0800715
$208$		−	0.319413i		−	0.0221473i
$209$	−8.54484	−	8.54484i	−0.591059	−	0.591059i
$210$	4.53720	−	1.97323i	0.313097	−	0.136166i
$211$	27.2170			1.87370			0.936848	−	0.349737i	$-0.113729\pi$
$211$	27.2170			1.87370			0.936848	+	0.349737i	$0.113729\pi$
$212$	3.03226	+	3.03226i	0.208257	+	0.208257i
$213$	2.32647	−	2.32647i	0.159407	−	0.159407i
$214$	1.55870	+	1.55870i	0.106551	+	0.106551i
$215$	−1.67057	−	3.84128i	−0.113932	−	0.261973i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$		−	21.2246i		−	1.44082i
$218$	4.24101	+	4.24101i	0.287237	+	0.287237i
$219$			12.0689i			0.815540i
$220$	−3.49748	−	8.04202i	−0.235800	−	0.542193i
$221$		−	0.400855i		−	0.0269644i
$222$	4.29403	−	4.30829i	0.288196	−	0.289153i
$223$	11.1865	+	11.1865i	0.749103	+	0.749103i	0.974311	−	0.225208i	$-0.0723061\pi$
$223$	11.1865	+	11.1865i	0.749103	+	0.749103i	−0.225208	+	0.974311i	$0.572306\pi$
$224$	−1.56460	−	1.56460i	−0.104539	−	0.104539i
$225$	−3.65728	−	3.40945i	−0.243818	−	0.227296i
$226$		−	16.5384i		−	1.10011i
$227$	1.74912			0.116093			0.0580467	−	0.998314i	$-0.481513\pi$
$227$	1.74912			0.116093			0.0580467	+	0.998314i	$0.481513\pi$
$228$			3.08122i			0.204058i
$229$			8.51464i			0.562663i	0.959611	+	0.281332i	$0.0907761\pi$
$229$			8.51464i			0.562663i	−0.959611	+	0.281332i	$0.909224\pi$
$230$	2.36228	−	1.02736i	0.155764	−	0.0677421i
$231$	8.67793			0.570966
$232$	1.22361	−	1.22361i	0.0803336	−	0.0803336i
$233$	−6.42533	+	6.42533i	−0.420938	+	0.420938i	−0.885526	−	0.464589i	$-0.846202\pi$
$233$	−6.42533	+	6.42533i	−0.420938	+	0.420938i	0.464589	+	0.885526i	$0.346202\pi$
$234$		−	0.319413i		−	0.0208807i
$235$	−5.65987	+	14.3716i	−0.369209	+	0.937497i
$236$	4.70399	−	4.70399i	0.306204	−	0.306204i
$237$			5.07811i			0.329859i
$238$	−1.96354	−	1.96354i	−0.127277	−	0.127277i
$239$	10.4976	−	10.4976i	0.679036	−	0.679036i	−0.280746	−	0.959782i	$-0.590582\pi$
$239$	10.4976	−	10.4976i	0.679036	−	0.679036i	0.959782	+	0.280746i	$0.0905818\pi$
$240$	−0.819367	+	2.08054i	−0.0528899	+	0.134298i
$241$	6.66851	+	6.66851i	0.429556	+	0.429556i	0.888477	−	0.458921i	$-0.151764\pi$
$241$	6.66851	+	6.66851i	0.429556	+	0.429556i	−0.458921	+	0.888477i	$0.651764\pi$
$242$		−	4.38131i		−	0.281641i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	5.56135	−	5.56135i	0.356029	−	0.356029i
$245$	1.87634	+	4.31440i	0.119875	+	0.275637i
$246$	2.77761	−	2.77761i	0.177094	−	0.177094i
$247$	0.695921	+	0.695921i	0.0442804	+	0.0442804i
$248$	6.78274	+	6.78274i	0.430704	+	0.430704i
$249$	1.59817			0.101280
$250$	10.5399	+	3.72972i	0.666601	+	0.235888i
$251$	19.9946	−	19.9946i	1.26205	−	1.26205i	0.311948	−	0.950099i	$-0.399019\pi$
$251$	19.9946	−	19.9946i	1.26205	−	1.26205i	0.950099	−	0.311948i	$-0.100981\pi$
$252$	−1.56460	−	1.56460i	−0.0985608	−	0.0985608i
$253$	4.51814			0.284053
$254$	7.06209	+	7.06209i	0.443115	+	0.443115i
$255$	−1.02828	+	2.61102i	−0.0643936	+	0.163508i
$256$	1.00000			0.0625000
$257$	31.3639			1.95642			0.978212	−	0.207609i	$-0.0665682\pi$
$257$	31.3639			1.95642			0.978212	+	0.207609i	$0.0665682\pi$
$258$	−1.32462	+	1.32462i	−0.0824673	+	0.0824673i
$259$	−9.53287	−	9.50133i	−0.592344	−	0.590384i
$260$	0.284847	+	0.654970i	0.0176655	+	0.0406195i
$261$	1.22361	−	1.22361i	0.0757393	−	0.0757393i
$262$	−9.32171	−	9.32171i	−0.575897	−	0.575897i
$263$	−7.40341	+	7.40341i	−0.456514	+	0.456514i	−0.897509	−	0.440995i	$-0.854626\pi$
$263$	−7.40341	+	7.40341i	−0.456514	+	0.456514i	0.440995	+	0.897509i	$0.354626\pi$
$264$	−2.77320	+	2.77320i	−0.170679	+	0.170679i
$265$	−8.92191	−	3.51366i	−0.548068	−	0.215843i
$266$	6.81776			0.418023
$267$	1.89234			0.115809
$268$	6.88391	+	6.88391i	0.420502	+	0.420502i
$269$		−	3.41947i		−	0.208489i	−0.994552	−	0.104244i	$-0.966758\pi$
$269$		−	3.41947i		−	0.208489i	0.994552	−	0.104244i	$-0.0332424\pi$
$270$	−0.819367	+	2.08054i	−0.0498651	+	0.126618i
$271$	17.8704			1.08555			0.542775	−	0.839878i	$-0.317374\pi$
$271$	17.8704			1.08555			0.542775	+	0.839878i	$0.317374\pi$
$272$	1.25497			0.0760940
$273$	−0.706760			−0.0427751
$274$	−14.5752	−	14.5752i	−0.880522	−	0.880522i
$275$	14.3435	+	13.3715i	0.864944	+	0.806333i
$276$	−0.814607	−	0.814607i	−0.0490336	−	0.0490336i
$277$			14.8527i			0.892410i	0.894931	+	0.446205i	$0.147225\pi$
$277$			14.8527i			0.892410i	−0.894931	+	0.446205i	$0.852775\pi$
$278$			1.20629i			0.0723486i
$279$	6.78274	+	6.78274i	0.406072	+	0.406072i
$280$	4.60357	+	1.81300i	0.275116	+	0.108347i
$281$	4.56193	+	4.56193i	0.272142	+	0.272142i	0.829962	−	0.557820i	$-0.188362\pi$
$281$	4.56193	+	4.56193i	0.272142	+	0.272142i	−0.557820	+	0.829962i	$0.688362\pi$
$282$	6.90761			0.411342
$283$	−32.3891			−1.92533			−0.962666	−	0.270692i	$-0.912748\pi$
$283$	−32.3891			−1.92533			−0.962666	+	0.270692i	$0.912748\pi$
$284$	3.29012			0.195233
$285$	−2.74778	−	6.31816i	−0.162764	−	0.374256i
$286$			1.25271i			0.0740741i
$287$	−6.14596	−	6.14596i	−0.362785	−	0.362785i
$288$	1.00000			0.0589256
$289$	−15.4250			−0.907355
$290$	−1.41786	+	3.60025i	−0.0832599	+	0.211414i
$291$	−2.84175	+	2.84175i	−0.166586	+	0.166586i
$292$	−8.53399	+	8.53399i	−0.499414	+	0.499414i
$293$	2.93182	+	2.93182i	0.171279	+	0.171279i	0.787541	−	0.616262i	$-0.211354\pi$
$293$	2.93182	+	2.93182i	0.171279	+	0.171279i	−0.616262	+	0.787541i	$0.711354\pi$
$294$	1.48777	−	1.48777i	0.0867688	−	0.0867688i
$295$	−5.45079	+	13.8407i	−0.317357	+	0.805835i
$296$	6.08275	−	0.0100817i	0.353553	−	0.000585988i
$297$	−2.77320	+	2.77320i	−0.160918	+	0.160918i
$298$	−0.425764			−0.0246639
$299$	−0.367973			−0.0212804
$300$	−0.175243	−	4.99693i	−0.0101176	−	0.288498i
$301$	2.93097	+	2.93097i	0.168938	+	0.168938i
$302$	−18.6559			−1.07353
$303$	−7.82575	−	7.82575i	−0.449578	−	0.449578i
$304$	−2.17875	+	2.17875i	−0.124960	+	0.124960i
$305$	−6.44427	+	16.3633i	−0.368998	+	0.936960i
$306$	1.25497			0.0717421
$307$	−0.225281	−	0.225281i	−0.0128575	−	0.0128575i	0.700649	−	0.713506i	$-0.252894\pi$
$307$	−0.225281	−	0.225281i	−0.0128575	−	0.0128575i	−0.713506	+	0.700649i	$0.752894\pi$
$308$	6.13622	+	6.13622i	0.349644	+	0.349644i
$309$	−9.76753	+	9.76753i	−0.555655	+	0.555655i
$310$	−19.9570	−	7.85956i	−1.13348	−	0.446393i
$311$	8.19803	−	8.19803i	0.464868	−	0.464868i	−0.435379	−	0.900247i	$-0.643386\pi$
$311$	8.19803	−	8.19803i	0.464868	−	0.464868i	0.900247	+	0.435379i	$0.143386\pi$
$312$	0.225859	−	0.225859i	0.0127868	−	0.0127868i
$313$		−	12.1187i		−	0.684987i	−0.939520	−	0.342494i	$-0.888729\pi$
$313$		−	12.1187i		−	0.684987i	0.939520	−	0.342494i	$-0.111271\pi$
$314$	6.23375	+	6.23375i	0.351791	+	0.351791i
$315$	4.60357	+	1.81300i	0.259382	+	0.102151i
$316$	−3.59077	+	3.59077i	−0.201996	+	0.201996i
$317$	5.46058	+	5.46058i	0.306697	+	0.306697i	0.843627	−	0.536930i	$-0.180416\pi$
$317$	5.46058	+	5.46058i	0.306697	+	0.306697i	−0.536930	+	0.843627i	$0.680416\pi$
$318$			4.28827i			0.240474i
$319$	−4.79886	+	4.79886i	−0.268685	+	0.268685i
$320$	−2.05054	+	0.891783i	−0.114629	+	0.0498522i
$321$			2.20433i			0.123034i
$322$	−1.80247	+	1.80247i	−0.100448	+	0.100448i
$323$	−2.73427	+	2.73427i	−0.152139	+	0.152139i
$324$	1.00000			0.0555556
$325$	−1.16818	−	1.08902i	−0.0647991	−	0.0604081i
$326$			15.4091i			0.853430i
$327$			5.99769i			0.331673i
$328$	3.92813			0.216895
$329$		−	15.2844i		−	0.842654i
$330$	3.21347	−	8.15967i	0.176896	−	0.449175i
$331$	14.2462	+	14.2462i	0.783041	+	0.783041i	0.980343	−	0.197302i	$-0.0632180\pi$
$331$	14.2462	+	14.2462i	0.783041	+	0.783041i	−0.197302	+	0.980343i	$0.563218\pi$
$332$	1.13008	+	1.13008i	0.0620211	+	0.0620211i
$333$	6.08275	−	0.0100817i	0.333333	−	0.000552474i
$334$			16.8371i			0.921285i
$335$	−20.2547	−	7.97679i	−1.10663	−	0.435819i
$336$		−	2.21268i		−	0.120712i
$337$	−23.4318	−	23.4318i	−1.27641	−	1.27641i	−0.942663	−	0.333746i	$-0.891687\pi$
$337$	−23.4318	−	23.4318i	−1.27641	−	1.27641i	−0.333746	−	0.942663i	$-0.608313\pi$
$338$			12.8980i			0.701557i
$339$	11.6944	−	11.6944i	0.635152	−	0.635152i
$340$	−2.57338	+	1.11916i	−0.139561	+	0.0606952i
$341$	−26.6012	−	26.6012i	−1.44054	−	1.44054i
$342$	−2.17875	+	2.17875i	−0.117813	+	0.117813i
$343$	−14.2442	−	14.2442i	−0.769115	−	0.769115i
$344$	−1.87330			−0.101001
$345$	2.39684	+	0.943934i	0.129041	+	0.0508197i
$346$	5.18404	+	5.18404i	0.278696	+	0.278696i
$347$		−	4.74393i		−	0.254667i	−0.991860	−	0.127334i	$-0.959358\pi$
$347$		−	4.74393i		−	0.254667i	0.991860	−	0.127334i	$-0.0406419\pi$
$348$	1.73044			0.0927613
$349$			14.8248i			0.793556i	0.917915	+	0.396778i	$0.129872\pi$
$349$			14.8248i			0.793556i	−0.917915	+	0.396778i	$0.870128\pi$
$350$	−11.0566	+	0.387756i	−0.591001	+	0.0207264i
$351$	0.225859	−	0.225859i	0.0120555	−	0.0120555i
$352$	−3.92190			−0.209038
$353$	−23.4920			−1.25035			−0.625177	−	0.780483i	$-0.714973\pi$
$353$	−23.4920			−1.25035			−0.625177	+	0.780483i	$0.714973\pi$
$354$	6.65245			0.353574
$355$	−6.74653	+	2.93407i	−0.358069	+	0.155725i
$356$	1.33809	+	1.33809i	0.0709185	+	0.0709185i
$357$		−	2.77686i		−	0.146967i
$358$	1.70251	−	1.70251i	0.0899805	−	0.0899805i
$359$		−	3.71905i		−	0.196284i	−0.995172	−	0.0981419i	$-0.968710\pi$
$359$		−	3.71905i		−	0.196284i	0.995172	−	0.0981419i	$-0.0312899\pi$
$360$	−2.05054	+	0.891783i	−0.108073	+	0.0470011i
$361$			9.50611i			0.500322i
$362$			8.75170i			0.459979i
$363$	3.09806	−	3.09806i	0.162606	−	0.162606i
$364$	−0.499755	−	0.499755i	−0.0261943	−	0.0261943i
$365$	9.88884	−	25.1098i	0.517606	−	1.31431i
$366$	7.86494			0.411107
$367$	20.2784	−	20.2784i	1.05852	−	1.05852i	0.0603458	−	0.998178i	$-0.480780\pi$
$367$	20.2784	−	20.2784i	1.05852	−	1.05852i	0.998178	−	0.0603458i	$-0.0192203\pi$
$368$		−	1.15203i		−	0.0600536i
$369$	3.92813			0.204490
$370$	−12.4640	+	5.44517i	−0.647970	+	0.283081i
$371$	9.48858			0.492623
$372$			9.59224i			0.497334i
$373$	17.0249	−	17.0249i	0.881515	−	0.881515i	−0.112174	−	0.993689i	$-0.535781\pi$
$373$	17.0249	−	17.0249i	0.881515	−	0.881515i	0.993689	+	0.112174i	$0.0357814\pi$
$374$	−4.92188			−0.254505
$375$	4.81552	+	10.0901i	0.248672	+	0.521052i
$376$	4.88442	+	4.88442i	0.251895	+	0.251895i
$377$	0.390836	−	0.390836i	0.0201291	−	0.0201291i
$378$		−	2.21268i		−	0.113808i
$379$		−	3.59500i		−	0.184663i	−0.995728	−	0.0923313i	$-0.970568\pi$
$379$		−	3.59500i		−	0.184663i	0.995728	−	0.0923313i	$-0.0294319\pi$
$380$	2.52465	−	6.41059i	0.129512	−	0.328856i
$381$			9.98731i			0.511665i
$382$	−4.56780	+	4.56780i	−0.233709	+	0.233709i
$383$		−	18.9973i		−	0.970715i	−0.874316	−	0.485358i	$-0.838689\pi$
$383$		−	18.9973i		−	0.970715i	0.874316	−	0.485358i	$-0.161311\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	−18.0548	−	7.11040i	−0.920156	−	0.362380i
$386$	5.51547			0.280730
$387$	−1.87330			−0.0952251
$388$	−4.01884			−0.204025
$389$	9.52518	−	9.52518i	0.482946	−	0.482946i	−0.423125	−	0.906071i	$-0.639067\pi$
$389$	9.52518	−	9.52518i	0.482946	−	0.482946i	0.906071	+	0.423125i	$0.139067\pi$
$390$	−0.261716	+	0.664551i	−0.0132525	+	0.0336509i
$391$		−	1.44577i		−	0.0731155i
$392$	2.10403			0.106270
$393$		−	13.1829i		−	0.664989i
$394$	−3.48510	−	3.48510i	−0.175577	−	0.175577i
$395$	4.16084	−	10.5652i	0.209354	−	0.531593i
$396$	−3.92190			−0.197083
$397$	6.55806	+	6.55806i	0.329139	+	0.329139i	0.852259	−	0.523120i	$-0.175232\pi$
$397$	6.55806	+	6.55806i	0.329139	+	0.329139i	−0.523120	+	0.852259i	$0.675232\pi$
$398$	11.0862	−	11.0862i	0.555703	−	0.555703i
$399$	4.82088	+	4.82088i	0.241346	+	0.241346i
$400$	3.40945	−	3.65728i	0.170472	−	0.182864i
$401$	−3.25081	+	3.25081i	−0.162337	+	0.162337i	−0.783601	−	0.621264i	$-0.786619\pi$
$401$	−3.25081	+	3.25081i	−0.162337	+	0.162337i	0.621264	+	0.783601i	$0.286619\pi$
$402$			9.73532i			0.485554i
$403$	2.16650	+	2.16650i	0.107921	+	0.107921i
$404$		−	11.0673i		−	0.550618i
$405$	−2.05054	+	0.891783i	−0.101892	+	0.0443130i
$406$		−	3.82892i		−	0.190026i
$407$	−23.8560	+	0.0395395i	−1.18250	+	0.00195990i
$408$	0.887401	+	0.887401i	0.0439329	+	0.0439329i
$409$	13.3605	+	13.3605i	0.660637	+	0.660637i	0.955530	−	0.294893i	$-0.0952842\pi$
$409$	13.3605	+	13.3605i	0.660637	+	0.660637i	−0.294893	+	0.955530i	$0.595284\pi$
$410$	−8.05479	+	3.50304i	−0.397798	+	0.173003i
$411$		−	20.6125i		−	1.01674i
$412$	−13.8134			−0.680536
$413$		−	14.7198i		−	0.724312i
$414$		−	1.15203i		−	0.0566191i
$415$	−3.32506	−	1.30949i	−0.163221	−	0.0642803i
$416$	0.319413			0.0156605
$417$	−0.852977	+	0.852977i	−0.0417705	+	0.0417705i
$418$	8.54484	−	8.54484i	0.417942	−	0.417942i
$419$			18.6060i			0.908963i	0.890756	+	0.454481i	$0.150175\pi$
$419$			18.6060i			0.908963i	−0.890756	+	0.454481i	$0.849825\pi$
$420$	1.97323	+	4.53720i	0.0962839	+	0.221393i
$421$	4.15626	−	4.15626i	0.202564	−	0.202564i	−0.598534	−	0.801098i	$-0.704250\pi$
$421$	4.15626	−	4.15626i	0.202564	−	0.202564i	0.801098	+	0.598534i	$0.204250\pi$
$422$			27.2170i			1.32490i
$423$	4.88442	+	4.88442i	0.237489	+	0.237489i
$424$	−3.03226	+	3.03226i	−0.147260	+	0.147260i
$425$	4.27877	−	4.58979i	0.207551	−	0.222637i
$426$	2.32647	+	2.32647i	0.112718	+	0.112718i
$427$		−	17.4026i		−	0.842172i
$428$	−1.55870	+	1.55870i	−0.0753426	+	0.0753426i
$429$	−0.885798	+	0.885798i	−0.0427667	+	0.0427667i
$430$	3.84128	−	1.67057i	0.185243	−	0.0805623i
$431$	−7.99513	+	7.99513i	−0.385112	+	0.385112i	−0.872940	−	0.487828i	$-0.837789\pi$
$431$	−7.99513	+	7.99513i	−0.385112	+	0.385112i	0.487828	+	0.872940i	$0.337789\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	21.8861	+	21.8861i	1.05178	+	1.05178i	0.998584	+	0.0531948i	$0.0169404\pi$
$433$	21.8861	+	21.8861i	1.05178	+	1.05178i	0.0531948	+	0.998584i	$0.483060\pi$
$434$	21.2246			1.01881
$435$	−3.54834	+	1.54318i	−0.170130	+	0.0739897i
$436$	−4.24101	+	4.24101i	−0.203107	+	0.203107i
$437$	2.50998	+	2.50998i	0.120069	+	0.120069i
$438$	−12.0689			−0.576674
$439$	−19.4929	−	19.4929i	−0.930345	−	0.930345i	0.0673822	−	0.997727i	$-0.478535\pi$
$439$	−19.4929	−	19.4929i	−0.930345	−	0.930345i	−0.997727	+	0.0673822i	$0.978535\pi$
$440$	8.04202	−	3.49748i	0.383388	−	0.166736i
$441$	2.10403			0.100192
$442$	0.400855			0.0190667
$443$	1.25482	−	1.25482i	0.0596181	−	0.0596181i	−0.676669	−	0.736287i	$-0.736577\pi$
$443$	1.25482	−	1.25482i	0.0596181	−	0.0596181i	0.736287	+	0.676669i	$0.236577\pi$
$444$	4.30829	+	4.29403i	0.204462	+	0.203786i
$445$	−3.93709	−	1.55052i	−0.186636	−	0.0735018i
$446$	−11.1865	+	11.1865i	−0.529696	+	0.529696i
$447$	−0.301061	−	0.301061i	−0.0142397	−	0.0142397i
$448$	1.56460	−	1.56460i	0.0739206	−	0.0739206i
$449$	5.51963	−	5.51963i	0.260487	−	0.260487i	−0.564765	−	0.825252i	$-0.691033\pi$
$449$	5.51963	−	5.51963i	0.260487	−	0.260487i	0.825252	+	0.564765i	$0.191033\pi$
$450$	3.40945	−	3.65728i	0.160723	−	0.172406i
$451$	−15.4057			−0.725427
$452$	16.5384			0.777899
$453$	−13.1917	−	13.1917i	−0.619801	−	0.619801i
$454$			1.74912i			0.0820905i
$455$	1.47044	+	0.579096i	0.0689354	+	0.0271484i
$456$	−3.08122			−0.144291
$457$	−6.65948			−0.311517			−0.155759	−	0.987795i	$-0.549782\pi$
$457$	−6.65948			−0.311517			−0.155759	+	0.987795i	$0.549782\pi$
$458$	−8.51464			−0.397863
$459$	0.887401	+	0.887401i	0.0414203	+	0.0414203i
$460$	1.02736	+	2.36228i	0.0479009	+	0.110142i
$461$	−24.8127	−	24.8127i	−1.15564	−	1.15564i	−0.985403	−	0.170240i	$-0.945546\pi$
$461$	−24.8127	−	24.8127i	−1.15564	−	1.15564i	−0.170240	−	0.985403i	$-0.554454\pi$
$462$			8.67793i			0.403734i
$463$			0.607120i			0.0282153i	0.999900	+	0.0141076i	$0.00449075\pi$
$463$			0.607120i			0.0282153i	−0.999900	+	0.0141076i	$0.995509\pi$
$464$	1.22361	+	1.22361i	0.0568045	+	0.0568045i
$465$	−8.55419	−	19.6693i	−0.396691	−	0.912141i
$466$	−6.42533	−	6.42533i	−0.297648	−	0.297648i
$467$	−14.2821			−0.660896			−0.330448	−	0.943824i	$-0.607200\pi$
$467$	−14.2821			−0.660896			−0.330448	+	0.943824i	$0.607200\pi$
$468$	0.319413			0.0147649
$469$	21.5412			0.994679
$470$	−14.3716	−	5.65987i	−0.662910	−	0.261070i
$471$			8.81585i			0.406213i
$472$	4.70399	+	4.70399i	0.216519	+	0.216519i
$473$	7.34689			0.337810
$474$	−5.07811			−0.233245
$475$	0.539960	+	15.3966i	0.0247751	+	0.706445i
$476$	1.96354	−	1.96354i	0.0899986	−	0.0899986i
$477$	−3.03226	+	3.03226i	−0.138838	+	0.138838i
$478$	10.4976	+	10.4976i	0.480151	+	0.480151i
$479$	12.8987	−	12.8987i	0.589358	−	0.589358i	−0.348100	−	0.937458i	$-0.613173\pi$
$479$	12.8987	−	12.8987i	0.589358	−	0.589358i	0.937458	+	0.348100i	$0.113173\pi$
$480$	−2.08054	−	0.819367i	−0.0949631	−	0.0373988i
$481$	1.94291	−	0.00322023i	0.0885891	−	0.000146830i
$482$	−6.66851	+	6.66851i	−0.303742	+	0.303742i
$483$	−2.54907			−0.115987
$484$	4.38131			0.199151
$485$	8.24079	−	3.58393i	0.374195	−	0.162738i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	0.169467			0.00767930			0.00383965	−	0.999993i	$-0.498778\pi$
$487$	0.169467			0.00767930			0.00383965	+	0.999993i	$0.498778\pi$
$488$	5.56135	+	5.56135i	0.251750	+	0.251750i
$489$	−10.8959	+	10.8959i	−0.492728	+	0.492728i
$490$	−4.31440	+	1.87634i	−0.194905	+	0.0847644i
$491$	11.6118			0.524033			0.262016	−	0.965063i	$-0.415613\pi$
$491$	11.6118			0.524033			0.262016	+	0.965063i	$0.415613\pi$
$492$	2.77761	+	2.77761i	0.125224	+	0.125224i
$493$	1.53559	+	1.53559i	0.0691596	+	0.0691596i
$494$	−0.695921	+	0.695921i	−0.0313110	+	0.0313110i
$495$	8.04202	−	3.49748i	0.361462	−	0.157200i
$496$	−6.78274	+	6.78274i	−0.304554	+	0.304554i
$497$	5.14774	−	5.14774i	0.230908	−	0.230908i
$498$			1.59817i			0.0716158i
$499$	−15.8556	−	15.8556i	−0.709793	−	0.709793i	0.256698	−	0.966492i	$-0.417365\pi$
$499$	−15.8556	−	15.8556i	−0.709793	−	0.709793i	−0.966492	+	0.256698i	$0.917365\pi$
$500$	−3.72972	+	10.5399i	−0.166798	+	0.471358i
$501$	−11.9056	+	11.9056i	−0.531904	+	0.531904i
$502$	19.9946	+	19.9946i	0.892402	+	0.892402i
$503$			22.2525i			0.992190i	0.868268	+	0.496095i	$0.165233\pi$
$503$			22.2525i			0.992190i	−0.868268	+	0.496095i	$0.834767\pi$
$504$	1.56460	−	1.56460i	0.0696930	−	0.0696930i
$505$	9.86962	+	22.6939i	0.439192	+	1.00987i
$506$			4.51814i			0.200856i
$507$	−9.12025	+	9.12025i	−0.405044	+	0.405044i
$508$	−7.06209	+	7.06209i	−0.313330	+	0.313330i
$509$	23.6164			1.04678			0.523390	−	0.852093i	$-0.324667\pi$
$509$	23.6164			1.04678			0.523390	+	0.852093i	$0.324667\pi$
$510$	−2.61102	−	1.02828i	−0.115618	−	0.0455332i
$511$			26.7046i			1.18134i
$512$			1.00000i			0.0441942i
$513$	−3.08122			−0.136039
$514$			31.3639i			1.38340i
$515$	28.3249	−	12.3185i	1.24814	−	0.542819i
$516$	−1.32462	−	1.32462i	−0.0583132	−	0.0583132i
$517$	−19.1562	−	19.1562i	−0.842489	−	0.842489i
$518$	9.50133	−	9.53287i	0.417464	−	0.418850i
$519$			7.33134i			0.321810i
$520$	−0.654970	+	0.284847i	−0.0287223	+	0.0124914i
$521$		−	17.0507i		−	0.747006i	−0.927629	−	0.373503i	$-0.878157\pi$
$521$		−	17.0507i		−	0.747006i	0.927629	−	0.373503i	$-0.121843\pi$
$522$	1.22361	+	1.22361i	0.0535558	+	0.0535558i
$523$		−	23.5794i		−	1.03105i	−0.856873	−	0.515527i	$-0.827596\pi$
$523$		−	23.5794i		−	1.03105i	0.856873	−	0.515527i	$-0.172404\pi$
$524$	9.32171	−	9.32171i	0.407221	−	0.407221i
$525$	−8.09240	−	7.54403i	−0.353181	−	0.329248i
$526$	−7.40341	−	7.40341i	−0.322804	−	0.322804i
$527$	−8.51216	+	8.51216i	−0.370795	+	0.370795i
$528$	−2.77320	−	2.77320i	−0.120688	−	0.120688i
$529$	21.6728			0.942297
$530$	3.51366	−	8.92191i	0.152624	−	0.387543i
$531$	4.70399	+	4.70399i	0.204136	+	0.204136i
$532$			6.81776i			0.295587i
$533$	1.25470			0.0543469
$534$			1.89234i			0.0818896i
$535$	1.80616	−	4.58620i	0.0780870	−	0.198279i
$536$	−6.88391	+	6.88391i	−0.297340	+	0.297340i
$537$	2.40771			0.103901
$538$	3.41947			0.147424
$539$	−8.25180			−0.355430
$540$	−2.08054	−	0.819367i	−0.0895321	−	0.0352599i
$541$	−10.2113	−	10.2113i	−0.439020	−	0.439020i	0.452662	−	0.891682i	$-0.350474\pi$
$541$	−10.2113	−	10.2113i	−0.439020	−	0.439020i	−0.891682	+	0.452662i	$0.850474\pi$
$542$			17.8704i			0.767600i
$543$	−6.18839	+	6.18839i	−0.265569	+	0.265569i
$544$			1.25497i			0.0538066i
$545$	4.91431	−	12.4784i	0.210506	−	0.534517i
$546$		−	0.706760i		−	0.0302465i
$547$		−	26.3899i		−	1.12835i	−0.825655	−	0.564176i	$-0.809194\pi$
$547$		−	26.3899i		−	1.12835i	0.825655	−	0.564176i	$-0.190806\pi$
$548$	14.5752	−	14.5752i	0.622623	−	0.622623i
$549$	5.56135	+	5.56135i	0.237353	+	0.237353i
$550$	−13.3715	+	14.3435i	−0.570163	+	0.611608i
$551$	−5.33186			−0.227145
$552$	0.814607	−	0.814607i	0.0346720	−	0.0346720i
$553$			11.2363i			0.477814i
$554$	−14.8527			−0.631029
$555$	−12.6637	−	4.96303i	−0.537543	−	0.210669i
$556$	−1.20629			−0.0511582
$557$			33.0054i			1.39849i	0.714885	+	0.699243i	$0.246479\pi$
$557$			33.0054i			1.39849i	−0.714885	+	0.699243i	$0.753521\pi$
$558$	−6.78274	+	6.78274i	−0.287136	+	0.287136i
$559$	−0.598356			−0.0253078
$560$	−1.81300	+	4.60357i	−0.0766132	+	0.194536i
$561$	−3.48030	−	3.48030i	−0.146938	−	0.146938i
$562$	−4.56193	+	4.56193i	−0.192434	+	0.192434i
$563$			2.41113i			0.101617i	0.998708	+	0.0508086i	$0.0161798\pi$
$563$			2.41113i			0.101617i	−0.998708	+	0.0508086i	$0.983820\pi$
$564$			6.90761i			0.290863i
$565$	−33.9126	+	14.7486i	−1.42671	+	0.620479i
$566$		−	32.3891i		−	1.36142i
$567$	1.56460	−	1.56460i	0.0657072	−	0.0657072i
$568$			3.29012i			0.138050i
$569$	−16.6810	−	16.6810i	−0.699306	−	0.699306i	0.264955	−	0.964261i	$-0.414643\pi$
$569$	−16.6810	−	16.6810i	−0.699306	−	0.699306i	−0.964261	+	0.264955i	$0.914643\pi$
$570$	6.31816	−	2.74778i	0.264639	−	0.115092i
$571$	−34.7939			−1.45608			−0.728041	−	0.685534i	$-0.759569\pi$
$571$	−34.7939			−1.45608			−0.728041	+	0.685534i	$0.759569\pi$
$572$	−1.25271			−0.0523783
$573$	−6.45984			−0.269864
$574$	6.14596	−	6.14596i	0.256528	−	0.256528i
$575$	−4.21329	−	3.92778i	−0.175706	−	0.163800i
$576$			1.00000i			0.0416667i
$577$	42.4452			1.76702			0.883509	−	0.468414i	$-0.155174\pi$
$577$	42.4452			1.76702			0.883509	+	0.468414i	$0.155174\pi$
$578$		−	15.4250i		−	0.641597i
$579$	3.90003	+	3.90003i	0.162080	+	0.162080i
$580$	−3.60025	−	1.41786i	−0.149492	−	0.0588736i
$581$	3.53625			0.146708
$582$	−2.84175	−	2.84175i	−0.117794	−	0.117794i
$583$	11.8922	−	11.8922i	0.492526	−	0.492526i
$584$	−8.53399	−	8.53399i	−0.353139	−	0.353139i
$585$	−0.654970	+	0.284847i	−0.0270797	+	0.0117770i
$586$	−2.93182	+	2.93182i	−0.121112	+	0.121112i
$587$			25.7512i			1.06287i	0.847100	+	0.531433i	$0.178346\pi$
$587$			25.7512i			1.06287i	−0.847100	+	0.531433i	$0.821654\pi$
$588$	1.48777	+	1.48777i	0.0613548	+	0.0613548i
$589$		−	29.5558i		−	1.21782i
$590$	−13.8407	−	5.45079i	−0.569811	−	0.224406i
$591$		−	4.92868i		−	0.202739i
$592$	0.0100817	+	6.08275i	0.000414356	+	0.250000i
$593$	−17.7350	−	17.7350i	−0.728289	−	0.728289i	0.241990	−	0.970279i	$-0.422200\pi$
$593$	−17.7350	−	17.7350i	−0.728289	−	0.728289i	−0.970279	+	0.241990i	$0.922200\pi$
$594$	−2.77320	−	2.77320i	−0.113786	−	0.113786i
$595$	−2.27527	+	5.77736i	−0.0932768	+	0.236849i
$596$		−	0.425764i		−	0.0174400i
$597$	15.6783			0.641671
$598$		−	0.367973i		−	0.0150475i
$599$			33.5799i			1.37204i	0.727583	+	0.686020i	$0.240644\pi$
$599$			33.5799i			1.37204i	−0.727583	+	0.686020i	$0.759356\pi$
$600$	4.99693	−	0.175243i	0.203999	−	0.00715425i
$601$	−28.5324			−1.16386			−0.581930	−	0.813239i	$-0.697702\pi$
$601$	−28.5324			−1.16386			−0.581930	+	0.813239i	$0.697702\pi$
$602$	−2.93097	+	2.93097i	−0.119457	+	0.119457i
$603$	−6.88391	+	6.88391i	−0.280334	+	0.280334i
$604$		−	18.6559i		−	0.759098i
$605$	−8.98406	+	3.90718i	−0.365254	+	0.158849i
$606$	7.82575	−	7.82575i	0.317900	−	0.317900i
$607$		−	26.3325i		−	1.06880i	−0.845231	−	0.534401i	$-0.820537\pi$
$607$		−	26.3325i		−	1.06880i	0.845231	−	0.534401i	$-0.179463\pi$
$608$	−2.17875	−	2.17875i	−0.0883599	−	0.0883599i
$609$	2.70745	−	2.70745i	0.109712	−	0.109712i
$610$	−16.3633	−	6.44427i	−0.662531	−	0.260921i
$611$	1.56015	+	1.56015i	0.0631168	+	0.0631168i
$612$			1.25497i			0.0507293i
$613$	−18.6885	+	18.6885i	−0.754820	+	0.754820i	−0.975375	−	0.220555i	$-0.929213\pi$
$613$	−18.6885	+	18.6885i	−0.754820	+	0.754820i	0.220555	+	0.975375i	$0.429213\pi$
$614$	0.225281	−	0.225281i	0.00909162	−	0.00909162i
$615$	−8.17262	−	3.21858i	−0.329552	−	0.129786i
$616$	−6.13622	+	6.13622i	−0.247235	+	0.247235i
$617$	−3.48887	−	3.48887i	−0.140457	−	0.140457i	0.633382	−	0.773839i	$-0.281666\pi$
$617$	−3.48887	−	3.48887i	−0.140457	−	0.140457i	−0.773839	+	0.633382i	$0.781666\pi$
$618$	−9.76753	−	9.76753i	−0.392907	−	0.392907i
$619$	3.83734			0.154236			0.0771178	−	0.997022i	$-0.475428\pi$
$619$	3.83734			0.154236			0.0771178	+	0.997022i	$0.475428\pi$
$620$	7.85956	−	19.9570i	0.315647	−	0.801493i
$621$	0.814607	−	0.814607i	0.0326891	−	0.0326891i
$622$	8.19803	+	8.19803i	0.328711	+	0.328711i
$623$	4.18715			0.167755
$624$	0.225859	+	0.225859i	0.00904160	+	0.00904160i
$625$	−1.75135	−	24.9386i	−0.0700540	−	0.997543i
$626$	12.1187			0.484359
$627$	12.0842			0.482597
$628$	−6.23375	+	6.23375i	−0.248754	+	0.248754i
$629$	0.0126523	+	7.63370i	0.000504480	+	0.304376i
$630$	−1.81300	+	4.60357i	−0.0722316	+	0.183411i
$631$	15.4358	−	15.4358i	0.614490	−	0.614490i	−0.329623	−	0.944113i	$-0.606922\pi$
$631$	15.4358	−	15.4358i	0.614490	−	0.614490i	0.944113	+	0.329623i	$0.106922\pi$
$632$	−3.59077	−	3.59077i	−0.142833	−	0.142833i
$633$	−19.2453	+	19.2453i	−0.764933	+	0.764933i
$634$	−5.46058	+	5.46058i	−0.216868	+	0.216868i
$635$	8.18326	−	20.7790i	0.324743	−	0.824588i
$636$	−4.28827			−0.170041
$637$	0.672055			0.0266278
$638$	−4.79886	−	4.79886i	−0.189989	−	0.189989i
$639$			3.29012i			0.130155i
$640$	−0.891783	−	2.05054i	−0.0352508	−	0.0810548i
$641$	−41.6890			−1.64662			−0.823309	−	0.567594i	$-0.807874\pi$
$641$	−41.6890			−1.64662			−0.823309	+	0.567594i	$0.807874\pi$
$642$	−2.20433			−0.0869982
$643$	−3.74780			−0.147799			−0.0738993	−	0.997266i	$-0.523544\pi$
$643$	−3.74780			−0.147799			−0.0738993	+	0.997266i	$0.523544\pi$
$644$	−1.80247	−	1.80247i	−0.0710272	−	0.0710272i
$645$	3.89747	+	1.53492i	0.153463	+	0.0604373i
$646$	−2.73427	−	2.73427i	−0.107579	−	0.107579i
$647$			3.49319i			0.137331i	0.997640	+	0.0686657i	$0.0218742\pi$
$647$			3.49319i			0.137331i	−0.997640	+	0.0686657i	$0.978126\pi$
$648$			1.00000i			0.0392837i
$649$	−18.4486	−	18.4486i	−0.724170	−	0.724170i
$650$	1.08902	−	1.16818i	0.0427150	−	0.0458199i
$651$	15.0080	+	15.0080i	0.588212	+	0.588212i
$652$	−15.4091			−0.603466
$653$	−32.5364			−1.27325			−0.636624	−	0.771175i	$-0.719670\pi$
$653$	−32.5364			−1.27325			−0.636624	+	0.771175i	$0.719670\pi$
$654$	−5.99769			−0.234528
$655$	−10.8016	+	27.4275i	−0.422054	+	1.07168i
$656$			3.92813i			0.153368i
$657$	−8.53399	−	8.53399i	−0.332943	−	0.332943i
$658$	15.2844			0.595847
$659$	2.62449			0.102236			0.0511178	−	0.998693i	$-0.483722\pi$
$659$	2.62449			0.102236			0.0511178	+	0.998693i	$0.483722\pi$
$660$	8.15967	+	3.21347i	0.317615	+	0.125084i
$661$	0.358911	−	0.358911i	0.0139600	−	0.0139600i	−0.700092	−	0.714052i	$-0.746858\pi$
$661$	0.358911	−	0.358911i	0.0139600	−	0.0139600i	0.714052	+	0.700092i	$0.246858\pi$
$662$	−14.2462	+	14.2462i	−0.553693	+	0.553693i
$663$	0.283447	+	0.283447i	0.0110082	+	0.0110082i
$664$	−1.13008	+	1.13008i	−0.0438556	+	0.0438556i
$665$	−6.07996	−	13.9801i	−0.235771	−	0.542125i
$666$	0.0100817	+	6.08275i	0.000390658	+	0.235702i
$667$	1.40963	−	1.40963i	0.0545810	−	0.0545810i
$668$	−16.8371			−0.651447
$669$	−15.8201			−0.611640
$670$	7.97679	−	20.2547i	0.308170	−	0.782507i
$671$	−21.8111	−	21.8111i	−0.842007	−	0.842007i
$672$	2.21268			0.0853561
$673$	−14.4928	−	14.4928i	−0.558658	−	0.558658i	0.370267	−	0.928925i	$-0.379266\pi$
$673$	−14.4928	−	14.4928i	−0.558658	−	0.558658i	−0.928925	+	0.370267i	$0.879266\pi$
$674$	23.4318	−	23.4318i	0.902557	−	0.902557i
$675$	4.99693	−	0.175243i	0.192332	−	0.00674509i
$676$	−12.8980			−0.496076
$677$	9.12580	+	9.12580i	0.350733	+	0.350733i	0.860382	−	0.509649i	$-0.170225\pi$
$677$	9.12580	+	9.12580i	0.350733	+	0.350733i	−0.509649	+	0.860382i	$0.670225\pi$
$678$	11.6944	+	11.6944i	0.449120	+	0.449120i
$679$	−6.28788	+	6.28788i	−0.241307	+	0.241307i
$680$	−1.11916	−	2.57338i	−0.0429180	−	0.0986845i
$681$	−1.23682	+	1.23682i	−0.0473949	+	0.0473949i
$682$	26.6012	−	26.6012i	1.01861	−	1.01861i
$683$			24.7098i			0.945493i	0.881199	+	0.472746i	$0.156737\pi$
$683$			24.7098i			0.945493i	−0.881199	+	0.472746i	$0.843263\pi$
$684$	−2.17875	−	2.17875i	−0.0833065	−	0.0833065i
$685$	−16.8892	+	42.8850i	−0.645302	+	1.63855i
$686$	14.2442	−	14.2442i	0.543846	−	0.543846i
$687$	−6.02076	−	6.02076i	−0.229706	−	0.229706i
$688$		−	1.87330i		−	0.0714188i
$689$	−0.968545	+	0.968545i	−0.0368986	+	0.0368986i
$690$	−0.943934	+	2.39684i	−0.0359349	+	0.0912461i
$691$			47.7183i			1.81529i	0.419739	+	0.907645i	$0.362121\pi$
$691$			47.7183i			1.81529i	−0.419739	+	0.907645i	$0.637879\pi$
$692$	−5.18404	+	5.18404i	−0.197068	+	0.197068i
$693$	−6.13622	+	6.13622i	−0.233096	+	0.233096i
$694$	4.74393			0.180077
$695$	2.47355	−	1.07575i	0.0938272	−	0.0408055i
$696$			1.73044i			0.0655921i
$697$			4.92970i			0.186726i
$698$	−14.8248			−0.561128
$699$		−	9.08679i		−	0.343694i
$700$	−0.387756	−	11.0566i	−0.0146558	−	0.417901i
$701$	−2.69605	−	2.69605i	−0.101828	−	0.101828i	0.654357	−	0.756186i	$-0.272939\pi$
$701$	−2.69605	−	2.69605i	−0.101828	−	0.101828i	−0.756186	+	0.654357i	$0.772939\pi$
$702$	0.225859	+	0.225859i	0.00852451	+	0.00852451i
$703$	−13.2748	−	13.2308i	−0.500667	−	0.499010i
$704$		−	3.92190i		−	0.147812i
$705$	−6.16009	−	14.1644i	−0.232002	−	0.533460i
$706$		−	23.4920i		−	0.884134i
$707$	−17.3159	−	17.3159i	−0.651232	−	0.651232i
$708$			6.65245i			0.250014i
$709$	20.0239	−	20.0239i	0.752014	−	0.752014i	−0.222841	−	0.974855i	$-0.571533\pi$
$709$	20.0239	−	20.0239i	0.752014	−	0.752014i	0.974855	+	0.222841i	$0.0715331\pi$
$710$	−2.93407	−	6.74653i	−0.110114	−	0.253193i
$711$	−3.59077	−	3.59077i	−0.134664	−	0.134664i
$712$	−1.33809	+	1.33809i	−0.0501470	+	0.0501470i
$713$	7.81391	+	7.81391i	0.292633	+	0.292633i
$714$	2.77686			0.103921
$715$	2.56873	−	1.11714i	0.0960650	−	0.0417788i
$716$	1.70251	+	1.70251i	0.0636258	+	0.0636258i
$717$			14.8459i			0.554431i
$718$	3.71905			0.138794
$719$			32.6337i			1.21703i	0.793541	+	0.608517i	$0.208235\pi$
$719$			32.6337i			1.21703i	−0.793541	+	0.608517i	$0.791765\pi$
$720$	−0.891783	−	2.05054i	−0.0332348	−	0.0764192i
$721$	−21.6124	+	21.6124i	−0.804889	+	0.804889i
$722$	−9.50611			−0.353781
$723$	−9.43070			−0.350731
$724$	−8.75170			−0.325254
$725$	8.64688	−	0.303247i	0.321137	−	0.0112623i
$726$	3.09806	+	3.09806i	0.114980	+	0.114980i
$727$			21.1503i			0.784422i	0.919875	+	0.392211i	$0.128290\pi$
$727$			21.1503i			0.784422i	−0.919875	+	0.392211i	$0.871710\pi$
$728$	0.499755	−	0.499755i	0.0185222	−	0.0185222i
$729$			1.00000i			0.0370370i
$730$	25.1098	+	9.88884i	0.929354	+	0.366002i
$731$		−	2.35094i		−	0.0869527i
$732$			7.86494i			0.290696i
$733$	−26.3403	+	26.3403i	−0.972902	+	0.972902i	−0.999642	−	0.0267403i	$-0.991487\pi$
$733$	−26.3403	+	26.3403i	−0.972902	+	0.972902i	0.0267403	+	0.999642i	$0.491487\pi$
$734$	20.2784	+	20.2784i	0.748489	+	0.748489i
$735$	−4.37752	−	1.72397i	−0.161467	−	0.0635897i
$736$	1.15203			0.0424643
$737$	26.9980	−	26.9980i	0.994485	−	0.994485i
$738$			3.92813i			0.144596i
$739$	−27.2865			−1.00375			−0.501876	−	0.864940i	$-0.667357\pi$
$739$	−27.2865			−1.00375			−0.501876	+	0.864940i	$0.667357\pi$
$740$	−5.44517	−	12.4640i	−0.200168	−	0.458184i
$741$	−0.984181			−0.0361548
$742$			9.48858i			0.348337i
$743$	18.6520	−	18.6520i	0.684276	−	0.684276i	−0.276684	−	0.960961i	$-0.589236\pi$
$743$	18.6520	−	18.6520i	0.684276	−	0.684276i	0.960961	+	0.276684i	$0.0892357\pi$
$744$	−9.59224			−0.351668
$745$	0.379689	+	0.873048i	0.0139107	+	0.0319860i
$746$	17.0249	+	17.0249i	0.623325	+	0.623325i
$747$	−1.13008	+	1.13008i	−0.0413474	+	0.0413474i
$748$		−	4.92188i		−	0.179962i
$749$			4.87750i			0.178220i
$750$	−10.0901	+	4.81552i	−0.368440	+	0.175838i
$751$		−	29.3632i		−	1.07148i	−0.844384	−	0.535738i	$-0.820033\pi$
$751$		−	29.3632i		−	1.07148i	0.844384	−	0.535738i	$-0.179967\pi$
$752$	−4.88442	+	4.88442i	−0.178116	+	0.178116i
$753$			28.2766i			1.03046i
$754$	0.390836	+	0.390836i	0.0142334	+	0.0142334i
$755$	16.6370	+	38.2547i	0.605483	+	1.39223i
$756$	2.21268			0.0804745
$757$	36.6279			1.33126			0.665631	−	0.746281i	$-0.268162\pi$
$757$	36.6279			1.33126			0.665631	+	0.746281i	$0.268162\pi$
$758$	3.59500			0.130576
$759$	−3.19481	+	3.19481i	−0.115964	+	0.115964i
$760$	6.41059	+	2.52465i	0.232536	+	0.0915785i
$761$		−	13.4727i		−	0.488386i	−0.969727	−	0.244193i	$-0.921477\pi$
$761$		−	13.4727i		−	0.488386i	0.969727	−	0.244193i	$-0.0785230\pi$
$762$	−9.98731			−0.361802
$763$			13.2710i			0.480442i
$764$	−4.56780	−	4.56780i	−0.165257	−	0.165257i
$765$	−1.11916	−	2.57338i	−0.0404635	−	0.0930407i
$766$	18.9973			0.686399
$767$	1.50252	+	1.50252i	0.0542527	+	0.0542527i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	11.9916	+	11.9916i	0.432427	+	0.432427i	0.889453	−	0.457026i	$-0.151085\pi$
$769$	11.9916	+	11.9916i	0.432427	+	0.432427i	−0.457026	+	0.889453i	$0.651085\pi$
$770$	7.11040	−	18.0548i	0.256241	−	0.650648i
$771$	−22.1776	+	22.1776i	−0.798707	+	0.798707i
$772$			5.51547i			0.198506i
$773$	14.0271	+	14.0271i	0.504520	+	0.504520i	0.912839	−	0.408319i	$-0.133885\pi$
$773$	14.0271	+	14.0271i	0.504520	+	0.504520i	−0.408319	+	0.912839i	$0.633885\pi$
$774$		−	1.87330i		−	0.0673343i
$775$	1.68097	+	47.9317i	0.0603822	+	1.72176i
$776$		−	4.01884i		−	0.144268i
$777$	13.4592	−	0.0223076i	0.482846	−	0.000800282i
$778$	9.52518	+	9.52518i	0.341494	+	0.341494i
$779$	−8.55840	−	8.55840i	−0.306637	−	0.306637i
$780$	−0.664551	−	0.261716i	−0.0237948	−	0.00937095i
$781$		−	12.9035i		−	0.461725i
$782$	1.44577			0.0517005
$783$			1.73044i			0.0618409i
$784$			2.10403i			0.0751440i
$785$	7.22341	−	18.3417i	0.257815	−	0.654644i
$786$	13.1829			0.470218
$787$	−7.13187	+	7.13187i	−0.254224	+	0.254224i	−0.822700	−	0.568476i	$-0.807533\pi$
$787$	−7.13187	+	7.13187i	−0.254224	+	0.254224i	0.568476	+	0.822700i	$0.307533\pi$
$788$	3.48510	−	3.48510i	0.124152	−	0.124152i
$789$		−	10.4700i		−	0.372742i
$790$	10.5652	+	4.16084i	0.375893	+	0.148036i
$791$	25.8760	−	25.8760i	0.920043	−	0.920043i
$792$		−	3.92190i		−	0.139359i
$793$	1.77637	+	1.77637i	0.0630807	+	0.0630807i
$794$	−6.55806	+	6.55806i	−0.232737	+	0.232737i
$795$	8.79328	−	3.82420i	0.311865	−	0.135631i
$796$	11.0862	+	11.0862i	0.392942	+	0.392942i
$797$		−	5.26825i		−	0.186611i	−0.995638	−	0.0933054i	$-0.970257\pi$
$797$		−	5.26825i		−	0.186611i	0.995638	−	0.0933054i	$-0.0297433\pi$
$798$	−4.82088	+	4.82088i	−0.170657	+	0.170657i
$799$	−6.12982	+	6.12982i	−0.216857	+	0.216857i
$800$	3.65728	+	3.40945i	0.129304	+	0.120542i
$801$	−1.33809	+	1.33809i	−0.0472790	+	0.0472790i
$802$	−3.25081	−	3.25081i	−0.114790	−	0.114790i
$803$	33.4695	+	33.4695i	1.18111	+	1.18111i
$804$	−9.73532			−0.343338
$805$	5.30345	+	2.08863i	0.186922	+	0.0736144i
$806$	−2.16650	+	2.16650i	−0.0763115	+	0.0763115i
$807$	2.41793	+	2.41793i	0.0851151	+	0.0851151i
$808$	11.0673			0.389346
$809$	7.49771	+	7.49771i	0.263605	+	0.263605i	0.826517	−	0.562912i	$-0.190319\pi$
$809$	7.49771	+	7.49771i	0.263605	+	0.263605i	−0.562912	+	0.826517i	$0.690319\pi$
$810$	−0.891783	−	2.05054i	−0.0313341	−	0.0720487i
$811$	17.4655			0.613296			0.306648	−	0.951823i	$-0.400793\pi$
$811$	17.4655			0.613296			0.306648	+	0.951823i	$0.400793\pi$
$812$	3.82892			0.134369
$813$	−12.6363	+	12.6363i	−0.443174	+	0.443174i
$814$	−0.0395395	−	23.8560i	−0.00138586	−	0.836151i
$815$	31.5970	−	13.7416i	1.10679	−	0.481346i
$816$	−0.887401	+	0.887401i	−0.0310652	+	0.0310652i
$817$	4.08144	+	4.08144i	0.142792	+	0.142792i
$818$	−13.3605	+	13.3605i	−0.467141	+	0.467141i
$819$	0.499755	−	0.499755i	0.0174629	−	0.0174629i
$820$	−3.50304	−	8.05479i	−0.122331	−	0.281286i
$821$	−30.4173			−1.06157			−0.530786	−	0.847506i	$-0.678103\pi$
$821$	−30.4173			−1.06157			−0.530786	+	0.847506i	$0.678103\pi$
$822$	20.6125			0.718943
$823$	34.7921	+	34.7921i	1.21278	+	1.21278i	0.970110	+	0.242667i	$0.0780221\pi$
$823$	34.7921	+	34.7921i	1.21278	+	1.21278i	0.242667	+	0.970110i	$0.421978\pi$
$824$		−	13.8134i		−	0.481211i
$825$	−19.5975	+	0.687284i	−0.682296	+	0.0239282i
$826$	14.7198			0.512166
$827$	−37.5059			−1.30421			−0.652104	−	0.758129i	$-0.726114\pi$
$827$	−37.5059			−1.30421			−0.652104	+	0.758129i	$0.726114\pi$
$828$	1.15203			0.0400358
$829$	38.6319	+	38.6319i	1.34174	+	1.34174i	0.894327	+	0.447414i	$0.147655\pi$
$829$	38.6319	+	38.6319i	1.34174	+	1.34174i	0.447414	+	0.894327i	$0.352345\pi$
$830$	1.30949	−	3.32506i	0.0454530	−	0.115414i
$831$	−10.5024	−	10.5024i	−0.364325	−	0.364325i
$832$			0.319413i			0.0110737i
$833$			2.64050i			0.0914881i
$834$	−0.852977	−	0.852977i	−0.0295362	−	0.0295362i
$835$	34.5252	−	15.0150i	1.19479	−	0.519617i
$836$	8.54484	+	8.54484i	0.295529	+	0.295529i
$837$	−9.59224			−0.331556
$838$	−18.6060			−0.642734
$839$	14.2744			0.492807			0.246404	−	0.969167i	$-0.420751\pi$
$839$	14.2744			0.492807			0.246404	+	0.969167i	$0.420751\pi$
$840$	−4.53720	+	1.97323i	−0.156548	+	0.0680830i
$841$		−	26.0056i		−	0.896744i
$842$	4.15626	+	4.15626i	0.143234	+	0.143234i
$843$	−6.45155			−0.222203
$844$	−27.2170			−0.936848
$845$	26.4478	−	11.5022i	0.909833	−	0.395687i
$846$	−4.88442	+	4.88442i	−0.167930	+	0.167930i
$847$	6.85502	−	6.85502i	0.235541	−	0.235541i
$848$	−3.03226	−	3.03226i	−0.104128	−	0.104128i
$849$	22.9026	−	22.9026i	0.786014	−	0.786014i
$850$	4.58979	+	4.27877i	0.157428	+	0.146760i
$851$	7.00751	−	0.0116144i	0.240214	−	0.000398137i
$852$	−2.32647	+	2.32647i	−0.0797035	+	0.0797035i
$853$	37.6236			1.28821			0.644104	−	0.764938i	$-0.277231\pi$
$853$	37.6236			1.28821			0.644104	+	0.764938i	$0.277231\pi$
$854$	17.4026			0.595505
$855$	6.41059	+	2.52465i	0.219237	+	0.0863410i
$856$	−1.55870	−	1.55870i	−0.0532753	−	0.0532753i
$857$	25.5393			0.872405			0.436202	−	0.899849i	$-0.356323\pi$
$857$	25.5393			0.872405			0.436202	+	0.899849i	$0.356323\pi$
$858$	−0.885798	−	0.885798i	−0.0302406	−	0.0302406i
$859$	−35.0362	+	35.0362i	−1.19542	+	1.19542i	−0.219897	+	0.975523i	$0.570572\pi$
$859$	−35.0362	+	35.0362i	−1.19542	+	1.19542i	−0.975523	+	0.219897i	$0.929428\pi$
$860$	1.67057	+	3.84128i	0.0569661	+	0.130986i
$861$	8.69170			0.296212
$862$	−7.99513	−	7.99513i	−0.272315	−	0.272315i
$863$	−34.9362	−	34.9362i	−1.18924	−	1.18924i	−0.977277	−	0.211964i	$-0.932014\pi$
$863$	−34.9362	−	34.9362i	−1.18924	−	1.18924i	−0.211964	−	0.977277i	$-0.567986\pi$
$864$	−0.707107	+	0.707107i	−0.0240563	+	0.0240563i
$865$	6.00706	−	15.2531i	0.204246	−	0.518622i
$866$	−21.8861	+	21.8861i	−0.743720	+	0.743720i
$867$	10.9072	−	10.9072i	0.370426	−	0.370426i
$868$			21.2246i			0.720409i
$869$	14.0826	+	14.0826i	0.477721	+	0.477721i
$870$	−1.54318	−	3.54834i	−0.0523186	−	0.120300i
$871$	−2.19881	+	2.19881i	−0.0745039	+	0.0745039i
$872$	−4.24101	−	4.24101i	−0.143619	−	0.143619i
$873$		−	4.01884i		−	0.136017i
$874$	−2.50998	+	2.50998i	−0.0849014	+	0.0849014i
$875$	10.6552	+	22.3263i	0.360212	+	0.754766i
$876$		−	12.0689i		−	0.407770i
$877$	−36.4441	+	36.4441i	−1.23063	+	1.23063i	−0.266909	+	0.963722i	$0.586002\pi$
$877$	−36.4441	+	36.4441i	−1.23063	+	1.23063i	−0.963722	+	0.266909i	$0.913998\pi$
$878$	19.4929	−	19.4929i	0.657853	−	0.657853i
$879$	−4.14622			−0.139848
$880$	3.49748	+	8.04202i	0.117900	+	0.271097i
$881$		−	41.8468i		−	1.40986i	−0.709279	−	0.704928i	$-0.750979\pi$
$881$		−	41.8468i		−	1.40986i	0.709279	−	0.704928i	$-0.249021\pi$
$882$			2.10403i			0.0708464i
$883$	6.73598			0.226684			0.113342	−	0.993556i	$-0.463844\pi$
$883$	6.73598			0.226684			0.113342	+	0.993556i	$0.463844\pi$
$884$			0.400855i			0.0134822i
$885$	−5.93254	−	13.6411i	−0.199420	−	0.458541i
$886$	1.25482	+	1.25482i	0.0421564	+	0.0421564i
$887$	−5.08587	−	5.08587i	−0.170767	−	0.170767i	0.616549	−	0.787316i	$-0.288530\pi$
$887$	−5.08587	−	5.08587i	−0.170767	−	0.170767i	−0.787316	+	0.616549i	$0.788530\pi$
$888$	−4.29403	+	4.30829i	−0.144098	+	0.144577i
$889$			22.0987i			0.741168i
$890$	1.55052	−	3.93709i	0.0519736	−	0.131972i
$891$		−	3.92190i		−	0.131389i
$892$	−11.1865	−	11.1865i	−0.374551	−	0.374551i
$893$		−	21.2838i		−	0.712237i
$894$	0.301061	−	0.301061i	0.0100690	−	0.0100690i
$895$	−5.00934	−	1.97280i	−0.167444	−	0.0659435i
$896$	1.56460	+	1.56460i	0.0522697	+	0.0522697i
$897$	0.260196	−	0.260196i	0.00868770	−	0.00868770i
$898$	5.51963	+	5.51963i	0.184192	+	0.184192i
$899$	−16.5988			−0.553601
$900$	3.65728	+	3.40945i	0.121909	+	0.113648i
$901$	−3.80541	−	3.80541i	−0.126777	−	0.126777i
$902$		−	15.4057i		−	0.512955i
$903$	−4.14502			−0.137937
$904$			16.5384i			0.550057i
$905$	17.9457	−	7.80462i	0.596536	−	0.259434i
$906$	13.1917	−	13.1917i	0.438265	−	0.438265i
$907$	−5.02600			−0.166886			−0.0834428	−	0.996513i	$-0.526592\pi$
$907$	−5.02600			−0.166886			−0.0834428	+	0.996513i	$0.526592\pi$
$908$	−1.74912			−0.0580467
$909$	11.0673			0.367079
$910$	−0.579096	+	1.47044i	−0.0191968	+	0.0487447i
$911$	−6.78195	−	6.78195i	−0.224696	−	0.224696i	0.585777	−	0.810473i	$-0.300790\pi$
$911$	−6.78195	−	6.78195i	−0.224696	−	0.224696i	−0.810473	+	0.585777i	$0.800790\pi$
$912$		−	3.08122i		−	0.102029i
$913$	4.43206	−	4.43206i	0.146680	−	0.146680i
$914$		−	6.65948i		−	0.220276i
$915$	−7.01382	−	16.1274i	−0.231870	−	0.533155i
$916$		−	8.51464i		−	0.281332i
$917$		−	29.1696i		−	0.963264i
$918$	−0.887401	+	0.887401i	−0.0292886	+	0.0292886i
$919$	5.23943	+	5.23943i	0.172833	+	0.172833i	0.788223	−	0.615390i	$-0.211001\pi$
$919$	5.23943	+	5.23943i	0.172833	+	0.172833i	−0.615390	+	0.788223i	$0.711001\pi$
$920$	−2.36228	+	1.02736i	−0.0778822	+	0.0338710i
$921$	0.318596			0.0104981
$922$	24.8127	−	24.8127i	0.817163	−	0.817163i
$923$			1.05091i			0.0345911i
$924$	−8.67793			−0.285483
$925$	22.2807	+	20.7020i	0.732585	+	0.680676i
$926$	−0.607120			−0.0199512
$927$		−	13.8134i		−	0.453690i
$928$	−1.22361	+	1.22361i	−0.0401668	+	0.0401668i
$929$	−41.3020			−1.35507			−0.677537	−	0.735488i	$-0.736953\pi$
$929$	−41.3020			−1.35507			−0.677537	+	0.735488i	$0.736953\pi$
$930$	19.6693	−	8.55419i	0.644981	−	0.280503i
$931$	−4.58415	−	4.58415i	−0.150240	−	0.150240i
$932$	6.42533	−	6.42533i	0.210469	−	0.210469i
$933$			11.5938i			0.379563i
$934$		−	14.2821i		−	0.467324i
$935$	4.38925	+	10.0925i	0.143544	+	0.330061i
$936$			0.319413i			0.0104403i
$937$	30.8614	−	30.8614i	1.00820	−	1.00820i	0.00823050	−	0.999966i	$-0.497380\pi$
$937$	30.8614	−	30.8614i	1.00820	−	1.00820i	0.999966	−	0.00823050i	$-0.00261988\pi$
$938$			21.5412i			0.703344i
$939$	8.56918	+	8.56918i	0.279645	+	0.279645i
$940$	5.65987	−	14.3716i	0.184605	−	0.468748i
$941$	−5.06512			−0.165118			−0.0825590	−	0.996586i	$-0.526309\pi$
$941$	−5.06512			−0.165118			−0.0825590	+	0.996586i	$0.526309\pi$
$942$	−8.81585			−0.287236
$943$	4.52532			0.147365
$944$	−4.70399	+	4.70399i	−0.153102	+	0.153102i
$945$	−4.53720	+	1.97323i	−0.147595	+	0.0641893i
$946$			7.34689i			0.238868i
$947$	59.8123			1.94364			0.971819	−	0.235726i	$-0.0757469\pi$
$947$	59.8123			1.94364			0.971819	+	0.235726i	$0.0757469\pi$
$948$		−	5.07811i		−	0.164929i
$949$	−2.72587	−	2.72587i	−0.0884855	−	0.0884855i
$950$	−15.3966	+	0.539960i	−0.499532	+	0.0175186i
$951$	−7.72243			−0.250417
$952$	1.96354	+	1.96354i	0.0636386	+	0.0636386i
$953$	−17.6361	+	17.6361i	−0.571291	+	0.571291i	−0.932489	−	0.361198i	$-0.882368\pi$
$953$	−17.6361	+	17.6361i	−0.571291	+	0.571291i	0.361198	+	0.932489i	$0.382368\pi$
$954$	−3.03226	−	3.03226i	−0.0981732	−	0.0981732i
$955$	13.4399	+	5.29298i	0.434906	+	0.171277i
$956$	−10.4976	+	10.4976i	−0.339518	+	0.339518i
$957$		−	6.78661i		−	0.219380i
$958$	12.8987	+	12.8987i	0.416739	+	0.416739i
$959$		−	45.6089i		−	1.47279i
$960$	0.819367	−	2.08054i	0.0264449	−	0.0671491i
$961$		−	61.0110i		−	1.96810i
$962$	0.00322023	+	1.94291i	0.000103824	+	0.0626420i
$963$	−1.55870	−	1.55870i	−0.0502284	−	0.0502284i
$964$	−6.66851	−	6.66851i	−0.214778	−	0.214778i
$965$	−4.91860	−	11.3097i	−0.158335	−	0.364072i
$966$		−	2.54907i		−	0.0820151i
$967$	39.1113			1.25773			0.628867	−	0.777513i	$-0.283519\pi$
$967$	39.1113			1.25773			0.628867	+	0.777513i	$0.283519\pi$
$968$			4.38131i			0.140821i
$969$		−	3.86685i		−	0.124221i
$970$	3.58393	+	8.24079i	0.115073	+	0.264596i
$971$	49.6084			1.59201			0.796004	−	0.605291i	$-0.206943\pi$
$971$	49.6084			1.59201			0.796004	+	0.605291i	$0.206943\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−1.88737	+	1.88737i	−0.0605063	+	0.0605063i
$974$			0.169467i			0.00543009i
$975$	1.59608	−	0.0559748i	0.0511156	−	0.00179263i
$976$	−5.56135	+	5.56135i	−0.178014	+	0.178014i
$977$			17.0944i			0.546899i	0.961886	+	0.273450i	$0.0881646\pi$
$977$			17.0944i			0.546899i	−0.961886	+	0.273450i	$0.911835\pi$
$978$	−10.8959	−	10.8959i	−0.348411	−	0.348411i
$979$	5.24785	−	5.24785i	0.167722	−	0.167722i
$980$	−1.87634	−	4.31440i	−0.0599374	−	0.137819i
$981$	−4.24101	−	4.24101i	−0.135405	−	0.135405i
$982$			11.6118i			0.370547i
$983$	−14.4506	+	14.4506i	−0.460901	+	0.460901i	−0.898951	−	0.438050i	$-0.855669\pi$
$983$	−14.4506	+	14.4506i	−0.460901	+	0.460901i	0.438050	+	0.898951i	$0.355669\pi$
$984$	−2.77761	+	2.77761i	−0.0885468	+	0.0885468i
$985$	−4.03839	+	10.2543i	−0.128674	+	0.326729i
$986$	−1.53559	+	1.53559i	−0.0489033	+	0.0489033i
$987$	10.8077	+	10.8077i	0.344012	+	0.344012i
$988$	−0.695921	−	0.695921i	−0.0221402	−	0.0221402i
$989$	−2.15809			−0.0686233
$990$	3.49748	+	8.04202i	0.111157	+	0.255592i
$991$	−10.9464	+	10.9464i	−0.347723	+	0.347723i	−0.859261	−	0.511538i	$-0.829076\pi$
$991$	−10.9464	+	10.9464i	−0.347723	+	0.347723i	0.511538	+	0.859261i	$0.329076\pi$
$992$	−6.78274	−	6.78274i	−0.215352	−	0.215352i
$993$	−20.1471			−0.639350
$994$	5.14774	+	5.14774i	0.163276	+	0.163276i
$995$	−32.6193	−	12.8463i	−1.03410	−	0.407255i
$996$	−1.59817			−0.0506400
$997$	32.8775			1.04124			0.520621	−	0.853788i	$-0.325701\pi$
$997$	32.8775			1.04124			0.520621	+	0.853788i	$0.325701\pi$
$998$	15.8556	−	15.8556i	0.501899	−	0.501899i
$999$	−4.29403	+	4.30829i	−0.135857	+	0.136308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.a.43.8	✓	36
5.2	odd	4		1110.2.o.a.487.11	yes	36
37.31	odd	4		1110.2.o.a.253.11	yes	36
185.142	even	4	inner	1110.2.l.a.697.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.8	✓	36	1.1	even	1	trivial
1110.2.l.a.697.8	yes	36	185.142	even	4	inner
1110.2.o.a.253.11	yes	36	37.31	odd	4
1110.2.o.a.487.11	yes	36	5.2	odd	4

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.05054 - 0.891783i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.56460 + 1.56460i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.05054 - 0.891783i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.56460 + 1.56460i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(0.891783 + 2.05054i) q^{10} +3.92190i q^{11} +(0.707107 - 0.707107i) q^{12} -0.319413i q^{13} +(-1.56460 - 1.56460i) q^{14} +(-0.819367 + 2.08054i) q^{15} +1.00000 q^{16} +1.25497 q^{17} +1.00000 q^{18} +(-2.17875 + 2.17875i) q^{19} +(-2.05054 + 0.891783i) q^{20} -2.21268i q^{21} -3.92190 q^{22} -1.15203i q^{23} +(0.707107 + 0.707107i) q^{24} +(3.40945 - 3.65728i) q^{25} +0.319413 q^{26} +(0.707107 + 0.707107i) q^{27} +(1.56460 - 1.56460i) q^{28} +(1.22361 + 1.22361i) q^{29} +(-2.08054 - 0.819367i) q^{30} +(-6.78274 + 6.78274i) q^{31} +1.00000i q^{32} +(-2.77320 - 2.77320i) q^{33} +1.25497i q^{34} +(-1.81300 + 4.60357i) q^{35} +1.00000i q^{36} +(0.0100817 + 6.08275i) q^{37} +(-2.17875 - 2.17875i) q^{38} +(0.225859 + 0.225859i) q^{39} +(-0.891783 - 2.05054i) q^{40} +3.92813i q^{41} +2.21268 q^{42} -1.87330i q^{43} -3.92190i q^{44} +(-0.891783 - 2.05054i) q^{45} +1.15203 q^{46} +(-4.88442 + 4.88442i) q^{47} +(-0.707107 + 0.707107i) q^{48} +2.10403i q^{49} +(3.65728 + 3.40945i) q^{50} +(-0.887401 + 0.887401i) q^{51} +0.319413i q^{52} +(-3.03226 - 3.03226i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(3.49748 + 8.04202i) q^{55} +(1.56460 + 1.56460i) q^{56} -3.08122i q^{57} +(-1.22361 + 1.22361i) q^{58} +(-4.70399 + 4.70399i) q^{59} +(0.819367 - 2.08054i) q^{60} +(-5.56135 + 5.56135i) q^{61} +(-6.78274 - 6.78274i) q^{62} +(1.56460 + 1.56460i) q^{63} -1.00000 q^{64} +(-0.284847 - 0.654970i) q^{65} +(2.77320 - 2.77320i) q^{66} +(-6.88391 - 6.88391i) q^{67} -1.25497 q^{68} +(0.814607 + 0.814607i) q^{69} +(-4.60357 - 1.81300i) q^{70} -3.29012 q^{71} -1.00000 q^{72} +(8.53399 - 8.53399i) q^{73} +(-6.08275 + 0.0100817i) q^{74} +(0.175243 + 4.99693i) q^{75} +(2.17875 - 2.17875i) q^{76} +(-6.13622 - 6.13622i) q^{77} +(-0.225859 + 0.225859i) q^{78} +(3.59077 - 3.59077i) q^{79} +(2.05054 - 0.891783i) q^{80} -1.00000 q^{81} -3.92813 q^{82} +(-1.13008 - 1.13008i) q^{83} +2.21268i q^{84} +(2.57338 - 1.11916i) q^{85} +1.87330 q^{86} -1.73044 q^{87} +3.92190 q^{88} +(-1.33809 - 1.33809i) q^{89} +(2.05054 - 0.891783i) q^{90} +(0.499755 + 0.499755i) q^{91} +1.15203i q^{92} -9.59224i q^{93} +(-4.88442 - 4.88442i) q^{94} +(-2.52465 + 6.41059i) q^{95} +(-0.707107 - 0.707107i) q^{96} +4.01884 q^{97} -2.10403 q^{98} +3.92190 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) \) 36 * q - 36 * q^4 + 4 * q^7	\( 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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