LMFDB - Embedded newform 665.2.i.h.596.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [665,2,Mod(106,665)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(665, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("665.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 665 = 5 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	665.i (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:	$5.31005173442$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
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} - 3 x^{19} + 20 x^{18} - 43 x^{17} + 207 x^{16} - 401 x^{15} + 1351 x^{14} - 2135 x^{13} + \cdots + 1024 $ x^20 - 3x^19 + 20x^18 - 43x^17 + 207x^16 - 401x^15 + 1351x^14 - 2135x^13 + 5714x^12 - 7983x^11 + 16723x^10 - 18718x^9 + 30867x^8 - 28726x^7 + 37857x^6 - 24848x^5 + 21360x^4 - 7488x^3 + 5888x^2 - 1536*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			596.1
Root			$-1.26008 - 2.18252i$ of defining polynomial
Character	$\chi$	$=$	665.596
Dual form			665.2.i.h.106.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26008 - 2.18252i) q^{2} +(-0.424874 - 0.735903i) q^{3} +(-2.17561 + 3.76826i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.07075 + 1.85460i) q^{6} -1.00000 q^{7} +5.92545 q^{8} +(1.13896 - 1.97274i) q^{9} +O(q^{10})$	\(q+(-1.26008 - 2.18252i) q^{2} +(-0.424874 - 0.735903i) q^{3} +(-2.17561 + 3.76826i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.07075 + 1.85460i) q^{6} -1.00000 q^{7} +5.92545 q^{8} +(1.13896 - 1.97274i) q^{9} +(1.26008 - 2.18252i) q^{10} +0.646997 q^{11} +3.69744 q^{12} +(1.20769 - 2.09179i) q^{13} +(1.26008 + 2.18252i) q^{14} +(0.424874 - 0.735903i) q^{15} +(-3.11532 - 5.39590i) q^{16} +(-1.90373 - 3.29735i) q^{17} -5.74075 q^{18} +(4.23737 + 1.02211i) q^{19} -4.35122 q^{20} +(0.424874 + 0.735903i) q^{21} +(-0.815269 - 1.41209i) q^{22} +(3.54502 - 6.14016i) q^{23} +(-2.51757 - 4.36056i) q^{24} +(-0.500000 + 0.866025i) q^{25} -6.08717 q^{26} -4.48491 q^{27} +(2.17561 - 3.76826i) q^{28} +(-2.56944 + 4.45040i) q^{29} -2.14150 q^{30} -8.45403 q^{31} +(-1.92568 + 3.33537i) q^{32} +(-0.274892 - 0.476127i) q^{33} +(-4.79770 + 8.30985i) q^{34} +(-0.500000 - 0.866025i) q^{35} +(4.95588 + 8.58383i) q^{36} -9.88242 q^{37} +(-3.10865 - 10.5361i) q^{38} -2.05247 q^{39} +(2.96272 + 5.13159i) q^{40} +(-5.09340 - 8.82202i) q^{41} +(1.07075 - 1.85460i) q^{42} +(2.21493 + 3.83637i) q^{43} +(-1.40761 + 2.43806i) q^{44} +2.27793 q^{45} -17.8681 q^{46} +(4.29059 - 7.43152i) q^{47} +(-2.64724 + 4.58516i) q^{48} +1.00000 q^{49} +2.52016 q^{50} +(-1.61769 + 2.80192i) q^{51} +(5.25494 + 9.10183i) q^{52} +(-0.550523 + 0.953533i) q^{53} +(5.65135 + 9.78842i) q^{54} +(0.323499 + 0.560316i) q^{55} -5.92545 q^{56} +(-1.04817 - 3.55256i) q^{57} +12.9508 q^{58} +(4.96489 + 8.59945i) q^{59} +(1.84872 + 3.20207i) q^{60} +(1.87689 - 3.25087i) q^{61} +(10.6528 + 18.4511i) q^{62} +(-1.13896 + 1.97274i) q^{63} -2.75526 q^{64} +2.41539 q^{65} +(-0.692773 + 1.19992i) q^{66} +(2.93233 - 5.07894i) q^{67} +16.5670 q^{68} -6.02475 q^{69} +(-1.26008 + 2.18252i) q^{70} +(2.84771 + 4.93237i) q^{71} +(6.74887 - 11.6894i) q^{72} +(-4.97630 - 8.61920i) q^{73} +(12.4527 + 21.5686i) q^{74} +0.849748 q^{75} +(-13.0704 + 13.7438i) q^{76} -0.646997 q^{77} +(2.58628 + 4.47957i) q^{78} +(-8.15293 - 14.1213i) q^{79} +(3.11532 - 5.39590i) q^{80} +(-1.51137 - 2.61777i) q^{81} +(-12.8362 + 22.2329i) q^{82} +6.25385 q^{83} -3.69744 q^{84} +(1.90373 - 3.29735i) q^{85} +(5.58198 - 9.66827i) q^{86} +4.36675 q^{87} +3.83375 q^{88} +(1.54661 - 2.67881i) q^{89} +(-2.87037 - 4.97163i) q^{90} +(-1.20769 + 2.09179i) q^{91} +(15.4252 + 26.7171i) q^{92} +(3.59190 + 6.22135i) q^{93} -21.6260 q^{94} +(1.23351 + 4.18072i) q^{95} +3.27268 q^{96} +(2.85767 + 4.94963i) q^{97} +(-1.26008 - 2.18252i) q^{98} +(0.736906 - 1.27636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3 q^{2} - q^{3} - 11 q^{4} + 10 q^{5} - 6 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) $ 20 * q + 3 * q^2 - q^3 - 11 * q^4 + 10 * q^5 - 6 * q^6 - 20 * q^7 - 9 * q^9	\( 20 q + 3 q^{2} - q^{3} - 11 q^{4} + 10 q^{5} - 6 q^{6} - 20 q^{7} - 9 q^{9} - 3 q^{10} + 2 q^{11} - 4 q^{12} + 6 q^{13} - 3 q^{14} + q^{15} - 5 q^{16} + 8 q^{17} - 76 q^{18} + 17 q^{19} - 22 q^{20} + q^{21} - 4 q^{22} + 3 q^{23} - 6 q^{24} - 10 q^{25} + 18 q^{26} + 20 q^{27} + 11 q^{28} + q^{29} - 12 q^{30} + 10 q^{31} + 18 q^{32} + q^{33} - 26 q^{34} - 10 q^{35} - 19 q^{36} - 66 q^{37} + 19 q^{38} + 34 q^{39} - 29 q^{41} + 6 q^{42} + q^{43} - 28 q^{44} - 18 q^{45} + 6 q^{46} - 7 q^{47} + 15 q^{48} + 20 q^{49} - 6 q^{50} + 16 q^{51} - 6 q^{52} + 40 q^{53} + 35 q^{54} + q^{55} + 24 q^{57} - 18 q^{58} - 9 q^{59} - 2 q^{60} + 10 q^{61} - 8 q^{62} + 9 q^{63} + 44 q^{64} + 12 q^{65} - 19 q^{66} + 22 q^{67} - 42 q^{68} + 60 q^{69} + 3 q^{70} - 8 q^{71} + 18 q^{72} + 14 q^{73} - 24 q^{74} + 2 q^{75} - 49 q^{76} - 2 q^{77} + 23 q^{78} + 9 q^{79} + 5 q^{80} - 42 q^{81} - 5 q^{82} - 54 q^{83} + 4 q^{84} - 8 q^{85} + 37 q^{86} + 18 q^{87} - 28 q^{88} - 25 q^{89} - 38 q^{90} - 6 q^{91} + 68 q^{92} + 11 q^{93} - 118 q^{94} + 10 q^{95} + 102 q^{96} + 29 q^{97} + 3 q^{98} + 34 q^{99}+O(q^{100}) \) 20 * q + 3 * q^2 - q^3 - 11 * q^4 + 10 * q^5 - 6 * q^6 - 20 * q^7 - 9 * q^9 - 3 * q^10 + 2 * q^11 - 4 * q^12 + 6 * q^13 - 3 * q^14 + q^15 - 5 * q^16 + 8 * q^17 - 76 * q^18 + 17 * q^19 - 22 * q^20 + q^21 - 4 * q^22 + 3 * q^23 - 6 * q^24 - 10 * q^25 + 18 * q^26 + 20 * q^27 + 11 * q^28 + q^29 - 12 * q^30 + 10 * q^31 + 18 * q^32 + q^33 - 26 * q^34 - 10 * q^35 - 19 * q^36 - 66 * q^37 + 19 * q^38 + 34 * q^39 - 29 * q^41 + 6 * q^42 + q^43 - 28 * q^44 - 18 * q^45 + 6 * q^46 - 7 * q^47 + 15 * q^48 + 20 * q^49 - 6 * q^50 + 16 * q^51 - 6 * q^52 + 40 * q^53 + 35 * q^54 + q^55 + 24 * q^57 - 18 * q^58 - 9 * q^59 - 2 * q^60 + 10 * q^61 - 8 * q^62 + 9 * q^63 + 44 * q^64 + 12 * q^65 - 19 * q^66 + 22 * q^67 - 42 * q^68 + 60 * q^69 + 3 * q^70 - 8 * q^71 + 18 * q^72 + 14 * q^73 - 24 * q^74 + 2 * q^75 - 49 * q^76 - 2 * q^77 + 23 * q^78 + 9 * q^79 + 5 * q^80 - 42 * q^81 - 5 * q^82 - 54 * q^83 + 4 * q^84 - 8 * q^85 + 37 * q^86 + 18 * q^87 - 28 * q^88 - 25 * q^89 - 38 * q^90 - 6 * q^91 + 68 * q^92 + 11 * q^93 - 118 * q^94 + 10 * q^95 + 102 * q^96 + 29 * q^97 + 3 * q^98 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/665\mathbb{Z}\right)^\times$.

$n$	$211$	$267$	$381$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	−1.26008	−	2.18252i	−0.891012	−	1.54328i	−0.838664	−	0.544649i	$-0.816663\pi$
$2$	−1.26008	−	2.18252i	−0.891012	−	1.54328i	−0.0523476	−	0.998629i	$-0.516670\pi$
$3$	−0.424874	−	0.735903i	−0.245301	−	0.424874i	0.716915	−	0.697160i	$-0.245554\pi$
$3$	−0.424874	−	0.735903i	−0.245301	−	0.424874i	−0.962216	+	0.272286i	$0.912220\pi$
$4$	−2.17561	+	3.76826i	−1.08780	+	1.88413i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.07075	+	1.85460i	−0.437132	+	0.757136i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	5.92545			2.09496
$9$	1.13896	−	1.97274i	0.379655	−	0.657581i
$10$	1.26008	−	2.18252i	0.398473	−	0.690175i
$11$	0.646997			0.195077			0.0975385	−	0.995232i	$-0.468903\pi$
$11$	0.646997			0.195077			0.0975385	+	0.995232i	$0.468903\pi$
$12$	3.69744			1.06736
$13$	1.20769	−	2.09179i	0.334954	−	0.580158i	−0.648522	−	0.761196i	$-0.724612\pi$
$13$	1.20769	−	2.09179i	0.334954	−	0.580158i	0.983476	+	0.181038i	$0.0579458\pi$
$14$	1.26008	+	2.18252i	0.336771	+	0.583304i
$15$	0.424874	−	0.735903i	0.109702	−	0.190009i
$16$	−3.11532	−	5.39590i	−0.778831	−	1.34898i
$17$	−1.90373	−	3.29735i	−0.461721	−	0.799725i	0.537326	−	0.843375i	$-0.319435\pi$
$17$	−1.90373	−	3.29735i	−0.461721	−	0.799725i	−0.999047	+	0.0436503i	$0.986101\pi$
$18$	−5.74075			−1.35311
$19$	4.23737	+	1.02211i	0.972119	+	0.234488i
$19$	4.23737	+	1.02211i	0.972119	+	0.234488i
$20$	−4.35122			−0.972962
$21$	0.424874	+	0.735903i	0.0927151	+	0.160587i
$22$	−0.815269	−	1.41209i	−0.173816	−	0.301058i
$23$	3.54502	−	6.14016i	0.739188	−	1.28031i	−0.213673	−	0.976905i	$-0.568543\pi$
$23$	3.54502	−	6.14016i	0.739188	−	1.28031i	0.952861	−	0.303406i	$-0.0981239\pi$
$24$	−2.51757	−	4.36056i	−0.513896	−	0.890095i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−6.08717			−1.19379
$27$	−4.48491			−0.863121
$28$	2.17561	−	3.76826i	0.411151	−	0.712135i
$29$	−2.56944	+	4.45040i	−0.477133	+	0.826418i	−0.999657	−	0.0262067i	$-0.991657\pi$
$29$	−2.56944	+	4.45040i	−0.477133	+	0.826418i	0.522524	+	0.852625i	$0.324991\pi$
$30$	−2.14150			−0.390983
$31$	−8.45403			−1.51839			−0.759194	−	0.650864i	$-0.774407\pi$
$31$	−8.45403			−1.51839			−0.759194	+	0.650864i	$0.774407\pi$
$32$	−1.92568	+	3.33537i	−0.340415	+	0.589616i
$33$	−0.274892	−	0.476127i	−0.0478526	−	0.0828831i
$34$	−4.79770	+	8.30985i	−0.822798	+	1.42513i
$35$	−0.500000	−	0.866025i	−0.0845154	−	0.146385i
$36$	4.95588	+	8.58383i	0.825980	+	1.43064i
$37$	−9.88242			−1.62466			−0.812330	−	0.583198i	$-0.801801\pi$
$37$	−9.88242			−1.62466			−0.812330	+	0.583198i	$0.801801\pi$
$38$	−3.10865	−	10.5361i	−0.504290	−	1.70918i
$39$	−2.05247			−0.328659
$40$	2.96272	+	5.13159i	0.468448	+	0.811375i
$41$	−5.09340	−	8.82202i	−0.795455	−	1.37777i	−0.922550	−	0.385878i	$-0.873899\pi$
$41$	−5.09340	−	8.82202i	−0.795455	−	1.37777i	0.127095	−	0.991891i	$-0.459435\pi$
$42$	1.07075	−	1.85460i	0.165221	−	0.286170i
$43$	2.21493	+	3.83637i	0.337773	+	0.585041i	0.984014	−	0.178093i	$-0.0569929\pi$
$43$	2.21493	+	3.83637i	0.337773	+	0.585041i	−0.646240	+	0.763134i	$0.723660\pi$
$44$	−1.40761	+	2.43806i	−0.212205	+	0.367551i
$45$	2.27793			0.339573
$46$	−17.8681			−2.63450
$47$	4.29059	−	7.43152i	0.625847	−	1.08400i	−0.362530	−	0.931972i	$-0.618087\pi$
$47$	4.29059	−	7.43152i	0.625847	−	1.08400i	0.988377	−	0.152026i	$-0.0485797\pi$
$48$	−2.64724	+	4.58516i	−0.382096	+	0.661810i
$49$	1.00000			0.142857
$50$	2.52016			0.356405
$51$	−1.61769	+	2.80192i	−0.226521	+	0.392347i
$52$	5.25494	+	9.10183i	0.728729	+	1.26220i
$53$	−0.550523	+	0.953533i	−0.0756201	+	0.130978i	−0.901356	−	0.433079i	$-0.857427\pi$
$53$	−0.550523	+	0.953533i	−0.0756201	+	0.130978i	0.825736	+	0.564057i	$0.190760\pi$
$54$	5.65135	+	9.78842i	0.769051	+	1.33204i
$55$	0.323499	+	0.560316i	0.0436205	+	0.0755530i
$56$	−5.92545			−0.791821
$57$	−1.04817	−	3.55256i	−0.138834	−	0.470548i
$58$	12.9508			1.70052
$59$	4.96489	+	8.59945i	0.646374	+	1.11955i	0.983982	+	0.178266i	$0.0570487\pi$
$59$	4.96489	+	8.59945i	0.646374	+	1.11955i	−0.337608	+	0.941287i	$0.609618\pi$
$60$	1.84872	+	3.20207i	0.238669	+	0.413386i
$61$	1.87689	−	3.25087i	0.240312	−	0.416232i	−0.720491	−	0.693464i	$-0.756084\pi$
$61$	1.87689	−	3.25087i	0.240312	−	0.416232i	0.960803	+	0.277232i	$0.0894171\pi$
$62$	10.6528	+	18.4511i	1.35290	+	2.34329i
$63$	−1.13896	+	1.97274i	−0.143496	+	0.248542i
$64$	−2.75526			−0.344407
$65$	2.41539			0.299592
$66$	−0.692773	+	1.19992i	−0.0852745	+	0.147700i
$67$	2.93233	−	5.07894i	0.358241	−	0.620491i	−0.629426	−	0.777060i	$-0.716710\pi$
$67$	2.93233	−	5.07894i	0.358241	−	0.620491i	0.987667	+	0.156569i	$0.0500434\pi$
$68$	16.5670			2.00905
$69$	−6.02475			−0.725295
$70$	−1.26008	+	2.18252i	−0.150608	+	0.260862i
$71$	2.84771	+	4.93237i	0.337961	+	0.585365i	0.984049	−	0.177898i	$-0.0569296\pi$
$71$	2.84771	+	4.93237i	0.337961	+	0.585365i	−0.646088	+	0.763263i	$0.723596\pi$
$72$	6.74887	−	11.6894i	0.795362	−	1.37761i
$73$	−4.97630	−	8.61920i	−0.582432	−	1.00880i	−0.995190	−	0.0979609i	$-0.968768\pi$
$73$	−4.97630	−	8.61920i	−0.582432	−	1.00880i	0.412758	−	0.910841i	$-0.364565\pi$
$74$	12.4527	+	21.5686i	1.44759	+	2.50730i
$75$	0.849748			0.0981205
$76$	−13.0704	+	13.7438i	−1.49928	+	1.57652i
$77$	−0.646997			−0.0737322
$78$	2.58628	+	4.47957i	0.292839	+	0.507212i
$79$	−8.15293	−	14.1213i	−0.917277	−	1.58877i	−0.803534	−	0.595259i	$-0.797049\pi$
$79$	−8.15293	−	14.1213i	−0.917277	−	1.58877i	−0.113743	−	0.993510i	$-0.536284\pi$
$80$	3.11532	−	5.39590i	0.348304	−	0.603280i
$81$	−1.51137	−	2.61777i	−0.167930	−	0.290863i
$82$	−12.8362	+	22.2329i	−1.41752	+	2.45522i
$83$	6.25385			0.686449			0.343224	−	0.939253i	$-0.388481\pi$
$83$	6.25385			0.686449			0.343224	+	0.939253i	$0.388481\pi$
$84$	−3.69744			−0.403424
$85$	1.90373	−	3.29735i	0.206488	−	0.357648i
$86$	5.58198	−	9.66827i	0.601920	−	1.04256i
$87$	4.36675			0.468165
$88$	3.83375			0.408679
$89$	1.54661	−	2.67881i	0.163940	−	0.283953i	−0.772338	−	0.635212i	$-0.780913\pi$
$89$	1.54661	−	2.67881i	0.163940	−	0.283953i	0.936278	+	0.351259i	$0.114246\pi$
$90$	−2.87037	−	4.97163i	−0.302564	−	0.524056i
$91$	−1.20769	+	2.09179i	−0.126601	+	0.219279i
$92$	15.4252	+	26.7171i	1.60818	+	2.78546i
$93$	3.59190	+	6.22135i	0.372462	+	0.645124i
$94$	−21.6260			−2.23055
$95$	1.23351	+	4.18072i	0.126556	+	0.428933i
$96$	3.27268			0.334017
$97$	2.85767	+	4.94963i	0.290152	+	0.502559i	0.973846	−	0.227211i	$-0.0729607\pi$
$97$	2.85767	+	4.94963i	0.290152	+	0.502559i	−0.683693	+	0.729770i	$0.739627\pi$
$98$	−1.26008	−	2.18252i	−0.127287	−	0.220468i
$99$	0.736906	−	1.27636i	0.0740619	−	0.128279i
$100$	−2.17561	−	3.76826i	−0.217561	−	0.376826i
$101$	2.70286	−	4.68150i	0.268945	−	0.465826i	−0.699645	−	0.714491i	$-0.746658\pi$
$101$	2.70286	−	4.68150i	0.268945	−	0.465826i	0.968590	+	0.248665i	$0.0799917\pi$
$102$	8.15367			0.807333
$103$	−11.4121			−1.12446			−0.562232	−	0.826980i	$-0.690057\pi$
$103$	−11.4121			−1.12446			−0.562232	+	0.826980i	$0.690057\pi$
$104$	7.15613	−	12.3948i	0.701716	−	1.21541i
$105$	−0.424874	+	0.735903i	−0.0414635	+	0.0718168i
$106$	2.77481			0.269514
$107$	4.47626			0.432736			0.216368	−	0.976312i	$-0.430579\pi$
$107$	4.47626			0.432736			0.216368	+	0.976312i	$0.430579\pi$
$108$	9.75741	−	16.9003i	0.938907	−	1.62623i
$109$	−0.309618	−	0.536274i	−0.0296560	−	0.0513658i	0.850816	−	0.525463i	$-0.176108\pi$
$109$	−0.309618	−	0.536274i	−0.0296560	−	0.0513658i	−0.880473	+	0.474097i	$0.842775\pi$
$110$	0.815269	−	1.41209i	0.0777328	−	0.134637i
$111$	4.19879	+	7.27251i	0.398531	+	0.690276i
$112$	3.11532	+	5.39590i	0.294371	+	0.509865i
$113$	−9.51243			−0.894854			−0.447427	−	0.894321i	$-0.647660\pi$
$113$	−9.51243			−0.894854			−0.447427	+	0.894321i	$0.647660\pi$
$114$	−6.43277	+	6.76418i	−0.602484	+	0.633524i
$115$	7.09004			0.661150
$116$	−11.1802	−	19.3646i	−1.03805	−	1.79796i
$117$	−2.75104	−	4.76494i	−0.254334	−	0.440519i
$118$	12.5123	−	21.6720i	1.15185	−	1.99507i
$119$	1.90373	+	3.29735i	0.174514	+	0.302267i
$120$	2.51757	−	4.36056i	0.229821	−	0.398062i
$121$	−10.5814			−0.961945
$122$	−9.46015			−0.856482
$123$	−4.32810	+	7.49650i	−0.390252	+	0.675936i
$124$	18.3927	−	31.8570i	1.65171	−	2.86084i
$125$	−1.00000			−0.0894427
$126$	5.74075			0.511426
$127$	−3.52799	+	6.11065i	−0.313058	+	0.542232i	−0.979023	−	0.203751i	$-0.934687\pi$
$127$	−3.52799	+	6.11065i	−0.313058	+	0.542232i	0.665965	+	0.745983i	$0.268020\pi$
$128$	7.32321	+	12.6842i	0.647286	+	1.12113i
$129$	1.88213	−	3.25995i	0.165712	−	0.287022i
$130$	−3.04359	−	5.27165i	−0.266940	−	0.462354i
$131$	−4.71583	−	8.16806i	−0.412024	−	0.713647i	0.583087	−	0.812410i	$-0.301845\pi$
$131$	−4.71583	−	8.16806i	−0.412024	−	0.713647i	−0.995111	+	0.0987632i	$0.968511\pi$
$132$	2.39223			0.208217
$133$	−4.23737	−	1.02211i	−0.367426	−	0.0886281i
$134$	−14.7799			−1.27679
$135$	−2.24245	−	3.88405i	−0.193000	−	0.334285i
$136$	−11.2804	−	19.5383i	−0.967288	−	1.67539i
$137$	1.40328	−	2.43056i	0.119891	−	0.207656i	−0.799834	−	0.600222i	$-0.795079\pi$
$137$	1.40328	−	2.43056i	0.119891	−	0.207656i	0.919724	+	0.392565i	$0.128412\pi$
$138$	7.59167	+	13.1492i	0.646246	+	1.11933i
$139$	0.599945	−	1.03913i	0.0508867	−	0.0881383i	−0.839460	−	0.543421i	$-0.817129\pi$
$139$	0.599945	−	1.03913i	0.0508867	−	0.0881383i	0.890347	+	0.455283i	$0.150462\pi$
$140$	4.35122			0.367745
$141$	−7.29184			−0.614084
$142$	7.17668	−	12.4304i	0.602254	−	1.04313i
$143$	0.781375	−	1.35338i	0.0653419	−	0.113175i
$144$	−14.1930			−1.18275
$145$	−5.13888			−0.426760
$146$	−12.5411	+	21.7218i	−1.03791	+	1.79771i
$147$	−0.424874	−	0.735903i	−0.0350430	−	0.0606963i
$148$	21.5003	−	37.2396i	1.76731	−	3.06107i
$149$	5.24567	+	9.08577i	0.429742	+	0.744335i	0.996850	−	0.0793080i	$-0.0252711\pi$
$149$	5.24567	+	9.08577i	0.429742	+	0.744335i	−0.567108	+	0.823644i	$0.691938\pi$
$150$	−1.07075	−	1.85460i	−0.0874265	−	0.151427i
$151$	18.8484			1.53386			0.766932	−	0.641729i	$-0.221782\pi$
$151$	18.8484			1.53386			0.766932	+	0.641729i	$0.221782\pi$
$152$	25.1083	+	6.05645i	2.03655	+	0.491243i
$153$	−8.67310			−0.701179
$154$	0.815269	+	1.41209i	0.0656962	+	0.113789i
$155$	−4.22701	−	7.32140i	−0.339522	−	0.588069i
$156$	4.46538	−	7.73426i	0.357516	−	0.619236i
$157$	−7.88731	−	13.6612i	−0.629476	−	1.09028i	−0.987657	−	0.156632i	$-0.949936\pi$
$157$	−7.88731	−	13.6612i	−0.629476	−	1.09028i	0.358181	−	0.933652i	$-0.383397\pi$
$158$	−20.5467	+	35.5879i	−1.63461	+	2.83122i
$159$	0.935611			0.0741988
$160$	−3.85136			−0.304476
$161$	−3.54502	+	6.14016i	−0.279387	+	0.483912i
$162$	−3.80890	+	6.59721i	−0.299255	+	0.518326i
$163$	−0.402159			−0.0314995			−0.0157498	−	0.999876i	$-0.505014\pi$
$163$	−0.402159			−0.0314995			−0.0157498	+	0.999876i	$0.505014\pi$
$164$	44.3249			3.46120
$165$	0.274892	−	0.476127i	0.0214003	−	0.0370665i
$166$	−7.88035	−	13.6492i	−0.611634	−	1.05938i
$167$	8.89895	−	15.4134i	0.688621	−	1.19273i	−0.283663	−	0.958924i	$-0.591550\pi$
$167$	8.89895	−	15.4134i	0.688621	−	1.19273i	0.972284	−	0.233803i	$-0.0751171\pi$
$168$	2.51757	+	4.36056i	0.194235	+	0.336424i
$169$	3.58295	+	6.20584i	0.275611	+	0.477373i
$170$	−9.59539			−0.735933
$171$	6.84257	−	7.19510i	0.523264	−	0.550223i
$172$	−19.2753			−1.46972
$173$	−7.92675	−	13.7295i	−0.602660	−	1.04384i	−0.992417	−	0.122920i	$-0.960774\pi$
$173$	−7.92675	−	13.7295i	−0.602660	−	1.04384i	0.389757	−	0.920918i	$-0.372559\pi$
$174$	−5.50246	−	9.53054i	−0.417140	−	0.722508i
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	−2.01561	−	3.49113i	−0.151932	−	0.263154i
$177$	4.21891	−	7.30736i	0.317113	−	0.549255i
$178$	−7.79541			−0.584291
$179$	13.6796			1.02246			0.511229	−	0.859444i	$-0.329190\pi$
$179$	13.6796			1.02246			0.511229	+	0.859444i	$0.329190\pi$
$180$	−4.95588	+	8.58383i	−0.369389	+	0.639801i
$181$	−1.65438	+	2.86547i	−0.122969	+	0.212989i	−0.920937	−	0.389711i	$-0.872575\pi$
$181$	−1.65438	+	2.86547i	−0.122969	+	0.212989i	0.797968	+	0.602700i	$0.205908\pi$
$182$	6.08717			0.451211
$183$	−3.18977			−0.235795
$184$	21.0058	−	36.3832i	1.54857	−	2.68220i
$185$	−4.94121	−	8.55843i	−0.363285	−	0.629228i
$186$	9.05216	−	15.6788i	0.663737	−	1.14963i
$187$	−1.23170	−	2.13338i	−0.0900712	−	0.156008i
$188$	18.6693	+	32.3361i	1.36160	+	2.35835i
$189$	4.48491			0.326229
$190$	7.57020	−	7.96022i	0.549200	−	0.577495i
$191$	19.2877			1.39561			0.697806	−	0.716287i	$-0.254160\pi$
$191$	19.2877			1.39561			0.697806	+	0.716287i	$0.254160\pi$
$192$	1.17064	+	2.02761i	0.0844835	+	0.146330i
$193$	10.6815	+	18.5008i	0.768869	+	1.33172i	0.938177	+	0.346157i	$0.112513\pi$
$193$	10.6815	+	18.5008i	0.768869	+	1.33172i	−0.169308	+	0.985563i	$0.554153\pi$
$194$	7.20179	−	12.4739i	0.517058	−	0.895571i
$195$	−1.02624	−	1.77749i	−0.0734903	−	0.127289i
$196$	−2.17561	+	3.76826i	−0.155401	+	0.269162i
$197$	−23.5603			−1.67860			−0.839301	−	0.543667i	$-0.817036\pi$
$197$	−23.5603			−1.67860			−0.839301	+	0.543667i	$0.817036\pi$
$198$	−3.71425			−0.263960
$199$	4.82962	−	8.36514i	0.342362	−	0.592989i	−0.642509	−	0.766279i	$-0.722106\pi$
$199$	4.82962	−	8.36514i	0.342362	−	0.592989i	0.984871	+	0.173289i	$0.0554396\pi$
$200$	−2.96272	+	5.13159i	−0.209496	+	0.362858i
$201$	−4.98348			−0.351507
$202$	−13.6233			−0.958533
$203$	2.56944	−	4.45040i	0.180339	−	0.312357i
$204$	−7.03891	−	12.1917i	−0.492822	−	0.853593i
$205$	5.09340	−	8.82202i	0.355738	−	0.616157i
$206$	14.3801	+	24.9071i	1.00191	+	1.73536i
$207$	−8.07530	−	13.9868i	−0.561272	−	0.972152i
$208$	−15.0494			−1.04349
$209$	2.74157	+	0.661301i	0.189638	+	0.0457432i
$210$	2.14150			0.147778
$211$	0.569667	+	0.986692i	0.0392175	+	0.0679267i	0.884968	−	0.465652i	$-0.154180\pi$
$211$	0.569667	+	0.986692i	0.0392175	+	0.0679267i	−0.845750	+	0.533579i	$0.820847\pi$
$212$	−2.39544	−	4.14903i	−0.164520	−	0.284957i
$213$	2.41983	−	4.19127i	0.165804	−	0.287181i
$214$	−5.64045	−	9.76955i	−0.385573	−	0.667832i
$215$	−2.21493	+	3.83637i	−0.151057	+	0.261638i
$216$	−26.5751			−1.80821
$217$	8.45403			0.573897
$218$	−0.780288	+	1.35150i	−0.0528478	+	0.0915350i
$219$	−4.22860	+	7.32415i	−0.285742	+	0.494920i
$220$	−2.81522			−0.189802
$221$	−9.19648			−0.618622
$222$	10.5816	−	18.3279i	0.710192	−	1.23009i
$223$	−0.0656005	−	0.113623i	−0.00439293	−	0.00760878i	0.863821	−	0.503800i	$-0.168065\pi$
$223$	−0.0656005	−	0.113623i	−0.00439293	−	0.00760878i	−0.868214	+	0.496191i	$0.834732\pi$
$224$	1.92568	−	3.33537i	0.128665	−	0.222854i
$225$	1.13896	+	1.97274i	0.0759309	+	0.131516i
$226$	11.9864	+	20.7611i	0.797325	+	1.38101i
$227$	16.5936			1.10136			0.550678	−	0.834717i	$-0.314369\pi$
$227$	16.5936			1.10136			0.550678	+	0.834717i	$0.314369\pi$
$228$	15.6674	+	3.77918i	1.03760	+	0.250283i
$229$	2.06710			0.136598			0.0682989	−	0.997665i	$-0.478243\pi$
$229$	2.06710			0.136598			0.0682989	+	0.997665i	$0.478243\pi$
$230$	−8.93403	−	15.4742i	−0.589092	−	1.02034i
$231$	0.274892	+	0.476127i	0.0180866	+	0.0313269i
$232$	−15.2251	+	26.3706i	−0.999574	+	1.73131i
$233$	13.0706	+	22.6390i	0.856286	+	1.48313i	0.875447	+	0.483315i	$0.160567\pi$
$233$	13.0706	+	22.6390i	0.856286	+	1.48313i	−0.0191604	+	0.999816i	$0.506099\pi$
$234$	−6.93307	+	12.0084i	−0.453229	+	0.785016i
$235$	8.58118			0.559774
$236$	−43.2066			−2.81251
$237$	−6.92794	+	11.9995i	−0.450018	+	0.779454i
$238$	4.79770	−	8.30985i	0.310988	−	0.538648i
$239$	9.15414			0.592132			0.296066	−	0.955167i	$-0.404325\pi$
$239$	9.15414			0.592132			0.296066	+	0.955167i	$0.404325\pi$
$240$	−5.29448			−0.341757
$241$	−12.9151	+	22.3697i	−0.831937	+	1.44096i	0.0645638	+	0.997914i	$0.479434\pi$
$241$	−12.9151	+	22.3697i	−0.831937	+	1.44096i	−0.896500	+	0.443043i	$0.853899\pi$
$242$	13.3334	+	23.0942i	0.857104	+	1.48455i
$243$	−8.01165	+	13.8766i	−0.513947	+	0.890183i
$244$	8.16677	+	14.1453i	0.522824	+	0.905557i
$245$	0.500000	+	0.866025i	0.0319438	+	0.0553283i
$246$	21.8150			1.39088
$247$	7.25548	−	7.62929i	0.461655	−	0.485440i
$248$	−50.0939			−3.18096
$249$	−2.65710	−	4.60223i	−0.168387	−	0.291654i
$250$	1.26008	+	2.18252i	0.0796945	+	0.138035i
$251$	−3.80081	+	6.58319i	−0.239905	+	0.415527i	−0.960687	−	0.277635i	$-0.910450\pi$
$251$	−3.80081	+	6.58319i	−0.239905	+	0.415527i	0.720782	+	0.693162i	$0.243783\pi$
$252$	−4.95588	−	8.58383i	−0.312191	−	0.540731i
$253$	2.29362	−	3.97266i	0.144199	−	0.249759i
$254$	17.7822			1.11575
$255$	−3.23537			−0.202607
$256$	15.7004	−	27.1939i	0.981275	−	1.69962i
$257$	6.66300	−	11.5407i	0.415626	−	0.719886i	−0.579868	−	0.814711i	$-0.696896\pi$
$257$	6.66300	−	11.5407i	0.415626	−	0.719886i	0.995494	+	0.0948247i	$0.0302291\pi$
$258$	−9.48655			−0.590607
$259$	9.88242			0.614064
$260$	−5.25494	+	9.10183i	−0.325898	+	0.564471i
$261$	5.85299	+	10.1377i	0.362291	+	0.627507i
$262$	−11.8847	+	20.5848i	−0.734237	+	1.27174i
$263$	13.3064	+	23.0473i	0.820505	+	1.42116i	0.905307	+	0.424759i	$0.139641\pi$
$263$	13.3064	+	23.0473i	0.820505	+	1.42116i	−0.0848015	+	0.996398i	$0.527026\pi$
$264$	−1.62886	−	2.82127i	−0.100249	−	0.173637i
$265$	−1.10105			−0.0676367
$266$	3.10865	+	10.5361i	0.190604	+	0.646010i
$267$	−2.62846			−0.160859
$268$	12.7592	+	22.0996i	0.779391	+	1.34994i
$269$	7.64035	+	13.2335i	0.465840	+	0.806859i	0.999239	−	0.0390050i	$-0.0124188\pi$
$269$	7.64035	+	13.2335i	0.465840	+	0.806859i	−0.533399	+	0.845864i	$0.679085\pi$
$270$	−5.65135	+	9.78842i	−0.343930	+	0.595704i
$271$	−8.71692	−	15.0981i	−0.529515	−	0.917147i	−0.999407	−	0.0344231i	$-0.989041\pi$
$271$	−8.71692	−	15.0981i	−0.529515	−	0.917147i	0.469892	−	0.882724i	$-0.344293\pi$
$272$	−11.8614	+	20.5446i	−0.719206	+	1.24570i
$273$	2.05247			0.124221
$274$	−7.07300			−0.427295
$275$	−0.323499	+	0.560316i	−0.0195077	+	0.0337883i
$276$	13.1075	−	22.7028i	0.788978	−	1.36655i
$277$	11.5813			0.695856			0.347928	−	0.937521i	$-0.386885\pi$
$277$	11.5813			0.695856			0.347928	+	0.937521i	$0.386885\pi$
$278$	−3.02392			−0.181362
$279$	−9.62883	+	16.6776i	−0.576463	+	0.998464i
$280$	−2.96272	−	5.13159i	−0.177057	−	0.306671i
$281$	16.4060	−	28.4160i	0.978698	−	1.69515i	0.311547	−	0.950231i	$-0.399153\pi$
$281$	16.4060	−	28.4160i	0.978698	−	1.69515i	0.667150	−	0.744923i	$-0.267514\pi$
$282$	9.18831	+	15.9146i	0.547156	+	0.947701i
$283$	9.63692	+	16.6916i	0.572855	+	0.992214i	0.996271	+	0.0862789i	$0.0274976\pi$
$283$	9.63692	+	16.6916i	0.572855	+	0.992214i	−0.423416	+	0.905935i	$0.639169\pi$
$284$	−24.7820			−1.47054
$285$	2.55252	−	2.68403i	0.151198	−	0.158988i
$286$	−3.93838			−0.232881
$287$	5.09340	+	8.82202i	0.300654	+	0.520748i
$288$	4.38656	+	7.59774i	0.258480	+	0.447701i
$289$	1.25166	−	2.16794i	0.0736271	−	0.127526i
$290$	6.47540	+	11.2157i	0.380249	+	0.658610i
$291$	2.42830	−	4.20594i	0.142349	−	0.246556i
$292$	43.3059			2.53429
$293$	−14.6557			−0.856194			−0.428097	−	0.903733i	$-0.640816\pi$
$293$	−14.6557			−0.856194			−0.428097	+	0.903733i	$0.640816\pi$
$294$	−1.07075	+	1.85460i	−0.0624475	+	0.108162i
$295$	−4.96489	+	8.59945i	−0.289067	+	0.500679i
$296$	−58.5578			−3.40360
$297$	−2.90172			−0.168375
$298$	13.2199	−	22.8976i	0.765811	−	1.32642i
$299$	−8.56261	−	14.8309i	−0.495188	−	0.857691i
$300$	−1.84872	+	3.20207i	−0.106736	+	0.184872i
$301$	−2.21493	−	3.83637i	−0.127666	−	0.221125i
$302$	−23.7505	−	41.1372i	−1.36669	−	2.36718i
$303$	−4.59351			−0.263890
$304$	−7.68558	−	26.0486i	−0.440798	−	1.49399i
$305$	3.75379			0.214941
$306$	10.9288	+	18.9292i	0.624758	+	1.08211i
$307$	−9.49724	−	16.4497i	−0.542036	−	0.938834i	−0.998787	−	0.0492395i	$-0.984320\pi$
$307$	−9.49724	−	16.4497i	−0.542036	−	0.938834i	0.456751	−	0.889595i	$-0.349013\pi$
$308$	1.40761	−	2.43806i	0.0802061	−	0.138921i
$309$	4.84869	+	8.39817i	0.275832	+	0.477755i
$310$	−10.6528	+	18.4511i	−0.605036	+	1.04795i
$311$	6.29739			0.357092			0.178546	−	0.983932i	$-0.442861\pi$
$311$	6.29739			0.357092			0.178546	+	0.983932i	$0.442861\pi$
$312$	−12.1618			−0.688527
$313$	−2.91886	+	5.05561i	−0.164984	+	0.285760i	−0.936649	−	0.350268i	$-0.886090\pi$
$313$	−2.91886	+	5.05561i	−0.164984	+	0.285760i	0.771666	+	0.636028i	$0.219424\pi$
$314$	−19.8773	+	34.4285i	−1.12174	+	1.94291i
$315$	−2.27793			−0.128347
$316$	70.9503			3.99127
$317$	7.61447	−	13.1887i	0.427671	−	0.740748i	−0.568994	−	0.822341i	$-0.692667\pi$
$317$	7.61447	−	13.1887i	0.427671	−	0.740748i	0.996666	+	0.0815929i	$0.0260007\pi$
$318$	−1.17895	−	2.04199i	−0.0661120	−	0.114509i
$319$	−1.66242	+	2.87939i	−0.0930776	+	0.161215i
$320$	−1.37763	−	2.38612i	−0.0770119	−	0.133388i
$321$	−1.90185	−	3.29409i	−0.106151	−	0.183858i
$322$	17.8681			0.995748
$323$	−4.69654	−	15.9179i	−0.261322	−	0.885696i
$324$	13.1526			0.730700
$325$	1.20769	+	2.09179i	0.0669909	+	0.116032i
$326$	0.506753	+	0.877722i	0.0280665	+	0.0486125i
$327$	−0.263097	+	0.455698i	−0.0145493	+	0.0252002i
$328$	−30.1806	−	52.2744i	−1.66645	−	2.88637i
$329$	−4.29059	+	7.43152i	−0.236548	+	0.409713i
$330$	−1.38555			−0.0762718
$331$	16.8944			0.928598			0.464299	−	0.885678i	$-0.346306\pi$
$331$	16.8944			0.928598			0.464299	+	0.885678i	$0.346306\pi$
$332$	−13.6059	+	23.5661i	−0.746722	+	1.29336i
$333$	−11.2557	+	19.4955i	−0.616810	+	1.06835i
$334$	−44.8536			−2.45428
$335$	5.86465			0.320420
$336$	2.64724	−	4.58516i	0.144419	−	0.250141i
$337$	8.15082	+	14.1176i	0.444003	+	0.769037i	0.997982	−	0.0634942i	$-0.0202245\pi$
$337$	8.15082	+	14.1176i	0.444003	+	0.769037i	−0.553979	+	0.832531i	$0.686891\pi$
$338$	9.02960	−	15.6397i	0.491146	−	0.850689i
$339$	4.04158	+	7.00023i	0.219509	+	0.380200i
$340$	8.28352	+	14.3475i	0.449237	+	0.778101i
$341$	−5.46973			−0.296203
$342$	−24.3257	−	5.86767i	−1.31538	−	0.317287i
$343$	−1.00000			−0.0539949
$344$	13.1244	+	22.7322i	0.707622	+	1.22564i
$345$	−3.01237	−	5.21759i	−0.162181	−	0.280905i
$346$	−19.9767	+	34.6007i	−1.07395	+	1.86014i
$347$	12.1908	+	21.1151i	0.654438	+	1.13352i	0.982034	+	0.188702i	$0.0604282\pi$
$347$	12.1908	+	21.1151i	0.654438	+	1.13352i	−0.327596	+	0.944818i	$0.606239\pi$
$348$	−9.50034	+	16.4551i	−0.509271	+	0.882084i
$349$	20.2804			1.08558			0.542792	−	0.839867i	$-0.317367\pi$
$349$	20.2804			1.08558			0.542792	+	0.839867i	$0.317367\pi$
$350$	−2.52016			−0.134708
$351$	−5.41640	+	9.38148i	−0.289106	+	0.500747i
$352$	−1.24591	+	2.15798i	−0.0664071	+	0.115020i
$353$	6.15345			0.327515			0.163757	−	0.986501i	$-0.447639\pi$
$353$	6.15345			0.327515			0.163757	+	0.986501i	$0.447639\pi$
$354$	−21.2647			−1.13020
$355$	−2.84771	+	4.93237i	−0.151141	+	0.261783i
$356$	6.72963	+	11.6561i	0.356670	+	0.617770i
$357$	1.61769	−	2.80192i	0.0856171	−	0.148293i
$358$	−17.2374	−	29.8560i	−0.911022	−	1.57794i
$359$	−0.544557	−	0.943200i	−0.0287406	−	0.0497802i	0.851297	−	0.524684i	$-0.175816\pi$
$359$	−0.544557	−	0.943200i	−0.0287406	−	0.0497802i	−0.880038	+	0.474903i	$0.842483\pi$
$360$	13.4977			0.711393
$361$	16.9106	+	8.66210i	0.890031	+	0.455900i
$362$	8.33862			0.438268
$363$	4.49576	+	7.78688i	0.235966	+	0.408705i
$364$	−5.25494	−	9.10183i	−0.275434	−	0.477065i
$365$	4.97630	−	8.61920i	0.260471	−	0.451150i
$366$	4.01937	+	6.96176i	0.210096	+	0.363897i
$367$	−10.1818	+	17.6353i	−0.531483	+	0.920556i	0.467841	+	0.883813i	$0.345032\pi$
$367$	−10.1818	+	17.6353i	−0.531483	+	0.920556i	−0.999325	+	0.0367438i	$0.988301\pi$
$368$	−44.1756			−2.30281
$369$	−23.2048			−1.20799
$370$	−12.4527	+	21.5686i	−0.647383	+	1.12130i
$371$	0.550523	−	0.953533i	0.0285817	−	0.0495050i
$372$	−31.2582			−1.62066
$373$	−23.4100			−1.21212			−0.606062	−	0.795417i	$-0.707252\pi$
$373$	−23.4100			−1.21212			−0.606062	+	0.795417i	$0.707252\pi$
$374$	−3.10410	+	5.37645i	−0.160509	+	0.278010i
$375$	0.424874	+	0.735903i	0.0219404	+	0.0380019i
$376$	25.4236	−	44.0350i	1.31112	−	2.27093i
$377$	6.20619	+	10.7494i	0.319635	+	0.553624i
$378$	−5.65135	−	9.78842i	−0.290674	−	0.503462i
$379$	−3.55669			−0.182695			−0.0913475	−	0.995819i	$-0.529117\pi$
$379$	−3.55669			−0.182695			−0.0913475	+	0.995819i	$0.529117\pi$
$380$	−18.4377	−	4.44742i	−0.945834	−	0.228148i
$381$	5.99580			0.307174
$382$	−24.3041	−	42.0959i	−1.24351	−	2.15382i
$383$	−2.48938	−	4.31173i	−0.127201	−	0.220319i	0.795390	−	0.606098i	$-0.207266\pi$
$383$	−2.48938	−	4.31173i	−0.127201	−	0.220319i	−0.922591	+	0.385779i	$0.873933\pi$
$384$	6.22288	−	10.7783i	0.317560	−	0.550030i
$385$	−0.323499	−	0.560316i	−0.0164870	−	0.0285563i
$386$	26.9190	−	46.6251i	1.37014	−	2.37316i
$387$	10.0909			0.512949
$388$	−24.8687			−1.26252
$389$	9.64167	−	16.6999i	0.488852	−	0.846716i	−0.511066	−	0.859542i	$-0.670749\pi$
$389$	9.64167	−	16.6999i	0.488852	−	0.846716i	0.999918	+	0.0128252i	$0.00408249\pi$
$390$	−2.58628	+	4.47957i	−0.130961	+	0.226832i
$391$	−26.9950			−1.36520
$392$	5.92545			0.299280
$393$	−4.00727	+	6.94079i	−0.202140	+	0.350117i
$394$	29.6879	+	51.4210i	1.49565	+	2.59055i
$395$	8.15293	−	14.1213i	0.410219	−	0.710519i
$396$	3.20644	+	5.55372i	0.161130	+	0.279085i
$397$	−9.80571	−	16.9840i	−0.492135	−	0.852402i	0.507824	−	0.861461i	$-0.330450\pi$
$397$	−9.80571	−	16.9840i	−0.492135	−	0.852402i	−0.999959	+	0.00905859i	$0.997117\pi$
$398$	−24.3428			−1.22020
$399$	1.04817	+	3.55256i	0.0524744	+	0.177851i
$400$	6.23065			0.311532
$401$	−14.7234	−	25.5016i	−0.735250	−	1.27349i	−0.954613	−	0.297847i	$-0.903731\pi$
$401$	−14.7234	−	25.5016i	−0.735250	−	1.27349i	0.219363	−	0.975643i	$-0.429602\pi$
$402$	6.27958	+	10.8766i	0.313197	+	0.542473i
$403$	−10.2099	+	17.6840i	−0.508591	+	0.880905i
$404$	11.7607	+	20.3702i	0.585119	+	1.01346i
$405$	1.51137	−	2.61777i	0.0751006	−	0.130078i
$406$	−12.9508			−0.642737
$407$	−6.39390			−0.316934
$408$	−9.58552	+	16.6026i	−0.474554	+	0.821951i
$409$	−7.08910	+	12.2787i	−0.350534	+	0.607142i	−0.986343	−	0.164704i	$-0.947333\pi$
$409$	−7.08910	+	12.2787i	−0.350534	+	0.607142i	0.635809	+	0.771846i	$0.280666\pi$
$410$	−25.6724			−1.26787
$411$	−2.38487			−0.117637
$412$	24.8282	−	43.0036i	1.22320	−	2.11864i
$413$	−4.96489	−	8.59945i	−0.244306	−	0.423151i
$414$	−20.3511	+	35.2491i	−1.00020	+	1.73240i
$415$	3.12692	+	5.41599i	0.153495	+	0.265860i
$416$	4.65126	+	8.05622i	0.228047	+	0.394989i
$417$	−1.01960			−0.0499302
$418$	−2.01129	−	6.81683i	−0.0983753	−	0.333422i
$419$	−14.6584			−0.716109			−0.358055	−	0.933701i	$-0.616560\pi$
$419$	−14.6584			−0.716109			−0.358055	+	0.933701i	$0.616560\pi$
$420$	−1.84872	−	3.20207i	−0.0902082	−	0.156245i
$421$	4.31940	+	7.48143i	0.210515	+	0.364622i	0.951876	−	0.306484i	$-0.0991526\pi$
$421$	4.31940	+	7.48143i	0.210515	+	0.364622i	−0.741361	+	0.671107i	$0.765819\pi$
$422$	1.43565	−	2.48662i	0.0698865	−	0.121047i
$423$	−9.77365	−	16.9285i	−0.475211	−	0.823090i
$424$	−3.26209	+	5.65011i	−0.158421	+	0.274394i
$425$	3.80745			0.184688
$426$	−12.1967			−0.590934
$427$	−1.87689	+	3.25087i	−0.0908292	+	0.157321i
$428$	−9.73859	+	16.8677i	−0.470732	+	0.815332i
$429$	−1.32794			−0.0641137
$430$	11.1640			0.538374
$431$	−7.67179	+	13.2879i	−0.369537	+	0.640057i	−0.989493	−	0.144579i	$-0.953817\pi$
$431$	−7.67179	+	13.2879i	−0.369537	+	0.640057i	0.619956	+	0.784637i	$0.287150\pi$
$432$	13.9719	+	24.2001i	0.672226	+	1.16433i
$433$	5.50758	−	9.53941i	0.264677	−	0.458435i	−0.702802	−	0.711386i	$-0.748068\pi$
$433$	5.50758	−	9.53941i	0.264677	−	0.458435i	0.967479	+	0.252951i	$0.0814012\pi$
$434$	−10.6528	−	18.4511i	−0.511349	−	0.885682i
$435$	2.18337	+	3.78172i	0.104685	+	0.181319i
$436$	2.69443			0.129040
$437$	21.2975	−	22.3947i	1.01880	−	1.07128i
$438$	21.3135			1.01840
$439$	1.38718	+	2.40267i	0.0662065	+	0.114673i	0.897229	−	0.441566i	$-0.145577\pi$
$439$	1.38718	+	2.40267i	0.0662065	+	0.114673i	−0.831022	+	0.556239i	$0.812244\pi$
$440$	1.91687	+	3.32012i	0.0913833	+	0.158281i
$441$	1.13896	−	1.97274i	0.0542364	−	0.0939402i
$442$	11.5883	+	20.0715i	0.551199	+	0.954706i
$443$	−7.51899	+	13.0233i	−0.357238	+	0.618754i	−0.987498	−	0.157630i	$-0.949615\pi$
$443$	−7.51899	+	13.0233i	−0.357238	+	0.618754i	0.630260	+	0.776384i	$0.282948\pi$
$444$	−36.5396			−1.73409
$445$	3.09322			0.146633
$446$	−0.165324	+	0.286349i	−0.00782831	+	0.0135590i
$447$	4.45750	−	7.72062i	0.210833	−	0.365173i
$448$	2.75526			0.130174
$449$	20.2821			0.957169			0.478585	−	0.878041i	$-0.341150\pi$
$449$	20.2821			0.957169			0.478585	+	0.878041i	$0.341150\pi$
$450$	2.87037	−	4.97163i	0.135311	−	0.234365i
$451$	−3.29541	−	5.70782i	−0.155175	−	0.268771i
$452$	20.6953	−	35.8453i	0.973426	−	1.68602i
$453$	−8.00821	−	13.8706i	−0.376258	−	0.651699i
$454$	−20.9093	−	36.2160i	−0.981322	−	1.69970i
$455$	−2.41539			−0.113235
$456$	−6.21090	−	21.0505i	−0.290852	−	0.985780i
$457$	−2.88806			−0.135098			−0.0675488	−	0.997716i	$-0.521518\pi$
$457$	−2.88806			−0.135098			−0.0675488	+	0.997716i	$0.521518\pi$
$458$	−2.60471	−	4.51150i	−0.121710	−	0.210808i
$459$	8.53804	+	14.7883i	0.398521	+	0.690259i
$460$	−15.4252	+	26.7171i	−0.719201	+	1.24569i
$461$	7.14575	+	12.3768i	0.332811	+	0.576445i	0.983062	−	0.183274i	$-0.0586697\pi$
$461$	7.14575	+	12.3768i	0.332811	+	0.576445i	−0.650251	+	0.759719i	$0.725336\pi$
$462$	0.692773	−	1.19992i	0.0322307	−	0.0558252i
$463$	26.6799			1.23992			0.619959	−	0.784634i	$-0.287149\pi$
$463$	26.6799			1.23992			0.619959	+	0.784634i	$0.287149\pi$
$464$	32.0185			1.48642
$465$	−3.59190	+	6.22135i	−0.166570	+	0.288508i
$466$	32.9401	−	57.0540i	1.52592	−	2.64297i
$467$	21.0193			0.972657			0.486328	−	0.873776i	$-0.338336\pi$
$467$	21.0193			0.972657			0.486328	+	0.873776i	$0.338336\pi$
$468$	23.9408			1.10666
$469$	−2.93233	+	5.07894i	−0.135402	+	0.234523i
$470$	−10.8130	−	18.7286i	−0.498765	−	0.863887i
$471$	−6.70223	+	11.6086i	−0.308822	+	0.534896i
$472$	29.4192	+	50.9556i	1.35413	+	2.34542i
$473$	1.43305	+	2.48212i	0.0658918	+	0.114128i
$474$	34.9191			1.60389
$475$	−3.00386	+	3.15861i	−0.137826	+	0.144927i
$476$	−16.5670			−0.759349
$477$	1.25405	+	2.17208i	0.0574191	+	0.0994527i
$478$	−11.5350	−	19.9791i	−0.527597	−	0.913825i
$479$	−3.68051	+	6.37483i	−0.168167	+	0.291273i	−0.937775	−	0.347243i	$-0.887118\pi$
$479$	−3.68051	+	6.37483i	−0.168167	+	0.291273i	0.769609	+	0.638516i	$0.220451\pi$
$480$	1.63634	+	2.83423i	0.0746884	+	0.129364i
$481$	−11.9350	+	20.6719i	−0.544187	+	0.942560i
$482$	65.0964			2.96506
$483$	6.02475			0.274136
$484$	23.0210	−	39.8735i	1.04641	−	1.81243i
$485$	−2.85767	+	4.94963i	−0.129760	+	0.224751i
$486$	40.3813			1.83173
$487$	−17.2766			−0.782879			−0.391439	−	0.920204i	$-0.628023\pi$
$487$	−17.2766			−0.782879			−0.391439	+	0.920204i	$0.628023\pi$
$488$	11.1214	−	19.2629i	0.503443	−	0.871990i
$489$	0.170867	+	0.295950i	0.00772687	+	0.0133833i
$490$	1.26008	−	2.18252i	0.0569247	−	0.0985964i
$491$	5.00946	+	8.67663i	0.226074	+	0.391571i	0.956641	−	0.291270i	$-0.0940777\pi$
$491$	5.00946	+	8.67663i	0.226074	+	0.391571i	−0.730567	+	0.682841i	$0.760744\pi$
$492$	−18.8325	−	32.6189i	−0.849035	−	1.47057i
$493$	19.5660			0.881209
$494$	−25.7936	−	6.22175i	−1.16051	−	0.279930i
$495$	1.47381			0.0662430
$496$	26.3370	+	45.6171i	1.18257	+	2.04827i
$497$	−2.84771	−	4.93237i	−0.127737	−	0.221247i
$498$	−6.69631	+	11.5984i	−0.300069	+	0.519735i
$499$	20.5923	+	35.6669i	0.921839	+	1.59667i	0.796568	+	0.604549i	$0.206647\pi$
$499$	20.5923	+	35.6669i	0.921839	+	1.59667i	0.125271	+	0.992123i	$0.460020\pi$
$500$	2.17561	−	3.76826i	0.0972962	−	0.168522i
$501$	−15.1237			−0.675678
$502$	19.1573			0.855032
$503$	13.8592	−	24.0048i	0.617951	−	1.07032i	−0.371908	−	0.928269i	$-0.621296\pi$
$503$	13.8592	−	24.0048i	0.617951	−	1.07032i	0.989859	−	0.142053i	$-0.0453702\pi$
$504$	−6.74887	+	11.6894i	−0.300619	+	0.520687i
$505$	5.40573			0.240552
$506$	−11.5606			−0.513930
$507$	3.04460	−	5.27340i	0.135216	−	0.234200i
$508$	−15.3510	−	26.5888i	−0.681092	−	1.17969i
$509$	1.28181	−	2.22016i	0.0568153	−	0.0984069i	−0.836219	−	0.548396i	$-0.815239\pi$
$509$	1.28181	−	2.22016i	0.0568153	−	0.0984069i	0.893034	+	0.449989i	$0.148572\pi$
$510$	4.07683	+	7.06128i	0.180525	+	0.312679i
$511$	4.97630	+	8.61920i	0.220139	+	0.381291i
$512$	−49.8423			−2.20274
$513$	−19.0042	−	4.58406i	−0.839057	−	0.202391i
$514$	−33.5837			−1.48131
$515$	−5.70603	−	9.88313i	−0.251438	−	0.435503i
$516$	8.18956	+	14.1847i	0.360525	+	0.624448i
$517$	2.77600	−	4.80817i	0.122088	−	0.211463i
$518$	−12.4527	−	21.5686i	−0.547138	−	0.947671i
$519$	−6.73574	+	11.6666i	−0.295666	+	0.512109i
$520$	14.3123			0.627634
$521$	3.99936			0.175215			0.0876075	−	0.996155i	$-0.472078\pi$
$521$	3.99936			0.175215			0.0876075	+	0.996155i	$0.472078\pi$
$522$	14.7505	−	25.5486i	0.645612	−	1.11823i
$523$	−15.2930	+	26.4882i	−0.668716	+	1.15825i	0.309547	+	0.950884i	$0.399822\pi$
$523$	−15.2930	+	26.4882i	−0.668716	+	1.15825i	−0.978263	+	0.207366i	$0.933511\pi$
$524$	41.0392			1.79281
$525$	−0.849748			−0.0370860
$526$	33.5342	−	58.0829i	1.46216	−	2.53253i
$527$	16.0941	+	27.8759i	0.701072	+	1.21429i
$528$	−1.71276	+	2.96658i	−0.0745382	+	0.129104i
$529$	−13.6344	−	23.6154i	−0.592798	−	1.02676i
$530$	1.38741	+	2.40306i	0.0602651	+	0.104382i
$531$	22.6193			0.981596
$532$	13.0704	−	13.7438i	0.566675	−	0.595870i
$533$	−24.6051			−1.06576
$534$	3.31207	+	5.73667i	0.143327	+	0.248250i
$535$	2.23813	+	3.87655i	0.0967628	+	0.167598i
$536$	17.3753	−	30.0950i	0.750500	−	1.29990i
$537$	−5.81209	−	10.0668i	−0.250810	−	0.434416i
$538$	19.2549	−	33.3505i	0.830138	−	1.43784i
$539$	0.646997			0.0278681
$540$	19.5148			0.839784
$541$	15.9825	−	27.6825i	0.687142	−	1.19016i	−0.285617	−	0.958344i	$-0.592198\pi$
$541$	15.9825	−	27.6825i	0.687142	−	1.19016i	0.972759	−	0.231821i	$-0.0744683\pi$
$542$	−21.9680	+	38.0498i	−0.943608	+	1.63438i
$543$	2.81161			0.120658
$544$	14.6638			0.628707
$545$	0.309618	−	0.536274i	0.0132626	−	0.0229715i
$546$	−2.58628	−	4.47957i	−0.110683	−	0.191708i
$547$	7.97687	−	13.8163i	0.341066	−	0.590744i	−0.643565	−	0.765392i	$-0.722545\pi$
$547$	7.97687	−	13.8163i	0.341066	−	0.590744i	0.984631	+	0.174648i	$0.0558786\pi$
$548$	6.10599	+	10.5759i	0.260835	+	0.451779i
$549$	−4.27543	−	7.40526i	−0.182471	−	0.316049i
$550$	1.63054			0.0695263
$551$	−15.4364	+	16.2317i	−0.657615	+	0.691495i
$552$	−35.6993			−1.51946
$553$	8.15293	+	14.1213i	0.346698	+	0.600498i
$554$	−14.5934	−	25.2766i	−0.620016	−	1.07390i
$555$	−4.19879	+	7.27251i	−0.178229	+	0.308701i
$556$	2.61049	+	4.52150i	0.110709	+	0.191754i
$557$	−10.8612	+	18.8121i	−0.460203	+	0.797095i	−0.998971	−	0.0453597i	$-0.985557\pi$
$557$	−10.8612	+	18.8121i	−0.460203	+	0.797095i	0.538768	+	0.842454i	$0.318890\pi$
$558$	48.5324			2.05454
$559$	10.6998			0.452555
$560$	−3.11532	+	5.39590i	−0.131647	+	0.228018i
$561$	−1.04664	+	1.81283i	−0.0441891	+	0.0765378i
$562$	−82.6914			−3.48812
$563$	42.8982			1.80794			0.903971	−	0.427593i	$-0.140638\pi$
$563$	42.8982			1.80794			0.903971	+	0.427593i	$0.140638\pi$
$564$	15.8642	−	27.4776i	0.668003	−	1.15701i
$565$	−4.75621	−	8.23800i	−0.200095	−	0.346575i
$566$	24.2866	−	42.0656i	1.02084	−	1.76815i
$567$	1.51137	+	2.61777i	0.0634716	+	0.109936i
$568$	16.8739	+	29.2265i	0.708014	+	1.22632i
$569$	11.5690			0.484997			0.242498	−	0.970152i	$-0.422033\pi$
$569$	11.5690			0.484997			0.242498	+	0.970152i	$0.422033\pi$
$570$	−9.07434	−	2.18885i	−0.380082	−	0.0916808i
$571$	40.5125			1.69540			0.847699	−	0.530478i	$-0.177988\pi$
$571$	40.5125			1.69540			0.847699	+	0.530478i	$0.177988\pi$
$572$	3.39993	+	5.88885i	0.142158	+	0.246225i
$573$	−8.19486	−	14.1939i	−0.342345	−	0.592959i
$574$	12.8362	−	22.2329i	0.535772	−	0.927984i
$575$	3.54502	+	6.14016i	0.147838	+	0.256062i
$576$	−3.13814	+	5.43542i	−0.130756	+	0.226476i
$577$	−13.5844			−0.565526			−0.282763	−	0.959190i	$-0.591251\pi$
$577$	−13.5844			−0.565526			−0.282763	+	0.959190i	$0.591251\pi$
$578$	−6.30877			−0.262410
$579$	9.07656	−	15.7211i	0.377209	−	0.653345i
$580$	11.1802	−	19.3646i	0.464232	−	0.804073i
$581$	−6.25385			−0.259453
$582$	−12.2394			−0.507340
$583$	−0.356187	+	0.616933i	−0.0147517	+	0.0255508i
$584$	−29.4868	−	51.0726i	−1.22017	−	2.11340i
$585$	2.75104	−	4.76494i	0.113742	−	0.197006i
$586$	18.4673	+	31.9864i	0.762879	+	1.32135i
$587$	−19.7388	−	34.1887i	−0.814709	−	1.41112i	−0.909537	−	0.415623i	$-0.863563\pi$
$587$	−19.7388	−	34.1887i	−0.814709	−	1.41112i	0.0948280	−	0.995494i	$-0.469770\pi$
$588$	3.69744			0.152480
$589$	−35.8228	−	8.64094i	−1.47605	−	0.356044i
$590$	25.0247			1.03025
$591$	10.0102	+	17.3381i	0.411763	+	0.713195i
$592$	30.7870	+	53.3246i	1.26534	+	2.19163i
$593$	−11.0363	+	19.1155i	−0.453208	+	0.784979i	−0.998583	−	0.0532129i	$-0.983054\pi$
$593$	−11.0363	+	19.1155i	−0.453208	+	0.784979i	0.545375	+	0.838192i	$0.316387\pi$
$594$	3.65641	+	6.33308i	0.150024	+	0.259849i
$595$	−1.90373	+	3.29735i	−0.0780451	+	0.135178i
$596$	−45.6501			−1.86990
$597$	−8.20791			−0.335928
$598$	−21.5792	+	37.3762i	−0.882437	+	1.52843i
$599$	10.8900	−	18.8621i	0.444954	−	0.770683i	−0.553095	−	0.833118i	$-0.686553\pi$
$599$	10.8900	−	18.8621i	0.444954	−	0.770683i	0.998049	+	0.0624351i	$0.0198867\pi$
$600$	5.03514			0.205559
$601$	5.11819			0.208775			0.104388	−	0.994537i	$-0.466712\pi$
$601$	5.11819			0.208775			0.104388	+	0.994537i	$0.466712\pi$
$602$	−5.58198	+	9.66827i	−0.227504	+	0.394049i
$603$	−6.67963	−	11.5695i	−0.272015	−	0.471145i
$604$	−41.0068	+	71.0259i	−1.66854	+	2.89000i
$605$	−5.29070	−	9.16376i	−0.215097	−	0.372560i
$606$	5.78819	+	10.0254i	0.235129	+	0.407256i
$607$	−7.95136			−0.322736			−0.161368	−	0.986894i	$-0.551591\pi$
$607$	−7.95136			−0.322736			−0.161368	+	0.986894i	$0.551591\pi$
$608$	−11.5689	+	12.1649i	−0.469182	+	0.493354i
$609$	−4.36675			−0.176950
$610$	−4.73008	−	8.19273i	−0.191515	−	0.331714i
$611$	−10.3634	−	17.9500i	−0.419260	−	0.726180i
$612$	18.8693	−	32.6825i	0.762745	−	1.32111i
$613$	1.89160	+	3.27635i	0.0764011	+	0.132331i	0.901695	−	0.432373i	$-0.142324\pi$
$613$	1.89160	+	3.27635i	0.0764011	+	0.132331i	−0.825294	+	0.564704i	$0.808990\pi$
$614$	−23.9346	+	41.4559i	−0.965921	+	1.67302i
$615$	−8.65621			−0.349052
$616$	−3.83375			−0.154466
$617$	4.88725	−	8.46496i	0.196753	−	0.340787i	−0.750721	−	0.660620i	$-0.770294\pi$
$617$	4.88725	−	8.46496i	0.196753	−	0.340787i	0.947474	+	0.319833i	$0.103627\pi$
$618$	12.2195	−	21.1648i	0.491539	−	0.851371i
$619$	0.103122			0.00414483			0.00207241	−	0.999998i	$-0.499340\pi$
$619$	0.103122			0.00414483			0.00207241	+	0.999998i	$0.499340\pi$
$620$	36.7853			1.47733
$621$	−15.8991	+	27.5380i	−0.638009	+	1.10506i
$622$	−7.93522	−	13.7442i	−0.318173	−	0.551092i
$623$	−1.54661	+	2.67881i	−0.0619636	+	0.107324i
$624$	6.39412	+	11.0749i	0.255970	+	0.443352i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	14.7120			0.588009
$627$	−0.678166	−	2.29850i	−0.0270833	−	0.0917931i
$628$	68.6388			2.73899
$629$	18.8134	+	32.5858i	0.750140	+	1.29928i
$630$	2.87037	+	4.97163i	0.114358	+	0.198075i
$631$	−12.2295	+	21.1822i	−0.486850	+	0.843248i	−0.999886	−	0.0151187i	$-0.995187\pi$
$631$	−12.2295	+	21.1822i	−0.486850	+	0.843248i	0.513036	+	0.858367i	$0.328521\pi$
$632$	−48.3098	−	83.6750i	−1.92166	−	3.32841i
$633$	0.484073	−	0.838440i	0.0192402	−	0.0333250i
$634$	−38.3794			−1.52424
$635$	−7.05597			−0.280008
$636$	−2.03552	+	3.52563i	−0.0807138	+	0.139800i
$637$	1.20769	−	2.09179i	0.0478506	−	0.0828797i
$638$	8.37913			0.331733
$639$	12.9737			0.513233
$640$	−7.32321	+	12.6842i	−0.289475	+	0.501386i
$641$	−18.5896	−	32.1981i	−0.734244	−	1.27175i	−0.955054	−	0.296431i	$-0.904203\pi$
$641$	−18.5896	−	32.1981i	−0.734244	−	1.27175i	0.220810	−	0.975317i	$-0.429130\pi$
$642$	−4.79296	+	8.30165i	−0.189163	+	0.327640i
$643$	5.81123	+	10.0653i	0.229173	+	0.396938i	0.957563	−	0.288224i	$-0.0930647\pi$
$643$	5.81123	+	10.0653i	0.229173	+	0.396938i	−0.728391	+	0.685162i	$0.759731\pi$
$644$	−15.4252	−	26.7171i	−0.607836	−	1.05280i
$645$	3.76426			0.148218
$646$	−28.8232	+	30.3081i	−1.13403	+	1.19246i
$647$	−41.4596			−1.62994			−0.814972	−	0.579501i	$-0.803248\pi$
$647$	−41.4596			−1.62994			−0.814972	+	0.579501i	$0.803248\pi$
$648$	−8.95555	−	15.5115i	−0.351807	−	0.609348i
$649$	3.21227	+	5.56382i	0.126093	+	0.218399i
$650$	3.04359	−	5.27165i	0.119379	−	0.206771i
$651$	−3.59190	−	6.22135i	−0.140778	−	0.243834i
$652$	0.874941	−	1.51544i	0.0342653	−	0.0593493i
$653$	−48.3225			−1.89101			−0.945503	−	0.325613i	$-0.894429\pi$
$653$	−48.3225			−1.89101			−0.945503	+	0.325613i	$0.894429\pi$
$654$	1.32610			0.0518545
$655$	4.71583	−	8.16806i	0.184263	−	0.319152i
$656$	−31.7352	+	54.9669i	−1.23905	+	2.14610i
$657$	−22.6713			−0.884492
$658$	21.6260			0.843067
$659$	−15.4787	+	26.8098i	−0.602963	+	1.04436i	0.389407	+	0.921066i	$0.372680\pi$
$659$	−15.4787	+	26.8098i	−0.602963	+	1.04436i	−0.992370	+	0.123297i	$0.960653\pi$
$660$	1.19612	+	2.07173i	0.0465587	+	0.0806421i
$661$	13.1126	−	22.7117i	0.510022	−	0.883384i	−0.489911	−	0.871773i	$-0.662971\pi$
$661$	13.1126	−	22.7117i	0.510022	−	0.883384i	0.999933	−	0.0116113i	$-0.00369609\pi$
$662$	−21.2883	−	36.8724i	−0.827392	−	1.43308i
$663$	3.90734	+	6.76772i	0.151749	+	0.262836i
$664$	37.0568			1.43808
$665$	−1.23351	−	4.18072i	−0.0478336	−	0.162121i
$666$	56.7325			2.19834
$667$	18.2174	+	31.5535i	0.705381	+	1.22176i
$668$	38.7213	+	67.0672i	1.49817	+	2.59491i
$669$	−0.0557439	+	0.0965512i	−0.00215518	+	0.00373289i
$670$	−7.38993	−	12.7997i	−0.285498	−	0.494497i
$671$	1.21434	−	2.10331i	0.0468792	−	0.0811972i
$672$	−3.27268			−0.126246
$673$	16.9063			0.651691			0.325846	−	0.945423i	$-0.394351\pi$
$673$	16.9063			0.651691			0.325846	+	0.945423i	$0.394351\pi$
$674$	20.5414	−	35.5787i	0.791225	−	1.37044i
$675$	2.24245	−	3.88405i	0.0863121	−	0.149497i
$676$	−31.1803			−1.19924
$677$	−19.2187			−0.738633			−0.369317	−	0.929304i	$-0.620408\pi$
$677$	−19.2187			−0.738633			−0.369317	+	0.929304i	$0.620408\pi$
$678$	10.1854	−	17.6417i	0.391170	−	0.677526i
$679$	−2.85767	−	4.94963i	−0.109667	−	0.189949i
$680$	11.2804	−	19.5383i	0.432584	−	0.749258i
$681$	−7.05020	−	12.2113i	−0.270164	−	0.467938i
$682$	6.89230	+	11.9378i	0.263920	+	0.457123i
$683$	−12.8676			−0.492366			−0.246183	−	0.969223i	$-0.579176\pi$
$683$	−12.8676			−0.492366			−0.246183	+	0.969223i	$0.579176\pi$
$684$	12.2263	+	41.4383i	0.467483	+	1.58443i
$685$	2.80657			0.107233
$686$	1.26008	+	2.18252i	0.0481101	+	0.0833292i
$687$	−0.878257	−	1.52119i	−0.0335076	−	0.0580369i
$688$	13.8004	−	23.9031i	0.526137	−	0.911296i
$689$	1.32973	+	2.30315i	0.0506586	+	0.0877432i
$690$	−7.59167	+	13.1492i	−0.289010	+	0.500580i
$691$	−18.0598			−0.687028			−0.343514	−	0.939147i	$-0.611617\pi$
$691$	−18.0598			−0.687028			−0.343514	+	0.939147i	$0.611617\pi$
$692$	68.9820			2.62230
$693$	−0.736906	+	1.27636i	−0.0279928	+	0.0484849i
$694$	30.7229	−	53.2136i	1.16622	−	2.01996i
$695$	1.19989			0.0455144
$696$	25.8749			0.980787
$697$	−19.3929	+	33.5894i	−0.734557	+	1.27229i
$698$	−25.5549	−	44.2624i	−0.967268	−	1.67536i
$699$	11.1068	−	19.2375i	0.420096	−	0.727628i
$700$	2.17561	+	3.76826i	0.0822303	+	0.142427i
$701$	8.72049	+	15.1043i	0.329368	+	0.570482i	0.982387	−	0.186860i	$-0.0598309\pi$
$701$	8.72049	+	15.1043i	0.329368	+	0.570482i	−0.653018	+	0.757342i	$0.726498\pi$
$702$	27.3004			1.03039
$703$	−41.8755	−	10.1009i	−1.57936	−	0.380963i
$704$	−1.78264			−0.0671860
$705$	−3.64592	−	6.31492i	−0.137313	−	0.237834i
$706$	−7.75384	−	13.4300i	−0.291820	−	0.505446i
$707$	−2.70286	+	4.68150i	−0.101652	+	0.176066i
$708$	18.3574	+	31.7959i	0.689913	+	1.19496i
$709$	18.1042	−	31.3573i	0.679916	−	1.17765i	−0.295090	−	0.955469i	$-0.595350\pi$
$709$	18.1042	−	31.3573i	0.679916	−	1.17765i	0.975006	−	0.222179i	$-0.0713170\pi$
$710$	14.3534			0.538672
$711$	−37.1436			−1.39299
$712$	9.16435	−	15.8731i	0.343449	−	0.594870i
$713$	−29.9697	+	51.9091i	−1.12237	+	1.94401i
$714$	−8.15367			−0.305143
$715$	1.56275			0.0584435
$716$	−29.7614	+	51.5482i	−1.11223	+	1.92645i
$717$	−3.88936	−	6.73657i	−0.145251	−	0.251582i
$718$	−1.37237	+	2.37702i	−0.0512164	+	0.0887095i
$719$	−13.4948	−	23.3736i	−0.503270	−	0.871689i	−0.999993	−	0.00377967i	$-0.998797\pi$
$719$	−13.4948	−	23.3736i	−0.503270	−	0.871689i	0.496723	−	0.867909i	$-0.334536\pi$
$720$	−7.09649	−	12.2915i	−0.264470	−	0.458076i
$721$	11.4121			0.425007
$722$	−2.40346	−	47.8227i	−0.0894475	−	1.77978i
$723$	21.9492			0.816300
$724$	−7.19857	−	12.4683i	−0.267533	−	0.463380i
$725$	−2.56944	−	4.45040i	−0.0954265	−	0.165284i
$726$	11.3300	−	19.6242i	0.420497	−	0.728323i
$727$	−8.15754	−	14.1293i	−0.302546	−	0.524026i	0.674166	−	0.738580i	$-0.264503\pi$
$727$	−8.15754	−	14.1293i	−0.302546	−	0.524026i	−0.976712	+	0.214555i	$0.931170\pi$
$728$	−7.15613	+	12.3948i	−0.265224	+	0.459381i
$729$	4.54754			0.168427
$730$	−25.0822			−0.928332
$731$	8.43323	−	14.6068i	0.311914	−	0.540251i
$732$	6.93970	−	12.0199i	0.256499	−	0.444269i
$733$	44.3334			1.63749			0.818746	−	0.574156i	$-0.194670\pi$
$733$	44.3334			1.63749			0.818746	+	0.574156i	$0.194670\pi$
$734$	51.3194			1.89423
$735$	0.424874	−	0.735903i	0.0156717	−	0.0271442i
$736$	13.6531	+	23.6479i	0.503261	+	0.871674i
$737$	1.89721	−	3.28606i	0.0698845	−	0.121043i
$738$	29.2399	+	50.6450i	1.07634	+	1.86427i
$739$	−8.54593	−	14.8020i	−0.314367	−	0.544500i	0.664936	−	0.746901i	$-0.268459\pi$
$739$	−8.54593	−	14.8020i	−0.314367	−	0.544500i	−0.979303	+	0.202401i	$0.935126\pi$
$740$	43.0006			1.58073
$741$	−8.69708	−	2.09785i	−0.319495	−	0.0770665i
$742$	−2.77481			−0.101867
$743$	−3.11326	−	5.39233i	−0.114214	−	0.197825i	0.803251	−	0.595641i	$-0.203102\pi$
$743$	−3.11326	−	5.39233i	−0.114214	−	0.197825i	−0.917465	+	0.397815i	$0.869768\pi$
$744$	21.2836	+	36.8643i	0.780294	+	1.35151i
$745$	−5.24567	+	9.08577i	−0.192187	+	0.332877i
$746$	29.4985	+	51.0929i	1.08002	+	1.87064i
$747$	7.12291	−	12.3372i	0.260614	−	0.451396i
$748$	10.7188			0.391919
$749$	−4.47626			−0.163559
$750$	1.07075	−	1.85460i	0.0390983	−	0.0677203i
$751$	−24.9588	+	43.2298i	−0.910758	+	1.57748i	−0.0977621	+	0.995210i	$0.531168\pi$
$751$	−24.9588	+	43.2298i	−0.910758	+	1.57748i	−0.812996	+	0.582269i	$0.802165\pi$
$752$	−53.4663			−1.94972
$753$	6.45945			0.235396
$754$	15.6406	−	27.0903i	0.569598	−	0.986572i
$755$	9.42421	+	16.3232i	0.342982	+	0.594063i
$756$	−9.75741	+	16.9003i	−0.354873	+	0.614659i
$757$	−6.59163	−	11.4170i	−0.239577	−	0.414960i	0.721016	−	0.692918i	$-0.243675\pi$
$757$	−6.59163	−	11.4170i	−0.239577	−	0.414960i	−0.960593	+	0.277959i	$0.910342\pi$
$758$	4.48172	+	7.76257i	0.162783	+	0.281949i
$759$	−3.89800			−0.141488
$760$	7.30911	+	24.7726i	0.265129	+	0.898598i
$761$	33.6334			1.21921			0.609605	−	0.792705i	$-0.291328\pi$
$761$	33.6334			1.21921			0.609605	+	0.792705i	$0.291328\pi$
$762$	−7.55519	−	13.0860i	−0.273696	−	0.474055i
$763$	0.309618	+	0.536274i	0.0112089	+	0.0194144i
$764$	−41.9625	+	72.6813i	−1.51815	+	2.62952i
$765$	−4.33655	−	7.51112i	−0.156788	−	0.271565i
$766$	−6.27364	+	10.8663i	−0.226676	+	0.392614i
$767$	23.9843			0.866023
$768$	−26.6828			−0.962832
$769$	−6.49213	+	11.2447i	−0.234112	+	0.405494i	−0.959014	−	0.283358i	$-0.908552\pi$
$769$	−6.49213	+	11.2447i	−0.234112	+	0.405494i	0.724902	+	0.688852i	$0.241885\pi$
$770$	−0.815269	+	1.41209i	−0.0293802	+	0.0508881i
$771$	−11.3237			−0.407815
$772$	−92.9547			−3.34551
$773$	−0.984097	+	1.70451i	−0.0353955	+	0.0613068i	−0.883180	−	0.469033i	$-0.844602\pi$
$773$	−0.984097	+	1.70451i	−0.0353955	+	0.0613068i	0.847785	+	0.530340i	$0.177936\pi$
$774$	−12.7153	−	22.0236i	−0.457044	−	0.791623i
$775$	4.22701	−	7.32140i	0.151839	−	0.262993i
$776$	16.9330	+	29.3288i	0.607858	+	1.05284i
$777$	−4.19879	−	7.27251i	−0.150631	−	0.260900i
$778$	−48.5971			−1.74229
$779$	−12.5655	−	42.5882i	−0.450207	−	1.52588i
$780$	8.93075			0.319772
$781$	1.84246	+	3.19123i	0.0659283	+	0.114191i
$782$	34.0159	+	58.9172i	1.21640	+	2.10688i
$783$	11.5237	−	19.9596i	0.411823	−	0.713299i
$784$	−3.11532	−	5.39590i	−0.111262	−	0.192711i
$785$	7.88731	−	13.6612i	0.281510	−	0.487590i
$786$	20.1979			0.720436
$787$	39.7072			1.41541			0.707704	−	0.706509i	$-0.249731\pi$
$787$	39.7072			1.41541			0.707704	+	0.706509i	$0.249731\pi$
$788$	51.2580	−	88.7815i	1.82599	−	3.16271i
$789$	11.3071	−	19.5844i	0.402542	−	0.697223i
$790$	−41.0934			−1.46204
$791$	9.51243			0.338223
$792$	4.36650	−	7.56300i	0.155157	−	0.268739i
$793$	−4.53343	−	7.85213i	−0.160987	−	0.278837i
$794$	−24.7120	+	42.8024i	−0.876995	+	1.51900i
$795$	0.467806	+	0.810263i	0.0165914	+	0.0287371i
$796$	21.0147	+	36.3985i	0.744846	+	1.29011i
$797$	−1.09478			−0.0387789			−0.0193895	−	0.999812i	$-0.506172\pi$
$797$	−1.09478			−0.0387789			−0.0193895	+	0.999812i	$0.506172\pi$
$798$	6.43277	−	6.76418i	0.227717	−	0.239449i
$799$	−32.6724			−1.15587
$800$	−1.92568	−	3.33537i	−0.0680830	−	0.117923i
$801$	−3.52307	−	6.10213i	−0.124481	−	0.215608i
$802$	−37.1053	+	64.2682i	−1.31023	+	2.26939i
$803$	−3.21965	−	5.57660i	−0.113619	−	0.196794i
$804$	10.8421	−	18.7791i	0.382371	−	0.662286i
$805$	−7.09004			−0.249891
$806$	51.4611			1.81264
$807$	6.49237	−	11.2451i	0.228542	−	0.395847i
$808$	16.0157	−	27.7400i	0.563429	−	0.975888i
$809$	32.1786			1.13134			0.565670	−	0.824632i	$-0.308618\pi$
$809$	32.1786			1.13134			0.565670	+	0.824632i	$0.308618\pi$
$810$	−7.61780			−0.267662
$811$	−9.23381	+	15.9934i	−0.324243	+	0.561605i	−0.981359	−	0.192184i	$-0.938443\pi$
$811$	−9.23381	+	15.9934i	−0.324243	+	0.561605i	0.657116	+	0.753790i	$0.271776\pi$
$812$	11.1802	+	19.3646i	0.392347	+	0.679566i
$813$	−7.40718	+	12.8296i	−0.259781	+	0.449954i
$814$	8.05683	+	13.9548i	0.282392	+	0.489117i
$815$	−0.201080	−	0.348280i	−0.00704351	−	0.0121997i
$816$	20.1585			0.705688
$817$	5.46428	+	18.5200i	0.191171	+	0.647933i
$818$	35.7314			1.24932
$819$	2.75104	+	4.76494i	0.0961292	+	0.166501i
$820$	22.1625	+	38.3865i	0.773947	+	1.34052i
$821$	−7.90769	+	13.6965i	−0.275980	+	0.478012i	−0.970382	−	0.241576i	$-0.922336\pi$
$821$	−7.90769	+	13.6965i	−0.275980	+	0.478012i	0.694402	+	0.719588i	$0.255669\pi$
$822$	3.00513	+	5.20504i	0.104816	+	0.181547i
$823$	−25.8194	+	44.7206i	−0.900009	+	1.55886i	−0.0725280	+	0.997366i	$0.523107\pi$
$823$	−25.8194	+	44.7206i	−0.900009	+	1.55886i	−0.827481	+	0.561494i	$0.810227\pi$
$824$	−67.6215			−2.35571
$825$	0.549785			0.0191410
$826$	−12.5123	+	21.6720i	−0.435360	+	0.754065i
$827$	−15.5529	+	26.9384i	−0.540828	+	0.936741i	0.458029	+	0.888937i	$0.348556\pi$
$827$	−15.5529	+	26.9384i	−0.540828	+	0.936741i	−0.998857	+	0.0478036i	$0.984778\pi$
$828$	70.2748			2.44222
$829$	−18.5607			−0.644640			−0.322320	−	0.946631i	$-0.604463\pi$
$829$	−18.5607			−0.644640			−0.322320	+	0.946631i	$0.604463\pi$
$830$	7.88035	−	13.6492i	0.273531	−	0.473770i
$831$	−4.92061	−	8.52275i	−0.170694	−	0.295651i
$832$	−3.32751	+	5.76342i	−0.115361	+	0.199811i
$833$	−1.90373	−	3.29735i	−0.0659602	−	0.114246i
$834$	1.28478	+	2.22531i	0.0444884	+	0.0770562i
$835$	17.7979			0.615922
$836$	−8.45653	+	8.89221i	−0.292475	+	0.307543i
$837$	37.9156			1.31055
$838$	18.4708	+	31.9923i	0.638062	+	1.10516i
$839$	21.5567	+	37.3373i	0.744221	+	1.28903i	0.950558	+	0.310547i	$0.100512\pi$
$839$	21.5567	+	37.3373i	0.744221	+	1.28903i	−0.206337	+	0.978481i	$0.566154\pi$
$840$	−2.51757	+	4.36056i	−0.0868643	+	0.150453i
$841$	1.29598	+	2.24470i	0.0446890	+	0.0774036i
$842$	10.8856	−	18.8544i	0.375142	−	0.649766i
$843$	−27.8819			−0.960302
$844$	−4.95749			−0.170644
$845$	−3.58295	+	6.20584i	−0.123257	+	0.213488i
$846$	−24.6312	+	42.6625i	−0.846838	+	1.46677i
$847$	10.5814			0.363581
$848$	6.86023			0.235581
$849$	8.18895	−	14.1837i	0.281044	−	0.486783i
$850$	−4.79770	−	8.30985i	−0.164560	−	0.285026i
$851$	−35.0334	+	60.6796i	−1.20093	+	2.08007i
$852$	10.5292	+	18.2371i	0.360725	+	0.624794i
$853$	1.65993	+	2.87509i	0.0568350	+	0.0984412i	0.893043	−	0.449971i	$-0.148566\pi$
$853$	1.65993	+	2.87509i	0.0568350	+	0.0984412i	−0.836208	+	0.548412i	$0.815232\pi$
$854$	9.46015			0.323720
$855$	9.65242	+	2.32829i	0.330106	+	0.0796258i
$856$	26.5238			0.906566
$857$	−17.9789	−	31.1403i	−0.614147	−	1.06373i	−0.990534	−	0.137271i	$-0.956167\pi$
$857$	−17.9789	−	31.1403i	−0.614147	−	1.06373i	0.376387	−	0.926463i	$-0.377166\pi$
$858$	1.67332	+	2.89827i	0.0571261	+	0.0989453i
$859$	9.84876	−	17.0586i	0.336035	−	0.582030i	−0.647648	−	0.761940i	$-0.724247\pi$
$859$	9.84876	−	17.0586i	0.336035	−	0.582030i	0.983683	+	0.179910i	$0.0575805\pi$
$860$	−9.63763	−	16.6929i	−0.328640	−	0.569222i
$861$	4.32810	−	7.49650i	0.147501	−	0.255480i
$862$	38.6683			1.31705
$863$	−4.19551			−0.142817			−0.0714084	−	0.997447i	$-0.522749\pi$
$863$	−4.19551			−0.142817			−0.0714084	+	0.997447i	$0.522749\pi$
$864$	8.63649	−	14.9588i	0.293819	−	0.508910i
$865$	7.92675	−	13.7295i	0.269518	−	0.466818i
$866$	−27.7600			−0.943323
$867$	−2.12719			−0.0722432
$868$	−18.3927	+	31.8570i	−0.624287	+	1.08130i
$869$	−5.27492	−	9.13644i	−0.178940	−	0.309932i
$870$	5.50246	−	9.53054i	0.186551	−	0.323115i
$871$	−7.08271	−	12.2676i	−0.239988	−	0.415672i
$872$	−1.83463	−	3.17766i	−0.0621282	−	0.107609i
$873$	13.0191			0.440631
$874$	−75.7135	−	18.2631i	−2.56105	−	0.617758i
$875$	1.00000			0.0338062
$876$	−18.3996	−	31.8690i	−0.621663	−	1.07675i
$877$	21.5389	+	37.3066i	0.727319	+	1.25975i	0.958013	+	0.286726i	$0.0925671\pi$
$877$	21.5389	+	37.3066i	0.727319	+	1.25975i	−0.230694	+	0.973026i	$0.574100\pi$
$878$	3.49592	−	6.05511i	0.117982	−	0.204350i
$879$	6.22682	+	10.7852i	0.210025	+	0.363775i
$880$	2.01561	−	3.49113i	0.0679461	−	0.117686i
$881$	−48.0180			−1.61777			−0.808883	−	0.587969i	$-0.799928\pi$
$881$	−48.0180			−1.61777			−0.808883	+	0.587969i	$0.799928\pi$
$882$	−5.74075			−0.193301
$883$	0.881302	−	1.52646i	0.0296582	−	0.0513694i	−0.850815	−	0.525465i	$-0.823891\pi$
$883$	0.881302	−	1.52646i	0.0296582	−	0.0513694i	0.880474	+	0.474095i	$0.157225\pi$
$884$	20.0079	−	34.6548i	0.672940	−	1.16557i
$885$	8.43782			0.283634
$886$	37.8981			1.27321
$887$	15.4340	−	26.7324i	0.518222	−	0.897587i	−0.481554	−	0.876417i	$-0.659927\pi$
$887$	15.4340	−	26.7324i	0.518222	−	0.897587i	0.999776	−	0.0211704i	$-0.00673927\pi$
$888$	24.8797	+	43.0929i	0.834907	+	1.44610i
$889$	3.52799	−	6.11065i	0.118325	−	0.204945i
$890$	−3.89771	−	6.75102i	−0.130651	−	0.226295i
$891$	−0.977852	−	1.69369i	−0.0327593	−	0.0567408i
$892$	0.570884			0.0191146
$893$	25.7766	−	27.1046i	0.862582	−	0.907022i
$894$	−22.4672			−0.751417
$895$	6.83978	+	11.8468i	0.228629	+	0.395996i
$896$	−7.32321	−	12.6842i	−0.244651	−	0.423748i
$897$	−7.27606	+	12.6025i	−0.242941	+	0.420785i
$898$	−25.5570	−	44.2661i	−0.852849	−	1.47718i
$899$	21.7221	−	37.6238i	0.724473	−	1.25482i
$900$	−9.91176			−0.330392
$901$	4.19218			0.139662
$902$	−8.30497	+	14.3846i	−0.276525	+	0.478956i
$903$	−1.88213	+	3.25995i	−0.0626334	+	0.108484i
$904$	−56.3654			−1.87468
$905$	−3.30876			−0.109987
$906$	−20.1820	+	34.9562i	−0.670501	+	1.16134i
$907$	6.22627	+	10.7842i	0.206740	+	0.358084i	0.950686	−	0.310156i	$-0.100381\pi$
$907$	6.22627	+	10.7842i	0.206740	+	0.358084i	−0.743946	+	0.668240i	$0.767048\pi$
$908$	−36.1012	+	62.5291i	−1.19806	+	2.07510i
$909$	−6.15693	−	10.6641i	−0.204212	−	0.353706i
$910$	3.04359	+	5.27165i	0.100894	+	0.174753i
$911$	−42.4187			−1.40540			−0.702698	−	0.711488i	$-0.748021\pi$
$911$	−42.4187			−1.40540			−0.702698	+	0.711488i	$0.748021\pi$
$912$	−15.9039	+	16.7232i	−0.526630	+	0.553762i
$913$	4.04622			0.133910
$914$	3.63918	+	6.30325i	0.120373	+	0.208493i
$915$	−1.59489	−	2.76242i	−0.0527253	−	0.0913229i
$916$	−4.49720	+	7.78938i	−0.148592	+	0.257368i
$917$	4.71583	+	8.16806i	0.155730	+	0.269733i
$918$	21.5172	−	37.2689i	0.710174	−	1.23006i
$919$	25.1084			0.828251			0.414126	−	0.910220i	$-0.364087\pi$
$919$	25.1084			0.828251			0.414126	+	0.910220i	$0.364087\pi$
$920$	42.0117			1.38508
$921$	−8.07026	+	13.9781i	−0.265924	+	0.460594i
$922$	18.0084	−	31.1915i	0.593076	−	1.02724i
$923$	13.7566			0.452805
$924$	−2.39223			−0.0786986
$925$	4.94121	−	8.55843i	0.162466	−	0.281399i
$926$	−33.6188	−	58.2294i	−1.10478	−	1.91354i
$927$	−12.9979	+	22.5131i	−0.426908	+	0.739426i
$928$	−9.89582	−	17.1401i	−0.324846	−	0.562650i
$929$	−19.7068	−	34.1332i	−0.646559	−	1.11987i	−0.983939	−	0.178504i	$-0.942874\pi$
$929$	−19.7068	−	34.1332i	−0.646559	−	1.11987i	0.337380	−	0.941368i	$-0.390459\pi$
$930$	18.1043			0.593664
$931$	4.23737	+	1.02211i	0.138874	+	0.0334983i
$932$	−113.746			−3.72589
$933$	−2.67560	−	4.63427i	−0.0875951	−	0.151719i
$934$	−26.4860	−	45.8751i	−0.866649	−	1.50108i
$935$	1.23170	−	2.13338i	0.0402810	−	0.0697688i
$936$	−16.3012	−	28.2344i	−0.532820	−	0.922871i
$937$	−21.3154	+	36.9194i	−0.696345	+	1.20611i	0.273380	+	0.961906i	$0.411858\pi$
$937$	−21.3154	+	36.9194i	−0.696345	+	1.20611i	−0.969725	+	0.244199i	$0.921475\pi$
$938$	14.7799			0.482580
$939$	4.96059			0.161883
$940$	−18.6693	+	32.3361i	−0.608925	+	1.05469i
$941$	17.5658	−	30.4249i	0.572629	−	0.991822i	−0.423666	−	0.905818i	$-0.639257\pi$
$941$	17.5658	−	30.4249i	0.572629	−	0.991822i	0.996295	−	0.0860036i	$-0.0274097\pi$
$942$	33.7814			1.10066
$943$	−72.2248			−2.35196
$944$	30.9345	−	53.5801i	1.00683	−	1.74389i
$945$	2.24245	+	3.88405i	0.0729471	+	0.126348i
$946$	3.61152	−	6.25534i	0.117421	−	0.203379i
$947$	−21.5425	−	37.3128i	−0.700039	−	1.21250i	−0.968452	−	0.249199i	$-0.919833\pi$
$947$	−21.5425	−	37.3128i	−0.700039	−	1.21250i	0.268414	−	0.963304i	$-0.413501\pi$
$948$	−30.1450	−	52.2126i	−0.979063	−	1.69579i
$949$	−24.0394			−0.780352
$950$	10.6789	+	2.57588i	0.346468	+	0.0835726i
$951$	−12.9408			−0.419633
$952$	11.2804	+	19.5383i	0.365601	+	0.633239i
$953$	−6.18810	−	10.7181i	−0.200452	−	0.347194i	0.748222	−	0.663448i	$-0.230908\pi$
$953$	−6.18810	−	10.7181i	−0.200452	−	0.347194i	−0.948674	+	0.316255i	$0.897574\pi$
$954$	3.16041	−	5.47400i	0.102322	−	0.177227i
$955$	9.64387	+	16.7037i	0.312068	+	0.540518i
$956$	−19.9158	+	34.4952i	−0.644124	+	1.11566i
$957$	2.82527			0.0913281
$958$	18.5509			0.599354
$959$	−1.40328	+	2.43056i	−0.0453144	+	0.0784868i
$960$	−1.17064	+	2.02761i	−0.0377822	+	0.0654407i
$961$	40.4706			1.30550
$962$	60.1560			1.93951
$963$	5.09830	−	8.83051i	0.164290	−	0.284559i
$964$	−56.1965	−	97.3352i	−1.80997	−	3.13496i
$965$	−10.6815	+	18.5008i	−0.343849	+	0.595563i
$966$	−7.59167	−	13.1492i	−0.244258	−	0.423067i
$967$	−9.38110	−	16.2485i	−0.301676	−	0.522518i	0.674840	−	0.737964i	$-0.264213\pi$
$967$	−9.38110	−	16.2485i	−0.301676	−	0.522518i	−0.976516	+	0.215446i	$0.930879\pi$
$968$	−62.6995			−2.01524
$969$	−9.71860	+	10.2193i	−0.312206	+	0.328291i
$970$	14.4036			0.462471
$971$	12.2335	+	21.1891i	0.392592	+	0.679989i	0.992791	−	0.119862i	$-0.0382451\pi$
$971$	12.2335	+	21.1891i	0.392592	+	0.679989i	−0.600199	+	0.799851i	$0.704912\pi$
$972$	−34.8604	−	60.3800i	−1.11815	−	1.93669i
$973$	−0.599945	+	1.03913i	−0.0192333	+	0.0333131i
$974$	21.7699	+	37.7067i	0.697554	+	1.20820i
$975$	1.02624	−	1.77749i	0.0328659	−	0.0569254i
$976$	−23.3885			−0.748649
$977$	1.81215			0.0579758			0.0289879	−	0.999580i	$-0.490772\pi$
$977$	1.81215			0.0579758			0.0289879	+	0.999580i	$0.490772\pi$
$978$	0.430612	−	0.745843i	0.0137695	−	0.0238494i
$979$	1.00065	−	1.73318i	0.0319810	−	0.0553927i
$980$	−4.35122			−0.138995
$981$	−1.41058			−0.0450362
$982$	12.6246	−	21.8665i	0.402868	−	0.697789i
$983$	−14.0369	−	24.3126i	−0.447707	−	0.775451i	0.550530	−	0.834816i	$-0.314426\pi$
$983$	−14.0369	−	24.3126i	−0.447707	−	0.775451i	−0.998236	+	0.0593649i	$0.981092\pi$
$984$	−25.6459	+	44.4201i	−0.817563	+	1.41606i
$985$	−11.7802	−	20.4038i	−0.375347	−	0.650120i
$986$	−24.6548	−	42.7033i	−0.785168	−	1.35995i
$987$	7.29184			0.232102
$988$	12.9641	+	43.9389i	0.412442	+	1.39788i
$989$	31.4079			0.998712
$990$	−1.85712	−	3.21663i	−0.0590233	−	0.102231i
$991$	12.4252	+	21.5211i	0.394701	+	0.683641i	0.993063	−	0.117584i	$-0.0375150\pi$
$991$	12.4252	+	21.5211i	0.394701	+	0.683641i	−0.598362	+	0.801226i	$0.704182\pi$
$992$	16.2797	−	28.1973i	0.516882	−	0.895266i
$993$	−7.17798	−	12.4326i	−0.227786	−	0.394537i
$994$	−7.17668	+	12.4304i	−0.227631	+	0.394268i
$995$	9.65923			0.306218
$996$	23.1232			0.732687
$997$	−29.8561	+	51.7123i	−0.945553	+	1.63775i	−0.190913	+	0.981607i	$0.561145\pi$
$997$	−29.8561	+	51.7123i	−0.945553	+	1.63775i	−0.754640	+	0.656139i	$0.772189\pi$
$998$	51.8960	−	89.8865i	1.64274	−	2.84531i
$999$	44.3218			1.40228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	665.2.i.h.596.1	yes	20
19.11	even	3	inner	665.2.i.h.106.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
665.2.i.h.106.1	✓	20	19.11	even	3	inner
665.2.i.h.596.1	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 665 = 5 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	665.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26008 - 2.18252i) q^{2} +(-0.424874 - 0.735903i) q^{3} +(-2.17561 + 3.76826i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.07075 + 1.85460i) q^{6} -1.00000 q^{7} +5.92545 q^{8} +(1.13896 - 1.97274i) q^{9} +O(q^{10})\)	\(q+(-1.26008 - 2.18252i) q^{2} +(-0.424874 - 0.735903i) q^{3} +(-2.17561 + 3.76826i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.07075 + 1.85460i) q^{6} -1.00000 q^{7} +5.92545 q^{8} +(1.13896 - 1.97274i) q^{9} +(1.26008 - 2.18252i) q^{10} +0.646997 q^{11} +3.69744 q^{12} +(1.20769 - 2.09179i) q^{13} +(1.26008 + 2.18252i) q^{14} +(0.424874 - 0.735903i) q^{15} +(-3.11532 - 5.39590i) q^{16} +(-1.90373 - 3.29735i) q^{17} -5.74075 q^{18} +(4.23737 + 1.02211i) q^{19} -4.35122 q^{20} +(0.424874 + 0.735903i) q^{21} +(-0.815269 - 1.41209i) q^{22} +(3.54502 - 6.14016i) q^{23} +(-2.51757 - 4.36056i) q^{24} +(-0.500000 + 0.866025i) q^{25} -6.08717 q^{26} -4.48491 q^{27} +(2.17561 - 3.76826i) q^{28} +(-2.56944 + 4.45040i) q^{29} -2.14150 q^{30} -8.45403 q^{31} +(-1.92568 + 3.33537i) q^{32} +(-0.274892 - 0.476127i) q^{33} +(-4.79770 + 8.30985i) q^{34} +(-0.500000 - 0.866025i) q^{35} +(4.95588 + 8.58383i) q^{36} -9.88242 q^{37} +(-3.10865 - 10.5361i) q^{38} -2.05247 q^{39} +(2.96272 + 5.13159i) q^{40} +(-5.09340 - 8.82202i) q^{41} +(1.07075 - 1.85460i) q^{42} +(2.21493 + 3.83637i) q^{43} +(-1.40761 + 2.43806i) q^{44} +2.27793 q^{45} -17.8681 q^{46} +(4.29059 - 7.43152i) q^{47} +(-2.64724 + 4.58516i) q^{48} +1.00000 q^{49} +2.52016 q^{50} +(-1.61769 + 2.80192i) q^{51} +(5.25494 + 9.10183i) q^{52} +(-0.550523 + 0.953533i) q^{53} +(5.65135 + 9.78842i) q^{54} +(0.323499 + 0.560316i) q^{55} -5.92545 q^{56} +(-1.04817 - 3.55256i) q^{57} +12.9508 q^{58} +(4.96489 + 8.59945i) q^{59} +(1.84872 + 3.20207i) q^{60} +(1.87689 - 3.25087i) q^{61} +(10.6528 + 18.4511i) q^{62} +(-1.13896 + 1.97274i) q^{63} -2.75526 q^{64} +2.41539 q^{65} +(-0.692773 + 1.19992i) q^{66} +(2.93233 - 5.07894i) q^{67} +16.5670 q^{68} -6.02475 q^{69} +(-1.26008 + 2.18252i) q^{70} +(2.84771 + 4.93237i) q^{71} +(6.74887 - 11.6894i) q^{72} +(-4.97630 - 8.61920i) q^{73} +(12.4527 + 21.5686i) q^{74} +0.849748 q^{75} +(-13.0704 + 13.7438i) q^{76} -0.646997 q^{77} +(2.58628 + 4.47957i) q^{78} +(-8.15293 - 14.1213i) q^{79} +(3.11532 - 5.39590i) q^{80} +(-1.51137 - 2.61777i) q^{81} +(-12.8362 + 22.2329i) q^{82} +6.25385 q^{83} -3.69744 q^{84} +(1.90373 - 3.29735i) q^{85} +(5.58198 - 9.66827i) q^{86} +4.36675 q^{87} +3.83375 q^{88} +(1.54661 - 2.67881i) q^{89} +(-2.87037 - 4.97163i) q^{90} +(-1.20769 + 2.09179i) q^{91} +(15.4252 + 26.7171i) q^{92} +(3.59190 + 6.22135i) q^{93} -21.6260 q^{94} +(1.23351 + 4.18072i) q^{95} +3.27268 q^{96} +(2.85767 + 4.94963i) q^{97} +(-1.26008 - 2.18252i) q^{98} +(0.736906 - 1.27636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3 q^{2} - q^{3} - 11 q^{4} + 10 q^{5} - 6 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) \) 20 * q + 3 * q^2 - q^3 - 11 * q^4 + 10 * q^5 - 6 * q^6 - 20 * q^7 - 9 * q^9	\( 20 q + 3 q^{2} - q^{3} - 11 q^{4} + 10 q^{5} - 6 q^{6} - 20 q^{7} - 9 q^{9} - 3 q^{10} + 2 q^{11} - 4 q^{12} + 6 q^{13} - 3 q^{14} + q^{15} - 5 q^{16} + 8 q^{17} - 76 q^{18} + 17 q^{19} - 22 q^{20} + q^{21} - 4 q^{22} + 3 q^{23} - 6 q^{24} - 10 q^{25} + 18 q^{26} + 20 q^{27} + 11 q^{28} + q^{29} - 12 q^{30} + 10 q^{31} + 18 q^{32} + q^{33} - 26 q^{34} - 10 q^{35} - 19 q^{36} - 66 q^{37} + 19 q^{38} + 34 q^{39} - 29 q^{41} + 6 q^{42} + q^{43} - 28 q^{44} - 18 q^{45} + 6 q^{46} - 7 q^{47} + 15 q^{48} + 20 q^{49} - 6 q^{50} + 16 q^{51} - 6 q^{52} + 40 q^{53} + 35 q^{54} + q^{55} + 24 q^{57} - 18 q^{58} - 9 q^{59} - 2 q^{60} + 10 q^{61} - 8 q^{62} + 9 q^{63} + 44 q^{64} + 12 q^{65} - 19 q^{66} + 22 q^{67} - 42 q^{68} + 60 q^{69} + 3 q^{70} - 8 q^{71} + 18 q^{72} + 14 q^{73} - 24 q^{74} + 2 q^{75} - 49 q^{76} - 2 q^{77} + 23 q^{78} + 9 q^{79} + 5 q^{80} - 42 q^{81} - 5 q^{82} - 54 q^{83} + 4 q^{84} - 8 q^{85} + 37 q^{86} + 18 q^{87} - 28 q^{88} - 25 q^{89} - 38 q^{90} - 6 q^{91} + 68 q^{92} + 11 q^{93} - 118 q^{94} + 10 q^{95} + 102 q^{96} + 29 q^{97} + 3 q^{98} + 34 q^{99}+O(q^{100}) \) 20 * q + 3 * q^2 - q^3 - 11 * q^4 + 10 * q^5 - 6 * q^6 - 20 * q^7 - 9 * q^9 - 3 * q^10 + 2 * q^11 - 4 * q^12 + 6 * q^13 - 3 * q^14 + q^15 - 5 * q^16 + 8 * q^17 - 76 * q^18 + 17 * q^19 - 22 * q^20 + q^21 - 4 * q^22 + 3 * q^23 - 6 * q^24 - 10 * q^25 + 18 * q^26 + 20 * q^27 + 11 * q^28 + q^29 - 12 * q^30 + 10 * q^31 + 18 * q^32 + q^33 - 26 * q^34 - 10 * q^35 - 19 * q^36 - 66 * q^37 + 19 * q^38 + 34 * q^39 - 29 * q^41 + 6 * q^42 + q^43 - 28 * q^44 - 18 * q^45 + 6 * q^46 - 7 * q^47 + 15 * q^48 + 20 * q^49 - 6 * q^50 + 16 * q^51 - 6 * q^52 + 40 * q^53 + 35 * q^54 + q^55 + 24 * q^57 - 18 * q^58 - 9 * q^59 - 2 * q^60 + 10 * q^61 - 8 * q^62 + 9 * q^63 + 44 * q^64 + 12 * q^65 - 19 * q^66 + 22 * q^67 - 42 * q^68 + 60 * q^69 + 3 * q^70 - 8 * q^71 + 18 * q^72 + 14 * q^73 - 24 * q^74 + 2 * q^75 - 49 * q^76 - 2 * q^77 + 23 * q^78 + 9 * q^79 + 5 * q^80 - 42 * q^81 - 5 * q^82 - 54 * q^83 + 4 * q^84 - 8 * q^85 + 37 * q^86 + 18 * q^87 - 28 * q^88 - 25 * q^89 - 38 * q^90 - 6 * q^91 + 68 * q^92 + 11 * q^93 - 118 * q^94 + 10 * q^95 + 102 * q^96 + 29 * q^97 + 3 * q^98 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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