LMFDB - Embedded newform 147.3.h.c.116.1

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			116.1
Root			$-0.279898 - 3.02113i$ of defining polynomial
Character	$\chi$	$=$	147.116
Dual form			147.3.h.c.128.1

$q$-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 $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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	−0.518337	+	0.855177i	$0.673449\pi$
$2$	−3.03622	+	1.75296i	−1.51811	+	0.876481i	−0.999773	+	0.0213043i	$0.993218\pi$
$3$	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	$-0.706302\pi$
$5$	−1.07558	+	0.620984i	−0.215115	+	0.124197i	0.388571	+	0.921419i	$0.372969\pi$
$6$	−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	0.749944	−	0.661501i	$-0.230080\pi$
$11$	6.07244	+	3.50592i	0.552040	+	0.318720i	−0.197904	+	0.980221i	$0.563414\pi$
$12$	17.3043	−	17.8690i	1.44203	−	1.48909i
$13$	11.6458			0.895827			0.447914	−	0.894077i	$-0.352167\pi$
$13$	11.6458			0.895827			0.447914	+	0.894077i	$0.352167\pi$
$14$		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	$-0.290816\pi$
$17$	3.92129	+	2.26395i	0.230664	+	0.133174i	−0.380214	+	0.924898i	$0.624150\pi$
$18$	−31.5371	+	1.01293i	−1.75206	+	0.0562740i
$19$	8.11438	+	14.0545i	0.427073	+	0.739711i	0.996611	−	0.0822530i	$-0.0262116\pi$
$19$	8.11438	+	14.0545i	0.427073	+	0.739711i	−0.569539	+	0.821964i	$0.692878\pi$
$20$			10.2978i			0.514889i
$21$		0			0
$22$	−24.5830			−1.11741
$23$	−22.1386	+	12.7817i	−0.962548	+	0.555727i	−0.896956	−	0.442119i	$-0.854227\pi$
$23$	−22.1386	+	12.7817i	−0.962548	+	0.555727i	−0.0655916	+	0.997847i	$0.520893\pi$
$24$	−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	$0.0523495\pi$
$29$			9.49579i			0.327441i	−0.986507	+	0.163720i	$0.947650\pi$
$30$	9.08729	−	9.38385i	0.302910	−	0.312795i
$31$	14.3542	−	24.8623i	0.463040	−	0.802009i	−0.536070	−	0.844173i	$-0.680092\pi$
$31$	14.3542	−	24.8623i	0.463040	−	0.802009i	0.999111	+	0.0421640i	$0.0134252\pi$
$32$	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	0.998155	−	0.0607187i	$-0.0193393\pi$
$37$	16.5203	+	28.6139i	0.446493	+	0.773349i	−0.551661	+	0.834068i	$0.686006\pi$
$38$	−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	$-0.552431\pi$
$47$	28.5921	−	16.5076i	0.608342	−	0.351226i	0.772316	+	0.635238i	$0.219098\pi$
$48$	−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	0.618926	−	0.785450i	$-0.287568\pi$
$53$	13.1530	+	7.59387i	0.248169	+	0.143281i	−0.370756	+	0.928730i	$0.620902\pi$
$54$	−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	$-0.0470131\pi$
$59$	80.0173	+	46.1980i	1.35623	+	0.783017i	0.367112	+	0.930177i	$0.380346\pi$
$60$	−7.51572	+	29.9652i	−0.125262	+	0.499420i
$61$	−28.7601	−	49.8140i	−0.471478	−	0.816623i	0.527990	−	0.849251i	$-0.322946\pi$
$61$	−28.7601	−	49.8140i	−0.471478	−	0.816623i	−0.999468	+	0.0326275i	$0.989612\pi$
$62$			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	−0.917050	−	0.398771i	$-0.869437\pi$
$67$	−7.58301	+	13.1342i	−0.113179	+	0.196032i	0.803871	+	0.594803i	$0.202770\pi$
$68$	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	$-0.834475\pi$
$71$		−	70.5584i		−	0.993781i	0.867813	−	0.496890i	$-0.165525\pi$
$72$	−63.9061	+	119.383i	−0.887584	+	1.65809i
$73$	−38.3948	+	66.5017i	−0.525956	+	0.910982i	0.473587	+	0.880747i	$0.342959\pi$
$73$	−38.3948	+	66.5017i	−0.525956	+	0.910982i	−0.999543	+	0.0302350i	$0.990374\pi$
$74$	−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	−0.916047	−	0.401071i	$-0.868638\pi$
$79$	−63.6235	−	110.199i	−0.805361	−	1.39493i	0.110686	−	0.993855i	$-0.464695\pi$
$80$	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	$-0.412819\pi$
$89$	110.312	−	63.6887i	1.23946	−	0.715603i	0.968984	+	0.247124i	$0.0794854\pi$
$90$	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	$-0.461899\pi$
$97$	23.1660			0.238825			0.119412	+	0.992845i	$0.461899\pi$
$98$		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	$-0.566121\pi$
$101$	−116.833	−	67.4535i	−1.15676	−	0.667857i	−0.950526	+	0.310646i	$0.899455\pi$
$102$	−46.1927	−	11.5858i	−0.452870	−	0.113587i
$103$	−59.8745	−	103.706i	−0.581306	−	1.00685i	−0.995325	−	0.0965831i	$-0.969209\pi$
$103$	−59.8745	−	103.706i	−0.581306	−	1.00685i	0.414019	−	0.910268i	$-0.364125\pi$
$104$			175.218i			1.68479i
$105$		0			0
$106$	−53.2470			−0.502331
$107$	−67.4239	+	38.9272i	−0.630130	+	0.363806i	−0.780802	−	0.624778i	$-0.785189\pi$
$107$	−67.4239	+	38.9272i	−0.630130	+	0.363806i	0.150673	+	0.988584i	$0.451856\pi$
$108$	213.202	−	68.2853i	1.97409	−	0.632272i
$109$	18.2693	−	31.6433i	0.167608	−	0.290306i	−0.769970	−	0.638080i	$-0.779729\pi$
$109$	18.2693	−	31.6433i	0.167608	−	0.290306i	0.937578	+	0.347774i	$0.113062\pi$
$110$	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	$0.0306949\pi$
$113$			21.7596i			0.192563i	−0.995354	+	0.0962815i	$0.969305\pi$
$114$	−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	$-0.912990\pi$
$131$	−158.578	+	91.5550i	−1.21052	+	0.698893i	−0.247646	+	0.968850i	$0.579657\pi$
$132$	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	0.392006	−	0.919962i	$-0.371781\pi$
$137$	−28.5921	−	16.5076i	−0.208701	−	0.120494i	−0.600708	+	0.799469i	$0.705114\pi$
$138$	187.044	−	193.148i	1.35539	−	1.39962i
$139$	−64.6418			−0.465049			−0.232525	−	0.972591i	$-0.574699\pi$
$139$	−64.6418			−0.465049			−0.232525	+	0.972591i	$0.574699\pi$
$140$		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	0.191815	−	0.981431i	$-0.438563\pi$
$149$	169.512	−	97.8680i	1.13767	−	0.656832i	0.945852	+	0.324599i	$0.105229\pi$
$150$	60.0221	−	239.308i	0.400147	−	1.59539i
$151$	−51.1255	+	88.5519i	−0.338579	+	0.586437i	−0.984166	−	0.177251i	$-0.943280\pi$
$151$	−51.1255	+	88.5519i	−0.338579	+	0.586437i	0.645586	+	0.763687i	$0.276613\pi$
$152$	−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	$-0.725099\pi$
$157$	52.3614	−	90.6926i	0.333512	−	0.577660i	0.983198	+	0.182543i	$0.0584328\pi$
$158$	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	0.954094	−	0.299506i	$-0.0968220\pi$
$163$	35.4797	+	61.4527i	0.217667	+	0.377011i	−0.736427	+	0.676517i	$0.763489\pi$
$164$	−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	$-0.768161\pi$
$173$	−93.9323	+	54.2318i	−0.542961	+	0.313479i	0.203317	+	0.979113i	$0.434828\pi$
$174$	−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	0.0622383	−	0.998061i	$-0.480176\pi$
$179$	−138.007	−	79.6784i	−0.770989	−	0.445131i	−0.833227	+	0.552931i	$0.813509\pi$
$180$	−43.7395	+	81.7096i	−0.242997	+	0.453942i
$181$	233.889			1.29220			0.646102	−	0.763251i	$-0.276398\pi$
$181$	233.889			1.29220			0.646102	+	0.763251i	$0.276398\pi$
$182$		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	−0.981559	−	0.191158i	$-0.938776\pi$
$191$	−249.597	+	144.105i	−1.30679	+	0.754476i	−0.325232	+	0.945634i	$0.605442\pi$
$192$	141.488	+	35.4873i	0.736917	+	0.184830i
$193$	−38.5608	+	66.7892i	−0.199797	+	0.346058i	−0.948462	−	0.316890i	$-0.897362\pi$
$193$	−38.5608	+	66.7892i	−0.199797	+	0.346058i	0.748666	+	0.662948i	$0.230695\pi$
$194$	−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	$-0.887446\pi$
$197$		−	136.433i		−	0.692554i	0.938132	−	0.346277i	$-0.112554\pi$
$198$	−195.058	−	104.416i	−0.985142	−	0.527351i
$199$	43.2915	−	74.9831i	0.217545	−	0.376799i	−0.736512	−	0.676425i	$-0.763528\pi$
$199$	43.2915	−	74.9831i	0.217545	−	0.376799i	0.954057	+	0.299625i	$0.0968617\pi$
$200$	−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	$-0.628378\pi$
$223$	−175.041			−0.784935			−0.392468	+	0.919766i	$0.628378\pi$
$224$		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	$-0.461250\pi$
$227$	−153.784	−	88.7870i	−0.677461	−	0.391132i	−0.798898	+	0.601467i	$0.794583\pi$
$228$	391.554	+	98.2076i	1.71734	+	0.430735i
$229$	20.4059	+	35.3440i	0.0891087	+	0.154341i	0.907135	−	0.420841i	$-0.138265\pi$
$229$	20.4059	+	35.3440i	0.0891087	+	0.154341i	−0.818026	+	0.575181i	$0.804931\pi$
$230$			111.310i			0.483955i
$231$		0			0
$232$	−142.871			−0.615821
$233$	335.754	−	193.848i	1.44101	−	0.831965i	0.443088	−	0.896478i	$-0.353883\pi$
$233$	335.754	−	193.848i	1.44101	−	0.831965i	0.997917	+	0.0645131i	$0.0205494\pi$
$234$	−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	$-0.966962\pi$
$239$		−	49.5229i		−	0.207209i	0.994619	−	0.103604i	$-0.0330376\pi$
$240$	52.4153	+	50.7588i	0.218397	+	0.211495i
$241$	162.624	−	281.672i	0.674786	−	1.16876i	−0.301745	−	0.953389i	$-0.597569\pi$
$241$	162.624	−	281.672i	0.674786	−	1.16876i	0.976531	−	0.215376i	$-0.0690976\pi$
$242$	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	$-0.571638\pi$
$257$	130.926	−	75.5904i	0.509442	−	0.294126i	0.732604	+	0.680655i	$0.238305\pi$
$258$	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	0.299699	−	0.954034i	$-0.403114\pi$
$263$	−99.0641	−	57.1947i	−0.376670	−	0.217470i	−0.676368	+	0.736564i	$0.736447\pi$
$264$	−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	$-0.330516\pi$
$269$	4.12375	+	2.38085i	0.0153299	+	0.00885074i	−0.492315	+	0.870417i	$0.663849\pi$
$270$	111.962	−	35.8598i	0.414675	−	0.132814i
$271$	−259.350	−	449.208i	−0.957012	−	1.65759i	−0.729695	−	0.683773i	$-0.760338\pi$
$271$	−259.350	−	449.208i	−0.957012	−	1.65759i	−0.227318	−	0.973821i	$-0.572996\pi$
$272$		−	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	−0.735805	−	0.677194i	$-0.763196\pi$
$277$	60.5425	−	104.863i	0.218565	−	0.378566i	0.954369	+	0.298628i	$0.0965291\pi$
$278$	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	$0.258000\pi$
$281$			407.255i			1.44931i	−0.689113	+	0.724654i	$0.742000\pi$
$282$	−241.567	+	249.451i	−0.856622	+	0.884577i
$283$	−199.317	+	345.227i	−0.704300	+	1.21988i	0.262643	+	0.964893i	$0.415406\pi$
$283$	−199.317	+	345.227i	−0.704300	+	1.21988i	−0.966943	+	0.254991i	$0.917928\pi$
$284$	−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	$-0.544855\pi$
$307$	−86.2366			−0.280901			−0.140451	+	0.990088i	$0.544855\pi$
$308$		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	$-0.254869\pi$
$311$	131.442	+	75.8884i	0.422645	+	0.244014i	−0.273564	+	0.961854i	$0.588202\pi$
$312$	−127.881	+	509.862i	−0.409875	+	1.63417i
$313$	159.059	+	275.498i	0.508175	+	0.880185i	0.999955	+	0.00946567i	$0.00301306\pi$
$313$	159.059	+	275.498i	0.508175	+	0.880185i	−0.491780	+	0.870719i	$0.663654\pi$
$314$			367.150i			1.16927i
$315$		0			0
$316$	−1055.07			−3.33883
$317$	315.251	−	182.010i	0.994482	−	0.574164i	0.0878710	−	0.996132i	$-0.471994\pi$
$317$	315.251	−	182.010i	0.994482	−	0.574164i	0.906611	+	0.421967i	$0.138660\pi$
$318$	−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	0.725559	−	0.688160i	$-0.241582\pi$
$331$	−77.1843	−	133.687i	−0.233185	−	0.403889i	−0.958744	+	0.284272i	$0.908248\pi$
$332$	−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	0.955110	−	0.296252i	$-0.0957370\pi$
$347$	408.108	+	235.621i	1.17610	+	0.679023i	0.220993	+	0.975275i	$0.429070\pi$
$348$	169.680	+	164.318i	0.487587	+	0.472178i
$349$	364.516			1.04446			0.522230	−	0.852805i	$-0.325100\pi$
$349$	364.516			1.04446			0.522230	+	0.852805i	$0.325100\pi$
$350$		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	$-0.372360\pi$
$353$	−74.7744	−	43.1710i	−0.211825	−	0.122297i	−0.602159	+	0.798376i	$0.705693\pi$
$354$	−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	0.0211451	−	0.999776i	$-0.493269\pi$
$359$	322.220	−	186.034i	0.897549	−	0.518200i	0.876404	+	0.481576i	$0.159935\pi$
$360$	−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	$-0.904075\pi$
$367$	−80.8928	+	140.110i	−0.220416	+	0.381772i	0.734518	+	0.678589i	$0.237408\pi$
$368$	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	−0.999967	−	0.00814693i	$-0.997407\pi$
$373$	−189.125	−	327.575i	−0.507039	−	0.878217i	0.492928	−	0.870070i	$-0.335927\pi$
$374$	−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	$-0.713956\pi$
$383$	−98.1910	+	56.6906i	−0.256373	+	0.148017i	0.366306	+	0.930495i	$0.380622\pi$
$384$	−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	0.988099	+	0.153817i	$0.0491565\pi$
$389$	628.374	+	362.792i	1.61536	+	0.932628i	0.627259	+	0.778811i	$0.284177\pi$
$390$	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	$-0.204579\pi$
$397$	−47.1732	−	81.7064i	−0.118824	−	0.205809i	−0.919302	+	0.393553i	$0.871246\pi$
$398$			303.553i			0.762697i
$399$		0			0
$400$	459.369			1.14842
$401$	−586.875	+	338.833i	−1.46353	+	0.844969i	−0.999172	−	0.0406787i	$-0.987048\pi$
$401$	−586.875	+	338.833i	−1.46353	+	0.844969i	−0.464357	+	0.885648i	$0.653715\pi$
$402$	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	$-0.826576\pi$
$409$	8.68233	−	15.0382i	0.0212282	−	0.0367683i	0.876444	+	0.481503i	$0.159909\pi$
$410$	−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	0.117569	−	0.993065i	$-0.462490\pi$
$431$	−294.660	−	170.122i	−0.683666	−	0.394715i	−0.801235	+	0.598350i	$0.795823\pi$
$432$	112.102	−	516.721i	0.259495	−	1.19611i
$433$	−159.166			−0.367589			−0.183794	−	0.982965i	$-0.558838\pi$
$433$	−159.166			−0.367589			−0.183794	+	0.982965i	$0.558838\pi$
$434$		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	$-0.120069\pi$
$439$	64.0366	+	110.915i	0.145869	+	0.252653i	−0.783828	+	0.620978i	$0.786735\pi$
$440$		−	131.025i		−	0.297785i
$441$		0			0
$442$	−184.871			−0.418259
$443$	−170.901	+	98.6700i	−0.385782	+	0.222731i	−0.680331	−	0.732905i	$-0.738164\pi$
$443$	−170.901	+	98.6700i	−0.385782	+	0.222731i	0.294549	+	0.955636i	$0.404831\pi$
$444$	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	$0.0527377\pi$
$449$			148.101i			0.329847i	−0.986306	+	0.164923i	$0.947262\pi$
$450$	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	0.925105	−	0.379710i	$-0.123976\pi$
$457$	61.1072	+	105.841i	0.133714	+	0.231599i	−0.791392	+	0.611310i	$0.790643\pi$
$458$	−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	$-0.359550\pi$
$467$	664.853	−	383.853i	1.42367	−	0.821955i	0.996610	+	0.0822701i	$0.0262170\pi$
$468$	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	$-0.198470\pi$
$479$	341.089	+	196.928i	0.712085	+	0.411122i	−0.0997478	+	0.995013i	$0.531804\pi$
$480$	−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	0.405685	+	0.914013i	$0.367033\pi$
$487$	−286.705	+	496.587i	−0.588716	+	1.01969i	−0.994401	+	0.105673i	$0.966300\pi$
$488$	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	$-0.944354\pi$
$491$		−	170.796i		−	0.347853i	0.984759	−	0.173927i	$-0.0556455\pi$
$492$	−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	0.881643	+	0.471917i	$0.156438\pi$
$499$	423.907	+	734.229i	0.849513	+	1.47140i	−0.0321299	+	0.999484i	$0.510229\pi$
$500$	−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	$-0.827032\pi$
$509$	−425.606	+	245.724i	−0.836162	+	0.482758i	0.0197959	+	0.999804i	$0.493698\pi$
$510$	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	$-0.0188343\pi$
$521$	753.451	+	435.005i	1.44616	+	0.834942i	0.447912	+	0.894078i	$0.352168\pi$
$522$	−9.61859	−	299.469i	−0.0184264	−	0.573696i
$523$	399.354	+	691.701i	0.763582	+	1.32256i	0.940993	+	0.338426i	$0.109895\pi$
$523$	399.354	+	691.701i	0.763582	+	1.32256i	−0.177411	+	0.984137i	$0.556772\pi$
$524$			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	0.974845	+	0.222885i	$0.0715475\pi$
$541$	368.122	+	637.605i	0.680446	+	1.17857i	−0.294398	+	0.955683i	$0.595119\pi$
$542$	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	−0.413798	−	0.910369i	$-0.635798\pi$
$557$	−784.869	−	453.144i	−1.40910	−	0.813544i	−0.995301	+	0.0968243i	$0.969131\pi$
$558$	−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	$-0.466862\pi$
$563$	−397.173	−	229.308i	−0.705459	−	0.407297i	−0.809377	+	0.587289i	$0.800195\pi$
$564$	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	−0.870280	−	0.492557i	$-0.836062\pi$
$569$	−500.067	+	288.714i	−0.878853	+	0.507406i	−0.00857275	+	0.999963i	$0.502729\pi$
$570$	205.623	+	51.5733i	0.360742	+	0.0904795i
$571$	51.5608	−	89.3059i	0.0902991	−	0.156403i	−0.817338	−	0.576159i	$-0.804551\pi$
$571$	51.5608	−	89.3059i	0.0902991	−	0.156403i	0.907637	+	0.419756i	$0.137884\pi$
$572$	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	0.408419	+	0.912795i	$0.366080\pi$
$577$	−338.292	+	585.938i	−0.586294	+	1.01549i	−0.994713	+	0.102696i	$0.967253\pi$
$578$	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	$-0.377433\pi$
$593$	810.055	−	467.686i	1.36603	−	0.788677i	0.990418	+	0.138100i	$0.0440995\pi$
$594$	−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	0.445726	−	0.895169i	$-0.352946\pi$
$599$	−63.8836	−	36.8832i	−0.106650	−	0.0615747i	−0.552376	+	0.833595i	$0.686279\pi$
$600$	−760.609	−	736.571i	−1.26768	−	1.22762i
$601$	934.280			1.55454			0.777271	−	0.629166i	$-0.216603\pi$
$601$	934.280			1.55454			0.777271	+	0.629166i	$0.216603\pi$
$602$		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	$-0.214464\pi$
$607$	−90.8039	−	157.277i	−0.149595	−	0.259105i	−0.931078	+	0.364821i	$0.881130\pi$
$608$			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	−0.223434	−	0.974719i	$-0.571727\pi$
$613$	448.970	−	777.639i	0.732414	−	1.26858i	0.955849	−	0.293860i	$-0.0949398\pi$
$614$	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	$0.396780\pi$
$617$			1169.69i			1.89576i	−0.318622	+	0.947882i	$0.603220\pi$
$618$	904.778	+	876.184i	1.46404	+	1.41777i
$619$	604.483	−	1047.00i	0.976548	−	1.69143i	0.301817	−	0.953366i	$-0.402407\pi$
$619$	604.483	−	1047.00i	0.976548	−	1.69143i	0.674730	−	0.738064i	$-0.264260\pi$
$620$	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	0.0984103	−	0.995146i	$-0.468624\pi$
$641$	−457.806	−	264.315i	−0.714206	−	0.412347i	−0.812616	+	0.582799i	$0.801958\pi$
$642$	569.648	−	588.238i	0.887302	−	0.916259i
$643$	−33.4392			−0.0520050			−0.0260025	−	0.999662i	$-0.508278\pi$
$643$	−33.4392			−0.0520050			−0.0260025	+	0.999662i	$0.508278\pi$
$644$		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	$-0.541224\pi$
$647$	−680.962	−	393.154i	−1.05249	−	0.607657i	−0.923346	+	0.383969i	$0.874557\pi$
$648$	−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	−0.733519	−	0.679669i	$-0.762123\pi$
$653$	−334.119	+	192.904i	−0.511668	+	0.295412i	0.221851	+	0.975081i	$0.428790\pi$
$654$	−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	$-0.976490\pi$
$659$		−	97.2583i		−	0.147585i	0.997274	−	0.0737924i	$-0.0235102\pi$
$660$	−150.695	+	155.612i	−0.228325	+	0.235776i
$661$	−480.752	+	832.687i	−0.727311	+	1.25974i	0.230705	+	0.973024i	$0.425897\pi$
$661$	−480.752	+	832.687i	−0.727311	+	1.25974i	−0.958016	+	0.286715i	$0.907437\pi$
$662$	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	−0.611258	+	0.791432i	$0.709336\pi$
$677$	−1084.75	+	626.279i	−1.60229	+	0.925080i	−0.991029	+	0.133649i	$0.957331\pi$
$678$	−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	0.267910	−	0.963444i	$-0.413667\pi$
$683$	−295.398	−	170.548i	−0.432501	−	0.249705i	−0.700412	+	0.713739i	$0.747000\pi$
$684$	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	−0.996855	−	0.0792411i	$-0.974750\pi$
$691$	−391.833	−	678.675i	−0.567053	−	0.982164i	0.429803	−	0.902923i	$-0.358583\pi$
$692$			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	$-0.601187\pi$
$701$		−	1331.76i		−	1.89979i	0.312562	−	0.949897i	$-0.398813\pi$
$702$	−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	−0.998971	−	0.0453517i	$-0.985559\pi$
$709$	−381.982	−	661.612i	−0.538761	−	0.933162i	0.460210	−	0.887810i	$-0.347774\pi$
$710$	−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	$-0.523861\pi$
$719$	540.153	−	311.858i	0.751256	−	0.433738i	0.826148	+	0.563454i	$0.190528\pi$
$720$	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	$-0.654536\pi$
$727$	−678.494			−0.933279			−0.466640	+	0.884448i	$0.654536\pi$
$728$		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	$-0.253498\pi$
$733$	−197.483	−	342.051i	−0.269417	−	0.466645i	−0.968712	+	0.248189i	$0.920164\pi$
$734$		−	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	−0.947782	−	0.318919i	$-0.896680\pi$
$739$	−146.099	+	253.051i	−0.197699	+	0.342424i	0.750083	+	0.661344i	$0.230013\pi$
$740$	−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	$0.0830776\pi$
$743$			383.452i			0.516086i	−0.966133	+	0.258043i	$0.916922\pi$
$744$	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	0.999137	−	0.0415293i	$-0.0132230\pi$
$751$	348.166	+	603.041i	0.463603	+	0.802984i	−0.535534	+	0.844514i	$0.679890\pi$
$752$	−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	$-0.685439\pi$
$761$	−77.6876	+	44.8529i	−0.102086	+	0.0589395i	0.448088	+	0.893990i	$0.352105\pi$
$762$	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	$-0.705718\pi$
$769$	−926.219			−1.20445			−0.602223	+	0.798328i	$0.705718\pi$
$770$		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	$-0.421792\pi$
$773$	−367.303	−	212.063i	−0.475166	−	0.274337i	−0.718400	+	0.695631i	$0.755125\pi$
$774$	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	$-0.864910\pi$
$787$	−77.9444	+	135.004i	−0.0990399	+	0.171542i	0.812248	+	0.583313i	$0.198244\pi$
$788$	−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	0.382077	−	0.924130i	$-0.375209\pi$
$809$	−183.808	−	106.122i	−0.227204	−	0.131176i	−0.609282	+	0.792954i	$0.708542\pi$
$810$	351.967	−	22.6329i	0.434527	−	0.0279418i
$811$	−1058.66			−1.30538			−0.652690	−	0.757625i	$-0.726359\pi$
$811$	−1058.66			−1.30538			−0.652690	+	0.757625i	$0.726359\pi$
$812$		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	−0.865171	−	0.501478i	$-0.832790\pi$
$821$	−708.903	+	409.286i	−0.863463	+	0.498521i	0.00170721	+	0.999999i	$0.499457\pi$
$822$	336.814	+	84.4781i	0.409750	+	0.102771i
$823$	−103.425	+	179.137i	−0.125668	+	0.217664i	−0.921994	−	0.387204i	$-0.873441\pi$
$823$	−103.425	+	179.137i	−0.125668	+	0.217664i	0.796326	+	0.604868i	$0.206774\pi$
$824$	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	$0.0854376\pi$
$827$			438.639i			0.530398i	−0.964194	+	0.265199i	$0.914562\pi$
$828$	−900.291	+	1681.83i	−1.08731	+	2.03119i
$829$	327.402	−	567.077i	0.394936	−	0.684049i	−0.598157	−	0.801379i	$-0.704100\pi$
$829$	327.402	−	567.077i	0.394936	−	0.684049i	0.993093	+	0.117330i	$0.0374334\pi$
$830$	−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	$-0.326626\pi$
$853$	883.941			1.03627			0.518137	+	0.855298i	$0.326626\pi$
$854$		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	$-0.228073\pi$
$857$	481.961	+	278.260i	0.562382	+	0.324691i	−0.191719	+	0.981450i	$0.561406\pi$
$858$	−833.059	−	208.944i	−0.970931	−	0.243524i
$859$	−321.539	−	556.922i	−0.374318	−	0.648338i	0.615907	−	0.787819i	$-0.288790\pi$
$859$	−321.539	−	556.922i	−0.374318	−	0.648338i	−0.990225	+	0.139481i	$0.955457\pi$
$860$		−	248.439i		−	0.288883i
$861$		0			0
$862$	1192.87			1.38384
$863$	177.442	−	102.446i	0.205611	−	0.118709i	−0.393659	−	0.919256i	$-0.628791\pi$
$863$	177.442	−	102.446i	0.205611	−	0.118709i	0.599270	+	0.800547i	$0.295458\pi$
$864$	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	0.919029	−	0.394190i	$-0.128975\pi$
$877$	103.605	+	179.450i	0.118136	+	0.204617i	−0.800893	+	0.598807i	$0.795641\pi$
$878$	−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	$-0.693514\pi$
$887$	−129.426	+	74.7243i	−0.145915	+	0.0842439i	0.425265	+	0.905069i	$0.360181\pi$
$888$	−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	−0.981975	−	0.189013i	$-0.939471\pi$
$907$	−296.859	+	514.174i	−0.327297	+	0.566896i	0.654677	+	0.755909i	$0.272805\pi$
$908$	−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	$0.213783\pi$
$911$			1133.75i			1.24451i	−0.782815	+	0.622254i	$0.786217\pi$
$912$	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	0.989977	−	0.141228i	$-0.0451051\pi$
$919$	342.494	+	593.217i	0.372681	+	0.645503i	−0.617296	+	0.786731i	$0.711772\pi$
$920$	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	$-0.633660\pi$
$929$	166.551	−	96.1584i	0.179280	−	0.103507i	0.586954	+	0.809620i	$0.300327\pi$
$930$	−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	$-0.262914\pi$
$937$	1270.28			1.35569			0.677844	+	0.735206i	$0.262914\pi$
$938$		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	$-0.306757\pi$
$941$	135.923	+	78.4754i	0.144446	+	0.0833957i	−0.426035	+	0.904706i	$0.640090\pi$
$942$	−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	−0.0404090	−	0.999183i	$-0.512866\pi$
$947$	762.055	−	439.973i	0.804704	−	0.464596i	0.845114	+	0.534587i	$0.179533\pi$
$948$	−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	$0.0954955\pi$
$953$			563.276i			0.591056i	−0.955334	+	0.295528i	$0.904505\pi$
$954$	−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	$-0.420859\pi$
$971$	1173.46	−	677.498i	1.20851	−	0.697732i	0.962433	+	0.271519i	$0.0875258\pi$
$972$	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	0.702598	−	0.711587i	$-0.252023\pi$
$977$	427.579	+	246.863i	0.437645	+	0.252674i	−0.264953	+	0.964261i	$0.585357\pi$
$978$	−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	$-0.619300\pi$
$983$	−1331.99	−	769.026i	−1.35503	−	0.782325i	−0.988949	+	0.148259i	$0.952633\pi$
$984$	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	0.176403	+	0.984318i	$0.443554\pi$
$991$	−757.365	+	1311.79i	−0.764243	+	1.32371i	−0.940646	+	0.339389i	$0.889780\pi$
$992$	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	0.110481	−	0.993878i	$-0.464761\pi$
$997$	913.216	−	1581.74i	0.915964	−	1.58650i	0.805484	−	0.592618i	$-0.201906\pi$
$998$	−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.c.116.1		8
3.2	odd	2	inner	147.3.h.c.116.4		8
7.2	even	3	inner	147.3.h.c.128.4		8
7.3	odd	6		21.3.b.a.8.1	✓	4
7.4	even	3		147.3.b.f.50.1		4
7.5	odd	6		147.3.h.e.128.4		8
7.6	odd	2		147.3.h.e.116.1		8
21.2	odd	6	inner	147.3.h.c.128.1		8
21.5	even	6		147.3.h.e.128.1		8
21.11	odd	6		147.3.b.f.50.4		4
21.17	even	6		21.3.b.a.8.4	yes	4
21.20	even	2		147.3.h.e.116.4		8
28.3	even	6		336.3.d.c.113.1		4
35.3	even	12		525.3.f.a.449.2		8
35.17	even	12		525.3.f.a.449.7		8
35.24	odd	6		525.3.c.a.176.4		4
56.3	even	6		1344.3.d.b.449.4		4
56.45	odd	6		1344.3.d.f.449.1		4
63.31	odd	6		567.3.r.c.512.4		8
63.38	even	6		567.3.r.c.134.4		8
63.52	odd	6		567.3.r.c.134.1		8
63.59	even	6		567.3.r.c.512.1		8
84.59	odd	6		336.3.d.c.113.2		4
105.17	odd	12		525.3.f.a.449.1		8
105.38	odd	12		525.3.f.a.449.8		8
105.59	even	6		525.3.c.a.176.1		4
168.59	odd	6		1344.3.d.b.449.3		4
168.101	even	6		1344.3.d.f.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.b.a.8.1	✓	4	7.3	odd	6
21.3.b.a.8.4	yes	4	21.17	even	6
147.3.b.f.50.1		4	7.4	even	3
147.3.b.f.50.4		4	21.11	odd	6
147.3.h.c.116.1		8	1.1	even	1	trivial
147.3.h.c.116.4		8	3.2	odd	2	inner
147.3.h.c.128.1		8	21.2	odd	6	inner
147.3.h.c.128.4		8	7.2	even	3	inner
147.3.h.e.116.1		8	7.6	odd	2
147.3.h.e.116.4		8	21.20	even	2
147.3.h.e.128.1		8	21.5	even	6
147.3.h.e.128.4		8	7.5	odd	6
336.3.d.c.113.1		4	28.3	even	6
336.3.d.c.113.2		4	84.59	odd	6
525.3.c.a.176.1		4	105.59	even	6
525.3.c.a.176.4		4	35.24	odd	6
525.3.f.a.449.1		8	105.17	odd	12
525.3.f.a.449.2		8	35.3	even	12
525.3.f.a.449.7		8	35.17	even	12
525.3.f.a.449.8		8	105.38	odd	12
567.3.r.c.134.1		8	63.52	odd	6
567.3.r.c.134.4		8	63.38	even	6
567.3.r.c.512.1		8	63.59	even	6
567.3.r.c.512.4		8	63.31	odd	6
1344.3.d.b.449.3		4	168.59	odd	6
1344.3.d.b.449.4		4	56.3	even	6
1344.3.d.f.449.1		4	56.45	odd	6
1344.3.d.f.449.2		4	168.101	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