LMFDB - Embedded newform 143.4.g.a.21.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(21,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("143.21");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.1
Character	$\chi$	$=$	143.21
Dual form			143.4.g.a.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.84534 + 3.84534i) q^{2} +4.01609 q^{3} -21.5733i q^{4} +(8.40231 + 8.40231i) q^{5} +(-15.4432 + 15.4432i) q^{6} +(-18.8709 - 18.8709i) q^{7} +(52.1938 + 52.1938i) q^{8} -10.8710 q^{9} +O(q^{10})$	\(q+(-3.84534 + 3.84534i) q^{2} +4.01609 q^{3} -21.5733i q^{4} +(8.40231 + 8.40231i) q^{5} +(-15.4432 + 15.4432i) q^{6} +(-18.8709 - 18.8709i) q^{7} +(52.1938 + 52.1938i) q^{8} -10.8710 q^{9} -64.6194 q^{10} +(32.9394 - 15.6843i) q^{11} -86.6402i q^{12} +(38.2898 - 27.0349i) q^{13} +145.130 q^{14} +(33.7445 + 33.7445i) q^{15} -228.819 q^{16} +58.6264 q^{17} +(41.8026 - 41.8026i) q^{18} +(89.7651 - 89.7651i) q^{19} +(181.265 - 181.265i) q^{20} +(-75.7872 - 75.7872i) q^{21} +(-66.3519 + 186.974i) q^{22} +50.3721i q^{23} +(209.615 + 209.615i) q^{24} +16.1975i q^{25} +(-43.2789 + 251.196i) q^{26} -152.093 q^{27} +(-407.106 + 407.106i) q^{28} +97.9106i q^{29} -259.518 q^{30} +(151.554 + 151.554i) q^{31} +(462.338 - 462.338i) q^{32} +(132.288 - 62.9895i) q^{33} +(-225.439 + 225.439i) q^{34} -317.118i q^{35} +234.522i q^{36} +(201.650 - 201.650i) q^{37} +690.355i q^{38} +(153.776 - 108.575i) q^{39} +877.096i q^{40} +(-237.968 + 237.968i) q^{41} +582.855 q^{42} +127.836 q^{43} +(-338.361 - 710.610i) q^{44} +(-91.3413 - 91.3413i) q^{45} +(-193.698 - 193.698i) q^{46} +(360.019 - 360.019i) q^{47} -918.960 q^{48} +369.219i q^{49} +(-62.2851 - 62.2851i) q^{50} +235.449 q^{51} +(-583.232 - 826.036i) q^{52} -314.543 q^{53} +(584.851 - 584.851i) q^{54} +(408.551 + 144.983i) q^{55} -1969.88i q^{56} +(360.505 - 360.505i) q^{57} +(-376.499 - 376.499i) q^{58} +(43.9596 - 43.9596i) q^{59} +(727.978 - 727.978i) q^{60} +38.7839i q^{61} -1165.55 q^{62} +(205.145 + 205.145i) q^{63} +1725.14i q^{64} +(548.879 + 94.5671i) q^{65} +(-266.475 + 750.907i) q^{66} +(250.107 + 250.107i) q^{67} -1264.76i q^{68} +202.299i q^{69} +(1219.42 + 1219.42i) q^{70} +(132.858 + 132.858i) q^{71} +(-567.398 - 567.398i) q^{72} +(-516.739 - 516.739i) q^{73} +1550.82i q^{74} +65.0509i q^{75} +(-1936.53 - 1936.53i) q^{76} +(-917.570 - 325.619i) q^{77} +(-173.812 + 1008.83i) q^{78} -101.043i q^{79} +(-1922.61 - 1922.61i) q^{80} -317.305 q^{81} -1830.14i q^{82} +(-70.7756 + 70.7756i) q^{83} +(-1634.98 + 1634.98i) q^{84} +(492.597 + 492.597i) q^{85} +(-491.573 + 491.573i) q^{86} +393.218i q^{87} +(2537.85 + 900.611i) q^{88} +(-269.410 + 269.410i) q^{89} +702.477 q^{90} +(-1232.74 - 212.389i) q^{91} +1086.69 q^{92} +(608.656 + 608.656i) q^{93} +2768.79i q^{94} +1508.47 q^{95} +(1856.79 - 1856.79i) q^{96} +(234.483 + 234.483i) q^{97} +(-1419.77 - 1419.77i) q^{98} +(-358.084 + 170.503i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9}+O(q^{10}) $ 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9	$ 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9} + 14 q^{11} + 280 q^{14} - 80 q^{15} - 952 q^{16} - 200 q^{20} - 424 q^{22} - 508 q^{26} - 848 q^{27} + 208 q^{31} + 860 q^{33} - 232 q^{34} - 340 q^{37} + 1308 q^{42} - 644 q^{44} - 1148 q^{45} - 280 q^{47} + 2420 q^{48} + 2976 q^{53} + 1652 q^{55} - 1972 q^{58} - 84 q^{59} + 1484 q^{60} - 4924 q^{66} + 2468 q^{67} - 3540 q^{70} + 1704 q^{71} + 2368 q^{78} - 3544 q^{80} + 6160 q^{81} + 32 q^{86} + 424 q^{89} - 5868 q^{91} - 164 q^{92} + 3944 q^{93} - 4936 q^{97} - 3750 q^{99}+O(q^{100}) $ 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9 + 14 * q^11 + 280 * q^14 - 80 * q^15 - 952 * q^16 - 200 * q^20 - 424 * q^22 - 508 * q^26 - 848 * q^27 + 208 * q^31 + 860 * q^33 - 232 * q^34 - 340 * q^37 + 1308 * q^42 - 644 * q^44 - 1148 * q^45 - 280 * q^47 + 2420 * q^48 + 2976 * q^53 + 1652 * q^55 - 1972 * q^58 - 84 * q^59 + 1484 * q^60 - 4924 * q^66 + 2468 * q^67 - 3540 * q^70 + 1704 * q^71 + 2368 * q^78 - 3544 * q^80 + 6160 * q^81 + 32 * q^86 + 424 * q^89 - 5868 * q^91 - 164 * q^92 + 3944 * q^93 - 4936 * q^97 - 3750 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−3.84534	+	3.84534i	−1.35953	+	1.35953i	−0.485041	+	0.874491i	$0.661195\pi$
$2$	−3.84534	+	3.84534i	−1.35953	+	1.35953i	−0.874491	+	0.485041i	$0.838805\pi$
$3$	4.01609			0.772898			0.386449	−	0.922311i	$-0.373702\pi$
$3$	4.01609			0.772898			0.386449	+	0.922311i	$0.373702\pi$
$4$		−	21.5733i		−	2.69666i
$5$	8.40231	+	8.40231i	0.751525	+	0.751525i	0.974764	−	0.223239i	$-0.0716629\pi$
$5$	8.40231	+	8.40231i	0.751525	+	0.751525i	−0.223239	+	0.974764i	$0.571663\pi$
$6$	−15.4432	+	15.4432i	−1.05078	+	1.05078i
$7$	−18.8709	−	18.8709i	−1.01893	−	1.01893i	−0.999817	−	0.0191135i	$-0.993916\pi$
$7$	−18.8709	−	18.8709i	−1.01893	−	1.01893i	−0.0191135	−	0.999817i	$-0.506084\pi$
$8$	52.1938	+	52.1938i	2.30666	+	2.30666i
$9$	−10.8710			−0.402629
$10$	−64.6194			−2.04345
$11$	32.9394	−	15.6843i	0.902873	−	0.429907i
$11$	32.9394	−	15.6843i	0.902873	−	0.429907i
$12$		−	86.6402i		−	2.08424i
$13$	38.2898	−	27.0349i	0.816899	−	0.576780i
$13$	38.2898	−	27.0349i	0.816899	−	0.576780i
$14$	145.130			2.77054
$15$	33.7445	+	33.7445i	0.580852	+	0.580852i
$16$	−228.819			−3.57530
$17$	58.6264			0.836412			0.418206	−	0.908352i	$-0.362659\pi$
$17$	58.6264			0.836412			0.418206	+	0.908352i	$0.362659\pi$
$18$	41.8026	−	41.8026i	0.547387	−	0.547387i
$19$	89.7651	−	89.7651i	1.08387	−	1.08387i	0.0877254	−	0.996145i	$-0.472040\pi$
$19$	89.7651	−	89.7651i	1.08387	−	1.08387i	0.996145	−	0.0877254i	$-0.0279598\pi$
$20$	181.265	−	181.265i	2.02661	−	2.02661i
$21$	−75.7872	−	75.7872i	−0.787529	−	0.787529i
$22$	−66.3519	+	186.974i	−0.643012	+	1.81196i
$23$			50.3721i			0.456666i	0.973583	+	0.228333i	$0.0733275\pi$
$23$			50.3721i			0.456666i	−0.973583	+	0.228333i	$0.926673\pi$
$24$	209.615	+	209.615i	1.78281	+	1.78281i
$25$			16.1975i			0.129580i
$26$	−43.2789	+	251.196i	−0.326449	+	1.89475i
$27$	−152.093			−1.08409
$28$	−407.106	+	407.106i	−2.74771	+	2.74771i
$29$			97.9106i			0.626950i	0.949597	+	0.313475i	$0.101493\pi$
$29$			97.9106i			0.626950i	−0.949597	+	0.313475i	$0.898507\pi$
$30$	−259.518			−1.57937
$31$	151.554	+	151.554i	0.878062	+	0.878062i	0.993334	−	0.115272i	$-0.0367739\pi$
$31$	151.554	+	151.554i	0.878062	+	0.878062i	−0.115272	+	0.993334i	$0.536774\pi$
$32$	462.338	−	462.338i	2.55408	−	2.55408i
$33$	132.288	−	62.9895i	0.697829	−	0.332275i
$34$	−225.439	+	225.439i	−1.13713	+	1.13713i
$35$		−	317.118i		−	1.53150i
$36$			234.522i			1.08575i
$37$	201.650	−	201.650i	0.895974	−	0.895974i	−0.0991029	−	0.995077i	$-0.531597\pi$
$37$	201.650	−	201.650i	0.895974	−	0.895974i	0.995077	+	0.0991029i	$0.0315973\pi$
$38$			690.355i			2.94711i
$39$	153.776	−	108.575i	0.631380	−	0.445792i
$40$			877.096i			3.46703i
$41$	−237.968	+	237.968i	−0.906448	+	0.906448i	−0.995984	−	0.0895357i	$-0.971462\pi$
$41$	−237.968	+	237.968i	−0.906448	+	0.906448i	0.0895357	+	0.995984i	$0.471462\pi$
$42$	582.855			2.14134
$43$	127.836			0.453368			0.226684	−	0.973968i	$-0.427212\pi$
$43$	127.836			0.453368			0.226684	+	0.973968i	$0.427212\pi$
$44$	−338.361	−	710.610i	−1.15931	−	2.43474i
$45$	−91.3413	−	91.3413i	−0.302586	−	0.302586i
$46$	−193.698	−	193.698i	−0.620852	−	0.620852i
$47$	360.019	−	360.019i	1.11732	−	1.11732i	0.125190	−	0.992133i	$-0.460046\pi$
$47$	360.019	−	360.019i	1.11732	−	1.11732i	0.992133	−	0.125190i	$-0.0399542\pi$
$48$	−918.960			−2.76334
$49$			369.219i			1.07644i
$50$	−62.2851	−	62.2851i	−0.176169	−	0.176169i
$51$	235.449			0.646461
$52$	−583.232	−	826.036i	−1.55538	−	2.20290i
$53$	−314.543			−0.815204			−0.407602	−	0.913160i	$-0.633635\pi$
$53$	−314.543			−0.815204			−0.407602	+	0.913160i	$0.633635\pi$
$54$	584.851	−	584.851i	1.47385	−	1.47385i
$55$	408.551	+	144.983i	1.00162	+	0.355446i
$56$		−	1969.88i		−	4.70065i
$57$	360.505	−	360.505i	0.837721	−	0.837721i
$58$	−376.499	−	376.499i	−0.852358	−	0.852358i
$59$	43.9596	−	43.9596i	0.0970010	−	0.0970010i	−0.656941	−	0.753942i	$-0.728150\pi$
$59$	43.9596	−	43.9596i	0.0970010	−	0.0970010i	0.753942	+	0.656941i	$0.228150\pi$
$60$	727.978	−	727.978i	1.56636	−	1.56636i
$61$			38.7839i			0.0814061i	0.999171	+	0.0407030i	$0.0129598\pi$
$61$			38.7839i			0.0814061i	−0.999171	+	0.0407030i	$0.987040\pi$
$62$	−1165.55			−2.38751
$63$	205.145	+	205.145i	0.410251	+	0.410251i
$64$			1725.14i			3.36940i
$65$	548.879	+	94.5671i	1.04739	+	0.180455i
$66$	−266.475	+	750.907i	−0.496983	+	1.40046i
$67$	250.107	+	250.107i	0.456052	+	0.456052i	0.897357	−	0.441305i	$-0.145484\pi$
$67$	250.107	+	250.107i	0.456052	+	0.456052i	−0.441305	+	0.897357i	$0.645484\pi$
$68$		−	1264.76i		−	2.25552i
$69$			202.299i			0.352956i
$70$	1219.42	+	1219.42i	2.08213	+	2.08213i
$71$	132.858	+	132.858i	0.222075	+	0.222075i	0.809372	−	0.587297i	$-0.199808\pi$
$71$	132.858	+	132.858i	0.222075	+	0.222075i	−0.587297	+	0.809372i	$0.699808\pi$
$72$	−567.398	−	567.398i	−0.928728	−	0.928728i
$73$	−516.739	−	516.739i	−0.828489	−	0.828489i	0.158819	−	0.987308i	$-0.449231\pi$
$73$	−516.739	−	516.739i	−0.828489	−	0.828489i	−0.987308	+	0.158819i	$0.949231\pi$
$74$			1550.82i			2.43621i
$75$			65.0509i			0.100152i
$76$	−1936.53	−	1936.53i	−2.92283	−	2.92283i
$77$	−917.570	−	325.619i	−1.35801	−	0.481919i
$78$	−173.812	+	1008.83i	−0.252312	+	1.46445i
$79$		−	101.043i		−	0.143901i	−0.997408	−	0.0719505i	$-0.977078\pi$
$79$		−	101.043i		−	0.143901i	0.997408	−	0.0719505i	$-0.0229224\pi$
$80$	−1922.61	−	1922.61i	−2.68693	−	2.68693i
$81$	−317.305			−0.435261
$82$		−	1830.14i		−	2.46469i
$83$	−70.7756	+	70.7756i	−0.0935980	+	0.0935980i	−0.752355	−	0.658757i	$-0.771082\pi$
$83$	−70.7756	+	70.7756i	−0.0935980	+	0.0935980i	0.658757	+	0.752355i	$0.271082\pi$
$84$	−1634.98	+	1634.98i	−2.12370	+	2.12370i
$85$	492.597	+	492.597i	0.628585	+	0.628585i
$86$	−491.573	+	491.573i	−0.616368	+	0.616368i
$87$			393.218i			0.484568i
$88$	2537.85	+	900.611i	3.07427	+	1.09097i
$89$	−269.410	+	269.410i	−0.320870	+	0.320870i	−0.849101	−	0.528231i	$-0.822856\pi$
$89$	−269.410	+	269.410i	−0.320870	+	0.320870i	0.528231	+	0.849101i	$0.322856\pi$
$90$	702.477			0.822751
$91$	−1232.74	−	212.389i	−1.42006	−	0.244664i
$92$	1086.69			1.23147
$93$	608.656	+	608.656i	0.678652	+	0.678652i
$94$			2768.79i			3.03807i
$95$	1508.47			1.62911
$96$	1856.79	−	1856.79i	1.97404	−	1.97404i
$97$	234.483	+	234.483i	0.245445	+	0.245445i	0.819098	−	0.573653i	$-0.194474\pi$
$97$	234.483	+	234.483i	0.245445	+	0.245445i	−0.573653	+	0.819098i	$0.694474\pi$
$98$	−1419.77	−	1419.77i	−1.46346	−	1.46346i
$99$	−358.084	+	170.503i	−0.363523	+	0.173093i
$100$	349.434			0.349434
$101$	278.643			0.274515			0.137257	−	0.990535i	$-0.456171\pi$
$101$	278.643			0.274515			0.137257	+	0.990535i	$0.456171\pi$
$102$	−905.383	+	905.383i	−0.878885	+	0.878885i
$103$		−	1195.90i		−	1.14404i	−0.820241	−	0.572018i	$-0.806161\pi$
$103$		−	1195.90i		−	1.14404i	0.820241	−	0.572018i	$-0.193839\pi$
$104$	3409.55	+	587.435i	3.21475	+	0.553873i
$105$		−	1273.57i		−	1.18370i
$106$	1209.52	−	1209.52i	1.10830	−	1.10830i
$107$		−	1673.99i		−	1.51244i	−0.654317	−	0.756220i	$-0.727044\pi$
$107$		−	1673.99i		−	1.51244i	0.654317	−	0.756220i	$-0.272956\pi$
$108$			3281.15i			2.92342i
$109$	387.639	−	387.639i	0.340633	−	0.340633i	−0.515972	−	0.856605i	$-0.672569\pi$
$109$	387.639	−	387.639i	0.340633	−	0.340633i	0.856605	+	0.515972i	$0.172569\pi$
$110$	−2128.53	+	1013.51i	−1.84497	+	0.878493i
$111$	809.845	−	809.845i	0.692497	−	0.692497i
$112$	4318.02	+	4318.02i	3.64299	+	3.64299i
$113$	−863.835			−0.719139			−0.359570	−	0.933118i	$-0.617077\pi$
$113$	−863.835			−0.719139			−0.359570	+	0.933118i	$0.617077\pi$
$114$			2772.53i			2.27782i
$115$	−423.242	+	423.242i	−0.343196	+	0.343196i
$116$	2112.25			1.69067
$117$	−416.248	+	293.896i	−0.328907	+	0.232229i
$118$			338.079i			0.263752i
$119$	−1106.33	−	1106.33i	−0.852246	−	0.852246i
$120$			3522.50i			2.67966i
$121$	839.008	−	1033.26i	0.630359	−	0.776304i
$122$	−149.137	−	149.137i	−0.110674	−	0.110674i
$123$	−955.702	+	955.702i	−0.700592	+	0.700592i
$124$	3269.52	−	3269.52i	2.36783	−	2.36783i
$125$	914.192	−	914.192i	0.654142	−	0.654142i
$126$	−1577.70			−1.11550
$127$	−1160.89			−0.811122			−0.405561	−	0.914068i	$-0.632924\pi$
$127$	−1160.89			−0.811122			−0.405561	+	0.914068i	$0.632924\pi$
$128$	−2935.03	−	2935.03i	−2.02674	−	2.02674i
$129$	513.401			0.350407
$130$	−2474.27	+	1746.98i	−1.66929	+	1.17862i
$131$			2415.75i			1.61119i	0.592469	+	0.805593i	$0.298153\pi$
$131$			2415.75i			1.61119i	−0.592469	+	0.805593i	$0.701847\pi$
$132$	−1358.89	−	2853.88i	−0.896030	−	1.88180i
$133$	−3387.89			−2.20878
$134$	−1923.49			−1.24003
$135$	−1277.94	−	1277.94i	−0.814720	−	0.814720i
$136$	3059.94	+	3059.94i	1.92932	+	1.92932i
$137$	−585.632	+	585.632i	−0.365211	+	0.365211i	−0.865727	−	0.500516i	$-0.833144\pi$
$137$	−585.632	+	585.632i	−0.365211	+	0.365211i	0.500516	+	0.865727i	$0.333144\pi$
$138$	−777.909	−	777.909i	−0.479855	−	0.479855i
$139$			177.164i			0.108107i	0.998538	+	0.0540533i	$0.0172141\pi$
$139$			177.164i			0.108107i	−0.998538	+	0.0540533i	$0.982786\pi$
$140$	−6841.26			−4.12994
$141$	1445.87	−	1445.87i	0.863577	−	0.863577i
$142$	−1021.76			−0.603835
$143$	837.221	−	1491.06i	0.489594	−	0.871950i
$144$	2487.49			1.43952
$145$	−822.675	+	822.675i	−0.471168	+	0.471168i
$146$	3974.07			2.25271
$147$			1482.82i			0.831978i
$148$	−4350.25	−	4350.25i	−2.41614	−	2.41614i
$149$	25.8732	−	25.8732i	0.0142256	−	0.0142256i	−0.699958	−	0.714184i	$-0.746798\pi$
$149$	25.8732	−	25.8732i	0.0142256	−	0.0142256i	0.714184	+	0.699958i	$0.246798\pi$
$150$	−250.143	−	250.143i	−0.136160	−	0.136160i
$151$	554.955	+	554.955i	0.299083	+	0.299083i	0.840655	−	0.541571i	$-0.182170\pi$
$151$	554.955	+	554.955i	0.299083	+	0.299083i	−0.541571	+	0.840655i	$0.682170\pi$
$152$	9370.36			5.00024
$153$	−637.327			−0.336764
$154$	4780.49	−	2276.25i	2.50144	−	1.19108i
$155$			2546.81i			1.31977i
$156$	−2342.31	−	3317.44i	−1.20215	−	1.70261i
$157$	−1709.79			−0.869149			−0.434575	−	0.900636i	$-0.643101\pi$
$157$	−1709.79			−0.869149			−0.434575	+	0.900636i	$0.643101\pi$
$158$	388.543	+	388.543i	0.195638	+	0.195638i
$159$	−1263.23			−0.630069
$160$	7769.41			3.83891
$161$	950.566	−	950.566i	0.465311	−	0.465311i
$162$	1220.15	−	1220.15i	0.591751	−	0.591751i
$163$	−2439.18	+	2439.18i	−1.17209	+	1.17209i	−0.190382	+	0.981710i	$0.560973\pi$
$163$	−2439.18	+	2439.18i	−1.17209	+	1.17209i	−0.981710	+	0.190382i	$0.939027\pi$
$164$	5133.75	+	5133.75i	2.44438	+	2.44438i
$165$	1640.78	+	582.265i	0.774148	+	0.274723i
$166$		−	544.313i		−	0.254499i
$167$	−86.7346	−	86.7346i	−0.0401900	−	0.0401900i	0.686726	−	0.726916i	$-0.259047\pi$
$167$	−86.7346	−	86.7346i	−0.0401900	−	0.0401900i	−0.726916	+	0.686726i	$0.759047\pi$
$168$		−	7911.24i		−	3.63313i
$169$	735.223	−	2070.33i	0.334649	−	0.942343i
$170$	−3788.41			−1.70916
$171$	−975.835	+	975.835i	−0.436398	+	0.436398i
$172$		−	2757.84i		−	1.22258i
$173$	−1317.50			−0.579004			−0.289502	−	0.957177i	$-0.593490\pi$
$173$	−1317.50			−0.579004			−0.289502	+	0.957177i	$0.593490\pi$
$174$	−1512.06	−	1512.06i	−0.658786	−	0.658786i
$175$	305.662	−	305.662i	0.132033	−	0.132033i
$176$	−7537.17	+	3588.86i	−3.22804	+	1.53705i
$177$	176.546	−	176.546i	0.0749718	−	0.0749718i
$178$		−	2071.95i		−	0.872466i
$179$		−	1944.91i		−	0.812119i	−0.913847	−	0.406059i	$-0.866903\pi$
$179$		−	1944.91i		−	0.812119i	0.913847	−	0.406059i	$-0.133097\pi$
$180$	−1970.53	+	1970.53i	−0.815970	+	0.815970i
$181$			3488.54i			1.43260i	0.697790	+	0.716302i	$0.254167\pi$
$181$			3488.54i			1.43260i	−0.697790	+	0.716302i	$0.745833\pi$
$182$	5556.99	−	3923.57i	2.26325	−	1.59799i
$183$			155.760i			0.0629186i
$184$	−2629.11	+	2629.11i	−1.05337	+	1.05337i
$185$	3388.65			1.34669
$186$	−4680.97			−1.84530
$187$	1931.12	−	919.512i	0.755174	−	0.359580i
$188$	−7766.79	−	7766.79i	−3.01304	−	3.01304i
$189$	2870.13	+	2870.13i	1.10461	+	1.10461i
$190$	−5800.57	+	5800.57i	−2.21483	+	2.21483i
$191$	−998.114			−0.378121			−0.189060	−	0.981965i	$-0.560544\pi$
$191$	−998.114			−0.378121			−0.189060	+	0.981965i	$0.560544\pi$
$192$			6928.31i			2.60421i
$193$	1433.22	+	1433.22i	0.534536	+	0.534536i	0.921919	−	0.387383i	$-0.126621\pi$
$193$	1433.22	+	1433.22i	0.534536	+	0.534536i	−0.387383	+	0.921919i	$0.626621\pi$
$194$	−1803.33			−0.667380
$195$	2204.35	+	379.790i	0.809522	+	0.139474i
$196$	7965.25			2.90279
$197$	204.596	−	204.596i	0.0739942	−	0.0739942i	−0.669141	−	0.743135i	$-0.733338\pi$
$197$	204.596	−	204.596i	0.0739942	−	0.0739942i	0.743135	+	0.669141i	$0.233338\pi$
$198$	721.310	−	2032.60i	0.258895	−	0.729547i
$199$		−	1889.21i		−	0.672978i	−0.941687	−	0.336489i	$-0.890761\pi$
$199$		−	1889.21i		−	0.672978i	0.941687	−	0.336489i	$-0.109239\pi$
$200$	−845.411	+	845.411i	−0.298898	+	0.298898i
$201$	1004.45	+	1004.45i	0.352481	+	0.352481i
$202$	−1071.48	+	1071.48i	−0.373212	+	0.373212i
$203$	1847.66	−	1847.66i	0.638818	−	0.638818i
$204$		−	5079.41i		−	1.74328i
$205$	−3998.96			−1.36244
$206$	4598.65	+	4598.65i	1.55535	+	1.55535i
$207$		−	547.595i		−	0.183867i
$208$	−8761.46	+	6186.12i	−2.92066	+	2.06216i
$209$	1548.91	−	4364.71i	0.512633	−	1.44456i
$210$	4897.32	+	4897.32i	1.60927	+	1.60927i
$211$			3631.00i			1.18468i	0.805686	+	0.592342i	$0.201797\pi$
$211$			3631.00i			1.18468i	−0.805686	+	0.592342i	$0.798203\pi$
$212$			6785.72i			2.19832i
$213$	533.569	+	533.569i	0.171641	+	0.171641i
$214$	6437.07	+	6437.07i	2.05621	+	2.05621i
$215$	1074.12	+	1074.12i	0.340717	+	0.340717i
$216$	−7938.33	−	7938.33i	−2.50062	−	2.50062i
$217$		−	5719.91i		−	1.78937i
$218$			2981.20i			0.926204i
$219$	−2075.27	−	2075.27i	−0.640337	−	0.640337i
$220$	3127.76	−	8813.77i	0.958515	−	2.70102i
$221$	2244.80	−	1584.96i	0.683264	−	0.482426i
$222$			6228.26i			1.88294i
$223$	2755.78	+	2755.78i	0.827536	+	0.827536i	0.987175	−	0.159639i	$-0.0510330\pi$
$223$	2755.78	+	2755.78i	0.827536	+	0.827536i	−0.159639	+	0.987175i	$0.551033\pi$
$224$	−17449.4			−5.20486
$225$		−	176.083i		−	0.0521728i
$226$	3321.74	−	3321.74i	0.977693	−	0.977693i
$227$	−1066.62	+	1066.62i	−0.311869	+	0.311869i	−0.845633	−	0.533764i	$-0.820777\pi$
$227$	−1066.62	+	1066.62i	−0.311869	+	0.311869i	0.533764	+	0.845633i	$0.320777\pi$
$228$	−7777.27	−	7777.27i	−2.25905	−	2.25905i
$229$	−2738.77	+	2738.77i	−0.790319	+	0.790319i	−0.981546	−	0.191227i	$-0.938753\pi$
$229$	−2738.77	+	2738.77i	−0.790319	+	0.790319i	0.191227	+	0.981546i	$0.438753\pi$
$230$		−	3255.02i		−	0.933172i
$231$	−3685.05	−	1307.72i	−1.04960	−	0.372474i
$232$	−5110.32	+	5110.32i	−1.44616	+	1.44616i
$233$	−2911.29			−0.818562			−0.409281	−	0.912408i	$-0.634220\pi$
$233$	−2911.29			−0.818562			−0.409281	+	0.912408i	$0.634220\pi$
$234$	470.484	−	2730.75i	0.131438	−	0.762882i
$235$	6049.98			1.67939
$236$	−948.352	−	948.352i	−0.261578	−	0.261578i
$237$		−	405.796i		−	0.111221i
$238$	8508.44			2.31731
$239$	−655.459	+	655.459i	−0.177398	+	0.177398i	−0.790221	−	0.612823i	$-0.790034\pi$
$239$	−655.459	+	655.459i	−0.177398	+	0.177398i	0.612823	+	0.790221i	$0.290034\pi$
$240$	−7721.39	−	7721.39i	−2.07672	−	2.07672i
$241$	2134.48	+	2134.48i	0.570514	+	0.570514i	0.932272	−	0.361758i	$-0.117823\pi$
$241$	2134.48	+	2134.48i	0.570514	+	0.570514i	−0.361758	+	0.932272i	$0.617823\pi$
$242$	746.965	+	7199.50i	0.198416	+	1.91240i
$243$	2832.20			0.747677
$244$	836.695			0.219524
$245$	−3102.29	+	3102.29i	−0.808972	+	0.808972i
$246$		−	7350.00i		−	1.90495i
$247$	1010.30	−	5863.89i	0.260258	−	1.51057i
$248$			15820.4i			4.05078i
$249$	−284.242	+	284.242i	−0.0723417	+	0.0723417i
$250$			7030.75i			1.77866i
$251$			6514.84i			1.63830i	0.573581	+	0.819149i	$0.305554\pi$
$251$			6514.84i			1.63830i	−0.573581	+	0.819149i	$0.694446\pi$
$252$	4425.64	−	4425.64i	1.10631	−	1.10631i
$253$	790.050	+	1659.23i	0.196324	+	0.412311i
$254$	4464.02	−	4464.02i	1.10275	−	1.10275i
$255$	1978.32	+	1978.32i	0.485832	+	0.485832i
$256$	8771.26			2.14142
$257$			1733.09i			0.420651i	0.977631	+	0.210326i	$0.0674524\pi$
$257$			1733.09i			0.420651i	−0.977631	+	0.210326i	$0.932548\pi$
$258$	−1974.20	+	1974.20i	−0.476389	+	0.476389i
$259$	−7610.62			−1.82587
$260$	2040.12	−	11841.1i	0.486626	−	2.82444i
$261$		−	1064.38i		−	0.252428i
$262$	−9289.40	−	9289.40i	−2.19046	−	2.19046i
$263$		−	88.7618i		−	0.0208110i	−0.999946	−	0.0104055i	$-0.996688\pi$
$263$		−	88.7618i		−	0.0208110i	0.999946	−	0.0104055i	$-0.00331223\pi$
$264$	10192.3	+	3616.94i	2.37610	+	0.843209i
$265$	−2642.89	−	2642.89i	−0.612646	−	0.612646i
$266$	13027.6	−	13027.6i	3.00290	−	3.00290i
$267$	−1081.98	+	1081.98i	−0.248000	+	0.248000i
$268$	5395.63	−	5395.63i	1.22982	−	1.22982i
$269$	4098.06			0.928859			0.464429	−	0.885610i	$-0.346259\pi$
$269$	4098.06			0.928859			0.464429	+	0.885610i	$0.346259\pi$
$270$	9828.19			2.21528
$271$	1079.20	+	1079.20i	0.241908	+	0.241908i	0.817639	−	0.575731i	$-0.195283\pi$
$271$	1079.20	+	1079.20i	0.241908	+	0.241908i	−0.575731	+	0.817639i	$0.695283\pi$
$272$	−13414.9			−2.99043
$273$	−4950.78	−	852.976i	−1.09756	−	0.189101i
$274$		−	4503.91i		−	0.993033i
$275$	254.047	+	533.538i	0.0557076	+	0.116995i
$276$	4364.26			0.951802
$277$	−6857.45			−1.48745			−0.743726	−	0.668485i	$-0.766943\pi$
$277$	−6857.45			−1.48745			−0.743726	+	0.668485i	$0.766943\pi$
$278$	−681.254	−	681.254i	−0.146974	−	0.146974i
$279$	−1647.54	−	1647.54i	−0.353533	−	0.353533i
$280$	16551.6	−	16551.6i	3.53266	−	3.53266i
$281$	−4128.79	−	4128.79i	−0.876524	−	0.876524i	0.116649	−	0.993173i	$-0.462785\pi$
$281$	−4128.79	−	4128.79i	−0.876524	−	0.876524i	−0.993173	+	0.116649i	$0.962785\pi$
$282$			11119.7i			2.34812i
$283$	1851.89			0.388988			0.194494	−	0.980904i	$-0.437693\pi$
$283$	1851.89			0.388988			0.194494	+	0.980904i	$0.437693\pi$
$284$	2866.17	−	2866.17i	0.598859	−	0.598859i
$285$	6058.15			1.25914
$286$	2514.24	+	8953.04i	0.519826	+	1.85106i
$287$	8981.32			1.84722
$288$	−5026.07	+	5026.07i	−1.02835	+	1.02835i
$289$	−1475.94			−0.300415
$290$		−	6326.93i		−	1.28114i
$291$	941.706	+	941.706i	0.189704	+	0.189704i
$292$	−11147.7	+	11147.7i	−2.23415	+	2.23415i
$293$	−838.073	−	838.073i	−0.167102	−	0.167102i	0.618603	−	0.785704i	$-0.287699\pi$
$293$	−838.073	−	838.073i	−0.167102	−	0.167102i	−0.785704	+	0.618603i	$0.787699\pi$
$294$	−5701.94	−	5701.94i	−1.13110	−	1.13110i
$295$	738.725			0.145797
$296$	21049.7			4.13342
$297$	−5009.87	+	2385.47i	−0.978795	+	0.466058i
$298$			198.982i			0.0386803i
$299$	1361.81	+	1928.74i	0.263396	+	0.373050i
$300$	1403.36			0.270077
$301$	−2412.38	−	2412.38i	−0.461950	−	0.461950i
$302$	−4267.98			−0.813227
$303$	1119.06			0.212172
$304$	−20540.0	+	20540.0i	−3.87516	+	3.87516i
$305$	−325.874	+	325.874i	−0.0611787	+	0.0611787i
$306$	2450.74	−	2450.74i	0.457841	−	0.457841i
$307$	4038.15	+	4038.15i	0.750715	+	0.750715i	0.974613	−	0.223898i	$-0.0718783\pi$
$307$	4038.15	+	4038.15i	0.750715	+	0.750715i	−0.223898	+	0.974613i	$0.571878\pi$
$308$	−7024.67	+	19795.0i	−1.29957	+	3.66209i
$309$		−	4802.86i		−	0.884223i
$310$	−9793.34	−	9793.34i	−1.79427	−	1.79427i
$311$			6924.18i			1.26249i	0.775584	+	0.631245i	$0.217456\pi$
$311$			6924.18i			1.26249i	−0.775584	+	0.631245i	$0.782544\pi$
$312$	13693.1	+	2359.20i	2.48467	+	0.428087i
$313$	−10099.0			−1.82374			−0.911869	−	0.410481i	$-0.865361\pi$
$313$	−10099.0			−1.82374			−0.911869	+	0.410481i	$0.865361\pi$
$314$	6574.74	−	6574.74i	1.18164	−	1.18164i
$315$			3447.38i			0.616628i
$316$	−2179.82			−0.388052
$317$	3132.09	+	3132.09i	0.554938	+	0.554938i	0.927862	−	0.372924i	$-0.121645\pi$
$317$	3132.09	+	3132.09i	0.554938	+	0.554938i	−0.372924	+	0.927862i	$0.621645\pi$
$318$	4857.56	−	4857.56i	0.856599	−	0.856599i
$319$	1535.65	+	3225.12i	0.269530	+	0.566056i
$320$	−14495.1	+	14495.1i	−2.53219	+	2.53219i
$321$		−	6722.92i		−	1.16896i
$322$			7310.50i			1.26521i
$323$	5262.61	−	5262.61i	0.906562	−	0.906562i
$324$			6845.31i			1.17375i
$325$	437.900	+	620.202i	0.0747394	+	0.105854i
$326$		−	18758.9i		−	3.18699i
$327$	1556.79	−	1556.79i	0.263275	−	0.263275i
$328$	−24840.9			−4.18173
$329$	−13587.7			−2.27695
$330$	−8548.36	+	4070.34i	−1.42597	+	0.678985i
$331$	3877.85	+	3877.85i	0.643946	+	0.643946i	0.951523	−	0.307578i	$-0.0995183\pi$
$331$	3877.85	+	3877.85i	0.643946	+	0.643946i	−0.307578	+	0.951523i	$0.599518\pi$
$332$	1526.86	+	1526.86i	0.252402	+	0.252402i
$333$	−2192.13	+	2192.13i	−0.360745	+	0.360745i
$334$	667.048			0.109279
$335$			4202.96i			0.685469i
$336$	17341.6	+	17341.6i	2.81566	+	2.81566i
$337$	2822.10			0.456171			0.228085	−	0.973641i	$-0.426754\pi$
$337$	2822.10			0.456171			0.228085	+	0.973641i	$0.426754\pi$
$338$	5133.93	+	10788.3i	0.826180	+	1.73611i
$339$	−3469.24			−0.555821
$340$	10626.9	−	10626.9i	1.69508	−	1.69508i
$341$	7369.12	+	2615.09i	1.17026	+	0.415293i
$342$		−	7504.83i		−	1.18659i
$343$	494.774	−	494.774i	0.0778871	−	0.0778871i
$344$	6672.24	+	6672.24i	1.04577	+	1.04577i
$345$	−1699.78	+	1699.78i	−0.265255	+	0.265255i
$346$	5066.23	−	5066.23i	0.787174	−	0.787174i
$347$			9749.76i			1.50834i	0.656678	+	0.754171i	$0.271961\pi$
$347$			9749.76i			1.50834i	−0.656678	+	0.754171i	$0.728039\pi$
$348$	8483.00			1.30671
$349$	−3242.92	−	3242.92i	−0.497391	−	0.497391i	0.413234	−	0.910625i	$-0.364399\pi$
$349$	−3242.92	−	3242.92i	−0.497391	−	0.497391i	−0.910625	+	0.413234i	$0.864399\pi$
$350$			2350.75i			0.359008i
$351$	−5823.63	+	4111.84i	−0.885591	+	0.625281i
$352$	7977.70	−	22480.6i	1.20799	−	3.40403i
$353$	2494.72	+	2494.72i	0.376149	+	0.376149i	0.869711	−	0.493561i	$-0.164305\pi$
$353$	2494.72	+	2494.72i	0.376149	+	0.376149i	−0.493561	+	0.869711i	$0.664305\pi$
$354$			1357.76i			0.203853i
$355$			2232.62i			0.333789i
$356$	5812.05	+	5812.05i	0.865276	+	0.865276i
$357$	−4443.13	−	4443.13i	−0.658699	−	0.658699i
$358$	7478.83	+	7478.83i	1.10410	+	1.10410i
$359$	4994.47	+	4994.47i	0.734256	+	0.734256i	0.971460	−	0.237204i	$-0.0762310\pi$
$359$	4994.47	+	4994.47i	0.734256	+	0.734256i	−0.237204	+	0.971460i	$0.576231\pi$
$360$		−	9534.90i		−	1.39593i
$361$		−	9256.56i		−	1.34955i
$362$	−13414.6	−	13414.6i	−1.94767	−	1.94767i
$363$	3369.54	−	4149.67i	0.487203	−	0.600003i
$364$	−4581.93	+	26594.1i	−0.659776	+	3.82942i
$365$		−	8683.59i		−	1.24526i
$366$	−598.949	−	598.949i	−0.0855398	−	0.0855398i
$367$	6400.34			0.910341			0.455171	−	0.890404i	$-0.349578\pi$
$367$	6400.34			0.910341			0.455171	+	0.890404i	$0.349578\pi$
$368$		−	11526.1i		−	1.63272i
$369$	2586.95	−	2586.95i	0.364962	−	0.364962i
$370$	−13030.5	+	13030.5i	−1.83088	+	1.83088i
$371$	5935.70	+	5935.70i	0.830636	+	0.830636i
$372$	13130.7	−	13130.7i	1.83009	−	1.83009i
$373$		−	9655.51i		−	1.34033i	−0.742212	−	0.670165i	$-0.766223\pi$
$373$		−	9655.51i		−	1.34033i	0.742212	−	0.670165i	$-0.233777\pi$
$374$	−3889.97	+	10961.6i	−0.537823	+	1.51554i
$375$	3671.48	−	3671.48i	0.505585	−	0.505585i
$376$	37581.5			5.15457
$377$	2647.01	+	3748.98i	0.361612	+	0.512155i
$378$	−22073.3			−3.00351
$379$	−8091.70	−	8091.70i	−1.09668	−	1.09668i	−0.994796	−	0.101887i	$-0.967512\pi$
$379$	−8091.70	−	8091.70i	−1.09668	−	1.09668i	−0.101887	−	0.994796i	$-0.532488\pi$
$380$		−	32542.6i		−	4.39316i
$381$	−4662.25			−0.626915
$382$	3838.09	−	3838.09i	0.514067	−	0.514067i
$383$	−1389.18	−	1389.18i	−0.185336	−	0.185336i	0.608340	−	0.793676i	$-0.291836\pi$
$383$	−1389.18	−	1389.18i	−0.185336	−	0.185336i	−0.793676	+	0.608340i	$0.791836\pi$
$384$	−11787.3	−	11787.3i	−1.56646	−	1.56646i
$385$	−4973.75	−	10445.7i	−0.658405	−	1.38275i
$386$	−11022.4			−1.45344
$387$	−1389.70			−0.182539
$388$	5058.56	−	5058.56i	0.661880	−	0.661880i
$389$			7640.69i			0.995883i	0.867211	+	0.497941i	$0.165911\pi$
$389$			7640.69i			0.995883i	−0.867211	+	0.497941i	$0.834089\pi$
$390$	−9936.89	+	7016.05i	−1.29019	+	0.910952i
$391$			2953.14i			0.381961i
$392$	−19270.9	+	19270.9i	−2.48298	+	2.48298i
$393$			9701.90i			1.24528i
$394$			1573.48i			0.201195i
$395$	848.991	−	848.991i	0.108145	−	0.108145i
$396$	3678.31	+	7725.03i	0.466773	+	0.980296i
$397$	4117.67	−	4117.67i	0.520554	−	0.520554i	−0.397185	−	0.917739i	$-0.630013\pi$
$397$	4117.67	−	4117.67i	0.520554	−	0.520554i	0.917739	+	0.397185i	$0.130013\pi$
$398$	7264.65	+	7264.65i	0.914935	+	0.914935i
$399$	−13606.1			−1.70716
$400$		−	3706.31i		−	0.463289i
$401$	−8913.72	+	8913.72i	−1.11005	+	1.11005i	−0.116907	+	0.993143i	$0.537298\pi$
$401$	−8913.72	+	8913.72i	−1.11005	+	1.11005i	−0.993143	+	0.116907i	$0.962702\pi$
$402$	−7724.94			−0.958420
$403$	9900.24	+	1705.73i	1.22374	+	0.210839i
$404$		−	6011.23i		−	0.740272i
$405$	−2666.10	−	2666.10i	−0.327110	−	0.327110i
$406$			14209.7i			1.73699i
$407$	3479.50	−	9804.96i	0.423765	−	1.19414i
$408$	12289.0	+	12289.0i	1.49117	+	1.49117i
$409$	1950.24	−	1950.24i	0.235778	−	0.235778i	−0.579321	−	0.815099i	$-0.696682\pi$
$409$	1950.24	−	1950.24i	0.235778	−	0.235778i	0.815099	+	0.579321i	$0.196682\pi$
$410$	15377.4	−	15377.4i	1.85228	−	1.85228i
$411$	−2351.95	+	2351.95i	−0.282271	+	0.282271i
$412$	−25799.5			−3.08507
$413$	−1659.11			−0.197675
$414$	2105.69	+	2105.69i	0.249973	+	0.249973i
$415$	−1189.36			−0.140683
$416$	5203.56	−	30202.1i	0.613283	−	3.55957i
$417$			711.505i			0.0835553i
$418$	10827.7	+	22739.9i	1.26699	+	2.66087i
$419$	3708.19			0.432356			0.216178	−	0.976354i	$-0.430641\pi$
$419$	3708.19			0.432356			0.216178	+	0.976354i	$0.430641\pi$
$420$	−27475.1			−3.19202
$421$	−10657.4	−	10657.4i	−1.23376	−	1.23376i	−0.962509	−	0.271249i	$-0.912563\pi$
$421$	−10657.4	−	10657.4i	−1.23376	−	1.23376i	−0.271249	−	0.962509i	$-0.587437\pi$
$422$	−13962.4	−	13962.4i	−1.61062	−	1.61062i
$423$	−3913.76	+	3913.76i	−0.449867	+	0.449867i
$424$	−16417.2	−	16417.2i	−1.88040	−	1.88040i
$425$			949.605i			0.108383i
$426$	−4103.50			−0.466703
$427$	731.886	−	731.886i	0.0829471	−	0.0829471i
$428$	−36113.5			−4.07853
$429$	3362.36	−	5988.25i	0.378406	−	0.673929i
$430$	−8260.69			−0.926432
$431$	10387.5	−	10387.5i	1.16090	−	1.16090i	0.176618	−	0.984279i	$-0.443484\pi$
$431$	10387.5	−	10387.5i	1.16090	−	1.16090i	0.984279	−	0.176618i	$-0.0565157\pi$
$432$	34801.9			3.87595
$433$			9710.50i			1.07773i	0.842392	+	0.538865i	$0.181147\pi$
$433$			9710.50i			1.07773i	−0.842392	+	0.538865i	$0.818853\pi$
$434$	21995.0	+	21995.0i	2.43271	+	2.43271i
$435$	−3303.94	+	3303.94i	−0.364165	+	0.364165i
$436$	−8362.63	−	8362.63i	−0.918572	−	0.918572i
$437$	4521.66	+	4521.66i	0.494967	+	0.494967i
$438$	15960.2			1.74112
$439$	14377.4			1.56309			0.781547	−	0.623847i	$-0.214431\pi$
$439$	14377.4			1.56309			0.781547	+	0.623847i	$0.214431\pi$
$440$	13756.6	+	28891.0i	1.49050	+	3.13028i
$441$		−	4013.77i		−	0.433406i
$442$	−2537.29	+	14726.7i	−0.273046	+	1.58479i
$443$	−15025.2			−1.61144			−0.805719	−	0.592298i	$-0.798221\pi$
$443$	−15025.2			−1.61144			−0.805719	+	0.592298i	$0.798221\pi$
$444$	−17471.0	−	17471.0i	−1.86743	−	1.86743i
$445$	−4527.33			−0.482283
$446$	−21193.8			−2.25013
$447$	103.909	−	103.909i	0.0109949	−	0.0109949i
$448$	32554.8	−	32554.8i	3.43319	−	3.43319i
$449$	6443.19	−	6443.19i	0.677222	−	0.677222i	−0.282148	−	0.959371i	$-0.591047\pi$
$449$	6443.19	−	6443.19i	0.677222	−	0.677222i	0.959371	+	0.282148i	$0.0910470\pi$
$450$	677.100	+	677.100i	0.0709306	+	0.0709306i
$451$	−4106.17	+	11570.9i	−0.428719	+	1.20810i
$452$			18635.7i			1.93927i
$453$	2228.75	+	2228.75i	0.231161	+	0.231161i
$454$		−	8203.06i		−	0.847993i
$455$	−8573.26	−	12142.4i	−0.883342	−	1.25108i
$456$	37632.3			3.86467
$457$	−981.369	+	981.369i	−0.100452	+	0.100452i	−0.755547	−	0.655095i	$-0.772629\pi$
$457$	−981.369	+	981.369i	−0.100452	+	0.100452i	0.655095	+	0.755547i	$0.272629\pi$
$458$		−	21063.0i		−	2.14893i
$459$	−8916.70			−0.906745
$460$	9130.71	+	9130.71i	0.925482	+	0.925482i
$461$	−2592.57	+	2592.57i	−0.261926	+	0.261926i	−0.825836	−	0.563910i	$-0.809296\pi$
$461$	−2592.57	+	2592.57i	−0.261926	+	0.261926i	0.563910	+	0.825836i	$0.309296\pi$
$462$	19198.9	−	9141.64i	1.93336	−	0.920580i
$463$	7330.81	−	7330.81i	0.735835	−	0.735835i	−0.235934	−	0.971769i	$-0.575815\pi$
$463$	7330.81	−	7330.81i	0.735835	−	0.735835i	0.971769	+	0.235934i	$0.0758149\pi$
$464$		−	22403.8i		−	2.24153i
$465$			10228.2i			1.02005i
$466$	11194.9	−	11194.9i	1.11286	−	1.11286i
$467$		−	14490.7i		−	1.43586i	−0.696114	−	0.717931i	$-0.745089\pi$
$467$		−	14490.7i		−	1.43586i	0.696114	−	0.717931i	$-0.254911\pi$
$468$	6340.30	+	8979.83i	0.626241	+	0.886950i
$469$		−	9439.48i		−	0.929371i
$470$	−23264.2	+	23264.2i	−2.28319	+	2.28319i
$471$	−6866.69			−0.671763
$472$	4588.84			0.447497
$473$	4210.84	−	2005.01i	0.409333	−	0.194906i
$474$	1560.42	+	1560.42i	0.151208	+	0.151208i
$475$	1453.98	+	1453.98i	0.140448	+	0.140448i
$476$	−23867.2	+	23867.2i	−2.29821	+	2.29821i
$477$	3419.39			0.328225
$478$		−	5040.93i		−	0.482357i
$479$	2759.57	+	2759.57i	0.263232	+	0.263232i	0.826366	−	0.563134i	$-0.190404\pi$
$479$	2759.57	+	2759.57i	0.263232	+	0.263232i	−0.563134	+	0.826366i	$0.690404\pi$
$480$	31202.7			2.96708
$481$	2269.55	−	13172.7i	0.215140	−	1.24870i
$482$	−16415.6			−1.55126
$483$	3817.56	−	3817.56i	0.359638	−	0.359638i
$484$	−22290.8	−	18100.1i	−2.09342	−	1.69986i
$485$			3940.40i			0.368916i
$486$	−10890.8	+	10890.8i	−1.01649	+	1.01649i
$487$	6141.09	+	6141.09i	0.571415	+	0.571415i	0.932524	−	0.361109i	$-0.117602\pi$
$487$	6141.09	+	6141.09i	0.571415	+	0.571415i	−0.361109	+	0.932524i	$0.617602\pi$
$488$	−2024.28	+	2024.28i	−0.187776	+	0.187776i
$489$	−9795.96	+	9795.96i	−0.905907	+	0.905907i
$490$		−	23858.7i		−	2.19965i
$491$	−6400.37			−0.588278			−0.294139	−	0.955763i	$-0.595033\pi$
$491$	−6400.37			−0.588278			−0.294139	+	0.955763i	$0.595033\pi$
$492$	20617.6	+	20617.6i	1.88926	+	1.88926i
$493$			5740.15i			0.524388i
$494$	18663.7	+	26433.6i	1.69984	+	2.40749i
$495$	−4441.35	−	1576.11i	−0.403280	−	0.143113i
$496$	−34678.5	−	34678.5i	−3.13934	−	3.13934i
$497$		−	5014.27i		−	0.452557i
$498$		−	2186.01i		−	0.196702i
$499$	−2222.58	−	2222.58i	−0.199391	−	0.199391i	0.600348	−	0.799739i	$-0.295029\pi$
$499$	−2222.58	−	2222.58i	−0.199391	−	0.199391i	−0.799739	+	0.600348i	$0.795029\pi$
$500$	−19722.1	−	19722.1i	−1.76400	−	1.76400i
$501$	−348.335	−	348.335i	−0.0310628	−	0.0310628i
$502$	−25051.7	−	25051.7i	−2.22732	−	2.22732i
$503$		−	2989.89i		−	0.265035i	−0.991181	−	0.132517i	$-0.957694\pi$
$503$		−	2989.89i		−	0.265035i	0.991181	−	0.132517i	$-0.0423061\pi$
$504$			21414.6i			1.89262i
$505$	2341.24	+	2341.24i	0.206305	+	0.206305i
$506$	−9418.30	−	3342.29i	−0.827460	−	0.293642i
$507$	2952.73	−	8314.63i	0.258649	−	0.728335i
$508$			25044.2i			2.18732i
$509$	4900.61	+	4900.61i	0.426750	+	0.426750i	0.887520	−	0.460770i	$-0.152427\pi$
$509$	4900.61	+	4900.61i	0.426750	+	0.426750i	−0.460770	+	0.887520i	$0.652427\pi$
$510$	−15214.6			−1.32101
$511$			19502.6i			1.68835i
$512$	−10248.3	+	10248.3i	−0.884597	+	0.884597i
$513$	−13652.7	+	13652.7i	−1.17501	+	1.17501i
$514$	−6664.33	−	6664.33i	−0.571889	−	0.571889i
$515$	10048.3	−	10048.3i	0.859772	−	0.859772i
$516$		−	11075.7i		−	0.944927i
$517$	6212.18	−	17505.4i	0.528455	−	1.48915i
$518$	29265.4	−	29265.4i	2.48233	−	2.48233i
$519$	−5291.20			−0.447511
$520$	23712.2	+	33583.9i	1.99971	+	2.83221i
$521$	9820.91			0.825838			0.412919	−	0.910768i	$-0.364509\pi$
$521$	9820.91			0.825838			0.412919	+	0.910768i	$0.364509\pi$
$522$	4092.92	+	4092.92i	0.343184	+	0.343184i
$523$			12527.9i			1.04743i	0.851893	+	0.523715i	$0.175454\pi$
$523$			12527.9i			1.04743i	−0.851893	+	0.523715i	$0.824546\pi$
$524$	52115.7			4.34482
$525$	1227.57	−	1227.57i	0.102048	−	0.102048i
$526$	341.319	+	341.319i	0.0282932	+	0.0282932i
$527$	8885.08	+	8885.08i	0.734422	+	0.734422i
$528$	−30270.0	+	14413.2i	−2.49495	+	1.18798i
$529$	9629.65			0.791456
$530$	20325.6			1.66582
$531$	−477.884	+	477.884i	−0.0390554	+	0.0390554i
$532$			73087.8i			5.95631i
$533$	−2678.30	+	15545.2i	−0.217655	+	1.26330i
$534$		−	8321.13i		−	0.674327i
$535$	14065.4	−	14065.4i	1.13664	−	1.13664i
$536$			26108.1i			2.10391i
$537$		−	7810.94i		−	0.627685i
$538$	−15758.4	+	15758.4i	−1.26281	+	1.26281i
$539$	5790.93	+	12161.8i	0.462770	+	0.971889i
$540$	−27569.2	+	27569.2i	−2.19702	+	2.19702i
$541$	6625.62	+	6625.62i	0.526539	+	0.526539i	0.919539	−	0.393000i	$-0.128563\pi$
$541$	6625.62	+	6625.62i	0.526539	+	0.526539i	−0.393000	+	0.919539i	$0.628563\pi$
$542$	−8299.81			−0.657763
$543$			14010.3i			1.10726i
$544$	27105.2	−	27105.2i	2.13626	−	2.13626i
$545$	6514.12			0.511989
$546$	22317.4	−	15757.4i	1.74926	−	1.23508i
$547$		−	24560.3i		−	1.91979i	−0.280365	−	0.959893i	$-0.590456\pi$
$547$		−	24560.3i		−	1.91979i	0.280365	−	0.959893i	$-0.409544\pi$
$548$	12634.0	+	12634.0i	0.984849	+	0.984849i
$549$		−	421.619i		−	0.0327764i
$550$	−3028.53	−	1074.74i	−0.234794	−	0.0833217i
$551$	8788.96	+	8788.96i	0.679532	+	0.679532i
$552$	−10558.8	+	10558.8i	−0.814150	+	0.814150i
$553$	−1906.76	+	1906.76i	−0.146625	+	0.146625i
$554$	26369.2	−	26369.2i	2.02224	−	2.02224i
$555$	13609.1			1.04086
$556$	3821.99			0.291526
$557$	−11826.4	−	11826.4i	−0.899642	−	0.899642i	0.0957623	−	0.995404i	$-0.469471\pi$
$557$	−11826.4	−	11826.4i	−0.899642	−	0.899642i	−0.995404	+	0.0957623i	$0.969471\pi$
$558$	12670.7			0.961280
$559$	4894.82	−	3456.04i	0.370356	−	0.261494i
$560$			72562.6i			5.47559i
$561$	7755.56	−	3692.85i	0.583672	−	0.277918i
$562$	31753.2			2.38332
$563$	−18332.3			−1.37232			−0.686160	−	0.727451i	$-0.740705\pi$
$563$	−18332.3			−1.37232			−0.686160	+	0.727451i	$0.740705\pi$
$564$	−31192.1	−	31192.1i	−2.32877	−	2.32877i
$565$	−7258.21	−	7258.21i	−0.540451	−	0.540451i
$566$	−7121.16	+	7121.16i	−0.528842	+	0.528842i
$567$	5987.82	+	5987.82i	0.443501	+	0.443501i
$568$			13868.7i			1.02450i
$569$	−5787.77			−0.426425			−0.213213	−	0.977006i	$-0.568393\pi$
$569$	−5787.77			−0.426425			−0.213213	+	0.977006i	$0.568393\pi$
$570$	−23295.6	+	23295.6i	−1.71184	+	1.71184i
$571$	−19371.3			−1.41973			−0.709864	−	0.704339i	$-0.751244\pi$
$571$	−19371.3			−1.41973			−0.709864	+	0.704339i	$0.751244\pi$
$572$	−32167.1	−	18061.6i	−2.35135	−	1.32027i
$573$	−4008.52			−0.292249
$574$	−34536.2	+	34536.2i	−2.51135	+	2.51135i
$575$	−815.905			−0.0591750
$576$		−	18753.9i		−	1.35662i
$577$	−5640.02	−	5640.02i	−0.406927	−	0.406927i	0.473738	−	0.880666i	$-0.342904\pi$
$577$	−5640.02	−	5640.02i	−0.406927	−	0.406927i	−0.880666	+	0.473738i	$0.842904\pi$
$578$	5675.49	−	5675.49i	0.408424	−	0.408424i
$579$	5755.94	+	5755.94i	0.413141	+	0.413141i
$580$	17747.8	+	17747.8i	1.27058	+	1.27058i
$581$	2671.20			0.190740
$582$	−7242.36			−0.515817
$583$	−10360.9	+	4933.37i	−0.736025	+	0.350462i
$584$		−	53941.1i		−	3.82208i
$585$	−5966.85	−	1028.04i	−0.421708	−	0.0726566i
$586$	6445.35			0.454360
$587$	7627.59	+	7627.59i	0.536327	+	0.536327i	0.922448	−	0.386121i	$-0.126185\pi$
$587$	7627.59	+	7627.59i	0.536327	+	0.536327i	−0.386121	+	0.922448i	$0.626185\pi$
$588$	31989.2			2.24356
$589$	27208.5			1.90341
$590$	−2840.65	+	2840.65i	−0.198216	+	0.198216i
$591$	821.677	−	821.677i	0.0571899	−	0.0571899i
$592$	−46141.4	+	46141.4i	−3.20338	+	3.20338i
$593$	−14504.4	−	14504.4i	−1.00443	−	1.00443i	−0.999990	−	0.00443858i	$-0.998587\pi$
$593$	−14504.4	−	14504.4i	−1.00443	−	1.00443i	−0.00443858	−	0.999990i	$-0.501413\pi$
$594$	10091.7	−	28437.6i	0.697082	−	1.96432i
$595$		−	18591.5i		−	1.28097i
$596$	−558.169	−	558.169i	−0.0383615	−	0.0383615i
$597$		−	7587.25i		−	0.520143i
$598$	−12653.3	−	2180.05i	−0.865269	−	0.149078i
$599$	4850.42			0.330856			0.165428	−	0.986222i	$-0.447099\pi$
$599$	4850.42			0.330856			0.165428	+	0.986222i	$0.447099\pi$
$600$	−3395.25	+	3395.25i	−0.231018	+	0.231018i
$601$			24079.1i			1.63429i	0.576435	+	0.817143i	$0.304443\pi$
$601$			24079.1i			1.63429i	−0.576435	+	0.817143i	$0.695557\pi$
$602$	18552.8			1.25607
$603$	−2718.91	−	2718.91i	−0.183620	−	0.183620i
$604$	11972.2	−	11972.2i	0.806525	−	0.806525i
$605$	15731.4	−	1632.17i	1.05714	−	0.109681i
$606$	−4303.15	+	4303.15i	−0.288455	+	0.288455i
$607$			12549.1i			0.839132i	0.907725	+	0.419566i	$0.137818\pi$
$607$			12549.1i			0.839132i	−0.907725	+	0.419566i	$0.862182\pi$
$608$		−	83003.6i		−	5.53658i
$609$	7420.37	−	7420.37i	0.493741	−	0.493741i
$610$		−	2506.19i		−	0.166349i
$611$	4051.98	−	23518.2i	0.268290	−	1.55719i
$612$			13749.2i			0.908136i
$613$	9941.58	−	9941.58i	0.655035	−	0.655035i	−0.299166	−	0.954201i	$-0.596708\pi$
$613$	9941.58	−	9941.58i	0.655035	−	0.655035i	0.954201	+	0.299166i	$0.0967084\pi$
$614$	−31056.1			−2.04124
$615$	−16060.2			−1.05302
$616$	−30896.2	−	64886.8i	−2.02085	−	4.24409i
$617$	14605.7	+	14605.7i	0.953001	+	0.953001i	0.998944	−	0.0459429i	$-0.0146292\pi$
$617$	14605.7	+	14605.7i	0.953001	+	0.953001i	−0.0459429	+	0.998944i	$0.514629\pi$
$618$	18468.6	+	18468.6i	1.20213	+	1.20213i
$619$	−19868.5	+	19868.5i	−1.29012	+	1.29012i	−0.355406	+	0.934712i	$0.615658\pi$
$619$	−19868.5	+	19868.5i	−1.29012	+	1.29012i	−0.934712	+	0.355406i	$0.884342\pi$
$620$	54943.0			3.55897
$621$		−	7661.27i		−	0.495067i
$622$	−26625.8	−	26625.8i	−1.71640	−	1.71640i
$623$	10168.0			0.653888
$624$	−35186.8	+	24844.0i	−2.25737	+	1.59384i
$625$	17387.3			1.11279
$626$	38834.1	−	38834.1i	2.47943	−	2.47943i
$627$	6220.57	−	17529.1i	0.396213	−	1.11650i
$628$			36885.8i			2.34380i
$629$	11822.0	−	11822.0i	0.749404	−	0.749404i
$630$	−13256.3	−	13256.3i	−0.838326	−	0.838326i
$631$	507.116	−	507.116i	0.0319936	−	0.0319936i	−0.690929	−	0.722923i	$-0.742798\pi$
$631$	507.116	−	507.116i	0.0319936	−	0.0319936i	0.722923	+	0.690929i	$0.242798\pi$
$632$	5273.79	−	5273.79i	0.331931	−	0.331931i
$633$			14582.4i			0.915640i
$634$	−24087.9			−1.50891
$635$	−9754.18	−	9754.18i	−0.609579	−	0.609579i
$636$			27252.1i			1.69908i
$637$	9981.81	+	14137.3i	0.620869	+	0.879343i
$638$	−18306.8	−	6496.55i	−1.13601	−	0.403136i
$639$	−1444.29	−	1444.29i	−0.0894137	−	0.0894137i
$640$		−	49322.0i		−	3.04629i
$641$		−	14565.3i		−	0.897495i	−0.893659	−	0.448748i	$-0.851870\pi$
$641$		−	14565.3i		−	0.897495i	0.893659	−	0.448748i	$-0.148130\pi$
$642$	25851.9	+	25851.9i	1.58924	+	1.58924i
$643$	18123.0	+	18123.0i	1.11151	+	1.11151i	0.992947	+	0.118563i	$0.0378286\pi$
$643$	18123.0	+	18123.0i	1.11151	+	1.11151i	0.118563	+	0.992947i	$0.462171\pi$
$644$	−20506.8	−	20506.8i	−1.25478	−	1.25478i
$645$	4313.76	+	4313.76i	0.263340	+	0.263340i
$646$			40473.0i			2.46500i
$647$			11894.6i			0.722761i	0.932418	+	0.361380i	$0.117694\pi$
$647$			11894.6i			0.722761i	−0.932418	+	0.361380i	$0.882306\pi$
$648$	−16561.4	−	16561.4i	−1.00400	−	1.00400i
$649$	758.530	−	2137.48i	0.0458781	−	0.129281i
$650$	−4068.76	−	701.012i	−0.245523	−	0.0423014i
$651$		−	22971.7i		−	1.38300i
$652$	52621.0	+	52621.0i	3.16073	+	3.16073i
$653$	8226.62			0.493005			0.246503	−	0.969142i	$-0.420719\pi$
$653$	8226.62			0.493005			0.246503	+	0.969142i	$0.420719\pi$
$654$			11972.8i			0.715861i
$655$	−20297.9	+	20297.9i	−1.21085	+	1.21085i
$656$	54451.7	−	54451.7i	3.24083	−	3.24083i
$657$	5617.46	+	5617.46i	0.333574	+	0.333574i
$658$	52249.5	−	52249.5i	3.09559	−	3.09559i
$659$			24391.9i			1.44184i	0.693019	+	0.720920i	$0.256280\pi$
$659$			24391.9i			1.44184i	−0.693019	+	0.720920i	$0.743720\pi$
$660$	12561.4	−	35397.0i	0.740834	−	2.08761i
$661$	−3644.43	+	3644.43i	−0.214451	+	0.214451i	−0.806155	−	0.591704i	$-0.798455\pi$
$661$	−3644.43	+	3644.43i	−0.214451	+	0.214451i	0.591704	+	0.806155i	$0.298455\pi$
$662$	−29823.3			−1.75093
$663$	9015.32	−	6365.36i	0.528093	−	0.372866i
$664$	−7388.10			−0.431798
$665$	−28466.1	−	28466.1i	−1.65995	−	1.65995i
$666$		−	16859.0i		−	0.980890i
$667$	−4931.97			−0.286307
$668$	−1871.15	+	1871.15i	−0.108379	+	0.108379i
$669$	11067.5	+	11067.5i	0.639601	+	0.639601i
$670$	−16161.8	−	16161.8i	−0.931917	−	0.931917i
$671$	608.297	+	1277.52i	0.0349971	+	0.0734993i
$672$	−70078.5			−4.02282
$673$	14606.1			0.836589			0.418295	−	0.908311i	$-0.362628\pi$
$673$	14606.1			0.836589			0.418295	+	0.908311i	$0.362628\pi$
$674$	−10851.9	+	10851.9i	−0.620179	+	0.620179i
$675$		−	2463.54i		−	0.140477i
$676$	−44663.7	−	15861.2i	−2.54118	−	0.902433i
$677$		−	10202.1i		−	0.579171i	−0.957152	−	0.289586i	$-0.906482\pi$
$677$		−	10202.1i		−	0.579171i	0.957152	−	0.289586i	$-0.0935175\pi$
$678$	13340.4	−	13340.4i	0.755657	−	0.755657i
$679$		−	8849.79i		−	0.500183i
$680$			51421.0i			2.89986i
$681$	−4283.66	+	4283.66i	−0.241043	+	0.241043i
$682$	−38392.6	+	18280.8i	−2.15562	+	1.02641i
$683$	11470.6	−	11470.6i	0.642621	−	0.642621i	−0.308578	−	0.951199i	$-0.599853\pi$
$683$	11470.6	−	11470.6i	0.642621	−	0.642621i	0.951199	+	0.308578i	$0.0998532\pi$
$684$	21051.9	+	21051.9i	1.17681	+	1.17681i
$685$	−9841.33			−0.548931
$686$			3805.14i			0.211780i
$687$	−10999.2	+	10999.2i	−0.610836	+	0.610836i
$688$	−29251.3			−1.62093
$689$	−12043.8	+	8503.65i	−0.665939	+	0.470194i
$690$		−	13072.5i		−	0.721247i
$691$	−7815.48	−	7815.48i	−0.430267	−	0.430267i	0.458452	−	0.888719i	$-0.348404\pi$
$691$	−7815.48	−	7815.48i	−0.430267	−	0.430267i	−0.888719	+	0.458452i	$0.848404\pi$
$692$			28422.7i			1.56137i
$693$	9974.89	+	3539.80i	0.546775	+	0.194035i
$694$	−37491.1	−	37491.1i	−2.05064	−	2.05064i
$695$	−1488.58	+	1488.58i	−0.0812448	+	0.0812448i
$696$	−20523.5	+	20523.5i	−1.11773	+	1.11773i
$697$	−13951.2	+	13951.2i	−0.758164	+	0.758164i
$698$	24940.2			1.35244
$699$	−11692.0			−0.632665
$700$	−6594.12	−	6594.12i	−0.356049	−	0.356049i
$701$	2554.70			0.137646			0.0688229	−	0.997629i	$-0.478076\pi$
$701$	2554.70			0.137646			0.0688229	+	0.997629i	$0.478076\pi$
$702$	6582.43	−	38205.3i	0.353900	−	2.05408i
$703$		−	36202.3i		−	1.94224i
$704$	27057.5	+	56824.9i	1.44853	+	3.04214i
$705$	24297.3			1.29800
$706$	−19186.1			−1.02277
$707$	−5258.23	−	5258.23i	−0.279712	−	0.279712i
$708$	−3808.67	−	3808.67i	−0.202173	−	0.202173i
$709$	−12242.0	+	12242.0i	−0.648458	+	0.648458i	−0.952620	−	0.304162i	$-0.901624\pi$
$709$	−12242.0	+	12242.0i	−0.648458	+	0.648458i	0.304162	+	0.952620i	$0.401624\pi$
$710$	−8585.18	−	8585.18i	−0.453797	−	0.453797i
$711$			1098.43i			0.0579387i
$712$	−28123.1			−1.48028
$713$	−7634.11	+	7634.11i	−0.400981	+	0.400981i
$714$	34170.7			1.79105
$715$	19563.0	−	5493.78i	1.02324	−	0.287351i
$716$	−41958.0			−2.19001
$717$	−2632.39	+	2632.39i	−0.137111	+	0.137111i
$718$	−38410.8			−1.99649
$719$		−	14413.3i		−	0.747600i	−0.927509	−	0.373800i	$-0.878055\pi$
$719$		−	14413.3i		−	0.747600i	0.927509	−	0.373800i	$-0.121945\pi$
$720$	20900.7	+	20900.7i	1.08184	+	1.08184i
$721$	−22567.7	+	22567.7i	−1.16569	+	1.16569i
$722$	35594.6	+	35594.6i	1.83476	+	1.83476i
$723$	8572.26	+	8572.26i	0.440949	+	0.440949i
$724$	75259.2			3.86324
$725$	−1585.91			−0.0812404
$726$	2999.88	+	28913.9i	0.153355	+	1.47809i
$727$		−	21440.6i		−	1.09379i	−0.837200	−	0.546897i	$-0.815809\pi$
$727$		−	21440.6i		−	1.09379i	0.837200	−	0.546897i	$-0.184191\pi$
$728$	−53255.7	−	75426.5i	−2.71125	−	3.83996i
$729$	19941.6			1.01314
$730$	33391.4	+	33391.4i	1.69297	+	1.69297i
$731$	7494.57			0.379202
$732$	3360.25			0.169670
$733$	13608.8	−	13608.8i	0.685748	−	0.685748i	−0.275541	−	0.961289i	$-0.588857\pi$
$733$	13608.8	−	13608.8i	0.685748	−	0.685748i	0.961289	+	0.275541i	$0.0888571\pi$
$734$	−24611.5	+	24611.5i	−1.23764	+	1.23764i
$735$	−12459.1	+	12459.1i	−0.625253	+	0.625253i
$736$	23288.9	+	23288.9i	1.16636	+	1.16636i
$737$	12161.1	+	4315.64i	0.607817	+	0.215697i
$738$			19895.4i			0.992356i
$739$	−125.607	−	125.607i	−0.00625240	−	0.00625240i	0.703974	−	0.710226i	$-0.251407\pi$
$739$	−125.607	−	125.607i	−0.00625240	−	0.00625240i	−0.710226	+	0.703974i	$0.751407\pi$
$740$		−	73104.2i		−	3.63157i
$741$	4057.45	−	23549.9i	0.201153	−	1.16751i
$742$	−45649.5			−2.25855
$743$	−1275.37	+	1275.37i	−0.0629726	+	0.0629726i	−0.737892	−	0.674919i	$-0.764178\pi$
$743$	−1275.37	+	1275.37i	−0.0629726	+	0.0629726i	0.674919	+	0.737892i	$0.264178\pi$
$744$			63536.1i			3.13084i
$745$	434.789			0.0213818
$746$	37128.7	+	37128.7i	1.82222	+	1.82222i
$747$	769.401	−	769.401i	0.0376853	−	0.0376853i
$748$	−19836.9	−	41660.5i	−0.969663	−	2.03644i
$749$	−31589.7	+	31589.7i	−1.54107	+	1.54107i
$750$			28236.2i			1.37472i
$751$		−	6766.80i		−	0.328794i	−0.986394	−	0.164397i	$-0.947432\pi$
$751$		−	6766.80i		−	0.328794i	0.986394	−	0.164397i	$-0.0525678\pi$
$752$	−82379.3	+	82379.3i	−3.99477	+	3.99477i
$753$			26164.2i			1.26624i
$754$	−24594.7	−	4237.46i	−1.18791	−	0.204667i
$755$			9325.80i			0.449537i
$756$	61918.2	−	61918.2i	2.97876	−	2.97876i
$757$	−39001.9			−1.87259			−0.936293	−	0.351220i	$-0.885767\pi$
$757$	−39001.9			−1.87259			−0.936293	+	0.351220i	$0.885767\pi$
$758$	62230.7			2.98195
$759$	3172.91	+	6663.62i	0.151738	+	0.318675i
$760$	78732.6	+	78732.6i	3.75781	+	3.75781i
$761$	7513.94	+	7513.94i	0.357924	+	0.357924i	0.863047	−	0.505123i	$-0.168553\pi$
$761$	7513.94	+	7513.94i	0.357924	+	0.357924i	−0.505123	+	0.863047i	$0.668553\pi$
$762$	17927.9	−	17927.9i	0.852311	−	0.852311i
$763$	−14630.1			−0.694164
$764$			21532.6i			1.01966i
$765$	−5355.02	−	5355.02i	−0.253086	−	0.253086i
$766$	10683.7			0.503941
$767$	494.761	−	2871.65i	0.0232918	−	0.135188i
$768$	35226.2			1.65510
$769$	−12904.4	+	12904.4i	−0.605130	+	0.605130i	−0.941669	−	0.336540i	$-0.890743\pi$
$769$	−12904.4	+	12904.4i	−0.605130	+	0.605130i	0.336540	+	0.941669i	$0.390743\pi$
$770$	59292.9	+	21041.3i	2.77502	+	0.984776i
$771$			6960.26i			0.325120i
$772$	30919.2	−	30919.2i	1.44146	−	1.44146i
$773$	−17305.0	−	17305.0i	−0.805197	−	0.805197i	0.178705	−	0.983903i	$-0.442809\pi$
$773$	−17305.0	−	17305.0i	−0.805197	−	0.805197i	−0.983903	+	0.178705i	$0.942809\pi$
$774$	5343.88	−	5343.88i	0.248168	−	0.248168i
$775$	−2454.81	+	2454.81i	−0.113780	+	0.113780i
$776$			24477.1i			1.13232i
$777$	−30565.0			−1.41121
$778$	−29381.0	−	29381.0i	−1.35393	−	1.35393i
$779$			42722.5i			1.96494i
$780$	8193.31	−	47555.0i	0.376112	−	2.18300i
$781$	6460.02	+	2292.48i	0.295977	+	0.105034i
$782$	−11355.8	−	11355.8i	−0.519288	−	0.519288i
$783$		−	14891.6i		−	0.679669i
$784$		−	84484.4i		−	3.84860i
$785$	−14366.2	−	14366.2i	−0.653187	−	0.653187i
$786$	−37307.1	−	37307.1i	−1.69300	−	1.69300i
$787$	15466.9	+	15466.9i	0.700554	+	0.700554i	0.964529	−	0.263975i	$-0.0850337\pi$
$787$	15466.9	+	15466.9i	0.700554	+	0.700554i	−0.263975	+	0.964529i	$0.585034\pi$
$788$	−4413.80	−	4413.80i	−0.199537	−	0.199537i
$789$		−	356.476i		−	0.0160848i
$790$			6529.31i			0.294054i
$791$	16301.3	+	16301.3i	0.732753	+	0.732753i
$792$	−27588.9	−	9790.52i	−1.23779	−	0.439256i
$793$	1048.52	+	1485.03i	0.0469534	+	0.0665005i
$794$			31667.7i			1.41542i
$795$	−10614.1	−	10614.1i	−0.473513	−	0.473513i
$796$	−40756.4			−1.81479
$797$		−	21260.5i		−	0.944899i	−0.881358	−	0.472450i	$-0.843370\pi$
$797$		−	21260.5i		−	0.944899i	0.881358	−	0.472450i	$-0.156630\pi$
$798$	52320.0	−	52320.0i	2.32094	−	2.32094i
$799$	21106.6	−	21106.6i	0.934542	−	0.934542i
$800$	7488.74	+	7488.74i	0.330959	+	0.330959i
$801$	2928.75	−	2928.75i	0.129191	−	0.129191i
$802$		−	68552.6i		−	3.01830i
$803$	−25125.7	−	8916.40i	−1.10419	−	0.391847i
$804$	21669.4	−	21669.4i	0.950522	−	0.950522i
$805$	15973.9			0.699386
$806$	−44628.9	+	31510.7i	−1.95035	+	1.37707i
$807$	16458.2			0.717913
$808$	14543.4	+	14543.4i	0.633212	+	0.633212i
$809$			36617.5i			1.59135i	0.605723	+	0.795676i	$0.292884\pi$
$809$			36617.5i			1.59135i	−0.605723	+	0.795676i	$0.707116\pi$
$810$	20504.1			0.889432
$811$	−3310.12	+	3310.12i	−0.143322	+	0.143322i	−0.775127	−	0.631805i	$-0.782314\pi$
$811$	−3310.12	+	3310.12i	−0.143322	+	0.143322i	0.631805	+	0.775127i	$0.282314\pi$
$812$	−39860.0	−	39860.0i	−1.72267	−	1.72267i
$813$	4334.19	+	4334.19i	0.186970	+	0.186970i
$814$	24323.5	+	51083.2i	1.04735	+	2.19959i
$815$	−40989.4			−1.76171
$816$	−53875.4			−2.31129
$817$	11475.2	−	11475.2i	0.491392	−	0.491392i
$818$			14998.7i			0.641095i
$819$	13401.0	+	2308.88i	0.571759	+	0.0985090i
$820$			86270.6i			3.67403i
$821$	−27279.2	+	27279.2i	−1.15962	+	1.15962i	−0.175067	+	0.984557i	$0.556014\pi$
$821$	−27279.2	+	27279.2i	−1.15962	+	1.15962i	−0.984557	+	0.175067i	$0.943986\pi$
$822$		−	18088.1i		−	0.767513i
$823$		−	14244.9i		−	0.603338i	−0.953413	−	0.301669i	$-0.902456\pi$
$823$		−	14244.9i		−	0.603338i	0.953413	−	0.301669i	$-0.0975438\pi$
$824$	62418.6	−	62418.6i	2.63890	−	2.63890i
$825$	1020.28	+	2142.74i	0.0430563	+	0.0904249i
$826$	6379.85	−	6379.85i	0.268745	−	0.268745i
$827$	−21153.0	−	21153.0i	−0.889434	−	0.889434i	0.105034	−	0.994469i	$-0.466505\pi$
$827$	−21153.0	−	21153.0i	−0.889434	−	0.889434i	−0.994469	+	0.105034i	$0.966505\pi$
$828$	−11813.4			−0.495826
$829$			18683.0i			0.782735i	0.920235	+	0.391367i	$0.127998\pi$
$829$			18683.0i			0.782735i	−0.920235	+	0.391367i	$0.872002\pi$
$830$	4573.48	−	4573.48i	0.191263	−	0.191263i
$831$	−27540.2			−1.14965
$832$	46638.9	+	66055.1i	1.94341	+	2.75246i
$833$			21646.0i			0.900347i
$834$	−2735.98	−	2735.98i	−0.113596	−	0.113596i
$835$		−	1457.54i		−	0.0604076i
$836$	−94161.0	−	33415.0i	−3.89549	−	1.38240i
$837$	−23050.4	−	23050.4i	−0.951897	−	0.951897i
$838$	−14259.3	+	14259.3i	−0.587802	+	0.587802i
$839$	−9456.61	+	9456.61i	−0.389128	+	0.389128i	−0.874376	−	0.485248i	$-0.838729\pi$
$839$	−9456.61	+	9456.61i	−0.389128	+	0.389128i	0.485248	+	0.874376i	$0.338729\pi$
$840$	66472.6	−	66472.6i	2.73039	−	2.73039i
$841$	14802.5			0.606934
$842$	81963.0			3.35467
$843$	−16581.6	−	16581.6i	−0.677463	−	0.677463i
$844$	78332.5			3.19469
$845$	23573.1	−	11218.0i	0.959691	−	0.456698i
$846$		−	30099.5i		−	1.22322i
$847$	−35331.3	+	3665.70i	−1.43329	+	0.148707i
$848$	71973.5			2.91460
$849$	7437.38			0.300648
$850$	−3651.55	−	3651.55i	−0.147350	−	0.147350i
$851$	10157.5	+	10157.5i	0.409161	+	0.409161i
$852$	11510.8	−	11510.8i	0.462857	−	0.462857i
$853$	24650.1	+	24650.1i	0.989451	+	0.989451i	0.999945	−	0.0104938i	$-0.00334033\pi$
$853$	24650.1	+	24650.1i	0.989451	+	0.989451i	−0.0104938	+	0.999945i	$0.503340\pi$
$854$			5628.70i			0.225539i
$855$	−16398.5			−0.655928
$856$	87372.0	−	87372.0i	3.48869	−	3.48869i
$857$	−8677.81			−0.345891			−0.172945	−	0.984931i	$-0.555328\pi$
$857$	−8677.81			−0.345891			−0.172945	+	0.984931i	$0.555328\pi$
$858$	10097.4	+	35956.3i	0.401772	+	1.43068i
$859$	19061.3			0.757118			0.378559	−	0.925577i	$-0.376420\pi$
$859$	19061.3			0.757118			0.378559	+	0.925577i	$0.376420\pi$
$860$	23172.2	−	23172.2i	0.918797	−	0.918797i
$861$	36069.9			1.42771
$862$			79886.7i			3.15656i
$863$	−1937.33	−	1937.33i	−0.0764165	−	0.0764165i	0.667865	−	0.744282i	$-0.267208\pi$
$863$	−1937.33	−	1937.33i	−0.0764165	−	0.0764165i	−0.744282	+	0.667865i	$0.767208\pi$
$864$	−70318.5	+	70318.5i	−2.76885	+	2.76885i
$865$	−11070.0	−	11070.0i	−0.435136	−	0.435136i
$866$	−37340.2	−	37340.2i	−1.46521	−	1.46521i
$867$	−5927.51			−0.232190
$868$	−123397.			−4.82531
$869$	−1584.78	−	3328.28i	−0.0618641	−	0.129924i
$870$		−	25409.5i		−	0.990188i
$871$	16338.2	+	2814.93i	0.635590	+	0.109507i
$872$	40464.6			1.57145
$873$	−2549.06	−	2549.06i	−0.0988232	−	0.0988232i
$874$	−34774.6			−1.34585
$875$	−34503.2			−1.33305
$876$	−44770.4	+	44770.4i	−1.72677	+	1.72677i
$877$	−8637.56	+	8637.56i	−0.332577	+	0.332577i	−0.853564	−	0.520988i	$-0.825564\pi$
$877$	−8637.56	+	8637.56i	−0.332577	+	0.332577i	0.520988	+	0.853564i	$0.325564\pi$
$878$	−55286.1	+	55286.1i	−2.12508	+	2.12508i
$879$	−3365.78	−	3365.78i	−0.129152	−	0.129152i
$880$	−93484.4	−	33174.9i	−3.58109	−	1.27083i
$881$			6615.94i			0.253004i	0.991966	+	0.126502i	$0.0403750\pi$
$881$			6615.94i			0.253004i	−0.991966	+	0.126502i	$0.959625\pi$
$882$	15434.3	+	15434.3i	0.589229	+	0.589229i
$883$			16129.5i			0.614722i	0.951593	+	0.307361i	$0.0994459\pi$
$883$			16129.5i			0.614722i	−0.951593	+	0.307361i	$0.900554\pi$
$884$	−34192.8	−	48427.6i	−1.30094	−	1.84253i
$885$	2966.79			0.112686
$886$	57776.8	−	57776.8i	2.19080	−	2.19080i
$887$			1225.16i			0.0463776i	0.999731	+	0.0231888i	$0.00738189\pi$
$887$			1225.16i			0.0463776i	−0.999731	+	0.0231888i	$0.992618\pi$
$888$	84537.8			3.19471
$889$	21907.0	+	21907.0i	0.826478	+	0.826478i
$890$	17409.1	−	17409.1i	0.655680	−	0.655680i
$891$	−10451.8	+	4976.70i	−0.392985	+	0.187122i
$892$	59451.1	−	59451.1i	2.23158	−	2.23158i
$893$		−	64634.3i		−	2.42207i
$894$			799.132i			0.0298959i
$895$	16341.7	−	16341.7i	0.610328	−	0.610328i
$896$			110773.i			4.13021i
$897$	5469.15	+	7746.01i	0.203578	+	0.288330i
$898$			49552.5i			1.84141i
$899$	−14838.8	+	14838.8i	−0.550501	+	0.550501i
$900$	−3798.69			−0.140692
$901$	−18440.5			−0.681846
$902$	−28704.3	−	60283.6i	−1.05959	−	2.22530i
$903$	−9688.33	−	9688.33i	−0.357040	−	0.357040i
$904$	−45086.8	−	45086.8i	−1.65881	−	1.65881i
$905$	−29311.8	+	29311.8i	−1.07664	+	1.07664i
$906$	−17140.6			−0.628541
$907$		−	54559.1i		−	1.99736i	−0.0513695	−	0.998680i	$-0.516359\pi$
$907$		−	54559.1i		−	1.99736i	0.0513695	−	0.998680i	$-0.483641\pi$
$908$	23010.5	+	23010.5i	0.841004	+	0.841004i
$909$	−3029.12			−0.110528
$910$	79658.6	+	13724.5i	2.90182	+	0.499959i
$911$	−25406.6			−0.923992			−0.461996	−	0.886882i	$-0.652867\pi$
$911$	−25406.6			−0.923992			−0.461996	+	0.886882i	$0.652867\pi$
$912$	−82490.6	+	82490.6i	−2.99511	+	2.99511i
$913$	−1221.24	+	3441.37i	−0.0442686	+	0.124746i
$914$		−	7547.39i		−	0.273135i
$915$	−1308.74	+	1308.74i	−0.0472849	+	0.0472849i
$916$	59084.2	+	59084.2i	2.13122	+	2.13122i
$917$	45587.4	−	45587.4i	1.64169	−	1.64169i
$918$	34287.7	−	34287.7i	1.23275	−	1.23275i
$919$		−	49928.6i		−	1.79216i	−0.443894	−	0.896079i	$-0.646403\pi$
$919$		−	49928.6i		−	1.79216i	0.443894	−	0.896079i	$-0.353597\pi$
$920$	−44181.2			−1.58327
$921$	16217.6	+	16217.6i	0.580226	+	0.580226i
$922$		−	19938.6i		−	0.712194i
$923$	8678.89	+	1495.30i	0.309501	+	0.0533243i
$924$	−28211.7	+	79498.5i	−1.00444	+	2.83042i
$925$	3266.24	+	3266.24i	0.116101	+	0.116101i
$926$			56378.9i			2.00078i
$927$			13000.6i			0.460622i
$928$	45267.8	+	45267.8i	1.60128	+	1.60128i
$929$	22735.3	+	22735.3i	0.802929	+	0.802929i	0.983552	−	0.180624i	$-0.0578116\pi$
$929$	22735.3	+	22735.3i	0.802929	+	0.802929i	−0.180624	+	0.983552i	$0.557812\pi$
$930$	−39331.0	−	39331.0i	−1.38679	−	1.38679i
$931$	33143.0	+	33143.0i	1.16672	+	1.16672i
$932$			62806.0i			2.20738i
$933$			27808.2i			0.975776i
$934$	55721.5	+	55721.5i	1.95210	+	1.95210i
$935$	23951.9	+	8499.84i	0.837765	+	0.297299i
$936$	−37065.1	−	6386.00i	−1.29435	−	0.223005i
$937$		−	30685.6i		−	1.06985i	−0.844898	−	0.534927i	$-0.820339\pi$
$937$		−	30685.6i		−	1.06985i	0.844898	−	0.534927i	$-0.179661\pi$
$938$	36298.0	+	36298.0i	1.26351	+	1.26351i
$939$	−40558.6			−1.40956
$940$		−	130518.i		−	4.52875i
$941$	25386.6	−	25386.6i	0.879469	−	0.879469i	−0.114011	−	0.993480i	$-0.536370\pi$
$941$	25386.6	−	25386.6i	0.879469	−	0.879469i	0.993480	+	0.114011i	$0.0363698\pi$
$942$	26404.8	−	26404.8i	0.913284	−	0.913284i
$943$	−11987.0	−	11987.0i	−0.413944	−	0.413944i
$944$	−10058.8	+	10058.8i	−0.346808	+	0.346808i
$945$			48231.5i			1.66029i
$946$	−8482.16	+	23902.1i	−0.291521	+	0.821483i
$947$	−29134.3	+	29134.3i	−0.999722	+	0.999722i	−1.00000		0.000277800i	$-0.999912\pi$
$947$	−29134.3	+	29134.3i	−0.999722	+	0.999722i	0.000277800		1.00000i	$0.499912\pi$
$948$	−8754.35			−0.299924
$949$	−33755.8	−	5815.84i	−1.15465	−	0.198936i
$950$	−11182.1			−0.381888
$951$	12578.8	+	12578.8i	0.428911	+	0.428911i
$952$		−	115487.i		−	3.93168i
$953$	−28320.9			−0.962647			−0.481323	−	0.876543i	$-0.659844\pi$
$953$	−28320.9			−0.962647			−0.481323	+	0.876543i	$0.659844\pi$
$954$	−13148.7	+	13148.7i	−0.446232	+	0.446232i
$955$	−8386.46	−	8386.46i	−0.284167	−	0.284167i
$956$	14140.4	+	14140.4i	0.478382	+	0.478382i
$957$	6167.34	+	12952.4i	0.208319	+	0.437503i
$958$	−21223.0			−0.715745
$959$	22102.8			0.744250
$960$	−58213.8	+	58213.8i	−1.95713	+	1.95713i
$961$			16146.3i			0.541986i
$962$	41926.5	+	59380.8i	1.40516	+	1.99014i
$963$			18198.0i			0.608952i
$964$	46047.6	−	46047.6i	1.53848	−	1.53848i
$965$			24084.7i			0.803434i
$966$			29359.6i			0.977879i
$967$	−723.422	+	723.422i	−0.0240576	+	0.0240576i	−0.719033	−	0.694976i	$-0.755415\pi$
$967$	−723.422	+	723.422i	−0.0240576	+	0.0240576i	0.694976	+	0.719033i	$0.255415\pi$
$968$	97720.7	−	10138.7i	3.24469	−	0.336644i
$969$	21135.1	−	21135.1i	0.700680	−	0.700680i
$970$	−15152.2	−	15152.2i	−0.501553	−	0.501553i
$971$	−59172.3			−1.95564			−0.977822	−	0.209437i	$-0.932837\pi$
$971$	−59172.3			−1.95564			−0.977822	+	0.209437i	$0.932837\pi$
$972$		−	61099.7i		−	2.01623i
$973$	3343.23	−	3343.23i	0.110153	−	0.110153i
$974$	−47229.1			−1.55371
$975$	1758.65	+	2490.79i	0.0577659	+	0.0818144i
$976$		−	8874.51i		−	0.291051i
$977$	−26915.0	−	26915.0i	−0.881360	−	0.881360i	0.112313	−	0.993673i	$-0.464174\pi$
$977$	−26915.0	−	26915.0i	−0.881360	−	0.881360i	−0.993673	+	0.112313i	$0.964174\pi$
$978$		−	75337.6i		−	2.46322i
$979$	−4648.71	+	13099.7i	−0.151760	+	0.427649i
$980$	66926.5	+	66926.5i	2.18152	+	2.18152i
$981$	−4214.01	+	4214.01i	−0.137149	+	0.137149i
$982$	24611.6	−	24611.6i	0.799783	−	0.799783i
$983$	24964.9	−	24964.9i	0.810027	−	0.810027i	−0.174611	−	0.984638i	$-0.555867\pi$
$983$	24964.9	−	24964.9i	0.810027	−	0.810027i	0.984638	+	0.174611i	$0.0558668\pi$
$984$	−99763.4			−3.23205
$985$	3438.16			0.111217
$986$	−22072.8	−	22072.8i	−0.712923	−	0.712923i
$987$	−54569.7			−1.75985
$988$	−126503.	−	21795.4i	−4.07348	−	0.701826i
$989$			6439.37i			0.207038i
$990$	23139.2	−	11017.8i	0.742839	−	0.353707i
$991$	4279.32			0.137172			0.0685858	−	0.997645i	$-0.478151\pi$
$991$	4279.32			0.137172			0.0685858	+	0.997645i	$0.478151\pi$
$992$	140138.			4.48528
$993$	15573.8	+	15573.8i	0.497704	+	0.497704i
$994$	19281.6	+	19281.6i	0.615266	+	0.615266i
$995$	15873.7	−	15873.7i	0.505760	−	0.505760i
$996$	6132.02	+	6132.02i	0.195081	+	0.195081i
$997$		−	32564.7i		−	1.03444i	−0.855853	−	0.517219i	$-0.826967\pi$
$997$		−	32564.7i		−	1.03444i	0.855853	−	0.517219i	$-0.173033\pi$
$998$	17093.1			0.542158
$999$	−30669.6	+	30669.6i	−0.971316	+	0.971316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.g.a.21.1	✓	80
11.10	odd	2	inner	143.4.g.a.21.40	yes	80
13.5	odd	4	inner	143.4.g.a.109.40	yes	80
143.109	even	4	inner	143.4.g.a.109.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.g.a.21.1	✓	80	1.1	even	1	trivial
143.4.g.a.21.40	yes	80	11.10	odd	2	inner
143.4.g.a.109.1	yes	80	143.109	even	4	inner
143.4.g.a.109.40	yes	80	13.5	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.84534 + 3.84534i) q^{2} +4.01609 q^{3} -21.5733i q^{4} +(8.40231 + 8.40231i) q^{5} +(-15.4432 + 15.4432i) q^{6} +(-18.8709 - 18.8709i) q^{7} +(52.1938 + 52.1938i) q^{8} -10.8710 q^{9} +O(q^{10})\)	\(q+(-3.84534 + 3.84534i) q^{2} +4.01609 q^{3} -21.5733i q^{4} +(8.40231 + 8.40231i) q^{5} +(-15.4432 + 15.4432i) q^{6} +(-18.8709 - 18.8709i) q^{7} +(52.1938 + 52.1938i) q^{8} -10.8710 q^{9} -64.6194 q^{10} +(32.9394 - 15.6843i) q^{11} -86.6402i q^{12} +(38.2898 - 27.0349i) q^{13} +145.130 q^{14} +(33.7445 + 33.7445i) q^{15} -228.819 q^{16} +58.6264 q^{17} +(41.8026 - 41.8026i) q^{18} +(89.7651 - 89.7651i) q^{19} +(181.265 - 181.265i) q^{20} +(-75.7872 - 75.7872i) q^{21} +(-66.3519 + 186.974i) q^{22} +50.3721i q^{23} +(209.615 + 209.615i) q^{24} +16.1975i q^{25} +(-43.2789 + 251.196i) q^{26} -152.093 q^{27} +(-407.106 + 407.106i) q^{28} +97.9106i q^{29} -259.518 q^{30} +(151.554 + 151.554i) q^{31} +(462.338 - 462.338i) q^{32} +(132.288 - 62.9895i) q^{33} +(-225.439 + 225.439i) q^{34} -317.118i q^{35} +234.522i q^{36} +(201.650 - 201.650i) q^{37} +690.355i q^{38} +(153.776 - 108.575i) q^{39} +877.096i q^{40} +(-237.968 + 237.968i) q^{41} +582.855 q^{42} +127.836 q^{43} +(-338.361 - 710.610i) q^{44} +(-91.3413 - 91.3413i) q^{45} +(-193.698 - 193.698i) q^{46} +(360.019 - 360.019i) q^{47} -918.960 q^{48} +369.219i q^{49} +(-62.2851 - 62.2851i) q^{50} +235.449 q^{51} +(-583.232 - 826.036i) q^{52} -314.543 q^{53} +(584.851 - 584.851i) q^{54} +(408.551 + 144.983i) q^{55} -1969.88i q^{56} +(360.505 - 360.505i) q^{57} +(-376.499 - 376.499i) q^{58} +(43.9596 - 43.9596i) q^{59} +(727.978 - 727.978i) q^{60} +38.7839i q^{61} -1165.55 q^{62} +(205.145 + 205.145i) q^{63} +1725.14i q^{64} +(548.879 + 94.5671i) q^{65} +(-266.475 + 750.907i) q^{66} +(250.107 + 250.107i) q^{67} -1264.76i q^{68} +202.299i q^{69} +(1219.42 + 1219.42i) q^{70} +(132.858 + 132.858i) q^{71} +(-567.398 - 567.398i) q^{72} +(-516.739 - 516.739i) q^{73} +1550.82i q^{74} +65.0509i q^{75} +(-1936.53 - 1936.53i) q^{76} +(-917.570 - 325.619i) q^{77} +(-173.812 + 1008.83i) q^{78} -101.043i q^{79} +(-1922.61 - 1922.61i) q^{80} -317.305 q^{81} -1830.14i q^{82} +(-70.7756 + 70.7756i) q^{83} +(-1634.98 + 1634.98i) q^{84} +(492.597 + 492.597i) q^{85} +(-491.573 + 491.573i) q^{86} +393.218i q^{87} +(2537.85 + 900.611i) q^{88} +(-269.410 + 269.410i) q^{89} +702.477 q^{90} +(-1232.74 - 212.389i) q^{91} +1086.69 q^{92} +(608.656 + 608.656i) q^{93} +2768.79i q^{94} +1508.47 q^{95} +(1856.79 - 1856.79i) q^{96} +(234.483 + 234.483i) q^{97} +(-1419.77 - 1419.77i) q^{98} +(-358.084 + 170.503i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9}+O(q^{10}) \) 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9	\( 80 q - 8 q^{3} - 4 q^{5} + 640 q^{9} + 14 q^{11} + 280 q^{14} - 80 q^{15} - 952 q^{16} - 200 q^{20} - 424 q^{22} - 508 q^{26} - 848 q^{27} + 208 q^{31} + 860 q^{33} - 232 q^{34} - 340 q^{37} + 1308 q^{42} - 644 q^{44} - 1148 q^{45} - 280 q^{47} + 2420 q^{48} + 2976 q^{53} + 1652 q^{55} - 1972 q^{58} - 84 q^{59} + 1484 q^{60} - 4924 q^{66} + 2468 q^{67} - 3540 q^{70} + 1704 q^{71} + 2368 q^{78} - 3544 q^{80} + 6160 q^{81} + 32 q^{86} + 424 q^{89} - 5868 q^{91} - 164 q^{92} + 3944 q^{93} - 4936 q^{97} - 3750 q^{99}+O(q^{100}) \) 80 * q - 8 * q^3 - 4 * q^5 + 640 * q^9 + 14 * q^11 + 280 * q^14 - 80 * q^15 - 952 * q^16 - 200 * q^20 - 424 * q^22 - 508 * q^26 - 848 * q^27 + 208 * q^31 + 860 * q^33 - 232 * q^34 - 340 * q^37 + 1308 * q^42 - 644 * q^44 - 1148 * q^45 - 280 * q^47 + 2420 * q^48 + 2976 * q^53 + 1652 * q^55 - 1972 * q^58 - 84 * q^59 + 1484 * q^60 - 4924 * q^66 + 2468 * q^67 - 3540 * q^70 + 1704 * q^71 + 2368 * q^78 - 3544 * q^80 + 6160 * q^81 + 32 * q^86 + 424 * q^89 - 5868 * q^91 - 164 * q^92 + 3944 * q^93 - 4936 * q^97 - 3750 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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