LMFDB - Embedded newform 1110.2.l.a.43.17

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			43.17
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.a.697.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.0484605 - 2.23554i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.77693 - 2.77693i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.0484605 - 2.23554i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.77693 - 2.77693i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(2.23554 - 0.0484605i) q^{10} +2.74073i q^{11} +(-0.707107 + 0.707107i) q^{12} -2.09781i q^{13} +(2.77693 + 2.77693i) q^{14} +(-1.61503 - 1.54650i) q^{15} +1.00000 q^{16} -4.54367 q^{17} +1.00000 q^{18} +(3.00837 - 3.00837i) q^{19} +(0.0484605 + 2.23554i) q^{20} -3.92718i q^{21} -2.74073 q^{22} -1.09307i q^{23} +(-0.707107 - 0.707107i) q^{24} +(-4.99530 + 0.216671i) q^{25} +2.09781 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.77693 + 2.77693i) q^{28} +(3.41798 + 3.41798i) q^{29} +(1.54650 - 1.61503i) q^{30} +(-0.444286 + 0.444286i) q^{31} +1.00000i q^{32} +(1.93799 + 1.93799i) q^{33} -4.54367i q^{34} +(-6.34253 - 6.07338i) q^{35} +1.00000i q^{36} +(-5.20783 - 3.14301i) q^{37} +(3.00837 + 3.00837i) q^{38} +(-1.48338 - 1.48338i) q^{39} +(-2.23554 + 0.0484605i) q^{40} -3.49239i q^{41} +3.92718 q^{42} -2.64615i q^{43} -2.74073i q^{44} +(-2.23554 + 0.0484605i) q^{45} +1.09307 q^{46} +(-4.28090 + 4.28090i) q^{47} +(0.707107 - 0.707107i) q^{48} -8.42272i q^{49} +(-0.216671 - 4.99530i) q^{50} +(-3.21286 + 3.21286i) q^{51} +2.09781i q^{52} +(-4.10770 - 4.10770i) q^{53} +(0.707107 - 0.707107i) q^{54} +(6.12703 - 0.132817i) q^{55} +(-2.77693 - 2.77693i) q^{56} -4.25447i q^{57} +(-3.41798 + 3.41798i) q^{58} +(10.1179 - 10.1179i) q^{59} +(1.61503 + 1.54650i) q^{60} +(-4.77382 + 4.77382i) q^{61} +(-0.444286 - 0.444286i) q^{62} +(-2.77693 - 2.77693i) q^{63} -1.00000 q^{64} +(-4.68975 + 0.101661i) q^{65} +(-1.93799 + 1.93799i) q^{66} +(3.42538 + 3.42538i) q^{67} +4.54367 q^{68} +(-0.772920 - 0.772920i) q^{69} +(6.07338 - 6.34253i) q^{70} +0.512824 q^{71} -1.00000 q^{72} +(9.57090 - 9.57090i) q^{73} +(3.14301 - 5.20783i) q^{74} +(-3.37900 + 3.68542i) q^{75} +(-3.00837 + 3.00837i) q^{76} +(7.61083 + 7.61083i) q^{77} +(1.48338 - 1.48338i) q^{78} +(4.84570 - 4.84570i) q^{79} +(-0.0484605 - 2.23554i) q^{80} -1.00000 q^{81} +3.49239 q^{82} +(4.09292 + 4.09292i) q^{83} +3.92718i q^{84} +(0.220188 + 10.1576i) q^{85} +2.64615 q^{86} +4.83375 q^{87} +2.74073 q^{88} +(9.59900 + 9.59900i) q^{89} +(-0.0484605 - 2.23554i) q^{90} +(-5.82548 - 5.82548i) q^{91} +1.09307i q^{92} +0.628315i q^{93} +(-4.28090 - 4.28090i) q^{94} +(-6.87112 - 6.57954i) q^{95} +(0.707107 + 0.707107i) q^{96} -5.08514 q^{97} +8.42272 q^{98} +2.74073 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	−0.0484605	−	2.23554i	−0.0216722	−	0.999765i
$5$	−0.0484605	−	2.23554i	−0.0216722	−	0.999765i
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	2.77693	−	2.77693i	1.04958	−	1.04958i	0.0508772	−	0.998705i	$-0.483798\pi$
$7$	2.77693	−	2.77693i	1.04958	−	1.04958i	0.998705	−	0.0508772i	$-0.0162017\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	2.23554	−	0.0484605i	0.706941	−	0.0153246i
$11$			2.74073i			0.826362i	0.910649	+	0.413181i	$0.135582\pi$
$11$			2.74073i			0.826362i	−0.910649	+	0.413181i	$0.864418\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$		−	2.09781i		−	0.581828i	−0.956749	−	0.290914i	$-0.906041\pi$
$13$		−	2.09781i		−	0.581828i	0.956749	−	0.290914i	$-0.0939594\pi$
$14$	2.77693	+	2.77693i	0.742167	+	0.742167i
$15$	−1.61503	−	1.54650i	−0.417000	−	0.399305i
$16$	1.00000			0.250000
$17$	−4.54367			−1.10200			−0.551001	−	0.834505i	$-0.685754\pi$
$17$	−4.54367			−1.10200			−0.551001	+	0.834505i	$0.685754\pi$
$18$	1.00000			0.235702
$19$	3.00837	−	3.00837i	0.690166	−	0.690166i	−0.272102	−	0.962268i	$-0.587719\pi$
$19$	3.00837	−	3.00837i	0.690166	−	0.690166i	0.962268	+	0.272102i	$0.0877188\pi$
$20$	0.0484605	+	2.23554i	0.0108361	+	0.499883i
$21$		−	3.92718i		−	0.856980i
$22$	−2.74073			−0.584326
$23$		−	1.09307i		−	0.227922i	−0.993485	−	0.113961i	$-0.963646\pi$
$23$		−	1.09307i		−	0.227922i	0.993485	−	0.113961i	$-0.0363538\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	−4.99530	+	0.216671i	−0.999061	+	0.0433342i
$26$	2.09781			0.411415
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−2.77693	+	2.77693i	−0.524791	+	0.524791i
$29$	3.41798	+	3.41798i	0.634703	+	0.634703i	0.949244	−	0.314541i	$-0.101851\pi$
$29$	3.41798	+	3.41798i	0.634703	+	0.634703i	−0.314541	+	0.949244i	$0.601851\pi$
$30$	1.54650	−	1.61503i	0.282351	−	0.294864i
$31$	−0.444286	+	0.444286i	−0.0797961	+	0.0797961i	−0.745878	−	0.666082i	$-0.767970\pi$
$31$	−0.444286	+	0.444286i	−0.0797961	+	0.0797961i	0.666082	+	0.745878i	$0.267970\pi$
$32$			1.00000i			0.176777i
$33$	1.93799	+	1.93799i	0.337361	+	0.337361i
$34$		−	4.54367i		−	0.779232i
$35$	−6.34253	−	6.07338i	−1.07208	−	1.02659i
$36$			1.00000i			0.166667i
$37$	−5.20783	−	3.14301i	−0.856162	−	0.516708i
$37$	−5.20783	−	3.14301i	−0.856162	−	0.516708i
$38$	3.00837	+	3.00837i	0.488021	+	0.488021i
$39$	−1.48338	−	1.48338i	−0.237530	−	0.237530i
$40$	−2.23554	+	0.0484605i	−0.353470	+	0.00766228i
$41$		−	3.49239i		−	0.545420i	−0.962096	−	0.272710i	$-0.912080\pi$
$41$		−	3.49239i		−	0.545420i	0.962096	−	0.272710i	$-0.0879200\pi$
$42$	3.92718			0.605977
$43$		−	2.64615i		−	0.403534i	−0.979434	−	0.201767i	$-0.935332\pi$
$43$		−	2.64615i		−	0.403534i	0.979434	−	0.201767i	$-0.0646683\pi$
$44$		−	2.74073i		−	0.413181i
$45$	−2.23554	+	0.0484605i	−0.333255	+	0.00722407i
$46$	1.09307			0.161165
$47$	−4.28090	+	4.28090i	−0.624434	+	0.624434i	−0.946662	−	0.322228i	$-0.895568\pi$
$47$	−4.28090	+	4.28090i	−0.624434	+	0.624434i	0.322228	+	0.946662i	$0.395568\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$		−	8.42272i		−	1.20325i
$50$	−0.216671	−	4.99530i	−0.0306419	−	0.706443i
$51$	−3.21286	+	3.21286i	−0.449890	+	0.449890i
$52$			2.09781i			0.290914i
$53$	−4.10770	−	4.10770i	−0.564235	−	0.564235i	0.366272	−	0.930508i	$-0.380634\pi$
$53$	−4.10770	−	4.10770i	−0.564235	−	0.564235i	−0.930508	+	0.366272i	$0.880634\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	6.12703	−	0.132817i	0.826168	−	0.0179091i
$56$	−2.77693	−	2.77693i	−0.371083	−	0.371083i
$57$		−	4.25447i		−	0.563519i
$58$	−3.41798	+	3.41798i	−0.448803	+	0.448803i
$59$	10.1179	−	10.1179i	1.31724	−	1.31724i	0.401282	−	0.915954i	$-0.368565\pi$
$59$	10.1179	−	10.1179i	1.31724	−	1.31724i	0.915954	−	0.401282i	$-0.131435\pi$
$60$	1.61503	+	1.54650i	0.208500	+	0.199652i
$61$	−4.77382	+	4.77382i	−0.611226	+	0.611226i	−0.943265	−	0.332040i	$-0.892263\pi$
$61$	−4.77382	+	4.77382i	−0.611226	+	0.611226i	0.332040	+	0.943265i	$0.392263\pi$
$62$	−0.444286	−	0.444286i	−0.0564243	−	0.0564243i
$63$	−2.77693	−	2.77693i	−0.349861	−	0.349861i
$64$	−1.00000			−0.125000
$65$	−4.68975	+	0.101661i	−0.581692	+	0.0126095i
$66$	−1.93799	+	1.93799i	−0.238550	+	0.238550i
$67$	3.42538	+	3.42538i	0.418476	+	0.418476i	0.884678	−	0.466202i	$-0.154378\pi$
$67$	3.42538	+	3.42538i	0.418476	+	0.418476i	−0.466202	+	0.884678i	$0.654378\pi$
$68$	4.54367			0.551001
$69$	−0.772920	−	0.772920i	−0.0930486	−	0.0930486i
$70$	6.07338	−	6.34253i	0.725908	−	0.758077i
$71$	0.512824			0.0608611			0.0304305	−	0.999537i	$-0.490312\pi$
$71$	0.512824			0.0608611			0.0304305	+	0.999537i	$0.490312\pi$
$72$	−1.00000			−0.117851
$73$	9.57090	−	9.57090i	1.12019	−	1.12019i	0.128477	−	0.991713i	$-0.458991\pi$
$73$	9.57090	−	9.57090i	1.12019	−	1.12019i	0.991713	−	0.128477i	$-0.0410088\pi$
$74$	3.14301	−	5.20783i	0.365368	−	0.605398i
$75$	−3.37900	+	3.68542i	−0.390174	+	0.425556i
$76$	−3.00837	+	3.00837i	−0.345083	+	0.345083i
$77$	7.61083	+	7.61083i	0.867335	+	0.867335i
$78$	1.48338	−	1.48338i	0.167959	−	0.167959i
$79$	4.84570	−	4.84570i	0.545184	−	0.545184i	−0.379860	−	0.925044i	$-0.624028\pi$
$79$	4.84570	−	4.84570i	0.545184	−	0.545184i	0.925044	+	0.379860i	$0.124028\pi$
$80$	−0.0484605	−	2.23554i	−0.00541805	−	0.249941i
$81$	−1.00000			−0.111111
$82$	3.49239			0.385670
$83$	4.09292	+	4.09292i	0.449256	+	0.449256i	0.895107	−	0.445851i	$-0.147099\pi$
$83$	4.09292	+	4.09292i	0.449256	+	0.449256i	−0.445851	+	0.895107i	$0.647099\pi$
$84$			3.92718i			0.428490i
$85$	0.220188	+	10.1576i	0.0238828	+	1.10174i
$86$	2.64615			0.285341
$87$	4.83375			0.518233
$88$	2.74073			0.292163
$89$	9.59900	+	9.59900i	1.01749	+	1.01749i	0.999844	+	0.0176477i	$0.00561773\pi$
$89$	9.59900	+	9.59900i	1.01749	+	1.01749i	0.0176477	+	0.999844i	$0.494382\pi$
$90$	−0.0484605	−	2.23554i	−0.00510819	−	0.235647i
$91$	−5.82548	−	5.82548i	−0.610677	−	0.610677i
$92$			1.09307i			0.113961i
$93$			0.628315i			0.0651532i
$94$	−4.28090	−	4.28090i	−0.441541	−	0.441541i
$95$	−6.87112	−	6.57954i	−0.704962	−	0.675047i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	−5.08514			−0.516318			−0.258159	−	0.966102i	$-0.583116\pi$
$97$	−5.08514			−0.516318			−0.258159	+	0.966102i	$0.583116\pi$
$98$	8.42272			0.850823
$99$	2.74073			0.275454
$100$	4.99530	−	0.216671i	0.499530	−	0.0216671i
$101$			14.3173i			1.42463i	0.701861	+	0.712314i	$0.252353\pi$
$101$			14.3173i			1.42463i	−0.701861	+	0.712314i	$0.747647\pi$
$102$	−3.21286	−	3.21286i	−0.318120	−	0.318120i
$103$	8.41065			0.828726			0.414363	−	0.910112i	$-0.364004\pi$
$103$	8.41065			0.828726			0.414363	+	0.910112i	$0.364004\pi$
$104$	−2.09781			−0.205707
$105$	−8.77937	+	0.190313i	−0.856779	+	0.0185726i
$106$	4.10770	−	4.10770i	0.398975	−	0.398975i
$107$	4.88230	−	4.88230i	0.471990	−	0.471990i	−0.430568	−	0.902558i	$-0.641687\pi$
$107$	4.88230	−	4.88230i	0.471990	−	0.471990i	0.902558	+	0.430568i	$0.141687\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	9.37338	−	9.37338i	0.897806	−	0.897806i	−0.0974354	−	0.995242i	$-0.531064\pi$
$109$	9.37338	−	9.37338i	0.897806	−	0.897806i	0.995242	+	0.0974354i	$0.0310639\pi$
$110$	0.132817	+	6.12703i	0.0126636	+	0.584189i
$111$	−5.90494	+	1.46004i	−0.560472	+	0.138581i
$112$	2.77693	−	2.77693i	0.262396	−	0.262396i
$113$	−4.08857			−0.384620			−0.192310	−	0.981334i	$-0.561598\pi$
$113$	−4.08857			−0.384620			−0.192310	+	0.981334i	$0.561598\pi$
$114$	4.25447			0.398468
$115$	−2.44361	+	0.0529709i	−0.227868	+	0.00493956i
$116$	−3.41798	−	3.41798i	−0.317352	−	0.317352i
$117$	−2.09781			−0.193943
$118$	10.1179	+	10.1179i	0.931427	+	0.931427i
$119$	−12.6175	+	12.6175i	−1.15664	+	1.15664i
$120$	−1.54650	+	1.61503i	−0.141176	+	0.147432i
$121$	3.48838			0.317126
$122$	−4.77382	−	4.77382i	−0.432202	−	0.432202i
$123$	−2.46949	−	2.46949i	−0.222667	−	0.222667i
$124$	0.444286	−	0.444286i	0.0398980	−	0.0398980i
$125$	0.726452	+	11.1567i	0.0649759	+	0.997887i
$126$	2.77693	−	2.77693i	0.247389	−	0.247389i
$127$	−8.71272	+	8.71272i	−0.773129	+	0.773129i	−0.978652	−	0.205523i	$-0.934110\pi$
$127$	−8.71272	+	8.71272i	−0.773129	+	0.773129i	0.205523	+	0.978652i	$0.434110\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−1.87111	−	1.87111i	−0.164742	−	0.164742i
$130$	−0.101661	−	4.68975i	−0.00891626	−	0.411318i
$131$	−15.0456	+	15.0456i	−1.31454	+	1.31454i	−0.396507	+	0.918032i	$0.629778\pi$
$131$	−15.0456	+	15.0456i	−1.31454	+	1.31454i	−0.918032	+	0.396507i	$0.870222\pi$
$132$	−1.93799	−	1.93799i	−0.168680	−	0.168680i
$133$		−	16.7081i		−	1.44877i
$134$	−3.42538	+	3.42538i	−0.295908	+	0.295908i
$135$	−1.54650	+	1.61503i	−0.133102	+	0.139000i
$136$			4.54367i			0.389616i
$137$	7.51357	−	7.51357i	0.641928	−	0.641928i	−0.309101	−	0.951029i	$-0.600028\pi$
$137$	7.51357	−	7.51357i	0.641928	−	0.641928i	0.951029	+	0.309101i	$0.100028\pi$
$138$	0.772920	−	0.772920i	0.0657953	−	0.0657953i
$139$	−7.58286			−0.643170			−0.321585	−	0.946881i	$-0.604216\pi$
$139$	−7.58286			−0.643170			−0.321585	+	0.946881i	$0.604216\pi$
$140$	6.34253	+	6.07338i	0.536041	+	0.513294i
$141$			6.05411i			0.509848i
$142$			0.512824i			0.0430353i
$143$	5.74954			0.480801
$144$		−	1.00000i		−	0.0833333i
$145$	7.47541	−	7.80668i	0.620799	−	0.648309i
$146$	9.57090	+	9.57090i	0.792093	+	0.792093i
$147$	−5.95576	−	5.95576i	−0.491223	−	0.491223i
$148$	5.20783	+	3.14301i	0.428081	+	0.258354i
$149$			18.5418i			1.51901i	0.650503	+	0.759504i	$0.274558\pi$
$149$			18.5418i			1.51901i	−0.650503	+	0.759504i	$0.725442\pi$
$150$	−3.68542	−	3.37900i	−0.300913	−	0.275894i
$151$			4.53529i			0.369077i	0.982825	+	0.184538i	$0.0590790\pi$
$151$			4.53529i			0.369077i	−0.982825	+	0.184538i	$0.940921\pi$
$152$	−3.00837	−	3.00837i	−0.244011	−	0.244011i
$153$			4.54367i			0.367334i
$154$	−7.61083	+	7.61083i	−0.613298	+	0.613298i
$155$	1.01475	+	0.971689i	0.0815067	+	0.0780480i
$156$	1.48338	+	1.48338i	0.118765	+	0.118765i
$157$	−2.15926	+	2.15926i	−0.172328	+	0.172328i	−0.788001	−	0.615674i	$-0.788884\pi$
$157$	−2.15926	+	2.15926i	−0.172328	+	0.172328i	0.615674	+	0.788001i	$0.288884\pi$
$158$	4.84570	+	4.84570i	0.385503	+	0.385503i
$159$	−5.80916			−0.460696
$160$	2.23554	−	0.0484605i	0.176735	−	0.00383114i
$161$	−3.03539	−	3.03539i	−0.239222	−	0.239222i
$162$		−	1.00000i		−	0.0785674i
$163$	13.2270			1.03602			0.518011	−	0.855374i	$-0.326673\pi$
$163$	13.2270			1.03602			0.518011	+	0.855374i	$0.326673\pi$
$164$			3.49239i			0.272710i
$165$	4.23855	−	4.42638i	0.329970	−	0.344593i
$166$	−4.09292	+	4.09292i	−0.317672	+	0.317672i
$167$	−2.15667			−0.166888			−0.0834441	−	0.996512i	$-0.526592\pi$
$167$	−2.15667			−0.166888			−0.0834441	+	0.996512i	$0.526592\pi$
$168$	−3.92718			−0.302988
$169$	8.59918			0.661476
$170$	−10.1576	+	0.220188i	−0.779049	+	0.0168877i
$171$	−3.00837	−	3.00837i	−0.230055	−	0.230055i
$172$			2.64615i			0.201767i
$173$	12.7830	−	12.7830i	0.971877	−	0.971877i	−0.0277386	−	0.999615i	$-0.508831\pi$
$173$	12.7830	−	12.7830i	0.971877	−	0.971877i	0.999615	+	0.0277386i	$0.00883062\pi$
$174$			4.83375i			0.366446i
$175$	−13.2699	+	14.4733i	−1.00311	+	1.09408i
$176$			2.74073i			0.206591i
$177$		−	14.3089i		−	1.07552i
$178$	−9.59900	+	9.59900i	−0.719475	+	0.719475i
$179$	−8.92829	−	8.92829i	−0.667332	−	0.667332i	0.289766	−	0.957098i	$-0.406423\pi$
$179$	−8.92829	−	8.92829i	−0.667332	−	0.667332i	−0.957098	+	0.289766i	$0.906423\pi$
$180$	2.23554	−	0.0484605i	0.166628	−	0.00361203i
$181$	8.76543			0.651530			0.325765	−	0.945451i	$-0.394378\pi$
$181$	8.76543			0.651530			0.325765	+	0.945451i	$0.394378\pi$
$182$	5.82548	−	5.82548i	0.431814	−	0.431814i
$183$			6.75121i			0.499064i
$184$	−1.09307			−0.0805825
$185$	−6.77397	+	11.7946i	−0.498032	+	0.867159i
$186$	−0.628315			−0.0460703
$187$		−	12.4530i		−	0.910652i
$188$	4.28090	−	4.28090i	0.312217	−	0.312217i
$189$	−3.92718			−0.285660
$190$	6.57954	−	6.87112i	0.477330	−	0.498483i
$191$	3.29001	+	3.29001i	0.238057	+	0.238057i	0.816045	−	0.577988i	$-0.196162\pi$
$191$	3.29001	+	3.29001i	0.238057	+	0.238057i	−0.577988	+	0.816045i	$0.696162\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$		−	19.3985i		−	1.39634i	−0.715934	−	0.698168i	$-0.753999\pi$
$193$		−	19.3985i		−	1.39634i	0.715934	−	0.698168i	$-0.246001\pi$
$194$		−	5.08514i		−	0.365092i
$195$	−3.24427	+	3.38804i	−0.232327	+	0.242622i
$196$			8.42272i			0.601623i
$197$	−12.6528	+	12.6528i	−0.901476	+	0.901476i	−0.995564	−	0.0940878i	$-0.970007\pi$
$197$	−12.6528	+	12.6528i	−0.901476	+	0.901476i	0.0940878	+	0.995564i	$0.470007\pi$
$198$			2.74073i			0.194775i
$199$	−3.25794	−	3.25794i	−0.230949	−	0.230949i	0.582140	−	0.813089i	$-0.302216\pi$
$199$	−3.25794	−	3.25794i	−0.230949	−	0.230949i	−0.813089	+	0.582140i	$0.802216\pi$
$200$	0.216671	+	4.99530i	0.0153210	+	0.353221i
$201$	4.84421			0.341685
$202$	−14.3173			−1.00736
$203$	18.9830			1.33235
$204$	3.21286	−	3.21286i	0.224945	−	0.224945i
$205$	−7.80739	+	0.169243i	−0.545292	+	0.0118205i
$206$			8.41065i			0.585998i
$207$	−1.09307			−0.0759739
$208$		−	2.09781i		−	0.145457i
$209$	8.24513	+	8.24513i	0.570327	+	0.570327i
$210$	−0.190313	−	8.77937i	−0.0131328	−	0.605834i
$211$	−1.48256			−0.102064			−0.0510319	−	0.998697i	$-0.516251\pi$
$211$	−1.48256			−0.102064			−0.0510319	+	0.998697i	$0.516251\pi$
$212$	4.10770	+	4.10770i	0.282118	+	0.282118i
$213$	0.362622	−	0.362622i	0.0248464	−	0.0248464i
$214$	4.88230	+	4.88230i	0.333747	+	0.333747i
$215$	−5.91557	+	0.128234i	−0.403439	+	0.00874546i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$			2.46750i			0.167505i
$218$	9.37338	+	9.37338i	0.634845	+	0.634845i
$219$		−	13.5353i		−	0.914631i
$220$	−6.12703	+	0.132817i	−0.413084	+	0.00895454i
$221$			9.53176i			0.641175i
$222$	−1.46004	−	5.90494i	−0.0979918	−	0.396313i
$223$	6.90996	+	6.90996i	0.462725	+	0.462725i	0.899548	−	0.436822i	$-0.143896\pi$
$223$	6.90996	+	6.90996i	0.462725	+	0.462725i	−0.436822	+	0.899548i	$0.643896\pi$
$224$	2.77693	+	2.77693i	0.185542	+	0.185542i
$225$	0.216671	+	4.99530i	0.0144447	+	0.333020i
$226$		−	4.08857i		−	0.271967i
$227$	−0.338896			−0.0224933			−0.0112467	−	0.999937i	$-0.503580\pi$
$227$	−0.338896			−0.0224933			−0.0112467	+	0.999937i	$0.503580\pi$
$228$			4.25447i			0.281759i
$229$			6.86738i			0.453810i	0.973917	+	0.226905i	$0.0728606\pi$
$229$			6.86738i			0.453810i	−0.973917	+	0.226905i	$0.927139\pi$
$230$	−0.0529709	−	2.44361i	−0.00349280	−	0.161127i
$231$	10.7633			0.708176
$232$	3.41798	−	3.41798i	0.224401	−	0.224401i
$233$	−11.8523	+	11.8523i	−0.776470	+	0.776470i	−0.979229	−	0.202758i	$-0.935009\pi$
$233$	−11.8523	+	11.8523i	−0.776470	+	0.776470i	0.202758	+	0.979229i	$0.435009\pi$
$234$		−	2.09781i		−	0.137138i
$235$	9.77759	+	9.36269i	0.637820	+	0.610754i
$236$	−10.1179	+	10.1179i	−0.658618	+	0.658618i
$237$		−	6.85285i		−	0.445141i
$238$	−12.6175	−	12.6175i	−0.817868	−	0.817868i
$239$	−11.8453	+	11.8453i	−0.766207	+	0.766207i	−0.977437	−	0.211229i	$-0.932253\pi$
$239$	−11.8453	+	11.8453i	−0.766207	+	0.766207i	0.211229	+	0.977437i	$0.432253\pi$
$240$	−1.61503	−	1.54650i	−0.104250	−	0.0998262i
$241$	−1.06176	−	1.06176i	−0.0683939	−	0.0683939i	0.672082	−	0.740476i	$-0.265400\pi$
$241$	−1.06176	−	1.06176i	−0.0683939	−	0.0683939i	−0.740476	+	0.672082i	$0.765400\pi$
$242$			3.48838i			0.224242i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	4.77382	−	4.77382i	0.305613	−	0.305613i
$245$	−18.8293	+	0.408169i	−1.20296	+	0.0260770i
$246$	2.46949	−	2.46949i	0.157449	−	0.157449i
$247$	−6.31099	−	6.31099i	−0.401558	−	0.401558i
$248$	0.444286	+	0.444286i	0.0282122	+	0.0282122i
$249$	5.78826			0.366816
$250$	−11.1567	+	0.726452i	−0.705613	+	0.0459449i
$251$	10.3290	−	10.3290i	0.651960	−	0.651960i	−0.301505	−	0.953465i	$-0.597489\pi$
$251$	10.3290	−	10.3290i	0.651960	−	0.651960i	0.953465	+	0.301505i	$0.0974890\pi$
$252$	2.77693	+	2.77693i	0.174930	+	0.174930i
$253$	2.99582			0.188346
$254$	−8.71272	−	8.71272i	−0.546685	−	0.546685i
$255$	7.33818	+	7.02678i	0.459534	+	0.440034i
$256$	1.00000			0.0625000
$257$	28.1460			1.75570			0.877848	−	0.478939i	$-0.158978\pi$
$257$	28.1460			1.75570			0.877848	+	0.478939i	$0.158978\pi$
$258$	1.87111	−	1.87111i	0.116490	−	0.116490i
$259$	−23.1897	+	5.73385i	−1.44094	+	0.356284i
$260$	4.68975	−	0.101661i	0.290846	−	0.00630475i
$261$	3.41798	−	3.41798i	0.211568	−	0.211568i
$262$	−15.0456	−	15.0456i	−0.929519	−	0.929519i
$263$	1.14169	−	1.14169i	0.0703994	−	0.0703994i	−0.671030	−	0.741430i	$-0.734148\pi$
$263$	1.14169	−	1.14169i	0.0703994	−	0.0703994i	0.741430	+	0.671030i	$0.234148\pi$
$264$	1.93799	−	1.93799i	0.119275	−	0.119275i
$265$	−8.98387	+	9.38199i	−0.551875	+	0.576331i
$266$	16.7081			1.02444
$267$	13.5750			0.830779
$268$	−3.42538	−	3.42538i	−0.209238	−	0.209238i
$269$			0.755375i			0.0460560i	0.999735	+	0.0230280i	$0.00733069\pi$
$269$			0.755375i			0.0460560i	−0.999735	+	0.0230280i	$0.992669\pi$
$270$	−1.61503	−	1.54650i	−0.0982879	−	0.0941170i
$271$	13.0803			0.794573			0.397286	−	0.917695i	$-0.369952\pi$
$271$	13.0803			0.794573			0.397286	+	0.917695i	$0.369952\pi$
$272$	−4.54367			−0.275500
$273$	−8.23848			−0.498615
$274$	7.51357	+	7.51357i	0.453912	+	0.453912i
$275$	−0.593838	−	13.6908i	−0.0358097	−	0.825586i
$276$	0.772920	+	0.772920i	0.0465243	+	0.0465243i
$277$		−	27.8958i		−	1.67610i	−0.545597	−	0.838048i	$-0.683697\pi$
$277$		−	27.8958i		−	1.67610i	0.545597	−	0.838048i	$-0.316303\pi$
$278$		−	7.58286i		−	0.454790i
$279$	0.444286	+	0.444286i	0.0265987	+	0.0265987i
$280$	−6.07338	+	6.34253i	−0.362954	+	0.379038i
$281$	3.25168	+	3.25168i	0.193979	+	0.193979i	0.797413	−	0.603434i	$-0.206201\pi$
$281$	3.25168	+	3.25168i	0.193979	+	0.193979i	−0.603434	+	0.797413i	$0.706201\pi$
$282$	−6.05411			−0.360517
$283$	−12.8597			−0.764431			−0.382216	−	0.924073i	$-0.624839\pi$
$283$	−12.8597			−0.764431			−0.382216	+	0.924073i	$0.624839\pi$
$284$	−0.512824			−0.0304305
$285$	−9.51105	+	0.206174i	−0.563386	+	0.0122127i
$286$			5.74954i			0.339978i
$287$	−9.69814	−	9.69814i	−0.572463	−	0.572463i
$288$	1.00000			0.0589256
$289$	3.64491			0.214406
$290$	7.80668	+	7.47541i	0.458424	+	0.438971i
$291$	−3.59574	+	3.59574i	−0.210786	+	0.210786i
$292$	−9.57090	+	9.57090i	−0.560095	+	0.560095i
$293$	−8.19264	−	8.19264i	−0.478619	−	0.478619i	0.426071	−	0.904690i	$-0.359897\pi$
$293$	−8.19264	−	8.19264i	−0.478619	−	0.478619i	−0.904690	+	0.426071i	$0.859897\pi$
$294$	5.95576	−	5.95576i	0.347347	−	0.347347i
$295$	−23.1093	−	22.1287i	−1.34547	−	1.28838i
$296$	−3.14301	+	5.20783i	−0.182684	+	0.302699i
$297$	1.93799	−	1.93799i	0.112454	−	0.112454i
$298$	−18.5418			−1.07410
$299$	−2.29306			−0.132611
$300$	3.37900	−	3.68542i	0.195087	−	0.212778i
$301$	−7.34817	−	7.34817i	−0.423542	−	0.423542i
$302$	−4.53529			−0.260977
$303$	10.1239	+	10.1239i	0.581602	+	0.581602i
$304$	3.00837	−	3.00837i	0.172542	−	0.172542i
$305$	10.9034	+	10.4407i	0.624329	+	0.597835i
$306$	−4.54367			−0.259744
$307$	−1.93471	−	1.93471i	−0.110420	−	0.110420i	0.649738	−	0.760158i	$-0.274879\pi$
$307$	−1.93471	−	1.93471i	−0.110420	−	0.110420i	−0.760158	+	0.649738i	$0.774879\pi$
$308$	−7.61083	−	7.61083i	−0.433667	−	0.433667i
$309$	5.94723	−	5.94723i	0.338326	−	0.338326i
$310$	−0.971689	+	1.01475i	−0.0551882	+	0.0576339i
$311$	−24.0063	+	24.0063i	−1.36127	+	1.36127i	−0.488974	+	0.872298i	$0.662629\pi$
$311$	−24.0063	+	24.0063i	−1.36127	+	1.36127i	−0.872298	+	0.488974i	$0.837371\pi$
$312$	−1.48338	+	1.48338i	−0.0839797	+	0.0839797i
$313$			28.6636i			1.62016i	0.586319	+	0.810080i	$0.300576\pi$
$313$			28.6636i			1.62016i	−0.586319	+	0.810080i	$0.699424\pi$
$314$	−2.15926	−	2.15926i	−0.121854	−	0.121854i
$315$	−6.07338	+	6.34253i	−0.342196	+	0.357361i
$316$	−4.84570	+	4.84570i	−0.272592	+	0.272592i
$317$	14.0253	+	14.0253i	0.787739	+	0.787739i	0.981123	−	0.193384i	$-0.0619464\pi$
$317$	14.0253	+	14.0253i	0.787739	+	0.787739i	−0.193384	+	0.981123i	$0.561946\pi$
$318$		−	5.80916i		−	0.325761i
$319$	−9.36777	+	9.36777i	−0.524495	+	0.524495i
$320$	0.0484605	+	2.23554i	0.00270902	+	0.124971i
$321$		−	6.90462i		−	0.385378i
$322$	3.03539	−	3.03539i	0.169156	−	0.169156i
$323$	−13.6690	+	13.6690i	−0.760564	+	0.760564i
$324$	1.00000			0.0555556
$325$	0.454535	+	10.4792i	0.0252131	+	0.581282i
$326$			13.2270i			0.732578i
$327$		−	13.2560i		−	0.733056i
$328$	−3.49239			−0.192835
$329$			23.7756i			1.31079i
$330$	4.42638	+	4.23855i	0.243664	+	0.233324i
$331$	−5.28358	−	5.28358i	−0.290412	−	0.290412i	0.546831	−	0.837243i	$-0.315834\pi$
$331$	−5.28358	−	5.28358i	−0.290412	−	0.290412i	−0.837243	+	0.546831i	$0.815834\pi$
$332$	−4.09292	−	4.09292i	−0.224628	−	0.224628i
$333$	−3.14301	+	5.20783i	−0.172236	+	0.285387i
$334$		−	2.15667i		−	0.118008i
$335$	7.49158	−	7.82357i	0.409309	−	0.427447i
$336$		−	3.92718i		−	0.214245i
$337$	15.8649	+	15.8649i	0.864216	+	0.864216i	0.991825	−	0.127609i	$-0.0407301\pi$
$337$	15.8649	+	15.8649i	0.864216	+	0.864216i	−0.127609	+	0.991825i	$0.540730\pi$
$338$			8.59918i			0.467734i
$339$	−2.89105	+	2.89105i	−0.157020	+	0.157020i
$340$	−0.220188	−	10.1576i	−0.0119414	−	0.550871i
$341$	−1.21767	−	1.21767i	−0.0659404	−	0.0659404i
$342$	3.00837	−	3.00837i	0.162674	−	0.162674i
$343$	−3.95079	−	3.95079i	−0.213323	−	0.213323i
$344$	−2.64615			−0.142671
$345$	−1.69044	+	1.76535i	−0.0910102	+	0.0950433i
$346$	12.7830	+	12.7830i	0.687221	+	0.687221i
$347$		−	20.2697i		−	1.08814i	−0.839041	−	0.544068i	$-0.816884\pi$
$347$		−	20.2697i		−	1.08814i	0.839041	−	0.544068i	$-0.183116\pi$
$348$	−4.83375			−0.259116
$349$			23.3133i			1.24793i	0.781452	+	0.623965i	$0.214479\pi$
$349$			23.3133i			1.24793i	−0.781452	+	0.623965i	$0.785521\pi$
$350$	−14.4733	−	13.2699i	−0.773631	−	0.709308i
$351$	−1.48338	+	1.48338i	−0.0791768	+	0.0791768i
$352$	−2.74073			−0.146082
$353$	35.1904			1.87300			0.936499	−	0.350671i	$-0.114047\pi$
$353$	35.1904			1.87300			0.936499	+	0.350671i	$0.114047\pi$
$354$	14.3089			0.760507
$355$	−0.0248517	−	1.14644i	−0.00131899	−	0.0608468i
$356$	−9.59900	−	9.59900i	−0.508746	−	0.508746i
$357$			17.8438i			0.944393i
$358$	8.92829	−	8.92829i	0.471875	−	0.471875i
$359$		−	34.3706i		−	1.81401i	−0.421118	−	0.907006i	$-0.638362\pi$
$359$		−	34.3706i		−	1.81401i	0.421118	−	0.907006i	$-0.361638\pi$
$360$	0.0484605	+	2.23554i	0.00255409	+	0.117823i
$361$			0.899470i			0.0473405i
$362$			8.76543i			0.460701i
$363$	2.46666	−	2.46666i	0.129466	−	0.129466i
$364$	5.82548	+	5.82548i	0.305338	+	0.305338i
$365$	−21.8600	−	20.9323i	−1.14420	−	1.09565i
$366$	−6.75121			−0.352891
$367$	−15.7170	+	15.7170i	−0.820421	+	0.820421i	−0.986168	−	0.165747i	$-0.946996\pi$
$367$	−15.7170	+	15.7170i	−0.820421	+	0.820421i	0.165747	+	0.986168i	$0.446996\pi$
$368$		−	1.09307i		−	0.0569804i
$369$	−3.49239			−0.181807
$370$	−11.7946	−	6.77397i	−0.613174	−	0.352162i
$371$	−22.8136			−1.18442
$372$		−	0.628315i		−	0.0325766i
$373$	−5.59113	+	5.59113i	−0.289498	+	0.289498i	−0.836882	−	0.547384i	$-0.815624\pi$
$373$	−5.59113	+	5.59113i	−0.289498	+	0.289498i	0.547384	+	0.836882i	$0.315624\pi$
$374$	12.4530			0.643928
$375$	8.40267	+	7.37531i	0.433912	+	0.380859i
$376$	4.28090	+	4.28090i	0.220771	+	0.220771i
$377$	7.17028	−	7.17028i	0.369288	−	0.369288i
$378$		−	3.92718i		−	0.201992i
$379$			20.7595i			1.06634i	0.846007	+	0.533171i	$0.179000\pi$
$379$			20.7595i			1.06634i	−0.846007	+	0.533171i	$0.821000\pi$
$380$	6.87112	+	6.57954i	0.352481	+	0.337523i
$381$			12.3216i			0.631257i
$382$	−3.29001	+	3.29001i	−0.168331	+	0.168331i
$383$			19.9351i			1.01863i	0.860579	+	0.509317i	$0.170102\pi$
$383$			19.9351i			1.01863i	−0.860579	+	0.509317i	$0.829898\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	16.6455	−	17.3832i	0.848334	−	0.885928i
$386$	19.3985			0.987358
$387$	−2.64615			−0.134511
$388$	5.08514			0.258159
$389$	−2.00735	+	2.00735i	−0.101777	+	0.101777i	−0.756162	−	0.654385i	$-0.772928\pi$
$389$	−2.00735	+	2.00735i	−0.101777	+	0.101777i	0.654385	+	0.756162i	$0.272928\pi$
$390$	−3.38804	−	3.24427i	−0.171560	−	0.164280i
$391$			4.96656i			0.251170i
$392$	−8.42272			−0.425412
$393$			21.2777i			1.07332i
$394$	−12.6528	−	12.6528i	−0.637440	−	0.637440i
$395$	−11.0676	−	10.5979i	−0.556871	−	0.533240i
$396$	−2.74073			−0.137727
$397$	21.4010	+	21.4010i	1.07408	+	1.07408i	0.997027	+	0.0770566i	$0.0245522\pi$
$397$	21.4010	+	21.4010i	1.07408	+	1.07408i	0.0770566	+	0.997027i	$0.475448\pi$
$398$	3.25794	−	3.25794i	0.163306	−	0.163306i
$399$	−11.8144	−	11.8144i	−0.591459	−	0.591459i
$400$	−4.99530	+	0.216671i	−0.249765	+	0.0108336i
$401$	18.1649	−	18.1649i	0.907111	−	0.907111i	−0.0889270	−	0.996038i	$-0.528344\pi$
$401$	18.1649	−	18.1649i	0.907111	−	0.907111i	0.996038	+	0.0889270i	$0.0283438\pi$
$402$			4.84421i			0.241607i
$403$	0.932028	+	0.932028i	0.0464276	+	0.0464276i
$404$		−	14.3173i		−	0.712314i
$405$	0.0484605	+	2.23554i	0.00240802	+	0.111085i
$406$			18.9830i			0.942111i
$407$	8.61416	−	14.2733i	0.426988	−	0.707499i
$408$	3.21286	+	3.21286i	0.159060	+	0.159060i
$409$	20.7880	+	20.7880i	1.02790	+	1.02790i	0.999599	+	0.0283030i	$0.00901031\pi$
$409$	20.7880	+	20.7880i	1.02790	+	1.02790i	0.0283030	+	0.999599i	$0.490990\pi$
$410$	−0.169243	−	7.80739i	−0.00835832	−	0.385580i
$411$		−	10.6258i		−	0.524132i
$412$	−8.41065			−0.414363
$413$		−	56.1934i		−	2.76510i
$414$		−	1.09307i		−	0.0537216i
$415$	8.95155	−	9.34824i	0.439414	−	0.458887i
$416$	2.09781			0.102854
$417$	−5.36189	+	5.36189i	−0.262573	+	0.262573i
$418$	−8.24513	+	8.24513i	−0.403282	+	0.403282i
$419$			6.01083i			0.293648i	0.989163	+	0.146824i	$0.0469051\pi$
$419$			6.01083i			0.293648i	−0.989163	+	0.146824i	$0.953095\pi$
$420$	8.77937	−	0.190313i	0.428389	−	0.00928632i
$421$	−14.1798	+	14.1798i	−0.691081	+	0.691081i	−0.962470	−	0.271389i	$-0.912517\pi$
$421$	−14.1798	+	14.1798i	−0.691081	+	0.691081i	0.271389	+	0.962470i	$0.412517\pi$
$422$		−	1.48256i		−	0.0721700i
$423$	4.28090	+	4.28090i	0.208145	+	0.208145i
$424$	−4.10770	+	4.10770i	−0.199487	+	0.199487i
$425$	22.6970	−	0.984481i	1.10097	−	0.0477543i
$426$	0.362622	+	0.362622i	0.0175691	+	0.0175691i
$427$			26.5132i			1.28306i
$428$	−4.88230	+	4.88230i	−0.235995	+	0.235995i
$429$	4.06554	−	4.06554i	0.196286	−	0.196286i
$430$	−0.128234	−	5.91557i	−0.00618397	−	0.285274i
$431$	19.4897	−	19.4897i	0.938784	−	0.938784i	−0.0594472	−	0.998231i	$-0.518934\pi$
$431$	19.4897	−	19.4897i	0.938784	−	0.938784i	0.998231	+	0.0594472i	$0.0189338\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	−27.2929	−	27.2929i	−1.31161	−	1.31161i	−0.920226	−	0.391387i	$-0.871995\pi$
$433$	−27.2929	−	27.2929i	−1.31161	−	1.31161i	−0.391387	−	0.920226i	$-0.628005\pi$
$434$	−2.46750			−0.118444
$435$	−0.234246	−	10.8061i	−0.0112312	−	0.518111i
$436$	−9.37338	+	9.37338i	−0.448903	+	0.448903i
$437$	−3.28837	−	3.28837i	−0.157304	−	0.157304i
$438$	13.5353			0.646742
$439$	27.9211	+	27.9211i	1.33260	+	1.33260i	0.903036	+	0.429564i	$0.141333\pi$
$439$	27.9211	+	27.9211i	1.33260	+	1.33260i	0.429564	+	0.903036i	$0.358667\pi$
$440$	−0.132817	−	6.12703i	−0.00633182	−	0.292094i
$441$	−8.42272			−0.401082
$442$	−9.53176			−0.453380
$443$	−13.8772	+	13.8772i	−0.659326	+	0.659326i	−0.955221	−	0.295894i	$-0.904382\pi$
$443$	−13.8772	+	13.8772i	−0.659326	+	0.659326i	0.295894	+	0.955221i	$0.404382\pi$
$444$	5.90494	−	1.46004i	0.280236	−	0.0692907i
$445$	20.9938	−	21.9241i	0.995202	−	1.03930i
$446$	−6.90996	+	6.90996i	−0.327196	+	0.327196i
$447$	13.1111	+	13.1111i	0.620132	+	0.620132i
$448$	−2.77693	+	2.77693i	−0.131198	+	0.131198i
$449$	4.29038	−	4.29038i	0.202475	−	0.202475i	−0.598584	−	0.801060i	$-0.704270\pi$
$449$	4.29038	−	4.29038i	0.202475	−	0.202475i	0.801060	+	0.598584i	$0.204270\pi$
$450$	−4.99530	+	0.216671i	−0.235481	+	0.0102140i
$451$	9.57172			0.450715
$452$	4.08857			0.192310
$453$	3.20694	+	3.20694i	0.150675	+	0.150675i
$454$		−	0.338896i		−	0.0159052i
$455$	−12.7408	+	13.3054i	−0.597299	+	0.623768i
$456$	−4.25447			−0.199234
$457$	37.1873			1.73955			0.869775	−	0.493449i	$-0.164264\pi$
$457$	37.1873			1.73955			0.869775	+	0.493449i	$0.164264\pi$
$458$	−6.86738			−0.320892
$459$	3.21286	+	3.21286i	0.149963	+	0.149963i
$460$	2.44361	−	0.0529709i	0.113934	−	0.00246978i
$461$	−13.3683	−	13.3683i	−0.622625	−	0.622625i	0.323577	−	0.946202i	$-0.395115\pi$
$461$	−13.3683	−	13.3683i	−0.622625	−	0.622625i	−0.946202	+	0.323577i	$0.895115\pi$
$462$			10.7633i			0.500756i
$463$		−	41.3804i		−	1.92311i	−0.274614	−	0.961554i	$-0.588550\pi$
$463$		−	41.3804i		−	1.92311i	0.274614	−	0.961554i	$-0.411450\pi$
$464$	3.41798	+	3.41798i	0.158676	+	0.158676i
$465$	1.40462	−	0.0304485i	0.0651379	−	0.00141201i
$466$	−11.8523	−	11.8523i	−0.549047	−	0.549047i
$467$	32.7500			1.51549			0.757744	−	0.652552i	$-0.226302\pi$
$467$	32.7500			1.51549			0.757744	+	0.652552i	$0.226302\pi$
$468$	2.09781			0.0969714
$469$	19.0241			0.878451
$470$	−9.36269	+	9.77759i	−0.431868	+	0.451007i
$471$			3.05366i			0.140705i
$472$	−10.1179	−	10.1179i	−0.465713	−	0.465713i
$473$	7.25238			0.333465
$474$	6.85285			0.314762
$475$	−14.3759	+	15.6795i	−0.659610	+	0.719426i
$476$	12.6175	−	12.6175i	0.578320	−	0.578320i
$477$	−4.10770	+	4.10770i	−0.188078	+	0.188078i
$478$	−11.8453	−	11.8453i	−0.541790	−	0.541790i
$479$	−16.6994	+	16.6994i	−0.763017	+	0.763017i	−0.976867	−	0.213849i	$-0.931400\pi$
$479$	−16.6994	+	16.6994i	−0.763017	+	0.763017i	0.213849	+	0.976867i	$0.431400\pi$
$480$	1.54650	−	1.61503i	0.0705878	−	0.0737159i
$481$	−6.59345	+	10.9250i	−0.300635	+	0.498139i
$482$	1.06176	−	1.06176i	0.0483618	−	0.0483618i
$483$	−4.29269			−0.195324
$484$	−3.48838			−0.158563
$485$	0.246429	+	11.3681i	0.0111897	+	0.516197i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	0.862986			0.0391056			0.0195528	−	0.999809i	$-0.493776\pi$
$487$	0.862986			0.0391056			0.0195528	+	0.999809i	$0.493776\pi$
$488$	4.77382	+	4.77382i	0.216101	+	0.216101i
$489$	9.35293	−	9.35293i	0.422954	−	0.422954i
$490$	−0.408169	−	18.8293i	−0.0184392	−	0.850623i
$491$	−27.6627			−1.24840			−0.624201	−	0.781264i	$-0.714575\pi$
$491$	−27.6627			−1.24840			−0.624201	+	0.781264i	$0.714575\pi$
$492$	2.46949	+	2.46949i	0.111333	+	0.111333i
$493$	−15.5302	−	15.5302i	−0.699443	−	0.699443i
$494$	6.31099	−	6.31099i	0.283945	−	0.283945i
$495$	−0.132817	−	6.12703i	−0.00596969	−	0.275389i
$496$	−0.444286	+	0.444286i	−0.0199490	+	0.0199490i
$497$	1.42408	−	1.42408i	0.0638787	−	0.0638787i
$498$			5.78826i			0.259378i
$499$	−3.33614	−	3.33614i	−0.149346	−	0.149346i	0.628480	−	0.777826i	$-0.283678\pi$
$499$	−3.33614	−	3.33614i	−0.149346	−	0.149346i	−0.777826	+	0.628480i	$0.783678\pi$
$500$	−0.726452	−	11.1567i	−0.0324879	−	0.498943i
$501$	−1.52500	+	1.52500i	−0.0681318	+	0.0681318i
$502$	10.3290	+	10.3290i	0.461005	+	0.461005i
$503$		−	25.4113i		−	1.13303i	−0.824050	−	0.566516i	$-0.808291\pi$
$503$		−	25.4113i		−	1.13303i	0.824050	−	0.566516i	$-0.191709\pi$
$504$	−2.77693	+	2.77693i	−0.123694	+	0.123694i
$505$	32.0070	−	0.693825i	1.42429	−	0.0308748i
$506$			2.99582i			0.133181i
$507$	6.08054	−	6.08054i	0.270046	−	0.270046i
$508$	8.71272	−	8.71272i	0.386565	−	0.386565i
$509$	15.9962			0.709020			0.354510	−	0.935052i	$-0.384648\pi$
$509$	15.9962			0.709020			0.354510	+	0.935052i	$0.384648\pi$
$510$	−7.02678	+	7.33818i	−0.311151	+	0.324940i
$511$		−	53.1555i		−	2.35146i
$512$			1.00000i			0.0441942i
$513$	−4.25447			−0.187840
$514$			28.1460i			1.24146i
$515$	−0.407584	−	18.8024i	−0.0179603	−	0.828531i
$516$	1.87111	+	1.87111i	0.0823709	+	0.0823709i
$517$	−11.7328	−	11.7328i	−0.516008	−	0.516008i
$518$	−5.73385	−	23.1897i	−0.251931	−	1.01890i
$519$		−	18.0779i		−	0.793534i
$520$	0.101661	+	4.68975i	0.00445813	+	0.205659i
$521$			41.9890i			1.83957i	0.392421	+	0.919786i	$0.371638\pi$
$521$			41.9890i			1.83957i	−0.392421	+	0.919786i	$0.628362\pi$
$522$	3.41798	+	3.41798i	0.149601	+	0.149601i
$523$		−	16.7289i		−	0.731505i	−0.930712	−	0.365753i	$-0.880812\pi$
$523$		−	16.7289i		−	0.731505i	0.930712	−	0.365753i	$-0.119188\pi$
$524$	15.0456	−	15.0456i	0.657269	−	0.657269i
$525$	0.850906	+	19.6174i	0.0371366	+	0.856175i
$526$	1.14169	+	1.14169i	0.0497799	+	0.0497799i
$527$	2.01869	−	2.01869i	0.0879353	−	0.0879353i
$528$	1.93799	+	1.93799i	0.0843402	+	0.0843402i
$529$	21.8052			0.948052
$530$	−9.38199	−	8.98387i	−0.407528	−	0.390234i
$531$	−10.1179	−	10.1179i	−0.439079	−	0.439079i
$532$			16.7081i			0.724386i
$533$	−7.32638			−0.317341
$534$			13.5750i			0.587449i
$535$	−11.1512	−	10.6780i	−0.482108	−	0.461650i
$536$	3.42538	−	3.42538i	0.147954	−	0.147954i
$537$	−12.6265			−0.544874
$538$	−0.755375			−0.0325665
$539$	23.0844			0.994316
$540$	1.54650	−	1.61503i	0.0665508	−	0.0695000i
$541$	5.79651	+	5.79651i	0.249212	+	0.249212i	0.820647	−	0.571435i	$-0.193613\pi$
$541$	5.79651	+	5.79651i	0.249212	+	0.249212i	−0.571435	+	0.820647i	$0.693613\pi$
$542$			13.0803i			0.561848i
$543$	6.19810	−	6.19810i	0.265986	−	0.265986i
$544$		−	4.54367i		−	0.194808i
$545$	−21.4088	−	20.5003i	−0.917053	−	0.878138i
$546$		−	8.23848i		−	0.352574i
$547$		−	20.4569i		−	0.874675i	−0.899298	−	0.437337i	$-0.855922\pi$
$547$		−	20.4569i		−	0.874675i	0.899298	−	0.437337i	$-0.144078\pi$
$548$	−7.51357	+	7.51357i	−0.320964	+	0.320964i
$549$	4.77382	+	4.77382i	0.203742	+	0.203742i
$550$	13.6908	−	0.593838i	0.583777	−	0.0253213i
$551$	20.5651			0.876102
$552$	−0.772920	+	0.772920i	−0.0328977	+	0.0328977i
$553$		−	26.9124i		−	1.14443i
$554$	27.8958			1.18518
$555$	3.55015	+	13.1300i	0.150695	+	0.557337i
$556$	7.58286			0.321585
$557$		−	5.28270i		−	0.223835i	−0.993717	−	0.111918i	$-0.964301\pi$
$557$		−	5.28270i		−	0.223835i	0.993717	−	0.111918i	$-0.0356993\pi$
$558$	−0.444286	+	0.444286i	−0.0188081	+	0.0188081i
$559$	−5.55112			−0.234787
$560$	−6.34253	−	6.07338i	−0.268021	−	0.256647i
$561$	−8.80558	−	8.80558i	−0.371772	−	0.371772i
$562$	−3.25168	+	3.25168i	−0.137164	+	0.137164i
$563$			21.9241i			0.923990i	0.886882	+	0.461995i	$0.152866\pi$
$563$			21.9241i			0.923990i	−0.886882	+	0.461995i	$0.847134\pi$
$564$		−	6.05411i		−	0.254924i
$565$	0.198134	+	9.14016i	0.00833556	+	0.384530i
$566$		−	12.8597i		−	0.540534i
$567$	−2.77693	+	2.77693i	−0.116620	+	0.116620i
$568$		−	0.512824i		−	0.0215176i
$569$	−13.2365	−	13.2365i	−0.554904	−	0.554904i	0.372948	−	0.927852i	$-0.378347\pi$
$569$	−13.2365	−	13.2365i	−0.554904	−	0.554904i	−0.927852	+	0.372948i	$0.878347\pi$
$570$	−0.206174	−	9.51105i	−0.00863567	−	0.398374i
$571$	−7.69386			−0.321978			−0.160989	−	0.986956i	$-0.551468\pi$
$571$	−7.69386			−0.321978			−0.160989	+	0.986956i	$0.551468\pi$
$572$	−5.74954			−0.240400
$573$	4.65277			0.194372
$574$	9.69814	−	9.69814i	0.404793	−	0.404793i
$575$	0.236837	+	5.46023i	0.00987680	+	0.227708i
$576$			1.00000i			0.0416667i
$577$	6.45917			0.268899			0.134449	−	0.990920i	$-0.457073\pi$
$577$	6.45917			0.268899			0.134449	+	0.990920i	$0.457073\pi$
$578$			3.64491i			0.151608i
$579$	−13.7168	−	13.7168i	−0.570051	−	0.570051i
$580$	−7.47541	+	7.80668i	−0.310399	+	0.324155i
$581$	22.7315			0.943062
$582$	−3.59574	−	3.59574i	−0.149048	−	0.149048i
$583$	11.2581	−	11.2581i	0.466263	−	0.466263i
$584$	−9.57090	−	9.57090i	−0.396047	−	0.396047i
$585$	0.101661	+	4.68975i	0.00420317	+	0.193897i
$586$	8.19264	−	8.19264i	0.338435	−	0.338435i
$587$		−	30.4031i		−	1.25487i	−0.778669	−	0.627435i	$-0.784105\pi$
$587$		−	30.4031i		−	1.25487i	0.778669	−	0.627435i	$-0.215895\pi$
$588$	5.95576	+	5.95576i	0.245611	+	0.245611i
$589$			2.67315i			0.110145i
$590$	22.1287	−	23.1093i	0.911022	−	0.951394i
$591$			17.8938i			0.736052i
$592$	−5.20783	−	3.14301i	−0.214040	−	0.129177i
$593$	4.55951	+	4.55951i	0.187237	+	0.187237i	0.794500	−	0.607264i	$-0.207733\pi$
$593$	4.55951	+	4.55951i	0.187237	+	0.187237i	−0.607264	+	0.794500i	$0.707733\pi$
$594$	1.93799	+	1.93799i	0.0795167	+	0.0795167i
$595$	28.8183	+	27.5954i	1.18144	+	1.13130i
$596$		−	18.5418i		−	0.759504i
$597$	−4.60742			−0.188569
$598$		−	2.29306i		−	0.0937703i
$599$		−	20.9262i		−	0.855023i	−0.904010	−	0.427511i	$-0.859390\pi$
$599$		−	20.9262i		−	0.855023i	0.904010	−	0.427511i	$-0.140610\pi$
$600$	3.68542	+	3.37900i	0.150457	+	0.137947i
$601$	46.3008			1.88865			0.944325	−	0.329013i	$-0.106716\pi$
$601$	46.3008			1.88865			0.944325	+	0.329013i	$0.106716\pi$
$602$	7.34817	−	7.34817i	0.299489	−	0.299489i
$603$	3.42538	−	3.42538i	0.139492	−	0.139492i
$604$		−	4.53529i		−	0.184538i
$605$	−0.169049	−	7.79843i	−0.00687281	−	0.317051i
$606$	−10.1239	+	10.1239i	−0.411255	+	0.411255i
$607$			20.3014i			0.824007i	0.911182	+	0.412004i	$0.135171\pi$
$607$			20.3014i			0.824007i	−0.911182	+	0.412004i	$0.864829\pi$
$608$	3.00837	+	3.00837i	0.122005	+	0.122005i
$609$	13.4230	−	13.4230i	0.543928	−	0.543928i
$610$	−10.4407	+	10.9034i	−0.422734	+	0.441467i
$611$	8.98053	+	8.98053i	0.363313	+	0.363313i
$612$		−	4.54367i		−	0.183667i
$613$	−11.6147	+	11.6147i	−0.469115	+	0.469115i	−0.901628	−	0.432513i	$-0.857627\pi$
$613$	−11.6147	+	11.6147i	−0.469115	+	0.469115i	0.432513	+	0.901628i	$0.357627\pi$
$614$	1.93471	−	1.93471i	0.0780787	−	0.0780787i
$615$	−5.40099	+	5.64033i	−0.217789	+	0.227440i
$616$	7.61083	−	7.61083i	0.306649	−	0.306649i
$617$	−5.70622	−	5.70622i	−0.229724	−	0.229724i	0.582853	−	0.812577i	$-0.301936\pi$
$617$	−5.70622	−	5.70622i	−0.229724	−	0.229724i	−0.812577	+	0.582853i	$0.801936\pi$
$618$	5.94723	+	5.94723i	0.239233	+	0.239233i
$619$	10.0488			0.403896			0.201948	−	0.979396i	$-0.435273\pi$
$619$	10.0488			0.403896			0.201948	+	0.979396i	$0.435273\pi$
$620$	−1.01475	−	0.971689i	−0.0407533	−	0.0390240i
$621$	−0.772920	+	0.772920i	−0.0310162	+	0.0310162i
$622$	−24.0063	−	24.0063i	−0.962565	−	0.962565i
$623$	53.3116			2.13588
$624$	−1.48338	−	1.48338i	−0.0593826	−	0.0593826i
$625$	24.9061	−	2.16468i	0.996244	−	0.0865870i
$626$	−28.6636			−1.14563
$627$	11.6604			0.465670
$628$	2.15926	−	2.15926i	0.0861639	−	0.0861639i
$629$	23.6626	+	14.2808i	0.943491	+	0.569413i
$630$	−6.34253	−	6.07338i	−0.252692	−	0.241969i
$631$	14.4480	−	14.4480i	0.575166	−	0.575166i	−0.358402	−	0.933568i	$-0.616678\pi$
$631$	14.4480	−	14.4480i	0.575166	−	0.575166i	0.933568	+	0.358402i	$0.116678\pi$
$632$	−4.84570	−	4.84570i	−0.192752	−	0.192752i
$633$	−1.04833	+	1.04833i	−0.0416674	+	0.0416674i
$634$	−14.0253	+	14.0253i	−0.557016	+	0.557016i
$635$	19.8999	+	19.0554i	0.789703	+	0.756192i
$636$	5.80916			0.230348
$637$	−17.6693			−0.700082
$638$	−9.36777	−	9.36777i	−0.370874	−	0.370874i
$639$		−	0.512824i		−	0.0202870i
$640$	−2.23554	+	0.0484605i	−0.0883676	+	0.00191557i
$641$	−37.9442			−1.49870			−0.749352	−	0.662171i	$-0.769635\pi$
$641$	−37.9442			−1.49870			−0.749352	+	0.662171i	$0.769635\pi$
$642$	6.90462			0.272504
$643$	−27.7110			−1.09281			−0.546407	−	0.837520i	$-0.684005\pi$
$643$	−27.7110			−1.09281			−0.546407	+	0.837520i	$0.684005\pi$
$644$	3.03539	+	3.03539i	0.119611	+	0.119611i
$645$	−4.09227	+	4.27362i	−0.161133	+	0.168273i
$646$	−13.6690	−	13.6690i	−0.537800	−	0.537800i
$647$		−	13.3729i		−	0.525745i	−0.964831	−	0.262872i	$-0.915330\pi$
$647$		−	13.3729i		−	0.525745i	0.964831	−	0.262872i	$-0.0846698\pi$
$648$			1.00000i			0.0392837i
$649$	27.7304	+	27.7304i	1.08851	+	1.08851i
$650$	−10.4792	+	0.454535i	−0.411028	+	0.0178283i
$651$	1.74479	+	1.74479i	0.0683837	+	0.0683837i
$652$	−13.2270			−0.518011
$653$	−10.9215			−0.427391			−0.213695	−	0.976900i	$-0.568550\pi$
$653$	−10.9215			−0.427391			−0.213695	+	0.976900i	$0.568550\pi$
$654$	13.2560			0.518349
$655$	34.3642	+	32.9059i	1.34272	+	1.28574i
$656$		−	3.49239i		−	0.136355i
$657$	−9.57090	−	9.57090i	−0.373396	−	0.373396i
$658$	−23.7756			−0.926868
$659$	−29.6060			−1.15329			−0.576644	−	0.816996i	$-0.695638\pi$
$659$	−29.6060			−1.15329			−0.576644	+	0.816996i	$0.695638\pi$
$660$	−4.23855	+	4.42638i	−0.164985	+	0.172297i
$661$	31.8938	−	31.8938i	1.24053	−	1.24053i	0.280744	−	0.959783i	$-0.409419\pi$
$661$	31.8938	−	31.8938i	1.24053	−	1.24053i	0.959783	−	0.280744i	$-0.0905812\pi$
$662$	5.28358	−	5.28358i	0.205352	−	0.205352i
$663$	6.73997	+	6.73997i	0.261759	+	0.261759i
$664$	4.09292	−	4.09292i	0.158836	−	0.158836i
$665$	−37.3516	+	0.809681i	−1.44843	+	0.0313981i
$666$	−5.20783	−	3.14301i	−0.201799	−	0.121789i
$667$	3.73610	−	3.73610i	0.144663	−	0.144663i
$668$	2.15667			0.0834441
$669$	9.77217			0.377814
$670$	7.82357	+	7.49158i	0.302251	+	0.289425i
$671$	−13.0838	−	13.0838i	−0.505094	−	0.505094i
$672$	3.92718			0.151494
$673$	20.0029	+	20.0029i	0.771053	+	0.771053i	0.978291	−	0.207237i	$-0.0664472\pi$
$673$	20.0029	+	20.0029i	0.771053	+	0.771053i	−0.207237	+	0.978291i	$0.566447\pi$
$674$	−15.8649	+	15.8649i	−0.611093	+	0.611093i
$675$	3.68542	+	3.37900i	0.141852	+	0.130058i
$676$	−8.59918			−0.330738
$677$	−4.10184	−	4.10184i	−0.157646	−	0.157646i	0.623876	−	0.781523i	$-0.285557\pi$
$677$	−4.10184	−	4.10184i	−0.157646	−	0.157646i	−0.781523	+	0.623876i	$0.785557\pi$
$678$	−2.89105	−	2.89105i	−0.111030	−	0.111030i
$679$	−14.1211	+	14.1211i	−0.541918	+	0.541918i
$680$	10.1576	−	0.220188i	0.389525	−	0.00844384i
$681$	−0.239636	+	0.239636i	−0.00918287	+	0.00918287i
$682$	1.21767	−	1.21767i	0.0466269	−	0.0466269i
$683$			26.9295i			1.03043i	0.857061	+	0.515215i	$0.172288\pi$
$683$			26.9295i			1.03043i	−0.857061	+	0.515215i	$0.827712\pi$
$684$	3.00837	+	3.00837i	0.115028	+	0.115028i
$685$	−17.1610	−	16.4328i	−0.655689	−	0.627865i
$686$	3.95079	−	3.95079i	0.150842	−	0.150842i
$687$	4.85597	+	4.85597i	0.185267	+	0.185267i
$688$		−	2.64615i		−	0.100883i
$689$	−8.61717	+	8.61717i	−0.328288	+	0.328288i
$690$	−1.76535	−	1.69044i	−0.0672058	−	0.0643539i
$691$			4.39008i			0.167007i	0.996508	+	0.0835033i	$0.0266109\pi$
$691$			4.39008i			0.167007i	−0.996508	+	0.0835033i	$0.973389\pi$
$692$	−12.7830	+	12.7830i	−0.485938	+	0.485938i
$693$	7.61083	−	7.61083i	0.289112	−	0.289112i
$694$	20.2697			0.769428
$695$	0.367469	+	16.9518i	0.0139389	+	0.643019i
$696$		−	4.83375i		−	0.183223i
$697$			15.8683i			0.601054i
$698$	−23.3133			−0.882420
$699$			16.7617i			0.633985i
$700$	13.2699	−	14.4733i	0.501557	−	0.547040i
$701$	7.67375	+	7.67375i	0.289834	+	0.289834i	0.837014	−	0.547181i	$-0.184299\pi$
$701$	7.67375	+	7.67375i	0.289834	+	0.289834i	−0.547181	+	0.837014i	$0.684299\pi$
$702$	−1.48338	−	1.48338i	−0.0559865	−	0.0559865i
$703$	−25.1224	+	6.21172i	−0.947509	+	0.234279i
$704$		−	2.74073i		−	0.103295i
$705$	13.5342	−	0.293385i	0.509728	−	0.0110495i
$706$			35.1904i			1.32441i
$707$	39.7583	+	39.7583i	1.49526	+	1.49526i
$708$			14.3089i			0.537760i
$709$	−4.72562	+	4.72562i	−0.177474	+	0.177474i	−0.790254	−	0.612779i	$-0.790051\pi$
$709$	−4.72562	+	4.72562i	−0.177474	+	0.177474i	0.612779	+	0.790254i	$0.290051\pi$
$710$	1.14644	−	0.0248517i	0.0430252	−	0.000932669i
$711$	−4.84570	−	4.84570i	−0.181728	−	0.181728i
$712$	9.59900	−	9.59900i	0.359738	−	0.359738i
$713$	0.485637	+	0.485637i	0.0181872	+	0.0181872i
$714$	−17.8438			−0.667787
$715$	−0.278626	−	12.8533i	−0.0104200	−	0.480688i
$716$	8.92829	+	8.92829i	0.333666	+	0.333666i
$717$			16.7517i			0.625606i
$718$	34.3706			1.28270
$719$		−	48.1348i		−	1.79513i	−0.440887	−	0.897563i	$-0.645336\pi$
$719$		−	48.1348i		−	1.79513i	0.440887	−	0.897563i	$-0.354664\pi$
$720$	−2.23554	+	0.0484605i	−0.0833138	+	0.00180602i
$721$	23.3558	−	23.3558i	0.869816	−	0.869816i
$722$	−0.899470			−0.0334748
$723$	−1.50155			−0.0558433
$724$	−8.76543			−0.325765
$725$	−17.8144	−	16.3333i	−0.661611	−	0.606603i
$726$	2.46666	+	2.46666i	0.0915463	+	0.0915463i
$727$			30.0659i			1.11508i	0.830150	+	0.557541i	$0.188255\pi$
$727$			30.0659i			1.11508i	−0.830150	+	0.557541i	$0.811745\pi$
$728$	−5.82548	+	5.82548i	−0.215907	+	0.215907i
$729$			1.00000i			0.0370370i
$730$	20.9323	−	21.8600i	0.774741	−	0.809074i
$731$			12.0232i			0.444694i
$732$		−	6.75121i		−	0.249532i
$733$	0.507990	−	0.507990i	0.0187630	−	0.0187630i	−0.697663	−	0.716426i	$-0.745777\pi$
$733$	0.507990	−	0.507990i	0.0187630	−	0.0187630i	0.716426	+	0.697663i	$0.245777\pi$
$734$	−15.7170	−	15.7170i	−0.580125	−	0.580125i
$735$	−13.0257	+	13.6030i	−0.480462	+	0.501753i
$736$	1.09307			0.0402912
$737$	−9.38804	+	9.38804i	−0.345813	+	0.345813i
$738$		−	3.49239i		−	0.128557i
$739$	−33.1591			−1.21978			−0.609889	−	0.792487i	$-0.708786\pi$
$739$	−33.1591			−1.21978			−0.609889	+	0.792487i	$0.708786\pi$
$740$	6.77397	−	11.7946i	0.249016	−	0.433579i
$741$	−8.92508			−0.327871
$742$		−	22.8136i		−	0.837513i
$743$	−7.44969	+	7.44969i	−0.273303	+	0.273303i	−0.830428	−	0.557126i	$-0.811904\pi$
$743$	−7.44969	+	7.44969i	−0.273303	+	0.273303i	0.557126	+	0.830428i	$0.311904\pi$
$744$	0.628315			0.0230351
$745$	41.4511	−	0.898547i	1.51865	−	0.0329202i
$746$	−5.59113	−	5.59113i	−0.204706	−	0.204706i
$747$	4.09292	−	4.09292i	0.149752	−	0.149752i
$748$			12.4530i			0.455326i
$749$		−	27.1157i		−	0.990785i
$750$	−7.37531	+	8.40267i	−0.269308	+	0.306822i
$751$			40.2247i			1.46782i	0.679246	+	0.733911i	$0.262307\pi$
$751$			40.2247i			1.46782i	−0.679246	+	0.733911i	$0.737693\pi$
$752$	−4.28090	+	4.28090i	−0.156108	+	0.156108i
$753$		−	14.6074i		−	0.532323i
$754$	7.17028	+	7.17028i	0.261126	+	0.261126i
$755$	10.1388	−	0.219783i	0.368990	−	0.00799871i
$756$	3.92718			0.142830
$757$	4.85976			0.176631			0.0883156	−	0.996093i	$-0.471852\pi$
$757$	4.85976			0.176631			0.0883156	+	0.996093i	$0.471852\pi$
$758$	−20.7595			−0.754018
$759$	2.11837	−	2.11837i	0.0768918	−	0.0768918i
$760$	−6.57954	+	6.87112i	−0.238665	+	0.249242i
$761$		−	10.4339i		−	0.378230i	−0.981955	−	0.189115i	$-0.939438\pi$
$761$		−	10.4339i		−	0.378230i	0.981955	−	0.189115i	$-0.0605618\pi$
$762$	−12.3216			−0.446366
$763$		−	52.0585i		−	1.88464i
$764$	−3.29001	−	3.29001i	−0.119028	−	0.119028i
$765$	10.1576	−	0.220188i	0.367247	−	0.00796093i
$766$	−19.9351			−0.720284
$767$	−21.2254	−	21.2254i	−0.766406	−	0.766406i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−29.8513	−	29.8513i	−1.07647	−	1.07647i	−0.996823	−	0.0796432i	$-0.974622\pi$
$769$	−29.8513	−	29.8513i	−1.07647	−	1.07647i	−0.0796432	−	0.996823i	$-0.525378\pi$
$770$	17.3832	+	16.6455i	0.626446	+	0.599863i
$771$	19.9022	−	19.9022i	0.716760	−	0.716760i
$772$			19.3985i			0.698168i
$773$	−31.7498	−	31.7498i	−1.14196	−	1.14196i	−0.988091	−	0.153868i	$-0.950827\pi$
$773$	−31.7498	−	31.7498i	−1.14196	−	1.14196i	−0.153868	−	0.988091i	$-0.549173\pi$
$774$		−	2.64615i		−	0.0951138i
$775$	2.12308	−	2.31561i	0.0762632	−	0.0831790i
$776$			5.08514i			0.182546i
$777$	−12.3432	+	20.4521i	−0.442809	+	0.733714i
$778$	−2.00735	−	2.00735i	−0.0719671	−	0.0719671i
$779$	−10.5064	−	10.5064i	−0.376431	−	0.376431i
$780$	3.24427	−	3.38804i	0.116163	−	0.121311i
$781$			1.40551i			0.0502933i
$782$	−4.96656			−0.177604
$783$		−	4.83375i		−	0.172744i
$784$		−	8.42272i		−	0.300811i
$785$	4.93176	+	4.72248i	0.176022	+	0.168553i
$786$	−21.2777			−0.758949
$787$	−26.3501	+	26.3501i	−0.939280	+	0.939280i	−0.998259	−	0.0589790i	$-0.981215\pi$
$787$	−26.3501	+	26.3501i	−0.939280	+	0.939280i	0.0589790	+	0.998259i	$0.481215\pi$
$788$	12.6528	−	12.6528i	0.450738	−	0.450738i
$789$		−	1.61459i		−	0.0574808i
$790$	10.5979	−	11.0676i	0.377058	−	0.393767i
$791$	−11.3537	+	11.3537i	−0.403690	+	0.403690i
$792$		−	2.74073i		−	0.0973877i
$793$	10.0146	+	10.0146i	0.355628	+	0.355628i
$794$	−21.4010	+	21.4010i	−0.759492	+	0.759492i
$795$	0.281515	+	12.9866i	0.00998430	+	0.460588i
$796$	3.25794	+	3.25794i	0.115474	+	0.115474i
$797$			18.4042i			0.651912i	0.945385	+	0.325956i	$0.105686\pi$
$797$			18.4042i			0.651912i	−0.945385	+	0.325956i	$0.894314\pi$
$798$	11.8144	−	11.8144i	0.418225	−	0.418225i
$799$	19.4510	−	19.4510i	0.688127	−	0.688127i
$800$	−0.216671	−	4.99530i	−0.00766048	−	0.176611i
$801$	9.59900	−	9.59900i	0.339164	−	0.339164i
$802$	18.1649	+	18.1649i	0.641424	+	0.641424i
$803$	26.2313	+	26.2313i	0.925682	+	0.925682i
$804$	−4.84421			−0.170842
$805$	−6.63865	+	6.93285i	−0.233982	+	0.244351i
$806$	−0.932028	+	0.932028i	−0.0328293	+	0.0328293i
$807$	0.534131	+	0.534131i	0.0188023	+	0.0188023i
$808$	14.3173			0.503682
$809$	−32.1862	−	32.1862i	−1.13161	−	1.13161i	−0.989910	−	0.141697i	$-0.954744\pi$
$809$	−32.1862	−	32.1862i	−1.13161	−	1.13161i	−0.141697	−	0.989910i	$-0.545256\pi$
$810$	−2.23554	+	0.0484605i	−0.0785490	+	0.00170273i
$811$	−39.7904			−1.39723			−0.698616	−	0.715497i	$-0.746200\pi$
$811$	−39.7904			−1.39723			−0.698616	+	0.715497i	$0.746200\pi$
$812$	−18.9830			−0.666173
$813$	9.24918	−	9.24918i	0.324383	−	0.324383i
$814$	14.2733	+	8.61416i	0.500278	+	0.301926i
$815$	−0.640989	−	29.5696i	−0.0224529	−	1.03578i
$816$	−3.21286	+	3.21286i	−0.112473	+	0.112473i
$817$	−7.96058	−	7.96058i	−0.278505	−	0.278505i
$818$	−20.7880	+	20.7880i	−0.726837	+	0.726837i
$819$	−5.82548	+	5.82548i	−0.203559	+	0.203559i
$820$	7.80739	−	0.169243i	0.272646	−	0.00591023i
$821$	−10.6472			−0.371591			−0.185796	−	0.982588i	$-0.559486\pi$
$821$	−10.6472			−0.371591			−0.185796	+	0.982588i	$0.559486\pi$
$822$	10.6258			0.370617
$823$	−23.8488	−	23.8488i	−0.831316	−	0.831316i	0.156381	−	0.987697i	$-0.450017\pi$
$823$	−23.8488	−	23.8488i	−0.831316	−	0.831316i	−0.987697	+	0.156381i	$0.950017\pi$
$824$		−	8.41065i		−	0.292999i
$825$	−10.1008	−	9.26094i	−0.351663	−	0.322425i
$826$	56.1934			1.95522
$827$	9.17793			0.319148			0.159574	−	0.987186i	$-0.448988\pi$
$827$	9.17793			0.319148			0.159574	+	0.987186i	$0.448988\pi$
$828$	1.09307			0.0379869
$829$	−38.2927	−	38.2927i	−1.32996	−	1.32996i	−0.905398	−	0.424564i	$-0.860428\pi$
$829$	−38.2927	−	38.2927i	−1.32996	−	1.32996i	−0.424564	−	0.905398i	$-0.639572\pi$
$830$	9.34824	+	8.95155i	0.324482	+	0.310713i
$831$	−19.7253	−	19.7253i	−0.684263	−	0.684263i
$832$			2.09781i			0.0727285i
$833$			38.2700i			1.32598i
$834$	−5.36189	−	5.36189i	−0.185667	−	0.185667i
$835$	0.104513	+	4.82133i	0.00361683	+	0.166849i
$836$	−8.24513	−	8.24513i	−0.285164	−	0.285164i
$837$	0.628315			0.0217177
$838$	−6.01083			−0.207641
$839$	8.64494			0.298457			0.149228	−	0.988803i	$-0.452321\pi$
$839$	8.64494			0.298457			0.149228	+	0.988803i	$0.452321\pi$
$840$	0.190313	+	8.77937i	0.00656642	+	0.302917i
$841$		−	5.63482i		−	0.194304i
$842$	−14.1798	−	14.1798i	−0.488668	−	0.488668i
$843$	4.59858			0.158383
$844$	1.48256			0.0510319
$845$	−0.416721	−	19.2238i	−0.0143356	−	0.661320i
$846$	−4.28090	+	4.28090i	−0.147180	+	0.147180i
$847$	9.68701	−	9.68701i	0.332850	−	0.332850i
$848$	−4.10770	−	4.10770i	−0.141059	−	0.141059i
$849$	−9.09320	+	9.09320i	−0.312078	+	0.312078i
$850$	0.984481	+	22.6970i	0.0337674	+	0.778500i
$851$	−3.43554	+	5.69254i	−0.117769	+	0.195138i
$852$	−0.362622	+	0.362622i	−0.0124232	+	0.0124232i
$853$	37.4151			1.28107			0.640535	−	0.767929i	$-0.278713\pi$
$853$	37.4151			1.28107			0.640535	+	0.767929i	$0.278713\pi$
$854$	−26.5132			−0.907263
$855$	−6.57954	+	6.87112i	−0.225016	+	0.234987i
$856$	−4.88230	−	4.88230i	−0.166874	−	0.166874i
$857$	37.7547			1.28967			0.644837	−	0.764320i	$-0.276925\pi$
$857$	37.7547			1.28967			0.644837	+	0.764320i	$0.276925\pi$
$858$	4.06554	+	4.06554i	0.138795	+	0.138795i
$859$	−9.37733	+	9.37733i	−0.319950	+	0.319950i	−0.848748	−	0.528798i	$-0.822643\pi$
$859$	−9.37733	+	9.37733i	−0.319950	+	0.319950i	0.528798	+	0.848748i	$0.322643\pi$
$860$	5.91557	−	0.128234i	0.201719	−	0.00437273i
$861$	−13.7152			−0.467414
$862$	19.4897	+	19.4897i	0.663821	+	0.663821i
$863$	−31.0440	−	31.0440i	−1.05675	−	1.05675i	−0.998290	−	0.0584611i	$-0.981381\pi$
$863$	−31.0440	−	31.0440i	−1.05675	−	1.05675i	−0.0584611	−	0.998290i	$-0.518619\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	−29.1965	−	27.9576i	−0.992711	−	0.950586i
$866$	27.2929	−	27.2929i	0.927451	−	0.927451i
$867$	2.57734	−	2.57734i	0.0875310	−	0.0875310i
$868$		−	2.46750i		−	0.0837525i
$869$	13.2808	+	13.2808i	0.450519	+	0.450519i
$870$	10.8061	−	0.234246i	0.366360	−	0.00794169i
$871$	7.18580	−	7.18580i	0.243481	−	0.243481i
$872$	−9.37338	−	9.37338i	−0.317423	−	0.317423i
$873$			5.08514i			0.172106i
$874$	3.28837	−	3.28837i	0.111231	−	0.111231i
$875$	32.9988	+	28.9641i	1.11556	+	0.979167i
$876$			13.5353i			0.457315i
$877$	−13.1731	+	13.1731i	−0.444825	+	0.444825i	−0.893630	−	0.448805i	$-0.851850\pi$
$877$	−13.1731	+	13.1731i	−0.444825	+	0.444825i	0.448805	+	0.893630i	$0.351850\pi$
$878$	−27.9211	+	27.9211i	−0.942291	+	0.942291i
$879$	−11.5861			−0.390791
$880$	6.12703	−	0.132817i	0.206542	−	0.00447727i
$881$			19.6288i			0.661311i	0.943752	+	0.330655i	$0.107270\pi$
$881$			19.6288i			0.661311i	−0.943752	+	0.330655i	$0.892730\pi$
$882$		−	8.42272i		−	0.283608i
$883$	14.8323			0.499145			0.249573	−	0.968356i	$-0.419710\pi$
$883$	14.8323			0.499145			0.249573	+	0.968356i	$0.419710\pi$
$884$		−	9.53176i		−	0.320588i
$885$	−31.9881	+	0.693414i	−1.07527	+	0.0233089i
$886$	−13.8772	−	13.8772i	−0.466214	−	0.466214i
$887$	−22.6343	−	22.6343i	−0.759985	−	0.759985i	0.216335	−	0.976319i	$-0.430590\pi$
$887$	−22.6343	−	22.6343i	−0.759985	−	0.759985i	−0.976319	+	0.216335i	$0.930590\pi$
$888$	1.46004	+	5.90494i	0.0489959	+	0.198157i
$889$			48.3893i			1.62292i
$890$	21.9241	+	20.9938i	0.734899	+	0.703714i
$891$		−	2.74073i		−	0.0918180i
$892$	−6.90996	−	6.90996i	−0.231363	−	0.231363i
$893$			25.7570i			0.861926i
$894$	−13.1111	+	13.1111i	−0.438500	+	0.438500i
$895$	−19.5269	+	20.3922i	−0.652712	+	0.681637i
$896$	−2.77693	−	2.77693i	−0.0927708	−	0.0927708i
$897$	−1.62144	+	1.62144i	−0.0541383	+	0.0541383i
$898$	4.29038	+	4.29038i	0.143172	+	0.143172i
$899$	−3.03712			−0.101294
$900$	−0.216671	−	4.99530i	−0.00722237	−	0.166510i
$901$	18.6640	+	18.6640i	0.621788	+	0.621788i
$902$			9.57172i			0.318703i
$903$	−10.3919			−0.345820
$904$			4.08857i			0.135984i
$905$	−0.424777	−	19.5955i	−0.0141201	−	0.651377i
$906$	−3.20694	+	3.20694i	−0.106543	+	0.106543i
$907$	−45.0345			−1.49535			−0.747673	−	0.664067i	$-0.768829\pi$
$907$	−45.0345			−1.49535			−0.747673	+	0.664067i	$0.768829\pi$
$908$	0.338896			0.0112467
$909$	14.3173			0.474876
$910$	−13.3054	−	12.7408i	−0.441071	−	0.422354i
$911$	−18.3283	−	18.3283i	−0.607244	−	0.607244i	0.334981	−	0.942225i	$-0.391270\pi$
$911$	−18.3283	−	18.3283i	−0.607244	−	0.607244i	−0.942225	+	0.334981i	$0.891270\pi$
$912$		−	4.25447i		−	0.140880i
$913$	−11.2176	+	11.2176i	−0.371248	+	0.371248i
$914$			37.1873i			1.23005i
$915$	15.0926	−	0.327167i	0.498946	−	0.0108158i
$916$		−	6.86738i		−	0.226905i
$917$			83.5612i			2.75943i
$918$	−3.21286	+	3.21286i	−0.106040	+	0.106040i
$919$	−24.5868	−	24.5868i	−0.811045	−	0.811045i	0.173746	−	0.984791i	$-0.444413\pi$
$919$	−24.5868	−	24.5868i	−0.811045	−	0.811045i	−0.984791	+	0.173746i	$0.944413\pi$
$920$	0.0529709	+	2.44361i	0.00174640	+	0.0805635i
$921$	−2.73610			−0.0901575
$922$	13.3683	−	13.3683i	0.440262	−	0.440262i
$923$		−	1.07581i		−	0.0354107i
$924$	−10.7633			−0.354088
$925$	26.6957	+	14.5719i	0.877749	+	0.479122i
$926$	41.3804			1.35984
$927$		−	8.41065i		−	0.276242i
$928$	−3.41798	+	3.41798i	−0.112201	+	0.112201i
$929$	−56.6055			−1.85717			−0.928583	−	0.371124i	$-0.878972\pi$
$929$	−56.6055			−1.85717			−0.928583	+	0.371124i	$0.878972\pi$
$930$	0.0304485	+	1.40462i	0.000998444	+	0.0460595i
$931$	−25.3386	−	25.3386i	−0.830440	−	0.830440i
$932$	11.8523	−	11.8523i	0.388235	−	0.388235i
$933$			33.9500i			1.11147i
$934$			32.7500i			1.07161i
$935$	−27.8392	+	0.603478i	−0.910438	+	0.0197358i
$936$			2.09781i			0.0685691i
$937$	−3.72209	+	3.72209i	−0.121596	+	0.121596i	−0.765286	−	0.643690i	$-0.777402\pi$
$937$	−3.72209	+	3.72209i	−0.121596	+	0.121596i	0.643690	+	0.765286i	$0.277402\pi$
$938$			19.0241i			0.621159i
$939$	20.2682	+	20.2682i	0.661428	+	0.661428i
$940$	−9.77759	−	9.36269i	−0.318910	−	0.305377i
$941$	−12.1814			−0.397102			−0.198551	−	0.980091i	$-0.563624\pi$
$941$	−12.1814			−0.397102			−0.198551	+	0.980091i	$0.563624\pi$
$942$	−3.05366			−0.0994935
$943$	−3.81744			−0.124313
$944$	10.1179	−	10.1179i	0.329309	−	0.329309i
$945$	0.190313	+	8.77937i	0.00619088	+	0.285593i
$946$			7.25238i			0.235795i
$947$	10.2614			0.333450			0.166725	−	0.986003i	$-0.446681\pi$
$947$	10.2614			0.333450			0.166725	+	0.986003i	$0.446681\pi$
$948$			6.85285i			0.222570i
$949$	−20.0780	−	20.0780i	−0.651758	−	0.651758i
$950$	−15.6795	−	14.3759i	−0.508711	−	0.466415i
$951$	19.8348			0.643186
$952$	12.6175	+	12.6175i	0.408934	+	0.408934i
$953$	21.4108	−	21.4108i	0.693564	−	0.693564i	−0.269451	−	0.963014i	$-0.586842\pi$
$953$	21.4108	−	21.4108i	0.693564	−	0.693564i	0.963014	+	0.269451i	$0.0868421\pi$
$954$	−4.10770	−	4.10770i	−0.132992	−	0.132992i
$955$	7.19552	−	7.51439i	0.232841	−	0.243160i
$956$	11.8453	−	11.8453i	0.383104	−	0.383104i
$957$			13.2480i			0.428248i
$958$	−16.6994	−	16.6994i	−0.539535	−	0.539535i
$959$		−	41.7294i		−	1.34751i
$960$	1.61503	+	1.54650i	0.0521250	+	0.0499131i
$961$			30.6052i			0.987265i
$962$	−10.9250	−	6.59345i	−0.352238	−	0.212581i
$963$	−4.88230	−	4.88230i	−0.157330	−	0.157330i
$964$	1.06176	+	1.06176i	0.0341969	+	0.0341969i
$965$	−43.3662	+	0.940061i	−1.39601	+	0.0302616i
$966$		−	4.29269i		−	0.138115i
$967$	4.67326			0.150282			0.0751409	−	0.997173i	$-0.476059\pi$
$967$	4.67326			0.150282			0.0751409	+	0.997173i	$0.476059\pi$
$968$		−	3.48838i		−	0.112121i
$969$			19.3309i			0.620998i
$970$	−11.3681	+	0.246429i	−0.365006	+	0.00791234i
$971$	−17.6883			−0.567643			−0.283822	−	0.958877i	$-0.591602\pi$
$971$	−17.6883			−0.567643			−0.283822	+	0.958877i	$0.591602\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−21.0571	+	21.0571i	−0.675060	+	0.675060i
$974$			0.862986i			0.0276519i
$975$	7.73132	+	7.08851i	0.247601	+	0.227014i
$976$	−4.77382	+	4.77382i	−0.152806	+	0.152806i
$977$		−	17.8116i		−	0.569845i	−0.958551	−	0.284922i	$-0.908032\pi$
$977$		−	17.8116i		−	0.569845i	0.958551	−	0.284922i	$-0.0919678\pi$
$978$	9.35293	+	9.35293i	0.299074	+	0.299074i
$979$	−26.3083	+	26.3083i	−0.840817	+	0.840817i
$980$	18.8293	−	0.408169i	0.601481	−	0.0130385i
$981$	−9.37338	−	9.37338i	−0.299269	−	0.299269i
$982$		−	27.6627i		−	0.882754i
$983$	−12.7706	+	12.7706i	−0.407318	+	0.407318i	−0.880802	−	0.473484i	$-0.842996\pi$
$983$	−12.7706	+	12.7706i	−0.407318	+	0.407318i	0.473484	+	0.880802i	$0.342996\pi$
$984$	−2.46949	+	2.46949i	−0.0787246	+	0.0787246i
$985$	28.8991	+	27.6728i	0.920801	+	0.881727i
$986$	15.5302	−	15.5302i	0.494581	−	0.494581i
$987$	16.8119	+	16.8119i	0.535127	+	0.535127i
$988$	6.31099	+	6.31099i	0.200779	+	0.200779i
$989$	−2.89243			−0.0919740
$990$	6.12703	−	0.132817i	0.194730	−	0.00422121i
$991$	−24.4516	+	24.4516i	−0.776731	+	0.776731i	−0.979273	−	0.202543i	$-0.935079\pi$
$991$	−24.4516	+	24.4516i	−0.776731	+	0.776731i	0.202543	+	0.979273i	$0.435079\pi$
$992$	−0.444286	−	0.444286i	−0.0141061	−	0.0141061i
$993$	−7.47211			−0.237120
$994$	1.42408	+	1.42408i	0.0451691	+	0.0451691i
$995$	−7.12537	+	7.44114i	−0.225890	+	0.235900i
$996$	−5.78826			−0.183408
$997$	−12.2888			−0.389189			−0.194594	−	0.980884i	$-0.562339\pi$
$997$	−12.2888			−0.389189			−0.194594	+	0.980884i	$0.562339\pi$
$998$	3.33614	−	3.33614i	0.105604	−	0.105604i
$999$	1.46004	+	5.90494i	0.0461938	+	0.186824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.a.43.17	✓	36
5.2	odd	4		1110.2.o.a.487.1	yes	36
37.31	odd	4		1110.2.o.a.253.1	yes	36
185.142	even	4	inner	1110.2.l.a.697.17	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.17	✓	36	1.1	even	1	trivial
1110.2.l.a.697.17	yes	36	185.142	even	4	inner
1110.2.o.a.253.1	yes	36	37.31	odd	4
1110.2.o.a.487.1	yes	36	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.0484605 - 2.23554i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.77693 - 2.77693i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.0484605 - 2.23554i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.77693 - 2.77693i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(2.23554 - 0.0484605i) q^{10} +2.74073i q^{11} +(-0.707107 + 0.707107i) q^{12} -2.09781i q^{13} +(2.77693 + 2.77693i) q^{14} +(-1.61503 - 1.54650i) q^{15} +1.00000 q^{16} -4.54367 q^{17} +1.00000 q^{18} +(3.00837 - 3.00837i) q^{19} +(0.0484605 + 2.23554i) q^{20} -3.92718i q^{21} -2.74073 q^{22} -1.09307i q^{23} +(-0.707107 - 0.707107i) q^{24} +(-4.99530 + 0.216671i) q^{25} +2.09781 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.77693 + 2.77693i) q^{28} +(3.41798 + 3.41798i) q^{29} +(1.54650 - 1.61503i) q^{30} +(-0.444286 + 0.444286i) q^{31} +1.00000i q^{32} +(1.93799 + 1.93799i) q^{33} -4.54367i q^{34} +(-6.34253 - 6.07338i) q^{35} +1.00000i q^{36} +(-5.20783 - 3.14301i) q^{37} +(3.00837 + 3.00837i) q^{38} +(-1.48338 - 1.48338i) q^{39} +(-2.23554 + 0.0484605i) q^{40} -3.49239i q^{41} +3.92718 q^{42} -2.64615i q^{43} -2.74073i q^{44} +(-2.23554 + 0.0484605i) q^{45} +1.09307 q^{46} +(-4.28090 + 4.28090i) q^{47} +(0.707107 - 0.707107i) q^{48} -8.42272i q^{49} +(-0.216671 - 4.99530i) q^{50} +(-3.21286 + 3.21286i) q^{51} +2.09781i q^{52} +(-4.10770 - 4.10770i) q^{53} +(0.707107 - 0.707107i) q^{54} +(6.12703 - 0.132817i) q^{55} +(-2.77693 - 2.77693i) q^{56} -4.25447i q^{57} +(-3.41798 + 3.41798i) q^{58} +(10.1179 - 10.1179i) q^{59} +(1.61503 + 1.54650i) q^{60} +(-4.77382 + 4.77382i) q^{61} +(-0.444286 - 0.444286i) q^{62} +(-2.77693 - 2.77693i) q^{63} -1.00000 q^{64} +(-4.68975 + 0.101661i) q^{65} +(-1.93799 + 1.93799i) q^{66} +(3.42538 + 3.42538i) q^{67} +4.54367 q^{68} +(-0.772920 - 0.772920i) q^{69} +(6.07338 - 6.34253i) q^{70} +0.512824 q^{71} -1.00000 q^{72} +(9.57090 - 9.57090i) q^{73} +(3.14301 - 5.20783i) q^{74} +(-3.37900 + 3.68542i) q^{75} +(-3.00837 + 3.00837i) q^{76} +(7.61083 + 7.61083i) q^{77} +(1.48338 - 1.48338i) q^{78} +(4.84570 - 4.84570i) q^{79} +(-0.0484605 - 2.23554i) q^{80} -1.00000 q^{81} +3.49239 q^{82} +(4.09292 + 4.09292i) q^{83} +3.92718i q^{84} +(0.220188 + 10.1576i) q^{85} +2.64615 q^{86} +4.83375 q^{87} +2.74073 q^{88} +(9.59900 + 9.59900i) q^{89} +(-0.0484605 - 2.23554i) q^{90} +(-5.82548 - 5.82548i) q^{91} +1.09307i q^{92} +0.628315i q^{93} +(-4.28090 - 4.28090i) q^{94} +(-6.87112 - 6.57954i) q^{95} +(0.707107 + 0.707107i) q^{96} -5.08514 q^{97} +8.42272 q^{98} +2.74073 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

Related objects

Downloads

Learn more