LMFDB - Embedded newform 1110.2.l.b.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.1
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.b.697.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.71586 + 1.43381i) q^{5} +(0.707107 + 0.707107i) q^{6} +(3.31235 - 3.31235i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.71586 + 1.43381i) q^{5} +(0.707107 + 0.707107i) q^{6} +(3.31235 - 3.31235i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(1.43381 - 1.71586i) q^{10} -4.55611i q^{11} +(0.707107 - 0.707107i) q^{12} -0.0409247i q^{13} +(-3.31235 - 3.31235i) q^{14} +(-2.22716 + 0.199442i) q^{15} +1.00000 q^{16} -3.39111 q^{17} -1.00000 q^{18} +(-1.42708 + 1.42708i) q^{19} +(-1.71586 - 1.43381i) q^{20} +4.68437i q^{21} -4.55611 q^{22} -6.74310i q^{23} +(-0.707107 - 0.707107i) q^{24} +(0.888377 + 4.92045i) q^{25} -0.0409247 q^{26} +(0.707107 + 0.707107i) q^{27} +(-3.31235 + 3.31235i) q^{28} +(2.73847 + 2.73847i) q^{29} +(0.199442 + 2.22716i) q^{30} +(2.17364 - 2.17364i) q^{31} -1.00000i q^{32} +(3.22166 + 3.22166i) q^{33} +3.39111i q^{34} +(10.4328 - 0.934260i) q^{35} +1.00000i q^{36} +(-1.32873 + 5.93586i) q^{37} +(1.42708 + 1.42708i) q^{38} +(0.0289381 + 0.0289381i) q^{39} +(-1.43381 + 1.71586i) q^{40} -4.17400i q^{41} +4.68437 q^{42} -8.29512i q^{43} +4.55611i q^{44} +(1.43381 - 1.71586i) q^{45} -6.74310 q^{46} +(1.79848 - 1.79848i) q^{47} +(-0.707107 + 0.707107i) q^{48} -14.9433i q^{49} +(4.92045 - 0.888377i) q^{50} +(2.39788 - 2.39788i) q^{51} +0.0409247i q^{52} +(-5.35361 - 5.35361i) q^{53} +(0.707107 - 0.707107i) q^{54} +(6.53260 - 7.81767i) q^{55} +(3.31235 + 3.31235i) q^{56} -2.01820i q^{57} +(2.73847 - 2.73847i) q^{58} +(-7.59479 + 7.59479i) q^{59} +(2.22716 - 0.199442i) q^{60} +(4.71353 - 4.71353i) q^{61} +(-2.17364 - 2.17364i) q^{62} +(-3.31235 - 3.31235i) q^{63} -1.00000 q^{64} +(0.0586782 - 0.0702211i) q^{65} +(3.22166 - 3.22166i) q^{66} +(10.3850 + 10.3850i) q^{67} +3.39111 q^{68} +(4.76809 + 4.76809i) q^{69} +(-0.934260 - 10.4328i) q^{70} +3.26527 q^{71} +1.00000 q^{72} +(3.99226 - 3.99226i) q^{73} +(5.93586 + 1.32873i) q^{74} +(-4.10746 - 2.85110i) q^{75} +(1.42708 - 1.42708i) q^{76} +(-15.0914 - 15.0914i) q^{77} +(0.0289381 - 0.0289381i) q^{78} +(-3.34318 + 3.34318i) q^{79} +(1.71586 + 1.43381i) q^{80} -1.00000 q^{81} -4.17400 q^{82} +(1.21753 + 1.21753i) q^{83} -4.68437i q^{84} +(-5.81869 - 4.86221i) q^{85} -8.29512 q^{86} -3.87278 q^{87} +4.55611 q^{88} +(-9.81417 - 9.81417i) q^{89} +(-1.71586 - 1.43381i) q^{90} +(-0.135557 - 0.135557i) q^{91} +6.74310i q^{92} +3.07399i q^{93} +(-1.79848 - 1.79848i) q^{94} +(-4.49484 + 0.402513i) q^{95} +(0.707107 + 0.707107i) q^{96} +16.9894 q^{97} -14.9433 q^{98} -4.55611 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) $ 40 * q - 40 * q^4 - 4 * q^7	$ 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) $ 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	1.71586	+	1.43381i	0.767358	+	0.641219i
$5$	1.71586	+	1.43381i	0.767358	+	0.641219i
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	3.31235	−	3.31235i	1.25195	−	1.25195i	0.297105	−	0.954845i	$-0.403979\pi$
$7$	3.31235	−	3.31235i	1.25195	−	1.25195i	0.954845	−	0.297105i	$-0.0960213\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	1.43381	−	1.71586i	0.453411	−	0.542604i
$11$		−	4.55611i		−	1.37372i	−0.726790	−	0.686860i	$-0.758989\pi$
$11$		−	4.55611i		−	1.37372i	0.726790	−	0.686860i	$-0.241011\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$		−	0.0409247i		−	0.0113505i	−0.999984	−	0.00567523i	$-0.998194\pi$
$13$		−	0.0409247i		−	0.0113505i	0.999984	−	0.00567523i	$-0.00180649\pi$
$14$	−3.31235	−	3.31235i	−0.885262	−	0.885262i
$15$	−2.22716	+	0.199442i	−0.575049	+	0.0514957i
$16$	1.00000			0.250000
$17$	−3.39111			−0.822466			−0.411233	−	0.911530i	$-0.634902\pi$
$17$	−3.39111			−0.822466			−0.411233	+	0.911530i	$0.634902\pi$
$18$	−1.00000			−0.235702
$19$	−1.42708	+	1.42708i	−0.327395	+	0.327395i	−0.851595	−	0.524200i	$-0.824364\pi$
$19$	−1.42708	+	1.42708i	−0.327395	+	0.327395i	0.524200	+	0.851595i	$0.324364\pi$
$20$	−1.71586	−	1.43381i	−0.383679	−	0.320610i
$21$			4.68437i			1.02221i
$22$	−4.55611			−0.971367
$23$		−	6.74310i		−	1.40603i	−0.711173	−	0.703017i	$-0.751836\pi$
$23$		−	6.74310i		−	1.40603i	0.711173	−	0.703017i	$-0.248164\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	0.888377	+	4.92045i	0.177675	+	0.984089i
$26$	−0.0409247			−0.00802598
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−3.31235	+	3.31235i	−0.625975	+	0.625975i
$29$	2.73847	+	2.73847i	0.508521	+	0.508521i	0.914072	−	0.405551i	$-0.132920\pi$
$29$	2.73847	+	2.73847i	0.508521	+	0.508521i	−0.405551	+	0.914072i	$0.632920\pi$
$30$	0.199442	+	2.22716i	0.0364130	+	0.406621i
$31$	2.17364	−	2.17364i	0.390397	−	0.390397i	−0.484432	−	0.874829i	$-0.660974\pi$
$31$	2.17364	−	2.17364i	0.390397	−	0.390397i	0.874829	+	0.484432i	$0.160974\pi$
$32$		−	1.00000i		−	0.176777i
$33$	3.22166	+	3.22166i	0.560819	+	0.560819i
$34$			3.39111i			0.581571i
$35$	10.4328	−	0.934260i	1.76347	−	0.157919i
$36$			1.00000i			0.166667i
$37$	−1.32873	+	5.93586i	−0.218442	+	0.975850i
$37$	−1.32873	+	5.93586i	−0.218442	+	0.975850i
$38$	1.42708	+	1.42708i	0.231503	+	0.231503i
$39$	0.0289381	+	0.0289381i	0.00463380	+	0.00463380i
$40$	−1.43381	+	1.71586i	−0.226705	+	0.271302i
$41$		−	4.17400i		−	0.651869i	−0.945392	−	0.325935i	$-0.894321\pi$
$41$		−	4.17400i		−	0.651869i	0.945392	−	0.325935i	$-0.105679\pi$
$42$	4.68437			0.722814
$43$		−	8.29512i		−	1.26499i	−0.774563	−	0.632497i	$-0.782030\pi$
$43$		−	8.29512i		−	1.26499i	0.774563	−	0.632497i	$-0.217970\pi$
$44$			4.55611i			0.686860i
$45$	1.43381	−	1.71586i	0.213740	−	0.255786i
$46$	−6.74310			−0.994216
$47$	1.79848	−	1.79848i	0.262335	−	0.262335i	−0.563667	−	0.826002i	$-0.690610\pi$
$47$	1.79848	−	1.79848i	0.262335	−	0.262335i	0.826002	+	0.563667i	$0.190610\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		−	14.9433i		−	2.13476i
$50$	4.92045	−	0.888377i	0.695856	−	0.125636i
$51$	2.39788	−	2.39788i	0.335770	−	0.335770i
$52$			0.0409247i			0.00567523i
$53$	−5.35361	−	5.35361i	−0.735375	−	0.735375i	0.236304	−	0.971679i	$-0.424064\pi$
$53$	−5.35361	−	5.35361i	−0.735375	−	0.735375i	−0.971679	+	0.236304i	$0.924064\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	6.53260	−	7.81767i	0.880856	−	1.05413i
$56$	3.31235	+	3.31235i	0.442631	+	0.442631i
$57$		−	2.01820i		−	0.267317i
$58$	2.73847	−	2.73847i	0.359579	−	0.359579i
$59$	−7.59479	+	7.59479i	−0.988757	+	0.988757i	−0.999938	−	0.0111802i	$-0.996441\pi$
$59$	−7.59479	+	7.59479i	−0.988757	+	0.988757i	0.0111802	+	0.999938i	$0.496441\pi$
$60$	2.22716	−	0.199442i	0.287525	−	0.0257479i
$61$	4.71353	−	4.71353i	0.603505	−	0.603505i	−0.337736	−	0.941241i	$-0.609661\pi$
$61$	4.71353	−	4.71353i	0.603505	−	0.603505i	0.941241	+	0.337736i	$0.109661\pi$
$62$	−2.17364	−	2.17364i	−0.276052	−	0.276052i
$63$	−3.31235	−	3.31235i	−0.417317	−	0.417317i
$64$	−1.00000			−0.125000
$65$	0.0586782	−	0.0702211i	0.00727813	−	0.00870986i
$66$	3.22166	−	3.22166i	0.396559	−	0.396559i
$67$	10.3850	+	10.3850i	1.26873	+	1.26873i	0.946747	+	0.321979i	$0.104348\pi$
$67$	10.3850	+	10.3850i	1.26873	+	1.26873i	0.321979	+	0.946747i	$0.395652\pi$
$68$	3.39111			0.411233
$69$	4.76809	+	4.76809i	0.574011	+	0.574011i
$70$	−0.934260	−	10.4328i	−0.111665	−	1.24696i
$71$	3.26527			0.387516			0.193758	−	0.981049i	$-0.437932\pi$
$71$	3.26527			0.387516			0.193758	+	0.981049i	$0.437932\pi$
$72$	1.00000			0.117851
$73$	3.99226	−	3.99226i	0.467258	−	0.467258i	−0.433767	−	0.901025i	$-0.642816\pi$
$73$	3.99226	−	3.99226i	0.467258	−	0.467258i	0.901025	+	0.433767i	$0.142816\pi$
$74$	5.93586	+	1.32873i	0.690030	+	0.154462i
$75$	−4.10746	−	2.85110i	−0.474288	−	0.329217i
$76$	1.42708	−	1.42708i	0.163697	−	0.163697i
$77$	−15.0914	−	15.0914i	−1.71983	−	1.71983i
$78$	0.0289381	−	0.0289381i	0.00327659	−	0.00327659i
$79$	−3.34318	+	3.34318i	−0.376137	+	0.376137i	−0.869706	−	0.493569i	$-0.835692\pi$
$79$	−3.34318	+	3.34318i	−0.376137	+	0.376137i	0.493569	+	0.869706i	$0.335692\pi$
$80$	1.71586	+	1.43381i	0.191839	+	0.160305i
$81$	−1.00000			−0.111111
$82$	−4.17400			−0.460941
$83$	1.21753	+	1.21753i	0.133641	+	0.133641i	0.770763	−	0.637122i	$-0.219875\pi$
$83$	1.21753	+	1.21753i	0.133641	+	0.133641i	−0.637122	+	0.770763i	$0.719875\pi$
$84$		−	4.68437i		−	0.511107i
$85$	−5.81869	−	4.86221i	−0.631125	−	0.527381i
$86$	−8.29512			−0.894486
$87$	−3.87278			−0.415206
$88$	4.55611			0.485683
$89$	−9.81417	−	9.81417i	−1.04030	−	1.04030i	−0.999153	−	0.0411466i	$-0.986899\pi$
$89$	−9.81417	−	9.81417i	−1.04030	−	1.04030i	−0.0411466	−	0.999153i	$-0.513101\pi$
$90$	−1.71586	−	1.43381i	−0.180868	−	0.151137i
$91$	−0.135557	−	0.135557i	−0.0142102	−	0.0142102i
$92$			6.74310i			0.703017i
$93$			3.07399i			0.318758i
$94$	−1.79848	−	1.79848i	−0.185499	−	0.185499i
$95$	−4.49484	+	0.402513i	−0.461161	+	0.0412970i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	16.9894			1.72502			0.862508	−	0.506043i	$-0.168892\pi$
$97$	16.9894			1.72502			0.862508	+	0.506043i	$0.168892\pi$
$98$	−14.9433			−1.50950
$99$	−4.55611			−0.457907
$100$	−0.888377	−	4.92045i	−0.0888377	−	0.492045i
$101$			0.926044i			0.0921448i	0.998938	+	0.0460724i	$0.0146705\pi$
$101$			0.926044i			0.0921448i	−0.998938	+	0.0460724i	$0.985330\pi$
$102$	−2.39788	−	2.39788i	−0.237425	−	0.237425i
$103$	8.34187			0.821948			0.410974	−	0.911647i	$-0.365189\pi$
$103$	8.34187			0.821948			0.410974	+	0.911647i	$0.365189\pi$
$104$	0.0409247			0.00401299
$105$	−6.71649	+	8.03774i	−0.655463	+	0.784403i
$106$	−5.35361	+	5.35361i	−0.519989	+	0.519989i
$107$	9.26659	−	9.26659i	0.895835	−	0.895835i	−0.0992296	−	0.995065i	$-0.531638\pi$
$107$	9.26659	−	9.26659i	0.895835	−	0.895835i	0.995065	+	0.0992296i	$0.0316378\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	−10.9135	+	10.9135i	−1.04532	+	1.04532i	−0.0463985	+	0.998923i	$0.514774\pi$
$109$	−10.9135	+	10.9135i	−1.04532	+	1.04532i	−0.998923	+	0.0463985i	$0.985226\pi$
$110$	−7.81767	−	6.53260i	−0.745386	−	0.622859i
$111$	−3.25773	−	5.13684i	−0.309210	−	0.487568i
$112$	3.31235	−	3.31235i	0.312988	−	0.312988i
$113$	16.0314			1.50810			0.754052	−	0.656814i	$-0.228096\pi$
$113$	16.0314			1.50810			0.754052	+	0.656814i	$0.228096\pi$
$114$	−2.01820			−0.189021
$115$	9.66833	−	11.5702i	0.901576	−	1.07893i
$116$	−2.73847	−	2.73847i	−0.254261	−	0.254261i
$117$	−0.0409247			−0.00378349
$118$	7.59479	+	7.59479i	0.699157	+	0.699157i
$119$	−11.2325	+	11.2325i	−1.02969	+	1.02969i
$120$	−0.199442	−	2.22716i	−0.0182065	−	0.203311i
$121$	−9.75818			−0.887107
$122$	−4.71353	−	4.71353i	−0.426743	−	0.426743i
$123$	2.95146	+	2.95146i	0.266124	+	0.266124i
$124$	−2.17364	+	2.17364i	−0.195198	+	0.195198i
$125$	−5.53065	+	9.71658i	−0.494676	+	0.869077i
$126$	−3.31235	+	3.31235i	−0.295087	+	0.295087i
$127$	4.76379	−	4.76379i	0.422718	−	0.422718i	−0.463420	−	0.886139i	$-0.653378\pi$
$127$	4.76379	−	4.76379i	0.422718	−	0.422718i	0.886139	+	0.463420i	$0.153378\pi$
$128$			1.00000i			0.0883883i
$129$	5.86553	+	5.86553i	0.516431	+	0.516431i
$130$	−0.0702211	−	0.0586782i	−0.00615880	−	0.00514642i
$131$	−13.9425	+	13.9425i	−1.21816	+	1.21816i	−0.249885	+	0.968275i	$0.580393\pi$
$131$	−13.9425	+	13.9425i	−1.21816	+	1.21816i	−0.968275	+	0.249885i	$0.919607\pi$
$132$	−3.22166	−	3.22166i	−0.280409	−	0.280409i
$133$			9.45398i			0.819764i
$134$	10.3850	−	10.3850i	0.897125	−	0.897125i
$135$	0.199442	+	2.22716i	0.0171652	+	0.191683i
$136$		−	3.39111i		−	0.290786i
$137$	−9.48384	+	9.48384i	−0.810259	+	0.810259i	−0.984673	−	0.174413i	$-0.944197\pi$
$137$	−9.48384	+	9.48384i	−0.810259	+	0.810259i	0.174413	+	0.984673i	$0.444197\pi$
$138$	4.76809	−	4.76809i	0.405887	−	0.405887i
$139$	15.4619			1.31146			0.655730	−	0.754995i	$-0.272361\pi$
$139$	15.4619			1.31146			0.655730	+	0.754995i	$0.272361\pi$
$140$	−10.4328	+	0.934260i	−0.881734	+	0.0789594i
$141$			2.54343i			0.214196i
$142$		−	3.26527i		−	0.274015i
$143$	−0.186457			−0.0155924
$144$		−	1.00000i		−	0.0833333i
$145$	0.772396	+	8.62529i	0.0641440	+	0.716291i
$146$	−3.99226	−	3.99226i	−0.330401	−	0.330401i
$147$	10.5665	+	10.5665i	0.871511	+	0.871511i
$148$	1.32873	−	5.93586i	0.109221	−	0.487925i
$149$			5.01498i			0.410843i	0.978674	+	0.205422i	$0.0658566\pi$
$149$			5.01498i			0.410843i	−0.978674	+	0.205422i	$0.934143\pi$
$150$	−2.85110	+	4.10746i	−0.232792	+	0.335373i
$151$			4.65633i			0.378927i	0.981888	+	0.189463i	$0.0606749\pi$
$151$			4.65633i			0.378927i	−0.981888	+	0.189463i	$0.939325\pi$
$152$	−1.42708	−	1.42708i	−0.115752	−	0.115752i
$153$			3.39111i			0.274155i
$154$	−15.0914	+	15.0914i	−1.21610	+	1.21610i
$155$	6.84625	−	0.613083i	0.549904	−	0.0492440i
$156$	−0.0289381	−	0.0289381i	−0.00231690	−	0.00231690i
$157$	11.3905	−	11.3905i	0.909057	−	0.909057i	−0.0871391	−	0.996196i	$-0.527772\pi$
$157$	11.3905	−	11.3905i	0.909057	−	0.909057i	0.996196	+	0.0871391i	$0.0277725\pi$
$158$	3.34318	+	3.34318i	0.265969	+	0.265969i
$159$	7.57115			0.600431
$160$	1.43381	−	1.71586i	0.113353	−	0.135651i
$161$	−22.3355	−	22.3355i	−1.76028	−	1.76028i
$162$			1.00000i			0.0785674i
$163$	−9.11221			−0.713723			−0.356862	−	0.934157i	$-0.616153\pi$
$163$	−9.11221			−0.713723			−0.356862	+	0.934157i	$0.616153\pi$
$164$			4.17400i			0.325935i
$165$	0.908681	+	10.1472i	0.0707407	+	0.789957i
$166$	1.21753	−	1.21753i	0.0944988	−	0.0944988i
$167$	−5.03912			−0.389939			−0.194969	−	0.980809i	$-0.562461\pi$
$167$	−5.03912			−0.389939			−0.194969	+	0.980809i	$0.562461\pi$
$168$	−4.68437			−0.361407
$169$	12.9983			0.999871
$170$	−4.86221	+	5.81869i	−0.372915	+	0.446273i
$171$	1.42708	+	1.42708i	0.109132	+	0.109132i
$172$			8.29512i			0.632497i
$173$	12.1162	−	12.1162i	0.921180	−	0.921180i	−0.0759333	−	0.997113i	$-0.524194\pi$
$173$	12.1162	−	12.1162i	0.921180	−	0.921180i	0.997113	+	0.0759333i	$0.0241936\pi$
$174$			3.87278i			0.293595i
$175$	19.2408	+	13.3556i	1.45447	+	1.00959i
$176$		−	4.55611i		−	0.343430i
$177$		−	10.7407i		−	0.807317i
$178$	−9.81417	+	9.81417i	−0.735603	+	0.735603i
$179$	−2.44720	−	2.44720i	−0.182912	−	0.182912i	0.609711	−	0.792623i	$-0.291285\pi$
$179$	−2.44720	−	2.44720i	−0.182912	−	0.182912i	−0.792623	+	0.609711i	$0.791285\pi$
$180$	−1.43381	+	1.71586i	−0.106870	+	0.127893i
$181$	−17.1218			−1.27265			−0.636325	−	0.771421i	$-0.719546\pi$
$181$	−17.1218			−1.27265			−0.636325	+	0.771421i	$0.719546\pi$
$182$	−0.135557	+	0.135557i	−0.0100481	+	0.0100481i
$183$			6.66593i			0.492760i
$184$	6.74310			0.497108
$185$	−10.7908	+	8.27998i	−0.793357	+	0.608757i
$186$	3.07399			0.225396
$187$			15.4503i			1.12984i
$188$	−1.79848	+	1.79848i	−0.131167	+	0.131167i
$189$	4.68437			0.340738
$190$	0.402513	+	4.49484i	0.0292014	+	0.326090i
$191$	7.96286	+	7.96286i	0.576172	+	0.576172i	0.933846	−	0.357674i	$-0.116430\pi$
$191$	7.96286	+	7.96286i	0.576172	+	0.576172i	−0.357674	+	0.933846i	$0.616430\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$			24.4915i			1.76294i	0.472244	+	0.881468i	$0.343444\pi$
$193$			24.4915i			1.76294i	−0.472244	+	0.881468i	$0.656556\pi$
$194$		−	16.9894i		−	1.21977i
$195$	0.00816210	+	0.0911456i	0.000584500	+	0.00652707i
$196$			14.9433i			1.06738i
$197$	−13.9774	+	13.9774i	−0.995845	+	0.995845i	−0.999991	−	0.00414607i	$-0.998680\pi$
$197$	−13.9774	+	13.9774i	−0.995845	+	0.995845i	0.00414607	+	0.999991i	$0.498680\pi$
$198$			4.55611i			0.323789i
$199$	−11.0246	−	11.0246i	−0.781514	−	0.781514i	0.198573	−	0.980086i	$-0.436369\pi$
$199$	−11.0246	−	11.0246i	−0.781514	−	0.781514i	−0.980086	+	0.198573i	$0.936369\pi$
$200$	−4.92045	+	0.888377i	−0.347928	+	0.0628178i
$201$	−14.6866			−1.03591
$202$	0.926044			0.0651562
$203$	18.1415			1.27329
$204$	−2.39788	+	2.39788i	−0.167885	+	0.167885i
$205$	5.98472	−	7.16201i	0.417991	−	0.500217i
$206$		−	8.34187i		−	0.581205i
$207$	−6.74310			−0.468678
$208$		−	0.0409247i		−	0.00283761i
$209$	6.50194	+	6.50194i	0.449749	+	0.449749i
$210$	8.03774	+	6.71649i	0.554657	+	0.463482i
$211$	6.36095			0.437906			0.218953	−	0.975735i	$-0.429736\pi$
$211$	6.36095			0.437906			0.218953	+	0.975735i	$0.429736\pi$
$212$	5.35361	+	5.35361i	0.367688	+	0.367688i
$213$	−2.30889	+	2.30889i	−0.158203	+	0.158203i
$214$	−9.26659	−	9.26659i	−0.633451	−	0.633451i
$215$	11.8936	−	14.2333i	0.811138	−	0.970702i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$		−	14.3997i		−	0.977515i
$218$	10.9135	+	10.9135i	0.739154	+	0.739154i
$219$			5.64590i			0.381515i
$220$	−6.53260	+	7.81767i	−0.440428	+	0.527067i
$221$			0.138780i			0.00933536i
$222$	−5.13684	+	3.25773i	−0.344762	+	0.218645i
$223$	0.324273	+	0.324273i	0.0217149	+	0.0217149i	0.717881	−	0.696166i	$-0.245112\pi$
$223$	0.324273	+	0.324273i	0.0217149	+	0.0217149i	−0.696166	+	0.717881i	$0.745112\pi$
$224$	−3.31235	−	3.31235i	−0.221316	−	0.221316i
$225$	4.92045	−	0.888377i	0.328030	−	0.0592252i
$226$		−	16.0314i		−	1.06639i
$227$	8.46323			0.561724			0.280862	−	0.959748i	$-0.409380\pi$
$227$	8.46323			0.561724			0.280862	+	0.959748i	$0.409380\pi$
$228$			2.01820i			0.133658i
$229$			15.8612i			1.04814i	0.851677	+	0.524068i	$0.175586\pi$
$229$			15.8612i			1.04814i	−0.851677	+	0.524068i	$0.824414\pi$
$230$	−11.5702	−	9.66833i	−0.762919	−	0.637511i
$231$	21.3425			1.40423
$232$	−2.73847	+	2.73847i	−0.179789	+	0.179789i
$233$	−5.31862	+	5.31862i	−0.348435	+	0.348435i	−0.859526	−	0.511092i	$-0.829241\pi$
$233$	−5.31862	+	5.31862i	−0.348435	+	0.348435i	0.511092	+	0.859526i	$0.329241\pi$
$234$			0.0409247i			0.00267533i
$235$	5.66462	−	0.507267i	0.369519	−	0.0330905i
$236$	7.59479	−	7.59479i	0.494379	−	0.494379i
$237$		−	4.72797i		−	0.307114i
$238$	11.2325	+	11.2325i	0.728098	+	0.728098i
$239$	−21.1771	+	21.1771i	−1.36983	+	1.36983i	−0.509158	+	0.860673i	$0.670043\pi$
$239$	−21.1771	+	21.1771i	−1.36983	+	1.36983i	−0.860673	+	0.509158i	$0.829957\pi$
$240$	−2.22716	+	0.199442i	−0.143762	+	0.0128739i
$241$	1.31443	+	1.31443i	0.0846701	+	0.0846701i	0.748173	−	0.663503i	$-0.230931\pi$
$241$	1.31443	+	1.31443i	0.0846701	+	0.0846701i	−0.663503	+	0.748173i	$0.730931\pi$
$242$			9.75818i			0.627279i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−4.71353	+	4.71353i	−0.301753	+	0.301753i
$245$	21.4259	−	25.6407i	1.36885	−	1.63812i
$246$	2.95146	−	2.95146i	0.188178	−	0.188178i
$247$	0.0584028	+	0.0584028i	0.00371608	+	0.00371608i
$248$	2.17364	+	2.17364i	0.138026	+	0.138026i
$249$	−1.72185			−0.109118
$250$	9.71658	+	5.53065i	0.614530	+	0.349789i
$251$	4.79145	−	4.79145i	0.302434	−	0.302434i	−0.539532	−	0.841965i	$-0.681399\pi$
$251$	4.79145	−	4.79145i	0.302434	−	0.302434i	0.841965	+	0.539532i	$0.181399\pi$
$252$	3.31235	+	3.31235i	0.208658	+	0.208658i
$253$	−30.7223			−1.93150
$254$	−4.76379	−	4.76379i	−0.298907	−	0.298907i
$255$	7.55254	−	0.676331i	0.472958	−	0.0423535i
$256$	1.00000			0.0625000
$257$	−1.92054			−0.119800			−0.0599000	−	0.998204i	$-0.519078\pi$
$257$	−1.92054			−0.119800			−0.0599000	+	0.998204i	$0.519078\pi$
$258$	5.86553	−	5.86553i	0.365172	−	0.365172i
$259$	15.2604	+	24.0629i	0.948237	+	1.49519i
$260$	−0.0586782	+	0.0702211i	−0.00363907	+	0.00435493i
$261$	2.73847	−	2.73847i	0.169507	−	0.169507i
$262$	13.9425	+	13.9425i	0.861370	+	0.861370i
$263$	−9.34281	+	9.34281i	−0.576102	+	0.576102i	−0.933827	−	0.357725i	$-0.883553\pi$
$263$	−9.34281	+	9.34281i	−0.576102	+	0.576102i	0.357725	+	0.933827i	$0.383553\pi$
$264$	−3.22166	+	3.22166i	−0.198279	+	0.198279i
$265$	−1.51001	−	16.8621i	−0.0927590	−	1.03583i
$266$	9.45398			0.579660
$267$	13.8793			0.849401
$268$	−10.3850	−	10.3850i	−0.634363	−	0.634363i
$269$		−	21.1755i		−	1.29109i	−0.763721	−	0.645546i	$-0.776630\pi$
$269$		−	21.1755i		−	1.29109i	0.763721	−	0.645546i	$-0.223370\pi$
$270$	2.22716	−	0.199442i	0.135540	−	0.0121377i
$271$	6.66480			0.404858			0.202429	−	0.979297i	$-0.435116\pi$
$271$	6.66480			0.404858			0.202429	+	0.979297i	$0.435116\pi$
$272$	−3.39111			−0.205616
$273$	0.191706			0.0116026
$274$	9.48384	+	9.48384i	0.572940	+	0.572940i
$275$	22.4181	−	4.04755i	1.35186	−	0.244076i
$276$	−4.76809	−	4.76809i	−0.287005	−	0.287005i
$277$			19.1249i			1.14910i	0.818469	+	0.574551i	$0.194823\pi$
$277$			19.1249i			1.14910i	−0.818469	+	0.574551i	$0.805177\pi$
$278$		−	15.4619i		−	0.927342i
$279$	−2.17364	−	2.17364i	−0.130132	−	0.130132i
$280$	0.934260	+	10.4328i	0.0558327	+	0.623480i
$281$	−16.4877	−	16.4877i	−0.983574	−	0.983574i	0.0162937	−	0.999867i	$-0.494813\pi$
$281$	−16.4877	−	16.4877i	−0.983574	−	0.983574i	−0.999867	+	0.0162937i	$0.994813\pi$
$282$	2.54343			0.151459
$283$	−8.89666			−0.528851			−0.264426	−	0.964406i	$-0.585182\pi$
$283$	−8.89666			−0.528851			−0.264426	+	0.964406i	$0.585182\pi$
$284$	−3.26527			−0.193758
$285$	2.89371	−	3.46295i	0.171409	−	0.205127i
$286$			0.186457i			0.0110255i
$287$	−13.8257	−	13.8257i	−0.816108	−	0.816108i
$288$	−1.00000			−0.0589256
$289$	−5.50035			−0.323550
$290$	8.62529	−	0.772396i	0.506494	−	0.0453566i
$291$	−12.0133	+	12.0133i	−0.704235	+	0.704235i
$292$	−3.99226	+	3.99226i	−0.233629	+	0.233629i
$293$	20.1484	+	20.1484i	1.17708	+	1.17708i	0.980485	+	0.196596i	$0.0629887\pi$
$293$	20.1484	+	20.1484i	1.17708	+	1.17708i	0.196596	+	0.980485i	$0.437011\pi$
$294$	10.5665	−	10.5665i	0.616252	−	0.616252i
$295$	−23.9211	+	2.14214i	−1.39274	+	0.124720i
$296$	−5.93586	−	1.32873i	−0.345015	−	0.0772310i
$297$	3.22166	−	3.22166i	0.186940	−	0.186940i
$298$	5.01498			0.290510
$299$	−0.275959			−0.0159591
$300$	4.10746	+	2.85110i	0.237144	+	0.164608i
$301$	−27.4763	−	27.4763i	−1.58371	−	1.58371i
$302$	4.65633			0.267942
$303$	−0.654812	−	0.654812i	−0.0376179	−	0.0376179i
$304$	−1.42708	+	1.42708i	−0.0818487	+	0.0818487i
$305$	14.8461	−	1.32947i	0.850084	−	0.0761251i
$306$	3.39111			0.193857
$307$	16.3116	+	16.3116i	0.930950	+	0.930950i	0.997765	−	0.0668151i	$-0.0212838\pi$
$307$	16.3116	+	16.3116i	0.930950	+	0.930950i	−0.0668151	+	0.997765i	$0.521284\pi$
$308$	15.0914	+	15.0914i	0.859915	+	0.859915i
$309$	−5.89859	+	5.89859i	−0.335559	+	0.335559i
$310$	−0.613083	−	6.84625i	−0.0348208	−	0.388841i
$311$	−9.24730	+	9.24730i	−0.524366	+	0.524366i	−0.918887	−	0.394521i	$-0.870911\pi$
$311$	−9.24730	+	9.24730i	−0.524366	+	0.524366i	0.394521	+	0.918887i	$0.370911\pi$
$312$	−0.0289381	+	0.0289381i	−0.00163830	+	0.00163830i
$313$		−	11.1765i		−	0.631735i	−0.948803	−	0.315868i	$-0.897704\pi$
$313$		−	11.1765i		−	0.631735i	0.948803	−	0.315868i	$-0.102296\pi$
$314$	−11.3905	−	11.3905i	−0.642800	−	0.642800i
$315$	−0.934260	−	10.4328i	−0.0526396	−	0.587823i
$316$	3.34318	−	3.34318i	0.188068	−	0.188068i
$317$	−2.44424	−	2.44424i	−0.137282	−	0.137282i	0.635126	−	0.772408i	$-0.280948\pi$
$317$	−2.44424	−	2.44424i	−0.137282	−	0.137282i	−0.772408	+	0.635126i	$0.780948\pi$
$318$		−	7.57115i		−	0.424569i
$319$	12.4768	−	12.4768i	0.698566	−	0.698566i
$320$	−1.71586	−	1.43381i	−0.0959197	−	0.0801524i
$321$			13.1049i			0.731446i
$322$	−22.3355	+	22.3355i	−1.24471	+	1.24471i
$323$	4.83939	−	4.83939i	0.269271	−	0.269271i
$324$	1.00000			0.0555556
$325$	0.201368	−	0.0363565i	0.0111699	−	0.00201670i
$326$			9.11221i			0.504679i
$327$		−	15.4340i		−	0.853501i
$328$	4.17400			0.230471
$329$		−	11.9144i		−	0.656860i
$330$	10.1472	−	0.908681i	0.558584	−	0.0500213i
$331$	19.5512	+	19.5512i	1.07463	+	1.07463i	0.996981	+	0.0776480i	$0.0247410\pi$
$331$	19.5512	+	19.5512i	1.07463	+	1.07463i	0.0776480	+	0.996981i	$0.475259\pi$
$332$	−1.21753	−	1.21753i	−0.0668207	−	0.0668207i
$333$	5.93586	+	1.32873i	0.325283	+	0.0728141i
$334$			5.03912i			0.275728i
$335$	2.92912	+	32.7093i	0.160035	+	1.78710i
$336$			4.68437i			0.255553i
$337$	−11.6161	−	11.6161i	−0.632771	−	0.632771i	0.315991	−	0.948762i	$-0.397663\pi$
$337$	−11.6161	−	11.6161i	−0.632771	−	0.632771i	−0.948762	+	0.315991i	$0.897663\pi$
$338$		−	12.9983i		−	0.707016i
$339$	−11.3359	+	11.3359i	−0.615681	+	0.615681i
$340$	5.81869	+	4.86221i	0.315563	+	0.263690i
$341$	−9.90334	−	9.90334i	−0.536296	−	0.536296i
$342$	1.42708	−	1.42708i	0.0771677	−	0.0771677i
$343$	−26.3110	−	26.3110i	−1.42066	−	1.42066i
$344$	8.29512			0.447243
$345$	1.34486	+	15.0179i	0.0724047	+	0.808538i
$346$	−12.1162	−	12.1162i	−0.651372	−	0.651372i
$347$		−	2.18154i		−	0.117111i	−0.998284	−	0.0585555i	$-0.981351\pi$
$347$		−	2.18154i		−	0.117111i	0.998284	−	0.0585555i	$-0.0186495\pi$
$348$	3.87278			0.207603
$349$			14.4187i			0.771814i	0.922538	+	0.385907i	$0.126111\pi$
$349$			14.4187i			0.771814i	−0.922538	+	0.385907i	$0.873889\pi$
$350$	13.3556	−	19.2408i	0.713888	−	1.02847i
$351$	0.0289381	−	0.0289381i	0.00154460	−	0.00154460i
$352$	−4.55611			−0.242842
$353$	11.4476			0.609292			0.304646	−	0.952466i	$-0.401462\pi$
$353$	11.4476			0.609292			0.304646	+	0.952466i	$0.401462\pi$
$354$	−10.7407			−0.570859
$355$	5.60276	+	4.68178i	0.297363	+	0.248483i
$356$	9.81417	+	9.81417i	0.520150	+	0.520150i
$357$		−	15.8852i		−	0.840735i
$358$	−2.44720	+	2.44720i	−0.129338	+	0.129338i
$359$		−	4.83560i		−	0.255213i	−0.991825	−	0.127607i	$-0.959270\pi$
$359$		−	4.83560i		−	0.255213i	0.991825	−	0.127607i	$-0.0407295\pi$
$360$	1.71586	+	1.43381i	0.0904340	+	0.0755684i
$361$			14.9269i			0.785625i
$362$			17.1218i			0.899900i
$363$	6.90007	−	6.90007i	0.362160	−	0.362160i
$364$	0.135557	+	0.135557i	0.00710510	+	0.00710510i
$365$	12.5743	−	1.12603i	0.658169	−	0.0589391i
$366$	6.66593			0.348434
$367$	11.6170	−	11.6170i	0.606404	−	0.606404i	−0.335600	−	0.942005i	$-0.608939\pi$
$367$	11.6170	−	11.6170i	0.606404	−	0.606404i	0.942005	+	0.335600i	$0.108939\pi$
$368$		−	6.74310i		−	0.351508i
$369$	−4.17400			−0.217290
$370$	8.27998	+	10.7908i	0.430456	+	0.560988i
$371$	−35.4661			−1.84131
$372$		−	3.07399i		−	0.159379i
$373$	−7.48841	+	7.48841i	−0.387735	+	0.387735i	−0.873879	−	0.486144i	$-0.838403\pi$
$373$	−7.48841	+	7.48841i	−0.387735	+	0.387735i	0.486144	+	0.873879i	$0.338403\pi$
$374$	15.4503			0.798916
$375$	−2.95990	−	10.7814i	−0.152849	−	0.556750i
$376$	1.79848	+	1.79848i	0.0927494	+	0.0927494i
$377$	0.112071	−	0.112071i	0.00577195	−	0.00577195i
$378$		−	4.68437i		−	0.240938i
$379$			22.8790i			1.17521i	0.809147	+	0.587607i	$0.199930\pi$
$379$			22.8790i			1.17521i	−0.809147	+	0.587607i	$0.800070\pi$
$380$	4.49484	−	0.402513i	0.230580	−	0.0206485i
$381$			6.73702i			0.345148i
$382$	7.96286	−	7.96286i	0.407415	−	0.407415i
$383$			21.6612i			1.10683i	0.832904	+	0.553417i	$0.186677\pi$
$383$			21.6612i			1.10683i	−0.832904	+	0.553417i	$0.813323\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	−4.25660	−	47.5331i	−0.216936	−	2.42251i
$386$	24.4915			1.24658
$387$	−8.29512			−0.421665
$388$	−16.9894			−0.862508
$389$	−26.3679	+	26.3679i	−1.33691	+	1.33691i	−0.437866	+	0.899040i	$0.644265\pi$
$389$	−26.3679	+	26.3679i	−1.33691	+	1.33691i	−0.899040	+	0.437866i	$0.855735\pi$
$390$	0.0911456	−	0.00816210i	0.00461534	−	0.000413304i
$391$			22.8666i			1.15641i
$392$	14.9433			0.754751
$393$		−	19.7177i		−	0.994624i
$394$	13.9774	+	13.9774i	0.704169	+	0.704169i
$395$	−10.5299	+	0.942956i	−0.529818	+	0.0474453i
$396$	4.55611			0.228953
$397$	−15.0917	−	15.0917i	−0.757432	−	0.757432i	0.218423	−	0.975854i	$-0.429909\pi$
$397$	−15.0917	−	15.0917i	−0.757432	−	0.757432i	−0.975854	+	0.218423i	$0.929909\pi$
$398$	−11.0246	+	11.0246i	−0.552614	+	0.552614i
$399$	−6.68497	−	6.68497i	−0.334667	−	0.334667i
$400$	0.888377	+	4.92045i	0.0444189	+	0.246022i
$401$	−27.7959	+	27.7959i	−1.38806	+	1.38806i	−0.558670	+	0.829390i	$0.688688\pi$
$401$	−27.7959	+	27.7959i	−1.38806	+	1.38806i	−0.829390	+	0.558670i	$0.811312\pi$
$402$			14.6866i			0.732499i
$403$	−0.0889554	−	0.0889554i	−0.00443118	−	0.00443118i
$404$		−	0.926044i		−	0.0460724i
$405$	−1.71586	−	1.43381i	−0.0852620	−	0.0712466i
$406$		−	18.1415i		−	0.900349i
$407$	27.0445	+	6.05385i	1.34054	+	0.300078i
$408$	2.39788	+	2.39788i	0.118713	+	0.118713i
$409$	16.2210	+	16.2210i	0.802078	+	0.802078i	0.983420	−	0.181342i	$-0.0580440\pi$
$409$	16.2210	+	16.2210i	0.802078	+	0.802078i	−0.181342	+	0.983420i	$0.558044\pi$
$410$	−7.16201	−	5.98472i	−0.353707	−	0.295564i
$411$		−	13.4122i		−	0.661574i
$412$	−8.34187			−0.410974
$413$			50.3132i			2.47575i
$414$			6.74310i			0.331405i
$415$	0.343409	+	3.83483i	0.0168573	+	0.188244i
$416$	−0.0409247			−0.00200650
$417$	−10.9332	+	10.9332i	−0.535401	+	0.535401i
$418$	6.50194	−	6.50194i	0.318020	−	0.318020i
$419$		−	7.84481i		−	0.383244i	−0.981469	−	0.191622i	$-0.938625\pi$
$419$		−	7.84481i		−	0.383244i	0.981469	−	0.191622i	$-0.0613748\pi$
$420$	6.71649	−	8.03774i	0.327731	−	0.392201i
$421$	−5.92395	+	5.92395i	−0.288716	+	0.288716i	−0.836572	−	0.547857i	$-0.815444\pi$
$421$	−5.92395	+	5.92395i	−0.288716	+	0.288716i	0.547857	+	0.836572i	$0.315444\pi$
$422$		−	6.36095i		−	0.309646i
$423$	−1.79848	−	1.79848i	−0.0874450	−	0.0874450i
$424$	5.35361	−	5.35361i	0.259994	−	0.259994i
$425$	−3.01259	−	16.6858i	−0.146132	−	0.809380i
$426$	2.30889	+	2.30889i	0.111866	+	0.111866i
$427$		−	31.2257i		−	1.51112i
$428$	−9.26659	+	9.26659i	−0.447917	+	0.447917i
$429$	0.131845	−	0.131845i	0.00636555	−	0.00636555i
$430$	−14.2333	−	11.8936i	−0.686390	−	0.573561i
$431$	−2.98464	+	2.98464i	−0.143765	+	0.143765i	−0.775326	−	0.631561i	$-0.782414\pi$
$431$	−2.98464	+	2.98464i	−0.143765	+	0.143765i	0.631561	+	0.775326i	$0.282414\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−18.8382	−	18.8382i	−0.905305	−	0.905305i	0.0905839	−	0.995889i	$-0.471127\pi$
$433$	−18.8382	−	18.8382i	−0.905305	−	0.905305i	−0.995889	+	0.0905839i	$0.971127\pi$
$434$	−14.3997			−0.691207
$435$	−6.64517	−	5.55283i	−0.318611	−	0.266238i
$436$	10.9135	−	10.9135i	0.522661	−	0.522661i
$437$	9.62295	+	9.62295i	0.460328	+	0.460328i
$438$	5.64590			0.269772
$439$	−15.6159	−	15.6159i	−0.745307	−	0.745307i	0.228287	−	0.973594i	$-0.426688\pi$
$439$	−15.6159	−	15.6159i	−0.745307	−	0.745307i	−0.973594	+	0.228287i	$0.926688\pi$
$440$	7.81767	+	6.53260i	0.372693	+	0.311430i
$441$	−14.9433			−0.711586
$442$	0.138780			0.00660110
$443$	15.3424	−	15.3424i	0.728940	−	0.728940i	−0.241469	−	0.970409i	$-0.577629\pi$
$443$	15.3424	−	15.3424i	0.728940	−	0.728940i	0.970409	+	0.241469i	$0.0776291\pi$
$444$	3.25773	+	5.13684i	0.154605	+	0.243784i
$445$	−2.76812	−	30.9114i	−0.131222	−	1.46534i
$446$	0.324273	−	0.324273i	0.0153548	−	0.0153548i
$447$	−3.54613	−	3.54613i	−0.167726	−	0.167726i
$448$	−3.31235	+	3.31235i	−0.156494	+	0.156494i
$449$	−10.9677	+	10.9677i	−0.517597	+	0.517597i	−0.916844	−	0.399246i	$-0.869272\pi$
$449$	−10.9677	+	10.9677i	−0.517597	+	0.517597i	0.399246	+	0.916844i	$0.369272\pi$
$450$	−0.888377	−	4.92045i	−0.0418785	−	0.231952i
$451$	−19.0172			−0.895486
$452$	−16.0314			−0.754052
$453$	−3.29252	−	3.29252i	−0.154696	−	0.154696i
$454$		−	8.46323i		−	0.397199i
$455$	−0.0382343	−	0.426959i	−0.00179245	−	0.0200162i
$456$	2.01820			0.0945107
$457$	31.4188			1.46971			0.734854	−	0.678225i	$-0.237250\pi$
$457$	31.4188			1.46971			0.734854	+	0.678225i	$0.237250\pi$
$458$	15.8612			0.741144
$459$	−2.39788	−	2.39788i	−0.111923	−	0.111923i
$460$	−9.66833	+	11.5702i	−0.450788	+	0.539465i
$461$	−4.21869	−	4.21869i	−0.196484	−	0.196484i	0.602007	−	0.798491i	$-0.294368\pi$
$461$	−4.21869	−	4.21869i	−0.196484	−	0.196484i	−0.798491	+	0.602007i	$0.794368\pi$
$462$		−	21.3425i		−	0.992944i
$463$		−	6.43379i		−	0.299003i	−0.988761	−	0.149502i	$-0.952233\pi$
$463$		−	6.43379i		−	0.299003i	0.988761	−	0.149502i	$-0.0477669\pi$
$464$	2.73847	+	2.73847i	0.127130	+	0.127130i
$465$	−4.40751	+	5.27454i	−0.204394	+	0.244601i
$466$	5.31862	+	5.31862i	0.246380	+	0.246380i
$467$	31.3277			1.44967			0.724836	−	0.688922i	$-0.241916\pi$
$467$	31.3277			1.44967			0.724836	+	0.688922i	$0.241916\pi$
$468$	0.0409247			0.00189174
$469$	68.7973			3.17676
$470$	−0.507267	−	5.66462i	−0.0233985	−	0.261289i
$471$			16.1085i			0.742242i
$472$	−7.59479	−	7.59479i	−0.349579	−	0.349579i
$473$	−37.7935			−1.73775
$474$	−4.72797			−0.217163
$475$	−8.28966	−	5.75409i	−0.380356	−	0.264016i
$476$	11.2325	−	11.2325i	0.514843	−	0.514843i
$477$	−5.35361	+	5.35361i	−0.245125	+	0.245125i
$478$	21.1771	+	21.1771i	0.968617	+	0.968617i
$479$	3.24558	−	3.24558i	0.148294	−	0.148294i	−0.629061	−	0.777356i	$-0.716561\pi$
$479$	3.24558	−	3.24558i	0.148294	−	0.148294i	0.777356	+	0.629061i	$0.216561\pi$
$480$	0.199442	+	2.22716i	0.00910325	+	0.101655i
$481$	0.242923	+	0.0543779i	0.0110763	+	0.00247942i
$482$	1.31443	−	1.31443i	0.0598708	−	0.0598708i
$483$	31.5872			1.43727
$484$	9.75818			0.443554
$485$	29.1516	+	24.3596i	1.32370	+	1.10611i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	−9.00283			−0.407957			−0.203979	−	0.978975i	$-0.565387\pi$
$487$	−9.00283			−0.407957			−0.203979	+	0.978975i	$0.565387\pi$
$488$	4.71353	+	4.71353i	0.213371	+	0.213371i
$489$	6.44330	−	6.44330i	0.291376	−	0.291376i
$490$	−25.6407	−	21.4259i	−1.15833	−	0.967922i
$491$	19.5352			0.881610			0.440805	−	0.897603i	$-0.354693\pi$
$491$	19.5352			0.881610			0.440805	+	0.897603i	$0.354693\pi$
$492$	−2.95146	−	2.95146i	−0.133062	−	0.133062i
$493$	−9.28646	−	9.28646i	−0.418241	−	0.418241i
$494$	0.0584028	−	0.0584028i	0.00262766	−	0.00262766i
$495$	−7.81767	−	6.53260i	−0.351378	−	0.293619i
$496$	2.17364	−	2.17364i	0.0975992	−	0.0975992i
$497$	10.8157	−	10.8157i	0.485151	−	0.485151i
$498$			1.72185i			0.0771579i
$499$	−13.5238	−	13.5238i	−0.605410	−	0.605410i	0.336333	−	0.941743i	$-0.390813\pi$
$499$	−13.5238	−	13.5238i	−0.605410	−	0.605410i	−0.941743	+	0.336333i	$0.890813\pi$
$500$	5.53065	−	9.71658i	0.247338	−	0.434539i
$501$	3.56320	−	3.56320i	0.159192	−	0.159192i
$502$	−4.79145	−	4.79145i	−0.213853	−	0.213853i
$503$		−	16.8585i		−	0.751685i	−0.926683	−	0.375843i	$-0.877353\pi$
$503$		−	16.8585i		−	0.751685i	0.926683	−	0.375843i	$-0.122647\pi$
$504$	3.31235	−	3.31235i	0.147544	−	0.147544i
$505$	−1.32777	+	1.58896i	−0.0590850	+	0.0707080i
$506$			30.7223i			1.36577i
$507$	−9.19120	+	9.19120i	−0.408196	+	0.408196i
$508$	−4.76379	+	4.76379i	−0.211359	+	0.211359i
$509$	29.4961			1.30739			0.653697	−	0.756757i	$-0.273217\pi$
$509$	29.4961			1.30739			0.653697	+	0.756757i	$0.273217\pi$
$510$	−0.676331	−	7.55254i	−0.0299484	−	0.334432i
$511$		−	26.4475i		−	1.16997i
$512$		−	1.00000i		−	0.0441942i
$513$	−2.01820			−0.0891055
$514$			1.92054i			0.0847113i
$515$	14.3135	+	11.9607i	0.630728	+	0.527049i
$516$	−5.86553	−	5.86553i	−0.258216	−	0.258216i
$517$	−8.19407	−	8.19407i	−0.360375	−	0.360375i
$518$	24.0629	−	15.2604i	1.05726	−	0.670505i
$519$			17.1349i			0.752140i
$520$	0.0702211	+	0.0586782i	0.00307940	+	0.00257321i
$521$		−	8.58275i		−	0.376017i	−0.982167	−	0.188009i	$-0.939797\pi$
$521$		−	8.58275i		−	0.376017i	0.982167	−	0.188009i	$-0.0602033\pi$
$522$	−2.73847	−	2.73847i	−0.119860	−	0.119860i
$523$			42.1005i			1.84093i	0.390830	+	0.920463i	$0.372188\pi$
$523$			42.1005i			1.84093i	−0.390830	+	0.920463i	$0.627812\pi$
$524$	13.9425	−	13.9425i	0.609080	−	0.609080i
$525$	−23.0492	+	4.16149i	−1.00595	+	0.181622i
$526$	9.34281	+	9.34281i	0.407366	+	0.407366i
$527$	−7.37105	+	7.37105i	−0.321088	+	0.321088i
$528$	3.22166	+	3.22166i	0.140205	+	0.140205i
$529$	−22.4694			−0.976931
$530$	−16.8621	+	1.51001i	−0.732444	+	0.0655905i
$531$	7.59479	+	7.59479i	0.329586	+	0.329586i
$532$		−	9.45398i		−	0.409882i
$533$	−0.170819			−0.00739901
$534$		−	13.8793i		−	0.600617i
$535$	29.1867	−	2.61368i	1.26185	−	0.112999i
$536$	−10.3850	+	10.3850i	−0.448562	+	0.448562i
$537$	3.46086			0.149347
$538$	−21.1755			−0.912940
$539$	−68.0834			−2.93256
$540$	−0.199442	−	2.22716i	−0.00858262	−	0.0958415i
$541$	−23.1999	−	23.1999i	−0.997443	−	0.997443i	0.00255363	−	0.999997i	$-0.499187\pi$
$541$	−23.1999	−	23.1999i	−0.997443	−	0.997443i	−0.999997	+	0.00255363i	$0.999187\pi$
$542$		−	6.66480i		−	0.286278i
$543$	12.1069	−	12.1069i	0.519557	−	0.519557i
$544$			3.39111i			0.145393i
$545$	−34.3739	+	3.07819i	−1.47242	+	0.131855i
$546$		−	0.191706i		−	0.00820427i
$547$		−	5.37380i		−	0.229767i	−0.993379	−	0.114884i	$-0.963351\pi$
$547$		−	5.37380i		−	0.229767i	0.993379	−	0.114884i	$-0.0366495\pi$
$548$	9.48384	−	9.48384i	0.405130	−	0.405130i
$549$	−4.71353	−	4.71353i	−0.201168	−	0.201168i
$550$	−4.04755	−	22.4181i	−0.172588	−	0.955912i
$551$	−7.81603			−0.332974
$552$	−4.76809	+	4.76809i	−0.202943	+	0.202943i
$553$			22.1475i			0.941809i
$554$	19.1249			0.812538
$555$	1.77543	−	13.4851i	0.0753629	−	0.572410i
$556$	−15.4619			−0.655730
$557$			3.16102i			0.133937i	0.997755	+	0.0669685i	$0.0213327\pi$
$557$			3.16102i			0.133937i	−0.997755	+	0.0669685i	$0.978667\pi$
$558$	−2.17364	+	2.17364i	−0.0920174	+	0.0920174i
$559$	−0.339475			−0.0143583
$560$	10.4328	−	0.934260i	0.440867	−	0.0394797i
$561$	−10.9250	−	10.9250i	−0.461254	−	0.461254i
$562$	−16.4877	+	16.4877i	−0.695492	+	0.695492i
$563$		−	24.6271i		−	1.03791i	−0.854802	−	0.518954i	$-0.826322\pi$
$563$		−	24.6271i		−	1.03791i	0.854802	−	0.518954i	$-0.173678\pi$
$564$		−	2.54343i		−	0.107098i
$565$	27.5077	+	22.9859i	1.15726	+	0.967026i
$566$			8.89666i			0.373954i
$567$	−3.31235	+	3.31235i	−0.139106	+	0.139106i
$568$			3.26527i			0.137008i
$569$	1.29571	+	1.29571i	0.0543191	+	0.0543191i	0.733745	−	0.679425i	$-0.237771\pi$
$569$	1.29571	+	1.29571i	0.0543191	+	0.0543191i	−0.679425	+	0.733745i	$0.737771\pi$
$570$	−3.46295	−	2.89371i	−0.145047	−	0.121204i
$571$	−16.7314			−0.700186			−0.350093	−	0.936715i	$-0.613850\pi$
$571$	−16.7314			−0.700186			−0.350093	+	0.936715i	$0.613850\pi$
$572$	0.186457			0.00779618
$573$	−11.2612			−0.470443
$574$	−13.8257	+	13.8257i	−0.577075	+	0.577075i
$575$	33.1791	−	5.99042i	1.38366	−	0.249818i
$576$			1.00000i			0.0416667i
$577$	14.3010			0.595359			0.297680	−	0.954666i	$-0.403787\pi$
$577$	14.3010			0.595359			0.297680	+	0.954666i	$0.403787\pi$
$578$			5.50035i			0.228784i
$579$	−17.3181	−	17.3181i	−0.719715	−	0.719715i
$580$	−0.772396	−	8.62529i	−0.0320720	−	0.358146i
$581$	8.06578			0.334625
$582$	12.0133	+	12.0133i	0.497969	+	0.497969i
$583$	−24.3917	+	24.3917i	−1.01020	+	1.01020i
$584$	3.99226	+	3.99226i	0.165201	+	0.165201i
$585$	−0.0702211	−	0.0586782i	−0.00290329	−	0.00242604i
$586$	20.1484	−	20.1484i	0.832322	−	0.832322i
$587$		−	33.8637i		−	1.39770i	−0.715266	−	0.698852i	$-0.753695\pi$
$587$		−	33.8637i		−	1.39770i	0.715266	−	0.698852i	$-0.246305\pi$
$588$	−10.5665	−	10.5665i	−0.435756	−	0.435756i
$589$			6.20391i			0.255628i
$590$	2.14214	+	23.9211i	0.0881905	+	0.984816i
$591$		−	19.7670i		−	0.813104i
$592$	−1.32873	+	5.93586i	−0.0546105	+	0.243962i
$593$	1.07792	+	1.07792i	0.0442650	+	0.0442650i	0.728893	−	0.684628i	$-0.240035\pi$
$593$	1.07792	+	1.07792i	0.0442650	+	0.0442650i	−0.684628	+	0.728893i	$0.740035\pi$
$594$	−3.22166	−	3.22166i	−0.132186	−	0.132186i
$595$	−35.3789	+	3.16818i	−1.45039	+	0.129883i
$596$		−	5.01498i		−	0.205422i
$597$	15.5911			0.638103
$598$			0.275959i			0.0112848i
$599$		−	37.1518i		−	1.51798i	−0.651102	−	0.758990i	$-0.725693\pi$
$599$		−	37.1518i		−	1.51798i	0.651102	−	0.758990i	$-0.274307\pi$
$600$	2.85110	−	4.10746i	0.116396	−	0.167686i
$601$	38.4844			1.56981			0.784906	−	0.619615i	$-0.212711\pi$
$601$	38.4844			1.56981			0.784906	+	0.619615i	$0.212711\pi$
$602$	−27.4763	+	27.4763i	−1.11985	+	1.11985i
$603$	10.3850	−	10.3850i	0.422909	−	0.422909i
$604$		−	4.65633i		−	0.189463i
$605$	−16.7437	−	13.9914i	−0.680728	−	0.568830i
$606$	−0.654812	+	0.654812i	−0.0265999	+	0.0265999i
$607$		−	0.856739i		−	0.0347740i	−0.999849	−	0.0173870i	$-0.994465\pi$
$607$		−	0.856739i		−	0.0347740i	0.999849	−	0.0173870i	$-0.00553473\pi$
$608$	1.42708	+	1.42708i	0.0578758	+	0.0578758i
$609$	−12.8280	+	12.8280i	−0.519817	+	0.519817i
$610$	−1.32947	−	14.8461i	−0.0538286	−	0.601100i
$611$	−0.0736021	−	0.0736021i	−0.00297762	−	0.00297762i
$612$		−	3.39111i		−	0.137078i
$613$	−15.7342	+	15.7342i	−0.635497	+	0.635497i	−0.949441	−	0.313945i	$-0.898349\pi$
$613$	−15.7342	+	15.7342i	−0.635497	+	0.635497i	0.313945	+	0.949441i	$0.398349\pi$
$614$	16.3116	−	16.3116i	0.658281	−	0.658281i
$615$	0.832471	+	9.29614i	0.0335685	+	0.374857i
$616$	15.0914	−	15.0914i	0.608051	−	0.608051i
$617$	−19.6618	−	19.6618i	−0.791555	−	0.791555i	0.190192	−	0.981747i	$-0.439089\pi$
$617$	−19.6618	−	19.6618i	−0.791555	−	0.791555i	−0.981747	+	0.190192i	$0.939089\pi$
$618$	5.89859	+	5.89859i	0.237276	+	0.237276i
$619$	1.20670			0.0485013			0.0242507	−	0.999706i	$-0.492280\pi$
$619$	1.20670			0.0485013			0.0242507	+	0.999706i	$0.492280\pi$
$620$	−6.84625	+	0.613083i	−0.274952	+	0.0246220i
$621$	4.76809	−	4.76809i	0.191337	−	0.191337i
$622$	9.24730	+	9.24730i	0.370783	+	0.370783i
$623$	−65.0159			−2.60481
$624$	0.0289381	+	0.0289381i	0.00115845	+	0.00115845i
$625$	−23.4216	+	8.74243i	−0.936863	+	0.349697i
$626$	−11.1765			−0.446704
$627$	−9.19513			−0.367218
$628$	−11.3905	+	11.3905i	−0.454529	+	0.454529i
$629$	4.50588	−	20.1292i	0.179661	−	0.802603i
$630$	−10.4328	+	0.934260i	−0.415653	+	0.0372218i
$631$	7.06484	−	7.06484i	0.281247	−	0.281247i	−0.552359	−	0.833606i	$-0.686272\pi$
$631$	7.06484	−	7.06484i	0.281247	−	0.281247i	0.833606	+	0.552359i	$0.186272\pi$
$632$	−3.34318	−	3.34318i	−0.132984	−	0.132984i
$633$	−4.49787	+	4.49787i	−0.178774	+	0.178774i
$634$	−2.44424	+	2.44424i	−0.0970731	+	0.0970731i
$635$	15.0044	−	1.34365i	0.595431	−	0.0533210i
$636$	−7.57115			−0.300216
$637$	−0.611550			−0.0242305
$638$	−12.4768	−	12.4768i	−0.493961	−	0.493961i
$639$		−	3.26527i		−	0.129172i
$640$	−1.43381	+	1.71586i	−0.0566763	+	0.0678255i
$641$	−22.4471			−0.886605			−0.443303	−	0.896372i	$-0.646193\pi$
$641$	−22.4471			−0.886605			−0.443303	+	0.896372i	$0.646193\pi$
$642$	13.1049			0.517211
$643$	−8.37987			−0.330470			−0.165235	−	0.986254i	$-0.552838\pi$
$643$	−8.37987			−0.330470			−0.165235	+	0.986254i	$0.552838\pi$
$644$	22.3355	+	22.3355i	0.880142	+	0.880142i
$645$	1.65440	+	18.4745i	0.0651418	+	0.727433i
$646$	−4.83939	−	4.83939i	−0.190403	−	0.190403i
$647$			3.24353i			0.127516i	0.997965	+	0.0637582i	$0.0203087\pi$
$647$			3.24353i			0.127516i	−0.997965	+	0.0637582i	$0.979691\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	34.6027	+	34.6027i	1.35828	+	1.35828i
$650$	−0.0363565	−	0.201368i	−0.00142602	−	0.00789828i
$651$	10.1821	+	10.1821i	0.399069	+	0.399069i
$652$	9.11221			0.356862
$653$	−6.24042			−0.244206			−0.122103	−	0.992517i	$-0.538964\pi$
$653$	−6.24042			−0.244206			−0.122103	+	0.992517i	$0.538964\pi$
$654$	−15.4340			−0.603517
$655$	−43.9143	+	3.93253i	−1.71587	+	0.153657i
$656$		−	4.17400i		−	0.162967i
$657$	−3.99226	−	3.99226i	−0.155753	−	0.155753i
$658$	−11.9144			−0.464470
$659$	27.3061			1.06370			0.531848	−	0.846840i	$-0.321498\pi$
$659$	27.3061			1.06370			0.531848	+	0.846840i	$0.321498\pi$
$660$	−0.908681	−	10.1472i	−0.0353704	−	0.394978i
$661$	29.4103	−	29.4103i	1.14393	−	1.14393i	0.156201	−	0.987725i	$-0.450075\pi$
$661$	29.4103	−	29.4103i	1.14393	−	1.14393i	0.987725	−	0.156201i	$-0.0499249\pi$
$662$	19.5512	−	19.5512i	0.759877	−	0.759877i
$663$	−0.0981324	−	0.0981324i	−0.00381115	−	0.00381115i
$664$	−1.21753	+	1.21753i	−0.0472494	+	0.0472494i
$665$	−13.5552	+	16.2217i	−0.525648	+	0.629052i
$666$	1.32873	−	5.93586i	0.0514873	−	0.230010i
$667$	18.4658	−	18.4658i	0.714998	−	0.714998i
$668$	5.03912			0.194969
$669$	−0.458591			−0.0177302
$670$	32.7093	−	2.92912i	1.26367	−	0.113162i
$671$	−21.4754	−	21.4754i	−0.829048	−	0.829048i
$672$	4.68437			0.180703
$673$	−16.0004	−	16.0004i	−0.616770	−	0.616770i	0.327932	−	0.944701i	$-0.393648\pi$
$673$	−16.0004	−	16.0004i	−0.616770	−	0.616770i	−0.944701	+	0.327932i	$0.893648\pi$
$674$	−11.6161	+	11.6161i	−0.447437	+	0.447437i
$675$	−2.85110	+	4.10746i	−0.109739	+	0.158096i
$676$	−12.9983			−0.499936
$677$	3.31711	+	3.31711i	0.127487	+	0.127487i	0.767971	−	0.640484i	$-0.221266\pi$
$677$	3.31711	+	3.31711i	0.127487	+	0.127487i	−0.640484	+	0.767971i	$0.721266\pi$
$678$	11.3359	+	11.3359i	0.435352	+	0.435352i
$679$	56.2749	−	56.2749i	2.15963	−	2.15963i
$680$	4.86221	−	5.81869i	0.186457	−	0.223137i
$681$	−5.98441	+	5.98441i	−0.229323	+	0.229323i
$682$	−9.90334	+	9.90334i	−0.379219	+	0.379219i
$683$			21.9331i			0.839246i	0.907698	+	0.419623i	$0.137838\pi$
$683$			21.9331i			0.839246i	−0.907698	+	0.419623i	$0.862162\pi$
$684$	−1.42708	−	1.42708i	−0.0545658	−	0.0545658i
$685$	−29.8710	+	2.67495i	−1.14131	+	0.102205i
$686$	−26.3110	+	26.3110i	−1.00456	+	1.00456i
$687$	−11.2155	−	11.2155i	−0.427899	−	0.427899i
$688$		−	8.29512i		−	0.316248i
$689$	−0.219095	+	0.219095i	−0.00834685	+	0.00834685i
$690$	15.0179	−	1.34486i	0.571723	−	0.0511979i
$691$		−	2.64115i		−	0.100474i	−0.998737	−	0.0502371i	$-0.984002\pi$
$691$		−	2.64115i		−	0.100474i	0.998737	−	0.0502371i	$-0.0159977\pi$
$692$	−12.1162	+	12.1162i	−0.460590	+	0.460590i
$693$	−15.0914	+	15.0914i	−0.573276	+	0.573276i
$694$	−2.18154			−0.0828100
$695$	26.5305	+	22.1694i	1.00636	+	0.840934i
$696$		−	3.87278i		−	0.146797i
$697$			14.1545i			0.536140i
$698$	14.4187			0.545755
$699$		−	7.52167i		−	0.284496i
$700$	−19.2408	−	13.3556i	−0.727236	−	0.504795i
$701$	16.2769	+	16.2769i	0.614770	+	0.614770i	0.944185	−	0.329415i	$-0.106852\pi$
$701$	16.2769	+	16.2769i	0.614770	+	0.614770i	−0.329415	+	0.944185i	$0.606852\pi$
$702$	−0.0289381	−	0.0289381i	−0.00109220	−	0.00109220i
$703$	−6.57475	−	10.3672i	−0.247971	−	0.391005i
$704$			4.55611i			0.171715i
$705$	−3.64680	+	4.36418i	−0.137346	+	0.164365i
$706$		−	11.4476i		−	0.430834i
$707$	3.06738	+	3.06738i	0.115361	+	0.115361i
$708$			10.7407i			0.403658i
$709$	−9.99325	+	9.99325i	−0.375304	+	0.375304i	−0.869405	−	0.494100i	$-0.835497\pi$
$709$	−9.99325	+	9.99325i	−0.375304	+	0.375304i	0.494100	+	0.869405i	$0.335497\pi$
$710$	4.68178	−	5.60276i	0.175704	−	0.210268i
$711$	3.34318	+	3.34318i	0.125379	+	0.125379i
$712$	9.81417	−	9.81417i	0.367802	−	0.367802i
$713$	−14.6571	−	14.6571i	−0.548911	−	0.548911i
$714$	−15.8852			−0.594490
$715$	−0.319936	−	0.267344i	−0.0119649	−	0.00999812i
$716$	2.44720	+	2.44720i	0.0914560	+	0.0914560i
$717$		−	29.9489i		−	1.11846i
$718$	−4.83560			−0.180463
$719$		−	23.5961i		−	0.879987i	−0.898001	−	0.439994i	$-0.854981\pi$
$719$		−	23.5961i		−	0.879987i	0.898001	−	0.439994i	$-0.145019\pi$
$720$	1.43381	−	1.71586i	0.0534349	−	0.0639465i
$721$	27.6312	−	27.6312i	1.02904	−	1.02904i
$722$	14.9269			0.555521
$723$	−1.85889			−0.0691328
$724$	17.1218			0.636325
$725$	−11.0417	+	15.9073i	−0.410078	+	0.590782i
$726$	−6.90007	−	6.90007i	−0.256086	−	0.256086i
$727$		−	39.5442i		−	1.46661i	−0.679897	−	0.733307i	$-0.737976\pi$
$727$		−	39.5442i		−	1.46661i	0.679897	−	0.733307i	$-0.262024\pi$
$728$	0.135557	−	0.135557i	0.00502407	−	0.00502407i
$729$			1.00000i			0.0370370i
$730$	−1.12603	−	12.5743i	−0.0416763	−	0.465396i
$731$			28.1297i			1.04041i
$732$		−	6.66593i		−	0.246380i
$733$	32.9017	−	32.9017i	1.21525	−	1.21525i	0.245976	−	0.969276i	$-0.420892\pi$
$733$	32.9017	−	32.9017i	1.21525	−	1.21525i	0.969276	−	0.245976i	$-0.0791083\pi$
$734$	−11.6170	−	11.6170i	−0.428793	−	0.428793i
$735$	2.98033	+	33.2811i	0.109931	+	1.22759i
$736$	−6.74310			−0.248554
$737$	47.3151	−	47.3151i	1.74287	−	1.74287i
$738$			4.17400i			0.153647i
$739$	−17.2951			−0.636211			−0.318105	−	0.948055i	$-0.603047\pi$
$739$	−17.2951			−0.636211			−0.318105	+	0.948055i	$0.603047\pi$
$740$	10.7908	−	8.27998i	0.396679	−	0.304378i
$741$	−0.0825940			−0.00303417
$742$			35.4661i			1.30200i
$743$	11.4904	−	11.4904i	0.421540	−	0.421540i	−0.464194	−	0.885734i	$-0.653656\pi$
$743$	11.4904	−	11.4904i	0.421540	−	0.421540i	0.885734	+	0.464194i	$0.153656\pi$
$744$	−3.07399			−0.112698
$745$	−7.19053	+	8.60503i	−0.263441	+	0.315264i
$746$	7.48841	+	7.48841i	0.274170	+	0.274170i
$747$	1.21753	−	1.21753i	0.0445471	−	0.0445471i
$748$		−	15.4503i		−	0.564919i
$749$		−	61.3883i		−	2.24308i
$750$	−10.7814	+	2.95990i	−0.393682	+	0.108080i
$751$			10.9358i			0.399052i	0.979892	+	0.199526i	$0.0639403\pi$
$751$			10.9358i			0.399052i	−0.979892	+	0.199526i	$0.936060\pi$
$752$	1.79848	−	1.79848i	0.0655837	−	0.0655837i
$753$			6.77614i			0.246936i
$754$	−0.112071	−	0.112071i	−0.00408138	−	0.00408138i
$755$	−6.67630	+	7.98963i	−0.242975	+	0.290772i
$756$	−4.68437			−0.170369
$757$	42.3878			1.54061			0.770305	−	0.637676i	$-0.220104\pi$
$757$	42.3878			1.54061			0.770305	+	0.637676i	$0.220104\pi$
$758$	22.8790			0.831001
$759$	21.7240	−	21.7240i	0.788530	−	0.788530i
$760$	−0.402513	−	4.49484i	−0.0146007	−	0.163045i
$761$			42.5455i			1.54227i	0.636670	+	0.771136i	$0.280311\pi$
$761$			42.5455i			1.54227i	−0.636670	+	0.771136i	$0.719689\pi$
$762$	6.73702			0.244057
$763$			72.2985i			2.61738i
$764$	−7.96286	−	7.96286i	−0.288086	−	0.288086i
$765$	−4.86221	+	5.81869i	−0.175794	+	0.210375i
$766$	21.6612			0.782650
$767$	0.310814	+	0.310814i	0.0112228	+	0.0112228i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	21.9376	+	21.9376i	0.791090	+	0.791090i	0.981671	−	0.190582i	$-0.0610374\pi$
$769$	21.9376	+	21.9376i	0.791090	+	0.791090i	−0.190582	+	0.981671i	$0.561037\pi$
$770$	−47.5331	+	4.25660i	−1.71297	+	0.153397i
$771$	1.35803	−	1.35803i	0.0489081	−	0.0489081i
$772$		−	24.4915i		−	0.881468i
$773$	8.34646	+	8.34646i	0.300201	+	0.300201i	0.841093	−	0.540891i	$-0.181913\pi$
$773$	8.34646	+	8.34646i	0.300201	+	0.300201i	−0.540891	+	0.841093i	$0.681913\pi$
$774$			8.29512i			0.298162i
$775$	12.6263	+	8.76426i	0.453549	+	0.314821i
$776$			16.9894i			0.609885i
$777$	−27.8058	−	6.22427i	−0.997526	−	0.223294i
$778$	26.3679	+	26.3679i	0.945335	+	0.945335i
$779$	5.95663	+	5.95663i	0.213418	+	0.213418i
$780$	−0.00816210	−	0.0911456i	−0.000292250	−	0.00326354i
$781$		−	14.8769i		−	0.532339i
$782$	22.8666			0.817709
$783$			3.87278i			0.138402i
$784$		−	14.9433i		−	0.533690i
$785$	35.8762	−	3.21272i	1.28048	−	0.114667i
$786$	−19.7177			−0.703305
$787$	−18.1655	+	18.1655i	−0.647530	+	0.647530i	−0.952395	−	0.304866i	$-0.901388\pi$
$787$	−18.1655	+	18.1655i	−0.647530	+	0.647530i	0.304866	+	0.952395i	$0.401388\pi$
$788$	13.9774	−	13.9774i	0.497923	−	0.497923i
$789$		−	13.2127i		−	0.470386i
$790$	0.942956	+	10.5299i	0.0335489	+	0.374638i
$791$	53.1015	−	53.1015i	1.88807	−	1.88807i
$792$		−	4.55611i		−	0.161894i
$793$	−0.192899	−	0.192899i	−0.00685006	−	0.00685006i
$794$	−15.0917	+	15.0917i	−0.535585	+	0.535585i
$795$	12.9911	+	10.8556i	0.460746	+	0.385008i
$796$	11.0246	+	11.0246i	0.390757	+	0.390757i
$797$			39.2307i			1.38962i	0.719191	+	0.694812i	$0.244513\pi$
$797$			39.2307i			1.38962i	−0.719191	+	0.694812i	$0.755487\pi$
$798$	−6.68497	+	6.68497i	−0.236645	+	0.236645i
$799$	−6.09884	+	6.09884i	−0.215761	+	0.215761i
$800$	4.92045	−	0.888377i	0.173964	−	0.0314089i
$801$	−9.81417	+	9.81417i	−0.346767	+	0.346767i
$802$	27.7959	+	27.7959i	0.981507	+	0.981507i
$803$	−18.1892	−	18.1892i	−0.641882	−	0.641882i
$804$	14.6866			0.517955
$805$	−6.29981	−	70.3495i	−0.222039	−	2.47950i
$806$	−0.0889554	+	0.0889554i	−0.00313332	+	0.00313332i
$807$	14.9733	+	14.9733i	0.527086	+	0.527086i
$808$	−0.926044			−0.0325781
$809$	2.17686	+	2.17686i	0.0765345	+	0.0765345i	0.744338	−	0.667803i	$-0.232765\pi$
$809$	2.17686	+	2.17686i	0.0765345	+	0.0765345i	−0.667803	+	0.744338i	$0.732765\pi$
$810$	−1.43381	+	1.71586i	−0.0503790	+	0.0602893i
$811$	−15.5660			−0.546595			−0.273298	−	0.961929i	$-0.588114\pi$
$811$	−15.5660			−0.546595			−0.273298	+	0.961929i	$0.588114\pi$
$812$	−18.1415			−0.636643
$813$	−4.71273	+	4.71273i	−0.165283	+	0.165283i
$814$	6.05385	−	27.0445i	0.212187	−	0.947908i
$815$	−15.6353	−	13.0652i	−0.547681	−	0.457653i
$816$	2.39788	−	2.39788i	0.0839426	−	0.0839426i
$817$	11.8378	+	11.8378i	0.414152	+	0.414152i
$818$	16.2210	−	16.2210i	0.567155	−	0.567155i
$819$	−0.135557	+	0.135557i	−0.00473674	+	0.00473674i
$820$	−5.98472	+	7.16201i	−0.208996	+	0.250108i
$821$	32.8977			1.14814			0.574069	−	0.818807i	$-0.305364\pi$
$821$	32.8977			1.14814			0.574069	+	0.818807i	$0.305364\pi$
$822$	−13.4122			−0.467803
$823$	−17.9986	−	17.9986i	−0.627393	−	0.627393i	0.320018	−	0.947411i	$-0.396311\pi$
$823$	−17.9986	−	17.9986i	−0.627393	−	0.627393i	−0.947411	+	0.320018i	$0.896311\pi$
$824$			8.34187i			0.290603i
$825$	−12.9900	+	18.7140i	−0.452252	+	0.651540i
$826$	50.3132			1.75062
$827$	20.3386			0.707242			0.353621	−	0.935389i	$-0.384950\pi$
$827$	20.3386			0.707242			0.353621	+	0.935389i	$0.384950\pi$
$828$	6.74310			0.234339
$829$	6.12311	+	6.12311i	0.212664	+	0.212664i	0.805398	−	0.592734i	$-0.201951\pi$
$829$	6.12311	+	6.12311i	0.212664	+	0.212664i	−0.592734	+	0.805398i	$0.701951\pi$
$830$	3.83483	−	0.343409i	0.133109	−	0.0119199i
$831$	−13.5233	−	13.5233i	−0.469119	−	0.469119i
$832$			0.0409247i			0.00141881i
$833$			50.6744i			1.75577i
$834$	10.9332	+	10.9332i	0.378586	+	0.378586i
$835$	−8.64645	−	7.22514i	−0.299223	−	0.250036i
$836$	−6.50194	−	6.50194i	−0.224874	−	0.224874i
$837$	3.07399			0.106253
$838$	−7.84481			−0.270995
$839$	56.2254			1.94111			0.970557	−	0.240870i	$-0.0774328\pi$
$839$	56.2254			1.94111			0.970557	+	0.240870i	$0.0774328\pi$
$840$	−8.03774	−	6.71649i	−0.277328	−	0.231741i
$841$		−	14.0016i		−	0.482812i
$842$	5.92395	+	5.92395i	0.204153	+	0.204153i
$843$	23.3171			0.803084
$844$	−6.36095			−0.218953
$845$	22.3034	+	18.6371i	0.767259	+	0.641137i
$846$	−1.79848	+	1.79848i	−0.0618329	+	0.0618329i
$847$	−32.3225	+	32.3225i	−1.11061	+	1.11061i
$848$	−5.35361	−	5.35361i	−0.183844	−	0.183844i
$849$	6.29089	−	6.29089i	0.215903	−	0.215903i
$850$	−16.6858	+	3.01259i	−0.572318	+	0.103331i
$851$	40.0261	+	8.95977i	1.37208	+	0.307137i
$852$	2.30889	−	2.30889i	0.0791014	−	0.0791014i
$853$	21.4218			0.733467			0.366734	−	0.930326i	$-0.380476\pi$
$853$	21.4218			0.733467			0.366734	+	0.930326i	$0.380476\pi$
$854$	−31.2257			−1.06852
$855$	0.402513	+	4.49484i	0.0137657	+	0.153720i
$856$	9.26659	+	9.26659i	0.316725	+	0.316725i
$857$	5.96951			0.203915			0.101957	−	0.994789i	$-0.467490\pi$
$857$	5.96951			0.203915			0.101957	+	0.994789i	$0.467490\pi$
$858$	−0.131845	−	0.131845i	−0.00450112	−	0.00450112i
$859$	11.4153	−	11.4153i	0.389485	−	0.389485i	−0.485019	−	0.874504i	$-0.661187\pi$
$859$	11.4153	−	11.4153i	0.389485	−	0.389485i	0.874504	+	0.485019i	$0.161187\pi$
$860$	−11.8936	+	14.2333i	−0.405569	+	0.485351i
$861$	19.5525			0.666349
$862$	2.98464	+	2.98464i	0.101657	+	0.101657i
$863$	−4.18842	−	4.18842i	−0.142575	−	0.142575i	0.632216	−	0.774792i	$-0.282145\pi$
$863$	−4.18842	−	4.18842i	−0.142575	−	0.142575i	−0.774792	+	0.632216i	$0.782145\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	38.1622	−	3.41743i	1.29755	−	0.116196i
$866$	−18.8382	+	18.8382i	−0.640147	+	0.640147i
$867$	3.88934	−	3.88934i	0.132089	−	0.132089i
$868$			14.3997i			0.488757i
$869$	15.2319	+	15.2319i	0.516707	+	0.516707i
$870$	−5.55283	+	6.64517i	−0.188259	+	0.225292i
$871$	0.425001	−	0.425001i	0.0144006	−	0.0144006i
$872$	−10.9135	−	10.9135i	−0.369577	−	0.369577i
$873$		−	16.9894i		−	0.575005i
$874$	9.62295	−	9.62295i	0.325501	−	0.325501i
$875$	13.8653	+	50.5041i	0.468731	+	1.70735i
$876$		−	5.64590i		−	0.190757i
$877$	2.03666	−	2.03666i	0.0687731	−	0.0687731i	−0.671884	−	0.740657i	$-0.734515\pi$
$877$	2.03666	−	2.03666i	0.0687731	−	0.0687731i	0.740657	+	0.671884i	$0.234515\pi$
$878$	−15.6159	+	15.6159i	−0.527012	+	0.527012i
$879$	−28.4941			−0.961082
$880$	6.53260	−	7.81767i	0.220214	−	0.263534i
$881$		−	17.6461i		−	0.594514i	−0.954798	−	0.297257i	$-0.903928\pi$
$881$		−	17.6461i		−	0.594514i	0.954798	−	0.297257i	$-0.0960718\pi$
$882$			14.9433i			0.503167i
$883$	−14.6660			−0.493551			−0.246776	−	0.969073i	$-0.579371\pi$
$883$	−14.6660			−0.493551			−0.246776	+	0.969073i	$0.579371\pi$
$884$		−	0.138780i		−	0.00466768i
$885$	15.4001	−	18.4295i	0.517667	−	0.619501i
$886$	−15.3424	−	15.3424i	−0.515438	−	0.515438i
$887$	−4.08796	−	4.08796i	−0.137260	−	0.137260i	0.635138	−	0.772398i	$-0.280943\pi$
$887$	−4.08796	−	4.08796i	−0.137260	−	0.137260i	−0.772398	+	0.635138i	$0.780943\pi$
$888$	5.13684	−	3.25773i	0.172381	−	0.109322i
$889$		−	31.5587i		−	1.05844i
$890$	−30.9114	+	2.76812i	−1.03615	+	0.0927877i
$891$			4.55611i			0.152636i
$892$	−0.324273	−	0.324273i	−0.0108575	−	0.0108575i
$893$			5.13314i			0.171774i
$894$	−3.54613	+	3.54613i	−0.118600	+	0.118600i
$895$	−0.690241	−	7.70787i	−0.0230722	−	0.257646i
$896$	3.31235	+	3.31235i	0.110658	+	0.110658i
$897$	0.195133	−	0.195133i	0.00651529	−	0.00651529i
$898$	10.9677	+	10.9677i	0.365997	+	0.365997i
$899$	11.9049			0.397050
$900$	−4.92045	+	0.888377i	−0.164015	+	0.0296126i
$901$	18.1547	+	18.1547i	0.604821	+	0.604821i
$902$			19.0172i			0.633204i
$903$	38.8574			1.29309
$904$			16.0314i			0.533196i
$905$	−29.3786	−	24.5494i	−0.976578	−	0.816048i
$906$	−3.29252	+	3.29252i	−0.109387	+	0.109387i
$907$	−40.2497			−1.33647			−0.668234	−	0.743951i	$-0.732950\pi$
$907$	−40.2497			−1.33647			−0.668234	+	0.743951i	$0.732950\pi$
$908$	−8.46323			−0.280862
$909$	0.926044			0.0307149
$910$	−0.426959	+	0.0382343i	−0.0141536	+	0.00126745i
$911$	25.8593	+	25.8593i	0.856757	+	0.856757i	0.990955	−	0.134198i	$-0.0428458\pi$
$911$	25.8593	+	25.8593i	0.856757	+	0.856757i	−0.134198	+	0.990955i	$0.542846\pi$
$912$		−	2.01820i		−	0.0668292i
$913$	5.54721	−	5.54721i	0.183586	−	0.183586i
$914$		−	31.4188i		−	1.03924i
$915$	−9.55768	+	11.4378i	−0.315967	+	0.378123i
$916$		−	15.8612i		−	0.524068i
$917$			92.3648i			3.05015i
$918$	−2.39788	+	2.39788i	−0.0791418	+	0.0791418i
$919$	14.1196	+	14.1196i	0.465763	+	0.465763i	0.900539	−	0.434776i	$-0.143172\pi$
$919$	14.1196	+	14.1196i	0.465763	+	0.465763i	−0.434776	+	0.900539i	$0.643172\pi$
$920$	11.5702	+	9.66833i	0.381460	+	0.318755i
$921$	−23.0680			−0.760118
$922$	−4.21869	+	4.21869i	−0.138935	+	0.138935i
$923$		−	0.133630i		−	0.00439849i
$924$	−21.3425			−0.702117
$925$	−30.3875	−	1.26467i	−0.999135	−	0.0415820i
$926$	−6.43379			−0.211427
$927$		−	8.34187i		−	0.273983i
$928$	2.73847	−	2.73847i	0.0898947	−	0.0898947i
$929$	−32.4012			−1.06305			−0.531524	−	0.847043i	$-0.678380\pi$
$929$	−32.4012			−1.06305			−0.531524	+	0.847043i	$0.678380\pi$
$930$	5.27454	+	4.40751i	0.172959	+	0.144528i
$931$	21.3253	+	21.3253i	0.698909	+	0.698909i
$932$	5.31862	−	5.31862i	0.174217	−	0.174217i
$933$		−	13.0777i		−	0.428143i
$934$		−	31.3277i		−	1.02507i
$935$	−22.1528	+	26.5106i	−0.724474	+	0.866990i
$936$		−	0.0409247i		−	0.00133766i
$937$	−30.9225	+	30.9225i	−1.01019	+	1.01019i	−0.0102456	+	0.999948i	$0.503261\pi$
$937$	−30.9225	+	30.9225i	−1.01019	+	1.01019i	−0.999948	+	0.0102456i	$0.996739\pi$
$938$		−	68.7973i		−	2.24631i
$939$	7.90300	+	7.90300i	0.257905	+	0.257905i
$940$	−5.66462	+	0.507267i	−0.184759	+	0.0165452i
$941$	−41.3078			−1.34660			−0.673298	−	0.739371i	$-0.735123\pi$
$941$	−41.3078			−1.34660			−0.673298	+	0.739371i	$0.735123\pi$
$942$	16.1085			0.524844
$943$	−28.1457			−0.916550
$944$	−7.59479	+	7.59479i	−0.247189	+	0.247189i
$945$	8.03774	+	6.71649i	0.261468	+	0.218488i
$946$			37.7935i			1.22877i
$947$	43.2125			1.40422			0.702109	−	0.712069i	$-0.252242\pi$
$947$	43.2125			1.40422			0.702109	+	0.712069i	$0.252242\pi$
$948$			4.72797i			0.153557i
$949$	−0.163382	−	0.163382i	−0.00530359	−	0.00530359i
$950$	−5.75409	+	8.28966i	−0.186687	+	0.268952i
$951$	3.45667			0.112090
$952$	−11.2325	−	11.2325i	−0.364049	−	0.364049i
$953$	−30.7535	+	30.7535i	−0.996204	+	0.996204i	−0.999993	−	0.00378868i	$-0.998794\pi$
$953$	−30.7535	+	30.7535i	−0.996204	+	0.996204i	0.00378868	+	0.999993i	$0.498794\pi$
$954$	5.35361	+	5.35361i	0.173330	+	0.173330i
$955$	2.24596	+	25.0804i	0.0726774	+	0.811583i
$956$	21.1771	−	21.1771i	0.684916	−	0.684916i
$957$			17.6448i			0.570377i
$958$	−3.24558	−	3.24558i	−0.104860	−	0.104860i
$959$			62.8276i			2.02881i
$960$	2.22716	−	0.199442i	0.0718811	−	0.00643697i
$961$			21.5506i			0.695181i
$962$	0.0543779	−	0.242923i	0.00175321	−	0.00783216i
$963$	−9.26659	−	9.26659i	−0.298612	−	0.298612i
$964$	−1.31443	−	1.31443i	−0.0423350	−	0.0423350i
$965$	−35.1161	+	42.0240i	−1.13043	+	1.35280i
$966$		−	31.5872i		−	1.01630i
$967$	−55.3457			−1.77980			−0.889899	−	0.456157i	$-0.849225\pi$
$967$	−55.3457			−1.77980			−0.889899	+	0.456157i	$0.849225\pi$
$968$		−	9.75818i		−	0.313640i
$969$			6.84393i			0.219859i
$970$	24.3596	−	29.1516i	0.782141	−	0.936000i
$971$	9.04099			0.290139			0.145070	−	0.989421i	$-0.453659\pi$
$971$	9.04099			0.290139			0.145070	+	0.989421i	$0.453659\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	51.2152	−	51.2152i	1.64188	−	1.64188i
$974$			9.00283i			0.288469i
$975$	−0.116680	+	0.168096i	−0.00373676	+	0.00538339i
$976$	4.71353	−	4.71353i	0.150876	−	0.150876i
$977$			46.7156i			1.49456i	0.664507	+	0.747282i	$0.268642\pi$
$977$			46.7156i			1.49456i	−0.664507	+	0.747282i	$0.731358\pi$
$978$	−6.44330	−	6.44330i	−0.206034	−	0.206034i
$979$	−44.7145	+	44.7145i	−1.42908	+	1.42908i
$980$	−21.4259	+	25.6407i	−0.684424	+	0.819062i
$981$	10.9135	+	10.9135i	0.348441	+	0.348441i
$982$		−	19.5352i		−	0.623392i
$983$	38.8849	−	38.8849i	1.24024	−	1.24024i	0.280334	−	0.959903i	$-0.409555\pi$
$983$	38.8849	−	38.8849i	1.24024	−	1.24024i	0.959903	−	0.280334i	$-0.0904451\pi$
$984$	−2.95146	+	2.95146i	−0.0940892	+	0.0940892i
$985$	−44.0241	+	3.94237i	−1.40272	+	0.125614i
$986$	−9.28646	+	9.28646i	−0.295741	+	0.295741i
$987$	8.42473	+	8.42473i	0.268162	+	0.268162i
$988$	−0.0584028	−	0.0584028i	−0.00185804	−	0.00185804i
$989$	−55.9348			−1.77862
$990$	−6.53260	+	7.81767i	−0.207620	+	0.248462i
$991$	2.57457	−	2.57457i	0.0817840	−	0.0817840i	−0.665031	−	0.746815i	$-0.731582\pi$
$991$	2.57457	−	2.57457i	0.0817840	−	0.0817840i	0.746815	+	0.665031i	$0.231582\pi$
$992$	−2.17364	−	2.17364i	−0.0690131	−	0.0690131i
$993$	−27.6495			−0.877431
$994$	−10.8157	−	10.8157i	−0.343053	−	0.343053i
$995$	−3.10953	−	34.7239i	−0.0985788	−	1.10082i
$996$	1.72185			0.0545589
$997$	−50.8696			−1.61106			−0.805529	−	0.592557i	$-0.798118\pi$
$997$	−50.8696			−1.61106			−0.805529	+	0.592557i	$0.798118\pi$
$998$	−13.5238	+	13.5238i	−0.428090	+	0.428090i
$999$	−5.13684	+	3.25773i	−0.162523	+	0.103070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.b.43.1	✓	40
5.2	odd	4		1110.2.o.b.487.20	yes	40
37.31	odd	4		1110.2.o.b.253.20	yes	40
185.142	even	4	inner	1110.2.l.b.697.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.1	✓	40	1.1	even	1	trivial
1110.2.l.b.697.1	yes	40	185.142	even	4	inner
1110.2.o.b.253.20	yes	40	37.31	odd	4
1110.2.o.b.487.20	yes	40	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.71586 + 1.43381i) q^{5} +(0.707107 + 0.707107i) q^{6} +(3.31235 - 3.31235i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.71586 + 1.43381i) q^{5} +(0.707107 + 0.707107i) q^{6} +(3.31235 - 3.31235i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(1.43381 - 1.71586i) q^{10} -4.55611i q^{11} +(0.707107 - 0.707107i) q^{12} -0.0409247i q^{13} +(-3.31235 - 3.31235i) q^{14} +(-2.22716 + 0.199442i) q^{15} +1.00000 q^{16} -3.39111 q^{17} -1.00000 q^{18} +(-1.42708 + 1.42708i) q^{19} +(-1.71586 - 1.43381i) q^{20} +4.68437i q^{21} -4.55611 q^{22} -6.74310i q^{23} +(-0.707107 - 0.707107i) q^{24} +(0.888377 + 4.92045i) q^{25} -0.0409247 q^{26} +(0.707107 + 0.707107i) q^{27} +(-3.31235 + 3.31235i) q^{28} +(2.73847 + 2.73847i) q^{29} +(0.199442 + 2.22716i) q^{30} +(2.17364 - 2.17364i) q^{31} -1.00000i q^{32} +(3.22166 + 3.22166i) q^{33} +3.39111i q^{34} +(10.4328 - 0.934260i) q^{35} +1.00000i q^{36} +(-1.32873 + 5.93586i) q^{37} +(1.42708 + 1.42708i) q^{38} +(0.0289381 + 0.0289381i) q^{39} +(-1.43381 + 1.71586i) q^{40} -4.17400i q^{41} +4.68437 q^{42} -8.29512i q^{43} +4.55611i q^{44} +(1.43381 - 1.71586i) q^{45} -6.74310 q^{46} +(1.79848 - 1.79848i) q^{47} +(-0.707107 + 0.707107i) q^{48} -14.9433i q^{49} +(4.92045 - 0.888377i) q^{50} +(2.39788 - 2.39788i) q^{51} +0.0409247i q^{52} +(-5.35361 - 5.35361i) q^{53} +(0.707107 - 0.707107i) q^{54} +(6.53260 - 7.81767i) q^{55} +(3.31235 + 3.31235i) q^{56} -2.01820i q^{57} +(2.73847 - 2.73847i) q^{58} +(-7.59479 + 7.59479i) q^{59} +(2.22716 - 0.199442i) q^{60} +(4.71353 - 4.71353i) q^{61} +(-2.17364 - 2.17364i) q^{62} +(-3.31235 - 3.31235i) q^{63} -1.00000 q^{64} +(0.0586782 - 0.0702211i) q^{65} +(3.22166 - 3.22166i) q^{66} +(10.3850 + 10.3850i) q^{67} +3.39111 q^{68} +(4.76809 + 4.76809i) q^{69} +(-0.934260 - 10.4328i) q^{70} +3.26527 q^{71} +1.00000 q^{72} +(3.99226 - 3.99226i) q^{73} +(5.93586 + 1.32873i) q^{74} +(-4.10746 - 2.85110i) q^{75} +(1.42708 - 1.42708i) q^{76} +(-15.0914 - 15.0914i) q^{77} +(0.0289381 - 0.0289381i) q^{78} +(-3.34318 + 3.34318i) q^{79} +(1.71586 + 1.43381i) q^{80} -1.00000 q^{81} -4.17400 q^{82} +(1.21753 + 1.21753i) q^{83} -4.68437i q^{84} +(-5.81869 - 4.86221i) q^{85} -8.29512 q^{86} -3.87278 q^{87} +4.55611 q^{88} +(-9.81417 - 9.81417i) q^{89} +(-1.71586 - 1.43381i) q^{90} +(-0.135557 - 0.135557i) q^{91} +6.74310i q^{92} +3.07399i q^{93} +(-1.79848 - 1.79848i) q^{94} +(-4.49484 + 0.402513i) q^{95} +(0.707107 + 0.707107i) q^{96} +16.9894 q^{97} -14.9433 q^{98} -4.55611 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) \) 40 * q - 40 * q^4 - 4 * q^7	\( 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) \) 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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