LMFDB - Embedded newform 403.2.h.b.118.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, 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("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.11
Character	$\chi$	$=$	403.118
Dual form			403.2.h.b.222.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.28826 q^{2} +(1.07551 + 1.86284i) q^{3} -0.340382 q^{4} +(-1.69851 + 2.94190i) q^{5} +(1.38554 + 2.39982i) q^{6} +(0.278041 + 0.481581i) q^{7} -3.01502 q^{8} +(-0.813438 + 1.40892i) q^{9} +O(q^{10})$	\(q+1.28826 q^{2} +(1.07551 + 1.86284i) q^{3} -0.340382 q^{4} +(-1.69851 + 2.94190i) q^{5} +(1.38554 + 2.39982i) q^{6} +(0.278041 + 0.481581i) q^{7} -3.01502 q^{8} +(-0.813438 + 1.40892i) q^{9} +(-2.18812 + 3.78994i) q^{10} +(2.38925 - 4.13830i) q^{11} +(-0.366083 - 0.634075i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(0.358189 + 0.620402i) q^{14} -7.30704 q^{15} -3.20338 q^{16} +(3.25861 + 5.64408i) q^{17} +(-1.04792 + 1.81505i) q^{18} +(1.33011 + 2.30381i) q^{19} +(0.578141 - 1.00137i) q^{20} +(-0.598070 + 1.03589i) q^{21} +(3.07798 - 5.33122i) q^{22} -7.99721 q^{23} +(-3.24268 - 5.61649i) q^{24} +(-3.26986 - 5.66356i) q^{25} +(-0.644131 + 1.11567i) q^{26} +2.95361 q^{27} +(-0.0946400 - 0.163921i) q^{28} +3.90984 q^{29} -9.41338 q^{30} +(4.90883 + 2.62744i) q^{31} +1.90326 q^{32} +10.2786 q^{33} +(4.19794 + 7.27105i) q^{34} -1.88902 q^{35} +(0.276879 - 0.479569i) q^{36} +(5.44537 + 9.43166i) q^{37} +(1.71352 + 2.96791i) q^{38} -2.15102 q^{39} +(5.12104 - 8.86990i) q^{40} +(6.00876 - 10.4075i) q^{41} +(-0.770471 + 1.33450i) q^{42} +(-4.19272 - 7.26200i) q^{43} +(-0.813257 + 1.40860i) q^{44} +(-2.76326 - 4.78611i) q^{45} -10.3025 q^{46} +4.74715 q^{47} +(-3.44526 - 5.96736i) q^{48} +(3.34539 - 5.79438i) q^{49} +(-4.21243 - 7.29615i) q^{50} +(-7.00933 + 12.1405i) q^{51} +(0.170191 - 0.294779i) q^{52} +(2.19963 - 3.80988i) q^{53} +3.80503 q^{54} +(8.11632 + 14.0579i) q^{55} +(-0.838300 - 1.45198i) q^{56} +(-2.86108 + 4.95554i) q^{57} +5.03690 q^{58} +(-3.33135 - 5.77007i) q^{59} +2.48718 q^{60} -8.01209 q^{61} +(6.32385 + 3.38483i) q^{62} -0.904675 q^{63} +8.85865 q^{64} +(-1.69851 - 2.94190i) q^{65} +13.2416 q^{66} +(-2.05361 + 3.55695i) q^{67} +(-1.10917 - 1.92114i) q^{68} +(-8.60107 - 14.8975i) q^{69} -2.43355 q^{70} +(-1.84977 + 3.20390i) q^{71} +(2.45253 - 4.24791i) q^{72} +(-5.46321 + 9.46256i) q^{73} +(7.01507 + 12.1505i) q^{74} +(7.03352 - 12.1824i) q^{75} +(-0.452744 - 0.784175i) q^{76} +2.65724 q^{77} -2.77107 q^{78} +(-1.00465 - 1.74011i) q^{79} +(5.44096 - 9.42402i) q^{80} +(5.61695 + 9.72885i) q^{81} +(7.74086 - 13.4076i) q^{82} +(4.62578 - 8.01208i) q^{83} +(0.203572 - 0.352597i) q^{84} -22.1391 q^{85} +(-5.40132 - 9.35536i) q^{86} +(4.20507 + 7.28339i) q^{87} +(-7.20365 + 12.4771i) q^{88} -5.05334 q^{89} +(-3.55980 - 6.16576i) q^{90} -0.556082 q^{91} +2.72210 q^{92} +(0.385000 + 11.9702i) q^{93} +6.11557 q^{94} -9.03678 q^{95} +(2.04697 + 3.54546i) q^{96} -3.19323 q^{97} +(4.30973 - 7.46468i) q^{98} +(3.88701 + 6.73250i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) $ 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.28826			0.910939			0.455469	−	0.890251i	$-0.349471\pi$
$2$	1.28826			0.910939			0.455469	+	0.890251i	$0.349471\pi$
$3$	1.07551	+	1.86284i	0.620945	+	1.07551i	0.989310	+	0.145827i	$0.0465844\pi$
$3$	1.07551	+	1.86284i	0.620945	+	1.07551i	−0.368365	+	0.929681i	$0.620082\pi$
$4$	−0.340382			−0.170191
$5$	−1.69851	+	2.94190i	−0.759596	+	1.31566i	0.183461	+	0.983027i	$0.441270\pi$
$5$	−1.69851	+	2.94190i	−0.759596	+	1.31566i	−0.943057	+	0.332631i	$0.892063\pi$
$6$	1.38554	+	2.39982i	0.565643	+	0.979722i
$7$	0.278041	+	0.481581i	0.105090	+	0.182020i	0.913775	−	0.406221i	$-0.133154\pi$
$7$	0.278041	+	0.481581i	0.105090	+	0.182020i	−0.808685	+	0.588242i	$0.799820\pi$
$8$	−3.01502			−1.06597
$9$	−0.813438	+	1.40892i	−0.271146	+	0.469639i
$10$	−2.18812	+	3.78994i	−0.691945	+	1.19848i
$11$	2.38925	−	4.13830i	0.720386	−	1.24775i	−0.240459	−	0.970659i	$-0.577298\pi$
$11$	2.38925	−	4.13830i	0.720386	−	1.24775i	0.960845	−	0.277086i	$-0.0893687\pi$
$12$	−0.366083	−	0.634075i	−0.105679	−	0.183042i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	0.358189	+	0.620402i	0.0957301	+	0.165809i
$15$	−7.30704			−1.88667
$16$	−3.20338			−0.800844
$17$	3.25861	+	5.64408i	0.790329	+	1.36889i	0.925763	+	0.378104i	$0.123424\pi$
$17$	3.25861	+	5.64408i	0.790329	+	1.36889i	−0.135434	+	0.990786i	$0.543243\pi$
$18$	−1.04792	+	1.81505i	−0.246997	+	0.427812i
$19$	1.33011	+	2.30381i	0.305147	+	0.528531i	0.977294	−	0.211887i	$-0.0679610\pi$
$19$	1.33011	+	2.30381i	0.305147	+	0.528531i	−0.672147	+	0.740418i	$0.734628\pi$
$20$	0.578141	−	1.00137i	0.129276	−	0.223913i
$21$	−0.598070	+	1.03589i	−0.130510	+	0.226049i
$22$	3.07798	−	5.33122i	0.656227	−	1.13662i
$23$	−7.99721			−1.66753			−0.833767	−	0.552117i	$-0.813820\pi$
$23$	−7.99721			−1.66753			−0.833767	+	0.552117i	$0.813820\pi$
$24$	−3.24268	−	5.61649i	−0.661910	−	1.14646i
$25$	−3.26986	−	5.66356i	−0.653971	−	1.13271i
$26$	−0.644131	+	1.11567i	−0.126324	+	0.218800i
$27$	2.95361			0.568423
$28$	−0.0946400	−	0.163921i	−0.0178853	−	0.0309782i
$29$	3.90984			0.726039			0.363019	−	0.931782i	$-0.381746\pi$
$29$	3.90984			0.726039			0.363019	+	0.931782i	$0.381746\pi$
$30$	−9.41338			−1.71864
$31$	4.90883	+	2.62744i	0.881651	+	0.471902i
$31$	4.90883	+	2.62744i	0.881651	+	0.471902i
$32$	1.90326			0.336452
$33$	10.2786			1.78928
$34$	4.19794	+	7.27105i	0.719942	+	1.24698i
$35$	−1.88902			−0.319302
$36$	0.276879	−	0.479569i	0.0461466	−	0.0799282i
$37$	5.44537	+	9.43166i	0.895214	+	1.55056i	0.833540	+	0.552460i	$0.186311\pi$
$37$	5.44537	+	9.43166i	0.895214	+	1.55056i	0.0616742	+	0.998096i	$0.480356\pi$
$38$	1.71352	+	2.96791i	0.277970	+	0.481459i
$39$	−2.15102			−0.344438
$40$	5.12104	−	8.86990i	0.809708	−	1.40246i
$41$	6.00876	−	10.4075i	0.938411	−	1.62538i	0.169976	−	0.985448i	$-0.445631\pi$
$41$	6.00876	−	10.4075i	0.938411	−	1.62538i	0.768435	−	0.639927i	$-0.221036\pi$
$42$	−0.770471	+	1.33450i	−0.118886	+	0.205917i
$43$	−4.19272	−	7.26200i	−0.639383	−	1.10744i	−0.985568	−	0.169278i	$-0.945856\pi$
$43$	−4.19272	−	7.26200i	−0.639383	−	1.10744i	0.346185	−	0.938166i	$-0.387477\pi$
$44$	−0.813257	+	1.40860i	−0.122603	+	0.212355i
$45$	−2.76326	−	4.78611i	−0.411923	−	0.713471i
$46$	−10.3025			−1.51902
$47$	4.74715			0.692443			0.346221	−	0.938153i	$-0.387465\pi$
$47$	4.74715			0.692443			0.346221	+	0.938153i	$0.387465\pi$
$48$	−3.44526	−	5.96736i	−0.497280	−	0.861315i
$49$	3.34539	−	5.79438i	0.477912	−	0.827769i
$50$	−4.21243	−	7.29615i	−0.595728	−	1.03183i
$51$	−7.00933	+	12.1405i	−0.981503	+	1.70001i
$52$	0.170191	−	0.294779i	0.0236012	−	0.0408785i
$53$	2.19963	−	3.80988i	0.302143	−	0.523327i	−0.674478	−	0.738295i	$-0.735631\pi$
$53$	2.19963	−	3.80988i	0.302143	−	0.523327i	0.976621	+	0.214968i	$0.0689647\pi$
$54$	3.80503			0.517799
$55$	8.11632	+	14.0579i	1.09440	+	1.89556i
$56$	−0.838300	−	1.45198i	−0.112022	−	0.194029i
$57$	−2.86108	+	4.95554i	−0.378959	+	0.656377i
$58$	5.03690			0.661377
$59$	−3.33135	−	5.77007i	−0.433705	−	0.751200i	0.563484	−	0.826127i	$-0.309461\pi$
$59$	−3.33135	−	5.77007i	−0.433705	−	0.751200i	−0.997189	+	0.0749276i	$0.976127\pi$
$60$	2.48718			0.321094
$61$	−8.01209			−1.02584			−0.512921	−	0.858436i	$-0.671437\pi$
$61$	−8.01209			−1.02584			−0.512921	+	0.858436i	$0.671437\pi$
$62$	6.32385	+	3.38483i	0.803130	+	0.429874i
$63$	−0.904675			−0.113978
$64$	8.85865			1.10733
$65$	−1.69851	−	2.94190i	−0.210674	−	0.364898i
$66$	13.2416			1.62993
$67$	−2.05361	+	3.55695i	−0.250888	+	0.434551i	−0.963771	−	0.266733i	$-0.914056\pi$
$67$	−2.05361	+	3.55695i	−0.250888	+	0.434551i	0.712882	+	0.701284i	$0.247389\pi$
$68$	−1.10917	−	1.92114i	−0.134507	−	0.232973i
$69$	−8.60107	−	14.8975i	−1.03545	−	1.79345i
$70$	−2.43355			−0.290865
$71$	−1.84977	+	3.20390i	−0.219528	+	0.380233i	−0.954664	−	0.297686i	$-0.903785\pi$
$71$	−1.84977	+	3.20390i	−0.219528	+	0.380233i	0.735136	+	0.677920i	$0.237118\pi$
$72$	2.45253	−	4.24791i	0.289034	−	0.500622i
$73$	−5.46321	+	9.46256i	−0.639420	+	1.10751i	0.346140	+	0.938183i	$0.387492\pi$
$73$	−5.46321	+	9.46256i	−0.639420	+	1.10751i	−0.985560	+	0.169325i	$0.945841\pi$
$74$	7.01507	+	12.1505i	0.815485	+	1.41246i
$75$	7.03352	−	12.1824i	0.812161	−	1.40670i
$76$	−0.452744	−	0.784175i	−0.0519333	−	0.0899511i
$77$	2.65724			0.302820
$78$	−2.77107			−0.313762
$79$	−1.00465	−	1.74011i	−0.113032	−	0.195777i	0.803959	−	0.594684i	$-0.202723\pi$
$79$	−1.00465	−	1.74011i	−0.113032	−	0.195777i	−0.916991	+	0.398907i	$0.869390\pi$
$80$	5.44096	−	9.42402i	0.608318	−	1.05364i
$81$	5.61695	+	9.72885i	0.624106	+	1.08098i
$82$	7.74086	−	13.4076i	0.854835	−	1.48062i
$83$	4.62578	−	8.01208i	0.507745	−	0.879440i	−0.492215	−	0.870474i	$-0.663813\pi$
$83$	4.62578	−	8.01208i	0.507745	−	0.879440i	0.999960	−	0.00896614i	$-0.00285405\pi$
$84$	0.203572	−	0.352597i	0.0222116	−	0.0384715i
$85$	−22.1391			−2.40132
$86$	−5.40132	−	9.35536i	−0.582439	−	1.00881i
$87$	4.20507	+	7.28339i	0.450830	+	0.780861i
$88$	−7.20365	+	12.4771i	−0.767911	+	1.33006i
$89$	−5.05334			−0.535653			−0.267827	−	0.963467i	$-0.586305\pi$
$89$	−5.05334			−0.535653			−0.267827	+	0.963467i	$0.586305\pi$
$90$	−3.55980	−	6.16576i	−0.375236	−	0.649928i
$91$	−0.556082			−0.0582932
$92$	2.72210			0.283799
$93$	0.385000	+	11.9702i	0.0399227	+	1.24125i
$94$	6.11557			0.630773
$95$	−9.03678			−0.927154
$96$	2.04697	+	3.54546i	0.208918	+	0.361857i
$97$	−3.19323			−0.324224			−0.162112	−	0.986772i	$-0.551831\pi$
$97$	−3.19323			−0.324224			−0.162112	+	0.986772i	$0.551831\pi$
$98$	4.30973	−	7.46468i	0.435349	−	0.754046i
$99$	3.88701	+	6.73250i	0.390659	+	0.676642i
$100$	1.11300	+	1.92777i	0.111300	+	0.192777i
$101$	−0.564935			−0.0562132			−0.0281066	−	0.999605i	$-0.508948\pi$
$101$	−0.564935			−0.0562132			−0.0281066	+	0.999605i	$0.508948\pi$
$102$	−9.02985	+	15.6402i	−0.894089	+	1.54861i
$103$	−5.04132	+	8.73182i	−0.496736	+	0.860372i	−0.999993	−	0.00376467i	$-0.998802\pi$
$103$	−5.04132	+	8.73182i	−0.496736	+	0.860372i	0.503257	+	0.864137i	$0.332135\pi$
$104$	1.50751	−	2.61109i	0.147824	−	0.256038i
$105$	−2.03165	−	3.51893i	−0.198269	−	0.343412i
$106$	2.83370	−	4.90812i	0.275234	−	0.476719i
$107$	−4.07492	−	7.05796i	−0.393937	−	0.682319i	0.599028	−	0.800728i	$-0.295554\pi$
$107$	−4.07492	−	7.05796i	−0.393937	−	0.682319i	−0.992965	+	0.118409i	$0.962220\pi$
$108$	−1.00536			−0.0967405
$109$	11.0090			1.05447			0.527236	−	0.849719i	$-0.323228\pi$
$109$	11.0090			1.05447			0.527236	+	0.849719i	$0.323228\pi$
$110$	10.4559	+	18.1102i	0.996935	+	1.72674i
$111$	−11.7131	+	20.2877i	−1.11176	+	1.92562i
$112$	−0.890669	−	1.54268i	−0.0841603	−	0.145770i
$113$	0.333706	−	0.577996i	0.0313924	−	0.0543733i	−0.849902	−	0.526940i	$-0.823339\pi$
$113$	0.333706	−	0.577996i	0.0313924	−	0.0543733i	0.881295	+	0.472567i	$0.156673\pi$
$114$	−3.68582	+	6.38403i	−0.345209	+	0.597919i
$115$	13.5833	−	23.5270i	1.26665	−	2.19390i
$116$	−1.33084			−0.123565
$117$	−0.813438	−	1.40892i	−0.0752024	−	0.130254i
$118$	−4.29166	−	7.43336i	−0.395079	−	0.684297i
$119$	−1.81205	+	3.13857i	−0.166111	+	0.287712i
$120$	22.0309			2.01114
$121$	−5.91703	−	10.2486i	−0.537912	−	0.931691i
$122$	−10.3217			−0.934479
$123$	25.8499			2.33081
$124$	−1.67087	−	0.894332i	−0.150049	−	0.0803134i
$125$	5.23043			0.467824
$126$	−1.16546			−0.103827
$127$	−9.95414	−	17.2411i	−0.883287	−	1.52990i	−0.847665	−	0.530532i	$-0.821992\pi$
$127$	−9.95414	−	17.2411i	−0.883287	−	1.52990i	−0.0356223	−	0.999365i	$-0.511341\pi$
$128$	7.60574			0.672259
$129$	9.01861	−	15.6207i	0.794044	−	1.37532i
$130$	−2.18812	−	3.78994i	−0.191911	−	0.332400i
$131$	−4.12049	−	7.13691i	−0.360009	−	0.623554i	0.627953	−	0.778252i	$-0.283893\pi$
$131$	−4.12049	−	7.13691i	−0.360009	−	0.623554i	−0.987962	+	0.154697i	$0.950560\pi$
$132$	−3.49866			−0.304519
$133$	−0.739647	+	1.28111i	−0.0641356	+	0.111086i
$134$	−2.64558	+	4.58229i	−0.228544	+	0.395849i
$135$	−5.01674	+	8.68924i	−0.431772	+	0.747851i
$136$	−9.82479	−	17.0170i	−0.842469	−	1.45920i
$137$	−0.407109	+	0.705134i	−0.0347817	+	0.0602436i	−0.882892	−	0.469576i	$-0.844407\pi$
$137$	−0.407109	+	0.705134i	−0.0347817	+	0.0602436i	0.848111	+	0.529819i	$0.177740\pi$
$138$	−11.0804	−	19.1919i	−0.943228	−	1.63372i
$139$	4.25650			0.361031			0.180516	−	0.983572i	$-0.442223\pi$
$139$	4.25650			0.361031			0.180516	+	0.983572i	$0.442223\pi$
$140$	0.642987			0.0543423
$141$	5.10560	+	8.84316i	0.429969	+	0.744728i
$142$	−2.38299	+	4.12747i	−0.199976	+	0.346369i
$143$	2.38925	+	4.13830i	0.199799	+	0.346062i
$144$	2.60575	−	4.51329i	0.217146	−	0.376107i
$145$	−6.64089	+	11.5024i	−0.551496	+	0.955219i
$146$	−7.03804	+	12.1902i	−0.582473	+	1.00887i
$147$	14.3920			1.18703
$148$	−1.85351	−	3.21037i	−0.152357	−	0.263890i
$149$	−7.21838	−	12.5026i	−0.591353	−	1.02425i	−0.994050	−	0.108920i	$-0.965261\pi$
$149$	−7.21838	−	12.5026i	−0.591353	−	1.02425i	0.402697	−	0.915333i	$-0.368073\pi$
$150$	9.06101	−	15.6941i	0.739829	−	1.28142i
$151$	23.9202			1.94659			0.973297	−	0.229549i	$-0.0737251\pi$
$151$	23.9202			1.94659			0.973297	+	0.229549i	$0.0737251\pi$
$152$	−4.01030	−	6.94605i	−0.325278	−	0.563399i
$153$	−10.6027			−0.857178
$154$	3.42321			0.275851
$155$	−16.0673	+	9.97856i	−1.29056	+	0.801497i
$156$	0.732167			0.0586203
$157$	−8.67546			−0.692377			−0.346189	−	0.938165i	$-0.612524\pi$
$157$	−8.67546			−0.692377			−0.346189	+	0.938165i	$0.612524\pi$
$158$	−1.29425	−	2.24171i	−0.102965	−	0.178341i
$159$	9.46290			0.750457
$160$	−3.23270	+	5.59921i	−0.255568	+	0.442656i
$161$	−2.22355	−	3.85130i	−0.175240	−	0.303525i
$162$	7.23610	+	12.5333i	0.568522	+	0.984709i
$163$	−14.6951			−1.15101			−0.575505	−	0.817798i	$-0.695195\pi$
$163$	−14.6951			−1.15101			−0.575505	+	0.817798i	$0.695195\pi$
$164$	−2.04527	+	3.54252i	−0.159709	+	0.276624i
$165$	−17.4583	+	30.2387i	−1.35913	+	2.35408i
$166$	5.95921	−	10.3217i	0.462524	−	0.801116i
$167$	9.69086	+	16.7851i	0.749901	+	1.29887i	0.947870	+	0.318658i	$0.103232\pi$
$167$	9.69086	+	16.7851i	0.749901	+	1.29887i	−0.197969	+	0.980208i	$0.563434\pi$
$168$	1.80320	−	3.12323i	0.139120	−	0.240962i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−28.5210			−2.18746
$171$	−4.32783			−0.330958
$172$	1.42712	+	2.47185i	0.108817	+	0.188477i
$173$	−0.664824	+	1.15151i	−0.0505456	+	0.0875476i	−0.890191	−	0.455587i	$-0.849429\pi$
$173$	−0.664824	+	1.15151i	−0.0505456	+	0.0875476i	0.839646	+	0.543135i	$0.182763\pi$
$174$	5.41723	+	9.38291i	0.410679	+	0.711317i
$175$	1.81831	−	3.14940i	0.137451	−	0.238072i
$176$	−7.65367	+	13.2565i	−0.576917	+	0.999249i
$177$	7.16580	−	12.4115i	0.538614	−	0.932908i
$178$	−6.51003			−0.487947
$179$	−8.98982	−	15.5708i	−0.671931	−	1.16382i	−0.977356	−	0.211602i	$-0.932132\pi$
$179$	−8.98982	−	15.5708i	−0.671931	−	1.16382i	0.305425	−	0.952216i	$-0.401201\pi$
$180$	0.940563	+	1.62910i	0.0701055	+	0.121426i
$181$	2.59517	−	4.49497i	0.192897	−	0.334108i	−0.753312	−	0.657664i	$-0.771545\pi$
$181$	2.59517	−	4.49497i	0.192897	−	0.334108i	0.946209	+	0.323555i	$0.104878\pi$
$182$	−0.716379			−0.0531015
$183$	−8.61707	−	14.9252i	−0.636992	−	1.10330i
$184$	24.1118			1.77754
$185$	−36.9960			−2.72000
$186$	0.495981	+	15.4207i	0.0363671	+	1.13070i
$187$	31.1426			2.27737
$188$	−1.61584			−0.117847
$189$	0.821225	+	1.42240i	0.0597353	+	0.103465i
$190$	−11.6417			−0.844581
$191$	2.84969	−	4.93580i	0.206196	−	0.357142i	−0.744317	−	0.667826i	$-0.767225\pi$
$191$	2.84969	−	4.93580i	0.206196	−	0.357142i	0.950513	+	0.310684i	$0.100558\pi$
$192$	9.52756	+	16.5022i	0.687592	+	1.19094i
$193$	6.47978	+	11.2233i	0.466425	+	0.807871i	0.999265	−	0.0383450i	$-0.0122086\pi$
$193$	6.47978	+	11.2233i	0.466425	+	0.807871i	−0.532840	+	0.846216i	$0.678875\pi$
$194$	−4.11372			−0.295348
$195$	3.65352	−	6.32808i	0.261634	−	0.453163i
$196$	−1.13871	+	1.97230i	−0.0813363	+	0.140879i
$197$	1.51535	−	2.62466i	0.107964	−	0.186999i	−0.806981	−	0.590577i	$-0.798900\pi$
$197$	1.51535	−	2.62466i	0.107964	−	0.186999i	0.914945	+	0.403578i	$0.132234\pi$
$198$	5.00749	+	8.67323i	0.355867	+	0.616379i
$199$	5.59389	−	9.68891i	0.396541	−	0.686828i	−0.596756	−	0.802423i	$-0.703544\pi$
$199$	5.59389	−	9.68891i	0.396541	−	0.686828i	0.993297	+	0.115594i	$0.0368773\pi$
$200$	9.85870	+	17.0758i	0.697115	+	1.20744i
$201$	−8.83469			−0.623151
$202$	−0.727784			−0.0512067
$203$	1.08709	+	1.88290i	0.0762991	+	0.132154i
$204$	2.38585	−	4.13241i	0.167043	−	0.289327i
$205$	20.4119	+	35.3544i	1.42563	+	2.46926i
$206$	−6.49454	+	11.2489i	−0.452496	+	0.783746i
$207$	6.50523	−	11.2674i	0.452145	−	0.783138i
$208$	1.60169	−	2.77421i	0.111057	−	0.192357i
$209$	12.7118			0.879295
$210$	−2.61730	−	4.53330i	−0.180611	−	0.312828i
$211$	12.9316	+	22.3983i	0.890251	+	1.54196i	0.839574	+	0.543245i	$0.182804\pi$
$211$	12.9316	+	22.3983i	0.890251	+	1.54196i	0.0506765	+	0.998715i	$0.483862\pi$
$212$	−0.748715	+	1.29681i	−0.0514220	+	0.0890655i
$213$	−7.95780			−0.545259
$214$	−5.24956	−	9.09250i	−0.358852	−	0.621550i
$215$	28.4855			1.94269
$216$	−8.90522			−0.605923
$217$	0.0995304	+	3.09453i	0.00675656	+	0.210070i
$218$	14.1825			0.960560
$219$	−23.5029			−1.58818
$220$	−2.76265	−	4.78504i	−0.186258	−	0.322608i
$221$	−6.51722			−0.438396
$222$	−15.0895	+	26.1358i	−1.01274	+	1.75412i
$223$	−6.75524	−	11.7004i	−0.452365	−	0.783519i	0.546168	−	0.837676i	$-0.316086\pi$
$223$	−6.75524	−	11.7004i	−0.452365	−	0.783519i	−0.998532	+	0.0541573i	$0.982753\pi$
$224$	0.529184	+	0.916574i	0.0353576	+	0.0612411i
$225$	10.6393			0.709287
$226$	0.429901	−	0.744610i	0.0285966	−	0.0495307i
$227$	−2.75995	+	4.78038i	−0.183184	+	0.317285i	−0.942963	−	0.332897i	$-0.891974\pi$
$227$	−2.75995	+	4.78038i	−0.183184	+	0.317285i	0.759779	+	0.650182i	$0.225307\pi$
$228$	0.973860	−	1.68677i	0.0644954	−	0.111709i
$229$	1.56376	+	2.70850i	0.103336	+	0.178983i	0.913057	−	0.407832i	$-0.133715\pi$
$229$	1.56376	+	2.70850i	0.103336	+	0.178983i	−0.809721	+	0.586815i	$0.800382\pi$
$230$	17.4989	−	30.3089i	1.15384	−	1.99851i
$231$	2.85788	+	4.94999i	0.188035	+	0.325686i
$232$	−11.7883			−0.773937
$233$	1.16805			0.0765212			0.0382606	−	0.999268i	$-0.487818\pi$
$233$	1.16805			0.0765212			0.0382606	+	0.999268i	$0.487818\pi$
$234$	−1.04792	−	1.81505i	−0.0685047	−	0.118654i
$235$	−8.06307	+	13.9656i	−0.525976	+	0.911018i
$236$	1.13393	+	1.96403i	0.0738127	+	0.127847i
$237$	2.16102	−	3.74300i	0.140373	−	0.243134i
$238$	−2.33440	+	4.04330i	−0.151317	+	0.262088i
$239$	8.67505	−	15.0256i	0.561143	−	0.971927i	−0.436255	−	0.899823i	$-0.643695\pi$
$239$	8.67505	−	15.0256i	0.561143	−	0.971927i	0.997397	−	0.0721041i	$-0.0229714\pi$
$240$	23.4072			1.51093
$241$	4.95865	+	8.58864i	0.319415	+	0.553243i	0.980366	−	0.197186i	$-0.0631803\pi$
$241$	4.95865	+	8.58864i	0.319415	+	0.553243i	−0.660951	+	0.750429i	$0.729847\pi$
$242$	−7.62268	−	13.2029i	−0.490005	−	0.848713i
$243$	−7.65174	+	13.2532i	−0.490859	+	0.850193i
$244$	2.72717			0.174589
$245$	11.3643	+	19.6836i	0.726040	+	1.25754i
$246$	33.3014			2.12322
$247$	−2.66021			−0.169265
$248$	−14.8002	−	7.92179i	−0.939815	−	0.503034i
$249$	19.9002			1.26113
$250$	6.73817			0.426159
$251$	−7.13022	−	12.3499i	−0.450055	−	0.779519i	0.548334	−	0.836260i	$-0.315262\pi$
$251$	−7.13022	−	12.3499i	−0.450055	−	0.779519i	−0.998389	+	0.0567411i	$0.981929\pi$
$252$	0.307935			0.0193981
$253$	−19.1073	+	33.0949i	−1.20127	+	2.08066i
$254$	−12.8235	−	22.2110i	−0.804620	−	1.39364i
$255$	−23.8108	−	41.2415i	−1.49109	−	2.58264i
$256$	−7.91912			−0.494945
$257$	−8.39783	+	14.5455i	−0.523842	+	0.907322i	0.475772	+	0.879568i	$0.342169\pi$
$257$	−8.39783	+	14.5455i	−0.523842	+	0.907322i	−0.999615	+	0.0277531i	$0.991165\pi$
$258$	11.6183	−	20.1235i	0.723325	−	1.25284i
$259$	−3.02807	+	5.24477i	−0.188155	+	0.325894i
$260$	0.578141	+	1.00137i	0.0358548	+	0.0621023i
$261$	−3.18041	+	5.50863i	−0.196862	+	0.340976i
$262$	−5.30828	−	9.19420i	−0.327946	−	0.568020i
$263$	−7.89727			−0.486966			−0.243483	−	0.969905i	$-0.578290\pi$
$263$	−7.89727			−0.486966			−0.243483	+	0.969905i	$0.578290\pi$
$264$	−30.9903			−1.90732
$265$	7.47219	+	12.9422i	0.459013	+	0.795034i
$266$	−0.952859	+	1.65040i	−0.0584236	+	0.101193i
$267$	−5.43491	−	9.41354i	−0.332611	−	0.576100i
$268$	0.699011	−	1.21072i	0.0426989	−	0.0739566i
$269$	0.139069	−	0.240875i	0.00847919	−	0.0146864i	−0.861755	−	0.507325i	$-0.830634\pi$
$269$	0.139069	−	0.240875i	0.00847919	−	0.0146864i	0.870234	+	0.492639i	$0.163968\pi$
$270$	−6.46287	+	11.1940i	−0.393318	+	0.681246i
$271$	14.7643			0.896865			0.448432	−	0.893817i	$-0.351983\pi$
$271$	14.7643			0.896865			0.448432	+	0.893817i	$0.351983\pi$
$272$	−10.4386	−	18.0801i	−0.632931	−	1.09627i
$273$	−0.598070	−	1.03589i	−0.0361969	−	0.0626948i
$274$	−0.524463	+	0.908397i	−0.0316840	+	0.0548783i
$275$	−31.2500			−1.88445
$276$	2.92765	+	5.07083i	0.176224	+	0.305228i
$277$	−27.7571			−1.66776			−0.833882	−	0.551943i	$-0.813887\pi$
$277$	−27.7571			−1.66776			−0.833882	+	0.551943i	$0.813887\pi$
$278$	5.48348			0.328877
$279$	−7.69486	+	4.77886i	−0.460679	+	0.286103i
$280$	5.69543			0.340367
$281$	5.14865			0.307143			0.153571	−	0.988138i	$-0.450923\pi$
$281$	5.14865			0.307143			0.153571	+	0.988138i	$0.450923\pi$
$282$	6.57735	+	11.3923i	0.391675	+	0.678401i
$283$	11.9313			0.709244			0.354622	−	0.935010i	$-0.384610\pi$
$283$	11.9313			0.709244			0.354622	+	0.935010i	$0.384610\pi$
$284$	0.629630	−	1.09055i	0.0373616	−	0.0647123i
$285$	−9.71914	−	16.8340i	−0.575712	−	0.997162i
$286$	3.07798	+	5.33122i	0.182005	+	0.315241i
$287$	6.68272			0.394469
$288$	−1.54818	+	2.68153i	−0.0912276	+	0.158011i
$289$	−12.7371	+	22.0613i	−0.749241	+	1.29772i
$290$	−8.55521	+	14.8181i	−0.502379	+	0.870146i
$291$	−3.43435	−	5.94847i	−0.201325	−	0.348705i
$292$	1.85958	−	3.22088i	0.108823	−	0.188488i
$293$	−3.13875	−	5.43647i	−0.183367	−	0.317602i	0.759658	−	0.650323i	$-0.225366\pi$
$293$	−3.13875	−	5.43647i	−0.183367	−	0.317602i	−0.943025	+	0.332721i	$0.892033\pi$
$294$	18.5406			1.08131
$295$	22.6333			1.31776
$296$	−16.4179	−	28.4367i	−0.954273	−	1.65285i
$297$	7.05692	−	12.2229i	0.409484	−	0.709247i
$298$	−9.29917	−	16.1066i	−0.538686	−	0.933032i
$299$	3.99860	−	6.92579i	0.231245	−	0.400528i
$300$	−2.39408	+	4.14667i	−0.138222	+	0.239408i
$301$	2.33149	−	4.03826i	0.134385	−	0.232762i
$302$	30.8154			1.77323
$303$	−0.607593	−	1.05238i	−0.0349053	−	0.0604577i
$304$	−4.26083	−	7.37998i	−0.244375	−	0.423271i
$305$	13.6086	−	23.5708i	0.779226	−	1.34966i
$306$	−13.6591			−0.780837
$307$	11.7575	+	20.3647i	0.671038	+	1.16227i	0.977610	+	0.210425i	$0.0674848\pi$
$307$	11.7575	+	20.3647i	0.671038	+	1.16227i	−0.306572	+	0.951848i	$0.599182\pi$
$308$	−0.904474			−0.0515372
$309$	−21.6879			−1.23378
$310$	−20.6989	+	12.8550i	−1.17562	+	0.730115i
$311$	5.95141			0.337473			0.168737	−	0.985661i	$-0.446031\pi$
$311$	5.95141			0.337473			0.168737	+	0.985661i	$0.446031\pi$
$312$	6.48537			0.367162
$313$	12.5991	+	21.8223i	0.712145	+	1.23347i	0.964051	+	0.265719i	$0.0856093\pi$
$313$	12.5991	+	21.8223i	0.712145	+	1.23347i	−0.251906	+	0.967752i	$0.581057\pi$
$314$	−11.1763			−0.630713
$315$	1.53660	−	2.66147i	0.0865775	−	0.149957i
$316$	0.341965	+	0.592300i	0.0192370	+	0.0333195i
$317$	2.57366	+	4.45770i	0.144551	+	0.250369i	0.929205	−	0.369564i	$-0.120493\pi$
$317$	2.57366	+	4.45770i	0.144551	+	0.250369i	−0.784654	+	0.619933i	$0.787160\pi$
$318$	12.1907			0.683620
$319$	9.34158	−	16.1801i	0.523028	−	0.905912i
$320$	−15.0465	+	26.0613i	−0.841124	+	1.45687i
$321$	8.76521	−	15.1818i	0.489226	−	0.847365i
$322$	−2.86451	−	4.96148i	−0.159633	−	0.276493i
$323$	−8.66860	+	15.0145i	−0.482334	+	0.835426i
$324$	−1.91191	−	3.31152i	−0.106217	−	0.183973i
$325$	6.53971			0.362758
$326$	−18.9312			−1.04850
$327$	11.8403	+	20.5080i	0.654770	+	1.13409i
$328$	−18.1166	+	31.3788i	−1.00032	+	1.73260i
$329$	1.31990	+	2.28613i	0.0727685	+	0.126039i
$330$	−22.4909	+	38.9554i	−1.23808	+	2.14442i
$331$	7.84954	−	13.5958i	0.431449	−	0.747292i	−0.565549	−	0.824715i	$-0.691336\pi$
$331$	7.84954	−	13.5958i	0.431449	−	0.747292i	0.996998	+	0.0774223i	$0.0246690\pi$
$332$	−1.57453	+	2.72716i	−0.0864135	+	0.149673i
$333$	−17.7179			−0.970934
$334$	12.4844	+	21.6235i	0.683114	+	1.18319i
$335$	−6.97614	−	12.0830i	−0.381147	−	0.660166i
$336$	1.91585	−	3.31834i	0.104518	−	0.181030i
$337$	−7.20525			−0.392495			−0.196247	−	0.980554i	$-0.562876\pi$
$337$	−7.20525			−0.392495			−0.196247	+	0.980554i	$0.562876\pi$
$338$	−0.644131	−	1.11567i	−0.0350361	−	0.0606843i
$339$	1.43562			0.0779719
$340$	7.53575			0.408683
$341$	22.6015	−	14.0366i	1.22394	−	0.760125i
$342$	−5.57538			−0.301482
$343$	7.61319			0.411073
$344$	12.6411	+	21.8951i	0.681565	+	1.18050i
$345$	58.4359			3.14608
$346$	−0.856467	+	1.48344i	−0.0460439	+	0.0797505i
$347$	−9.57121	−	16.5778i	−0.513810	−	0.889944i	−0.999872	−	0.0160200i	$-0.994900\pi$
$347$	−9.57121	−	16.5778i	−0.513810	−	0.889944i	0.486062	−	0.873924i	$-0.338433\pi$
$348$	−1.43133	−	2.47913i	−0.0767272	−	0.132895i
$349$	−13.3373			−0.713927			−0.356963	−	0.934118i	$-0.616188\pi$
$349$	−13.3373			−0.713927			−0.356963	+	0.934118i	$0.616188\pi$
$350$	2.34246	−	4.05725i	0.125210	−	0.216869i
$351$	−1.47681	+	2.55791i	−0.0788261	+	0.136531i
$352$	4.54737	−	7.87627i	0.242375	−	0.419806i
$353$	−14.7712	−	25.5845i	−0.786191	−	1.36172i	−0.928285	−	0.371870i	$-0.878717\pi$
$353$	−14.7712	−	25.5845i	−0.786191	−	1.36172i	0.142094	−	0.989853i	$-0.454617\pi$
$354$	9.23142	−	15.9893i	0.490645	−	0.849822i
$355$	−6.28371	−	10.8837i	−0.333505	−	0.577647i
$356$	1.72006			0.0911633
$357$	−7.79552			−0.412583
$358$	−11.5812	−	20.0593i	−0.612088	−	1.06017i
$359$	4.08018	−	7.06708i	0.215344	−	0.372986i	−0.738035	−	0.674762i	$-0.764246\pi$
$359$	4.08018	−	7.06708i	0.215344	−	0.372986i	0.953379	+	0.301776i	$0.0975795\pi$
$360$	8.33130	+	14.4302i	0.439098	+	0.760540i
$361$	5.96164	−	10.3259i	0.313770	−	0.543466i
$362$	3.34326	−	5.79069i	0.175718	−	0.304352i
$363$	12.7276	−	22.0449i	0.668028	−	1.15706i
$364$	0.189280			0.00992097
$365$	−18.5586	−	32.1444i	−0.971402	−	1.68252i
$366$	−11.1010	−	19.2276i	−0.580261	−	1.00504i
$367$	−2.38972	+	4.13911i	−0.124742	+	0.216060i	−0.921632	−	0.388065i	$-0.873144\pi$
$367$	−2.38972	+	4.13911i	−0.124742	+	0.216060i	0.796890	+	0.604125i	$0.206477\pi$
$368$	25.6181			1.33543
$369$	9.77551	+	16.9317i	0.508893	+	0.881428i
$370$	−47.6606			−2.47776
$371$	2.44635			0.127008
$372$	−0.131047	−	4.07443i	−0.00679447	−	0.211249i
$373$	−2.23562			−0.115756			−0.0578781	−	0.998324i	$-0.518433\pi$
$373$	−2.23562			−0.115756			−0.0578781	+	0.998324i	$0.518433\pi$
$374$	40.1198			2.07454
$375$	5.62538	+	9.74344i	0.290493	+	0.503149i
$376$	−14.3128			−0.738124
$377$	−1.95492	+	3.38602i	−0.100683	+	0.174389i
$378$	1.05795	+	1.83243i	0.0544152	+	0.0942499i
$379$	−1.86488	−	3.23007i	−0.0957925	−	0.165917i	0.814147	−	0.580659i	$-0.197205\pi$
$379$	−1.86488	−	3.23007i	−0.0957925	−	0.165917i	−0.909939	+	0.414742i	$0.863872\pi$
$380$	3.07596			0.157793
$381$	21.4115	−	37.0858i	1.09695	−	1.89997i
$382$	3.67114	−	6.35860i	0.187832	−	0.325334i
$383$	−10.1268	+	17.5401i	−0.517454	+	0.896257i	0.482340	+	0.875984i	$0.339787\pi$
$383$	−10.1268	+	17.5401i	−0.517454	+	0.896257i	−0.999794	+	0.0202728i	$0.993547\pi$
$384$	8.18004	+	14.1682i	0.417436	+	0.723020i
$385$	−4.51334	+	7.81733i	−0.230021	+	0.398408i
$386$	8.34765	+	14.4586i	0.424884	+	0.735921i
$387$	13.6421			0.693465
$388$	1.08692			0.0551799
$389$	−6.68884	−	11.5854i	−0.339137	−	0.587403i	0.645133	−	0.764070i	$-0.276802\pi$
$389$	−6.68884	−	11.5854i	−0.339137	−	0.587403i	−0.984271	+	0.176667i	$0.943468\pi$
$390$	4.70669	−	8.15223i	0.238332	−	0.412804i
$391$	−26.0598	−	45.1369i	−1.31790	−	2.28267i
$392$	−10.0864	+	17.4702i	−0.509441	+	0.882378i
$393$	8.86326	−	15.3516i	0.447092	−	0.774386i
$394$	1.95216	−	3.38125i	0.0983486	−	0.170345i
$395$	6.82563			0.343435
$396$	−1.32307	−	2.29162i	−0.0664867	−	0.115158i
$397$	4.46105	+	7.72677i	0.223894	+	0.387795i	0.955987	−	0.293409i	$-0.0947898\pi$
$397$	4.46105	+	7.72677i	0.223894	+	0.387795i	−0.732093	+	0.681205i	$0.761456\pi$
$398$	7.20640	−	12.4818i	0.361224	−	0.625659i
$399$	−3.18199			−0.159299
$400$	10.4746	+	18.1425i	0.523729	+	0.907126i
$401$	−5.56728			−0.278017			−0.139008	−	0.990291i	$-0.544391\pi$
$401$	−5.56728			−0.278017			−0.139008	+	0.990291i	$0.544391\pi$
$402$	−11.3814			−0.567653
$403$	−4.72984	+	2.93745i	−0.235610	+	0.146325i
$404$	0.192294			0.00956697
$405$	−38.1617			−1.89627
$406$	1.40046	+	2.42567i	0.0695038	+	0.120384i
$407$	52.0414			2.57960
$408$	21.1333	−	36.6040i	1.04625	−	1.81217i
$409$	10.6233	+	18.4000i	0.525287	+	0.909824i	0.999566	+	0.0294492i	$0.00937534\pi$
$409$	10.6233	+	18.4000i	0.525287	+	0.909824i	−0.474279	+	0.880374i	$0.657291\pi$
$410$	26.2958	+	45.5457i	1.29866	+	2.24934i
$411$	−1.75140			−0.0863901
$412$	1.71597	−	2.97215i	0.0845399	−	0.146427i
$413$	1.85250	−	3.20863i	0.0911558	−	0.157886i
$414$	8.38044	−	14.5153i	0.411876	−	0.713390i
$415$	15.7138	+	27.2172i	0.771362	+	1.33604i
$416$	−0.951630	+	1.64827i	−0.0466575	+	0.0808132i
$417$	4.57790	+	7.92916i	0.224181	+	0.388292i
$418$	16.3762			0.800984
$419$	9.77903			0.477737			0.238869	−	0.971052i	$-0.423224\pi$
$419$	9.77903			0.477737			0.238869	+	0.971052i	$0.423224\pi$
$420$	0.691538	+	1.19778i	0.0337436	+	0.0584456i
$421$	−9.29415	+	16.0979i	−0.452969	+	0.784565i	−0.998569	−	0.0534804i	$-0.982969\pi$
$421$	−9.29415	+	16.0979i	−0.452969	+	0.784565i	0.545600	+	0.838046i	$0.316302\pi$
$422$	16.6593	+	28.8548i	0.810964	+	1.40463i
$423$	−3.86151	+	6.68833i	−0.187753	+	0.325198i
$424$	−6.63195	+	11.4869i	−0.322076	+	0.557852i
$425$	21.3104	−	36.9107i	1.03371	−	1.79043i
$426$	−10.2517			−0.496698
$427$	−2.22769	−	3.85847i	−0.107805	−	0.186724i
$428$	1.38703	+	2.40240i	0.0670445	+	0.116124i
$429$	−5.13932	+	8.90156i	−0.248129	+	0.429771i
$430$	36.6967			1.76967
$431$	−1.49908	−	2.59648i	−0.0722081	−	0.125068i	0.827661	−	0.561229i	$-0.189671\pi$
$431$	−1.49908	−	2.59648i	−0.0722081	−	0.125068i	−0.899869	+	0.436161i	$0.856338\pi$
$432$	−9.46154			−0.455219
$433$	25.0436			1.20352			0.601759	−	0.798677i	$-0.294467\pi$
$433$	25.0436			1.20352			0.601759	+	0.798677i	$0.294467\pi$
$434$	0.128221	+	3.98657i	0.00615481	+	0.191361i
$435$	−28.5693			−1.36980
$436$	−3.74727			−0.179462
$437$	−10.6371	−	18.4241i	−0.508843	−	0.881342i
$438$	−30.2779			−1.44673
$439$	3.15891	−	5.47140i	0.150767	−	0.261136i	−0.780743	−	0.624853i	$-0.785159\pi$
$439$	3.15891	−	5.47140i	0.150767	−	0.261136i	0.931510	+	0.363717i	$0.118492\pi$
$440$	−24.4709	−	42.3848i	−1.16660	−	2.02062i
$441$	5.44253	+	9.42673i	0.259168	+	0.448892i
$442$	−8.39589			−0.399352
$443$	−0.761832	+	1.31953i	−0.0361957	+	0.0626928i	−0.883556	−	0.468326i	$-0.844857\pi$
$443$	−0.761832	+	1.31953i	−0.0361957	+	0.0626928i	0.847360	+	0.531019i	$0.178191\pi$
$444$	3.98692	−	6.90555i	0.189211	−	0.327723i
$445$	8.58314	−	14.8664i	0.406880	−	0.704737i
$446$	−8.70252	−	15.0732i	−0.412076	−	0.713737i
$447$	15.5269	−	26.8933i	0.734396	−	1.27201i
$448$	2.46307	+	4.26616i	0.116369	+	0.201557i
$449$	25.8776			1.22124			0.610621	−	0.791923i	$-0.290920\pi$
$449$	25.8776			1.22124			0.610621	+	0.791923i	$0.290920\pi$
$450$	13.7062			0.646117
$451$	−28.7129	−	49.7322i	−1.35204	−	2.34180i
$452$	−0.113587	+	0.196739i	−0.00534271	+	0.00925384i
$453$	25.7263	+	44.5593i	1.20873	+	2.09358i
$454$	−3.55554	+	6.15838i	−0.166870	+	0.289027i
$455$	0.944509	−	1.63594i	0.0442793	−	0.0766939i
$456$	8.62623	−	14.9411i	0.403960	−	0.699680i
$457$	3.70424			0.173277			0.0866386	−	0.996240i	$-0.472387\pi$
$457$	3.70424			0.173277			0.0866386	+	0.996240i	$0.472387\pi$
$458$	2.01453	+	3.48926i	0.0941327	+	0.163043i
$459$	9.62468	+	16.6704i	0.449242	+	0.778109i
$460$	−4.62351	+	8.00816i	−0.215572	+	0.373382i
$461$	−4.70201			−0.218994			−0.109497	−	0.993987i	$-0.534924\pi$
$461$	−4.70201			−0.218994			−0.109497	+	0.993987i	$0.534924\pi$
$462$	3.68170	+	6.37689i	0.171288	+	0.296680i
$463$	−2.93054			−0.136194			−0.0680968	−	0.997679i	$-0.521693\pi$
$463$	−2.93054			−0.136194			−0.0680968	+	0.997679i	$0.521693\pi$
$464$	−12.5247			−0.581444
$465$	−35.8690	−	19.1988i	−1.66338	−	0.890323i
$466$	1.50475			0.0697061
$467$	−10.4504			−0.483586			−0.241793	−	0.970328i	$-0.577735\pi$
$467$	−10.4504			−0.483586			−0.241793	+	0.970328i	$0.577735\pi$
$468$	0.276879	+	0.479569i	0.0127988	+	0.0221681i
$469$	−2.28395			−0.105463
$470$	−10.3873	+	17.9914i	−0.479132	+	0.829881i
$471$	−9.33053	−	16.1610i	−0.429928	−	0.744658i
$472$	10.0441	+	17.3969i	0.462318	+	0.800758i
$473$	−40.0698			−1.84241
$474$	2.78396	−	4.82196i	0.127872	−	0.221480i
$475$	8.69851	−	15.0663i	0.399115	−	0.691288i
$476$	0.616790	−	1.06831i	0.0282705	−	0.0489660i
$477$	3.57853	+	6.19820i	0.163850	+	0.283796i
$478$	11.1757	−	19.3569i	0.511166	−	0.885366i
$479$	−1.32556	−	2.29594i	−0.0605665	−	0.104904i	0.834152	−	0.551534i	$-0.185957\pi$
$479$	−1.32556	−	2.29594i	−0.0605665	−	0.104904i	−0.894719	+	0.446630i	$0.852624\pi$
$480$	−13.9072			−0.634774
$481$	−10.8907			−0.496575
$482$	6.38804	+	11.0644i	0.290967	+	0.503970i
$483$	4.78289	−	8.28422i	0.217629	−	0.376945i
$484$	2.01405	+	3.48844i	0.0915477	+	0.158565i
$485$	5.42373	−	9.39418i	0.246279	−	0.426568i
$486$	−9.85744	+	17.0736i	−0.447143	+	0.774474i
$487$	18.0760	−	31.3085i	0.819101	−	1.41872i	−0.0872448	−	0.996187i	$-0.527806\pi$
$487$	18.0760	−	31.3085i	0.819101	−	1.41872i	0.906346	−	0.422537i	$-0.138860\pi$
$488$	24.1566			1.09352
$489$	−15.8047	−	27.3746i	−0.714715	−	1.23792i
$490$	14.6402	+	25.3576i	0.661378	+	1.14554i
$491$	−5.35437	+	9.27404i	−0.241639	+	0.418532i	−0.961181	−	0.275917i	$-0.911018\pi$
$491$	−5.35437	+	9.27404i	−0.241639	+	0.418532i	0.719542	+	0.694449i	$0.244352\pi$
$492$	−8.79883			−0.396682
$493$	12.7406	+	22.0674i	0.573810	+	0.993868i
$494$	−3.42705			−0.154190
$495$	−26.4085			−1.18697
$496$	−15.7248	−	8.41667i	−0.706065	−	0.377920i
$497$	−2.05725			−0.0922803
$498$	25.6367			1.14881
$499$	4.74370	+	8.21632i	0.212357	+	0.367813i	0.952452	−	0.304689i	$-0.0985527\pi$
$499$	4.74370	+	8.21632i	0.212357	+	0.367813i	−0.740095	+	0.672503i	$0.765219\pi$
$500$	−1.78034			−0.0796194
$501$	−20.8452	+	36.1049i	−0.931295	+	1.61305i
$502$	−9.18558	−	15.9099i	−0.409973	−	0.710094i
$503$	−10.0778	−	17.4552i	−0.449346	−	0.778290i	0.548997	−	0.835824i	$-0.315010\pi$
$503$	−10.0778	−	17.4552i	−0.449346	−	0.778290i	−0.998344	+	0.0575337i	$0.981676\pi$
$504$	2.72762			0.121498
$505$	0.959547	−	1.66198i	0.0426993	−	0.0739573i
$506$	−24.6152	+	42.6348i	−1.09428	+	1.89535i
$507$	1.07551	−	1.86284i	0.0477650	−	0.0827314i
$508$	3.38821	+	5.86855i	0.150327	+	0.260375i
$509$	−19.5271	+	33.8218i	−0.865521	+	1.49913i	0.00100720	+	0.999999i	$0.499679\pi$
$509$	−19.5271	+	33.8218i	−0.865521	+	1.49913i	−0.866529	+	0.499127i	$0.833654\pi$
$510$	−30.6745	−	53.1299i	−1.35829	−	2.35263i
$511$	−6.07598			−0.268785
$512$	−25.4134			−1.12312
$513$	3.92862	+	6.80457i	0.173453	+	0.300429i
$514$	−10.8186	+	18.7384i	−0.477188	+	0.826514i
$515$	−17.1254	−	29.6621i	−0.754637	−	1.30707i
$516$	−3.06977	+	5.31700i	−0.135139	+	0.234068i
$517$	11.3421	−	19.6451i	0.498826	−	0.863992i
$518$	−3.90095	+	6.75664i	−0.171398	+	0.296870i
$519$	−2.86009			−0.125544
$520$	5.12104	+	8.86990i	0.224573	+	0.388971i
$521$	−9.22697	−	15.9816i	−0.404241	−	0.700166i	0.589992	−	0.807409i	$-0.299131\pi$
$521$	−9.22697	−	15.9816i	−0.404241	−	0.700166i	−0.994233	+	0.107243i	$0.965798\pi$
$522$	−4.09720	+	7.09656i	−0.179330	+	0.310608i
$523$	−8.69059			−0.380013			−0.190006	−	0.981783i	$-0.560851\pi$
$523$	−8.69059			−0.380013			−0.190006	+	0.981783i	$0.560851\pi$
$524$	1.40254	+	2.42927i	0.0612703	+	0.106123i
$525$	7.82242			0.341398
$526$	−10.1737			−0.443597
$527$	1.16649	+	36.2676i	0.0508130	+	1.57984i
$528$	−32.9263			−1.43294
$529$	40.9553			1.78067
$530$	9.62614	+	16.6730i	0.418133	+	0.724227i
$531$	10.8394			0.470390
$532$	0.251762	−	0.436065i	0.0109153	−	0.0189058i
$533$	6.00876	+	10.4075i	0.260268	+	0.450798i
$534$	−7.00159	−	12.1271i	−0.302988	−	0.524791i
$535$	27.6851			1.19693
$536$	6.19168	−	10.7243i	0.267440	−	0.463219i
$537$	19.3373	−	33.4931i	0.834464	−	1.44533i
$538$	0.179157	−	0.310310i	0.00772402	−	0.0133784i
$539$	−15.9859	−	27.6884i	−0.688563	−	1.19263i
$540$	1.70761	−	2.95766i	0.0734836	−	0.127277i
$541$	7.83771	+	13.5753i	0.336969	+	0.583648i	0.983861	−	0.178934i	$-0.0572648\pi$
$541$	7.83771	+	13.5753i	0.336969	+	0.583648i	−0.646892	+	0.762582i	$0.723931\pi$
$542$	19.0202			0.816989
$543$	11.1645			0.479115
$544$	6.20199	+	10.7422i	0.265908	+	0.460566i
$545$	−18.6989	+	32.3875i	−0.800973	+	1.38733i
$546$	−0.770471	−	1.33450i	−0.0329731	−	0.0571111i
$547$	−3.74731	+	6.49053i	−0.160223	+	0.277515i	−0.934949	−	0.354783i	$-0.884555\pi$
$547$	−3.74731	+	6.49053i	−0.160223	+	0.277515i	0.774725	+	0.632298i	$0.217888\pi$
$548$	0.138573	−	0.240015i	0.00591952	−	0.0102529i
$549$	6.51733	−	11.2884i	0.278153	−	0.481775i
$550$	−40.2582			−1.71662
$551$	5.20050	+	9.00753i	0.221549	+	0.383734i
$552$	25.9324	+	44.9163i	1.10376	+	1.91176i
$553$	0.558668	−	0.967641i	0.0237570	−	0.0411483i
$554$	−35.7584			−1.51923
$555$	−39.7896	−	68.9175i	−1.68897	−	2.92539i
$556$	−1.44883			−0.0614442
$557$	5.52145			0.233951			0.116976	−	0.993135i	$-0.462680\pi$
$557$	5.52145			0.233951			0.116976	+	0.993135i	$0.462680\pi$
$558$	−9.91300	+	6.15643i	−0.419651	+	0.260622i
$559$	8.38543			0.354666
$560$	6.05124			0.255711
$561$	33.4941	+	58.0135i	1.41412	+	2.44933i
$562$	6.63281			0.279788
$563$	1.13056	−	1.95818i	0.0476472	−	0.0825274i	−0.841218	−	0.540696i	$-0.818161\pi$
$563$	1.13056	−	1.95818i	0.0476472	−	0.0825274i	0.888865	+	0.458168i	$0.151494\pi$
$564$	−1.73785	−	3.01005i	−0.0731768	−	0.126746i
$565$	1.13361	+	1.96346i	0.0476911	+	0.0826035i
$566$	15.3707			0.646078
$567$	−3.12348	+	5.41003i	−0.131174	+	0.227200i
$568$	5.57712	−	9.65985i	0.234011	−	0.405318i
$569$	−11.6134	+	20.1149i	−0.486858	+	0.843262i	−0.999886	−	0.0151096i	$-0.995190\pi$
$569$	−11.6134	+	20.1149i	−0.486858	+	0.843262i	0.513028	+	0.858372i	$0.328524\pi$
$570$	−12.5208	−	21.6866i	−0.524438	−	0.908354i
$571$	−3.97157	+	6.87896i	−0.166205	+	0.287876i	−0.937083	−	0.349108i	$-0.886485\pi$
$571$	−3.97157	+	6.87896i	−0.166205	+	0.287876i	0.770877	+	0.636983i	$0.219818\pi$
$572$	−0.813257	−	1.40860i	−0.0340040	−	0.0588966i
$573$	12.2594			0.512146
$574$	8.60910			0.359337
$575$	26.1497	+	45.2927i	1.09052	+	1.88883i
$576$	−7.20596	+	12.4811i	−0.300248	+	0.520046i
$577$	−5.34226	−	9.25307i	−0.222401	−	0.385211i	0.733135	−	0.680083i	$-0.238056\pi$
$577$	−5.34226	−	9.25307i	−0.222401	−	0.385211i	−0.955537	+	0.294872i	$0.904723\pi$
$578$	−16.4087	+	28.4207i	−0.682513	+	1.18215i
$579$	−13.9381	+	24.1415i	−0.579248	+	1.00329i
$580$	2.26044	−	3.91519i	0.0938596	−	0.162570i
$581$	5.14462			0.213435
$582$	−4.42434	−	7.66319i	−0.183395	−	0.317649i
$583$	−10.5110	−	18.2055i	−0.435319	−	0.753995i
$584$	16.4717	−	28.5298i	0.681604	−	1.18057i
$585$	5.52652			0.228494
$586$	−4.04353	−	7.00359i	−0.167037	−	0.289316i
$587$	22.4935			0.928405			0.464202	−	0.885729i	$-0.346341\pi$
$587$	22.4935			0.928405			0.464202	+	0.885729i	$0.346341\pi$
$588$	−4.89876			−0.202022
$589$	0.476139	+	14.8038i	0.0196190	+	0.609979i
$590$	29.1576			1.20040
$591$	6.51907			0.268159
$592$	−17.4436	−	30.2132i	−0.716927	−	1.24175i
$593$	0.141633			0.00581615			0.00290808	−	0.999996i	$-0.499074\pi$
$593$	0.141633			0.00581615			0.00290808	+	0.999996i	$0.499074\pi$
$594$	9.09116	−	15.7464i	0.373015	−	0.646081i
$595$	−6.15557	−	10.6618i	−0.252354	−	0.437090i
$596$	2.45701	+	4.25566i	0.100643	+	0.174319i
$597$	24.0651			0.984920
$598$	5.15125	−	8.92222i	0.210650	−	0.364857i
$599$	−4.99372	+	8.64938i	−0.204038	+	0.353404i	−0.949826	−	0.312779i	$-0.898740\pi$
$599$	−4.99372	+	8.64938i	−0.204038	+	0.353404i	0.745788	+	0.666183i	$0.232073\pi$
$600$	−21.2062	+	36.7303i	−0.865741	+	1.49951i
$601$	−10.0860	−	17.4695i	−0.411418	−	0.712597i	0.583627	−	0.812022i	$-0.301633\pi$
$601$	−10.0860	−	17.4695i	−0.411418	−	0.712597i	−0.995045	+	0.0994246i	$0.968300\pi$
$602$	3.00357	−	5.20234i	0.122416	−	0.212032i
$603$	−3.34097	−	5.78672i	−0.136055	−	0.235654i
$604$	−8.14198			−0.331293
$605$	40.2005			1.63438
$606$	−0.782738	−	1.35574i	−0.0317966	−	0.0550733i
$607$	−0.334064	+	0.578615i	−0.0135592	+	0.0234853i	−0.872725	−	0.488211i	$-0.837650\pi$
$607$	−0.334064	+	0.578615i	−0.0135592	+	0.0234853i	0.859166	+	0.511697i	$0.170983\pi$
$608$	2.53154	+	4.38475i	0.102667	+	0.177825i
$609$	−2.33836	+	4.05016i	−0.0947551	+	0.164121i
$610$	17.5314	−	30.3653i	0.709827	−	1.22946i
$611$	−2.37357	+	4.11115i	−0.0960245	+	0.166319i
$612$	3.60897			0.145884
$613$	−6.57392	−	11.3864i	−0.265518	−	0.459891i	0.702181	−	0.711998i	$-0.252210\pi$
$613$	−6.57392	−	11.3864i	−0.265518	−	0.459891i	−0.967699	+	0.252107i	$0.918876\pi$
$614$	15.1468	+	26.2350i	0.611275	+	1.05876i
$615$	−43.9063	+	76.0479i	−1.77047	+	3.06655i
$616$	−8.01163			−0.322798
$617$	−13.8967	−	24.0699i	−0.559462	−	0.969017i	−0.997541	−	0.0700803i	$-0.977674\pi$
$617$	−13.8967	−	24.0699i	−0.559462	−	0.969017i	0.438079	−	0.898936i	$-0.355659\pi$
$618$	−27.9397			−1.12390
$619$	−35.9015			−1.44300			−0.721501	−	0.692413i	$-0.756548\pi$
$619$	−35.9015			−1.44300			−0.721501	+	0.692413i	$0.756548\pi$
$620$	5.46903	−	3.39652i	0.219641	−	0.136407i
$621$	−23.6207			−0.947865
$622$	7.66697			0.307418
$623$	−1.40503	−	2.43359i	−0.0562915	−	0.0974998i
$624$	6.89052			0.275842
$625$	7.46536	−	12.9304i	0.298614	−	0.517215i
$626$	16.2310	+	28.1129i	0.648720	+	1.12362i
$627$	13.6717	+	23.6800i	0.545994	+	0.945690i
$628$	2.95297			0.117836
$629$	−35.4887	+	61.4683i	−1.41503	+	2.45090i
$630$	1.97954	−	3.42867i	0.0788668	−	0.136601i
$631$	2.24715	−	3.89218i	0.0894577	−	0.154945i	−0.817824	−	0.575468i	$-0.804820\pi$
$631$	2.24715	−	3.89218i	0.0894577	−	0.154945i	0.907282	+	0.420523i	$0.138153\pi$
$632$	3.02905	+	5.24646i	0.120489	+	0.208693i
$633$	−27.8162	+	48.1790i	−1.10559	+	1.91495i
$634$	3.31554	+	5.74269i	0.131677	+	0.228071i
$635$	67.6287			2.68376
$636$	−3.22100			−0.127721
$637$	3.34539	+	5.79438i	0.132549	+	0.229582i
$638$	12.0344	−	20.8442i	0.476447	−	0.825230i
$639$	−3.00935	−	5.21235i	−0.119048	−	0.206198i
$640$	−12.9184	+	22.3753i	−0.510645	+	0.884463i
$641$	−19.3448	+	33.5063i	−0.764076	+	1.32342i	0.176658	+	0.984272i	$0.443471\pi$
$641$	−19.3448	+	33.5063i	−0.764076	+	1.32342i	−0.940734	+	0.339145i	$0.889862\pi$
$642$	11.2919	−	19.5581i	0.445655	−	0.771898i
$643$	21.3222			0.840867			0.420433	−	0.907323i	$-0.361878\pi$
$643$	21.3222			0.840867			0.420433	+	0.907323i	$0.361878\pi$
$644$	0.756856	+	1.31091i	0.0298243	+	0.0516572i
$645$	30.6364	+	53.0637i	1.20631	+	2.08938i
$646$	−11.1674	+	19.3425i	−0.439376	+	0.761022i
$647$	−16.4679			−0.647422			−0.323711	−	0.946156i	$-0.604930\pi$
$647$	−16.4679			−0.647422			−0.323711	+	0.946156i	$0.604930\pi$
$648$	−16.9352	−	29.3327i	−0.665279	−	1.15230i
$649$	−31.8377			−1.24974
$650$	8.42486			0.330450
$651$	−5.65756	+	3.51360i	−0.221737	+	0.137709i
$652$	5.00195			0.195892
$653$	−33.6345			−1.31622			−0.658110	−	0.752922i	$-0.728644\pi$
$653$	−33.6345			−1.31622			−0.658110	+	0.752922i	$0.728644\pi$
$654$	15.2534	+	26.4197i	0.596455	+	1.03309i
$655$	27.9948			1.09385
$656$	−19.2483	+	33.3391i	−0.751521	+	1.30167i
$657$	−8.88796	−	15.3944i	−0.346752	−	0.600593i
$658$	1.70038	+	2.94514i	0.0662876	+	0.114814i
$659$	−8.87797			−0.345837			−0.172918	−	0.984936i	$-0.555320\pi$
$659$	−8.87797			−0.345837			−0.172918	+	0.984936i	$0.555320\pi$
$660$	5.94250	−	10.2927i	0.231312	−	0.400643i
$661$	−15.8836	+	27.5112i	−0.617801	+	1.07006i	0.372085	+	0.928199i	$0.378643\pi$
$661$	−15.8836	+	27.5112i	−0.617801	+	1.07006i	−0.989886	+	0.141864i	$0.954690\pi$
$662$	10.1123	−	17.5149i	0.393024	−	0.680738i
$663$	−7.00933	−	12.1405i	−0.272220	−	0.471499i
$664$	−13.9468	+	24.1566i	−0.541242	+	0.937458i
$665$	−2.51259	−	4.35194i	−0.0974342	−	0.168761i
$666$	−22.8253			−0.884462
$667$	−31.2678			−1.21069
$668$	−3.29859	−	5.71333i	−0.127626	−	0.221055i
$669$	14.5306	−	25.1678i	0.561787	−	0.973044i
$670$	−8.98709	−	15.5661i	−0.347202	−	0.601371i
$671$	−19.1429	+	33.1564i	−0.739002	+	1.27999i
$672$	−1.13828	+	1.97157i	−0.0439103	+	0.0760548i
$673$	−12.5128	+	21.6728i	−0.482334	+	0.835426i	−0.999794	−	0.0202805i	$-0.993544\pi$
$673$	−12.5128	+	21.6728i	−0.482334	+	0.835426i	0.517461	+	0.855707i	$0.326877\pi$
$674$	−9.28224			−0.357539
$675$	−9.65790	−	16.7280i	−0.371733	−	0.643860i
$676$	0.170191	+	0.294779i	0.00654580	+	0.0113377i
$677$	16.8637	−	29.2088i	0.648124	−	1.12258i	−0.335446	−	0.942059i	$-0.608887\pi$
$677$	16.8637	−	29.2088i	0.648124	−	1.12258i	0.983570	−	0.180524i	$-0.0577795\pi$
$678$	1.84945			0.0710277
$679$	−0.887849	−	1.53780i	−0.0340725	−	0.0590153i
$680$	66.7499			2.55974
$681$	−11.8734			−0.454990
$682$	29.1167	−	18.0828i	1.11494	−	0.692427i
$683$	11.2620			0.430927			0.215464	−	0.976512i	$-0.430874\pi$
$683$	11.2620			0.430927			0.215464	+	0.976512i	$0.430874\pi$
$684$	1.47312			0.0563260
$685$	−1.38296	−	2.39535i	−0.0528400	−	0.0915216i
$686$	9.80778			0.374463
$687$	−3.36367	+	5.82604i	−0.128332	+	0.222277i
$688$	13.4309	+	23.2629i	0.512047	+	0.886891i
$689$	2.19963	+	3.80988i	0.0837994	+	0.145145i
$690$	75.2807			2.86589
$691$	−0.00437220	+	0.00757288i	−0.000166326	+	0.000288086i	−0.866109	−	0.499856i	$-0.833386\pi$
$691$	−0.00437220	+	0.00757288i	−0.000166326	+	0.000288086i	0.865942	+	0.500144i	$0.166720\pi$
$692$	0.226294	−	0.391952i	0.00860240	−	0.0148998i
$693$	−2.16150	+	3.74382i	−0.0821084	+	0.142216i
$694$	−12.3302	−	21.3566i	−0.468049	−	0.810685i
$695$	−7.22969	+	12.5222i	−0.274238	+	0.474994i
$696$	−12.6784	−	21.9596i	−0.480573	−	0.832376i
$697$	78.3209			2.96662
$698$	−17.1819			−0.650343
$699$	1.25624	+	2.17588i	0.0475155	+	0.0822992i
$700$	−0.618918	+	1.07200i	−0.0233929	+	0.0405177i
$701$	12.3747	+	21.4336i	0.467386	+	0.809536i	0.999306	−	0.0372584i	$-0.0118625\pi$
$701$	12.3747	+	21.4336i	0.467386	+	0.809536i	−0.531920	+	0.846795i	$0.678529\pi$
$702$	−1.90251	+	3.29525i	−0.0718058	+	0.124371i
$703$	−14.4858	+	25.0902i	−0.546344	+	0.946296i
$704$	21.1655	−	36.6598i	0.797706	−	1.38167i
$705$	−34.6876			−1.30641
$706$	−19.0292	−	32.9595i	−0.716172	−	1.24045i
$707$	−0.157075	−	0.272062i	−0.00590741	−	0.0102319i
$708$	−2.43911	+	4.22466i	−0.0916673	+	0.158772i
$709$	−43.2844			−1.62558			−0.812790	−	0.582557i	$-0.802052\pi$
$709$	−43.2844			−1.62558			−0.812790	+	0.582557i	$0.802052\pi$
$710$	−8.09507	−	14.0211i	−0.303802	−	0.526201i
$711$	3.26888			0.122593
$712$	15.2359			0.570991
$713$	−39.2569	−	21.0122i	−1.47018	−	0.786912i
$714$	−10.0427			−0.375837
$715$	−16.2326			−0.607066
$716$	3.05997	+	5.30002i	0.114356	+	0.198071i
$717$	37.3204			1.39376
$718$	5.25634	−	9.10425i	0.196165	−	0.339768i
$719$	0.693219	+	1.20069i	0.0258527	+	0.0447782i	0.878662	−	0.477444i	$-0.158437\pi$
$719$	0.693219	+	1.20069i	0.0258527	+	0.0447782i	−0.852810	+	0.522222i	$0.825103\pi$
$720$	8.85177	+	15.3317i	0.329886	+	0.571379i
$721$	−5.60677			−0.208807
$722$	7.68015	−	13.3024i	0.285825	−	0.495064i
$723$	−10.6662	+	18.4743i	−0.396678	+	0.687067i
$724$	−0.883348	+	1.53000i	−0.0328294	+	0.0568621i
$725$	−12.7846	−	22.1436i	−0.474809	−	0.822393i
$726$	16.3965	−	28.3996i	0.608532	−	1.05401i
$727$	11.5948	+	20.0828i	0.430027	+	0.744829i	0.996875	−	0.0789932i	$-0.0251705\pi$
$727$	11.5948	+	20.0828i	0.430027	+	0.744829i	−0.566848	+	0.823823i	$0.691837\pi$
$728$	1.67660			0.0621389
$729$	0.783665			0.0290246
$730$	−23.9083	−	41.4105i	−0.884887	−	1.53267i
$731$	27.3249	−	47.3281i	1.01065	−	1.75049i
$732$	2.93309	+	5.08026i	0.108410	+	0.187772i
$733$	0.552407	−	0.956796i	0.0204036	−	0.0353401i	−0.855643	−	0.517566i	$-0.826838\pi$
$733$	0.552407	−	0.956796i	0.0204036	−	0.0353401i	0.876047	+	0.482226i	$0.160172\pi$
$734$	−3.07858	+	5.33226i	−0.113633	+	0.196817i
$735$	−24.4449	+	42.3398i	−0.901663	+	1.56173i
$736$	−15.2208			−0.561045
$737$	9.81317	+	16.9969i	0.361473	+	0.626089i
$738$	12.5934	+	21.8124i	0.463570	+	0.802927i
$739$	13.0859	−	22.6655i	0.481373	−	0.833763i	−0.518398	−	0.855139i	$-0.673472\pi$
$739$	13.0859	−	22.6655i	0.481373	−	0.833763i	0.999771	+	0.0213765i	$0.00680488\pi$
$740$	12.5928			0.462920
$741$	−2.86108	−	4.95554i	−0.105104	−	0.182046i
$742$	3.15154			0.115697
$743$	52.7509			1.93524			0.967621	−	0.252409i	$-0.0812228\pi$
$743$	52.7509			1.93524			0.967621	+	0.252409i	$0.0812228\pi$
$744$	−1.16079	−	36.0903i	−0.0425565	−	1.32314i
$745$	49.0419			1.79676
$746$	−2.88007			−0.105447
$747$	7.52556	+	13.0347i	0.275346	+	0.476913i
$748$	−10.6004			−0.387587
$749$	2.26599	−	3.92480i	0.0827973	−	0.143409i
$750$	7.24696	+	12.5521i	0.264621	+	0.458338i
$751$	1.62856	+	2.82074i	0.0594269	+	0.102930i	0.894208	−	0.447651i	$-0.147739\pi$
$751$	1.62856	+	2.82074i	0.0594269	+	0.102930i	−0.834781	+	0.550582i	$0.814406\pi$
$752$	−15.2069			−0.554539
$753$	15.3372	−	26.5648i	0.558919	−	0.968077i
$754$	−2.51845	+	4.36208i	−0.0917165	+	0.158858i
$755$	−40.6286	+	70.3707i	−1.47862	+	2.56105i
$756$	−0.279530	−	0.484160i	−0.0101664	−	0.0176087i
$757$	11.7390	−	20.3325i	0.426660	−	0.738997i	−0.569914	−	0.821705i	$-0.693023\pi$
$757$	11.7390	−	20.3325i	0.426660	−	0.738997i	0.996574	+	0.0827074i	$0.0263567\pi$
$758$	−2.40246	−	4.16117i	−0.0872611	−	0.151141i
$759$	−82.2004			−2.98369
$760$	27.2461			0.988320
$761$	−26.8997	−	46.5917i	−0.975114	−	1.68895i	−0.679558	−	0.733621i	$-0.737829\pi$
$761$	−26.8997	−	46.5917i	−0.975114	−	1.68895i	−0.295556	−	0.955326i	$-0.595505\pi$
$762$	27.5836	−	47.7763i	0.999250	−	1.73075i
$763$	3.06096	+	5.30173i	0.110814	+	0.191936i
$764$	−0.969981	+	1.68006i	−0.0350927	+	0.0607823i
$765$	18.0088	−	31.1921i	0.651109	−	1.12775i
$766$	−13.0459	+	22.5962i	−0.471369	+	0.816435i
$767$	6.66271			0.240576
$768$	−8.51708	−	14.7520i	−0.307334	−	0.532318i
$769$	21.5619	+	37.3463i	0.777542	+	1.34674i	0.933355	+	0.358955i	$0.116867\pi$
$769$	21.5619	+	37.3463i	0.777542	+	1.34674i	−0.155813	+	0.987787i	$0.549800\pi$
$770$	−5.81436	+	10.0708i	−0.209535	+	0.362925i
$771$	−36.1278			−1.30111
$772$	−2.20560	−	3.82021i	−0.0793812	−	0.137492i
$773$	−9.78376			−0.351897			−0.175949	−	0.984399i	$-0.556299\pi$
$773$	−9.78376			−0.351897			−0.175949	+	0.984399i	$0.556299\pi$
$774$	17.5745			0.631704
$775$	−1.17051	−	36.3928i	−0.0420460	−	1.30727i
$776$	9.62768			0.345613
$777$	−13.0269			−0.467336
$778$	−8.61697	−	14.9250i	−0.308933	−	0.535088i
$779$	31.9692			1.14541
$780$	−1.24359	+	2.15396i	−0.0445277	+	0.0771243i
$781$	8.83915	+	15.3099i	0.316290	+	0.547830i
$782$	−33.5718	−	58.1481i	−1.20053	−	2.07937i
$783$	11.5482			0.412697
$784$	−10.7165	+	18.5616i	−0.382733	+	0.662914i
$785$	14.7353	−	25.5224i	0.525927	−	0.910932i
$786$	11.4182	−	19.7769i	0.407273	−	0.705418i
$787$	−24.7449	−	42.8595i	−0.882062	−	1.52778i	−0.849044	−	0.528321i	$-0.822822\pi$
$787$	−24.7449	−	42.8595i	−0.882062	−	1.52778i	−0.0330175	−	0.999455i	$-0.510512\pi$
$788$	−0.515796	+	0.893385i	−0.0183745	+	0.0318255i
$789$	−8.49358	−	14.7113i	−0.302380	−	0.523737i
$790$	8.79319			0.312848
$791$	0.371136			0.0131961
$792$	−11.7194	−	20.2987i	−0.416432	−	0.721281i
$793$	4.00604	−	6.93867i	0.142259	−	0.246399i
$794$	5.74700	+	9.95410i	0.203954	+	0.353258i
$795$	−16.0728	+	27.8389i	−0.570044	+	0.987345i
$796$	−1.90406	+	3.29793i	−0.0674876	+	0.116892i
$797$	−24.4511	+	42.3506i	−0.866103	+	1.50013i	−0.000154661		1.00000i	$0.500049\pi$
$797$	−24.4511	+	42.3506i	−0.866103	+	1.50013i	−0.865948	+	0.500134i	$0.833284\pi$
$798$	−4.09923			−0.145111
$799$	15.4691	+	26.7933i	0.547258	+	0.947878i
$800$	−6.22339	−	10.7792i	−0.220030	−	0.381103i
$801$	4.11058	−	7.11973i	0.145240	−	0.251563i
$802$	−7.17211			−0.253256
$803$	26.1059	+	45.2168i	0.921259	+	1.59567i
$804$	3.00717			0.106055
$805$	15.1069			0.532447
$806$	−6.09327	+	3.78420i	−0.214626	+	0.133293i
$807$	0.598280			0.0210604
$808$	1.70329			0.0599217
$809$	−9.38613	−	16.2572i	−0.329999	−	0.571574i	0.652513	−	0.757778i	$-0.273715\pi$
$809$	−9.38613	−	16.2572i	−0.329999	−	0.571574i	−0.982511	+	0.186204i	$0.940382\pi$
$810$	−49.1623			−1.72739
$811$	−9.09532	+	15.7536i	−0.319380	+	0.553182i	−0.980359	−	0.197222i	$-0.936808\pi$
$811$	−9.09532	+	15.7536i	−0.319380	+	0.553182i	0.660979	+	0.750405i	$0.270141\pi$
$812$	−0.370027	−	0.640906i	−0.0129854	−	0.0224914i
$813$	15.8791	+	27.5034i	0.556904	+	0.964586i
$814$	67.0430			2.34986
$815$	24.9598	−	43.2316i	0.874303	−	1.51434i
$816$	22.4535	−	38.8906i	0.786031	−	1.36145i
$817$	11.1535	−	19.3185i	0.390212	−	0.675867i
$818$	13.6856	+	23.7041i	0.478504	+	0.828793i
$819$	0.452338	−	0.783472i	0.0158060	−	0.0273767i
$820$	−6.94782	−	12.0340i	−0.242629	−	0.420245i
$821$	6.16241			0.215070			0.107535	−	0.994201i	$-0.465704\pi$
$821$	6.16241			0.215070			0.107535	+	0.994201i	$0.465704\pi$
$822$	−2.25626			−0.0786961
$823$	−23.3225	−	40.3958i	−0.812972	−	1.40811i	−0.910775	−	0.412903i	$-0.864515\pi$
$823$	−23.3225	−	40.3958i	−0.812972	−	1.40811i	0.0978030	−	0.995206i	$-0.468818\pi$
$824$	15.1997	−	26.3267i	0.529507	−	0.917133i
$825$	−33.6097	−	58.2137i	−1.17014	−	2.02674i
$826$	2.38651	−	4.13356i	0.0830373	−	0.143825i
$827$	−13.8759	+	24.0338i	−0.482513	+	0.835737i	−0.999798	−	0.0200761i	$-0.993609\pi$
$827$	−13.8759	+	24.0338i	−0.482513	+	0.835737i	0.517286	+	0.855813i	$0.326942\pi$
$828$	−2.21426	+	3.83521i	−0.0769509	+	0.133283i
$829$	−24.2338			−0.841674			−0.420837	−	0.907136i	$-0.638264\pi$
$829$	−24.2338			−0.841674			−0.420837	+	0.907136i	$0.638264\pi$
$830$	20.2435	+	35.0628i	0.702663	+	1.21705i
$831$	−29.8530	−	51.7070i	−1.03559	−	1.79369i
$832$	−4.42933	+	7.67182i	−0.153559	+	0.265972i
$833$	43.6053			1.51083
$834$	5.89753	+	10.2148i	0.204215	+	0.353711i
$835$	−65.8400			−2.27849
$836$	−4.32687			−0.149648
$837$	14.4988	+	7.76044i	0.501151	+	0.268240i
$838$	12.5980			0.435189
$839$	21.3491			0.737053			0.368527	−	0.929617i	$-0.379862\pi$
$839$	21.3491			0.737053			0.368527	+	0.929617i	$0.379862\pi$
$840$	6.12549	+	10.6097i	0.211349	+	0.366068i
$841$	−13.7132			−0.472868
$842$	−11.9733	+	20.7384i	−0.412627	+	0.714691i
$843$	5.53742	+	9.59109i	0.190719	+	0.330335i
$844$	−4.40169	−	7.62396i	−0.151513	−	0.262427i
$845$	3.39702			0.116861
$846$	−4.97463	+	8.61632i	−0.171031	+	0.296235i
$847$	3.29035	−	5.69906i	0.113058	−	0.195822i
$848$	−7.04626	+	12.2045i	−0.241969	+	0.419103i
$849$	12.8322	+	22.2261i	0.440402	+	0.762798i
$850$	27.4534	−	47.5506i	0.941642	−	1.63097i
$851$	−43.5478	−	75.4270i	−1.49280	−	2.58560i
$852$	2.70869			0.0927981
$853$	−43.4816			−1.48878			−0.744390	−	0.667745i	$-0.767260\pi$
$853$	−43.4816			−1.48878			−0.744390	+	0.667745i	$0.767260\pi$
$854$	−2.86984	−	4.97071i	−0.0982040	−	0.170094i
$855$	7.35086	−	12.7321i	0.251394	−	0.435427i
$856$	12.2860	+	21.2799i	0.419926	+	0.727333i
$857$	26.1690	−	45.3260i	0.893916	−	1.54831i	0.0587746	−	0.998271i	$-0.481281\pi$
$857$	26.1690	−	45.3260i	0.893916	−	1.54831i	0.835141	−	0.550036i	$-0.185386\pi$
$858$	−6.62079	+	11.4675i	−0.226030	+	0.391495i
$859$	9.41096	−	16.3003i	0.321098	−	0.556158i	−0.659617	−	0.751602i	$-0.729281\pi$
$859$	9.41096	−	16.3003i	0.321098	−	0.556158i	0.980715	+	0.195444i	$0.0626148\pi$
$860$	−9.69593			−0.330628
$861$	7.18733	+	12.4488i	0.244943	+	0.424255i
$862$	−1.93121	−	3.34495i	−0.0657772	−	0.113929i
$863$	19.2792	−	33.3926i	0.656273	−	1.13670i	−0.325301	−	0.945611i	$-0.605465\pi$
$863$	19.2792	−	33.3926i	0.656273	−	1.13670i	0.981573	−	0.191087i	$-0.0612012\pi$
$864$	5.62150			0.191247
$865$	−2.25842	−	3.91169i	−0.0767885	−	0.133002i
$866$	32.2627			1.09633
$867$	−54.7955			−1.86095
$868$	−0.0338783	−	1.05332i	−0.00114991	−	0.0357521i
$869$	−9.60145			−0.325707
$870$	−36.8048			−1.24780
$871$	−2.05361	−	3.55695i	−0.0695839	−	0.120523i
$872$	−33.1925			−1.12404
$873$	2.59750	−	4.49900i	0.0879120	−	0.152268i
$874$	−13.7034	−	23.7350i	−0.463525	−	0.802849i
$875$	1.45427	+	2.51888i	0.0491634	+	0.0851535i
$876$	7.99996			0.270294
$877$	−2.12228	+	3.67590i	−0.0716643	+	0.124126i	−0.899631	−	0.436651i	$-0.856164\pi$
$877$	−2.12228	+	3.67590i	−0.0716643	+	0.124126i	0.827967	+	0.560777i	$0.189498\pi$
$878$	4.06951	−	7.04859i	0.137339	−	0.237879i
$879$	6.75150	−	11.6939i	0.227722	−	0.394427i
$880$	−25.9996	−	45.0327i	−0.876447	−	1.51805i
$881$	8.02271	−	13.8957i	0.270292	−	0.468159i	−0.698645	−	0.715469i	$-0.746213\pi$
$881$	8.02271	−	13.8957i	0.270292	−	0.468159i	0.968937	+	0.247309i	$0.0795464\pi$
$882$	7.01140	+	12.1441i	0.236086	+	0.408913i
$883$	33.2272			1.11819			0.559093	−	0.829105i	$-0.311150\pi$
$883$	33.2272			1.11819			0.559093	+	0.829105i	$0.311150\pi$
$884$	2.21834			0.0746110
$885$	24.3423	+	42.1622i	0.818258	+	1.41727i
$886$	−0.981438	+	1.69990i	−0.0329721	+	0.0571093i
$887$	22.7170	+	39.3469i	0.762761	+	1.32114i	0.941422	+	0.337230i	$0.109490\pi$
$887$	22.7170	+	39.3469i	0.762761	+	1.32114i	−0.178662	+	0.983911i	$0.557177\pi$
$888$	35.3153	−	61.1678i	1.18510	−	2.05266i
$889$	5.53531	−	9.58744i	0.185648	−	0.321552i
$890$	11.0573	−	19.1519i	0.370643	−	0.641972i
$891$	53.6812			1.79839
$892$	2.29936	+	3.98261i	0.0769883	+	0.133348i
$893$	6.31421	+	10.9365i	0.211297	+	0.365977i
$894$	20.0027	−	34.6456i	0.668989	−	1.15872i
$895$	61.0771			2.04158
$896$	2.11471	+	3.66278i	0.0706474	+	0.122365i
$897$	17.2021			0.574362
$898$	33.3372			1.11248
$899$	19.1927	+	10.2729i	0.640113	+	0.342619i
$900$	−3.62142			−0.120714
$901$	28.6710			0.955170
$902$	−36.9897	−	64.0680i	−1.23162	−	2.13323i
$903$	10.0302			0.333783
$904$	−1.00613	+	1.74267i	−0.0334635	+	0.0579604i
$905$	8.81583	+	15.2695i	0.293048	+	0.507574i
$906$	33.1422	+	57.4041i	1.10108	+	1.90712i
$907$	−1.94838			−0.0646950			−0.0323475	−	0.999477i	$-0.510298\pi$
$907$	−1.94838			−0.0646950			−0.0323475	+	0.999477i	$0.510298\pi$
$908$	0.939437	−	1.62715i	0.0311763	−	0.0539990i
$909$	0.459540	−	0.795946i	0.0152420	−	0.0263999i
$910$	1.21677	−	2.10752i	0.0403357	−	0.0698635i
$911$	28.7585	+	49.8111i	0.952810	+	1.65032i	0.739301	+	0.673375i	$0.235156\pi$
$911$	28.7585	+	49.8111i	0.952810	+	1.65032i	0.213509	+	0.976941i	$0.431511\pi$
$912$	9.16512	−	15.8745i	0.303487	−	0.525656i
$913$	−22.1043	−	38.2857i	−0.731544	−	1.26707i
$914$	4.77204			0.157845
$915$	58.5446			1.93543
$916$	−0.532274	−	0.921926i	−0.0175868	−	0.0304613i
$917$	2.29133	−	3.96870i	0.0756664	−	0.131058i
$918$	12.3991	+	21.4759i	0.409232	+	0.708810i
$919$	−21.7436	+	37.6610i	−0.717255	+	1.24232i	0.244828	+	0.969566i	$0.421268\pi$
$919$	−21.7436	+	37.6610i	−0.717255	+	1.24232i	−0.962083	+	0.272756i	$0.912065\pi$
$920$	−40.9540	+	70.9345i	−1.35021	+	2.33864i
$921$	−25.2907	+	43.8047i	−0.833356	+	1.44342i
$922$	−6.05742			−0.199490
$923$	−1.84977	−	3.20390i	−0.0608861	−	0.105458i
$924$	−0.972770	−	1.68489i	−0.0320018	−	0.0554287i
$925$	35.6112	−	61.6804i	1.17089	−	2.02804i
$926$	−3.77530			−0.124064
$927$	−8.20160	−	14.2056i	−0.269376	−	0.466573i
$928$	7.44144			0.244277
$929$	19.9614			0.654913			0.327456	−	0.944866i	$-0.393809\pi$
$929$	19.9614			0.654913			0.327456	+	0.944866i	$0.393809\pi$
$930$	−46.2086	−	24.7331i	−1.51524	−	0.811029i
$931$	17.7989			0.583335
$932$	−0.397581			−0.0130232
$933$	6.40079	+	11.0865i	0.209553	+	0.362956i
$934$	−13.4628			−0.440517
$935$	−52.8959	+	91.6183i	−1.72988	+	2.99624i
$936$	2.45253	+	4.24791i	0.0801636	+	0.138847i
$937$	−28.0248	−	48.5403i	−0.915529	−	1.58574i	−0.806125	−	0.591745i	$-0.798439\pi$
$937$	−28.0248	−	48.5403i	−0.915529	−	1.58574i	−0.109403	−	0.993997i	$-0.534894\pi$
$938$	−2.94232			−0.0960702
$939$	−27.1009	+	46.9402i	−0.884406	+	1.53184i
$940$	2.74452	−	4.75365i	0.0895164	−	0.155047i
$941$	−22.3829	+	38.7684i	−0.729663	+	1.26381i	0.227363	+	0.973810i	$0.426990\pi$
$941$	−22.3829	+	38.7684i	−0.729663	+	1.26381i	−0.957026	+	0.290003i	$0.906344\pi$
$942$	−12.0202	−	20.8195i	−0.391638	−	0.678337i
$943$	−48.0533	+	83.2308i	−1.56483	+	2.71037i
$944$	10.6716	+	18.4837i	0.347330	+	0.601594i
$945$	−5.57943			−0.181499
$946$	−51.6204			−1.67832
$947$	−8.94810	−	15.4986i	−0.290774	−	0.503636i	0.683219	−	0.730214i	$-0.260580\pi$
$947$	−8.94810	−	15.4986i	−0.290774	−	0.503636i	−0.973993	+	0.226578i	$0.927246\pi$
$948$	−0.735572	+	1.27405i	−0.0238903	+	0.0413792i
$949$	−5.46321	−	9.46256i	−0.177343	−	0.307168i
$950$	11.2060	−	19.4093i	0.363569	−	0.629721i
$951$	−5.53598	+	9.58859i	−0.179516	+	0.310931i
$952$	5.46339	−	9.46286i	0.177069	−	0.306693i
$953$	1.14600			0.0371226			0.0185613	−	0.999828i	$-0.494091\pi$
$953$	1.14600			0.0371226			0.0185613	+	0.999828i	$0.494091\pi$
$954$	4.61008	+	7.98490i	0.149257	+	0.258521i
$955$	9.68043	+	16.7670i	0.313251	+	0.542567i
$956$	−2.95283	+	5.11445i	−0.0955013	+	0.165413i
$957$	40.1878			1.29909
$958$	−1.70767	−	2.95778i	−0.0551724	−	0.0955614i
$959$	−0.452772			−0.0146208
$960$	−64.7305			−2.08917
$961$	17.1931	+	25.7953i	0.554618	+	0.832105i
$962$	−14.0301			−0.452350
$963$	13.2588			0.427258
$964$	−1.68783	−	2.92342i	−0.0543615	−	0.0941569i
$965$	−44.0238			−1.41718
$966$	6.16162	−	10.6722i	0.198247	−	0.343374i
$967$	−8.84212	−	15.3150i	−0.284343	−	0.492497i	0.688106	−	0.725610i	$-0.258442\pi$
$967$	−8.84212	−	15.3150i	−0.284343	−	0.492497i	−0.972450	+	0.233113i	$0.925109\pi$
$968$	17.8400	+	30.8998i	0.573399	+	0.993156i
$969$	−37.2926			−1.19801
$970$	6.98719	−	12.1022i	0.224345	−	0.388577i
$971$	3.11829	−	5.40103i	0.100071	−	0.173327i	−0.811643	−	0.584154i	$-0.801426\pi$
$971$	3.11829	−	5.40103i	0.100071	−	0.173327i	0.911714	+	0.410827i	$0.134760\pi$
$972$	2.60451	−	4.51115i	0.0835397	−	0.144695i
$973$	1.18348	+	2.04985i	0.0379406	+	0.0657151i
$974$	23.2866	−	40.3336i	0.746151	−	1.29237i
$975$	7.03352	+	12.1824i	0.225253	+	0.390149i
$976$	25.6657			0.821540
$977$	2.16636			0.0693080			0.0346540	−	0.999399i	$-0.488967\pi$
$977$	2.16636			0.0693080			0.0346540	+	0.999399i	$0.488967\pi$
$978$	−20.3606	−	35.2656i	−0.651061	−	1.12767i
$979$	−12.0737	+	20.9123i	−0.385877	+	0.668359i
$980$	−3.86821	−	6.69994i	−0.123565	−	0.214022i
$981$	−8.95515	+	15.5108i	−0.285916	+	0.495221i
$982$	−6.89783	+	11.9474i	−0.220119	+	0.381257i
$983$	3.58502	−	6.20944i	0.114344	−	0.198050i	−0.803173	−	0.595746i	$-0.796857\pi$
$983$	3.58502	−	6.20944i	0.114344	−	0.198050i	0.917517	+	0.397695i	$0.130190\pi$
$984$	−77.9381			−2.48458
$985$	5.14766	+	8.91600i	0.164018	+	0.284087i
$986$	16.4133	+	28.4287i	0.522706	+	0.905353i
$987$	−2.83913	+	4.91752i	−0.0903705	+	0.156526i
$988$	0.905487			0.0288074
$989$	33.5300	+	58.0757i	1.06619	+	1.84670i
$990$	−34.0210			−1.08126
$991$	−18.8450			−0.598631			−0.299316	−	0.954154i	$-0.596758\pi$
$991$	−18.8450			−0.598631			−0.299316	+	0.954154i	$0.596758\pi$
$992$	9.34277	+	5.00070i	0.296633	+	0.158772i
$993$	33.7690			1.07163
$994$	−2.65028			−0.0840617
$995$	19.0025	+	32.9134i	0.602421	+	1.04342i
$996$	−6.77368			−0.214632
$997$	6.97667	−	12.0839i	0.220953	−	0.382702i	−0.734144	−	0.678993i	$-0.762416\pi$
$997$	6.97667	−	12.0839i	0.220953	−	0.382702i	0.955098	+	0.296291i	$0.0957498\pi$
$998$	6.11112	+	10.5848i	0.193444	+	0.335055i
$999$	16.0835	+	27.8575i	0.508860	+	0.881372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.b.118.11	✓	34
31.5	even	3	inner	403.2.h.b.222.11	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.b.118.11	✓	34	1.1	even	1	trivial
403.2.h.b.222.11	yes	34	31.5	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.28826 q^{2} +(1.07551 + 1.86284i) q^{3} -0.340382 q^{4} +(-1.69851 + 2.94190i) q^{5} +(1.38554 + 2.39982i) q^{6} +(0.278041 + 0.481581i) q^{7} -3.01502 q^{8} +(-0.813438 + 1.40892i) q^{9} +O(q^{10})\)	\(q+1.28826 q^{2} +(1.07551 + 1.86284i) q^{3} -0.340382 q^{4} +(-1.69851 + 2.94190i) q^{5} +(1.38554 + 2.39982i) q^{6} +(0.278041 + 0.481581i) q^{7} -3.01502 q^{8} +(-0.813438 + 1.40892i) q^{9} +(-2.18812 + 3.78994i) q^{10} +(2.38925 - 4.13830i) q^{11} +(-0.366083 - 0.634075i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(0.358189 + 0.620402i) q^{14} -7.30704 q^{15} -3.20338 q^{16} +(3.25861 + 5.64408i) q^{17} +(-1.04792 + 1.81505i) q^{18} +(1.33011 + 2.30381i) q^{19} +(0.578141 - 1.00137i) q^{20} +(-0.598070 + 1.03589i) q^{21} +(3.07798 - 5.33122i) q^{22} -7.99721 q^{23} +(-3.24268 - 5.61649i) q^{24} +(-3.26986 - 5.66356i) q^{25} +(-0.644131 + 1.11567i) q^{26} +2.95361 q^{27} +(-0.0946400 - 0.163921i) q^{28} +3.90984 q^{29} -9.41338 q^{30} +(4.90883 + 2.62744i) q^{31} +1.90326 q^{32} +10.2786 q^{33} +(4.19794 + 7.27105i) q^{34} -1.88902 q^{35} +(0.276879 - 0.479569i) q^{36} +(5.44537 + 9.43166i) q^{37} +(1.71352 + 2.96791i) q^{38} -2.15102 q^{39} +(5.12104 - 8.86990i) q^{40} +(6.00876 - 10.4075i) q^{41} +(-0.770471 + 1.33450i) q^{42} +(-4.19272 - 7.26200i) q^{43} +(-0.813257 + 1.40860i) q^{44} +(-2.76326 - 4.78611i) q^{45} -10.3025 q^{46} +4.74715 q^{47} +(-3.44526 - 5.96736i) q^{48} +(3.34539 - 5.79438i) q^{49} +(-4.21243 - 7.29615i) q^{50} +(-7.00933 + 12.1405i) q^{51} +(0.170191 - 0.294779i) q^{52} +(2.19963 - 3.80988i) q^{53} +3.80503 q^{54} +(8.11632 + 14.0579i) q^{55} +(-0.838300 - 1.45198i) q^{56} +(-2.86108 + 4.95554i) q^{57} +5.03690 q^{58} +(-3.33135 - 5.77007i) q^{59} +2.48718 q^{60} -8.01209 q^{61} +(6.32385 + 3.38483i) q^{62} -0.904675 q^{63} +8.85865 q^{64} +(-1.69851 - 2.94190i) q^{65} +13.2416 q^{66} +(-2.05361 + 3.55695i) q^{67} +(-1.10917 - 1.92114i) q^{68} +(-8.60107 - 14.8975i) q^{69} -2.43355 q^{70} +(-1.84977 + 3.20390i) q^{71} +(2.45253 - 4.24791i) q^{72} +(-5.46321 + 9.46256i) q^{73} +(7.01507 + 12.1505i) q^{74} +(7.03352 - 12.1824i) q^{75} +(-0.452744 - 0.784175i) q^{76} +2.65724 q^{77} -2.77107 q^{78} +(-1.00465 - 1.74011i) q^{79} +(5.44096 - 9.42402i) q^{80} +(5.61695 + 9.72885i) q^{81} +(7.74086 - 13.4076i) q^{82} +(4.62578 - 8.01208i) q^{83} +(0.203572 - 0.352597i) q^{84} -22.1391 q^{85} +(-5.40132 - 9.35536i) q^{86} +(4.20507 + 7.28339i) q^{87} +(-7.20365 + 12.4771i) q^{88} -5.05334 q^{89} +(-3.55980 - 6.16576i) q^{90} -0.556082 q^{91} +2.72210 q^{92} +(0.385000 + 11.9702i) q^{93} +6.11557 q^{94} -9.03678 q^{95} +(2.04697 + 3.54546i) q^{96} -3.19323 q^{97} +(4.30973 - 7.46468i) q^{98} +(3.88701 + 6.73250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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