LMFDB - Embedded newform 147.3.h.e.116.4

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			116.4
Root			$2.10277 - 0.136187i$ of defining polynomial
Character	$\chi$	$=$	147.116
Dual form			147.3.h.e.128.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.03622 - 1.75296i) q^{2} +(2.08699 + 2.15510i) q^{3} +(4.14575 - 7.18065i) q^{4} +(-1.07558 + 0.620984i) q^{5} +(10.1144 + 2.88494i) q^{6} -15.0457i q^{8} +(-0.288920 + 8.99536i) q^{9} +O(q^{10})$	\(q+(3.03622 - 1.75296i) q^{2} +(2.08699 + 2.15510i) q^{3} +(4.14575 - 7.18065i) q^{4} +(-1.07558 + 0.620984i) q^{5} +(10.1144 + 2.88494i) q^{6} -15.0457i q^{8} +(-0.288920 + 8.99536i) q^{9} +(-2.17712 + 3.77089i) q^{10} +(-6.07244 - 3.50592i) q^{11} +(24.1272 - 6.05146i) q^{12} -11.6458 q^{13} +(-3.58301 - 1.02199i) q^{15} +(-9.79150 - 16.9594i) q^{16} +(3.92129 + 2.26395i) q^{17} +(14.8913 + 27.8184i) q^{18} +(-8.11438 - 14.0545i) q^{19} +10.2978i q^{20} -24.5830 q^{22} +(22.1386 - 12.7817i) q^{23} +(32.4250 - 31.4002i) q^{24} +(-11.7288 + 20.3148i) q^{25} +(-35.3591 + 20.4146i) q^{26} +(-19.9889 + 18.1506i) q^{27} -9.49579i q^{29} +(-12.6703 + 3.17790i) q^{30} +(-14.3542 + 24.8623i) q^{31} +(-7.33853 - 4.23690i) q^{32} +(-5.11752 - 20.4036i) q^{33} +15.8745 q^{34} +(63.3948 + 39.3672i) q^{36} +(16.5203 + 28.6139i) q^{37} +(-49.2741 - 28.4484i) q^{38} +(-24.3046 - 25.0978i) q^{39} +(9.34313 + 16.1828i) q^{40} -67.1946i q^{41} -24.1255 q^{43} +(-50.3496 + 29.0694i) q^{44} +(-5.27522 - 9.85462i) q^{45} +(44.8118 - 77.6162i) q^{46} +(28.5921 - 16.5076i) q^{47} +(16.1144 - 56.4958i) q^{48} +82.2403i q^{50} +(3.30464 + 13.1756i) q^{51} +(-48.2804 + 83.6241i) q^{52} +(-13.1530 - 7.59387i) q^{53} +(-28.8733 + 90.1490i) q^{54} +8.70850 q^{55} +(13.3542 - 46.8190i) q^{57} +(-16.6458 - 28.8313i) q^{58} +(80.0173 + 46.1980i) q^{59} +(-22.1928 + 21.4914i) q^{60} +(28.7601 + 49.8140i) q^{61} +100.650i q^{62} +48.6235 q^{64} +(12.5259 - 7.23183i) q^{65} +(-51.3046 - 52.9789i) q^{66} +(-7.58301 + 13.1342i) q^{67} +(32.5133 - 18.7716i) q^{68} +(73.7490 + 21.0355i) q^{69} +70.5584i q^{71} +(135.341 + 4.34700i) q^{72} +(38.3948 - 66.5017i) q^{73} +(100.318 + 57.9188i) q^{74} +(-68.2583 + 17.1202i) q^{75} -134.561 q^{76} +(-117.790 - 33.5973i) q^{78} +(-63.6235 - 110.199i) q^{79} +(21.0630 + 12.1607i) q^{80} +(-80.8331 - 5.19788i) q^{81} +(-117.790 - 204.017i) q^{82} -74.2844i q^{83} -5.62352 q^{85} +(-73.2503 + 42.2911i) q^{86} +(20.4644 - 19.8176i) q^{87} +(-52.7490 + 91.3640i) q^{88} +(110.312 - 63.6887i) q^{89} +(-33.2915 - 20.6735i) q^{90} -211.959i q^{92} +(-83.5380 + 20.9526i) q^{93} +(57.8745 - 100.242i) q^{94} +(17.4553 + 10.0778i) q^{95} +(-6.18451 - 24.6576i) 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	$-0.326551\pi$
$2$	3.03622	−	1.75296i	1.51811	−	0.876481i	0.999773	−	0.0213043i	$-0.00678187\pi$
$3$	2.08699	+	2.15510i	0.695664	+	0.718367i
$3$	2.08699	+	2.15510i	0.695664	+	0.718367i
$4$	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
$9$	−0.288920	+	8.99536i	−0.0321022	+	0.999485i
$10$	−2.17712	+	3.77089i	−0.217712	+	0.377089i
$11$	−6.07244	−	3.50592i	−0.552040	−	0.318720i	0.197904	−	0.980221i	$-0.436586\pi$
$11$	−6.07244	−	3.50592i	−0.552040	−	0.318720i	−0.749944	+	0.661501i	$0.769920\pi$
$12$	24.1272	−	6.05146i	2.01060	−	0.504288i
$13$	−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	$-0.290816\pi$
$17$	3.92129	+	2.26395i	0.230664	+	0.133174i	−0.380214	+	0.924898i	$0.624150\pi$
$18$	14.8913	+	27.8184i	0.827295	+	1.54546i
$19$	−8.11438	−	14.0545i	−0.427073	−	0.739711i	0.569539	−	0.821964i	$-0.307122\pi$
$19$	−8.11438	−	14.0545i	−0.427073	−	0.739711i	−0.996611	+	0.0822530i	$0.973788\pi$
$20$			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	$-0.479107\pi$
$23$	22.1386	−	12.7817i	0.962548	−	0.555727i	0.896956	+	0.442119i	$0.145773\pi$
$24$	32.4250	−	31.4002i	1.35104	−	1.30834i
$25$	−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	$-0.0523495\pi$
$30$	−12.6703	+	3.17790i	−0.422343	+	0.105930i
$31$	−14.3542	+	24.8623i	−0.463040	+	0.802009i	−0.999111	−	0.0421640i	$-0.986575\pi$
$31$	−14.3542	+	24.8623i	−0.463040	+	0.802009i	0.536070	+	0.844173i	$0.319908\pi$
$32$	−7.33853	−	4.23690i	−0.229329	−	0.132403i
$33$	−5.11752	−	20.4036i	−0.155076	−	0.618290i
$34$	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
$39$	−24.3046	−	25.0978i	−0.623195	−	0.643533i
$40$	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
$45$	−5.27522	−	9.85462i	−0.117227	−	0.218991i
$46$	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
$51$	3.30464	+	13.1756i	0.0647969	+	0.258346i
$52$	−48.2804	+	83.6241i	−0.928469	+	1.60816i
$53$	−13.1530	−	7.59387i	−0.248169	−	0.143281i	0.370756	−	0.928730i	$-0.379098\pi$
$53$	−13.1530	−	7.59387i	−0.248169	−	0.143281i	−0.618926	+	0.785450i	$0.712432\pi$
$54$	−28.8733	+	90.1490i	−0.534691	+	1.66943i
$55$	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	$0.380346\pi$
$60$	−22.1928	+	21.4914i	−0.369880	+	0.358190i
$61$	28.7601	+	49.8140i	0.471478	+	0.816623i	0.999468	−	0.0326275i	$-0.0103875\pi$
$61$	28.7601	+	49.8140i	0.471478	+	0.816623i	−0.527990	+	0.849251i	$0.677054\pi$
$62$			100.650i			1.62338i
$63$		0			0
$64$	48.6235			0.759743
$65$	12.5259	−	7.23183i	0.192706	−	0.111259i
$66$	−51.3046	−	52.9789i	−0.777342	−	0.802710i
$67$	−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	$0.165525\pi$
$71$			70.5584i			0.993781i	−0.867813	+	0.496890i	$0.834475\pi$
$72$	135.341	+	4.34700i	1.87974	+	0.0603750i
$73$	38.3948	−	66.5017i	0.525956	−	0.910982i	−0.473587	−	0.880747i	$-0.657041\pi$
$73$	38.3948	−	66.5017i	0.525956	−	0.910982i	0.999543	−	0.0302350i	$-0.00962558\pi$
$74$	100.318	+	57.9188i	1.35565	+	0.782686i
$75$	−68.2583	+	17.1202i	−0.910110	+	0.228269i
$76$	−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
$81$	−80.8331	−	5.19788i	−0.997939	−	0.0641714i
$82$	−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
$87$	20.4644	−	19.8176i	0.235223	−	0.227789i
$88$	−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
$93$	−83.5380	+	20.9526i	−0.898258	+	0.225296i
$94$	57.8745	−	100.242i	0.615686	−	1.06640i
$95$	17.4553	+	10.0778i	0.183740	+	0.106082i
$96$	−6.18451	−	24.6576i	−0.0644219	−	0.256850i
$97$	−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	$-0.566121\pi$
$101$	−116.833	−	67.4535i	−1.15676	−	0.667857i	−0.950526	+	0.310646i	$0.899455\pi$
$102$	33.1300	+	34.2112i	0.324804	+	0.335404i
$103$	59.8745	+	103.706i	0.581306	+	1.00685i	0.995325	+	0.0965831i	$0.0307914\pi$
$103$	59.8745	+	103.706i	0.581306	+	1.00685i	−0.414019	+	0.910268i	$0.635875\pi$
$104$			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	$-0.548144\pi$
$107$	67.4239	−	38.9272i	0.630130	−	0.363806i	0.780802	+	0.624778i	$0.214811\pi$
$108$	47.4642	+	218.781i	0.439484	+	2.02575i
$109$	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	$-0.969305\pi$
$113$		−	21.7596i		−	0.192563i	0.995354	−	0.0962815i	$-0.0306949\pi$
$114$	−41.5255	−	165.562i	−0.364258	−	1.45230i
$115$	−15.8745	+	27.4955i	−0.138039	+	0.239091i
$116$	−68.1859	−	39.3672i	−0.587810	−	0.339372i
$117$	3.36469	−	104.758i	0.0287581	−	0.895365i
$118$	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
$123$	144.811	−	140.235i	1.17733	−	1.14012i
$124$	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
$129$	−50.3497	−	51.9929i	−0.390308	−	0.403046i
$130$	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
$135$	10.2283	−	31.9352i	0.0757655	−	0.236557i
$136$	34.0627	−	58.9984i	0.250461	−	0.433812i
$137$	28.5921	+	16.5076i	0.208701	+	0.120494i	0.600708	−	0.799469i	$-0.294886\pi$
$137$	28.5921	+	16.5076i	0.208701	+	0.120494i	−0.392006	+	0.919962i	$0.628219\pi$
$138$	260.793	−	65.4107i	1.88980	−	0.473991i
$139$	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
$144$	155.385	−	83.1782i	1.07906	−	0.577626i
$145$	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	$-0.894771\pi$
$149$	−169.512	+	97.8680i	−1.13767	+	0.656832i	−0.191815	+	0.981431i	$0.561437\pi$
$150$	−177.236	+	171.635i	−1.18157	+	1.14423i
$151$	−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
$156$	−280.979	+	70.4738i	−1.80115	+	0.451755i
$157$	−52.3614	+	90.6926i	−0.333512	+	0.577660i	−0.983198	−	0.182543i	$-0.941567\pi$
$157$	−52.3614	+	90.6926i	−0.333512	+	0.577660i	0.649686	+	0.760203i	$0.274901\pi$
$158$	−386.350	−	223.059i	−2.44525	−	1.41177i
$159$	−11.0846	−	44.1943i	−0.0697144	−	0.277952i
$160$	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
$165$	18.1746	+	18.7677i	0.110149	+	0.113744i
$166$	−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
$171$	128.770	−	68.9311i	0.753040	−	0.403106i
$172$	−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
$177$	67.4342	+	268.860i	0.380984	+	1.51898i
$178$	223.288	−	386.745i	1.25442	−	2.17273i
$179$	138.007	+	79.6784i	0.770989	+	0.445131i	0.833227	−	0.552931i	$-0.186491\pi$
$179$	138.007	+	79.6784i	0.770989	+	0.445131i	−0.0622383	+	0.998061i	$0.519824\pi$
$180$	−92.6323	−	2.97524i	−0.514624	−	0.0165291i
$181$	−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
$186$	−216.910	+	210.055i	−1.16619	+	1.12933i
$187$	−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	$-0.394558\pi$
$191$	249.597	−	144.105i	1.30679	−	0.754476i	0.981559	+	0.191158i	$0.0612244\pi$
$192$	101.477	+	104.789i	0.528526	+	0.545774i
$193$	−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	$0.112554\pi$
$197$			136.433i			0.692554i	−0.938132	+	0.346277i	$0.887446\pi$
$198$	7.10253	−	221.133i	0.0358713	−	1.11683i
$199$	−43.2915	+	74.9831i	−0.217545	+	0.376799i	−0.954057	−	0.299625i	$-0.903138\pi$
$199$	−43.2915	+	74.9831i	−0.217545	+	0.376799i	0.736512	+	0.676425i	$0.236472\pi$
$200$	305.650	+	176.467i	1.52825	+	0.882336i
$201$	−44.1311	+	11.0687i	−0.219558	+	0.0550684i
$202$	−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
$207$	108.580	+	202.838i	0.524541	+	0.979892i
$208$	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
$213$	−152.061	+	147.255i	−0.713899	+	0.691338i
$214$	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
$219$	223.447	−	56.0440i	1.02031	−	0.255908i
$220$	36.1033	−	62.5327i	0.164106	−	0.284239i
$221$	−45.6663	−	26.3655i	−0.206635	−	0.119301i
$222$	84.5427	+	337.072i	0.380823	+	1.51834i
$223$	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	$-0.461250\pi$
$227$	−153.784	−	88.7870i	−0.677461	−	0.391132i	−0.798898	+	0.601467i	$0.794583\pi$
$228$	−280.827	−	289.992i	−1.23170	−	1.27189i
$229$	−20.4059	−	35.3440i	−0.0891087	−	0.154341i	0.818026	−	0.575181i	$-0.195069\pi$
$229$	−20.4059	−	35.3440i	−0.0891087	−	0.154341i	−0.907135	+	0.420841i	$0.861735\pi$
$230$			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	$-0.979451\pi$
$233$	−335.754	+	193.848i	−1.44101	+	0.831965i	−0.443088	+	0.896478i	$0.646117\pi$
$234$	−173.420	−	323.966i	−0.741113	−	1.38447i
$235$	−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	$0.966962\pi$
$240$	17.7508	+	70.7723i	0.0739615	+	0.294885i
$241$	−162.624	+	281.672i	−0.674786	+	1.16876i	0.301745	+	0.953389i	$0.402431\pi$
$241$	−162.624	+	281.672i	−0.674786	+	1.16876i	−0.976531	+	0.215376i	$0.930902\pi$
$242$	−218.104	−	125.922i	−0.901255	−	0.520340i
$243$	−157.496	−	185.051i	−0.648132	−	0.761528i
$244$	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
$249$	160.090	−	155.031i	0.642933	−	0.622614i
$250$	−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
$255$	−11.7363	−	12.1193i	−0.0460245	−	0.0475265i
$256$	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
$261$	85.4180	+	2.74352i	0.327272	+	0.0105116i
$262$	−320.985	+	555.962i	−1.22513	+	2.12199i
$263$	99.0641	+	57.1947i	0.376670	+	0.217470i	0.676368	−	0.736564i	$-0.263553\pi$
$263$	99.0641	+	57.1947i	0.376670	+	0.217470i	−0.299699	+	0.954034i	$0.596886\pi$
$264$	−306.985	+	76.9965i	−1.16282	+	0.291654i
$265$	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	$0.663849\pi$
$270$	−24.9256	−	114.892i	−0.0923172	−	0.425526i
$271$	259.350	+	449.208i	0.957012	+	1.65759i	0.729695	+	0.683773i	$0.239662\pi$
$271$	259.350	+	449.208i	0.957012	+	1.65759i	0.227318	+	0.973821i	$0.427004\pi$
$272$		−	88.6701i		−	0.325993i
$273$		0			0
$274$	115.749			0.422442
$275$	142.444	−	82.2403i	0.517979	−	0.299055i
$276$	456.794	−	442.358i	1.65505	−	1.60275i
$277$	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	$-0.742000\pi$
$281$		−	407.255i		−	1.44931i	0.689113	−	0.724654i	$-0.258000\pi$
$282$	336.814	−	84.4781i	1.19438	−	0.299568i
$283$	199.317	−	345.227i	0.704300	−	1.21988i	−0.262643	−	0.964893i	$-0.584594\pi$
$283$	199.317	−	345.227i	0.704300	−	1.21988i	0.966943	−	0.254991i	$-0.0820724\pi$
$284$	506.656	+	292.518i	1.78400	+	1.02999i
$285$	14.7103	+	58.6502i	0.0516152	+	0.205790i
$286$	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
$291$	−48.3473	−	49.9251i	−0.166142	−	0.171564i
$292$	−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
$297$	185.016	−	40.1389i	0.622949	−	0.135148i
$298$	−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
$303$	−98.4604	−	392.562i	−0.324952	−	1.29558i
$304$	−158.904	+	275.230i	−0.522710	+	0.905361i
$305$	−61.8674	−	35.7192i	−0.202844	−	0.117112i
$306$	−4.58647	+	142.797i	−0.0149885	+	0.466657i
$307$	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	$-0.254869\pi$
$311$	131.442	+	75.8884i	0.422645	+	0.244014i	−0.273564	+	0.961854i	$0.588202\pi$
$312$	−377.613	+	365.679i	−1.21030	+	1.17205i
$313$	−159.059	−	275.498i	−0.508175	−	0.880185i	−0.999955	−	0.00946567i	$-0.996987\pi$
$313$	−159.059	−	275.498i	−0.508175	−	0.880185i	0.491780	−	0.870719i	$-0.336346\pi$
$314$			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	$-0.861340\pi$
$317$	−315.251	+	182.010i	−0.994482	+	0.574164i	−0.0878710	+	0.996132i	$0.528006\pi$
$318$	−111.126	−	114.753i	−0.349454	−	0.360858i
$319$	−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
$324$	−372.438	+	558.885i	−1.14950	+	1.72495i
$325$	136.590	−	236.581i	0.420277	−	0.727942i
$326$	215.449	+	124.389i	0.660885	+	0.381562i
$327$	106.322	−	26.6672i	0.325145	−	0.0815512i
$328$	−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
$333$	−262.166	+	140.339i	−0.787284	+	0.421437i
$334$	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
$339$	46.8942	−	45.4122i	0.138331	−	0.133959i
$340$	−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
$345$	−92.3855	+	23.1717i	−0.267784	+	0.0671642i
$346$	−190.133	+	329.319i	−0.549516	+	0.951790i
$347$	−408.108	−	235.621i	−1.17610	−	0.679023i	−0.220993	−	0.975275i	$-0.570930\pi$
$347$	−408.108	−	235.621i	−1.17610	−	0.679023i	−0.955110	+	0.296252i	$0.904263\pi$
$348$	−57.4633	−	229.107i	−0.165125	−	0.658352i
$349$	−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	$-0.372360\pi$
$353$	−74.7744	−	43.1710i	−0.211825	−	0.122297i	−0.602159	+	0.798376i	$0.705693\pi$
$354$	676.047	+	698.109i	1.90974	+	1.97206i
$355$	−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	$-0.840065\pi$
$359$	−322.220	+	186.034i	−0.897549	+	0.518200i	−0.0211451	+	0.999776i	$0.506731\pi$
$360$	−148.269	+	79.3693i	−0.411859	+	0.220470i
$361$	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
$366$	147.180	+	586.809i	0.402132	+	1.60330i
$367$	80.8928	−	140.110i	0.220416	−	0.381772i	−0.734518	−	0.678589i	$-0.762592\pi$
$367$	80.8928	−	140.110i	0.220416	−	0.381772i	0.954934	+	0.296817i	$0.0959251\pi$
$368$	−433.540	−	250.305i	−1.17810	−	0.680176i
$369$	604.439	+	19.4139i	1.63805	+	0.0526121i
$370$	−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
$375$	129.700	−	125.601i	0.345866	−	0.334936i
$376$	−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
$381$	−32.1752	−	33.2252i	−0.0844492	−	0.0872052i
$382$	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
$387$	6.97034	−	217.018i	0.0180112	−	0.560769i
$388$	−96.0405	+	166.347i	−0.247527	+	0.428730i
$389$	−628.374	−	362.792i	−1.61536	−	0.932628i	−0.988099	−	0.153817i	$-0.950843\pi$
$389$	−628.374	−	362.792i	−1.61536	−	0.932628i	−0.627259	−	0.778811i	$-0.715823\pi$
$390$	147.555	−	37.0090i	0.378346	−	0.0948949i
$391$	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
$396$	−246.943	−	461.312i	−0.623592	−	1.16493i
$397$	47.1732	+	81.7064i	0.118824	+	0.205809i	0.919302	−	0.393553i	$-0.128754\pi$
$397$	47.1732	+	81.7064i	0.118824	+	0.205809i	−0.800478	+	0.599362i	$0.795421\pi$
$398$			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	$-0.346285\pi$
$401$	586.875	−	338.833i	1.46353	−	0.844969i	0.999172	+	0.0406787i	$0.0129520\pi$
$402$	−114.589	+	110.967i	−0.285046	+	0.276038i
$403$	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
$408$	198.236	−	49.7206i	0.485873	−	0.121864i
$409$	−8.68233	+	15.0382i	−0.0212282	+	0.0367683i	−0.876444	−	0.481503i	$-0.840091\pi$
$409$	−8.68233	+	15.0382i	−0.0212282	+	0.0367683i	0.855216	+	0.518271i	$0.173424\pi$
$410$	253.383	+	146.291i	0.618008	+	0.356807i
$411$	24.0958	+	96.0701i	0.0586273	+	0.233747i
$412$	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
$417$	134.907	+	139.310i	0.323518	+	0.334076i
$418$	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
$423$	140.231	+	261.965i	0.331516	+	0.619303i
$424$	−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
$429$	59.5973	+	237.615i	0.138922	+	0.553881i
$430$	52.5242	−	90.9746i	0.122149	−	0.211569i
$431$	294.660	+	170.122i	0.683666	+	0.394715i	0.801235	−	0.598350i	$-0.204177\pi$
$431$	294.660	+	170.122i	0.683666	+	0.394715i	−0.117569	+	0.993065i	$0.537510\pi$
$432$	503.544	+	161.277i	1.16561	+	0.373327i
$433$	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
$438$	580.193	−	561.857i	1.32464	−	1.28278i
$439$	−64.0366	−	110.915i	−0.145869	−	0.252653i	0.783828	−	0.620978i	$-0.213265\pi$
$439$	−64.0366	−	110.915i	−0.145869	−	0.252653i	−0.929697	+	0.368326i	$0.879931\pi$
$440$		−	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	$-0.595169\pi$
$443$	170.901	−	98.6700i	0.385782	−	0.222731i	0.680331	+	0.732905i	$0.261836\pi$
$444$	571.743	+	590.402i	1.28771	+	1.32973i
$445$	−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	$-0.0527377\pi$
$450$	−739.781	−	23.7609i	−1.64396	−	0.0528019i
$451$	−235.579	+	408.035i	−0.522348	+	0.904734i
$452$	−156.248	−	90.2100i	−0.345682	−	0.199580i
$453$	−297.537	+	74.6267i	−0.656814	+	0.164739i
$454$	−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
$459$	−119.474	+	25.9198i	−0.260293	+	0.0564701i
$460$	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
$465$	76.8403	−	74.4119i	0.165248	−	0.160026i
$466$	−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
$471$	−304.730	+	76.4308i	−0.646985	+	0.162273i
$472$	695.080	−	1203.91i	1.47263	−	2.55067i
$473$	146.501	+	84.5821i	0.309726	+	0.178821i
$474$	−325.594	−	1298.15i	−0.686908	−	2.73870i
$475$	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	$0.531804\pi$
$480$	21.9639	+	22.6807i	0.0457582	+	0.0472515i
$481$	−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
$486$	−802.580	−	285.772i	−1.65140	−	0.588008i
$487$	−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	$0.0556455\pi$
$491$			170.796i			0.347853i	−0.984759	+	0.173927i	$0.944354\pi$
$492$	−406.625	−	1621.22i	−0.826474	−	3.29515i
$493$	21.4980	−	37.2357i	0.0436066	−	0.0755288i
$494$	573.833	+	331.303i	1.16161	+	0.670654i
$495$	−2.51606	+	78.3361i	−0.00508295	+	0.158255i
$496$	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
$501$	−446.088	+	431.990i	−0.890395	+	0.862255i
$502$	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
$507$	−69.6565	−	71.9297i	−0.137389	−	0.141873i
$508$	−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
$513$	417.295	+	133.653i	0.813441	+	0.260533i
$514$	265.014	−	459.018i	0.515592	−	0.893032i
$515$	−128.799	−	74.3623i	−0.250096	−	0.144393i
$516$	−582.080	+	145.994i	−1.12806	+	0.282935i
$517$	−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	$0.352168\pi$
$522$	264.157	−	141.405i	0.506048	−	0.270890i
$523$	−399.354	−	691.701i	−0.763582	−	1.32256i	−0.940993	−	0.338426i	$-0.890105\pi$
$523$	−399.354	−	691.701i	−0.763582	−	1.32256i	0.177411	−	0.984137i	$-0.443228\pi$
$524$			1518.26i			2.89744i
$525$		0			0
$526$	401.041			0.762434
$527$	−112.574	+	64.9947i	−0.213613	+	0.123330i
$528$	−295.923	+	286.571i	−0.560461	+	0.542749i
$529$	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
$534$	1299.47	−	325.928i	2.43347	−	0.610352i
$535$	−48.3464	+	83.7384i	−0.0903671	+	0.156520i
$536$	197.612	+	114.091i	0.368680	+	0.212857i
$537$	116.305	+	463.707i	0.216582	+	0.863515i
$538$	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
$543$	−488.124	−	504.054i	−0.898940	−	0.928276i
$544$	−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
$549$	−456.404	+	244.315i	−0.831338	+	0.445019i
$550$	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
$555$	−29.9491	−	119.407i	−0.0539624	−	0.215148i
$556$	267.989	−	464.170i	0.481994	−	0.834839i
$557$	784.869	+	453.144i	1.40910	+	0.813544i	0.995301	−	0.0968243i	$-0.0308685\pi$
$557$	784.869	+	453.144i	1.40910	+	0.813544i	0.413798	+	0.910369i	$0.364202\pi$
$558$	−905.381	−	29.0798i	−1.62255	−	0.0521143i
$559$	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	$0.800195\pi$
$564$	589.951	−	571.306i	1.04601	−	1.01295i
$565$	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	$-0.497271\pi$
$569$	500.067	−	288.714i	0.878853	−	0.507406i	0.870280	+	0.492557i	$0.163938\pi$
$570$	147.475	+	152.288i	0.258729	+	0.267172i
$571$	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
$576$	−14.0483	+	437.386i	−0.0243894	+	0.759351i
$577$	338.292	−	585.938i	0.586294	−	1.01549i	−0.408419	−	0.912795i	$-0.633920\pi$
$577$	338.292	−	585.938i	0.586294	−	1.01549i	0.994713	−	0.102696i	$-0.0327469\pi$
$578$	−815.219	−	470.667i	−1.41041	−	0.814302i
$579$	−224.414	+	56.2863i	−0.387588	+	0.0972129i
$580$	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
$585$	61.4339	+	114.764i	0.105015	+	0.196178i
$586$	−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
$591$	−294.027	+	284.735i	−0.497508	+	0.481785i
$592$	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
$597$	−251.945	+	63.1916i	−0.422019	+	0.105849i
$598$	−521.867	+	903.900i	−0.872687	+	1.51154i
$599$	63.8836	+	36.8832i	0.106650	+	0.0615747i	0.552376	−	0.833595i	$-0.313721\pi$
$599$	63.8836	+	36.8832i	0.106650	+	0.0615747i	−0.445726	+	0.895169i	$0.647054\pi$
$600$	257.585	+	1026.99i	0.429308	+	1.71165i
$601$	−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
$606$	−987.093	−	1019.31i	−1.62887	−	1.68202i
$607$	90.8039	+	157.277i	0.149595	+	0.259105i	0.931078	−	0.364821i	$-0.118870\pi$
$607$	90.8039	+	157.277i	0.149595	+	0.259105i	−0.781483	+	0.623926i	$0.785536\pi$
$608$			137.519i			0.226183i
$609$		0			0
$610$	−250.458			−0.410586
$611$	−332.976	+	192.244i	−0.544969	+	0.314638i
$612$	159.463	+	297.893i	0.260561	+	0.486753i
$613$	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	$-0.603220\pi$
$617$		−	1169.69i		−	1.89576i	0.318622	−	0.947882i	$-0.396780\pi$
$618$	306.409	+	1221.65i	0.495807	+	1.97678i
$619$	−604.483	+	1047.00i	−0.976548	+	1.69143i	−0.301817	+	0.953366i	$0.597593\pi$
$619$	−604.483	+	1047.00i	−0.976548	+	1.69143i	−0.674730	+	0.738064i	$0.735740\pi$
$620$	−256.027	−	147.817i	−0.412946	−	0.238415i
$621$	−210.530	+	657.321i	−0.339018	+	1.05849i
$622$	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
$627$	−245.237	+	237.486i	−0.391127	+	0.378766i
$628$	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
$633$	40.5231	+	41.8456i	0.0640176	+	0.0661068i
$634$	−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
$639$	−634.699	−	20.3858i	−0.993269	−	0.0319026i
$640$	−126.908	+	219.811i	−0.198294	+	0.343454i
$641$	457.806	+	264.315i	0.714206	+	0.412347i	0.812616	−	0.582799i	$-0.198042\pi$
$641$	457.806	+	264.315i	0.714206	+	0.412347i	−0.0984103	+	0.995146i	$0.531376\pi$
$642$	794.253	−	199.211i	1.23715	−	0.310297i
$643$	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	$-0.541224\pi$
$647$	−680.962	−	393.154i	−1.05249	−	0.607657i	−0.923346	+	0.383969i	$0.874557\pi$
$648$	−78.2057	+	1216.19i	−0.120688	+	1.87683i
$649$	−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	$-0.571210\pi$
$653$	334.119	−	192.904i	0.511668	−	0.295412i	0.733519	+	0.679669i	$0.237877\pi$
$654$	276.071	−	267.347i	0.422128	−	0.408787i
$655$	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	$0.976490\pi$
$660$	210.112	−	52.6991i	0.318351	−	0.0798471i
$661$	480.752	−	832.687i	0.727311	−	1.25974i	−0.230705	−	0.973024i	$-0.574103\pi$
$661$	480.752	−	832.687i	0.727311	−	1.25974i	0.958016	−	0.286715i	$-0.0925633\pi$
$662$	−468.697	−	270.602i	−0.708001	−	0.408765i
$663$	−38.4851	−	153.440i	−0.0580468	−	0.231433i
$664$	−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
$669$	365.308	+	377.230i	0.546051	+	0.563871i
$670$	−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
$675$	−134.281	−	618.954i	−0.198935	−	0.916969i
$676$	−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
$681$	−129.600	−	516.717i	−0.190309	−	0.758762i
$682$	352.871	−	611.190i	0.517406	−	0.896173i
$683$	295.398	+	170.548i	0.432501	+	0.249705i	0.700412	−	0.713739i	$-0.253000\pi$
$683$	295.398	+	170.548i	0.432501	+	0.249705i	−0.267910	+	0.963444i	$0.586333\pi$
$684$	38.8773	−	1210.42i	0.0568382	−	1.76962i
$685$	−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
$690$	−239.883	+	232.302i	−0.347657	+	0.336670i
$691$	391.833	+	678.675i	0.567053	+	0.982164i	0.996855	+	0.0792411i	$0.0252497\pi$
$691$	391.833	+	678.675i	0.567053	+	0.982164i	−0.429803	+	0.902923i	$0.641417\pi$
$692$			899.327i			1.29961i
$693$		0			0
$694$	−1652.14			−2.38060
$695$	−69.5272	+	40.1416i	−0.100039	+	0.0577576i
$696$	−298.170	−	307.901i	−0.428405	−	0.442386i
$697$	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	$0.601187\pi$
$702$	336.252	−	1049.85i	0.478991	−	1.49552i
$703$	268.103	−	464.368i	0.381370	−	0.660553i
$704$	−295.263	−	170.470i	−0.419408	−	0.242145i
$705$	−119.316	+	29.9263i	−0.169243	+	0.0424486i
$706$	−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
$711$	1009.66	−	540.478i	1.42006	−	0.760166i
$712$	−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
$717$	−106.727	+	103.354i	−0.148852	+	0.144148i
$718$	−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
$723$	−946.426	+	237.378i	−1.30903	+	0.328323i
$724$	−969.645	+	1679.47i	−1.33929	+	2.31972i
$725$	192.905	+	111.374i	0.266076	+	0.153619i
$726$	−183.806	−	732.834i	−0.253176	−	1.00941i
$727$	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
$732$	995.348	+	1027.83i	1.35977	+	1.40414i
$733$	197.483	+	342.051i	0.269417	+	0.466645i	0.968712	−	0.248189i	$-0.0798355\pi$
$733$	197.483	+	342.051i	0.269417	+	0.466645i	−0.699294	+	0.714834i	$0.746502\pi$
$734$		−	567.208i		−	0.772763i
$735$		0			0
$736$	−216.620			−0.294320
$737$	92.0947	−	53.1709i	0.124959	−	0.0721450i
$738$	1869.24	−	1000.61i	2.53285	−	1.35585i
$739$	−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	$-0.916922\pi$
$743$		−	383.452i		−	0.516086i	0.966133	−	0.258043i	$-0.0830776\pi$
$744$	315.246	+	1256.89i	0.423717	+	1.68936i
$745$	121.549	−	210.529i	0.163153	−	0.282589i
$746$	−1148.45	−	663.060i	−1.53948	−	0.888820i
$747$	668.215	+	21.4622i	0.894531	+	0.0287313i
$748$	−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
$753$	−568.370	+	550.408i	−0.754808	+	0.730953i
$754$	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
$759$	−374.087	−	386.295i	−0.492869	−	0.508953i
$760$	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
$765$	1.62475	−	50.5856i	0.00212386	−	0.0661250i
$766$	−198.753	+	344.250i	−0.259469	+	0.449413i
$767$	−931.861	−	538.010i	−1.21494	−	0.701448i
$768$	1518.94	−	380.973i	1.97779	−	0.496058i
$769$	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	$-0.421792\pi$
$773$	−367.303	−	212.063i	−0.475166	−	0.274337i	−0.718400	+	0.695631i	$0.755125\pi$
$774$	−359.260	−	671.131i	−0.464160	−	0.867095i
$775$	−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
$780$	258.452	−	250.284i	0.331348	−	0.320876i
$781$	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
$786$	−1868.05	+	468.534i	−2.37665	+	0.596100i
$787$	77.9444	−	135.004i	0.0990399	−	0.171542i	−0.812248	−	0.583313i	$-0.801756\pi$
$787$	77.9444	−	135.004i	0.0990399	−	0.171542i	0.911288	+	0.411771i	$0.135090\pi$
$788$	979.679	+	565.618i	1.24325	+	0.717789i
$789$	83.4858	+	332.858i	0.105812	+	0.421873i
$790$	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
$795$	39.3663	+	40.6510i	0.0495174	+	0.0511334i
$796$	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
$801$	541.031	+	1010.70i	0.675445	+	1.26179i
$802$	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
$807$	3.47527	+	13.8559i	0.00430641	+	0.0171697i
$808$	−1014.88	+	1757.83i	−1.25604	+	2.17553i
$809$	183.808	+	106.122i	0.227204	+	0.131176i	0.609282	−	0.792954i	$-0.291458\pi$
$809$	183.808	+	106.122i	0.227204	+	0.131176i	−0.382077	+	0.924130i	$0.624791\pi$
$810$	195.584	−	293.496i	0.241462	−	0.362341i
$811$	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
$816$	191.093	−	185.054i	0.234183	−	0.226782i
$817$	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	$-0.500543\pi$
$821$	708.903	−	409.286i	0.863463	−	0.498521i	0.865171	+	0.501478i	$0.167210\pi$
$822$	241.567	+	249.451i	0.293878	+	0.303468i
$823$	−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	$-0.914562\pi$
$827$		−	438.639i		−	0.530398i	0.964194	−	0.265199i	$-0.0854376\pi$
$828$	1906.65	+	61.2394i	2.30272	+	0.0739606i
$829$	−327.402	+	567.077i	−0.394936	+	0.684049i	−0.993093	−	0.117330i	$-0.962567\pi$
$829$	−327.402	+	567.077i	−0.394936	+	0.684049i	0.598157	+	0.801379i	$0.295900\pi$
$830$	280.118	+	161.726i	0.337492	+	0.194851i
$831$	352.341	−	88.3725i	0.423997	−	0.106345i
$832$	−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
$837$	−164.340	−	757.508i	−0.196344	−	0.905027i
$838$	−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
$843$	877.676	−	849.939i	1.04113	−	1.00823i
$844$	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
$849$	1159.97	−	290.938i	1.36628	−	0.342684i
$850$	−186.188	+	322.487i	−0.219045	+	0.379397i
$851$	731.471	+	422.315i	0.859543	+	0.496257i
$852$	426.981	+	1702.38i	0.501152	+	1.99809i
$853$	−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	$-0.228073\pi$
$857$	481.961	+	278.260i	0.562382	+	0.324691i	−0.191719	+	0.981450i	$0.561406\pi$
$858$	597.480	+	616.979i	0.696364	+	0.719089i
$859$	321.539	+	556.922i	0.374318	+	0.648338i	0.990225	−	0.139481i	$-0.0445435\pi$
$859$	321.539	+	556.922i	0.374318	+	0.648338i	−0.615907	+	0.787819i	$0.711210\pi$
$860$		−	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	$-0.704542\pi$
$863$	−177.442	+	102.446i	−0.205611	+	0.118709i	0.393659	+	0.919256i	$0.371209\pi$
$864$	223.591	−	48.5078i	0.258786	−	0.0561433i
$865$	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
$870$	30.1766	+	120.314i	0.0346858	+	0.138292i
$871$	88.3098	−	152.957i	0.101389	−	0.175611i
$872$	−476.095	−	274.874i	−0.545981	−	0.315222i
$873$	6.69313	−	208.387i	0.00766681	−	0.238702i
$874$	−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
$879$	5.46159	−	5.28898i	0.00621341	−	0.00601705i
$880$	−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
$885$	−239.489	−	247.304i	−0.270609	−	0.279440i
$886$	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
$891$	472.630	+	314.958i	0.530449	+	0.353489i
$892$	725.674	−	1256.91i	0.813536	−	1.40909i
$893$	−464.014	−	267.898i	−0.519612	−	0.299998i
$894$	−1996.85	+	500.841i	−2.23362	+	0.560225i
$895$	−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
$900$	−1543.28	+	826.124i	−1.71475	+	0.917916i
$901$	−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
$906$	−772.570	+	748.154i	−0.852726	+	0.825777i
$907$	−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	$-0.786217\pi$
$911$		−	1133.75i		−	1.24451i	0.782815	−	0.622254i	$-0.213783\pi$
$912$	−924.779	+	231.948i	−1.01401	+	0.254329i
$913$	−260.435	+	451.087i	−0.285252	+	0.494071i
$914$	371.070	+	214.237i	0.405984	+	0.234395i
$915$	−52.1385	−	207.876i	−0.0569819	−	0.227187i
$916$	−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
$921$	179.975	+	185.849i	0.195413	+	0.201790i
$922$	−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
$927$	−950.169	+	508.630i	−1.02499	+	0.548684i
$928$	−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
$933$	110.772	+	441.650i	0.118727	+	0.473366i
$934$	1345.76	−	2330.92i	1.44086	−	2.49563i
$935$	34.1485	+	19.7156i	0.0365225	+	0.0210863i
$936$	−1576.15	−	50.6241i	−1.68392	−	0.0540856i
$937$	−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	$-0.306757\pi$
$941$	135.923	+	78.4754i	0.144446	+	0.0833957i	−0.426035	+	0.904706i	$0.640090\pi$
$942$	−791.246	+	766.240i	−0.839964	+	0.813418i
$943$	−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	$-0.820467\pi$
$947$	−762.055	+	439.973i	−0.804704	+	0.464596i	0.0404090	+	0.999183i	$0.487134\pi$
$948$	−2201.92	−	2273.78i	−2.32270	−	2.39850i
$949$	−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	$-0.0954955\pi$
$954$	15.3841	−	478.976i	0.0161259	−	0.502072i
$955$	−178.974	+	309.992i	−0.187407	+	0.324599i
$956$	355.607	+	205.310i	0.371974	+	0.214759i
$957$	−193.748	+	48.5948i	−0.202453	+	0.0507783i
$958$	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
$963$	330.684	+	617.749i	0.343390	+	0.641484i
$964$	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
$969$	158.362	−	153.357i	0.163428	−	0.158263i
$970$	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
$975$	794.919	−	199.378i	0.815302	−	0.204490i
$976$	563.210	−	975.508i	0.577059	−	0.999496i
$977$	−427.579	−	246.863i	−0.437645	−	0.252674i	0.264953	−	0.964261i	$-0.414643\pi$
$977$	−427.579	−	246.863i	−0.437645	−	0.252674i	−0.702598	+	0.711587i	$0.747977\pi$
$978$	181.568	+	723.913i	0.185653	+	0.740197i
$979$	−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	$0.952633\pi$
$984$	−2109.93	−	2178.78i	−2.14423	−	2.21421i
$985$	−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
$990$	129.681	+	242.256i	0.130991	+	0.244703i
$991$	−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
$996$	−449.529	−	1792.27i	−0.451334	−	1.79947i
$997$	−913.216	+	1581.74i	−0.915964	+	1.58650i	−0.110481	+	0.993878i	$0.535239\pi$
$997$	−913.216	+	1581.74i	−0.915964	+	1.58650i	−0.805484	+	0.592618i	$0.798094\pi$
$998$	2574.15	+	1486.19i	2.57931	+	1.48916i
$999$	−849.582	−	272.108i	−0.850432	−	0.272380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.3.h.e.116.4		8
3.2	odd	2	inner	147.3.h.e.116.1		8
7.2	even	3	inner	147.3.h.e.128.1		8
7.3	odd	6		147.3.b.f.50.4		4
7.4	even	3		21.3.b.a.8.4	yes	4
7.5	odd	6		147.3.h.c.128.1		8
7.6	odd	2		147.3.h.c.116.4		8
21.2	odd	6	inner	147.3.h.e.128.4		8
21.5	even	6		147.3.h.c.128.4		8
21.11	odd	6		21.3.b.a.8.1	✓	4
21.17	even	6		147.3.b.f.50.1		4
21.20	even	2		147.3.h.c.116.1		8
28.11	odd	6		336.3.d.c.113.2		4
35.4	even	6		525.3.c.a.176.1		4
35.18	odd	12		525.3.f.a.449.8		8
35.32	odd	12		525.3.f.a.449.1		8
56.11	odd	6		1344.3.d.b.449.3		4
56.53	even	6		1344.3.d.f.449.2		4
63.4	even	3		567.3.r.c.512.1		8
63.11	odd	6		567.3.r.c.134.1		8
63.25	even	3		567.3.r.c.134.4		8
63.32	odd	6		567.3.r.c.512.4		8
84.11	even	6		336.3.d.c.113.1		4
105.32	even	12		525.3.f.a.449.7		8
105.53	even	12		525.3.f.a.449.2		8
105.74	odd	6		525.3.c.a.176.4		4
168.11	even	6		1344.3.d.b.449.4		4
168.53	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	21.11	odd	6
21.3.b.a.8.4	yes	4	7.4	even	3
147.3.b.f.50.1		4	21.17	even	6
147.3.b.f.50.4		4	7.3	odd	6
147.3.h.c.116.1		8	21.20	even	2
147.3.h.c.116.4		8	7.6	odd	2
147.3.h.c.128.1		8	7.5	odd	6
147.3.h.c.128.4		8	21.5	even	6
147.3.h.e.116.1		8	3.2	odd	2	inner
147.3.h.e.116.4		8	1.1	even	1	trivial
147.3.h.e.128.1		8	7.2	even	3	inner
147.3.h.e.128.4		8	21.2	odd	6	inner
336.3.d.c.113.1		4	84.11	even	6
336.3.d.c.113.2		4	28.11	odd	6
525.3.c.a.176.1		4	35.4	even	6
525.3.c.a.176.4		4	105.74	odd	6
525.3.f.a.449.1		8	35.32	odd	12
525.3.f.a.449.2		8	105.53	even	12
525.3.f.a.449.7		8	105.32	even	12
525.3.f.a.449.8		8	35.18	odd	12
567.3.r.c.134.1		8	63.11	odd	6
567.3.r.c.134.4		8	63.25	even	3
567.3.r.c.512.1		8	63.4	even	3
567.3.r.c.512.4		8	63.32	odd	6
1344.3.d.b.449.3		4	56.11	odd	6
1344.3.d.b.449.4		4	168.11	even	6
1344.3.d.f.449.1		4	168.53	odd	6
1344.3.d.f.449.2		4	56.53	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)

\(f(q)\)	\(=\)	\(q+(3.03622 - 1.75296i) q^{2} +(2.08699 + 2.15510i) q^{3} +(4.14575 - 7.18065i) q^{4} +(-1.07558 + 0.620984i) q^{5} +(10.1144 + 2.88494i) q^{6} -15.0457i q^{8} +(-0.288920 + 8.99536i) q^{9} +O(q^{10})\)	\(q+(3.03622 - 1.75296i) q^{2} +(2.08699 + 2.15510i) q^{3} +(4.14575 - 7.18065i) q^{4} +(-1.07558 + 0.620984i) q^{5} +(10.1144 + 2.88494i) q^{6} -15.0457i q^{8} +(-0.288920 + 8.99536i) q^{9} +(-2.17712 + 3.77089i) q^{10} +(-6.07244 - 3.50592i) q^{11} +(24.1272 - 6.05146i) q^{12} -11.6458 q^{13} +(-3.58301 - 1.02199i) q^{15} +(-9.79150 - 16.9594i) q^{16} +(3.92129 + 2.26395i) q^{17} +(14.8913 + 27.8184i) q^{18} +(-8.11438 - 14.0545i) q^{19} +10.2978i q^{20} -24.5830 q^{22} +(22.1386 - 12.7817i) q^{23} +(32.4250 - 31.4002i) q^{24} +(-11.7288 + 20.3148i) q^{25} +(-35.3591 + 20.4146i) q^{26} +(-19.9889 + 18.1506i) q^{27} -9.49579i q^{29} +(-12.6703 + 3.17790i) q^{30} +(-14.3542 + 24.8623i) q^{31} +(-7.33853 - 4.23690i) q^{32} +(-5.11752 - 20.4036i) q^{33} +15.8745 q^{34} +(63.3948 + 39.3672i) q^{36} +(16.5203 + 28.6139i) q^{37} +(-49.2741 - 28.4484i) q^{38} +(-24.3046 - 25.0978i) q^{39} +(9.34313 + 16.1828i) q^{40} -67.1946i q^{41} -24.1255 q^{43} +(-50.3496 + 29.0694i) q^{44} +(-5.27522 - 9.85462i) q^{45} +(44.8118 - 77.6162i) q^{46} +(28.5921 - 16.5076i) q^{47} +(16.1144 - 56.4958i) q^{48} +82.2403i q^{50} +(3.30464 + 13.1756i) q^{51} +(-48.2804 + 83.6241i) q^{52} +(-13.1530 - 7.59387i) q^{53} +(-28.8733 + 90.1490i) q^{54} +8.70850 q^{55} +(13.3542 - 46.8190i) q^{57} +(-16.6458 - 28.8313i) q^{58} +(80.0173 + 46.1980i) q^{59} +(-22.1928 + 21.4914i) q^{60} +(28.7601 + 49.8140i) q^{61} +100.650i q^{62} +48.6235 q^{64} +(12.5259 - 7.23183i) q^{65} +(-51.3046 - 52.9789i) q^{66} +(-7.58301 + 13.1342i) q^{67} +(32.5133 - 18.7716i) q^{68} +(73.7490 + 21.0355i) q^{69} +70.5584i q^{71} +(135.341 + 4.34700i) q^{72} +(38.3948 - 66.5017i) q^{73} +(100.318 + 57.9188i) q^{74} +(-68.2583 + 17.1202i) q^{75} -134.561 q^{76} +(-117.790 - 33.5973i) q^{78} +(-63.6235 - 110.199i) q^{79} +(21.0630 + 12.1607i) q^{80} +(-80.8331 - 5.19788i) q^{81} +(-117.790 - 204.017i) q^{82} -74.2844i q^{83} -5.62352 q^{85} +(-73.2503 + 42.2911i) q^{86} +(20.4644 - 19.8176i) q^{87} +(-52.7490 + 91.3640i) q^{88} +(110.312 - 63.6887i) q^{89} +(-33.2915 - 20.6735i) q^{90} -211.959i q^{92} +(-83.5380 + 20.9526i) q^{93} +(57.8745 - 100.242i) q^{94} +(17.4553 + 10.0778i) q^{95} +(-6.18451 - 24.6576i) 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

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