LMFDB - Embedded newform 338.4.e.g.23.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,4,Mod(23,338)] 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([5])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.23"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	338.e (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,6,16,0,0,0,0,-118,76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$19.9426455819$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.45979465625856.49
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 109x^{6} + 8965x^{4} - 317844x^{2} + 8503056 $ x^8 - 109x^6 + 8965x^4 - 317844*x^2 + 8503056
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.3
Root			$6.81169 + 3.93273i$ of defining polynomial
Character	$\chi$	$=$	338.23
Dual form			338.4.e.g.147.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 - 1.00000i) q^{2} +(-2.93273 - 5.07964i) q^{3} +(2.00000 - 3.46410i) q^{4} +2.13454i q^{5} +(-10.1593 - 5.86546i) q^{6} +(-3.34759 - 1.93273i) q^{7} -8.00000i q^{8} +(-3.70181 + 6.41172i) q^{9} +(2.13454 + 3.69713i) q^{10} +(-46.0663 + 26.5964i) q^{11} -23.4618 q^{12} -7.73092 q^{14} +(10.8427 - 6.26003i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-21.6636 + 37.5225i) q^{17} +14.8072i q^{18} +(-128.506 - 74.1928i) q^{19} +(7.39426 + 4.26908i) q^{20} +22.6727i q^{21} +(-53.1928 + 92.1326i) q^{22} +(61.3273 + 106.222i) q^{23} +(-40.6371 + 23.4618i) q^{24} +120.444 q^{25} -114.942 q^{27} +(-13.3903 + 7.73092i) q^{28} +(-41.9418 - 72.6453i) q^{29} +(12.5201 - 21.6854i) q^{30} +190.269i q^{31} +(-27.7128 - 16.0000i) q^{32} +(270.200 + 156.000i) q^{33} +86.6546i q^{34} +(4.12549 - 7.14556i) q^{35} +(14.8072 + 25.6469i) q^{36} +(114.067 - 65.8564i) q^{37} -296.771 q^{38} +17.0763 q^{40} +(-335.753 + 193.847i) q^{41} +(22.6727 + 39.2703i) q^{42} +(-37.3182 + 64.6371i) q^{43} +212.771i q^{44} +(-13.6861 - 7.90166i) q^{45} +(212.444 + 122.655i) q^{46} +298.789i q^{47} +(-46.9237 + 81.2742i) q^{48} +(-164.029 - 284.107i) q^{49} +(208.615 - 120.444i) q^{50} +254.135 q^{51} +100.386 q^{53} +(-199.085 + 114.942i) q^{54} +(-56.7710 - 98.3303i) q^{55} +(-15.4618 + 26.7807i) q^{56} +870.349i q^{57} +(-145.291 - 83.8836i) q^{58} +(415.094 + 239.655i) q^{59} -50.0802i q^{60} +(239.906 - 415.529i) q^{61} +(190.269 + 329.556i) q^{62} +(24.7843 - 14.3092i) q^{63} -64.0000 q^{64} +624.000 q^{66} +(-359.637 + 207.636i) q^{67} +(86.6546 + 150.090i) q^{68} +(359.713 - 623.041i) q^{69} -16.5020i q^{70} +(-254.564 - 146.973i) q^{71} +(51.2938 + 29.6145i) q^{72} -106.727i q^{73} +(131.713 - 228.133i) q^{74} +(-353.229 - 611.811i) q^{75} +(-514.023 + 296.771i) q^{76} +205.614 q^{77} -906.044 q^{79} +(29.5771 - 17.0763i) q^{80} +(437.042 + 756.979i) q^{81} +(-387.695 + 671.507i) q^{82} -22.1605i q^{83} +(78.5405 + 45.3454i) q^{84} +(-80.0934 - 46.2419i) q^{85} +149.273i q^{86} +(-246.008 + 426.098i) q^{87} +(212.771 + 368.530i) q^{88} +(-576.282 + 332.717i) q^{89} -31.6066 q^{90} +490.618 q^{92} +(966.498 - 558.008i) q^{93} +(298.789 + 517.518i) q^{94} +(158.367 - 274.300i) q^{95} +187.695i q^{96} +(-1086.20 - 627.120i) q^{97} +(-568.214 - 328.058i) q^{98} -393.819i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 16 q^{4} - 118 q^{9} + 76 q^{10} + 48 q^{12} + 56 q^{14} - 64 q^{16} - 26 q^{17} - 72 q^{22} + 196 q^{23} - 156 q^{25} - 1332 q^{27} - 748 q^{29} - 548 q^{30} - 350 q^{35} + 472 q^{36} - 960 q^{38}+ \cdots - 324 q^{95}+O(q^{100}) $ 8 * q + 6 * q^3 + 16 * q^4 - 118 * q^9 + 76 * q^10 + 48 * q^12 + 56 * q^14 - 64 * q^16 - 26 * q^17 - 72 * q^22 + 196 * q^23 - 156 * q^25 - 1332 * q^27 - 748 * q^29 - 548 * q^30 - 350 * q^35 + 472 * q^36 - 960 * q^38 + 608 * q^40 + 476 * q^42 + 438 * q^43 + 96 * q^48 - 1106 * q^49 + 2092 * q^51 + 96 * q^53 + 960 * q^55 + 112 * q^56 + 564 * q^61 + 1640 * q^62 - 512 * q^64 + 4992 * q^66 + 104 * q^68 + 1876 * q^69 + 52 * q^74 - 4240 * q^75 + 2352 * q^77 - 2888 * q^79 + 668 * q^81 - 1216 * q^82 + 4160 * q^87 + 288 * q^88 - 7088 * q^90 + 1568 * q^92 + 1860 * q^94 - 324 * q^95

Character values

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

$n$	$171$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	−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
$5$			2.13454i			0.190919i	0.995433	+	0.0954595i	$0.0304321\pi$
$5$			2.13454i			0.190919i	−0.995433	+	0.0954595i	$0.969568\pi$
$6$	−10.1593	−	5.86546i	−0.691251	−	0.399094i
$7$	−3.34759	−	1.93273i	−0.180753	−	0.104358i	0.406894	−	0.913476i	$-0.366612\pi$
$7$	−3.34759	−	1.93273i	−0.180753	−	0.104358i	−0.587646	+	0.809118i	$0.699945\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−3.70181	+	6.41172i	−0.137104	+	0.237471i
$10$	2.13454	+	3.69713i	0.0675001	+	0.116914i
$11$	−46.0663	+	26.5964i	−1.26268	+	0.729010i	−0.973593	−	0.228292i	$-0.926686\pi$
$11$	−46.0663	+	26.5964i	−1.26268	+	0.729010i	−0.289090	+	0.957302i	$0.593353\pi$
$12$	−23.4618			−0.564404
$13$		0			0
$13$		0			0
$14$	−7.73092			−0.147584
$15$	10.8427	−	6.26003i	0.186638	−	0.107756i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−21.6636	+	37.5225i	−0.309071	+	0.535327i	−0.978159	−	0.207856i	$-0.933351\pi$
$17$	−21.6636	+	37.5225i	−0.309071	+	0.535327i	0.669088	+	0.743183i	$0.266685\pi$
$18$			14.8072i			0.193894i
$19$	−128.506	−	74.1928i	−1.55164	−	0.895841i	−0.998008	−	0.0630816i	$-0.979907\pi$
$19$	−128.506	−	74.1928i	−1.55164	−	0.895841i	−0.553634	−	0.832760i	$-0.686759\pi$
$20$	7.39426	+	4.26908i	0.0826704	+	0.0477298i
$21$			22.6727i			0.235599i
$22$	−53.1928	+	92.1326i	−0.515488	+	0.892851i
$23$	61.3273	+	106.222i	0.555984	+	0.962992i	0.997826	+	0.0658995i	$0.0209917\pi$
$23$	61.3273	+	106.222i	0.555984	+	0.962992i	−0.441843	+	0.897093i	$0.645675\pi$
$24$	−40.6371	+	23.4618i	−0.345626	+	0.199547i
$25$	120.444			0.963550
$26$		0			0
$27$	−114.942			−0.819280
$28$	−13.3903	+	7.73092i	−0.0903763	+	0.0521788i
$29$	−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
$31$			190.269i			1.10237i	0.834384	+	0.551183i	$0.185823\pi$
$31$			190.269i			1.10237i	−0.834384	+	0.551183i	$0.814177\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	270.200	+	156.000i	1.42533	+	0.822913i
$34$			86.6546i			0.437092i
$35$	4.12549	−	7.14556i	0.0199239	−	0.0345091i
$36$	14.8072	+	25.6469i	0.0685520	+	0.118736i
$37$	114.067	−	65.8564i	0.506823	−	0.292614i	−0.224704	−	0.974427i	$-0.572141\pi$
$37$	114.067	−	65.8564i	0.506823	−	0.292614i	0.731527	+	0.681813i	$0.238808\pi$
$38$	−296.771			−1.26691
$39$		0			0
$40$	17.0763			0.0675001
$41$	−335.753	+	193.847i	−1.27892	+	0.738387i	−0.976651	−	0.214834i	$-0.931079\pi$
$41$	−335.753	+	193.847i	−1.27892	+	0.738387i	−0.302273	+	0.953221i	$0.597746\pi$
$42$	22.6727	+	39.2703i	0.0832970	+	0.144275i
$43$	−37.3182	+	64.6371i	−0.132348	+	0.229234i	−0.924581	−	0.380985i	$-0.875585\pi$
$43$	−37.3182	+	64.6371i	−0.132348	+	0.229234i	0.792233	+	0.610219i	$0.208918\pi$
$44$			212.771i			0.729010i
$45$	−13.6861	−	7.90166i	−0.0453378	−	0.0261758i
$46$	212.444	+	122.655i	0.680938	+	0.393140i
$47$			298.789i			0.927295i	0.886020	+	0.463648i	$0.153460\pi$
$47$			298.789i			0.927295i	−0.886020	+	0.463648i	$0.846540\pi$
$48$	−46.9237	+	81.2742i	−0.141101	+	0.244394i
$49$	−164.029	−	284.107i	−0.478219	−	0.828300i
$50$	208.615	−	120.444i	0.590051	−	0.340666i
$51$	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	$0.458475\pi$
$54$	−199.085	+	114.942i	−0.501704	+	0.289659i
$55$	−56.7710	−	98.3303i	−0.139182	−	0.241070i
$56$	−15.4618	+	26.7807i	−0.0368960	+	0.0639057i
$57$			870.349i			2.02247i
$58$	−145.291	−	83.8836i	−0.328924	−	0.189904i
$59$	415.094	+	239.655i	0.915943	+	0.528820i	0.882338	−	0.470615i	$-0.155968\pi$
$59$	415.094	+	239.655i	0.915943	+	0.528820i	0.0336044	+	0.999435i	$0.489301\pi$
$60$		−	50.0802i		−	0.107756i
$61$	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
$63$	24.7843	−	14.3092i	0.0495639	−	0.0286157i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	624.000			1.16377
$67$	−359.637	+	207.636i	−0.655771	+	0.378609i	−0.790664	−	0.612251i	$-0.790264\pi$
$67$	−359.637	+	207.636i	−0.655771	+	0.378609i	0.134893	+	0.990860i	$0.456931\pi$
$68$	86.6546	+	150.090i	0.154535	+	0.267663i
$69$	359.713	−	623.041i	0.627599	−	1.08703i
$70$		−	16.5020i		−	0.0281766i
$71$	−254.564	−	146.973i	−0.425510	−	0.245669i	0.271922	−	0.962319i	$-0.412341\pi$
$71$	−254.564	−	146.973i	−0.425510	−	0.245669i	−0.697432	+	0.716651i	$0.745674\pi$
$72$	51.2938	+	29.6145i	0.0839588	+	0.0484736i
$73$		−	106.727i		−	0.171116i	−0.996333	−	0.0855579i	$-0.972733\pi$
$73$		−	106.727i		−	0.171116i	0.996333	−	0.0855579i	$-0.0272673\pi$
$74$	131.713	−	228.133i	0.206910	−	0.358378i
$75$	−353.229	−	611.811i	−0.543832	−	0.941944i
$76$	−514.023	+	296.771i	−0.775821	+	0.447921i
$77$	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	$0.723216\pi$
$80$	29.5771	−	17.0763i	0.0413352	−	0.0238649i
$81$	437.042	+	756.979i	0.599509	+	1.03838i
$82$	−387.695	+	671.507i	−0.522119	+	0.904336i
$83$		−	22.1605i		−	0.0293064i	−0.999893	−	0.0146532i	$-0.995336\pi$
$83$		−	22.1605i		−	0.0293064i	0.999893	−	0.0146532i	$-0.00466442\pi$
$84$	78.5405	+	45.3454i	0.102018	+	0.0588999i
$85$	−80.0934	−	46.2419i	−0.102204	−	0.0590075i
$86$			149.273i			0.187169i
$87$	−246.008	+	426.098i	−0.303159	+	0.525086i
$88$	212.771	+	368.530i	0.257744	+	0.446426i
$89$	−576.282	+	332.717i	−0.686357	+	0.396269i	−0.802246	−	0.596994i	$-0.796362\pi$
$89$	−576.282	+	332.717i	−0.686357	+	0.396269i	0.115889	+	0.993262i	$0.463028\pi$
$90$	−31.6066			−0.0370181
$91$		0			0
$92$	490.618			0.555984
$93$	966.498	−	558.008i	1.07765	−	0.622180i
$94$	298.789	+	517.518i	0.327848	+	0.567850i
$95$	158.367	−	274.300i	0.171033	−	0.296238i
$96$			187.695i			0.199547i
$97$	−1086.20	−	627.120i	−1.13698	−	0.656437i	−0.191301	−	0.981531i	$-0.561271\pi$
$97$	−1086.20	−	627.120i	−1.13698	−	0.656437i	−0.945682	+	0.325094i	$0.894604\pi$
$98$	−568.214	−	328.058i	−0.585696	−	0.338152i
$99$		−	393.819i		−	0.399801i
$100$	240.887	−	417.229i	0.240887	−	0.417229i
$101$	−878.604	−	1521.79i	−0.865588	−	1.49924i	−0.866462	−	0.499243i	$-0.833612\pi$
$101$	−878.604	−	1521.79i	−0.865588	−	1.49924i	0.000874171	−	1.00000i	$-0.499722\pi$
$102$	440.174	−	254.135i	0.427291	−	0.246697i
$103$	−86.2769			−0.0825351			−0.0412676	−	0.999148i	$-0.513140\pi$
$103$	−86.2769			−0.0825351			−0.0412676	+	0.999148i	$0.513140\pi$
$104$		0			0
$105$	−48.3958			−0.0449804
$106$	173.873	−	100.386i	0.159321	−	0.0919840i
$107$	−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
$109$		−	2166.87i		−	1.90411i	−0.305920	−	0.952057i	$-0.598964\pi$
$109$		−	2166.87i		−	1.90411i	0.305920	−	0.952057i	$-0.401036\pi$
$110$	−196.661	−	113.542i	−0.170462	−	0.0984165i
$111$	−669.053	−	386.278i	−0.572106	−	0.330305i
$112$			61.8474i			0.0521788i
$113$	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
$115$	−226.735	+	130.906i	−0.183854	+	0.106148i
$116$	−335.534			−0.268565
$117$		0			0
$118$	958.618			0.747864
$119$	145.042	−	83.7400i	0.111731	−	0.0645078i
$120$	−50.0802	−	86.7415i	−0.0380973	−	0.0659865i
$121$	749.235	−	1297.71i	0.562911	−	0.974991i
$122$		−	959.622i		−	0.712132i
$123$	1969.35	+	1137.00i	1.44366	+	0.833497i
$124$	659.111	+	380.538i	0.477338	+	0.275591i
$125$			523.909i			0.374879i
$126$	28.6184	−	49.5685i	0.0202344	−	0.0350469i
$127$	498.833	+	864.004i	0.348538	+	0.603685i	0.985990	−	0.166805i	$-0.0533450\pi$
$127$	498.833	+	864.004i	0.348538	+	0.603685i	−0.637452	+	0.770490i	$0.720012\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	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	$0.689403\pi$
$132$	1080.80	−	624.000i	0.712663	−	0.411456i
$133$	286.789	+	496.733i	0.186976	+	0.323851i
$134$	−415.273	+	719.274i	−0.267717	+	0.463700i
$135$		−	245.348i		−	0.156416i
$136$	300.180	+	173.309i	0.189267	+	0.109273i
$137$	−1367.09	−	789.291i	−0.852544	−	0.492217i	0.00896417	−	0.999960i	$-0.497147\pi$
$137$	−1367.09	−	789.291i	−0.852544	−	0.492217i	−0.861509	+	0.507743i	$0.830480\pi$
$138$		−	1438.85i		−	0.887559i
$139$	−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
$141$	1517.74	−	876.268i	0.906502	−	0.523369i
$142$	−587.891			−0.347428
$143$		0			0
$144$	118.458			0.0685520
$145$	155.064	−	89.5264i	0.0888096	−	0.0512742i
$146$	−106.727	−	184.857i	−0.0604986	−	0.104787i
$147$	−962.106	+	1666.42i	−0.539818	+	0.934991i
$148$		−	526.851i		−	0.292614i
$149$	2363.96	+	1364.83i	1.29975	+	0.750413i	0.980361	−	0.197210i	$-0.0631881\pi$
$149$	2363.96	+	1364.83i	1.29975	+	0.750413i	0.319392	+	0.947623i	$0.396521\pi$
$150$	−1223.62	−	706.458i	−0.666055	−	0.384547i
$151$		−	484.316i		−	0.261014i	−0.991447	−	0.130507i	$-0.958340\pi$
$151$		−	484.316i		−	0.261014i	0.991447	−	0.130507i	$-0.0416604\pi$
$152$	−593.542	+	1028.05i	−0.316728	+	0.548589i
$153$	−160.389	−	277.803i	−0.0847498	−	0.146791i
$154$	356.135	−	205.614i	0.186352	−	0.107590i
$155$	−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	$0.480913\pi$
$158$	−1569.31	+	906.044i	−0.790177	+	0.456209i
$159$	−294.404	−	509.922i	−0.146841	−	0.254336i
$160$	34.1526	−	59.1541i	0.0168750	−	0.0292284i
$161$		−	474.116i		−	0.232085i
$162$	1513.96	+	874.084i	0.734246	+	0.423917i
$163$	−1260.26	−	727.611i	−0.605589	−	0.349637i	0.165648	−	0.986185i	$-0.447028\pi$
$163$	−1260.26	−	727.611i	−0.605589	−	0.349637i	−0.771237	+	0.636548i	$0.780362\pi$
$164$			1550.78i			0.738387i
$165$	−332.988	+	576.753i	−0.157110	+	0.272122i
$166$	−22.1605	−	38.3831i	−0.0103614	−	0.0179464i
$167$	1412.07	−	815.259i	0.654307	−	0.377764i	−0.135798	−	0.990737i	$-0.543360\pi$
$167$	1412.07	−	815.259i	0.654307	−	0.377764i	0.790104	+	0.612972i	$0.210026\pi$
$168$	181.382			0.0832970
$169$		0			0
$170$	−184.968			−0.0834493
$171$	951.407	−	549.295i	0.425473	−	0.245647i
$172$	149.273	+	258.548i	0.0661742	+	0.114617i
$173$	480.120	−	831.593i	0.210999	−	0.365461i	−0.741028	−	0.671474i	$-0.765662\pi$
$173$	480.120	−	831.593i	0.210999	−	0.365461i	0.952028	+	0.306012i	$0.0989949\pi$
$174$			984.031i			0.428731i
$175$	−403.196	−	232.785i	−0.174164	−	0.100554i
$176$	737.060	+	425.542i	0.315671	+	0.182253i
$177$		−	2811.37i		−	1.19387i
$178$	−665.433	+	1152.56i	−0.280204	+	0.485328i
$179$	1050.16	+	1818.93i	0.438506	+	0.759515i	0.997575	−	0.0696067i	$-0.0221744\pi$
$179$	1050.16	+	1818.93i	0.438506	+	0.759515i	−0.559068	+	0.829122i	$0.688841\pi$
$180$	−54.7443	+	31.6066i	−0.0226689	+	0.0130879i
$181$	3385.80			1.39041			0.695206	−	0.718811i	$-0.255313\pi$
$181$	3385.80			1.39041			0.695206	+	0.718811i	$0.255313\pi$
$182$		0			0
$183$	−2814.31			−1.13683
$184$	849.776	−	490.618i	0.340469	−	0.196570i
$185$	140.573	+	243.480i	0.0558656	+	0.0967621i
$186$	1116.02	−	1933.00i	0.439948	−	0.762011i
$187$		−	2304.70i		−	0.901263i
$188$	1035.04	+	597.578i	0.401531	+	0.231824i
$189$	384.778	+	222.151i	0.148087	+	0.0854981i
$190$		−	633.470i		−	0.241877i
$191$	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
$193$	−2228.46	+	1286.60i	−0.831129	+	0.479852i	−0.854239	−	0.519881i	$-0.825976\pi$
$193$	−2228.46	+	1286.60i	−0.831129	+	0.479852i	0.0231102	+	0.999733i	$0.492643\pi$
$194$	−2508.48			−0.928343
$195$		0			0
$196$	−1312.23			−0.478219
$197$	−1681.42	+	970.770i	−0.608104	+	0.351089i	−0.772223	−	0.635352i	$-0.780855\pi$
$197$	−1681.42	+	970.770i	−0.608104	+	0.351089i	0.164119	+	0.986440i	$0.447522\pi$
$198$	−393.819	−	682.114i	−0.141351	−	0.244827i
$199$	−1145.35	+	1983.80i	−0.407997	+	0.706671i	−0.994665	−	0.103156i	$-0.967106\pi$
$199$	−1145.35	+	1983.80i	−0.407997	+	0.706671i	0.586668	+	0.809827i	$0.300439\pi$
$200$		−	963.550i		−	0.340666i
$201$	2109.44	+	1217.88i	0.740240	+	0.427378i
$202$	−3043.57	−	1757.21i	−1.06012	−	0.612063i
$203$			324.249i			0.112107i
$204$	508.269	−	880.348i	0.174441	−	0.302141i
$205$	−413.775	−	716.679i	−0.140972	−	0.244171i
$206$	−149.436	+	86.2769i	−0.0505422	+	0.0291806i
$207$	−908.088			−0.304911
$208$		0			0
$209$	7893.04			2.61231
$210$	−83.8240	+	48.3958i	−0.0275448	+	0.0159030i
$211$	−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
$213$			1724.13i			0.554625i
$214$	−3638.92	−	2100.93i	−1.16239	−	0.671106i
$215$	−137.970	−	79.6573i	−0.0437652	−	0.0252678i
$216$			919.534i			0.289659i
$217$	367.739	−	636.942i	0.115040	−	0.199256i
$218$	−2166.87	−	3753.13i	−0.673206	−	1.16603i
$219$	−542.134	+	313.001i	−0.167279	+	0.0965784i
$220$	−454.168			−0.139182
$221$		0			0
$222$	−1545.11			−0.467122
$223$	3767.97	−	2175.44i	1.13149	−	0.653265i	0.187180	−	0.982326i	$-0.440065\pi$
$223$	3767.97	−	2175.44i	1.13149	−	0.653265i	0.944309	+	0.329060i	$0.106732\pi$
$224$	61.8474	+	107.123i	0.0184480	+	0.0319529i
$225$	−445.860	+	772.252i	−0.132107	+	0.228815i
$226$		−	713.558i		−	0.210023i
$227$	−3157.40	−	1822.93i	−0.923189	−	0.533003i	−0.0385380	−	0.999257i	$-0.512270\pi$
$227$	−3157.40	−	1822.93i	−0.923189	−	0.533003i	−0.884651	+	0.466254i	$0.845603\pi$
$228$	3014.98	+	1740.70i	0.875754	+	0.505617i
$229$			3239.15i			0.934713i	0.884069	+	0.467357i	$0.154794\pi$
$229$			3239.15i			0.934713i	−0.884069	+	0.467357i	$0.845206\pi$
$230$	−261.811	+	453.470i	−0.0750579	+	0.130004i
$231$	−603.012	−	1044.45i	−0.171754	−	0.297487i
$232$	−581.162	+	335.534i	−0.164462	+	0.0949522i
$233$	−2182.68			−0.613700			−0.306850	−	0.951758i	$-0.599275\pi$
$233$	−2182.68			−0.613700			−0.306850	+	0.951758i	$0.599275\pi$
$234$		0			0
$235$	−637.777			−0.177038
$236$	1660.38	−	958.618i	0.457971	−	0.264410i
$237$	2657.18	+	4602.38i	0.728281	+	1.26142i
$238$	167.480	−	290.084i	0.0456139	−	0.0790056i
$239$		−	58.8048i		−	0.0159153i	−0.999968	−	0.00795767i	$-0.997467\pi$
$239$		−	58.8048i		−	0.0159153i	0.999968	−	0.00795767i	$-0.00253303\pi$
$240$	−173.483	−	100.160i	−0.0466595	−	0.0269389i
$241$	−175.163	−	101.131i	−0.0468185	−	0.0270307i	0.476408	−	0.879224i	$-0.341939\pi$
$241$	−175.163	−	101.131i	−0.0468185	−	0.0270307i	−0.523227	+	0.852194i	$0.675272\pi$
$242$		−	2996.94i		−	0.796077i
$243$	1011.74	−	1752.38i	0.267091	−	0.462615i
$244$	−959.622	−	1662.11i	−0.251777	−	0.436090i
$245$	606.437	−	350.127i	0.158138	−	0.0913011i
$246$	4548.02			1.17874
$247$		0			0
$248$	1522.15			0.389745
$249$	−112.567	+	64.9907i	−0.0286492	+	0.0165406i
$250$	523.909	+	907.438i	0.132540	+	0.229566i
$251$	−56.9961	+	98.7201i	−0.0143329	+	0.0248253i	−0.873103	−	0.487536i	$-0.837896\pi$
$251$	−56.9961	+	98.7201i	−0.0143329	+	0.0248253i	0.858770	+	0.512361i	$0.171229\pi$
$252$		−	114.474i		−	0.0286157i
$253$	−5650.24	−	3262.17i	−1.40406	−	0.810635i
$254$	1728.01	+	997.666i	0.426870	+	0.246453i
$255$			542.460i			0.133216i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	2117.36	+	3667.38i	0.513920	+	0.890136i	0.999870	+	0.0161491i	$0.00514064\pi$
$257$	2117.36	+	3667.38i	0.513920	+	0.890136i	−0.485949	+	0.873987i	$0.661526\pi$
$258$	758.253	−	437.777i	0.182972	−	0.105639i
$259$	−509.131			−0.122146
$260$		0			0
$261$	621.042			0.147286
$262$	−2911.36	+	1680.88i	−0.686507	+	0.396355i
$263$	−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
$265$			214.277i			0.0496714i
$266$	993.467	+	573.578i	0.228998	+	0.132212i
$267$	3380.16	+	1951.54i	0.774766	+	0.447311i
$268$			1661.09i			0.378609i
$269$	−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
$271$	−5101.87	+	2945.57i	−1.14360	+	0.660260i	−0.947320	−	0.320288i	$-0.896220\pi$
$271$	−5101.87	+	2945.57i	−1.14360	+	0.660260i	−0.196283	+	0.980547i	$0.562887\pi$
$272$	693.237			0.154535
$273$		0			0
$274$	−3157.16			−0.696100
$275$	−5548.40	+	3203.37i	−1.21666	+	0.702438i
$276$	−1438.85	−	2492.16i	−0.313800	−	0.543517i
$277$	3069.70	−	5316.87i	0.665849	−	1.15328i	−0.313205	−	0.949685i	$-0.601403\pi$
$277$	3069.70	−	5316.87i	0.665849	−	1.15328i	0.979054	−	0.203599i	$-0.0652638\pi$
$278$			3448.14i			0.743905i
$279$	−1219.95	−	704.340i	−0.261780	−	0.151139i
$280$	−57.1645	−	33.0039i	−0.0122008	−	0.00704415i
$281$			1852.24i			0.393221i	0.980482	+	0.196611i	$0.0629935\pi$
$281$			1852.24i			0.393221i	−0.980482	+	0.196611i	$0.937006\pi$
$282$	1752.54	−	3035.48i	0.370078	−	0.640994i
$283$	86.1448	+	149.207i	0.0180946	+	0.0313408i	0.874931	−	0.484248i	$-0.160907\pi$
$283$	86.1448	+	149.207i	0.0180946	+	0.0313408i	−0.856836	+	0.515589i	$0.827573\pi$
$284$	−1018.26	+	587.891i	−0.212755	+	0.122834i
$285$	−1857.80			−0.386127
$286$		0			0
$287$	1498.62			0.308225
$288$	205.175	−	118.458i	0.0419794	−	0.0242368i
$289$	1517.87	+	2629.03i	0.308950	+	0.535118i
$290$	179.053	−	310.129i	0.0362564	−	0.0627979i
$291$			7356.70i			1.48198i
$292$	−369.713	−	213.454i	−0.0740953	−	0.0427789i
$293$	4958.00	+	2862.50i	0.988564	+	0.570748i	0.904845	−	0.425742i	$-0.139987\pi$
$293$	4958.00	+	2862.50i	0.988564	+	0.570748i	0.0837193	+	0.996489i	$0.473320\pi$
$294$			3848.42i			0.763417i
$295$	−511.552	+	886.035i	−0.100962	+	0.174871i
$296$	−526.851	−	912.533i	−0.103455	−	0.179189i
$297$	5294.94	−	3057.04i	1.03449	−	0.597263i
$298$	5459.33			1.06124
$299$		0			0
$300$	−2825.83			−0.543832
$301$	249.852	−	144.252i	0.0478446	−	0.0276231i
$302$	−484.316	−	838.859i	−0.0922822	−	0.159837i
$303$	−5153.42	+	8925.98i	−0.977083	+	1.69236i
$304$			2374.17i			0.447921i
$305$	886.963	+	512.088i	0.166516	+	0.0961380i
$306$	−555.605	−	320.779i	−0.103797	−	0.0599271i
$307$		−	2115.94i		−	0.393364i	−0.980467	−	0.196682i	$-0.936983\pi$
$307$		−	2115.94i		−	0.393364i	0.980467	−	0.196682i	$-0.0630167\pi$
$308$	411.229	−	712.269i	0.0760777	−	0.131771i
$309$	253.027	+	438.255i	0.0465832	+	0.0806844i
$310$	−703.450	+	406.137i	−0.128882	+	0.0744098i
$311$	−3912.14			−0.713303			−0.356651	−	0.934238i	$-0.616082\pi$
$311$	−3912.14			−0.713303			−0.356651	+	0.934238i	$0.616082\pi$
$312$		0			0
$313$	3751.20			0.677413			0.338706	−	0.940892i	$-0.390011\pi$
$313$	3751.20			0.677413			0.338706	+	0.940892i	$0.390011\pi$
$314$	408.374	−	235.775i	0.0733946	−	0.0423744i
$315$	30.5436	+	52.9030i	0.00546328	+	0.00946269i
$316$	−1812.09	+	3138.63i	−0.322588	+	0.558739i
$317$			8277.14i			1.46653i	0.679942	+	0.733266i	$0.262005\pi$
$317$			8277.14i			1.46653i	−0.679942	+	0.733266i	$0.737995\pi$
$318$	−1019.84	−	588.807i	−0.179843	−	0.103832i
$319$	3864.20	+	2231.00i	0.678225	+	0.391574i
$320$		−	136.611i		−	0.0238649i
$321$	−6161.46	+	10672.0i	−1.07134	+	1.85561i
$322$	−474.116	−	821.194i	−0.0820543	−	0.142122i
$323$	5567.80	−	3214.57i	0.959136	−	0.553757i
$324$	3496.34			0.599509
$325$		0			0
$326$	−2910.44			−0.494462
$327$	−11006.9	+	6354.84i	−1.86142	+	1.07469i
$328$	1550.78	+	2686.03i	0.261059	+	0.452168i
$329$	577.479	−	1000.22i	0.0967703	−	0.167611i
$330$			1331.95i			0.222187i
$331$	768.271	+	443.562i	0.127577	+	0.0736567i	0.562430	−	0.826845i	$-0.309866\pi$
$331$	768.271	+	443.562i	0.127577	+	0.0736567i	−0.434853	+	0.900501i	$0.643200\pi$
$332$	−76.7661	−	44.3209i	−0.0126900	−	0.00732659i
$333$			975.152i			0.160474i
$334$	1630.52	−	2824.14i	0.267120	−	0.462665i
$335$	−443.208	−	767.660i	−0.0722838	−	0.125199i
$336$	314.162	−	181.382i	0.0510088	−	0.0294499i
$337$	−6563.94			−1.06101			−0.530506	−	0.847681i	$-0.677998\pi$
$337$	−6563.94			−1.06101			−0.530506	+	0.847681i	$0.677998\pi$
$338$		0			0
$339$	−2092.67			−0.335275
$340$	−320.373	+	184.968i	−0.0511020	+	0.0295038i
$341$	−5060.47	−	8764.99i	−0.803636	−	1.39194i
$342$	1098.59	−	1902.81i	0.173699	−	0.300855i
$343$			2593.95i			0.408338i
$344$	517.097	+	298.546i	0.0810465	+	0.0467922i
$345$	1329.91	+	767.821i	0.207535	+	0.119821i
$346$		−	1920.48i		−	0.298398i
$347$	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
$349$	−8810.54	+	5086.77i	−1.35134	+	0.780196i	−0.988437	−	0.151631i	$-0.951548\pi$
$349$	−8810.54	+	5086.77i	−1.35134	+	0.780196i	−0.362903	+	0.931827i	$0.618214\pi$
$350$	−931.141			−0.142204
$351$		0			0
$352$	1702.17			0.257744
$353$	798.137	−	460.805i	0.120342	−	0.0694792i	−0.438621	−	0.898672i	$-0.644533\pi$
$353$	798.137	−	460.805i	0.120342	−	0.0694792i	0.558962	+	0.829193i	$0.311200\pi$
$354$	−2811.37	−	4869.43i	−0.422098	−	0.731095i
$355$	313.719	−	543.378i	0.0469028	−	0.0812381i
$356$			2661.73i			0.396269i
$357$	−850.737	−	491.173i	−0.126123	−	0.0728170i
$358$	3637.86	+	2100.32i	0.537058	+	0.310071i
$359$			2056.77i			0.302374i	0.988505	+	0.151187i	$0.0483096\pi$
$359$			2056.77i			0.302374i	−0.988505	+	0.151187i	$0.951690\pi$
$360$	−63.2133	+	109.489i	−0.00925454	+	0.0160293i
$361$	7579.63	+	13128.3i	1.10506	+	1.91403i
$362$	5864.37	−	3385.80i	0.851449	−	0.491585i
$363$	−8789.21			−1.27084
$364$		0			0
$365$	227.813			0.0326693
$366$	−4874.53	+	2814.31i	−0.696164	+	0.401930i
$367$	−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
$369$		−	2870.34i		−	0.404944i
$370$	486.960	+	281.146i	0.0684212	+	0.0395030i
$371$	−336.049	−	194.018i	−0.0470264	−	0.0271507i
$372$		−	4464.06i		−	0.622180i
$373$	−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
$375$	2661.27	−	1536.49i	0.366473	−	0.211583i
$376$	2390.31			0.327848
$377$		0			0
$378$	888.606			0.120913
$379$	10599.2	−	6119.48i	1.43653	−	0.829384i	0.438928	−	0.898522i	$-0.355358\pi$
$379$	10599.2	−	6119.48i	1.43653	−	0.829384i	0.997607	+	0.0691388i	$0.0220251\pi$
$380$	−633.470	−	1097.20i	−0.0855166	−	0.148119i
$381$	2925.89	−	5067.78i	0.393432	−	0.681445i
$382$		−	7456.14i		−	0.998664i
$383$	6265.43	+	3617.35i	0.835897	+	0.482605i	0.855867	−	0.517195i	$-0.173024\pi$
$383$	6265.43	+	3617.35i	0.835897	+	0.482605i	−0.0199705	+	0.999801i	$0.506357\pi$
$384$	650.194	+	375.389i	0.0864064	+	0.0498867i
$385$			438.892i			0.0580988i
$386$	−2573.20	+	4456.91i	−0.339307	+	0.587697i
$387$	−276.290	−	478.549i	−0.0362910	−	0.0628579i
$388$	−4344.82	+	2508.48i	−0.568491	+	0.328219i
$389$	11781.1			1.53554			0.767768	−	0.640728i	$-0.221367\pi$
$389$	11781.1			1.53554			0.767768	+	0.640728i	$0.221367\pi$
$390$		0			0
$391$	−5314.29			−0.687354
$392$	−2272.85	+	1312.23i	−0.292848	+	0.169076i
$393$	4929.56	+	8538.25i	0.632731	+	1.09592i
$394$	−1941.54	+	3362.85i	−0.248257	+	0.429994i
$395$		−	1933.99i		−	0.246353i
$396$	−1364.23	−	787.638i	−0.173119	−	0.0999502i
$397$	−10153.3	−	5862.01i	−1.28358	−	0.741072i	−0.306075	−	0.952007i	$-0.599016\pi$
$397$	−10153.3	−	5862.01i	−1.28358	−	0.741072i	−0.977500	+	0.210935i	$0.932349\pi$
$398$			4581.38i			0.576995i
$399$	1682.15	−	2913.57i	0.211060	−	0.365566i
$400$	−963.550	−	1668.92i	−0.120444	−	0.208615i
$401$	1479.16	−	853.995i	0.184204	−	0.106350i	−0.405062	−	0.914289i	$-0.632750\pi$
$401$	1479.16	−	853.995i	0.184204	−	0.106350i	0.589266	+	0.807939i	$0.299417\pi$
$402$	4871.53			0.604403
$403$		0			0
$404$	−7028.83			−0.865588
$405$	−1615.80	+	932.884i	−0.198247	+	0.114458i
$406$	324.249	+	561.615i	0.0396359	+	0.0686514i
$407$	−3503.08	+	6067.52i	−0.426637	+	0.738958i
$408$		−	2033.08i		−	0.246697i
$409$	−8319.96	−	4803.53i	−1.00586	−	0.580732i	−0.0958812	−	0.995393i	$-0.530567\pi$
$409$	−8319.96	−	4803.53i	−1.00586	−	0.580732i	−0.909976	+	0.414661i	$0.863900\pi$
$410$	−1433.36	−	827.550i	−0.172655	−	0.0996824i
$411$			9259.11i			1.11124i
$412$	−172.554	+	298.872i	−0.0206338	+	0.0357388i
$413$	−926.375	−	1604.53i	−0.110373	−	0.191171i
$414$	−1572.85	+	908.088i	−0.186719	+	0.107802i
$415$	47.3024			0.00559514
$416$		0			0
$417$	10112.5			1.18755
$418$	13671.1	−	7893.04i	1.59971	−	0.923591i
$419$	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
$421$		−	10957.4i		−	1.26848i	−0.773137	−	0.634239i	$-0.781314\pi$
$421$		−	10957.4i		−	1.26848i	0.773137	−	0.634239i	$-0.218686\pi$
$422$	−2035.55	−	1175.23i	−0.234808	−	0.135567i
$423$	−1915.75	−	1106.06i	−0.220206	−	0.127136i
$424$		−	803.084i		−	0.0919840i
$425$	−2609.25	+	4519.36i	−0.297805	+	0.515814i
$426$	1724.13	+	2986.28i	0.196090	+	0.339637i
$427$	−1606.21	+	927.345i	−0.182037	+	0.105099i
$428$	−8403.73			−0.949087
$429$		0			0
$430$	−318.629			−0.0357341
$431$	8238.61	−	4756.56i	0.920742	−	0.531591i	0.0368705	−	0.999320i	$-0.488261\pi$
$431$	8238.61	−	4756.56i	0.920742	−	0.531591i	0.883872	+	0.467729i	$0.154928\pi$
$432$	919.534	+	1592.68i	0.102410	+	0.177379i
$433$	−3635.66	+	6297.16i	−0.403508	+	0.698896i	−0.994147	−	0.108040i	$-0.965543\pi$
$433$	−3635.66	+	6297.16i	−0.403508	+	0.698896i	0.590639	+	0.806936i	$0.298876\pi$
$434$		−	1470.96i		−	0.162691i
$435$	−909.523	−	525.114i	−0.100249	−	0.0578788i
$436$	−7506.26	−	4333.74i	−0.824506	−	0.476029i
$437$		−	18200.2i		−	1.99229i
$438$	−626.003	+	1084.27i	−0.0682913	+	0.118284i
$439$	−4807.62	−	8327.05i	−0.522677	−	0.905304i	−0.999652	−	0.0263867i	$-0.991600\pi$
$439$	−4807.62	−	8327.05i	−0.522677	−	0.905304i	0.476974	−	0.878917i	$-0.341733\pi$
$440$	−786.643	+	454.168i	−0.0852312	+	0.0492082i
$441$	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	$0.582557\pi$
$444$	−2676.21	+	1545.11i	−0.286053	+	0.165153i
$445$	−710.197	−	1230.10i	−0.0756552	−	0.131039i
$446$	4350.88	−	7535.94i	0.461928	−	0.800083i
$447$		−	16010.7i		−	1.69414i
$448$	214.246	+	123.695i	0.0225941	+	0.0130447i
$449$	5948.49	+	3434.36i	0.625226	+	0.360974i	0.778901	−	0.627147i	$-0.215778\pi$
$449$	5948.49	+	3434.36i	0.625226	+	0.360974i	−0.153675	+	0.988121i	$0.549111\pi$
$450$			1783.44i			0.186827i
$451$	10311.3	−	17859.7i	1.07658	−	1.86470i
$452$	−713.558	−	1235.92i	−0.0742543	−	0.128612i
$453$	−2460.15	+	1420.37i	−0.255161	+	0.147317i
$454$	−7291.70			−0.753781
$455$		0			0
$456$	6962.79			0.715050
$457$	7275.89	−	4200.74i	0.744752	−	0.429983i	−0.0790424	−	0.996871i	$-0.525186\pi$
$457$	7275.89	−	4200.74i	0.744752	−	0.429983i	0.823795	+	0.566888i	$0.191853\pi$
$458$	3239.15	+	5610.38i	0.330471	+	0.572393i
$459$	2490.06	−	4312.91i	0.253216	−	0.438582i
$460$			1047.24i			0.106148i
$461$	13796.2	+	7965.23i	1.39382	+	0.804723i	0.993736	−	0.111754i	$-0.0356469\pi$
$461$	13796.2	+	7965.23i	1.39382	+	0.804723i	0.400086	+	0.916478i	$0.368980\pi$
$462$	−2088.89	−	1206.02i	−0.210355	−	0.121449i
$463$		−	11572.2i		−	1.16156i	−0.814060	−	0.580781i	$-0.802747\pi$
$463$		−	11572.2i		−	1.16156i	0.814060	−	0.580781i	$-0.197253\pi$
$464$	−671.068	+	1162.32i	−0.0671413	+	0.116292i
$465$	1191.09	+	2063.03i	0.118786	+	0.205743i
$466$	−3780.51	+	2182.68i	−0.375813	+	0.216976i
$467$	10862.4			1.07634			0.538169	−	0.842837i	$-0.319116\pi$
$467$	10862.4			1.07634			0.538169	+	0.842837i	$0.319116\pi$
$468$		0			0
$469$	1605.22			0.158043
$470$	−1104.66	+	637.777i	−0.108413	+	0.0625925i
$471$	−691.464	−	1197.65i	−0.0676454	−	0.117165i
$472$	1917.24	−	3320.75i	0.186966	−	0.323835i
$473$		−	3970.12i		−	0.385933i
$474$	9204.75	+	5314.36i	0.891958	+	0.514972i
$475$	−15477.7	−	8936.05i	−1.49509	−	0.863188i
$476$		−	669.920i		−	0.0645078i
$477$	−371.608	+	643.644i	−0.0356704	+	0.0617829i
$478$	−58.8048	−	101.853i	−0.00562692	−	0.00974612i
$479$	−1806.28	+	1042.86i	−0.172299	+	0.0994769i	−0.583669	−	0.811991i	$-0.698384\pi$
$479$	−1806.28	+	1042.86i	−0.172299	+	0.0994769i	0.411370	+	0.911468i	$0.365050\pi$
$480$	−400.642			−0.0380973
$481$		0			0
$482$	−404.522			−0.0382272
$483$	−2408.34	+	1390.46i	−0.226880	+	0.130989i
$484$	−2996.94	−	5190.85i	−0.281456	−	0.487495i
$485$	1338.61	−	2318.55i	0.125326	−	0.217072i
$486$		−	4046.96i		−	0.377723i
$487$	−10244.7	−	5914.78i	−0.953247	−	0.550358i	−0.0591591	−	0.998249i	$-0.518842\pi$
$487$	−10244.7	−	5914.78i	−0.953247	−	0.550358i	−0.894088	+	0.447891i	$0.852175\pi$
$488$	−3324.23	−	1919.24i	−0.308362	−	0.178033i
$489$			8535.54i			0.789347i
$490$	700.253	−	1212.87i	0.0645596	−	0.111821i
$491$	1350.02	+	2338.30i	0.124085	+	0.214921i	0.921375	−	0.388675i	$-0.127067\pi$
$491$	1350.02	+	2338.30i	0.124085	+	0.214921i	−0.797290	+	0.603596i	$0.793734\pi$
$492$	7877.39	−	4548.02i	0.721830	−	0.416749i
$493$	3634.45			0.332023
$494$		0			0
$495$	840.622			0.0763296
$496$	2636.45	−	1522.15i	0.238669	−	0.137796i
$497$	568.118	+	984.009i	0.0512748	+	0.0888105i
$498$	−129.981	+	225.134i	−0.0116960	+	0.0202581i
$499$		−	3013.67i		−	0.270361i	−0.990821	−	0.135181i	$-0.956839\pi$
$499$		−	3013.67i		−	0.270361i	0.990821	−	0.135181i	$-0.0431615\pi$
$500$	1814.88	+	1047.82i	0.162327	+	0.0937198i
$501$	−8282.44	−	4781.87i	−0.738587	−	0.426423i
$502$			227.984i			0.0202698i
$503$	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
$505$	3248.32	−	1875.42i	0.286234	−	0.165257i
$506$	−13048.7			−1.14641
$507$		0			0
$508$	3990.67			0.348538
$509$	−1412.20	+	815.332i	−0.122975	+	0.0709999i	−0.560226	−	0.828340i	$-0.689286\pi$
$509$	−1412.20	+	815.332i	−0.122975	+	0.0709999i	0.437250	+	0.899340i	$0.355952\pi$
$510$	542.460	+	939.569i	0.0470991	+	0.0815781i
$511$	−206.274	+	357.278i	−0.0178572	+	0.0309296i
$512$			512.000i			0.0441942i
$513$	14770.7	+	8527.85i	1.27123	+	0.733945i
$514$	7334.76	+	4234.73i	0.629421	+	0.363397i
$515$		−	184.162i		−	0.0157575i
$516$	875.555	−	1516.51i	0.0746980	−	0.129381i
$517$	−7946.71	−	13764.1i	−0.676008	−	1.17088i
$518$	−881.840	+	509.131i	−0.0747989	+	0.0431852i
$519$	−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	$0.381447\pi$
$522$	1075.68	−	621.042i	0.0901936	−	0.0520733i
$523$	−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
$525$			2730.78i			0.227012i
$526$	−395.741	−	228.481i	−0.0328045	−	0.0189397i
$527$	−7139.38	−	4121.92i	−0.590126	−	0.340709i
$528$		−	4992.00i		−	0.411456i
$529$	−1438.58	+	2491.69i	−0.118236	+	0.204790i
$530$	214.277	+	371.139i	0.0175615	+	0.0304174i
$531$	−3073.20	+	1774.31i	−0.251159	+	0.145007i
$532$	2294.31			0.186976
$533$		0			0
$534$	7806.15			0.632594
$535$	3883.71	−	2242.26i	0.313846	−	0.181199i
$536$	1661.09	+	2877.10i	0.133859	+	0.231850i
$537$	6159.67	−	10668.9i	0.494989	−	0.857347i
$538$			2438.61i			0.195420i
$539$	15112.4	+	8725.16i	1.20768	+	0.697253i
$540$	−849.910	−	490.696i	−0.0677302	−	0.0391040i
$541$			5004.07i			0.397674i	0.980033	+	0.198837i	$0.0637165\pi$
$541$			5004.07i			0.397674i	−0.980033	+	0.198837i	$0.936284\pi$
$542$	−5891.13	+	10203.7i	−0.466874	+	0.808650i
$543$	−9929.63	−	17198.6i	−0.784754	−	1.35923i
$544$	1200.72	−	693.237i	0.0946333	−	0.0546365i
$545$	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	$0.639479\pi$
$548$	−5468.37	+	3157.16i	−0.426272	+	0.246108i
$549$	1776.17	+	3076.42i	0.138078	+	0.239159i
$550$	−6406.73	+	11096.8i	−0.496698	+	0.860307i
$551$			12447.1i			0.962368i
$552$	−4984.33	−	2877.70i	−0.384324	−	0.221890i
$553$	3033.06	+	1751.14i	0.233235	+	0.134658i
$554$		−	12278.8i		−	0.941653i
$555$	824.526	−	1428.12i	0.0630616	−	0.109226i
$556$	3448.14	+	5972.35i	0.263010	+	0.455547i
$557$	19991.2	−	11541.9i	1.52074	−	0.878001i	0.521042	−	0.853531i	$-0.325543\pi$
$557$	19991.2	−	11541.9i	1.52074	−	0.878001i	0.999701	−	0.0244704i	$-0.00778994\pi$
$558$	−2817.36			−0.213743
$559$		0			0
$560$	−132.016			−0.00996193
$561$	−11707.0	+	6759.06i	−0.881054	+	0.508677i
$562$	1852.24	+	3208.17i	0.139025	+	0.240798i
$563$	−7747.97	+	13419.9i	−0.579996	+	1.00458i	0.415483	+	0.909601i	$0.363613\pi$
$563$	−7747.97	+	13419.9i	−0.579996	+	1.00458i	−0.995479	+	0.0949820i	$0.969721\pi$
$564$		−	7010.14i		−	0.523369i
$565$	659.529	+	380.779i	0.0491090	+	0.0283531i
$566$	298.414	+	172.290i	0.0221613	+	0.0127948i
$567$		−	3378.74i		−	0.250253i
$568$	−1175.78	+	2036.52i	−0.0868570	+	0.150441i
$569$	9082.73	+	15731.7i	0.669188	+	1.15907i	0.978132	+	0.207987i	$0.0666911\pi$
$569$	9082.73	+	15731.7i	0.669188	+	1.15907i	−0.308944	+	0.951080i	$0.599976\pi$
$570$	−3217.80	+	1857.80i	−0.236454	+	0.136517i
$571$	8289.75			0.607557			0.303779	−	0.952743i	$-0.401752\pi$
$571$	8289.75			0.607557			0.303779	+	0.952743i	$0.401752\pi$
$572$		0			0
$573$	−21866.9			−1.59424
$574$	2595.68	−	1498.62i	0.188749	−	0.108974i
$575$	7386.49	+	12793.8i	0.535718	+	0.927891i
$576$	236.916	−	410.350i	0.0171380	−	0.0296839i
$577$		−	5336.46i		−	0.385026i	−0.981294	−	0.192513i	$-0.938336\pi$
$577$		−	5336.46i		−	0.385026i	0.981294	−	0.192513i	$-0.0616637\pi$
$578$	5258.06	+	3035.75i	0.378385	+	0.218461i
$579$	13070.9	+	7546.50i	0.938185	+	0.541661i
$580$		−	716.211i		−	0.0512742i
$581$	−42.8302	+	74.1841i	−0.00305834	+	0.00529720i
$582$	7356.70	+	12742.2i	0.523960	+	0.907526i
$583$	−4624.39	+	2669.89i	−0.328512	+	0.189667i
$584$	−853.816			−0.0604986
$585$		0			0
$586$	11450.0			0.807159
$587$	−5956.28	+	3438.86i	−0.418811	+	0.241800i	−0.694568	−	0.719427i	$-0.744405\pi$
$587$	−5956.28	+	3438.86i	−0.418811	+	0.241800i	0.275758	+	0.961227i	$0.411071\pi$
$588$	3848.42	+	6665.67i	0.269909	+	0.467496i
$589$	14116.6	−	24450.6i	0.987545	−	1.71048i
$590$			2046.21i			0.142782i
$591$	9862.32	+	5694.01i	0.686432	+	0.396312i
$592$	−1825.07	−	1053.70i	−0.126706	−	0.0731536i
$593$			8358.37i			0.578814i	0.957206	+	0.289407i	$0.0934582\pi$
$593$			8358.37i			0.578814i	−0.957206	+	0.289407i	$0.906542\pi$
$594$	6114.07	−	10589.9i	0.422329	−	0.731495i
$595$	178.746	+	309.598i	0.0123158	+	0.0213315i
$596$	9455.84	−	5459.33i	0.649876	−	0.375206i
$597$	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	$0.669631\pi$
$600$	−4894.48	+	2825.83i	−0.333027	+	0.192273i
$601$	−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
$603$		−	3074.52i		−	0.207636i
$604$	−1677.72	−	968.631i	−0.113022	−	0.0652534i
$605$	2770.02	+	1599.27i	0.186144	+	0.107470i
$606$			20613.7i			1.38180i
$607$	−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
$609$	1647.06	−	950.933i	0.109594	−	0.0632738i
$610$	2048.35			0.135960
$611$		0			0
$612$	−1283.12			−0.0847498
$613$	10462.4	−	6040.47i	0.689352	−	0.397997i	−0.114018	−	0.993479i	$-0.536372\pi$
$613$	10462.4	−	6040.47i	0.689352	−	0.397997i	0.803369	+	0.595481i	$0.203039\pi$
$614$	−2115.94	−	3664.91i	−0.139075	−	0.240885i
$615$	−2426.98	+	4203.65i	−0.159131	+	0.275622i
$616$		−	1644.92i		−	0.107590i
$617$	−18276.9	−	10552.1i	−1.19254	−	0.688514i	−0.233660	−	0.972318i	$-0.575070\pi$
$617$	−18276.9	−	10552.1i	−1.19254	−	0.688514i	−0.958882	+	0.283804i	$0.908403\pi$
$618$	876.511	+	506.054i	0.0570525	+	0.0329393i
$619$		−	12516.1i		−	0.812706i	−0.913716	−	0.406353i	$-0.866800\pi$
$619$		−	12516.1i		−	0.812706i	0.913716	−	0.406353i	$-0.133200\pi$
$620$	−812.274	+	1406.90i	−0.0526157	+	0.0911330i
$621$	−7049.07	−	12209.3i	−0.455506	−	0.788960i
$622$	−6776.03	+	3912.14i	−0.436807	+	0.252191i
$623$	2572.21			0.165415
$624$		0			0
$625$	13937.2			0.891978
$626$	6497.27	−	3751.20i	0.414829	−	0.239502i
$627$	−23148.1	−	40093.8i	−1.47440	−	2.55373i
$628$	471.550	−	816.748i	0.0299632	−	0.0518978i
$629$			5706.76i			0.361754i
$630$	105.806	+	61.0871i	0.00669113	+	0.00386313i
$631$	8720.58	+	5034.83i	0.550176	+	0.317644i	0.749193	−	0.662352i	$-0.230442\pi$
$631$	8720.58	+	5034.83i	0.550176	+	0.317644i	−0.199017	+	0.979996i	$0.563775\pi$
$632$			7248.35i			0.456209i
$633$	−3446.62	+	5969.72i	−0.216415	+	0.374842i
$634$	8277.14	+	14336.4i	0.518497	+	0.898064i
$635$	−1844.25	+	1064.78i	−0.115255	+	0.0665425i
$636$	−2355.23			−0.146841
$637$		0			0
$638$	8924.00			0.553769
$639$	1884.70	−	1088.13i	0.116678	−	0.0673643i
$640$	−136.611	−	236.616i	−0.00843751	−	0.0146142i
$641$	−1694.43	+	2934.84i	−0.104409	+	0.180842i	−0.913497	−	0.406846i	$-0.866628\pi$
$641$	−1694.43	+	2934.84i	−0.104409	+	0.180842i	0.809088	+	0.587688i	$0.199962\pi$
$642$			24645.9i			1.51510i
$643$	−21333.1	−	12316.7i	−1.30839	−	0.755400i	−0.326563	−	0.945175i	$-0.605891\pi$
$643$	−21333.1	−	12316.7i	−1.30839	−	0.755400i	−0.981827	+	0.189776i	$0.939224\pi$
$644$	−1642.39	−	948.233i	−0.100496	−	0.0580211i
$645$			934.453i			0.0570451i
$646$	6429.14	−	11135.6i	0.391565	−	0.678211i
$647$	954.062	+	1652.48i	0.0579723	+	0.100411i	0.893555	−	0.448954i	$-0.148203\pi$
$647$	954.062	+	1652.48i	0.0579723	+	0.100411i	−0.835583	+	0.549365i	$0.814870\pi$
$648$	6055.83	−	3496.34i	0.367123	−	0.211958i
$649$	−25495.8			−1.54206
$650$		0			0
$651$	−4313.91			−0.259717
$652$	−5041.03	+	2910.44i	−0.302795	+	0.174819i
$653$	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
$655$		−	3587.90i		−	0.214032i
$656$	5372.06	+	3101.56i	0.319731	+	0.184597i
$657$	684.304	+	395.083i	0.0406351	+	0.0234607i
$658$		−	2309.91i		−	0.136854i
$659$	−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
$661$	−24805.6	+	14321.5i	−1.45964	+	0.842726i	−0.998993	−	0.0448562i	$-0.985717\pi$
$661$	−24805.6	+	14321.5i	−1.45964	+	0.842726i	−0.460650	+	0.887582i	$0.652384\pi$
$662$	1774.25			0.104166
$663$		0			0
$664$	−177.284			−0.0103614
$665$	−1060.30	+	612.163i	−0.0618294	+	0.0356972i
$666$	975.152	+	1689.01i	0.0567363	+	0.0982701i
$667$	5144.35	−	8910.28i	0.298636	−	0.517252i
$668$		−	6522.07i		−	0.377764i
$669$	−22100.9	−	12759.9i	−1.27723	−	0.737411i
$670$	−1535.32	−	886.417i	−0.0885292	−	0.0511123i
$671$			25522.5i			1.46838i
$672$	362.763	−	628.324i	0.0208242	−	0.0360687i
$673$	−9186.40	−	15911.3i	−0.526166	−	0.911346i	−0.999535	−	0.0304820i	$-0.990296\pi$
$673$	−9186.40	−	15911.3i	−0.526166	−	0.911346i	0.473369	−	0.880864i	$-0.343038\pi$
$674$	−11369.1	+	6563.94i	−0.649734	+	0.375124i
$675$	−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	$0.618722\pi$
$678$	−3624.61	+	2092.67i	−0.205313	+	0.118538i
$679$	2424.11	+	4198.68i	0.137008	+	0.237306i
$680$	−369.935	+	640.747i	−0.0208623	+	0.0361346i
$681$			21384.6i			1.20332i
$682$	−17530.0	−	10120.9i	−0.984249	−	0.568256i
$683$	10586.9	+	6112.37i	0.593116	+	0.342436i	0.766329	−	0.642449i	$-0.222081\pi$
$683$	10586.9	+	6112.37i	0.593116	+	0.342436i	−0.173213	+	0.984884i	$0.555415\pi$
$684$		−	4394.36i		−	0.245647i
$685$	1684.77	−	2918.11i	0.0939736	−	0.162767i
$686$	2593.95	+	4492.85i	0.144369	+	0.250055i
$687$	16453.7	−	9499.56i	0.913754	−	0.527556i
$688$	1194.18			0.0661742
$689$		0			0
$690$	3071.29			0.169452
$691$	−6636.35	+	3831.50i	−0.365352	+	0.210936i	−0.671426	−	0.741072i	$-0.734318\pi$
$691$	−6636.35	+	3831.50i	−0.365352	+	0.210936i	0.306074	+	0.952008i	$0.400985\pi$
$692$	−1920.48	−	3326.37i	−0.105500	−	0.182731i
$693$	−761.146	+	1318.34i	−0.0417223	+	0.0722651i
$694$		−	17308.1i		−	0.946694i
$695$	−3187.06	−	1840.05i	−0.173945	−	0.100427i
$696$	3408.78	+	1968.06i	0.185646	+	0.107183i
$697$		−	16797.8i		−	0.912856i
$698$	−10173.5	+	17621.1i	−0.551682	+	0.955542i
$699$	6401.21	+	11087.2i	0.346375	+	0.599939i
$700$	−1612.78	+	931.141i	−0.0870821	+	0.0502769i
$701$	15215.8			0.819818			0.409909	−	0.912126i	$-0.365560\pi$
$701$	15215.8			0.819818			0.409909	+	0.912126i	$0.365560\pi$
$702$		0			0
$703$	−19544.3			−1.04854
$704$	2948.24	−	1702.17i	0.157835	−	0.0911263i
$705$	1870.43	+	3239.68i	0.0999212	+	0.173069i
$706$	921.610	−	1596.27i	0.0491292	−	0.0850943i
$707$			6792.42i			0.361323i
$708$	−9738.87	−	5622.74i	−0.516962	−	0.298468i
$709$	13346.2	+	7705.43i	0.706949	+	0.408157i	0.809930	−	0.586526i	$-0.199505\pi$
$709$	13346.2	+	7705.43i	0.706949	+	0.408157i	−0.102981	+	0.994683i	$0.532838\pi$
$710$		−	1254.88i		−	0.0663306i
$711$	3354.00	−	5809.30i	0.176913	−	0.306422i
$712$	2661.73	+	4610.26i	0.140102	+	0.242664i
$713$	−20210.8	+	11668.7i	−1.06157	+	0.612897i
$714$	−1964.69			−0.102979
$715$		0			0
$716$	8401.27			0.438506
$717$	−298.707	+	172.459i	−0.0155585	+	0.00898268i
$718$	2056.77	+	3562.44i	0.106905	+	0.185166i
$719$	577.894	−	1000.94i	0.0299747	−	0.0519177i	−0.850649	−	0.525734i	$-0.823791\pi$
$719$	577.894	−	1000.94i	0.0299747	−	0.0519177i	0.880624	+	0.473816i	$0.157124\pi$
$720$			252.853i			0.0130879i
$721$	288.819	+	166.750i	0.0149184	+	0.00861317i
$722$	26256.6	+	15159.3i	1.35342	+	0.781398i
$723$			1186.36i			0.0610249i
$724$	6771.60	−	11728.7i	0.347603	−	0.602066i
$725$	−5051.62	−	8749.67i	−0.258776	−	0.448213i
$726$	−15223.4	+	8789.21i	−0.778226	+	0.449309i
$727$	−18048.8			−0.920759			−0.460379	−	0.887722i	$-0.652287\pi$
$727$	−18048.8			−0.920759			−0.460379	+	0.887722i	$0.652287\pi$
$728$		0			0
$729$	11731.6			0.596029
$730$	394.584	−	227.813i	0.0200058	−	0.0115503i
$731$	−1616.90	−	2800.55i	−0.0818101	−	0.141699i
$732$	−5628.63	+	9749.07i	−0.284208	+	0.492262i
$733$			7855.68i			0.395847i	0.980217	+	0.197924i	$0.0634198\pi$
$733$			7855.68i			0.395847i	−0.980217	+	0.197924i	$0.936580\pi$
$734$	−3830.96	−	2211.81i	−0.192648	−	0.111225i
$735$	−3557.03	−	2053.65i	−0.178508	−	0.103061i
$736$		−	3924.95i		−	0.196570i
$737$	11044.8	−	19130.1i	0.552020	−	0.956127i
$738$	−2870.34	−	4971.58i	−0.143169	−	0.247976i
$739$	262.234	−	151.401i	0.0130533	−	0.00753635i	−0.493459	−	0.869769i	$-0.664268\pi$
$739$	262.234	−	151.401i	0.0130533	−	0.00753635i	0.506512	+	0.862233i	$0.330934\pi$
$740$	1124.59			0.0558656
$741$		0			0
$742$	−776.072			−0.0383969
$743$	−14895.6	+	8599.96i	−0.735485	+	0.424633i	−0.820426	−	0.571753i	$-0.806263\pi$
$743$	−14895.6	+	8599.96i	−0.735485	+	0.424633i	0.0849402	+	0.996386i	$0.472930\pi$
$744$	−4464.06	−	7731.98i	−0.219974	−	0.381006i
$745$	−2913.29	+	5045.97i	−0.143268	+	0.248148i
$746$			21092.2i			1.03518i
$747$	142.087	+	82.0339i	0.00695942	+	0.00401802i
$748$	−7983.71	−	4609.40i	−0.390258	−	0.225316i
$749$			8121.07i			0.396178i
$750$	3072.97	−	5322.54i	0.149612	−	0.259136i
$751$	6499.83	+	11258.0i	0.315822	+	0.547019i	0.979612	−	0.200900i	$-0.0643865\pi$
$751$	6499.83	+	11258.0i	0.315822	+	0.547019i	−0.663790	+	0.747919i	$0.731053\pi$
$752$	4140.14	−	2390.31i	0.200765	−	0.115912i
$753$	668.616			0.0323582
$754$		0			0
$755$	1033.79			0.0498325
$756$	1539.11	−	888.606i	0.0740435	−	0.0427490i
$757$	−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
$759$			38268.2i			1.83010i
$760$	−2194.40	−	1266.94i	−0.104736	−	0.0604694i
$761$	−23298.1	−	13451.1i	−1.10979	−	0.640740i	−0.171019	−	0.985268i	$-0.554706\pi$
$761$	−23298.1	−	13451.1i	−1.10979	−	0.640740i	−0.938776	+	0.344527i	$0.888039\pi$
$762$		−	11703.5i		−	0.556397i
$763$	−4187.97	+	7253.78i	−0.198709	+	0.344174i
$764$	−7456.14	−	12914.4i	−0.353081	−	0.611554i
$765$	592.981	−	342.358i	0.0280252	−	0.0161804i
$766$	14469.4			0.682507
$767$		0			0
$768$	1501.56			0.0705505
$769$	−1791.19	+	1034.14i	−0.0839947	+	0.0484943i	−0.541409	−	0.840759i	$-0.682109\pi$
$769$	−1791.19	+	1034.14i	−0.0839947	+	0.0484943i	0.457414	+	0.889254i	$0.348776\pi$
$770$	438.892	+	760.184i	0.0205410	+	0.0355781i
$771$	12419.3	−	21510.9i	0.580118	−	1.00479i
$772$			10292.8i			0.479852i
$773$	−7265.71	−	4194.86i	−0.338072	−	0.195186i	0.321347	−	0.946961i	$-0.395864\pi$
$773$	−7265.71	−	4194.86i	−0.338072	−	0.195186i	−0.659419	+	0.751776i	$0.729198\pi$
$774$	−957.097	−	552.580i	−0.0444472	−	0.0256616i
$775$			22916.7i			1.06218i
$776$	−5016.96	+	8689.63i	−0.232086	+	0.401984i
$777$	1493.14	+	2586.20i	0.0689398	+	0.119407i
$778$	20405.4	−	11781.1i	0.940320	−	0.542894i
$779$	57528.3			2.64591
$780$		0			0
$781$	15635.8			0.716379
$782$	−9204.62	+	5314.29i	−0.420917	+	0.243016i
$783$	4820.86	+	8349.98i	0.220030	+	0.381103i
$784$	−2624.47	+	4545.71i	−0.119555	+	0.207075i
$785$			503.271i			0.0228822i
$786$	17076.5	+	9859.12i	0.774934	+	0.447409i
$787$	18583.5	+	10729.2i	0.841714	+	0.485964i	0.857847	−	0.513906i	$-0.171802\pi$
$787$	18583.5	+	10729.2i	0.841714	+	0.485964i	−0.0161324	+	0.999870i	$0.505135\pi$
$788$			7766.16i			0.351089i
$789$	−670.074	+	1160.60i	−0.0302348	+	0.0523683i
$790$	−1933.99	−	3349.76i	−0.0870990	−	0.150860i
$791$	−1194.35	+	689.557i	−0.0536866	+	0.0309960i
$792$	−3150.55			−0.141351
$793$		0			0
$794$	−23448.0			−1.04803
$795$	1088.45	−	628.416i	0.0485576	−	0.0280348i
$796$	4581.38	+	7935.19i	0.203998	+	0.353336i
$797$	−3024.86	+	5239.21i	−0.134437	+	0.232851i	−0.925382	−	0.379036i	$-0.876256\pi$
$797$	−3024.86	+	5239.21i	−0.134437	+	0.232851i	0.790945	+	0.611887i	$0.209589\pi$
$798$		−	6728.60i		−	0.298484i
$799$	−11211.3	−	6472.86i	−0.496406	−	0.286600i
$800$	−3337.83	−	1927.10i	−0.147513	−	0.0851666i
$801$		−	4926.62i		−	0.217320i
$802$	1707.99	−	2958.32i	0.0752010	−	0.130252i
$803$	2838.55	+	4916.52i	0.124745	+	0.216065i
$804$	8437.74	−	4871.53i	0.370120	−	0.213689i
$805$	1012.02			0.0443094
$806$		0			0
$807$	7151.78			0.311964
$808$	−12174.3	+	7028.83i	−0.530062	+	0.306032i
$809$	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
$811$		−	2210.77i		−	0.0957221i	−0.998854	−	0.0478611i	$-0.984760\pi$
$811$		−	2210.77i		−	0.0957221i	0.998854	−	0.0478611i	$-0.0152405\pi$
$812$	1123.23	+	648.497i	0.0485439	+	0.0280268i
$813$	29924.8	+	17277.1i	1.29091	+	0.745307i
$814$			14012.3i			0.603356i
$815$	1553.11	−	2690.07i	0.0667524	−	0.115619i
$816$	−2033.08	−	3521.39i	−0.0872205	−	0.151070i
$817$	9591.21	−	5537.49i	0.410715	−	0.237126i
$818$	−19214.1			−0.821279
$819$		0			0
$820$	−3310.20			−0.140972
$821$	−21999.6	+	12701.5i	−0.935189	+	0.539932i	−0.888449	−	0.458976i	$-0.848217\pi$
$821$	−21999.6	+	12701.5i	−0.935189	+	0.539932i	−0.0467399	+	0.998907i	$0.514883\pi$
$822$	9259.11	+	16037.3i	0.392881	+	0.680491i
$823$	−21015.5	+	36399.8i	−0.890100	+	1.54170i	−0.0503464	+	0.998732i	$0.516033\pi$
$823$	−21015.5	+	36399.8i	−0.890100	+	1.54170i	−0.839754	+	0.542967i	$0.817301\pi$
$824$			690.215i			0.0291806i
$825$	32543.9	+	18789.2i	1.37337	+	0.792917i
$826$	−3209.06	−	1852.75i	−0.135178	−	0.0780453i
$827$		−	27713.0i		−	1.16527i	−0.812735	−	0.582633i	$-0.802022\pi$
$827$		−	27713.0i		−	1.16527i	0.812735	−	0.582633i	$-0.197978\pi$
$828$	−1816.18	+	3145.71i	−0.0762276	+	0.132030i
$829$	−11789.9	−	20420.6i	−0.493943	−	0.855534i	0.506033	−	0.862514i	$-0.331111\pi$
$829$	−11789.9	−	20420.6i	−0.493943	−	0.855534i	−0.999976	+	0.00698019i	$0.997778\pi$
$830$	81.9302	−	47.3024i	0.00342631	−	0.00197818i
$831$	−36010.4			−1.50323
$832$		0			0
$833$	14213.9			0.591214
$834$	17515.3	−	10112.5i	0.727225	−	0.419863i
$835$	1740.20	+	3014.12i	0.0721224	+	0.124920i
$836$	15786.1	−	27342.3i	0.653077	−	1.13116i
$837$		−	21869.9i		−	0.903146i
$838$	4691.56	+	2708.67i	0.193397	+	0.111658i
$839$	7489.42	+	4324.02i	0.308180	+	0.177928i	0.646112	−	0.763243i	$-0.276394\pi$
$839$	7489.42	+	4324.02i	0.308180	+	0.177928i	−0.337932	+	0.941171i	$0.609727\pi$
$840$			387.166i			0.0159030i
$841$	8676.27	−	15027.7i	0.355745	−	0.616169i
$842$	−10957.4	−	18978.7i	−0.448474	−	0.776781i
$843$	9408.70	−	5432.11i	0.384404	−	0.221936i
$844$	−4700.91			−0.191720
$845$		0			0
$846$	−4424.24			−0.179797
$847$	−5016.26	+	2896.14i	−0.203495	+	0.117488i
$848$	−803.084	−	1390.98i	−0.0325213	−	0.0563285i
$849$	505.279	−	875.169i	0.0204254	−	0.0353778i
$850$			10437.0i			0.421160i
$851$	13990.8	+	8077.59i	0.563570	+	0.325378i
$852$	5972.55	+	3448.25i	0.240160	+	0.138656i
$853$			23117.7i			0.927942i	0.885851	+	0.463971i	$0.153576\pi$
$853$			23117.7i			0.927942i	−0.885851	+	0.463971i	$0.846424\pi$
$854$	−1854.69	+	3212.42i	−0.0743164	+	0.128720i
$855$	1172.49	+	2030.82i	0.0468987	+	0.0812309i
$856$	−14555.7	+	8403.73i	−0.581195	+	0.335553i
$857$	−3246.65			−0.129409			−0.0647045	−	0.997904i	$-0.520610\pi$
$857$	−3246.65			−0.129409			−0.0647045	+	0.997904i	$0.520610\pi$
$858$		0			0
$859$	29452.5			1.16986			0.584928	−	0.811085i	$-0.301123\pi$
$859$	29452.5			1.16986			0.584928	+	0.811085i	$0.301123\pi$
$860$	−551.882	+	318.629i	−0.0218826	+	0.0126339i
$861$	−4395.04	−	7612.44i	−0.173964	−	0.301314i
$862$	9513.13	−	16477.2i	0.375891	−	0.651063i
$863$		−	15485.4i		−	0.610809i	−0.952223	−	0.305405i	$-0.901208\pi$
$863$		−	15485.4i		−	0.610809i	0.952223	−	0.305405i	$-0.0987917\pi$
$864$	3185.36	+	1839.07i	0.125426	+	0.0724148i
$865$	1775.07	+	1024.84i	0.0697736	+	0.0402838i
$866$			14542.7i			0.570646i
$867$	8903.02	−	15420.5i	0.348746	−	0.604045i
$868$	−1470.96	−	2547.77i	−0.0575201	−	0.0996278i
$869$	41738.1	−	24097.5i	1.62931	−	0.940681i
$870$	−2100.45			−0.0818530
$871$		0			0
$872$	−17335.0			−0.673206
$873$	8041.84	−	4642.96i	0.311770	−	0.180000i
$874$	−18200.2	−	31523.6i	−0.704382	−	1.22003i
$875$	1012.58	−	1753.83i	0.0391215	−	0.0677604i
$876$			2504.01i			0.0965784i
$877$	11866.3	+	6851.03i	0.456896	+	0.263789i	0.710738	−	0.703457i	$-0.248361\pi$
$877$	11866.3	+	6851.03i	0.456896	+	0.263789i	−0.253842	+	0.967246i	$0.581694\pi$
$878$	−16654.1	−	9615.25i	−0.640147	−	0.369589i
$879$		−	33579.8i		−	1.28853i
$880$	−908.337	+	1573.29i	−0.0347955	+	0.0602675i
$881$	8434.32	+	14608.7i	0.322542	+	0.558659i	0.981012	−	0.193948i	$-0.0621294\pi$
$881$	8434.32	+	14608.7i	0.322542	+	0.558659i	−0.658470	+	0.752607i	$0.728796\pi$
$882$	4206.84	−	2428.82i	0.160603	−	0.0927240i
$883$	−15162.4			−0.577867			−0.288934	−	0.957349i	$-0.593301\pi$
$883$	−15162.4			−0.577867			−0.288934	+	0.957349i	$0.593301\pi$
$884$		0			0
$885$	6000.98			0.227933
$886$	−8283.61	+	4782.54i	−0.314101	+	0.181346i
$887$	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
$889$		−	3856.44i		−	0.145490i
$890$	−2460.20	−	1420.39i	−0.0926584	−	0.0534963i
$891$	−40265.8	−	23247.5i	−1.51398	−	0.874096i
$892$		−	17403.5i		−	0.653265i
$893$	22168.0	−	38396.1i	0.830709	−	1.43883i
$894$	−16010.7	−	27731.4i	−0.598970	−	1.03745i
$895$	−3882.58	+	2241.61i	−0.145006	+	0.0837192i
$896$	494.779			0.0184480
$897$		0			0
$898$	13737.4			0.510495
$899$	13822.2	−	7980.22i	0.512786	−	0.296057i
$900$	1783.44	+	3089.01i	0.0660533	+	0.114408i
$901$	−2174.72	+	3766.72i	−0.0804110	+	0.139276i
$902$		−	41245.1i		−	1.52252i
$903$	−1465.50	−	846.105i	−0.0540074	−	0.0311812i
$904$	−2471.84	−	1427.12i	−0.0909425	−	0.0525057i
$905$			7227.12i			0.265456i
$906$	−2840.73	+	4920.29i	−0.104169	+	0.180426i
$907$	16095.0	+	27877.4i	0.589225	+	1.02057i	0.994334	+	0.106300i	$0.0339003\pi$
$907$	16095.0	+	27877.4i	0.589225	+	1.02057i	−0.405109	+	0.914268i	$0.632766\pi$
$908$	−12629.6	+	7291.70i	−0.461595	+	0.266502i
$909$	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	$0.420180\pi$
$912$	12059.9	−	6962.79i	0.437877	−	0.252808i
$913$	589.388	+	1020.85i	0.0213646	+	0.0370046i
$914$	8401.47	−	14551.8i	0.304044	−	0.526619i
$915$		−	6007.26i		−	0.217043i
$916$	11220.8	+	6478.31i	0.404743	+	0.233678i
$917$	5626.88	+	3248.68i	0.202635	+	0.116991i
$918$		−	9960.23i		−	0.358101i
$919$	−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
$921$	−10748.2	+	6205.47i	−0.384544	+	0.222016i
$922$	31860.9			1.13805
$923$		0			0
$924$	−4824.09			−0.171754
$925$	13738.6	−	7931.99i	0.488349	−	0.281948i
$926$	−11572.2	−	20043.6i	−0.410674	−	0.711309i
$927$	319.381	−	553.184i	0.0113159	−	0.0195997i
$928$			2684.27i			0.0949522i
$929$	−3713.08	−	2143.75i	−0.131133	−	0.0757094i	0.432999	−	0.901395i	$-0.357455\pi$
$929$	−3713.08	−	2143.75i	−0.131133	−	0.0757094i	−0.564131	+	0.825685i	$0.690789\pi$
$930$	4126.06	+	2382.18i	0.145483	+	0.0839944i
$931$			48679.1i			1.71363i
$932$	−4365.36	+	7561.03i	−0.153425	+	0.265740i
$933$	11473.3	+	19872.3i	0.402591	+	0.697308i
$934$	18814.2	−	10862.4i	0.659120	−	0.380543i
$935$	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	$0.579475\pi$
$938$	2780.32	−	1605.22i	0.0967813	−	0.0558767i
$939$	−11001.3	−	19054.7i	−0.382335	−	0.662223i
$940$	−1275.55	+	2209.33i	−0.0442596	+	0.0766598i
$941$		−	11317.1i		−	0.392058i	−0.980598	−	0.196029i	$-0.937195\pi$
$941$		−	11317.1i		−	0.392058i	0.980598	−	0.196029i	$-0.0628047\pi$
$942$	−2395.30	−	1382.93i	−0.0828484	−	0.0478325i
$943$	−41181.7	−	23776.3i	−1.42212	−	0.821062i
$944$		−	7668.95i		−	0.264410i
$945$	−474.191	+	821.323i	−0.0163232	+	0.0282726i
$946$	−3970.12	−	6876.45i	−0.136448	−	0.236335i
$947$	−35086.4	+	20257.2i	−1.20397	+	0.695110i	−0.961435	−	0.275034i	$-0.911311\pi$
$947$	−35086.4	+	20257.2i	−1.20397	+	0.695110i	−0.242531	+	0.970144i	$0.577978\pi$
$948$	21257.5			0.728281
$949$		0			0
$950$	−35744.2			−1.22073
$951$	42044.9	−	24274.6i	1.43365	−	0.827717i
$952$	−669.920	−	1160.34i	−0.0228070	−	0.0395028i
$953$	−24740.0	+	42850.9i	−0.840930	+	1.45653i	0.0481798	+	0.998839i	$0.484658\pi$
$953$	−24740.0	+	42850.9i	−0.840930	+	1.45653i	−0.889110	+	0.457694i	$0.848675\pi$
$954$			1486.43i			0.0504455i
$955$	6891.59	+	3978.86i	0.233515	+	0.134820i
$956$	−203.706	−	117.610i	−0.00689155	−	0.00397884i
$957$		−	26171.7i		−	0.884023i
$958$	−2085.72	+	3612.57i	−0.0703408	+	0.121834i
$959$	3050.97	+	5284.44i	0.102733	+	0.177939i
$960$	−693.932	+	400.642i	−0.0233298	+	0.0134694i
$961$	−6411.32			−0.215210
$962$		0			0
$963$	15554.5			0.520495
$964$	−700.654	+	404.522i	−0.0234093	+	0.0135153i
$965$	−2746.30	−	4756.73i	−0.0916130	−	0.158678i
$966$	−2780.91	+	4816.68i	−0.0926235	+	0.160429i
$967$		−	46779.9i		−	1.55568i	−0.628465	−	0.777838i	$-0.716316\pi$
$967$		−	46779.9i		−	1.55568i	0.628465	−	0.777838i	$-0.283684\pi$
$968$	−10381.7	−	5993.88i	−0.344711	−	0.199019i
$969$	−32657.7	−	18854.9i	−1.08268	−	0.625086i
$970$		−	5354.45i		−	0.177238i
$971$	−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
$973$	5771.47	−	3332.16i	0.190159	−	0.109788i
$974$	−23659.1			−0.778323
$975$		0			0
$976$	−7676.98			−0.251777
$977$	20990.4	−	12118.8i	0.687351	−	0.396842i	−0.115268	−	0.993334i	$-0.536773\pi$
$977$	20990.4	−	12118.8i	0.687351	−	0.396842i	0.802619	+	0.596492i	$0.203439\pi$
$978$	8535.54	+	14784.0i	0.279076	+	0.483374i
$979$	17698.1	−	30654.0i	0.577768	−	1.00072i
$980$		−	2801.01i		−	0.0913011i
$981$	13893.4	+	8021.34i	0.452172	+	0.261062i
$982$	4676.60	+	2700.04i	0.151972	+	0.0877410i
$983$		−	32953.2i		−	1.06922i	−0.845098	−	0.534611i	$-0.820458\pi$
$983$		−	32953.2i		−	1.06922i	0.845098	−	0.534611i	$-0.179542\pi$
$984$	9096.03	−	15754.8i	0.294686	−	0.510411i
$985$	−2072.15	−	3589.06i	−0.0670295	−	0.116099i
$986$	6295.05	−	3634.45i	0.203322	−	0.117388i
$987$	−6774.36			−0.218470
$988$		0			0
$989$	−9154.51			−0.294334
$990$	1456.00	−	840.622i	0.0467422	−	0.0269866i
$991$	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
$993$		−	5203.39i		−	0.166288i
$994$	1968.02	+	1136.24i	0.0627985	+	0.0362567i
$995$	−4234.49	−	2444.79i	−0.134917	−	0.0778944i
$996$			519.925i			0.0165406i
$997$	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
$999$	−13111.0	+	7569.65i	−0.415230	+	0.239733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.4.e.g.23.3		8
13.2	odd	12		338.4.a.i.1.2		2
13.3	even	3		26.4.b.a.25.4	yes	4
13.4	even	6	inner	338.4.e.g.147.3		8
13.5	odd	4		338.4.c.h.315.1		4
13.6	odd	12		338.4.c.h.191.1		4
13.7	odd	12		338.4.c.i.191.1		4
13.8	odd	4		338.4.c.i.315.1		4
13.9	even	3	inner	338.4.e.g.147.1		8
13.10	even	6		26.4.b.a.25.2	✓	4
13.11	odd	12		338.4.a.f.1.2		2
13.12	even	2	inner	338.4.e.g.23.1		8
39.23	odd	6		234.4.b.b.181.3		4
39.29	odd	6		234.4.b.b.181.2		4
52.3	odd	6		208.4.f.d.129.2		4
52.23	odd	6		208.4.f.d.129.1		4
65.3	odd	12		650.4.c.f.649.3		4
65.23	odd	12		650.4.c.e.649.3		4
65.29	even	6		650.4.d.d.51.1		4
65.42	odd	12		650.4.c.e.649.2		4
65.49	even	6		650.4.d.d.51.3		4
65.62	odd	12		650.4.c.f.649.2		4
104.3	odd	6		832.4.f.h.129.3		4
104.29	even	6		832.4.f.j.129.1		4
104.75	odd	6		832.4.f.h.129.4		4
104.101	even	6		832.4.f.j.129.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.b.a.25.2	✓	4	13.10	even	6
26.4.b.a.25.4	yes	4	13.3	even	3
208.4.f.d.129.1		4	52.23	odd	6
208.4.f.d.129.2		4	52.3	odd	6
234.4.b.b.181.2		4	39.29	odd	6
234.4.b.b.181.3		4	39.23	odd	6
338.4.a.f.1.2		2	13.11	odd	12
338.4.a.i.1.2		2	13.2	odd	12
338.4.c.h.191.1		4	13.6	odd	12
338.4.c.h.315.1		4	13.5	odd	4
338.4.c.i.191.1		4	13.7	odd	12
338.4.c.i.315.1		4	13.8	odd	4
338.4.e.g.23.1		8	13.12	even	2	inner
338.4.e.g.23.3		8	1.1	even	1	trivial
338.4.e.g.147.1		8	13.9	even	3	inner
338.4.e.g.147.3		8	13.4	even	6	inner
650.4.c.e.649.2		4	65.42	odd	12
650.4.c.e.649.3		4	65.23	odd	12
650.4.c.f.649.2		4	65.62	odd	12
650.4.c.f.649.3		4	65.3	odd	12
650.4.d.d.51.1		4	65.29	even	6
650.4.d.d.51.3		4	65.49	even	6
832.4.f.h.129.3		4	104.3	odd	6
832.4.f.h.129.4		4	104.75	odd	6
832.4.f.j.129.1		4	104.29	even	6
832.4.f.j.129.2		4	104.101	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	338.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(-2.93273 - 5.07964i) q^{3} +(2.00000 - 3.46410i) q^{4} +2.13454i q^{5} +(-10.1593 - 5.86546i) q^{6} +(-3.34759 - 1.93273i) q^{7} -8.00000i q^{8} +(-3.70181 + 6.41172i) q^{9} +(2.13454 + 3.69713i) q^{10} +(-46.0663 + 26.5964i) q^{11} -23.4618 q^{12} -7.73092 q^{14} +(10.8427 - 6.26003i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-21.6636 + 37.5225i) q^{17} +14.8072i q^{18} +(-128.506 - 74.1928i) q^{19} +(7.39426 + 4.26908i) q^{20} +22.6727i q^{21} +(-53.1928 + 92.1326i) q^{22} +(61.3273 + 106.222i) q^{23} +(-40.6371 + 23.4618i) q^{24} +120.444 q^{25} -114.942 q^{27} +(-13.3903 + 7.73092i) q^{28} +(-41.9418 - 72.6453i) q^{29} +(12.5201 - 21.6854i) q^{30} +190.269i q^{31} +(-27.7128 - 16.0000i) q^{32} +(270.200 + 156.000i) q^{33} +86.6546i q^{34} +(4.12549 - 7.14556i) q^{35} +(14.8072 + 25.6469i) q^{36} +(114.067 - 65.8564i) q^{37} -296.771 q^{38} +17.0763 q^{40} +(-335.753 + 193.847i) q^{41} +(22.6727 + 39.2703i) q^{42} +(-37.3182 + 64.6371i) q^{43} +212.771i q^{44} +(-13.6861 - 7.90166i) q^{45} +(212.444 + 122.655i) q^{46} +298.789i q^{47} +(-46.9237 + 81.2742i) q^{48} +(-164.029 - 284.107i) q^{49} +(208.615 - 120.444i) q^{50} +254.135 q^{51} +100.386 q^{53} +(-199.085 + 114.942i) q^{54} +(-56.7710 - 98.3303i) q^{55} +(-15.4618 + 26.7807i) q^{56} +870.349i q^{57} +(-145.291 - 83.8836i) q^{58} +(415.094 + 239.655i) q^{59} -50.0802i q^{60} +(239.906 - 415.529i) q^{61} +(190.269 + 329.556i) q^{62} +(24.7843 - 14.3092i) q^{63} -64.0000 q^{64} +624.000 q^{66} +(-359.637 + 207.636i) q^{67} +(86.6546 + 150.090i) q^{68} +(359.713 - 623.041i) q^{69} -16.5020i q^{70} +(-254.564 - 146.973i) q^{71} +(51.2938 + 29.6145i) q^{72} -106.727i q^{73} +(131.713 - 228.133i) q^{74} +(-353.229 - 611.811i) q^{75} +(-514.023 + 296.771i) q^{76} +205.614 q^{77} -906.044 q^{79} +(29.5771 - 17.0763i) q^{80} +(437.042 + 756.979i) q^{81} +(-387.695 + 671.507i) q^{82} -22.1605i q^{83} +(78.5405 + 45.3454i) q^{84} +(-80.0934 - 46.2419i) q^{85} +149.273i q^{86} +(-246.008 + 426.098i) q^{87} +(212.771 + 368.530i) q^{88} +(-576.282 + 332.717i) q^{89} -31.6066 q^{90} +490.618 q^{92} +(966.498 - 558.008i) q^{93} +(298.789 + 517.518i) q^{94} +(158.367 - 274.300i) q^{95} +187.695i q^{96} +(-1086.20 - 627.120i) q^{97} +(-568.214 - 328.058i) q^{98} -393.819i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 16 q^{4} - 118 q^{9} + 76 q^{10} + 48 q^{12} + 56 q^{14} - 64 q^{16} - 26 q^{17} - 72 q^{22} + 196 q^{23} - 156 q^{25} - 1332 q^{27} - 748 q^{29} - 548 q^{30} - 350 q^{35} + 472 q^{36} - 960 q^{38}+ \cdots - 324 q^{95}+O(q^{100}) \) 8 * q + 6 * q^3 + 16 * q^4 - 118 * q^9 + 76 * q^10 + 48 * q^12 + 56 * q^14 - 64 * q^16 - 26 * q^17 - 72 * q^22 + 196 * q^23 - 156 * q^25 - 1332 * q^27 - 748 * q^29 - 548 * q^30 - 350 * q^35 + 472 * q^36 - 960 * q^38 + 608 * q^40 + 476 * q^42 + 438 * q^43 + 96 * q^48 - 1106 * q^49 + 2092 * q^51 + 96 * q^53 + 960 * q^55 + 112 * q^56 + 564 * q^61 + 1640 * q^62 - 512 * q^64 + 4992 * q^66 + 104 * q^68 + 1876 * q^69 + 52 * q^74 - 4240 * q^75 + 2352 * q^77 - 2888 * q^79 + 668 * q^81 - 1216 * q^82 + 4160 * q^87 + 288 * q^88 - 7088 * q^90 + 1568 * q^92 + 1860 * q^94 - 324 * q^95

Introduction

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