LMFDB - Embedded newform 39.4.e.c.16.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,4,Mod(16,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("39.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	39.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.30107449022$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 29x^{6} + 2x^{5} + 595x^{4} - 288x^{3} + 2526x^{2} + 1872x + 6084 $ x^8 - 2x^7 + 29x^6 + 2x^5 + 595x^4 - 288x^3 + 2526x^2 + 1872*x + 6084
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.4
Root			$-2.11303 - 3.65987i$ of defining polynomial
Character	$\chi$	$=$	39.16
Dual form			39.4.e.c.22.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.11303 + 3.65987i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-4.92977 + 8.53861i) q^{4} -5.85953 q^{5} +(-6.33908 + 10.9796i) q^{6} +(12.0627 - 20.8932i) q^{7} -7.85849 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(2.11303 + 3.65987i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-4.92977 + 8.53861i) q^{4} -5.85953 q^{5} +(-6.33908 + 10.9796i) q^{6} +(12.0627 - 20.8932i) q^{7} -7.85849 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-12.3814 - 21.4451i) q^{10} +(16.9446 + 29.3489i) q^{11} -29.5786 q^{12} +(-40.8020 - 23.0694i) q^{13} +101.955 q^{14} +(-8.78930 - 15.2235i) q^{15} +(22.8329 + 39.5478i) q^{16} +(24.6978 - 42.7779i) q^{17} -38.0345 q^{18} +(38.4274 - 66.5582i) q^{19} +(28.8861 - 50.0322i) q^{20} +72.3763 q^{21} +(-71.6088 + 124.030i) q^{22} +(-3.14582 - 5.44871i) q^{23} +(-11.7877 - 20.4169i) q^{24} -90.6659 q^{25} +(-1.78447 - 198.076i) q^{26} -27.0000 q^{27} +(118.933 + 205.998i) q^{28} +(-50.4977 - 87.4645i) q^{29} +(37.1441 - 64.3354i) q^{30} -307.580 q^{31} +(-127.927 + 221.576i) q^{32} +(-50.8338 + 88.0467i) q^{33} +208.749 q^{34} +(-70.6819 + 122.425i) q^{35} +(-44.3679 - 76.8475i) q^{36} +(38.0095 + 65.8343i) q^{37} +324.793 q^{38} +(-1.26677 - 140.611i) q^{39} +46.0471 q^{40} +(257.209 + 445.499i) q^{41} +(152.933 + 264.888i) q^{42} +(134.092 - 232.254i) q^{43} -334.132 q^{44} +(26.3679 - 45.6705i) q^{45} +(13.2944 - 23.0266i) q^{46} -460.912 q^{47} +(-68.4988 + 118.643i) q^{48} +(-119.519 - 207.012i) q^{49} +(-191.579 - 331.825i) q^{50} +148.187 q^{51} +(398.125 - 234.665i) q^{52} +67.8057 q^{53} +(-57.0517 - 98.8165i) q^{54} +(-99.2874 - 171.971i) q^{55} +(-94.7947 + 164.189i) q^{56} +230.564 q^{57} +(213.406 - 369.630i) q^{58} +(-12.6010 + 21.8256i) q^{59} +173.317 q^{60} +(294.416 - 509.944i) q^{61} +(-649.925 - 1125.70i) q^{62} +(108.565 + 188.039i) q^{63} -715.927 q^{64} +(239.080 + 135.176i) q^{65} -429.653 q^{66} +(502.230 + 869.888i) q^{67} +(243.509 + 421.770i) q^{68} +(9.43745 - 16.3461i) q^{69} -597.411 q^{70} +(-447.740 + 775.509i) q^{71} +(35.3632 - 61.2508i) q^{72} +968.599 q^{73} +(-160.630 + 278.219i) q^{74} +(-135.999 - 235.557i) q^{75} +(378.876 + 656.233i) q^{76} +817.592 q^{77} +(511.941 - 301.751i) q^{78} -119.053 q^{79} +(-133.790 - 231.732i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-1086.98 + 1882.70i) q^{82} +480.784 q^{83} +(-356.798 + 617.993i) q^{84} +(-144.718 + 250.658i) q^{85} +1133.36 q^{86} +(151.493 - 262.394i) q^{87} +(-133.159 - 230.638i) q^{88} +(-542.954 - 940.423i) q^{89} +222.864 q^{90} +(-974.179 + 574.205i) q^{91} +62.0325 q^{92} +(-461.370 - 799.116i) q^{93} +(-973.920 - 1686.88i) q^{94} +(-225.167 + 390.000i) q^{95} -767.563 q^{96} +(8.32761 - 14.4239i) q^{97} +(505.092 - 874.845i) q^{98} -305.003 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 12 q^{3} - 22 q^{4} - 12 q^{5} + 6 q^{6} + 14 q^{7} + 108 q^{8} - 36 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 12 * q^3 - 22 * q^4 - 12 * q^5 + 6 * q^6 + 14 * q^7 + 108 * q^8 - 36 * q^9	\( 8 q - 2 q^{2} + 12 q^{3} - 22 q^{4} - 12 q^{5} + 6 q^{6} + 14 q^{7} + 108 q^{8} - 36 q^{9} + 62 q^{10} - 40 q^{11} - 132 q^{12} - 60 q^{13} + 80 q^{14} - 18 q^{15} - 122 q^{16} - 98 q^{17} + 36 q^{18} - 124 q^{19} + 466 q^{20} + 84 q^{21} - 220 q^{22} - 104 q^{23} + 162 q^{24} - 116 q^{25} + 14 q^{26} - 216 q^{27} + 144 q^{28} - 194 q^{29} - 186 q^{30} + 52 q^{31} - 654 q^{32} + 120 q^{33} + 2124 q^{34} - 88 q^{35} - 198 q^{36} - 102 q^{37} + 664 q^{38} + 342 q^{39} - 1996 q^{40} + 1054 q^{41} + 120 q^{42} - 450 q^{43} - 88 q^{44} + 54 q^{45} + 172 q^{46} - 192 q^{47} + 366 q^{48} - 1070 q^{49} - 996 q^{50} - 588 q^{51} + 2280 q^{52} + 524 q^{53} + 54 q^{54} - 204 q^{55} - 2164 q^{56} - 744 q^{57} - 722 q^{58} - 308 q^{59} + 2796 q^{60} + 928 q^{61} - 2780 q^{62} + 126 q^{63} + 2052 q^{64} + 2346 q^{65} - 1320 q^{66} + 1134 q^{67} - 1786 q^{68} + 312 q^{69} - 4648 q^{70} - 1064 q^{71} - 486 q^{72} + 1904 q^{73} - 1158 q^{74} - 174 q^{75} + 1708 q^{76} + 5016 q^{77} + 480 q^{78} - 1492 q^{79} + 2922 q^{80} - 324 q^{81} - 1734 q^{82} - 808 q^{83} - 432 q^{84} + 1394 q^{85} + 6336 q^{86} + 582 q^{87} - 3060 q^{88} - 1620 q^{89} - 1116 q^{90} + 3278 q^{91} + 664 q^{92} + 78 q^{93} + 772 q^{94} - 2204 q^{95} - 3924 q^{96} - 2166 q^{97} + 1906 q^{98} + 720 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 12 * q^3 - 22 * q^4 - 12 * q^5 + 6 * q^6 + 14 * q^7 + 108 * q^8 - 36 * q^9 + 62 * q^10 - 40 * q^11 - 132 * q^12 - 60 * q^13 + 80 * q^14 - 18 * q^15 - 122 * q^16 - 98 * q^17 + 36 * q^18 - 124 * q^19 + 466 * q^20 + 84 * q^21 - 220 * q^22 - 104 * q^23 + 162 * q^24 - 116 * q^25 + 14 * q^26 - 216 * q^27 + 144 * q^28 - 194 * q^29 - 186 * q^30 + 52 * q^31 - 654 * q^32 + 120 * q^33 + 2124 * q^34 - 88 * q^35 - 198 * q^36 - 102 * q^37 + 664 * q^38 + 342 * q^39 - 1996 * q^40 + 1054 * q^41 + 120 * q^42 - 450 * q^43 - 88 * q^44 + 54 * q^45 + 172 * q^46 - 192 * q^47 + 366 * q^48 - 1070 * q^49 - 996 * q^50 - 588 * q^51 + 2280 * q^52 + 524 * q^53 + 54 * q^54 - 204 * q^55 - 2164 * q^56 - 744 * q^57 - 722 * q^58 - 308 * q^59 + 2796 * q^60 + 928 * q^61 - 2780 * q^62 + 126 * q^63 + 2052 * q^64 + 2346 * q^65 - 1320 * q^66 + 1134 * q^67 - 1786 * q^68 + 312 * q^69 - 4648 * q^70 - 1064 * q^71 - 486 * q^72 + 1904 * q^73 - 1158 * q^74 - 174 * q^75 + 1708 * q^76 + 5016 * q^77 + 480 * q^78 - 1492 * q^79 + 2922 * q^80 - 324 * q^81 - 1734 * q^82 - 808 * q^83 - 432 * q^84 + 1394 * q^85 + 6336 * q^86 + 582 * q^87 - 3060 * q^88 - 1620 * q^89 - 1116 * q^90 + 3278 * q^91 + 664 * q^92 + 78 * q^93 + 772 * q^94 - 2204 * q^95 - 3924 * q^96 - 2166 * q^97 + 1906 * q^98 + 720 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.11303	+	3.65987i	0.747068	+	1.29396i	0.949222	+	0.314606i	$0.101872\pi$
$2$	2.11303	+	3.65987i	0.747068	+	1.29396i	−0.202155	+	0.979354i	$0.564794\pi$
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	−4.92977	+	8.53861i	−0.616221	+	1.06733i
$5$	−5.85953			−0.524093			−0.262046	−	0.965055i	$-0.584397\pi$
$5$	−5.85953			−0.524093			−0.262046	+	0.965055i	$0.584397\pi$
$6$	−6.33908	+	10.9796i	−0.431320	+	0.747068i
$7$	12.0627	−	20.8932i	0.651326	−	1.12813i	−0.331476	−	0.943464i	$-0.607546\pi$
$7$	12.0627	−	20.8932i	0.651326	−	1.12813i	0.982801	−	0.184666i	$-0.0591202\pi$
$8$	−7.85849			−0.347299
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−12.3814	−	21.4451i	−0.391533	−	0.678155i
$11$	16.9446	+	29.3489i	0.464453	+	0.804457i	0.999177	−	0.0405703i	$-0.0129175\pi$
$11$	16.9446	+	29.3489i	0.464453	+	0.804457i	−0.534723	+	0.845027i	$0.679584\pi$
$12$	−29.5786			−0.711551
$13$	−40.8020	−	23.0694i	−0.870495	−	0.492178i
$13$	−40.8020	−	23.0694i	−0.870495	−	0.492178i
$14$	101.955			1.94634
$15$	−8.78930	−	15.2235i	−0.151292	−	0.262046i
$16$	22.8329	+	39.5478i	0.356765	+	0.617934i
$17$	24.6978	−	42.7779i	0.352359	−	0.610303i	−0.634303	−	0.773084i	$-0.718713\pi$
$17$	24.6978	−	42.7779i	0.352359	−	0.610303i	0.986662	+	0.162781i	$0.0520463\pi$
$18$	−38.0345			−0.498045
$19$	38.4274	−	66.5582i	0.463992	−	0.803658i	−0.535163	−	0.844749i	$-0.679750\pi$
$19$	38.4274	−	66.5582i	0.463992	−	0.803658i	0.999155	+	0.0410905i	$0.0130832\pi$
$20$	28.8861	−	50.0322i	0.322957	−	0.559377i
$21$	72.3763			0.752086
$22$	−71.6088	+	124.030i	−0.693957	+	1.20197i
$23$	−3.14582	−	5.44871i	−0.0285195	−	0.0493972i	0.851413	−	0.524495i	$-0.175746\pi$
$23$	−3.14582	−	5.44871i	−0.0285195	−	0.0493972i	−0.879933	+	0.475098i	$0.842413\pi$
$24$	−11.7877	−	20.4169i	−0.100257	−	0.173650i
$25$	−90.6659			−0.725327
$26$	−1.78447	−	198.076i	−0.0134602	−	1.49408i
$27$	−27.0000			−0.192450
$28$	118.933	+	205.998i	0.802721	+	1.39035i
$29$	−50.4977	−	87.4645i	−0.323351	−	0.560061i	0.657826	−	0.753170i	$-0.271476\pi$
$29$	−50.4977	−	87.4645i	−0.323351	−	0.560061i	−0.981177	+	0.193109i	$0.938143\pi$
$30$	37.1441	−	64.3354i	0.226052	−	0.391533i
$31$	−307.580			−1.78203			−0.891016	−	0.453972i	$-0.850007\pi$
$31$	−307.580			−1.78203			−0.891016	+	0.453972i	$0.850007\pi$
$32$	−127.927	+	221.576i	−0.706704	+	1.22405i
$33$	−50.8338	+	88.0467i	−0.268152	+	0.464453i
$34$	208.749			1.05294
$35$	−70.6819	+	122.425i	−0.341355	+	0.591244i
$36$	−44.3679	−	76.8475i	−0.205407	−	0.355775i
$37$	38.0095	+	65.8343i	0.168884	+	0.292516i	0.938028	−	0.346560i	$-0.112650\pi$
$37$	38.0095	+	65.8343i	0.168884	+	0.292516i	−0.769144	+	0.639076i	$0.779317\pi$
$38$	324.793			1.38653
$39$	−1.26677	−	140.611i	−0.00520115	−	0.577327i
$40$	46.0471			0.182017
$41$	257.209	+	445.499i	0.979740	+	1.69696i	0.663312	+	0.748343i	$0.269150\pi$
$41$	257.209	+	445.499i	0.979740	+	1.69696i	0.316427	+	0.948617i	$0.397517\pi$
$42$	152.933	+	264.888i	0.561859	+	0.973169i
$43$	134.092	−	232.254i	0.475554	−	0.823684i	−0.524054	−	0.851685i	$-0.675581\pi$
$43$	134.092	−	232.254i	0.475554	−	0.823684i	0.999608	+	0.0280012i	$0.00891422\pi$
$44$	−334.132			−1.14482
$45$	26.3679	−	45.6705i	0.0873488	−	0.151292i
$46$	13.2944	−	23.0266i	0.0426120	−	0.0738061i
$47$	−460.912			−1.43045			−0.715223	−	0.698896i	$-0.753675\pi$
$47$	−460.912			−1.43045			−0.715223	+	0.698896i	$0.753675\pi$
$48$	−68.4988	+	118.643i	−0.205978	+	0.356765i
$49$	−119.519	−	207.012i	−0.348451	−	0.603534i
$50$	−191.579	−	331.825i	−0.541868	−	0.938544i
$51$	148.187			0.406869
$52$	398.125	−	234.665i	1.06173	−	0.625811i
$53$	67.8057			0.175733			0.0878663	−	0.996132i	$-0.471995\pi$
$53$	67.8057			0.175733			0.0878663	+	0.996132i	$0.471995\pi$
$54$	−57.0517	−	98.8165i	−0.143773	−	0.249023i
$55$	−99.2874	−	171.971i	−0.243417	−	0.421610i
$56$	−94.7947	+	164.189i	−0.226205	+	0.391799i
$57$	230.564			0.535772
$58$	213.406	−	369.630i	0.483130	−	0.836806i
$59$	−12.6010	+	21.8256i	−0.0278053	+	0.0481603i	−0.879593	−	0.475727i	$-0.842185\pi$
$59$	−12.6010	+	21.8256i	−0.0278053	+	0.0481603i	0.851788	+	0.523887i	$0.175519\pi$
$60$	173.317			0.372918
$61$	294.416	−	509.944i	0.617969	−	1.07035i	−0.371886	−	0.928278i	$-0.621289\pi$
$61$	294.416	−	509.944i	0.617969	−	1.07035i	0.989856	−	0.142076i	$-0.0453778\pi$
$62$	−649.925	−	1125.70i	−1.33130	−	2.30588i
$63$	108.565	+	188.039i	0.217109	+	0.376043i
$64$	−715.927			−1.39830
$65$	239.080	+	135.176i	0.456220	+	0.257947i
$66$	−429.653			−0.801312
$67$	502.230	+	869.888i	0.915778	+	1.58617i	0.805758	+	0.592245i	$0.201758\pi$
$67$	502.230	+	869.888i	0.915778	+	1.58617i	0.110021	+	0.993929i	$0.464908\pi$
$68$	243.509	+	421.770i	0.434262	+	0.752163i
$69$	9.43745	−	16.3461i	0.0164657	−	0.0285195i
$70$	−597.411			−1.02006
$71$	−447.740	+	775.509i	−0.748408	+	1.29628i	0.200177	+	0.979760i	$0.435848\pi$
$71$	−447.740	+	775.509i	−0.748408	+	1.29628i	−0.948585	+	0.316522i	$0.897485\pi$
$72$	35.3632	−	61.2508i	0.0578832	−	0.100257i
$73$	968.599			1.55296			0.776479	−	0.630143i	$-0.217004\pi$
$73$	968.599			1.55296			0.776479	+	0.630143i	$0.217004\pi$
$74$	−160.630	+	278.219i	−0.252336	+	0.437059i
$75$	−135.999	−	235.557i	−0.209384	−	0.362663i
$76$	378.876	+	656.233i	0.571843	+	0.990462i
$77$	817.592			1.21004
$78$	511.941	−	301.751i	0.743152	−	0.438032i
$79$	−119.053			−0.169551			−0.0847755	−	0.996400i	$-0.527017\pi$
$79$	−119.053			−0.169551			−0.0847755	+	0.996400i	$0.527017\pi$
$80$	−133.790	−	231.732i	−0.186978	−	0.323855i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−1086.98	+	1882.70i	−1.46386	+	2.53549i
$83$	480.784			0.635818			0.317909	−	0.948121i	$-0.397019\pi$
$83$	480.784			0.635818			0.317909	+	0.948121i	$0.397019\pi$
$84$	−356.798	+	617.993i	−0.463451	+	0.802721i
$85$	−144.718	+	250.658i	−0.184669	+	0.319856i
$86$	1133.36			1.42109
$87$	151.493	−	262.394i	0.186687	−	0.323351i
$88$	−133.159	−	230.638i	−0.161304	−	0.279387i
$89$	−542.954	−	940.423i	−0.646663	−	1.12005i	−0.983915	−	0.178638i	$-0.942831\pi$
$89$	−542.954	−	940.423i	−0.646663	−	1.12005i	0.337252	−	0.941414i	$-0.390503\pi$
$90$	222.864			0.261022
$91$	−974.179	+	574.205i	−1.12222	+	0.661462i
$92$	62.0325			0.0702972
$93$	−461.370	−	799.116i	−0.514428	−	0.891016i
$94$	−973.920	−	1686.88i	−1.06864	−	1.85094i
$95$	−225.167	+	390.000i	−0.243175	+	0.421191i
$96$	−767.563			−0.816032
$97$	8.32761	−	14.4239i	0.00871692	−	0.0150981i	−0.861634	−	0.507530i	$-0.830559\pi$
$97$	8.32761	−	14.4239i	0.00871692	−	0.0150981i	0.870351	+	0.492432i	$0.163892\pi$
$98$	505.092	−	874.845i	0.520632	−	0.901762i
$99$	−305.003			−0.309636
$100$	446.962	−	774.160i	0.446962	−	0.774160i
$101$	479.002	+	829.655i	0.471906	+	0.817364i	0.999483	−	0.0321423i	$-0.0102330\pi$
$101$	479.002	+	829.655i	0.471906	+	0.817364i	−0.527578	+	0.849507i	$0.676900\pi$
$102$	313.123	+	542.345i	0.303959	+	0.526472i
$103$	−2.70560			−0.00258826			−0.00129413	−	0.999999i	$-0.500412\pi$
$103$	−2.70560			−0.00258826			−0.00129413	+	0.999999i	$0.500412\pi$
$104$	320.642	+	181.291i	0.302322	+	0.170933i
$105$	−424.092			−0.394163
$106$	143.275	+	248.160i	0.131284	+	0.227391i
$107$	−675.642	−	1170.25i	−0.610437	−	1.05731i	−0.991167	−	0.132621i	$-0.957661\pi$
$107$	−675.642	−	1170.25i	−0.610437	−	1.05731i	0.380730	−	0.924686i	$-0.375673\pi$
$108$	133.104	−	230.542i	0.118592	−	0.205407i
$109$	448.455			0.394075			0.197037	−	0.980396i	$-0.436868\pi$
$109$	448.455			0.394075			0.197037	+	0.980396i	$0.436868\pi$
$110$	419.594	−	726.758i	0.363697	−	0.629942i
$111$	−114.028	+	197.503i	−0.0975054	+	0.168884i
$112$	1101.71			0.929480
$113$	−699.423	+	1211.44i	−0.582267	+	1.00852i	0.412943	+	0.910757i	$0.364501\pi$
$113$	−699.423	+	1211.44i	−0.582267	+	1.00852i	−0.995210	+	0.0977596i	$0.968832\pi$
$114$	487.189	+	843.836i	0.400258	+	0.693267i
$115$	18.4330	+	31.9269i	0.0149468	+	0.0258887i
$116$	995.767			0.797023
$117$	363.417	−	214.207i	0.287162	−	0.169260i
$118$	−106.505			−0.0830899
$119$	−595.846	−	1032.04i	−0.459001	−	0.795013i
$120$	69.0706	+	119.634i	0.0525438	+	0.0910085i
$121$	91.2613	−	158.069i	0.0685659	−	0.118760i
$122$	2488.44			1.84666
$123$	−771.628	+	1336.50i	−0.565653	+	0.979740i
$124$	1516.30	−	2626.30i	1.09813	−	1.90201i
$125$	1263.70			0.904231
$126$	−458.799	+	794.664i	−0.324390	+	0.561859i
$127$	59.7522	+	103.494i	0.0417492	+	0.0723118i	0.886145	−	0.463408i	$-0.153374\pi$
$127$	59.7522	+	103.494i	0.0417492	+	0.0723118i	−0.844396	+	0.535720i	$0.820040\pi$
$128$	−489.356	−	847.590i	−0.337917	−	0.585290i
$129$	804.552			0.549123
$130$	10.4562	+	1160.63i	0.00705437	+	0.783034i
$131$	−2251.70			−1.50177			−0.750886	−	0.660432i	$-0.770373\pi$
$131$	−2251.70			−1.50177			−0.750886	+	0.660432i	$0.770373\pi$
$132$	−501.197	−	868.099i	−0.330482	−	0.572412i
$133$	−927.078	−	1605.75i	−0.604420	−	1.04689i
$134$	−2122.45	+	3676.19i	−1.36830	+	2.36996i
$135$	158.207			0.100862
$136$	−194.087	+	336.169i	−0.122374	+	0.211958i
$137$	−565.310	+	979.146i	−0.352538	+	0.610614i	−0.986693	−	0.162592i	$-0.948015\pi$
$137$	−565.310	+	979.146i	−0.352538	+	0.610614i	0.634155	+	0.773206i	$0.281348\pi$
$138$	79.7663			0.0492041
$139$	297.644	−	515.534i	0.181624	−	0.314583i	−0.760809	−	0.648975i	$-0.775198\pi$
$139$	297.644	−	515.534i	0.181624	−	0.314583i	0.942434	+	0.334393i	$0.108531\pi$
$140$	−696.891	−	1207.05i	−0.420700	−	0.728674i
$141$	−691.368	−	1197.49i	−0.412934	−	0.715223i
$142$	−3784.35			−2.23645
$143$	−14.3099	−	1588.40i	−0.00836821	−	0.928869i
$144$	−410.993			−0.237843
$145$	295.893	+	512.501i	0.169466	+	0.293524i
$146$	2046.68	+	3544.95i	1.16017	+	2.00947i
$147$	358.556	−	621.037i	0.201178	−	0.348451i
$148$	−749.511			−0.416280
$149$	396.587	−	686.910i	0.218052	−	0.377677i	−0.736161	−	0.676807i	$-0.763363\pi$
$149$	396.587	−	686.910i	0.218052	−	0.377677i	0.954212	+	0.299130i	$0.0966965\pi$
$150$	574.738	−	995.476i	0.312848	−	0.541868i
$151$	−134.213			−0.0723317			−0.0361659	−	0.999346i	$-0.511514\pi$
$151$	−134.213			−0.0723317			−0.0361659	+	0.999346i	$0.511514\pi$
$152$	−301.981	+	523.047i	−0.161144	+	0.279110i
$153$	222.280	+	385.001i	0.117453	+	0.203434i
$154$	1727.59	+	2992.28i	0.903984	+	1.56575i
$155$	1802.28			0.933950
$156$	1206.87	+	682.362i	0.619401	+	0.350209i
$157$	1509.07			0.767114			0.383557	−	0.923517i	$-0.374699\pi$
$157$	1509.07			0.767114			0.383557	+	0.923517i	$0.374699\pi$
$158$	−251.563	−	435.719i	−0.126666	−	0.219392i
$159$	101.709	+	176.164i	0.0507297	+	0.0878663i
$160$	749.593	−	1298.33i	0.370379	−	0.641514i
$161$	−151.788			−0.0743019
$162$	171.155	−	296.449i	0.0830075	−	0.143773i
$163$	−587.540	+	1017.65i	−0.282329	+	0.489009i	−0.971958	−	0.235155i	$-0.924440\pi$
$163$	−587.540	+	1017.65i	−0.282329	+	0.489009i	0.689629	+	0.724163i	$0.257774\pi$
$164$	−5071.93			−2.41494
$165$	297.862	−	515.913i	0.140537	−	0.243417i
$166$	1015.91	+	1759.61i	0.474999	+	0.822723i
$167$	−737.007	−	1276.53i	−0.341505	−	0.591504i	0.643208	−	0.765692i	$-0.277603\pi$
$167$	−737.007	−	1276.53i	−0.341505	−	0.591504i	−0.984712	+	0.174188i	$0.944270\pi$
$168$	−568.768			−0.261199
$169$	1132.60	+	1882.56i	0.515522	+	0.856877i
$170$	−1223.17			−0.551840
$171$	345.847	+	599.024i	0.154664	+	0.267886i
$172$	1322.08	+	2289.92i	0.586093	+	1.01514i
$173$	1164.15	−	2016.37i	0.511612	−	0.886139i	−0.488297	−	0.872678i	$-0.662382\pi$
$173$	1164.15	−	2016.37i	0.511612	−	0.886139i	0.999909	−	0.0134612i	$-0.00428497\pi$
$174$	1280.44			0.557871
$175$	−1093.68	+	1894.30i	−0.472424	+	0.818263i
$176$	−773.790	+	1340.24i	−0.331401	+	0.574004i
$177$	−75.6062			−0.0321069
$178$	2294.55	−	3974.28i	0.966202	−	1.67351i
$179$	1066.93	+	1847.97i	0.445508	+	0.771642i	0.998087	−	0.0618183i	$-0.0196899\pi$
$179$	1066.93	+	1847.97i	0.445508	+	0.771642i	−0.552580	+	0.833460i	$0.686357\pi$
$180$	259.975	+	450.290i	0.107652	+	0.186459i
$181$	−2485.41			−1.02066			−0.510329	−	0.859979i	$-0.670476\pi$
$181$	−2485.41			−1.02066			−0.510329	+	0.859979i	$0.670476\pi$
$182$	−4159.98	−	2352.06i	−1.69428	−	0.957945i
$183$	1766.50			0.713570
$184$	24.7214	+	42.8186i	0.00990479	+	0.0171556i
$185$	−222.718	−	385.758i	−0.0885110	−	0.153305i
$186$	1949.77	−	3377.11i	0.768626	−	1.33130i
$187$	1673.98			0.654617
$188$	2272.19	−	3935.55i	0.881471	−	1.52675i
$189$	−325.694	+	564.118i	−0.125348	+	0.217109i
$190$	−1903.13			−0.726673
$191$	1162.53	−	2013.57i	0.440408	−	0.762809i	−0.557311	−	0.830304i	$-0.688167\pi$
$191$	1162.53	−	2013.57i	0.440408	−	0.762809i	0.997720	+	0.0674941i	$0.0215004\pi$
$192$	−1073.89	−	1860.03i	−0.403653	−	0.699148i
$193$	−1675.06	−	2901.29i	−0.624732	−	1.08207i	−0.988593	−	0.150614i	$-0.951875\pi$
$193$	−1675.06	−	2901.29i	−0.624732	−	1.08207i	0.363860	−	0.931453i	$-0.381458\pi$
$194$	70.3859			0.0260485
$195$	7.42266	+	823.914i	0.00272588	+	0.302573i
$196$	2356.79			0.858890
$197$	1929.65	+	3342.25i	0.697878	+	1.20876i	0.969201	+	0.246272i	$0.0792056\pi$
$197$	1929.65	+	3342.25i	0.697878	+	1.20876i	−0.271323	+	0.962488i	$0.587461\pi$
$198$	−644.479	−	1116.27i	−0.231319	−	0.400656i
$199$	2041.80	−	3536.50i	0.727333	−	1.25978i	−0.230673	−	0.973031i	$-0.574093\pi$
$199$	2041.80	−	3536.50i	0.727333	−	1.25978i	0.958006	−	0.286747i	$-0.0925739\pi$
$200$	712.497			0.251906
$201$	−1506.69	+	2609.66i	−0.528725	+	0.915778i
$202$	−2024.29	+	3506.17i	−0.705091	+	1.22125i
$203$	−2436.56			−0.842428
$204$	−730.527	+	1265.31i	−0.250721	+	0.434262i
$205$	−1507.13	−	2610.42i	−0.513474	−	0.889364i
$206$	−5.71700	−	9.90214i	−0.00193360	−	0.00334910i
$207$	56.6247			0.0190130
$208$	−19.2827	−	2140.37i	−0.00642794	−	0.713500i
$209$	2604.55			0.862011
$210$	−896.117	−	1552.12i	−0.294466	−	0.510031i
$211$	−1513.65	−	2621.72i	−0.493857	−	0.855386i	0.506118	−	0.862464i	$-0.331080\pi$
$211$	−1513.65	−	2621.72i	−0.493857	−	0.855386i	−0.999975	+	0.00707871i	$0.997747\pi$
$212$	−334.266	+	578.966i	−0.108290	+	0.187564i
$213$	−2686.44			−0.864188
$214$	2855.30	−	4945.52i	0.912076	−	1.57976i
$215$	−785.716	+	1360.90i	−0.249234	+	0.431687i
$216$	212.179			0.0668378
$217$	−3710.25	+	6426.34i	−1.16068	+	2.01036i
$218$	947.597	+	1641.29i	0.294401	+	0.509917i
$219$	1452.90	+	2516.49i	0.448300	+	0.776479i
$220$	1957.86			0.599994
$221$	−1994.58	+	1175.66i	−0.607104	+	0.357843i
$222$	−963.780			−0.291372
$223$	862.379	+	1493.68i	0.258965	+	0.448540i	0.965965	−	0.258673i	$-0.0832853\pi$
$223$	862.379	+	1493.68i	0.258965	+	0.448540i	−0.707000	+	0.707213i	$0.749952\pi$
$224$	3086.30	+	5345.63i	0.920590	+	1.59451i
$225$	407.996	−	706.671i	0.120888	−	0.209384i
$226$	−5911.60			−1.73997
$227$	961.637	−	1665.60i	0.281172	−	0.487005i	−0.690502	−	0.723331i	$-0.742610\pi$
$227$	961.637	−	1665.60i	0.281172	−	0.487005i	0.971674	+	0.236326i	$0.0759435\pi$
$228$	−1136.63	+	1968.70i	−0.330154	+	0.571843i
$229$	373.993			0.107922			0.0539610	−	0.998543i	$-0.482815\pi$
$229$	373.993			0.107922			0.0539610	+	0.998543i	$0.482815\pi$
$230$	−77.8989	+	134.925i	−0.0223326	+	0.0386812i
$231$	1226.39	+	2124.17i	0.349309	+	0.605021i
$232$	396.835	+	687.339i	0.112300	+	0.194509i
$233$	3094.49			0.870073			0.435036	−	0.900413i	$-0.356735\pi$
$233$	3094.49			0.870073			0.435036	+	0.900413i	$0.356735\pi$
$234$	1551.88	+	877.435i	0.433546	+	0.245127i
$235$	2700.73			0.749686
$236$	−124.240	−	215.191i	−0.0342685	−	0.0593547i
$237$	−178.580	−	309.309i	−0.0489452	−	0.0847755i
$238$	2518.08	−	4361.44i	0.685810	−	1.18786i
$239$	−1221.18			−0.330510			−0.165255	−	0.986251i	$-0.552845\pi$
$239$	−1221.18			−0.330510			−0.165255	+	0.986251i	$0.552845\pi$
$240$	401.371	−	695.195i	0.107952	−	0.186978i
$241$	−72.7003	+	125.921i	−0.0194317	+	0.0336567i	−0.875578	−	0.483077i	$-0.839519\pi$
$241$	−72.7003	+	125.921i	−0.0194317	+	0.0336567i	0.856146	+	0.516734i	$0.172852\pi$
$242$	771.350			0.204894
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	2902.81	+	5027.81i	0.761611	+	1.31915i
$245$	700.323	+	1212.99i	0.182620	+	0.316308i
$246$	−6521.88			−1.69033
$247$	−3103.38	+	1829.21i	−0.799446	+	0.471213i
$248$	2417.11			0.618899
$249$	721.176	+	1249.11i	0.183545	+	0.317909i
$250$	2670.24	+	4624.98i	0.675522	+	1.17004i
$251$	492.835	−	853.615i	0.123934	−	0.214660i	−0.797382	−	0.603475i	$-0.793782\pi$
$251$	492.835	−	853.615i	0.123934	−	0.214660i	0.921316	+	0.388815i	$0.127116\pi$
$252$	−2140.79			−0.535147
$253$	106.609	−	184.652i	0.0264919	−	0.0458854i
$254$	−252.516	+	437.371i	−0.0623790	+	0.108044i
$255$	−868.306			−0.213237
$256$	−795.663	+	1378.13i	−0.194254	+	0.336457i
$257$	−1464.66	−	2536.86i	−0.355498	−	0.615740i	0.631705	−	0.775209i	$-0.282355\pi$
$257$	−1464.66	−	2536.86i	−0.355498	−	0.615740i	−0.987203	+	0.159469i	$0.949022\pi$
$258$	1700.04	+	2944.55i	0.410232	+	0.710543i
$259$	1833.99			0.439995
$260$	−2332.83	+	1375.03i	−0.556445	+	0.327983i
$261$	908.958			0.215567
$262$	−4757.91	−	8240.94i	−1.12193	−	1.94323i
$263$	−1119.00	−	1938.17i	−0.262360	−	0.454420i	0.704509	−	0.709695i	$-0.251167\pi$
$263$	−1119.00	−	1938.17i	−0.262360	−	0.454420i	−0.966869	+	0.255275i	$0.917834\pi$
$264$	399.477	−	691.914i	0.0931291	−	0.161304i
$265$	−397.310			−0.0921002
$266$	3917.88	−	6785.97i	0.903086	−	1.56419i
$267$	1628.86	−	2821.27i	0.373351	−	0.646663i
$268$	−9903.50			−2.25729
$269$	−962.992	+	1667.95i	−0.218270	+	0.378055i	−0.954279	−	0.298917i	$-0.903375\pi$
$269$	−962.992	+	1667.95i	−0.218270	+	0.378055i	0.736009	+	0.676972i	$0.236708\pi$
$270$	334.296	+	579.019i	0.0753505	+	0.130511i
$271$	1781.14	+	3085.03i	0.399250	+	0.691521i	0.993634	−	0.112660i	$-0.0359372\pi$
$271$	1781.14	+	3085.03i	0.399250	+	0.691521i	−0.594384	+	0.804182i	$0.702604\pi$
$272$	2255.69			0.502837
$273$	−2953.10	−	1669.68i	−0.654687	−	0.370160i
$274$	−4778.06			−1.05348
$275$	−1536.30	−	2660.94i	−0.336881	−	0.583494i
$276$	93.0488	+	161.165i	0.0202930	+	0.0351486i
$277$	718.712	−	1244.85i	0.155896	−	0.270020i	−0.777489	−	0.628897i	$-0.783507\pi$
$277$	718.712	−	1244.85i	0.155896	−	0.270020i	0.933385	+	0.358877i	$0.116840\pi$
$278$	2515.72			0.542743
$279$	1384.11	−	2397.35i	0.297005	−	0.514428i
$280$	555.453	−	962.073i	0.118552	−	0.205339i
$281$	−3913.51			−0.830820			−0.415410	−	0.909634i	$-0.636362\pi$
$281$	−3913.51			−0.830820			−0.415410	+	0.909634i	$0.636362\pi$
$282$	2921.76	−	5060.64i	0.616980	−	1.06864i
$283$	1606.16	+	2781.94i	0.337371	+	0.584344i	0.983937	−	0.178514i	$-0.0571289\pi$
$283$	1606.16	+	2781.94i	0.337371	+	0.584344i	−0.646566	+	0.762858i	$0.723796\pi$
$284$	−4414.51	−	7646.16i	−0.922370	−	1.59759i
$285$	−1351.00			−0.280794
$286$	5783.08	−	3408.69i	1.19567	−	0.704756i
$287$	12410.6			2.55252
$288$	−1151.34	−	1994.19i	−0.235568	−	0.408016i
$289$	1236.54	+	2141.74i	0.251686	+	0.435934i
$290$	−1250.46	+	2165.86i	−0.253205	+	0.438564i
$291$	49.9657			0.0100654
$292$	−4774.97	+	8270.49i	−0.956965	+	1.65751i
$293$	2450.89	−	4245.06i	0.488677	−	0.846413i	−0.511238	−	0.859439i	$-0.670813\pi$
$293$	2450.89	−	4245.06i	0.488677	−	0.846413i	0.999915	+	0.0130260i	$0.00414642\pi$
$294$	3030.55			0.601175
$295$	73.8362	−	127.888i	0.0145726	−	0.0252404i
$296$	−298.697	−	517.358i	−0.0586534	−	0.101591i
$297$	−457.504	−	792.420i	−0.0893841	−	0.154818i
$298$	3352.00			0.651598
$299$	2.65667	+	294.890i	0.000513844	+	0.0570366i
$300$	2681.77			0.516107
$301$	−3235.03	−	5603.23i	−0.619481	−	1.07297i
$302$	−283.595	−	491.202i	−0.0540367	−	0.0935943i
$303$	−1437.01	+	2488.97i	−0.272455	+	0.471906i
$304$	3509.64			0.662144
$305$	−1725.14	+	2988.03i	−0.323873	+	0.560965i
$306$	−939.369	+	1627.03i	−0.175491	+	0.303959i
$307$	5800.63			1.07837			0.539185	−	0.842188i	$-0.318733\pi$
$307$	5800.63			1.07837			0.539185	+	0.842188i	$0.318733\pi$
$308$	−4030.54	+	6981.09i	−0.745653	+	1.29151i
$309$	−4.05840	−	7.02935i	−0.000747165	−	0.00129413i
$310$	3808.26	+	6596.09i	0.697724	+	1.20849i
$311$	−4913.51			−0.895884			−0.447942	−	0.894063i	$-0.647843\pi$
$311$	−4913.51			−0.895884			−0.447942	+	0.894063i	$0.647843\pi$
$312$	9.95486	+	1104.99i	0.00180636	+	0.200505i
$313$	−8104.97			−1.46364			−0.731822	−	0.681496i	$-0.761330\pi$
$313$	−8104.97			−1.46364			−0.731822	+	0.681496i	$0.761330\pi$
$314$	3188.71	+	5523.00i	0.573086	+	0.992615i
$315$	−636.137	−	1101.82i	−0.113785	−	0.197081i
$316$	586.904	−	1016.55i	0.104481	−	0.180966i
$317$	5149.92			0.912455			0.456227	−	0.889863i	$-0.349200\pi$
$317$	5149.92			0.912455			0.456227	+	0.889863i	$0.349200\pi$
$318$	−429.826	+	744.480i	−0.0757970	+	0.131284i
$319$	1711.33	−	2964.10i	0.300363	−	0.520244i
$320$	4195.00			0.732836
$321$	2026.93	−	3510.74i	0.352436	−	0.610437i
$322$	−320.733	−	555.526i	−0.0555085	−	0.0961436i
$323$	−1898.15	−	3287.69i	−0.326984	−	0.566352i
$324$	798.622			0.136938
$325$	3699.35	+	2091.61i	0.631393	+	0.356990i
$326$	−4965.95			−0.843676
$327$	672.682	+	1165.12i	0.113760	+	0.197037i
$328$	−2021.28	−	3500.95i	−0.340263	−	0.589353i
$329$	−5559.86	+	9629.96i	−0.931687	+	1.61373i
$330$	2517.56			0.419962
$331$	−3030.99	+	5249.83i	−0.503318	+	0.871772i	0.496675	+	0.867937i	$0.334554\pi$
$331$	−3030.99	+	5249.83i	−0.503318	+	0.871772i	−0.999993	+	0.00383535i	$0.998779\pi$
$332$	−2370.15	+	4105.23i	−0.391804	+	0.678625i
$333$	−684.170			−0.112589
$334$	3114.63	−	5394.70i	0.510255	−	0.883787i
$335$	−2942.83	−	5097.14i	−0.479953	−	0.831302i
$336$	1652.56	+	2862.33i	0.268318	+	0.464740i
$337$	3743.50			0.605108			0.302554	−	0.953132i	$-0.402161\pi$
$337$	3743.50			0.605108			0.302554	+	0.953132i	$0.402161\pi$
$338$	−4496.70	+	8123.07i	−0.723634	+	1.30721i
$339$	−4196.54			−0.672344
$340$	−1426.85	−	2471.37i	−0.227593	−	0.394203i
$341$	−5211.82	−	9027.13i	−0.827671	−	1.43357i
$342$	−1461.57	+	2531.51i	−0.231089	+	0.400258i
$343$	2508.15			0.394832
$344$	−1053.76	+	1825.17i	−0.165160	+	0.286065i
$345$	−55.2990	+	95.7807i	−0.00862956	+	0.0149468i
$346$	9839.55			1.52884
$347$	1260.20	−	2182.74i	0.194961	−	0.337682i	−0.751927	−	0.659246i	$-0.770875\pi$
$347$	1260.20	−	2182.74i	0.194961	−	0.337682i	0.946888	+	0.321565i	$0.104209\pi$
$348$	1493.65	+	2587.08i	0.230081	+	0.398511i
$349$	−5325.37	−	9223.82i	−0.816793	−	1.41473i	−0.908033	−	0.418898i	$-0.862417\pi$
$349$	−5325.37	−	9223.82i	−0.816793	−	1.41473i	0.0912407	−	0.995829i	$-0.470917\pi$
$350$	−9243.88			−1.41173
$351$	1101.65	+	622.875i	0.167527	+	0.0947197i
$352$	−8670.70			−1.31293
$353$	4501.41	+	7796.67i	0.678714	+	1.17557i	0.975368	+	0.220582i	$0.0707956\pi$
$353$	4501.41	+	7796.67i	0.678714	+	1.17557i	−0.296655	+	0.954985i	$0.595871\pi$
$354$	−159.758	−	276.709i	−0.0239860	−	0.0415450i
$355$	2623.55	−	4544.12i	0.392235	−	0.679371i
$356$	10706.5			1.59395
$357$	1787.54	−	3096.11i	0.265004	−	0.459001i
$358$	−4508.89	+	7809.63i	−0.665649	+	1.15294i
$359$	−11360.9			−1.67021			−0.835106	−	0.550089i	$-0.814594\pi$
$359$	−11360.9			−1.67021			−0.835106	+	0.550089i	$0.814594\pi$
$360$	−207.212	+	358.901i	−0.0303362	+	0.0525438i
$361$	476.168	+	824.747i	0.0694224	+	0.120243i
$362$	−5251.74	−	9096.27i	−0.762500	−	1.32069i
$363$	547.568			0.0791731
$364$	−100.440	−	11148.8i	−0.0144629	−	1.60538i
$365$	−5675.54			−0.813894
$366$	3732.66	+	6465.15i	0.533085	+	0.923330i
$367$	6969.42	+	12071.4i	0.991283	+	1.71695i	0.609743	+	0.792599i	$0.291273\pi$
$367$	6969.42	+	12071.4i	0.991283	+	1.71695i	0.381540	+	0.924352i	$0.375394\pi$
$368$	143.656	−	248.820i	0.0203495	−	0.0352463i
$369$	−4629.77			−0.653160
$370$	941.217	−	1630.24i	0.132247	−	0.229059i
$371$	817.922	−	1416.68i	0.114459	−	0.198249i
$372$	9097.78			1.26801
$373$	−796.535	+	1379.64i	−0.110571	+	0.191515i	−0.916001	−	0.401177i	$-0.868601\pi$
$373$	−796.535	+	1379.64i	−0.110571	+	0.191515i	0.805430	+	0.592691i	$0.201935\pi$
$374$	3537.16	+	6126.54i	0.489043	+	0.847048i
$375$	1895.55	+	3283.19i	0.261029	+	0.452116i
$376$	3622.07			0.496793
$377$	42.6458	+	4733.68i	0.00582592	+	0.646676i
$378$	−2752.80			−0.374573
$379$	−4568.78	−	7913.36i	−0.619215	−	1.07251i	−0.989629	−	0.143645i	$-0.954118\pi$
$379$	−4568.78	−	7913.36i	−0.619215	−	1.07251i	0.370414	−	0.928867i	$-0.379216\pi$
$380$	−2220.04	−	3845.22i	−0.299699	−	0.519094i
$381$	−179.257	+	310.482i	−0.0241039	+	0.0417492i
$382$	9825.86			1.31606
$383$	−4775.53	+	8271.47i	−0.637124	+	1.10353i	0.348937	+	0.937146i	$0.386543\pi$
$383$	−4775.53	+	8271.47i	−0.637124	+	1.10353i	−0.986061	+	0.166385i	$0.946791\pi$
$384$	1468.07	−	2542.77i	0.195097	−	0.337917i
$385$	−4790.71			−0.634174
$386$	7078.88	−	12261.0i	0.933435	−	1.61676i
$387$	1206.83	+	2090.29i	0.158518	+	0.274561i
$388$	82.1064	+	142.212i	0.0107431	+	0.0186076i
$389$	7366.50			0.960145			0.480072	−	0.877229i	$-0.340610\pi$
$389$	7366.50			0.960145			0.480072	+	0.877229i	$0.340610\pi$
$390$	−2999.73	+	1768.12i	−0.389480	+	0.229570i
$391$	−310.779			−0.0401964
$392$	939.235	+	1626.80i	0.121017	+	0.209607i
$393$	−3377.55	−	5850.10i	−0.433524	−	0.750886i
$394$	−8154.81	+	14124.5i	−1.04272	+	1.80605i
$395$	697.596			0.0888604
$396$	1503.59	−	2604.30i	0.190804	−	0.330482i
$397$	5848.24	−	10129.4i	0.739332	−	1.28056i	−0.213465	−	0.976951i	$-0.568475\pi$
$397$	5848.24	−	10129.4i	0.739332	−	1.28056i	0.952797	−	0.303609i	$-0.0981917\pi$
$398$	17257.5			2.17347
$399$	2781.24	−	4817.24i	0.348962	−	0.604420i
$400$	−2070.17	−	3585.64i	−0.258771	−	0.448205i
$401$	7083.82	+	12269.5i	0.882167	+	1.52796i	0.848927	+	0.528510i	$0.177249\pi$
$401$	7083.82	+	12269.5i	0.882167	+	1.52796i	0.0332399	+	0.999447i	$0.489417\pi$
$402$	−12734.7			−1.57997
$403$	12549.9	+	7095.70i	1.55125	+	0.877077i
$404$	−9445.47			−1.16319
$405$	237.311	+	411.035i	0.0291163	+	0.0504308i
$406$	−5148.51	−	8917.48i	−0.629351	−	1.09007i
$407$	−1288.11	+	2231.07i	−0.156878	+	0.271720i
$408$	−1164.52			−0.141305
$409$	−1351.85	+	2341.47i	−0.163434	+	0.283076i	−0.936098	−	0.351739i	$-0.885590\pi$
$409$	−1351.85	+	2341.47i	−0.163434	+	0.283076i	0.772664	+	0.634815i	$0.218924\pi$
$410$	6369.20	−	11031.8i	0.767200	−	1.32883i
$411$	−3391.86			−0.407076
$412$	13.3380	−	23.1020i	0.00159494	−	0.00276251i
$413$	304.006	+	526.553i	0.0362207	+	0.0627361i
$414$	119.649	+	207.239i	0.0142040	+	0.0246020i
$415$	−2817.17			−0.333228
$416$	10331.3	−	6089.54i	1.21763	−	0.717703i
$417$	1785.86			0.209722
$418$	5503.48	+	9532.31i	0.643981	+	1.11541i
$419$	−3571.26	−	6185.61i	−0.416390	−	0.721209i	0.579183	−	0.815198i	$-0.303372\pi$
$419$	−3571.26	−	6185.61i	−0.416390	−	0.721209i	−0.995573	+	0.0939884i	$0.970038\pi$
$420$	2090.67	−	3621.15i	0.242891	−	0.420700i
$421$	−3406.45			−0.394347			−0.197174	−	0.980369i	$-0.563176\pi$
$421$	−3406.45			−0.394347			−0.197174	+	0.980369i	$0.563176\pi$
$422$	6396.76	−	11079.5i	0.737890	−	1.27806i
$423$	2074.11	−	3592.46i	0.238408	−	0.412934i
$424$	−532.850			−0.0610318
$425$	−2239.25	+	3878.49i	−0.255575	+	0.442670i
$426$	−5676.52	−	9832.03i	−0.645607	−	1.11822i
$427$	−7102.92	−	12302.6i	−0.804999	−	1.39430i
$428$	13323.0			1.50466
$429$	4105.31	−	2419.77i	0.462019	−	0.272326i
$430$	−6640.96			−0.744780
$431$	−2586.48	−	4479.92i	−0.289064	−	0.500673i	0.684523	−	0.728992i	$-0.260011\pi$
$431$	−2586.48	−	4479.92i	−0.289064	−	0.500673i	−0.973587	+	0.228318i	$0.926677\pi$
$432$	−616.489	−	1067.79i	−0.0686594	−	0.118922i
$433$	−5477.49	+	9487.28i	−0.607924	+	1.05296i	0.383658	+	0.923475i	$0.374664\pi$
$433$	−5477.49	+	9487.28i	−0.607924	+	1.05296i	−0.991582	+	0.129480i	$0.958669\pi$
$434$	−31359.4			−3.46844
$435$	−887.678	+	1537.50i	−0.0978412	+	0.169466i
$436$	−2210.78	+	3829.18i	−0.242837	+	0.420606i
$437$	−483.542			−0.0529313
$438$	−6140.03	+	10634.8i	−0.669822	+	1.16017i
$439$	−5916.22	−	10247.2i	−0.643202	−	1.11406i	−0.984714	−	0.174181i	$-0.944272\pi$
$439$	−5916.22	−	10247.2i	−0.643202	−	1.11406i	0.341511	−	0.939878i	$-0.389061\pi$
$440$	780.249	+	1351.43i	0.0845384	+	0.146425i
$441$	2151.33			0.232300
$442$	−8517.35	−	4815.72i	−0.916582	−	0.518236i
$443$	13479.8			1.44570			0.722852	−	0.691003i	$-0.242831\pi$
$443$	13479.8			1.44570			0.722852	+	0.691003i	$0.242831\pi$
$444$	−1124.27	−	1947.29i	−0.120170	−	0.208140i
$445$	3181.46	+	5510.44i	0.338911	+	0.587011i
$446$	−3644.46	+	6312.39i	−0.386929	+	0.670180i
$447$	2379.52			0.251784
$448$	−8636.03	+	14958.0i	−0.910746	+	1.57746i
$449$	3387.17	−	5866.75i	0.356014	−	0.616635i	−0.631277	−	0.775558i	$-0.717469\pi$
$449$	3387.17	−	5866.75i	0.356014	−	0.616635i	0.987291	+	0.158923i	$0.0508021\pi$
$450$	3448.43			0.361246
$451$	−8716.61	+	15097.6i	−0.910087	+	1.57632i
$452$	−6895.99	−	11944.2i	−0.717610	−	1.24294i
$453$	−201.319	−	348.695i	−0.0208804	−	0.0361659i
$454$	8127.86			0.840219
$455$	5708.23	−	3364.57i	0.588145	−	0.346667i
$456$	−1811.89			−0.186073
$457$	2321.18	+	4020.40i	0.237594	+	0.411524i	0.960023	−	0.279920i	$-0.0903080\pi$
$457$	2321.18	+	4020.40i	0.237594	+	0.411524i	−0.722430	+	0.691444i	$0.756975\pi$
$458$	790.257	+	1368.76i	0.0806250	+	0.139647i
$459$	−666.841	+	1155.00i	−0.0678115	+	0.117453i
$460$	−363.482			−0.0368422
$461$	−1230.18	+	2130.74i	−0.124285	+	0.215268i	−0.921453	−	0.388489i	$-0.872997\pi$
$461$	−1230.18	+	2130.74i	−0.124285	+	0.215268i	0.797168	+	0.603757i	$0.206330\pi$
$462$	−5182.78	+	8976.84i	−0.521915	+	0.903984i
$463$	4290.01			0.430613			0.215306	−	0.976547i	$-0.430925\pi$
$463$	4290.01			0.430613			0.215306	+	0.976547i	$0.430925\pi$
$464$	2306.02	−	3994.14i	0.230720	−	0.399620i
$465$	2703.41	+	4682.45i	0.269608	+	0.466975i
$466$	6538.75	+	11325.4i	0.650003	+	1.12584i
$467$	−8798.99			−0.871882			−0.435941	−	0.899975i	$-0.643584\pi$
$467$	−8798.99			−0.871882			−0.435941	+	0.899975i	$0.643584\pi$
$468$	37.4692	+	4159.07i	0.00370088	+	0.410797i
$469$	24233.0			2.38588
$470$	5706.72	+	9884.32i	0.560066	+	0.970064i
$471$	2263.61	+	3920.68i	0.221447	+	0.383557i
$472$	99.0251	−	171.517i	0.00965678	−	0.0167260i
$473$	9088.54			0.883491
$474$	754.688	−	1307.16i	0.0731307	−	0.126666i
$475$	−3484.05	+	6034.56i	−0.336546	+	0.582915i
$476$	11749.5			1.13138
$477$	−305.126	+	528.493i	−0.0292888	+	0.0507297i
$478$	−2580.39	−	4469.37i	−0.246913	−	0.427666i
$479$	5486.68	+	9503.21i	0.523367	+	0.906499i	0.999630	+	0.0271958i	$0.00865776\pi$
$479$	5486.68	+	9503.21i	0.523367	+	0.906499i	−0.476263	+	0.879303i	$0.658009\pi$
$480$	4497.56			0.427676
$481$	−32.0994	−	3563.03i	−0.00304284	−	0.337755i
$482$	−614.470			−0.0580671
$483$	−227.683	−	394.358i	−0.0214491	−	0.0371509i
$484$	899.793	+	1558.49i	0.0845035	+	0.146364i
$485$	−48.7959	+	84.5170i	−0.00456847	+	0.00791283i
$486$	1026.93			0.0958489
$487$	2604.79	−	4511.62i	0.242370	−	0.419797i	−0.719019	−	0.694991i	$-0.755409\pi$
$487$	2604.79	−	4511.62i	0.242370	−	0.419797i	0.961389	+	0.275193i	$0.0887419\pi$
$488$	−2313.67	+	4007.39i	−0.214620	+	0.371733i
$489$	−3525.24			−0.326006
$490$	−2959.60	+	5126.18i	−0.272860	+	0.472607i
$491$	4389.61	+	7603.03i	0.403463	+	0.698819i	0.994141	−	0.108089i	$-0.0344730\pi$
$491$	4389.61	+	7603.03i	0.403463	+	0.698819i	−0.590678	+	0.806907i	$0.701140\pi$
$492$	−7607.89	−	13177.3i	−0.697134	−	1.20747i
$493$	−4988.73			−0.455742
$494$	−13252.2	−	7492.79i	−1.20697	−	0.682422i
$495$	1787.17			0.162278
$496$	−7022.95	−	12164.1i	−0.635766	−	1.10118i
$497$	10801.9	+	18709.5i	0.974915	+	1.68860i
$498$	−3047.73	+	5278.82i	−0.274241	+	0.474999i
$499$	−15590.1			−1.39861			−0.699305	−	0.714823i	$-0.746507\pi$
$499$	−15590.1			−1.39861			−0.699305	+	0.714823i	$0.746507\pi$
$500$	−6229.75	+	10790.2i	−0.557206	+	0.965109i
$501$	2211.02	−	3829.60i	0.197168	−	0.341505i
$502$	4165.49			0.370349
$503$	32.1955	−	55.7642i	0.00285393	−	0.00494314i	−0.864595	−	0.502470i	$-0.832425\pi$
$503$	32.1955	−	55.7642i	0.00285393	−	0.00494314i	0.867449	+	0.497526i	$0.165758\pi$
$504$	−853.153	−	1477.70i	−0.0754017	−	0.130600i
$505$	−2806.73	−	4861.39i	−0.247322	−	0.428375i
$506$	901.072			0.0791651
$507$	−3192.13	+	5766.42i	−0.279620	+	0.505120i
$508$	−1178.26			−0.102907
$509$	−1607.08	−	2783.54i	−0.139946	−	0.242393i	0.787530	−	0.616276i	$-0.211359\pi$
$509$	−1607.08	−	2783.54i	−0.139946	−	0.242393i	−0.927476	+	0.373883i	$0.878026\pi$
$510$	−1834.75	−	3177.89i	−0.159303	−	0.275920i
$511$	11683.9	−	20237.2i	1.01148	−	1.75194i
$512$	−14554.7			−1.25632
$513$	−1037.54	+	1797.07i	−0.0892954	+	0.154664i
$514$	6189.73	−	10720.9i	0.531162	−	0.919999i
$515$	15.8535			0.00135649
$516$	−3966.25	+	6869.75i	−0.338381	+	0.586093i
$517$	−7809.97	−	13527.3i	−0.664376	−	1.15073i
$518$	3875.27	+	6712.17i	0.328706	+	0.569335i
$519$	6984.92			0.590759
$520$	−1878.81	−	1062.28i	−0.158445	−	0.0895848i
$521$	−3053.01			−0.256727			−0.128363	−	0.991727i	$-0.540972\pi$
$521$	−3053.01			−0.256727			−0.128363	+	0.991727i	$0.540972\pi$
$522$	1920.65	+	3326.67i	0.161043	+	0.278935i
$523$	−2548.01	−	4413.28i	−0.213034	−	0.368985i	0.739629	−	0.673015i	$-0.235001\pi$
$523$	−2548.01	−	4413.28i	−0.213034	−	0.368985i	−0.952663	+	0.304030i	$0.901668\pi$
$524$	11100.4	−	19226.4i	0.925423	−	1.60288i
$525$	−6562.06			−0.545508
$526$	4728.96	−	8190.80i	0.392001	−	0.678966i
$527$	−7596.55	+	13157.6i	−0.627915	+	1.08758i
$528$	−4642.74			−0.382669
$529$	6063.71	−	10502.6i	0.498373	−	0.863208i
$530$	−839.526	−	1454.10i	−0.0688051	−	0.119174i
$531$	−113.409	−	196.431i	−0.00926845	−	0.0160534i
$532$	18281.1			1.48983
$533$	−217.216	−	24110.9i	−0.0176523	−	1.95940i
$534$	13767.3			1.11567
$535$	3958.95	+	6857.09i	0.319925	+	0.554127i
$536$	−3946.77	−	6836.00i	−0.318049	−	0.550877i
$537$	−3200.78	+	5543.91i	−0.257214	+	0.445508i
$538$	−8139.31			−0.652250
$539$	4050.39	−	7015.48i	0.323678	−	0.560627i
$540$	−779.925	+	1350.87i	−0.0621531	+	0.107652i
$541$	7861.99			0.624793			0.312397	−	0.949952i	$-0.398868\pi$
$541$	7861.99			0.624793			0.312397	+	0.949952i	$0.398868\pi$
$542$	−7527.21	+	13037.5i	−0.596534	+	1.03323i
$543$	−3728.11	−	6457.28i	−0.294638	−	0.510329i
$544$	6319.04	+	10944.9i	0.498027	+	0.862608i
$545$	−2627.73			−0.206532
$546$	−129.154	−	14336.0i	−0.0101232	−	1.12367i
$547$	−6317.48			−0.493814			−0.246907	−	0.969039i	$-0.579414\pi$
$547$	−6317.48			−0.493814			−0.246907	+	0.969039i	$0.579414\pi$
$548$	−5573.70	−	9653.93i	−0.434483	−	0.752546i
$549$	2649.75	+	4589.49i	0.205990	+	0.356785i
$550$	6492.47	−	11245.3i	0.503345	−	0.871820i
$551$	−7761.98			−0.600130
$552$	−74.1641	+	128.456i	−0.00571854	+	0.00990479i
$553$	−1436.11	+	2487.41i	−0.110433	+	0.191275i
$554$	6074.63			0.465860
$555$	668.153	−	1157.28i	0.0511018	−	0.0885110i
$556$	2934.63	+	5082.92i	0.223842	+	0.387705i
$557$	485.617	+	841.113i	0.0369412	+	0.0639840i	0.883905	−	0.467667i	$-0.154905\pi$
$557$	485.617	+	841.113i	0.0369412	+	0.0639840i	−0.846964	+	0.531651i	$0.821572\pi$
$558$	11698.6			0.887533
$559$	−10829.2	+	6383.00i	−0.819367	+	0.482955i
$560$	−6455.50			−0.487134
$561$	2510.97	+	4349.12i	0.188972	+	0.327309i
$562$	−8269.35	−	14322.9i	−0.620679	−	1.07505i
$563$	−4664.24	+	8078.71i	−0.349155	+	0.604755i	−0.986100	−	0.166155i	$-0.946865\pi$
$563$	−4664.24	+	8078.71i	−0.349155	+	0.604755i	0.636944	+	0.770910i	$0.280198\pi$
$564$	13633.1			1.01783
$565$	4098.29	−	7098.45i	0.305162	−	0.528556i
$566$	−6787.70	+	11756.6i	−0.504079	+	0.873090i
$567$	−1954.16			−0.144739
$568$	3518.56	−	6094.33i	0.259922	−	0.450198i
$569$	−8726.08	−	15114.0i	−0.642911	−	1.11355i	−0.984780	−	0.173807i	$-0.944393\pi$
$569$	−8726.08	−	15114.0i	−0.642911	−	1.11355i	0.341869	−	0.939748i	$-0.388940\pi$
$570$	−2854.70	−	4944.49i	−0.209772	−	0.363336i
$571$	−20181.4			−1.47910			−0.739548	−	0.673103i	$-0.764961\pi$
$571$	−20181.4			−1.47910			−0.739548	+	0.673103i	$0.764961\pi$
$572$	13633.2	+	7708.23i	0.996563	+	0.563457i
$573$	6975.20			0.508540
$574$	26223.9	+	45421.1i	1.90691	+	3.30286i
$575$	285.218	+	494.012i	0.0206859	+	0.0358291i
$576$	3221.67	−	5580.10i	0.233049	−	0.403653i
$577$	6382.72			0.460513			0.230257	−	0.973130i	$-0.426043\pi$
$577$	6382.72			0.460513			0.230257	+	0.973130i	$0.426043\pi$
$578$	−5225.67	+	9051.12i	−0.376054	+	0.651344i
$579$	5025.17	−	8703.86i	0.360689	−	0.624732i
$580$	−5834.73			−0.417714
$581$	5799.57	−	10045.1i	0.414125	−	0.717285i
$582$	105.579	+	182.868i	0.00751956	+	0.0130243i
$583$	1148.94	+	1990.02i	0.0816197	+	0.141369i
$584$	−7611.72			−0.539341
$585$	−2129.46	+	1255.16i	−0.150499	+	0.0887082i
$586$	20715.2			1.46030
$587$	387.763	+	671.626i	0.0272653	+	0.0472248i	0.879336	−	0.476202i	$-0.157987\pi$
$587$	387.763	+	671.626i	0.0272653	+	0.0472248i	−0.852071	+	0.523427i	$0.824653\pi$
$588$	3535.19	+	6123.13i	0.247940	+	0.429445i
$589$	−11819.5	+	20472.0i	−0.826849	+	1.43214i
$590$	624.072			0.0435468
$591$	−5788.95	+	10026.8i	−0.402920	+	0.697878i
$592$	−1735.74	+	3006.38i	−0.120504	+	0.208719i
$593$	−17843.3			−1.23564			−0.617821	−	0.786319i	$-0.711984\pi$
$593$	−17843.3			−1.23564			−0.617821	+	0.786319i	$0.711984\pi$
$594$	1933.44	−	3348.81i	0.133552	−	0.231319i
$595$	3491.38	+	6047.24i	0.240559	+	0.416660i
$596$	3910.17	+	6772.61i	0.268736	+	0.465464i
$597$	12250.8			0.839852
$598$	−1073.65	+	632.835i	−0.0734192	+	0.0432751i
$599$	−24373.3			−1.66255			−0.831274	−	0.555863i	$-0.812388\pi$
$599$	−24373.3			−1.66255			−0.831274	+	0.555863i	$0.812388\pi$
$600$	1068.74	+	1851.12i	0.0727189	+	0.125953i
$601$	1763.50	+	3054.46i	0.119691	+	0.207311i	0.919645	−	0.392750i	$-0.128476\pi$
$601$	1763.50	+	3054.46i	0.119691	+	0.207311i	−0.799954	+	0.600061i	$0.795143\pi$
$602$	13671.4	−	23679.6i	0.925589	−	1.60317i
$603$	−9040.14			−0.610519
$604$	661.638	−	1145.99i	0.0445723	−	0.0772015i
$605$	−534.748	+	926.211i	−0.0359349	+	0.0622411i
$606$	−12145.7			−0.814169
$607$	−3995.77	+	6920.88i	−0.267189	+	0.462784i	−0.968135	−	0.250430i	$-0.919428\pi$
$607$	−3995.77	+	6920.88i	−0.267189	+	0.462784i	0.700946	+	0.713214i	$0.252761\pi$
$608$	9831.82	+	17029.2i	0.655811	+	1.13590i
$609$	−3654.84	−	6330.36i	−0.243188	−	0.421214i
$610$	−14581.1			−0.967821
$611$	18806.1	+	10633.0i	1.24520	+	0.704034i
$612$	−4383.16			−0.289508
$613$	8166.09	+	14144.1i	0.538051	+	0.931932i	0.999009	+	0.0445098i	$0.0141726\pi$
$613$	8166.09	+	14144.1i	0.538051	+	0.931932i	−0.460958	+	0.887422i	$0.652494\pi$
$614$	12256.9	+	21229.5i	0.805615	+	1.39537i
$615$	4521.38	−	7831.26i	0.296455	−	0.513474i
$616$	−6425.04			−0.420247
$617$	9676.82	−	16760.8i	0.631401	−	1.09362i	−0.355865	−	0.934537i	$-0.615814\pi$
$617$	9676.82	−	16760.8i	0.631401	−	1.09362i	0.987266	−	0.159081i	$-0.0508530\pi$
$618$	17.1510	−	29.7064i	0.00111637	−	0.00193360i
$619$	−9982.52			−0.648193			−0.324096	−	0.946024i	$-0.605060\pi$
$619$	−9982.52			−0.648193			−0.324096	+	0.946024i	$0.605060\pi$
$620$	−8884.79	+	15388.9i	−0.575519	+	0.996829i
$621$	84.9370	+	147.115i	0.00548858	+	0.00950649i
$622$	−10382.4	−	17982.8i	−0.669286	−	1.15924i
$623$	−26198.0			−1.68475
$624$	5531.92	−	3260.66i	0.354895	−	0.209184i
$625$	3928.53			0.251426
$626$	−17126.0	−	29663.2i	−1.09344	−	1.89389i
$627$	3906.82	+	6766.81i	0.248841	+	0.431006i
$628$	−7439.36	+	12885.4i	−0.472712	+	0.818761i
$629$	3755.00			0.238031
$630$	2688.35	−	4656.36i	0.170010	−	0.294466i
$631$	287.887	−	498.636i	0.0181626	−	0.0314586i	−0.856801	−	0.515647i	$-0.827552\pi$
$631$	287.887	−	498.636i	0.0181626	−	0.0314586i	0.874964	+	0.484188i	$0.160885\pi$
$632$	935.578			0.0588850
$633$	4540.95	−	7865.15i	0.285129	−	0.493857i
$634$	10881.9	+	18848.0i	0.681666	+	1.18068i
$635$	−350.120	−	606.426i	−0.0218805	−	0.0378981i
$636$	−2005.60			−0.125043
$637$	100.935	+	11203.7i	0.00627814	+	0.696873i
$638$	14464.3			0.897566
$639$	−4029.66	−	6979.58i	−0.249469	−	0.432094i
$640$	2867.40	+	4966.48i	0.177100	+	0.306746i
$641$	12260.9	−	21236.5i	0.755500	−	1.30856i	−0.189625	−	0.981857i	$-0.560727\pi$
$641$	12260.9	−	21236.5i	0.755500	−	1.30856i	0.945125	−	0.326708i	$-0.105939\pi$
$642$	17131.8			1.05317
$643$	11333.5	−	19630.2i	0.695099	−	1.20395i	−0.275048	−	0.961431i	$-0.588694\pi$
$643$	11333.5	−	19630.2i	0.695099	−	1.20395i	0.970147	−	0.242517i	$-0.0779730\pi$
$644$	748.281	−	1296.06i	0.0457864	−	0.0793043i
$645$	−4714.30			−0.287791
$646$	8021.67	−	13893.9i	0.488558	−	0.846207i
$647$	1198.73	+	2076.25i	0.0728389	+	0.126161i	0.900144	−	0.435592i	$-0.143461\pi$
$647$	1198.73	+	2076.25i	0.0728389	+	0.126161i	−0.827306	+	0.561752i	$0.810127\pi$
$648$	318.269	+	551.258i	0.0192944	+	0.0334189i
$649$	−854.078			−0.0516572
$650$	161.791	+	17958.8i	0.00976302	+	1.08369i
$651$	−22261.5			−1.34024
$652$	−5792.87	−	10033.5i	−0.347954	−	0.602674i
$653$	−10001.0	−	17322.3i	−0.599342	−	1.03809i	−0.992918	−	0.118799i	$-0.962095\pi$
$653$	−10001.0	−	17322.3i	−0.599342	−	1.03809i	0.393576	−	0.919292i	$-0.371238\pi$
$654$	−2842.79	+	4923.86i	−0.169972	+	0.294401i
$655$	13193.9			0.787068
$656$	−11745.7	+	20344.1i	−0.699073	+	1.21083i
$657$	−4358.70	+	7549.48i	−0.258826	+	0.448300i
$658$	−46992.5			−2.78413
$659$	1758.98	−	3046.64i	0.103976	−	0.180091i	−0.809343	−	0.587336i	$-0.800177\pi$
$659$	1758.98	−	3046.64i	0.103976	−	0.180091i	0.913319	+	0.407244i	$0.133510\pi$
$660$	2936.78	+	5086.66i	0.173203	+	0.299997i
$661$	−6791.71	−	11763.6i	−0.399647	−	0.692209i	0.594035	−	0.804439i	$-0.297534\pi$
$661$	−6791.71	−	11763.6i	−0.399647	−	0.692209i	−0.993682	+	0.112230i	$0.964201\pi$
$662$	−25618.2			−1.50405
$663$	−6046.32	−	3418.59i	−0.354177	−	0.200252i
$664$	−3778.24			−0.220819
$665$	5432.25	+	9408.93i	0.316772	+	0.548665i
$666$	−1445.67	−	2503.97i	−0.0841120	−	0.145686i
$667$	−317.713	+	550.295i	−0.0184436	+	0.0319453i
$668$	14533.1			0.841770
$669$	−2587.14	+	4481.05i	−0.149513	+	0.258965i
$670$	12436.6	−	21540.8i	0.717114	−	1.24208i
$671$	19955.1			1.14807
$672$	−9258.90	+	16036.9i	−0.531503	+	0.920590i
$673$	5447.92	+	9436.07i	0.312038	+	0.540466i	0.978804	−	0.204801i	$-0.0656549\pi$
$673$	5447.92	+	9436.07i	0.312038	+	0.540466i	−0.666765	+	0.745268i	$0.732322\pi$
$674$	7910.11	+	13700.7i	0.452057	+	0.782985i
$675$	2447.98			0.139589
$676$	−21657.9	+	390.264i	−1.23224	+	0.0222044i
$677$	1449.03			0.0822609			0.0411305	−	0.999154i	$-0.486904\pi$
$677$	1449.03			0.0822609			0.0411305	+	0.999154i	$0.486904\pi$
$678$	−8867.40	−	15358.8i	−0.502287	−	0.869986i
$679$	−200.907	−	347.982i	−0.0113551	−	0.0196676i
$680$	1137.26	−	1969.80i	0.0641353	−	0.111086i
$681$	5769.82			0.324670
$682$	22025.4	−	38149.2i	1.23665	−	2.14195i
$683$	7683.21	−	13307.7i	0.430439	−	0.745543i	−0.566472	−	0.824081i	$-0.691692\pi$
$683$	7683.21	−	13307.7i	0.430439	−	0.745543i	0.996911	+	0.0785385i	$0.0250253\pi$
$684$	−6819.77			−0.381229
$685$	3312.45	−	5737.34i	0.184763	−	0.320018i
$686$	5299.79	+	9179.51i	0.294966	+	0.510897i
$687$	560.989	+	971.661i	0.0311544	+	0.0539610i
$688$	12246.9			0.678644
$689$	−2766.61	−	1564.24i	−0.152974	−	0.0864918i
$690$	−467.393			−0.0257875
$691$	1009.85	+	1749.12i	0.0555957	+	0.0962946i	0.892484	−	0.451079i	$-0.148961\pi$
$691$	1009.85	+	1749.12i	0.0555957	+	0.0962946i	−0.836888	+	0.547374i	$0.815628\pi$
$692$	11478.0	+	19880.5i	0.630532	+	1.09211i
$693$	−3679.16	+	6372.50i	−0.201674	+	0.349309i
$694$	10651.4			0.582595
$695$	−1744.05	+	3020.79i	−0.0951880	+	0.164870i
$696$	−1190.51	+	2062.02i	−0.0648362	+	0.112300i
$697$	25410.0			1.38088
$698$	22505.3	−	38980.3i	1.22040	−	2.11379i
$699$	4641.74	+	8039.73i	0.251168	+	0.435036i
$700$	−10783.1	−	18677.0i	−0.582235	−	1.00846i
$701$	28031.6			1.51033			0.755164	−	0.655536i	$-0.227557\pi$
$701$	28031.6			1.51033			0.755164	+	0.655536i	$0.227557\pi$
$702$	48.1808	+	5348.06i	0.00259041	+	0.287535i
$703$	5842.42			0.313444
$704$	−12131.1	−	21011.7i	−0.649443	−	1.12487i
$705$	4051.10	+	7016.70i	0.216416	+	0.374843i
$706$	−19023.2	+	32949.2i	−1.01409	+	1.75646i
$707$	23112.3			1.22946
$708$	372.721	−	645.572i	0.0197849	−	0.0342685i
$709$	−9802.22	+	16977.9i	−0.519224	+	0.899323i	0.480526	+	0.876980i	$0.340446\pi$
$709$	−9802.22	+	16977.9i	−0.519224	+	0.899323i	−0.999750	+	0.0223423i	$0.992888\pi$
$710$	22174.5			1.17211
$711$	535.739	−	927.928i	0.0282585	−	0.0489452i
$712$	4266.79	+	7390.31i	0.224586	+	0.388994i
$713$	967.590	+	1675.91i	0.0508226	+	0.0880274i
$714$	15108.5			0.791905
$715$	83.8493	+	9307.26i	0.00438571	+	0.486813i
$716$	−21038.8			−1.09812
$717$	−1831.77	−	3172.73i	−0.0954099	−	0.165255i
$718$	−24005.9	−	41579.5i	−1.24776	−	2.16119i
$719$	7363.71	−	12754.3i	0.381947	−	0.661552i	−0.609393	−	0.792868i	$-0.708587\pi$
$719$	7363.71	−	12754.3i	0.381947	−	0.661552i	0.991341	+	0.131316i	$0.0419203\pi$
$720$	2408.23			0.124652
$721$	−32.6369	+	56.5287i	−0.00168580	+	0.00291989i
$722$	−2012.31	+	3485.43i	−0.103726	+	0.179659i
$723$	−436.202			−0.0224378
$724$	12252.5	−	21221.9i	0.628950	−	1.08937i
$725$	4578.42	+	7930.05i	0.234535	+	0.406227i
$726$	1157.03	+	2004.03i	0.0591477	+	0.102447i
$727$	−16890.5			−0.861668			−0.430834	−	0.902431i	$-0.641781\pi$
$727$	−16890.5			−0.861668			−0.430834	+	0.902431i	$0.641781\pi$
$728$	7655.57	−	4512.38i	0.389745	−	0.229725i
$729$	729.000			0.0370370
$730$	−11992.6	−	20771.7i	−0.608034	−	1.05315i
$731$	−6623.56	−	11472.3i	−0.335131	−	0.580465i
$732$	−8708.42	+	15083.4i	−0.439716	+	0.761611i
$733$	12553.6			0.632578			0.316289	−	0.948663i	$-0.397563\pi$
$733$	12553.6			0.632578			0.316289	+	0.948663i	$0.397563\pi$
$734$	−29453.1	+	51014.3i	−1.48111	+	2.56536i
$735$	−2100.97	+	3638.98i	−0.105436	+	0.182620i
$736$	1609.74			0.0806194
$737$	−17020.2	+	29479.8i	−0.850673	+	1.47341i
$738$	−9782.82	−	16944.3i	−0.487955	−	0.845163i
$739$	18937.4	+	32800.5i	0.942656	+	1.63273i	0.760378	+	0.649481i	$0.225014\pi$
$739$	18937.4	+	32800.5i	0.942656	+	1.63273i	0.182278	+	0.983247i	$0.441653\pi$
$740$	4391.78			0.218169
$741$	−9407.48	−	5319.00i	−0.466387	−	0.263695i
$742$	6913.16			0.342035
$743$	−17941.3	−	31075.3i	−0.885872	−	1.53438i	−0.844711	−	0.535223i	$-0.820227\pi$
$743$	−17941.3	−	31075.3i	−0.885872	−	1.53438i	−0.0411616	−	0.999153i	$-0.513106\pi$
$744$	3625.67	+	6279.84i	0.178661	+	0.309449i
$745$	−2323.82	+	4024.97i	−0.114279	+	0.197938i
$746$	−6732.40			−0.330416
$747$	−2163.53	+	3747.34i	−0.105970	+	0.183545i
$748$	−8252.32	+	14293.4i	−0.403389	+	0.698690i
$749$	−32600.3			−1.59037
$750$	−8010.71	+	13874.9i	−0.390013	+	0.675522i
$751$	90.8447	+	157.348i	0.00441407	+	0.00764540i	0.868224	−	0.496172i	$-0.165262\pi$
$751$	90.8447	+	157.348i	0.00441407	+	0.00764540i	−0.863810	+	0.503818i	$0.831928\pi$
$752$	−10524.0	−	18228.1i	−0.510333	−	0.883922i
$753$	2957.01			0.143107
$754$	−17234.5	+	10158.5i	−0.832420	+	0.490649i
$755$	786.425			0.0379085
$756$	−3211.19	−	5561.94i	−0.154484	−	0.267574i
$757$	245.526	+	425.264i	0.0117884	+	0.0204181i	0.871859	−	0.489756i	$-0.162914\pi$
$757$	245.526	+	425.264i	0.0117884	+	0.0204181i	−0.860071	+	0.510174i	$0.829581\pi$
$758$	19307.9	−	33442.3i	0.925191	−	1.60248i
$759$	639.655			0.0305903
$760$	1769.47	−	3064.81i	0.0844545	−	0.146279i
$761$	4056.50	−	7026.07i	0.193230	−	0.334684i	−0.753089	−	0.657919i	$-0.771437\pi$
$761$	4056.50	−	7026.07i	0.193230	−	0.334684i	0.946319	+	0.323235i	$0.104770\pi$
$762$	−1515.10			−0.0720291
$763$	5409.58	−	9369.67i	0.256671	−	0.444567i
$764$	11462.0	+	19852.8i	0.542777	+	0.940118i
$765$	−1302.46	−	2255.93i	−0.0615562	−	0.106619i
$766$	−40363.3			−1.90390
$767$	1017.65	−	599.830i	0.0479078	−	0.0282381i
$768$	−4773.98			−0.224305
$769$	−9932.33	−	17203.3i	−0.465759	−	0.806719i	0.533476	−	0.845815i	$-0.320885\pi$
$769$	−9932.33	−	17203.3i	−0.465759	−	0.806719i	−0.999235	+	0.0390962i	$0.987552\pi$
$770$	−10122.9	−	17533.4i	−0.473771	−	0.820596i
$771$	4393.98	−	7610.59i	0.205247	−	0.355498i
$772$	33030.6			1.53989
$773$	−4523.71	+	7835.29i	−0.210487	+	0.364574i	−0.951867	−	0.306511i	$-0.900838\pi$
$773$	−4523.71	+	7835.29i	−0.210487	+	0.364574i	0.741380	+	0.671085i	$0.234172\pi$
$774$	−5100.12	+	8833.66i	−0.236848	+	0.410232i
$775$	27887.0			1.29256
$776$	−65.4424	+	113.350i	−0.00302738	+	0.00524358i
$777$	2750.99	+	4764.85i	0.127016	+	0.219997i
$778$	15565.6	+	26960.4i	0.717293	+	1.24239i
$779$	39535.5			1.81837
$780$	−7071.67	−	3998.32i	−0.324623	−	0.183542i
$781$	−30347.1			−1.39040
$782$	−656.685	−	1137.41i	−0.0300294	−	0.0520125i
$783$	1363.44	+	2361.54i	0.0622289	+	0.107784i
$784$	5457.92	−	9453.39i	0.248630	−	0.430639i
$785$	−8842.45			−0.402039
$786$	14273.7	−	24722.8i	0.647744	−	1.12193i
$787$	7509.20	−	13006.3i	0.340120	−	0.589105i	−0.644335	−	0.764743i	$-0.722866\pi$
$787$	7509.20	−	13006.3i	0.340120	−	0.589105i	0.984455	+	0.175639i	$0.0561991\pi$
$788$	−38050.9			−1.72019
$789$	3357.00	−	5814.50i	0.151473	−	0.262360i
$790$	1474.04	+	2553.11i	0.0663848	+	0.114982i
$791$	16873.9	+	29226.4i	0.758491	+	1.31375i
$792$	2396.86			0.107536
$793$	−23776.9	+	14014.7i	−1.06474	+	0.627587i
$794$	49429.9			2.20932
$795$	−595.965	−	1032.24i	−0.0265870	−	0.0460501i
$796$	20131.2	+	34868.2i	0.896396	+	1.55260i
$797$	−15970.5	+	27661.8i	−0.709794	+	1.22940i	0.255139	+	0.966904i	$0.417879\pi$
$797$	−15970.5	+	27661.8i	−0.709794	+	1.22940i	−0.964933	+	0.262495i	$0.915455\pi$
$798$	23507.3			1.04279
$799$	−11383.5	+	19716.9i	−0.504030	+	0.873006i
$800$	11598.6	−	20089.4i	0.512592	−	0.887835i
$801$	9773.17			0.431108
$802$	−29936.6	+	51851.7i	−1.31808	+	2.28298i
$803$	16412.5	+	28427.3i	0.721277	+	1.24929i
$804$	−14855.3	−	25730.1i	−0.651623	−	1.12864i
$805$	889.409			0.0389411
$806$	548.868	+	60924.3i	0.0239864	+	2.66249i
$807$	−5777.95			−0.252037
$808$	−3764.23	−	6519.84i	−0.163892	−	0.283870i
$809$	−13630.0	−	23607.9i	−0.592344	−	1.02597i	−0.993916	−	0.110142i	$-0.964869\pi$
$809$	−13630.0	−	23607.9i	−0.592344	−	1.02597i	0.401572	−	0.915827i	$-0.368464\pi$
$810$	−1002.89	+	1737.06i	−0.0435036	+	0.0753505i
$811$	−20707.8			−0.896607			−0.448303	−	0.893881i	$-0.647972\pi$
$811$	−20707.8			−0.896607			−0.448303	+	0.893881i	$0.647972\pi$
$812$	12011.7	−	20804.8i	0.519121	−	0.899145i
$813$	−5343.43	+	9255.09i	−0.230507	+	0.399250i
$814$	−10887.2			−0.468793
$815$	3442.71	−	5962.95i	0.147967	−	0.256286i
$816$	3383.54	+	5860.47i	0.145156	+	0.251418i
$817$	−10305.6	−	17849.8i	−0.441307	−	0.764366i
$818$	−11426.0			−0.488385
$819$	−91.6839	−	10176.9i	−0.00391171	−	0.434200i
$820$	29719.1			1.26565
$821$	−7829.28	−	13560.7i	−0.332818	−	0.576458i	0.650245	−	0.759724i	$-0.274666\pi$
$821$	−7829.28	−	13560.7i	−0.332818	−	0.576458i	−0.983063	+	0.183267i	$0.941333\pi$
$822$	−7167.10	−	12413.8i	−0.304113	−	0.526740i
$823$	2053.29	−	3556.40i	0.0869662	−	0.150630i	−0.819261	−	0.573421i	$-0.805616\pi$
$823$	2053.29	−	3556.40i	0.0869662	−	0.150630i	0.906227	+	0.422791i	$0.138949\pi$
$824$	21.2619			0.000898900
$825$	4608.89	−	7982.83i	0.194498	−	0.336881i
$826$	−1284.74	+	2225.24i	−0.0541186	+	0.0937362i
$827$	16747.3			0.704184			0.352092	−	0.935965i	$-0.385470\pi$
$827$	16747.3			0.704184			0.352092	+	0.935965i	$0.385470\pi$
$828$	−279.146	+	483.496i	−0.0117162	+	0.0202930i
$829$	14578.5	+	25250.8i	0.610776	+	1.05790i	0.991110	+	0.133046i	$0.0424758\pi$
$829$	14578.5	+	25250.8i	0.610776	+	1.05790i	−0.380334	+	0.924849i	$0.624191\pi$
$830$	−5952.76	−	10310.5i	−0.248944	−	0.431183i
$831$	4312.27			0.180013
$832$	29211.2	+	16516.0i	1.21721	+	0.688210i
$833$	−11807.4			−0.491119
$834$	3773.57	+	6536.02i	0.156676	+	0.271372i
$835$	4318.52	+	7479.89i	0.178980	+	0.310003i
$836$	−12839.8	+	22239.2i	−0.531189	+	0.920047i
$837$	8304.66			0.342952
$838$	15092.3	−	26140.7i	0.622144	−	1.07758i
$839$	−22909.7	+	39680.8i	−0.942707	+	1.63282i	−0.182429	+	0.983219i	$0.558396\pi$
$839$	−22909.7	+	39680.8i	−0.942707	+	1.63282i	−0.760278	+	0.649598i	$0.774937\pi$
$840$	3332.72			0.136892
$841$	7094.47	−	12288.0i	0.290888	−	0.503833i
$842$	−7197.92	−	12467.2i	−0.294604	−	0.510270i
$843$	−5870.26	−	10167.6i	−0.239837	−	0.415410i
$844$	29847.7			1.21730
$845$	−6636.51	−	11030.9i	−0.270181	−	0.449083i
$846$	17530.6			0.712427
$847$	−2201.72	−	3813.49i	−0.0893175	−	0.154703i
$848$	1548.20	+	2681.57i	0.0626952	+	0.108591i
$849$	−4818.47	+	8345.83i	−0.194781	+	0.337371i
$850$	−18926.4			−0.763729
$851$	239.142	−	414.205i	0.00963298	−	0.0166848i
$852$	13243.5	−	22938.5i	0.532530	−	0.922370i
$853$	17351.1			0.696471			0.348235	−	0.937407i	$-0.386781\pi$
$853$	17351.1			0.696471			0.348235	+	0.937407i	$0.386781\pi$
$854$	30017.3	−	51991.5i	1.20278	−	2.08327i
$855$	−2026.50	−	3510.00i	−0.0810583	−	0.140397i
$856$	5309.52	+	9196.36i	0.212004	+	0.367202i
$857$	−21768.1			−0.867659			−0.433829	−	0.900995i	$-0.642838\pi$
$857$	−21768.1			−0.867659			−0.433829	+	0.900995i	$0.642838\pi$
$858$	17530.7	+	9911.85i	0.697538	+	0.394388i
$859$	−29878.4			−1.18677			−0.593387	−	0.804918i	$-0.702209\pi$
$859$	−29878.4			−1.18677			−0.593387	+	0.804918i	$0.702209\pi$
$860$	−7746.80	−	13417.8i	−0.307167	−	0.532029i
$861$	18615.9	+	32243.6i	0.736849	+	1.27626i
$862$	10930.6	−	18932.4i	0.431901	−	0.748074i
$863$	−15067.7			−0.594335			−0.297168	−	0.954825i	$-0.596042\pi$
$863$	−15067.7			−0.594335			−0.297168	+	0.954825i	$0.596042\pi$
$864$	3454.03	−	5982.56i	0.136005	−	0.235568i
$865$	−6821.40	+	11815.0i	−0.268132	+	0.464419i
$866$	−46296.3			−1.81664
$867$	−3709.61	+	6425.23i	−0.145311	+	0.251686i
$868$	−36581.4	−	63360.8i	−1.43047	−	2.47765i
$869$	−2017.31	−	3494.08i	−0.0787486	−	0.136397i
$870$	−7502.75			−0.292376
$871$	−424.138	−	47079.3i	−0.0164999	−	1.83148i
$872$	−3524.17			−0.136862
$873$	74.9485	+	129.815i	0.00290564	+	0.00503272i
$874$	−1021.74	−	1769.70i	−0.0395432	−	0.0684909i
$875$	15243.7	−	26402.8i	0.588949	−	1.02009i
$876$	−28649.8			−1.10501
$877$	10559.8	−	18290.1i	0.406588	−	0.704232i	−0.587917	−	0.808922i	$-0.700052\pi$
$877$	10559.8	−	18290.1i	0.406588	−	0.704232i	0.994505	+	0.104690i	$0.0333850\pi$
$878$	25002.3	−	43305.2i	0.961032	−	1.66456i
$879$	14705.3			0.564275
$880$	4534.05	−	7853.20i	0.173685	−	0.300831i
$881$	−15826.2	−	27411.9i	−0.605221	−	1.04827i	−0.992016	−	0.126108i	$-0.959751\pi$
$881$	−15826.2	−	27411.9i	−0.605221	−	1.04827i	0.386795	−	0.922166i	$-0.373582\pi$
$882$	4545.83	+	7873.60i	0.173544	+	0.300587i
$883$	11701.6			0.445969			0.222984	−	0.974822i	$-0.428420\pi$
$883$	11701.6			0.445969			0.222984	+	0.974822i	$0.428420\pi$
$884$	−205.646	−	22826.7i	−0.00782423	−	0.868488i
$885$	443.017			0.0168270
$886$	28483.3	+	49334.5i	1.08004	+	1.87068i
$887$	−11254.0	−	19492.4i	−0.426010	−	0.737871i	0.570504	−	0.821295i	$-0.306748\pi$
$887$	−11254.0	−	19492.4i	−0.426010	−	0.737871i	−0.996514	+	0.0834239i	$0.973414\pi$
$888$	896.091	−	1552.07i	0.0338635	−	0.0586534i
$889$	2883.10			0.108769
$890$	−13445.0	+	23287.4i	−0.506379	+	0.877075i
$891$	1372.51	−	2377.26i	0.0516059	−	0.0893841i
$892$	−17005.3			−0.638318
$893$	−17711.7	+	30677.5i	−0.663716	+	1.14959i
$894$	5028.00	+	8708.75i	0.188100	+	0.325799i
$895$	−6251.69	−	10828.2i	−0.233487	−	0.404412i
$896$	−23611.9			−0.880377
$897$	−762.163	+	449.238i	−0.0283700	+	0.0167220i
$898$	28628.7			1.06387
$899$	15532.1	+	26902.3i	0.576222	+	0.998046i
$900$	4022.65	+	6967.44i	0.148987	+	0.258053i
$901$	1674.65	−	2900.58i	0.0619210	−	0.107250i
$902$	−73673.8			−2.71959
$903$	9705.08	−	16809.7i	0.357658	−	0.619481i
$904$	5496.41	−	9520.06i	0.202221	−	0.350257i
$905$	14563.3			0.534919
$906$	850.786	−	1473.61i	0.0311981	−	0.0540367i
$907$	−9359.32	−	16210.8i	−0.342636	−	0.593464i	0.642285	−	0.766466i	$-0.277987\pi$
$907$	−9359.32	−	16210.8i	−0.342636	−	0.593464i	−0.984921	+	0.173002i	$0.944653\pi$
$908$	9481.29	+	16422.1i	0.346528	+	0.600205i
$909$	−8622.03			−0.314604
$910$	24375.6	+	13781.9i	0.887958	+	0.502052i
$911$	18616.7			0.677057			0.338529	−	0.940956i	$-0.390071\pi$
$911$	18616.7			0.677057			0.338529	+	0.940956i	$0.390071\pi$
$912$	5264.46	+	9118.32i	0.191145	+	0.331072i
$913$	8146.69	+	14110.5i	0.295308	+	0.511488i
$914$	−9809.44	+	16990.4i	−0.354997	+	0.614873i
$915$	−10350.8			−0.373977
$916$	−1843.70	+	3193.38i	−0.0665038	+	0.115188i
$917$	−27161.7	+	47045.4i	−0.978143	+	1.69419i
$918$	−5636.21			−0.202639
$919$	27382.2	−	47427.3i	0.982867	−	1.70238i	0.331812	−	0.943346i	$-0.392340\pi$
$919$	27382.2	−	47427.3i	0.982867	−	1.70238i	0.651056	−	0.759030i	$-0.274326\pi$
$920$	−144.856	−	250.897i	−0.00519103	−	0.00899113i
$921$	8700.94	+	15070.5i	0.311298	+	0.539185i
$922$	−10397.6			−0.371397
$923$	36159.2	−	21313.2i	1.28949	−	0.760056i
$924$	−24183.2			−0.861006
$925$	−3446.16	−	5968.93i	−0.122496	−	0.212170i
$926$	9064.90	+	15700.9i	0.321697	+	0.557195i
$927$	12.1752	−	21.0880i	0.000431376	−	0.000747165i
$928$	25840.1			0.914055
$929$	15916.0	−	27567.4i	0.562097	−	0.973581i	−0.435216	−	0.900326i	$-0.643328\pi$
$929$	15916.0	−	27567.4i	0.562097	−	0.973581i	0.997313	−	0.0732550i	$-0.0233387\pi$
$930$	−11424.8	+	19788.3i	−0.402831	+	0.697724i
$931$	−18371.2			−0.646713
$932$	−15255.1	+	26422.7i	−0.536157	+	0.928651i
$933$	−7370.27	−	12765.7i	−0.258619	−	0.447942i
$934$	−18592.5	−	32203.2i	−0.651355	−	1.12818i
$935$	−9808.73			−0.343080
$936$	−2855.91	+	1683.35i	−0.0997312	+	0.0587841i
$937$	−27408.7			−0.955607			−0.477803	−	0.878467i	$-0.658567\pi$
$937$	−27408.7			−0.955607			−0.477803	+	0.878467i	$0.658567\pi$
$938$	51205.1	+	88689.8i	1.78241	+	3.08723i
$939$	−12157.5	−	21057.3i	−0.422517	−	0.731822i
$940$	−13314.0	+	23060.5i	−0.461972	+	0.800159i
$941$	54837.8			1.89975			0.949874	−	0.312634i	$-0.101211\pi$
$941$	54837.8			1.89975			0.949874	+	0.312634i	$0.101211\pi$
$942$	−9566.12	+	16569.0i	−0.330872	+	0.573086i
$943$	1618.27	−	2802.92i	0.0558833	−	0.0967928i
$944$	−1150.87			−0.0396799
$945$	1908.41	−	3305.47i	0.0656938	−	0.113785i
$946$	19204.3	+	33262.9i	0.660028	+	1.14320i
$947$	19853.9	+	34388.0i	0.681273	+	1.18000i	0.974593	+	0.223984i	$0.0719065\pi$
$947$	19853.9	+	34388.0i	0.681273	+	1.18000i	−0.293320	+	0.956014i	$0.594760\pi$
$948$	3521.43			0.120644
$949$	−39520.8	−	22345.0i	−1.35184	−	0.764332i
$950$	−29447.6			−1.00569
$951$	7724.88	+	13379.9i	0.263403	+	0.456227i
$952$	4682.45	+	8110.24i	0.159411	+	0.276107i
$953$	8553.32	−	14814.8i	0.290734	−	0.503566i	−0.683250	−	0.730185i	$-0.739434\pi$
$953$	8553.32	−	14814.8i	0.290734	−	0.503566i	0.973983	+	0.226619i	$0.0727673\pi$
$954$	−2578.96			−0.0875228
$955$	−6811.90	+	11798.6i	−0.230815	+	0.399783i
$956$	6020.15	−	10427.2i	0.203667	−	0.352761i
$957$	10268.0			0.346829
$958$	−23187.0	+	40161.1i	−0.781982	+	1.35443i
$959$	13638.4	+	23622.3i	0.459234	+	0.795417i
$960$	6292.50	+	10898.9i	0.211552	+	0.366418i
$961$	64814.4			2.17564
$962$	12972.4	−	7646.25i	0.434768	−	0.256263i
$963$	12161.6			0.406958
$964$	−716.791	−	1241.52i	−0.0239484	−	0.0414799i
$965$	9815.06	+	17000.2i	0.327417	+	0.567104i
$966$	962.199	−	1666.58i	0.0320479	−	0.0555085i
$967$	−23417.5			−0.778756			−0.389378	−	0.921078i	$-0.627310\pi$
$967$	−23417.5			−0.778756			−0.389378	+	0.921078i	$0.627310\pi$
$968$	−717.175	+	1242.18i	−0.0238129	+	0.0412452i
$969$	5694.44	−	9863.06i	0.188784	−	0.326984i
$970$	−412.428			−0.0136518
$971$	−8215.31	+	14229.3i	−0.271516	+	0.470279i	−0.969250	−	0.246077i	$-0.920858\pi$
$971$	−8215.31	+	14229.3i	−0.271516	+	0.470279i	0.697734	+	0.716357i	$0.254192\pi$
$972$	1197.93	+	2074.88i	0.0395306	+	0.0684690i
$973$	−7180.78	−	12437.5i	−0.236593	−	0.409792i
$974$	22015.9			0.724267
$975$	114.852	+	12748.6i	0.00377254	+	0.418751i
$976$	26889.5			0.881879
$977$	5277.32	+	9140.58i	0.172811	+	0.299318i	0.939402	−	0.342819i	$-0.111382\pi$
$977$	5277.32	+	9140.58i	0.172811	+	0.299318i	−0.766591	+	0.642136i	$0.778048\pi$
$978$	−7448.92	−	12901.9i	−0.243548	−	0.421838i
$979$	18400.3	−	31870.2i	0.600689	−	1.04042i
$980$	−13809.7			−0.450138
$981$	−2018.05	+	3495.36i	−0.0656791	+	0.113760i
$982$	−18550.7	+	32130.8i	−0.602829	+	1.04413i
$983$	1534.33			0.0497839			0.0248919	−	0.999690i	$-0.492076\pi$
$983$	1534.33			0.0497839			0.0248919	+	0.999690i	$0.492076\pi$
$984$	6063.83	−	10502.9i	0.196451	−	0.340263i
$985$	−11306.9	−	19584.1i	−0.365753	−	0.633502i
$986$	−10541.3	−	18258.1i	−0.340471	−	0.589712i
$987$	−33359.1			−1.07582
$988$	−319.965	−	35516.1i	−0.0103031	−	1.14364i
$989$	−1687.31			−0.0542502
$990$	3776.35	+	6540.82i	0.121232	+	0.209981i
$991$	9009.08	+	15604.2i	0.288782	+	0.500185i	0.973519	−	0.228605i	$-0.0734165\pi$
$991$	9009.08	+	15604.2i	0.288782	+	0.500185i	−0.684737	+	0.728790i	$0.740083\pi$
$992$	39347.8	−	68152.5i	1.25937	−	2.18129i
$993$	−18185.9			−0.581181
$994$	−45649.6	+	79067.3i	−1.45666	+	2.52300i
$995$	−11964.0	+	20722.2i	−0.381190	+	0.660240i
$996$	−14220.9			−0.452417
$997$	−24143.8	+	41818.4i	−0.766944	+	1.32839i	0.172269	+	0.985050i	$0.444890\pi$
$997$	−24143.8	+	41818.4i	−0.766944	+	1.32839i	−0.939213	+	0.343336i	$0.888443\pi$
$998$	−32942.2	−	57057.6i	−1.04486	−	1.80975i
$999$	−1026.26	−	1777.53i	−0.0325018	−	0.0562947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.e.c.16.4	✓	8
3.2	odd	2		117.4.g.e.55.1		8
4.3	odd	2		624.4.q.i.289.2		8
13.2	odd	12		507.4.b.h.337.7		8
13.3	even	3		507.4.a.m.1.1		4
13.9	even	3	inner	39.4.e.c.22.4	yes	8
13.10	even	6		507.4.a.i.1.4		4
13.11	odd	12		507.4.b.h.337.2		8
39.23	odd	6		1521.4.a.bb.1.1		4
39.29	odd	6		1521.4.a.v.1.4		4
39.35	odd	6		117.4.g.e.100.1		8
52.35	odd	6		624.4.q.i.529.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.e.c.16.4	✓	8	1.1	even	1	trivial
39.4.e.c.22.4	yes	8	13.9	even	3	inner
117.4.g.e.55.1		8	3.2	odd	2
117.4.g.e.100.1		8	39.35	odd	6
507.4.a.i.1.4		4	13.10	even	6
507.4.a.m.1.1		4	13.3	even	3
507.4.b.h.337.2		8	13.11	odd	12
507.4.b.h.337.7		8	13.2	odd	12
624.4.q.i.289.2		8	4.3	odd	2
624.4.q.i.529.2		8	52.35	odd	6
1521.4.a.v.1.4		4	39.29	odd	6
1521.4.a.bb.1.1		4	39.23	odd	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:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	39.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.11303 + 3.65987i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-4.92977 + 8.53861i) q^{4} -5.85953 q^{5} +(-6.33908 + 10.9796i) q^{6} +(12.0627 - 20.8932i) q^{7} -7.85849 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(2.11303 + 3.65987i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-4.92977 + 8.53861i) q^{4} -5.85953 q^{5} +(-6.33908 + 10.9796i) q^{6} +(12.0627 - 20.8932i) q^{7} -7.85849 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-12.3814 - 21.4451i) q^{10} +(16.9446 + 29.3489i) q^{11} -29.5786 q^{12} +(-40.8020 - 23.0694i) q^{13} +101.955 q^{14} +(-8.78930 - 15.2235i) q^{15} +(22.8329 + 39.5478i) q^{16} +(24.6978 - 42.7779i) q^{17} -38.0345 q^{18} +(38.4274 - 66.5582i) q^{19} +(28.8861 - 50.0322i) q^{20} +72.3763 q^{21} +(-71.6088 + 124.030i) q^{22} +(-3.14582 - 5.44871i) q^{23} +(-11.7877 - 20.4169i) q^{24} -90.6659 q^{25} +(-1.78447 - 198.076i) q^{26} -27.0000 q^{27} +(118.933 + 205.998i) q^{28} +(-50.4977 - 87.4645i) q^{29} +(37.1441 - 64.3354i) q^{30} -307.580 q^{31} +(-127.927 + 221.576i) q^{32} +(-50.8338 + 88.0467i) q^{33} +208.749 q^{34} +(-70.6819 + 122.425i) q^{35} +(-44.3679 - 76.8475i) q^{36} +(38.0095 + 65.8343i) q^{37} +324.793 q^{38} +(-1.26677 - 140.611i) q^{39} +46.0471 q^{40} +(257.209 + 445.499i) q^{41} +(152.933 + 264.888i) q^{42} +(134.092 - 232.254i) q^{43} -334.132 q^{44} +(26.3679 - 45.6705i) q^{45} +(13.2944 - 23.0266i) q^{46} -460.912 q^{47} +(-68.4988 + 118.643i) q^{48} +(-119.519 - 207.012i) q^{49} +(-191.579 - 331.825i) q^{50} +148.187 q^{51} +(398.125 - 234.665i) q^{52} +67.8057 q^{53} +(-57.0517 - 98.8165i) q^{54} +(-99.2874 - 171.971i) q^{55} +(-94.7947 + 164.189i) q^{56} +230.564 q^{57} +(213.406 - 369.630i) q^{58} +(-12.6010 + 21.8256i) q^{59} +173.317 q^{60} +(294.416 - 509.944i) q^{61} +(-649.925 - 1125.70i) q^{62} +(108.565 + 188.039i) q^{63} -715.927 q^{64} +(239.080 + 135.176i) q^{65} -429.653 q^{66} +(502.230 + 869.888i) q^{67} +(243.509 + 421.770i) q^{68} +(9.43745 - 16.3461i) q^{69} -597.411 q^{70} +(-447.740 + 775.509i) q^{71} +(35.3632 - 61.2508i) q^{72} +968.599 q^{73} +(-160.630 + 278.219i) q^{74} +(-135.999 - 235.557i) q^{75} +(378.876 + 656.233i) q^{76} +817.592 q^{77} +(511.941 - 301.751i) q^{78} -119.053 q^{79} +(-133.790 - 231.732i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-1086.98 + 1882.70i) q^{82} +480.784 q^{83} +(-356.798 + 617.993i) q^{84} +(-144.718 + 250.658i) q^{85} +1133.36 q^{86} +(151.493 - 262.394i) q^{87} +(-133.159 - 230.638i) q^{88} +(-542.954 - 940.423i) q^{89} +222.864 q^{90} +(-974.179 + 574.205i) q^{91} +62.0325 q^{92} +(-461.370 - 799.116i) q^{93} +(-973.920 - 1686.88i) q^{94} +(-225.167 + 390.000i) q^{95} -767.563 q^{96} +(8.32761 - 14.4239i) q^{97} +(505.092 - 874.845i) q^{98} -305.003 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 12 q^{3} - 22 q^{4} - 12 q^{5} + 6 q^{6} + 14 q^{7} + 108 q^{8} - 36 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 12 * q^3 - 22 * q^4 - 12 * q^5 + 6 * q^6 + 14 * q^7 + 108 * q^8 - 36 * q^9	\( 8 q - 2 q^{2} + 12 q^{3} - 22 q^{4} - 12 q^{5} + 6 q^{6} + 14 q^{7} + 108 q^{8} - 36 q^{9} + 62 q^{10} - 40 q^{11} - 132 q^{12} - 60 q^{13} + 80 q^{14} - 18 q^{15} - 122 q^{16} - 98 q^{17} + 36 q^{18} - 124 q^{19} + 466 q^{20} + 84 q^{21} - 220 q^{22} - 104 q^{23} + 162 q^{24} - 116 q^{25} + 14 q^{26} - 216 q^{27} + 144 q^{28} - 194 q^{29} - 186 q^{30} + 52 q^{31} - 654 q^{32} + 120 q^{33} + 2124 q^{34} - 88 q^{35} - 198 q^{36} - 102 q^{37} + 664 q^{38} + 342 q^{39} - 1996 q^{40} + 1054 q^{41} + 120 q^{42} - 450 q^{43} - 88 q^{44} + 54 q^{45} + 172 q^{46} - 192 q^{47} + 366 q^{48} - 1070 q^{49} - 996 q^{50} - 588 q^{51} + 2280 q^{52} + 524 q^{53} + 54 q^{54} - 204 q^{55} - 2164 q^{56} - 744 q^{57} - 722 q^{58} - 308 q^{59} + 2796 q^{60} + 928 q^{61} - 2780 q^{62} + 126 q^{63} + 2052 q^{64} + 2346 q^{65} - 1320 q^{66} + 1134 q^{67} - 1786 q^{68} + 312 q^{69} - 4648 q^{70} - 1064 q^{71} - 486 q^{72} + 1904 q^{73} - 1158 q^{74} - 174 q^{75} + 1708 q^{76} + 5016 q^{77} + 480 q^{78} - 1492 q^{79} + 2922 q^{80} - 324 q^{81} - 1734 q^{82} - 808 q^{83} - 432 q^{84} + 1394 q^{85} + 6336 q^{86} + 582 q^{87} - 3060 q^{88} - 1620 q^{89} - 1116 q^{90} + 3278 q^{91} + 664 q^{92} + 78 q^{93} + 772 q^{94} - 2204 q^{95} - 3924 q^{96} - 2166 q^{97} + 1906 q^{98} + 720 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 12 * q^3 - 22 * q^4 - 12 * q^5 + 6 * q^6 + 14 * q^7 + 108 * q^8 - 36 * q^9 + 62 * q^10 - 40 * q^11 - 132 * q^12 - 60 * q^13 + 80 * q^14 - 18 * q^15 - 122 * q^16 - 98 * q^17 + 36 * q^18 - 124 * q^19 + 466 * q^20 + 84 * q^21 - 220 * q^22 - 104 * q^23 + 162 * q^24 - 116 * q^25 + 14 * q^26 - 216 * q^27 + 144 * q^28 - 194 * q^29 - 186 * q^30 + 52 * q^31 - 654 * q^32 + 120 * q^33 + 2124 * q^34 - 88 * q^35 - 198 * q^36 - 102 * q^37 + 664 * q^38 + 342 * q^39 - 1996 * q^40 + 1054 * q^41 + 120 * q^42 - 450 * q^43 - 88 * q^44 + 54 * q^45 + 172 * q^46 - 192 * q^47 + 366 * q^48 - 1070 * q^49 - 996 * q^50 - 588 * q^51 + 2280 * q^52 + 524 * q^53 + 54 * q^54 - 204 * q^55 - 2164 * q^56 - 744 * q^57 - 722 * q^58 - 308 * q^59 + 2796 * q^60 + 928 * q^61 - 2780 * q^62 + 126 * q^63 + 2052 * q^64 + 2346 * q^65 - 1320 * q^66 + 1134 * q^67 - 1786 * q^68 + 312 * q^69 - 4648 * q^70 - 1064 * q^71 - 486 * q^72 + 1904 * q^73 - 1158 * q^74 - 174 * q^75 + 1708 * q^76 + 5016 * q^77 + 480 * q^78 - 1492 * q^79 + 2922 * q^80 - 324 * q^81 - 1734 * q^82 - 808 * q^83 - 432 * q^84 + 1394 * q^85 + 6336 * q^86 + 582 * q^87 - 3060 * q^88 - 1620 * q^89 - 1116 * q^90 + 3278 * q^91 + 664 * q^92 + 78 * q^93 + 772 * q^94 - 2204 * q^95 - 3924 * q^96 - 2166 * q^97 + 1906 * q^98 + 720 * q^99

Introduction

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