LMFDB - Embedded newform 644.4.i.b.93.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,4,Mod(93,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("644.93");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	644.i (of order $3$, 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:	$37.9972300437$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.7
Character	$\chi$	$=$	644.93
Dual form			644.4.i.b.277.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91623 - 3.31900i) q^{3} +(8.26993 - 14.3239i) q^{5} +(17.5855 - 5.80951i) q^{7} +(6.15616 - 10.6628i) q^{9} +O(q^{10})$	\(q+(-1.91623 - 3.31900i) q^{3} +(8.26993 - 14.3239i) q^{5} +(17.5855 - 5.80951i) q^{7} +(6.15616 - 10.6628i) q^{9} +(-22.5405 - 39.0412i) q^{11} -80.5239 q^{13} -63.3882 q^{15} +(-7.80256 - 13.5144i) q^{17} +(0.883825 - 1.53083i) q^{19} +(-52.9795 - 47.2339i) q^{21} +(11.5000 - 19.9186i) q^{23} +(-74.2836 - 128.663i) q^{25} -150.663 q^{27} +137.860 q^{29} +(12.7620 + 22.1045i) q^{31} +(-86.3853 + 149.624i) q^{33} +(62.2158 - 299.938i) q^{35} +(-122.218 + 211.688i) q^{37} +(154.302 + 267.259i) q^{39} +415.158 q^{41} +293.578 q^{43} +(-101.822 - 176.361i) q^{45} +(30.5772 - 52.9613i) q^{47} +(275.499 - 204.326i) q^{49} +(-29.9029 + 51.7934i) q^{51} +(-124.000 - 214.774i) q^{53} -745.633 q^{55} -6.77443 q^{57} +(185.926 + 322.033i) q^{59} +(-131.422 + 227.630i) q^{61} +(46.3136 - 223.274i) q^{63} +(-665.927 + 1153.42i) q^{65} +(-280.029 - 485.024i) q^{67} -88.1464 q^{69} -683.628 q^{71} +(109.322 + 189.352i) q^{73} +(-284.688 + 493.095i) q^{75} +(-623.196 - 555.611i) q^{77} +(-360.333 + 624.114i) q^{79} +(122.487 + 212.154i) q^{81} +205.649 q^{83} -258.107 q^{85} +(-264.170 - 457.557i) q^{87} +(-472.604 + 818.574i) q^{89} +(-1416.05 + 467.804i) q^{91} +(48.9099 - 84.7144i) q^{93} +(-14.6183 - 25.3197i) q^{95} -63.4193 q^{97} -555.051 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9}+O(q^{10}) $ 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9	$ 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9} + 28 q^{11} - 152 q^{13} + 208 q^{15} - 52 q^{17} + 38 q^{19} - 10 q^{21} + 506 q^{23} - 516 q^{25} - 876 q^{27} - 100 q^{29} + 230 q^{31} + 424 q^{33} + 98 q^{35} + 18 q^{37} - 350 q^{39} + 784 q^{41} - 336 q^{43} + 1156 q^{45} + 452 q^{47} + 546 q^{49} - 498 q^{51} - 508 q^{53} - 3084 q^{55} - 1916 q^{57} + 508 q^{59} + 1386 q^{61} + 1290 q^{63} + 360 q^{65} - 1896 q^{67} + 552 q^{69} - 3352 q^{71} + 990 q^{73} + 3328 q^{75} + 1328 q^{77} + 524 q^{79} - 4486 q^{81} - 1120 q^{83} - 5296 q^{85} + 3700 q^{87} + 1216 q^{89} + 1438 q^{91} + 366 q^{93} + 90 q^{95} + 716 q^{97} + 5716 q^{99}+O(q^{100}) $ 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9 + 28 * q^11 - 152 * q^13 + 208 * q^15 - 52 * q^17 + 38 * q^19 - 10 * q^21 + 506 * q^23 - 516 * q^25 - 876 * q^27 - 100 * q^29 + 230 * q^31 + 424 * q^33 + 98 * q^35 + 18 * q^37 - 350 * q^39 + 784 * q^41 - 336 * q^43 + 1156 * q^45 + 452 * q^47 + 546 * q^49 - 498 * q^51 - 508 * q^53 - 3084 * q^55 - 1916 * q^57 + 508 * q^59 + 1386 * q^61 + 1290 * q^63 + 360 * q^65 - 1896 * q^67 + 552 * q^69 - 3352 * q^71 + 990 * q^73 + 3328 * q^75 + 1328 * q^77 + 524 * q^79 - 4486 * q^81 - 1120 * q^83 - 5296 * q^85 + 3700 * q^87 + 1216 * q^89 + 1438 * q^91 + 366 * q^93 + 90 * q^95 + 716 * q^97 + 5716 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.91623	−	3.31900i	−0.368778	−	0.638742i	0.620597	−	0.784130i	$-0.286890\pi$
$3$	−1.91623	−	3.31900i	−0.368778	−	0.638742i	−0.989375	+	0.145388i	$0.953557\pi$
$4$		0			0
$5$	8.26993	−	14.3239i	0.739685	−	1.28117i	−0.212951	−	0.977063i	$-0.568308\pi$
$5$	8.26993	−	14.3239i	0.739685	−	1.28117i	0.952637	−	0.304110i	$-0.0983590\pi$
$6$		0			0
$7$	17.5855	−	5.80951i	0.949527	−	0.313684i
$7$	17.5855	−	5.80951i	0.949527	−	0.313684i
$8$		0			0
$9$	6.15616	−	10.6628i	0.228006	−	0.394918i
$10$		0			0
$11$	−22.5405	−	39.0412i	−0.617837	−	1.07013i	−0.989880	−	0.141910i	$-0.954676\pi$
$11$	−22.5405	−	39.0412i	−0.617837	−	1.07013i	0.372042	−	0.928216i	$-0.378658\pi$
$12$		0			0
$13$	−80.5239			−1.71795			−0.858973	−	0.512020i	$-0.828897\pi$
$13$	−80.5239			−1.71795			−0.858973	+	0.512020i	$0.828897\pi$
$14$		0			0
$15$	−63.3882			−1.09112
$16$		0			0
$17$	−7.80256	−	13.5144i	−0.111318	−	0.192808i	0.804984	−	0.593296i	$-0.202174\pi$
$17$	−7.80256	−	13.5144i	−0.111318	−	0.192808i	−0.916302	+	0.400489i	$0.868840\pi$
$18$		0			0
$19$	0.883825	−	1.53083i	0.0106718	−	0.0184840i	−0.860640	−	0.509214i	$-0.829936\pi$
$19$	0.883825	−	1.53083i	0.0106718	−	0.0184840i	0.871312	+	0.490730i	$0.163270\pi$
$20$		0			0
$21$	−52.9795	−	47.2339i	−0.550528	−	0.490823i
$22$		0			0
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$24$		0			0
$25$	−74.2836	−	128.663i	−0.594269	−	1.02930i
$26$		0			0
$27$	−150.663			−1.07389
$28$		0			0
$29$	137.860			0.882756			0.441378	−	0.897321i	$-0.354490\pi$
$29$	137.860			0.882756			0.441378	+	0.897321i	$0.354490\pi$
$30$		0			0
$31$	12.7620	+	22.1045i	0.0739396	+	0.128067i	0.900625	−	0.434598i	$-0.143109\pi$
$31$	12.7620	+	22.1045i	0.0739396	+	0.128067i	−0.826685	+	0.562665i	$0.809776\pi$
$32$		0			0
$33$	−86.3853	+	149.624i	−0.455689	+	0.789277i
$34$		0			0
$35$	62.2158	−	299.938i	0.300468	−	1.44854i
$36$		0			0
$37$	−122.218	+	211.688i	−0.543042	+	0.940576i	0.455686	+	0.890141i	$0.349394\pi$
$37$	−122.218	+	211.688i	−0.543042	+	0.940576i	−0.998727	+	0.0504350i	$0.983939\pi$
$38$		0			0
$39$	154.302	+	267.259i	0.633541	+	1.09732i
$40$		0			0
$41$	415.158			1.58138			0.790692	−	0.612214i	$-0.209721\pi$
$41$	415.158			1.58138			0.790692	+	0.612214i	$0.209721\pi$
$42$		0			0
$43$	293.578			1.04117			0.520584	−	0.853810i	$-0.325714\pi$
$43$	293.578			1.04117			0.520584	+	0.853810i	$0.325714\pi$
$44$		0			0
$45$	−101.822	−	176.361i	−0.337305	−	0.584230i
$46$		0			0
$47$	30.5772	−	52.9613i	0.0948967	−	0.164366i	−0.814669	−	0.579926i	$-0.803081\pi$
$47$	30.5772	−	52.9613i	0.0948967	−	0.164366i	0.909565	+	0.415561i	$0.136415\pi$
$48$		0			0
$49$	275.499	−	204.326i	0.803205	−	0.595703i
$50$		0			0
$51$	−29.9029	+	51.7934i	−0.0821029	+	0.142206i
$52$		0			0
$53$	−124.000	−	214.774i	−0.321372	−	0.556633i	0.659399	−	0.751793i	$-0.270811\pi$
$53$	−124.000	−	214.774i	−0.321372	−	0.556633i	−0.980771	+	0.195160i	$0.937477\pi$
$54$		0			0
$55$	−745.633			−1.82802
$56$		0			0
$57$	−6.77443			−0.0157420
$58$		0			0
$59$	185.926	+	322.033i	0.410262	+	0.710595i	0.994918	−	0.100686i	$-0.0321038\pi$
$59$	185.926	+	322.033i	0.410262	+	0.710595i	−0.584656	+	0.811281i	$0.698770\pi$
$60$		0			0
$61$	−131.422	+	227.630i	−0.275851	+	0.477787i	−0.970349	−	0.241707i	$-0.922293\pi$
$61$	−131.422	+	227.630i	−0.275851	+	0.477787i	0.694499	+	0.719494i	$0.255626\pi$
$62$		0			0
$63$	46.3136	−	223.274i	0.0926184	−	0.446507i
$64$		0			0
$65$	−665.927	+	1153.42i	−1.27074	+	2.20099i
$66$		0			0
$67$	−280.029	−	485.024i	−0.510611	−	0.884405i	−0.999924	−	0.0122966i	$-0.996086\pi$
$67$	−280.029	−	485.024i	−0.510611	−	0.884405i	0.489313	−	0.872108i	$-0.337248\pi$
$68$		0			0
$69$	−88.1464			−0.153791
$70$		0			0
$71$	−683.628			−1.14270			−0.571350	−	0.820706i	$-0.693580\pi$
$71$	−683.628			−1.14270			−0.571350	+	0.820706i	$0.693580\pi$
$72$		0			0
$73$	109.322	+	189.352i	0.175277	+	0.303589i	0.940257	−	0.340465i	$-0.110585\pi$
$73$	109.322	+	189.352i	0.175277	+	0.303589i	−0.764980	+	0.644054i	$0.777251\pi$
$74$		0			0
$75$	−284.688	+	493.095i	−0.438307	+	0.759169i
$76$		0			0
$77$	−623.196	−	555.611i	−0.922335	−	0.822308i
$78$		0			0
$79$	−360.333	+	624.114i	−0.513172	+	0.888840i	0.486711	+	0.873563i	$0.338196\pi$
$79$	−360.333	+	624.114i	−0.513172	+	0.888840i	−0.999883	+	0.0152772i	$0.995137\pi$
$80$		0			0
$81$	122.487	+	212.154i	0.168021	+	0.291021i
$82$		0			0
$83$	205.649			0.271962			0.135981	−	0.990711i	$-0.456581\pi$
$83$	205.649			0.271962			0.135981	+	0.990711i	$0.456581\pi$
$84$		0			0
$85$	−258.107			−0.329360
$86$		0			0
$87$	−264.170	−	457.557i	−0.325541	−	0.563853i
$88$		0			0
$89$	−472.604	+	818.574i	−0.562876	+	0.974929i	0.434368	+	0.900735i	$0.356972\pi$
$89$	−472.604	+	818.574i	−0.562876	+	0.974929i	−0.997244	+	0.0741940i	$0.976362\pi$
$90$		0			0
$91$	−1416.05	+	467.804i	−1.63124	+	0.538893i
$92$		0			0
$93$	48.9099	−	84.7144i	0.0545346	−	0.0944567i
$94$		0			0
$95$	−14.6183	−	25.3197i	−0.0157875	−	0.0273447i
$96$		0			0
$97$	−63.4193			−0.0663841			−0.0331921	−	0.999449i	$-0.510567\pi$
$97$	−63.4193			−0.0663841			−0.0331921	+	0.999449i	$0.510567\pi$
$98$		0			0
$99$	−555.051			−0.563482
$100$		0			0
$101$	832.928	+	1442.67i	0.820588	+	1.42130i	0.905245	+	0.424890i	$0.139687\pi$
$101$	832.928	+	1442.67i	0.820588	+	1.42130i	−0.0846564	+	0.996410i	$0.526979\pi$
$102$		0			0
$103$	830.291	−	1438.11i	0.794282	−	1.37574i	−0.129013	−	0.991643i	$-0.541181\pi$
$103$	830.291	−	1438.11i	0.794282	−	1.37574i	0.923294	−	0.384093i	$-0.125486\pi$
$104$		0			0
$105$	−1114.71	+	368.255i	−1.03605	+	0.342266i
$106$		0			0
$107$	912.732	−	1580.90i	0.824646	−	1.42833i	−0.0775436	−	0.996989i	$-0.524708\pi$
$107$	912.732	−	1580.90i	0.824646	−	1.42833i	0.902190	−	0.431340i	$-0.141959\pi$
$108$		0			0
$109$	−362.126	−	627.221i	−0.318215	−	0.551164i	0.661901	−	0.749591i	$-0.269750\pi$
$109$	−362.126	−	627.221i	−0.318215	−	0.551164i	−0.980116	+	0.198427i	$0.936417\pi$
$110$		0			0
$111$	936.790			0.801047
$112$		0			0
$113$	−597.983			−0.497818			−0.248909	−	0.968527i	$-0.580072\pi$
$113$	−597.983			−0.497818			−0.248909	+	0.968527i	$0.580072\pi$
$114$		0			0
$115$	−190.208	−	329.451i	−0.154235	−	0.267143i
$116$		0			0
$117$	−495.718	+	858.608i	−0.391702	+	0.678448i
$118$		0			0
$119$	−215.724	−	192.329i	−0.166180	−	0.148158i
$120$		0			0
$121$	−350.646	+	607.337i	−0.263446	+	0.456301i
$122$		0			0
$123$	−795.536	−	1377.91i	−0.583179	−	1.01010i
$124$		0			0
$125$	−389.800			−0.278918
$126$		0			0
$127$	−1914.45			−1.33764			−0.668819	−	0.743425i	$-0.733200\pi$
$127$	−1914.45			−1.33764			−0.668819	+	0.743425i	$0.733200\pi$
$128$		0			0
$129$	−562.562	−	974.386i	−0.383960	−	0.665038i
$130$		0			0
$131$	335.186	−	580.559i	0.223552	−	0.387203i	−0.732332	−	0.680948i	$-0.761568\pi$
$131$	335.186	−	580.559i	0.223552	−	0.387203i	0.955884	+	0.293744i	$0.0949014\pi$
$132$		0			0
$133$	6.64913	−	32.0550i	0.00433498	−	0.0208986i
$134$		0			0
$135$	−1245.97	+	2158.08i	−0.794341	+	1.37584i
$136$		0			0
$137$	551.623	+	955.440i	0.344003	+	0.595830i	0.985172	−	0.171569i	$-0.0548838\pi$
$137$	551.623	+	955.440i	0.344003	+	0.595830i	−0.641169	+	0.767399i	$0.721550\pi$
$138$		0			0
$139$	−1650.06			−1.00688			−0.503441	−	0.864030i	$-0.667933\pi$
$139$	−1650.06			−1.00688			−0.503441	+	0.864030i	$0.667933\pi$
$140$		0			0
$141$	−234.371			−0.139983
$142$		0			0
$143$	1815.05	+	3143.75i	1.06141	+	1.83842i
$144$		0			0
$145$	1140.09	−	1974.70i	0.652962	−	1.13096i
$146$		0			0
$147$	−1206.08	−	522.847i	−0.676705	−	0.293358i
$148$		0			0
$149$	1383.87	−	2396.94i	0.760882	−	1.31789i	−0.181514	−	0.983388i	$-0.558100\pi$
$149$	1383.87	−	2396.94i	0.760882	−	1.31789i	0.942396	−	0.334498i	$-0.108567\pi$
$150$		0			0
$151$	−958.189	−	1659.63i	−0.516400	−	0.894430i	−0.999819	−	0.0190414i	$-0.993939\pi$
$151$	−958.189	−	1659.63i	−0.516400	−	0.894430i	0.483419	−	0.875389i	$-0.339395\pi$
$152$		0			0
$153$	−192.135			−0.101524
$154$		0			0
$155$	422.165			0.218768
$156$		0			0
$157$	17.3279	+	30.0128i	0.00880838	+	0.0152566i	0.870396	−	0.492352i	$-0.163863\pi$
$157$	17.3279	+	30.0128i	0.00880838	+	0.0152566i	−0.861588	+	0.507609i	$0.830530\pi$
$158$		0			0
$159$	−475.224	+	823.112i	−0.237030	+	0.410548i
$160$		0			0
$161$	86.5160	−	417.088i	0.0423504	−	0.204168i
$162$		0			0
$163$	−1306.17	+	2262.34i	−0.627649	+	1.08712i	0.360373	+	0.932808i	$0.382649\pi$
$163$	−1306.17	+	2262.34i	−0.627649	+	1.08712i	−0.988022	+	0.154312i	$0.950684\pi$
$164$		0			0
$165$	1428.80	+	2474.76i	0.674133	+	1.16763i
$166$		0			0
$167$	625.325			0.289755			0.144878	−	0.989450i	$-0.453721\pi$
$167$	625.325			0.289755			0.144878	+	0.989450i	$0.453721\pi$
$168$		0			0
$169$	4287.10			1.95134
$170$		0			0
$171$	−10.8819	−	18.8481i	−0.00486644	−	0.00842893i
$172$		0			0
$173$	−438.054	+	758.732i	−0.192512	+	0.333441i	−0.946082	−	0.323927i	$-0.894997\pi$
$173$	−438.054	+	758.732i	−0.192512	+	0.333441i	0.753570	+	0.657368i	$0.228330\pi$
$174$		0			0
$175$	−2053.78	−	1831.05i	−0.887151	−	0.790940i
$176$		0			0
$177$	712.552	−	1234.18i	0.302591	−	0.524104i
$178$		0			0
$179$	−2235.61	−	3872.20i	−0.933506	−	1.61688i	−0.777276	−	0.629160i	$-0.783399\pi$
$179$	−2235.61	−	3872.20i	−0.933506	−	1.61688i	−0.156230	−	0.987721i	$-0.549934\pi$
$180$		0			0
$181$	2744.63			1.12711			0.563554	−	0.826079i	$-0.309434\pi$
$181$	2744.63			1.12711			0.563554	+	0.826079i	$0.309434\pi$
$182$		0			0
$183$	1007.34			0.406910
$184$		0			0
$185$	2021.47	+	3501.29i	0.803360	+	1.39146i
$186$		0			0
$187$	−351.747	+	609.243i	−0.137552	+	0.238248i
$188$		0			0
$189$	−2649.48	+	875.276i	−1.01969	+	0.336862i
$190$		0			0
$191$	−1672.63	+	2897.08i	−0.633650	+	1.09751i	0.353149	+	0.935567i	$0.385111\pi$
$191$	−1672.63	+	2897.08i	−0.633650	+	1.09751i	−0.986799	+	0.161947i	$0.948222\pi$
$192$		0			0
$193$	1098.83	+	1903.23i	0.409820	+	0.709830i	0.994869	−	0.101168i	$-0.0322580\pi$
$193$	1098.83	+	1903.23i	0.409820	+	0.709830i	−0.585049	+	0.810998i	$0.698925\pi$
$194$		0			0
$195$	5104.27			1.87448
$196$		0			0
$197$	−3111.20			−1.12520			−0.562599	−	0.826730i	$-0.690198\pi$
$197$	−3111.20			−1.12520			−0.562599	+	0.826730i	$0.690198\pi$
$198$		0			0
$199$	229.551	+	397.594i	0.0817711	+	0.141632i	0.904011	−	0.427510i	$-0.140609\pi$
$199$	229.551	+	397.594i	0.0817711	+	0.141632i	−0.822240	+	0.569141i	$0.807276\pi$
$200$		0			0
$201$	−1073.20	+	1858.83i	−0.376604	+	0.652298i
$202$		0			0
$203$	2424.33	−	800.898i	0.838201	−	0.276906i
$204$		0			0
$205$	3433.33	−	5946.70i	1.16973	−	2.02603i
$206$		0			0
$207$	−141.592	−	245.244i	−0.0475425	−	0.0823460i
$208$		0			0
$209$	−79.6873			−0.0263736
$210$		0			0
$211$	−3851.04			−1.25648			−0.628238	−	0.778021i	$-0.716223\pi$
$211$	−3851.04			−1.25648			−0.628238	+	0.778021i	$0.716223\pi$
$212$		0			0
$213$	1309.99	+	2268.96i	0.421403	+	0.729891i
$214$		0			0
$215$	2427.87	−	4205.20i	0.770137	−	1.33392i
$216$		0			0
$217$	352.843	+	314.577i	0.110380	+	0.0984097i
$218$		0			0
$219$	418.973	−	725.682i	0.129276	−	0.223913i
$220$		0			0
$221$	628.293	+	1088.23i	0.191238	+	0.331233i
$222$		0			0
$223$	3463.35			1.04001			0.520007	−	0.854162i	$-0.325929\pi$
$223$	3463.35			1.04001			0.520007	+	0.854162i	$0.325929\pi$
$224$		0			0
$225$	−1829.21			−0.541987
$226$		0			0
$227$	−2516.67	−	4359.00i	−0.735847	−	1.27452i	−0.954351	−	0.298688i	$-0.903451\pi$
$227$	−2516.67	−	4359.00i	−0.735847	−	1.27452i	0.218504	−	0.975836i	$-0.429882\pi$
$228$		0			0
$229$	2483.43	−	4301.43i	0.716637	−	1.24125i	−0.245688	−	0.969349i	$-0.579014\pi$
$229$	2483.43	−	4301.43i	0.716637	−	1.24125i	0.962325	−	0.271903i	$-0.0876529\pi$
$230$		0			0
$231$	−649.887	+	3133.06i	−0.185106	+	0.892383i
$232$		0			0
$233$	2239.31	−	3878.60i	0.629623	−	1.09054i	−0.358005	−	0.933720i	$-0.616543\pi$
$233$	2239.31	−	3878.60i	0.629623	−	1.09054i	0.987627	−	0.156819i	$-0.0501239\pi$
$234$		0			0
$235$	−505.743	−	875.972i	−0.140387	−	0.243158i
$236$		0			0
$237$	2761.91			0.756986
$238$		0			0
$239$	−5082.93			−1.37568			−0.687840	−	0.725862i	$-0.741441\pi$
$239$	−5082.93			−1.37568			−0.687840	+	0.725862i	$0.741441\pi$
$240$		0			0
$241$	2341.42	+	4055.45i	0.625826	+	1.08396i	0.988381	+	0.151999i	$0.0485711\pi$
$241$	2341.42	+	4055.45i	0.625826	+	1.08396i	−0.362555	+	0.931962i	$0.618096\pi$
$242$		0			0
$243$	−1564.52	+	2709.83i	−0.413020	+	0.715372i
$244$		0			0
$245$	−648.397	−	5636.00i	−0.169080	−	1.46968i
$246$		0			0
$247$	−71.1690	+	123.268i	−0.0183335	+	0.0317546i
$248$		0			0
$249$	−394.069	−	682.548i	−0.100294	−	0.173714i
$250$		0			0
$251$	3315.17			0.833673			0.416836	−	0.908982i	$-0.363139\pi$
$251$	3315.17			0.833673			0.416836	+	0.908982i	$0.363139\pi$
$252$		0			0
$253$	−1036.86			−0.257656
$254$		0			0
$255$	494.591	+	856.656i	0.121461	+	0.210376i
$256$		0			0
$257$	−1693.99	+	2934.08i	−0.411160	+	0.712151i	−0.995017	−	0.0997061i	$-0.968210\pi$
$257$	−1693.99	+	2934.08i	−0.411160	+	0.712151i	0.583856	+	0.811857i	$0.301543\pi$
$258$		0			0
$259$	−919.463	+	4432.67i	−0.220589	+	1.06345i
$260$		0			0
$261$	848.687	−	1469.97i	0.201273	−	0.348616i
$262$		0			0
$263$	543.392	+	941.182i	0.127403	+	0.220668i	0.922670	−	0.385591i	$-0.126003\pi$
$263$	543.392	+	941.182i	0.127403	+	0.220668i	−0.795267	+	0.606260i	$0.792669\pi$
$264$		0			0
$265$	−4101.89			−0.950857
$266$		0			0
$267$	3622.47			0.830304
$268$		0			0
$269$	57.9131	+	100.308i	0.0131265	+	0.0227357i	0.872514	−	0.488589i	$-0.162488\pi$
$269$	57.9131	+	100.308i	0.0131265	+	0.0227357i	−0.859388	+	0.511325i	$0.829155\pi$
$270$		0			0
$271$	3112.06	−	5390.25i	0.697581	−	1.20825i	−0.271722	−	0.962376i	$-0.587593\pi$
$271$	3112.06	−	5390.25i	0.697581	−	1.20825i	0.969303	−	0.245869i	$-0.0790734\pi$
$272$		0			0
$273$	4266.12	+	3803.46i	0.945777	+	0.843208i
$274$		0			0
$275$	−3348.78	+	5800.25i	−0.734323	+	1.27189i
$276$		0			0
$277$	−3201.02	−	5544.32i	−0.694333	−	1.20262i	−0.970405	−	0.241484i	$-0.922366\pi$
$277$	−3201.02	−	5544.32i	−0.694333	−	1.20262i	0.276071	−	0.961137i	$-0.410967\pi$
$278$		0			0
$279$	314.260			0.0674347
$280$		0			0
$281$	7464.65			1.58471			0.792355	−	0.610060i	$-0.208855\pi$
$281$	7464.65			1.58471			0.792355	+	0.610060i	$0.208855\pi$
$282$		0			0
$283$	−2654.41	−	4597.58i	−0.557556	−	0.965716i	−0.997700	−	0.0677883i	$-0.978406\pi$
$283$	−2654.41	−	4597.58i	−0.557556	−	0.965716i	0.440144	−	0.897927i	$-0.354928\pi$
$284$		0			0
$285$	−56.0241	+	97.0366i	−0.0116441	+	0.0201682i
$286$		0			0
$287$	7300.75	−	2411.86i	1.50157	−	0.496055i
$288$		0			0
$289$	2334.74	−	4043.89i	0.475217	−	0.823100i
$290$		0			0
$291$	121.526	+	210.489i	0.0244810	+	0.0424023i
$292$		0			0
$293$	477.108			0.0951296			0.0475648	−	0.998868i	$-0.484854\pi$
$293$	477.108			0.0951296			0.0475648	+	0.998868i	$0.484854\pi$
$294$		0			0
$295$	6150.38			1.21386
$296$		0			0
$297$	3396.01	+	5882.05i	0.663489	+	1.14920i
$298$		0			0
$299$	−926.025	+	1603.92i	−0.179108	+	0.310225i
$300$		0			0
$301$	5162.72	−	1705.55i	0.988618	−	0.326598i
$302$		0			0
$303$	3192.16	−	5528.98i	0.605230	−	1.04829i
$304$		0			0
$305$	2173.71	+	3764.97i	0.408085	+	0.706825i
$306$		0			0
$307$	−9087.34			−1.68939			−0.844694	−	0.535250i	$-0.820217\pi$
$307$	−9087.34			−1.68939			−0.844694	+	0.535250i	$0.820217\pi$
$308$		0			0
$309$	−6364.10			−1.17165
$310$		0			0
$311$	3071.11	+	5319.31i	0.559957	+	0.969873i	0.997499	+	0.0706756i	$0.0225155\pi$
$311$	3071.11	+	5319.31i	0.559957	+	0.969873i	−0.437543	+	0.899198i	$0.644151\pi$
$312$		0			0
$313$	−4568.33	+	7912.58i	−0.824975	+	1.42890i	0.0769629	+	0.997034i	$0.475478\pi$
$313$	−4568.33	+	7912.58i	−0.824975	+	1.42890i	−0.901938	+	0.431865i	$0.857856\pi$
$314$		0			0
$315$	−2815.16	−	2509.86i	−0.503544	−	0.448935i
$316$		0			0
$317$	1838.02	−	3183.54i	0.325657	−	0.564055i	−0.655988	−	0.754771i	$-0.727748\pi$
$317$	1838.02	−	3183.54i	0.325657	−	0.564055i	0.981645	+	0.190717i	$0.0610811\pi$
$318$		0			0
$319$	−3107.42	−	5382.22i	−0.545399	−	0.944659i
$320$		0			0
$321$	−6996.00			−1.21644
$322$		0			0
$323$	−27.5844			−0.00475181
$324$		0			0
$325$	5981.61	+	10360.4i	1.02092	+	1.76829i
$326$		0			0
$327$	−1387.83	+	2403.79i	−0.234701	+	0.406514i
$328$		0			0
$329$	230.036	−	1108.99i	0.0385480	−	0.185837i
$330$		0			0
$331$	1198.94	−	2076.63i	0.199093	−	0.344839i	−0.749142	−	0.662410i	$-0.769534\pi$
$331$	1198.94	−	2076.63i	0.199093	−	0.344839i	0.948235	+	0.317571i	$0.102867\pi$
$332$		0			0
$333$	1504.79	+	2606.37i	0.247633	+	0.428914i
$334$		0			0
$335$	−9263.28			−1.51077
$336$		0			0
$337$	7258.26			1.17324			0.586621	−	0.809862i	$-0.300458\pi$
$337$	7258.26			1.17324			0.586621	+	0.809862i	$0.300458\pi$
$338$		0			0
$339$	1145.87	+	1984.70i	0.183584	+	0.317977i
$340$		0			0
$341$	575.325	−	996.492i	0.0913653	−	0.158249i
$342$		0			0
$343$	3657.75	−	5193.69i	0.575802	−	0.817589i
$344$		0			0
$345$	−728.965	+	1262.60i	−0.113757	+	0.197033i
$346$		0			0
$347$	2513.10	+	4352.82i	0.388791	+	0.673406i	0.992287	−	0.123960i	$-0.0395594\pi$
$347$	2513.10	+	4352.82i	0.388791	+	0.673406i	−0.603496	+	0.797366i	$0.706226\pi$
$348$		0			0
$349$	−1649.35			−0.252973			−0.126487	−	0.991968i	$-0.540370\pi$
$349$	−1649.35			−0.252973			−0.126487	+	0.991968i	$0.540370\pi$
$350$		0			0
$351$	12131.9			1.84489
$352$		0			0
$353$	−3189.28	−	5523.99i	−0.480873	−	0.832897i	0.518886	−	0.854843i	$-0.326347\pi$
$353$	−3189.28	−	5523.99i	−0.480873	−	0.832897i	−0.999759	+	0.0219468i	$0.993014\pi$
$354$		0			0
$355$	−5653.56	+	9792.25i	−0.845239	+	1.46400i
$356$		0			0
$357$	−224.964	+	1084.53i	−0.0333511	+	0.160783i
$358$		0			0
$359$	5320.27	−	9214.97i	0.782153	−	1.35473i	−0.148532	−	0.988908i	$-0.547455\pi$
$359$	5320.27	−	9214.97i	0.782153	−	1.35473i	0.930685	−	0.365822i	$-0.119212\pi$
$360$		0			0
$361$	3427.94	+	5937.36i	0.499772	+	0.865631i
$362$		0			0
$363$	2687.67			0.388612
$364$		0			0
$365$	3616.36			0.518599
$366$		0			0
$367$	−2740.27	−	4746.29i	−0.389757	−	0.675080i	0.602659	−	0.797999i	$-0.294108\pi$
$367$	−2740.27	−	4746.29i	−0.389757	−	0.675080i	−0.992417	+	0.122919i	$0.960775\pi$
$368$		0			0
$369$	2555.78	−	4426.73i	0.360565	−	0.624517i
$370$		0			0
$371$	−3428.34	−	3056.53i	−0.479758	−	0.427729i
$372$		0			0
$373$	−1203.80	+	2085.05i	−0.167106	+	0.289436i	−0.937401	−	0.348251i	$-0.886776\pi$
$373$	−1203.80	+	2085.05i	−0.167106	+	0.289436i	0.770295	+	0.637688i	$0.220109\pi$
$374$		0			0
$375$	746.944	+	1293.75i	0.102859	+	0.178157i
$376$		0			0
$377$	−11101.0			−1.51653
$378$		0			0
$379$	3655.03			0.495373			0.247686	−	0.968840i	$-0.420330\pi$
$379$	3655.03			0.495373			0.247686	+	0.968840i	$0.420330\pi$
$380$		0			0
$381$	3668.52	+	6354.06i	0.493291	+	0.854405i
$382$		0			0
$383$	4422.97	−	7660.81i	0.590087	−	1.02206i	−0.404133	−	0.914700i	$-0.632427\pi$
$383$	4422.97	−	7660.81i	0.590087	−	1.02206i	0.994220	−	0.107360i	$-0.0342398\pi$
$384$		0			0
$385$	−13112.3	+	4331.76i	−1.73576	+	0.573421i
$386$		0			0
$387$	1807.31	−	3130.36i	0.237393	−	0.411176i
$388$		0			0
$389$	2309.17	+	3999.60i	0.300976	+	0.521305i	0.976357	−	0.216163i	$-0.0693544\pi$
$389$	2309.17	+	3999.60i	0.300976	+	0.521305i	−0.675382	+	0.737468i	$0.736021\pi$
$390$		0			0
$391$	−358.918			−0.0464226
$392$		0			0
$393$	−2569.17			−0.329764
$394$		0			0
$395$	5959.86	+	10322.8i	0.759172	+	1.31492i
$396$		0			0
$397$	4278.12	−	7409.93i	0.540838	−	0.936759i	−0.458018	−	0.888943i	$-0.651440\pi$
$397$	4278.12	−	7409.93i	0.540838	−	0.936759i	0.998856	−	0.0478164i	$-0.0152262\pi$
$398$		0			0
$399$	−119.132	+	39.3561i	−0.0149475	+	0.00493802i
$400$		0			0
$401$	−1891.68	+	3276.49i	−0.235576	+	0.408030i	−0.959440	−	0.281913i	$-0.909031\pi$
$401$	−1891.68	+	3276.49i	−0.235576	+	0.408030i	0.723864	+	0.689943i	$0.242364\pi$
$402$		0			0
$403$	−1027.65	−	1779.94i	−0.127024	−	0.220013i
$404$		0			0
$405$	4051.84			0.497130
$406$		0			0
$407$	11019.4			1.34205
$408$		0			0
$409$	5058.27	+	8761.18i	0.611529	+	1.05920i	0.990983	+	0.133989i	$0.0427786\pi$
$409$	5058.27	+	8761.18i	0.611529	+	1.05920i	−0.379454	+	0.925211i	$0.623888\pi$
$410$		0			0
$411$	2114.07	−	3661.68i	0.253721	−	0.439458i
$412$		0			0
$413$	5140.45	+	4582.97i	0.612458	+	0.546037i
$414$		0			0
$415$	1700.70	−	2945.70i	0.201167	−	0.348431i
$416$		0			0
$417$	3161.89	+	5476.56i	0.371315	+	0.643137i
$418$		0			0
$419$	−4122.53			−0.480665			−0.240332	−	0.970691i	$-0.577256\pi$
$419$	−4122.53			−0.480665			−0.240332	+	0.970691i	$0.577256\pi$
$420$		0			0
$421$	−10226.3			−1.18385			−0.591924	−	0.805993i	$-0.701632\pi$
$421$	−10226.3			−1.18385			−0.591924	+	0.805993i	$0.701632\pi$
$422$		0			0
$423$	−376.476	−	652.076i	−0.0432740	−	0.0749527i
$424$		0			0
$425$	−1159.21	+	2007.80i	−0.132305	+	0.229159i
$426$		0			0
$427$	−988.706	+	4766.48i	−0.112053	+	0.540202i
$428$		0			0
$429$	6956.08	−	12048.3i	0.782850	−	1.35594i
$430$		0			0
$431$	−3290.30	−	5698.96i	−0.367722	−	0.636912i	0.621487	−	0.783424i	$-0.286529\pi$
$431$	−3290.30	−	5698.96i	−0.367722	−	0.636912i	−0.989209	+	0.146512i	$0.953195\pi$
$432$		0			0
$433$	−877.437			−0.0973832			−0.0486916	−	0.998814i	$-0.515505\pi$
$433$	−877.437			−0.0973832			−0.0486916	+	0.998814i	$0.515505\pi$
$434$		0			0
$435$	−8738.69			−0.963191
$436$		0			0
$437$	−20.3280	−	35.2091i	−0.00222521	−	0.00385418i
$438$		0			0
$439$	2262.20	−	3918.25i	0.245943	−	0.425986i	−0.716453	−	0.697635i	$-0.754236\pi$
$439$	2262.20	−	3918.25i	0.245943	−	0.425986i	0.962396	+	0.271649i	$0.0875690\pi$
$440$		0			0
$441$	−482.668	−	4195.45i	−0.0521184	−	0.453024i
$442$		0			0
$443$	7496.95	−	12985.1i	0.804043	−	1.39264i	−0.112892	−	0.993607i	$-0.536012\pi$
$443$	7496.95	−	12985.1i	0.804043	−	1.39264i	0.916935	−	0.399036i	$-0.130655\pi$
$444$		0			0
$445$	7816.81	+	13539.1i	0.832702	+	1.44228i
$446$		0			0
$447$	−10607.3			−1.12239
$448$		0			0
$449$	−10940.0			−1.14987			−0.574935	−	0.818199i	$-0.694973\pi$
$449$	−10940.0			−1.14987			−0.574935	+	0.818199i	$0.694973\pi$
$450$		0			0
$451$	−9357.85	−	16208.3i	−0.977038	−	1.69228i
$452$		0			0
$453$	−3672.21	+	6360.46i	−0.380873	+	0.659692i
$454$		0			0
$455$	−5009.86	+	24152.2i	−0.516188	+	2.48851i
$456$		0			0
$457$	8352.23	−	14466.5i	0.854925	−	1.48077i	−0.0217898	−	0.999763i	$-0.506936\pi$
$457$	8352.23	−	14466.5i	0.854925	−	1.48077i	0.876715	−	0.481011i	$-0.159730\pi$
$458$		0			0
$459$	1175.55	+	2036.12i	0.119543	+	0.207054i
$460$		0			0
$461$	−6992.06			−0.706405			−0.353203	−	0.935547i	$-0.614907\pi$
$461$	−6992.06			−0.706405			−0.353203	+	0.935547i	$0.614907\pi$
$462$		0			0
$463$	1402.15			0.140741			0.0703707	−	0.997521i	$-0.477582\pi$
$463$	1402.15			0.140741			0.0703707	+	0.997521i	$0.477582\pi$
$464$		0			0
$465$	−808.963	−	1401.17i	−0.0806769	−	0.139736i
$466$		0			0
$467$	2481.73	−	4298.49i	0.245912	−	0.425932i	−0.716476	−	0.697612i	$-0.754246\pi$
$467$	2481.73	−	4298.49i	0.245912	−	0.425932i	0.962388	+	0.271680i	$0.0875792\pi$
$468$		0			0
$469$	−7742.20	−	6902.56i	−0.762263	−	0.679596i
$470$		0			0
$471$	66.4083	−	115.023i	0.00649667	−	0.0112526i
$472$		0			0
$473$	−6617.39	−	11461.7i	−0.643273	−	1.11418i
$474$		0			0
$475$	−262.615			−0.0253676
$476$		0			0
$477$	−3053.46			−0.293099
$478$		0			0
$479$	2219.68	+	3844.60i	0.211732	+	0.366731i	0.952257	−	0.305298i	$-0.0987561\pi$
$479$	2219.68	+	3844.60i	0.211732	+	0.366731i	−0.740524	+	0.672029i	$0.765423\pi$
$480$		0			0
$481$	9841.48	−	17045.9i	0.932917	−	1.61586i
$482$		0			0
$483$	−1550.10	+	512.087i	−0.146029	+	0.0482418i
$484$		0			0
$485$	−524.474	+	908.415i	−0.0491034	+	0.0850495i
$486$		0			0
$487$	3026.85	+	5242.65i	0.281642	+	0.487818i	0.971789	−	0.235851i	$-0.0757877\pi$
$487$	3026.85	+	5242.65i	0.281642	+	0.487818i	−0.690148	+	0.723669i	$0.742454\pi$
$488$		0			0
$489$	10011.6			0.925852
$490$		0			0
$491$	−464.323			−0.0426774			−0.0213387	−	0.999772i	$-0.506793\pi$
$491$	−464.323			−0.0426774			−0.0213387	+	0.999772i	$0.506793\pi$
$492$		0			0
$493$	−1075.66	−	1863.10i	−0.0982662	−	0.170202i
$494$		0			0
$495$	−4590.24	+	7950.52i	−0.416799	+	0.721918i
$496$		0			0
$497$	−12021.9	+	3971.54i	−1.08503	+	0.358447i
$498$		0			0
$499$	3122.60	−	5408.50i	0.280134	−	0.485206i	−0.691284	−	0.722583i	$-0.742955\pi$
$499$	3122.60	−	5408.50i	0.280134	−	0.485206i	0.971417	+	0.237378i	$0.0762879\pi$
$500$		0			0
$501$	−1198.26	−	2075.45i	−0.106855	−	0.185079i
$502$		0			0
$503$	−14848.4			−1.31621			−0.658107	−	0.752924i	$-0.728643\pi$
$503$	−14848.4			−1.31621			−0.658107	+	0.752924i	$0.728643\pi$
$504$		0			0
$505$	27553.0			2.42791
$506$		0			0
$507$	−8215.05	−	14228.9i	−0.719611	−	1.24640i
$508$		0			0
$509$	−6675.96	+	11563.1i	−0.581349	+	1.00693i	0.413971	+	0.910290i	$0.364142\pi$
$509$	−6675.96	+	11563.1i	−0.581349	+	1.00693i	−0.995320	+	0.0966360i	$0.969192\pi$
$510$		0			0
$511$	3022.53	+	2694.74i	0.261661	+	0.233284i
$512$		0			0
$513$	−133.159	+	230.639i	−0.0114603	+	0.0198498i
$514$		0			0
$515$	−13732.9	−	23786.1i	−1.17504	−	2.03522i
$516$		0			0
$517$	−2756.90			−0.234523
$518$		0			0
$519$	3357.64			0.283977
$520$		0			0
$521$	5566.89	+	9642.13i	0.468118	+	0.810805i	0.999336	−	0.0364304i	$-0.0115987\pi$
$521$	5566.89	+	9642.13i	0.468118	+	0.810805i	−0.531218	+	0.847235i	$0.678265\pi$
$522$		0			0
$523$	3805.32	−	6591.01i	0.318155	−	0.551061i	−0.661948	−	0.749550i	$-0.730270\pi$
$523$	3805.32	−	6591.01i	0.318155	−	0.551061i	0.980103	+	0.198489i	$0.0636033\pi$
$524$		0			0
$525$	−2141.75	+	10325.2i	−0.178045	+	0.858342i
$526$		0			0
$527$	199.153	−	344.943i	0.0164616	−	0.0285123i
$528$		0			0
$529$	−264.500	−	458.127i	−0.0217391	−	0.0376533i
$530$		0			0
$531$	4578.36			0.374169
$532$		0			0
$533$	−33430.1			−2.71673
$534$		0			0
$535$	−15096.5	−	26147.8i	−1.21996	−	2.11303i
$536$		0			0
$537$	−8567.88	+	14840.0i	−0.688513	+	1.19254i
$538$		0			0
$539$	−14187.0	−	6150.22i	−1.13373	−	0.491482i
$540$		0			0
$541$	−4023.24	+	6968.45i	−0.319727	+	0.553784i	−0.980431	−	0.196863i	$-0.936925\pi$
$541$	−4023.24	+	6968.45i	−0.319727	+	0.553784i	0.660704	+	0.750647i	$0.270258\pi$
$542$		0			0
$543$	−5259.33	−	9109.42i	−0.415652	−	0.719931i
$544$		0			0
$545$	−11979.0			−0.941515
$546$		0			0
$547$	−6783.55			−0.530245			−0.265122	−	0.964215i	$-0.585412\pi$
$547$	−6783.55			−0.530245			−0.265122	+	0.964215i	$0.585412\pi$
$548$		0			0
$549$	1618.11	+	2802.65i	0.125791	+	0.217877i
$550$		0			0
$551$	121.844	−	211.040i	0.00942055	−	0.0163169i
$552$		0			0
$553$	−2710.83	+	13068.7i	−0.208456	+	1.00495i
$554$		0			0
$555$	7747.19	−	13418.5i	0.592523	−	1.02628i
$556$		0			0
$557$	5185.38	+	8981.34i	0.394455	+	0.683217i	0.993031	−	0.117849i	$-0.0376000\pi$
$557$	5185.38	+	8981.34i	0.394455	+	0.683217i	−0.598576	+	0.801066i	$0.704267\pi$
$558$		0			0
$559$	−23640.1			−1.78867
$560$		0			0
$561$	2696.11			0.202905
$562$		0			0
$563$	10410.6	+	18031.6i	0.779312	+	1.34981i	0.932339	+	0.361587i	$0.117765\pi$
$563$	10410.6	+	18031.6i	0.779312	+	1.34981i	−0.153026	+	0.988222i	$0.548902\pi$
$564$		0			0
$565$	−4945.28	+	8565.47i	−0.368229	+	0.637791i
$566$		0			0
$567$	3386.51	+	3019.24i	0.250829	+	0.223627i
$568$		0			0
$569$	−6596.49	+	11425.5i	−0.486009	+	0.841792i	−0.999871	−	0.0160807i	$-0.994881\pi$
$569$	−6596.49	+	11425.5i	−0.486009	+	0.841792i	0.513862	+	0.857873i	$0.328214\pi$
$570$		0			0
$571$	−6782.16	−	11747.0i	−0.497065	−	0.860943i	0.502929	−	0.864328i	$-0.332256\pi$
$571$	−6782.16	−	11747.0i	−0.497065	−	0.860943i	−0.999994	+	0.00338520i	$0.998922\pi$
$572$		0			0
$573$	12820.5			0.934705
$574$		0			0
$575$	−3417.05			−0.247827
$576$		0			0
$577$	2840.28	+	4919.51i	0.204926	+	0.354942i	0.950109	−	0.311918i	$-0.100971\pi$
$577$	2840.28	+	4919.51i	0.204926	+	0.354942i	−0.745183	+	0.666860i	$0.767638\pi$
$578$		0			0
$579$	4211.20	−	7294.02i	0.302265	−	0.523539i
$580$		0			0
$581$	3616.43	−	1194.72i	0.258236	−	0.0853102i
$582$		0			0
$583$	−5590.04	+	9682.23i	−0.397111	+	0.687817i
$584$		0			0
$585$	8199.11	+	14201.3i	0.579472	+	1.00368i
$586$		0			0
$587$	−14174.5			−0.996667			−0.498334	−	0.866985i	$-0.666054\pi$
$587$	−14174.5			−0.996667			−0.498334	+	0.866985i	$0.666054\pi$
$588$		0			0
$589$	45.1176			0.00315626
$590$		0			0
$591$	5961.77	+	10326.1i	0.414948	+	0.718711i
$592$		0			0
$593$	−3735.35	+	6469.81i	−0.258672	+	0.448032i	−0.965886	−	0.258966i	$-0.916618\pi$
$593$	−3735.35	+	6469.81i	−0.258672	+	0.448032i	0.707215	+	0.706999i	$0.249951\pi$
$594$		0			0
$595$	−4538.93	+	1499.47i	−0.312736	+	0.103315i
$596$		0			0
$597$	879.744	−	1523.76i	0.0603107	−	0.104461i
$598$		0			0
$599$	7787.69	+	13488.7i	0.531213	+	0.920087i	0.999336	+	0.0364245i	$0.0115968\pi$
$599$	7787.69	+	13488.7i	0.531213	+	0.920087i	−0.468124	+	0.883663i	$0.655070\pi$
$600$		0			0
$601$	25262.3			1.71460			0.857298	−	0.514821i	$-0.172141\pi$
$601$	25262.3			1.71460			0.857298	+	0.514821i	$0.172141\pi$
$602$		0			0
$603$	−6895.61			−0.465690
$604$		0			0
$605$	5799.64	+	10045.3i	0.389734	+	0.675039i
$606$		0			0
$607$	7486.58	−	12967.1i	0.500611	−	0.867084i	−0.499388	−	0.866378i	$-0.666442\pi$
$607$	7486.58	−	12967.1i	0.500611	−	0.867084i	1.00000		0.000706110i	$-0.000224762\pi$
$608$		0			0
$609$	−7303.75	−	6511.66i	−0.485982	−	0.433277i
$610$		0			0
$611$	−2462.20	+	4264.65i	−0.163027	+	0.282372i
$612$		0			0
$613$	−1009.49	−	1748.49i	−0.0665138	−	0.115205i	0.830851	−	0.556495i	$-0.187854\pi$
$613$	−1009.49	−	1748.49i	−0.0665138	−	0.115205i	−0.897365	+	0.441290i	$0.854521\pi$
$614$		0			0
$615$	−26316.1			−1.72548
$616$		0			0
$617$	17854.9			1.16501			0.582506	−	0.812826i	$-0.302072\pi$
$617$	17854.9			1.16501			0.582506	+	0.812826i	$0.302072\pi$
$618$		0			0
$619$	3406.40	+	5900.06i	0.221187	+	0.383107i	0.955169	−	0.296062i	$-0.0956735\pi$
$619$	3406.40	+	5900.06i	0.221187	+	0.383107i	−0.733982	+	0.679169i	$0.762340\pi$
$620$		0			0
$621$	−1732.62	+	3000.98i	−0.111961	+	0.193922i
$622$		0			0
$623$	−3555.46	+	17140.6i	−0.228646	+	1.10229i
$624$		0			0
$625$	6061.84	−	10499.4i	0.387958	−	0.671962i
$626$		0			0
$627$	152.699	+	264.482i	0.00972601	+	0.0168459i
$628$		0			0
$629$	3814.46			0.241800
$630$		0			0
$631$	21951.4			1.38490			0.692448	−	0.721467i	$-0.256532\pi$
$631$	21951.4			1.38490			0.692448	+	0.721467i	$0.256532\pi$
$632$		0			0
$633$	7379.46	+	12781.6i	0.463360	+	0.802564i
$634$		0			0
$635$	−15832.4	+	27422.5i	−0.989431	+	1.71375i
$636$		0			0
$637$	−22184.3	+	16453.1i	−1.37986	+	1.02339i
$638$		0			0
$639$	−4208.52	+	7289.38i	−0.260542	+	0.451273i
$640$		0			0
$641$	−13924.3	−	24117.7i	−0.858001	−	1.48610i	−0.873833	−	0.486226i	$-0.838373\pi$
$641$	−13924.3	−	24117.7i	−0.858001	−	1.48610i	0.0158325	−	0.999875i	$-0.494960\pi$
$642$		0			0
$643$	−9672.83			−0.593249			−0.296624	−	0.954994i	$-0.595861\pi$
$643$	−9672.83			−0.593249			−0.296624	+	0.954994i	$0.595861\pi$
$644$		0			0
$645$	−18609.4			−1.13604
$646$		0			0
$647$	6887.87	+	11930.1i	0.418532	+	0.724918i	0.995792	−	0.0916420i	$-0.0292115\pi$
$647$	6887.87	+	11930.1i	0.418532	+	0.724918i	−0.577260	+	0.816560i	$0.695878\pi$
$648$		0			0
$649$	8381.71	−	14517.6i	0.506951	−	0.878064i
$650$		0			0
$651$	367.955	−	1773.89i	0.0221525	−	0.106796i
$652$		0			0
$653$	−1174.61	+	2034.49i	−0.0703922	+	0.121923i	−0.899073	−	0.437798i	$-0.855758\pi$
$653$	−1174.61	+	2034.49i	−0.0703922	+	0.121923i	0.828681	+	0.559721i	$0.189092\pi$
$654$		0			0
$655$	−5543.93	−	9602.37i	−0.330716	−	0.572817i
$656$		0			0
$657$	2692.02			0.159857
$658$		0			0
$659$	20057.6			1.18563			0.592816	−	0.805338i	$-0.298016\pi$
$659$	20057.6			1.18563			0.592816	+	0.805338i	$0.298016\pi$
$660$		0			0
$661$	−14824.6	−	25677.0i	−0.872331	−	1.51092i	−0.859579	−	0.511003i	$-0.829274\pi$
$661$	−14824.6	−	25677.0i	−0.872331	−	1.51092i	−0.0127517	−	0.999919i	$-0.504059\pi$
$662$		0			0
$663$	2407.90	−	4170.61i	0.141048	−	0.244303i
$664$		0			0
$665$	−404.166	−	360.334i	−0.0235682	−	0.0210123i
$666$		0			0
$667$	1585.39	−	2745.97i	0.0920337	−	0.159407i
$668$		0			0
$669$	−6636.56	−	11494.9i	−0.383534	−	0.664301i
$670$		0			0
$671$	11849.3			0.681723
$672$		0			0
$673$	9178.85			0.525733			0.262867	−	0.964832i	$-0.415332\pi$
$673$	9178.85			0.525733			0.262867	+	0.964832i	$0.415332\pi$
$674$		0			0
$675$	11191.8	+	19384.7i	0.638179	+	1.10536i
$676$		0			0
$677$	231.272	−	400.574i	0.0131292	−	0.0227405i	−0.859386	−	0.511327i	$-0.829154\pi$
$677$	231.272	−	400.574i	0.0131292	−	0.0227405i	0.872515	+	0.488587i	$0.162487\pi$
$678$		0			0
$679$	−1115.26	+	368.435i	−0.0630335	+	0.0208236i
$680$		0			0
$681$	−9645.02	+	16705.7i	−0.542728	+	0.940033i
$682$		0			0
$683$	−9437.01	−	16345.4i	−0.528693	−	0.915723i	−0.999440	−	0.0334549i	$-0.989349\pi$
$683$	−9437.01	−	16345.4i	−0.528693	−	0.915723i	0.470747	−	0.882268i	$-0.343984\pi$
$684$		0			0
$685$	18247.6			1.01781
$686$		0			0
$687$	−19035.3			−1.05712
$688$		0			0
$689$	9984.97	+	17294.5i	0.552100	+	0.956265i
$690$		0			0
$691$	3099.69	−	5368.81i	0.170648	−	0.295571i	−0.767999	−	0.640451i	$-0.778747\pi$
$691$	3099.69	−	5368.81i	0.170648	−	0.295571i	0.938647	+	0.344881i	$0.112081\pi$
$692$		0			0
$693$	−9760.85	+	3224.57i	−0.535042	+	0.176755i
$694$		0			0
$695$	−13645.9	+	23635.4i	−0.744775	+	1.28999i
$696$		0			0
$697$	−3239.29	−	5610.62i	−0.176036	−	0.304903i
$698$		0			0
$699$	−17164.1			−0.928764
$700$		0			0
$701$	−7422.22			−0.399905			−0.199952	−	0.979806i	$-0.564079\pi$
$701$	−7422.22			−0.399905			−0.199952	+	0.979806i	$0.564079\pi$
$702$		0			0
$703$	216.039	+	374.190i	0.0115904	+	0.0200752i
$704$		0			0
$705$	−1938.24	+	3357.12i	−0.103543	+	0.179343i
$706$		0			0
$707$	23028.7	+	20531.2i	1.22501	+	1.09216i
$708$		0			0
$709$	−1616.03	+	2799.04i	−0.0856010	+	0.148265i	−0.905647	−	0.424032i	$-0.860614\pi$
$709$	−1616.03	+	2799.04i	−0.0856010	+	0.148265i	0.820046	+	0.572297i	$0.193948\pi$
$710$		0			0
$711$	4436.53	+	7684.30i	0.234012	+	0.405321i
$712$		0			0
$713$	587.054			0.0308350
$714$		0			0
$715$	60041.3			3.14044
$716$		0			0
$717$	9740.05	+	16870.3i	0.507320	+	0.878705i
$718$		0			0
$719$	−10474.7	+	18142.7i	−0.543309	+	0.941039i	0.455402	+	0.890286i	$0.349496\pi$
$719$	−10474.7	+	18142.7i	−0.543309	+	0.941039i	−0.998711	+	0.0507532i	$0.983838\pi$
$720$		0			0
$721$	6246.39	−	30113.4i	0.322646	−	1.55545i
$722$		0			0
$723$	8973.37	−	15542.3i	0.461581	−	0.799482i
$724$		0			0
$725$	−10240.7	−	17737.5i	−0.524595	−	0.908624i
$726$		0			0
$727$	8068.72			0.411626			0.205813	−	0.978591i	$-0.434016\pi$
$727$	8068.72			0.411626			0.205813	+	0.978591i	$0.434016\pi$
$728$		0			0
$729$	18606.2			0.945292
$730$		0			0
$731$	−2290.66	−	3967.54i	−0.115900	−	0.200745i
$732$		0			0
$733$	18918.3	−	32767.5i	0.953293	−	1.65115i	0.215067	−	0.976599i	$-0.431003\pi$
$733$	18918.3	−	32767.5i	0.953293	−	1.65115i	0.738226	−	0.674553i	$-0.235664\pi$
$734$		0			0
$735$	−17463.4	+	12951.9i	−0.876391	+	0.649983i
$736$		0			0
$737$	−12624.0	+	21865.3i	−0.630949	+	1.09284i
$738$		0			0
$739$	−6615.47	−	11458.3i	−0.329302	−	0.570367i	0.653072	−	0.757296i	$-0.273480\pi$
$739$	−6615.47	−	11458.3i	−0.329302	−	0.570367i	−0.982373	+	0.186929i	$0.940147\pi$
$740$		0			0
$741$	545.503			0.0270440
$742$		0			0
$743$	−3367.17			−0.166257			−0.0831287	−	0.996539i	$-0.526491\pi$
$743$	−3367.17			−0.166257			−0.0831287	+	0.996539i	$0.526491\pi$
$744$		0			0
$745$	−22889.1	−	39645.1i	−1.12563	−	1.94964i
$746$		0			0
$747$	1266.01	−	2192.79i	0.0620090	−	0.107403i
$748$		0			0
$749$	6866.60	−	33103.4i	0.334980	−	1.61492i
$750$		0			0
$751$	−188.264	+	326.084i	−0.00914763	+	0.0158442i	−0.870563	−	0.492057i	$-0.836245\pi$
$751$	−188.264	+	326.084i	−0.00914763	+	0.0158442i	0.861415	+	0.507901i	$0.169578\pi$
$752$		0			0
$753$	−6352.62	−	11003.1i	−0.307440	−	0.532502i
$754$		0			0
$755$	−31696.7			−1.52789
$756$		0			0
$757$	20874.3			1.00223			0.501116	−	0.865380i	$-0.332923\pi$
$757$	20874.3			1.00223			0.501116	+	0.865380i	$0.332923\pi$
$758$		0			0
$759$	1986.86	+	3441.34i	0.0950178	+	0.164576i
$760$		0			0
$761$	9568.68	−	16573.4i	0.455801	−	0.789470i	−0.542933	−	0.839776i	$-0.682686\pi$
$761$	9568.68	−	16573.4i	0.455801	−	0.789470i	0.998734	+	0.0503060i	$0.0160197\pi$
$762$		0			0
$763$	−10012.0	−	8926.21i	−0.475045	−	0.423526i
$764$		0			0
$765$	−1588.95	+	2752.13i	−0.0750960	+	0.130070i
$766$		0			0
$767$	−14971.5	−	25931.4i	−0.704809	−	1.22077i
$768$		0			0
$769$	−12455.0			−0.584055			−0.292028	−	0.956410i	$-0.594330\pi$
$769$	−12455.0			−0.584055			−0.292028	+	0.956410i	$0.594330\pi$
$770$		0			0
$771$	12984.3			0.606507
$772$		0			0
$773$	−2517.35	−	4360.18i	−0.117132	−	0.202878i	0.801498	−	0.597997i	$-0.204037\pi$
$773$	−2517.35	−	4360.18i	−0.117132	−	0.202878i	−0.918630	+	0.395119i	$0.870703\pi$
$774$		0			0
$775$	1896.02	−	3284.00i	0.0878801	−	0.152213i
$776$		0			0
$777$	16473.9	−	5442.29i	0.760616	−	0.251276i
$778$		0			0
$779$	366.927	−	635.536i	0.0168761	−	0.0292303i
$780$		0			0
$781$	15409.3	+	26689.7i	0.706003	+	1.22283i
$782$		0			0
$783$	−20770.3			−0.947982
$784$		0			0
$785$	573.202			0.0260617
$786$		0			0
$787$	5294.79	+	9170.85i	0.239821	+	0.415382i	0.960663	−	0.277718i	$-0.0895779\pi$
$787$	5294.79	+	9170.85i	0.239821	+	0.415382i	−0.720842	+	0.693100i	$0.756245\pi$
$788$		0			0
$789$	2082.52	−	3607.04i	0.0939668	−	0.162755i
$790$		0			0
$791$	−10515.8	+	3473.99i	−0.472692	+	0.156158i
$792$		0			0
$793$	10582.6	−	18329.6i	0.473897	−	0.820813i
$794$		0			0
$795$	7860.15	+	13614.2i	0.350655	+	0.607352i
$796$		0			0
$797$	−38998.4			−1.73324			−0.866621	−	0.498967i	$-0.833713\pi$
$797$	−38998.4			−1.73324			−0.866621	+	0.498967i	$0.833713\pi$
$798$		0			0
$799$	−954.322			−0.0422547
$800$		0			0
$801$	5818.85	+	10078.5i	0.256678	+	0.444579i
$802$		0			0
$803$	4928.36	−	8536.16i	0.216585	−	0.375137i
$804$		0			0
$805$	−5258.86	−	4688.54i	−0.230249	−	0.205279i
$806$		0			0
$807$	221.949	−	384.427i	0.00968151	−	0.0167689i
$808$		0			0
$809$	−18992.6	−	32896.1i	−0.825394	−	1.42962i	−0.901618	−	0.432533i	$-0.857620\pi$
$809$	−18992.6	−	32896.1i	−0.825394	−	1.42962i	0.0762240	−	0.997091i	$-0.475714\pi$
$810$		0			0
$811$	43986.7			1.90454			0.952270	−	0.305256i	$-0.0987421\pi$
$811$	43986.7			1.90454			0.952270	+	0.305256i	$0.0987421\pi$
$812$		0			0
$813$	−23853.7			−1.02901
$814$		0			0
$815$	21603.8	+	37418.9i	0.928525	+	1.60825i
$816$		0			0
$817$	259.472	−	449.418i	0.0111111	−	0.0192450i
$818$		0			0
$819$	−3729.35	+	17978.9i	−0.159114	+	0.767075i
$820$		0			0
$821$	10088.6	−	17474.0i	0.428861	−	0.742808i	−0.567912	−	0.823090i	$-0.692248\pi$
$821$	10088.6	−	17474.0i	0.428861	−	0.742808i	0.996772	+	0.0802811i	$0.0255818\pi$
$822$		0			0
$823$	−5162.23	−	8941.25i	−0.218644	−	0.378703i	0.735750	−	0.677254i	$-0.236830\pi$
$823$	−5162.23	−	8941.25i	−0.218644	−	0.378703i	−0.954394	+	0.298551i	$0.903497\pi$
$824$		0			0
$825$	25668.1			1.08321
$826$		0			0
$827$	−7744.33			−0.325631			−0.162815	−	0.986657i	$-0.552057\pi$
$827$	−7744.33			−0.325631			−0.162815	+	0.986657i	$0.552057\pi$
$828$		0			0
$829$	13443.0	+	23284.0i	0.563204	+	0.975499i	0.997214	+	0.0745904i	$0.0237649\pi$
$829$	13443.0	+	23284.0i	0.563204	+	0.975499i	−0.434010	+	0.900908i	$0.642902\pi$
$830$		0			0
$831$	−12267.7	+	21248.3i	−0.512109	+	0.887000i
$832$		0			0
$833$	−4910.95	−	2128.95i	−0.204267	−	0.0885518i
$834$		0			0
$835$	5171.40	−	8957.12i	0.214328	−	0.371226i
$836$		0			0
$837$	−1922.76	−	3330.32i	−0.0794030	−	0.137530i
$838$		0			0
$839$	24127.6			0.992822			0.496411	−	0.868088i	$-0.334651\pi$
$839$	24127.6			0.992822			0.496411	+	0.868088i	$0.334651\pi$
$840$		0			0
$841$	−5383.68			−0.220742
$842$		0			0
$843$	−14303.9	−	24775.2i	−0.584406	−	1.01222i
$844$		0			0
$845$	35454.0	−	61408.2i	1.44338	−	2.50001i
$846$		0			0
$847$	−2637.96	+	12717.4i	−0.107014	+	0.515909i
$848$		0			0
$849$	−10172.9	+	17620.0i	−0.411229	+	0.712269i
$850$		0			0
$851$	2811.02	+	4868.83i	0.113232	+	0.196124i
$852$		0			0
$853$	−24949.2			−1.00146			−0.500729	−	0.865604i	$-0.666935\pi$
$853$	−24949.2			−1.00146			−0.500729	+	0.865604i	$0.666935\pi$
$854$		0			0
$855$	−359.971			−0.0143986
$856$		0			0
$857$	14919.3	+	25841.0i	0.594672	+	1.03000i	0.993593	+	0.113017i	$0.0360515\pi$
$857$	14919.3	+	25841.0i	0.594672	+	1.03000i	−0.398921	+	0.916985i	$0.630615\pi$
$858$		0			0
$859$	17720.3	−	30692.4i	0.703851	−	1.21910i	−0.263254	−	0.964726i	$-0.584796\pi$
$859$	17720.3	−	30692.4i	0.703851	−	1.21910i	0.967105	−	0.254378i	$-0.0818708\pi$
$860$		0			0
$861$	−21994.9	−	19609.5i	−0.870596	−	0.776180i
$862$		0			0
$863$	−11403.5	+	19751.5i	−0.449804	+	0.779083i	−0.998373	−	0.0570224i	$-0.981839\pi$
$863$	−11403.5	+	19751.5i	−0.449804	+	0.779083i	0.548569	+	0.836105i	$0.315173\pi$
$864$		0			0
$865$	7245.36	+	12549.3i	0.284797	+	0.493283i
$866$		0			0
$867$	−17895.6			−0.700998
$868$		0			0
$869$	32488.3			1.26823
$870$		0			0
$871$	22549.0	+	39056.0i	0.877203	+	1.51936i
$872$		0			0
$873$	−390.420	+	676.226i	−0.0151360	+	0.0262163i
$874$		0			0
$875$	−6854.82	+	2264.55i	−0.264840	+	0.0874921i
$876$		0			0
$877$	17451.9	−	30227.6i	0.671960	−	1.16387i	−0.305388	−	0.952228i	$-0.598786\pi$
$877$	17451.9	−	30227.6i	0.671960	−	1.16387i	0.977348	−	0.211641i	$-0.0678806\pi$
$878$		0			0
$879$	−914.247	−	1583.52i	−0.0350817	−	0.0607632i
$880$		0			0
$881$	41523.3			1.58792			0.793960	−	0.607971i	$-0.208016\pi$
$881$	41523.3			1.58792			0.793960	+	0.607971i	$0.208016\pi$
$882$		0			0
$883$	50289.6			1.91662			0.958312	−	0.285724i	$-0.0922341\pi$
$883$	50289.6			1.91662			0.958312	+	0.285724i	$0.0922341\pi$
$884$		0			0
$885$	−11785.5	−	20413.1i	−0.447645	−	0.775344i
$886$		0			0
$887$	5310.11	−	9197.39i	0.201010	−	0.348160i	−0.747844	−	0.663875i	$-0.768911\pi$
$887$	5310.11	−	9197.39i	0.201010	−	0.348160i	0.948854	+	0.315715i	$0.102244\pi$
$888$		0			0
$889$	−33666.6	+	11122.0i	−1.27012	+	0.419596i
$890$		0			0
$891$	5521.84	−	9564.10i	0.207619	−	0.359607i
$892$		0			0
$893$	−54.0498	−	93.6169i	−0.00202543	−	0.00350814i
$894$		0			0
$895$	−73953.5			−2.76200
$896$		0			0
$897$	7097.89			0.264205
$898$		0			0
$899$	1759.37	+	3047.32i	0.0652707	+	0.113052i
$900$		0			0
$901$	−1935.04	+	3351.58i	−0.0715487	+	0.123926i
$902$		0			0
$903$	−15553.6	−	13866.9i	−0.573192	−	0.511030i
$904$		0			0
$905$	22697.9	−	39313.9i	0.833706	−	1.44402i
$906$		0			0
$907$	871.549	+	1509.57i	0.0319066	+	0.0552639i	0.881538	−	0.472113i	$-0.156509\pi$
$907$	871.549	+	1509.57i	0.0319066	+	0.0552639i	−0.849631	+	0.527377i	$0.823175\pi$
$908$		0			0
$909$	20510.5			0.748396
$910$		0			0
$911$	14466.5			0.526120			0.263060	−	0.964780i	$-0.415268\pi$
$911$	14466.5			0.526120			0.263060	+	0.964780i	$0.415268\pi$
$912$		0			0
$913$	−4635.42	−	8028.78i	−0.168028	−	0.291034i
$914$		0			0
$915$	8330.62	−	14429.1i	0.300986	−	0.521322i
$916$		0			0
$917$	2521.65	−	12156.7i	0.0908092	−	0.437785i
$918$		0			0
$919$	−11657.3	+	20191.0i	−0.418430	+	0.724742i	−0.995782	−	0.0917533i	$-0.970753\pi$
$919$	−11657.3	+	20191.0i	−0.418430	+	0.724742i	0.577352	+	0.816496i	$0.304086\pi$
$920$		0			0
$921$	17413.4	+	30160.9i	0.623008	+	1.07908i
$922$		0			0
$923$	55048.4			1.96310
$924$		0			0
$925$	36315.2			1.29085
$926$		0			0
$927$	−10222.8	−	17706.4i	−0.362202	−	0.627352i
$928$		0			0
$929$	−1597.28	+	2766.57i	−0.0564102	+	0.0977054i	−0.892852	−	0.450351i	$-0.851299\pi$
$929$	−1597.28	+	2766.57i	−0.0564102	+	0.0977054i	0.836441	+	0.548057i	$0.184632\pi$
$930$		0			0
$931$	−69.2955	−	602.331i	−0.00243939	−	0.0212036i
$932$		0			0
$933$	11769.9	−	20386.0i	0.412999	−	0.715335i
$934$		0			0
$935$	5817.85	+	10076.8i	0.203491	+	0.352457i
$936$		0			0
$937$	40.7704			0.00142146			0.000710732	−	1.00000i	$-0.499774\pi$
$937$	40.7704			0.00142146			0.000710732		1.00000i	$0.499774\pi$
$938$		0			0
$939$	35015.8			1.21693
$940$		0			0
$941$	17664.4	+	30595.6i	0.611948	+	1.05992i	0.990912	+	0.134513i	$0.0429471\pi$
$941$	17664.4	+	30595.6i	0.611948	+	1.05992i	−0.378964	+	0.925411i	$0.623720\pi$
$942$		0			0
$943$	4774.31	−	8269.35i	0.164871	−	0.285564i
$944$		0			0
$945$	−9373.59	+	45189.4i	−0.322670	+	1.55557i
$946$		0			0
$947$	−8027.32	+	13903.7i	−0.275452	+	0.477097i	−0.970249	−	0.242109i	$-0.922161\pi$
$947$	−8027.32	+	13903.7i	−0.275452	+	0.477097i	0.694797	+	0.719206i	$0.255494\pi$
$948$		0			0
$949$	−8803.06	−	15247.4i	−0.301116	−	0.521549i
$950$		0			0
$951$	−14088.2			−0.480381
$952$		0			0
$953$	16044.6			0.545369			0.272685	−	0.962103i	$-0.412088\pi$
$953$	16044.6			0.545369			0.272685	+	0.962103i	$0.412088\pi$
$954$		0			0
$955$	27665.1	+	47917.3i	0.937404	+	1.62363i
$956$		0			0
$957$	−11909.1	+	20627.1i	−0.402262	+	0.696739i
$958$		0			0
$959$	15251.2	+	13597.2i	0.513542	+	0.457849i
$960$		0			0
$961$	14569.8	−	25235.6i	0.489066	−	0.847087i
$962$		0			0
$963$	−11237.8	−	19464.5i	−0.376048	−	0.651335i
$964$		0			0
$965$	36348.9			1.21255
$966$		0			0
$967$	−3588.51			−0.119337			−0.0596684	−	0.998218i	$-0.519004\pi$
$967$	−3588.51			−0.119337			−0.0596684	+	0.998218i	$0.519004\pi$
$968$		0			0
$969$	52.8579	+	91.5526i	0.00175236	+	0.00303518i
$970$		0			0
$971$	−1002.71	+	1736.74i	−0.0331394	+	0.0573991i	−0.882119	−	0.471026i	$-0.843884\pi$
$971$	−1002.71	+	1736.74i	−0.0331394	+	0.0573991i	0.848980	+	0.528425i	$0.177217\pi$
$972$		0			0
$973$	−29017.2	+	9586.05i	−0.956061	+	0.315843i
$974$		0			0
$975$	22924.2	−	39705.9i	0.752987	−	1.30421i
$976$		0			0
$977$	19855.2	+	34390.2i	0.650178	+	1.12614i	0.983079	+	0.183180i	$0.0586392\pi$
$977$	19855.2	+	34390.2i	0.650178	+	1.12614i	−0.332901	+	0.942962i	$0.608027\pi$
$978$		0			0
$979$	42610.9			1.39106
$980$		0			0
$981$	−8917.22			−0.290219
$982$		0			0
$983$	22461.3	+	38904.2i	0.728795	+	1.26231i	0.957393	+	0.288789i	$0.0932526\pi$
$983$	22461.3	+	38904.2i	0.728795	+	1.26231i	−0.228598	+	0.973521i	$0.573414\pi$
$984$		0			0
$985$	−25729.4	+	44564.7i	−0.832292	+	1.44157i
$986$		0			0
$987$	−4121.53	+	1361.58i	−0.132918	+	0.0439105i
$988$		0			0
$989$	3376.15	−	5847.66i	0.108549	−	0.188013i
$990$		0			0
$991$	7436.19	+	12879.9i	0.238364	+	0.412858i	0.960245	−	0.279159i	$-0.0900557\pi$
$991$	7436.19	+	12879.9i	0.238364	+	0.412858i	−0.721881	+	0.692017i	$0.756722\pi$
$992$		0			0
$993$	−9189.77			−0.293684
$994$		0			0
$995$	7593.49			0.241940
$996$		0			0
$997$	22894.2	+	39654.0i	0.727249	+	1.25963i	0.958042	+	0.286629i	$0.0925348\pi$
$997$	22894.2	+	39654.0i	0.727249	+	1.25963i	−0.230792	+	0.973003i	$0.574132\pi$
$998$		0			0
$999$	18413.7	−	31893.5i	0.583167	−	1.01007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.4.i.b.93.7	✓	44
7.4	even	3	inner	644.4.i.b.277.7	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.4.i.b.93.7	✓	44	1.1	even	1	trivial
644.4.i.b.277.7	yes	44	7.4	even	3	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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	644.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.91623 - 3.31900i) q^{3} +(8.26993 - 14.3239i) q^{5} +(17.5855 - 5.80951i) q^{7} +(6.15616 - 10.6628i) q^{9} +O(q^{10})\)	\(q+(-1.91623 - 3.31900i) q^{3} +(8.26993 - 14.3239i) q^{5} +(17.5855 - 5.80951i) q^{7} +(6.15616 - 10.6628i) q^{9} +(-22.5405 - 39.0412i) q^{11} -80.5239 q^{13} -63.3882 q^{15} +(-7.80256 - 13.5144i) q^{17} +(0.883825 - 1.53083i) q^{19} +(-52.9795 - 47.2339i) q^{21} +(11.5000 - 19.9186i) q^{23} +(-74.2836 - 128.663i) q^{25} -150.663 q^{27} +137.860 q^{29} +(12.7620 + 22.1045i) q^{31} +(-86.3853 + 149.624i) q^{33} +(62.2158 - 299.938i) q^{35} +(-122.218 + 211.688i) q^{37} +(154.302 + 267.259i) q^{39} +415.158 q^{41} +293.578 q^{43} +(-101.822 - 176.361i) q^{45} +(30.5772 - 52.9613i) q^{47} +(275.499 - 204.326i) q^{49} +(-29.9029 + 51.7934i) q^{51} +(-124.000 - 214.774i) q^{53} -745.633 q^{55} -6.77443 q^{57} +(185.926 + 322.033i) q^{59} +(-131.422 + 227.630i) q^{61} +(46.3136 - 223.274i) q^{63} +(-665.927 + 1153.42i) q^{65} +(-280.029 - 485.024i) q^{67} -88.1464 q^{69} -683.628 q^{71} +(109.322 + 189.352i) q^{73} +(-284.688 + 493.095i) q^{75} +(-623.196 - 555.611i) q^{77} +(-360.333 + 624.114i) q^{79} +(122.487 + 212.154i) q^{81} +205.649 q^{83} -258.107 q^{85} +(-264.170 - 457.557i) q^{87} +(-472.604 + 818.574i) q^{89} +(-1416.05 + 467.804i) q^{91} +(48.9099 - 84.7144i) q^{93} +(-14.6183 - 25.3197i) q^{95} -63.4193 q^{97} -555.051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9}+O(q^{10}) \) 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9	\( 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9} + 28 q^{11} - 152 q^{13} + 208 q^{15} - 52 q^{17} + 38 q^{19} - 10 q^{21} + 506 q^{23} - 516 q^{25} - 876 q^{27} - 100 q^{29} + 230 q^{31} + 424 q^{33} + 98 q^{35} + 18 q^{37} - 350 q^{39} + 784 q^{41} - 336 q^{43} + 1156 q^{45} + 452 q^{47} + 546 q^{49} - 498 q^{51} - 508 q^{53} - 3084 q^{55} - 1916 q^{57} + 508 q^{59} + 1386 q^{61} + 1290 q^{63} + 360 q^{65} - 1896 q^{67} + 552 q^{69} - 3352 q^{71} + 990 q^{73} + 3328 q^{75} + 1328 q^{77} + 524 q^{79} - 4486 q^{81} - 1120 q^{83} - 5296 q^{85} + 3700 q^{87} + 1216 q^{89} + 1438 q^{91} + 366 q^{93} + 90 q^{95} + 716 q^{97} + 5716 q^{99}+O(q^{100}) \) 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9 + 28 * q^11 - 152 * q^13 + 208 * q^15 - 52 * q^17 + 38 * q^19 - 10 * q^21 + 506 * q^23 - 516 * q^25 - 876 * q^27 - 100 * q^29 + 230 * q^31 + 424 * q^33 + 98 * q^35 + 18 * q^37 - 350 * q^39 + 784 * q^41 - 336 * q^43 + 1156 * q^45 + 452 * q^47 + 546 * q^49 - 498 * q^51 - 508 * q^53 - 3084 * q^55 - 1916 * q^57 + 508 * q^59 + 1386 * q^61 + 1290 * q^63 + 360 * q^65 - 1896 * q^67 + 552 * q^69 - 3352 * q^71 + 990 * q^73 + 3328 * q^75 + 1328 * q^77 + 524 * q^79 - 4486 * q^81 - 1120 * q^83 - 5296 * q^85 + 3700 * q^87 + 1216 * q^89 + 1438 * q^91 + 366 * q^93 + 90 * q^95 + 716 * q^97 + 5716 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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