LMFDB - Embedded newform 245.2.e.i.116.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,2,Mod(116,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("245.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.e (of order $3$, degree $2$, not 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:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.1
Root			$-0.780776 - 1.35234i$ of defining polynomial
Character	$\chi$	$=$	245.116
Dual form			245.2.e.i.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780776 - 1.35234i) q^{2} +(1.28078 - 2.21837i) q^{3} +(-0.219224 + 0.379706i) q^{4} +(-0.500000 - 0.866025i) q^{5} -4.00000 q^{6} -2.43845 q^{8} +(-1.78078 - 3.08440i) q^{9} +O(q^{10})$	\(q+(-0.780776 - 1.35234i) q^{2} +(1.28078 - 2.21837i) q^{3} +(-0.219224 + 0.379706i) q^{4} +(-0.500000 - 0.866025i) q^{5} -4.00000 q^{6} -2.43845 q^{8} +(-1.78078 - 3.08440i) q^{9} +(-0.780776 + 1.35234i) q^{10} +(-1.28078 + 2.21837i) q^{11} +(0.561553 + 0.972638i) q^{12} +4.56155 q^{13} -2.56155 q^{15} +(2.34233 + 4.05703i) q^{16} +(2.28078 - 3.95042i) q^{17} +(-2.78078 + 4.81645i) q^{18} +(-0.561553 - 0.972638i) q^{19} +0.438447 q^{20} +4.00000 q^{22} +(2.56155 + 4.43674i) q^{23} +(-3.12311 + 5.40938i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.56155 - 6.16879i) q^{26} -1.43845 q^{27} -5.68466 q^{29} +(2.00000 + 3.46410i) q^{30} +(1.21922 - 2.11176i) q^{32} +(3.28078 + 5.68247i) q^{33} -7.12311 q^{34} +1.56155 q^{36} +(-3.00000 - 5.19615i) q^{37} +(-0.876894 + 1.51883i) q^{38} +(5.84233 - 10.1192i) q^{39} +(1.21922 + 2.11176i) q^{40} -3.12311 q^{41} +9.12311 q^{43} +(-0.561553 - 0.972638i) q^{44} +(-1.78078 + 3.08440i) q^{45} +(4.00000 - 6.92820i) q^{46} +(-1.84233 - 3.19101i) q^{47} +12.0000 q^{48} +1.56155 q^{50} +(-5.84233 - 10.1192i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-1.56155 + 2.70469i) q^{53} +(1.12311 + 1.94528i) q^{54} +2.56155 q^{55} -2.87689 q^{57} +(4.43845 + 7.68762i) q^{58} +(2.00000 - 3.46410i) q^{59} +(0.561553 - 0.972638i) q^{60} +(4.68466 + 8.11407i) q^{61} +5.56155 q^{64} +(-2.28078 - 3.95042i) q^{65} +(5.12311 - 8.87348i) q^{66} +(3.12311 - 5.40938i) q^{67} +(1.00000 + 1.73205i) q^{68} +13.1231 q^{69} +8.00000 q^{71} +(4.34233 + 7.52113i) q^{72} +(-2.12311 + 3.67733i) q^{73} +(-4.68466 + 8.11407i) q^{74} +(1.28078 + 2.21837i) q^{75} +0.492423 q^{76} -18.2462 q^{78} +(3.28078 + 5.68247i) q^{79} +(2.34233 - 4.05703i) q^{80} +(3.50000 - 6.06218i) q^{81} +(2.43845 + 4.22351i) q^{82} +4.00000 q^{83} -4.56155 q^{85} +(-7.12311 - 12.3376i) q^{86} +(-7.28078 + 12.6107i) q^{87} +(3.12311 - 5.40938i) q^{88} +(-3.56155 - 6.16879i) q^{89} +5.56155 q^{90} -2.24621 q^{92} +(-2.87689 + 4.98293i) q^{94} +(-0.561553 + 0.972638i) q^{95} +(-3.12311 - 5.40938i) q^{96} -14.8078 q^{97} +9.12311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} - 5 q^{4} - 2 q^{5} - 16 q^{6} - 18 q^{8} - 3 q^{9}+O(q^{10}) $ 4 * q + q^2 + q^3 - 5 * q^4 - 2 * q^5 - 16 * q^6 - 18 * q^8 - 3 * q^9	$ 4 q + q^{2} + q^{3} - 5 q^{4} - 2 q^{5} - 16 q^{6} - 18 q^{8} - 3 q^{9} + q^{10} - q^{11} - 6 q^{12} + 10 q^{13} - 2 q^{15} - 3 q^{16} + 5 q^{17} - 7 q^{18} + 6 q^{19} + 10 q^{20} + 16 q^{22} + 2 q^{23} + 4 q^{24} - 2 q^{25} - 6 q^{26} - 14 q^{27} + 2 q^{29} + 8 q^{30} + 9 q^{32} + 9 q^{33} - 12 q^{34} - 2 q^{36} - 12 q^{37} - 20 q^{38} + 11 q^{39} + 9 q^{40} + 4 q^{41} + 20 q^{43} + 6 q^{44} - 3 q^{45} + 16 q^{46} + 5 q^{47} + 48 q^{48} - 2 q^{50} - 11 q^{51} - 4 q^{52} + 2 q^{53} - 12 q^{54} + 2 q^{55} - 28 q^{57} + 26 q^{58} + 8 q^{59} - 6 q^{60} - 6 q^{61} + 14 q^{64} - 5 q^{65} + 4 q^{66} - 4 q^{67} + 4 q^{68} + 36 q^{69} + 32 q^{71} + 5 q^{72} + 8 q^{73} + 6 q^{74} + q^{75} - 64 q^{76} - 40 q^{78} + 9 q^{79} - 3 q^{80} + 14 q^{81} + 18 q^{82} + 16 q^{83} - 10 q^{85} - 12 q^{86} - 25 q^{87} - 4 q^{88} - 6 q^{89} + 14 q^{90} + 24 q^{92} - 28 q^{94} + 6 q^{95} + 4 q^{96} - 18 q^{97} + 20 q^{99}+O(q^{100}) $ 4 * q + q^2 + q^3 - 5 * q^4 - 2 * q^5 - 16 * q^6 - 18 * q^8 - 3 * q^9 + q^10 - q^11 - 6 * q^12 + 10 * q^13 - 2 * q^15 - 3 * q^16 + 5 * q^17 - 7 * q^18 + 6 * q^19 + 10 * q^20 + 16 * q^22 + 2 * q^23 + 4 * q^24 - 2 * q^25 - 6 * q^26 - 14 * q^27 + 2 * q^29 + 8 * q^30 + 9 * q^32 + 9 * q^33 - 12 * q^34 - 2 * q^36 - 12 * q^37 - 20 * q^38 + 11 * q^39 + 9 * q^40 + 4 * q^41 + 20 * q^43 + 6 * q^44 - 3 * q^45 + 16 * q^46 + 5 * q^47 + 48 * q^48 - 2 * q^50 - 11 * q^51 - 4 * q^52 + 2 * q^53 - 12 * q^54 + 2 * q^55 - 28 * q^57 + 26 * q^58 + 8 * q^59 - 6 * q^60 - 6 * q^61 + 14 * q^64 - 5 * q^65 + 4 * q^66 - 4 * q^67 + 4 * q^68 + 36 * q^69 + 32 * q^71 + 5 * q^72 + 8 * q^73 + 6 * q^74 + q^75 - 64 * q^76 - 40 * q^78 + 9 * q^79 - 3 * q^80 + 14 * q^81 + 18 * q^82 + 16 * q^83 - 10 * q^85 - 12 * q^86 - 25 * q^87 - 4 * q^88 - 6 * q^89 + 14 * q^90 + 24 * q^92 - 28 * q^94 + 6 * q^95 + 4 * q^96 - 18 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.780776	−	1.35234i	−0.552092	−	0.956252i	−0.998123	−	0.0612344i	$-0.980496\pi$
$2$	−0.780776	−	1.35234i	−0.552092	−	0.956252i	0.446031	−	0.895017i	$-0.352837\pi$
$3$	1.28078	−	2.21837i	0.739457	−	1.28078i	−0.213284	−	0.976990i	$-0.568416\pi$
$3$	1.28078	−	2.21837i	0.739457	−	1.28078i	0.952740	−	0.303786i	$-0.0982508\pi$
$4$	−0.219224	+	0.379706i	−0.109612	+	0.189853i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−4.00000			−1.63299
$7$		0			0
$7$		0			0
$8$	−2.43845			−0.862121
$9$	−1.78078	−	3.08440i	−0.593592	−	1.02813i
$10$	−0.780776	+	1.35234i	−0.246903	+	0.427649i
$11$	−1.28078	+	2.21837i	−0.386169	+	0.668864i	−0.991931	−	0.126782i	$-0.959535\pi$
$11$	−1.28078	+	2.21837i	−0.386169	+	0.668864i	0.605762	+	0.795646i	$0.292868\pi$
$12$	0.561553	+	0.972638i	0.162106	+	0.280776i
$13$	4.56155			1.26515			0.632574	−	0.774500i	$-0.281999\pi$
$13$	4.56155			1.26515			0.632574	+	0.774500i	$0.281999\pi$
$14$		0			0
$15$	−2.56155			−0.661390
$16$	2.34233	+	4.05703i	0.585582	+	1.01426i
$17$	2.28078	−	3.95042i	0.553170	−	0.958118i	−0.444874	−	0.895593i	$-0.646752\pi$
$17$	2.28078	−	3.95042i	0.553170	−	0.958118i	0.998043	−	0.0625245i	$-0.0199152\pi$
$18$	−2.78078	+	4.81645i	−0.655435	+	1.13525i
$19$	−0.561553	−	0.972638i	−0.128829	−	0.223138i	0.794394	−	0.607403i	$-0.207789\pi$
$19$	−0.561553	−	0.972638i	−0.128829	−	0.223138i	−0.923223	+	0.384264i	$0.874455\pi$
$20$	0.438447			0.0980398
$21$		0			0
$22$	4.00000			0.852803
$23$	2.56155	+	4.43674i	0.534121	+	0.925124i	0.999205	+	0.0398580i	$0.0126905\pi$
$23$	2.56155	+	4.43674i	0.534121	+	0.925124i	−0.465085	+	0.885266i	$0.653976\pi$
$24$	−3.12311	+	5.40938i	−0.637501	+	1.10418i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−3.56155	−	6.16879i	−0.698478	−	1.20980i
$27$	−1.43845			−0.276829
$28$		0			0
$29$	−5.68466			−1.05561			−0.527807	−	0.849364i	$-0.676986\pi$
$29$	−5.68466			−1.05561			−0.527807	+	0.849364i	$0.676986\pi$
$30$	2.00000	+	3.46410i	0.365148	+	0.632456i
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	1.21922	−	2.11176i	0.215530	−	0.373309i
$33$	3.28078	+	5.68247i	0.571110	+	0.989191i
$34$	−7.12311			−1.22160
$35$		0			0
$36$	1.56155			0.260259
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	0.506772	−	0.862080i	$-0.330838\pi$
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	−0.999969	+	0.00783774i	$0.997505\pi$
$38$	−0.876894	+	1.51883i	−0.142251	+	0.246386i
$39$	5.84233	−	10.1192i	0.935521	−	1.62037i
$40$	1.21922	+	2.11176i	0.192776	+	0.333898i
$41$	−3.12311			−0.487747			−0.243874	−	0.969807i	$-0.578418\pi$
$41$	−3.12311			−0.487747			−0.243874	+	0.969807i	$0.578418\pi$
$42$		0			0
$43$	9.12311			1.39126			0.695630	−	0.718400i	$-0.255125\pi$
$43$	9.12311			1.39126			0.695630	+	0.718400i	$0.255125\pi$
$44$	−0.561553	−	0.972638i	−0.0846573	−	0.146631i
$45$	−1.78078	+	3.08440i	−0.265462	+	0.459794i
$46$	4.00000	−	6.92820i	0.589768	−	1.02151i
$47$	−1.84233	−	3.19101i	−0.268731	−	0.465456i	0.699803	−	0.714336i	$-0.253271\pi$
$47$	−1.84233	−	3.19101i	−0.268731	−	0.465456i	−0.968534	+	0.248879i	$0.919938\pi$
$48$	12.0000			1.73205
$49$		0			0
$50$	1.56155			0.220837
$51$	−5.84233	−	10.1192i	−0.818090	−	1.41697i
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−1.56155	+	2.70469i	−0.214496	+	0.371518i	−0.953116	−	0.302604i	$-0.902144\pi$
$53$	−1.56155	+	2.70469i	−0.214496	+	0.371518i	0.738621	+	0.674121i	$0.235477\pi$
$54$	1.12311	+	1.94528i	0.152835	+	0.264719i
$55$	2.56155			0.345400
$56$		0			0
$57$	−2.87689			−0.381054
$58$	4.43845	+	7.68762i	0.582797	+	1.00943i
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$	0.561553	−	0.972638i	0.0724962	−	0.125567i
$61$	4.68466	+	8.11407i	0.599809	+	1.03890i	0.992849	+	0.119378i	$0.0380901\pi$
$61$	4.68466	+	8.11407i	0.599809	+	1.03890i	−0.393040	+	0.919521i	$0.628577\pi$
$62$		0			0
$63$		0			0
$64$	5.56155			0.695194
$65$	−2.28078	−	3.95042i	−0.282895	−	0.489989i
$66$	5.12311	−	8.87348i	0.630611	−	1.09225i
$67$	3.12311	−	5.40938i	0.381548	−	0.660861i	−0.609736	−	0.792605i	$-0.708724\pi$
$67$	3.12311	−	5.40938i	0.381548	−	0.660861i	0.991284	+	0.131744i	$0.0420577\pi$
$68$	1.00000	+	1.73205i	0.121268	+	0.210042i
$69$	13.1231			1.57984
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$	4.34233	+	7.52113i	0.511748	+	0.886374i
$73$	−2.12311	+	3.67733i	−0.248491	+	0.430399i	−0.963107	−	0.269118i	$-0.913268\pi$
$73$	−2.12311	+	3.67733i	−0.248491	+	0.430399i	0.714617	+	0.699516i	$0.246601\pi$
$74$	−4.68466	+	8.11407i	−0.544580	+	0.943241i
$75$	1.28078	+	2.21837i	0.147891	+	0.256155i
$76$	0.492423			0.0564847
$77$		0			0
$78$	−18.2462			−2.06598
$79$	3.28078	+	5.68247i	0.369116	+	0.639328i	0.989428	−	0.145028i	$-0.0463271\pi$
$79$	3.28078	+	5.68247i	0.369116	+	0.639328i	−0.620311	+	0.784356i	$0.712994\pi$
$80$	2.34233	−	4.05703i	0.261880	−	0.453590i
$81$	3.50000	−	6.06218i	0.388889	−	0.673575i
$82$	2.43845	+	4.22351i	0.269281	+	0.466409i
$83$	4.00000			0.439057			0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000			0.439057			0.219529	+	0.975606i	$0.429548\pi$
$84$		0			0
$85$	−4.56155			−0.494770
$86$	−7.12311	−	12.3376i	−0.768104	−	1.33040i
$87$	−7.28078	+	12.6107i	−0.780581	+	1.35201i
$88$	3.12311	−	5.40938i	0.332924	−	0.576642i
$89$	−3.56155	−	6.16879i	−0.377524	−	0.653890i	0.613177	−	0.789945i	$-0.289891\pi$
$89$	−3.56155	−	6.16879i	−0.377524	−	0.653890i	−0.990701	+	0.136055i	$0.956558\pi$
$90$	5.56155			0.586239
$91$		0			0
$92$	−2.24621			−0.234184
$93$		0			0
$94$	−2.87689	+	4.98293i	−0.296729	+	0.513950i
$95$	−0.561553	+	0.972638i	−0.0576141	+	0.0997906i
$96$	−3.12311	−	5.40938i	−0.318751	−	0.552092i
$97$	−14.8078			−1.50350			−0.751750	−	0.659448i	$-0.770790\pi$
$97$	−14.8078			−1.50350			−0.751750	+	0.659448i	$0.770790\pi$
$98$		0			0
$99$	9.12311			0.916907
$100$	−0.219224	−	0.379706i	−0.0219224	−	0.0379706i
$101$	−0.123106	+	0.213225i	−0.0122495	+	0.0212167i	−0.872085	−	0.489354i	$-0.837233\pi$
$101$	−0.123106	+	0.213225i	−0.0122495	+	0.0212167i	0.859836	+	0.510571i	$0.170566\pi$
$102$	−9.12311	+	15.8017i	−0.903322	+	1.56460i
$103$	−0.719224	−	1.24573i	−0.0708672	−	0.122746i	0.828414	−	0.560116i	$-0.189243\pi$
$103$	−0.719224	−	1.24573i	−0.0708672	−	0.122746i	−0.899282	+	0.437370i	$0.855910\pi$
$104$	−11.1231			−1.09071
$105$		0			0
$106$	4.87689			0.473686
$107$	5.68466	+	9.84612i	0.549557	+	0.951860i	0.998305	+	0.0582018i	$0.0185367\pi$
$107$	5.68466	+	9.84612i	0.549557	+	0.951860i	−0.448748	+	0.893658i	$0.648130\pi$
$108$	0.315342	−	0.546188i	0.0303438	−	0.0525569i
$109$	−8.84233	+	15.3154i	−0.846942	+	1.46695i	0.0369828	+	0.999316i	$0.488225\pi$
$109$	−8.84233	+	15.3154i	−0.846942	+	1.46695i	−0.883924	+	0.467630i	$0.845108\pi$
$110$	−2.00000	−	3.46410i	−0.190693	−	0.330289i
$111$	−15.3693			−1.45879
$112$		0			0
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$	2.24621	+	3.89055i	0.210377	+	0.364384i
$115$	2.56155	−	4.43674i	0.238866	−	0.413728i
$116$	1.24621	−	2.15850i	0.115708	−	0.200412i
$117$	−8.12311	−	14.0696i	−0.750981	−	1.30074i
$118$	−6.24621			−0.575010
$119$		0			0
$120$	6.24621			0.570198
$121$	2.21922	+	3.84381i	0.201748	+	0.349437i
$122$	7.31534	−	12.6705i	0.662300	−	1.14714i
$123$	−4.00000	+	6.92820i	−0.360668	+	0.624695i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	10.2462			0.909204			0.454602	−	0.890695i	$-0.349781\pi$
$127$	10.2462			0.909204			0.454602	+	0.890695i	$0.349781\pi$
$128$	−6.78078	−	11.7446i	−0.599342	−	1.03809i
$129$	11.6847	−	20.2384i	1.02878	−	1.78189i
$130$	−3.56155	+	6.16879i	−0.312369	+	0.541039i
$131$	4.56155	+	7.90084i	0.398545	+	0.690300i	0.993547	−	0.113425i	$-0.0361820\pi$
$131$	4.56155	+	7.90084i	0.398545	+	0.690300i	−0.595002	+	0.803724i	$0.702849\pi$
$132$	−2.87689			−0.250402
$133$		0			0
$134$	−9.75379			−0.842599
$135$	0.719224	+	1.24573i	0.0619009	+	0.107216i
$136$	−5.56155	+	9.63289i	−0.476899	+	0.826014i
$137$	4.43845	−	7.68762i	0.379202	−	0.656797i	−0.611744	−	0.791056i	$-0.709532\pi$
$137$	4.43845	−	7.68762i	0.379202	−	0.656797i	0.990946	+	0.134258i	$0.0428652\pi$
$138$	−10.2462	−	17.7470i	−0.872215	−	1.51072i
$139$	−6.87689			−0.583291			−0.291645	−	0.956527i	$-0.594203\pi$
$139$	−6.87689			−0.583291			−0.291645	+	0.956527i	$0.594203\pi$
$140$		0			0
$141$	−9.43845			−0.794861
$142$	−6.24621	−	10.8188i	−0.524170	−	0.907890i
$143$	−5.84233	+	10.1192i	−0.488560	+	0.846211i
$144$	8.34233	−	14.4493i	0.695194	−	1.20411i
$145$	2.84233	+	4.92306i	0.236043	+	0.408838i
$146$	6.63068			0.548759
$147$		0			0
$148$	2.63068			0.216241
$149$	2.12311	+	3.67733i	0.173932	+	0.301258i	0.939791	−	0.341750i	$-0.111020\pi$
$149$	2.12311	+	3.67733i	0.173932	+	0.301258i	−0.765859	+	0.643008i	$0.777686\pi$
$150$	2.00000	−	3.46410i	0.163299	−	0.282843i
$151$	−10.9654	+	18.9927i	−0.892354	+	1.54560i	−0.0553094	+	0.998469i	$0.517615\pi$
$151$	−10.9654	+	18.9927i	−0.892354	+	1.54560i	−0.837045	+	0.547134i	$0.815719\pi$
$152$	1.36932	+	2.37173i	0.111066	+	0.192372i
$153$	−16.2462			−1.31343
$154$		0			0
$155$		0			0
$156$	2.56155	+	4.43674i	0.205088	+	0.355223i
$157$	−1.87689	+	3.25088i	−0.149792	+	0.259448i	−0.931151	−	0.364635i	$-0.881194\pi$
$157$	−1.87689	+	3.25088i	−0.149792	+	0.259448i	0.781358	+	0.624083i	$0.214527\pi$
$158$	5.12311	−	8.87348i	0.407572	−	0.705936i
$159$	4.00000	+	6.92820i	0.317221	+	0.549442i
$160$	−2.43845			−0.192776
$161$		0			0
$162$	−10.9309			−0.858810
$163$	−0.561553	−	0.972638i	−0.0439842	−	0.0761829i	0.843195	−	0.537608i	$-0.180672\pi$
$163$	−0.561553	−	0.972638i	−0.0439842	−	0.0761829i	−0.887179	+	0.461425i	$0.847338\pi$
$164$	0.684658	−	1.18586i	0.0534628	−	0.0926004i
$165$	3.28078	−	5.68247i	0.255408	−	0.442380i
$166$	−3.12311	−	5.40938i	−0.242400	−	0.419849i
$167$	21.9309			1.69706			0.848531	−	0.529146i	$-0.177488\pi$
$167$	21.9309			1.69706			0.848531	+	0.529146i	$0.177488\pi$
$168$		0			0
$169$	7.80776			0.600597
$170$	3.56155	+	6.16879i	0.273159	+	0.473125i
$171$	−2.00000	+	3.46410i	−0.152944	+	0.264906i
$172$	−2.00000	+	3.46410i	−0.152499	+	0.264135i
$173$	4.28078	+	7.41452i	0.325461	+	0.563716i	0.981606	−	0.190920i	$-0.0611470\pi$
$173$	4.28078	+	7.41452i	0.325461	+	0.563716i	−0.656144	+	0.754636i	$0.727814\pi$
$174$	22.7386			1.72381
$175$		0			0
$176$	−12.0000			−0.904534
$177$	−5.12311	−	8.87348i	−0.385076	−	0.666972i
$178$	−5.56155	+	9.63289i	−0.416856	+	0.722016i
$179$	−10.0000	+	17.3205i	−0.747435	+	1.29460i	0.201613	+	0.979465i	$0.435382\pi$
$179$	−10.0000	+	17.3205i	−0.747435	+	1.29460i	−0.949048	+	0.315130i	$0.897952\pi$
$180$	−0.780776	−	1.35234i	−0.0581956	−	0.100798i
$181$	23.6155			1.75533			0.877664	−	0.479276i	$-0.159101\pi$
$181$	23.6155			1.75533			0.877664	+	0.479276i	$0.159101\pi$
$182$		0			0
$183$	24.0000			1.77413
$184$	−6.24621	−	10.8188i	−0.460477	−	0.797569i
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$		0			0
$187$	5.84233	+	10.1192i	0.427233	+	0.739990i
$188$	1.61553			0.117824
$189$		0			0
$190$	1.75379			0.127233
$191$	4.71922	+	8.17394i	0.341471	+	0.591445i	0.984706	−	0.174224i	$-0.0557415\pi$
$191$	4.71922	+	8.17394i	0.341471	+	0.591445i	−0.643235	+	0.765669i	$0.722408\pi$
$192$	7.12311	−	12.3376i	0.514066	−	0.890388i
$193$	2.68466	−	4.64996i	0.193246	−	0.334712i	−0.753078	−	0.657931i	$-0.771432\pi$
$193$	2.68466	−	4.64996i	0.193246	−	0.334712i	0.946324	+	0.323219i	$0.104765\pi$
$194$	11.5616	+	20.0252i	0.830071	+	1.43773i
$195$	−11.6847			−0.836756
$196$		0			0
$197$	−7.12311			−0.507500			−0.253750	−	0.967270i	$-0.581664\pi$
$197$	−7.12311			−0.507500			−0.253750	+	0.967270i	$0.581664\pi$
$198$	−7.12311	−	12.3376i	−0.506217	−	0.876794i
$199$	9.12311	−	15.8017i	0.646720	−	1.12015i	−0.337182	−	0.941440i	$-0.609474\pi$
$199$	9.12311	−	15.8017i	0.646720	−	1.12015i	0.983901	−	0.178712i	$-0.0571930\pi$
$200$	1.21922	−	2.11176i	0.0862121	−	0.149324i
$201$	−8.00000	−	13.8564i	−0.564276	−	0.977356i
$202$	0.384472			0.0270513
$203$		0			0
$204$	5.12311			0.358689
$205$	1.56155	+	2.70469i	0.109064	+	0.188904i
$206$	−1.12311	+	1.94528i	−0.0782505	+	0.135534i
$207$	9.12311	−	15.8017i	0.634100	−	1.09829i
$208$	10.6847	+	18.5064i	0.740848	+	1.28319i
$209$	2.87689			0.198999
$210$		0			0
$211$	−23.0540			−1.58710			−0.793551	−	0.608504i	$-0.791770\pi$
$211$	−23.0540			−1.58710			−0.793551	+	0.608504i	$0.791770\pi$
$212$	−0.684658	−	1.18586i	−0.0470225	−	0.0814454i
$213$	10.2462	−	17.7470i	0.702059	−	1.21600i
$214$	8.87689	−	15.3752i	0.606812	−	1.05103i
$215$	−4.56155	−	7.90084i	−0.311095	−	0.538833i
$216$	3.50758			0.238660
$217$		0			0
$218$	27.6155			1.87036
$219$	5.43845	+	9.41967i	0.367496	+	0.636522i
$220$	−0.561553	+	0.972638i	−0.0378599	+	0.0655752i
$221$	10.4039	−	18.0201i	0.699841	−	1.21216i
$222$	12.0000	+	20.7846i	0.805387	+	1.39497i
$223$	−6.56155			−0.439394			−0.219697	−	0.975568i	$-0.570507\pi$
$223$	−6.56155			−0.439394			−0.219697	+	0.975568i	$0.570507\pi$
$224$		0			0
$225$	3.56155			0.237437
$226$	10.9309	+	18.9328i	0.727111	+	1.25939i
$227$	−11.8423	+	20.5115i	−0.786003	+	1.36140i	0.142395	+	0.989810i	$0.454520\pi$
$227$	−11.8423	+	20.5115i	−0.786003	+	1.36140i	−0.928398	+	0.371587i	$0.878814\pi$
$228$	0.630683	−	1.09238i	0.0417680	−	0.0723443i
$229$	−9.56155	−	16.5611i	−0.631845	−	1.09439i	−0.987174	−	0.159647i	$-0.948965\pi$
$229$	−9.56155	−	16.5611i	−0.631845	−	1.09439i	0.355329	−	0.934741i	$-0.384369\pi$
$230$	−8.00000			−0.527504
$231$		0			0
$232$	13.8617			0.910068
$233$	1.56155	+	2.70469i	0.102301	+	0.177190i	0.912632	−	0.408782i	$-0.134046\pi$
$233$	1.56155	+	2.70469i	0.102301	+	0.177190i	−0.810331	+	0.585972i	$0.800713\pi$
$234$	−12.6847	+	21.9705i	−0.829222	+	1.43625i
$235$	−1.84233	+	3.19101i	−0.120180	+	0.208158i
$236$	0.876894	+	1.51883i	0.0570810	+	0.0988671i
$237$	16.8078			1.09178
$238$		0			0
$239$	−0.807764			−0.0522499			−0.0261250	−	0.999659i	$-0.508317\pi$
$239$	−0.807764			−0.0522499			−0.0261250	+	0.999659i	$0.508317\pi$
$240$	−6.00000	−	10.3923i	−0.387298	−	0.670820i
$241$	−6.12311	+	10.6055i	−0.394424	+	0.683162i	−0.993027	−	0.117883i	$-0.962389\pi$
$241$	−6.12311	+	10.6055i	−0.394424	+	0.683162i	0.598604	+	0.801045i	$0.295722\pi$
$242$	3.46543	−	6.00231i	0.222767	−	0.385843i
$243$	−11.1231	−	19.2658i	−0.713548	−	1.23590i
$244$	−4.10795			−0.262985
$245$		0			0
$246$	12.4924			0.796488
$247$	−2.56155	−	4.43674i	−0.162988	−	0.282303i
$248$		0			0
$249$	5.12311	−	8.87348i	0.324664	−	0.562334i
$250$	−0.780776	−	1.35234i	−0.0493806	−	0.0855298i
$251$	−17.1231			−1.08080			−0.540400	−	0.841408i	$-0.681727\pi$
$251$	−17.1231			−1.08080			−0.540400	+	0.841408i	$0.681727\pi$
$252$		0			0
$253$	−13.1231			−0.825043
$254$	−8.00000	−	13.8564i	−0.501965	−	0.869428i
$255$	−5.84233	+	10.1192i	−0.365861	+	0.633690i
$256$	−5.02699	+	8.70700i	−0.314187	+	0.544187i
$257$	−11.2462	−	19.4790i	−0.701519	−	1.21507i	−0.967933	−	0.251208i	$-0.919172\pi$
$257$	−11.2462	−	19.4790i	−0.701519	−	1.21507i	0.266414	−	0.963859i	$-0.414161\pi$
$258$	−36.4924			−2.27192
$259$		0			0
$260$	2.00000			0.124035
$261$	10.1231	+	17.5337i	0.626605	+	1.08531i
$262$	7.12311	−	12.3376i	0.440067	−	0.762218i
$263$	10.5616	−	18.2931i	0.651253	−	1.12800i	−0.331566	−	0.943432i	$-0.607577\pi$
$263$	10.5616	−	18.2931i	0.651253	−	1.12800i	0.982819	−	0.184572i	$-0.0590898\pi$
$264$	−8.00000	−	13.8564i	−0.492366	−	0.852803i
$265$	3.12311			0.191851
$266$		0			0
$267$	−18.2462			−1.11665
$268$	1.36932	+	2.37173i	0.0836443	+	0.144876i
$269$	−14.3693	+	24.8884i	−0.876113	+	1.51747i	−0.0205400	+	0.999789i	$0.506539\pi$
$269$	−14.3693	+	24.8884i	−0.876113	+	1.51747i	−0.855573	+	0.517683i	$0.826795\pi$
$270$	1.12311	−	1.94528i	0.0683500	−	0.118386i
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$	21.3693			1.29571
$273$		0			0
$274$	−13.8617			−0.837418
$275$	−1.28078	−	2.21837i	−0.0772337	−	0.133773i
$276$	−2.87689	+	4.98293i	−0.173169	+	0.299937i
$277$	−8.12311	+	14.0696i	−0.488070	+	0.845362i	−0.999906	−	0.0137211i	$-0.995632\pi$
$277$	−8.12311	+	14.0696i	−0.488070	+	0.845362i	0.511836	+	0.859083i	$0.328966\pi$
$278$	5.36932	+	9.29993i	0.322030	+	0.557773i
$279$		0			0
$280$		0			0
$281$	16.5616			0.987979			0.493990	−	0.869468i	$-0.335538\pi$
$281$	16.5616			0.987979			0.493990	+	0.869468i	$0.335538\pi$
$282$	7.36932	+	12.7640i	0.438836	+	0.760087i
$283$	11.8423	−	20.5115i	0.703953	−	1.21928i	−0.263115	−	0.964765i	$-0.584750\pi$
$283$	11.8423	−	20.5115i	0.703953	−	1.21928i	0.967068	−	0.254518i	$-0.0819170\pi$
$284$	−1.75379	+	3.03765i	−0.104068	+	0.180251i
$285$	1.43845	+	2.49146i	0.0852063	+	0.147582i
$286$	18.2462			1.07892
$287$		0			0
$288$	−8.68466			−0.511748
$289$	−1.90388	−	3.29762i	−0.111993	−	0.193978i
$290$	4.43845	−	7.68762i	0.260635	−	0.451432i
$291$	−18.9654	+	32.8491i	−1.11177	+	1.92565i
$292$	−0.930870	−	1.61231i	−0.0544750	−	0.0943535i
$293$	9.68466			0.565784			0.282892	−	0.959152i	$-0.408706\pi$
$293$	9.68466			0.565784			0.282892	+	0.959152i	$0.408706\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$	7.31534	+	12.6705i	0.425196	+	0.736460i
$297$	1.84233	−	3.19101i	0.106903	−	0.185161i
$298$	3.31534	−	5.74234i	0.192053	−	0.332645i
$299$	11.6847	+	20.2384i	0.675741	+	1.17042i
$300$	−1.12311			−0.0648425
$301$		0			0
$302$	34.2462			1.97065
$303$	0.315342	+	0.546188i	0.0181159	+	0.0313777i
$304$	2.63068	−	4.55648i	0.150880	−	0.261332i
$305$	4.68466	−	8.11407i	0.268243	−	0.464610i
$306$	12.6847	+	21.9705i	0.725134	+	1.25597i
$307$	−31.6847			−1.80834			−0.904169	−	0.427174i	$-0.859509\pi$
$307$	−31.6847			−1.80834			−0.904169	+	0.427174i	$0.859509\pi$
$308$		0			0
$309$	−3.68466			−0.209613
$310$		0			0
$311$	4.80776	−	8.32729i	0.272623	−	0.472197i	−0.696909	−	0.717159i	$-0.745442\pi$
$311$	4.80776	−	8.32729i	0.272623	−	0.472197i	0.969533	+	0.244962i	$0.0787754\pi$
$312$	−14.2462	+	24.6752i	−0.806533	+	1.39696i
$313$	−15.6501	−	27.1068i	−0.884596	−	1.53216i	−0.846176	−	0.532903i	$-0.821101\pi$
$313$	−15.6501	−	27.1068i	−0.884596	−	1.53216i	−0.0384191	−	0.999262i	$-0.512232\pi$
$314$	5.86174			0.330797
$315$		0			0
$316$	−2.87689			−0.161838
$317$	11.2462	+	19.4790i	0.631650	+	1.09405i	0.987214	+	0.159398i	$0.0509554\pi$
$317$	11.2462	+	19.4790i	0.631650	+	1.09405i	−0.355564	+	0.934652i	$0.615711\pi$
$318$	6.24621	−	10.8188i	0.350270	−	0.606686i
$319$	7.28078	−	12.6107i	0.407645	−	0.706062i
$320$	−2.78078	−	4.81645i	−0.155450	−	0.269248i
$321$	29.1231			1.62549
$322$		0			0
$323$	−5.12311			−0.285057
$324$	1.53457	+	2.65794i	0.0852536	+	0.147664i
$325$	−2.28078	+	3.95042i	−0.126515	+	0.219130i
$326$	−0.876894	+	1.51883i	−0.0485667	+	0.0841200i
$327$	22.6501	+	39.2311i	1.25255	+	2.16949i
$328$	7.61553			0.420497
$329$		0			0
$330$	−10.2462			−0.564035
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	0.652680	−	0.757634i	$-0.273645\pi$
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	−0.982470	+	0.186421i	$0.940311\pi$
$332$	−0.876894	+	1.51883i	−0.0481258	+	0.0833564i
$333$	−10.6847	+	18.5064i	−0.585516	+	1.01414i
$334$	−17.1231	−	29.6581i	−0.936935	−	1.62282i
$335$	−6.24621			−0.341267
$336$		0			0
$337$	−34.4924			−1.87892			−0.939461	−	0.342656i	$-0.888674\pi$
$337$	−34.4924			−1.87892			−0.939461	+	0.342656i	$0.888674\pi$
$338$	−6.09612	−	10.5588i	−0.331585	−	0.574322i
$339$	−17.9309	+	31.0572i	−0.973871	+	1.68679i
$340$	1.00000	−	1.73205i	0.0542326	−	0.0939336i
$341$		0			0
$342$	6.24621			0.337756
$343$		0			0
$344$	−22.2462			−1.19944
$345$	−6.56155	−	11.3649i	−0.353262	−	0.611868i
$346$	6.68466	−	11.5782i	0.359369	−	0.622446i
$347$	0.561553	−	0.972638i	0.0301457	−	0.0522139i	−0.850559	−	0.525880i	$-0.823736\pi$
$347$	0.561553	−	0.972638i	0.0301457	−	0.0522139i	0.880705	+	0.473666i	$0.157070\pi$
$348$	−3.19224	−	5.52911i	−0.171122	−	0.296392i
$349$	−22.4924			−1.20399			−0.601996	−	0.798499i	$-0.705628\pi$
$349$	−22.4924			−1.20399			−0.601996	+	0.798499i	$0.705628\pi$
$350$		0			0
$351$	−6.56155			−0.350230
$352$	3.12311	+	5.40938i	0.166462	+	0.288321i
$353$	7.40388	−	12.8239i	0.394069	−	0.682547i	−0.598913	−	0.800814i	$-0.704400\pi$
$353$	7.40388	−	12.8239i	0.394069	−	0.682547i	0.992982	+	0.118267i	$0.0377338\pi$
$354$	−8.00000	+	13.8564i	−0.425195	+	0.736460i
$355$	−4.00000	−	6.92820i	−0.212298	−	0.367711i
$356$	3.12311			0.165524
$357$		0			0
$358$	31.2311			1.65061
$359$	−4.00000	−	6.92820i	−0.211112	−	0.365657i	0.740951	−	0.671559i	$-0.234375\pi$
$359$	−4.00000	−	6.92820i	−0.211112	−	0.365657i	−0.952063	+	0.305903i	$0.901042\pi$
$360$	4.34233	−	7.52113i	0.228861	−	0.396399i
$361$	8.86932	−	15.3621i	0.466806	−	0.808532i
$362$	−18.4384	−	31.9363i	−0.969103	−	1.67854i
$363$	11.3693			0.596734
$364$		0			0
$365$	4.24621			0.222257
$366$	−18.7386	−	32.4563i	−0.979484	−	1.69652i
$367$	−1.84233	+	3.19101i	−0.0961688	+	0.166569i	−0.910096	−	0.414398i	$-0.863992\pi$
$367$	−1.84233	+	3.19101i	−0.0961688	+	0.166569i	0.813927	+	0.580967i	$0.197326\pi$
$368$	−12.0000	+	20.7846i	−0.625543	+	1.08347i
$369$	5.56155	+	9.63289i	0.289523	+	0.501468i
$370$	9.36932			0.487088
$371$		0			0
$372$		0			0
$373$	−14.6847	−	25.4346i	−0.760343	−	1.31695i	−0.942674	−	0.333715i	$-0.891698\pi$
$373$	−14.6847	−	25.4346i	−0.760343	−	1.31695i	0.182331	−	0.983237i	$-0.441636\pi$
$374$	9.12311	−	15.8017i	0.471745	−	0.817086i
$375$	1.28078	−	2.21837i	0.0661390	−	0.114556i
$376$	4.49242	+	7.78110i	0.231679	+	0.401280i
$377$	−25.9309			−1.33551
$378$		0			0
$379$	16.4924			0.847159			0.423579	−	0.905859i	$-0.360773\pi$
$379$	16.4924			0.847159			0.423579	+	0.905859i	$0.360773\pi$
$380$	−0.246211	−	0.426450i	−0.0126304	−	0.0218764i
$381$	13.1231	−	22.7299i	0.672317	−	1.16449i
$382$	7.36932	−	12.7640i	0.377047	−	0.653065i
$383$	5.12311	+	8.87348i	0.261778	+	0.453414i	0.966715	−	0.255857i	$-0.0823577\pi$
$383$	5.12311	+	8.87348i	0.261778	+	0.453414i	−0.704936	+	0.709271i	$0.749024\pi$
$384$	−34.7386			−1.77275
$385$		0			0
$386$	−8.38447			−0.426758
$387$	−16.2462	−	28.1393i	−0.825841	−	1.43040i
$388$	3.24621	−	5.62260i	0.164801	−	0.285444i
$389$	−1.96543	+	3.40423i	−0.0996515	+	0.172601i	−0.911540	−	0.411210i	$-0.865106\pi$
$389$	−1.96543	+	3.40423i	−0.0996515	+	0.172601i	0.811889	+	0.583812i	$0.198439\pi$
$390$	9.12311	+	15.8017i	0.461966	+	0.800149i
$391$	23.3693			1.18184
$392$		0			0
$393$	23.3693			1.17883
$394$	5.56155	+	9.63289i	0.280187	+	0.485298i
$395$	3.28078	−	5.68247i	0.165074	−	0.285916i
$396$	−2.00000	+	3.46410i	−0.100504	+	0.174078i
$397$	−11.7192	−	20.2983i	−0.588171	−	1.01874i	−0.994472	−	0.105003i	$-0.966515\pi$
$397$	−11.7192	−	20.2983i	−0.588171	−	1.01874i	0.406301	−	0.913739i	$-0.366818\pi$
$398$	−28.4924			−1.42820
$399$		0			0
$400$	−4.68466			−0.234233
$401$	−13.7192	−	23.7624i	−0.685105	−	1.18664i	−0.973404	−	0.229097i	$-0.926423\pi$
$401$	−13.7192	−	23.7624i	−0.685105	−	1.18664i	0.288298	−	0.957541i	$-0.406911\pi$
$402$	−12.4924	+	21.6375i	−0.623065	+	1.07918i
$403$		0			0
$404$	−0.0539753	−	0.0934880i	−0.00268537	−	0.00465120i
$405$	−7.00000			−0.347833
$406$		0			0
$407$	15.3693			0.761829
$408$	14.2462	+	24.6752i	0.705293	+	1.22160i
$409$	13.2462	−	22.9431i	0.654983	−	1.13446i	−0.326915	−	0.945054i	$-0.606009\pi$
$409$	13.2462	−	22.9431i	0.654983	−	1.13446i	0.981898	−	0.189410i	$-0.0606576\pi$
$410$	2.43845	−	4.22351i	0.120426	−	0.208585i
$411$	−11.3693	−	19.6922i	−0.560807	−	0.971346i
$412$	0.630683			0.0310715
$413$		0			0
$414$	−28.4924			−1.40033
$415$	−2.00000	−	3.46410i	−0.0981761	−	0.170046i
$416$	5.56155	−	9.63289i	0.272678	−	0.472291i
$417$	−8.80776	+	15.2555i	−0.431318	+	0.747065i
$418$	−2.24621	−	3.89055i	−0.109866	−	0.190293i
$419$	9.75379			0.476504			0.238252	−	0.971203i	$-0.423426\pi$
$419$	9.75379			0.476504			0.238252	+	0.971203i	$0.423426\pi$
$420$		0			0
$421$	9.68466			0.472001			0.236001	−	0.971753i	$-0.424163\pi$
$421$	9.68466			0.472001			0.236001	+	0.971753i	$0.424163\pi$
$422$	18.0000	+	31.1769i	0.876226	+	1.51767i
$423$	−6.56155	+	11.3649i	−0.319034	+	0.552582i
$424$	3.80776	−	6.59524i	0.184921	−	0.320293i
$425$	2.28078	+	3.95042i	0.110634	+	0.191624i
$426$	−32.0000			−1.55041
$427$		0			0
$428$	−4.98485			−0.240952
$429$	14.9654	+	25.9209i	0.722538	+	1.25147i
$430$	−7.12311	+	12.3376i	−0.343507	+	0.594971i
$431$	−0.403882	+	0.699544i	−0.0194543	+	0.0336959i	−0.875589	−	0.483057i	$-0.839526\pi$
$431$	−0.403882	+	0.699544i	−0.0194543	+	0.0336959i	0.856134	+	0.516753i	$0.172860\pi$
$432$	−3.36932	−	5.83583i	−0.162106	−	0.280776i
$433$	−8.24621			−0.396288			−0.198144	−	0.980173i	$-0.563491\pi$
$433$	−8.24621			−0.396288			−0.198144	+	0.980173i	$0.563491\pi$
$434$		0			0
$435$	14.5616			0.698173
$436$	−3.87689	−	6.71498i	−0.185670	−	0.321589i
$437$	2.87689	−	4.98293i	0.137621	−	0.238366i
$438$	8.49242	−	14.7093i	0.405784	−	0.702838i
$439$	7.68466	+	13.3102i	0.366769	+	0.635262i	0.989058	−	0.147525i	$-0.0471307\pi$
$439$	7.68466	+	13.3102i	0.366769	+	0.635262i	−0.622290	+	0.782787i	$0.713797\pi$
$440$	−6.24621			−0.297776
$441$		0			0
$442$	−32.4924			−1.54551
$443$	13.6847	+	23.7025i	0.650178	+	1.12614i	0.983080	+	0.183179i	$0.0586389\pi$
$443$	13.6847	+	23.7025i	0.650178	+	1.12614i	−0.332902	+	0.942962i	$0.608028\pi$
$444$	3.36932	−	5.83583i	0.159901	−	0.276956i
$445$	−3.56155	+	6.16879i	−0.168834	+	0.292429i
$446$	5.12311	+	8.87348i	0.242586	+	0.420171i
$447$	10.8769			0.514459
$448$		0			0
$449$	18.8078			0.887593			0.443797	−	0.896128i	$-0.353631\pi$
$449$	18.8078			0.887593			0.443797	+	0.896128i	$0.353631\pi$
$450$	−2.78078	−	4.81645i	−0.131087	−	0.227049i
$451$	4.00000	−	6.92820i	0.188353	−	0.326236i
$452$	3.06913	−	5.31589i	0.144360	−	0.250038i
$453$	28.0885	+	48.6508i	1.31971	+	2.28581i
$454$	36.9848			1.73578
$455$		0			0
$456$	7.01515			0.328515
$457$	4.43845	+	7.68762i	0.207622	+	0.359612i	0.950965	−	0.309299i	$-0.100094\pi$
$457$	4.43845	+	7.68762i	0.207622	+	0.359612i	−0.743343	+	0.668910i	$0.766761\pi$
$458$	−14.9309	+	25.8610i	−0.697674	+	1.20841i
$459$	−3.28078	+	5.68247i	−0.153134	+	0.265235i
$460$	1.12311	+	1.94528i	0.0523651	+	0.0906990i
$461$	−4.87689			−0.227140			−0.113570	−	0.993530i	$-0.536229\pi$
$461$	−4.87689			−0.227140			−0.113570	+	0.993530i	$0.536229\pi$
$462$		0			0
$463$	−20.4924			−0.952364			−0.476182	−	0.879347i	$-0.657980\pi$
$463$	−20.4924			−0.952364			−0.476182	+	0.879347i	$0.657980\pi$
$464$	−13.3153	−	23.0628i	−0.618149	−	1.07067i
$465$		0			0
$466$	2.43845	−	4.22351i	0.112959	−	0.195651i
$467$	−13.2808	−	23.0030i	−0.614561	−	1.06445i	−0.990461	−	0.137791i	$-0.956000\pi$
$467$	−13.2808	−	23.0030i	−0.614561	−	1.06445i	0.375900	−	0.926660i	$-0.377334\pi$
$468$	7.12311			0.329266
$469$		0			0
$470$	5.75379			0.265402
$471$	4.80776	+	8.32729i	0.221530	+	0.383701i
$472$	−4.87689	+	8.44703i	−0.224477	+	0.388806i
$473$	−11.6847	+	20.2384i	−0.537261	+	0.930564i
$474$	−13.1231	−	22.7299i	−0.602764	−	1.04402i
$475$	1.12311			0.0515316
$476$		0			0
$477$	11.1231			0.509292
$478$	0.630683	+	1.09238i	0.0288468	+	0.0499641i
$479$	−6.56155	+	11.3649i	−0.299805	+	0.519277i	−0.976091	−	0.217362i	$-0.930255\pi$
$479$	−6.56155	+	11.3649i	−0.299805	+	0.519277i	0.676286	+	0.736639i	$0.263588\pi$
$480$	−3.12311	+	5.40938i	−0.142550	+	0.246903i
$481$	−13.6847	−	23.7025i	−0.623967	−	1.08074i
$482$	19.1231			0.871034
$483$		0			0
$484$	−1.94602			−0.0884557
$485$	7.40388	+	12.8239i	0.336193	+	0.582303i
$486$	−17.3693	+	30.0845i	−0.787888	+	1.36466i
$487$	−2.56155	+	4.43674i	−0.116075	+	0.201048i	−0.918209	−	0.396096i	$-0.870365\pi$
$487$	−2.56155	+	4.43674i	−0.116075	+	0.201048i	0.802134	+	0.597144i	$0.203698\pi$
$488$	−11.4233	−	19.7857i	−0.517108	−	0.895658i
$489$	−2.87689			−0.130098
$490$		0			0
$491$	4.17708			0.188509			0.0942545	−	0.995548i	$-0.469953\pi$
$491$	4.17708			0.188509			0.0942545	+	0.995548i	$0.469953\pi$
$492$	−1.75379	−	3.03765i	−0.0790669	−	0.136948i
$493$	−12.9654	+	22.4568i	−0.583934	+	1.01140i
$494$	−4.00000	+	6.92820i	−0.179969	+	0.311715i
$495$	−4.56155	−	7.90084i	−0.205027	−	0.355116i
$496$		0			0
$497$		0			0
$498$	−16.0000			−0.716977
$499$	2.08854	+	3.61746i	0.0934959	+	0.161940i	0.908980	−	0.416840i	$-0.136862\pi$
$499$	2.08854	+	3.61746i	0.0934959	+	0.161940i	−0.815484	+	0.578780i	$0.803529\pi$
$500$	−0.219224	+	0.379706i	−0.00980398	+	0.0169810i
$501$	28.0885	−	48.6508i	1.25490	−	2.17356i
$502$	13.3693	+	23.1563i	0.596702	+	1.03352i
$503$	10.0691			0.448960			0.224480	−	0.974479i	$-0.427932\pi$
$503$	10.0691			0.448960			0.224480	+	0.974479i	$0.427932\pi$
$504$		0			0
$505$	0.246211			0.0109563
$506$	10.2462	+	17.7470i	0.455500	+	0.788949i
$507$	10.0000	−	17.3205i	0.444116	−	0.769231i
$508$	−2.24621	+	3.89055i	−0.0996595	+	0.172615i
$509$	14.1231	+	24.4619i	0.625996	+	1.08426i	0.988347	+	0.152215i	$0.0486406\pi$
$509$	14.1231	+	24.4619i	0.625996	+	1.08426i	−0.362352	+	0.932041i	$0.618026\pi$
$510$	18.2462			0.807956
$511$		0			0
$512$	−11.4233			−0.504843
$513$	0.807764	+	1.39909i	0.0356637	+	0.0617713i
$514$	−17.5616	+	30.4175i	−0.774607	+	1.34166i
$515$	−0.719224	+	1.24573i	−0.0316928	+	0.0548935i
$516$	5.12311	+	8.87348i	0.225532	+	0.390633i
$517$	9.43845			0.415102
$518$		0			0
$519$	21.9309			0.962658
$520$	5.56155	+	9.63289i	0.243890	+	0.422430i
$521$	−5.00000	+	8.66025i	−0.219054	+	0.379413i	−0.954519	−	0.298150i	$-0.903630\pi$
$521$	−5.00000	+	8.66025i	−0.219054	+	0.379413i	0.735465	+	0.677563i	$0.236964\pi$
$522$	15.8078	−	27.3799i	0.691887	−	1.19838i
$523$	−3.75379	−	6.50175i	−0.164142	−	0.284302i	0.772208	−	0.635369i	$-0.219152\pi$
$523$	−3.75379	−	6.50175i	−0.164142	−	0.284302i	−0.936350	+	0.351067i	$0.885819\pi$
$524$	−4.00000			−0.174741
$525$		0			0
$526$	−32.9848			−1.43821
$527$		0			0
$528$	−15.3693	+	26.6204i	−0.668864	+	1.15851i
$529$	−1.62311	+	2.81130i	−0.0705698	+	0.122230i
$530$	−2.43845	−	4.22351i	−0.105919	−	0.183458i
$531$	−14.2462			−0.618233
$532$		0			0
$533$	−14.2462			−0.617072
$534$	14.2462	+	24.6752i	0.616494	+	1.06780i
$535$	5.68466	−	9.84612i	0.245769	−	0.425685i
$536$	−7.61553	+	13.1905i	−0.328941	+	0.569742i
$537$	25.6155	+	44.3674i	1.10539	+	1.91459i
$538$	44.8769			1.93478
$539$		0			0
$540$	−0.630683			−0.0271403
$541$	8.59612	+	14.8889i	0.369576	+	0.640124i	0.989499	−	0.144538i	$-0.0461696\pi$
$541$	8.59612	+	14.8889i	0.369576	+	0.640124i	−0.619923	+	0.784662i	$0.712836\pi$
$542$	12.4924	−	21.6375i	0.536595	−	0.929411i
$543$	30.2462	−	52.3880i	1.29799	−	2.24818i
$544$	−5.56155	−	9.63289i	−0.238450	−	0.413007i
$545$	17.6847			0.757528
$546$		0			0
$547$	14.2462			0.609124			0.304562	−	0.952493i	$-0.401490\pi$
$547$	14.2462			0.609124			0.304562	+	0.952493i	$0.401490\pi$
$548$	1.94602	+	3.37061i	0.0831301	+	0.143985i
$549$	16.6847	−	28.8987i	0.712084	−	1.23337i
$550$	−2.00000	+	3.46410i	−0.0852803	+	0.147710i
$551$	3.19224	+	5.52911i	0.135994	+	0.235548i
$552$	−32.0000			−1.36201
$553$		0			0
$554$	25.3693			1.07784
$555$	7.68466	+	13.3102i	0.326196	+	0.564987i
$556$	1.50758	−	2.61120i	0.0639355	−	0.110740i
$557$	2.43845	−	4.22351i	0.103320	−	0.178956i	−0.809730	−	0.586802i	$-0.800387\pi$
$557$	2.43845	−	4.22351i	0.103320	−	0.178956i	0.913051	+	0.407846i	$0.133720\pi$
$558$		0			0
$559$	41.6155			1.76015
$560$		0			0
$561$	29.9309			1.26368
$562$	−12.9309	−	22.3969i	−0.545456	−	0.944757i
$563$	14.0000	−	24.2487i	0.590030	−	1.02196i	−0.404198	−	0.914671i	$-0.632449\pi$
$563$	14.0000	−	24.2487i	0.590030	−	1.02196i	0.994228	−	0.107290i	$-0.0342173\pi$
$564$	2.06913	−	3.58384i	0.0871261	−	0.150907i
$565$	7.00000	+	12.1244i	0.294492	+	0.510075i
$566$	−36.9848			−1.55459
$567$		0			0
$568$	−19.5076			−0.818520
$569$	−17.4924	−	30.2978i	−0.733320	−	1.27015i	−0.955456	−	0.295133i	$-0.904636\pi$
$569$	−17.4924	−	30.2978i	−0.733320	−	1.27015i	0.222136	−	0.975016i	$-0.428697\pi$
$570$	2.24621	−	3.89055i	0.0940834	−	0.162957i
$571$	−3.75379	+	6.50175i	−0.157091	+	0.272090i	−0.933819	−	0.357747i	$-0.883545\pi$
$571$	−3.75379	+	6.50175i	−0.157091	+	0.272090i	0.776727	+	0.629837i	$0.216878\pi$
$572$	−2.56155	−	4.43674i	−0.107104	−	0.185509i
$573$	24.1771			1.01001
$574$		0			0
$575$	−5.12311			−0.213648
$576$	−9.90388	−	17.1540i	−0.412662	−	0.714751i
$577$	−6.52699	+	11.3051i	−0.271722	+	0.470636i	−0.969303	−	0.245870i	$-0.920926\pi$
$577$	−6.52699	+	11.3051i	−0.271722	+	0.470636i	0.697581	+	0.716506i	$0.254260\pi$
$578$	−2.97301	+	5.14941i	−0.123661	+	0.214187i
$579$	−6.87689	−	11.9111i	−0.285794	−	0.495010i
$580$	−2.49242			−0.103492
$581$		0			0
$582$	59.2311			2.45521
$583$	−4.00000	−	6.92820i	−0.165663	−	0.286937i
$584$	5.17708	−	8.96697i	0.214229	−	0.371056i
$585$	−8.12311	+	14.0696i	−0.335849	+	0.581708i
$586$	−7.56155	−	13.0970i	−0.312365	−	0.541032i
$587$	−9.75379			−0.402582			−0.201291	−	0.979531i	$-0.564514\pi$
$587$	−9.75379			−0.402582			−0.201291	+	0.979531i	$0.564514\pi$
$588$		0			0
$589$		0			0
$590$	3.12311	+	5.40938i	0.128576	+	0.222701i
$591$	−9.12311	+	15.8017i	−0.375274	+	0.649994i
$592$	14.0540	−	24.3422i	0.577615	−	1.00046i
$593$	11.7192	+	20.2983i	0.481251	+	0.833551i	0.999769	−	0.0215160i	$-0.00684929\pi$
$593$	11.7192	+	20.2983i	0.481251	+	0.833551i	−0.518518	+	0.855067i	$0.673516\pi$
$594$	−5.75379			−0.236081
$595$		0			0
$596$	−1.86174			−0.0762598
$597$	−23.3693	−	40.4768i	−0.956442	−	1.65661i
$598$	18.2462	−	31.6034i	0.746143	−	1.29236i
$599$	−4.40388	+	7.62775i	−0.179938	+	0.311661i	−0.941859	−	0.336008i	$-0.890923\pi$
$599$	−4.40388	+	7.62775i	−0.179938	+	0.311661i	0.761921	+	0.647670i	$0.224256\pi$
$600$	−3.12311	−	5.40938i	−0.127500	−	0.220837i
$601$	−26.4924			−1.08065			−0.540324	−	0.841457i	$-0.681698\pi$
$601$	−26.4924			−1.08065			−0.540324	+	0.841457i	$0.681698\pi$
$602$		0			0
$603$	−22.2462			−0.905936
$604$	−4.80776	−	8.32729i	−0.195625	−	0.338833i
$605$	2.21922	−	3.84381i	0.0902243	−	0.156273i
$606$	0.492423	−	0.852901i	0.0200033	−	0.0346467i
$607$	2.47301	+	4.28338i	0.100376	+	0.173857i	0.911840	−	0.410546i	$-0.134662\pi$
$607$	2.47301	+	4.28338i	0.100376	+	0.173857i	−0.811463	+	0.584403i	$0.801329\pi$
$608$	−2.73863			−0.111066
$609$		0			0
$610$	−14.6307			−0.592379
$611$	−8.40388	−	14.5560i	−0.339985	−	0.588871i
$612$	3.56155	−	6.16879i	0.143967	−	0.249359i
$613$	4.36932	−	7.56788i	0.176475	−	0.305664i	−0.764196	−	0.644984i	$-0.776864\pi$
$613$	4.36932	−	7.56788i	0.176475	−	0.305664i	0.940671	+	0.339321i	$0.110197\pi$
$614$	24.7386	+	42.8486i	0.998370	+	1.72923i
$615$	8.00000			0.322591
$616$		0			0
$617$	15.7538			0.634224			0.317112	−	0.948388i	$-0.397287\pi$
$617$	15.7538			0.634224			0.317112	+	0.948388i	$0.397287\pi$
$618$	2.87689	+	4.98293i	0.115726	+	0.200443i
$619$	21.0540	−	36.4666i	0.846231	−	1.46571i	−0.0383174	−	0.999266i	$-0.512200\pi$
$619$	21.0540	−	36.4666i	0.846231	−	1.46571i	0.884548	−	0.466449i	$-0.154467\pi$
$620$		0			0
$621$	−3.68466	−	6.38202i	−0.147860	−	0.256101i
$622$	−15.0152			−0.602053
$623$		0			0
$624$	54.7386			2.19130
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−24.4384	+	42.3286i	−0.976757	+	1.69179i
$627$	3.68466	−	6.38202i	0.147151	−	0.254873i
$628$	−0.822919	−	1.42534i	−0.0328380	−	0.0568772i
$629$	−27.3693			−1.09129
$630$		0			0
$631$	8.80776			0.350632			0.175316	−	0.984512i	$-0.443905\pi$
$631$	8.80776			0.350632			0.175316	+	0.984512i	$0.443905\pi$
$632$	−8.00000	−	13.8564i	−0.318223	−	0.551178i
$633$	−29.5270	+	51.1422i	−1.17359	+	2.03272i
$634$	17.5616	−	30.4175i	0.697458	−	1.20803i
$635$	−5.12311	−	8.87348i	−0.203304	−	0.352133i
$636$	−3.50758			−0.139084
$637$		0			0
$638$	−22.7386			−0.900231
$639$	−14.2462	−	24.6752i	−0.563571	−	0.976134i
$640$	−6.78078	+	11.7446i	−0.268034	+	0.464248i
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	−0.885098	−	0.465404i	$-0.845909\pi$
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	0.845601	+	0.533816i	$0.179242\pi$
$642$	−22.7386	−	39.3845i	−0.897422	−	1.55438i
$643$	−2.56155			−0.101018			−0.0505089	−	0.998724i	$-0.516084\pi$
$643$	−2.56155			−0.101018			−0.0505089	+	0.998724i	$0.516084\pi$
$644$		0			0
$645$	−23.3693			−0.920166
$646$	4.00000	+	6.92820i	0.157378	+	0.272587i
$647$	−1.75379	+	3.03765i	−0.0689486	+	0.119422i	−0.898439	−	0.439099i	$-0.855298\pi$
$647$	−1.75379	+	3.03765i	−0.0689486	+	0.119422i	0.829490	+	0.558521i	$0.188631\pi$
$648$	−8.53457	+	14.7823i	−0.335269	+	0.580704i
$649$	5.12311	+	8.87348i	0.201099	+	0.348315i
$650$	7.12311			0.279391
$651$		0			0
$652$	0.492423			0.0192848
$653$	−24.6155	−	42.6353i	−0.963280	−	1.66845i	−0.714167	−	0.699976i	$-0.753194\pi$
$653$	−24.6155	−	42.6353i	−0.963280	−	1.66845i	−0.249113	−	0.968474i	$-0.580139\pi$
$654$	35.3693	−	61.2615i	1.38305	−	2.39551i
$655$	4.56155	−	7.90084i	0.178235	−	0.308711i
$656$	−7.31534	−	12.6705i	−0.285616	−	0.494702i
$657$	15.1231			0.590009
$658$		0			0
$659$	−36.1771			−1.40926			−0.704629	−	0.709575i	$-0.748887\pi$
$659$	−36.1771			−1.40926			−0.704629	+	0.709575i	$0.748887\pi$
$660$	1.43845	+	2.49146i	0.0559915	+	0.0969801i
$661$	−1.56155	+	2.70469i	−0.0607374	+	0.105200i	−0.894795	−	0.446477i	$-0.852679\pi$
$661$	−1.56155	+	2.70469i	−0.0607374	+	0.105200i	0.834058	+	0.551677i	$0.186012\pi$
$662$	−9.36932	+	16.2281i	−0.364149	+	0.630724i
$663$	−26.6501	−	46.1593i	−1.03500	−	1.79268i
$664$	−9.75379			−0.378520
$665$		0			0
$666$	33.3693			1.29303
$667$	−14.5616	−	25.2213i	−0.563826	−	0.976575i
$668$	−4.80776	+	8.32729i	−0.186018	+	0.322193i
$669$	−8.40388	+	14.5560i	−0.324913	+	0.562766i
$670$	4.87689	+	8.44703i	0.188411	+	0.326337i
$671$	−24.0000			−0.926510
$672$		0			0
$673$	−25.8617			−0.996897			−0.498448	−	0.866919i	$-0.666097\pi$
$673$	−25.8617			−0.996897			−0.498448	+	0.866919i	$0.666097\pi$
$674$	26.9309	+	46.6456i	1.03734	+	1.79672i
$675$	0.719224	−	1.24573i	0.0276829	−	0.0479482i
$676$	−1.71165	+	2.96466i	−0.0658325	+	0.114025i
$677$	11.9654	+	20.7247i	0.459869	+	0.796517i	0.998954	−	0.0457351i	$-0.0145630\pi$
$677$	11.9654	+	20.7247i	0.459869	+	0.796517i	−0.539085	+	0.842252i	$0.681230\pi$
$678$	56.0000			2.15067
$679$		0			0
$680$	11.1231			0.426552
$681$	30.3348	+	52.5413i	1.16243	+	2.01339i
$682$		0			0
$683$	−21.3693	+	37.0127i	−0.817674	+	1.41625i	0.0897175	+	0.995967i	$0.471404\pi$
$683$	−21.3693	+	37.0127i	−0.817674	+	1.41625i	−0.907392	+	0.420286i	$0.861930\pi$
$684$	−0.876894	−	1.51883i	−0.0335289	−	0.0580737i
$685$	−8.87689			−0.339169
$686$		0			0
$687$	−48.9848			−1.86889
$688$	21.3693	+	37.0127i	0.814698	+	1.41110i
$689$	−7.12311	+	12.3376i	−0.271369	+	0.470024i
$690$	−10.2462	+	17.7470i	−0.390067	+	0.675615i
$691$	−4.24621	−	7.35465i	−0.161533	−	0.279784i	0.773885	−	0.633326i	$-0.218311\pi$
$691$	−4.24621	−	7.35465i	−0.161533	−	0.279784i	−0.935419	+	0.353542i	$0.884977\pi$
$692$	−3.75379			−0.142698
$693$		0			0
$694$	−1.75379			−0.0665729
$695$	3.43845	+	5.95557i	0.130428	+	0.225907i
$696$	17.7538	−	30.7505i	0.672956	−	1.16559i
$697$	−7.12311	+	12.3376i	−0.269807	+	0.467319i
$698$	17.5616	+	30.4175i	0.664715	+	1.15132i
$699$	8.00000			0.302588
$700$		0			0
$701$	0.0691303			0.00261102			0.00130551	−	0.999999i	$-0.499584\pi$
$701$	0.0691303			0.00261102			0.00130551	+	0.999999i	$0.499584\pi$
$702$	5.12311	+	8.87348i	0.193359	+	0.334908i
$703$	−3.36932	+	5.83583i	−0.127076	+	0.220102i
$704$	−7.12311	+	12.3376i	−0.268462	+	0.464990i
$705$	4.71922	+	8.17394i	0.177736	+	0.307848i
$706$	−23.1231			−0.870250
$707$		0			0
$708$	4.49242			0.168836
$709$	9.08854	+	15.7418i	0.341327	+	0.591196i	0.984679	−	0.174374i	$-0.0557902\pi$
$709$	9.08854	+	15.7418i	0.341327	+	0.591196i	−0.643352	+	0.765570i	$0.722457\pi$
$710$	−6.24621	+	10.8188i	−0.234416	+	0.406021i
$711$	11.6847	−	20.2384i	0.438209	−	0.759000i
$712$	8.68466	+	15.0423i	0.325471	+	0.563733i
$713$		0			0
$714$		0			0
$715$	11.6847			0.436981
$716$	−4.38447	−	7.59413i	−0.163855	−	0.283806i
$717$	−1.03457	+	1.79192i	−0.0386365	+	0.0669205i
$718$	−6.24621	+	10.8188i	−0.233107	+	0.403752i
$719$	−24.8078	−	42.9683i	−0.925173	−	1.60245i	−0.791282	−	0.611451i	$-0.790586\pi$
$719$	−24.8078	−	42.9683i	−0.925173	−	1.60245i	−0.133892	−	0.990996i	$-0.542747\pi$
$720$	−16.6847			−0.621801
$721$		0			0
$722$	−27.6998			−1.03088
$723$	15.6847	+	27.1666i	0.583319	+	1.01034i
$724$	−5.17708	+	8.96697i	−0.192405	+	0.333255i
$725$	2.84233	−	4.92306i	0.105561	−	0.182838i
$726$	−8.87689	−	15.3752i	−0.329452	−	0.570628i
$727$	19.5076			0.723496			0.361748	−	0.932276i	$-0.382180\pi$
$727$	19.5076			0.723496			0.361748	+	0.932276i	$0.382180\pi$
$728$		0			0
$729$	−35.9848			−1.33277
$730$	−3.31534	−	5.74234i	−0.122706	−	0.212534i
$731$	20.8078	−	36.0401i	0.769603	−	1.33299i
$732$	−5.26137	+	9.11295i	−0.194466	+	0.336824i
$733$	2.84233	+	4.92306i	0.104984	+	0.181837i	0.913732	−	0.406318i	$-0.133188\pi$
$733$	2.84233	+	4.92306i	0.104984	+	0.181837i	−0.808748	+	0.588156i	$0.799854\pi$
$734$	5.75379			0.212376
$735$		0			0
$736$	12.4924			0.460477
$737$	8.00000	+	13.8564i	0.294684	+	0.510407i
$738$	8.68466	−	15.0423i	0.319687	−	0.553714i
$739$	−3.03457	+	5.25602i	−0.111628	+	0.193346i	−0.916427	−	0.400202i	$-0.868940\pi$
$739$	−3.03457	+	5.25602i	−0.111628	+	0.193346i	0.804799	+	0.593548i	$0.202273\pi$
$740$	−1.31534	−	2.27824i	−0.0483529	−	0.0837497i
$741$	−13.1231			−0.482089
$742$		0			0
$743$	32.9848			1.21010			0.605048	−	0.796189i	$-0.293154\pi$
$743$	32.9848			1.21010			0.605048	+	0.796189i	$0.293154\pi$
$744$		0			0
$745$	2.12311	−	3.67733i	0.0777846	−	0.134727i
$746$	−22.9309	+	39.7174i	−0.839559	+	1.45416i
$747$	−7.12311	−	12.3376i	−0.260621	−	0.451408i
$748$	−5.12311			−0.187319
$749$		0			0
$750$	−4.00000			−0.146059
$751$	−22.9654	−	39.7773i	−0.838021	−	1.45149i	−0.891547	−	0.452928i	$-0.850380\pi$
$751$	−22.9654	−	39.7773i	−0.838021	−	1.45149i	0.0535265	−	0.998566i	$-0.482954\pi$
$752$	8.63068	−	14.9488i	0.314729	−	0.545126i
$753$	−21.9309	+	37.9854i	−0.799205	+	1.38426i
$754$	20.2462	+	35.0675i	0.737324	+	1.27708i
$755$	21.9309			0.798146
$756$		0			0
$757$	14.6307			0.531761			0.265881	−	0.964006i	$-0.414337\pi$
$757$	14.6307			0.531761			0.265881	+	0.964006i	$0.414337\pi$
$758$	−12.8769	−	22.3034i	−0.467710	−	0.810097i
$759$	−16.8078	+	29.1119i	−0.610083	+	1.05670i
$760$	1.36932	−	2.37173i	0.0496703	−	0.0860316i
$761$	−15.8769	−	27.4996i	−0.575537	−	0.996859i	−0.995983	−	0.0895418i	$-0.971460\pi$
$761$	−15.8769	−	27.4996i	−0.575537	−	0.996859i	0.420446	−	0.907318i	$-0.361874\pi$
$762$	−40.9848			−1.48472
$763$		0			0
$764$	−4.13826			−0.149717
$765$	8.12311	+	14.0696i	0.293692	+	0.508689i
$766$	8.00000	−	13.8564i	0.289052	−	0.500652i
$767$	9.12311	−	15.8017i	0.329416	−	0.570566i
$768$	12.8769	+	22.3034i	0.464655	+	0.804806i
$769$	−9.50758			−0.342852			−0.171426	−	0.985197i	$-0.554837\pi$
$769$	−9.50758			−0.342852			−0.171426	+	0.985197i	$0.554837\pi$
$770$		0			0
$771$	−57.6155			−2.07497
$772$	1.17708	+	2.03876i	0.0423641	+	0.0733767i
$773$	−4.03457	+	6.98807i	−0.145113	+	0.251343i	−0.929415	−	0.369036i	$-0.879688\pi$
$773$	−4.03457	+	6.98807i	−0.145113	+	0.251343i	0.784302	+	0.620379i	$0.213021\pi$
$774$	−25.3693	+	43.9409i	−0.911881	+	1.57942i
$775$		0			0
$776$	36.1080			1.29620
$777$		0			0
$778$	6.13826			0.220067
$779$	1.75379	+	3.03765i	0.0628360	+	0.108835i
$780$	2.56155	−	4.43674i	0.0917183	−	0.158861i
$781$	−10.2462	+	17.7470i	−0.366638	+	0.635036i
$782$	−18.2462	−	31.6034i	−0.652483	−	1.13013i
$783$	8.17708			0.292225
$784$		0			0
$785$	3.75379			0.133978
$786$	−18.2462	−	31.6034i	−0.650821	−	1.12725i
$787$	1.91146	−	3.31075i	0.0681362	−	0.118015i	−0.829945	−	0.557846i	$-0.811628\pi$
$787$	1.91146	−	3.31075i	0.0681362	−	0.118015i	0.898081	+	0.439830i	$0.144961\pi$
$788$	1.56155	−	2.70469i	0.0556280	−	0.0963505i
$789$	−27.0540	−	46.8589i	−0.963147	−	1.66822i
$790$	−10.2462			−0.364544
$791$		0			0
$792$	−22.2462			−0.790485
$793$	21.3693	+	37.0127i	0.758847	+	1.31436i
$794$	−18.3002	+	31.6969i	−0.649449	+	1.12488i
$795$	4.00000	−	6.92820i	0.141865	−	0.245718i
$796$	4.00000	+	6.92820i	0.141776	+	0.245564i
$797$	−13.0540			−0.462396			−0.231198	−	0.972907i	$-0.574264\pi$
$797$	−13.0540			−0.462396			−0.231198	+	0.972907i	$0.574264\pi$
$798$		0			0
$799$	−16.8078			−0.594616
$800$	1.21922	+	2.11176i	0.0431061	+	0.0746619i
$801$	−12.6847	+	21.9705i	−0.448190	+	0.776288i
$802$	−21.4233	+	37.1062i	−0.756483	+	1.31027i
$803$	−5.43845	−	9.41967i	−0.191919	−	0.332413i
$804$	7.01515			0.247405
$805$		0			0
$806$		0			0
$807$	36.8078	+	63.7529i	1.29569	+	2.24421i
$808$	0.300187	−	0.519938i	0.0105605	−	0.0182914i
$809$	26.7732	−	46.3725i	0.941296	−	1.63037i	0.178292	−	0.983978i	$-0.442943\pi$
$809$	26.7732	−	46.3725i	0.941296	−	1.63037i	0.763004	−	0.646394i	$-0.223724\pi$
$810$	5.46543	+	9.46641i	0.192036	+	0.332616i
$811$	−21.6155			−0.759024			−0.379512	−	0.925187i	$-0.623908\pi$
$811$	−21.6155			−0.759024			−0.379512	+	0.925187i	$0.623908\pi$
$812$		0			0
$813$	40.9848			1.43740
$814$	−12.0000	−	20.7846i	−0.420600	−	0.728500i
$815$	−0.561553	+	0.972638i	−0.0196703	+	0.0340700i
$816$	27.3693	−	47.4050i	0.958118	−	1.65951i
$817$	−5.12311	−	8.87348i	−0.179235	−	0.310444i
$818$	−41.3693			−1.44644
$819$		0			0
$820$	−1.36932			−0.0478186
$821$	−20.2116	−	35.0076i	−0.705391	−	1.22177i	−0.966550	−	0.256478i	$-0.917438\pi$
$821$	−20.2116	−	35.0076i	−0.705391	−	1.22177i	0.261159	−	0.965296i	$-0.415895\pi$
$822$	−17.7538	+	30.7505i	−0.619234	+	1.07255i
$823$	1.75379	−	3.03765i	0.0611332	−	0.105886i	−0.833839	−	0.552008i	$-0.813862\pi$
$823$	1.75379	−	3.03765i	0.0611332	−	0.105886i	0.894972	+	0.446122i	$0.147195\pi$
$824$	1.75379	+	3.03765i	0.0610961	+	0.105822i
$825$	−6.56155			−0.228444
$826$		0			0
$827$	19.3693			0.673537			0.336769	−	0.941587i	$-0.390666\pi$
$827$	19.3693			0.673537			0.336769	+	0.941587i	$0.390666\pi$
$828$	4.00000	+	6.92820i	0.139010	+	0.240772i
$829$	−21.5616	+	37.3457i	−0.748864	+	1.29707i	0.199504	+	0.979897i	$0.436067\pi$
$829$	−21.5616	+	37.3457i	−0.748864	+	1.29707i	−0.948368	+	0.317173i	$0.897266\pi$
$830$	−3.12311	+	5.40938i	−0.108405	+	0.187762i
$831$	20.8078	+	36.0401i	0.721813	+	1.25022i
$832$	25.3693			0.879523
$833$		0			0
$834$	27.5076			0.952510
$835$	−10.9654	−	18.9927i	−0.379475	−	0.657269i
$836$	−0.630683	+	1.09238i	−0.0218126	+	0.0377806i
$837$		0			0
$838$	−7.61553	−	13.1905i	−0.263074	−	0.455658i
$839$	−37.1231			−1.28163			−0.640816	−	0.767695i	$-0.721404\pi$
$839$	−37.1231			−1.28163			−0.640816	+	0.767695i	$0.721404\pi$
$840$		0			0
$841$	3.31534			0.114322
$842$	−7.56155	−	13.0970i	−0.260588	−	0.451352i
$843$	21.2116	−	36.7396i	0.730568	−	1.26538i
$844$	5.05398	−	8.75374i	0.173965	−	0.301316i
$845$	−3.90388	−	6.76172i	−0.134298	−	0.232610i
$846$	20.4924			0.704544
$847$		0			0
$848$	−14.6307			−0.502420
$849$	−30.3348	−	52.5413i	−1.04109	−	1.80321i
$850$	3.56155	−	6.16879i	0.122160	−	0.211588i
$851$	15.3693	−	26.6204i	0.526853	−	0.912537i
$852$	4.49242	+	7.78110i	0.153908	+	0.266576i
$853$	−56.7386			−1.94269			−0.971347	−	0.237666i	$-0.923618\pi$
$853$	−56.7386			−1.94269			−0.971347	+	0.237666i	$0.923618\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$	−13.8617	−	24.0092i	−0.473784	−	0.820619i
$857$	16.1231	−	27.9260i	0.550755	−	0.953935i	−0.447466	−	0.894301i	$-0.647673\pi$
$857$	16.1231	−	27.9260i	0.550755	−	0.953935i	0.998220	−	0.0596341i	$-0.0189934\pi$
$858$	23.3693	−	40.4768i	0.797815	−	1.38186i
$859$	−8.24621	−	14.2829i	−0.281357	−	0.487325i	0.690362	−	0.723464i	$-0.257451\pi$
$859$	−8.24621	−	14.2829i	−0.281357	−	0.487325i	−0.971719	+	0.236139i	$0.924118\pi$
$860$	4.00000			0.136399
$861$		0			0
$862$	1.26137			0.0429623
$863$	21.1231	+	36.5863i	0.719039	+	1.24541i	0.961381	+	0.275221i	$0.0887510\pi$
$863$	21.1231	+	36.5863i	0.719039	+	1.24541i	−0.242342	+	0.970191i	$0.577916\pi$
$864$	−1.75379	+	3.03765i	−0.0596651	+	0.103343i
$865$	4.28078	−	7.41452i	0.145551	−	0.252101i
$866$	6.43845	+	11.1517i	0.218787	+	0.378951i
$867$	−9.75379			−0.331256
$868$		0			0
$869$	−16.8078			−0.570164
$870$	−11.3693	−	19.6922i	−0.385456	−	0.667629i
$871$	14.2462	−	24.6752i	0.482714	−	0.836086i
$872$	21.5616	−	37.3457i	0.730166	−	1.26469i
$873$	26.3693	+	45.6730i	0.892466	+	1.54580i
$874$	−8.98485			−0.303917
$875$		0			0
$876$	−4.76894			−0.161128
$877$	11.8769	+	20.5714i	0.401054	+	0.694646i	0.993853	−	0.110704i	$-0.0353106\pi$
$877$	11.8769	+	20.5714i	0.401054	+	0.694646i	−0.592799	+	0.805350i	$0.701977\pi$
$878$	12.0000	−	20.7846i	0.404980	−	0.701447i
$879$	12.4039	−	21.4842i	0.418373	−	0.724643i
$880$	6.00000	+	10.3923i	0.202260	+	0.350325i
$881$	45.8617			1.54512			0.772561	−	0.634941i	$-0.218976\pi$
$881$	45.8617			1.54512			0.772561	+	0.634941i	$0.218976\pi$
$882$		0			0
$883$	24.4924			0.824236			0.412118	−	0.911131i	$-0.364789\pi$
$883$	24.4924			0.824236			0.412118	+	0.911131i	$0.364789\pi$
$884$	4.56155	+	7.90084i	0.153422	+	0.265734i
$885$	−5.12311	+	8.87348i	−0.172211	+	0.298279i
$886$	21.3693	−	37.0127i	0.717916	−	1.24347i
$887$	6.24621	+	10.8188i	0.209727	+	0.363258i	0.951629	−	0.307251i	$-0.0994091\pi$
$887$	6.24621	+	10.8188i	0.209727	+	0.363258i	−0.741901	+	0.670509i	$0.766076\pi$
$888$	37.4773			1.25765
$889$		0			0
$890$	11.1231			0.372847
$891$	8.96543	+	15.5286i	0.300353	+	0.520227i
$892$	1.43845	−	2.49146i	0.0481628	−	0.0834204i
$893$	−2.06913	+	3.58384i	−0.0692408	+	0.119929i
$894$	−8.49242	−	14.7093i	−0.284029	−	0.491953i
$895$	20.0000			0.668526
$896$		0			0
$897$	59.8617			1.99873
$898$	−14.6847	−	25.4346i	−0.490033	−	0.848763i
$899$		0			0
$900$	−0.780776	+	1.35234i	−0.0260259	+	0.0450781i
$901$	7.12311	+	12.3376i	0.237305	+	0.411024i
$902$	−12.4924			−0.415952
$903$		0			0
$904$	34.1383			1.13542
$905$	−11.8078	−	20.4516i	−0.392503	−	0.679836i
$906$	43.8617	−	75.9708i	1.45721	−	2.52396i
$907$	−25.0540	+	43.3948i	−0.831904	+	1.44090i	0.0646232	+	0.997910i	$0.479415\pi$
$907$	−25.0540	+	43.3948i	−0.831904	+	1.44090i	−0.896527	+	0.442990i	$0.853918\pi$
$908$	−5.19224	−	8.99322i	−0.172310	−	0.298450i
$909$	0.876894			0.0290848
$910$		0			0
$911$	4.49242			0.148841			0.0744203	−	0.997227i	$-0.476289\pi$
$911$	4.49242			0.148841			0.0744203	+	0.997227i	$0.476289\pi$
$912$	−6.73863	−	11.6717i	−0.223138	−	0.386487i
$913$	−5.12311	+	8.87348i	−0.169550	+	0.293669i
$914$	6.93087	−	12.0046i	0.229253	−	0.397077i
$915$	−12.0000	−	20.7846i	−0.396708	−	0.687118i
$916$	8.38447			0.277031
$917$		0			0
$918$	10.2462			0.338175
$919$	6.65009	+	11.5183i	0.219366	+	0.379954i	0.954614	−	0.297844i	$-0.0962677\pi$
$919$	6.65009	+	11.5183i	0.219366	+	0.379954i	−0.735248	+	0.677798i	$0.762934\pi$
$920$	−6.24621	+	10.8188i	−0.205931	+	0.356684i
$921$	−40.5810	+	70.2883i	−1.33719	+	2.31608i
$922$	3.80776	+	6.59524i	0.125402	+	0.217203i
$923$	36.4924			1.20116
$924$		0			0
$925$	6.00000			0.197279
$926$	16.0000	+	27.7128i	0.525793	+	0.910700i
$927$	−2.56155	+	4.43674i	−0.0841324	+	0.145722i
$928$	−6.93087	+	12.0046i	−0.227517	+	0.394071i
$929$	26.0540	+	45.1268i	0.854803	+	1.48056i	0.876827	+	0.480805i	$0.159656\pi$
$929$	26.0540	+	45.1268i	0.854803	+	1.48056i	−0.0220243	+	0.999757i	$0.507011\pi$
$930$		0			0
$931$		0			0
$932$	−1.36932			−0.0448535
$933$	−12.3153	−	21.3308i	−0.403186	−	0.698339i
$934$	−20.7386	+	35.9204i	−0.678589	+	1.17535i
$935$	5.84233	−	10.1192i	0.191065	−	0.330934i
$936$	19.8078	+	34.3081i	0.647437	+	1.12139i
$937$	22.6695			0.740580			0.370290	−	0.928916i	$-0.379258\pi$
$937$	22.6695			0.740580			0.370290	+	0.928916i	$0.379258\pi$
$938$		0			0
$939$	−80.1771			−2.61648
$940$	−0.807764	−	1.39909i	−0.0263464	−	0.0456332i
$941$	6.93087	−	12.0046i	0.225940	−	0.391339i	−0.730661	−	0.682740i	$-0.760788\pi$
$941$	6.93087	−	12.0046i	0.225940	−	0.391339i	0.956601	+	0.291401i	$0.0941214\pi$
$942$	7.50758	−	13.0035i	0.244610	−	0.423677i
$943$	−8.00000	−	13.8564i	−0.260516	−	0.451227i
$944$	18.7386			0.609891
$945$		0			0
$946$	36.4924			1.18647
$947$	−2.00000	−	3.46410i	−0.0649913	−	0.112568i	0.831699	−	0.555227i	$-0.187369\pi$
$947$	−2.00000	−	3.46410i	−0.0649913	−	0.112568i	−0.896690	+	0.442659i	$0.854035\pi$
$948$	−3.68466	+	6.38202i	−0.119672	+	0.207278i
$949$	−9.68466	+	16.7743i	−0.314377	+	0.544517i
$950$	−0.876894	−	1.51883i	−0.0284502	−	0.0492772i
$951$	57.6155			1.86831
$952$		0			0
$953$	−24.8769			−0.805842			−0.402921	−	0.915235i	$-0.632005\pi$
$953$	−24.8769			−0.805842			−0.402921	+	0.915235i	$0.632005\pi$
$954$	−8.68466	−	15.0423i	−0.281176	−	0.487011i
$955$	4.71922	−	8.17394i	0.152710	−	0.264502i
$956$	0.177081	−	0.306713i	0.00572721	−	0.00991981i
$957$	−18.6501	−	32.3029i	−0.602872	−	1.04420i
$958$	20.4924			0.662080
$959$		0			0
$960$	−14.2462			−0.459794
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	−21.3693	+	37.0127i	−0.688974	+	1.19334i
$963$	20.2462	−	35.0675i	0.652425	−	1.13003i
$964$	−2.68466	−	4.64996i	−0.0864670	−	0.149765i
$965$	−5.36932			−0.172844
$966$		0			0
$967$	−26.8769			−0.864303			−0.432151	−	0.901801i	$-0.642245\pi$
$967$	−26.8769			−0.864303			−0.432151	+	0.901801i	$0.642245\pi$
$968$	−5.41146	−	9.37292i	−0.173931	−	0.301257i
$969$	−6.56155	+	11.3649i	−0.210787	+	0.365095i
$970$	11.5616	−	20.0252i	0.371219	−	0.642970i
$971$	24.7386	+	42.8486i	0.793901	+	1.37508i	0.923535	+	0.383514i	$0.125286\pi$
$971$	24.7386	+	42.8486i	0.793901	+	1.37508i	−0.129634	+	0.991562i	$0.541380\pi$
$972$	9.75379			0.312853
$973$		0			0
$974$	8.00000			0.256337
$975$	5.84233	+	10.1192i	0.187104	+	0.324074i
$976$	−21.9460	+	38.0116i	−0.702475	+	1.21672i
$977$	24.6155	−	42.6353i	0.787521	−	1.36403i	−0.139961	−	0.990157i	$-0.544698\pi$
$977$	24.6155	−	42.6353i	0.787521	−	1.36403i	0.927482	−	0.373869i	$-0.121969\pi$
$978$	2.24621	+	3.89055i	0.0718259	+	0.124406i
$979$	18.2462			0.583151
$980$		0			0
$981$	62.9848			2.01095
$982$	−3.26137	−	5.64885i	−0.104074	−	0.180262i
$983$	5.21165	−	9.02684i	0.166226	−	0.287911i	−0.770864	−	0.637000i	$-0.780175\pi$
$983$	5.21165	−	9.02684i	0.166226	−	0.287911i	0.937090	+	0.349088i	$0.113509\pi$
$984$	9.75379	−	16.8941i	0.310939	−	0.538563i
$985$	3.56155	+	6.16879i	0.113481	+	0.196554i
$986$	40.4924			1.28954
$987$		0			0
$988$	2.24621			0.0714615
$989$	23.3693	+	40.4768i	0.743101	+	1.28709i
$990$	−7.12311	+	12.3376i	−0.226387	+	0.392114i
$991$	10.2462	−	17.7470i	0.325482	−	0.563751i	−0.656128	−	0.754650i	$-0.727807\pi$
$991$	10.2462	−	17.7470i	0.325482	−	0.563751i	0.981610	+	0.190899i	$0.0611402\pi$
$992$		0			0
$993$	−30.7386			−0.975461
$994$		0			0
$995$	−18.2462			−0.578444
$996$	2.24621	+	3.89055i	0.0711739	+	0.123277i
$997$	−4.84233	+	8.38716i	−0.153358	+	0.265624i	−0.932460	−	0.361273i	$-0.882342\pi$
$997$	−4.84233	+	8.38716i	−0.153358	+	0.265624i	0.779102	+	0.626897i	$0.215675\pi$
$998$	3.26137	−	5.64885i	0.103237	−	0.178811i
$999$	4.31534	+	7.47439i	0.136531	+	0.236479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.e.i.116.1		4
7.2	even	3	inner	245.2.e.i.226.1		4
7.3	odd	6		245.2.a.d.1.2		2
7.4	even	3		35.2.a.b.1.2	✓	2
7.5	odd	6		245.2.e.h.226.1		4
7.6	odd	2		245.2.e.h.116.1		4
21.11	odd	6		315.2.a.e.1.1		2
21.17	even	6		2205.2.a.x.1.1		2
28.3	even	6		3920.2.a.bs.1.1		2
28.11	odd	6		560.2.a.i.1.2		2
35.3	even	12		1225.2.b.f.99.2		4
35.4	even	6		175.2.a.f.1.1		2
35.17	even	12		1225.2.b.f.99.3		4
35.18	odd	12		175.2.b.b.99.2		4
35.24	odd	6		1225.2.a.s.1.1		2
35.32	odd	12		175.2.b.b.99.3		4
56.11	odd	6		2240.2.a.bd.1.1		2
56.53	even	6		2240.2.a.bh.1.2		2
77.32	odd	6		4235.2.a.m.1.1		2
84.11	even	6		5040.2.a.bt.1.2		2
91.25	even	6		5915.2.a.l.1.1		2
105.32	even	12		1575.2.d.e.1324.2		4
105.53	even	12		1575.2.d.e.1324.3		4
105.74	odd	6		1575.2.a.p.1.2		2
140.39	odd	6		2800.2.a.bi.1.1		2
140.67	even	12		2800.2.g.t.449.1		4
140.123	even	12		2800.2.g.t.449.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.a.b.1.2	✓	2	7.4	even	3
175.2.a.f.1.1		2	35.4	even	6
175.2.b.b.99.2		4	35.18	odd	12
175.2.b.b.99.3		4	35.32	odd	12
245.2.a.d.1.2		2	7.3	odd	6
245.2.e.h.116.1		4	7.6	odd	2
245.2.e.h.226.1		4	7.5	odd	6
245.2.e.i.116.1		4	1.1	even	1	trivial
245.2.e.i.226.1		4	7.2	even	3	inner
315.2.a.e.1.1		2	21.11	odd	6
560.2.a.i.1.2		2	28.11	odd	6
1225.2.a.s.1.1		2	35.24	odd	6
1225.2.b.f.99.2		4	35.3	even	12
1225.2.b.f.99.3		4	35.17	even	12
1575.2.a.p.1.2		2	105.74	odd	6
1575.2.d.e.1324.2		4	105.32	even	12
1575.2.d.e.1324.3		4	105.53	even	12
2205.2.a.x.1.1		2	21.17	even	6
2240.2.a.bd.1.1		2	56.11	odd	6
2240.2.a.bh.1.2		2	56.53	even	6
2800.2.a.bi.1.1		2	140.39	odd	6
2800.2.g.t.449.1		4	140.67	even	12
2800.2.g.t.449.4		4	140.123	even	12
3920.2.a.bs.1.1		2	28.3	even	6
4235.2.a.m.1.1		2	77.32	odd	6
5040.2.a.bt.1.2		2	84.11	even	6
5915.2.a.l.1.1		2	91.25	even	6

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.780776 - 1.35234i) q^{2} +(1.28078 - 2.21837i) q^{3} +(-0.219224 + 0.379706i) q^{4} +(-0.500000 - 0.866025i) q^{5} -4.00000 q^{6} -2.43845 q^{8} +(-1.78078 - 3.08440i) q^{9} +O(q^{10})\)	\(q+(-0.780776 - 1.35234i) q^{2} +(1.28078 - 2.21837i) q^{3} +(-0.219224 + 0.379706i) q^{4} +(-0.500000 - 0.866025i) q^{5} -4.00000 q^{6} -2.43845 q^{8} +(-1.78078 - 3.08440i) q^{9} +(-0.780776 + 1.35234i) q^{10} +(-1.28078 + 2.21837i) q^{11} +(0.561553 + 0.972638i) q^{12} +4.56155 q^{13} -2.56155 q^{15} +(2.34233 + 4.05703i) q^{16} +(2.28078 - 3.95042i) q^{17} +(-2.78078 + 4.81645i) q^{18} +(-0.561553 - 0.972638i) q^{19} +0.438447 q^{20} +4.00000 q^{22} +(2.56155 + 4.43674i) q^{23} +(-3.12311 + 5.40938i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.56155 - 6.16879i) q^{26} -1.43845 q^{27} -5.68466 q^{29} +(2.00000 + 3.46410i) q^{30} +(1.21922 - 2.11176i) q^{32} +(3.28078 + 5.68247i) q^{33} -7.12311 q^{34} +1.56155 q^{36} +(-3.00000 - 5.19615i) q^{37} +(-0.876894 + 1.51883i) q^{38} +(5.84233 - 10.1192i) q^{39} +(1.21922 + 2.11176i) q^{40} -3.12311 q^{41} +9.12311 q^{43} +(-0.561553 - 0.972638i) q^{44} +(-1.78078 + 3.08440i) q^{45} +(4.00000 - 6.92820i) q^{46} +(-1.84233 - 3.19101i) q^{47} +12.0000 q^{48} +1.56155 q^{50} +(-5.84233 - 10.1192i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-1.56155 + 2.70469i) q^{53} +(1.12311 + 1.94528i) q^{54} +2.56155 q^{55} -2.87689 q^{57} +(4.43845 + 7.68762i) q^{58} +(2.00000 - 3.46410i) q^{59} +(0.561553 - 0.972638i) q^{60} +(4.68466 + 8.11407i) q^{61} +5.56155 q^{64} +(-2.28078 - 3.95042i) q^{65} +(5.12311 - 8.87348i) q^{66} +(3.12311 - 5.40938i) q^{67} +(1.00000 + 1.73205i) q^{68} +13.1231 q^{69} +8.00000 q^{71} +(4.34233 + 7.52113i) q^{72} +(-2.12311 + 3.67733i) q^{73} +(-4.68466 + 8.11407i) q^{74} +(1.28078 + 2.21837i) q^{75} +0.492423 q^{76} -18.2462 q^{78} +(3.28078 + 5.68247i) q^{79} +(2.34233 - 4.05703i) q^{80} +(3.50000 - 6.06218i) q^{81} +(2.43845 + 4.22351i) q^{82} +4.00000 q^{83} -4.56155 q^{85} +(-7.12311 - 12.3376i) q^{86} +(-7.28078 + 12.6107i) q^{87} +(3.12311 - 5.40938i) q^{88} +(-3.56155 - 6.16879i) q^{89} +5.56155 q^{90} -2.24621 q^{92} +(-2.87689 + 4.98293i) q^{94} +(-0.561553 + 0.972638i) q^{95} +(-3.12311 - 5.40938i) q^{96} -14.8078 q^{97} +9.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} - 5 q^{4} - 2 q^{5} - 16 q^{6} - 18 q^{8} - 3 q^{9}+O(q^{10}) \) 4 * q + q^2 + q^3 - 5 * q^4 - 2 * q^5 - 16 * q^6 - 18 * q^8 - 3 * q^9	\( 4 q + q^{2} + q^{3} - 5 q^{4} - 2 q^{5} - 16 q^{6} - 18 q^{8} - 3 q^{9} + q^{10} - q^{11} - 6 q^{12} + 10 q^{13} - 2 q^{15} - 3 q^{16} + 5 q^{17} - 7 q^{18} + 6 q^{19} + 10 q^{20} + 16 q^{22} + 2 q^{23} + 4 q^{24} - 2 q^{25} - 6 q^{26} - 14 q^{27} + 2 q^{29} + 8 q^{30} + 9 q^{32} + 9 q^{33} - 12 q^{34} - 2 q^{36} - 12 q^{37} - 20 q^{38} + 11 q^{39} + 9 q^{40} + 4 q^{41} + 20 q^{43} + 6 q^{44} - 3 q^{45} + 16 q^{46} + 5 q^{47} + 48 q^{48} - 2 q^{50} - 11 q^{51} - 4 q^{52} + 2 q^{53} - 12 q^{54} + 2 q^{55} - 28 q^{57} + 26 q^{58} + 8 q^{59} - 6 q^{60} - 6 q^{61} + 14 q^{64} - 5 q^{65} + 4 q^{66} - 4 q^{67} + 4 q^{68} + 36 q^{69} + 32 q^{71} + 5 q^{72} + 8 q^{73} + 6 q^{74} + q^{75} - 64 q^{76} - 40 q^{78} + 9 q^{79} - 3 q^{80} + 14 q^{81} + 18 q^{82} + 16 q^{83} - 10 q^{85} - 12 q^{86} - 25 q^{87} - 4 q^{88} - 6 q^{89} + 14 q^{90} + 24 q^{92} - 28 q^{94} + 6 q^{95} + 4 q^{96} - 18 q^{97} + 20 q^{99}+O(q^{100}) \) 4 * q + q^2 + q^3 - 5 * q^4 - 2 * q^5 - 16 * q^6 - 18 * q^8 - 3 * q^9 + q^10 - q^11 - 6 * q^12 + 10 * q^13 - 2 * q^15 - 3 * q^16 + 5 * q^17 - 7 * q^18 + 6 * q^19 + 10 * q^20 + 16 * q^22 + 2 * q^23 + 4 * q^24 - 2 * q^25 - 6 * q^26 - 14 * q^27 + 2 * q^29 + 8 * q^30 + 9 * q^32 + 9 * q^33 - 12 * q^34 - 2 * q^36 - 12 * q^37 - 20 * q^38 + 11 * q^39 + 9 * q^40 + 4 * q^41 + 20 * q^43 + 6 * q^44 - 3 * q^45 + 16 * q^46 + 5 * q^47 + 48 * q^48 - 2 * q^50 - 11 * q^51 - 4 * q^52 + 2 * q^53 - 12 * q^54 + 2 * q^55 - 28 * q^57 + 26 * q^58 + 8 * q^59 - 6 * q^60 - 6 * q^61 + 14 * q^64 - 5 * q^65 + 4 * q^66 - 4 * q^67 + 4 * q^68 + 36 * q^69 + 32 * q^71 + 5 * q^72 + 8 * q^73 + 6 * q^74 + q^75 - 64 * q^76 - 40 * q^78 + 9 * q^79 - 3 * q^80 + 14 * q^81 + 18 * q^82 + 16 * q^83 - 10 * q^85 - 12 * q^86 - 25 * q^87 - 4 * q^88 - 6 * q^89 + 14 * q^90 + 24 * q^92 - 28 * q^94 + 6 * q^95 + 4 * q^96 - 18 * q^97 + 20 * q^99

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