LMFDB - Embedded newform 1110.2.o.a.487.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			487.4
Character	$\chi$	$=$	1110.487
Dual form			1110.2.o.a.253.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	1.00000			0.500000
$5$	−0.530977	−	2.17211i	−0.237460	−	0.971397i
$5$	−0.530977	−	2.17211i	−0.237460	−	0.971397i
$6$	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	$0.922896\pi$
$8$	−1.00000			−0.353553
$9$			1.00000i			0.333333i
$10$	0.530977	+	2.17211i	0.167910	+	0.686882i
$11$			2.54109i			0.766168i	0.923714	+	0.383084i	$0.125138\pi$
$11$			2.54109i			0.766168i	−0.923714	+	0.383084i	$0.874862\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	−2.64021			−0.732261			−0.366131	−	0.930563i	$-0.619318\pi$
$13$	−2.64021			−0.732261			−0.366131	+	0.930563i	$0.619318\pi$
$14$	1.93388	+	1.93388i	0.516850	+	0.516850i
$15$	−1.16046	+	1.91137i	−0.299629	+	0.493514i
$16$	1.00000			0.250000
$17$			3.60448i			0.874214i	0.899410	+	0.437107i	$0.143997\pi$
$17$			3.60448i			0.874214i	−0.899410	+	0.437107i	$0.856003\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−2.47157	+	2.47157i	−0.567017	+	0.567017i	−0.931291	−	0.364275i	$-0.881317\pi$
$19$	−2.47157	+	2.47157i	−0.567017	+	0.567017i	0.364275	+	0.931291i	$0.381317\pi$
$20$	−0.530977	−	2.17211i	−0.118730	−	0.485699i
$21$			2.73491i			0.596807i
$22$		−	2.54109i		−	0.541763i
$23$	−4.49206			−0.936659			−0.468329	−	0.883554i	$-0.655144\pi$
$23$	−4.49206			−0.936659			−0.468329	+	0.883554i	$0.655144\pi$
$24$	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	$-0.0441530\pi$
$29$	4.58885	+	4.58885i	0.852129	+	0.852129i	−0.138266	+	0.990395i	$0.544153\pi$
$30$	1.16046	−	1.91137i	0.211869	−	0.348967i
$31$	7.33111	−	7.33111i	1.31671	−	1.31671i	0.400338	−	0.916368i	$-0.368893\pi$
$31$	7.33111	−	7.33111i	1.31671	−	1.31671i	0.916368	−	0.400338i	$-0.131107\pi$
$32$	−1.00000			−0.176777
$33$	1.79682	−	1.79682i	0.312787	−	0.312787i
$34$		−	3.60448i		−	0.618163i
$35$	−3.17375	+	5.22744i	−0.536461	+	0.883598i
$36$			1.00000i			0.166667i
$37$	5.87071	−	1.59211i	0.965138	−	0.261741i
$37$	5.87071	−	1.59211i	0.965138	−	0.261741i
$38$	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	$0.109524\pi$
$41$			4.31993i			0.674660i	−0.941387	+	0.337330i	$0.890476\pi$
$42$		−	2.73491i		−	0.422006i
$43$	−3.12360			−0.476344			−0.238172	−	0.971223i	$-0.576548\pi$
$43$	−3.12360			−0.476344			−0.238172	+	0.971223i	$0.576548\pi$
$44$			2.54109i			0.383084i
$45$	2.17211	−	0.530977i	0.323799	−	0.0791534i
$46$	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
$50$	4.43613	−	2.30668i	0.627363	−	0.326214i
$51$	2.54875	−	2.54875i	0.356896	−	0.356896i
$52$	−2.64021			−0.366131
$53$	−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
$55$	5.51953	−	1.34926i	0.744253	−	0.181934i
$56$	1.93388	+	1.93388i	0.258425	+	0.258425i
$57$	3.49532			0.462967
$58$	−4.58885	−	4.58885i	−0.602546	−	0.602546i
$59$	−0.813625	+	0.813625i	−0.105925	+	0.105925i	−0.758083	−	0.652158i	$-0.773864\pi$
$59$	−0.813625	+	0.813625i	−0.105925	+	0.105925i	0.652158	+	0.758083i	$0.273864\pi$
$60$	−1.16046	+	1.91137i	−0.149814	+	0.246757i
$61$	−0.867564	+	0.867564i	−0.111080	+	0.111080i	−0.760462	−	0.649382i	$-0.775028\pi$
$61$	−0.867564	+	0.867564i	−0.111080	+	0.111080i	0.649382	+	0.760462i	$0.275028\pi$
$62$	−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	−0.260293	−	0.965530i	$-0.583819\pi$
$67$	5.77261	−	5.77261i	0.705237	−	0.705237i	0.965530	+	0.260293i	$0.0838191\pi$
$68$			3.60448i			0.437107i
$69$	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	$0.543639\pi$
$72$		−	1.00000i		−	0.117851i
$73$	−3.70992	−	3.70992i	−0.434213	−	0.434213i	0.455846	−	0.890059i	$-0.349337\pi$
$73$	−3.70992	−	3.70992i	−0.434213	−	0.434213i	−0.890059	+	0.455846i	$0.849337\pi$
$74$	−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	$-0.872009\pi$
$79$	−4.70094	+	4.70094i	−0.528897	+	0.528897i	0.391347	+	0.920243i	$0.372009\pi$
$80$	−0.530977	−	2.17211i	−0.0593651	−	0.242849i
$81$	−1.00000			−0.111111
$82$		−	4.31993i		−	0.477056i
$83$	−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
$87$		−	6.48962i		−	0.695760i
$88$		−	2.54109i		−	0.270881i
$89$	6.69075	+	6.69075i	0.709218	+	0.709218i	0.966371	−	0.257153i	$-0.0827844\pi$
$89$	6.69075	+	6.69075i	0.709218	+	0.709218i	−0.257153	+	0.966371i	$0.582784\pi$
$90$	−2.17211	+	0.530977i	−0.228961	+	0.0559699i
$91$	5.10583	+	5.10583i	0.535237	+	0.535237i
$92$	−4.49206			−0.468329
$93$	−10.3677			−1.07509
$94$	−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
$97$			17.0294i			1.72908i	0.502565	+	0.864539i	$0.332390\pi$
$97$			17.0294i			1.72908i	−0.502565	+	0.864539i	$0.667610\pi$
$98$		−	0.479758i		−	0.0484628i
$99$	−2.54109			−0.255389
$100$	−4.43613	+	2.30668i	−0.443613	+	0.230668i
$101$			18.0572i			1.79675i	0.439225	+	0.898377i	$0.355253\pi$
$101$			18.0572i			1.79675i	−0.439225	+	0.898377i	$0.644747\pi$
$102$	−2.54875	+	2.54875i	−0.252364	+	0.252364i
$103$			2.66961i			0.263044i	0.991313	+	0.131522i	$0.0419864\pi$
$103$			2.66961i			0.263044i	−0.991313	+	0.131522i	$0.958014\pi$
$104$	2.64021			0.258894
$105$	5.94054	−	1.45218i	0.579737	−	0.141718i
$106$	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	$-0.772652\pi$
$109$	−1.04982	+	1.04982i	−0.100554	+	0.100554i	0.655040	+	0.755594i	$0.272652\pi$
$110$	−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
$113$			5.71763i			0.537869i	0.963158	+	0.268935i	$0.0866715\pi$
$113$			5.71763i			0.537869i	−0.963158	+	0.268935i	$0.913328\pi$
$114$	−3.49532			−0.327367
$115$	2.38518	+	9.75725i	0.222419	+	0.909868i
$116$	4.58885	+	4.58885i	0.426064	+	0.426064i
$117$		−	2.64021i		−	0.244087i
$118$	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
$125$	7.36585	+	8.41096i	0.658822	+	0.752299i
$126$	−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	$0.686513\pi$
$128$	−1.00000			−0.0883883
$129$	2.20872	+	2.20872i	0.194467	+	0.194467i
$130$	−1.40189	−	5.73482i	−0.122954	−	0.502977i
$131$	−12.5592	+	12.5592i	−1.09730	+	1.09730i	−0.102577	+	0.994725i	$0.532709\pi$
$131$	−12.5592	+	12.5592i	−1.09730	+	1.09730i	−0.994725	+	0.102577i	$0.967291\pi$
$132$	1.79682	−	1.79682i	0.156393	−	0.156393i
$133$	9.55941			0.828906
$134$	−5.77261	+	5.77261i	−0.498678	+	0.498678i
$135$	−1.91137	−	1.16046i	−0.164505	−	0.0998762i
$136$		−	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	$-0.551846\pi$
$139$	−3.82368			−0.324321			−0.162160	+	0.986764i	$0.551846\pi$
$140$	−3.17375	+	5.22744i	−0.268231	+	0.441799i
$141$		−	6.38074i		−	0.537355i
$142$	2.30317			0.193278
$143$		−	6.70901i		−	0.561035i
$144$			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
$148$	5.87071	−	1.59211i	0.482569	−	0.130870i
$149$			4.92924i			0.403819i	0.979404	+	0.201909i	$0.0647147\pi$
$149$			4.92924i			0.403819i	−0.979404	+	0.201909i	$0.935285\pi$
$150$	−4.76789	−	1.50574i	−0.389296	−	0.122943i
$151$		−	2.56917i		−	0.209076i	−0.994521	−	0.104538i	$-0.966664\pi$
$151$		−	2.56917i		−	0.209076i	0.994521	−	0.104538i	$-0.0333363\pi$
$152$	2.47157	−	2.47157i	0.200471	−	0.200471i
$153$	−3.60448			−0.291405
$154$	−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
$162$	1.00000			0.0785674
$163$		−	2.00094i		−	0.156726i	−0.996925	−	0.0783628i	$-0.975031\pi$
$163$		−	2.00094i		−	0.156726i	0.996925	−	0.0783628i	$-0.0249693\pi$
$164$			4.31993i			0.337330i
$165$	−4.85697	−	2.94883i	−0.378115	−	0.229566i
$166$	0.524568	−	0.524568i	0.0407144	−	0.0407144i
$167$			3.34903i			0.259156i	0.991569	+	0.129578i	$0.0413622\pi$
$167$			3.34903i			0.259156i	−0.991569	+	0.129578i	$0.958638\pi$
$168$		−	2.73491i		−	0.211003i
$169$	−6.02931			−0.463793
$170$	−7.82932	+	1.91389i	−0.600481	+	0.146789i
$171$	−2.47157	−	2.47157i	−0.189006	−	0.189006i
$172$	−3.12360			−0.238172
$173$	7.11846	+	7.11846i	0.541206	+	0.541206i	0.923882	−	0.382676i	$-0.124998\pi$
$173$	7.11846	+	7.11846i	0.541206	+	0.541206i	−0.382676	+	0.923882i	$0.624998\pi$
$174$			6.48962i			0.491977i
$175$	13.0398	+	4.11808i	0.985713	+	0.311298i
$176$			2.54109i			0.191542i
$177$	1.15064			0.0864873
$178$	−6.69075	−	6.69075i	−0.501493	−	0.501493i
$179$	−8.68094	−	8.68094i	−0.648844	−	0.648844i	0.303869	−	0.952714i	$-0.401721\pi$
$179$	−8.68094	−	8.68094i	−0.648844	−	0.648844i	−0.952714	+	0.303869i	$0.901721\pi$
$180$	2.17211	−	0.530977i	0.161900	−	0.0395767i
$181$	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
$183$	1.22692			0.0906966
$184$	4.49206			0.331159
$185$	−6.57544	−	11.9064i	−0.483436	−	0.875380i
$186$	10.3677			0.760200
$187$	−9.15930			−0.669795
$188$	4.51187	+	4.51187i	0.329062	+	0.329062i
$189$	−2.73491			−0.198936
$190$	−6.68086	−	4.05617i	−0.484681	−	0.294266i
$191$	−1.64289	−	1.64289i	−0.118876	−	0.118876i	0.645166	−	0.764042i	$-0.276788\pi$
$191$	−1.64289	−	1.64289i	−0.118876	−	0.118876i	−0.764042	+	0.645166i	$0.776788\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−13.9313			−1.00280			−0.501398	−	0.865217i	$-0.667181\pi$
$193$	−13.9313			−1.00280			−0.501398	+	0.865217i	$0.667181\pi$
$194$		−	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	$0.354231\pi$
$198$	2.54109			0.180588
$199$	3.23872	+	3.23872i	0.229587	+	0.229587i	0.812520	−	0.582933i	$-0.198095\pi$
$199$	3.23872	+	3.23872i	0.229587	+	0.229587i	−0.582933	+	0.812520i	$0.698095\pi$
$200$	4.43613	−	2.30668i	0.313681	−	0.163107i
$201$	−8.16371			−0.575824
$202$		−	18.0572i		−	1.27050i
$203$		−	17.7486i		−	1.24570i
$204$	2.54875	−	2.54875i	0.178448	−	0.178448i
$205$	9.38336	−	2.29378i	0.655362	−	0.160205i
$206$		−	2.66961i		−	0.186000i
$207$		−	4.49206i		−	0.312220i
$208$	−2.64021			−0.183065
$209$	−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
$217$	−28.3549			−1.92486
$218$	1.04982	−	1.04982i	0.0711026	−	0.0711026i
$219$			5.24662i			0.354534i
$220$	5.51953	−	1.34926i	0.372127	−	0.0909672i
$221$		−	9.51656i		−	0.640153i
$222$	5.27701	+	3.02543i	0.354169	+	0.203053i
$223$	−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
$227$		−	20.3161i		−	1.34843i	−0.738535	−	0.674215i	$-0.764482\pi$
$227$		−	20.3161i		−	1.34843i	0.738535	−	0.674215i	$-0.235518\pi$
$228$	3.49532			0.231484
$229$		−	23.8741i		−	1.57764i	−0.614623	−	0.788821i	$-0.710692\pi$
$229$		−	23.8741i		−	1.57764i	0.614623	−	0.788821i	$-0.289308\pi$
$230$	−2.38518	−	9.75725i	−0.157274	−	0.643374i
$231$	−6.94967			−0.457255
$232$	−4.58885	−	4.58885i	−0.301273	−	0.301273i
$233$	−0.0502450	−	0.0502450i	−0.00329166	−	0.00329166i	0.705459	−	0.708751i	$-0.250741\pi$
$233$	−0.0502450	−	0.0502450i	−0.00329166	−	0.00329166i	−0.708751	+	0.705459i	$0.750741\pi$
$234$			2.64021i			0.172596i
$235$	7.40457	−	12.1960i	0.483021	−	0.795577i
$236$	−0.813625	+	0.813625i	−0.0529625	+	0.0529625i
$237$	6.64813			0.431842
$238$	−6.97061	+	6.97061i	−0.451838	+	0.451838i
$239$	−11.3273	+	11.3273i	−0.732705	+	0.732705i	−0.971155	−	0.238450i	$-0.923361\pi$
$239$	−11.3273	+	11.3273i	−0.732705	+	0.732705i	0.238450	+	0.971155i	$0.423361\pi$
$240$	−1.16046	+	1.91137i	−0.0749071	+	0.123379i
$241$	−3.69272	−	3.69272i	−0.237869	−	0.237869i	0.578098	−	0.815967i	$-0.303795\pi$
$241$	−3.69272	−	3.69272i	−0.237869	−	0.237869i	−0.815967	+	0.578098i	$0.803795\pi$
$242$	−4.54285			−0.292026
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−0.867564	+	0.867564i	−0.0555401	+	0.0555401i
$245$	1.04209	−	0.254740i	0.0665765	−	0.0162748i
$246$	−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	−0.918595	−	0.395199i	$-0.870675\pi$
$251$	−8.29215	+	8.29215i	−0.523396	+	0.523396i	0.395199	+	0.918595i	$0.370675\pi$
$252$	1.93388	−	1.93388i	0.121823	−	0.121823i
$253$		−	11.4147i		−	0.717638i
$254$	−3.15767	−	3.15767i	−0.198130	−	0.198130i
$255$	−6.88949	−	4.18284i	−0.431437	−	0.261939i
$256$	1.00000			0.0625000
$257$			1.06813i			0.0666279i	0.999445	+	0.0333140i	$0.0106061\pi$
$257$			1.06813i			0.0666279i	−0.999445	+	0.0333140i	$0.989394\pi$
$258$	−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	$-0.827592\pi$
$263$	−22.2567	−	22.2567i	−1.37240	−	1.37240i	−0.515538	−	0.856867i	$-0.672408\pi$
$264$	−1.79682	+	1.79682i	−0.110587	+	0.110587i
$265$	0.814742	+	0.494656i	0.0500492	+	0.0303865i
$266$	−9.55941			−0.586125
$267$		−	9.46214i		−	0.579074i
$268$	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	$0.710398\pi$
$272$			3.60448i			0.218553i
$273$		−	7.22074i		−	0.437019i
$274$	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
$277$	−26.8225			−1.61161			−0.805805	−	0.592181i	$-0.798267\pi$
$277$	−26.8225			−1.61161			−0.805805	+	0.592181i	$0.798267\pi$
$278$	3.82368			0.229329
$279$	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	0.965616	−	0.259974i	$-0.0837140\pi$
$281$	11.8287	+	11.8287i	0.705642	+	0.705642i	−0.259974	+	0.965616i	$0.583714\pi$
$282$			6.38074i			0.379968i
$283$			20.4845i			1.21768i	0.793293	+	0.608840i	$0.208365\pi$
$283$			20.4845i			1.21768i	−0.793293	+	0.608840i	$0.791635\pi$
$284$	−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
$288$		−	1.00000i		−	0.0589256i
$289$	4.00775			0.235750
$290$	−7.53092	+	12.4041i	−0.442231	+	0.728392i
$291$	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
$298$		−	4.92924i		−	0.285543i
$299$	11.8600			0.685879
$300$	4.76789	+	1.50574i	0.275274	+	0.0869342i
$301$	6.04066	+	6.04066i	0.348178	+	0.348178i
$302$			2.56917i			0.147839i
$303$	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	$-0.385632\pi$
$307$	22.5634	−	22.5634i	1.28776	−	1.28776i	0.936144	−	0.351616i	$-0.114368\pi$
$308$	4.91416	−	4.91416i	0.280010	−	0.280010i
$309$	1.88770	−	1.88770i	0.107387	−	0.107387i
$310$	19.8166	+	12.0313i	1.12551	+	0.683333i
$311$	17.2148	−	17.2148i	0.976159	−	0.976159i	−0.0235634	−	0.999722i	$-0.507501\pi$
$311$	17.2148	−	17.2148i	0.976159	−	0.976159i	0.999722	+	0.0235634i	$0.00750115\pi$
$312$	−1.86691	−	1.86691i	−0.105693	−	0.105693i
$313$	−30.7702			−1.73923			−0.869616	−	0.493729i	$-0.835634\pi$
$313$	−30.7702			−1.73923			−0.869616	+	0.493729i	$0.835634\pi$
$314$	−10.7956	−	10.7956i	−0.609233	−	0.609233i
$315$	−5.22744	−	3.17375i	−0.294533	−	0.178820i
$316$	−4.70094	+	4.70094i	−0.264448	+	0.264448i
$317$	12.5932	−	12.5932i	0.707307	−	0.707307i	−0.258661	−	0.965968i	$-0.583281\pi$
$317$	12.5932	−	12.5932i	0.707307	−	0.707307i	0.965968	+	0.258661i	$0.0832813\pi$
$318$	−0.426260			−0.0239035
$319$	−11.6607	+	11.6607i	−0.652874	+	0.652874i
$320$	−0.530977	−	2.17211i	−0.0296825	−	0.121425i
$321$			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
$325$	11.7123	−	6.09012i	0.649681	−	0.337819i
$326$			2.00094i			0.110822i
$327$	1.48467			0.0821022
$328$		−	4.31993i		−	0.238528i
$329$		−	17.4508i		−	0.962093i
$330$	4.85697	+	2.94883i	0.267367	+	0.162327i
$331$	12.4856	+	12.4856i	0.686272	+	0.686272i	0.961406	−	0.275134i	$-0.0887222\pi$
$331$	12.4856	+	12.4856i	0.686272	+	0.686272i	−0.275134	+	0.961406i	$0.588722\pi$
$332$	−0.524568	+	0.524568i	−0.0287894	+	0.0287894i
$333$	1.59211	+	5.87071i	0.0872469	+	0.321713i
$334$		−	3.34903i		−	0.183251i
$335$	−15.6039	−	9.47363i	−0.852531	−	0.517599i
$336$			2.73491i			0.149202i
$337$	2.01004	−	2.01004i	0.109494	−	0.109494i	−0.650237	−	0.759731i	$-0.725331\pi$
$337$	2.01004	−	2.01004i	0.109494	−	0.109494i	0.759731	+	0.650237i	$0.225331\pi$
$338$	6.02931			0.327951
$339$	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
$347$	15.1173			0.811539			0.405770	−	0.913975i	$-0.367004\pi$
$347$	15.1173			0.811539			0.405770	+	0.913975i	$0.367004\pi$
$348$		−	6.48962i		−	0.347880i
$349$			13.6893i			0.732771i	0.930463	+	0.366386i	$0.119405\pi$
$349$			13.6893i			0.732771i	−0.930463	+	0.366386i	$0.880595\pi$
$350$	−13.0398	−	4.11808i	−0.697005	−	0.220121i
$351$	−1.86691	+	1.86691i	−0.0996482	+	0.0996482i
$352$		−	2.54109i		−	0.135441i
$353$			31.3775i			1.67006i	0.550206	+	0.835029i	$0.314549\pi$
$353$			31.3775i			1.67006i	−0.550206	+	0.835029i	$0.685451\pi$
$354$	−1.15064			−0.0611558
$355$	1.22293	+	5.00274i	0.0649065	+	0.265518i
$356$	6.69075	+	6.69075i	0.354609	+	0.354609i
$357$	−9.85793			−0.521737
$358$	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
$362$	−14.0432			−0.738096
$363$	−3.21228	−	3.21228i	−0.168601	−	0.168601i
$364$	5.10583	+	5.10583i	0.267618	+	0.267618i
$365$	−6.08847	+	10.0282i	−0.318685	+	0.524902i
$366$	−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	$0.634298\pi$
$368$	−4.49206			−0.234165
$369$	−4.31993			−0.224887
$370$	6.57544	+	11.9064i	0.341841	+	0.618987i
$371$	1.16579			0.0605245
$372$	−10.3677			−0.537543
$373$	21.6306	+	21.6306i	1.11999	+	1.11999i	0.991742	+	0.128250i	$0.0409359\pi$
$373$	21.6306	+	21.6306i	1.11999	+	1.11999i	0.128250	+	0.991742i	$0.459064\pi$
$374$	9.15930			0.473616
$375$	0.739003	−	11.1559i	0.0381620	−	0.576088i
$376$	−4.51187	−	4.51187i	−0.232682	−	0.232682i
$377$	−12.1155	−	12.1155i	−0.623981	−	0.623981i
$378$	2.73491			0.140669
$379$			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
$383$	1.75588			0.0897211			0.0448606	−	0.998993i	$-0.485716\pi$
$383$	1.75588			0.0897211			0.0448606	+	0.998993i	$0.485716\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	−13.2834	−	8.06479i	−0.676985	−	0.411020i
$386$	13.9313			0.709084
$387$		−	3.12360i		−	0.158781i
$388$			17.0294i			0.864539i
$389$	11.3156	−	11.3156i	0.573722	−	0.573722i	−0.359445	−	0.933166i	$-0.617034\pi$
$389$	11.3156	−	11.3156i	0.573722	−	0.573722i	0.933166	+	0.359445i	$0.117034\pi$
$390$	−3.06384	+	5.04642i	−0.155144	+	0.255535i
$391$		−	16.1915i		−	0.818840i
$392$		−	0.479758i		−	0.0242314i
$393$	17.7614			0.895943
$394$	−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	−0.921015	−	0.389527i	$-0.872639\pi$
$397$	−10.5898	+	10.5898i	−0.531488	+	0.531488i	0.389527	+	0.921015i	$0.372639\pi$
$398$	−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	−0.517164	−	0.855886i	$-0.673012\pi$
$401$	6.78291	−	6.78291i	0.338722	−	0.338722i	0.855886	+	0.517164i	$0.173012\pi$
$402$	8.16371			0.407169
$403$	−19.3556	+	19.3556i	−0.964173	+	0.964173i
$404$			18.0572i			0.898377i
$405$	0.530977	+	2.17211i	0.0263845	+	0.107933i
$406$			17.7486i			0.880846i
$407$	4.04569	+	14.9180i	0.200537	+	0.739458i
$408$	−2.54875	+	2.54875i	−0.126182	+	0.126182i
$409$	−12.5316	−	12.5316i	−0.619650	−	0.619650i	0.325792	−	0.945442i	$-0.394369\pi$
$409$	−12.5316	−	12.5316i	−0.619650	−	0.619650i	−0.945442	+	0.325792i	$0.894369\pi$
$410$	−9.38336	+	2.29378i	−0.463411	+	0.113282i
$411$			18.0818i			0.891910i
$412$			2.66961i			0.131522i
$413$	3.14690			0.154849
$414$			4.49206i			0.220773i
$415$	1.41795	+	0.860886i	0.0696046	+	0.0422592i
$416$	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	$0.824854\pi$
$420$	5.94054	−	1.45218i	0.289868	−	0.0708590i
$421$	10.7024	−	10.7024i	0.521601	−	0.521601i	−0.396454	−	0.918055i	$-0.629759\pi$
$421$	10.7024	−	10.7024i	0.521601	−	0.521601i	0.918055	+	0.396454i	$0.129759\pi$
$422$	13.4040			0.652495
$423$	−4.51187	+	4.51187i	−0.219374	+	0.219374i
$424$	0.301411	−	0.301411i	0.0146378	−	0.0146378i
$425$	−8.31438	−	15.9899i	−0.403307	−	0.775625i
$426$	−1.62859	−	1.62859i	−0.0789053	−	0.0789053i
$427$	3.35552			0.162385
$428$	−0.404456	−	0.404456i	−0.0195501	−	0.0195501i
$429$	−4.74398	+	4.74398i	−0.229042	+	0.229042i
$430$	−1.65856	−	6.78480i	−0.0799829	−	0.327192i
$431$	−11.7768	+	11.7768i	−0.567266	+	0.567266i	−0.931362	−	0.364095i	$-0.881378\pi$
$431$	−11.7768	+	11.7768i	−0.567266	+	0.567266i	0.364095	+	0.931362i	$0.381378\pi$
$432$	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
$438$		−	5.24662i		−	0.250693i
$439$	−12.6631	−	12.6631i	−0.604375	−	0.604375i	0.337095	−	0.941471i	$-0.390556\pi$
$439$	−12.6631	−	12.6631i	−0.604375	−	0.604375i	−0.941471	+	0.337095i	$0.890556\pi$
$440$	−5.51953	+	1.34926i	−0.263133	+	0.0643235i
$441$	−0.479758			−0.0228456
$442$			9.51656i			0.452657i
$443$	−19.8789	−	19.8789i	−0.944476	−	0.944476i	0.0540616	−	0.998538i	$-0.482783\pi$
$443$	−19.8789	−	19.8789i	−0.944476	−	0.944476i	−0.998538	+	0.0540616i	$0.982783\pi$
$444$	−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	$-0.861224\pi$
$449$	−10.2591	+	10.2591i	−0.484159	+	0.484159i	0.422298	+	0.906457i	$0.361224\pi$
$450$	2.30668	+	4.43613i	0.108738	+	0.209121i
$451$	−10.9773			−0.516902
$452$			5.71763i			0.268935i
$453$	−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
$457$		−	3.03992i		−	0.142202i	−0.997469	−	0.0711008i	$-0.977349\pi$
$457$		−	3.03992i		−	0.142202i	0.997469	−	0.0711008i	$-0.0226512\pi$
$458$			23.8741i			1.11556i
$459$	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	0.655666	−	0.755051i	$-0.272388\pi$
$461$	−2.13391	−	2.13391i	−0.0993859	−	0.0993859i	−0.755051	+	0.655666i	$0.772388\pi$
$462$	6.94967			0.323328
$463$	−20.8314			−0.968118			−0.484059	−	0.875035i	$-0.660838\pi$
$463$	−20.8314			−0.968118			−0.484059	+	0.875035i	$0.660838\pi$
$464$	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
$467$			30.6842i			1.41990i	0.704253	+	0.709949i	$0.251282\pi$
$467$			30.6842i			1.41990i	−0.704253	+	0.709949i	$0.748718\pi$
$468$		−	2.64021i		−	0.122044i
$469$	−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
$473$		−	7.93735i		−	0.364960i
$474$	−6.64813			−0.305359
$475$	5.26306	−	16.6653i	0.241486	−	0.764657i
$476$	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	$-0.711586\pi$
$479$	3.72623	−	3.72623i	0.170256	−	0.170256i	0.787092	+	0.616836i	$0.211586\pi$
$480$	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
$483$		−	12.2854i		−	0.559005i
$484$	4.54285			0.206493
$485$	36.9898	−	9.04225i	1.67962	−	0.410587i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$			19.2486i			0.872239i	0.899889	+	0.436120i	$0.143648\pi$
$487$			19.2486i			0.872239i	−0.899889	+	0.436120i	$0.856352\pi$
$488$	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
$495$	1.34926	+	5.51953i	0.0606448	+	0.248084i
$496$	7.33111	−	7.33111i	0.329176	−	0.329176i
$497$	4.45405	+	4.45405i	0.199791	+	0.199791i
$498$	−0.741852			−0.0332432
$499$	8.46141	+	8.46141i	0.378785	+	0.378785i	0.870664	−	0.491879i	$-0.163690\pi$
$499$	8.46141	+	8.46141i	0.378785	+	0.378785i	−0.491879	+	0.870664i	$0.663690\pi$
$500$	7.36585	+	8.41096i	0.329411	+	0.376150i
$501$	2.36812	−	2.36812i	0.105800	−	0.105800i
$502$	8.29215	−	8.29215i	0.370097	−	0.370097i
$503$	−16.8793			−0.752612			−0.376306	−	0.926495i	$-0.622806\pi$
$503$	−16.8793			−0.752612			−0.376306	+	0.926495i	$0.622806\pi$
$504$	−1.93388	+	1.93388i	−0.0861417	+	0.0861417i
$505$	39.2221	−	9.58794i	1.74536	−	0.426658i
$506$			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	$-0.685245\pi$
$509$	−24.8021			−1.09933			−0.549667	+	0.835384i	$0.685245\pi$
$510$	6.88949	+	4.18284i	0.305072	+	0.185219i
$511$			14.3491i			0.634765i
$512$	−1.00000			−0.0441942
$513$			3.49532i			0.154322i
$514$		−	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
$518$	14.4322	+	8.27428i	0.634113	+	0.363551i
$519$		−	10.0670i		−	0.441893i
$520$	−1.40189	−	5.73482i	−0.0614769	−	0.251488i
$521$			25.4431i			1.11468i	0.830283	+	0.557342i	$0.188179\pi$
$521$			25.4431i			1.11468i	−0.830283	+	0.557342i	$0.811821\pi$
$522$	4.58885	−	4.58885i	0.200849	−	0.200849i
$523$	43.8527			1.91755			0.958773	−	0.284174i	$-0.0917195\pi$
$523$	43.8527			1.91755			0.958773	+	0.284174i	$0.0917195\pi$
$524$	−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
$532$	9.55941			0.414453
$533$		−	11.4055i		−	0.494027i
$534$			9.46214i			0.409467i
$535$	−0.663765	+	1.09328i	−0.0286971	+	0.0472666i
$536$	−5.77261	+	5.77261i	−0.249339	+	0.249339i
$537$			12.2767i			0.529779i
$538$			1.98048i			0.0853845i
$539$	−1.21911			−0.0525107
$540$	−1.91137	−	1.16046i	−0.0822523	−	0.0499381i
$541$	25.4345	+	25.4345i	1.09351	+	1.09351i	0.995150	+	0.0983645i	$0.0313611\pi$
$541$	25.4345	+	25.4345i	1.09351	+	1.09351i	0.0983645	+	0.995150i	$0.468639\pi$
$542$	20.2119			0.868177
$543$	−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
$547$	−13.3671			−0.571538			−0.285769	−	0.958299i	$-0.592249\pi$
$547$	−13.3671			−0.571538			−0.285769	+	0.958299i	$0.592249\pi$
$548$	−12.7858	−	12.7858i	−0.546181	−	0.546181i
$549$	−0.867564	−	0.867564i	−0.0370267	−	0.0370267i
$550$	5.86149	+	11.2726i	0.249935	+	0.480665i
$551$	−22.6833			−0.966342
$552$	−3.17637	−	3.17637i	−0.135195	−	0.135195i
$553$	18.1821			0.773180
$554$	26.8225			1.13958
$555$	−3.76959	+	13.0687i	−0.160010	+	0.554734i
$556$	−3.82368			−0.162160
$557$	17.4429			0.739080			0.369540	−	0.929215i	$-0.379515\pi$
$557$	17.4429			0.739080			0.369540	+	0.929215i	$0.379515\pi$
$558$	−7.33111	−	7.33111i	−0.310350	−	0.310350i
$559$	8.24695			0.348809
$560$	−3.17375	+	5.22744i	−0.134115	+	0.220900i
$561$	6.47661	+	6.47661i	0.273442	+	0.273442i
$562$	−11.8287	−	11.8287i	−0.498964	−	0.498964i
$563$	2.58551			0.108966			0.0544831	−	0.998515i	$-0.482649\pi$
$563$	2.58551			0.108966			0.0544831	+	0.998515i	$0.482649\pi$
$564$		−	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
$568$	2.30317			0.0966389
$569$	−19.1350	−	19.1350i	−0.802180	−	0.802180i	0.181256	−	0.983436i	$-0.441984\pi$
$569$	−19.1350	−	19.1350i	−0.802180	−	0.802180i	−0.983436	+	0.181256i	$0.941984\pi$
$570$	1.85594	+	7.59223i	0.0777367	+	0.318004i
$571$	6.72822			0.281567			0.140784	−	0.990040i	$-0.455038\pi$
$571$	6.72822			0.281567			0.140784	+	0.990040i	$0.455038\pi$
$572$		−	6.70901i		−	0.280518i
$573$			2.32340i			0.0970616i
$574$	−8.35421	+	8.35421i	−0.348698	+	0.348698i
$575$	19.9273	−	10.3618i	0.831027	−	0.432115i
$576$			1.00000i			0.0416667i
$577$			32.3098i			1.34507i	0.740063	+	0.672537i	$0.234796\pi$
$577$			32.3098i			1.34507i	−0.740063	+	0.672537i	$0.765204\pi$
$578$	−4.00775			−0.166701
$579$	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
$587$	13.1138			0.541266			0.270633	−	0.962683i	$-0.412767\pi$
$587$	13.1138			0.541266			0.270633	+	0.962683i	$0.412767\pi$
$588$	0.339240	−	0.339240i	0.0139900	−	0.0139900i
$589$			36.2386i			1.49319i
$590$	−2.19930	−	1.33527i	−0.0905437	−	0.0549721i
$591$		−	26.5798i		−	1.09335i
$592$	5.87071	−	1.59211i	0.241285	−	0.0654352i
$593$	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
$597$		−	4.58024i		−	0.187457i
$598$	−11.8600			−0.484990
$599$		−	13.3830i		−	0.546815i	−0.961898	−	0.273407i	$-0.911849\pi$
$599$		−	13.3830i		−	0.546815i	0.961898	−	0.273407i	$-0.0881507\pi$
$600$	−4.76789	−	1.50574i	−0.194648	−	0.0614717i
$601$	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
$605$	−2.41215	−	9.86758i	−0.0980679	−	0.401174i
$606$	−12.7683	+	12.7683i	−0.518678	+	0.518678i
$607$	−34.6374			−1.40589			−0.702944	−	0.711246i	$-0.748131\pi$
$607$	−34.6374			−1.40589			−0.702944	+	0.711246i	$0.748131\pi$
$608$	2.47157	−	2.47157i	0.100235	−	0.100235i
$609$	−12.5501	+	12.5501i	−0.508557	+	0.508557i
$610$	−2.34510	−	1.42379i	−0.0949504	−	0.0576475i
$611$	−11.9123	−	11.9123i	−0.481918	−	0.481918i
$612$	−3.60448			−0.145702
$613$	13.5656	+	13.5656i	0.547908	+	0.547908i	0.925835	−	0.377928i	$-0.123363\pi$
$613$	13.5656	+	13.5656i	0.547908	+	0.547908i	−0.377928	+	0.925835i	$0.623363\pi$
$614$	−22.5634	+	22.5634i	−0.910584	+	0.910584i
$615$	−8.25699	−	5.01309i	−0.332954	−	0.202147i
$616$	−4.91416	+	4.91416i	−0.197997	+	0.197997i
$617$	−29.4000	+	29.4000i	−1.18360	+	1.18360i	−0.204793	+	0.978805i	$0.565652\pi$
$617$	−29.4000	+	29.4000i	−1.18360	+	1.18360i	−0.978805	+	0.204793i	$0.934348\pi$
$618$	−1.88770	+	1.88770i	−0.0759343	+	0.0759343i
$619$	−8.71796			−0.350404			−0.175202	−	0.984532i	$-0.556058\pi$
$619$	−8.71796			−0.350404			−0.175202	+	0.984532i	$0.556058\pi$
$620$	−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
$623$		−	25.8782i		−	1.03679i
$624$	1.86691	+	1.86691i	0.0747361	+	0.0747361i
$625$	14.3584	−	20.4655i	0.574337	−	0.818619i
$626$	30.7702			1.22982
$627$			8.88194i			0.354710i
$628$	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	−0.984764	−	0.173897i	$-0.944364\pi$
$631$	−20.3687	+	20.3687i	−0.810867	+	0.810867i	0.173897	+	0.984764i	$0.444364\pi$
$632$	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
$635$	5.18216	−	8.53546i	0.205648	−	0.338719i
$636$	0.426260			0.0169023
$637$		−	1.26666i		−	0.0501869i
$638$	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	$0.372658\pi$
$642$		−	0.571987i		−	0.0225745i
$643$			30.0934i			1.18677i	0.804919	+	0.593384i	$0.202209\pi$
$643$			30.0934i			1.18677i	−0.804919	+	0.593384i	$0.797791\pi$
$644$	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
$647$	3.58012			0.140749			0.0703746	−	0.997521i	$-0.477581\pi$
$647$	3.58012			0.140749			0.0703746	+	0.997521i	$0.477581\pi$
$648$	1.00000			0.0392837
$649$	−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
$652$		−	2.00094i		−	0.0783628i
$653$		−	21.6461i		−	0.847079i	−0.905878	−	0.423540i	$-0.860787\pi$
$653$		−	21.6461i		−	0.847079i	0.905878	−	0.423540i	$-0.139213\pi$
$654$	−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
$658$			17.4508i			0.680302i
$659$	−24.8071			−0.966346			−0.483173	−	0.875525i	$-0.660516\pi$
$659$	−24.8071			−0.966346			−0.483173	+	0.875525i	$0.660516\pi$
$660$	−4.85697	−	2.94883i	−0.189057	−	0.114783i
$661$	−7.55751	+	7.55751i	−0.293953	+	0.293953i	−0.838640	−	0.544687i	$-0.816649\pi$
$661$	−7.55751	+	7.55751i	−0.293953	+	0.293953i	0.544687	+	0.838640i	$0.316649\pi$
$662$	−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
$668$			3.34903i			0.129578i
$669$	25.8168			0.998135
$670$	15.6039	+	9.47363i	0.602830	+	0.365998i
$671$	−2.20456	−	2.20456i	−0.0851061	−	0.0851061i
$672$		−	2.73491i		−	0.105502i
$673$	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	$0.506524\pi$
$677$	−26.5470	+	26.5470i	−1.02028	+	1.02028i	−0.999790	+	0.0204933i	$0.993476\pi$
$678$	−4.04297	+	4.04297i	−0.155269	+	0.155269i
$679$	32.9329	−	32.9329i	1.26385	−	1.26385i
$680$	−7.82932	+	1.91389i	−0.300241	+	0.0733945i
$681$	−14.3657	+	14.3657i	−0.550494	+	0.550494i
$682$	−18.6290	−	18.6290i	−0.713342	−	0.713342i
$683$	−26.8136			−1.02599			−0.512997	−	0.858390i	$-0.671465\pi$
$683$	−26.8136			−1.02599			−0.512997	+	0.858390i	$0.671465\pi$
$684$	−2.47157	−	2.47157i	−0.0945028	−	0.0945028i
$685$	−20.9831	+	34.5610i	−0.801725	+	1.32051i
$686$	12.6093	−	12.6093i	0.481427	−	0.481427i
$687$	−16.8815	+	16.8815i	−0.644070	+	0.644070i
$688$	−3.12360			−0.119086
$689$	0.795788	−	0.795788i	0.0303171	−	0.0303171i
$690$	−5.21284	+	8.58599i	−0.198449	+	0.326863i
$691$		−	39.2996i		−	1.49503i	−0.664246	−	0.747514i	$-0.731247\pi$
$691$		−	39.2996i		−	1.49503i	0.664246	−	0.747514i	$-0.268753\pi$
$692$	7.11846	+	7.11846i	0.270603	+	0.270603i
$693$	4.91416	+	4.91416i	0.186673	+	0.186673i
$694$	−15.1173			−0.573845
$695$	2.03029	+	8.30546i	0.0770133	+	0.315044i
$696$			6.48962i			0.245988i
$697$	−15.5711			−0.589797
$698$		−	13.6893i		−	0.518148i
$699$			0.0710572i			0.00268763i
$700$	13.0398	+	4.11808i	0.492857	+	0.155649i
$701$	−19.5030	−	19.5030i	−0.736617	−	0.736617i	0.235305	−	0.971922i	$-0.424391\pi$
$701$	−19.5030	−	19.5030i	−0.736617	−	0.736617i	−0.971922	+	0.235305i	$0.924391\pi$
$702$	1.86691	−	1.86691i	0.0704619	−	0.0704619i
$703$	−10.5748	+	18.4448i	−0.398838	+	0.695661i
$704$			2.54109i			0.0957710i
$705$	−13.8597	+	3.38803i	−0.521986	+	0.127601i
$706$		−	31.3775i		−	1.18091i
$707$	34.9203	−	34.9203i	1.31331	−	1.31331i
$708$	1.15064			0.0432437
$709$	8.21814	−	8.21814i	0.308639	−	0.308639i	−0.535743	−	0.844381i	$-0.679968\pi$
$709$	8.21814	−	8.21814i	0.308639	−	0.308639i	0.844381	+	0.535743i	$0.179968\pi$
$710$	−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
$717$	16.0193			0.598251
$718$			32.4157i			1.20974i
$719$		−	9.15541i		−	0.341439i	−0.985320	−	0.170720i	$-0.945391\pi$
$719$		−	9.15541i		−	0.341439i	0.985320	−	0.170720i	$-0.0546092\pi$
$720$	2.17211	−	0.530977i	0.0809498	−	0.0197884i
$721$	5.16269	−	5.16269i	0.192269	−	0.192269i
$722$		−	6.78271i		−	0.252426i
$723$			5.22229i			0.194219i
$724$	14.0432			0.521912
$725$	−30.9418	−	9.77171i	−1.14915	−	0.362912i
$726$	3.21228	+	3.21228i	0.119219	+	0.119219i
$727$	−32.4114			−1.20207			−0.601036	−	0.799222i	$-0.705245\pi$
$727$	−32.4114			−1.20207			−0.601036	+	0.799222i	$0.705245\pi$
$728$	−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
$732$	1.22692			0.0453483
$733$	35.1555	+	35.1555i	1.29850	+	1.29850i	0.929384	+	0.369115i	$0.120339\pi$
$733$	35.1555	+	35.1555i	1.29850	+	1.29850i	0.369115	+	0.929384i	$0.379661\pi$
$734$	−9.63234	−	9.63234i	−0.355536	−	0.355536i
$735$	−0.916995	−	0.556738i	−0.0338239	−	0.0205356i
$736$	4.49206			0.165579
$737$	14.6687	+	14.6687i	0.540330	+	0.540330i
$738$	4.31993			0.159019
$739$	11.5902			0.426351			0.213176	−	0.977014i	$-0.431619\pi$
$739$	11.5902			0.426351			0.213176	+	0.977014i	$0.431619\pi$
$740$	−6.57544	−	11.9064i	−0.241718	−	0.437690i
$741$	−9.22838			−0.339013
$742$	−1.16579			−0.0427973
$743$	21.4779	+	21.4779i	0.787949	+	0.787949i	0.981158	−	0.193209i	$-0.0618895\pi$
$743$	21.4779	+	21.4779i	0.787949	+	0.787949i	−0.193209	+	0.981158i	$0.561890\pi$
$744$	10.3677			0.380100
$745$	10.7068	−	2.61731i	0.392269	−	0.0958909i
$746$	−21.6306	−	21.6306i	−0.791954	−	0.791954i
$747$	−0.524568	−	0.524568i	−0.0191929	−	0.0191929i
$748$	−9.15930			−0.334897
$749$			1.56433i			0.0571595i
$750$	−0.739003	+	11.1559i	−0.0269846	+	0.407355i
$751$		−	46.7182i		−	1.70477i	−0.522914	−	0.852385i	$-0.675155\pi$
$751$		−	46.7182i		−	1.70477i	0.522914	−	0.852385i	$-0.324845\pi$
$752$	4.51187	+	4.51187i	0.164531	+	0.164531i
$753$	11.7269			0.427351
$754$	12.1155	+	12.1155i	0.441221	+	0.441221i
$755$	−5.58051	+	1.36417i	−0.203096	+	0.0496472i
$756$	−2.73491			−0.0994679
$757$		−	28.5100i		−	1.03622i	−0.855315	−	0.518108i	$-0.826637\pi$
$757$		−	28.5100i		−	1.03622i	0.855315	−	0.518108i	$-0.173363\pi$
$758$		−	0.115662i		−	0.00420103i
$759$	−8.07143	+	8.07143i	−0.292974	+	0.292974i
$760$	−6.68086	−	4.05617i	−0.242340	−	0.147133i
$761$		−	19.7514i		−	0.715988i	−0.933724	−	0.357994i	$-0.883461\pi$
$761$		−	19.7514i		−	0.715988i	0.933724	−	0.357994i	$-0.116539\pi$
$762$			4.46562i			0.161772i
$763$	4.06043			0.146998
$764$	−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	$-0.0124665\pi$
$769$	26.6238	+	26.6238i	0.960078	+	0.960078i	−0.0391547	+	0.999233i	$0.512467\pi$
$770$	13.2834	+	8.06479i	0.478700	+	0.290635i
$771$	0.755280	−	0.755280i	0.0272007	−	0.0272007i
$772$	−13.9313			−0.501398
$773$	−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
$775$	−15.6112	+	49.4322i	−0.560770	+	1.77566i
$776$		−	17.0294i		−	0.611322i
$777$	4.35428	+	16.0559i	0.156209	+	0.576002i
$778$	−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
$782$			16.1915i			0.579007i
$783$	6.48962			0.231920
$784$			0.479758i			0.0171342i
$785$	17.7171	−	29.1816i	0.632350	−	1.04153i
$786$	−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
$790$	−12.7070	−	7.71486i	−0.452096	−	0.274483i
$791$	11.0572	−	11.0572i	0.393148	−	0.393148i
$792$	2.54109			0.0902938
$793$	2.29055	−	2.29055i	0.0813398	−	0.0813398i
$794$	10.5898	−	10.5898i	0.375819	−	0.375819i
$795$	−0.226334	−	0.925884i	−0.00802726	−	0.0328377i
$796$	3.23872	+	3.23872i	0.114793	+	0.114793i
$797$	3.20231			0.113432			0.0567159	−	0.998390i	$-0.481937\pi$
$797$	3.20231			0.113432			0.0567159	+	0.998390i	$0.481937\pi$
$798$	6.75953	+	6.75953i	0.239285	+	0.239285i
$799$	−16.2629	+	16.2629i	−0.575341	+	0.575341i
$800$	4.43613	−	2.30668i	0.156841	−	0.0815535i
$801$	−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
$808$		−	18.0572i		−	0.635249i
$809$	−6.69579	−	6.69579i	−0.235412	−	0.235412i	0.579535	−	0.814947i	$-0.303234\pi$
$809$	−6.69579	−	6.69579i	−0.235412	−	0.235412i	−0.814947	+	0.579535i	$0.803234\pi$
$810$	−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	$0.410092\pi$
$812$		−	17.7486i		−	0.622852i
$813$	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
$820$	9.38336	−	2.29378i	0.327681	−	0.0801024i
$821$	−46.5456			−1.62445			−0.812227	−	0.583342i	$-0.801745\pi$
$821$	−46.5456			−1.62445			−0.812227	+	0.583342i	$0.801745\pi$
$822$		−	18.0818i		−	0.630675i
$823$	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
$827$		−	28.5690i		−	0.993443i	−0.867910	−	0.496721i	$-0.834537\pi$
$827$		−	28.5690i		−	0.993443i	0.867910	−	0.496721i	$-0.165463\pi$
$828$		−	4.49206i		−	0.156110i
$829$	−28.7820	−	28.7820i	−0.999640	−	0.999640i	0.000360408	−	1.00000i	$-0.499885\pi$
$829$	−28.7820	−	28.7820i	−0.999640	−	0.999640i	−1.00000		0.000360408i	$0.999885\pi$
$830$	−1.41795	−	0.860886i	−0.0492179	−	0.0298818i
$831$	18.9664	+	18.9664i	0.657937	+	0.657937i
$832$	−2.64021			−0.0915327
$833$	−1.72927			−0.0599158
$834$	−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
$837$		−	10.3677i		−	0.358362i
$838$		−	21.4066i		−	0.739479i
$839$	29.3296			1.01257			0.506285	−	0.862366i	$-0.331018\pi$
$839$	29.3296			1.01257			0.506285	+	0.862366i	$0.331018\pi$
$840$	−5.94054	+	1.45218i	−0.204968	+	0.0501049i
$841$			13.1152i			0.452247i
$842$	−10.7024	+	10.7024i	−0.368827	+	0.368827i
$843$		−	16.7283i		−	0.576154i
$844$	−13.4040			−0.461384
$845$	3.20143	+	13.0963i	0.110132	+	0.450527i
$846$	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
$853$		−	10.7137i		−	0.366831i	−0.983035	−	0.183416i	$-0.941285\pi$
$853$		−	10.7137i		−	0.366831i	0.983035	−	0.183416i	$-0.0587154\pi$
$854$	−3.35552			−0.114824
$855$	−4.05617	+	6.68086i	−0.138718	+	0.228481i
$856$	0.404456	+	0.404456i	0.0138240	+	0.0138240i
$857$			31.9152i			1.09020i	0.838371	+	0.545101i	$0.183509\pi$
$857$			31.9152i			1.09020i	−0.838371	+	0.545101i	$0.816491\pi$
$858$	4.74398	−	4.74398i	0.161957	−	0.161957i
$859$	30.9778	−	30.9778i	1.05695	−	1.05695i	0.0586704	−	0.998277i	$-0.481314\pi$
$859$	30.9778	−	30.9778i	1.05695	−	1.05695i	0.998277	−	0.0586704i	$-0.0186861\pi$
$860$	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
$865$	11.6823	−	19.2418i	0.397211	−	0.654241i
$866$	−12.9115	+	12.9115i	−0.438751	+	0.438751i
$867$	−2.83391	−	2.83391i	−0.0962446	−	0.0962446i
$868$	−28.3549			−0.962428
$869$	−11.9455	−	11.9455i	−0.405224	−	0.405224i
$870$	14.0962	−	3.44584i	0.477905	−	0.116825i
$871$	−15.2409	+	15.2409i	−0.516418	+	0.516418i
$872$	1.04982	−	1.04982i	0.0355513	−	0.0355513i
$873$	−17.0294			−0.576360
$874$	−11.1024	+	11.1024i	−0.375545	+	0.375545i
$875$	2.02111	−	30.5104i	0.0683260	−	1.03144i
$876$			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
$880$	5.51953	−	1.34926i	0.186063	−	0.0454836i
$881$		−	23.6087i		−	0.795397i	−0.917516	−	0.397699i	$-0.869809\pi$
$881$		−	23.6087i		−	0.795397i	0.917516	−	0.397699i	$-0.130191\pi$
$882$	0.479758			0.0161543
$883$			15.7413i			0.529737i	0.964285	+	0.264868i	$0.0853285\pi$
$883$			15.7413i			0.529737i	−0.964285	+	0.264868i	$0.914671\pi$
$884$		−	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	−0.414450	−	0.910072i	$-0.636026\pi$
$887$	14.7609	−	14.7609i	0.495622	−	0.495622i	0.910072	+	0.414450i	$0.136026\pi$
$888$	5.27701	+	3.02543i	0.177085	+	0.101527i
$889$		−	12.2131i		−	0.409614i
$890$	−10.9804	+	18.0857i	−0.368064	+	0.606233i
$891$		−	2.54109i		−	0.0851298i
$892$	−18.2552	+	18.2552i	−0.611231	+	0.611231i
$893$	−22.3028			−0.746334
$894$	−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
$902$	10.9773			0.365505
$903$		−	8.54278i		−	0.284286i
$904$		−	5.71763i		−	0.190165i
$905$	−7.45663	−	30.5034i	−0.247867	−	1.01397i
$906$	1.81667	−	1.81667i	0.0603550	−	0.0603550i
$907$			46.5171i			1.54457i	0.635274	+	0.772287i	$0.280887\pi$
$907$			46.5171i			1.54457i	−0.635274	+	0.772287i	$0.719113\pi$
$908$		−	20.3161i		−	0.674215i
$909$	−18.0572			−0.598918
$910$	−8.37935	+	13.8015i	−0.277773	+	0.457516i
$911$	−35.8371	−	35.8371i	−1.18734	−	1.18734i	−0.977801	−	0.209534i	$-0.932805\pi$
$911$	−35.8371	−	35.8371i	−1.18734	−	1.18734i	−0.209534	−	0.977801i	$-0.567195\pi$
$912$	3.49532			0.115742
$913$	−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
$917$	48.5759			1.60412
$918$	−2.54875	−	2.54875i	−0.0841213	−	0.0841213i
$919$	−22.7714	−	22.7714i	−0.751160	−	0.751160i	0.223536	−	0.974696i	$-0.428240\pi$
$919$	−22.7714	−	22.7714i	−0.751160	−	0.751160i	−0.974696	+	0.223536i	$0.928240\pi$
$920$	−2.38518	−	9.75725i	−0.0786371	−	0.321687i
$921$	−31.9094			−1.05145
$922$	2.13391	+	2.13391i	0.0702765	+	0.0702765i
$923$	6.08085			0.200153
$924$	−6.94967			−0.228627
$925$	−22.3707	+	20.6046i	−0.735544	+	0.677476i
$926$	20.8314			0.684563
$927$	−2.66961			−0.0876814
$928$	−4.58885	−	4.58885i	−0.150637	−	0.150637i
$929$	17.7432			0.582135			0.291068	−	0.956702i	$-0.405989\pi$
$929$	17.7432			0.582135			0.291068	+	0.956702i	$0.405989\pi$
$930$	−5.50504	−	22.5199i	−0.180517	−	0.738456i
$931$	−1.18575	−	1.18575i	−0.0388615	−	0.0388615i
$932$	−0.0502450	−	0.0502450i	−0.00164583	−	0.00164583i
$933$	−24.3453			−0.797030
$934$		−	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	$-0.556961\pi$
$938$	22.3270			0.729004
$939$	21.7578	+	21.7578i	0.710038	+	0.710038i
$940$	7.40457	−	12.1960i	0.241511	−	0.397789i
$941$	18.2845			0.596058			0.298029	−	0.954557i	$-0.403671\pi$
$941$	18.2845			0.596058			0.298029	+	0.954557i	$0.403671\pi$
$942$			15.2673i			0.497437i
$943$		−	19.4054i		−	0.631926i
$944$	−0.813625	+	0.813625i	−0.0264812	+	0.0264812i
$945$	1.45218	+	5.94054i	0.0472393	+	0.193246i
$946$			7.93735i			0.258066i
$947$			14.1055i			0.458368i	0.973383	+	0.229184i	$0.0736058\pi$
$947$			14.1055i			0.458368i	−0.973383	+	0.229184i	$0.926394\pi$
$948$	6.64813			0.215921
$949$	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	0.762774	−	0.646665i	$-0.223837\pi$
$953$	3.58438	+	3.58438i	0.116109	+	0.116109i	−0.646665	+	0.762774i	$0.723837\pi$
$954$	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
$957$	16.4907			0.533069
$958$	−3.72623	+	3.72623i	−0.120389	+	0.120389i
$959$			49.4522i			1.59689i
$960$	−1.16046	+	1.91137i	−0.0374536	+	0.0616893i
$961$		−	76.4902i		−	2.46743i
$962$	15.4999	−	4.20349i	0.499736	−	0.135526i
$963$	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
$967$			21.6520i			0.696280i	0.937442	+	0.348140i	$0.113187\pi$
$967$			21.6520i			0.696280i	−0.937442	+	0.348140i	$0.886813\pi$
$968$	−4.54285			−0.146013
$969$			12.5988i			0.404732i
$970$	−36.9898	+	9.04225i	−1.18767	+	0.290329i
$971$	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
$975$	−12.5882	−	3.97547i	−0.403145	−	0.127317i
$976$	−0.867564	+	0.867564i	−0.0277701	+	0.0277701i
$977$	−62.4861			−1.99911			−0.999553	−	0.0298845i	$-0.990486\pi$
$977$	−62.4861			−1.99911			−0.999553	+	0.0298845i	$0.990486\pi$
$978$	1.41488	−	1.41488i	0.0452428	−	0.0452428i
$979$	−17.0018	+	17.0018i	−0.543380	+	0.543380i
$980$	1.04209	−	0.254740i	0.0332882	−	0.00813738i
$981$	−1.04982	−	1.04982i	−0.0335181	−	0.0335181i
$982$	7.57274			0.241656
$983$	9.77180	+	9.77180i	0.311672	+	0.311672i	0.845557	−	0.533885i	$-0.179268\pi$
$983$	9.77180	+	9.77180i	0.311672	+	0.311672i	−0.533885	+	0.845557i	$0.679268\pi$
$984$	−3.05465	+	3.05465i	−0.0973787	+	0.0973787i
$985$	30.8447	−	50.8038i	0.982792	−	1.61874i
$986$	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	−0.293883	+	0.955842i	$0.594947\pi$
$991$	−39.3415	+	39.3415i	−1.24972	+	1.24972i	−0.955842	+	0.293883i	$0.905053\pi$
$992$	−7.33111	+	7.33111i	−0.232763	+	0.232763i
$993$		−	17.6573i		−	0.560339i
$994$	−4.45405	−	4.45405i	−0.141274	−	0.141274i
$995$	5.31516	−	8.75453i	0.168502	−	0.277537i
$996$	0.741852			0.0235065
$997$			3.43255i			0.108710i	0.998522	+	0.0543550i	$0.0173103\pi$
$997$			3.43255i			0.108710i	−0.998522	+	0.0543550i	$0.982690\pi$
$998$	−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.o.a.487.4	yes	36
5.3	odd	4		1110.2.l.a.43.15	✓	36
37.31	odd	4		1110.2.l.a.697.15	yes	36
185.68	even	4	inner	1110.2.o.a.253.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.15	✓	36	5.3	odd	4
1110.2.l.a.697.15	yes	36	37.31	odd	4
1110.2.o.a.253.4	yes	36	185.68	even	4	inner
1110.2.o.a.487.4	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more