LMFDB - Embedded newform 1110.2.u.f.401.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(191,1110)]

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([2, 0, 3]))

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

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

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.u (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:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			401.10
Character	$\chi$	$=$	1110.401
Dual form			1110.2.u.f.191.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.55108 - 0.770820i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(1.64183 - 0.551724i) q^{6} +4.38167 q^{7} +(0.707107 + 0.707107i) q^{8} +(1.81167 + 2.39120i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.55108 - 0.770820i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(1.64183 - 0.551724i) q^{6} +4.38167 q^{7} +(0.707107 + 0.707107i) q^{8} +(1.81167 + 2.39120i) q^{9} -1.00000 q^{10} +4.49999 q^{11} +(-0.770820 + 1.55108i) q^{12} +(1.45588 - 1.45588i) q^{13} +(-3.09831 + 3.09831i) q^{14} +(-0.551724 - 1.64183i) q^{15} -1.00000 q^{16} +(1.09123 + 1.09123i) q^{17} +(-2.97188 - 0.409787i) q^{18} +(-0.737671 + 0.737671i) q^{19} +(0.707107 - 0.707107i) q^{20} +(-6.79630 - 3.37748i) q^{21} +(-3.18197 + 3.18197i) q^{22} +(-1.56045 - 1.56045i) q^{23} +(-0.551724 - 1.64183i) q^{24} +1.00000i q^{25} +2.05893i q^{26} +(-0.966859 - 5.10541i) q^{27} -4.38167i q^{28} +(-3.68128 + 3.68128i) q^{29} +(1.55108 + 0.770820i) q^{30} +(-0.303265 - 0.303265i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.97982 - 3.46868i) q^{33} -1.54323 q^{34} +(3.09831 + 3.09831i) q^{35} +(2.39120 - 1.81167i) q^{36} +(0.167677 + 6.08045i) q^{37} -1.04322i q^{38} +(-3.38041 + 1.13596i) q^{39} +1.00000i q^{40} -1.99260 q^{41} +(7.19395 - 2.41747i) q^{42} +(0.568955 - 0.568955i) q^{43} -4.49999i q^{44} +(-0.409787 + 2.97188i) q^{45} +2.20681 q^{46} -8.83045i q^{47} +(1.55108 + 0.770820i) q^{48} +12.1990 q^{49} +(-0.707107 - 0.707107i) q^{50} +(-0.851438 - 2.53372i) q^{51} +(-1.45588 - 1.45588i) q^{52} -8.07611i q^{53} +(4.29374 + 2.92640i) q^{54} +(3.18197 + 3.18197i) q^{55} +(3.09831 + 3.09831i) q^{56} +(1.71280 - 0.575573i) q^{57} -5.20612i q^{58} +(9.81764 + 9.81764i) q^{59} +(-1.64183 + 0.551724i) q^{60} +(0.496818 + 0.496818i) q^{61} +0.428882 q^{62} +(7.93815 + 10.4774i) q^{63} +1.00000i q^{64} +2.05893 q^{65} +(7.38821 - 2.48275i) q^{66} +7.31837i q^{67} +(1.09123 - 1.09123i) q^{68} +(1.21755 + 3.62320i) q^{69} -4.38167 q^{70} +13.3890i q^{71} +(-0.409787 + 2.97188i) q^{72} -12.3051i q^{73} +(-4.41809 - 4.18096i) q^{74} +(0.770820 - 1.55108i) q^{75} +(0.737671 + 0.737671i) q^{76} +19.7174 q^{77} +(1.58706 - 3.19355i) q^{78} +(-2.04760 + 2.04760i) q^{79} +(-0.707107 - 0.707107i) q^{80} +(-2.43568 + 8.66415i) q^{81} +(1.40898 - 1.40898i) q^{82} -10.2732i q^{83} +(-3.37748 + 6.79630i) q^{84} +1.54323i q^{85} +0.804623i q^{86} +(8.54756 - 2.87234i) q^{87} +(3.18197 + 3.18197i) q^{88} +(11.8187 - 11.8187i) q^{89} +(-1.81167 - 2.39120i) q^{90} +(6.37919 - 6.37919i) q^{91} +(-1.56045 + 1.56045i) q^{92} +(0.236625 + 0.704150i) q^{93} +(6.24407 + 6.24407i) q^{94} -1.04322 q^{95} +(-1.64183 + 0.551724i) q^{96} +(-0.766039 + 0.766039i) q^{97} +(-8.62600 + 8.62600i) q^{98} +(8.15251 + 10.7604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{7} - 8 q^{9}+O(q^{10}) $ 40 * q + 24 * q^7 - 8 * q^9	$ 40 q + 24 q^{7} - 8 q^{9} - 40 q^{10} + 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 16 q^{22} - 8 q^{31} + 24 q^{33} + 24 q^{34} + 32 q^{37} + 16 q^{39} + 12 q^{42} + 32 q^{43} + 8 q^{45} - 56 q^{46} - 32 q^{49} - 44 q^{51} - 16 q^{52} - 24 q^{54} + 16 q^{55} + 8 q^{57} - 72 q^{61} + 24 q^{63} - 28 q^{66} + 16 q^{69} - 24 q^{70} + 8 q^{72} - 16 q^{76} - 48 q^{79} + 120 q^{81} - 24 q^{82} - 24 q^{84} + 20 q^{87} + 16 q^{88} + 8 q^{90} - 92 q^{93} - 8 q^{94} - 40 q^{97}+O(q^{100}) $ 40 * q + 24 * q^7 - 8 * q^9 - 40 * q^10 + 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 16 * q^22 - 8 * q^31 + 24 * q^33 + 24 * q^34 + 32 * q^37 + 16 * q^39 + 12 * q^42 + 32 * q^43 + 8 * q^45 - 56 * q^46 - 32 * q^49 - 44 * q^51 - 16 * q^52 - 24 * q^54 + 16 * q^55 + 8 * q^57 - 72 * q^61 + 24 * q^63 - 28 * q^66 + 16 * q^69 - 24 * q^70 + 8 * q^72 - 16 * q^76 - 48 * q^79 + 120 * q^81 - 24 * q^82 - 24 * q^84 + 20 * q^87 + 16 * q^88 + 8 * q^90 - 92 * q^93 - 8 * q^94 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.55108	−	0.770820i	−0.895514	−	0.445033i
$3$	−1.55108	−	0.770820i	−0.895514	−	0.445033i
$4$		−	1.00000i		−	0.500000i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	1.64183	−	0.551724i	0.670274	−	0.225241i
$7$	4.38167			1.65611			0.828057	−	0.560643i	$-0.189446\pi$
$7$	4.38167			1.65611			0.828057	+	0.560643i	$0.189446\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.81167	+	2.39120i	0.603891	+	0.797067i
$10$	−1.00000			−0.316228
$11$	4.49999			1.35680			0.678399	−	0.734694i	$-0.262674\pi$
$11$	4.49999			1.35680			0.678399	+	0.734694i	$0.262674\pi$
$12$	−0.770820	+	1.55108i	−0.222517	+	0.447757i
$13$	1.45588	−	1.45588i	0.403789	−	0.403789i	−0.475777	−	0.879566i	$-0.657833\pi$
$13$	1.45588	−	1.45588i	0.403789	−	0.403789i	0.879566	+	0.475777i	$0.157833\pi$
$14$	−3.09831	+	3.09831i	−0.828057	+	0.828057i
$15$	−0.551724	−	1.64183i	−0.142455	−	0.423918i
$16$	−1.00000			−0.250000
$17$	1.09123	+	1.09123i	0.264662	+	0.264662i	0.826945	−	0.562283i	$-0.190077\pi$
$17$	1.09123	+	1.09123i	0.264662	+	0.264662i	−0.562283	+	0.826945i	$0.690077\pi$
$18$	−2.97188	−	0.409787i	−0.700479	−	0.0965878i
$19$	−0.737671	+	0.737671i	−0.169233	+	0.169233i	−0.786642	−	0.617409i	$-0.788182\pi$
$19$	−0.737671	+	0.737671i	−0.169233	+	0.169233i	0.617409	+	0.786642i	$0.288182\pi$
$20$	0.707107	−	0.707107i	0.158114	−	0.158114i
$21$	−6.79630	−	3.37748i	−1.48307	−	0.737026i
$22$	−3.18197	+	3.18197i	−0.678399	+	0.678399i
$23$	−1.56045	−	1.56045i	−0.325376	−	0.325376i	0.525449	−	0.850825i	$-0.323897\pi$
$23$	−1.56045	−	1.56045i	−0.325376	−	0.325376i	−0.850825	+	0.525449i	$0.823897\pi$
$24$	−0.551724	−	1.64183i	−0.112620	−	0.335137i
$25$			1.00000i			0.200000i
$26$			2.05893i			0.403789i
$27$	−0.966859	−	5.10541i	−0.186072	−	0.982536i
$28$		−	4.38167i		−	0.828057i
$29$	−3.68128	+	3.68128i	−0.683597	+	0.683597i	−0.960809	−	0.277212i	$-0.910590\pi$
$29$	−3.68128	+	3.68128i	−0.683597	+	0.683597i	0.277212	+	0.960809i	$0.410590\pi$
$30$	1.55108	+	0.770820i	0.283186	+	0.140732i
$31$	−0.303265	−	0.303265i	−0.0544680	−	0.0544680i	0.679348	−	0.733816i	$-0.262263\pi$
$31$	−0.303265	−	0.303265i	−0.0544680	−	0.0544680i	−0.733816	+	0.679348i	$0.762263\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−6.97982	−	3.46868i	−1.21503	−	0.603820i
$34$	−1.54323			−0.264662
$35$	3.09831	+	3.09831i	0.523709	+	0.523709i
$36$	2.39120	−	1.81167i	0.398533	−	0.301946i
$37$	0.167677	+	6.08045i	0.0275659	+	0.999620i
$37$	0.167677	+	6.08045i	0.0275659	+	0.999620i
$38$		−	1.04322i		−	0.169233i
$39$	−3.38041	+	1.13596i	−0.541298	+	0.181899i
$40$			1.00000i			0.158114i
$41$	−1.99260			−0.311192			−0.155596	−	0.987821i	$-0.549730\pi$
$41$	−1.99260			−0.311192			−0.155596	+	0.987821i	$0.549730\pi$
$42$	7.19395	−	2.41747i	1.11005	−	0.373024i
$43$	0.568955	−	0.568955i	0.0867648	−	0.0867648i	−0.662392	−	0.749157i	$-0.730459\pi$
$43$	0.568955	−	0.568955i	0.0867648	−	0.0867648i	0.749157	+	0.662392i	$0.230459\pi$
$44$		−	4.49999i		−	0.678399i
$45$	−0.409787	+	2.97188i	−0.0610875	+	0.443022i
$46$	2.20681			0.325376
$47$		−	8.83045i		−	1.28805i	−0.765003	−	0.644027i	$-0.777262\pi$
$47$		−	8.83045i		−	1.28805i	0.765003	−	0.644027i	$-0.222738\pi$
$48$	1.55108	+	0.770820i	0.223879	+	0.111258i
$49$	12.1990			1.74272
$50$	−0.707107	−	0.707107i	−0.100000	−	0.100000i
$51$	−0.851438	−	2.53372i	−0.119225	−	0.354791i
$52$	−1.45588	−	1.45588i	−0.201894	−	0.201894i
$53$		−	8.07611i		−	1.10934i	−0.832071	−	0.554670i	$-0.812845\pi$
$53$		−	8.07611i		−	1.10934i	0.832071	−	0.554670i	$-0.187155\pi$
$54$	4.29374	+	2.92640i	0.584304	+	0.398232i
$55$	3.18197	+	3.18197i	0.429057	+	0.429057i
$56$	3.09831	+	3.09831i	0.414029	+	0.414029i
$57$	1.71280	−	0.575573i	0.226865	−	0.0762365i
$58$		−	5.20612i		−	0.683597i
$59$	9.81764	+	9.81764i	1.27815	+	1.27815i	0.941703	+	0.336445i	$0.109224\pi$
$59$	9.81764	+	9.81764i	1.27815	+	1.27815i	0.336445	+	0.941703i	$0.390776\pi$
$60$	−1.64183	+	0.551724i	−0.211959	+	0.0712273i
$61$	0.496818	+	0.496818i	0.0636110	+	0.0636110i	0.738197	−	0.674586i	$-0.235678\pi$
$61$	0.496818	+	0.496818i	0.0636110	+	0.0636110i	−0.674586	+	0.738197i	$0.735678\pi$
$62$	0.428882			0.0544680
$63$	7.93815	+	10.4774i	1.00011	+	1.32003i
$64$			1.00000i			0.125000i
$65$	2.05893			0.255378
$66$	7.38821	−	2.48275i	0.909425	−	0.305606i
$67$			7.31837i			0.894081i	0.894514	+	0.447040i	$0.147522\pi$
$67$			7.31837i			0.894081i	−0.894514	+	0.447040i	$0.852478\pi$
$68$	1.09123	−	1.09123i	0.132331	−	0.132331i
$69$	1.21755	+	3.62320i	0.146576	+	0.436182i
$70$	−4.38167			−0.523709
$71$			13.3890i			1.58898i	0.607280	+	0.794488i	$0.292261\pi$
$71$			13.3890i			1.58898i	−0.607280	+	0.794488i	$0.707739\pi$
$72$	−0.409787	+	2.97188i	−0.0482939	+	0.350239i
$73$		−	12.3051i		−	1.44021i	−0.693867	−	0.720104i	$-0.744094\pi$
$73$		−	12.3051i		−	1.44021i	0.693867	−	0.720104i	$-0.255906\pi$
$74$	−4.41809	−	4.18096i	−0.513593	−	0.486027i
$75$	0.770820	−	1.55108i	0.0890066	−	0.179103i
$76$	0.737671	+	0.737671i	0.0846167	+	0.0846167i
$77$	19.7174			2.24701
$78$	1.58706	−	3.19355i	0.179699	−	0.361599i
$79$	−2.04760	+	2.04760i	−0.230373	+	0.230373i	−0.812848	−	0.582475i	$-0.802084\pi$
$79$	−2.04760	+	2.04760i	−0.230373	+	0.230373i	0.582475	+	0.812848i	$0.302084\pi$
$80$	−0.707107	−	0.707107i	−0.0790569	−	0.0790569i
$81$	−2.43568	+	8.66415i	−0.270631	+	0.962683i
$82$	1.40898	−	1.40898i	0.155596	−	0.155596i
$83$		−	10.2732i		−	1.12763i	−0.825903	−	0.563813i	$-0.809334\pi$
$83$		−	10.2732i		−	1.12763i	0.825903	−	0.563813i	$-0.190666\pi$
$84$	−3.37748	+	6.79630i	−0.368513	+	0.741537i
$85$			1.54323i			0.167387i
$86$			0.804623i			0.0867648i
$87$	8.54756	−	2.87234i	0.916394	−	0.307948i
$88$	3.18197	+	3.18197i	0.339199	+	0.339199i
$89$	11.8187	−	11.8187i	1.25278	−	1.25278i	0.298316	−	0.954467i	$-0.403575\pi$
$89$	11.8187	−	11.8187i	1.25278	−	1.25278i	0.954467	−	0.298316i	$-0.0964250\pi$
$90$	−1.81167	−	2.39120i	−0.190967	−	0.252055i
$91$	6.37919	−	6.37919i	0.668721	−	0.668721i
$92$	−1.56045	+	1.56045i	−0.162688	+	0.162688i
$93$	0.236625	+	0.704150i	0.0245368	+	0.0730170i
$94$	6.24407	+	6.24407i	0.644027	+	0.644027i
$95$	−1.04322			−0.107033
$96$	−1.64183	+	0.551724i	−0.167568	+	0.0563101i
$97$	−0.766039	+	0.766039i	−0.0777795	+	0.0777795i	−0.744926	−	0.667147i	$-0.767515\pi$
$97$	−0.766039	+	0.766039i	−0.0777795	+	0.0777795i	0.667147	+	0.744926i	$0.267515\pi$
$98$	−8.62600	+	8.62600i	−0.871358	+	0.871358i
$99$	8.15251	+	10.7604i	0.819358	+	1.08146i
$100$	1.00000			0.100000
$101$	−12.5125			−1.24504			−0.622519	−	0.782604i	$-0.713891\pi$
$101$	−12.5125			−1.24504			−0.622519	+	0.782604i	$0.713891\pi$
$102$	2.39367	+	1.18955i	0.237008	+	0.117783i
$103$	6.46547	+	6.46547i	0.637062	+	0.637062i	0.949830	−	0.312768i	$-0.101256\pi$
$103$	6.46547	+	6.46547i	0.637062	+	0.637062i	−0.312768	+	0.949830i	$0.601256\pi$
$104$	2.05893			0.201894
$105$	−2.41747	−	7.19395i	−0.235921	−	0.702057i
$106$	5.71067	+	5.71067i	0.554670	+	0.554670i
$107$			0.550155i			0.0531855i	0.999646	+	0.0265928i	$0.00846573\pi$
$107$			0.550155i			0.0531855i	−0.999646	+	0.0265928i	$0.991534\pi$
$108$	−5.10541	+	0.966859i	−0.491268	+	0.0930361i
$109$	−6.68407	+	6.68407i	−0.640217	+	0.640217i	−0.950609	−	0.310391i	$-0.899540\pi$
$109$	−6.68407	+	6.68407i	−0.640217	+	0.640217i	0.310391	+	0.950609i	$0.399540\pi$
$110$	−4.49999			−0.429057
$111$	4.42685	−	9.56049i	0.420178	−	0.907442i
$112$	−4.38167			−0.414029
$113$	−6.11267	+	6.11267i	−0.575032	+	0.575032i	−0.933530	−	0.358499i	$-0.883289\pi$
$113$	−6.11267	+	6.11267i	−0.575032	+	0.575032i	0.358499	+	0.933530i	$0.383289\pi$
$114$	−0.804138	+	1.61812i	−0.0753145	+	0.151551i
$115$		−	2.20681i		−	0.205786i
$116$	3.68128	+	3.68128i	0.341799	+	0.341799i
$117$	6.11889	+	0.843722i	0.565691	+	0.0780021i
$118$	−13.8842			−1.27815
$119$	4.78140	+	4.78140i	0.438310	+	0.438310i
$120$	0.770820	−	1.55108i	0.0703659	−	0.141593i
$121$	9.24988			0.840898
$122$	−0.702607			−0.0636110
$123$	3.09068	+	1.53594i	0.278677	+	0.138491i
$124$	−0.303265	+	0.303265i	−0.0272340	+	0.0272340i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	−13.0218	−	1.79555i	−1.16007	−	0.159960i
$127$	18.8279			1.67070			0.835352	−	0.549716i	$-0.185264\pi$
$127$	18.8279			1.67070			0.835352	+	0.549716i	$0.185264\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−1.32105	+	0.443930i	−0.116312	+	0.0390859i
$130$	−1.45588	+	1.45588i	−0.127689	+	0.127689i
$131$	−6.50740	+	6.50740i	−0.568554	+	0.568554i	−0.931723	−	0.363169i	$-0.881695\pi$
$131$	−6.50740	+	6.50740i	−0.568554	+	0.568554i	0.363169	+	0.931723i	$0.381695\pi$
$132$	−3.46868	+	6.97982i	−0.301910	+	0.607516i
$133$	−3.23223	+	3.23223i	−0.280270	+	0.280270i
$134$	−5.17487	−	5.17487i	−0.447040	−	0.447040i
$135$	2.92640	−	4.29374i	0.251864	−	0.369546i
$136$			1.54323i			0.132331i
$137$		−	19.5068i		−	1.66658i	−0.552838	−	0.833289i	$-0.686455\pi$
$137$		−	19.5068i		−	1.66658i	0.552838	−	0.833289i	$-0.313545\pi$
$138$	−3.42293	−	1.70105i	−0.291379	−	0.144803i
$139$			17.7979i			1.50960i	0.655954	+	0.754801i	$0.272266\pi$
$139$			17.7979i			1.50960i	−0.655954	+	0.754801i	$0.727734\pi$
$140$	3.09831	−	3.09831i	0.261855	−	0.261855i
$141$	−6.80669	+	13.6967i	−0.573227	+	1.15347i
$142$	−9.46742	−	9.46742i	−0.794488	−	0.794488i
$143$	6.55145	−	6.55145i	0.547860	−	0.547860i
$144$	−1.81167	−	2.39120i	−0.150973	−	0.199267i
$145$	−5.20612			−0.432345
$146$	8.70104	+	8.70104i	0.720104	+	0.720104i
$147$	−18.9216	−	9.40324i	−1.56063	−	0.775566i
$148$	6.08045	−	0.167677i	0.499810	−	0.0137830i
$149$		−	19.3712i		−	1.58695i	−0.608602	−	0.793476i	$-0.708269\pi$
$149$		−	19.3712i		−	1.58695i	0.608602	−	0.793476i	$-0.291731\pi$
$150$	0.551724	+	1.64183i	0.0450481	+	0.134055i
$151$		−	12.1984i		−	0.992693i	−0.868124	−	0.496347i	$-0.834675\pi$
$151$		−	12.1984i		−	0.992693i	0.868124	−	0.496347i	$-0.165325\pi$
$152$	−1.04322			−0.0846167
$153$	−0.632396	+	4.58629i	−0.0511262	+	0.370780i
$154$	−13.9423	+	13.9423i	−1.12351	+	1.12351i
$155$		−	0.428882i		−	0.0344486i
$156$	1.13596	+	3.38041i	0.0909496	+	0.270649i
$157$	−7.11091			−0.567512			−0.283756	−	0.958896i	$-0.591581\pi$
$157$	−7.11091			−0.567512			−0.283756	+	0.958896i	$0.591581\pi$
$158$		−	2.89575i		−	0.230373i
$159$	−6.22523	+	12.5267i	−0.493692	+	0.993429i
$160$	1.00000			0.0790569
$161$	−6.83737	−	6.83737i	−0.538860	−	0.538860i
$162$	−4.40419	−	7.84876i	−0.346026	−	0.616657i
$163$	−3.95330	−	3.95330i	−0.309646	−	0.309646i	0.535126	−	0.844772i	$-0.320264\pi$
$163$	−3.95330	−	3.95330i	−0.309646	−	0.309646i	−0.844772	+	0.535126i	$0.820264\pi$
$164$			1.99260i			0.155596i
$165$	−2.48275	−	7.38821i	−0.193282	−	0.575171i
$166$	7.26422	+	7.26422i	0.563813	+	0.563813i
$167$	−1.00757	−	1.00757i	−0.0779683	−	0.0779683i	0.667047	−	0.745015i	$-0.267558\pi$
$167$	−1.00757	−	1.00757i	−0.0779683	−	0.0779683i	−0.745015	+	0.667047i	$0.767558\pi$
$168$	−2.41747	−	7.19395i	−0.186512	−	0.555025i
$169$			8.76082i			0.673909i
$170$	−1.09123	−	1.09123i	−0.0836934	−	0.0836934i
$171$	−3.10034	−	0.427500i	−0.237089	−	0.0326918i
$172$	−0.568955	−	0.568955i	−0.0433824	−	0.0433824i
$173$	−1.51433			−0.115132			−0.0575660	−	0.998342i	$-0.518334\pi$
$173$	−1.51433			−0.115132			−0.0575660	+	0.998342i	$0.518334\pi$
$174$	−4.01298	+	8.07509i	−0.304223	+	0.612171i
$175$			4.38167i			0.331223i
$176$	−4.49999			−0.339199
$177$	−7.66027	−	22.7955i	−0.575782	−	1.71342i
$178$			16.7142i			1.25278i
$179$	2.61668	−	2.61668i	0.195580	−	0.195580i	−0.602522	−	0.798102i	$-0.705838\pi$
$179$	2.61668	−	2.61668i	0.195580	−	0.195580i	0.798102	+	0.602522i	$0.205838\pi$
$180$	2.97188	+	0.409787i	0.221511	+	0.0305437i
$181$	−8.02378			−0.596403			−0.298201	−	0.954503i	$-0.596387\pi$
$181$	−8.02378			−0.596403			−0.298201	+	0.954503i	$0.596387\pi$
$182$			9.02154i			0.668721i
$183$	−0.387645	−	1.15356i	−0.0286556	−	0.0852736i
$184$		−	2.20681i		−	0.162688i
$185$	−4.18096	+	4.41809i	−0.307390	+	0.324825i
$186$	−0.665228	−	0.330591i	−0.0487769	−	0.0242401i
$187$	4.91051	+	4.91051i	0.359092	+	0.359092i
$188$	−8.83045			−0.644027
$189$	−4.23646	−	22.3702i	−0.308157	−	1.62719i
$190$	0.737671	−	0.737671i	0.0535163	−	0.0535163i
$191$	−3.71929	−	3.71929i	−0.269118	−	0.269118i	0.559627	−	0.828745i	$-0.310945\pi$
$191$	−3.71929	−	3.71929i	−0.269118	−	0.269118i	−0.828745	+	0.559627i	$0.810945\pi$
$192$	0.770820	−	1.55108i	0.0556291	−	0.111939i
$193$	11.4367	−	11.4367i	0.823235	−	0.823235i	−0.163336	−	0.986571i	$-0.552225\pi$
$193$	11.4367	−	11.4367i	0.823235	−	0.823235i	0.986571	+	0.163336i	$0.0522253\pi$
$194$		−	1.08334i		−	0.0777795i
$195$	−3.19355	−	1.58706i	−0.228695	−	0.113652i
$196$		−	12.1990i		−	0.871358i
$197$			12.8748i			0.917293i	0.888619	+	0.458646i	$0.151666\pi$
$197$			12.8748i			0.917293i	−0.888619	+	0.458646i	$0.848334\pi$
$198$	−13.3734	−	1.84404i	−0.950408	−	0.131050i
$199$	16.5646	+	16.5646i	1.17423	+	1.17423i	0.981190	+	0.193044i	$0.0618359\pi$
$199$	16.5646	+	16.5646i	1.17423	+	1.17423i	0.193044	+	0.981190i	$0.438164\pi$
$200$	−0.707107	+	0.707107i	−0.0500000	+	0.0500000i
$201$	5.64114	−	11.3513i	0.397895	−	0.800662i
$202$	8.84766	−	8.84766i	0.622519	−	0.622519i
$203$	−16.1302	+	16.1302i	−1.13212	+	1.13212i
$204$	−2.53372	+	0.851438i	−0.177396	+	0.0596126i
$205$	−1.40898	−	1.40898i	−0.0984076	−	0.0984076i
$206$	−9.14355			−0.637062
$207$	0.904321	−	6.55837i	0.0628547	−	0.455838i
$208$	−1.45588	+	1.45588i	−0.100947	+	0.100947i
$209$	−3.31951	+	3.31951i	−0.229615	+	0.229615i
$210$	6.79630	+	3.37748i	0.468989	+	0.233068i
$211$	−9.22945			−0.635382			−0.317691	−	0.948194i	$-0.602907\pi$
$211$	−9.22945			−0.635382			−0.317691	+	0.948194i	$0.602907\pi$
$212$	−8.07611			−0.554670
$213$	10.3205	−	20.7673i	0.707147	−	1.42295i
$214$	−0.389018	−	0.389018i	−0.0265928	−	0.0265928i
$215$	0.804623			0.0548749
$216$	2.92640	−	4.29374i	0.199116	−	0.292152i
$217$	−1.32881	−	1.32881i	−0.0902053	−	0.0902053i
$218$		−	9.45270i		−	0.640217i
$219$	−9.48504	+	19.0862i	−0.640940	+	1.28973i
$220$	3.18197	−	3.18197i	0.214528	−	0.214528i
$221$	3.17740			0.213735
$222$	3.63003	+	9.89054i	0.243632	+	0.663810i
$223$	−21.7378			−1.45567			−0.727837	−	0.685750i	$-0.759474\pi$
$223$	−21.7378			−1.45567			−0.727837	+	0.685750i	$0.759474\pi$
$224$	3.09831	−	3.09831i	0.207014	−	0.207014i
$225$	−2.39120	+	1.81167i	−0.159413	+	0.120778i
$226$		−	8.64462i		−	0.575032i
$227$	11.6318	+	11.6318i	0.772032	+	0.772032i	0.978462	−	0.206429i	$-0.0661843\pi$
$227$	11.6318	+	11.6318i	0.772032	+	0.772032i	−0.206429	+	0.978462i	$0.566184\pi$
$228$	−0.575573	−	1.71280i	−0.0381182	−	0.113433i
$229$	10.0261			0.662545			0.331272	−	0.943535i	$-0.392522\pi$
$229$	10.0261			0.662545			0.331272	+	0.943535i	$0.392522\pi$
$230$	1.56045	+	1.56045i	0.102893	+	0.102893i
$231$	−30.5833	−	15.1986i	−2.01223	−	0.999994i
$232$	−5.20612			−0.341799
$233$	−14.0316			−0.919243			−0.459622	−	0.888115i	$-0.652015\pi$
$233$	−14.0316			−0.919243			−0.459622	+	0.888115i	$0.652015\pi$
$234$	−4.92331	+	3.73010i	−0.321847	+	0.243845i
$235$	6.24407	−	6.24407i	0.407318	−	0.407318i
$236$	9.81764	−	9.81764i	0.639074	−	0.639074i
$237$	4.75432	−	1.59765i	0.308826	−	0.103779i
$238$	−6.76192			−0.438310
$239$	−1.89394	−	1.89394i	−0.122509	−	0.122509i	0.643194	−	0.765703i	$-0.277609\pi$
$239$	−1.89394	−	1.89394i	−0.122509	−	0.122509i	−0.765703	+	0.643194i	$0.777609\pi$
$240$	0.551724	+	1.64183i	0.0356137	+	0.105980i
$241$	11.7784	−	11.7784i	0.758715	−	0.758715i	−0.217373	−	0.976089i	$-0.569749\pi$
$241$	11.7784	−	11.7784i	0.758715	−	0.758715i	0.976089	+	0.217373i	$0.0697489\pi$
$242$	−6.54065	+	6.54065i	−0.420449	+	0.420449i
$243$	10.4564	−	11.5613i	0.670780	−	0.741657i
$244$	0.496818	−	0.496818i	0.0318055	−	0.0318055i
$245$	8.62600	+	8.62600i	0.551095	+	0.551095i
$246$	−3.27151	+	1.09937i	−0.208584	+	0.0700931i
$247$			2.14792i			0.136669i
$248$		−	0.428882i		−	0.0272340i
$249$	−7.91876	+	15.9345i	−0.501831	+	1.00980i
$250$		−	1.00000i		−	0.0632456i
$251$	10.9133	−	10.9133i	0.688839	−	0.688839i	−0.273136	−	0.961975i	$-0.588061\pi$
$251$	10.9133	−	10.9133i	0.688839	−	0.688839i	0.961975	+	0.273136i	$0.0880610\pi$
$252$	10.4774	−	7.93815i	0.660017	−	0.500057i
$253$	−7.02200	−	7.02200i	−0.441469	−	0.441469i
$254$	−13.3133	+	13.3133i	−0.835352	+	0.835352i
$255$	1.18955	−	2.39367i	0.0744926	−	0.149897i
$256$	1.00000			0.0625000
$257$	−16.7640	−	16.7640i	−1.04571	−	1.04571i	−0.998904	−	0.0468078i	$-0.985095\pi$
$257$	−16.7640	−	16.7640i	−1.04571	−	1.04571i	−0.0468078	−	0.998904i	$-0.514905\pi$
$258$	0.620220	−	1.24803i	0.0386132	−	0.0776991i
$259$	0.734705	+	26.6425i	0.0456524	+	1.65549i
$260$		−	2.05893i		−	0.127689i
$261$	−15.4720	−	2.13340i	−0.957691	−	0.132054i
$262$		−	9.20286i		−	0.568554i
$263$	16.2544			1.00229			0.501145	−	0.865363i	$-0.332912\pi$
$263$	16.2544			1.00229			0.501145	+	0.865363i	$0.332912\pi$
$264$	−2.48275	−	7.38821i	−0.152803	−	0.454713i
$265$	5.71067	−	5.71067i	0.350804	−	0.350804i
$266$		−	4.57106i		−	0.280270i
$267$	−27.4419	+	9.22164i	−1.67942	+	0.564355i
$268$	7.31837			0.447040
$269$			14.2889i			0.871212i	0.900137	+	0.435606i	$0.143466\pi$
$269$			14.2889i			0.871212i	−0.900137	+	0.435606i	$0.856534\pi$
$270$	0.966859	+	5.10541i	0.0588412	+	0.310705i
$271$	20.3803			1.23802			0.619008	−	0.785385i	$-0.287535\pi$
$271$	20.3803			1.23802			0.619008	+	0.785385i	$0.287535\pi$
$272$	−1.09123	−	1.09123i	−0.0661654	−	0.0661654i
$273$	−14.8118	+	4.97740i	−0.896452	+	0.301246i
$274$	13.7934	+	13.7934i	0.833289	+	0.833289i
$275$			4.49999i			0.271359i
$276$	3.62320	−	1.21755i	0.218091	−	0.0732879i
$277$	−17.5786	−	17.5786i	−1.05619	−	1.05619i	−0.998324	−	0.0578693i	$-0.981569\pi$
$277$	−17.5786	−	17.5786i	−1.05619	−	1.05619i	−0.0578693	−	0.998324i	$-0.518431\pi$
$278$	−12.5850	−	12.5850i	−0.754801	−	0.754801i
$279$	0.175750	−	1.27459i	0.0105219	−	0.0763074i
$280$			4.38167i			0.261855i
$281$	1.34583	+	1.34583i	0.0802855	+	0.0802855i	0.746109	−	0.665824i	$-0.231920\pi$
$281$	1.34583	+	1.34583i	0.0802855	+	0.0802855i	−0.665824	+	0.746109i	$0.731920\pi$
$282$	−4.87198	−	14.4981i	−0.290122	−	0.863349i
$283$	0.275222	+	0.275222i	0.0163602	+	0.0163602i	0.715240	−	0.698879i	$-0.246318\pi$
$283$	0.275222	+	0.275222i	0.0163602	+	0.0163602i	−0.698879	+	0.715240i	$0.746318\pi$
$284$	13.3890			0.794488
$285$	1.61812	+	0.804138i	0.0958492	+	0.0476330i
$286$			9.26515i			0.547860i
$287$	−8.73092			−0.515370
$288$	2.97188	+	0.409787i	0.175120	+	0.0241469i
$289$		−	14.6184i		−	0.859908i
$290$	3.68128	−	3.68128i	0.216172	−	0.216172i
$291$	1.77866	−	0.597707i	0.104267	−	0.0350382i
$292$	−12.3051			−0.720104
$293$			3.04158i			0.177691i	0.996045	+	0.0888455i	$0.0283178\pi$
$293$			3.04158i			0.177691i	−0.996045	+	0.0888455i	$0.971682\pi$
$294$	20.0287	−	6.73049i	1.16810	−	0.392530i
$295$			13.8842i			0.808372i
$296$	−4.18096	+	4.41809i	−0.243014	+	0.256796i
$297$	−4.35085	−	22.9743i	−0.252462	−	1.33310i
$298$	13.6975	+	13.6975i	0.793476	+	0.793476i
$299$	−4.54366			−0.262766
$300$	−1.55108	−	0.770820i	−0.0895514	−	0.0445033i
$301$	2.49297	−	2.49297i	0.143692	−	0.143692i
$302$	8.62559	+	8.62559i	0.496347	+	0.496347i
$303$	19.4078	+	9.64487i	1.11495	+	0.554083i
$304$	0.737671	−	0.737671i	0.0423084	−	0.0423084i
$305$			0.702607i			0.0402311i
$306$	−2.79583	−	3.69017i	−0.159827	−	0.210953i
$307$			13.1974i			0.753217i	0.926373	+	0.376608i	$0.122910\pi$
$307$			13.1974i			0.753217i	−0.926373	+	0.376608i	$0.877090\pi$
$308$		−	19.7174i		−	1.12351i
$309$	−5.04472	−	15.0121i	−0.286984	−	0.854011i
$310$	0.303265	+	0.303265i	0.0172243	+	0.0172243i
$311$	16.5296	−	16.5296i	0.937307	−	0.937307i	−0.0608406	−	0.998147i	$-0.519378\pi$
$311$	16.5296	−	16.5296i	0.937307	−	0.937307i	0.998147	+	0.0608406i	$0.0193781\pi$
$312$	−3.19355	−	1.58706i	−0.180799	−	0.0898497i
$313$	4.43787	−	4.43787i	0.250843	−	0.250843i	−0.570473	−	0.821316i	$-0.693240\pi$
$313$	4.43787	−	4.43787i	0.250843	−	0.250843i	0.821316	+	0.570473i	$0.193240\pi$
$314$	5.02817	−	5.02817i	0.283756	−	0.283756i
$315$	−1.79555	+	13.0218i	−0.101168	+	0.733695i
$316$	2.04760	+	2.04760i	0.115187	+	0.115187i
$317$	−3.18702			−0.179001			−0.0895003	−	0.995987i	$-0.528527\pi$
$317$	−3.18702			−0.179001			−0.0895003	+	0.995987i	$0.528527\pi$
$318$	−4.45579	−	13.2596i	−0.249868	−	0.743561i
$319$	−16.5657	+	16.5657i	−0.927503	+	0.927503i
$320$	−0.707107	+	0.707107i	−0.0395285	+	0.0395285i
$321$	0.424070	−	0.853332i	0.0236693	−	0.0476284i
$322$	9.66950			0.538860
$323$	−1.60994			−0.0895792
$324$	8.66415	+	2.43568i	0.481342	+	0.135315i
$325$	1.45588	+	1.45588i	0.0807578	+	0.0807578i
$326$	5.59081			0.309646
$327$	15.5197	−	5.21528i	0.858242	−	0.288406i
$328$	−1.40898	−	1.40898i	−0.0777981	−	0.0777981i
$329$		−	38.6921i		−	2.13317i
$330$	6.97982	+	3.46868i	0.384227	+	0.190944i
$331$	−13.9140	+	13.9140i	−0.764780	+	0.764780i	−0.977182	−	0.212402i	$-0.931871\pi$
$331$	−13.9140	+	13.9140i	−0.764780	+	0.764780i	0.212402	+	0.977182i	$0.431871\pi$
$332$	−10.2732			−0.563813
$333$	−14.2358	+	11.4167i	−0.780117	+	0.625634i
$334$	1.42492			0.0779683
$335$	−5.17487	+	5.17487i	−0.282733	+	0.282733i
$336$	6.79630	+	3.37748i	0.370769	+	0.184256i
$337$			22.2998i			1.21475i	0.794416	+	0.607374i	$0.207777\pi$
$337$			22.2998i			1.21475i	−0.794416	+	0.607374i	$0.792223\pi$
$338$	−6.19483	−	6.19483i	−0.336955	−	0.336955i
$339$	14.1930	−	4.76945i	0.770857	−	0.259041i
$340$	1.54323			0.0836934
$341$	−1.36469	−	1.36469i	−0.0739021	−	0.0739021i
$342$	2.49456	−	1.88998i	0.134890	−	0.102199i
$343$	22.7803			1.23002
$344$	0.804623			0.0433824
$345$	−1.70105	+	3.42293i	−0.0915815	+	0.184284i
$346$	1.07079	−	1.07079i	0.0575660	−	0.0575660i
$347$	−8.92530	+	8.92530i	−0.479135	+	0.479135i	−0.904855	−	0.425720i	$-0.860021\pi$
$347$	−8.92530	+	8.92530i	−0.479135	+	0.479135i	0.425720	+	0.904855i	$0.360021\pi$
$348$	−2.87234	−	8.54756i	−0.153974	−	0.458197i
$349$	−7.54456			−0.403851			−0.201926	−	0.979401i	$-0.564720\pi$
$349$	−7.54456			−0.403851			−0.201926	+	0.979401i	$0.564720\pi$
$350$	−3.09831	−	3.09831i	−0.165611	−	0.165611i
$351$	−8.84050	−	6.02524i	−0.471871	−	0.321603i
$352$	3.18197	−	3.18197i	0.169600	−	0.169600i
$353$	−4.41933	+	4.41933i	−0.235217	+	0.235217i	−0.814866	−	0.579649i	$-0.803190\pi$
$353$	−4.41933	+	4.41933i	−0.235217	+	0.235217i	0.579649	+	0.814866i	$0.303190\pi$
$354$	21.5355	+	10.7022i	1.14460	+	0.568818i
$355$	−9.46742	+	9.46742i	−0.502478	+	0.502478i
$356$	−11.8187	−	11.8187i	−0.626392	−	0.626392i
$357$	−3.73072	−	11.1019i	−0.197450	−	0.587575i
$358$			3.70055i			0.195580i
$359$		−	24.0431i		−	1.26895i	−0.772944	−	0.634474i	$-0.781217\pi$
$359$		−	24.0431i		−	1.26895i	0.772944	−	0.634474i	$-0.218783\pi$
$360$	−2.39120	+	1.81167i	−0.126027	+	0.0954836i
$361$			17.9117i			0.942720i
$362$	5.67367	−	5.67367i	0.298201	−	0.298201i
$363$	−14.3473	−	7.12999i	−0.753036	−	0.374228i
$364$	−6.37919	−	6.37919i	−0.334360	−	0.334360i
$365$	8.70104	−	8.70104i	0.455433	−	0.455433i
$366$	1.08980	+	0.541583i	0.0569646	+	0.0283090i
$367$	−23.6025			−1.23204			−0.616020	−	0.787730i	$-0.711256\pi$
$367$	−23.6025			−1.23204			−0.616020	+	0.787730i	$0.711256\pi$
$368$	1.56045	+	1.56045i	0.0813440	+	0.0813440i
$369$	−3.60995	−	4.76471i	−0.187926	−	0.248041i
$370$	−0.167677	−	6.08045i	−0.00871712	−	0.316108i
$371$		−	35.3868i		−	1.83719i
$372$	0.704150	−	0.236625i	0.0365085	−	0.0122684i
$373$		−	36.5693i		−	1.89349i	−0.321991	−	0.946743i	$-0.604352\pi$
$373$		−	36.5693i		−	1.89349i	0.321991	−	0.946743i	$-0.395648\pi$
$374$	−6.94451			−0.359092
$375$	1.64183	−	0.551724i	0.0847836	−	0.0284909i
$376$	6.24407	−	6.24407i	0.322014	−	0.322014i
$377$			10.7190i			0.552058i
$378$	18.8137	+	12.8225i	0.967675	+	0.659518i
$379$	−36.7825			−1.88939			−0.944695	−	0.327950i	$-0.893642\pi$
$379$	−36.7825			−1.88939			−0.944695	+	0.327950i	$0.893642\pi$
$380$			1.04322i			0.0535163i
$381$	−29.2035	−	14.5129i	−1.49614	−	0.743518i
$382$	5.25987			0.269118
$383$	7.74910	+	7.74910i	0.395960	+	0.395960i	0.876806	−	0.480845i	$-0.159670\pi$
$383$	7.74910	+	7.74910i	0.395960	+	0.395960i	−0.480845	+	0.876806i	$0.659670\pi$
$384$	0.551724	+	1.64183i	0.0281551	+	0.0837842i
$385$	13.9423	+	13.9423i	0.710567	+	0.710567i
$386$			16.1740i			0.823235i
$387$	2.39124	+	0.329724i	0.121554	+	0.0167608i
$388$	0.766039	+	0.766039i	0.0388897	+	0.0388897i
$389$	16.8656	+	16.8656i	0.855119	+	0.855119i	0.990758	−	0.135640i	$-0.0433089\pi$
$389$	16.8656	+	16.8656i	0.855119	+	0.855119i	−0.135640	+	0.990758i	$0.543309\pi$
$390$	3.38041	−	1.13596i	0.171173	−	0.0575216i
$391$		−	3.40561i		−	0.172229i
$392$	8.62600	+	8.62600i	0.435679	+	0.435679i
$393$	15.1095	−	5.07744i	0.762174	−	0.256123i
$394$	−9.10387	−	9.10387i	−0.458646	−	0.458646i
$395$	−2.89575			−0.145701
$396$	10.7604	−	8.15251i	0.540729	−	0.409679i
$397$		−	2.62029i		−	0.131509i	−0.997836	−	0.0657543i	$-0.979055\pi$
$397$		−	2.62029i		−	0.131509i	0.997836	−	0.0657543i	$-0.0209453\pi$
$398$	−23.4259			−1.17423
$399$	7.50490	−	2.52197i	0.375715	−	0.126256i
$400$		−	1.00000i		−	0.0500000i
$401$	−23.7337	+	23.7337i	−1.18521	+	1.18521i	−0.206830	+	0.978377i	$0.566315\pi$
$401$	−23.7337	+	23.7337i	−1.18521	+	1.18521i	−0.978377	+	0.206830i	$0.933685\pi$
$402$	4.03772	+	12.0155i	0.201383	+	0.599279i
$403$	−0.883036			−0.0439872
$404$			12.5125i			0.622519i
$405$	−7.84876	+	4.40419i	−0.390008	+	0.218846i
$406$		−	22.8115i		−	1.13212i
$407$	0.754545	+	27.3619i	0.0374014	+	1.35628i
$408$	1.18955	−	2.39367i	0.0588916	−	0.118504i
$409$	−8.35272	−	8.35272i	−0.413015	−	0.413015i	0.469772	−	0.882788i	$-0.344336\pi$
$409$	−8.35272	−	8.35272i	−0.413015	−	0.413015i	−0.882788	+	0.469772i	$0.844336\pi$
$410$	1.99260			0.0984076
$411$	−15.0362	+	30.2565i	−0.741682	+	1.49244i
$412$	6.46547	−	6.46547i	0.318531	−	0.318531i
$413$	43.0176	+	43.0176i	2.11676	+	2.11676i
$414$	3.99801	+	5.27692i	0.196492	+	0.259346i
$415$	7.26422	−	7.26422i	0.356587	−	0.356587i
$416$		−	2.05893i		−	0.100947i
$417$	13.7190	−	27.6060i	0.671823	−	1.35187i
$418$		−	4.69450i		−	0.229615i
$419$		−	21.3828i		−	1.04462i	−0.852757	−	0.522309i	$-0.825071\pi$
$419$		−	21.3828i		−	1.04462i	0.852757	−	0.522309i	$-0.174929\pi$
$420$	−7.19395	+	2.41747i	−0.351029	+	0.117961i
$421$	−24.9099	−	24.9099i	−1.21404	−	1.21404i	−0.969688	−	0.244348i	$-0.921426\pi$
$421$	−24.9099	−	24.9099i	−1.21404	−	1.21404i	−0.244348	−	0.969688i	$-0.578574\pi$
$422$	6.52621	−	6.52621i	0.317691	−	0.317691i
$423$	21.1154	−	15.9979i	1.02667	−	0.777845i
$424$	5.71067	−	5.71067i	0.277335	−	0.277335i
$425$	−1.09123	+	1.09123i	−0.0529323	+	0.0529323i
$426$	7.38701	+	21.9824i	0.357902	+	1.06505i
$427$	2.17689	+	2.17689i	0.105347	+	0.105347i
$428$	0.550155			0.0265928
$429$	−15.2118	+	5.11181i	−0.734432	+	0.246800i
$430$	−0.568955	+	0.568955i	−0.0274374	+	0.0274374i
$431$	−13.1558	+	13.1558i	−0.633692	+	0.633692i	−0.948992	−	0.315300i	$-0.897895\pi$
$431$	−13.1558	+	13.1558i	−0.633692	+	0.633692i	0.315300	+	0.948992i	$0.397895\pi$
$432$	0.966859	+	5.10541i	0.0465180	+	0.245634i
$433$	40.5145			1.94700			0.973502	−	0.228679i	$-0.0734405\pi$
$433$	40.5145			1.94700			0.973502	+	0.228679i	$0.0734405\pi$
$434$	1.87922			0.0902053
$435$	8.07509	+	4.01298i	0.387171	+	0.192408i
$436$	6.68407	+	6.68407i	0.320109	+	0.320109i
$437$	2.30220			0.110129
$438$	−6.78904	−	20.2029i	−0.324393	−	0.965333i
$439$	−16.5074	−	16.5074i	−0.787857	−	0.787857i	0.193285	−	0.981143i	$-0.438086\pi$
$439$	−16.5074	−	16.5074i	−0.787857	−	0.787857i	−0.981143	+	0.193285i	$0.938086\pi$
$440$			4.49999i			0.214528i
$441$	22.1006	+	29.1703i	1.05241	+	1.38906i
$442$	−2.24676	+	2.24676i	−0.106867	+	0.106867i
$443$	−17.2944			−0.821681			−0.410841	−	0.911707i	$-0.634765\pi$
$443$	−17.2944			−0.821681			−0.410841	+	0.911707i	$0.634765\pi$
$444$	−9.56049	−	4.42685i	−0.453721	−	0.210089i
$445$	16.7142			0.792330
$446$	15.3710	−	15.3710i	0.727837	−	0.727837i
$447$	−14.9317	+	30.0462i	−0.706246	+	1.42114i
$448$			4.38167i			0.207014i
$449$	5.59586	+	5.59586i	0.264085	+	0.264085i	0.826711	−	0.562626i	$-0.190209\pi$
$449$	5.59586	+	5.59586i	0.264085	+	0.264085i	−0.562626	+	0.826711i	$0.690209\pi$
$450$	0.409787	−	2.97188i	0.0193176	−	0.140096i
$451$	−8.96669			−0.422225
$452$	6.11267	+	6.11267i	0.287516	+	0.287516i
$453$	−9.40278	+	18.9207i	−0.441781	+	0.888971i
$454$	−16.4499			−0.772032
$455$	9.02154			0.422936
$456$	1.61812	+	0.804138i	0.0757755	+	0.0376572i
$457$	−21.3020	+	21.3020i	−0.996467	+	0.996467i	−0.999994	−	0.00352675i	$-0.998877\pi$
$457$	−21.3020	+	21.3020i	−0.996467	+	0.996467i	0.00352675	+	0.999994i	$0.498877\pi$
$458$	−7.08954	+	7.08954i	−0.331272	+	0.331272i
$459$	4.51610	−	6.62623i	0.210794	−	0.309286i
$460$	−2.20681			−0.102893
$461$	15.6647	+	15.6647i	0.729576	+	0.729576i	0.970535	−	0.240959i	$-0.0774620\pi$
$461$	15.6647	+	15.6647i	0.729576	+	0.729576i	−0.240959	+	0.970535i	$0.577462\pi$
$462$	32.3727	−	10.8786i	1.50611	−	0.506118i
$463$	12.1234	−	12.1234i	0.563420	−	0.563420i	−0.366857	−	0.930277i	$-0.619566\pi$
$463$	12.1234	−	12.1234i	0.563420	−	0.563420i	0.930277	+	0.366857i	$0.119566\pi$
$464$	3.68128	−	3.68128i	0.170899	−	0.170899i
$465$	−0.330591	+	0.665228i	−0.0153308	+	0.0308492i
$466$	9.92187	−	9.92187i	0.459622	−	0.459622i
$467$	12.9695	+	12.9695i	0.600158	+	0.600158i	0.940355	−	0.340196i	$-0.110493\pi$
$467$	12.9695	+	12.9695i	0.600158	+	0.600158i	−0.340196	+	0.940355i	$0.610493\pi$
$468$	0.843722	−	6.11889i	0.0390011	−	0.282846i
$469$			32.0667i			1.48070i
$470$			8.83045i			0.407318i
$471$	11.0296	+	5.48123i	0.508215	+	0.252562i
$472$			13.8842i			0.639074i
$473$	2.56029	−	2.56029i	0.117722	−	0.117722i
$474$	−2.23210	+	4.49152i	−0.102524	+	0.206303i
$475$	−0.737671	−	0.737671i	−0.0338467	−	0.0338467i
$476$	4.78140	−	4.78140i	0.219155	−	0.219155i
$477$	19.3116	−	14.6313i	0.884217	−	0.669920i
$478$	2.67843			0.122509
$479$	20.6435	+	20.6435i	0.943226	+	0.943226i	0.998473	−	0.0552467i	$-0.0175945\pi$
$479$	20.6435	+	20.6435i	0.943226	+	0.943226i	−0.0552467	+	0.998473i	$0.517595\pi$
$480$	−1.55108	−	0.770820i	−0.0707966	−	0.0351829i
$481$	9.09653	+	8.60830i	0.414766	+	0.392505i
$482$			16.6572i			0.758715i
$483$	5.33490	+	15.8757i	0.242746	+	0.722367i
$484$		−	9.24988i		−	0.420449i
$485$	−1.08334			−0.0491921
$486$	0.781259	+	15.5689i	0.0354386	+	0.706218i
$487$	−20.1438	+	20.1438i	−0.912801	+	0.912801i	−0.996492	−	0.0836904i	$-0.973329\pi$
$487$	−20.1438	+	20.1438i	−0.912801	+	0.912801i	0.0836904	+	0.996492i	$0.473329\pi$
$488$			0.702607i			0.0318055i
$489$	3.08458	+	9.17914i	0.139490	+	0.415095i
$490$	−12.1990			−0.551095
$491$		−	35.5626i		−	1.60492i	−0.596707	−	0.802460i	$-0.703524\pi$
$491$		−	35.5626i		−	1.60492i	0.596707	−	0.802460i	$-0.296476\pi$
$492$	1.53594	−	3.09068i	0.0692454	−	0.139339i
$493$	−8.03424			−0.361844
$494$	−1.51881	−	1.51881i	−0.0683346	−	0.0683346i
$495$	−1.84404	+	13.3734i	−0.0828833	+	0.601091i
$496$	0.303265	+	0.303265i	0.0136170	+	0.0136170i
$497$			58.6659i			2.63153i
$498$	−5.66795	−	16.8668i	−0.253987	−	0.755818i
$499$	−5.43817	−	5.43817i	−0.243446	−	0.243446i	0.574828	−	0.818274i	$-0.305069\pi$
$499$	−5.43817	−	5.43817i	−0.243446	−	0.243446i	−0.818274	+	0.574828i	$0.805069\pi$
$500$	0.707107	+	0.707107i	0.0316228	+	0.0316228i
$501$	0.786165	+	2.33948i	0.0351233	+	0.104520i
$502$			15.4337i			0.688839i
$503$	18.5290	+	18.5290i	0.826166	+	0.826166i	0.986984	−	0.160818i	$-0.0514133\pi$
$503$	18.5290	+	18.5290i	0.826166	+	0.826166i	−0.160818	+	0.986984i	$0.551413\pi$
$504$	−1.79555	+	13.0218i	−0.0799802	+	0.580037i
$505$	−8.84766	−	8.84766i	−0.393716	−	0.393716i
$506$	9.93060			0.441469
$507$	6.75301	−	13.5887i	0.299912	−	0.603495i
$508$		−	18.8279i		−	0.835352i
$509$	−29.5711			−1.31072			−0.655358	−	0.755318i	$-0.727482\pi$
$509$	−29.5711			−1.31072			−0.655358	+	0.755318i	$0.727482\pi$
$510$	0.851438	+	2.53372i	0.0377023	+	0.112195i
$511$		−	53.9170i		−	2.38515i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	4.47934	+	3.05289i	0.197768	+	0.134788i
$514$	23.7079			1.04571
$515$			9.14355i			0.402913i
$516$	0.443930	+	1.32105i	0.0195429	+	0.0581561i
$517$		−	39.7369i		−	1.74763i
$518$	−19.3586	−	18.3196i	−0.850569	−	0.804917i
$519$	2.34883	+	1.16727i	0.103102	+	0.0512376i
$520$	1.45588	+	1.45588i	0.0638446	+	0.0638446i
$521$	3.80161			0.166552			0.0832759	−	0.996527i	$-0.473462\pi$
$521$	3.80161			0.166552			0.0832759	+	0.996527i	$0.473462\pi$
$522$	12.4489	−	9.43179i	0.544873	−	0.412818i
$523$	−18.5143	+	18.5143i	−0.809573	+	0.809573i	−0.984569	−	0.174996i	$-0.944009\pi$
$523$	−18.5143	+	18.5143i	−0.809573	+	0.809573i	0.174996	+	0.984569i	$0.444009\pi$
$524$	6.50740	+	6.50740i	0.284277	+	0.284277i
$525$	3.37748	−	6.79630i	0.147405	−	0.296615i
$526$	−11.4936	+	11.4936i	−0.501145	+	0.501145i
$527$		−	0.661863i		−	0.0288312i
$528$	6.97982	+	3.46868i	0.303758	+	0.150955i
$529$		−	18.1300i		−	0.788261i
$530$			8.07611i			0.350804i
$531$	−5.68958	+	41.2623i	−0.246907	+	1.79063i
$532$	3.23223	+	3.23223i	0.140135	+	0.140135i
$533$	−2.90099	+	2.90099i	−0.125656	+	0.125656i
$534$	12.8836	−	25.9250i	0.557530	−	1.12189i
$535$	−0.389018	+	0.389018i	−0.0168187	+	0.0168187i
$536$	−5.17487	+	5.17487i	−0.223520	+	0.223520i
$537$	−6.07566	+	2.04168i	−0.262184	+	0.0881051i
$538$	−10.1038	−	10.1038i	−0.435606	−	0.435606i
$539$	54.8954			2.36451
$540$	−4.29374	−	2.92640i	−0.184773	−	0.125932i
$541$	−26.4175	+	26.4175i	−1.13578	+	1.13578i	−0.146576	+	0.989199i	$0.546825\pi$
$541$	−26.4175	+	26.4175i	−1.13578	+	1.13578i	−0.989199	+	0.146576i	$0.953175\pi$
$542$	−14.4111	+	14.4111i	−0.619008	+	0.619008i
$543$	12.4455	+	6.18489i	0.534087	+	0.265419i
$544$	1.54323			0.0661654
$545$	−9.45270			−0.404909
$546$	6.95398	−	13.9931i	0.297603	−	0.598849i
$547$	13.2147	+	13.2147i	0.565018	+	0.565018i	0.930729	−	0.365710i	$-0.119174\pi$
$547$	13.2147	+	13.2147i	0.565018	+	0.565018i	−0.365710	+	0.930729i	$0.619174\pi$
$548$	−19.5068			−0.833289
$549$	−0.287919	+	2.08806i	−0.0122881	+	0.0891164i
$550$	−3.18197	−	3.18197i	−0.135680	−	0.135680i
$551$		−	5.43115i		−	0.231375i
$552$	−1.70105	+	3.42293i	−0.0724015	+	0.145689i
$553$	−8.97191	+	8.97191i	−0.381525	+	0.381525i
$554$	24.8598			1.05619
$555$	9.89054	−	3.63003i	0.419830	−	0.154086i
$556$	17.7979			0.754801
$557$	−17.3259	+	17.3259i	−0.734123	+	0.734123i	−0.971434	−	0.237311i	$-0.923734\pi$
$557$	−17.3259	+	17.3259i	−0.734123	+	0.734123i	0.237311	+	0.971434i	$0.423734\pi$
$558$	0.776994	+	1.02554i	0.0328928	+	0.0434147i
$559$		−	1.65666i		−	0.0700693i
$560$	−3.09831	−	3.09831i	−0.130927	−	0.130927i
$561$	−3.83146	−	11.4017i	−0.161764	−	0.481380i
$562$	−1.90329			−0.0802855
$563$	12.6771	+	12.6771i	0.534276	+	0.534276i	0.921842	−	0.387566i	$-0.126684\pi$
$563$	12.6771	+	12.6771i	0.534276	+	0.534276i	−0.387566	+	0.921842i	$0.626684\pi$
$564$	13.6967	+	6.80669i	0.576735	+	0.286613i
$565$	−8.64462			−0.363682
$566$	−0.389222			−0.0163602
$567$	−10.6723	+	37.9634i	−0.448196	+	1.59431i
$568$	−9.46742	+	9.46742i	−0.397244	+	0.397244i
$569$	−19.4272	+	19.4272i	−0.814430	+	0.814430i	−0.985295	−	0.170864i	$-0.945344\pi$
$569$	−19.4272	+	19.4272i	−0.814430	+	0.814430i	0.170864	+	0.985295i	$0.445344\pi$
$570$	−1.71280	+	0.575573i	−0.0717411	+	0.0241081i
$571$	18.7824			0.786020			0.393010	−	0.919534i	$-0.371434\pi$
$571$	18.7824			0.786020			0.393010	+	0.919534i	$0.371434\pi$
$572$	−6.55145	−	6.55145i	−0.273930	−	0.273930i
$573$	2.90200	+	8.63580i	0.121233	+	0.360766i
$574$	6.17369	−	6.17369i	0.257685	−	0.257685i
$575$	1.56045	−	1.56045i	0.0650752	−	0.0650752i
$576$	−2.39120	+	1.81167i	−0.0996333	+	0.0754864i
$577$	15.0730	−	15.0730i	0.627496	−	0.627496i	−0.319941	−	0.947437i	$-0.603663\pi$
$577$	15.0730	−	15.0730i	0.627496	−	0.627496i	0.947437	+	0.319941i	$0.103663\pi$
$578$	10.3368	+	10.3368i	0.429954	+	0.429954i
$579$	−26.5549	+	8.92359i	−1.10359	+	0.370852i
$580$			5.20612i			0.216172i
$581$		−	45.0136i		−	1.86748i
$582$	−0.835062	+	1.68035i	−0.0346144	+	0.0696526i
$583$		−	36.3424i		−	1.50515i
$584$	8.70104	−	8.70104i	0.360052	−	0.360052i
$585$	3.73010	+	4.92331i	0.154221	+	0.203554i
$586$	−2.15072	−	2.15072i	−0.0888455	−	0.0888455i
$587$	−28.6854	+	28.6854i	−1.18397	+	1.18397i	−0.205266	+	0.978706i	$0.565806\pi$
$587$	−28.6854	+	28.6854i	−1.18397	+	1.18397i	−0.978706	+	0.205266i	$0.934194\pi$
$588$	−9.40324	+	18.9216i	−0.387783	+	0.780313i
$589$	0.447420			0.0184356
$590$	−9.81764	−	9.81764i	−0.404186	−	0.404186i
$591$	9.92416	−	19.9698i	0.408226	−	0.821449i
$592$	−0.167677	−	6.08045i	−0.00689149	−	0.249905i
$593$			19.5396i			0.802396i	0.915991	+	0.401198i	$0.131406\pi$
$593$			19.5396i			0.802396i	−0.915991	+	0.401198i	$0.868594\pi$
$594$	19.3218	+	13.1687i	0.792782	+	0.540320i
$595$			6.76192i			0.277212i
$596$	−19.3712			−0.793476
$597$	−12.9246	−	38.4613i	−0.528970	−	1.57412i
$598$	3.21285	−	3.21285i	0.131383	−	0.131383i
$599$		−	19.5959i		−	0.800668i	−0.916369	−	0.400334i	$-0.868894\pi$
$599$		−	19.5959i		−	0.800668i	0.916369	−	0.400334i	$-0.131106\pi$
$600$	1.64183	−	0.551724i	0.0670274	−	0.0225241i
$601$	−21.1149			−0.861294			−0.430647	−	0.902520i	$-0.641715\pi$
$601$	−21.1149			−0.861294			−0.430647	+	0.902520i	$0.641715\pi$
$602$			3.52559i			0.143692i
$603$	−17.4997	+	13.2585i	−0.712642	+	0.539928i
$604$	−12.1984			−0.496347
$605$	6.54065	+	6.54065i	0.265915	+	0.265915i
$606$	−20.5433	+	6.90344i	−0.834516	+	0.280433i
$607$	−26.0839	−	26.0839i	−1.05871	−	1.05871i	−0.998165	−	0.0605486i	$-0.980715\pi$
$607$	−26.0839	−	26.0839i	−1.05871	−	1.05871i	−0.0605486	−	0.998165i	$-0.519285\pi$
$608$			1.04322i			0.0423084i
$609$	37.4526	−	12.5857i	1.51765	−	0.509997i
$610$	−0.496818	−	0.496818i	−0.0201156	−	0.0201156i
$611$	−12.8561	−	12.8561i	−0.520102	−	0.520102i
$612$	4.58629	+	0.632396i	0.185390	+	0.0255631i
$613$		−	8.19734i		−	0.331087i	−0.986202	−	0.165544i	$-0.947062\pi$
$613$		−	8.19734i		−	0.331087i	0.986202	−	0.165544i	$-0.0529379\pi$
$614$	−9.33199	−	9.33199i	−0.376608	−	0.376608i
$615$	1.09937	+	3.27151i	0.0443308	+	0.131920i
$616$	13.9423	+	13.9423i	0.561753	+	0.561753i
$617$	25.5042			1.02676			0.513379	−	0.858162i	$-0.328393\pi$
$617$	25.5042			1.02676			0.513379	+	0.858162i	$0.328393\pi$
$618$	14.1823	+	7.04803i	0.570498	+	0.283513i
$619$		−	29.5707i		−	1.18855i	−0.804262	−	0.594274i	$-0.797439\pi$
$619$		−	29.5707i		−	1.18855i	0.804262	−	0.594274i	$-0.202561\pi$
$620$	−0.428882			−0.0172243
$621$	−6.45799	+	9.47546i	−0.259150	+	0.380237i
$622$			23.3764i			0.937307i
$623$	51.7858	−	51.7858i	2.07475	−	2.07475i
$624$	3.38041	−	1.13596i	0.135325	−	0.0454748i
$625$	−1.00000			−0.0400000
$626$			6.27610i			0.250843i
$627$	7.70756	−	2.59007i	0.307810	−	0.103437i
$628$			7.11091i			0.283756i
$629$	−6.45219	+	6.81813i	−0.257265	+	0.271857i
$630$	−7.93815	−	10.4774i	−0.316264	−	0.417431i
$631$	−2.03316	−	2.03316i	−0.0809387	−	0.0809387i	0.665478	−	0.746417i	$-0.268228\pi$
$631$	−2.03316	−	2.03316i	−0.0809387	−	0.0809387i	−0.746417	+	0.665478i	$0.768228\pi$
$632$	−2.89575			−0.115187
$633$	14.3156	+	7.11424i	0.568993	+	0.282766i
$634$	2.25356	−	2.25356i	0.0895003	−	0.0895003i
$635$	13.3133	+	13.3133i	0.528323	+	0.528323i
$636$	12.5267	+	6.22523i	0.496714	+	0.246846i
$637$	17.7603	−	17.7603i	0.703689	−	0.703689i
$638$		−	23.4275i		−	0.927503i
$639$	−32.0157	+	24.2564i	−1.26652	+	0.959569i
$640$		−	1.00000i		−	0.0395285i
$641$			6.05439i			0.239134i	0.992826	+	0.119567i	$0.0381507\pi$
$641$			6.05439i			0.239134i	−0.992826	+	0.119567i	$0.961849\pi$
$642$	0.303534	+	0.903260i	0.0119795	+	0.0356488i
$643$	−13.8840	−	13.8840i	−0.547530	−	0.547530i	0.378196	−	0.925726i	$-0.376545\pi$
$643$	−13.8840	−	13.8840i	−0.547530	−	0.547530i	−0.925726	+	0.378196i	$0.876545\pi$
$644$	−6.83737	+	6.83737i	−0.269430	+	0.269430i
$645$	−1.24803	−	0.620220i	−0.0491412	−	0.0244211i
$646$	1.13840	−	1.13840i	0.0447896	−	0.0447896i
$647$	15.4482	−	15.4482i	0.607330	−	0.607330i	−0.334917	−	0.942248i	$-0.608708\pi$
$647$	15.4482	−	15.4482i	0.607330	−	0.607330i	0.942248	+	0.334917i	$0.108708\pi$
$648$	−7.84876	+	4.40419i	−0.308329	+	0.173013i
$649$	44.1793	+	44.1793i	1.73419	+	1.73419i
$650$	−2.05893			−0.0807578
$651$	1.03681	+	3.08535i	0.0406358	+	0.120924i
$652$	−3.95330	+	3.95330i	−0.154823	+	0.154823i
$653$	14.5821	−	14.5821i	0.570642	−	0.570642i	−0.361666	−	0.932308i	$-0.617792\pi$
$653$	14.5821	−	14.5821i	0.570642	−	0.570642i	0.932308	+	0.361666i	$0.117792\pi$
$654$	−7.28633	+	14.6619i	−0.284918	+	0.573324i
$655$	−9.20286			−0.359585
$656$	1.99260			0.0777981
$657$	29.4240	−	22.2929i	1.14794	−	0.869728i
$658$	27.3595	+	27.3595i	1.06658	+	1.06658i
$659$	14.6678			0.571375			0.285688	−	0.958323i	$-0.407778\pi$
$659$	14.6678			0.571375			0.285688	+	0.958323i	$0.407778\pi$
$660$	−7.38821	+	2.48275i	−0.287586	+	0.0966410i
$661$	−32.3272	−	32.3272i	−1.25738	−	1.25738i	−0.952338	−	0.305044i	$-0.901329\pi$
$661$	−32.3272	−	32.3272i	−1.25738	−	1.25738i	−0.305044	−	0.952338i	$-0.598671\pi$
$662$		−	19.6773i		−	0.764780i
$663$	−4.92839	−	2.44920i	−0.191403	−	0.0951191i
$664$	7.26422	−	7.26422i	0.281906	−	0.281906i
$665$	−4.57106			−0.177258
$666$	1.99337	−	18.1391i	0.0772417	−	0.702875i
$667$	11.4889			0.444852
$668$	−1.00757	+	1.00757i	−0.0389842	+	0.0389842i
$669$	33.7171	+	16.7560i	1.30358	+	0.647823i
$670$		−	7.31837i		−	0.282733i
$671$	2.23567	+	2.23567i	0.0863073	+	0.0863073i
$672$	−7.19395	+	2.41747i	−0.277512	+	0.0932561i
$673$	−11.1901			−0.431345			−0.215673	−	0.976466i	$-0.569194\pi$
$673$	−11.1901			−0.431345			−0.215673	+	0.976466i	$0.569194\pi$
$674$	−15.7683	−	15.7683i	−0.607374	−	0.607374i
$675$	5.10541	−	0.966859i	0.196507	−	0.0372144i
$676$	8.76082			0.336955
$677$	13.6262			0.523699			0.261850	−	0.965109i	$-0.415668\pi$
$677$	13.6262			0.523699			0.261850	+	0.965109i	$0.415668\pi$
$678$	−6.66344	+	13.4085i	−0.255908	+	0.514949i
$679$	−3.35653	+	3.35653i	−0.128812	+	0.128812i
$680$	−1.09123	+	1.09123i	−0.0418467	+	0.0418467i
$681$	−9.07582	−	27.0079i	−0.347786	−	1.03495i
$682$	1.92996			0.0739021
$683$	−19.9135	−	19.9135i	−0.761970	−	0.761970i	0.214708	−	0.976678i	$-0.431120\pi$
$683$	−19.9135	−	19.9135i	−0.761970	−	0.761970i	−0.976678	+	0.214708i	$0.931120\pi$
$684$	−0.427500	+	3.10034i	−0.0163459	+	0.118544i
$685$	13.7934	−	13.7934i	0.527018	−	0.527018i
$686$	−16.1081	+	16.1081i	−0.615012	+	0.615012i
$687$	−15.5513	−	7.72833i	−0.593318	−	0.294854i
$688$	−0.568955	+	0.568955i	−0.0216912	+	0.0216912i
$689$	−11.7579	−	11.7579i	−0.447939	−	0.447939i
$690$	−1.21755	−	3.62320i	−0.0463513	−	0.137933i
$691$		−	18.2283i		−	0.693436i	−0.937969	−	0.346718i	$-0.887296\pi$
$691$		−	18.2283i		−	0.693436i	0.937969	−	0.346718i	$-0.112704\pi$
$692$			1.51433i			0.0575660i
$693$	35.7216	+	47.1484i	1.35695	+	1.79102i
$694$		−	12.6223i		−	0.479135i
$695$	−12.5850	+	12.5850i	−0.477378	+	0.477378i
$696$	8.07509	+	4.01298i	0.306085	+	0.152112i
$697$	−2.17438	−	2.17438i	−0.0823607	−	0.0823607i
$698$	5.33481	−	5.33481i	0.201926	−	0.201926i
$699$	21.7641	+	10.8159i	0.823195	+	0.409094i
$700$	4.38167			0.165611
$701$	17.6579	+	17.6579i	0.666930	+	0.666930i	0.957004	−	0.290074i	$-0.0936799\pi$
$701$	17.6579	+	17.6579i	0.666930	+	0.666930i	−0.290074	+	0.957004i	$0.593680\pi$
$702$	10.5117	−	1.99069i	0.396737	−	0.0751338i
$703$	−4.60906	−	4.36168i	−0.173834	−	0.164504i
$704$			4.49999i			0.169600i
$705$	−14.4981	+	4.87198i	−0.546030	+	0.183489i
$706$		−	6.24988i		−	0.235217i
$707$	−54.8255			−2.06193
$708$	−22.7955	+	7.66027i	−0.856709	+	0.287891i
$709$	8.86406	−	8.86406i	0.332897	−	0.332897i	−0.520789	−	0.853686i	$-0.674362\pi$
$709$	8.86406	−	8.86406i	0.332897	−	0.332897i	0.853686	+	0.520789i	$0.174362\pi$
$710$		−	13.3890i		−	0.502478i
$711$	−8.60581	−	1.18664i	−0.322743	−	0.0445025i
$712$	16.7142			0.626392
$713$			0.946460i			0.0354452i
$714$	10.4883	+	5.21222i	0.392513	+	0.195062i
$715$	9.26515			0.346497
$716$	−2.61668	−	2.61668i	−0.0977900	−	0.0977900i
$717$	1.47776	+	4.39753i	0.0551879	+	0.164229i
$718$	17.0011	+	17.0011i	0.634474	+	0.634474i
$719$		−	36.0585i		−	1.34476i	−0.740208	−	0.672378i	$-0.765273\pi$
$719$		−	36.0585i		−	1.34476i	0.740208	−	0.672378i	$-0.234727\pi$
$720$	0.409787	−	2.97188i	0.0152719	−	0.110755i
$721$	28.3295	+	28.3295i	1.05505	+	1.05505i
$722$	−12.6655	−	12.6655i	−0.471360	−	0.471360i
$723$	−27.3483	+	9.19019i	−1.01709	+	0.341787i
$724$			8.02378i			0.298201i
$725$	−3.68128	−	3.68128i	−0.136719	−	0.136719i
$726$	15.1867	−	5.10339i	0.563632	−	0.189404i
$727$	−4.79330	−	4.79330i	−0.177774	−	0.177774i	0.612611	−	0.790385i	$-0.290119\pi$
$727$	−4.79330	−	4.79330i	−0.177774	−	0.177774i	−0.790385	+	0.612611i	$0.790119\pi$
$728$	9.02154			0.334360
$729$	−25.1304	+	9.87242i	−0.930754	+	0.365645i
$730$			12.3051i			0.455433i
$731$	1.24172			0.0459266
$732$	−1.15356	+	0.387645i	−0.0426368	+	0.0143278i
$733$			3.58673i			0.132479i	0.997804	+	0.0662394i	$0.0211001\pi$
$733$			3.58673i			0.132479i	−0.997804	+	0.0662394i	$0.978900\pi$
$734$	16.6895	−	16.6895i	0.616020	−	0.616020i
$735$	−6.73049	−	20.0287i	−0.248258	−	0.738769i
$736$	−2.20681			−0.0813440
$737$			32.9326i			1.21309i
$738$	5.92178	+	0.816543i	0.217984	+	0.0300574i
$739$			38.9164i			1.43156i	0.698324	+	0.715781i	$0.253929\pi$
$739$			38.9164i			1.43156i	−0.698324	+	0.715781i	$0.746071\pi$
$740$	4.41809	+	4.18096i	0.162412	+	0.153695i
$741$	1.65566	−	3.33159i	0.0608223	−	0.122389i
$742$	25.0223	+	25.0223i	0.918596	+	0.918596i
$743$	−25.3462			−0.929863			−0.464931	−	0.885347i	$-0.653921\pi$
$743$	−25.3462			−0.929863			−0.464931	+	0.885347i	$0.653921\pi$
$744$	−0.330591	+	0.665228i	−0.0121200	+	0.0243885i
$745$	13.6975	−	13.6975i	0.501838	−	0.501838i
$746$	25.8584	+	25.8584i	0.946743	+	0.946743i
$747$	24.5652	−	18.6116i	0.898793	−	0.680963i
$748$	4.91051	−	4.91051i	0.179546	−	0.179546i
$749$			2.41060i			0.0880813i
$750$	−0.770820	+	1.55108i	−0.0281464	+	0.0566373i
$751$		−	12.8037i		−	0.467215i	−0.972331	−	0.233608i	$-0.924947\pi$
$751$		−	12.8037i		−	0.467215i	0.972331	−	0.233608i	$-0.0750531\pi$
$752$			8.83045i			0.322014i
$753$	−25.3395	+	8.51514i	−0.923421	+	0.310309i
$754$	−7.57950	−	7.57950i	−0.276029	−	0.276029i
$755$	8.62559	−	8.62559i	0.313917	−	0.313917i
$756$	−22.3702	+	4.23646i	−0.813596	+	0.154078i
$757$	0.841475	−	0.841475i	0.0305839	−	0.0305839i	−0.691649	−	0.722233i	$-0.743116\pi$
$757$	0.841475	−	0.841475i	0.0305839	−	0.0305839i	0.722233	+	0.691649i	$0.243116\pi$
$758$	26.0092	−	26.0092i	0.944695	−	0.944695i
$759$	5.47896	+	16.3043i	0.198874	+	0.591810i
$760$	−0.737671	−	0.737671i	−0.0267582	−	0.0267582i
$761$	45.4549			1.64774			0.823870	−	0.566779i	$-0.191811\pi$
$761$	45.4549			1.64774			0.823870	+	0.566779i	$0.191811\pi$
$762$	30.9121	−	10.3878i	1.11983	−	0.376310i
$763$	−29.2874	+	29.2874i	−1.06027	+	1.06027i
$764$	−3.71929	+	3.71929i	−0.134559	+	0.134559i
$765$	−3.69017	+	2.79583i	−0.133418	+	0.101083i
$766$	−10.9589			−0.395960
$767$	28.5866			1.03220
$768$	−1.55108	−	0.770820i	−0.0559696	−	0.0278146i
$769$	−35.9501	−	35.9501i	−1.29639	−	1.29639i	−0.930759	−	0.365634i	$-0.880852\pi$
$769$	−35.9501	−	35.9501i	−1.29639	−	1.29639i	−0.365634	−	0.930759i	$-0.619148\pi$
$770$	−19.7174			−0.710567
$771$	13.0802	+	38.9243i	0.471073	+	1.40183i
$772$	−11.4367	−	11.4367i	−0.411617	−	0.411617i
$773$			3.80731i			0.136939i	0.997653	+	0.0684697i	$0.0218116\pi$
$773$			3.80731i			0.136939i	−0.997653	+	0.0684697i	$0.978188\pi$
$774$	−1.92402	+	1.45772i	−0.0691573	+	0.0523965i
$775$	0.303265	−	0.303265i	0.0108936	−	0.0108936i
$776$	−1.08334			−0.0388897
$777$	19.3970	−	41.8909i	0.695863	−	1.50283i
$778$	−23.8515			−0.855119
$779$	1.46989	−	1.46989i	0.0526641	−	0.0526641i
$780$	−1.58706	+	3.19355i	−0.0568259	+	0.114348i
$781$			60.2501i			2.15592i
$782$	2.40813	+	2.40813i	0.0861146	+	0.0861146i
$783$	22.3537	+	15.2352i	0.798857	+	0.544461i
$784$	−12.1990			−0.435679
$785$	−5.02817	−	5.02817i	−0.179463	−	0.179463i
$786$	−7.09374	+	14.2743i	−0.253025	+	0.509148i
$787$	2.17346			0.0774755			0.0387378	−	0.999249i	$-0.487666\pi$
$787$	2.17346			0.0774755			0.0387378	+	0.999249i	$0.487666\pi$
$788$	12.8748			0.458646
$789$	−25.2118	−	12.5292i	−0.897565	−	0.446052i
$790$	2.04760	−	2.04760i	0.0728504	−	0.0728504i
$791$	−26.7837	+	26.7837i	−0.952318	+	0.952318i
$792$	−1.84404	+	13.3734i	−0.0655250	+	0.475204i
$793$	1.44662			0.0513708
$794$	1.85282	+	1.85282i	0.0657543	+	0.0657543i
$795$	−13.2596	+	4.45579i	−0.470269	+	0.158030i
$796$	16.5646	−	16.5646i	0.587117	−	0.587117i
$797$	−11.8159	+	11.8159i	−0.418540	+	0.418540i	−0.884700	−	0.466160i	$-0.845637\pi$
$797$	−11.8159	+	11.8159i	−0.418540	+	0.418540i	0.466160	+	0.884700i	$0.345637\pi$
$798$	−3.52347	+	7.09007i	−0.124729	+	0.250986i
$799$	9.63604	−	9.63604i	0.340899	−	0.340899i
$800$	0.707107	+	0.707107i	0.0250000	+	0.0250000i
$801$	49.6726	+	6.84927i	1.75510	+	0.242007i
$802$		−	33.5646i		−	1.18521i
$803$		−	55.3729i		−	1.95407i
$804$	−11.3513	−	5.64114i	−0.400331	−	0.198948i
$805$		−	9.66950i		−	0.340805i
$806$	0.624401	−	0.624401i	0.0219936	−	0.0219936i
$807$	11.0142	−	22.1632i	0.387718	−	0.780183i
$808$	−8.84766	−	8.84766i	−0.311260	−	0.311260i
$809$	−10.9733	+	10.9733i	−0.385800	+	0.385800i	−0.873186	−	0.487386i	$-0.837950\pi$
$809$	−10.9733	+	10.9733i	−0.385800	+	0.385800i	0.487386	+	0.873186i	$0.337950\pi$
$810$	2.43568	−	8.66415i	0.0855810	−	0.304427i
$811$	10.1575			0.356678			0.178339	−	0.983969i	$-0.442928\pi$
$811$	10.1575			0.356678			0.178339	+	0.983969i	$0.442928\pi$
$812$	16.1302	+	16.1302i	0.566058	+	0.566058i
$813$	−31.6114	−	15.7096i	−1.10866	−	0.550958i
$814$	−19.8814	−	18.8143i	−0.696841	−	0.659440i
$815$		−	5.59081i		−	0.195837i
$816$	0.851438	+	2.53372i	0.0298063	+	0.0886979i
$817$			0.839403i			0.0293670i
$818$	11.8125			0.413015
$819$	26.8109	+	3.69691i	0.936850	+	0.129180i
$820$	−1.40898	+	1.40898i	−0.0492038	+	0.0492038i
$821$		−	44.8407i		−	1.56495i	−0.622681	−	0.782476i	$-0.713957\pi$
$821$		−	44.8407i		−	1.56495i	0.622681	−	0.782476i	$-0.286043\pi$
$822$	−10.7624	−	32.0268i	−0.375381	−	1.11706i
$823$	31.0456			1.08218			0.541090	−	0.840965i	$-0.318012\pi$
$823$	31.0456			1.08218			0.541090	+	0.840965i	$0.318012\pi$
$824$			9.14355i			0.318531i
$825$	3.46868	−	6.97982i	0.120764	−	0.243006i
$826$	−60.8361			−2.11676
$827$	−28.1012	−	28.1012i	−0.977176	−	0.977176i	0.0225692	−	0.999745i	$-0.492815\pi$
$827$	−28.1012	−	28.1012i	−0.977176	−	0.977176i	−0.999745	+	0.0225692i	$0.992815\pi$
$828$	−6.55837	−	0.904321i	−0.227919	−	0.0314273i
$829$	−5.40746	−	5.40746i	−0.187809	−	0.187809i	0.606939	−	0.794748i	$-0.292397\pi$
$829$	−5.40746	−	5.40746i	−0.187809	−	0.187809i	−0.794748	+	0.606939i	$0.792397\pi$
$830$			10.2732i			0.356587i
$831$	13.7158	+	40.8156i	0.475795	+	1.41588i
$832$	1.45588	+	1.45588i	0.0504736	+	0.0504736i
$833$	13.3119	+	13.3119i	0.461230	+	0.461230i
$834$	9.81956	+	29.2212i	0.340024	+	1.01185i
$835$		−	1.42492i		−	0.0493115i
$836$	3.31951	+	3.31951i	0.114808	+	0.114808i
$837$	−1.25508	+	1.84151i	−0.0433818	+	0.0636518i
$838$	15.1199	+	15.1199i	0.522309	+	0.522309i
$839$	7.42372			0.256295			0.128148	−	0.991755i	$-0.459097\pi$
$839$	7.42372			0.256295			0.128148	+	0.991755i	$0.459097\pi$
$840$	3.37748	−	6.79630i	0.116534	−	0.234495i
$841$			1.89630i			0.0653897i
$842$	35.2280			1.21404
$843$	−1.05009	−	3.12488i	−0.0361671	−	0.107626i
$844$			9.22945i			0.317691i
$845$	−6.19483	+	6.19483i	−0.213109	+	0.213109i
$846$	−3.61861	+	26.2431i	−0.124410	+	0.902255i
$847$	40.5299			1.39262
$848$			8.07611i			0.277335i
$849$	−0.214743	−	0.639036i	−0.00736997	−	0.0219317i
$850$		−	1.54323i		−	0.0529323i
$851$	9.22658	−	9.74988i	0.316283	−	0.334222i
$852$	−20.7673	−	10.3205i	−0.711475	−	0.353573i
$853$	−0.927344	−	0.927344i	−0.0317516	−	0.0317516i	0.691053	−	0.722804i	$-0.257147\pi$
$853$	−0.927344	−	0.927344i	−0.0317516	−	0.0317516i	−0.722804	+	0.691053i	$0.757147\pi$
$854$	−3.07859			−0.105347
$855$	−1.88998	−	2.49456i	−0.0646360	−	0.0853121i
$856$	−0.389018	+	0.389018i	−0.0132964	+	0.0132964i
$857$	−23.2850	−	23.2850i	−0.795402	−	0.795402i	0.186965	−	0.982367i	$-0.440135\pi$
$857$	−23.2850	−	23.2850i	−0.795402	−	0.795402i	−0.982367	+	0.186965i	$0.940135\pi$
$858$	7.14176	−	14.3709i	0.243816	−	0.490616i
$859$	21.9971	−	21.9971i	0.750532	−	0.750532i	−0.224047	−	0.974578i	$-0.571927\pi$
$859$	21.9971	−	21.9971i	0.750532	−	0.750532i	0.974578	+	0.224047i	$0.0719268\pi$
$860$		−	0.804623i		−	0.0274374i
$861$	13.5423	+	6.72997i	0.461521	+	0.229357i
$862$		−	18.6051i		−	0.633692i
$863$			7.25558i			0.246983i	0.992346	+	0.123491i	$0.0394092\pi$
$863$			7.25558i			0.246983i	−0.992346	+	0.123491i	$0.960591\pi$
$864$	−4.29374	−	2.92640i	−0.146076	−	0.0995580i
$865$	−1.07079	−	1.07079i	−0.0364079	−	0.0364079i
$866$	−28.6481	+	28.6481i	−0.973502	+	0.973502i
$867$	−11.2682	+	22.6743i	−0.382688	+	0.770060i
$868$	−1.32881	+	1.32881i	−0.0451027	+	0.0451027i
$869$	−9.21418	+	9.21418i	−0.312570	+	0.312570i
$870$	−8.54756	+	2.87234i	−0.289789	+	0.0973816i
$871$	10.6547	+	10.6547i	0.361020	+	0.361020i
$872$	−9.45270			−0.320109
$873$	−3.21957	−	0.443940i	−0.108966	−	0.0150251i
$874$	−1.62790	+	1.62790i	−0.0550645	+	0.0550645i
$875$	−3.09831	+	3.09831i	−0.104742	+	0.104742i
$876$	19.0862	+	9.48504i	0.644863	+	0.320470i
$877$	−46.4154			−1.56734			−0.783668	−	0.621179i	$-0.786654\pi$
$877$	−46.4154			−1.56734			−0.783668	+	0.621179i	$0.786654\pi$
$878$	23.3451			0.787857
$879$	2.34451	−	4.71772i	0.0790784	−	0.159125i
$880$	−3.18197	−	3.18197i	−0.107264	−	0.107264i
$881$	−23.1046			−0.778413			−0.389206	−	0.921151i	$-0.627251\pi$
$881$	−23.1046			−0.778413			−0.389206	+	0.921151i	$0.627251\pi$
$882$	−36.2540	−	4.99900i	−1.22074	−	0.168325i
$883$	−39.2707	−	39.2707i	−1.32156	−	1.32156i	−0.912511	−	0.409052i	$-0.865859\pi$
$883$	−39.2707	−	39.2707i	−1.32156	−	1.32156i	−0.409052	−	0.912511i	$-0.634141\pi$
$884$		−	3.17740i		−	0.106867i
$885$	10.7022	−	21.5355i	0.359752	−	0.723908i
$886$	12.2290	−	12.2290i	0.410841	−	0.410841i
$887$	−28.2672			−0.949120			−0.474560	−	0.880223i	$-0.657393\pi$
$887$	−28.2672			−0.949120			−0.474560	+	0.880223i	$0.657393\pi$
$888$	9.89054	−	3.63003i	0.331905	−	0.121816i
$889$	82.4975			2.76688
$890$	−11.8187	+	11.8187i	−0.396165	+	0.396165i
$891$	−10.9605	+	38.9886i	−0.367191	+	1.30617i
$892$			21.7378i			0.727837i
$893$	6.51397	+	6.51397i	0.217982	+	0.217982i
$894$	−10.6876	−	31.8042i	−0.357446	−	1.06369i
$895$	3.70055			0.123696
$896$	−3.09831	−	3.09831i	−0.103507	−	0.103507i
$897$	7.04756	+	3.50234i	0.235311	+	0.116940i
$898$	−7.91374			−0.264085
$899$	2.23281			0.0744684
$900$	1.81167	+	2.39120i	0.0603891	+	0.0797067i
$901$	8.81288	−	8.81288i	0.293600	−	0.293600i
$902$	6.34040	−	6.34040i	0.211112	−	0.211112i
$903$	−5.78842	+	1.94516i	−0.192626	+	0.0647307i
$904$	−8.64462			−0.287516
$905$	−5.67367	−	5.67367i	−0.188599	−	0.188599i
$906$	−6.73017	−	20.0277i	−0.223595	−	0.665376i
$907$	−12.3328	+	12.3328i	−0.409504	+	0.409504i	−0.881566	−	0.472061i	$-0.843510\pi$
$907$	−12.3328	+	12.3328i	−0.409504	+	0.409504i	0.472061	+	0.881566i	$0.343510\pi$
$908$	11.6318	−	11.6318i	0.386016	−	0.386016i
$909$	−22.6685	−	29.9199i	−0.751868	−	0.992379i
$910$	−6.37919	+	6.37919i	−0.211468	+	0.211468i
$911$	−1.77565	−	1.77565i	−0.0588297	−	0.0588297i	0.677080	−	0.735910i	$-0.263245\pi$
$911$	−1.77565	−	1.77565i	−0.0588297	−	0.0588297i	−0.735910	+	0.677080i	$0.763245\pi$
$912$	−1.71280	+	0.575573i	−0.0567163	+	0.0190591i
$913$		−	46.2291i		−	1.52996i
$914$		−	30.1256i		−	0.996467i
$915$	0.541583	−	1.08980i	0.0179042	−	0.0360276i
$916$		−	10.0261i		−	0.331272i
$917$	−28.5133	+	28.5133i	−0.941591	+	0.941591i
$918$	1.49209	+	7.87882i	0.0492462	+	0.260040i
$919$	−22.7873	−	22.7873i	−0.751682	−	0.751682i	0.223111	−	0.974793i	$-0.428379\pi$
$919$	−22.7873	−	22.7873i	−0.751682	−	0.751682i	−0.974793	+	0.223111i	$0.928379\pi$
$920$	1.56045	−	1.56045i	0.0514465	−	0.0514465i
$921$	10.1728	−	20.4702i	0.335206	−	0.674516i
$922$	−22.1532			−0.729576
$923$	19.4927	+	19.4927i	0.641611	+	0.641611i
$924$	−15.1986	+	30.5833i	−0.499997	+	1.00612i
$925$	−6.08045	+	0.167677i	−0.199924	+	0.00551319i
$926$			17.1450i			0.563420i
$927$	−3.74691	+	27.1736i	−0.123065	+	0.892497i
$928$			5.20612i			0.170899i
$929$	−45.6654			−1.49823			−0.749116	−	0.662439i	$-0.769522\pi$
$929$	−45.6654			−1.49823			−0.749116	+	0.662439i	$0.769522\pi$
$930$	−0.236625	−	0.704150i	−0.00775923	−	0.0230900i
$931$	−8.99886	+	8.99886i	−0.294926	+	0.294926i
$932$			14.0316i			0.459622i
$933$	−38.3800	+	12.8973i	−1.25650	+	0.422239i
$934$	−18.3417			−0.600158
$935$			6.94451i			0.227110i
$936$	3.73010	+	4.92331i	0.121922	+	0.160923i
$937$	19.6515			0.641988			0.320994	−	0.947081i	$-0.395983\pi$
$937$	19.6515			0.641988			0.320994	+	0.947081i	$0.395983\pi$
$938$	−22.6745	−	22.6745i	−0.740350	−	0.740350i
$939$	−10.3043	+	3.46268i	−0.336268	+	0.113000i
$940$	−6.24407	−	6.24407i	−0.203659	−	0.203659i
$941$			17.0041i			0.554317i	0.960824	+	0.277159i	$0.0893927\pi$
$941$			17.0041i			0.554317i	−0.960824	+	0.277159i	$0.910607\pi$
$942$	−11.6749	+	3.92326i	−0.380388	+	0.127827i
$943$	3.10935	+	3.10935i	0.101254	+	0.101254i
$944$	−9.81764	−	9.81764i	−0.319537	−	0.319537i
$945$	12.8225	−	18.8137i	0.417116	−	0.612011i
$946$			3.62079i			0.117722i
$947$	3.04029	+	3.04029i	0.0987962	+	0.0987962i	0.754777	−	0.655981i	$-0.227745\pi$
$947$	3.04029	+	3.04029i	0.0987962	+	0.0987962i	−0.655981	+	0.754777i	$0.727745\pi$
$948$	−1.59765	−	4.75432i	−0.0518894	−	0.154413i
$949$	−17.9148	−	17.9148i	−0.581540	−	0.581540i
$950$	1.04322			0.0338467
$951$	4.94330	+	2.45662i	0.160298	+	0.0796612i
$952$			6.76192i			0.219155i
$953$	7.48439			0.242443			0.121222	−	0.992625i	$-0.461319\pi$
$953$	7.48439			0.242443			0.121222	+	0.992625i	$0.461319\pi$
$954$	−3.30949	+	24.0012i	−0.107149	+	0.777069i
$955$		−	5.25987i		−	0.170205i
$956$	−1.89394	+	1.89394i	−0.0612544	+	0.0612544i
$957$	38.4639	−	12.9255i	1.24336	−	0.417822i
$958$	−29.1943			−0.943226
$959$		−	85.4723i		−	2.76004i
$960$	1.64183	−	0.551724i	0.0529898	−	0.0178068i
$961$		−	30.8161i		−	0.994066i
$962$	−12.5192	+	0.345235i	−0.403635	+	0.0111308i
$963$	−1.31553	+	0.996702i	−0.0423924	+	0.0321183i
$964$	−11.7784	−	11.7784i	−0.379358	−	0.379358i
$965$	16.1740			0.520659
$966$	−14.9981	−	7.45344i	−0.482557	−	0.239810i
$967$	−16.0066	+	16.0066i	−0.514738	+	0.514738i	−0.915974	−	0.401237i	$-0.868581\pi$
$967$	−16.0066	+	16.0066i	−0.514738	+	0.514738i	0.401237	+	0.915974i	$0.368581\pi$
$968$	6.54065	+	6.54065i	0.210225	+	0.210225i
$969$	2.49713	+	1.24097i	0.0802194	+	0.0398657i
$970$	0.766039	−	0.766039i	0.0245960	−	0.0245960i
$971$		−	13.5254i		−	0.434049i	−0.976166	−	0.217025i	$-0.930365\pi$
$971$		−	13.5254i		−	0.434049i	0.976166	−	0.217025i	$-0.0696352\pi$
$972$	−11.5613	−	10.4564i	−0.370828	−	0.335390i
$973$			77.9847i			2.50007i
$974$		−	28.4876i		−	0.912801i
$975$	−1.13596	−	3.38041i	−0.0363799	−	0.108260i
$976$	−0.496818	−	0.496818i	−0.0159028	−	0.0159028i
$977$	23.7197	−	23.7197i	0.758861	−	0.758861i	−0.217254	−	0.976115i	$-0.569710\pi$
$977$	23.7197	−	23.7197i	0.758861	−	0.758861i	0.976115	+	0.217254i	$0.0697101\pi$
$978$	−8.67177	−	4.30950i	−0.277292	−	0.137803i
$979$	53.1841	−	53.1841i	1.69977	−	1.69977i
$980$	8.62600	−	8.62600i	0.275548	−	0.275548i
$981$	−28.0923	−	3.87359i	−0.896918	−	0.123674i
$982$	25.1466	+	25.1466i	0.802460	+	0.802460i
$983$	10.5567			0.336707			0.168353	−	0.985727i	$-0.446155\pi$
$983$	10.5567			0.336707			0.168353	+	0.985727i	$0.446155\pi$
$984$	1.09937	+	3.27151i	0.0350466	+	0.104292i
$985$	−9.10387	+	9.10387i	−0.290073	+	0.290073i
$986$	5.68107	−	5.68107i	0.180922	−	0.180922i
$987$	−29.8247	+	60.0144i	−0.949329	+	1.91028i
$988$	2.14792			0.0683346
$989$	−1.77565			−0.0564623
$990$	−8.15251	−	10.7604i	−0.259104	−	0.341987i
$991$	20.8171	+	20.8171i	0.661278	+	0.661278i	0.955681	−	0.294403i	$-0.0951208\pi$
$991$	20.8171	+	20.8171i	0.661278	+	0.661278i	−0.294403	+	0.955681i	$0.595121\pi$
$992$	−0.428882			−0.0136170
$993$	32.3068	−	10.8564i	1.02522	−	0.344519i
$994$	−41.4831	−	41.4831i	−1.31576	−	1.31576i
$995$			23.4259i			0.742651i
$996$	15.9345	+	7.91876i	0.504902	+	0.250915i
$997$	−18.2060	+	18.2060i	−0.576588	+	0.576588i	−0.933962	−	0.357373i	$-0.883672\pi$
$997$	−18.2060	+	18.2060i	−0.576588	+	0.576588i	0.357373	+	0.933962i	$0.383672\pi$
$998$	7.69073			0.243446
$999$	30.8811	−	6.73500i	0.977033	−	0.213086i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.f.401.10	yes	40
3.2	odd	2	inner	1110.2.u.f.401.17	yes	40
37.6	odd	4	inner	1110.2.u.f.191.17	yes	40
111.80	even	4	inner	1110.2.u.f.191.10	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.f.191.10	✓	40	111.80	even	4	inner
1110.2.u.f.191.17	yes	40	37.6	odd	4	inner
1110.2.u.f.401.10	yes	40	1.1	even	1	trivial
1110.2.u.f.401.17	yes	40	3.2	odd	2	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.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.55108 - 0.770820i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(1.64183 - 0.551724i) q^{6} +4.38167 q^{7} +(0.707107 + 0.707107i) q^{8} +(1.81167 + 2.39120i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.55108 - 0.770820i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(1.64183 - 0.551724i) q^{6} +4.38167 q^{7} +(0.707107 + 0.707107i) q^{8} +(1.81167 + 2.39120i) q^{9} -1.00000 q^{10} +4.49999 q^{11} +(-0.770820 + 1.55108i) q^{12} +(1.45588 - 1.45588i) q^{13} +(-3.09831 + 3.09831i) q^{14} +(-0.551724 - 1.64183i) q^{15} -1.00000 q^{16} +(1.09123 + 1.09123i) q^{17} +(-2.97188 - 0.409787i) q^{18} +(-0.737671 + 0.737671i) q^{19} +(0.707107 - 0.707107i) q^{20} +(-6.79630 - 3.37748i) q^{21} +(-3.18197 + 3.18197i) q^{22} +(-1.56045 - 1.56045i) q^{23} +(-0.551724 - 1.64183i) q^{24} +1.00000i q^{25} +2.05893i q^{26} +(-0.966859 - 5.10541i) q^{27} -4.38167i q^{28} +(-3.68128 + 3.68128i) q^{29} +(1.55108 + 0.770820i) q^{30} +(-0.303265 - 0.303265i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.97982 - 3.46868i) q^{33} -1.54323 q^{34} +(3.09831 + 3.09831i) q^{35} +(2.39120 - 1.81167i) q^{36} +(0.167677 + 6.08045i) q^{37} -1.04322i q^{38} +(-3.38041 + 1.13596i) q^{39} +1.00000i q^{40} -1.99260 q^{41} +(7.19395 - 2.41747i) q^{42} +(0.568955 - 0.568955i) q^{43} -4.49999i q^{44} +(-0.409787 + 2.97188i) q^{45} +2.20681 q^{46} -8.83045i q^{47} +(1.55108 + 0.770820i) q^{48} +12.1990 q^{49} +(-0.707107 - 0.707107i) q^{50} +(-0.851438 - 2.53372i) q^{51} +(-1.45588 - 1.45588i) q^{52} -8.07611i q^{53} +(4.29374 + 2.92640i) q^{54} +(3.18197 + 3.18197i) q^{55} +(3.09831 + 3.09831i) q^{56} +(1.71280 - 0.575573i) q^{57} -5.20612i q^{58} +(9.81764 + 9.81764i) q^{59} +(-1.64183 + 0.551724i) q^{60} +(0.496818 + 0.496818i) q^{61} +0.428882 q^{62} +(7.93815 + 10.4774i) q^{63} +1.00000i q^{64} +2.05893 q^{65} +(7.38821 - 2.48275i) q^{66} +7.31837i q^{67} +(1.09123 - 1.09123i) q^{68} +(1.21755 + 3.62320i) q^{69} -4.38167 q^{70} +13.3890i q^{71} +(-0.409787 + 2.97188i) q^{72} -12.3051i q^{73} +(-4.41809 - 4.18096i) q^{74} +(0.770820 - 1.55108i) q^{75} +(0.737671 + 0.737671i) q^{76} +19.7174 q^{77} +(1.58706 - 3.19355i) q^{78} +(-2.04760 + 2.04760i) q^{79} +(-0.707107 - 0.707107i) q^{80} +(-2.43568 + 8.66415i) q^{81} +(1.40898 - 1.40898i) q^{82} -10.2732i q^{83} +(-3.37748 + 6.79630i) q^{84} +1.54323i q^{85} +0.804623i q^{86} +(8.54756 - 2.87234i) q^{87} +(3.18197 + 3.18197i) q^{88} +(11.8187 - 11.8187i) q^{89} +(-1.81167 - 2.39120i) q^{90} +(6.37919 - 6.37919i) q^{91} +(-1.56045 + 1.56045i) q^{92} +(0.236625 + 0.704150i) q^{93} +(6.24407 + 6.24407i) q^{94} -1.04322 q^{95} +(-1.64183 + 0.551724i) q^{96} +(-0.766039 + 0.766039i) q^{97} +(-8.62600 + 8.62600i) q^{98} +(8.15251 + 10.7604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{7} - 8 q^{9}+O(q^{10}) \) 40 * q + 24 * q^7 - 8 * q^9	\( 40 q + 24 q^{7} - 8 q^{9} - 40 q^{10} + 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 16 q^{22} - 8 q^{31} + 24 q^{33} + 24 q^{34} + 32 q^{37} + 16 q^{39} + 12 q^{42} + 32 q^{43} + 8 q^{45} - 56 q^{46} - 32 q^{49} - 44 q^{51} - 16 q^{52} - 24 q^{54} + 16 q^{55} + 8 q^{57} - 72 q^{61} + 24 q^{63} - 28 q^{66} + 16 q^{69} - 24 q^{70} + 8 q^{72} - 16 q^{76} - 48 q^{79} + 120 q^{81} - 24 q^{82} - 24 q^{84} + 20 q^{87} + 16 q^{88} + 8 q^{90} - 92 q^{93} - 8 q^{94} - 40 q^{97}+O(q^{100}) \) 40 * q + 24 * q^7 - 8 * q^9 - 40 * q^10 + 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 16 * q^22 - 8 * q^31 + 24 * q^33 + 24 * q^34 + 32 * q^37 + 16 * q^39 + 12 * q^42 + 32 * q^43 + 8 * q^45 - 56 * q^46 - 32 * q^49 - 44 * q^51 - 16 * q^52 - 24 * q^54 + 16 * q^55 + 8 * q^57 - 72 * q^61 + 24 * q^63 - 28 * q^66 + 16 * q^69 - 24 * q^70 + 8 * q^72 - 16 * q^76 - 48 * q^79 + 120 * q^81 - 24 * q^82 - 24 * q^84 + 20 * q^87 + 16 * q^88 + 8 * q^90 - 92 * q^93 - 8 * q^94 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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