LMFDB - Embedded newform 338.4.c.i.315.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,4,Mod(191,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.191"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	338.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,3,-8,-38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.9426455819$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{217})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 55x^{2} + 54x + 2916 $ x^4 - x^3 + 55x^2 + 54x + 2916
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			315.1
Root			$-3.43273 - 5.94566i$ of defining polynomial
Character	$\chi$	$=$	338.315
Dual form			338.4.c.i.191.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.93273 - 5.07964i) q^{3} +(-2.00000 + 3.46410i) q^{4} -2.13454 q^{5} +(5.86546 - 10.1593i) q^{6} +(-1.93273 + 3.34759i) q^{7} -8.00000 q^{8} +(-3.70181 + 6.41172i) q^{9} +(-2.13454 - 3.69713i) q^{10} +(26.5964 + 46.0663i) q^{11} +23.4618 q^{12} -7.73092 q^{14} +(6.26003 + 10.8427i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(21.6636 - 37.5225i) q^{17} -14.8072 q^{18} +(74.1928 - 128.506i) q^{19} +(4.26908 - 7.39426i) q^{20} +22.6727 q^{21} +(-53.1928 + 92.1326i) q^{22} +(-61.3273 - 106.222i) q^{23} +(23.4618 + 40.6371i) q^{24} -120.444 q^{25} -114.942 q^{27} +(-7.73092 - 13.3903i) q^{28} +(-41.9418 - 72.6453i) q^{29} +(-12.5201 + 21.6854i) q^{30} -190.269 q^{31} +(16.0000 - 27.7128i) q^{32} +(156.000 - 270.200i) q^{33} +86.6546 q^{34} +(4.12549 - 7.14556i) q^{35} +(-14.8072 - 25.6469i) q^{36} +(-65.8564 - 114.067i) q^{37} +296.771 q^{38} +17.0763 q^{40} +(-193.847 - 335.753i) q^{41} +(22.6727 + 39.2703i) q^{42} +(37.3182 - 64.6371i) q^{43} -212.771 q^{44} +(7.90166 - 13.6861i) q^{45} +(122.655 - 212.444i) q^{46} +298.789 q^{47} +(-46.9237 + 81.2742i) q^{48} +(164.029 + 284.107i) q^{49} +(-120.444 - 208.615i) q^{50} -254.135 q^{51} +100.386 q^{53} +(-114.942 - 199.085i) q^{54} +(-56.7710 - 98.3303i) q^{55} +(15.4618 - 26.7807i) q^{56} -870.349 q^{57} +(83.8836 - 145.291i) q^{58} +(239.655 - 415.094i) q^{59} -50.0802 q^{60} +(239.906 - 415.529i) q^{61} +(-190.269 - 329.556i) q^{62} +(-14.3092 - 24.7843i) q^{63} +64.0000 q^{64} +624.000 q^{66} +(-207.636 - 359.637i) q^{67} +(86.6546 + 150.090i) q^{68} +(-359.713 + 623.041i) q^{69} +16.5020 q^{70} +(146.973 - 254.564i) q^{71} +(29.6145 - 51.2938i) q^{72} -106.727 q^{73} +(131.713 - 228.133i) q^{74} +(353.229 + 611.811i) q^{75} +(296.771 + 514.023i) q^{76} -205.614 q^{77} -906.044 q^{79} +(17.0763 + 29.5771i) q^{80} +(437.042 + 756.979i) q^{81} +(387.695 - 671.507i) q^{82} +22.1605 q^{83} +(-45.3454 + 78.5405i) q^{84} +(-46.2419 + 80.0934i) q^{85} +149.273 q^{86} +(-246.008 + 426.098i) q^{87} +(-212.771 - 368.530i) q^{88} +(332.717 + 576.282i) q^{89} +31.6066 q^{90} +490.618 q^{92} +(558.008 + 966.498i) q^{93} +(298.789 + 517.518i) q^{94} +(-158.367 + 274.300i) q^{95} -187.695 q^{96} +(627.120 - 1086.20i) q^{97} +(-328.058 + 568.214i) q^{98} -393.819 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 3 q^{3} - 8 q^{4} - 38 q^{5} - 6 q^{6} + 7 q^{7} - 32 q^{8} - 59 q^{9} - 38 q^{10} + 18 q^{11} - 24 q^{12} + 28 q^{14} - 137 q^{15} - 32 q^{16} + 13 q^{17} - 236 q^{18} + 120 q^{19} + 76 q^{20}+ \cdots + 2844 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 3 * q^3 - 8 * q^4 - 38 * q^5 - 6 * q^6 + 7 * q^7 - 32 * q^8 - 59 * q^9 - 38 * q^10 + 18 * q^11 - 24 * q^12 + 28 * q^14 - 137 * q^15 - 32 * q^16 + 13 * q^17 - 236 * q^18 + 120 * q^19 + 76 * q^20 + 238 * q^21 - 36 * q^22 - 98 * q^23 - 24 * q^24 + 78 * q^25 - 666 * q^27 + 28 * q^28 - 374 * q^29 + 274 * q^30 - 820 * q^31 + 64 * q^32 + 624 * q^33 + 52 * q^34 - 175 * q^35 - 236 * q^36 - 13 * q^37 + 480 * q^38 + 304 * q^40 - 304 * q^41 + 238 * q^42 - 219 * q^43 - 144 * q^44 + 886 * q^45 + 196 * q^46 + 930 * q^47 + 48 * q^48 + 553 * q^49 + 78 * q^50 - 1046 * q^51 + 48 * q^53 - 666 * q^54 + 480 * q^55 - 56 * q^56 - 2244 * q^57 + 748 * q^58 + 664 * q^59 + 1096 * q^60 + 282 * q^61 - 820 * q^62 + 532 * q^63 + 256 * q^64 + 2496 * q^66 - 94 * q^67 + 52 * q^68 - 938 * q^69 - 700 * q^70 - 75 * q^71 + 472 * q^72 - 1900 * q^73 + 26 * q^74 + 2120 * q^75 + 480 * q^76 - 1176 * q^77 - 1444 * q^79 + 304 * q^80 + 334 * q^81 + 608 * q^82 - 2504 * q^83 - 476 * q^84 + 419 * q^85 - 876 * q^86 + 2080 * q^87 - 144 * q^88 - 702 * q^89 + 3544 * q^90 + 784 * q^92 - 832 * q^93 + 930 * q^94 + 162 * q^95 + 192 * q^96 + 564 * q^97 - 1106 * q^98 + 2844 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$	−2.93273	−	5.07964i	−0.564404	−	0.977577i	−0.997105	−	0.0760390i	$-0.975773\pi$
$3$	−2.93273	−	5.07964i	−0.564404	−	0.977577i	0.432701	−	0.901538i	$-0.357561\pi$
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−2.13454			−0.190919			−0.0954595	−	0.995433i	$-0.530432\pi$
$5$	−2.13454			−0.190919			−0.0954595	+	0.995433i	$0.530432\pi$
$6$	5.86546	−	10.1593i	0.399094	−	0.691251i
$7$	−1.93273	+	3.34759i	−0.104358	+	0.180753i	−0.913476	−	0.406894i	$-0.866612\pi$
$7$	−1.93273	+	3.34759i	−0.104358	+	0.180753i	0.809118	+	0.587646i	$0.199945\pi$
$8$	−8.00000			−0.353553
$9$	−3.70181	+	6.41172i	−0.137104	+	0.237471i
$10$	−2.13454	−	3.69713i	−0.0675001	−	0.116914i
$11$	26.5964	+	46.0663i	0.729010	+	1.26268i	0.957302	+	0.289090i	$0.0933526\pi$
$11$	26.5964	+	46.0663i	0.729010	+	1.26268i	−0.228292	+	0.973593i	$0.573314\pi$
$12$	23.4618			0.564404
$13$		0			0
$13$		0			0
$14$	−7.73092			−0.147584
$15$	6.26003	+	10.8427i	0.107756	+	0.186638i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	21.6636	−	37.5225i	0.309071	−	0.535327i	−0.669088	−	0.743183i	$-0.733315\pi$
$17$	21.6636	−	37.5225i	0.309071	−	0.535327i	0.978159	+	0.207856i	$0.0666486\pi$
$18$	−14.8072			−0.193894
$19$	74.1928	−	128.506i	0.895841	−	1.55164i	0.0630816	−	0.998008i	$-0.479907\pi$
$19$	74.1928	−	128.506i	0.895841	−	1.55164i	0.832760	−	0.553634i	$-0.186759\pi$
$20$	4.26908	−	7.39426i	0.0477298	−	0.0826704i
$21$	22.6727			0.235599
$22$	−53.1928	+	92.1326i	−0.515488	+	0.892851i
$23$	−61.3273	−	106.222i	−0.555984	−	0.962992i	−0.997826	−	0.0658995i	$-0.979008\pi$
$23$	−61.3273	−	106.222i	−0.555984	−	0.962992i	0.441843	−	0.897093i	$-0.354325\pi$
$24$	23.4618	+	40.6371i	0.199547	+	0.345626i
$25$	−120.444			−0.963550
$26$		0			0
$27$	−114.942			−0.819280
$28$	−7.73092	−	13.3903i	−0.0521788	−	0.0903763i
$29$	−41.9418	−	72.6453i	−0.268565	−	0.465169i	0.699926	−	0.714215i	$-0.253216\pi$
$29$	−41.9418	−	72.6453i	−0.268565	−	0.465169i	−0.968492	+	0.249046i	$0.919883\pi$
$30$	−12.5201	+	21.6854i	−0.0761947	+	0.131973i
$31$	−190.269			−1.10237			−0.551183	−	0.834384i	$-0.685823\pi$
$31$	−190.269			−1.10237			−0.551183	+	0.834384i	$0.685823\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	156.000	−	270.200i	0.822913	−	1.42533i
$34$	86.6546			0.437092
$35$	4.12549	−	7.14556i	0.0199239	−	0.0345091i
$36$	−14.8072	−	25.6469i	−0.0685520	−	0.118736i
$37$	−65.8564	−	114.067i	−0.292614	−	0.506823i	0.681813	−	0.731527i	$-0.261192\pi$
$37$	−65.8564	−	114.067i	−0.292614	−	0.506823i	−0.974427	+	0.224704i	$0.927859\pi$
$38$	296.771			1.26691
$39$		0			0
$40$	17.0763			0.0675001
$41$	−193.847	−	335.753i	−0.738387	−	1.27892i	−0.953221	−	0.302273i	$-0.902254\pi$
$41$	−193.847	−	335.753i	−0.738387	−	1.27892i	0.214834	−	0.976651i	$-0.431079\pi$
$42$	22.6727	+	39.2703i	0.0832970	+	0.144275i
$43$	37.3182	−	64.6371i	0.132348	−	0.229234i	−0.792233	−	0.610219i	$-0.791082\pi$
$43$	37.3182	−	64.6371i	0.132348	−	0.229234i	0.924581	+	0.380985i	$0.124415\pi$
$44$	−212.771			−0.729010
$45$	7.90166	−	13.6861i	0.0261758	−	0.0453378i
$46$	122.655	−	212.444i	0.393140	−	0.680938i
$47$	298.789			0.927295			0.463648	−	0.886020i	$-0.346540\pi$
$47$	298.789			0.927295			0.463648	+	0.886020i	$0.346540\pi$
$48$	−46.9237	+	81.2742i	−0.141101	+	0.244394i
$49$	164.029	+	284.107i	0.478219	+	0.828300i
$50$	−120.444	−	208.615i	−0.340666	−	0.590051i
$51$	−254.135			−0.697764
$52$		0			0
$53$	100.386			0.260170			0.130085	−	0.991503i	$-0.458475\pi$
$53$	100.386			0.260170			0.130085	+	0.991503i	$0.458475\pi$
$54$	−114.942	−	199.085i	−0.289659	−	0.501704i
$55$	−56.7710	−	98.3303i	−0.139182	−	0.241070i
$56$	15.4618	−	26.7807i	0.0368960	−	0.0639057i
$57$	−870.349			−2.02247
$58$	83.8836	−	145.291i	0.189904	−	0.328924i
$59$	239.655	−	415.094i	0.528820	−	0.915943i	−0.470615	−	0.882338i	$-0.655968\pi$
$59$	239.655	−	415.094i	0.528820	−	0.915943i	0.999435	−	0.0336044i	$-0.0106986\pi$
$60$	−50.0802			−0.107756
$61$	239.906	−	415.529i	0.503553	−	0.872180i	−0.496438	−	0.868072i	$-0.665359\pi$
$61$	239.906	−	415.529i	0.503553	−	0.872180i	0.999992	−	0.00410807i	$-0.00130764\pi$
$62$	−190.269	−	329.556i	−0.389745	−	0.675058i
$63$	−14.3092	−	24.7843i	−0.0286157	−	0.0495639i
$64$	64.0000			0.125000
$65$		0			0
$66$	624.000			1.16377
$67$	−207.636	−	359.637i	−0.378609	−	0.655771i	0.612251	−	0.790664i	$-0.290264\pi$
$67$	−207.636	−	359.637i	−0.378609	−	0.655771i	−0.990860	+	0.134893i	$0.956931\pi$
$68$	86.6546	+	150.090i	0.154535	+	0.267663i
$69$	−359.713	+	623.041i	−0.627599	+	1.08703i
$70$	16.5020			0.0281766
$71$	146.973	−	254.564i	0.245669	−	0.425510i	−0.716651	−	0.697432i	$-0.754326\pi$
$71$	146.973	−	254.564i	0.245669	−	0.425510i	0.962319	+	0.271922i	$0.0876592\pi$
$72$	29.6145	−	51.2938i	0.0484736	−	0.0839588i
$73$	−106.727			−0.171116			−0.0855579	−	0.996333i	$-0.527267\pi$
$73$	−106.727			−0.171116			−0.0855579	+	0.996333i	$0.527267\pi$
$74$	131.713	−	228.133i	0.206910	−	0.358378i
$75$	353.229	+	611.811i	0.543832	+	0.941944i
$76$	296.771	+	514.023i	0.447921	+	0.775821i
$77$	−205.614			−0.304311
$78$		0			0
$79$	−906.044			−1.29035			−0.645177	−	0.764033i	$-0.723216\pi$
$79$	−906.044			−1.29035			−0.645177	+	0.764033i	$0.723216\pi$
$80$	17.0763	+	29.5771i	0.0238649	+	0.0413352i
$81$	437.042	+	756.979i	0.599509	+	1.03838i
$82$	387.695	−	671.507i	0.522119	−	0.904336i
$83$	22.1605			0.0293064			0.0146532	−	0.999893i	$-0.495336\pi$
$83$	22.1605			0.0293064			0.0146532	+	0.999893i	$0.495336\pi$
$84$	−45.3454	+	78.5405i	−0.0588999	+	0.102018i
$85$	−46.2419	+	80.0934i	−0.0590075	+	0.102204i
$86$	149.273			0.187169
$87$	−246.008	+	426.098i	−0.303159	+	0.525086i
$88$	−212.771	−	368.530i	−0.257744	−	0.446426i
$89$	332.717	+	576.282i	0.396269	+	0.686357i	0.993262	−	0.115889i	$-0.0369716\pi$
$89$	332.717	+	576.282i	0.396269	+	0.686357i	−0.596994	+	0.802246i	$0.703638\pi$
$90$	31.6066			0.0370181
$91$		0			0
$92$	490.618			0.555984
$93$	558.008	+	966.498i	0.622180	+	1.07765i
$94$	298.789	+	517.518i	0.327848	+	0.567850i
$95$	−158.367	+	274.300i	−0.171033	+	0.296238i
$96$	−187.695			−0.199547
$97$	627.120	−	1086.20i	0.656437	−	1.13698i	−0.325094	−	0.945682i	$-0.605396\pi$
$97$	627.120	−	1086.20i	0.656437	−	1.13698i	0.981531	−	0.191301i	$-0.0612707\pi$
$98$	−328.058	+	568.214i	−0.338152	+	0.585696i
$99$	−393.819			−0.399801
$100$	240.887	−	417.229i	0.240887	−	0.417229i
$101$	878.604	+	1521.79i	0.865588	+	1.49924i	0.866462	+	0.499243i	$0.166388\pi$
$101$	878.604	+	1521.79i	0.865588	+	1.49924i	−0.000874171		1.00000i	$0.500278\pi$
$102$	−254.135	−	440.174i	−0.246697	−	0.427291i
$103$	86.2769			0.0825351			0.0412676	−	0.999148i	$-0.486860\pi$
$103$	86.2769			0.0825351			0.0412676	+	0.999148i	$0.486860\pi$
$104$		0			0
$105$	−48.3958			−0.0449804
$106$	100.386	+	173.873i	0.0919840	+	0.159321i
$107$	−1050.47	−	1819.46i	−0.949087	−	1.64387i	−0.747353	−	0.664427i	$-0.768675\pi$
$107$	−1050.47	−	1819.46i	−0.949087	−	1.64387i	−0.201735	−	0.979440i	$-0.564658\pi$
$108$	229.884	−	398.170i	0.204820	−	0.354759i
$109$	2166.87			1.90411			0.952057	−	0.305920i	$-0.0989642\pi$
$109$	2166.87			1.90411			0.952057	+	0.305920i	$0.0989642\pi$
$110$	113.542	−	196.661i	0.0984165	−	0.170462i
$111$	−386.278	+	669.053i	−0.330305	+	0.572106i
$112$	61.8474			0.0521788
$113$	178.389	−	308.980i	0.148509	−	0.257224i	−0.782168	−	0.623068i	$-0.785886\pi$
$113$	178.389	−	308.980i	0.148509	−	0.257224i	0.930676	+	0.365843i	$0.119219\pi$
$114$	−870.349	−	1507.49i	−0.715050	−	1.23850i
$115$	130.906	+	226.735i	0.106148	+	0.183854i
$116$	335.534			0.268565
$117$		0			0
$118$	958.618			0.747864
$119$	83.7400	+	145.042i	0.0645078	+	0.111731i
$120$	−50.0802	−	86.7415i	−0.0380973	−	0.0659865i
$121$	−749.235	+	1297.71i	−0.562911	+	0.974991i
$122$	959.622			0.712132
$123$	−1137.00	+	1969.35i	−0.833497	+	1.44366i
$124$	380.538	−	659.111i	0.275591	−	0.477338i
$125$	523.909			0.374879
$126$	28.6184	−	49.5685i	0.0202344	−	0.0350469i
$127$	−498.833	−	864.004i	−0.348538	−	0.603685i	0.637452	−	0.770490i	$-0.279988\pi$
$127$	−498.833	−	864.004i	−0.348538	−	0.603685i	−0.985990	+	0.166805i	$0.946655\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	−437.777			−0.298792
$130$		0			0
$131$	−1680.88			−1.12106			−0.560530	−	0.828134i	$-0.689403\pi$
$131$	−1680.88			−1.12106			−0.560530	+	0.828134i	$0.689403\pi$
$132$	624.000	+	1080.80i	0.411456	+	0.712663i
$133$	286.789	+	496.733i	0.186976	+	0.323851i
$134$	415.273	−	719.274i	0.267717	−	0.463700i
$135$	245.348			0.156416
$136$	−173.309	+	300.180i	−0.109273	+	0.189267i
$137$	−789.291	+	1367.09i	−0.492217	+	0.852544i	−0.999960	−	0.00896417i	$-0.997147\pi$
$137$	−789.291	+	1367.09i	−0.492217	+	0.852544i	0.507743	+	0.861509i	$0.330480\pi$
$138$	−1438.85			−0.887559
$139$	−862.035	+	1493.09i	−0.526021	+	0.911094i	0.473520	+	0.880783i	$0.342983\pi$
$139$	−862.035	+	1493.09i	−0.526021	+	0.911094i	−0.999541	+	0.0303112i	$0.990350\pi$
$140$	16.5020	+	28.5822i	0.00996193	+	0.0172546i
$141$	−876.268	−	1517.74i	−0.523369	−	0.906502i
$142$	587.891			0.347428
$143$		0			0
$144$	118.458			0.0685520
$145$	89.5264	+	155.064i	0.0512742	+	0.0888096i
$146$	−106.727	−	184.857i	−0.0604986	−	0.104787i
$147$	962.106	−	1666.42i	0.539818	−	0.934991i
$148$	526.851			0.292614
$149$	−1364.83	+	2363.96i	−0.750413	+	1.29975i	0.197210	+	0.980361i	$0.436812\pi$
$149$	−1364.83	+	2363.96i	−0.750413	+	1.29975i	−0.947623	+	0.319392i	$0.896521\pi$
$150$	−706.458	+	1223.62i	−0.384547	+	0.666055i
$151$	−484.316			−0.261014			−0.130507	−	0.991447i	$-0.541660\pi$
$151$	−484.316			−0.261014			−0.130507	+	0.991447i	$0.541660\pi$
$152$	−593.542	+	1028.05i	−0.316728	+	0.548589i
$153$	160.389	+	277.803i	0.0847498	+	0.146791i
$154$	−205.614	−	356.135i	−0.107590	−	0.186352i
$155$	406.137			0.210463
$156$		0			0
$157$	235.775			0.119853			0.0599264	−	0.998203i	$-0.480913\pi$
$157$	235.775			0.119853			0.0599264	+	0.998203i	$0.480913\pi$
$158$	−906.044	−	1569.31i	−0.456209	−	0.790177i
$159$	−294.404	−	509.922i	−0.146841	−	0.254336i
$160$	−34.1526	+	59.1541i	−0.0168750	+	0.0292284i
$161$	474.116			0.232085
$162$	−874.084	+	1513.96i	−0.423917	+	0.734246i
$163$	−727.611	+	1260.26i	−0.349637	+	0.605589i	−0.986185	−	0.165648i	$-0.947028\pi$
$163$	−727.611	+	1260.26i	−0.349637	+	0.605589i	0.636548	+	0.771237i	$0.280362\pi$
$164$	1550.78			0.738387
$165$	−332.988	+	576.753i	−0.157110	+	0.272122i
$166$	22.1605	+	38.3831i	0.0103614	+	0.0179464i
$167$	−815.259	−	1412.07i	−0.377764	−	0.654307i	0.612972	−	0.790104i	$-0.289974\pi$
$167$	−815.259	−	1412.07i	−0.377764	−	0.654307i	−0.990737	+	0.135798i	$0.956640\pi$
$168$	−181.382			−0.0832970
$169$		0			0
$170$	−184.968			−0.0834493
$171$	549.295	+	951.407i	0.245647	+	0.425473i
$172$	149.273	+	258.548i	0.0661742	+	0.114617i
$173$	−480.120	+	831.593i	−0.210999	+	0.365461i	−0.952028	−	0.306012i	$-0.901005\pi$
$173$	−480.120	+	831.593i	−0.210999	+	0.365461i	0.741028	+	0.671474i	$0.234338\pi$
$174$	−984.031			−0.428731
$175$	232.785	−	403.196i	0.100554	−	0.174164i
$176$	425.542	−	737.060i	0.182253	−	0.315671i
$177$	−2811.37			−1.19387
$178$	−665.433	+	1152.56i	−0.280204	+	0.485328i
$179$	−1050.16	−	1818.93i	−0.438506	−	0.759515i	0.559068	−	0.829122i	$-0.311159\pi$
$179$	−1050.16	−	1818.93i	−0.438506	−	0.759515i	−0.997575	+	0.0696067i	$0.977826\pi$
$180$	31.6066	+	54.7443i	0.0130879	+	0.0226689i
$181$	−3385.80			−1.39041			−0.695206	−	0.718811i	$-0.744687\pi$
$181$	−3385.80			−1.39041			−0.695206	+	0.718811i	$0.744687\pi$
$182$		0			0
$183$	−2814.31			−1.13683
$184$	490.618	+	849.776i	0.196570	+	0.340469i
$185$	140.573	+	243.480i	0.0558656	+	0.0967621i
$186$	−1116.02	+	1933.00i	−0.439948	+	0.762011i
$187$	2304.70			0.901263
$188$	−597.578	+	1035.04i	−0.231824	+	0.401531i
$189$	222.151	−	384.778i	0.0854981	−	0.148087i
$190$	−633.470			−0.241877
$191$	1864.04	−	3228.61i	0.706162	−	1.22311i	−0.260109	−	0.965579i	$-0.583758\pi$
$191$	1864.04	−	3228.61i	0.706162	−	1.22311i	0.966271	−	0.257529i	$-0.0829083\pi$
$192$	−187.695	−	325.097i	−0.0705505	−	0.122197i
$193$	1286.60	+	2228.46i	0.479852	+	0.831129i	0.999733	−	0.0231102i	$-0.00735687\pi$
$193$	1286.60	+	2228.46i	0.479852	+	0.831129i	−0.519881	+	0.854239i	$0.674024\pi$
$194$	2508.48			0.928343
$195$		0			0
$196$	−1312.23			−0.478219
$197$	−970.770	−	1681.42i	−0.351089	−	0.608104i	0.635352	−	0.772223i	$-0.280855\pi$
$197$	−970.770	−	1681.42i	−0.351089	−	0.608104i	−0.986440	+	0.164119i	$0.947522\pi$
$198$	−393.819	−	682.114i	−0.141351	−	0.244827i
$199$	1145.35	−	1983.80i	0.407997	−	0.706671i	−0.586668	−	0.809827i	$-0.699561\pi$
$199$	1145.35	−	1983.80i	0.407997	−	0.706671i	0.994665	+	0.103156i	$0.0328941\pi$
$200$	963.550			0.340666
$201$	−1217.88	+	2109.44i	−0.427378	+	0.740240i
$202$	−1757.21	+	3043.57i	−0.612063	+	1.06012i
$203$	324.249			0.112107
$204$	508.269	−	880.348i	0.174441	−	0.302141i
$205$	413.775	+	716.679i	0.140972	+	0.244171i
$206$	86.2769	+	149.436i	0.0291806	+	0.0505422i
$207$	908.088			0.304911
$208$		0			0
$209$	7893.04			2.61231
$210$	−48.3958	−	83.8240i	−0.0159030	−	0.0275448i
$211$	−587.613	−	1017.78i	−0.191720	−	0.332069i	0.754100	−	0.656759i	$-0.228073\pi$
$211$	−587.613	−	1017.78i	−0.191720	−	0.332069i	−0.945820	+	0.324690i	$0.894740\pi$
$212$	−200.771	+	347.746i	−0.0650425	+	0.112657i
$213$	−1724.13			−0.554625
$214$	2100.93	−	3638.92i	0.671106	−	1.16239i
$215$	−79.6573	+	137.970i	−0.0252678	+	0.0437652i
$216$	919.534			0.289659
$217$	367.739	−	636.942i	0.115040	−	0.199256i
$218$	2166.87	+	3753.13i	0.673206	+	1.16603i
$219$	313.001	+	542.134i	0.0965784	+	0.167279i
$220$	454.168			0.139182
$221$		0			0
$222$	−1545.11			−0.467122
$223$	2175.44	+	3767.97i	0.653265	+	1.13149i	0.982326	+	0.187180i	$0.0599347\pi$
$223$	2175.44	+	3767.97i	0.653265	+	1.13149i	−0.329060	+	0.944309i	$0.606732\pi$
$224$	61.8474	+	107.123i	0.0184480	+	0.0319529i
$225$	445.860	−	772.252i	0.132107	−	0.228815i
$226$	713.558			0.210023
$227$	1822.93	−	3157.40i	0.533003	−	0.923189i	−0.466254	−	0.884651i	$-0.654397\pi$
$227$	1822.93	−	3157.40i	0.533003	−	0.923189i	0.999257	−	0.0385380i	$-0.0122701\pi$
$228$	1740.70	−	3014.98i	0.505617	−	0.875754i
$229$	3239.15			0.934713			0.467357	−	0.884069i	$-0.345206\pi$
$229$	3239.15			0.934713			0.467357	+	0.884069i	$0.345206\pi$
$230$	−261.811	+	453.470i	−0.0750579	+	0.130004i
$231$	603.012	+	1044.45i	0.171754	+	0.297487i
$232$	335.534	+	581.162i	0.0949522	+	0.164462i
$233$	2182.68			0.613700			0.306850	−	0.951758i	$-0.400725\pi$
$233$	2182.68			0.613700			0.306850	+	0.951758i	$0.400725\pi$
$234$		0			0
$235$	−637.777			−0.177038
$236$	958.618	+	1660.38i	0.264410	+	0.457971i
$237$	2657.18	+	4602.38i	0.728281	+	1.26142i
$238$	−167.480	+	290.084i	−0.0456139	+	0.0790056i
$239$	58.8048			0.0159153			0.00795767	−	0.999968i	$-0.497467\pi$
$239$	58.8048			0.0159153			0.00795767	+	0.999968i	$0.497467\pi$
$240$	100.160	−	173.483i	0.0269389	−	0.0466595i
$241$	−101.131	+	175.163i	−0.0270307	+	0.0468185i	−0.879224	−	0.476408i	$-0.841939\pi$
$241$	−101.131	+	175.163i	−0.0270307	+	0.0468185i	0.852194	+	0.523227i	$0.175272\pi$
$242$	−2996.94			−0.796077
$243$	1011.74	−	1752.38i	0.267091	−	0.462615i
$244$	959.622	+	1662.11i	0.251777	+	0.436090i
$245$	−350.127	−	606.437i	−0.0913011	−	0.158138i
$246$	−4548.02			−1.17874
$247$		0			0
$248$	1522.15			0.389745
$249$	−64.9907	−	112.567i	−0.0165406	−	0.0286492i
$250$	523.909	+	907.438i	0.132540	+	0.229566i
$251$	56.9961	−	98.7201i	0.0143329	−	0.0248253i	−0.858770	−	0.512361i	$-0.828771\pi$
$251$	56.9961	−	98.7201i	0.0143329	−	0.0248253i	0.873103	+	0.487536i	$0.162104\pi$
$252$	114.474			0.0286157
$253$	3262.17	−	5650.24i	0.810635	−	1.40406i
$254$	997.666	−	1728.01i	0.246453	−	0.426870i
$255$	542.460			0.133216
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−2117.36	−	3667.38i	−0.513920	−	0.890136i	−0.999870	−	0.0161491i	$-0.994859\pi$
$257$	−2117.36	−	3667.38i	−0.513920	−	0.890136i	0.485949	−	0.873987i	$-0.338474\pi$
$258$	−437.777	−	758.253i	−0.105639	−	0.182972i
$259$	509.131			0.122146
$260$		0			0
$261$	621.042			0.147286
$262$	−1680.88	−	2911.36i	−0.396355	−	0.686507i
$263$	−114.241	−	197.871i	−0.0267847	−	0.0463925i	0.852322	−	0.523017i	$-0.175194\pi$
$263$	−114.241	−	197.871i	−0.0267847	−	0.0463925i	−0.879107	+	0.476624i	$0.841860\pi$
$264$	−1248.00	+	2161.60i	−0.290944	+	0.503929i
$265$	−214.277			−0.0496714
$266$	−573.578	+	993.467i	−0.132212	+	0.228998i
$267$	1951.54	−	3380.16i	0.447311	−	0.774766i
$268$	1661.09			0.378609
$269$	−609.652	+	1055.95i	−0.138183	+	0.239339i	−0.926809	−	0.375534i	$-0.877459\pi$
$269$	−609.652	+	1055.95i	−0.138183	+	0.239339i	0.788626	+	0.614873i	$0.210793\pi$
$270$	245.348	+	424.955i	0.0553015	+	0.0957849i
$271$	2945.57	+	5101.87i	0.660260	+	1.14360i	0.980547	+	0.196283i	$0.0628871\pi$
$271$	2945.57	+	5101.87i	0.660260	+	1.14360i	−0.320288	+	0.947320i	$0.603780\pi$
$272$	−693.237			−0.154535
$273$		0			0
$274$	−3157.16			−0.696100
$275$	−3203.37	−	5548.40i	−0.702438	−	1.21666i
$276$	−1438.85	−	2492.16i	−0.313800	−	0.543517i
$277$	−3069.70	+	5316.87i	−0.665849	+	1.15328i	0.313205	+	0.949685i	$0.398597\pi$
$277$	−3069.70	+	5316.87i	−0.665849	+	1.15328i	−0.979054	+	0.203599i	$0.934736\pi$
$278$	−3448.14			−0.743905
$279$	704.340	−	1219.95i	0.151139	−	0.261780i
$280$	−33.0039	+	57.1645i	−0.00704415	+	0.0122008i
$281$	1852.24			0.393221			0.196611	−	0.980482i	$-0.437006\pi$
$281$	1852.24			0.393221			0.196611	+	0.980482i	$0.437006\pi$
$282$	1752.54	−	3035.48i	0.370078	−	0.640994i
$283$	−86.1448	−	149.207i	−0.0180946	−	0.0313408i	0.856836	−	0.515589i	$-0.172427\pi$
$283$	−86.1448	−	149.207i	−0.0180946	−	0.0313408i	−0.874931	+	0.484248i	$0.839093\pi$
$284$	587.891	+	1018.26i	0.122834	+	0.212755i
$285$	1857.80			0.386127
$286$		0			0
$287$	1498.62			0.308225
$288$	118.458	+	205.175i	0.0242368	+	0.0419794i
$289$	1517.87	+	2629.03i	0.308950	+	0.535118i
$290$	−179.053	+	310.129i	−0.0362564	+	0.0627979i
$291$	−7356.70			−1.48198
$292$	213.454	−	369.713i	0.0427789	−	0.0740953i
$293$	2862.50	−	4958.00i	0.570748	−	0.988564i	−0.425742	−	0.904845i	$-0.639987\pi$
$293$	2862.50	−	4958.00i	0.570748	−	0.988564i	0.996489	−	0.0837193i	$-0.0266799\pi$
$294$	3848.42			0.763417
$295$	−511.552	+	886.035i	−0.100962	+	0.174871i
$296$	526.851	+	912.533i	0.103455	+	0.179189i
$297$	−3057.04	−	5294.94i	−0.597263	−	1.03449i
$298$	−5459.33			−1.06124
$299$		0			0
$300$	−2825.83			−0.543832
$301$	144.252	+	249.852i	0.0276231	+	0.0478446i
$302$	−484.316	−	838.859i	−0.0922822	−	0.159837i
$303$	5153.42	−	8925.98i	0.977083	−	1.69236i
$304$	−2374.17			−0.447921
$305$	−512.088	+	886.963i	−0.0961380	+	0.166516i
$306$	−320.779	+	555.605i	−0.0599271	+	0.103797i
$307$	−2115.94			−0.393364			−0.196682	−	0.980467i	$-0.563017\pi$
$307$	−2115.94			−0.393364			−0.196682	+	0.980467i	$0.563017\pi$
$308$	411.229	−	712.269i	0.0760777	−	0.131771i
$309$	−253.027	−	438.255i	−0.0465832	−	0.0806844i
$310$	406.137	+	703.450i	0.0744098	+	0.128882i
$311$	3912.14			0.713303			0.356651	−	0.934238i	$-0.383918\pi$
$311$	3912.14			0.713303			0.356651	+	0.934238i	$0.383918\pi$
$312$		0			0
$313$	3751.20			0.677413			0.338706	−	0.940892i	$-0.390011\pi$
$313$	3751.20			0.677413			0.338706	+	0.940892i	$0.390011\pi$
$314$	235.775	+	408.374i	0.0423744	+	0.0733946i
$315$	30.5436	+	52.9030i	0.00546328	+	0.00946269i
$316$	1812.09	−	3138.63i	0.322588	−	0.558739i
$317$	−8277.14			−1.46653			−0.733266	−	0.679942i	$-0.762005\pi$
$317$	−8277.14			−1.46653			−0.733266	+	0.679942i	$0.762005\pi$
$318$	588.807	−	1019.84i	0.103832	−	0.179843i
$319$	2231.00	−	3864.20i	0.391574	−	0.678225i
$320$	−136.611			−0.0238649
$321$	−6161.46	+	10672.0i	−1.07134	+	1.85561i
$322$	474.116	+	821.194i	0.0820543	+	0.142122i
$323$	−3214.57	−	5567.80i	−0.553757	−	0.959136i
$324$	−3496.34			−0.599509
$325$		0			0
$326$	−2910.44			−0.494462
$327$	−6354.84	−	11006.9i	−1.07469	−	1.86142i
$328$	1550.78	+	2686.03i	0.261059	+	0.452168i
$329$	−577.479	+	1000.22i	−0.0967703	+	0.167611i
$330$	−1331.95			−0.222187
$331$	−443.562	+	768.271i	−0.0736567	+	0.127577i	−0.900501	−	0.434853i	$-0.856800\pi$
$331$	−443.562	+	768.271i	−0.0736567	+	0.127577i	0.826845	+	0.562430i	$0.190134\pi$
$332$	−44.3209	+	76.7661i	−0.00732659	+	0.0126900i
$333$	975.152			0.160474
$334$	1630.52	−	2824.14i	0.267120	−	0.462665i
$335$	443.208	+	767.660i	0.0722838	+	0.125199i
$336$	−181.382	−	314.162i	−0.0294499	−	0.0510088i
$337$	6563.94			1.06101			0.530506	−	0.847681i	$-0.322002\pi$
$337$	6563.94			1.06101			0.530506	+	0.847681i	$0.322002\pi$
$338$		0			0
$339$	−2092.67			−0.335275
$340$	−184.968	−	320.373i	−0.0295038	−	0.0511020i
$341$	−5060.47	−	8764.99i	−0.803636	−	1.39194i
$342$	−1098.59	+	1902.81i	−0.173699	+	0.300855i
$343$	−2593.95			−0.408338
$344$	−298.546	+	517.097i	−0.0467922	+	0.0810465i
$345$	767.821	−	1329.91i	0.119821	−	0.207535i
$346$	−1920.48			−0.298398
$347$	4327.02	−	7494.62i	0.669414	−	1.15946i	−0.308654	−	0.951174i	$-0.599879\pi$
$347$	4327.02	−	7494.62i	0.669414	−	1.15946i	0.978068	−	0.208285i	$-0.0667881\pi$
$348$	−984.031	−	1704.39i	−0.151579	−	0.262543i
$349$	5086.77	+	8810.54i	0.780196	+	1.35134i	0.931827	+	0.362903i	$0.118214\pi$
$349$	5086.77	+	8810.54i	0.780196	+	1.35134i	−0.151631	+	0.988437i	$0.548452\pi$
$350$	931.141			0.142204
$351$		0			0
$352$	1702.17			0.257744
$353$	460.805	+	798.137i	0.0694792	+	0.120342i	0.898672	−	0.438621i	$-0.144533\pi$
$353$	460.805	+	798.137i	0.0694792	+	0.120342i	−0.829193	+	0.558962i	$0.811200\pi$
$354$	−2811.37	−	4869.43i	−0.422098	−	0.731095i
$355$	−313.719	+	543.378i	−0.0469028	+	0.0812381i
$356$	−2661.73			−0.396269
$357$	491.173	−	850.737i	0.0728170	−	0.126123i
$358$	2100.32	−	3637.86i	0.310071	−	0.537058i
$359$	2056.77			0.302374			0.151187	−	0.988505i	$-0.451690\pi$
$359$	2056.77			0.302374			0.151187	+	0.988505i	$0.451690\pi$
$360$	−63.2133	+	109.489i	−0.00925454	+	0.0160293i
$361$	−7579.63	−	13128.3i	−1.10506	−	1.91403i
$362$	−3385.80	−	5864.37i	−0.491585	−	0.851449i
$363$	8789.21			1.27084
$364$		0			0
$365$	227.813			0.0326693
$366$	−2814.31	−	4874.53i	−0.401930	−	0.696164i
$367$	−1105.90	−	1915.48i	−0.157296	−	0.272445i	0.776597	−	0.629998i	$-0.216944\pi$
$367$	−1105.90	−	1915.48i	−0.157296	−	0.272445i	−0.933893	+	0.357553i	$0.883611\pi$
$368$	−981.237	+	1699.55i	−0.138996	+	0.240748i
$369$	2870.34			0.404944
$370$	−281.146	+	486.960i	−0.0395030	+	0.0684212i
$371$	−194.018	+	336.049i	−0.0271507	+	0.0470264i
$372$	−4464.06			−0.622180
$373$	−5273.06	+	9133.21i	−0.731981	+	1.26783i	0.224055	+	0.974577i	$0.428071\pi$
$373$	−5273.06	+	9133.21i	−0.731981	+	1.26783i	−0.956035	+	0.293251i	$0.905263\pi$
$374$	2304.70	+	3991.86i	0.318645	+	0.551909i
$375$	−1536.49	−	2661.27i	−0.211583	−	0.366473i
$376$	−2390.31			−0.327848
$377$		0			0
$378$	888.606			0.120913
$379$	6119.48	+	10599.2i	0.829384	+	1.43653i	0.898522	+	0.438928i	$0.144642\pi$
$379$	6119.48	+	10599.2i	0.829384	+	1.43653i	−0.0691388	+	0.997607i	$0.522025\pi$
$380$	−633.470	−	1097.20i	−0.0855166	−	0.148119i
$381$	−2925.89	+	5067.78i	−0.393432	+	0.681445i
$382$	7456.14			0.998664
$383$	−3617.35	+	6265.43i	−0.482605	+	0.835897i	−0.999801	−	0.0199705i	$-0.993643\pi$
$383$	−3617.35	+	6265.43i	−0.482605	+	0.835897i	0.517195	+	0.855867i	$0.326976\pi$
$384$	375.389	−	650.194i	0.0498867	−	0.0864064i
$385$	438.892			0.0580988
$386$	−2573.20	+	4456.91i	−0.339307	+	0.587697i
$387$	276.290	+	478.549i	0.0362910	+	0.0628579i
$388$	2508.48	+	4344.82i	0.328219	+	0.568491i
$389$	−11781.1			−1.53554			−0.767768	−	0.640728i	$-0.778633\pi$
$389$	−11781.1			−1.53554			−0.767768	+	0.640728i	$0.778633\pi$
$390$		0			0
$391$	−5314.29			−0.687354
$392$	−1312.23	−	2272.85i	−0.169076	−	0.292848i
$393$	4929.56	+	8538.25i	0.632731	+	1.09592i
$394$	1941.54	−	3362.85i	0.248257	−	0.429994i
$395$	1933.99			0.246353
$396$	787.638	−	1364.23i	0.0999502	−	0.173119i
$397$	−5862.01	+	10153.3i	−0.741072	+	1.28358i	0.210935	+	0.977500i	$0.432349\pi$
$397$	−5862.01	+	10153.3i	−0.741072	+	1.28358i	−0.952007	+	0.306075i	$0.900984\pi$
$398$	4581.38			0.576995
$399$	1682.15	−	2913.57i	0.211060	−	0.365566i
$400$	963.550	+	1668.92i	0.120444	+	0.208615i
$401$	−853.995	−	1479.16i	−0.106350	−	0.184204i	0.807939	−	0.589266i	$-0.200583\pi$
$401$	−853.995	−	1479.16i	−0.106350	−	0.184204i	−0.914289	+	0.405062i	$0.867250\pi$
$402$	−4871.53			−0.604403
$403$		0			0
$404$	−7028.83			−0.865588
$405$	−932.884	−	1615.80i	−0.114458	−	0.198247i
$406$	324.249	+	561.615i	0.0396359	+	0.0686514i
$407$	3503.08	−	6067.52i	0.426637	−	0.738958i
$408$	2033.08			0.246697
$409$	4803.53	−	8319.96i	0.580732	−	1.00586i	−0.414661	−	0.909976i	$-0.636100\pi$
$409$	4803.53	−	8319.96i	0.580732	−	1.00586i	0.995393	−	0.0958812i	$-0.0305669\pi$
$410$	−827.550	+	1433.36i	−0.0996824	+	0.172655i
$411$	9259.11			1.11124
$412$	−172.554	+	298.872i	−0.0206338	+	0.0357388i
$413$	926.375	+	1604.53i	0.110373	+	0.191171i
$414$	908.088	+	1572.85i	0.107802	+	0.186719i
$415$	−47.3024			−0.00559514
$416$		0			0
$417$	10112.5			1.18755
$418$	7893.04	+	13671.1i	0.923591	+	1.59971i
$419$	1354.34	+	2345.78i	0.157908	+	0.273505i	0.934114	−	0.356974i	$-0.116192\pi$
$419$	1354.34	+	2345.78i	0.157908	+	0.273505i	−0.776206	+	0.630480i	$0.782858\pi$
$420$	96.7916	−	167.648i	0.0112451	−	0.0194771i
$421$	10957.4			1.26848			0.634239	−	0.773137i	$-0.281314\pi$
$421$	10957.4			1.26848			0.634239	+	0.773137i	$0.281314\pi$
$422$	1175.23	−	2035.55i	0.135567	−	0.234808i
$423$	−1106.06	+	1915.75i	−0.127136	+	0.220206i
$424$	−803.084			−0.0919840
$425$	−2609.25	+	4519.36i	−0.297805	+	0.515814i
$426$	−1724.13	−	2986.28i	−0.196090	−	0.339637i
$427$	927.345	+	1606.21i	0.105099	+	0.182037i
$428$	8403.73			0.949087
$429$		0			0
$430$	−318.629			−0.0357341
$431$	4756.56	+	8238.61i	0.531591	+	0.920742i	0.999320	+	0.0368705i	$0.0117389\pi$
$431$	4756.56	+	8238.61i	0.531591	+	0.920742i	−0.467729	+	0.883872i	$0.654928\pi$
$432$	919.534	+	1592.68i	0.102410	+	0.177379i
$433$	3635.66	−	6297.16i	0.403508	−	0.698896i	−0.590639	−	0.806936i	$-0.701124\pi$
$433$	3635.66	−	6297.16i	0.403508	−	0.698896i	0.994147	+	0.108040i	$0.0344575\pi$
$434$	1470.96			0.162691
$435$	525.114	−	909.523i	0.0578788	−	0.100249i
$436$	−4333.74	+	7506.26i	−0.476029	+	0.824506i
$437$	−18200.2			−1.99229
$438$	−626.003	+	1084.27i	−0.0682913	+	0.118284i
$439$	4807.62	+	8327.05i	0.522677	+	0.905304i	0.999652	+	0.0263867i	$0.00840013\pi$
$439$	4807.62	+	8327.05i	0.522677	+	0.905304i	−0.476974	+	0.878917i	$0.658267\pi$
$440$	454.168	+	786.643i	0.0492082	+	0.0852312i
$441$	−2428.82			−0.262263
$442$		0			0
$443$	−4782.54			−0.512924			−0.256462	−	0.966554i	$-0.582557\pi$
$443$	−4782.54			−0.512924			−0.256462	+	0.966554i	$0.582557\pi$
$444$	−1545.11	−	2676.21i	−0.165153	−	0.286053i
$445$	−710.197	−	1230.10i	−0.0756552	−	0.131039i
$446$	−4350.88	+	7535.94i	−0.461928	+	0.800083i
$447$	16010.7			1.69414
$448$	−123.695	+	214.246i	−0.0130447	+	0.0225941i
$449$	3434.36	−	5948.49i	0.360974	−	0.625226i	−0.627147	−	0.778901i	$-0.715778\pi$
$449$	3434.36	−	5948.49i	0.360974	−	0.625226i	0.988121	+	0.153675i	$0.0491109\pi$
$450$	1783.44			0.186827
$451$	10311.3	−	17859.7i	1.07658	−	1.86470i
$452$	713.558	+	1235.92i	0.0742543	+	0.128612i
$453$	1420.37	+	2460.15i	0.147317	+	0.255161i
$454$	7291.70			0.753781
$455$		0			0
$456$	6962.79			0.715050
$457$	4200.74	+	7275.89i	0.429983	+	0.744752i	0.996871	−	0.0790424i	$-0.0251862\pi$
$457$	4200.74	+	7275.89i	0.429983	+	0.744752i	−0.566888	+	0.823795i	$0.691853\pi$
$458$	3239.15	+	5610.38i	0.330471	+	0.572393i
$459$	−2490.06	+	4312.91i	−0.253216	+	0.438582i
$460$	−1047.24			−0.106148
$461$	−7965.23	+	13796.2i	−0.804723	+	1.39382i	0.111754	+	0.993736i	$0.464353\pi$
$461$	−7965.23	+	13796.2i	−0.804723	+	1.39382i	−0.916478	+	0.400086i	$0.868980\pi$
$462$	−1206.02	+	2088.89i	−0.121449	+	0.210355i
$463$	−11572.2			−1.16156			−0.580781	−	0.814060i	$-0.697253\pi$
$463$	−11572.2			−1.16156			−0.580781	+	0.814060i	$0.697253\pi$
$464$	−671.068	+	1162.32i	−0.0671413	+	0.116292i
$465$	−1191.09	−	2063.03i	−0.118786	−	0.205743i
$466$	2182.68	+	3780.51i	0.216976	+	0.375813i
$467$	−10862.4			−1.07634			−0.538169	−	0.842837i	$-0.680884\pi$
$467$	−10862.4			−1.07634			−0.538169	+	0.842837i	$0.680884\pi$
$468$		0			0
$469$	1605.22			0.158043
$470$	−637.777	−	1104.66i	−0.0625925	−	0.108413i
$471$	−691.464	−	1197.65i	−0.0676454	−	0.117165i
$472$	−1917.24	+	3320.75i	−0.186966	+	0.323835i
$473$	3970.12			0.385933
$474$	−5314.36	+	9204.75i	−0.514972	+	0.891958i
$475$	−8936.05	+	15477.7i	−0.863188	+	1.49509i
$476$	−669.920			−0.0645078
$477$	−371.608	+	643.644i	−0.0356704	+	0.0617829i
$478$	58.8048	+	101.853i	0.00562692	+	0.00974612i
$479$	1042.86	+	1806.28i	0.0994769	+	0.172299i	0.911468	−	0.411370i	$-0.134950\pi$
$479$	1042.86	+	1806.28i	0.0994769	+	0.172299i	−0.811991	+	0.583669i	$0.801616\pi$
$480$	400.642			0.0380973
$481$		0			0
$482$	−404.522			−0.0382272
$483$	−1390.46	−	2408.34i	−0.130989	−	0.226880i
$484$	−2996.94	−	5190.85i	−0.281456	−	0.487495i
$485$	−1338.61	+	2318.55i	−0.125326	+	0.217072i
$486$	4046.96			0.377723
$487$	5914.78	−	10244.7i	0.550358	−	0.953247i	−0.447891	−	0.894088i	$-0.647825\pi$
$487$	5914.78	−	10244.7i	0.550358	−	0.953247i	0.998249	−	0.0591591i	$-0.0188419\pi$
$488$	−1919.24	+	3324.23i	−0.178033	+	0.308362i
$489$	8535.54			0.789347
$490$	700.253	−	1212.87i	0.0645596	−	0.111821i
$491$	−1350.02	−	2338.30i	−0.124085	−	0.214921i	0.797290	−	0.603596i	$-0.206266\pi$
$491$	−1350.02	−	2338.30i	−0.124085	−	0.214921i	−0.921375	+	0.388675i	$0.872933\pi$
$492$	−4548.02	−	7877.39i	−0.416749	−	0.721830i
$493$	−3634.45			−0.332023
$494$		0			0
$495$	840.622			0.0763296
$496$	1522.15	+	2636.45i	0.137796	+	0.238669i
$497$	568.118	+	984.009i	0.0512748	+	0.0888105i
$498$	129.981	−	225.134i	0.0116960	−	0.0202581i
$499$	3013.67			0.270361			0.135181	−	0.990821i	$-0.456839\pi$
$499$	3013.67			0.270361			0.135181	+	0.990821i	$0.456839\pi$
$500$	−1047.82	+	1814.88i	−0.0937198	+	0.162327i
$501$	−4781.87	+	8282.44i	−0.426423	+	0.738587i
$502$	227.984			0.0202698
$503$	6951.00	−	12039.5i	0.616163	−	1.06723i	−0.374016	−	0.927422i	$-0.622020\pi$
$503$	6951.00	−	12039.5i	0.616163	−	1.06723i	0.990179	−	0.139803i	$-0.0446471\pi$
$504$	114.474	+	198.274i	0.0101172	+	0.0175235i
$505$	−1875.42	−	3248.32i	−0.165257	−	0.286234i
$506$	13048.7			1.14641
$507$		0			0
$508$	3990.67			0.348538
$509$	−815.332	−	1412.20i	−0.0709999	−	0.122975i	0.828340	−	0.560226i	$-0.189286\pi$
$509$	−815.332	−	1412.20i	−0.0709999	−	0.122975i	−0.899340	+	0.437250i	$0.855952\pi$
$510$	542.460	+	939.569i	0.0470991	+	0.0815781i
$511$	206.274	−	357.278i	0.0178572	−	0.0309296i
$512$	−512.000			−0.0441942
$513$	−8527.85	+	14770.7i	−0.733945	+	1.27123i
$514$	4234.73	−	7334.76i	0.363397	−	0.629421i
$515$	−184.162			−0.0157575
$516$	875.555	−	1516.51i	0.0746980	−	0.129381i
$517$	7946.71	+	13764.1i	0.676008	+	1.17088i
$518$	509.131	+	881.840i	0.0431852	+	0.0747989i
$519$	5632.25			0.476355
$520$		0			0
$521$	8654.86			0.727785			0.363893	−	0.931441i	$-0.381447\pi$
$521$	8654.86			0.727785			0.363893	+	0.931441i	$0.381447\pi$
$522$	621.042	+	1075.68i	0.0520733	+	0.0901936i
$523$	−2546.50	−	4410.67i	−0.212908	−	0.368767i	0.739716	−	0.672920i	$-0.234960\pi$
$523$	−2546.50	−	4410.67i	−0.212908	−	0.368767i	−0.952623	+	0.304153i	$0.901627\pi$
$524$	3361.75	−	5822.73i	0.280265	−	0.485433i
$525$	−2730.78			−0.227012
$526$	228.481	−	395.741i	0.0189397	−	0.0328045i
$527$	−4121.92	+	7139.38i	−0.340709	+	0.590126i
$528$	−4992.00			−0.411456
$529$	−1438.58	+	2491.69i	−0.118236	+	0.204790i
$530$	−214.277	−	371.139i	−0.0175615	−	0.0304174i
$531$	1774.31	+	3073.20i	0.145007	+	0.251159i
$532$	−2294.31			−0.186976
$533$		0			0
$534$	7806.15			0.632594
$535$	2242.26	+	3883.71i	0.181199	+	0.313846i
$536$	1661.09	+	2877.10i	0.133859	+	0.231850i
$537$	−6159.67	+	10668.9i	−0.494989	+	0.857347i
$538$	−2438.61			−0.195420
$539$	−8725.16	+	15112.4i	−0.697253	+	1.20768i
$540$	−490.696	+	849.910i	−0.0391040	+	0.0677302i
$541$	5004.07			0.397674			0.198837	−	0.980033i	$-0.436284\pi$
$541$	5004.07			0.397674			0.198837	+	0.980033i	$0.436284\pi$
$542$	−5891.13	+	10203.7i	−0.466874	+	0.808650i
$543$	9929.63	+	17198.6i	0.784754	+	1.35923i
$544$	−693.237	−	1200.72i	−0.0546365	−	0.0946333i
$545$	−4625.27			−0.363532
$546$		0			0
$547$	−10856.3			−0.848598			−0.424299	−	0.905522i	$-0.639479\pi$
$547$	−10856.3			−0.848598			−0.424299	+	0.905522i	$0.639479\pi$
$548$	−3157.16	−	5468.37i	−0.246108	−	0.426272i
$549$	1776.17	+	3076.42i	0.138078	+	0.239159i
$550$	6406.73	−	11096.8i	0.496698	−	0.860307i
$551$	−12447.1			−0.962368
$552$	2877.70	−	4984.33i	0.221890	−	0.384324i
$553$	1751.14	−	3033.06i	0.134658	−	0.233235i
$554$	−12278.8			−0.941653
$555$	824.526	−	1428.12i	0.0630616	−	0.109226i
$556$	−3448.14	−	5972.35i	−0.263010	−	0.455547i
$557$	−11541.9	−	19991.2i	−0.878001	−	1.52074i	−0.853531	−	0.521042i	$-0.825543\pi$
$557$	−11541.9	−	19991.2i	−0.878001	−	1.52074i	−0.0244704	−	0.999701i	$-0.507790\pi$
$558$	2817.36			0.213743
$559$		0			0
$560$	−132.016			−0.00996193
$561$	−6759.06	−	11707.0i	−0.508677	−	0.881054i
$562$	1852.24	+	3208.17i	0.139025	+	0.240798i
$563$	7747.97	−	13419.9i	0.579996	−	1.00458i	−0.415483	−	0.909601i	$-0.636387\pi$
$563$	7747.97	−	13419.9i	0.579996	−	1.00458i	0.995479	−	0.0949820i	$-0.0302793\pi$
$564$	7010.14			0.523369
$565$	−380.779	+	659.529i	−0.0283531	+	0.0491090i
$566$	172.290	−	298.414i	0.0127948	−	0.0221613i
$567$	−3378.74			−0.250253
$568$	−1175.78	+	2036.52i	−0.0868570	+	0.150441i
$569$	−9082.73	−	15731.7i	−0.669188	−	1.15907i	−0.978132	−	0.207987i	$-0.933309\pi$
$569$	−9082.73	−	15731.7i	−0.669188	−	1.15907i	0.308944	−	0.951080i	$-0.400024\pi$
$570$	1857.80	+	3217.80i	0.136517	+	0.236454i
$571$	−8289.75			−0.607557			−0.303779	−	0.952743i	$-0.598248\pi$
$571$	−8289.75			−0.607557			−0.303779	+	0.952743i	$0.598248\pi$
$572$		0			0
$573$	−21866.9			−1.59424
$574$	1498.62	+	2595.68i	0.108974	+	0.188749i
$575$	7386.49	+	12793.8i	0.535718	+	0.927891i
$576$	−236.916	+	410.350i	−0.0171380	+	0.0296839i
$577$	5336.46			0.385026			0.192513	−	0.981294i	$-0.438336\pi$
$577$	5336.46			0.385026			0.192513	+	0.981294i	$0.438336\pi$
$578$	−3035.75	+	5258.06i	−0.218461	+	0.378385i
$579$	7546.50	−	13070.9i	0.541661	−	0.938185i
$580$	−716.211			−0.0512742
$581$	−42.8302	+	74.1841i	−0.00305834	+	0.00529720i
$582$	−7356.70	−	12742.2i	−0.523960	−	0.907526i
$583$	2669.89	+	4624.39i	0.189667	+	0.328512i
$584$	853.816			0.0604986
$585$		0			0
$586$	11450.0			0.807159
$587$	−3438.86	−	5956.28i	−0.241800	−	0.418811i	0.719427	−	0.694568i	$-0.244405\pi$
$587$	−3438.86	−	5956.28i	−0.241800	−	0.418811i	−0.961227	+	0.275758i	$0.911071\pi$
$588$	3848.42	+	6665.67i	0.269909	+	0.467496i
$589$	−14116.6	+	24450.6i	−0.987545	+	1.71048i
$590$	−2046.21			−0.142782
$591$	−5694.01	+	9862.32i	−0.396312	+	0.686432i
$592$	−1053.70	+	1825.07i	−0.0731536	+	0.126706i
$593$	8358.37			0.578814			0.289407	−	0.957206i	$-0.406542\pi$
$593$	8358.37			0.578814			0.289407	+	0.957206i	$0.406542\pi$
$594$	6114.07	−	10589.9i	0.422329	−	0.731495i
$595$	−178.746	−	309.598i	−0.0123158	−	0.0213315i
$596$	−5459.33	−	9455.84i	−0.375206	−	0.649876i
$597$	−13436.0			−0.921101
$598$		0			0
$599$	−14896.0			−1.01609			−0.508043	−	0.861332i	$-0.669631\pi$
$599$	−14896.0			−1.01609			−0.508043	+	0.861332i	$0.669631\pi$
$600$	−2825.83	−	4894.48i	−0.192273	−	0.333027i
$601$	−3830.80	−	6635.14i	−0.260003	−	0.450338i	0.706240	−	0.707973i	$-0.250390\pi$
$601$	−3830.80	−	6635.14i	−0.260003	−	0.450338i	−0.966242	+	0.257635i	$0.917057\pi$
$602$	−288.504	+	499.704i	−0.0195325	+	0.0338313i
$603$	3074.52			0.207636
$604$	968.631	−	1677.72i	0.0652534	−	0.113022i
$605$	1599.27	−	2770.02i	0.107470	−	0.186144i
$606$	20613.7			1.38180
$607$	−11359.1	+	19674.5i	−0.759558	+	1.31559i	0.183519	+	0.983016i	$0.441251\pi$
$607$	−11359.1	+	19674.5i	−0.759558	+	1.31559i	−0.943076	+	0.332576i	$0.892082\pi$
$608$	−2374.17	−	4112.18i	−0.158364	−	0.274294i
$609$	−950.933	−	1647.06i	−0.0632738	−	0.109594i
$610$	−2048.35			−0.135960
$611$		0			0
$612$	−1283.12			−0.0847498
$613$	6040.47	+	10462.4i	0.397997	+	0.689352i	0.993479	−	0.114018i	$-0.0363720\pi$
$613$	6040.47	+	10462.4i	0.397997	+	0.689352i	−0.595481	+	0.803369i	$0.703039\pi$
$614$	−2115.94	−	3664.91i	−0.139075	−	0.240885i
$615$	2426.98	−	4203.65i	0.159131	−	0.275622i
$616$	1644.92			0.107590
$617$	10552.1	−	18276.9i	0.688514	−	1.19254i	−0.283804	−	0.958882i	$-0.591597\pi$
$617$	10552.1	−	18276.9i	0.688514	−	1.19254i	0.972318	−	0.233660i	$-0.0750702\pi$
$618$	506.054	−	876.511i	0.0329393	−	0.0570525i
$619$	−12516.1			−0.812706			−0.406353	−	0.913716i	$-0.633200\pi$
$619$	−12516.1			−0.812706			−0.406353	+	0.913716i	$0.633200\pi$
$620$	−812.274	+	1406.90i	−0.0526157	+	0.0911330i
$621$	7049.07	+	12209.3i	0.455506	+	0.788960i
$622$	3912.14	+	6776.03i	0.252191	+	0.436807i
$623$	−2572.21			−0.165415
$624$		0			0
$625$	13937.2			0.891978
$626$	3751.20	+	6497.27i	0.239502	+	0.414829i
$627$	−23148.1	−	40093.8i	−1.47440	−	2.55373i
$628$	−471.550	+	816.748i	−0.0299632	+	0.0518978i
$629$	−5706.76			−0.361754
$630$	−61.0871	+	105.806i	−0.00386313	+	0.00669113i
$631$	5034.83	−	8720.58i	0.317644	−	0.550176i	−0.662352	−	0.749193i	$-0.730442\pi$
$631$	5034.83	−	8720.58i	0.317644	−	0.550176i	0.979996	+	0.199017i	$0.0637749\pi$
$632$	7248.35			0.456209
$633$	−3446.62	+	5969.72i	−0.216415	+	0.374842i
$634$	−8277.14	−	14336.4i	−0.518497	−	0.898064i
$635$	1064.78	+	1844.25i	0.0665425	+	0.115255i
$636$	2355.23			0.146841
$637$		0			0
$638$	8924.00			0.553769
$639$	1088.13	+	1884.70i	0.0673643	+	0.116678i
$640$	−136.611	−	236.616i	−0.00843751	−	0.0146142i
$641$	1694.43	−	2934.84i	0.104409	−	0.180842i	−0.809088	−	0.587688i	$-0.800038\pi$
$641$	1694.43	−	2934.84i	0.104409	−	0.180842i	0.913497	+	0.406846i	$0.133372\pi$
$642$	−24645.9			−1.51510
$643$	12316.7	−	21333.1i	0.755400	−	1.30839i	−0.189776	−	0.981827i	$-0.560776\pi$
$643$	12316.7	−	21333.1i	0.755400	−	1.30839i	0.945175	−	0.326563i	$-0.105891\pi$
$644$	−948.233	+	1642.39i	−0.0580211	+	0.100496i
$645$	934.453			0.0570451
$646$	6429.14	−	11135.6i	0.391565	−	0.678211i
$647$	−954.062	−	1652.48i	−0.0579723	−	0.100411i	0.835583	−	0.549365i	$-0.185130\pi$
$647$	−954.062	−	1652.48i	−0.0579723	−	0.100411i	−0.893555	+	0.448954i	$0.851797\pi$
$648$	−3496.34	−	6055.83i	−0.211958	−	0.367123i
$649$	25495.8			1.54206
$650$		0			0
$651$	−4313.91			−0.259717
$652$	−2910.44	−	5041.03i	−0.174819	−	0.302795i
$653$	5165.70	+	8947.26i	0.309570	+	0.536192i	0.978268	−	0.207342i	$-0.0664814\pi$
$653$	5165.70	+	8947.26i	0.309570	+	0.536192i	−0.668698	+	0.743534i	$0.733148\pi$
$654$	12709.7	−	22013.8i	0.759921	−	1.31622i
$655$	3587.90			0.214032
$656$	−3101.56	+	5372.06i	−0.184597	+	0.319731i
$657$	395.083	−	684.304i	0.0234607	−	0.0406351i
$658$	−2309.91			−0.136854
$659$	−9519.92	+	16489.0i	−0.562737	+	0.974688i	0.434520	+	0.900662i	$0.356918\pi$
$659$	−9519.92	+	16489.0i	−0.562737	+	0.974688i	−0.997256	+	0.0740261i	$0.976415\pi$
$660$	−1331.95	−	2307.01i	−0.0785548	−	0.136061i
$661$	14321.5	+	24805.6i	0.842726	+	1.45964i	0.887582	+	0.460650i	$0.152384\pi$
$661$	14321.5	+	24805.6i	0.842726	+	1.45964i	−0.0448562	+	0.998993i	$0.514283\pi$
$662$	−1774.25			−0.104166
$663$		0			0
$664$	−177.284			−0.0103614
$665$	−612.163	−	1060.30i	−0.0356972	−	0.0618294i
$666$	975.152	+	1689.01i	0.0567363	+	0.0982701i
$667$	−5144.35	+	8910.28i	−0.298636	+	0.517252i
$668$	6522.07			0.377764
$669$	12759.9	−	22100.9i	0.737411	−	1.27723i
$670$	−886.417	+	1535.32i	−0.0511123	+	0.0885292i
$671$	25522.5			1.46838
$672$	362.763	−	628.324i	0.0208242	−	0.0360687i
$673$	9186.40	+	15911.3i	0.526166	+	0.911346i	0.999535	+	0.0304820i	$0.00970424\pi$
$673$	9186.40	+	15911.3i	0.526166	+	0.911346i	−0.473369	+	0.880864i	$0.656962\pi$
$674$	6563.94	+	11369.1i	0.375124	+	0.649734i
$675$	13844.0			0.789417
$676$		0			0
$677$	−12837.4			−0.728779			−0.364389	−	0.931247i	$-0.618722\pi$
$677$	−12837.4			−0.728779			−0.364389	+	0.931247i	$0.618722\pi$
$678$	−2092.67	−	3624.61i	−0.118538	−	0.205313i
$679$	2424.11	+	4198.68i	0.137008	+	0.237306i
$680$	369.935	−	640.747i	0.0208623	−	0.0361346i
$681$	−21384.6			−1.20332
$682$	10120.9	−	17530.0i	0.568256	−	0.984249i
$683$	6112.37	−	10586.9i	0.342436	−	0.593116i	−0.642449	−	0.766329i	$-0.722081\pi$
$683$	6112.37	−	10586.9i	0.342436	−	0.593116i	0.984884	+	0.173213i	$0.0554148\pi$
$684$	−4394.36			−0.245647
$685$	1684.77	−	2918.11i	0.0939736	−	0.162767i
$686$	−2593.95	−	4492.85i	−0.144369	−	0.250055i
$687$	−9499.56	−	16453.7i	−0.527556	−	0.913754i
$688$	−1194.18			−0.0661742
$689$		0			0
$690$	3071.29			0.169452
$691$	−3831.50	−	6636.35i	−0.210936	−	0.365352i	0.741072	−	0.671426i	$-0.234318\pi$
$691$	−3831.50	−	6636.35i	−0.210936	−	0.365352i	−0.952008	+	0.306074i	$0.900985\pi$
$692$	−1920.48	−	3326.37i	−0.105500	−	0.182731i
$693$	761.146	−	1318.34i	0.0417223	−	0.0722651i
$694$	17308.1			0.946694
$695$	1840.05	−	3187.06i	0.100427	−	0.173945i
$696$	1968.06	−	3408.78i	0.107183	−	0.185646i
$697$	−16797.8			−0.912856
$698$	−10173.5	+	17621.1i	−0.551682	+	0.955542i
$699$	−6401.21	−	11087.2i	−0.346375	−	0.599939i
$700$	931.141	+	1612.78i	0.0502769	+	0.0870821i
$701$	−15215.8			−0.819818			−0.409909	−	0.912126i	$-0.634440\pi$
$701$	−15215.8			−0.819818			−0.409909	+	0.912126i	$0.634440\pi$
$702$		0			0
$703$	−19544.3			−1.04854
$704$	1702.17	+	2948.24i	0.0911263	+	0.157835i
$705$	1870.43	+	3239.68i	0.0999212	+	0.173069i
$706$	−921.610	+	1596.27i	−0.0491292	+	0.0850943i
$707$	−6792.42			−0.361323
$708$	5622.74	−	9738.87i	0.298468	−	0.516962i
$709$	7705.43	−	13346.2i	0.408157	−	0.706949i	−0.586526	−	0.809930i	$-0.699505\pi$
$709$	7705.43	−	13346.2i	0.408157	−	0.706949i	0.994683	+	0.102981i	$0.0328382\pi$
$710$	−1254.88			−0.0663306
$711$	3354.00	−	5809.30i	0.176913	−	0.306422i
$712$	−2661.73	−	4610.26i	−0.140102	−	0.242664i
$713$	11668.7	+	20210.8i	0.612897	+	1.06157i
$714$	1964.69			0.102979
$715$		0			0
$716$	8401.27			0.438506
$717$	−172.459	−	298.707i	−0.00898268	−	0.0155585i
$718$	2056.77	+	3562.44i	0.106905	+	0.185166i
$719$	−577.894	+	1000.94i	−0.0299747	+	0.0519177i	−0.880624	−	0.473816i	$-0.842876\pi$
$719$	−577.894	+	1000.94i	−0.0299747	+	0.0519177i	0.850649	+	0.525734i	$0.176209\pi$
$720$	−252.853			−0.0130879
$721$	−166.750	+	288.819i	−0.00861317	+	0.0149184i
$722$	15159.3	−	26256.6i	0.781398	−	1.35342i
$723$	1186.36			0.0610249
$724$	6771.60	−	11728.7i	0.347603	−	0.602066i
$725$	5051.62	+	8749.67i	0.258776	+	0.448213i
$726$	8789.21	+	15223.4i	0.449309	+	0.778226i
$727$	18048.8			0.920759			0.460379	−	0.887722i	$-0.347713\pi$
$727$	18048.8			0.920759			0.460379	+	0.887722i	$0.347713\pi$
$728$		0			0
$729$	11731.6			0.596029
$730$	227.813	+	394.584i	0.0115503	+	0.0200058i
$731$	−1616.90	−	2800.55i	−0.0818101	−	0.141699i
$732$	5628.63	−	9749.07i	0.284208	−	0.492262i
$733$	−7855.68			−0.395847			−0.197924	−	0.980217i	$-0.563420\pi$
$733$	−7855.68			−0.395847			−0.197924	+	0.980217i	$0.563420\pi$
$734$	2211.81	−	3830.96i	0.111225	−	0.192648i
$735$	−2053.65	+	3557.03i	−0.103061	+	0.178508i
$736$	−3924.95			−0.196570
$737$	11044.8	−	19130.1i	0.552020	−	0.956127i
$738$	2870.34	+	4971.58i	0.143169	+	0.247976i
$739$	−151.401	−	262.234i	−0.00753635	−	0.0130533i	0.862233	−	0.506512i	$-0.169066\pi$
$739$	−151.401	−	262.234i	−0.00753635	−	0.0130533i	−0.869769	+	0.493459i	$0.835732\pi$
$740$	−1124.59			−0.0558656
$741$		0			0
$742$	−776.072			−0.0383969
$743$	−8599.96	−	14895.6i	−0.424633	−	0.735485i	0.571753	−	0.820426i	$-0.306263\pi$
$743$	−8599.96	−	14895.6i	−0.424633	−	0.735485i	−0.996386	+	0.0849402i	$0.972930\pi$
$744$	−4464.06	−	7731.98i	−0.219974	−	0.381006i
$745$	2913.29	−	5045.97i	0.143268	−	0.248148i
$746$	−21092.2			−1.03518
$747$	−82.0339	+	142.087i	−0.00401802	+	0.00695942i
$748$	−4609.40	+	7983.71i	−0.225316	+	0.390258i
$749$	8121.07			0.396178
$750$	3072.97	−	5322.54i	0.149612	−	0.259136i
$751$	−6499.83	−	11258.0i	−0.315822	−	0.547019i	0.663790	−	0.747919i	$-0.268947\pi$
$751$	−6499.83	−	11258.0i	−0.315822	−	0.547019i	−0.979612	+	0.200900i	$0.935614\pi$
$752$	−2390.31	−	4140.14i	−0.115912	−	0.200765i
$753$	−668.616			−0.0323582
$754$		0			0
$755$	1033.79			0.0498325
$756$	888.606	+	1539.11i	0.0427490	+	0.0740435i
$757$	−3023.40	−	5236.69i	−0.145162	−	0.251428i	0.784272	−	0.620418i	$-0.213037\pi$
$757$	−3023.40	−	5236.69i	−0.145162	−	0.251428i	−0.929433	+	0.368990i	$0.879704\pi$
$758$	−12239.0	+	21198.5i	−0.586463	+	1.01578i
$759$	−38268.2			−1.83010
$760$	1266.94	−	2194.40i	0.0604694	−	0.104736i
$761$	−13451.1	+	23298.1i	−0.640740	+	1.10979i	0.344527	+	0.938776i	$0.388039\pi$
$761$	−13451.1	+	23298.1i	−0.640740	+	1.10979i	−0.985268	+	0.171019i	$0.945294\pi$
$762$	−11703.5			−0.556397
$763$	−4187.97	+	7253.78i	−0.198709	+	0.344174i
$764$	7456.14	+	12914.4i	0.353081	+	0.611554i
$765$	−342.358	−	592.981i	−0.0161804	−	0.0280252i
$766$	−14469.4			−0.682507
$767$		0			0
$768$	1501.56			0.0705505
$769$	−1034.14	−	1791.19i	−0.0484943	−	0.0839947i	0.840759	−	0.541409i	$-0.182109\pi$
$769$	−1034.14	−	1791.19i	−0.0484943	−	0.0839947i	−0.889254	+	0.457414i	$0.848776\pi$
$770$	438.892	+	760.184i	0.0205410	+	0.0355781i
$771$	−12419.3	+	21510.9i	−0.580118	+	1.00479i
$772$	−10292.8			−0.479852
$773$	4194.86	−	7265.71i	0.195186	−	0.338072i	−0.751776	−	0.659419i	$-0.770802\pi$
$773$	4194.86	−	7265.71i	0.195186	−	0.338072i	0.946961	+	0.321347i	$0.104136\pi$
$774$	−552.580	+	957.097i	−0.0256616	+	0.0444472i
$775$	22916.7			1.06218
$776$	−5016.96	+	8689.63i	−0.232086	+	0.401984i
$777$	−1493.14	−	2586.20i	−0.0689398	−	0.119407i
$778$	−11781.1	−	20405.4i	−0.542894	−	0.940320i
$779$	−57528.3			−2.64591
$780$		0			0
$781$	15635.8			0.716379
$782$	−5314.29	−	9204.62i	−0.243016	−	0.420917i
$783$	4820.86	+	8349.98i	0.220030	+	0.381103i
$784$	2624.47	−	4545.71i	0.119555	−	0.207075i
$785$	−503.271			−0.0228822
$786$	−9859.12	+	17076.5i	−0.447409	+	0.774934i
$787$	10729.2	−	18583.5i	0.485964	−	0.841714i	−0.513906	−	0.857847i	$-0.671802\pi$
$787$	10729.2	−	18583.5i	0.485964	−	0.841714i	0.999870	+	0.0161324i	$0.00513532\pi$
$788$	7766.16			0.351089
$789$	−670.074	+	1160.60i	−0.0302348	+	0.0523683i
$790$	1933.99	+	3349.76i	0.0870990	+	0.150860i
$791$	689.557	+	1194.35i	0.0309960	+	0.0536866i
$792$	3150.55			0.141351
$793$		0			0
$794$	−23448.0			−1.04803
$795$	628.416	+	1088.45i	0.0280348	+	0.0485576i
$796$	4581.38	+	7935.19i	0.203998	+	0.353336i
$797$	3024.86	−	5239.21i	0.134437	−	0.232851i	−0.790945	−	0.611887i	$-0.790411\pi$
$797$	3024.86	−	5239.21i	0.134437	−	0.232851i	0.925382	+	0.379036i	$0.123744\pi$
$798$	6728.60			0.298484
$799$	6472.86	−	11211.3i	0.286600	−	0.496406i
$800$	−1927.10	+	3337.83i	−0.0851666	+	0.147513i
$801$	−4926.62			−0.217320
$802$	1707.99	−	2958.32i	0.0752010	−	0.130252i
$803$	−2838.55	−	4916.52i	−0.124745	−	0.216065i
$804$	−4871.53	−	8437.74i	−0.213689	−	0.370120i
$805$	−1012.02			−0.0443094
$806$		0			0
$807$	7151.78			0.311964
$808$	−7028.83	−	12174.3i	−0.306032	−	0.530062i
$809$	16682.1	+	28894.2i	0.724981	+	1.25570i	0.958982	+	0.283468i	$0.0914850\pi$
$809$	16682.1	+	28894.2i	0.724981	+	1.25570i	−0.234000	+	0.972237i	$0.575182\pi$
$810$	1865.77	−	3231.60i	0.0809338	−	0.140181i
$811$	2210.77			0.0957221			0.0478611	−	0.998854i	$-0.484760\pi$
$811$	2210.77			0.0957221			0.0478611	+	0.998854i	$0.484760\pi$
$812$	−648.497	+	1123.23i	−0.0280268	+	0.0485439i
$813$	17277.1	−	29924.8i	0.745307	−	1.29091i
$814$	14012.3			0.603356
$815$	1553.11	−	2690.07i	0.0667524	−	0.115619i
$816$	2033.08	+	3521.39i	0.0872205	+	0.151070i
$817$	−5537.49	−	9591.21i	−0.237126	−	0.410715i
$818$	19214.1			0.821279
$819$		0			0
$820$	−3310.20			−0.140972
$821$	−12701.5	−	21999.6i	−0.539932	−	0.935189i	−0.998907	−	0.0467399i	$-0.985117\pi$
$821$	−12701.5	−	21999.6i	−0.539932	−	0.935189i	0.458976	−	0.888449i	$-0.348217\pi$
$822$	9259.11	+	16037.3i	0.392881	+	0.680491i
$823$	21015.5	−	36399.8i	0.890100	−	1.54170i	0.0503464	−	0.998732i	$-0.483967\pi$
$823$	21015.5	−	36399.8i	0.890100	−	1.54170i	0.839754	−	0.542967i	$-0.182699\pi$
$824$	−690.215			−0.0291806
$825$	−18789.2	+	32543.9i	−0.792917	+	1.37337i
$826$	−1852.75	+	3209.06i	−0.0780453	+	0.135178i
$827$	−27713.0			−1.16527			−0.582633	−	0.812735i	$-0.697978\pi$
$827$	−27713.0			−1.16527			−0.582633	+	0.812735i	$0.697978\pi$
$828$	−1816.18	+	3145.71i	−0.0762276	+	0.132030i
$829$	11789.9	+	20420.6i	0.493943	+	0.855534i	0.999976	−	0.00698019i	$-0.00222188\pi$
$829$	11789.9	+	20420.6i	0.493943	+	0.855534i	−0.506033	+	0.862514i	$0.668889\pi$
$830$	−47.3024	−	81.9302i	−0.00197818	−	0.00342631i
$831$	36010.4			1.50323
$832$		0			0
$833$	14213.9			0.591214
$834$	10112.5	+	17515.3i	0.419863	+	0.727225i
$835$	1740.20	+	3014.12i	0.0721224	+	0.124920i
$836$	−15786.1	+	27342.3i	−0.653077	+	1.13116i
$837$	21869.9			0.903146
$838$	−2708.67	+	4691.56i	−0.111658	+	0.193397i
$839$	4324.02	−	7489.42i	0.177928	−	0.308180i	−0.763243	−	0.646112i	$-0.776394\pi$
$839$	4324.02	−	7489.42i	0.177928	−	0.308180i	0.941171	+	0.337932i	$0.109727\pi$
$840$	387.166			0.0159030
$841$	8676.27	−	15027.7i	0.355745	−	0.616169i
$842$	10957.4	+	18978.7i	0.448474	+	0.776781i
$843$	−5432.11	−	9408.70i	−0.221936	−	0.384404i
$844$	4700.91			0.191720
$845$		0			0
$846$	−4424.24			−0.179797
$847$	−2896.14	−	5016.26i	−0.117488	−	0.203495i
$848$	−803.084	−	1390.98i	−0.0325213	−	0.0563285i
$849$	−505.279	+	875.169i	−0.0204254	+	0.0353778i
$850$	−10437.0			−0.421160
$851$	−8077.59	+	13990.8i	−0.325378	+	0.563570i
$852$	3448.25	−	5972.55i	0.138656	−	0.240160i
$853$	23117.7			0.927942			0.463971	−	0.885851i	$-0.346424\pi$
$853$	23117.7			0.927942			0.463971	+	0.885851i	$0.346424\pi$
$854$	−1854.69	+	3212.42i	−0.0743164	+	0.128720i
$855$	−1172.49	−	2030.82i	−0.0468987	−	0.0812309i
$856$	8403.73	+	14555.7i	0.335553	+	0.581195i
$857$	3246.65			0.129409			0.0647045	−	0.997904i	$-0.479390\pi$
$857$	3246.65			0.129409			0.0647045	+	0.997904i	$0.479390\pi$
$858$		0			0
$859$	29452.5			1.16986			0.584928	−	0.811085i	$-0.301123\pi$
$859$	29452.5			1.16986			0.584928	+	0.811085i	$0.301123\pi$
$860$	−318.629	−	551.882i	−0.0126339	−	0.0218826i
$861$	−4395.04	−	7612.44i	−0.173964	−	0.301314i
$862$	−9513.13	+	16477.2i	−0.375891	+	0.651063i
$863$	15485.4			0.610809			0.305405	−	0.952223i	$-0.401208\pi$
$863$	15485.4			0.610809			0.305405	+	0.952223i	$0.401208\pi$
$864$	−1839.07	+	3185.36i	−0.0724148	+	0.125426i
$865$	1024.84	−	1775.07i	0.0402838	−	0.0697736i
$866$	14542.7			0.570646
$867$	8903.02	−	15420.5i	0.348746	−	0.604045i
$868$	1470.96	+	2547.77i	0.0575201	+	0.0996278i
$869$	−24097.5	−	41738.1i	−0.940681	−	1.62931i
$870$	2100.45			0.0818530
$871$		0			0
$872$	−17335.0			−0.673206
$873$	4642.96	+	8041.84i	0.180000	+	0.311770i
$874$	−18200.2	−	31523.6i	−0.704382	−	1.22003i
$875$	−1012.58	+	1753.83i	−0.0391215	+	0.0677604i
$876$	−2504.01			−0.0965784
$877$	−6851.03	+	11866.3i	−0.263789	+	0.456896i	−0.967246	−	0.253842i	$-0.918306\pi$
$877$	−6851.03	+	11866.3i	−0.263789	+	0.456896i	0.703457	+	0.710738i	$0.251639\pi$
$878$	−9615.25	+	16654.1i	−0.369589	+	0.640147i
$879$	−33579.8			−1.28853
$880$	−908.337	+	1573.29i	−0.0347955	+	0.0602675i
$881$	−8434.32	−	14608.7i	−0.322542	−	0.558659i	0.658470	−	0.752607i	$-0.271204\pi$
$881$	−8434.32	−	14608.7i	−0.322542	−	0.558659i	−0.981012	+	0.193948i	$0.937871\pi$
$882$	−2428.82	−	4206.84i	−0.0927240	−	0.160603i
$883$	15162.4			0.577867			0.288934	−	0.957349i	$-0.406699\pi$
$883$	15162.4			0.577867			0.288934	+	0.957349i	$0.406699\pi$
$884$		0			0
$885$	6000.98			0.227933
$886$	−4782.54	−	8283.61i	−0.181346	−	0.314101i
$887$	6586.93	+	11408.9i	0.249343	+	0.431875i	0.963344	−	0.268270i	$-0.0864519\pi$
$887$	6586.93	+	11408.9i	0.249343	+	0.431875i	−0.714001	+	0.700145i	$0.753119\pi$
$888$	3090.23	−	5352.43i	0.116781	−	0.202270i
$889$	3856.44			0.145490
$890$	1420.39	−	2460.20i	0.0534963	−	0.0926584i
$891$	−23247.5	+	40265.8i	−0.874096	+	1.51398i
$892$	−17403.5			−0.653265
$893$	22168.0	−	38396.1i	0.830709	−	1.43883i
$894$	16010.7	+	27731.4i	0.598970	+	1.03745i
$895$	2241.61	+	3882.58i	0.0837192	+	0.145006i
$896$	−494.779			−0.0184480
$897$		0			0
$898$	13737.4			0.510495
$899$	7980.22	+	13822.2i	0.296057	+	0.512786i
$900$	1783.44	+	3089.01i	0.0660533	+	0.114408i
$901$	2174.72	−	3766.72i	0.0804110	−	0.139276i
$902$	41245.1			1.52252
$903$	846.105	−	1465.50i	0.0311812	−	0.0540074i
$904$	−1427.12	+	2471.84i	−0.0525057	+	0.0909425i
$905$	7227.12			0.265456
$906$	−2840.73	+	4920.29i	−0.104169	+	0.180426i
$907$	−16095.0	−	27877.4i	−0.589225	−	1.02057i	−0.994334	−	0.106300i	$-0.966100\pi$
$907$	−16095.0	−	27877.4i	−0.589225	−	1.02057i	0.405109	−	0.914268i	$-0.367234\pi$
$908$	7291.70	+	12629.6i	0.266502	+	0.461595i
$909$	−13009.7			−0.474703
$910$		0			0
$911$	13646.0			0.496281			0.248141	−	0.968724i	$-0.420180\pi$
$911$	13646.0			0.496281			0.248141	+	0.968724i	$0.420180\pi$
$912$	6962.79	+	12059.9i	0.252808	+	0.437877i
$913$	589.388	+	1020.85i	0.0213646	+	0.0370046i
$914$	−8401.47	+	14551.8i	−0.304044	+	0.526619i
$915$	6007.26			0.217043
$916$	−6478.31	+	11220.8i	−0.233678	+	0.404743i
$917$	3248.68	−	5626.88i	0.116991	−	0.202635i
$918$	−9960.23			−0.358101
$919$	−17461.8	+	30244.7i	−0.626780	+	1.08561i	0.361414	+	0.932406i	$0.382294\pi$
$919$	−17461.8	+	30244.7i	−0.626780	+	1.08561i	−0.988194	+	0.153209i	$0.951039\pi$
$920$	−1047.24	−	1813.88i	−0.0375289	−	0.0650020i
$921$	6205.47	+	10748.2i	0.222016	+	0.384544i
$922$	−31860.9			−1.13805
$923$		0			0
$924$	−4824.09			−0.171754
$925$	7931.99	+	13738.6i	0.281948	+	0.488349i
$926$	−11572.2	−	20043.6i	−0.410674	−	0.711309i
$927$	−319.381	+	553.184i	−0.0113159	+	0.0195997i
$928$	−2684.27			−0.0949522
$929$	2143.75	−	3713.08i	0.0757094	−	0.131133i	−0.825685	−	0.564131i	$-0.809211\pi$
$929$	2143.75	−	3713.08i	0.0757094	−	0.131133i	0.901395	+	0.432999i	$0.142545\pi$
$930$	2382.18	−	4126.06i	0.0839944	−	0.145483i
$931$	48679.1			1.71363
$932$	−4365.36	+	7561.03i	−0.153425	+	0.265740i
$933$	−11473.3	−	19872.3i	−0.402591	−	0.697308i
$934$	−10862.4	−	18814.2i	−0.380543	−	0.659120i
$935$	−4919.47			−0.172068
$936$		0			0
$937$	−14174.1			−0.494182			−0.247091	−	0.968992i	$-0.579475\pi$
$937$	−14174.1			−0.494182			−0.247091	+	0.968992i	$0.579475\pi$
$938$	1605.22	+	2780.32i	0.0558767	+	0.0967813i
$939$	−11001.3	−	19054.7i	−0.382335	−	0.662223i
$940$	1275.55	−	2209.33i	0.0442596	−	0.0766598i
$941$	11317.1			0.392058			0.196029	−	0.980598i	$-0.437195\pi$
$941$	11317.1			0.392058			0.196029	+	0.980598i	$0.437195\pi$
$942$	1382.93	−	2395.30i	0.0478325	−	0.0828484i
$943$	−23776.3	+	41181.7i	−0.821062	+	1.42212i
$944$	−7668.95			−0.264410
$945$	−474.191	+	821.323i	−0.0163232	+	0.0282726i
$946$	3970.12	+	6876.45i	0.136448	+	0.236335i
$947$	20257.2	+	35086.4i	0.695110	+	1.20397i	0.970144	+	0.242531i	$0.0779776\pi$
$947$	20257.2	+	35086.4i	0.695110	+	1.20397i	−0.275034	+	0.961435i	$0.588689\pi$
$948$	−21257.5			−0.728281
$949$		0			0
$950$	−35744.2			−1.22073
$951$	24274.6	+	42044.9i	0.827717	+	1.43365i
$952$	−669.920	−	1160.34i	−0.0228070	−	0.0395028i
$953$	24740.0	−	42850.9i	0.840930	−	1.45653i	−0.0481798	−	0.998839i	$-0.515342\pi$
$953$	24740.0	−	42850.9i	0.840930	−	1.45653i	0.889110	−	0.457694i	$-0.151325\pi$
$954$	−1486.43			−0.0504455
$955$	−3978.86	+	6891.59i	−0.134820	+	0.233515i
$956$	−117.610	+	203.706i	−0.00397884	+	0.00689155i
$957$	−26171.7			−0.884023
$958$	−2085.72	+	3612.57i	−0.0703408	+	0.121834i
$959$	−3050.97	−	5284.44i	−0.102733	−	0.177939i
$960$	400.642	+	693.932i	0.0134694	+	0.0233298i
$961$	6411.32			0.215210
$962$		0			0
$963$	15554.5			0.520495
$964$	−404.522	−	700.654i	−0.0135153	−	0.0234093i
$965$	−2746.30	−	4756.73i	−0.0916130	−	0.158678i
$966$	2780.91	−	4816.68i	0.0926235	−	0.160429i
$967$	46779.9			1.55568			0.777838	−	0.628465i	$-0.216316\pi$
$967$	46779.9			1.55568			0.777838	+	0.628465i	$0.216316\pi$
$968$	5993.88	−	10381.7i	0.199019	−	0.344711i
$969$	−18854.9	+	32657.7i	−0.625086	+	1.08268i
$970$	−5354.45			−0.177238
$971$	−12189.3	+	21112.4i	−0.402855	+	0.697766i	−0.994069	−	0.108749i	$-0.965316\pi$
$971$	−12189.3	+	21112.4i	−0.402855	+	0.697766i	0.591214	+	0.806515i	$0.298649\pi$
$972$	4046.96	+	7009.53i	0.133545	+	0.231307i
$973$	−3332.16	−	5771.47i	−0.109788	−	0.190159i
$974$	23659.1			0.778323
$975$		0			0
$976$	−7676.98			−0.251777
$977$	12118.8	+	20990.4i	0.396842	+	0.687351i	0.993334	−	0.115268i	$-0.0367726\pi$
$977$	12118.8	+	20990.4i	0.396842	+	0.687351i	−0.596492	+	0.802619i	$0.703439\pi$
$978$	8535.54	+	14784.0i	0.279076	+	0.483374i
$979$	−17698.1	+	30654.0i	−0.577768	+	1.00072i
$980$	2801.01			0.0913011
$981$	−8021.34	+	13893.4i	−0.261062	+	0.452172i
$982$	2700.04	−	4676.60i	0.0877410	−	0.151972i
$983$	−32953.2			−1.06922			−0.534611	−	0.845098i	$-0.679542\pi$
$983$	−32953.2			−1.06922			−0.534611	+	0.845098i	$0.679542\pi$
$984$	9096.03	−	15754.8i	0.294686	−	0.510411i
$985$	2072.15	+	3589.06i	0.0670295	+	0.116099i
$986$	−3634.45	−	6295.05i	−0.117388	−	0.203322i
$987$	6774.36			0.218470
$988$		0			0
$989$	−9154.51			−0.294334
$990$	840.622	+	1456.00i	0.0269866	+	0.0467422i
$991$	15127.4	+	26201.4i	0.484902	+	0.839875i	0.999850	−	0.0173469i	$-0.00552196\pi$
$991$	15127.4	+	26201.4i	0.484902	+	0.839875i	−0.514948	+	0.857222i	$0.672189\pi$
$992$	−3044.31	+	5272.89i	−0.0974363	+	0.168765i
$993$	5203.39			0.166288
$994$	−1136.24	+	1968.02i	−0.0362567	+	0.0627985i
$995$	−2444.79	+	4234.49i	−0.0778944	+	0.134917i
$996$	519.925			0.0165406
$997$	2397.23	−	4152.12i	0.0761495	−	0.131895i	−0.825436	−	0.564496i	$-0.809071\pi$
$997$	2397.23	−	4152.12i	0.0761495	−	0.131895i	0.901586	+	0.432601i	$0.142404\pi$
$998$	3013.67	+	5219.83i	0.0955872	+	0.165562i
$999$	7569.65	+	13111.0i	0.239733	+	0.415230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.4.c.i.315.1		4
13.2	odd	12		26.4.b.a.25.4	yes	4
13.3	even	3		338.4.a.f.1.2		2
13.4	even	6		338.4.c.h.191.1		4
13.5	odd	4		338.4.e.g.23.3		8
13.6	odd	12		338.4.e.g.147.1		8
13.7	odd	12		338.4.e.g.147.3		8
13.8	odd	4		338.4.e.g.23.1		8
13.9	even	3	inner	338.4.c.i.191.1		4
13.10	even	6		338.4.a.i.1.2		2
13.11	odd	12		26.4.b.a.25.2	✓	4
13.12	even	2		338.4.c.h.315.1		4
39.2	even	12		234.4.b.b.181.2		4
39.11	even	12		234.4.b.b.181.3		4
52.11	even	12		208.4.f.d.129.1		4
52.15	even	12		208.4.f.d.129.2		4
65.2	even	12		650.4.c.e.649.2		4
65.24	odd	12		650.4.d.d.51.3		4
65.28	even	12		650.4.c.f.649.3		4
65.37	even	12		650.4.c.f.649.2		4
65.54	odd	12		650.4.d.d.51.1		4
65.63	even	12		650.4.c.e.649.3		4
104.11	even	12		832.4.f.h.129.4		4
104.37	odd	12		832.4.f.j.129.2		4
104.67	even	12		832.4.f.h.129.3		4
104.93	odd	12		832.4.f.j.129.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.b.a.25.2	✓	4	13.11	odd	12
26.4.b.a.25.4	yes	4	13.2	odd	12
208.4.f.d.129.1		4	52.11	even	12
208.4.f.d.129.2		4	52.15	even	12
234.4.b.b.181.2		4	39.2	even	12
234.4.b.b.181.3		4	39.11	even	12
338.4.a.f.1.2		2	13.3	even	3
338.4.a.i.1.2		2	13.10	even	6
338.4.c.h.191.1		4	13.4	even	6
338.4.c.h.315.1		4	13.12	even	2
338.4.c.i.191.1		4	13.9	even	3	inner
338.4.c.i.315.1		4	1.1	even	1	trivial
338.4.e.g.23.1		8	13.8	odd	4
338.4.e.g.23.3		8	13.5	odd	4
338.4.e.g.147.1		8	13.6	odd	12
338.4.e.g.147.3		8	13.7	odd	12
650.4.c.e.649.2		4	65.2	even	12
650.4.c.e.649.3		4	65.63	even	12
650.4.c.f.649.2		4	65.37	even	12
650.4.c.f.649.3		4	65.28	even	12
650.4.d.d.51.1		4	65.54	odd	12
650.4.d.d.51.3		4	65.24	odd	12
832.4.f.h.129.3		4	104.67	even	12
832.4.f.h.129.4		4	104.11	even	12
832.4.f.j.129.1		4	104.93	odd	12
832.4.f.j.129.2		4	104.37	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	338.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.93273 - 5.07964i) q^{3} +(-2.00000 + 3.46410i) q^{4} -2.13454 q^{5} +(5.86546 - 10.1593i) q^{6} +(-1.93273 + 3.34759i) q^{7} -8.00000 q^{8} +(-3.70181 + 6.41172i) q^{9} +(-2.13454 - 3.69713i) q^{10} +(26.5964 + 46.0663i) q^{11} +23.4618 q^{12} -7.73092 q^{14} +(6.26003 + 10.8427i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(21.6636 - 37.5225i) q^{17} -14.8072 q^{18} +(74.1928 - 128.506i) q^{19} +(4.26908 - 7.39426i) q^{20} +22.6727 q^{21} +(-53.1928 + 92.1326i) q^{22} +(-61.3273 - 106.222i) q^{23} +(23.4618 + 40.6371i) q^{24} -120.444 q^{25} -114.942 q^{27} +(-7.73092 - 13.3903i) q^{28} +(-41.9418 - 72.6453i) q^{29} +(-12.5201 + 21.6854i) q^{30} -190.269 q^{31} +(16.0000 - 27.7128i) q^{32} +(156.000 - 270.200i) q^{33} +86.6546 q^{34} +(4.12549 - 7.14556i) q^{35} +(-14.8072 - 25.6469i) q^{36} +(-65.8564 - 114.067i) q^{37} +296.771 q^{38} +17.0763 q^{40} +(-193.847 - 335.753i) q^{41} +(22.6727 + 39.2703i) q^{42} +(37.3182 - 64.6371i) q^{43} -212.771 q^{44} +(7.90166 - 13.6861i) q^{45} +(122.655 - 212.444i) q^{46} +298.789 q^{47} +(-46.9237 + 81.2742i) q^{48} +(164.029 + 284.107i) q^{49} +(-120.444 - 208.615i) q^{50} -254.135 q^{51} +100.386 q^{53} +(-114.942 - 199.085i) q^{54} +(-56.7710 - 98.3303i) q^{55} +(15.4618 - 26.7807i) q^{56} -870.349 q^{57} +(83.8836 - 145.291i) q^{58} +(239.655 - 415.094i) q^{59} -50.0802 q^{60} +(239.906 - 415.529i) q^{61} +(-190.269 - 329.556i) q^{62} +(-14.3092 - 24.7843i) q^{63} +64.0000 q^{64} +624.000 q^{66} +(-207.636 - 359.637i) q^{67} +(86.6546 + 150.090i) q^{68} +(-359.713 + 623.041i) q^{69} +16.5020 q^{70} +(146.973 - 254.564i) q^{71} +(29.6145 - 51.2938i) q^{72} -106.727 q^{73} +(131.713 - 228.133i) q^{74} +(353.229 + 611.811i) q^{75} +(296.771 + 514.023i) q^{76} -205.614 q^{77} -906.044 q^{79} +(17.0763 + 29.5771i) q^{80} +(437.042 + 756.979i) q^{81} +(387.695 - 671.507i) q^{82} +22.1605 q^{83} +(-45.3454 + 78.5405i) q^{84} +(-46.2419 + 80.0934i) q^{85} +149.273 q^{86} +(-246.008 + 426.098i) q^{87} +(-212.771 - 368.530i) q^{88} +(332.717 + 576.282i) q^{89} +31.6066 q^{90} +490.618 q^{92} +(558.008 + 966.498i) q^{93} +(298.789 + 517.518i) q^{94} +(-158.367 + 274.300i) q^{95} -187.695 q^{96} +(627.120 - 1086.20i) q^{97} +(-328.058 + 568.214i) q^{98} -393.819 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 3 q^{3} - 8 q^{4} - 38 q^{5} - 6 q^{6} + 7 q^{7} - 32 q^{8} - 59 q^{9} - 38 q^{10} + 18 q^{11} - 24 q^{12} + 28 q^{14} - 137 q^{15} - 32 q^{16} + 13 q^{17} - 236 q^{18} + 120 q^{19} + 76 q^{20}+ \cdots + 2844 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 3 * q^3 - 8 * q^4 - 38 * q^5 - 6 * q^6 + 7 * q^7 - 32 * q^8 - 59 * q^9 - 38 * q^10 + 18 * q^11 - 24 * q^12 + 28 * q^14 - 137 * q^15 - 32 * q^16 + 13 * q^17 - 236 * q^18 + 120 * q^19 + 76 * q^20 + 238 * q^21 - 36 * q^22 - 98 * q^23 - 24 * q^24 + 78 * q^25 - 666 * q^27 + 28 * q^28 - 374 * q^29 + 274 * q^30 - 820 * q^31 + 64 * q^32 + 624 * q^33 + 52 * q^34 - 175 * q^35 - 236 * q^36 - 13 * q^37 + 480 * q^38 + 304 * q^40 - 304 * q^41 + 238 * q^42 - 219 * q^43 - 144 * q^44 + 886 * q^45 + 196 * q^46 + 930 * q^47 + 48 * q^48 + 553 * q^49 + 78 * q^50 - 1046 * q^51 + 48 * q^53 - 666 * q^54 + 480 * q^55 - 56 * q^56 - 2244 * q^57 + 748 * q^58 + 664 * q^59 + 1096 * q^60 + 282 * q^61 - 820 * q^62 + 532 * q^63 + 256 * q^64 + 2496 * q^66 - 94 * q^67 + 52 * q^68 - 938 * q^69 - 700 * q^70 - 75 * q^71 + 472 * q^72 - 1900 * q^73 + 26 * q^74 + 2120 * q^75 + 480 * q^76 - 1176 * q^77 - 1444 * q^79 + 304 * q^80 + 334 * q^81 + 608 * q^82 - 2504 * q^83 - 476 * q^84 + 419 * q^85 - 876 * q^86 + 2080 * q^87 - 144 * q^88 - 702 * q^89 + 3544 * q^90 + 784 * q^92 - 832 * q^93 + 930 * q^94 + 162 * q^95 + 192 * q^96 + 564 * q^97 - 1106 * q^98 + 2844 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more