LMFDB - Embedded newform 370.2.h.e.117.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(117,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("370.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.h (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} + \cdots + 256 $ x^20 - 4x^19 + 8x^18 + 4x^17 + 103x^16 - 394x^15 + 760x^14 + 278x^13 + 2009x^12 - 7362x^11 + 13826x^10 + 4848x^9 + 13544x^8 - 44248x^7 + 76384x^6 + 24512x^5 + 28432x^4 - 61952x^3 + 61952x^2 - 5632*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			117.1
Root			$-2.09082 + 2.09082i$ of defining polynomial
Character	$\chi$	$=$	370.117
Dual form			370.2.h.e.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-2.09082 - 2.09082i) q^{3} +1.00000 q^{4} +(-1.81614 + 1.30447i) q^{5} +(2.09082 + 2.09082i) q^{6} +(-0.643605 - 0.643605i) q^{7} -1.00000 q^{8} +5.74304i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-2.09082 - 2.09082i) q^{3} +1.00000 q^{4} +(-1.81614 + 1.30447i) q^{5} +(2.09082 + 2.09082i) q^{6} +(-0.643605 - 0.643605i) q^{7} -1.00000 q^{8} +5.74304i q^{9} +(1.81614 - 1.30447i) q^{10} +1.88405i q^{11} +(-2.09082 - 2.09082i) q^{12} -0.536082 q^{13} +(0.643605 + 0.643605i) q^{14} +(6.52462 + 1.06980i) q^{15} +1.00000 q^{16} +0.334703i q^{17} -5.74304i q^{18} +(1.08518 - 1.08518i) q^{19} +(-1.81614 + 1.30447i) q^{20} +2.69132i q^{21} -1.88405i q^{22} +4.65098 q^{23} +(2.09082 + 2.09082i) q^{24} +(1.59670 - 4.73820i) q^{25} +0.536082 q^{26} +(5.73519 - 5.73519i) q^{27} +(-0.643605 - 0.643605i) q^{28} +(3.33033 + 3.33033i) q^{29} +(-6.52462 - 1.06980i) q^{30} +(4.90948 - 4.90948i) q^{31} -1.00000 q^{32} +(3.93919 - 3.93919i) q^{33} -0.334703i q^{34} +(2.00844 + 0.329310i) q^{35} +5.74304i q^{36} +(-0.819646 + 6.02729i) q^{37} +(-1.08518 + 1.08518i) q^{38} +(1.12085 + 1.12085i) q^{39} +(1.81614 - 1.30447i) q^{40} +8.26486i q^{41} -2.69132i q^{42} +11.9117 q^{43} +1.88405i q^{44} +(-7.49163 - 10.4301i) q^{45} -4.65098 q^{46} +(-0.141535 - 0.141535i) q^{47} +(-2.09082 - 2.09082i) q^{48} -6.17154i q^{49} +(-1.59670 + 4.73820i) q^{50} +(0.699803 - 0.699803i) q^{51} -0.536082 q^{52} +(-5.03296 + 5.03296i) q^{53} +(-5.73519 + 5.73519i) q^{54} +(-2.45768 - 3.42168i) q^{55} +(0.643605 + 0.643605i) q^{56} -4.53784 q^{57} +(-3.33033 - 3.33033i) q^{58} +(-4.10789 + 4.10789i) q^{59} +(6.52462 + 1.06980i) q^{60} +(-8.90180 + 8.90180i) q^{61} +(-4.90948 + 4.90948i) q^{62} +(3.69625 - 3.69625i) q^{63} +1.00000 q^{64} +(0.973599 - 0.699305i) q^{65} +(-3.93919 + 3.93919i) q^{66} +(-3.61956 + 3.61956i) q^{67} +0.334703i q^{68} +(-9.72436 - 9.72436i) q^{69} +(-2.00844 - 0.329310i) q^{70} +15.5121 q^{71} -5.74304i q^{72} +(6.82739 + 6.82739i) q^{73} +(0.819646 - 6.02729i) q^{74} +(-13.2451 + 6.56829i) q^{75} +(1.08518 - 1.08518i) q^{76} +(1.21258 - 1.21258i) q^{77} +(-1.12085 - 1.12085i) q^{78} +(-5.73637 + 5.73637i) q^{79} +(-1.81614 + 1.30447i) q^{80} -6.75336 q^{81} -8.26486i q^{82} +(-7.90475 + 7.90475i) q^{83} +2.69132i q^{84} +(-0.436611 - 0.607866i) q^{85} -11.9117 q^{86} -13.9262i q^{87} -1.88405i q^{88} +(1.21521 + 1.21521i) q^{89} +(7.49163 + 10.4301i) q^{90} +(0.345025 + 0.345025i) q^{91} +4.65098 q^{92} -20.5297 q^{93} +(0.141535 + 0.141535i) q^{94} +(-0.555249 + 3.38643i) q^{95} +(2.09082 + 2.09082i) q^{96} -17.1767i q^{97} +6.17154i q^{98} -10.8201 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8} + 4 q^{10} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 6 q^{19} - 4 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} - 20 q^{27} - 2 q^{28} + 18 q^{29} + 4 q^{30} + 12 q^{31} - 20 q^{32} + 4 q^{33} - 12 q^{35} - 32 q^{37} - 6 q^{38} + 6 q^{39} + 4 q^{40} + 16 q^{43} + 22 q^{45} + 4 q^{46} - 22 q^{47} + 4 q^{48} - 10 q^{50} + 8 q^{51} - 4 q^{53} + 20 q^{54} + 16 q^{55} + 2 q^{56} + 24 q^{57} - 18 q^{58} - 10 q^{59} - 4 q^{60} + 10 q^{61} - 12 q^{62} - 2 q^{63} + 20 q^{64} + 20 q^{65} - 4 q^{66} + 8 q^{67} - 34 q^{69} + 12 q^{70} + 16 q^{71} - 6 q^{73} + 32 q^{74} - 26 q^{75} + 6 q^{76} - 4 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} - 28 q^{81} + 6 q^{83} + 10 q^{85} - 16 q^{86} - 44 q^{89} - 22 q^{90} - 40 q^{91} - 4 q^{92} - 40 q^{93} + 22 q^{94} + 50 q^{95} - 4 q^{96} - 20 q^{99}+O(q^{100}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8 + 4 * q^10 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 6 * q^19 - 4 * q^20 - 4 * q^23 - 4 * q^24 + 10 * q^25 - 20 * q^27 - 2 * q^28 + 18 * q^29 + 4 * q^30 + 12 * q^31 - 20 * q^32 + 4 * q^33 - 12 * q^35 - 32 * q^37 - 6 * q^38 + 6 * q^39 + 4 * q^40 + 16 * q^43 + 22 * q^45 + 4 * q^46 - 22 * q^47 + 4 * q^48 - 10 * q^50 + 8 * q^51 - 4 * q^53 + 20 * q^54 + 16 * q^55 + 2 * q^56 + 24 * q^57 - 18 * q^58 - 10 * q^59 - 4 * q^60 + 10 * q^61 - 12 * q^62 - 2 * q^63 + 20 * q^64 + 20 * q^65 - 4 * q^66 + 8 * q^67 - 34 * q^69 + 12 * q^70 + 16 * q^71 - 6 * q^73 + 32 * q^74 - 26 * q^75 + 6 * q^76 - 4 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 - 28 * q^81 + 6 * q^83 + 10 * q^85 - 16 * q^86 - 44 * q^89 - 22 * q^90 - 40 * q^91 - 4 * q^92 - 40 * q^93 + 22 * q^94 + 50 * q^95 - 4 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−2.09082	−	2.09082i	−1.20713	−	1.20713i	−0.971951	−	0.235183i	$-0.924431\pi$
$3$	−2.09082	−	2.09082i	−1.20713	−	1.20713i	−0.235183	−	0.971951i	$-0.575569\pi$
$4$	1.00000			0.500000
$5$	−1.81614	+	1.30447i	−0.812201	+	0.583378i
$5$	−1.81614	+	1.30447i	−0.812201	+	0.583378i
$6$	2.09082	+	2.09082i	0.853573	+	0.853573i
$7$	−0.643605	−	0.643605i	−0.243260	−	0.243260i	0.574937	−	0.818197i	$-0.305026\pi$
$7$	−0.643605	−	0.643605i	−0.243260	−	0.243260i	−0.818197	+	0.574937i	$0.805026\pi$
$8$	−1.00000			−0.353553
$9$			5.74304i			1.91435i
$10$	1.81614	−	1.30447i	0.574313	−	0.412510i
$11$			1.88405i			0.568061i	0.958815	+	0.284030i	$0.0916717\pi$
$11$			1.88405i			0.568061i	−0.958815	+	0.284030i	$0.908328\pi$
$12$	−2.09082	−	2.09082i	−0.603567	−	0.603567i
$13$	−0.536082			−0.148683			−0.0743413	−	0.997233i	$-0.523685\pi$
$13$	−0.536082			−0.148683			−0.0743413	+	0.997233i	$0.523685\pi$
$14$	0.643605	+	0.643605i	0.172011	+	0.172011i
$15$	6.52462	+	1.06980i	1.68465	+	0.276220i
$16$	1.00000			0.250000
$17$			0.334703i			0.0811774i	0.999176	+	0.0405887i	$0.0129233\pi$
$17$			0.334703i			0.0811774i	−0.999176	+	0.0405887i	$0.987077\pi$
$18$		−	5.74304i		−	1.35365i
$19$	1.08518	−	1.08518i	0.248958	−	0.248958i	−0.571585	−	0.820543i	$-0.693671\pi$
$19$	1.08518	−	1.08518i	0.248958	−	0.248958i	0.820543	+	0.571585i	$0.193671\pi$
$20$	−1.81614	+	1.30447i	−0.406101	+	0.291689i
$21$			2.69132i			0.587295i
$22$		−	1.88405i		−	0.401680i
$23$	4.65098			0.969797			0.484899	−	0.874570i	$-0.338856\pi$
$23$	4.65098			0.969797			0.484899	+	0.874570i	$0.338856\pi$
$24$	2.09082	+	2.09082i	0.426786	+	0.426786i
$25$	1.59670	−	4.73820i	0.319341	−	0.947640i
$26$	0.536082			0.105134
$27$	5.73519	−	5.73519i	1.10374	−	1.10374i
$28$	−0.643605	−	0.643605i	−0.121630	−	0.121630i
$29$	3.33033	+	3.33033i	0.618427	+	0.618427i	0.945128	−	0.326701i	$-0.105937\pi$
$29$	3.33033	+	3.33033i	0.618427	+	0.618427i	−0.326701	+	0.945128i	$0.605937\pi$
$30$	−6.52462	−	1.06980i	−1.19123	−	0.195317i
$31$	4.90948	−	4.90948i	0.881769	−	0.881769i	−0.111945	−	0.993714i	$-0.535708\pi$
$31$	4.90948	−	4.90948i	0.881769	−	0.881769i	0.993714	+	0.111945i	$0.0357081\pi$
$32$	−1.00000			−0.176777
$33$	3.93919	−	3.93919i	0.685726	−	0.685726i
$34$		−	0.334703i		−	0.0574011i
$35$	2.00844	+	0.329310i	0.339488	+	0.0556635i
$36$			5.74304i			0.957173i
$37$	−0.819646	+	6.02729i	−0.134749	+	0.990880i
$37$	−0.819646	+	6.02729i	−0.134749	+	0.990880i
$38$	−1.08518	+	1.08518i	−0.176040	+	0.176040i
$39$	1.12085	+	1.12085i	0.179480	+	0.179480i
$40$	1.81614	−	1.30447i	0.287156	−	0.206255i
$41$			8.26486i			1.29075i	0.763864	+	0.645377i	$0.223300\pi$
$41$			8.26486i			1.29075i	−0.763864	+	0.645377i	$0.776700\pi$
$42$		−	2.69132i		−	0.415280i
$43$	11.9117			1.81652			0.908259	−	0.418409i	$-0.137412\pi$
$43$	11.9117			1.81652			0.908259	+	0.418409i	$0.137412\pi$
$44$			1.88405i			0.284030i
$45$	−7.49163	−	10.4301i	−1.11679	−	1.55483i
$46$	−4.65098			−0.685750
$47$	−0.141535	−	0.141535i	−0.0206450	−	0.0206450i	0.696709	−	0.717354i	$-0.254647\pi$
$47$	−0.141535	−	0.141535i	−0.0206450	−	0.0206450i	−0.717354	+	0.696709i	$0.754647\pi$
$48$	−2.09082	−	2.09082i	−0.301784	−	0.301784i
$49$		−	6.17154i		−	0.881649i
$50$	−1.59670	+	4.73820i	−0.225808	+	0.670083i
$51$	0.699803	−	0.699803i	0.0979920	−	0.0979920i
$52$	−0.536082			−0.0743413
$53$	−5.03296	+	5.03296i	−0.691330	+	0.691330i	−0.962525	−	0.271194i	$-0.912581\pi$
$53$	−5.03296	+	5.03296i	−0.691330	+	0.691330i	0.271194	+	0.962525i	$0.412581\pi$
$54$	−5.73519	+	5.73519i	−0.780460	+	0.780460i
$55$	−2.45768	−	3.42168i	−0.331394	−	0.461380i
$56$	0.643605	+	0.643605i	0.0860054	+	0.0860054i
$57$	−4.53784			−0.601051
$58$	−3.33033	−	3.33033i	−0.437294	−	0.437294i
$59$	−4.10789	+	4.10789i	−0.534802	+	0.534802i	−0.921998	−	0.387195i	$-0.873444\pi$
$59$	−4.10789	+	4.10789i	−0.534802	+	0.534802i	0.387195	+	0.921998i	$0.373444\pi$
$60$	6.52462	+	1.06980i	0.842325	+	0.138110i
$61$	−8.90180	+	8.90180i	−1.13976	+	1.13976i	−0.151265	+	0.988493i	$0.548335\pi$
$61$	−8.90180	+	8.90180i	−1.13976	+	1.13976i	−0.988493	+	0.151265i	$0.951665\pi$
$62$	−4.90948	+	4.90948i	−0.623505	+	0.623505i
$63$	3.69625	−	3.69625i	0.465683	−	0.465683i
$64$	1.00000			0.125000
$65$	0.973599	−	0.699305i	0.120760	−	0.0867381i
$66$	−3.93919	+	3.93919i	−0.484881	+	0.484881i
$67$	−3.61956	+	3.61956i	−0.442199	+	0.442199i	−0.892751	−	0.450551i	$-0.851227\pi$
$67$	−3.61956	+	3.61956i	−0.442199	+	0.442199i	0.450551	+	0.892751i	$0.351227\pi$
$68$			0.334703i			0.0405887i
$69$	−9.72436	−	9.72436i	−1.17068	−	1.17068i
$70$	−2.00844	−	0.329310i	−0.240054	−	0.0393601i
$71$	15.5121			1.84095			0.920477	−	0.390798i	$-0.127801\pi$
$71$	15.5121			1.84095			0.920477	+	0.390798i	$0.127801\pi$
$72$		−	5.74304i		−	0.676823i
$73$	6.82739	+	6.82739i	0.799086	+	0.799086i	0.982951	−	0.183866i	$-0.0588611\pi$
$73$	6.82739	+	6.82739i	0.799086	+	0.799086i	−0.183866	+	0.982951i	$0.558861\pi$
$74$	0.819646	−	6.02729i	0.0952819	−	0.700658i
$75$	−13.2451	+	6.56829i	−1.52942	+	0.758441i
$76$	1.08518	−	1.08518i	0.124479	−	0.124479i
$77$	1.21258	−	1.21258i	0.138186	−	0.138186i
$78$	−1.12085	−	1.12085i	−0.126911	−	0.126911i
$79$	−5.73637	+	5.73637i	−0.645392	+	0.645392i	−0.951876	−	0.306484i	$-0.900847\pi$
$79$	−5.73637	+	5.73637i	−0.645392	+	0.645392i	0.306484	+	0.951876i	$0.400847\pi$
$80$	−1.81614	+	1.30447i	−0.203050	+	0.145844i
$81$	−6.75336			−0.750373
$82$		−	8.26486i		−	0.912701i
$83$	−7.90475	+	7.90475i	−0.867659	+	0.867659i	−0.992213	−	0.124554i	$-0.960250\pi$
$83$	−7.90475	+	7.90475i	−0.867659	+	0.867659i	0.124554	+	0.992213i	$0.460250\pi$
$84$			2.69132i			0.293647i
$85$	−0.436611	−	0.607866i	−0.0473571	−	0.0659323i
$86$	−11.9117			−1.28447
$87$		−	13.9262i		−	1.49305i
$88$		−	1.88405i		−	0.200840i
$89$	1.21521	+	1.21521i	0.128812	+	0.128812i	0.768574	−	0.639761i	$-0.220967\pi$
$89$	1.21521	+	1.21521i	0.128812	+	0.128812i	−0.639761	+	0.768574i	$0.720967\pi$
$90$	7.49163	+	10.4301i	0.789687	+	1.09943i
$91$	0.345025	+	0.345025i	0.0361685	+	0.0361685i
$92$	4.65098			0.484899
$93$	−20.5297			−2.12883
$94$	0.141535	+	0.141535i	0.0145982	+	0.0145982i
$95$	−0.555249	+	3.38643i	−0.0569674	+	0.347440i
$96$	2.09082	+	2.09082i	0.213393	+	0.213393i
$97$		−	17.1767i		−	1.74403i	−0.489477	−	0.872016i	$-0.662812\pi$
$97$		−	17.1767i		−	1.74403i	0.489477	−	0.872016i	$-0.337188\pi$
$98$			6.17154i			0.623420i
$99$	−10.8201			−1.08746
$100$	1.59670	−	4.73820i	0.159670	−	0.473820i
$101$		−	13.4676i		−	1.34008i	−0.742324	−	0.670041i	$-0.766277\pi$
$101$		−	13.4676i		−	1.34008i	0.742324	−	0.670041i	$-0.233723\pi$
$102$	−0.699803	+	0.699803i	−0.0692908	+	0.0692908i
$103$			12.6201i			1.24350i	0.783216	+	0.621749i	$0.213578\pi$
$103$			12.6201i			1.24350i	−0.783216	+	0.621749i	$0.786422\pi$
$104$	0.536082			0.0525672
$105$	−3.51075	−	4.88781i	−0.342615	−	0.477001i
$106$	5.03296	−	5.03296i	0.488844	−	0.488844i
$107$	−1.64796	−	1.64796i	−0.159314	−	0.159314i	0.622949	−	0.782263i	$-0.285935\pi$
$107$	−1.64796	−	1.64796i	−0.159314	−	0.159314i	−0.782263	+	0.622949i	$0.785935\pi$
$108$	5.73519	−	5.73519i	0.551869	−	0.551869i
$109$	7.06206	−	7.06206i	0.676422	−	0.676422i	−0.282766	−	0.959189i	$-0.591252\pi$
$109$	7.06206	−	7.06206i	0.676422	−	0.676422i	0.959189	+	0.282766i	$0.0912521\pi$
$110$	2.45768	+	3.42168i	0.234331	+	0.326245i
$111$	14.3157	−	10.8882i	1.35878	−	1.03346i
$112$	−0.643605	−	0.643605i	−0.0608150	−	0.0608150i
$113$			15.1701i			1.42709i	0.700612	+	0.713543i	$0.252911\pi$
$113$			15.1701i			1.42709i	−0.700612	+	0.713543i	$0.747089\pi$
$114$	4.53784			0.425007
$115$	−8.44682	+	6.06708i	−0.787670	+	0.565758i
$116$	3.33033	+	3.33033i	0.309213	+	0.309213i
$117$		−	3.07874i		−	0.284630i
$118$	4.10789	−	4.10789i	0.378162	−	0.378162i
$119$	0.215416	−	0.215416i	0.0197472	−	0.0197472i
$120$	−6.52462	−	1.06980i	−0.595614	−	0.0976587i
$121$	7.45037			0.677307
$122$	8.90180	−	8.90180i	0.805931	−	0.805931i
$123$	17.2803	−	17.2803i	1.55811	−	1.55811i
$124$	4.90948	−	4.90948i	0.440885	−	0.440885i
$125$	3.28101	+	10.6881i	0.293463	+	0.955970i
$126$	−3.69625	+	3.69625i	−0.329288	+	0.329288i
$127$	−3.59805	−	3.59805i	−0.319275	−	0.319275i	0.529213	−	0.848489i	$-0.322487\pi$
$127$	−3.59805	−	3.59805i	−0.319275	−	0.319275i	−0.848489	+	0.529213i	$0.822487\pi$
$128$	−1.00000			−0.0883883
$129$	−24.9052	−	24.9052i	−2.19278	−	2.19278i
$130$	−0.973599	+	0.699305i	−0.0853903	+	0.0613331i
$131$	7.63639	−	7.63639i	0.667194	−	0.667194i	−0.289871	−	0.957066i	$-0.593613\pi$
$131$	7.63639	−	7.63639i	0.667194	−	0.667194i	0.957066	+	0.289871i	$0.0936126\pi$
$132$	3.93919	−	3.93919i	0.342863	−	0.342863i
$133$	−1.39686			−0.121123
$134$	3.61956	−	3.61956i	0.312682	−	0.312682i
$135$	−2.93449	+	17.8973i	−0.252561	+	1.54035i
$136$		−	0.334703i		−	0.0287005i
$137$	5.48037	+	5.48037i	0.468220	+	0.468220i	0.901337	−	0.433118i	$-0.142587\pi$
$137$	5.48037	+	5.48037i	0.468220	+	0.468220i	−0.433118	+	0.901337i	$0.642587\pi$
$138$	9.72436	+	9.72436i	0.827793	+	0.827793i
$139$	4.24414			0.359983			0.179991	−	0.983668i	$-0.442393\pi$
$139$	4.24414			0.359983			0.179991	+	0.983668i	$0.442393\pi$
$140$	2.00844	+	0.329310i	0.169744	+	0.0278318i
$141$			0.591849i			0.0498427i
$142$	−15.5121			−1.30175
$143$		−	1.01000i		−	0.0844607i
$144$			5.74304i			0.478586i
$145$	−10.3927	−	1.70401i	−0.863063	−	0.141510i
$146$	−6.82739	−	6.82739i	−0.565039	−	0.565039i
$147$	−12.9036	+	12.9036i	−1.06427	+	1.06427i
$148$	−0.819646	+	6.02729i	−0.0673745	+	0.495440i
$149$			20.3080i			1.66370i	0.555002	+	0.831849i	$0.312718\pi$
$149$			20.3080i			1.66370i	−0.555002	+	0.831849i	$0.687282\pi$
$150$	13.2451	−	6.56829i	1.08146	−	0.536299i
$151$			13.8362i			1.12597i	0.826466	+	0.562987i	$0.190348\pi$
$151$			13.8362i			1.12597i	−0.826466	+	0.562987i	$0.809652\pi$
$152$	−1.08518	+	1.08518i	−0.0880199	+	0.0880199i
$153$	−1.92221			−0.155402
$154$	−1.21258	+	1.21258i	−0.0977126	+	0.0977126i
$155$	−2.51201	+	15.3206i	−0.201769	+	1.23058i
$156$	1.12085	+	1.12085i	0.0897399	+	0.0897399i
$157$	13.2682	+	13.2682i	1.05892	+	1.05892i	0.998152	+	0.0607691i	$0.0193553\pi$
$157$	13.2682	+	13.2682i	1.05892	+	1.05892i	0.0607691	+	0.998152i	$0.480645\pi$
$158$	5.73637	−	5.73637i	0.456361	−	0.456361i
$159$	21.0460			1.66906
$160$	1.81614	−	1.30447i	0.143578	−	0.103128i
$161$	−2.99340	−	2.99340i	−0.235913	−	0.235913i
$162$	6.75336			0.530594
$163$		−	1.48487i		−	0.116304i	−0.998308	−	0.0581520i	$-0.981479\pi$
$163$		−	1.48487i		−	0.116304i	0.998308	−	0.0581520i	$-0.0185208\pi$
$164$			8.26486i			0.645377i
$165$	−2.01555	+	12.2927i	−0.156910	+	0.956984i
$166$	7.90475	−	7.90475i	0.613527	−	0.613527i
$167$		−	4.69210i		−	0.363086i	−0.983383	−	0.181543i	$-0.941891\pi$
$167$		−	4.69210i		−	0.363086i	0.983383	−	0.181543i	$-0.0581091\pi$
$168$		−	2.69132i		−	0.207640i
$169$	−12.7126			−0.977894
$170$	0.436611	+	0.607866i	0.0334865	+	0.0466212i
$171$	6.23224	+	6.23224i	0.476591	+	0.476591i
$172$	11.9117			0.908259
$173$	−1.68127	−	1.68127i	−0.127825	−	0.127825i	0.640300	−	0.768125i	$-0.278810\pi$
$173$	−1.68127	−	1.68127i	−0.127825	−	0.127825i	−0.768125	+	0.640300i	$0.778810\pi$
$174$			13.9262i			1.05574i
$175$	−4.07718	+	2.02188i	−0.308206	+	0.152840i
$176$			1.88405i			0.142015i
$177$	17.1777			1.29116
$178$	−1.21521	−	1.21521i	−0.0910840	−	0.0910840i
$179$	−13.0168	−	13.0168i	−0.972921	−	0.972921i	0.0267216	−	0.999643i	$-0.491493\pi$
$179$	−13.0168	−	13.0168i	−0.972921	−	0.972921i	−0.999643	+	0.0267216i	$0.991493\pi$
$180$	−7.49163	−	10.4301i	−0.558393	−	0.777417i
$181$	5.91911			0.439964			0.219982	−	0.975504i	$-0.429400\pi$
$181$	5.91911			0.439964			0.219982	+	0.975504i	$0.429400\pi$
$182$	−0.345025	−	0.345025i	−0.0255750	−	0.0255750i
$183$	37.2241			2.75168
$184$	−4.65098			−0.342875
$185$	−6.37384	−	12.0156i	−0.468614	−	0.883403i
$186$	20.5297			1.50531
$187$	−0.630595			−0.0461137
$188$	−0.141535	−	0.141535i	−0.0103225	−	0.0103225i
$189$	−7.38239			−0.536990
$190$	0.555249	−	3.38643i	0.0402820	−	0.245677i
$191$	−8.14150	−	8.14150i	−0.589099	−	0.589099i	0.348289	−	0.937387i	$-0.386763\pi$
$191$	−8.14150	−	8.14150i	−0.589099	−	0.589099i	−0.937387	+	0.348289i	$0.886763\pi$
$192$	−2.09082	−	2.09082i	−0.150892	−	0.150892i
$193$	15.8717			1.14247			0.571235	−	0.820787i	$-0.306465\pi$
$193$	15.8717			1.14247			0.571235	+	0.820787i	$0.306465\pi$
$194$			17.1767i			1.23322i
$195$	−3.49774	−	0.573499i	−0.250478	−	0.0410691i
$196$		−	6.17154i		−	0.440825i
$197$	3.60225	+	3.60225i	0.256650	+	0.256650i	0.823690	−	0.567040i	$-0.191912\pi$
$197$	3.60225	+	3.60225i	0.256650	+	0.256650i	−0.567040	+	0.823690i	$0.691912\pi$
$198$	10.8201			0.768954
$199$	−1.14697	−	1.14697i	−0.0813064	−	0.0813064i	0.665284	−	0.746590i	$-0.268310\pi$
$199$	−1.14697	−	1.14697i	−0.0813064	−	0.0813064i	−0.746590	+	0.665284i	$0.768310\pi$
$200$	−1.59670	+	4.73820i	−0.112904	+	0.335041i
$201$	15.1357			1.06759
$202$			13.4676i			0.947581i
$203$		−	4.28683i		−	0.300877i
$204$	0.699803	−	0.699803i	0.0489960	−	0.0489960i
$205$	−10.7813	−	15.0101i	−0.752997	−	1.04835i
$206$		−	12.6201i		−	0.879286i
$207$			26.7108i			1.85653i
$208$	−0.536082			−0.0371706
$209$	2.04453	+	2.04453i	0.141423	+	0.141423i
$210$	3.51075	+	4.88781i	0.242265	+	0.337291i
$211$	3.19579			0.220008			0.110004	−	0.993931i	$-0.464914\pi$
$211$	3.19579			0.220008			0.110004	+	0.993931i	$0.464914\pi$
$212$	−5.03296	+	5.03296i	−0.345665	+	0.345665i
$213$	−32.4331	−	32.4331i	−2.22228	−	2.22228i
$214$	1.64796	+	1.64796i	0.112652	+	0.112652i
$215$	−21.6333	+	15.5385i	−1.47538	+	1.05972i
$216$	−5.73519	+	5.73519i	−0.390230	+	0.390230i
$217$	−6.31954			−0.428998
$218$	−7.06206	+	7.06206i	−0.478303	+	0.478303i
$219$		−	28.5497i		−	1.92921i
$220$	−2.45768	−	3.42168i	−0.165697	−	0.230690i
$221$		−	0.179428i		−	0.0120697i
$222$	−14.3157	+	10.8882i	−0.960806	+	0.730770i
$223$	−7.29909	+	7.29909i	−0.488783	+	0.488783i	−0.907922	−	0.419139i	$-0.862332\pi$
$223$	−7.29909	+	7.29909i	−0.488783	+	0.488783i	0.419139	+	0.907922i	$0.362332\pi$
$224$	0.643605	+	0.643605i	0.0430027	+	0.0430027i
$225$	27.2117	+	9.16993i	1.81411	+	0.611329i
$226$		−	15.1701i		−	1.00910i
$227$		−	19.6620i		−	1.30501i	−0.757783	−	0.652507i	$-0.773717\pi$
$227$		−	19.6620i		−	1.30501i	0.757783	−	0.652507i	$-0.226283\pi$
$228$	−4.53784			−0.300526
$229$			13.4975i			0.891940i	0.895048	+	0.445970i	$0.147141\pi$
$229$			13.4975i			0.891940i	−0.895048	+	0.445970i	$0.852859\pi$
$230$	8.44682	−	6.06708i	0.556967	−	0.400051i
$231$	−5.07057			−0.333619
$232$	−3.33033	−	3.33033i	−0.218647	−	0.218647i
$233$	−1.10924	−	1.10924i	−0.0726687	−	0.0726687i	0.669838	−	0.742507i	$-0.266363\pi$
$233$	−1.10924	−	1.10924i	−0.0726687	−	0.0726687i	−0.742507	+	0.669838i	$0.766363\pi$
$234$			3.07874i			0.201264i
$235$	0.441676	+	0.0724186i	0.0288118	+	0.00472407i
$236$	−4.10789	+	4.10789i	−0.267401	+	0.267401i
$237$	23.9874			1.55815
$238$	−0.215416	+	0.215416i	−0.0139634	+	0.0139634i
$239$	10.5161	−	10.5161i	0.680230	−	0.680230i	−0.279822	−	0.960052i	$-0.590275\pi$
$239$	10.5161	−	10.5161i	0.680230	−	0.680230i	0.960052	+	0.279822i	$0.0902754\pi$
$240$	6.52462	+	1.06980i	0.421163	+	0.0690551i
$241$	−18.7617	−	18.7617i	−1.20855	−	1.20855i	−0.971498	−	0.237047i	$-0.923820\pi$
$241$	−18.7617	−	18.7617i	−1.20855	−	1.20855i	−0.237047	−	0.971498i	$-0.576180\pi$
$242$	−7.45037			−0.478928
$243$	−3.08553	−	3.08553i	−0.197937	−	0.197937i
$244$	−8.90180	+	8.90180i	−0.569879	+	0.569879i
$245$	8.05061	+	11.2084i	0.514334	+	0.716076i
$246$	−17.2803	+	17.2803i	−1.10175	+	1.10175i
$247$	−0.581747	+	0.581747i	−0.0370157	+	0.0370157i
$248$	−4.90948	+	4.90948i	−0.311752	+	0.311752i
$249$	33.0548			2.09476
$250$	−3.28101	−	10.6881i	−0.207510	−	0.675973i
$251$	9.09164	−	9.09164i	0.573859	−	0.573859i	−0.359346	−	0.933205i	$-0.617000\pi$
$251$	9.09164	−	9.09164i	0.573859	−	0.573859i	0.933205	+	0.359346i	$0.117000\pi$
$252$	3.69625	−	3.69625i	0.232842	−	0.232842i
$253$			8.76267i			0.550904i
$254$	3.59805	+	3.59805i	0.225762	+	0.225762i
$255$	−0.358064	+	2.18381i	−0.0224228	+	0.136756i
$256$	1.00000			0.0625000
$257$		−	2.08454i		−	0.130030i	−0.997884	−	0.0650151i	$-0.979290\pi$
$257$		−	2.08454i		−	0.130030i	0.997884	−	0.0650151i	$-0.0207096\pi$
$258$	24.9052	+	24.9052i	1.55053	+	1.55053i
$259$	4.40672	−	3.35166i	0.273820	−	0.208262i
$260$	0.973599	−	0.699305i	0.0603800	−	0.0433690i
$261$	−19.1262	+	19.1262i	−1.18388	+	1.18388i
$262$	−7.63639	+	7.63639i	−0.471778	+	0.471778i
$263$	−6.41417	−	6.41417i	−0.395515	−	0.395515i	0.481133	−	0.876648i	$-0.340225\pi$
$263$	−6.41417	−	6.41417i	−0.395515	−	0.395515i	−0.876648	+	0.481133i	$0.840225\pi$
$264$	−3.93919	+	3.93919i	−0.242441	+	0.242441i
$265$	2.57519	−	15.7059i	0.158192	−	0.964806i
$266$	1.39686			0.0856469
$267$		−	5.08157i		−	0.310987i
$268$	−3.61956	+	3.61956i	−0.221100	+	0.221100i
$269$		−	10.5529i		−	0.643424i	−0.946838	−	0.321712i	$-0.895742\pi$
$269$		−	10.5529i		−	0.643424i	0.946838	−	0.321712i	$-0.104258\pi$
$270$	2.93449	−	17.8973i	0.178588	−	1.08919i
$271$	19.2734			1.17078			0.585389	−	0.810753i	$-0.300942\pi$
$271$	19.2734			1.17078			0.585389	+	0.810753i	$0.300942\pi$
$272$			0.334703i			0.0202943i
$273$		−	1.44277i		−	0.0873204i
$274$	−5.48037	−	5.48037i	−0.331081	−	0.331081i
$275$	8.92698	+	3.00826i	0.538317	+	0.181405i
$276$	−9.72436	−	9.72436i	−0.585338	−	0.585338i
$277$	7.82056			0.469892			0.234946	−	0.972008i	$-0.424509\pi$
$277$	7.82056			0.469892			0.234946	+	0.972008i	$0.424509\pi$
$278$	−4.24414			−0.254546
$279$	28.1953	+	28.1953i	1.68801	+	1.68801i
$280$	−2.00844	−	0.329310i	−0.120027	−	0.0196800i
$281$	−10.4788	−	10.4788i	−0.625110	−	0.625110i	0.321723	−	0.946834i	$-0.395738\pi$
$281$	−10.4788	−	10.4788i	−0.625110	−	0.625110i	−0.946834	+	0.321723i	$0.895738\pi$
$282$		−	0.591849i		−	0.0352441i
$283$		−	26.3960i		−	1.56908i	−0.620079	−	0.784539i	$-0.712900\pi$
$283$		−	26.3960i		−	1.56908i	0.620079	−	0.784539i	$-0.287100\pi$
$284$	15.5121			0.920477
$285$	8.24133	−	5.91948i	0.488174	−	0.350640i
$286$			1.01000i			0.0597228i
$287$	5.31930	−	5.31930i	0.313989	−	0.313989i
$288$		−	5.74304i		−	0.338412i
$289$	16.8880			0.993410
$290$	10.3927	+	1.70401i	0.610278	+	0.100063i
$291$	−35.9134	+	35.9134i	−2.10528	+	2.10528i
$292$	6.82739	+	6.82739i	0.399543	+	0.399543i
$293$	−22.4956	+	22.4956i	−1.31421	+	1.31421i	−0.395928	+	0.918281i	$0.629577\pi$
$293$	−22.4956	+	22.4956i	−1.31421	+	1.31421i	−0.918281	+	0.395928i	$0.870423\pi$
$294$	12.9036	−	12.9036i	0.752552	−	0.752552i
$295$	2.10186	−	12.8191i	0.122375	−	0.746359i
$296$	0.819646	−	6.02729i	0.0476410	−	0.350329i
$297$	10.8054	+	10.8054i	0.626990	+	0.626990i
$298$		−	20.3080i		−	1.17641i
$299$	−2.49331			−0.144192
$300$	−13.2451	+	6.56829i	−0.764708	+	0.379221i
$301$	−7.66643	−	7.66643i	−0.441886	−	0.441886i
$302$		−	13.8362i		−	0.796183i
$303$	−28.1584	+	28.1584i	−1.61766	+	1.61766i
$304$	1.08518	−	1.08518i	0.0622395	−	0.0622395i
$305$	4.55473	−	27.7790i	0.260803	−	1.59062i
$306$	1.92221			0.109885
$307$	−17.4358	+	17.4358i	−0.995111	+	0.995111i	−0.999988	−	0.00487690i	$-0.998448\pi$
$307$	−17.4358	+	17.4358i	−0.995111	+	0.995111i	0.00487690	+	0.999988i	$0.498448\pi$
$308$	1.21258	−	1.21258i	0.0690932	−	0.0690932i
$309$	26.3864	−	26.3864i	1.50107	−	1.50107i
$310$	2.51201	−	15.3206i	0.142672	−	0.870150i
$311$	−3.97519	+	3.97519i	−0.225412	+	0.225412i	−0.810773	−	0.585361i	$-0.800953\pi$
$311$	−3.97519	+	3.97519i	−0.225412	+	0.225412i	0.585361	+	0.810773i	$0.300953\pi$
$312$	−1.12085	−	1.12085i	−0.0634557	−	0.0634557i
$313$	15.8472			0.895735			0.447867	−	0.894100i	$-0.352184\pi$
$313$	15.8472			0.895735			0.447867	+	0.894100i	$0.352184\pi$
$314$	−13.2682	−	13.2682i	−0.748770	−	0.748770i
$315$	−1.89124	+	11.5345i	−0.106559	+	0.649898i
$316$	−5.73637	+	5.73637i	−0.322696	+	0.322696i
$317$	0.950144	−	0.950144i	0.0533654	−	0.0533654i	−0.679920	−	0.733286i	$-0.737986\pi$
$317$	0.950144	−	0.950144i	0.0533654	−	0.0533654i	0.733286	+	0.679920i	$0.237986\pi$
$318$	−21.0460			−1.18020
$319$	−6.27449	+	6.27449i	−0.351304	+	0.351304i
$320$	−1.81614	+	1.30447i	−0.101525	+	0.0729222i
$321$			6.89116i			0.384627i
$322$	2.99340	+	2.99340i	0.166816	+	0.166816i
$323$	0.363214	+	0.363214i	0.0202097	+	0.0202097i
$324$	−6.75336			−0.375186
$325$	−0.855965	+	2.54007i	−0.0474804	+	0.140897i
$326$			1.48487i			0.0822394i
$327$	−29.5309			−1.63306
$328$		−	8.26486i		−	0.456350i
$329$			0.182186i			0.0100442i
$330$	2.01555	−	12.2927i	0.110952	−	0.676690i
$331$	−19.3735	−	19.3735i	−1.06486	−	1.06486i	−0.997745	−	0.0671177i	$-0.978620\pi$
$331$	−19.3735	−	19.3735i	−1.06486	−	1.06486i	−0.0671177	−	0.997745i	$-0.521380\pi$
$332$	−7.90475	+	7.90475i	−0.433829	+	0.433829i
$333$	−34.6149	−	4.70726i	−1.89689	−	0.257956i
$334$			4.69210i			0.256740i
$335$	1.85200	−	11.2952i	0.101186	−	0.617124i
$336$			2.69132i			0.146824i
$337$	−3.21128	+	3.21128i	−0.174929	+	0.174929i	−0.789141	−	0.614212i	$-0.789474\pi$
$337$	−3.21128	+	3.21128i	−0.174929	+	0.174929i	0.614212	+	0.789141i	$0.289474\pi$
$338$	12.7126			0.691475
$339$	31.7180	−	31.7180i	1.72268	−	1.72268i
$340$	−0.436611	−	0.607866i	−0.0236785	−	0.0329662i
$341$	9.24969	+	9.24969i	0.500899	+	0.500899i
$342$	−6.23224	−	6.23224i	−0.337001	−	0.337001i
$343$	−8.47727	+	8.47727i	−0.457730	+	0.457730i
$344$	−11.9117			−0.642236
$345$	30.3459	+	4.97561i	1.63377	+	0.267878i
$346$	1.68127	+	1.68127i	0.0903856	+	0.0903856i
$347$	−18.4401			−0.989915			−0.494957	−	0.868917i	$-0.664816\pi$
$347$	−18.4401			−0.989915			−0.494957	+	0.868917i	$0.664816\pi$
$348$		−	13.9262i		−	0.746524i
$349$			21.3314i			1.14184i	0.821005	+	0.570921i	$0.193414\pi$
$349$			21.3314i			1.14184i	−0.821005	+	0.570921i	$0.806586\pi$
$350$	4.07718	−	2.02188i	0.217934	−	0.108074i
$351$	−3.07453	+	3.07453i	−0.164106	+	0.164106i
$352$		−	1.88405i		−	0.100420i
$353$			11.9150i			0.634173i	0.948397	+	0.317086i	$0.102704\pi$
$353$			11.9150i			0.634173i	−0.948397	+	0.317086i	$0.897296\pi$
$354$	−17.1777			−0.912985
$355$	−28.1722	+	20.2352i	−1.49522	+	1.07397i
$356$	1.21521	+	1.21521i	0.0644061	+	0.0644061i
$357$	−0.900793			−0.0476750
$358$	13.0168	+	13.0168i	0.687959	+	0.687959i
$359$			24.9976i			1.31932i	0.751562	+	0.659662i	$0.229301\pi$
$359$			24.9976i			1.31932i	−0.751562	+	0.659662i	$0.770699\pi$
$360$	7.49163	+	10.4301i	0.394844	+	0.549717i
$361$			16.6448i			0.876040i
$362$	−5.91911			−0.311101
$363$	−15.5774	−	15.5774i	−0.817600	−	0.817600i
$364$	0.345025	+	0.345025i	0.0180842	+	0.0180842i
$365$	−21.3056	−	3.49333i	−1.11519	−	0.182849i
$366$	−37.2241			−1.94573
$367$	0.228241	+	0.228241i	0.0119141	+	0.0119141i	0.713039	−	0.701125i	$-0.247318\pi$
$367$	0.228241	+	0.228241i	0.0119141	+	0.0119141i	−0.701125	+	0.713039i	$0.747318\pi$
$368$	4.65098			0.242449
$369$	−47.4654			−2.47095
$370$	6.37384	+	12.0156i	0.331360	+	0.624660i
$371$	6.47848			0.336346
$372$	−20.5297			−1.06441
$373$	5.32431	+	5.32431i	0.275682	+	0.275682i	0.831383	−	0.555700i	$-0.187550\pi$
$373$	5.32431	+	5.32431i	0.275682	+	0.275682i	−0.555700	+	0.831383i	$0.687550\pi$
$374$	0.630595			0.0326073
$375$	15.4868	−	29.2068i	0.799735	−	1.50823i
$376$	0.141535	+	0.141535i	0.00729912	+	0.00729912i
$377$	−1.78533	−	1.78533i	−0.0919492	−	0.0919492i
$378$	7.38239			0.379709
$379$			7.62224i			0.391528i	0.980651	+	0.195764i	$0.0627187\pi$
$379$			7.62224i			0.391528i	−0.980651	+	0.195764i	$0.937281\pi$
$380$	−0.555249	+	3.38643i	−0.0284837	+	0.173720i
$381$			15.0457i			0.770816i
$382$	8.14150	+	8.14150i	0.416556	+	0.416556i
$383$	9.60774			0.490933			0.245466	−	0.969405i	$-0.421059\pi$
$383$	9.60774			0.490933			0.245466	+	0.969405i	$0.421059\pi$
$384$	2.09082	+	2.09082i	0.106697	+	0.106697i
$385$	−0.620435	+	3.78399i	−0.0316203	+	0.192850i
$386$	−15.8717			−0.807848
$387$			68.4093i			3.47744i
$388$		−	17.1767i		−	0.872016i
$389$	−12.3615	+	12.3615i	−0.626751	+	0.626751i	−0.947249	−	0.320498i	$-0.896150\pi$
$389$	−12.3615	+	12.3615i	−0.626751	+	0.626751i	0.320498	+	0.947249i	$0.396150\pi$
$390$	3.49774	+	0.573499i	0.177115	+	0.0290403i
$391$			1.55670i			0.0787256i
$392$			6.17154i			0.311710i
$393$	−31.9326			−1.61079
$394$	−3.60225	−	3.60225i	−0.181479	−	0.181479i
$395$	2.93510	−	17.9010i	0.147681	−	0.900695i
$396$	−10.8201			−0.543732
$397$	22.1034	−	22.1034i	1.10934	−	1.10934i	0.116100	−	0.993238i	$-0.462961\pi$
$397$	22.1034	−	22.1034i	1.10934	−	1.10934i	0.993238	−	0.116100i	$-0.0370394\pi$
$398$	1.14697	+	1.14697i	0.0574923	+	0.0574923i
$399$	2.92058	+	2.92058i	0.146212	+	0.146212i
$400$	1.59670	−	4.73820i	0.0798352	−	0.236910i
$401$	11.3365	−	11.3365i	0.566118	−	0.566118i	−0.364921	−	0.931039i	$-0.618904\pi$
$401$	11.3365	−	11.3365i	0.566118	−	0.566118i	0.931039	+	0.364921i	$0.118904\pi$
$402$	−15.1357			−0.754899
$403$	−2.63189	+	2.63189i	−0.131104	+	0.131104i
$404$		−	13.4676i		−	0.670041i
$405$	12.2650	−	8.80956i	0.609454	−	0.437751i
$406$			4.28683i			0.212752i
$407$	−11.3557	−	1.54425i	−0.562880	−	0.0765456i
$408$	−0.699803	+	0.699803i	−0.0346454	+	0.0346454i
$409$	−10.2703	−	10.2703i	−0.507834	−	0.507834i	0.406027	−	0.913861i	$-0.366914\pi$
$409$	−10.2703	−	10.2703i	−0.507834	−	0.507834i	−0.913861	+	0.406027i	$0.866914\pi$
$410$	10.7813	+	15.0101i	0.532449	+	0.741297i
$411$		−	22.9169i		−	1.13041i
$412$			12.6201i			0.621749i
$413$	5.28772			0.260192
$414$		−	26.7108i		−	1.31276i
$415$	4.04458	−	24.6676i	0.198541	−	1.21089i
$416$	0.536082			0.0262836
$417$	−8.87372	−	8.87372i	−0.434548	−	0.434548i
$418$	−2.04453	−	2.04453i	−0.100001	−	0.100001i
$419$		−	13.8549i		−	0.676854i	−0.940993	−	0.338427i	$-0.890105\pi$
$419$		−	13.8549i		−	0.676854i	0.940993	−	0.338427i	$-0.109895\pi$
$420$	−3.51075	−	4.88781i	−0.171307	−	0.238501i
$421$	−25.5907	+	25.5907i	−1.24722	+	1.24722i	−0.290273	+	0.956944i	$0.593746\pi$
$421$	−25.5907	+	25.5907i	−1.24722	+	1.24722i	−0.956944	+	0.290273i	$0.906254\pi$
$422$	−3.19579			−0.155569
$423$	0.812842	−	0.812842i	0.0395217	−	0.0395217i
$424$	5.03296	−	5.03296i	0.244422	−	0.244422i
$425$	1.58589	+	0.534422i	0.0769269	+	0.0259233i
$426$	32.4331	+	32.4331i	1.57139	+	1.57139i
$427$	11.4585			0.554515
$428$	−1.64796	−	1.64796i	−0.0796571	−	0.0796571i
$429$	−2.11173	+	2.11173i	−0.101955	+	0.101955i
$430$	21.6333	−	15.5385i	1.04325	−	0.749332i
$431$	16.4247	−	16.4247i	0.791148	−	0.791148i	−0.190533	−	0.981681i	$-0.561021\pi$
$431$	16.4247	−	16.4247i	0.791148	−	0.791148i	0.981681	+	0.190533i	$0.0610215\pi$
$432$	5.73519	−	5.73519i	0.275934	−	0.275934i
$433$	7.66855	−	7.66855i	0.368527	−	0.368527i	−0.498413	−	0.866940i	$-0.666084\pi$
$433$	7.66855	−	7.66855i	0.368527	−	0.368527i	0.866940	+	0.498413i	$0.166084\pi$
$434$	6.31954			0.303347
$435$	18.1664	+	25.2919i	0.871011	+	1.21265i
$436$	7.06206	−	7.06206i	0.338211	−	0.338211i
$437$	5.04717	−	5.04717i	0.241439	−	0.241439i
$438$			28.5497i			1.36416i
$439$	22.6564	+	22.6564i	1.08133	+	1.08133i	0.996385	+	0.0849471i	$0.0270721\pi$
$439$	22.6564	+	22.6564i	1.08133	+	1.08133i	0.0849471	+	0.996385i	$0.472928\pi$
$440$	2.45768	+	3.42168i	0.117166	+	0.163122i
$441$	35.4434			1.68778
$442$			0.179428i			0.00853453i
$443$	10.4105	+	10.4105i	0.494616	+	0.494616i	0.909757	−	0.415141i	$-0.136268\pi$
$443$	10.4105	+	10.4105i	0.494616	+	0.494616i	−0.415141	+	0.909757i	$0.636268\pi$
$444$	14.3157	−	10.8882i	0.679392	−	0.516732i
$445$	−3.79220	−	0.621781i	−0.179768	−	0.0294753i
$446$	7.29909	−	7.29909i	0.345622	−	0.345622i
$447$	42.4604	−	42.4604i	2.00831	−	2.00831i
$448$	−0.643605	−	0.643605i	−0.0304075	−	0.0304075i
$449$	−16.6573	+	16.6573i	−0.786107	+	0.786107i	−0.980854	−	0.194746i	$-0.937612\pi$
$449$	−16.6573	+	16.6573i	−0.786107	+	0.786107i	0.194746	+	0.980854i	$0.437612\pi$
$450$	−27.2117	−	9.16993i	−1.28277	−	0.432275i
$451$	−15.5714			−0.733227
$452$			15.1701i			0.713543i
$453$	28.9290	−	28.9290i	1.35920	−	1.35920i
$454$			19.6620i			0.922784i
$455$	−1.07669	−	0.176537i	−0.0504760	−	0.00827619i
$456$	4.53784			0.212504
$457$			39.7899i			1.86129i	0.365919	+	0.930647i	$0.380755\pi$
$457$			39.7899i			1.86129i	−0.365919	+	0.930647i	$0.619245\pi$
$458$		−	13.4975i		−	0.630697i
$459$	1.91958	+	1.91958i	0.0895985	+	0.0895985i
$460$	−8.44682	+	6.06708i	−0.393835	+	0.282879i
$461$	7.71541	+	7.71541i	0.359342	+	0.359342i	0.863570	−	0.504228i	$-0.168223\pi$
$461$	7.71541	+	7.71541i	0.359342	+	0.359342i	−0.504228	+	0.863570i	$0.668223\pi$
$462$	5.07057			0.235904
$463$	14.7430			0.685164			0.342582	−	0.939488i	$-0.388698\pi$
$463$	14.7430			0.685164			0.342582	+	0.939488i	$0.388698\pi$
$464$	3.33033	+	3.33033i	0.154607	+	0.154607i
$465$	37.2847	−	26.7804i	1.72904	−	1.24191i
$466$	1.10924	+	1.10924i	0.0513845	+	0.0513845i
$467$		−	28.4840i		−	1.31808i	−0.752107	−	0.659041i	$-0.770962\pi$
$467$		−	28.4840i		−	1.31808i	0.752107	−	0.659041i	$-0.229038\pi$
$468$		−	3.07874i		−	0.142315i
$469$	4.65913			0.215139
$470$	−0.441676	−	0.0724186i	−0.0203730	−	0.00334042i
$471$		−	55.4829i		−	2.55652i
$472$	4.10789	−	4.10789i	0.189081	−	0.189081i
$473$			22.4422i			1.03189i
$474$	−23.9874			−1.10178
$475$	−3.40909	−	6.87453i	−0.156420	−	0.315425i
$476$	0.215416	−	0.215416i	0.00987360	−	0.00987360i
$477$	−28.9045	−	28.9045i	−1.32344	−	1.32344i
$478$	−10.5161	+	10.5161i	−0.480995	+	0.480995i
$479$	2.09957	−	2.09957i	0.0959318	−	0.0959318i	−0.657512	−	0.753444i	$-0.728391\pi$
$479$	2.09957	−	2.09957i	0.0959318	−	0.0959318i	0.753444	+	0.657512i	$0.228391\pi$
$480$	−6.52462	−	1.06980i	−0.297807	−	0.0488293i
$481$	0.439398	−	3.23112i	0.0200348	−	0.147326i
$482$	18.7617	+	18.7617i	0.854571	+	0.854571i
$483$			12.5173i			0.569557i
$484$	7.45037			0.338653
$485$	22.4066	+	31.1953i	1.01743	+	1.41651i
$486$	3.08553	+	3.08553i	0.139962	+	0.139962i
$487$			17.7878i			0.806044i	0.915190	+	0.403022i	$0.132040\pi$
$487$			17.7878i			0.806044i	−0.915190	+	0.403022i	$0.867960\pi$
$488$	8.90180	−	8.90180i	0.402965	−	0.402965i
$489$	−3.10459	+	3.10459i	−0.140395	+	0.140395i
$490$	−8.05061	−	11.2084i	−0.363689	−	0.506342i
$491$	11.1728			0.504221			0.252110	−	0.967698i	$-0.418875\pi$
$491$	11.1728			0.504221			0.252110	+	0.967698i	$0.418875\pi$
$492$	17.2803	−	17.2803i	0.779056	−	0.779056i
$493$	−1.11467	+	1.11467i	−0.0502022	+	0.0502022i
$494$	0.581747	−	0.581747i	0.0261740	−	0.0261740i
$495$	19.6509	−	14.1146i	0.883240	−	0.634403i
$496$	4.90948	−	4.90948i	0.220442	−	0.220442i
$497$	−9.98370	−	9.98370i	−0.447830	−	0.447830i
$498$	−33.0548			−1.48122
$499$	9.60201	+	9.60201i	0.429845	+	0.429845i	0.888576	−	0.458730i	$-0.151696\pi$
$499$	9.60201	+	9.60201i	0.429845	+	0.429845i	−0.458730	+	0.888576i	$0.651696\pi$
$500$	3.28101	+	10.6881i	0.146731	+	0.477985i
$501$	−9.81033	+	9.81033i	−0.438293	+	0.438293i
$502$	−9.09164	+	9.09164i	−0.405780	+	0.405780i
$503$	−14.7806			−0.659035			−0.329518	−	0.944149i	$-0.606886\pi$
$503$	−14.7806			−0.659035			−0.329518	+	0.944149i	$0.606886\pi$
$504$	−3.69625	+	3.69625i	−0.164644	+	0.164644i
$505$	17.5682	+	24.4591i	0.781773	+	1.08842i
$506$		−	8.76267i		−	0.389548i
$507$	26.5798	+	26.5798i	1.18045	+	1.18045i
$508$	−3.59805	−	3.59805i	−0.159638	−	0.159638i
$509$	4.49759			0.199352			0.0996760	−	0.995020i	$-0.468219\pi$
$509$	4.49759			0.199352			0.0996760	+	0.995020i	$0.468219\pi$
$510$	0.358064	−	2.18381i	0.0158553	−	0.0967007i
$511$		−	8.78829i		−	0.388771i
$512$	−1.00000			−0.0441942
$513$		−	12.4475i		−	0.549568i
$514$			2.08454i			0.0919453i
$515$	−16.4626	−	22.9199i	−0.725429	−	1.00997i
$516$	−24.9052	−	24.9052i	−1.09639	−	1.09639i
$517$	0.266659	−	0.266659i	0.0117276	−	0.0117276i
$518$	−4.40672	+	3.35166i	−0.193620	+	0.147264i
$519$			7.03045i			0.308603i
$520$	−0.973599	+	0.699305i	−0.0426951	+	0.0306665i
$521$			14.5173i			0.636014i	0.948088	+	0.318007i	$0.103014\pi$
$521$			14.5173i			0.636014i	−0.948088	+	0.318007i	$0.896986\pi$
$522$	19.1262	−	19.1262i	0.837131	−	0.837131i
$523$	27.3756			1.19705			0.598526	−	0.801103i	$-0.295753\pi$
$523$	27.3756			1.19705			0.598526	+	0.801103i	$0.295753\pi$
$524$	7.63639	−	7.63639i	0.333597	−	0.333597i
$525$	12.7520	+	4.29725i	0.556544	+	0.187547i
$526$	6.41417	+	6.41417i	0.279671	+	0.279671i
$527$	1.64322	+	1.64322i	0.0715797	+	0.0715797i
$528$	3.93919	−	3.93919i	0.171431	−	0.171431i
$529$	−1.36834			−0.0594930
$530$	−2.57519	+	15.7059i	−0.111859	+	0.682221i
$531$	−23.5918	−	23.5918i	−1.02380	−	1.02380i
$532$	−1.39686			−0.0605615
$533$		−	4.43064i		−	0.191913i
$534$			5.08157i			0.219901i
$535$	5.14264	+	0.843202i	0.222336	+	0.0364548i
$536$	3.61956	−	3.61956i	0.156341	−	0.156341i
$537$			54.4315i			2.34889i
$538$			10.5529i			0.454970i
$539$	11.6275			0.500831
$540$	−2.93449	+	17.8973i	−0.126280	+	0.770176i
$541$	15.0886	+	15.0886i	0.648708	+	0.648708i	0.952681	−	0.303973i	$-0.0983133\pi$
$541$	15.0886	+	15.0886i	0.648708	+	0.648708i	−0.303973	+	0.952681i	$0.598313\pi$
$542$	−19.2734			−0.827865
$543$	−12.3758	−	12.3758i	−0.531095	−	0.531095i
$544$		−	0.334703i		−	0.0143503i
$545$	−3.61340	+	22.0379i	−0.154781	+	0.944001i
$546$			1.44277i			0.0617449i
$547$	−24.9954			−1.06873			−0.534363	−	0.845255i	$-0.679448\pi$
$547$	−24.9954			−1.06873			−0.534363	+	0.845255i	$0.679448\pi$
$548$	5.48037	+	5.48037i	0.234110	+	0.234110i
$549$	−51.1233	−	51.1233i	−2.18189	−	2.18189i
$550$	−8.92698	−	3.00826i	−0.380648	−	0.128273i
$551$	7.22803			0.307924
$552$	9.72436	+	9.72436i	0.413896	+	0.413896i
$553$	7.38391			0.313996
$554$	−7.82056			−0.332264
$555$	−11.7959	+	38.4489i	−0.500706	+	1.63207i
$556$	4.24414			0.179991
$557$	12.4355			0.526909			0.263455	−	0.964672i	$-0.415138\pi$
$557$	12.4355			0.526909			0.263455	+	0.964672i	$0.415138\pi$
$558$	−28.1953	−	28.1953i	−1.19360	−	1.19360i
$559$	−6.38565			−0.270084
$560$	2.00844	+	0.329310i	0.0848721	+	0.0139159i
$561$	1.31846	+	1.31846i	0.0556654	+	0.0556654i
$562$	10.4788	+	10.4788i	0.442020	+	0.442020i
$563$	9.73552			0.410303			0.205152	−	0.978730i	$-0.434231\pi$
$563$	9.73552			0.410303			0.205152	+	0.978730i	$0.434231\pi$
$564$			0.591849i			0.0249213i
$565$	−19.7890	−	27.5510i	−0.832530	−	1.15908i
$566$			26.3960i			1.10951i
$567$	4.34649	+	4.34649i	0.182536	+	0.182536i
$568$	−15.5121			−0.650875
$569$	−10.5582	−	10.5582i	−0.442624	−	0.442624i	0.450269	−	0.892893i	$-0.351328\pi$
$569$	−10.5582	−	10.5582i	−0.442624	−	0.442624i	−0.892893	+	0.450269i	$0.851328\pi$
$570$	−8.24133	+	5.91948i	−0.345191	+	0.247940i
$571$	13.3170			0.557301			0.278650	−	0.960393i	$-0.410113\pi$
$571$	13.3170			0.557301			0.278650	+	0.960393i	$0.410113\pi$
$572$		−	1.01000i		−	0.0422304i
$573$			34.0448i			1.42224i
$574$	−5.31930	+	5.31930i	−0.222023	+	0.222023i
$575$	7.42625	−	22.0373i	0.309696	−	0.919019i
$576$			5.74304i			0.239293i
$577$		−	4.76082i		−	0.198195i	−0.995078	−	0.0990977i	$-0.968404\pi$
$577$		−	4.76082i		−	0.198195i	0.995078	−	0.0990977i	$-0.0315956\pi$
$578$	−16.8880			−0.702447
$579$	−33.1848	−	33.1848i	−1.37911	−	1.37911i
$580$	−10.3927	−	1.70401i	−0.431532	−	0.0707552i
$581$	10.1751			0.422133
$582$	35.9134	−	35.9134i	1.48866	−	1.48866i
$583$	−9.48232	−	9.48232i	−0.392718	−	0.392718i
$584$	−6.82739	−	6.82739i	−0.282519	−	0.282519i
$585$	4.01613	+	5.59141i	0.166047	+	0.231177i
$586$	22.4956	−	22.4956i	0.929287	−	0.929287i
$587$	−2.41574			−0.0997081			−0.0498540	−	0.998757i	$-0.515876\pi$
$587$	−2.41574			−0.0997081			−0.0498540	+	0.998757i	$0.515876\pi$
$588$	−12.9036	+	12.9036i	−0.532134	+	0.532134i
$589$		−	10.6554i		−	0.439047i
$590$	−2.10186	+	12.8191i	−0.0865324	+	0.527755i
$591$		−	15.0633i		−	0.619621i
$592$	−0.819646	+	6.02729i	−0.0336872	+	0.247720i
$593$	1.14068	−	1.14068i	0.0468420	−	0.0468420i	−0.683298	−	0.730140i	$-0.739455\pi$
$593$	1.14068	−	1.14068i	0.0468420	−	0.0468420i	0.730140	+	0.683298i	$0.239455\pi$
$594$	−10.8054	−	10.8054i	−0.443349	−	0.443349i
$595$	−0.110221	+	0.672231i	−0.00451862	+	0.0275588i
$596$			20.3080i			0.831849i
$597$			4.79620i			0.196295i
$598$	2.49331			0.101959
$599$		−	40.0185i		−	1.63511i	−0.575851	−	0.817555i	$-0.695329\pi$
$599$		−	40.0185i		−	1.63511i	0.575851	−	0.817555i	$-0.304671\pi$
$600$	13.2451	−	6.56829i	0.540730	−	0.268149i
$601$	−11.7034			−0.477393			−0.238696	−	0.971094i	$-0.576720\pi$
$601$	−11.7034			−0.477393			−0.238696	+	0.971094i	$0.576720\pi$
$602$	7.66643	+	7.66643i	0.312460	+	0.312460i
$603$	−20.7873	−	20.7873i	−0.846522	−	0.846522i
$604$			13.8362i			0.562987i
$605$	−13.5309	+	9.71881i	−0.550109	+	0.395126i
$606$	28.1584	−	28.1584i	1.14386	−	1.14386i
$607$	24.3851			0.989761			0.494881	−	0.868961i	$-0.335212\pi$
$607$	24.3851			0.989761			0.494881	+	0.868961i	$0.335212\pi$
$608$	−1.08518	+	1.08518i	−0.0440100	+	0.0440100i
$609$	−8.96299	+	8.96299i	−0.363199	+	0.363199i
$610$	−4.55473	+	27.7790i	−0.184416	+	1.12474i
$611$	0.0758746	+	0.0758746i	0.00306956	+	0.00306956i
$612$	−1.92221			−0.0777008
$613$	18.3951	+	18.3951i	0.742971	+	0.742971i	0.973149	−	0.230178i	$-0.0739308\pi$
$613$	18.3951	+	18.3951i	0.742971	+	0.742971i	−0.230178	+	0.973149i	$0.573931\pi$
$614$	17.4358	−	17.4358i	0.703650	−	0.703650i
$615$	−8.84172	+	53.9251i	−0.356533	+	2.17447i
$616$	−1.21258	+	1.21258i	−0.0488563	+	0.0488563i
$617$	31.2896	−	31.2896i	1.25967	−	1.25967i	0.308421	−	0.951250i	$-0.400199\pi$
$617$	31.2896	−	31.2896i	1.25967	−	1.25967i	0.951250	−	0.308421i	$-0.0998006\pi$
$618$	−26.3864	+	26.3864i	−1.06142	+	1.06142i
$619$	−39.6915			−1.59534			−0.797669	−	0.603096i	$-0.793934\pi$
$619$	−39.6915			−1.59534			−0.797669	+	0.603096i	$0.793934\pi$
$620$	−2.51201	+	15.3206i	−0.100885	+	0.615289i
$621$	26.6743	−	26.6743i	1.07040	−	1.07040i
$622$	3.97519	−	3.97519i	0.159391	−	0.159391i
$623$		−	1.56423i		−	0.0626697i
$624$	1.12085	+	1.12085i	0.0448699	+	0.0448699i
$625$	−19.9011	−	15.1310i	−0.796043	−	0.605240i
$626$	−15.8472			−0.633380
$627$		−	8.54949i		−	0.341434i
$628$	13.2682	+	13.2682i	0.529460	+	0.529460i
$629$	−2.01735	−	0.274338i	−0.0804370	−	0.0109386i
$630$	1.89124	−	11.5345i	0.0753488	−	0.459547i
$631$	−29.5138	+	29.5138i	−1.17493	+	1.17493i	−0.193907	+	0.981020i	$0.562116\pi$
$631$	−29.5138	+	29.5138i	−1.17493	+	1.17493i	−0.981020	+	0.193907i	$0.937884\pi$
$632$	5.73637	−	5.73637i	0.228181	−	0.228181i
$633$	−6.68182	−	6.68182i	−0.265579	−	0.265579i
$634$	−0.950144	+	0.950144i	−0.0377350	+	0.0377350i
$635$	11.2281	+	1.84099i	0.445574	+	0.0730576i
$636$	21.0460			0.834528
$637$			3.30846i			0.131086i
$638$	6.27449	−	6.27449i	0.248409	−	0.248409i
$639$			89.0868i			3.52422i
$640$	1.81614	−	1.30447i	0.0717891	−	0.0515638i
$641$	−36.0367			−1.42336			−0.711681	−	0.702503i	$-0.752066\pi$
$641$	−36.0367			−1.42336			−0.711681	+	0.702503i	$0.752066\pi$
$642$		−	6.89116i		−	0.271973i
$643$			36.2733i			1.43048i	0.698880	+	0.715239i	$0.253682\pi$
$643$			36.2733i			1.43048i	−0.698880	+	0.715239i	$0.746318\pi$
$644$	−2.99340	−	2.99340i	−0.117956	−	0.117956i
$645$	77.7194	+	12.7431i	3.06020	+	0.501759i
$646$	−0.363214	−	0.363214i	−0.0142905	−	0.0142905i
$647$	20.1761			0.793203			0.396602	−	0.917991i	$-0.370189\pi$
$647$	20.1761			0.793203			0.396602	+	0.917991i	$0.370189\pi$
$648$	6.75336			0.265297
$649$	−7.73946	−	7.73946i	−0.303800	−	0.303800i
$650$	0.855965	−	2.54007i	0.0335737	−	0.0996296i
$651$	13.2130	+	13.2130i	0.517858	+	0.517858i
$652$		−	1.48487i		−	0.0581520i
$653$		−	45.2272i		−	1.76988i	−0.465706	−	0.884939i	$-0.654200\pi$
$653$		−	45.2272i		−	1.76988i	0.465706	−	0.884939i	$-0.345800\pi$
$654$	29.5309			1.15475
$655$	−3.90727	+	23.8302i	−0.152670	+	0.931122i
$656$			8.26486i			0.322688i
$657$	−39.2100	+	39.2100i	−1.52973	+	1.52973i
$658$		−	0.182186i		−	0.00710234i
$659$	−3.64301			−0.141911			−0.0709557	−	0.997479i	$-0.522605\pi$
$659$	−3.64301			−0.141911			−0.0709557	+	0.997479i	$0.522605\pi$
$660$	−2.01555	+	12.2927i	−0.0784550	+	0.478492i
$661$	0.359733	−	0.359733i	0.0139920	−	0.0139920i	−0.700076	−	0.714068i	$-0.746851\pi$
$661$	0.359733	−	0.359733i	0.0139920	−	0.0139920i	0.714068	+	0.700076i	$0.246851\pi$
$662$	19.3735	+	19.3735i	0.752972	+	0.752972i
$663$	−0.375152	+	0.375152i	−0.0145697	+	0.0145697i
$664$	7.90475	−	7.90475i	0.306764	−	0.306764i
$665$	2.53689	−	1.82216i	0.0983762	−	0.0706604i
$666$	34.6149	+	4.70726i	1.34130	+	0.182402i
$667$	15.4893	+	15.4893i	0.599749	+	0.599749i
$668$		−	4.69210i		−	0.181543i
$669$	30.5221			1.18005
$670$	−1.85200	+	11.2952i	−0.0715490	+	0.436373i
$671$	−16.7714	−	16.7714i	−0.647452	−	0.647452i
$672$		−	2.69132i		−	0.103820i
$673$	12.3228	−	12.3228i	0.475011	−	0.475011i	−0.428521	−	0.903532i	$-0.640965\pi$
$673$	12.3228	−	12.3228i	0.475011	−	0.475011i	0.903532	+	0.428521i	$0.140965\pi$
$674$	3.21128	−	3.21128i	0.123694	−	0.123694i
$675$	−18.0171	−	36.3319i	−0.693477	−	1.39841i
$676$	−12.7126			−0.488947
$677$	13.3890	−	13.3890i	0.514579	−	0.514579i	−0.401347	−	0.915926i	$-0.631458\pi$
$677$	13.3890	−	13.3890i	0.514579	−	0.514579i	0.915926	+	0.401347i	$0.131458\pi$
$678$	−31.7180	+	31.7180i	−1.21812	+	1.21812i
$679$	−11.0550	+	11.0550i	−0.424253	+	0.424253i
$680$	0.436611	+	0.607866i	0.0167433	+	0.0233106i
$681$	−41.1097	+	41.1097i	−1.57533	+	1.57533i
$682$	−9.24969	−	9.24969i	−0.354189	−	0.354189i
$683$	26.4505			1.01210			0.506050	−	0.862504i	$-0.331105\pi$
$683$	26.4505			1.01210			0.506050	+	0.862504i	$0.331105\pi$
$684$	6.23224	+	6.23224i	0.238296	+	0.238296i
$685$	−17.1021	−	2.80411i	−0.653437	−	0.107140i
$686$	8.47727	−	8.47727i	0.323664	−	0.323664i
$687$	28.2208	−	28.2208i	1.07669	−	1.07669i
$688$	11.9117			0.454129
$689$	2.69808	−	2.69808i	0.102789	−	0.102789i
$690$	−30.3459	−	4.97561i	−1.15525	−	0.189418i
$691$		−	8.34143i		−	0.317323i	−0.987333	−	0.158661i	$-0.949282\pi$
$691$		−	8.34143i		−	0.317323i	0.987333	−	0.158661i	$-0.0507178\pi$
$692$	−1.68127	−	1.68127i	−0.0639123	−	0.0639123i
$693$	6.96390	+	6.96390i	0.264537	+	0.264537i
$694$	18.4401			0.699976
$695$	−7.70793	+	5.53636i	−0.292379	+	0.210006i
$696$			13.9262i			0.527872i
$697$	−2.76627			−0.104780
$698$		−	21.3314i		−	0.807405i
$699$			4.63843i			0.175442i
$700$	−4.07718	+	2.02188i	−0.154103	+	0.0764200i
$701$	15.0534	+	15.0534i	0.568560	+	0.568560i	0.931725	−	0.363165i	$-0.118304\pi$
$701$	15.0534	+	15.0534i	0.568560	+	0.568560i	−0.363165	+	0.931725i	$0.618304\pi$
$702$	3.07453	−	3.07453i	0.116041	−	0.116041i
$703$	5.65124	+	7.43017i	0.213141	+	0.280234i
$704$			1.88405i			0.0710076i
$705$	−0.772050	−	1.07488i	−0.0290771	−	0.0404823i
$706$		−	11.9150i		−	0.448428i
$707$	−8.66785	+	8.66785i	−0.325988	+	0.325988i
$708$	17.1777			0.645578
$709$	26.5041	−	26.5041i	0.995384	−	0.995384i	−0.00460560	−	0.999989i	$-0.501466\pi$
$709$	26.5041	−	26.5041i	0.995384	−	0.995384i	0.999989	+	0.00460560i	$0.00146601\pi$
$710$	28.1722	−	20.2352i	1.05728	−	0.759412i
$711$	−32.9442	−	32.9442i	−1.23550	−	1.23550i
$712$	−1.21521	−	1.21521i	−0.0455420	−	0.0455420i
$713$	22.8339	−	22.8339i	0.855137	−	0.855137i
$714$	0.900793			0.0337113
$715$	1.31752	+	1.83430i	0.0492725	+	0.0685991i
$716$	−13.0168	−	13.0168i	−0.486461	−	0.486461i
$717$	−43.9745			−1.64226
$718$		−	24.9976i		−	0.932903i
$719$		−	17.0904i		−	0.637364i	−0.947862	−	0.318682i	$-0.896760\pi$
$719$		−	17.0904i		−	0.637364i	0.947862	−	0.318682i	$-0.103240\pi$
$720$	−7.49163	−	10.4301i	−0.279197	−	0.388708i
$721$	8.12238	−	8.12238i	0.302493	−	0.302493i
$722$		−	16.6448i		−	0.619454i
$723$			78.4545i			2.91775i
$724$	5.91911			0.219982
$725$	21.0973	−	10.4622i	0.783535	−	0.388557i
$726$	15.5774	+	15.5774i	0.578131	+	0.578131i
$727$	−49.5068			−1.83611			−0.918053	−	0.396457i	$-0.870240\pi$
$727$	−49.5068			−1.83611			−0.918053	+	0.396457i	$0.870240\pi$
$728$	−0.345025	−	0.345025i	−0.0127875	−	0.0127875i
$729$			33.1626i			1.22825i
$730$	21.3056	+	3.49333i	0.788556	+	0.129294i
$731$			3.98688i			0.147460i
$732$	37.2241			1.37584
$733$	8.80945	+	8.80945i	0.325385	+	0.325385i	0.850828	−	0.525444i	$-0.176101\pi$
$733$	8.80945	+	8.80945i	0.325385	+	0.325385i	−0.525444	+	0.850828i	$0.676101\pi$
$734$	−0.228241	−	0.228241i	−0.00842451	−	0.00842451i
$735$	6.60230	−	40.2670i	0.243530	−	1.48527i
$736$	−4.65098			−0.171438
$737$	−6.81941	−	6.81941i	−0.251196	−	0.251196i
$738$	47.4654			1.74722
$739$	−44.3001			−1.62961			−0.814803	−	0.579738i	$-0.803155\pi$
$739$	−44.3001			−1.62961			−0.814803	+	0.579738i	$0.803155\pi$
$740$	−6.37384	−	12.0156i	−0.234307	−	0.441702i
$741$	2.43265			0.0893658
$742$	−6.47848			−0.237832
$743$	−16.9715	−	16.9715i	−0.622623	−	0.622623i	0.323579	−	0.946201i	$-0.395114\pi$
$743$	−16.9715	−	16.9715i	−0.622623	−	0.622623i	−0.946201	+	0.323579i	$0.895114\pi$
$744$	20.5297			0.752654
$745$	−26.4913	−	36.8822i	−0.970564	−	1.35126i
$746$	−5.32431	−	5.32431i	−0.194937	−	0.194937i
$747$	−45.3972	−	45.3972i	−1.66100	−	1.66100i
$748$	−0.630595			−0.0230568
$749$			2.12127i			0.0775095i
$750$	−15.4868	+	29.2068i	−0.565498	+	1.06648i
$751$			10.2040i			0.372350i	0.982517	+	0.186175i	$0.0596091\pi$
$751$			10.2040i			0.372350i	−0.982517	+	0.186175i	$0.940391\pi$
$752$	−0.141535	−	0.141535i	−0.00516126	−	0.00516126i
$753$	−38.0179			−1.38545
$754$	1.78533	+	1.78533i	0.0650179	+	0.0650179i
$755$	−18.0489	−	25.1284i	−0.656868	−	0.914517i
$756$	−7.38239			−0.268495
$757$			6.71387i			0.244020i	0.992529	+	0.122010i	$0.0389340\pi$
$757$			6.71387i			0.244020i	−0.992529	+	0.122010i	$0.961066\pi$
$758$		−	7.62224i		−	0.276852i
$759$	18.3211	−	18.3211i	0.665015	−	0.665015i
$760$	0.555249	−	3.38643i	0.0201410	−	0.122839i
$761$			1.33026i			0.0482218i	0.999709	+	0.0241109i	$0.00767549\pi$
$761$			1.33026i			0.0482218i	−0.999709	+	0.0241109i	$0.992325\pi$
$762$		−	15.0457i		−	0.545049i
$763$	−9.09035			−0.329093
$764$	−8.14150	−	8.14150i	−0.294549	−	0.294549i
$765$	3.49100	−	2.50747i	0.126217	−	0.0906578i
$766$	−9.60774			−0.347142
$767$	2.20217	−	2.20217i	0.0795157	−	0.0795157i
$768$	−2.09082	−	2.09082i	−0.0754459	−	0.0754459i
$769$	18.1678	+	18.1678i	0.655148	+	0.655148i	0.954228	−	0.299080i	$-0.0966797\pi$
$769$	18.1678	+	18.1678i	0.655148	+	0.655148i	−0.299080	+	0.954228i	$0.596680\pi$
$770$	0.620435	−	3.78399i	0.0223589	−	0.136366i
$771$	−4.35840	+	4.35840i	−0.156964	+	0.156964i
$772$	15.8717			0.571235
$773$	19.9474	−	19.9474i	0.717458	−	0.717458i	−0.250626	−	0.968084i	$-0.580637\pi$
$773$	19.9474	−	19.9474i	0.717458	−	0.717458i	0.968084	+	0.250626i	$0.0806365\pi$
$774$		−	68.4093i		−	2.45892i
$775$	−15.4231	−	31.1011i	−0.554015	−	1.11718i
$776$			17.1767i			0.616609i
$777$	−16.2214	−	2.20593i	−0.581938	−	0.0791373i
$778$	12.3615	−	12.3615i	0.443180	−	0.443180i
$779$	8.96888	+	8.96888i	0.321343	+	0.321343i
$780$	−3.49774	−	0.573499i	−0.125239	−	0.0205346i
$781$			29.2256i			1.04577i
$782$		−	1.55670i		−	0.0556674i
$783$	38.2001			1.36516
$784$		−	6.17154i		−	0.220412i
$785$	−41.4050	−	6.78889i	−1.47781	−	0.242306i
$786$	31.9326			1.13900
$787$	34.1482	+	34.1482i	1.21725	+	1.21725i	0.968590	+	0.248663i	$0.0799912\pi$
$787$	34.1482	+	34.1482i	1.21725	+	1.21725i	0.248663	+	0.968590i	$0.420009\pi$
$788$	3.60225	+	3.60225i	0.128325	+	0.128325i
$789$			26.8217i			0.954878i
$790$	−2.93510	+	17.9010i	−0.104426	+	0.636888i
$791$	9.76357	−	9.76357i	0.347153	−	0.347153i
$792$	10.8201			0.384477
$793$	4.77210	−	4.77210i	0.169462	−	0.169462i
$794$	−22.1034	+	22.1034i	−0.784420	+	0.784420i
$795$	−38.2224	+	27.4539i	−1.35561	+	0.973690i
$796$	−1.14697	−	1.14697i	−0.0406532	−	0.0406532i
$797$	−48.5605			−1.72010			−0.860050	−	0.510209i	$-0.829568\pi$
$797$	−48.5605			−1.72010			−0.860050	+	0.510209i	$0.829568\pi$
$798$	−2.92058	−	2.92058i	−0.103387	−	0.103387i
$799$	0.0473723	−	0.0473723i	0.00167591	−	0.00167591i
$800$	−1.59670	+	4.73820i	−0.0564520	+	0.167521i
$801$	−6.97901	+	6.97901i	−0.246591	+	0.246591i
$802$	−11.3365	+	11.3365i	−0.400306	+	0.400306i
$803$	−12.8631	+	12.8631i	−0.453929	+	0.453929i
$804$	15.1357			0.533794
$805$	9.34122	+	1.53162i	0.329235	+	0.0539824i
$806$	2.63189	−	2.63189i	0.0927043	−	0.0927043i
$807$	−22.0643	+	22.0643i	−0.776699	+	0.776699i
$808$			13.4676i			0.473790i
$809$	18.4675	+	18.4675i	0.649284	+	0.649284i	0.952820	−	0.303536i	$-0.0981674\pi$
$809$	18.4675	+	18.4675i	0.649284	+	0.649284i	−0.303536	+	0.952820i	$0.598167\pi$
$810$	−12.2650	+	8.80956i	−0.430949	+	0.309537i
$811$	−41.1929			−1.44648			−0.723238	−	0.690598i	$-0.757347\pi$
$811$	−41.1929			−1.44648			−0.723238	+	0.690598i	$0.757347\pi$
$812$		−	4.28683i		−	0.150438i
$813$	−40.2972	−	40.2972i	−1.41329	−	1.41329i
$814$	11.3557	+	1.54425i	0.398016	+	0.0541259i
$815$	1.93697	+	2.69673i	0.0678492	+	0.0944623i
$816$	0.699803	−	0.699803i	0.0244980	−	0.0244980i
$817$	12.9264	−	12.9264i	0.452236	−	0.452236i
$818$	10.2703	+	10.2703i	0.359093	+	0.359093i
$819$	−1.98149	+	1.98149i	−0.0692390	+	0.0692390i
$820$	−10.7813	−	15.0101i	−0.376498	−	0.524176i
$821$	54.6337			1.90673			0.953364	−	0.301822i	$-0.0975948\pi$
$821$	54.6337			1.90673			0.953364	+	0.301822i	$0.0975948\pi$
$822$			22.9169i			0.799319i
$823$	38.9987	−	38.9987i	1.35941	−	1.35941i	0.484768	−	0.874643i	$-0.338904\pi$
$823$	38.9987	−	38.9987i	1.35941	−	1.35941i	0.874643	−	0.484768i	$-0.161096\pi$
$824$		−	12.6201i		−	0.439643i
$825$	−12.3750	−	24.9544i	−0.430841	−	0.868801i
$826$	−5.28772			−0.183983
$827$		−	1.62207i		−	0.0564050i	−0.999602	−	0.0282025i	$-0.991022\pi$
$827$		−	1.62207i		−	0.0564050i	0.999602	−	0.0282025i	$-0.00897832\pi$
$828$			26.7108i			0.928264i
$829$	28.1215	+	28.1215i	0.976699	+	0.976699i	0.999735	−	0.0230357i	$-0.00733314\pi$
$829$	28.1215	+	28.1215i	0.976699	+	0.976699i	−0.0230357	+	0.999735i	$0.507333\pi$
$830$	−4.04458	+	24.6676i	−0.140389	+	0.856226i
$831$	−16.3514	−	16.3514i	−0.567222	−	0.567222i
$832$	−0.536082			−0.0185853
$833$	2.06563			0.0715700
$834$	8.87372	+	8.87372i	0.307272	+	0.307272i
$835$	6.12071	+	8.52150i	0.211816	+	0.294899i
$836$	2.04453	+	2.04453i	0.0707116	+	0.0707116i
$837$		−	56.3136i		−	1.94648i
$838$			13.8549i			0.478608i
$839$	−35.3409			−1.22010			−0.610052	−	0.792361i	$-0.708851\pi$
$839$	−35.3409			−1.22010			−0.610052	+	0.792361i	$0.708851\pi$
$840$	3.51075	+	4.88781i	0.121133	+	0.168645i
$841$		−	6.81781i		−	0.235097i
$842$	25.5907	−	25.5907i	0.881915	−	0.881915i
$843$			43.8183i			1.50918i
$844$	3.19579			0.110004
$845$	23.0878	−	16.5833i	0.794246	−	0.570481i
$846$	−0.812842	+	0.812842i	−0.0279461	+	0.0279461i
$847$	−4.79510	−	4.79510i	−0.164762	−	0.164762i
$848$	−5.03296	+	5.03296i	−0.172833	+	0.172833i
$849$	−55.1892	+	55.1892i	−1.89409	+	1.89409i
$850$	−1.58589	−	0.534422i	−0.0543955	−	0.0183305i
$851$	−3.81216	+	28.0328i	−0.130679	+	0.960953i
$852$	−32.4331	−	32.4331i	−1.11114	−	1.11114i
$853$		−	42.8331i		−	1.46658i	−0.679917	−	0.733289i	$-0.737984\pi$
$853$		−	42.8331i		−	1.46658i	0.679917	−	0.733289i	$-0.262016\pi$
$854$	−11.4585			−0.392101
$855$	−19.4484	−	3.18882i	−0.665121	−	0.109055i
$856$	1.64796	+	1.64796i	0.0563261	+	0.0563261i
$857$		−	9.21841i		−	0.314895i	−0.987527	−	0.157447i	$-0.949674\pi$
$857$		−	9.21841i		−	0.314895i	0.987527	−	0.157447i	$-0.0503265\pi$
$858$	2.11173	−	2.11173i	0.0720934	−	0.0720934i
$859$	−26.7930	+	26.7930i	−0.914167	+	0.914167i	−0.996597	−	0.0824302i	$-0.973732\pi$
$859$	−26.7930	+	26.7930i	−0.914167	+	0.914167i	0.0824302	+	0.996597i	$0.473732\pi$
$860$	−21.6333	+	15.5385i	−0.737689	+	0.529858i
$861$	−22.2434			−0.758053
$862$	−16.4247	+	16.4247i	−0.559426	+	0.559426i
$863$	−28.1937	+	28.1937i	−0.959726	+	0.959726i	−0.999220	−	0.0394943i	$-0.987425\pi$
$863$	−28.1937	+	28.1937i	−0.959726	+	0.959726i	0.0394943	+	0.999220i	$0.487425\pi$
$864$	−5.73519	+	5.73519i	−0.195115	+	0.195115i
$865$	5.24658	+	0.860246i	0.178389	+	0.0292492i
$866$	−7.66855	+	7.66855i	−0.260588	+	0.260588i
$867$	−35.3097	−	35.3097i	−1.19918	−	1.19918i
$868$	−6.31954			−0.214499
$869$	−10.8076	−	10.8076i	−0.366622	−	0.366622i
$870$	−18.1664	−	25.2919i	−0.615898	−	0.857476i
$871$	1.94038	−	1.94038i	0.0657473	−	0.0657473i
$872$	−7.06206	+	7.06206i	−0.239151	+	0.239151i
$873$	98.6466			3.33868
$874$	−5.04717	+	5.04717i	−0.170723	+	0.170723i
$875$	4.76722	−	8.99058i	0.161162	−	0.303937i
$876$		−	28.5497i		−	0.964604i
$877$	19.0689	+	19.0689i	0.643910	+	0.643910i	0.951514	−	0.307604i	$-0.0995274\pi$
$877$	19.0689	+	19.0689i	0.643910	+	0.643910i	−0.307604	+	0.951514i	$0.599527\pi$
$878$	−22.6564	−	22.6564i	−0.764618	−	0.764618i
$879$	94.0686			3.17285
$880$	−2.45768	−	3.42168i	−0.0828485	−	0.115345i
$881$		−	2.04078i		−	0.0687555i	−0.999409	−	0.0343777i	$-0.989055\pi$
$881$		−	2.04078i		−	0.0687555i	0.999409	−	0.0343777i	$-0.0109449\pi$
$882$	−35.4434			−1.19344
$883$		−	46.2566i		−	1.55666i	−0.627857	−	0.778329i	$-0.716068\pi$
$883$		−	46.2566i		−	1.55666i	0.627857	−	0.778329i	$-0.283932\pi$
$884$		−	0.179428i		−	0.00603483i
$885$	−31.1971	+	22.4078i	−1.04868	+	0.753232i
$886$	−10.4105	−	10.4105i	−0.349746	−	0.349746i
$887$	−31.6807	+	31.6807i	−1.06373	+	1.06373i	−0.0659094	+	0.997826i	$0.520995\pi$
$887$	−31.6807	+	31.6807i	−1.06373	+	1.06373i	−0.997826	+	0.0659094i	$0.979005\pi$
$888$	−14.3157	+	10.8882i	−0.480403	+	0.365385i
$889$			4.63145i			0.155334i
$890$	3.79220	+	0.621781i	0.127115	+	0.0208421i
$891$		−	12.7236i		−	0.426258i
$892$	−7.29909	+	7.29909i	−0.244392	+	0.244392i
$893$	−0.307183			−0.0102795
$894$	−42.4604	+	42.4604i	−1.42009	+	1.42009i
$895$	40.6203	+	6.66024i	1.35779	+	0.222627i
$896$	0.643605	+	0.643605i	0.0215013	+	0.0215013i
$897$	5.21306	+	5.21306i	0.174059	+	0.174059i
$898$	16.6573	−	16.6573i	0.555862	−	0.555862i
$899$	32.7004			1.09062
$900$	27.2117	+	9.16993i	0.907055	+	0.305664i
$901$	−1.68455	−	1.68455i	−0.0561204	−	0.0561204i
$902$	15.5714			0.518470
$903$			32.0582i			1.06683i
$904$		−	15.1701i		−	0.504551i
$905$	−10.7499	+	7.72131i	−0.357339	+	0.256665i
$906$	−28.9290	+	28.9290i	−0.961100	+	0.961100i
$907$		−	36.2975i		−	1.20524i	−0.798029	−	0.602620i	$-0.794124\pi$
$907$		−	36.2975i		−	1.20524i	0.798029	−	0.602620i	$-0.205876\pi$
$908$		−	19.6620i		−	0.652507i
$909$	77.3452			2.56538
$910$	1.07669	+	0.176537i	0.0356919	+	0.00585215i
$911$	−5.83123	−	5.83123i	−0.193197	−	0.193197i	0.603879	−	0.797076i	$-0.293621\pi$
$911$	−5.83123	−	5.83123i	−0.193197	−	0.193197i	−0.797076	+	0.603879i	$0.793621\pi$
$912$	−4.53784			−0.150263
$913$	−14.8929	−	14.8929i	−0.492883	−	0.492883i
$914$		−	39.7899i		−	1.31613i
$915$	−67.6040	+	48.5578i	−2.23492	+	1.60527i
$916$			13.4975i			0.445970i
$917$	−9.82963			−0.324603
$918$	−1.91958	−	1.91958i	−0.0633557	−	0.0633557i
$919$	−10.4404	−	10.4404i	−0.344396	−	0.344396i	0.513621	−	0.858017i	$-0.328304\pi$
$919$	−10.4404	−	10.4404i	−0.344396	−	0.344396i	−0.858017	+	0.513621i	$0.828304\pi$
$920$	8.44682	−	6.06708i	0.278484	−	0.200026i
$921$	72.9100			2.40247
$922$	−7.71541	−	7.71541i	−0.254093	−	0.254093i
$923$	−8.31579			−0.273718
$924$	−5.07057			−0.166810
$925$	27.2498	+	13.5074i	0.895966	+	0.444122i
$926$	−14.7430			−0.484484
$927$	−72.4779			−2.38049
$928$	−3.33033	−	3.33033i	−0.109323	−	0.109323i
$929$	−24.9525			−0.818666			−0.409333	−	0.912385i	$-0.634239\pi$
$929$	−24.9525			−0.818666			−0.409333	+	0.912385i	$0.634239\pi$
$930$	−37.2847	+	26.7804i	−1.22261	+	0.878163i
$931$	−6.69725	−	6.69725i	−0.219494	−	0.219494i
$932$	−1.10924	−	1.10924i	−0.0363343	−	0.0363343i
$933$	16.6228			0.544206
$934$			28.4840i			0.932025i
$935$	1.14525	−	0.822594i	0.0374536	−	0.0269017i
$936$			3.07874i			0.100632i
$937$	−27.8220	−	27.8220i	−0.908904	−	0.908904i	0.0872802	−	0.996184i	$-0.472182\pi$
$937$	−27.8220	−	27.8220i	−0.908904	−	0.908904i	−0.996184	+	0.0872802i	$0.972182\pi$
$938$	−4.65913			−0.152126
$939$	−33.1335	−	33.1335i	−1.08127	−	1.08127i
$940$	0.441676	+	0.0724186i	0.0144059	+	0.00236203i
$941$	29.9817			0.977374			0.488687	−	0.872459i	$-0.337476\pi$
$941$	29.9817			0.977374			0.488687	+	0.872459i	$0.337476\pi$
$942$			55.4829i			1.80773i
$943$			38.4397i			1.25177i
$944$	−4.10789	+	4.10789i	−0.133701	+	0.133701i
$945$	13.4074	−	9.63013i	0.436144	−	0.313268i
$946$		−	22.4422i		−	0.729658i
$947$		−	26.4941i		−	0.860941i	−0.902605	−	0.430471i	$-0.858348\pi$
$947$		−	26.4941i		−	0.860941i	0.902605	−	0.430471i	$-0.141652\pi$
$948$	23.9874			0.779075
$949$	−3.66004	−	3.66004i	−0.118810	−	0.118810i
$950$	3.40909	+	6.87453i	0.110606	+	0.223039i
$951$	−3.97316			−0.128838
$952$	−0.215416	+	0.215416i	−0.00698169	+	0.00698169i
$953$	−16.5640	−	16.5640i	−0.536561	−	0.536561i	0.385956	−	0.922517i	$-0.373872\pi$
$953$	−16.5640	−	16.5640i	−0.536561	−	0.536561i	−0.922517	+	0.385956i	$0.873872\pi$
$954$	28.9045	+	28.9045i	0.935817	+	0.935817i
$955$	25.4064	+	4.16572i	0.822133	+	0.134800i
$956$	10.5161	−	10.5161i	0.340115	−	0.340115i
$957$	26.2376			0.848142
$958$	−2.09957	+	2.09957i	−0.0678340	+	0.0678340i
$959$		−	7.05439i		−	0.227798i
$960$	6.52462	+	1.06980i	0.210581	+	0.0345276i
$961$		−	17.2060i		−	0.555033i
$962$	−0.439398	+	3.23112i	−0.0141668	+	0.104176i
$963$	9.46429	−	9.46429i	0.304982	−	0.304982i
$964$	−18.7617	−	18.7617i	−0.604273	−	0.604273i
$965$	−28.8252	+	20.7042i	−0.927915	+	0.666491i
$966$		−	12.5173i		−	0.402737i
$967$			4.61124i			0.148288i	0.997248	+	0.0741438i	$0.0236224\pi$
$967$			4.61124i			0.148288i	−0.997248	+	0.0741438i	$0.976378\pi$
$968$	−7.45037			−0.239464
$969$		−	1.51883i		−	0.0487918i
$970$	−22.4066	−	31.1953i	−0.719432	−	1.00162i
$971$	−27.9365			−0.896524			−0.448262	−	0.893902i	$-0.647957\pi$
$971$	−27.9365			−0.896524			−0.448262	+	0.893902i	$0.647957\pi$
$972$	−3.08553	−	3.08553i	−0.0989684	−	0.0989684i
$973$	−2.73155	−	2.73155i	−0.0875694	−	0.0875694i
$974$		−	17.7878i		−	0.569959i
$975$	7.10048	−	3.52115i	0.227397	−	0.112767i
$976$	−8.90180	+	8.90180i	−0.284940	+	0.284940i
$977$	6.07748			0.194436			0.0972180	−	0.995263i	$-0.469006\pi$
$977$	6.07748			0.194436			0.0972180	+	0.995263i	$0.469006\pi$
$978$	3.10459	−	3.10459i	0.0992739	−	0.0992739i
$979$	−2.28951	+	2.28951i	−0.0731732	+	0.0731732i
$980$	8.05061	+	11.2084i	0.257167	+	0.358038i
$981$	40.5576	+	40.5576i	1.29491	+	1.29491i
$982$	−11.1728			−0.356538
$983$	18.5414	+	18.5414i	0.591379	+	0.591379i	0.938004	−	0.346625i	$-0.112672\pi$
$983$	18.5414	+	18.5414i	0.591379	+	0.591379i	−0.346625	+	0.938004i	$0.612672\pi$
$984$	−17.2803	+	17.2803i	−0.550876	+	0.550876i
$985$	−11.2412	−	1.84314i	−0.358175	−	0.0587274i
$986$	1.11467	−	1.11467i	0.0354983	−	0.0354983i
$987$	0.380917	−	0.380917i	0.0121247	−	0.0121247i
$988$	−0.581747	+	0.581747i	−0.0185078	+	0.0185078i
$989$	55.4011			1.76165
$990$	−19.6509	+	14.1146i	−0.624545	+	0.448590i
$991$	−8.80348	+	8.80348i	−0.279652	+	0.279652i	−0.832970	−	0.553318i	$-0.813361\pi$
$991$	−8.80348	+	8.80348i	−0.279652	+	0.279652i	0.553318	+	0.832970i	$0.313361\pi$
$992$	−4.90948	+	4.90948i	−0.155876	+	0.155876i
$993$			81.0128i			2.57086i
$994$	9.98370	+	9.98370i	0.316664	+	0.316664i
$995$	3.57924	+	0.586863i	0.113469	+	0.0186048i
$996$	33.0548			1.04738
$997$		−	31.7260i		−	1.00477i	−0.864644	−	0.502386i	$-0.832456\pi$
$997$		−	31.7260i		−	1.00477i	0.864644	−	0.502386i	$-0.167544\pi$
$998$	−9.60201	−	9.60201i	−0.303946	−	0.303946i
$999$	29.8668	+	39.2684i	0.944944	+	1.24240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.h.e.117.1	yes	20
5.3	odd	4		370.2.g.e.43.10	✓	20
37.31	odd	4		370.2.g.e.327.10	yes	20
185.68	even	4	inner	370.2.h.e.253.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.10	✓	20	5.3	odd	4
370.2.g.e.327.10	yes	20	37.31	odd	4
370.2.h.e.117.1	yes	20	1.1	even	1	trivial
370.2.h.e.253.1	yes	20	185.68	even	4	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-2.09082 - 2.09082i) q^{3} +1.00000 q^{4} +(-1.81614 + 1.30447i) q^{5} +(2.09082 + 2.09082i) q^{6} +(-0.643605 - 0.643605i) q^{7} -1.00000 q^{8} +5.74304i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-2.09082 - 2.09082i) q^{3} +1.00000 q^{4} +(-1.81614 + 1.30447i) q^{5} +(2.09082 + 2.09082i) q^{6} +(-0.643605 - 0.643605i) q^{7} -1.00000 q^{8} +5.74304i q^{9} +(1.81614 - 1.30447i) q^{10} +1.88405i q^{11} +(-2.09082 - 2.09082i) q^{12} -0.536082 q^{13} +(0.643605 + 0.643605i) q^{14} +(6.52462 + 1.06980i) q^{15} +1.00000 q^{16} +0.334703i q^{17} -5.74304i q^{18} +(1.08518 - 1.08518i) q^{19} +(-1.81614 + 1.30447i) q^{20} +2.69132i q^{21} -1.88405i q^{22} +4.65098 q^{23} +(2.09082 + 2.09082i) q^{24} +(1.59670 - 4.73820i) q^{25} +0.536082 q^{26} +(5.73519 - 5.73519i) q^{27} +(-0.643605 - 0.643605i) q^{28} +(3.33033 + 3.33033i) q^{29} +(-6.52462 - 1.06980i) q^{30} +(4.90948 - 4.90948i) q^{31} -1.00000 q^{32} +(3.93919 - 3.93919i) q^{33} -0.334703i q^{34} +(2.00844 + 0.329310i) q^{35} +5.74304i q^{36} +(-0.819646 + 6.02729i) q^{37} +(-1.08518 + 1.08518i) q^{38} +(1.12085 + 1.12085i) q^{39} +(1.81614 - 1.30447i) q^{40} +8.26486i q^{41} -2.69132i q^{42} +11.9117 q^{43} +1.88405i q^{44} +(-7.49163 - 10.4301i) q^{45} -4.65098 q^{46} +(-0.141535 - 0.141535i) q^{47} +(-2.09082 - 2.09082i) q^{48} -6.17154i q^{49} +(-1.59670 + 4.73820i) q^{50} +(0.699803 - 0.699803i) q^{51} -0.536082 q^{52} +(-5.03296 + 5.03296i) q^{53} +(-5.73519 + 5.73519i) q^{54} +(-2.45768 - 3.42168i) q^{55} +(0.643605 + 0.643605i) q^{56} -4.53784 q^{57} +(-3.33033 - 3.33033i) q^{58} +(-4.10789 + 4.10789i) q^{59} +(6.52462 + 1.06980i) q^{60} +(-8.90180 + 8.90180i) q^{61} +(-4.90948 + 4.90948i) q^{62} +(3.69625 - 3.69625i) q^{63} +1.00000 q^{64} +(0.973599 - 0.699305i) q^{65} +(-3.93919 + 3.93919i) q^{66} +(-3.61956 + 3.61956i) q^{67} +0.334703i q^{68} +(-9.72436 - 9.72436i) q^{69} +(-2.00844 - 0.329310i) q^{70} +15.5121 q^{71} -5.74304i q^{72} +(6.82739 + 6.82739i) q^{73} +(0.819646 - 6.02729i) q^{74} +(-13.2451 + 6.56829i) q^{75} +(1.08518 - 1.08518i) q^{76} +(1.21258 - 1.21258i) q^{77} +(-1.12085 - 1.12085i) q^{78} +(-5.73637 + 5.73637i) q^{79} +(-1.81614 + 1.30447i) q^{80} -6.75336 q^{81} -8.26486i q^{82} +(-7.90475 + 7.90475i) q^{83} +2.69132i q^{84} +(-0.436611 - 0.607866i) q^{85} -11.9117 q^{86} -13.9262i q^{87} -1.88405i q^{88} +(1.21521 + 1.21521i) q^{89} +(7.49163 + 10.4301i) q^{90} +(0.345025 + 0.345025i) q^{91} +4.65098 q^{92} -20.5297 q^{93} +(0.141535 + 0.141535i) q^{94} +(-0.555249 + 3.38643i) q^{95} +(2.09082 + 2.09082i) q^{96} -17.1767i q^{97} +6.17154i q^{98} -10.8201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8} + 4 q^{10} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 6 q^{19} - 4 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} - 20 q^{27} - 2 q^{28} + 18 q^{29} + 4 q^{30} + 12 q^{31} - 20 q^{32} + 4 q^{33} - 12 q^{35} - 32 q^{37} - 6 q^{38} + 6 q^{39} + 4 q^{40} + 16 q^{43} + 22 q^{45} + 4 q^{46} - 22 q^{47} + 4 q^{48} - 10 q^{50} + 8 q^{51} - 4 q^{53} + 20 q^{54} + 16 q^{55} + 2 q^{56} + 24 q^{57} - 18 q^{58} - 10 q^{59} - 4 q^{60} + 10 q^{61} - 12 q^{62} - 2 q^{63} + 20 q^{64} + 20 q^{65} - 4 q^{66} + 8 q^{67} - 34 q^{69} + 12 q^{70} + 16 q^{71} - 6 q^{73} + 32 q^{74} - 26 q^{75} + 6 q^{76} - 4 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} - 28 q^{81} + 6 q^{83} + 10 q^{85} - 16 q^{86} - 44 q^{89} - 22 q^{90} - 40 q^{91} - 4 q^{92} - 40 q^{93} + 22 q^{94} + 50 q^{95} - 4 q^{96} - 20 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8 + 4 * q^10 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 6 * q^19 - 4 * q^20 - 4 * q^23 - 4 * q^24 + 10 * q^25 - 20 * q^27 - 2 * q^28 + 18 * q^29 + 4 * q^30 + 12 * q^31 - 20 * q^32 + 4 * q^33 - 12 * q^35 - 32 * q^37 - 6 * q^38 + 6 * q^39 + 4 * q^40 + 16 * q^43 + 22 * q^45 + 4 * q^46 - 22 * q^47 + 4 * q^48 - 10 * q^50 + 8 * q^51 - 4 * q^53 + 20 * q^54 + 16 * q^55 + 2 * q^56 + 24 * q^57 - 18 * q^58 - 10 * q^59 - 4 * q^60 + 10 * q^61 - 12 * q^62 - 2 * q^63 + 20 * q^64 + 20 * q^65 - 4 * q^66 + 8 * q^67 - 34 * q^69 + 12 * q^70 + 16 * q^71 - 6 * q^73 + 32 * q^74 - 26 * q^75 + 6 * q^76 - 4 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 - 28 * q^81 + 6 * q^83 + 10 * q^85 - 16 * q^86 - 44 * q^89 - 22 * q^90 - 40 * q^91 - 4 * q^92 - 40 * q^93 + 22 * q^94 + 50 * q^95 - 4 * q^96 - 20 * q^99

Introduction

L-functions

Modular forms

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Database

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