LMFDB - Embedded newform 1110.2.o.a.253.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (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			253.11
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.a.487.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	1.00000			0.500000
$5$	−0.891783	−	2.05054i	−0.398817	−	0.917030i
$5$	−0.891783	−	2.05054i	−0.398817	−	0.917030i
$6$	−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	$0.387324\pi$
$8$	−1.00000			−0.353553
$9$		−	1.00000i		−	0.333333i
$10$	0.891783	+	2.05054i	0.282007	+	0.648438i
$11$		−	3.92190i		−	1.18250i	−0.806489	−	0.591249i	$-0.798635\pi$
$11$		−	3.92190i		−	1.18250i	0.806489	−	0.591249i	$-0.201365\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−0.319413			−0.0885893			−0.0442946	−	0.999019i	$-0.514104\pi$
$13$	−0.319413			−0.0885893			−0.0442946	+	0.999019i	$0.514104\pi$
$14$	1.56460	−	1.56460i	0.418158	−	0.418158i
$15$	−2.08054	−	0.819367i	−0.537193	−	0.211560i
$16$	1.00000			0.250000
$17$		−	1.25497i		−	0.304376i	−0.988352	−	0.152188i	$-0.951368\pi$
$17$		−	1.25497i		−	0.304376i	0.988352	−	0.152188i	$-0.0486319\pi$
$18$			1.00000i			0.235702i
$19$	2.17875	+	2.17875i	0.499839	+	0.499839i	0.911388	−	0.411549i	$-0.135012\pi$
$19$	2.17875	+	2.17875i	0.499839	+	0.499839i	−0.411549	+	0.911388i	$0.635012\pi$
$20$	−0.891783	−	2.05054i	−0.199409	−	0.458515i
$21$			2.21268i			0.482847i
$22$			3.92190i			0.836152i
$23$	−1.15203			−0.240215			−0.120107	−	0.992761i	$-0.538324\pi$
$23$	−1.15203			−0.240215			−0.120107	+	0.992761i	$0.538324\pi$
$24$	−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	$-0.801365\pi$
$29$	−1.22361	+	1.22361i	−0.227218	+	0.227218i	0.584312	+	0.811529i	$0.301365\pi$
$30$	2.08054	+	0.819367i	0.379853	+	0.149595i
$31$	−6.78274	−	6.78274i	−1.21822	−	1.21822i	−0.968256	−	0.249959i	$-0.919583\pi$
$31$	−6.78274	−	6.78274i	−1.21822	−	1.21822i	−0.249959	−	0.968256i	$-0.580417\pi$
$32$	−1.00000			−0.176777
$33$	−2.77320	−	2.77320i	−0.482753	−	0.482753i
$34$			1.25497i			0.215226i
$35$	4.60357	+	1.81300i	0.778146	+	0.306453i
$36$		−	1.00000i		−	0.166667i
$37$	−6.08275	−	0.0100817i	−0.999999	−	0.00165742i
$37$	−6.08275	−	0.0100817i	−0.999999	−	0.00165742i
$38$	−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	$-0.900763\pi$
$41$		−	3.92813i		−	0.613470i	0.951795	−	0.306735i	$-0.0992366\pi$
$42$		−	2.21268i		−	0.341425i
$43$	−1.87330			−0.285675			−0.142838	−	0.989746i	$-0.545623\pi$
$43$	−1.87330			−0.285675			−0.142838	+	0.989746i	$0.545623\pi$
$44$		−	3.92190i		−	0.591249i
$45$	−2.05054	+	0.891783i	−0.305677	+	0.132939i
$46$	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
$50$	3.40945	−	3.65728i	0.482169	−	0.517217i
$51$	−0.887401	−	0.887401i	−0.124261	−	0.124261i
$52$	−0.319413			−0.0442946
$53$	−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
$55$	−8.04202	+	3.49748i	−1.08439	+	0.471601i
$56$	1.56460	−	1.56460i	0.209079	−	0.209079i
$57$	3.08122			0.408117
$58$	1.22361	−	1.22361i	0.160667	−	0.160667i
$59$	4.70399	+	4.70399i	0.612407	+	0.612407i	0.943573	−	0.331165i	$-0.107442\pi$
$59$	4.70399	+	4.70399i	0.612407	+	0.612407i	−0.331165	+	0.943573i	$0.607442\pi$
$60$	−2.08054	−	0.819367i	−0.268596	−	0.105780i
$61$	−5.56135	−	5.56135i	−0.712058	−	0.712058i	0.254908	−	0.966965i	$-0.417955\pi$
$61$	−5.56135	−	5.56135i	−0.712058	−	0.712058i	−0.966965	+	0.254908i	$0.917955\pi$
$62$	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	0.988989	−	0.147986i	$-0.0472791\pi$
$67$	6.88391	+	6.88391i	0.841003	+	0.841003i	−0.147986	+	0.988989i	$0.547279\pi$
$68$		−	1.25497i		−	0.152188i
$69$	−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	$0.562546\pi$
$72$			1.00000i			0.117851i
$73$	−8.53399	+	8.53399i	−0.998828	+	0.998828i	−0.999999	−	0.00117124i	$-0.999627\pi$
$73$	−8.53399	+	8.53399i	−0.998828	+	0.998828i	0.00117124	+	0.999999i	$0.499627\pi$
$74$	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	$-0.342215\pi$
$79$	−3.59077	−	3.59077i	−0.403993	−	0.403993i	−0.879638	+	0.475645i	$0.842215\pi$
$80$	−0.891783	−	2.05054i	−0.0997044	−	0.229258i
$81$	−1.00000			−0.111111
$82$			3.92813i			0.433789i
$83$	−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
$87$			1.73044i			0.185523i
$88$			3.92190i			0.418076i
$89$	1.33809	−	1.33809i	0.141837	−	0.141837i	−0.632623	−	0.774460i	$-0.718022\pi$
$89$	1.33809	−	1.33809i	0.141837	−	0.141837i	0.774460	+	0.632623i	$0.218022\pi$
$90$	2.05054	−	0.891783i	0.216146	−	0.0940022i
$91$	0.499755	−	0.499755i	0.0523886	−	0.0523886i
$92$	−1.15203			−0.120107
$93$	−9.59224			−0.994669
$94$	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
$97$		−	4.01884i		−	0.408051i	−0.978966	−	0.204025i	$-0.934597\pi$
$97$		−	4.01884i		−	0.408051i	0.978966	−	0.204025i	$-0.0654025\pi$
$98$		−	2.10403i		−	0.212539i
$99$	−3.92190			−0.394166
$100$	−3.40945	+	3.65728i	−0.340945	+	0.365728i
$101$		−	11.0673i		−	1.10124i	−0.834757	−	0.550618i	$-0.814392\pi$
$101$		−	11.0673i		−	1.10124i	0.834757	−	0.550618i	$-0.185608\pi$
$102$	0.887401	+	0.887401i	0.0878658	+	0.0878658i
$103$			13.8134i			1.36107i	0.732715	+	0.680536i	$0.238253\pi$
$103$			13.8134i			1.36107i	−0.732715	+	0.680536i	$0.761747\pi$
$104$	0.319413			0.0313210
$105$	4.53720	−	1.97323i	0.442785	−	0.192568i
$106$	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	$-0.342737\pi$
$109$	−4.24101	−	4.24101i	−0.406215	−	0.406215i	−0.880416	+	0.474201i	$0.842737\pi$
$110$	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
$113$		−	16.5384i		−	1.55580i	−0.628390	−	0.777899i	$-0.716286\pi$
$113$		−	16.5384i		−	1.55580i	0.628390	−	0.777899i	$-0.283714\pi$
$114$	−3.08122			−0.288582
$115$	1.02736	+	2.36228i	0.0958018	+	0.220284i
$116$	−1.22361	+	1.22361i	−0.113609	+	0.113609i
$117$			0.319413i			0.0295298i
$118$	−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
$125$	10.5399	+	3.72972i	0.942716	+	0.333596i
$126$	−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	$0.103873\pi$
$128$	−1.00000			−0.0883883
$129$	−1.32462	+	1.32462i	−0.116626	+	0.116626i
$130$	−0.284847	−	0.654970i	−0.0249828	−	0.0574447i
$131$	−9.32171	−	9.32171i	−0.814442	−	0.814442i	0.170855	−	0.985296i	$-0.445347\pi$
$131$	−9.32171	−	9.32171i	−0.814442	−	0.814442i	−0.985296	+	0.170855i	$0.945347\pi$
$132$	−2.77320	−	2.77320i	−0.241376	−	0.241376i
$133$	−6.81776			−0.591174
$134$	−6.88391	−	6.88391i	−0.594679	−	0.594679i
$135$	−0.819367	+	2.08054i	−0.0705198	+	0.179064i
$136$			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	$-0.516291\pi$
$139$	−1.20629			−0.102316			−0.0511582	+	0.998691i	$0.516291\pi$
$140$	4.60357	+	1.81300i	0.389073	+	0.153226i
$141$			6.90761i			0.581726i
$142$	3.29012			0.276101
$143$			1.25271i			0.104757i
$144$		−	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
$148$	−6.08275	−	0.0100817i	−0.499999	−	0.000828712i
$149$			0.425764i			0.0348800i	0.999848	+	0.0174400i	$0.00555160\pi$
$149$			0.425764i			0.0348800i	−0.999848	+	0.0174400i	$0.994448\pi$
$150$	−0.175243	−	4.99693i	−0.0143085	−	0.407997i
$151$		−	18.6559i		−	1.51820i	−0.650976	−	0.759098i	$-0.725640\pi$
$151$		−	18.6559i		−	1.51820i	0.650976	−	0.759098i	$-0.274360\pi$
$152$	−2.17875	−	2.17875i	−0.176720	−	0.176720i
$153$	−1.25497			−0.101459
$154$	−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
$162$	1.00000			0.0785674
$163$			15.4091i			1.20693i	0.797389	+	0.603466i	$0.206214\pi$
$163$			15.4091i			1.20693i	−0.797389	+	0.603466i	$0.793786\pi$
$164$		−	3.92813i		−	0.306735i
$165$	−3.21347	+	8.15967i	−0.250169	+	0.635229i
$166$	1.13008	+	1.13008i	0.0877111	+	0.0877111i
$167$		−	16.8371i		−	1.30289i	−0.758694	−	0.651447i	$-0.774162\pi$
$167$		−	16.8371i		−	1.30289i	0.758694	−	0.651447i	$-0.225838\pi$
$168$		−	2.21268i		−	0.170712i
$169$	−12.8980			−0.992152
$170$	2.57338	−	1.11916i	0.197369	−	0.0858360i
$171$	2.17875	−	2.17875i	0.166613	−	0.166613i
$172$	−1.87330			−0.142838
$173$	−5.18404	+	5.18404i	−0.394136	+	0.394136i	−0.876159	−	0.482023i	$-0.839902\pi$
$173$	−5.18404	+	5.18404i	−0.394136	+	0.394136i	0.482023	+	0.876159i	$0.339902\pi$
$174$		−	1.73044i		−	0.131184i
$175$	−0.387756	−	11.0566i	−0.0293116	−	0.835802i
$176$		−	3.92190i		−	0.295624i
$177$	6.65245			0.500029
$178$	−1.33809	+	1.33809i	−0.100294	+	0.100294i
$179$	1.70251	−	1.70251i	0.127252	−	0.127252i	−0.640613	−	0.767864i	$-0.721320\pi$
$179$	1.70251	−	1.70251i	0.127252	−	0.127252i	0.767864	+	0.640613i	$0.221320\pi$
$180$	−2.05054	+	0.891783i	−0.152838	+	0.0664696i
$181$	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
$183$	−7.86494			−0.581393
$184$	1.15203			0.0849287
$185$	5.40382	+	12.4819i	0.397297	+	0.917690i
$186$	9.59224			0.703337
$187$	−4.92188			−0.359924
$188$	−4.88442	+	4.88442i	−0.356233	+	0.356233i
$189$	2.21268			0.160949
$190$	−2.52465	+	6.41059i	−0.183157	+	0.465073i
$191$	4.56780	−	4.56780i	0.330514	−	0.330514i	−0.522268	−	0.852782i	$-0.674914\pi$
$191$	4.56780	−	4.56780i	0.330514	−	0.330514i	0.852782	+	0.522268i	$0.174914\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−5.51547			−0.397012			−0.198506	−	0.980100i	$-0.563609\pi$
$193$	−5.51547			−0.397012			−0.198506	+	0.980100i	$0.563609\pi$
$194$			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	$0.306179\pi$
$198$	3.92190			0.278717
$199$	11.0862	−	11.0862i	0.785883	−	0.785883i	−0.194933	−	0.980817i	$-0.562449\pi$
$199$	11.0862	−	11.0862i	0.785883	−	0.785883i	0.980817	+	0.194933i	$0.0624490\pi$
$200$	3.40945	−	3.65728i	0.241084	−	0.258609i
$201$	9.73532			0.686676
$202$			11.0673i			0.778692i
$203$		−	3.82892i		−	0.268737i
$204$	−0.887401	−	0.887401i	−0.0621305	−	0.0621305i
$205$	−8.05479	+	3.50304i	−0.562571	+	0.244663i
$206$		−	13.8134i		−	0.962423i
$207$			1.15203i			0.0800715i
$208$	−0.319413			−0.0221473
$209$	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
$217$	21.2246			1.44082
$218$	4.24101	+	4.24101i	0.287237	+	0.287237i
$219$			12.0689i			0.815540i
$220$	−8.04202	+	3.49748i	−0.542193	+	0.235800i
$221$			0.400855i			0.0269644i
$222$	4.30829	−	4.29403i	0.289153	−	0.288196i
$223$	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
$227$		−	1.74912i		−	0.116093i	−0.998314	−	0.0580467i	$-0.981513\pi$
$227$		−	1.74912i		−	0.116093i	0.998314	−	0.0580467i	$-0.0184872\pi$
$228$	3.08122			0.204058
$229$			8.51464i			0.562663i	0.959611	+	0.281332i	$0.0907761\pi$
$229$			8.51464i			0.562663i	−0.959611	+	0.281332i	$0.909224\pi$
$230$	−1.02736	−	2.36228i	−0.0677421	−	0.155764i
$231$	8.67793			0.570966
$232$	1.22361	−	1.22361i	0.0803336	−	0.0803336i
$233$	6.42533	−	6.42533i	0.420938	−	0.420938i	−0.464589	−	0.885526i	$-0.653798\pi$
$233$	6.42533	−	6.42533i	0.420938	−	0.420938i	0.885526	+	0.464589i	$0.153798\pi$
$234$		−	0.319413i		−	0.0208807i
$235$	14.3716	+	5.65987i	0.937497	+	0.369209i
$236$	4.70399	+	4.70399i	0.306204	+	0.306204i
$237$	−5.07811			−0.329859
$238$	−1.96354	−	1.96354i	−0.127277	−	0.127277i
$239$	−10.4976	−	10.4976i	−0.679036	−	0.679036i	0.280746	−	0.959782i	$-0.409418\pi$
$239$	−10.4976	−	10.4976i	−0.679036	−	0.679036i	−0.959782	+	0.280746i	$0.909418\pi$
$240$	−2.08054	−	0.819367i	−0.134298	−	0.0528899i
$241$	6.66851	−	6.66851i	0.429556	−	0.429556i	−0.458921	−	0.888477i	$-0.651764\pi$
$241$	6.66851	−	6.66851i	0.429556	−	0.429556i	0.888477	+	0.458921i	$0.151764\pi$
$242$	4.38131			0.281641
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−5.56135	−	5.56135i	−0.356029	−	0.356029i
$245$	4.31440	−	1.87634i	0.275637	−	0.119875i
$246$	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	0.950099	+	0.311948i	$0.100981\pi$
$251$	19.9946	+	19.9946i	1.26205	+	1.26205i	0.311948	+	0.950099i	$0.399019\pi$
$252$	1.56460	+	1.56460i	0.0985608	+	0.0985608i
$253$			4.51814i			0.284053i
$254$	−7.06209	+	7.06209i	−0.443115	+	0.443115i
$255$	−1.02828	+	2.61102i	−0.0643936	+	0.163508i
$256$	1.00000			0.0625000
$257$		−	31.3639i		−	1.95642i	−0.207609	−	0.978212i	$-0.566568\pi$
$257$		−	31.3639i		−	1.95642i	0.207609	−	0.978212i	$-0.433432\pi$
$258$	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	−0.440995	−	0.897509i	$-0.645374\pi$
$263$	7.40341	−	7.40341i	0.456514	−	0.456514i	0.897509	+	0.440995i	$0.145374\pi$
$264$	2.77320	+	2.77320i	0.170679	+	0.170679i
$265$	−3.51366	+	8.92191i	−0.215843	+	0.548068i
$266$	6.81776			0.418023
$267$		−	1.89234i		−	0.115809i
$268$	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	$0.317374\pi$
$272$		−	1.25497i		−	0.0760940i
$273$		−	0.706760i		−	0.0427751i
$274$	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
$277$	−14.8527			−0.892410			−0.446205	−	0.894931i	$-0.647225\pi$
$277$	−14.8527			−0.892410			−0.446205	+	0.894931i	$0.647225\pi$
$278$	1.20629			0.0723486
$279$	−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	−0.557820	−	0.829962i	$-0.688362\pi$
$281$	4.56193	−	4.56193i	0.272142	−	0.272142i	0.829962	+	0.557820i	$0.188362\pi$
$282$		−	6.90761i		−	0.411342i
$283$		−	32.3891i		−	1.92533i	−0.270692	−	0.962666i	$-0.587252\pi$
$283$		−	32.3891i		−	1.92533i	0.270692	−	0.962666i	$-0.412748\pi$
$284$	−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
$288$			1.00000i			0.0589256i
$289$	15.4250			0.907355
$290$	−3.60025	−	1.41786i	−0.211414	−	0.0832599i
$291$	−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
$298$		−	0.425764i		−	0.0246639i
$299$	0.367973			0.0212804
$300$	0.175243	+	4.99693i	0.0101176	+	0.288498i
$301$	2.93097	−	2.93097i	0.168938	−	0.168938i
$302$			18.6559i			1.07353i
$303$	−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	0.713506	−	0.700649i	$-0.247106\pi$
$307$	0.225281	+	0.225281i	0.0128575	+	0.0128575i	−0.700649	+	0.713506i	$0.747106\pi$
$308$	6.13622	+	6.13622i	0.349644	+	0.349644i
$309$	9.76753	+	9.76753i	0.555655	+	0.555655i
$310$	7.85956	−	19.9570i	0.446393	−	1.13348i
$311$	8.19803	+	8.19803i	0.464868	+	0.464868i	0.900247	−	0.435379i	$-0.143386\pi$
$311$	8.19803	+	8.19803i	0.464868	+	0.464868i	−0.435379	+	0.900247i	$0.643386\pi$
$312$	0.225859	−	0.225859i	0.0127868	−	0.0127868i
$313$	−12.1187			−0.684987			−0.342494	−	0.939520i	$-0.611271\pi$
$313$	−12.1187			−0.684987			−0.342494	+	0.939520i	$0.611271\pi$
$314$	−6.23375	+	6.23375i	−0.351791	+	0.351791i
$315$	1.81300	−	4.60357i	0.102151	−	0.259382i
$316$	−3.59077	−	3.59077i	−0.201996	−	0.201996i
$317$	−5.46058	−	5.46058i	−0.306697	−	0.306697i	0.536930	−	0.843627i	$-0.319584\pi$
$317$	−5.46058	−	5.46058i	−0.306697	−	0.306697i	−0.843627	+	0.536930i	$0.819584\pi$
$318$	4.28827			0.240474
$319$	4.79886	+	4.79886i	0.268685	+	0.268685i
$320$	−0.891783	−	2.05054i	−0.0498522	−	0.114629i
$321$		−	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
$325$	1.08902	−	1.16818i	0.0604081	−	0.0647991i
$326$		−	15.4091i		−	0.853430i
$327$	−5.99769			−0.331673
$328$			3.92813i			0.216895i
$329$		−	15.2844i		−	0.842654i
$330$	3.21347	−	8.15967i	0.176896	−	0.449175i
$331$	14.2462	−	14.2462i	0.783041	−	0.783041i	−0.197302	−	0.980343i	$-0.563218\pi$
$331$	14.2462	−	14.2462i	0.783041	−	0.783041i	0.980343	+	0.197302i	$0.0632180\pi$
$332$	−1.13008	−	1.13008i	−0.0620211	−	0.0620211i
$333$	−0.0100817	+	6.08275i	−0.000552474	+	0.333333i
$334$			16.8371i			0.921285i
$335$	7.97679	−	20.2547i	0.435819	−	1.10663i
$336$			2.21268i			0.120712i
$337$	23.4318	+	23.4318i	1.27641	+	1.27641i	0.942663	+	0.333746i	$0.108313\pi$
$337$	23.4318	+	23.4318i	1.27641	+	1.27641i	0.333746	+	0.942663i	$0.391687\pi$
$338$	12.8980			0.701557
$339$	−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
$347$	4.74393			0.254667			0.127334	−	0.991860i	$-0.459358\pi$
$347$	4.74393			0.254667			0.127334	+	0.991860i	$0.459358\pi$
$348$			1.73044i			0.0927613i
$349$			14.8248i			0.793556i	0.917915	+	0.396778i	$0.129872\pi$
$349$			14.8248i			0.793556i	−0.917915	+	0.396778i	$0.870128\pi$
$350$	0.387756	+	11.0566i	0.0207264	+	0.591001i
$351$	0.225859	+	0.225859i	0.0120555	+	0.0120555i
$352$			3.92190i			0.209038i
$353$		−	23.4920i		−	1.25035i	−0.780483	−	0.625177i	$-0.785027\pi$
$353$		−	23.4920i		−	1.25035i	0.780483	−	0.625177i	$-0.214973\pi$
$354$	−6.65245			−0.353574
$355$	2.93407	+	6.74653i	0.155725	+	0.358069i
$356$	1.33809	−	1.33809i	0.0709185	−	0.0709185i
$357$	2.77686			0.146967
$358$	−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
$362$	−8.75170			−0.459979
$363$	−3.09806	+	3.09806i	−0.162606	+	0.162606i
$364$	0.499755	−	0.499755i	0.0261943	−	0.0261943i
$365$	25.1098	+	9.88884i	1.31431	+	0.517606i
$366$	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	$-0.0192203\pi$
$368$	−1.15203			−0.0600536
$369$	−3.92813			−0.204490
$370$	−5.40382	−	12.4819i	−0.280931	−	0.648905i
$371$	9.48858			0.492623
$372$	−9.59224			−0.497334
$373$	−17.0249	+	17.0249i	−0.881515	+	0.881515i	−0.993689	−	0.112174i	$-0.964219\pi$
$373$	−17.0249	+	17.0249i	−0.881515	+	0.881515i	0.112174	+	0.993689i	$0.464219\pi$
$374$	4.92188			0.254505
$375$	10.0901	−	4.81552i	0.521052	−	0.248672i
$376$	4.88442	−	4.88442i	0.251895	−	0.251895i
$377$	0.390836	−	0.390836i	0.0201291	−	0.0201291i
$378$	−2.21268			−0.113808
$379$		−	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
$383$	−18.9973			−0.970715			−0.485358	−	0.874316i	$-0.661311\pi$
$383$	−18.9973			−0.970715			−0.485358	+	0.874316i	$0.661311\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	7.11040	−	18.0548i	0.362380	−	0.920156i
$386$	5.51547			0.280730
$387$			1.87330i			0.0952251i
$388$		−	4.01884i		−	0.204025i
$389$	−9.52518	−	9.52518i	−0.482946	−	0.482946i	0.423125	−	0.906071i	$-0.360933\pi$
$389$	−9.52518	−	9.52518i	−0.482946	−	0.482946i	−0.906071	+	0.423125i	$0.860933\pi$
$390$	−0.664551	−	0.261716i	−0.0336509	−	0.0132525i
$391$			1.44577i			0.0731155i
$392$		−	2.10403i		−	0.106270i
$393$	−13.1829			−0.664989
$394$	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	0.523120	−	0.852259i	$-0.324768\pi$
$397$	−6.55806	−	6.55806i	−0.329139	−	0.329139i	−0.852259	+	0.523120i	$0.824768\pi$
$398$	−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	0.621264	−	0.783601i	$-0.286619\pi$
$401$	−3.25081	−	3.25081i	−0.162337	−	0.162337i	−0.783601	+	0.621264i	$0.786619\pi$
$402$	−9.73532			−0.485554
$403$	2.16650	+	2.16650i	0.107921	+	0.107921i
$404$		−	11.0673i		−	0.550618i
$405$	0.891783	+	2.05054i	0.0443130	+	0.101892i
$406$			3.82892i			0.190026i
$407$	−0.0395395	+	23.8560i	−0.00195990	+	1.18250i
$408$	0.887401	+	0.887401i	0.0439329	+	0.0439329i
$409$	−13.3605	+	13.3605i	−0.660637	+	0.660637i	−0.955530	−	0.294893i	$-0.904716\pi$
$409$	−13.3605	+	13.3605i	−0.660637	+	0.660637i	0.294893	+	0.955530i	$0.404716\pi$
$410$	8.05479	−	3.50304i	0.397798	−	0.173003i
$411$			20.6125i			1.01674i
$412$			13.8134i			0.680536i
$413$	−14.7198			−0.724312
$414$		−	1.15203i		−	0.0566191i
$415$	−1.30949	+	3.32506i	−0.0642803	+	0.163221i
$416$	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	$0.849825\pi$
$420$	4.53720	−	1.97323i	0.221393	−	0.0962839i
$421$	4.15626	+	4.15626i	0.202564	+	0.202564i	0.801098	−	0.598534i	$-0.204250\pi$
$421$	4.15626	+	4.15626i	0.202564	+	0.202564i	−0.598534	+	0.801098i	$0.704250\pi$
$422$	−27.2170			−1.32490
$423$	4.88442	+	4.88442i	0.237489	+	0.237489i
$424$	3.03226	+	3.03226i	0.147260	+	0.147260i
$425$	4.58979	+	4.27877i	0.222637	+	0.207551i
$426$	2.32647	−	2.32647i	0.112718	−	0.112718i
$427$	17.4026			0.842172
$428$	1.55870	−	1.55870i	0.0753426	−	0.0753426i
$429$	0.885798	+	0.885798i	0.0427667	+	0.0427667i
$430$	−1.67057	−	3.84128i	−0.0805623	−	0.185243i
$431$	−7.99513	−	7.99513i	−0.385112	−	0.385112i	0.487828	−	0.872940i	$-0.337789\pi$
$431$	−7.99513	−	7.99513i	−0.385112	−	0.385112i	−0.872940	+	0.487828i	$0.837789\pi$
$432$	−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
$438$		−	12.0689i		−	0.576674i
$439$	19.4929	−	19.4929i	0.930345	−	0.930345i	−0.0673822	−	0.997727i	$-0.521465\pi$
$439$	19.4929	−	19.4929i	0.930345	−	0.930345i	0.997727	+	0.0673822i	$0.0214647\pi$
$440$	8.04202	−	3.49748i	0.383388	−	0.166736i
$441$	2.10403			0.100192
$442$		−	0.400855i		−	0.0190667i
$443$	−1.25482	+	1.25482i	−0.0596181	+	0.0596181i	−0.736287	−	0.676669i	$-0.763423\pi$
$443$	−1.25482	+	1.25482i	−0.0596181	+	0.0596181i	0.676669	+	0.736287i	$0.263423\pi$
$444$	−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	$-0.308967\pi$
$449$	−5.51963	−	5.51963i	−0.260487	−	0.260487i	−0.825252	+	0.564765i	$0.808967\pi$
$450$	−3.65728	−	3.40945i	−0.172406	−	0.160723i
$451$	−15.4057			−0.725427
$452$		−	16.5384i		−	0.777899i
$453$	−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
$457$			6.65948i			0.311517i	0.987795	+	0.155759i	$0.0497822\pi$
$457$			6.65948i			0.311517i	−0.987795	+	0.155759i	$0.950218\pi$
$458$		−	8.51464i		−	0.397863i
$459$	−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	−0.170240	+	0.985403i	$0.554454\pi$
$461$	−24.8127	+	24.8127i	−1.15564	+	1.15564i	−0.985403	+	0.170240i	$0.945546\pi$
$462$	−8.67793			−0.403734
$463$	0.607120			0.0282153			0.0141076	−	0.999900i	$-0.495509\pi$
$463$	0.607120			0.0282153			0.0141076	+	0.999900i	$0.495509\pi$
$464$	−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
$467$			14.2821i			0.660896i	0.943824	+	0.330448i	$0.107200\pi$
$467$			14.2821i			0.660896i	−0.943824	+	0.330448i	$0.892800\pi$
$468$			0.319413i			0.0147649i
$469$	−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
$473$			7.34689i			0.337810i
$474$	5.07811			0.233245
$475$	−15.3966	+	0.539960i	−0.706445	+	0.0247751i
$476$	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	$-0.386827\pi$
$479$	−12.8987	−	12.8987i	−0.589358	−	0.589358i	−0.937458	+	0.348100i	$0.886827\pi$
$480$	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
$483$		−	2.54907i		−	0.115987i
$484$	−4.38131			−0.199151
$485$	−8.24079	+	3.58393i	−0.374195	+	0.162738i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$		−	0.169467i		−	0.00767930i	−0.999993	−	0.00383965i	$-0.998778\pi$
$487$		−	0.169467i		−	0.00767930i	0.999993	−	0.00383965i	$-0.00122220\pi$
$488$	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
$495$	3.49748	+	8.04202i	0.157200	+	0.361462i
$496$	−6.78274	−	6.78274i	−0.304554	−	0.304554i
$497$	5.14774	−	5.14774i	0.230908	−	0.230908i
$498$	1.59817			0.0716158
$499$	15.8556	−	15.8556i	0.709793	−	0.709793i	−0.256698	−	0.966492i	$-0.582635\pi$
$499$	15.8556	−	15.8556i	0.709793	−	0.709793i	0.966492	+	0.256698i	$0.0826347\pi$
$500$	10.5399	+	3.72972i	0.471358	+	0.166798i
$501$	−11.9056	−	11.9056i	−0.531904	−	0.531904i
$502$	−19.9946	−	19.9946i	−0.892402	−	0.892402i
$503$	22.2525			0.992190			0.496095	−	0.868268i	$-0.334767\pi$
$503$	22.2525			0.992190			0.496095	+	0.868268i	$0.334767\pi$
$504$	−1.56460	−	1.56460i	−0.0696930	−	0.0696930i
$505$	−22.6939	+	9.86962i	−1.00987	+	0.439192i
$506$		−	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	$-0.675333\pi$
$509$	−23.6164			−1.04678			−0.523390	+	0.852093i	$0.675333\pi$
$510$	1.02828	−	2.61102i	0.0455332	−	0.115618i
$511$		−	26.7046i		−	1.18134i
$512$	−1.00000			−0.0441942
$513$		−	3.08122i		−	0.136039i
$514$			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
$518$	−9.53287	+	9.50133i	−0.418850	+	0.417464i
$519$			7.33134i			0.321810i
$520$	−0.284847	−	0.654970i	−0.0124914	−	0.0287223i
$521$			17.0507i			0.747006i	0.927629	+	0.373503i	$0.121843\pi$
$521$			17.0507i			0.747006i	−0.927629	+	0.373503i	$0.878157\pi$
$522$	−1.22361	−	1.22361i	−0.0535558	−	0.0535558i
$523$	−23.5794			−1.03105			−0.515527	−	0.856873i	$-0.672404\pi$
$523$	−23.5794			−1.03105			−0.515527	+	0.856873i	$0.672404\pi$
$524$	−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
$532$	−6.81776			−0.295587
$533$			1.25470i			0.0543469i
$534$			1.89234i			0.0818896i
$535$	−4.58620	−	1.80616i	−0.198279	−	0.0780870i
$536$	−6.88391	−	6.88391i	−0.297340	−	0.297340i
$537$		−	2.40771i		−	0.103901i
$538$			3.41947i			0.147424i
$539$	8.25180			0.355430
$540$	−0.819367	+	2.08054i	−0.0352599	+	0.0895321i
$541$	−10.2113	+	10.2113i	−0.439020	+	0.439020i	−0.891682	−	0.452662i	$-0.850474\pi$
$541$	−10.2113	+	10.2113i	−0.439020	+	0.439020i	0.452662	+	0.891682i	$0.350474\pi$
$542$	−17.8704			−0.767600
$543$	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
$547$	26.3899			1.12835			0.564176	−	0.825655i	$-0.309194\pi$
$547$	26.3899			1.12835			0.564176	+	0.825655i	$0.309194\pi$
$548$	−14.5752	+	14.5752i	−0.622623	+	0.622623i
$549$	−5.56135	+	5.56135i	−0.237353	+	0.237353i
$550$	−14.3435	−	13.3715i	−0.611608	−	0.570163i
$551$	−5.33186			−0.227145
$552$	0.814607	−	0.814607i	0.0346720	−	0.0346720i
$553$	11.2363			0.477814
$554$	14.8527			0.631029
$555$	12.6471	+	5.00498i	0.536841	+	0.212450i
$556$	−1.20629			−0.0511582
$557$	−33.0054			−1.39849			−0.699243	−	0.714885i	$-0.746479\pi$
$557$	−33.0054			−1.39849			−0.699243	+	0.714885i	$0.746479\pi$
$558$	6.78274	−	6.78274i	0.287136	−	0.287136i
$559$	0.598356			0.0253078
$560$	4.60357	+	1.81300i	0.194536	+	0.0766132i
$561$	−3.48030	+	3.48030i	−0.146938	+	0.146938i
$562$	−4.56193	+	4.56193i	−0.192434	+	0.192434i
$563$	2.41113			0.101617			0.0508086	−	0.998708i	$-0.483820\pi$
$563$	2.41113			0.101617			0.0508086	+	0.998708i	$0.483820\pi$
$564$			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
$568$	3.29012			0.138050
$569$	16.6810	−	16.6810i	0.699306	−	0.699306i	−0.264955	−	0.964261i	$-0.585357\pi$
$569$	16.6810	−	16.6810i	0.699306	−	0.699306i	0.964261	+	0.264955i	$0.0853571\pi$
$570$	2.74778	+	6.31816i	0.115092	+	0.264639i
$571$	−34.7939			−1.45608			−0.728041	−	0.685534i	$-0.759569\pi$
$571$	−34.7939			−1.45608			−0.728041	+	0.685534i	$0.759569\pi$
$572$			1.25271i			0.0523783i
$573$		−	6.45984i		−	0.269864i
$574$	−6.14596	−	6.14596i	−0.256528	−	0.256528i
$575$	3.92778	−	4.21329i	0.163800	−	0.175706i
$576$		−	1.00000i		−	0.0416667i
$577$		−	42.4452i		−	1.76702i	−0.468414	−	0.883509i	$-0.655174\pi$
$577$		−	42.4452i		−	1.76702i	0.468414	−	0.883509i	$-0.344826\pi$
$578$	−15.4250			−0.641597
$579$	−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
$587$	−25.7512			−1.06287			−0.531433	−	0.847100i	$-0.678346\pi$
$587$	−25.7512			−1.06287			−0.531433	+	0.847100i	$0.678346\pi$
$588$	1.48777	+	1.48777i	0.0613548	+	0.0613548i
$589$		−	29.5558i		−	1.21782i
$590$	−5.45079	+	13.8407i	−0.224406	+	0.569811i
$591$			4.92868i			0.202739i
$592$	−6.08275	−	0.0100817i	−0.250000	−	0.000414356i
$593$	−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
$597$		−	15.6783i		−	0.641671i
$598$	−0.367973			−0.0150475
$599$			33.5799i			1.37204i	0.727583	+	0.686020i	$0.240644\pi$
$599$			33.5799i			1.37204i	−0.727583	+	0.686020i	$0.759356\pi$
$600$	−0.175243	−	4.99693i	−0.00715425	−	0.203999i
$601$	−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
$605$	3.90718	+	8.98406i	0.158849	+	0.365254i
$606$	7.82575	+	7.82575i	0.317900	+	0.317900i
$607$	26.3325			1.06880			0.534401	−	0.845231i	$-0.320537\pi$
$607$	26.3325			1.06880			0.534401	+	0.845231i	$0.320537\pi$
$608$	−2.17875	−	2.17875i	−0.0883599	−	0.0883599i
$609$	−2.70745	−	2.70745i	−0.109712	−	0.109712i
$610$	6.44427	−	16.3633i	0.260921	−	0.662531i
$611$	1.56015	−	1.56015i	0.0631168	−	0.0631168i
$612$	−1.25497			−0.0507293
$613$	18.6885	−	18.6885i	0.754820	−	0.754820i	−0.220555	−	0.975375i	$-0.570787\pi$
$613$	18.6885	−	18.6885i	0.754820	−	0.754820i	0.975375	+	0.220555i	$0.0707868\pi$
$614$	−0.225281	−	0.225281i	−0.00909162	−	0.00909162i
$615$	−3.21858	+	8.17262i	−0.129786	+	0.329552i
$616$	−6.13622	−	6.13622i	−0.247235	−	0.247235i
$617$	3.48887	+	3.48887i	0.140457	+	0.140457i	0.773839	−	0.633382i	$-0.218334\pi$
$617$	3.48887	+	3.48887i	0.140457	+	0.140457i	−0.633382	+	0.773839i	$0.718334\pi$
$618$	−9.76753	−	9.76753i	−0.392907	−	0.392907i
$619$	−3.83734			−0.154236			−0.0771178	−	0.997022i	$-0.524572\pi$
$619$	−3.83734			−0.154236			−0.0771178	+	0.997022i	$0.524572\pi$
$620$	−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
$623$			4.18715i			0.167755i
$624$	−0.225859	+	0.225859i	−0.00904160	+	0.00904160i
$625$	−1.75135	−	24.9386i	−0.0700540	−	0.997543i
$626$	12.1187			0.484359
$627$		−	12.0842i		−	0.482597i
$628$	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	0.944113	−	0.329623i	$-0.106922\pi$
$631$	15.4358	+	15.4358i	0.614490	+	0.614490i	−0.329623	+	0.944113i	$0.606922\pi$
$632$	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
$635$	−20.7790	−	8.18326i	−0.824588	−	0.324743i
$636$	−4.28827			−0.170041
$637$		−	0.672055i		−	0.0266278i
$638$	−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	$0.807874\pi$
$642$			2.20433i			0.0869982i
$643$		−	3.74780i		−	0.147799i	−0.997266	−	0.0738993i	$-0.976456\pi$
$643$		−	3.74780i		−	0.147799i	0.997266	−	0.0738993i	$-0.0235443\pi$
$644$	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
$647$	−3.49319			−0.137331			−0.0686657	−	0.997640i	$-0.521874\pi$
$647$	−3.49319			−0.137331			−0.0686657	+	0.997640i	$0.521874\pi$
$648$	1.00000			0.0392837
$649$	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
$652$			15.4091i			0.603466i
$653$		−	32.5364i		−	1.27325i	−0.771175	−	0.636624i	$-0.780330\pi$
$653$		−	32.5364i		−	1.27325i	0.771175	−	0.636624i	$-0.219670\pi$
$654$	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
$658$			15.2844i			0.595847i
$659$	−2.62449			−0.102236			−0.0511178	−	0.998693i	$-0.516278\pi$
$659$	−2.62449			−0.102236			−0.0511178	+	0.998693i	$0.516278\pi$
$660$	−3.21347	+	8.15967i	−0.125084	+	0.317615i
$661$	0.358911	+	0.358911i	0.0139600	+	0.0139600i	0.714052	−	0.700092i	$-0.246858\pi$
$661$	0.358911	+	0.358911i	0.0139600	+	0.0139600i	−0.700092	+	0.714052i	$0.746858\pi$
$662$	−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
$668$		−	16.8371i		−	0.651447i
$669$	15.8201			0.611640
$670$	−7.97679	+	20.2547i	−0.308170	+	0.782507i
$671$	−21.8111	+	21.8111i	−0.842007	+	0.842007i
$672$		−	2.21268i		−	0.0853561i
$673$	−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	0.509649	−	0.860382i	$-0.329775\pi$
$677$	−9.12580	−	9.12580i	−0.350733	−	0.350733i	−0.860382	+	0.509649i	$0.829775\pi$
$678$	11.6944	+	11.6944i	0.449120	+	0.449120i
$679$	6.28788	+	6.28788i	0.241307	+	0.241307i
$680$	2.57338	−	1.11916i	0.0986845	−	0.0429180i
$681$	−1.23682	−	1.23682i	−0.0473949	−	0.0473949i
$682$	26.6012	−	26.6012i	1.01861	−	1.01861i
$683$	24.7098			0.945493			0.472746	−	0.881199i	$-0.343263\pi$
$683$	24.7098			0.945493			0.472746	+	0.881199i	$0.343263\pi$
$684$	2.17875	−	2.17875i	0.0833065	−	0.0833065i
$685$	42.8850	+	16.8892i	1.63855	+	0.645302i
$686$	14.2442	+	14.2442i	0.543846	+	0.543846i
$687$	6.02076	+	6.02076i	0.229706	+	0.229706i
$688$	−1.87330			−0.0714188
$689$	0.968545	+	0.968545i	0.0368986	+	0.0368986i
$690$	−2.39684	−	0.943934i	−0.0912461	−	0.0359349i
$691$		−	47.7183i		−	1.81529i	−0.419739	−	0.907645i	$-0.637879\pi$
$691$		−	47.7183i		−	1.81529i	0.419739	−	0.907645i	$-0.362121\pi$
$692$	−5.18404	+	5.18404i	−0.197068	+	0.197068i
$693$	6.13622	−	6.13622i	0.233096	−	0.233096i
$694$	−4.74393			−0.180077
$695$	1.07575	+	2.47355i	0.0408055	+	0.0938272i
$696$		−	1.73044i		−	0.0655921i
$697$	−4.92970			−0.186726
$698$		−	14.8248i		−	0.561128i
$699$		−	9.08679i		−	0.343694i
$700$	−0.387756	−	11.0566i	−0.0146558	−	0.417901i
$701$	−2.69605	+	2.69605i	−0.101828	+	0.101828i	−0.756186	−	0.654357i	$-0.772939\pi$
$701$	−2.69605	+	2.69605i	−0.101828	+	0.101828i	0.654357	+	0.756186i	$0.272939\pi$
$702$	−0.225859	−	0.225859i	−0.00852451	−	0.00852451i
$703$	−13.2308	−	13.2748i	−0.499010	−	0.500667i
$704$		−	3.92190i		−	0.147812i
$705$	14.1644	−	6.16009i	0.533460	−	0.232002i
$706$			23.4920i			0.884134i
$707$	17.3159	+	17.3159i	0.651232	+	0.651232i
$708$	6.65245			0.250014
$709$	−20.0239	−	20.0239i	−0.752014	−	0.752014i	0.222841	−	0.974855i	$-0.428467\pi$
$709$	−20.0239	−	20.0239i	−0.752014	−	0.752014i	−0.974855	+	0.222841i	$0.928467\pi$
$710$	−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
$717$	−14.8459			−0.554431
$718$			3.71905i			0.138794i
$719$			32.6337i			1.21703i	0.793541	+	0.608517i	$0.208235\pi$
$719$			32.6337i			1.21703i	−0.793541	+	0.608517i	$0.791765\pi$
$720$	−2.05054	+	0.891783i	−0.0764192	+	0.0332348i
$721$	−21.6124	−	21.6124i	−0.804889	−	0.804889i
$722$			9.50611i			0.353781i
$723$		−	9.43070i		−	0.350731i
$724$	8.75170			0.325254
$725$	−0.303247	−	8.64688i	−0.0112623	−	0.321137i
$726$	3.09806	−	3.09806i	0.114980	−	0.114980i
$727$	−21.1503			−0.784422			−0.392211	−	0.919875i	$-0.628290\pi$
$727$	−21.1503			−0.784422			−0.392211	+	0.919875i	$0.628290\pi$
$728$	−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
$732$	−7.86494			−0.290696
$733$	26.3403	−	26.3403i	0.972902	−	0.972902i	−0.0267403	−	0.999642i	$-0.508513\pi$
$733$	26.3403	−	26.3403i	0.972902	−	0.972902i	0.999642	+	0.0267403i	$0.00851273\pi$
$734$	−20.2784	+	20.2784i	−0.748489	+	0.748489i
$735$	1.72397	−	4.37752i	0.0635897	−	0.161467i
$736$	1.15203			0.0424643
$737$	26.9980	−	26.9980i	0.994485	−	0.994485i
$738$	3.92813			0.144596
$739$	27.2865			1.00375			0.501876	−	0.864940i	$-0.332643\pi$
$739$	27.2865			1.00375			0.501876	+	0.864940i	$0.332643\pi$
$740$	5.40382	+	12.4819i	0.198648	+	0.458845i
$741$	−0.984181			−0.0361548
$742$	−9.48858			−0.348337
$743$	−18.6520	+	18.6520i	−0.684276	+	0.684276i	−0.960961	−	0.276684i	$-0.910764\pi$
$743$	−18.6520	+	18.6520i	−0.684276	+	0.684276i	0.276684	+	0.960961i	$0.410764\pi$
$744$	9.59224			0.351668
$745$	0.873048	−	0.379689i	0.0319860	−	0.0139107i
$746$	17.0249	−	17.0249i	0.623325	−	0.623325i
$747$	−1.13008	+	1.13008i	−0.0413474	+	0.0413474i
$748$	−4.92188			−0.179962
$749$			4.87750i			0.178220i
$750$	−10.0901	+	4.81552i	−0.368440	+	0.175838i
$751$			29.3632i			1.07148i	0.844384	+	0.535738i	$0.179967\pi$
$751$			29.3632i			1.07148i	−0.844384	+	0.535738i	$0.820033\pi$
$752$	−4.88442	+	4.88442i	−0.178116	+	0.178116i
$753$	28.2766			1.03046
$754$	−0.390836	+	0.390836i	−0.0142334	+	0.0142334i
$755$	−38.2547	+	16.6370i	−1.39223	+	0.605483i
$756$	2.21268			0.0804745
$757$		−	36.6279i		−	1.33126i	−0.746281	−	0.665631i	$-0.768162\pi$
$757$		−	36.6279i		−	1.33126i	0.746281	−	0.665631i	$-0.231838\pi$
$758$			3.59500i			0.130576i
$759$	3.19481	+	3.19481i	0.115964	+	0.115964i
$760$	−2.52465	+	6.41059i	−0.0915785	+	0.232536i
$761$			13.4727i			0.488386i	0.969727	+	0.244193i	$0.0785230\pi$
$761$			13.4727i			0.488386i	−0.969727	+	0.244193i	$0.921477\pi$
$762$			9.98731i			0.361802i
$763$	13.2710			0.480442
$764$	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	$-0.848915\pi$
$769$	−11.9916	+	11.9916i	−0.432427	+	0.432427i	0.457026	+	0.889453i	$0.348915\pi$
$770$	−7.11040	+	18.0548i	−0.256241	+	0.650648i
$771$	−22.1776	−	22.1776i	−0.798707	−	0.798707i
$772$	−5.51547			−0.198506
$773$	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
$775$	47.9317	−	1.68097i	1.72176	−	0.0603822i
$776$			4.01884i			0.144268i
$777$	0.0223076	−	13.4592i	0.000800282	−	0.482846i
$778$	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
$782$		−	1.44577i		−	0.0517005i
$783$	1.73044			0.0618409
$784$			2.10403i			0.0751440i
$785$	−18.3417	−	7.22341i	−0.654644	−	0.257815i
$786$	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
$790$	4.16084	−	10.5652i	0.148036	−	0.375893i
$791$	25.8760	+	25.8760i	0.920043	+	0.920043i
$792$	3.92190			0.139359
$793$	1.77637	+	1.77637i	0.0630807	+	0.0630807i
$794$	6.55806	+	6.55806i	0.232737	+	0.232737i
$795$	3.82420	+	8.79328i	0.135631	+	0.311865i
$796$	11.0862	−	11.0862i	0.392942	−	0.392942i
$797$	5.26825			0.186611			0.0933054	−	0.995638i	$-0.470257\pi$
$797$	5.26825			0.186611			0.0933054	+	0.995638i	$0.470257\pi$
$798$	4.82088	−	4.82088i	0.170657	−	0.170657i
$799$	6.12982	+	6.12982i	0.216857	+	0.216857i
$800$	3.40945	−	3.65728i	0.120542	−	0.129304i
$801$	−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
$808$			11.0673i			0.389346i
$809$	−7.49771	+	7.49771i	−0.263605	+	0.263605i	−0.826517	−	0.562912i	$-0.809681\pi$
$809$	−7.49771	+	7.49771i	−0.263605	+	0.263605i	0.562912	+	0.826517i	$0.309681\pi$
$810$	−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	$0.400793\pi$
$812$		−	3.82892i		−	0.134369i
$813$	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
$820$	−8.05479	+	3.50304i	−0.281286	+	0.122331i
$821$	−30.4173			−1.06157			−0.530786	−	0.847506i	$-0.678103\pi$
$821$	−30.4173			−1.06157			−0.530786	+	0.847506i	$0.678103\pi$
$822$		−	20.6125i		−	0.718943i
$823$	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
$827$			37.5059i			1.30421i	0.758129	+	0.652104i	$0.226114\pi$
$827$			37.5059i			1.30421i	−0.758129	+	0.652104i	$0.773886\pi$
$828$			1.15203i			0.0400358i
$829$	−38.6319	+	38.6319i	−1.34174	+	1.34174i	−0.447414	+	0.894327i	$0.647655\pi$
$829$	−38.6319	+	38.6319i	−1.34174	+	1.34174i	−0.894327	+	0.447414i	$0.852345\pi$
$830$	1.30949	−	3.32506i	0.0454530	−	0.115414i
$831$	−10.5024	+	10.5024i	−0.364325	+	0.364325i
$832$	−0.319413			−0.0110737
$833$	2.64050			0.0914881
$834$	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
$837$			9.59224i			0.331556i
$838$		−	18.6060i		−	0.642734i
$839$	−14.2744			−0.492807			−0.246404	−	0.969167i	$-0.579249\pi$
$839$	−14.2744			−0.492807			−0.246404	+	0.969167i	$0.579249\pi$
$840$	−4.53720	+	1.97323i	−0.156548	+	0.0680830i
$841$			26.0056i			0.896744i
$842$	−4.15626	−	4.15626i	−0.143234	−	0.143234i
$843$		−	6.45155i		−	0.222203i
$844$	27.2170			0.936848
$845$	11.5022	+	26.4478i	0.395687	+	0.909833i
$846$	−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
$853$			37.6236i			1.28821i	0.764938	+	0.644104i	$0.222769\pi$
$853$			37.6236i			1.28821i	−0.764938	+	0.644104i	$0.777231\pi$
$854$	−17.4026			−0.595505
$855$	−6.41059	−	2.52465i	−0.219237	−	0.0863410i
$856$	−1.55870	+	1.55870i	−0.0532753	+	0.0532753i
$857$		−	25.5393i		−	0.872405i	−0.899849	−	0.436202i	$-0.856323\pi$
$857$		−	25.5393i		−	0.872405i	0.899849	−	0.436202i	$-0.143677\pi$
$858$	−0.885798	−	0.885798i	−0.0302406	−	0.0302406i
$859$	35.0362	+	35.0362i	1.19542	+	1.19542i	0.975523	+	0.219897i	$0.0705722\pi$
$859$	35.0362	+	35.0362i	1.19542	+	1.19542i	0.219897	+	0.975523i	$0.429428\pi$
$860$	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
$865$	15.2531	+	6.00706i	0.518622	+	0.204246i
$866$	−21.8861	−	21.8861i	−0.743720	−	0.743720i
$867$	10.9072	−	10.9072i	0.370426	−	0.370426i
$868$	21.2246			0.720409
$869$	−14.0826	+	14.0826i	−0.477721	+	0.477721i
$870$	−3.54834	+	1.54318i	−0.120300	+	0.0523186i
$871$	−2.19881	−	2.19881i	−0.0745039	−	0.0745039i
$872$	4.24101	+	4.24101i	0.143619	+	0.143619i
$873$	−4.01884			−0.136017
$874$	2.50998	+	2.50998i	0.0849014	+	0.0849014i
$875$	−22.3263	+	10.6552i	−0.754766	+	0.360212i
$876$			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
$880$	−8.04202	+	3.49748i	−0.271097	+	0.117900i
$881$			41.8468i			1.40986i	0.709279	+	0.704928i	$0.249021\pi$
$881$			41.8468i			1.40986i	−0.709279	+	0.704928i	$0.750979\pi$
$882$	−2.10403			−0.0708464
$883$			6.73598i			0.226684i	0.993556	+	0.113342i	$0.0361555\pi$
$883$			6.73598i			0.226684i	−0.993556	+	0.113342i	$0.963844\pi$
$884$			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	0.787316	−	0.616549i	$-0.211470\pi$
$887$	5.08587	+	5.08587i	0.170767	+	0.170767i	−0.616549	+	0.787316i	$0.711470\pi$
$888$	4.30829	−	4.29403i	0.144577	−	0.144098i
$889$			22.0987i			0.741168i
$890$	3.93709	+	1.55052i	0.131972	+	0.0519736i
$891$			3.92190i			0.131389i
$892$	11.1865	+	11.1865i	0.374551	+	0.374551i
$893$	−21.2838			−0.712237
$894$	−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
$902$	15.4057			0.512955
$903$		−	4.14502i		−	0.137937i
$904$			16.5384i			0.550057i
$905$	−7.80462	−	17.9457i	−0.259434	−	0.596536i
$906$	13.1917	+	13.1917i	0.438265	+	0.438265i
$907$			5.02600i			0.166886i	0.996513	+	0.0834428i	$0.0265916\pi$
$907$			5.02600i			0.166886i	−0.996513	+	0.0834428i	$0.973408\pi$
$908$		−	1.74912i		−	0.0580467i
$909$	−11.0673			−0.367079
$910$	1.47044	+	0.579096i	0.0487447	+	0.0191968i
$911$	−6.78195	+	6.78195i	−0.224696	+	0.224696i	−0.810473	−	0.585777i	$-0.800790\pi$
$911$	−6.78195	+	6.78195i	−0.224696	+	0.224696i	0.585777	+	0.810473i	$0.300790\pi$
$912$	3.08122			0.102029
$913$	−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
$917$	29.1696			0.963264
$918$	0.887401	−	0.887401i	0.0292886	−	0.0292886i
$919$	−5.23943	+	5.23943i	−0.172833	+	0.172833i	−0.788223	−	0.615390i	$-0.788999\pi$
$919$	−5.23943	+	5.23943i	−0.172833	+	0.172833i	0.615390	+	0.788223i	$0.288999\pi$
$920$	−1.02736	−	2.36228i	−0.0338710	−	0.0778822i
$921$	0.318596			0.0104981
$922$	24.8127	−	24.8127i	0.817163	−	0.817163i
$923$	1.05091			0.0345911
$924$	8.67793			0.285483
$925$	20.7757	−	22.2119i	0.683101	−	0.730324i
$926$	−0.607120			−0.0199512
$927$	13.8134			0.453690
$928$	1.22361	−	1.22361i	0.0401668	−	0.0401668i
$929$	41.3020			1.35507			0.677537	−	0.735488i	$-0.263047\pi$
$929$	41.3020			1.35507			0.677537	+	0.735488i	$0.263047\pi$
$930$	−8.55419	−	19.6693i	−0.280503	−	0.644981i
$931$	−4.58415	+	4.58415i	−0.150240	+	0.150240i
$932$	6.42533	−	6.42533i	0.210469	−	0.210469i
$933$	11.5938			0.379563
$934$		−	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	$-0.00261988\pi$
$938$	21.5412			0.703344
$939$	−8.56918	+	8.56918i	−0.279645	+	0.279645i
$940$	14.3716	+	5.65987i	0.468748	+	0.184605i
$941$	−5.06512			−0.165118			−0.0825590	−	0.996586i	$-0.526309\pi$
$941$	−5.06512			−0.165118			−0.0825590	+	0.996586i	$0.526309\pi$
$942$			8.81585i			0.287236i
$943$			4.52532i			0.147365i
$944$	4.70399	+	4.70399i	0.153102	+	0.153102i
$945$	−1.97323	−	4.53720i	−0.0641893	−	0.147595i
$946$		−	7.34689i		−	0.238868i
$947$		−	59.8123i		−	1.94364i	−0.235726	−	0.971819i	$-0.575747\pi$
$947$		−	59.8123i		−	1.94364i	0.235726	−	0.971819i	$-0.424253\pi$
$948$	−5.07811			−0.164929
$949$	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	−0.361198	−	0.932489i	$-0.617632\pi$
$953$	17.6361	−	17.6361i	0.571291	−	0.571291i	0.932489	+	0.361198i	$0.117632\pi$
$954$	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
$957$	6.78661			0.219380
$958$	12.8987	+	12.8987i	0.416739	+	0.416739i
$959$		−	45.6089i		−	1.47279i
$960$	−2.08054	−	0.819367i	−0.0671491	−	0.0264449i
$961$			61.0110i			1.96810i
$962$	−1.94291	−	0.00322023i	−0.0626420	−	0.000103824i
$963$	−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
$967$		−	39.1113i		−	1.25773i	−0.777513	−	0.628867i	$-0.783519\pi$
$967$		−	39.1113i		−	1.25773i	0.777513	−	0.628867i	$-0.216481\pi$
$968$	4.38131			0.140821
$969$		−	3.86685i		−	0.124221i
$970$	8.24079	−	3.58393i	0.264596	−	0.115073i
$971$	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
$975$	−0.0559748	−	1.59608i	−0.00179263	−	0.0511156i
$976$	−5.56135	−	5.56135i	−0.178014	−	0.178014i
$977$	−17.0944			−0.546899			−0.273450	−	0.961886i	$-0.588165\pi$
$977$	−17.0944			−0.546899			−0.273450	+	0.961886i	$0.588165\pi$
$978$	−10.8959	−	10.8959i	−0.348411	−	0.348411i
$979$	−5.24785	−	5.24785i	−0.167722	−	0.167722i
$980$	4.31440	−	1.87634i	0.137819	−	0.0599374i
$981$	−4.24101	+	4.24101i	−0.135405	+	0.135405i
$982$	−11.6118			−0.370547
$983$	14.4506	−	14.4506i	0.460901	−	0.460901i	−0.438050	−	0.898951i	$-0.644331\pi$
$983$	14.4506	−	14.4506i	0.460901	−	0.460901i	0.898951	+	0.438050i	$0.144331\pi$
$984$	2.77761	+	2.77761i	0.0885468	+	0.0885468i
$985$	10.2543	+	4.03839i	0.326729	+	0.128674i
$986$	−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	0.511538	−	0.859261i	$-0.329076\pi$
$991$	−10.9464	−	10.9464i	−0.347723	−	0.347723i	−0.859261	+	0.511538i	$0.829076\pi$
$992$	6.78274	+	6.78274i	0.215352	+	0.215352i
$993$		−	20.1471i		−	0.639350i
$994$	−5.14774	+	5.14774i	−0.163276	+	0.163276i
$995$	−32.6193	−	12.8463i	−1.03410	−	0.407255i
$996$	−1.59817			−0.0506400
$997$		−	32.8775i		−	1.04124i	−0.853788	−	0.520621i	$-0.825701\pi$
$997$		−	32.8775i		−	1.04124i	0.853788	−	0.520621i	$-0.174299\pi$
$998$	−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.o.a.253.11	yes	36
5.2	odd	4		1110.2.l.a.697.8	yes	36
37.6	odd	4		1110.2.l.a.43.8	✓	36
185.117	even	4	inner	1110.2.o.a.487.11	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.8	✓	36	37.6	odd	4
1110.2.l.a.697.8	yes	36	5.2	odd	4
1110.2.o.a.253.11	yes	36	1.1	even	1	trivial
1110.2.o.a.487.11	yes	36	185.117	even	4	inner

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.o (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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