LMFDB - Embedded newform 240.2.s.c.61.1

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			61.1
Root			$-1.38431 + 0.289262i$ of defining polynomial
Character	$\chi$	$=$	240.61
Dual form			240.2.s.c.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38431 + 0.289262i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.83266 - 0.800859i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.18340 + 0.774320i) q^{6} -2.60796i q^{7} +(-2.30531 + 1.63876i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.38431 + 0.289262i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.83266 - 0.800859i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.18340 + 0.774320i) q^{6} -2.60796i q^{7} +(-2.30531 + 1.63876i) q^{8} +1.00000i q^{9} +(0.774320 - 1.18340i) q^{10} +(0.702458 - 0.702458i) q^{11} +(-1.86218 - 0.729591i) q^{12} +(-2.12440 - 2.12440i) q^{13} +(0.754384 + 3.61024i) q^{14} +1.00000 q^{15} +(2.71725 - 2.93540i) q^{16} -2.33676 q^{17} +(-0.289262 - 1.38431i) q^{18} +(-3.46869 - 3.46869i) q^{19} +(-0.729591 + 1.86218i) q^{20} +(-1.84411 + 1.84411i) q^{21} +(-0.769229 + 1.17562i) q^{22} -8.48753i q^{23} +(2.78888 + 0.471327i) q^{24} -1.00000i q^{25} +(3.55535 + 2.32633i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.08861 - 4.77950i) q^{28} +(-5.11647 - 5.11647i) q^{29} +(-1.38431 + 0.289262i) q^{30} +5.61685 q^{31} +(-2.91243 + 4.84951i) q^{32} -0.993426 q^{33} +(3.23481 - 0.675935i) q^{34} +(1.84411 + 1.84411i) q^{35} +(0.800859 + 1.83266i) q^{36} +(-0.967355 + 0.967355i) q^{37} +(5.80512 + 3.79840i) q^{38} +3.00436i q^{39} +(0.471327 - 2.78888i) q^{40} +3.19212i q^{41} +(2.01940 - 3.08626i) q^{42} +(-2.92929 + 2.92929i) q^{43} +(0.724794 - 1.84993i) q^{44} +(-0.707107 - 0.707107i) q^{45} +(2.45512 + 11.7494i) q^{46} +8.59369 q^{47} +(-3.99702 + 0.154251i) q^{48} +0.198520 q^{49} +(0.289262 + 1.38431i) q^{50} +(1.65234 + 1.65234i) q^{51} +(-5.59464 - 2.19195i) q^{52} +(-3.45092 + 3.45092i) q^{53} +(-0.774320 + 1.18340i) q^{54} +0.993426i q^{55} +(4.27382 + 6.01218i) q^{56} +4.90547i q^{57} +(8.56281 + 5.60281i) q^{58} +(-5.32136 + 5.32136i) q^{59} +(1.83266 - 0.800859i) q^{60} +(9.33498 + 9.33498i) q^{61} +(-7.77549 + 1.62474i) q^{62} +2.60796 q^{63} +(2.62895 - 7.55570i) q^{64} +3.00436 q^{65} +(1.37521 - 0.287360i) q^{66} +(-0.273754 - 0.273754i) q^{67} +(-4.28247 + 1.87141i) q^{68} +(-6.00159 + 6.00159i) q^{69} +(-3.08626 - 2.01940i) q^{70} -15.3079i q^{71} +(-1.63876 - 2.30531i) q^{72} +8.55384i q^{73} +(1.05931 - 1.61894i) q^{74} +(-0.707107 + 0.707107i) q^{75} +(-9.13485 - 3.57899i) q^{76} +(-1.83199 - 1.83199i) q^{77} +(-0.869046 - 4.15898i) q^{78} -4.46759 q^{79} +(0.154251 + 3.99702i) q^{80} -1.00000 q^{81} +(-0.923357 - 4.41889i) q^{82} +(9.85305 + 9.85305i) q^{83} +(-1.90275 + 4.85649i) q^{84} +(1.65234 - 1.65234i) q^{85} +(3.20773 - 4.90240i) q^{86} +7.23578i q^{87} +(-0.468228 + 2.77055i) q^{88} -7.30907i q^{89} +(1.18340 + 0.774320i) q^{90} +(-5.54037 + 5.54037i) q^{91} +(-6.79731 - 15.5547i) q^{92} +(-3.97171 - 3.97171i) q^{93} +(-11.8964 + 2.48583i) q^{94} +4.90547 q^{95} +(5.48852 - 1.36972i) q^{96} +18.1677 q^{97} +(-0.274814 + 0.0574243i) q^{98} +(0.702458 + 0.702458i) 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 $

$2$	−1.38431	+	0.289262i	−0.978858	+	0.204539i
$2$	−1.38431	+	0.289262i	−0.978858	+	0.204539i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	1.83266	−	0.800859i	0.916328	−	0.400429i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	1.18340	+	0.774320i	0.483120	+	0.316115i
$7$		−	2.60796i		−	0.985718i	−0.870109	−	0.492859i	$-0.835952\pi$
$7$		−	2.60796i		−	0.985718i	0.870109	−	0.492859i	$-0.164048\pi$
$8$	−2.30531	+	1.63876i	−0.815052	+	0.579388i
$9$			1.00000i			0.333333i
$10$	0.774320	−	1.18340i	0.244861	−	0.374223i
$11$	0.702458	−	0.702458i	0.211799	−	0.211799i	−0.593232	−	0.805031i	$-0.702148\pi$
$11$	0.702458	−	0.702458i	0.211799	−	0.211799i	0.805031	+	0.593232i	$0.202148\pi$
$12$	−1.86218	−	0.729591i	−0.537564	−	0.210615i
$13$	−2.12440	−	2.12440i	−0.589203	−	0.589203i	0.348212	−	0.937416i	$-0.386789\pi$
$13$	−2.12440	−	2.12440i	−0.589203	−	0.589203i	−0.937416	+	0.348212i	$0.886789\pi$
$14$	0.754384	+	3.61024i	0.201618	+	0.964878i
$15$	1.00000			0.258199
$16$	2.71725	−	2.93540i	0.679313	−	0.733849i
$17$	−2.33676			−0.566747			−0.283374	−	0.959010i	$-0.591454\pi$
$17$	−2.33676			−0.566747			−0.283374	+	0.959010i	$0.591454\pi$
$18$	−0.289262	−	1.38431i	−0.0681796	−	0.326286i
$19$	−3.46869	−	3.46869i	−0.795773	−	0.795773i	0.186653	−	0.982426i	$-0.440236\pi$
$19$	−3.46869	−	3.46869i	−0.795773	−	0.795773i	−0.982426	+	0.186653i	$0.940236\pi$
$20$	−0.729591	+	1.86218i	−0.163141	+	0.416395i
$21$	−1.84411	+	1.84411i	−0.402418	+	0.402418i
$22$	−0.769229	+	1.17562i	−0.164000	+	0.250642i
$23$		−	8.48753i		−	1.76977i	−0.465806	−	0.884887i	$-0.654236\pi$
$23$		−	8.48753i		−	1.76977i	0.465806	−	0.884887i	$-0.345764\pi$
$24$	2.78888	+	0.471327i	0.569278	+	0.0962092i
$25$		−	1.00000i		−	0.200000i
$26$	3.55535	+	2.32633i	0.697261	+	0.456232i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−2.08861	−	4.77950i	−0.394710	−	0.903241i
$29$	−5.11647	−	5.11647i	−0.950105	−	0.950105i	0.0487081	−	0.998813i	$-0.484490\pi$
$29$	−5.11647	−	5.11647i	−0.950105	−	0.950105i	−0.998813	+	0.0487081i	$0.984490\pi$
$30$	−1.38431	+	0.289262i	−0.252740	+	0.0528117i
$31$	5.61685			1.00882			0.504408	−	0.863465i	$-0.331711\pi$
$31$	5.61685			1.00882			0.504408	+	0.863465i	$0.331711\pi$
$32$	−2.91243	+	4.84951i	−0.514850	+	0.857280i
$33$	−0.993426			−0.172933
$34$	3.23481	−	0.675935i	0.554765	−	0.115922i
$35$	1.84411	+	1.84411i	0.311711	+	0.311711i
$36$	0.800859	+	1.83266i	0.133476	+	0.305443i
$37$	−0.967355	+	0.967355i	−0.159032	+	0.159032i	−0.782138	−	0.623106i	$-0.785871\pi$
$37$	−0.967355	+	0.967355i	−0.159032	+	0.159032i	0.623106	+	0.782138i	$0.285871\pi$
$38$	5.80512	+	3.79840i	0.941715	+	0.616182i
$39$			3.00436i			0.481082i
$40$	0.471327	−	2.78888i	0.0745233	−	0.440961i
$41$			3.19212i			0.498525i	0.968436	+	0.249262i	$0.0801882\pi$
$41$			3.19212i			0.498525i	−0.968436	+	0.249262i	$0.919812\pi$
$42$	2.01940	−	3.08626i	0.311600	−	0.476220i
$43$	−2.92929	+	2.92929i	−0.446713	+	0.446713i	−0.894260	−	0.447547i	$-0.852298\pi$
$43$	−2.92929	+	2.92929i	−0.446713	+	0.446713i	0.447547	+	0.894260i	$0.352298\pi$
$44$	0.724794	−	1.84993i	0.109267	−	0.278888i
$45$	−0.707107	−	0.707107i	−0.105409	−	0.105409i
$46$	2.45512	+	11.7494i	0.361987	+	1.73236i
$47$	8.59369			1.25352			0.626759	−	0.779213i	$-0.284381\pi$
$47$	8.59369			1.25352			0.626759	+	0.779213i	$0.284381\pi$
$48$	−3.99702	+	0.154251i	−0.576921	+	0.0222642i
$49$	0.198520			0.0283600
$50$	0.289262	+	1.38431i	0.0409078	+	0.195772i
$51$	1.65234	+	1.65234i	0.231374	+	0.231374i
$52$	−5.59464	−	2.19195i	−0.775837	−	0.303969i
$53$	−3.45092	+	3.45092i	−0.474020	+	0.474020i	−0.903213	−	0.429193i	$-0.858798\pi$
$53$	−3.45092	+	3.45092i	−0.474020	+	0.474020i	0.429193	+	0.903213i	$0.358798\pi$
$54$	−0.774320	+	1.18340i	−0.105372	+	0.161040i
$55$			0.993426i			0.133953i
$56$	4.27382	+	6.01218i	0.571113	+	0.803411i
$57$			4.90547i			0.649746i
$58$	8.56281	+	5.60281i	1.12435	+	0.735685i
$59$	−5.32136	+	5.32136i	−0.692781	+	0.692781i	−0.962843	−	0.270062i	$-0.912956\pi$
$59$	−5.32136	+	5.32136i	−0.692781	+	0.692781i	0.270062	+	0.962843i	$0.412956\pi$
$60$	1.83266	−	0.800859i	0.236595	−	0.103390i
$61$	9.33498	+	9.33498i	1.19522	+	1.19522i	0.975581	+	0.219641i	$0.0704886\pi$
$61$	9.33498	+	9.33498i	1.19522	+	1.19522i	0.219641	+	0.975581i	$0.429511\pi$
$62$	−7.77549	+	1.62474i	−0.987488	+	0.206342i
$63$	2.60796			0.328573
$64$	2.62895	−	7.55570i	0.328619	−	0.944463i
$65$	3.00436			0.372645
$66$	1.37521	−	0.287360i	0.169277	−	0.0353716i
$67$	−0.273754	−	0.273754i	−0.0334443	−	0.0334443i	0.690187	−	0.723631i	$-0.257528\pi$
$67$	−0.273754	−	0.273754i	−0.0334443	−	0.0334443i	−0.723631	+	0.690187i	$0.757528\pi$
$68$	−4.28247	+	1.87141i	−0.519326	+	0.226942i
$69$	−6.00159	+	6.00159i	−0.722507	+	0.722507i
$70$	−3.08626	−	2.01940i	−0.368878	−	0.241364i
$71$		−	15.3079i		−	1.81671i	−0.418201	−	0.908355i	$-0.637339\pi$
$71$		−	15.3079i		−	1.81671i	0.418201	−	0.908355i	$-0.362661\pi$
$72$	−1.63876	−	2.30531i	−0.193129	−	0.271684i
$73$			8.55384i			1.00115i	0.865693	+	0.500576i	$0.166878\pi$
$73$			8.55384i			1.00115i	−0.865693	+	0.500576i	$0.833122\pi$
$74$	1.05931	−	1.61894i	0.123142	−	0.188198i
$75$	−0.707107	+	0.707107i	−0.0816497	+	0.0816497i
$76$	−9.13485	−	3.57899i	−1.04784	−	0.410538i
$77$	−1.83199	−	1.83199i	−0.208774	−	0.208774i
$78$	−0.869046	−	4.15898i	−0.0984001	−	0.470912i
$79$	−4.46759			−0.502643			−0.251321	−	0.967904i	$-0.580865\pi$
$79$	−4.46759			−0.502643			−0.251321	+	0.967904i	$0.580865\pi$
$80$	0.154251	+	3.99702i	0.0172458	+	0.446881i
$81$	−1.00000			−0.111111
$82$	−0.923357	−	4.41889i	−0.101968	−	0.487985i
$83$	9.85305	+	9.85305i	1.08151	+	1.08151i	0.996369	+	0.0851436i	$0.0271349\pi$
$83$	9.85305	+	9.85305i	1.08151	+	1.08151i	0.0851436	+	0.996369i	$0.472865\pi$
$84$	−1.90275	+	4.85649i	−0.207607	+	0.529886i
$85$	1.65234	−	1.65234i	0.179221	−	0.179221i
$86$	3.20773	−	4.90240i	0.345899	−	0.528639i
$87$			7.23578i			0.775757i
$88$	−0.468228	+	2.77055i	−0.0499133	+	0.295341i
$89$		−	7.30907i		−	0.774760i	−0.921920	−	0.387380i	$-0.873380\pi$
$89$		−	7.30907i		−	0.774760i	0.921920	−	0.387380i	$-0.126620\pi$
$90$	1.18340	+	0.774320i	0.124741	+	0.0816204i
$91$	−5.54037	+	5.54037i	−0.580788	+	0.580788i
$92$	−6.79731	−	15.5547i	−0.708669	−	1.62169i
$93$	−3.97171	−	3.97171i	−0.411848	−	0.411848i
$94$	−11.8964	+	2.48583i	−1.22702	+	0.256393i
$95$	4.90547			0.503291
$96$	5.48852	−	1.36972i	0.560170	−	0.139796i
$97$	18.1677			1.84465			0.922323	−	0.386420i	$-0.126288\pi$
$97$	18.1677			1.84465			0.922323	+	0.386420i	$0.126288\pi$
$98$	−0.274814	+	0.0574243i	−0.0277604	+	0.00580073i
$99$	0.702458	+	0.702458i	0.0705997	+	0.0705997i
$100$	−0.800859	−	1.83266i	−0.0800859	−	0.183266i
$101$	8.41665	−	8.41665i	0.837488	−	0.837488i	−0.151039	−	0.988528i	$-0.548262\pi$
$101$	8.41665	−	8.41665i	0.837488	−	0.837488i	0.988528	+	0.151039i	$0.0482620\pi$
$102$	−2.76531	−	1.80940i	−0.273807	−	0.179157i
$103$		−	9.13102i		−	0.899706i	−0.893103	−	0.449853i	$-0.851476\pi$
$103$		−	9.13102i		−	0.899706i	0.893103	−	0.449853i	$-0.148524\pi$
$104$	8.37879	+	1.41604i	0.821608	+	0.138854i
$105$		−	2.60796i		−	0.254511i
$106$	3.77894	−	5.77538i	0.367043	−	0.560954i
$107$	6.88197	−	6.88197i	0.665305	−	0.665305i	−0.291320	−	0.956626i	$-0.594095\pi$
$107$	6.88197	−	6.88197i	0.665305	−	0.665305i	0.956626	+	0.291320i	$0.0940946\pi$
$108$	0.729591	−	1.86218i	0.0702049	−	0.179188i
$109$	−12.5747	−	12.5747i	−1.20444	−	1.20444i	−0.972804	−	0.231632i	$-0.925594\pi$
$109$	−12.5747	−	12.5747i	−1.20444	−	1.20444i	−0.231632	−	0.972804i	$-0.574406\pi$
$110$	−0.287360	−	1.37521i	−0.0273987	−	0.131122i
$111$	1.36805			0.129849
$112$	−7.65541	−	7.08650i	−0.723368	−	0.669611i
$113$	1.01506			0.0954887			0.0477443	−	0.998860i	$-0.484797\pi$
$113$	1.01506			0.0954887			0.0477443	+	0.998860i	$0.484797\pi$
$114$	−1.41896	−	6.79072i	−0.132898	−	0.636009i
$115$	6.00159	+	6.00159i	0.559651	+	0.559651i
$116$	−13.4743	−	5.27916i	−1.25106	−	0.490158i
$117$	2.12440	−	2.12440i	0.196401	−	0.196401i
$118$	5.82717	−	8.90570i	0.536434	−	0.819836i
$119$			6.09418i			0.558653i
$120$	−2.30531	+	1.63876i	−0.210445	+	0.149597i
$121$			10.0131i			0.910282i
$122$	−15.6228	−	10.2223i	−1.41442	−	0.925483i
$123$	2.25717	−	2.25717i	0.203522	−	0.203522i
$124$	10.2938	−	4.49830i	0.924406	−	0.403960i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−3.61024	+	0.754384i	−0.321626	+	0.0672059i
$127$	−12.3908			−1.09951			−0.549754	−	0.835327i	$-0.685279\pi$
$127$	−12.3908			−1.09951			−0.549754	+	0.835327i	$0.685279\pi$
$128$	−1.45372	+	11.2199i	−0.128492	+	0.991711i
$129$	4.14265			0.364740
$130$	−4.15898	+	0.869046i	−0.364767	+	0.0762204i
$131$	−9.53320	−	9.53320i	−0.832919	−	0.832919i	0.154996	−	0.987915i	$-0.450464\pi$
$131$	−9.53320	−	9.53320i	−0.832919	−	0.832919i	−0.987915	+	0.154996i	$0.950464\pi$
$132$	−1.82061	+	0.795593i	−0.158463	+	0.0692475i
$133$	−9.04623	+	9.04623i	−0.784407	+	0.784407i
$134$	0.458148	+	0.299775i	0.0395779	+	0.0258966i
$135$			1.00000i			0.0860663i
$136$	5.38696	−	3.82938i	0.461928	−	0.328367i
$137$			12.7888i			1.09262i	0.837583	+	0.546309i	$0.183968\pi$
$137$			12.7888i			1.09262i	−0.837583	+	0.546309i	$0.816032\pi$
$138$	6.57206	−	10.0441i	0.559451	−	0.855013i
$139$	−5.52252	+	5.52252i	−0.468414	+	0.468414i	−0.901400	−	0.432987i	$-0.857460\pi$
$139$	−5.52252	+	5.52252i	−0.468414	+	0.468414i	0.432987	+	0.901400i	$0.357460\pi$
$140$	4.85649	+	1.90275i	0.410448	+	0.160811i
$141$	−6.07666	−	6.07666i	−0.511747	−	0.511747i
$142$	4.42798	+	21.1909i	0.371588	+	1.77830i
$143$	−2.98461			−0.249585
$144$	2.93540	+	2.71725i	0.244616	+	0.226438i
$145$	7.23578			0.600899
$146$	−2.47430	−	11.8412i	−0.204774	−	0.979985i
$147$	−0.140375	−	0.140375i	−0.0115779	−	0.0115779i
$148$	−0.998114	+	2.54754i	−0.0820445	+	0.209407i
$149$	7.91718	−	7.91718i	0.648600	−	0.648600i	−0.304054	−	0.952655i	$-0.598340\pi$
$149$	7.91718	−	7.91718i	0.648600	−	0.648600i	0.952655	+	0.304054i	$0.0983404\pi$
$150$	0.774320	−	1.18340i	0.0632229	−	0.0966240i
$151$			17.1529i			1.39588i	0.716154	+	0.697942i	$0.245901\pi$
$151$			17.1529i			1.39588i	−0.716154	+	0.697942i	$0.754099\pi$
$152$	13.6808	+	2.31208i	1.10966	+	0.187535i
$153$		−	2.33676i		−	0.188916i
$154$	3.06597	+	2.00612i	0.247063	+	0.161658i
$155$	−3.97171	+	3.97171i	−0.319016	+	0.319016i
$156$	2.40607	+	5.50595i	0.192639	+	0.440829i
$157$	2.21453	+	2.21453i	0.176738	+	0.176738i	0.789932	−	0.613194i	$-0.210116\pi$
$157$	2.21453	+	2.21453i	0.176738	+	0.176738i	−0.613194	+	0.789932i	$0.710116\pi$
$158$	6.18455	−	1.29230i	0.492016	−	0.102810i
$159$	4.88033			0.387036
$160$	−1.36972	−	5.48852i	−0.108286	−	0.433906i
$161$	−22.1352			−1.74450
$162$	1.38431	−	0.289262i	0.108762	−	0.0227265i
$163$	−9.85832	−	9.85832i	−0.772163	−	0.772163i	0.206321	−	0.978484i	$-0.433851\pi$
$163$	−9.85832	−	9.85832i	−0.772163	−	0.772163i	−0.978484	+	0.206321i	$0.933851\pi$
$164$	2.55643	+	5.85005i	0.199624	+	0.456812i
$165$	0.702458	−	0.702458i	0.0546863	−	0.0546863i
$166$	−16.4898	−	10.7896i	−1.27986	−	0.837436i
$167$		−	5.61117i		−	0.434206i	−0.976149	−	0.217103i	$-0.930339\pi$
$167$		−	5.61117i		−	0.434206i	0.976149	−	0.217103i	$-0.0696607\pi$
$168$	1.22920	−	7.27330i	0.0948352	−	0.561147i
$169$		−	3.97383i		−	0.305679i
$170$	−1.80940	+	2.76531i	−0.138774	+	0.212090i
$171$	3.46869	−	3.46869i	0.265258	−	0.265258i
$172$	−3.02244	+	7.71434i	−0.230459	+	0.588213i
$173$	2.30263	+	2.30263i	0.175066	+	0.175066i	0.789201	−	0.614135i	$-0.210495\pi$
$173$	2.30263	+	2.30263i	0.175066	+	0.175066i	−0.614135	+	0.789201i	$0.710495\pi$
$174$	−2.09303	−	10.0166i	−0.158673	−	0.759357i
$175$	−2.60796			−0.197144
$176$	−0.153237	−	3.97075i	−0.0115507	−	0.299306i
$177$	7.52553			0.565654
$178$	2.11423	+	10.1181i	0.158469	+	0.758380i
$179$	11.1129	+	11.1129i	0.830621	+	0.830621i	0.987602	−	0.156981i	$-0.0501761\pi$
$179$	11.1129	+	11.1129i	0.830621	+	0.830621i	−0.156981	+	0.987602i	$0.550176\pi$
$180$	−1.86218	−	0.729591i	−0.138798	−	0.0543805i
$181$	−1.60636	+	1.60636i	−0.119400	+	0.119400i	−0.764282	−	0.644882i	$-0.776906\pi$
$181$	−1.60636	+	1.60636i	−0.119400	+	0.119400i	0.644882	+	0.764282i	$0.276906\pi$
$182$	6.06700	−	9.27223i	0.449716	−	0.687303i
$183$		−	13.2017i		−	0.975894i
$184$	13.9090	+	19.5664i	1.02539	+	1.44246i
$185$		−	1.36805i		−	0.100581i
$186$	6.64697	+	4.34924i	0.487379	+	0.318902i
$187$	−1.64148	+	1.64148i	−0.120037	+	0.120037i
$188$	15.7493	−	6.88233i	1.14863	−	0.501946i
$189$	−1.84411	−	1.84411i	−0.134139	−	0.134139i
$190$	−6.79072	+	1.41896i	−0.492650	+	0.102943i
$191$	−6.76545			−0.489531			−0.244765	−	0.969582i	$-0.578711\pi$
$191$	−6.76545			−0.489531			−0.244765	+	0.969582i	$0.578711\pi$
$192$	−7.20164	+	3.48374i	−0.519733	+	0.251417i
$193$	26.6787			1.92038			0.960189	−	0.279351i	$-0.0901192\pi$
$193$	26.6787			1.92038			0.960189	+	0.279351i	$0.0901192\pi$
$194$	−25.1498	+	5.25521i	−1.80565	+	0.377302i
$195$	−2.12440	−	2.12440i	−0.152132	−	0.152132i
$196$	0.363819	−	0.158987i	0.0259871	−	0.0113562i
$197$	8.58027	−	8.58027i	0.611319	−	0.611319i	−0.331970	−	0.943290i	$-0.607713\pi$
$197$	8.58027	−	8.58027i	0.611319	−	0.611319i	0.943290	+	0.331970i	$0.107713\pi$
$198$	−1.17562	−	0.769229i	−0.0835475	−	0.0546667i
$199$			7.84846i			0.556362i	0.960529	+	0.278181i	$0.0897316\pi$
$199$			7.84846i			0.556362i	−0.960529	+	0.278181i	$0.910268\pi$
$200$	1.63876	+	2.30531i	0.115878	+	0.163010i
$201$			0.387146i			0.0273072i
$202$	−9.21668	+	14.0859i	−0.648484	+	0.991082i
$203$	−13.3436	+	13.3436i	−0.936536	+	0.936536i
$204$	4.35146	+	1.70488i	0.304663	+	0.119365i
$205$	−2.25717	−	2.25717i	−0.157647	−	0.157647i
$206$	2.64125	+	12.6402i	0.184025	+	0.880684i
$207$	8.48753			0.589924
$208$	−12.0085	+	0.463426i	−0.832639	+	0.0321328i
$209$	−4.87322			−0.337088
$210$	0.754384	+	3.61024i	0.0520575	+	0.249131i
$211$	−9.73022	−	9.73022i	−0.669856	−	0.669856i	0.287826	−	0.957683i	$-0.407067\pi$
$211$	−9.73022	−	9.73022i	−0.669856	−	0.669856i	−0.957683	+	0.287826i	$0.907067\pi$
$212$	−3.56065	+	9.08804i	−0.244546	+	0.624169i
$213$	−10.8243	+	10.8243i	−0.741668	+	0.741668i
$214$	−7.53612	+	11.5175i	−0.515159	+	0.787320i
$215$		−	4.14265i		−	0.282526i
$216$	−0.471327	+	2.78888i	−0.0320697	+	0.189759i
$217$		−	14.6486i		−	0.994408i
$218$	21.0447	+	13.7699i	1.42533	+	0.932618i
$219$	6.04848	−	6.04848i	0.408718	−	0.408718i
$220$	0.795593	+	1.82061i	0.0536389	+	0.122745i
$221$	4.96422	+	4.96422i	0.333929	+	0.333929i
$222$	−1.89381	+	0.395724i	−0.127104	+	0.0265592i
$223$	−5.76312			−0.385927			−0.192963	−	0.981206i	$-0.561810\pi$
$223$	−5.76312			−0.385927			−0.192963	+	0.981206i	$0.561810\pi$
$224$	12.6473	+	7.59552i	0.845036	+	0.507497i
$225$	1.00000			0.0666667
$226$	−1.40516	+	0.293618i	−0.0934699	+	0.0195312i
$227$	8.88428	+	8.88428i	0.589671	+	0.589671i	0.937542	−	0.347872i	$-0.113095\pi$
$227$	8.88428	+	8.88428i	0.589671	+	0.589671i	−0.347872	+	0.937542i	$0.613095\pi$
$228$	3.92859	+	8.99004i	0.260177	+	0.595380i
$229$	20.6876	−	20.6876i	1.36707	−	1.36707i	0.502493	−	0.864581i	$-0.332416\pi$
$229$	20.6876	−	20.6876i	1.36707	−	1.36707i	0.864581	−	0.502493i	$-0.167584\pi$
$230$	−10.0441	−	6.57206i	−0.662290	−	0.433349i
$231$			2.59082i			0.170463i
$232$	20.1797	+	3.41042i	1.32486	+	0.223905i
$233$			18.4775i			1.21050i	0.796036	+	0.605249i	$0.206927\pi$
$233$			18.4775i			1.21050i	−0.796036	+	0.605249i	$0.793073\pi$
$234$	−2.32633	+	3.55535i	−0.152077	+	0.232420i
$235$	−6.07666	+	6.07666i	−0.396397	+	0.396397i
$236$	−5.49056	+	14.0139i	−0.357405	+	0.912225i
$237$	3.15906	+	3.15906i	0.205203	+	0.205203i
$238$	−1.76281	−	8.43627i	−0.114266	−	0.546842i
$239$	−11.7690			−0.761271			−0.380636	−	0.924725i	$-0.624295\pi$
$239$	−11.7690			−0.761271			−0.380636	+	0.924725i	$0.624295\pi$
$240$	2.71725	−	2.93540i	0.175398	−	0.189479i
$241$	−1.34327			−0.0865279			−0.0432639	−	0.999064i	$-0.513776\pi$
$241$	−1.34327			−0.0865279			−0.0432639	+	0.999064i	$0.513776\pi$
$242$	−2.89641	−	13.8613i	−0.186188	−	0.891038i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	24.5838	+	9.63180i	1.57382	+	0.616613i
$245$	−0.140375	+	0.140375i	−0.00896822	+	0.00896822i
$246$	−2.47172	+	3.77754i	−0.157591	+	0.240847i
$247$			14.7378i			0.937743i
$248$	−12.9486	+	9.20466i	−0.822237	+	0.584496i
$249$		−	13.9343i		−	0.883051i
$250$	−1.18340	−	0.774320i	−0.0748446	−	0.0489723i
$251$	−0.0990218	+	0.0990218i	−0.00625020	+	0.00625020i	−0.710225	−	0.703975i	$-0.751407\pi$
$251$	−0.0990218	+	0.0990218i	−0.00625020	+	0.00625020i	0.703975	+	0.710225i	$0.251407\pi$
$252$	4.77950	−	2.08861i	0.301080	−	0.131570i
$253$	−5.96214	−	5.96214i	−0.374836	−	0.374836i
$254$	17.1528	−	3.58419i	1.07626	−	0.224892i
$255$	−2.33676			−0.146334
$256$	−1.23309	−	15.9524i	−0.0770682	−	0.997026i
$257$	−18.6669			−1.16441			−0.582205	−	0.813042i	$-0.697810\pi$
$257$	−18.6669			−1.16441			−0.582205	+	0.813042i	$0.697810\pi$
$258$	−5.73473	+	1.19831i	−0.357029	+	0.0746035i
$259$	2.52283	+	2.52283i	0.156761	+	0.156761i
$260$	5.50595	−	2.40607i	0.341465	−	0.149218i
$261$	5.11647	−	5.11647i	0.316702	−	0.316702i
$262$	15.9545	+	10.4394i	0.985675	+	0.644946i
$263$		−	10.3497i		−	0.638191i	−0.947723	−	0.319096i	$-0.896621\pi$
$263$		−	10.3497i		−	0.638191i	0.947723	−	0.319096i	$-0.103379\pi$
$264$	2.29016	−	1.62798i	0.140950	−	0.100195i
$265$		−	4.88033i		−	0.299797i
$266$	9.90610	−	15.1396i	0.607382	−	0.928266i
$267$	−5.16829	+	5.16829i	−0.316294	+	0.316294i
$268$	−0.720934	−	0.282458i	−0.0440381	−	0.0172539i
$269$	6.45646	+	6.45646i	0.393657	+	0.393657i	0.875989	−	0.482331i	$-0.160210\pi$
$269$	6.45646	+	6.45646i	0.393657	+	0.393657i	−0.482331	+	0.875989i	$0.660210\pi$
$270$	−0.289262	−	1.38431i	−0.0176039	−	0.0842467i
$271$	5.56932			0.338312			0.169156	−	0.985589i	$-0.445896\pi$
$271$	5.56932			0.338312			0.169156	+	0.985589i	$0.445896\pi$
$272$	−6.34956	+	6.85931i	−0.384999	+	0.415907i
$273$	7.83526			0.474212
$274$	−3.69930	−	17.7037i	−0.223483	−	1.06952i
$275$	−0.702458	−	0.702458i	−0.0423598	−	0.0423598i
$276$	−6.19242	+	15.8053i	−0.372740	+	0.951366i
$277$	5.34171	−	5.34171i	0.320952	−	0.320952i	−0.528180	−	0.849132i	$-0.677125\pi$
$277$	5.34171	−	5.34171i	0.320952	−	0.320952i	0.849132	+	0.528180i	$0.177125\pi$
$278$	6.04745	−	9.24236i	0.362702	−	0.554320i
$279$			5.61685i			0.336272i
$280$	−7.27330	−	1.22920i	−0.434663	−	0.0734590i
$281$		−	24.0978i		−	1.43755i	−0.695242	−	0.718776i	$-0.744703\pi$
$281$		−	24.0978i		−	1.43755i	0.695242	−	0.718776i	$-0.255297\pi$
$282$	10.1698	+	6.65426i	0.605600	+	0.396256i
$283$	11.6783	−	11.6783i	0.694201	−	0.694201i	−0.268952	−	0.963153i	$-0.586677\pi$
$283$	11.6783	−	11.6783i	0.694201	−	0.694201i	0.963153	+	0.268952i	$0.0866774\pi$
$284$	−12.2594	−	28.0540i	−0.727463	−	1.66470i
$285$	−3.46869	−	3.46869i	−0.205468	−	0.205468i
$286$	4.13164	−	0.863332i	0.244309	−	0.0510499i
$287$	8.32493			0.491405
$288$	−4.84951	−	2.91243i	−0.285760	−	0.171617i
$289$	−11.5396			−0.678798
$290$	−10.0166	+	2.09303i	−0.588195	+	0.122907i
$291$	−12.8465	−	12.8465i	−0.753073	−	0.753073i
$292$	6.85042	+	15.6762i	0.400890	+	0.917383i
$293$	−3.11332	+	3.11332i	−0.181882	+	0.181882i	−0.792175	−	0.610294i	$-0.791051\pi$
$293$	−3.11332	+	3.11332i	−0.181882	+	0.181882i	0.610294	+	0.792175i	$0.291051\pi$
$294$	0.234928	+	0.153718i	0.0137013	+	0.00896502i
$295$		−	7.52553i		−	0.438153i
$296$	0.644798	−	3.81532i	0.0374781	−	0.221761i
$297$		−	0.993426i		−	0.0576444i
$298$	−8.66973	+	13.2500i	−0.502224	+	0.767552i
$299$	−18.0309	+	18.0309i	−1.04276	+	1.04276i
$300$	−0.729591	+	1.86218i	−0.0421229	+	0.107513i
$301$	7.63950	+	7.63950i	0.440333	+	0.440333i
$302$	−4.96168	−	23.7450i	−0.285513	−	1.36637i
$303$	−11.9029			−0.683806
$304$	−19.6073	+	0.756674i	−1.12456	+	0.0433983i
$305$	−13.2017			−0.755925
$306$	0.675935	+	3.23481i	0.0386406	+	0.184922i
$307$	−17.3883	−	17.3883i	−0.992405	−	0.992405i	0.00756633	−	0.999971i	$-0.497592\pi$
$307$	−17.3883	−	17.3883i	−0.992405	−	0.992405i	−0.999971	+	0.00756633i	$0.997592\pi$
$308$	−4.82456	−	1.89024i	−0.274905	−	0.107706i
$309$	−6.45660	+	6.45660i	−0.367303	+	0.367303i
$310$	4.34924	−	6.64697i	0.247020	−	0.377522i
$311$			8.10508i			0.459597i	0.973238	+	0.229799i	$0.0738067\pi$
$311$			8.10508i			0.459597i	−0.973238	+	0.229799i	$0.926193\pi$
$312$	−4.92341	−	6.92599i	−0.278733	−	0.392107i
$313$		−	30.9243i		−	1.74795i	−0.485974	−	0.873973i	$-0.661535\pi$
$313$		−	30.9243i		−	1.74795i	0.485974	−	0.873973i	$-0.338465\pi$
$314$	−3.70618	−	2.42502i	−0.209152	−	0.136852i
$315$	−1.84411	+	1.84411i	−0.103904	+	0.103904i
$316$	−8.18755	+	3.57790i	−0.460585	+	0.201273i
$317$	16.9428	+	16.9428i	0.951603	+	0.951603i	0.998882	−	0.0472784i	$-0.0150548\pi$
$317$	16.9428	+	16.9428i	0.951603	+	0.951603i	−0.0472784	+	0.998882i	$0.515055\pi$
$318$	−6.75592	+	1.41169i	−0.378853	+	0.0791639i
$319$	−7.18821			−0.402463
$320$	3.48374	+	7.20164i	0.194747	+	0.402584i
$321$	−9.73258			−0.543219
$322$	30.6421	−	6.40286i	1.70762	−	0.356818i
$323$	8.10550	+	8.10550i	0.451002	+	0.451002i
$324$	−1.83266	+	0.800859i	−0.101814	+	0.0444921i
$325$	−2.12440	+	2.12440i	−0.117841	+	0.117841i
$326$	16.4987	+	10.7954i	0.913776	+	0.597901i
$327$			17.7833i			0.983417i
$328$	−5.23110	−	7.35883i	−0.288839	−	0.406323i
$329$		−	22.4120i		−	1.23562i
$330$	−0.769229	+	1.17562i	−0.0423447	+	0.0647156i
$331$	15.3934	−	15.3934i	0.846098	−	0.846098i	−0.143545	−	0.989644i	$-0.545850\pi$
$331$	15.3934	−	15.3934i	0.846098	−	0.846098i	0.989644	+	0.143545i	$0.0458503\pi$
$332$	25.9481	+	10.1663i	1.42409	+	0.557950i
$333$	−0.967355	−	0.967355i	−0.0530108	−	0.0530108i
$334$	1.62310	+	7.76763i	0.0888120	+	0.425026i
$335$	0.387146			0.0211521
$336$	0.402281	+	10.4241i	0.0219463	+	0.568681i
$337$	−20.4632			−1.11470			−0.557351	−	0.830277i	$-0.688182\pi$
$337$	−20.4632			−1.11470			−0.557351	+	0.830277i	$0.688182\pi$
$338$	1.14948	+	5.50103i	0.0625233	+	0.299217i
$339$	−0.717755	−	0.717755i	−0.0389831	−	0.0389831i
$340$	1.70488	−	4.35146i	0.0924599	−	0.235991i
$341$	3.94560	−	3.94560i	0.213666	−	0.213666i
$342$	−3.79840	+	5.80512i	−0.205394	+	0.313905i
$343$		−	18.7735i		−	1.01367i
$344$	1.95254	−	11.5533i	0.105274	−	0.622915i
$345$		−	8.48753i		−	0.456953i
$346$	−3.85363	−	2.52150i	−0.207172	−	0.135557i
$347$	9.11287	−	9.11287i	0.489205	−	0.489205i	−0.418851	−	0.908055i	$-0.637567\pi$
$347$	9.11287	−	9.11287i	0.489205	−	0.489205i	0.908055	+	0.418851i	$0.137567\pi$
$348$	5.79484	+	13.2607i	0.310636	+	0.710848i
$349$	12.6103	+	12.6103i	0.675013	+	0.675013i	0.958867	−	0.283854i	$-0.0916131\pi$
$349$	12.6103	+	12.6103i	0.675013	+	0.675013i	−0.283854	+	0.958867i	$0.591613\pi$
$350$	3.61024	−	0.754384i	0.192976	−	0.0403235i
$351$	−3.00436			−0.160361
$352$	1.36071	+	5.45244i	0.0725263	+	0.290616i
$353$	17.3831			0.925209			0.462605	−	0.886565i	$-0.346915\pi$
$353$	17.3831			0.925209			0.462605	+	0.886565i	$0.346915\pi$
$354$	−10.4177	+	2.17685i	−0.553695	+	0.115698i
$355$	10.8243	+	10.8243i	0.574494	+	0.574494i
$356$	−5.85353	−	13.3950i	−0.310236	−	0.709934i
$357$	4.30924	−	4.30924i	0.228069	−	0.228069i
$358$	−18.5984	−	12.1693i	−0.982954	−	0.643166i
$359$			20.4165i			1.07754i	0.842453	+	0.538770i	$0.181111\pi$
$359$			20.4165i			1.07754i	−0.842453	+	0.538770i	$0.818889\pi$
$360$	2.78888	+	0.471327i	0.146987	+	0.0248411i
$361$			5.06365i			0.266508i
$362$	1.75905	−	2.68837i	0.0924538	−	0.141298i
$363$	7.08033	−	7.08033i	0.371621	−	0.371621i
$364$	−5.71653	+	14.5906i	−0.299628	+	0.764757i
$365$	−6.04848	−	6.04848i	−0.316592	−	0.316592i
$366$	3.81873	+	18.2752i	0.199608	+	0.955262i
$367$	5.83031			0.304340			0.152170	−	0.988354i	$-0.451374\pi$
$367$	5.83031			0.304340			0.152170	+	0.988354i	$0.451374\pi$
$368$	−24.9143	−	23.0628i	−1.29875	−	1.20223i
$369$	−3.19212			−0.166175
$370$	0.395724	+	1.89381i	0.0205727	+	0.0984544i
$371$	8.99987	+	8.99987i	0.467250	+	0.467250i
$372$	−10.4596	−	4.09800i	−0.542303	−	0.212471i
$373$	−26.3488	+	26.3488i	−1.36429	+	1.36429i	−0.495921	+	0.868368i	$0.665169\pi$
$373$	−26.3488	+	26.3488i	−1.36429	+	1.36429i	−0.868368	+	0.495921i	$0.834831\pi$
$374$	1.79750	−	2.74713i	0.0929466	−	0.142051i
$375$		−	1.00000i		−	0.0516398i
$376$	−19.8112	+	14.0830i	−1.02168	+	0.726274i
$377$			21.7389i			1.11961i
$378$	3.08626	+	2.01940i	0.158740	+	0.103867i
$379$	17.3158	−	17.3158i	0.889455	−	0.889455i	−0.105015	−	0.994471i	$-0.533489\pi$
$379$	17.3158	−	17.3158i	0.889455	−	0.889455i	0.994471	+	0.105015i	$0.0334891\pi$
$380$	8.99004	−	3.92859i	0.461179	−	0.201532i
$381$	8.76164	+	8.76164i	0.448872	+	0.448872i
$382$	9.36551	−	1.95699i	0.479181	−	0.100128i
$383$	−17.2683			−0.882370			−0.441185	−	0.897416i	$-0.645442\pi$
$383$	−17.2683			−0.882370			−0.441185	+	0.897416i	$0.645442\pi$
$384$	8.96162	−	6.90575i	0.457321	−	0.352408i
$385$	2.59082			0.132040
$386$	−36.9318	+	7.71714i	−1.87978	+	0.392792i
$387$	−2.92929	−	2.92929i	−0.148904	−	0.148904i
$388$	33.2950	−	14.5497i	1.69030	−	0.738650i
$389$	11.0035	−	11.0035i	0.557901	−	0.557901i	−0.370809	−	0.928709i	$-0.620919\pi$
$389$	11.0035	−	11.0035i	0.557901	−	0.557901i	0.928709	+	0.370809i	$0.120919\pi$
$390$	3.55535	+	2.32633i	0.180032	+	0.117798i
$391$			19.8333i			1.00301i
$392$	−0.457651	+	0.325326i	−0.0231149	+	0.0164315i
$393$			13.4820i			0.680076i
$394$	−9.39586	+	14.3597i	−0.473356	+	0.723434i
$395$	3.15906	−	3.15906i	0.158950	−	0.158950i
$396$	1.84993	+	0.724794i	0.0929626	+	0.0364223i
$397$	−15.3110	−	15.3110i	−0.768439	−	0.768439i	0.209393	−	0.977832i	$-0.432851\pi$
$397$	−15.3110	−	15.3110i	−0.768439	−	0.768439i	−0.977832	+	0.209393i	$0.932851\pi$
$398$	−2.27026	−	10.8647i	−0.113798	−	0.544600i
$399$	12.7933			0.640466
$400$	−2.93540	−	2.71725i	−0.146770	−	0.135863i
$401$	−31.4249			−1.56928			−0.784642	−	0.619950i	$-0.787153\pi$
$401$	−31.4249			−1.56928			−0.784642	+	0.619950i	$0.787153\pi$
$402$	−0.111987	−	0.535932i	−0.00558538	−	0.0267299i
$403$	−11.9325	−	11.9325i	−0.594398	−	0.594398i
$404$	8.68428	−	22.1654i	0.432059	−	1.10277i
$405$	0.707107	−	0.707107i	0.0351364	−	0.0351364i
$406$	14.6119	−	22.3315i	0.725178	−	1.10829i
$407$			1.35905i			0.0673658i
$408$	−6.51694	−	1.10138i	−0.322637	−	0.0545263i
$409$			27.2731i			1.34857i	0.738471	+	0.674285i	$0.235548\pi$
$409$			27.2731i			1.34857i	−0.738471	+	0.674285i	$0.764452\pi$
$410$	3.77754	+	2.47172i	0.186559	+	0.122069i
$411$	9.04303	−	9.04303i	0.446060	−	0.446060i
$412$	−7.31265	−	16.7340i	−0.360268	−	0.824425i
$413$	13.8779	+	13.8779i	0.682887	+	0.682887i
$414$	−11.7494	+	2.45512i	−0.577452	+	0.120662i
$415$	−13.9343			−0.684008
$416$	16.4895	−	4.11512i	0.808464	−	0.201761i
$417$	7.81002			0.382458
$418$	6.74607	−	1.40964i	0.329961	−	0.0689476i
$419$	−2.75602	−	2.75602i	−0.134640	−	0.134640i	0.636575	−	0.771215i	$-0.280351\pi$
$419$	−2.75602	−	2.75602i	−0.134640	−	0.134640i	−0.771215	+	0.636575i	$0.780351\pi$
$420$	−2.08861	−	4.77950i	−0.101914	−	0.233216i
$421$	−1.44979	+	1.44979i	−0.0706586	+	0.0706586i	−0.741553	−	0.670894i	$-0.765910\pi$
$421$	−1.44979	+	1.44979i	−0.0706586	+	0.0706586i	0.670894	+	0.741553i	$0.265910\pi$
$422$	16.2843	+	10.6551i	0.792706	+	0.518683i
$423$			8.59369i			0.417840i
$424$	2.30023	−	13.6107i	0.111709	−	0.660992i
$425$			2.33676i			0.113349i
$426$	11.8532	−	18.1153i	0.574288	−	0.877688i
$427$	24.3453	−	24.3453i	1.17815	−	1.17815i
$428$	7.10080	−	18.1238i	0.343230	−	0.876045i
$429$	2.11044	+	2.11044i	0.101893	+	0.101893i
$430$	1.19831	+	5.73473i	0.0577876	+	0.276553i
$431$	−3.76741			−0.181470			−0.0907348	−	0.995875i	$-0.528922\pi$
$431$	−3.76741			−0.181470			−0.0907348	+	0.995875i	$0.528922\pi$
$432$	−0.154251	−	3.99702i	−0.00742141	−	0.192307i
$433$	5.25544			0.252560			0.126280	−	0.991995i	$-0.459696\pi$
$433$	5.25544			0.252560			0.126280	+	0.991995i	$0.459696\pi$
$434$	4.23726	+	20.2782i	0.203395	+	0.973385i
$435$	−5.11647	−	5.11647i	−0.245316	−	0.245316i
$436$	−33.1156	−	12.9745i	−1.58595	−	0.621366i
$437$	−29.4406	+	29.4406i	−1.40834	+	1.40834i
$438$	−6.62341	+	10.1226i	−0.316479	+	0.483676i
$439$			3.82927i			0.182761i	0.995816	+	0.0913806i	$0.0291280\pi$
$439$			3.82927i			0.182761i	−0.995816	+	0.0913806i	$0.970872\pi$
$440$	−1.62798	−	2.29016i	−0.0776111	−	0.109179i
$441$			0.198520i			0.00945334i
$442$	−8.30799	−	5.43608i	−0.395171	−	0.258568i
$443$	3.69729	−	3.69729i	0.175663	−	0.175663i	−0.613799	−	0.789462i	$-0.710359\pi$
$443$	3.69729	−	3.69729i	0.175663	−	0.175663i	0.789462	+	0.613799i	$0.210359\pi$
$444$	2.50716	−	1.09561i	0.118984	−	0.0519955i
$445$	5.16829	+	5.16829i	0.245001	+	0.245001i
$446$	7.97797	−	1.66705i	0.377768	−	0.0789371i
$447$	−11.1966			−0.529580
$448$	−19.7050	−	6.85621i	−0.930974	−	0.323925i
$449$	22.6361			1.06826			0.534132	−	0.845401i	$-0.320639\pi$
$449$	22.6361			1.06826			0.534132	+	0.845401i	$0.320639\pi$
$450$	−1.38431	+	0.289262i	−0.0652572	+	0.0136359i
$451$	2.24233	+	2.24233i	0.105587	+	0.105587i
$452$	1.86025	−	0.812918i	0.0874989	−	0.0382365i
$453$	12.1289	−	12.1289i	0.569867	−	0.569867i
$454$	−14.8685	−	9.72876i	−0.697815	−	0.456593i
$455$		−	7.83526i		−	0.367323i
$456$	−8.03888	−	11.3087i	−0.376455	−	0.529576i
$457$		−	21.2035i		−	0.991860i	−0.868363	−	0.495930i	$-0.834827\pi$
$457$		−	21.2035i		−	0.991860i	0.868363	−	0.495930i	$-0.165173\pi$
$458$	−22.6540	+	34.6223i	−1.05855	+	1.61779i
$459$	−1.65234	+	1.65234i	−0.0771245	+	0.0771245i
$460$	15.8053	+	6.19242i	0.736925	+	0.288723i
$461$	4.36137	+	4.36137i	0.203129	+	0.203129i	0.801339	−	0.598210i	$-0.204121\pi$
$461$	4.36137	+	4.36137i	0.203129	+	0.203129i	−0.598210	+	0.801339i	$0.704121\pi$
$462$	−0.749425	−	3.58651i	−0.0348664	−	0.166860i
$463$	39.7287			1.84635			0.923175	−	0.384380i	$-0.125585\pi$
$463$	39.7287			1.84635			0.923175	+	0.384380i	$0.125585\pi$
$464$	−28.9216	+	1.11613i	−1.34265	+	0.0518149i
$465$	5.61685			0.260475
$466$	−5.34482	−	25.5786i	−0.247594	−	1.18491i
$467$	−8.42639	−	8.42639i	−0.389927	−	0.389927i	0.484734	−	0.874661i	$-0.338916\pi$
$467$	−8.42639	−	8.42639i	−0.389927	−	0.389927i	−0.874661	+	0.484734i	$0.838916\pi$
$468$	2.19195	−	5.59464i	0.101323	−	0.258612i
$469$	−0.713940	+	0.713940i	−0.0329667	+	0.0329667i
$470$	6.65426	−	10.1698i	0.306938	−	0.469096i
$471$		−	3.13181i		−	0.144306i
$472$	3.54699	−	20.9878i	0.163263	−	0.966042i
$473$			4.11541i			0.189227i
$474$	−5.28693	−	3.45934i	−0.242837	−	0.158893i
$475$	−3.46869	+	3.46869i	−0.159155	+	0.159155i
$476$	4.88058	+	11.1685i	0.223701	+	0.511909i
$477$	−3.45092	−	3.45092i	−0.158007	−	0.158007i
$478$	16.2920	−	3.40431i	0.745177	−	0.155710i
$479$	13.9093			0.635532			0.317766	−	0.948169i	$-0.397067\pi$
$479$	13.9093			0.635532			0.317766	+	0.948169i	$0.397067\pi$
$480$	−2.91243	+	4.84951i	−0.132934	+	0.221349i
$481$	4.11010			0.187405
$482$	1.85951	−	0.388558i	0.0846985	−	0.0176983i
$483$	15.6519	+	15.6519i	0.712188	+	0.712188i
$484$	8.01908	+	18.3506i	0.364504	+	0.834117i
$485$	−12.8465	+	12.8465i	−0.583328	+	0.583328i
$486$	−1.18340	−	0.774320i	−0.0536800	−	0.0351238i
$487$			3.48598i			0.157965i	0.996876	+	0.0789825i	$0.0251671\pi$
$487$			3.48598i			0.157965i	−0.996876	+	0.0789825i	$0.974833\pi$
$488$	−36.8178	−	6.22230i	−1.66666	−	0.281670i
$489$			13.9418i			0.630469i
$490$	0.153718	−	0.234928i	0.00694427	−	0.0106130i
$491$	13.1079	−	13.1079i	0.591550	−	0.591550i	−0.346500	−	0.938050i	$-0.612630\pi$
$491$	13.1079	−	13.1079i	0.591550	−	0.591550i	0.938050	+	0.346500i	$0.112630\pi$
$492$	2.32894	−	5.94428i	0.104997	−	0.267989i
$493$	11.9560	+	11.9560i	0.538469	+	0.538469i
$494$	−4.26308	−	20.4017i	−0.191805	−	0.917918i
$495$	−0.993426			−0.0446512
$496$	15.2624	−	16.4877i	0.685302	−	0.740319i
$497$	−39.9224			−1.79076
$498$	4.03066	+	19.2895i	0.180618	+	0.864382i
$499$	27.0251	+	27.0251i	1.20981	+	1.20981i	0.971088	+	0.238720i	$0.0767280\pi$
$499$	27.0251	+	27.0251i	1.20981	+	1.20981i	0.238720	+	0.971088i	$0.423272\pi$
$500$	1.86218	+	0.729591i	0.0832790	+	0.0326283i
$501$	−3.96770	+	3.96770i	−0.177264	+	0.177264i
$502$	0.108434	−	0.165721i	0.00483965	−	0.00739647i
$503$		−	30.2210i		−	1.34749i	−0.738965	−	0.673743i	$-0.764685\pi$
$503$		−	30.2210i		−	1.34749i	0.738965	−	0.673743i	$-0.235315\pi$
$504$	−6.01218	+	4.27382i	−0.267804	+	0.190371i
$505$			11.9029i			0.529674i
$506$	9.97809	+	6.52886i	0.443580	+	0.290243i
$507$	−2.80992	+	2.80992i	−0.124793	+	0.124793i
$508$	−22.7081	+	9.92330i	−1.00751	+	0.440275i
$509$	22.8520	+	22.8520i	1.01290	+	1.01290i	0.999916	+	0.0129834i	$0.00413286\pi$
$509$	22.8520	+	22.8520i	1.01290	+	1.01290i	0.0129834	+	0.999916i	$0.495867\pi$
$510$	3.23481	−	0.675935i	0.143240	−	0.0299309i
$511$	22.3081			0.986853
$512$	6.32141	+	21.7265i	0.279369	+	0.960184i
$513$	−4.90547			−0.216582
$514$	25.8409	−	5.39962i	1.13979	−	0.238167i
$515$	6.45660	+	6.45660i	0.284512	+	0.284512i
$516$	7.59205	−	3.31768i	0.334221	−	0.146053i
$517$	6.03671	−	6.03671i	0.265494	−	0.265494i
$518$	−4.22215	−	2.76263i	−0.185510	−	0.121383i
$519$		−	3.25641i		−	0.142941i
$520$	−6.92599	+	4.92341i	−0.303725	+	0.215906i
$521$			40.3144i			1.76620i	0.469181	+	0.883102i	$0.344549\pi$
$521$			40.3144i			1.76620i	−0.469181	+	0.883102i	$0.655451\pi$
$522$	−5.60281	+	8.56281i	−0.245228	+	0.374784i
$523$	−7.85539	+	7.85539i	−0.343492	+	0.343492i	−0.857679	−	0.514186i	$-0.828094\pi$
$523$	−7.85539	+	7.85539i	−0.343492	+	0.343492i	0.514186	+	0.857679i	$0.328094\pi$
$524$	−25.1058	−	9.83632i	−1.09675	−	0.429702i
$525$	1.84411	+	1.84411i	0.0804835	+	0.0804835i
$526$	2.99378	+	14.3273i	0.130535	+	0.624699i
$527$	−13.1252			−0.571744
$528$	−2.69939	+	2.91610i	−0.117476	+	0.126907i
$529$	−49.0382			−2.13210
$530$	1.41169	+	6.75592i	0.0613201	+	0.293458i
$531$	−5.32136	−	5.32136i	−0.230927	−	0.230927i
$532$	−9.33387	+	23.8234i	−0.404674	+	1.03287i
$533$	6.78134	−	6.78134i	0.293732	−	0.293732i
$534$	5.65956	−	8.64953i	0.244913	−	0.374302i
$535$			9.73258i			0.420776i
$536$	1.07970	+	0.182472i	0.0466361	+	0.00788161i
$537$		−	15.7161i		−	0.678199i
$538$	−10.8054	−	7.07017i	−0.465853	−	0.304817i
$539$	0.139452	−	0.139452i	0.00600663	−	0.00600663i
$540$	0.800859	+	1.83266i	0.0344635	+	0.0788649i
$541$	10.7511	+	10.7511i	0.462226	+	0.462226i	0.899384	−	0.437159i	$-0.144015\pi$
$541$	10.7511	+	10.7511i	0.462226	+	0.462226i	−0.437159	+	0.899384i	$0.644015\pi$
$542$	−7.70970	+	1.61099i	−0.331160	+	0.0691980i
$543$	2.27174			0.0974897
$544$	6.80566	−	11.3321i	0.291790	−	0.485861i
$545$	17.7833			0.761752
$546$	−10.8465	+	2.26644i	−0.464186	+	0.0969947i
$547$	−7.97598	−	7.97598i	−0.341028	−	0.341028i	0.515726	−	0.856754i	$-0.327522\pi$
$547$	−7.97598	−	7.97598i	−0.341028	−	0.341028i	−0.856754	+	0.515726i	$0.827522\pi$
$548$	10.2420	+	23.4374i	0.437517	+	1.00120i
$549$	−9.33498	+	9.33498i	−0.398407	+	0.398407i
$550$	1.17562	+	0.769229i	0.0501285	+	0.0328000i
$551$			35.4949i			1.51213i
$552$	4.00040	−	23.6707i	0.170269	−	1.00749i
$553$			11.6513i			0.495464i
$554$	−5.84946	+	8.93976i	−0.248520	+	0.379814i
$555$	−0.967355	+	0.967355i	−0.0410620	+	0.0410620i
$556$	−5.69812	+	14.5436i	−0.241654	+	0.616787i
$557$	4.48769	+	4.48769i	0.190149	+	0.190149i	0.795761	−	0.605611i	$-0.207071\pi$
$557$	4.48769	+	4.48769i	0.190149	+	0.190149i	−0.605611	+	0.795761i	$0.707071\pi$
$558$	−1.62474	−	7.77549i	−0.0687807	−	0.329163i
$559$	12.4460			0.526410
$560$	10.4241	−	0.402281i	0.440499	−	0.0169995i
$561$	2.32140			0.0980094
$562$	6.97056	+	33.3589i	0.294035	+	1.40716i
$563$	18.2741	+	18.2741i	0.770162	+	0.770162i	0.978135	−	0.207973i	$-0.0666866\pi$
$563$	18.2741	+	18.2741i	0.770162	+	0.770162i	−0.207973	+	0.978135i	$0.566687\pi$
$564$	−16.0030	−	6.26988i	−0.673846	−	0.264009i
$565$	−0.717755	+	0.717755i	−0.0301962	+	0.0301962i
$566$	−12.7883	+	19.5445i	−0.537533	+	0.821516i
$567$			2.60796i			0.109524i
$568$	25.0859	+	35.2894i	1.05258	+	1.48071i
$569$		−	17.7045i		−	0.742213i	−0.928590	−	0.371106i	$-0.878979\pi$
$569$		−	17.7045i		−	0.742213i	0.928590	−	0.371106i	$-0.121021\pi$
$570$	5.80512	+	3.79840i	0.243150	+	0.159098i
$571$	19.6327	−	19.6327i	0.821605	−	0.821605i	−0.164733	−	0.986338i	$-0.552676\pi$
$571$	19.6327	−	19.6327i	0.821605	−	0.821605i	0.986338	+	0.164733i	$0.0526763\pi$
$572$	−5.46976	+	2.39025i	−0.228702	+	0.0999413i
$573$	4.78390	+	4.78390i	0.199850	+	0.199850i
$574$	−11.5243	+	2.40808i	−0.481016	+	0.100511i
$575$	−8.48753			−0.353955
$576$	7.55570	+	2.62895i	0.314821	+	0.109540i
$577$	−37.0303			−1.54159			−0.770797	−	0.637081i	$-0.780142\pi$
$577$	−37.0303			−1.54159			−0.770797	+	0.637081i	$0.780142\pi$
$578$	15.9744	−	3.33795i	0.664447	−	0.138841i
$579$	−18.8647	−	18.8647i	−0.783991	−	0.783991i
$580$	13.2607	−	5.79484i	0.550620	−	0.240618i
$581$	25.6964	−	25.6964i	1.06607	−	1.06607i
$582$	21.4996	+	14.0676i	0.891185	+	0.583120i
$583$			4.84825i			0.200794i
$584$	−14.0177	−	19.7193i	−0.580055	−	0.815990i
$585$			3.00436i			0.124215i
$586$	3.40925	−	5.21037i	0.140835	−	0.215238i
$587$	−3.50754	+	3.50754i	−0.144772	+	0.144772i	−0.775778	−	0.631006i	$-0.782642\pi$
$587$	−3.50754	+	3.50754i	−0.144772	+	0.144772i	0.631006	+	0.775778i	$0.282642\pi$
$588$	−0.369679	−	0.144838i	−0.0152453	−	0.00597303i
$589$	−19.4831	−	19.4831i	−0.802788	−	0.802788i
$590$	2.17685	+	10.4177i	0.0896194	+	0.428890i
$591$	−12.1343			−0.499140
$592$	0.211023	+	5.46812i	0.00867298	+	0.224738i
$593$	11.9915			0.492431			0.246215	−	0.969215i	$-0.420813\pi$
$593$	11.9915			0.492431			0.246215	+	0.969215i	$0.420813\pi$
$594$	0.287360	+	1.37521i	0.0117905	+	0.0564257i
$595$	−4.30924	−	4.30924i	−0.176662	−	0.176662i
$596$	8.16892	−	20.8500i	0.334612	−	0.854049i
$597$	5.54970	−	5.54970i	0.227134	−	0.227134i
$598$	19.7448	−	30.1762i	0.807426	−	1.23399i
$599$		−	4.94416i		−	0.202013i	−0.994886	−	0.101006i	$-0.967794\pi$
$599$		−	4.94416i		−	0.202013i	0.994886	−	0.101006i	$-0.0322062\pi$
$600$	0.471327	−	2.78888i	0.0192418	−	0.113856i
$601$		−	7.83460i		−	0.319580i	−0.987151	−	0.159790i	$-0.948918\pi$
$601$		−	7.83460i		−	0.319580i	0.987151	−	0.159790i	$-0.0510817\pi$
$602$	−12.7853	−	8.36566i	−0.521089	−	0.340959i
$603$	0.273754	−	0.273754i	0.0111481	−	0.0111481i
$604$	13.7371	+	31.4354i	0.558953	+	1.27909i
$605$	−7.08033	−	7.08033i	−0.287857	−	0.287857i
$606$	16.4774	−	3.44307i	0.669350	−	0.139865i
$607$	−31.6374			−1.28412			−0.642060	−	0.766654i	$-0.721920\pi$
$607$	−31.6374			−1.28412			−0.642060	+	0.766654i	$0.721920\pi$
$608$	26.9238	−	6.71911i	1.09190	−	0.272496i
$609$	18.8707			0.764678
$610$	18.2752	−	3.81873i	0.739943	−	0.154616i
$611$	−18.2565	−	18.2565i	−0.738577	−	0.738577i
$612$	−1.87141	−	4.28247i	−0.0756474	−	0.173109i
$613$	−17.8222	+	17.8222i	−0.719830	+	0.719830i	−0.968570	−	0.248740i	$-0.919983\pi$
$613$	−17.8222	+	17.8222i	−0.719830	+	0.719830i	0.248740	+	0.968570i	$0.419983\pi$
$614$	29.1007	+	19.0412i	1.17441	+	0.768439i
$615$			3.19212i			0.128719i
$616$	7.22548	+	1.22112i	0.291123	+	0.0492005i
$617$			6.50086i			0.261715i	0.991401	+	0.130857i	$0.0417730\pi$
$617$			6.50086i			0.261715i	−0.991401	+	0.130857i	$0.958227\pi$
$618$	7.07032	−	10.8056i	0.284410	−	0.434666i
$619$	20.2361	−	20.2361i	0.813358	−	0.813358i	−0.171778	−	0.985136i	$-0.554951\pi$
$619$	20.2361	−	20.2361i	0.813358	−	0.813358i	0.985136	+	0.171778i	$0.0549510\pi$
$620$	−4.09800	+	10.4596i	−0.164580	+	0.420066i
$621$	−6.00159	−	6.00159i	−0.240836	−	0.240836i
$622$	−2.34449	−	11.2200i	−0.0940055	−	0.449880i
$623$	−19.0618			−0.763695
$624$	8.81898	+	8.16360i	0.353042	+	0.326805i
$625$	−1.00000			−0.0400000
$626$	8.94523	+	42.8090i	0.357523	+	1.71099i
$627$	3.44589	+	3.44589i	0.137616	+	0.137616i
$628$	5.83199	+	2.28494i	0.232722	+	0.0911791i
$629$	2.26048	−	2.26048i	0.0901311	−	0.0901311i
$630$	2.01940	−	3.08626i	0.0804547	−	0.122959i
$631$			24.6616i			0.981765i	0.871226	+	0.490882i	$0.163325\pi$
$631$			24.6616i			0.981765i	−0.871226	+	0.490882i	$0.836675\pi$
$632$	10.2992	−	7.32129i	0.409680	−	0.291225i
$633$			13.7606i			0.546935i
$634$	−28.3551	−	18.5533i	−1.12612	−	0.736845i
$635$	8.76164	−	8.76164i	0.347695	−	0.347695i
$636$	8.94397	−	3.90846i	0.354652	−	0.154980i
$637$	−0.421737	−	0.421737i	−0.0167098	−	0.0167098i
$638$	9.95075	−	2.07927i	0.393954	−	0.0823193i
$639$	15.3079			0.605570
$640$	−6.90575	−	8.96162i	−0.272974	−	0.354239i
$641$	16.6134			0.656191			0.328096	−	0.944645i	$-0.393593\pi$
$641$	16.6134			0.656191			0.328096	+	0.944645i	$0.393593\pi$
$642$	13.4729	−	2.81526i	0.531735	−	0.111109i
$643$	30.5822	+	30.5822i	1.20605	+	1.20605i	0.972297	+	0.233748i	$0.0750991\pi$
$643$	30.5822	+	30.5822i	1.20605	+	1.20605i	0.233748	+	0.972297i	$0.424901\pi$
$644$	−40.5662	+	17.7272i	−1.59853	+	0.698548i
$645$	−2.92929	+	2.92929i	−0.115341	+	0.115341i
$646$	−13.5652	−	8.87595i	−0.533714	−	0.349220i
$647$		−	41.3821i		−	1.62690i	−0.581636	−	0.813449i	$-0.697587\pi$
$647$		−	41.3821i		−	1.62690i	0.581636	−	0.813449i	$-0.302413\pi$
$648$	2.30531	−	1.63876i	0.0905613	−	0.0643765i
$649$			7.47606i			0.293461i
$650$	2.32633	−	3.55535i	0.0912463	−	0.139452i
$651$	−10.3581	+	10.3581i	−0.405966	+	0.405966i
$652$	−25.9620	−	10.1718i	−1.01675	−	0.398358i
$653$	−31.4145	−	31.4145i	−1.22934	−	1.22934i	−0.964212	−	0.265132i	$-0.914585\pi$
$653$	−31.4145	−	31.4145i	−1.22934	−	1.22934i	−0.265132	−	0.964212i	$-0.585415\pi$
$654$	−5.14402	−	24.6176i	−0.201147	−	0.962626i
$655$	13.4820			0.526784
$656$	9.37012	+	8.67378i	0.365842	+	0.338654i
$657$	−8.55384			−0.333717
$658$	6.48294	+	31.0253i	0.252732	+	1.20949i
$659$	−23.1025	−	23.1025i	−0.899945	−	0.899945i	0.0954854	−	0.995431i	$-0.469560\pi$
$659$	−23.1025	−	23.1025i	−0.899945	−	0.899945i	−0.995431	+	0.0954854i	$0.969560\pi$
$660$	0.724794	−	1.84993i	0.0282126	−	0.0720085i
$661$	−1.90735	+	1.90735i	−0.0741873	+	0.0741873i	−0.743227	−	0.669040i	$-0.766706\pi$
$661$	−1.90735	+	1.90735i	−0.0741873	+	0.0741873i	0.669040	+	0.743227i	$0.266706\pi$
$662$	−16.8566	+	25.7621i	−0.655150	+	1.00127i
$663$		−	7.02046i		−	0.272652i
$664$	−38.8611	−	6.56762i	−1.50810	−	0.254873i
$665$		−	12.7933i		−	0.496103i
$666$	1.61894	+	1.05931i	0.0627328	+	0.0410473i
$667$	−43.4262	+	43.4262i	−1.68147	+	1.68147i
$668$	−4.49376	−	10.2833i	−0.173869	−	0.397875i
$669$	4.07514	+	4.07514i	0.157554	+	0.157554i
$670$	−0.535932	+	0.111987i	−0.0207049	+	0.00432642i
$671$	13.1149			0.506294
$672$	−3.57218	−	14.3139i	−0.137800	−	0.552170i
$673$	−0.419477			−0.0161696			−0.00808482	−	0.999967i	$-0.502574\pi$
$673$	−0.419477			−0.0161696			−0.00808482	+	0.999967i	$0.502574\pi$
$674$	28.3275	−	5.91922i	1.09114	−	0.228000i
$675$	−0.707107	−	0.707107i	−0.0272166	−	0.0272166i
$676$	−3.18248	−	7.28266i	−0.122403	−	0.280102i
$677$	15.2420	−	15.2420i	0.585799	−	0.585799i	−0.350692	−	0.936491i	$-0.614054\pi$
$677$	15.2420	−	15.2420i	0.585799	−	0.585799i	0.936491	+	0.350692i	$0.114054\pi$
$678$	1.20122	+	0.785980i	0.0461325	+	0.0301854i
$679$		−	47.3806i		−	1.81830i
$680$	−1.10138	+	6.51694i	−0.0422359	+	0.249913i
$681$		−	12.5643i		−	0.481464i
$682$	−4.32064	+	6.60327i	−0.165446	+	0.252852i
$683$	−2.27719	+	2.27719i	−0.0871343	+	0.0871343i	−0.749330	−	0.662196i	$-0.769625\pi$
$683$	−2.27719	+	2.27719i	−0.0871343	+	0.0871343i	0.662196	+	0.749330i	$0.269625\pi$
$684$	3.57899	−	9.13485i	0.136846	−	0.349280i
$685$	−9.04303	−	9.04303i	−0.345516	−	0.345516i
$686$	5.43045	+	25.9884i	0.207336	+	0.992242i
$687$	−29.2567			−1.11621
$688$	0.639008	+	16.5583i	0.0243620	+	0.631278i
$689$	14.6623			0.558588
$690$	2.45512	+	11.7494i	0.0934648	+	0.447293i
$691$	−7.20242	−	7.20242i	−0.273993	−	0.273993i	0.556712	−	0.830705i	$-0.312063\pi$
$691$	−7.20242	−	7.20242i	−0.273993	−	0.273993i	−0.830705	+	0.556712i	$0.812063\pi$
$692$	6.06401	+	2.37585i	0.230519	+	0.0903161i
$693$	1.83199	−	1.83199i	0.0695914	−	0.0695914i
$694$	−9.97908	+	15.2511i	−0.378801	+	0.578923i
$695$		−	7.81002i		−	0.296251i
$696$	−11.8577	−	16.6808i	−0.449465	−	0.632282i
$697$		−	7.45921i		−	0.282538i
$698$	−21.1043	−	13.8089i	−0.798809	−	0.522676i
$699$	13.0655	−	13.0655i	0.494184	−	0.494184i
$700$	−4.77950	+	2.08861i	−0.180648	+	0.0789421i
$701$	−7.76614	−	7.76614i	−0.293323	−	0.293323i	0.545068	−	0.838392i	$-0.316504\pi$
$701$	−7.76614	−	7.76614i	−0.293323	−	0.293323i	−0.838392	+	0.545068i	$0.816504\pi$
$702$	4.15898	−	0.869046i	0.156971	−	0.0328000i
$703$	6.71092			0.253107
$704$	−3.46084	−	7.15429i	−0.130435	−	0.269637i
$705$	8.59369			0.323657
$706$	−24.0637	+	5.02826i	−0.905649	+	0.189241i
$707$	−21.9503	−	21.9503i	−0.825527	−	0.825527i
$708$	13.7917	−	6.02689i	0.518324	−	0.226504i
$709$	−17.6106	+	17.6106i	−0.661380	+	0.661380i	−0.955705	−	0.294325i	$-0.904905\pi$
$709$	−17.6106	+	17.6106i	−0.661380	+	0.661380i	0.294325	+	0.955705i	$0.404905\pi$
$710$	−18.1153	−	11.8532i	−0.679854	−	0.444842i
$711$		−	4.46759i		−	0.167548i
$712$	11.9778	+	16.8497i	0.448887	+	0.631469i
$713$		−	47.6732i		−	1.78538i
$714$	−4.71885	+	7.21184i	−0.176598	+	0.269896i
$715$	2.11044	−	2.11044i	0.0789258	−	0.0789258i
$716$	29.2661	+	11.4663i	1.09373	+	0.428516i
$717$	8.32192	+	8.32192i	0.310788	+	0.310788i
$718$	−5.90570	−	28.2628i	−0.220399	−	1.05476i
$719$	−14.1187			−0.526540			−0.263270	−	0.964722i	$-0.584801\pi$
$719$	−14.1187			−0.526540			−0.263270	+	0.964722i	$0.584801\pi$
$720$	−3.99702	+	0.154251i	−0.148960	+	0.00574860i
$721$	−23.8134			−0.886856
$722$	−1.46472	−	7.00968i	−0.0545112	−	0.260873i
$723$	0.949838	+	0.949838i	0.0353248	+	0.0353248i
$724$	−1.65744	+	4.23038i	−0.0615983	+	0.157221i
$725$	−5.11647	+	5.11647i	−0.190021	+	0.190021i
$726$	−7.75334	+	11.8495i	−0.287754	+	0.439776i
$727$		−	4.45104i		−	0.165080i	−0.996588	−	0.0825400i	$-0.973697\pi$
$727$		−	4.45104i		−	0.165080i	0.996588	−	0.0825400i	$-0.0263032\pi$
$728$	3.69297	−	21.8516i	0.136871	−	0.809874i
$729$		−	1.00000i		−	0.0370370i
$730$	10.1226	+	6.62341i	0.374654	+	0.245143i
$731$	6.84506	−	6.84506i	0.253174	−	0.253174i
$732$	−10.5727	−	24.1941i	−0.390777	−	0.894239i
$733$	−22.0904	−	22.0904i	−0.815928	−	0.815928i	0.169587	−	0.985515i	$-0.445757\pi$
$733$	−22.0904	−	22.0904i	−0.815928	−	0.815928i	−0.985515	+	0.169587i	$0.945757\pi$
$734$	−8.07099	+	1.68649i	−0.297906	+	0.0622494i
$735$	0.198520			0.00732252
$736$	41.1604	+	24.7194i	1.51719	+	0.911169i
$737$	−0.384601			−0.0141670
$738$	4.41889	−	0.923357i	0.162662	−	0.0339892i
$739$	14.8923	+	14.8923i	0.547823	+	0.547823i	0.925811	−	0.377988i	$-0.123384\pi$
$739$	14.8923	+	14.8923i	0.547823	+	0.547823i	−0.377988	+	0.925811i	$0.623384\pi$
$740$	−1.09561	−	2.50716i	−0.0402755	−	0.0921650i
$741$	10.4212	−	10.4212i	0.382832	−	0.382832i
$742$	−15.0620	−	9.85534i	−0.552943	−	0.361801i
$743$		−	10.7372i		−	0.393908i	−0.980413	−	0.196954i	$-0.936895\pi$
$743$		−	10.7372i		−	0.393908i	0.980413	−	0.196954i	$-0.0631050\pi$
$744$	15.6647	+	2.64737i	0.574297	+	0.0970574i
$745$			11.1966i			0.410211i
$746$	28.8533	−	44.0967i	1.05640	−	1.61450i
$747$	−9.85305	+	9.85305i	−0.360504	+	0.360504i
$748$	−1.69367	+	4.32285i	−0.0619267	+	0.158059i
$749$	−17.9479	−	17.9479i	−0.655803	−	0.655803i
$750$	0.289262	+	1.38431i	0.0105623	+	0.0505480i
$751$	−5.40613			−0.197272			−0.0986362	−	0.995124i	$-0.531448\pi$
$751$	−5.40613			−0.197272			−0.0986362	+	0.995124i	$0.531448\pi$
$752$	23.3512	−	25.2259i	0.851531	−	0.919893i
$753$	0.140038			0.00510327
$754$	−6.28823	−	30.0935i	−0.229004	−	1.09594i
$755$	−12.1289	−	12.1289i	−0.441417	−	0.441417i
$756$	−4.85649	−	1.90275i	−0.176629	−	0.0692022i
$757$	−0.195858	+	0.195858i	−0.00711857	+	0.00711857i	−0.710657	−	0.703539i	$-0.751602\pi$
$757$	−0.195858	+	0.195858i	−0.00711857	+	0.00711857i	0.703539	+	0.710657i	$0.251602\pi$
$758$	−18.9618	+	28.9794i	−0.688723	+	1.05258i
$759$			8.43174i			0.306053i
$760$	−11.3087	+	8.03888i	−0.410208	+	0.291601i
$761$		−	3.78500i		−	0.137206i	−0.997644	−	0.0686030i	$-0.978146\pi$
$761$		−	3.78500i		−	0.137206i	0.997644	−	0.0686030i	$-0.0218542\pi$
$762$	−14.6633	−	9.59446i	−0.531194	−	0.347571i
$763$	−32.7943	+	32.7943i	−1.18723	+	1.18723i
$764$	−12.3987	+	5.41817i	−0.448571	+	0.196022i
$765$	1.65234	+	1.65234i	0.0597404	+	0.0597404i
$766$	23.9048	−	4.99506i	0.863716	−	0.180479i
$767$	22.6094			0.816378
$768$	−10.4081	+	12.1520i	−0.375571	+	0.438497i
$769$	37.9204			1.36744			0.683721	−	0.729743i	$-0.260360\pi$
$769$	37.9204			1.36744			0.683721	+	0.729743i	$0.260360\pi$
$770$	−3.58651	+	0.749425i	−0.129249	+	0.0270074i
$771$	13.1995	+	13.1995i	0.475368	+	0.475368i
$772$	48.8930	−	21.3659i	1.75970	−	0.768976i
$773$	32.7905	−	32.7905i	1.17939	−	1.17939i	0.199492	−	0.979900i	$-0.436071\pi$
$773$	32.7905	−	32.7905i	1.17939	−	1.17939i	0.979900	−	0.199492i	$-0.0639291\pi$
$774$	4.90240	+	3.20773i	0.176213	+	0.115300i
$775$		−	5.61685i		−	0.201763i
$776$	−41.8822	+	29.7724i	−1.50348	+	1.06877i
$777$		−	3.56782i		−	0.127995i
$778$	−12.0494	+	18.4152i	−0.431993	+	0.660218i
$779$	11.0725	−	11.0725i	0.396712	−	0.396712i
$780$	−5.59464	−	2.19195i	−0.200320	−	0.0784845i
$781$	−10.7531	−	10.7531i	−0.384777	−	0.384777i
$782$	−5.73702	−	27.4556i	−0.205155	−	0.981809i
$783$	−7.23578			−0.258586
$784$	0.539429	−	0.582735i	0.0192653	−	0.0208120i
$785$	−3.13181			−0.111779
$786$	−3.89982	−	18.6633i	−0.139102	−	0.665698i
$787$	−0.345189	−	0.345189i	−0.0123047	−	0.0123047i	0.700928	−	0.713232i	$-0.252770\pi$
$787$	−0.345189	−	0.345189i	−0.0123047	−	0.0123047i	−0.713232	+	0.700928i	$0.752770\pi$
$788$	8.85310	−	22.5963i	0.315379	−	0.804959i
$789$	−7.31836	+	7.31836i	−0.260541	+	0.260541i
$790$	−3.45934	+	5.28693i	−0.123078	+	0.188101i
$791$		−	2.64724i		−	0.0941249i
$792$	−2.77055	−	0.468228i	−0.0984470	−	0.0166378i
$793$		−	39.6625i		−	1.40846i
$794$	25.6242	+	16.7664i	0.909368	+	0.595017i
$795$	−3.45092	+	3.45092i	−0.122391	+	0.122391i
$796$	6.28550	+	14.3835i	0.222784	+	0.509810i
$797$	−1.70354	−	1.70354i	−0.0603426	−	0.0603426i	0.676292	−	0.736634i	$-0.263586\pi$
$797$	−1.70354	−	1.70354i	−0.0603426	−	0.0603426i	−0.736634	+	0.676292i	$0.763586\pi$
$798$	−17.7099	+	3.70061i	−0.626925	+	0.131000i
$799$	−20.0814			−0.710428
$800$	4.84951	+	2.91243i	0.171456	+	0.102970i
$801$	7.30907			0.258253
$802$	43.5019	−	9.09001i	1.53611	−	0.320979i
$803$	6.00871	+	6.00871i	0.212043	+	0.212043i
$804$	0.310049	+	0.709506i	0.0109346	+	0.0250223i
$805$	15.6519	−	15.6519i	0.551659	−	0.551659i
$806$	19.9699	+	13.0667i	0.703409	+	0.460254i
$807$		−	9.13082i		−	0.321420i
$808$	−5.61018	+	33.1959i	−0.197365	+	1.16783i
$809$			10.1344i			0.356305i	0.984003	+	0.178152i	$0.0570120\pi$
$809$			10.1344i			0.356305i	−0.984003	+	0.178152i	$0.942988\pi$
$810$	−0.774320	+	1.18340i	−0.0272068	+	0.0415803i
$811$	−4.48583	+	4.48583i	−0.157519	+	0.157519i	−0.781466	−	0.623947i	$-0.785528\pi$
$811$	−4.48583	+	4.48583i	−0.157519	+	0.157519i	0.623947	+	0.781466i	$0.285528\pi$
$812$	−13.7679	+	35.1405i	−0.483157	+	1.23319i
$813$	−3.93811	−	3.93811i	−0.138115	−	0.138115i
$814$	−0.393122	−	1.88136i	−0.0137789	−	0.0659416i
$815$	13.9418			0.488359
$816$	9.34008	−	0.360448i	0.326968	−	0.0126182i
$817$	20.3216			0.710964
$818$	−7.88907	−	37.7546i	−0.275835	−	1.32006i
$819$	−5.54037	−	5.54037i	−0.193596	−	0.193596i
$820$	−5.94428	−	2.32894i	−0.207583	−	0.0813300i
$821$	8.79662	−	8.79662i	0.307004	−	0.307004i	−0.536742	−	0.843746i	$-0.680345\pi$
$821$	8.79662	−	8.79662i	0.307004	−	0.307004i	0.843746	+	0.536742i	$0.180345\pi$
$822$	−9.90260	+	15.1342i	−0.345393	+	0.527866i
$823$			28.1188i			0.980159i	0.871678	+	0.490080i	$0.163032\pi$
$823$			28.1188i			0.980159i	−0.871678	+	0.490080i	$0.836968\pi$
$824$	14.9635	+	21.0499i	0.521279	+	0.733307i
$825$			0.993426i			0.0345866i
$826$	−23.2257	−	15.1970i	−0.808127	−	0.528773i
$827$	23.8356	−	23.8356i	0.828843	−	0.828843i	−0.158513	−	0.987357i	$-0.550670\pi$
$827$	23.8356	−	23.8356i	0.828843	−	0.828843i	0.987357	+	0.158513i	$0.0506701\pi$
$828$	15.5547	−	6.79731i	0.540564	−	0.236223i
$829$	12.6450	+	12.6450i	0.439179	+	0.439179i	0.891736	−	0.452557i	$-0.149488\pi$
$829$	12.6450	+	12.6450i	0.439179	+	0.439179i	−0.452557	+	0.891736i	$0.649488\pi$
$830$	19.2895	−	4.03066i	0.669547	−	0.139906i
$831$	−7.55432			−0.262056
$832$	−21.6363	+	10.4664i	−0.750104	+	0.362857i
$833$	−0.463894			−0.0160730
$834$	−10.8115	+	2.25914i	−0.374373	+	0.0782276i
$835$	3.96770	+	3.96770i	0.137308	+	0.137308i
$836$	−8.93094	+	3.90276i	−0.308883	+	0.134980i
$837$	3.97171	−	3.97171i	0.137283	−	0.137283i
$838$	4.61241	+	3.01799i	0.159333	+	0.104255i
$839$			56.2799i			1.94300i	0.237045	+	0.971499i	$0.423821\pi$
$839$			56.2799i			1.94300i	−0.237045	+	0.971499i	$0.576179\pi$
$840$	4.27382	+	6.01218i	0.147461	+	0.207440i
$841$			23.3566i			0.805399i
$842$	1.58760	−	2.42634i	0.0547123	−	0.0836172i
$843$	−17.0397	+	17.0397i	−0.586878	+	0.586878i
$844$	−25.6247	−	10.0396i	−0.882038	−	0.345578i
$845$	2.80992	+	2.80992i	0.0966643	+	0.0966643i
$846$	−2.48583	−	11.8964i	−0.0854644	−	0.409006i
$847$	26.1138			0.897282
$848$	0.752797	+	19.5068i	0.0258512	+	0.669867i
$849$	−16.5156			−0.566813
$850$	−0.675935	−	3.23481i	−0.0231844	−	0.110953i
$851$	8.21046	+	8.21046i	0.281451	+	0.281451i
$852$	−11.1685	+	28.5059i	−0.382626	+	0.976597i
$853$	−25.2565	+	25.2565i	−0.864766	+	0.864766i	−0.991887	−	0.127121i	$-0.959426\pi$
$853$	−25.2565	+	25.2565i	−0.864766	+	0.864766i	0.127121	+	0.991887i	$0.459426\pi$
$854$	−26.6594	+	40.7437i	−0.912266	+	1.39422i
$855$			4.90547i			0.167764i
$856$	−4.58723	+	27.1430i	−0.156788	+	0.927728i
$857$		−	24.8247i		−	0.847996i	−0.905663	−	0.423998i	$-0.860626\pi$
$857$		−	24.8247i		−	0.847996i	0.905663	−	0.423998i	$-0.139374\pi$
$858$	−3.53198	−	2.31104i	−0.120580	−	0.0788976i
$859$	−3.35276	+	3.35276i	−0.114395	+	0.114395i	−0.761987	−	0.647592i	$-0.775776\pi$
$859$	−3.35276	+	3.35276i	−0.114395	+	0.114395i	0.647592	+	0.761987i	$0.275776\pi$
$860$	−3.31768	−	7.59205i	−0.113132	−	0.258887i
$861$	−5.88661	−	5.88661i	−0.200615	−	0.200615i
$862$	5.21528	−	1.08977i	0.177633	−	0.0371176i
$863$	−17.0990			−0.582057			−0.291028	−	0.956714i	$-0.593997\pi$
$863$	−17.0990			−0.582057			−0.291028	+	0.956714i	$0.593997\pi$
$864$	1.36972	+	5.48852i	0.0465988	+	0.186723i
$865$	−3.25641			−0.110721
$866$	−7.27519	+	1.52020i	−0.247221	+	0.0516584i
$867$	8.15970	+	8.15970i	0.277118	+	0.277118i
$868$	−11.7314	−	26.8457i	−0.398190	−	0.911204i
$869$	−3.13829	+	3.13829i	−0.106459	+	0.106459i
$870$	8.56281	+	5.60281i	0.290306	+	0.189953i
$871$			1.16313i			0.0394110i
$872$	49.5954	+	8.38174i	1.67951	+	0.283841i
$873$			18.1677i			0.614882i
$874$	32.2391	−	49.2712i	1.09050	−	1.66662i
$875$	1.84411	−	1.84411i	0.0623423	−	0.0623423i
$876$	6.24080	−	15.9288i	0.210857	−	0.538183i
$877$	5.96256	+	5.96256i	0.201341	+	0.201341i	0.800575	−	0.599233i	$-0.204528\pi$
$877$	5.96256	+	5.96256i	0.201341	+	0.201341i	−0.599233	+	0.800575i	$0.704528\pi$
$878$	−1.10766	−	5.30092i	−0.0373818	−	0.178897i
$879$	4.40289			0.148506
$880$	2.91610	+	2.69939i	0.0983016	+	0.0909963i
$881$	34.3910			1.15866			0.579332	−	0.815092i	$-0.303314\pi$
$881$	34.3910			1.15866			0.579332	+	0.815092i	$0.303314\pi$
$882$	−0.0574243	−	0.274814i	−0.00193358	−	0.00925348i
$883$	−1.76029	−	1.76029i	−0.0592386	−	0.0592386i	0.676867	−	0.736105i	$-0.263337\pi$
$883$	−1.76029	−	1.76029i	−0.0592386	−	0.0592386i	−0.736105	+	0.676867i	$0.763337\pi$
$884$	13.0733	+	5.12206i	0.439704	+	0.172274i
$885$	−5.32136	+	5.32136i	−0.178875	+	0.178875i
$886$	−4.04873	+	6.18769i	−0.136020	+	0.207880i
$887$			33.8325i			1.13598i	0.823034	+	0.567992i	$0.192279\pi$
$887$			33.8325i			1.13598i	−0.823034	+	0.567992i	$0.807721\pi$
$888$	−3.15378	+	2.24190i	−0.105834	+	0.0752331i
$889$			32.3148i			1.08381i
$890$	−8.64953	−	5.65956i	−0.289933	−	0.189709i
$891$	−0.702458	+	0.702458i	−0.0235332	+	0.0235332i
$892$	−10.5618	+	4.61544i	−0.353636	+	0.154536i
$893$	−29.8089	−	29.8089i	−0.997516	−	0.997516i
$894$	15.4996	−	3.23874i	0.518384	−	0.108320i
$895$	−15.7161			−0.525331
$896$	29.2612	+	3.79124i	0.977547	+	0.126657i
$897$	25.4996			0.851407
$898$	−31.3355	+	6.54776i	−1.04568	+	0.218501i
$899$	−28.7385	−	28.7385i	−0.958481	−	0.958481i
$900$	1.83266	−	0.800859i	0.0610885	−	0.0266953i
$901$	8.06396	−	8.06396i	0.268650	−	0.268650i
$902$	−3.75271	−	2.45547i	−0.124951	−	0.0817581i
$903$		−	10.8039i		−	0.359531i
$904$	−2.34003	+	1.66344i	−0.0778282	+	0.0553250i
$905$		−	2.27174i		−	0.0755152i
$906$	−13.2818	+	20.2987i	−0.441259	+	0.674379i
$907$	−12.2217	+	12.2217i	−0.405816	+	0.405816i	−0.880277	−	0.474461i	$-0.842643\pi$
$907$	−12.2217	+	12.2217i	−0.405816	+	0.405816i	0.474461	+	0.880277i	$0.342643\pi$
$908$	23.3969	+	9.16677i	0.776453	+	0.304210i
$909$	8.41665	+	8.41665i	0.279163	+	0.279163i
$910$	2.26644	+	10.8465i	0.0751318	+	0.359557i
$911$	−18.5029			−0.613028			−0.306514	−	0.951866i	$-0.599163\pi$
$911$	−18.5029			−0.613028			−0.306514	+	0.951866i	$0.599163\pi$
$912$	14.3995	+	13.3294i	0.476815	+	0.441380i
$913$	13.8427			0.458127
$914$	6.13337	+	29.3524i	0.202874	+	0.970890i
$915$	9.33498	+	9.33498i	0.308605	+	0.308605i
$916$	21.3454	−	54.4811i	0.705271	−	1.80010i
$917$	−24.8622	+	24.8622i	−0.821024	+	0.821024i
$918$	1.80940	−	2.76531i	0.0597190	−	0.0912690i
$919$		−	53.1645i		−	1.75373i	−0.480733	−	0.876867i	$-0.659630\pi$
$919$		−	53.1645i		−	1.75373i	0.480733	−	0.876867i	$-0.340370\pi$
$920$	−23.6707	−	4.00040i	−0.780400	−	0.131889i
$921$			24.5908i			0.810295i
$922$	−7.29909	−	4.77593i	−0.240383	−	0.157287i
$923$	−32.5201	+	32.5201i	−1.07041	+	1.07041i
$924$	2.07488	+	4.74808i	0.0682585	+	0.156200i
$925$	0.967355	+	0.967355i	0.0318065	+	0.0318065i
$926$	−54.9970	+	11.4920i	−1.80732	+	0.377650i
$927$	9.13102			0.299902
$928$	39.7138	−	9.91098i	1.30367	−	0.325344i
$929$	38.2816			1.25598			0.627989	−	0.778222i	$-0.283878\pi$
$929$	38.2816			1.25598			0.627989	+	0.778222i	$0.283878\pi$
$930$	−7.77549	+	1.62474i	−0.254968	+	0.0532773i
$931$	−0.688605	−	0.688605i	−0.0225681	−	0.0225681i
$932$	14.7978	+	33.8628i	0.484719	+	1.10921i
$933$	5.73116	−	5.73116i	0.187630	−	0.187630i
$934$	14.1022	+	9.22735i	0.461439	+	0.301928i
$935$		−	2.32140i		−	0.0759178i
$936$	−1.41604	+	8.37879i	−0.0462846	+	0.273869i
$937$			41.1475i			1.34423i	0.740447	+	0.672115i	$0.234614\pi$
$937$			41.1475i			1.34423i	−0.740447	+	0.672115i	$0.765386\pi$
$938$	0.781802	−	1.19483i	0.0255268	−	0.0390127i
$939$	−21.8668	+	21.8668i	−0.713596	+	0.713596i
$940$	−6.26988	+	16.0030i	−0.204501	+	0.521959i
$941$	23.1721	+	23.1721i	0.755389	+	0.755389i	0.975479	−	0.220090i	$-0.0706352\pi$
$941$	23.1721	+	23.1721i	0.755389	+	0.755389i	−0.220090	+	0.975479i	$0.570635\pi$
$942$	0.905914	+	4.33542i	0.0295163	+	0.141255i
$943$	27.0932			0.882276
$944$	1.16082	+	30.0797i	0.0377815	+	0.979012i
$945$	2.60796			0.0848371
$946$	−1.19043	−	5.69703i	−0.0387043	−	0.185226i
$947$	24.4290	+	24.4290i	0.793837	+	0.793837i	0.982116	−	0.188279i	$-0.0602908\pi$
$947$	24.4290	+	24.4290i	0.793837	+	0.793837i	−0.188279	+	0.982116i	$0.560291\pi$
$948$	8.31943	+	3.25951i	0.270203	+	0.105864i
$949$	18.1718	−	18.1718i	0.589882	−	0.589882i
$950$	3.79840	−	5.80512i	0.123236	−	0.188343i
$951$		−	23.9608i		−	0.776981i
$952$	−9.98689	−	14.0490i	−0.323677	−	0.455331i
$953$		−	21.6582i		−	0.701579i	−0.936454	−	0.350789i	$-0.885913\pi$
$953$		−	21.6582i		−	0.701579i	0.936454	−	0.350789i	$-0.114087\pi$
$954$	5.77538	+	3.77894i	0.186985	+	0.122348i
$955$	4.78390	−	4.78390i	0.154803	−	0.154803i
$956$	−21.5685	+	9.42528i	−0.697574	+	0.304835i
$957$	5.08283	+	5.08283i	0.164305	+	0.164305i
$958$	−19.2548	+	4.02343i	−0.622096	+	0.129991i
$959$	33.3527			1.07701
$960$	2.62895	−	7.55570i	0.0848490	−	0.243859i
$961$	0.549021			0.0177104
$962$	−5.68968	+	1.18890i	−0.183443	+	0.0383315i
$963$	6.88197	+	6.88197i	0.221768	+	0.221768i
$964$	−2.46176	+	1.07577i	−0.0792879	+	0.0346483i
$965$	−18.8647	+	18.8647i	−0.607277	+	0.607277i
$966$	−26.1947	−	17.1397i	−0.842801	−	0.551461i
$967$			4.89396i			0.157379i	0.996899	+	0.0786896i	$0.0250736\pi$
$967$			4.89396i			0.157379i	−0.996899	+	0.0786896i	$0.974926\pi$
$968$	−16.4090	−	23.0834i	−0.527407	−	0.741927i
$969$		−	11.4629i		−	0.368242i
$970$	14.0676	−	21.4996i	0.451682	−	0.690309i
$971$	−39.2227	+	39.2227i	−1.25872	+	1.25872i	−0.307010	+	0.951706i	$0.599329\pi$
$971$	−39.2227	+	39.2227i	−1.25872	+	1.25872i	−0.951706	+	0.307010i	$0.900671\pi$
$972$	1.86218	+	0.729591i	0.0597293	+	0.0234016i
$973$	14.4025	+	14.4025i	0.461724	+	0.461724i
$974$	−1.00836	−	4.82570i	−0.0323100	−	0.154625i
$975$	3.00436			0.0962165
$976$	52.7673	−	2.03637i	1.68904	−	0.0651826i
$977$	35.4735			1.13490			0.567449	−	0.823409i	$-0.307930\pi$
$977$	35.4735			1.13490			0.567449	+	0.823409i	$0.307930\pi$
$978$	−4.03282	−	19.2998i	−0.128955	−	0.617140i
$979$	−5.13431	−	5.13431i	−0.164093	−	0.164093i
$980$	−0.144838	+	0.369679i	−0.00462669	+	0.0118090i
$981$	12.5747	−	12.5747i	0.401478	−	0.401478i
$982$	−14.3538	+	21.9370i	−0.458049	+	0.700038i
$983$			19.2936i			0.615369i	0.951488	+	0.307684i	$0.0995541\pi$
$983$			19.2936i			0.615369i	−0.951488	+	0.307684i	$0.900446\pi$
$984$	−1.50453	+	8.90243i	−0.0479627	+	0.283799i
$985$			12.1343i			0.386632i
$986$	−20.0092	−	13.0924i	−0.637223	−	0.416947i
$987$	−15.8477	+	15.8477i	−0.504438	+	0.504438i
$988$	11.8029	+	27.0093i	0.375500	+	0.859280i
$989$	24.8625	+	24.8625i	0.790581	+	0.790581i
$990$	1.37521	−	0.287360i	0.0437072	−	0.00913290i
$991$	1.76023			0.0559155			0.0279577	−	0.999609i	$-0.491100\pi$
$991$	1.76023			0.0559155			0.0279577	+	0.999609i	$0.491100\pi$
$992$	−16.3587	+	27.2390i	−0.519390	+	0.864838i
$993$	−21.7696			−0.690836
$994$	55.2651	−	11.5480i	1.75290	−	0.366281i
$995$	−5.54970	−	5.54970i	−0.175937	−	0.175937i
$996$	−11.1594	−	25.5368i	−0.353599	−	0.809164i
$997$	24.9267	−	24.9267i	0.789435	−	0.789435i	−0.191966	−	0.981402i	$-0.561486\pi$
$997$	24.9267	−	24.9267i	0.789435	−	0.789435i	0.981402	+	0.191966i	$0.0614864\pi$
$998$	−45.2285	−	29.5939i	−1.43168	−	0.936779i
$999$			1.36805i			0.0432831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.s.c.61.1	✓	20
3.2	odd	2		720.2.t.d.541.10		20
4.3	odd	2		960.2.s.c.721.9		20
8.3	odd	2		1920.2.s.f.1441.4		20
8.5	even	2		1920.2.s.e.1441.7		20
12.11	even	2		2880.2.t.d.721.9		20
16.3	odd	4		1920.2.s.f.481.2		20
16.5	even	4	inner	240.2.s.c.181.1	yes	20
16.11	odd	4		960.2.s.c.241.7		20
16.13	even	4		1920.2.s.e.481.9		20
48.5	odd	4		720.2.t.d.181.10		20
48.11	even	4		2880.2.t.d.2161.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.c.61.1	✓	20	1.1	even	1	trivial
240.2.s.c.181.1	yes	20	16.5	even	4	inner
720.2.t.d.181.10		20	48.5	odd	4
720.2.t.d.541.10		20	3.2	odd	2
960.2.s.c.241.7		20	16.11	odd	4
960.2.s.c.721.9		20	4.3	odd	2
1920.2.s.e.481.9		20	16.13	even	4
1920.2.s.e.1441.7		20	8.5	even	2
1920.2.s.f.481.2		20	16.3	odd	4
1920.2.s.f.1441.4		20	8.3	odd	2
2880.2.t.d.721.9		20	12.11	even	2
2880.2.t.d.2161.7		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)

\(f(q)\)	\(=\)	\(q+(-1.38431 + 0.289262i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.83266 - 0.800859i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.18340 + 0.774320i) q^{6} -2.60796i q^{7} +(-2.30531 + 1.63876i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-1.38431 + 0.289262i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.83266 - 0.800859i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.18340 + 0.774320i) q^{6} -2.60796i q^{7} +(-2.30531 + 1.63876i) q^{8} +1.00000i q^{9} +(0.774320 - 1.18340i) q^{10} +(0.702458 - 0.702458i) q^{11} +(-1.86218 - 0.729591i) q^{12} +(-2.12440 - 2.12440i) q^{13} +(0.754384 + 3.61024i) q^{14} +1.00000 q^{15} +(2.71725 - 2.93540i) q^{16} -2.33676 q^{17} +(-0.289262 - 1.38431i) q^{18} +(-3.46869 - 3.46869i) q^{19} +(-0.729591 + 1.86218i) q^{20} +(-1.84411 + 1.84411i) q^{21} +(-0.769229 + 1.17562i) q^{22} -8.48753i q^{23} +(2.78888 + 0.471327i) q^{24} -1.00000i q^{25} +(3.55535 + 2.32633i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.08861 - 4.77950i) q^{28} +(-5.11647 - 5.11647i) q^{29} +(-1.38431 + 0.289262i) q^{30} +5.61685 q^{31} +(-2.91243 + 4.84951i) q^{32} -0.993426 q^{33} +(3.23481 - 0.675935i) q^{34} +(1.84411 + 1.84411i) q^{35} +(0.800859 + 1.83266i) q^{36} +(-0.967355 + 0.967355i) q^{37} +(5.80512 + 3.79840i) q^{38} +3.00436i q^{39} +(0.471327 - 2.78888i) q^{40} +3.19212i q^{41} +(2.01940 - 3.08626i) q^{42} +(-2.92929 + 2.92929i) q^{43} +(0.724794 - 1.84993i) q^{44} +(-0.707107 - 0.707107i) q^{45} +(2.45512 + 11.7494i) q^{46} +8.59369 q^{47} +(-3.99702 + 0.154251i) q^{48} +0.198520 q^{49} +(0.289262 + 1.38431i) q^{50} +(1.65234 + 1.65234i) q^{51} +(-5.59464 - 2.19195i) q^{52} +(-3.45092 + 3.45092i) q^{53} +(-0.774320 + 1.18340i) q^{54} +0.993426i q^{55} +(4.27382 + 6.01218i) q^{56} +4.90547i q^{57} +(8.56281 + 5.60281i) q^{58} +(-5.32136 + 5.32136i) q^{59} +(1.83266 - 0.800859i) q^{60} +(9.33498 + 9.33498i) q^{61} +(-7.77549 + 1.62474i) q^{62} +2.60796 q^{63} +(2.62895 - 7.55570i) q^{64} +3.00436 q^{65} +(1.37521 - 0.287360i) q^{66} +(-0.273754 - 0.273754i) q^{67} +(-4.28247 + 1.87141i) q^{68} +(-6.00159 + 6.00159i) q^{69} +(-3.08626 - 2.01940i) q^{70} -15.3079i q^{71} +(-1.63876 - 2.30531i) q^{72} +8.55384i q^{73} +(1.05931 - 1.61894i) q^{74} +(-0.707107 + 0.707107i) q^{75} +(-9.13485 - 3.57899i) q^{76} +(-1.83199 - 1.83199i) q^{77} +(-0.869046 - 4.15898i) q^{78} -4.46759 q^{79} +(0.154251 + 3.99702i) q^{80} -1.00000 q^{81} +(-0.923357 - 4.41889i) q^{82} +(9.85305 + 9.85305i) q^{83} +(-1.90275 + 4.85649i) q^{84} +(1.65234 - 1.65234i) q^{85} +(3.20773 - 4.90240i) q^{86} +7.23578i q^{87} +(-0.468228 + 2.77055i) q^{88} -7.30907i q^{89} +(1.18340 + 0.774320i) q^{90} +(-5.54037 + 5.54037i) q^{91} +(-6.79731 - 15.5547i) q^{92} +(-3.97171 - 3.97171i) q^{93} +(-11.8964 + 2.48583i) q^{94} +4.90547 q^{95} +(5.48852 - 1.36972i) q^{96} +18.1677 q^{97} +(-0.274814 + 0.0574243i) q^{98} +(0.702458 + 0.702458i) 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

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