LMFDB - Embedded newform 169.4.c.e.22.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(22,169)]

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([4]))

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

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

chi := DirichletCharacter("169.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.c (of order $3$, 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	169.22
Dual form			169.4.c.e.146.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.50000 - 4.33013i) q^{2} +(3.50000 - 6.06218i) q^{3} +(-8.50000 - 14.7224i) q^{4} -7.00000 q^{5} +(-17.5000 - 30.3109i) q^{6} +(6.50000 + 11.2583i) q^{7} -45.0000 q^{8} +(-11.0000 - 19.0526i) q^{9} +O(q^{10})$	\(q+(2.50000 - 4.33013i) q^{2} +(3.50000 - 6.06218i) q^{3} +(-8.50000 - 14.7224i) q^{4} -7.00000 q^{5} +(-17.5000 - 30.3109i) q^{6} +(6.50000 + 11.2583i) q^{7} -45.0000 q^{8} +(-11.0000 - 19.0526i) q^{9} +(-17.5000 + 30.3109i) q^{10} +(13.0000 - 22.5167i) q^{11} -119.000 q^{12} +65.0000 q^{14} +(-24.5000 + 42.4352i) q^{15} +(-44.5000 + 77.0763i) q^{16} +(-38.5000 - 66.6840i) q^{17} -110.000 q^{18} +(63.0000 + 109.119i) q^{19} +(59.5000 + 103.057i) q^{20} +91.0000 q^{21} +(-65.0000 - 112.583i) q^{22} +(48.0000 - 83.1384i) q^{23} +(-157.500 + 272.798i) q^{24} -76.0000 q^{25} +35.0000 q^{27} +(110.500 - 191.392i) q^{28} +(41.0000 - 71.0141i) q^{29} +(122.500 + 212.176i) q^{30} +196.000 q^{31} +(42.5000 + 73.6122i) q^{32} +(-91.0000 - 157.617i) q^{33} -385.000 q^{34} +(-45.5000 - 78.8083i) q^{35} +(-187.000 + 323.894i) q^{36} +(65.5000 - 113.449i) q^{37} +630.000 q^{38} +315.000 q^{40} +(-168.000 + 290.985i) q^{41} +(227.500 - 394.042i) q^{42} +(100.500 + 174.071i) q^{43} -442.000 q^{44} +(77.0000 + 133.368i) q^{45} +(-240.000 - 415.692i) q^{46} -105.000 q^{47} +(311.500 + 539.534i) q^{48} +(87.0000 - 150.688i) q^{49} +(-190.000 + 329.090i) q^{50} -539.000 q^{51} -432.000 q^{53} +(87.5000 - 151.554i) q^{54} +(-91.0000 + 157.617i) q^{55} +(-292.500 - 506.625i) q^{56} +882.000 q^{57} +(-205.000 - 355.070i) q^{58} +(147.000 + 254.611i) q^{59} +833.000 q^{60} +(28.0000 + 48.4974i) q^{61} +(490.000 - 848.705i) q^{62} +(143.000 - 247.683i) q^{63} -287.000 q^{64} -910.000 q^{66} +(-239.000 + 413.960i) q^{67} +(-654.500 + 1133.63i) q^{68} +(-336.000 - 581.969i) q^{69} -455.000 q^{70} +(-4.50000 - 7.79423i) q^{71} +(495.000 + 857.365i) q^{72} +98.0000 q^{73} +(-327.500 - 567.247i) q^{74} +(-266.000 + 460.726i) q^{75} +(1071.00 - 1855.03i) q^{76} +338.000 q^{77} +1304.00 q^{79} +(311.500 - 539.534i) q^{80} +(419.500 - 726.595i) q^{81} +(840.000 + 1454.92i) q^{82} -308.000 q^{83} +(-773.500 - 1339.74i) q^{84} +(269.500 + 466.788i) q^{85} +1005.00 q^{86} +(-287.000 - 497.099i) q^{87} +(-585.000 + 1013.25i) q^{88} +(595.000 - 1030.57i) q^{89} +770.000 q^{90} -1632.00 q^{92} +(686.000 - 1188.19i) q^{93} +(-262.500 + 454.663i) q^{94} +(-441.000 - 763.834i) q^{95} +595.000 q^{96} +(-35.0000 - 60.6218i) q^{97} +(-435.000 - 753.442i) q^{98} -572.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 5 q^{2} + 7 q^{3} - 17 q^{4} - 14 q^{5} - 35 q^{6} + 13 q^{7} - 90 q^{8} - 22 q^{9}+O(q^{10}) $ 2 * q + 5 * q^2 + 7 * q^3 - 17 * q^4 - 14 * q^5 - 35 * q^6 + 13 * q^7 - 90 * q^8 - 22 * q^9	\( 2 q + 5 q^{2} + 7 q^{3} - 17 q^{4} - 14 q^{5} - 35 q^{6} + 13 q^{7} - 90 q^{8} - 22 q^{9} - 35 q^{10} + 26 q^{11} - 238 q^{12} + 130 q^{14} - 49 q^{15} - 89 q^{16} - 77 q^{17} - 220 q^{18} + 126 q^{19} + 119 q^{20} + 182 q^{21} - 130 q^{22} + 96 q^{23} - 315 q^{24} - 152 q^{25} + 70 q^{27} + 221 q^{28} + 82 q^{29} + 245 q^{30} + 392 q^{31} + 85 q^{32} - 182 q^{33} - 770 q^{34} - 91 q^{35} - 374 q^{36} + 131 q^{37} + 1260 q^{38} + 630 q^{40} - 336 q^{41} + 455 q^{42} + 201 q^{43} - 884 q^{44} + 154 q^{45} - 480 q^{46} - 210 q^{47} + 623 q^{48} + 174 q^{49} - 380 q^{50} - 1078 q^{51} - 864 q^{53} + 175 q^{54} - 182 q^{55} - 585 q^{56} + 1764 q^{57} - 410 q^{58} + 294 q^{59} + 1666 q^{60} + 56 q^{61} + 980 q^{62} + 286 q^{63} - 574 q^{64} - 1820 q^{66} - 478 q^{67} - 1309 q^{68} - 672 q^{69} - 910 q^{70} - 9 q^{71} + 990 q^{72} + 196 q^{73} - 655 q^{74} - 532 q^{75} + 2142 q^{76} + 676 q^{77} + 2608 q^{79} + 623 q^{80} + 839 q^{81} + 1680 q^{82} - 616 q^{83} - 1547 q^{84} + 539 q^{85} + 2010 q^{86} - 574 q^{87} - 1170 q^{88} + 1190 q^{89} + 1540 q^{90} - 3264 q^{92} + 1372 q^{93} - 525 q^{94} - 882 q^{95} + 1190 q^{96} - 70 q^{97} - 870 q^{98} - 1144 q^{99}+O(q^{100}) \) 2 * q + 5 * q^2 + 7 * q^3 - 17 * q^4 - 14 * q^5 - 35 * q^6 + 13 * q^7 - 90 * q^8 - 22 * q^9 - 35 * q^10 + 26 * q^11 - 238 * q^12 + 130 * q^14 - 49 * q^15 - 89 * q^16 - 77 * q^17 - 220 * q^18 + 126 * q^19 + 119 * q^20 + 182 * q^21 - 130 * q^22 + 96 * q^23 - 315 * q^24 - 152 * q^25 + 70 * q^27 + 221 * q^28 + 82 * q^29 + 245 * q^30 + 392 * q^31 + 85 * q^32 - 182 * q^33 - 770 * q^34 - 91 * q^35 - 374 * q^36 + 131 * q^37 + 1260 * q^38 + 630 * q^40 - 336 * q^41 + 455 * q^42 + 201 * q^43 - 884 * q^44 + 154 * q^45 - 480 * q^46 - 210 * q^47 + 623 * q^48 + 174 * q^49 - 380 * q^50 - 1078 * q^51 - 864 * q^53 + 175 * q^54 - 182 * q^55 - 585 * q^56 + 1764 * q^57 - 410 * q^58 + 294 * q^59 + 1666 * q^60 + 56 * q^61 + 980 * q^62 + 286 * q^63 - 574 * q^64 - 1820 * q^66 - 478 * q^67 - 1309 * q^68 - 672 * q^69 - 910 * q^70 - 9 * q^71 + 990 * q^72 + 196 * q^73 - 655 * q^74 - 532 * q^75 + 2142 * q^76 + 676 * q^77 + 2608 * q^79 + 623 * q^80 + 839 * q^81 + 1680 * q^82 - 616 * q^83 - 1547 * q^84 + 539 * q^85 + 2010 * q^86 - 574 * q^87 - 1170 * q^88 + 1190 * q^89 + 1540 * q^90 - 3264 * q^92 + 1372 * q^93 - 525 * q^94 - 882 * q^95 + 1190 * q^96 - 70 * q^97 - 870 * q^98 - 1144 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.50000	−	4.33013i	0.883883	−	1.53093i	0.0368954	−	0.999319i	$-0.488253\pi$
$2$	2.50000	−	4.33013i	0.883883	−	1.53093i	0.846988	−	0.531612i	$-0.178414\pi$
$3$	3.50000	−	6.06218i	0.673575	−	1.16667i	−0.303308	−	0.952893i	$-0.598091\pi$
$3$	3.50000	−	6.06218i	0.673575	−	1.16667i	0.976883	−	0.213774i	$-0.0685756\pi$
$4$	−8.50000	−	14.7224i	−1.06250	−	1.84030i
$5$	−7.00000			−0.626099			−0.313050	−	0.949737i	$-0.601351\pi$
$5$	−7.00000			−0.626099			−0.313050	+	0.949737i	$0.601351\pi$
$6$	−17.5000	−	30.3109i	−1.19072	−	2.06239i
$7$	6.50000	+	11.2583i	0.350967	+	0.607893i	0.986419	−	0.164248i	$-0.0525196\pi$
$7$	6.50000	+	11.2583i	0.350967	+	0.607893i	−0.635452	+	0.772140i	$0.719186\pi$
$8$	−45.0000			−1.98874
$9$	−11.0000	−	19.0526i	−0.407407	−	0.705650i
$10$	−17.5000	+	30.3109i	−0.553399	+	0.958514i
$11$	13.0000	−	22.5167i	0.356332	−	0.617184i	−0.631013	−	0.775772i	$-0.717361\pi$
$11$	13.0000	−	22.5167i	0.356332	−	0.617184i	0.987345	+	0.158588i	$0.0506940\pi$
$12$	−119.000			−2.86270
$13$		0			0
$13$		0			0
$14$	65.0000			1.24086
$15$	−24.5000	+	42.4352i	−0.421725	+	0.730449i
$16$	−44.5000	+	77.0763i	−0.695312	+	1.20432i
$17$	−38.5000	−	66.6840i	−0.549272	−	0.951367i	−0.998325	−	0.0578615i	$-0.981572\pi$
$17$	−38.5000	−	66.6840i	−0.549272	−	0.951367i	0.449053	−	0.893505i	$-0.351762\pi$
$18$	−110.000			−1.44040
$19$	63.0000	+	109.119i	0.760694	+	1.31756i	0.942493	+	0.334225i	$0.108475\pi$
$19$	63.0000	+	109.119i	0.760694	+	1.31756i	−0.181799	+	0.983336i	$0.558192\pi$
$20$	59.5000	+	103.057i	0.665230	+	1.15221i
$21$	91.0000			0.945611
$22$	−65.0000	−	112.583i	−0.629911	−	1.09104i
$23$	48.0000	−	83.1384i	0.435161	−	0.753720i	−0.562148	−	0.827037i	$-0.690025\pi$
$23$	48.0000	−	83.1384i	0.435161	−	0.753720i	0.997309	+	0.0733164i	$0.0233583\pi$
$24$	−157.500	+	272.798i	−1.33956	+	2.32019i
$25$	−76.0000			−0.608000
$26$		0			0
$27$	35.0000			0.249472
$28$	110.500	−	191.392i	0.745805	−	1.29177i
$29$	41.0000	−	71.0141i	0.262535	−	0.454724i	−0.704380	−	0.709823i	$-0.748775\pi$
$29$	41.0000	−	71.0141i	0.262535	−	0.454724i	0.966915	+	0.255099i	$0.0821082\pi$
$30$	122.500	+	212.176i	0.745511	+	1.29126i
$31$	196.000			1.13557			0.567785	−	0.823177i	$-0.307801\pi$
$31$	196.000			1.13557			0.567785	+	0.823177i	$0.307801\pi$
$32$	42.5000	+	73.6122i	0.234782	+	0.406654i
$33$	−91.0000	−	157.617i	−0.480032	−	0.831440i
$34$	−385.000			−1.94197
$35$	−45.5000	−	78.8083i	−0.219740	−	0.380601i
$36$	−187.000	+	323.894i	−0.865741	+	1.49951i
$37$	65.5000	−	113.449i	0.291031	−	0.504080i	−0.683023	−	0.730397i	$-0.739335\pi$
$37$	65.5000	−	113.449i	0.291031	−	0.504080i	0.974054	+	0.226317i	$0.0726685\pi$
$38$	630.000			2.68946
$39$		0			0
$40$	315.000			1.24515
$41$	−168.000	+	290.985i	−0.639932	+	1.10839i	0.345516	+	0.938413i	$0.387704\pi$
$41$	−168.000	+	290.985i	−0.639932	+	1.10839i	−0.985447	+	0.169981i	$0.945629\pi$
$42$	227.500	−	394.042i	0.835810	−	1.44767i
$43$	100.500	+	174.071i	0.356421	+	0.617339i	0.987360	−	0.158493i	$-0.0506635\pi$
$43$	100.500	+	174.071i	0.356421	+	0.617339i	−0.630939	+	0.775832i	$0.717330\pi$
$44$	−442.000			−1.51441
$45$	77.0000	+	133.368i	0.255077	+	0.441807i
$46$	−240.000	−	415.692i	−0.769262	−	1.33240i
$47$	−105.000			−0.325869			−0.162934	−	0.986637i	$-0.552096\pi$
$47$	−105.000			−0.325869			−0.162934	+	0.986637i	$0.552096\pi$
$48$	311.500	+	539.534i	0.936691	+	1.62240i
$49$	87.0000	−	150.688i	0.253644	−	0.439325i
$50$	−190.000	+	329.090i	−0.537401	+	0.930806i
$51$	−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	$0.689126\pi$
$54$	87.5000	−	151.554i	0.220504	−	0.381925i
$55$	−91.0000	+	157.617i	−0.223099	+	0.386419i
$56$	−292.500	−	506.625i	−0.697981	−	1.20894i
$57$	882.000			2.04954
$58$	−205.000	−	355.070i	−0.464100	−	0.803845i
$59$	147.000	+	254.611i	0.324369	+	0.561824i	0.981384	−	0.192054i	$-0.0615147\pi$
$59$	147.000	+	254.611i	0.324369	+	0.561824i	−0.657015	+	0.753877i	$0.728181\pi$
$60$	833.000			1.79233
$61$	28.0000	+	48.4974i	0.0587710	+	0.101794i	0.893914	−	0.448239i	$-0.147948\pi$
$61$	28.0000	+	48.4974i	0.0587710	+	0.101794i	−0.835143	+	0.550033i	$0.814615\pi$
$62$	490.000	−	848.705i	1.00371	−	1.73848i
$63$	143.000	−	247.683i	0.285973	−	0.495320i
$64$	−287.000			−0.560547
$65$		0			0
$66$	−910.000			−1.69717
$67$	−239.000	+	413.960i	−0.435798	+	0.754825i	−0.997360	−	0.0726096i	$-0.976867\pi$
$67$	−239.000	+	413.960i	−0.435798	+	0.754825i	0.561562	+	0.827435i	$0.310201\pi$
$68$	−654.500	+	1133.63i	−1.16720	+	2.02165i
$69$	−336.000	−	581.969i	−0.586227	−	1.01537i
$70$	−455.000			−0.776899
$71$	−4.50000	−	7.79423i	−0.00752186	−	0.0130282i	0.862240	−	0.506500i	$-0.169061\pi$
$71$	−4.50000	−	7.79423i	−0.00752186	−	0.0130282i	−0.869762	+	0.493472i	$0.835728\pi$
$72$	495.000	+	857.365i	0.810227	+	1.40335i
$73$	98.0000			0.157124			0.0785619	−	0.996909i	$-0.474967\pi$
$73$	98.0000			0.157124			0.0785619	+	0.996909i	$0.474967\pi$
$74$	−327.500	−	567.247i	−0.514474	−	0.891096i
$75$	−266.000	+	460.726i	−0.409534	+	0.709333i
$76$	1071.00	−	1855.03i	1.61648	−	2.79982i
$77$	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	$0.121053\pi$
$80$	311.500	−	539.534i	0.435334	−	0.754021i
$81$	419.500	−	726.595i	0.575446	−	0.996701i
$82$	840.000	+	1454.92i	1.13125	+	1.95938i
$83$	−308.000			−0.407318			−0.203659	−	0.979042i	$-0.565283\pi$
$83$	−308.000			−0.407318			−0.203659	+	0.979042i	$0.565283\pi$
$84$	−773.500	−	1339.74i	−1.00471	−	1.74021i
$85$	269.500	+	466.788i	0.343899	+	0.595650i
$86$	1005.00			1.26014
$87$	−287.000	−	497.099i	−0.353674	−	0.612581i
$88$	−585.000	+	1013.25i	−0.708650	+	1.22742i
$89$	595.000	−	1030.57i	0.708650	−	1.22742i	−0.256708	−	0.966489i	$-0.582638\pi$
$89$	595.000	−	1030.57i	0.708650	−	1.22742i	0.965358	−	0.260929i	$-0.0840289\pi$
$90$	770.000			0.901835
$91$		0			0
$92$	−1632.00			−1.84943
$93$	686.000	−	1188.19i	0.764891	−	1.32483i
$94$	−262.500	+	454.663i	−0.288030	+	0.498882i
$95$	−441.000	−	763.834i	−0.476270	−	0.824924i
$96$	595.000			0.632572
$97$	−35.0000	−	60.6218i	−0.0366362	−	0.0634558i	0.847126	−	0.531392i	$-0.178331\pi$
$97$	−35.0000	−	60.6218i	−0.0366362	−	0.0634558i	−0.883762	+	0.467936i	$0.844998\pi$
$98$	−435.000	−	753.442i	−0.448384	−	0.776624i
$99$	−572.000			−0.580689
$100$	646.000	+	1118.90i	0.646000	+	1.11890i
$101$	−210.000	+	363.731i	−0.206889	+	0.358342i	−0.950733	−	0.310011i	$-0.899667\pi$
$101$	−210.000	+	363.731i	−0.206889	+	0.358342i	0.743844	+	0.668353i	$0.233001\pi$
$102$	−1347.50	+	2333.94i	−1.30806	+	2.26563i
$103$	588.000			0.562499			0.281249	−	0.959635i	$-0.409251\pi$
$103$	588.000			0.562499			0.281249	+	0.959635i	$0.409251\pi$
$104$		0			0
$105$	−637.000			−0.592046
$106$	−1080.00	+	1870.61i	−0.989612	+	1.71406i
$107$	342.000	−	592.361i	0.308994	−	0.535194i	−0.669148	−	0.743129i	$-0.733341\pi$
$107$	342.000	−	592.361i	0.308994	−	0.535194i	0.978143	+	0.207935i	$0.0666743\pi$
$108$	−297.500	−	515.285i	−0.265064	−	0.459105i
$109$	373.000			0.327770			0.163885	−	0.986479i	$-0.447597\pi$
$109$	373.000			0.327770			0.163885	+	0.986479i	$0.447597\pi$
$110$	455.000	+	788.083i	0.394387	+	0.683098i
$111$	−458.500	−	794.145i	−0.392062	−	0.679071i
$112$	−1157.00			−0.976127
$113$	867.000	+	1501.69i	0.721774	+	1.25015i	0.960288	+	0.279011i	$0.0900065\pi$
$113$	867.000	+	1501.69i	0.721774	+	1.25015i	−0.238514	+	0.971139i	$0.576660\pi$
$114$	2205.00	−	3819.17i	1.81155	−	3.13770i
$115$	−336.000	+	581.969i	−0.272454	+	0.471903i
$116$	−1394.00			−1.11577
$117$		0			0
$118$	1470.00			1.14682
$119$	500.500	−	866.891i	0.385553	−	0.667797i
$120$	1102.50	−	1909.59i	0.838700	−	1.45267i
$121$	327.500	+	567.247i	0.246056	+	0.426181i
$122$	280.000			0.207787
$123$	1176.00	+	2036.89i	0.862084	+	1.49317i
$124$	−1666.00	−	2885.60i	−1.20654	−	2.08979i
$125$	1407.00			1.00677
$126$	−715.000	−	1238.42i	−0.505534	−	0.875610i
$127$	−946.000	+	1638.52i	−0.660976	+	1.14484i	0.319384	+	0.947625i	$0.396524\pi$
$127$	−946.000	+	1638.52i	−0.660976	+	1.14484i	−0.980360	+	0.197218i	$0.936809\pi$
$128$	−1057.50	+	1831.64i	−0.730240	+	1.26481i
$129$	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	$0.341167\pi$
$132$	−1547.00	+	2679.48i	−1.02007	+	1.76681i
$133$	−819.000	+	1418.55i	−0.533957	+	0.924841i
$134$	1195.00	+	2069.80i	0.770390	+	1.33435i
$135$	−245.000			−0.156194
$136$	1732.50	+	3000.78i	1.09236	+	1.89202i
$137$	888.000	+	1538.06i	0.553773	+	0.959164i	0.997998	+	0.0632482i	$0.0201460\pi$
$137$	888.000	+	1538.06i	0.553773	+	0.959164i	−0.444224	+	0.895916i	$0.646521\pi$
$138$	−3360.00			−2.07262
$139$	934.500	+	1618.60i	0.570239	+	0.987683i	0.996541	+	0.0831023i	$0.0264828\pi$
$139$	934.500	+	1618.60i	0.570239	+	0.987683i	−0.426302	+	0.904581i	$0.640184\pi$
$140$	−773.500	+	1339.74i	−0.466948	+	0.808777i
$141$	−367.500	+	636.529i	−0.219497	+	0.380180i
$142$	−45.0000			−0.0265938
$143$		0			0
$144$	1958.00			1.13310
$145$	−287.000	+	497.099i	−0.164373	+	0.284702i
$146$	245.000	−	424.352i	0.138879	−	0.240546i
$147$	−609.000	−	1054.82i	−0.341697	−	0.591837i
$148$	−2227.00			−1.23688
$149$	−1233.00	−	2135.62i	−0.677928	−	1.17421i	−0.975604	−	0.219539i	$-0.929545\pi$
$149$	−1233.00	−	2135.62i	−0.677928	−	1.17421i	0.297676	−	0.954667i	$-0.403789\pi$
$150$	1330.00	+	2303.63i	0.723960	+	1.25394i
$151$	−3323.00			−1.79087			−0.895437	−	0.445189i	$-0.853137\pi$
$151$	−3323.00			−1.79087			−0.895437	+	0.445189i	$0.853137\pi$
$152$	−2835.00	−	4910.36i	−1.51282	−	2.62028i
$153$	−847.000	+	1467.05i	−0.447555	+	0.775188i
$154$	845.000	−	1463.58i	0.442156	−	0.765837i
$155$	−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	$0.744099\pi$
$158$	3260.00	−	5646.49i	1.64147	−	2.84310i
$159$	−1512.00	+	2618.86i	−0.754147	+	1.30622i
$160$	−297.500	−	515.285i	−0.146997	−	0.254605i
$161$	1248.00			0.610908
$162$	−2097.50	−	3632.98i	−1.01725	−	1.76194i
$163$	272.000	+	471.118i	0.130704	+	0.226385i	0.923948	−	0.382518i	$-0.124943\pi$
$163$	272.000	+	471.118i	0.130704	+	0.226385i	−0.793244	+	0.608903i	$0.791610\pi$
$164$	5712.00			2.71971
$165$	637.000	+	1103.32i	0.300548	+	0.520564i
$166$	−770.000	+	1333.68i	−0.360022	+	0.623576i
$167$	−812.000	+	1406.43i	−0.376254	+	0.651691i	−0.990514	−	0.137413i	$-0.956121\pi$
$167$	−812.000	+	1406.43i	−0.376254	+	0.651691i	0.614260	+	0.789104i	$0.289455\pi$
$168$	−4095.00			−1.88057
$169$		0			0
$170$	2695.00			1.21587
$171$	1386.00	−	2400.62i	0.619825	−	1.07357i
$172$	1708.50	−	2959.21i	0.757395	−	1.31185i
$173$	168.000	+	290.985i	0.0738312	+	0.127879i	0.900577	−	0.434696i	$-0.143144\pi$
$173$	168.000	+	290.985i	0.0738312	+	0.127879i	−0.826746	+	0.562575i	$0.809811\pi$
$174$	−2870.00			−1.25043
$175$	−494.000	−	855.633i	−0.213388	−	0.369599i
$176$	1157.00	+	2003.98i	0.495524	+	0.858272i
$177$	2058.00			0.873948
$178$	−2975.00	−	5152.85i	−1.25273	−	2.16979i
$179$	1514.50	−	2623.19i	0.632397	−	1.09534i	−0.354663	−	0.934994i	$-0.615405\pi$
$179$	1514.50	−	2623.19i	0.632397	−	1.09534i	0.987060	−	0.160350i	$-0.0512621\pi$
$180$	1309.00	−	2267.25i	0.542039	−	0.938840i
$181$	−28.0000			−0.0114985			−0.00574924	−	0.999983i	$-0.501830\pi$
$181$	−28.0000			−0.0114985			−0.00574924	+	0.999983i	$0.501830\pi$
$182$		0			0
$183$	392.000			0.158347
$184$	−2160.00	+	3741.23i	−0.865420	+	1.49895i
$185$	−458.500	+	794.145i	−0.182214	+	0.315604i
$186$	−3430.00	−	5940.93i	−1.35215	−	2.34199i
$187$	−2002.00			−0.782892
$188$	892.500	+	1545.86i	0.346235	+	0.599697i
$189$	227.500	+	394.042i	0.0875566	+	0.151652i
$190$	−4410.00			−1.68387
$191$	−211.000	−	365.463i	−0.0799342	−	0.138450i	0.823287	−	0.567625i	$-0.192138\pi$
$191$	−211.000	−	365.463i	−0.0799342	−	0.138450i	−0.903221	+	0.429175i	$0.858804\pi$
$192$	−1004.50	+	1739.85i	−0.377571	+	0.653971i
$193$	−246.000	+	426.084i	−0.0917485	+	0.158913i	−0.908247	−	0.418435i	$-0.862579\pi$
$193$	−246.000	+	426.084i	−0.0917485	+	0.158913i	0.816498	+	0.577348i	$0.195912\pi$
$194$	−350.000			−0.129529
$195$		0			0
$196$	−2958.00			−1.07799
$197$	−1495.50	+	2590.28i	−0.540863	+	0.936802i	0.457992	+	0.888956i	$0.348569\pi$
$197$	−1495.50	+	2590.28i	−0.540863	+	0.936802i	−0.998855	+	0.0478455i	$0.984765\pi$
$198$	−1430.00	+	2476.83i	−0.513261	+	0.888994i
$199$	35.0000	+	60.6218i	0.0124678	+	0.0215948i	0.872192	−	0.489164i	$-0.162698\pi$
$199$	35.0000	+	60.6218i	0.0124678	+	0.0215948i	−0.859724	+	0.510759i	$0.829365\pi$
$200$	3420.00			1.20915
$201$	1673.00	+	2897.72i	0.587086	+	1.01686i
$202$	1050.00	+	1818.65i	0.365731	+	0.633465i
$203$	1066.00			0.368564
$204$	4581.50	+	7935.39i	1.57240	+	2.72347i
$205$	1176.00	−	2036.89i	0.400661	−	0.693964i
$206$	1470.00	−	2546.11i	0.497183	−	0.861147i
$207$	−2112.00			−0.709150
$208$		0			0
$209$	3276.00			1.08424
$210$	−1592.50	+	2758.29i	−0.523300	+	0.906382i
$211$	−1425.50	+	2469.04i	−0.465097	+	0.805572i	−0.999206	−	0.0398440i	$-0.987314\pi$
$211$	−1425.50	+	2469.04i	−0.465097	+	0.805572i	0.534109	+	0.845416i	$0.320647\pi$
$212$	3672.00	+	6360.09i	1.18959	+	2.06044i
$213$	−63.0000			−0.0202661
$214$	−1710.00	−	2961.81i	−0.546230	−	0.946098i
$215$	−703.500	−	1218.50i	−0.223155	−	0.386516i
$216$	−1575.00			−0.496135
$217$	1274.00	+	2206.63i	0.398547	+	0.690304i
$218$	932.500	−	1615.14i	0.289710	−	0.501793i
$219$	343.000	−	594.093i	0.105835	−	0.183311i
$220$	3094.00			0.948170
$221$		0			0
$222$	−4585.00			−1.38615
$223$	−108.500	+	187.928i	−0.0325816	+	0.0564330i	−0.881856	−	0.471518i	$-0.843706\pi$
$223$	−108.500	+	187.928i	−0.0325816	+	0.0564330i	0.849275	+	0.527951i	$0.177040\pi$
$224$	−552.500	+	956.958i	−0.164801	+	0.285444i
$225$	836.000	+	1447.99i	0.247704	+	0.429035i
$226$	8670.00			2.55186
$227$	1288.00	+	2230.88i	0.376597	+	0.652285i	0.990565	−	0.137046i	$-0.0437608\pi$
$227$	1288.00	+	2230.88i	0.376597	+	0.652285i	−0.613968	+	0.789331i	$0.710427\pi$
$228$	−7497.00	−	12985.2i	−2.17764	−	3.77178i
$229$	455.000			0.131298			0.0656490	−	0.997843i	$-0.479088\pi$
$229$	455.000			0.131298			0.0656490	+	0.997843i	$0.479088\pi$
$230$	1680.00	+	2909.85i	0.481634	+	0.834215i
$231$	1183.00	−	2049.02i	0.336951	−	0.583616i
$232$	−1845.00	+	3195.63i	−0.522113	+	0.904326i
$233$	3061.00			0.860656			0.430328	−	0.902673i	$-0.358398\pi$
$233$	3061.00			0.860656			0.430328	+	0.902673i	$0.358398\pi$
$234$		0			0
$235$	735.000			0.204026
$236$	2499.00	−	4328.39i	0.689284	−	1.19388i
$237$	4564.00	−	7905.08i	1.25090	−	2.16662i
$238$	−2502.50	−	4334.46i	−0.681567	−	1.18051i
$239$	−3477.00			−0.941039			−0.470520	−	0.882389i	$-0.655934\pi$
$239$	−3477.00			−0.941039			−0.470520	+	0.882389i	$0.655934\pi$
$240$	−2180.50	−	3776.74i	−0.586461	−	1.01578i
$241$	805.000	+	1394.30i	0.215164	+	0.372676i	0.953323	−	0.301951i	$-0.0976379\pi$
$241$	805.000	+	1394.30i	0.215164	+	0.372676i	−0.738159	+	0.674627i	$0.764305\pi$
$242$	3275.00			0.869938
$243$	−2464.00	−	4267.77i	−0.650476	−	1.12666i
$244$	476.000	−	824.456i	0.124888	−	0.216313i
$245$	−609.000	+	1054.82i	−0.158806	+	0.275061i
$246$	11760.0			3.04793
$247$		0			0
$248$	−8820.00			−2.25835
$249$	−1078.00	+	1867.15i	−0.274359	+	0.475204i
$250$	3517.50	−	6092.49i	0.889865	−	1.54129i
$251$	−504.000	−	872.954i	−0.126742	−	0.219523i	0.795671	−	0.605730i	$-0.207119\pi$
$251$	−504.000	−	872.954i	−0.126742	−	0.219523i	−0.922412	+	0.386206i	$0.873785\pi$
$252$	−4862.00			−1.21539
$253$	−1248.00	−	2161.60i	−0.310123	−	0.537149i
$254$	4730.00	+	8192.60i	1.16845	+	2.02382i
$255$	3773.00			0.926566
$256$	4139.50	+	7169.82i	1.01062	+	1.75045i
$257$	−3020.50	+	5231.66i	−0.733127	+	1.26981i	0.222413	+	0.974952i	$0.428607\pi$
$257$	−3020.50	+	5231.66i	−0.733127	+	1.26981i	−0.955540	+	0.294861i	$0.904727\pi$
$258$	3517.50	−	6092.49i	0.848798	−	1.47016i
$259$	1703.00			0.408569
$260$		0			0
$261$	−1804.00			−0.427834
$262$	3587.50	−	6213.73i	0.845941	−	1.46521i
$263$	1854.00	−	3211.22i	0.434686	−	0.752899i	−0.562584	−	0.826740i	$-0.690193\pi$
$263$	1854.00	−	3211.22i	0.434686	−	0.752899i	0.997270	+	0.0738414i	$0.0235259\pi$
$264$	4095.00	+	7092.75i	0.954658	+	1.65352i
$265$	3024.00			0.700992
$266$	4095.00	+	7092.75i	0.943912	+	1.63490i
$267$	−4165.00	−	7213.99i	−0.954659	−	1.65352i
$268$	8126.00			1.85214
$269$	−4172.00	−	7226.12i	−0.945618	−	1.63786i	−0.754508	−	0.656290i	$-0.772125\pi$
$269$	−4172.00	−	7226.12i	−0.945618	−	1.63786i	−0.191110	−	0.981569i	$-0.561209\pi$
$270$	−612.500	+	1060.88i	−0.138058	+	0.239123i
$271$	808.500	−	1400.36i	0.181228	−	0.313897i	−0.761071	−	0.648669i	$-0.775326\pi$
$271$	808.500	−	1400.36i	0.181228	−	0.313897i	0.942299	+	0.334772i	$0.108659\pi$
$272$	6853.00			1.52766
$273$		0			0
$274$	8880.00			1.95788
$275$	−988.000	+	1711.27i	−0.216650	+	0.375248i
$276$	−5712.00	+	9893.47i	−1.24573	+	2.15767i
$277$	1910.00	+	3308.22i	0.414299	+	0.717587i	0.995355	−	0.0962771i	$-0.0306935\pi$
$277$	1910.00	+	3308.22i	0.414299	+	0.717587i	−0.581056	+	0.813864i	$0.697360\pi$
$278$	9345.00			2.01610
$279$	−2156.00	−	3734.30i	−0.462639	−	0.801315i
$280$	2047.50	+	3546.37i	0.437005	+	0.756916i
$281$	−6214.00			−1.31920			−0.659602	−	0.751615i	$-0.729275\pi$
$281$	−6214.00			−1.31920			−0.659602	+	0.751615i	$0.729275\pi$
$282$	1837.50	+	3182.64i	0.388020	+	0.672070i
$283$	2646.00	−	4583.01i	0.555789	−	0.962655i	−0.442052	−	0.896989i	$-0.645749\pi$
$283$	2646.00	−	4583.01i	0.555789	−	0.962655i	0.997842	−	0.0656661i	$-0.0209172\pi$
$284$	−76.5000	+	132.502i	−0.0159839	+	0.0276850i
$285$	−6174.00			−1.28321
$286$		0			0
$287$	−4368.00			−0.898379
$288$	935.000	−	1619.47i	0.191303	−	0.331347i
$289$	−508.000	+	879.882i	−0.103399	+	0.179093i
$290$	1435.00	+	2485.49i	0.290573	+	0.503287i
$291$	−490.000			−0.0987090
$292$	−833.000	−	1442.80i	−0.166944	−	0.289155i
$293$	451.500	+	782.021i	0.0900236	+	0.155925i	0.907521	−	0.420007i	$-0.137972\pi$
$293$	451.500	+	782.021i	0.0900236	+	0.155925i	−0.817497	+	0.575933i	$0.804639\pi$
$294$	−6090.00			−1.20808
$295$	−1029.00	−	1782.28i	−0.203087	−	0.351757i
$296$	−2947.50	+	5105.22i	−0.578784	+	1.00248i
$297$	455.000	−	788.083i	0.0888949	−	0.153970i
$298$	−12330.0			−2.39684
$299$		0			0
$300$	9044.00			1.74052
$301$	−1306.50	+	2262.92i	−0.250184	+	0.433332i
$302$	−8307.50	+	14389.0i	−1.58292	+	2.74170i
$303$	1470.00	+	2546.11i	0.278711	+	0.482741i
$304$	−11214.0			−2.11568
$305$	−196.000	−	339.482i	−0.0367965	−	0.0637334i
$306$	4235.00	+	7335.24i	0.791173	+	1.37035i
$307$	2114.00			0.393004			0.196502	−	0.980503i	$-0.437042\pi$
$307$	2114.00			0.393004			0.196502	+	0.980503i	$0.437042\pi$
$308$	−2873.00	−	4976.18i	−0.531508	−	0.920598i
$309$	2058.00	−	3564.56i	0.378885	−	0.656248i
$310$	−3430.00	+	5940.93i	−0.628422	+	1.08846i
$311$	3402.00			0.620288			0.310144	−	0.950690i	$-0.399623\pi$
$311$	3402.00			0.620288			0.310144	+	0.950690i	$0.399623\pi$
$312$		0			0
$313$	−10689.0			−1.93028			−0.965141	−	0.261732i	$-0.915706\pi$
$313$	−10689.0			−1.93028			−0.965141	+	0.261732i	$0.915706\pi$
$314$	−6825.00	+	11821.2i	−1.22661	+	2.12456i
$315$	−1001.00	+	1733.78i	−0.179047	+	0.310119i
$316$	−11084.0	−	19198.1i	−1.97318	−	3.41764i
$317$	−7054.00			−1.24982			−0.624909	−	0.780698i	$-0.714864\pi$
$317$	−7054.00			−1.24982			−0.624909	+	0.780698i	$0.714864\pi$
$318$	7560.00	+	13094.3i	1.33316	+	2.30909i
$319$	−1066.00	−	1846.37i	−0.187099	−	0.324065i
$320$	2009.00			0.350958
$321$	−2394.00	−	4146.53i	−0.416262	−	0.720987i
$322$	3120.00	−	5404.00i	0.539971	−	0.935258i
$323$	4851.00	−	8402.18i	0.835656	−	1.44740i
$324$	−14263.0			−2.44564
$325$		0			0
$326$	2720.00			0.462107
$327$	1305.50	−	2261.19i	0.220778	−	0.382398i
$328$	7560.00	−	13094.3i	1.27266	−	2.20430i
$329$	−682.500	−	1182.12i	−0.114369	−	0.198093i
$330$	6370.00			1.06260
$331$	−4852.00	−	8403.91i	−0.805710	−	1.39553i	−0.915811	−	0.401610i	$-0.868451\pi$
$331$	−4852.00	−	8403.91i	−0.805710	−	1.39553i	0.110101	−	0.993920i	$-0.464883\pi$
$332$	2618.00	+	4534.51i	0.432775	+	0.749589i
$333$	−2882.00			−0.474272
$334$	4060.00	+	7032.13i	0.665130	+	1.15204i
$335$	1673.00	−	2897.72i	0.272853	−	0.472595i
$336$	−4049.50	+	7013.94i	−0.657495	+	1.13881i
$337$	−10449.0			−1.68900			−0.844500	−	0.535555i	$-0.820103\pi$
$337$	−10449.0			−1.68900			−0.844500	+	0.535555i	$0.820103\pi$
$338$		0			0
$339$	12138.0			1.94468
$340$	4581.50	−	7935.39i	0.730784	−	1.26576i
$341$	2548.00	−	4413.27i	0.404639	−	0.700855i
$342$	−6930.00	−	12003.1i	−1.09571	−	1.89782i
$343$	6721.00			1.05802
$344$	−4522.50	−	7833.20i	−0.708828	−	1.22773i
$345$	2352.00	+	4073.78i	0.367036	+	0.635725i
$346$	1680.00			0.261033
$347$	310.500	+	537.802i	0.0480361	+	0.0832009i	0.889044	−	0.457822i	$-0.151370\pi$
$347$	310.500	+	537.802i	0.0480361	+	0.0832009i	−0.841008	+	0.541023i	$0.818037\pi$
$348$	−4879.00	+	8450.68i	−0.751557	+	1.30173i
$349$	−6240.50	+	10808.9i	−0.957153	+	1.65784i	−0.227790	+	0.973710i	$0.573150\pi$
$349$	−6240.50	+	10808.9i	−0.957153	+	1.65784i	−0.729363	+	0.684127i	$0.760183\pi$
$350$	−4940.00			−0.754440
$351$		0			0
$352$	2210.00			0.334640
$353$	700.000	−	1212.44i	0.105545	−	0.182809i	−0.808416	−	0.588612i	$-0.799675\pi$
$353$	700.000	−	1212.44i	0.105545	−	0.182809i	0.913961	+	0.405803i	$0.133008\pi$
$354$	5145.00	−	8911.40i	0.772468	−	1.33795i
$355$	31.5000	+	54.5596i	0.00470943	+	0.00815697i
$356$	−20230.0			−3.01176
$357$	−3503.50	−	6068.24i	−0.519397	−	0.899623i
$358$	−7572.50	−	13116.0i	−1.11793	−	1.93631i
$359$	−4968.00			−0.730365			−0.365182	−	0.930936i	$-0.618993\pi$
$359$	−4968.00			−0.730365			−0.365182	+	0.930936i	$0.618993\pi$
$360$	−3465.00	−	6001.56i	−0.507282	−	0.878638i
$361$	−4508.50	+	7808.95i	−0.657312	+	1.13850i
$362$	−70.0000	+	121.244i	−0.0101633	+	0.0176034i
$363$	4585.00			0.662948
$364$		0			0
$365$	−686.000			−0.0983750
$366$	980.000	−	1697.41i	0.139960	−	0.242418i
$367$	−4361.00	+	7553.47i	−0.620279	+	1.07435i	0.369155	+	0.929368i	$0.379647\pi$
$367$	−4361.00	+	7553.47i	−0.620279	+	1.07435i	−0.989434	+	0.144987i	$0.953686\pi$
$368$	4272.00	+	7399.32i	0.605145	+	1.04814i
$369$	7392.00			1.04285
$370$	2292.50	+	3970.73i	0.322112	+	0.557914i
$371$	−2808.00	−	4863.60i	−0.392949	−	0.680608i
$372$	−23324.0			−3.25079
$373$	−5006.00	−	8670.65i	−0.694908	−	1.20362i	−0.970212	−	0.242259i	$-0.922112\pi$
$373$	−5006.00	−	8670.65i	−0.694908	−	1.20362i	0.275303	−	0.961357i	$-0.411222\pi$
$374$	−5005.00	+	8668.91i	−0.691985	+	1.19855i
$375$	4924.50	−	8529.48i	0.678134	−	1.17456i
$376$	4725.00			0.648067
$377$		0			0
$378$	2275.00			0.309559
$379$	1686.00	−	2920.24i	0.228507	−	0.395785i	−0.728859	−	0.684664i	$-0.759949\pi$
$379$	1686.00	−	2920.24i	0.228507	−	0.395785i	0.957366	+	0.288879i	$0.0932824\pi$
$380$	−7497.00	+	12985.2i	−1.01207	+	1.75296i
$381$	6622.00	+	11469.6i	0.890434	+	1.54228i
$382$	−2110.00			−0.282610
$383$	423.500	+	733.524i	0.0565009	+	0.0978624i	0.892892	−	0.450270i	$-0.148672\pi$
$383$	423.500	+	733.524i	0.0565009	+	0.0978624i	−0.836392	+	0.548132i	$0.815339\pi$
$384$	7402.50	+	12821.5i	0.983743	+	1.70389i
$385$	−2366.00			−0.313201
$386$	1230.00	+	2130.42i	0.162190	+	0.280921i
$387$	2211.00	−	3829.56i	0.290417	−	0.503017i
$388$	−595.000	+	1030.57i	−0.0778519	+	0.134843i
$389$	11314.0			1.47466			0.737330	−	0.675533i	$-0.236086\pi$
$389$	11314.0			1.47466			0.737330	+	0.675533i	$0.236086\pi$
$390$		0			0
$391$	−7392.00			−0.956086
$392$	−3915.00	+	6780.98i	−0.504432	+	0.873702i
$393$	5022.50	−	8699.23i	0.644661	−	1.11658i
$394$	7477.50	+	12951.4i	0.956119	+	1.65605i
$395$	−9128.00			−1.16273
$396$	4862.00	+	8421.23i	0.616982	+	1.06864i
$397$	−931.000	−	1612.54i	−0.117697	−	0.203856i	0.801158	−	0.598453i	$-0.204218\pi$
$397$	−931.000	−	1612.54i	−0.117697	−	0.203856i	−0.918854	+	0.394597i	$0.870884\pi$
$398$	350.000			0.0440802
$399$	5733.00	+	9929.85i	0.719321	+	1.24590i
$400$	3382.00	−	5857.80i	0.422750	−	0.732224i
$401$	−3410.00	+	5906.29i	−0.424657	+	0.735527i	−0.996388	−	0.0849139i	$-0.972938\pi$
$401$	−3410.00	+	5906.29i	−0.424657	+	0.735527i	0.571732	+	0.820441i	$0.306272\pi$
$402$	16730.0			2.07566
$403$		0			0
$404$	7140.00			0.879278
$405$	−2936.50	+	5086.17i	−0.360286	+	0.624034i
$406$	2665.00	−	4615.92i	0.325768	−	0.564246i
$407$	−1703.00	−	2949.68i	−0.207407	−	0.359239i
$408$	24255.0			2.94314
$409$	6496.00	+	11251.4i	0.785346	+	1.36026i	0.928792	+	0.370601i	$0.120848\pi$
$409$	6496.00	+	11251.4i	0.785346	+	1.36026i	−0.143446	+	0.989658i	$0.545818\pi$
$410$	−5880.00	−	10184.5i	−0.708274	−	1.22677i
$411$	12432.0			1.49203
$412$	−4998.00	−	8656.79i	−0.597655	−	1.03517i
$413$	−1911.00	+	3309.95i	−0.227686	+	0.394363i
$414$	−5280.00	+	9145.23i	−0.626806	+	1.08566i
$415$	2156.00			0.255021
$416$		0			0
$417$	13083.0			1.53640
$418$	8190.00	−	14185.5i	0.958340	−	1.65989i
$419$	3671.50	−	6359.22i	0.428078	−	0.741452i	−0.568625	−	0.822597i	$-0.692524\pi$
$419$	3671.50	−	6359.22i	0.428078	−	0.741452i	0.996702	+	0.0811449i	$0.0258577\pi$
$420$	5414.50	+	9378.19i	0.629049	+	1.08954i
$421$	−5059.00			−0.585655			−0.292827	−	0.956165i	$-0.594596\pi$
$421$	−5059.00			−0.585655			−0.292827	+	0.956165i	$0.594596\pi$
$422$	7127.50	+	12345.2i	0.822183	+	1.42406i
$423$	1155.00	+	2000.52i	0.132761	+	0.229949i
$424$	19440.0			2.22663
$425$	2926.00	+	5067.98i	0.333957	+	0.578431i
$426$	−157.500	+	272.798i	−0.0179129	+	0.0310261i
$427$	−364.000	+	630.466i	−0.0412534	+	0.0714530i
$428$	−11628.0			−1.31323
$429$		0			0
$430$	−7035.00			−0.788972
$431$	−1621.50	+	2808.52i	−0.181218	+	0.313879i	−0.942296	−	0.334782i	$-0.891337\pi$
$431$	−1621.50	+	2808.52i	−0.181218	+	0.313879i	0.761078	+	0.648661i	$0.224671\pi$
$432$	−1557.50	+	2697.67i	−0.173461	+	0.300444i
$433$	−5799.50	−	10045.0i	−0.643663	−	1.11486i	−0.984609	−	0.174774i	$-0.944080\pi$
$433$	−5799.50	−	10045.0i	−0.643663	−	1.11486i	0.340945	−	0.940083i	$-0.389253\pi$
$434$	12740.0			1.40908
$435$	2009.00	+	3479.69i	0.221435	+	0.383536i
$436$	−3170.50	−	5491.47i	−0.348256	−	0.603196i
$437$	12096.0			1.32410
$438$	−1715.00	−	2970.47i	−0.187091	−	0.324051i
$439$	8687.00	−	15046.3i	0.944437	−	1.63581i	0.187563	−	0.982253i	$-0.439941\pi$
$439$	8687.00	−	15046.3i	0.944437	−	1.63581i	0.756874	−	0.653560i	$-0.226725\pi$
$440$	4095.00	−	7092.75i	0.443685	−	0.768485i
$441$	−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	$0.483111\pi$
$444$	−7794.50	+	13500.5i	−0.833132	+	1.44303i
$445$	−4165.00	+	7213.99i	−0.443685	+	0.768485i
$446$	542.500	+	939.638i	0.0575967	+	0.0997604i
$447$	−17262.0			−1.82654
$448$	−1865.50	−	3231.14i	−0.196733	−	0.340752i
$449$	7237.00	+	12534.9i	0.760657	+	1.31750i	0.942512	+	0.334172i	$0.108457\pi$
$449$	7237.00	+	12534.9i	0.760657	+	1.31750i	−0.181855	+	0.983325i	$0.558210\pi$
$450$	8360.00			0.875765
$451$	4368.00	+	7565.60i	0.456056	+	0.789912i
$452$	14739.0	−	25528.7i	1.53377	−	2.65657i
$453$	−11630.5	+	20144.6i	−1.20629	+	2.08935i
$454$	12880.0			1.33147
$455$		0			0
$456$	−39690.0			−4.07600
$457$	797.000	−	1380.44i	0.0815801	−	0.141301i	−0.822349	−	0.568984i	$-0.807337\pi$
$457$	797.000	−	1380.44i	0.0815801	−	0.141301i	0.903929	+	0.427683i	$0.140670\pi$
$458$	1137.50	−	1970.21i	0.116052	−	0.201008i
$459$	−1347.50	−	2333.94i	−0.137028	−	0.237340i
$460$	11424.0			1.15793
$461$	2957.50	+	5122.54i	0.298795	+	0.517528i	0.975861	−	0.218395i	$-0.0700820\pi$
$461$	2957.50	+	5122.54i	0.298795	+	0.517528i	−0.677066	+	0.735923i	$0.736749\pi$
$462$	−5915.00	−	10245.1i	−0.595651	−	1.03170i
$463$	−11072.0			−1.11136			−0.555680	−	0.831396i	$-0.687542\pi$
$463$	−11072.0			−1.11136			−0.555680	+	0.831396i	$0.687542\pi$
$464$	3649.00	+	6320.25i	0.365087	+	0.632350i
$465$	−4802.00	+	8317.31i	−0.478898	+	0.829475i
$466$	7652.50	−	13254.5i	0.760719	−	1.31760i
$467$	1260.00			0.124852			0.0624260	−	0.998050i	$-0.480116\pi$
$467$	1260.00			0.124852			0.0624260	+	0.998050i	$0.480116\pi$
$468$		0			0
$469$	−6214.00			−0.611804
$470$	1837.50	−	3182.64i	0.180335	−	0.312350i
$471$	−9555.00	+	16549.7i	−0.934758	+	1.61905i
$472$	−6615.00	−	11457.5i	−0.645085	−	1.11732i
$473$	5226.00			0.508016
$474$	−22820.0	−	39525.4i	−2.21130	−	3.83009i
$475$	−4788.00	−	8293.06i	−0.462502	−	0.801077i
$476$	−17017.0			−1.63860
$477$	4752.00	+	8230.71i	0.456141	+	0.790059i
$478$	−8692.50	+	15055.9i	−0.831769	+	1.44067i
$479$	6016.50	−	10420.9i	0.573906	−	0.994034i	−0.422254	−	0.906478i	$-0.638761\pi$
$479$	6016.50	−	10420.9i	0.573906	−	0.994034i	0.996160	−	0.0875564i	$-0.0279058\pi$
$480$	−4165.00			−0.396053
$481$		0			0
$482$	8050.00			0.760721
$483$	4368.00	−	7565.60i	0.411493	−	0.712726i
$484$	5567.50	−	9643.19i	0.522868	−	0.905634i
$485$	245.000	+	424.352i	0.0229379	+	0.0397296i
$486$	−24640.0			−2.29978
$487$	1140.00	+	1974.54i	0.106075	+	0.183727i	0.914177	−	0.405316i	$-0.132838\pi$
$487$	1140.00	+	1974.54i	0.106075	+	0.183727i	−0.808102	+	0.589042i	$0.799505\pi$
$488$	−1260.00	−	2182.38i	−0.116880	−	0.202442i
$489$	3808.00			0.352155
$490$	3045.00	+	5274.09i	0.280733	+	0.486243i
$491$	−8383.50	+	14520.6i	−0.770554	+	1.33464i	0.166706	+	0.986007i	$0.446687\pi$
$491$	−8383.50	+	14520.6i	−0.770554	+	1.33464i	−0.937260	+	0.348632i	$0.886646\pi$
$492$	19992.0	−	34627.2i	1.83193	−	3.17299i
$493$	−6314.00			−0.576812
$494$		0			0
$495$	4004.00			0.363569
$496$	−8722.00	+	15106.9i	−0.789575	+	1.36758i
$497$	58.5000	−	101.325i	0.00527985	−	0.00914496i
$498$	5390.00	+	9335.75i	0.485003	+	0.840050i
$499$	12840.0			1.15190			0.575949	−	0.817485i	$-0.304633\pi$
$499$	12840.0			1.15190			0.575949	+	0.817485i	$0.304633\pi$
$500$	−11959.5	−	20714.5i	−1.06969	−	1.85276i
$501$	5684.00	+	9844.98i	0.506871	+	0.877926i
$502$	−5040.00			−0.448100
$503$	1099.00	+	1903.52i	0.0974195	+	0.168735i	0.910616	−	0.413254i	$-0.135608\pi$
$503$	1099.00	+	1903.52i	0.0974195	+	0.168735i	−0.813196	+	0.581989i	$0.802274\pi$
$504$	−6435.00	+	11145.7i	−0.568726	+	0.985062i
$505$	1470.00	−	2546.11i	0.129533	−	0.224358i
$506$	−12480.0			−1.09645
$507$		0			0
$508$	32164.0			2.80915
$509$	8533.00	−	14779.6i	0.743062	−	1.28702i	−0.208033	−	0.978122i	$-0.566706\pi$
$509$	8533.00	−	14779.6i	0.743062	−	1.28702i	0.951095	−	0.308899i	$-0.0999606\pi$
$510$	9432.50	−	16337.6i	0.818977	−	1.41851i
$511$	637.000	+	1103.32i	0.0551452	+	0.0955144i
$512$	24475.0			2.11260
$513$	2205.00	+	3819.17i	0.189772	+	0.328695i
$514$	15102.5	+	26158.3i	1.29600	+	2.24473i
$515$	−4116.00			−0.352180
$516$	−11959.5	−	20714.5i	−1.02032	−	1.76725i
$517$	−1365.00	+	2364.25i	−0.116117	+	0.201121i
$518$	4257.50	−	7374.21i	0.361127	−	0.625490i
$519$	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	$0.465363\pi$
$522$	−4510.00	+	7811.55i	−0.378156	+	0.654985i
$523$	−9310.00	+	16125.4i	−0.778390	+	1.34821i	0.154480	+	0.987996i	$0.450630\pi$
$523$	−9310.00	+	16125.4i	−0.778390	+	1.34821i	−0.932869	+	0.360215i	$0.882703\pi$
$524$	−12197.5	−	21126.7i	−1.01689	−	1.76130i
$525$	−6916.00			−0.574931
$526$	−9270.00	−	16056.1i	−0.768424	−	1.33095i
$527$	−7546.00	−	13070.1i	−0.623736	−	1.08034i
$528$	16198.0			1.33509
$529$	1475.50	+	2555.64i	0.121271	+	0.210047i
$530$	7560.00	−	13094.3i	0.619595	−	1.07317i
$531$	3234.00	−	5601.45i	0.264301	−	0.457782i
$532$	27846.0			2.26932
$533$		0			0
$534$	−41650.0			−3.37523
$535$	−2394.00	+	4146.53i	−0.193461	+	0.335084i
$536$	10755.0	−	18628.2i	0.866689	−	1.50115i
$537$	−10601.5	−	18362.3i	−0.851934	−	1.47559i
$538$	−41720.0			−3.34327
$539$	−2262.00	−	3917.90i	−0.180763	−	0.313091i
$540$	2082.50	+	3607.00i	0.165957	+	0.287445i
$541$	−16833.0			−1.33772			−0.668861	−	0.743388i	$-0.733218\pi$
$541$	−16833.0			−1.33772			−0.668861	+	0.743388i	$0.733218\pi$
$542$	−4042.50	−	7001.82i	−0.320369	−	0.554896i
$543$	−98.0000	+	169.741i	−0.00774509	+	0.0134149i
$544$	3272.50	−	5668.14i	0.257918	−	0.446727i
$545$	−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	$0.609311\pi$
$548$	15096.0	−	26147.0i	1.17677	−	2.03822i
$549$	616.000	−	1066.94i	0.0478875	−	0.0829436i
$550$	4940.00	+	8556.33i	0.382986	+	0.663351i
$551$	10332.0			0.798835
$552$	15120.0	+	26188.6i	1.16585	+	2.01931i
$553$	8476.00	+	14680.9i	0.651783	+	1.12892i
$554$	19100.0			1.46477
$555$	3209.50	+	5559.02i	0.245470	+	0.425166i
$556$	15886.5	−	27516.2i	1.21176	−	2.09883i
$557$	−4267.50	+	7391.53i	−0.324632	+	0.562278i	−0.981438	−	0.191781i	$-0.938574\pi$
$557$	−4267.50	+	7391.53i	−0.324632	+	0.562278i	0.656806	+	0.754059i	$0.271907\pi$
$558$	−21560.0			−1.63568
$559$		0			0
$560$	8099.00			0.611152
$561$	−7007.00	+	12136.5i	−0.527336	+	0.913374i
$562$	−15535.0	+	26907.4i	−1.16602	+	2.01961i
$563$	2320.50	+	4019.22i	0.173708	+	0.300871i	0.939713	−	0.341963i	$-0.111092\pi$
$563$	2320.50	+	4019.22i	0.173708	+	0.300871i	−0.766006	+	0.642834i	$0.777759\pi$
$564$	12495.0			0.932862
$565$	−6069.00	−	10511.8i	−0.451902	−	0.782718i
$566$	−13230.0	−	22915.0i	−0.982506	−	1.70175i
$567$	10907.0			0.807850
$568$	202.500	+	350.740i	0.0149590	+	0.0259097i
$569$	2396.50	−	4150.86i	0.176567	−	0.305823i	−0.764136	−	0.645056i	$-0.776834\pi$
$569$	2396.50	−	4150.86i	0.176567	−	0.305823i	0.940702	+	0.339233i	$0.110168\pi$
$570$	−15435.0	+	26734.2i	−1.13421	+	1.96451i
$571$	−5563.00			−0.407713			−0.203857	−	0.979001i	$-0.565348\pi$
$571$	−5563.00			−0.407713			−0.203857	+	0.979001i	$0.565348\pi$
$572$		0			0
$573$	−2954.00			−0.215367
$574$	−10920.0	+	18914.0i	−0.794063	+	1.37536i
$575$	−3648.00	+	6318.52i	−0.264578	+	0.458262i
$576$	3157.00	+	5468.08i	0.228371	+	0.395550i
$577$	24038.0			1.73434			0.867171	−	0.498011i	$-0.165936\pi$
$577$	24038.0			1.73434			0.867171	+	0.498011i	$0.165936\pi$
$578$	2540.00	+	4399.41i	0.182786	+	0.316594i
$579$	1722.00	+	2982.59i	0.123599	+	0.214080i
$580$	9758.00			0.698584
$581$	−2002.00	−	3467.57i	−0.142955	−	0.247606i
$582$	−1225.00	+	2121.76i	−0.0872472	+	0.151117i
$583$	−5616.00	+	9727.20i	−0.398955	+	0.691011i
$584$	−4410.00			−0.312478
$585$		0			0
$586$	4515.00			0.318281
$587$	10612.0	−	18380.5i	0.746174	−	1.29241i	−0.203470	−	0.979081i	$-0.565222\pi$
$587$	10612.0	−	18380.5i	0.746174	−	1.29241i	0.949644	−	0.313330i	$-0.101445\pi$
$588$	−10353.0	+	17931.9i	−0.726106	+	1.25765i
$589$	12348.0	+	21387.4i	0.863821	+	1.49618i
$590$	−10290.0			−0.718021
$591$	10468.5	+	18132.0i	0.728624	+	1.26201i
$592$	5829.50	+	10097.0i	0.404714	+	0.700986i
$593$	4354.00			0.301513			0.150757	−	0.988571i	$-0.451829\pi$
$593$	4354.00			0.301513			0.150757	+	0.988571i	$0.451829\pi$
$594$	−2275.00	−	3940.42i	−0.157145	−	0.272184i
$595$	−3503.50	+	6068.24i	−0.241394	+	0.418107i
$596$	−20961.0	+	36305.5i	−1.44060	+	2.49519i
$597$	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	$0.419795\pi$
$600$	11970.0	−	20732.6i	0.814455	−	1.41068i
$601$	3797.50	−	6577.46i	0.257743	−	0.446423i	−0.707894	−	0.706318i	$-0.750355\pi$
$601$	3797.50	−	6577.46i	0.257743	−	0.446423i	0.965637	+	0.259895i	$0.0836880\pi$
$602$	6532.50	+	11314.6i	0.442267	+	0.766029i
$603$	10516.0			0.710190
$604$	28245.5	+	48922.6i	1.90280	+	3.29575i
$605$	−2292.50	−	3970.73i	−0.154055	−	0.266831i
$606$	14700.0			0.985391
$607$	413.000	+	715.337i	0.0276164	+	0.0478330i	0.879503	−	0.475893i	$-0.157875\pi$
$607$	413.000	+	715.337i	0.0276164	+	0.0478330i	−0.851887	+	0.523726i	$0.824542\pi$
$608$	−5355.00	+	9275.13i	−0.357194	+	0.618678i
$609$	3731.00	−	6462.28i	0.248256	−	0.429992i
$610$	−1960.00			−0.130095
$611$		0			0
$612$	28798.0			1.90211
$613$	−7295.00	+	12635.3i	−0.480656	+	0.832521i	−0.999754	−	0.0221940i	$-0.992935\pi$
$613$	−7295.00	+	12635.3i	−0.480656	+	0.832521i	0.519097	+	0.854715i	$0.326268\pi$
$614$	5285.00	−	9153.89i	0.347370	−	0.601663i
$615$	−8232.00	−	14258.2i	−0.539750	−	0.934875i
$616$	−15210.0			−0.994851
$617$	−2444.00	−	4233.13i	−0.159468	−	0.276207i	0.775209	−	0.631705i	$-0.217645\pi$
$617$	−2444.00	−	4233.13i	−0.159468	−	0.276207i	−0.934677	+	0.355498i	$0.884311\pi$
$618$	−10290.0	−	17822.8i	−0.669781	−	1.16009i
$619$	−11004.0			−0.714520			−0.357260	−	0.934005i	$-0.616289\pi$
$619$	−11004.0			−0.714520			−0.357260	+	0.934005i	$0.616289\pi$
$620$	11662.0	+	20199.2i	0.755415	+	1.30842i
$621$	1680.00	−	2909.85i	0.108561	−	0.188032i
$622$	8505.00	−	14731.1i	0.548263	−	0.949619i
$623$	15470.0			0.994851
$624$		0			0
$625$	−349.000			−0.0223360
$626$	−26722.5	+	46284.7i	−1.70614	+	2.95513i
$627$	11466.0	−	19859.7i	0.730316	−	1.26494i
$628$	23205.0	+	40192.2i	1.47449	+	2.55389i
$629$	−10087.0			−0.639420
$630$	5005.00	+	8668.91i	0.316514	+	0.548219i
$631$	2487.50	+	4308.48i	0.156935	+	0.271819i	0.933762	−	0.357895i	$-0.116505\pi$
$631$	2487.50	+	4308.48i	0.156935	+	0.271819i	−0.776827	+	0.629714i	$0.783172\pi$
$632$	−58680.0			−3.69330
$633$	9978.50	+	17283.3i	0.626556	+	1.08523i
$634$	−17635.0	+	30544.7i	−1.10469	+	1.91338i
$635$	6622.00	−	11469.6i	0.413836	−	0.716786i
$636$	51408.0			3.20513
$637$		0			0
$638$	−10660.0			−0.661494
$639$	−99.0000	+	171.473i	−0.00612892	+	0.0106156i
$640$	7402.50	−	12821.5i	0.457202	−	0.791898i
$641$	−1975.00	−	3420.80i	−0.121697	−	0.210785i	0.798740	−	0.601676i	$-0.205500\pi$
$641$	−1975.00	−	3420.80i	−0.121697	−	0.210785i	−0.920437	+	0.390891i	$0.872167\pi$
$642$	−23940.0			−1.47171
$643$	1841.00	+	3188.71i	0.112911	+	0.195568i	0.916943	−	0.399019i	$-0.130649\pi$
$643$	1841.00	+	3188.71i	0.112911	+	0.195568i	−0.804032	+	0.594587i	$0.797316\pi$
$644$	−10608.0	−	18373.6i	−0.649090	−	1.12426i
$645$	−9849.00			−0.601247
$646$	−24255.0	−	42010.9i	−1.47724	−	2.55866i
$647$	−5201.00	+	9008.40i	−0.316032	+	0.547383i	−0.979656	−	0.200683i	$-0.935684\pi$
$647$	−5201.00	+	9008.40i	−0.316032	+	0.547383i	0.663625	+	0.748066i	$0.269017\pi$
$648$	−18877.5	+	32696.8i	−1.14441	+	1.98218i
$649$	7644.00			0.462332
$650$		0			0
$651$	17836.0			1.07381
$652$	4624.00	−	8009.00i	0.277745	−	0.481069i
$653$	15840.0	−	27435.7i	0.949260	−	1.64417i	0.202273	−	0.979329i	$-0.435167\pi$
$653$	15840.0	−	27435.7i	0.949260	−	1.64417i	0.746987	−	0.664838i	$-0.231500\pi$
$654$	−6527.50	−	11306.0i	−0.390284	−	0.675991i
$655$	−10045.0			−0.599222
$656$	−14952.0	−	25897.6i	−0.889905	−	1.54136i
$657$	−1078.00	−	1867.15i	−0.0640134	−	0.110874i
$658$	−6825.00			−0.404356
$659$	−10970.0	−	19000.6i	−0.648453	−	1.12315i	−0.983492	−	0.180949i	$-0.942083\pi$
$659$	−10970.0	−	19000.6i	−0.648453	−	1.12315i	0.335039	−	0.942204i	$-0.391250\pi$
$660$	10829.0	−	18756.4i	0.638664	−	1.10620i
$661$	15687.0	−	27170.7i	0.923077	−	1.59882i	0.128451	−	0.991716i	$-0.459000\pi$
$661$	15687.0	−	27170.7i	0.923077	−	1.59882i	0.794626	−	0.607100i	$-0.207667\pi$
$662$	−48520.0			−2.84862
$663$		0			0
$664$	13860.0			0.810049
$665$	5733.00	−	9929.85i	0.334310	−	0.579042i
$666$	−7205.00	+	12479.4i	−0.419201	+	0.726078i
$667$	−3936.00	−	6817.35i	−0.228490	−	0.395756i
$668$	27608.0			1.59908
$669$	759.500	+	1315.49i	0.0438923	+	0.0760237i
$670$	−8365.00	−	14488.6i	−0.482341	−	0.835438i
$671$	1456.00			0.0837679
$672$	3867.50	+	6698.71i	0.222012	+	0.384536i
$673$	−9006.50	+	15599.7i	−0.515862	+	0.893499i	0.483969	+	0.875085i	$0.339195\pi$
$673$	−9006.50	+	15599.7i	−0.515862	+	0.893499i	−0.999830	+	0.0184136i	$0.994138\pi$
$674$	−26122.5	+	45245.5i	−1.49288	+	2.58574i
$675$	−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	$0.597659\pi$
$678$	30345.0	−	52559.1i	1.71887	−	2.97717i
$679$	455.000	−	788.083i	0.0257162	−	0.0445418i
$680$	−12127.5	−	21005.4i	−0.683924	−	1.18459i
$681$	18032.0			1.01467
$682$	−12740.0	−	22066.3i	−0.715308	−	1.23895i
$683$	4668.00	+	8085.21i	0.261517	+	0.452961i	0.966645	−	0.256119i	$-0.0824439\pi$
$683$	4668.00	+	8085.21i	0.261517	+	0.452961i	−0.705128	+	0.709080i	$0.749111\pi$
$684$	−47124.0			−2.63426
$685$	−6216.00	−	10766.4i	−0.346717	−	0.600531i
$686$	16802.5	−	29102.8i	0.935164	−	1.61975i
$687$	1592.50	−	2758.29i	0.0884391	−	0.153181i
$688$	−17889.0			−0.991296
$689$		0			0
$690$	23520.0			1.29767
$691$	−2100.00	+	3637.31i	−0.115612	+	0.200246i	−0.918024	−	0.396524i	$-0.870216\pi$
$691$	−2100.00	+	3637.31i	−0.115612	+	0.200246i	0.802412	+	0.596770i	$0.203550\pi$
$692$	2856.00	−	4946.74i	0.156891	−	0.271744i
$693$	−3718.00	−	6439.76i	−0.203803	−	0.352996i
$694$	3105.00			0.169833
$695$	−6541.50	−	11330.2i	−0.357026	−	0.618388i
$696$	12915.0	+	22369.4i	0.703365	+	1.21826i
$697$	25872.0			1.40599
$698$	31202.5	+	54044.3i	1.69202	+	2.93067i
$699$	10713.5	−	18556.3i	0.579716	−	1.00410i
$700$	−8398.00	+	14545.8i	−0.453449	+	0.785397i
$701$	9872.00			0.531898			0.265949	−	0.963987i	$-0.414315\pi$
$701$	9872.00			0.531898			0.265949	+	0.963987i	$0.414315\pi$
$702$		0			0
$703$	16506.0			0.885541
$704$	−3731.00	+	6462.28i	−0.199741	+	0.345961i
$705$	2572.50	−	4455.70i	0.137427	−	0.238030i
$706$	−3500.00	−	6062.18i	−0.186578	−	0.323163i
$707$	−5460.00			−0.290445
$708$	−17493.0	−	30298.8i	−0.928569	−	1.60833i
$709$	−14225.0	−	24638.4i	−0.753499	−	1.30510i	−0.946117	−	0.323825i	$-0.895031\pi$
$709$	−14225.0	−	24638.4i	−0.753499	−	1.30510i	0.192617	−	0.981274i	$-0.438302\pi$
$710$	315.000			0.0166503
$711$	−14344.0	−	24844.5i	−0.756599	−	1.31047i
$712$	−26775.0	+	46375.7i	−1.40932	+	2.44101i
$713$	9408.00	−	16295.1i	0.494155	−	0.855901i
$714$	−35035.0			−1.83635
$715$		0			0
$716$	−51493.0			−2.68769
$717$	−12169.5	+	21078.2i	−0.633861	+	1.09788i
$718$	−12420.0	+	21512.1i	−0.645557	+	1.11814i
$719$	−16359.0	−	28334.6i	−0.848523	−	1.46968i	−0.882527	−	0.470263i	$-0.844159\pi$
$719$	−16359.0	−	28334.6i	−0.848523	−	1.46968i	0.0340039	−	0.999422i	$-0.489174\pi$
$720$	−13706.0			−0.709434
$721$	3822.00	+	6619.90i	0.197418	+	0.341939i
$722$	22542.5	+	39044.8i	1.16197	+	2.01260i
$723$	11270.0			0.579718
$724$	238.000	+	412.228i	0.0122171	+	0.0211607i
$725$	−3116.00	+	5397.07i	−0.159621	+	0.276472i
$726$	11462.5	−	19853.6i	0.585969	−	1.01493i
$727$	−22834.0			−1.16488			−0.582439	−	0.812874i	$-0.697901\pi$
$727$	−22834.0			−1.16488			−0.582439	+	0.812874i	$0.697901\pi$
$728$		0			0
$729$	−11843.0			−0.601687
$730$	−1715.00	+	2970.47i	−0.0869521	+	0.150605i
$731$	7738.50	−	13403.5i	0.391544	−	0.678174i
$732$	−3332.00	−	5771.19i	−0.168244	−	0.291406i
$733$	7875.00			0.396821			0.198410	−	0.980119i	$-0.436422\pi$
$733$	7875.00			0.396821			0.198410	+	0.980119i	$0.436422\pi$
$734$	21805.0	+	37767.4i	1.09651	+	1.89921i
$735$	4263.00	+	7383.73i	0.213936	+	0.370548i
$736$	8160.00			0.408671
$737$	6214.00	+	10763.0i	0.310578	+	0.537936i
$738$	18480.0	−	32008.3i	0.921759	−	1.59653i
$739$	1070.00	−	1853.29i	0.0532620	−	0.0922524i	−0.838165	−	0.545416i	$-0.816371\pi$
$739$	1070.00	−	1853.29i	0.0532620	−	0.0922524i	0.891427	+	0.453164i	$0.149705\pi$
$740$	15589.0			0.774410
$741$		0			0
$742$	−28080.0			−1.38928
$743$	−15985.5	+	27687.7i	−0.789302	+	1.36711i	0.137094	+	0.990558i	$0.456224\pi$
$743$	−15985.5	+	27687.7i	−0.789302	+	1.36711i	−0.926395	+	0.376552i	$0.877109\pi$
$744$	−30870.0	+	53468.4i	−1.52117	+	2.63474i
$745$	8631.00	+	14949.3i	0.424450	+	0.735169i
$746$	−50060.0			−2.45687
$747$	3388.00	+	5868.19i	0.165944	+	0.287424i
$748$	17017.0	+	29474.3i	0.831822	+	1.44076i
$749$	8892.00			0.433787
$750$	−24622.5	−	42647.4i	−1.19878	−	2.07635i
$751$	3716.00	−	6436.30i	0.180558	−	0.312735i	−0.761513	−	0.648150i	$-0.775543\pi$
$751$	3716.00	−	6436.30i	0.180558	−	0.312735i	0.942071	+	0.335415i	$0.108876\pi$
$752$	4672.50	−	8093.01i	0.226581	−	0.392449i
$753$	−7056.00			−0.341481
$754$		0			0
$755$	23261.0			1.12126
$756$	3867.50	−	6698.71i	0.186058	−	0.322261i
$757$	−10088.0	+	17472.9i	−0.484352	+	0.838923i	−0.999838	−	0.0179753i	$-0.994278\pi$
$757$	−10088.0	+	17472.9i	−0.484352	+	0.838923i	0.515486	+	0.856898i	$0.327611\pi$
$758$	−8430.00	−	14601.2i	−0.403946	−	0.699656i
$759$	−17472.0			−0.835564
$760$	19845.0	+	34372.5i	0.947176	+	1.64056i
$761$	4739.00	+	8208.19i	0.225741	+	0.390994i	0.956541	−	0.291597i	$-0.0941865\pi$
$761$	4739.00	+	8208.19i	0.225741	+	0.390994i	−0.730801	+	0.682591i	$0.760853\pi$
$762$	66220.0			3.14816
$763$	2424.50	+	4199.36i	0.115036	+	0.199249i
$764$	−3587.00	+	6212.87i	−0.169860	+	0.294206i
$765$	5929.00	−	10269.3i	0.280214	−	0.485344i
$766$	4235.00			0.199761
$767$		0			0
$768$	57953.0			2.72292
$769$	6048.00	−	10475.4i	0.283610	−	0.491228i	−0.688661	−	0.725084i	$-0.741801\pi$
$769$	6048.00	−	10475.4i	0.283610	−	0.491228i	0.972271	+	0.233856i	$0.0751344\pi$
$770$	−5915.00	+	10245.1i	−0.276834	+	0.479490i
$771$	21143.5	+	36621.6i	0.987632	+	1.71063i
$772$	8364.00			0.389931
$773$	−8970.50	−	15537.4i	−0.417395	−	0.722950i	0.578281	−	0.815837i	$-0.303724\pi$
$773$	−8970.50	−	15537.4i	−0.417395	−	0.722950i	−0.995677	+	0.0928877i	$0.970390\pi$
$774$	−11055.0	−	19147.8i	−0.513390	−	0.889217i
$775$	−14896.0			−0.690426
$776$	1575.00	+	2727.98i	0.0728598	+	0.126197i
$777$	5960.50	−	10323.9i	0.275202	−	0.476663i
$778$	28285.0	−	48991.1i	1.30343	−	2.25760i
$779$	−42336.0			−1.94717
$780$		0			0
$781$	−234.000			−0.0107211
$782$	−18480.0	+	32008.3i	−0.845068	+	1.46370i
$783$	1435.00	−	2485.49i	0.0654952	−	0.113441i
$784$	7743.00	+	13411.3i	0.352724	+	0.610936i
$785$	19110.0			0.868873
$786$	−25112.5	−	43496.1i	−1.13961	−	1.97386i
$787$	−3332.00	−	5771.19i	−0.150919	−	0.261399i	0.780647	−	0.624972i	$-0.214890\pi$
$787$	−3332.00	−	5771.19i	−0.150919	−	0.261399i	−0.931565	+	0.363574i	$0.881556\pi$
$788$	50847.0			2.29867
$789$	−12978.0	−	22478.6i	−0.585588	−	1.01427i
$790$	−22820.0	+	39525.4i	−1.02772	+	1.78006i
$791$	−11271.0	+	19521.9i	−0.506638	+	0.877523i
$792$	25740.0			1.15484
$793$		0			0
$794$	−9310.00			−0.416120
$795$	10584.0	−	18332.0i	0.472171	−	0.817824i
$796$	595.000	−	1030.57i	0.0264940	−	0.0458889i
$797$	721.000	+	1248.81i	0.0320441	+	0.0555020i	0.881603	−	0.471992i	$-0.156465\pi$
$797$	721.000	+	1248.81i	0.0320441	+	0.0555020i	−0.849559	+	0.527494i	$0.823132\pi$
$798$	57330.0			2.54318
$799$	4042.50	+	7001.82i	0.178990	+	0.310021i
$800$	−3230.00	−	5594.52i	−0.142747	−	0.247245i
$801$	−26180.0			−1.15484
$802$	17050.0	+	29531.5i	0.750694	+	1.30024i
$803$	1274.00	−	2206.63i	0.0559881	−	0.0969743i
$804$	28441.0	−	49261.3i	1.24756	−	2.16083i
$805$	−8736.00			−0.382489
$806$		0			0
$807$	−58408.0			−2.54778
$808$	9450.00	−	16367.9i	0.411448	−	0.712649i
$809$	−15103.5	+	26160.0i	−0.656379	+	1.13688i	0.325167	+	0.945657i	$0.394580\pi$
$809$	−15103.5	+	26160.0i	−0.656379	+	1.13688i	−0.981546	+	0.191226i	$0.938754\pi$
$810$	14682.5	+	25430.8i	0.636902	+	1.10315i
$811$	21140.0			0.915322			0.457661	−	0.889127i	$-0.348687\pi$
$811$	21140.0			0.915322			0.457661	+	0.889127i	$0.348687\pi$
$812$	−9061.00	−	15694.1i	−0.391599	−	0.678270i
$813$	−5659.50	−	9802.54i	−0.244142	−	0.422866i
$814$	−17030.0			−0.733294
$815$	−1904.00	−	3297.82i	−0.0818334	−	0.141740i
$816$	23985.5	−	41544.1i	1.02900	−	1.78227i
$817$	−12663.0	+	21933.0i	−0.542255	+	0.939213i
$818$	64960.0			2.77662
$819$		0			0
$820$	−39984.0			−1.70281
$821$	−284.500	+	492.768i	−0.0120939	+	0.0209473i	−0.872009	−	0.489490i	$-0.837183\pi$
$821$	−284.500	+	492.768i	−0.0120939	+	0.0209473i	0.859915	+	0.510437i	$0.170516\pi$
$822$	31080.0	−	53832.1i	1.31878	−	2.28420i
$823$	4269.00	+	7394.12i	0.180812	+	0.313175i	0.942157	−	0.335171i	$-0.108794\pi$
$823$	4269.00	+	7394.12i	0.180812	+	0.313175i	−0.761346	+	0.648346i	$0.775461\pi$
$824$	−26460.0			−1.11866
$825$	6916.00	+	11978.9i	0.291860	+	0.505516i
$826$	9555.00	+	16549.7i	0.402495	+	0.697142i
$827$	−32702.0			−1.37504			−0.687521	−	0.726164i	$-0.741301\pi$
$827$	−32702.0			−1.37504			−0.687521	+	0.726164i	$0.741301\pi$
$828$	17952.0	+	31093.8i	0.753472	+	1.30505i
$829$	10577.0	−	18319.9i	0.443130	−	0.767523i	−0.554790	−	0.831990i	$-0.687202\pi$
$829$	10577.0	−	18319.9i	0.443130	−	0.767523i	0.997920	+	0.0644673i	$0.0205348\pi$
$830$	5390.00	−	9335.75i	0.225409	−	0.390420i
$831$	26740.0			1.11625
$832$		0			0
$833$	−13398.0			−0.557279
$834$	32707.5	−	56651.1i	1.35800	−	2.35212i
$835$	5684.00	−	9844.98i	0.235572	−	0.408023i
$836$	−27846.0	−	48230.7i	−1.15200	−	1.99533i
$837$	6860.00			0.283293
$838$	−18357.5	−	31796.1i	−0.756741	−	1.31071i
$839$	1092.00	+	1891.40i	0.0449345	+	0.0778288i	0.887618	−	0.460581i	$-0.152359\pi$
$839$	1092.00	+	1891.40i	0.0449345	+	0.0778288i	−0.842683	+	0.538409i	$0.819025\pi$
$840$	28665.0			1.17742
$841$	8832.50	+	15298.3i	0.362151	+	0.627264i
$842$	−12647.5	+	21906.1i	−0.517650	+	0.896597i
$843$	−21749.0	+	37670.4i	−0.888583	+	1.53907i
$844$	48467.0			1.97666
$845$		0			0
$846$	11550.0			0.469382
$847$	−4257.50	+	7374.21i	−0.172715	+	0.299151i
$848$	19224.0	−	33296.9i	0.778485	−	1.34837i
$849$	−18522.0	−	32081.0i	−0.748732	−	1.29684i
$850$	29260.0			1.18072
$851$	−6288.00	−	10891.1i	−0.253290	−	0.438711i
$852$	535.500	+	927.513i	0.0215328	+	0.0372959i
$853$	36687.0			1.47261			0.736307	−	0.676648i	$-0.236568\pi$
$853$	36687.0			1.47261			0.736307	+	0.676648i	$0.236568\pi$
$854$	1820.00	+	3152.33i	0.0729264	+	0.126312i
$855$	−9702.00	+	16804.4i	−0.388072	+	0.672160i
$856$	−15390.0	+	26656.3i	−0.614509	+	1.06436i
$857$	36806.0			1.46706			0.733529	−	0.679658i	$-0.237872\pi$
$857$	36806.0			1.46706			0.733529	+	0.679658i	$0.237872\pi$
$858$		0			0
$859$	4900.00			0.194628			0.0973142	−	0.995254i	$-0.468975\pi$
$859$	4900.00			0.194628			0.0973142	+	0.995254i	$0.468975\pi$
$860$	−11959.5	+	20714.5i	−0.474204	+	0.821346i
$861$	−15288.0	+	26479.6i	−0.605126	+	1.04811i
$862$	8107.50	+	14042.6i	0.320351	+	0.554864i
$863$	−13697.0			−0.540268			−0.270134	−	0.962823i	$-0.587068\pi$
$863$	−13697.0			−0.540268			−0.270134	+	0.962823i	$0.587068\pi$
$864$	1487.50	+	2576.43i	0.0585715	+	0.101449i
$865$	−1176.00	−	2036.89i	−0.0462257	−	0.0800652i
$866$	−57995.0			−2.27569
$867$	3556.00	+	6159.17i	0.139294	+	0.241265i
$868$	21658.0	−	37512.8i	0.846913	−	1.46690i
$869$	16952.0	−	29361.7i	0.661746	−	1.14618i
$870$	20090.0			0.782891
$871$		0			0
$872$	−16785.0			−0.651848
$873$	−770.000	+	1333.68i	−0.0298517	+	0.0517047i
$874$	30240.0	−	52377.2i	1.17035	−	2.02710i
$875$	9145.50	+	15840.5i	0.353342	+	0.612006i
$876$	−11662.0			−0.449797
$877$	−3119.50	−	5403.13i	−0.120112	−	0.208040i	0.799700	−	0.600400i	$-0.204992\pi$
$877$	−3119.50	−	5403.13i	−0.120112	−	0.208040i	−0.919812	+	0.392360i	$0.871659\pi$
$878$	−43435.0	−	75231.6i	−1.66954	−	2.89174i
$879$	6321.00			0.242551
$880$	−8099.00	−	14027.9i	−0.310247	−	0.537363i
$881$	−66.5000	+	115.181i	−0.00254307	+	0.00440472i	−0.867294	−	0.497796i	$-0.834143\pi$
$881$	−66.5000	+	115.181i	−0.00254307	+	0.00440472i	0.864751	+	0.502201i	$0.167476\pi$
$882$	−9570.00	+	16575.7i	−0.365350	+	0.632805i
$883$	−26003.0			−0.991020			−0.495510	−	0.868602i	$-0.665019\pi$
$883$	−26003.0			−0.991020			−0.495510	+	0.868602i	$0.665019\pi$
$884$		0			0
$885$	−14406.0			−0.547178
$886$	2472.50	−	4282.50i	0.0937531	−	0.162385i
$887$	15624.0	−	27061.6i	0.591435	−	1.02439i	−0.402605	−	0.915374i	$-0.631895\pi$
$887$	15624.0	−	27061.6i	0.591435	−	1.02439i	0.994039	−	0.109021i	$-0.0347716\pi$
$888$	20632.5	+	35736.5i	0.779709	+	1.35050i
$889$	−24596.0			−0.927923
$890$	20825.0	+	36070.0i	0.784332	+	1.35850i
$891$	−10907.0	−	18891.5i	−0.410099	−	0.710312i
$892$	3689.00			0.138472
$893$	−6615.00	−	11457.5i	−0.247886	−	0.429352i
$894$	−43155.0	+	74746.7i	−1.61445	+	2.79631i
$895$	−10601.5	+	18362.3i	−0.395943	+	0.685794i
$896$	−27495.0			−1.02516
$897$		0			0
$898$	72370.0			2.68933
$899$	8036.00	−	13918.8i	0.298126	−	0.516370i
$900$	14212.0	−	24615.9i	0.526370	−	0.911700i
$901$	16632.0	+	28807.5i	0.614975	+	1.06517i
$902$	43680.0			1.61240
$903$	9145.50	+	15840.5i	0.337036	+	0.583763i
$904$	−39015.0	−	67576.0i	−1.43542	−	2.48622i
$905$	196.000			0.00719918
$906$	58152.5	+	100723.i	2.13244	+	3.69349i
$907$	19126.5	−	33128.1i	0.700204	−	1.21279i	−0.268191	−	0.963366i	$-0.586426\pi$
$907$	19126.5	−	33128.1i	0.700204	−	1.21279i	0.968395	−	0.249423i	$-0.0802410\pi$
$908$	21896.0	−	37925.0i	0.800269	−	1.38611i
$909$	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	$0.269950\pi$
$912$	−39249.0	+	67981.3i	−1.42507	+	2.46829i
$913$	−4004.00	+	6935.13i	−0.145140	+	0.251390i
$914$	−3985.00	−	6902.22i	−0.144215	−	0.249787i
$915$	−2744.00			−0.0991408
$916$	−3867.50	−	6698.71i	−0.139504	−	0.241628i
$917$	9327.50	+	16155.7i	0.335901	+	0.581798i
$918$	−13475.0			−0.484468
$919$	13824.0	+	23943.9i	0.496204	+	0.859451i	0.999990	−	0.00437745i	$-0.00139339\pi$
$919$	13824.0	+	23943.9i	0.496204	+	0.859451i	−0.503786	+	0.863828i	$0.668060\pi$
$920$	15120.0	−	26188.6i	0.541839	−	0.938492i
$921$	7399.00	−	12815.4i	0.264718	−	0.458505i
$922$	29575.0			1.05640
$923$		0			0
$924$	−40222.0			−1.43204
$925$	−4978.00	+	8622.15i	−0.176947	+	0.306481i
$926$	−27680.0	+	47943.2i	−0.982312	+	1.70141i
$927$	−6468.00	−	11202.9i	−0.229166	−	0.396927i
$928$	6970.00			0.246553
$929$	−378.000	−	654.715i	−0.0133496	−	0.0231222i	0.859273	−	0.511517i	$-0.170916\pi$
$929$	−378.000	−	654.715i	−0.0133496	−	0.0231222i	−0.872623	+	0.488394i	$0.837583\pi$
$930$	24010.0	+	41586.5i	0.846579	+	1.46632i
$931$	21924.0			0.771783
$932$	−26018.5	−	45065.4i	−0.914447	−	1.58387i
$933$	11907.0	−	20623.5i	0.417811	−	0.723670i
$934$	3150.00	−	5455.96i	0.110355	−	0.191140i
$935$	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	$0.381616\pi$
$938$	−15535.0	+	26907.4i	−0.540763	+	0.936629i
$939$	−37411.5	+	64798.6i	−1.30019	+	2.25199i
$940$	−6247.50	−	10821.0i	−0.216778	−	0.375470i
$941$	−41321.0			−1.43148			−0.715742	−	0.698365i	$-0.753911\pi$
$941$	−41321.0			−1.43148			−0.715742	+	0.698365i	$0.753911\pi$
$942$	47775.0	+	82748.7i	1.65243	+	2.86210i
$943$	16128.0	+	27934.5i	0.556946	+	0.964659i
$944$	−26166.0			−0.902151
$945$	−1592.50	−	2758.29i	−0.0548191	−	0.0949494i
$946$	13065.0	−	22629.2i	0.449027	−	0.777738i
$947$	−27483.0	+	47602.0i	−0.943060	+	1.63343i	−0.183469	+	0.983025i	$0.558733\pi$
$947$	−27483.0	+	47602.0i	−0.943060	+	1.63343i	−0.759590	+	0.650402i	$0.774601\pi$
$948$	−155176.			−5.31633
$949$		0			0
$950$	−47880.0			−1.63519
$951$	−24689.0	+	42762.6i	−0.841846	+	1.45812i
$952$	−22522.5	+	39010.1i	−0.766763	+	1.32807i
$953$	22276.5	+	38584.0i	0.757195	+	1.31150i	0.944276	+	0.329155i	$0.106764\pi$
$953$	22276.5	+	38584.0i	0.757195	+	1.31150i	−0.187081	+	0.982344i	$0.559903\pi$
$954$	47520.0			1.61270
$955$	1477.00	+	2558.24i	0.0500467	+	0.0866834i
$956$	29554.5	+	51189.9i	0.999854	+	1.73180i
$957$	−14924.0			−0.504101
$958$	−30082.5	−	52104.4i	−1.01453	−	1.75722i
$959$	−11544.0	+	19994.8i	−0.388712	+	0.673270i
$960$	7031.50	−	12178.9i	0.236397	−	0.409451i
$961$	8625.00			0.289517
$962$		0			0
$963$	−15048.0			−0.503546
$964$	13685.0	−	23703.1i	0.457224	−	0.791936i
$965$	1722.00	−	2982.59i	0.0574437	−	0.0994954i
$966$	−21840.0	−	37828.0i	−0.727423	−	1.25993i
$967$	−27907.0			−0.928054			−0.464027	−	0.885821i	$-0.653596\pi$
$967$	−27907.0			−0.928054			−0.464027	+	0.885821i	$0.653596\pi$
$968$	−14737.5	−	25526.1i	−0.489340	−	0.847562i
$969$	−33957.0	−	58815.2i	−1.12575	−	1.94986i
$970$	2450.00			0.0810977
$971$	8221.50	+	14240.1i	0.271720	+	0.470634i	0.969302	−	0.245871i	$-0.0790741\pi$
$971$	8221.50	+	14240.1i	0.271720	+	0.470634i	−0.697582	+	0.716505i	$0.745741\pi$
$972$	−41888.0	+	72552.1i	−1.38226	+	2.39415i
$973$	−12148.5	+	21041.8i	−0.400270	+	0.693289i
$974$	11400.0			0.375030
$975$		0			0
$976$	−4984.00			−0.163457
$977$	22707.0	−	39329.7i	0.743563	−	1.28789i	−0.207300	−	0.978277i	$-0.566468\pi$
$977$	22707.0	−	39329.7i	0.743563	−	1.28789i	0.950863	−	0.309612i	$-0.100199\pi$
$978$	9520.00	−	16489.1i	0.311264	−	0.539125i
$979$	−15470.0	−	26794.8i	−0.505029	−	0.874736i
$980$	20706.0			0.674927
$981$	−4103.00	−	7106.60i	−0.133536	−	0.231291i
$982$	41917.5	+	72603.2i	1.36216	+	2.35933i
$983$	−8981.00			−0.291403			−0.145702	−	0.989329i	$-0.546544\pi$
$983$	−8981.00			−0.291403			−0.145702	+	0.989329i	$0.546544\pi$
$984$	−52920.0	−	91660.1i	−1.71446	−	2.96953i
$985$	10468.5	−	18132.0i	0.338634	−	0.586531i
$986$	−15785.0	+	27340.4i	−0.509834	+	0.883059i
$987$	−9555.00			−0.308145
$988$		0			0
$989$	19296.0			0.620402
$990$	10010.0	−	17337.8i	0.321352	−	0.556598i
$991$	8707.00	−	15081.0i	0.279099	−	0.483413i	−0.692062	−	0.721838i	$-0.743298\pi$
$991$	8707.00	−	15081.0i	0.279099	−	0.483413i	0.971161	+	0.238424i	$0.0766309\pi$
$992$	8330.00	+	14428.0i	0.266611	+	0.461783i
$993$	−67928.0			−2.17083
$994$	−292.500	−	506.625i	−0.00933354	−	0.0161662i
$995$	−245.000	−	424.352i	−0.00780605	−	0.0135205i
$996$	36652.0			1.16603
$997$	11851.0	+	20526.5i	0.376454	+	0.652038i	0.990544	−	0.137199i	$-0.0438099\pi$
$997$	11851.0	+	20526.5i	0.376454	+	0.652038i	−0.614089	+	0.789237i	$0.710477\pi$
$998$	32100.0	−	55598.8i	1.01814	−	1.76348i
$999$	2292.50	−	3970.73i	0.0726041	−	0.125754i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.c.e.22.1		2
13.2	odd	12		169.4.e.e.23.2		4
13.3	even	3	inner	169.4.c.e.146.1		2
13.4	even	6		169.4.a.e.1.1		1
13.5	odd	4		169.4.e.e.147.1		4
13.6	odd	12		169.4.b.a.168.2		2
13.7	odd	12		169.4.b.a.168.1		2
13.8	odd	4		169.4.e.e.147.2		4
13.9	even	3		13.4.a.a.1.1	✓	1
13.10	even	6		169.4.c.a.146.1		2
13.11	odd	12		169.4.e.e.23.1		4
13.12	even	2		169.4.c.a.22.1		2
39.17	odd	6		1521.4.a.a.1.1		1
39.35	odd	6		117.4.a.b.1.1		1
52.35	odd	6		208.4.a.g.1.1		1
65.9	even	6		325.4.a.d.1.1		1
65.22	odd	12		325.4.b.b.274.1		2
65.48	odd	12		325.4.b.b.274.2		2
91.48	odd	6		637.4.a.a.1.1		1
104.35	odd	6		832.4.a.a.1.1		1
104.61	even	6		832.4.a.r.1.1		1
143.87	odd	6		1573.4.a.a.1.1		1
156.35	even	6		1872.4.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.a.a.1.1	✓	1	13.9	even	3
117.4.a.b.1.1		1	39.35	odd	6
169.4.a.e.1.1		1	13.4	even	6
169.4.b.a.168.1		2	13.7	odd	12
169.4.b.a.168.2		2	13.6	odd	12
169.4.c.a.22.1		2	13.12	even	2
169.4.c.a.146.1		2	13.10	even	6
169.4.c.e.22.1		2	1.1	even	1	trivial
169.4.c.e.146.1		2	13.3	even	3	inner
169.4.e.e.23.1		4	13.11	odd	12
169.4.e.e.23.2		4	13.2	odd	12
169.4.e.e.147.1		4	13.5	odd	4
169.4.e.e.147.2		4	13.8	odd	4
208.4.a.g.1.1		1	52.35	odd	6
325.4.a.d.1.1		1	65.9	even	6
325.4.b.b.274.1		2	65.22	odd	12
325.4.b.b.274.2		2	65.48	odd	12
637.4.a.a.1.1		1	91.48	odd	6
832.4.a.a.1.1		1	104.35	odd	6
832.4.a.r.1.1		1	104.61	even	6
1521.4.a.a.1.1		1	39.17	odd	6
1573.4.a.a.1.1		1	143.87	odd	6
1872.4.a.k.1.1		1	156.35	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.50000 - 4.33013i) q^{2} +(3.50000 - 6.06218i) q^{3} +(-8.50000 - 14.7224i) q^{4} -7.00000 q^{5} +(-17.5000 - 30.3109i) q^{6} +(6.50000 + 11.2583i) q^{7} -45.0000 q^{8} +(-11.0000 - 19.0526i) q^{9} +O(q^{10})\)	\(q+(2.50000 - 4.33013i) q^{2} +(3.50000 - 6.06218i) q^{3} +(-8.50000 - 14.7224i) q^{4} -7.00000 q^{5} +(-17.5000 - 30.3109i) q^{6} +(6.50000 + 11.2583i) q^{7} -45.0000 q^{8} +(-11.0000 - 19.0526i) q^{9} +(-17.5000 + 30.3109i) q^{10} +(13.0000 - 22.5167i) q^{11} -119.000 q^{12} +65.0000 q^{14} +(-24.5000 + 42.4352i) q^{15} +(-44.5000 + 77.0763i) q^{16} +(-38.5000 - 66.6840i) q^{17} -110.000 q^{18} +(63.0000 + 109.119i) q^{19} +(59.5000 + 103.057i) q^{20} +91.0000 q^{21} +(-65.0000 - 112.583i) q^{22} +(48.0000 - 83.1384i) q^{23} +(-157.500 + 272.798i) q^{24} -76.0000 q^{25} +35.0000 q^{27} +(110.500 - 191.392i) q^{28} +(41.0000 - 71.0141i) q^{29} +(122.500 + 212.176i) q^{30} +196.000 q^{31} +(42.5000 + 73.6122i) q^{32} +(-91.0000 - 157.617i) q^{33} -385.000 q^{34} +(-45.5000 - 78.8083i) q^{35} +(-187.000 + 323.894i) q^{36} +(65.5000 - 113.449i) q^{37} +630.000 q^{38} +315.000 q^{40} +(-168.000 + 290.985i) q^{41} +(227.500 - 394.042i) q^{42} +(100.500 + 174.071i) q^{43} -442.000 q^{44} +(77.0000 + 133.368i) q^{45} +(-240.000 - 415.692i) q^{46} -105.000 q^{47} +(311.500 + 539.534i) q^{48} +(87.0000 - 150.688i) q^{49} +(-190.000 + 329.090i) q^{50} -539.000 q^{51} -432.000 q^{53} +(87.5000 - 151.554i) q^{54} +(-91.0000 + 157.617i) q^{55} +(-292.500 - 506.625i) q^{56} +882.000 q^{57} +(-205.000 - 355.070i) q^{58} +(147.000 + 254.611i) q^{59} +833.000 q^{60} +(28.0000 + 48.4974i) q^{61} +(490.000 - 848.705i) q^{62} +(143.000 - 247.683i) q^{63} -287.000 q^{64} -910.000 q^{66} +(-239.000 + 413.960i) q^{67} +(-654.500 + 1133.63i) q^{68} +(-336.000 - 581.969i) q^{69} -455.000 q^{70} +(-4.50000 - 7.79423i) q^{71} +(495.000 + 857.365i) q^{72} +98.0000 q^{73} +(-327.500 - 567.247i) q^{74} +(-266.000 + 460.726i) q^{75} +(1071.00 - 1855.03i) q^{76} +338.000 q^{77} +1304.00 q^{79} +(311.500 - 539.534i) q^{80} +(419.500 - 726.595i) q^{81} +(840.000 + 1454.92i) q^{82} -308.000 q^{83} +(-773.500 - 1339.74i) q^{84} +(269.500 + 466.788i) q^{85} +1005.00 q^{86} +(-287.000 - 497.099i) q^{87} +(-585.000 + 1013.25i) q^{88} +(595.000 - 1030.57i) q^{89} +770.000 q^{90} -1632.00 q^{92} +(686.000 - 1188.19i) q^{93} +(-262.500 + 454.663i) q^{94} +(-441.000 - 763.834i) q^{95} +595.000 q^{96} +(-35.0000 - 60.6218i) q^{97} +(-435.000 - 753.442i) q^{98} -572.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 5 q^{2} + 7 q^{3} - 17 q^{4} - 14 q^{5} - 35 q^{6} + 13 q^{7} - 90 q^{8} - 22 q^{9}+O(q^{10}) \) 2 * q + 5 * q^2 + 7 * q^3 - 17 * q^4 - 14 * q^5 - 35 * q^6 + 13 * q^7 - 90 * q^8 - 22 * q^9	\( 2 q + 5 q^{2} + 7 q^{3} - 17 q^{4} - 14 q^{5} - 35 q^{6} + 13 q^{7} - 90 q^{8} - 22 q^{9} - 35 q^{10} + 26 q^{11} - 238 q^{12} + 130 q^{14} - 49 q^{15} - 89 q^{16} - 77 q^{17} - 220 q^{18} + 126 q^{19} + 119 q^{20} + 182 q^{21} - 130 q^{22} + 96 q^{23} - 315 q^{24} - 152 q^{25} + 70 q^{27} + 221 q^{28} + 82 q^{29} + 245 q^{30} + 392 q^{31} + 85 q^{32} - 182 q^{33} - 770 q^{34} - 91 q^{35} - 374 q^{36} + 131 q^{37} + 1260 q^{38} + 630 q^{40} - 336 q^{41} + 455 q^{42} + 201 q^{43} - 884 q^{44} + 154 q^{45} - 480 q^{46} - 210 q^{47} + 623 q^{48} + 174 q^{49} - 380 q^{50} - 1078 q^{51} - 864 q^{53} + 175 q^{54} - 182 q^{55} - 585 q^{56} + 1764 q^{57} - 410 q^{58} + 294 q^{59} + 1666 q^{60} + 56 q^{61} + 980 q^{62} + 286 q^{63} - 574 q^{64} - 1820 q^{66} - 478 q^{67} - 1309 q^{68} - 672 q^{69} - 910 q^{70} - 9 q^{71} + 990 q^{72} + 196 q^{73} - 655 q^{74} - 532 q^{75} + 2142 q^{76} + 676 q^{77} + 2608 q^{79} + 623 q^{80} + 839 q^{81} + 1680 q^{82} - 616 q^{83} - 1547 q^{84} + 539 q^{85} + 2010 q^{86} - 574 q^{87} - 1170 q^{88} + 1190 q^{89} + 1540 q^{90} - 3264 q^{92} + 1372 q^{93} - 525 q^{94} - 882 q^{95} + 1190 q^{96} - 70 q^{97} - 870 q^{98} - 1144 q^{99}+O(q^{100}) \) 2 * q + 5 * q^2 + 7 * q^3 - 17 * q^4 - 14 * q^5 - 35 * q^6 + 13 * q^7 - 90 * q^8 - 22 * q^9 - 35 * q^10 + 26 * q^11 - 238 * q^12 + 130 * q^14 - 49 * q^15 - 89 * q^16 - 77 * q^17 - 220 * q^18 + 126 * q^19 + 119 * q^20 + 182 * q^21 - 130 * q^22 + 96 * q^23 - 315 * q^24 - 152 * q^25 + 70 * q^27 + 221 * q^28 + 82 * q^29 + 245 * q^30 + 392 * q^31 + 85 * q^32 - 182 * q^33 - 770 * q^34 - 91 * q^35 - 374 * q^36 + 131 * q^37 + 1260 * q^38 + 630 * q^40 - 336 * q^41 + 455 * q^42 + 201 * q^43 - 884 * q^44 + 154 * q^45 - 480 * q^46 - 210 * q^47 + 623 * q^48 + 174 * q^49 - 380 * q^50 - 1078 * q^51 - 864 * q^53 + 175 * q^54 - 182 * q^55 - 585 * q^56 + 1764 * q^57 - 410 * q^58 + 294 * q^59 + 1666 * q^60 + 56 * q^61 + 980 * q^62 + 286 * q^63 - 574 * q^64 - 1820 * q^66 - 478 * q^67 - 1309 * q^68 - 672 * q^69 - 910 * q^70 - 9 * q^71 + 990 * q^72 + 196 * q^73 - 655 * q^74 - 532 * q^75 + 2142 * q^76 + 676 * q^77 + 2608 * q^79 + 623 * q^80 + 839 * q^81 + 1680 * q^82 - 616 * q^83 - 1547 * q^84 + 539 * q^85 + 2010 * q^86 - 574 * q^87 - 1170 * q^88 + 1190 * q^89 + 1540 * q^90 - 3264 * q^92 + 1372 * q^93 - 525 * q^94 - 882 * q^95 + 1190 * q^96 - 70 * q^97 - 870 * q^98 - 1144 * q^99

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