LMFDB - Embedded newform 128.4.k.a.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(5,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("128.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.k (of order $32$, degree $16$, 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:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$752$
Relative dimension:	$47$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			5.3
Character	$\chi$	$=$	128.5
Dual form			128.4.k.a.77.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.73119 + 0.735238i) q^{2} +(-2.99224 - 0.907685i) q^{3} +(6.91885 - 4.01616i) q^{4} +(20.1386 + 1.98348i) q^{5} +(8.83975 + 0.279059i) q^{6} +(-4.42679 - 6.62516i) q^{7} +(-15.9439 + 16.0559i) q^{8} +(-14.3201 - 9.56838i) q^{9} +O(q^{10})$	\(q+(-2.73119 + 0.735238i) q^{2} +(-2.99224 - 0.907685i) q^{3} +(6.91885 - 4.01616i) q^{4} +(20.1386 + 1.98348i) q^{5} +(8.83975 + 0.279059i) q^{6} +(-4.42679 - 6.62516i) q^{7} +(-15.9439 + 16.0559i) q^{8} +(-14.3201 - 9.56838i) q^{9} +(-56.4608 + 9.38941i) q^{10} +(2.24857 - 4.20677i) q^{11} +(-24.3482 + 5.73715i) q^{12} +(3.42203 + 34.7444i) q^{13} +(16.9615 + 14.8399i) q^{14} +(-58.4592 - 24.2146i) q^{15} +(31.7410 - 55.5744i) q^{16} +(115.947 - 48.0269i) q^{17} +(46.1460 + 15.6044i) q^{18} +(16.2002 - 19.7400i) q^{19} +(147.302 - 67.1564i) q^{20} +(7.23244 + 23.8422i) q^{21} +(-3.04829 + 13.1427i) q^{22} +(-31.7855 - 159.797i) q^{23} +(62.2816 - 33.5710i) q^{24} +(279.032 + 55.5029i) q^{25} +(-34.8916 - 92.3778i) q^{26} +(87.7232 + 106.891i) q^{27} +(-57.2359 - 28.0598i) q^{28} +(-21.0446 + 11.2486i) q^{29} +(177.467 + 23.1533i) q^{30} +(-13.6670 - 13.6670i) q^{31} +(-45.8304 + 175.122i) q^{32} +(-10.5467 + 10.5467i) q^{33} +(-281.363 + 216.420i) q^{34} +(-76.0086 - 142.202i) q^{35} +(-137.507 - 8.69047i) q^{36} +(226.234 - 185.666i) q^{37} +(-29.7323 + 65.8247i) q^{38} +(21.2975 - 107.070i) q^{39} +(-352.935 + 291.719i) q^{40} +(-165.586 + 32.9371i) q^{41} +(-37.2829 - 59.8000i) q^{42} +(394.786 - 119.757i) q^{43} +(-1.33756 - 38.1366i) q^{44} +(-269.408 - 221.098i) q^{45} +(204.301 + 413.066i) q^{46} +(93.4867 + 225.697i) q^{47} +(-145.421 + 137.481i) q^{48} +(106.964 - 258.234i) q^{49} +(-802.898 + 53.5656i) q^{50} +(-390.535 + 38.4643i) q^{51} +(163.215 + 226.648i) q^{52} +(163.009 + 87.1301i) q^{53} +(-318.179 - 227.443i) q^{54} +(53.6271 - 80.2586i) q^{55} +(176.953 + 34.5547i) q^{56} +(-66.3925 + 44.3620i) q^{57} +(49.2066 - 46.1949i) q^{58} +(75.6616 - 768.205i) q^{59} +(-501.720 + 67.2441i) q^{60} +(-23.4833 + 77.4142i) q^{61} +(47.3757 + 27.2787i) q^{62} +137.230i q^{63} +(-3.58414 - 511.987i) q^{64} +706.492i q^{65} +(21.0507 - 36.5593i) q^{66} +(-133.350 + 439.595i) q^{67} +(609.338 - 797.953i) q^{68} +(-49.9352 + 507.001i) q^{69} +(312.146 + 332.497i) q^{70} +(-805.116 + 537.961i) q^{71} +(381.947 - 77.3647i) q^{72} +(-246.257 + 368.550i) q^{73} +(-481.382 + 673.425i) q^{74} +(-784.550 - 419.351i) q^{75} +(32.8078 - 201.640i) q^{76} +(-37.8244 + 3.72538i) q^{77} +(20.5541 + 308.087i) q^{78} +(-254.214 + 613.726i) q^{79} +(749.451 - 1056.23i) q^{80} +(12.4869 + 30.1460i) q^{81} +(428.031 - 211.703i) q^{82} +(-868.642 - 712.876i) q^{83} +(145.794 + 135.914i) q^{84} +(2430.28 - 737.217i) q^{85} +(-990.187 + 617.341i) q^{86} +(73.1807 - 14.5566i) q^{87} +(31.6926 + 103.175i) q^{88} +(-152.199 + 765.157i) q^{89} +(898.366 + 405.782i) q^{90} +(215.039 - 176.478i) q^{91} +(-861.688 - 977.954i) q^{92} +(28.4895 + 53.3002i) q^{93} +(-421.271 - 547.687i) q^{94} +(365.403 - 365.403i) q^{95} +(296.091 - 482.406i) q^{96} +(-175.993 - 175.993i) q^{97} +(-102.276 + 783.932i) q^{98} +(-72.4516 + 38.7262i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 5696 q^{50} - 16 q^{51} + 6608 q^{52} - 16 q^{53} + 3440 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 4768 q^{58} - 16 q^{59} - 9808 q^{60} - 16 q^{61} - 5872 q^{62} - 12112 q^{64} - 10960 q^{66} - 16 q^{67} - 4144 q^{68} - 16 q^{69} - 4048 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 5248 q^{74} - 16 q^{75} + 11888 q^{76} - 16 q^{77} + 14096 q^{78} - 16 q^{79} + 10016 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 5696 * q^50 - 16 * q^51 + 6608 * q^52 - 16 * q^53 + 3440 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 4768 * q^58 - 16 * q^59 - 9808 * q^60 - 16 * q^61 - 5872 * q^62 - 12112 * q^64 - 10960 * q^66 - 16 * q^67 - 4144 * q^68 - 16 * q^69 - 4048 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 5248 * q^74 - 16 * q^75 + 11888 * q^76 - 16 * q^77 + 14096 * q^78 - 16 * q^79 + 10016 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{1}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.73119	+	0.735238i	−0.965623	+	0.259946i
$2$	−2.73119	+	0.735238i	−0.965623	+	0.259946i
$3$	−2.99224	−	0.907685i	−0.575856	−	0.174684i	−0.0110950	−	0.999938i	$-0.503532\pi$
$3$	−2.99224	−	0.907685i	−0.575856	−	0.174684i	−0.564761	+	0.825254i	$0.691032\pi$
$4$	6.91885	−	4.01616i	0.864856	−	0.502019i
$5$	20.1386	+	1.98348i	1.80125	+	0.177408i	0.942328	−	0.334692i	$-0.108632\pi$
$5$	20.1386	+	1.98348i	1.80125	+	0.177408i	0.858926	+	0.512100i	$0.171132\pi$
$6$	8.83975	+	0.279059i	0.601469	+	0.0189876i
$7$	−4.42679	−	6.62516i	−0.239024	−	0.357725i	0.692492	−	0.721426i	$-0.256513\pi$
$7$	−4.42679	−	6.62516i	−0.239024	−	0.357725i	−0.931516	+	0.363701i	$0.881513\pi$
$8$	−15.9439	+	16.0559i	−0.704627	+	0.709577i
$9$	−14.3201	−	9.56838i	−0.530374	−	0.354384i
$10$	−56.4608	+	9.38941i	−1.78545	+	0.296919i
$11$	2.24857	−	4.20677i	0.0616335	−	0.115308i	−0.849218	−	0.528042i	$-0.822926\pi$
$11$	2.24857	−	4.20677i	0.0616335	−	0.115308i	0.910851	+	0.412734i	$0.135426\pi$
$12$	−24.3482	+	5.73715i	−0.585728	+	0.138014i
$13$	3.42203	+	34.7444i	0.0730076	+	0.741259i	0.960098	+	0.279663i	$0.0902229\pi$
$13$	3.42203	+	34.7444i	0.0730076	+	0.741259i	−0.887090	+	0.461596i	$0.847277\pi$
$14$	16.9615	+	14.8399i	0.323796	+	0.283294i
$15$	−58.4592	−	24.2146i	−1.00627	−	0.416812i
$16$	31.7410	−	55.5744i	0.495953	−	0.868349i
$17$	115.947	−	48.0269i	1.65420	−	0.685191i	0.656584	−	0.754253i	$-0.272001\pi$
$17$	115.947	−	48.0269i	1.65420	−	0.685191i	0.997612	+	0.0690623i	$0.0220007\pi$
$18$	46.1460	+	15.6044i	0.604262	+	0.204333i
$19$	16.2002	−	19.7400i	0.195609	−	0.238351i	−0.665964	−	0.745984i	$-0.731980\pi$
$19$	16.2002	−	19.7400i	0.195609	−	0.238351i	0.861573	+	0.507633i	$0.169480\pi$
$20$	147.302	−	67.1564i	1.64689	−	0.750832i
$21$	7.23244	+	23.8422i	0.0751547	+	0.247752i
$22$	−3.04829	+	13.1427i	−0.0295408	+	0.127366i
$23$	−31.7855	−	159.797i	−0.288163	−	1.44869i	−0.805340	−	0.592814i	$-0.798017\pi$
$23$	−31.7855	−	159.797i	−0.288163	−	1.44869i	0.517177	−	0.855879i	$-0.326983\pi$
$24$	62.2816	−	33.5710i	0.529716	−	0.285527i
$25$	279.032	+	55.5029i	2.23226	+	0.444023i
$26$	−34.8916	−	92.3778i	−0.263185	−	0.696799i
$27$	87.7232	+	106.891i	0.625271	+	0.761895i
$28$	−57.2359	−	28.0598i	−0.386306	−	0.189386i
$29$	−21.0446	+	11.2486i	−0.134755	+	0.0720280i	−0.537396	−	0.843330i	$-0.680592\pi$
$29$	−21.0446	+	11.2486i	−0.134755	+	0.0720280i	0.402642	+	0.915358i	$0.368092\pi$
$30$	177.467	+	23.1533i	1.08003	+	0.140907i
$31$	−13.6670	−	13.6670i	−0.0791827	−	0.0791827i	0.666406	−	0.745589i	$-0.267832\pi$
$31$	−13.6670	−	13.6670i	−0.0791827	−	0.0791827i	−0.745589	+	0.666406i	$0.767832\pi$
$32$	−45.8304	+	175.122i	−0.253180	+	0.967419i
$33$	−10.5467	+	10.5467i	−0.0556345	+	0.0556345i
$34$	−281.363	+	216.420i	−1.41922	+	1.09164i
$35$	−76.0086	−	142.202i	−0.367080	−	0.686758i
$36$	−137.507	−	8.69047i	−0.636605	−	0.0402337i
$37$	226.234	−	185.666i	1.00521	−	0.824953i	0.0206103	−	0.999788i	$-0.493439\pi$
$37$	226.234	−	185.666i	1.00521	−	0.824953i	0.984598	+	0.174835i	$0.0559391\pi$
$38$	−29.7323	+	65.8247i	−0.126927	+	0.281005i
$39$	21.2975	−	107.070i	0.0874442	−	0.439612i
$40$	−352.935	+	291.719i	−1.39510	+	1.15312i
$41$	−165.586	+	32.9371i	−0.630736	+	0.125461i	−0.500098	−	0.865969i	$-0.666703\pi$
$41$	−165.586	+	32.9371i	−0.630736	+	0.125461i	−0.130638	+	0.991430i	$0.541703\pi$
$42$	−37.2829	−	59.8000i	−0.136973	−	0.219699i
$43$	394.786	−	119.757i	1.40010	−	0.424715i	0.502137	−	0.864788i	$-0.332547\pi$
$43$	394.786	−	119.757i	1.40010	−	0.424715i	0.897962	+	0.440073i	$0.145047\pi$
$44$	−1.33756	−	38.1366i	−0.00458282	−	0.130666i
$45$	−269.408	−	221.098i	−0.892467	−	0.732429i
$46$	204.301	+	413.066i	0.654838	+	1.32398i
$47$	93.4867	+	225.697i	0.290137	+	0.700452i	0.999992	−	0.00389501i	$-0.00123982\pi$
$47$	93.4867	+	225.697i	0.290137	+	0.700452i	−0.709856	+	0.704347i	$0.751240\pi$
$48$	−145.421	+	137.481i	−0.437284	+	0.413409i
$49$	106.964	−	258.234i	0.311849	−	0.752870i
$50$	−802.898	+	53.5656i	−2.27094	+	0.151506i
$51$	−390.535	+	38.4643i	−1.07227	+	0.105610i
$52$	163.215	+	226.648i	0.435268	+	0.604431i
$53$	163.009	+	87.1301i	0.422472	+	0.225816i	0.668911	−	0.743342i	$-0.266761\pi$
$53$	163.009	+	87.1301i	0.422472	+	0.225816i	−0.246439	+	0.969158i	$0.579261\pi$
$54$	−318.179	−	227.443i	−0.801828	−	0.573167i
$55$	53.6271	−	80.2586i	0.131474	−	0.196765i
$56$	176.953	+	34.5547i	0.422256	+	0.0824566i
$57$	−66.3925	+	44.3620i	−0.154279	+	0.103086i
$58$	49.2066	−	46.1949i	0.111399	−	0.104581i
$59$	75.6616	−	768.205i	0.166954	−	1.69512i	−0.438096	−	0.898928i	$-0.644347\pi$
$59$	75.6616	−	768.205i	0.166954	−	1.69512i	0.605051	−	0.796187i	$-0.293153\pi$
$60$	−501.720	+	67.2441i	−1.07953	+	0.144686i
$61$	−23.4833	+	77.4142i	−0.0492907	+	0.162490i	−0.978131	−	0.207992i	$-0.933307\pi$
$61$	−23.4833	+	77.4142i	−0.0492907	+	0.162490i	0.928840	+	0.370481i	$0.120807\pi$
$62$	47.3757	+	27.2787i	0.0970438	+	0.0558774i
$63$			137.230i			0.274434i
$64$	−3.58414	−	511.987i	−0.00700027	−	0.999975i
$65$			706.492i			1.34815i
$66$	21.0507	−	36.5593i	0.0392600	−	0.0681839i
$67$	−133.350	+	439.595i	−0.243153	+	0.801568i	0.747392	+	0.664383i	$0.231306\pi$
$67$	−133.350	+	439.595i	−0.243153	+	0.801568i	−0.990545	+	0.137185i	$0.956194\pi$
$68$	609.338	−	797.953i	1.08666	−	1.42303i
$69$	−49.9352	+	507.001i	−0.0871231	+	0.884576i
$70$	312.146	+	332.497i	0.532981	+	0.567728i
$71$	−805.116	+	537.961i	−1.34577	+	0.899215i	−0.999246	−	0.0388256i	$-0.987638\pi$
$71$	−805.116	+	537.961i	−1.34577	+	0.899215i	−0.346525	+	0.938041i	$0.612638\pi$
$72$	381.947	−	77.3647i	0.625179	−	0.126632i
$73$	−246.257	+	368.550i	−0.394825	+	0.590898i	−0.974620	−	0.223865i	$-0.928133\pi$
$73$	−246.257	+	368.550i	−0.394825	+	0.590898i	0.579795	+	0.814762i	$0.303133\pi$
$74$	−481.382	+	673.425i	−0.756209	+	1.05789i
$75$	−784.550	−	419.351i	−1.20789	−	0.645633i
$76$	32.8078	−	201.640i	0.0495173	−	0.304339i
$77$	−37.8244	+	3.72538i	−0.0559805	+	0.00551359i
$78$	20.5541	+	308.087i	0.0298371	+	0.447230i
$79$	−254.214	+	613.726i	−0.362041	+	0.874045i	0.632960	+	0.774184i	$0.281840\pi$
$79$	−254.214	+	613.726i	−0.362041	+	0.874045i	−0.995001	+	0.0998607i	$0.968160\pi$
$80$	749.451	−	1056.23i	1.04739	−	1.47613i
$81$	12.4869	+	30.1460i	0.0171288	+	0.0413525i
$82$	428.031	−	211.703i	0.576440	−	0.285105i
$83$	−868.642	−	712.876i	−1.14875	−	0.942751i	−0.149802	−	0.988716i	$-0.547864\pi$
$83$	−868.642	−	712.876i	−1.14875	−	0.942751i	−0.998943	+	0.0459650i	$0.985364\pi$
$84$	145.794	+	135.914i	0.189374	+	0.176541i
$85$	2430.28	−	737.217i	3.10119	−	0.940734i
$86$	−990.187	+	617.341i	−1.24156	+	0.774065i
$87$	73.1807	−	14.5566i	0.0901816	−	0.0179382i
$88$	31.6926	+	103.175i	0.0383914	+	0.124983i
$89$	−152.199	+	765.157i	−0.181270	+	0.911308i	0.777880	+	0.628413i	$0.216295\pi$
$89$	−152.199	+	765.157i	−0.181270	+	0.911308i	−0.959151	+	0.282896i	$0.908705\pi$
$90$	898.366	+	405.782i	1.05218	+	0.475257i
$91$	215.039	−	176.478i	0.247716	−	0.203295i
$92$	−861.688	−	977.954i	−0.976491	−	1.10825i
$93$	28.4895	+	53.3002i	0.0317659	+	0.0594298i
$94$	−421.271	−	547.687i	−0.462242	−	0.600953i
$95$	365.403	−	365.403i	0.394627	−	0.394627i
$96$	296.091	−	482.406i	0.314788	−	0.512868i
$97$	−175.993	−	175.993i	−0.184220	−	0.184220i	0.608972	−	0.793192i	$-0.291582\pi$
$97$	−175.993	−	175.993i	−0.184220	−	0.184220i	−0.793192	+	0.608972i	$0.791582\pi$
$98$	−102.276	+	783.932i	−0.105423	+	0.808052i
$99$	−72.4516	+	38.7262i	−0.0735522	+	0.0393144i
$100$	2153.49	−	736.619i	2.15349	−	0.736619i
$101$	−361.800	−	440.854i	−0.356440	−	0.434323i	0.563660	−	0.826007i	$-0.309393\pi$
$101$	−361.800	−	440.854i	−0.356440	−	0.434323i	−0.920100	+	0.391684i	$0.871893\pi$
$102$	1038.35	−	392.190i	1.00796	−	0.380711i
$103$	1432.98	+	285.038i	1.37084	+	0.272676i	0.824960	−	0.565191i	$-0.191197\pi$
$103$	1432.98	+	285.038i	1.37084	+	0.272676i	0.545875	+	0.837867i	$0.316197\pi$
$104$	−612.413	−	499.018i	−0.577424	−	0.470507i
$105$	98.3610	+	494.494i	0.0914195	+	0.459597i
$106$	−509.271	−	118.119i	−0.466649	−	0.108233i
$107$	148.412	+	489.247i	0.134089	+	0.442031i	0.998112	−	0.0614207i	$-0.0195631\pi$
$107$	148.412	+	489.247i	0.134089	+	0.442031i	−0.864023	+	0.503452i	$0.832063\pi$
$108$	1036.23	+	387.253i	0.923256	+	0.345032i
$109$	−489.066	+	595.928i	−0.429762	+	0.523666i	−0.942197	−	0.335060i	$-0.891243\pi$
$109$	−489.066	+	595.928i	−0.429762	+	0.523666i	0.512435	+	0.858726i	$0.328743\pi$
$110$	−87.4568	+	258.631i	−0.0758062	+	0.224177i
$111$	−845.473	+	350.206i	−0.722962	+	0.299460i
$112$	−508.699	+	35.7269i	−0.429175	+	0.0301417i
$113$	−404.030	−	167.355i	−0.336353	−	0.139322i	0.208113	−	0.978105i	$-0.433268\pi$
$113$	−404.030	−	167.355i	−0.336353	−	0.139322i	−0.544466	+	0.838783i	$0.683268\pi$
$114$	148.714	−	169.976i	0.122179	−	0.139646i
$115$	−323.163	−	3281.13i	−0.262045	−	2.66058i
$116$	−100.429	+	162.346i	−0.0803842	+	0.129943i
$117$	283.444	−	530.286i	0.223969	−	0.419017i
$118$	358.167	+	2153.75i	0.279423	+	1.68024i
$119$	−831.460	−	555.564i	−0.640502	−	0.427970i
$120$	1320.85	−	552.540i	1.00481	−	0.420331i
$121$	726.823	+	1087.77i	0.546073	+	0.817256i
$122$	7.21973	−	228.699i	0.00535773	−	0.169717i
$123$	525.369	+	51.7443i	0.385129	+	0.0379319i
$124$	−149.449	−	39.6711i	−0.108233	−	0.0287304i
$125$	3088.64	+	936.929i	2.21005	+	0.670412i
$126$	−100.897	−	374.802i	−0.0713380	−	0.265000i
$127$	546.792			0.382047			0.191023	−	0.981585i	$-0.438819\pi$
$127$	546.792			0.382047			0.191023	+	0.981585i	$0.438819\pi$
$128$	386.222	+	1395.70i	0.266699	+	0.963780i
$129$	−1289.99			−0.880447
$130$	−519.440	−	1929.57i	−0.350445	−	1.30180i
$131$	−1472.66	−	446.727i	−0.982192	−	0.297945i	−0.241953	−	0.970288i	$-0.577788\pi$
$131$	−1472.66	−	446.727i	−0.982192	−	0.297945i	−0.740239	+	0.672343i	$0.765288\pi$
$132$	−30.6138	+	115.328i	−0.0201862	+	0.0760455i
$133$	−202.495	−	19.9440i	−0.132019	−	0.0130028i
$134$	40.9971	−	1298.66i	0.0264299	−	0.837219i
$135$	1554.61	+	2326.63i	0.991106	+	1.48329i
$136$	−1077.54	+	2627.37i	−0.679396	+	1.65658i
$137$	−2335.34	−	1560.43i	−1.45636	−	0.973111i	−0.996365	−	0.0851916i	$-0.972850\pi$
$137$	−2335.34	−	1560.43i	−1.45636	−	0.973111i	−0.459999	−	0.887919i	$-0.652150\pi$
$138$	−236.383	−	1421.43i	−0.145814	−	0.876814i
$139$	−1470.88	+	2751.83i	−0.897544	+	1.67919i	−0.178830	+	0.983880i	$0.557231\pi$
$139$	−1470.88	+	2751.83i	−0.897544	+	1.67919i	−0.718714	+	0.695306i	$0.755269\pi$
$140$	−1097.00	−	678.612i	−0.662237	−	0.409666i
$141$	−74.8726	−	760.195i	−0.0447192	−	0.454042i
$142$	1803.40	−	2061.23i	1.06576	−	1.21813i
$143$	153.856	+	63.7294i	0.0899729	+	0.0372680i
$144$	−986.290	+	492.120i	−0.570770	+	0.284792i
$145$	−446.121	+	184.790i	−0.255506	+	0.105834i
$146$	401.605	−	1187.64i	0.227651	−	0.673218i
$147$	−554.458	+	675.609i	−0.311095	+	0.379070i
$148$	819.619	−	2193.19i	0.455218	−	1.21810i
$149$	−163.142	−	537.806i	−0.0896986	−	0.295697i	0.900601	−	0.434647i	$-0.143127\pi$
$149$	−163.142	−	537.806i	−0.0896986	−	0.295697i	−0.990299	+	0.138951i	$0.955627\pi$
$150$	2451.08	+	568.498i	1.33420	+	0.309451i
$151$	125.789	+	632.384i	0.0677918	+	0.340812i	0.999764	−	0.0217169i	$-0.00691325\pi$
$151$	125.789	+	632.384i	0.0677918	+	0.340812i	−0.931972	+	0.362529i	$0.881913\pi$
$152$	58.6492	+	574.841i	0.0312965	+	0.306748i
$153$	−2119.91	−	421.677i	−1.12016	−	0.222814i
$154$	100.567	−	37.9847i	0.0526228	−	0.0198759i
$155$	−248.126	−	302.342i	−0.128580	−	0.156676i
$156$	−282.654	−	826.333i	−0.145067	−	0.424100i
$157$	−1350.58	+	721.899i	−0.686547	+	0.366967i	−0.777495	−	0.628889i	$-0.783510\pi$
$157$	−1350.58	+	721.899i	−0.686547	+	0.366967i	0.0909487	+	0.995856i	$0.471010\pi$
$158$	243.072	−	1863.11i	0.122391	−	0.938109i
$159$	−408.675	−	408.675i	−0.203837	−	0.203837i
$160$	−1270.31	+	3435.80i	−0.627669	+	1.69765i
$161$	−917.970	+	917.970i	−0.449355	+	0.449355i
$162$	−56.2685	−	73.1537i	−0.0272893	−	0.0354784i
$163$	982.212	+	1837.59i	0.471980	+	0.883013i	0.999441	+	0.0334335i	$0.0106442\pi$
$163$	982.212	+	1837.59i	0.471980	+	0.883013i	−0.527461	+	0.849579i	$0.676856\pi$
$164$	−1013.38	+	892.905i	−0.482512	+	0.425147i
$165$	−233.314	+	191.476i	−0.110082	+	0.0903418i
$166$	2896.56	+	1308.35i	1.35432	+	0.611731i
$167$	−80.5462	+	404.933i	−0.0373224	+	0.187633i	−0.994949	−	0.100379i	$-0.967994\pi$
$167$	−80.5462	+	404.933i	−0.0373224	+	0.187633i	0.957627	+	0.288012i	$0.0929943\pi$
$168$	−498.121	−	264.014i	−0.228755	−	0.121245i
$169$	959.321	−	190.821i	0.436651	−	0.0868552i
$170$	−6095.54	+	3800.32i	−2.75004	+	1.71454i
$171$	−420.868	+	127.669i	−0.188214	+	0.0570940i
$172$	2250.50	−	2414.10i	0.997669	−	1.07019i
$173$	1497.94	+	1229.33i	0.658303	+	0.540255i	0.903160	−	0.429304i	$-0.141241\pi$
$173$	1497.94	+	1229.33i	0.658303	+	0.540255i	−0.244857	+	0.969559i	$0.578741\pi$
$174$	−189.168	+	93.5620i	−0.0824185	+	0.0407639i
$175$	−867.500	−	2094.33i	−0.374725	−	0.904665i
$176$	−162.417	−	258.490i	−0.0695604	−	0.110707i
$177$	−923.686	+	2229.97i	−0.392251	+	0.946978i
$178$	−146.887	−	2201.69i	−0.0618518	−	0.927101i
$179$	2093.08	−	206.150i	0.873990	−	0.0860805i	0.348933	−	0.937148i	$-0.386544\pi$
$179$	2093.08	−	206.150i	0.873990	−	0.0860805i	0.525057	+	0.851067i	$0.324044\pi$
$180$	−2751.96	−	447.756i	−1.13955	−	0.185410i
$181$	−1553.06	−	830.130i	−0.637781	−	0.340901i	0.120611	−	0.992700i	$-0.461515\pi$
$181$	−1553.06	−	830.130i	−0.637781	−	0.340901i	−0.758392	+	0.651799i	$0.774015\pi$
$182$	−457.559	+	640.099i	−0.186355	+	0.260700i
$183$	140.535	−	210.326i	0.0567687	−	0.0849604i
$184$	3072.47	+	2037.44i	1.23101	+	0.816315i
$185$	4924.31	−	3290.32i	1.95699	−	1.30762i
$186$	−116.999	−	124.627i	−0.0461224	−	0.0491294i
$187$	58.6768	−	595.755i	0.0229458	−	0.232973i
$188$	1553.25	+	1186.11i	0.602567	+	0.460136i
$189$	319.838	−	1054.36i	0.123094	−	0.405786i
$190$	−729.329	+	1266.65i	−0.278480	+	0.483643i
$191$			360.457i			0.136554i	0.997666	+	0.0682768i	$0.0217501\pi$
$191$			360.457i			0.136554i	−0.997666	+	0.0682768i	$0.978250\pi$
$192$	−453.999	+	1535.24i	−0.170649	+	0.577065i
$193$			21.2307i			0.00791824i	0.999992	+	0.00395912i	$0.00126023\pi$
$193$			21.2307i			0.00791824i	−0.999992	+	0.00395912i	$0.998740\pi$
$194$	610.067	+	351.274i	0.225774	+	0.130000i
$195$	641.273	−	2113.99i	0.235500	−	0.776339i
$196$	−297.040	−	2216.27i	−0.108251	−	0.807678i
$197$	7.74011	−	78.5867i	0.00279929	−	0.0284217i	−0.993684	−	0.112218i	$-0.964205\pi$
$197$	7.74011	−	78.5867i	0.00279929	−	0.0284217i	0.996483	+	0.0837963i	$0.0267045\pi$
$198$	169.407	−	159.038i	0.0608040	−	0.0570825i
$199$	242.115	−	161.776i	0.0862465	−	0.0576281i	−0.511699	−	0.859165i	$-0.670984\pi$
$199$	242.115	−	161.776i	0.0862465	−	0.0576281i	0.597946	+	0.801537i	$0.295984\pi$
$200$	−5340.01	+	3595.18i	−1.88798	+	1.27109i
$201$	798.027	−	1194.33i	0.280042	−	0.419113i
$202$	1312.28	+	938.050i	0.457087	+	0.326737i
$203$	167.684	+	89.6289i	0.0579759	+	0.0309887i
$204$	−2547.57	+	1834.58i	−0.874343	+	0.629638i
$205$	−3400.00	+	334.871i	−1.15837	+	0.114090i
$206$	−4123.33	+	275.089i	−1.39459	+	0.0930405i
$207$	−1073.82	+	2592.44i	−0.360560	+	0.870469i
$208$	2039.52	+	912.645i	0.679880	+	0.304233i
$209$	−46.6144	−	112.537i	−0.0154277	−	0.0372457i
$210$	−632.214	−	1278.24i	−0.207747	−	0.420033i
$211$	−1183.03	−	970.889i	−0.385987	−	0.316771i	0.421310	−	0.906917i	$-0.361570\pi$
$211$	−1183.03	−	970.889i	−0.385987	−	0.316771i	−0.807297	+	0.590145i	$0.799070\pi$
$212$	1477.76	−	51.8292i	0.478741	−	0.0167908i
$213$	2897.40	−	878.916i	0.932049	−	0.282734i
$214$	−765.054	−	1227.11i	−0.244383	−	0.391980i
$215$	8187.98	−	1628.69i	2.59728	−	0.516631i
$216$	−3114.88	−	295.784i	−0.981207	−	0.0931740i
$217$	−30.0451	+	151.047i	−0.00939904	+	0.0472522i
$218$	897.585	−	1987.18i	0.278863	−	0.617379i
$219$	1071.39	−	879.265i	0.330583	−	0.271303i
$220$	48.7067	−	770.672i	0.0149264	−	0.236176i
$221$	2065.44	+	3864.17i	0.628673	+	1.17616i
$222$	2051.67	−	1578.11i	0.620265	−	0.477097i
$223$	−1889.04	+	1889.04i	−0.567262	+	0.567262i	−0.931361	−	0.364098i	$-0.881377\pi$
$223$	−1889.04	+	1889.04i	−0.567262	+	0.567262i	0.364098	+	0.931361i	$0.381377\pi$
$224$	1363.09	−	471.592i	0.406586	−	0.140668i
$225$	−3464.69	−	3464.69i	−1.02657	−	1.02657i
$226$	1226.53	+	160.020i	0.361007	+	0.0470990i
$227$	3767.08	−	2013.55i	1.10145	−	0.588739i	0.182540	−	0.983198i	$-0.441568\pi$
$227$	3767.08	−	2013.55i	1.10145	−	0.588739i	0.918913	+	0.394459i	$0.129068\pi$
$228$	−281.195	+	573.577i	−0.0816780	+	0.166606i
$229$	−3866.29	−	4711.08i	−1.11568	−	1.35946i	−0.925958	−	0.377626i	$-0.876741\pi$
$229$	−3866.29	−	4711.08i	−1.11568	−	1.35946i	−0.189725	−	0.981837i	$-0.560759\pi$
$230$	3295.04	+	8723.81i	0.944644	+	2.50100i
$231$	116.561	+	23.1855i	0.0331998	+	0.00660386i
$232$	154.927	−	517.237i	0.0438426	−	0.146372i
$233$	578.573	+	2908.68i	0.162676	+	0.817829i	0.972814	+	0.231589i	$0.0743925\pi$
$233$	578.573	+	2908.68i	0.162676	+	0.817829i	−0.810137	+	0.586240i	$0.800608\pi$
$234$	−384.254	+	1656.71i	−0.107348	+	0.462832i
$235$	1435.03	+	4730.65i	0.398344	+	1.31316i
$236$	−2561.74	−	5618.97i	−0.706589	−	1.54985i
$237$	1317.74	−	1605.67i	0.361166	−	0.440082i
$238$	2679.35	+	906.032i	0.729733	+	0.246762i
$239$	2068.15	−	856.657i	0.559739	−	0.231851i	−0.0848329	−	0.996395i	$-0.527036\pi$
$239$	2068.15	−	856.657i	0.559739	−	0.231851i	0.644572	+	0.764544i	$0.277036\pi$
$240$	−3201.26	+	2480.24i	−0.861002	+	0.667077i
$241$	−3563.59	−	1476.09i	−0.952495	−	0.394536i	−0.148327	−	0.988938i	$-0.547389\pi$
$241$	−3563.59	−	1476.09i	−0.952495	−	0.394536i	−0.804168	+	0.594402i	$0.797389\pi$
$242$	−2784.86	−	2436.52i	−0.739743	−	0.647212i
$243$	−375.950	−	3817.09i	−0.0992478	−	1.00768i
$244$	148.430	+	629.930i	0.0389436	+	0.165275i
$245$	2666.31	−	4988.32i	0.695284	−	1.30078i
$246$	−1472.93	+	244.947i	−0.381750	+	0.0634848i
$247$	741.292	+	495.315i	0.190961	+	0.127596i
$248$	437.341	−	1.53077i	0.111981	−	0.000391952i
$249$	1952.12	+	2921.55i	0.496829	+	0.743557i
$250$	−9124.55	−	288.050i	−2.30835	−	0.0728715i
$251$	−3403.21	−	335.187i	−0.855812	−	0.0842901i	−0.339412	−	0.940638i	$-0.610228\pi$
$251$	−3403.21	−	335.187i	−0.855812	−	0.0842901i	−0.516400	+	0.856348i	$0.672728\pi$
$252$	551.137	+	949.474i	0.137771	+	0.237346i
$253$	−743.700	−	225.599i	−0.184806	−	0.0560604i
$254$	−1493.39	+	402.022i	−0.368913	+	0.0993114i
$255$	−7941.13			−1.95017
$256$	−2081.02	−	3527.97i	−0.508061	−	0.861321i
$257$	−7523.96			−1.82619			−0.913097	−	0.407743i	$-0.866316\pi$
$257$	−7523.96			−1.82619			−0.913097	+	0.407743i	$0.866316\pi$
$258$	3523.22	−	948.452i	0.850180	−	0.228868i
$259$	−2231.56	−	676.935i	−0.535375	−	0.162404i
$260$	2837.38	+	4888.11i	0.676796	+	1.16595i
$261$	408.992	+	40.2822i	0.0969960	+	0.00955328i
$262$	4350.58	+	137.342i	1.02588	+	0.0323856i
$263$	4047.96	+	6058.20i	0.949079	+	1.42040i	0.906928	+	0.421286i	$0.138421\pi$
$263$	4047.96	+	6058.20i	0.949079	+	1.42040i	0.0421517	+	0.999111i	$0.486579\pi$
$264$	−1.18128	−	337.491i	−0.000275389	−	0.0786786i
$265$	3109.96	+	2078.01i	0.720917	+	0.481702i
$266$	567.718	−	94.4111i	0.130861	−	0.0217621i
$267$	1149.94	−	2151.38i	0.263577	−	0.493117i
$268$	842.855	+	3577.04i	0.192110	+	0.815309i
$269$	129.077	+	1310.55i	0.0292565	+	0.297046i	0.998668	+	0.0516036i	$0.0164332\pi$
$269$	129.077	+	1310.55i	0.0292565	+	0.297046i	−0.969411	+	0.245442i	$0.921067\pi$
$270$	−5956.57	−	5211.49i	−1.34261	−	1.17467i
$271$	7652.63	+	3169.83i	1.71537	+	0.710528i	0.999930	+	0.0118512i	$0.00377244\pi$
$271$	7652.63	+	3169.83i	1.71537	+	0.710528i	0.715437	+	0.698677i	$0.246228\pi$
$272$	1011.21	−	7968.12i	0.225419	−	1.77624i
$273$	−803.632	+	332.875i	−0.178161	+	0.0737968i
$274$	7525.56	+	2544.80i	1.65925	+	0.561083i
$275$	860.910	−	1049.02i	0.188781	−	0.230030i
$276$	1690.70	+	3708.41i	0.368725	+	0.808769i
$277$	306.796	+	1011.37i	0.0665473	+	0.219377i	0.983907	−	0.178683i	$-0.0571836\pi$
$277$	306.796	+	1011.37i	0.0665473	+	0.219377i	−0.917359	+	0.398060i	$0.869684\pi$
$278$	1994.02	−	8597.22i	0.430192	−	1.85477i
$279$	64.9416	+	326.483i	0.0139353	+	0.0700575i
$280$	3495.05	+	1046.87i	0.745962	+	0.223437i
$281$	−5404.69	−	1075.06i	−1.14739	−	0.228230i	−0.415462	−	0.909611i	$-0.636380\pi$
$281$	−5404.69	−	1075.06i	−1.14739	−	0.228230i	−0.731930	+	0.681380i	$0.761380\pi$
$282$	763.416	+	2021.19i	0.161208	+	0.426809i
$283$	4910.88	+	5983.93i	1.03152	+	1.25692i	0.965857	+	0.259075i	$0.0834177\pi$
$283$	4910.88	+	5983.93i	1.03152	+	1.25692i	0.0656677	+	0.997842i	$0.479082\pi$
$284$	−3409.94	+	6955.55i	−0.712475	+	1.45330i
$285$	−1425.04	+	761.702i	−0.296184	+	0.158313i
$286$	−467.068	−	60.9364i	−0.0965675	−	0.0125988i
$287$	951.227	+	951.227i	0.195642	+	0.195642i
$288$	2331.93	−	2069.23i	0.477118	−	0.423371i
$289$	7663.16	−	7663.16i	1.55977	−	1.55977i
$290$	1082.58	−	832.702i	0.219211	−	0.168614i
$291$	366.866	+	686.358i	0.0739040	+	0.138265i
$292$	−223.663	+	3538.95i	−0.0448250	+	0.709252i
$293$	5450.38	−	4473.01i	1.08674	−	0.891864i	0.0921493	−	0.995745i	$-0.470626\pi$
$293$	5450.38	−	4473.01i	1.08674	−	0.891864i	0.994590	+	0.103882i	$0.0331263\pi$
$294$	1017.60	−	2252.88i	0.201862	−	0.446906i
$295$	3047.44	−	15320.5i	0.601454	−	3.02371i
$296$	−626.026	+	6592.63i	−0.122929	+	1.29456i
$297$	646.917	−	128.680i	0.126390	−	0.0251406i
$298$	840.987	+	1348.91i	0.163480	+	0.262215i
$299$	5443.27	−	1651.20i	1.05282	−	0.319369i
$300$	−7112.37	+	249.450i	−1.36878	+	0.0480067i
$301$	−2541.04	−	2085.38i	−0.486589	−	0.399333i
$302$	−808.507	−	1634.68i	−0.154054	−	0.311474i
$303$	682.433	+	1647.54i	0.129389	+	0.312372i
$304$	−582.827	−	1526.88i	−0.109959	−	0.288068i
$305$	−626.472	+	1512.44i	−0.117612	+	0.283941i
$306$	6099.93	−	406.959i	1.13958	−	0.0760271i
$307$	4629.52	−	455.968i	0.860654	−	0.0847670i	0.341947	−	0.939719i	$-0.388914\pi$
$307$	4629.52	−	455.968i	0.860654	−	0.0847670i	0.518707	+	0.854952i	$0.326414\pi$
$308$	−246.740	+	177.684i	−0.0456471	+	0.0328717i
$309$	−4029.10	−	2153.60i	−0.741772	−	0.396485i
$310$	899.974	+	643.324i	0.164887	+	0.117866i
$311$	−5218.25	+	7809.66i	−0.951446	+	1.42394i	−0.0462573	+	0.998930i	$0.514729\pi$
$311$	−5218.25	+	7809.66i	−0.951446	+	1.42394i	−0.905189	+	0.425010i	$0.860271\pi$
$312$	1379.54	+	2049.06i	0.250323	+	0.371811i
$313$	−1903.59	+	1271.94i	−0.343761	+	0.229694i	−0.715451	−	0.698663i	$-0.753779\pi$
$313$	−1903.59	+	1271.94i	−0.343761	+	0.229694i	0.371689	+	0.928357i	$0.378779\pi$
$314$	3157.92	−	2964.64i	0.567554	−	0.532817i
$315$	−272.193	+	2763.62i	−0.0486868	+	0.494326i
$316$	705.953	+	5267.24i	0.125674	+	0.937675i
$317$	2084.50	−	6871.69i	0.369330	−	1.21752i	−0.553677	−	0.832732i	$-0.686776\pi$
$317$	2084.50	−	6871.69i	0.369330	−	1.21752i	0.923006	−	0.384785i	$-0.125724\pi$
$318$	1416.64	+	815.697i	0.249816	+	0.143843i
$319$			113.823i			0.0199777i
$320$	943.338	−	10317.8i	0.164794	−	1.80245i
$321$		−	1598.66i		−	0.277970i
$322$	1832.23	−	3182.08i	0.317100	−	0.550716i
$323$	930.316	−	3066.84i	0.160261	−	0.528308i
$324$	207.466	+	158.426i	0.0355737	+	0.0271650i
$325$	−973.561	+	9884.73i	−0.166164	+	1.68710i
$326$	−4033.68	−	4296.66i	−0.685291	−	0.729968i
$327$	2004.32	−	1339.24i	0.338957	−	0.226484i
$328$	2111.25	−	3183.78i	0.355409	−	0.535959i
$329$	1081.43	−	1618.48i	0.181219	−	0.271214i
$330$	496.447	−	694.501i	0.0828136	−	0.115852i
$331$	−9076.70	−	4851.60i	−1.50725	−	0.805644i	−0.508781	−	0.860896i	$-0.669904\pi$
$331$	−9076.70	−	4851.60i	−1.50725	−	0.805644i	−0.998472	+	0.0552526i	$0.982404\pi$
$332$	−8873.03	−	1443.68i	−1.46678	−	0.238652i
$333$	−5016.22	+	494.054i	−0.825486	+	0.0813033i
$334$	−77.7347	−	1165.17i	−0.0127349	−	0.190884i
$335$	−3557.41	+	8588.34i	−0.580185	+	1.40069i
$336$	1554.58	+	354.836i	0.252408	+	0.0576127i
$337$	3783.01	+	9132.99i	0.611495	+	1.47628i	0.861359	+	0.507997i	$0.169614\pi$
$337$	3783.01	+	9132.99i	0.611495	+	1.47628i	−0.249864	+	0.968281i	$0.580386\pi$
$338$	−2479.79	+	1226.50i	−0.399062	+	0.197375i
$339$	1057.05	+	867.496i	0.169354	+	0.138985i
$340$	13854.0	−	14861.1i	2.20981	−	2.37046i
$341$	−88.2250	+	26.7628i	−0.0140107	+	0.00425010i
$342$	1055.60	−	658.126i	0.166902	−	0.104057i
$343$	−4864.86	+	967.681i	−0.765825	+	0.152332i
$344$	−4371.62	+	8248.03i	−0.685180	+	1.29274i
$345$	−2011.25	+	10111.3i	−0.313862	+	1.57789i
$346$	−4995.02	−	2256.19i	−0.776110	−	0.350560i
$347$	592.422	−	486.189i	0.0916510	−	0.0752160i	−0.587452	−	0.809259i	$-0.699869\pi$
$347$	592.422	−	486.189i	0.0916510	−	0.0752160i	0.679103	+	0.734043i	$0.262369\pi$
$348$	447.865	−	394.620i	0.0689888	−	0.0607869i
$349$	−215.874	−	403.871i	−0.0331102	−	0.0619448i	0.864822	−	0.502078i	$-0.167431\pi$
$349$	−215.874	−	403.871i	−0.0331102	−	0.0619448i	−0.897932	+	0.440134i	$0.854931\pi$
$350$	3909.14	+	5082.20i	0.597007	+	0.776158i
$351$	−3413.67	+	3413.67i	−0.519112	+	0.519112i
$352$	633.644	+	586.571i	0.0959469	+	0.0888191i
$353$	−6903.33	−	6903.33i	−1.04087	−	1.04087i	−0.999128	−	0.0417417i	$-0.986709\pi$
$353$	−6903.33	−	6903.33i	−1.04087	−	1.04087i	−0.0417417	−	0.999128i	$-0.513291\pi$
$354$	883.204	−	6769.62i	0.132604	−	1.01639i
$355$	−17281.0	+	9236.87i	−2.58360	+	1.38096i
$356$	2019.94	+	5905.26i	0.300722	+	0.879152i
$357$	1983.65	+	2417.08i	0.294078	+	0.358335i
$358$	−5565.04	+	2101.95i	−0.821569	+	0.310311i
$359$	8415.02	+	1673.85i	1.23712	+	0.246079i	0.769961	−	0.638091i	$-0.220276\pi$
$359$	8415.02	+	1673.85i	1.23712	+	0.246079i	0.467164	+	0.884171i	$0.345276\pi$
$360$	7845.34	−	800.435i	1.14857	−	0.117185i
$361$	1210.90	+	6087.62i	0.176542	+	0.887538i
$362$	4852.06	+	1125.38i	0.704472	+	0.163393i
$363$	−1187.48	−	3914.59i	−0.171698	−	0.566012i
$364$	779.058	−	2084.65i	0.112181	−	0.300180i
$365$	−5690.30	+	6933.65i	−0.816010	+	0.994312i
$366$	−229.190	+	677.769i	−0.0327321	+	0.0967965i
$367$	−2939.76	+	1217.69i	−0.418132	+	0.173196i	−0.581823	−	0.813316i	$-0.697660\pi$
$367$	−2939.76	+	1217.69i	−0.418132	+	0.173196i	0.163690	+	0.986512i	$0.447660\pi$
$368$	−9889.51	−	3305.64i	−1.40089	−	0.468257i
$369$	2686.36	+	1112.73i	0.378987	+	0.156982i
$370$	−11030.1	+	12607.1i	−1.54980	+	1.77138i
$371$	−144.356	−	1465.67i	−0.0202010	−	0.205104i
$372$	411.177	+	254.357i	0.0573078	+	0.0354511i
$373$	−838.601	+	1568.91i	−0.116410	+	0.217789i	−0.933378	−	0.358895i	$-0.883154\pi$
$373$	−838.601	+	1568.91i	−0.116410	+	0.217789i	0.816967	+	0.576684i	$0.195654\pi$
$374$	277.764	+	1670.26i	0.0384033	+	0.230929i
$375$	−8391.51	−	5607.03i	−1.15556	−	0.772122i
$376$	−5114.31	−	2097.47i	−0.701463	−	0.287683i
$377$	−462.841	−	692.691i	−0.0632295	−	0.0946297i
$378$	−98.3310	+	3114.83i	−0.0133799	+	0.423835i
$379$	5466.10	+	538.364i	0.740831	+	0.0729655i	0.461390	−	0.887197i	$-0.347351\pi$
$379$	5466.10	+	538.364i	0.740831	+	0.0729655i	0.279441	+	0.960163i	$0.409851\pi$
$380$	1060.65	−	3995.69i	0.143185	−	0.539407i
$381$	−1636.13	−	496.315i	−0.220004	−	0.0667375i
$382$	−265.021	−	984.477i	−0.0354965	−	0.131859i
$383$	−5535.85			−0.738561			−0.369281	−	0.929318i	$-0.620396\pi$
$383$	−5535.85			−0.738561			−0.369281	+	0.929318i	$0.620396\pi$
$384$	111.192	−	4526.84i	0.0147767	−	0.601587i
$385$	−769.121			−0.101813
$386$	−15.6096	−	57.9853i	−0.00205831	−	0.00764604i
$387$	−6799.25	−	2062.53i	−0.893088	−	0.270915i
$388$	−1924.48	−	510.853i	−0.251806	−	0.0668418i
$389$	5542.52	+	545.890i	0.722408	+	0.0711510i	0.452537	−	0.891745i	$-0.350519\pi$
$389$	5542.52	+	545.890i	0.722408	+	0.0711510i	0.269871	+	0.962896i	$0.413019\pi$
$390$	−197.153	+	6245.21i	−0.0255980	+	0.810868i
$391$	−11360.0	−	17001.4i	−1.46931	−	2.19898i
$392$	2440.76	+	5834.67i	0.314482	+	0.751774i
$393$	4001.07	+	2673.43i	0.513555	+	0.343147i
$394$	36.6401	+	220.326i	0.00468503	+	0.0281723i
$395$	−6336.83	+	11855.4i	−0.807191	+	1.51015i
$396$	−345.752	+	558.918i	−0.0438754	+	0.0709260i
$397$	1032.59	+	10484.1i	0.130540	+	1.32539i	0.807717	+	0.589571i	$0.200703\pi$
$397$	1032.59	+	10484.1i	0.130540	+	1.32539i	−0.677177	+	0.735820i	$0.736797\pi$
$398$	−542.319	+	619.853i	−0.0683014	+	0.0780664i
$399$	587.811	+	243.479i	0.0737528	+	0.0305494i
$400$	11941.3	−	13745.3i	1.49266	−	1.71816i
$401$	−4490.63	+	1860.08i	−0.559230	+	0.231641i	−0.644351	−	0.764730i	$-0.722872\pi$
$401$	−4490.63	+	1860.08i	−0.559230	+	0.231641i	0.0851210	+	0.996371i	$0.472872\pi$
$402$	−1301.45	+	3848.69i	−0.161469	+	0.477501i
$403$	428.082	−	521.620i	0.0529139	−	0.0644758i
$404$	−4273.78	−	1597.16i	−0.526308	−	0.196687i
$405$	191.674	+	631.866i	0.0235170	+	0.0775251i
$406$	−523.876	−	121.506i	−0.0640382	−	0.0148529i
$407$	−272.350	−	1369.20i	−0.0331693	−	0.166753i
$408$	5609.07	−	6883.66i	0.680614	−	0.835275i
$409$	6903.41	+	1373.17i	0.834600	+	0.166012i	0.593851	−	0.804575i	$-0.297607\pi$
$409$	6903.41	+	1373.17i	0.834600	+	0.166012i	0.240749	+	0.970587i	$0.422607\pi$
$410$	9039.86	−	3414.41i	1.08889	−	0.411282i
$411$	5571.52	+	6788.92i	0.668669	+	0.814776i
$412$	11059.4	−	3782.95i	1.32246	−	0.452360i
$413$	−5424.42	+	2899.41i	−0.646291	+	0.345450i
$414$	1026.76	−	7869.97i	0.121890	−	0.934271i
$415$	−16079.3	−	16079.3i	−1.90193	−	1.90193i
$416$	−6241.33	−	993.081i	−0.735592	−	0.117043i
$417$	6899.02	−	6899.02i	0.810183	−	0.810183i
$418$	210.055	+	273.088i	0.0245792	+	0.0319550i
$419$	2212.84	+	4139.93i	0.258006	+	0.482694i	0.977258	−	0.212055i	$-0.0680154\pi$
$419$	2212.84	+	4139.93i	0.258006	+	0.482694i	−0.719252	+	0.694749i	$0.755515\pi$
$420$	2666.51	+	3026.30i	0.309791	+	0.351591i
$421$	−3971.56	+	3259.38i	−0.459768	+	0.377322i	−0.835575	−	0.549376i	$-0.814865\pi$
$421$	−3971.56	+	3259.38i	−0.459768	+	0.377322i	0.375807	+	0.926698i	$0.377365\pi$
$422$	3944.92	+	1781.88i	0.455061	+	0.205546i
$423$	820.815	−	4126.51i	0.0943484	−	0.474321i
$424$	−3997.95	+	1228.06i	−0.457919	+	0.140660i
$425$	35018.6	−	6965.64i	3.99683	−	0.795019i
$426$	−7267.15	+	4530.77i	−0.826513	+	0.515297i
$427$	616.837	−	187.115i	0.0699083	−	0.0212064i
$428$	2991.73	+	2788.99i	0.337876	+	0.314978i
$429$	−402.529	−	330.347i	−0.0453013	−	0.0371778i
$430$	−21165.5	+	10468.4i	−2.37370	+	1.17402i
$431$	−923.701	−	2230.01i	−0.103232	−	0.249225i	0.863821	−	0.503799i	$-0.168065\pi$
$431$	−923.701	−	2230.01i	−0.103232	−	0.249225i	−0.967053	+	0.254574i	$0.918065\pi$
$432$	8724.82	−	1482.33i	0.971697	−	0.165090i
$433$	4917.82	−	11872.7i	0.545810	−	1.31770i	−0.374760	−	0.927122i	$-0.622275\pi$
$433$	4917.82	−	11872.7i	0.545810	−	1.31770i	0.920569	−	0.390579i	$-0.127725\pi$
$434$	−28.9964	−	434.628i	−0.00320707	−	0.0480710i
$435$	1502.63	−	147.996i	0.165622	−	0.0163124i
$436$	−990.432	+	6087.30i	−0.108792	+	0.668645i
$437$	−3669.32	−	1961.29i	−0.401664	−	0.214694i
$438$	−2279.70	+	3189.17i	−0.248695	+	0.347910i
$439$	368.790	−	551.934i	0.0400943	−	0.0600054i	−0.810881	−	0.585211i	$-0.801012\pi$
$439$	368.790	−	551.934i	0.0400943	−	0.0600054i	0.850975	+	0.525206i	$0.176012\pi$
$440$	433.600	+	2140.67i	0.0469797	+	0.231937i
$441$	−4002.62	+	2674.47i	−0.432202	+	0.288788i
$442$	−8482.21	−	9035.21i	−0.912800	−	0.972310i
$443$	−928.803	+	9430.29i	−0.0996135	+	1.01139i	0.807319	+	0.590116i	$0.200918\pi$
$443$	−928.803	+	9430.29i	−0.0996135	+	1.01139i	−0.906932	+	0.421277i	$0.861582\pi$
$444$	−4443.22	+	5818.58i	−0.474923	+	0.621931i
$445$	−4582.75	+	15107.3i	−0.488187	+	1.60934i
$446$	3770.44	−	6548.23i	0.400304	−	0.695219i
$447$			1757.32i			0.185948i
$448$	−3376.13	+	2290.21i	−0.356043	+	0.241522i
$449$		−	14501.2i		−	1.52417i	−0.647475	−	0.762087i	$-0.724175\pi$
$449$		−	14501.2i		−	1.52417i	0.647475	−	0.762087i	$-0.275825\pi$
$450$	12010.1	+	6915.37i	1.25814	+	0.724431i
$451$	−233.772	+	770.643i	−0.0244077	+	0.0804615i
$452$	−3467.54	+	464.745i	−0.360840	+	0.0483623i
$453$	197.615	−	2006.42i	0.0204962	−	0.208101i
$454$	−8808.20	+	8269.09i	−0.910549	+	0.854818i
$455$	4680.62	−	3127.49i	0.482266	−	0.322240i
$456$	346.282	−	1773.30i	0.0355618	−	0.182110i
$457$	−1852.54	+	2772.52i	−0.189624	+	0.283792i	−0.914084	−	0.405524i	$-0.867089\pi$
$457$	−1852.54	+	2772.52i	−0.189624	+	0.283792i	0.724460	+	0.689316i	$0.242089\pi$
$458$	14023.3	+	10024.2i	1.43072	+	1.02271i
$459$	15304.9	+	8180.64i	1.55637	+	0.831895i
$460$	−15413.5	−	21403.8i	−1.56230	−	2.16947i
$461$	−635.866	+	62.6274i	−0.0642413	+	0.00632722i	−0.130087	−	0.991503i	$-0.541526\pi$
$461$	−635.866	+	62.6274i	−0.0642413	+	0.00632722i	0.0658454	+	0.997830i	$0.479026\pi$
$462$	−335.398	+	22.3762i	−0.0337752	+	0.00225332i
$463$	5606.86	−	13536.2i	0.562792	−	1.35870i	−0.344732	−	0.938701i	$-0.612030\pi$
$463$	5606.86	−	13536.2i	0.562792	−	1.35870i	0.907524	−	0.420000i	$-0.137970\pi$
$464$	−42.8442	+	1526.58i	−0.00428662	+	0.152737i
$465$	468.020	+	1129.90i	0.0466751	+	0.112684i
$466$	−3718.77	−	7518.79i	−0.369675	−	0.747428i
$467$	−3756.98	−	3083.27i	−0.372274	−	0.305518i	0.429590	−	0.903024i	$-0.358658\pi$
$467$	−3756.98	−	3083.27i	−0.372274	−	0.305518i	−0.801864	+	0.597507i	$0.796158\pi$
$468$	−168.606	−	4807.33i	−0.0166535	−	0.474826i
$469$	3502.70	−	1062.53i	0.344860	−	0.104612i
$470$	−7397.49	−	11865.2i	−0.726002	−	1.16447i
$471$	4696.50	−	934.193i	0.459455	−	0.0913914i
$472$	11127.9	+	13463.0i	1.08517	+	1.31289i
$473$	383.912	−	1930.05i	0.0373198	−	0.187619i
$474$	−2418.45	+	5354.24i	−0.234352	+	0.518836i
$475$	5616.00	−	4608.93i	0.542483	−	0.445204i
$476$	−7983.98	−	504.590i	−0.768792	−	0.0485879i
$477$	−1500.61	−	2807.44i	−0.144042	−	0.269484i
$478$	−5018.68	+	3860.28i	−0.480228	+	0.369383i
$479$	2033.64	−	2033.64i	0.193986	−	0.193986i	−0.603430	−	0.797416i	$-0.706200\pi$
$479$	2033.64	−	2033.64i	0.193986	−	0.193986i	0.797416	+	0.603430i	$0.206200\pi$
$480$	6919.71	−	9127.70i	0.658000	−	0.867959i
$481$	7225.03	+	7225.03i	0.684892	+	0.684892i
$482$	10818.1	+	1411.40i	1.02231	+	0.133376i
$483$	3580.01	−	1913.56i	0.337259	−	0.180269i
$484$	9397.42	+	4607.07i	0.882553	+	0.432670i
$485$	−3195.17	−	3893.33i	−0.299145	−	0.364509i
$486$	3833.26	+	10148.8i	0.357778	+	0.947240i
$487$	−837.475	−	166.584i	−0.0779253	−	0.0155003i	0.155974	−	0.987761i	$-0.450149\pi$
$487$	−837.475	−	166.584i	−0.0779253	−	0.0155003i	−0.233899	+	0.972261i	$0.575149\pi$
$488$	−868.539	−	1611.33i	−0.0805674	−	0.149470i
$489$	−1271.06	−	6390.04i	−0.117544	−	0.590936i
$490$	−3614.62	+	15584.5i	−0.333249	+	1.43680i
$491$	−1387.59	−	4574.27i	−0.127538	−	0.420435i	0.869796	−	0.493412i	$-0.164250\pi$
$491$	−1387.59	−	4574.27i	−0.127538	−	0.420435i	−0.997334	+	0.0729761i	$0.976750\pi$
$492$	3842.76	−	1751.95i	0.352124	−	0.160537i
$493$	−1899.83	+	2314.95i	−0.173558	+	0.211481i
$494$	−2388.79	−	807.777i	−0.217564	−	0.0735700i
$495$	−1535.89	+	636.186i	−0.139461	+	0.0577665i
$496$	−1193.34	+	325.730i	−0.108029	+	0.0294873i
$497$	7128.16	+	2952.58i	0.643343	+	0.266481i
$498$	−7479.64	−	6544.05i	−0.673034	−	0.588847i
$499$	−1140.00	−	11574.6i	−0.102271	−	1.03837i	−0.900157	−	0.435566i	$-0.856548\pi$
$499$	−1140.00	−	11574.6i	−0.102271	−	1.03837i	0.797886	−	0.602808i	$-0.205952\pi$
$500$	25132.7	−	5921.99i	2.24794	−	0.529679i
$501$	608.565	−	1138.54i	0.0542688	−	0.101530i
$502$	9541.28	−	1586.71i	0.848303	−	0.141072i
$503$	8080.48	+	5399.20i	0.716283	+	0.478605i	0.859532	−	0.511081i	$-0.170755\pi$
$503$	8080.48	+	5399.20i	0.716283	+	0.478605i	−0.143249	+	0.989687i	$0.545755\pi$
$504$	−2203.35	−	2187.98i	−0.194732	−	0.193374i
$505$	−6411.72	−	9595.82i	−0.564986	−	0.845561i
$506$	2197.06	+	69.3582i	0.193026	+	0.00609358i
$507$	−3043.72	−	299.780i	−0.266620	−	0.0262598i
$508$	3783.17	−	2196.00i	0.330415	−	0.191795i
$509$	8510.47	+	2581.62i	0.741100	+	0.224810i	0.638188	−	0.769880i	$-0.279684\pi$
$509$	8510.47	+	2581.62i	0.741100	+	0.224810i	0.102912	+	0.994691i	$0.467184\pi$
$510$	21688.8	−	5838.62i	1.88313	−	0.506938i
$511$	3531.83			0.305752
$512$	8277.57	+	8105.53i	0.714493	+	0.699643i
$513$	3531.16			0.303907
$514$	20549.4	−	5531.90i	1.76341	−	0.474711i
$515$	28292.9	+	8582.57i	2.42085	+	0.734356i
$516$	−8925.27	+	5180.82i	−0.761460	+	0.442001i
$517$	1159.67	+	114.217i	0.0986500	+	0.00971617i
$518$	6592.52	+	208.117i	0.559187	+	0.0176528i
$519$	−3366.35	−	5038.10i	−0.284714	−	0.426104i
$520$	−11343.4	−	11264.2i	−0.956615	−	0.949942i
$521$	−3403.83	−	2274.37i	−0.286227	−	0.191251i	0.404165	−	0.914686i	$-0.367562\pi$
$521$	−3403.83	−	2274.37i	−0.286227	−	0.191251i	−0.690392	+	0.723435i	$0.742562\pi$
$522$	−1146.65	+	190.688i	−0.0961450	+	0.0159889i
$523$	−659.925	+	1234.63i	−0.0551750	+	0.103225i	−0.907997	−	0.418976i	$-0.862389\pi$
$523$	−659.925	+	1234.63i	−0.0551750	+	0.103225i	0.852822	+	0.522201i	$0.174889\pi$
$524$	−11983.3	+	2823.60i	−0.999029	+	0.235400i
$525$	694.773	+	7054.15i	0.0577569	+	0.586416i
$526$	−15510.0	−	13569.9i	−1.28568	−	1.12486i
$527$	−2241.03	−	928.266i	−0.185239	−	0.0767285i
$528$	251.363	+	920.886i	0.0207181	+	0.0759023i
$529$	−13283.8	+	5502.34i	−1.09179	+	0.452235i
$530$	−10021.7	−	3388.88i	−0.821351	−	0.277743i
$531$	−8433.96	+	10276.8i	−0.689270	+	0.839878i
$532$	−1481.13	+	675.263i	−0.120705	+	0.0550307i
$533$	−1711.02	−	5640.47i	−0.139048	−	0.458379i
$534$	−1558.93	+	6721.32i	−0.126332	+	0.544681i
$535$	2018.39	+	10147.1i	0.163108	+	0.819999i
$536$	−4931.98	−	9149.90i	−0.397442	−	0.737343i
$537$	−6450.11	−	1283.01i	−0.518330	−	0.103102i
$538$	−1316.10	−	3484.45i	−0.105467	−	0.279229i
$539$	−845.817	−	1030.63i	−0.0675917	−	0.0823607i
$540$	20100.2	+	9854.09i	1.60181	+	0.785283i
$541$	14768.6	−	7893.98i	1.17366	−	0.627336i	0.234940	−	0.972010i	$-0.424511\pi$
$541$	14768.6	−	7893.98i	1.17366	−	0.627336i	0.938722	+	0.344674i	$0.112011\pi$
$542$	−23231.4	−	3030.90i	−1.84110	−	0.240200i
$543$	3893.64	+	3893.64i	0.307720	+	0.307720i
$544$	3096.64	+	22506.0i	0.244057	+	1.77378i
$545$	−11031.1	+	11031.1i	−0.867012	+	0.867012i
$546$	1950.13	−	1500.01i	0.152854	−	0.117572i
$547$	−3582.60	−	6702.56i	−0.280038	−	0.523914i	0.702100	−	0.712079i	$-0.252246\pi$
$547$	−3582.60	−	6702.56i	−0.280038	−	0.523914i	−0.982137	+	0.188165i	$0.939746\pi$
$548$	−22424.8	−	1417.26i	−1.74807	−	0.110478i
$549$	1077.01	−	883.881i	0.0837263	−	0.0687124i
$550$	−1580.03	+	3498.06i	−0.122496	+	0.271196i
$551$	−118.880	+	597.650i	−0.00919139	+	0.0462083i
$552$	−7344.20	−	8885.33i	−0.566286	−	0.685117i
$553$	5191.38	−	1032.63i	0.399204	−	0.0794067i
$554$	−1581.52	−	2536.68i	−0.121286	−	0.194537i
$555$	−17721.3	+	5375.69i	−1.35536	+	0.411145i
$556$	874.951	+	24946.8i	0.0667378	+	1.90284i
$557$	−9270.71	−	7608.28i	−0.705229	−	0.578767i	0.211931	−	0.977285i	$-0.432025\pi$
$557$	−9270.71	−	7608.28i	−0.705229	−	0.578767i	−0.917161	+	0.398518i	$0.869525\pi$
$558$	−417.411	−	843.942i	−0.0316674	−	0.0640267i
$559$	5511.85	+	13306.8i	0.417042	+	1.00683i
$560$	−10315.4	−	289.505i	−0.778400	−	0.0218461i
$561$	−716.333	+	1729.38i	−0.0539102	+	0.130151i
$562$	15551.7	−	1037.54i	1.16728	−	0.0778751i
$563$	5510.86	−	542.772i	0.412531	−	0.0406308i	0.110377	−	0.993890i	$-0.464794\pi$
$563$	5510.86	−	542.772i	0.412531	−	0.0406308i	0.302154	+	0.953259i	$0.402294\pi$
$564$	−3571.09	−	4958.97i	−0.266614	−	0.370231i
$565$	−7804.66	−	4171.68i	−0.581140	−	0.310626i
$566$	−17812.2	−	12732.6i	−1.32279	−	0.945567i
$567$	144.445	−	216.177i	0.0106986	−	0.0160116i
$568$	4199.23	−	21504.1i	0.310204	−	1.58854i
$569$	−1347.04	+	900.062i	−0.0992456	+	0.0663138i	−0.604203	−	0.796831i	$-0.706508\pi$
$569$	−1347.04	+	900.062i	−0.0992456	+	0.0663138i	0.504957	+	0.863144i	$0.331508\pi$
$570$	3332.04	−	3128.10i	0.244849	−	0.229863i
$571$	−1195.17	+	12134.7i	−0.0875941	+	0.889358i	0.846514	+	0.532367i	$0.178697\pi$
$571$	−1195.17	+	12134.7i	−0.0875941	+	0.889358i	−0.934108	+	0.356991i	$0.883803\pi$
$572$	1320.46	−	176.977i	0.0965229	−	0.0129367i
$573$	327.181	−	1078.57i	0.0238537	−	0.0786352i
$574$	−3297.36	−	1898.61i	−0.239772	−	0.138060i
$575$		−	46352.6i		−	3.36180i
$576$	−4847.56	+	7366.00i	−0.350663	+	0.532842i
$577$			9621.34i			0.694180i	0.937832	+	0.347090i	$0.112830\pi$
$577$			9621.34i			0.694180i	−0.937832	+	0.347090i	$0.887170\pi$
$578$	−15295.3	+	26563.8i	−1.10070	+	1.91161i
$579$	19.2708	−	63.5274i	0.00138319	−	0.00455977i
$580$	−2344.50	+	3070.22i	−0.167845	+	0.219800i
$581$	−877.622	+	8910.64i	−0.0626676	+	0.636275i
$582$	−1506.62	−	1604.84i	−0.107305	−	0.114300i
$583$	733.073	−	489.824i	0.0520768	−	0.0347966i
$584$	−1991.10	−	9830.01i	−0.141083	−	0.696522i
$585$	6759.99	−	10117.0i	0.477762	−	0.715022i
$586$	−11597.3	+	16224.0i	−0.817544	+	1.14370i
$587$	−10724.9	−	5732.56i	−0.754110	−	0.403080i	0.0490861	−	0.998795i	$-0.484369\pi$
$587$	−10724.9	−	5732.56i	−0.754110	−	0.403080i	−0.803197	+	0.595714i	$0.796869\pi$
$588$	−1122.86	+	6901.22i	−0.0787517	+	0.484016i
$589$	−491.194	+	48.3783i	−0.0343621	+	0.00338437i
$590$	2941.07	+	44083.9i	0.205224	+	3.07611i
$591$	−94.4922	+	228.124i	−0.00657680	+	0.0158778i
$592$	−3137.35	−	18466.0i	−0.217812	−	1.28201i
$593$	1480.68	+	3574.69i	0.102537	+	0.247546i	0.966819	−	0.255461i	$-0.0822271\pi$
$593$	1480.68	+	3574.69i	0.102537	+	0.247546i	−0.864283	+	0.503007i	$0.832227\pi$
$594$	−1672.25	+	827.088i	−0.115510	+	0.0571310i
$595$	−15642.5	−	12837.5i	−1.07778	−	0.884513i
$596$	−3288.67	−	3065.80i	−0.226022	−	0.210705i
$597$	−871.306	+	264.308i	−0.0597323	+	0.0181196i
$598$	−13652.6	+	8511.85i	−0.933607	+	0.582066i
$599$	−10065.0	+	2002.05i	−0.686551	+	0.136563i	−0.526026	−	0.850468i	$-0.676319\pi$
$599$	−10065.0	+	2002.05i	−0.686551	+	0.136563i	−0.160525	+	0.987032i	$0.551319\pi$
$600$	19241.9	−	5910.58i	1.30924	−	0.402164i
$601$	1024.23	−	5149.16i	0.0695163	−	0.349482i	−0.930335	−	0.366710i	$-0.880484\pi$
$601$	1024.23	−	5149.16i	0.0695163	−	0.349482i	0.999852	+	0.0172281i	$0.00548415\pi$
$602$	8473.33	+	3827.31i	0.573666	+	0.259118i
$603$	6115.79	−	5019.10i	0.413025	−	0.338961i
$604$	3410.07	+	3870.18i	0.229725	+	0.260721i
$605$	12479.7	+	23347.8i	0.838628	+	1.56896i
$606$	−3075.19	−	3998.00i	−0.206140	−	0.268000i
$607$	−14340.1	+	14340.1i	−0.958891	+	0.958891i	−0.999188	−	0.0402967i	$-0.987170\pi$
$607$	−14340.1	+	14340.1i	−0.958891	+	0.958891i	0.0402967	+	0.999188i	$0.487170\pi$
$608$	2714.44	+	3741.69i	0.181061	+	0.249582i
$609$	−420.395	−	420.395i	−0.0279725	−	0.0279725i
$610$	599.016	−	4591.37i	0.0397597	−	0.304752i
$611$	−7521.79	+	4020.48i	−0.498034	+	0.266205i
$612$	−16360.9	+	5596.39i	−1.08064	+	0.369641i
$613$	9665.58	+	11777.5i	0.636850	+	0.776004i	0.987005	−	0.160688i	$-0.0513712\pi$
$613$	9665.58	+	11777.5i	0.636850	+	0.776004i	−0.350155	+	0.936692i	$0.613871\pi$
$614$	−12308.9	+	4649.14i	−0.809032	+	0.305576i
$615$	10477.6	+	2084.12i	0.686986	+	0.136650i
$616$	543.255	−	666.703i	0.0355330	−	0.0436075i
$617$	−3179.83	−	15986.1i	−0.207480	−	1.04307i	−0.934366	−	0.356314i	$-0.884033\pi$
$617$	−3179.83	−	15986.1i	−0.207480	−	1.04307i	0.726886	−	0.686758i	$-0.240967\pi$
$618$	12587.7	+	2919.55i	0.819337	+	0.190035i
$619$	−5830.36	−	19220.1i	−0.378582	−	1.24802i	−0.914790	−	0.403931i	$-0.867644\pi$
$619$	−5830.36	−	19220.1i	−0.378582	−	1.24802i	0.536208	−	0.844086i	$-0.319856\pi$
$620$	−2931.00	−	1095.35i	−0.189858	−	0.0709521i
$621$	14292.5	−	17415.5i	0.923572	−	1.12538i
$622$	8510.09	−	25166.4i	0.548591	−	1.62231i
$623$	5743.03	−	2378.84i	0.369326	−	0.152980i
$624$	−5274.32	−	4582.09i	−0.338368	−	0.293959i
$625$	27487.3	+	11385.6i	1.75919	+	0.728680i
$626$	4263.90	−	4873.50i	0.272236	−	0.311157i
$627$	37.3331	+	379.049i	0.00237789	+	0.0241431i
$628$	−6445.19	+	10418.8i	−0.409540	+	0.662033i
$629$	17314.3	−	32392.8i	1.09756	−	2.05339i
$630$	−1288.51	−	7748.12i	−0.0814848	−	0.489988i
$631$	2.71363	+	1.81319i	0.000171201	+	0.000114393i	0.555656	−	0.831412i	$-0.312467\pi$
$631$	2.71363	+	1.81319i	0.000171201	+	0.000114393i	−0.555485	+	0.831527i	$0.687467\pi$
$632$	−5800.77	−	13866.8i	−0.365098	−	0.872773i
$633$	2658.65	+	3978.95i	0.166938	+	0.249840i
$634$	−640.861	+	20300.5i	−0.0401449	+	1.27167i
$635$	11011.6	+	1084.55i	0.688163	+	0.0677781i
$636$	−4468.86	−	1186.26i	−0.278619	−	0.0739594i
$637$	9338.23	+	2832.72i	0.580839	+	0.176196i
$638$	−83.6871	−	310.873i	−0.00519311	−	0.0192909i
$639$	16676.8			1.03243
$640$	5009.62	+	28873.6i	0.309410	+	1.78333i
$641$	−1694.21			−0.104395			−0.0521977	−	0.998637i	$-0.516623\pi$
$641$	−1694.21			−0.104395			−0.0521977	+	0.998637i	$0.516623\pi$
$642$	1175.39	+	4366.24i	0.0722570	+	0.268414i
$643$	−439.169	−	133.220i	−0.0269349	−	0.00817060i	0.276788	−	0.960931i	$-0.410730\pi$
$643$	−439.169	−	133.220i	−0.0269349	−	0.00817060i	−0.303723	+	0.952760i	$0.598230\pi$
$644$	−2664.59	+	10038.0i	−0.163043	+	0.614213i
$645$	−25978.7	−	2558.68i	−1.58591	−	0.156198i
$646$	−286.017	+	9060.15i	−0.0174198	+	0.551806i
$647$	17289.0	+	25874.8i	1.05054	+	1.57224i	0.796109	+	0.605153i	$0.206888\pi$
$647$	17289.0	+	25874.8i	1.05054	+	1.57224i	0.254431	+	0.967091i	$0.418112\pi$
$648$	−683.110	−	280.156i	−0.0414122	−	0.0169839i
$649$	−3061.53	−	2045.65i	−0.185171	−	0.123727i
$650$	−4608.64	−	27712.9i	−0.278101	−	1.67229i
$651$	227.005	−	424.696i	0.0136667	−	0.0255686i
$652$	14175.8	+	8769.29i	0.851485	+	0.526736i
$653$	−1413.43	−	14350.8i	−0.0847039	−	0.860013i	−0.939841	−	0.341612i	$-0.889027\pi$
$653$	−1413.43	−	14350.8i	−0.0847039	−	0.860013i	0.855137	−	0.518402i	$-0.173473\pi$
$654$	−4489.52	+	5131.38i	−0.268431	+	0.306809i
$655$	−28771.3	−	11917.5i	−1.71632	−	0.710923i
$656$	−3425.40	+	10247.8i	−0.203871	+	0.609922i
$657$	7052.86	−	2921.39i	0.418810	−	0.173477i
$658$	−1763.63	+	5215.48i	−0.104489	+	0.308998i
$659$	15685.6	−	19113.0i	0.927202	−	1.12980i	−0.0640677	−	0.997946i	$-0.520407\pi$
$659$	15685.6	−	19113.0i	0.927202	−	1.12980i	0.991269	−	0.131853i	$-0.0420926\pi$
$660$	−845.270	+	2261.82i	−0.0498516	+	0.133396i
$661$	3718.64	+	12258.7i	0.218817	+	0.721344i	0.995778	+	0.0917947i	$0.0292603\pi$
$661$	3718.64	+	12258.7i	0.218817	+	0.721344i	−0.776961	+	0.629549i	$0.783240\pi$
$662$	28357.3	+	6577.13i	1.66486	+	0.386144i
$663$	−2672.84	−	13437.3i	−0.156568	−	0.787120i
$664$	25295.4	−	2580.81i	1.47839	−	0.150836i
$665$	−4038.42	−	803.291i	−0.235493	−	0.0468426i
$666$	13337.0	−	5037.47i	0.775974	−	0.293090i
$667$	2466.40	+	3005.32i	0.143178	+	0.174463i
$668$	1068.99	+	3125.16i	0.0619167	+	0.181012i
$669$	7367.11	−	3937.80i	0.425753	−	0.227570i
$670$	3401.50	−	26072.0i	0.196136	−	1.50336i
$671$	272.860	+	272.860i	0.0156984	+	0.0156984i
$672$	−4506.74	+	173.860i	−0.258707	+	0.00998033i
$673$	−16326.4	+	16326.4i	−0.935120	+	0.935120i	−0.998020	−	0.0628996i	$-0.979965\pi$
$673$	−16326.4	+	16326.4i	−0.935120	+	0.935120i	0.0628996	+	0.998020i	$0.479965\pi$
$674$	−17047.1	−	22162.6i	−0.974226	−	1.26657i
$675$	18544.8	+	34694.9i	1.05747	+	1.97838i
$676$	5871.03	−	5173.05i	0.334037	−	0.294324i
$677$	−13109.0	+	10758.2i	−0.744192	+	0.610742i	−0.928156	−	0.372190i	$-0.878607\pi$
$677$	−13109.0	+	10758.2i	−0.744192	+	0.610742i	0.183965	+	0.982933i	$0.441107\pi$
$678$	−3524.82	−	1592.12i	−0.199660	−	0.0901844i
$679$	−386.897	+	1945.06i	−0.0218671	+	0.109933i
$680$	−26911.4	+	50774.4i	−1.51766	+	2.86340i
$681$	−13099.7	+	2605.69i	−0.737122	+	0.146623i
$682$	221.283	−	137.961i	0.0124243	−	0.00774602i
$683$	−23197.2	+	7036.78i	−1.29958	+	0.394224i	−0.862892	−	0.505388i	$-0.831349\pi$
$683$	−23197.2	+	7036.78i	−1.29958	+	0.394224i	−0.436690	+	0.899612i	$0.643849\pi$
$684$	−2399.18	+	2573.59i	−0.134116	+	0.143865i
$685$	−43935.5	−	36057.0i	−2.45064	−	2.01119i
$686$	12575.4	−	6219.76i	0.699900	−	0.346168i
$687$	7292.66	+	17606.0i	0.404996	+	0.977747i
$688$	5875.47	−	25741.2i	0.325582	−	1.42641i
$689$	−2469.46	+	5961.81i	−0.136544	+	0.329647i
$690$	−1941.05	−	29094.6i	−0.107094	−	1.60523i
$691$	−11670.9	+	1149.49i	−0.642524	+	0.0632831i	−0.414031	−	0.910263i	$-0.635880\pi$
$691$	−11670.9	+	1149.49i	−0.642524	+	0.0632831i	−0.228492	+	0.973546i	$0.573380\pi$
$692$	15301.2	+	2489.58i	0.840556	+	0.136762i
$693$	577.295	+	308.571i	0.0316445	+	0.0169143i
$694$	−1260.56	+	1763.45i	−0.0689483	+	0.0964547i
$695$	−35079.7	+	52500.5i	−1.91460	+	2.86541i
$696$	−933.068	+	1407.07i	−0.0508159	+	0.0766306i
$697$	−17617.4	+	11771.5i	−0.957396	+	0.639712i
$698$	886.534	+	944.332i	0.0480742	+	0.0512084i
$699$	908.941	−	9228.63i	0.0491836	−	0.499369i
$700$	−14413.3	−	11006.3i	−0.778243	−	0.594287i
$701$	−8178.75	+	26961.7i	−0.440667	+	1.45268i	0.402694	+	0.915335i	$0.368074\pi$
$701$	−8178.75	+	26961.7i	−0.440667	+	1.45268i	−0.843360	+	0.537348i	$0.819426\pi$
$702$	6813.54	−	11833.3i	0.366326	−	0.636208i
$703$		−	7473.68i		−	0.400961i
$704$	−2161.87	−	1136.16i	−0.115737	−	0.0608248i
$705$		−	15457.8i		−	0.825778i
$706$	23929.9	+	13778.7i	1.27566	+	0.734519i
$707$	−1319.12	+	4348.55i	−0.0701704	+	0.231321i
$708$	2565.08	+	19138.5i	0.136161	+	1.01592i
$709$	−2997.61	+	30435.2i	−0.158783	+	1.61215i	0.504245	+	0.863561i	$0.331771\pi$
$709$	−2997.61	+	30435.2i	−0.158783	+	1.61215i	−0.663028	+	0.748594i	$0.730729\pi$
$710$	40406.4	−	37933.3i	2.13581	−	2.00509i
$711$	9512.72	−	6356.20i	0.501765	−	0.335269i
$712$	−9858.63	−	14643.3i	−0.518916	−	0.770758i
$713$	−1749.53	+	2618.35i	−0.0918938	+	0.137529i
$714$	−7194.86	−	5143.07i	−0.377116	−	0.269572i
$715$	2972.05	+	1588.59i	0.155452	+	0.0830910i
$716$	13653.8	−	9832.46i	0.712662	−	0.513207i
$717$	−6965.97	+	686.089i	−0.362830	+	0.0357356i
$718$	−24213.7	+	1615.43i	−1.25856	+	0.0839654i
$719$	−3719.79	+	8980.36i	−0.192941	+	0.465801i	−0.990512	−	0.137424i	$-0.956118\pi$
$719$	−3719.79	+	8980.36i	−0.192941	+	0.465801i	0.797571	+	0.603225i	$0.206118\pi$
$720$	−20838.6	+	7954.33i	−1.07863	+	0.411723i
$721$	−4455.09	−	10755.5i	−0.230120	−	0.555558i
$722$	−7783.06	−	15736.2i	−0.401185	−	0.811136i
$723$	9323.29	+	7651.43i	0.479581	+	0.393582i
$724$	−14079.4	+	493.801i	−0.722728	+	0.0253480i
$725$	−6496.46	+	1970.68i	−0.332789	+	0.100951i
$726$	6121.38	+	9818.42i	0.312928	+	0.501922i
$727$	−2314.51	+	460.386i	−0.118075	+	0.0234866i	−0.253774	−	0.967264i	$-0.581672\pi$
$727$	−2314.51	+	460.386i	−0.118075	+	0.0234866i	0.135699	+	0.990750i	$0.456672\pi$
$728$	−595.046	+	6266.38i	−0.0302938	+	0.319021i
$729$	−2167.91	+	10898.8i	−0.110141	+	0.553716i
$730$	10443.4	−	23120.9i	0.529491	−	1.17225i
$731$	40022.8	−	32845.8i	2.02503	−	1.66190i
$732$	127.641	−	2019.63i	0.00644502	−	0.101978i
$733$	5353.48	+	10015.7i	0.269762	+	0.504689i	0.979930	−	0.199343i	$-0.0638809\pi$
$733$	5353.48	+	10015.7i	0.269762	+	0.504689i	−0.710168	+	0.704032i	$0.751381\pi$
$734$	7133.78	−	5487.18i	0.358736	−	0.275934i
$735$	−12506.1	+	12506.1i	−0.627610	+	0.627610i
$736$	29440.6	+	1757.22i	1.47445	+	0.0880054i
$737$	1549.43	+	1549.43i	0.0774409	+	0.0774409i
$738$	−8155.09	−	1063.96i	−0.406765	−	0.0530690i
$739$	103.964	−	55.5697i	0.00517505	−	0.00276612i	−0.468807	−	0.883301i	$-0.655316\pi$
$739$	103.964	−	55.5697i	0.00517505	−	0.00276612i	0.473982	+	0.880534i	$0.342816\pi$
$740$	20856.1	−	42542.1i	1.03606	−	2.11335i
$741$	−1768.53	−	2154.96i	−0.0876769	−	0.106835i
$742$	1471.88	+	3896.89i	0.0728225	+	0.192802i
$743$	−18356.8	−	3651.40i	−0.906388	−	0.180292i	−0.280180	−	0.959948i	$-0.590394\pi$
$743$	−18356.8	−	3651.40i	−0.906388	−	0.180292i	−0.626208	+	0.779656i	$0.715394\pi$
$744$	−1310.02	−	392.387i	−0.0645531	−	0.0193355i
$745$	−2218.72	−	11154.3i	−0.109111	−	0.548538i
$746$	1136.86	−	4901.57i	0.0557954	−	0.240562i
$747$	5617.96	+	18519.9i	0.275168	+	0.907108i
$748$	−1986.67	−	4357.60i	−0.0971121	−	0.213007i
$749$	2584.35	−	3149.05i	0.126075	−	0.153623i
$750$	27041.4	+	9144.13i	1.31655	+	0.445195i
$751$	32884.1	−	13621.0i	1.59781	−	0.661836i	0.606710	−	0.794924i	$-0.292489\pi$
$751$	32884.1	−	13621.0i	1.59781	−	0.661836i	0.991104	+	0.133087i	$0.0424891\pi$
$752$	15510.3	+	1968.38i	0.752131	+	0.0954512i
$753$	9878.97	+	4092.00i	0.478101	+	0.198036i
$754$	1773.40	+	1551.57i	0.0856545	+	0.0749403i
$755$	1278.90	+	12984.8i	0.0616474	+	0.625916i
$756$	−2021.58	−	8579.50i	−0.0972541	−	0.412743i
$757$	13728.0	−	25683.3i	0.659119	−	1.23312i	−0.301025	−	0.953616i	$-0.597329\pi$
$757$	13728.0	−	25683.3i	0.659119	−	1.23312i	0.960143	−	0.279508i	$-0.0901713\pi$
$758$	−15324.8	+	2548.51i	−0.734330	+	0.122119i
$759$	2020.55	+	1350.09i	0.0966291	+	0.0645655i
$760$	40.9270	+	11692.8i	0.00195339	+	0.558084i
$761$	−12954.8	−	19388.3i	−0.617099	−	0.923554i	0.382901	−	0.923790i	$-0.374925\pi$
$761$	−12954.8	−	19388.3i	−0.617099	−	0.923554i	−1.00000		0.000235094i	$0.999925\pi$
$762$	4833.50	+	152.587i	0.229789	+	0.00725414i
$763$	6113.11	+	602.089i	0.290052	+	0.0285676i
$764$	1447.65	+	2493.94i	0.0685525	+	0.118099i
$765$	−41855.8	−	12696.8i	−1.97817	−	0.600071i
$766$	15119.5	−	4070.17i	0.713172	−	0.191986i
$767$	26949.8			1.26871
$768$	3024.62	+	12445.4i	0.142111	+	0.584747i
$769$	3106.48			0.145673			0.0728366	−	0.997344i	$-0.476795\pi$
$769$	3106.48			0.145673			0.0728366	+	0.997344i	$0.476795\pi$
$770$	2100.62	−	565.487i	0.0983131	−	0.0264659i
$771$	22513.5	+	6829.39i	1.05163	+	0.319007i
$772$	85.2659	+	146.892i	0.00397511	+	0.00684814i
$773$	−9891.28	−	974.206i	−0.460239	−	0.0453296i	−0.134759	−	0.990878i	$-0.543026\pi$
$773$	−9891.28	−	974.206i	−0.460239	−	0.0453296i	−0.325480	+	0.945549i	$0.605526\pi$
$774$	20086.5	+	634.105i	0.932810	+	0.0294476i
$775$	−3054.97	−	4572.08i	−0.141597	−	0.211915i
$776$	5631.73	−	19.7121i	0.260525	−	0.000911884i
$777$	6062.90	+	4051.10i	0.279930	+	0.187043i
$778$	−15539.1	+	2584.14i	−0.716070	+	0.119082i
$779$	−2032.34	+	3802.25i	−0.0934741	+	0.174878i
$780$	−4053.25	−	17201.8i	−0.186064	−	0.789647i
$781$	452.724	+	4596.58i	0.0207423	+	0.210600i
$782$	43526.4	+	38081.9i	1.99041	+	1.74144i
$783$	−3048.47	−	1262.72i	−0.139136	−	0.0576321i
$784$	−10956.1	−	14141.1i	−0.499092	−	0.644182i
$785$	−28630.6	+	11859.2i	−1.30175	+	0.539201i
$786$	−12893.3	−	4359.92i	−0.585100	−	0.197854i
$787$	6088.54	−	7418.91i	0.275773	−	0.336030i	−0.616644	−	0.787242i	$-0.711508\pi$
$787$	6088.54	−	7418.91i	0.275773	−	0.336030i	0.892417	+	0.451212i	$0.149008\pi$
$788$	−262.064	−	574.815i	−0.0118472	−	0.0259860i
$789$	−6613.52	−	21801.8i	−0.298412	−	0.983734i
$790$	8590.59	−	37038.4i	0.386886	−	1.66806i
$791$	679.803	+	3417.60i	0.0305576	+	0.153623i
$792$	533.377	−	1780.72i	0.0239302	−	0.0798930i
$793$	−2770.07	−	551.001i	−0.124046	−	0.0246742i
$794$	−10528.5	−	27874.8i	−0.470582	−	1.24589i
$795$	−7419.55	−	9040.75i	−0.330999	−	0.403324i
$796$	1025.44	−	2091.67i	0.0456604	−	0.0931374i
$797$	31623.4	−	16903.0i	1.40547	−	0.751237i	0.417908	−	0.908489i	$-0.362763\pi$
$797$	31623.4	−	16903.0i	1.40547	−	0.751237i	0.987559	+	0.157252i	$0.0502635\pi$
$798$	−1784.44	−	232.808i	−0.0791586	−	0.0103275i
$799$	21679.0	+	21679.0i	0.959887	+	0.959887i
$800$	−22507.9	+	46320.8i	−0.994719	+	2.04711i
$801$	9500.81	−	9500.81i	0.419094	−	0.419094i
$802$	10897.2	−	8381.91i	0.479791	−	0.369047i
$803$	996.680	+	1864.66i	0.0438009	+	0.0819456i
$804$	724.807	−	11468.4i	0.0317935	−	0.503059i
$805$	−20307.4	+	16665.9i	−0.889122	+	0.729684i
$806$	−785.662	+	1739.39i	−0.0343347	+	0.0760141i
$807$	803.332	−	4038.62i	0.0350417	−	0.176166i
$808$	12846.8	+	1219.91i	0.559343	+	0.0531144i
$809$	3747.60	−	745.445i	0.162866	−	0.0323961i	−0.112984	−	0.993597i	$-0.536041\pi$
$809$	3747.60	−	745.445i	0.162866	−	0.0323961i	0.275850	+	0.961201i	$0.411041\pi$
$810$	−988.071	−	1584.82i	−0.0428609	−	0.0687469i
$811$	−32209.0	+	9770.49i	−1.39459	+	0.423043i	−0.896099	−	0.443854i	$-0.853611\pi$
$811$	−32209.0	+	9770.49i	−1.39459	+	0.423043i	−0.498488	+	0.866897i	$0.666111\pi$
$812$	1520.14	−	53.3156i	0.0656977	−	0.00230420i
$813$	−20021.3	−	16431.1i	−0.863687	−	0.708809i
$814$	1750.53	+	3539.30i	0.0753759	+	0.152399i
$815$	16135.6	+	38954.7i	0.693503	+	1.67426i
$816$	−10258.3	+	22924.6i	−0.440090	+	0.983483i
$817$	4031.60	−	9733.15i	0.172641	−	0.416793i
$818$	−19864.2	+	1325.24i	−0.849064	+	0.0566455i
$819$	−4767.98	+	469.605i	−0.203427	+	0.0200358i
$820$	−22179.2	+	15971.9i	−0.944551	+	0.680197i
$821$	19917.6	+	10646.2i	0.846684	+	0.452562i	0.836878	−	0.547390i	$-0.184378\pi$
$821$	19917.6	+	10646.2i	0.846684	+	0.452562i	0.00980648	+	0.999952i	$0.496878\pi$
$822$	−20208.4	−	14445.5i	−0.857480	−	0.612949i
$823$	21106.7	−	31588.3i	0.893963	−	1.33791i	−0.0468207	−	0.998903i	$-0.514909\pi$
$823$	21106.7	−	31588.3i	0.893963	−	1.33791i	0.940784	−	0.339007i	$-0.110091\pi$
$824$	−27423.9	+	18463.2i	−1.15941	+	0.780579i
$825$	−3528.23	+	2357.49i	−0.148893	+	0.0994874i
$826$	12683.4	−	11907.1i	0.534275	−	0.501575i
$827$	−736.555	+	7478.37i	−0.0309704	+	0.314448i	0.967202	+	0.254010i	$0.0817497\pi$
$827$	−736.555	+	7478.37i	−0.0309704	+	0.314448i	−0.998172	+	0.0604378i	$0.980750\pi$
$828$	2982.02	+	22249.3i	0.125160	+	0.933838i
$829$	−431.953	+	1423.96i	−0.0180969	+	0.0596575i	−0.965524	−	0.260315i	$-0.916174\pi$
$829$	−431.953	+	1423.96i	−0.0180969	+	0.0596575i	0.947427	+	0.319972i	$0.103674\pi$
$830$	55737.8	+	32093.6i	2.33095	+	1.34215i
$831$		−	3304.74i		−	0.137954i
$832$	17776.4	−	1876.56i	0.740730	−	0.0781949i
$833$		−	35078.7i		−	1.45907i
$834$	−13770.1	+	23915.0i	−0.571728	+	0.992935i
$835$	−2425.27	+	7995.03i	−0.100515	+	0.331353i
$836$	−774.485	−	591.417i	−0.0320408	−	0.0244672i
$837$	261.966	−	2659.79i	0.0108183	−	0.109840i
$838$	−9087.53	−	9680.00i	−0.374611	−	0.399034i
$839$	3924.10	−	2622.00i	0.161472	−	0.107892i	−0.472209	−	0.881487i	$-0.656543\pi$
$839$	3924.10	−	2622.00i	0.161472	−	0.107892i	0.633681	+	0.773594i	$0.281543\pi$
$840$	−9507.80	−	6304.89i	−0.390536	−	0.258975i
$841$	−13233.5	+	19805.3i	−0.542599	+	0.812057i
$842$	8450.70	−	11822.0i	0.345879	−	0.483865i
$843$	15196.3	+	8122.60i	0.620864	+	0.331859i
$844$	−12084.5	−	1966.20i	−0.492848	−	0.0801887i
$845$	19697.9	−	1940.07i	0.801927	−	0.0789829i
$846$	792.164	+	11873.8i	0.0321929	+	0.482541i
$847$	3989.14	−	9630.63i	0.161828	−	0.390688i
$848$	10016.3	−	6293.53i	0.405613	−	0.254859i
$849$	−9263.00	−	22362.9i	−0.374447	−	0.903994i
$850$	−90521.3	+	44771.5i	−3.65277	+	1.80665i
$851$	−36859.8	−	30250.0i	−1.48477	−	1.21852i
$852$	16516.8	−	17717.5i	0.664151	−	0.712431i
$853$	19188.4	−	5820.75i	0.770223	−	0.233644i	0.119371	−	0.992850i	$-0.461912\pi$
$853$	19188.4	−	5820.75i	0.770223	−	0.233644i	0.650851	+	0.759205i	$0.274412\pi$
$854$	−1547.13	+	964.571i	−0.0619925	+	0.0386498i
$855$	−8728.93	+	1736.29i	−0.349150	+	0.0694502i
$856$	−10221.6	−	5417.63i	−0.408138	−	0.216321i
$857$	−8894.07	+	44713.5i	−0.354511	+	1.78225i	0.232427	+	0.972614i	$0.425333\pi$
$857$	−8894.07	+	44713.5i	−0.354511	+	1.78225i	−0.586938	+	0.809632i	$0.699667\pi$
$858$	1342.27	+	606.287i	0.0534082	+	0.0241239i
$859$	25537.0	−	20957.6i	1.01433	−	0.832440i	0.0284004	−	0.999597i	$-0.490959\pi$
$859$	25537.0	−	20957.6i	1.01433	−	0.832440i	0.985930	+	0.167157i	$0.0534586\pi$
$860$	50110.3	−	44152.9i	1.98692	−	1.75070i
$861$	−1982.88	−	3709.71i	−0.0784860	−	0.146837i
$862$	4162.40	+	5411.46i	0.164468	+	0.213822i
$863$	2790.75	−	2790.75i	0.110079	−	0.110079i	−0.649922	−	0.760001i	$-0.725198\pi$
$863$	2790.75	−	2790.75i	0.110079	−	0.110079i	0.760001	+	0.649922i	$0.225198\pi$
$864$	−22739.3	+	10463.4i	−0.895378	+	0.412003i
$865$	27728.1	+	27728.1i	1.08992	+	1.08992i
$866$	−4702.29	+	36042.4i	−0.184516	+	1.41428i
$867$	−29885.7	+	15974.3i	−1.17067	+	0.625737i
$868$	398.750	+	1165.74i	0.0155927	+	0.0455848i
$869$	2010.19	+	2449.42i	0.0784706	+	0.0956167i
$870$	−3995.17	+	1509.00i	−0.155688	+	0.0588044i
$871$	−15729.8	−	3128.85i	−0.611921	−	0.121719i
$872$	−1770.55	−	17353.8i	−0.0687598	−	0.673939i
$873$	836.266	+	4204.20i	0.0324208	+	0.162990i
$874$	11463.6	+	2658.85i	0.443665	+	0.102903i
$875$	−7465.46	−	24610.3i	−0.288433	−	0.950835i
$876$	3881.51	−	10386.4i	0.149708	−	0.400597i
$877$	7560.14	−	9212.06i	0.291092	−	0.354697i	−0.606845	−	0.794820i	$-0.707565\pi$
$877$	7560.14	−	9212.06i	0.291092	−	0.354697i	0.897937	+	0.440123i	$0.145065\pi$
$878$	−601.436	+	1778.59i	−0.0231179	+	0.0683649i
$879$	−20368.9	+	8437.08i	−0.781600	+	0.323749i
$880$	−2758.14	−	5527.78i	−0.105656	−	0.211752i
$881$	29508.5	+	12222.8i	1.12845	+	0.467420i	0.867254	−	0.497866i	$-0.165883\pi$
$881$	29508.5	+	12222.8i	1.12845	+	0.467420i	0.261197	+	0.965285i	$0.415883\pi$
$882$	8965.57	−	10247.4i	0.342275	−	0.391209i
$883$	3336.09	+	33871.9i	0.127144	+	1.29092i	0.821052	+	0.570853i	$0.193387\pi$
$883$	3336.09	+	33871.9i	0.127144	+	1.29092i	−0.693908	+	0.720064i	$0.744113\pi$
$884$	29809.6	+	18440.5i	1.13417	+	0.701607i
$885$	−23024.9	+	43076.5i	−0.874546	+	1.63616i
$886$	−4396.77	−	26438.9i	−0.166718	−	1.00252i
$887$	−42523.7	−	28413.4i	−1.60970	−	1.07557i	−0.944301	−	0.329084i	$-0.893260\pi$
$887$	−42523.7	−	28413.4i	−1.60970	−	1.07557i	−0.665402	−	0.746485i	$-0.731740\pi$
$888$	7857.25	−	19158.5i	0.296928	−	0.724005i
$889$	−2420.53	−	3622.58i	−0.0913184	−	0.136668i
$890$	1408.92	−	44630.4i	0.0530643	−	1.68092i
$891$	154.895	+	15.2558i	0.00582398	+	0.000573612i
$892$	−5483.31	+	20656.7i	−0.205824	+	0.775377i
$893$	5969.75	+	1810.90i	0.223707	+	0.0678607i
$894$	−1292.05	−	4799.60i	−0.0483363	−	0.179555i
$895$	42560.7			1.58955
$896$	7537.03	−	8737.26i	0.281020	−	0.325771i
$897$	−17786.3			−0.662060
$898$	10661.8	+	39605.6i	0.396203	+	1.47178i
$899$	441.351	+	133.882i	0.0163736	+	0.00496688i
$900$	−37886.4	−	10056.9i	−1.40320	−	0.372479i
$901$	23085.0	+	2273.68i	0.853578	+	0.0840701i
$902$	71.8710	−	2276.65i	0.00265304	−	0.0840402i
$903$	5710.53	+	8546.41i	0.210448	+	0.314958i
$904$	9128.84	−	3818.78i	0.335863	−	0.140498i
$905$	−29630.0	−	19798.2i	−1.08833	−	0.727197i
$906$	935.470	+	5625.22i	0.0343034	+	0.206275i
$907$	20349.2	−	38070.7i	0.744967	−	1.39374i	−0.168035	−	0.985781i	$-0.553742\pi$
$907$	20349.2	−	38070.7i	0.744967	−	1.39374i	0.913002	−	0.407955i	$-0.133758\pi$
$908$	17977.2	−	29060.6i	0.657040	−	1.06213i
$909$	962.744	+	9774.90i	0.0351289	+	0.356670i
$910$	−10484.2	+	11983.2i	−0.381922	+	0.436525i
$911$	18966.0	+	7855.97i	0.689760	+	0.285708i	0.699900	−	0.714241i	$-0.253228\pi$
$911$	18966.0	+	7855.97i	0.689760	+	0.285708i	−0.0101400	+	0.999949i	$0.503228\pi$
$912$	358.029	+	5097.81i	0.0129995	+	0.185094i
$913$	−4952.11	+	2051.23i	−0.179508	+	0.0743546i
$914$	3021.18	−	8934.35i	0.109335	−	0.323328i
$915$	3247.37	−	3956.93i	0.117328	−	0.142964i
$916$	−45670.7	−	17067.7i	−1.64738	−	0.615646i
$917$	3559.53	+	11734.2i	0.128185	+	0.422570i
$918$	−47815.4	−	11090.2i	−1.71911	−	0.398726i
$919$	4027.45	+	20247.4i	0.144563	+	0.726768i	0.983266	+	0.182178i	$0.0583146\pi$
$919$	4027.45	+	20247.4i	0.144563	+	0.726768i	−0.838703	+	0.544590i	$0.816685\pi$
$920$	57834.0	+	47125.4i	2.07253	+	1.68878i
$921$	−14266.5	−	2837.78i	−0.510420	−	0.101529i
$922$	1690.63	−	638.561i	0.0603882	−	0.0228090i
$923$	−21446.3	−	26132.4i	−0.764803	−	0.931915i
$924$	899.586	−	307.711i	0.0320283	−	0.0109556i
$925$	73431.6	−	39250.0i	2.61018	−	1.39517i
$926$	−5361.13	+	41092.3i	−0.190257	+	1.45829i
$927$	−17793.1	−	17793.1i	−0.630423	−	0.630423i
$928$	−1005.39	−	4200.90i	−0.0355640	−	0.148600i
$929$	−16669.5	+	16669.5i	−0.588707	+	0.588707i	−0.937281	−	0.348574i	$-0.886666\pi$
$929$	−16669.5	+	16669.5i	−0.588707	+	0.588707i	0.348574	+	0.937281i	$0.386666\pi$
$930$	−2109.00	−	2741.87i	−0.0743622	−	0.0966769i
$931$	−3364.70	−	6294.92i	−0.118446	−	0.221598i
$932$	15684.8	+	17801.1i	0.551258	+	0.625638i
$933$	22702.9	−	18631.8i	0.796636	−	0.653782i
$934$	12528.0	+	5658.74i	0.438895	+	0.198244i
$935$	2363.34	−	11881.3i	0.0826625	−	0.415573i
$936$	3995.03	+	13005.8i	0.139510	+	0.454174i
$937$	−20877.2	+	4152.73i	−0.727884	+	0.144785i	−0.545104	−	0.838369i	$-0.683510\pi$
$937$	−20877.2	+	4152.73i	−0.727884	+	0.144785i	−0.182781	+	0.983154i	$0.558510\pi$
$938$	−8785.33	+	5477.29i	−0.305811	+	0.190661i
$939$	6850.51	−	2078.08i	0.238081	−	0.0722211i
$940$	28927.8	+	26967.4i	1.00374	+	0.935722i
$941$	17705.5	+	14530.5i	0.613372	+	0.503382i	0.889015	−	0.457879i	$-0.151391\pi$
$941$	17705.5	+	14530.5i	0.613372	+	0.503382i	−0.275642	+	0.961260i	$0.588891\pi$
$942$	−12140.2	+	6004.51i	−0.419904	+	0.207683i
$943$	10526.5	+	25413.2i	0.363509	+	0.877589i
$944$	−40290.9	−	28588.4i	−1.38915	−	0.985672i
$945$	8532.40	−	20599.0i	0.293713	−	0.709086i
$946$	370.511	+	5553.62i	0.0127340	+	0.190871i
$947$	−14578.0	+	1435.81i	−0.500233	+	0.0492687i	−0.344988	−	0.938607i	$-0.612117\pi$
$947$	−14578.0	+	1435.81i	−0.500233	+	0.0492687i	−0.155246	+	0.987876i	$0.549617\pi$
$948$	2668.62	−	16401.6i	0.0914268	−	0.561919i
$949$	−13647.8	−	7294.88i	−0.466834	−	0.249528i
$950$	−11949.7	+	16717.0i	−0.408105	+	0.570916i
$951$	−12474.7	+	18669.7i	−0.425361	+	0.636598i
$952$	22176.8	−	4491.99i	0.754994	−	0.152927i
$953$	−8128.71	+	5431.43i	−0.276301	+	0.184618i	−0.685998	−	0.727603i	$-0.740634\pi$
$953$	−8128.71	+	5431.43i	−0.276301	+	0.184618i	0.409697	+	0.912221i	$0.365634\pi$
$954$	6162.60	+	6564.37i	0.209142	+	0.222777i
$955$	−714.959	+	7259.10i	−0.0242257	+	0.245967i
$956$	10868.8	−	14233.1i	0.367700	−	0.481518i
$957$	103.316	−	340.586i	0.00348978	−	0.0115043i
$958$	−4059.05	+	7049.47i	−0.136892	+	0.237743i
$959$			22379.7i			0.753574i
$960$	−12188.0	+	30017.1i	−0.409757	+	1.00917i
$961$		−	29417.4i		−	0.987460i
$962$	−25045.1	−	14420.8i	−0.839382	−	0.483313i
$963$	2556.04	−	8426.13i	0.0855318	−	0.281961i
$964$	−30584.2	+	4099.11i	−1.02184	+	0.136954i
$965$	−42.1108	+	427.558i	−0.00140476	+	0.0142628i
$966$	−8370.79	+	7858.46i	−0.278805	+	0.261741i
$967$	−34219.6	+	22864.8i	−1.13798	+	0.760376i	−0.974103	−	0.226104i	$-0.927401\pi$
$967$	−34219.6	+	22864.8i	−1.13798	+	0.760376i	−0.163880	+	0.986480i	$0.552401\pi$
$968$	−29053.5	−	5673.46i	−0.964684	−	0.188380i
$969$	−5567.45	+	8332.28i	−0.184574	+	0.276235i
$970$	11589.2	+	8284.23i	0.383614	+	0.274217i
$971$	−18119.8	−	9685.21i	−0.598857	−	0.320096i	0.143967	−	0.989583i	$-0.454014\pi$
$971$	−18119.8	−	9685.21i	−0.598857	−	0.320096i	−0.742824	+	0.669487i	$0.766514\pi$
$972$	−17931.2	−	24900.0i	−0.591710	−	0.821674i
$973$	24742.6	−	2436.93i	0.815221	−	0.0802923i
$974$	2409.79	−	160.770i	0.0792757	−	0.00528890i
$975$	11885.4	−	28693.8i	0.390396	−	0.942499i
$976$	3556.86	+	3762.27i	0.116652	+	0.123389i
$977$	15839.7	+	38240.4i	0.518686	+	1.25222i	0.938711	+	0.344706i	$0.112021\pi$
$977$	15839.7	+	38240.4i	0.518686	+	1.25222i	−0.420025	+	0.907513i	$0.637979\pi$
$978$	8169.71	+	16517.9i	0.267115	+	0.540066i
$979$	2876.61	+	2360.77i	0.0939089	+	0.0770690i
$980$	−1586.05	−	45221.8i	−0.0516986	−	1.47404i
$981$	12705.5	−	3854.18i	0.413513	−	0.125438i
$982$	7152.95	+	11473.0i	0.232444	+	0.372829i
$983$	6410.61	−	1275.15i	0.208003	−	0.0413743i	−0.0899891	−	0.995943i	$-0.528683\pi$
$983$	6410.61	−	1275.15i	0.208003	−	0.0413743i	0.297992	+	0.954568i	$0.403683\pi$
$984$	−9207.23	+	7610.26i	−0.298288	+	0.246551i
$985$	311.750	−	1567.28i	0.0100845	−	0.0506980i
$986$	3486.77	−	7719.42i	0.112618	−	0.249327i
$987$	−4704.96	+	3861.26i	−0.151733	+	0.124524i
$988$	7118.15	+	449.869i	0.229209	+	0.0144861i
$989$	−31685.2	−	59278.9i	−1.01874	−	1.90593i
$990$	3727.06	−	2866.79i	0.119650	−	0.0920330i
$991$	−16301.0	+	16301.0i	−0.522522	+	0.522522i	−0.918332	−	0.395810i	$-0.870464\pi$
$991$	−16301.0	+	16301.0i	−0.522522	+	0.522522i	0.395810	+	0.918332i	$0.370464\pi$
$992$	3019.75	−	1767.02i	0.0966503	−	0.0565554i
$993$	22755.9	+	22755.9i	0.727228	+	0.727228i
$994$	−21639.2	−	2823.18i	−0.690498	−	0.0900863i
$995$	5196.74	−	2777.71i	0.165576	−	0.0885020i
$996$	25239.8	+	12373.8i	0.802965	+	0.393652i
$997$	34825.1	+	42434.5i	1.10624	+	1.34796i	0.931666	+	0.363316i	$0.118355\pi$
$997$	34825.1	+	42434.5i	1.10624	+	1.34796i	0.174576	+	0.984644i	$0.444145\pi$
$998$	11623.6	+	30774.2i	0.368676	+	0.976093i
$999$	39692.0	+	7895.23i	1.25706	+	0.250044i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.k.a.5.3	✓	752
128.77	even	32	inner	128.4.k.a.77.3	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.4.k.a.5.3	✓	752	1.1	even	1	trivial
128.4.k.a.77.3	yes	752	128.77	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.k (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.73119 + 0.735238i) q^{2} +(-2.99224 - 0.907685i) q^{3} +(6.91885 - 4.01616i) q^{4} +(20.1386 + 1.98348i) q^{5} +(8.83975 + 0.279059i) q^{6} +(-4.42679 - 6.62516i) q^{7} +(-15.9439 + 16.0559i) q^{8} +(-14.3201 - 9.56838i) q^{9} +O(q^{10})\)	\(q+(-2.73119 + 0.735238i) q^{2} +(-2.99224 - 0.907685i) q^{3} +(6.91885 - 4.01616i) q^{4} +(20.1386 + 1.98348i) q^{5} +(8.83975 + 0.279059i) q^{6} +(-4.42679 - 6.62516i) q^{7} +(-15.9439 + 16.0559i) q^{8} +(-14.3201 - 9.56838i) q^{9} +(-56.4608 + 9.38941i) q^{10} +(2.24857 - 4.20677i) q^{11} +(-24.3482 + 5.73715i) q^{12} +(3.42203 + 34.7444i) q^{13} +(16.9615 + 14.8399i) q^{14} +(-58.4592 - 24.2146i) q^{15} +(31.7410 - 55.5744i) q^{16} +(115.947 - 48.0269i) q^{17} +(46.1460 + 15.6044i) q^{18} +(16.2002 - 19.7400i) q^{19} +(147.302 - 67.1564i) q^{20} +(7.23244 + 23.8422i) q^{21} +(-3.04829 + 13.1427i) q^{22} +(-31.7855 - 159.797i) q^{23} +(62.2816 - 33.5710i) q^{24} +(279.032 + 55.5029i) q^{25} +(-34.8916 - 92.3778i) q^{26} +(87.7232 + 106.891i) q^{27} +(-57.2359 - 28.0598i) q^{28} +(-21.0446 + 11.2486i) q^{29} +(177.467 + 23.1533i) q^{30} +(-13.6670 - 13.6670i) q^{31} +(-45.8304 + 175.122i) q^{32} +(-10.5467 + 10.5467i) q^{33} +(-281.363 + 216.420i) q^{34} +(-76.0086 - 142.202i) q^{35} +(-137.507 - 8.69047i) q^{36} +(226.234 - 185.666i) q^{37} +(-29.7323 + 65.8247i) q^{38} +(21.2975 - 107.070i) q^{39} +(-352.935 + 291.719i) q^{40} +(-165.586 + 32.9371i) q^{41} +(-37.2829 - 59.8000i) q^{42} +(394.786 - 119.757i) q^{43} +(-1.33756 - 38.1366i) q^{44} +(-269.408 - 221.098i) q^{45} +(204.301 + 413.066i) q^{46} +(93.4867 + 225.697i) q^{47} +(-145.421 + 137.481i) q^{48} +(106.964 - 258.234i) q^{49} +(-802.898 + 53.5656i) q^{50} +(-390.535 + 38.4643i) q^{51} +(163.215 + 226.648i) q^{52} +(163.009 + 87.1301i) q^{53} +(-318.179 - 227.443i) q^{54} +(53.6271 - 80.2586i) q^{55} +(176.953 + 34.5547i) q^{56} +(-66.3925 + 44.3620i) q^{57} +(49.2066 - 46.1949i) q^{58} +(75.6616 - 768.205i) q^{59} +(-501.720 + 67.2441i) q^{60} +(-23.4833 + 77.4142i) q^{61} +(47.3757 + 27.2787i) q^{62} +137.230i q^{63} +(-3.58414 - 511.987i) q^{64} +706.492i q^{65} +(21.0507 - 36.5593i) q^{66} +(-133.350 + 439.595i) q^{67} +(609.338 - 797.953i) q^{68} +(-49.9352 + 507.001i) q^{69} +(312.146 + 332.497i) q^{70} +(-805.116 + 537.961i) q^{71} +(381.947 - 77.3647i) q^{72} +(-246.257 + 368.550i) q^{73} +(-481.382 + 673.425i) q^{74} +(-784.550 - 419.351i) q^{75} +(32.8078 - 201.640i) q^{76} +(-37.8244 + 3.72538i) q^{77} +(20.5541 + 308.087i) q^{78} +(-254.214 + 613.726i) q^{79} +(749.451 - 1056.23i) q^{80} +(12.4869 + 30.1460i) q^{81} +(428.031 - 211.703i) q^{82} +(-868.642 - 712.876i) q^{83} +(145.794 + 135.914i) q^{84} +(2430.28 - 737.217i) q^{85} +(-990.187 + 617.341i) q^{86} +(73.1807 - 14.5566i) q^{87} +(31.6926 + 103.175i) q^{88} +(-152.199 + 765.157i) q^{89} +(898.366 + 405.782i) q^{90} +(215.039 - 176.478i) q^{91} +(-861.688 - 977.954i) q^{92} +(28.4895 + 53.3002i) q^{93} +(-421.271 - 547.687i) q^{94} +(365.403 - 365.403i) q^{95} +(296.091 - 482.406i) q^{96} +(-175.993 - 175.993i) q^{97} +(-102.276 + 783.932i) q^{98} +(-72.4516 + 38.7262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 5696 q^{50} - 16 q^{51} + 6608 q^{52} - 16 q^{53} + 3440 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 4768 q^{58} - 16 q^{59} - 9808 q^{60} - 16 q^{61} - 5872 q^{62} - 12112 q^{64} - 10960 q^{66} - 16 q^{67} - 4144 q^{68} - 16 q^{69} - 4048 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 5248 q^{74} - 16 q^{75} + 11888 q^{76} - 16 q^{77} + 14096 q^{78} - 16 q^{79} + 10016 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 5696 * q^50 - 16 * q^51 + 6608 * q^52 - 16 * q^53 + 3440 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 4768 * q^58 - 16 * q^59 - 9808 * q^60 - 16 * q^61 - 5872 * q^62 - 12112 * q^64 - 10960 * q^66 - 16 * q^67 - 4144 * q^68 - 16 * q^69 - 4048 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 5248 * q^74 - 16 * q^75 + 11888 * q^76 - 16 * q^77 + 14096 * q^78 - 16 * q^79 + 10016 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

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