LMFDB - Embedded newform 1110.2.l.a.697.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			697.15
Character	$\chi$	$=$	1110.697
Dual form			1110.2.l.a.43.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.17211 + 0.530977i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.93388 - 1.93388i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.17211 + 0.530977i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.93388 - 1.93388i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(0.530977 + 2.17211i) q^{10} -2.54109i q^{11} +(-0.707107 - 0.707107i) q^{12} +2.64021i q^{13} +(-1.93388 + 1.93388i) q^{14} +(-1.91137 - 1.16046i) q^{15} +1.00000 q^{16} +3.60448 q^{17} +1.00000 q^{18} +(2.47157 + 2.47157i) q^{19} +(2.17211 - 0.530977i) q^{20} -2.73491i q^{21} -2.54109 q^{22} +4.49206i q^{23} +(-0.707107 + 0.707107i) q^{24} +(4.43613 - 2.30668i) q^{25} +2.64021 q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.93388 + 1.93388i) q^{28} +(-4.58885 + 4.58885i) q^{29} +(-1.16046 + 1.91137i) q^{30} +(7.33111 + 7.33111i) q^{31} -1.00000i q^{32} +(1.79682 - 1.79682i) q^{33} -3.60448i q^{34} +(5.22744 + 3.17375i) q^{35} -1.00000i q^{36} +(-1.59211 + 5.87071i) q^{37} +(2.47157 - 2.47157i) q^{38} +(-1.86691 + 1.86691i) q^{39} +(-0.530977 - 2.17211i) q^{40} -4.31993i q^{41} -2.73491 q^{42} +3.12360i q^{43} +2.54109i q^{44} +(-0.530977 - 2.17211i) q^{45} +4.49206 q^{46} +(4.51187 + 4.51187i) q^{47} +(0.707107 + 0.707107i) q^{48} +0.479758i q^{49} +(-2.30668 - 4.43613i) q^{50} +(2.54875 + 2.54875i) q^{51} -2.64021i q^{52} +(-0.301411 + 0.301411i) q^{53} +(0.707107 + 0.707107i) q^{54} +(1.34926 + 5.51953i) q^{55} +(1.93388 - 1.93388i) q^{56} +3.49532i q^{57} +(4.58885 + 4.58885i) q^{58} +(0.813625 + 0.813625i) q^{59} +(1.91137 + 1.16046i) q^{60} +(-0.867564 - 0.867564i) q^{61} +(7.33111 - 7.33111i) q^{62} +(1.93388 - 1.93388i) q^{63} -1.00000 q^{64} +(-1.40189 - 5.73482i) q^{65} +(-1.79682 - 1.79682i) q^{66} +(-5.77261 + 5.77261i) q^{67} -3.60448 q^{68} +(-3.17637 + 3.17637i) q^{69} +(3.17375 - 5.22744i) q^{70} -2.30317 q^{71} -1.00000 q^{72} +(3.70992 + 3.70992i) q^{73} +(5.87071 + 1.59211i) q^{74} +(4.76789 + 1.50574i) q^{75} +(-2.47157 - 2.47157i) q^{76} +(-4.91416 + 4.91416i) q^{77} +(1.86691 + 1.86691i) q^{78} +(4.70094 + 4.70094i) q^{79} +(-2.17211 + 0.530977i) q^{80} -1.00000 q^{81} -4.31993 q^{82} +(-0.524568 + 0.524568i) q^{83} +2.73491i q^{84} +(-7.82932 + 1.91389i) q^{85} +3.12360 q^{86} -6.48962 q^{87} +2.54109 q^{88} +(-6.69075 + 6.69075i) q^{89} +(-2.17211 + 0.530977i) q^{90} +(5.10583 - 5.10583i) q^{91} -4.49206i q^{92} +10.3677i q^{93} +(4.51187 - 4.51187i) q^{94} +(-6.68086 - 4.05617i) q^{95} +(0.707107 - 0.707107i) q^{96} +17.0294 q^{97} +0.479758 q^{98} +2.54109 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) $ 36 * q - 36 * q^4 + 4 * q^7	$ 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	−2.17211	+	0.530977i	−0.971397	+	0.237460i
$5$	−2.17211	+	0.530977i	−0.971397	+	0.237460i
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	−1.93388	−	1.93388i	−0.730937	−	0.730937i	0.239869	−	0.970805i	$-0.422896\pi$
$7$	−1.93388	−	1.93388i	−0.730937	−	0.730937i	−0.970805	+	0.239869i	$0.922896\pi$
$8$			1.00000i			0.353553i
$9$			1.00000i			0.333333i
$10$	0.530977	+	2.17211i	0.167910	+	0.686882i
$11$		−	2.54109i		−	0.766168i	−0.923714	−	0.383084i	$-0.874862\pi$
$11$		−	2.54109i		−	0.766168i	0.923714	−	0.383084i	$-0.125138\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$			2.64021i			0.732261i	0.930563	+	0.366131i	$0.119318\pi$
$13$			2.64021i			0.732261i	−0.930563	+	0.366131i	$0.880682\pi$
$14$	−1.93388	+	1.93388i	−0.516850	+	0.516850i
$15$	−1.91137	−	1.16046i	−0.493514	−	0.299629i
$16$	1.00000			0.250000
$17$	3.60448			0.874214			0.437107	−	0.899410i	$-0.356003\pi$
$17$	3.60448			0.874214			0.437107	+	0.899410i	$0.356003\pi$
$18$	1.00000			0.235702
$19$	2.47157	+	2.47157i	0.567017	+	0.567017i	0.931291	−	0.364275i	$-0.118683\pi$
$19$	2.47157	+	2.47157i	0.567017	+	0.567017i	−0.364275	+	0.931291i	$0.618683\pi$
$20$	2.17211	−	0.530977i	0.485699	−	0.118730i
$21$		−	2.73491i		−	0.596807i
$22$	−2.54109			−0.541763
$23$			4.49206i			0.936659i	0.883554	+	0.468329i	$0.155144\pi$
$23$			4.49206i			0.936659i	−0.883554	+	0.468329i	$0.844856\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	4.43613	−	2.30668i	0.887225	−	0.461336i
$26$	2.64021			0.517787
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.93388	+	1.93388i	0.365468	+	0.365468i
$29$	−4.58885	+	4.58885i	−0.852129	+	0.852129i	−0.990395	−	0.138266i	$-0.955847\pi$
$29$	−4.58885	+	4.58885i	−0.852129	+	0.852129i	0.138266	+	0.990395i	$0.455847\pi$
$30$	−1.16046	+	1.91137i	−0.211869	+	0.348967i
$31$	7.33111	+	7.33111i	1.31671	+	1.31671i	0.916368	+	0.400338i	$0.131107\pi$
$31$	7.33111	+	7.33111i	1.31671	+	1.31671i	0.400338	+	0.916368i	$0.368893\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.79682	−	1.79682i	0.312787	−	0.312787i
$34$		−	3.60448i		−	0.618163i
$35$	5.22744	+	3.17375i	0.883598	+	0.536461i
$36$		−	1.00000i		−	0.166667i
$37$	−1.59211	+	5.87071i	−0.261741	+	0.965138i
$37$	−1.59211	+	5.87071i	−0.261741	+	0.965138i
$38$	2.47157	−	2.47157i	0.400941	−	0.400941i
$39$	−1.86691	+	1.86691i	−0.298944	+	0.298944i
$40$	−0.530977	−	2.17211i	−0.0839549	−	0.343441i
$41$		−	4.31993i		−	0.674660i	−0.941387	−	0.337330i	$-0.890476\pi$
$41$		−	4.31993i		−	0.674660i	0.941387	−	0.337330i	$-0.109524\pi$
$42$	−2.73491			−0.422006
$43$			3.12360i			0.476344i	0.971223	+	0.238172i	$0.0765483\pi$
$43$			3.12360i			0.476344i	−0.971223	+	0.238172i	$0.923452\pi$
$44$			2.54109i			0.383084i
$45$	−0.530977	−	2.17211i	−0.0791534	−	0.323799i
$46$	4.49206			0.662318
$47$	4.51187	+	4.51187i	0.658123	+	0.658123i	0.954936	−	0.296812i	$-0.0959236\pi$
$47$	4.51187	+	4.51187i	0.658123	+	0.658123i	−0.296812	+	0.954936i	$0.595924\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$			0.479758i			0.0685368i
$50$	−2.30668	−	4.43613i	−0.326214	−	0.627363i
$51$	2.54875	+	2.54875i	0.356896	+	0.356896i
$52$		−	2.64021i		−	0.366131i
$53$	−0.301411	+	0.301411i	−0.0414020	+	0.0414020i	−0.727505	−	0.686103i	$-0.759320\pi$
$53$	−0.301411	+	0.301411i	−0.0414020	+	0.0414020i	0.686103	+	0.727505i	$0.259320\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	1.34926	+	5.51953i	0.181934	+	0.744253i
$56$	1.93388	−	1.93388i	0.258425	−	0.258425i
$57$			3.49532i			0.462967i
$58$	4.58885	+	4.58885i	0.602546	+	0.602546i
$59$	0.813625	+	0.813625i	0.105925	+	0.105925i	0.758083	−	0.652158i	$-0.226136\pi$
$59$	0.813625	+	0.813625i	0.105925	+	0.105925i	−0.652158	+	0.758083i	$0.726136\pi$
$60$	1.91137	+	1.16046i	0.246757	+	0.149814i
$61$	−0.867564	−	0.867564i	−0.111080	−	0.111080i	0.649382	−	0.760462i	$-0.275028\pi$
$61$	−0.867564	−	0.867564i	−0.111080	−	0.111080i	−0.760462	+	0.649382i	$0.775028\pi$
$62$	7.33111	−	7.33111i	0.931051	−	0.931051i
$63$	1.93388	−	1.93388i	0.243646	−	0.243646i
$64$	−1.00000			−0.125000
$65$	−1.40189	−	5.73482i	−0.173883	−	0.711317i
$66$	−1.79682	−	1.79682i	−0.221174	−	0.221174i
$67$	−5.77261	+	5.77261i	−0.705237	+	0.705237i	−0.965530	−	0.260293i	$-0.916181\pi$
$67$	−5.77261	+	5.77261i	−0.705237	+	0.705237i	0.260293	+	0.965530i	$0.416181\pi$
$68$	−3.60448			−0.437107
$69$	−3.17637	+	3.17637i	−0.382389	+	0.382389i
$70$	3.17375	−	5.22744i	0.379336	−	0.624798i
$71$	−2.30317			−0.273336			−0.136668	−	0.990617i	$-0.543639\pi$
$71$	−2.30317			−0.273336			−0.136668	+	0.990617i	$0.543639\pi$
$72$	−1.00000			−0.117851
$73$	3.70992	+	3.70992i	0.434213	+	0.434213i	0.890059	−	0.455846i	$-0.150663\pi$
$73$	3.70992	+	3.70992i	0.434213	+	0.434213i	−0.455846	+	0.890059i	$0.650663\pi$
$74$	5.87071	+	1.59211i	0.682456	+	0.185079i
$75$	4.76789	+	1.50574i	0.550548	+	0.173868i
$76$	−2.47157	−	2.47157i	−0.283508	−	0.283508i
$77$	−4.91416	+	4.91416i	−0.560020	+	0.560020i
$78$	1.86691	+	1.86691i	0.211386	+	0.211386i
$79$	4.70094	+	4.70094i	0.528897	+	0.528897i	0.920243	−	0.391347i	$-0.127991\pi$
$79$	4.70094	+	4.70094i	0.528897	+	0.528897i	−0.391347	+	0.920243i	$0.627991\pi$
$80$	−2.17211	+	0.530977i	−0.242849	+	0.0593651i
$81$	−1.00000			−0.111111
$82$	−4.31993			−0.477056
$83$	−0.524568	+	0.524568i	−0.0575788	+	0.0575788i	−0.735310	−	0.677731i	$-0.762963\pi$
$83$	−0.524568	+	0.524568i	−0.0575788	+	0.0575788i	0.677731	+	0.735310i	$0.262963\pi$
$84$			2.73491i			0.298404i
$85$	−7.82932	+	1.91389i	−0.849209	+	0.207591i
$86$	3.12360			0.336826
$87$	−6.48962			−0.695760
$88$	2.54109			0.270881
$89$	−6.69075	+	6.69075i	−0.709218	+	0.709218i	−0.966371	−	0.257153i	$-0.917216\pi$
$89$	−6.69075	+	6.69075i	−0.709218	+	0.709218i	0.257153	+	0.966371i	$0.417216\pi$
$90$	−2.17211	+	0.530977i	−0.228961	+	0.0559699i
$91$	5.10583	−	5.10583i	0.535237	−	0.535237i
$92$		−	4.49206i		−	0.468329i
$93$			10.3677i			1.07509i
$94$	4.51187	−	4.51187i	0.465363	−	0.465363i
$95$	−6.68086	−	4.05617i	−0.685442	−	0.416154i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	17.0294			1.72908			0.864539	−	0.502565i	$-0.167610\pi$
$97$	17.0294			1.72908			0.864539	+	0.502565i	$0.167610\pi$
$98$	0.479758			0.0484628
$99$	2.54109			0.255389
$100$	−4.43613	+	2.30668i	−0.443613	+	0.230668i
$101$		−	18.0572i		−	1.79675i	−0.439225	−	0.898377i	$-0.644747\pi$
$101$		−	18.0572i		−	1.79675i	0.439225	−	0.898377i	$-0.355253\pi$
$102$	2.54875	−	2.54875i	0.252364	−	0.252364i
$103$	−2.66961			−0.263044			−0.131522	−	0.991313i	$-0.541986\pi$
$103$	−2.66961			−0.263044			−0.131522	+	0.991313i	$0.541986\pi$
$104$	−2.64021			−0.258894
$105$	1.45218	+	5.94054i	0.141718	+	0.579737i
$106$	0.301411	+	0.301411i	0.0292757	+	0.0292757i
$107$	−0.404456	−	0.404456i	−0.0391002	−	0.0391002i	0.687286	−	0.726387i	$-0.258802\pi$
$107$	−0.404456	−	0.404456i	−0.0391002	−	0.0391002i	−0.726387	+	0.687286i	$0.758802\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	1.04982	+	1.04982i	0.100554	+	0.100554i	0.755594	−	0.655040i	$-0.227348\pi$
$109$	1.04982	+	1.04982i	0.100554	+	0.100554i	−0.655040	+	0.755594i	$0.727348\pi$
$110$	5.51953	−	1.34926i	0.526267	−	0.128647i
$111$	−5.27701	+	3.02543i	−0.500871	+	0.287161i
$112$	−1.93388	−	1.93388i	−0.182734	−	0.182734i
$113$	−5.71763			−0.537869			−0.268935	−	0.963158i	$-0.586672\pi$
$113$	−5.71763			−0.537869			−0.268935	+	0.963158i	$0.586672\pi$
$114$	3.49532			0.327367
$115$	−2.38518	−	9.75725i	−0.222419	−	0.909868i
$116$	4.58885	−	4.58885i	0.426064	−	0.426064i
$117$	−2.64021			−0.244087
$118$	0.813625	−	0.813625i	0.0749002	−	0.0749002i
$119$	−6.97061	−	6.97061i	−0.638995	−	0.638995i
$120$	1.16046	−	1.91137i	0.105935	−	0.174484i
$121$	4.54285			0.412987
$122$	−0.867564	+	0.867564i	−0.0785456	+	0.0785456i
$123$	3.05465	−	3.05465i	0.275429	−	0.275429i
$124$	−7.33111	−	7.33111i	−0.658353	−	0.658353i
$125$	−8.41096	+	7.36585i	−0.752299	+	0.658822i
$126$	−1.93388	−	1.93388i	−0.172283	−	0.172283i
$127$	3.15767	+	3.15767i	0.280198	+	0.280198i	0.833188	−	0.552990i	$-0.186513\pi$
$127$	3.15767	+	3.15767i	0.280198	+	0.280198i	−0.552990	+	0.833188i	$0.686513\pi$
$128$			1.00000i			0.0883883i
$129$	−2.20872	+	2.20872i	−0.194467	+	0.194467i
$130$	−5.73482	+	1.40189i	−0.502977	+	0.122954i
$131$	−12.5592	−	12.5592i	−1.09730	−	1.09730i	−0.994725	−	0.102577i	$-0.967291\pi$
$131$	−12.5592	−	12.5592i	−1.09730	−	1.09730i	−0.102577	−	0.994725i	$-0.532709\pi$
$132$	−1.79682	+	1.79682i	−0.156393	+	0.156393i
$133$		−	9.55941i		−	0.828906i
$134$	5.77261	+	5.77261i	0.498678	+	0.498678i
$135$	1.16046	−	1.91137i	0.0998762	−	0.164505i
$136$			3.60448i			0.309081i
$137$	−12.7858	−	12.7858i	−1.09236	−	1.09236i	−0.995276	−	0.0970857i	$-0.969048\pi$
$137$	−12.7858	−	12.7858i	−1.09236	−	1.09236i	−0.0970857	−	0.995276i	$-0.530952\pi$
$138$	3.17637	+	3.17637i	0.270390	+	0.270390i
$139$	3.82368			0.324321			0.162160	−	0.986764i	$-0.448154\pi$
$139$	3.82368			0.324321			0.162160	+	0.986764i	$0.448154\pi$
$140$	−5.22744	−	3.17375i	−0.441799	−	0.268231i
$141$			6.38074i			0.537355i
$142$			2.30317i			0.193278i
$143$	6.70901			0.561035
$144$			1.00000i			0.0833333i
$145$	7.53092	−	12.4041i	0.625409	−	1.03010i
$146$	3.70992	−	3.70992i	0.307035	−	0.307035i
$147$	−0.339240	+	0.339240i	−0.0279800	+	0.0279800i
$148$	1.59211	−	5.87071i	0.130870	−	0.482569i
$149$			4.92924i			0.403819i	0.979404	+	0.201909i	$0.0647147\pi$
$149$			4.92924i			0.403819i	−0.979404	+	0.201909i	$0.935285\pi$
$150$	1.50574	−	4.76789i	0.122943	−	0.389296i
$151$			2.56917i			0.209076i	0.994521	+	0.104538i	$0.0333363\pi$
$151$			2.56917i			0.209076i	−0.994521	+	0.104538i	$0.966664\pi$
$152$	−2.47157	+	2.47157i	−0.200471	+	0.200471i
$153$			3.60448i			0.291405i
$154$	4.91416	+	4.91416i	0.395994	+	0.395994i
$155$	−19.8166	−	12.0313i	−1.59171	−	0.966379i
$156$	1.86691	−	1.86691i	0.149472	−	0.149472i
$157$	10.7956	+	10.7956i	0.861586	+	0.861586i	0.991522	−	0.129937i	$-0.0414774\pi$
$157$	10.7956	+	10.7956i	0.861586	+	0.861586i	−0.129937	+	0.991522i	$0.541477\pi$
$158$	4.70094	−	4.70094i	0.373986	−	0.373986i
$159$	−0.426260			−0.0338046
$160$	0.530977	+	2.17211i	0.0419774	+	0.171720i
$161$	8.68709	−	8.68709i	0.684638	−	0.684638i
$162$			1.00000i			0.0785674i
$163$	2.00094			0.156726			0.0783628	−	0.996925i	$-0.475031\pi$
$163$	2.00094			0.156726			0.0783628	+	0.996925i	$0.475031\pi$
$164$			4.31993i			0.337330i
$165$	−2.94883	+	4.85697i	−0.229566	+	0.378115i
$166$	0.524568	+	0.524568i	0.0407144	+	0.0407144i
$167$	3.34903			0.259156			0.129578	−	0.991569i	$-0.458638\pi$
$167$	3.34903			0.259156			0.129578	+	0.991569i	$0.458638\pi$
$168$	2.73491			0.211003
$169$	6.02931			0.463793
$170$	1.91389	+	7.82932i	0.146789	+	0.600481i
$171$	−2.47157	+	2.47157i	−0.189006	+	0.189006i
$172$		−	3.12360i		−	0.238172i
$173$	−7.11846	−	7.11846i	−0.541206	−	0.541206i	0.382676	−	0.923882i	$-0.375002\pi$
$173$	−7.11846	−	7.11846i	−0.541206	−	0.541206i	−0.923882	+	0.382676i	$0.875002\pi$
$174$			6.48962i			0.491977i
$175$	−13.0398	−	4.11808i	−0.985713	−	0.311298i
$176$		−	2.54109i		−	0.191542i
$177$			1.15064i			0.0864873i
$178$	6.69075	+	6.69075i	0.501493	+	0.501493i
$179$	8.68094	−	8.68094i	0.648844	−	0.648844i	−0.303869	−	0.952714i	$-0.598279\pi$
$179$	8.68094	−	8.68094i	0.648844	−	0.648844i	0.952714	+	0.303869i	$0.0982787\pi$
$180$	0.530977	+	2.17211i	0.0395767	+	0.161900i
$181$	14.0432			1.04382			0.521912	−	0.852999i	$-0.325219\pi$
$181$	14.0432			1.04382			0.521912	+	0.852999i	$0.325219\pi$
$182$	−5.10583	−	5.10583i	−0.378470	−	0.378470i
$183$		−	1.22692i		−	0.0906966i
$184$	−4.49206			−0.331159
$185$	0.341020	−	13.5972i	0.0250723	−	0.999686i
$186$	10.3677			0.760200
$187$		−	9.15930i		−	0.669795i
$188$	−4.51187	−	4.51187i	−0.329062	−	0.329062i
$189$	2.73491			0.198936
$190$	−4.05617	+	6.68086i	−0.294266	+	0.484681i
$191$	−1.64289	+	1.64289i	−0.118876	+	0.118876i	−0.764042	−	0.645166i	$-0.776788\pi$
$191$	−1.64289	+	1.64289i	−0.118876	+	0.118876i	0.645166	+	0.764042i	$0.276788\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$			13.9313i			1.00280i	0.865217	+	0.501398i	$0.167181\pi$
$193$			13.9313i			1.00280i	−0.865217	+	0.501398i	$0.832819\pi$
$194$		−	17.0294i		−	1.22264i
$195$	3.06384	−	5.04642i	0.219406	−	0.361381i
$196$		−	0.479758i		−	0.0342684i
$197$	18.7947	+	18.7947i	1.33907	+	1.33907i	0.896962	+	0.442107i	$0.145769\pi$
$197$	18.7947	+	18.7947i	1.33907	+	1.33907i	0.442107	+	0.896962i	$0.354231\pi$
$198$		−	2.54109i		−	0.180588i
$199$	−3.23872	+	3.23872i	−0.229587	+	0.229587i	−0.812520	−	0.582933i	$-0.801905\pi$
$199$	−3.23872	+	3.23872i	−0.229587	+	0.229587i	0.582933	+	0.812520i	$0.301905\pi$
$200$	2.30668	+	4.43613i	0.163107	+	0.313681i
$201$	−8.16371			−0.575824
$202$	−18.0572			−1.27050
$203$	17.7486			1.24570
$204$	−2.54875	−	2.54875i	−0.178448	−	0.178448i
$205$	2.29378	+	9.38336i	0.160205	+	0.655362i
$206$			2.66961i			0.186000i
$207$	−4.49206			−0.312220
$208$			2.64021i			0.183065i
$209$	6.28048	−	6.28048i	0.434430	−	0.434430i
$210$	5.94054	−	1.45218i	0.409936	−	0.100210i
$211$	−13.4040			−0.922767			−0.461384	−	0.887201i	$-0.652647\pi$
$211$	−13.4040			−0.922767			−0.461384	+	0.887201i	$0.652647\pi$
$212$	0.301411	−	0.301411i	0.0207010	−	0.0207010i
$213$	−1.62859	−	1.62859i	−0.111589	−	0.111589i
$214$	−0.404456	+	0.404456i	−0.0276480	+	0.0276480i
$215$	−1.65856	−	6.78480i	−0.113113	−	0.462720i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$		−	28.3549i		−	1.92486i
$218$	1.04982	−	1.04982i	0.0711026	−	0.0711026i
$219$			5.24662i			0.354534i
$220$	−1.34926	−	5.51953i	−0.0909672	−	0.372127i
$221$			9.51656i			0.640153i
$222$	3.02543	+	5.27701i	0.203053	+	0.354169i
$223$	−18.2552	+	18.2552i	−1.22246	+	1.22246i	−0.255707	+	0.966754i	$0.582308\pi$
$223$	−18.2552	+	18.2552i	−1.22246	+	1.22246i	−0.966754	+	0.255707i	$0.917692\pi$
$224$	−1.93388	+	1.93388i	−0.129213	+	0.129213i
$225$	2.30668	+	4.43613i	0.153779	+	0.295742i
$226$			5.71763i			0.380331i
$227$	−20.3161			−1.34843			−0.674215	−	0.738535i	$-0.735518\pi$
$227$	−20.3161			−1.34843			−0.674215	+	0.738535i	$0.735518\pi$
$228$		−	3.49532i		−	0.231484i
$229$		−	23.8741i		−	1.57764i	−0.614623	−	0.788821i	$-0.710692\pi$
$229$		−	23.8741i		−	1.57764i	0.614623	−	0.788821i	$-0.289308\pi$
$230$	−9.75725	+	2.38518i	−0.643374	+	0.157274i
$231$	−6.94967			−0.457255
$232$	−4.58885	−	4.58885i	−0.301273	−	0.301273i
$233$	0.0502450	+	0.0502450i	0.00329166	+	0.00329166i	0.708751	−	0.705459i	$-0.249259\pi$
$233$	0.0502450	+	0.0502450i	0.00329166	+	0.00329166i	−0.705459	+	0.708751i	$0.749259\pi$
$234$			2.64021i			0.172596i
$235$	−12.1960	−	7.40457i	−0.795577	−	0.483021i
$236$	−0.813625	−	0.813625i	−0.0529625	−	0.0529625i
$237$			6.64813i			0.431842i
$238$	−6.97061	+	6.97061i	−0.451838	+	0.451838i
$239$	11.3273	+	11.3273i	0.732705	+	0.732705i	0.971155	−	0.238450i	$-0.0766394\pi$
$239$	11.3273	+	11.3273i	0.732705	+	0.732705i	−0.238450	+	0.971155i	$0.576639\pi$
$240$	−1.91137	−	1.16046i	−0.123379	−	0.0749071i
$241$	−3.69272	+	3.69272i	−0.237869	+	0.237869i	−0.815967	−	0.578098i	$-0.803795\pi$
$241$	−3.69272	+	3.69272i	−0.237869	+	0.237869i	0.578098	+	0.815967i	$0.303795\pi$
$242$		−	4.54285i		−	0.292026i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	0.867564	+	0.867564i	0.0555401	+	0.0555401i
$245$	−0.254740	−	1.04209i	−0.0162748	−	0.0665765i
$246$	−3.05465	−	3.05465i	−0.194757	−	0.194757i
$247$	−6.52545	+	6.52545i	−0.415204	+	0.415204i
$248$	−7.33111	+	7.33111i	−0.465526	+	0.465526i
$249$	−0.741852			−0.0470129
$250$	7.36585	+	8.41096i	0.465857	+	0.531956i
$251$	−8.29215	−	8.29215i	−0.523396	−	0.523396i	0.395199	−	0.918595i	$-0.370675\pi$
$251$	−8.29215	−	8.29215i	−0.523396	−	0.523396i	−0.918595	+	0.395199i	$0.870675\pi$
$252$	−1.93388	+	1.93388i	−0.121823	+	0.121823i
$253$	11.4147			0.717638
$254$	3.15767	−	3.15767i	0.198130	−	0.198130i
$255$	−6.88949	−	4.18284i	−0.431437	−	0.261939i
$256$	1.00000			0.0625000
$257$	1.06813			0.0666279			0.0333140	−	0.999445i	$-0.489394\pi$
$257$	1.06813			0.0666279			0.0333140	+	0.999445i	$0.489394\pi$
$258$	2.20872	+	2.20872i	0.137509	+	0.137509i
$259$	14.4322	−	8.27428i	0.896771	−	0.514139i
$260$	1.40189	+	5.73482i	0.0869415	+	0.355658i
$261$	−4.58885	−	4.58885i	−0.284043	−	0.284043i
$262$	−12.5592	+	12.5592i	−0.775909	+	0.775909i
$263$	22.2567	+	22.2567i	1.37240	+	1.37240i	0.856867	+	0.515538i	$0.172408\pi$
$263$	22.2567	+	22.2567i	1.37240	+	1.37240i	0.515538	+	0.856867i	$0.327592\pi$
$264$	1.79682	+	1.79682i	0.110587	+	0.110587i
$265$	0.494656	−	0.814742i	0.0303865	−	0.0500492i
$266$	−9.55941			−0.586125
$267$	−9.46214			−0.579074
$268$	5.77261	−	5.77261i	0.352618	−	0.352618i
$269$		−	1.98048i		−	0.120752i	−0.998176	−	0.0603760i	$-0.980770\pi$
$269$		−	1.98048i		−	0.120752i	0.998176	−	0.0603760i	$-0.0192300\pi$
$270$	−1.91137	−	1.16046i	−0.116322	−	0.0706231i
$271$	−20.2119			−1.22779			−0.613894	−	0.789389i	$-0.710398\pi$
$271$	−20.2119			−1.22779			−0.613894	+	0.789389i	$0.710398\pi$
$272$	3.60448			0.218553
$273$	7.22074			0.437019
$274$	−12.7858	+	12.7858i	−0.772416	+	0.772416i
$275$	−5.86149	−	11.2726i	−0.353461	−	0.679763i
$276$	3.17637	−	3.17637i	0.191195	−	0.191195i
$277$		−	26.8225i		−	1.61161i	−0.592181	−	0.805805i	$-0.701733\pi$
$277$		−	26.8225i		−	1.61161i	0.592181	−	0.805805i	$-0.298267\pi$
$278$		−	3.82368i		−	0.229329i
$279$	−7.33111	+	7.33111i	−0.438902	+	0.438902i
$280$	−3.17375	+	5.22744i	−0.189668	+	0.312399i
$281$	11.8287	−	11.8287i	0.705642	−	0.705642i	−0.259974	−	0.965616i	$-0.583714\pi$
$281$	11.8287	−	11.8287i	0.705642	−	0.705642i	0.965616	+	0.259974i	$0.0837140\pi$
$282$	6.38074			0.379968
$283$	−20.4845			−1.21768			−0.608840	−	0.793293i	$-0.708365\pi$
$283$	−20.4845			−1.21768			−0.608840	+	0.793293i	$0.708365\pi$
$284$	2.30317			0.136668
$285$	−1.85594	−	7.59223i	−0.109936	−	0.449725i
$286$		−	6.70901i		−	0.396712i
$287$	−8.35421	+	8.35421i	−0.493133	+	0.493133i
$288$	1.00000			0.0589256
$289$	−4.00775			−0.235750
$290$	−12.4041	−	7.53092i	−0.728392	−	0.442231i
$291$	12.0416	+	12.0416i	0.705893	+	0.705893i
$292$	−3.70992	−	3.70992i	−0.217107	−	0.217107i
$293$	−18.0953	+	18.0953i	−1.05714	+	1.05714i	−0.0588702	+	0.998266i	$0.518750\pi$
$293$	−18.0953	+	18.0953i	−1.05714	+	1.05714i	−0.998266	+	0.0588702i	$0.981250\pi$
$294$	0.339240	+	0.339240i	0.0197849	+	0.0197849i
$295$	−2.19930	−	1.33527i	−0.128048	−	0.0777422i
$296$	−5.87071	−	1.59211i	−0.341228	−	0.0925393i
$297$	1.79682	+	1.79682i	0.104262	+	0.104262i
$298$	4.92924			0.285543
$299$	−11.8600			−0.685879
$300$	−4.76789	−	1.50574i	−0.275274	−	0.0869342i
$301$	6.04066	−	6.04066i	0.348178	−	0.348178i
$302$	2.56917			0.147839
$303$	12.7683	−	12.7683i	0.733522	−	0.733522i
$304$	2.47157	+	2.47157i	0.141754	+	0.141754i
$305$	2.34510	+	1.42379i	0.134280	+	0.0815259i
$306$	3.60448			0.206054
$307$	−22.5634	+	22.5634i	−1.28776	+	1.28776i	−0.351616	+	0.936144i	$0.614368\pi$
$307$	−22.5634	+	22.5634i	−1.28776	+	1.28776i	−0.936144	+	0.351616i	$0.885632\pi$
$308$	4.91416	−	4.91416i	0.280010	−	0.280010i
$309$	−1.88770	−	1.88770i	−0.107387	−	0.107387i
$310$	−12.0313	+	19.8166i	−0.683333	+	1.12551i
$311$	17.2148	+	17.2148i	0.976159	+	0.976159i	0.999722	−	0.0235634i	$-0.00750115\pi$
$311$	17.2148	+	17.2148i	0.976159	+	0.976159i	−0.0235634	+	0.999722i	$0.507501\pi$
$312$	−1.86691	−	1.86691i	−0.105693	−	0.105693i
$313$			30.7702i			1.73923i	0.493729	+	0.869616i	$0.335634\pi$
$313$			30.7702i			1.73923i	−0.493729	+	0.869616i	$0.664366\pi$
$314$	10.7956	−	10.7956i	0.609233	−	0.609233i
$315$	−3.17375	+	5.22744i	−0.178820	+	0.294533i
$316$	−4.70094	−	4.70094i	−0.264448	−	0.264448i
$317$	−12.5932	+	12.5932i	−0.707307	+	0.707307i	−0.965968	−	0.258661i	$-0.916719\pi$
$317$	−12.5932	+	12.5932i	−0.707307	+	0.707307i	0.258661	+	0.965968i	$0.416719\pi$
$318$			0.426260i			0.0239035i
$319$	11.6607	+	11.6607i	0.652874	+	0.652874i
$320$	2.17211	−	0.530977i	0.121425	−	0.0296825i
$321$		−	0.571987i		−	0.0319252i
$322$	−8.68709	−	8.68709i	−0.484112	−	0.484112i
$323$	8.90871	+	8.90871i	0.495694	+	0.495694i
$324$	1.00000			0.0555556
$325$	6.09012	+	11.7123i	0.337819	+	0.649681i
$326$		−	2.00094i		−	0.110822i
$327$			1.48467i			0.0821022i
$328$	4.31993			0.238528
$329$		−	17.4508i		−	0.962093i
$330$	4.85697	+	2.94883i	0.267367	+	0.162327i
$331$	12.4856	−	12.4856i	0.686272	−	0.686272i	−0.275134	−	0.961406i	$-0.588722\pi$
$331$	12.4856	−	12.4856i	0.686272	−	0.686272i	0.961406	+	0.275134i	$0.0887222\pi$
$332$	0.524568	−	0.524568i	0.0287894	−	0.0287894i
$333$	−5.87071	−	1.59211i	−0.321713	−	0.0872469i
$334$		−	3.34903i		−	0.183251i
$335$	9.47363	−	15.6039i	0.517599	−	0.852531i
$336$		−	2.73491i		−	0.149202i
$337$	−2.01004	+	2.01004i	−0.109494	+	0.109494i	−0.759731	−	0.650237i	$-0.774669\pi$
$337$	−2.01004	+	2.01004i	−0.109494	+	0.109494i	0.650237	+	0.759731i	$0.274669\pi$
$338$		−	6.02931i		−	0.327951i
$339$	−4.04297	−	4.04297i	−0.219584	−	0.219584i
$340$	7.82932	−	1.91389i	0.424604	−	0.103796i
$341$	18.6290	−	18.6290i	1.00882	−	1.00882i
$342$	2.47157	+	2.47157i	0.133647	+	0.133647i
$343$	−12.6093	+	12.6093i	−0.680841	+	0.680841i
$344$	−3.12360			−0.168413
$345$	5.21284	−	8.58599i	0.280650	−	0.462254i
$346$	−7.11846	+	7.11846i	−0.382691	+	0.382691i
$347$			15.1173i			0.811539i	0.913975	+	0.405770i	$0.132996\pi$
$347$			15.1173i			0.811539i	−0.913975	+	0.405770i	$0.867004\pi$
$348$	6.48962			0.347880
$349$			13.6893i			0.732771i	0.930463	+	0.366386i	$0.119405\pi$
$349$			13.6893i			0.732771i	−0.930463	+	0.366386i	$0.880595\pi$
$350$	−4.11808	+	13.0398i	−0.220121	+	0.697005i
$351$	−1.86691	−	1.86691i	−0.0996482	−	0.0996482i
$352$	−2.54109			−0.135441
$353$	−31.3775			−1.67006			−0.835029	−	0.550206i	$-0.814549\pi$
$353$	−31.3775			−1.67006			−0.835029	+	0.550206i	$0.814549\pi$
$354$	1.15064			0.0611558
$355$	5.00274	−	1.22293i	0.265518	−	0.0649065i
$356$	6.69075	−	6.69075i	0.354609	−	0.354609i
$357$		−	9.85793i		−	0.521737i
$358$	−8.68094	−	8.68094i	−0.458802	−	0.458802i
$359$		−	32.4157i		−	1.71083i	−0.517941	−	0.855416i	$-0.673301\pi$
$359$		−	32.4157i		−	1.71083i	0.517941	−	0.855416i	$-0.326699\pi$
$360$	2.17211	−	0.530977i	0.114480	−	0.0279850i
$361$		−	6.78271i		−	0.356985i
$362$		−	14.0432i		−	0.738096i
$363$	3.21228	+	3.21228i	0.168601	+	0.168601i
$364$	−5.10583	+	5.10583i	−0.267618	+	0.267618i
$365$	−10.0282	−	6.08847i	−0.524902	−	0.318685i
$366$	−1.22692			−0.0641322
$367$	9.63234	+	9.63234i	0.502804	+	0.502804i	0.912308	−	0.409504i	$-0.134298\pi$
$367$	9.63234	+	9.63234i	0.502804	+	0.502804i	−0.409504	+	0.912308i	$0.634298\pi$
$368$			4.49206i			0.234165i
$369$	4.31993			0.224887
$370$	−13.5972	−	0.341020i	−0.706884	−	0.0177288i
$371$	1.16579			0.0605245
$372$		−	10.3677i		−	0.537543i
$373$	−21.6306	−	21.6306i	−1.11999	−	1.11999i	−0.991742	−	0.128250i	$-0.959064\pi$
$373$	−21.6306	−	21.6306i	−1.11999	−	1.11999i	−0.128250	−	0.991742i	$-0.540936\pi$
$374$	−9.15930			−0.473616
$375$	−11.1559	−	0.739003i	−0.576088	−	0.0381620i
$376$	−4.51187	+	4.51187i	−0.232682	+	0.232682i
$377$	−12.1155	−	12.1155i	−0.623981	−	0.623981i
$378$		−	2.73491i		−	0.140669i
$379$			0.115662i			0.00594116i	0.999996	+	0.00297058i	$0.000945566\pi$
$379$			0.115662i			0.00594116i	−0.999996	+	0.00297058i	$0.999054\pi$
$380$	6.68086	+	4.05617i	0.342721	+	0.208077i
$381$			4.46562i			0.228781i
$382$	1.64289	+	1.64289i	0.0840578	+	0.0840578i
$383$		−	1.75588i		−	0.0897211i	−0.998993	−	0.0448606i	$-0.985716\pi$
$383$		−	1.75588i		−	0.0897211i	0.998993	−	0.0448606i	$-0.0142844\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	8.06479	−	13.2834i	0.411020	−	0.676985i
$386$	13.9313			0.709084
$387$	−3.12360			−0.158781
$388$	−17.0294			−0.864539
$389$	−11.3156	−	11.3156i	−0.573722	−	0.573722i	0.359445	−	0.933166i	$-0.382966\pi$
$389$	−11.3156	−	11.3156i	−0.573722	−	0.573722i	−0.933166	+	0.359445i	$0.882966\pi$
$390$	−5.04642	−	3.06384i	−0.255535	−	0.155144i
$391$			16.1915i			0.818840i
$392$	−0.479758			−0.0242314
$393$		−	17.7614i		−	0.895943i
$394$	18.7947	−	18.7947i	0.946865	−	0.946865i
$395$	−12.7070	−	7.71486i	−0.639361	−	0.388177i
$396$	−2.54109			−0.127695
$397$	10.5898	−	10.5898i	0.531488	−	0.531488i	−0.389527	−	0.921015i	$-0.627361\pi$
$397$	10.5898	−	10.5898i	0.531488	−	0.531488i	0.921015	+	0.389527i	$0.127361\pi$
$398$	3.23872	+	3.23872i	0.162342	+	0.162342i
$399$	6.75953	−	6.75953i	0.338400	−	0.338400i
$400$	4.43613	−	2.30668i	0.221806	−	0.115334i
$401$	6.78291	+	6.78291i	0.338722	+	0.338722i	0.855886	−	0.517164i	$-0.173012\pi$
$401$	6.78291	+	6.78291i	0.338722	+	0.338722i	−0.517164	+	0.855886i	$0.673012\pi$
$402$			8.16371i			0.407169i
$403$	−19.3556	+	19.3556i	−0.964173	+	0.964173i
$404$			18.0572i			0.898377i
$405$	2.17211	−	0.530977i	0.107933	−	0.0263845i
$406$		−	17.7486i		−	0.880846i
$407$	14.9180	+	4.04569i	0.739458	+	0.200537i
$408$	−2.54875	+	2.54875i	−0.126182	+	0.126182i
$409$	12.5316	−	12.5316i	0.619650	−	0.619650i	−0.325792	−	0.945442i	$-0.605631\pi$
$409$	12.5316	−	12.5316i	0.619650	−	0.619650i	0.945442	+	0.325792i	$0.105631\pi$
$410$	9.38336	−	2.29378i	0.463411	−	0.113282i
$411$		−	18.0818i		−	0.891910i
$412$	2.66961			0.131522
$413$		−	3.14690i		−	0.154849i
$414$			4.49206i			0.220773i
$415$	0.860886	−	1.41795i	0.0422592	−	0.0696046i
$416$	2.64021			0.129447
$417$	2.70375	+	2.70375i	0.132403	+	0.132403i
$418$	−6.28048	−	6.28048i	−0.307188	−	0.307188i
$419$			21.4066i			1.04578i	0.852400	+	0.522891i	$0.175146\pi$
$419$			21.4066i			1.04578i	−0.852400	+	0.522891i	$0.824854\pi$
$420$	−1.45218	−	5.94054i	−0.0708590	−	0.289868i
$421$	10.7024	+	10.7024i	0.521601	+	0.521601i	0.918055	−	0.396454i	$-0.129759\pi$
$421$	10.7024	+	10.7024i	0.521601	+	0.521601i	−0.396454	+	0.918055i	$0.629759\pi$
$422$			13.4040i			0.652495i
$423$	−4.51187	+	4.51187i	−0.219374	+	0.219374i
$424$	−0.301411	−	0.301411i	−0.0146378	−	0.0146378i
$425$	15.9899	−	8.31438i	0.775625	−	0.403307i
$426$	−1.62859	+	1.62859i	−0.0789053	+	0.0789053i
$427$			3.35552i			0.162385i
$428$	0.404456	+	0.404456i	0.0195501	+	0.0195501i
$429$	4.74398	+	4.74398i	0.229042	+	0.229042i
$430$	−6.78480	+	1.65856i	−0.327192	+	0.0799829i
$431$	−11.7768	−	11.7768i	−0.567266	−	0.567266i	0.364095	−	0.931362i	$-0.381378\pi$
$431$	−11.7768	−	11.7768i	−0.567266	−	0.567266i	−0.931362	+	0.364095i	$0.881378\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	12.9115	−	12.9115i	0.620487	−	0.620487i	−0.325169	−	0.945656i	$-0.605421\pi$
$433$	12.9115	−	12.9115i	0.620487	−	0.620487i	0.945656	+	0.325169i	$0.105421\pi$
$434$	−28.3549			−1.36108
$435$	14.0962	−	3.44584i	0.675860	−	0.165215i
$436$	−1.04982	−	1.04982i	−0.0502771	−	0.0502771i
$437$	−11.1024	+	11.1024i	−0.531101	+	0.531101i
$438$	5.24662			0.250693
$439$	12.6631	−	12.6631i	0.604375	−	0.604375i	−0.337095	−	0.941471i	$-0.609444\pi$
$439$	12.6631	−	12.6631i	0.604375	−	0.604375i	0.941471	+	0.337095i	$0.109444\pi$
$440$	−5.51953	+	1.34926i	−0.263133	+	0.0643235i
$441$	−0.479758			−0.0228456
$442$	9.51656			0.452657
$443$	19.8789	+	19.8789i	0.944476	+	0.944476i	0.998538	−	0.0540616i	$-0.0172167\pi$
$443$	19.8789	+	19.8789i	0.944476	+	0.944476i	−0.0540616	+	0.998538i	$0.517217\pi$
$444$	5.27701	−	3.02543i	0.250436	−	0.143580i
$445$	10.9804	−	18.0857i	0.520521	−	0.857343i
$446$	18.2552	+	18.2552i	0.864411	+	0.864411i
$447$	−3.48550	+	3.48550i	−0.164858	+	0.164858i
$448$	1.93388	+	1.93388i	0.0913671	+	0.0913671i
$449$	10.2591	+	10.2591i	0.484159	+	0.484159i	0.906457	−	0.422298i	$-0.138776\pi$
$449$	10.2591	+	10.2591i	0.484159	+	0.484159i	−0.422298	+	0.906457i	$0.638776\pi$
$450$	4.43613	−	2.30668i	0.209121	−	0.108738i
$451$	−10.9773			−0.516902
$452$	5.71763			0.268935
$453$	−1.81667	+	1.81667i	−0.0853548	+	0.0853548i
$454$			20.3161i			0.953483i
$455$	−8.37935	+	13.8015i	−0.392830	+	0.647025i
$456$	−3.49532			−0.163684
$457$	−3.03992			−0.142202			−0.0711008	−	0.997469i	$-0.522651\pi$
$457$	−3.03992			−0.142202			−0.0711008	+	0.997469i	$0.522651\pi$
$458$	−23.8741			−1.11556
$459$	−2.54875	+	2.54875i	−0.118965	+	0.118965i
$460$	2.38518	+	9.75725i	0.111210	+	0.454934i
$461$	−2.13391	+	2.13391i	−0.0993859	+	0.0993859i	−0.755051	−	0.655666i	$-0.772388\pi$
$461$	−2.13391	+	2.13391i	−0.0993859	+	0.0993859i	0.655666	+	0.755051i	$0.272388\pi$
$462$			6.94967i			0.323328i
$463$			20.8314i			0.968118i	0.875035	+	0.484059i	$0.160838\pi$
$463$			20.8314i			0.968118i	−0.875035	+	0.484059i	$0.839162\pi$
$464$	−4.58885	+	4.58885i	−0.213032	+	0.213032i
$465$	−5.50504	−	22.5199i	−0.255290	−	1.04434i
$466$	0.0502450	−	0.0502450i	0.00232756	−	0.00232756i
$467$	30.6842			1.41990			0.709949	−	0.704253i	$-0.248718\pi$
$467$	30.6842			1.41990			0.709949	+	0.704253i	$0.248718\pi$
$468$	2.64021			0.122044
$469$	22.3270			1.03097
$470$	−7.40457	+	12.1960i	−0.341547	+	0.562558i
$471$			15.2673i			0.703482i
$472$	−0.813625	+	0.813625i	−0.0374501	+	0.0374501i
$473$	7.93735			0.364960
$474$	6.64813			0.305359
$475$	16.6653	+	5.26306i	0.764657	+	0.241486i
$476$	6.97061	+	6.97061i	0.319497	+	0.319497i
$477$	−0.301411	−	0.301411i	−0.0138007	−	0.0138007i
$478$	11.3273	−	11.3273i	0.518100	−	0.518100i
$479$	−3.72623	−	3.72623i	−0.170256	−	0.170256i	0.616836	−	0.787092i	$-0.288414\pi$
$479$	−3.72623	−	3.72623i	−0.170256	−	0.170256i	−0.787092	+	0.616836i	$0.788414\pi$
$480$	−1.16046	+	1.91137i	−0.0529673	+	0.0872418i
$481$	−15.4999	−	4.20349i	−0.706734	−	0.191663i
$482$	3.69272	+	3.69272i	0.168199	+	0.168199i
$483$	12.2854			0.559005
$484$	−4.54285			−0.206493
$485$	−36.9898	+	9.04225i	−1.67962	+	0.410587i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	19.2486			0.872239			0.436120	−	0.899889i	$-0.356352\pi$
$487$	19.2486			0.872239			0.436120	+	0.899889i	$0.356352\pi$
$488$	0.867564	−	0.867564i	0.0392728	−	0.0392728i
$489$	1.41488	+	1.41488i	0.0639830	+	0.0639830i
$490$	−1.04209	+	0.254740i	−0.0470767	+	0.0115080i
$491$	−7.57274			−0.341753			−0.170877	−	0.985292i	$-0.554660\pi$
$491$	−7.57274			−0.341753			−0.170877	+	0.985292i	$0.554660\pi$
$492$	−3.05465	+	3.05465i	−0.137714	+	0.137714i
$493$	−16.5404	+	16.5404i	−0.744943	+	0.744943i
$494$	6.52545	+	6.52545i	0.293594	+	0.293594i
$495$	−5.51953	+	1.34926i	−0.248084	+	0.0606448i
$496$	7.33111	+	7.33111i	0.329176	+	0.329176i
$497$	4.45405	+	4.45405i	0.199791	+	0.199791i
$498$			0.741852i			0.0332432i
$499$	−8.46141	+	8.46141i	−0.378785	+	0.378785i	−0.870664	−	0.491879i	$-0.836310\pi$
$499$	−8.46141	+	8.46141i	−0.378785	+	0.378785i	0.491879	+	0.870664i	$0.336310\pi$
$500$	8.41096	−	7.36585i	0.376150	−	0.329411i
$501$	2.36812	+	2.36812i	0.105800	+	0.105800i
$502$	−8.29215	+	8.29215i	−0.370097	+	0.370097i
$503$			16.8793i			0.752612i	0.926495	+	0.376306i	$0.122806\pi$
$503$			16.8793i			0.752612i	−0.926495	+	0.376306i	$0.877194\pi$
$504$	1.93388	+	1.93388i	0.0861417	+	0.0861417i
$505$	9.58794	+	39.2221i	0.426658	+	1.74536i
$506$		−	11.4147i		−	0.507447i
$507$	4.26337	+	4.26337i	0.189343	+	0.189343i
$508$	−3.15767	−	3.15767i	−0.140099	−	0.140099i
$509$	24.8021			1.09933			0.549667	−	0.835384i	$-0.314755\pi$
$509$	24.8021			1.09933			0.549667	+	0.835384i	$0.314755\pi$
$510$	−4.18284	+	6.88949i	−0.185219	+	0.305072i
$511$		−	14.3491i		−	0.634765i
$512$		−	1.00000i		−	0.0441942i
$513$	−3.49532			−0.154322
$514$		−	1.06813i		−	0.0471131i
$515$	5.79868	−	1.41750i	0.255520	−	0.0624625i
$516$	2.20872	−	2.20872i	0.0972334	−	0.0972334i
$517$	11.4651	−	11.4651i	0.504233	−	0.504233i
$518$	−8.27428	−	14.4322i	−0.363551	−	0.634113i
$519$		−	10.0670i		−	0.441893i
$520$	5.73482	−	1.40189i	0.251488	−	0.0614769i
$521$		−	25.4431i		−	1.11468i	−0.830283	−	0.557342i	$-0.811821\pi$
$521$		−	25.4431i		−	1.11468i	0.830283	−	0.557342i	$-0.188179\pi$
$522$	−4.58885	+	4.58885i	−0.200849	+	0.200849i
$523$		−	43.8527i		−	1.91755i	−0.284174	−	0.958773i	$-0.591720\pi$
$523$		−	43.8527i		−	1.91755i	0.284174	−	0.958773i	$-0.408280\pi$
$524$	12.5592	+	12.5592i	0.548651	+	0.548651i
$525$	−6.30858	−	12.1324i	−0.275329	−	0.529502i
$526$	22.2567	−	22.2567i	0.970437	−	0.970437i
$527$	26.4248	+	26.4248i	1.15108	+	1.15108i
$528$	1.79682	−	1.79682i	0.0781967	−	0.0781967i
$529$	2.82141			0.122670
$530$	−0.814742	−	0.494656i	−0.0353901	−	0.0214865i
$531$	−0.813625	+	0.813625i	−0.0353083	+	0.0353083i
$532$			9.55941i			0.414453i
$533$	11.4055			0.494027
$534$			9.46214i			0.409467i
$535$	1.09328	+	0.663765i	0.0472666	+	0.0286971i
$536$	−5.77261	−	5.77261i	−0.249339	−	0.249339i
$537$	12.2767			0.529779
$538$	−1.98048			−0.0853845
$539$	1.21911			0.0525107
$540$	−1.16046	+	1.91137i	−0.0499381	+	0.0822523i
$541$	25.4345	−	25.4345i	1.09351	−	1.09351i	0.0983645	−	0.995150i	$-0.468639\pi$
$541$	25.4345	−	25.4345i	1.09351	−	1.09351i	0.995150	−	0.0983645i	$-0.0313611\pi$
$542$			20.2119i			0.868177i
$543$	9.93006	+	9.93006i	0.426140	+	0.426140i
$544$		−	3.60448i		−	0.154541i
$545$	−2.83775	−	1.72289i	−0.121556	−	0.0738005i
$546$		−	7.22074i		−	0.309019i
$547$		−	13.3671i		−	0.571538i	−0.958299	−	0.285769i	$-0.907751\pi$
$547$		−	13.3671i		−	0.571538i	0.958299	−	0.285769i	$-0.0922489\pi$
$548$	12.7858	+	12.7858i	0.546181	+	0.546181i
$549$	0.867564	−	0.867564i	0.0370267	−	0.0370267i
$550$	−11.2726	+	5.86149i	−0.480665	+	0.249935i
$551$	−22.6833			−0.966342
$552$	−3.17637	−	3.17637i	−0.135195	−	0.135195i
$553$		−	18.1821i		−	0.773180i
$554$	−26.8225			−1.13958
$555$	9.85581	−	9.37353i	0.418356	−	0.397884i
$556$	−3.82368			−0.162160
$557$			17.4429i			0.739080i	0.929215	+	0.369540i	$0.120485\pi$
$557$			17.4429i			0.739080i	−0.929215	+	0.369540i	$0.879515\pi$
$558$	7.33111	+	7.33111i	0.310350	+	0.310350i
$559$	−8.24695			−0.348809
$560$	5.22744	+	3.17375i	0.220900	+	0.134115i
$561$	6.47661	−	6.47661i	0.273442	−	0.273442i
$562$	−11.8287	−	11.8287i	−0.498964	−	0.498964i
$563$		−	2.58551i		−	0.108966i	−0.998515	−	0.0544831i	$-0.982649\pi$
$563$		−	2.58551i		−	0.108966i	0.998515	−	0.0544831i	$-0.0173511\pi$
$564$		−	6.38074i		−	0.268678i
$565$	12.4193	−	3.03593i	0.522485	−	0.127723i
$566$			20.4845i			0.861029i
$567$	1.93388	+	1.93388i	0.0812152	+	0.0812152i
$568$		−	2.30317i		−	0.0966389i
$569$	19.1350	−	19.1350i	0.802180	−	0.802180i	−0.181256	−	0.983436i	$-0.558016\pi$
$569$	19.1350	−	19.1350i	0.802180	−	0.802180i	0.983436	+	0.181256i	$0.0580162\pi$
$570$	−7.59223	+	1.85594i	−0.318004	+	0.0777367i
$571$	6.72822			0.281567			0.140784	−	0.990040i	$-0.455038\pi$
$571$	6.72822			0.281567			0.140784	+	0.990040i	$0.455038\pi$
$572$	−6.70901			−0.280518
$573$	−2.32340			−0.0970616
$574$	8.35421	+	8.35421i	0.348698	+	0.348698i
$575$	10.3618	+	19.9273i	0.432115	+	0.831027i
$576$		−	1.00000i		−	0.0416667i
$577$	32.3098			1.34507			0.672537	−	0.740063i	$-0.265204\pi$
$577$	32.3098			1.34507			0.672537	+	0.740063i	$0.265204\pi$
$578$			4.00775i			0.166701i
$579$	−9.85090	+	9.85090i	−0.409390	+	0.409390i
$580$	−7.53092	+	12.4041i	−0.312704	+	0.515051i
$581$	2.02890			0.0841730
$582$	12.0416	−	12.0416i	0.499142	−	0.499142i
$583$	0.765914	+	0.765914i	0.0317209	+	0.0317209i
$584$	−3.70992	+	3.70992i	−0.153518	+	0.153518i
$585$	5.73482	−	1.40189i	0.237106	−	0.0579610i
$586$	18.0953	+	18.0953i	0.747508	+	0.747508i
$587$			13.1138i			0.541266i	0.962683	+	0.270633i	$0.0872330\pi$
$587$			13.1138i			0.541266i	−0.962683	+	0.270633i	$0.912767\pi$
$588$	0.339240	−	0.339240i	0.0139900	−	0.0139900i
$589$			36.2386i			1.49319i
$590$	−1.33527	+	2.19930i	−0.0549721	+	0.0905437i
$591$			26.5798i			1.09335i
$592$	−1.59211	+	5.87071i	−0.0654352	+	0.241285i
$593$	28.5182	−	28.5182i	1.17110	−	1.17110i	0.189155	−	0.981947i	$-0.439425\pi$
$593$	28.5182	−	28.5182i	1.17110	−	1.17110i	0.981947	−	0.189155i	$-0.0605749\pi$
$594$	1.79682	−	1.79682i	0.0737245	−	0.0737245i
$595$	18.8422	+	11.4397i	0.772454	+	0.468982i
$596$		−	4.92924i		−	0.201909i
$597$	−4.58024			−0.187457
$598$			11.8600i			0.484990i
$599$		−	13.3830i		−	0.546815i	−0.961898	−	0.273407i	$-0.911849\pi$
$599$		−	13.3830i		−	0.546815i	0.961898	−	0.273407i	$-0.0881507\pi$
$600$	−1.50574	+	4.76789i	−0.0614717	+	0.194648i
$601$	11.5916			0.472833			0.236417	−	0.971652i	$-0.424027\pi$
$601$	11.5916			0.472833			0.236417	+	0.971652i	$0.424027\pi$
$602$	−6.04066	−	6.04066i	−0.246199	−	0.246199i
$603$	−5.77261	−	5.77261i	−0.235079	−	0.235079i
$604$		−	2.56917i		−	0.104538i
$605$	−9.86758	+	2.41215i	−0.401174	+	0.0980679i
$606$	−12.7683	−	12.7683i	−0.518678	−	0.518678i
$607$		−	34.6374i		−	1.40589i	−0.711246	−	0.702944i	$-0.751869\pi$
$607$		−	34.6374i		−	1.40589i	0.711246	−	0.702944i	$-0.248131\pi$
$608$	2.47157	−	2.47157i	0.100235	−	0.100235i
$609$	12.5501	+	12.5501i	0.508557	+	0.508557i
$610$	1.42379	−	2.34510i	0.0576475	−	0.0949504i
$611$	−11.9123	+	11.9123i	−0.481918	+	0.481918i
$612$		−	3.60448i		−	0.145702i
$613$	−13.5656	−	13.5656i	−0.547908	−	0.547908i	0.377928	−	0.925835i	$-0.376637\pi$
$613$	−13.5656	−	13.5656i	−0.547908	−	0.547908i	−0.925835	+	0.377928i	$0.876637\pi$
$614$	22.5634	+	22.5634i	0.910584	+	0.910584i
$615$	−5.01309	+	8.25699i	−0.202147	+	0.332954i
$616$	−4.91416	−	4.91416i	−0.197997	−	0.197997i
$617$	29.4000	−	29.4000i	1.18360	−	1.18360i	0.204793	−	0.978805i	$-0.434348\pi$
$617$	29.4000	−	29.4000i	1.18360	−	1.18360i	0.978805	−	0.204793i	$-0.0656522\pi$
$618$	−1.88770	+	1.88770i	−0.0759343	+	0.0759343i
$619$	8.71796			0.350404			0.175202	−	0.984532i	$-0.443942\pi$
$619$	8.71796			0.350404			0.175202	+	0.984532i	$0.443942\pi$
$620$	19.8166	+	12.0313i	0.795855	+	0.483189i
$621$	−3.17637	−	3.17637i	−0.127463	−	0.127463i
$622$	17.2148	−	17.2148i	0.690249	−	0.690249i
$623$	25.8782			1.03679
$624$	−1.86691	+	1.86691i	−0.0747361	+	0.0747361i
$625$	14.3584	−	20.4655i	0.574337	−	0.818619i
$626$	30.7702			1.22982
$627$	8.88194			0.354710
$628$	−10.7956	−	10.7956i	−0.430793	−	0.430793i
$629$	−5.73871	+	21.1608i	−0.228817	+	0.843737i
$630$	5.22744	+	3.17375i	0.208266	+	0.126445i
$631$	−20.3687	−	20.3687i	−0.810867	−	0.810867i	0.173897	−	0.984764i	$-0.444364\pi$
$631$	−20.3687	−	20.3687i	−0.810867	−	0.810867i	−0.984764	+	0.173897i	$0.944364\pi$
$632$	−4.70094	+	4.70094i	−0.186993	+	0.186993i
$633$	−9.47804	−	9.47804i	−0.376718	−	0.376718i
$634$	12.5932	+	12.5932i	0.500141	+	0.500141i
$635$	−8.53546	−	5.18216i	−0.338719	−	0.205648i
$636$	0.426260			0.0169023
$637$	−1.26666			−0.0501869
$638$	11.6607	−	11.6607i	0.461651	−	0.461651i
$639$		−	2.30317i		−	0.0911120i
$640$	−0.530977	−	2.17211i	−0.0209887	−	0.0858602i
$641$	19.7213			0.778944			0.389472	−	0.921038i	$-0.372658\pi$
$641$	19.7213			0.778944			0.389472	+	0.921038i	$0.372658\pi$
$642$	−0.571987			−0.0225745
$643$	−30.0934			−1.18677			−0.593384	−	0.804919i	$-0.702209\pi$
$643$	−30.0934			−1.18677			−0.593384	+	0.804919i	$0.702209\pi$
$644$	−8.68709	+	8.68709i	−0.342319	+	0.342319i
$645$	3.62480	−	5.97036i	0.142726	−	0.235083i
$646$	8.90871	−	8.90871i	0.350508	−	0.350508i
$647$			3.58012i			0.140749i	0.997521	+	0.0703746i	$0.0224195\pi$
$647$			3.58012i			0.140749i	−0.997521	+	0.0703746i	$0.977581\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	2.06750	−	2.06750i	0.0811563	−	0.0811563i
$650$	11.7123	−	6.09012i	0.459394	−	0.238874i
$651$	20.0499	−	20.0499i	0.785819	−	0.785819i
$652$	−2.00094			−0.0783628
$653$	21.6461			0.847079			0.423540	−	0.905878i	$-0.360787\pi$
$653$	21.6461			0.847079			0.423540	+	0.905878i	$0.360787\pi$
$654$	1.48467			0.0580550
$655$	33.9486	+	20.6113i	1.32648	+	0.805350i
$656$		−	4.31993i		−	0.168665i
$657$	−3.70992	+	3.70992i	−0.144738	+	0.144738i
$658$	−17.4508			−0.680302
$659$	24.8071			0.966346			0.483173	−	0.875525i	$-0.339484\pi$
$659$	24.8071			0.966346			0.483173	+	0.875525i	$0.339484\pi$
$660$	2.94883	−	4.85697i	0.114783	−	0.189057i
$661$	−7.55751	−	7.55751i	−0.293953	−	0.293953i	0.544687	−	0.838640i	$-0.316649\pi$
$661$	−7.55751	−	7.55751i	−0.293953	−	0.293953i	−0.838640	+	0.544687i	$0.816649\pi$
$662$	−12.4856	−	12.4856i	−0.485267	−	0.485267i
$663$	−6.72922	+	6.72922i	−0.261341	+	0.261341i
$664$	−0.524568	−	0.524568i	−0.0203572	−	0.0203572i
$665$	5.07583	+	20.7641i	0.196832	+	0.805197i
$666$	−1.59211	+	5.87071i	−0.0616929	+	0.227485i
$667$	−20.6134	−	20.6134i	−0.798154	−	0.798154i
$668$	−3.34903			−0.129578
$669$	−25.8168			−0.998135
$670$	−15.6039	−	9.47363i	−0.602830	−	0.365998i
$671$	−2.20456	+	2.20456i	−0.0851061	+	0.0851061i
$672$	−2.73491			−0.105502
$673$	23.8195	−	23.8195i	0.918173	−	0.918173i	−0.0787239	−	0.996896i	$-0.525085\pi$
$673$	23.8195	−	23.8195i	0.918173	−	0.918173i	0.996896	+	0.0787239i	$0.0250846\pi$
$674$	2.01004	+	2.01004i	0.0774237	+	0.0774237i
$675$	−1.50574	+	4.76789i	−0.0579561	+	0.183516i
$676$	−6.02931			−0.231897
$677$	26.5470	−	26.5470i	1.02028	−	1.02028i	0.0204933	−	0.999790i	$-0.493476\pi$
$677$	26.5470	−	26.5470i	1.02028	−	1.02028i	0.999790	−	0.0204933i	$-0.00652367\pi$
$678$	−4.04297	+	4.04297i	−0.155269	+	0.155269i
$679$	−32.9329	−	32.9329i	−1.26385	−	1.26385i
$680$	−1.91389	−	7.82932i	−0.0733945	−	0.300241i
$681$	−14.3657	−	14.3657i	−0.550494	−	0.550494i
$682$	−18.6290	−	18.6290i	−0.713342	−	0.713342i
$683$			26.8136i			1.02599i	0.858390	+	0.512997i	$0.171465\pi$
$683$			26.8136i			1.02599i	−0.858390	+	0.512997i	$0.828535\pi$
$684$	2.47157	−	2.47157i	0.0945028	−	0.0945028i
$685$	34.5610	+	20.9831i	1.32051	+	0.801725i
$686$	12.6093	+	12.6093i	0.481427	+	0.481427i
$687$	16.8815	−	16.8815i	0.644070	−	0.644070i
$688$			3.12360i			0.119086i
$689$	−0.795788	−	0.795788i	−0.0303171	−	0.0303171i
$690$	−8.58599	−	5.21284i	−0.326863	−	0.198449i
$691$			39.2996i			1.49503i	0.664246	+	0.747514i	$0.268753\pi$
$691$			39.2996i			1.49503i	−0.664246	+	0.747514i	$0.731247\pi$
$692$	7.11846	+	7.11846i	0.270603	+	0.270603i
$693$	−4.91416	−	4.91416i	−0.186673	−	0.186673i
$694$	15.1173			0.573845
$695$	−8.30546	+	2.03029i	−0.315044	+	0.0770133i
$696$		−	6.48962i		−	0.245988i
$697$		−	15.5711i		−	0.589797i
$698$	13.6893			0.518148
$699$			0.0710572i			0.00268763i
$700$	13.0398	+	4.11808i	0.492857	+	0.155649i
$701$	−19.5030	+	19.5030i	−0.736617	+	0.736617i	−0.971922	−	0.235305i	$-0.924391\pi$
$701$	−19.5030	+	19.5030i	−0.736617	+	0.736617i	0.235305	+	0.971922i	$0.424391\pi$
$702$	−1.86691	+	1.86691i	−0.0704619	+	0.0704619i
$703$	−18.4448	+	10.5748i	−0.695661	+	0.398838i
$704$			2.54109i			0.0957710i
$705$	−3.38803	−	13.8597i	−0.127601	−	0.521986i
$706$			31.3775i			1.18091i
$707$	−34.9203	+	34.9203i	−1.31331	+	1.31331i
$708$		−	1.15064i		−	0.0432437i
$709$	−8.21814	−	8.21814i	−0.308639	−	0.308639i	0.535743	−	0.844381i	$-0.320032\pi$
$709$	−8.21814	−	8.21814i	−0.308639	−	0.308639i	−0.844381	+	0.535743i	$0.820032\pi$
$710$	−1.22293	−	5.00274i	−0.0458958	−	0.187750i
$711$	−4.70094	+	4.70094i	−0.176299	+	0.176299i
$712$	−6.69075	−	6.69075i	−0.250746	−	0.250746i
$713$	−32.9318	+	32.9318i	−1.23330	+	1.23330i
$714$	−9.85793			−0.368924
$715$	−14.5727	+	3.56233i	−0.544988	+	0.133224i
$716$	−8.68094	+	8.68094i	−0.324422	+	0.324422i
$717$			16.0193i			0.598251i
$718$	−32.4157			−1.20974
$719$		−	9.15541i		−	0.341439i	−0.985320	−	0.170720i	$-0.945391\pi$
$719$		−	9.15541i		−	0.341439i	0.985320	−	0.170720i	$-0.0546092\pi$
$720$	−0.530977	−	2.17211i	−0.0197884	−	0.0809498i
$721$	5.16269	+	5.16269i	0.192269	+	0.192269i
$722$	−6.78271			−0.252426
$723$	−5.22229			−0.194219
$724$	−14.0432			−0.521912
$725$	−9.77171	+	30.9418i	−0.362912	+	1.14915i
$726$	3.21228	−	3.21228i	0.119219	−	0.119219i
$727$		−	32.4114i		−	1.20207i	−0.799222	−	0.601036i	$-0.794755\pi$
$727$		−	32.4114i		−	1.20207i	0.799222	−	0.601036i	$-0.205245\pi$
$728$	5.10583	+	5.10583i	0.189235	+	0.189235i
$729$		−	1.00000i		−	0.0370370i
$730$	−6.08847	+	10.0282i	−0.225344	+	0.371162i
$731$			11.2589i			0.416427i
$732$			1.22692i			0.0453483i
$733$	−35.1555	−	35.1555i	−1.29850	−	1.29850i	−0.929384	−	0.369115i	$-0.879661\pi$
$733$	−35.1555	−	35.1555i	−1.29850	−	1.29850i	−0.369115	−	0.929384i	$-0.620339\pi$
$734$	9.63234	−	9.63234i	0.355536	−	0.355536i
$735$	0.556738	−	0.916995i	0.0205356	−	0.0338239i
$736$	4.49206			0.165579
$737$	14.6687	+	14.6687i	0.540330	+	0.540330i
$738$		−	4.31993i		−	0.159019i
$739$	−11.5902			−0.426351			−0.213176	−	0.977014i	$-0.568381\pi$
$739$	−11.5902			−0.426351			−0.213176	+	0.977014i	$0.568381\pi$
$740$	−0.341020	+	13.5972i	−0.0125361	+	0.499843i
$741$	−9.22838			−0.339013
$742$		−	1.16579i		−	0.0427973i
$743$	−21.4779	−	21.4779i	−0.787949	−	0.787949i	0.193209	−	0.981158i	$-0.438110\pi$
$743$	−21.4779	−	21.4779i	−0.787949	−	0.787949i	−0.981158	+	0.193209i	$0.938110\pi$
$744$	−10.3677			−0.380100
$745$	−2.61731	−	10.7068i	−0.0958909	−	0.392269i
$746$	−21.6306	+	21.6306i	−0.791954	+	0.791954i
$747$	−0.524568	−	0.524568i	−0.0191929	−	0.0191929i
$748$			9.15930i			0.334897i
$749$			1.56433i			0.0571595i
$750$	−0.739003	+	11.1559i	−0.0269846	+	0.407355i
$751$			46.7182i			1.70477i	0.522914	+	0.852385i	$0.324845\pi$
$751$			46.7182i			1.70477i	−0.522914	+	0.852385i	$0.675155\pi$
$752$	4.51187	+	4.51187i	0.164531	+	0.164531i
$753$		−	11.7269i		−	0.427351i
$754$	−12.1155	+	12.1155i	−0.441221	+	0.441221i
$755$	−1.36417	−	5.58051i	−0.0496472	−	0.203096i
$756$	−2.73491			−0.0994679
$757$	−28.5100			−1.03622			−0.518108	−	0.855315i	$-0.673363\pi$
$757$	−28.5100			−1.03622			−0.518108	+	0.855315i	$0.673363\pi$
$758$	0.115662			0.00420103
$759$	8.07143	+	8.07143i	0.292974	+	0.292974i
$760$	4.05617	−	6.68086i	0.147133	−	0.242340i
$761$			19.7514i			0.715988i	0.933724	+	0.357994i	$0.116539\pi$
$761$			19.7514i			0.715988i	−0.933724	+	0.357994i	$0.883461\pi$
$762$	4.46562			0.161772
$763$		−	4.06043i		−	0.146998i
$764$	1.64289	−	1.64289i	0.0594378	−	0.0594378i
$765$	−1.91389	−	7.82932i	−0.0691970	−	0.283070i
$766$	−1.75588			−0.0634424
$767$	−2.14814	+	2.14814i	−0.0775647	+	0.0775647i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−26.6238	+	26.6238i	−0.960078	+	0.960078i	−0.999233	−	0.0391547i	$-0.987533\pi$
$769$	−26.6238	+	26.6238i	−0.960078	+	0.960078i	0.0391547	+	0.999233i	$0.487533\pi$
$770$	−13.2834	−	8.06479i	−0.478700	−	0.290635i
$771$	0.755280	+	0.755280i	0.0272007	+	0.0272007i
$772$		−	13.9313i		−	0.501398i
$773$	−1.41448	+	1.41448i	−0.0508753	+	0.0508753i	−0.732087	−	0.681211i	$-0.761453\pi$
$773$	−1.41448	+	1.41448i	−0.0508753	+	0.0508753i	0.681211	+	0.732087i	$0.261453\pi$
$774$			3.12360i			0.112275i
$775$	49.4322	+	15.6112i	1.77566	+	0.560770i
$776$			17.0294i			0.611322i
$777$	16.0559	+	4.35428i	0.576002	+	0.156209i
$778$	−11.3156	+	11.3156i	−0.405683	+	0.405683i
$779$	10.6770	−	10.6770i	0.382543	−	0.382543i
$780$	−3.06384	+	5.04642i	−0.109703	+	0.180691i
$781$			5.85257i			0.209421i
$782$	16.1915			0.579007
$783$		−	6.48962i		−	0.231920i
$784$			0.479758i			0.0171342i
$785$	−29.1816	−	17.7171i	−1.04153	−	0.632350i
$786$	−17.7614			−0.633527
$787$	22.3671	+	22.3671i	0.797301	+	0.797301i	0.982669	−	0.185368i	$-0.0593479\pi$
$787$	22.3671	+	22.3671i	0.797301	+	0.797301i	−0.185368	+	0.982669i	$0.559348\pi$
$788$	−18.7947	−	18.7947i	−0.669535	−	0.669535i
$789$			31.4757i			1.12056i
$790$	−7.71486	+	12.7070i	−0.274483	+	0.452096i
$791$	11.0572	+	11.0572i	0.393148	+	0.393148i
$792$			2.54109i			0.0902938i
$793$	2.29055	−	2.29055i	0.0813398	−	0.0813398i
$794$	−10.5898	−	10.5898i	−0.375819	−	0.375819i
$795$	0.925884	−	0.226334i	0.0328377	−	0.00802726i
$796$	3.23872	−	3.23872i	0.114793	−	0.114793i
$797$			3.20231i			0.113432i	0.998390	+	0.0567159i	$0.0180629\pi$
$797$			3.20231i			0.113432i	−0.998390	+	0.0567159i	$0.981937\pi$
$798$	−6.75953	−	6.75953i	−0.239285	−	0.239285i
$799$	16.2629	+	16.2629i	0.575341	+	0.575341i
$800$	−2.30668	−	4.43613i	−0.0815535	−	0.156841i
$801$	−6.69075	−	6.69075i	−0.236406	−	0.236406i
$802$	6.78291	−	6.78291i	0.239513	−	0.239513i
$803$	9.42725	−	9.42725i	0.332680	−	0.332680i
$804$	8.16371			0.287912
$805$	−14.2567	+	23.4820i	−0.502481	+	0.827630i
$806$	19.3556	+	19.3556i	0.681773	+	0.681773i
$807$	1.40041	−	1.40041i	0.0492968	−	0.0492968i
$808$	18.0572			0.635249
$809$	6.69579	−	6.69579i	0.235412	−	0.235412i	−0.579535	−	0.814947i	$-0.696766\pi$
$809$	6.69579	−	6.69579i	0.235412	−	0.235412i	0.814947	+	0.579535i	$0.196766\pi$
$810$	−0.530977	−	2.17211i	−0.0186566	−	0.0763202i
$811$	15.8744			0.557425			0.278712	−	0.960375i	$-0.410092\pi$
$811$	15.8744			0.557425			0.278712	+	0.960375i	$0.410092\pi$
$812$	−17.7486			−0.622852
$813$	−14.2920	−	14.2920i	−0.501242	−	0.501242i
$814$	4.04569	−	14.9180i	0.141801	−	0.522876i
$815$	−4.34626	+	1.06245i	−0.152243	+	0.0372161i
$816$	2.54875	+	2.54875i	0.0892241	+	0.0892241i
$817$	−7.72019	+	7.72019i	−0.270095	+	0.270095i
$818$	−12.5316	−	12.5316i	−0.438159	−	0.438159i
$819$	5.10583	+	5.10583i	0.178412	+	0.178412i
$820$	−2.29378	−	9.38336i	−0.0801024	−	0.327681i
$821$	−46.5456			−1.62445			−0.812227	−	0.583342i	$-0.801745\pi$
$821$	−46.5456			−1.62445			−0.812227	+	0.583342i	$0.801745\pi$
$822$	−18.0818			−0.630675
$823$	15.5996	−	15.5996i	0.543767	−	0.543767i	−0.380864	−	0.924631i	$-0.624373\pi$
$823$	15.5996	−	15.5996i	0.543767	−	0.543767i	0.924631	+	0.380864i	$0.124373\pi$
$824$		−	2.66961i		−	0.0930001i
$825$	3.82623	−	12.1156i	0.133212	−	0.421812i
$826$	−3.14690			−0.109495
$827$	−28.5690			−0.993443			−0.496721	−	0.867910i	$-0.665463\pi$
$827$	−28.5690			−0.993443			−0.496721	+	0.867910i	$0.665463\pi$
$828$	4.49206			0.156110
$829$	28.7820	−	28.7820i	0.999640	−	0.999640i	−0.000360408	−	1.00000i	$-0.500115\pi$
$829$	28.7820	−	28.7820i	0.999640	−	0.999640i	1.00000		0.000360408i	$0.000114722\pi$
$830$	−1.41795	−	0.860886i	−0.0492179	−	0.0298818i
$831$	18.9664	−	18.9664i	0.657937	−	0.657937i
$832$		−	2.64021i		−	0.0915327i
$833$			1.72927i			0.0599158i
$834$	2.70375	−	2.70375i	0.0936233	−	0.0936233i
$835$	−7.27446	+	1.77826i	−0.251743	+	0.0615392i
$836$	−6.28048	+	6.28048i	−0.217215	+	0.217215i
$837$	−10.3677			−0.358362
$838$	21.4066			0.739479
$839$	−29.3296			−1.01257			−0.506285	−	0.862366i	$-0.668982\pi$
$839$	−29.3296			−1.01257			−0.506285	+	0.862366i	$0.668982\pi$
$840$	−5.94054	+	1.45218i	−0.204968	+	0.0501049i
$841$		−	13.1152i		−	0.452247i
$842$	10.7024	−	10.7024i	0.368827	−	0.368827i
$843$	16.7283			0.576154
$844$	13.4040			0.461384
$845$	−13.0963	+	3.20143i	−0.450527	+	0.110132i
$846$	4.51187	+	4.51187i	0.155121	+	0.155121i
$847$	−8.78532	−	8.78532i	−0.301867	−	0.301867i
$848$	−0.301411	+	0.301411i	−0.0103505	+	0.0103505i
$849$	−14.4848	−	14.4848i	−0.497115	−	0.497115i
$850$	−8.31438	−	15.9899i	−0.285181	−	0.548449i
$851$	−26.3716	−	7.15184i	−0.904005	−	0.245162i
$852$	1.62859	+	1.62859i	0.0557945	+	0.0557945i
$853$	10.7137			0.366831			0.183416	−	0.983035i	$-0.441285\pi$
$853$	10.7137			0.366831			0.183416	+	0.983035i	$0.441285\pi$
$854$	3.35552			0.114824
$855$	4.05617	−	6.68086i	0.138718	−	0.228481i
$856$	0.404456	−	0.404456i	0.0138240	−	0.0138240i
$857$	31.9152			1.09020			0.545101	−	0.838371i	$-0.316491\pi$
$857$	31.9152			1.09020			0.545101	+	0.838371i	$0.316491\pi$
$858$	4.74398	−	4.74398i	0.161957	−	0.161957i
$859$	−30.9778	−	30.9778i	−1.05695	−	1.05695i	−0.998277	−	0.0586704i	$-0.981314\pi$
$859$	−30.9778	−	30.9778i	−1.05695	−	1.05695i	−0.0586704	−	0.998277i	$-0.518686\pi$
$860$	1.65856	+	6.78480i	0.0565564	+	0.231360i
$861$	−11.8146			−0.402642
$862$	−11.7768	+	11.7768i	−0.401118	+	0.401118i
$863$	29.6917	−	29.6917i	1.01072	−	1.01072i	0.0107769	−	0.999942i	$-0.496570\pi$
$863$	29.6917	−	29.6917i	1.01072	−	1.01072i	0.999942	−	0.0107769i	$-0.00343045\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	19.2418	+	11.6823i	0.654241	+	0.397211i
$866$	−12.9115	−	12.9115i	−0.438751	−	0.438751i
$867$	−2.83391	−	2.83391i	−0.0962446	−	0.0962446i
$868$			28.3549i			0.962428i
$869$	11.9455	−	11.9455i	0.405224	−	0.405224i
$870$	−3.44584	−	14.0962i	−0.116825	−	0.477905i
$871$	−15.2409	−	15.2409i	−0.516418	−	0.516418i
$872$	−1.04982	+	1.04982i	−0.0355513	+	0.0355513i
$873$			17.0294i			0.576360i
$874$	11.1024	+	11.1024i	0.375545	+	0.375545i
$875$	30.5104	+	2.02111i	1.03144	+	0.0683260i
$876$		−	5.24662i		−	0.177267i
$877$	13.3438	+	13.3438i	0.450587	+	0.450587i	0.895549	−	0.444962i	$-0.146783\pi$
$877$	13.3438	+	13.3438i	0.450587	+	0.450587i	−0.444962	+	0.895549i	$0.646783\pi$
$878$	−12.6631	−	12.6631i	−0.427358	−	0.427358i
$879$	−25.5905			−0.863148
$880$	1.34926	+	5.51953i	0.0454836	+	0.186063i
$881$			23.6087i			0.795397i	0.917516	+	0.397699i	$0.130191\pi$
$881$			23.6087i			0.795397i	−0.917516	+	0.397699i	$0.869809\pi$
$882$			0.479758i			0.0161543i
$883$	−15.7413			−0.529737			−0.264868	−	0.964285i	$-0.585329\pi$
$883$	−15.7413			−0.529737			−0.264868	+	0.964285i	$0.585329\pi$
$884$		−	9.51656i		−	0.320077i
$885$	−0.610963	−	2.49932i	−0.0205373	−	0.0840136i
$886$	19.8789	−	19.8789i	0.667845	−	0.667845i
$887$	−14.7609	+	14.7609i	−0.495622	+	0.495622i	−0.910072	−	0.414450i	$-0.863974\pi$
$887$	−14.7609	+	14.7609i	−0.495622	+	0.495622i	0.414450	+	0.910072i	$0.363974\pi$
$888$	−3.02543	−	5.27701i	−0.101527	−	0.177085i
$889$		−	12.2131i		−	0.409614i
$890$	−18.0857	−	10.9804i	−0.606233	−	0.368064i
$891$			2.54109i			0.0851298i
$892$	18.2552	−	18.2552i	0.611231	−	0.611231i
$893$			22.3028i			0.746334i
$894$	3.48550	+	3.48550i	0.116572	+	0.116572i
$895$	−14.2466	+	23.4654i	−0.476211	+	0.784360i
$896$	1.93388	−	1.93388i	0.0646063	−	0.0646063i
$897$	−8.38626	−	8.38626i	−0.280009	−	0.280009i
$898$	10.2591	−	10.2591i	0.342352	−	0.342352i
$899$	−67.2827			−2.24401
$900$	−2.30668	−	4.43613i	−0.0768894	−	0.147871i
$901$	−1.08643	+	1.08643i	−0.0361942	+	0.0361942i
$902$			10.9773i			0.365505i
$903$	8.54278			0.284286
$904$		−	5.71763i		−	0.190165i
$905$	−30.5034	+	7.45663i	−1.01397	+	0.247867i
$906$	1.81667	+	1.81667i	0.0603550	+	0.0603550i
$907$	46.5171			1.54457			0.772287	−	0.635274i	$-0.219113\pi$
$907$	46.5171			1.54457			0.772287	+	0.635274i	$0.219113\pi$
$908$	20.3161			0.674215
$909$	18.0572			0.598918
$910$	13.8015	+	8.37935i	0.457516	+	0.277773i
$911$	−35.8371	+	35.8371i	−1.18734	+	1.18734i	−0.209534	+	0.977801i	$0.567195\pi$
$911$	−35.8371	+	35.8371i	−1.18734	+	1.18734i	−0.977801	+	0.209534i	$0.932805\pi$
$912$			3.49532i			0.115742i
$913$	1.33298	+	1.33298i	0.0441151	+	0.0441151i
$914$			3.03992i			0.100552i
$915$	0.651467	+	2.66501i	0.0215368	+	0.0881025i
$916$			23.8741i			0.788821i
$917$			48.5759i			1.60412i
$918$	2.54875	+	2.54875i	0.0841213	+	0.0841213i
$919$	22.7714	−	22.7714i	0.751160	−	0.751160i	−0.223536	−	0.974696i	$-0.571760\pi$
$919$	22.7714	−	22.7714i	0.751160	−	0.751160i	0.974696	+	0.223536i	$0.0717599\pi$
$920$	9.75725	−	2.38518i	0.321687	−	0.0786371i
$921$	−31.9094			−1.05145
$922$	2.13391	+	2.13391i	0.0702765	+	0.0702765i
$923$		−	6.08085i		−	0.200153i
$924$	6.94967			0.228627
$925$	6.47907	+	29.7157i	0.213030	+	0.977046i
$926$	20.8314			0.684563
$927$		−	2.66961i		−	0.0876814i
$928$	4.58885	+	4.58885i	0.150637	+	0.150637i
$929$	−17.7432			−0.582135			−0.291068	−	0.956702i	$-0.594011\pi$
$929$	−17.7432			−0.582135			−0.291068	+	0.956702i	$0.594011\pi$
$930$	−22.5199	+	5.50504i	−0.738456	+	0.180517i
$931$	−1.18575	+	1.18575i	−0.0388615	+	0.0388615i
$932$	−0.0502450	−	0.0502450i	−0.00164583	−	0.00164583i
$933$			24.3453i			0.797030i
$934$		−	30.6842i		−	1.00402i
$935$	4.86338	+	19.8950i	0.159050	+	0.650637i
$936$		−	2.64021i		−	0.0862978i
$937$	−35.5702	−	35.5702i	−1.16203	−	1.16203i	−0.984031	−	0.177996i	$-0.943039\pi$
$937$	−35.5702	−	35.5702i	−1.16203	−	1.16203i	−0.177996	−	0.984031i	$-0.556961\pi$
$938$		−	22.3270i		−	0.729004i
$939$	−21.7578	+	21.7578i	−0.710038	+	0.710038i
$940$	12.1960	+	7.40457i	0.397789	+	0.241511i
$941$	18.2845			0.596058			0.298029	−	0.954557i	$-0.403671\pi$
$941$	18.2845			0.596058			0.298029	+	0.954557i	$0.403671\pi$
$942$	15.2673			0.497437
$943$	19.4054			0.631926
$944$	0.813625	+	0.813625i	0.0264812	+	0.0264812i
$945$	−5.94054	+	1.45218i	−0.193246	+	0.0472393i
$946$		−	7.93735i		−	0.258066i
$947$	14.1055			0.458368			0.229184	−	0.973383i	$-0.426394\pi$
$947$	14.1055			0.458368			0.229184	+	0.973383i	$0.426394\pi$
$948$		−	6.64813i		−	0.215921i
$949$	−9.79495	+	9.79495i	−0.317958	+	0.317958i
$950$	5.26306	−	16.6653i	0.170756	−	0.540694i
$951$	−17.8095			−0.577514
$952$	6.97061	−	6.97061i	0.225919	−	0.225919i
$953$	−3.58438	−	3.58438i	−0.116109	−	0.116109i	0.646665	−	0.762774i	$-0.276163\pi$
$953$	−3.58438	−	3.58438i	−0.116109	−	0.116109i	−0.762774	+	0.646665i	$0.776163\pi$
$954$	−0.301411	+	0.301411i	−0.00975856	+	0.00975856i
$955$	2.69621	−	4.44089i	0.0872473	−	0.143704i
$956$	−11.3273	−	11.3273i	−0.366352	−	0.366352i
$957$			16.4907i			0.533069i
$958$	−3.72623	+	3.72623i	−0.120389	+	0.120389i
$959$			49.4522i			1.59689i
$960$	1.91137	+	1.16046i	0.0616893	+	0.0374536i
$961$			76.4902i			2.46743i
$962$	−4.20349	+	15.4999i	−0.135526	+	0.499736i
$963$	0.404456	−	0.404456i	0.0130334	−	0.0130334i
$964$	3.69272	−	3.69272i	0.118934	−	0.118934i
$965$	−7.39719	−	30.2603i	−0.238124	−	0.974113i
$966$		−	12.2854i		−	0.395276i
$967$	21.6520			0.696280			0.348140	−	0.937442i	$-0.386813\pi$
$967$	21.6520			0.696280			0.348140	+	0.937442i	$0.386813\pi$
$968$			4.54285i			0.146013i
$969$			12.5988i			0.404732i
$970$	9.04225	+	36.9898i	0.290329	+	1.18767i
$971$	10.5284			0.337872			0.168936	−	0.985627i	$-0.445967\pi$
$971$	10.5284			0.337872			0.168936	+	0.985627i	$0.445967\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	−7.39453	−	7.39453i	−0.237058	−	0.237058i
$974$		−	19.2486i		−	0.616766i
$975$	−3.97547	+	12.5882i	−0.127317	+	0.403145i
$976$	−0.867564	−	0.867564i	−0.0277701	−	0.0277701i
$977$		−	62.4861i		−	1.99911i	−0.0298845	−	0.999553i	$-0.509514\pi$
$977$		−	62.4861i		−	1.99911i	0.0298845	−	0.999553i	$-0.490486\pi$
$978$	1.41488	−	1.41488i	0.0452428	−	0.0452428i
$979$	17.0018	+	17.0018i	0.543380	+	0.543380i
$980$	0.254740	+	1.04209i	0.00813738	+	0.0332882i
$981$	−1.04982	+	1.04982i	−0.0335181	+	0.0335181i
$982$			7.57274i			0.241656i
$983$	−9.77180	−	9.77180i	−0.311672	−	0.311672i	0.533885	−	0.845557i	$-0.320732\pi$
$983$	−9.77180	−	9.77180i	−0.311672	−	0.311672i	−0.845557	+	0.533885i	$0.820732\pi$
$984$	3.05465	+	3.05465i	0.0973787	+	0.0973787i
$985$	−50.8038	−	30.8447i	−1.61874	−	0.982792i
$986$	16.5404	+	16.5404i	0.526754	+	0.526754i
$987$	12.3396	−	12.3396i	0.392773	−	0.392773i
$988$	6.52545	−	6.52545i	0.207602	−	0.207602i
$989$	−14.0314			−0.446172
$990$	1.34926	+	5.51953i	0.0428824	+	0.175422i
$991$	−39.3415	−	39.3415i	−1.24972	−	1.24972i	−0.955842	−	0.293883i	$-0.905053\pi$
$991$	−39.3415	−	39.3415i	−1.24972	−	1.24972i	−0.293883	−	0.955842i	$-0.594947\pi$
$992$	7.33111	−	7.33111i	0.232763	−	0.232763i
$993$	17.6573			0.560339
$994$	4.45405	−	4.45405i	0.141274	−	0.141274i
$995$	5.31516	−	8.75453i	0.168502	−	0.277537i
$996$	0.741852			0.0235065
$997$	3.43255			0.108710			0.0543550	−	0.998522i	$-0.482690\pi$
$997$	3.43255			0.108710			0.0543550	+	0.998522i	$0.482690\pi$
$998$	8.46141	+	8.46141i	0.267841	+	0.267841i
$999$	−3.02543	−	5.27701i	−0.0957203	−	0.166957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.a.697.15	yes	36
5.3	odd	4		1110.2.o.a.253.4	yes	36
37.6	odd	4		1110.2.o.a.487.4	yes	36
185.43	even	4	inner	1110.2.l.a.43.15	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.15	✓	36	185.43	even	4	inner
1110.2.l.a.697.15	yes	36	1.1	even	1	trivial
1110.2.o.a.253.4	yes	36	5.3	odd	4
1110.2.o.a.487.4	yes	36	37.6	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.17211 + 0.530977i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.93388 - 1.93388i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.17211 + 0.530977i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-1.93388 - 1.93388i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(0.530977 + 2.17211i) q^{10} -2.54109i q^{11} +(-0.707107 - 0.707107i) q^{12} +2.64021i q^{13} +(-1.93388 + 1.93388i) q^{14} +(-1.91137 - 1.16046i) q^{15} +1.00000 q^{16} +3.60448 q^{17} +1.00000 q^{18} +(2.47157 + 2.47157i) q^{19} +(2.17211 - 0.530977i) q^{20} -2.73491i q^{21} -2.54109 q^{22} +4.49206i q^{23} +(-0.707107 + 0.707107i) q^{24} +(4.43613 - 2.30668i) q^{25} +2.64021 q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.93388 + 1.93388i) q^{28} +(-4.58885 + 4.58885i) q^{29} +(-1.16046 + 1.91137i) q^{30} +(7.33111 + 7.33111i) q^{31} -1.00000i q^{32} +(1.79682 - 1.79682i) q^{33} -3.60448i q^{34} +(5.22744 + 3.17375i) q^{35} -1.00000i q^{36} +(-1.59211 + 5.87071i) q^{37} +(2.47157 - 2.47157i) q^{38} +(-1.86691 + 1.86691i) q^{39} +(-0.530977 - 2.17211i) q^{40} -4.31993i q^{41} -2.73491 q^{42} +3.12360i q^{43} +2.54109i q^{44} +(-0.530977 - 2.17211i) q^{45} +4.49206 q^{46} +(4.51187 + 4.51187i) q^{47} +(0.707107 + 0.707107i) q^{48} +0.479758i q^{49} +(-2.30668 - 4.43613i) q^{50} +(2.54875 + 2.54875i) q^{51} -2.64021i q^{52} +(-0.301411 + 0.301411i) q^{53} +(0.707107 + 0.707107i) q^{54} +(1.34926 + 5.51953i) q^{55} +(1.93388 - 1.93388i) q^{56} +3.49532i q^{57} +(4.58885 + 4.58885i) q^{58} +(0.813625 + 0.813625i) q^{59} +(1.91137 + 1.16046i) q^{60} +(-0.867564 - 0.867564i) q^{61} +(7.33111 - 7.33111i) q^{62} +(1.93388 - 1.93388i) q^{63} -1.00000 q^{64} +(-1.40189 - 5.73482i) q^{65} +(-1.79682 - 1.79682i) q^{66} +(-5.77261 + 5.77261i) q^{67} -3.60448 q^{68} +(-3.17637 + 3.17637i) q^{69} +(3.17375 - 5.22744i) q^{70} -2.30317 q^{71} -1.00000 q^{72} +(3.70992 + 3.70992i) q^{73} +(5.87071 + 1.59211i) q^{74} +(4.76789 + 1.50574i) q^{75} +(-2.47157 - 2.47157i) q^{76} +(-4.91416 + 4.91416i) q^{77} +(1.86691 + 1.86691i) q^{78} +(4.70094 + 4.70094i) q^{79} +(-2.17211 + 0.530977i) q^{80} -1.00000 q^{81} -4.31993 q^{82} +(-0.524568 + 0.524568i) q^{83} +2.73491i q^{84} +(-7.82932 + 1.91389i) q^{85} +3.12360 q^{86} -6.48962 q^{87} +2.54109 q^{88} +(-6.69075 + 6.69075i) q^{89} +(-2.17211 + 0.530977i) q^{90} +(5.10583 - 5.10583i) q^{91} -4.49206i q^{92} +10.3677i q^{93} +(4.51187 - 4.51187i) q^{94} +(-6.68086 - 4.05617i) q^{95} +(0.707107 - 0.707107i) q^{96} +17.0294 q^{97} +0.479758 q^{98} +2.54109 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) \) 36 * q - 36 * q^4 + 4 * q^7	\( 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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