LMFDB - Embedded newform 343.2.g.i.312.4

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			312.4
Character	$\chi$	$=$	343.312
Dual form			343.2.g.i.177.4

$q$-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 $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{20}{21}\right)$

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	0.424430	−	0.905461i	$-0.360474\pi$
$2$	1.92202	−	1.78338i	1.35908	−	1.26104i	0.934647	−	0.355578i	$-0.115716\pi$
$3$	1.46134	−	0.220261i	0.843703	−	0.127168i	0.287053	−	0.957915i	$-0.407325\pi$
$3$	1.46134	−	0.220261i	0.843703	−	0.127168i	0.556650	+	0.830747i	$0.312086\pi$
$4$	0.364281	−	4.86099i	0.182140	−	2.43049i
$5$	−0.754391	+	1.92216i	−0.337374	+	0.859615i	0.657020	+	0.753873i	$0.271817\pi$
$5$	−0.754391	+	1.92216i	−0.337374	+	0.859615i	−0.994394	+	0.105741i	$0.966278\pi$
$6$	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	0.552016	−	0.833833i	$-0.313859\pi$
$11$	1.78567	+	0.550805i	0.538399	+	0.166074i	−0.0136176	+	0.999907i	$0.504335\pi$
$12$	−0.538349	−	7.18377i	−0.155408	−	2.07378i
$13$	−0.677236	−	2.96716i	−0.187831	−	0.822943i	−0.977757	−	0.209741i	$-0.932738\pi$
$13$	−0.677236	−	2.96716i	−0.187831	−	0.822943i	0.789926	−	0.613203i	$-0.210119\pi$
$14$		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	−0.695779	−	0.718256i	$-0.744941\pi$
$17$	−1.16012	+	0.790958i	−0.281371	+	0.191835i	0.414408	+	0.910091i	$0.363988\pi$
$18$	−1.06973	+	1.85283i	−0.252139	+	0.436717i
$19$	2.73229	+	4.73247i	0.626831	+	1.08570i	0.988184	+	0.153274i	$0.0489816\pi$
$19$	2.73229	+	4.73247i	0.626831	+	1.08570i	−0.361353	+	0.932429i	$0.617685\pi$
$20$	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	0.545649	−	0.838014i	$-0.316283\pi$
$23$	−0.168275	−	0.114728i	−0.0350878	−	0.0239225i	−0.580737	+	0.814091i	$0.697236\pi$
$24$	−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	0.578480	−	0.815696i	$-0.303646\pi$
$29$	1.62320	+	0.781691i	0.301420	+	0.145156i	−0.277060	+	0.960853i	$0.589360\pi$
$30$	4.00056	+	6.92917i	0.730398	+	1.26509i
$31$	−2.57807	+	4.46535i	−0.463035	+	0.802000i	−0.999110	−	0.0421697i	$-0.986573\pi$
$31$	−2.57807	+	4.46535i	−0.463035	+	0.802000i	0.536075	+	0.844170i	$0.319906\pi$
$32$	−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	0.828621	+	0.559810i	$0.189126\pi$
$37$	0.563813	+	7.52356i	0.0926903	+	1.23687i	−0.735931	+	0.677057i	$0.763255\pi$
$38$	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	−0.987325	−	0.158714i	$-0.949265\pi$
$41$	−5.90598	−	7.40586i	−0.922359	−	1.15660i	0.0649659	−	0.997887i	$-0.479306\pi$
$42$		0			0
$43$	1.60000	−	2.00633i	0.243997	−	0.305963i	−0.644720	−	0.764419i	$-0.723026\pi$
$43$	1.60000	−	2.00633i	0.243997	−	0.305963i	0.888717	+	0.458456i	$0.151597\pi$
$44$	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	−0.764034	−	0.645176i	$-0.776784\pi$
$47$	−1.21865	+	1.13074i	−0.177758	+	0.164936i	0.586276	+	0.810112i	$0.300594\pi$
$48$	−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	−0.828112	−	0.560563i	$-0.810585\pi$
$53$	0.540899	−	7.21780i	0.0742982	−	0.991441i	0.902410	−	0.430878i	$-0.141796\pi$
$54$	−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	−0.979967	−	0.199159i	$-0.936179\pi$
$59$	−3.04990	−	7.77102i	−0.397063	−	1.01170i	0.582904	−	0.812541i	$-0.301916\pi$
$60$	14.2145	+	4.38458i	1.83508	+	0.566047i
$61$	−0.493546	−	6.58591i	−0.0631920	−	0.843239i	−0.935284	−	0.353898i	$-0.884856\pi$
$61$	−0.493546	−	6.58591i	−0.0631920	−	0.843239i	0.872092	−	0.489342i	$-0.162763\pi$
$62$	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	−0.954399	−	0.298534i	$-0.903502\pi$
$67$	−1.78982	+	3.10006i	−0.218661	+	0.378732i	0.735738	+	0.677267i	$0.236836\pi$
$68$	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	−0.755592	−	0.655043i	$-0.772651\pi$
$71$	−6.02101	+	2.89956i	−0.714562	+	0.344115i	0.0410295	+	0.999158i	$0.486936\pi$
$72$	5.08149	+	3.46450i	0.598859	+	0.408295i
$73$	0.129576	+	0.120229i	0.0151657	+	0.0140717i	0.687719	−	0.725977i	$-0.258612\pi$
$73$	0.129576	+	0.120229i	0.0151657	+	0.0140717i	−0.672553	+	0.740049i	$0.734803\pi$
$74$	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	−0.850816	−	0.525463i	$-0.823892\pi$
$79$	−7.82581	−	13.5547i	−0.880473	−	1.52502i	−0.0296560	−	0.999560i	$-0.509441\pi$
$80$	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	−0.709691	−	0.704514i	$-0.751165\pi$
$83$	2.14456	−	9.39591i	0.235396	−	1.03134i	0.945086	−	0.326822i	$-0.105978\pi$
$84$		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	−0.357058	−	0.934082i	$-0.616220\pi$
$89$	−1.18760	+	0.366325i	−0.125885	+	0.0388304i	0.231173	+	0.972913i	$0.425744\pi$
$90$	−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	−0.0831241	−	0.996539i	$-0.526490\pi$
$101$	1.31834	−	0.198708i	0.131180	−	0.0197722i	0.214304	+	0.976767i	$0.431252\pi$
$102$	−0.406580	+	5.42543i	−0.0402574	+	0.537198i
$103$	2.78726	−	7.10182i	0.274637	−	0.699763i	−0.725299	−	0.688434i	$-0.758298\pi$
$103$	2.78726	−	7.10182i	0.274637	−	0.699763i	0.999936	−	0.0113292i	$-0.00360626\pi$
$104$	−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	−0.219398	−	0.975635i	$-0.570409\pi$
$107$	1.54046	−	0.475169i	0.148922	−	0.0459364i	0.368320	+	0.929699i	$0.379933\pi$
$108$	10.0432	+	25.5897i	0.966410	+	2.46237i
$109$	9.74415	+	3.00567i	0.933320	+	0.287891i	0.723876	−	0.689930i	$-0.242359\pi$
$109$	9.74415	+	3.00567i	0.933320	+	0.287891i	0.209444	+	0.977821i	$0.432835\pi$
$110$	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	0.845886	+	0.533364i	$0.179072\pi$
$113$	−1.56953	+	6.87656i	−0.147649	+	0.646893i	−0.993535	+	0.113528i	$0.963785\pi$
$114$	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	0.430984	−	0.902359i	$-0.358166\pi$
$127$	−0.0652974	−	0.0314456i	−0.00579421	−	0.00279034i	−0.436779	+	0.899569i	$0.643881\pi$
$128$	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	0.890750	−	0.454493i	$-0.150179\pi$
$131$	18.4040	+	2.77395i	1.60796	+	0.242361i	0.717213	+	0.696854i	$0.245418\pi$
$132$	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	0.999642	−	0.0267444i	$-0.00851402\pi$
$137$	2.91051	+	7.41586i	0.248662	+	0.633580i	−0.750980	+	0.660324i	$0.770419\pi$
$138$	−0.754104	+	0.232610i	−0.0641936	+	0.0198011i
$139$	11.8104	+	14.8098i	1.00175	+	1.25615i	0.966472	+	0.256772i	$0.0826590\pi$
$139$	11.8104	+	14.8098i	1.00175	+	1.25615i	0.0352743	+	0.999378i	$0.488770\pi$
$140$		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	−0.539328	+	0.842096i	$0.681322\pi$
$149$	−17.3257	+	16.0759i	−1.41937	+	1.31699i	−0.880045	+	0.474890i	$0.842488\pi$
$150$	2.82081	−	0.425169i	0.230318	−	0.0347149i
$151$	−0.664285	+	8.86426i	−0.0540587	+	0.721364i	0.902661	+	0.430352i	$0.141611\pi$
$151$	−0.664285	+	8.86426i	−0.0540587	+	0.721364i	−0.956720	+	0.291011i	$0.906008\pi$
$152$	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	0.905952	−	0.423380i	$-0.139156\pi$
$157$	−0.577998	−	1.47272i	−0.0461293	−	0.117535i	−0.952081	+	0.305844i	$0.901061\pi$
$158$	−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	0.725185	−	0.688554i	$-0.241754\pi$
$163$	15.5146	+	2.33845i	1.21520	+	0.183162i	0.490013	+	0.871715i	$0.336992\pi$
$164$	−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	0.186877	−	0.982383i	$-0.440163\pi$
$167$	−6.00479	−	2.89175i	−0.464664	−	0.223771i	−0.651542	+	0.758613i	$0.725878\pi$
$168$		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	−0.325248	−	0.945629i	$-0.605448\pi$
$173$	−17.4189	−	11.8760i	−1.32434	−	0.902917i	−0.999087	+	0.0427122i	$0.986400\pi$
$174$	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	−0.992032	−	0.125986i	$-0.959790\pi$
$179$	−16.5524	+	11.2852i	−1.23718	+	0.843498i	−0.245153	+	0.969484i	$0.578838\pi$
$180$	−8.12160	−	1.22413i	−0.605349	−	0.0912416i
$181$	1.67180	−	7.32462i	0.124264	−	0.544435i	−0.874021	−	0.485888i	$-0.838496\pi$
$181$	1.67180	−	7.32462i	0.124264	−	0.544435i	0.998285	−	0.0585468i	$-0.0186467\pi$
$182$		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	−0.979082	−	0.203465i	$-0.934780\pi$
$191$	−1.69952	+	4.33031i	−0.122973	+	0.313330i	0.856109	+	0.516795i	$0.172875\pi$
$192$	−1.02533	+	13.6820i	−0.0739966	+	0.987417i
$193$	21.7036	−	3.27129i	1.56226	−	0.235472i	0.689740	−	0.724057i	$-0.257725\pi$
$193$	21.7036	−	3.27129i	1.56226	−	0.235472i	0.872516	+	0.488585i	$0.162487\pi$
$194$	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	0.0805964	−	0.996747i	$-0.474318\pi$
$199$	6.36790	−	0.959806i	0.451408	−	0.0680389i	0.370812	+	0.928708i	$0.379079\pi$
$200$	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	−0.764527	−	0.644591i	$-0.777028\pi$
$211$	2.96277	−	12.9808i	0.203966	−	0.893632i	0.968493	−	0.249041i	$-0.0801154\pi$
$212$	−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	−0.855959	−	0.517044i	$-0.827032\pi$
$223$	−14.7151	+	7.08644i	−0.985399	+	0.474543i	−0.129440	+	0.991587i	$0.541318\pi$
$224$		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	−0.510959	−	0.859605i	$-0.670710\pi$
$227$	7.36693	−	12.7599i	0.488960	−	0.846904i	0.999919	+	0.0127013i	$0.00404304\pi$
$228$	32.5260	−	22.1759i	2.15409	−	1.46863i
$229$	−6.56085	−	0.988890i	−0.433553	−	0.0653477i	−0.0713600	−	0.997451i	$-0.522734\pi$
$229$	−6.56085	−	0.988890i	−0.433553	−	0.0653477i	−0.362193	+	0.932103i	$0.617972\pi$
$230$	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	−0.999975	−	0.00710913i	$-0.997737\pi$
$233$	−0.186659	−	2.49079i	−0.0122285	−	0.163177i	0.987746	−	0.156068i	$-0.0498820\pi$
$234$	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	−0.431846	−	0.901947i	$-0.642138\pi$
$239$	8.40358	−	10.5378i	0.543583	−	0.681631i	0.975428	+	0.220316i	$0.0707090\pi$
$240$	11.1628	−	28.4424i	0.720557	−	1.83595i
$241$	−1.81042	+	24.1583i	−0.116619	+	1.55617i	0.565386	+	0.824827i	$0.308727\pi$
$241$	−1.81042	+	24.1583i	−0.116619	+	1.55617i	−0.682005	+	0.731348i	$0.738892\pi$
$242$	−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	−0.598362	−	0.801226i	$-0.704182\pi$
$251$	5.00516	−	6.27627i	0.315923	−	0.396155i	0.914285	+	0.405071i	$0.132753\pi$
$252$		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	0.872439	+	0.488724i	$0.162537\pi$
$257$	1.32394	+	17.6667i	0.0825849	+	1.10202i	−0.789854	+	0.613295i	$0.789844\pi$
$258$	−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	−0.395321	−	0.918543i	$-0.629367\pi$
$263$	9.69503	−	16.7923i	0.597821	−	1.03546i	0.993142	−	0.116913i	$-0.0373000\pi$
$264$	−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	0.972017	+	0.234909i	$0.0754793\pi$
$269$	20.9757	+	19.4626i	1.27891	+	1.18665i	0.306891	+	0.951745i	$0.400711\pi$
$270$	−22.3816	−	20.7671i	−1.36210	−	1.26385i
$271$	−22.1894	−	15.1285i	−1.34791	−	0.918990i	−0.348081	−	0.937464i	$-0.613167\pi$
$271$	−22.1894	−	15.1285i	−1.34791	−	0.918990i	−0.999829	+	0.0184744i	$0.994119\pi$
$272$	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	−0.260551	−	0.965460i	$-0.583904\pi$
$277$	9.03698	−	6.16131i	0.542980	−	0.370197i	0.803531	+	0.595263i	$0.202952\pi$
$278$	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	0.861817	+	0.507219i	$0.169327\pi$
$281$	5.11979	+	22.4313i	0.305421	+	1.33814i	−0.556396	+	0.830917i	$0.687816\pi$
$282$	0.481385	+	6.42363i	0.0286660	+	0.382522i
$283$	−1.25063	−	0.385767i	−0.0743419	−	0.0229315i	0.257361	−	0.966315i	$-0.417147\pi$
$283$	−1.25063	−	0.385767i	−0.0743419	−	0.0229315i	−0.331703	+	0.943384i	$0.607623\pi$
$284$	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	0.952344	+	0.305025i	$0.0986647\pi$
$307$	3.97135	+	17.3996i	0.226657	+	0.993049i	−0.725687	+	0.688025i	$0.758478\pi$
$308$		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	−0.422340	−	0.906438i	$-0.638791\pi$
$311$	4.71108	−	3.21196i	0.267141	−	0.182134i	0.689481	+	0.724304i	$0.257839\pi$
$312$	−16.9501	+	29.3584i	−0.959608	+	1.66209i
$313$	10.7377	+	18.5983i	0.606933	+	1.05124i	0.991743	+	0.128242i	$0.0409335\pi$
$313$	10.7377	+	18.5983i	0.606933	+	1.05124i	−0.384810	+	0.922996i	$0.625733\pi$
$314$	−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	0.698256	−	0.715848i	$-0.253960\pi$
$317$	5.10976	+	3.48378i	0.286993	+	0.195668i	−0.411263	+	0.911517i	$0.634912\pi$
$318$	−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	0.994265	−	0.106947i	$-0.0341074\pi$
$331$	−0.0879555	−	1.17368i	−0.00483447	−	0.0645115i	−0.999099	+	0.0424352i	$0.986488\pi$
$332$	−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	−0.865634	−	0.500678i	$-0.833084\pi$
$337$	−3.39407	+	4.25603i	−0.184887	+	0.231841i	0.680747	+	0.732519i	$0.261655\pi$
$338$	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	0.984833	+	0.173505i	$0.0555092\pi$
$347$	−0.276806	+	3.69373i	−0.0148597	+	0.198290i	−0.999693	+	0.0247850i	$0.992110\pi$
$348$	4.74164	−	12.0815i	0.254179	−	0.647636i
$349$	15.1210	−	18.9611i	0.809406	−	1.01496i	−0.190043	−	0.981776i	$-0.560863\pi$
$349$	15.1210	−	18.9611i	0.809406	−	1.01496i	0.999449	−	0.0331876i	$-0.0105659\pi$
$350$		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	0.852724	+	0.522362i	$0.174949\pi$
$353$	10.9523	+	27.9059i	0.582929	+	1.48528i	−0.269794	+	0.962918i	$0.586956\pi$
$354$	−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	−0.111924	−	0.993717i	$-0.535701\pi$
$359$	−9.69681	−	1.46156i	−0.511778	−	0.0771381i	−0.399854	+	0.916579i	$0.630939\pi$
$360$	−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	0.925852	−	0.377885i	$-0.123349\pi$
$367$	11.8433	+	10.9889i	0.618213	+	0.573618i	−0.307640	+	0.951503i	$0.599539\pi$
$368$	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	0.999934	−	0.0114488i	$-0.00364435\pi$
$373$	9.46448	+	16.3930i	0.490052	+	0.848795i	−0.509882	+	0.860244i	$0.670311\pi$
$374$	−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	−0.953182	−	0.302398i	$-0.902213\pi$
$379$	−4.39197	−	19.2425i	−0.225600	−	0.988420i	0.727581	−	0.686021i	$-0.240644\pi$
$380$	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	−0.536968	−	0.843602i	$-0.680431\pi$
$383$	−9.89115	+	3.05102i	−0.505414	+	0.155900i	0.0315540	+	0.999502i	$0.489954\pi$
$384$	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	−0.603631	−	0.797264i	$-0.706280\pi$
$389$	−18.6471	+	2.81060i	−0.945446	+	0.142503i	−0.341815	+	0.939767i	$0.611042\pi$
$390$	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	−0.933941	−	0.357428i	$-0.883654\pi$
$397$	−0.123550	+	0.314801i	−0.00620082	+	0.0157994i	0.927740	+	0.373228i	$0.121749\pi$
$398$	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	0.315552	−	0.948908i	$-0.397810\pi$
$401$	22.2440	−	6.86136i	1.11081	−	0.342640i	0.795260	+	0.606268i	$0.207334\pi$
$402$	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	−0.808802	−	0.588081i	$-0.799884\pi$
$409$	−11.2618	+	7.67818i	−0.556861	+	0.379662i	0.251941	+	0.967743i	$0.418931\pi$
$410$	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	−0.235256	−	0.971934i	$-0.575593\pi$
$419$	7.73651	−	3.72571i	0.377953	−	0.182013i	0.613209	+	0.789921i	$0.289878\pi$
$420$		0			0
$421$	5.75293	+	2.77046i	0.280381	+	0.135024i	0.568789	−	0.822483i	$-0.307412\pi$
$421$	5.75293	+	2.77046i	0.280381	+	0.135024i	−0.288409	+	0.957507i	$0.593126\pi$
$422$	−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	−0.678411	−	0.734683i	$-0.737331\pi$
$431$	−14.1340	−	36.0129i	−0.680812	−	1.73468i	−0.00240092	−	0.999997i	$-0.500764\pi$
$432$	53.9570	−	16.6435i	2.59601	−	0.800762i
$433$	0.316460	+	0.396828i	0.0152081	+	0.0190703i	0.789377	−	0.613908i	$-0.210404\pi$
$433$	0.316460	+	0.396828i	0.0152081	+	0.0190703i	−0.774169	+	0.632979i	$0.781832\pi$
$434$		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	−0.571828	−	0.820374i	$-0.693766\pi$
$439$	4.26419	−	3.95659i	0.203519	−	0.188838i	0.775347	+	0.631536i	$0.217575\pi$
$440$	29.0830			1.38648
$441$		0			0
$442$	11.2045			0.532942
$443$	4.78541	−	4.44021i	0.227362	−	0.210961i	−0.558263	−	0.829664i	$-0.688532\pi$
$443$	4.78541	−	4.44021i	0.227362	−	0.210961i	0.785625	+	0.618703i	$0.212342\pi$
$444$	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	0.474592	−	0.880206i	$-0.342596\pi$
$449$	−10.3649	−	12.9972i	−0.489152	−	0.613377i	−0.963744	+	0.266829i	$0.914024\pi$
$450$	−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	0.981413	−	0.191905i	$-0.0614666\pi$
$457$	39.8191	+	6.00177i	1.86266	+	0.280751i	0.881247	+	0.472656i	$0.156705\pi$
$458$	−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	0.531056	−	0.847337i	$-0.321795\pi$
$461$	4.28753	+	2.06477i	0.199690	+	0.0961657i	−0.331366	+	0.943502i	$0.607510\pi$
$462$		0			0
$463$	21.6387	−	10.4207i	1.00564	−	0.484289i	0.142789	−	0.989753i	$-0.454393\pi$
$463$	21.6387	−	10.4207i	1.00564	−	0.484289i	0.862848	+	0.505464i	$0.168679\pi$
$464$	−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	0.132970	−	0.991120i	$-0.457549\pi$
$467$	−16.0144	−	10.9184i	−0.741059	−	0.505245i	−0.874028	+	0.485875i	$0.838501\pi$
$468$	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	0.245167	−	0.969481i	$-0.421157\pi$
$479$	−2.15347	−	0.664257i	−0.0983945	−	0.0303507i	−0.343562	+	0.939130i	$0.611633\pi$
$480$	−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	−0.0357190	−	0.999362i	$-0.511372\pi$
$487$	4.95905	−	0.747457i	0.224716	−	0.0338705i	0.260435	+	0.965491i	$0.416134\pi$
$488$	−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	−0.818739	−	0.574166i	$-0.805327\pi$
$499$	−26.1755	+	8.07406i	−1.17177	+	0.361444i	−0.353035	+	0.935610i	$0.614850\pi$
$500$	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	0.910196	−	0.414179i	$-0.135931\pi$
$503$	−2.00879	−	8.80109i	−0.0895676	−	0.392421i	−0.999763	+	0.0217571i	$0.993074\pi$
$504$		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	−0.999223	−	0.0394096i	$-0.987452\pi$
$509$	−12.0418	−	20.8569i	−0.533741	−	0.924467i	0.465482	−	0.885057i	$-0.345881\pi$
$510$	−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	−0.594054	−	0.804425i	$-0.702473\pi$
$521$	9.12162	−	15.7991i	0.399626	−	0.692172i	0.993680	+	0.112253i	$0.0358068\pi$
$522$	−3.18473	+	2.17131i	−0.139392	+	0.0950357i
$523$	−4.05307	−	0.610901i	−0.177228	−	0.0267129i	0.0598285	−	0.998209i	$-0.480945\pi$
$523$	−4.05307	−	0.610901i	−0.177228	−	0.0267129i	−0.237057	+	0.971496i	$0.576183\pi$
$524$	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	−0.898306	−	0.439370i	$-0.855202\pi$
$541$	−12.2646	+	11.3799i	−0.527296	+	0.489259i	0.371011	+	0.928629i	$0.379011\pi$
$542$	−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	0.793855	−	0.608108i	$-0.208071\pi$
$547$	0.569364	+	0.713960i	0.0243443	+	0.0305267i	−0.769510	+	0.638634i	$0.779500\pi$
$548$	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	−0.222089	+	0.975026i	$0.571288\pi$
$557$	−22.5492	+	39.0564i	−0.955442	+	1.65487i	−0.733353	+	0.679848i	$0.762046\pi$
$558$	−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	0.0196708	−	0.999807i	$-0.493738\pi$
$563$	−23.1551	−	21.4848i	−0.975870	−	0.905475i	−0.995541	+	0.0943315i	$0.969929\pi$
$564$	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	0.633297	−	0.773909i	$-0.281701\pi$
$569$	−8.43410	−	14.6083i	−0.353576	−	0.612412i	−0.986873	+	0.161497i	$0.948368\pi$
$570$	−21.8614	+	37.8650i	−0.915672	+	1.58599i
$571$	7.77392	−	5.30017i	0.325328	−	0.221805i	−0.389631	−	0.920971i	$-0.627398\pi$
$571$	7.77392	−	5.30017i	0.325328	−	0.221805i	0.714959	+	0.699166i	$0.246445\pi$
$572$	−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	0.0584675	−	0.998289i	$-0.481379\pi$
$577$	−10.9434	−	3.37560i	−0.455581	−	0.140528i	−0.514048	+	0.857761i	$0.671855\pi$
$578$	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	−0.164058	−	0.986451i	$-0.552459\pi$
$593$	15.2724	−	38.9134i	0.627162	−	1.59798i	0.791220	−	0.611531i	$-0.209446\pi$
$594$	−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	0.123670	−	0.992323i	$-0.460534\pi$
$599$	−8.15355	−	2.51504i	−0.333145	−	0.102762i	−0.456815	+	0.889562i	$0.651010\pi$
$600$	−0.612813	−	8.17742i	−0.0250180	−	0.333842i
$601$	3.88880	+	17.0379i	0.158627	+	0.694992i	0.990209	+	0.139590i	$0.0445784\pi$
$601$	3.88880	+	17.0379i	0.158627	+	0.694992i	−0.831582	+	0.555402i	$0.812564\pi$
$602$		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	0.998838	+	0.0482033i	$0.0153495\pi$
$607$	13.3329	+	23.0932i	0.541164	+	0.937324i	−0.457673	+	0.889120i	$0.651317\pi$
$608$	−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	0.235456	−	0.971885i	$-0.424342\pi$
$613$	−17.7302	−	16.4512i	−0.716116	−	0.664458i	−0.951572	+	0.307427i	$0.900532\pi$
$614$	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	0.859823	−	0.510592i	$-0.170574\pi$
$617$	24.7579	+	11.9228i	0.996717	+	0.479994i	0.136894	+	0.990586i	$0.456288\pi$
$618$	−14.7809	−	25.6013i	−0.594575	−	1.02983i
$619$	−4.78591	+	8.28944i	−0.192362	+	0.333181i	−0.946033	−	0.324072i	$-0.894948\pi$
$619$	−4.78591	+	8.28944i	−0.192362	+	0.333181i	0.753671	+	0.657252i	$0.228281\pi$
$620$	−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	−0.679727	−	0.733465i	$-0.737902\pi$
$631$	4.68739	−	5.87780i	0.186602	−	0.233992i	0.866329	+	0.499474i	$0.166473\pi$
$632$	−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	−0.994127	−	0.108219i	$-0.965485\pi$
$641$	0.127237	−	1.69786i	0.00502556	−	0.0670614i	0.999153	+	0.0411571i	$0.0131044\pi$
$642$	2.28212	−	5.81474i	0.0900679	−	0.229489i
$643$	1.53076	−	1.91951i	0.0603672	−	0.0756981i	−0.750731	−	0.660608i	$-0.770299\pi$
$643$	1.53076	−	1.91951i	0.0603672	−	0.0756981i	0.811098	+	0.584910i	$0.198870\pi$
$644$		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	−0.975555	−	0.219753i	$-0.929475\pi$
$647$	−10.4261	−	26.5653i	−0.409893	−	1.04439i	0.565662	−	0.824637i	$-0.308621\pi$
$648$	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	−0.0157719	−	0.999876i	$-0.505021\pi$
$653$	−8.31936	−	1.25394i	−0.325562	−	0.0490705i	−0.309790	+	0.950805i	$0.600259\pi$
$654$	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	−0.846846	−	0.531838i	$-0.821502\pi$
$659$	−24.6195	+	11.8561i	−0.959039	+	0.461849i	−0.112193	+	0.993686i	$0.535787\pi$
$660$	22.9672	+	15.6588i	0.893999	+	0.609518i
$661$	14.8873	+	13.8134i	0.579048	+	0.537278i	0.914398	−	0.404815i	$-0.132664\pi$
$661$	14.8873	+	13.8134i	0.579048	+	0.537278i	−0.335350	+	0.942093i	$0.608855\pi$
$662$	−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	0.999380	−	0.0352021i	$-0.0112075\pi$
$673$	2.17126	+	9.51293i	0.0836961	+	0.366697i	−0.915684	+	0.401899i	$0.868350\pi$
$674$	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	0.215507	−	0.976502i	$-0.430860\pi$
$677$	24.5530	−	7.57361i	0.943650	−	0.291077i	0.728143	+	0.685425i	$0.240384\pi$
$678$	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	−0.596608	−	0.802533i	$-0.703485\pi$
$683$	−24.3090	+	3.66399i	−0.930159	+	0.140199i	−0.333551	+	0.942732i	$0.608247\pi$
$684$	−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	−0.908717	−	0.417413i	$-0.862937\pi$
$691$	1.08651	−	2.76839i	0.0413329	−	0.105315i	0.950050	+	0.312099i	$0.101032\pi$
$692$	−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	−0.969306	−	0.245858i	$-0.920930\pi$
$701$	0.282827	−	1.23914i	0.0106822	−	0.0468018i	0.979988	+	0.199056i	$0.0637875\pi$
$702$	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	−0.993821	−	0.110994i	$-0.964597\pi$
$709$	−38.8815	−	26.5090i	−1.46023	−	0.995565i	−0.466405	−	0.884571i	$-0.654451\pi$
$710$	−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	−0.0533356	−	0.998577i	$-0.516985\pi$
$719$	−10.6891	−	1.61113i	−0.398637	−	0.0600849i	−0.345302	+	0.938492i	$0.612223\pi$
$720$	−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	0.978422	−	0.206615i	$-0.0662449\pi$
$727$	15.0795	+	18.9091i	0.559268	+	0.701300i	−0.419155	+	0.907915i	$0.637673\pi$
$728$		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	−0.922133	−	0.386872i	$-0.873555\pi$
$733$	−16.3866	+	15.2046i	−0.605254	+	0.561594i	0.316879	+	0.948466i	$0.397365\pi$
$734$	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	−0.997994	−	0.0633058i	$-0.979836\pi$
$739$	−0.0465273	+	0.620863i	−0.00171153	+	0.0228388i	0.996283	+	0.0861446i	$0.0274547\pi$
$740$	−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	0.437122	−	0.899402i	$-0.355998\pi$
$743$	−14.6375	−	18.3549i	−0.536999	−	0.673375i	−0.974121	+	0.226027i	$0.927426\pi$
$744$	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	−0.786102	−	0.618097i	$-0.787904\pi$
$751$	−47.1209	−	7.10234i	−1.71947	−	0.259168i	−0.933365	+	0.358929i	$0.883142\pi$
$752$	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	−0.498968	−	0.866620i	$-0.666287\pi$
$757$	−3.64606	+	1.75585i	−0.132518	+	0.0638175i	0.366450	+	0.930438i	$0.380573\pi$
$758$	−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	0.978342	−	0.206995i	$-0.0663684\pi$
$761$	31.5334	+	21.4991i	1.14308	+	0.779342i	0.164742	+	0.986337i	$0.447321\pi$
$762$	−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	0.487496	+	0.873125i	$0.337910\pi$
$769$	−9.16664	+	40.1617i	−0.330558	+	1.44827i	−0.818054	+	0.575142i	$0.804947\pi$
$770$		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	0.516136	−	0.856507i	$-0.327370\pi$
$773$	12.7921	+	3.94584i	0.460100	+	0.141922i	−0.0560357	+	0.998429i	$0.517846\pi$
$774$	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	0.314940	−	0.949111i	$-0.398016\pi$
$787$	25.1260	−	3.78713i	0.895644	−	0.134997i	0.580704	+	0.814115i	$0.302777\pi$
$788$	−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	0.946316	−	0.323242i	$-0.104773\pi$
$797$	−1.31373	−	5.75582i	−0.0465347	−	0.203882i	−0.992851	+	0.119360i	$0.961916\pi$
$798$		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	0.521346	−	0.853346i	$-0.325430\pi$
$809$	−8.26704	−	7.67070i	−0.290654	−	0.269687i	−0.811999	+	0.583658i	$0.801621\pi$
$810$	−26.3308	−	17.9521i	−0.925171	−	0.630771i
$811$	16.3734	−	7.88502i	0.574948	−	0.276881i	−0.123731	−	0.992316i	$-0.539486\pi$
$811$	16.3734	−	7.88502i	0.574948	−	0.276881i	0.698679	+	0.715435i	$0.253772\pi$
$812$		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	0.617197	+	0.786809i	$0.288268\pi$
$821$	3.55761	+	47.4730i	0.124161	+	1.65682i	−0.493036	+	0.870009i	$0.664113\pi$
$822$	29.4976	+	9.09881i	1.02885	+	0.317357i
$823$	−4.30931	−	10.9800i	−0.150213	−	0.382737i	0.835884	−	0.548906i	$-0.184956\pi$
$823$	−4.30931	−	10.9800i	−0.150213	−	0.382737i	−0.986097	+	0.166169i	$0.946860\pi$
$824$	−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	−0.978780	−	0.204913i	$-0.934309\pi$
$827$	−16.1389	+	20.2376i	−0.561206	+	0.703730i	0.417575	+	0.908643i	$0.362880\pi$
$828$	0.295961	−	0.754097i	0.0102854	−	0.0262067i
$829$	0.847463	−	11.3086i	0.0294336	−	0.392764i	−0.962959	−	0.269649i	$-0.913092\pi$
$829$	0.847463	−	11.3086i	0.0294336	−	0.392764i	0.992392	−	0.123115i	$-0.0392885\pi$
$830$	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	−0.537061	−	0.843543i	$-0.680465\pi$
$839$	11.7264	−	14.7044i	0.404840	−	0.507654i	0.941901	+	0.335890i	$0.109037\pi$
$840$		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	0.287531	−	0.957771i	$-0.407166\pi$
$853$	−8.23650	−	3.96649i	−0.282012	−	0.135810i	−0.569543	+	0.821961i	$0.692880\pi$
$854$		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	0.430367	−	0.902654i	$-0.358384\pi$
$857$	−12.8106	−	11.8865i	−0.437601	−	0.406034i	−0.867968	+	0.496619i	$0.834574\pi$
$858$	−16.1545	−	14.9892i	−0.551504	−	0.511721i
$859$	−10.6109	−	7.23437i	−0.362038	−	0.246833i	0.368615	−	0.929582i	$-0.379832\pi$
$859$	−10.6109	−	7.23437i	−0.362038	−	0.246833i	−0.730653	+	0.682749i	$0.760784\pi$
$860$	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	0.972886	+	0.231287i	$0.0742936\pi$
$863$	20.1744	+	34.9430i	0.686743	+	1.18947i	−0.286142	+	0.958187i	$0.592373\pi$
$864$	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	−0.698179	−	0.715924i	$-0.746006\pi$
$877$	8.90126	−	22.6800i	0.300574	−	0.765850i	0.998753	−	0.0499269i	$-0.0158988\pi$
$878$	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	0.250381	+	0.968147i	$0.419444\pi$
$887$	−17.6214	+	44.8986i	−0.591669	+	1.50755i	−0.842050	+	0.539400i	$0.818651\pi$
$888$	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	0.400851	−	0.916143i	$-0.368715\pi$
$907$	−14.5395	−	13.4907i	−0.482775	−	0.447950i	−0.883626	+	0.468193i	$0.844905\pi$
$908$	−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	0.889057	−	0.457797i	$-0.151361\pi$
$911$	32.7621	+	15.7774i	1.08546	+	0.522728i	0.196398	+	0.980524i	$0.437075\pi$
$912$	−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	0.962292	+	0.272020i	$0.0876917\pi$
$919$	1.55487	+	20.7483i	0.0512905	+	0.684424i	−0.911001	+	0.412404i	$0.864689\pi$
$920$	−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	−0.682318	−	0.731055i	$-0.739028\pi$
$929$	−0.130972	+	0.121524i	−0.00429706	+	0.00398709i	0.678021	+	0.735042i	$0.262838\pi$
$930$	−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	−0.610790	−	0.791792i	$-0.709148\pi$
$937$	9.09326	−	11.4026i	0.297064	−	0.372506i	0.907854	+	0.419286i	$0.137720\pi$
$938$		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	0.994787	+	0.101972i	$0.0325153\pi$
$941$	10.2738	+	26.1771i	0.334915	+	0.853350i	−0.659872	+	0.751378i	$0.729389\pi$
$942$	−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	0.397998	−	0.917386i	$-0.369705\pi$
$947$	15.6301	+	2.35586i	0.507909	+	0.0765550i	0.109912	+	0.993941i	$0.464943\pi$
$948$	−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	0.362104	−	0.932138i	$-0.382058\pi$
$953$	40.6458	−	19.5740i	1.31665	−	0.634064i	0.954543	+	0.298074i	$0.0963442\pi$
$954$	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	0.724886	+	0.688869i	$0.241893\pi$
$967$	11.5268	+	50.5020i	0.370675	+	1.62403i	−0.354210	+	0.935166i	$0.615250\pi$
$968$	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	−0.841269	−	0.540616i	$-0.818191\pi$
$971$	−38.3845	+	11.8401i	−1.23182	+	0.379966i	−0.390549	+	0.920582i	$0.627715\pi$
$972$	−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	0.219711	−	0.975565i	$-0.429488\pi$
$977$	22.4180	−	3.37897i	0.717215	−	0.108103i	0.497503	+	0.867462i	$0.334250\pi$
$978$	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	0.137068	−	0.990562i	$-0.456232\pi$
$983$	17.5582	−	2.64648i	0.560021	−	0.0844095i	0.422952	+	0.906152i	$0.360994\pi$
$984$	−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	0.160799	−	0.986987i	$-0.448593\pi$
$991$	−8.25826	−	2.54734i	−0.262332	−	0.0809188i	−0.423131	+	0.906068i	$0.639069\pi$
$992$	−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	−0.396500	−	0.918035i	$-0.629775\pi$
$997$	9.88991	−	6.74283i	0.313217	−	0.213547i	0.709717	+	0.704487i	$0.248823\pi$
$998$	−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.312.4		48
7.2	even	3		49.2.g.a.2.1	✓	48
7.3	odd	6		343.2.e.c.246.8		48
7.4	even	3		343.2.e.d.246.8		48
7.5	odd	6		343.2.g.g.128.1		48
7.6	odd	2		343.2.g.h.312.4		48
21.2	odd	6		441.2.bb.d.100.4		48
28.23	odd	6		784.2.bg.c.737.3		48
49.3	odd	42		2401.2.a.i.1.1		24
49.9	even	21	inner	343.2.g.i.177.4		48
49.15	even	7		49.2.g.a.25.1	yes	48
49.24	odd	42		343.2.e.c.99.8		48
49.25	even	21		343.2.e.d.99.8		48
49.34	odd	14		343.2.g.g.67.1		48
49.40	odd	42		343.2.g.h.177.4		48
49.46	even	21		2401.2.a.h.1.1		24
147.113	odd	14		441.2.bb.d.172.4		48
196.15	odd	14		784.2.bg.c.417.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.2.1	✓	48	7.2	even	3
49.2.g.a.25.1	yes	48	49.15	even	7
343.2.e.c.99.8		48	49.24	odd	42
343.2.e.c.246.8		48	7.3	odd	6
343.2.e.d.99.8		48	49.25	even	21
343.2.e.d.246.8		48	7.4	even	3
343.2.g.g.67.1		48	49.34	odd	14
343.2.g.g.128.1		48	7.5	odd	6
343.2.g.h.177.4		48	49.40	odd	42
343.2.g.h.312.4		48	7.6	odd	2
343.2.g.i.177.4		48	49.9	even	21	inner
343.2.g.i.312.4		48	1.1	even	1	trivial
441.2.bb.d.100.4		48	21.2	odd	6
441.2.bb.d.172.4		48	147.113	odd	14
784.2.bg.c.417.3		48	196.15	odd	14
784.2.bg.c.737.3		48	28.23	odd	6
2401.2.a.h.1.1		24	49.46	even	21
2401.2.a.i.1.1		24	49.3	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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