LMFDB - Embedded newform 1110.2.x.c.751.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(751,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1110.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{13} + 398 x^{12} - 136 x^{11} + 32 x^{10} - 824 x^{9} + 17825 x^{8} - 11480 x^{7} + \cdots + 20736 $ x^16 - 8x^13 + 398x^12 - 136x^11 + 32x^10 - 824x^9 + 17825x^8 - 11480x^7 + 3104x^6 + 11296x^5 + 68320x^4 - 21120x^3 + 4608x^2 + 13824*x + 20736
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.4
Root			$-0.917697 - 0.917697i$ of defining polynomial
Character	$\chi$	$=$	1110.751
Dual form			1110.2.x.c.841.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(1.35869 - 2.35332i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(1.35869 - 2.35332i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} -3.71738 q^{11} +(0.500000 + 0.866025i) q^{12} +(0.0894976 + 0.0516714i) q^{13} +2.71738i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-4.85218 + 2.80141i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-0.581796 - 0.335900i) q^{19} +(0.866025 - 0.500000i) q^{20} +(1.35869 + 2.35332i) q^{21} +(3.21935 - 1.85869i) q^{22} +4.33273i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -0.103343 q^{26} +1.00000 q^{27} +(-1.35869 - 2.35332i) q^{28} +6.22458i q^{29} +(0.500000 - 0.866025i) q^{30} +5.43958i q^{31} +(0.866025 + 0.500000i) q^{32} +(1.85869 - 3.21935i) q^{33} +(2.80141 - 4.85218i) q^{34} +(2.35332 - 1.35869i) q^{35} -1.00000 q^{36} +(3.02255 + 5.27865i) q^{37} +0.671801 q^{38} +(-0.0894976 + 0.0516714i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(4.16034 - 7.20592i) q^{41} +(-2.35332 - 1.35869i) q^{42} +10.6337i q^{43} +(-1.85869 + 3.21935i) q^{44} -1.00000i q^{45} +(-2.16637 - 3.75226i) q^{46} +0.896377 q^{47} +1.00000 q^{48} +(-0.192082 - 0.332697i) q^{49} +(-0.866025 - 0.500000i) q^{50} -5.60282i q^{51} +(0.0894976 - 0.0516714i) q^{52} +(6.66754 + 11.5485i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-3.21935 - 1.85869i) q^{55} +(2.35332 + 1.35869i) q^{56} +(0.581796 - 0.335900i) q^{57} +(-3.11229 - 5.39064i) q^{58} +(-3.08579 + 1.78158i) q^{59} +1.00000i q^{60} +(-7.20592 - 4.16034i) q^{61} +(-2.71979 - 4.71081i) q^{62} -2.71738 q^{63} -1.00000 q^{64} +(0.0516714 + 0.0894976i) q^{65} +3.71738i q^{66} +(3.52476 - 6.10506i) q^{67} +5.60282i q^{68} +(-3.75226 - 2.16637i) q^{69} +(-1.35869 + 2.35332i) q^{70} +(-6.90850 + 11.9659i) q^{71} +(0.866025 - 0.500000i) q^{72} +14.8636 q^{73} +(-5.25693 - 3.06017i) q^{74} -1.00000 q^{75} +(-0.581796 + 0.335900i) q^{76} +(-5.05077 + 8.74820i) q^{77} +(0.0516714 - 0.0894976i) q^{78} +(-11.3555 - 6.55611i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +8.32068i q^{82} +(-2.96354 - 5.13301i) q^{83} +2.71738 q^{84} -5.60282 q^{85} +(-5.31686 - 9.20908i) q^{86} +(-5.39064 - 3.11229i) q^{87} -3.71738i q^{88} +(-15.9168 + 9.18954i) q^{89} +(0.500000 + 0.866025i) q^{90} +(0.243199 - 0.140411i) q^{91} +(3.75226 + 2.16637i) q^{92} +(-4.71081 - 2.71979i) q^{93} +(-0.776285 + 0.448189i) q^{94} +(-0.335900 - 0.581796i) q^{95} +(-0.866025 + 0.500000i) q^{96} +6.98265i q^{97} +(0.332697 + 0.192082i) q^{98} +(1.85869 + 3.21935i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} + 8 q^{12} - 12 q^{13} - 8 q^{16} - 6 q^{17} + 6 q^{19} - 2 q^{21} - 6 q^{22} + 8 q^{25} + 16 q^{27} + 2 q^{28} + 8 q^{30} + 6 q^{33} - 4 q^{34} - 6 q^{35} - 16 q^{36} + 18 q^{37} + 12 q^{38} + 12 q^{39} - 8 q^{40} + 6 q^{42} - 6 q^{44} - 4 q^{46} - 60 q^{47} + 16 q^{48} - 4 q^{49} - 12 q^{52} + 12 q^{53} + 6 q^{55} - 6 q^{56} - 6 q^{57} - 12 q^{58} + 12 q^{59} - 4 q^{62} + 4 q^{63} - 16 q^{64} + 22 q^{67} - 6 q^{69} + 2 q^{70} + 2 q^{71} + 24 q^{73} - 8 q^{74} - 16 q^{75} + 6 q^{76} - 58 q^{77} - 36 q^{79} - 8 q^{81} - 8 q^{83} - 4 q^{84} + 8 q^{85} - 2 q^{86} - 42 q^{89} + 8 q^{90} + 6 q^{92} - 6 q^{93} + 6 q^{94} - 6 q^{95} - 12 q^{98} + 6 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 + 8 * q^12 - 12 * q^13 - 8 * q^16 - 6 * q^17 + 6 * q^19 - 2 * q^21 - 6 * q^22 + 8 * q^25 + 16 * q^27 + 2 * q^28 + 8 * q^30 + 6 * q^33 - 4 * q^34 - 6 * q^35 - 16 * q^36 + 18 * q^37 + 12 * q^38 + 12 * q^39 - 8 * q^40 + 6 * q^42 - 6 * q^44 - 4 * q^46 - 60 * q^47 + 16 * q^48 - 4 * q^49 - 12 * q^52 + 12 * q^53 + 6 * q^55 - 6 * q^56 - 6 * q^57 - 12 * q^58 + 12 * q^59 - 4 * q^62 + 4 * q^63 - 16 * q^64 + 22 * q^67 - 6 * q^69 + 2 * q^70 + 2 * q^71 + 24 * q^73 - 8 * q^74 - 16 * q^75 + 6 * q^76 - 58 * q^77 - 36 * q^79 - 8 * q^81 - 8 * q^83 - 4 * q^84 + 8 * q^85 - 2 * q^86 - 42 * q^89 + 8 * q^90 + 6 * q^92 - 6 * q^93 + 6 * q^94 - 6 * q^95 - 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$		−	1.00000i		−	0.408248i
$7$	1.35869	−	2.35332i	0.513537	−	0.889472i	−0.486340	−	0.873770i	$-0.661668\pi$
$7$	1.35869	−	2.35332i	0.513537	−	0.889472i	0.999877	−	0.0157023i	$-0.00499840\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00000			−0.316228
$11$	−3.71738			−1.12083			−0.560416	−	0.828211i	$-0.689359\pi$
$11$	−3.71738			−1.12083			−0.560416	+	0.828211i	$0.689359\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	0.0894976	+	0.0516714i	0.0248222	+	0.0143311i	0.512360	−	0.858771i	$-0.328771\pi$
$13$	0.0894976	+	0.0516714i	0.0248222	+	0.0143311i	−0.487538	+	0.873102i	$0.662105\pi$
$14$			2.71738i			0.726251i
$15$	−0.866025	+	0.500000i	−0.223607	+	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.85218	+	2.80141i	−1.17683	+	0.679441i	−0.955278	−	0.295708i	$-0.904444\pi$
$17$	−4.85218	+	2.80141i	−1.17683	+	0.679441i	−0.221549	+	0.975149i	$0.571111\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	−0.581796	−	0.335900i	−0.133473	−	0.0770608i	0.431777	−	0.901981i	$-0.357887\pi$
$19$	−0.581796	−	0.335900i	−0.133473	−	0.0770608i	−0.565250	+	0.824920i	$0.691220\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	1.35869	+	2.35332i	0.296491	+	0.513537i
$22$	3.21935	−	1.85869i	0.686367	−	0.396274i
$23$			4.33273i			0.903437i	0.892160	+	0.451719i	$0.149189\pi$
$23$			4.33273i			0.903437i	−0.892160	+	0.451719i	$0.850811\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−0.103343			−0.0202672
$27$	1.00000			0.192450
$28$	−1.35869	−	2.35332i	−0.256768	−	0.444736i
$29$			6.22458i			1.15587i	0.816081	+	0.577937i	$0.196142\pi$
$29$			6.22458i			1.15587i	−0.816081	+	0.577937i	$0.803858\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$			5.43958i			0.976977i	0.872570	+	0.488489i	$0.162452\pi$
$31$			5.43958i			0.976977i	−0.872570	+	0.488489i	$0.837548\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	1.85869	−	3.21935i	0.323557	−	0.560416i
$34$	2.80141	−	4.85218i	0.480438	−	0.832142i
$35$	2.35332	−	1.35869i	0.397784	−	0.229661i
$36$	−1.00000			−0.166667
$37$	3.02255	+	5.27865i	0.496904	+	0.867806i
$37$	3.02255	+	5.27865i	0.496904	+	0.867806i
$38$	0.671801			0.108980
$39$	−0.0894976	+	0.0516714i	−0.0143311	+	0.00827405i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	4.16034	−	7.20592i	0.649736	−	1.12538i	−0.333450	−	0.942768i	$-0.608213\pi$
$41$	4.16034	−	7.20592i	0.649736	−	1.12538i	0.983186	−	0.182608i	$-0.0584540\pi$
$42$	−2.35332	−	1.35869i	−0.363125	−	0.209651i
$43$			10.6337i			1.62163i	0.585303	+	0.810814i	$0.300975\pi$
$43$			10.6337i			1.62163i	−0.585303	+	0.810814i	$0.699025\pi$
$44$	−1.85869	+	3.21935i	−0.280208	+	0.485335i
$45$		−	1.00000i		−	0.149071i
$46$	−2.16637	−	3.75226i	−0.319413	−	0.553240i
$47$	0.896377			0.130750			0.0653750	−	0.997861i	$-0.479176\pi$
$47$	0.896377			0.130750			0.0653750	+	0.997861i	$0.479176\pi$
$48$	1.00000			0.144338
$49$	−0.192082	−	0.332697i	−0.0274404	−	0.0475281i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$		−	5.60282i		−	0.784551i
$52$	0.0894976	−	0.0516714i	0.0124111	−	0.00716554i
$53$	6.66754	+	11.5485i	0.915856	+	1.58631i	0.805642	+	0.592402i	$0.201820\pi$
$53$	6.66754	+	11.5485i	0.915856	+	1.58631i	0.110214	+	0.993908i	$0.464846\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	−3.21935	−	1.85869i	−0.434097	−	0.250626i
$56$	2.35332	+	1.35869i	0.314476	+	0.181563i
$57$	0.581796	−	0.335900i	0.0770608	−	0.0444911i
$58$	−3.11229	−	5.39064i	−0.408663	−	0.707826i
$59$	−3.08579	+	1.78158i	−0.401735	+	0.231942i	−0.687232	−	0.726438i	$-0.741175\pi$
$59$	−3.08579	+	1.78158i	−0.401735	+	0.231942i	0.285497	+	0.958380i	$0.407841\pi$
$60$			1.00000i			0.129099i
$61$	−7.20592	−	4.16034i	−0.922624	−	0.532677i	−0.0381527	−	0.999272i	$-0.512147\pi$
$61$	−7.20592	−	4.16034i	−0.922624	−	0.532677i	−0.884471	+	0.466595i	$0.845481\pi$
$62$	−2.71979	−	4.71081i	−0.345414	−	0.598274i
$63$	−2.71738			−0.342358
$64$	−1.00000			−0.125000
$65$	0.0516714	+	0.0894976i	0.00640905	+	0.0111008i
$66$			3.71738i			0.457578i
$67$	3.52476	−	6.10506i	0.430617	−	0.745851i	−0.566309	−	0.824193i	$-0.691629\pi$
$67$	3.52476	−	6.10506i	0.430617	−	0.745851i	0.996927	+	0.0783416i	$0.0249625\pi$
$68$			5.60282i			0.679441i
$69$	−3.75226	−	2.16637i	−0.451719	−	0.260800i
$70$	−1.35869	+	2.35332i	−0.162395	+	0.281276i
$71$	−6.90850	+	11.9659i	−0.819889	+	1.42009i	0.0858751	+	0.996306i	$0.472631\pi$
$71$	−6.90850	+	11.9659i	−0.819889	+	1.42009i	−0.905764	+	0.423783i	$0.860702\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	14.8636			1.73965			0.869827	−	0.493358i	$-0.164231\pi$
$73$	14.8636			1.73965			0.869827	+	0.493358i	$0.164231\pi$
$74$	−5.25693	−	3.06017i	−0.611106	−	0.355738i
$75$	−1.00000			−0.115470
$76$	−0.581796	+	0.335900i	−0.0667366	+	0.0385304i
$77$	−5.05077	+	8.74820i	−0.575589	+	0.996949i
$78$	0.0516714	−	0.0894976i	0.00585064	−	0.0101336i
$79$	−11.3555	−	6.55611i	−1.27760	−	0.737620i	−0.301190	−	0.953564i	$-0.597384\pi$
$79$	−11.3555	−	6.55611i	−1.27760	−	0.737620i	−0.976406	+	0.215944i	$0.930717\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$			8.32068i			0.918866i
$83$	−2.96354	−	5.13301i	−0.325291	−	0.563421i	0.656280	−	0.754517i	$-0.272129\pi$
$83$	−2.96354	−	5.13301i	−0.325291	−	0.563421i	−0.981571	+	0.191097i	$0.938796\pi$
$84$	2.71738			0.296491
$85$	−5.60282			−0.607711
$86$	−5.31686	−	9.20908i	−0.573332	−	0.993041i
$87$	−5.39064	−	3.11229i	−0.577937	−	0.333672i
$88$		−	3.71738i		−	0.396274i
$89$	−15.9168	+	9.18954i	−1.68717	+	0.974089i	−0.730505	+	0.682908i	$0.760715\pi$
$89$	−15.9168	+	9.18954i	−1.68717	+	0.974089i	−0.956668	+	0.291182i	$0.905952\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	0.243199	−	0.140411i	0.0254942	−	0.0147191i
$92$	3.75226	+	2.16637i	0.391200	+	0.225859i
$93$	−4.71081	−	2.71979i	−0.488489	−	0.282029i
$94$	−0.776285	+	0.448189i	−0.0800677	+	0.0462271i
$95$	−0.335900	−	0.581796i	−0.0344626	−	0.0596911i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$			6.98265i			0.708981i	0.935060	+	0.354490i	$0.115346\pi$
$97$			6.98265i			0.708981i	−0.935060	+	0.354490i	$0.884654\pi$
$98$	0.332697	+	0.192082i	0.0336074	+	0.0194033i
$99$	1.85869	+	3.21935i	0.186805	+	0.323557i
$100$	1.00000			0.100000
$101$	11.3761			1.13197			0.565983	−	0.824417i	$-0.308497\pi$
$101$	11.3761			1.13197			0.565983	+	0.824417i	$0.308497\pi$
$102$	2.80141	+	4.85218i	0.277381	+	0.480438i
$103$		−	14.4717i		−	1.42594i	−0.701193	−	0.712972i	$-0.747349\pi$
$103$		−	14.4717i		−	1.42594i	0.701193	−	0.712972i	$-0.252651\pi$
$104$	−0.0516714	+	0.0894976i	−0.00506680	+	0.00877596i
$105$			2.71738i			0.265189i
$106$	−11.5485	−	6.66754i	−1.12169	−	0.647608i
$107$	−0.502002	+	0.869493i	−0.0485304	+	0.0840571i	−0.889270	−	0.457382i	$-0.848787\pi$
$107$	−0.502002	+	0.869493i	−0.0485304	+	0.0840571i	0.840740	+	0.541439i	$0.182120\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−11.6471	+	6.72445i	−1.11559	+	0.644086i	−0.940271	−	0.340426i	$-0.889429\pi$
$109$	−11.6471	+	6.72445i	−1.11559	+	0.644086i	−0.175318	+	0.984512i	$0.556095\pi$
$110$	3.71738			0.354438
$111$	−6.08272	−	0.0217234i	−0.577347	−	0.00206189i
$112$	−2.71738			−0.256768
$113$	−1.71969	+	0.992866i	−0.161775	+	0.0934010i	−0.578702	−	0.815539i	$-0.696441\pi$
$113$	−1.71969	+	0.992866i	−0.161775	+	0.0934010i	0.416927	+	0.908940i	$0.363107\pi$
$114$	−0.335900	+	0.581796i	−0.0314600	+	0.0544902i
$115$	−2.16637	+	3.75226i	−0.202015	+	0.349900i
$116$	5.39064	+	3.11229i	0.500508	+	0.288969i
$117$		−	0.103343i		−	0.00955405i
$118$	1.78158	−	3.08579i	0.164008	−	0.284070i
$119$			15.2250i			1.39567i
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	2.81893			0.256266
$122$	8.32068			0.753319
$123$	4.16034	+	7.20592i	0.375125	+	0.649736i
$124$	4.71081	+	2.71979i	0.423043	+	0.244244i
$125$			1.00000i			0.0894427i
$126$	2.35332	−	1.35869i	0.209651	−	0.121042i
$127$	−6.43022	−	11.1375i	−0.570590	−	0.988291i	−0.996505	−	0.0835276i	$-0.973381\pi$
$127$	−6.43022	−	11.1375i	−0.570590	−	0.988291i	0.425916	−	0.904763i	$-0.359952\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−9.20908	−	5.31686i	−0.810814	−	0.468124i
$130$	−0.0894976	−	0.0516714i	−0.00784945	−	0.00453188i
$131$	11.6872	−	6.74763i	1.02112	−	0.589543i	0.106691	−	0.994292i	$-0.465974\pi$
$131$	11.6872	−	6.74763i	1.02112	−	0.589543i	0.914428	+	0.404749i	$0.132641\pi$
$132$	−1.85869	−	3.21935i	−0.161778	−	0.280208i
$133$	−1.58096	+	0.912770i	−0.137087	+	0.0791472i
$134$			7.04951i			0.608985i
$135$	0.866025	+	0.500000i	0.0745356	+	0.0430331i
$136$	−2.80141	−	4.85218i	−0.240219	−	0.416071i
$137$	15.7687			1.34722			0.673608	−	0.739089i	$-0.264744\pi$
$137$	15.7687			1.34722			0.673608	+	0.739089i	$0.264744\pi$
$138$	4.33273			0.368827
$139$	−2.81271	−	4.87175i	−0.238571	−	0.413216i	0.721734	−	0.692171i	$-0.243345\pi$
$139$	−2.81271	−	4.87175i	−0.238571	−	0.413216i	−0.960304	+	0.278954i	$0.910012\pi$
$140$		−	2.71738i		−	0.229661i
$141$	−0.448189	+	0.776285i	−0.0377443	+	0.0653750i
$142$		−	13.8170i		−	1.15950i
$143$	−0.332697	−	0.192082i	−0.0278215	−	0.0160627i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−3.11229	+	5.39064i	−0.258461	+	0.447668i
$146$	−12.8723	+	7.43180i	−1.06532	+	0.615060i
$147$	0.384165			0.0316854
$148$	6.08272	+	0.0217234i	0.499997	+	0.00178565i
$149$	−16.9725			−1.39044			−0.695222	−	0.718795i	$-0.744694\pi$
$149$	−16.9725			−1.39044			−0.695222	+	0.718795i	$0.744694\pi$
$150$	0.866025	−	0.500000i	0.0707107	−	0.0408248i
$151$	−1.76946	+	3.06479i	−0.143996	+	0.249409i	−0.928998	−	0.370084i	$-0.879329\pi$
$151$	−1.76946	+	3.06479i	−0.143996	+	0.249409i	0.785002	+	0.619494i	$0.212662\pi$
$152$	0.335900	−	0.581796i	0.0272451	−	0.0471899i
$153$	4.85218	+	2.80141i	0.392276	+	0.226480i
$154$		−	10.1015i		−	0.814006i
$155$	−2.71979	+	4.71081i	−0.218459	+	0.378382i
$156$			0.103343i			0.00827405i
$157$	10.4553	+	18.1091i	0.834422	+	1.44526i	0.894500	+	0.447068i	$0.147532\pi$
$157$	10.4553	+	18.1091i	0.834422	+	1.44526i	−0.0600781	+	0.998194i	$0.519135\pi$
$158$	13.1122			1.04315
$159$	−13.3351			−1.05754
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	10.1963	+	5.88685i	0.803582	+	0.463948i
$162$		−	1.00000i		−	0.0785674i
$163$	−9.85826	+	5.69167i	−0.772158	+	0.445806i	−0.833644	−	0.552302i	$-0.813749\pi$
$163$	−9.85826	+	5.69167i	−0.772158	+	0.445806i	0.0614858	+	0.998108i	$0.480416\pi$
$164$	−4.16034	−	7.20592i	−0.324868	−	0.562688i
$165$	3.21935	−	1.85869i	0.250626	−	0.144699i
$166$	5.13301	+	2.96354i	0.398399	+	0.230016i
$167$	2.40769	+	1.39008i	0.186313	+	0.107568i	0.590255	−	0.807217i	$-0.299027\pi$
$167$	2.40769	+	1.39008i	0.186313	+	0.107568i	−0.403942	+	0.914784i	$0.632360\pi$
$168$	−2.35332	+	1.35869i	−0.181563	+	0.104825i
$169$	−6.49466	−	11.2491i	−0.499589	−	0.865314i
$170$	4.85218	−	2.80141i	0.372145	−	0.214858i
$171$			0.671801i			0.0513739i
$172$	9.20908	+	5.31686i	0.702186	+	0.405407i
$173$	−3.46352	−	5.99899i	−0.263327	−	0.456095i	0.703797	−	0.710401i	$-0.251486\pi$
$173$	−3.46352	−	5.99899i	−0.263327	−	0.456095i	−0.967124	+	0.254306i	$0.918153\pi$
$174$	6.22458			0.471884
$175$	2.71738			0.205415
$176$	1.85869	+	3.21935i	0.140104	+	0.242667i
$177$		−	3.56316i		−	0.267824i
$178$	9.18954	−	15.9168i	0.688785	−	1.19301i
$179$		−	9.57411i		−	0.715603i	−0.933798	−	0.357801i	$-0.883526\pi$
$179$		−	9.57411i		−	0.715603i	0.933798	−	0.357801i	$-0.116474\pi$
$180$	−0.866025	−	0.500000i	−0.0645497	−	0.0372678i
$181$	9.99350	−	17.3093i	0.742811	−	1.28659i	−0.208399	−	0.978044i	$-0.566825\pi$
$181$	9.99350	−	17.3093i	0.742811	−	1.28659i	0.951210	−	0.308543i	$-0.0998414\pi$
$182$	−0.140411	+	0.243199i	−0.0104080	+	0.0180271i
$183$	7.20592	−	4.16034i	0.532677	−	0.307541i
$184$	−4.33273			−0.319413
$185$	−0.0217234	+	6.08272i	−0.00159713	+	0.447211i
$186$	5.43958			0.398849
$187$	18.0374	−	10.4139i	1.31903	−	0.761540i
$188$	0.448189	−	0.776285i	0.0326875	−	0.0566164i
$189$	1.35869	−	2.35332i	0.0988302	−	0.171179i
$190$	0.581796	+	0.335900i	0.0422080	+	0.0243688i
$191$		−	20.4388i		−	1.47890i	−0.673213	−	0.739449i	$-0.735086\pi$
$191$		−	20.4388i		−	1.47890i	0.673213	−	0.739449i	$-0.264914\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$			17.1929i			1.23757i	0.785561	+	0.618784i	$0.212374\pi$
$193$			17.1929i			1.23757i	−0.785561	+	0.618784i	$0.787626\pi$
$194$	−3.49133	−	6.04715i	−0.250663	−	0.434160i
$195$	−0.103343			−0.00740054
$196$	−0.384165			−0.0274404
$197$	4.22710	+	7.32155i	0.301168	+	0.521638i	0.976401	−	0.215966i	$-0.0692901\pi$
$197$	4.22710	+	7.32155i	0.301168	+	0.521638i	−0.675233	+	0.737605i	$0.735957\pi$
$198$	−3.21935	−	1.85869i	−0.228789	−	0.132091i
$199$		−	10.1762i		−	0.721371i	−0.932688	−	0.360685i	$-0.882543\pi$
$199$		−	10.1762i		−	0.721371i	0.932688	−	0.360685i	$-0.117457\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	3.52476	+	6.10506i	0.248617	+	0.430617i
$202$	−9.85201	+	5.68806i	−0.693185	+	0.400210i
$203$	14.6484	+	8.45728i	1.02812	+	0.593584i
$204$	−4.85218	−	2.80141i	−0.339721	−	0.196138i
$205$	7.20592	−	4.16034i	0.503283	−	0.290571i
$206$	7.23587	+	12.5329i	0.504147	+	0.873208i
$207$	3.75226	−	2.16637i	0.260800	−	0.150573i
$208$		−	0.103343i		−	0.00716554i
$209$	2.16276	+	1.24867i	0.149601	+	0.0863723i
$210$	−1.35869	−	2.35332i	−0.0937586	−	0.162395i
$211$	9.24185			0.636235			0.318118	−	0.948051i	$-0.396949\pi$
$211$	9.24185			0.636235			0.318118	+	0.948051i	$0.396949\pi$
$212$	13.3351			0.915856
$213$	−6.90850	−	11.9659i	−0.473363	−	0.819889i
$214$		−	1.00400i		−	0.0686323i
$215$	−5.31686	+	9.20908i	−0.362607	+	0.628054i
$216$			1.00000i			0.0680414i
$217$	12.8011	+	7.39071i	0.868994	+	0.501714i
$218$	6.72445	−	11.6471i	0.455437	−	0.788841i
$219$	−7.43180	+	12.8723i	−0.502195	+	0.869827i
$220$	−3.21935	+	1.85869i	−0.217048	+	0.125313i
$221$	−0.579011			−0.0389485
$222$	5.27865	−	3.02255i	0.354280	−	0.202860i
$223$	−9.79917			−0.656201			−0.328101	−	0.944643i	$-0.606409\pi$
$223$	−9.79917			−0.656201			−0.328101	+	0.944643i	$0.606409\pi$
$224$	2.35332	−	1.35869i	0.157238	−	0.0907814i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	0.992866	−	1.71969i	0.0660444	−	0.114392i
$227$	−2.75424	−	1.59016i	−0.182805	−	0.105543i	0.405805	−	0.913960i	$-0.366991\pi$
$227$	−2.75424	−	1.59016i	−0.182805	−	0.105543i	−0.588610	+	0.808417i	$0.700325\pi$
$228$		−	0.671801i		−	0.0444911i
$229$	0.796621	−	1.37979i	0.0526422	−	0.0911789i	−0.838504	−	0.544896i	$-0.816569\pi$
$229$	0.796621	−	1.37979i	0.0526422	−	0.0911789i	0.891146	+	0.453717i	$0.149902\pi$
$230$		−	4.33273i		−	0.285692i
$231$	−5.05077	−	8.74820i	−0.332316	−	0.575589i
$232$	−6.22458			−0.408663
$233$	−3.04213			−0.199297			−0.0996484	−	0.995023i	$-0.531772\pi$
$233$	−3.04213			−0.199297			−0.0996484	+	0.995023i	$0.531772\pi$
$234$	0.0516714	+	0.0894976i	0.00337787	+	0.00585064i
$235$	0.776285	+	0.448189i	0.0506393	+	0.0292366i
$236$			3.56316i			0.231942i
$237$	11.3555	−	6.55611i	0.737620	−	0.425865i
$238$	−7.61250	−	13.1852i	−0.493445	−	0.854672i
$239$	−0.726353	+	0.419360i	−0.0469839	+	0.0271262i	−0.523308	−	0.852144i	$-0.675302\pi$
$239$	−0.726353	+	0.419360i	−0.0469839	+	0.0271262i	0.476324	+	0.879270i	$0.341969\pi$
$240$	0.866025	+	0.500000i	0.0559017	+	0.0322749i
$241$	2.29842	+	1.32699i	0.148054	+	0.0854791i	0.572197	−	0.820116i	$-0.306091\pi$
$241$	2.29842	+	1.32699i	0.148054	+	0.0854791i	−0.424143	+	0.905595i	$0.639425\pi$
$242$	−2.44126	+	1.40946i	−0.156930	+	0.0906038i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−7.20592	+	4.16034i	−0.461312	+	0.266339i
$245$		−	0.384165i		−	0.0245434i
$246$	−7.20592	−	4.16034i	−0.459433	−	0.265254i
$247$	−0.0347129	−	0.0601245i	−0.00220873	−	0.00382563i
$248$	−5.43958			−0.345414
$249$	5.92709			0.375614
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$			16.4136i			1.03602i	0.855375	+	0.518009i	$0.173327\pi$
$251$			16.4136i			1.03602i	−0.855375	+	0.518009i	$0.826673\pi$
$252$	−1.35869	+	2.35332i	−0.0855895	+	0.148245i
$253$		−	16.1064i		−	1.01260i
$254$	11.1375	+	6.43022i	0.698827	+	0.403468i
$255$	2.80141	−	4.85218i	0.175431	−	0.303855i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−18.8467	+	10.8811i	−1.17562	+	0.678746i	−0.954998	−	0.296613i	$-0.904143\pi$
$257$	−18.8467	+	10.8811i	−1.17562	+	0.678746i	−0.220624	+	0.975359i	$0.570810\pi$
$258$	10.6337			0.662027
$259$	16.5291	+	0.0590307i	1.02707	+	0.00366799i
$260$	0.103343			0.00640905
$261$	5.39064	−	3.11229i	0.333672	−	0.192646i
$262$	−6.74763	+	11.6872i	−0.416870	+	0.722040i
$263$	13.7167	−	23.7580i	0.845809	−	1.46498i	−0.0391079	−	0.999235i	$-0.512452\pi$
$263$	13.7167	−	23.7580i	0.845809	−	1.46498i	0.884917	−	0.465749i	$-0.154215\pi$
$264$	3.21935	+	1.85869i	0.198137	+	0.114395i
$265$			13.3351i			0.819167i
$266$	0.912770	−	1.58096i	0.0559655	−	0.0969351i
$267$		−	18.3791i		−	1.12478i
$268$	−3.52476	−	6.10506i	−0.215309	−	0.372926i
$269$	4.30997			0.262784			0.131392	−	0.991331i	$-0.458055\pi$
$269$	4.30997			0.262784			0.131392	+	0.991331i	$0.458055\pi$
$270$	−1.00000			−0.0608581
$271$	9.15167	+	15.8512i	0.555924	+	0.962889i	0.997831	+	0.0658280i	$0.0209689\pi$
$271$	9.15167	+	15.8512i	0.555924	+	0.962889i	−0.441907	+	0.897061i	$0.645698\pi$
$272$	4.85218	+	2.80141i	0.294207	+	0.169860i
$273$			0.280822i			0.0169961i
$274$	−13.6561	+	7.88437i	−0.824997	+	0.476312i
$275$	−1.85869	−	3.21935i	−0.112083	−	0.194134i
$276$	−3.75226	+	2.16637i	−0.225859	+	0.130400i
$277$	7.61381	+	4.39583i	0.457469	+	0.264120i	0.710980	−	0.703213i	$-0.248252\pi$
$277$	7.61381	+	4.39583i	0.457469	+	0.264120i	−0.253510	+	0.967333i	$0.581585\pi$
$278$	4.87175	+	2.81271i	0.292188	+	0.168695i
$279$	4.71081	−	2.71979i	0.282029	−	0.162830i
$280$	1.35869	+	2.35332i	0.0811973	+	0.140638i
$281$	16.7977	−	9.69815i	1.00207	−	0.578543i	0.0932069	−	0.995647i	$-0.470288\pi$
$281$	16.7977	−	9.69815i	1.00207	−	0.578543i	0.908859	+	0.417104i	$0.136955\pi$
$282$		−	0.896377i		−	0.0533785i
$283$	−0.885281	−	0.511117i	−0.0526245	−	0.0303828i	0.473457	−	0.880817i	$-0.343006\pi$
$283$	−0.885281	−	0.511117i	−0.0526245	−	0.0303828i	−0.526081	+	0.850434i	$0.676339\pi$
$284$	6.90850	+	11.9659i	0.409944	+	0.710044i
$285$	0.671801			0.0397940
$286$	0.384165			0.0227161
$287$	−11.3052	−	19.5812i	−0.667327	−	1.15584i
$288$		−	1.00000i		−	0.0589256i
$289$	7.19578	−	12.4635i	0.423281	−	0.733145i
$290$		−	6.22458i		−	0.365520i
$291$	−6.04715	−	3.49133i	−0.354490	−	0.204665i
$292$	7.43180	−	12.8723i	0.434913	−	0.753292i
$293$	−1.24506	+	2.15651i	−0.0727374	+	0.125985i	−0.900100	−	0.435683i	$-0.856507\pi$
$293$	−1.24506	+	2.15651i	−0.0727374	+	0.125985i	0.827363	+	0.561668i	$0.189840\pi$
$294$	−0.332697	+	0.192082i	−0.0194033	+	0.0112025i
$295$	−3.56316			−0.207455
$296$	−5.27865	+	3.02255i	−0.306816	+	0.175682i
$297$	−3.71738			−0.215704
$298$	14.6986	−	8.48626i	0.851469	−	0.491596i
$299$	−0.223879	+	0.387769i	−0.0129472	+	0.0224253i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	25.0246	+	14.4480i	1.44239	+	0.832766i
$302$		−	3.53892i		−	0.203642i
$303$	−5.68806	+	9.85201i	−0.326770	+	0.565983i
$304$			0.671801i			0.0385304i
$305$	−4.16034	−	7.20592i	−0.238220	−	0.412610i
$306$	−5.60282			−0.320292
$307$	1.32779			0.0757810			0.0378905	−	0.999282i	$-0.487936\pi$
$307$	1.32779			0.0757810			0.0378905	+	0.999282i	$0.487936\pi$
$308$	5.05077	+	8.74820i	0.287795	+	0.498475i
$309$	12.5329	+	7.23587i	0.712972	+	0.411634i
$310$		−	5.43958i		−	0.308947i
$311$	1.82785	−	1.05531i	0.103648	−	0.0598410i	−0.447280	−	0.894394i	$-0.647607\pi$
$311$	1.82785	−	1.05531i	0.103648	−	0.0598410i	0.550928	+	0.834553i	$0.314274\pi$
$312$	−0.0516714	−	0.0894976i	−0.00292532	−	0.00506680i
$313$	3.64727	−	2.10575i	0.206156	−	0.119024i	−0.393368	−	0.919381i	$-0.628690\pi$
$313$	3.64727	−	2.10575i	0.206156	−	0.119024i	0.599524	+	0.800357i	$0.295357\pi$
$314$	−18.1091	−	10.4553i	−1.02195	−	0.590025i
$315$	−2.35332	−	1.35869i	−0.132595	−	0.0765536i
$316$	−11.3555	+	6.55611i	−0.638798	+	0.368810i
$317$	−2.08780	−	3.61617i	−0.117262	−	0.203105i	0.801419	−	0.598103i	$-0.204079\pi$
$317$	−2.08780	−	3.61617i	−0.117262	−	0.203105i	−0.918682	+	0.394998i	$0.870745\pi$
$318$	11.5485	−	6.66754i	0.647608	−	0.373897i
$319$		−	23.1391i		−	1.29554i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	−0.502002	−	0.869493i	−0.0280190	−	0.0485304i
$322$	−11.7737			−0.656122
$323$	3.76398			0.209433
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$			0.103343i			0.00573243i
$326$	5.69167	−	9.85826i	0.315232	−	0.545998i
$327$		−	13.4489i		−	0.743726i
$328$	7.20592	+	4.16034i	0.397881	+	0.229716i
$329$	1.21790	−	2.10946i	0.0671450	−	0.116299i
$330$	−1.85869	+	3.21935i	−0.102318	+	0.177219i
$331$	25.7646	−	14.8752i	1.41615	−	0.817616i	0.420194	−	0.907434i	$-0.361962\pi$
$331$	25.7646	−	14.8752i	1.41615	−	0.817616i	0.995958	+	0.0898189i	$0.0286288\pi$
$332$	−5.92709			−0.325291
$333$	3.06017	−	5.25693i	0.167697	−	0.288078i
$334$	−2.78016			−0.152124
$335$	6.10506	−	3.52476i	0.333555	−	0.192578i
$336$	1.35869	−	2.35332i	0.0741227	−	0.128384i
$337$	2.76374	−	4.78693i	0.150550	−	0.260761i	−0.780880	−	0.624682i	$-0.785229\pi$
$337$	2.76374	−	4.78693i	0.150550	−	0.260761i	0.931430	+	0.363921i	$0.118562\pi$
$338$	11.2491	+	6.49466i	0.611869	+	0.353263i
$339$		−	1.98573i		−	0.107850i
$340$	−2.80141	+	4.85218i	−0.151928	+	0.263147i
$341$		−	20.2210i		−	1.09503i
$342$	−0.335900	−	0.581796i	−0.0181634	−	0.0314600i
$343$	17.9778			0.970707
$344$	−10.6337			−0.573332
$345$	−2.16637	−	3.75226i	−0.116633	−	0.202015i
$346$	5.99899	+	3.46352i	0.322508	+	0.186200i
$347$		−	18.5686i		−	0.996816i	−0.866943	−	0.498408i	$-0.833918\pi$
$347$		−	18.5686i		−	0.996816i	0.866943	−	0.498408i	$-0.166082\pi$
$348$	−5.39064	+	3.11229i	−0.288969	+	0.166836i
$349$	15.6950	+	27.1845i	0.840134	+	1.45515i	0.889781	+	0.456387i	$0.150857\pi$
$349$	15.6950	+	27.1845i	0.840134	+	1.45515i	−0.0496474	+	0.998767i	$0.515810\pi$
$350$	−2.35332	+	1.35869i	−0.125790	+	0.0726251i
$351$	0.0894976	+	0.0516714i	0.00477703	+	0.00275802i
$352$	−3.21935	−	1.85869i	−0.171592	−	0.0990686i
$353$	−15.1392	+	8.74065i	−0.805781	+	0.465218i	−0.845488	−	0.533994i	$-0.820691\pi$
$353$	−15.1392	+	8.74065i	−0.805781	+	0.465218i	0.0397078	+	0.999211i	$0.487357\pi$
$354$	1.78158	+	3.08579i	0.0946899	+	0.164008i
$355$	−11.9659	+	6.90850i	−0.635083	+	0.366665i
$356$			18.3791i			0.974089i
$357$	−13.1852	−	7.61250i	−0.697836	−	0.402896i
$358$	4.78706	+	8.29143i	0.253004	+	0.438215i
$359$	−10.7506			−0.567396			−0.283698	−	0.958914i	$-0.591561\pi$
$359$	−10.7506			−0.567396			−0.283698	+	0.958914i	$0.591561\pi$
$360$	1.00000			0.0527046
$361$	−9.27434	−	16.0636i	−0.488123	−	0.845454i
$362$			19.9870i			1.05049i
$363$	−1.40946	+	2.44126i	−0.0739777	+	0.128133i
$364$		−	0.280822i		−	0.0147191i
$365$	12.8723	+	7.43180i	0.673765	+	0.388998i
$366$	−4.16034	+	7.20592i	−0.217465	+	0.376660i
$367$	−9.52657	+	16.5005i	−0.497283	+	0.861319i	−0.999995	−	0.00313453i	$-0.999002\pi$
$367$	−9.52657	+	16.5005i	−0.497283	+	0.861319i	0.502712	+	0.864454i	$0.332336\pi$
$368$	3.75226	−	2.16637i	0.195600	−	0.112930i
$369$	−8.32068			−0.433157
$370$	−3.02255	−	5.27865i	−0.157135	−	0.274424i
$371$	36.2365			1.88130
$372$	−4.71081	+	2.71979i	−0.244244	+	0.141014i
$373$	−12.1097	+	20.9746i	−0.627016	+	1.08602i	0.361132	+	0.932515i	$0.382391\pi$
$373$	−12.1097	+	20.9746i	−0.627016	+	1.08602i	−0.988147	+	0.153508i	$0.950943\pi$
$374$	−10.4139	+	18.0374i	−0.538490	+	0.932692i
$375$	−0.866025	−	0.500000i	−0.0447214	−	0.0258199i
$376$			0.896377i			0.0462271i
$377$	−0.321633	+	0.557084i	−0.0165649	+	0.0286913i
$378$			2.71738i			0.139767i
$379$	−1.27807	−	2.21369i	−0.0656501	−	0.113709i	0.831332	−	0.555776i	$-0.187579\pi$
$379$	−1.27807	−	2.21369i	−0.0656501	−	0.113709i	−0.896982	+	0.442067i	$0.854245\pi$
$380$	−0.671801			−0.0344626
$381$	12.8604			0.658860
$382$	10.2194	+	17.7005i	0.522869	+	0.905636i
$383$	−19.1348	−	11.0475i	−0.977744	−	0.564501i	−0.0761560	−	0.997096i	$-0.524265\pi$
$383$	−19.1348	−	11.0475i	−0.977744	−	0.564501i	−0.901588	+	0.432595i	$0.857598\pi$
$384$			1.00000i			0.0510310i
$385$	−8.74820	+	5.05077i	−0.445849	+	0.257411i
$386$	−8.59643	−	14.8894i	−0.437547	−	0.757853i
$387$	9.20908	−	5.31686i	0.468124	−	0.270271i
$388$	6.04715	+	3.49133i	0.306998	+	0.177245i
$389$	29.0097	+	16.7488i	1.47085	+	0.849196i	0.999464	−	0.0327305i	$-0.0104203\pi$
$389$	29.0097	+	16.7488i	1.47085	+	0.849196i	0.471387	+	0.881927i	$0.343754\pi$
$390$	0.0894976	−	0.0516714i	0.00453188	−	0.00261648i
$391$	−12.1378	−	21.0232i	−0.613833	−	1.06319i
$392$	0.332697	−	0.192082i	0.0168037	−	0.00970163i
$393$			13.4953i			0.680746i
$394$	−7.32155	−	4.22710i	−0.368854	−	0.212958i
$395$	−6.55611	−	11.3555i	−0.329874	−	0.571358i
$396$	3.71738			0.186805
$397$	−9.29412			−0.466458			−0.233229	−	0.972422i	$-0.574929\pi$
$397$	−9.29412			−0.466458			−0.233229	+	0.972422i	$0.574929\pi$
$398$	5.08809	+	8.81284i	0.255043	+	0.441748i
$399$		−	1.82554i		−	0.0913913i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$		−	13.0216i		−	0.650267i	−0.945668	−	0.325133i	$-0.894591\pi$
$401$		−	13.0216i		−	0.650267i	0.945668	−	0.325133i	$-0.105409\pi$
$402$	−6.10506	−	3.52476i	−0.304493	−	0.175799i
$403$	−0.281071	+	0.486829i	−0.0140011	+	0.0242507i
$404$	5.68806	−	9.85201i	0.282992	−	0.490156i
$405$	−0.866025	+	0.500000i	−0.0430331	+	0.0248452i
$406$	−16.9146			−0.839455
$407$	−11.2360	−	19.6228i	−0.556946	−	0.972665i
$408$	5.60282			0.277381
$409$	−24.7591	+	14.2947i	−1.22426	+	0.706826i	−0.965823	−	0.259203i	$-0.916540\pi$
$409$	−24.7591	+	14.2947i	−1.22426	+	0.706826i	−0.258435	+	0.966029i	$0.583207\pi$
$410$	−4.16034	+	7.20592i	−0.205465	+	0.355875i
$411$	−7.88437	+	13.6561i	−0.388907	+	0.673608i
$412$	−12.5329	−	7.23587i	−0.617451	−	0.356486i
$413$			9.68247i			0.476443i
$414$	−2.16637	+	3.75226i	−0.106471	+	0.184413i
$415$		−	5.92709i		−	0.290949i
$416$	0.0516714	+	0.0894976i	0.00253340	+	0.00438798i
$417$	5.62541			0.275478
$418$	−2.49734			−0.122149
$419$	3.19419	+	5.53249i	0.156046	+	0.270280i	0.933439	−	0.358735i	$-0.116792\pi$
$419$	3.19419	+	5.53249i	0.156046	+	0.270280i	−0.777393	+	0.629015i	$0.783458\pi$
$420$	2.35332	+	1.35869i	0.114830	+	0.0662973i
$421$			31.2270i			1.52191i	0.648803	+	0.760956i	$0.275270\pi$
$421$			31.2270i			1.52191i	−0.648803	+	0.760956i	$0.724730\pi$
$422$	−8.00368	+	4.62092i	−0.389613	+	0.224943i
$423$	−0.448189	−	0.776285i	−0.0217917	−	0.0377443i
$424$	−11.5485	+	6.66754i	−0.560845	+	0.323804i
$425$	−4.85218	−	2.80141i	−0.235365	−	0.135888i
$426$	11.9659	+	6.90850i	0.579749	+	0.334718i
$427$	−19.5812	+	11.3052i	−0.947603	+	0.547099i
$428$	0.502002	+	0.869493i	0.0242652	+	0.0420285i
$429$	0.332697	−	0.192082i	0.0160627	−	0.00927383i
$430$		−	10.6337i		−	0.512804i
$431$	−25.9818	−	15.0006i	−1.25150	−	0.722553i	−0.280092	−	0.959973i	$-0.590365\pi$
$431$	−25.9818	−	15.0006i	−1.25150	−	0.722553i	−0.971407	+	0.237420i	$0.923698\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	30.4411			1.46291			0.731453	−	0.681892i	$-0.238843\pi$
$433$	30.4411			1.46291			0.731453	+	0.681892i	$0.238843\pi$
$434$	−14.7814			−0.709530
$435$	−3.11229	−	5.39064i	−0.149223	−	0.258461i
$436$			13.4489i			0.644086i
$437$	1.45537	−	2.52077i	0.0696196	−	0.120585i
$438$		−	14.8636i		−	0.710210i
$439$	11.6906	+	6.74956i	0.557961	+	0.322139i	0.752327	−	0.658790i	$-0.228932\pi$
$439$	11.6906	+	6.74956i	0.557961	+	0.322139i	−0.194366	+	0.980929i	$0.562265\pi$
$440$	1.85869	−	3.21935i	0.0886096	−	0.153476i
$441$	−0.192082	+	0.332697i	−0.00914678	+	0.0158427i
$442$	0.501438	−	0.289506i	0.0238510	−	0.0137704i
$443$	−9.89115			−0.469943			−0.234971	−	0.972002i	$-0.575500\pi$
$443$	−9.89115			−0.469943			−0.234971	+	0.972002i	$0.575500\pi$
$444$	−3.06017	+	5.25693i	−0.145229	+	0.249483i
$445$	−18.3791			−0.871252
$446$	8.48633	−	4.89959i	0.401840	−	0.232002i
$447$	8.48626	−	14.6986i	0.401387	−	0.695222i
$448$	−1.35869	+	2.35332i	−0.0641921	+	0.111184i
$449$	−18.1212	−	10.4623i	−0.855194	−	0.493747i	0.00720566	−	0.999974i	$-0.497706\pi$
$449$	−18.1212	−	10.4623i	−0.855194	−	0.493747i	−0.862400	+	0.506227i	$0.831040\pi$
$450$			1.00000i			0.0471405i
$451$	−15.4656	+	26.7872i	−0.728246	+	1.26136i
$452$			1.98573i			0.0934010i
$453$	−1.76946	−	3.06479i	−0.0831364	−	0.143996i
$454$	3.18032			0.149260
$455$	0.280822			0.0131651
$456$	0.335900	+	0.581796i	0.0157300	+	0.0272451i
$457$	−13.4450	−	7.76248i	−0.628931	−	0.363113i	0.151407	−	0.988472i	$-0.451620\pi$
$457$	−13.4450	−	7.76248i	−0.628931	−	0.363113i	−0.780338	+	0.625358i	$0.784953\pi$
$458$			1.59324i			0.0744473i
$459$	−4.85218	+	2.80141i	−0.226480	+	0.130759i
$460$	2.16637	+	3.75226i	0.101007	+	0.174950i
$461$	22.2831	−	12.8651i	1.03783	−	0.599190i	0.118610	−	0.992941i	$-0.462156\pi$
$461$	22.2831	−	12.8651i	1.03783	−	0.599190i	0.919217	+	0.393751i	$0.128823\pi$
$462$	8.74820	+	5.05077i	0.407003	+	0.234983i
$463$	21.0016	+	12.1253i	0.976027	+	0.563509i	0.901068	−	0.433677i	$-0.142784\pi$
$463$	21.0016	+	12.1253i	0.976027	+	0.563509i	0.0749587	+	0.997187i	$0.476117\pi$
$464$	5.39064	−	3.11229i	0.250254	−	0.144484i
$465$	−2.71979	−	4.71081i	−0.126127	−	0.218459i
$466$	2.63457	−	1.52107i	0.122044	−	0.0704621i
$467$			25.0329i			1.15839i	0.815190	+	0.579193i	$0.196632\pi$
$467$			25.0329i			1.15839i	−0.815190	+	0.579193i	$0.803368\pi$
$468$	−0.0894976	−	0.0516714i	−0.00413703	−	0.00238851i
$469$	−9.57811	−	16.5898i	−0.442276	−	0.766044i
$470$	−0.896377			−0.0413468
$471$	−20.9106			−0.963508
$472$	−1.78158	−	3.08579i	−0.0820039	−	0.142035i
$473$		−	39.5296i		−	1.81757i
$474$	−6.55611	+	11.3555i	−0.301132	+	0.521576i
$475$		−	0.671801i		−	0.0308243i
$476$	13.1852	+	7.61250i	0.604344	+	0.348918i
$477$	6.66754	−	11.5485i	0.305285	−	0.528770i
$478$	0.419360	−	0.726353i	0.0191811	−	0.0332226i
$479$	−26.5119	+	15.3066i	−1.21136	+	0.699379i	−0.963055	−	0.269304i	$-0.913206\pi$
$479$	−26.5119	+	15.3066i	−1.21136	+	0.699379i	−0.248304	+	0.968682i	$0.579873\pi$
$480$	−1.00000			−0.0456435
$481$	−0.00224496	+	0.628606i	−0.000102361	+	0.0286620i
$482$	−2.65399			−0.120886
$483$	−10.1963	+	5.88685i	−0.463948	+	0.267861i
$484$	1.40946	−	2.44126i	0.0640666	−	0.110967i
$485$	−3.49133	+	6.04715i	−0.158533	+	0.274587i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$			13.9987i			0.634342i	0.948368	+	0.317171i	$0.102733\pi$
$487$			13.9987i			0.634342i	−0.948368	+	0.317171i	$0.897267\pi$
$488$	4.16034	−	7.20592i	0.188330	−	0.326197i
$489$		−	11.3833i		−	0.514772i
$490$	0.192082	+	0.332697i	0.00867740	+	0.0150297i
$491$	−24.4717			−1.10439			−0.552197	−	0.833714i	$-0.686210\pi$
$491$	−24.4717			−1.10439			−0.552197	+	0.833714i	$0.686210\pi$
$492$	8.32068			0.375125
$493$	−17.4376	−	30.2028i	−0.785349	−	1.36026i
$494$	0.0601245	+	0.0347129i	0.00270513	+	0.00156181i
$495$			3.71738i			0.167084i
$496$	4.71081	−	2.71979i	0.211522	−	0.122122i
$497$	18.7730	+	32.5159i	0.842086	+	1.45854i
$498$	−5.13301	+	2.96354i	−0.230016	+	0.132800i
$499$	−9.81210	−	5.66502i	−0.439250	−	0.253601i	0.264029	−	0.964515i	$-0.414948\pi$
$499$	−9.81210	−	5.66502i	−0.439250	−	0.253601i	−0.703279	+	0.710914i	$0.748282\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	−2.40769	+	1.39008i	−0.107568	+	0.0621043i
$502$	−8.20681	−	14.2146i	−0.366288	−	0.634429i
$503$	−11.8081	+	6.81738i	−0.526495	+	0.303972i	−0.739588	−	0.673060i	$-0.764980\pi$
$503$	−11.8081	+	6.81738i	−0.526495	+	0.303972i	0.213093	+	0.977032i	$0.431646\pi$
$504$		−	2.71738i		−	0.121042i
$505$	9.85201	+	5.68806i	0.438409	+	0.253115i
$506$	8.05321	+	13.9486i	0.358009	+	0.620090i
$507$	12.9893			0.576876
$508$	−12.8604			−0.570590
$509$	12.0608	+	20.8900i	0.534588	+	0.925933i	0.999183	+	0.0404099i	$0.0128664\pi$
$509$	12.0608	+	20.8900i	0.534588	+	0.925933i	−0.464596	+	0.885523i	$0.653800\pi$
$510$			5.60282i			0.248097i
$511$	20.1950	−	34.9788i	0.893376	−	1.54737i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.581796	−	0.335900i	−0.0256869	−	0.0148304i
$514$	10.8811	−	18.8467i	0.479946	−	0.831290i
$515$	7.23587	−	12.5329i	0.318851	−	0.552265i
$516$	−9.20908	+	5.31686i	−0.405407	+	0.234062i
$517$	−3.33218			−0.146549
$518$	−14.3441	+	8.21342i	−0.630245	+	0.360877i
$519$	6.92704			0.304063
$520$	−0.0894976	+	0.0516714i	−0.00392473	+	0.00226594i
$521$	1.87061	−	3.23999i	0.0819529	−	0.141947i	−0.822136	−	0.569291i	$-0.807218\pi$
$521$	1.87061	−	3.23999i	0.0819529	−	0.141947i	0.904089	+	0.427345i	$0.140551\pi$
$522$	−3.11229	+	5.39064i	−0.136221	+	0.235942i
$523$	7.68204	+	4.43523i	0.335912	+	0.193939i	0.658463	−	0.752613i	$-0.271207\pi$
$523$	7.68204	+	4.43523i	0.335912	+	0.193939i	−0.322551	+	0.946552i	$0.604540\pi$
$524$		−	13.4953i		−	0.589543i
$525$	−1.35869	+	2.35332i	−0.0592981	+	0.102707i
$526$			27.4334i			1.19615i
$527$	−15.2385	−	26.3938i	−0.663799	−	1.14973i
$528$	−3.71738			−0.161778
$529$	4.22742			0.183801
$530$	−6.66754	−	11.5485i	−0.289619	−	0.501635i
$531$	3.08579	+	1.78158i	0.133912	+	0.0773140i
$532$			1.82554i			0.0791472i
$533$	0.744681	−	0.429942i	0.0322557	−	0.0186228i
$534$	9.18954	+	15.9168i	0.397670	+	0.688785i
$535$	−0.869493	+	0.502002i	−0.0375915	+	0.0217034i
$536$	6.10506	+	3.52476i	0.263698	+	0.152246i
$537$	8.29143	+	4.78706i	0.357801	+	0.206577i
$538$	−3.73255	+	2.15499i	−0.160922	+	0.0929081i
$539$	0.714044	+	1.23676i	0.0307560	+	0.0532710i
$540$	0.866025	−	0.500000i	0.0372678	−	0.0215166i
$541$			30.2437i			1.30028i	0.759815	+	0.650140i	$0.225290\pi$
$541$			30.2437i			1.30028i	−0.759815	+	0.650140i	$0.774710\pi$
$542$	−15.8512	−	9.15167i	−0.680865	−	0.393098i
$543$	9.99350	+	17.3093i	0.428862	+	0.742811i
$544$	−5.60282			−0.240219
$545$	−13.4489			−0.576088
$546$	−0.140411	−	0.243199i	−0.00600904	−	0.0104080i
$547$			31.7454i			1.35734i	0.734445	+	0.678668i	$0.237442\pi$
$547$			31.7454i			1.35734i	−0.734445	+	0.678668i	$0.762558\pi$
$548$	7.88437	−	13.6561i	0.336804	−	0.583361i
$549$			8.32068i			0.355118i
$550$	3.21935	+	1.85869i	0.137273	+	0.0792549i
$551$	2.09084	−	3.62144i	0.0890727	−	0.154278i
$552$	2.16637	−	3.75226i	0.0922067	−	0.159707i
$553$	−30.8573	+	17.8155i	−1.31218	+	0.757590i
$554$	−8.79167			−0.373522
$555$	−5.25693	−	3.06017i	−0.223144	−	0.129897i
$556$	−5.62541			−0.238571
$557$	30.4246	−	17.5656i	1.28913	−	0.744280i	0.310631	−	0.950530i	$-0.399460\pi$
$557$	30.4246	−	17.5656i	1.28913	−	0.744280i	0.978499	+	0.206251i	$0.0661262\pi$
$558$	−2.71979	+	4.71081i	−0.115138	+	0.199425i
$559$	−0.549460	+	0.951693i	−0.0232397	+	0.0402523i
$560$	−2.35332	−	1.35869i	−0.0994460	−	0.0574152i
$561$			20.8278i			0.879351i
$562$	−9.69815	+	16.7977i	−0.409092	+	0.708567i
$563$		−	25.2798i		−	1.06542i	−0.846298	−	0.532709i	$-0.821174\pi$
$563$		−	25.2798i		−	1.06542i	0.846298	−	0.532709i	$-0.178826\pi$
$564$	0.448189	+	0.776285i	0.0188721	+	0.0326875i
$565$	−1.98573			−0.0835404
$566$	1.02223			0.0429677
$567$	1.35869	+	2.35332i	0.0570597	+	0.0988302i
$568$	−11.9659	−	6.90850i	−0.502077	−	0.289874i
$569$		−	24.1032i		−	1.01046i	−0.862986	−	0.505229i	$-0.831408\pi$
$569$		−	24.1032i		−	1.01046i	0.862986	−	0.505229i	$-0.168592\pi$
$570$	−0.581796	+	0.335900i	−0.0243688	+	0.0140693i
$571$	−0.160325	−	0.277691i	−0.00670940	−	0.0116210i	0.862651	−	0.505799i	$-0.168802\pi$
$571$	−0.160325	−	0.277691i	−0.00670940	−	0.0116210i	−0.869361	+	0.494178i	$0.835469\pi$
$572$	−0.332697	+	0.192082i	−0.0139107	+	0.00803137i
$573$	17.7005	+	10.2194i	0.739449	+	0.426921i
$574$	19.5812	+	11.3052i	0.817305	+	0.471871i
$575$	−3.75226	+	2.16637i	−0.156480	+	0.0903437i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−26.5450	+	15.3258i	−1.10508	+	0.638021i	−0.937552	−	0.347846i	$-0.886913\pi$
$577$	−26.5450	+	15.3258i	−1.10508	+	0.638021i	−0.167533	+	0.985866i	$0.553580\pi$
$578$			14.3916i			0.598610i
$579$	−14.8894	−	8.59643i	−0.618784	−	0.357255i
$580$	3.11229	+	5.39064i	0.129231	+	0.223834i
$581$	−16.1062			−0.668196
$582$	6.98265			0.289440
$583$	−24.7858	−	42.9302i	−1.02652	−	1.77799i
$584$			14.8636i			0.615060i
$585$	0.0516714	−	0.0894976i	0.00213635	−	0.00370027i
$586$		−	2.49013i		−	0.102866i
$587$	−11.6126	−	6.70456i	−0.479305	−	0.276727i	0.240822	−	0.970569i	$-0.422583\pi$
$587$	−11.6126	−	6.70456i	−0.479305	−	0.276727i	−0.720127	+	0.693843i	$0.755916\pi$
$588$	0.192082	−	0.332697i	0.00792135	−	0.0137202i
$589$	1.82716	−	3.16473i	0.0752867	−	0.130400i
$590$	3.08579	−	1.78158i	0.127040	−	0.0733465i
$591$	−8.45419			−0.347759
$592$	3.06017	−	5.25693i	0.125772	−	0.216059i
$593$	31.3384			1.28691			0.643457	−	0.765483i	$-0.277500\pi$
$593$	31.3384			1.28691			0.643457	+	0.765483i	$0.277500\pi$
$594$	3.21935	−	1.85869i	0.132091	−	0.0762630i
$595$	−7.61250	+	13.1852i	−0.312082	+	0.540542i
$596$	−8.48626	+	14.6986i	−0.347611	+	0.602080i
$597$	8.81284	+	5.08809i	0.360685	+	0.208242i
$598$		−	0.447757i		−	0.0183102i
$599$	−16.2777	+	28.1939i	−0.665090	+	1.15197i	0.314171	+	0.949366i	$0.398274\pi$
$599$	−16.2777	+	28.1939i	−0.665090	+	1.15197i	−0.979261	+	0.202603i	$0.935060\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	2.15756	+	3.73701i	0.0880088	+	0.152436i	0.906669	−	0.421842i	$-0.138616\pi$
$601$	2.15756	+	3.73701i	0.0880088	+	0.152436i	−0.818661	+	0.574278i	$0.805283\pi$
$602$	−28.8959			−1.17771
$603$	−7.04951			−0.287078
$604$	1.76946	+	3.06479i	0.0719982	+	0.124705i
$605$	2.44126	+	1.40946i	0.0992515	+	0.0573029i
$606$		−	11.3761i		−	0.462123i
$607$	11.3305	−	6.54167i	0.459891	−	0.265518i	−0.252107	−	0.967699i	$-0.581124\pi$
$607$	11.3305	−	6.54167i	0.459891	−	0.265518i	0.711998	+	0.702181i	$0.247790\pi$
$608$	−0.335900	−	0.581796i	−0.0136226	−	0.0235950i
$609$	−14.6484	+	8.45728i	−0.593584	+	0.342706i
$610$	7.20592	+	4.16034i	0.291759	+	0.168447i
$611$	0.0802236	+	0.0463171i	0.00324550	+	0.00187379i
$612$	4.85218	−	2.80141i	0.196138	−	0.113240i
$613$	5.50909	+	9.54202i	0.222510	+	0.385399i	0.955569	−	0.294766i	$-0.0952417\pi$
$613$	5.50909	+	9.54202i	0.222510	+	0.385399i	−0.733060	+	0.680165i	$0.761908\pi$
$614$	−1.14990	+	0.663895i	−0.0464062	+	0.0267926i
$615$			8.32068i			0.335522i
$616$	−8.74820	−	5.05077i	−0.352475	−	0.203501i
$617$	−23.0402	−	39.9067i	−0.927562	−	1.60659i	−0.787387	−	0.616458i	$-0.788567\pi$
$617$	−23.0402	−	39.9067i	−0.927562	−	1.60659i	−0.140175	−	0.990127i	$-0.544767\pi$
$618$	−14.4717			−0.582139
$619$	41.0739			1.65090			0.825450	−	0.564476i	$-0.190922\pi$
$619$	41.0739			1.65090			0.825450	+	0.564476i	$0.190922\pi$
$620$	2.71979	+	4.71081i	0.109229	+	0.189191i
$621$			4.33273i			0.173867i
$622$	−1.05531	+	1.82785i	−0.0423140	+	0.0732900i
$623$			49.9430i			2.00092i
$624$	0.0894976	+	0.0516714i	0.00358277	+	0.00206851i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−2.10575	+	3.64727i	−0.0841627	+	0.145774i
$627$	−2.16276	+	1.24867i	−0.0863723	+	0.0498671i
$628$	20.9106			0.834422
$629$	−29.4536	−	17.1456i	−1.17439	−	0.683640i
$630$	2.71738			0.108263
$631$	8.22377	−	4.74799i	0.327383	−	0.189015i	−0.327296	−	0.944922i	$-0.606137\pi$
$631$	8.22377	−	4.74799i	0.327383	−	0.189015i	0.654679	+	0.755907i	$0.272804\pi$
$632$	6.55611	−	11.3555i	0.260788	−	0.451698i
$633$	−4.62092	+	8.00368i	−0.183665	+	0.318118i
$634$	3.61617	+	2.08780i	0.143617	+	0.0829171i
$635$		−	12.8604i		−	0.510351i
$636$	−6.66754	+	11.5485i	−0.264385	+	0.457928i
$637$		−	0.0397007i		−	0.00157300i
$638$	11.5696	+	20.0391i	0.458043	+	0.793354i
$639$	13.8170			0.546592
$640$	1.00000			0.0395285
$641$	12.4599	+	21.5812i	0.492136	+	0.852404i	0.999959	−	0.00905693i	$-0.00288295\pi$
$641$	12.4599	+	21.5812i	0.492136	+	0.852404i	−0.507823	+	0.861461i	$0.669550\pi$
$642$	0.869493	+	0.502002i	0.0343162	+	0.0198124i
$643$			14.5374i			0.573298i	0.958036	+	0.286649i	$0.0925413\pi$
$643$			14.5374i			0.573298i	−0.958036	+	0.286649i	$0.907459\pi$
$644$	10.1963	−	5.88685i	0.401791	−	0.231974i
$645$	−5.31686	−	9.20908i	−0.209351	−	0.362607i
$646$	−3.25970	+	1.88199i	−0.128251	+	0.0740458i
$647$	−2.06391	−	1.19160i	−0.0811407	−	0.0468466i	0.458881	−	0.888498i	$-0.348251\pi$
$647$	−2.06391	−	1.19160i	−0.0811407	−	0.0468466i	−0.540021	+	0.841651i	$0.681584\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	11.4710	−	6.62281i	0.450278	−	0.259968i
$650$	−0.0516714	−	0.0894976i	−0.00202672	−	0.00351038i
$651$	−12.8011	+	7.39071i	−0.501714	+	0.289665i
$652$			11.3833i			0.445806i
$653$	36.3633	+	20.9943i	1.42300	+	0.821572i	0.996555	−	0.0829397i	$-0.0264309\pi$
$653$	36.3633	+	20.9943i	1.42300	+	0.821572i	0.426449	+	0.904511i	$0.359764\pi$
$654$	6.72445	+	11.6471i	0.262947	+	0.455437i
$655$	13.4953			0.527304
$656$	−8.32068			−0.324868
$657$	−7.43180	−	12.8723i	−0.289942	−	0.502195i
$658$			2.43580i			0.0949573i
$659$	12.2157	−	21.1582i	0.475857	−	0.824208i	−0.523761	−	0.851865i	$-0.675471\pi$
$659$	12.2157	−	21.1582i	0.475857	−	0.824208i	0.999617	+	0.0276576i	$0.00880480\pi$
$660$		−	3.71738i		−	0.144699i
$661$	−1.29567	−	0.748053i	−0.0503956	−	0.0290959i	0.474591	−	0.880207i	$-0.342596\pi$
$661$	−1.29567	−	0.748053i	−0.0503956	−	0.0290959i	−0.524986	+	0.851111i	$0.675929\pi$
$662$	−14.8752	+	25.7646i	−0.578142	+	1.00137i
$663$	0.289506	−	0.501438i	0.0112435	−	0.0194743i
$664$	5.13301	−	2.96354i	0.199199	−	0.115008i
$665$	−1.82554			−0.0707914
$666$	−0.0217234	+	6.08272i	−0.000841763	+	0.235701i
$667$	−26.9694			−1.04426
$668$	2.40769	−	1.39008i	0.0931564	−	0.0537839i
$669$	4.89959	−	8.48633i	0.189429	−	0.328101i
$670$	−3.52476	+	6.10506i	−0.136173	+	0.235859i
$671$	26.7872	+	15.4656i	1.03411	+	0.597042i
$672$			2.71738i			0.104825i
$673$	4.92756	−	8.53478i	0.189943	−	0.328992i	−0.755288	−	0.655393i	$-0.772503\pi$
$673$	4.92756	−	8.53478i	0.189943	−	0.328992i	0.945231	+	0.326402i	$0.105836\pi$
$674$			5.52747i			0.212910i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−12.9893			−0.499589
$677$	3.49219			0.134216			0.0671078	−	0.997746i	$-0.478623\pi$
$677$	3.49219			0.134216			0.0671078	+	0.997746i	$0.478623\pi$
$678$	0.992866	+	1.71969i	0.0381308	+	0.0660444i
$679$	16.4324	+	9.48727i	0.630619	+	0.364088i
$680$		−	5.60282i		−	0.214858i
$681$	2.75424	−	1.59016i	0.105543	−	0.0609351i
$682$	10.1105	+	17.5119i	0.387151	+	0.670565i
$683$	−24.1798	+	13.9602i	−0.925214	+	0.534172i	−0.885295	−	0.465031i	$-0.846043\pi$
$683$	−24.1798	+	13.9602i	−0.925214	+	0.534172i	−0.0399190	+	0.999203i	$0.512710\pi$
$684$	0.581796	+	0.335900i	0.0222455	+	0.0128435i
$685$	13.6561	+	7.88437i	0.521774	+	0.301246i
$686$	−15.5692	+	8.98888i	−0.594434	+	0.343197i
$687$	0.796621	+	1.37979i	0.0303930	+	0.0526422i
$688$	9.20908	−	5.31686i	0.351093	−	0.202704i
$689$			1.37808i			0.0525008i
$690$	3.75226	+	2.16637i	0.142846	+	0.0824722i
$691$	16.5354	+	28.6402i	0.629036	+	1.08952i	0.987745	+	0.156074i	$0.0498837\pi$
$691$	16.5354	+	28.6402i	0.629036	+	1.08952i	−0.358709	+	0.933449i	$0.616783\pi$
$692$	−6.92704			−0.263327
$693$	10.1015			0.383726
$694$	9.28431	+	16.0809i	0.352428	+	0.610422i
$695$		−	5.62541i		−	0.213384i
$696$	3.11229	−	5.39064i	0.117971	−	0.204332i
$697$			46.6193i			1.76583i
$698$	−27.1845	−	15.6950i	−1.02895	−	0.594064i
$699$	1.52107	−	2.63457i	0.0575320	−	0.0996484i
$700$	1.35869	−	2.35332i	0.0513537	−	0.0889472i
$701$	−4.50375	+	2.60024i	−0.170104	+	0.0982097i	−0.582635	−	0.812734i	$-0.697978\pi$
$701$	−4.50375	+	2.60024i	−0.170104	+	0.0982097i	0.412531	+	0.910944i	$0.364645\pi$
$702$	−0.103343			−0.00390043
$703$	0.0145938	−	4.08638i	0.000550415	−	0.154121i
$704$	3.71738			0.140104
$705$	−0.776285	+	0.448189i	−0.0292366	+	0.0168798i
$706$	8.74065	−	15.1392i	0.328959	−	0.569773i
$707$	15.4566	−	26.7717i	0.581306	−	1.00685i
$708$	−3.08579	−	1.78158i	−0.115971	−	0.0669559i
$709$		−	32.5299i		−	1.22169i	−0.791752	−	0.610843i	$-0.790831\pi$
$709$		−	32.5299i		−	1.22169i	0.791752	−	0.610843i	$-0.209169\pi$
$710$	6.90850	−	11.9659i	0.259272	−	0.449072i
$711$			13.1122i			0.491747i
$712$	−9.18954	−	15.9168i	−0.344393	−	0.596505i
$713$	−23.5682			−0.882638
$714$	15.2250			0.569781
$715$	−0.192082	−	0.332697i	−0.00718348	−	0.0124421i
$716$	−8.29143	−	4.78706i	−0.309865	−	0.178901i
$717$		−	0.838720i		−	0.0313226i
$718$	9.31031	−	5.37531i	0.347458	−	0.200605i
$719$	18.1047	+	31.3582i	0.675190	+	1.16946i	0.976413	+	0.215909i	$0.0692716\pi$
$719$	18.1047	+	31.3582i	0.675190	+	1.16946i	−0.301224	+	0.953554i	$0.597395\pi$
$720$	−0.866025	+	0.500000i	−0.0322749	+	0.0186339i
$721$	−34.0567	−	19.6626i	−1.26834	−	0.732274i
$722$	16.0636	+	9.27434i	0.597826	+	0.345155i
$723$	−2.29842	+	1.32699i	−0.0854791	+	0.0493514i
$724$	−9.99350	−	17.3093i	−0.371406	−	0.643294i
$725$	−5.39064	+	3.11229i	−0.200203	+	0.115587i
$726$		−	2.81893i		−	0.104620i
$727$	14.0006	+	8.08328i	0.519255	+	0.299792i	0.736630	−	0.676296i	$-0.236416\pi$
$727$	14.0006	+	8.08328i	0.519255	+	0.299792i	−0.217375	+	0.976088i	$0.569749\pi$
$728$	0.140411	+	0.243199i	0.00520398	+	0.00901356i
$729$	1.00000			0.0370370
$730$	−14.8636			−0.550127
$731$	−29.7894	−	51.5968i	−1.10180	−	1.90838i
$732$		−	8.32068i		−	0.307541i
$733$	14.6192	−	25.3213i	0.539974	−	0.935262i	−0.458931	−	0.888472i	$-0.651767\pi$
$733$	14.6192	−	25.3213i	0.539974	−	0.935262i	0.998905	−	0.0467901i	$-0.0148992\pi$
$734$		−	19.0531i		−	0.703264i
$735$	0.332697	+	0.192082i	0.0122717	+	0.00708507i
$736$	−2.16637	+	3.75226i	−0.0798533	+	0.138310i
$737$	−13.1029	+	22.6948i	−0.482650	+	0.835975i
$738$	7.20592	−	4.16034i	0.265254	−	0.153144i
$739$	−7.32606			−0.269494			−0.134747	−	0.990880i	$-0.543022\pi$
$739$	−7.32606			−0.269494			−0.134747	+	0.990880i	$0.543022\pi$
$740$	5.25693	+	3.06017i	0.193249	+	0.112494i
$741$	0.0694258			0.00255042
$742$	−31.3817	+	18.1182i	−1.15206	+	0.665142i
$743$	−17.7643	+	30.7687i	−0.651709	+	1.12879i	0.330999	+	0.943631i	$0.392614\pi$
$743$	−17.7643	+	30.7687i	−0.651709	+	1.12879i	−0.982708	+	0.185162i	$0.940719\pi$
$744$	2.71979	−	4.71081i	0.0997123	−	0.172707i
$745$	−14.6986	−	8.48626i	−0.538517	−	0.310913i
$746$		−	24.2194i		−	0.886734i
$747$	−2.96354	+	5.13301i	−0.108430	+	0.187807i
$748$		−	20.8278i		−	0.761540i
$749$	1.36413	+	2.36275i	0.0498443	+	0.0863328i
$750$	1.00000			0.0365148
$751$	−4.52526			−0.165129			−0.0825646	−	0.996586i	$-0.526311\pi$
$751$	−4.52526			−0.165129			−0.0825646	+	0.996586i	$0.526311\pi$
$752$	−0.448189	−	0.776285i	−0.0163438	−	0.0283082i
$753$	−14.2146	−	8.20681i	−0.518009	−	0.299073i
$754$		−	0.643266i		−	0.0234264i
$755$	−3.06479	+	1.76946i	−0.111539	+	0.0643972i
$756$	−1.35869	−	2.35332i	−0.0494151	−	0.0855895i
$757$	−8.43550	+	4.87024i	−0.306593	+	0.177012i	−0.645401	−	0.763844i	$-0.723310\pi$
$757$	−8.43550	+	4.87024i	−0.306593	+	0.177012i	0.338808	+	0.940856i	$0.389976\pi$
$758$	2.21369	+	1.27807i	0.0804047	+	0.0464217i
$759$	13.9486	+	8.05321i	0.506301	+	0.292313i
$760$	0.581796	−	0.335900i	0.0211040	−	0.0121844i
$761$	−25.4151	−	44.0203i	−0.921298	−	1.59574i	−0.797409	−	0.603440i	$-0.793796\pi$
$761$	−25.4151	−	44.0203i	−0.921298	−	1.59574i	−0.123890	−	0.992296i	$-0.539537\pi$
$762$	−11.1375	+	6.43022i	−0.403468	+	0.232942i
$763$			36.5458i			1.32305i
$764$	−17.7005	−	10.2194i	−0.640381	−	0.369724i
$765$	2.80141	+	4.85218i	0.101285	+	0.175431i
$766$	22.0950			0.798325
$767$	−0.368227			−0.0132959
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$		−	23.2177i		−	0.837250i	−0.908159	−	0.418625i	$-0.862512\pi$
$769$		−	23.2177i		−	0.837250i	0.908159	−	0.418625i	$-0.137488\pi$
$770$	5.05077	−	8.74820i	0.182017	−	0.315263i
$771$		−	21.7622i		−	0.783748i
$772$	14.8894	+	8.59643i	0.535883	+	0.309392i
$773$	23.0478	−	39.9199i	0.828971	−	1.43582i	−0.0698760	−	0.997556i	$-0.522260\pi$
$773$	23.0478	−	39.9199i	0.828971	−	1.43582i	0.898847	−	0.438263i	$-0.144406\pi$
$774$	−5.31686	+	9.20908i	−0.191111	+	0.331014i
$775$	−4.71081	+	2.71979i	−0.169217	+	0.0976977i
$776$	−6.98265			−0.250663
$777$	−8.31566	+	14.2851i	−0.298323	+	0.512475i
$778$	−33.4975			−1.20094
$779$	−4.84094	+	2.79492i	−0.173445	+	0.100138i
$780$	−0.0516714	+	0.0894976i	−0.00185013	+	0.00320453i
$781$	25.6816	−	44.4818i	0.918958	−	1.59168i
$782$	21.0232	+	12.1378i	0.751789	+	0.434045i
$783$			6.22458i			0.222448i
$784$	−0.192082	+	0.332697i	−0.00686009	+	0.0118820i
$785$			20.9106i			0.746330i
$786$	−6.74763	−	11.6872i	−0.240680	−	0.416870i
$787$	−15.4267			−0.549904			−0.274952	−	0.961458i	$-0.588662\pi$
$787$	−15.4267			−0.549904			−0.274952	+	0.961458i	$0.588662\pi$
$788$	8.45419			0.301168
$789$	13.7167	+	23.7580i	0.488328	+	0.845809i
$790$	11.3555	+	6.55611i	0.404011	+	0.233256i
$791$			5.39599i			0.191859i
$792$	−3.21935	+	1.85869i	−0.114395	+	0.0660457i
$793$	−0.429942	−	0.744681i	−0.0152677	−	0.0264444i
$794$	8.04894	−	4.64706i	0.285646	−	0.164918i
$795$	−11.5485	−	6.66754i	−0.409583	−	0.236473i
$796$	−8.81284	−	5.08809i	−0.312363	−	0.180343i
$797$	17.8782	−	10.3220i	0.633277	−	0.365623i	−0.148743	−	0.988876i	$-0.547523\pi$
$797$	17.8782	−	10.3220i	0.633277	−	0.365623i	0.782020	+	0.623253i	$0.214189\pi$
$798$	0.912770	+	1.58096i	0.0323117	+	0.0559655i
$799$	−4.34938	+	2.51112i	−0.153870	+	0.0888370i
$800$			1.00000i			0.0353553i
$801$	15.9168	+	9.18954i	0.562391	+	0.324696i
$802$	6.51079	+	11.2770i	0.229904	+	0.398206i
$803$	−55.2537			−1.94986
$804$	7.04951			0.248617
$805$	5.88685	+	10.1963i	0.207484	+	0.359373i
$806$		−	0.562142i		−	0.0198006i
$807$	−2.15499	+	3.73255i	−0.0758591	+	0.131392i
$808$			11.3761i			0.400210i
$809$	36.1382	+	20.8644i	1.27055	+	0.733552i	0.975091	−	0.221803i	$-0.0711943\pi$
$809$	36.1382	+	20.8644i	1.27055	+	0.733552i	0.295458	+	0.955356i	$0.404528\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	6.31799	−	10.9431i	0.221855	−	0.384264i	−0.733516	−	0.679672i	$-0.762122\pi$
$811$	6.31799	−	10.9431i	0.221855	−	0.384264i	0.955371	+	0.295408i	$0.0954556\pi$
$812$	14.6484	−	8.45728i	0.514059	−	0.296792i
$813$	−18.3033			−0.641926
$814$	19.5420	+	11.3758i	0.684948	+	0.398723i
$815$	−11.3833			−0.398741
$816$	−4.85218	+	2.80141i	−0.169860	+	0.0980689i
$817$	3.57187	−	6.18667i	0.124964	−	0.216444i
$818$	14.2947	−	24.7591i	0.499801	−	0.865681i
$819$	−0.243199	−	0.140411i	−0.00849806	−	0.00490636i
$820$		−	8.32068i		−	0.290571i
$821$	8.58217	−	14.8648i	0.299520	−	0.518784i	−0.676506	−	0.736437i	$-0.736507\pi$
$821$	8.58217	−	14.8648i	0.299520	−	0.518784i	0.976026	+	0.217653i	$0.0698401\pi$
$822$		−	15.7687i		−	0.549998i
$823$	6.90383	+	11.9578i	0.240652	+	0.416822i	0.960900	−	0.276895i	$-0.0893053\pi$
$823$	6.90383	+	11.9578i	0.240652	+	0.416822i	−0.720248	+	0.693717i	$0.755972\pi$
$824$	14.4717			0.504147
$825$	3.71738			0.129423
$826$	−4.84123	−	8.38526i	−0.168448	−	0.291761i
$827$	16.6863	+	9.63385i	0.580240	+	0.335002i	0.761229	−	0.648483i	$-0.224596\pi$
$827$	16.6863	+	9.63385i	0.580240	+	0.335002i	−0.180989	+	0.983485i	$0.557930\pi$
$828$		−	4.33273i		−	0.150573i
$829$	19.1687	−	11.0670i	0.665756	−	0.384374i	−0.128711	−	0.991682i	$-0.541084\pi$
$829$	19.1687	−	11.0670i	0.665756	−	0.384374i	0.794466	+	0.607308i	$0.207751\pi$
$830$	2.96354	+	5.13301i	0.102866	+	0.178169i
$831$	−7.61381	+	4.39583i	−0.264120	+	0.152490i
$832$	−0.0894976	−	0.0516714i	−0.00310277	−	0.00179138i
$833$	1.86404	+	1.07620i	0.0645851	+	0.0372882i
$834$	−4.87175	+	2.81271i	−0.168695	+	0.0973960i
$835$	1.39008	+	2.40769i	0.0481058	+	0.0833216i
$836$	2.16276	−	1.24867i	0.0748006	−	0.0431862i
$837$			5.43958i			0.188019i
$838$	−5.53249	−	3.19419i	−0.191117	−	0.110341i
$839$	22.2989	+	38.6228i	0.769843	+	1.33341i	0.937648	+	0.347588i	$0.112999\pi$
$839$	22.2989	+	38.6228i	0.769843	+	1.33341i	−0.167804	+	0.985820i	$0.553668\pi$
$840$	−2.71738			−0.0937586
$841$	−9.74535			−0.336047
$842$	−15.6135	−	27.0434i	−0.538077	−	0.931977i
$843$			19.3963i			0.668044i
$844$	4.62092	−	8.00368i	0.159059	−	0.275498i
$845$		−	12.9893i		−	0.446846i
$846$	0.776285	+	0.448189i	0.0266892	+	0.0154090i
$847$	3.83005	−	6.63385i	0.131602	−	0.227942i
$848$	6.66754	−	11.5485i	0.228964	−	0.396577i
$849$	0.885281	−	0.511117i	0.0303828	−	0.0175415i
$850$	5.60282			0.192175
$851$	−22.8710	+	13.0959i	−0.784008	+	0.448922i
$852$	−13.8170			−0.473363
$853$	−1.70575	+	0.984814i	−0.0584037	+	0.0337194i	−0.528918	−	0.848673i	$-0.677402\pi$
$853$	−1.70575	+	0.984814i	−0.0584037	+	0.0337194i	0.470514	+	0.882393i	$0.344069\pi$
$854$	11.3052	−	19.5812i	0.386857	−	0.670056i
$855$	−0.335900	+	0.581796i	−0.0114875	+	0.0198970i
$856$	−0.869493	−	0.502002i	−0.0297187	−	0.0171581i
$857$		−	35.8811i		−	1.22568i	−0.790209	−	0.612838i	$-0.790028\pi$
$857$		−	35.8811i		−	1.22568i	0.790209	−	0.612838i	$-0.209972\pi$
$858$	−0.192082	+	0.332697i	−0.00655759	+	0.0113581i
$859$		−	28.6655i		−	0.978056i	−0.872268	−	0.489028i	$-0.837352\pi$
$859$		−	28.6655i		−	0.978056i	0.872268	−	0.489028i	$-0.162648\pi$
$860$	5.31686	+	9.20908i	0.181304	+	0.314027i
$861$	22.6105			0.770563
$862$	30.0012			1.02184
$863$	−20.5916	−	35.6658i	−0.700948	−	1.21408i	−0.968134	−	0.250432i	$-0.919427\pi$
$863$	−20.5916	−	35.6658i	−0.700948	−	1.21408i	0.267186	−	0.963645i	$-0.413906\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$		−	6.92704i		−	0.235526i
$866$	−26.3628	+	15.2206i	−0.895843	+	0.517215i
$867$	7.19578	+	12.4635i	0.244382	+	0.423281i
$868$	12.8011	−	7.39071i	0.434497	−	0.250857i
$869$	42.2128	+	24.3716i	1.43197	+	0.826749i
$870$	5.39064	+	3.11229i	0.182760	+	0.105516i
$871$	0.630914	−	0.364258i	0.0213777	−	0.0123424i
$872$	−6.72445	−	11.6471i	−0.227719	−	0.394420i
$873$	6.04715	−	3.49133i	0.204665	−	0.118163i
$874$			2.91073i			0.0984570i
$875$	2.35332	+	1.35869i	0.0795568	+	0.0459321i
$876$	7.43180	+	12.8723i	0.251097	+	0.434913i
$877$	−23.6842			−0.799760			−0.399880	−	0.916567i	$-0.630948\pi$
$877$	−23.6842			−0.799760			−0.399880	+	0.916567i	$0.630948\pi$
$878$	−13.4991			−0.455573
$879$	−1.24506	−	2.15651i	−0.0419949	−	0.0727374i
$880$			3.71738i			0.125313i
$881$	−1.34540	+	2.33030i	−0.0453277	+	0.0785099i	−0.887799	−	0.460231i	$-0.847767\pi$
$881$	−1.34540	+	2.33030i	−0.0453277	+	0.0785099i	0.842471	+	0.538741i	$0.181100\pi$
$882$		−	0.384165i		−	0.0129355i
$883$	−32.4400	−	18.7292i	−1.09169	−	0.630289i	−0.157666	−	0.987492i	$-0.550397\pi$
$883$	−32.4400	−	18.7292i	−1.09169	−	0.630289i	−0.934027	+	0.357203i	$0.883730\pi$
$884$	−0.289506	+	0.501438i	−0.00973713	+	0.0168652i
$885$	1.78158	−	3.08579i	0.0598872	−	0.103728i
$886$	8.56599	−	4.94558i	0.287780	−	0.166150i
$887$	−10.5345			−0.353715			−0.176858	−	0.984236i	$-0.556593\pi$
$887$	−10.5345			−0.353715			−0.176858	+	0.984236i	$0.556593\pi$
$888$	0.0217234	−	6.08272i	0.000728989	−	0.204123i
$889$	−34.9467			−1.17208
$890$	15.9168	−	9.18954i	0.533531	−	0.308034i
$891$	1.85869	−	3.21935i	0.0622685	−	0.107852i
$892$	−4.89959	+	8.48633i	−0.164050	+	0.284143i
$893$	−0.521509	−	0.301093i	−0.0174516	−	0.0100757i
$894$			16.9725i			0.567646i
$895$	4.78706	−	8.29143i	0.160014	−	0.277152i
$896$		−	2.71738i		−	0.0907814i
$897$	−0.223879	−	0.387769i	−0.00747509	−	0.0129472i
$898$	20.9246			0.698263
$899$	−33.8591			−1.12926
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−64.7042	−	37.3570i	−2.15561	−	1.24454i
$902$		−	30.9312i		−	1.02989i
$903$	−25.0246	+	14.4480i	−0.832766	+	0.480798i
$904$	−0.992866	−	1.71969i	−0.0330222	−	0.0571962i
$905$	17.3093	−	9.99350i	0.575379	−	0.332195i
$906$	3.06479	+	1.76946i	0.101821	+	0.0587863i
$907$	13.2909	+	7.67353i	0.441318	+	0.254795i	0.704157	−	0.710045i	$-0.251325\pi$
$907$	13.2909	+	7.67353i	0.441318	+	0.254795i	−0.262838	+	0.964840i	$0.584659\pi$
$908$	−2.75424	+	1.59016i	−0.0914026	+	0.0527713i
$909$	−5.68806	−	9.85201i	−0.188661	−	0.326770i
$910$	−0.243199	+	0.140411i	−0.00806197	+	0.00465458i
$911$		−	27.5829i		−	0.913863i	−0.889502	−	0.456931i	$-0.848949\pi$
$911$		−	27.5829i		−	0.913863i	0.889502	−	0.456931i	$-0.151051\pi$
$912$	−0.581796	−	0.335900i	−0.0192652	−	0.0111228i
$913$	11.0166	+	19.0813i	0.364597	+	0.631500i
$914$	15.5250			0.513520
$915$	8.32068			0.275073
$916$	−0.796621	−	1.37979i	−0.0263211	−	0.0455895i
$917$		−	36.6718i		−	1.21101i
$918$	2.80141	−	4.85218i	0.0924603	−	0.160146i
$919$		−	23.6011i		−	0.778529i	−0.921126	−	0.389264i	$-0.872729\pi$
$919$		−	23.6011i		−	0.778529i	0.921126	−	0.389264i	$-0.127271\pi$
$920$	−3.75226	−	2.16637i	−0.123708	−	0.0714230i
$921$	−0.663895	+	1.14990i	−0.0218761	+	0.0378905i
$922$	−12.8651	+	22.2831i	−0.423691	+	0.733854i
$923$	−1.23659	+	0.713945i	−0.0407028	+	0.0234998i
$924$	−10.1015			−0.332316
$925$	−3.06017	+	5.25693i	−0.100618	+	0.172847i
$926$	−24.2506			−0.796923
$927$	−12.5329	+	7.23587i	−0.411634	+	0.237657i
$928$	−3.11229	+	5.39064i	−0.102166	+	0.176956i
$929$	3.70073	−	6.40986i	0.121417	−	0.210301i	−0.798910	−	0.601451i	$-0.794589\pi$
$929$	3.70073	−	6.40986i	0.121417	−	0.210301i	0.920327	+	0.391150i	$0.127923\pi$
$930$	4.71081	+	2.71979i	0.154474	+	0.0891854i
$931$			0.258082i			0.00845830i
$932$	−1.52107	+	2.63457i	−0.0498242	+	0.0862981i
$933$			2.11062i			0.0690984i
$934$	−12.5165	−	21.6792i	−0.409551	−	0.709364i
$935$	20.8278			0.681142
$936$	0.103343			0.00337787
$937$	11.3165	+	19.6008i	0.369694	+	0.640329i	0.989518	−	0.144412i	$-0.0461291\pi$
$937$	11.3165	+	19.6008i	0.369694	+	0.640329i	−0.619823	+	0.784741i	$0.712796\pi$
$938$	16.5898	+	9.57811i	0.541675	+	0.312736i
$939$			4.21150i			0.137437i
$940$	0.776285	−	0.448189i	0.0253196	−	0.0146183i
$941$	10.5491	+	18.2716i	0.343891	+	0.595637i	0.985152	−	0.171686i	$-0.0549215\pi$
$941$	10.5491	+	18.2716i	0.343891	+	0.595637i	−0.641260	+	0.767323i	$0.721588\pi$
$942$	18.1091	−	10.4553i	0.590025	−	0.340651i
$943$	31.2213	+	18.0257i	1.01671	+	0.586996i
$944$	3.08579	+	1.78158i	0.100434	+	0.0579855i
$945$	2.35332	−	1.35869i	0.0765536	−	0.0441982i
$946$	19.7648	+	34.2337i	0.642610	+	1.11303i
$947$	32.4819	−	18.7535i	1.05552	−	0.609406i	0.131331	−	0.991339i	$-0.458075\pi$
$947$	32.4819	−	18.7535i	1.05552	−	0.609406i	0.924190	+	0.381933i	$0.124741\pi$
$948$		−	13.1122i		−	0.425865i
$949$	1.33026	+	0.768024i	0.0431819	+	0.0249311i
$950$	0.335900	+	0.581796i	0.0108980	+	0.0188760i
$951$	4.17560			0.135403
$952$	−15.2250			−0.493445
$953$	15.6316	+	27.0748i	0.506358	+	0.877038i	0.999973	+	0.00735751i	$0.00234199\pi$
$953$	15.6316	+	27.0748i	0.506358	+	0.877038i	−0.493615	+	0.869681i	$0.664325\pi$
$954$			13.3351i			0.431739i
$955$	10.2194	−	17.7005i	0.330692	−	0.572774i
$956$			0.838720i			0.0271262i
$957$	20.0391	+	11.5696i	0.647771	+	0.373991i
$958$	15.3066	−	26.5119i	0.494535	−	0.856560i
$959$	21.4249	−	37.1089i	0.691845	−	1.19831i
$960$	0.866025	−	0.500000i	0.0279508	−	0.0161374i
$961$	1.41099			0.0455157
$962$	−0.312359	−	0.545511i	−0.0100709	−	0.0175880i
$963$	1.00400			0.0323536
$964$	2.29842	−	1.32699i	0.0740271	−	0.0427396i
$965$	−8.59643	+	14.8894i	−0.276729	+	0.479308i
$966$	5.88685	−	10.1963i	0.189406	−	0.328061i
$967$	34.8644	+	20.1290i	1.12116	+	0.647304i	0.941698	−	0.336461i	$-0.109230\pi$
$967$	34.8644	+	20.1290i	1.12116	+	0.647304i	0.179465	+	0.983764i	$0.442563\pi$
$968$			2.81893i			0.0906038i
$969$	−1.88199	+	3.25970i	−0.0604582	+	0.104717i
$970$		−	6.98265i		−	0.224199i
$971$	15.2847	+	26.4738i	0.490509	+	0.849586i	0.999940	−	0.0109250i	$-0.00347759\pi$
$971$	15.2847	+	26.4738i	0.490509	+	0.849586i	−0.509431	+	0.860511i	$0.670144\pi$
$972$	−1.00000			−0.0320750
$973$	−15.2864			−0.490059
$974$	−6.99935	−	12.1232i	−0.224274	−	0.388454i
$975$	−0.0894976	−	0.0516714i	−0.00286622	−	0.00165481i
$976$			8.32068i			0.266339i
$977$	10.3715	−	5.98798i	0.331813	−	0.191573i	−0.324833	−	0.945772i	$-0.605308\pi$
$977$	10.3715	−	5.98798i	0.331813	−	0.191573i	0.656646	+	0.754199i	$0.271975\pi$
$978$	5.69167	+	9.85826i	0.181999	+	0.315232i
$979$	59.1686	−	34.1610i	1.89104	−	1.09179i
$980$	−0.332697	−	0.192082i	−0.0106276	−	0.00613585i
$981$	11.6471	+	6.72445i	0.371863	+	0.214695i
$982$	21.1931	−	12.2359i	0.676300	−	0.390462i
$983$	−13.7519	−	23.8189i	−0.438616	−	0.759705i	0.558967	−	0.829190i	$-0.311198\pi$
$983$	−13.7519	−	23.8189i	−0.438616	−	0.759705i	−0.997583	+	0.0694845i	$0.977865\pi$
$984$	−7.20592	+	4.16034i	−0.229716	+	0.132627i
$985$			8.45419i			0.269373i
$986$	30.2028	+	17.4376i	0.961852	+	0.555326i
$987$	1.21790	+	2.10946i	0.0387662	+	0.0671450i
$988$	−0.0694258			−0.00220873
$989$	−46.0731			−1.46504
$990$	−1.85869	−	3.21935i	−0.0590731	−	0.102318i
$991$		−	23.4519i		−	0.744975i	−0.928037	−	0.372488i	$-0.878505\pi$
$991$		−	23.4519i		−	0.744975i	0.928037	−	0.372488i	$-0.121495\pi$
$992$	−2.71979	+	4.71081i	−0.0863534	+	0.149568i
$993$			29.7504i			0.944101i
$994$	−32.5159	−	18.7730i	−1.03134	−	0.595445i
$995$	5.08809	−	8.81284i	0.161303	−	0.279386i
$996$	2.96354	−	5.13301i	0.0939035	−	0.162646i
$997$	23.3821	−	13.4996i	0.740518	−	0.427538i	−0.0817399	−	0.996654i	$-0.526048\pi$
$997$	23.3821	−	13.4996i	0.740518	−	0.427538i	0.822257	+	0.569116i	$0.192714\pi$
$998$	11.3300			0.358646
$999$	3.02255	+	5.27865i	0.0956292	+	0.167009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.c.751.4	✓	16
37.27	even	6	inner	1110.2.x.c.841.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.c.751.4	✓	16	1.1	even	1	trivial
1110.2.x.c.841.4	yes	16	37.27	even	6	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.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(1.35869 - 2.35332i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(1.35869 - 2.35332i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} -3.71738 q^{11} +(0.500000 + 0.866025i) q^{12} +(0.0894976 + 0.0516714i) q^{13} +2.71738i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-4.85218 + 2.80141i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-0.581796 - 0.335900i) q^{19} +(0.866025 - 0.500000i) q^{20} +(1.35869 + 2.35332i) q^{21} +(3.21935 - 1.85869i) q^{22} +4.33273i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -0.103343 q^{26} +1.00000 q^{27} +(-1.35869 - 2.35332i) q^{28} +6.22458i q^{29} +(0.500000 - 0.866025i) q^{30} +5.43958i q^{31} +(0.866025 + 0.500000i) q^{32} +(1.85869 - 3.21935i) q^{33} +(2.80141 - 4.85218i) q^{34} +(2.35332 - 1.35869i) q^{35} -1.00000 q^{36} +(3.02255 + 5.27865i) q^{37} +0.671801 q^{38} +(-0.0894976 + 0.0516714i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(4.16034 - 7.20592i) q^{41} +(-2.35332 - 1.35869i) q^{42} +10.6337i q^{43} +(-1.85869 + 3.21935i) q^{44} -1.00000i q^{45} +(-2.16637 - 3.75226i) q^{46} +0.896377 q^{47} +1.00000 q^{48} +(-0.192082 - 0.332697i) q^{49} +(-0.866025 - 0.500000i) q^{50} -5.60282i q^{51} +(0.0894976 - 0.0516714i) q^{52} +(6.66754 + 11.5485i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-3.21935 - 1.85869i) q^{55} +(2.35332 + 1.35869i) q^{56} +(0.581796 - 0.335900i) q^{57} +(-3.11229 - 5.39064i) q^{58} +(-3.08579 + 1.78158i) q^{59} +1.00000i q^{60} +(-7.20592 - 4.16034i) q^{61} +(-2.71979 - 4.71081i) q^{62} -2.71738 q^{63} -1.00000 q^{64} +(0.0516714 + 0.0894976i) q^{65} +3.71738i q^{66} +(3.52476 - 6.10506i) q^{67} +5.60282i q^{68} +(-3.75226 - 2.16637i) q^{69} +(-1.35869 + 2.35332i) q^{70} +(-6.90850 + 11.9659i) q^{71} +(0.866025 - 0.500000i) q^{72} +14.8636 q^{73} +(-5.25693 - 3.06017i) q^{74} -1.00000 q^{75} +(-0.581796 + 0.335900i) q^{76} +(-5.05077 + 8.74820i) q^{77} +(0.0516714 - 0.0894976i) q^{78} +(-11.3555 - 6.55611i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +8.32068i q^{82} +(-2.96354 - 5.13301i) q^{83} +2.71738 q^{84} -5.60282 q^{85} +(-5.31686 - 9.20908i) q^{86} +(-5.39064 - 3.11229i) q^{87} -3.71738i q^{88} +(-15.9168 + 9.18954i) q^{89} +(0.500000 + 0.866025i) q^{90} +(0.243199 - 0.140411i) q^{91} +(3.75226 + 2.16637i) q^{92} +(-4.71081 - 2.71979i) q^{93} +(-0.776285 + 0.448189i) q^{94} +(-0.335900 - 0.581796i) q^{95} +(-0.866025 + 0.500000i) q^{96} +6.98265i q^{97} +(0.332697 + 0.192082i) q^{98} +(1.85869 + 3.21935i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} + 8 q^{12} - 12 q^{13} - 8 q^{16} - 6 q^{17} + 6 q^{19} - 2 q^{21} - 6 q^{22} + 8 q^{25} + 16 q^{27} + 2 q^{28} + 8 q^{30} + 6 q^{33} - 4 q^{34} - 6 q^{35} - 16 q^{36} + 18 q^{37} + 12 q^{38} + 12 q^{39} - 8 q^{40} + 6 q^{42} - 6 q^{44} - 4 q^{46} - 60 q^{47} + 16 q^{48} - 4 q^{49} - 12 q^{52} + 12 q^{53} + 6 q^{55} - 6 q^{56} - 6 q^{57} - 12 q^{58} + 12 q^{59} - 4 q^{62} + 4 q^{63} - 16 q^{64} + 22 q^{67} - 6 q^{69} + 2 q^{70} + 2 q^{71} + 24 q^{73} - 8 q^{74} - 16 q^{75} + 6 q^{76} - 58 q^{77} - 36 q^{79} - 8 q^{81} - 8 q^{83} - 4 q^{84} + 8 q^{85} - 2 q^{86} - 42 q^{89} + 8 q^{90} + 6 q^{92} - 6 q^{93} + 6 q^{94} - 6 q^{95} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 + 8 * q^12 - 12 * q^13 - 8 * q^16 - 6 * q^17 + 6 * q^19 - 2 * q^21 - 6 * q^22 + 8 * q^25 + 16 * q^27 + 2 * q^28 + 8 * q^30 + 6 * q^33 - 4 * q^34 - 6 * q^35 - 16 * q^36 + 18 * q^37 + 12 * q^38 + 12 * q^39 - 8 * q^40 + 6 * q^42 - 6 * q^44 - 4 * q^46 - 60 * q^47 + 16 * q^48 - 4 * q^49 - 12 * q^52 + 12 * q^53 + 6 * q^55 - 6 * q^56 - 6 * q^57 - 12 * q^58 + 12 * q^59 - 4 * q^62 + 4 * q^63 - 16 * q^64 + 22 * q^67 - 6 * q^69 + 2 * q^70 + 2 * q^71 + 24 * q^73 - 8 * q^74 - 16 * q^75 + 6 * q^76 - 58 * q^77 - 36 * q^79 - 8 * q^81 - 8 * q^83 - 4 * q^84 + 8 * q^85 - 2 * q^86 - 42 * q^89 + 8 * q^90 + 6 * q^92 - 6 * q^93 + 6 * q^94 - 6 * q^95 - 12 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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