LMFDB - Embedded newform 147.3.h.e.128.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,3,Mod(116,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("147.116");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	147.h (of order $6$, 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:	$4.00545988610$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.39033114624.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 6x^{6} - 30x^{5} + 34x^{4} - 102x^{3} + 486x^{2} - 730x + 373 $ x^8 - 2x^7 + 6x^6 - 30x^5 + 34x^4 - 102x^3 + 486x^2 - 730*x + 373
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			128.1
Root			$-0.279898 + 3.02113i$ of defining polynomial
Character	$\chi$	$=$	147.128
Dual form			147.3.h.e.116.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.03622 - 1.75296i) q^{2} +(-2.90987 + 0.729839i) q^{3} +(4.14575 + 7.18065i) q^{4} +(1.07558 + 0.620984i) q^{5} +(10.1144 + 2.88494i) q^{6} -15.0457i q^{8} +(7.93467 - 4.24747i) q^{9} +O(q^{10})$	\(q+(-3.03622 - 1.75296i) q^{2} +(-2.90987 + 0.729839i) q^{3} +(4.14575 + 7.18065i) q^{4} +(1.07558 + 0.620984i) q^{5} +(10.1144 + 2.88494i) q^{6} -15.0457i q^{8} +(7.93467 - 4.24747i) q^{9} +(-2.17712 - 3.77089i) q^{10} +(6.07244 - 3.50592i) q^{11} +(-17.3043 - 17.8690i) q^{12} -11.6458 q^{13} +(-3.58301 - 1.02199i) q^{15} +(-9.79150 + 16.9594i) q^{16} +(-3.92129 + 2.26395i) q^{17} +(-31.5371 - 1.01293i) q^{18} +(-8.11438 + 14.0545i) q^{19} +10.2978i q^{20} -24.5830 q^{22} +(-22.1386 - 12.7817i) q^{23} +(10.9809 + 43.7810i) q^{24} +(-11.7288 - 20.3148i) q^{25} +(35.3591 + 20.4146i) q^{26} +(-19.9889 + 18.1506i) q^{27} -9.49579i q^{29} +(9.08729 + 9.38385i) q^{30} +(-14.3542 - 24.8623i) q^{31} +(7.33853 - 4.23690i) q^{32} +(-15.1112 + 14.6337i) q^{33} +15.8745 q^{34} +(63.3948 + 39.3672i) q^{36} +(16.5203 - 28.6139i) q^{37} +(49.2741 - 28.4484i) q^{38} +(33.8876 - 8.49952i) q^{39} +(9.34313 - 16.1828i) q^{40} -67.1946i q^{41} -24.1255 q^{43} +(50.3496 + 29.0694i) q^{44} +(11.1720 + 0.358830i) q^{45} +(44.8118 + 77.6162i) q^{46} +(-28.5921 - 16.5076i) q^{47} +(16.1144 - 56.4958i) q^{48} +82.2403i q^{50} +(9.75810 - 9.44972i) q^{51} +(-48.2804 - 83.6241i) q^{52} +(13.1530 - 7.59387i) q^{53} +(92.5080 - 20.0695i) q^{54} +8.70850 q^{55} +(13.3542 - 46.8190i) q^{57} +(-16.6458 + 28.8313i) q^{58} +(-80.0173 + 46.1980i) q^{59} +(-7.51572 - 29.9652i) q^{60} +(28.7601 - 49.8140i) q^{61} +100.650i q^{62} +48.6235 q^{64} +(-12.5259 - 7.23183i) q^{65} +(71.5333 - 17.9416i) q^{66} +(-7.58301 - 13.1342i) q^{67} +(-32.5133 - 18.7716i) q^{68} +(73.7490 + 21.0355i) q^{69} +70.5584i q^{71} +(-63.9061 - 119.383i) q^{72} +(38.3948 + 66.5017i) q^{73} +(-100.318 + 57.9188i) q^{74} +(48.9557 + 50.5533i) q^{75} -134.561 q^{76} +(-117.790 - 33.5973i) q^{78} +(-63.6235 + 110.199i) q^{79} +(-21.0630 + 12.1607i) q^{80} +(44.9180 - 67.4045i) q^{81} +(-117.790 + 204.017i) q^{82} -74.2844i q^{83} -5.62352 q^{85} +(73.2503 + 42.2911i) q^{86} +(6.93039 + 27.6315i) q^{87} +(-52.7490 - 91.3640i) q^{88} +(-110.312 - 63.6887i) q^{89} +(-33.2915 - 20.6735i) q^{90} -211.959i q^{92} +(59.9144 + 61.8697i) q^{93} +(57.8745 + 100.242i) q^{94} +(-17.4553 + 10.0778i) q^{95} +(-18.2619 + 17.6848i) q^{96} -23.1660 q^{97} +(33.2915 - 53.6108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 12 q^{4} + 28 q^{6} + 20 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 12 * q^4 + 28 * q^6 + 20 * q^9	$ 8 q + 2 q^{3} + 12 q^{4} + 28 q^{6} + 20 q^{9} - 28 q^{10} + 22 q^{12} - 72 q^{13} + 56 q^{15} - 36 q^{16} - 56 q^{18} - 12 q^{19} - 112 q^{22} + 126 q^{24} + 12 q^{25} + 20 q^{27} + 28 q^{30} - 136 q^{31} - 28 q^{33} + 232 q^{36} - 16 q^{37} - 4 q^{39} - 84 q^{40} - 320 q^{43} + 140 q^{45} + 168 q^{46} + 76 q^{48} + 84 q^{51} - 164 q^{52} + 154 q^{54} + 112 q^{55} + 128 q^{57} - 112 q^{58} - 140 q^{60} + 156 q^{61} + 8 q^{64} + 28 q^{66} + 24 q^{67} + 336 q^{69} + 32 q^{73} - 146 q^{75} - 632 q^{76} - 392 q^{78} - 128 q^{79} + 68 q^{81} - 392 q^{82} + 336 q^{85} - 28 q^{87} - 168 q^{88} - 224 q^{90} + 96 q^{93} + 336 q^{94} + 98 q^{96} - 16 q^{97} + 224 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 12 * q^4 + 28 * q^6 + 20 * q^9 - 28 * q^10 + 22 * q^12 - 72 * q^13 + 56 * q^15 - 36 * q^16 - 56 * q^18 - 12 * q^19 - 112 * q^22 + 126 * q^24 + 12 * q^25 + 20 * q^27 + 28 * q^30 - 136 * q^31 - 28 * q^33 + 232 * q^36 - 16 * q^37 - 4 * q^39 - 84 * q^40 - 320 * q^43 + 140 * q^45 + 168 * q^46 + 76 * q^48 + 84 * q^51 - 164 * q^52 + 154 * q^54 + 112 * q^55 + 128 * q^57 - 112 * q^58 - 140 * q^60 + 156 * q^61 + 8 * q^64 + 28 * q^66 + 24 * q^67 + 336 * q^69 + 32 * q^73 - 146 * q^75 - 632 * q^76 - 392 * q^78 - 128 * q^79 + 68 * q^81 - 392 * q^82 + 336 * q^85 - 28 * q^87 - 168 * q^88 - 224 * q^90 + 96 * q^93 + 336 * q^94 + 98 * q^96 - 16 * q^97 + 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−3.03622	−	1.75296i	−1.51811	−	0.876481i	−0.999773	−	0.0213043i	$-0.993218\pi$
$2$	−3.03622	−	1.75296i	−1.51811	−	0.876481i	−0.518337	−	0.855177i	$-0.673449\pi$
$3$	−2.90987	+	0.729839i	−0.969956	+	0.243280i
$3$	−2.90987	+	0.729839i	−0.969956	+	0.243280i
$4$	4.14575	+	7.18065i	1.03644	+	1.79516i
$5$	1.07558	+	0.620984i	0.215115	+	0.124197i	0.603686	−	0.797222i	$-0.293698\pi$
$5$	1.07558	+	0.620984i	0.215115	+	0.124197i	−0.388571	+	0.921419i	$0.627031\pi$
$6$	10.1144	+	2.88494i	1.68573	+	0.480823i
$7$		0			0
$7$		0			0
$8$		−	15.0457i		−	1.88071i
$9$	7.93467	−	4.24747i	0.881630	−	0.471941i
$10$	−2.17712	−	3.77089i	−0.217712	−	0.377089i
$11$	6.07244	−	3.50592i	0.552040	−	0.318720i	−0.197904	−	0.980221i	$-0.563414\pi$
$11$	6.07244	−	3.50592i	0.552040	−	0.318720i	0.749944	+	0.661501i	$0.230080\pi$
$12$	−17.3043	−	17.8690i	−1.44203	−	1.48909i
$13$	−11.6458			−0.895827			−0.447914	−	0.894077i	$-0.647833\pi$
$13$	−11.6458			−0.895827			−0.447914	+	0.894077i	$0.647833\pi$
$14$		0			0
$15$	−3.58301	−	1.02199i	−0.238867	−	0.0681324i
$16$	−9.79150	+	16.9594i	−0.611969	+	1.05996i
$17$	−3.92129	+	2.26395i	−0.230664	+	0.133174i	−0.610878	−	0.791725i	$-0.709184\pi$
$17$	−3.92129	+	2.26395i	−0.230664	+	0.133174i	0.380214	+	0.924898i	$0.375850\pi$
$18$	−31.5371	−	1.01293i	−1.75206	−	0.0562740i
$19$	−8.11438	+	14.0545i	−0.427073	+	0.739711i	−0.996611	−	0.0822530i	$-0.973788\pi$
$19$	−8.11438	+	14.0545i	−0.427073	+	0.739711i	0.569539	+	0.821964i	$0.307122\pi$
$20$			10.2978i			0.514889i
$21$		0			0
$22$	−24.5830			−1.11741
$23$	−22.1386	−	12.7817i	−0.962548	−	0.555727i	−0.0655916	−	0.997847i	$-0.520893\pi$
$23$	−22.1386	−	12.7817i	−0.962548	−	0.555727i	−0.896956	+	0.442119i	$0.854227\pi$
$24$	10.9809	+	43.7810i	0.457538	+	1.82421i
$25$	−11.7288	−	20.3148i	−0.469150	−	0.812592i
$26$	35.3591	+	20.4146i	1.35996	+	0.785175i
$27$	−19.9889	+	18.1506i	−0.740329	+	0.672245i
$28$		0			0
$29$		−	9.49579i		−	0.327441i	−0.986507	−	0.163720i	$-0.947650\pi$
$29$		−	9.49579i		−	0.327441i	0.986507	−	0.163720i	$-0.0523495\pi$
$30$	9.08729	+	9.38385i	0.302910	+	0.312795i
$31$	−14.3542	−	24.8623i	−0.463040	−	0.802009i	0.536070	−	0.844173i	$-0.319908\pi$
$31$	−14.3542	−	24.8623i	−0.463040	−	0.802009i	−0.999111	+	0.0421640i	$0.986575\pi$
$32$	7.33853	−	4.23690i	0.229329	−	0.132403i
$33$	−15.1112	+	14.6337i	−0.457916	+	0.443445i
$34$	15.8745			0.466897
$35$		0			0
$36$	63.3948	+	39.3672i	1.76097	+	1.09353i
$37$	16.5203	−	28.6139i	0.446493	−	0.773349i	−0.551661	−	0.834068i	$-0.686006\pi$
$37$	16.5203	−	28.6139i	0.446493	−	0.773349i	0.998155	+	0.0607187i	$0.0193393\pi$
$38$	49.2741	−	28.4484i	1.29669	−	0.748642i
$39$	33.8876	−	8.49952i	0.868913	−	0.217936i
$40$	9.34313	−	16.1828i	0.233578	−	0.404570i
$41$		−	67.1946i		−	1.63889i	−0.573156	−	0.819446i	$-0.694281\pi$
$41$		−	67.1946i		−	1.63889i	0.573156	−	0.819446i	$-0.305719\pi$
$42$		0			0
$43$	−24.1255			−0.561058			−0.280529	−	0.959846i	$-0.590510\pi$
$43$	−24.1255			−0.561058			−0.280529	+	0.959846i	$0.590510\pi$
$44$	50.3496	+	29.0694i	1.14431	+	0.660668i
$45$	11.1720	+	0.358830i	0.248266	+	0.00797400i
$46$	44.8118	+	77.6162i	0.974169	+	1.68731i
$47$	−28.5921	−	16.5076i	−0.608342	−	0.351226i	0.163974	−	0.986465i	$-0.447569\pi$
$47$	−28.5921	−	16.5076i	−0.608342	−	0.351226i	−0.772316	+	0.635238i	$0.780902\pi$
$48$	16.1144	−	56.4958i	0.335716	−	1.17700i
$49$		0			0
$50$			82.2403i			1.64481i
$51$	9.75810	−	9.44972i	0.191335	−	0.185289i
$52$	−48.2804	−	83.6241i	−0.928469	−	1.60816i
$53$	13.1530	−	7.59387i	0.248169	−	0.143281i	−0.370756	−	0.928730i	$-0.620902\pi$
$53$	13.1530	−	7.59387i	0.248169	−	0.143281i	0.618926	+	0.785450i	$0.287568\pi$
$54$	92.5080	−	20.0695i	1.71311	−	0.371657i
$55$	8.70850			0.158336
$56$		0			0
$57$	13.3542	−	46.8190i	0.234285	−	0.821386i
$58$	−16.6458	+	28.8313i	−0.286996	+	0.497091i
$59$	−80.0173	+	46.1980i	−1.35623	+	0.783017i	−0.989113	−	0.147160i	$-0.952987\pi$
$59$	−80.0173	+	46.1980i	−1.35623	+	0.783017i	−0.367112	+	0.930177i	$0.619654\pi$
$60$	−7.51572	−	29.9652i	−0.125262	−	0.499420i
$61$	28.7601	−	49.8140i	0.471478	−	0.816623i	−0.527990	−	0.849251i	$-0.677054\pi$
$61$	28.7601	−	49.8140i	0.471478	−	0.816623i	0.999468	+	0.0326275i	$0.0103875\pi$
$62$			100.650i			1.62338i
$63$		0			0
$64$	48.6235			0.759743
$65$	−12.5259	−	7.23183i	−0.192706	−	0.111259i
$66$	71.5333	−	17.9416i	1.08384	−	0.271843i
$67$	−7.58301	−	13.1342i	−0.113179	−	0.196032i	0.803871	−	0.594803i	$-0.202770\pi$
$67$	−7.58301	−	13.1342i	−0.113179	−	0.196032i	−0.917050	+	0.398771i	$0.869437\pi$
$68$	−32.5133	−	18.7716i	−0.478137	−	0.276053i
$69$	73.7490	+	21.0355i	1.06883	+	0.304863i
$70$		0			0
$71$			70.5584i			0.993781i	0.867813	+	0.496890i	$0.165525\pi$
$71$			70.5584i			0.993781i	−0.867813	+	0.496890i	$0.834475\pi$
$72$	−63.9061	−	119.383i	−0.887584	−	1.65809i
$73$	38.3948	+	66.5017i	0.525956	+	0.910982i	0.999543	+	0.0302350i	$0.00962558\pi$
$73$	38.3948	+	66.5017i	0.525956	+	0.910982i	−0.473587	+	0.880747i	$0.657041\pi$
$74$	−100.318	+	57.9188i	−1.35565	+	0.782686i
$75$	48.9557	+	50.5533i	0.652742	+	0.674044i
$76$	−134.561			−1.77054
$77$		0			0
$78$	−117.790	−	33.5973i	−1.51012	−	0.430734i
$79$	−63.6235	+	110.199i	−0.805361	+	1.39493i	0.110686	+	0.993855i	$0.464695\pi$
$79$	−63.6235	+	110.199i	−0.805361	+	1.39493i	−0.916047	+	0.401071i	$0.868638\pi$
$80$	−21.0630	+	12.1607i	−0.263288	+	0.152009i
$81$	44.9180	−	67.4045i	0.554544	−	0.832155i
$82$	−117.790	+	204.017i	−1.43646	+	2.48802i
$83$		−	74.2844i		−	0.894992i	−0.894286	−	0.447496i	$-0.852316\pi$
$83$		−	74.2844i		−	0.894992i	0.894286	−	0.447496i	$-0.147684\pi$
$84$		0			0
$85$	−5.62352			−0.0661591
$86$	73.2503	+	42.2911i	0.851747	+	0.491757i
$87$	6.93039	+	27.6315i	0.0796597	+	0.317603i
$88$	−52.7490	−	91.3640i	−0.599421	−	1.03823i
$89$	−110.312	−	63.6887i	−1.23946	−	0.715603i	−0.270477	−	0.962727i	$-0.587181\pi$
$89$	−110.312	−	63.6887i	−1.23946	−	0.715603i	−0.968984	+	0.247124i	$0.920515\pi$
$90$	−33.2915	−	20.6735i	−0.369906	−	0.229706i
$91$		0			0
$92$		−	211.959i		−	2.30391i
$93$	59.9144	+	61.8697i	0.644241	+	0.665266i
$94$	57.8745	+	100.242i	0.615686	+	1.06640i
$95$	−17.4553	+	10.0778i	−0.183740	+	0.106082i
$96$	−18.2619	+	17.6848i	−0.190228	+	0.184216i
$97$	−23.1660			−0.238825			−0.119412	−	0.992845i	$-0.538101\pi$
$97$	−23.1660			−0.238825			−0.119412	+	0.992845i	$0.538101\pi$
$98$		0			0
$99$	33.2915	−	53.6108i	0.336278	−	0.541524i
$100$	97.2490	−	168.440i	0.972490	−	1.68440i
$101$	116.833	−	67.4535i	1.15676	−	0.667857i	0.206236	−	0.978502i	$-0.433879\pi$
$101$	116.833	−	67.4535i	1.15676	−	0.667857i	0.950526	+	0.310646i	$0.100545\pi$
$102$	−46.1927	+	11.5858i	−0.452870	+	0.113587i
$103$	59.8745	−	103.706i	0.581306	−	1.00685i	−0.414019	−	0.910268i	$-0.635875\pi$
$103$	59.8745	−	103.706i	0.581306	−	1.00685i	0.995325	−	0.0965831i	$-0.0307914\pi$
$104$			175.218i			1.68479i
$105$		0			0
$106$	−53.2470			−0.502331
$107$	−67.4239	−	38.9272i	−0.630130	−	0.363806i	0.150673	−	0.988584i	$-0.451856\pi$
$107$	−67.4239	−	38.9272i	−0.630130	−	0.363806i	−0.780802	+	0.624778i	$0.785189\pi$
$108$	−213.202	−	68.2853i	−1.97409	−	0.632272i
$109$	18.2693	+	31.6433i	0.167608	+	0.290306i	0.937578	−	0.347774i	$-0.113062\pi$
$109$	18.2693	+	31.6433i	0.167608	+	0.290306i	−0.769970	+	0.638080i	$0.779729\pi$
$110$	−26.4409	−	15.2657i	−0.240372	−	0.138779i
$111$	−27.1882	+	95.3199i	−0.244939	+	0.858738i
$112$		0			0
$113$		−	21.7596i		−	0.192563i	−0.995354	−	0.0962815i	$-0.969305\pi$
$113$		−	21.7596i		−	0.192563i	0.995354	−	0.0962815i	$-0.0306949\pi$
$114$	−122.618	+	118.743i	−1.07560	+	1.04161i
$115$	−15.8745	−	27.4955i	−0.138039	−	0.239091i
$116$	68.1859	−	39.3672i	0.587810	−	0.339372i
$117$	−92.4052	+	49.4650i	−0.789788	+	0.422777i
$118$	323.933			2.74520
$119$		0			0
$120$	−15.3765	+	53.9088i	−0.128137	+	0.449240i
$121$	−35.9170	+	62.2101i	−0.296835	+	0.514133i
$122$	−174.644	+	100.831i	−1.43151	+	0.826482i
$123$	49.0412	+	195.527i	0.398709	+	1.58965i
$124$	119.018	−	206.146i	0.959825	−	1.66247i
$125$		−	60.1827i		−	0.481462i
$126$		0			0
$127$	−15.4170			−0.121394			−0.0606968	−	0.998156i	$-0.519332\pi$
$127$	−15.4170			−0.121394			−0.0606968	+	0.998156i	$0.519332\pi$
$128$	−176.986	−	102.183i	−1.38270	−	0.798303i
$129$	70.2020	−	17.6077i	0.544202	−	0.136494i
$130$	25.3542	+	43.9148i	0.195033	+	0.337807i
$131$	158.578	+	91.5550i	1.21052	+	0.698893i	0.962872	−	0.269957i	$-0.0870095\pi$
$131$	158.578	+	91.5550i	1.21052	+	0.698893i	0.247646	+	0.968850i	$0.420343\pi$
$132$	−167.727	−	47.8410i	−1.27066	−	0.362432i
$133$		0			0
$134$			53.1709i			0.396798i
$135$	−32.7708	+	7.10958i	−0.242747	+	0.0526635i
$136$	34.0627	+	58.9984i	0.250461	+	0.433812i
$137$	−28.5921	+	16.5076i	−0.208701	+	0.120494i	−0.600708	−	0.799469i	$-0.705114\pi$
$137$	−28.5921	+	16.5076i	−0.208701	+	0.120494i	0.392006	+	0.919962i	$0.371781\pi$
$138$	−187.044	−	193.148i	−1.35539	−	1.39962i
$139$	64.6418			0.465049			0.232525	−	0.972591i	$-0.425301\pi$
$139$	64.6418			0.465049			0.232525	+	0.972591i	$0.425301\pi$
$140$		0			0
$141$	95.2470	+	27.1675i	0.675511	+	0.192677i
$142$	123.686	−	214.231i	0.871030	−	1.50867i
$143$	−70.7181	+	40.8291i	−0.494532	+	0.285518i
$144$	−5.65793	+	176.156i	−0.0392912	+	1.22331i
$145$	5.89674	−	10.2134i	0.0406671	−	0.0704376i
$146$		−	269.218i		−	1.84396i
$147$		0			0
$148$	273.956			1.85105
$149$	169.512	+	97.8680i	1.13767	+	0.656832i	0.945852	−	0.324599i	$-0.105229\pi$
$149$	169.512	+	97.8680i	1.13767	+	0.656832i	0.191815	+	0.981431i	$0.438563\pi$
$150$	−60.0221	−	239.308i	−0.400147	−	1.59539i
$151$	−51.1255	−	88.5519i	−0.338579	−	0.586437i	0.645586	−	0.763687i	$-0.276613\pi$
$151$	−51.1255	−	88.5519i	−0.338579	−	0.586437i	−0.984166	+	0.177251i	$0.943280\pi$
$152$	211.460	+	122.086i	1.39118	+	0.803200i
$153$	−21.4980	+	34.6193i	−0.140510	+	0.226270i
$154$		0			0
$155$		−	35.6551i		−	0.230033i
$156$	201.522	+	208.098i	1.29181	+	1.33396i
$157$	−52.3614	−	90.6926i	−0.333512	−	0.577660i	0.649686	−	0.760203i	$-0.274901\pi$
$157$	−52.3614	−	90.6926i	−0.333512	−	0.577660i	−0.983198	+	0.182543i	$0.941567\pi$
$158$	386.350	−	223.059i	2.44525	−	1.41177i
$159$	−32.7311	+	31.6967i	−0.205856	+	0.199350i
$160$	10.5242			0.0657762
$161$		0			0
$162$	−254.539	+	125.915i	−1.57123	+	0.777255i
$163$	35.4797	−	61.4527i	0.217667	−	0.377011i	−0.736427	−	0.676517i	$-0.763489\pi$
$163$	35.4797	−	61.4527i	0.217667	−	0.377011i	0.954094	+	0.299506i	$0.0968220\pi$
$164$	482.501	−	278.572i	2.94208	−	1.69861i
$165$	−25.3406	+	6.35580i	−0.153579	+	0.0385200i
$166$	−130.218	+	225.544i	−0.784444	+	1.35870i
$167$			206.992i			1.23947i	0.784811	+	0.619735i	$0.212760\pi$
$167$			206.992i			1.23947i	−0.784811	+	0.619735i	$0.787240\pi$
$168$		0			0
$169$	−33.3765			−0.197494
$170$	17.0743	+	9.85782i	0.100437	+	0.0579872i
$171$	−4.68882	+	145.984i	−0.0274200	+	0.853705i
$172$	−100.018	−	173.237i	−0.581502	−	1.00719i
$173$	93.9323	+	54.2318i	0.542961	+	0.313479i	0.746278	−	0.665634i	$-0.231839\pi$
$173$	93.9323	+	54.2318i	0.542961	+	0.313479i	−0.203317	+	0.979113i	$0.565172\pi$
$174$	27.3948	−	96.0440i	0.157441	−	0.551977i
$175$		0			0
$176$			137.313i			0.780188i
$177$	199.123	−	192.830i	1.12499	−	1.08943i
$178$	223.288	+	386.745i	1.25442	+	2.17273i
$179$	−138.007	+	79.6784i	−0.770989	+	0.445131i	−0.833227	−	0.552931i	$-0.813509\pi$
$179$	−138.007	+	79.6784i	−0.770989	+	0.445131i	0.0622383	+	0.998061i	$0.480176\pi$
$180$	43.7395	+	81.7096i	0.242997	+	0.453942i
$181$	−233.889			−1.29220			−0.646102	−	0.763251i	$-0.723602\pi$
$181$	−233.889			−1.29220			−0.646102	+	0.763251i	$0.723602\pi$
$182$		0			0
$183$	−47.3320	+	165.942i	−0.258645	+	0.906789i
$184$	−192.310	+	333.090i	−1.04516	+	1.81027i
$185$	35.5376	−	20.5176i	0.192095	−	0.110906i
$186$	−73.4581	−	292.878i	−0.394936	−	1.57461i
$187$	−15.8745	+	27.4955i	−0.0848904	+	0.147035i
$188$		−	273.746i		−	1.45610i
$189$		0			0
$190$	70.6640			0.371916
$191$	−249.597	−	144.105i	−1.30679	−	0.754476i	−0.325232	−	0.945634i	$-0.605442\pi$
$191$	−249.597	−	144.105i	−1.30679	−	0.754476i	−0.981559	+	0.191158i	$0.938776\pi$
$192$	−141.488	+	35.4873i	−0.736917	+	0.184830i
$193$	−38.5608	−	66.7892i	−0.199797	−	0.346058i	0.748666	−	0.662948i	$-0.230695\pi$
$193$	−38.5608	−	66.7892i	−0.199797	−	0.346058i	−0.948462	+	0.316890i	$0.897362\pi$
$194$	70.3371	+	40.6091i	0.362562	+	0.209325i
$195$	41.7268	+	11.9018i	0.213984	+	0.0610348i
$196$		0			0
$197$			136.433i			0.692554i	0.938132	+	0.346277i	$0.112554\pi$
$197$			136.433i			0.692554i	−0.938132	+	0.346277i	$0.887446\pi$
$198$	−195.058	+	104.416i	−0.985142	+	0.527351i
$199$	−43.2915	−	74.9831i	−0.217545	−	0.376799i	0.736512	−	0.676425i	$-0.236472\pi$
$199$	−43.2915	−	74.9831i	−0.217545	−	0.376799i	−0.954057	+	0.299625i	$0.903138\pi$
$200$	−305.650	+	176.467i	−1.52825	+	0.882336i
$201$	31.6514	+	32.6843i	0.157469	+	0.162608i
$202$	−472.974			−2.34145
$203$		0			0
$204$	108.310	+	30.8934i	0.530930	+	0.151438i
$205$	41.7268	−	72.2729i	0.203545	−	0.352551i
$206$	−363.584	+	209.915i	−1.76497	+	1.01901i
$207$	−229.953	−	7.38580i	−1.11088	−	0.0356802i
$208$	114.029	−	197.505i	0.548218	−	0.949542i
$209$			113.794i			0.544467i
$210$		0			0
$211$	19.4170			0.0920237			0.0460118	−	0.998941i	$-0.485349\pi$
$211$	19.4170			0.0920237			0.0460118	+	0.998941i	$0.485349\pi$
$212$	109.058	+	62.9646i	0.514424	+	0.297003i
$213$	−51.4963	−	205.316i	−0.241767	−	0.963924i
$214$	136.476	+	236.383i	0.637737	+	1.10459i
$215$	−25.9488	−	14.9816i	−0.120692	−	0.0696817i
$216$	273.088	+	300.746i	1.26430	+	1.39234i
$217$		0			0
$218$		−	128.101i		−	0.587621i
$219$	−160.259	−	165.489i	−0.731777	−	0.755658i
$220$	36.1033	+	62.5327i	0.164106	+	0.284239i
$221$	45.6663	−	26.3655i	0.206635	−	0.119301i
$222$	249.642	−	241.752i	1.12451	−	1.08897i
$223$	175.041			0.784935			0.392468	−	0.919766i	$-0.371622\pi$
$223$	175.041			0.784935			0.392468	+	0.919766i	$0.371622\pi$
$224$		0			0
$225$	−179.350	−	111.374i	−0.797112	−	0.494994i
$226$	−38.1438	+	66.0670i	−0.168778	+	0.292332i
$227$	153.784	−	88.7870i	0.677461	−	0.391132i	−0.121437	−	0.992599i	$-0.538750\pi$
$227$	153.784	−	88.7870i	0.677461	−	0.391132i	0.798898	+	0.601467i	$0.205417\pi$
$228$	391.554	−	98.2076i	1.71734	−	0.430735i
$229$	−20.4059	+	35.3440i	−0.0891087	+	0.154341i	−0.907135	−	0.420841i	$-0.861735\pi$
$229$	−20.4059	+	35.3440i	−0.0891087	+	0.154341i	0.818026	+	0.575181i	$0.195069\pi$
$230$			111.310i			0.483955i
$231$		0			0
$232$	−142.871			−0.615821
$233$	335.754	+	193.848i	1.44101	+	0.831965i	0.997917	−	0.0645131i	$-0.0205494\pi$
$233$	335.754	+	193.848i	1.44101	+	0.831965i	0.443088	+	0.896478i	$0.353883\pi$
$234$	367.273	+	11.7964i	1.56954	+	0.0504118i
$235$	−20.5020	−	35.5105i	−0.0872424	−	0.151108i
$236$	−663.463	−	383.051i	−2.81129	−	1.62310i
$237$	104.708	−	367.100i	0.441808	−	1.54895i
$238$		0			0
$239$			49.5229i			0.207209i	0.994619	+	0.103604i	$0.0330376\pi$
$239$			49.5229i			0.207209i	−0.994619	+	0.103604i	$0.966962\pi$
$240$	52.4153	−	50.7588i	0.218397	−	0.211495i
$241$	−162.624	−	281.672i	−0.674786	−	1.16876i	−0.976531	−	0.215376i	$-0.930902\pi$
$241$	−162.624	−	281.672i	−0.674786	−	1.16876i	0.301745	−	0.953389i	$-0.402431\pi$
$242$	218.104	−	125.922i	0.901255	−	0.520340i
$243$	−81.5111	+	228.921i	−0.335437	+	0.942063i
$244$	476.929			1.95463
$245$		0			0
$246$	193.852	−	679.631i	0.788017	−	2.76273i
$247$	94.4980	−	163.675i	0.382583	−	0.662653i
$248$	−374.070	+	215.969i	−1.50835	+	0.870845i
$249$	54.2156	+	216.158i	0.217733	+	0.868103i
$250$	−105.498	+	182.728i	−0.421992	+	0.730912i
$251$			263.732i			1.05073i	0.850878	+	0.525364i	$0.176071\pi$
$251$			263.732i			1.05073i	−0.850878	+	0.525364i	$0.823929\pi$
$252$		0			0
$253$	−179.247			−0.708486
$254$	46.8094	+	27.0254i	0.184289	+	0.106399i
$255$	16.3637	−	4.10426i	0.0641714	−	0.0160952i
$256$	260.998	+	452.062i	1.01952	+	1.76587i
$257$	−130.926	−	75.5904i	−0.509442	−	0.294126i	0.223162	−	0.974781i	$-0.428362\pi$
$257$	−130.926	−	75.5904i	−0.509442	−	0.294126i	−0.732604	+	0.680655i	$0.761695\pi$
$258$	−244.014	−	69.6006i	−0.945792	−	0.269770i
$259$		0			0
$260$		−	119.925i		−	0.461252i
$261$	−40.3331	−	75.3459i	−0.154533	−	0.288682i
$262$	−320.985	−	555.962i	−1.22513	−	2.12199i
$263$	−99.0641	+	57.1947i	−0.376670	+	0.217470i	−0.676368	−	0.736564i	$-0.736447\pi$
$263$	−99.0641	+	57.1947i	−0.376670	+	0.217470i	0.299699	+	0.954034i	$0.403114\pi$
$264$	220.174	+	227.359i	0.833991	+	0.861208i
$265$	18.8627			0.0711800
$266$		0			0
$267$	367.476	+	104.816i	1.37631	+	0.392568i
$268$	62.8745	−	108.902i	0.234606	−	0.406350i
$269$	−4.12375	+	2.38085i	−0.0153299	+	0.00885074i	−0.507645	−	0.861566i	$-0.669484\pi$
$269$	−4.12375	+	2.38085i	−0.0153299	+	0.00885074i	0.492315	+	0.870417i	$0.336151\pi$
$270$	111.962	+	35.8598i	0.414675	+	0.132814i
$271$	259.350	−	449.208i	0.957012	−	1.65759i	0.227318	−	0.973821i	$-0.427004\pi$
$271$	259.350	−	449.208i	0.957012	−	1.65759i	0.729695	−	0.683773i	$-0.239662\pi$
$272$		−	88.6701i		−	0.325993i
$273$		0			0
$274$	115.749			0.422442
$275$	−142.444	−	82.2403i	−0.517979	−	0.299055i
$276$	154.696	+	616.774i	0.560493	+	2.23469i
$277$	60.5425	+	104.863i	0.218565	+	0.378566i	0.954369	−	0.298628i	$-0.0965291\pi$
$277$	60.5425	+	104.863i	0.218565	+	0.378566i	−0.735805	+	0.677194i	$0.763196\pi$
$278$	−196.267	−	113.315i	−0.705995	−	0.407607i
$279$	−219.498	−	136.305i	−0.786731	−	0.488548i
$280$		0			0
$281$		−	407.255i		−	1.44931i	−0.689113	−	0.724654i	$-0.742000\pi$
$281$		−	407.255i		−	1.44931i	0.689113	−	0.724654i	$-0.258000\pi$
$282$	−241.567	−	249.451i	−0.856622	−	0.884577i
$283$	199.317	+	345.227i	0.704300	+	1.21988i	0.966943	+	0.254991i	$0.0820724\pi$
$283$	199.317	+	345.227i	0.704300	+	1.21988i	−0.262643	+	0.964893i	$0.584594\pi$
$284$	−506.656	+	292.518i	−1.78400	+	1.02999i
$285$	43.4374	−	42.0646i	0.152412	−	0.147595i
$286$	286.288			1.00101
$287$		0			0
$288$	40.2327	−	64.7886i	0.139697	−	0.224960i
$289$	−134.249	+	232.526i	−0.464529	+	0.804589i
$290$	−35.8076	+	20.6735i	−0.123474	+	0.0712880i
$291$	67.4100	−	16.9074i	0.231650	−	0.0581012i
$292$	−318.350	+	551.399i	−1.09024	+	1.88835i
$293$		−	2.53426i		−	0.00864935i	−0.999991	−	0.00432468i	$-0.998623\pi$
$293$		−	2.53426i		−	0.00864935i	0.999991	−	0.00432468i	$-0.00137659\pi$
$294$		0			0
$295$	−114.753			−0.388993
$296$	−430.516	−	248.559i	−1.45445	−	0.839725i
$297$	−57.7466	+	180.298i	−0.194433	+	0.607064i
$298$	−343.118	−	594.297i	−1.15140	−	1.99429i
$299$	257.821	+	148.853i	0.862276	+	0.497835i
$300$	−160.048	+	561.115i	−0.533492	+	1.87038i
$301$		0			0
$302$			358.484i			1.18703i
$303$	−290.738	+	281.550i	−0.959532	+	0.929208i
$304$	−158.904	−	275.230i	−0.522710	−	0.905361i
$305$	61.8674	−	35.7192i	0.202844	−	0.117112i
$306$	125.959	−	67.4265i	0.411631	−	0.220348i
$307$	86.2366			0.280901			0.140451	−	0.990088i	$-0.455145\pi$
$307$	86.2366			0.280901			0.140451	+	0.990088i	$0.455145\pi$
$308$		0			0
$309$	−98.5385	+	345.469i	−0.318895	+	1.11802i
$310$	−62.5020	+	108.257i	−0.201619	+	0.349215i
$311$	−131.442	+	75.8884i	−0.422645	+	0.244014i	−0.696208	−	0.717840i	$-0.745131\pi$
$311$	−131.442	+	75.8884i	−0.422645	+	0.244014i	0.273564	+	0.961854i	$0.411798\pi$
$312$	−127.881	−	509.862i	−0.409875	−	1.63417i
$313$	−159.059	+	275.498i	−0.508175	+	0.880185i	0.491780	+	0.870719i	$0.336346\pi$
$313$	−159.059	+	275.498i	−0.508175	+	0.880185i	−0.999955	+	0.00946567i	$0.996987\pi$
$314$			367.150i			1.16927i
$315$		0			0
$316$	−1055.07			−3.33883
$317$	315.251	+	182.010i	0.994482	+	0.574164i	0.906611	−	0.421967i	$-0.138660\pi$
$317$	315.251	+	182.010i	0.994482	+	0.574164i	0.0878710	+	0.996132i	$0.471994\pi$
$318$	154.942	−	38.8617i	0.487239	−	0.122207i
$319$	−33.2915	−	57.6626i	−0.104362	−	0.180760i
$320$	52.2983	+	30.1945i	0.163432	+	0.0943577i
$321$	224.605	+	64.0645i	0.699705	+	0.199578i
$322$		0			0
$323$		−	73.4823i		−	0.227500i
$324$	670.227	+	43.0983i	2.06860	+	0.133019i
$325$	136.590	+	236.581i	0.420277	+	0.727942i
$326$	−215.449	+	124.389i	−0.660885	+	0.381562i
$327$	−76.2557	−	78.7443i	−0.233198	−	0.240808i
$328$	−1010.99			−3.08228
$329$		0			0
$330$	88.0810	+	25.1235i	0.266912	+	0.0761318i
$331$	−77.1843	+	133.687i	−0.233185	+	0.403889i	−0.958744	−	0.284272i	$-0.908248\pi$
$331$	−77.1843	+	133.687i	−0.233185	+	0.403889i	0.725559	+	0.688160i	$0.241582\pi$
$332$	533.410	−	307.964i	1.60666	−	0.927604i
$333$	9.54607	−	297.211i	0.0286669	−	0.892527i
$334$	362.848	−	628.472i	1.08637	−	1.88165i
$335$		−	18.8357i		−	0.0562260i
$336$		0			0
$337$	403.041			1.19597			0.597983	−	0.801509i	$-0.295969\pi$
$337$	403.041			1.19597			0.597983	+	0.801509i	$0.295969\pi$
$338$	101.338	+	58.5077i	0.299817	+	0.173100i
$339$	15.8810	+	63.3176i	0.0468466	+	0.186778i
$340$	−23.3137	−	40.3806i	−0.0685698	−	0.118766i
$341$	−174.331	−	100.650i	−0.511233	−	0.295161i
$342$	270.140	−	435.019i	0.789883	−	1.27198i
$343$		0			0
$344$			362.984i			1.05519i
$345$	66.2600	+	68.4223i	0.192058	+	0.198326i
$346$	−190.133	−	329.319i	−0.549516	−	0.951790i
$347$	408.108	−	235.621i	1.17610	−	0.679023i	0.220993	−	0.975275i	$-0.429070\pi$
$347$	408.108	−	235.621i	1.17610	−	0.679023i	0.955110	+	0.296252i	$0.0957370\pi$
$348$	−169.680	+	164.318i	−0.487587	+	0.472178i
$349$	−364.516			−1.04446			−0.522230	−	0.852805i	$-0.674900\pi$
$349$	−364.516			−1.04446			−0.522230	+	0.852805i	$0.674900\pi$
$350$		0			0
$351$	232.786	−	211.377i	0.663207	−	0.602215i
$352$	29.7085	−	51.4566i	0.0843991	−	0.146184i
$353$	74.7744	−	43.1710i	0.211825	−	0.122297i	−0.390334	−	0.920673i	$-0.627640\pi$
$353$	74.7744	−	43.1710i	0.211825	−	0.122297i	0.602159	+	0.798376i	$0.294307\pi$
$354$	−942.603	+	236.419i	−2.66272	+	0.667850i
$355$	−43.8157	+	75.8910i	−0.123425	+	0.213778i
$356$		−	1056.15i		−	2.96671i
$357$		0			0
$358$	558.693			1.56059
$359$	322.220	+	186.034i	0.897549	+	0.518200i	0.876404	−	0.481576i	$-0.159935\pi$
$359$	322.220	+	186.034i	0.897549	+	0.518200i	0.0211451	+	0.999776i	$0.493269\pi$
$360$	5.39884	−	168.090i	0.0149968	−	0.466916i
$361$	48.8137	+	84.5479i	0.135218	+	0.234205i
$362$	710.138	+	409.998i	1.96171	+	1.13259i
$363$	59.1104	−	207.237i	0.162839	−	0.570900i
$364$		0			0
$365$			95.3702i			0.261288i
$366$	434.601	−	420.866i	1.18744	−	1.14991i
$367$	80.8928	+	140.110i	0.220416	+	0.381772i	0.954934	−	0.296817i	$-0.0959251\pi$
$367$	80.8928	+	140.110i	0.220416	+	0.381772i	−0.734518	+	0.678589i	$0.762592\pi$
$368$	433.540	−	250.305i	1.17810	−	0.680176i
$369$	−285.407	−	533.167i	−0.773460	−	1.44490i
$370$	−143.867			−0.388829
$371$		0			0
$372$	−195.875	+	686.721i	−0.526544	+	1.84602i
$373$	−189.125	+	327.575i	−0.507039	+	0.878217i	0.492928	+	0.870070i	$0.335927\pi$
$373$	−189.125	+	327.575i	−0.507039	+	0.878217i	−0.999967	+	0.00814693i	$0.997407\pi$
$374$	96.3970	−	55.6548i	0.257746	−	0.148810i
$375$	43.9237	+	175.124i	0.117130	+	0.466997i
$376$	−248.369	+	430.187i	−0.660555	+	1.14411i
$377$			110.586i			0.293330i
$378$		0			0
$379$	−50.7974			−0.134030			−0.0670151	−	0.997752i	$-0.521348\pi$
$379$	−50.7974			−0.134030			−0.0670151	+	0.997752i	$0.521348\pi$
$380$	−144.730	−	83.5602i	−0.380870	−	0.219895i
$381$	44.8614	−	11.2519i	0.117747	−	0.0295326i
$382$	505.221	+	875.068i	1.32257	+	2.29075i
$383$	98.1910	+	56.6906i	0.256373	+	0.148017i	0.622679	−	0.782477i	$-0.286044\pi$
$383$	98.1910	+	56.6906i	0.256373	+	0.148017i	−0.366306	+	0.930495i	$0.619378\pi$
$384$	589.582	+	168.167i	1.53537	+	0.437936i
$385$		0			0
$386$			270.382i			0.700472i
$387$	−191.428	+	102.472i	−0.494646	+	0.264786i
$388$	−96.0405	−	166.347i	−0.247527	−	0.428730i
$389$	628.374	−	362.792i	1.61536	−	0.932628i	0.627259	−	0.778811i	$-0.284177\pi$
$389$	628.374	−	362.792i	1.61536	−	0.932628i	0.988099	−	0.153817i	$-0.0491565\pi$
$390$	−105.828	−	109.282i	−0.271355	−	0.280210i
$391$	115.749			0.296033
$392$		0			0
$393$	−528.261	−	150.677i	−1.34418	−	0.383402i
$394$	239.162	−	414.241i	0.607010	−	1.05137i
$395$	−136.864	+	79.0184i	−0.346491	+	0.200047i
$396$	522.979	+	16.7975i	1.32065	+	0.0424178i
$397$	47.1732	−	81.7064i	0.118824	−	0.205809i	−0.800478	−	0.599362i	$-0.795421\pi$
$397$	47.1732	−	81.7064i	0.118824	−	0.205809i	0.919302	+	0.393553i	$0.128754\pi$
$398$			303.553i			0.762697i
$399$		0			0
$400$	459.369			1.14842
$401$	−586.875	−	338.833i	−1.46353	−	0.844969i	−0.464357	−	0.885648i	$-0.653715\pi$
$401$	−586.875	−	338.833i	−1.46353	−	0.844969i	−0.999172	+	0.0406787i	$0.987048\pi$
$402$	−38.8062	−	154.720i	−0.0965327	−	0.384876i
$403$	167.166	+	289.540i	0.414804	+	0.718462i
$404$	968.721	+	559.291i	2.39782	+	1.38438i
$405$	90.1699	−	44.6053i	0.222642	−	0.110137i
$406$		0			0
$407$		−	231.675i		−	0.569226i
$408$	−142.177	−	146.817i	−0.348474	−	0.359846i
$409$	−8.68233	−	15.0382i	−0.0212282	−	0.0367683i	0.855216	−	0.518271i	$-0.173424\pi$
$409$	−8.68233	−	15.0382i	−0.0212282	−	0.0367683i	−0.876444	+	0.481503i	$0.840091\pi$
$410$	−253.383	+	146.291i	−0.618008	+	0.356807i
$411$	71.1512	−	68.9026i	0.173117	−	0.167646i
$412$	992.899			2.40995
$413$		0			0
$414$	685.239	+	425.523i	1.65517	+	1.02783i
$415$	46.1294	−	79.8985i	0.111155	−	0.192527i
$416$	−85.4626	+	49.3419i	−0.205439	+	0.118610i
$417$	−188.099	+	47.1781i	−0.451077	+	0.113137i
$418$	199.476	−	345.502i	0.477215	−	0.826560i
$419$		−	136.071i		−	0.324752i	−0.986729	−	0.162376i	$-0.948084\pi$
$419$		−	136.071i		−	0.324752i	0.986729	−	0.162376i	$-0.0519157\pi$
$420$		0			0
$421$	423.992			1.00711			0.503554	−	0.863964i	$-0.332026\pi$
$421$	423.992			1.00711			0.503554	+	0.863964i	$0.332026\pi$
$422$	−58.9543	−	34.0373i	−0.139702	−	0.0806570i
$423$	−296.984	−	9.53878i	−0.702090	−	0.0225503i
$424$	−114.255	−	197.895i	−0.269469	−	0.466734i
$425$	91.9836	+	53.1068i	0.216432	+	0.124957i
$426$	−203.557	+	713.655i	−0.477833	+	1.67525i
$427$		0			0
$428$		−	645.530i		−	1.50825i
$429$	175.982	−	170.420i	0.410214	−	0.397250i
$430$	52.5242	+	90.9746i	0.122149	+	0.211569i
$431$	−294.660	+	170.122i	−0.683666	+	0.394715i	−0.801235	−	0.598350i	$-0.795823\pi$
$431$	−294.660	+	170.122i	−0.683666	+	0.394715i	0.117569	+	0.993065i	$0.462490\pi$
$432$	−112.102	−	516.721i	−0.259495	−	1.19611i
$433$	159.166			0.367589			0.183794	−	0.982965i	$-0.441162\pi$
$433$	159.166			0.367589			0.183794	+	0.982965i	$0.441162\pi$
$434$		0			0
$435$	−9.70456	+	34.0235i	−0.0223093	+	0.0782148i
$436$	−151.480	+	262.371i	−0.347431	+	0.601767i
$437$	359.282	−	207.432i	0.822155	−	0.474672i
$438$	196.486	+	783.390i	0.448598	+	1.78856i
$439$	−64.0366	+	110.915i	−0.145869	+	0.252653i	−0.929697	−	0.368326i	$-0.879931\pi$
$439$	−64.0366	+	110.915i	−0.145869	+	0.252653i	0.783828	+	0.620978i	$0.213265\pi$
$440$		−	131.025i		−	0.297785i
$441$		0			0
$442$	−184.871			−0.418259
$443$	−170.901	−	98.6700i	−0.385782	−	0.222731i	0.294549	−	0.955636i	$-0.404831\pi$
$443$	−170.901	−	98.6700i	−0.385782	−	0.222731i	−0.680331	+	0.732905i	$0.738164\pi$
$444$	−797.175	+	199.943i	−1.79544	+	0.450323i
$445$	−79.0993	−	137.004i	−0.177751	−	0.307874i
$446$	−531.461	−	306.839i	−1.19162	−	0.687981i
$447$	−564.686	−	161.066i	−1.26328	−	0.360327i
$448$		0			0
$449$		−	148.101i		−	0.329847i	−0.986306	−	0.164923i	$-0.947262\pi$
$449$		−	148.101i		−	0.329847i	0.986306	−	0.164923i	$-0.0527377\pi$
$450$	349.313	+	652.549i	0.776251	+	1.45011i
$451$	−235.579	−	408.035i	−0.522348	−	0.904734i
$452$	156.248	−	90.2100i	0.345682	−	0.199580i
$453$	213.397	+	220.361i	0.471075	+	0.486449i
$454$	−622.561			−1.37128
$455$		0			0
$456$	−704.423	−	200.924i	−1.54479	−	0.440622i
$457$	61.1072	−	105.841i	0.133714	−	0.231599i	−0.791392	−	0.611310i	$-0.790643\pi$
$457$	61.1072	−	105.841i	0.133714	−	0.231599i	0.925105	+	0.379710i	$0.123976\pi$
$458$	123.913	−	71.5415i	0.270553	−	0.156204i
$459$	37.2900	−	116.428i	0.0812418	−	0.253655i
$460$	131.624	−	227.979i	0.286138	−	0.495606i
$461$		−	602.089i		−	1.30605i	−0.757337	−	0.653025i	$-0.773500\pi$
$461$		−	602.089i		−	1.30605i	0.757337	−	0.653025i	$-0.226500\pi$
$462$		0			0
$463$	−637.061			−1.37594			−0.687971	−	0.725738i	$-0.741498\pi$
$463$	−637.061			−1.37594			−0.687971	+	0.725738i	$0.741498\pi$
$464$	161.043	+	92.9780i	0.347075	+	0.200384i
$465$	26.0224	+	103.752i	0.0559622	+	0.223122i
$466$	−679.616	−	1177.13i	−1.45840	−	2.52603i
$467$	−664.853	−	383.853i	−1.42367	−	0.821955i	−0.427057	−	0.904225i	$-0.640450\pi$
$467$	−664.853	−	383.853i	−1.42367	−	0.821955i	−0.996610	+	0.0822701i	$0.973783\pi$
$468$	−738.280	−	458.460i	−1.57752	−	0.979616i
$469$		0			0
$470$			143.757i			0.305865i
$471$	218.556	+	225.688i	0.464025	+	0.479168i
$472$	695.080	+	1203.91i	1.47263	+	2.55067i
$473$	−146.501	+	84.5821i	−0.309726	+	0.178821i
$474$	−961.430	+	931.046i	−2.02833	+	1.96423i
$475$	380.686			0.801445
$476$		0			0
$477$	72.1097	−	116.122i	0.151173	−	0.243442i
$478$	86.8118	−	150.362i	0.181615	−	0.314566i
$479$	−341.089	+	196.928i	−0.712085	+	0.411122i	−0.811832	−	0.583890i	$-0.801530\pi$
$479$	−341.089	+	196.928i	−0.712085	+	0.411122i	0.0997478	+	0.995013i	$0.468196\pi$
$480$	−30.6240	+	7.68096i	−0.0638001	+	0.0160020i
$481$	−192.391	+	333.231i	−0.399981	+	0.692787i
$482$			1140.29i			2.36575i
$483$		0			0
$484$	−595.612			−1.23060
$485$	−24.9168	−	14.3857i	−0.0513749	−	0.0296613i
$486$	648.776	−	552.169i	1.33493	−	1.13615i
$487$	−286.705	−	496.587i	−0.588716	−	1.01969i	−0.994401	−	0.105673i	$-0.966300\pi$
$487$	−286.705	−	496.587i	−0.588716	−	1.01969i	0.405685	−	0.914013i	$-0.367033\pi$
$488$	−749.486	−	432.716i	−1.53583	−	0.886713i
$489$	−58.3908	+	204.714i	−0.119409	+	0.418638i
$490$		0			0
$491$			170.796i			0.347853i	0.984759	+	0.173927i	$0.0556455\pi$
$491$			170.796i			0.347853i	−0.984759	+	0.173927i	$0.944354\pi$
$492$	−1200.70	+	1162.76i	−2.44045	+	2.36332i
$493$	21.4980	+	37.2357i	0.0436066	+	0.0755288i
$494$	−573.833	+	331.303i	−1.16161	+	0.670654i
$495$	69.0991	−	36.9891i	0.139594	−	0.0747254i
$496$	562.199			1.13347
$497$		0			0
$498$	214.306	−	751.340i	0.430333	−	1.50871i
$499$	423.907	−	734.229i	0.849513	−	1.47140i	−0.0321299	−	0.999484i	$-0.510229\pi$
$499$	423.907	−	734.229i	0.849513	−	1.47140i	0.881643	−	0.471917i	$-0.156438\pi$
$500$	432.151	−	249.503i	0.864302	−	0.499005i
$501$	−151.070	−	602.318i	−0.301538	−	1.20223i
$502$	462.313	−	800.750i	0.920942	−	1.59512i
$503$		−	197.624i		−	0.392891i	−0.980515	−	0.196445i	$-0.937060\pi$
$503$		−	197.624i		−	0.392891i	0.980515	−	0.196445i	$-0.0629398\pi$
$504$		0			0
$505$	167.550			0.331783
$506$	544.233	+	314.213i	1.07556	+	0.620975i
$507$	97.1212	−	24.3594i	0.191560	−	0.0480462i
$508$	−63.9150	−	110.704i	−0.125817	−	0.217921i
$509$	425.606	+	245.724i	0.836162	+	0.482758i	0.855958	−	0.517046i	$-0.172968\pi$
$509$	425.606	+	245.724i	0.836162	+	0.482758i	−0.0197959	+	0.999804i	$0.506302\pi$
$510$	−56.8784	−	16.2235i	−0.111526	−	0.0318108i
$511$		0			0
$512$		−	1012.62i		−	1.97777i
$513$	−92.9006	−	428.215i	−0.181093	−	0.834727i
$514$	265.014	+	459.018i	0.515592	+	0.893032i
$515$	128.799	−	74.3623i	0.250096	−	0.144393i
$516$	417.475	+	431.099i	0.809060	+	0.835463i
$517$	−231.498			−0.447772
$518$		0			0
$519$	−312.911	−	89.2521i	−0.602912	−	0.171969i
$520$	−108.808	+	188.461i	−0.209246	+	0.362424i
$521$	−753.451	+	435.005i	−1.44616	+	0.834942i	−0.998250	−	0.0591353i	$-0.981166\pi$
$521$	−753.451	+	435.005i	−1.44616	+	0.834942i	−0.447912	+	0.894078i	$0.647832\pi$
$522$	−9.61859	+	299.469i	−0.0184264	+	0.573696i
$523$	−399.354	+	691.701i	−0.763582	+	1.32256i	0.177411	+	0.984137i	$0.443228\pi$
$523$	−399.354	+	691.701i	−0.763582	+	1.32256i	−0.940993	+	0.338426i	$0.890105\pi$
$524$			1518.26i			2.89744i
$525$		0			0
$526$	401.041			0.762434
$527$	112.574	+	64.9947i	0.213613	+	0.123330i
$528$	−100.216	−	399.563i	−0.189804	−	0.756748i
$529$	62.2451	+	107.812i	0.117666	+	0.203803i
$530$	−57.2713	−	33.0656i	−0.108059	−	0.0623879i
$531$	−438.686	+	706.437i	−0.826151	+	1.33039i
$532$		0			0
$533$			782.531i			1.46816i
$534$	−931.999	−	962.414i	−1.74532	−	1.80227i
$535$	−48.3464	−	83.7384i	−0.0903671	−	0.156520i
$536$	−197.612	+	114.091i	−0.368680	+	0.212857i
$537$	343.430	−	332.576i	0.639534	−	0.619323i
$538$	16.6941			0.0310300
$539$		0			0
$540$	−186.911	−	205.841i	−0.346132	−	0.381188i
$541$	368.122	−	637.605i	0.680446	−	1.17857i	−0.294398	−	0.955683i	$-0.595119\pi$
$541$	368.122	−	637.605i	0.680446	−	1.17857i	0.974845	−	0.222885i	$-0.0715475\pi$
$542$	−1574.89	+	909.262i	−2.90570	+	1.67761i
$543$	680.586	−	170.701i	1.25338	−	0.314367i
$544$	−19.1843	+	33.2282i	−0.0352653	+	0.0610812i
$545$			45.3797i			0.0832656i
$546$		0			0
$547$	−228.952			−0.418559			−0.209279	−	0.977856i	$-0.567112\pi$
$547$	−228.952			−0.418559			−0.209279	+	0.977856i	$0.567112\pi$
$548$	−237.071	−	136.873i	−0.432612	−	0.249768i
$549$	16.6188	−	517.416i	0.0302710	−	0.942469i
$550$	288.328	+	499.399i	0.524233	+	0.907998i
$551$	133.459	+	77.0524i	0.242212	+	0.139841i
$552$	316.494	−	1109.60i	0.573359	−	2.01015i
$553$		0			0
$554$		−	424.515i		−	0.766272i
$555$	−88.4352	+	85.6404i	−0.159343	+	0.154307i
$556$	267.989	+	464.170i	0.481994	+	0.834839i
$557$	−784.869	+	453.144i	−1.40910	+	0.813544i	−0.995301	−	0.0968243i	$-0.969131\pi$
$557$	−784.869	+	453.144i	−1.40910	+	0.813544i	−0.413798	+	0.910369i	$0.635798\pi$
$558$	427.507	+	798.623i	0.766141	+	1.43122i
$559$	280.959			0.502611
$560$		0			0
$561$	26.1255	−	91.5940i	0.0465695	−	0.163269i
$562$	−713.903	+	1236.52i	−1.27029	+	2.20021i
$563$	397.173	−	229.308i	0.705459	−	0.407297i	−0.103919	−	0.994586i	$-0.533138\pi$
$563$	397.173	−	229.308i	0.705459	−	0.407297i	0.809377	+	0.587289i	$0.199805\pi$
$564$	199.790	+	796.565i	0.354238	+	1.41235i
$565$	13.5124	−	23.4041i	0.0239157	−	0.0414233i
$566$		−	1397.58i		−	2.46922i
$567$		0			0
$568$	1061.60			1.86901
$569$	−500.067	−	288.714i	−0.878853	−	0.507406i	−0.00857275	−	0.999963i	$-0.502729\pi$
$569$	−500.067	−	288.714i	−0.878853	−	0.507406i	−0.870280	+	0.492557i	$0.836062\pi$
$570$	−205.623	+	51.5733i	−0.360742	+	0.0904795i
$571$	51.5608	+	89.3059i	0.0902991	+	0.156403i	0.907637	−	0.419756i	$-0.137884\pi$
$571$	51.5608	+	89.3059i	0.0902991	+	0.156403i	−0.817338	+	0.576159i	$0.804551\pi$
$572$	−586.359	−	338.535i	−1.02510	−	0.591844i
$573$	831.468	+	237.161i	1.45108	+	0.413893i
$574$		0			0
$575$			599.655i			1.04288i
$576$	385.812	−	206.527i	0.669812	−	0.358554i
$577$	338.292	+	585.938i	0.586294	+	1.01549i	0.994713	+	0.102696i	$0.0327469\pi$
$577$	338.292	+	585.938i	0.586294	+	1.01549i	−0.408419	+	0.912795i	$0.633920\pi$
$578$	815.219	−	470.667i	1.41041	−	0.814302i
$579$	160.952	+	166.205i	0.277983	+	0.287055i
$580$	97.7856			0.168596
$581$		0			0
$582$	−234.310	−	66.8325i	−0.402594	−	0.114833i
$583$	53.2470	−	92.2266i	0.0913328	−	0.158193i
$584$	1000.56	−	577.675i	1.71329	−	0.989170i
$585$	−130.106	−	4.17884i	−0.222403	−	0.00714332i
$586$	−4.44246	+	7.69457i	−0.00758099	+	0.0131307i
$587$		−	158.683i		−	0.270329i	−0.990823	−	0.135164i	$-0.956844\pi$
$587$		−	158.683i		−	0.270329i	0.990823	−	0.135164i	$-0.0431563\pi$
$588$		0			0
$589$	465.903			0.791007
$590$	348.415	+	201.158i	0.590534	+	0.340945i
$591$	−99.5741	−	397.002i	−0.168484	−	0.671747i
$592$	323.516	+	560.347i	0.546480	+	0.946532i
$593$	−810.055	−	467.686i	−1.36603	−	0.788677i	−0.375611	−	0.926777i	$-0.622567\pi$
$593$	−810.055	−	467.686i	−1.36603	−	0.788677i	−0.990418	+	0.138100i	$0.955900\pi$
$594$	491.387	−	446.196i	0.827251	−	0.751172i
$595$		0			0
$596$			1622.94i			2.72306i
$597$	180.698	+	186.595i	0.302677	+	0.312555i
$598$	−521.867	−	903.900i	−0.872687	−	1.51154i
$599$	−63.8836	+	36.8832i	−0.106650	+	0.0615747i	−0.552376	−	0.833595i	$-0.686279\pi$
$599$	−63.8836	+	36.8832i	−0.106650	+	0.0615747i	0.445726	+	0.895169i	$0.352946\pi$
$600$	760.609	−	736.571i	1.26768	−	1.22762i
$601$	−934.280			−1.55454			−0.777271	−	0.629166i	$-0.783397\pi$
$601$	−934.280			−1.55454			−0.777271	+	0.629166i	$0.783397\pi$
$602$		0			0
$603$	−115.956	−	72.0066i	−0.192298	−	0.119414i
$604$	423.907	−	734.229i	0.701833	−	1.21561i
$605$	−77.2630	+	44.6078i	−0.127707	+	0.0737319i
$606$	1376.29	−	345.195i	2.27111	−	0.569628i
$607$	90.8039	−	157.277i	0.149595	−	0.259105i	−0.781483	−	0.623926i	$-0.785536\pi$
$607$	90.8039	−	157.277i	0.149595	−	0.259105i	0.931078	+	0.364821i	$0.118870\pi$
$608$			137.519i			0.226183i
$609$		0			0
$610$	−250.458			−0.410586
$611$	332.976	+	192.244i	0.544969	+	0.314638i
$612$	−337.714	−	10.8470i	−0.551821	−	0.0177238i
$613$	448.970	+	777.639i	0.732414	+	1.26858i	0.955849	+	0.293860i	$0.0949398\pi$
$613$	448.970	+	777.639i	0.732414	+	1.26858i	−0.223434	+	0.974719i	$0.571727\pi$
$614$	−261.833	−	151.170i	−0.426439	−	0.246204i
$615$	−68.6719	+	240.759i	−0.111662	+	0.391477i
$616$		0			0
$617$		−	1169.69i		−	1.89576i	−0.318622	−	0.947882i	$-0.603220\pi$
$617$		−	1169.69i		−	1.89576i	0.318622	−	0.947882i	$-0.396780\pi$
$618$	904.778	−	876.184i	1.46404	−	1.41777i
$619$	−604.483	−	1047.00i	−0.976548	−	1.69143i	−0.674730	−	0.738064i	$-0.735740\pi$
$619$	−604.483	−	1047.00i	−0.976548	−	1.69143i	−0.301817	−	0.953366i	$-0.597593\pi$
$620$	256.027	−	147.817i	0.412946	−	0.238415i
$621$	674.522	−	146.336i	1.08619	−	0.235647i
$622$	532.118			0.855495
$623$		0			0
$624$	−187.664	+	657.936i	−0.300744	+	1.05438i
$625$	−255.846	+	443.139i	−0.409354	+	0.709022i
$626$	965.875	−	557.648i	1.54293	−	0.890812i
$627$	−83.0509	−	331.124i	−0.132458	−	0.528109i
$628$	434.155	−	751.978i	0.691329	−	1.19742i
$629$			149.604i			0.237845i
$630$		0			0
$631$	901.223			1.42825			0.714123	−	0.700020i	$-0.246826\pi$
$631$	901.223			1.42825			0.714123	+	0.700020i	$0.246826\pi$
$632$	1658.02	+	957.259i	2.62345	+	1.51465i
$633$	−56.5009	+	14.1713i	−0.0892589	+	0.0223875i
$634$	−638.114	−	1105.25i	−1.00649	−	1.74329i
$635$	−16.5822	−	9.57371i	−0.0261136	−	0.0150767i
$636$	−363.298	−	103.624i	−0.571223	−	0.162931i
$637$		0			0
$638$			233.435i			0.365886i
$639$	299.695	+	559.858i	0.469006	+	0.876147i
$640$	−126.908	−	219.811i	−0.198294	−	0.343454i
$641$	−457.806	+	264.315i	−0.714206	+	0.412347i	−0.812616	−	0.582799i	$-0.801958\pi$
$641$	−457.806	+	264.315i	−0.714206	+	0.412347i	0.0984103	+	0.995146i	$0.468624\pi$
$642$	−569.648	−	588.238i	−0.887302	−	0.916259i
$643$	33.4392			0.0520050			0.0260025	−	0.999662i	$-0.491722\pi$
$643$	33.4392			0.0520050			0.0260025	+	0.999662i	$0.491722\pi$
$644$		0			0
$645$	86.4418	+	24.6559i	0.134018	+	0.0382262i
$646$	−128.812	+	223.109i	−0.199399	+	0.345369i
$647$	680.962	−	393.154i	1.05249	−	0.607657i	0.129146	−	0.991626i	$-0.458776\pi$
$647$	680.962	−	393.154i	1.05249	−	0.607657i	0.923346	+	0.383969i	$0.125443\pi$
$648$	−1014.15	−	675.822i	−1.56504	−	1.04294i
$649$	−323.933	+	561.069i	−0.499127	+	0.864513i
$650$		−	957.750i		−	1.47346i
$651$		0			0
$652$	588.361			0.902394
$653$	−334.119	−	192.904i	−0.511668	−	0.295412i	0.221851	−	0.975081i	$-0.428790\pi$
$653$	−334.119	−	192.904i	−0.511668	−	0.295412i	−0.733519	+	0.679669i	$0.762123\pi$
$654$	93.4933	+	372.758i	0.142956	+	0.569967i
$655$	113.708	+	196.949i	0.173601	+	0.300685i
$656$	1139.58	+	657.936i	1.73716	+	1.00295i
$657$	587.114	+	364.588i	0.893628	+	0.554929i
$658$		0			0
$659$			97.2583i			0.147585i	0.997274	+	0.0737924i	$0.0235102\pi$
$659$			97.2583i			0.147585i	−0.997274	+	0.0737924i	$0.976490\pi$
$660$	−150.695	−	155.612i	−0.228325	−	0.235776i
$661$	480.752	+	832.687i	0.727311	+	1.25974i	0.958016	+	0.286715i	$0.0925633\pi$
$661$	480.752	+	832.687i	0.727311	+	1.25974i	−0.230705	+	0.973024i	$0.574103\pi$
$662$	468.697	−	270.602i	0.708001	−	0.408765i
$663$	−113.640	+	110.049i	−0.171403	+	0.165986i
$664$	−1117.66			−1.68322
$665$		0			0
$666$	−549.984	+	885.665i	−0.825802	+	1.32983i
$667$	−121.373	+	210.223i	−0.181968	+	0.315178i
$668$	−1486.33	+	858.136i	−2.22505	+	1.28463i
$669$	−509.345	+	127.751i	−0.761353	+	0.190959i
$670$	−33.0183	+	57.1894i	−0.0492810	+	0.0853572i
$671$		−	403.323i		−	0.601078i
$672$		0			0
$673$	−1089.81			−1.61933			−0.809663	−	0.586895i	$-0.800350\pi$
$673$	−1089.81			−1.61933			−0.809663	+	0.586895i	$0.800350\pi$
$674$	−1223.72	−	706.515i	−1.81561	−	1.04824i
$675$	603.171	+	193.186i	0.893586	+	0.286202i
$676$	−138.371	−	239.665i	−0.204690	−	0.354534i
$677$	1084.75	+	626.279i	1.60229	+	0.925080i	0.991029	+	0.133649i	$0.0426694\pi$
$677$	1084.75	+	626.279i	1.60229	+	0.925080i	0.611258	+	0.791432i	$0.290664\pi$
$678$	62.7752	−	220.085i	0.0925888	−	0.324609i
$679$		0			0
$680$			84.6097i			0.124426i
$681$	−382.690	+	370.596i	−0.561953	+	0.544193i
$682$	352.871	+	611.190i	0.517406	+	0.896173i
$683$	−295.398	+	170.548i	−0.432501	+	0.249705i	−0.700412	−	0.713739i	$-0.747000\pi$
$683$	−295.398	+	170.548i	−0.432501	+	0.249705i	0.267910	+	0.963444i	$0.413667\pi$
$684$	−1067.70	+	571.543i	−1.56096	+	0.835589i
$685$	−41.0039			−0.0598598
$686$		0			0
$687$	33.5830	−	117.739i	0.0488836	−	0.171382i
$688$	236.225	−	409.153i	0.343350	−	0.594700i
$689$	−153.176	+	88.4363i	−0.222317	+	0.128355i
$690$	−81.2381	−	323.896i	−0.117736	−	0.469415i
$691$	391.833	−	678.675i	0.567053	−	0.982164i	−0.429803	−	0.902923i	$-0.641417\pi$
$691$	391.833	−	678.675i	0.567053	−	0.982164i	0.996855	−	0.0792411i	$-0.0252497\pi$
$692$			899.327i			1.29961i
$693$		0			0
$694$	−1652.14			−2.38060
$695$	69.5272	+	40.1416i	0.100039	+	0.0577576i
$696$	415.735	−	104.272i	0.597320	−	0.149817i
$697$	152.125	+	263.489i	0.218258	+	0.378033i
$698$	1106.75	+	638.983i	1.58560	+	0.915449i
$699$	−1118.48	−	319.025i	−1.60011	−	0.456402i
$700$		0			0
$701$			1331.76i			1.89979i	0.312562	+	0.949897i	$0.398813\pi$
$701$			1331.76i			1.89979i	−0.312562	+	0.949897i	$0.601187\pi$
$702$	−1077.32	+	233.724i	−1.53465	+	0.332940i
$703$	268.103	+	464.368i	0.381370	+	0.660553i
$704$	295.263	−	170.470i	0.419408	−	0.242145i
$705$	85.5749	+	88.3676i	0.121383	+	0.125344i
$706$	−302.708			−0.428766
$707$		0			0
$708$	2210.16	+	630.406i	3.12169	+	0.890404i
$709$	−381.982	+	661.612i	−0.538761	+	0.933162i	0.460210	+	0.887810i	$0.347774\pi$
$709$	−381.982	+	661.612i	−0.538761	+	0.933162i	−0.998971	+	0.0453517i	$0.985559\pi$
$710$	266.068	−	153.615i	0.374744	−	0.216358i
$711$	−36.7642	+	1144.63i	−0.0517078	+	1.60989i
$712$	−958.239	+	1659.72i	−1.34584	+	2.33107i
$713$			733.888i			1.02930i
$714$		0			0
$715$	−101.417			−0.141842
$716$	−1144.29	−	660.654i	−1.59816	−	0.922701i
$717$	−36.1437	−	144.105i	−0.0504097	−	0.200983i
$718$	−652.221	−	1129.68i	−0.908386	−	1.57337i
$719$	−540.153	−	311.858i	−0.751256	−	0.433738i	0.0748915	−	0.997192i	$-0.476139\pi$
$719$	−540.153	−	311.858i	−0.751256	−	0.433738i	−0.826148	+	0.563454i	$0.809472\pi$
$720$	−115.476	+	185.956i	−0.160383	+	0.258272i
$721$		0			0
$722$		−	342.274i		−	0.474064i
$723$	678.788	+	700.940i	0.938850	+	0.969489i
$724$	−969.645	−	1679.47i	−1.33929	−	2.31972i
$725$	−192.905	+	111.374i	−0.266076	+	0.153619i
$726$	−542.750	+	525.598i	−0.747590	+	0.723964i
$727$	678.494			0.933279			0.466640	−	0.884448i	$-0.345464\pi$
$727$	678.494			0.933279			0.466640	+	0.884448i	$0.345464\pi$
$728$		0			0
$729$	70.1111	−	725.621i	0.0961744	−	0.995364i
$730$	167.180	−	289.565i	0.229014	−	0.396664i
$731$	94.6029	−	54.6190i	0.129416	−	0.0747182i
$732$	−1387.80	+	348.081i	−1.89590	+	0.475521i
$733$	197.483	−	342.051i	0.269417	−	0.466645i	−0.699294	−	0.714834i	$-0.746502\pi$
$733$	197.483	−	342.051i	0.269417	−	0.466645i	0.968712	+	0.248189i	$0.0798355\pi$
$734$		−	567.208i		−	0.772763i
$735$		0			0
$736$	−216.620			−0.294320
$737$	−92.0947	−	53.1709i	−0.124959	−	0.0721450i
$738$	−68.0636	+	2119.12i	−0.0922270	+	2.87143i
$739$	−146.099	−	253.051i	−0.197699	−	0.342424i	0.750083	−	0.661344i	$-0.230013\pi$
$739$	−146.099	−	253.051i	−0.197699	−	0.342424i	−0.947782	+	0.318919i	$0.896680\pi$
$740$	294.660	+	170.122i	0.398189	+	0.229895i
$741$	−155.520	+	545.242i	−0.209879	+	0.735819i
$742$		0			0
$743$		−	383.452i		−	0.516086i	−0.966133	−	0.258043i	$-0.916922\pi$
$743$		−	383.452i		−	0.516086i	0.966133	−	0.258043i	$-0.0830776\pi$
$744$	930.872	−	901.454i	1.25117	−	1.21163i
$745$	121.549	+	210.529i	0.163153	+	0.282589i
$746$	1148.45	−	663.060i	1.53948	−	0.888820i
$747$	−315.520	−	589.422i	−0.422383	−	0.789052i
$748$	−263.247			−0.351935
$749$		0			0
$750$	173.624	−	608.711i	0.231498	−	0.811614i
$751$	348.166	−	603.041i	0.463603	−	0.802984i	−0.535534	−	0.844514i	$-0.679890\pi$
$751$	348.166	−	603.041i	0.463603	−	0.802984i	0.999137	+	0.0415293i	$0.0132230\pi$
$752$	559.918	−	323.269i	0.744572	−	0.429879i
$753$	−192.482	−	767.427i	−0.255620	−	1.01916i
$754$	193.852	−	335.762i	0.257099	−	0.445308i
$755$		−	126.993i		−	0.168202i
$756$		0			0
$757$	967.357			1.27788			0.638941	−	0.769256i	$-0.279373\pi$
$757$	967.357			1.27788			0.638941	+	0.769256i	$0.279373\pi$
$758$	154.232	+	89.0459i	0.203472	+	0.117475i
$759$	521.585	−	130.821i	0.687201	−	0.172360i
$760$	151.627	+	262.626i	0.199510	+	0.345561i
$761$	77.6876	+	44.8529i	0.102086	+	0.0589395i	0.550174	−	0.835050i	$-0.314561\pi$
$761$	77.6876	+	44.8529i	0.102086	+	0.0589395i	−0.448088	+	0.893990i	$0.647895\pi$
$762$	−155.933	−	44.4771i	−0.204637	−	0.0583689i
$763$		0			0
$764$		−	2389.69i		−	3.12787i
$765$	−44.6208	+	23.8857i	−0.0583279	+	0.0312232i
$766$	−198.753	−	344.250i	−0.259469	−	0.449413i
$767$	931.861	−	538.010i	1.21494	−	0.701448i
$768$	−1089.40	−	1124.95i	−1.41849	−	1.46478i
$769$	926.219			1.20445			0.602223	−	0.798328i	$-0.294282\pi$
$769$	926.219			1.20445			0.602223	+	0.798328i	$0.294282\pi$
$770$		0			0
$771$	436.148	+	124.403i	0.565691	+	0.161353i
$772$	319.727	−	553.783i	0.414154	−	0.717336i
$773$	367.303	−	212.063i	0.475166	−	0.274337i	−0.243234	−	0.969968i	$-0.578208\pi$
$773$	367.303	−	212.063i	0.475166	−	0.274337i	0.718400	+	0.695631i	$0.244875\pi$
$774$	760.847	+	24.4375i	0.983006	+	0.0315730i
$775$	−336.715	+	583.207i	−0.434471	+	0.752526i
$776$			348.548i			0.449160i
$777$		0			0
$778$	−2543.84			−3.26972
$779$	944.387	+	545.242i	1.21231	+	0.699926i
$780$	87.5262	+	348.967i	0.112213	+	0.447394i
$781$	247.373	+	428.462i	0.316738	+	0.548607i
$782$	−351.439	−	202.904i	−0.449411	−	0.259468i
$783$	172.354	+	189.810i	0.220120	+	0.242414i
$784$		0			0
$785$		−	130.063i		−	0.165685i
$786$	1339.79	+	1383.51i	1.70456	+	1.76019i
$787$	77.9444	+	135.004i	0.0990399	+	0.171542i	0.911288	−	0.411771i	$-0.135090\pi$
$787$	77.9444	+	135.004i	0.0990399	+	0.171542i	−0.812248	+	0.583313i	$0.801756\pi$
$788$	−979.679	+	565.618i	−1.24325	+	0.717789i
$789$	246.521	−	238.730i	0.312447	−	0.302573i
$790$	554.065			0.701348
$791$		0			0
$792$	−806.612	−	500.893i	−1.01845	−	0.632441i
$793$	−334.933	+	580.122i	−0.422362	+	0.731553i
$794$	−286.456	+	165.386i	−0.360776	+	0.208294i
$795$	−54.8880	+	13.7667i	−0.0690415	+	0.0173166i
$796$	358.952	−	621.722i	0.450944	−	0.781058i
$797$		−	719.191i		−	0.902373i	−0.892430	−	0.451186i	$-0.851001\pi$
$797$		−	719.191i		−	0.902373i	0.892430	−	0.451186i	$-0.148999\pi$
$798$		0			0
$799$	149.490			0.187097
$800$	−172.144	−	99.3871i	−0.215179	−	0.124234i
$801$	−1145.80	−	36.8019i	−1.43047	−	0.0459449i
$802$	1187.92	+	2057.54i	1.48120	+	2.56551i
$803$	466.300	+	269.218i	0.580697	+	0.335266i
$804$	−103.476	+	362.778i	−0.128701	+	0.451217i
$805$		0			0
$806$		−	1172.14i		−	1.45427i
$807$	10.2619	−	9.93763i	0.0127162	−	0.0123143i
$808$	−1014.88	−	1757.83i	−1.25604	−	2.17553i
$809$	−183.808	+	106.122i	−0.227204	+	0.131176i	−0.609282	−	0.792954i	$-0.708542\pi$
$809$	−183.808	+	106.122i	−0.227204	+	0.131176i	0.382077	+	0.924130i	$0.375209\pi$
$810$	−351.967	−	22.6329i	−0.434527	−	0.0279418i
$811$	1058.66			1.30538			0.652690	−	0.757625i	$-0.273641\pi$
$811$	1058.66			1.30538			0.652690	+	0.757625i	$0.273641\pi$
$812$		0			0
$813$	−426.826	+	1496.42i	−0.525001	+	1.84061i
$814$	−406.118	+	703.416i	−0.498916	+	0.864148i
$815$	76.3224	−	44.0647i	0.0936471	−	0.0540672i
$816$	64.7148	+	258.018i	0.0793074	+	0.316199i
$817$	195.763	−	339.072i	0.239612	−	0.415021i
$818$			60.8792i			0.0744244i
$819$		0			0
$820$	691.956			0.843848
$821$	−708.903	−	409.286i	−0.863463	−	0.498521i	0.00170721	−	0.999999i	$-0.499457\pi$
$821$	−708.903	−	409.286i	−0.863463	−	0.498521i	−0.865171	+	0.501478i	$0.832790\pi$
$822$	−336.814	+	84.4781i	−0.409750	+	0.102771i
$823$	−103.425	−	179.137i	−0.125668	−	0.217664i	0.796326	−	0.604868i	$-0.206774\pi$
$823$	−103.425	−	179.137i	−0.125668	−	0.217664i	−0.921994	+	0.387204i	$0.873441\pi$
$824$	−1560.32	−	900.853i	−1.89360	−	1.09327i
$825$	474.516	+	135.347i	0.575171	+	0.164057i
$826$		0			0
$827$		−	438.639i		−	0.530398i	−0.964194	−	0.265199i	$-0.914562\pi$
$827$		−	438.639i		−	0.530398i	0.964194	−	0.265199i	$-0.0854376\pi$
$828$	−900.291	−	1681.83i	−1.08731	−	2.03119i
$829$	−327.402	−	567.077i	−0.394936	−	0.684049i	0.598157	−	0.801379i	$-0.295900\pi$
$829$	−327.402	−	567.077i	−0.394936	−	0.684049i	−0.993093	+	0.117330i	$0.962567\pi$
$830$	−280.118	+	161.726i	−0.337492	+	0.194851i
$831$	−252.703	−	260.950i	−0.304096	−	0.314020i
$832$	−566.257			−0.680598
$833$		0			0
$834$	653.812	+	186.488i	0.783947	+	0.223606i
$835$	−128.539	+	222.635i	−0.153938	+	0.266629i
$836$	−817.112	+	471.760i	−0.977407	+	0.564306i
$837$	738.191	+	236.431i	0.881949	+	0.282475i
$838$	−238.527	+	413.142i	−0.284639	+	0.493009i
$839$			50.9710i			0.0607521i	0.999539	+	0.0303761i	$0.00967049\pi$
$839$			50.9710i			0.0607521i	−0.999539	+	0.0303761i	$0.990330\pi$
$840$		0			0
$841$	750.830			0.892782
$842$	−1287.33	−	743.242i	−1.52890	−	0.882710i
$843$	297.231	+	1185.06i	0.352587	+	1.40576i
$844$	80.4980	+	139.427i	0.0953768	+	0.165197i
$845$	−35.8990	−	20.7263i	−0.0424840	−	0.0245281i
$846$	884.988	+	549.564i	1.04609	+	0.649603i
$847$		0			0
$848$			297.422i			0.350733i
$849$	−831.946	−	859.096i	−0.979913	−	1.01189i
$850$	−186.188	−	322.487i	−0.219045	−	0.379397i
$851$	−731.471	+	422.315i	−0.859543	+	0.496257i
$852$	1260.81	−	1220.97i	1.47982	−	1.43306i
$853$	−883.941			−1.03627			−0.518137	−	0.855298i	$-0.673374\pi$
$853$	−883.941			−1.03627			−0.518137	+	0.855298i	$0.673374\pi$
$854$		0			0
$855$	−95.6967	+	154.105i	−0.111926	+	0.180240i
$856$	−585.686	+	1014.44i	−0.684213	+	1.18509i
$857$	−481.961	+	278.260i	−0.562382	+	0.324691i	−0.754101	−	0.656759i	$-0.771927\pi$
$857$	−481.961	+	278.260i	−0.562382	+	0.324691i	0.191719	+	0.981450i	$0.438594\pi$
$858$	−833.059	+	208.944i	−0.970931	+	0.243524i
$859$	321.539	−	556.922i	0.374318	−	0.648338i	−0.615907	−	0.787819i	$-0.711210\pi$
$859$	321.539	−	556.922i	0.374318	−	0.648338i	0.990225	+	0.139481i	$0.0445435\pi$
$860$		−	248.439i		−	0.288883i
$861$		0			0
$862$	1192.87			1.38384
$863$	177.442	+	102.446i	0.205611	+	0.118709i	0.599270	−	0.800547i	$-0.295458\pi$
$863$	177.442	+	102.446i	0.205611	+	0.118709i	−0.393659	+	0.919256i	$0.628791\pi$
$864$	−69.7867	+	217.890i	−0.0807716	+	0.252187i
$865$	67.3542	+	116.661i	0.0778662	+	0.134868i
$866$	−483.263	−	279.012i	−0.558040	−	0.322185i
$867$	220.940	−	774.601i	0.254833	−	0.893426i
$868$		0			0
$869$			892.237i			1.02674i
$870$	89.1070	−	86.2909i	0.102422	−	0.0991850i
$871$	88.3098	+	152.957i	0.101389	+	0.175611i
$872$	476.095	−	274.874i	0.545981	−	0.315222i
$873$	−183.815	+	98.3969i	−0.210555	+	0.112711i
$874$	−1454.48			−1.66416
$875$		0			0
$876$	523.925	−	1836.84i	0.598088	−	2.09685i
$877$	103.605	−	179.450i	0.118136	−	0.204617i	−0.800893	−	0.598807i	$-0.795641\pi$
$877$	103.605	−	179.450i	0.118136	−	0.204617i	0.919029	+	0.394190i	$0.128975\pi$
$878$	388.858	−	224.507i	0.442891	−	0.255703i
$879$	1.84960	+	7.37437i	0.00210421	+	0.00838949i
$880$	−85.2693	+	147.691i	−0.0968969	+	0.167830i
$881$			1391.37i			1.57931i	0.613552	+	0.789654i	$0.289740\pi$
$881$			1391.37i			1.57931i	−0.613552	+	0.789654i	$0.710260\pi$
$882$		0			0
$883$	−1091.99			−1.23668			−0.618342	−	0.785909i	$-0.712195\pi$
$883$	−1091.99			−1.23668			−0.618342	+	0.785909i	$0.712195\pi$
$884$	378.642	+	218.609i	0.428328	+	0.247296i
$885$	333.916	−	83.7511i	0.377306	−	0.0946340i
$886$	345.929	+	599.167i	0.390439	+	0.676261i
$887$	129.426	+	74.7243i	0.145915	+	0.0842439i	0.571180	−	0.820825i	$-0.306486\pi$
$887$	129.426	+	74.7243i	0.145915	+	0.0842439i	−0.425265	+	0.905069i	$0.639819\pi$
$888$	1434.15	+	409.066i	1.61504	+	0.460659i
$889$		0			0
$890$			554.632i			0.623183i
$891$	36.4468	−	566.789i	0.0409055	−	0.636127i
$892$	725.674	+	1256.91i	0.813536	+	1.40909i
$893$	464.014	−	267.898i	0.519612	−	0.299998i
$894$	1432.17	+	1478.91i	1.60198	+	1.65426i
$895$	−197.916			−0.221135
$896$		0			0
$897$	−858.863	−	244.975i	−0.957483	−	0.273104i
$898$	−259.616	+	449.667i	−0.289104	+	0.500743i
$899$	−236.087	+	136.305i	−0.262611	+	0.151618i
$900$	56.1944	−	1749.58i	0.0624382	−	1.94398i
$901$	−34.3844	+	59.5554i	−0.0381624	+	0.0660993i
$902$			1651.84i			1.83131i
$903$		0			0
$904$	−327.388			−0.362155
$905$	−251.565	−	145.241i	−0.277973	−	0.160488i
$906$	−261.636	−	1043.14i	−0.288781	−	1.15137i
$907$	−296.859	−	514.174i	−0.327297	−	0.566896i	0.654677	−	0.755909i	$-0.272805\pi$
$907$	−296.859	−	514.174i	−0.327297	−	0.566896i	−0.981975	+	0.189013i	$0.939471\pi$
$908$	1275.10	+	736.177i	1.40429	+	0.810768i
$909$	640.524	−	1031.47i	0.704647	−	1.13473i
$910$		0			0
$911$		−	1133.75i		−	1.24451i	−0.782815	−	0.622254i	$-0.786217\pi$
$911$		−	1133.75i		−	1.24451i	0.782815	−	0.622254i	$-0.213783\pi$
$912$	663.263	+	684.908i	0.727262	+	0.750996i
$913$	−260.435	−	451.087i	−0.285252	−	0.494071i
$914$	−371.070	+	214.237i	−0.405984	+	0.234395i
$915$	−153.957	+	149.091i	−0.168259	+	0.162941i
$916$	−338.391			−0.369422
$917$		0			0
$918$	−317.314	+	288.132i	−0.345658	+	0.313869i
$919$	342.494	−	593.217i	0.372681	−	0.645503i	−0.617296	−	0.786731i	$-0.711772\pi$
$919$	342.494	−	593.217i	0.372681	−	0.645503i	0.989977	+	0.141228i	$0.0451051\pi$
$920$	−413.688	+	238.843i	−0.449661	+	0.259612i
$921$	−250.937	+	62.9388i	−0.272462	+	0.0683375i
$922$	−1055.44	+	1828.07i	−1.14473	+	1.98273i
$923$		−	821.706i		−	0.890256i
$924$		0			0
$925$	−775.048			−0.837890
$926$	1934.26	+	1116.74i	2.08883	+	1.20599i
$927$	34.5979	−	1077.19i	0.0373224	−	1.16201i
$928$	−40.2327	−	69.6851i	−0.0433542	−	0.0750917i
$929$	−166.551	−	96.1584i	−0.179280	−	0.103507i	0.407674	−	0.913127i	$-0.366340\pi$
$929$	−166.551	−	96.1584i	−0.179280	−	0.103507i	−0.586954	+	0.809620i	$0.699673\pi$
$930$	102.863	−	360.629i	0.110605	−	0.387773i
$931$		0			0
$932$			3214.58i			3.44912i
$933$	327.094	−	316.757i	0.350583	−	0.339504i
$934$	1345.76	+	2330.92i	1.44086	+	2.49563i
$935$	−34.1485	+	19.7156i	−0.0365225	+	0.0210863i
$936$	744.234	+	1390.30i	0.795122	+	1.48536i
$937$	−1270.28			−1.35569			−0.677844	−	0.735206i	$-0.737086\pi$
$937$	−1270.28			−1.35569			−0.677844	+	0.735206i	$0.737086\pi$
$938$		0			0
$939$	261.771	−	917.750i	0.278777	−	0.977370i
$940$	169.992	−	294.435i	0.180843	−	0.313229i
$941$	−135.923	+	78.4754i	−0.144446	+	0.0833957i	−0.570481	−	0.821311i	$-0.693243\pi$
$941$	−135.923	+	78.4754i	−0.144446	+	0.0833957i	0.426035	+	0.904706i	$0.359910\pi$
$942$	−267.960	−	1068.36i	−0.284459	−	1.13414i
$943$	−858.863	+	1487.59i	−0.910777	+	1.57751i
$944$		−	1809.39i		−	1.91673i
$945$		0			0
$946$	593.077			0.626931
$947$	762.055	+	439.973i	0.804704	+	0.464596i	0.845114	−	0.534587i	$-0.179533\pi$
$947$	762.055	+	439.973i	0.804704	+	0.464596i	−0.0404090	+	0.999183i	$0.512866\pi$
$948$	3070.11	−	770.030i	3.23852	−	0.812268i
$949$	−447.136	−	774.462i	−0.471165	−	0.816082i
$950$	−1155.85	−	667.329i	−1.21668	−	0.702451i
$951$	−1050.18	−	299.543i	−1.10429	−	0.314977i
$952$		0			0
$953$		−	563.276i		−	0.591056i	−0.955334	−	0.295528i	$-0.904505\pi$
$953$		−	563.276i		−	0.591056i	0.955334	−	0.295528i	$-0.0954955\pi$
$954$	−422.498	+	226.165i	−0.442870	+	0.237070i
$955$	−178.974	−	309.992i	−0.187407	−	0.324599i
$956$	−355.607	+	205.310i	−0.371974	+	0.214759i
$957$	138.958	+	143.493i	0.145202	+	0.149941i
$958$	1380.83			1.44136
$959$		0			0
$960$	−174.218	−	49.6926i	−0.181477	−	0.0517631i
$961$	68.4111	−	118.491i	0.0711874	−	0.123300i
$962$	1168.28	−	674.508i	1.21443	−	0.701151i
$963$	−700.328	−	22.4937i	−0.727236	−	0.0233580i
$964$	1348.39	−	2335.49i	1.39875	−	2.42270i
$965$		−	95.7826i		−	0.0992566i
$966$		0			0
$967$	237.676			0.245787			0.122893	−	0.992420i	$-0.460783\pi$
$967$	237.676			0.245787			0.122893	+	0.992420i	$0.460783\pi$
$968$	935.993	+	540.396i	0.966935	+	0.558260i
$969$	53.6302	+	213.824i	0.0553460	+	0.220665i
$970$	50.4353	+	87.3565i	0.0519951	+	0.0900582i
$971$	−1173.46	−	677.498i	−1.20851	−	0.697732i	−0.246075	−	0.969251i	$-0.579141\pi$
$971$	−1173.46	−	677.498i	−1.20851	−	0.697732i	−0.962433	+	0.271519i	$0.912474\pi$
$972$	−1981.73	+	363.748i	−2.03882	+	0.374226i
$973$		0			0
$974$			2010.33i			2.06399i
$975$	−570.126	−	588.731i	−0.584744	−	0.603827i
$976$	563.210	+	975.508i	0.577059	+	0.999496i
$977$	427.579	−	246.863i	0.437645	−	0.252674i	−0.264953	−	0.964261i	$-0.585357\pi$
$977$	427.579	−	246.863i	0.437645	−	0.252674i	0.702598	+	0.711587i	$0.252023\pi$
$978$	536.143	−	519.199i	0.548203	−	0.530878i
$979$	−893.150			−0.912309
$980$		0			0
$981$	279.365	+	173.481i	0.284775	+	0.176841i
$982$	299.399	−	518.574i	0.304887	−	0.528079i
$983$	1331.99	−	769.026i	1.35503	−	0.782325i	0.366078	−	0.930584i	$-0.380700\pi$
$983$	1331.99	−	769.026i	1.35503	−	0.782325i	0.988949	+	0.148259i	$0.0473670\pi$
$984$	2941.84	−	737.858i	2.98968	−	0.749856i
$985$	−84.7229	+	146.744i	−0.0860130	+	0.148979i
$986$		−	150.741i		−	0.152881i
$987$		0			0
$988$	1567.06			1.58609
$989$	534.105	+	308.365i	0.540045	+	0.311795i
$990$	−274.640	−	8.82112i	−0.277414	−	0.00891022i
$991$	−757.365	−	1311.79i	−0.764243	−	1.32371i	−0.940646	−	0.339389i	$-0.889780\pi$
$991$	−757.365	−	1311.79i	−0.764243	−	1.32371i	0.176403	−	0.984318i	$-0.443554\pi$
$992$	−210.678	−	121.635i	−0.212377	−	0.122616i
$993$	127.026	−	445.344i	0.127922	−	0.448483i
$994$		0			0
$995$		−	107.533i		−	0.108074i
$996$	−1327.39	+	1285.44i	−1.33272	+	1.29060i
$997$	−913.216	−	1581.74i	−0.915964	−	1.58650i	−0.805484	−	0.592618i	$-0.798094\pi$
$997$	−913.216	−	1581.74i	−0.915964	−	1.58650i	−0.110481	−	0.993878i	$-0.535239\pi$
$998$	−2574.15	+	1486.19i	−2.57931	+	1.48916i
$999$	189.139	+	871.813i	0.189328	+	0.872686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.3.h.e.128.1		8
3.2	odd	2	inner	147.3.h.e.128.4		8
7.2	even	3		21.3.b.a.8.4	yes	4
7.3	odd	6		147.3.h.c.116.4		8
7.4	even	3	inner	147.3.h.e.116.4		8
7.5	odd	6		147.3.b.f.50.4		4
7.6	odd	2		147.3.h.c.128.1		8
21.2	odd	6		21.3.b.a.8.1	✓	4
21.5	even	6		147.3.b.f.50.1		4
21.11	odd	6	inner	147.3.h.e.116.1		8
21.17	even	6		147.3.h.c.116.1		8
21.20	even	2		147.3.h.c.128.4		8
28.23	odd	6		336.3.d.c.113.2		4
35.2	odd	12		525.3.f.a.449.1		8
35.9	even	6		525.3.c.a.176.1		4
35.23	odd	12		525.3.f.a.449.8		8
56.37	even	6		1344.3.d.f.449.2		4
56.51	odd	6		1344.3.d.b.449.3		4
63.2	odd	6		567.3.r.c.134.1		8
63.16	even	3		567.3.r.c.134.4		8
63.23	odd	6		567.3.r.c.512.4		8
63.58	even	3		567.3.r.c.512.1		8
84.23	even	6		336.3.d.c.113.1		4
105.2	even	12		525.3.f.a.449.7		8
105.23	even	12		525.3.f.a.449.2		8
105.44	odd	6		525.3.c.a.176.4		4
168.107	even	6		1344.3.d.b.449.4		4
168.149	odd	6		1344.3.d.f.449.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.b.a.8.1	✓	4	21.2	odd	6
21.3.b.a.8.4	yes	4	7.2	even	3
147.3.b.f.50.1		4	21.5	even	6
147.3.b.f.50.4		4	7.5	odd	6
147.3.h.c.116.1		8	21.17	even	6
147.3.h.c.116.4		8	7.3	odd	6
147.3.h.c.128.1		8	7.6	odd	2
147.3.h.c.128.4		8	21.20	even	2
147.3.h.e.116.1		8	21.11	odd	6	inner
147.3.h.e.116.4		8	7.4	even	3	inner
147.3.h.e.128.1		8	1.1	even	1	trivial
147.3.h.e.128.4		8	3.2	odd	2	inner
336.3.d.c.113.1		4	84.23	even	6
336.3.d.c.113.2		4	28.23	odd	6
525.3.c.a.176.1		4	35.9	even	6
525.3.c.a.176.4		4	105.44	odd	6
525.3.f.a.449.1		8	35.2	odd	12
525.3.f.a.449.2		8	105.23	even	12
525.3.f.a.449.7		8	105.2	even	12
525.3.f.a.449.8		8	35.23	odd	12
567.3.r.c.134.1		8	63.2	odd	6
567.3.r.c.134.4		8	63.16	even	3
567.3.r.c.512.1		8	63.58	even	3
567.3.r.c.512.4		8	63.23	odd	6
1344.3.d.b.449.3		4	56.51	odd	6
1344.3.d.b.449.4		4	168.107	even	6
1344.3.d.f.449.1		4	168.149	odd	6
1344.3.d.f.449.2		4	56.37	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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	147.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.03622 - 1.75296i) q^{2} +(-2.90987 + 0.729839i) q^{3} +(4.14575 + 7.18065i) q^{4} +(1.07558 + 0.620984i) q^{5} +(10.1144 + 2.88494i) q^{6} -15.0457i q^{8} +(7.93467 - 4.24747i) q^{9} +O(q^{10})\)	\(q+(-3.03622 - 1.75296i) q^{2} +(-2.90987 + 0.729839i) q^{3} +(4.14575 + 7.18065i) q^{4} +(1.07558 + 0.620984i) q^{5} +(10.1144 + 2.88494i) q^{6} -15.0457i q^{8} +(7.93467 - 4.24747i) q^{9} +(-2.17712 - 3.77089i) q^{10} +(6.07244 - 3.50592i) q^{11} +(-17.3043 - 17.8690i) q^{12} -11.6458 q^{13} +(-3.58301 - 1.02199i) q^{15} +(-9.79150 + 16.9594i) q^{16} +(-3.92129 + 2.26395i) q^{17} +(-31.5371 - 1.01293i) q^{18} +(-8.11438 + 14.0545i) q^{19} +10.2978i q^{20} -24.5830 q^{22} +(-22.1386 - 12.7817i) q^{23} +(10.9809 + 43.7810i) q^{24} +(-11.7288 - 20.3148i) q^{25} +(35.3591 + 20.4146i) q^{26} +(-19.9889 + 18.1506i) q^{27} -9.49579i q^{29} +(9.08729 + 9.38385i) q^{30} +(-14.3542 - 24.8623i) q^{31} +(7.33853 - 4.23690i) q^{32} +(-15.1112 + 14.6337i) q^{33} +15.8745 q^{34} +(63.3948 + 39.3672i) q^{36} +(16.5203 - 28.6139i) q^{37} +(49.2741 - 28.4484i) q^{38} +(33.8876 - 8.49952i) q^{39} +(9.34313 - 16.1828i) q^{40} -67.1946i q^{41} -24.1255 q^{43} +(50.3496 + 29.0694i) q^{44} +(11.1720 + 0.358830i) q^{45} +(44.8118 + 77.6162i) q^{46} +(-28.5921 - 16.5076i) q^{47} +(16.1144 - 56.4958i) q^{48} +82.2403i q^{50} +(9.75810 - 9.44972i) q^{51} +(-48.2804 - 83.6241i) q^{52} +(13.1530 - 7.59387i) q^{53} +(92.5080 - 20.0695i) q^{54} +8.70850 q^{55} +(13.3542 - 46.8190i) q^{57} +(-16.6458 + 28.8313i) q^{58} +(-80.0173 + 46.1980i) q^{59} +(-7.51572 - 29.9652i) q^{60} +(28.7601 - 49.8140i) q^{61} +100.650i q^{62} +48.6235 q^{64} +(-12.5259 - 7.23183i) q^{65} +(71.5333 - 17.9416i) q^{66} +(-7.58301 - 13.1342i) q^{67} +(-32.5133 - 18.7716i) q^{68} +(73.7490 + 21.0355i) q^{69} +70.5584i q^{71} +(-63.9061 - 119.383i) q^{72} +(38.3948 + 66.5017i) q^{73} +(-100.318 + 57.9188i) q^{74} +(48.9557 + 50.5533i) q^{75} -134.561 q^{76} +(-117.790 - 33.5973i) q^{78} +(-63.6235 + 110.199i) q^{79} +(-21.0630 + 12.1607i) q^{80} +(44.9180 - 67.4045i) q^{81} +(-117.790 + 204.017i) q^{82} -74.2844i q^{83} -5.62352 q^{85} +(73.2503 + 42.2911i) q^{86} +(6.93039 + 27.6315i) q^{87} +(-52.7490 - 91.3640i) q^{88} +(-110.312 - 63.6887i) q^{89} +(-33.2915 - 20.6735i) q^{90} -211.959i q^{92} +(59.9144 + 61.8697i) q^{93} +(57.8745 + 100.242i) q^{94} +(-17.4553 + 10.0778i) q^{95} +(-18.2619 + 17.6848i) q^{96} -23.1660 q^{97} +(33.2915 - 53.6108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 12 q^{4} + 28 q^{6} + 20 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 12 * q^4 + 28 * q^6 + 20 * q^9	\( 8 q + 2 q^{3} + 12 q^{4} + 28 q^{6} + 20 q^{9} - 28 q^{10} + 22 q^{12} - 72 q^{13} + 56 q^{15} - 36 q^{16} - 56 q^{18} - 12 q^{19} - 112 q^{22} + 126 q^{24} + 12 q^{25} + 20 q^{27} + 28 q^{30} - 136 q^{31} - 28 q^{33} + 232 q^{36} - 16 q^{37} - 4 q^{39} - 84 q^{40} - 320 q^{43} + 140 q^{45} + 168 q^{46} + 76 q^{48} + 84 q^{51} - 164 q^{52} + 154 q^{54} + 112 q^{55} + 128 q^{57} - 112 q^{58} - 140 q^{60} + 156 q^{61} + 8 q^{64} + 28 q^{66} + 24 q^{67} + 336 q^{69} + 32 q^{73} - 146 q^{75} - 632 q^{76} - 392 q^{78} - 128 q^{79} + 68 q^{81} - 392 q^{82} + 336 q^{85} - 28 q^{87} - 168 q^{88} - 224 q^{90} + 96 q^{93} + 336 q^{94} + 98 q^{96} - 16 q^{97} + 224 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 12 * q^4 + 28 * q^6 + 20 * q^9 - 28 * q^10 + 22 * q^12 - 72 * q^13 + 56 * q^15 - 36 * q^16 - 56 * q^18 - 12 * q^19 - 112 * q^22 + 126 * q^24 + 12 * q^25 + 20 * q^27 + 28 * q^30 - 136 * q^31 - 28 * q^33 + 232 * q^36 - 16 * q^37 - 4 * q^39 - 84 * q^40 - 320 * q^43 + 140 * q^45 + 168 * q^46 + 76 * q^48 + 84 * q^51 - 164 * q^52 + 154 * q^54 + 112 * q^55 + 128 * q^57 - 112 * q^58 - 140 * q^60 + 156 * q^61 + 8 * q^64 + 28 * q^66 + 24 * q^67 + 336 * q^69 + 32 * q^73 - 146 * q^75 - 632 * q^76 - 392 * q^78 - 128 * q^79 + 68 * q^81 - 392 * q^82 + 336 * q^85 - 28 * q^87 - 168 * q^88 - 224 * q^90 + 96 * q^93 + 336 * q^94 + 98 * q^96 - 16 * q^97 + 224 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more