LMFDB - Embedded newform 26.4.e.a.23.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,4,Mod(17,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("26.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	26.e (of order $6$, 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:	$1.53404966015$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
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} + 122x^{6} + 5305x^{4} + 97056x^{2} + 627264 $ x^8 + 122x^6 + 5305x^4 + 97056*x^2 + 627264
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.4
Root			$5.87513i$ of defining polynomial
Character	$\chi$	$=$	26.23
Dual form			26.4.e.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 - 1.00000i) q^{2} +(2.43757 + 4.22199i) q^{3} +(2.00000 - 3.46410i) q^{4} -0.110135i q^{5} +(8.44398 + 4.87513i) q^{6} +(-14.0246 - 8.09712i) q^{7} -8.00000i q^{8} +(1.61655 - 2.79994i) q^{9} +O(q^{10})$	\(q+(1.73205 - 1.00000i) q^{2} +(2.43757 + 4.22199i) q^{3} +(2.00000 - 3.46410i) q^{4} -0.110135i q^{5} +(8.44398 + 4.87513i) q^{6} +(-14.0246 - 8.09712i) q^{7} -8.00000i q^{8} +(1.61655 - 2.79994i) q^{9} +(-0.110135 - 0.190760i) q^{10} +(-33.6077 + 19.4034i) q^{11} +19.5005 q^{12} +(-23.6233 + 40.4838i) q^{13} -32.3885 q^{14} +(0.464989 - 0.268462i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(47.2228 - 81.7923i) q^{17} -6.46618i q^{18} +(33.5104 + 19.3472i) q^{19} +(-0.381520 - 0.220270i) q^{20} -78.9491i q^{21} +(-38.8068 + 67.2154i) q^{22} +(46.2232 + 80.0610i) q^{23} +(33.7759 - 19.5005i) q^{24} +124.988 q^{25} +(-0.433024 + 93.7433i) q^{26} +147.390 q^{27} +(-56.0985 + 32.3885i) q^{28} +(-96.2678 - 166.741i) q^{29} +(0.536924 - 0.929979i) q^{30} +158.597i q^{31} +(-27.7128 - 16.0000i) q^{32} +(-163.842 - 94.5942i) q^{33} -188.891i q^{34} +(-0.891778 + 1.54460i) q^{35} +(-6.46618 - 11.1998i) q^{36} +(-248.280 + 143.344i) q^{37} +77.3889 q^{38} +(-228.506 - 1.05553i) q^{39} -0.881082 q^{40} +(202.882 - 117.134i) q^{41} +(-78.9491 - 136.744i) q^{42} +(-262.935 + 455.417i) q^{43} +155.227i q^{44} +(-0.308372 - 0.178039i) q^{45} +(160.122 + 92.4465i) q^{46} -320.423i q^{47} +(39.0011 - 67.5518i) q^{48} +(-40.3733 - 69.9286i) q^{49} +(216.485 - 124.988i) q^{50} +460.435 q^{51} +(92.9933 + 162.801i) q^{52} +414.352 q^{53} +(255.287 - 147.390i) q^{54} +(2.13700 + 3.70139i) q^{55} +(-64.7770 + 112.197i) q^{56} +188.641i q^{57} +(-333.482 - 192.536i) q^{58} +(-223.006 - 128.753i) q^{59} -2.14769i q^{60} +(-71.6545 + 124.109i) q^{61} +(158.597 + 274.698i) q^{62} +(-45.3429 + 26.1787i) q^{63} -64.0000 q^{64} +(4.45869 + 2.60176i) q^{65} -378.377 q^{66} +(392.729 - 226.742i) q^{67} +(-188.891 - 327.169i) q^{68} +(-225.344 + 390.308i) q^{69} +3.56711i q^{70} +(-654.631 - 377.952i) q^{71} +(-22.3995 - 12.9324i) q^{72} -641.108i q^{73} +(-286.689 + 496.559i) q^{74} +(304.666 + 527.697i) q^{75} +(134.042 - 77.3889i) q^{76} +628.447 q^{77} +(-396.839 + 226.677i) q^{78} -588.290 q^{79} +(-1.52608 + 0.881082i) q^{80} +(315.627 + 546.682i) q^{81} +(234.267 - 405.763i) q^{82} -744.654i q^{83} +(-273.488 - 157.898i) q^{84} +(-9.00822 - 5.20090i) q^{85} +1051.74i q^{86} +(469.318 - 812.883i) q^{87} +(155.227 + 268.861i) q^{88} +(-1081.79 + 624.570i) q^{89} -0.712154 q^{90} +(659.111 - 376.489i) q^{91} +369.786 q^{92} +(-669.593 + 386.590i) q^{93} +(-320.423 - 554.990i) q^{94} +(2.13081 - 3.69067i) q^{95} -156.004i q^{96} +(1043.14 + 602.258i) q^{97} +(-139.857 - 80.7466i) q^{98} +125.466i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} + 16 q^{4} + 18 q^{7} - 22 q^{9}+O(q^{10}) $ 8 * q - 6 * q^3 + 16 * q^4 + 18 * q^7 - 22 * q^9	\( 8 q - 6 q^{3} + 16 q^{4} + 18 q^{7} - 22 q^{9} - 8 q^{10} - 18 q^{11} - 48 q^{12} - 130 q^{13} + 80 q^{14} - 192 q^{15} - 64 q^{16} + 112 q^{17} + 594 q^{19} + 72 q^{20} - 72 q^{22} - 230 q^{23} - 180 q^{25} - 184 q^{26} + 468 q^{27} + 72 q^{28} + 32 q^{29} + 328 q^{30} - 42 q^{33} - 128 q^{35} + 88 q^{36} - 768 q^{37} - 576 q^{38} - 230 q^{39} - 64 q^{40} - 564 q^{41} - 688 q^{42} - 114 q^{43} + 630 q^{45} + 576 q^{46} - 96 q^{48} - 110 q^{49} + 1968 q^{50} + 1300 q^{51} - 104 q^{52} + 36 q^{53} + 648 q^{54} + 1248 q^{55} + 160 q^{56} - 1848 q^{58} - 1110 q^{59} + 900 q^{61} + 1064 q^{62} - 1980 q^{63} - 512 q^{64} + 1870 q^{65} - 2400 q^{66} + 510 q^{67} - 448 q^{68} - 2402 q^{69} - 1470 q^{71} + 576 q^{72} - 680 q^{74} - 862 q^{75} + 2376 q^{76} + 2340 q^{77} + 1016 q^{78} + 784 q^{79} + 288 q^{80} + 1868 q^{81} + 704 q^{82} - 2136 q^{84} - 2898 q^{85} + 1598 q^{87} + 288 q^{88} - 4434 q^{89} - 2384 q^{90} - 886 q^{91} - 1840 q^{92} + 3108 q^{93} - 2568 q^{94} - 816 q^{95} + 1854 q^{97} + 4272 q^{98}+O(q^{100}) \) 8 * q - 6 * q^3 + 16 * q^4 + 18 * q^7 - 22 * q^9 - 8 * q^10 - 18 * q^11 - 48 * q^12 - 130 * q^13 + 80 * q^14 - 192 * q^15 - 64 * q^16 + 112 * q^17 + 594 * q^19 + 72 * q^20 - 72 * q^22 - 230 * q^23 - 180 * q^25 - 184 * q^26 + 468 * q^27 + 72 * q^28 + 32 * q^29 + 328 * q^30 - 42 * q^33 - 128 * q^35 + 88 * q^36 - 768 * q^37 - 576 * q^38 - 230 * q^39 - 64 * q^40 - 564 * q^41 - 688 * q^42 - 114 * q^43 + 630 * q^45 + 576 * q^46 - 96 * q^48 - 110 * q^49 + 1968 * q^50 + 1300 * q^51 - 104 * q^52 + 36 * q^53 + 648 * q^54 + 1248 * q^55 + 160 * q^56 - 1848 * q^58 - 1110 * q^59 + 900 * q^61 + 1064 * q^62 - 1980 * q^63 - 512 * q^64 + 1870 * q^65 - 2400 * q^66 + 510 * q^67 - 448 * q^68 - 2402 * q^69 - 1470 * q^71 + 576 * q^72 - 680 * q^74 - 862 * q^75 + 2376 * q^76 + 2340 * q^77 + 1016 * q^78 + 784 * q^79 + 288 * q^80 + 1868 * q^81 + 704 * q^82 - 2136 * q^84 - 2898 * q^85 + 1598 * q^87 + 288 * q^88 - 4434 * q^89 - 2384 * q^90 - 886 * q^91 - 1840 * q^92 + 3108 * q^93 - 2568 * q^94 - 816 * q^95 + 1854 * q^97 + 4272 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	2.43757	+	4.22199i	0.469110	+	0.812522i	0.999376	−	0.0353090i	$-0.0112415\pi$
$3$	2.43757	+	4.22199i	0.469110	+	0.812522i	−0.530267	+	0.847831i	$0.677908\pi$
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$		−	0.110135i		−	0.00985079i	−0.999988	−	0.00492540i	$-0.998432\pi$
$5$		−	0.110135i		−	0.00985079i	0.999988	−	0.00492540i	$-0.00156781\pi$
$6$	8.44398	+	4.87513i	0.574540	+	0.331711i
$7$	−14.0246	−	8.09712i	−0.757258	−	0.437203i	0.0710521	−	0.997473i	$-0.477364\pi$
$7$	−14.0246	−	8.09712i	−0.757258	−	0.437203i	−0.828311	+	0.560269i	$0.810698\pi$
$8$		−	8.00000i		−	0.353553i
$9$	1.61655	−	2.79994i	0.0598720	−	0.103701i
$10$	−0.110135	−	0.190760i	−0.00348278	−	0.00603235i
$11$	−33.6077	+	19.4034i	−0.921191	+	0.531850i	−0.884015	−	0.467459i	$-0.845170\pi$
$11$	−33.6077	+	19.4034i	−0.921191	+	0.531850i	−0.0371760	+	0.999309i	$0.511836\pi$
$12$	19.5005			0.469110
$13$	−23.6233	+	40.4838i	−0.503995	+	0.863707i
$13$	−23.6233	+	40.4838i	−0.503995	+	0.863707i
$14$	−32.3885			−0.618299
$15$	0.464989	−	0.268462i	0.00800398	−	0.00462110i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	47.2228	−	81.7923i	0.673719	−	1.16692i	−0.303123	−	0.952951i	$-0.598029\pi$
$17$	47.2228	−	81.7923i	0.673719	−	1.16692i	0.976842	−	0.213964i	$-0.0686374\pi$
$18$		−	6.46618i		−	0.0846719i
$19$	33.5104	+	19.3472i	0.404622	+	0.233608i	0.688476	−	0.725259i	$-0.258280\pi$
$19$	33.5104	+	19.3472i	0.404622	+	0.233608i	−0.283855	+	0.958867i	$0.591613\pi$
$20$	−0.381520	−	0.220270i	−0.00426552	−	0.00246270i
$21$		−	78.9491i		−	0.820385i
$22$	−38.8068	+	67.2154i	−0.376075	+	0.651380i
$23$	46.2232	+	80.0610i	0.419053	+	0.725820i	0.995844	−	0.0910708i	$-0.0290290\pi$
$23$	46.2232	+	80.0610i	0.419053	+	0.725820i	−0.576792	+	0.816891i	$0.695696\pi$
$24$	33.7759	−	19.5005i	0.287270	−	0.165855i
$25$	124.988			0.999903
$26$	−0.433024	+	93.7433i	−0.00326627	+	0.707099i
$27$	147.390			1.05057
$28$	−56.0985	+	32.3885i	−0.378629	+	0.218602i
$29$	−96.2678	−	166.741i	−0.616431	−	1.06769i	−0.990132	−	0.140140i	$-0.955245\pi$
$29$	−96.2678	−	166.741i	−0.616431	−	1.06769i	0.373701	−	0.927549i	$-0.378089\pi$
$30$	0.536924	−	0.929979i	0.00326761	−	0.00565967i
$31$			158.597i			0.918865i	0.888213	+	0.459432i	$0.151947\pi$
$31$			158.597i			0.918865i	−0.888213	+	0.459432i	$0.848053\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	−163.842	−	94.5942i	−0.864279	−	0.498992i
$34$		−	188.891i		−	0.952782i
$35$	−0.891778	+	1.54460i	−0.00430680	+	0.00745959i
$36$	−6.46618	−	11.1998i	−0.0299360	−	0.0518507i
$37$	−248.280	+	143.344i	−1.10316	+	0.636910i	−0.937049	−	0.349197i	$-0.886454\pi$
$37$	−248.280	+	143.344i	−1.10316	+	0.636910i	−0.166111	+	0.986107i	$0.553121\pi$
$38$	77.3889			0.330372
$39$	−228.506	−	1.05553i	−0.938210	−	0.00433383i
$40$	−0.881082			−0.00348278
$41$	202.882	−	117.134i	0.772800	−	0.446176i	−0.0610728	−	0.998133i	$-0.519452\pi$
$41$	202.882	−	117.134i	0.772800	−	0.446176i	0.833872	+	0.551957i	$0.186119\pi$
$42$	−78.9491	−	136.744i	−0.290050	−	0.502381i
$43$	−262.935	+	455.417i	−0.932494	+	1.61513i	−0.153450	+	0.988156i	$0.549039\pi$
$43$	−262.935	+	455.417i	−0.932494	+	1.61513i	−0.779043	+	0.626970i	$0.784295\pi$
$44$			155.227i			0.531850i
$45$	−0.308372	−	0.178039i	−0.00102154	−	0.000589787i
$46$	160.122	+	92.4465i	0.513233	+	0.296315i
$47$		−	320.423i		−	0.994437i	−0.867625	−	0.497219i	$-0.834355\pi$
$47$		−	320.423i		−	0.994437i	0.867625	−	0.497219i	$-0.165645\pi$
$48$	39.0011	−	67.5518i	0.117277	−	0.203130i
$49$	−40.3733	−	69.9286i	−0.117706	−	0.203874i
$50$	216.485	−	124.988i	0.612313	−	0.353519i
$51$	460.435			1.26419
$52$	92.9933	+	162.801i	0.247997	+	0.434163i
$53$	414.352			1.07388			0.536940	−	0.843620i	$-0.319580\pi$
$53$	414.352			1.07388			0.536940	+	0.843620i	$0.319580\pi$
$54$	255.287	−	147.390i	0.643338	−	0.371431i
$55$	2.13700	+	3.70139i	0.00523914	+	0.00907446i
$56$	−64.7770	+	112.197i	−0.154575	+	0.267731i
$57$			188.641i			0.438352i
$58$	−333.482	−	192.536i	−0.754970	−	0.435882i
$59$	−223.006	−	128.753i	−0.492084	−	0.284105i	0.233355	−	0.972392i	$-0.425030\pi$
$59$	−223.006	−	128.753i	−0.492084	−	0.284105i	−0.725438	+	0.688287i	$0.758363\pi$
$60$		−	2.14769i		−	0.00462110i
$61$	−71.6545	+	124.109i	−0.150400	+	0.260501i	−0.931375	−	0.364062i	$-0.881390\pi$
$61$	−71.6545	+	124.109i	−0.150400	+	0.260501i	0.780974	+	0.624563i	$0.214723\pi$
$62$	158.597	+	274.698i	0.324868	+	0.562687i
$63$	−45.3429	+	26.1787i	−0.0906772	+	0.0523525i
$64$	−64.0000			−0.125000
$65$	4.45869	+	2.60176i	0.00850819	+	0.00496475i
$66$	−378.377			−0.705681
$67$	392.729	−	226.742i	0.716111	−	0.413447i	−0.0972086	−	0.995264i	$-0.530991\pi$
$67$	392.729	−	226.742i	0.716111	−	0.413447i	0.813320	+	0.581817i	$0.197658\pi$
$68$	−188.891	−	327.169i	−0.336859	−	0.583458i
$69$	−225.344	+	390.308i	−0.393163	+	0.680979i
$70$			3.56711i			0.00609073i
$71$	−654.631	−	377.952i	−1.09423	−	0.631755i	−0.159532	−	0.987193i	$-0.550998\pi$
$71$	−654.631	−	377.952i	−1.09423	−	0.631755i	−0.934700	+	0.355438i	$0.884332\pi$
$72$	−22.3995	−	12.9324i	−0.0366640	−	0.0211680i
$73$		−	641.108i		−	1.02789i	−0.857823	−	0.513945i	$-0.828183\pi$
$73$		−	641.108i		−	1.02789i	0.857823	−	0.513945i	$-0.171817\pi$
$74$	−286.689	+	496.559i	−0.450363	+	0.780052i
$75$	304.666	+	527.697i	0.469064	+	0.812443i
$76$	134.042	−	77.3889i	0.202311	−	0.116804i
$77$	628.447			0.930106
$78$	−396.839	+	226.677i	−0.576066	+	0.329053i
$79$	−588.290			−0.837820			−0.418910	−	0.908028i	$-0.637588\pi$
$79$	−588.290			−0.837820			−0.418910	+	0.908028i	$0.637588\pi$
$80$	−1.52608	+	0.881082i	−0.00213276	+	0.00123135i
$81$	315.627	+	546.682i	0.432959	+	0.749906i
$82$	234.267	−	405.763i	0.315494	−	0.546452i
$83$		−	744.654i		−	0.984776i	−0.870376	−	0.492388i	$-0.836124\pi$
$83$		−	744.654i		−	0.984776i	0.870376	−	0.492388i	$-0.163876\pi$
$84$	−273.488	−	157.898i	−0.355237	−	0.205096i
$85$	−9.00822	−	5.20090i	−0.0114950	−	0.00663666i
$86$			1051.74i			1.31875i
$87$	469.318	−	812.883i	0.578347	−	1.00173i
$88$	155.227	+	268.861i	0.188037	+	0.325690i
$89$	−1081.79	+	624.570i	−1.28842	+	0.743869i	−0.978372	−	0.206853i	$-0.933678\pi$
$89$	−1081.79	+	624.570i	−1.28842	+	0.743869i	−0.310046	+	0.950721i	$0.600345\pi$
$90$	−0.712154			−0.000834085
$91$	659.111	−	376.489i	0.759270	−	0.433701i
$92$	369.786			0.419053
$93$	−669.593	+	386.590i	−0.746598	+	0.431048i
$94$	−320.423	−	554.990i	−0.351587	−	0.608966i
$95$	2.13081	−	3.69067i	0.00230123	−	0.00398584i
$96$		−	156.004i		−	0.165855i
$97$	1043.14	+	602.258i	1.09191	+	0.630412i	0.934083	−	0.357055i	$-0.116219\pi$
$97$	1043.14	+	602.258i	1.09191	+	0.630412i	0.157823	+	0.987467i	$0.449552\pi$
$98$	−139.857	−	80.7466i	−0.144160	−	0.0832310i
$99$			125.466i			0.127372i
$100$	249.976	−	432.971i	0.249976	−	0.432971i
$101$	−313.860	−	543.622i	−0.309210	−	0.535568i	0.668979	−	0.743281i	$-0.266731\pi$
$101$	−313.860	−	543.622i	−0.309210	−	0.535568i	−0.978190	+	0.207713i	$0.933398\pi$
$102$	797.497	−	460.435i	0.774156	−	0.446959i
$103$	532.283			0.509198			0.254599	−	0.967047i	$-0.418057\pi$
$103$	532.283			0.509198			0.254599	+	0.967047i	$0.418057\pi$
$104$	323.870	+	188.987i	0.305366	+	0.178189i
$105$	−8.69507			−0.00808145
$106$	717.679	−	414.352i	0.657615	−	0.379674i
$107$	741.335	+	1284.03i	0.669790	+	1.16011i	0.977963	+	0.208780i	$0.0669492\pi$
$107$	741.335	+	1284.03i	0.669790	+	1.16011i	−0.308173	+	0.951330i	$0.599717\pi$
$108$	294.781	−	510.575i	0.262641	−	0.454908i
$109$		−	72.2452i		−	0.0634847i	−0.999496	−	0.0317424i	$-0.989894\pi$
$109$		−	72.2452i		−	0.0634847i	0.999496	−	0.0317424i	$-0.0101056\pi$
$110$	7.40278	+	4.27400i	0.00641661	+	0.00370463i
$111$	−1210.40	−	698.823i	−1.03501	−	0.597561i
$112$			259.108i			0.218602i
$113$	−293.899	+	509.048i	−0.244670	+	0.423781i	−0.962039	−	0.272913i	$-0.912013\pi$
$113$	−293.899	+	509.048i	−0.244670	+	0.423781i	0.717369	+	0.696694i	$0.245346\pi$
$114$	188.641	+	326.735i	0.154981	+	0.268435i
$115$	8.81753	−	5.09080i	0.00714990	−	0.00412800i
$116$	−770.143			−0.616431
$117$	75.1639	+	131.588i	0.0593924	+	0.103977i
$118$	−515.011			−0.401785
$119$	−1324.56	+	764.738i	−1.02036	+	0.589104i
$120$	−2.14769	−	3.71992i	−0.00163381	−	0.00282984i
$121$	87.4844	−	151.527i	0.0657283	−	0.113845i
$122$			286.618i			0.212698i
$123$	989.075	+	571.042i	0.725056	+	0.418611i
$124$	549.395	+	317.193i	0.397880	+	0.229716i
$125$		−	27.5325i		−	0.0197006i
$126$	−52.3574	+	90.6857i	−0.0370188	+	0.0641185i
$127$	−1126.21	−	1950.65i	−0.786888	−	1.36293i	−0.927864	−	0.372918i	$-0.878357\pi$
$127$	−1126.21	−	1950.65i	−0.786888	−	1.36293i	0.140976	−	0.990013i	$-0.454976\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	−2563.69			−1.74977
$130$	10.3244	+	0.0476912i	0.00696549	+	3.21754e-5i
$131$	−201.795			−0.134587			−0.0672935	−	0.997733i	$-0.521436\pi$
$131$	−201.795			−0.134587			−0.0672935	+	0.997733i	$0.521436\pi$
$132$	−655.368	+	378.377i	−0.432140	+	0.249496i
$133$	−313.314	−	542.675i	−0.204269	−	0.353804i
$134$	453.484	−	785.457i	0.292351	−	0.506367i
$135$		−	16.2329i		−	0.0103489i
$136$	−654.339	−	377.783i	−0.412567	−	0.238196i
$137$	1663.44	+	960.387i	1.03735	+	0.598915i	0.919082	−	0.394066i	$-0.128932\pi$
$137$	1663.44	+	960.387i	1.03735	+	0.598915i	0.118269	+	0.992982i	$0.462265\pi$
$138$			901.377i			0.556017i
$139$	112.070	−	194.110i	0.0683857	−	0.118448i	−0.829805	−	0.558053i	$-0.811548\pi$
$139$	112.070	−	194.110i	0.0683857	−	0.118448i	0.898191	+	0.439606i	$0.144882\pi$
$140$	3.56711	+	6.17842i	0.00215340	+	0.00372980i
$141$	1352.82	−	781.053i	0.808002	−	0.466500i
$142$	−1511.81			−0.893437
$143$	8.40215	−	1818.94i	0.00491345	−	1.06369i
$144$	−51.7294			−0.0299360
$145$	−18.3640	+	10.6025i	−0.0105176	+	0.00607233i
$146$	−641.108	−	1110.43i	−0.363414	−	0.629452i
$147$	196.825	−	340.911i	0.110434	−	0.191278i
$148$			1146.75i			0.636910i
$149$	2008.37	+	1159.53i	1.10424	+	0.637533i	0.937331	−	0.348439i	$-0.113288\pi$
$149$	2008.37	+	1159.53i	1.10424	+	0.637533i	0.166909	+	0.985972i	$0.446621\pi$
$150$	1055.39	+	609.332i	0.574484	+	0.331679i
$151$			1961.99i			1.05738i	0.848815	+	0.528690i	$0.177316\pi$
$151$			1961.99i			1.05738i	−0.848815	+	0.528690i	$0.822684\pi$
$152$	154.778	−	268.083i	0.0825930	−	0.143055i
$153$	−152.676	−	264.442i	−0.0806738	−	0.139731i
$154$	1088.50	−	628.447i	0.569571	−	0.328842i
$155$	17.4671			0.00905154
$156$	−460.668	+	789.455i	−0.236429	+	0.405173i
$157$	2499.22			1.27044			0.635221	−	0.772330i	$-0.280909\pi$
$157$	2499.22			1.27044			0.635221	+	0.772330i	$0.280909\pi$
$158$	−1018.95	+	588.290i	−0.513058	+	0.296214i
$159$	1010.01	+	1749.39i	0.503768	+	0.872551i
$160$	−1.76216	+	3.05216i	−0.000870695	+	0.00150809i
$161$		−	1497.10i		−	0.732845i
$162$	1093.36	+	631.254i	0.530264	+	0.306148i
$163$	2288.75	+	1321.41i	1.09981	+	0.634975i	0.936171	−	0.351545i	$-0.114344\pi$
$163$	2288.75	+	1321.41i	1.09981	+	0.634975i	0.163638	+	0.986520i	$0.447677\pi$
$164$		−	937.070i		−	0.446176i
$165$	−10.4181	+	18.0448i	−0.00491546	+	0.00851383i
$166$	−744.654	−	1289.78i	−0.348171	−	0.603050i
$167$	−743.976	+	429.535i	−0.344734	+	0.199032i	−0.662364	−	0.749183i	$-0.730447\pi$
$167$	−743.976	+	429.535i	−0.344734	+	0.199032i	0.317629	+	0.948215i	$0.397113\pi$
$168$	−631.592			−0.290050
$169$	−1080.88	−	1912.72i	−0.491978	−	0.870608i
$170$	−20.8036			−0.00938566
$171$	108.342	−	62.5513i	0.0484510	−	0.0279732i
$172$	1051.74	+	1821.67i	0.466247	+	0.807563i
$173$	1056.57	−	1830.03i	0.464331	−	0.804244i	−0.534840	−	0.844953i	$-0.679628\pi$
$173$	1056.57	−	1830.03i	0.464331	−	0.804244i	0.999171	+	0.0407087i	$0.0129616\pi$
$174$		−	1877.27i		−	0.817906i
$175$	−1752.91	−	1012.04i	−0.757185	−	0.437161i
$176$	537.723	+	310.455i	0.230298	+	0.132962i
$177$		−	1255.37i		−	0.533105i
$178$	−1249.14	+	2163.58i	−0.525995	+	0.911050i
$179$	−104.764	−	181.456i	−0.0437453	−	0.0757691i	0.843324	−	0.537406i	$-0.180596\pi$
$179$	−104.764	−	181.456i	−0.0437453	−	0.0757691i	−0.887069	+	0.461637i	$0.847262\pi$
$180$	−1.23349	+	0.712154i	−0.000510771	+	0.000294894i
$181$	−4500.28			−1.84808			−0.924041	−	0.382293i	$-0.875135\pi$
$181$	−4500.28			−1.84808			−0.924041	+	0.382293i	$0.875135\pi$
$182$	765.124	−	1311.21i	0.311620	−	0.534029i
$183$	−698.650			−0.282217
$184$	640.488	−	369.786i	0.256616	−	0.148157i
$185$	15.7873	+	27.3443i	0.00627407	+	0.0108670i
$186$	−773.180	+	1339.19i	−0.304797	+	0.527924i
$187$			3665.14i			1.43327i
$188$	−1109.98	−	640.847i	−0.430604	−	0.248609i
$189$	−2067.09	−	1193.44i	−0.795550	−	0.459311i
$190$		−	8.52324i		−	0.00325443i
$191$	32.2122	−	55.7932i	0.0122031	−	0.0211364i	−0.859859	−	0.510531i	$-0.829449\pi$
$191$	32.2122	−	55.7932i	0.0122031	−	0.0211364i	0.872062	+	0.489395i	$0.162782\pi$
$192$	−156.004	−	270.207i	−0.0586387	−	0.101565i
$193$	−1893.47	+	1093.19i	−0.706190	+	0.407719i	−0.809649	−	0.586915i	$-0.800342\pi$
$193$	−1893.47	+	1093.19i	−0.706190	+	0.407719i	0.103459	+	0.994634i	$0.467009\pi$
$194$	2409.03			0.891538
$195$	−0.116250	+	25.1665i	−4.26916e−5	+	0.00924211i
$196$	−322.986			−0.117706
$197$	−1173.25	+	677.376i	−0.424318	+	0.244980i	−0.696923	−	0.717146i	$-0.745448\pi$
$197$	−1173.25	+	677.376i	−0.424318	+	0.244980i	0.272605	+	0.962126i	$0.412115\pi$
$198$	125.466	+	217.313i	0.0450327	+	0.0779989i
$199$	−703.491	+	1218.48i	−0.250599	+	0.434050i	−0.963691	−	0.267020i	$-0.913961\pi$
$199$	−703.491	+	1218.48i	−0.250599	+	0.434050i	0.713092	+	0.701071i	$0.247294\pi$
$200$		−	999.903i		−	0.353519i
$201$	1914.60	+	1105.40i	0.671869	+	0.387904i
$202$	−1087.24	−	627.720i	−0.378704	−	0.218645i
$203$			3117.97i			1.07802i
$204$	920.870	−	1594.99i	0.316048	−	0.547411i
$205$	−12.9005	−	22.3444i	−0.00439519	−	0.00761269i
$206$	921.940	−	532.283i	0.311819	−	0.180029i
$207$	298.888			0.100358
$208$	749.947	+	3.46419i	0.249997	+	0.00115480i
$209$	−1501.61			−0.496978
$210$	−15.0603	+	8.69507i	−0.00494885	+	0.00285722i
$211$	204.037	+	353.402i	0.0665709	+	0.115304i	0.897390	−	0.441239i	$-0.145461\pi$
$211$	204.037	+	353.402i	0.0665709	+	0.115304i	−0.830819	+	0.556543i	$0.812127\pi$
$212$	828.705	−	1435.36i	0.268470	−	0.465004i
$213$		−	3685.13i		−	1.18545i
$214$	2568.06	+	1482.67i	0.820322	+	0.473613i
$215$	50.1574	+	28.9584i	0.0159103	+	0.00918580i
$216$		−	1179.12i		−	0.371431i
$217$	1284.18	−	2224.26i	0.401731	−	0.695818i
$218$	−72.2452	−	125.132i	−0.0224452	−	0.0388763i
$219$	2706.75	−	1562.74i	0.835184	−	0.482194i
$220$	17.0960			0.00523914
$221$	2195.70	+	3843.97i	0.668321	+	1.17001i
$222$	−2795.29			−0.845079
$223$	2246.35	−	1296.93i	0.674560	−	0.389457i	−0.123242	−	0.992377i	$-0.539329\pi$
$223$	2246.35	−	1296.93i	0.674560	−	0.389457i	0.797802	+	0.602919i	$0.205996\pi$
$224$	259.108	+	448.788i	0.0772874	+	0.133866i
$225$	202.049	−	349.958i	0.0598662	−	0.103691i
$226$			1175.60i			0.346015i
$227$	−4509.90	−	2603.79i	−1.31865	−	0.761320i	−0.335135	−	0.942170i	$-0.608782\pi$
$227$	−4509.90	−	2603.79i	−1.31865	−	0.761320i	−0.983511	+	0.180850i	$0.942115\pi$
$228$	653.470	+	377.281i	0.189812	+	0.109588i
$229$			2454.17i			0.708193i	0.935209	+	0.354097i	$0.115212\pi$
$229$			2454.17i			0.708193i	−0.935209	+	0.354097i	$0.884788\pi$
$230$	10.1816	−	17.6351i	0.00291894	−	0.00505575i
$231$	1531.88	+	2653.30i	0.436322	+	0.755732i
$232$	−1333.93	+	770.143i	−0.377485	+	0.217941i
$233$	4251.72			1.19545			0.597724	−	0.801702i	$-0.296072\pi$
$233$	4251.72			1.19545			0.597724	+	0.801702i	$0.296072\pi$
$234$	261.776	+	152.753i	0.0731316	+	0.0426742i
$235$	−35.2899			−0.00979599
$236$	−892.025	+	515.011i	−0.246042	+	0.142052i
$237$	−1434.00	−	2483.75i	−0.393029	−	0.680747i
$238$	−1529.48	+	2649.13i	−0.416560	+	0.721502i
$239$		−	302.969i		−	0.0819977i	−0.999159	−	0.0409988i	$-0.986946\pi$
$239$		−	302.969i		−	0.0819977i	0.999159	−	0.0409988i	$-0.0130540\pi$
$240$	−7.43983	−	4.29539i	−0.00200100	−	0.00115528i
$241$	−874.074	−	504.647i	−0.233627	−	0.134884i	0.378617	−	0.925553i	$-0.376400\pi$
$241$	−874.074	−	504.647i	−0.233627	−	0.134884i	−0.612244	+	0.790669i	$0.709733\pi$
$242$		−	349.938i		−	0.0929539i
$243$	451.047	−	781.236i	0.119073	−	0.206240i
$244$	286.618	+	496.437i	0.0752002	+	0.130251i
$245$	−7.70160	+	4.44652i	−0.00200832	+	0.00115950i
$246$	2284.17			0.592005
$247$	−1574.88	+	899.582i	−0.405696	+	0.231737i
$248$	1268.77			0.324868
$249$	3143.92	−	1815.14i	0.800152	−	0.461968i
$250$	−27.5325	−	47.6876i	−0.00696522	−	0.0120641i
$251$	1661.62	−	2878.02i	0.417852	−	0.723741i	−0.577871	−	0.816128i	$-0.696116\pi$
$251$	1661.62	−	2878.02i	0.417852	−	0.723741i	0.995723	+	0.0923872i	$0.0294498\pi$
$252$			209.430i			0.0523525i
$253$	−3106.91	−	1793.78i	−0.772055	−	0.445746i
$254$	−3901.30	−	2252.42i	−0.963738	−	0.556414i
$255$		−	50.7101i		−	0.0124533i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	3204.14	+	5549.73i	0.777698	+	1.34701i	0.933265	+	0.359188i	$0.116946\pi$
$257$	3204.14	+	5549.73i	0.777698	+	1.34701i	−0.155567	+	0.987825i	$0.549720\pi$
$258$	−4440.44	+	2563.69i	−1.07151	+	0.618636i
$259$	4642.70			1.11384
$260$	17.9301	−	10.2418i	0.00427685	−	0.00244297i
$261$	−622.485			−0.147628
$262$	−349.519	+	201.795i	−0.0824173	+	0.0475837i
$263$	−2142.32	−	3710.61i	−0.502286	−	0.869985i	−0.999997	−	0.00264167i	$-0.999159\pi$
$263$	−2142.32	−	3710.61i	−0.502286	−	0.869985i	0.497710	−	0.867343i	$-0.334174\pi$
$264$	−756.753	+	1310.74i	−0.176420	+	0.305569i
$265$		−	45.6348i		−	0.0105786i
$266$	−1085.35	−	626.627i	−0.250177	−	0.144440i
$267$	−5273.86	−	3044.86i	−1.20882	−	0.697912i
$268$		−	1813.94i		−	0.413447i
$269$	−2840.56	+	4920.00i	−0.643837	+	1.11516i	0.340732	+	0.940160i	$0.389325\pi$
$269$	−2840.56	+	4920.00i	−0.643837	+	1.11516i	−0.984569	+	0.174997i	$0.944008\pi$
$270$	−16.2329	−	28.1161i	−0.00365889	−	0.00633738i
$271$	4255.71	−	2457.03i	0.953933	−	0.550753i	0.0596325	−	0.998220i	$-0.481007\pi$
$271$	4255.71	−	2457.03i	0.953933	−	0.550753i	0.894300	+	0.447467i	$0.147674\pi$
$272$	−1511.13			−0.336859
$273$	3196.16	+	1865.04i	0.708572	+	0.413470i
$274$	3841.55			0.846994
$275$	−4200.55	+	2425.19i	−0.921101	+	0.531798i
$276$	901.377	+	1561.23i	0.196582	+	0.340489i
$277$	−3869.67	+	6702.46i	−0.839371	+	1.45383i	0.0510496	+	0.998696i	$0.483743\pi$
$277$	−3869.67	+	6702.46i	−0.839371	+	1.45383i	−0.890421	+	0.455138i	$0.849590\pi$
$278$		−	448.278i		−	0.0967120i
$279$	444.061	+	256.379i	0.0952876	+	0.0550143i
$280$	12.3568	+	7.13422i	0.00263737	+	0.00152268i
$281$		−	4205.91i		−	0.892895i	−0.894810	−	0.446447i	$-0.852689\pi$
$281$		−	4205.91i		−	0.892895i	0.894810	−	0.446447i	$-0.147311\pi$
$282$	1562.11	−	2705.65i	0.329866	−	0.571344i
$283$	−1672.67	−	2897.15i	−0.351343	−	0.608543i	0.635142	−	0.772395i	$-0.280941\pi$
$283$	−1672.67	−	2897.15i	−0.351343	−	0.608543i	−0.986485	+	0.163852i	$0.947608\pi$
$284$	−2618.53	+	1511.81i	−0.547116	+	0.315878i
$285$	20.7760			0.00431811
$286$	−1804.39	−	3158.90i	−0.373062	−	0.653110i
$287$	−3793.78			−0.780279
$288$	−89.5980	+	51.7294i	−0.0183320	+	0.0105840i
$289$	−2003.49	−	3470.15i	−0.407794	−	0.706320i
$290$	−21.2050	+	36.7281i	−0.00429378	+	0.00743705i
$291$			5872.17i			1.18293i
$292$	−2220.86	−	1282.22i	−0.445090	−	0.256973i
$293$	4787.46	+	2764.04i	0.954561	+	0.551116i	0.894495	−	0.447078i	$-0.147535\pi$
$293$	4787.46	+	2764.04i	0.954561	+	0.551116i	0.0600664	+	0.998194i	$0.480869\pi$
$294$		−	787.301i		−	0.156178i
$295$	−14.1802	+	24.5608i	−0.00279865	+	0.00484741i
$296$	1146.75	+	1986.24i	0.225182	+	0.390026i
$297$	−4953.45	+	2859.87i	−0.967772	+	0.558743i
$298$	4638.12			0.901608
$299$	−4333.12	−	20.0158i	−0.838096	−	0.00387138i
$300$	2437.33			0.469064
$301$	7375.13	−	4258.03i	1.41228	−	0.815379i
$302$	1961.99	+	3398.26i	0.373840	+	0.647510i
$303$	1530.11	−	2650.23i	0.290107	−	0.502480i
$304$		−	619.111i		−	0.116804i
$305$	13.6688	+	7.89168i	0.00256614	+	0.00148156i
$306$	−528.884	−	305.351i	−0.0988049	−	0.0570450i
$307$		−	10085.6i		−	1.87497i	−0.348030	−	0.937484i	$-0.613149\pi$
$307$		−	10085.6i		−	1.87497i	0.348030	−	0.937484i	$-0.386851\pi$
$308$	1256.89	−	2177.00i	0.232527	−	0.402748i
$309$	1297.47	+	2247.29i	0.238870	+	0.413734i
$310$	30.2539	−	17.4671i	0.00554292	−	0.00320020i
$311$	6397.41			1.16644			0.583222	−	0.812313i	$-0.301792\pi$
$311$	6397.41			1.16644			0.583222	+	0.812313i	$0.301792\pi$
$312$	−8.44420	+	1828.04i	−0.00153224	+	0.331707i
$313$	2987.39			0.539480			0.269740	−	0.962933i	$-0.413062\pi$
$313$	2987.39			0.539480			0.269740	+	0.962933i	$0.413062\pi$
$314$	4328.77	−	2499.22i	0.777984	−	0.449169i
$315$	2.88320	+	4.99385i	0.000515714	+	0.000893242i
$316$	−1176.58	+	2037.90i	−0.209455	+	0.362787i
$317$		−	841.335i		−	0.149067i	−0.997219	−	0.0745333i	$-0.976253\pi$
$317$		−	841.335i		−	0.149067i	0.997219	−	0.0745333i	$-0.0237467\pi$
$318$	3498.78	+	2020.02i	0.616987	+	0.356218i
$319$	6470.68	+	3735.85i	1.13570	+	0.655697i
$320$			7.04865i			0.00123135i
$321$	−3614.10	+	6259.81i	−0.628410	+	1.08844i
$322$	−1497.10	−	2593.05i	−0.259100	−	0.448774i
$323$	3164.91	−	1827.26i	0.545202	−	0.314773i
$324$	2525.01			0.432959
$325$	−2952.63	+	5059.98i	−0.503946	+	0.863623i
$326$	5285.65			0.897990
$327$	305.018	−	176.102i	0.0515827	−	0.0297813i
$328$	−937.070	−	1623.05i	−0.157747	−	0.273226i
$329$	−2594.51	+	4493.82i	−0.434771	+	0.753046i
$330$			41.6726i			0.00695152i
$331$	−2586.21	−	1493.15i	−0.429459	−	0.247948i	0.269657	−	0.962956i	$-0.413090\pi$
$331$	−2586.21	−	1493.15i	−0.429459	−	0.247948i	−0.699116	+	0.715008i	$0.746423\pi$
$332$	−2579.56	−	1489.31i	−0.426421	−	0.246194i
$333$			926.890i			0.152532i
$334$	−859.070	+	1487.95i	−0.140737	+	0.243764i
$335$	−24.9723	−	43.2532i	−0.00407278	−	0.00705426i
$336$	−1093.95	+	631.592i	−0.177619	+	0.102548i
$337$	−8483.23			−1.37125			−0.685625	−	0.727955i	$-0.740471\pi$
$337$	−8483.23			−1.37125			−0.685625	+	0.727955i	$0.740471\pi$
$338$	−3784.86	−	2232.06i	−0.609080	−	0.359196i
$339$	−2865.59			−0.459108
$340$	−36.0329	+	20.8036i	−0.00574752	+	0.00331833i
$341$	−3077.32	−	5330.07i	−0.488698	−	0.846450i
$342$	125.103	−	216.684i	0.0197801	−	0.0342601i
$343$			6862.25i			1.08025i
$344$	3643.34	+	2103.48i	0.571033	+	0.329686i
$345$	42.9866	+	24.8183i	0.00670818	+	0.00387297i
$346$		−	4226.26i		−	0.656663i
$347$	1054.36	−	1826.21i	0.163115	−	0.282524i	−0.772869	−	0.634566i	$-0.781179\pi$
$347$	1054.36	−	1826.21i	0.163115	−	0.282524i	0.935984	+	0.352041i	$0.114512\pi$
$348$	−1877.27	−	3251.53i	−0.289174	−	0.500863i
$349$	7978.73	−	4606.52i	1.22376	−	0.706537i	0.258042	−	0.966134i	$-0.416923\pi$
$349$	7978.73	−	4606.52i	1.22376	−	0.706537i	0.965717	+	0.259596i	$0.0835895\pi$
$350$	−4048.17			−0.618239
$351$	−3481.85	+	5966.92i	−0.529480	+	0.907381i
$352$	1241.82			0.188037
$353$	347.274	−	200.499i	0.0523613	−	0.0302308i	−0.473591	−	0.880745i	$-0.657042\pi$
$353$	347.274	−	200.499i	0.0523613	−	0.0302308i	0.525952	+	0.850514i	$0.323709\pi$
$354$	−1255.37	−	2174.37i	−0.188481	−	0.326459i
$355$	−41.6258	+	72.0980i	−0.00622329	+	0.0107790i
$356$			4996.56i			0.743869i
$357$	−6457.43	−	3728.20i	−0.957320	−	0.552709i
$358$	−362.912	−	209.528i	−0.0535769	−	0.0309326i
$359$		−	2709.95i		−	0.398400i	−0.979959	−	0.199200i	$-0.936166\pi$
$359$		−	2709.95i		−	0.398400i	0.979959	−	0.199200i	$-0.0638344\pi$
$360$	−1.42431	+	2.46697i	−0.000208521	+	0.000361169i
$361$	−2680.87	−	4643.40i	−0.390854	−	0.676979i
$362$	−7794.71	+	4500.28i	−1.13171	+	0.653396i
$363$	852.996			0.123335
$364$	14.0250	−	3036.20i	0.00201953	−	0.437199i
$365$	−70.6086			−0.0101255
$366$	−1210.10	+	698.650i	−0.172822	+	0.0997788i
$367$	183.562	+	317.939i	0.0261087	+	0.0452215i	0.878785	−	0.477219i	$-0.158355\pi$
$367$	183.562	+	317.939i	0.0261087	+	0.0452215i	−0.852676	+	0.522440i	$0.825022\pi$
$368$	739.572	−	1280.98i	0.104763	−	0.181455i
$369$		−	757.408i		−	0.106854i
$370$	54.6887	+	31.5745i	0.00768413	+	0.00443643i
$371$	−5811.13	−	3355.06i	−0.813205	−	0.469504i
$372$			3092.72i			0.431048i
$373$	−1399.02	+	2423.17i	−0.194205	+	0.336373i	−0.946640	−	0.322294i	$-0.895546\pi$
$373$	−1399.02	+	2423.17i	−0.194205	+	0.336373i	0.752435	+	0.658667i	$0.228879\pi$
$374$	3665.14	+	6348.20i	0.506737	+	0.877694i
$375$	116.242	−	67.1122i	0.0160072	−	0.00924176i
$376$	−2563.39			−0.351587
$377$	9024.47	+	41.6863i	1.23285	+	0.00569484i
$378$	−4773.75			−0.649564
$379$	−3786.81	+	2186.32i	−0.513234	+	0.296316i	−0.734162	−	0.678975i	$-0.762425\pi$
$379$	−3786.81	+	2186.32i	−0.513234	+	0.296316i	0.220928	+	0.975290i	$0.429091\pi$
$380$	−8.52324	−	14.7627i	−0.00115061	−	0.00199292i
$381$	5490.41	−	9509.68i	0.738274	−	1.27873i
$382$		−	128.849i		−	0.0172578i
$383$	8471.57	+	4891.06i	1.13023	+	0.652537i	0.943992	−	0.329968i	$-0.107038\pi$
$383$	8471.57	+	4891.06i	1.13023	+	0.652537i	0.186235	+	0.982505i	$0.440371\pi$
$384$	−540.414	−	312.008i	−0.0718175	−	0.0414638i
$385$		−	69.2141i		−	0.00916228i
$386$	−2186.39	+	3786.93i	−0.288301	+	0.499352i
$387$	850.093	+	1472.40i	0.111661	+	0.193402i
$388$	4172.56	−	2409.03i	0.545953	−	0.315206i
$389$	−1150.89			−0.150007			−0.0750033	−	0.997183i	$-0.523897\pi$
$389$	−1150.89			−0.150007			−0.0750033	+	0.997183i	$0.523897\pi$
$390$	24.9652	+	43.7059i	0.00324143	+	0.00567470i
$391$	8731.17			1.12929
$392$	−559.429	+	322.986i	−0.0720802	+	0.0416155i
$393$	−491.888	−	851.975i	−0.0631361	−	0.109355i
$394$	−1354.75	+	2346.50i	−0.173227	+	0.300038i
$395$			64.7914i			0.00825319i
$396$	434.627	+	250.932i	0.0551536	+	0.0318429i
$397$	8339.28	+	4814.69i	1.05425	+	0.608671i	0.923836	−	0.382789i	$-0.125036\pi$
$397$	8339.28	+	4814.69i	1.05425	+	0.608671i	0.130413	+	0.991460i	$0.458370\pi$
$398$			2813.97i			0.354400i
$399$	1527.45	−	2645.61i	0.191649	−	0.331946i
$400$	−999.903	−	1731.88i	−0.124988	−	0.216485i
$401$	−5373.63	+	3102.47i	−0.669192	+	0.386358i	−0.795771	−	0.605598i	$-0.792934\pi$
$401$	−5373.63	+	3102.47i	−0.669192	+	0.386358i	0.126578	+	0.991957i	$0.459601\pi$
$402$	4421.59			0.548579
$403$	−6420.60	−	3746.58i	−0.793630	−	0.463103i
$404$	−2510.88			−0.309210
$405$	60.2089	−	34.7616i	0.00738717	−	0.00426499i
$406$	3117.97	+	5400.48i	0.381138	+	0.660151i
$407$	5562.74	−	9634.94i	0.677481	−	1.17343i
$408$		−	3683.48i		−	0.446959i
$409$	4901.86	+	2830.09i	0.592619	+	0.342149i	0.766132	−	0.642683i	$-0.222179\pi$
$409$	4901.86	+	2830.09i	0.592619	+	0.342149i	−0.173513	+	0.984832i	$0.555512\pi$
$410$	−44.6888	−	25.8011i	−0.00538298	−	0.00310787i
$411$			9364.02i			1.12383i
$412$	1064.57	−	1843.88i	0.127299	−	0.220489i
$413$	2085.05	+	3611.41i	0.248423	+	0.430281i
$414$	517.689	−	298.888i	0.0614566	−	0.0354820i
$415$	−82.0127			−0.00970083
$416$	1302.41	−	743.947i	0.153500	−	0.0876802i
$417$	1092.71			0.128322
$418$	−2600.86	+	1501.61i	−0.304336	+	0.175708i
$419$	1834.51	+	3177.47i	0.213895	+	0.370477i	0.952930	−	0.303190i	$-0.0980517\pi$
$419$	1834.51	+	3177.47i	0.213895	+	0.370477i	−0.739035	+	0.673667i	$0.764718\pi$
$420$	−17.3901	+	30.1206i	−0.00202036	+	0.00349937i
$421$		−	13716.5i		−	1.58789i	−0.607991	−	0.793944i	$-0.708024\pi$
$421$		−	13716.5i		−	1.58789i	0.607991	−	0.793944i	$-0.291976\pi$
$422$	706.804	+	408.073i	0.0815324	+	0.0470728i
$423$	−897.166	−	517.979i	−0.103125	−	0.0595390i
$424$		−	3314.82i		−	0.379674i
$425$	5902.28	−	10223.1i	0.673653	−	1.16680i
$426$	−3685.13	−	6382.83i	−0.419120	−	0.725937i
$427$	2009.86	−	1160.39i	0.227784	−	0.131511i
$428$	5930.68			0.669790
$429$	7700.02	−	4398.31i	0.866575	−	0.494994i
$430$	115.834			0.0129907
$431$	−13180.5	+	7609.74i	−1.47304	+	0.850460i	−0.999540	−	0.0303334i	$-0.990343\pi$
$431$	−13180.5	+	7609.74i	−1.47304	+	0.850460i	−0.473500	+	0.880794i	$0.657010\pi$
$432$	−1179.12	−	2042.30i	−0.131321	−	0.227454i
$433$	−8097.51	+	14025.3i	−0.898710	+	1.55661i	−0.0695656	+	0.997577i	$0.522161\pi$
$433$	−8097.51	+	14025.3i	−0.898710	+	1.55661i	−0.829145	+	0.559034i	$0.811172\pi$
$434$		−	5136.71i		−	0.568133i
$435$	−89.5270	−	51.6885i	−0.00986780	−	0.00569718i
$436$	−250.265	−	144.490i	−0.0274897	−	0.0158712i
$437$			3577.17i			0.391577i
$438$	3125.49	−	5413.50i	0.340962	−	0.590564i
$439$	−1136.17	−	1967.90i	−0.123522	−	0.213947i	0.797632	−	0.603144i	$-0.206086\pi$
$439$	−1136.17	−	1967.90i	−0.123522	−	0.213947i	−0.921154	+	0.389197i	$0.872752\pi$
$440$	29.6111	−	17.0960i	0.00320831	−	0.00185232i
$441$	−261.061			−0.0281893
$442$	7647.04	+	4462.24i	0.822924	+	0.480197i
$443$	−13195.8			−1.41524			−0.707622	−	0.706591i	$-0.750232\pi$
$443$	−13195.8			−1.41524			−0.707622	+	0.706591i	$0.750232\pi$
$444$	−4841.58	+	2795.29i	−0.517503	+	0.298781i
$445$	68.7872	+	119.143i	0.00732770	+	0.0126919i
$446$	2593.86	−	4492.70i	0.275388	−	0.476986i
$447$			11305.7i			1.19629i
$448$	897.576	+	518.216i	0.0946573	+	0.0546504i
$449$	−12667.8	−	7313.74i	−1.33147	−	0.768724i	−0.345944	−	0.938255i	$-0.612441\pi$
$449$	−12667.8	−	7313.74i	−1.33147	−	0.768724i	−0.985525	+	0.169532i	$0.945775\pi$
$450$		−	808.194i		−	0.0846636i
$451$	−4545.59	+	7873.19i	−0.474597	+	0.822027i
$452$	1175.60	+	2036.19i	0.122335	+	0.211890i
$453$	−8283.49	+	4782.47i	−0.859144	+	0.496027i
$454$	−10415.2			−1.07667
$455$	−41.4647	−	72.5913i	−0.00427230	−	0.00747941i
$456$	1509.12			0.154981
$457$	2790.63	−	1611.17i	0.285646	−	0.164918i	−0.350331	−	0.936626i	$-0.613931\pi$
$457$	2790.63	−	1611.17i	0.285646	−	0.164918i	0.635977	+	0.771708i	$0.280598\pi$
$458$	2454.17	+	4250.75i	0.250384	+	0.433678i
$459$	6960.19	−	12055.4i	0.707786	−	1.22592i
$460$		−	40.7264i		−	0.00412800i
$461$	1134.40	+	654.948i	0.114608	+	0.0661691i	0.556208	−	0.831043i	$-0.312256\pi$
$461$	1134.40	+	654.948i	0.114608	+	0.0661691i	−0.441600	+	0.897212i	$0.645589\pi$
$462$	5306.59	+	3063.76i	0.534383	+	0.308526i
$463$			16084.0i			1.61444i	0.590249	+	0.807221i	$0.299030\pi$
$463$			16084.0i			1.61444i	−0.590249	+	0.807221i	$0.700970\pi$
$464$	−1540.29	+	2667.85i	−0.154108	+	0.266922i
$465$	42.5772	+	73.7458i	0.00424617	+	0.00735458i
$466$	7364.20	−	4251.72i	0.732060	−	0.422655i
$467$	−10100.7			−1.00087			−0.500435	−	0.865774i	$-0.666827\pi$
$467$	−10100.7			−1.00087			−0.500435	+	0.865774i	$0.666827\pi$
$468$	606.161	+	2.80001i	0.0598714	+	0.000276561i
$469$	−7343.83			−0.723042
$470$	−61.1239	+	35.2899i	−0.00599880	+	0.00346341i
$471$	6092.01	+	10551.7i	0.595977	+	1.03226i
$472$	−1030.02	+	1784.05i	−0.100446	+	0.173978i
$473$		−	20407.3i		−	1.98379i
$474$	−4967.50	−	2867.99i	−0.481361	−	0.277914i
$475$	4188.39	+	2418.17i	0.404582	+	0.233586i
$476$			6117.90i			0.589104i
$477$	669.819	−	1160.16i	0.0642954	−	0.111363i
$478$	−302.969	−	524.758i	−0.0289906	−	0.0502131i
$479$	7343.90	−	4240.00i	0.700525	−	0.404448i	−0.107018	−	0.994257i	$-0.534130\pi$
$479$	7343.90	−	4240.00i	0.700525	−	0.404448i	0.807543	+	0.589809i	$0.200797\pi$
$480$	−17.1816			−0.00163381
$481$	62.0716	−	13437.6i	0.00588404	−	1.27381i
$482$	−2018.59			−0.190755
$483$	6320.74	−	3649.28i	0.595453	−	0.343785i
$484$	−349.938	−	606.110i	−0.0328642	−	0.0569224i
$485$	66.3298	−	114.887i	0.00621006	−	0.0107561i
$486$		−	1804.19i		−	0.168394i
$487$	−5865.01	−	3386.17i	−0.545727	−	0.315076i	0.201670	−	0.979454i	$-0.435363\pi$
$487$	−5865.01	−	3386.17i	−0.545727	−	0.315076i	−0.747397	+	0.664378i	$0.768697\pi$
$488$	992.874	+	573.236i	0.0921010	+	0.0531745i
$489$			12884.1i			1.19149i
$490$	−8.89304	+	15.4032i	−0.000819891	+	0.00142009i
$491$	−4212.80	−	7296.79i	−0.387212	−	0.670671i	0.604861	−	0.796331i	$-0.293229\pi$
$491$	−4212.80	−	7296.79i	−0.387212	−	0.670671i	−0.992073	+	0.125660i	$0.959895\pi$
$492$	3956.30	−	2284.17i	0.362528	−	0.209306i
$493$	−18184.2			−1.66120
$494$	−1828.18	+	3133.00i	−0.166506	+	0.285345i
$495$	13.8182			0.00125471
$496$	2197.58	−	1268.77i	0.198940	−	0.114858i
$497$	6120.64	+	10601.3i	0.552411	+	0.956804i
$498$	3630.29	−	6287.84i	0.326661	−	0.565793i
$499$			12421.7i			1.11437i	0.830388	+	0.557186i	$0.188119\pi$
$499$			12421.7i			1.11437i	−0.830388	+	0.557186i	$0.811881\pi$
$500$	−95.3752	−	55.0649i	−0.00853062	−	0.00492516i
$501$	−3626.98	−	2094.04i	−0.323436	−	0.186736i
$502$		−	6646.50i		−	0.590932i
$503$	5642.87	−	9773.74i	0.500205	−	0.866381i	−0.499795	−	0.866144i	$-0.666591\pi$
$503$	5642.87	−	9773.74i	0.500205	−	0.866381i	1.00000		0.000236966i	$-7.54285e-5\pi$
$504$	209.430	+	362.743i	0.0185094	+	0.0320592i
$505$	−59.8719	+	34.5670i	−0.00527577	+	0.00304597i
$506$	−7175.11			−0.630380
$507$	5440.80	−	9225.84i	0.476596	−	0.808154i
$508$	−9009.67			−0.786888
$509$	9718.44	−	5610.95i	0.846292	−	0.488607i	−0.0131062	−	0.999914i	$-0.504172\pi$
$509$	9718.44	−	5610.95i	0.846292	−	0.488607i	0.859398	+	0.511307i	$0.170839\pi$
$510$	−50.7101	−	87.8325i	−0.00440290	−	0.00762605i
$511$	−5191.13	+	8991.30i	−0.449397	+	0.778379i
$512$			512.000i			0.0441942i
$513$	4939.11	+	2851.59i	0.425082	+	0.245421i
$514$	11099.5	+	6408.27i	0.952482	+	0.549916i
$515$		−	58.6230i		−	0.00501600i
$516$	−5127.37	+	8880.87i	−0.437442	+	0.757672i
$517$	6217.31	+	10768.7i	0.528891	+	0.916067i
$518$	8041.40	−	4642.70i	0.682083	−	0.393801i
$519$	10301.8			0.871288
$520$	20.8141	−	35.6695i	0.00175530	−	0.00300810i
$521$	9592.88			0.806664			0.403332	−	0.915054i	$-0.367852\pi$
$521$	9592.88			0.806664			0.403332	+	0.915054i	$0.367852\pi$
$522$	−1078.18	+	622.485i	−0.0904032	+	0.0521943i
$523$	265.667	+	460.149i	0.0222119	+	0.0384721i	0.876918	−	0.480641i	$-0.159596\pi$
$523$	265.667	+	460.149i	0.0222119	+	0.0384721i	−0.854706	+	0.519113i	$0.826262\pi$
$524$	−403.590	+	699.038i	−0.0336467	+	0.0582779i
$525$		−	9867.67i		−	0.820306i
$526$	−7421.22	−	4284.64i	−0.615172	−	0.355170i
$527$	12972.0	+	7489.39i	1.07224	+	0.619056i
$528$			3027.01i			0.249496i
$529$	1810.33	−	3135.58i	0.148790	−	0.257712i
$530$	−45.6348	−	79.0417i	−0.00374009	−	0.00647803i
$531$	−720.999	+	416.269i	−0.0589241	+	0.0340198i
$532$	−2506.51			−0.204269
$533$	−50.7218	+	10980.5i	−0.00412196	+	0.892343i
$534$	−12179.5			−0.986997
$535$	141.417	−	81.6470i	0.0114280	−	0.00659796i
$536$	−1813.94	−	3141.83i	−0.146176	−	0.253184i
$537$	510.737	−	884.623i	0.0410427	−	0.0710881i
$538$			11362.2i			0.910522i
$539$	2713.71	+	1566.76i	0.216860	+	0.125204i
$540$	−56.2323	−	32.4657i	−0.00448121	−	0.00258723i
$541$		−	3385.98i		−	0.269085i	−0.990908	−	0.134542i	$-0.957044\pi$
$541$		−	3385.98i		−	0.269085i	0.990908	−	0.134542i	$-0.0429564\pi$
$542$	4914.07	−	8511.42i	0.389441	−	0.674532i
$543$	−10969.7	−	19000.1i	−0.866954	−	1.50161i
$544$	−2617.36	+	1511.13i	−0.206283	+	0.119098i
$545$	−7.95674			−0.000625375
$546$	7400.95	+	34.1869i	0.580094	+	0.00267960i
$547$	21727.3			1.69834			0.849169	−	0.528121i	$-0.177103\pi$
$547$	21727.3			1.69834			0.849169	+	0.528121i	$0.177103\pi$
$548$	6653.75	−	3841.55i	0.518676	−	0.299458i
$549$	231.666	+	401.256i	0.0180096	+	0.0311935i
$550$	−4850.38	+	8401.11i	−0.376038	+	0.651317i
$551$		−	7450.06i		−	0.576013i
$552$	3122.46	+	1802.75i	0.240762	+	0.139004i
$553$	8250.54	+	4763.45i	0.634446	+	0.366298i
$554$			15478.7i			1.18705i
$555$	−76.9650	+	133.307i	−0.00588645	+	0.0101956i
$556$	−448.278	−	776.441i	−0.0341929	−	0.0592238i
$557$	2201.34	−	1270.94i	0.167457	−	0.0966816i	−0.413929	−	0.910309i	$-0.635844\pi$
$557$	2201.34	−	1270.94i	0.167457	−	0.0966816i	0.581386	+	0.813628i	$0.302510\pi$
$558$	1025.51			0.0778020
$559$	−12225.6	−	21403.1i	−0.925023	−	1.61942i
$560$	28.5369			0.00215340
$561$	−15474.2	+	8934.01i	−1.16456	+	0.672360i
$562$	−4205.91	−	7284.85i	−0.315686	−	0.546784i
$563$	−4573.52	+	7921.57i	−0.342364	+	0.592992i	−0.984871	−	0.173288i	$-0.944561\pi$
$563$	−4573.52	+	7921.57i	−0.342364	+	0.592992i	0.642507	+	0.766280i	$0.277894\pi$
$564$		−	6248.43i		−	0.466500i
$565$	56.0641	+	32.3686i	0.00417457	+	0.00241019i
$566$	−5794.30	−	3345.34i	−0.430305	−	0.248437i
$567$		−	10222.7i		−	0.757164i
$568$	−3023.61	+	5237.05i	−0.223359	+	0.386869i
$569$	−4178.43	−	7237.25i	−0.307854	−	0.533219i	0.670039	−	0.742326i	$-0.266278\pi$
$569$	−4178.43	−	7237.25i	−0.307854	−	0.533219i	−0.977893	+	0.209107i	$0.932944\pi$
$570$	35.9850	−	20.7760i	0.00264429	−	0.00152668i
$571$	−1254.50			−0.0919427			−0.0459713	−	0.998943i	$-0.514638\pi$
$571$	−1254.50			−0.0919427			−0.0459713	+	0.998943i	$0.514638\pi$
$572$	−6284.19	−	3666.99i	−0.459362	−	0.268050i
$573$	314.078			0.0228984
$574$	−6571.03	+	3793.78i	−0.477821	+	0.275870i
$575$	5777.34	+	10006.7i	0.419012	+	0.725750i
$576$	−103.459	+	179.196i	−0.00748401	+	0.0129627i
$577$			8182.68i			0.590381i	0.955438	+	0.295190i	$0.0953830\pi$
$577$			8182.68i			0.590381i	−0.955438	+	0.295190i	$0.904617\pi$
$578$	−6940.30	−	4006.98i	−0.499444	−	0.288354i
$579$	−9230.90	−	5329.46i	−0.662561	−	0.382530i
$580$			84.8198i			0.00607233i
$581$	−6029.56	+	10443.5i	−0.430548	+	0.745730i
$582$	5872.17	+	10170.9i	0.418229	+	0.724394i
$583$	−13925.4	+	8039.85i	−0.989249	+	0.571143i
$584$	−5128.86			−0.363414
$585$	14.4924	−	8.27820i	0.00102425	−	0.000585062i
$586$	11056.2			0.779396
$587$	−8583.51	+	4955.69i	−0.603543	+	0.348455i	−0.770434	−	0.637520i	$-0.779960\pi$
$587$	−8583.51	+	4955.69i	−0.603543	+	0.348455i	0.166891	+	0.985975i	$0.446627\pi$
$588$	−787.301	−	1363.64i	−0.0552172	−	0.0956391i
$589$	−3068.41	+	5314.64i	−0.214655	+	0.371793i
$590$			56.7208i			0.00395790i
$591$	−5719.75	−	3302.30i	−0.398103	−	0.229845i
$592$	3972.47	+	2293.51i	0.275790	+	0.159227i
$593$		−	16356.5i		−	1.13268i	−0.824170	−	0.566342i	$-0.808358\pi$
$593$		−	16356.5i		−	1.13268i	0.824170	−	0.566342i	$-0.191642\pi$
$594$	−5719.75	+	9906.89i	−0.395091	+	0.684318i
$595$	84.2246	+	145.881i	0.00580314	+	0.0100513i
$596$	8033.47	−	4638.12i	0.552120	−	0.318767i
$597$	−6859.23			−0.470234
$598$	−7525.20	+	4298.45i	−0.514596	+	0.293941i
$599$	−20073.9			−1.36928			−0.684640	−	0.728881i	$-0.740041\pi$
$599$	−20073.9			−1.36928			−0.684640	+	0.728881i	$0.740041\pi$
$600$	4221.58	−	2437.33i	0.287242	−	0.165839i
$601$	3286.93	+	5693.13i	0.223089	+	0.386402i	0.955745	−	0.294198i	$-0.0950525\pi$
$601$	3286.93	+	5693.13i	0.223089	+	0.386402i	−0.732655	+	0.680600i	$0.761719\pi$
$602$	8516.07	−	14750.3i	0.576560	−	0.998631i
$603$		−	1466.15i		−	0.0990157i
$604$	6796.52	+	3923.98i	0.457859	+	0.264345i
$605$	−16.6885	−	9.63511i	−0.00112146	−	0.000647476i
$606$		−	6120.44i		−	0.410274i
$607$	7187.22	−	12448.6i	0.480593	−	0.832412i	−0.519159	−	0.854678i	$-0.673755\pi$
$607$	7187.22	−	12448.6i	0.480593	−	0.832412i	0.999752	+	0.0222657i	$0.00708797\pi$
$608$	−619.111	−	1072.33i	−0.0412965	−	0.0715277i
$609$	−13164.0	+	7600.25i	−0.875917	+	0.505711i
$610$	31.5667			0.00209525
$611$	12972.0	+	7569.47i	0.858902	+	0.501191i
$612$	−1221.41			−0.0806738
$613$	1095.61	−	632.550i	0.0721879	−	0.0416777i	−0.463472	−	0.886112i	$-0.653396\pi$
$613$	1095.61	−	632.550i	0.0721879	−	0.0416777i	0.535660	+	0.844434i	$0.320063\pi$
$614$	−10085.6	−	17468.8i	−0.662901	−	1.14818i
$615$	62.8919	−	108.932i	0.00412365	−	0.00714237i
$616$		−	5027.57i		−	0.328842i
$617$	16903.7	+	9759.33i	1.10294	+	0.636784i	0.936992	−	0.349350i	$-0.113598\pi$
$617$	16903.7	+	9759.33i	1.10294	+	0.636784i	0.165950	+	0.986134i	$0.446931\pi$
$618$	4494.58	+	2594.95i	0.292554	+	0.168906i
$619$		−	16094.2i		−	1.04504i	−0.852626	−	0.522521i	$-0.824992\pi$
$619$		−	16094.2i		−	1.04504i	0.852626	−	0.522521i	$-0.175008\pi$
$620$	34.9342	−	60.5077i	0.00226289	−	0.00391943i
$621$	6812.86	+	11800.2i	0.440242	+	0.762522i
$622$	11080.6	−	6397.41i	0.714298	−	0.412400i
$623$	20228.9			1.30089
$624$	1813.42	+	3174.71i	0.116338	+	0.203670i
$625$	15620.5			0.999709
$626$	5174.31	−	2987.39i	0.330362	−	0.190735i
$627$	−3660.27	−	6339.77i	−0.233137	−	0.403806i
$628$	4998.44	−	8657.55i	0.317610	−	0.550118i
$629$			27076.5i			1.71639i
$630$	9.98769	+	5.76640i	0.000631618	+	0.000364665i
$631$	−14480.6	−	8360.35i	−0.913569	−	0.527449i	−0.0319910	−	0.999488i	$-0.510185\pi$
$631$	−14480.6	−	8360.35i	−0.913569	−	0.527449i	−0.881578	+	0.472039i	$0.843518\pi$
$632$			4706.32i			0.296214i
$633$	−994.706	+	1722.88i	−0.0624581	+	0.108181i
$634$	−841.335	−	1457.24i	−0.0527030	−	0.0912842i
$635$	−214.835	+	124.035i	−0.0134259	+	0.00775147i
$636$	8080.09			0.503768
$637$	3784.73	+	17.4826i	0.235410	+	0.00108742i
$638$	14943.4			0.927295
$639$	−2116.48	+	1221.95i	−0.131028	+	0.0756489i
$640$	7.04865	+	12.2086i	0.000435348	+	0.000754044i
$641$	−4882.19	+	8456.20i	−0.300834	+	0.521060i	−0.976325	−	0.216308i	$-0.930598\pi$
$641$	−4882.19	+	8456.20i	−0.300834	+	0.521060i	0.675491	+	0.737368i	$0.263932\pi$
$642$			14456.4i			0.888706i
$643$	3455.26	+	1994.90i	0.211916	+	0.122350i	0.602202	−	0.798344i	$-0.294290\pi$
$643$	3455.26	+	1994.90i	0.211916	+	0.122350i	−0.390285	+	0.920694i	$0.627624\pi$
$644$	−5186.11	−	2994.20i	−0.317331	−	0.183211i
$645$			282.352i			0.0172366i
$646$	3654.52	−	6329.82i	0.222578	−	0.385516i
$647$	−193.788	−	335.650i	−0.0117752	−	0.0203953i	0.860078	−	0.510163i	$-0.170415\pi$
$647$	−193.788	−	335.650i	−0.0117752	−	0.0203953i	−0.871853	+	0.489768i	$0.837082\pi$
$648$	4373.45	−	2525.01i	0.265132	−	0.153074i
$649$	9992.96			0.604404
$650$	−54.1228	+	11716.8i	−0.00326595	+	0.707031i
$651$	12521.1			0.753823
$652$	9155.01	−	5285.65i	0.549905	−	0.317488i
$653$	−7564.69	−	13102.4i	−0.453337	−	0.785203i	0.545254	−	0.838271i	$-0.316433\pi$
$653$	−7564.69	−	13102.4i	−0.453337	−	0.785203i	−0.998591	+	0.0530682i	$0.983100\pi$
$654$	352.205	−	610.037i	0.0210586	−	0.0364745i
$655$			22.2247i			0.00132579i
$656$	−3246.11	−	1874.14i	−0.193200	−	0.111544i
$657$	−1795.06	−	1036.38i	−0.106594	−	0.0615419i
$658$			10378.0i			0.614860i
$659$	−4997.61	+	8656.12i	−0.295416	+	0.511676i	−0.975082	−	0.221846i	$-0.928792\pi$
$659$	−4997.61	+	8656.12i	−0.295416	+	0.511676i	0.679665	+	0.733522i	$0.262125\pi$
$660$	41.6726	+	72.1790i	0.00245773	+	0.00425692i
$661$	4915.76	−	2838.11i	0.289260	−	0.167004i	−0.348348	−	0.937365i	$-0.613257\pi$
$661$	4915.76	−	2838.11i	0.289260	−	0.167004i	0.637608	+	0.770361i	$0.279924\pi$
$662$	−5972.59			−0.350652
$663$	−10877.0	+	18640.2i	−0.637147	+	1.09189i
$664$	−5957.24			−0.348171
$665$	−59.7676	+	34.5069i	−0.00348525	+	0.00201221i
$666$	926.890	+	1605.42i	0.0539283	+	0.0934066i
$667$	8899.62	−	15414.6i	0.516634	−	0.894836i
$668$			3436.28i			0.199032i
$669$	10951.3	+	6322.71i	0.632885	+	0.365397i
$670$	−86.5065	−	49.9445i	−0.00498812	−	0.00287989i
$671$		−	5561.37i		−	0.319962i
$672$	−1263.18	+	2187.90i	−0.0725125	+	0.125595i
$673$	−4590.03	−	7950.17i	−0.262901	−	0.455359i	0.704110	−	0.710091i	$-0.251346\pi$
$673$	−4590.03	−	7950.17i	−0.262901	−	0.455359i	−0.967012	+	0.254732i	$0.918013\pi$
$674$	−14693.4	+	8483.23i	−0.839715	+	0.484810i
$675$	18422.0			1.05046
$676$	−8787.62	−	81.1863i	−0.499979	−	0.00461916i
$677$	−25308.1			−1.43673			−0.718366	−	0.695665i	$-0.755110\pi$
$677$	−25308.1			−1.43673			−0.718366	+	0.695665i	$0.755110\pi$
$678$	−4963.35	+	2865.59i	−0.281145	+	0.162319i
$679$	−9753.11	−	16892.9i	−0.551237	−	0.954770i
$680$	−41.6072	+	72.0657i	−0.00234641	+	0.00406411i
$681$		−	25387.7i		−	1.42857i
$682$	−10660.1	−	6154.63i	−0.598530	−	0.345562i
$683$	−13192.5	−	7616.72i	−0.739090	−	0.426714i	0.0826483	−	0.996579i	$-0.473662\pi$
$683$	−13192.5	−	7616.72i	−0.739090	−	0.426714i	−0.821738	+	0.569865i	$0.806996\pi$
$684$		−	500.411i		−	0.0279732i
$685$	105.772	−	183.203i	0.00589979	−	0.0102187i
$686$	6862.25	+	11885.8i	0.381927	+	0.661517i
$687$	−10361.5	+	5982.20i	−0.575422	+	0.332220i
$688$	8413.92			0.466247
$689$	−9788.38	+	16774.6i	−0.541230	+	0.927518i
$690$	99.2734			0.00547721
$691$	10818.4	−	6246.03i	0.595590	−	0.343864i	−0.171715	−	0.985147i	$-0.554931\pi$
$691$	10818.4	−	6246.03i	0.595590	−	0.343864i	0.767305	+	0.641283i	$0.221597\pi$
$692$	−4226.26	−	7320.10i	−0.232165	−	0.402122i
$693$	1015.91	−	1759.61i	0.0556874	−	0.0964533i
$694$		−	4217.44i		−	0.230680i
$695$	−21.3784	−	12.3428i	−0.00116680	−	0.000673654i
$696$	−6503.07	−	3754.55i	−0.354164	−	0.204477i
$697$		−	22125.5i		−	1.20239i
$698$	9213.05	−	15957.5i	0.499597	−	0.865328i
$699$	10363.9	+	17950.7i	0.560797	+	0.971328i
$700$	−7011.63	+	4048.17i	−0.378592	+	0.218580i
$701$	11945.1			0.643597			0.321799	−	0.946808i	$-0.395713\pi$
$701$	11945.1			0.643597			0.321799	+	0.946808i	$0.395713\pi$
$702$	−63.8236	+	13816.9i	−0.00343143	+	0.742854i
$703$	−11093.3			−0.595150
$704$	2150.89	−	1241.82i	0.115149	−	0.0664812i
$705$	−86.0214	−	148.993i	−0.00459540	−	0.00795946i
$706$	400.998	−	694.549i	0.0213764	−	0.0370251i
$707$			10165.5i			0.540751i
$708$	−4348.74	−	2510.74i	−0.230841	−	0.133276i
$709$	3204.65	+	1850.20i	0.169750	+	0.0980054i	0.582468	−	0.812854i	$-0.302087\pi$
$709$	3204.65	+	1850.20i	0.169750	+	0.0980054i	−0.412718	+	0.910859i	$0.635420\pi$
$710$			166.503i			0.00880106i
$711$	−950.997	+	1647.18i	−0.0501620	+	0.0868831i
$712$	4996.56	+	8654.30i	0.262997	+	0.455525i
$713$	−12697.4	+	7330.85i	−0.666931	+	0.385053i
$714$	−14912.8			−0.781649
$715$	−200.329	−	0.925372i	−0.0104782	−	4.84013e-5i
$716$	−838.111			−0.0437453
$717$	1279.13	−	738.507i	0.0666249	−	0.0384659i
$718$	−2709.95	−	4693.77i	−0.140856	−	0.243969i
$719$	−1756.18	+	3041.79i	−0.0910910	+	0.157774i	−0.907970	−	0.419034i	$-0.862369\pi$
$719$	−1756.18	+	3041.79i	−0.0910910	+	0.157774i	0.816879	+	0.576808i	$0.195702\pi$
$720$			5.69723i			0.000294894i
$721$	−7465.06	−	4309.96i	−0.385594	−	0.222623i
$722$	−9286.80	−	5361.74i	−0.478697	−	0.276376i
$723$		−	4920.44i		−	0.253102i
$724$	−9000.55	+	15589.4i	−0.462021	+	0.800243i
$725$	−12032.3	−	20840.6i	−0.616371	−	1.06759i
$726$	1477.43	−	852.996i	0.0755271	−	0.0436056i
$727$	9484.80			0.483868			0.241934	−	0.970293i	$-0.422218\pi$
$727$	9484.80			0.483868			0.241934	+	0.970293i	$0.422218\pi$
$728$	−3011.91	−	5272.88i	−0.153336	−	0.268442i
$729$	21441.7			1.08935
$730$	−122.298	+	70.6086i	−0.00620060	+	0.00357992i
$731$	24833.1	+	43012.2i	1.25648	+	2.17628i
$732$	−1397.30	+	2420.20i	−0.0705543	+	0.122204i
$733$			11063.5i			0.557490i	0.960365	+	0.278745i	$0.0899184\pi$
$733$			11063.5i			0.557490i	−0.960365	+	0.278745i	$0.910082\pi$
$734$	635.879	+	367.125i	0.0319765	+	0.0184616i
$735$	−37.5463	−	21.6774i	−0.00188424	−	0.00108787i
$736$		−	2958.29i		−	0.148157i
$737$	−8799.14	+	15240.5i	−0.439783	+	0.761727i
$738$	−757.408	−	1311.87i	−0.0377786	−	0.0654344i
$739$	7104.94	−	4102.04i	0.353666	−	0.204189i	−0.312633	−	0.949874i	$-0.601211\pi$
$739$	7104.94	−	4102.04i	0.353666	−	0.204189i	0.666299	+	0.745685i	$0.267878\pi$
$740$	126.298			0.00627407
$741$	−7636.89	−	4456.32i	−0.378607	−	0.220927i
$742$	−13420.2			−0.663979
$743$	7119.87	−	4110.66i	0.351552	−	0.202968i	−0.313817	−	0.949484i	$-0.601608\pi$
$743$	7119.87	−	4110.66i	0.351552	−	0.202968i	0.665368	+	0.746515i	$0.268274\pi$
$744$	3092.72	+	5356.75i	0.152399	+	0.263962i
$745$	127.705	−	221.192i	0.00628021	−	0.0108776i
$746$			5596.08i			0.274648i
$747$	−2084.99	−	1203.77i	−0.102123	−	0.0589606i
$748$	12696.4	+	7330.27i	0.620624	+	0.358317i
$749$		−	24010.7i		−	1.17134i
$750$	134.224	−	232.483i	0.00653491	−	0.0113188i
$751$	6732.53	+	11661.1i	0.327129	+	0.566603i	0.981941	−	0.189188i	$-0.0605856\pi$
$751$	6732.53	+	11661.1i	0.327129	+	0.566603i	−0.654812	+	0.755792i	$0.727252\pi$
$752$	−4439.92	+	2563.39i	−0.215302	+	0.124305i
$753$	16201.3			0.784074
$754$	15672.5	−	8952.26i	0.756976	−	0.432390i
$755$	216.084			0.0104160
$756$	−8268.37	+	4773.75i	−0.397775	+	0.229655i
$757$	−12027.9	−	20832.9i	−0.577491	−	1.00024i	−0.995766	−	0.0919236i	$-0.970698\pi$
$757$	−12027.9	−	20832.9i	−0.577491	−	1.00024i	0.418275	−	0.908321i	$-0.362635\pi$
$758$	−4372.64	+	7573.63i	−0.209527	+	0.362911i
$759$		−	17489.8i		−	0.836415i
$760$	−29.5254	−	17.0465i	−0.00140921	−	0.000813607i
$761$	−21161.7	−	12217.7i	−1.00803	−	0.581987i	−0.0974168	−	0.995244i	$-0.531058\pi$
$761$	−21161.7	−	12217.7i	−1.00803	−	0.581987i	−0.910615	+	0.413256i	$0.864391\pi$
$762$		−	21961.7i		−	1.04408i
$763$	−584.978	+	1013.21i	−0.0277557	+	0.0480743i
$764$	−128.849	−	223.173i	−0.00610156	−	0.0105682i
$765$	−29.1244	+	16.8150i	−0.00137646	+	0.000794701i
$766$	19564.3			0.922827
$767$	10480.5	−	5986.57i	0.493391	−	0.281828i
$768$	−1248.03			−0.0586387
$769$	12584.3	−	7265.54i	0.590118	−	0.340705i	−0.175026	−	0.984564i	$-0.556001\pi$
$769$	12584.3	−	7265.54i	0.590118	−	0.340705i	0.765144	+	0.643859i	$0.222668\pi$
$770$	−69.2141	−	119.882i	−0.00323936	−	0.00561073i
$771$	−15620.6	+	27055.6i	−0.729652	+	1.26379i
$772$			8745.55i			0.407719i
$773$	−5022.43	−	2899.70i	−0.233692	−	0.134922i	0.378582	−	0.925568i	$-0.376412\pi$
$773$	−5022.43	−	2899.70i	−0.233692	−	0.134922i	−0.612274	+	0.790645i	$0.709745\pi$
$774$	2944.81	+	1700.19i	0.136756	+	0.0789560i
$775$			19822.7i			0.918776i
$776$	4818.06	−	8345.13i	0.222884	−	0.386047i
$777$	11316.9	+	19601.4i	0.522512	+	0.905017i
$778$	−1993.40	+	1150.89i	−0.0918599	+	0.0530353i
$779$	9064.86			0.416922
$780$	86.9468	+	50.7357i	0.00399128	+	0.00232901i
$781$	29334.2			1.34400
$782$	15122.8	−	8731.17i	0.691549	−	0.399266i
$783$	−14188.9	−	24576.0i	−0.647601	−	1.12168i
$784$	−645.973	+	1118.86i	−0.0294266	+	0.0509684i
$785$		−	275.252i		−	0.0125149i
$786$	−1703.95	−	983.776i	−0.0773256	−	0.0446439i
$787$	4078.30	+	2354.61i	0.184722	+	0.106649i	0.589509	−	0.807762i	$-0.299321\pi$
$787$	4078.30	+	2354.61i	0.184722	+	0.106649i	−0.404788	+	0.914411i	$0.632655\pi$
$788$			5419.01i			0.244980i
$789$	10444.1	−	18089.7i	0.471255	−	0.816237i
$790$	64.7914	+	112.222i	0.00291794	+	0.00505403i
$791$	8243.65	−	4759.47i	0.370557	−	0.213941i
$792$	1003.73			0.0450327
$793$	−3331.70	−	5832.72i	−0.149195	−	0.261193i
$794$	19258.7			0.860790
$795$	192.669	−	111.238i	0.00859532	−	0.00496251i
$796$	2813.97	+	4873.93i	0.125299	+	0.217025i
$797$	2892.14	−	5009.34i	0.128538	−	0.222635i	−0.794572	−	0.607170i	$-0.792305\pi$
$797$	2892.14	−	5009.34i	0.128538	−	0.222635i	0.923110	+	0.384535i	$0.125638\pi$
$798$		−	6109.78i		−	0.271033i
$799$	−26208.2	−	15131.3i	−1.16042	−	0.669971i
$800$	−3463.77	−	1999.81i	−0.153078	−	0.0883798i
$801$			4038.58i			0.178148i
$802$	−6204.93	+	10747.3i	−0.273197	+	0.473191i
$803$	12439.7	+	21546.2i	0.546683	+	0.946884i
$804$	7658.42	−	4421.59i	0.335935	−	0.193952i
$805$	−164.883			−0.00721910
$806$	−14867.4	−	68.6762i	−0.649729	−	0.00300126i
$807$	−27696.2			−1.20812
$808$	−4348.97	+	2510.88i	−0.189352	+	0.109322i
$809$	4513.56	+	7817.71i	0.196154	+	0.339748i	0.947278	−	0.320413i	$-0.103822\pi$
$809$	4513.56	+	7817.71i	0.196154	+	0.339748i	−0.751125	+	0.660161i	$0.770488\pi$
$810$	69.5232	−	120.418i	0.00301580	−	0.00522352i
$811$			8982.87i			0.388941i	0.980908	+	0.194471i	$0.0622989\pi$
$811$			8982.87i			0.388941i	−0.980908	+	0.194471i	$0.937701\pi$
$812$	10801.0	+	6235.94i	0.466797	+	0.269506i
$813$	20747.1	+	11978.4i	0.894999	+	0.516728i
$814$		−	22250.9i		−	0.958102i
$815$	145.534	−	252.072i	0.00625501	−	0.0108340i
$816$	−3683.48	−	6379.98i	−0.158024	−	0.273706i
$817$	−17622.1	+	10174.1i	−0.754614	+	0.435677i
$818$	11320.4			0.483871
$819$	11.3360	−	2454.08i	0.000483654	−	0.104704i
$820$	−103.204			−0.00439519
$821$	4440.94	−	2563.98i	0.188782	−	0.108993i	−0.402630	−	0.915363i	$-0.631904\pi$
$821$	4440.94	−	2563.98i	0.188782	−	0.108993i	0.591412	+	0.806369i	$0.298571\pi$
$822$	9364.02	+	16219.0i	0.397333	+	0.688201i
$823$	−18012.0	+	31197.7i	−0.762890	+	1.32136i	0.178465	+	0.983946i	$0.442887\pi$
$823$	−18012.0	+	31197.7i	−0.762890	+	1.32136i	−0.941355	+	0.337418i	$0.890447\pi$
$824$		−	4258.26i		−	0.180029i
$825$	−20478.3	−	11823.1i	−0.864195	−	0.498943i
$826$	7222.83	+	4170.10i	0.304255	+	0.175662i
$827$			11728.0i			0.493136i	0.969126	+	0.246568i	$0.0793028\pi$
$827$			11728.0i			0.493136i	−0.969126	+	0.246568i	$0.920697\pi$
$828$	597.776	−	1035.38i	0.0250895	−	0.0434564i
$829$	−7543.28	−	13065.3i	−0.316030	−	0.547380i	0.663626	−	0.748065i	$-0.269017\pi$
$829$	−7543.28	−	13065.3i	−0.316030	−	0.547380i	−0.979656	+	0.200684i	$0.935683\pi$
$830$	−142.050	+	82.0127i	−0.00594052	+	0.00342976i
$831$	−37730.3			−1.57503
$832$	1511.89	−	2590.96i	0.0629994	−	0.107963i
$833$	−7626.17			−0.317204
$834$	1892.63	−	1092.71i	0.0785806	−	0.0453686i
$835$	47.3069	+	81.9380i	0.00196063	+	0.00339590i
$836$	−3003.22	+	5201.73i	−0.124245	+	0.215198i
$837$			23375.6i			0.965328i
$838$	6354.94	+	3669.03i	0.261966	+	0.151246i
$839$	23716.0	+	13692.5i	0.975886	+	0.563428i	0.901025	−	0.433766i	$-0.142816\pi$
$839$	23716.0	+	13692.5i	0.975886	+	0.563428i	0.0748602	+	0.997194i	$0.476149\pi$
$840$			69.5606i			0.00285722i
$841$	−6340.49	+	10982.0i	−0.259973	+	0.450287i
$842$	−13716.5	−	23757.7i	−0.561403	−	0.972379i
$843$	17757.3	−	10252.2i	0.725497	−	0.418866i
$844$	1632.29			0.0665709
$845$	−210.658	+	119.042i	−0.00857617	+	0.00484637i
$846$	−2071.92			−0.0842009
$847$	−2453.87	+	1416.74i	−0.0995467	+	0.0574733i
$848$	−3314.82	−	5741.43i	−0.134235	−	0.232502i
$849$	8154.49	−	14124.0i	0.329636	−	0.570947i
$850$		−	23609.1i		−	0.952690i
$851$	−22952.6	−	13251.7i	−0.924564	−	0.533797i
$852$	−12765.7	−	7370.26i	−0.513315	−	0.296362i
$853$			30583.1i			1.22760i	0.789460	+	0.613802i	$0.210361\pi$
$853$			30583.1i			1.22760i	−0.789460	+	0.613802i	$0.789639\pi$
$854$	2320.78	−	4019.71i	0.0929924	−	0.161068i
$855$	−6.88910	−	11.9323i	−0.000275558	−	0.000477281i
$856$	10272.2	−	5930.68i	0.410161	−	0.236807i
$857$	−19542.8			−0.778962			−0.389481	−	0.921035i	$-0.627346\pi$
$857$	−19542.8			−0.778962			−0.389481	+	0.921035i	$0.627346\pi$
$858$	8938.52	−	15318.1i	0.355660	−	0.609501i
$859$	−3593.03			−0.142716			−0.0713578	−	0.997451i	$-0.522733\pi$
$859$	−3593.03			−0.142716			−0.0713578	+	0.997451i	$0.522733\pi$
$860$	200.630	−	115.834i	0.00795514	−	0.00459290i
$861$	−9247.60	−	16017.3i	−0.366036	−	0.633994i
$862$	−15219.5	+	26360.9i	−0.601366	+	1.04160i
$863$		−	22652.3i		−	0.893501i	−0.894658	−	0.446751i	$-0.852581\pi$
$863$		−	22652.3i		−	0.893501i	0.894658	−	0.446751i	$-0.147419\pi$
$864$	−4084.60	−	2358.24i	−0.160834	−	0.0928578i
$865$	−201.550	−	116.365i	−0.00792244	−	0.00457402i
$866$			32390.0i			1.27097i
$867$	9767.29	−	16917.4i	0.382600	−	0.662683i
$868$	−5136.71	−	8897.04i	−0.200865	−	0.347909i
$869$	19771.1	−	11414.8i	0.771792	−	0.445594i
$870$	−206.754			−0.00805703
$871$	−98.1848	+	21255.6i	−0.00381959	+	0.826885i
$872$	−577.961			−0.0224452
$873$	3372.57	−	1947.15i	0.130749	−	0.0754882i
$874$	3577.17	+	6195.83i	0.138443	+	0.239791i
$875$	−222.934	+	386.132i	−0.00861318	+	0.0149185i
$876$		−	12501.9i		−	0.482194i
$877$	3379.00	+	1950.86i	0.130103	+	0.0751152i	0.563639	−	0.826021i	$-0.309401\pi$
$877$	3379.00	+	1950.86i	0.130103	+	0.0751152i	−0.433536	+	0.901136i	$0.642734\pi$
$878$	−3935.80	−	2272.34i	−0.151283	−	0.0873436i
$879$			26950.1i			1.03414i
$880$	34.1920	−	59.2222i	0.00130979	−	0.00226861i
$881$	−18576.6	−	32175.6i	−0.710398	−	1.23044i	−0.964708	−	0.263322i	$-0.915182\pi$
$881$	−18576.6	−	32175.6i	−0.710398	−	1.23044i	0.254310	−	0.967123i	$-0.418152\pi$
$882$	−452.171	+	261.061i	−0.0172623	+	0.00996642i
$883$	−32883.2			−1.25324			−0.626618	−	0.779326i	$-0.715561\pi$
$883$	−32883.2			−1.25324			−0.626618	+	0.779326i	$0.715561\pi$
$884$	17707.3	+	81.7945i	0.673712	+	0.00311205i
$885$	−138.261			−0.00525150
$886$	−22855.9	+	13195.8i	−0.866657	+	0.500365i
$887$	−12940.4	−	22413.5i	−0.489850	−	0.848445i	0.510082	−	0.860126i	$-0.329615\pi$
$887$	−12940.4	−	22413.5i	−0.489850	−	0.848445i	−0.999932	+	0.0116807i	$0.996282\pi$
$888$	−5590.58	+	9683.17i	−0.211270	+	0.365930i
$889$			36476.2i			1.37612i
$890$	238.286	+	137.574i	0.00897456	+	0.00518146i
$891$	−21215.0	−	12248.5i	−0.797675	−	0.460538i
$892$		−	10375.5i		−	0.389457i
$893$	6199.31	−	10737.5i	0.232309	−	0.402371i
$894$	11305.7	+	19582.1i	0.422953	+	0.732577i
$895$	−19.9847	+	11.5382i	−0.000746386	+	0.000430926i
$896$	2072.86			0.0772874
$897$	−10477.8	−	18343.2i	−0.390014	−	0.682788i
$898$	−29255.0			−1.08714
$899$	26444.5	−	15267.8i	0.981062	−	0.566416i
$900$	−808.194	−	1399.83i	−0.0299331	−	0.0518457i
$901$	19566.9	−	33890.8i	0.723493	−	1.25313i
$902$			18182.4i			0.671182i
$903$	35954.7	+	20758.5i	1.32503	+	0.765004i
$904$	4072.38	+	2351.19i	0.149829	+	0.0865039i
$905$			495.639i			0.0182051i
$906$	−9564.95	+	16567.0i	−0.350744	+	0.607507i
$907$	11049.2	+	19137.8i	0.404502	+	0.700617i	0.994263	−	0.106960i	$-0.0341117\pi$
$907$	11049.2	+	19137.8i	0.404502	+	0.700617i	−0.589762	+	0.807577i	$0.700778\pi$
$908$	−18039.6	+	10415.2i	−0.659323	+	0.380660i
$909$	−2029.48			−0.0740522
$910$	−144.410	−	84.2671i	−0.00526061	−	0.00306970i
$911$	43509.4			1.58236			0.791180	−	0.611583i	$-0.209467\pi$
$911$	43509.4			1.58236			0.791180	+	0.611583i	$0.209467\pi$
$912$	2613.88	−	1509.12i	0.0949060	−	0.0547940i
$913$	14448.8	+	25026.1i	0.523753	+	0.907167i
$914$	3222.34	−	5581.26i	0.116614	−	0.201982i
$915$			76.9460i			0.00278006i
$916$	8501.50	+	4908.34i	0.306657	+	0.177048i
$917$	2830.10	+	1633.96i	0.101917	+	0.0588419i
$918$		−	27840.7i		−	1.00096i
$919$	6442.74	−	11159.2i	0.231258	−	0.400551i	−0.726920	−	0.686722i	$-0.759049\pi$
$919$	6442.74	−	11159.2i	0.231258	−	0.400551i	0.958179	+	0.286170i	$0.0923824\pi$
$920$	−40.7264	−	70.5403i	−0.00145947	−	0.00252787i
$921$	42581.2	−	24584.3i	1.52345	−	0.879565i
$922$	2619.79			0.0935773
$923$	30765.5	−	17573.5i	1.09714	−	0.626694i
$924$	12255.0			0.436322
$925$	−31031.9	+	17916.3i	−1.10305	+	0.636848i
$926$	16084.0	+	27858.3i	0.570792	+	0.988640i
$927$	860.459	−	1490.36i	0.0304867	−	0.0528045i
$928$			6161.14i			0.217941i
$929$	9246.24	+	5338.32i	0.326544	+	0.188530i	0.654306	−	0.756230i	$-0.272961\pi$
$929$	9246.24	+	5338.32i	0.326544	+	0.188530i	−0.327762	+	0.944760i	$0.606294\pi$
$930$	147.492	+	85.1543i	0.00520047	+	0.00300249i
$931$		−	3124.45i		−	0.109989i
$932$	8503.44	−	14728.4i	0.298862	−	0.517644i
$933$	15594.1	+	27009.8i	0.547190	+	0.947761i
$934$	−17495.0	+	10100.7i	−0.612905	+	0.353861i
$935$	403.660			0.0141188
$936$	1052.70	−	601.312i	0.0367614	−	0.0209984i
$937$	−39125.1			−1.36410			−0.682050	−	0.731306i	$-0.738911\pi$
$937$	−39125.1			−1.36410			−0.682050	+	0.731306i	$0.738911\pi$
$938$	−12719.9	+	7343.83i	−0.442771	+	0.255634i
$939$	7281.95	+	12612.7i	0.253075	+	0.438339i
$940$	−70.5798	+	122.248i	−0.00244900	+	0.00424179i
$941$		−	22571.0i		−	0.781926i	−0.920406	−	0.390963i	$-0.872142\pi$
$941$		−	22571.0i		−	0.781926i	0.920406	−	0.390963i	$-0.127858\pi$
$942$	21103.3	+	12184.0i	0.729919	+	0.421419i
$943$	18755.7	+	10828.6i	0.647687	+	0.373942i
$944$			4120.09i			0.142052i
$945$	−131.439	+	227.660i	−0.00452458	+	0.00783680i
$946$	−20407.3	−	35346.6i	−0.701374	−	1.21482i
$947$	4052.60	−	2339.77i	0.139062	−	0.0802874i	−0.428855	−	0.903373i	$-0.641083\pi$
$947$	4052.60	−	2339.77i	0.139062	−	0.0802874i	0.567917	+	0.823086i	$0.307750\pi$
$948$	−11472.0			−0.393029
$949$	25954.5	+	15145.1i	0.887796	+	0.518052i
$950$	9672.68			0.330340
$951$	3552.11	−	2050.81i	0.121120	−	0.0699286i
$952$	6117.90	+	10596.5i	0.208280	+	0.360751i
$953$	16683.0	−	28895.9i	0.567069	−	0.982192i	−0.429785	−	0.902931i	$-0.641411\pi$
$953$	16683.0	−	28895.9i	0.567069	−	0.982192i	0.996854	−	0.0792605i	$-0.0252559\pi$
$954$		−	2679.28i		−	0.0909275i
$955$	−6.14479	−	3.54770i	−0.000208210	−	0.000120210i
$956$	−1049.52	−	605.938i	−0.0355060	−	0.0204994i
$957$			36425.5i			1.23038i
$958$	8480.01	−	14687.8i	0.285988	−	0.495346i
$959$	−15552.7	−	26938.1i	−0.523695	−	0.907067i
$960$	−29.7593	+	17.1816i	−0.00100050	+	0.000577638i
$961$	4638.09			0.155688
$962$	−13330.1	−	23336.6i	−0.446755	−	0.782124i
$963$	4793.60			0.160407
$964$	−3496.29	+	2018.59i	−0.116813	+	0.0674422i
$965$	120.399	+	208.537i	0.00401635	+	0.00695653i
$966$	7298.56	−	12641.5i	0.243092	−	0.421049i
$967$		−	56075.3i		−	1.86480i	−0.361431	−	0.932399i	$-0.617712\pi$
$967$		−	56075.3i		−	1.86480i	0.361431	−	0.932399i	$-0.382288\pi$
$968$	−1212.22	−	699.875i	−0.0402502	−	0.0232385i
$969$	15429.4	+	8908.14i	0.511519	+	0.295326i
$970$		−	265.319i		−	0.00878235i
$971$	−25273.7	+	43775.3i	−0.835294	+	1.44677i	0.0584964	+	0.998288i	$0.481369\pi$
$971$	−25273.7	+	43775.3i	−0.835294	+	1.44677i	−0.893791	+	0.448484i	$0.851964\pi$
$972$	−1804.19	−	3124.94i	−0.0595363	−	0.103120i
$973$	−3143.47	+	1814.88i	−0.103571	+	0.0597969i
$974$	−13544.7			−0.445584
$975$	−28560.4	−	131.928i	−0.938118	−	0.00433341i
$976$	2292.94			0.0752002
$977$	−27148.1	+	15673.9i	−0.888990	+	0.513259i	−0.873612	−	0.486623i	$-0.838229\pi$
$977$	−27148.1	+	15673.9i	−0.888990	+	0.513259i	−0.0153782	+	0.999882i	$0.504895\pi$
$978$	12884.1	+	22315.9i	0.421256	+	0.729637i
$979$	24237.6	−	41980.7i	0.791253	−	1.37049i
$980$			35.5722i			0.00115950i
$981$	−202.282	−	116.788i	−0.00658345	−	0.00380096i
$982$	−14593.6	−	8425.61i	−0.474236	−	0.273800i
$983$		−	6770.66i		−	0.219685i	−0.993949	−	0.109843i	$-0.964965\pi$
$983$		−	6770.66i		−	0.219685i	0.993949	−	0.109843i	$-0.0350346\pi$
$984$	4568.34	−	7912.60i	0.148001	−	0.256346i
$985$	74.6030	+	129.216i	0.00241325	+	0.00417987i
$986$	−31495.9	+	18184.2i	−1.01728	+	0.587324i
$987$	−25297.1			−0.815822
$988$	−33.5113	+	7254.70i	−0.00107909	+	0.233606i
$989$	−48614.8			−1.56306
$990$	23.9339	−	13.8182i	0.000768351	−	0.000443608i
$991$	3421.43	+	5926.09i	0.109672	+	0.189958i	0.915638	−	0.402005i	$-0.131686\pi$
$991$	3421.43	+	5926.09i	0.109672	+	0.189958i	−0.805965	+	0.591963i	$0.798353\pi$
$992$	2537.55	−	4395.16i	0.0812169	−	0.140672i
$993$		−	14558.6i		−	0.465259i
$994$	21202.5	+	12241.3i	0.676562	+	0.390613i
$995$	134.198	+	77.4792i	0.00427574	+	0.00246860i
$996$		−	14521.2i		−	0.461968i
$997$	−11882.5	+	20581.1i	−0.377455	+	0.653771i	−0.990691	−	0.136129i	$-0.956534\pi$
$997$	−11882.5	+	20581.1i	−0.377455	+	0.653771i	0.613237	+	0.789899i	$0.289867\pi$
$998$	12421.7	+	21515.0i	0.393990	+	0.682410i
$999$	−36594.0	+	21127.6i	−1.15894	+	0.669116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.4.e.a.23.4	yes	8
3.2	odd	2		234.4.l.b.127.2		8
4.3	odd	2		208.4.w.d.49.1		8
13.2	odd	12		338.4.a.m.1.1		4
13.3	even	3		338.4.b.g.337.5		8
13.4	even	6	inner	26.4.e.a.17.4	✓	8
13.5	odd	4		338.4.c.m.315.4		8
13.6	odd	12		338.4.c.m.191.4		8
13.7	odd	12		338.4.c.n.191.4		8
13.8	odd	4		338.4.c.n.315.4		8
13.9	even	3		338.4.e.e.147.2		8
13.10	even	6		338.4.b.g.337.1		8
13.11	odd	12		338.4.a.l.1.1		4
13.12	even	2		338.4.e.e.23.2		8
39.17	odd	6		234.4.l.b.199.1		8
52.43	odd	6		208.4.w.d.17.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.e.a.17.4	✓	8	13.4	even	6	inner
26.4.e.a.23.4	yes	8	1.1	even	1	trivial
208.4.w.d.17.1		8	52.43	odd	6
208.4.w.d.49.1		8	4.3	odd	2
234.4.l.b.127.2		8	3.2	odd	2
234.4.l.b.199.1		8	39.17	odd	6
338.4.a.l.1.1		4	13.11	odd	12
338.4.a.m.1.1		4	13.2	odd	12
338.4.b.g.337.1		8	13.10	even	6
338.4.b.g.337.5		8	13.3	even	3
338.4.c.m.191.4		8	13.6	odd	12
338.4.c.m.315.4		8	13.5	odd	4
338.4.c.n.191.4		8	13.7	odd	12
338.4.c.n.315.4		8	13.8	odd	4
338.4.e.e.23.2		8	13.12	even	2
338.4.e.e.147.2		8	13.9	even	3

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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	26.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(2.43757 + 4.22199i) q^{3} +(2.00000 - 3.46410i) q^{4} -0.110135i q^{5} +(8.44398 + 4.87513i) q^{6} +(-14.0246 - 8.09712i) q^{7} -8.00000i q^{8} +(1.61655 - 2.79994i) q^{9} +O(q^{10})\)	\(q+(1.73205 - 1.00000i) q^{2} +(2.43757 + 4.22199i) q^{3} +(2.00000 - 3.46410i) q^{4} -0.110135i q^{5} +(8.44398 + 4.87513i) q^{6} +(-14.0246 - 8.09712i) q^{7} -8.00000i q^{8} +(1.61655 - 2.79994i) q^{9} +(-0.110135 - 0.190760i) q^{10} +(-33.6077 + 19.4034i) q^{11} +19.5005 q^{12} +(-23.6233 + 40.4838i) q^{13} -32.3885 q^{14} +(0.464989 - 0.268462i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(47.2228 - 81.7923i) q^{17} -6.46618i q^{18} +(33.5104 + 19.3472i) q^{19} +(-0.381520 - 0.220270i) q^{20} -78.9491i q^{21} +(-38.8068 + 67.2154i) q^{22} +(46.2232 + 80.0610i) q^{23} +(33.7759 - 19.5005i) q^{24} +124.988 q^{25} +(-0.433024 + 93.7433i) q^{26} +147.390 q^{27} +(-56.0985 + 32.3885i) q^{28} +(-96.2678 - 166.741i) q^{29} +(0.536924 - 0.929979i) q^{30} +158.597i q^{31} +(-27.7128 - 16.0000i) q^{32} +(-163.842 - 94.5942i) q^{33} -188.891i q^{34} +(-0.891778 + 1.54460i) q^{35} +(-6.46618 - 11.1998i) q^{36} +(-248.280 + 143.344i) q^{37} +77.3889 q^{38} +(-228.506 - 1.05553i) q^{39} -0.881082 q^{40} +(202.882 - 117.134i) q^{41} +(-78.9491 - 136.744i) q^{42} +(-262.935 + 455.417i) q^{43} +155.227i q^{44} +(-0.308372 - 0.178039i) q^{45} +(160.122 + 92.4465i) q^{46} -320.423i q^{47} +(39.0011 - 67.5518i) q^{48} +(-40.3733 - 69.9286i) q^{49} +(216.485 - 124.988i) q^{50} +460.435 q^{51} +(92.9933 + 162.801i) q^{52} +414.352 q^{53} +(255.287 - 147.390i) q^{54} +(2.13700 + 3.70139i) q^{55} +(-64.7770 + 112.197i) q^{56} +188.641i q^{57} +(-333.482 - 192.536i) q^{58} +(-223.006 - 128.753i) q^{59} -2.14769i q^{60} +(-71.6545 + 124.109i) q^{61} +(158.597 + 274.698i) q^{62} +(-45.3429 + 26.1787i) q^{63} -64.0000 q^{64} +(4.45869 + 2.60176i) q^{65} -378.377 q^{66} +(392.729 - 226.742i) q^{67} +(-188.891 - 327.169i) q^{68} +(-225.344 + 390.308i) q^{69} +3.56711i q^{70} +(-654.631 - 377.952i) q^{71} +(-22.3995 - 12.9324i) q^{72} -641.108i q^{73} +(-286.689 + 496.559i) q^{74} +(304.666 + 527.697i) q^{75} +(134.042 - 77.3889i) q^{76} +628.447 q^{77} +(-396.839 + 226.677i) q^{78} -588.290 q^{79} +(-1.52608 + 0.881082i) q^{80} +(315.627 + 546.682i) q^{81} +(234.267 - 405.763i) q^{82} -744.654i q^{83} +(-273.488 - 157.898i) q^{84} +(-9.00822 - 5.20090i) q^{85} +1051.74i q^{86} +(469.318 - 812.883i) q^{87} +(155.227 + 268.861i) q^{88} +(-1081.79 + 624.570i) q^{89} -0.712154 q^{90} +(659.111 - 376.489i) q^{91} +369.786 q^{92} +(-669.593 + 386.590i) q^{93} +(-320.423 - 554.990i) q^{94} +(2.13081 - 3.69067i) q^{95} -156.004i q^{96} +(1043.14 + 602.258i) q^{97} +(-139.857 - 80.7466i) q^{98} +125.466i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} + 16 q^{4} + 18 q^{7} - 22 q^{9}+O(q^{10}) \) 8 * q - 6 * q^3 + 16 * q^4 + 18 * q^7 - 22 * q^9	\( 8 q - 6 q^{3} + 16 q^{4} + 18 q^{7} - 22 q^{9} - 8 q^{10} - 18 q^{11} - 48 q^{12} - 130 q^{13} + 80 q^{14} - 192 q^{15} - 64 q^{16} + 112 q^{17} + 594 q^{19} + 72 q^{20} - 72 q^{22} - 230 q^{23} - 180 q^{25} - 184 q^{26} + 468 q^{27} + 72 q^{28} + 32 q^{29} + 328 q^{30} - 42 q^{33} - 128 q^{35} + 88 q^{36} - 768 q^{37} - 576 q^{38} - 230 q^{39} - 64 q^{40} - 564 q^{41} - 688 q^{42} - 114 q^{43} + 630 q^{45} + 576 q^{46} - 96 q^{48} - 110 q^{49} + 1968 q^{50} + 1300 q^{51} - 104 q^{52} + 36 q^{53} + 648 q^{54} + 1248 q^{55} + 160 q^{56} - 1848 q^{58} - 1110 q^{59} + 900 q^{61} + 1064 q^{62} - 1980 q^{63} - 512 q^{64} + 1870 q^{65} - 2400 q^{66} + 510 q^{67} - 448 q^{68} - 2402 q^{69} - 1470 q^{71} + 576 q^{72} - 680 q^{74} - 862 q^{75} + 2376 q^{76} + 2340 q^{77} + 1016 q^{78} + 784 q^{79} + 288 q^{80} + 1868 q^{81} + 704 q^{82} - 2136 q^{84} - 2898 q^{85} + 1598 q^{87} + 288 q^{88} - 4434 q^{89} - 2384 q^{90} - 886 q^{91} - 1840 q^{92} + 3108 q^{93} - 2568 q^{94} - 816 q^{95} + 1854 q^{97} + 4272 q^{98}+O(q^{100}) \) 8 * q - 6 * q^3 + 16 * q^4 + 18 * q^7 - 22 * q^9 - 8 * q^10 - 18 * q^11 - 48 * q^12 - 130 * q^13 + 80 * q^14 - 192 * q^15 - 64 * q^16 + 112 * q^17 + 594 * q^19 + 72 * q^20 - 72 * q^22 - 230 * q^23 - 180 * q^25 - 184 * q^26 + 468 * q^27 + 72 * q^28 + 32 * q^29 + 328 * q^30 - 42 * q^33 - 128 * q^35 + 88 * q^36 - 768 * q^37 - 576 * q^38 - 230 * q^39 - 64 * q^40 - 564 * q^41 - 688 * q^42 - 114 * q^43 + 630 * q^45 + 576 * q^46 - 96 * q^48 - 110 * q^49 + 1968 * q^50 + 1300 * q^51 - 104 * q^52 + 36 * q^53 + 648 * q^54 + 1248 * q^55 + 160 * q^56 - 1848 * q^58 - 1110 * q^59 + 900 * q^61 + 1064 * q^62 - 1980 * q^63 - 512 * q^64 + 1870 * q^65 - 2400 * q^66 + 510 * q^67 - 448 * q^68 - 2402 * q^69 - 1470 * q^71 + 576 * q^72 - 680 * q^74 - 862 * q^75 + 2376 * q^76 + 2340 * q^77 + 1016 * q^78 + 784 * q^79 + 288 * q^80 + 1868 * q^81 + 704 * q^82 - 2136 * q^84 - 2898 * q^85 + 1598 * q^87 + 288 * q^88 - 4434 * q^89 - 2384 * q^90 - 886 * q^91 - 1840 * q^92 + 3108 * q^93 - 2568 * q^94 - 816 * q^95 + 1854 * q^97 + 4272 * q^98

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