LMFDB - Embedded newform 240.2.s.c.61.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(61,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))

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

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

chi := DirichletCharacter("240.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.s (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:	$1.91640964851$
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} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^18 - 4x^17 + 7x^16 + 16x^15 + 6x^14 - 36x^13 - 42x^12 + 40x^11 + 136x^10 + 80x^9 - 168x^8 - 288x^7 + 96x^6 + 512x^5 + 448x^4 - 512x^3 - 512*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			61.3
Root			$-1.04932 - 0.948122i$ of defining polynomial
Character	$\chi$	$=$	240.61
Dual form			240.2.s.c.181.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04932 - 0.948122i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(0.202128 + 1.98976i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.0715547 + 1.41240i) q^{6} +0.740019i q^{7} +(1.67444 - 2.27953i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.04932 - 0.948122i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(0.202128 + 1.98976i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.0715547 + 1.41240i) q^{6} +0.740019i q^{7} +(1.67444 - 2.27953i) q^{8} +1.00000i q^{9} +(1.41240 - 0.0715547i) q^{10} +(-3.83476 + 3.83476i) q^{11} +(1.26405 - 1.54990i) q^{12} +(3.31314 + 3.31314i) q^{13} +(0.701629 - 0.776514i) q^{14} +1.00000 q^{15} +(-3.91829 + 0.804372i) q^{16} +2.93893 q^{17} +(0.948122 - 1.04932i) q^{18} +(5.02789 + 5.02789i) q^{19} +(-1.54990 - 1.26405i) q^{20} +(0.523272 - 0.523272i) q^{21} +(7.65970 - 0.388053i) q^{22} -5.45159i q^{23} +(-2.79588 + 0.427863i) q^{24} -1.00000i q^{25} +(-0.335268 - 6.61779i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.47246 + 0.149579i) q^{28} +(2.64012 + 2.64012i) q^{29} +(-1.04932 - 0.948122i) q^{30} -5.94837 q^{31} +(4.87417 + 2.87098i) q^{32} +5.42317 q^{33} +(-3.08387 - 2.78647i) q^{34} +(-0.523272 - 0.523272i) q^{35} +(-1.98976 + 0.202128i) q^{36} +(-0.479352 + 0.479352i) q^{37} +(-0.508791 - 10.0429i) q^{38} -4.68548i q^{39} +(0.427863 + 2.79588i) q^{40} +10.1918i q^{41} +(-1.04520 + 0.0529518i) q^{42} +(-4.93728 + 4.93728i) q^{43} +(-8.40537 - 6.85514i) q^{44} +(-0.707107 - 0.707107i) q^{45} +(-5.16877 + 5.72044i) q^{46} -8.15706 q^{47} +(3.33943 + 2.20187i) q^{48} +6.45237 q^{49} +(-0.948122 + 1.04932i) q^{50} +(-2.07814 - 2.07814i) q^{51} +(-5.92267 + 7.26203i) q^{52} +(-5.05247 + 5.05247i) q^{53} +(-1.41240 + 0.0715547i) q^{54} -5.42317i q^{55} +(1.68689 + 1.23912i) q^{56} -7.11052i q^{57} +(-0.267163 - 5.27348i) q^{58} +(3.83709 - 3.83709i) q^{59} +(0.202128 + 1.98976i) q^{60} +(-4.87697 - 4.87697i) q^{61} +(6.24172 + 5.63978i) q^{62} -0.740019 q^{63} +(-2.39250 - 7.63387i) q^{64} -4.68548 q^{65} +(-5.69062 - 5.14183i) q^{66} +(-3.99222 - 3.99222i) q^{67} +(0.594040 + 5.84777i) q^{68} +(-3.85485 + 3.85485i) q^{69} +(0.0529518 + 1.04520i) q^{70} -3.55343i q^{71} +(2.27953 + 1.67444i) q^{72} -11.1655i q^{73} +(0.957475 - 0.0485073i) q^{74} +(-0.707107 + 0.707107i) q^{75} +(-8.98803 + 11.0206i) q^{76} +(-2.83780 - 2.83780i) q^{77} +(-4.44241 + 4.91655i) q^{78} +10.7776 q^{79} +(2.20187 - 3.33943i) q^{80} -1.00000 q^{81} +(9.66309 - 10.6944i) q^{82} +(4.61002 + 4.61002i) q^{83} +(1.14695 + 0.935419i) q^{84} +(-2.07814 + 2.07814i) q^{85} +(9.86192 - 0.499621i) q^{86} -3.73370i q^{87} +(2.32037 + 15.1625i) q^{88} +2.62476i q^{89} +(0.0715547 + 1.41240i) q^{90} +(-2.45179 + 2.45179i) q^{91} +(10.8473 - 1.10192i) q^{92} +(4.20613 + 4.20613i) q^{93} +(8.55934 + 7.73389i) q^{94} -7.11052 q^{95} +(-1.41647 - 5.47664i) q^{96} +1.67846 q^{97} +(-6.77058 - 6.11764i) q^{98} +(-3.83476 - 3.83476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4} + 12 q^{8}+O(q^{10}) $ 20 * q + 4 * q^4 + 12 * q^8	$ 20 q + 4 q^{4} + 12 q^{8} + 8 q^{11} - 4 q^{14} + 20 q^{15} - 20 q^{16} - 24 q^{17} - 4 q^{18} - 4 q^{19} - 8 q^{20} + 8 q^{22} + 28 q^{26} - 8 q^{28} + 16 q^{29} - 40 q^{32} + 16 q^{33} - 44 q^{34} + 16 q^{37} - 8 q^{38} + 12 q^{40} + 12 q^{42} - 8 q^{43} + 24 q^{44} - 12 q^{46} - 16 q^{48} - 52 q^{49} + 4 q^{50} + 4 q^{51} - 56 q^{52} - 16 q^{53} + 64 q^{56} + 72 q^{58} - 16 q^{59} + 4 q^{60} - 4 q^{61} - 44 q^{62} - 8 q^{63} - 56 q^{64} - 32 q^{66} - 8 q^{67} - 32 q^{68} - 4 q^{69} + 20 q^{70} + 4 q^{72} + 60 q^{74} + 28 q^{76} - 40 q^{77} - 28 q^{78} + 56 q^{79} - 16 q^{80} - 20 q^{81} - 24 q^{82} - 48 q^{83} + 24 q^{84} + 4 q^{85} + 64 q^{86} + 40 q^{88} - 8 q^{91} + 88 q^{92} + 16 q^{93} - 20 q^{94} + 56 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) $ 20 * q + 4 * q^4 + 12 * q^8 + 8 * q^11 - 4 * q^14 + 20 * q^15 - 20 * q^16 - 24 * q^17 - 4 * q^18 - 4 * q^19 - 8 * q^20 + 8 * q^22 + 28 * q^26 - 8 * q^28 + 16 * q^29 - 40 * q^32 + 16 * q^33 - 44 * q^34 + 16 * q^37 - 8 * q^38 + 12 * q^40 + 12 * q^42 - 8 * q^43 + 24 * q^44 - 12 * q^46 - 16 * q^48 - 52 * q^49 + 4 * q^50 + 4 * q^51 - 56 * q^52 - 16 * q^53 + 64 * q^56 + 72 * q^58 - 16 * q^59 + 4 * q^60 - 4 * q^61 - 44 * q^62 - 8 * q^63 - 56 * q^64 - 32 * q^66 - 8 * q^67 - 32 * q^68 - 4 * q^69 + 20 * q^70 + 4 * q^72 + 60 * q^74 + 28 * q^76 - 40 * q^77 - 28 * q^78 + 56 * q^79 - 16 * q^80 - 20 * q^81 - 24 * q^82 - 48 * q^83 + 24 * q^84 + 4 * q^85 + 64 * q^86 + 40 * q^88 - 8 * q^91 + 88 * q^92 + 16 * q^93 - 20 * q^94 + 56 * q^97 - 48 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.04932	−	0.948122i	−0.741978	−	0.670424i
$2$	−1.04932	−	0.948122i	−0.741978	−	0.670424i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	0.202128	+	1.98976i	0.101064	+	0.994880i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	0.0715547	+	1.41240i	0.0292121	+	0.576611i
$7$			0.740019i			0.279701i	0.990173	+	0.139850i	$0.0446622\pi$
$7$			0.740019i			0.279701i	−0.990173	+	0.139850i	$0.955338\pi$
$8$	1.67444	−	2.27953i	0.592004	−	0.805935i
$9$			1.00000i			0.333333i
$10$	1.41240	−	0.0715547i	0.446641	−	0.0226276i
$11$	−3.83476	+	3.83476i	−1.15622	+	1.15622i	−0.170943	+	0.985281i	$0.554682\pi$
$11$	−3.83476	+	3.83476i	−1.15622	+	1.15622i	−0.985281	+	0.170943i	$0.945318\pi$
$12$	1.26405	−	1.54990i	0.364899	−	0.447417i
$13$	3.31314	+	3.31314i	0.918899	+	0.918899i	0.996949	−	0.0780503i	$-0.0248695\pi$
$13$	3.31314	+	3.31314i	0.918899	+	0.918899i	−0.0780503	+	0.996949i	$0.524869\pi$
$14$	0.701629	−	0.776514i	0.187518	−	0.207532i
$15$	1.00000			0.258199
$16$	−3.91829	+	0.804372i	−0.979572	+	0.201093i
$17$	2.93893			0.712796			0.356398	−	0.934334i	$-0.384005\pi$
$17$	2.93893			0.712796			0.356398	+	0.934334i	$0.384005\pi$
$18$	0.948122	−	1.04932i	0.223475	−	0.247326i
$19$	5.02789	+	5.02789i	1.15348	+	1.15348i	0.985850	+	0.167628i	$0.0536107\pi$
$19$	5.02789	+	5.02789i	1.15348	+	1.15348i	0.167628	+	0.985850i	$0.446389\pi$
$20$	−1.54990	−	1.26405i	−0.346568	−	0.282649i
$21$	0.523272	−	0.523272i	0.114187	−	0.114187i
$22$	7.65970	−	0.388053i	1.63305	−	0.0827332i
$23$		−	5.45159i		−	1.13673i	−0.822775	−	0.568367i	$-0.807575\pi$
$23$		−	5.45159i		−	1.13673i	0.822775	−	0.568367i	$-0.192425\pi$
$24$	−2.79588	+	0.427863i	−0.570706	+	0.0873371i
$25$		−	1.00000i		−	0.200000i
$26$	−0.335268	−	6.61779i	−0.0657515	−	1.29786i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−1.47246	+	0.149579i	−0.278269	+	0.0282677i
$29$	2.64012	+	2.64012i	0.490258	+	0.490258i	0.908388	−	0.418129i	$-0.137314\pi$
$29$	2.64012	+	2.64012i	0.490258	+	0.490258i	−0.418129	+	0.908388i	$0.637314\pi$
$30$	−1.04932	−	0.948122i	−0.191578	−	0.173103i
$31$	−5.94837			−1.06836			−0.534179	−	0.845371i	$-0.679379\pi$
$31$	−5.94837			−1.06836			−0.534179	+	0.845371i	$0.679379\pi$
$32$	4.87417	+	2.87098i	0.861639	+	0.507522i
$33$	5.42317			0.944053
$34$	−3.08387	−	2.78647i	−0.528879	−	0.477875i
$35$	−0.523272	−	0.523272i	−0.0884492	−	0.0884492i
$36$	−1.98976	+	0.202128i	−0.331627	+	0.0336880i
$37$	−0.479352	+	0.479352i	−0.0788049	+	0.0788049i	−0.745411	−	0.666606i	$-0.767747\pi$
$37$	−0.479352	+	0.479352i	−0.0788049	+	0.0788049i	0.666606	+	0.745411i	$0.267747\pi$
$38$	−0.508791	−	10.0429i	−0.0825368	−	1.62918i
$39$		−	4.68548i		−	0.750278i
$40$	0.427863	+	2.79588i	0.0676510	+	0.442067i
$41$			10.1918i			1.59169i	0.605497	+	0.795847i	$0.292974\pi$
$41$			10.1918i			1.59169i	−0.605497	+	0.795847i	$0.707026\pi$
$42$	−1.04520	+	0.0529518i	−0.161279	+	0.00817064i
$43$	−4.93728	+	4.93728i	−0.752929	+	0.752929i	−0.975025	−	0.222096i	$-0.928710\pi$
$43$	−4.93728	+	4.93728i	−0.752929	+	0.752929i	0.222096	+	0.975025i	$0.428710\pi$
$44$	−8.40537	−	6.85514i	−1.26716	−	1.03345i
$45$	−0.707107	−	0.707107i	−0.105409	−	0.105409i
$46$	−5.16877	+	5.72044i	−0.762094	+	0.843432i
$47$	−8.15706			−1.18983			−0.594915	−	0.803789i	$-0.702814\pi$
$47$	−8.15706			−1.18983			−0.594915	+	0.803789i	$0.702814\pi$
$48$	3.33943	+	2.20187i	0.482005	+	0.317813i
$49$	6.45237			0.921767
$50$	−0.948122	+	1.04932i	−0.134085	+	0.148396i
$51$	−2.07814	−	2.07814i	−0.290998	−	0.290998i
$52$	−5.92267	+	7.26203i	−0.821327	+	1.00706i
$53$	−5.05247	+	5.05247i	−0.694010	+	0.694010i	−0.963112	−	0.269102i	$-0.913273\pi$
$53$	−5.05247	+	5.05247i	−0.694010	+	0.694010i	0.269102	+	0.963112i	$0.413273\pi$
$54$	−1.41240	+	0.0715547i	−0.192204	+	0.00973736i
$55$		−	5.42317i		−	0.731260i
$56$	1.68689	+	1.23912i	0.225421	+	0.165584i
$57$		−	7.11052i		−	0.941811i
$58$	−0.267163	−	5.27348i	−0.0350803	−	0.692442i
$59$	3.83709	−	3.83709i	0.499547	−	0.499547i	−0.411750	−	0.911297i	$-0.635082\pi$
$59$	3.83709	−	3.83709i	0.499547	−	0.499547i	0.911297	+	0.411750i	$0.135082\pi$
$60$	0.202128	+	1.98976i	0.0260946	+	0.256877i
$61$	−4.87697	−	4.87697i	−0.624432	−	0.624432i	0.322229	−	0.946662i	$-0.395568\pi$
$61$	−4.87697	−	4.87697i	−0.624432	−	0.624432i	−0.946662	+	0.322229i	$0.895568\pi$
$62$	6.24172	+	5.63978i	0.792699	+	0.716253i
$63$	−0.740019			−0.0932336
$64$	−2.39250	−	7.63387i	−0.299063	−	0.954233i
$65$	−4.68548			−0.581163
$66$	−5.69062	−	5.14183i	−0.700467	−	0.632916i
$67$	−3.99222	−	3.99222i	−0.487728	−	0.487728i	0.419861	−	0.907588i	$-0.362079\pi$
$67$	−3.99222	−	3.99222i	−0.487728	−	0.487728i	−0.907588	+	0.419861i	$0.862079\pi$
$68$	0.594040	+	5.84777i	0.0720379	+	0.709146i
$69$	−3.85485	+	3.85485i	−0.464070	+	0.464070i
$70$	0.0529518	+	1.04520i	0.00632895	+	0.124926i
$71$		−	3.55343i		−	0.421715i	−0.977517	−	0.210857i	$-0.932374\pi$
$71$		−	3.55343i		−	0.421715i	0.977517	−	0.210857i	$-0.0676255\pi$
$72$	2.27953	+	1.67444i	0.268645	+	0.197335i
$73$		−	11.1655i		−	1.30683i	−0.757002	−	0.653413i	$-0.773337\pi$
$73$		−	11.1655i		−	1.30683i	0.757002	−	0.653413i	$-0.226663\pi$
$74$	0.957475	−	0.0485073i	0.111304	−	0.00563886i
$75$	−0.707107	+	0.707107i	−0.0816497	+	0.0816497i
$76$	−8.98803	+	11.0206i	−1.03100	+	1.26415i
$77$	−2.83780	−	2.83780i	−0.323397	−	0.323397i
$78$	−4.44241	+	4.91655i	−0.503004	+	0.556690i
$79$	10.7776			1.21258			0.606288	−	0.795245i	$-0.292658\pi$
$79$	10.7776			1.21258			0.606288	+	0.795245i	$0.292658\pi$
$80$	2.20187	−	3.33943i	0.246177	−	0.373359i
$81$	−1.00000			−0.111111
$82$	9.66309	−	10.6944i	1.06711	−	1.18100i
$83$	4.61002	+	4.61002i	0.506016	+	0.506016i	0.913301	−	0.407285i	$-0.133525\pi$
$83$	4.61002	+	4.61002i	0.506016	+	0.506016i	−0.407285	+	0.913301i	$0.633525\pi$
$84$	1.14695	+	0.935419i	0.125143	+	0.102063i
$85$	−2.07814	+	2.07814i	−0.225406	+	0.225406i
$86$	9.86192	−	0.499621i	1.06344	−	0.0538756i
$87$		−	3.73370i		−	0.400294i
$88$	2.32037	+	15.1625i	0.247353	+	1.61633i
$89$			2.62476i			0.278224i	0.990277	+	0.139112i	$0.0444247\pi$
$89$			2.62476i			0.278224i	−0.990277	+	0.139112i	$0.955575\pi$
$90$	0.0715547	+	1.41240i	0.00754252	+	0.148880i
$91$	−2.45179	+	2.45179i	−0.257017	+	0.257017i
$92$	10.8473	−	1.10192i	1.13091	−	0.114883i
$93$	4.20613	+	4.20613i	0.436156	+	0.436156i
$94$	8.55934	+	7.73389i	0.882828	+	0.797690i
$95$	−7.11052			−0.729524
$96$	−1.41647	−	5.47664i	−0.144568	−	0.558958i
$97$	1.67846			0.170422			0.0852108	−	0.996363i	$-0.472844\pi$
$97$	1.67846			0.170422			0.0852108	+	0.996363i	$0.472844\pi$
$98$	−6.77058	−	6.11764i	−0.683932	−	0.617975i
$99$	−3.83476	−	3.83476i	−0.385408	−	0.385408i
$100$	1.98976	−	0.202128i	0.198976	−	0.0202128i
$101$	6.52161	−	6.52161i	0.648925	−	0.648925i	−0.303808	−	0.952733i	$-0.598258\pi$
$101$	6.52161	−	6.52161i	0.648925	−	0.648925i	0.952733	+	0.303808i	$0.0982583\pi$
$102$	0.210294	+	4.15095i	0.0208222	+	0.411006i
$103$		−	0.302418i		−	0.0297981i	−0.999889	−	0.0148991i	$-0.995257\pi$
$103$		−	0.302418i		−	0.0297981i	0.999889	−	0.0148991i	$-0.00474269\pi$
$104$	13.1000	−	2.00474i	1.28456	−	0.196581i
$105$			0.740019i			0.0722185i
$106$	10.0920	−	0.511278i	0.980222	−	0.0496597i
$107$	−1.20078	+	1.20078i	−0.116084	+	0.116084i	−0.762762	−	0.646679i	$-0.776157\pi$
$107$	−1.20078	+	1.20078i	−0.116084	+	0.116084i	0.646679	+	0.762762i	$0.276157\pi$
$108$	1.54990	+	1.26405i	0.149139	+	0.121633i
$109$	−6.99992	−	6.99992i	−0.670471	−	0.670471i	0.287353	−	0.957825i	$-0.407225\pi$
$109$	−6.99992	−	6.99992i	−0.670471	−	0.670471i	−0.957825	+	0.287353i	$0.907225\pi$
$110$	−5.14183	+	5.69062i	−0.490254	+	0.542579i
$111$	0.677905			0.0643439
$112$	−0.595251	−	2.89961i	−0.0562459	−	0.273987i
$113$	15.1350			1.42378			0.711892	−	0.702289i	$-0.247839\pi$
$113$	15.1350			1.42378			0.711892	+	0.702289i	$0.247839\pi$
$114$	−6.74164	+	7.46118i	−0.631412	+	0.698803i
$115$	3.85485	+	3.85485i	0.359467	+	0.359467i
$116$	−4.71957	+	5.78685i	−0.438201	+	0.537296i
$117$	−3.31314	+	3.31314i	−0.306300	+	0.306300i
$118$	−7.66436	+	0.388289i	−0.705561	+	0.0357449i
$119$			2.17486i			0.199370i
$120$	1.67444	−	2.27953i	0.152855	−	0.208092i
$121$		−	18.4108i		−	1.67371i
$122$	0.493518	+	9.74145i	0.0446811	+	0.881950i
$123$	7.20670	−	7.20670i	0.649807	−	0.649807i
$124$	−1.20233	−	11.8358i	−0.107973	−	1.06289i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	0.776514	+	0.701629i	0.0691773	+	0.0625060i
$127$	8.94547			0.793782			0.396891	−	0.917866i	$-0.370089\pi$
$127$	8.94547			0.793782			0.396891	+	0.917866i	$0.370089\pi$
$128$	−4.72735	+	10.2787i	−0.417843	+	0.908519i
$129$	6.98237			0.614764
$130$	4.91655	+	4.44241i	0.431210	+	0.389625i
$131$	9.63786	+	9.63786i	0.842064	+	0.842064i	0.989127	−	0.147063i	$-0.0469821\pi$
$131$	9.63786	+	9.63786i	0.842064	+	0.842064i	−0.147063	+	0.989127i	$0.546982\pi$
$132$	1.09617	+	10.7908i	0.0954098	+	0.939220i
$133$	−3.72074	+	3.72074i	−0.322629	+	0.322629i
$134$	0.403987	+	7.97422i	0.0348992	+	0.688867i
$135$			1.00000i			0.0860663i
$136$	4.92106	−	6.69938i	0.421978	−	0.574467i
$137$			6.92180i			0.591370i	0.955286	+	0.295685i	$0.0955478\pi$
$137$			6.92180i			0.591370i	−0.955286	+	0.295685i	$0.904452\pi$
$138$	7.69983	−	0.390086i	0.655453	−	0.0332064i
$139$	6.50393	−	6.50393i	0.551657	−	0.551657i	−0.375262	−	0.926919i	$-0.622447\pi$
$139$	6.50393	−	6.50393i	0.551657	−	0.551657i	0.926919	+	0.375262i	$0.122447\pi$
$140$	0.935419	−	1.14695i	0.0790573	−	0.0969353i
$141$	5.76791	+	5.76791i	0.485746	+	0.485746i
$142$	−3.36909	+	3.72867i	−0.282728	+	0.312903i
$143$	−25.4102			−2.12491
$144$	−0.804372	−	3.91829i	−0.0670310	−	0.326524i
$145$	−3.73370			−0.310067
$146$	−10.5863	+	11.7162i	−0.876127	+	0.969636i
$147$	−4.56252	−	4.56252i	−0.376310	−	0.376310i
$148$	−1.05068	−	0.856904i	−0.0863658	−	0.0704371i
$149$	−5.75043	+	5.75043i	−0.471094	+	0.471094i	−0.902268	−	0.431175i	$-0.858099\pi$
$149$	−5.75043	+	5.75043i	−0.471094	+	0.471094i	0.431175	+	0.902268i	$0.358099\pi$
$150$	1.41240	−	0.0715547i	0.115322	−	0.00584241i
$151$		−	0.185782i		−	0.0151187i	−0.999971	−	0.00755935i	$-0.997594\pi$
$151$		−	0.185782i		−	0.0151187i	0.999971	−	0.00755935i	$-0.00240624\pi$
$152$	19.8801	−	3.04232i	1.61249	−	0.246765i
$153$			2.93893i			0.237599i
$154$	0.287167	+	5.66832i	0.0231406	+	0.456767i
$155$	4.20613	−	4.20613i	0.337845	−	0.337845i
$156$	9.32299	−	0.947067i	0.746437	−	0.0758261i
$157$	−11.8717	−	11.8717i	−0.947462	−	0.947462i	0.0512256	−	0.998687i	$-0.483687\pi$
$157$	−11.8717	−	11.8717i	−0.947462	−	0.947462i	−0.998687	+	0.0512256i	$0.983687\pi$
$158$	−11.3091	−	10.2185i	−0.899705	−	0.812940i
$159$	7.14527			0.566657
$160$	−5.47664	+	1.41647i	−0.432967	+	0.111982i
$161$	4.03428			0.317946
$162$	1.04932	+	0.948122i	0.0824420	+	0.0744915i
$163$	11.3813	+	11.3813i	0.891454	+	0.891454i	0.994660	−	0.103206i	$-0.0329101\pi$
$163$	11.3813	+	11.3813i	0.891454	+	0.891454i	−0.103206	+	0.994660i	$0.532910\pi$
$164$	−20.2793	+	2.06005i	−1.58354	+	0.160863i
$165$	−3.83476	+	3.83476i	−0.298536	+	0.298536i
$166$	−0.466505	−	9.20823i	−0.0362078	−	0.714698i
$167$		−	12.8924i		−	0.997644i	−0.866705	−	0.498822i	$-0.833766\pi$
$167$		−	12.8924i		−	0.997644i	0.866705	−	0.498822i	$-0.166234\pi$
$168$	−0.316626	−	2.06900i	−0.0244283	−	0.159627i
$169$			8.95377i			0.688751i
$170$	4.15095	−	0.210294i	0.318364	−	0.0161288i
$171$	−5.02789	+	5.02789i	−0.384493	+	0.384493i
$172$	−10.8220	−	8.82604i	−0.825167	−	0.672980i
$173$	−12.1023	−	12.1023i	−0.920122	−	0.920122i	0.0769156	−	0.997038i	$-0.475493\pi$
$173$	−12.1023	−	12.1023i	−0.920122	−	0.920122i	−0.997038	+	0.0769156i	$0.975493\pi$
$174$	−3.54000	+	3.91783i	−0.268367	+	0.297010i
$175$	0.740019			0.0559402
$176$	11.9411	−	18.1103i	0.900096	−	1.36511i
$177$	−5.42647			−0.407878
$178$	2.48859	−	2.75420i	0.186528	−	0.206436i
$179$	15.5558	+	15.5558i	1.16269	+	1.16269i	0.983884	+	0.178809i	$0.0572244\pi$
$179$	15.5558	+	15.5558i	1.16269	+	1.16269i	0.178809	+	0.983884i	$0.442776\pi$
$180$	1.26405	−	1.54990i	0.0942165	−	0.115523i
$181$	10.5970	−	10.5970i	0.787670	−	0.787670i	−0.193442	−	0.981112i	$-0.561965\pi$
$181$	10.5970	−	10.5970i	0.787670	−	0.787670i	0.981112	+	0.193442i	$0.0619651\pi$
$182$	4.89729	−	0.248105i	0.363011	−	0.0183908i
$183$			6.89708i			0.509847i
$184$	−12.4270	−	9.12835i	−0.916134	−	0.672951i
$185$		−	0.677905i		−	0.0498406i
$186$	−0.425634	−	8.40149i	−0.0312090	−	0.616027i
$187$	−11.2701	+	11.2701i	−0.824151	+	0.824151i
$188$	−1.64877	−	16.2306i	−0.120249	−	1.18374i
$189$	0.523272	+	0.523272i	0.0380625	+	0.0380625i
$190$	7.46118	+	6.74164i	0.541291	+	0.489090i
$191$	8.84439			0.639958			0.319979	−	0.947425i	$-0.396324\pi$
$191$	8.84439			0.639958			0.319979	+	0.947425i	$0.396324\pi$
$192$	−3.70620	+	7.08971i	−0.267472	+	0.511656i
$193$	14.0714			1.01289			0.506443	−	0.862274i	$-0.330960\pi$
$193$	14.0714			1.01289			0.506443	+	0.862274i	$0.330960\pi$
$194$	−1.76123	−	1.59138i	−0.126449	−	0.114255i
$195$	3.31314	+	3.31314i	0.237259	+	0.237259i
$196$	1.30420	+	12.8387i	0.0931575	+	0.917048i
$197$	8.15230	−	8.15230i	0.580827	−	0.580827i	−0.354303	−	0.935131i	$-0.615282\pi$
$197$	8.15230	−	8.15230i	0.580827	−	0.580827i	0.935131	+	0.354303i	$0.115282\pi$
$198$	0.388053	+	7.65970i	0.0275777	+	0.544351i
$199$			11.3466i			0.804340i	0.915565	+	0.402170i	$0.131744\pi$
$199$			11.3466i			0.804340i	−0.915565	+	0.402170i	$0.868256\pi$
$200$	−2.27953	−	1.67444i	−0.161187	−	0.118401i
$201$			5.64585i			0.398228i
$202$	−13.0265	+	0.659945i	−0.916543	+	0.0464336i
$203$	−1.95374	+	1.95374i	−0.137126	+	0.137126i
$204$	3.71495	−	4.55505i	0.260098	−	0.318917i
$205$	−7.20670	−	7.20670i	−0.503338	−	0.503338i
$206$	−0.286729	+	0.317332i	−0.0199774	+	0.0221096i
$207$	5.45159			0.378911
$208$	−15.6468	−	10.3168i	−1.08491	−	0.715344i
$209$	−38.5616			−2.66736
$210$	0.701629	−	0.776514i	0.0484170	−	0.0535845i
$211$	−15.6416	−	15.6416i	−1.07681	−	1.07681i	−0.996793	−	0.0800209i	$-0.974501\pi$
$211$	−15.6416	−	15.6416i	−1.07681	−	1.07681i	−0.0800209	−	0.996793i	$-0.525499\pi$
$212$	−11.0744	−	9.03196i	−0.760596	−	0.620317i
$213$	−2.51265	+	2.51265i	−0.172164	+	0.172164i
$214$	2.39848	−	0.121511i	0.163957	−	0.00830632i
$215$		−	6.98237i		−	0.476194i
$216$	−0.427863	−	2.79588i	−0.0291124	−	0.190235i
$217$		−	4.40191i		−	0.298821i
$218$	0.708347	+	13.9819i	0.0479753	+	0.946975i
$219$	−7.89522	+	7.89522i	−0.533509	+	0.533509i
$220$	10.7908	−	1.09617i	0.727516	−	0.0739041i
$221$	9.73708	+	9.73708i	0.654987	+	0.654987i
$222$	−0.711337	−	0.642737i	−0.0477418	−	0.0431377i
$223$	−10.2773			−0.688219			−0.344110	−	0.938929i	$-0.611819\pi$
$223$	−10.2773			−0.688219			−0.344110	+	0.938929i	$0.611819\pi$
$224$	−2.12458	+	3.60698i	−0.141954	+	0.241001i
$225$	1.00000			0.0666667
$226$	−15.8814	−	14.3499i	−1.05642	−	0.954539i
$227$	−13.8323	−	13.8323i	−0.918082	−	0.918082i	0.0788077	−	0.996890i	$-0.474889\pi$
$227$	−13.8323	−	13.8323i	−0.918082	−	0.918082i	−0.996890	+	0.0788077i	$0.974889\pi$
$228$	14.1482	−	1.43723i	0.936989	−	0.0951832i
$229$	−11.3025	+	11.3025i	−0.746890	+	0.746890i	−0.973894	−	0.227004i	$-0.927107\pi$
$229$	−11.3025	+	11.3025i	−0.746890	+	0.746890i	0.227004	+	0.973894i	$0.427107\pi$
$230$	−0.390086	−	7.69983i	−0.0257215	−	0.507712i
$231$			4.01325i			0.264053i
$232$	10.4390	−	1.59751i	0.685351	−	0.104882i
$233$		−	0.638284i		−	0.0418154i	−0.999781	−	0.0209077i	$-0.993344\pi$
$233$		−	0.638284i		−	0.0418154i	0.999781	−	0.0209077i	$-0.00665561\pi$
$234$	6.61779	−	0.335268i	0.432618	−	0.0219172i
$235$	5.76791	−	5.76791i	0.376257	−	0.376257i
$236$	8.41048	+	6.85931i	0.547475	+	0.446503i
$237$	−7.62092	−	7.62092i	−0.495032	−	0.495032i
$238$	2.06204	−	2.28212i	0.133662	−	0.147928i
$239$	27.2255			1.76107			0.880534	−	0.473983i	$-0.157184\pi$
$239$	27.2255			1.76107			0.880534	+	0.473983i	$0.157184\pi$
$240$	−3.91829	+	0.804372i	−0.252924	+	0.0519220i
$241$	−14.0821			−0.907106			−0.453553	−	0.891229i	$-0.649844\pi$
$241$	−14.0821			−0.907106			−0.453553	+	0.891229i	$0.649844\pi$
$242$	−17.4557	+	19.3187i	−1.12209	+	1.24186i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	8.71823	−	10.6898i	0.558128	−	0.684343i
$245$	−4.56252	+	4.56252i	−0.291488	+	0.291488i
$246$	−14.3949	+	0.729272i	−0.917788	+	0.0464967i
$247$			33.3162i			2.11986i
$248$	−9.96019	+	13.5595i	−0.632473	+	0.861028i
$249$		−	6.51956i		−	0.413160i
$250$	−0.0715547	−	1.41240i	−0.00452551	−	0.0893282i
$251$	1.61761	−	1.61761i	0.102103	−	0.102103i	−0.654210	−	0.756313i	$-0.726999\pi$
$251$	1.61761	−	1.61761i	0.102103	−	0.102103i	0.756313	+	0.654210i	$0.226999\pi$
$252$	−0.149579	−	1.47246i	−0.00942256	−	0.0927563i
$253$	20.9055	+	20.9055i	1.31432	+	1.31432i
$254$	−9.38663	−	8.48140i	−0.588969	−	0.532170i
$255$	2.93893			0.184043
$256$	14.7060	−	6.30352i	0.919123	−	0.393970i
$257$	4.53176			0.282683			0.141342	−	0.989961i	$-0.454858\pi$
$257$	4.53176			0.282683			0.141342	+	0.989961i	$0.454858\pi$
$258$	−7.32671	−	6.62014i	−0.456141	−	0.412152i
$259$	−0.354729	−	0.354729i	−0.0220418	−	0.0220418i
$260$	−0.947067	−	9.32299i	−0.0587346	−	0.578187i
$261$	−2.64012	+	2.64012i	−0.163419	+	0.163419i
$262$	−0.975289	−	19.2510i	−0.0602536	−	1.18933i
$263$		−	8.25620i		−	0.509099i	−0.967060	−	0.254550i	$-0.918073\pi$
$263$		−	8.25620i		−	0.509099i	0.967060	−	0.254550i	$-0.0819272\pi$
$264$	9.08078	−	12.3623i	0.558883	−	0.760846i
$265$		−	7.14527i		−	0.438931i
$266$	7.43194	−	0.376515i	0.455682	−	0.0230856i
$267$	1.85598	−	1.85598i	0.113584	−	0.113584i
$268$	7.13662	−	8.75050i	0.435939	−	0.534522i
$269$	−14.8352	−	14.8352i	−0.904520	−	0.904520i	0.0913029	−	0.995823i	$-0.470897\pi$
$269$	−14.8352	−	14.8352i	−0.904520	−	0.904520i	−0.995823	+	0.0913029i	$0.970897\pi$
$270$	0.948122	−	1.04932i	0.0577009	−	0.0638593i
$271$	32.0786			1.94864			0.974319	−	0.225172i	$-0.0722944\pi$
$271$	32.0786			1.94864			0.974319	+	0.225172i	$0.0722944\pi$
$272$	−11.5156	+	2.36399i	−0.698235	+	0.143338i
$273$	3.46735			0.209853
$274$	6.56272	−	7.26316i	0.396468	−	0.438784i
$275$	3.83476	+	3.83476i	0.231245	+	0.231245i
$276$	−8.44941	−	6.89106i	−0.508594	−	0.414793i
$277$	−14.6755	+	14.6755i	−0.881763	+	0.881763i	−0.993714	−	0.111951i	$-0.964290\pi$
$277$	−14.6755	+	14.6755i	−0.881763	+	0.881763i	0.111951	+	0.993714i	$0.464290\pi$
$278$	−12.9912	+	0.658156i	−0.779161	+	0.0394736i
$279$		−	5.94837i		−	0.356120i
$280$	−2.06900	+	0.316626i	−0.123647	+	0.0189220i
$281$			24.6456i			1.47023i	0.677942	+	0.735116i	$0.262872\pi$
$281$			24.6456i			1.47023i	−0.677942	+	0.735116i	$0.737128\pi$
$282$	−0.583676	−	11.5211i	−0.0347574	−	0.686069i
$283$	−0.116449	+	0.116449i	−0.00692219	+	0.00692219i	−0.710559	−	0.703637i	$-0.751558\pi$
$283$	−0.116449	+	0.116449i	−0.00692219	+	0.00692219i	0.703637	+	0.710559i	$0.251558\pi$
$284$	7.07047	−	0.718248i	0.419555	−	0.0426202i
$285$	5.02789	+	5.02789i	0.297827	+	0.297827i
$286$	26.6633	+	24.0920i	1.57664	+	1.42459i
$287$	−7.54214			−0.445198
$288$	−2.87098	+	4.87417i	−0.169174	+	0.287213i
$289$	−8.36268			−0.491923
$290$	3.91783	+	3.54000i	0.230063	+	0.207876i
$291$	−1.18685	−	1.18685i	−0.0695743	−	0.0695743i
$292$	22.2167	−	2.25686i	1.30013	−	0.132073i
$293$	21.5697	−	21.5697i	1.26012	−	1.26012i	0.309079	−	0.951036i	$-0.399979\pi$
$293$	21.5697	−	21.5697i	1.26012	−	1.26012i	0.951036	−	0.309079i	$-0.100021\pi$
$294$	0.461697	+	9.11334i	0.0269267	+	0.531501i
$295$			5.42647i			0.315941i
$296$	0.290050	+	1.89534i	0.0168588	+	0.110164i
$297$			5.42317i			0.314684i
$298$	11.4861	−	0.581907i	0.665374	−	0.0337090i
$299$	18.0619	−	18.0619i	1.04454	−	1.04454i
$300$	−1.54990	−	1.26405i	−0.0894834	−	0.0729798i
$301$	−3.65368	−	3.65368i	−0.210595	−	0.210595i
$302$	−0.176144	+	0.194944i	−0.0101359	+	0.0112177i
$303$	−9.22295			−0.529845
$304$	−23.7450	−	15.6564i	−1.36187	−	0.897959i
$305$	6.89708			0.394926
$306$	2.78647	−	3.08387i	0.159292	−	0.176293i
$307$	11.7544	+	11.7544i	0.670856	+	0.670856i	0.957913	−	0.287057i	$-0.0926770\pi$
$307$	11.7544	+	11.7544i	0.670856	+	0.670856i	−0.287057	+	0.957913i	$0.592677\pi$
$308$	5.07294	−	6.22013i	0.289057	−	0.354425i
$309$	−0.213842	+	0.213842i	−0.0121650	+	0.0121650i
$310$	−8.40149	+	0.425634i	−0.477173	+	0.0241744i
$311$			15.8798i			0.900462i	0.892912	+	0.450231i	$0.148658\pi$
$311$			15.8798i			0.900462i	−0.892912	+	0.450231i	$0.851342\pi$
$312$	−10.6807	−	7.84556i	−0.604675	−	0.444167i
$313$		−	32.5435i		−	1.83947i	−0.392542	−	0.919734i	$-0.628404\pi$
$313$		−	32.5435i		−	1.83947i	0.392542	−	0.919734i	$-0.371596\pi$
$314$	1.20134	+	23.7129i	0.0677953	+	1.33820i
$315$	0.523272	−	0.523272i	0.0294831	−	0.0294831i
$316$	2.17846	+	21.4449i	0.122548	+	1.20637i
$317$	13.8078	+	13.8078i	0.775523	+	0.775523i	0.979066	−	0.203543i	$-0.0652458\pi$
$317$	13.8078	+	13.8078i	0.775523	+	0.775523i	−0.203543	+	0.979066i	$0.565246\pi$
$318$	−7.49765	−	6.77459i	−0.420447	−	0.379900i
$319$	−20.2485			−1.13370
$320$	7.08971	+	3.70620i	0.396327	+	0.207183i
$321$	1.69816			0.0947818
$322$	−4.23323	−	3.82499i	−0.235909	−	0.213158i
$323$	14.7766	+	14.7766i	0.822194	+	0.822194i
$324$	−0.202128	−	1.98976i	−0.0112293	−	0.110542i
$325$	3.31314	−	3.31314i	0.183780	−	0.183780i
$326$	−1.15172	−	22.7335i	−0.0637877	−	1.25909i
$327$			9.89939i			0.547437i
$328$	23.2325	+	17.0656i	1.28280	+	0.942289i
$329$		−	6.03638i		−	0.332796i
$330$	7.65970	−	0.388053i	0.421653	−	0.0213616i
$331$	−5.85148	+	5.85148i	−0.321627	+	0.321627i	−0.849391	−	0.527764i	$-0.823030\pi$
$331$	−5.85148	+	5.85148i	−0.321627	+	0.321627i	0.527764	+	0.849391i	$0.323030\pi$
$332$	−8.24102	+	10.1047i	−0.452285	+	0.554565i
$333$	−0.479352	−	0.479352i	−0.0262683	−	0.0262683i
$334$	−12.2236	+	13.5282i	−0.668844	+	0.740230i
$335$	5.64585			0.308466
$336$	−1.62943	+	2.47124i	−0.0888925	+	0.134817i
$337$	−19.3223			−1.05255			−0.526276	−	0.850314i	$-0.676412\pi$
$337$	−19.3223			−1.05255			−0.526276	+	0.850314i	$0.676412\pi$
$338$	8.48927	−	9.39533i	0.461755	−	0.511039i
$339$	−10.7021	−	10.7021i	−0.581257	−	0.581257i
$340$	−4.55505	−	3.71495i	−0.247032	−	0.201471i
$341$	22.8106	−	22.8106i	1.23526	−	1.23526i
$342$	10.0429	−	0.508791i	0.543058	−	0.0275123i
$343$			9.95501i			0.537520i
$344$	2.98750	+	19.5219i	0.161075	+	1.05255i
$345$		−	5.45159i		−	0.293504i
$346$	1.22468	+	24.1736i	0.0658390	+	1.29958i
$347$	6.92151	−	6.92151i	0.371566	−	0.371566i	−0.496481	−	0.868047i	$-0.665375\pi$
$347$	6.92151	−	6.92151i	0.371566	−	0.371566i	0.868047	+	0.496481i	$0.165375\pi$
$348$	7.42916	−	0.754684i	0.398245	−	0.0404553i
$349$	13.2497	+	13.2497i	0.709241	+	0.709241i	0.966376	−	0.257135i	$-0.0827784\pi$
$349$	13.2497	+	13.2497i	0.709241	+	0.709241i	−0.257135	+	0.966376i	$0.582778\pi$
$350$	−0.776514	−	0.701629i	−0.0415064	−	0.0375036i
$351$	4.68548			0.250093
$352$	−29.7008	+	7.68175i	−1.58306	+	0.409439i
$353$	−21.8789			−1.16450			−0.582249	−	0.813010i	$-0.697827\pi$
$353$	−21.8789			−1.16450			−0.582249	+	0.813010i	$0.697827\pi$
$354$	5.69408	+	5.14496i	0.302637	+	0.273451i
$355$	2.51265	+	2.51265i	0.133358	+	0.133358i
$356$	−5.22263	+	0.530537i	−0.276799	+	0.0281184i
$357$	1.53786	−	1.53786i	0.0813923	−	0.0813923i
$358$	−1.57414	−	31.0717i	−0.0831961	−	1.64219i
$359$		−	6.94782i		−	0.366692i	−0.983048	−	0.183346i	$-0.941307\pi$
$359$		−	6.94782i		−	0.366692i	0.983048	−	0.183346i	$-0.0586928\pi$
$360$	−2.79588	+	0.427863i	−0.147356	+	0.0225503i
$361$			31.5595i			1.66102i
$362$	−21.1669	+	1.07235i	−1.11251	+	0.0563615i
$363$	−13.0184	+	13.0184i	−0.683289	+	0.683289i
$364$	−5.37404	−	4.38289i	−0.281676	−	0.229726i
$365$	7.89522	+	7.89522i	0.413254	+	0.413254i
$366$	6.53928	−	7.23722i	0.341813	−	0.378295i
$367$	17.0448			0.889730			0.444865	−	0.895598i	$-0.353252\pi$
$367$	17.0448			0.889730			0.444865	+	0.895598i	$0.353252\pi$
$368$	4.38510	+	21.3609i	0.228589	+	1.11351i
$369$	−10.1918			−0.530565
$370$	−0.642737	+	0.711337i	−0.0334143	+	0.0369807i
$371$	−3.73892	−	3.73892i	−0.194115	−	0.194115i
$372$	−7.51902	+	9.21937i	−0.389843	+	0.478002i
$373$	−14.3704	+	14.3704i	−0.744071	+	0.744071i	−0.973359	−	0.229287i	$-0.926360\pi$
$373$	−14.3704	+	14.3704i	−0.744071	+	0.744071i	0.229287	+	0.973359i	$0.426360\pi$
$374$	22.5113	−	1.14046i	1.16403	−	0.0589719i
$375$		−	1.00000i		−	0.0516398i
$376$	−13.6585	+	18.5943i	−0.704384	+	0.958926i
$377$			17.4942i			0.900996i
$378$	−0.0529518	−	1.04520i	−0.00272355	−	0.0537595i
$379$	2.97499	−	2.97499i	0.152815	−	0.152815i	−0.626559	−	0.779374i	$-0.715537\pi$
$379$	2.97499	−	2.97499i	0.152815	−	0.152815i	0.779374	+	0.626559i	$0.215537\pi$
$380$	−1.43723	−	14.1482i	−0.0737286	−	0.725788i
$381$	−6.32540	−	6.32540i	−0.324060	−	0.324060i
$382$	−9.28056	−	8.38557i	−0.474835	−	0.429043i
$383$	−20.4810			−1.04653			−0.523266	−	0.852170i	$-0.675286\pi$
$383$	−20.4810			−1.04653			−0.523266	+	0.852170i	$0.675286\pi$
$384$	10.6109	−	3.92542i	0.541485	−	0.200318i
$385$	4.01325			0.204534
$386$	−14.7654	−	13.3415i	−0.751539	−	0.679062i
$387$	−4.93728	−	4.93728i	−0.250976	−	0.250976i
$388$	0.339263	+	3.33973i	0.0172235	+	0.169549i
$389$	11.8703	−	11.8703i	0.601848	−	0.601848i	−0.338955	−	0.940803i	$-0.610073\pi$
$389$	11.8703	−	11.8703i	0.601848	−	0.601848i	0.940803	+	0.338955i	$0.110073\pi$
$390$	−0.335268	−	6.61779i	−0.0169770	−	0.335105i
$391$		−	16.0218i		−	0.810259i
$392$	10.8041	−	14.7084i	0.545690	−	0.742885i
$393$		−	13.6300i		−	0.687542i
$394$	−16.2837	+	0.824960i	−0.820361	+	0.0415609i
$395$	−7.62092	+	7.62092i	−0.383450	+	0.383450i
$396$	6.85514	−	8.40537i	0.344484	−	0.422386i
$397$	19.1282	+	19.1282i	0.960019	+	0.960019i	0.999231	−	0.0392118i	$-0.0124847\pi$
$397$	19.1282	+	19.1282i	0.960019	+	0.960019i	−0.0392118	+	0.999231i	$0.512485\pi$
$398$	10.7580	−	11.9062i	0.539249	−	0.596803i
$399$	5.26192			0.263425
$400$	0.804372	+	3.91829i	0.0402186	+	0.195914i
$401$	−16.0874			−0.803368			−0.401684	−	0.915778i	$-0.631575\pi$
$401$	−16.0874			−0.803368			−0.401684	+	0.915778i	$0.631575\pi$
$402$	5.35296	−	5.92429i	0.266981	−	0.295477i
$403$	−19.7078	−	19.7078i	−0.981714	−	0.981714i
$404$	14.2946	+	11.6582i	0.711185	+	0.580019i
$405$	0.707107	−	0.707107i	0.0351364	−	0.0351364i
$406$	3.90248	−	0.197706i	0.193677	−	0.00981198i
$407$		−	3.67640i		−	0.182232i
$408$	−8.21689	+	1.25746i	−0.406797	+	0.0622535i
$409$			23.4524i			1.15964i	0.814743	+	0.579822i	$0.196878\pi$
$409$			23.4524i			1.15964i	−0.814743	+	0.579822i	$0.803122\pi$
$410$	0.729272	+	14.3949i	0.0360162	+	0.710916i
$411$	4.89445	−	4.89445i	0.241426	−	0.241426i
$412$	0.601739	−	0.0611271i	0.0296456	−	0.00301152i
$413$	2.83952	+	2.83952i	0.139724	+	0.139724i
$414$	−5.72044	−	5.16877i	−0.281144	−	0.254031i
$415$	−6.51956			−0.320032
$416$	6.63684	+	25.6607i	0.325398	+	1.25812i
$417$	−9.19795			−0.450426
$418$	40.4633	+	36.5611i	1.97912	+	1.78826i
$419$	−14.1654	−	14.1654i	−0.692027	−	0.692027i	0.270651	−	0.962678i	$-0.412761\pi$
$419$	−14.1654	−	14.1654i	−0.692027	−	0.692027i	−0.962678	+	0.270651i	$0.912761\pi$
$420$	−1.47246	+	0.149579i	−0.0718487	+	0.00729868i
$421$	21.2978	−	21.2978i	1.03799	−	1.03799i	0.0387434	−	0.999249i	$-0.487665\pi$
$421$	21.2978	−	21.2978i	1.03799	−	1.03799i	0.999249	−	0.0387434i	$-0.0123355\pi$
$422$	1.58283	+	31.2432i	0.0770511	+	1.52089i
$423$		−	8.15706i		−	0.396610i
$424$	3.05719	+	19.9773i	0.148470	+	0.970184i
$425$		−	2.93893i		−	0.142559i
$426$	5.01887	−	0.254265i	0.243165	−	0.0123192i
$427$	3.60905	−	3.60905i	0.174654	−	0.174654i
$428$	−2.63197	−	2.14655i	−0.127221	−	0.103757i
$429$	17.9677	+	17.9677i	0.867490	+	0.867490i
$430$	−6.62014	+	7.32671i	−0.319252	+	0.353326i
$431$	−21.0148			−1.01225			−0.506123	−	0.862462i	$-0.668922\pi$
$431$	−21.0148			−1.01225			−0.506123	+	0.862462i	$0.668922\pi$
$432$	−2.20187	+	3.33943i	−0.105938	+	0.160668i
$433$	16.2253			0.779738			0.389869	−	0.920870i	$-0.372520\pi$
$433$	16.2253			0.779738			0.389869	+	0.920870i	$0.372520\pi$
$434$	−4.17355	+	4.61899i	−0.200337	+	0.221719i
$435$	2.64012	+	2.64012i	0.126584	+	0.126584i
$436$	12.5133	−	15.3430i	0.599278	−	0.734799i
$437$	27.4100	−	27.4100i	1.31120	−	1.31120i
$438$	15.7702	−	0.798945i	0.753530	−	0.0381751i
$439$		−	3.33967i		−	0.159394i	−0.996819	−	0.0796970i	$-0.974605\pi$
$439$		−	3.33967i		−	0.159394i	0.996819	−	0.0796970i	$-0.0253953\pi$
$440$	−12.3623	−	9.08078i	−0.589348	−	0.432909i
$441$			6.45237i			0.307256i
$442$	−0.985330	−	19.4492i	−0.0468674	−	0.925105i
$443$	13.4671	−	13.4671i	0.639841	−	0.639841i	−0.310675	−	0.950516i	$-0.600555\pi$
$443$	13.4671	−	13.4671i	0.639841	−	0.639841i	0.950516	+	0.310675i	$0.100555\pi$
$444$	0.137024	+	1.34887i	0.00650285	+	0.0640145i
$445$	−1.85598	−	1.85598i	−0.0879820	−	0.0879820i
$446$	10.7841	+	9.74415i	0.510644	+	0.461399i
$447$	8.13234			0.384647
$448$	5.64921	−	1.77050i	0.266900	−	0.0836482i
$449$	19.2995			0.910799			0.455400	−	0.890287i	$-0.349496\pi$
$449$	19.2995			0.910799			0.455400	+	0.890287i	$0.349496\pi$
$450$	−1.04932	−	0.948122i	−0.0494652	−	0.0446949i
$451$	−39.0832	−	39.0832i	−1.84036	−	1.84036i
$452$	3.05921	+	30.1151i	0.143893	+	1.41649i
$453$	−0.131367	+	0.131367i	−0.00617218	+	0.00617218i
$454$	1.39974	+	27.6292i	0.0656931	+	1.29670i
$455$		−	3.46735i		−	0.162552i
$456$	−16.2086	−	11.9061i	−0.759039	−	0.557556i
$457$			21.0222i			0.983377i	0.870771	+	0.491688i	$0.163620\pi$
$457$			21.0222i			0.983377i	−0.870771	+	0.491688i	$0.836380\pi$
$458$	22.5760	−	1.14374i	1.05491	−	0.0534434i
$459$	2.07814	−	2.07814i	0.0969992	−	0.0969992i
$460$	−6.89106	+	8.44941i	−0.321297	+	0.393956i
$461$	−23.3056	−	23.3056i	−1.08545	−	1.08545i	−0.995990	−	0.0894616i	$-0.971485\pi$
$461$	−23.3056	−	23.3056i	−1.08545	−	1.08545i	−0.0894616	−	0.995990i	$-0.528515\pi$
$462$	3.80505	−	4.21117i	0.177027	−	0.195921i
$463$	−1.65187			−0.0767687			−0.0383844	−	0.999263i	$-0.512221\pi$
$463$	−1.65187			−0.0767687			−0.0383844	+	0.999263i	$0.512221\pi$
$464$	−12.4684	−	8.22112i	−0.578831	−	0.381656i
$465$	−5.94837			−0.275849
$466$	−0.605171	+	0.669762i	−0.0280340	+	0.0310261i
$467$	−14.4723	−	14.4723i	−0.669699	−	0.669699i	0.287948	−	0.957646i	$-0.407027\pi$
$467$	−14.4723	−	14.4723i	−0.669699	−	0.669699i	−0.957646	+	0.287948i	$0.907027\pi$
$468$	−7.26203	−	5.92267i	−0.335687	−	0.273776i
$469$	2.95432	−	2.95432i	0.136418	−	0.136418i
$470$	−11.5211	+	0.583676i	−0.531427	+	0.0269230i
$471$			16.7891i			0.773599i
$472$	−2.32178	−	15.1717i	−0.106869	−	0.698336i
$473$		−	37.8666i		−	1.74111i
$474$	0.771188	+	15.2223i	0.0354218	+	0.699184i
$475$	5.02789	−	5.02789i	0.230696	−	0.230696i
$476$	−4.32746	+	0.439601i	−0.198349	+	0.0201491i
$477$	−5.05247	−	5.05247i	−0.231337	−	0.231337i
$478$	−28.5681	−	25.8131i	−1.30667	−	1.18066i
$479$	6.07727			0.277678			0.138839	−	0.990315i	$-0.455663\pi$
$479$	6.07727			0.277678			0.138839	+	0.990315i	$0.455663\pi$
$480$	4.87417	+	2.87098i	0.222474	+	0.131042i
$481$	−3.17632			−0.144828
$482$	14.7765	+	13.3515i	0.673053	+	0.608145i
$483$	−2.85266	−	2.85266i	−0.129801	−	0.129801i
$484$	36.6331	−	3.72134i	1.66514	−	0.169152i
$485$	−1.18685	+	1.18685i	−0.0538921	+	0.0538921i
$486$	−0.0715547	−	1.41240i	−0.00324579	−	0.0640679i
$487$		−	10.1863i		−	0.461586i	−0.973003	−	0.230793i	$-0.925868\pi$
$487$		−	10.1863i		−	0.461586i	0.973003	−	0.230793i	$-0.0741320\pi$
$488$	−19.2834	+	2.95100i	−0.872918	+	0.133586i
$489$		−	16.0956i		−	0.727869i
$490$	9.11334	−	0.461697i	0.411699	−	0.0208574i
$491$	8.75035	−	8.75035i	0.394898	−	0.394898i	−0.481531	−	0.876429i	$-0.659919\pi$
$491$	8.75035	−	8.75035i	0.394898	−	0.394898i	0.876429	+	0.481531i	$0.159919\pi$
$492$	15.7963	+	12.8829i	0.712152	+	0.580807i
$493$	7.75914	+	7.75914i	0.349454	+	0.349454i
$494$	31.5879	−	34.9592i	1.42120	−	1.57289i
$495$	5.42317			0.243753
$496$	23.3074	−	4.78470i	1.04653	−	0.214840i
$497$	2.62961			0.117954
$498$	−6.18134	+	6.84107i	−0.276992	+	0.306556i
$499$	−23.8260	−	23.8260i	−1.06660	−	1.06660i	−0.997618	−	0.0689808i	$-0.978025\pi$
$499$	−23.8260	−	23.8260i	−1.06660	−	1.06660i	−0.0689808	−	0.997618i	$-0.521975\pi$
$500$	−1.26405	+	1.54990i	−0.0565299	+	0.0693136i
$501$	−9.11630	+	9.11630i	−0.407286	+	0.407286i
$502$	−3.23108	+	0.163692i	−0.144210	+	0.00730592i
$503$			9.42267i			0.420136i	0.977687	+	0.210068i	$0.0673685\pi$
$503$			9.42267i			0.420136i	−0.977687	+	0.210068i	$0.932631\pi$
$504$	−1.23912	+	1.68689i	−0.0551947	+	0.0751403i
$505$			9.22295i			0.410416i
$506$	−2.11551	−	41.7575i	−0.0940457	−	1.85635i
$507$	6.33127	−	6.33127i	0.281182	−	0.281182i
$508$	1.80813	+	17.7993i	0.0802228	+	0.789718i
$509$	−16.3129	−	16.3129i	−0.723055	−	0.723055i	0.246172	−	0.969226i	$-0.420827\pi$
$509$	−16.3129	−	16.3129i	−0.723055	−	0.723055i	−0.969226	+	0.246172i	$0.920827\pi$
$510$	−3.08387	−	2.78647i	−0.136556	−	0.123387i
$511$	8.26270			0.365520
$512$	−21.4077	−	7.32867i	−0.946097	−	0.323885i
$513$	7.11052			0.313937
$514$	−4.75525	−	4.29666i	−0.209745	−	0.189518i
$515$	0.213842	+	0.213842i	0.00942299	+	0.00942299i
$516$	1.41133	+	13.8932i	0.0621305	+	0.611616i
$517$	31.2804	−	31.2804i	1.37571	−	1.37571i
$518$	0.0358963	+	0.708550i	0.00157719	+	0.0311319i
$519$			17.1153i			0.751276i
$520$	−7.84556	+	10.6807i	−0.344051	+	0.468380i
$521$			10.7287i			0.470033i	0.971991	+	0.235016i	$0.0755144\pi$
$521$			10.7287i			0.470033i	−0.971991	+	0.235016i	$0.924486\pi$
$522$	5.27348	−	0.267163i	0.230814	−	0.0116934i
$523$	−16.3868	+	16.3868i	−0.716546	+	0.716546i	−0.967896	−	0.251351i	$-0.919125\pi$
$523$	−16.3868	+	16.3868i	−0.716546	+	0.716546i	0.251351	+	0.967896i	$0.419125\pi$
$524$	−17.2289	+	21.1251i	−0.752650	+	0.922855i
$525$	−0.523272	−	0.523272i	−0.0228375	−	0.0228375i
$526$	−7.82789	+	8.66337i	−0.341312	+	0.377741i
$527$	−17.4819			−0.761521
$528$	−21.2496	+	4.36225i	−0.924768	+	0.189843i
$529$	−6.71979			−0.292165
$530$	−6.77459	+	7.49765i	−0.294269	+	0.325677i
$531$	3.83709	+	3.83709i	0.166516	+	0.166516i
$532$	−8.15544	−	6.65131i	−0.353583	−	0.288371i
$533$	−33.7669	+	33.7669i	−1.46261	+	1.46261i
$534$	−3.70721	+	0.187814i	−0.160427	+	0.00812749i
$535$		−	1.69816i		−	0.0734177i
$536$	−15.7851	+	2.41565i	−0.681813	+	0.104340i
$537$		−	21.9992i		−	0.949335i
$538$	1.50123	+	29.6325i	0.0647227	+	1.27755i
$539$	−24.7433	+	24.7433i	−1.06577	+	1.06577i
$540$	−1.98976	+	0.202128i	−0.0856256	+	0.00869820i
$541$	11.4471	+	11.4471i	0.492148	+	0.492148i	0.908983	−	0.416834i	$-0.136860\pi$
$541$	11.4471	+	11.4471i	0.492148	+	0.492148i	−0.416834	+	0.908983i	$0.636860\pi$
$542$	−33.6606	−	30.4145i	−1.44585	−	1.30641i
$543$	−14.9864			−0.643130
$544$	14.3248	+	8.43760i	0.614172	+	0.361759i
$545$	9.89939			0.424043
$546$	−3.63834	−	3.28747i	−0.155707	−	0.140691i
$547$	9.67749	+	9.67749i	0.413780	+	0.413780i	0.883053	−	0.469273i	$-0.155484\pi$
$547$	9.67749	+	9.67749i	0.413780	+	0.413780i	−0.469273	+	0.883053i	$0.655484\pi$
$548$	−13.7727	+	1.39909i	−0.588342	+	0.0597662i
$549$	4.87697	−	4.87697i	0.208144	−	0.208144i
$550$	−0.388053	−	7.65970i	−0.0165466	−	0.326611i
$551$			26.5485i			1.13100i
$552$	2.33253	+	15.2420i	0.0992791	+	0.648741i
$553$			7.97564i			0.339159i
$554$	29.3133	−	1.48506i	1.24540	−	0.0630942i
$555$	−0.479352	+	0.479352i	−0.0203473	+	0.0203473i
$556$	14.2559	+	11.6266i	0.604585	+	0.493079i
$557$	10.0484	+	10.0484i	0.425762	+	0.425762i	0.887182	−	0.461420i	$-0.152660\pi$
$557$	10.0484	+	10.0484i	0.425762	+	0.425762i	−0.461420	+	0.887182i	$0.652660\pi$
$558$	−5.63978	+	6.24172i	−0.238751	+	0.264233i
$559$	−32.7158			−1.38373
$560$	2.47124	+	1.62943i	0.104429	+	0.0688558i
$561$	15.9383			0.672917
$562$	23.3670	−	25.8610i	0.985678	−	1.09088i
$563$	8.44120	+	8.44120i	0.355754	+	0.355754i	0.862245	−	0.506491i	$-0.169058\pi$
$563$	8.44120	+	8.44120i	0.355754	+	0.355754i	−0.506491	+	0.862245i	$0.669058\pi$
$564$	−10.3109	+	12.6426i	−0.434168	+	0.532350i
$565$	−10.7021	+	10.7021i	−0.450240	+	0.450240i
$566$	0.232600	−	0.0117839i	0.00977692	−	0.000495315i
$567$		−	0.740019i		−	0.0310779i
$568$	−8.10015	−	5.95001i	−0.339875	−	0.249657i
$569$		−	7.27300i		−	0.304900i	−0.988311	−	0.152450i	$-0.951284\pi$
$569$		−	7.27300i		−	0.304900i	0.988311	−	0.152450i	$-0.0487163\pi$
$570$	−0.508791	−	10.0429i	−0.0213109	−	0.420651i
$571$	−5.28045	+	5.28045i	−0.220980	+	0.220980i	−0.808911	−	0.587931i	$-0.799943\pi$
$571$	−5.28045	+	5.28045i	−0.220980	+	0.220980i	0.587931	+	0.808911i	$0.299943\pi$
$572$	−5.13611	−	50.5602i	−0.214752	−	2.11403i
$573$	−6.25393	−	6.25393i	−0.261262	−	0.261262i
$574$	7.91409	+	7.15087i	0.330328	+	0.298472i
$575$	−5.45159			−0.227347
$576$	7.63387	−	2.39250i	0.318078	−	0.0996876i
$577$	27.0550			1.12631			0.563157	−	0.826350i	$-0.309587\pi$
$577$	27.0550			1.12631			0.563157	+	0.826350i	$0.309587\pi$
$578$	8.77510	+	7.92885i	0.364996	+	0.329797i
$579$	−9.95002	−	9.95002i	−0.413509	−	0.413509i
$580$	−0.754684	−	7.42916i	−0.0313366	−	0.308479i
$581$	−3.41150	+	3.41150i	−0.141533	+	0.141533i
$582$	0.120102	+	2.37066i	0.00497837	+	0.0982670i
$583$		−	38.7500i		−	1.60486i
$584$	−25.4521	−	18.6960i	−1.05322	−	0.773646i
$585$		−	4.68548i		−	0.193721i
$586$	−43.0841	+	2.18272i	−1.77979	+	0.0901671i
$587$	−6.62135	+	6.62135i	−0.273292	+	0.273292i	−0.830424	−	0.557132i	$-0.811902\pi$
$587$	−6.62135	+	6.62135i	−0.273292	+	0.273292i	0.557132	+	0.830424i	$0.311902\pi$
$588$	8.15610	−	10.0005i	0.336352	−	0.412415i
$589$	−29.9078	−	29.9078i	−1.23233	−	1.23233i
$590$	5.14496	−	5.69408i	0.211815	−	0.234422i
$591$	−11.5291			−0.474243
$592$	1.49266	−	2.26381i	0.0613480	−	0.0930422i
$593$	−9.02017			−0.370414			−0.185207	−	0.982700i	$-0.559296\pi$
$593$	−9.02017			−0.370414			−0.185207	+	0.982700i	$0.559296\pi$
$594$	5.14183	−	5.69062i	0.210972	−	0.233489i
$595$	−1.53786	−	1.53786i	−0.0630462	−	0.0630462i
$596$	−12.6043	−	10.2797i	−0.516292	−	0.421071i
$597$	8.02327	−	8.02327i	0.328371	−	0.328371i
$598$	−36.0774	+	1.82774i	−1.47532	+	0.0747420i
$599$		−	7.68375i		−	0.313950i	−0.987603	−	0.156975i	$-0.949826\pi$
$599$		−	7.68375i		−	0.313950i	0.987603	−	0.156975i	$-0.0501742\pi$
$600$	0.427863	+	2.79588i	0.0174674	+	0.114141i
$601$		−	31.7822i		−	1.29642i	−0.761460	−	0.648212i	$-0.775517\pi$
$601$		−	31.7822i		−	1.29642i	0.761460	−	0.648212i	$-0.224483\pi$
$602$	0.369729	+	7.29801i	0.0150690	+	0.297445i
$603$	3.99222	−	3.99222i	0.162576	−	0.162576i
$604$	0.369661	−	0.0375517i	0.0150413	−	0.00152796i
$605$	13.0184	+	13.0184i	0.529273	+	0.529273i
$606$	9.67779	+	8.74449i	0.393133	+	0.355221i
$607$	25.7518			1.04524			0.522618	−	0.852567i	$-0.324956\pi$
$607$	25.7518			1.04524			0.522618	+	0.852567i	$0.324956\pi$
$608$	10.0718	+	38.9418i	0.408466	+	1.57930i
$609$	2.76301			0.111963
$610$	−7.23722	−	6.53928i	−0.293026	−	0.264768i
$611$	−27.0255	−	27.0255i	−1.09333	−	1.09333i
$612$	−5.84777	+	0.594040i	−0.236382	+	0.0240126i
$613$	−10.4967	+	10.4967i	−0.423956	+	0.423956i	−0.886563	−	0.462607i	$-0.846914\pi$
$613$	−10.4967	+	10.4967i	−0.423956	+	0.423956i	0.462607	+	0.886563i	$0.346914\pi$
$614$	−1.18947	−	23.4786i	−0.0480029	−	0.947519i
$615$			10.1918i			0.410974i
$616$	−11.2206	+	1.71712i	−0.452089	+	0.0691847i
$617$			29.2461i			1.17740i	0.808351	+	0.588701i	$0.200360\pi$
$617$			29.2461i			1.17740i	−0.808351	+	0.588701i	$0.799640\pi$
$618$	0.427136	−	0.0216394i	0.0171819	−	0.000870465i
$619$	21.9641	−	21.9641i	0.882814	−	0.882814i	−0.111006	−	0.993820i	$-0.535407\pi$
$619$	21.9641	−	21.9641i	0.882814	−	0.882814i	0.993820	+	0.111006i	$0.0354073\pi$
$620$	9.21937	+	7.51902i	0.370259	+	0.301971i
$621$	−3.85485	−	3.85485i	−0.154690	−	0.154690i
$622$	15.0560	−	16.6629i	0.603691	−	0.668123i
$623$	−1.94237			−0.0778194
$624$	3.76887	+	18.3591i	0.150876	+	0.734951i
$625$	−1.00000			−0.0400000
$626$	−30.8552	+	34.1484i	−1.23322	+	1.36485i
$627$	27.2671	+	27.2671i	1.08894	+	1.08894i
$628$	21.2222	−	26.0213i	0.846856	−	1.03836i
$629$	−1.40878	+	1.40878i	−0.0561718	+	0.0561718i
$630$	−1.04520	+	0.0529518i	−0.0416419	+	0.00210965i
$631$			6.46257i			0.257271i	0.991692	+	0.128635i	$0.0410597\pi$
$631$			6.46257i			0.257271i	−0.991692	+	0.128635i	$0.958940\pi$
$632$	18.0465	−	24.5679i	0.717850	−	0.977257i
$633$			22.1206i			0.879215i
$634$	−1.39726	−	27.5802i	−0.0554923	−	1.09535i
$635$	−6.32540	+	6.32540i	−0.251016	+	0.251016i
$636$	1.44426	+	14.2174i	0.0572686	+	0.563756i
$637$	21.3776	+	21.3776i	0.847011	+	0.847011i
$638$	21.2471	+	19.1980i	0.841179	+	0.760058i
$639$	3.55343			0.140572
$640$	−3.92542	−	10.6109i	−0.155166	−	0.419432i
$641$	−5.56318			−0.219732			−0.109866	−	0.993946i	$-0.535042\pi$
$641$	−5.56318			−0.219732			−0.109866	+	0.993946i	$0.535042\pi$
$642$	−1.78190	−	1.61006i	−0.0703261	−	0.0635440i
$643$	2.91681	+	2.91681i	0.115028	+	0.115028i	0.762278	−	0.647250i	$-0.224081\pi$
$643$	2.91681	+	2.91681i	0.115028	+	0.115028i	−0.647250	+	0.762278i	$0.724081\pi$
$644$	0.815440	+	8.02724i	0.0321328	+	0.316318i
$645$	−4.93728	+	4.93728i	−0.194405	+	0.194405i
$646$	−1.49530	−	29.5154i	−0.0588318	−	1.16127i
$647$			22.9740i			0.903201i	0.892220	+	0.451601i	$0.149147\pi$
$647$			22.9740i			0.903201i	−0.892220	+	0.451601i	$0.850853\pi$
$648$	−1.67444	+	2.27953i	−0.0657782	+	0.0895483i
$649$			29.4287i			1.15518i
$650$	−6.61779	+	0.335268i	−0.259571	+	0.0131503i
$651$	−3.11262	+	3.11262i	−0.121993	+	0.121993i
$652$	−20.3456	+	24.9466i	−0.796796	+	0.976984i
$653$	25.9783	+	25.9783i	1.01661	+	1.01661i	0.999860	+	0.0167495i	$0.00533179\pi$
$653$	25.9783	+	25.9783i	1.01661	+	1.01661i	0.0167495	+	0.999860i	$0.494668\pi$
$654$	9.38583	−	10.3876i	0.367015	−	0.406187i
$655$	−13.6300			−0.532568
$656$	−8.19801	−	39.9345i	−0.320079	−	1.55918i
$657$	11.1655			0.435608
$658$	−5.72323	+	6.33407i	−0.223115	+	0.246928i
$659$	28.1599	+	28.1599i	1.09695	+	1.09695i	0.994765	+	0.102189i	$0.0325848\pi$
$659$	28.1599	+	28.1599i	1.09695	+	1.09695i	0.102189	+	0.994765i	$0.467415\pi$
$660$	−8.40537	−	6.85514i	−0.327179	−	0.266836i
$661$	−24.8805	+	24.8805i	−0.967741	+	0.967741i	−0.999496	−	0.0317548i	$-0.989890\pi$
$661$	−24.8805	+	24.8805i	−0.967741	+	0.967741i	0.0317548	+	0.999496i	$0.489890\pi$
$662$	11.6880	−	0.592133i	0.454266	−	0.0230139i
$663$		−	13.7703i		−	0.534795i
$664$	18.2279	−	2.78947i	0.707379	−	0.108253i
$665$		−	5.26192i		−	0.204048i
$666$	0.0485073	+	0.957475i	0.00187962	+	0.0371014i
$667$	14.3929	−	14.3929i	0.557294	−	0.557294i
$668$	25.6528	−	2.60591i	0.992536	−	0.100826i
$669$	7.26715	+	7.26715i	0.280964	+	0.280964i
$670$	−5.92429	−	5.35296i	−0.228875	−	0.206803i
$671$	37.4041			1.44397
$672$	4.05282	−	1.04821i	0.156341	−	0.0404357i
$673$	−4.37152			−0.168510			−0.0842548	−	0.996444i	$-0.526851\pi$
$673$	−4.37152			−0.168510			−0.0842548	+	0.996444i	$0.526851\pi$
$674$	20.2752	+	18.3199i	0.780970	+	0.705655i
$675$	−0.707107	−	0.707107i	−0.0272166	−	0.0272166i
$676$	−17.8158	+	1.80981i	−0.685225	+	0.0696079i
$677$	−7.19018	+	7.19018i	−0.276341	+	0.276341i	−0.831646	−	0.555305i	$-0.812601\pi$
$677$	−7.19018	+	7.19018i	−0.276341	+	0.276341i	0.555305	+	0.831646i	$0.312601\pi$
$678$	1.08298	+	21.3768i	0.0415917	+	0.820969i
$679$			1.24209i			0.0476671i
$680$	1.25746	+	8.21689i	0.0482213	+	0.315103i
$681$			19.5618i			0.749611i
$682$	−45.5627	+	2.30828i	−1.74469	+	0.0883888i
$683$	27.3182	−	27.3182i	1.04530	−	1.04530i	0.0463792	−	0.998924i	$-0.485232\pi$
$683$	27.3182	−	27.3182i	1.04530	−	1.04530i	0.998924	−	0.0463792i	$-0.0147682\pi$
$684$	−11.0206	−	8.98803i	−0.421382	−	0.343666i
$685$	−4.89445	−	4.89445i	−0.187007	−	0.187007i
$686$	9.43857	−	10.4460i	0.360366	−	0.398828i
$687$	15.9841			0.609833
$688$	15.3743	−	23.3171i	0.586139	−	0.888957i
$689$	−33.4791			−1.27545
$690$	−5.16877	+	5.72044i	−0.196772	+	0.217773i
$691$	10.7859	+	10.7859i	0.410316	+	0.410316i	0.881849	−	0.471533i	$-0.156299\pi$
$691$	10.7859	+	10.7859i	0.410316	+	0.410316i	−0.471533	+	0.881849i	$0.656299\pi$
$692$	21.6345	−	26.5269i	0.822420	−	1.00840i
$693$	2.83780	−	2.83780i	0.107799	−	0.107799i
$694$	−13.8253	+	0.700412i	−0.524801	+	0.0265873i
$695$			9.19795i			0.348898i
$696$	−8.51107	−	6.25185i	−0.322611	−	0.236976i
$697$			29.9530i			1.13455i
$698$	−1.34079	−	26.4655i	−0.0507495	−	1.00173i
$699$	−0.451335	+	0.451335i	−0.0170711	+	0.0170711i
$700$	0.149579	+	1.47246i	0.00565354	+	0.0556538i
$701$	−7.34496	−	7.34496i	−0.277415	−	0.277415i	0.554661	−	0.832076i	$-0.312848\pi$
$701$	−7.34496	−	7.34496i	−0.277415	−	0.277415i	−0.832076	+	0.554661i	$0.812848\pi$
$702$	−4.91655	−	4.44241i	−0.185563	−	0.167668i
$703$	−4.82026			−0.181799
$704$	38.4487	+	20.0994i	1.44909	+	0.757524i
$705$	−8.15706			−0.307213
$706$	22.9579	+	20.7439i	0.864033	+	0.780707i
$707$	4.82612	+	4.82612i	0.181505	+	0.181505i
$708$	−1.09684	−	10.7974i	−0.0412218	−	0.405790i
$709$	36.8251	−	36.8251i	1.38299	−	1.38299i	0.543740	−	0.839254i	$-0.317008\pi$
$709$	36.8251	−	36.8251i	1.38299	−	1.38299i	0.839254	−	0.543740i	$-0.182992\pi$
$710$	−0.254265	−	5.01887i	−0.00954238	−	0.188355i
$711$			10.7776i			0.404192i
$712$	5.98321	+	4.39500i	0.224230	+	0.164709i
$713$			32.4281i			1.21444i
$714$	−3.07178	+	0.155622i	−0.114959	+	0.00582400i
$715$	17.9677	−	17.9677i	0.671955	−	0.671955i
$716$	−27.8080	+	34.0965i	−1.03923	+	1.27425i
$717$	−19.2513	−	19.2513i	−0.718953	−	0.718953i
$718$	−6.58738	+	7.29046i	−0.245839	+	0.272077i
$719$	15.1515			0.565055			0.282527	−	0.959259i	$-0.408827\pi$
$719$	15.1515			0.565055			0.282527	+	0.959259i	$0.408827\pi$
$720$	3.33943	+	2.20187i	0.124453	+	0.0820589i
$721$	0.223795			0.00833456
$722$	29.9222	−	33.1158i	1.11359	−	1.23244i
$723$	9.95753	+	9.95753i	0.370324	+	0.370324i
$724$	23.2275	+	18.9436i	0.863242	+	0.704032i
$725$	2.64012	−	2.64012i	0.0980517	−	0.0980517i
$726$	26.0035	−	1.31738i	0.965079	−	0.0488925i
$727$		−	18.4900i		−	0.685756i	−0.939380	−	0.342878i	$-0.888598\pi$
$727$		−	18.4900i		−	0.685756i	0.939380	−	0.342878i	$-0.111402\pi$
$728$	1.48355	+	9.69428i	0.0549840	+	0.359294i
$729$		−	1.00000i		−	0.0370370i
$730$	−0.798945	−	15.7702i	−0.0295703	−	0.583682i
$731$	−14.5103	+	14.5103i	−0.536684	+	0.536684i
$732$	−13.7235	+	1.39409i	−0.507236	+	0.0515272i
$733$	−10.2992	−	10.2992i	−0.380409	−	0.380409i	0.490840	−	0.871250i	$-0.336690\pi$
$733$	−10.2992	−	10.2992i	−0.380409	−	0.380409i	−0.871250	+	0.490840i	$0.836690\pi$
$734$	−17.8854	−	16.1605i	−0.660161	−	0.596496i
$735$	6.45237			0.237999
$736$	15.6514	−	26.5719i	0.576917	−	0.979455i
$737$	30.6184			1.12784
$738$	10.6944	+	9.66309i	0.393668	+	0.355703i
$739$	25.4615	+	25.4615i	0.936618	+	0.936618i	0.998108	−	0.0614897i	$-0.0195851\pi$
$739$	25.4615	+	25.4615i	0.936618	+	0.936618i	−0.0614897	+	0.998108i	$0.519585\pi$
$740$	1.34887	−	0.137024i	0.0495854	−	0.00503709i
$741$	23.5581	−	23.5581i	0.865429	−	0.865429i
$742$	0.378355	+	7.46827i	0.0138899	+	0.274169i
$743$			46.0798i			1.69050i	0.534368	+	0.845252i	$0.320550\pi$
$743$			46.0798i			1.69050i	−0.534368	+	0.845252i	$0.679450\pi$
$744$	16.6309	−	2.54508i	0.609719	−	0.0933073i
$745$		−	8.13234i		−	0.297946i
$746$	28.7040	−	1.45419i	1.05093	−	0.0532418i
$747$	−4.61002	+	4.61002i	−0.168672	+	0.168672i
$748$	−24.7028	−	20.1468i	−0.903224	−	0.736640i
$749$	−0.888598	−	0.888598i	−0.0324687	−	0.0324687i
$750$	−0.948122	+	1.04932i	−0.0346205	+	0.0383156i
$751$	−16.4699			−0.600997			−0.300498	−	0.953782i	$-0.597153\pi$
$751$	−16.4699			−0.600997			−0.300498	+	0.953782i	$0.597153\pi$
$752$	31.9617	−	6.56131i	1.16552	−	0.239266i
$753$	−2.28765			−0.0833664
$754$	16.5866	−	18.3569i	0.604049	−	0.668520i
$755$	0.131367	+	0.131367i	0.00478095	+	0.00478095i
$756$	−0.935419	+	1.14695i	−0.0340208	+	0.0417143i
$757$	−21.4819	+	21.4819i	−0.780772	+	0.780772i	−0.979961	−	0.199189i	$-0.936169\pi$
$757$	−21.4819	+	21.4819i	−0.780772	+	0.780772i	0.199189	+	0.979961i	$0.436169\pi$
$758$	−5.94235	+	0.301050i	−0.215836	+	0.0109346i
$759$		−	29.5649i		−	1.07314i
$760$	−11.9061	+	16.2086i	−0.431881	+	0.587949i
$761$		−	10.1316i		−	0.367270i	−0.982994	−	0.183635i	$-0.941214\pi$
$761$		−	10.1316i		−	0.367270i	0.982994	−	0.183635i	$-0.0587865\pi$
$762$	0.640090	+	12.6346i	0.0231880	+	0.457703i
$763$	5.18008	−	5.18008i	0.187531	−	0.187531i
$764$	1.78770	+	17.5982i	0.0646767	+	0.636681i
$765$	−2.07814	−	2.07814i	−0.0751352	−	0.0751352i
$766$	21.4911	+	19.4185i	0.776504	+	0.701619i
$767$	25.4256			0.918067
$768$	−14.8560	−	5.94143i	−0.536068	−	0.214393i
$769$	33.2758			1.19996			0.599979	−	0.800016i	$-0.295176\pi$
$769$	33.2758			1.19996			0.599979	+	0.800016i	$0.295176\pi$
$770$	−4.21117	−	3.80505i	−0.151760	−	0.137125i
$771$	−3.20444	−	3.20444i	−0.115405	−	0.115405i
$772$	2.84423	+	27.9988i	0.102366	+	1.00770i
$773$	6.50648	−	6.50648i	0.234022	−	0.234022i	−0.580347	−	0.814369i	$-0.697083\pi$
$773$	6.50648	−	6.50648i	0.234022	−	0.234022i	0.814369	+	0.580347i	$0.197083\pi$
$774$	0.499621	+	9.86192i	0.0179585	+	0.354479i
$775$			5.94837i			0.213672i
$776$	2.81048	−	3.82609i	0.100890	−	0.137349i
$777$			0.501663i			0.0179971i
$778$	−23.7102	+	1.20120i	−0.850052	+	0.0430651i
$779$	−51.2434	+	51.2434i	−1.83598	+	1.83598i
$780$	−5.92267	+	7.26203i	−0.212066	+	0.260022i
$781$	13.6266	+	13.6266i	0.487597	+	0.487597i
$782$	−15.1907	+	16.8120i	−0.543217	+	0.601195i
$783$	3.73370			0.133431
$784$	−25.2823	+	5.19011i	−0.902938	+	0.185361i
$785$	16.7891			0.599227
$786$	−12.9229	+	14.3022i	−0.460945	+	0.510141i
$787$	−25.9368	−	25.9368i	−0.924547	−	0.924547i	0.0727995	−	0.997347i	$-0.476807\pi$
$787$	−25.9368	−	25.9368i	−0.924547	−	0.924547i	−0.997347	+	0.0727995i	$0.976807\pi$
$788$	17.8689	+	14.5733i	0.636554	+	0.519153i
$789$	−5.83802	+	5.83802i	−0.207839	+	0.207839i
$790$	15.2223	−	0.771188i	0.541586	−	0.0274376i
$791$			11.2002i			0.398234i
$792$	−15.1625	+	2.32037i	−0.538777	+	0.0824508i
$793$		−	32.3162i		−	1.14758i
$794$	−1.93566	−	38.2075i	−0.0686938	−	1.35593i
$795$	−5.05247	+	5.05247i	−0.179193	+	0.179193i
$796$	−22.5770	+	2.29347i	−0.800222	+	0.0812898i
$797$	−1.54315	−	1.54315i	−0.0546611	−	0.0546611i	0.679248	−	0.733909i	$-0.262306\pi$
$797$	−1.54315	−	1.54315i	−0.0546611	−	0.0546611i	−0.733909	+	0.679248i	$0.762306\pi$
$798$	−5.52141	−	4.98894i	−0.195456	−	0.176607i
$799$	−23.9730			−0.848105
$800$	2.87098	−	4.87417i	0.101504	−	0.172328i
$801$	−2.62476			−0.0927412
$802$	16.8808	+	15.2529i	0.596082	+	0.538597i
$803$	42.8171	+	42.8171i	1.51098	+	1.51098i
$804$	−11.2339	+	1.14119i	−0.396189	+	0.0402465i
$805$	−2.85266	+	2.85266i	−0.100543	+	0.100543i
$806$	1.99430	+	39.3651i	0.0702462	+	1.38658i
$807$			20.9802i			0.738538i
$808$	−3.94616	−	25.7863i	−0.138825	−	0.907157i
$809$		−	25.5155i		−	0.897076i	−0.893764	−	0.448538i	$-0.851945\pi$
$809$		−	25.5155i		−	0.897076i	0.893764	−	0.448538i	$-0.148055\pi$
$810$	−1.41240	+	0.0715547i	−0.0496268	+	0.00251417i
$811$	10.6605	−	10.6605i	0.374342	−	0.374342i	−0.494714	−	0.869056i	$-0.664727\pi$
$811$	10.6605	−	10.6605i	0.374342	−	0.374342i	0.869056	+	0.494714i	$0.164727\pi$
$812$	−4.28238	−	3.49257i	−0.150282	−	0.122565i
$813$	−22.6830	−	22.6830i	−0.795528	−	0.795528i
$814$	−3.48568	+	3.85770i	−0.122173	+	0.135212i
$815$	−16.0956			−0.563805
$816$	9.81434	+	6.47115i	0.343571	+	0.226536i
$817$	−49.6483			−1.73697
$818$	22.2357	−	24.6089i	0.777453	−	0.860431i
$819$	−2.45179	−	2.45179i	−0.0856723	−	0.0856723i
$820$	12.8829	−	15.7963i	0.449892	−	0.551630i
$821$	−34.9507	+	34.9507i	−1.21979	+	1.21979i	−0.252081	+	0.967706i	$0.581115\pi$
$821$	−34.9507	+	34.9507i	−1.21979	+	1.21979i	−0.967706	+	0.252081i	$0.918885\pi$
$822$	−9.77637	+	0.495287i	−0.340990	+	0.0172751i
$823$		−	35.6125i		−	1.24137i	−0.784059	−	0.620686i	$-0.786854\pi$
$823$		−	35.6125i		−	1.24137i	0.784059	−	0.620686i	$-0.213146\pi$
$824$	−0.689370	−	0.506381i	−0.0240154	−	0.0176406i
$825$		−	5.42317i		−	0.188811i
$826$	−0.287341	−	5.67177i	−0.00999789	−	0.197346i
$827$	−15.2133	+	15.2133i	−0.529019	+	0.529019i	−0.920280	−	0.391261i	$-0.872039\pi$
$827$	−15.2133	+	15.2133i	−0.529019	+	0.529019i	0.391261	+	0.920280i	$0.372039\pi$
$828$	1.10192	+	10.8473i	0.0382943	+	0.376971i
$829$	24.4188	+	24.4188i	0.848101	+	0.848101i	0.989896	−	0.141795i	$-0.0452874\pi$
$829$	24.4188	+	24.4188i	0.848101	+	0.848101i	−0.141795	+	0.989896i	$0.545287\pi$
$830$	6.84107	+	6.18134i	0.237457	+	0.214557i
$831$	20.7542			0.719956
$832$	17.3654	−	33.2187i	0.602036	−	1.15165i
$833$	18.9631			0.657032
$834$	9.65156	+	8.72078i	0.334206	+	0.301976i
$835$	9.11630	+	9.11630i	0.315483	+	0.315483i
$836$	−7.79437	−	76.7282i	−0.269574	−	2.65370i
$837$	−4.20613	+	4.20613i	−0.145385	+	0.145385i
$838$	1.43345	+	28.2946i	0.0495178	+	0.977420i
$839$		−	1.78206i		−	0.0615236i	−0.999527	−	0.0307618i	$-0.990207\pi$
$839$		−	1.78206i		−	0.0615236i	0.999527	−	0.0307618i	$-0.00979333\pi$
$840$	1.68689	+	1.23912i	0.0582034	+	0.0427536i
$841$		−	15.0595i		−	0.519293i
$842$	−42.5411	+	2.15520i	−1.46606	+	0.0742732i
$843$	17.4270	−	17.4270i	0.600219	−	0.600219i
$844$	27.9615	−	34.2847i	0.962474	−	1.18013i
$845$	−6.33127	−	6.33127i	−0.217802	−	0.217802i
$846$	−7.73389	+	8.55934i	−0.265897	+	0.294276i
$847$	13.6243			0.468138
$848$	15.7330	−	23.8611i	0.540272	−	0.819394i
$849$	0.164684			0.00565195
$850$	−2.78647	+	3.08387i	−0.0955750	+	0.105776i
$851$	2.61323	+	2.61323i	0.0895802	+	0.0895802i
$852$	−5.50746	−	4.49170i	−0.188682	−	0.153883i
$853$	−20.1759	+	20.1759i	−0.690809	+	0.690809i	−0.962410	−	0.271601i	$-0.912447\pi$
$853$	−20.1759	+	20.1759i	−0.690809	+	0.690809i	0.271601	+	0.962410i	$0.412447\pi$
$854$	−7.20886	+	0.365213i	−0.246682	+	0.0124973i
$855$		−	7.11052i		−	0.243175i
$856$	0.726577	+	4.74784i	0.0248339	+	0.162278i
$857$		−	40.0844i		−	1.36926i	−0.728893	−	0.684628i	$-0.759965\pi$
$857$		−	40.0844i		−	1.36926i	0.728893	−	0.684628i	$-0.240035\pi$
$858$	−1.81822	−	35.8894i	−0.0620729	−	1.22524i
$859$	−3.09121	+	3.09121i	−0.105471	+	0.105471i	−0.757873	−	0.652402i	$-0.773761\pi$
$859$	−3.09121	+	3.09121i	−0.105471	+	0.105471i	0.652402	+	0.757873i	$0.273761\pi$
$860$	13.8932	−	1.41133i	0.473756	−	0.0481260i
$861$	5.33310	+	5.33310i	0.181751	+	0.181751i
$862$	22.0511	+	19.9246i	0.751064	+	0.678633i
$863$	13.8844			0.472630			0.236315	−	0.971676i	$-0.424060\pi$
$863$	13.8844			0.472630			0.236315	+	0.971676i	$0.424060\pi$
$864$	5.47664	−	1.41647i	0.186319	−	0.0481892i
$865$	17.1153			0.581936
$866$	−17.0255	−	15.3836i	−0.578549	−	0.522755i
$867$	5.91331	+	5.91331i	0.200827	+	0.200827i
$868$	8.75874	−	0.889748i	0.297291	−	0.0302000i
$869$	−41.3296	+	41.3296i	−1.40201	+	1.40201i
$870$	−0.267163	−	5.27348i	−0.00905769	−	0.178788i
$871$		−	26.4536i		−	0.896345i
$872$	−27.6775	+	4.23558i	−0.937278	+	0.143435i
$873$			1.67846i			0.0568072i
$874$	−54.7498	+	2.77372i	−1.85194	+	0.0938224i
$875$	−0.523272	+	0.523272i	−0.0176898	+	0.0176898i
$876$	−17.3054	−	14.1137i	−0.584696	−	0.476859i
$877$	−21.3550	−	21.3550i	−0.721107	−	0.721107i	0.247724	−	0.968831i	$-0.420317\pi$
$877$	−21.3550	−	21.3550i	−0.721107	−	0.721107i	−0.968831	+	0.247724i	$0.920317\pi$
$878$	−3.16642	+	3.50437i	−0.106861	+	0.118267i
$879$	−30.5042			−1.02888
$880$	4.36225	+	21.2496i	0.147051	+	0.716322i
$881$	−25.1815			−0.848387			−0.424193	−	0.905572i	$-0.639442\pi$
$881$	−25.1815			−0.848387			−0.424193	+	0.905572i	$0.639442\pi$
$882$	6.11764	−	6.77058i	0.205992	−	0.227977i
$883$	4.36865	+	4.36865i	0.147017	+	0.147017i	0.776784	−	0.629767i	$-0.216850\pi$
$883$	4.36865	+	4.36865i	0.147017	+	0.147017i	−0.629767	+	0.776784i	$0.716850\pi$
$884$	−17.4063	+	21.3426i	−0.585438	+	0.717829i
$885$	3.83709	−	3.83709i	0.128982	−	0.128982i
$886$	−26.8997	+	1.36278i	−0.903713	+	0.0457836i
$887$		−	36.7638i		−	1.23441i	−0.786803	−	0.617204i	$-0.788265\pi$
$887$		−	36.7638i		−	1.23441i	0.786803	−	0.617204i	$-0.211735\pi$
$888$	1.13511	−	1.54531i	0.0380919	−	0.0518570i
$889$			6.61982i			0.222022i
$890$	0.187814	+	3.70721i	0.00629552	+	0.124266i
$891$	3.83476	−	3.83476i	0.128469	−	0.128469i
$892$	−2.07733	−	20.4494i	−0.0695542	−	0.684696i
$893$	−41.0129	−	41.0129i	−1.37244	−	1.37244i
$894$	−8.53339	−	7.71045i	−0.285399	−	0.257876i
$895$	−21.9992			−0.735351
$896$	−7.60645	−	3.49833i	−0.254114	−	0.116871i
$897$	−25.5433			−0.852867
$898$	−20.2513	−	18.2983i	−0.675793	−	0.610622i
$899$	−15.7044	−	15.7044i	−0.523772	−	0.523772i
$900$	0.202128	+	1.98976i	0.00673760	+	0.0663253i
$901$	−14.8489	+	14.8489i	−0.494687	+	0.494687i
$902$	3.95497	+	78.0663i	0.131686	+	2.59932i
$903$			5.16709i			0.171950i
$904$	25.3427	−	34.5007i	0.842886	−	1.14748i
$905$			14.9864i			0.498166i
$906$	0.262398	−	0.0132935i	0.00871760	−	0.000441648i
$907$	−24.5327	+	24.5327i	−0.814594	+	0.814594i	−0.985319	−	0.170725i	$-0.945389\pi$
$907$	−24.5327	+	24.5327i	−0.814594	+	0.814594i	0.170725	+	0.985319i	$0.445389\pi$
$908$	24.7271	−	30.3189i	0.820596	−	1.00617i
$909$	6.52161	+	6.52161i	0.216308	+	0.216308i
$910$	−3.28747	+	3.63834i	−0.108979	+	0.120610i
$911$	−0.221626			−0.00734279			−0.00367139	−	0.999993i	$-0.501169\pi$
$911$	−0.221626			−0.00734279			−0.00367139	+	0.999993i	$0.501169\pi$
$912$	5.71950	+	27.8611i	0.189392	+	0.922572i
$913$	−35.3567			−1.17014
$914$	19.9316	−	22.0589i	0.659279	−	0.729644i
$915$	−4.87697	−	4.87697i	−0.161228	−	0.161228i
$916$	−24.7738	−	20.2047i	−0.818549	−	0.667582i
$917$	−7.13220	+	7.13220i	−0.235526	+	0.235526i
$918$	−4.15095	+	0.210294i	−0.137002	+	0.00694074i
$919$			22.8234i			0.752874i	0.926442	+	0.376437i	$0.122851\pi$
$919$			22.8234i			0.752874i	−0.926442	+	0.376437i	$0.877149\pi$
$920$	15.2420	−	2.33253i	0.502513	−	0.0769012i
$921$		−	16.6232i		−	0.547752i
$922$	2.35838	+	46.5516i	0.0776692	+	1.53309i
$923$	11.7730	−	11.7730i	0.387513	−	0.387513i
$924$	−7.98541	+	0.811190i	−0.262701	+	0.0266862i
$925$	0.479352	+	0.479352i	0.0157610	+	0.0157610i
$926$	1.73333	+	1.56617i	0.0569607	+	0.0514676i
$927$	0.302418			0.00993271
$928$	5.28866	+	20.4481i	0.173609	+	0.671243i
$929$	12.9959			0.426383			0.213191	−	0.977010i	$-0.431614\pi$
$929$	12.9959			0.426383			0.213191	+	0.977010i	$0.431614\pi$
$930$	6.24172	+	5.63978i	0.204674	+	0.184936i
$931$	32.4418	+	32.4418i	1.06324	+	1.06324i
$932$	1.27003	−	0.129015i	0.0416013	−	0.00422603i
$933$	11.2287	−	11.2287i	0.367612	−	0.367612i
$934$	1.46450	+	28.9075i	0.0479201	+	0.945884i
$935$		−	15.9383i		−	0.521239i
$936$	2.00474	+	13.1000i	0.0655271	+	0.428188i
$937$		−	51.7244i		−	1.68976i	−0.534954	−	0.844881i	$-0.679671\pi$
$937$		−	51.7244i		−	1.68976i	0.534954	−	0.844881i	$-0.320329\pi$
$938$	−5.90107	+	0.298958i	−0.192677	+	0.00976133i
$939$	−23.0117	+	23.0117i	−0.750960	+	0.750960i
$940$	12.6426	+	10.3109i	0.412357	+	0.336305i
$941$	−11.9700	−	11.9700i	−0.390210	−	0.390210i	0.484552	−	0.874762i	$-0.338983\pi$
$941$	−11.9700	−	11.9700i	−0.390210	−	0.390210i	−0.874762	+	0.484552i	$0.838983\pi$
$942$	15.9181	−	17.6170i	0.518639	−	0.573994i
$943$	55.5616			1.80933
$944$	−11.9484	+	18.1213i	−0.388887	+	0.589798i
$945$	−0.740019			−0.0240728
$946$	−35.9022	+	39.7340i	−1.16728	+	1.29186i
$947$	3.97492	+	3.97492i	0.129168	+	0.129168i	0.768735	−	0.639567i	$-0.220887\pi$
$947$	3.97492	+	3.97492i	0.129168	+	0.129168i	−0.639567	+	0.768735i	$0.720887\pi$
$948$	13.6234	−	16.7042i	0.442467	−	0.542527i
$949$	36.9929	−	36.9929i	1.20084	−	1.20084i
$950$	−10.0429	+	0.508791i	−0.325835	+	0.0165074i
$951$		−	19.5272i		−	0.633211i
$952$	4.95767	+	3.64168i	0.160679	+	0.118028i
$953$		−	13.1913i		−	0.427308i	−0.976909	−	0.213654i	$-0.931463\pi$
$953$		−	13.1913i		−	0.427308i	0.976909	−	0.213654i	$-0.0685365\pi$
$954$	0.511278	+	10.0920i	0.0165532	+	0.326741i
$955$	−6.25393	+	6.25393i	−0.202372	+	0.202372i
$956$	5.50303	+	54.1721i	0.177981	+	1.75205i
$957$	14.3178	+	14.3178i	0.462830	+	0.462830i
$958$	−6.37698	−	5.76200i	−0.206031	−	0.186162i
$959$	−5.12227			−0.165407
$960$	−2.39250	−	7.63387i	−0.0772177	−	0.246382i
$961$	4.38311			0.141391
$962$	3.33296	+	3.01154i	0.107459	+	0.0970958i
$963$	−1.20078	−	1.20078i	−0.0386945	−	0.0386945i
$964$	−2.84638	−	28.0199i	−0.0916757	−	0.902461i
$965$	−9.95002	+	9.95002i	−0.320302	+	0.320302i
$966$	0.288671	+	5.69802i	0.00928785	+	0.183331i
$967$			5.07109i			0.163075i	0.996670	+	0.0815376i	$0.0259831\pi$
$967$			5.07109i			0.163075i	−0.996670	+	0.0815376i	$0.974017\pi$
$968$	−41.9679	−	30.8278i	−1.34890	−	0.990842i
$969$		−	20.8973i		−	0.671319i
$970$	2.37066	−	0.120102i	0.0761173	−	0.00385623i
$971$	2.07041	−	2.07041i	0.0664427	−	0.0664427i	−0.673105	−	0.739547i	$-0.735040\pi$
$971$	2.07041	−	2.07041i	0.0664427	−	0.0664427i	0.739547	+	0.673105i	$0.235040\pi$
$972$	−1.26405	+	1.54990i	−0.0405443	+	0.0497130i
$973$	4.81304	+	4.81304i	0.154299	+	0.154299i
$974$	−9.65787	+	10.6887i	−0.309458	+	0.342487i
$975$	−4.68548			−0.150056
$976$	23.0323	+	15.1865i	0.737246	+	0.486108i
$977$	−6.93371			−0.221829			−0.110914	−	0.993830i	$-0.535378\pi$
$977$	−6.93371			−0.221829			−0.110914	+	0.993830i	$0.535378\pi$
$978$	−15.2606	+	16.8894i	−0.487981	+	0.540063i
$979$	−10.0653	−	10.0653i	−0.321689	−	0.321689i
$980$	−10.0005	−	8.15610i	−0.319455	−	0.260537i
$981$	6.99992	−	6.99992i	0.223490	−	0.223490i
$982$	−17.4783	+	0.885479i	−0.557754	+	0.0282568i
$983$		−	49.6290i		−	1.58292i	−0.611221	−	0.791460i	$-0.709321\pi$
$983$		−	49.6290i		−	1.58292i	0.611221	−	0.791460i	$-0.290679\pi$
$984$	−4.36070	−	28.4951i	−0.139014	−	0.908390i
$985$			11.5291i			0.367347i
$986$	−0.785175	−	15.4984i	−0.0250051	−	0.493570i
$987$	−4.26837	+	4.26837i	−0.135864	+	0.135864i
$988$	−66.2913	+	6.73414i	−2.10901	+	0.214241i
$989$	26.9160	+	26.9160i	0.855880	+	0.855880i
$990$	−5.69062	−	5.14183i	−0.180860	−	0.163418i
$991$	47.6664			1.51417			0.757086	−	0.653315i	$-0.226622\pi$
$991$	47.6664			1.51417			0.757086	+	0.653315i	$0.226622\pi$
$992$	−28.9933	−	17.0776i	−0.920540	−	0.542215i
$993$	8.27525			0.262607
$994$	−2.75929	−	2.49319i	−0.0875193	−	0.0790791i
$995$	−8.02327	−	8.02327i	−0.254355	−	0.254355i
$996$	12.9724	−	1.31778i	0.411045	−	0.0417556i
$997$	4.46020	−	4.46020i	0.141256	−	0.141256i	−0.632943	−	0.774199i	$-0.718153\pi$
$997$	4.46020	−	4.46020i	0.141256	−	0.141256i	0.774199	+	0.632943i	$0.218153\pi$
$998$	2.41104	+	47.5910i	0.0763201	+	1.50647i
$999$			0.677905i			0.0214480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.s.c.61.3	✓	20
3.2	odd	2		720.2.t.d.541.8		20
4.3	odd	2		960.2.s.c.721.8		20
8.3	odd	2		1920.2.s.f.1441.3		20
8.5	even	2		1920.2.s.e.1441.8		20
12.11	even	2		2880.2.t.d.721.8		20
16.3	odd	4		1920.2.s.f.481.3		20
16.5	even	4	inner	240.2.s.c.181.3	yes	20
16.11	odd	4		960.2.s.c.241.8		20
16.13	even	4		1920.2.s.e.481.8		20
48.5	odd	4		720.2.t.d.181.8		20
48.11	even	4		2880.2.t.d.2161.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.c.61.3	✓	20	1.1	even	1	trivial
240.2.s.c.181.3	yes	20	16.5	even	4	inner
720.2.t.d.181.8		20	48.5	odd	4
720.2.t.d.541.8		20	3.2	odd	2
960.2.s.c.241.8		20	16.11	odd	4
960.2.s.c.721.8		20	4.3	odd	2
1920.2.s.e.481.8		20	16.13	even	4
1920.2.s.e.1441.8		20	8.5	even	2
1920.2.s.f.481.3		20	16.3	odd	4
1920.2.s.f.1441.3		20	8.3	odd	2
2880.2.t.d.721.8		20	12.11	even	2
2880.2.t.d.2161.8		20	48.11	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04932 - 0.948122i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(0.202128 + 1.98976i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.0715547 + 1.41240i) q^{6} +0.740019i q^{7} +(1.67444 - 2.27953i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-1.04932 - 0.948122i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(0.202128 + 1.98976i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.0715547 + 1.41240i) q^{6} +0.740019i q^{7} +(1.67444 - 2.27953i) q^{8} +1.00000i q^{9} +(1.41240 - 0.0715547i) q^{10} +(-3.83476 + 3.83476i) q^{11} +(1.26405 - 1.54990i) q^{12} +(3.31314 + 3.31314i) q^{13} +(0.701629 - 0.776514i) q^{14} +1.00000 q^{15} +(-3.91829 + 0.804372i) q^{16} +2.93893 q^{17} +(0.948122 - 1.04932i) q^{18} +(5.02789 + 5.02789i) q^{19} +(-1.54990 - 1.26405i) q^{20} +(0.523272 - 0.523272i) q^{21} +(7.65970 - 0.388053i) q^{22} -5.45159i q^{23} +(-2.79588 + 0.427863i) q^{24} -1.00000i q^{25} +(-0.335268 - 6.61779i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.47246 + 0.149579i) q^{28} +(2.64012 + 2.64012i) q^{29} +(-1.04932 - 0.948122i) q^{30} -5.94837 q^{31} +(4.87417 + 2.87098i) q^{32} +5.42317 q^{33} +(-3.08387 - 2.78647i) q^{34} +(-0.523272 - 0.523272i) q^{35} +(-1.98976 + 0.202128i) q^{36} +(-0.479352 + 0.479352i) q^{37} +(-0.508791 - 10.0429i) q^{38} -4.68548i q^{39} +(0.427863 + 2.79588i) q^{40} +10.1918i q^{41} +(-1.04520 + 0.0529518i) q^{42} +(-4.93728 + 4.93728i) q^{43} +(-8.40537 - 6.85514i) q^{44} +(-0.707107 - 0.707107i) q^{45} +(-5.16877 + 5.72044i) q^{46} -8.15706 q^{47} +(3.33943 + 2.20187i) q^{48} +6.45237 q^{49} +(-0.948122 + 1.04932i) q^{50} +(-2.07814 - 2.07814i) q^{51} +(-5.92267 + 7.26203i) q^{52} +(-5.05247 + 5.05247i) q^{53} +(-1.41240 + 0.0715547i) q^{54} -5.42317i q^{55} +(1.68689 + 1.23912i) q^{56} -7.11052i q^{57} +(-0.267163 - 5.27348i) q^{58} +(3.83709 - 3.83709i) q^{59} +(0.202128 + 1.98976i) q^{60} +(-4.87697 - 4.87697i) q^{61} +(6.24172 + 5.63978i) q^{62} -0.740019 q^{63} +(-2.39250 - 7.63387i) q^{64} -4.68548 q^{65} +(-5.69062 - 5.14183i) q^{66} +(-3.99222 - 3.99222i) q^{67} +(0.594040 + 5.84777i) q^{68} +(-3.85485 + 3.85485i) q^{69} +(0.0529518 + 1.04520i) q^{70} -3.55343i q^{71} +(2.27953 + 1.67444i) q^{72} -11.1655i q^{73} +(0.957475 - 0.0485073i) q^{74} +(-0.707107 + 0.707107i) q^{75} +(-8.98803 + 11.0206i) q^{76} +(-2.83780 - 2.83780i) q^{77} +(-4.44241 + 4.91655i) q^{78} +10.7776 q^{79} +(2.20187 - 3.33943i) q^{80} -1.00000 q^{81} +(9.66309 - 10.6944i) q^{82} +(4.61002 + 4.61002i) q^{83} +(1.14695 + 0.935419i) q^{84} +(-2.07814 + 2.07814i) q^{85} +(9.86192 - 0.499621i) q^{86} -3.73370i q^{87} +(2.32037 + 15.1625i) q^{88} +2.62476i q^{89} +(0.0715547 + 1.41240i) q^{90} +(-2.45179 + 2.45179i) q^{91} +(10.8473 - 1.10192i) q^{92} +(4.20613 + 4.20613i) q^{93} +(8.55934 + 7.73389i) q^{94} -7.11052 q^{95} +(-1.41647 - 5.47664i) q^{96} +1.67846 q^{97} +(-6.77058 - 6.11764i) q^{98} +(-3.83476 - 3.83476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} + 12 q^{8}+O(q^{10}) \) 20 * q + 4 * q^4 + 12 * q^8	\( 20 q + 4 q^{4} + 12 q^{8} + 8 q^{11} - 4 q^{14} + 20 q^{15} - 20 q^{16} - 24 q^{17} - 4 q^{18} - 4 q^{19} - 8 q^{20} + 8 q^{22} + 28 q^{26} - 8 q^{28} + 16 q^{29} - 40 q^{32} + 16 q^{33} - 44 q^{34} + 16 q^{37} - 8 q^{38} + 12 q^{40} + 12 q^{42} - 8 q^{43} + 24 q^{44} - 12 q^{46} - 16 q^{48} - 52 q^{49} + 4 q^{50} + 4 q^{51} - 56 q^{52} - 16 q^{53} + 64 q^{56} + 72 q^{58} - 16 q^{59} + 4 q^{60} - 4 q^{61} - 44 q^{62} - 8 q^{63} - 56 q^{64} - 32 q^{66} - 8 q^{67} - 32 q^{68} - 4 q^{69} + 20 q^{70} + 4 q^{72} + 60 q^{74} + 28 q^{76} - 40 q^{77} - 28 q^{78} + 56 q^{79} - 16 q^{80} - 20 q^{81} - 24 q^{82} - 48 q^{83} + 24 q^{84} + 4 q^{85} + 64 q^{86} + 40 q^{88} - 8 q^{91} + 88 q^{92} + 16 q^{93} - 20 q^{94} + 56 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) \) 20 * q + 4 * q^4 + 12 * q^8 + 8 * q^11 - 4 * q^14 + 20 * q^15 - 20 * q^16 - 24 * q^17 - 4 * q^18 - 4 * q^19 - 8 * q^20 + 8 * q^22 + 28 * q^26 - 8 * q^28 + 16 * q^29 - 40 * q^32 + 16 * q^33 - 44 * q^34 + 16 * q^37 - 8 * q^38 + 12 * q^40 + 12 * q^42 - 8 * q^43 + 24 * q^44 - 12 * q^46 - 16 * q^48 - 52 * q^49 + 4 * q^50 + 4 * q^51 - 56 * q^52 - 16 * q^53 + 64 * q^56 + 72 * q^58 - 16 * q^59 + 4 * q^60 - 4 * q^61 - 44 * q^62 - 8 * q^63 - 56 * q^64 - 32 * q^66 - 8 * q^67 - 32 * q^68 - 4 * q^69 + 20 * q^70 + 4 * q^72 + 60 * q^74 + 28 * q^76 - 40 * q^77 - 28 * q^78 + 56 * q^79 - 16 * q^80 - 20 * q^81 - 24 * q^82 - 48 * q^83 + 24 * q^84 + 4 * q^85 + 64 * q^86 + 40 * q^88 - 8 * q^91 + 88 * q^92 + 16 * q^93 - 20 * q^94 + 56 * q^97 - 48 * q^98 + 8 * q^99

Introduction

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