LMFDB - Embedded newform 245.2.e.i.226.2

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			226.2
Root			$1.28078 - 2.21837i$ of defining polynomial
Character	$\chi$	$=$	245.226
Dual form			245.2.e.i.116.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28078 - 2.21837i) q^{2} +(-0.780776 - 1.35234i) q^{3} +(-2.28078 - 3.95042i) q^{4} +(-0.500000 + 0.866025i) q^{5} -4.00000 q^{6} -6.56155 q^{8} +(0.280776 - 0.486319i) q^{9} +O(q^{10})$	\(q+(1.28078 - 2.21837i) q^{2} +(-0.780776 - 1.35234i) q^{3} +(-2.28078 - 3.95042i) q^{4} +(-0.500000 + 0.866025i) q^{5} -4.00000 q^{6} -6.56155 q^{8} +(0.280776 - 0.486319i) q^{9} +(1.28078 + 2.21837i) q^{10} +(0.780776 + 1.35234i) q^{11} +(-3.56155 + 6.16879i) q^{12} +0.438447 q^{13} +1.56155 q^{15} +(-3.84233 + 6.65511i) q^{16} +(0.219224 + 0.379706i) q^{17} +(-0.719224 - 1.24573i) q^{18} +(3.56155 - 6.16879i) q^{19} +4.56155 q^{20} +4.00000 q^{22} +(-1.56155 + 2.70469i) q^{23} +(5.12311 + 8.87348i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.561553 - 0.972638i) q^{26} -5.56155 q^{27} +6.68466 q^{29} +(2.00000 - 3.46410i) q^{30} +(3.28078 + 5.68247i) q^{32} +(1.21922 - 2.11176i) q^{33} +1.12311 q^{34} -2.56155 q^{36} +(-3.00000 + 5.19615i) q^{37} +(-9.12311 - 15.8017i) q^{38} +(-0.342329 - 0.592932i) q^{39} +(3.28078 - 5.68247i) q^{40} +5.12311 q^{41} +0.876894 q^{43} +(3.56155 - 6.16879i) q^{44} +(0.280776 + 0.486319i) q^{45} +(4.00000 + 6.92820i) q^{46} +(4.34233 - 7.52113i) q^{47} +12.0000 q^{48} -2.56155 q^{50} +(0.342329 - 0.592932i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(2.56155 + 4.43674i) q^{53} +(-7.12311 + 12.3376i) q^{54} -1.56155 q^{55} -11.1231 q^{57} +(8.56155 - 14.8290i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-3.56155 - 6.16879i) q^{60} +(-7.68466 + 13.3102i) q^{61} +1.43845 q^{64} +(-0.219224 + 0.379706i) q^{65} +(-3.12311 - 5.40938i) q^{66} +(-5.12311 - 8.87348i) q^{67} +(1.00000 - 1.73205i) q^{68} +4.87689 q^{69} +8.00000 q^{71} +(-1.84233 + 3.19101i) q^{72} +(6.12311 + 10.6055i) q^{73} +(7.68466 + 13.3102i) q^{74} +(-0.780776 + 1.35234i) q^{75} -32.4924 q^{76} -1.75379 q^{78} +(1.21922 - 2.11176i) q^{79} +(-3.84233 - 6.65511i) q^{80} +(3.50000 + 6.06218i) q^{81} +(6.56155 - 11.3649i) q^{82} +4.00000 q^{83} -0.438447 q^{85} +(1.12311 - 1.94528i) q^{86} +(-5.21922 - 9.03996i) q^{87} +(-5.12311 - 8.87348i) q^{88} +(0.561553 - 0.972638i) q^{89} +1.43845 q^{90} +14.2462 q^{92} +(-11.1231 - 19.2658i) q^{94} +(3.56155 + 6.16879i) q^{95} +(5.12311 - 8.87348i) q^{96} +5.80776 q^{97} +0.876894 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 $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.28078	−	2.21837i	0.905646	−	1.56862i	0.0855975	−	0.996330i	$-0.472720\pi$
$2$	1.28078	−	2.21837i	0.905646	−	1.56862i	0.820048	−	0.572295i	$-0.193947\pi$
$3$	−0.780776	−	1.35234i	−0.450781	−	0.780776i	0.547653	−	0.836705i	$-0.315521\pi$
$3$	−0.780776	−	1.35234i	−0.450781	−	0.780776i	−0.998435	+	0.0559290i	$0.982188\pi$
$4$	−2.28078	−	3.95042i	−1.14039	−	1.97521i
$5$	−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
$8$	−6.56155			−2.31986
$9$	0.280776	−	0.486319i	0.0935921	−	0.162106i
$10$	1.28078	+	2.21837i	0.405017	+	0.701510i
$11$	0.780776	+	1.35234i	0.235413	+	0.407747i	0.959393	−	0.282074i	$-0.0910224\pi$
$11$	0.780776	+	1.35234i	0.235413	+	0.407747i	−0.723980	+	0.689821i	$0.757689\pi$
$12$	−3.56155	+	6.16879i	−1.02813	+	1.78078i
$13$	0.438447			0.121603			0.0608017	−	0.998150i	$-0.480634\pi$
$13$	0.438447			0.121603			0.0608017	+	0.998150i	$0.480634\pi$
$14$		0			0
$15$	1.56155			0.403191
$16$	−3.84233	+	6.65511i	−0.960582	+	1.66378i
$17$	0.219224	+	0.379706i	0.0531695	+	0.0920923i	0.891385	−	0.453247i	$-0.149734\pi$
$17$	0.219224	+	0.379706i	0.0531695	+	0.0920923i	−0.838216	+	0.545339i	$0.816401\pi$
$18$	−0.719224	−	1.24573i	−0.169523	−	0.293622i
$19$	3.56155	−	6.16879i	0.817076	−	1.41522i	−0.0907512	−	0.995874i	$-0.528927\pi$
$19$	3.56155	−	6.16879i	0.817076	−	1.41522i	0.907827	−	0.419344i	$-0.137740\pi$
$20$	4.56155			1.01999
$21$		0			0
$22$	4.00000			0.852803
$23$	−1.56155	+	2.70469i	−0.325606	+	0.563967i	−0.981635	−	0.190769i	$-0.938902\pi$
$23$	−1.56155	+	2.70469i	−0.325606	+	0.563967i	0.656029	+	0.754736i	$0.272235\pi$
$24$	5.12311	+	8.87348i	1.04575	+	1.81129i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.561553	−	0.972638i	0.110130	−	0.190750i
$27$	−5.56155			−1.07032
$28$		0			0
$29$	6.68466			1.24131			0.620655	−	0.784084i	$-0.286867\pi$
$29$	6.68466			1.24131			0.620655	+	0.784084i	$0.286867\pi$
$30$	2.00000	−	3.46410i	0.365148	−	0.632456i
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	3.28078	+	5.68247i	0.579965	+	1.00453i
$33$	1.21922	−	2.11176i	0.212240	−	0.367610i
$34$	1.12311			0.192611
$35$		0			0
$36$	−2.56155			−0.426925
$37$	−3.00000	+	5.19615i	−0.493197	+	0.854242i	−0.999969	−	0.00783774i	$-0.997505\pi$
$37$	−3.00000	+	5.19615i	−0.493197	+	0.854242i	0.506772	+	0.862080i	$0.330838\pi$
$38$	−9.12311	−	15.8017i	−1.47996	−	2.56337i
$39$	−0.342329	−	0.592932i	−0.0548165	−	0.0949450i
$40$	3.28078	−	5.68247i	0.518736	−	0.898478i
$41$	5.12311			0.800095			0.400047	−	0.916494i	$-0.368994\pi$
$41$	5.12311			0.800095			0.400047	+	0.916494i	$0.368994\pi$
$42$		0			0
$43$	0.876894			0.133725			0.0668626	−	0.997762i	$-0.478701\pi$
$43$	0.876894			0.133725			0.0668626	+	0.997762i	$0.478701\pi$
$44$	3.56155	−	6.16879i	0.536924	−	0.929980i
$45$	0.280776	+	0.486319i	0.0418557	+	0.0724962i
$46$	4.00000	+	6.92820i	0.589768	+	1.02151i
$47$	4.34233	−	7.52113i	0.633394	−	1.09707i	−0.353459	−	0.935450i	$-0.614995\pi$
$47$	4.34233	−	7.52113i	0.633394	−	1.09707i	0.986853	−	0.161620i	$-0.0516720\pi$
$48$	12.0000			1.73205
$49$		0			0
$50$	−2.56155			−0.362258
$51$	0.342329	−	0.592932i	0.0479357	−	0.0830270i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	2.56155	+	4.43674i	0.351856	+	0.609433i	0.986575	−	0.163310i	$-0.0522172\pi$
$53$	2.56155	+	4.43674i	0.351856	+	0.609433i	−0.634718	+	0.772744i	$0.718884\pi$
$54$	−7.12311	+	12.3376i	−0.969332	+	1.67893i
$55$	−1.56155			−0.210560
$56$		0			0
$57$	−11.1231			−1.47329
$58$	8.56155	−	14.8290i	1.12419	−	1.94715i
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$	−3.56155	−	6.16879i	−0.459794	−	0.796387i
$61$	−7.68466	+	13.3102i	−0.983920	+	1.70420i	−0.337278	+	0.941405i	$0.609506\pi$
$61$	−7.68466	+	13.3102i	−0.983920	+	1.70420i	−0.646642	+	0.762794i	$0.723827\pi$
$62$		0			0
$63$		0			0
$64$	1.43845			0.179806
$65$	−0.219224	+	0.379706i	−0.0271913	+	0.0470968i
$66$	−3.12311	−	5.40938i	−0.384428	−	0.665848i
$67$	−5.12311	−	8.87348i	−0.625887	−	1.08407i	−0.988369	−	0.152077i	$-0.951404\pi$
$67$	−5.12311	−	8.87348i	−0.625887	−	1.08407i	0.362482	−	0.931991i	$-0.381930\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$	4.87689			0.587109
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$	−1.84233	+	3.19101i	−0.217121	+	0.376064i
$73$	6.12311	+	10.6055i	0.716655	+	1.24128i	0.962318	+	0.271928i	$0.0876612\pi$
$73$	6.12311	+	10.6055i	0.716655	+	1.24128i	−0.245662	+	0.969355i	$0.579005\pi$
$74$	7.68466	+	13.3102i	0.893323	+	1.54728i
$75$	−0.780776	+	1.35234i	−0.0901563	+	0.156155i
$76$	−32.4924			−3.72714
$77$		0			0
$78$	−1.75379			−0.198577
$79$	1.21922	−	2.11176i	0.137173	−	0.237591i	−0.789252	−	0.614069i	$-0.789532\pi$
$79$	1.21922	−	2.11176i	0.137173	−	0.237591i	0.926426	+	0.376478i	$0.122865\pi$
$80$	−3.84233	−	6.65511i	−0.429585	−	0.744064i
$81$	3.50000	+	6.06218i	0.388889	+	0.673575i
$82$	6.56155	−	11.3649i	0.724602	−	1.25505i
$83$	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
$85$	−0.438447			−0.0475563
$86$	1.12311	−	1.94528i	0.121108	−	0.209765i
$87$	−5.21922	−	9.03996i	−0.559560	−	0.969185i
$88$	−5.12311	−	8.87348i	−0.546125	−	0.945916i
$89$	0.561553	−	0.972638i	0.0595245	−	0.103099i	−0.834728	−	0.550663i	$-0.814375\pi$
$89$	0.561553	−	0.972638i	0.0595245	−	0.103099i	0.894252	+	0.447564i	$0.147708\pi$
$90$	1.43845			0.151626
$91$		0			0
$92$	14.2462			1.48527
$93$		0			0
$94$	−11.1231	−	19.2658i	−1.14726	−	1.98711i
$95$	3.56155	+	6.16879i	0.365408	+	0.632905i
$96$	5.12311	−	8.87348i	0.522875	−	0.905646i
$97$	5.80776			0.589689			0.294845	−	0.955545i	$-0.404732\pi$
$97$	5.80776			0.589689			0.294845	+	0.955545i	$0.404732\pi$
$98$		0			0
$99$	0.876894			0.0881312
$100$	−2.28078	+	3.95042i	−0.228078	+	0.395042i
$101$	8.12311	+	14.0696i	0.808279	+	1.39998i	0.914055	+	0.405591i	$0.132934\pi$
$101$	8.12311	+	14.0696i	0.808279	+	1.39998i	−0.105776	+	0.994390i	$0.533733\pi$
$102$	−0.876894	−	1.51883i	−0.0868255	−	0.150386i
$103$	−2.78078	+	4.81645i	−0.273998	+	0.474579i	−0.969882	−	0.243576i	$-0.921680\pi$
$103$	−2.78078	+	4.81645i	−0.273998	+	0.474579i	0.695884	+	0.718154i	$0.255013\pi$
$104$	−2.87689			−0.282103
$105$		0			0
$106$	13.1231			1.27463
$107$	−6.68466	+	11.5782i	−0.646230	+	1.11930i	0.337786	+	0.941223i	$0.390322\pi$
$107$	−6.68466	+	11.5782i	−0.646230	+	1.11930i	−0.984016	+	0.178081i	$0.943011\pi$
$108$	12.6847	+	21.9705i	1.22058	+	2.11411i
$109$	−2.65767	−	4.60322i	−0.254559	−	0.440909i	0.710217	−	0.703983i	$-0.248597\pi$
$109$	−2.65767	−	4.60322i	−0.254559	−	0.440909i	−0.964776	+	0.263074i	$0.915264\pi$
$110$	−2.00000	+	3.46410i	−0.190693	+	0.330289i
$111$	9.36932			0.889296
$112$		0			0
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$	−14.2462	+	24.6752i	−1.33428	+	2.31104i
$115$	−1.56155	−	2.70469i	−0.145616	−	0.252214i
$116$	−15.2462	−	26.4072i	−1.41558	−	2.45185i
$117$	0.123106	−	0.213225i	0.0113811	−	0.0197127i
$118$	10.2462			0.943240
$119$		0			0
$120$	−10.2462			−0.935347
$121$	4.28078	−	7.41452i	0.389161	−	0.674047i
$122$	19.6847	+	34.0948i	1.78217	+	3.08680i
$123$	−4.00000	−	6.92820i	−0.360668	−	0.624695i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−6.24621			−0.554262			−0.277131	−	0.960832i	$-0.589384\pi$
$127$	−6.24621			−0.554262			−0.277131	+	0.960832i	$0.589384\pi$
$128$	−4.71922	+	8.17394i	−0.417124	+	0.722481i
$129$	−0.684658	−	1.18586i	−0.0602808	−	0.104409i
$130$	0.561553	+	0.972638i	0.0492514	+	0.0853060i
$131$	0.438447	−	0.759413i	0.0383073	−	0.0663502i	−0.846236	−	0.532808i	$-0.821137\pi$
$131$	0.438447	−	0.759413i	0.0383073	−	0.0663502i	0.884543	+	0.466458i	$0.154470\pi$
$132$	−11.1231			−0.968142
$133$		0			0
$134$	−26.2462			−2.26733
$135$	2.78078	−	4.81645i	0.239331	−	0.414534i
$136$	−1.43845	−	2.49146i	−0.123346	−	0.213641i
$137$	8.56155	+	14.8290i	0.731463	+	1.26693i	0.956258	+	0.292525i	$0.0944954\pi$
$137$	8.56155	+	14.8290i	0.731463	+	1.26693i	−0.224795	+	0.974406i	$0.572171\pi$
$138$	6.24621	−	10.8188i	0.531713	−	0.920954i
$139$	−15.1231			−1.28273			−0.641363	−	0.767238i	$-0.721631\pi$
$139$	−15.1231			−1.28273			−0.641363	+	0.767238i	$0.721631\pi$
$140$		0			0
$141$	−13.5616			−1.14209
$142$	10.2462	−	17.7470i	0.859843	−	1.48929i
$143$	0.342329	+	0.592932i	0.0286270	+	0.0495834i
$144$	2.15767	+	3.73720i	0.179806	+	0.311433i
$145$	−3.34233	+	5.78908i	−0.277565	+	0.480757i
$146$	31.3693			2.59614
$147$		0			0
$148$	27.3693			2.24974
$149$	−6.12311	+	10.6055i	−0.501624	+	0.868839i	0.498374	+	0.866962i	$0.333931\pi$
$149$	−6.12311	+	10.6055i	−0.501624	+	0.868839i	−0.999998	+	0.00187666i	$0.999403\pi$
$150$	2.00000	+	3.46410i	0.163299	+	0.282843i
$151$	3.46543	+	6.00231i	0.282013	+	0.488461i	0.971880	−	0.235475i	$-0.0756645\pi$
$151$	3.46543	+	6.00231i	0.282013	+	0.488461i	−0.689867	+	0.723936i	$0.742331\pi$
$152$	−23.3693	+	40.4768i	−1.89550	+	3.28311i
$153$	0.246211			0.0199050
$154$		0			0
$155$		0			0
$156$	−1.56155	+	2.70469i	−0.125024	+	0.216548i
$157$	−10.1231	−	17.5337i	−0.807912	−	1.39934i	−0.914308	−	0.405020i	$-0.867264\pi$
$157$	−10.1231	−	17.5337i	−0.807912	−	1.39934i	0.106396	−	0.994324i	$-0.466069\pi$
$158$	−3.12311	−	5.40938i	−0.248461	−	0.430347i
$159$	4.00000	−	6.92820i	0.317221	−	0.549442i
$160$	−6.56155			−0.518736
$161$		0			0
$162$	17.9309			1.40878
$163$	3.56155	−	6.16879i	0.278962	−	0.483177i	−0.692165	−	0.721739i	$-0.743343\pi$
$163$	3.56155	−	6.16879i	0.278962	−	0.483177i	0.971127	+	0.238563i	$0.0766762\pi$
$164$	−11.6847	−	20.2384i	−0.912419	−	1.58036i
$165$	1.21922	+	2.11176i	0.0949164	+	0.164400i
$166$	5.12311	−	8.87348i	0.397630	−	0.688716i
$167$	−6.93087			−0.536327			−0.268163	−	0.963373i	$-0.586417\pi$
$167$	−6.93087			−0.536327			−0.268163	+	0.963373i	$0.586417\pi$
$168$		0			0
$169$	−12.8078			−0.985213
$170$	−0.561553	+	0.972638i	−0.0430691	+	0.0745979i
$171$	−2.00000	−	3.46410i	−0.152944	−	0.264906i
$172$	−2.00000	−	3.46410i	−0.152499	−	0.264135i
$173$	2.21922	−	3.84381i	0.168724	−	0.292239i	−0.769247	−	0.638951i	$-0.779369\pi$
$173$	2.21922	−	3.84381i	0.168724	−	0.292239i	0.937972	+	0.346712i	$0.112702\pi$
$174$	−26.7386			−2.02705
$175$		0			0
$176$	−12.0000			−0.904534
$177$	3.12311	−	5.40938i	0.234747	−	0.406594i
$178$	−1.43845	−	2.49146i	−0.107816	−	0.186743i
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	−0.949048	−	0.315130i	$-0.897952\pi$
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	0.201613	−	0.979465i	$-0.435382\pi$
$180$	1.28078	−	2.21837i	0.0954634	−	0.165348i
$181$	−17.6155			−1.30935			−0.654676	−	0.755910i	$-0.727195\pi$
$181$	−17.6155			−1.30935			−0.654676	+	0.755910i	$0.727195\pi$
$182$		0			0
$183$	24.0000			1.77413
$184$	10.2462	−	17.7470i	0.755361	−	1.30832i
$185$	−3.00000	−	5.19615i	−0.220564	−	0.382029i
$186$		0			0
$187$	−0.342329	+	0.592932i	−0.0250336	+	0.0433595i
$188$	−39.6155			−2.88926
$189$		0			0
$190$	18.2462			1.32372
$191$	6.78078	−	11.7446i	0.490640	−	0.849813i	−0.509302	−	0.860588i	$-0.670096\pi$
$191$	6.78078	−	11.7446i	0.490640	−	0.849813i	0.999942	+	0.0107748i	$0.00342978\pi$
$192$	−1.12311	−	1.94528i	−0.0810532	−	0.140388i
$193$	−9.68466	−	16.7743i	−0.697117	−	1.20744i	−0.969462	−	0.245242i	$-0.921132\pi$
$193$	−9.68466	−	16.7743i	−0.697117	−	1.20744i	0.272345	−	0.962200i	$-0.412201\pi$
$194$	7.43845	−	12.8838i	0.534049	−	0.925001i
$195$	0.684658			0.0490294
$196$		0			0
$197$	1.12311			0.0800180			0.0400090	−	0.999199i	$-0.487261\pi$
$197$	1.12311			0.0800180			0.0400090	+	0.999199i	$0.487261\pi$
$198$	1.12311	−	1.94528i	0.0798156	−	0.138245i
$199$	0.876894	+	1.51883i	0.0621614	+	0.107667i	0.895431	−	0.445200i	$-0.146867\pi$
$199$	0.876894	+	1.51883i	0.0621614	+	0.107667i	−0.833270	+	0.552866i	$0.813534\pi$
$200$	3.28078	+	5.68247i	0.231986	+	0.401811i
$201$	−8.00000	+	13.8564i	−0.564276	+	0.977356i
$202$	41.6155			2.92806
$203$		0			0
$204$	−3.12311			−0.218661
$205$	−2.56155	+	4.43674i	−0.178907	+	0.309875i
$206$	7.12311	+	12.3376i	0.496290	+	0.859600i
$207$	0.876894	+	1.51883i	0.0609484	+	0.105566i
$208$	−1.68466	+	2.91791i	−0.116810	+	0.202321i
$209$	11.1231			0.769401
$210$		0			0
$211$	14.0540			0.967516			0.483758	−	0.875202i	$-0.339272\pi$
$211$	14.0540			0.967516			0.483758	+	0.875202i	$0.339272\pi$
$212$	11.6847	−	20.2384i	0.802506	−	1.38998i
$213$	−6.24621	−	10.8188i	−0.427983	−	0.741289i
$214$	17.1231	+	29.6581i	1.17051	+	2.02739i
$215$	−0.438447	+	0.759413i	−0.0299018	+	0.0517915i
$216$	36.4924			2.48299
$217$		0			0
$218$	−13.6155			−0.922160
$219$	9.56155	−	16.5611i	0.646110	−	1.11910i
$220$	3.56155	+	6.16879i	0.240120	+	0.415900i
$221$	0.0961180	+	0.166481i	0.00646559	+	0.0111987i
$222$	12.0000	−	20.7846i	0.805387	−	1.39497i
$223$	−2.43845			−0.163291			−0.0816453	−	0.996661i	$-0.526017\pi$
$223$	−2.43845			−0.163291			−0.0816453	+	0.996661i	$0.526017\pi$
$224$		0			0
$225$	−0.561553			−0.0374369
$226$	−17.9309	+	31.0572i	−1.19274	+	2.06589i
$227$	−5.65767	−	9.79937i	−0.375513	−	0.650407i	0.614891	−	0.788612i	$-0.289200\pi$
$227$	−5.65767	−	9.79937i	−0.375513	−	0.650407i	−0.990404	+	0.138205i	$0.955867\pi$
$228$	25.3693	+	43.9409i	1.68012	+	2.91006i
$229$	−5.43845	+	9.41967i	−0.359383	+	0.622469i	−0.987858	−	0.155361i	$-0.950346\pi$
$229$	−5.43845	+	9.41967i	−0.359383	+	0.622469i	0.628475	+	0.777830i	$0.283679\pi$
$230$	−8.00000			−0.527504
$231$		0			0
$232$	−43.8617			−2.87966
$233$	−2.56155	+	4.43674i	−0.167813	+	0.290660i	−0.937651	−	0.347579i	$-0.887004\pi$
$233$	−2.56155	+	4.43674i	−0.167813	+	0.290660i	0.769838	+	0.638240i	$0.220337\pi$
$234$	−0.315342	−	0.546188i	−0.0206145	−	0.0357054i
$235$	4.34233	+	7.52113i	0.283262	+	0.490625i
$236$	9.12311	−	15.8017i	0.593864	−	1.02860i
$237$	−3.80776			−0.247341
$238$		0			0
$239$	19.8078			1.28126			0.640629	−	0.767851i	$-0.278674\pi$
$239$	19.8078			1.28126			0.640629	+	0.767851i	$0.278674\pi$
$240$	−6.00000	+	10.3923i	−0.387298	+	0.670820i
$241$	2.12311	+	3.67733i	0.136761	+	0.236877i	0.926269	−	0.376863i	$-0.122997\pi$
$241$	2.12311	+	3.67733i	0.136761	+	0.236877i	−0.789508	+	0.613741i	$0.789664\pi$
$242$	−10.9654	−	18.9927i	−0.704885	−	1.22090i
$243$	−2.87689	+	4.98293i	−0.184553	+	0.319655i
$244$	70.1080			4.48820
$245$		0			0
$246$	−20.4924			−1.30655
$247$	1.56155	−	2.70469i	0.0993592	−	0.172095i
$248$		0			0
$249$	−3.12311	−	5.40938i	−0.197919	−	0.342805i
$250$	1.28078	−	2.21837i	0.0810034	−	0.140302i
$251$	−8.87689			−0.560305			−0.280152	−	0.959956i	$-0.590385\pi$
$251$	−8.87689			−0.560305			−0.280152	+	0.959956i	$0.590385\pi$
$252$		0			0
$253$	−4.87689			−0.306608
$254$	−8.00000	+	13.8564i	−0.501965	+	0.869428i
$255$	0.342329	+	0.592932i	0.0214375	+	0.0371308i
$256$	13.5270	+	23.4294i	0.845437	+	1.46434i
$257$	5.24621	−	9.08670i	0.327250	−	0.566813i	−0.654715	−	0.755875i	$-0.727212\pi$
$257$	5.24621	−	9.08670i	0.327250	−	0.566813i	0.981965	+	0.189062i	$0.0605449\pi$
$258$	−3.50758			−0.218372
$259$		0			0
$260$	2.00000			0.124035
$261$	1.87689	−	3.25088i	0.116177	−	0.201224i
$262$	−1.12311	−	1.94528i	−0.0693857	−	0.120180i
$263$	6.43845	+	11.1517i	0.397012	+	0.687644i	0.993356	−	0.115085i	$-0.0367139\pi$
$263$	6.43845	+	11.1517i	0.397012	+	0.687644i	−0.596344	+	0.802729i	$0.703381\pi$
$264$	−8.00000	+	13.8564i	−0.492366	+	0.852803i
$265$	−5.12311			−0.314710
$266$		0			0
$267$	−1.75379			−0.107330
$268$	−23.3693	+	40.4768i	−1.42751	+	2.47252i
$269$	10.3693	+	17.9602i	0.632228	+	1.09505i	0.987095	+	0.160135i	$0.0511929\pi$
$269$	10.3693	+	17.9602i	0.632228	+	1.09505i	−0.354867	+	0.934917i	$0.615474\pi$
$270$	−7.12311	−	12.3376i	−0.433498	−	0.750841i
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	−3.36932			−0.204295
$273$		0			0
$274$	43.8617			2.64978
$275$	0.780776	−	1.35234i	0.0470826	−	0.0815494i
$276$	−11.1231	−	19.2658i	−0.669532	−	1.15966i
$277$	0.123106	+	0.213225i	0.00739670	+	0.0128115i	0.869700	−	0.493581i	$-0.164312\pi$
$277$	0.123106	+	0.213225i	0.00739670	+	0.0128115i	−0.862303	+	0.506392i	$0.830979\pi$
$278$	−19.3693	+	33.5486i	−1.16169	+	2.01211i
$279$		0			0
$280$		0			0
$281$	12.4384			0.742016			0.371008	−	0.928630i	$-0.379012\pi$
$281$	12.4384			0.742016			0.371008	+	0.928630i	$0.379012\pi$
$282$	−17.3693	+	30.0845i	−1.03433	+	1.79151i
$283$	5.65767	+	9.79937i	0.336314	+	0.582512i	0.983736	−	0.179619i	$-0.0574865\pi$
$283$	5.65767	+	9.79937i	0.336314	+	0.582512i	−0.647423	+	0.762131i	$0.724153\pi$
$284$	−18.2462	−	31.6034i	−1.08271	−	1.87531i
$285$	5.56155	−	9.63289i	0.329438	−	0.570603i
$286$	1.75379			0.103704
$287$		0			0
$288$	3.68466			0.217121
$289$	8.40388	−	14.5560i	0.494346	−	0.856232i
$290$	8.56155	+	14.8290i	0.502752	+	0.870791i
$291$	−4.53457	−	7.85410i	−0.265821	−	0.460415i
$292$	27.9309	−	48.3777i	1.63453	−	2.83109i
$293$	−2.68466			−0.156839			−0.0784197	−	0.996920i	$-0.524987\pi$
$293$	−2.68466			−0.156839			−0.0784197	+	0.996920i	$0.524987\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$	19.6847	−	34.0948i	1.14415	−	1.98172i
$297$	−4.34233	−	7.52113i	−0.251967	−	0.436421i
$298$	15.6847	+	27.1666i	0.908588	+	1.57372i
$299$	−0.684658	+	1.18586i	−0.0395948	+	0.0685802i
$300$	7.12311			0.411253
$301$		0			0
$302$	17.7538			1.02162
$303$	12.6847	−	21.9705i	0.728715	−	1.26217i
$304$	27.3693	+	47.4050i	1.56974	+	2.71887i
$305$	−7.68466	−	13.3102i	−0.440022	−	0.762141i
$306$	0.315342	−	0.546188i	0.0180269	−	0.0312235i
$307$	−19.3153			−1.10238			−0.551192	−	0.834378i	$-0.685827\pi$
$307$	−19.3153			−1.10238			−0.551192	+	0.834378i	$0.685827\pi$
$308$		0			0
$309$	8.68466			0.494053
$310$		0			0
$311$	−15.8078	−	27.3799i	−0.896376	−	1.55257i	−0.832092	−	0.554637i	$-0.812857\pi$
$311$	−15.8078	−	27.3799i	−0.896376	−	1.55257i	−0.0642838	−	0.997932i	$-0.520476\pi$
$312$	2.24621	+	3.89055i	0.127167	+	0.220259i
$313$	11.1501	−	19.3125i	0.630241	−	1.09161i	−0.357262	−	0.934004i	$-0.616290\pi$
$313$	11.1501	−	19.3125i	0.630241	−	1.09161i	0.987502	−	0.157604i	$-0.0503771\pi$
$314$	−51.8617			−2.92673
$315$		0			0
$316$	−11.1231			−0.625724
$317$	−5.24621	+	9.08670i	−0.294657	+	0.510360i	−0.974905	−	0.222622i	$-0.928539\pi$
$317$	−5.24621	+	9.08670i	−0.294657	+	0.510360i	0.680248	+	0.732982i	$0.261872\pi$
$318$	−10.2462	−	17.7470i	−0.574579	−	0.995200i
$319$	5.21922	+	9.03996i	0.292220	+	0.506141i
$320$	−0.719224	+	1.24573i	−0.0402058	+	0.0696385i
$321$	20.8769			1.16523
$322$		0			0
$323$	3.12311			0.173774
$324$	15.9654	−	27.6529i	0.886969	−	1.53627i
$325$	−0.219224	−	0.379706i	−0.0121603	−	0.0210623i
$326$	−9.12311	−	15.8017i	−0.505282	−	0.875174i
$327$	−4.15009	+	7.18817i	−0.229501	+	0.397507i
$328$	−33.6155			−1.85611
$329$		0			0
$330$	6.24621			0.343843
$331$	−6.00000	+	10.3923i	−0.329790	+	0.571213i	−0.982470	−	0.186421i	$-0.940311\pi$
$331$	−6.00000	+	10.3923i	−0.329790	+	0.571213i	0.652680	+	0.757634i	$0.273645\pi$
$332$	−9.12311	−	15.8017i	−0.500695	−	0.867230i
$333$	1.68466	+	2.91791i	0.0923187	+	0.159901i
$334$	−8.87689	+	15.3752i	−0.485722	+	0.841295i
$335$	10.2462			0.559810
$336$		0			0
$337$	−1.50758			−0.0821230			−0.0410615	−	0.999157i	$-0.513074\pi$
$337$	−1.50758			−0.0821230			−0.0410615	+	0.999157i	$0.513074\pi$
$338$	−16.4039	+	28.4124i	−0.892254	+	1.54543i
$339$	10.9309	+	18.9328i	0.593683	+	1.02829i
$340$	1.00000	+	1.73205i	0.0542326	+	0.0939336i
$341$		0			0
$342$	−10.2462			−0.554052
$343$		0			0
$344$	−5.75379			−0.310223
$345$	−2.43845	+	4.22351i	−0.131282	+	0.227386i
$346$	−5.68466	−	9.84612i	−0.305609	−	0.529331i
$347$	−3.56155	−	6.16879i	−0.191194	−	0.331158i	0.754452	−	0.656355i	$-0.227903\pi$
$347$	−3.56155	−	6.16879i	−0.191194	−	0.331158i	−0.945646	+	0.325197i	$0.894569\pi$
$348$	−23.8078	+	41.2363i	−1.27623	+	2.21050i
$349$	10.4924			0.561646			0.280823	−	0.959760i	$-0.409393\pi$
$349$	10.4924			0.561646			0.280823	+	0.959760i	$0.409393\pi$
$350$		0			0
$351$	−2.43845			−0.130155
$352$	−5.12311	+	8.87348i	−0.273062	+	0.472958i
$353$	−2.90388	−	5.02967i	−0.154558	−	0.267702i	0.778340	−	0.627843i	$-0.216062\pi$
$353$	−2.90388	−	5.02967i	−0.154558	−	0.267702i	−0.932898	+	0.360141i	$0.882729\pi$
$354$	−8.00000	−	13.8564i	−0.425195	−	0.736460i
$355$	−4.00000	+	6.92820i	−0.212298	+	0.367711i
$356$	−5.12311			−0.271524
$357$		0			0
$358$	−51.2311			−2.70765
$359$	−4.00000	+	6.92820i	−0.211112	+	0.365657i	−0.952063	−	0.305903i	$-0.901042\pi$
$359$	−4.00000	+	6.92820i	−0.211112	+	0.365657i	0.740951	+	0.671559i	$0.234375\pi$
$360$	−1.84233	−	3.19101i	−0.0970993	−	0.168181i
$361$	−15.8693	−	27.4865i	−0.835227	−	1.44666i
$362$	−22.5616	+	39.0778i	−1.18581	+	2.05388i
$363$	−13.3693			−0.701707
$364$		0			0
$365$	−12.2462			−0.640996
$366$	30.7386	−	53.2409i	1.60673	−	2.78295i
$367$	4.34233	+	7.52113i	0.226668	+	0.392600i	0.956818	−	0.290686i	$-0.0938835\pi$
$367$	4.34233	+	7.52113i	0.226668	+	0.392600i	−0.730151	+	0.683286i	$0.760550\pi$
$368$	−12.0000	−	20.7846i	−0.625543	−	1.08347i
$369$	1.43845	−	2.49146i	0.0748826	−	0.129700i
$370$	−15.3693			−0.799013
$371$		0			0
$372$		0			0
$373$	−2.31534	+	4.01029i	−0.119884	+	0.207645i	−0.919721	−	0.392572i	$-0.871586\pi$
$373$	−2.31534	+	4.01029i	−0.119884	+	0.207645i	0.799838	+	0.600216i	$0.204919\pi$
$374$	0.876894	+	1.51883i	0.0453431	+	0.0785366i
$375$	−0.780776	−	1.35234i	−0.0403191	−	0.0698348i
$376$	−28.4924	+	49.3503i	−1.46938	+	2.54505i
$377$	2.93087			0.150947
$378$		0			0
$379$	−16.4924			−0.847159			−0.423579	−	0.905859i	$-0.639227\pi$
$379$	−16.4924			−0.847159			−0.423579	+	0.905859i	$0.639227\pi$
$380$	16.2462	−	28.1393i	0.833413	−	1.44351i
$381$	4.87689	+	8.44703i	0.249851	+	0.432754i
$382$	−17.3693	−	30.0845i	−0.888692	−	1.53926i
$383$	−3.12311	+	5.40938i	−0.159583	+	0.276406i	−0.934718	−	0.355389i	$-0.884348\pi$
$383$	−3.12311	+	5.40938i	−0.159583	+	0.276406i	0.775135	+	0.631795i	$0.217682\pi$
$384$	14.7386			0.752128
$385$		0			0
$386$	−49.6155			−2.52536
$387$	0.246211	−	0.426450i	0.0125156	−	0.0216777i
$388$	−13.2462	−	22.9431i	−0.672474	−	1.16476i
$389$	12.4654	+	21.5908i	0.632023	+	1.09470i	0.987138	+	0.159873i	$0.0511084\pi$
$389$	12.4654	+	21.5908i	0.632023	+	1.09470i	−0.355115	+	0.934823i	$0.615558\pi$
$390$	0.876894	−	1.51883i	0.0444033	−	0.0769087i
$391$	−1.36932			−0.0692493
$392$		0			0
$393$	−1.36932			−0.0690729
$394$	1.43845	−	2.49146i	0.0724679	−	0.125518i
$395$	1.21922	+	2.11176i	0.0613458	+	0.106254i
$396$	−2.00000	−	3.46410i	−0.100504	−	0.174078i
$397$	−13.7808	+	23.8690i	−0.691637	+	1.19795i	0.279664	+	0.960098i	$0.409777\pi$
$397$	−13.7808	+	23.8690i	−0.691637	+	1.19795i	−0.971301	+	0.237853i	$0.923556\pi$
$398$	4.49242			0.225185
$399$		0			0
$400$	7.68466			0.384233
$401$	−15.7808	+	27.3331i	−0.788054	+	1.36495i	0.139103	+	0.990278i	$0.455578\pi$
$401$	−15.7808	+	27.3331i	−0.788054	+	1.36495i	−0.927157	+	0.374672i	$0.877755\pi$
$402$	20.4924	+	35.4939i	1.02207	+	1.77028i
$403$		0			0
$404$	37.0540	−	64.1794i	1.84350	−	3.19304i
$405$	−7.00000			−0.347833
$406$		0			0
$407$	−9.36932			−0.464420
$408$	−2.24621	+	3.89055i	−0.111204	+	0.192611i
$409$	−3.24621	−	5.62260i	−0.160515	−	0.278020i	0.774539	−	0.632527i	$-0.217982\pi$
$409$	−3.24621	−	5.62260i	−0.160515	−	0.278020i	−0.935053	+	0.354507i	$0.884649\pi$
$410$	6.56155	+	11.3649i	0.324052	+	0.561275i
$411$	13.3693	−	23.1563i	0.659460	−	1.14222i
$412$	25.3693			1.24986
$413$		0			0
$414$	4.49242			0.220791
$415$	−2.00000	+	3.46410i	−0.0981761	+	0.170046i
$416$	1.43845	+	2.49146i	0.0705257	+	0.122154i
$417$	11.8078	+	20.4516i	0.578229	+	1.00152i
$418$	14.2462	−	24.6752i	0.696805	−	1.20690i
$419$	26.2462			1.28221			0.641106	−	0.767453i	$-0.278476\pi$
$419$	26.2462			1.28221			0.641106	+	0.767453i	$0.278476\pi$
$420$		0			0
$421$	−2.68466			−0.130842			−0.0654211	−	0.997858i	$-0.520839\pi$
$421$	−2.68466			−0.130842			−0.0654211	+	0.997858i	$0.520839\pi$
$422$	18.0000	−	31.1769i	0.876226	−	1.51767i
$423$	−2.43845	−	4.22351i	−0.118561	−	0.205354i
$424$	−16.8078	−	29.1119i	−0.816257	−	1.41380i
$425$	0.219224	−	0.379706i	0.0106339	−	0.0184185i
$426$	−32.0000			−1.55041
$427$		0			0
$428$	60.9848			2.94781
$429$	0.534565	−	0.925894i	0.0258090	−	0.0447026i
$430$	1.12311	+	1.94528i	0.0541610	+	0.0938095i
$431$	9.90388	+	17.1540i	0.477053	+	0.826280i	0.999654	−	0.0262970i	$-0.00837156\pi$
$431$	9.90388	+	17.1540i	0.477053	+	0.826280i	−0.522601	+	0.852577i	$0.675038\pi$
$432$	21.3693	−	37.0127i	1.02813	−	1.78078i
$433$	8.24621			0.396288			0.198144	−	0.980173i	$-0.436509\pi$
$433$	8.24621			0.396288			0.198144	+	0.980173i	$0.436509\pi$
$434$		0			0
$435$	10.4384			0.500485
$436$	−12.1231	+	20.9978i	−0.580591	+	1.00561i
$437$	11.1231	+	19.2658i	0.532090	+	0.921607i
$438$	−24.4924	−	42.4221i	−1.17029	−	2.02701i
$439$	−4.68466	+	8.11407i	−0.223587	+	0.387263i	−0.955894	−	0.293710i	$-0.905110\pi$
$439$	−4.68466	+	8.11407i	−0.223587	+	0.387263i	0.732308	+	0.680974i	$0.238443\pi$
$440$	10.2462			0.488469
$441$		0			0
$442$	0.492423			0.0234221
$443$	1.31534	−	2.27824i	0.0624938	−	0.108242i	−0.833086	−	0.553144i	$-0.813428\pi$
$443$	1.31534	−	2.27824i	0.0624938	−	0.108242i	0.895580	+	0.444901i	$0.146761\pi$
$444$	−21.3693	−	37.0127i	−1.01414	−	1.75655i
$445$	0.561553	+	0.972638i	0.0266202	+	0.0461075i
$446$	−3.12311	+	5.40938i	−0.147883	+	0.256141i
$447$	19.1231			0.904492
$448$		0			0
$449$	−1.80776			−0.0853137			−0.0426568	−	0.999090i	$-0.513582\pi$
$449$	−1.80776			−0.0853137			−0.0426568	+	0.999090i	$0.513582\pi$
$450$	−0.719224	+	1.24573i	−0.0339045	+	0.0587244i
$451$	4.00000	+	6.92820i	0.188353	+	0.326236i
$452$	31.9309	+	55.3059i	1.50190	+	2.60137i
$453$	5.41146	−	9.37292i	0.254253	−	0.440378i
$454$	−28.9848			−1.36033
$455$		0			0
$456$	72.9848			3.41783
$457$	8.56155	−	14.8290i	0.400493	−	0.693673i	−0.593293	−	0.804987i	$-0.702172\pi$
$457$	8.56155	−	14.8290i	0.400493	−	0.693673i	0.993785	+	0.111313i	$0.0355057\pi$
$458$	13.9309	+	24.1290i	0.650947	+	1.12747i
$459$	−1.21922	−	2.11176i	−0.0569085	−	0.0985684i
$460$	−7.12311	+	12.3376i	−0.332117	+	0.575243i
$461$	−13.1231			−0.611204			−0.305602	−	0.952159i	$-0.598858\pi$
$461$	−13.1231			−0.611204			−0.305602	+	0.952159i	$0.598858\pi$
$462$		0			0
$463$	12.4924			0.580572			0.290286	−	0.956940i	$-0.406250\pi$
$463$	12.4924			0.580572			0.290286	+	0.956940i	$0.406250\pi$
$464$	−25.6847	+	44.4871i	−1.19238	+	2.06526i
$465$		0			0
$466$	6.56155	+	11.3649i	0.303958	+	0.526471i
$467$	−11.2192	+	19.4323i	−0.519164	+	0.899218i	0.480588	+	0.876946i	$0.340423\pi$
$467$	−11.2192	+	19.4323i	−0.519164	+	0.899218i	−0.999752	+	0.0222716i	$0.992910\pi$
$468$	−1.12311			−0.0519156
$469$		0			0
$470$	22.2462			1.02614
$471$	−15.8078	+	27.3799i	−0.728383	+	1.26160i
$472$	−13.1231	−	22.7299i	−0.604040	−	1.04623i
$473$	0.684658	+	1.18586i	0.0314806	+	0.0545260i
$474$	−4.87689	+	8.44703i	−0.224003	+	0.387985i
$475$	−7.12311			−0.326831
$476$		0			0
$477$	2.87689			0.131724
$478$	25.3693	−	43.9409i	1.16037	−	2.00981i
$479$	−2.43845	−	4.22351i	−0.111415	−	0.192977i	0.804926	−	0.593376i	$-0.202205\pi$
$479$	−2.43845	−	4.22351i	−0.111415	−	0.192977i	−0.916341	+	0.400398i	$0.868872\pi$
$480$	5.12311	+	8.87348i	0.233837	+	0.405017i
$481$	−1.31534	+	2.27824i	−0.0599744	+	0.103879i
$482$	10.8769			0.495429
$483$		0			0
$484$	−39.0540			−1.77518
$485$	−2.90388	+	5.02967i	−0.131858	+	0.228386i
$486$	7.36932	+	12.7640i	0.334279	+	0.578988i
$487$	1.56155	+	2.70469i	0.0707607	+	0.122561i	0.899235	−	0.437466i	$-0.144124\pi$
$487$	1.56155	+	2.70469i	0.0707607	+	0.122561i	−0.828474	+	0.560027i	$0.810791\pi$
$488$	50.4233	−	87.3357i	2.28256	−	3.95350i
$489$	−11.1231			−0.503004
$490$		0			0
$491$	−41.1771			−1.85830			−0.929148	−	0.369708i	$-0.879458\pi$
$491$	−41.1771			−1.85830			−0.929148	+	0.369708i	$0.879458\pi$
$492$	−18.2462	+	31.6034i	−0.822603	+	1.42479i
$493$	1.46543	+	2.53821i	0.0659999	+	0.114315i
$494$	−4.00000	−	6.92820i	−0.179969	−	0.311715i
$495$	−0.438447	+	0.759413i	−0.0197067	+	0.0341331i
$496$		0			0
$497$		0			0
$498$	−16.0000			−0.716977
$499$	−20.5885	+	35.6604i	−0.921670	+	1.59638i	−0.124838	+	0.992177i	$0.539841\pi$
$499$	−20.5885	+	35.6604i	−0.921670	+	1.59638i	−0.796832	+	0.604202i	$0.793492\pi$
$500$	−2.28078	−	3.95042i	−0.101999	−	0.176668i
$501$	5.41146	+	9.37292i	0.241766	+	0.418751i
$502$	−11.3693	+	19.6922i	−0.507437	+	0.878907i
$503$	38.9309			1.73584			0.867921	−	0.496703i	$-0.165456\pi$
$503$	38.9309			1.73584			0.867921	+	0.496703i	$0.165456\pi$
$504$		0			0
$505$	−16.2462			−0.722947
$506$	−6.24621	+	10.8188i	−0.277678	+	0.480952i
$507$	10.0000	+	17.3205i	0.444116	+	0.769231i
$508$	14.2462	+	24.6752i	0.632073	+	1.09478i
$509$	5.87689	−	10.1791i	0.260489	−	0.451180i	−0.705883	−	0.708328i	$-0.749450\pi$
$509$	5.87689	−	10.1791i	0.260489	−	0.451180i	0.966372	+	0.257149i	$0.0827830\pi$
$510$	1.75379			0.0776591
$511$		0			0
$512$	50.4233			2.22842
$513$	−19.8078	+	34.3081i	−0.874534	+	1.51474i
$514$	−13.4384	−	23.2761i	−0.592744	−	1.02666i
$515$	−2.78078	−	4.81645i	−0.122536	−	0.212238i
$516$	−3.12311	+	5.40938i	−0.137487	+	0.238135i
$517$	13.5616			0.596436
$518$		0			0
$519$	−6.93087			−0.304231
$520$	1.43845	−	2.49146i	0.0630801	−	0.109258i
$521$	−5.00000	−	8.66025i	−0.219054	−	0.379413i	0.735465	−	0.677563i	$-0.236964\pi$
$521$	−5.00000	−	8.66025i	−0.219054	−	0.379413i	−0.954519	+	0.298150i	$0.903630\pi$
$522$	−4.80776	−	8.32729i	−0.210430	−	0.364476i
$523$	−20.2462	+	35.0675i	−0.885305	+	1.53339i	−0.0399413	+	0.999202i	$0.512717\pi$
$523$	−20.2462	+	35.0675i	−0.885305	+	1.53339i	−0.845364	+	0.534191i	$0.820616\pi$
$524$	−4.00000			−0.174741
$525$		0			0
$526$	32.9848			1.43821
$527$		0			0
$528$	9.36932	+	16.2281i	0.407747	+	0.706239i
$529$	6.62311	+	11.4716i	0.287961	+	0.498763i
$530$	−6.56155	+	11.3649i	−0.285016	+	0.493662i
$531$	2.24621			0.0974773
$532$		0			0
$533$	2.24621			0.0972942
$534$	−2.24621	+	3.89055i	−0.0972031	+	0.168361i
$535$	−6.68466	−	11.5782i	−0.289003	−	0.500568i
$536$	33.6155	+	58.2238i	1.45197	+	2.51489i
$537$	−15.6155	+	27.0469i	−0.673860	+	1.16716i
$538$	53.1231			2.29030
$539$		0			0
$540$	−25.3693			−1.09172
$541$	18.9039	−	32.7425i	0.812741	−	1.40771i	−0.0981971	−	0.995167i	$-0.531308\pi$
$541$	18.9039	−	32.7425i	0.812741	−	1.40771i	0.910938	−	0.412542i	$-0.135359\pi$
$542$	−20.4924	−	35.4939i	−0.880225	−	1.52459i
$543$	13.7538	+	23.8223i	0.590232	+	1.02231i
$544$	−1.43845	+	2.49146i	−0.0616729	+	0.106821i
$545$	5.31534			0.227684
$546$		0			0
$547$	−2.24621			−0.0960411			−0.0480205	−	0.998846i	$-0.515291\pi$
$547$	−2.24621			−0.0960411			−0.0480205	+	0.998846i	$0.515291\pi$
$548$	39.0540	−	67.6435i	1.66830	−	2.88959i
$549$	4.31534	+	7.47439i	0.184174	+	0.318999i
$550$	−2.00000	−	3.46410i	−0.0852803	−	0.147710i
$551$	23.8078	−	41.2363i	1.01424	−	1.75672i
$552$	−32.0000			−1.36201
$553$		0			0
$554$	0.630683			0.0267952
$555$	−4.68466	+	8.11407i	−0.198853	+	0.344423i
$556$	34.4924	+	59.7426i	1.46280	+	2.53365i
$557$	6.56155	+	11.3649i	0.278022	+	0.481548i	0.970893	−	0.239513i	$-0.0769879\pi$
$557$	6.56155	+	11.3649i	0.278022	+	0.481548i	−0.692871	+	0.721061i	$0.743655\pi$
$558$		0			0
$559$	0.384472			0.0162614
$560$		0			0
$561$	1.06913			0.0451387
$562$	15.9309	−	27.5931i	0.672003	−	1.16394i
$563$	14.0000	+	24.2487i	0.590030	+	1.02196i	0.994228	+	0.107290i	$0.0342173\pi$
$563$	14.0000	+	24.2487i	0.590030	+	1.02196i	−0.404198	+	0.914671i	$0.632449\pi$
$564$	30.9309	+	53.5738i	1.30242	+	2.25587i
$565$	7.00000	−	12.1244i	0.294492	−	0.510075i
$566$	28.9848			1.21832
$567$		0			0
$568$	−52.4924			−2.20253
$569$	15.4924	−	26.8337i	0.649476	−	1.12493i	−0.333772	−	0.942654i	$-0.608322\pi$
$569$	15.4924	−	26.8337i	0.649476	−	1.12493i	0.983248	−	0.182272i	$-0.0583451\pi$
$570$	−14.2462	−	24.6752i	−0.596708	−	1.03353i
$571$	−20.2462	−	35.0675i	−0.847278	−	1.46753i	−0.883629	−	0.468189i	$-0.844907\pi$
$571$	−20.2462	−	35.0675i	−0.847278	−	1.46753i	0.0363509	−	0.999339i	$-0.488427\pi$
$572$	1.56155	−	2.70469i	0.0652918	−	0.113089i
$573$	−21.1771			−0.884685
$574$		0			0
$575$	3.12311			0.130243
$576$	0.403882	−	0.699544i	0.0168284	−	0.0291477i
$577$	12.0270	+	20.8314i	0.500690	+	0.867221i	1.00000		0.000796982i	$0.000253687\pi$
$577$	12.0270	+	20.8314i	0.500690	+	0.867221i	−0.499310	+	0.866424i	$0.666413\pi$
$578$	−21.5270	−	37.2858i	−0.895405	−	1.55089i
$579$	−15.1231	+	26.1940i	−0.628495	+	1.08858i
$580$	30.4924			1.26613
$581$		0			0
$582$	−23.2311			−0.962958
$583$	−4.00000	+	6.92820i	−0.165663	+	0.286937i
$584$	−40.1771	−	69.5887i	−1.66254	−	2.87960i
$585$	0.123106	+	0.213225i	0.00508979	+	0.00881578i
$586$	−3.43845	+	5.95557i	−0.142041	+	0.246022i
$587$	−26.2462			−1.08330			−0.541649	−	0.840605i	$-0.682200\pi$
$587$	−26.2462			−1.08330			−0.541649	+	0.840605i	$0.682200\pi$
$588$		0			0
$589$		0			0
$590$	−5.12311	+	8.87348i	−0.210915	+	0.365315i
$591$	−0.876894	−	1.51883i	−0.0360706	−	0.0624761i
$592$	−23.0540	−	39.9307i	−0.947513	−	1.64114i
$593$	13.7808	−	23.8690i	0.565909	−	0.980183i	−0.431056	−	0.902325i	$-0.641859\pi$
$593$	13.7808	−	23.8690i	0.565909	−	0.980183i	0.996965	−	0.0778573i	$-0.0248079\pi$
$594$	−22.2462			−0.912773
$595$		0			0
$596$	55.8617			2.28819
$597$	1.36932	−	2.37173i	0.0560424	−	0.0970683i
$598$	1.75379	+	3.03765i	0.0717178	+	0.124219i
$599$	5.90388	+	10.2258i	0.241226	+	0.417816i	0.961064	−	0.276327i	$-0.0891171\pi$
$599$	5.90388	+	10.2258i	0.241226	+	0.417816i	−0.719838	+	0.694142i	$0.755784\pi$
$600$	5.12311	−	8.87348i	0.209150	−	0.362258i
$601$	6.49242			0.264831			0.132416	−	0.991194i	$-0.457727\pi$
$601$	6.49242			0.264831			0.132416	+	0.991194i	$0.457727\pi$
$602$		0			0
$603$	−5.75379			−0.234312
$604$	15.8078	−	27.3799i	0.643209	−	1.11407i
$605$	4.28078	+	7.41452i	0.174038	+	0.301443i
$606$	−32.4924	−	56.2785i	−1.31991	−	2.28616i
$607$	21.0270	−	36.4198i	0.853459	−	1.47823i	−0.0246081	−	0.999697i	$-0.507834\pi$
$607$	21.0270	−	36.4198i	0.853459	−	1.47823i	0.878067	−	0.478537i	$-0.158833\pi$
$608$	46.7386			1.89550
$609$		0			0
$610$	−39.3693			−1.59402
$611$	1.90388	−	3.29762i	0.0770228	−	0.133407i
$612$	−0.561553	−	0.972638i	−0.0226994	−	0.0393166i
$613$	−20.3693	−	35.2807i	−0.822709	−	1.42497i	−0.903658	−	0.428255i	$-0.859128\pi$
$613$	−20.3693	−	35.2807i	−0.822709	−	1.42497i	0.0809488	−	0.996718i	$-0.474205\pi$
$614$	−24.7386	+	42.8486i	−0.998370	+	1.72923i
$615$	8.00000			0.322591
$616$		0			0
$617$	32.2462			1.29818			0.649092	−	0.760710i	$-0.275149\pi$
$617$	32.2462			1.29818			0.649092	+	0.760710i	$0.275149\pi$
$618$	11.1231	−	19.2658i	0.447437	−	0.774983i
$619$	−16.0540	−	27.8063i	−0.645264	−	1.11763i	−0.984241	−	0.176835i	$-0.943414\pi$
$619$	−16.0540	−	27.8063i	−0.645264	−	1.11763i	0.338977	−	0.940795i	$-0.389919\pi$
$620$		0			0
$621$	8.68466	−	15.0423i	0.348503	−	0.603625i
$622$	−80.9848			−3.24720
$623$		0			0
$624$	5.26137			0.210623
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−28.5616	−	49.4701i	−1.14155	−	1.97722i
$627$	−8.68466	−	15.0423i	−0.346832	−	0.600730i
$628$	−46.1771	+	79.9811i	−1.84267	+	3.19159i
$629$	−2.63068			−0.104892
$630$		0			0
$631$	−11.8078			−0.470060			−0.235030	−	0.971988i	$-0.575519\pi$
$631$	−11.8078			−0.470060			−0.235030	+	0.971988i	$0.575519\pi$
$632$	−8.00000	+	13.8564i	−0.318223	+	0.551178i
$633$	−10.9730	−	19.0058i	−0.436138	−	0.755413i
$634$	13.4384	+	23.2761i	0.533709	+	0.924411i
$635$	3.12311	−	5.40938i	0.123937	−	0.214665i
$636$	−36.4924			−1.44702
$637$		0			0
$638$	26.7386			1.05859
$639$	2.24621	−	3.89055i	0.0888587	−	0.153908i
$640$	−4.71922	−	8.17394i	−0.186544	−	0.323103i
$641$	−1.00000	−	1.73205i	−0.0394976	−	0.0684119i	0.845601	−	0.533816i	$-0.179242\pi$
$641$	−1.00000	−	1.73205i	−0.0394976	−	0.0684119i	−0.885098	+	0.465404i	$0.845909\pi$
$642$	26.7386	−	46.3127i	1.05529	−	1.82782i
$643$	1.56155			0.0615816			0.0307908	−	0.999526i	$-0.490197\pi$
$643$	1.56155			0.0615816			0.0307908	+	0.999526i	$0.490197\pi$
$644$		0			0
$645$	1.36932			0.0539168
$646$	4.00000	−	6.92820i	0.157378	−	0.272587i
$647$	−18.2462	−	31.6034i	−0.717333	−	1.24246i	−0.962053	−	0.272863i	$-0.912029\pi$
$647$	−18.2462	−	31.6034i	−0.717333	−	1.24246i	0.244720	−	0.969594i	$-0.421304\pi$
$648$	−22.9654	−	39.7773i	−0.902167	−	1.56260i
$649$	−3.12311	+	5.40938i	−0.122593	+	0.212337i
$650$	−1.12311			−0.0440518
$651$		0			0
$652$	−32.4924			−1.27250
$653$	16.6155	−	28.7789i	0.650216	−	1.12621i	−0.332854	−	0.942978i	$-0.608012\pi$
$653$	16.6155	−	28.7789i	0.650216	−	1.12621i	0.983070	−	0.183229i	$-0.0586549\pi$
$654$	10.6307	+	18.4129i	0.415693	+	0.720001i
$655$	0.438447	+	0.759413i	0.0171315	+	0.0296727i
$656$	−19.6847	+	34.0948i	−0.768557	+	1.33118i
$657$	6.87689			0.268293
$658$		0			0
$659$	9.17708			0.357488			0.178744	−	0.983896i	$-0.442797\pi$
$659$	9.17708			0.357488			0.178744	+	0.983896i	$0.442797\pi$
$660$	5.56155	−	9.63289i	0.216483	−	0.374960i
$661$	2.56155	+	4.43674i	0.0996329	+	0.172569i	0.911533	−	0.411228i	$-0.134900\pi$
$661$	2.56155	+	4.43674i	0.0996329	+	0.172569i	−0.811900	+	0.583797i	$0.801567\pi$
$662$	15.3693	+	26.6204i	0.597345	+	1.03463i
$663$	0.150093	−	0.259969i	0.00582914	−	0.0100964i
$664$	−26.2462			−1.01855
$665$		0			0
$666$	8.63068			0.334432
$667$	−10.4384	+	18.0799i	−0.404178	+	0.700057i
$668$	15.8078	+	27.3799i	0.611621	+	1.05936i
$669$	1.90388	+	3.29762i	0.0736083	+	0.127493i
$670$	13.1231	−	22.7299i	0.506990	−	0.878132i
$671$	−24.0000			−0.926510
$672$		0			0
$673$	31.8617			1.22818			0.614090	−	0.789236i	$-0.289523\pi$
$673$	31.8617			1.22818			0.614090	+	0.789236i	$0.289523\pi$
$674$	−1.93087	+	3.34436i	−0.0743743	+	0.128820i
$675$	2.78078	+	4.81645i	0.107032	+	0.185385i
$676$	29.2116	+	50.5961i	1.12352	+	1.94600i
$677$	−2.46543	+	4.27026i	−0.0947544	+	0.164119i	−0.909506	−	0.415691i	$-0.863540\pi$
$677$	−2.46543	+	4.27026i	−0.0947544	+	0.164119i	0.814752	+	0.579810i	$0.196873\pi$
$678$	56.0000			2.15067
$679$		0			0
$680$	2.87689			0.110324
$681$	−8.83475	+	15.3022i	−0.338548	+	0.586383i
$682$		0			0
$683$	3.36932	+	5.83583i	0.128923	+	0.223302i	0.923260	−	0.384176i	$-0.125515\pi$
$683$	3.36932	+	5.83583i	0.128923	+	0.223302i	−0.794336	+	0.607478i	$0.792181\pi$
$684$	−9.12311	+	15.8017i	−0.348831	+	0.604192i
$685$	−17.1231			−0.654240
$686$		0			0
$687$	16.9848			0.648012
$688$	−3.36932	+	5.83583i	−0.128454	+	0.222489i
$689$	1.12311	+	1.94528i	0.0427869	+	0.0741091i
$690$	6.24621	+	10.8188i	0.237789	+	0.411863i
$691$	12.2462	−	21.2111i	0.465868	−	0.806907i	−0.533372	−	0.845881i	$-0.679076\pi$
$691$	12.2462	−	21.2111i	0.465868	−	0.806907i	0.999240	+	0.0389738i	$0.0124089\pi$
$692$	−20.2462			−0.769645
$693$		0			0
$694$	−18.2462			−0.692617
$695$	7.56155	−	13.0970i	0.286826	−	0.496797i
$696$	34.2462	+	59.3162i	1.29810	+	2.24837i
$697$	1.12311	+	1.94528i	0.0425407	+	0.0736826i
$698$	13.4384	−	23.2761i	0.508653	−	0.881012i
$699$	8.00000			0.302588
$700$		0			0
$701$	28.9309			1.09270			0.546352	−	0.837556i	$-0.316016\pi$
$701$	28.9309			1.09270			0.546352	+	0.837556i	$0.316016\pi$
$702$	−3.12311	+	5.40938i	−0.117874	+	0.204164i
$703$	21.3693	+	37.0127i	0.805959	+	1.39596i
$704$	1.12311	+	1.94528i	0.0423286	+	0.0733153i
$705$	6.78078	−	11.7446i	0.255379	−	0.442329i
$706$	−14.8769			−0.559899
$707$		0			0
$708$	−28.4924			−1.07081
$709$	−13.5885	+	23.5360i	−0.510328	+	0.883915i	0.489600	+	0.871947i	$0.337143\pi$
$709$	−13.5885	+	23.5360i	−0.510328	+	0.883915i	−0.999928	+	0.0119675i	$0.996191\pi$
$710$	10.2462	+	17.7470i	0.384533	+	0.666031i
$711$	−0.684658	−	1.18586i	−0.0256767	−	0.0444733i
$712$	−3.68466	+	6.38202i	−0.138088	+	0.239176i
$713$		0			0
$714$		0			0
$715$	−0.684658			−0.0256048
$716$	−45.6155	+	79.0084i	−1.70473	+	2.95268i
$717$	−15.4654	−	26.7869i	−0.577567	−	1.00038i
$718$	10.2462	+	17.7470i	0.382385	+	0.662311i
$719$	−4.19224	+	7.26117i	−0.156344	+	0.270796i	−0.933548	−	0.358453i	$-0.883304\pi$
$719$	−4.19224	+	7.26117i	−0.156344	+	0.270796i	0.777204	+	0.629249i	$0.216638\pi$
$720$	−4.31534			−0.160823
$721$		0			0
$722$	−81.3002			−3.02568
$723$	3.31534	−	5.74234i	0.123299	−	0.213560i
$724$	40.1771	+	69.5887i	1.49317	+	2.58625i
$725$	−3.34233	−	5.78908i	−0.124131	−	0.215001i
$726$	−17.1231	+	29.6581i	−0.635498	+	1.10071i
$727$	52.4924			1.94684			0.973418	−	0.229035i	$-0.0735572\pi$
$727$	52.4924			1.94684			0.973418	+	0.229035i	$0.0735572\pi$
$728$		0			0
$729$	29.9848			1.11055
$730$	−15.6847	+	27.1666i	−0.580515	+	1.00548i
$731$	0.192236	+	0.332962i	0.00711010	+	0.0123151i
$732$	−54.7386	−	94.8101i	−2.02320	−	3.50428i
$733$	−3.34233	+	5.78908i	−0.123452	+	0.213825i	−0.921127	−	0.389263i	$-0.872730\pi$
$733$	−3.34233	+	5.78908i	−0.123452	+	0.213825i	0.797675	+	0.603088i	$0.206063\pi$
$734$	22.2462			0.821123
$735$		0			0
$736$	−20.4924			−0.755361
$737$	8.00000	−	13.8564i	0.294684	−	0.510407i
$738$	−3.68466	−	6.38202i	−0.135634	−	0.234925i
$739$	−17.4654	−	30.2510i	−0.642476	−	1.11280i	−0.984878	−	0.173248i	$-0.944574\pi$
$739$	−17.4654	−	30.2510i	−0.642476	−	1.11280i	0.342402	−	0.939554i	$-0.388760\pi$
$740$	−13.6847	+	23.7025i	−0.503058	+	0.871322i
$741$	−4.87689			−0.179157
$742$		0			0
$743$	−32.9848			−1.21010			−0.605048	−	0.796189i	$-0.706846\pi$
$743$	−32.9848			−1.21010			−0.605048	+	0.796189i	$0.706846\pi$
$744$		0			0
$745$	−6.12311	−	10.6055i	−0.224333	−	0.388557i
$746$	5.93087	+	10.2726i	0.217145	+	0.376105i
$747$	1.12311	−	1.94528i	0.0410923	−	0.0711739i
$748$	3.12311			0.114192
$749$		0			0
$750$	−4.00000			−0.146059
$751$	−8.53457	+	14.7823i	−0.311431	+	0.539414i	−0.978672	−	0.205428i	$-0.934142\pi$
$751$	−8.53457	+	14.7823i	−0.311431	+	0.539414i	0.667242	+	0.744841i	$0.267475\pi$
$752$	33.3693	+	57.7974i	1.21685	+	2.10765i
$753$	6.93087	+	12.0046i	0.252575	+	0.437473i
$754$	3.75379	−	6.50175i	0.136705	−	0.236780i
$755$	−6.93087			−0.252240
$756$		0			0
$757$	39.3693			1.43090			0.715451	−	0.698663i	$-0.246221\pi$
$757$	39.3693			1.43090			0.715451	+	0.698663i	$0.246221\pi$
$758$	−21.1231	+	36.5863i	−0.767226	+	1.32887i
$759$	3.80776	+	6.59524i	0.138213	+	0.239392i
$760$	−23.3693	−	40.4768i	−0.847694	−	1.46825i
$761$	−24.1231	+	41.7824i	−0.874462	+	1.51461i	−0.0171270	+	0.999853i	$0.505452\pi$
$761$	−24.1231	+	41.7824i	−0.874462	+	1.51461i	−0.857335	+	0.514759i	$0.827881\pi$
$762$	24.9848			0.905105
$763$		0			0
$764$	−61.8617			−2.23808
$765$	−0.123106	+	0.213225i	−0.00445089	+	0.00770917i
$766$	8.00000	+	13.8564i	0.289052	+	0.500652i
$767$	0.876894	+	1.51883i	0.0316628	+	0.0548416i
$768$	21.1231	−	36.5863i	0.762214	−	1.32019i
$769$	−42.4924			−1.53232			−0.766158	−	0.642652i	$-0.777834\pi$
$769$	−42.4924			−1.53232			−0.766158	+	0.642652i	$0.777834\pi$
$770$		0			0
$771$	−16.3845			−0.590072
$772$	−44.1771	+	76.5169i	−1.58997	+	2.75391i
$773$	−18.4654	−	31.9831i	−0.664156	−	1.15035i	−0.979514	−	0.201378i	$-0.935458\pi$
$773$	−18.4654	−	31.9831i	−0.664156	−	1.15035i	0.315358	−	0.948973i	$-0.397875\pi$
$774$	−0.630683	−	1.09238i	−0.0226694	−	0.0392646i
$775$		0			0
$776$	−38.1080			−1.36800
$777$		0			0
$778$	63.8617			2.28955
$779$	18.2462	−	31.6034i	0.653738	−	1.13231i
$780$	−1.56155	−	2.70469i	−0.0559126	−	0.0968434i
$781$	6.24621	+	10.8188i	0.223507	+	0.387125i
$782$	−1.75379	+	3.03765i	−0.0627154	+	0.108626i
$783$	−37.1771			−1.32860
$784$		0			0
$785$	20.2462			0.722618
$786$	−1.75379	+	3.03765i	−0.0625556	+	0.108349i
$787$	24.5885	+	42.5886i	0.876487	+	1.51812i	0.855170	+	0.518347i	$0.173452\pi$
$787$	24.5885	+	42.5886i	0.876487	+	1.51812i	0.0213164	+	0.999773i	$0.493214\pi$
$788$	−2.56155	−	4.43674i	−0.0912515	−	0.158052i
$789$	10.0540	−	17.4140i	0.357931	−	0.619955i
$790$	6.24621			0.222230
$791$		0			0
$792$	−5.75379			−0.204452
$793$	−3.36932	+	5.83583i	−0.119648	+	0.207236i
$794$	35.3002	+	61.1417i	1.25276	+	2.16984i
$795$	4.00000	+	6.92820i	0.141865	+	0.245718i
$796$	4.00000	−	6.92820i	0.141776	−	0.245564i
$797$	24.0540			0.852036			0.426018	−	0.904715i	$-0.359916\pi$
$797$	24.0540			0.852036			0.426018	+	0.904715i	$0.359916\pi$
$798$		0			0
$799$	3.80776			0.134709
$800$	3.28078	−	5.68247i	0.115993	−	0.200906i
$801$	−0.315342	−	0.546188i	−0.0111420	−	0.0192986i
$802$	40.4233	+	70.0152i	1.42740	+	2.47232i
$803$	−9.56155	+	16.5611i	−0.337420	+	0.584428i
$804$	72.9848			2.57398
$805$		0			0
$806$		0			0
$807$	16.1922	−	28.0458i	0.569994	−	0.987258i
$808$	−53.3002	−	92.3186i	−1.87509	−	3.24776i
$809$	−8.27320	−	14.3296i	−0.290870	−	0.503802i	0.683146	−	0.730282i	$-0.260611\pi$
$809$	−8.27320	−	14.3296i	−0.290870	−	0.503802i	−0.974016	+	0.226480i	$0.927278\pi$
$810$	−8.96543	+	15.5286i	−0.315013	+	0.545619i
$811$	19.6155			0.688794			0.344397	−	0.938824i	$-0.388083\pi$
$811$	19.6155			0.688794			0.344397	+	0.938824i	$0.388083\pi$
$812$		0			0
$813$	−24.9848			−0.876257
$814$	−12.0000	+	20.7846i	−0.420600	+	0.728500i
$815$	3.56155	+	6.16879i	0.124756	+	0.216083i
$816$	2.63068	+	4.55648i	0.0920923	+	0.159509i
$817$	3.12311	−	5.40938i	0.109264	−	0.189250i
$818$	−16.6307			−0.581478
$819$		0			0
$820$	23.3693			0.816092
$821$	10.7116	−	18.5531i	0.373839	−	0.647508i	−0.616314	−	0.787501i	$-0.711375\pi$
$821$	10.7116	−	18.5531i	0.373839	−	0.647508i	0.990153	+	0.139993i	$0.0447079\pi$
$822$	−34.2462	−	59.3162i	−1.19447	−	2.06889i
$823$	18.2462	+	31.6034i	0.636023	+	1.10162i	0.986297	+	0.164977i	$0.0527550\pi$
$823$	18.2462	+	31.6034i	0.636023	+	1.10162i	−0.350274	+	0.936647i	$0.613912\pi$
$824$	18.2462	−	31.6034i	0.635637	−	1.10096i
$825$	−2.43845			−0.0848958
$826$		0			0
$827$	−5.36932			−0.186709			−0.0933547	−	0.995633i	$-0.529759\pi$
$827$	−5.36932			−0.186709			−0.0933547	+	0.995633i	$0.529759\pi$
$828$	4.00000	−	6.92820i	0.139010	−	0.240772i
$829$	−17.4384	−	30.2043i	−0.605662	−	1.04904i	−0.991946	−	0.126658i	$-0.959575\pi$
$829$	−17.4384	−	30.2043i	−0.605662	−	1.04904i	0.386284	−	0.922380i	$-0.373758\pi$
$830$	5.12311	+	8.87348i	0.177826	+	0.308003i
$831$	0.192236	−	0.332962i	0.00666859	−	0.0115503i
$832$	0.630683			0.0218650
$833$		0			0
$834$	60.4924			2.09468
$835$	3.46543	−	6.00231i	0.119926	−	0.207718i
$836$	−25.3693	−	43.9409i	−0.877416	−	1.51973i
$837$		0			0
$838$	33.6155	−	58.2238i	1.16123	−	2.01131i
$839$	−28.8769			−0.996941			−0.498471	−	0.866907i	$-0.666105\pi$
$839$	−28.8769			−0.996941			−0.498471	+	0.866907i	$0.666105\pi$
$840$		0			0
$841$	15.6847			0.540850
$842$	−3.43845	+	5.95557i	−0.118497	+	0.205242i
$843$	−9.71165	−	16.8211i	−0.334487	−	0.579348i
$844$	−32.0540	−	55.5191i	−1.10334	−	1.91105i
$845$	6.40388	−	11.0918i	0.220300	−	0.381571i
$846$	−12.4924			−0.429498
$847$		0			0
$848$	−39.3693			−1.35195
$849$	8.83475	−	15.3022i	0.303208	−	0.525171i
$850$	−0.561553	−	0.972638i	−0.0192611	−	0.0333612i
$851$	−9.36932	−	16.2281i	−0.321176	−	0.556293i
$852$	−28.4924	+	49.3503i	−0.976134	+	1.69071i
$853$	−7.26137			−0.248624			−0.124312	−	0.992243i	$-0.539672\pi$
$853$	−7.26137			−0.248624			−0.124312	+	0.992243i	$0.539672\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$	43.8617	−	75.9708i	1.49916	−	2.59663i
$857$	7.87689	+	13.6432i	0.269070	+	0.466042i	0.968622	−	0.248539i	$-0.0799505\pi$
$857$	7.87689	+	13.6432i	0.269070	+	0.466042i	−0.699552	+	0.714581i	$0.746617\pi$
$858$	−1.36932	−	2.37173i	−0.0467477	−	0.0809694i
$859$	8.24621	−	14.2829i	0.281357	−	0.487325i	−0.690362	−	0.723464i	$-0.742549\pi$
$859$	8.24621	−	14.2829i	0.281357	−	0.487325i	0.971719	+	0.236139i	$0.0758821\pi$
$860$	4.00000			0.136399
$861$		0			0
$862$	50.7386			1.72816
$863$	12.8769	−	22.3034i	0.438335	−	0.759218i	−0.559227	−	0.829015i	$-0.688902\pi$
$863$	12.8769	−	22.3034i	0.438335	−	0.759218i	0.997561	+	0.0697971i	$0.0222352\pi$
$864$	−18.2462	−	31.6034i	−0.620749	−	1.07517i
$865$	2.21922	+	3.84381i	0.0754559	+	0.130693i
$866$	10.5616	−	18.2931i	0.358896	−	0.621626i
$867$	−26.2462			−0.891368
$868$		0			0
$869$	3.80776			0.129170
$870$	13.3693	−	23.1563i	0.453262	−	0.785073i
$871$	−2.24621	−	3.89055i	−0.0761100	−	0.131826i
$872$	17.4384	+	30.2043i	0.590540	+	1.02285i
$873$	1.63068	−	2.82443i	0.0551903	−	0.0955923i
$874$	56.9848			1.92754
$875$		0			0
$876$	−87.2311			−2.94726
$877$	20.1231	−	34.8542i	0.679509	−	1.17694i	−0.295620	−	0.955306i	$-0.595526\pi$
$877$	20.1231	−	34.8542i	0.679509	−	1.17694i	0.975129	−	0.221638i	$-0.0711405\pi$
$878$	12.0000	+	20.7846i	0.404980	+	0.701447i
$879$	2.09612	+	3.63058i	0.0707003	+	0.122457i
$880$	6.00000	−	10.3923i	0.202260	−	0.350325i
$881$	−11.8617			−0.399632			−0.199816	−	0.979833i	$-0.564034\pi$
$881$	−11.8617			−0.399632			−0.199816	+	0.979833i	$0.564034\pi$
$882$		0			0
$883$	−8.49242			−0.285793			−0.142896	−	0.989738i	$-0.545642\pi$
$883$	−8.49242			−0.285793			−0.142896	+	0.989738i	$0.545642\pi$
$884$	0.438447	−	0.759413i	0.0147466	−	0.0255418i
$885$	3.12311	+	5.40938i	0.104982	+	0.181834i
$886$	−3.36932	−	5.83583i	−0.113194	−	0.196058i
$887$	−10.2462	+	17.7470i	−0.344034	+	0.595885i	−0.985178	−	0.171536i	$-0.945127\pi$
$887$	−10.2462	+	17.7470i	−0.344034	+	0.595885i	0.641144	+	0.767421i	$0.278460\pi$
$888$	−61.4773			−2.06304
$889$		0			0
$890$	2.87689			0.0964337
$891$	−5.46543	+	9.46641i	−0.183099	+	0.317137i
$892$	5.56155	+	9.63289i	0.186215	+	0.322533i
$893$	−30.9309	−	53.5738i	−1.03506	−	1.79278i
$894$	24.4924	−	42.4221i	0.819149	−	1.41881i
$895$	20.0000			0.668526
$896$		0			0
$897$	2.13826			0.0713944
$898$	−2.31534	+	4.01029i	−0.0772639	+	0.133825i
$899$		0			0
$900$	1.28078	+	2.21837i	0.0426925	+	0.0739457i
$901$	−1.12311	+	1.94528i	−0.0374161	+	0.0648065i
$902$	20.4924			0.682323
$903$		0			0
$904$	91.8617			3.05528
$905$	8.80776	−	15.2555i	0.292780	−	0.507110i
$906$	−13.8617	−	24.0092i	−0.460525	−	0.797653i
$907$	12.0540	+	20.8781i	0.400246	+	0.693246i	0.993755	−	0.111581i	$-0.0355915\pi$
$907$	12.0540	+	20.8781i	0.400246	+	0.693246i	−0.593510	+	0.804827i	$0.702258\pi$
$908$	−25.8078	+	44.7004i	−0.856461	+	1.48343i
$909$	9.12311			0.302594
$910$		0			0
$911$	−28.4924			−0.943996			−0.471998	−	0.881600i	$-0.656467\pi$
$911$	−28.4924			−0.943996			−0.471998	+	0.881600i	$0.656467\pi$
$912$	42.7386	−	74.0255i	1.41522	−	2.45123i
$913$	3.12311	+	5.40938i	0.103360	+	0.179024i
$914$	−21.9309	−	37.9854i	−0.725409	−	1.25644i
$915$	−12.0000	+	20.7846i	−0.396708	+	0.687118i
$916$	49.6155			1.63934
$917$		0			0
$918$	−6.24621			−0.206156
$919$	−20.1501	+	34.9010i	−0.664690	+	1.15128i	0.314679	+	0.949198i	$0.398103\pi$
$919$	−20.1501	+	34.9010i	−0.664690	+	1.15128i	−0.979369	+	0.202079i	$0.935230\pi$
$920$	10.2462	+	17.7470i	0.337808	+	0.585100i
$921$	15.0810	+	26.1210i	0.496935	+	0.860716i
$922$	−16.8078	+	29.1119i	−0.553534	+	0.958749i
$923$	3.50758			0.115453
$924$		0			0
$925$	6.00000			0.197279
$926$	16.0000	−	27.7128i	0.525793	−	0.910700i
$927$	1.56155	+	2.70469i	0.0512881	+	0.0888336i
$928$	21.9309	+	37.9854i	0.719916	+	1.24693i
$929$	−11.0540	+	19.1460i	−0.362669	+	0.628161i	−0.988399	−	0.151878i	$-0.951468\pi$
$929$	−11.0540	+	19.1460i	−0.362669	+	0.628161i	0.625730	+	0.780040i	$0.284801\pi$
$930$		0			0
$931$		0			0
$932$	23.3693			0.765487
$933$	−24.6847	+	42.7551i	−0.808139	+	1.39974i
$934$	28.7386	+	49.7768i	0.940357	+	1.62875i
$935$	−0.342329	−	0.592932i	−0.0111954	−	0.0193909i
$936$	−0.807764	+	1.39909i	−0.0264026	+	0.0457306i
$937$	−55.6695			−1.81864			−0.909322	−	0.416094i	$-0.863399\pi$
$937$	−55.6695			−1.81864			−0.909322	+	0.416094i	$0.863399\pi$
$938$		0			0
$939$	−34.8229			−1.13640
$940$	19.8078	−	34.3081i	0.646058	−	1.11901i
$941$	−21.9309	−	37.9854i	−0.714926	−	1.23829i	−0.962988	−	0.269544i	$-0.913127\pi$
$941$	−21.9309	−	37.9854i	−0.714926	−	1.23829i	0.248062	−	0.968744i	$-0.420206\pi$
$942$	40.4924	+	70.1349i	1.31931	+	2.28512i
$943$	−8.00000	+	13.8564i	−0.260516	+	0.451227i
$944$	−30.7386			−1.00046
$945$		0			0
$946$	3.50758			0.114041
$947$	−2.00000	+	3.46410i	−0.0649913	+	0.112568i	−0.896690	−	0.442659i	$-0.854035\pi$
$947$	−2.00000	+	3.46410i	−0.0649913	+	0.112568i	0.831699	+	0.555227i	$0.187369\pi$
$948$	8.68466	+	15.0423i	0.282065	+	0.488550i
$949$	2.68466	+	4.64996i	0.0871477	+	0.150944i
$950$	−9.12311	+	15.8017i	−0.295993	+	0.512674i
$951$	16.3845			0.531303
$952$		0			0
$953$	−33.1231			−1.07296			−0.536481	−	0.843912i	$-0.680247\pi$
$953$	−33.1231			−1.07296			−0.536481	+	0.843912i	$0.680247\pi$
$954$	3.68466	−	6.38202i	0.119295	−	0.206625i
$955$	6.78078	+	11.7446i	0.219421	+	0.380048i
$956$	−45.1771	−	78.2490i	−1.46113	−	2.53075i
$957$	8.15009	−	14.1164i	0.263455	−	0.456318i
$958$	−12.4924			−0.403612
$959$		0			0
$960$	2.24621			0.0724962
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	3.36932	+	5.83583i	0.108631	+	0.188155i
$963$	3.75379	+	6.50175i	0.120964	+	0.209516i
$964$	9.68466	−	16.7743i	0.311922	−	0.540264i
$965$	19.3693			0.623520
$966$		0			0
$967$	−35.1231			−1.12948			−0.564741	−	0.825268i	$-0.691024\pi$
$967$	−35.1231			−1.12948			−0.564741	+	0.825268i	$0.691024\pi$
$968$	−28.0885	+	48.6508i	−0.902800	+	1.56370i
$969$	−2.43845	−	4.22351i	−0.0783342	−	0.135679i
$970$	7.43845	+	12.8838i	0.238834	+	0.413673i
$971$	−24.7386	+	42.8486i	−0.793901	+	1.37508i	0.129634	+	0.991562i	$0.458620\pi$
$971$	−24.7386	+	42.8486i	−0.793901	+	1.37508i	−0.923535	+	0.383514i	$0.874714\pi$
$972$	26.2462			0.841848
$973$		0			0
$974$	8.00000			0.256337
$975$	−0.342329	+	0.592932i	−0.0109633	+	0.0189890i
$976$	−59.0540	−	102.284i	−1.89027	−	3.27405i
$977$	−16.6155	−	28.7789i	−0.531578	−	0.920720i	−0.999321	−	0.0368552i	$-0.988266\pi$
$977$	−16.6155	−	28.7789i	−0.531578	−	0.920720i	0.467743	−	0.883865i	$-0.345067\pi$
$978$	−14.2462	+	24.6752i	−0.455544	+	0.789025i
$979$	1.75379			0.0560513
$980$		0			0
$981$	−2.98485			−0.0952988
$982$	−52.7386	+	91.3460i	−1.68296	+	2.91497i
$983$	−25.7116	−	44.5339i	−0.820074	−	1.42041i	−0.905626	−	0.424076i	$-0.860599\pi$
$983$	−25.7116	−	44.5339i	−0.820074	−	1.42041i	0.0855523	−	0.996334i	$-0.472735\pi$
$984$	26.2462	+	45.4598i	0.836699	+	1.44920i
$985$	−0.561553	+	0.972638i	−0.0178926	+	0.0309908i
$986$	7.50758			0.239090
$987$		0			0
$988$	−14.2462			−0.453232
$989$	−1.36932	+	2.37173i	−0.0435417	+	0.0754165i
$990$	1.12311	+	1.94528i	0.0356946	+	0.0618249i
$991$	−6.24621	−	10.8188i	−0.198417	−	0.343669i	0.749598	−	0.661893i	$-0.230247\pi$
$991$	−6.24621	−	10.8188i	−0.198417	−	0.343669i	−0.948015	+	0.318224i	$0.896914\pi$
$992$		0			0
$993$	18.7386			0.594653
$994$		0			0
$995$	−1.75379			−0.0555988
$996$	−14.2462	+	24.6752i	−0.451408	+	0.781862i
$997$	1.34233	+	2.32498i	0.0425120	+	0.0736329i	0.886498	−	0.462732i	$-0.153131\pi$
$997$	1.34233	+	2.32498i	0.0425120	+	0.0736329i	−0.843986	+	0.536364i	$0.819797\pi$
$998$	52.7386	+	91.3460i	1.66941	+	2.89151i
$999$	16.6847	−	28.8987i	0.527879	−	0.914314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.e.i.226.2		4
7.2	even	3		35.2.a.b.1.1	✓	2
7.3	odd	6		245.2.e.h.116.2		4
7.4	even	3	inner	245.2.e.i.116.2		4
7.5	odd	6		245.2.a.d.1.1		2
7.6	odd	2		245.2.e.h.226.2		4
21.2	odd	6		315.2.a.e.1.2		2
21.5	even	6		2205.2.a.x.1.2		2
28.19	even	6		3920.2.a.bs.1.2		2
28.23	odd	6		560.2.a.i.1.1		2
35.2	odd	12		175.2.b.b.99.1		4
35.9	even	6		175.2.a.f.1.2		2
35.12	even	12		1225.2.b.f.99.1		4
35.19	odd	6		1225.2.a.s.1.2		2
35.23	odd	12		175.2.b.b.99.4		4
35.33	even	12		1225.2.b.f.99.4		4
56.37	even	6		2240.2.a.bh.1.1		2
56.51	odd	6		2240.2.a.bd.1.2		2
77.65	odd	6		4235.2.a.m.1.2		2
84.23	even	6		5040.2.a.bt.1.1		2
91.51	even	6		5915.2.a.l.1.2		2
105.2	even	12		1575.2.d.e.1324.4		4
105.23	even	12		1575.2.d.e.1324.1		4
105.44	odd	6		1575.2.a.p.1.1		2
140.23	even	12		2800.2.g.t.449.2		4
140.79	odd	6		2800.2.a.bi.1.2		2
140.107	even	12		2800.2.g.t.449.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.a.b.1.1	✓	2	7.2	even	3
175.2.a.f.1.2		2	35.9	even	6
175.2.b.b.99.1		4	35.2	odd	12
175.2.b.b.99.4		4	35.23	odd	12
245.2.a.d.1.1		2	7.5	odd	6
245.2.e.h.116.2		4	7.3	odd	6
245.2.e.h.226.2		4	7.6	odd	2
245.2.e.i.116.2		4	7.4	even	3	inner
245.2.e.i.226.2		4	1.1	even	1	trivial
315.2.a.e.1.2		2	21.2	odd	6
560.2.a.i.1.1		2	28.23	odd	6
1225.2.a.s.1.2		2	35.19	odd	6
1225.2.b.f.99.1		4	35.12	even	12
1225.2.b.f.99.4		4	35.33	even	12
1575.2.a.p.1.1		2	105.44	odd	6
1575.2.d.e.1324.1		4	105.23	even	12
1575.2.d.e.1324.4		4	105.2	even	12
2205.2.a.x.1.2		2	21.5	even	6
2240.2.a.bd.1.2		2	56.51	odd	6
2240.2.a.bh.1.1		2	56.37	even	6
2800.2.a.bi.1.2		2	140.79	odd	6
2800.2.g.t.449.2		4	140.23	even	12
2800.2.g.t.449.3		4	140.107	even	12
3920.2.a.bs.1.2		2	28.19	even	6
4235.2.a.m.1.2		2	77.65	odd	6
5040.2.a.bt.1.1		2	84.23	even	6
5915.2.a.l.1.2		2	91.51	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)

\(f(q)\)	\(=\)	\(q+(1.28078 - 2.21837i) q^{2} +(-0.780776 - 1.35234i) q^{3} +(-2.28078 - 3.95042i) q^{4} +(-0.500000 + 0.866025i) q^{5} -4.00000 q^{6} -6.56155 q^{8} +(0.280776 - 0.486319i) q^{9} +O(q^{10})\)	\(q+(1.28078 - 2.21837i) q^{2} +(-0.780776 - 1.35234i) q^{3} +(-2.28078 - 3.95042i) q^{4} +(-0.500000 + 0.866025i) q^{5} -4.00000 q^{6} -6.56155 q^{8} +(0.280776 - 0.486319i) q^{9} +(1.28078 + 2.21837i) q^{10} +(0.780776 + 1.35234i) q^{11} +(-3.56155 + 6.16879i) q^{12} +0.438447 q^{13} +1.56155 q^{15} +(-3.84233 + 6.65511i) q^{16} +(0.219224 + 0.379706i) q^{17} +(-0.719224 - 1.24573i) q^{18} +(3.56155 - 6.16879i) q^{19} +4.56155 q^{20} +4.00000 q^{22} +(-1.56155 + 2.70469i) q^{23} +(5.12311 + 8.87348i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.561553 - 0.972638i) q^{26} -5.56155 q^{27} +6.68466 q^{29} +(2.00000 - 3.46410i) q^{30} +(3.28078 + 5.68247i) q^{32} +(1.21922 - 2.11176i) q^{33} +1.12311 q^{34} -2.56155 q^{36} +(-3.00000 + 5.19615i) q^{37} +(-9.12311 - 15.8017i) q^{38} +(-0.342329 - 0.592932i) q^{39} +(3.28078 - 5.68247i) q^{40} +5.12311 q^{41} +0.876894 q^{43} +(3.56155 - 6.16879i) q^{44} +(0.280776 + 0.486319i) q^{45} +(4.00000 + 6.92820i) q^{46} +(4.34233 - 7.52113i) q^{47} +12.0000 q^{48} -2.56155 q^{50} +(0.342329 - 0.592932i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(2.56155 + 4.43674i) q^{53} +(-7.12311 + 12.3376i) q^{54} -1.56155 q^{55} -11.1231 q^{57} +(8.56155 - 14.8290i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-3.56155 - 6.16879i) q^{60} +(-7.68466 + 13.3102i) q^{61} +1.43845 q^{64} +(-0.219224 + 0.379706i) q^{65} +(-3.12311 - 5.40938i) q^{66} +(-5.12311 - 8.87348i) q^{67} +(1.00000 - 1.73205i) q^{68} +4.87689 q^{69} +8.00000 q^{71} +(-1.84233 + 3.19101i) q^{72} +(6.12311 + 10.6055i) q^{73} +(7.68466 + 13.3102i) q^{74} +(-0.780776 + 1.35234i) q^{75} -32.4924 q^{76} -1.75379 q^{78} +(1.21922 - 2.11176i) q^{79} +(-3.84233 - 6.65511i) q^{80} +(3.50000 + 6.06218i) q^{81} +(6.56155 - 11.3649i) q^{82} +4.00000 q^{83} -0.438447 q^{85} +(1.12311 - 1.94528i) q^{86} +(-5.21922 - 9.03996i) q^{87} +(-5.12311 - 8.87348i) q^{88} +(0.561553 - 0.972638i) q^{89} +1.43845 q^{90} +14.2462 q^{92} +(-11.1231 - 19.2658i) q^{94} +(3.56155 + 6.16879i) q^{95} +(5.12311 - 8.87348i) q^{96} +5.80776 q^{97} +0.876894 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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