LMFDB - Embedded newform 343.2.g.i.177.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [343,2,Mod(30,343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(343, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([32]))

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

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

chi := DirichletCharacter("343.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	343.g (of order $21$, degree $12$, 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:	$2.73886878933$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			177.4
Character	$\chi$	$=$	343.177
Dual form			343.2.g.i.312.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.92202 + 1.78338i) q^{2} +(1.46134 + 0.220261i) q^{3} +(0.364281 + 4.86099i) q^{4} +(-0.754391 - 1.92216i) q^{5} +(2.41591 + 3.02946i) q^{6} +(-4.69930 + 5.89274i) q^{8} +(-0.779731 - 0.240515i) q^{9} +O(q^{10})$	\(q+(1.92202 + 1.78338i) q^{2} +(1.46134 + 0.220261i) q^{3} +(0.364281 + 4.86099i) q^{4} +(-0.754391 - 1.92216i) q^{5} +(2.41591 + 3.02946i) q^{6} +(-4.69930 + 5.89274i) q^{8} +(-0.779731 - 0.240515i) q^{9} +(1.97797 - 5.03980i) q^{10} +(1.78567 - 0.550805i) q^{11} +(-0.538349 + 7.18377i) q^{12} +(-0.677236 + 2.96716i) q^{13} +(-0.679042 - 2.97508i) q^{15} +(-9.90082 + 1.49231i) q^{16} +(-1.16012 - 0.790958i) q^{17} +(-1.06973 - 1.85283i) q^{18} +(2.73229 - 4.73247i) q^{19} +(9.06877 - 4.36729i) q^{20} +(4.41439 + 2.12586i) q^{22} +(-0.168275 + 0.114728i) q^{23} +(-8.16520 + 7.57620i) q^{24} +(0.539678 - 0.500748i) q^{25} +(-6.59324 + 4.49519i) q^{26} +(-5.08094 - 2.44685i) q^{27} +(1.62320 - 0.781691i) q^{29} +(4.00056 - 6.92917i) q^{30} +(-2.57807 - 4.46535i) q^{31} +(-9.23609 - 6.29706i) q^{32} +(2.73078 - 0.411599i) q^{33} +(-0.819206 - 3.58918i) q^{34} +(0.885100 - 3.87788i) q^{36} +(0.563813 - 7.52356i) q^{37} +(13.6913 - 4.22321i) q^{38} +(-1.64322 + 4.18685i) q^{39} +(14.8719 + 4.58737i) q^{40} +(-5.90598 + 7.40586i) q^{41} +(1.60000 + 2.00633i) q^{43} +(3.32794 + 8.47945i) q^{44} +(0.125914 + 1.68021i) q^{45} +(-0.528033 - 0.0795882i) q^{46} +(-1.21865 - 1.13074i) q^{47} -14.7971 q^{48} +1.93030 q^{50} +(-1.52111 - 1.41138i) q^{51} +(-14.6700 - 2.21115i) q^{52} +(0.540899 + 7.21780i) q^{53} +(-5.40203 - 13.7642i) q^{54} +(-2.40583 - 3.01681i) q^{55} +(5.03517 - 6.31391i) q^{57} +(4.51388 + 1.39235i) q^{58} +(-3.04990 + 7.77102i) q^{59} +(14.2145 - 4.38458i) q^{60} +(-0.493546 + 6.58591i) q^{61} +(3.00829 - 13.1802i) q^{62} +(-2.06590 - 9.05131i) q^{64} +(6.21425 - 0.936648i) q^{65} +(5.98266 + 4.07891i) q^{66} +(-1.78982 - 3.10006i) q^{67} +(3.42222 - 5.92747i) q^{68} +(-0.271177 + 0.130592i) q^{69} +(-6.02101 - 2.89956i) q^{71} +(5.08149 - 3.46450i) q^{72} +(0.129576 - 0.120229i) q^{73} +(14.5010 - 13.4550i) q^{74} +(0.898946 - 0.612891i) q^{75} +(23.9998 + 11.5577i) q^{76} +(-10.6251 + 5.11676i) q^{78} +(-7.82581 + 13.5547i) q^{79} +(10.3375 + 17.9052i) q^{80} +(-4.86342 - 3.31583i) q^{81} +(-24.5589 + 3.70166i) q^{82} +(2.14456 + 9.39591i) q^{83} +(-0.645159 + 2.82663i) q^{85} +(-0.502817 + 6.70962i) q^{86} +(2.54421 - 0.784786i) q^{87} +(-5.14564 + 13.1109i) q^{88} +(-1.18760 - 0.366325i) q^{89} +(-2.75444 + 3.45395i) q^{90} +(-0.618992 - 0.776191i) q^{92} +(-2.78388 - 7.09322i) q^{93} +(-0.325735 - 4.34663i) q^{94} +(-11.1578 - 1.68176i) q^{95} +(-12.1100 - 11.2365i) q^{96} +13.9109 q^{97} -1.52482 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} + 7 q^{3} + 12 q^{4} + 7 q^{5} - 20 q^{8} - 15 q^{9}+O(q^{10}) $ 48 * q + 8 * q^2 + 7 * q^3 + 12 * q^4 + 7 * q^5 - 20 * q^8 - 15 * q^9	$ 48 q + 8 q^{2} + 7 q^{3} + 12 q^{4} + 7 q^{5} - 20 q^{8} - 15 q^{9} + 7 q^{10} - 3 q^{11} - 63 q^{12} - 14 q^{13} - 12 q^{15} + 18 q^{16} + 14 q^{17} + 2 q^{18} + 21 q^{19} + 14 q^{20} - 20 q^{22} - 27 q^{23} - 77 q^{24} + 17 q^{25} - 21 q^{26} + 7 q^{27} + 12 q^{29} + 11 q^{30} + 35 q^{31} - 60 q^{32} + 7 q^{33} + 70 q^{34} - 12 q^{36} - 6 q^{37} + 35 q^{38} + 35 q^{39} + 105 q^{40} - 42 q^{41} - 30 q^{43} + 13 q^{44} - 35 q^{45} + 69 q^{46} - 42 q^{47} - 84 q^{48} + 40 q^{50} + 53 q^{51} - 7 q^{52} - 31 q^{53} + 70 q^{54} - 7 q^{55} - 12 q^{57} - 47 q^{58} + 35 q^{59} - 91 q^{60} - 14 q^{61} - 28 q^{62} - 32 q^{64} + 35 q^{65} - 35 q^{66} + 11 q^{67} + 77 q^{68} + 70 q^{69} + 19 q^{71} - 124 q^{72} - 35 q^{73} + 13 q^{74} - 119 q^{75} + 119 q^{76} + 28 q^{78} + 15 q^{79} + 70 q^{80} - 125 q^{81} - 98 q^{82} - 26 q^{85} + 9 q^{86} + 35 q^{87} + 49 q^{88} - 14 q^{89} - 182 q^{90} - 38 q^{92} + 46 q^{93} + 14 q^{94} + 128 q^{95} + 98 q^{96} - 16 q^{99}+O(q^{100}) $ 48 * q + 8 * q^2 + 7 * q^3 + 12 * q^4 + 7 * q^5 - 20 * q^8 - 15 * q^9 + 7 * q^10 - 3 * q^11 - 63 * q^12 - 14 * q^13 - 12 * q^15 + 18 * q^16 + 14 * q^17 + 2 * q^18 + 21 * q^19 + 14 * q^20 - 20 * q^22 - 27 * q^23 - 77 * q^24 + 17 * q^25 - 21 * q^26 + 7 * q^27 + 12 * q^29 + 11 * q^30 + 35 * q^31 - 60 * q^32 + 7 * q^33 + 70 * q^34 - 12 * q^36 - 6 * q^37 + 35 * q^38 + 35 * q^39 + 105 * q^40 - 42 * q^41 - 30 * q^43 + 13 * q^44 - 35 * q^45 + 69 * q^46 - 42 * q^47 - 84 * q^48 + 40 * q^50 + 53 * q^51 - 7 * q^52 - 31 * q^53 + 70 * q^54 - 7 * q^55 - 12 * q^57 - 47 * q^58 + 35 * q^59 - 91 * q^60 - 14 * q^61 - 28 * q^62 - 32 * q^64 + 35 * q^65 - 35 * q^66 + 11 * q^67 + 77 * q^68 + 70 * q^69 + 19 * q^71 - 124 * q^72 - 35 * q^73 + 13 * q^74 - 119 * q^75 + 119 * q^76 + 28 * q^78 + 15 * q^79 + 70 * q^80 - 125 * q^81 - 98 * q^82 - 26 * q^85 + 9 * q^86 + 35 * q^87 + 49 * q^88 - 14 * q^89 - 182 * q^90 - 38 * q^92 + 46 * q^93 + 14 * q^94 + 128 * q^95 + 98 * q^96 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{21}\right)$

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 $

$2$	1.92202	+	1.78338i	1.35908	+	1.26104i	0.934647	+	0.355578i	$0.115716\pi$
$2$	1.92202	+	1.78338i	1.35908	+	1.26104i	0.424430	+	0.905461i	$0.360474\pi$
$3$	1.46134	+	0.220261i	0.843703	+	0.127168i	0.556650	−	0.830747i	$-0.312086\pi$
$3$	1.46134	+	0.220261i	0.843703	+	0.127168i	0.287053	+	0.957915i	$0.407325\pi$
$4$	0.364281	+	4.86099i	0.182140	+	2.43049i
$5$	−0.754391	−	1.92216i	−0.337374	−	0.859615i	−0.994394	−	0.105741i	$-0.966278\pi$
$5$	−0.754391	−	1.92216i	−0.337374	−	0.859615i	0.657020	−	0.753873i	$-0.271817\pi$
$6$	2.41591	+	3.02946i	0.986293	+	1.23677i
$7$		0			0
$7$		0			0
$8$	−4.69930	+	5.89274i	−1.66146	+	2.08340i
$9$	−0.779731	−	0.240515i	−0.259910	−	0.0801718i
$10$	1.97797	−	5.03980i	0.625491	−	1.59372i
$11$	1.78567	−	0.550805i	0.538399	−	0.166074i	−0.0136176	−	0.999907i	$-0.504335\pi$
$11$	1.78567	−	0.550805i	0.538399	−	0.166074i	0.552016	+	0.833833i	$0.313859\pi$
$12$	−0.538349	+	7.18377i	−0.155408	+	2.07378i
$13$	−0.677236	+	2.96716i	−0.187831	+	0.822943i	0.789926	+	0.613203i	$0.210119\pi$
$13$	−0.677236	+	2.96716i	−0.187831	+	0.822943i	−0.977757	+	0.209741i	$0.932738\pi$
$14$		0			0
$15$	−0.679042	−	2.97508i	−0.175328	−	0.768162i
$16$	−9.90082	+	1.49231i	−2.47521	+	0.373077i
$17$	−1.16012	−	0.790958i	−0.281371	−	0.191835i	0.414408	−	0.910091i	$-0.363988\pi$
$17$	−1.16012	−	0.790958i	−0.281371	−	0.191835i	−0.695779	+	0.718256i	$0.744941\pi$
$18$	−1.06973	−	1.85283i	−0.252139	−	0.436717i
$19$	2.73229	−	4.73247i	0.626831	−	1.08570i	−0.361353	−	0.932429i	$-0.617685\pi$
$19$	2.73229	−	4.73247i	0.626831	−	1.08570i	0.988184	−	0.153274i	$-0.0489816\pi$
$20$	9.06877	−	4.36729i	2.02784	−	0.976555i
$21$		0			0
$22$	4.41439	+	2.12586i	0.941151	+	0.453234i
$23$	−0.168275	+	0.114728i	−0.0350878	+	0.0239225i	−0.580737	−	0.814091i	$-0.697236\pi$
$23$	−0.168275	+	0.114728i	−0.0350878	+	0.0239225i	0.545649	+	0.838014i	$0.316283\pi$
$24$	−8.16520	+	7.57620i	−1.66671	+	1.54649i
$25$	0.539678	−	0.500748i	0.107936	−	0.100150i
$26$	−6.59324	+	4.49519i	−1.29304	+	0.881580i
$27$	−5.08094	−	2.44685i	−0.977828	−	0.470897i
$28$		0			0
$29$	1.62320	−	0.781691i	0.301420	−	0.145156i	−0.277060	−	0.960853i	$-0.589360\pi$
$29$	1.62320	−	0.781691i	0.301420	−	0.145156i	0.578480	+	0.815696i	$0.303646\pi$
$30$	4.00056	−	6.92917i	0.730398	−	1.26509i
$31$	−2.57807	−	4.46535i	−0.463035	−	0.802000i	0.536075	−	0.844170i	$-0.319906\pi$
$31$	−2.57807	−	4.46535i	−0.463035	−	0.802000i	−0.999110	+	0.0421697i	$0.986573\pi$
$32$	−9.23609	−	6.29706i	−1.63273	−	1.11317i
$33$	2.73078	−	0.411599i	0.475368	−	0.0716502i
$34$	−0.819206	−	3.58918i	−0.140493	−	0.615539i
$35$		0			0
$36$	0.885100	−	3.87788i	0.147517	−	0.646313i
$37$	0.563813	−	7.52356i	0.0926903	−	1.23687i	−0.735931	−	0.677057i	$-0.763255\pi$
$37$	0.563813	−	7.52356i	0.0926903	−	1.23687i	0.828621	−	0.559810i	$-0.189126\pi$
$38$	13.6913	−	4.22321i	2.22102	−	0.685095i
$39$	−1.64322	+	4.18685i	−0.263126	+	0.670433i
$40$	14.8719	+	4.58737i	2.35145	+	0.725327i
$41$	−5.90598	+	7.40586i	−0.922359	+	1.15660i	0.0649659	+	0.997887i	$0.479306\pi$
$41$	−5.90598	+	7.40586i	−0.922359	+	1.15660i	−0.987325	+	0.158714i	$0.949265\pi$
$42$		0			0
$43$	1.60000	+	2.00633i	0.243997	+	0.305963i	0.888717	−	0.458456i	$-0.151597\pi$
$43$	1.60000	+	2.00633i	0.243997	+	0.305963i	−0.644720	+	0.764419i	$0.723026\pi$
$44$	3.32794	+	8.47945i	0.501706	+	1.27833i
$45$	0.125914	+	1.68021i	0.0187702	+	0.250471i
$46$	−0.528033	−	0.0795882i	−0.0778543	−	0.0117346i
$47$	−1.21865	−	1.13074i	−0.177758	−	0.164936i	0.586276	−	0.810112i	$-0.300594\pi$
$47$	−1.21865	−	1.13074i	−0.177758	−	0.164936i	−0.764034	+	0.645176i	$0.776784\pi$
$48$	−14.7971			−2.13578
$49$		0			0
$50$	1.93030			0.272985
$51$	−1.52111	−	1.41138i	−0.212998	−	0.197633i
$52$	−14.6700	−	2.21115i	−2.03437	−	0.306632i
$53$	0.540899	+	7.21780i	0.0742982	+	0.991441i	0.902410	+	0.430878i	$0.141796\pi$
$53$	0.540899	+	7.21780i	0.0742982	+	0.991441i	−0.828112	+	0.560563i	$0.810585\pi$
$54$	−5.40203	−	13.7642i	−0.735123	−	1.87306i
$55$	−2.40583	−	3.01681i	−0.324401	−	0.406786i
$56$		0			0
$57$	5.03517	−	6.31391i	0.666925	−	0.836298i
$58$	4.51388	+	1.39235i	0.592701	+	0.182824i
$59$	−3.04990	+	7.77102i	−0.397063	+	1.01170i	0.582904	+	0.812541i	$0.301916\pi$
$59$	−3.04990	+	7.77102i	−0.397063	+	1.01170i	−0.979967	+	0.199159i	$0.936179\pi$
$60$	14.2145	−	4.38458i	1.83508	−	0.566047i
$61$	−0.493546	+	6.58591i	−0.0631920	+	0.843239i	0.872092	+	0.489342i	$0.162763\pi$
$61$	−0.493546	+	6.58591i	−0.0631920	+	0.843239i	−0.935284	+	0.353898i	$0.884856\pi$
$62$	3.00829	−	13.1802i	0.382053	−	1.67389i
$63$		0			0
$64$	−2.06590	−	9.05131i	−0.258238	−	1.13141i
$65$	6.21425	−	0.936648i	0.770783	−	0.116177i
$66$	5.98266	+	4.07891i	0.736415	+	0.502079i
$67$	−1.78982	−	3.10006i	−0.218661	−	0.378732i	0.735738	−	0.677267i	$-0.236836\pi$
$67$	−1.78982	−	3.10006i	−0.218661	−	0.378732i	−0.954399	+	0.298534i	$0.903502\pi$
$68$	3.42222	−	5.92747i	0.415006	−	0.718811i
$69$	−0.271177	+	0.130592i	−0.0326459	+	0.0157214i
$70$		0			0
$71$	−6.02101	−	2.89956i	−0.714562	−	0.344115i	0.0410295	−	0.999158i	$-0.486936\pi$
$71$	−6.02101	−	2.89956i	−0.714562	−	0.344115i	−0.755592	+	0.655043i	$0.772651\pi$
$72$	5.08149	−	3.46450i	0.598859	−	0.408295i
$73$	0.129576	−	0.120229i	0.0151657	−	0.0140717i	−0.672553	−	0.740049i	$-0.734803\pi$
$73$	0.129576	−	0.120229i	0.0151657	−	0.0140717i	0.687719	+	0.725977i	$0.258612\pi$
$74$	14.5010	−	13.4550i	1.68571	−	1.56411i
$75$	0.898946	−	0.612891i	0.103801	−	0.0707706i
$76$	23.9998	+	11.5577i	2.75296	+	1.32576i
$77$		0			0
$78$	−10.6251	+	5.11676i	−1.20305	+	0.579358i
$79$	−7.82581	+	13.5547i	−0.880473	+	1.52502i	−0.0296560	+	0.999560i	$0.509441\pi$
$79$	−7.82581	+	13.5547i	−0.880473	+	1.52502i	−0.850816	+	0.525463i	$0.823892\pi$
$80$	10.3375	+	17.9052i	1.15577	+	2.00186i
$81$	−4.86342	−	3.31583i	−0.540381	−	0.368425i
$82$	−24.5589	+	3.70166i	−2.71208	+	0.408780i
$83$	2.14456	+	9.39591i	0.235396	+	1.03134i	0.945086	+	0.326822i	$0.105978\pi$
$83$	2.14456	+	9.39591i	0.235396	+	1.03134i	−0.709691	+	0.704514i	$0.751165\pi$
$84$		0			0
$85$	−0.645159	+	2.82663i	−0.0699773	+	0.306591i
$86$	−0.502817	+	6.70962i	−0.0542201	+	0.723517i
$87$	2.54421	−	0.784786i	0.272768	−	0.0841378i
$88$	−5.14564	+	13.1109i	−0.548527	+	1.39762i
$89$	−1.18760	−	0.366325i	−0.125885	−	0.0388304i	0.231173	−	0.972913i	$-0.425744\pi$
$89$	−1.18760	−	0.366325i	−0.125885	−	0.0388304i	−0.357058	+	0.934082i	$0.616220\pi$
$90$	−2.75444	+	3.45395i	−0.290343	+	0.364079i
$91$		0			0
$92$	−0.618992	−	0.776191i	−0.0645344	−	0.0809235i
$93$	−2.78388	−	7.09322i	−0.288675	−	0.735533i
$94$	−0.325735	−	4.34663i	−0.0335970	−	0.448320i
$95$	−11.1578	−	1.68176i	−1.14476	−	0.172545i
$96$	−12.1100	−	11.2365i	−1.23598	−	1.14682i
$97$	13.9109			1.41244			0.706218	−	0.707995i	$-0.250400\pi$
$97$	13.9109			1.41244			0.706218	+	0.707995i	$0.250400\pi$
$98$		0			0
$99$	−1.52482			−0.153250
$100$	2.63072	+	2.44096i	0.263072	+	0.244096i
$101$	1.31834	+	0.198708i	0.131180	+	0.0197722i	0.214304	−	0.976767i	$-0.431252\pi$
$101$	1.31834	+	0.198708i	0.131180	+	0.0197722i	−0.0831241	+	0.996539i	$0.526490\pi$
$102$	−0.406580	−	5.42543i	−0.0402574	−	0.537198i
$103$	2.78726	+	7.10182i	0.274637	+	0.699763i	0.999936	+	0.0113292i	$0.00360626\pi$
$103$	2.78726	+	7.10182i	0.274637	+	0.699763i	−0.725299	+	0.688434i	$0.758298\pi$
$104$	−14.3022	−	17.9344i	−1.40245	−	1.75861i
$105$		0			0
$106$	−11.8324	+	14.8374i	−1.14927	+	1.44114i
$107$	1.54046	+	0.475169i	0.148922	+	0.0459364i	0.368320	−	0.929699i	$-0.379933\pi$
$107$	1.54046	+	0.475169i	0.148922	+	0.0459364i	−0.219398	+	0.975635i	$0.570409\pi$
$108$	10.0432	−	25.5897i	0.966410	−	2.46237i
$109$	9.74415	−	3.00567i	0.933320	−	0.287891i	0.209444	−	0.977821i	$-0.432835\pi$
$109$	9.74415	−	3.00567i	0.933320	−	0.287891i	0.723876	+	0.689930i	$0.242359\pi$
$110$	0.756057	−	10.0889i	0.0720872	−	0.961937i
$111$	2.48107	−	10.8703i	0.235492	−	1.03176i
$112$		0			0
$113$	−1.56953	−	6.87656i	−0.147649	−	0.646893i	−0.993535	−	0.113528i	$-0.963785\pi$
$113$	−1.56953	−	6.87656i	−0.147649	−	0.646893i	0.845886	−	0.533364i	$-0.179072\pi$
$114$	20.9378	−	3.15587i	1.96101	−	0.295574i
$115$	0.347471	+	0.236902i	0.0324018	+	0.0220912i
$116$	4.39109	+	7.60559i	0.407702	+	0.706161i
$117$	1.24171	−	2.15070i	0.114796	−	0.198833i
$118$	−19.7206	+	9.49696i	−1.81543	+	0.874266i
$119$		0			0
$120$	20.7224	+	9.97938i	1.89169	+	0.910989i
$121$	−6.20341	+	4.22941i	−0.563946	+	0.384492i
$122$	−12.6938	+	11.7781i	−1.14924	+	1.06634i
$123$	−10.2618	+	9.52159i	−0.925279	+	0.858533i
$124$	20.7669	−	14.1586i	1.86492	−	1.27148i
$125$	−10.6717	−	5.13921i	−0.954504	−	0.459665i
$126$		0			0
$127$	−0.0652974	+	0.0314456i	−0.00579421	+	0.00279034i	−0.436779	−	0.899569i	$-0.643881\pi$
$127$	−0.0652974	+	0.0314456i	−0.00579421	+	0.00279034i	0.430984	+	0.902359i	$0.358166\pi$
$128$	0.992721	−	1.71944i	0.0877450	−	0.151979i
$129$	1.89622	+	3.28434i	0.166952	+	0.289170i
$130$	13.6143	+	9.28211i	1.19406	+	0.814095i
$131$	18.4040	−	2.77395i	1.60796	−	0.242361i	0.717213	−	0.696854i	$-0.245418\pi$
$131$	18.4040	−	2.77395i	1.60796	−	0.242361i	0.890750	+	0.454493i	$0.150179\pi$
$132$	2.99555	+	13.1243i	0.260729	+	1.14233i
$133$		0			0
$134$	2.08850	−	9.15032i	0.180419	−	0.790467i
$135$	−0.870218	+	11.6123i	−0.0748964	+	0.999423i
$136$	10.1127	−	3.11935i	0.867155	−	0.267482i
$137$	2.91051	−	7.41586i	0.248662	−	0.633580i	−0.750980	−	0.660324i	$-0.770419\pi$
$137$	2.91051	−	7.41586i	0.248662	−	0.633580i	0.999642	+	0.0267444i	$0.00851402\pi$
$138$	−0.754104	−	0.232610i	−0.0641936	−	0.0198011i
$139$	11.8104	−	14.8098i	1.00175	−	1.25615i	0.0352743	−	0.999378i	$-0.488770\pi$
$139$	11.8104	−	14.8098i	1.00175	−	1.25615i	0.966472	−	0.256772i	$-0.0826590\pi$
$140$		0			0
$141$	−1.53180	−	1.92081i	−0.129001	−	0.161762i
$142$	−6.40151	−	16.3108i	−0.537202	−	1.36877i
$143$	0.425012	+	5.67139i	0.0355413	+	0.474266i
$144$	8.07891	+	1.21770i	0.673242	+	0.101475i
$145$	−2.72706	−	2.53034i	−0.226470	−	0.210133i
$146$	0.463462			0.0383564
$147$		0			0
$148$	36.7773			3.02308
$149$	−17.3257	−	16.0759i	−1.41937	−	1.31699i	−0.880045	−	0.474890i	$-0.842488\pi$
$149$	−17.3257	−	16.0759i	−1.41937	−	1.31699i	−0.539328	−	0.842096i	$-0.681322\pi$
$150$	2.82081	+	0.425169i	0.230318	+	0.0347149i
$151$	−0.664285	−	8.86426i	−0.0540587	−	0.721364i	−0.956720	−	0.291011i	$-0.906008\pi$
$151$	−0.664285	−	8.86426i	−0.0540587	−	0.721364i	0.902661	−	0.430352i	$-0.141611\pi$
$152$	15.0473	+	38.3400i	1.22050	+	3.10979i
$153$	0.714346	+	0.895761i	0.0577514	+	0.0724180i
$154$		0			0
$155$	−6.63823	+	8.32408i	−0.533195	+	0.668606i
$156$	−20.9508	−	6.46248i	−1.67741	−	0.517412i
$157$	−0.577998	+	1.47272i	−0.0461293	+	0.117535i	−0.952081	−	0.305844i	$-0.901061\pi$
$157$	−0.577998	+	1.47272i	−0.0461293	+	0.117535i	0.905952	+	0.423380i	$0.139156\pi$
$158$	−39.2146	+	12.0961i	−3.11974	+	0.962313i
$159$	−0.799364	+	10.6668i	−0.0633937	+	0.845929i
$160$	−5.13631	+	22.5037i	−0.406061	+	1.77907i
$161$		0			0
$162$	−3.43425	−	15.0464i	−0.269820	−	1.18216i
$163$	15.5146	−	2.33845i	1.21520	−	0.183162i	0.490013	−	0.871715i	$-0.336992\pi$
$163$	15.5146	−	2.33845i	1.21520	−	0.183162i	0.725185	+	0.688554i	$0.241754\pi$
$164$	−38.1512	−	26.0111i	−2.97911	−	2.03112i
$165$	−2.85123	−	4.93848i	−0.221968	−	0.384460i
$166$	−12.6346	+	21.8837i	−0.980633	+	1.69851i
$167$	−6.00479	+	2.89175i	−0.464664	+	0.223771i	−0.651542	−	0.758613i	$-0.725878\pi$
$167$	−6.00479	+	2.89175i	−0.464664	+	0.223771i	0.186877	+	0.982383i	$0.440163\pi$
$168$		0			0
$169$	3.36718	+	1.62155i	0.259014	+	0.124735i
$170$	−6.28096	+	4.28228i	−0.481728	+	0.328436i
$171$	−3.26869	+	3.03290i	−0.249963	+	0.231931i
$172$	−9.16991	+	8.50843i	−0.699199	+	0.648762i
$173$	−17.4189	+	11.8760i	−1.32434	+	0.902917i	−0.999087	−	0.0427122i	$-0.986400\pi$
$173$	−17.4189	+	11.8760i	−1.32434	+	0.902917i	−0.325248	+	0.945629i	$0.605448\pi$
$174$	6.28961	+	3.02892i	0.476814	+	0.229622i
$175$		0			0
$176$	−16.8576	+	8.11819i	−1.27069	+	0.611932i
$177$	−6.16858	+	10.6843i	−0.463659	+	0.803080i
$178$	−1.62929	−	2.82202i	−0.122121	−	0.211519i
$179$	−16.5524	−	11.2852i	−1.23718	−	0.843498i	−0.245153	−	0.969484i	$-0.578838\pi$
$179$	−16.5524	−	11.2852i	−1.23718	−	0.843498i	−0.992032	+	0.125986i	$0.959790\pi$
$180$	−8.12160	+	1.22413i	−0.605349	+	0.0912416i
$181$	1.67180	+	7.32462i	0.124264	+	0.544435i	0.998285	+	0.0585468i	$0.0186467\pi$
$181$	1.67180	+	7.32462i	0.124264	+	0.544435i	−0.874021	+	0.485888i	$0.838496\pi$
$182$		0			0
$183$	−2.17185	+	9.51551i	−0.160548	+	0.703407i
$184$	0.114714	−	1.53075i	0.00845680	−	0.112848i
$185$	−14.8868	+	4.59197i	−1.09450	+	0.337608i
$186$	7.29920	−	18.5981i	0.535204	−	1.36368i
$187$	−2.50725	−	0.773386i	−0.183349	−	0.0565556i
$188$	5.05259	−	6.33575i	0.368498	−	0.462082i
$189$		0			0
$190$	−18.4463	−	23.1309i	−1.33823	−	1.67809i
$191$	−1.69952	−	4.33031i	−0.122973	−	0.313330i	0.856109	−	0.516795i	$-0.172875\pi$
$191$	−1.69952	−	4.33031i	−0.122973	−	0.313330i	−0.979082	+	0.203465i	$0.934780\pi$
$192$	−1.02533	−	13.6820i	−0.0739966	−	0.987417i
$193$	21.7036	+	3.27129i	1.56226	+	0.235472i	0.872516	−	0.488585i	$-0.162487\pi$
$193$	21.7036	+	3.27129i	1.56226	+	0.235472i	0.689740	+	0.724057i	$0.257725\pi$
$194$	26.7370	+	24.8083i	1.91961	+	1.78114i
$195$	9.28742			0.665086
$196$		0			0
$197$	−14.4765			−1.03141			−0.515705	−	0.856766i	$-0.672470\pi$
$197$	−14.4765			−1.03141			−0.515705	+	0.856766i	$0.672470\pi$
$198$	−2.93074	−	2.71933i	−0.208278	−	0.193254i
$199$	6.36790	+	0.959806i	0.451408	+	0.0680389i	0.370812	−	0.928708i	$-0.379079\pi$
$199$	6.36790	+	0.959806i	0.451408	+	0.0680389i	0.0805964	+	0.996747i	$0.474318\pi$
$200$	0.414667	+	5.53335i	0.0293214	+	0.391267i
$201$	−1.93271	−	4.92445i	−0.136323	−	0.347344i
$202$	2.17951	+	2.73302i	0.153350	+	0.192295i
$203$		0			0
$204$	6.30661	−	7.90824i	0.441551	−	0.553687i
$205$	18.6906	+	5.76530i	1.30541	+	0.402666i
$206$	−7.30805	+	18.6206i	−0.509176	+	1.29736i
$207$	0.158803	−	0.0489844i	0.0110376	−	0.00340465i
$208$	2.27727	−	30.3880i	0.157900	−	2.10703i
$209$	2.27229	−	9.95557i	0.157178	−	0.688642i
$210$		0			0
$211$	2.96277	+	12.9808i	0.203966	+	0.893632i	0.968493	+	0.249041i	$0.0801154\pi$
$211$	2.96277	+	12.9808i	0.203966	+	0.893632i	−0.764527	+	0.644591i	$0.777028\pi$
$212$	−34.8886	+	5.25861i	−2.39616	+	0.361163i
$213$	−8.16005	−	5.56343i	−0.559118	−	0.381200i
$214$	2.11340	+	3.66051i	0.144469	+	0.250227i
$215$	2.64946	−	4.58900i	0.180692	−	0.312967i
$216$	38.2956	−	18.4422i	2.60568	−	1.25483i
$217$		0			0
$218$	24.0887	+	11.6005i	1.63150	+	0.785687i
$219$	0.215836	−	0.147154i	0.0145848	−	0.00994377i
$220$	13.7883	−	12.7936i	0.929605	−	0.862548i
$221$	3.13258	−	2.90661i	0.210720	−	0.195520i
$222$	24.1545	−	16.4682i	1.62114	−	1.10528i
$223$	−14.7151	−	7.08644i	−0.985399	−	0.474543i	−0.129440	−	0.991587i	$-0.541318\pi$
$223$	−14.7151	−	7.08644i	−0.985399	−	0.474543i	−0.855959	+	0.517044i	$0.827032\pi$
$224$		0			0
$225$	−0.541241	+	0.260648i	−0.0360828	+	0.0173765i
$226$	9.24684	−	16.0160i	0.615090	−	1.06537i
$227$	7.36693	+	12.7599i	0.488960	+	0.846904i	0.999919	−	0.0127013i	$-0.00404304\pi$
$227$	7.36693	+	12.7599i	0.488960	+	0.846904i	−0.510959	+	0.859605i	$0.670710\pi$
$228$	32.5260	+	22.1759i	2.15409	+	1.46863i
$229$	−6.56085	+	0.988890i	−0.433553	+	0.0653477i	−0.362193	−	0.932103i	$-0.617972\pi$
$229$	−6.56085	+	0.988890i	−0.433553	+	0.0653477i	−0.0713600	+	0.997451i	$0.522734\pi$
$230$	0.245362	+	1.07500i	0.0161787	+	0.0708836i
$231$		0			0
$232$	−3.02160	+	13.2385i	−0.198378	+	0.869149i
$233$	−0.186659	+	2.49079i	−0.0122285	+	0.163177i	0.987746	+	0.156068i	$0.0498820\pi$
$233$	−0.186659	+	2.49079i	−0.0122285	+	0.163177i	−0.999975	+	0.00710913i	$0.997737\pi$
$234$	6.22212	−	1.91927i	0.406753	−	0.125467i
$235$	−1.25413	+	3.19546i	−0.0818101	+	0.208449i
$236$	−38.8858	−	11.9947i	−2.53125	−	0.780788i
$237$	−14.4217	+	18.0842i	−0.936791	+	1.17470i
$238$		0			0
$239$	8.40358	+	10.5378i	0.543583	+	0.681631i	0.975428	−	0.220316i	$-0.0707090\pi$
$239$	8.40358	+	10.5378i	0.543583	+	0.681631i	−0.431846	+	0.901947i	$0.642138\pi$
$240$	11.1628	+	28.4424i	0.720557	+	1.83595i
$241$	−1.81042	−	24.1583i	−0.116619	−	1.55617i	−0.682005	−	0.731348i	$-0.738892\pi$
$241$	−1.81042	−	24.1583i	−0.116619	−	1.55617i	0.565386	−	0.824827i	$-0.308727\pi$
$242$	−19.4657	−	2.93399i	−1.25131	−	0.188604i
$243$	6.02521	+	5.59058i	0.386518	+	0.358636i
$244$	−32.1938			−2.06100
$245$		0			0
$246$	−36.7041			−2.34017
$247$	12.1916	+	11.3122i	0.775733	+	0.719775i
$248$	38.4283	+	5.79213i	2.44020	+	0.367801i
$249$	1.06436	+	14.2029i	0.0674513	+	0.900075i
$250$	−11.3461	−	28.9093i	−0.717589	−	1.82839i
$251$	5.00516	+	6.27627i	0.315923	+	0.396155i	0.914285	−	0.405071i	$-0.132753\pi$
$251$	5.00516	+	6.27627i	0.315923	+	0.396155i	−0.598362	+	0.801226i	$0.704182\pi$
$252$		0			0
$253$	−0.237291	+	0.297553i	−0.0149183	+	0.0187070i
$254$	−0.181583	−	0.0560108i	−0.0113935	−	0.00351443i
$255$	−1.56539	+	3.98855i	−0.0980285	+	0.249773i
$256$	−12.7688	+	3.93865i	−0.798049	+	0.246166i
$257$	1.32394	−	17.6667i	0.0825849	−	1.10202i	−0.789854	−	0.613295i	$-0.789844\pi$
$257$	1.32394	−	17.6667i	0.0825849	−	1.10202i	0.872439	−	0.488724i	$-0.162537\pi$
$258$	−2.21265	+	9.69426i	−0.137754	+	0.603538i
$259$		0			0
$260$	6.81677	+	29.8662i	0.422758	+	1.85222i
$261$	−1.45367	+	0.219105i	−0.0899797	+	0.0135623i
$262$	40.3199	+	27.4897i	2.49097	+	1.69832i
$263$	9.69503	+	16.7923i	0.597821	+	1.03546i	0.993142	+	0.116913i	$0.0373000\pi$
$263$	9.69503	+	16.7923i	0.597821	+	1.03546i	−0.395321	+	0.918543i	$0.629367\pi$
$264$	−10.4073	+	18.0260i	−0.640526	+	1.10942i
$265$	13.4657	−	6.48473i	0.827191	−	0.398354i
$266$		0			0
$267$	−1.65479	−	0.796905i	−0.101272	−	0.0487698i
$268$	14.4173	−	9.82958i	0.880680	−	0.600437i
$269$	20.9757	−	19.4626i	1.27891	−	1.18665i	0.306891	−	0.951745i	$-0.400711\pi$
$269$	20.9757	−	19.4626i	1.27891	−	1.18665i	0.972017	−	0.234909i	$-0.0754793\pi$
$270$	−22.3816	+	20.7671i	−1.36210	+	1.26385i
$271$	−22.1894	+	15.1285i	−1.34791	+	0.918990i	−0.999829	−	0.0184744i	$-0.994119\pi$
$271$	−22.1894	+	15.1285i	−1.34791	+	0.918990i	−0.348081	+	0.937464i	$0.613167\pi$
$272$	12.6665	+	6.09987i	0.768020	+	0.369859i
$273$		0			0
$274$	18.8194	−	9.06293i	1.13692	−	0.547512i
$275$	0.687871	−	1.19143i	0.0414802	−	0.0718457i
$276$	−0.733590	−	1.27062i	−0.0441569	−	0.0764821i
$277$	9.03698	+	6.16131i	0.542980	+	0.370197i	0.803531	−	0.595263i	$-0.202952\pi$
$277$	9.03698	+	6.16131i	0.542980	+	0.370197i	−0.260551	+	0.965460i	$0.583904\pi$
$278$	49.1114	−	7.40235i	2.94550	−	0.443963i
$279$	0.936218	+	4.10184i	0.0560499	+	0.245571i
$280$		0			0
$281$	5.11979	−	22.4313i	0.305421	−	1.33814i	−0.556396	−	0.830917i	$-0.687816\pi$
$281$	5.11979	−	22.4313i	0.305421	−	1.33814i	0.861817	−	0.507219i	$-0.169327\pi$
$282$	0.481385	−	6.42363i	0.0286660	−	0.382522i
$283$	−1.25063	+	0.385767i	−0.0743419	+	0.0229315i	−0.331703	−	0.943384i	$-0.607623\pi$
$283$	−1.25063	+	0.385767i	−0.0743419	+	0.0229315i	0.257361	+	0.966315i	$0.417147\pi$
$284$	11.9014	−	30.3243i	0.706219	−	1.79942i
$285$	−15.9348	−	4.91524i	−0.943897	−	0.291154i
$286$	−9.29735	+	11.6585i	−0.549764	+	0.689382i
$287$		0			0
$288$	5.68713	+	7.13144i	0.335117	+	0.420224i
$289$	−5.49053	−	13.9896i	−0.322972	−	0.822920i
$290$	−0.728919	−	9.72675i	−0.0428036	−	0.571174i
$291$	20.3285	+	3.06402i	1.19168	+	0.179616i
$292$	0.631634	+	0.586070i	0.0369636	+	0.0342972i
$293$	4.00258			0.233833			0.116917	−	0.993142i	$-0.462699\pi$
$293$	4.00258			0.233833			0.116917	+	0.993142i	$0.462699\pi$
$294$		0			0
$295$	17.2379			1.00363
$296$	41.6849	+	38.6779i	2.42288	+	2.24811i
$297$	−10.4206	−	1.57065i	−0.604665	−	0.0911386i
$298$	−4.63100	−	61.7964i	−0.268267	−	3.57977i
$299$	−0.226455	−	0.576999i	−0.0130962	−	0.0333687i
$300$	3.30672	+	4.14650i	0.190914	+	0.239398i
$301$		0			0
$302$	14.5316	−	18.2220i	0.836198	−	1.04856i
$303$	1.88277	+	0.580758i	0.108162	+	0.0333637i
$304$	−19.9896	+	50.9328i	−1.14648	+	2.92119i
$305$	13.0315	−	4.01968i	0.746180	−	0.230166i
$306$	−0.224491	+	2.99562i	−0.0128333	+	0.171248i
$307$	3.97135	−	17.3996i	0.226657	−	0.993049i	−0.725687	−	0.688025i	$-0.758478\pi$
$307$	3.97135	−	17.3996i	0.226657	−	0.993049i	0.952344	−	0.305025i	$-0.0986647\pi$
$308$		0			0
$309$	2.50887	+	10.9921i	0.142724	+	0.625317i
$310$	−27.6038	+	4.16061i	−1.56779	+	0.236307i
$311$	4.71108	+	3.21196i	0.267141	+	0.182134i	0.689481	−	0.724304i	$-0.257839\pi$
$311$	4.71108	+	3.21196i	0.267141	+	0.182134i	−0.422340	+	0.906438i	$0.638791\pi$
$312$	−16.9501	−	29.3584i	−0.959608	−	1.66209i
$313$	10.7377	−	18.5983i	0.606933	−	1.05124i	−0.384810	−	0.922996i	$-0.625733\pi$
$313$	10.7377	−	18.5983i	0.606933	−	1.05124i	0.991743	−	0.128242i	$-0.0409335\pi$
$314$	−3.73734	+	1.79981i	−0.210910	+	0.101569i
$315$		0			0
$316$	−68.7400	−	33.1034i	−3.86693	−	1.86221i
$317$	5.10976	−	3.48378i	0.286993	−	0.195668i	−0.411263	−	0.911517i	$-0.634912\pi$
$317$	5.10976	−	3.48378i	0.286993	−	0.195668i	0.698256	+	0.715848i	$0.253960\pi$
$318$	−20.5593	+	19.0762i	−1.15291	+	1.06974i
$319$	2.46793	−	2.28990i	0.138178	−	0.128210i
$320$	−15.8395	+	10.7992i	−0.885457	+	0.603695i
$321$	2.14647	+	1.03369i	0.119804	+	0.0576947i
$322$		0			0
$323$	−6.91298	+	3.32911i	−0.384648	+	0.185237i
$324$	14.3465	−	24.8489i	0.797030	−	1.38050i
$325$	1.12031	+	1.94044i	0.0621437	+	0.107636i
$326$	33.9898	+	23.1739i	1.88252	+	1.28348i
$327$	14.9015	−	2.24604i	0.824055	−	0.124206i
$328$	−15.8868	−	69.6048i	−0.877204	−	3.84328i
$329$		0			0
$330$	3.32704	−	14.5767i	0.183147	−	0.802421i
$331$	−0.0879555	+	1.17368i	−0.00483447	+	0.0645115i	−0.999099	−	0.0424352i	$-0.986488\pi$
$331$	−0.0879555	+	1.17368i	−0.00483447	+	0.0645115i	0.994265	+	0.106947i	$0.0341074\pi$
$332$	−44.8922	+	13.8474i	−2.46378	+	0.759975i
$333$	−2.24915	+	5.73075i	−0.123253	+	0.314043i
$334$	−16.6984	−	5.15079i	−0.913698	−	0.281839i
$335$	−4.60858	+	5.77897i	−0.251793	+	0.315739i
$336$		0			0
$337$	−3.39407	−	4.25603i	−0.184887	−	0.231841i	0.680747	−	0.732519i	$-0.261655\pi$
$337$	−3.39407	−	4.25603i	−0.184887	−	0.231841i	−0.865634	+	0.500678i	$0.833084\pi$
$338$	3.57997	+	9.12162i	0.194725	+	0.496151i
$339$	−0.778973	−	10.3947i	−0.0423080	−	0.564561i
$340$	−13.9752	−	2.10643i	−0.757913	−	0.114237i
$341$	−7.06311	−	6.55361i	−0.382489	−	0.354898i
$342$	−11.6913			−0.632193
$343$		0			0
$344$	−19.3417			−1.04283
$345$	0.455592	+	0.422727i	0.0245282	+	0.0227589i
$346$	−54.6590	−	8.23852i	−2.93849	−	0.442906i
$347$	−0.276806	−	3.69373i	−0.0148597	−	0.198290i	−0.999693	−	0.0247850i	$-0.992110\pi$
$347$	−0.276806	−	3.69373i	−0.0148597	−	0.198290i	0.984833	−	0.173505i	$-0.0555092\pi$
$348$	4.74164	+	12.0815i	0.254179	+	0.647636i
$349$	15.1210	+	18.9611i	0.809406	+	1.01496i	0.999449	+	0.0331876i	$0.0105659\pi$
$349$	15.1210	+	18.9611i	0.809406	+	1.01496i	−0.190043	+	0.981776i	$0.560863\pi$
$350$		0			0
$351$	10.7012	−	13.4189i	0.571188	−	0.716247i
$352$	−19.9610	−	6.15716i	−1.06393	−	0.328178i
$353$	10.9523	−	27.9059i	0.582929	−	1.48528i	−0.269794	−	0.962918i	$-0.586956\pi$
$353$	10.9523	−	27.9059i	0.582929	−	1.48528i	0.852724	−	0.522362i	$-0.174949\pi$
$354$	−30.9103	+	9.53456i	−1.64286	+	0.506756i
$355$	−1.03122	+	13.7607i	−0.0547317	+	0.730344i
$356$	1.34808	−	5.90634i	0.0714483	−	0.313035i
$357$		0			0
$358$	−11.6883	−	51.2097i	−0.617745	−	2.70652i
$359$	−9.69681	+	1.46156i	−0.511778	+	0.0771381i	−0.399854	−	0.916579i	$-0.630939\pi$
$359$	−9.69681	+	1.46156i	−0.511778	+	0.0771381i	−0.111924	+	0.993717i	$0.535701\pi$
$360$	−10.4927	−	7.15383i	−0.553016	−	0.377040i
$361$	−5.43084	−	9.40650i	−0.285834	−	0.495079i
$362$	−9.84934	+	17.0596i	−0.517670	+	0.896630i
$363$	−9.99683	+	4.81422i	−0.524698	+	0.252681i
$364$		0			0
$365$	−0.328850	−	0.158366i	−0.0172128	−	0.00828925i
$366$	−21.1441	+	14.4158i	−1.10522	+	0.753527i
$367$	11.8433	−	10.9889i	0.618213	−	0.573618i	−0.307640	−	0.951503i	$-0.599539\pi$
$367$	11.8433	−	10.9889i	0.618213	−	0.573618i	0.925852	+	0.377885i	$0.123349\pi$
$368$	1.49485	−	1.38702i	0.0779247	−	0.0723036i
$369$	6.38630	−	4.35410i	0.332457	−	0.226666i
$370$	−36.8020	−	17.7229i	−1.91325	−	0.921371i
$371$		0			0
$372$	33.4659	−	16.1163i	1.73513	−	0.835594i
$373$	9.46448	−	16.3930i	0.490052	−	0.848795i	−0.509882	−	0.860244i	$-0.670311\pi$
$373$	9.46448	−	16.3930i	0.490052	−	0.848795i	0.999934	+	0.0114488i	$0.00364435\pi$
$374$	−3.43977	−	5.95785i	−0.177866	−	0.308073i
$375$	−14.4629	−	9.86066i	−0.746863	−	0.509202i
$376$	12.3900	−	1.86749i	0.638964	−	0.0963084i
$377$	1.22012	+	5.34568i	0.0628392	+	0.275317i
$378$		0			0
$379$	−4.39197	+	19.2425i	−0.225600	+	0.988420i	0.727581	+	0.686021i	$0.240644\pi$
$379$	−4.39197	+	19.2425i	−0.225600	+	0.988420i	−0.953182	+	0.302398i	$0.902213\pi$
$380$	4.11047	−	54.8504i	0.210863	−	2.81377i
$381$	−0.102348	+	0.0315701i	−0.00524343	+	0.00161738i
$382$	4.45606	−	11.3539i	0.227992	−	0.580914i
$383$	−9.89115	−	3.05102i	−0.505414	−	0.155900i	0.0315540	−	0.999502i	$-0.489954\pi$
$383$	−9.89115	−	3.05102i	−0.505414	−	0.155900i	−0.536968	+	0.843602i	$0.680431\pi$
$384$	1.82943	−	2.29403i	0.0933575	−	0.117067i
$385$		0			0
$386$	35.8808	+	44.9931i	1.82629	+	2.29009i
$387$	−0.765014	−	1.94922i	−0.0388878	−	0.0990846i
$388$	5.06746	+	67.6206i	0.257261	+	3.43291i
$389$	−18.6471	−	2.81060i	−0.945446	−	0.142503i	−0.341815	−	0.939767i	$-0.611042\pi$
$389$	−18.6471	−	2.81060i	−0.945446	−	0.142503i	−0.603631	+	0.797264i	$0.706280\pi$
$390$	17.8506	+	16.5630i	0.903903	+	0.838699i
$391$	0.285965			0.0144619
$392$		0			0
$393$	27.5054			1.38746
$394$	−27.8243	−	25.8171i	−1.40177	−	1.30065i
$395$	31.9580	+	4.81689i	1.60798	+	0.242364i
$396$	−0.555461	−	7.41212i	−0.0279130	−	0.372473i
$397$	−0.123550	−	0.314801i	−0.00620082	−	0.0157994i	0.927740	−	0.373228i	$-0.121749\pi$
$397$	−0.123550	−	0.314801i	−0.00620082	−	0.0157994i	−0.933941	+	0.357428i	$0.883654\pi$
$398$	10.5276	+	13.2011i	0.527699	+	0.661713i
$399$		0			0
$400$	−4.59599	+	5.76319i	−0.229799	+	0.288159i
$401$	22.2440	+	6.86136i	1.11081	+	0.342640i	0.795260	−	0.606268i	$-0.207334\pi$
$401$	22.2440	+	6.86136i	1.11081	+	0.342640i	0.315552	+	0.948908i	$0.397810\pi$
$402$	5.06746	−	12.9117i	0.252742	−	0.643975i
$403$	14.9954	−	4.62546i	0.746973	−	0.230411i
$404$	−0.485671	+	6.48083i	−0.0241630	+	0.322433i
$405$	−2.70462	+	11.8497i	−0.134393	+	0.588816i
$406$		0			0
$407$	−3.13724	−	13.7451i	−0.155507	−	0.681321i
$408$	15.4651	−	2.33099i	0.765636	−	0.115401i
$409$	−11.2618	−	7.67818i	−0.556861	−	0.379662i	0.251941	−	0.967743i	$-0.418931\pi$
$409$	−11.2618	−	7.67818i	−0.556861	−	0.379662i	−0.808802	+	0.588081i	$0.799884\pi$
$410$	25.6422	+	44.4135i	1.26638	+	2.19343i
$411$	5.88666	−	10.1960i	0.290368	−	0.502931i
$412$	−33.5065	+	16.1359i	−1.65075	+	0.794958i
$413$		0			0
$414$	0.392582	+	0.189057i	0.0192943	+	0.00929167i
$415$	16.4426	−	11.2104i	0.807135	−	0.550295i
$416$	24.9394	−	23.1404i	1.22276	−	1.13455i
$417$	20.5210	−	19.0407i	1.00492	−	0.932427i
$418$	22.1220	−	15.0825i	1.08202	−	0.737709i
$419$	7.73651	+	3.72571i	0.377953	+	0.182013i	0.613209	−	0.789921i	$-0.289878\pi$
$419$	7.73651	+	3.72571i	0.377953	+	0.182013i	−0.235256	+	0.971934i	$0.575593\pi$
$420$		0			0
$421$	5.75293	−	2.77046i	0.280381	−	0.135024i	−0.288409	−	0.957507i	$-0.593126\pi$
$421$	5.75293	−	2.77046i	0.280381	−	0.135024i	0.568789	+	0.822483i	$0.307412\pi$
$422$	−17.4551	+	30.2331i	−0.849700	+	1.47172i
$423$	0.678259	+	1.17478i	0.0329781	+	0.0571197i
$424$	−45.0745	−	30.7313i	−2.18901	−	1.49244i
$425$	−1.02216	+	0.154066i	−0.0495822	+	0.00747331i
$426$	−5.76212	−	25.2455i	−0.279176	−	1.22315i
$427$		0			0
$428$	−1.74863	+	7.66126i	−0.0845233	+	0.370321i
$429$	−0.628101	+	8.38142i	−0.0303250	+	0.404659i
$430$	13.2763	−	4.09518i	0.640238	−	0.197487i
$431$	−14.1340	+	36.0129i	−0.680812	+	1.73468i	−0.00240092	+	0.999997i	$0.500764\pi$
$431$	−14.1340	+	36.0129i	−0.680812	+	1.73468i	−0.678411	+	0.734683i	$0.737331\pi$
$432$	53.9570	+	16.6435i	2.59601	+	0.800762i
$433$	0.316460	−	0.396828i	0.0152081	−	0.0190703i	−0.774169	−	0.632979i	$-0.781832\pi$
$433$	0.316460	−	0.396828i	0.0152081	−	0.0190703i	0.789377	+	0.613908i	$0.210404\pi$
$434$		0			0
$435$	−3.42781	−	4.29834i	−0.164351	−	0.206090i
$436$	18.1601	+	46.2713i	0.869713	+	2.21599i
$437$	0.0831702	+	1.10983i	0.00397857	+	0.0530903i
$438$	0.677274	+	0.102083i	0.0323614	+	0.00487770i
$439$	4.26419	+	3.95659i	0.203519	+	0.188838i	0.775347	−	0.631536i	$-0.217575\pi$
$439$	4.26419	+	3.95659i	0.203519	+	0.188838i	−0.571828	+	0.820374i	$0.693766\pi$
$440$	29.0830			1.38648
$441$		0			0
$442$	11.2045			0.532942
$443$	4.78541	+	4.44021i	0.227362	+	0.210961i	0.785625	−	0.618703i	$-0.212342\pi$
$443$	4.78541	+	4.44021i	0.227362	+	0.210961i	−0.558263	+	0.829664i	$0.688532\pi$
$444$	53.7440	+	8.10061i	2.55058	+	0.384438i
$445$	0.191778	+	2.55910i	0.00909115	+	0.121313i
$446$	−15.6451	−	39.8630i	−0.740815	−	1.88757i
$447$	−21.7777	−	27.3084i	−1.03005	−	1.29164i
$448$		0			0
$449$	−10.3649	+	12.9972i	−0.489152	+	0.613377i	−0.963744	−	0.266829i	$-0.914024\pi$
$449$	−10.3649	+	12.9972i	−0.489152	+	0.613377i	0.474592	+	0.880206i	$0.342596\pi$
$450$	−1.50511	−	0.464266i	−0.0709517	−	0.0218857i
$451$	−6.46692	+	16.4774i	−0.304515	+	0.775893i
$452$	32.8551	−	10.1345i	1.54538	−	0.476685i
$453$	0.981708	−	13.1000i	0.0461247	−	0.615491i
$454$	−8.59630	+	37.6628i	−0.403444	+	1.76760i
$455$		0			0
$456$	13.5444	+	59.3420i	0.634275	+	2.77894i
$457$	39.8191	−	6.00177i	1.86266	−	0.280751i	0.881247	−	0.472656i	$-0.156705\pi$
$457$	39.8191	−	6.00177i	1.86266	−	0.280751i	0.981413	+	0.191905i	$0.0614666\pi$
$458$	−14.3737	−	9.79981i	−0.671638	−	0.457915i
$459$	3.95915	+	6.85746i	0.184798	+	0.320079i
$460$	−1.02500	+	1.77535i	−0.0477908	+	0.0827762i
$461$	4.28753	−	2.06477i	0.199690	−	0.0961657i	−0.331366	−	0.943502i	$-0.607510\pi$
$461$	4.28753	−	2.06477i	0.199690	−	0.0961657i	0.531056	+	0.847337i	$0.321795\pi$
$462$		0			0
$463$	21.6387	+	10.4207i	1.00564	+	0.484289i	0.862848	−	0.505464i	$-0.168679\pi$
$463$	21.6387	+	10.4207i	1.00564	+	0.484289i	0.142789	+	0.989753i	$0.454393\pi$
$464$	−14.9045	+	10.1617i	−0.691923	+	0.471745i
$465$	−11.5341	+	10.7021i	−0.534883	+	0.496299i
$466$	−4.80079	+	4.45448i	−0.222392	+	0.206350i
$467$	−16.0144	+	10.9184i	−0.741059	+	0.505245i	−0.874028	−	0.485875i	$-0.838501\pi$
$467$	−16.0144	+	10.9184i	−0.741059	+	0.505245i	0.132970	+	0.991120i	$0.457549\pi$
$468$	10.9069	+	5.25248i	0.504171	+	0.242796i
$469$		0			0
$470$	−8.10917	+	3.90517i	−0.374048	+	0.180132i
$471$	−1.16903	+	2.02482i	−0.0538661	+	0.0932988i
$472$	−31.4602	−	54.4906i	−1.44807	−	2.50813i
$473$	3.96216	+	2.70135i	0.182180	+	0.124208i
$474$	−59.9699	+	9.03901i	−2.75451	+	0.415176i
$475$	−0.895217	−	3.92220i	−0.0410754	−	0.179963i
$476$		0			0
$477$	1.31423	−	5.75804i	0.0601747	−	0.263642i
$478$	−2.64092	+	35.2406i	−0.120793	+	1.61187i
$479$	−2.15347	+	0.664257i	−0.0983945	+	0.0303507i	−0.343562	−	0.939130i	$-0.611633\pi$
$479$	−2.15347	+	0.664257i	−0.0983945	+	0.0303507i	0.245167	+	0.969481i	$0.421157\pi$
$480$	−12.4626	+	31.7541i	−0.568835	+	1.44937i
$481$	21.9418	+	6.76815i	1.00046	+	0.308601i
$482$	39.6038	−	49.6615i	1.80390	−	2.26202i
$483$		0			0
$484$	−22.8189	−	28.6140i	−1.03722	−	1.30064i
$485$	−10.4942	−	26.7389i	−0.476519	−	1.21415i
$486$	1.61049	+	21.4905i	0.0730532	+	0.974827i
$487$	4.95905	+	0.747457i	0.224716	+	0.0338705i	0.260435	−	0.965491i	$-0.416134\pi$
$487$	4.95905	+	0.747457i	0.224716	+	0.0338705i	−0.0357190	+	0.999362i	$0.511372\pi$
$488$	−36.4897	−	33.8575i	−1.65181	−	1.53266i
$489$	23.1871			1.04856
$490$		0			0
$491$	−3.79212			−0.171136			−0.0855680	−	0.996332i	$-0.527270\pi$
$491$	−3.79212			−0.171136			−0.0855680	+	0.996332i	$0.527270\pi$
$492$	−50.0225	−	46.4141i	−2.25519	−	2.09251i
$493$	−2.50139	−	0.377024i	−0.112657	−	0.0169803i
$494$	3.25871	+	43.4845i	0.146616	+	1.95646i
$495$	1.15031	+	2.93094i	0.0517025	+	0.131736i
$496$	32.1887	+	40.3634i	1.44532	+	1.81237i
$497$		0			0
$498$	−23.2835	+	29.1966i	−1.04336	+	1.30833i
$499$	−26.1755	−	8.07406i	−1.17177	−	0.361444i	−0.353035	−	0.935610i	$-0.614850\pi$
$499$	−26.1755	−	8.07406i	−1.17177	−	0.361444i	−0.818739	+	0.574166i	$0.805327\pi$
$500$	21.0941	−	53.7470i	0.943359	−	2.40364i
$501$	−9.41195	+	2.90320i	−0.420495	+	0.129706i
$502$	−1.57293	+	20.9893i	−0.0702032	+	0.936796i
$503$	−2.00879	+	8.80109i	−0.0895676	+	0.392421i	−0.999763	−	0.0217571i	$-0.993074\pi$
$503$	−2.00879	+	8.80109i	−0.0895676	+	0.392421i	0.910196	+	0.414179i	$0.135931\pi$
$504$		0			0
$505$	−0.612597	−	2.68396i	−0.0272602	−	0.119435i
$506$	−0.986729	+	0.148725i	−0.0438655	+	0.00661165i
$507$	4.56342	+	3.11129i	0.202669	+	0.138177i
$508$	−0.176643	−	0.305955i	−0.00783727	−	0.0135745i
$509$	−12.0418	+	20.8569i	−0.533741	+	0.924467i	0.465482	+	0.885057i	$0.345881\pi$
$509$	−12.0418	+	20.8569i	−0.533741	+	0.924467i	−0.999223	+	0.0394096i	$0.987452\pi$
$510$	−10.1218	+	4.87441i	−0.448201	+	0.215842i
$511$		0			0
$512$	−35.1437	−	16.9243i	−1.55315	−	0.747955i
$513$	−25.4623	+	17.3599i	−1.12419	+	0.766458i
$514$	34.0511	−	31.5948i	1.50193	−	1.39359i
$515$	11.5481	−	10.7151i	0.508871	−	0.472164i
$516$	−15.2744	+	10.4139i	−0.672417	+	0.458446i
$517$	−2.79892	−	1.34789i	−0.123096	−	0.0592801i
$518$		0			0
$519$	−28.0707	+	13.5181i	−1.23217	+	0.593380i
$520$	−23.6833	+	41.0206i	−1.03858	+	1.79887i
$521$	9.12162	+	15.7991i	0.399626	+	0.692172i	0.993680	−	0.112253i	$-0.0358068\pi$
$521$	9.12162	+	15.7991i	0.399626	+	0.692172i	−0.594054	+	0.804425i	$0.702473\pi$
$522$	−3.18473	−	2.17131i	−0.139392	−	0.0950357i
$523$	−4.05307	+	0.610901i	−0.177228	+	0.0267129i	−0.237057	−	0.971496i	$-0.576183\pi$
$523$	−4.05307	+	0.610901i	−0.177228	+	0.0267129i	0.0598285	+	0.998209i	$0.480945\pi$
$524$	20.1884	+	88.4510i	0.881933	+	3.86400i
$525$		0			0
$526$	−11.3129	+	49.5651i	−0.493266	+	2.16114i
$527$	−0.541026	+	7.21949i	−0.0235675	+	0.314486i
$528$	−26.4227	+	8.15033i	−1.14990	+	0.354698i
$529$	−8.38769	+	21.3715i	−0.364682	+	0.929195i
$530$	37.4461	+	11.5506i	1.62656	+	0.501726i
$531$	4.24715	−	5.32576i	0.184311	−	0.231118i
$532$		0			0
$533$	−17.9747	−	22.5395i	−0.778569	−	0.976295i
$534$	−1.75937	−	4.48279i	−0.0761352	−	0.193989i
$535$	−0.248760	−	3.31947i	−0.0107548	−	0.143513i
$536$	26.6788	+	4.02118i	1.15235	+	0.173688i
$537$	−21.7029	−	20.1374i	−0.936550	−	0.868992i
$538$	75.0249			3.23455
$539$		0			0
$540$	−56.7640			−2.44273
$541$	−12.2646	−	11.3799i	−0.527296	−	0.489259i	0.371011	−	0.928629i	$-0.379011\pi$
$541$	−12.2646	−	11.3799i	−0.527296	−	0.489259i	−0.898306	+	0.439370i	$0.855202\pi$
$542$	−69.6284	−	10.4948i	−2.99080	−	0.450790i
$543$	0.829729	+	11.0720i	0.0356071	+	0.475144i
$544$	5.73428	+	14.6107i	0.245855	+	0.626429i
$545$	−13.1283	−	16.4623i	−0.562353	−	0.705169i
$546$		0			0
$547$	0.569364	−	0.713960i	0.0243443	−	0.0305267i	−0.769510	−	0.638634i	$-0.779500\pi$
$547$	0.569364	−	0.713960i	0.0243443	−	0.0305267i	0.793855	+	0.608108i	$0.208071\pi$
$548$	37.1087	+	11.4465i	1.58520	+	0.488970i
$549$	1.96884	−	5.01653i	0.0840282	−	0.214100i
$550$	3.44687	−	1.06322i	0.146975	−	0.0453358i
$551$	0.735723	−	9.81754i	0.0313428	−	0.418241i
$552$	0.504799	−	2.21167i	0.0214857	−	0.0941348i
$553$		0			0
$554$	6.38136	+	27.9586i	0.271118	+	1.18785i
$555$	−22.7660	+	3.43143i	−0.966365	+	0.145656i
$556$	76.2925	+	52.0153i	3.23552	+	2.20594i
$557$	−22.5492	−	39.0564i	−0.955442	−	1.65487i	−0.733353	−	0.679848i	$-0.762046\pi$
$557$	−22.5492	−	39.0564i	−0.955442	−	1.65487i	−0.222089	−	0.975026i	$-0.571288\pi$
$558$	−5.51570	+	9.55346i	−0.233498	+	0.404430i
$559$	−7.03669	+	3.38869i	−0.297620	+	0.143326i
$560$		0			0
$561$	−3.49359	−	1.68243i	−0.147500	−	0.0710321i
$562$	49.8438	−	33.9829i	2.10253	−	1.43348i
$563$	−23.1551	+	21.4848i	−0.975870	+	0.905475i	−0.995541	−	0.0943315i	$-0.969929\pi$
$563$	−23.1551	+	21.4848i	−0.975870	+	0.905475i	0.0196708	+	0.999807i	$0.493738\pi$
$564$	8.77905	−	8.14577i	0.369665	−	0.342999i
$565$	−12.0338	+	8.20450i	−0.506266	+	0.345166i
$566$	−3.09170	−	1.48888i	−0.129954	−	0.0625825i
$567$		0			0
$568$	45.3809	−	21.8543i	1.90414	−	0.916986i
$569$	−8.43410	+	14.6083i	−0.353576	+	0.612412i	−0.986873	−	0.161497i	$-0.948368\pi$
$569$	−8.43410	+	14.6083i	−0.353576	+	0.612412i	0.633297	+	0.773909i	$0.281701\pi$
$570$	−21.8614	−	37.8650i	−0.915672	−	1.58599i
$571$	7.77392	+	5.30017i	0.325328	+	0.221805i	0.714959	−	0.699166i	$-0.246445\pi$
$571$	7.77392	+	5.30017i	0.325328	+	0.221805i	−0.389631	+	0.920971i	$0.627398\pi$
$572$	−27.4137	+	4.13196i	−1.14623	+	0.172766i
$573$	−1.52977	−	6.70238i	−0.0639072	−	0.279996i
$574$		0			0
$575$	−0.0333646	+	0.146180i	−0.00139140	+	0.00609612i
$576$	−0.566130	+	7.55447i	−0.0235887	+	0.314770i
$577$	−10.9434	+	3.37560i	−0.455581	+	0.140528i	−0.514048	−	0.857761i	$-0.671855\pi$
$577$	−10.9434	+	3.37560i	−0.455581	+	0.140528i	0.0584675	+	0.998289i	$0.481379\pi$
$578$	14.3959	−	36.6801i	0.598790	−	1.52569i
$579$	30.9956	+	9.56089i	1.28814	+	0.397337i
$580$	11.3065	−	14.1779i	0.469478	−	0.588707i
$581$		0			0
$582$	33.6075	+	42.1424i	1.39307	+	1.74686i
$583$	4.94147	+	12.5907i	0.204655	+	0.521452i
$584$	0.0995611	+	1.32855i	0.00411987	+	0.0549758i
$585$	−5.07073	−	0.764289i	−0.209649	−	0.0315995i
$586$	7.69305	+	7.13811i	0.317797	+	0.294873i
$587$	−28.6455			−1.18233			−0.591163	−	0.806552i	$-0.701331\pi$
$587$	−28.6455			−1.18233			−0.591163	+	0.806552i	$0.701331\pi$
$588$		0			0
$589$	−28.1762			−1.16098
$590$	33.1317	+	30.7417i	1.36401	+	1.26562i
$591$	−21.1551	−	3.18862i	−0.870204	−	0.131162i
$592$	5.64527	+	75.3308i	0.232019	+	3.09608i
$593$	15.2724	+	38.9134i	0.627162	+	1.59798i	0.791220	+	0.611531i	$0.209446\pi$
$593$	15.2724	+	38.9134i	0.627162	+	1.59798i	−0.164058	+	0.986451i	$0.552459\pi$
$594$	−17.2276	−	21.6027i	−0.706857	−	0.886370i
$595$		0			0
$596$	71.8331	−	90.0759i	2.94240	−	3.68965i
$597$	9.09423	+	2.80520i	0.372202	+	0.114809i
$598$	0.593754	−	1.51286i	0.0242804	−	0.0618655i
$599$	−8.15355	+	2.51504i	−0.333145	+	0.102762i	−0.456815	−	0.889562i	$-0.651010\pi$
$599$	−8.15355	+	2.51504i	−0.333145	+	0.102762i	0.123670	+	0.992323i	$0.460534\pi$
$600$	−0.612813	+	8.17742i	−0.0250180	+	0.333842i
$601$	3.88880	−	17.0379i	0.158627	−	0.694992i	−0.831582	−	0.555402i	$-0.812564\pi$
$601$	3.88880	−	17.0379i	0.158627	−	0.694992i	0.990209	−	0.139590i	$-0.0445784\pi$
$602$		0			0
$603$	0.649967	+	2.84769i	0.0264687	+	0.115967i
$604$	42.8471	−	6.45816i	1.74342	−	0.262779i
$605$	12.8094	+	8.73329i	0.520776	+	0.355059i
$606$	2.58302	+	4.47393i	0.104928	+	0.181741i
$607$	13.3329	−	23.0932i	0.541164	−	0.937324i	−0.457673	−	0.889120i	$-0.651317\pi$
$607$	13.3329	−	23.0932i	0.541164	−	0.937324i	0.998838	−	0.0482033i	$-0.0153495\pi$
$608$	−55.0363	+	26.5041i	−2.23202	+	1.07488i
$609$		0			0
$610$	32.2154	+	15.5141i	1.30436	+	0.628149i
$611$	4.18041	−	2.85016i	0.169121	−	0.115305i
$612$	−4.09406	+	3.79873i	−0.165493	+	0.153555i
$613$	−17.7302	+	16.4512i	−0.716116	+	0.664458i	−0.951572	−	0.307427i	$-0.900532\pi$
$613$	−17.7302	+	16.4512i	−0.716116	+	0.664458i	0.235456	+	0.971885i	$0.424342\pi$
$614$	38.6632	−	26.3601i	1.56032	−	1.06381i
$615$	26.0434	+	12.5419i	1.05017	+	0.505736i
$616$		0			0
$617$	24.7579	−	11.9228i	0.996717	−	0.479994i	0.136894	−	0.990586i	$-0.456288\pi$
$617$	24.7579	−	11.9228i	0.996717	−	0.479994i	0.859823	+	0.510592i	$0.170574\pi$
$618$	−14.7809	+	25.6013i	−0.594575	+	1.02983i
$619$	−4.78591	−	8.28944i	−0.192362	−	0.333181i	0.753671	−	0.657252i	$-0.228281\pi$
$619$	−4.78591	−	8.28944i	−0.192362	−	0.333181i	−0.946033	+	0.324072i	$0.894948\pi$
$620$	−42.8814	−	29.2360i	−1.72216	−	1.17415i
$621$	1.13572	−	0.171182i	0.0455749	−	0.00686931i
$622$	3.32667	+	14.5751i	0.133387	+	0.584409i
$623$		0			0
$624$	10.0211	−	43.9055i	0.401167	−	1.75763i
$625$	−1.55266	+	20.7189i	−0.0621066	+	0.828755i
$626$	53.8060	−	16.5970i	2.15052	−	0.663348i
$627$	5.51341	−	14.0479i	0.220184	−	0.561021i
$628$	−7.36940	−	2.27316i	−0.294071	−	0.0907090i
$629$	−6.60491	+	8.28230i	−0.263355	+	0.330237i
$630$		0			0
$631$	4.68739	+	5.87780i	0.186602	+	0.233992i	0.866329	−	0.499474i	$-0.166473\pi$
$631$	4.68739	+	5.87780i	0.186602	+	0.233992i	−0.679727	+	0.733465i	$0.737902\pi$
$632$	−43.0985	−	109.813i	−1.71437	−	4.36813i
$633$	1.47045	+	19.6218i	0.0584453	+	0.779898i
$634$	16.0340	+	2.41673i	0.636791	+	0.0959807i
$635$	0.109703	+	0.101790i	0.00435343	+	0.00403940i
$636$	−52.1422			−2.06757
$637$		0			0
$638$	8.82719			0.349472
$639$	3.99738	+	3.70903i	0.158134	+	0.146727i
$640$	−4.05394	−	0.611033i	−0.160246	−	0.0241532i
$641$	0.127237	+	1.69786i	0.00502556	+	0.0670614i	0.999153	−	0.0411571i	$-0.0131044\pi$
$641$	0.127237	+	1.69786i	0.00502556	+	0.0670614i	−0.994127	+	0.108219i	$0.965485\pi$
$642$	2.28212	+	5.81474i	0.0900679	+	0.229489i
$643$	1.53076	+	1.91951i	0.0603672	+	0.0756981i	0.811098	−	0.584910i	$-0.198870\pi$
$643$	1.53076	+	1.91951i	0.0603672	+	0.0756981i	−0.750731	+	0.660608i	$0.770299\pi$
$644$		0			0
$645$	4.88253	−	6.12250i	0.192250	−	0.241073i
$646$	−19.2240	−	5.92981i	−0.756357	−	0.233305i
$647$	−10.4261	+	26.5653i	−0.409893	+	1.04439i	0.565662	+	0.824637i	$0.308621\pi$
$647$	−10.4261	+	26.5653i	−0.409893	+	1.04439i	−0.975555	+	0.219753i	$0.929475\pi$
$648$	42.3940	−	13.0768i	1.66539	−	0.513706i
$649$	−1.16579	+	15.5563i	−0.0457611	+	0.610640i
$650$	−1.30727	+	5.72751i	−0.0512752	+	0.224651i
$651$		0			0
$652$	17.0188	+	74.5644i	0.666510	+	2.92017i
$653$	−8.31936	+	1.25394i	−0.325562	+	0.0490705i	−0.309790	−	0.950805i	$-0.600259\pi$
$653$	−8.31936	+	1.25394i	−0.325562	+	0.0490705i	−0.0157719	+	0.999876i	$0.505021\pi$
$654$	32.6466	+	22.2581i	1.27658	+	0.870359i
$655$	−19.2158	−	33.2827i	−0.750822	−	1.30046i
$656$	47.4222	−	82.1377i	1.85153	−	3.20694i
$657$	−0.129951	+	0.0625813i	−0.00506989	+	0.00244153i
$658$		0			0
$659$	−24.6195	−	11.8561i	−0.959039	−	0.461849i	−0.112193	−	0.993686i	$-0.535787\pi$
$659$	−24.6195	−	11.8561i	−0.959039	−	0.461849i	−0.846846	+	0.531838i	$0.821502\pi$
$660$	22.9672	−	15.6588i	0.893999	−	0.609518i
$661$	14.8873	−	13.8134i	0.579048	−	0.537278i	−0.335350	−	0.942093i	$-0.608855\pi$
$661$	14.8873	−	13.8134i	0.579048	−	0.537278i	0.914398	+	0.404815i	$0.132664\pi$
$662$	−2.26218	+	2.09899i	−0.0879219	+	0.0815796i
$663$	5.21796	−	3.55754i	0.202649	−	0.138164i
$664$	−65.4456	−	31.5169i	−2.53978	−	1.22309i
$665$		0			0
$666$	−14.5430	+	7.00355i	−0.563531	+	0.271382i
$667$	−0.183462	+	0.317766i	−0.00710368	+	0.0123039i
$668$	−16.2442	−	28.1358i	−0.628507	−	1.08861i
$669$	−19.9429	−	13.5968i	−0.771037	−	0.525684i
$670$	−19.1639	+	2.88849i	−0.740366	+	0.111592i
$671$	2.74625	+	12.0321i	0.106018	+	0.464494i
$672$		0			0
$673$	2.17126	−	9.51293i	0.0836961	−	0.366697i	−0.915684	−	0.401899i	$-0.868350\pi$
$673$	2.17126	−	9.51293i	0.0836961	−	0.366697i	0.999380	+	0.0352021i	$0.0112075\pi$
$674$	1.06662	−	14.2331i	0.0410848	−	0.548239i
$675$	−3.96733	+	1.22376i	−0.152703	+	0.0471025i
$676$	−6.65573	+	16.9585i	−0.255990	+	0.652251i
$677$	24.5530	+	7.57361i	0.943650	+	0.291077i	0.728143	−	0.685425i	$-0.240384\pi$
$677$	24.5530	+	7.57361i	0.943650	+	0.291077i	0.215507	+	0.976502i	$0.430860\pi$
$678$	17.0404	−	21.3680i	0.654434	−	0.820634i
$679$		0			0
$680$	−13.6248	−	17.0849i	−0.522487	−	0.655178i
$681$	7.95505	+	20.2691i	0.304838	+	0.776715i
$682$	−1.88791	−	25.1924i	−0.0722918	−	0.964667i
$683$	−24.3090	−	3.66399i	−0.930159	−	0.140199i	−0.333551	−	0.942732i	$-0.608247\pi$
$683$	−24.3090	−	3.66399i	−0.930159	−	0.140199i	−0.596608	+	0.802533i	$0.703485\pi$
$684$	−15.9336	−	14.7842i	−0.609236	−	0.565288i
$685$	−16.4501			−0.628527
$686$		0			0
$687$	−9.80542			−0.374100
$688$	−18.8354	−	17.4767i	−0.718091	−	0.666291i
$689$	−21.7827	−	3.28321i	−0.829855	−	0.125081i
$690$	0.121776	+	1.62498i	0.00463592	+	0.0618621i
$691$	1.08651	+	2.76839i	0.0413329	+	0.105315i	0.950050	−	0.312099i	$-0.101032\pi$
$691$	1.08651	+	2.76839i	0.0413329	+	0.105315i	−0.908717	+	0.417413i	$0.862937\pi$
$692$	−64.0745	−	80.3469i	−2.43575	−	3.05433i
$693$		0			0
$694$	6.05528	−	7.59308i	0.229855	−	0.288229i
$695$	−37.3764	−	11.5291i	−1.41777	−	0.437324i
$696$	−7.33149	+	18.6803i	−0.277899	+	0.708076i
$697$	12.7094	−	3.92032i	0.481402	−	0.148493i
$698$	−4.75193	+	63.4101i	−0.179863	+	2.40011i
$699$	−0.821396	+	3.59877i	−0.0310681	+	0.136118i
$700$		0			0
$701$	0.282827	+	1.23914i	0.0106822	+	0.0468018i	0.979988	−	0.199056i	$-0.0637875\pi$
$701$	0.282827	+	1.23914i	0.0106822	+	0.0468018i	−0.969306	+	0.245858i	$0.920930\pi$
$702$	44.4989	−	6.70714i	1.67950	−	0.253145i
$703$	−34.0645	−	23.2248i	−1.28477	−	0.875940i
$704$	−8.67453	−	15.0247i	−0.326933	−	0.566265i
$705$	−2.53653	+	4.39340i	−0.0955313	+	0.165465i
$706$	70.8172	−	34.1038i	2.66524	−	1.28351i
$707$		0			0
$708$	−54.1833	−	26.0933i	−2.03633	−	0.980646i
$709$	−38.8815	+	26.5090i	−1.46023	+	0.995565i	−0.466405	+	0.884571i	$0.654451\pi$
$709$	−38.8815	+	26.5090i	−1.46023	+	0.995565i	−0.993821	+	0.110994i	$0.964597\pi$
$710$	−26.5226	+	24.6094i	−0.995376	+	0.923574i
$711$	9.36214	−	8.68680i	0.351108	−	0.325780i
$712$	7.73954	−	5.27673i	0.290052	−	0.197754i
$713$	0.946127	+	0.455631i	0.0354327	+	0.0170635i
$714$		0			0
$715$	10.5807	−	5.09539i	0.395695	−	0.190557i
$716$	48.8277	−	84.5720i	1.82478	−	3.16060i
$717$	9.95940	+	17.2502i	0.371941	+	0.644220i
$718$	−21.2440	−	14.4839i	−0.792820	−	0.540535i
$719$	−10.6891	+	1.61113i	−0.398637	+	0.0600849i	−0.345302	−	0.938492i	$-0.612223\pi$
$719$	−10.6891	+	1.61113i	−0.398637	+	0.0600849i	−0.0533356	+	0.998577i	$0.516985\pi$
$720$	−3.75404	−	16.4475i	−0.139905	−	0.612964i
$721$		0			0
$722$	6.33713	−	27.7648i	0.235843	−	1.03330i
$723$	2.67551	−	35.7022i	0.0995032	−	1.32778i
$724$	−34.9959	+	10.7948i	−1.30061	+	0.401186i
$725$	0.484574	−	1.23467i	0.0179966	−	0.0458547i
$726$	−27.7997	−	8.57508i	−1.03175	−	0.318251i
$727$	15.0795	−	18.9091i	0.559268	−	0.701300i	−0.419155	−	0.907915i	$-0.637673\pi$
$727$	15.0795	−	18.9091i	0.559268	−	0.701300i	0.978422	+	0.206615i	$0.0662449\pi$
$728$		0			0
$729$	18.5835	+	23.3029i	0.688277	+	0.863072i
$730$	−0.349632	−	0.890847i	−0.0129404	−	0.0329717i
$731$	−0.269267	−	3.59312i	−0.00995920	−	0.132896i
$732$	−47.0459	−	7.09104i	−1.73887	−	0.262092i
$733$	−16.3866	−	15.2046i	−0.605254	−	0.561594i	0.316879	−	0.948466i	$-0.397365\pi$
$733$	−16.3866	−	15.2046i	−0.605254	−	0.561594i	−0.922133	+	0.386872i	$0.873555\pi$
$734$	42.3605			1.56355
$735$		0			0
$736$	2.27666			0.0839187
$737$	−4.90355	−	4.54983i	−0.180625	−	0.167595i
$738$	20.0396	+	3.02049i	0.737669	+	0.111186i
$739$	−0.0465273	−	0.620863i	−0.00171153	−	0.0228388i	0.996283	−	0.0861446i	$-0.0274547\pi$
$739$	−0.0465273	−	0.620863i	−0.00171153	−	0.0228388i	−0.997994	+	0.0633058i	$0.979836\pi$
$740$	−27.7445	−	70.6918i	−1.01991	−	2.59868i
$741$	15.3244	+	19.2162i	0.562956	+	0.705924i
$742$		0			0
$743$	−14.6375	+	18.3549i	−0.536999	+	0.673375i	−0.974121	−	0.226027i	$-0.927426\pi$
$743$	−14.6375	+	18.3549i	−0.536999	+	0.673375i	0.437122	+	0.899402i	$0.355998\pi$
$744$	54.8808	+	16.9285i	2.01203	+	0.620629i
$745$	−17.8300	+	45.4301i	−0.653241	+	1.66443i
$746$	47.4258	−	14.6289i	1.73638	−	0.535603i
$747$	0.587683	−	7.84208i	0.0215022	−	0.286927i
$748$	2.84607	−	12.4695i	0.104063	−	0.455929i
$749$		0			0
$750$	−10.2128	−	44.7453i	−0.372920	−	1.63387i
$751$	−47.1209	+	7.10234i	−1.71947	+	0.259168i	−0.933365	−	0.358929i	$-0.883142\pi$
$751$	−47.1209	+	7.10234i	−1.71947	+	0.259168i	−0.786102	+	0.618097i	$0.787904\pi$
$752$	13.7531	+	9.37668i	0.501522	+	0.341932i
$753$	5.93180	+	10.2742i	0.216167	+	0.374412i
$754$	−7.18828	+	12.4505i	−0.261782	+	0.453419i
$755$	−16.5374	+	7.96398i	−0.601857	+	0.289839i
$756$		0			0
$757$	−3.64606	−	1.75585i	−0.132518	−	0.0638175i	0.366450	−	0.930438i	$-0.380573\pi$
$757$	−3.64606	−	1.75585i	−0.132518	−	0.0638175i	−0.498968	+	0.866620i	$0.666287\pi$
$758$	−42.7581	+	29.1520i	−1.55304	+	1.05885i
$759$	−0.412301	+	0.382559i	−0.0149656	+	0.0138860i
$760$	62.3439	−	57.8467i	2.26145	−	2.09832i
$761$	31.5334	−	21.4991i	1.14308	−	0.779342i	0.164742	−	0.986337i	$-0.447321\pi$
$761$	31.5334	−	21.4991i	1.14308	−	0.779342i	0.978342	+	0.206995i	$0.0663684\pi$
$762$	−0.253016	−	0.121846i	−0.00916581	−	0.00441402i
$763$		0			0
$764$	20.4305	−	9.83880i	0.739149	−	0.355955i
$765$	1.18290	−	2.04884i	0.0427678	−	0.0740759i
$766$	−13.5699	−	23.5038i	−0.490301	−	0.849227i
$767$	−20.9924	−	14.3124i	−0.757991	−	0.516789i
$768$	−19.5270	+	2.94322i	−0.704620	+	0.106204i
$769$	−9.16664	−	40.1617i	−0.330558	−	1.44827i	−0.818054	−	0.575142i	$-0.804947\pi$
$769$	−9.16664	−	40.1617i	−0.330558	−	1.44827i	0.487496	−	0.873125i	$-0.337910\pi$
$770$		0			0
$771$	5.82600	−	25.5254i	0.209818	−	0.919274i
$772$	−7.99549	+	106.692i	−0.287764	+	3.83994i
$773$	12.7921	−	3.94584i	0.460100	−	0.141922i	−0.0560357	−	0.998429i	$-0.517846\pi$
$773$	12.7921	−	3.94584i	0.460100	−	0.141922i	0.516136	+	0.856507i	$0.327370\pi$
$774$	2.00583	−	5.11077i	0.0720980	−	0.183703i
$775$	−3.62734	−	1.11889i	−0.130298	−	0.0401916i
$776$	−65.3714	+	81.9732i	−2.34670	+	2.94267i
$777$		0			0
$778$	−30.8278	−	38.6569i	−1.10523	−	1.38592i
$779$	18.9112	+	48.1848i	0.677562	+	1.72640i
$780$	3.38323	+	45.1460i	0.121139	+	1.61649i
$781$	−12.3486	−	1.86125i	−0.441868	−	0.0666009i
$782$	0.549632	+	0.509984i	0.0196548	+	0.0182370i
$783$	−10.1601			−0.363091
$784$		0			0
$785$	3.26683			0.116598
$786$	52.8660	+	49.0525i	1.88567	+	1.74965i
$787$	25.1260	+	3.78713i	0.895644	+	0.134997i	0.580704	−	0.814115i	$-0.302777\pi$
$787$	25.1260	+	3.78713i	0.895644	+	0.134997i	0.314940	+	0.949111i	$0.398016\pi$
$788$	−5.27352	−	70.3703i	−0.187861	−	2.50684i
$789$	10.4690	+	26.6746i	0.372706	+	0.949641i
$790$	52.8337	+	66.2514i	1.87974	+	2.35712i
$791$		0			0
$792$	7.16558	−	8.98536i	0.254618	−	0.319281i
$793$	−19.2072	−	5.92464i	−0.682068	−	0.210390i
$794$	0.323943	−	0.825393i	0.0114963	−	0.0292921i
$795$	21.1062	−	6.51041i	0.748561	−	0.230900i
$796$	−2.34590	+	31.3039i	−0.0831483	+	1.10954i
$797$	−1.31373	+	5.75582i	−0.0465347	+	0.203882i	−0.992851	−	0.119360i	$-0.961916\pi$
$797$	−1.31373	+	5.75582i	−0.0465347	+	0.203882i	0.946316	+	0.323242i	$0.104773\pi$
$798$		0			0
$799$	0.519414	+	2.27570i	0.0183755	+	0.0805085i
$800$	−8.13776	+	1.22657i	−0.287713	+	0.0433658i
$801$	0.837900	+	0.571270i	0.0296057	+	0.0201848i
$802$	30.5171	+	52.8571i	1.07760	+	1.86645i
$803$	0.165157	−	0.286060i	0.00582826	−	0.0100948i
$804$	23.2337	−	11.1887i	0.819388	−	0.394596i
$805$		0			0
$806$	37.0705	+	17.8522i	1.30575	+	0.628817i
$807$	34.9393	−	23.8212i	1.22992	−	0.838547i
$808$	−7.36622	+	6.83486i	−0.259143	+	0.240449i
$809$	−8.26704	+	7.67070i	−0.290654	+	0.269687i	−0.811999	−	0.583658i	$-0.801621\pi$
$809$	−8.26704	+	7.67070i	−0.290654	+	0.269687i	0.521346	+	0.853346i	$0.325430\pi$
$810$	−26.3308	+	17.9521i	−0.925171	+	0.630771i
$811$	16.3734	+	7.88502i	0.574948	+	0.276881i	0.698679	−	0.715435i	$-0.253772\pi$
$811$	16.3734	+	7.88502i	0.574948	+	0.276881i	−0.123731	+	0.992316i	$0.539486\pi$
$812$		0			0
$813$	−35.7584	+	17.2203i	−1.25410	+	0.603943i
$814$	18.4829	−	32.0134i	0.647826	−	1.12207i
$815$	−16.1989	−	28.0574i	−0.567424	−	0.982808i
$816$	17.1665	+	11.7039i	0.600947	+	0.409718i
$817$	13.8666	−	2.09005i	0.485130	−	0.0731215i
$818$	−7.95240	−	34.8418i	−0.278049	−	1.21821i
$819$		0			0
$820$	−21.2164	+	92.9552i	−0.740909	+	3.24613i
$821$	3.55761	−	47.4730i	0.124161	−	1.65682i	−0.493036	−	0.870009i	$-0.664113\pi$
$821$	3.55761	−	47.4730i	0.124161	−	1.65682i	0.617197	−	0.786809i	$-0.288268\pi$
$822$	29.4976	−	9.09881i	1.02885	−	0.317357i
$823$	−4.30931	+	10.9800i	−0.150213	+	0.382737i	−0.986097	−	0.166169i	$-0.946860\pi$
$823$	−4.30931	+	10.9800i	−0.150213	+	0.382737i	0.835884	+	0.548906i	$0.184956\pi$
$824$	−54.9474	−	16.9490i	−1.91418	−	0.590447i
$825$	1.26763	−	1.58956i	0.0441334	−	0.0553415i
$826$		0			0
$827$	−16.1389	−	20.2376i	−0.561206	−	0.703730i	0.417575	−	0.908643i	$-0.362880\pi$
$827$	−16.1389	−	20.2376i	−0.561206	−	0.703730i	−0.978780	+	0.204913i	$0.934309\pi$
$828$	0.295961	+	0.754097i	0.0102854	+	0.0262067i
$829$	0.847463	+	11.3086i	0.0294336	+	0.392764i	0.992392	+	0.123115i	$0.0392885\pi$
$829$	0.847463	+	11.3086i	0.0294336	+	0.392764i	−0.962959	+	0.269649i	$0.913092\pi$
$830$	51.5954	+	7.77675i	1.79090	+	0.269935i
$831$	11.8490	+	10.9942i	0.411036	+	0.381386i
$832$	28.2558			0.979595
$833$		0			0
$834$	73.3986			2.54159
$835$	10.0884	+	9.36063i	0.349122	+	0.323938i
$836$	49.2217	+	7.41897i	1.70237	+	0.256591i
$837$	2.17298	+	28.9963i	0.0751090	+	1.00226i
$838$	8.22542	+	20.9580i	0.284142	+	0.723983i
$839$	11.7264	+	14.7044i	0.404840	+	0.507654i	0.941901	−	0.335890i	$-0.109037\pi$
$839$	11.7264	+	14.7044i	0.404840	+	0.507654i	−0.537061	+	0.843543i	$0.680465\pi$
$840$		0			0
$841$	−16.0575	+	20.1354i	−0.553706	+	0.694325i
$842$	15.9981	+	4.93475i	0.551329	+	0.170063i
$843$	12.4225	−	31.6519i	0.427852	−	1.09015i
$844$	−62.0200	+	19.1306i	−2.13482	+	0.658504i
$845$	0.576701	−	7.69554i	0.0198391	−	0.264734i
$846$	−0.791445	+	3.46755i	−0.0272104	+	0.119217i
$847$		0			0
$848$	−16.1265	−	70.6550i	−0.553787	−	2.42630i
$849$	−1.91255	+	0.288271i	−0.0656386	+	0.00989343i
$850$	−2.23938	−	1.52678i	−0.0768101	−	0.0523683i
$851$	0.768289	+	1.33072i	0.0263366	+	0.0456163i
$852$	24.0712	−	41.6926i	0.824666	−	1.42836i
$853$	−8.23650	+	3.96649i	−0.282012	+	0.135810i	−0.569543	−	0.821961i	$-0.692880\pi$
$853$	−8.23650	+	3.96649i	−0.282012	+	0.135810i	0.287531	+	0.957771i	$0.407166\pi$
$854$		0			0
$855$	8.29557	+	3.99494i	0.283702	+	0.136624i
$856$	−10.0391	+	6.84457i	−0.343131	+	0.233943i
$857$	−12.8106	+	11.8865i	−0.437601	+	0.406034i	−0.867968	−	0.496619i	$-0.834574\pi$
$857$	−12.8106	+	11.8865i	−0.437601	+	0.406034i	0.430367	+	0.902654i	$0.358384\pi$
$858$	−16.1545	+	14.9892i	−0.551504	+	0.511721i
$859$	−10.6109	+	7.23437i	−0.362038	+	0.246833i	−0.730653	−	0.682749i	$-0.760784\pi$
$859$	−10.6109	+	7.23437i	−0.362038	+	0.246833i	0.368615	+	0.929582i	$0.379832\pi$
$860$	23.2722	+	11.2073i	0.793577	+	0.382166i
$861$		0			0
$862$	−91.3905	+	44.0114i	−3.11277	+	1.49903i
$863$	20.1744	−	34.9430i	0.686743	−	1.18947i	−0.286142	−	0.958187i	$-0.592373\pi$
$863$	20.1744	−	34.9430i	0.686743	−	1.18947i	0.972886	−	0.231287i	$-0.0742936\pi$
$864$	31.5201	+	54.5944i	1.07233	+	1.85734i
$865$	35.9682	+	24.5227i	1.22296	+	0.833798i
$866$	1.31594	−	0.198346i	0.0447174	−	0.00674006i
$867$	−4.94213	−	21.6529i	−0.167844	−	0.735371i
$868$		0			0
$869$	−6.50829	+	28.5147i	−0.220779	+	0.967294i
$870$	1.07723	−	14.3746i	0.0365214	−	0.487345i
$871$	10.4105	−	3.21122i	0.352747	−	0.108808i
$872$	−28.0791	+	71.5443i	−0.950877	+	2.42280i
$873$	−10.8467	−	3.34578i	−0.367107	−	0.113237i
$874$	−1.81939	+	2.28144i	−0.0615418	+	0.0771710i
$875$		0			0
$876$	0.793940	+	0.995570i	0.0268248	+	0.0336372i
$877$	8.90126	+	22.6800i	0.300574	+	0.765850i	0.998753	+	0.0499269i	$0.0158988\pi$
$877$	8.90126	+	22.6800i	0.300574	+	0.765850i	−0.698179	+	0.715924i	$0.746006\pi$
$878$	1.13978	+	15.2093i	0.0384658	+	0.513290i
$879$	5.84911	+	0.881611i	0.197286	+	0.0297360i
$880$	28.3217	+	26.2787i	0.954723	+	0.885854i
$881$	−55.9997			−1.88668			−0.943339	−	0.331831i	$-0.892334\pi$
$881$	−55.9997			−1.88668			−0.943339	+	0.331831i	$0.892334\pi$
$882$		0			0
$883$	4.69302			0.157933			0.0789663	−	0.996877i	$-0.474838\pi$
$883$	4.69302			0.157933			0.0789663	+	0.996877i	$0.474838\pi$
$884$	15.2701	+	14.1686i	0.513589	+	0.476541i
$885$	25.1904	+	3.79684i	0.846766	+	0.127629i
$886$	1.27910	+	17.0684i	0.0429722	+	0.573424i
$887$	−17.6214	−	44.8986i	−0.591669	−	1.50755i	−0.842050	−	0.539400i	$-0.818651\pi$
$887$	−17.6214	−	44.8986i	−0.591669	−	1.50755i	0.250381	−	0.968147i	$-0.419444\pi$
$888$	52.3964	+	65.7030i	1.75831	+	2.20485i
$889$		0			0
$890$	−4.19524	+	5.26067i	−0.140625	+	0.176338i
$891$	−10.5108	−	3.24216i	−0.352126	−	0.108617i
$892$	29.0866	−	74.1116i	0.973893	−	2.48144i
$893$	−8.68091	+	2.67771i	−0.290496	+	0.0896060i
$894$	6.84389	−	91.3253i	0.228894	−	3.05438i
$895$	−9.20501	+	40.3298i	−0.307690	+	1.34808i
$896$		0			0
$897$	−0.203837	−	0.893068i	−0.00680592	−	0.0298187i
$898$	−43.1007	+	6.49638i	−1.43829	+	0.216787i
$899$	−7.67524	−	5.23289i	−0.255984	−	0.174527i
$900$	−1.46417	−	2.53602i	−0.0488057	−	0.0845339i
$901$	5.08146	−	8.80135i	0.169288	−	0.293216i
$902$	−41.8151	+	20.1371i	−1.39229	+	0.670492i
$903$		0			0
$904$	47.8975	+	23.0662i	1.59305	+	0.767171i
$905$	12.8179	−	8.73909i	0.426081	−	0.290497i
$906$	25.2491	−	23.4277i	0.838845	−	0.778334i
$907$	−14.5395	+	13.4907i	−0.482775	+	0.447950i	−0.883626	−	0.468193i	$-0.844905\pi$
$907$	−14.5395	+	13.4907i	−0.482775	+	0.447950i	0.400851	+	0.916143i	$0.368715\pi$
$908$	−59.3420	+	40.4587i	−1.96933	+	1.34267i
$909$	−0.980160	−	0.472020i	−0.0325099	−	0.0156559i
$910$		0			0
$911$	32.7621	−	15.7774i	1.08546	−	0.522728i	0.196398	−	0.980524i	$-0.437075\pi$
$911$	32.7621	−	15.7774i	1.08546	−	0.522728i	0.889057	+	0.457797i	$0.151361\pi$
$912$	−40.4301	+	70.0269i	−1.33877	+	2.31882i
$913$	9.00478	+	15.5967i	0.298015	+	0.516177i
$914$	87.2368	+	59.4770i	2.88554	+	1.96733i
$915$	19.9287	−	3.00377i	0.658824	−	0.0993017i
$916$	−7.19697	−	31.5320i	−0.237795	−	1.04185i
$917$		0			0
$918$	−4.61985	+	20.2409i	−0.152478	+	0.668048i
$919$	1.55487	−	20.7483i	0.0512905	−	0.684424i	−0.911001	−	0.412404i	$-0.864689\pi$
$919$	1.55487	−	20.7483i	0.0512905	−	0.684424i	0.962292	−	0.272020i	$-0.0876917\pi$
$920$	−3.02887	+	0.934284i	−0.0998590	+	0.0308024i
$921$	9.63594	−	24.5520i	0.317515	−	0.809015i
$922$	11.9230	+	3.67776i	0.392663	+	0.121121i
$923$	12.6811	−	15.9016i	0.417404	−	0.523409i
$924$		0			0
$925$	−3.46313	−	4.34263i	−0.113867	−	0.142785i
$926$	23.0062	+	58.6188i	0.756031	+	1.92633i
$927$	−0.465217	−	6.20789i	−0.0152797	−	0.203894i
$928$	−19.9144	−	3.00161i	−0.653721	−	0.0985325i
$929$	−0.130972	−	0.121524i	−0.00429706	−	0.00398709i	0.678021	−	0.735042i	$-0.262838\pi$
$929$	−0.130972	−	0.121524i	−0.00429706	−	0.00398709i	−0.682318	+	0.731055i	$0.739028\pi$
$930$	−41.2549			−1.35280
$931$		0			0
$932$	−12.1757			−0.398829
$933$	6.17700	+	5.73142i	0.202226	+	0.187638i
$934$	−50.2518	−	7.57424i	−1.64429	−	0.247837i
$935$	0.404882	+	5.40277i	0.0132411	+	0.176690i
$936$	6.83837	+	17.4239i	0.223519	+	0.569518i
$937$	9.09326	+	11.4026i	0.297064	+	0.372506i	0.907854	−	0.419286i	$-0.137720\pi$
$937$	9.09326	+	11.4026i	0.297064	+	0.372506i	−0.610790	+	0.791792i	$0.709148\pi$
$938$		0			0
$939$	19.7879	−	24.8133i	0.645754	−	0.809750i
$940$	−15.9899	−	4.93224i	−0.521534	−	0.160872i
$941$	10.2738	−	26.1771i	0.334915	−	0.853350i	−0.659872	−	0.751378i	$-0.729389\pi$
$941$	10.2738	−	26.1771i	0.334915	−	0.853350i	0.994787	−	0.101972i	$-0.0325153\pi$
$942$	−5.85793	+	1.80693i	−0.190862	+	0.0588730i
$943$	0.144169	−	1.92381i	0.00469480	−	0.0626478i
$944$	18.5998	−	81.4908i	0.605370	−	2.65230i
$945$		0			0
$946$	2.79783	+	12.2581i	0.0909653	+	0.398545i
$947$	15.6301	−	2.35586i	0.507909	−	0.0765550i	0.109912	−	0.993941i	$-0.464943\pi$
$947$	15.6301	−	2.35586i	0.507909	−	0.0765550i	0.397998	+	0.917386i	$0.369705\pi$
$948$	−93.1608	−	63.5160i	−3.02572	−	2.06290i
$949$	0.268986	+	0.465897i	0.00873164	+	0.0151236i
$950$	5.27414	−	9.13508i	0.171116	−	0.296381i
$951$	8.23442	−	3.96549i	0.267019	−	0.128590i
$952$		0			0
$953$	40.6458	+	19.5740i	1.31665	+	0.634064i	0.954543	−	0.298074i	$-0.0963442\pi$
$953$	40.6458	+	19.5740i	1.31665	+	0.634064i	0.362104	+	0.932138i	$0.382058\pi$
$954$	12.7948	−	8.72331i	0.414245	−	0.282428i
$955$	−7.04144	+	6.53350i	−0.227856	+	0.211419i
$956$	−48.1627	+	44.6884i	−1.55769	+	1.44533i
$957$	4.11085	−	2.80273i	0.132885	−	0.0905994i
$958$	−5.32364	−	2.56373i	−0.171999	−	0.0828304i
$959$		0			0
$960$	−25.5255	+	12.2925i	−0.823833	+	0.396737i
$961$	2.20710	−	3.82281i	0.0711969	−	0.123317i
$962$	30.1025	+	52.1391i	0.970544	+	1.68103i
$963$	−1.08686	−	0.741009i	−0.0350236	−	0.0238787i
$964$	116.774	−	17.6008i	3.76103	−	0.566884i
$965$	−10.0850	−	44.1855i	−0.324649	−	1.42238i
$966$		0			0
$967$	11.5268	−	50.5020i	0.370675	−	1.62403i	−0.354210	−	0.935166i	$-0.615250\pi$
$967$	11.5268	−	50.5020i	0.370675	−	1.62403i	0.724886	−	0.688869i	$-0.241893\pi$
$968$	4.22887	−	56.4304i	0.135921	−	1.81374i
$969$	−10.8355	+	3.34229i	−0.348085	+	0.107370i
$970$	27.5154	−	70.1080i	0.883465	−	2.25103i
$971$	−38.3845	−	11.8401i	−1.23182	−	0.379966i	−0.390549	−	0.920582i	$-0.627715\pi$
$971$	−38.3845	−	11.8401i	−1.23182	−	0.379966i	−0.841269	+	0.540616i	$0.818191\pi$
$972$	−24.9809	+	31.3250i	−0.801262	+	1.00475i
$973$		0			0
$974$	8.19842	+	10.2805i	0.262694	+	0.329408i
$975$	1.20975	+	3.08239i	0.0387430	+	0.0987156i
$976$	−4.94170	−	65.9424i	−0.158180	−	2.11077i
$977$	22.4180	+	3.37897i	0.717215	+	0.108103i	0.497503	−	0.867462i	$-0.334250\pi$
$977$	22.4180	+	3.37897i	0.717215	+	0.108103i	0.219711	+	0.975565i	$0.429488\pi$
$978$	44.5662	+	41.3514i	1.42507	+	1.32227i
$979$	−2.32243			−0.0742251
$980$		0			0
$981$	−8.32073			−0.265660
$982$	−7.28855	−	6.76279i	−0.232587	−	0.215809i
$983$	17.5582	+	2.64648i	0.560021	+	0.0844095i	0.422952	−	0.906152i	$-0.360994\pi$
$983$	17.5582	+	2.64648i	0.560021	+	0.0844095i	0.137068	+	0.990562i	$0.456232\pi$
$984$	−7.88479	−	105.215i	−0.251358	−	3.35414i
$985$	10.9210	+	27.8262i	0.347971	+	0.886616i
$986$	−4.13536	−	5.18558i	−0.131697	−	0.165142i
$987$		0			0
$988$	−50.5471	+	63.3840i	−1.60812	+	2.01651i
$989$	−0.499423	−	0.154052i	−0.0158807	−	0.00489856i
$990$	−3.01605	+	7.68477i	−0.0958564	+	0.244238i
$991$	−8.25826	+	2.54734i	−0.262332	+	0.0809188i	−0.423131	−	0.906068i	$-0.639069\pi$
$991$	−8.25826	+	2.54734i	−0.262332	+	0.0809188i	0.160799	+	0.986987i	$0.448593\pi$
$992$	−4.30728	+	57.4766i	−0.136756	+	1.82489i
$993$	−0.387049	+	1.69577i	−0.0122826	+	0.0538137i
$994$		0			0
$995$	−2.95899	−	12.9642i	−0.0938062	−	0.410992i
$996$	−68.6526	+	10.3477i	−2.17534	+	0.327880i
$997$	9.88991	+	6.74283i	0.313217	+	0.213547i	0.709717	−	0.704487i	$-0.248823\pi$
$997$	9.88991	+	6.74283i	0.313217	+	0.213547i	−0.396500	+	0.918035i	$0.629775\pi$
$998$	−35.9108	−	62.1993i	−1.13674	−	1.96888i
$999$	−21.2738	+	36.8472i	−0.673072	+	1.16579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.2.g.i.177.4		48
7.2	even	3		343.2.e.d.99.8		48
7.3	odd	6		343.2.g.g.67.1		48
7.4	even	3		49.2.g.a.25.1	yes	48
7.5	odd	6		343.2.e.c.99.8		48
7.6	odd	2		343.2.g.h.177.4		48
21.11	odd	6		441.2.bb.d.172.4		48
28.11	odd	6		784.2.bg.c.417.3		48
49.2	even	21		343.2.e.d.246.8		48
49.11	even	21	inner	343.2.g.i.312.4		48
49.13	odd	14		343.2.g.g.128.1		48
49.16	even	21		2401.2.a.h.1.1		24
49.33	odd	42		2401.2.a.i.1.1		24
49.36	even	7		49.2.g.a.2.1	✓	48
49.38	odd	42		343.2.g.h.312.4		48
49.47	odd	42		343.2.e.c.246.8		48
147.134	odd	14		441.2.bb.d.100.4		48
196.183	odd	14		784.2.bg.c.737.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.2.1	✓	48	49.36	even	7
49.2.g.a.25.1	yes	48	7.4	even	3
343.2.e.c.99.8		48	7.5	odd	6
343.2.e.c.246.8		48	49.47	odd	42
343.2.e.d.99.8		48	7.2	even	3
343.2.e.d.246.8		48	49.2	even	21
343.2.g.g.67.1		48	7.3	odd	6
343.2.g.g.128.1		48	49.13	odd	14
343.2.g.h.177.4		48	7.6	odd	2
343.2.g.h.312.4		48	49.38	odd	42
343.2.g.i.177.4		48	1.1	even	1	trivial
343.2.g.i.312.4		48	49.11	even	21	inner
441.2.bb.d.100.4		48	147.134	odd	14
441.2.bb.d.172.4		48	21.11	odd	6
784.2.bg.c.417.3		48	28.11	odd	6
784.2.bg.c.737.3		48	196.183	odd	14
2401.2.a.h.1.1		24	49.16	even	21
2401.2.a.i.1.1		24	49.33	odd	42

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:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	343.g (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.92202 + 1.78338i) q^{2} +(1.46134 + 0.220261i) q^{3} +(0.364281 + 4.86099i) q^{4} +(-0.754391 - 1.92216i) q^{5} +(2.41591 + 3.02946i) q^{6} +(-4.69930 + 5.89274i) q^{8} +(-0.779731 - 0.240515i) q^{9} +O(q^{10})\)	\(q+(1.92202 + 1.78338i) q^{2} +(1.46134 + 0.220261i) q^{3} +(0.364281 + 4.86099i) q^{4} +(-0.754391 - 1.92216i) q^{5} +(2.41591 + 3.02946i) q^{6} +(-4.69930 + 5.89274i) q^{8} +(-0.779731 - 0.240515i) q^{9} +(1.97797 - 5.03980i) q^{10} +(1.78567 - 0.550805i) q^{11} +(-0.538349 + 7.18377i) q^{12} +(-0.677236 + 2.96716i) q^{13} +(-0.679042 - 2.97508i) q^{15} +(-9.90082 + 1.49231i) q^{16} +(-1.16012 - 0.790958i) q^{17} +(-1.06973 - 1.85283i) q^{18} +(2.73229 - 4.73247i) q^{19} +(9.06877 - 4.36729i) q^{20} +(4.41439 + 2.12586i) q^{22} +(-0.168275 + 0.114728i) q^{23} +(-8.16520 + 7.57620i) q^{24} +(0.539678 - 0.500748i) q^{25} +(-6.59324 + 4.49519i) q^{26} +(-5.08094 - 2.44685i) q^{27} +(1.62320 - 0.781691i) q^{29} +(4.00056 - 6.92917i) q^{30} +(-2.57807 - 4.46535i) q^{31} +(-9.23609 - 6.29706i) q^{32} +(2.73078 - 0.411599i) q^{33} +(-0.819206 - 3.58918i) q^{34} +(0.885100 - 3.87788i) q^{36} +(0.563813 - 7.52356i) q^{37} +(13.6913 - 4.22321i) q^{38} +(-1.64322 + 4.18685i) q^{39} +(14.8719 + 4.58737i) q^{40} +(-5.90598 + 7.40586i) q^{41} +(1.60000 + 2.00633i) q^{43} +(3.32794 + 8.47945i) q^{44} +(0.125914 + 1.68021i) q^{45} +(-0.528033 - 0.0795882i) q^{46} +(-1.21865 - 1.13074i) q^{47} -14.7971 q^{48} +1.93030 q^{50} +(-1.52111 - 1.41138i) q^{51} +(-14.6700 - 2.21115i) q^{52} +(0.540899 + 7.21780i) q^{53} +(-5.40203 - 13.7642i) q^{54} +(-2.40583 - 3.01681i) q^{55} +(5.03517 - 6.31391i) q^{57} +(4.51388 + 1.39235i) q^{58} +(-3.04990 + 7.77102i) q^{59} +(14.2145 - 4.38458i) q^{60} +(-0.493546 + 6.58591i) q^{61} +(3.00829 - 13.1802i) q^{62} +(-2.06590 - 9.05131i) q^{64} +(6.21425 - 0.936648i) q^{65} +(5.98266 + 4.07891i) q^{66} +(-1.78982 - 3.10006i) q^{67} +(3.42222 - 5.92747i) q^{68} +(-0.271177 + 0.130592i) q^{69} +(-6.02101 - 2.89956i) q^{71} +(5.08149 - 3.46450i) q^{72} +(0.129576 - 0.120229i) q^{73} +(14.5010 - 13.4550i) q^{74} +(0.898946 - 0.612891i) q^{75} +(23.9998 + 11.5577i) q^{76} +(-10.6251 + 5.11676i) q^{78} +(-7.82581 + 13.5547i) q^{79} +(10.3375 + 17.9052i) q^{80} +(-4.86342 - 3.31583i) q^{81} +(-24.5589 + 3.70166i) q^{82} +(2.14456 + 9.39591i) q^{83} +(-0.645159 + 2.82663i) q^{85} +(-0.502817 + 6.70962i) q^{86} +(2.54421 - 0.784786i) q^{87} +(-5.14564 + 13.1109i) q^{88} +(-1.18760 - 0.366325i) q^{89} +(-2.75444 + 3.45395i) q^{90} +(-0.618992 - 0.776191i) q^{92} +(-2.78388 - 7.09322i) q^{93} +(-0.325735 - 4.34663i) q^{94} +(-11.1578 - 1.68176i) q^{95} +(-12.1100 - 11.2365i) q^{96} +13.9109 q^{97} -1.52482 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} + 7 q^{3} + 12 q^{4} + 7 q^{5} - 20 q^{8} - 15 q^{9}+O(q^{10}) \) 48 * q + 8 * q^2 + 7 * q^3 + 12 * q^4 + 7 * q^5 - 20 * q^8 - 15 * q^9	\( 48 q + 8 q^{2} + 7 q^{3} + 12 q^{4} + 7 q^{5} - 20 q^{8} - 15 q^{9} + 7 q^{10} - 3 q^{11} - 63 q^{12} - 14 q^{13} - 12 q^{15} + 18 q^{16} + 14 q^{17} + 2 q^{18} + 21 q^{19} + 14 q^{20} - 20 q^{22} - 27 q^{23} - 77 q^{24} + 17 q^{25} - 21 q^{26} + 7 q^{27} + 12 q^{29} + 11 q^{30} + 35 q^{31} - 60 q^{32} + 7 q^{33} + 70 q^{34} - 12 q^{36} - 6 q^{37} + 35 q^{38} + 35 q^{39} + 105 q^{40} - 42 q^{41} - 30 q^{43} + 13 q^{44} - 35 q^{45} + 69 q^{46} - 42 q^{47} - 84 q^{48} + 40 q^{50} + 53 q^{51} - 7 q^{52} - 31 q^{53} + 70 q^{54} - 7 q^{55} - 12 q^{57} - 47 q^{58} + 35 q^{59} - 91 q^{60} - 14 q^{61} - 28 q^{62} - 32 q^{64} + 35 q^{65} - 35 q^{66} + 11 q^{67} + 77 q^{68} + 70 q^{69} + 19 q^{71} - 124 q^{72} - 35 q^{73} + 13 q^{74} - 119 q^{75} + 119 q^{76} + 28 q^{78} + 15 q^{79} + 70 q^{80} - 125 q^{81} - 98 q^{82} - 26 q^{85} + 9 q^{86} + 35 q^{87} + 49 q^{88} - 14 q^{89} - 182 q^{90} - 38 q^{92} + 46 q^{93} + 14 q^{94} + 128 q^{95} + 98 q^{96} - 16 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 + 7 * q^3 + 12 * q^4 + 7 * q^5 - 20 * q^8 - 15 * q^9 + 7 * q^10 - 3 * q^11 - 63 * q^12 - 14 * q^13 - 12 * q^15 + 18 * q^16 + 14 * q^17 + 2 * q^18 + 21 * q^19 + 14 * q^20 - 20 * q^22 - 27 * q^23 - 77 * q^24 + 17 * q^25 - 21 * q^26 + 7 * q^27 + 12 * q^29 + 11 * q^30 + 35 * q^31 - 60 * q^32 + 7 * q^33 + 70 * q^34 - 12 * q^36 - 6 * q^37 + 35 * q^38 + 35 * q^39 + 105 * q^40 - 42 * q^41 - 30 * q^43 + 13 * q^44 - 35 * q^45 + 69 * q^46 - 42 * q^47 - 84 * q^48 + 40 * q^50 + 53 * q^51 - 7 * q^52 - 31 * q^53 + 70 * q^54 - 7 * q^55 - 12 * q^57 - 47 * q^58 + 35 * q^59 - 91 * q^60 - 14 * q^61 - 28 * q^62 - 32 * q^64 + 35 * q^65 - 35 * q^66 + 11 * q^67 + 77 * q^68 + 70 * q^69 + 19 * q^71 - 124 * q^72 - 35 * q^73 + 13 * q^74 - 119 * q^75 + 119 * q^76 + 28 * q^78 + 15 * q^79 + 70 * q^80 - 125 * q^81 - 98 * q^82 - 26 * q^85 + 9 * q^86 + 35 * q^87 + 49 * q^88 - 14 * q^89 - 182 * q^90 - 38 * q^92 + 46 * q^93 + 14 * q^94 + 128 * q^95 + 98 * q^96 - 16 * q^99

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