LMFDB - Embedded newform 169.4.e.e.23.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(23,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("169.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.e (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	169.23
Dual form			169.4.e.e.147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.33013 + 2.50000i) q^{2} +(3.50000 + 6.06218i) q^{3} +(8.50000 - 14.7224i) q^{4} -7.00000i q^{5} +(-30.3109 - 17.5000i) q^{6} +(-11.2583 - 6.50000i) q^{7} +45.0000i q^{8} +(-11.0000 + 19.0526i) q^{9} +O(q^{10})$	\(q+(-4.33013 + 2.50000i) q^{2} +(3.50000 + 6.06218i) q^{3} +(8.50000 - 14.7224i) q^{4} -7.00000i q^{5} +(-30.3109 - 17.5000i) q^{6} +(-11.2583 - 6.50000i) q^{7} +45.0000i q^{8} +(-11.0000 + 19.0526i) q^{9} +(17.5000 + 30.3109i) q^{10} +(22.5167 - 13.0000i) q^{11} +119.000 q^{12} +65.0000 q^{14} +(42.4352 - 24.5000i) q^{15} +(-44.5000 - 77.0763i) q^{16} +(38.5000 - 66.6840i) q^{17} -110.000i q^{18} +(109.119 + 63.0000i) q^{19} +(-103.057 - 59.5000i) q^{20} -91.0000i q^{21} +(-65.0000 + 112.583i) q^{22} +(-48.0000 - 83.1384i) q^{23} +(-272.798 + 157.500i) q^{24} +76.0000 q^{25} +35.0000 q^{27} +(-191.392 + 110.500i) q^{28} +(41.0000 + 71.0141i) q^{29} +(-122.500 + 212.176i) q^{30} +196.000i q^{31} +(73.6122 + 42.5000i) q^{32} +(157.617 + 91.0000i) q^{33} +385.000i q^{34} +(-45.5000 + 78.8083i) q^{35} +(187.000 + 323.894i) q^{36} +(113.449 - 65.5000i) q^{37} -630.000 q^{38} +315.000 q^{40} +(290.985 - 168.000i) q^{41} +(227.500 + 394.042i) q^{42} +(-100.500 + 174.071i) q^{43} -442.000i q^{44} +(133.368 + 77.0000i) q^{45} +(415.692 + 240.000i) q^{46} +105.000i q^{47} +(311.500 - 539.534i) q^{48} +(-87.0000 - 150.688i) q^{49} +(-329.090 + 190.000i) q^{50} +539.000 q^{51} -432.000 q^{53} +(-151.554 + 87.5000i) q^{54} +(-91.0000 - 157.617i) q^{55} +(292.500 - 506.625i) q^{56} +882.000i q^{57} +(-355.070 - 205.000i) q^{58} +(-254.611 - 147.000i) q^{59} -833.000i q^{60} +(28.0000 - 48.4974i) q^{61} +(-490.000 - 848.705i) q^{62} +(247.683 - 143.000i) q^{63} +287.000 q^{64} -910.000 q^{66} +(413.960 - 239.000i) q^{67} +(-654.500 - 1133.63i) q^{68} +(336.000 - 581.969i) q^{69} -455.000i q^{70} +(-7.79423 - 4.50000i) q^{71} +(-857.365 - 495.000i) q^{72} -98.0000i q^{73} +(-327.500 + 567.247i) q^{74} +(266.000 + 460.726i) q^{75} +(1855.03 - 1071.00i) q^{76} -338.000 q^{77} +1304.00 q^{79} +(-539.534 + 311.500i) q^{80} +(419.500 + 726.595i) q^{81} +(-840.000 + 1454.92i) q^{82} -308.000i q^{83} +(-1339.74 - 773.500i) q^{84} +(-466.788 - 269.500i) q^{85} -1005.00i q^{86} +(-287.000 + 497.099i) q^{87} +(585.000 + 1013.25i) q^{88} +(1030.57 - 595.000i) q^{89} -770.000 q^{90} -1632.00 q^{92} +(-1188.19 + 686.000i) q^{93} +(-262.500 - 454.663i) q^{94} +(441.000 - 763.834i) q^{95} +595.000i q^{96} +(-60.6218 - 35.0000i) q^{97} +(753.442 + 435.000i) q^{98} +572.000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 14 q^{3} + 34 q^{4} - 44 q^{9}+O(q^{10}) $ 4 * q + 14 * q^3 + 34 * q^4 - 44 * q^9	$ 4 q + 14 q^{3} + 34 q^{4} - 44 q^{9} + 70 q^{10} + 476 q^{12} + 260 q^{14} - 178 q^{16} + 154 q^{17} - 260 q^{22} - 192 q^{23} + 304 q^{25} + 140 q^{27} + 164 q^{29} - 490 q^{30} - 182 q^{35} + 748 q^{36} - 2520 q^{38} + 1260 q^{40} + 910 q^{42} - 402 q^{43} + 1246 q^{48} - 348 q^{49} + 2156 q^{51} - 1728 q^{53} - 364 q^{55} + 1170 q^{56} + 112 q^{61} - 1960 q^{62} + 1148 q^{64} - 3640 q^{66} - 2618 q^{68} + 1344 q^{69} - 1310 q^{74} + 1064 q^{75} - 1352 q^{77} + 5216 q^{79} + 1678 q^{81} - 3360 q^{82} - 1148 q^{87} + 2340 q^{88} - 3080 q^{90} - 6528 q^{92} - 1050 q^{94} + 1764 q^{95}+O(q^{100}) $ 4 * q + 14 * q^3 + 34 * q^4 - 44 * q^9 + 70 * q^10 + 476 * q^12 + 260 * q^14 - 178 * q^16 + 154 * q^17 - 260 * q^22 - 192 * q^23 + 304 * q^25 + 140 * q^27 + 164 * q^29 - 490 * q^30 - 182 * q^35 + 748 * q^36 - 2520 * q^38 + 1260 * q^40 + 910 * q^42 - 402 * q^43 + 1246 * q^48 - 348 * q^49 + 2156 * q^51 - 1728 * q^53 - 364 * q^55 + 1170 * q^56 + 112 * q^61 - 1960 * q^62 + 1148 * q^64 - 3640 * q^66 - 2618 * q^68 + 1344 * q^69 - 1310 * q^74 + 1064 * q^75 - 1352 * q^77 + 5216 * q^79 + 1678 * q^81 - 3360 * q^82 - 1148 * q^87 + 2340 * q^88 - 3080 * q^90 - 6528 * q^92 - 1050 * q^94 + 1764 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−4.33013	+	2.50000i	−1.53093	+	0.883883i	−0.531612	+	0.846988i	$0.678414\pi$
$2$	−4.33013	+	2.50000i	−1.53093	+	0.883883i	−0.999319	+	0.0368954i	$0.988253\pi$
$3$	3.50000	+	6.06218i	0.673575	+	1.16667i	0.976883	+	0.213774i	$0.0685756\pi$
$3$	3.50000	+	6.06218i	0.673575	+	1.16667i	−0.303308	+	0.952893i	$0.598091\pi$
$4$	8.50000	−	14.7224i	1.06250	−	1.84030i
$5$		−	7.00000i		−	0.626099i	−0.949737	−	0.313050i	$-0.898649\pi$
$5$		−	7.00000i		−	0.626099i	0.949737	−	0.313050i	$-0.101351\pi$
$6$	−30.3109	−	17.5000i	−2.06239	−	1.19072i
$7$	−11.2583	−	6.50000i	−0.607893	−	0.350967i	0.164248	−	0.986419i	$-0.447480\pi$
$7$	−11.2583	−	6.50000i	−0.607893	−	0.350967i	−0.772140	+	0.635452i	$0.780814\pi$
$8$			45.0000i			1.98874i
$9$	−11.0000	+	19.0526i	−0.407407	+	0.705650i
$10$	17.5000	+	30.3109i	0.553399	+	0.958514i
$11$	22.5167	−	13.0000i	0.617184	−	0.356332i	−0.158588	−	0.987345i	$-0.550694\pi$
$11$	22.5167	−	13.0000i	0.617184	−	0.356332i	0.775772	+	0.631013i	$0.217361\pi$
$12$	119.000			2.86270
$13$		0			0
$13$		0			0
$14$	65.0000			1.24086
$15$	42.4352	−	24.5000i	0.730449	−	0.421725i
$16$	−44.5000	−	77.0763i	−0.695312	−	1.20432i
$17$	38.5000	−	66.6840i	0.549272	−	0.951367i	−0.449053	−	0.893505i	$-0.648238\pi$
$17$	38.5000	−	66.6840i	0.549272	−	0.951367i	0.998325	−	0.0578615i	$-0.0184282\pi$
$18$		−	110.000i		−	1.44040i
$19$	109.119	+	63.0000i	1.31756	+	0.760694i	0.983336	−	0.181799i	$-0.0581920\pi$
$19$	109.119	+	63.0000i	1.31756	+	0.760694i	0.334225	+	0.942493i	$0.391525\pi$
$20$	−103.057	−	59.5000i	−1.15221	−	0.665230i
$21$		−	91.0000i		−	0.945611i
$22$	−65.0000	+	112.583i	−0.629911	+	1.09104i
$23$	−48.0000	−	83.1384i	−0.435161	−	0.753720i	0.562148	−	0.827037i	$-0.309975\pi$
$23$	−48.0000	−	83.1384i	−0.435161	−	0.753720i	−0.997309	+	0.0733164i	$0.976642\pi$
$24$	−272.798	+	157.500i	−2.32019	+	1.33956i
$25$	76.0000			0.608000
$26$		0			0
$27$	35.0000			0.249472
$28$	−191.392	+	110.500i	−1.29177	+	0.745805i
$29$	41.0000	+	71.0141i	0.262535	+	0.454724i	0.966915	−	0.255099i	$-0.0821082\pi$
$29$	41.0000	+	71.0141i	0.262535	+	0.454724i	−0.704380	+	0.709823i	$0.748775\pi$
$30$	−122.500	+	212.176i	−0.745511	+	1.29126i
$31$			196.000i			1.13557i	0.823177	+	0.567785i	$0.192199\pi$
$31$			196.000i			1.13557i	−0.823177	+	0.567785i	$0.807801\pi$
$32$	73.6122	+	42.5000i	0.406654	+	0.234782i
$33$	157.617	+	91.0000i	0.831440	+	0.480032i
$34$			385.000i			1.94197i
$35$	−45.5000	+	78.8083i	−0.219740	+	0.380601i
$36$	187.000	+	323.894i	0.865741	+	1.49951i
$37$	113.449	−	65.5000i	0.504080	−	0.291031i	−0.226317	−	0.974054i	$-0.572669\pi$
$37$	113.449	−	65.5000i	0.504080	−	0.291031i	0.730397	+	0.683023i	$0.239335\pi$
$38$	−630.000			−2.68946
$39$		0			0
$40$	315.000			1.24515
$41$	290.985	−	168.000i	1.10839	−	0.639932i	0.169981	−	0.985447i	$-0.445629\pi$
$41$	290.985	−	168.000i	1.10839	−	0.639932i	0.938413	+	0.345516i	$0.112296\pi$
$42$	227.500	+	394.042i	0.835810	+	1.44767i
$43$	−100.500	+	174.071i	−0.356421	+	0.617339i	−0.987360	−	0.158493i	$-0.949336\pi$
$43$	−100.500	+	174.071i	−0.356421	+	0.617339i	0.630939	+	0.775832i	$0.282670\pi$
$44$		−	442.000i		−	1.51441i
$45$	133.368	+	77.0000i	0.441807	+	0.255077i
$46$	415.692	+	240.000i	1.33240	+	0.769262i
$47$			105.000i			0.325869i	0.986637	+	0.162934i	$0.0520959\pi$
$47$			105.000i			0.325869i	−0.986637	+	0.162934i	$0.947904\pi$
$48$	311.500	−	539.534i	0.936691	−	1.62240i
$49$	−87.0000	−	150.688i	−0.253644	−	0.439325i
$50$	−329.090	+	190.000i	−0.930806	+	0.537401i
$51$	539.000			1.47990
$52$		0			0
$53$	−432.000			−1.11962			−0.559809	−	0.828622i	$-0.689126\pi$
$53$	−432.000			−1.11962			−0.559809	+	0.828622i	$0.689126\pi$
$54$	−151.554	+	87.5000i	−0.381925	+	0.220504i
$55$	−91.0000	−	157.617i	−0.223099	−	0.386419i
$56$	292.500	−	506.625i	0.697981	−	1.20894i
$57$			882.000i			2.04954i
$58$	−355.070	−	205.000i	−0.803845	−	0.464100i
$59$	−254.611	−	147.000i	−0.561824	−	0.324369i	0.192054	−	0.981384i	$-0.438485\pi$
$59$	−254.611	−	147.000i	−0.561824	−	0.324369i	−0.753877	+	0.657015i	$0.771819\pi$
$60$		−	833.000i		−	1.79233i
$61$	28.0000	−	48.4974i	0.0587710	−	0.101794i	−0.835143	−	0.550033i	$-0.814615\pi$
$61$	28.0000	−	48.4974i	0.0587710	−	0.101794i	0.893914	+	0.448239i	$0.147948\pi$
$62$	−490.000	−	848.705i	−1.00371	−	1.73848i
$63$	247.683	−	143.000i	0.495320	−	0.285973i
$64$	287.000			0.560547
$65$		0			0
$66$	−910.000			−1.69717
$67$	413.960	−	239.000i	0.754825	−	0.435798i	−0.0726096	−	0.997360i	$-0.523133\pi$
$67$	413.960	−	239.000i	0.754825	−	0.435798i	0.827435	+	0.561562i	$0.189799\pi$
$68$	−654.500	−	1133.63i	−1.16720	−	2.02165i
$69$	336.000	−	581.969i	0.586227	−	1.01537i
$70$		−	455.000i		−	0.776899i
$71$	−7.79423	−	4.50000i	−0.0130282	−	0.00752186i	0.493472	−	0.869762i	$-0.335728\pi$
$71$	−7.79423	−	4.50000i	−0.0130282	−	0.00752186i	−0.506500	+	0.862240i	$0.669061\pi$
$72$	−857.365	−	495.000i	−1.40335	−	0.810227i
$73$		−	98.0000i		−	0.157124i	−0.996909	−	0.0785619i	$-0.974967\pi$
$73$		−	98.0000i		−	0.157124i	0.996909	−	0.0785619i	$-0.0250328\pi$
$74$	−327.500	+	567.247i	−0.514474	+	0.891096i
$75$	266.000	+	460.726i	0.409534	+	0.709333i
$76$	1855.03	−	1071.00i	2.79982	−	1.61648i
$77$	−338.000			−0.500243
$78$		0			0
$79$	1304.00			1.85711			0.928554	−	0.371198i	$-0.121053\pi$
$79$	1304.00			1.85711			0.928554	+	0.371198i	$0.121053\pi$
$80$	−539.534	+	311.500i	−0.754021	+	0.435334i
$81$	419.500	+	726.595i	0.575446	+	0.996701i
$82$	−840.000	+	1454.92i	−1.13125	+	1.95938i
$83$		−	308.000i		−	0.407318i	−0.979042	−	0.203659i	$-0.934717\pi$
$83$		−	308.000i		−	0.407318i	0.979042	−	0.203659i	$-0.0652834\pi$
$84$	−1339.74	−	773.500i	−1.74021	−	1.00471i
$85$	−466.788	−	269.500i	−0.595650	−	0.343899i
$86$		−	1005.00i		−	1.26014i
$87$	−287.000	+	497.099i	−0.353674	+	0.612581i
$88$	585.000	+	1013.25i	0.708650	+	1.22742i
$89$	1030.57	−	595.000i	1.22742	−	0.708650i	0.260929	−	0.965358i	$-0.415971\pi$
$89$	1030.57	−	595.000i	1.22742	−	0.708650i	0.966489	+	0.256708i	$0.0826378\pi$
$90$	−770.000			−0.901835
$91$		0			0
$92$	−1632.00			−1.84943
$93$	−1188.19	+	686.000i	−1.32483	+	0.764891i
$94$	−262.500	−	454.663i	−0.288030	−	0.498882i
$95$	441.000	−	763.834i	0.476270	−	0.824924i
$96$			595.000i			0.632572i
$97$	−60.6218	−	35.0000i	−0.0634558	−	0.0366362i	0.467936	−	0.883762i	$-0.344998\pi$
$97$	−60.6218	−	35.0000i	−0.0634558	−	0.0366362i	−0.531392	+	0.847126i	$0.678331\pi$
$98$	753.442	+	435.000i	0.776624	+	0.448384i
$99$			572.000i			0.580689i
$100$	646.000	−	1118.90i	0.646000	−	1.11890i
$101$	210.000	+	363.731i	0.206889	+	0.358342i	0.950733	−	0.310011i	$-0.100333\pi$
$101$	210.000	+	363.731i	0.206889	+	0.358342i	−0.743844	+	0.668353i	$0.766999\pi$
$102$	−2333.94	+	1347.50i	−2.26563	+	1.30806i
$103$	−588.000			−0.562499			−0.281249	−	0.959635i	$-0.590749\pi$
$103$	−588.000			−0.562499			−0.281249	+	0.959635i	$0.590749\pi$
$104$		0			0
$105$	−637.000			−0.592046
$106$	1870.61	−	1080.00i	1.71406	−	0.989612i
$107$	342.000	+	592.361i	0.308994	+	0.535194i	0.978143	−	0.207935i	$-0.0666743\pi$
$107$	342.000	+	592.361i	0.308994	+	0.535194i	−0.669148	+	0.743129i	$0.733341\pi$
$108$	297.500	−	515.285i	0.265064	−	0.459105i
$109$			373.000i			0.327770i	0.986479	+	0.163885i	$0.0524026\pi$
$109$			373.000i			0.327770i	−0.986479	+	0.163885i	$0.947597\pi$
$110$	788.083	+	455.000i	0.683098	+	0.394387i
$111$	794.145	+	458.500i	0.679071	+	0.392062i
$112$			1157.00i			0.976127i
$113$	867.000	−	1501.69i	0.721774	−	1.25015i	−0.238514	−	0.971139i	$-0.576660\pi$
$113$	867.000	−	1501.69i	0.721774	−	1.25015i	0.960288	−	0.279011i	$-0.0900065\pi$
$114$	−2205.00	−	3819.17i	−1.81155	−	3.13770i
$115$	−581.969	+	336.000i	−0.471903	+	0.272454i
$116$	1394.00			1.11577
$117$		0			0
$118$	1470.00			1.14682
$119$	−866.891	+	500.500i	−0.667797	+	0.385553i
$120$	1102.50	+	1909.59i	0.838700	+	1.45267i
$121$	−327.500	+	567.247i	−0.246056	+	0.426181i
$122$			280.000i			0.207787i
$123$	2036.89	+	1176.00i	1.49317	+	0.862084i
$124$	2885.60	+	1666.00i	2.08979	+	1.20654i
$125$		−	1407.00i		−	1.00677i
$126$	−715.000	+	1238.42i	−0.505534	+	0.875610i
$127$	946.000	+	1638.52i	0.660976	+	1.14484i	0.980360	+	0.197218i	$0.0631907\pi$
$127$	946.000	+	1638.52i	0.660976	+	1.14484i	−0.319384	+	0.947625i	$0.603476\pi$
$128$	−1831.64	+	1057.50i	−1.26481	+	0.730240i
$129$	−1407.00			−0.960306
$130$		0			0
$131$	1435.00			0.957073			0.478536	−	0.878068i	$-0.341167\pi$
$131$	1435.00			0.957073			0.478536	+	0.878068i	$0.341167\pi$
$132$	2679.48	−	1547.00i	1.76681	−	1.02007i
$133$	−819.000	−	1418.55i	−0.533957	−	0.924841i
$134$	−1195.00	+	2069.80i	−0.770390	+	1.33435i
$135$		−	245.000i		−	0.156194i
$136$	3000.78	+	1732.50i	1.89202	+	1.09236i
$137$	−1538.06	−	888.000i	−0.959164	−	0.553773i	−0.0632482	−	0.997998i	$-0.520146\pi$
$137$	−1538.06	−	888.000i	−0.959164	−	0.553773i	−0.895916	+	0.444224i	$0.853479\pi$
$138$			3360.00i			2.07262i
$139$	934.500	−	1618.60i	0.570239	−	0.987683i	−0.426302	−	0.904581i	$-0.640184\pi$
$139$	934.500	−	1618.60i	0.570239	−	0.987683i	0.996541	−	0.0831023i	$-0.0264828\pi$
$140$	773.500	+	1339.74i	0.466948	+	0.808777i
$141$	−636.529	+	367.500i	−0.380180	+	0.219497i
$142$	45.0000			0.0265938
$143$		0			0
$144$	1958.00			1.13310
$145$	497.099	−	287.000i	0.284702	−	0.164373i
$146$	245.000	+	424.352i	0.138879	+	0.240546i
$147$	609.000	−	1054.82i	0.341697	−	0.591837i
$148$		−	2227.00i		−	1.23688i
$149$	−2135.62	−	1233.00i	−1.17421	−	0.677928i	−0.219539	−	0.975604i	$-0.570455\pi$
$149$	−2135.62	−	1233.00i	−1.17421	−	0.677928i	−0.954667	+	0.297676i	$0.903789\pi$
$150$	−2303.63	−	1330.00i	−1.25394	−	0.723960i
$151$			3323.00i			1.79087i	0.445189	+	0.895437i	$0.353137\pi$
$151$			3323.00i			1.79087i	−0.445189	+	0.895437i	$0.646863\pi$
$152$	−2835.00	+	4910.36i	−1.51282	+	2.62028i
$153$	847.000	+	1467.05i	0.447555	+	0.775188i
$154$	1463.58	−	845.000i	0.765837	−	0.442156i
$155$	1372.00			0.710979
$156$		0			0
$157$	−2730.00			−1.38776			−0.693878	−	0.720092i	$-0.744099\pi$
$157$	−2730.00			−1.38776			−0.693878	+	0.720092i	$0.744099\pi$
$158$	−5646.49	+	3260.00i	−2.84310	+	1.64147i
$159$	−1512.00	−	2618.86i	−0.754147	−	1.30622i
$160$	297.500	−	515.285i	0.146997	−	0.254605i
$161$			1248.00i			0.610908i
$162$	−3632.98	−	2097.50i	−1.76194	−	1.01725i
$163$	−471.118	−	272.000i	−0.226385	−	0.130704i	0.382518	−	0.923948i	$-0.375057\pi$
$163$	−471.118	−	272.000i	−0.226385	−	0.130704i	−0.608903	+	0.793244i	$0.708390\pi$
$164$		−	5712.00i		−	2.71971i
$165$	637.000	−	1103.32i	0.300548	−	0.520564i
$166$	770.000	+	1333.68i	0.360022	+	0.623576i
$167$	−1406.43	+	812.000i	−0.651691	+	0.376254i	−0.789104	−	0.614260i	$-0.789455\pi$
$167$	−1406.43	+	812.000i	−0.651691	+	0.376254i	0.137413	+	0.990514i	$0.456121\pi$
$168$	4095.00			1.88057
$169$		0			0
$170$	2695.00			1.21587
$171$	−2400.62	+	1386.00i	−1.07357	+	0.619825i
$172$	1708.50	+	2959.21i	0.757395	+	1.31185i
$173$	−168.000	+	290.985i	−0.0738312	+	0.127879i	−0.900577	−	0.434696i	$-0.856856\pi$
$173$	−168.000	+	290.985i	−0.0738312	+	0.127879i	0.826746	+	0.562575i	$0.190189\pi$
$174$		−	2870.00i		−	1.25043i
$175$	−855.633	−	494.000i	−0.369599	−	0.213388i
$176$	−2003.98	−	1157.00i	−0.858272	−	0.495524i
$177$		−	2058.00i		−	0.873948i
$178$	−2975.00	+	5152.85i	−1.25273	+	2.16979i
$179$	−1514.50	−	2623.19i	−0.632397	−	1.09534i	−0.987060	−	0.160350i	$-0.948738\pi$
$179$	−1514.50	−	2623.19i	−0.632397	−	1.09534i	0.354663	−	0.934994i	$-0.384595\pi$
$180$	2267.25	−	1309.00i	0.938840	−	0.542039i
$181$	28.0000			0.0114985			0.00574924	−	0.999983i	$-0.498170\pi$
$181$	28.0000			0.0114985			0.00574924	+	0.999983i	$0.498170\pi$
$182$		0			0
$183$	392.000			0.158347
$184$	3741.23	−	2160.00i	1.49895	−	0.865420i
$185$	−458.500	−	794.145i	−0.182214	−	0.315604i
$186$	3430.00	−	5940.93i	1.35215	−	2.34199i
$187$		−	2002.00i		−	0.782892i
$188$	1545.86	+	892.500i	0.599697	+	0.346235i
$189$	−394.042	−	227.500i	−0.151652	−	0.0875566i
$190$			4410.00i			1.68387i
$191$	−211.000	+	365.463i	−0.0799342	+	0.138450i	−0.903221	−	0.429175i	$-0.858804\pi$
$191$	−211.000	+	365.463i	−0.0799342	+	0.138450i	0.823287	+	0.567625i	$0.192138\pi$
$192$	1004.50	+	1739.85i	0.377571	+	0.653971i
$193$	−426.084	+	246.000i	−0.158913	+	0.0917485i	−0.577348	−	0.816498i	$-0.695912\pi$
$193$	−426.084	+	246.000i	−0.158913	+	0.0917485i	0.418435	+	0.908247i	$0.362579\pi$
$194$	350.000			0.129529
$195$		0			0
$196$	−2958.00			−1.07799
$197$	2590.28	−	1495.50i	0.936802	−	0.540863i	0.0478455	−	0.998855i	$-0.484765\pi$
$197$	2590.28	−	1495.50i	0.936802	−	0.540863i	0.888956	+	0.457992i	$0.151431\pi$
$198$	−1430.00	−	2476.83i	−0.513261	−	0.888994i
$199$	−35.0000	+	60.6218i	−0.0124678	+	0.0215948i	−0.872192	−	0.489164i	$-0.837302\pi$
$199$	−35.0000	+	60.6218i	−0.0124678	+	0.0215948i	0.859724	+	0.510759i	$0.170635\pi$
$200$			3420.00i			1.20915i
$201$	2897.72	+	1673.00i	1.01686	+	0.587086i
$202$	−1818.65	−	1050.00i	−0.633465	−	0.365731i
$203$		−	1066.00i		−	0.368564i
$204$	4581.50	−	7935.39i	1.57240	−	2.72347i
$205$	−1176.00	−	2036.89i	−0.400661	−	0.693964i
$206$	2546.11	−	1470.00i	0.861147	−	0.497183i
$207$	2112.00			0.709150
$208$		0			0
$209$	3276.00			1.08424
$210$	2758.29	−	1592.50i	0.906382	−	0.523300i
$211$	−1425.50	−	2469.04i	−0.465097	−	0.805572i	0.534109	−	0.845416i	$-0.320647\pi$
$211$	−1425.50	−	2469.04i	−0.465097	−	0.805572i	−0.999206	+	0.0398440i	$0.987314\pi$
$212$	−3672.00	+	6360.09i	−1.18959	+	2.06044i
$213$		−	63.0000i		−	0.0202661i
$214$	−2961.81	−	1710.00i	−0.946098	−	0.546230i
$215$	1218.50	+	703.500i	0.386516	+	0.223155i
$216$			1575.00i			0.496135i
$217$	1274.00	−	2206.63i	0.398547	−	0.690304i
$218$	−932.500	−	1615.14i	−0.289710	−	0.501793i
$219$	594.093	−	343.000i	0.183311	−	0.105835i
$220$	−3094.00			−0.948170
$221$		0			0
$222$	−4585.00			−1.38615
$223$	187.928	−	108.500i	0.0564330	−	0.0325816i	−0.471518	−	0.881856i	$-0.656294\pi$
$223$	187.928	−	108.500i	0.0564330	−	0.0325816i	0.527951	+	0.849275i	$0.322960\pi$
$224$	−552.500	−	956.958i	−0.164801	−	0.285444i
$225$	−836.000	+	1447.99i	−0.247704	+	0.429035i
$226$			8670.00i			2.55186i
$227$	2230.88	+	1288.00i	0.652285	+	0.376597i	0.789331	−	0.613968i	$-0.210427\pi$
$227$	2230.88	+	1288.00i	0.652285	+	0.376597i	−0.137046	+	0.990565i	$0.543761\pi$
$228$	12985.2	+	7497.00i	3.77178	+	2.17764i
$229$		−	455.000i		−	0.131298i	−0.997843	−	0.0656490i	$-0.979088\pi$
$229$		−	455.000i		−	0.131298i	0.997843	−	0.0656490i	$-0.0209118\pi$
$230$	1680.00	−	2909.85i	0.481634	−	0.834215i
$231$	−1183.00	−	2049.02i	−0.336951	−	0.583616i
$232$	−3195.63	+	1845.00i	−0.904326	+	0.522113i
$233$	−3061.00			−0.860656			−0.430328	−	0.902673i	$-0.641602\pi$
$233$	−3061.00			−0.860656			−0.430328	+	0.902673i	$0.641602\pi$
$234$		0			0
$235$	735.000			0.204026
$236$	−4328.39	+	2499.00i	−1.19388	+	0.689284i
$237$	4564.00	+	7905.08i	1.25090	+	2.16662i
$238$	2502.50	−	4334.46i	0.681567	−	1.18051i
$239$		−	3477.00i		−	0.941039i	−0.882389	−	0.470520i	$-0.844066\pi$
$239$		−	3477.00i		−	0.941039i	0.882389	−	0.470520i	$-0.155934\pi$
$240$	−3776.74	−	2180.50i	−1.01578	−	0.586461i
$241$	−1394.30	−	805.000i	−0.372676	−	0.215164i	0.301951	−	0.953323i	$-0.402362\pi$
$241$	−1394.30	−	805.000i	−0.372676	−	0.215164i	−0.674627	+	0.738159i	$0.735695\pi$
$242$		−	3275.00i		−	0.869938i
$243$	−2464.00	+	4267.77i	−0.650476	+	1.12666i
$244$	−476.000	−	824.456i	−0.124888	−	0.216313i
$245$	−1054.82	+	609.000i	−0.275061	+	0.158806i
$246$	−11760.0			−3.04793
$247$		0			0
$248$	−8820.00			−2.25835
$249$	1867.15	−	1078.00i	0.475204	−	0.274359i
$250$	3517.50	+	6092.49i	0.889865	+	1.54129i
$251$	504.000	−	872.954i	0.126742	−	0.219523i	−0.795671	−	0.605730i	$-0.792881\pi$
$251$	504.000	−	872.954i	0.126742	−	0.219523i	0.922412	+	0.386206i	$0.126215\pi$
$252$		−	4862.00i		−	1.21539i
$253$	−2161.60	−	1248.00i	−0.537149	−	0.310123i
$254$	−8192.60	−	4730.00i	−2.02382	−	1.16845i
$255$		−	3773.00i		−	0.926566i
$256$	4139.50	−	7169.82i	1.01062	−	1.75045i
$257$	3020.50	+	5231.66i	0.733127	+	1.26981i	0.955540	+	0.294861i	$0.0952732\pi$
$257$	3020.50	+	5231.66i	0.733127	+	1.26981i	−0.222413	+	0.974952i	$0.571393\pi$
$258$	6092.49	−	3517.50i	1.47016	−	0.848798i
$259$	−1703.00			−0.408569
$260$		0			0
$261$	−1804.00			−0.427834
$262$	−6213.73	+	3587.50i	−1.46521	+	0.845941i
$263$	1854.00	+	3211.22i	0.434686	+	0.752899i	0.997270	−	0.0738414i	$-0.0235259\pi$
$263$	1854.00	+	3211.22i	0.434686	+	0.752899i	−0.562584	+	0.826740i	$0.690193\pi$
$264$	−4095.00	+	7092.75i	−0.954658	+	1.65352i
$265$			3024.00i			0.700992i
$266$	7092.75	+	4095.00i	1.63490	+	0.943912i
$267$	7213.99	+	4165.00i	1.65352	+	0.954659i
$268$		−	8126.00i		−	1.85214i
$269$	−4172.00	+	7226.12i	−0.945618	+	1.63786i	−0.191110	+	0.981569i	$0.561209\pi$
$269$	−4172.00	+	7226.12i	−0.945618	+	1.63786i	−0.754508	+	0.656290i	$0.772125\pi$
$270$	612.500	+	1060.88i	0.138058	+	0.239123i
$271$	1400.36	−	808.500i	0.313897	−	0.181228i	−0.334772	−	0.942299i	$-0.608659\pi$
$271$	1400.36	−	808.500i	0.313897	−	0.181228i	0.648669	+	0.761071i	$0.275326\pi$
$272$	−6853.00			−1.52766
$273$		0			0
$274$	8880.00			1.95788
$275$	1711.27	−	988.000i	0.375248	−	0.216650i
$276$	−5712.00	−	9893.47i	−1.24573	−	2.15767i
$277$	−1910.00	+	3308.22i	−0.414299	+	0.717587i	−0.995355	−	0.0962771i	$-0.969306\pi$
$277$	−1910.00	+	3308.22i	−0.414299	+	0.717587i	0.581056	+	0.813864i	$0.302640\pi$
$278$			9345.00i			2.01610i
$279$	−3734.30	−	2156.00i	−0.801315	−	0.462639i
$280$	−3546.37	−	2047.50i	−0.756916	−	0.437005i
$281$			6214.00i			1.31920i	0.751615	+	0.659602i	$0.229275\pi$
$281$			6214.00i			1.31920i	−0.751615	+	0.659602i	$0.770725\pi$
$282$	1837.50	−	3182.64i	0.388020	−	0.672070i
$283$	−2646.00	−	4583.01i	−0.555789	−	0.962655i	−0.997842	−	0.0656661i	$-0.979083\pi$
$283$	−2646.00	−	4583.01i	−0.555789	−	0.962655i	0.442052	−	0.896989i	$-0.354251\pi$
$284$	−132.502	+	76.5000i	−0.0276850	+	0.0159839i
$285$	6174.00			1.28321
$286$		0			0
$287$	−4368.00			−0.898379
$288$	−1619.47	+	935.000i	−0.331347	+	0.191303i
$289$	−508.000	−	879.882i	−0.103399	−	0.179093i
$290$	−1435.00	+	2485.49i	−0.290573	+	0.503287i
$291$		−	490.000i		−	0.0987090i
$292$	−1442.80	−	833.000i	−0.289155	−	0.166944i
$293$	−782.021	−	451.500i	−0.155925	−	0.0900236i	0.420007	−	0.907521i	$-0.362028\pi$
$293$	−782.021	−	451.500i	−0.155925	−	0.0900236i	−0.575933	+	0.817497i	$0.695361\pi$
$294$			6090.00i			1.20808i
$295$	−1029.00	+	1782.28i	−0.203087	+	0.351757i
$296$	2947.50	+	5105.22i	0.578784	+	1.00248i
$297$	788.083	−	455.000i	0.153970	−	0.0888949i
$298$	12330.0			2.39684
$299$		0			0
$300$	9044.00			1.74052
$301$	2262.92	−	1306.50i	0.433332	−	0.250184i
$302$	−8307.50	−	14389.0i	−1.58292	−	2.74170i
$303$	−1470.00	+	2546.11i	−0.278711	+	0.482741i
$304$		−	11214.0i		−	2.11568i
$305$	−339.482	−	196.000i	−0.0637334	−	0.0367965i
$306$	−7335.24	−	4235.00i	−1.37035	−	0.791173i
$307$		−	2114.00i		−	0.393004i	−0.980503	−	0.196502i	$-0.937042\pi$
$307$		−	2114.00i		−	0.393004i	0.980503	−	0.196502i	$-0.0629583\pi$
$308$	−2873.00	+	4976.18i	−0.531508	+	0.920598i
$309$	−2058.00	−	3564.56i	−0.378885	−	0.656248i
$310$	−5940.93	+	3430.00i	−1.08846	+	0.628422i
$311$	−3402.00			−0.620288			−0.310144	−	0.950690i	$-0.600377\pi$
$311$	−3402.00			−0.620288			−0.310144	+	0.950690i	$0.600377\pi$
$312$		0			0
$313$	−10689.0			−1.93028			−0.965141	−	0.261732i	$-0.915706\pi$
$313$	−10689.0			−1.93028			−0.965141	+	0.261732i	$0.915706\pi$
$314$	11821.2	−	6825.00i	2.12456	−	1.22661i
$315$	−1001.00	−	1733.78i	−0.179047	−	0.310119i
$316$	11084.0	−	19198.1i	1.97318	−	3.41764i
$317$		−	7054.00i		−	1.24982i	−0.780698	−	0.624909i	$-0.785136\pi$
$317$		−	7054.00i		−	1.24982i	0.780698	−	0.624909i	$-0.214864\pi$
$318$	13094.3	+	7560.00i	2.30909	+	1.33316i
$319$	1846.37	+	1066.00i	0.324065	+	0.187099i
$320$		−	2009.00i		−	0.350958i
$321$	−2394.00	+	4146.53i	−0.416262	+	0.720987i
$322$	−3120.00	−	5404.00i	−0.539971	−	0.935258i
$323$	8402.18	−	4851.00i	1.44740	−	0.835656i
$324$	14263.0			2.44564
$325$		0			0
$326$	2720.00			0.462107
$327$	−2261.19	+	1305.50i	−0.382398	+	0.220778i
$328$	7560.00	+	13094.3i	1.27266	+	2.20430i
$329$	682.500	−	1182.12i	0.114369	−	0.198093i
$330$			6370.00i			1.06260i
$331$	−8403.91	−	4852.00i	−1.39553	−	0.805710i	−0.401610	−	0.915811i	$-0.631549\pi$
$331$	−8403.91	−	4852.00i	−1.39553	−	0.805710i	−0.993920	+	0.110101i	$0.964883\pi$
$332$	−4534.51	−	2618.00i	−0.749589	−	0.432775i
$333$			2882.00i			0.474272i
$334$	4060.00	−	7032.13i	0.665130	−	1.15204i
$335$	−1673.00	−	2897.72i	−0.272853	−	0.472595i
$336$	−7013.94	+	4049.50i	−1.13881	+	0.657495i
$337$	10449.0			1.68900			0.844500	−	0.535555i	$-0.179897\pi$
$337$	10449.0			1.68900			0.844500	+	0.535555i	$0.179897\pi$
$338$		0			0
$339$	12138.0			1.94468
$340$	−7935.39	+	4581.50i	−1.26576	+	0.730784i
$341$	2548.00	+	4413.27i	0.404639	+	0.700855i
$342$	6930.00	−	12003.1i	1.09571	−	1.89782i
$343$			6721.00i			1.05802i
$344$	−7833.20	−	4522.50i	−1.22773	−	0.708828i
$345$	−4073.78	−	2352.00i	−0.635725	−	0.367036i
$346$		−	1680.00i		−	0.261033i
$347$	310.500	−	537.802i	0.0480361	−	0.0832009i	−0.841008	−	0.541023i	$-0.818037\pi$
$347$	310.500	−	537.802i	0.0480361	−	0.0832009i	0.889044	+	0.457822i	$0.151370\pi$
$348$	4879.00	+	8450.68i	0.751557	+	1.30173i
$349$	−10808.9	+	6240.50i	−1.65784	+	0.957153i	−0.684127	+	0.729363i	$0.739817\pi$
$349$	−10808.9	+	6240.50i	−1.65784	+	0.957153i	−0.973710	+	0.227790i	$0.926850\pi$
$350$	4940.00			0.754440
$351$		0			0
$352$	2210.00			0.334640
$353$	−1212.44	+	700.000i	−0.182809	+	0.105545i	−0.588612	−	0.808416i	$-0.700325\pi$
$353$	−1212.44	+	700.000i	−0.182809	+	0.105545i	0.405803	+	0.913961i	$0.366992\pi$
$354$	5145.00	+	8911.40i	0.772468	+	1.33795i
$355$	−31.5000	+	54.5596i	−0.00470943	+	0.00815697i
$356$		−	20230.0i		−	3.01176i
$357$	−6068.24	−	3503.50i	−0.899623	−	0.519397i
$358$	13116.0	+	7572.50i	1.93631	+	1.11793i
$359$			4968.00i			0.730365i	0.930936	+	0.365182i	$0.118993\pi$
$359$			4968.00i			0.730365i	−0.930936	+	0.365182i	$0.881007\pi$
$360$	−3465.00	+	6001.56i	−0.507282	+	0.878638i
$361$	4508.50	+	7808.95i	0.657312	+	1.13850i
$362$	−121.244	+	70.0000i	−0.0176034	+	0.0101633i
$363$	−4585.00			−0.662948
$364$		0			0
$365$	−686.000			−0.0983750
$366$	−1697.41	+	980.000i	−0.242418	+	0.139960i
$367$	−4361.00	−	7553.47i	−0.620279	−	1.07435i	−0.989434	−	0.144987i	$-0.953686\pi$
$367$	−4361.00	−	7553.47i	−0.620279	−	1.07435i	0.369155	−	0.929368i	$-0.379647\pi$
$368$	−4272.00	+	7399.32i	−0.605145	+	1.04814i
$369$			7392.00i			1.04285i
$370$	3970.73	+	2292.50i	0.557914	+	0.322112i
$371$	4863.60	+	2808.00i	0.680608	+	0.392949i
$372$			23324.0i			3.25079i
$373$	−5006.00	+	8670.65i	−0.694908	+	1.20362i	0.275303	+	0.961357i	$0.411222\pi$
$373$	−5006.00	+	8670.65i	−0.694908	+	1.20362i	−0.970212	+	0.242259i	$0.922112\pi$
$374$	5005.00	+	8668.91i	0.691985	+	1.19855i
$375$	8529.48	−	4924.50i	1.17456	−	0.678134i
$376$	−4725.00			−0.648067
$377$		0			0
$378$	2275.00			0.309559
$379$	−2920.24	+	1686.00i	−0.395785	+	0.228507i	−0.684664	−	0.728859i	$-0.740051\pi$
$379$	−2920.24	+	1686.00i	−0.395785	+	0.228507i	0.288879	+	0.957366i	$0.406718\pi$
$380$	−7497.00	−	12985.2i	−1.01207	−	1.75296i
$381$	−6622.00	+	11469.6i	−0.890434	+	1.54228i
$382$		−	2110.00i		−	0.282610i
$383$	733.524	+	423.500i	0.0978624	+	0.0565009i	0.548132	−	0.836392i	$-0.315339\pi$
$383$	733.524	+	423.500i	0.0978624	+	0.0565009i	−0.450270	+	0.892892i	$0.648672\pi$
$384$	−12821.5	−	7402.50i	−1.70389	−	0.983743i
$385$			2366.00i			0.313201i
$386$	1230.00	−	2130.42i	0.162190	−	0.280921i
$387$	−2211.00	−	3829.56i	−0.290417	−	0.503017i
$388$	−1030.57	+	595.000i	−0.134843	+	0.0778519i
$389$	−11314.0			−1.47466			−0.737330	−	0.675533i	$-0.763914\pi$
$389$	−11314.0			−1.47466			−0.737330	+	0.675533i	$0.763914\pi$
$390$		0			0
$391$	−7392.00			−0.956086
$392$	6780.98	−	3915.00i	0.873702	−	0.504432i
$393$	5022.50	+	8699.23i	0.644661	+	1.11658i
$394$	−7477.50	+	12951.4i	−0.956119	+	1.65605i
$395$		−	9128.00i		−	1.16273i
$396$	8421.23	+	4862.00i	1.06864	+	0.616982i
$397$	1612.54	+	931.000i	0.203856	+	0.117697i	0.598453	−	0.801158i	$-0.295782\pi$
$397$	1612.54	+	931.000i	0.203856	+	0.117697i	−0.394597	+	0.918854i	$0.629116\pi$
$398$		−	350.000i		−	0.0440802i
$399$	5733.00	−	9929.85i	0.719321	−	1.24590i
$400$	−3382.00	−	5857.80i	−0.422750	−	0.732224i
$401$	−5906.29	+	3410.00i	−0.735527	+	0.424657i	−0.820441	−	0.571732i	$-0.806272\pi$
$401$	−5906.29	+	3410.00i	−0.735527	+	0.424657i	0.0849139	+	0.996388i	$0.472938\pi$
$402$	−16730.0			−2.07566
$403$		0			0
$404$	7140.00			0.879278
$405$	5086.17	−	2936.50i	0.624034	−	0.360286i
$406$	2665.00	+	4615.92i	0.325768	+	0.564246i
$407$	1703.00	−	2949.68i	0.207407	−	0.359239i
$408$			24255.0i			2.94314i
$409$	11251.4	+	6496.00i	1.36026	+	0.785346i	0.989658	−	0.143446i	$-0.0458184\pi$
$409$	11251.4	+	6496.00i	1.36026	+	0.785346i	0.370601	+	0.928792i	$0.379152\pi$
$410$	10184.5	+	5880.00i	1.22677	+	0.708274i
$411$		−	12432.0i		−	1.49203i
$412$	−4998.00	+	8656.79i	−0.597655	+	1.03517i
$413$	1911.00	+	3309.95i	0.227686	+	0.394363i
$414$	−9145.23	+	5280.00i	−1.08566	+	0.626806i
$415$	−2156.00			−0.255021
$416$		0			0
$417$	13083.0			1.53640
$418$	−14185.5	+	8190.00i	−1.65989	+	0.958340i
$419$	3671.50	+	6359.22i	0.428078	+	0.741452i	0.996702	−	0.0811449i	$-0.0258577\pi$
$419$	3671.50	+	6359.22i	0.428078	+	0.741452i	−0.568625	+	0.822597i	$0.692524\pi$
$420$	−5414.50	+	9378.19i	−0.629049	+	1.08954i
$421$		−	5059.00i		−	0.585655i	−0.956165	−	0.292827i	$-0.905404\pi$
$421$		−	5059.00i		−	0.585655i	0.956165	−	0.292827i	$-0.0945961\pi$
$422$	12345.2	+	7127.50i	1.42406	+	0.822183i
$423$	−2000.52	−	1155.00i	−0.229949	−	0.132761i
$424$		−	19440.0i		−	2.22663i
$425$	2926.00	−	5067.98i	0.333957	−	0.578431i
$426$	157.500	+	272.798i	0.0179129	+	0.0310261i
$427$	−630.466	+	364.000i	−0.0714530	+	0.0412534i
$428$	11628.0			1.31323
$429$		0			0
$430$	−7035.00			−0.788972
$431$	2808.52	−	1621.50i	0.313879	−	0.181218i	−0.334782	−	0.942296i	$-0.608663\pi$
$431$	2808.52	−	1621.50i	0.313879	−	0.181218i	0.648661	+	0.761078i	$0.275329\pi$
$432$	−1557.50	−	2697.67i	−0.173461	−	0.300444i
$433$	5799.50	−	10045.0i	0.643663	−	1.11486i	−0.340945	−	0.940083i	$-0.610747\pi$
$433$	5799.50	−	10045.0i	0.643663	−	1.11486i	0.984609	−	0.174774i	$-0.0559196\pi$
$434$			12740.0i			1.40908i
$435$	3479.69	+	2009.00i	0.383536	+	0.221435i
$436$	5491.47	+	3170.50i	0.603196	+	0.348256i
$437$		−	12096.0i		−	1.32410i
$438$	−1715.00	+	2970.47i	−0.187091	+	0.324051i
$439$	−8687.00	−	15046.3i	−0.944437	−	1.63581i	−0.756874	−	0.653560i	$-0.773275\pi$
$439$	−8687.00	−	15046.3i	−0.944437	−	1.63581i	−0.187563	−	0.982253i	$-0.560059\pi$
$440$	7092.75	−	4095.00i	0.768485	−	0.443685i
$441$	3828.00			0.413346
$442$		0			0
$443$	989.000			0.106070			0.0530348	−	0.998593i	$-0.483111\pi$
$443$	989.000			0.106070			0.0530348	+	0.998593i	$0.483111\pi$
$444$	13500.5	−	7794.50i	1.44303	−	0.833132i
$445$	−4165.00	−	7213.99i	−0.443685	−	0.768485i
$446$	−542.500	+	939.638i	−0.0575967	+	0.0997604i
$447$		−	17262.0i		−	1.82654i
$448$	−3231.14	−	1865.50i	−0.340752	−	0.196733i
$449$	−12534.9	−	7237.00i	−1.31750	−	0.760657i	−0.334172	−	0.942512i	$-0.608457\pi$
$449$	−12534.9	−	7237.00i	−1.31750	−	0.760657i	−0.983325	+	0.181855i	$0.941790\pi$
$450$		−	8360.00i		−	0.875765i
$451$	4368.00	−	7565.60i	0.456056	−	0.789912i
$452$	−14739.0	−	25528.7i	−1.53377	−	2.65657i
$453$	−20144.6	+	11630.5i	−2.08935	+	1.20629i
$454$	−12880.0			−1.33147
$455$		0			0
$456$	−39690.0			−4.07600
$457$	−1380.44	+	797.000i	−0.141301	+	0.0815801i	−0.568984	−	0.822349i	$-0.692663\pi$
$457$	−1380.44	+	797.000i	−0.141301	+	0.0815801i	0.427683	+	0.903929i	$0.359330\pi$
$458$	1137.50	+	1970.21i	0.116052	+	0.201008i
$459$	1347.50	−	2333.94i	0.137028	−	0.237340i
$460$			11424.0i			1.15793i
$461$	5122.54	+	2957.50i	0.517528	+	0.298795i	0.735923	−	0.677066i	$-0.236749\pi$
$461$	5122.54	+	2957.50i	0.517528	+	0.298795i	−0.218395	+	0.975861i	$0.570082\pi$
$462$	10245.1	+	5915.00i	1.03170	+	0.595651i
$463$			11072.0i			1.11136i	0.831396	+	0.555680i	$0.187542\pi$
$463$			11072.0i			1.11136i	−0.831396	+	0.555680i	$0.812458\pi$
$464$	3649.00	−	6320.25i	0.365087	−	0.632350i
$465$	4802.00	+	8317.31i	0.478898	+	0.829475i
$466$	13254.5	−	7652.50i	1.31760	−	0.760719i
$467$	−1260.00			−0.124852			−0.0624260	−	0.998050i	$-0.519884\pi$
$467$	−1260.00			−0.124852			−0.0624260	+	0.998050i	$0.519884\pi$
$468$		0			0
$469$	−6214.00			−0.611804
$470$	−3182.64	+	1837.50i	−0.312350	+	0.180335i
$471$	−9555.00	−	16549.7i	−0.934758	−	1.61905i
$472$	6615.00	−	11457.5i	0.645085	−	1.11732i
$473$			5226.00i			0.508016i
$474$	−39525.4	−	22820.0i	−3.83009	−	2.21130i
$475$	8293.06	+	4788.00i	0.801077	+	0.462502i
$476$			17017.0i			1.63860i
$477$	4752.00	−	8230.71i	0.456141	−	0.790059i
$478$	8692.50	+	15055.9i	0.831769	+	1.44067i
$479$	10420.9	−	6016.50i	0.994034	−	0.573906i	0.0875564	−	0.996160i	$-0.472094\pi$
$479$	10420.9	−	6016.50i	0.994034	−	0.573906i	0.906478	+	0.422254i	$0.138761\pi$
$480$	4165.00			0.396053
$481$		0			0
$482$	8050.00			0.760721
$483$	−7565.60	+	4368.00i	−0.712726	+	0.411493i
$484$	5567.50	+	9643.19i	0.522868	+	0.905634i
$485$	−245.000	+	424.352i	−0.0229379	+	0.0397296i
$486$		−	24640.0i		−	2.29978i
$487$	1974.54	+	1140.00i	0.183727	+	0.106075i	0.589042	−	0.808102i	$-0.299505\pi$
$487$	1974.54	+	1140.00i	0.183727	+	0.106075i	−0.405316	+	0.914177i	$0.632838\pi$
$488$	2182.38	+	1260.00i	0.202442	+	0.116880i
$489$		−	3808.00i		−	0.352155i
$490$	3045.00	−	5274.09i	0.280733	−	0.486243i
$491$	8383.50	+	14520.6i	0.770554	+	1.33464i	0.937260	+	0.348632i	$0.113354\pi$
$491$	8383.50	+	14520.6i	0.770554	+	1.33464i	−0.166706	+	0.986007i	$0.553313\pi$
$492$	34627.2	−	19992.0i	3.17299	−	1.83193i
$493$	6314.00			0.576812
$494$		0			0
$495$	4004.00			0.363569
$496$	15106.9	−	8722.00i	1.36758	−	0.789575i
$497$	58.5000	+	101.325i	0.00527985	+	0.00914496i
$498$	−5390.00	+	9335.75i	−0.485003	+	0.840050i
$499$			12840.0i			1.15190i	0.817485	+	0.575949i	$0.195367\pi$
$499$			12840.0i			1.15190i	−0.817485	+	0.575949i	$0.804633\pi$
$500$	−20714.5	−	11959.5i	−1.85276	−	1.06969i
$501$	−9844.98	−	5684.00i	−0.877926	−	0.506871i
$502$			5040.00i			0.448100i
$503$	1099.00	−	1903.52i	0.0974195	−	0.168735i	−0.813196	−	0.581989i	$-0.802274\pi$
$503$	1099.00	−	1903.52i	0.0974195	−	0.168735i	0.910616	+	0.413254i	$0.135608\pi$
$504$	6435.00	+	11145.7i	0.568726	+	0.985062i
$505$	2546.11	−	1470.00i	0.224358	−	0.129533i
$506$	12480.0			1.09645
$507$		0			0
$508$	32164.0			2.80915
$509$	−14779.6	+	8533.00i	−1.28702	+	0.743062i	−0.978122	−	0.208033i	$-0.933294\pi$
$509$	−14779.6	+	8533.00i	−1.28702	+	0.743062i	−0.308899	+	0.951095i	$0.599961\pi$
$510$	9432.50	+	16337.6i	0.818977	+	1.41851i
$511$	−637.000	+	1103.32i	−0.0551452	+	0.0955144i
$512$			24475.0i			2.11260i
$513$	3819.17	+	2205.00i	0.328695	+	0.189772i
$514$	−26158.3	−	15102.5i	−2.24473	−	1.29600i
$515$			4116.00i			0.352180i
$516$	−11959.5	+	20714.5i	−1.02032	+	1.76725i
$517$	1365.00	+	2364.25i	0.116117	+	0.201121i
$518$	7374.21	−	4257.50i	0.625490	−	0.361127i
$519$	−2352.00			−0.198924
$520$		0			0
$521$	2583.00			0.217204			0.108602	−	0.994085i	$-0.465363\pi$
$521$	2583.00			0.217204			0.108602	+	0.994085i	$0.465363\pi$
$522$	7811.55	−	4510.00i	0.654985	−	0.378156i
$523$	−9310.00	−	16125.4i	−0.778390	−	1.34821i	−0.932869	−	0.360215i	$-0.882703\pi$
$523$	−9310.00	−	16125.4i	−0.778390	−	1.34821i	0.154480	−	0.987996i	$-0.450630\pi$
$524$	12197.5	−	21126.7i	1.01689	−	1.76130i
$525$		−	6916.00i		−	0.574931i
$526$	−16056.1	−	9270.00i	−1.33095	−	0.768424i
$527$	13070.1	+	7546.00i	1.08034	+	0.623736i
$528$		−	16198.0i		−	1.33509i
$529$	1475.50	−	2555.64i	0.121271	−	0.210047i
$530$	−7560.00	−	13094.3i	−0.619595	−	1.07317i
$531$	5601.45	−	3234.00i	0.457782	−	0.264301i
$532$	−27846.0			−2.26932
$533$		0			0
$534$	−41650.0			−3.37523
$535$	4146.53	−	2394.00i	0.335084	−	0.193461i
$536$	10755.0	+	18628.2i	0.866689	+	1.50115i
$537$	10601.5	−	18362.3i	0.851934	−	1.47559i
$538$		−	41720.0i		−	3.34327i
$539$	−3917.90	−	2262.00i	−0.313091	−	0.180763i
$540$	−3607.00	−	2082.50i	−0.287445	−	0.165957i
$541$			16833.0i			1.33772i	0.743388	+	0.668861i	$0.233218\pi$
$541$			16833.0i			1.33772i	−0.743388	+	0.668861i	$0.766782\pi$
$542$	−4042.50	+	7001.82i	−0.320369	+	0.554896i
$543$	98.0000	+	169.741i	0.00774509	+	0.0134149i
$544$	5668.14	−	3272.50i	0.446727	−	0.257918i
$545$	2611.00			0.205216
$546$		0			0
$547$	−8615.00			−0.673402			−0.336701	−	0.941612i	$-0.609311\pi$
$547$	−8615.00			−0.673402			−0.336701	+	0.941612i	$0.609311\pi$
$548$	−26147.0	+	15096.0i	−2.03822	+	1.17677i
$549$	616.000	+	1066.94i	0.0478875	+	0.0829436i
$550$	−4940.00	+	8556.33i	−0.382986	+	0.663351i
$551$			10332.0i			0.798835i
$552$	26188.6	+	15120.0i	2.01931	+	1.16585i
$553$	−14680.9	−	8476.00i	−1.12892	−	0.651783i
$554$		−	19100.0i		−	1.46477i
$555$	3209.50	−	5559.02i	0.245470	−	0.425166i
$556$	−15886.5	−	27516.2i	−1.21176	−	2.09883i
$557$	−7391.53	+	4267.50i	−0.562278	+	0.324632i	−0.754059	−	0.656806i	$-0.771907\pi$
$557$	−7391.53	+	4267.50i	−0.562278	+	0.324632i	0.191781	+	0.981438i	$0.438574\pi$
$558$	21560.0			1.63568
$559$		0			0
$560$	8099.00			0.611152
$561$	12136.5	−	7007.00i	0.913374	−	0.527336i
$562$	−15535.0	−	26907.4i	−1.16602	−	2.01961i
$563$	−2320.50	+	4019.22i	−0.173708	+	0.300871i	−0.939713	−	0.341963i	$-0.888908\pi$
$563$	−2320.50	+	4019.22i	−0.173708	+	0.300871i	0.766006	+	0.642834i	$0.222241\pi$
$564$			12495.0i			0.932862i
$565$	−10511.8	−	6069.00i	−0.782718	−	0.451902i
$566$	22915.0	+	13230.0i	1.70175	+	0.982506i
$567$		−	10907.0i		−	0.807850i
$568$	202.500	−	350.740i	0.0149590	−	0.0259097i
$569$	−2396.50	−	4150.86i	−0.176567	−	0.305823i	0.764136	−	0.645056i	$-0.223166\pi$
$569$	−2396.50	−	4150.86i	−0.176567	−	0.305823i	−0.940702	+	0.339233i	$0.889832\pi$
$570$	−26734.2	+	15435.0i	−1.96451	+	1.13421i
$571$	5563.00			0.407713			0.203857	−	0.979001i	$-0.434652\pi$
$571$	5563.00			0.407713			0.203857	+	0.979001i	$0.434652\pi$
$572$		0			0
$573$	−2954.00			−0.215367
$574$	18914.0	−	10920.0i	1.37536	−	0.794063i
$575$	−3648.00	−	6318.52i	−0.264578	−	0.458262i
$576$	−3157.00	+	5468.08i	−0.228371	+	0.395550i
$577$			24038.0i			1.73434i	0.498011	+	0.867171i	$0.334064\pi$
$577$			24038.0i			1.73434i	−0.498011	+	0.867171i	$0.665936\pi$
$578$	4399.41	+	2540.00i	0.316594	+	0.182786i
$579$	−2982.59	−	1722.00i	−0.214080	−	0.123599i
$580$		−	9758.00i		−	0.698584i
$581$	−2002.00	+	3467.57i	−0.142955	+	0.247606i
$582$	1225.00	+	2121.76i	0.0872472	+	0.151117i
$583$	−9727.20	+	5616.00i	−0.691011	+	0.398955i
$584$	4410.00			0.312478
$585$		0			0
$586$	4515.00			0.318281
$587$	−18380.5	+	10612.0i	−1.29241	+	0.746174i	−0.979081	−	0.203470i	$-0.934778\pi$
$587$	−18380.5	+	10612.0i	−1.29241	+	0.746174i	−0.313330	+	0.949644i	$0.601445\pi$
$588$	−10353.0	−	17931.9i	−0.726106	−	1.25765i
$589$	−12348.0	+	21387.4i	−0.863821	+	1.49618i
$590$		−	10290.0i		−	0.718021i
$591$	18132.0	+	10468.5i	1.26201	+	0.728624i
$592$	−10097.0	−	5829.50i	−0.700986	−	0.404714i
$593$		−	4354.00i		−	0.301513i	−0.988571	−	0.150757i	$-0.951829\pi$
$593$		−	4354.00i		−	0.301513i	0.988571	−	0.150757i	$-0.0481710\pi$
$594$	−2275.00	+	3940.42i	−0.157145	+	0.272184i
$595$	3503.50	+	6068.24i	0.241394	+	0.418107i
$596$	−36305.5	+	20961.0i	−2.49519	+	1.44060i
$597$	−490.000			−0.0335919
$598$		0			0
$599$	7310.00			0.498629			0.249314	−	0.968423i	$-0.419795\pi$
$599$	7310.00			0.498629			0.249314	+	0.968423i	$0.419795\pi$
$600$	−20732.6	+	11970.0i	−1.41068	+	0.814455i
$601$	3797.50	+	6577.46i	0.257743	+	0.446423i	0.965637	−	0.259895i	$-0.0836880\pi$
$601$	3797.50	+	6577.46i	0.257743	+	0.446423i	−0.707894	+	0.706318i	$0.750355\pi$
$602$	−6532.50	+	11314.6i	−0.442267	+	0.766029i
$603$			10516.0i			0.710190i
$604$	48922.6	+	28245.5i	3.29575	+	1.90280i
$605$	3970.73	+	2292.50i	0.266831	+	0.154055i
$606$		−	14700.0i		−	0.985391i
$607$	413.000	−	715.337i	0.0276164	−	0.0478330i	−0.851887	−	0.523726i	$-0.824542\pi$
$607$	413.000	−	715.337i	0.0276164	−	0.0478330i	0.879503	+	0.475893i	$0.157875\pi$
$608$	5355.00	+	9275.13i	0.357194	+	0.618678i
$609$	6462.28	−	3731.00i	0.429992	−	0.248256i
$610$	1960.00			0.130095
$611$		0			0
$612$	28798.0			1.90211
$613$	12635.3	−	7295.00i	0.832521	−	0.480656i	−0.0221940	−	0.999754i	$-0.507065\pi$
$613$	12635.3	−	7295.00i	0.832521	−	0.480656i	0.854715	+	0.519097i	$0.173732\pi$
$614$	5285.00	+	9153.89i	0.347370	+	0.601663i
$615$	8232.00	−	14258.2i	0.539750	−	0.934875i
$616$		−	15210.0i		−	0.994851i
$617$	−4233.13	−	2444.00i	−0.276207	−	0.159468i	0.355498	−	0.934677i	$-0.384311\pi$
$617$	−4233.13	−	2444.00i	−0.276207	−	0.159468i	−0.631705	+	0.775209i	$0.717645\pi$
$618$	17822.8	+	10290.0i	1.16009	+	0.669781i
$619$			11004.0i			0.714520i	0.934005	+	0.357260i	$0.116289\pi$
$619$			11004.0i			0.714520i	−0.934005	+	0.357260i	$0.883711\pi$
$620$	11662.0	−	20199.2i	0.755415	−	1.30842i
$621$	−1680.00	−	2909.85i	−0.108561	−	0.188032i
$622$	14731.1	−	8505.00i	0.949619	−	0.548263i
$623$	−15470.0			−0.994851
$624$		0			0
$625$	−349.000			−0.0223360
$626$	46284.7	−	26722.5i	2.95513	−	1.70614i
$627$	11466.0	+	19859.7i	0.730316	+	1.26494i
$628$	−23205.0	+	40192.2i	−1.47449	+	2.55389i
$629$		−	10087.0i		−	0.639420i
$630$	8668.91	+	5005.00i	0.548219	+	0.316514i
$631$	−4308.48	−	2487.50i	−0.271819	−	0.156935i	0.357895	−	0.933762i	$-0.383495\pi$
$631$	−4308.48	−	2487.50i	−0.271819	−	0.156935i	−0.629714	+	0.776827i	$0.716828\pi$
$632$			58680.0i			3.69330i
$633$	9978.50	−	17283.3i	0.626556	−	1.08523i
$634$	17635.0	+	30544.7i	1.10469	+	1.91338i
$635$	11469.6	−	6622.00i	0.716786	−	0.413836i
$636$	−51408.0			−3.20513
$637$		0			0
$638$	−10660.0			−0.661494
$639$	171.473	−	99.0000i	0.0106156	−	0.00612892i
$640$	7402.50	+	12821.5i	0.457202	+	0.791898i
$641$	1975.00	−	3420.80i	0.121697	−	0.210785i	−0.798740	−	0.601676i	$-0.794500\pi$
$641$	1975.00	−	3420.80i	0.121697	−	0.210785i	0.920437	+	0.390891i	$0.127833\pi$
$642$		−	23940.0i		−	1.47171i
$643$	3188.71	+	1841.00i	0.195568	+	0.112911i	0.594587	−	0.804032i	$-0.297316\pi$
$643$	3188.71	+	1841.00i	0.195568	+	0.112911i	−0.399019	+	0.916943i	$0.630649\pi$
$644$	18373.6	+	10608.0i	1.12426	+	0.649090i
$645$			9849.00i			0.601247i
$646$	−24255.0	+	42010.9i	−1.47724	+	2.55866i
$647$	5201.00	+	9008.40i	0.316032	+	0.547383i	0.979656	−	0.200683i	$-0.0643161\pi$
$647$	5201.00	+	9008.40i	0.316032	+	0.547383i	−0.663625	+	0.748066i	$0.730983\pi$
$648$	−32696.8	+	18877.5i	−1.98218	+	1.14441i
$649$	−7644.00			−0.462332
$650$		0			0
$651$	17836.0			1.07381
$652$	−8009.00	+	4624.00i	−0.481069	+	0.277745i
$653$	15840.0	+	27435.7i	0.949260	+	1.64417i	0.746987	+	0.664838i	$0.231500\pi$
$653$	15840.0	+	27435.7i	0.949260	+	1.64417i	0.202273	+	0.979329i	$0.435167\pi$
$654$	6527.50	−	11306.0i	0.390284	−	0.675991i
$655$		−	10045.0i		−	0.599222i
$656$	−25897.6	−	14952.0i	−1.54136	−	0.889905i
$657$	1867.15	+	1078.00i	0.110874	+	0.0640134i
$658$			6825.00i			0.404356i
$659$	−10970.0	+	19000.6i	−0.648453	+	1.12315i	0.335039	+	0.942204i	$0.391250\pi$
$659$	−10970.0	+	19000.6i	−0.648453	+	1.12315i	−0.983492	+	0.180949i	$0.942083\pi$
$660$	−10829.0	−	18756.4i	−0.638664	−	1.10620i
$661$	27170.7	−	15687.0i	1.59882	−	0.923077i	0.607100	−	0.794626i	$-0.292333\pi$
$661$	27170.7	−	15687.0i	1.59882	−	0.923077i	0.991716	−	0.128451i	$-0.0410004\pi$
$662$	48520.0			2.84862
$663$		0			0
$664$	13860.0			0.810049
$665$	−9929.85	+	5733.00i	−0.579042	+	0.334310i
$666$	−7205.00	−	12479.4i	−0.419201	−	0.726078i
$667$	3936.00	−	6817.35i	0.228490	−	0.395756i
$668$			27608.0i			1.59908i
$669$	1315.49	+	759.500i	0.0760237	+	0.0438923i
$670$	14488.6	+	8365.00i	0.835438	+	0.482341i
$671$		−	1456.00i		−	0.0837679i
$672$	3867.50	−	6698.71i	0.222012	−	0.384536i
$673$	9006.50	+	15599.7i	0.515862	+	0.893499i	0.999830	+	0.0184136i	$0.00586157\pi$
$673$	9006.50	+	15599.7i	0.515862	+	0.893499i	−0.483969	+	0.875085i	$0.660805\pi$
$674$	−45245.5	+	26122.5i	−2.58574	+	1.49288i
$675$	2660.00			0.151679
$676$		0			0
$677$	−10640.0			−0.604030			−0.302015	−	0.953303i	$-0.597659\pi$
$677$	−10640.0			−0.604030			−0.302015	+	0.953303i	$0.597659\pi$
$678$	−52559.1	+	30345.0i	−2.97717	+	1.71887i
$679$	455.000	+	788.083i	0.0257162	+	0.0445418i
$680$	12127.5	−	21005.4i	0.683924	−	1.18459i
$681$			18032.0i			1.01467i
$682$	−22066.3	−	12740.0i	−1.23895	−	0.715308i
$683$	−8085.21	−	4668.00i	−0.452961	−	0.261517i	0.256119	−	0.966645i	$-0.417556\pi$
$683$	−8085.21	−	4668.00i	−0.452961	−	0.261517i	−0.709080	+	0.705128i	$0.750889\pi$
$684$			47124.0i			2.63426i
$685$	−6216.00	+	10766.4i	−0.346717	+	0.600531i
$686$	−16802.5	−	29102.8i	−0.935164	−	1.61975i
$687$	2758.29	−	1592.50i	0.153181	−	0.0884391i
$688$	17889.0			0.991296
$689$		0			0
$690$	23520.0			1.29767
$691$	3637.31	−	2100.00i	0.200246	−	0.115612i	−0.396524	−	0.918024i	$-0.629784\pi$
$691$	3637.31	−	2100.00i	0.200246	−	0.115612i	0.596770	+	0.802412i	$0.296450\pi$
$692$	2856.00	+	4946.74i	0.156891	+	0.271744i
$693$	3718.00	−	6439.76i	0.203803	−	0.352996i
$694$			3105.00i			0.169833i
$695$	−11330.2	−	6541.50i	−0.618388	−	0.357026i
$696$	−22369.4	−	12915.0i	−1.21826	−	0.703365i
$697$		−	25872.0i		−	1.40599i
$698$	31202.5	−	54044.3i	1.69202	−	2.93067i
$699$	−10713.5	−	18556.3i	−0.579716	−	1.00410i
$700$	−14545.8	+	8398.00i	−0.785397	+	0.453449i
$701$	−9872.00			−0.531898			−0.265949	−	0.963987i	$-0.585685\pi$
$701$	−9872.00			−0.531898			−0.265949	+	0.963987i	$0.585685\pi$
$702$		0			0
$703$	16506.0			0.885541
$704$	6462.28	−	3731.00i	0.345961	−	0.199741i
$705$	2572.50	+	4455.70i	0.137427	+	0.238030i
$706$	3500.00	−	6062.18i	0.186578	−	0.323163i
$707$		−	5460.00i		−	0.290445i
$708$	−30298.8	−	17493.0i	−1.60833	−	0.928569i
$709$	24638.4	+	14225.0i	1.30510	+	0.753499i	0.981274	−	0.192617i	$-0.0616976\pi$
$709$	24638.4	+	14225.0i	1.30510	+	0.753499i	0.323825	+	0.946117i	$0.395031\pi$
$710$		−	315.000i		−	0.0166503i
$711$	−14344.0	+	24844.5i	−0.756599	+	1.31047i
$712$	26775.0	+	46375.7i	1.40932	+	2.44101i
$713$	16295.1	−	9408.00i	0.855901	−	0.494155i
$714$	35035.0			1.83635
$715$		0			0
$716$	−51493.0			−2.68769
$717$	21078.2	−	12169.5i	1.09788	−	0.633861i
$718$	−12420.0	−	21512.1i	−0.645557	−	1.11814i
$719$	16359.0	−	28334.6i	0.848523	−	1.46968i	−0.0340039	−	0.999422i	$-0.510826\pi$
$719$	16359.0	−	28334.6i	0.848523	−	1.46968i	0.882527	−	0.470263i	$-0.155841\pi$
$720$		−	13706.0i		−	0.709434i
$721$	6619.90	+	3822.00i	0.341939	+	0.197418i
$722$	−39044.8	−	22542.5i	−2.01260	−	1.16197i
$723$		−	11270.0i		−	0.579718i
$724$	238.000	−	412.228i	0.0122171	−	0.0211607i
$725$	3116.00	+	5397.07i	0.159621	+	0.276472i
$726$	19853.6	−	11462.5i	1.01493	−	0.585969i
$727$	22834.0			1.16488			0.582439	−	0.812874i	$-0.302099\pi$
$727$	22834.0			1.16488			0.582439	+	0.812874i	$0.302099\pi$
$728$		0			0
$729$	−11843.0			−0.601687
$730$	2970.47	−	1715.00i	0.150605	−	0.0869521i
$731$	7738.50	+	13403.5i	0.391544	+	0.678174i
$732$	3332.00	−	5771.19i	0.168244	−	0.291406i
$733$			7875.00i			0.396821i	0.980119	+	0.198410i	$0.0635779\pi$
$733$			7875.00i			0.396821i	−0.980119	+	0.198410i	$0.936422\pi$
$734$	37767.4	+	21805.0i	1.89921	+	1.09651i
$735$	−7383.73	−	4263.00i	−0.370548	−	0.213936i
$736$		−	8160.00i		−	0.408671i
$737$	6214.00	−	10763.0i	0.310578	−	0.537936i
$738$	−18480.0	−	32008.3i	−0.921759	−	1.59653i
$739$	1853.29	−	1070.00i	0.0922524	−	0.0532620i	−0.453164	−	0.891427i	$-0.649705\pi$
$739$	1853.29	−	1070.00i	0.0922524	−	0.0532620i	0.545416	+	0.838165i	$0.316371\pi$
$740$	−15589.0			−0.774410
$741$		0			0
$742$	−28080.0			−1.38928
$743$	27687.7	−	15985.5i	1.36711	−	0.789302i	0.376552	−	0.926395i	$-0.377109\pi$
$743$	27687.7	−	15985.5i	1.36711	−	0.789302i	0.990558	+	0.137094i	$0.0437761\pi$
$744$	−30870.0	−	53468.4i	−1.52117	−	2.63474i
$745$	−8631.00	+	14949.3i	−0.424450	+	0.735169i
$746$		−	50060.0i		−	2.45687i
$747$	5868.19	+	3388.00i	0.287424	+	0.165944i
$748$	−29474.3	−	17017.0i	−1.44076	−	0.831822i
$749$		−	8892.00i		−	0.433787i
$750$	−24622.5	+	42647.4i	−1.19878	+	2.07635i
$751$	−3716.00	−	6436.30i	−0.180558	−	0.312735i	0.761513	−	0.648150i	$-0.224457\pi$
$751$	−3716.00	−	6436.30i	−0.180558	−	0.312735i	−0.942071	+	0.335415i	$0.891124\pi$
$752$	8093.01	−	4672.50i	0.392449	−	0.226581i
$753$	7056.00			0.341481
$754$		0			0
$755$	23261.0			1.12126
$756$	−6698.71	+	3867.50i	−0.322261	+	0.186058i
$757$	−10088.0	−	17472.9i	−0.484352	−	0.838923i	0.515486	−	0.856898i	$-0.327611\pi$
$757$	−10088.0	−	17472.9i	−0.484352	−	0.838923i	−0.999838	+	0.0179753i	$0.994278\pi$
$758$	8430.00	−	14601.2i	0.403946	−	0.699656i
$759$		−	17472.0i		−	0.835564i
$760$	34372.5	+	19845.0i	1.64056	+	0.947176i
$761$	−8208.19	−	4739.00i	−0.390994	−	0.225741i	0.291597	−	0.956541i	$-0.405814\pi$
$761$	−8208.19	−	4739.00i	−0.390994	−	0.225741i	−0.682591	+	0.730801i	$0.739147\pi$
$762$		−	66220.0i		−	3.14816i
$763$	2424.50	−	4199.36i	0.115036	−	0.199249i
$764$	3587.00	+	6212.87i	0.169860	+	0.294206i
$765$	10269.3	−	5929.00i	0.485344	−	0.280214i
$766$	−4235.00			−0.199761
$767$		0			0
$768$	57953.0			2.72292
$769$	−10475.4	+	6048.00i	−0.491228	+	0.283610i	−0.725084	−	0.688661i	$-0.758199\pi$
$769$	−10475.4	+	6048.00i	−0.491228	+	0.283610i	0.233856	+	0.972271i	$0.424866\pi$
$770$	−5915.00	−	10245.1i	−0.276834	−	0.479490i
$771$	−21143.5	+	36621.6i	−0.987632	+	1.71063i
$772$			8364.00i			0.389931i
$773$	−15537.4	−	8970.50i	−0.722950	−	0.417395i	0.0928877	−	0.995677i	$-0.470390\pi$
$773$	−15537.4	−	8970.50i	−0.722950	−	0.417395i	−0.815837	+	0.578281i	$0.803724\pi$
$774$	19147.8	+	11055.0i	0.889217	+	0.513390i
$775$			14896.0i			0.690426i
$776$	1575.00	−	2727.98i	0.0728598	−	0.126197i
$777$	−5960.50	−	10323.9i	−0.275202	−	0.476663i
$778$	48991.1	−	28285.0i	2.25760	−	1.30343i
$779$	42336.0			1.94717
$780$		0			0
$781$	−234.000			−0.0107211
$782$	32008.3	−	18480.0i	1.46370	−	0.845068i
$783$	1435.00	+	2485.49i	0.0654952	+	0.113441i
$784$	−7743.00	+	13411.3i	−0.352724	+	0.610936i
$785$			19110.0i			0.868873i
$786$	−43496.1	−	25112.5i	−1.97386	−	1.13961i
$787$	5771.19	+	3332.00i	0.261399	+	0.150919i	0.624972	−	0.780647i	$-0.285110\pi$
$787$	5771.19	+	3332.00i	0.261399	+	0.150919i	−0.363574	+	0.931565i	$0.618444\pi$
$788$		−	50847.0i		−	2.29867i
$789$	−12978.0	+	22478.6i	−0.585588	+	1.01427i
$790$	22820.0	+	39525.4i	1.02772	+	1.78006i
$791$	−19521.9	+	11271.0i	−0.877523	+	0.506638i
$792$	−25740.0			−1.15484
$793$		0			0
$794$	−9310.00			−0.416120
$795$	−18332.0	+	10584.0i	−0.817824	+	0.472171i
$796$	595.000	+	1030.57i	0.0264940	+	0.0458889i
$797$	−721.000	+	1248.81i	−0.0320441	+	0.0555020i	−0.881603	−	0.471992i	$-0.843535\pi$
$797$	−721.000	+	1248.81i	−0.0320441	+	0.0555020i	0.849559	+	0.527494i	$0.176868\pi$
$798$			57330.0i			2.54318i
$799$	7001.82	+	4042.50i	0.310021	+	0.178990i
$800$	5594.52	+	3230.00i	0.247245	+	0.142747i
$801$			26180.0i			1.15484i
$802$	17050.0	−	29531.5i	0.750694	−	1.30024i
$803$	−1274.00	−	2206.63i	−0.0559881	−	0.0969743i
$804$	49261.3	−	28441.0i	2.16083	−	1.24756i
$805$	8736.00			0.382489
$806$		0			0
$807$	−58408.0			−2.54778
$808$	−16367.9	+	9450.00i	−0.712649	+	0.411448i
$809$	−15103.5	−	26160.0i	−0.656379	−	1.13688i	−0.981546	−	0.191226i	$-0.938754\pi$
$809$	−15103.5	−	26160.0i	−0.656379	−	1.13688i	0.325167	−	0.945657i	$-0.394580\pi$
$810$	−14682.5	+	25430.8i	−0.636902	+	1.10315i
$811$			21140.0i			0.915322i	0.889127	+	0.457661i	$0.151313\pi$
$811$			21140.0i			0.915322i	−0.889127	+	0.457661i	$0.848687\pi$
$812$	−15694.1	−	9061.00i	−0.678270	−	0.391599i
$813$	9802.54	+	5659.50i	0.422866	+	0.244142i
$814$			17030.0i			0.733294i
$815$	−1904.00	+	3297.82i	−0.0818334	+	0.141740i
$816$	−23985.5	−	41544.1i	−1.02900	−	1.78227i
$817$	−21933.0	+	12663.0i	−0.939213	+	0.542255i
$818$	−64960.0			−2.77662
$819$		0			0
$820$	−39984.0			−1.70281
$821$	492.768	−	284.500i	0.0209473	−	0.0120939i	−0.489490	−	0.872009i	$-0.662817\pi$
$821$	492.768	−	284.500i	0.0209473	−	0.0120939i	0.510437	+	0.859915i	$0.329484\pi$
$822$	31080.0	+	53832.1i	1.31878	+	2.28420i
$823$	−4269.00	+	7394.12i	−0.180812	+	0.313175i	−0.942157	−	0.335171i	$-0.891206\pi$
$823$	−4269.00	+	7394.12i	−0.180812	+	0.313175i	0.761346	+	0.648346i	$0.224539\pi$
$824$		−	26460.0i		−	1.11866i
$825$	11978.9	+	6916.00i	0.505516	+	0.291860i
$826$	−16549.7	−	9555.00i	−0.697142	−	0.402495i
$827$			32702.0i			1.37504i	0.726164	+	0.687521i	$0.241301\pi$
$827$			32702.0i			1.37504i	−0.726164	+	0.687521i	$0.758699\pi$
$828$	17952.0	−	31093.8i	0.753472	−	1.30505i
$829$	−10577.0	−	18319.9i	−0.443130	−	0.767523i	0.554790	−	0.831990i	$-0.312798\pi$
$829$	−10577.0	−	18319.9i	−0.443130	−	0.767523i	−0.997920	+	0.0644673i	$0.979465\pi$
$830$	9335.75	−	5390.00i	0.390420	−	0.225409i
$831$	−26740.0			−1.11625
$832$		0			0
$833$	−13398.0			−0.557279
$834$	−56651.1	+	32707.5i	−2.35212	+	1.35800i
$835$	5684.00	+	9844.98i	0.235572	+	0.408023i
$836$	27846.0	−	48230.7i	1.15200	−	1.99533i
$837$			6860.00i			0.283293i
$838$	−31796.1	−	18357.5i	−1.31071	−	0.756741i
$839$	−1891.40	−	1092.00i	−0.0778288	−	0.0449345i	0.460581	−	0.887618i	$-0.347641\pi$
$839$	−1891.40	−	1092.00i	−0.0778288	−	0.0449345i	−0.538409	+	0.842683i	$0.680975\pi$
$840$		−	28665.0i		−	1.17742i
$841$	8832.50	−	15298.3i	0.362151	−	0.627264i
$842$	12647.5	+	21906.1i	0.517650	+	0.896597i
$843$	−37670.4	+	21749.0i	−1.53907	+	0.888583i
$844$	−48467.0			−1.97666
$845$		0			0
$846$	11550.0			0.469382
$847$	7374.21	−	4257.50i	0.299151	−	0.172715i
$848$	19224.0	+	33296.9i	0.778485	+	1.34837i
$849$	18522.0	−	32081.0i	0.748732	−	1.29684i
$850$			29260.0i			1.18072i
$851$	−10891.1	−	6288.00i	−0.438711	−	0.253290i
$852$	−927.513	−	535.500i	−0.0372959	−	0.0215328i
$853$		−	36687.0i		−	1.47261i	−0.676648	−	0.736307i	$-0.736568\pi$
$853$		−	36687.0i		−	1.47261i	0.676648	−	0.736307i	$-0.263432\pi$
$854$	1820.00	−	3152.33i	0.0729264	−	0.126312i
$855$	9702.00	+	16804.4i	0.388072	+	0.672160i
$856$	−26656.3	+	15390.0i	−1.06436	+	0.614509i
$857$	−36806.0			−1.46706			−0.733529	−	0.679658i	$-0.762128\pi$
$857$	−36806.0			−1.46706			−0.733529	+	0.679658i	$0.762128\pi$
$858$		0			0
$859$	4900.00			0.194628			0.0973142	−	0.995254i	$-0.468975\pi$
$859$	4900.00			0.194628			0.0973142	+	0.995254i	$0.468975\pi$
$860$	20714.5	−	11959.5i	0.821346	−	0.474204i
$861$	−15288.0	−	26479.6i	−0.605126	−	1.04811i
$862$	−8107.50	+	14042.6i	−0.320351	+	0.554864i
$863$		−	13697.0i		−	0.540268i	−0.962823	−	0.270134i	$-0.912932\pi$
$863$		−	13697.0i		−	0.540268i	0.962823	−	0.270134i	$-0.0870680\pi$
$864$	2576.43	+	1487.50i	0.101449	+	0.0585715i
$865$	2036.89	+	1176.00i	0.0800652	+	0.0462257i
$866$			57995.0i			2.27569i
$867$	3556.00	−	6159.17i	0.139294	−	0.241265i
$868$	−21658.0	−	37512.8i	−0.846913	−	1.46690i
$869$	29361.7	−	16952.0i	1.14618	−	0.661746i
$870$	−20090.0			−0.782891
$871$		0			0
$872$	−16785.0			−0.651848
$873$	1333.68	−	770.000i	0.0517047	−	0.0298517i
$874$	30240.0	+	52377.2i	1.17035	+	2.02710i
$875$	−9145.50	+	15840.5i	−0.353342	+	0.612006i
$876$		−	11662.0i		−	0.449797i
$877$	−5403.13	−	3119.50i	−0.208040	−	0.120112i	0.392360	−	0.919812i	$-0.371659\pi$
$877$	−5403.13	−	3119.50i	−0.208040	−	0.120112i	−0.600400	+	0.799700i	$0.704992\pi$
$878$	75231.6	+	43435.0i	2.89174	+	1.66954i
$879$		−	6321.00i		−	0.242551i
$880$	−8099.00	+	14027.9i	−0.310247	+	0.537363i
$881$	66.5000	+	115.181i	0.00254307	+	0.00440472i	0.867294	−	0.497796i	$-0.165857\pi$
$881$	66.5000	+	115.181i	0.00254307	+	0.00440472i	−0.864751	+	0.502201i	$0.832524\pi$
$882$	−16575.7	+	9570.00i	−0.632805	+	0.365350i
$883$	26003.0			0.991020			0.495510	−	0.868602i	$-0.334981\pi$
$883$	26003.0			0.991020			0.495510	+	0.868602i	$0.334981\pi$
$884$		0			0
$885$	−14406.0			−0.547178
$886$	−4282.50	+	2472.50i	−0.162385	+	0.0937531i
$887$	15624.0	+	27061.6i	0.591435	+	1.02439i	0.994039	+	0.109021i	$0.0347716\pi$
$887$	15624.0	+	27061.6i	0.591435	+	1.02439i	−0.402605	+	0.915374i	$0.631895\pi$
$888$	−20632.5	+	35736.5i	−0.779709	+	1.35050i
$889$		−	24596.0i		−	0.927923i
$890$	36070.0	+	20825.0i	1.35850	+	0.784332i
$891$	18891.5	+	10907.0i	0.710312	+	0.410099i
$892$		−	3689.00i		−	0.138472i
$893$	−6615.00	+	11457.5i	−0.247886	+	0.429352i
$894$	43155.0	+	74746.7i	1.61445	+	2.79631i
$895$	−18362.3	+	10601.5i	−0.685794	+	0.395943i
$896$	27495.0			1.02516
$897$		0			0
$898$	72370.0			2.68933
$899$	−13918.8	+	8036.00i	−0.516370	+	0.298126i
$900$	14212.0	+	24615.9i	0.526370	+	0.911700i
$901$	−16632.0	+	28807.5i	−0.614975	+	1.06517i
$902$			43680.0i			1.61240i
$903$	15840.5	+	9145.50i	0.583763	+	0.337036i
$904$	67576.0	+	39015.0i	2.48622	+	1.43542i
$905$		−	196.000i		−	0.00719918i
$906$	58152.5	−	100723.i	2.13244	−	3.69349i
$907$	−19126.5	−	33128.1i	−0.700204	−	1.21279i	−0.968395	−	0.249423i	$-0.919759\pi$
$907$	−19126.5	−	33128.1i	−0.700204	−	1.21279i	0.268191	−	0.963366i	$-0.413574\pi$
$908$	37925.0	−	21896.0i	1.38611	−	0.800269i
$909$	−9240.00			−0.337152
$910$		0			0
$911$	36374.0			1.32286			0.661429	−	0.750007i	$-0.269950\pi$
$911$	36374.0			1.32286			0.661429	+	0.750007i	$0.269950\pi$
$912$	67981.3	−	39249.0i	2.46829	−	1.42507i
$913$	−4004.00	−	6935.13i	−0.145140	−	0.251390i
$914$	3985.00	−	6902.22i	0.144215	−	0.249787i
$915$		−	2744.00i		−	0.0991408i
$916$	−6698.71	−	3867.50i	−0.241628	−	0.139504i
$917$	−16155.7	−	9327.50i	−0.581798	−	0.335901i
$918$			13475.0i			0.484468i
$919$	13824.0	−	23943.9i	0.496204	−	0.859451i	−0.503786	−	0.863828i	$-0.668060\pi$
$919$	13824.0	−	23943.9i	0.496204	−	0.859451i	0.999990	+	0.00437745i	$0.00139339\pi$
$920$	−15120.0	−	26188.6i	−0.541839	−	0.938492i
$921$	12815.4	−	7399.00i	0.458505	−	0.264718i
$922$	−29575.0			−1.05640
$923$		0			0
$924$	−40222.0			−1.43204
$925$	8622.15	−	4978.00i	0.306481	−	0.176947i
$926$	−27680.0	−	47943.2i	−0.982312	−	1.70141i
$927$	6468.00	−	11202.9i	0.229166	−	0.396927i
$928$			6970.00i			0.246553i
$929$	−654.715	−	378.000i	−0.0231222	−	0.0133496i	0.488394	−	0.872623i	$-0.337583\pi$
$929$	−654.715	−	378.000i	−0.0231222	−	0.0133496i	−0.511517	+	0.859273i	$0.670916\pi$
$930$	−41586.5	−	24010.0i	−1.46632	−	0.846579i
$931$		−	21924.0i		−	0.771783i
$932$	−26018.5	+	45065.4i	−0.914447	+	1.58387i
$933$	−11907.0	−	20623.5i	−0.417811	−	0.723670i
$934$	5455.96	−	3150.00i	0.191140	−	0.110355i
$935$	−14014.0			−0.490168
$936$		0			0
$937$	20846.0			0.726797			0.363399	−	0.931634i	$-0.381616\pi$
$937$	20846.0			0.726797			0.363399	+	0.931634i	$0.381616\pi$
$938$	26907.4	−	15535.0i	0.936629	−	0.540763i
$939$	−37411.5	−	64798.6i	−1.30019	−	2.25199i
$940$	6247.50	−	10821.0i	0.216778	−	0.375470i
$941$		−	41321.0i		−	1.43148i	−0.698365	−	0.715742i	$-0.746089\pi$
$941$		−	41321.0i		−	1.43148i	0.698365	−	0.715742i	$-0.253911\pi$
$942$	82748.7	+	47775.0i	2.86210	+	1.65243i
$943$	−27934.5	−	16128.0i	−0.964659	−	0.556946i
$944$			26166.0i			0.902151i
$945$	−1592.50	+	2758.29i	−0.0548191	+	0.0949494i
$946$	−13065.0	−	22629.2i	−0.449027	−	0.777738i
$947$	−47602.0	+	27483.0i	−1.63343	+	0.943060i	−0.650402	+	0.759590i	$0.725399\pi$
$947$	−47602.0	+	27483.0i	−1.63343	+	0.943060i	−0.983025	+	0.183469i	$0.941267\pi$
$948$	155176.			5.31633
$949$		0			0
$950$	−47880.0			−1.63519
$951$	42762.6	−	24689.0i	1.45812	−	0.841846i
$952$	−22522.5	−	39010.1i	−0.766763	−	1.32807i
$953$	−22276.5	+	38584.0i	−0.757195	+	1.31150i	0.187081	+	0.982344i	$0.440097\pi$
$953$	−22276.5	+	38584.0i	−0.757195	+	1.31150i	−0.944276	+	0.329155i	$0.893236\pi$
$954$			47520.0i			1.61270i
$955$	2558.24	+	1477.00i	0.0866834	+	0.0500467i
$956$	−51189.9	−	29554.5i	−1.73180	−	0.999854i
$957$			14924.0i			0.504101i
$958$	−30082.5	+	52104.4i	−1.01453	+	1.75722i
$959$	11544.0	+	19994.8i	0.388712	+	0.673270i
$960$	12178.9	−	7031.50i	0.409451	−	0.236397i
$961$	−8625.00			−0.289517
$962$		0			0
$963$	−15048.0			−0.503546
$964$	−23703.1	+	13685.0i	−0.791936	+	0.457224i
$965$	1722.00	+	2982.59i	0.0574437	+	0.0994954i
$966$	21840.0	−	37828.0i	0.727423	−	1.25993i
$967$		−	27907.0i		−	0.928054i	−0.885821	−	0.464027i	$-0.846404\pi$
$967$		−	27907.0i		−	0.928054i	0.885821	−	0.464027i	$-0.153596\pi$
$968$	−25526.1	−	14737.5i	−0.847562	−	0.489340i
$969$	58815.2	+	33957.0i	1.94986	+	1.12575i
$970$		−	2450.00i		−	0.0810977i
$971$	8221.50	−	14240.1i	0.271720	−	0.470634i	−0.697582	−	0.716505i	$-0.745741\pi$
$971$	8221.50	−	14240.1i	0.271720	−	0.470634i	0.969302	+	0.245871i	$0.0790741\pi$
$972$	41888.0	+	72552.1i	1.38226	+	2.39415i
$973$	−21041.8	+	12148.5i	−0.693289	+	0.400270i
$974$	−11400.0			−0.375030
$975$		0			0
$976$	−4984.00			−0.163457
$977$	−39329.7	+	22707.0i	−1.28789	+	0.743563i	−0.978277	−	0.207300i	$-0.933532\pi$
$977$	−39329.7	+	22707.0i	−1.28789	+	0.743563i	−0.309612	+	0.950863i	$0.600199\pi$
$978$	9520.00	+	16489.1i	0.311264	+	0.539125i
$979$	15470.0	−	26794.8i	0.505029	−	0.874736i
$980$			20706.0i			0.674927i
$981$	−7106.60	−	4103.00i	−0.231291	−	0.133536i
$982$	−72603.2	−	41917.5i	−2.35933	−	1.36216i
$983$			8981.00i			0.291403i	0.989329	+	0.145702i	$0.0465440\pi$
$983$			8981.00i			0.291403i	−0.989329	+	0.145702i	$0.953456\pi$
$984$	−52920.0	+	91660.1i	−1.71446	+	2.96953i
$985$	−10468.5	−	18132.0i	−0.338634	−	0.586531i
$986$	−27340.4	+	15785.0i	−0.883059	+	0.509834i
$987$	9555.00			0.308145
$988$		0			0
$989$	19296.0			0.620402
$990$	−17337.8	+	10010.0i	−0.556598	+	0.321352i
$991$	8707.00	+	15081.0i	0.279099	+	0.483413i	0.971161	−	0.238424i	$-0.0766309\pi$
$991$	8707.00	+	15081.0i	0.279099	+	0.483413i	−0.692062	+	0.721838i	$0.743298\pi$
$992$	−8330.00	+	14428.0i	−0.266611	+	0.461783i
$993$		−	67928.0i		−	2.17083i
$994$	−506.625	−	292.500i	−0.0161662	−	0.00933354i
$995$	424.352	+	245.000i	0.0135205	+	0.00780605i
$996$		−	36652.0i		−	1.16603i
$997$	11851.0	−	20526.5i	0.376454	−	0.652038i	−0.614089	−	0.789237i	$-0.710477\pi$
$997$	11851.0	−	20526.5i	0.376454	−	0.652038i	0.990544	+	0.137199i	$0.0438099\pi$
$998$	−32100.0	−	55598.8i	−1.01814	−	1.76348i
$999$	3970.73	−	2292.50i	0.125754	−	0.0726041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.e.e.23.1		4
13.2	odd	12		13.4.a.a.1.1	✓	1
13.3	even	3		169.4.b.a.168.1		2
13.4	even	6	inner	169.4.e.e.147.1		4
13.5	odd	4		169.4.c.e.146.1		2
13.6	odd	12		169.4.c.e.22.1		2
13.7	odd	12		169.4.c.a.22.1		2
13.8	odd	4		169.4.c.a.146.1		2
13.9	even	3	inner	169.4.e.e.147.2		4
13.10	even	6		169.4.b.a.168.2		2
13.11	odd	12		169.4.a.e.1.1		1
13.12	even	2	inner	169.4.e.e.23.2		4
39.2	even	12		117.4.a.b.1.1		1
39.11	even	12		1521.4.a.a.1.1		1
52.15	even	12		208.4.a.g.1.1		1
65.2	even	12		325.4.b.b.274.1		2
65.28	even	12		325.4.b.b.274.2		2
65.54	odd	12		325.4.a.d.1.1		1
91.41	even	12		637.4.a.a.1.1		1
104.67	even	12		832.4.a.a.1.1		1
104.93	odd	12		832.4.a.r.1.1		1
143.54	even	12		1573.4.a.a.1.1		1
156.119	odd	12		1872.4.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.a.a.1.1	✓	1	13.2	odd	12
117.4.a.b.1.1		1	39.2	even	12
169.4.a.e.1.1		1	13.11	odd	12
169.4.b.a.168.1		2	13.3	even	3
169.4.b.a.168.2		2	13.10	even	6
169.4.c.a.22.1		2	13.7	odd	12
169.4.c.a.146.1		2	13.8	odd	4
169.4.c.e.22.1		2	13.6	odd	12
169.4.c.e.146.1		2	13.5	odd	4
169.4.e.e.23.1		4	1.1	even	1	trivial
169.4.e.e.23.2		4	13.12	even	2	inner
169.4.e.e.147.1		4	13.4	even	6	inner
169.4.e.e.147.2		4	13.9	even	3	inner
208.4.a.g.1.1		1	52.15	even	12
325.4.a.d.1.1		1	65.54	odd	12
325.4.b.b.274.1		2	65.2	even	12
325.4.b.b.274.2		2	65.28	even	12
637.4.a.a.1.1		1	91.41	even	12
832.4.a.a.1.1		1	104.67	even	12
832.4.a.r.1.1		1	104.93	odd	12
1521.4.a.a.1.1		1	39.11	even	12
1573.4.a.a.1.1		1	143.54	even	12
1872.4.a.k.1.1		1	156.119	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.33013 + 2.50000i) q^{2} +(3.50000 + 6.06218i) q^{3} +(8.50000 - 14.7224i) q^{4} -7.00000i q^{5} +(-30.3109 - 17.5000i) q^{6} +(-11.2583 - 6.50000i) q^{7} +45.0000i q^{8} +(-11.0000 + 19.0526i) q^{9} +O(q^{10})\)	\(q+(-4.33013 + 2.50000i) q^{2} +(3.50000 + 6.06218i) q^{3} +(8.50000 - 14.7224i) q^{4} -7.00000i q^{5} +(-30.3109 - 17.5000i) q^{6} +(-11.2583 - 6.50000i) q^{7} +45.0000i q^{8} +(-11.0000 + 19.0526i) q^{9} +(17.5000 + 30.3109i) q^{10} +(22.5167 - 13.0000i) q^{11} +119.000 q^{12} +65.0000 q^{14} +(42.4352 - 24.5000i) q^{15} +(-44.5000 - 77.0763i) q^{16} +(38.5000 - 66.6840i) q^{17} -110.000i q^{18} +(109.119 + 63.0000i) q^{19} +(-103.057 - 59.5000i) q^{20} -91.0000i q^{21} +(-65.0000 + 112.583i) q^{22} +(-48.0000 - 83.1384i) q^{23} +(-272.798 + 157.500i) q^{24} +76.0000 q^{25} +35.0000 q^{27} +(-191.392 + 110.500i) q^{28} +(41.0000 + 71.0141i) q^{29} +(-122.500 + 212.176i) q^{30} +196.000i q^{31} +(73.6122 + 42.5000i) q^{32} +(157.617 + 91.0000i) q^{33} +385.000i q^{34} +(-45.5000 + 78.8083i) q^{35} +(187.000 + 323.894i) q^{36} +(113.449 - 65.5000i) q^{37} -630.000 q^{38} +315.000 q^{40} +(290.985 - 168.000i) q^{41} +(227.500 + 394.042i) q^{42} +(-100.500 + 174.071i) q^{43} -442.000i q^{44} +(133.368 + 77.0000i) q^{45} +(415.692 + 240.000i) q^{46} +105.000i q^{47} +(311.500 - 539.534i) q^{48} +(-87.0000 - 150.688i) q^{49} +(-329.090 + 190.000i) q^{50} +539.000 q^{51} -432.000 q^{53} +(-151.554 + 87.5000i) q^{54} +(-91.0000 - 157.617i) q^{55} +(292.500 - 506.625i) q^{56} +882.000i q^{57} +(-355.070 - 205.000i) q^{58} +(-254.611 - 147.000i) q^{59} -833.000i q^{60} +(28.0000 - 48.4974i) q^{61} +(-490.000 - 848.705i) q^{62} +(247.683 - 143.000i) q^{63} +287.000 q^{64} -910.000 q^{66} +(413.960 - 239.000i) q^{67} +(-654.500 - 1133.63i) q^{68} +(336.000 - 581.969i) q^{69} -455.000i q^{70} +(-7.79423 - 4.50000i) q^{71} +(-857.365 - 495.000i) q^{72} -98.0000i q^{73} +(-327.500 + 567.247i) q^{74} +(266.000 + 460.726i) q^{75} +(1855.03 - 1071.00i) q^{76} -338.000 q^{77} +1304.00 q^{79} +(-539.534 + 311.500i) q^{80} +(419.500 + 726.595i) q^{81} +(-840.000 + 1454.92i) q^{82} -308.000i q^{83} +(-1339.74 - 773.500i) q^{84} +(-466.788 - 269.500i) q^{85} -1005.00i q^{86} +(-287.000 + 497.099i) q^{87} +(585.000 + 1013.25i) q^{88} +(1030.57 - 595.000i) q^{89} -770.000 q^{90} -1632.00 q^{92} +(-1188.19 + 686.000i) q^{93} +(-262.500 - 454.663i) q^{94} +(441.000 - 763.834i) q^{95} +595.000i q^{96} +(-60.6218 - 35.0000i) q^{97} +(753.442 + 435.000i) q^{98} +572.000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 14 q^{3} + 34 q^{4} - 44 q^{9}+O(q^{10}) \) 4 * q + 14 * q^3 + 34 * q^4 - 44 * q^9	\( 4 q + 14 q^{3} + 34 q^{4} - 44 q^{9} + 70 q^{10} + 476 q^{12} + 260 q^{14} - 178 q^{16} + 154 q^{17} - 260 q^{22} - 192 q^{23} + 304 q^{25} + 140 q^{27} + 164 q^{29} - 490 q^{30} - 182 q^{35} + 748 q^{36} - 2520 q^{38} + 1260 q^{40} + 910 q^{42} - 402 q^{43} + 1246 q^{48} - 348 q^{49} + 2156 q^{51} - 1728 q^{53} - 364 q^{55} + 1170 q^{56} + 112 q^{61} - 1960 q^{62} + 1148 q^{64} - 3640 q^{66} - 2618 q^{68} + 1344 q^{69} - 1310 q^{74} + 1064 q^{75} - 1352 q^{77} + 5216 q^{79} + 1678 q^{81} - 3360 q^{82} - 1148 q^{87} + 2340 q^{88} - 3080 q^{90} - 6528 q^{92} - 1050 q^{94} + 1764 q^{95}+O(q^{100}) \) 4 * q + 14 * q^3 + 34 * q^4 - 44 * q^9 + 70 * q^10 + 476 * q^12 + 260 * q^14 - 178 * q^16 + 154 * q^17 - 260 * q^22 - 192 * q^23 + 304 * q^25 + 140 * q^27 + 164 * q^29 - 490 * q^30 - 182 * q^35 + 748 * q^36 - 2520 * q^38 + 1260 * q^40 + 910 * q^42 - 402 * q^43 + 1246 * q^48 - 348 * q^49 + 2156 * q^51 - 1728 * q^53 - 364 * q^55 + 1170 * q^56 + 112 * q^61 - 1960 * q^62 + 1148 * q^64 - 3640 * q^66 - 2618 * q^68 + 1344 * q^69 - 1310 * q^74 + 1064 * q^75 - 1352 * q^77 + 5216 * q^79 + 1678 * q^81 - 3360 * q^82 - 1148 * q^87 + 2340 * q^88 - 3080 * q^90 - 6528 * q^92 - 1050 * q^94 + 1764 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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