LMFDB - Embedded newform 471.2.e.c.169.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(169,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("471.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.e (of order $3$, 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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			169.6
Character	$\chi$	$=$	471.169
Dual form			471.2.e.c.301.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.907528 q^{2} +(-0.500000 - 0.866025i) q^{3} -1.17639 q^{4} +(-0.0276317 - 0.0478596i) q^{5} +(0.453764 + 0.785942i) q^{6} +1.18963 q^{7} +2.88267 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-0.907528 q^{2} +(-0.500000 - 0.866025i) q^{3} -1.17639 q^{4} +(-0.0276317 - 0.0478596i) q^{5} +(0.453764 + 0.785942i) q^{6} +1.18963 q^{7} +2.88267 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.0250766 + 0.0434339i) q^{10} +(1.02960 + 1.78331i) q^{11} +(0.588197 + 1.01879i) q^{12} +(-1.49254 + 2.58516i) q^{13} -1.07962 q^{14} +(-0.0276317 + 0.0478596i) q^{15} -0.263312 q^{16} +(-1.22856 - 2.12793i) q^{17} +(0.453764 - 0.785942i) q^{18} +(-2.30064 - 3.98483i) q^{19} +(0.0325058 + 0.0563017i) q^{20} +(-0.594813 - 1.03025i) q^{21} +(-0.934387 - 1.61841i) q^{22} +8.53195 q^{23} +(-1.44133 - 2.49646i) q^{24} +(2.49847 - 4.32748i) q^{25} +(1.35452 - 2.34611i) q^{26} +1.00000 q^{27} -1.39947 q^{28} +8.37411 q^{29} +(0.0250766 - 0.0434339i) q^{30} +(2.32680 - 4.03014i) q^{31} -5.52637 q^{32} +(1.02960 - 1.78331i) q^{33} +(1.11496 + 1.93116i) q^{34} +(-0.0328714 - 0.0569350i) q^{35} +(0.588197 - 1.01879i) q^{36} +(3.50575 - 6.07214i) q^{37} +(2.08790 + 3.61634i) q^{38} +2.98509 q^{39} +(-0.0796530 - 0.137963i) q^{40} +2.54715 q^{41} +(0.539810 + 0.934978i) q^{42} +(-4.70147 + 8.14318i) q^{43} +(-1.21121 - 2.09788i) q^{44} +0.0552635 q^{45} -7.74298 q^{46} +(5.23742 - 9.07147i) q^{47} +(0.131656 + 0.228035i) q^{48} -5.58479 q^{49} +(-2.26743 + 3.92731i) q^{50} +(-1.22856 + 2.12793i) q^{51} +(1.75582 - 3.04117i) q^{52} +(-0.611242 + 1.05870i) q^{53} -0.907528 q^{54} +(0.0568990 - 0.0985520i) q^{55} +3.42930 q^{56} +(-2.30064 + 3.98483i) q^{57} -7.59974 q^{58} +13.2674 q^{59} +(0.0325058 - 0.0563017i) q^{60} +(-5.08799 - 8.81266i) q^{61} +(-2.11164 + 3.65746i) q^{62} +(-0.594813 + 1.03025i) q^{63} +5.54196 q^{64} +0.164966 q^{65} +(-0.934387 + 1.61841i) q^{66} -8.62010 q^{67} +(1.44527 + 2.50329i) q^{68} +(-4.26597 - 7.38888i) q^{69} +(0.0298317 + 0.0516701i) q^{70} +(-6.41999 + 11.1198i) q^{71} +(-1.44133 + 2.49646i) q^{72} +(6.96746 + 12.0680i) q^{73} +(-3.18157 + 5.51063i) q^{74} -4.99695 q^{75} +(2.70646 + 4.68772i) q^{76} +(1.22483 + 2.12148i) q^{77} -2.70905 q^{78} +6.83192 q^{79} +(0.00727578 + 0.0126020i) q^{80} +(-0.500000 - 0.866025i) q^{81} -2.31161 q^{82} +(2.53415 - 4.38928i) q^{83} +(0.699734 + 1.21198i) q^{84} +(-0.0678947 + 0.117597i) q^{85} +(4.26671 - 7.39016i) q^{86} +(-4.18705 - 7.25219i) q^{87} +(2.96798 + 5.14069i) q^{88} +(4.02647 + 6.97406i) q^{89} -0.0501531 q^{90} +(-1.77557 + 3.07538i) q^{91} -10.0369 q^{92} -4.65360 q^{93} +(-4.75310 + 8.23261i) q^{94} +(-0.127141 + 0.220215i) q^{95} +(2.76318 + 4.78597i) q^{96} +(8.93896 - 15.4827i) q^{97} +5.06835 q^{98} -2.05919 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.907528			−0.641719			−0.320860	−	0.947127i	$-0.603972\pi$
$2$	−0.907528			−0.641719			−0.320860	+	0.947127i	$0.603972\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.17639			−0.588197
$5$	−0.0276317	−	0.0478596i	−0.0123573	−	0.0214034i	0.859781	−	0.510664i	$-0.170600\pi$
$5$	−0.0276317	−	0.0478596i	−0.0123573	−	0.0214034i	−0.872138	+	0.489260i	$0.837267\pi$
$6$	0.453764	+	0.785942i	0.185248	+	0.320860i
$7$	1.18963			0.449637			0.224818	−	0.974401i	$-0.427821\pi$
$7$	1.18963			0.449637			0.224818	+	0.974401i	$0.427821\pi$
$8$	2.88267			1.01918
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.0250766	+	0.0434339i	0.00792991	+	0.0137350i
$11$	1.02960	+	1.78331i	0.310435	+	0.537689i	0.978457	−	0.206453i	$-0.0661920\pi$
$11$	1.02960	+	1.78331i	0.310435	+	0.537689i	−0.668022	+	0.744142i	$0.732859\pi$
$12$	0.588197	+	1.01879i	0.169798	+	0.294098i
$13$	−1.49254	+	2.58516i	−0.413957	+	0.716995i	−0.995318	−	0.0966508i	$-0.969187\pi$
$13$	−1.49254	+	2.58516i	−0.413957	+	0.716995i	0.581361	+	0.813646i	$0.302520\pi$
$14$	−1.07962			−0.288540
$15$	−0.0276317	+	0.0478596i	−0.00713448	+	0.0123573i
$16$	−0.263312			−0.0658281
$17$	−1.22856	−	2.12793i	−0.297970	−	0.516100i	0.677701	−	0.735338i	$-0.262976\pi$
$17$	−1.22856	−	2.12793i	−0.297970	−	0.516100i	−0.975671	+	0.219238i	$0.929643\pi$
$18$	0.453764	−	0.785942i	0.106953	−	0.185248i
$19$	−2.30064	−	3.98483i	−0.527803	−	0.914182i	−0.999475	−	0.0324077i	$-0.989682\pi$
$19$	−2.30064	−	3.98483i	−0.527803	−	0.914182i	0.471671	−	0.881774i	$-0.343651\pi$
$20$	0.0325058	+	0.0563017i	0.00726851	+	0.0125894i
$21$	−0.594813	−	1.03025i	−0.129799	−	0.224818i
$22$	−0.934387	−	1.61841i	−0.199212	−	0.345045i
$23$	8.53195			1.77903			0.889517	−	0.456902i	$-0.151041\pi$
$23$	8.53195			1.77903			0.889517	+	0.456902i	$0.151041\pi$
$24$	−1.44133	−	2.49646i	−0.294211	−	0.509588i
$25$	2.49847	−	4.32748i	0.499695	−	0.865496i
$26$	1.35452	−	2.34611i	0.265644	−	0.460109i
$27$	1.00000			0.192450
$28$	−1.39947			−0.264475
$29$	8.37411			1.55503			0.777516	−	0.628863i	$-0.216479\pi$
$29$	8.37411			1.55503			0.777516	+	0.628863i	$0.216479\pi$
$30$	0.0250766	−	0.0434339i	0.00457833	−	0.00792991i
$31$	2.32680	−	4.03014i	0.417906	−	0.723834i	−0.577823	−	0.816162i	$-0.696098\pi$
$31$	2.32680	−	4.03014i	0.417906	−	0.723834i	0.995729	+	0.0923284i	$0.0294310\pi$
$32$	−5.52637			−0.976933
$33$	1.02960	−	1.78331i	0.179230	−	0.310435i
$34$	1.11496	+	1.93116i	0.191213	+	0.331191i
$35$	−0.0328714	−	0.0569350i	−0.00555629	−	0.00962377i
$36$	0.588197	−	1.01879i	0.0980328	−	0.169798i
$37$	3.50575	−	6.07214i	0.576342	−	0.998253i	−0.419553	−	0.907731i	$-0.637813\pi$
$37$	3.50575	−	6.07214i	0.576342	−	0.998253i	0.995894	−	0.0905223i	$-0.0288536\pi$
$38$	2.08790	+	3.61634i	0.338701	+	0.586648i
$39$	2.98509			0.477997
$40$	−0.0796530	−	0.137963i	−0.0125942	−	0.0218139i
$41$	2.54715			0.397798			0.198899	−	0.980020i	$-0.436263\pi$
$41$	2.54715			0.397798			0.198899	+	0.980020i	$0.436263\pi$
$42$	0.539810	+	0.934978i	0.0832944	+	0.144270i
$43$	−4.70147	+	8.14318i	−0.716967	+	1.24182i	0.245229	+	0.969465i	$0.421137\pi$
$43$	−4.70147	+	8.14318i	−0.716967	+	1.24182i	−0.962196	+	0.272358i	$0.912197\pi$
$44$	−1.21121	−	2.09788i	−0.182597	−	0.316267i
$45$	0.0552635			0.00823819
$46$	−7.74298			−1.14164
$47$	5.23742	−	9.07147i	0.763956	−	1.32321i	−0.176842	−	0.984239i	$-0.556588\pi$
$47$	5.23742	−	9.07147i	0.763956	−	1.32321i	0.940797	−	0.338970i	$-0.110079\pi$
$48$	0.131656	+	0.228035i	0.0190029	+	0.0329141i
$49$	−5.58479			−0.797827
$50$	−2.26743	+	3.92731i	−0.320664	+	0.555406i
$51$	−1.22856	+	2.12793i	−0.172033	+	0.297970i
$52$	1.75582	−	3.04117i	0.243488	−	0.421734i
$53$	−0.611242	+	1.05870i	−0.0839606	+	0.145424i	−0.904948	−	0.425523i	$-0.860090\pi$
$53$	−0.611242	+	1.05870i	−0.0839606	+	0.145424i	0.820987	+	0.570947i	$0.193424\pi$
$54$	−0.907528			−0.123499
$55$	0.0568990	−	0.0985520i	0.00767226	−	0.0132888i
$56$	3.42930			0.458259
$57$	−2.30064	+	3.98483i	−0.304727	+	0.527803i
$58$	−7.59974			−0.997894
$59$	13.2674			1.72726			0.863631	−	0.504124i	$-0.168184\pi$
$59$	13.2674			1.72726			0.863631	+	0.504124i	$0.168184\pi$
$60$	0.0325058	−	0.0563017i	0.00419648	−	0.00726851i
$61$	−5.08799	−	8.81266i	−0.651450	−	1.12835i	−0.982771	−	0.184827i	$-0.940828\pi$
$61$	−5.08799	−	8.81266i	−0.651450	−	1.12835i	0.331321	−	0.943518i	$-0.392506\pi$
$62$	−2.11164	+	3.65746i	−0.268178	+	0.464498i
$63$	−0.594813	+	1.03025i	−0.0749394	+	0.129799i
$64$	5.54196			0.692745
$65$	0.164966			0.0204615
$66$	−0.934387	+	1.61841i	−0.115015	+	0.199212i
$67$	−8.62010			−1.05311			−0.526556	−	0.850140i	$-0.676517\pi$
$67$	−8.62010			−1.05311			−0.526556	+	0.850140i	$0.676517\pi$
$68$	1.44527	+	2.50329i	0.175265	+	0.303568i
$69$	−4.26597	−	7.38888i	−0.513563	−	0.889517i
$70$	0.0298317	+	0.0516701i	0.00356558	+	0.00617576i
$71$	−6.41999	+	11.1198i	−0.761913	+	1.31967i	0.179950	+	0.983676i	$0.442406\pi$
$71$	−6.41999	+	11.1198i	−0.761913	+	1.31967i	−0.941863	+	0.335996i	$0.890927\pi$
$72$	−1.44133	+	2.49646i	−0.169863	+	0.294211i
$73$	6.96746	+	12.0680i	0.815479	+	1.41245i	0.908983	+	0.416832i	$0.136860\pi$
$73$	6.96746	+	12.0680i	0.815479	+	1.41245i	−0.0935044	+	0.995619i	$0.529807\pi$
$74$	−3.18157	+	5.51063i	−0.369850	+	0.640598i
$75$	−4.99695			−0.576998
$76$	2.70646	+	4.68772i	0.310452	+	0.537719i
$77$	1.22483	+	2.12148i	0.139583	+	0.241765i
$78$	−2.70905			−0.306739
$79$	6.83192			0.768651			0.384326	−	0.923198i	$-0.374434\pi$
$79$	6.83192			0.768651			0.384326	+	0.923198i	$0.374434\pi$
$80$	0.00727578	+	0.0126020i	0.000813457	+	0.00140895i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.31161			−0.255274
$83$	2.53415	−	4.38928i	0.278160	−	0.481787i	−0.692768	−	0.721161i	$-0.743609\pi$
$83$	2.53415	−	4.38928i	0.278160	−	0.481787i	0.970927	+	0.239374i	$0.0769423\pi$
$84$	0.699734	+	1.21198i	0.0763473	+	0.132237i
$85$	−0.0678947	+	0.117597i	−0.00736421	+	0.0127552i
$86$	4.26671	−	7.39016i	0.460091	−	0.796901i
$87$	−4.18705	−	7.25219i	−0.448899	−	0.777516i
$88$	2.96798	+	5.14069i	0.316388	+	0.548000i
$89$	4.02647	+	6.97406i	0.426805	+	0.739249i	0.996587	−	0.0825473i	$-0.0263056\pi$
$89$	4.02647	+	6.97406i	0.426805	+	0.739249i	−0.569782	+	0.821796i	$0.692972\pi$
$90$	−0.0501531			−0.00528660
$91$	−1.77557	+	3.07538i	−0.186130	+	0.322387i
$92$	−10.0369			−1.04642
$93$	−4.65360			−0.482556
$94$	−4.75310	+	8.23261i	−0.490245	+	0.849129i
$95$	−0.127141	+	0.220215i	−0.0130444	+	0.0225936i
$96$	2.76318	+	4.78597i	0.282016	+	0.488466i
$97$	8.93896	−	15.4827i	0.907614	−	1.57203i	0.0902435	−	0.995920i	$-0.471235\pi$
$97$	8.93896	−	15.4827i	0.907614	−	1.57203i	0.817370	−	0.576113i	$-0.195431\pi$
$98$	5.06835			0.511981
$99$	−2.05919			−0.206957
$100$	−2.93919	+	5.09082i	−0.293919	+	0.509082i
$101$	7.67205			0.763398			0.381699	−	0.924287i	$-0.375339\pi$
$101$	7.67205			0.763398			0.381699	+	0.924287i	$0.375339\pi$
$102$	1.11496	−	1.93116i	0.110397	−	0.191213i
$103$	−4.03517			−0.397597			−0.198798	−	0.980040i	$-0.563704\pi$
$103$	−4.03517			−0.397597			−0.198798	+	0.980040i	$0.563704\pi$
$104$	−4.30250	+	7.45216i	−0.421895	+	0.730744i
$105$	−0.0328714	+	0.0569350i	−0.00320792	+	0.00555629i
$106$	0.554719	−	0.960802i	0.0538791	−	0.0933213i
$107$	−6.86579	+	11.8919i	−0.663741	+	1.14963i	0.315883	+	0.948798i	$0.397699\pi$
$107$	−6.86579	+	11.8919i	−0.663741	+	1.14963i	−0.979625	+	0.200836i	$0.935634\pi$
$108$	−1.17639			−0.113198
$109$	−0.969400	−	1.67905i	−0.0928516	−	0.160824i	0.815858	−	0.578252i	$-0.196265\pi$
$109$	−0.969400	−	1.67905i	−0.0928516	−	0.160824i	−0.908710	+	0.417428i	$0.862932\pi$
$110$	−0.0516375	+	0.0894387i	−0.00492344	+	0.00852765i
$111$	−7.01150			−0.665502
$112$	−0.313244			−0.0295987
$113$	−5.13910	−	8.90118i	−0.483446	−	0.837353i	0.516373	−	0.856363i	$-0.327282\pi$
$113$	−5.13910	−	8.90118i	−0.483446	−	0.837353i	−0.999819	+	0.0190108i	$0.993948\pi$
$114$	2.08790	−	3.61634i	0.195549	−	0.338701i
$115$	−0.235752	−	0.408335i	−0.0219840	−	0.0380775i
$116$	−9.85124			−0.914665
$117$	−1.49254	−	2.58516i	−0.137986	−	0.238998i
$118$	−12.0405			−1.10842
$119$	−1.46153	−	2.53145i	−0.133978	−	0.232057i
$120$	−0.0796530	+	0.137963i	−0.00727129	+	0.0125942i
$121$	3.37986	−	5.85410i	0.307260	−	0.532191i
$122$	4.61749	+	7.99773i	0.418048	+	0.724081i
$123$	−1.27357	−	2.20589i	−0.114834	−	0.198899i
$124$	−2.73723	+	4.74102i	−0.245811	+	0.425756i
$125$	−0.552466			−0.0494140
$126$	0.539810	−	0.934978i	0.0480901	−	0.0832944i
$127$	−6.58638	+	11.4079i	−0.584446	+	1.01229i	0.410498	+	0.911862i	$0.365355\pi$
$127$	−6.58638	+	11.4079i	−0.584446	+	1.01229i	−0.994944	+	0.100429i	$0.967978\pi$
$128$	6.02325			0.532385
$129$	9.40293			0.827882
$130$	−0.149711			−0.0131306
$131$	−0.0322287	+	0.0558217i	−0.00281583	+	0.00487716i	−0.867430	−	0.497559i	$-0.834230\pi$
$131$	−0.0322287	+	0.0558217i	−0.00281583	+	0.00487716i	0.864614	+	0.502437i	$0.167563\pi$
$132$	−1.21121	+	2.09788i	−0.105422	+	0.182597i
$133$	−2.73690	−	4.74046i	−0.237320	−	0.411050i
$134$	7.82298			0.675803
$135$	−0.0276317	−	0.0478596i	−0.00237816	−	0.00411910i
$136$	−3.54154	−	6.13412i	−0.303684	−	0.525997i
$137$	4.05116	+	7.01682i	0.346114	+	0.599488i	0.985556	−	0.169352i	$-0.0541676\pi$
$137$	4.05116	+	7.01682i	0.346114	+	0.599488i	−0.639441	+	0.768840i	$0.720834\pi$
$138$	3.87149	+	6.70562i	0.329563	+	0.570820i
$139$	−9.08690	+	15.7390i	−0.770740	+	1.33496i	0.166417	+	0.986055i	$0.446780\pi$
$139$	−9.08690	+	15.7390i	−0.770740	+	1.33496i	−0.937158	+	0.348906i	$0.886553\pi$
$140$	0.0386697	+	0.0669780i	0.00326819	+	0.00566067i
$141$	−10.4748			−0.882140
$142$	5.82632	−	10.0915i	0.488934	−	0.846859i
$143$	−6.14687			−0.514027
$144$	0.131656	−	0.228035i	0.0109714	−	0.0190029i
$145$	−0.231391	−	0.400781i	−0.0192160	−	0.0332831i
$146$	−6.32316	−	10.9520i	−0.523308	−	0.906397i
$147$	2.79239	+	4.83657i	0.230313	+	0.398913i
$148$	−4.12414	+	7.14322i	−0.339002	+	0.587169i
$149$	−6.49693			−0.532250			−0.266125	−	0.963939i	$-0.585743\pi$
$149$	−6.49693			−0.532250			−0.266125	+	0.963939i	$0.585743\pi$
$150$	4.53487			0.370270
$151$	5.18633	+	8.98298i	0.422057	+	0.731025i	0.996141	−	0.0877722i	$-0.0279748\pi$
$151$	5.18633	+	8.98298i	0.422057	+	0.731025i	−0.574083	+	0.818797i	$0.694641\pi$
$152$	−6.63198	−	11.4869i	−0.537924	−	0.931713i
$153$	2.45713			0.198647
$154$	−1.11157	−	1.92530i	−0.0895730	−	0.155145i
$155$	−0.257174			−0.0206567
$156$	−3.51164			−0.281156
$157$	12.5299	−	0.0460596i	0.999993	−	0.00367596i
$157$	12.5299	−	0.0460596i	0.999993	−	0.00367596i
$158$	−6.20016			−0.493258
$159$	1.22248			0.0969493
$160$	0.152703	+	0.264489i	0.0120722	+	0.0209097i
$161$	10.1498			0.799919
$162$	0.453764	+	0.785942i	0.0356511	+	0.0617494i
$163$	1.10620	+	1.91599i	0.0866441	+	0.150072i	0.906091	−	0.423084i	$-0.139052\pi$
$163$	1.10620	+	1.91599i	0.0866441	+	0.150072i	−0.819447	+	0.573156i	$0.805719\pi$
$164$	−2.99645			−0.233983
$165$	−0.113798			−0.00885917
$166$	−2.29982	+	3.98340i	−0.178500	+	0.309172i
$167$	−10.7260	−	18.5780i	−0.830004	−	1.43761i	−0.898034	−	0.439926i	$-0.855005\pi$
$167$	−10.7260	−	18.5780i	−0.830004	−	1.43761i	0.0680305	−	0.997683i	$-0.478328\pi$
$168$	−1.71465	−	2.96986i	−0.132288	−	0.229129i
$169$	2.04463	+	3.54140i	0.157279	+	0.272415i
$170$	0.0616163	−	0.106723i	0.00472575	−	0.00818525i
$171$	4.60128			0.351869
$172$	5.53077	−	9.57958i	0.421717	−	0.730436i
$173$	−7.94107			−0.603748			−0.301874	−	0.953348i	$-0.597612\pi$
$173$	−7.94107			−0.603748			−0.301874	+	0.953348i	$0.597612\pi$
$174$	3.79987	+	6.58156i	0.288067	+	0.498947i
$175$	2.97225	−	5.14809i	0.224681	−	0.389159i
$176$	−0.271105	−	0.469568i	−0.0204353	−	0.0353951i
$177$	−6.63368	−	11.4899i	−0.498618	−	0.863631i
$178$	−3.65414	−	6.32915i	−0.273889	−	0.474390i
$179$	3.89827	+	6.75200i	0.291370	+	0.504668i	0.974134	−	0.225971i	$-0.0725555\pi$
$179$	3.89827	+	6.75200i	0.291370	+	0.504668i	−0.682764	+	0.730639i	$0.739222\pi$
$180$	−0.0650116			−0.00484568
$181$	7.75593	+	13.4337i	0.576494	+	0.998516i	0.995878	+	0.0907075i	$0.0289128\pi$
$181$	7.75593	+	13.4337i	0.576494	+	0.998516i	−0.419384	+	0.907809i	$0.637754\pi$
$182$	1.61138	−	2.79099i	0.119443	−	0.206882i
$183$	−5.08799	+	8.81266i	−0.376115	+	0.651450i
$184$	24.5947			1.81315
$185$	−0.387480			−0.0284881
$186$	4.22327			0.309665
$187$	2.52985	−	4.38183i	0.185001	−	0.320431i
$188$	−6.16126	+	10.6716i	−0.449356	+	0.778308i
$189$	1.18963			0.0865326
$190$	0.115384	−	0.199852i	0.00837086	−	0.0144988i
$191$	3.23419	+	5.60179i	0.234018	+	0.405331i	0.958987	−	0.283451i	$-0.0914792\pi$
$191$	3.23419	+	5.60179i	0.234018	+	0.405331i	−0.724969	+	0.688782i	$0.758146\pi$
$192$	−2.77098	−	4.79948i	−0.199978	−	0.346372i
$193$	4.80747	−	8.32678i	0.346049	−	0.599375i	−0.639495	−	0.768796i	$-0.720856\pi$
$193$	4.80747	−	8.32678i	0.346049	−	0.599375i	0.985544	+	0.169421i	$0.0541897\pi$
$194$	−8.11235	+	14.0510i	−0.582433	+	1.00880i
$195$	−0.0824831	−	0.142865i	−0.00590674	−	0.0102308i
$196$	6.56991			0.469279
$197$	−7.02585	−	12.1691i	−0.500571	−	0.867014i	−1.00000		0.000659372i	$-0.999790\pi$
$197$	−7.02585	−	12.1691i	−0.500571	−	0.867014i	0.499429	−	0.866355i	$-0.333543\pi$
$198$	1.86877			0.132808
$199$	−10.5150	−	18.2124i	−0.745386	−	1.29105i	−0.950014	−	0.312206i	$-0.898932\pi$
$199$	−10.5150	−	18.2124i	−0.745386	−	1.29105i	0.204629	−	0.978840i	$-0.434401\pi$
$200$	7.20226	−	12.4747i	0.509277	−	0.882093i
$201$	4.31005	+	7.46523i	0.304008	+	0.526556i
$202$	−6.96260			−0.489887
$203$	9.96206			0.699200
$204$	1.44527	−	2.50329i	0.101189	−	0.175265i
$205$	−0.0703821	−	0.121905i	−0.00491570	−	0.00851424i
$206$	3.66203			0.255146
$207$	−4.26597	+	7.38888i	−0.296506	+	0.513563i
$208$	0.393005	−	0.680705i	0.0272500	−	0.0471984i
$209$	4.73746	−	8.20552i	0.327697	−	0.567588i
$210$	0.0298317	−	0.0516701i	0.00205859	−	0.00356558i
$211$	16.2602			1.11940			0.559700	−	0.828695i	$-0.310916\pi$
$211$	16.2602			1.11940			0.559700	+	0.828695i	$0.310916\pi$
$212$	0.719061	−	1.24545i	0.0493853	−	0.0855379i
$213$	12.8400			0.879781
$214$	6.23090	−	10.7922i	0.425936	−	0.737742i
$215$	0.519638			0.0354391
$216$	2.88267			0.196141
$217$	2.76802	−	4.79436i	0.187906	−	0.325462i
$218$	0.879757	+	1.52378i	0.0595847	+	0.103204i
$219$	6.96746	−	12.0680i	0.470817	−	0.815479i
$220$	−0.0669356	+	0.115936i	−0.00451280	+	0.00781640i
$221$	7.33474			0.493388
$222$	6.36313			0.427065
$223$	−1.40656	+	2.43624i	−0.0941904	+	0.163143i	−0.909270	−	0.416206i	$-0.863360\pi$
$223$	−1.40656	+	2.43624i	−0.0941904	+	0.163143i	0.815080	+	0.579348i	$0.196693\pi$
$224$	−6.57431			−0.439265
$225$	2.49847	+	4.32748i	0.166565	+	0.288499i
$226$	4.66388	+	8.07807i	0.310236	+	0.537345i
$227$	−4.57414	−	7.92264i	−0.303596	−	0.525844i	0.673352	−	0.739322i	$-0.264854\pi$
$227$	−4.57414	−	7.92264i	−0.303596	−	0.525844i	−0.976948	+	0.213478i	$0.931521\pi$
$228$	2.70646	−	4.68772i	0.179240	−	0.310452i
$229$	−8.23031	+	14.2553i	−0.543874	+	0.942017i	0.454803	+	0.890592i	$0.349710\pi$
$229$	−8.23031	+	14.2553i	−0.543874	+	0.942017i	−0.998677	+	0.0514251i	$0.983624\pi$
$230$	0.213952	+	0.370576i	0.0141076	+	0.0244350i
$231$	1.22483	−	2.12148i	0.0805882	−	0.139583i
$232$	24.1398			1.58485
$233$	−10.7887	−	18.6866i	−0.706792	−	1.22420i	−0.966041	−	0.258389i	$-0.916808\pi$
$233$	−10.7887	−	18.6866i	−0.706792	−	1.22420i	0.259249	−	0.965811i	$-0.416525\pi$
$234$	1.35452	+	2.34611i	0.0885481	+	0.153370i
$235$	−0.578875			−0.0377617
$236$	−15.6076			−1.01597
$237$	−3.41596	−	5.91662i	−0.221891	−	0.384326i
$238$	1.32638	+	2.29736i	0.0859765	+	0.148916i
$239$	0.0544574			0.00352256			0.00176128	−	0.999998i	$-0.499439\pi$
$239$	0.0544574			0.00352256			0.00176128	+	0.999998i	$0.499439\pi$
$240$	0.00727578	−	0.0126020i	0.000469649	−	0.000813457i
$241$	−9.56415	−	16.5656i	−0.616081	−	1.06708i	−0.990194	−	0.139701i	$-0.955386\pi$
$241$	−9.56415	−	16.5656i	−0.616081	−	1.06708i	0.374113	−	0.927383i	$-0.377947\pi$
$242$	−3.06732	+	5.31276i	−0.197175	+	0.341517i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	5.98548	+	10.3672i	0.383181	+	0.663689i
$245$	0.154317	+	0.267286i	0.00985897	+	0.0170762i
$246$	1.15580	+	2.00191i	0.0736914	+	0.127637i
$247$	13.7352			0.873952
$248$	6.70738	−	11.6175i	0.425919	−	0.737714i
$249$	−5.06831			−0.321191
$250$	0.501378			0.0317099
$251$	−13.6456	+	23.6349i	−0.861303	+	1.49182i	0.00936830	+	0.999956i	$0.497018\pi$
$251$	−13.6456	+	23.6349i	−0.861303	+	1.49182i	−0.870672	+	0.491865i	$0.836315\pi$
$252$	0.699734	−	1.21198i	0.0440791	−	0.0763473i
$253$	8.78446	+	15.2151i	0.552274	+	0.956567i
$254$	5.97732	−	10.3530i	0.375050	−	0.649606i
$255$	0.135789			0.00850346
$256$	−16.5502			−1.03439
$257$	12.4088	−	21.4926i	0.774037	−	1.34067i	−0.161298	−	0.986906i	$-0.551568\pi$
$257$	12.4088	−	21.4926i	0.774037	−	1.34067i	0.935334	−	0.353765i	$-0.115099\pi$
$258$	−8.53342			−0.531268
$259$	4.17053	−	7.22358i	0.259144	−	0.448851i
$260$	−0.194065			−0.0120354
$261$	−4.18705	+	7.25219i	−0.259172	+	0.448899i
$262$	0.0292484	−	0.0506597i	0.00180697	−	0.00312977i
$263$	−11.7265	+	20.3110i	−0.723090	+	1.25243i	0.236666	+	0.971591i	$0.423945\pi$
$263$	−11.7265	+	20.3110i	−0.723090	+	1.25243i	−0.959755	+	0.280837i	$0.909388\pi$
$264$	2.96798	−	5.14069i	0.182667	−	0.316388i
$265$	0.0675587			0.00415010
$266$	2.48382	+	4.30210i	0.152293	+	0.263778i
$267$	4.02647	−	6.97406i	0.246416	−	0.426805i
$268$	10.1406			0.619437
$269$	15.1204			0.921907			0.460953	−	0.887424i	$-0.347507\pi$
$269$	15.1204			0.921907			0.460953	+	0.887424i	$0.347507\pi$
$270$	0.0250766	+	0.0434339i	0.00152611	+	0.00264330i
$271$	−8.18756	+	14.1813i	−0.497359	+	0.861451i	−0.999995	−	0.00304678i	$-0.999030\pi$
$271$	−8.18756	+	14.1813i	−0.497359	+	0.861451i	0.502636	+	0.864498i	$0.332364\pi$
$272$	0.323496	+	0.560312i	0.0196148	+	0.0339739i
$273$	3.55114			0.214925
$274$	−3.67654	−	6.36796i	−0.222108	−	0.384703i
$275$	10.2897			0.620491
$276$	5.01846	+	8.69223i	0.302076	+	0.523211i
$277$	6.36978	−	11.0328i	0.382723	−	0.662896i	−0.608727	−	0.793380i	$-0.708320\pi$
$277$	6.36978	−	11.0328i	0.382723	−	0.662896i	0.991450	+	0.130483i	$0.0416530\pi$
$278$	8.24661	−	14.2835i	0.494599	−	0.856670i
$279$	2.32680	+	4.03014i	0.139302	+	0.241278i
$280$	−0.0947574	−	0.164125i	−0.00566284	−	0.00980832i
$281$	−5.14326	+	8.90839i	−0.306821	+	0.531430i	−0.977665	−	0.210168i	$-0.932599\pi$
$281$	−5.14326	+	8.90839i	−0.306821	+	0.531430i	0.670844	+	0.741599i	$0.265932\pi$
$282$	9.50620			0.566086
$283$	6.31533	−	10.9385i	0.375407	−	0.650225i	−0.614981	−	0.788542i	$-0.710836\pi$
$283$	6.31533	−	10.9385i	0.375407	−	0.650225i	0.990388	+	0.138318i	$0.0441695\pi$
$284$	7.55244	−	13.0812i	0.448155	−	0.776227i
$285$	0.254283			0.0150624
$286$	5.57845			0.329861
$287$	3.03015			0.178864
$288$	2.76318	−	4.78597i	0.162822	−	0.282016i
$289$	5.48126	−	9.49383i	0.322427	−	0.558460i
$290$	0.209994	+	0.363720i	0.0123313	+	0.0213584i
$291$	−17.8779			−1.04802
$292$	−8.19647	−	14.1967i	−0.479662	−	0.830799i
$293$	−1.16721	−	2.02167i	−0.0681893	−	0.118107i	0.829915	−	0.557890i	$-0.188389\pi$
$293$	−1.16721	−	2.02167i	−0.0681893	−	0.118107i	−0.898104	+	0.439783i	$0.855056\pi$
$294$	−2.53418	−	4.38932i	−0.147796	−	0.255990i
$295$	−0.366600	−	0.634970i	−0.0213443	−	0.0369694i
$296$	10.1059	−	17.5039i	0.587394	−	1.01740i
$297$	1.02960	+	1.78331i	0.0597432	+	0.103478i
$298$	5.89615			0.341555
$299$	−12.7343	+	22.0565i	−0.736444	+	1.27556i
$300$	5.87837			0.339388
$301$	−5.59299	+	9.68734i	−0.322375	+	0.558369i
$302$	−4.70674	−	8.15231i	−0.270842	−	0.469112i
$303$	−3.83603	−	6.64419i	−0.220374	−	0.381699i
$304$	0.605787	+	1.04925i	0.0347443	+	0.0601789i
$305$	−0.281180	+	0.487018i	−0.0161003	+	0.0278866i
$306$	−2.22991			−0.127476
$307$	−20.2048			−1.15315			−0.576573	−	0.817045i	$-0.695610\pi$
$307$	−20.2048			−1.15315			−0.576573	+	0.817045i	$0.695610\pi$
$308$	−1.44089	−	2.49569i	−0.0821022	−	0.142205i
$309$	2.01758	+	3.49456i	0.114776	+	0.198798i
$310$	0.233393			0.0132558
$311$	−4.26588	−	7.38872i	−0.241896	−	0.418976i	0.719359	−	0.694639i	$-0.244436\pi$
$311$	−4.26588	−	7.38872i	−0.241896	−	0.418976i	−0.961254	+	0.275663i	$0.911103\pi$
$312$	8.60501			0.487163
$313$	6.66462			0.376707			0.188353	−	0.982101i	$-0.439685\pi$
$313$	6.66462			0.376707			0.188353	+	0.982101i	$0.439685\pi$
$314$	−11.3712	+	0.0418004i	−0.641715	+	0.00235893i
$315$	0.0657429			0.00370419
$316$	−8.03703			−0.452118
$317$	−2.01885	−	3.49676i	−0.113390	−	0.196397i	0.803745	−	0.594974i	$-0.202838\pi$
$317$	−2.01885	−	3.49676i	−0.113390	−	0.196397i	−0.917135	+	0.398577i	$0.869504\pi$
$318$	−1.10944			−0.0622142
$319$	8.62195	+	14.9337i	0.482736	+	0.836124i
$320$	−0.153134	−	0.265236i	−0.00856044	−	0.0148271i
$321$	13.7316			0.766423
$322$	−9.21125			−0.513323
$323$	−5.65297	+	9.79123i	−0.314540	+	0.544798i
$324$	0.588197	+	1.01879i	0.0326776	+	0.0565992i
$325$	7.45816	+	12.9179i	0.413704	+	0.716557i
$326$	−1.00390	−	1.73881i	−0.0556011	−	0.0963040i
$327$	−0.969400	+	1.67905i	−0.0536079	+	0.0928516i
$328$	7.34257			0.405426
$329$	6.23057	−	10.7917i	0.343502	−	0.594964i
$330$	0.103275			0.00568510
$331$	−6.79871	−	11.7757i	−0.373691	−	0.647252i	0.616439	−	0.787403i	$-0.288575\pi$
$331$	−6.79871	−	11.7757i	−0.373691	−	0.647252i	−0.990130	+	0.140151i	$0.955241\pi$
$332$	−2.98116	+	5.16352i	−0.163613	+	0.283385i
$333$	3.50575	+	6.07214i	0.192114	+	0.332751i
$334$	9.73416	+	16.8601i	0.532629	+	0.922541i
$335$	0.238188	+	0.412554i	0.0130136	+	0.0225402i
$336$	0.156622	+	0.271277i	0.00854442	+	0.0147994i
$337$	−22.9988			−1.25283			−0.626413	−	0.779492i	$-0.715477\pi$
$337$	−22.9988			−1.25283			−0.626413	+	0.779492i	$0.715477\pi$
$338$	−1.85556	−	3.21392i	−0.100929	−	0.174814i
$339$	−5.13910	+	8.90118i	−0.279118	+	0.483446i
$340$	0.0798708	−	0.138340i	0.00433160	−	0.00750256i
$341$	9.58265			0.518930
$342$	−4.17579			−0.225801
$343$	−14.9712			−0.808369
$344$	−13.5528	+	23.4741i	−0.730715	+	1.26564i
$345$	−0.235752	+	0.408335i	−0.0126925	+	0.0219840i
$346$	7.20674			0.387437
$347$	0.869438	−	1.50591i	0.0466739	−	0.0808416i	−0.841745	−	0.539876i	$-0.818471\pi$
$347$	0.869438	−	1.50591i	0.0466739	−	0.0808416i	0.888419	+	0.459034i	$0.151805\pi$
$348$	4.92562	+	8.53143i	0.264041	+	0.457333i
$349$	0.568715	+	0.985044i	0.0304426	+	0.0527282i	0.880845	−	0.473404i	$-0.156975\pi$
$349$	0.568715	+	0.985044i	0.0304426	+	0.0527282i	−0.850403	+	0.526132i	$0.823642\pi$
$350$	−2.69740	+	4.67203i	−0.144182	+	0.249731i
$351$	−1.49254	+	2.58516i	−0.0796661	+	0.137986i
$352$	−5.68993	−	9.85524i	−0.303274	−	0.525286i
$353$	−2.19638			−0.116902			−0.0584509	−	0.998290i	$-0.518616\pi$
$353$	−2.19638			−0.116902			−0.0584509	+	0.998290i	$0.518616\pi$
$354$	6.02025	+	10.4274i	0.319973	+	0.554209i
$355$	0.709582			0.0376607
$356$	−4.73672	−	8.20424i	−0.251046	−	0.434824i
$357$	−1.46153	+	2.53145i	−0.0773525	+	0.133978i
$358$	−3.53779	−	6.12763i	−0.186978	−	0.323855i
$359$	−4.45034			−0.234880			−0.117440	−	0.993080i	$-0.537469\pi$
$359$	−4.45034			−0.234880			−0.117440	+	0.993080i	$0.537469\pi$
$360$	0.159306			0.00839617
$361$	−1.08590	+	1.88083i	−0.0571526	+	0.0989912i
$362$	−7.03872	−	12.1914i	−0.369947	−	0.640767i
$363$	−6.75973			−0.354794
$364$	2.08877	−	3.61785i	0.109481	−	0.189627i
$365$	0.385046	−	0.666919i	0.0201542	−	0.0349081i
$366$	4.61749	−	7.99773i	0.241360	−	0.418048i
$367$	−9.42501	+	16.3246i	−0.491982	+	0.852137i	−0.999957	−	0.00923424i	$-0.997061\pi$
$367$	−9.42501	+	16.3246i	−0.491982	+	0.852137i	0.507976	+	0.861371i	$0.330394\pi$
$368$	−2.24657			−0.117110
$369$	−1.27357	+	2.20589i	−0.0662996	+	0.114834i
$370$	0.351649			0.0182813
$371$	−0.727150	+	1.25946i	−0.0377517	+	0.0653879i
$372$	5.47446			0.283838
$373$	−23.8098			−1.23282			−0.616412	−	0.787424i	$-0.711414\pi$
$373$	−23.8098			−1.23282			−0.616412	+	0.787424i	$0.711414\pi$
$374$	−2.29591	+	3.97663i	−0.118719	+	0.205627i
$375$	0.276233	+	0.478449i	0.0142646	+	0.0247070i
$376$	15.0977	−	26.1500i	0.778605	−	1.34858i
$377$	−12.4987	+	21.6484i	−0.643717	+	1.11495i
$378$	−1.07962			−0.0555296
$379$	−25.8832			−1.32953			−0.664766	−	0.747052i	$-0.731469\pi$
$379$	−25.8832			−1.32953			−0.664766	+	0.747052i	$0.731469\pi$
$380$	0.149568	−	0.259060i	0.00767269	−	0.0132895i
$381$	13.1728			0.674861
$382$	−2.93512	−	5.08378i	−0.150174	−	0.260109i
$383$	4.85612	+	8.41104i	0.248136	+	0.429784i	0.963009	−	0.269471i	$-0.0868487\pi$
$383$	4.85612	+	8.41104i	0.248136	+	0.429784i	−0.714873	+	0.699255i	$0.753515\pi$
$384$	−3.01163	−	5.21629i	−0.153686	−	0.266193i
$385$	0.0676886	−	0.117240i	0.00344973	−	0.00597511i
$386$	−4.36291	+	7.55678i	−0.222066	+	0.384630i
$387$	−4.70147	−	8.14318i	−0.238989	−	0.413941i
$388$	−10.5157	+	18.2138i	−0.533855	+	0.924664i
$389$	−30.9679			−1.57013			−0.785067	−	0.619411i	$-0.787371\pi$
$389$	−30.9679			−1.57013			−0.785067	+	0.619411i	$0.787371\pi$
$390$	0.0748557	+	0.129654i	0.00379047	+	0.00656528i
$391$	−10.4820	−	18.1554i	−0.530099	−	0.918159i
$392$	−16.0991			−0.813126
$393$	0.0644573			0.00325144
$394$	6.37615	+	11.0438i	0.321226	+	0.556380i
$395$	−0.188778	−	0.326973i	−0.00949844	−	0.0164518i
$396$	2.42242			0.121731
$397$	5.92391	−	10.2605i	0.297312	−	0.514960i	−0.678208	−	0.734870i	$-0.737243\pi$
$397$	5.92391	−	10.2605i	0.297312	−	0.514960i	0.975520	+	0.219910i	$0.0705764\pi$
$398$	9.54262	+	16.5283i	0.478328	+	0.828489i
$399$	−2.73690	+	4.74046i	−0.137017	+	0.237320i
$400$	−0.657879	+	1.13948i	−0.0328940	+	0.0569740i
$401$	13.4056	+	23.2192i	0.669445	+	1.15951i	0.978060	+	0.208325i	$0.0668012\pi$
$401$	13.4056	+	23.2192i	0.669445	+	1.15951i	−0.308615	+	0.951187i	$0.599865\pi$
$402$	−3.91149	−	6.77490i	−0.195087	−	0.337901i
$403$	6.94570	+	12.0303i	0.345990	+	0.599272i
$404$	−9.02535			−0.449028
$405$	−0.0276317	+	0.0478596i	−0.00137303	+	0.00237816i
$406$	−9.04085			−0.448690
$407$	14.4380			0.715666
$408$	−3.54154	+	6.13412i	−0.175332	+	0.303684i
$409$	−6.30639	+	10.9230i	−0.311831	+	0.540107i	−0.978759	−	0.205015i	$-0.934276\pi$
$409$	−6.30639	+	10.9230i	−0.311831	+	0.540107i	0.666928	+	0.745122i	$0.267609\pi$
$410$	0.0638737	+	0.110633i	0.00315450	+	0.00546375i
$411$	4.05116	−	7.01682i	0.199829	−	0.346114i
$412$	4.74695			0.233865
$413$	15.7832			0.776641
$414$	3.87149	−	6.70562i	0.190273	−	0.329563i
$415$	−0.280092			−0.0137492
$416$	8.24834	−	14.2866i	0.404408	−	0.700456i
$417$	18.1738			0.889974
$418$	−4.29938	+	7.44674i	−0.210289	+	0.364232i
$419$	−7.15714	+	12.3965i	−0.349649	+	0.605610i	−0.986187	−	0.165635i	$-0.947033\pi$
$419$	−7.15714	+	12.3965i	−0.349649	+	0.605610i	0.636538	+	0.771245i	$0.280366\pi$
$420$	0.0386697	−	0.0669780i	0.00188689	−	0.00326819i
$421$	−12.5845	+	21.7970i	−0.613332	+	1.06232i	0.377343	+	0.926074i	$0.376838\pi$
$421$	−12.5845	+	21.7970i	−0.613332	+	1.06232i	−0.990675	+	0.136248i	$0.956496\pi$
$422$	−14.7566			−0.718341
$423$	5.23742	+	9.07147i	0.254652	+	0.441070i
$424$	−1.76201	+	3.05189i	−0.0855706	+	0.148213i
$425$	−12.2781			−0.595577
$426$	−11.6526			−0.564572
$427$	−6.05281	−	10.4838i	−0.292916	−	0.507345i
$428$	8.07687	−	13.9896i	0.390410	−	0.676211i
$429$	3.07343	+	5.32334i	0.148387	+	0.257013i
$430$	−0.471586			−0.0227419
$431$	−2.93595	−	5.08522i	−0.141420	−	0.244946i	0.786612	−	0.617448i	$-0.211833\pi$
$431$	−2.93595	−	5.08522i	−0.141420	−	0.244946i	−0.928032	+	0.372502i	$0.878500\pi$
$432$	−0.263312			−0.0126686
$433$	−11.5948	−	20.0828i	−0.557211	−	0.965118i	−0.997728	−	0.0673735i	$-0.978538\pi$
$433$	−11.5948	−	20.0828i	−0.557211	−	0.965118i	0.440517	−	0.897744i	$-0.354795\pi$
$434$	−2.51206	+	4.35101i	−0.120583	+	0.208855i
$435$	−0.231391	+	0.400781i	−0.0110944	+	0.0192160i
$436$	1.14040	+	1.97522i	0.0546150	+	0.0945960i
$437$	−19.6289	−	33.9983i	−0.938980	−	1.62636i
$438$	−6.32316	+	10.9520i	−0.302132	+	0.523308i
$439$	39.5305			1.88669			0.943344	−	0.331815i	$-0.107661\pi$
$439$	39.5305			1.88669			0.943344	+	0.331815i	$0.107661\pi$
$440$	0.164021	−	0.284092i	0.00781939	−	0.0135436i
$441$	2.79239	−	4.83657i	0.132971	−	0.230313i
$442$	−6.65648			−0.316616
$443$	39.9989			1.90040			0.950202	−	0.311636i	$-0.100877\pi$
$443$	39.9989			1.90040			0.950202	+	0.311636i	$0.100877\pi$
$444$	8.24828			0.391446
$445$	0.222517	−	0.385411i	0.0105483	−	0.0182702i
$446$	1.27650	−	2.21095i	0.0604438	−	0.104692i
$447$	3.24847	+	5.62651i	0.153647	+	0.266125i
$448$	6.59286			0.311483
$449$	1.41980	+	2.45917i	0.0670047	+	0.116056i	0.897582	−	0.440849i	$-0.145322\pi$
$449$	1.41980	+	2.45917i	0.0670047	+	0.116056i	−0.830577	+	0.556904i	$0.811989\pi$
$450$	−2.26743	−	3.92731i	−0.106888	−	0.185135i
$451$	2.62253	+	4.54236i	0.123490	+	0.213891i
$452$	6.04560	+	10.4713i	0.284361	+	0.492528i
$453$	5.18633	−	8.98298i	0.243675	−	0.422057i
$454$	4.15116	+	7.19001i	0.194823	+	0.337444i
$455$	0.196248			0.00920026
$456$	−6.63198	+	11.4869i	−0.310571	+	0.537924i
$457$	4.11129			0.192318			0.0961591	−	0.995366i	$-0.469344\pi$
$457$	4.11129			0.192318			0.0961591	+	0.995366i	$0.469344\pi$
$458$	7.46923	−	12.9371i	0.349014	−	0.604510i
$459$	−1.22856	−	2.12793i	−0.0573444	−	0.0993235i
$460$	0.277338	+	0.480363i	0.0129309	+	0.0223970i
$461$	6.94644	+	12.0316i	0.323528	+	0.560367i	0.981213	−	0.192926i	$-0.0617977\pi$
$461$	6.94644	+	12.0316i	0.323528	+	0.560367i	−0.657685	+	0.753293i	$0.728464\pi$
$462$	−1.11157	+	1.92530i	−0.0517150	+	0.0895730i
$463$	−1.18195			−0.0549298			−0.0274649	−	0.999623i	$-0.508743\pi$
$463$	−1.18195			−0.0549298			−0.0274649	+	0.999623i	$0.508743\pi$
$464$	−2.20501			−0.102365
$465$	0.128587	+	0.222719i	0.00596308	+	0.0103284i
$466$	9.79106	+	16.9586i	0.453562	+	0.785593i
$467$	−14.6475			−0.677806			−0.338903	−	0.940821i	$-0.610056\pi$
$467$	−14.6475			−0.677806			−0.338903	+	0.940821i	$0.610056\pi$
$468$	1.75582	+	3.04117i	0.0811627	+	0.140578i
$469$	−10.2547			−0.473518
$470$	0.525345			0.0242324
$471$	−6.30483	−	10.8282i	−0.290511	−	0.498935i
$472$	38.2454			1.76039
$473$	−19.3624			−0.890286
$474$	3.10008	+	5.36950i	0.142391	+	0.246629i
$475$	−22.9924			−1.05496
$476$	1.71934	+	2.97798i	0.0788056	+	0.136495i
$477$	−0.611242	−	1.05870i	−0.0279869	−	0.0484747i
$478$	−0.0494216			−0.00226049
$479$	−5.05026			−0.230752			−0.115376	−	0.993322i	$-0.536807\pi$
$479$	−5.05026			−0.230752			−0.115376	+	0.993322i	$0.536807\pi$
$480$	0.152703	−	0.264489i	0.00696991	−	0.0120722i
$481$	10.4650	+	18.1259i	0.477162	+	0.826468i
$482$	8.67973	+	15.0337i	0.395351	+	0.684768i
$483$	−5.07492	−	8.79001i	−0.230917	−	0.399959i
$484$	−3.97605	+	6.88672i	−0.180730	+	0.313033i
$485$	−0.987995			−0.0448626
$486$	0.453764	−	0.785942i	0.0205831	−	0.0356511i
$487$	−24.2401			−1.09842			−0.549211	−	0.835684i	$-0.685072\pi$
$487$	−24.2401			−1.09842			−0.549211	+	0.835684i	$0.685072\pi$
$488$	−14.6670	−	25.4039i	−0.663943	−	1.14998i
$489$	1.10620	−	1.91599i	0.0500240	−	0.0866441i
$490$	−0.140047	−	0.242569i	−0.00632669	−	0.0109582i
$491$	16.2572	+	28.1583i	0.733678	+	1.27077i	0.955301	+	0.295636i	$0.0955314\pi$
$491$	16.2572	+	28.1583i	0.733678	+	1.27077i	−0.221622	+	0.975133i	$0.571135\pi$
$492$	1.49822	+	2.59500i	0.0675451	+	0.116992i
$493$	−10.2881	−	17.8196i	−0.463354	−	0.802552i
$494$	−12.4651			−0.560832
$495$	0.0568990	+	0.0985520i	0.00255742	+	0.00442958i
$496$	−0.612675	+	1.06118i	−0.0275099	+	0.0476486i
$497$	−7.63739	+	13.2284i	−0.342584	+	0.593373i
$498$	4.59963			0.206114
$499$	−11.5544			−0.517246			−0.258623	−	0.965978i	$-0.583269\pi$
$499$	−11.5544			−0.517246			−0.258623	+	0.965978i	$0.583269\pi$
$500$	0.649917			0.0290652
$501$	−10.7260	+	18.5780i	−0.479203	+	0.830004i
$502$	12.3838	−	21.4493i	0.552715	−	0.957330i
$503$	8.02582			0.357854			0.178927	−	0.983862i	$-0.442737\pi$
$503$	8.02582			0.357854			0.178927	+	0.983862i	$0.442737\pi$
$504$	−1.71465	+	2.96986i	−0.0763765	+	0.132288i
$505$	−0.211992	−	0.367181i	−0.00943352	−	0.0163393i
$506$	−7.97214	−	13.8082i	−0.354405	−	0.613847i
$507$	2.04463	−	3.54140i	0.0908051	−	0.157279i
$508$	7.74817	−	13.4202i	0.343769	−	0.595426i
$509$	10.0044	+	17.3282i	0.443438	+	0.768058i	0.997942	−	0.0641235i	$-0.0204252\pi$
$509$	10.0044	+	17.3282i	0.443438	+	0.768058i	−0.554504	+	0.832181i	$0.687092\pi$
$510$	−0.123233			−0.00545683
$511$	8.28867	+	14.3564i	0.366669	+	0.635090i
$512$	2.97324			0.131400
$513$	−2.30064	−	3.98483i	−0.101576	−	0.175934i
$514$	−11.2613	+	19.5051i	−0.496714	+	0.860334i
$515$	0.111499	+	0.193121i	0.00491322	+	0.00850995i
$516$	−11.0615			−0.486957
$517$	21.5697			0.948634
$518$	−3.78488	+	6.55560i	−0.166298	+	0.288036i
$519$	3.97054	+	6.87717i	0.174287	+	0.301874i
$520$	0.475542			0.0208539
$521$	6.85465	−	11.8726i	0.300307	−	0.520148i	−0.675898	−	0.736995i	$-0.736244\pi$
$521$	6.85465	−	11.8726i	0.300307	−	0.520148i	0.976206	+	0.216847i	$0.0695774\pi$
$522$	3.79987	−	6.58156i	0.166316	−	0.288067i
$523$	−12.4083	+	21.4918i	−0.542577	+	0.939771i	0.456178	+	0.889889i	$0.349218\pi$
$523$	−12.4083	+	21.4918i	−0.542577	+	0.939771i	−0.998755	+	0.0498825i	$0.984115\pi$
$524$	0.0379136	−	0.0656682i	0.00165626	−	0.00286873i
$525$	−5.94450			−0.259439
$526$	10.6422	−	18.4328i	0.464021	−	0.803707i
$527$	−11.4345			−0.498094
$528$	−0.271105	+	0.469568i	−0.0117984	+	0.0204353i
$529$	49.7941			2.16496
$530$	−0.0613114			−0.00266320
$531$	−6.63368	+	11.4899i	−0.287877	+	0.498618i
$532$	3.21968	+	5.57664i	0.139591	+	0.241778i
$533$	−3.80173	+	6.58479i	−0.164671	+	0.285219i
$534$	−3.65414	+	6.32915i	−0.158130	+	0.273889i
$535$	0.758855			0.0328082
$536$	−24.8489			−1.07331
$537$	3.89827	−	6.75200i	0.168223	−	0.291370i
$538$	−13.7222			−0.591605
$539$	−5.75008	−	9.95942i	−0.247673	−	0.428983i
$540$	0.0325058	+	0.0563017i	0.00139883	+	0.00242284i
$541$	14.8799	+	25.7727i	0.639735	+	1.10805i	0.985491	+	0.169729i	$0.0542893\pi$
$541$	14.8799	+	25.7727i	0.639735	+	1.10805i	−0.345755	+	0.938325i	$0.612377\pi$
$542$	7.43044	−	12.8699i	0.319165	−	0.552810i
$543$	7.75593	−	13.4337i	0.332839	−	0.576494i
$544$	6.78949	+	11.7597i	0.291097	+	0.504195i
$545$	−0.0535724	+	0.0927901i	−0.00229479	+	0.00397469i
$546$	−3.22276			−0.137921
$547$	−20.2250	−	35.0307i	−0.864758	−	1.49780i	−0.867288	−	0.497807i	$-0.834139\pi$
$547$	−20.2250	−	35.0307i	−0.864758	−	1.49780i	0.00253009	−	0.999997i	$-0.499195\pi$
$548$	−4.76576	−	8.25454i	−0.203583	−	0.352617i
$549$	10.1760			0.434300
$550$	−9.33816			−0.398181
$551$	−19.2658	−	33.3694i	−0.820751	−	1.42158i
$552$	−12.2974	−	21.2997i	−0.523411	−	0.906574i
$553$	8.12744			0.345614
$554$	−5.78076	+	10.0126i	−0.245601	+	0.425393i
$555$	0.193740	+	0.335567i	0.00822380	+	0.0142440i
$556$	10.6898	−	18.5152i	0.453347	−	0.785220i
$557$	−0.812453	+	1.40721i	−0.0344247	+	0.0596254i	−0.882724	−	0.469891i	$-0.844293\pi$
$557$	−0.812453	+	1.40721i	−0.0344247	+	0.0596254i	0.848300	+	0.529516i	$0.177627\pi$
$558$	−2.11164	−	3.65746i	−0.0893927	−	0.154833i
$559$	−14.0343	−	24.3081i	−0.593587	−	1.02812i
$560$	0.00865546	+	0.0149917i	0.000365760	+	0.000633515i
$561$	−5.05970			−0.213621
$562$	4.66766	−	8.08462i	0.196893	−	0.341029i
$563$	21.0766			0.888272			0.444136	−	0.895959i	$-0.353511\pi$
$563$	21.0766			0.888272			0.444136	+	0.895959i	$0.353511\pi$
$564$	12.3225			0.518872
$565$	−0.284004	+	0.491910i	−0.0119482	+	0.0206948i
$566$	−5.73134	+	9.92697i	−0.240906	+	0.417262i
$567$	−0.594813	−	1.03025i	−0.0249798	−	0.0432663i
$568$	−18.5067	+	32.0545i	−0.776523	+	1.34498i
$569$	0.148491			0.00622505			0.00311252	−	0.999995i	$-0.499009\pi$
$569$	0.148491			0.00622505			0.00311252	+	0.999995i	$0.499009\pi$
$570$	−0.230769			−0.00966584
$571$	−18.8200	+	32.5972i	−0.787592	+	1.36415i	0.139846	+	0.990173i	$0.455339\pi$
$571$	−18.8200	+	32.5972i	−0.787592	+	1.36415i	−0.927438	+	0.373977i	$0.877994\pi$
$572$	7.23113			0.302349
$573$	3.23419	−	5.60179i	0.135110	−	0.234018i
$574$	−2.74995			−0.114781
$575$	21.3168	−	36.9218i	0.888974	−	1.53975i
$576$	−2.77098	+	4.79948i	−0.115457	+	0.199978i
$577$	−2.82340	+	4.89028i	−0.117540	+	0.203585i	−0.918792	−	0.394742i	$-0.870834\pi$
$577$	−2.82340	+	4.89028i	−0.117540	+	0.203585i	0.801252	+	0.598327i	$0.204167\pi$
$578$	−4.97440	+	8.61591i	−0.206908	+	0.358375i
$579$	−9.61494			−0.399583
$580$	0.272207	+	0.471476i	0.0113028	+	0.0195770i
$581$	3.01470	−	5.22161i	0.125071	−	0.216629i
$582$	16.2247			0.672536
$583$	−2.51733			−0.104257
$584$	20.0848	+	34.7880i	0.831117	+	1.43954i
$585$	−0.0824831	+	0.142865i	−0.00341026	+	0.00590674i
$586$	1.05928	+	1.83472i	0.0437584	+	0.0757917i
$587$	39.1457			1.61572			0.807858	−	0.589377i	$-0.200627\pi$
$587$	39.1457			1.61572			0.807858	+	0.589377i	$0.200627\pi$
$588$	−3.28495	−	5.68971i	−0.135469	−	0.234640i
$589$	−21.4125			−0.882288
$590$	0.332700	+	0.576253i	0.0136970	+	0.0237240i
$591$	−7.02585	+	12.1691i	−0.289005	+	0.500571i
$592$	−0.923108	+	1.59887i	−0.0379395	+	0.0657131i
$593$	−16.9651	−	29.3844i	−0.696674	−	1.20667i	−0.969613	−	0.244643i	$-0.921329\pi$
$593$	−16.9651	−	29.3844i	−0.696674	−	1.20667i	0.272940	−	0.962031i	$-0.412004\pi$
$594$	−0.934387	−	1.61841i	−0.0383384	−	0.0664040i
$595$	−0.0807693	+	0.139897i	−0.00331122	+	0.00573520i
$596$	7.64295			0.313067
$597$	−10.5150	+	18.2124i	−0.430349	+	0.745386i
$598$	11.5567	−	20.0169i	0.472590	−	0.818550i
$599$	−2.77759			−0.113489			−0.0567446	−	0.998389i	$-0.518072\pi$
$599$	−2.77759			−0.113489			−0.0567446	+	0.998389i	$0.518072\pi$
$600$	−14.4045			−0.588062
$601$	37.0078			1.50958			0.754789	−	0.655968i	$-0.227739\pi$
$601$	37.0078			1.50958			0.754789	+	0.655968i	$0.227739\pi$
$602$	5.07579	−	8.79153i	0.206874	−	0.358316i
$603$	4.31005	−	7.46523i	0.175519	−	0.304008i
$604$	−6.10116	−	10.5675i	−0.248253	−	0.429986i
$605$	−0.373566			−0.0151876
$606$	3.48130	+	6.02979i	0.141418	+	0.244943i
$607$	−23.2687	−	40.3026i	−0.944448	−	1.63583i	−0.756853	−	0.653585i	$-0.773264\pi$
$607$	−23.2687	−	40.3026i	−0.944448	−	1.63583i	−0.187595	−	0.982246i	$-0.560069\pi$
$608$	12.7142	+	22.0216i	0.515628	+	0.893095i
$609$	−4.98103	−	8.62740i	−0.201842	−	0.349600i
$610$	0.255179	−	0.441982i	0.0103319	−	0.0178953i
$611$	15.6341	+	27.0791i	0.632490	+	1.09550i
$612$	−2.89055			−0.116843
$613$	10.8120	−	18.7269i	0.436693	−	0.756374i	−0.560740	−	0.827992i	$-0.689483\pi$
$613$	10.8120	−	18.7269i	0.436693	−	0.756374i	0.997432	+	0.0716186i	$0.0228164\pi$
$614$	18.3364			0.739996
$615$	−0.0703821	+	0.121905i	−0.00283808	+	0.00491570i
$616$	3.53079	+	6.11551i	0.142260	+	0.246401i
$617$	0.558716	+	0.967724i	0.0224931	+	0.0389591i	0.877053	−	0.480394i	$-0.159506\pi$
$617$	0.558716	+	0.967724i	0.0224931	+	0.0389591i	−0.854560	+	0.519353i	$0.826173\pi$
$618$	−1.83101	−	3.17141i	−0.0736542	−	0.127573i
$619$	11.2597	−	19.5023i	0.452565	−	0.783865i	−0.545980	−	0.837798i	$-0.683842\pi$
$619$	11.2597	−	19.5023i	0.452565	−	0.783865i	0.998545	+	0.0539332i	$0.0171758\pi$
$620$	0.302538			0.0121502
$621$	8.53195			0.342375
$622$	3.87140	+	6.70546i	0.155229	+	0.268865i
$623$	4.79000	+	8.29653i	0.191907	+	0.332393i
$624$	−0.786011			−0.0314656
$625$	−12.4771	−	21.6110i	−0.499084	−	0.864439i
$626$	−6.04833			−0.241740
$627$	−9.47492			−0.378392
$628$	−14.7401	+	0.0541843i	−0.588193	+	0.00216219i
$629$	−17.2281			−0.686931
$630$	−0.0596635			−0.00237705
$631$	0.799414	+	1.38463i	0.0318242	+	0.0551211i	0.881499	−	0.472186i	$-0.156535\pi$
$631$	0.799414	+	1.38463i	0.0318242	+	0.0551211i	−0.849675	+	0.527307i	$0.823202\pi$
$632$	19.6941			0.783391
$633$	−8.13012	−	14.0818i	−0.323143	−	0.559700i
$634$	1.83216	+	3.17340i	0.0727646	+	0.126032i
$635$	0.727972			0.0288887
$636$	−1.43812			−0.0570253
$637$	8.33554	−	14.4376i	0.330266	−	0.572038i
$638$	−7.82466	−	13.5527i	−0.309781	−	0.536557i
$639$	−6.41999	−	11.1198i	−0.253971	−	0.439891i
$640$	−0.166433	−	0.288270i	−0.00657884	−	0.0113949i
$641$	16.6439	−	28.8281i	0.657395	−	1.13864i	−0.323893	−	0.946094i	$-0.604992\pi$
$641$	16.6439	−	28.8281i	0.657395	−	1.13864i	0.981288	−	0.192548i	$-0.0616750\pi$
$642$	−12.4618			−0.491828
$643$	−19.7311	+	34.1752i	−0.778118	+	1.34774i	0.154907	+	0.987929i	$0.450492\pi$
$643$	−19.7311	+	34.1752i	−0.778118	+	1.34774i	−0.933025	+	0.359811i	$0.882841\pi$
$644$	−11.9402			−0.470510
$645$	−0.259819	−	0.450020i	−0.0102304	−	0.0177195i
$646$	5.13023	−	8.88581i	0.201846	−	0.349608i
$647$	2.37740	+	4.11778i	0.0934653	+	0.161887i	0.908967	−	0.416868i	$-0.136872\pi$
$647$	2.37740	+	4.11778i	0.0934653	+	0.161887i	−0.815502	+	0.578755i	$0.803539\pi$
$648$	−1.44133	−	2.49646i	−0.0566209	−	0.0980703i
$649$	13.6600	+	23.6598i	0.536203	+	0.928730i
$650$	−6.76849	−	11.7234i	−0.265482	−	0.459828i
$651$	−5.53605			−0.216975
$652$	−1.30132	−	2.25396i	−0.0509637	−	0.0882718i
$653$	−10.6368	+	18.4234i	−0.416249	+	0.720964i	−0.995559	−	0.0941432i	$-0.969989\pi$
$653$	−10.6368	+	18.4234i	−0.416249	+	0.720964i	0.579310	+	0.815108i	$0.303322\pi$
$654$	0.879757	−	1.52378i	0.0344012	−	0.0595847i
$655$	0.00356213			0.000139184
$656$	−0.670696			−0.0261863
$657$	−13.9349			−0.543653
$658$	−5.65441	+	9.79373i	−0.220432	+	0.381799i
$659$	−6.61362	+	11.4551i	−0.257630	+	0.446229i	−0.965607	−	0.260007i	$-0.916275\pi$
$659$	−6.61362	+	11.4551i	−0.257630	+	0.446229i	0.707976	+	0.706236i	$0.249608\pi$
$660$	0.133871			0.00521093
$661$	−1.41697	+	2.45427i	−0.0551138	+	0.0954599i	−0.892266	−	0.451510i	$-0.850885\pi$
$661$	−1.41697	+	2.45427i	−0.0551138	+	0.0954599i	0.837152	+	0.546970i	$0.184219\pi$
$662$	6.17002	+	10.6868i	0.239805	+	0.415354i
$663$	−3.66737	−	6.35207i	−0.142429	−	0.246694i
$664$	7.30512	−	12.6528i	0.283494	−	0.491025i
$665$	−0.151251	+	0.261974i	−0.00586525	+	0.0101589i
$666$	−3.18157	−	5.51063i	−0.123283	−	0.213533i
$667$	71.4474			2.76646
$668$	12.6180	+	21.8550i	0.488205	+	0.845597i
$669$	2.81313			0.108762
$670$	−0.216162	−	0.374404i	−0.00835109	−	0.0144645i
$671$	10.4771	−	18.1470i	0.404466	−	0.700555i
$672$	3.28716	+	5.69352i	0.126805	+	0.219632i
$673$	9.81925			0.378504			0.189252	−	0.981929i	$-0.439394\pi$
$673$	9.81925			0.378504			0.189252	+	0.981929i	$0.439394\pi$
$674$	20.8721			0.803962
$675$	2.49847	−	4.32748i	0.0961663	−	0.166565i
$676$	−2.40528	−	4.16608i	−0.0925110	−	0.160234i
$677$	−35.7690			−1.37471			−0.687357	−	0.726320i	$-0.741229\pi$
$677$	−35.7690			−1.37471			−0.687357	+	0.726320i	$0.741229\pi$
$678$	4.66388	−	8.07807i	0.179115	−	0.310236i
$679$	10.6340	−	18.4187i	0.408096	−	0.706843i
$680$	−0.195718	+	0.338993i	−0.00750543	+	0.0129998i
$681$	−4.57414	+	7.92264i	−0.175281	+	0.303596i
$682$	−8.69652			−0.333007
$683$	5.15810	−	8.93409i	0.197369	−	0.341853i	−0.750305	−	0.661091i	$-0.770094\pi$
$683$	5.15810	−	8.93409i	0.197369	−	0.341853i	0.947675	+	0.319238i	$0.103427\pi$
$684$	−5.41292			−0.206968
$685$	0.223881	−	0.387774i	0.00855407	−	0.0148161i
$686$	13.5868			0.518746
$687$	16.4606			0.628011
$688$	1.23795	−	2.14420i	0.0471966	−	0.0817469i
$689$	−1.82461	−	3.16032i	−0.0695122	−	0.120399i
$690$	0.213952	−	0.370576i	0.00814501	−	0.0141076i
$691$	−2.32281	+	4.02323i	−0.0883639	+	0.153051i	−0.906820	−	0.421519i	$-0.861497\pi$
$691$	−2.32281	+	4.02323i	−0.0883639	+	0.153051i	0.818456	+	0.574570i	$0.194831\pi$
$692$	9.34182			0.355123
$693$	−2.44967			−0.0930553
$694$	−0.789039	+	1.36666i	−0.0299515	+	0.0518776i
$695$	1.00435			0.0380970
$696$	−12.0699	−	20.9056i	−0.457507	−	0.792426i
$697$	−3.12933	−	5.42016i	−0.118532	−	0.205303i
$698$	−0.516125	−	0.893955i	−0.0195356	−	0.0338367i
$699$	−10.7887	+	18.6866i	−0.408067	+	0.706792i
$700$	−3.49653	+	6.05618i	−0.132157	+	0.228902i
$701$	23.8767	+	41.3557i	0.901811	+	1.56198i	0.825141	+	0.564926i	$0.191095\pi$
$701$	23.8767	+	41.3557i	0.901811	+	1.56198i	0.0766696	+	0.997057i	$0.475571\pi$
$702$	1.35452	−	2.34611i	0.0511232	−	0.0885481i
$703$	−32.2619			−1.21678
$704$	5.70598	+	9.88304i	0.215052	+	0.372481i
$705$	0.289438	+	0.501321i	0.0109009	+	0.0188808i
$706$	1.99328			0.0750181
$707$	9.12688			0.343251
$708$	7.80382	+	13.5166i	0.293285	+	0.507985i
$709$	−4.81943	−	8.34750i	−0.180998	−	0.313497i	0.761223	−	0.648490i	$-0.224599\pi$
$709$	−4.81943	−	8.34750i	−0.180998	−	0.313497i	−0.942221	+	0.334993i	$0.891266\pi$
$710$	−0.643965			−0.0241676
$711$	−3.41596	+	5.91662i	−0.128109	+	0.221891i
$712$	11.6070	+	20.1039i	0.434990	+	0.753425i
$713$	19.8521	−	34.3849i	0.743468	−	1.28772i
$714$	1.32638	−	2.29736i	0.0496386	−	0.0859765i
$715$	0.169849	+	0.294186i	0.00635198	+	0.0110019i
$716$	−4.58590	−	7.94301i	−0.171383	−	0.296844i
$717$	−0.0272287	−	0.0471615i	−0.00101688	−	0.00176128i
$718$	4.03881			0.150727
$719$	−3.93251	+	6.81131i	−0.146658	+	0.254019i	−0.929990	−	0.367584i	$-0.880185\pi$
$719$	−3.93251	+	6.81131i	−0.146658	+	0.254019i	0.783332	+	0.621603i	$0.213518\pi$
$720$	−0.0145516			−0.000542305
$721$	−4.80034			−0.178774
$722$	0.985484	−	1.70691i	0.0366759	−	0.0635245i
$723$	−9.56415	+	16.5656i	−0.355695	+	0.616081i
$724$	−9.12402	−	15.8033i	−0.339092	−	0.587324i
$725$	20.9225	−	36.2388i	0.777042	−	1.34588i
$726$	6.13464			0.227678
$727$	−19.5201			−0.723959			−0.361980	−	0.932186i	$-0.617899\pi$
$727$	−19.5201			−0.723959			−0.361980	+	0.932186i	$0.617899\pi$
$728$	−5.11837	+	8.86528i	−0.189700	+	0.328569i
$729$	1.00000			0.0370370
$730$	−0.349440	+	0.605247i	−0.0129333	+	0.0224012i
$731$	23.1042			0.854540
$732$	5.98548	−	10.3672i	0.221230	−	0.383181i
$733$	−9.93481	+	17.2076i	−0.366951	+	0.635577i	−0.989087	−	0.147332i	$-0.952932\pi$
$733$	−9.93481	+	17.2076i	−0.366951	+	0.635577i	0.622137	+	0.782909i	$0.286265\pi$
$734$	8.55346	−	14.8150i	0.315714	−	0.546833i
$735$	0.154317	−	0.267286i	0.00569208	−	0.00985897i
$736$	−47.1507			−1.73800
$737$	−8.87522	−	15.3723i	−0.326923	−	0.566247i
$738$	1.15580	−	2.00191i	0.0425457	−	0.0736914i
$739$	28.9625			1.06540			0.532701	−	0.846303i	$-0.321177\pi$
$739$	28.9625			1.06540			0.532701	+	0.846303i	$0.321177\pi$
$740$	0.455829			0.0167566
$741$	−6.86761	−	11.8951i	−0.252288	−	0.436976i
$742$	0.659909	−	1.14300i	0.0242260	−	0.0419607i
$743$	22.0208	+	38.1412i	0.807865	+	1.39926i	0.914340	+	0.404948i	$0.132710\pi$
$743$	22.0208	+	38.1412i	0.807865	+	1.39926i	−0.106474	+	0.994315i	$0.533956\pi$
$744$	−13.4148			−0.491809
$745$	0.179522	+	0.310940i	0.00657716	+	0.0113920i
$746$	21.6080			0.791126
$747$	2.53415	+	4.38928i	0.0927199	+	0.160596i
$748$	−2.97610	+	5.15475i	−0.108817	+	0.188476i
$749$	−8.16773	+	14.1469i	−0.298442	+	0.516917i
$750$	−0.250689	−	0.434206i	−0.00915387	−	0.0158550i
$751$	−7.67505	−	13.2936i	−0.280067	−	0.485089i	0.691334	−	0.722535i	$-0.257023\pi$
$751$	−7.67505	−	13.2936i	−0.280067	−	0.485089i	−0.971401	+	0.237446i	$0.923690\pi$
$752$	−1.37908	+	2.38863i	−0.0502898	+	0.0871044i
$753$	27.2912			0.994547
$754$	11.3429	−	19.6465i	0.413085	−	0.715485i
$755$	0.286614	−	0.496431i	0.0104310	−	0.0180670i
$756$	−1.39947			−0.0508982
$757$	−27.8099			−1.01077			−0.505384	−	0.862895i	$-0.668649\pi$
$757$	−27.8099			−1.01077			−0.505384	+	0.862895i	$0.668649\pi$
$758$	23.4897			0.853186
$759$	8.78446	−	15.2151i	0.318856	−	0.552274i
$760$	−0.366506	+	0.634807i	−0.0132946	+	0.0230269i
$761$	5.41241	+	9.37457i	0.196200	+	0.339828i	0.947293	−	0.320368i	$-0.103807\pi$
$761$	5.41241	+	9.37457i	0.196200	+	0.339828i	−0.751093	+	0.660196i	$0.770473\pi$
$762$	−11.9546			−0.433071
$763$	−1.15322	−	1.99744i	−0.0417495	−	0.0723123i
$764$	−3.80468	−	6.58990i	−0.137649	−	0.238414i
$765$	−0.0678947	−	0.117597i	−0.00245474	−	0.00425173i
$766$	−4.40706	−	7.63325i	−0.159234	−	0.275801i
$767$	−19.8021	+	34.2983i	−0.715013	+	1.23844i
$768$	8.27509	+	14.3329i	0.298602	+	0.517193i
$769$	16.2661			0.586571			0.293286	−	0.956025i	$-0.405251\pi$
$769$	16.2661			0.586571			0.293286	+	0.956025i	$0.405251\pi$
$770$	−0.0614293	+	0.106399i	−0.00221376	+	0.00383434i
$771$	−24.8175			−0.893781
$772$	−5.65547	+	9.79557i	−0.203545	+	0.352550i
$773$	9.96847	+	17.2659i	0.358541	+	0.621011i	0.987717	−	0.156251i	$-0.0499410\pi$
$773$	9.96847	+	17.2659i	0.358541	+	0.621011i	−0.629176	+	0.777263i	$0.716608\pi$
$774$	4.26671	+	7.39016i	0.153364	+	0.265634i
$775$	−11.6269	−	20.1384i	−0.417650	−	0.723391i
$776$	25.7680	−	44.6315i	0.925018	−	1.60218i
$777$	−8.34107			−0.299234
$778$	28.1042			1.00758
$779$	−5.86007	−	10.1499i	−0.209959	−	0.363660i
$780$	0.0970326	+	0.168065i	0.00347432	+	0.00601771i
$781$	−26.4400			−0.946097
$782$	9.51274	+	16.4766i	0.340175	+	0.589200i
$783$	8.37411			0.299266
$784$	1.47054			0.0525194
$785$	−0.348427	−	0.598402i	−0.0124359	−	0.0213579i
$786$	−0.0584968			−0.00208651
$787$	−6.24278			−0.222531			−0.111266	−	0.993791i	$-0.535490\pi$
$787$	−6.24278			−0.222531			−0.111266	+	0.993791i	$0.535490\pi$
$788$	8.26516	+	14.3157i	0.294434	+	0.509975i
$789$	23.4531			0.834952
$790$	0.171321	+	0.296737i	0.00609533	+	0.0105574i
$791$	−6.11361	−	10.5891i	−0.217375	−	0.376504i
$792$	−5.93596			−0.210925
$793$	30.3762			1.07869
$794$	−5.37611	+	9.31169i	−0.190791	+	0.330460i
$795$	−0.0337794	−	0.0585076i	−0.00119803	−	0.00207505i
$796$	12.3697	+	21.4250i	0.438433	+	0.759389i
$797$	−0.905859	−	1.56899i	−0.0320872	−	0.0555766i	0.849536	−	0.527531i	$-0.176882\pi$
$797$	−0.905859	−	1.56899i	−0.0320872	−	0.0555766i	−0.881623	+	0.471954i	$0.843549\pi$
$798$	2.48382	−	4.30210i	0.0879262	−	0.152293i
$799$	−25.7380			−0.910545
$800$	−13.8075	+	23.9153i	−0.488168	+	0.845532i
$801$	−8.05295			−0.284537
$802$	−12.1660	−	21.0721i	−0.429595	−	0.744081i
$803$	−14.3473	+	24.8503i	−0.506306	+	0.876948i
$804$	−5.07031	−	8.78204i	−0.178816	−	0.309719i
$805$	−0.280457	−	0.485766i	−0.00988482	−	0.0171210i
$806$	−6.30342	−	10.9178i	−0.222028	−	0.384564i
$807$	−7.56020	−	13.0946i	−0.266132	−	0.460953i
$808$	22.1160			0.778037
$809$	−21.8882	−	37.9114i	−0.769547	−	1.33289i	−0.937809	−	0.347152i	$-0.887149\pi$
$809$	−21.8882	−	37.9114i	−0.769547	−	1.33289i	0.168262	−	0.985742i	$-0.446184\pi$
$810$	0.0250766	−	0.0434339i	0.000881101	−	0.00152611i
$811$	−2.07174	+	3.58835i	−0.0727485	+	0.126004i	−0.900105	−	0.435673i	$-0.856510\pi$
$811$	−2.07174	+	3.58835i	−0.0727485	+	0.126004i	0.827356	+	0.561677i	$0.189844\pi$
$812$	−11.7193			−0.411267
$813$	16.3751			0.574301
$814$	−13.1029			−0.459257
$815$	0.0611323	−	0.105884i	0.00214137	−	0.00370896i
$816$	0.323496	−	0.560312i	0.0113246	−	0.0196148i
$817$	43.2655			1.51367
$818$	5.72322	−	9.91291i	0.200108	−	0.346597i
$819$	−1.77557	−	3.07538i	−0.0620434	−	0.107462i
$820$	0.0827970	+	0.143409i	0.00289140	+	0.00500805i
$821$	22.2759	−	38.5830i	0.777435	−	1.34656i	−0.155981	−	0.987760i	$-0.549854\pi$
$821$	22.2759	−	38.5830i	0.777435	−	1.34656i	0.933416	−	0.358797i	$-0.116813\pi$
$822$	−3.67654	+	6.36796i	−0.128234	+	0.222108i
$823$	21.6822	+	37.5547i	0.755794	+	1.30907i	0.944979	+	0.327132i	$0.106082\pi$
$823$	21.6822	+	37.5547i	0.755794	+	1.30907i	−0.189185	+	0.981942i	$0.560584\pi$
$824$	−11.6320			−0.405221
$825$	−5.14484	−	8.91112i	−0.179120	−	0.310245i
$826$	−14.3237			−0.498385
$827$	10.8266	+	18.7522i	0.376478	+	0.652079i	0.990547	−	0.137173i	$-0.0438016\pi$
$827$	10.8266	+	18.7522i	0.376478	+	0.652079i	−0.614069	+	0.789252i	$0.710468\pi$
$828$	5.01846	−	8.69223i	0.174404	−	0.302076i
$829$	−15.5892	−	27.0013i	−0.541435	−	0.937793i	−0.998822	−	0.0485253i	$-0.984548\pi$
$829$	−15.5892	−	27.0013i	−0.541435	−	0.937793i	0.457387	−	0.889268i	$-0.348785\pi$
$830$	0.254192			0.00882312
$831$	−12.7396			−0.441931
$832$	−8.27161	+	14.3269i	−0.286767	+	0.496694i
$833$	6.86127	+	11.8841i	0.237729	+	0.411758i
$834$	−16.4932			−0.571114
$835$	−0.592757	+	1.02668i	−0.0205132	+	0.0355299i
$836$	−5.57312	+	9.65292i	−0.192750	+	0.333853i
$837$	2.32680	−	4.03014i	0.0804260	−	0.139302i
$838$	6.49531	−	11.2502i	0.224377	−	0.388632i
$839$	19.9717			0.689501			0.344751	−	0.938694i	$-0.387964\pi$
$839$	19.9717			0.689501			0.344751	+	0.938694i	$0.387964\pi$
$840$	−0.0947574	+	0.164125i	−0.00326944	+	0.00566284i
$841$	41.1257			1.41813
$842$	11.4208	−	19.7814i	0.393587	−	0.681712i
$843$	10.2865			0.354287
$844$	−19.1284			−0.658428
$845$	0.112993	−	0.195710i	0.00388708	−	0.00673262i
$846$	−4.75310	−	8.23261i	−0.163415	−	0.283043i
$847$	4.02078	−	6.96419i	0.138156	−	0.239292i
$848$	0.160948	−	0.278770i	0.00552697	−	0.00957299i
$849$	−12.6307			−0.433483
$850$	11.1427			0.382193
$851$	29.9109	−	51.8072i	1.02533	−	1.77593i
$852$	−15.1049			−0.517484
$853$	16.3241	+	28.2742i	0.558927	+	0.968090i	0.997586	+	0.0694364i	$0.0221201\pi$
$853$	16.3241	+	28.2742i	0.558927	+	0.968090i	−0.438659	+	0.898653i	$0.644547\pi$
$854$	5.49309	+	9.51432i	0.187970	+	0.325573i
$855$	−0.127141	−	0.220215i	−0.00434814	−	0.00753121i
$856$	−19.7918	+	34.2804i	−0.676469	+	1.17168i
$857$	−18.4849	+	32.0168i	−0.631432	+	1.09367i	0.355827	+	0.934552i	$0.384199\pi$
$857$	−18.4849	+	32.0168i	−0.631432	+	1.09367i	−0.987259	+	0.159121i	$0.949134\pi$
$858$	−2.78923	−	4.83108i	−0.0952226	−	0.164930i
$859$	13.0043	−	22.5241i	0.443700	−	0.768512i	−0.554260	−	0.832343i	$-0.686999\pi$
$859$	13.0043	−	22.5241i	0.443700	−	0.768512i	0.997961	+	0.0638318i	$0.0203321\pi$
$860$	−0.611299			−0.0208451
$861$	−1.51508	−	2.62419i	−0.0516337	−	0.0894322i
$862$	2.66446	+	4.61498i	0.0907518	+	0.157187i
$863$	1.23797			0.0421411			0.0210706	−	0.999778i	$-0.493293\pi$
$863$	1.23797			0.0421411			0.0210706	+	0.999778i	$0.493293\pi$
$864$	−5.52637			−0.188011
$865$	0.219426	+	0.380056i	0.00746069	+	0.0129223i
$866$	10.5226	+	18.2257i	0.357573	+	0.619335i
$867$	−10.9625			−0.372307
$868$	−3.25628	+	5.64005i	−0.110525	+	0.191436i
$869$	7.03412	+	12.1835i	0.238616	+	0.413295i
$870$	0.209994	−	0.363720i	0.00711946	−	0.0123313i
$871$	12.8659	−	22.2844i	0.435944	−	0.755076i
$872$	−2.79445	−	4.84014i	−0.0946322	−	0.163908i
$873$	8.93896	+	15.4827i	0.302538	+	0.524011i
$874$	17.8138	+	30.8544i	0.602561	+	1.04367i
$875$	−0.657228			−0.0222184
$876$	−8.19647	+	14.1967i	−0.276933	+	0.479662i
$877$	−7.57774			−0.255882			−0.127941	−	0.991782i	$-0.540837\pi$
$877$	−7.57774			−0.255882			−0.127941	+	0.991782i	$0.540837\pi$
$878$	−35.8750			−1.21072
$879$	−1.16721	+	2.02167i	−0.0393691	+	0.0681893i
$880$	−0.0149822	+	0.0259500i	−0.000505051	+	0.000874773i
$881$	15.1461	+	26.2338i	0.510286	+	0.883840i	0.999929	+	0.0119177i	$0.00379362\pi$
$881$	15.1461	+	26.2338i	0.510286	+	0.883840i	−0.489643	+	0.871923i	$0.662873\pi$
$882$	−2.53418	+	4.38932i	−0.0853301	+	0.147796i
$883$	−21.0789			−0.709362			−0.354681	−	0.934987i	$-0.615411\pi$
$883$	−21.0789			−0.709362			−0.354681	+	0.934987i	$0.615411\pi$
$884$	−8.62854			−0.290209
$885$	−0.366600	+	0.634970i	−0.0123231	+	0.0213443i
$886$	−36.3001			−1.21952
$887$	−2.58574	+	4.47863i	−0.0868206	+	0.150378i	−0.906166	−	0.422923i	$-0.861004\pi$
$887$	−2.58574	+	4.47863i	−0.0868206	+	0.150378i	0.819345	+	0.573301i	$0.194337\pi$
$888$	−20.2118			−0.678264
$889$	−7.83533	+	13.5712i	−0.262788	+	0.455163i
$890$	−0.201940	+	0.349771i	−0.00676905	+	0.0117243i
$891$	1.02960	−	1.78331i	0.0344928	−	0.0597432i
$892$	1.65467	−	2.86597i	0.0554025	−	0.0959599i
$893$	−48.1977			−1.61287
$894$	−2.94807	−	5.10621i	−0.0985984	−	0.170777i
$895$	0.215432	−	0.373139i	0.00720109	−	0.0124727i
$896$	7.16542			0.239380
$897$	25.4686			0.850372
$898$	−1.28851	−	2.23177i	−0.0429982	−	0.0744751i
$899$	19.4849	−	33.7488i	0.649857	−	1.12559i
$900$	−2.93919	−	5.09082i	−0.0979729	−	0.169694i
$901$	3.00380			0.100071
$902$	−2.38002	−	4.12232i	−0.0792461	−	0.137258i
$903$	11.1860			0.372246
$904$	−14.8143	−	25.6591i	−0.492716	−	0.853410i
$905$	0.428620	−	0.742391i	0.0142478	−	0.0246779i
$906$	−4.70674	+	8.15231i	−0.156371	+	0.270842i
$907$	13.9530	+	24.1673i	0.463301	+	0.802461i	0.999123	−	0.0418703i	$-0.0133316\pi$
$907$	13.9530	+	24.1673i	0.463301	+	0.802461i	−0.535822	+	0.844331i	$0.679998\pi$
$908$	5.38098	+	9.32014i	0.178574	+	0.309300i
$909$	−3.83603	+	6.64419i	−0.127233	+	0.220374i
$910$	−0.178101			−0.00590398
$911$	9.57060	−	16.5768i	0.317088	−	0.549213i	−0.662791	−	0.748804i	$-0.730628\pi$
$911$	9.57060	−	16.5768i	0.317088	−	0.549213i	0.979879	+	0.199592i	$0.0639616\pi$
$912$	0.605787	−	1.04925i	0.0200596	−	0.0347443i
$913$	10.4366			0.345402
$914$	−3.73111			−0.123414
$915$	0.562360			0.0185910
$916$	9.68208	−	16.7698i	0.319905	−	0.554091i
$917$	−0.0383401	+	0.0664069i	−0.00126610	+	0.00219295i
$918$	1.11496	+	1.93116i	0.0367990	+	0.0637378i
$919$	20.0280			0.660664			0.330332	−	0.943865i	$-0.392839\pi$
$919$	20.0280			0.660664			0.330332	+	0.943865i	$0.392839\pi$
$920$	−0.679595	−	1.17709i	−0.0224056	−	0.0388076i
$921$	10.1024	+	17.4978i	0.332885	+	0.576573i
$922$	−6.30409	−	10.9190i	−0.207614	−	0.359598i
$923$	−19.1642	−	33.1934i	−0.630799	−	1.09258i
$924$	−1.44089	+	2.49569i	−0.0474017	+	0.0821022i
$925$	−17.5180	−	30.3421i	−0.575990	−	0.997644i
$926$	1.07265			0.0352495
$927$	2.01758	−	3.49456i	0.0662662	−	0.114776i
$928$	−46.2784			−1.51916
$929$	−17.1233	+	29.6584i	−0.561797	+	0.973061i	0.435543	+	0.900168i	$0.356557\pi$
$929$	−17.1233	+	29.6584i	−0.561797	+	0.973061i	−0.997340	+	0.0728931i	$0.976777\pi$
$930$	−0.116696	−	0.202124i	−0.00382662	−	0.00662790i
$931$	12.8486	+	22.2544i	0.421096	+	0.729359i
$932$	12.6918	+	21.9828i	0.415733	+	0.720070i
$933$	−4.26588	+	7.38872i	−0.139659	+	0.241896i
$934$	13.2930			0.434961
$935$	−0.279616			−0.00914443
$936$	−4.30250	−	7.45216i	−0.140632	−	0.243581i
$937$	−12.7373	−	22.0616i	−0.416109	−	0.720722i	0.579435	−	0.815018i	$-0.303273\pi$
$937$	−12.7373	−	22.0616i	−0.416109	−	0.720722i	−0.995544	+	0.0942965i	$0.969940\pi$
$938$	9.30643			0.303866
$939$	−3.33231	−	5.77173i	−0.108746	−	0.188353i
$940$	0.680985			0.0222113
$941$	−12.5564			−0.409328			−0.204664	−	0.978832i	$-0.565610\pi$
$941$	−12.5564			−0.409328			−0.204664	+	0.978832i	$0.565610\pi$
$942$	5.72181	+	9.82686i	0.186427	+	0.320176i
$943$	21.7321			0.707696
$944$	−3.49346			−0.113702
$945$	−0.0328714	−	0.0569350i	−0.00106931	−	0.00185210i
$946$	17.5720			0.571313
$947$	−18.2709	−	31.6461i	−0.593724	−	1.02836i	−0.993726	−	0.111846i	$-0.964324\pi$
$947$	−18.2709	−	31.6461i	−0.593724	−	1.02836i	0.400002	−	0.916514i	$-0.369010\pi$
$948$	4.01851	+	6.96027i	0.130515	+	0.226059i
$949$	−41.5969			−1.35029
$950$	20.8662			0.676989
$951$	−2.01885	+	3.49676i	−0.0654658	+	0.113390i
$952$	−4.21311	−	7.29732i	−0.136548	−	0.236507i
$953$	−5.04077	−	8.73088i	−0.163287	−	0.282821i	0.772759	−	0.634700i	$-0.218876\pi$
$953$	−5.04077	−	8.73088i	−0.163287	−	0.282821i	−0.936046	+	0.351879i	$0.885543\pi$
$954$	0.554719	+	0.960802i	0.0179597	+	0.0311071i
$955$	0.178733	−	0.309574i	0.00578365	−	0.0100176i
$956$	−0.0640634			−0.00207196
$957$	8.62195	−	14.9337i	0.278708	−	0.482736i
$958$	4.58325			0.148078
$959$	4.81937	+	8.34740i	0.155626	+	0.269552i
$960$	−0.153134	+	0.265236i	−0.00494237	+	0.00856044i
$961$	4.67201	+	8.09216i	0.150710	+	0.261037i
$962$	−9.49725	−	16.4497i	−0.306204	−	0.530360i
$963$	−6.86579	−	11.8919i	−0.221247	−	0.383211i
$964$	11.2512	+	19.4877i	0.362377	+	0.627655i
$965$	−0.531355			−0.0171049
$966$	4.60563	+	7.97718i	0.148184	+	0.256662i
$967$	−17.3578	+	30.0645i	−0.558188	+	0.966810i	0.439460	+	0.898262i	$0.355170\pi$
$967$	−17.3578	+	30.0645i	−0.558188	+	0.966810i	−0.997648	+	0.0685477i	$0.978163\pi$
$968$	9.74302	−	16.8754i	0.313152	−	0.542396i
$969$	11.3059			0.363199
$970$	0.896633			0.0287892
$971$	−34.6796			−1.11292			−0.556461	−	0.830874i	$-0.687841\pi$
$971$	−34.6796			−1.11292			−0.556461	+	0.830874i	$0.687841\pi$
$972$	0.588197	−	1.01879i	0.0188664	−	0.0326776i
$973$	−10.8100	+	18.7235i	−0.346553	+	0.600248i
$974$	21.9985			0.704879
$975$	7.45816	−	12.9179i	0.238852	−	0.413704i
$976$	1.33973	+	2.32048i	0.0428838	+	0.0742768i
$977$	14.8946	+	25.7983i	0.476522	+	0.825360i	0.999638	−	0.0269010i	$-0.00856390\pi$
$977$	14.8946	+	25.7983i	0.476522	+	0.825360i	−0.523116	+	0.852261i	$0.675231\pi$
$978$	−1.00390	+	1.73881i	−0.0321013	+	0.0556011i
$979$	−8.29128	+	14.3609i	−0.264991	+	0.458977i
$980$	−0.181538	−	0.314433i	−0.00579902	−	0.0100442i
$981$	1.93880			0.0619011
$982$	−14.7539	−	25.5545i	−0.470815	−	0.815476i
$983$	41.9434			1.33779			0.668893	−	0.743359i	$-0.266768\pi$
$983$	41.9434			1.33779			0.668893	+	0.743359i	$0.266768\pi$
$984$	−3.67129	−	6.35886i	−0.117036	−	0.202713i
$985$	−0.388273	+	0.672508i	−0.0123714	+	0.0214279i
$986$	9.33676	+	16.1717i	0.297343	+	0.515013i
$987$	−12.4611			−0.396642
$988$	−16.1580			−0.514055
$989$	−40.1127	+	69.4772i	−1.27551	+	2.20924i
$990$	−0.0516375	−	0.0894387i	−0.00164115	−	0.00284255i
$991$	−27.4541			−0.872110			−0.436055	−	0.899920i	$-0.643625\pi$
$991$	−27.4541			−0.872110			−0.436055	+	0.899920i	$0.643625\pi$
$992$	−12.8587	+	22.2720i	−0.408266	+	0.707137i
$993$	−6.79871	+	11.7757i	−0.215751	+	0.373691i
$994$	6.93115	−	12.0051i	0.219843	−	0.380779i
$995$	−0.581093	+	1.00648i	−0.0184219	+	0.0319076i
$996$	5.96232			0.188923
$997$	17.9777	−	31.1382i	0.569358	−	0.986157i	−0.427271	−	0.904123i	$-0.640525\pi$
$997$	17.9777	−	31.1382i	0.569358	−	0.986157i	0.996630	−	0.0820340i	$-0.0261416\pi$
$998$	10.4859			0.331927
$999$	3.50575	−	6.07214i	0.110917	−	0.192114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.e.c.169.6	✓	28
157.144	even	3	inner	471.2.e.c.301.6	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.e.c.169.6	✓	28	1.1	even	1	trivial
471.2.e.c.301.6	yes	28	157.144	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.907528 q^{2} +(-0.500000 - 0.866025i) q^{3} -1.17639 q^{4} +(-0.0276317 - 0.0478596i) q^{5} +(0.453764 + 0.785942i) q^{6} +1.18963 q^{7} +2.88267 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-0.907528 q^{2} +(-0.500000 - 0.866025i) q^{3} -1.17639 q^{4} +(-0.0276317 - 0.0478596i) q^{5} +(0.453764 + 0.785942i) q^{6} +1.18963 q^{7} +2.88267 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.0250766 + 0.0434339i) q^{10} +(1.02960 + 1.78331i) q^{11} +(0.588197 + 1.01879i) q^{12} +(-1.49254 + 2.58516i) q^{13} -1.07962 q^{14} +(-0.0276317 + 0.0478596i) q^{15} -0.263312 q^{16} +(-1.22856 - 2.12793i) q^{17} +(0.453764 - 0.785942i) q^{18} +(-2.30064 - 3.98483i) q^{19} +(0.0325058 + 0.0563017i) q^{20} +(-0.594813 - 1.03025i) q^{21} +(-0.934387 - 1.61841i) q^{22} +8.53195 q^{23} +(-1.44133 - 2.49646i) q^{24} +(2.49847 - 4.32748i) q^{25} +(1.35452 - 2.34611i) q^{26} +1.00000 q^{27} -1.39947 q^{28} +8.37411 q^{29} +(0.0250766 - 0.0434339i) q^{30} +(2.32680 - 4.03014i) q^{31} -5.52637 q^{32} +(1.02960 - 1.78331i) q^{33} +(1.11496 + 1.93116i) q^{34} +(-0.0328714 - 0.0569350i) q^{35} +(0.588197 - 1.01879i) q^{36} +(3.50575 - 6.07214i) q^{37} +(2.08790 + 3.61634i) q^{38} +2.98509 q^{39} +(-0.0796530 - 0.137963i) q^{40} +2.54715 q^{41} +(0.539810 + 0.934978i) q^{42} +(-4.70147 + 8.14318i) q^{43} +(-1.21121 - 2.09788i) q^{44} +0.0552635 q^{45} -7.74298 q^{46} +(5.23742 - 9.07147i) q^{47} +(0.131656 + 0.228035i) q^{48} -5.58479 q^{49} +(-2.26743 + 3.92731i) q^{50} +(-1.22856 + 2.12793i) q^{51} +(1.75582 - 3.04117i) q^{52} +(-0.611242 + 1.05870i) q^{53} -0.907528 q^{54} +(0.0568990 - 0.0985520i) q^{55} +3.42930 q^{56} +(-2.30064 + 3.98483i) q^{57} -7.59974 q^{58} +13.2674 q^{59} +(0.0325058 - 0.0563017i) q^{60} +(-5.08799 - 8.81266i) q^{61} +(-2.11164 + 3.65746i) q^{62} +(-0.594813 + 1.03025i) q^{63} +5.54196 q^{64} +0.164966 q^{65} +(-0.934387 + 1.61841i) q^{66} -8.62010 q^{67} +(1.44527 + 2.50329i) q^{68} +(-4.26597 - 7.38888i) q^{69} +(0.0298317 + 0.0516701i) q^{70} +(-6.41999 + 11.1198i) q^{71} +(-1.44133 + 2.49646i) q^{72} +(6.96746 + 12.0680i) q^{73} +(-3.18157 + 5.51063i) q^{74} -4.99695 q^{75} +(2.70646 + 4.68772i) q^{76} +(1.22483 + 2.12148i) q^{77} -2.70905 q^{78} +6.83192 q^{79} +(0.00727578 + 0.0126020i) q^{80} +(-0.500000 - 0.866025i) q^{81} -2.31161 q^{82} +(2.53415 - 4.38928i) q^{83} +(0.699734 + 1.21198i) q^{84} +(-0.0678947 + 0.117597i) q^{85} +(4.26671 - 7.39016i) q^{86} +(-4.18705 - 7.25219i) q^{87} +(2.96798 + 5.14069i) q^{88} +(4.02647 + 6.97406i) q^{89} -0.0501531 q^{90} +(-1.77557 + 3.07538i) q^{91} -10.0369 q^{92} -4.65360 q^{93} +(-4.75310 + 8.23261i) q^{94} +(-0.127141 + 0.220215i) q^{95} +(2.76318 + 4.78597i) q^{96} +(8.93896 - 15.4827i) q^{97} +5.06835 q^{98} -2.05919 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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