LMFDB - Embedded newform 128.4.k.a.5.20

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			5.20
Character	$\chi$	$=$	128.5
Dual form			128.4.k.a.77.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.668572 + 2.74827i) q^{2} +(-6.55625 - 1.98882i) q^{3} +(-7.10602 - 3.67484i) q^{4} +(-14.4435 - 1.42256i) q^{5} +(9.84915 - 16.6887i) q^{6} +(0.534510 + 0.799951i) q^{7} +(14.8504 - 17.0724i) q^{8} +(16.5794 + 11.0780i) q^{9} +O(q^{10})$	\(q+(-0.668572 + 2.74827i) q^{2} +(-6.55625 - 1.98882i) q^{3} +(-7.10602 - 3.67484i) q^{4} +(-14.4435 - 1.42256i) q^{5} +(9.84915 - 16.6887i) q^{6} +(0.534510 + 0.799951i) q^{7} +(14.8504 - 17.0724i) q^{8} +(16.5794 + 11.0780i) q^{9} +(13.5661 - 38.7437i) q^{10} +(-10.7650 + 20.1399i) q^{11} +(39.2803 + 38.2258i) q^{12} +(1.57776 + 16.0193i) q^{13} +(-2.55584 + 0.934156i) q^{14} +(91.8662 + 38.0522i) q^{15} +(36.9911 + 52.2270i) q^{16} +(86.9935 - 36.0339i) q^{17} +(-41.5299 + 38.1583i) q^{18} +(-42.8521 + 52.2154i) q^{19} +(97.4083 + 63.1864i) q^{20} +(-1.91343 - 6.30773i) q^{21} +(-48.1527 - 43.0501i) q^{22} +(-18.9060 - 95.0467i) q^{23} +(-131.317 + 82.3964i) q^{24} +(83.9935 + 16.7073i) q^{25} +(-45.0801 - 6.37391i) q^{26} +(30.6861 + 37.3911i) q^{27} +(-0.858551 - 7.64871i) q^{28} +(97.5274 - 52.1295i) q^{29} +(-165.997 + 227.033i) q^{30} +(-15.4742 - 15.4742i) q^{31} +(-168.265 + 66.7442i) q^{32} +(110.632 - 110.632i) q^{33} +(40.8696 + 263.173i) q^{34} +(-6.58223 - 12.3145i) q^{35} +(-77.1037 - 139.647i) q^{36} +(118.320 - 97.1029i) q^{37} +(-114.853 - 152.679i) q^{38} +(21.5152 - 108.164i) q^{39} +(-238.778 + 225.460i) q^{40} +(349.350 - 69.4901i) q^{41} +(18.6146 - 1.04146i) q^{42} +(-396.816 + 120.373i) q^{43} +(150.507 - 103.555i) q^{44} +(-223.706 - 183.591i) q^{45} +(273.854 + 11.5868i) q^{46} +(119.581 + 288.694i) q^{47} +(-138.653 - 415.982i) q^{48} +(130.906 - 316.036i) q^{49} +(-102.072 + 219.667i) q^{50} +(-642.016 + 63.2331i) q^{51} +(47.6566 - 119.631i) q^{52} +(274.329 + 146.632i) q^{53} +(-123.277 + 59.3352i) q^{54} +(184.134 - 275.577i) q^{55} +(21.5948 + 2.75418i) q^{56} +(384.796 - 257.112i) q^{57} +(78.0620 + 302.884i) q^{58} +(48.2557 - 489.948i) q^{59} +(-512.967 - 607.993i) q^{60} +(79.5550 - 262.258i) q^{61} +(52.8729 - 32.1817i) q^{62} +19.1840i q^{63} +(-70.9340 - 507.062i) q^{64} -233.619i q^{65} +(230.083 + 378.014i) q^{66} +(-13.3068 + 43.8665i) q^{67} +(-750.596 - 63.6294i) q^{68} +(-65.0783 + 660.751i) q^{69} +(38.2443 - 9.85666i) q^{70} +(663.138 - 443.095i) q^{71} +(435.338 - 118.538i) q^{72} +(-604.413 + 904.568i) q^{73} +(187.760 + 390.097i) q^{74} +(-517.455 - 276.585i) q^{75} +(496.391 - 213.569i) q^{76} +(-21.8649 + 2.15351i) q^{77} +(282.880 + 131.445i) q^{78} +(-386.533 + 933.172i) q^{79} +(-459.986 - 806.964i) q^{80} +(-332.850 - 803.570i) q^{81} +(-42.5880 + 1006.57i) q^{82} +(758.509 + 622.493i) q^{83} +(-9.58302 + 51.8544i) q^{84} +(-1307.75 + 396.702i) q^{85} +(-65.5174 - 1171.04i) q^{86} +(-743.090 + 147.810i) q^{87} +(183.972 + 482.868i) q^{88} +(-123.388 + 620.316i) q^{89} +(654.121 - 492.061i) q^{90} +(-11.9713 + 9.82459i) q^{91} +(-214.935 + 744.880i) q^{92} +(70.6773 + 132.228i) q^{93} +(-873.360 + 135.629i) q^{94} +(693.214 - 693.214i) q^{95} +(1235.93 - 102.943i) q^{96} +(1226.56 + 1226.56i) q^{97} +(781.032 + 571.059i) q^{98} +(-401.586 + 214.652i) 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 $

$2$	−0.668572	+	2.74827i	−0.236376	+	0.971662i
$2$	−0.668572	+	2.74827i	−0.236376	+	0.971662i
$3$	−6.55625	−	1.98882i	−1.26175	−	0.382748i	−0.412607	−	0.910909i	$-0.635382\pi$
$3$	−6.55625	−	1.98882i	−1.26175	−	0.382748i	−0.849144	+	0.528161i	$0.822882\pi$
$4$	−7.10602	−	3.67484i	−0.888253	−	0.459355i
$5$	−14.4435	−	1.42256i	−1.29187	−	0.127238i	−0.571369	−	0.820694i	$-0.693587\pi$
$5$	−14.4435	−	1.42256i	−1.29187	−	0.127238i	−0.720499	+	0.693456i	$0.756087\pi$
$6$	9.84915	−	16.6887i	0.670150	−	1.13552i
$7$	0.534510	+	0.799951i	0.0288609	+	0.0431933i	0.845620	−	0.533786i	$-0.179231\pi$
$7$	0.534510	+	0.799951i	0.0288609	+	0.0431933i	−0.816759	+	0.576979i	$0.804231\pi$
$8$	14.8504	−	17.0724i	0.656299	−	0.754501i
$9$	16.5794	+	11.0780i	0.614052	+	0.410296i
$10$	13.5661	−	38.7437i	0.428999	−	1.22518i
$11$	−10.7650	+	20.1399i	−0.295069	+	0.552036i	−0.985150	−	0.171697i	$-0.945075\pi$
$11$	−10.7650	+	20.1399i	−0.295069	+	0.552036i	0.690080	+	0.723733i	$0.257575\pi$
$12$	39.2803	+	38.2258i	0.944937	+	0.919569i
$13$	1.57776	+	16.0193i	0.0336609	+	0.341765i	0.997234	+	0.0743210i	$0.0236789\pi$
$13$	1.57776	+	16.0193i	0.0336609	+	0.341765i	−0.963573	+	0.267444i	$0.913821\pi$
$14$	−2.55584	+	0.934156i	−0.0487913	+	0.0178331i
$15$	91.8662	+	38.0522i	1.58132	+	0.655003i
$16$	36.9911	+	52.2270i	0.577986	+	0.816047i
$17$	86.9935	−	36.0339i	1.24112	−	0.514088i	0.337054	−	0.941485i	$-0.390569\pi$
$17$	86.9935	−	36.0339i	1.24112	−	0.514088i	0.904064	+	0.427397i	$0.140569\pi$
$18$	−41.5299	+	38.1583i	−0.543816	+	0.499666i
$19$	−42.8521	+	52.2154i	−0.517418	+	0.630475i	−0.964521	−	0.264007i	$-0.914956\pi$
$19$	−42.8521	+	52.2154i	−0.517418	+	0.630475i	0.447103	+	0.894483i	$0.352456\pi$
$20$	97.4083	+	63.1864i	1.08906	+	0.706445i
$21$	−1.91343	−	6.30773i	−0.0198831	−	0.0655457i
$22$	−48.1527	−	43.0501i	−0.466645	−	0.417196i
$23$	−18.9060	−	95.0467i	−0.171399	−	0.861679i	−0.966788	−	0.255580i	$-0.917734\pi$
$23$	−18.9060	−	95.0467i	−0.171399	−	0.861679i	0.795389	−	0.606099i	$-0.207266\pi$
$24$	−131.317	+	82.3964i	−1.11687	+	0.700795i
$25$	83.9935	+	16.7073i	0.671948	+	0.133659i
$26$	−45.0801	−	6.37391i	−0.340036	−	0.0480780i
$27$	30.6861	+	37.3911i	0.218724	+	0.266516i
$28$	−0.858551	−	7.64871i	−0.00579467	−	0.0516240i
$29$	97.5274	−	52.1295i	0.624496	−	0.333800i	−0.128614	−	0.991695i	$-0.541053\pi$
$29$	97.5274	−	52.1295i	0.624496	−	0.333800i	0.753110	+	0.657895i	$0.228553\pi$
$30$	−165.997	+	227.033i	−1.01023	+	1.38168i
$31$	−15.4742	−	15.4742i	−0.0896530	−	0.0896530i	0.660858	−	0.750511i	$-0.270193\pi$
$31$	−15.4742	−	15.4742i	−0.0896530	−	0.0896530i	−0.750511	+	0.660858i	$0.770193\pi$
$32$	−168.265	+	66.7442i	−0.929543	+	0.368713i
$33$	110.632	−	110.632i	0.583595	−	0.583595i
$34$	40.8696	+	263.173i	0.206149	+	1.32747i
$35$	−6.58223	−	12.3145i	−0.0317886	−	0.0594723i
$36$	−77.1037	−	139.647i	−0.356962	−	0.646515i
$37$	118.320	−	97.1029i	0.525722	−	0.431449i	−0.333727	−	0.942670i	$-0.608306\pi$
$37$	118.320	−	97.1029i	0.525722	−	0.431449i	0.859450	+	0.511221i	$0.170806\pi$
$38$	−114.853	−	152.679i	−0.490304	−	0.651784i
$39$	21.5152	−	108.164i	0.0883382	−	0.444106i
$40$	−238.778	+	225.460i	−0.943853	+	0.891209i
$41$	349.350	−	69.4901i	1.33072	−	0.264696i	0.522025	−	0.852930i	$-0.325177\pi$
$41$	349.350	−	69.4901i	1.33072	−	0.264696i	0.808690	+	0.588235i	$0.200177\pi$
$42$	18.6146	−	1.04146i	0.0683881	−	0.00382619i
$43$	−396.816	+	120.373i	−1.40730	+	0.426900i	−0.900384	−	0.435096i	$-0.856714\pi$
$43$	−396.816	+	120.373i	−1.40730	+	0.426900i	−0.506915	+	0.861996i	$0.669214\pi$
$44$	150.507	−	103.555i	0.515677	−	0.354806i
$45$	−223.706	−	183.591i	−0.741069	−	0.608179i
$46$	273.854	+	11.5868i	0.877775	+	0.0371387i
$47$	119.581	+	288.694i	0.371121	+	0.895966i	0.993561	+	0.113298i	$0.0361416\pi$
$47$	119.581	+	288.694i	0.371121	+	0.895966i	−0.622440	+	0.782668i	$0.713858\pi$
$48$	−138.653	−	415.982i	−0.416935	−	1.25087i
$49$	130.906	−	316.036i	0.381651	−	0.921386i
$50$	−102.072	+	219.667i	−0.288703	+	0.621312i
$51$	−642.016	+	63.2331i	−1.76275	+	0.173616i
$52$	47.6566	−	119.631i	0.127092	−	0.319036i
$53$	274.329	+	146.632i	0.710981	+	0.380027i	0.786895	−	0.617087i	$-0.211687\pi$
$53$	274.329	+	146.632i	0.710981	+	0.380027i	−0.0759139	+	0.997114i	$0.524187\pi$
$54$	−123.277	+	59.3352i	−0.310664	+	0.149528i
$55$	184.134	−	275.577i	0.451431	−	0.675614i
$56$	21.5948	+	2.75418i	0.0515307	+	0.00657220i
$57$	384.796	−	257.112i	0.894166	−	0.597463i
$58$	78.0620	+	302.884i	0.176725	+	0.685701i
$59$	48.2557	−	489.948i	0.106481	−	1.08112i	−0.782337	−	0.622855i	$-0.785973\pi$
$59$	48.2557	−	489.948i	0.106481	−	1.08112i	0.888818	−	0.458261i	$-0.151527\pi$
$60$	−512.967	−	607.993i	−1.10373	−	1.30819i
$61$	79.5550	−	262.258i	0.166983	−	0.550470i	−0.833013	−	0.553254i	$-0.813386\pi$
$61$	79.5550	−	262.258i	0.166983	−	0.550470i	0.999996	+	0.00278371i	$0.000886082\pi$
$62$	52.8729	−	32.1817i	0.108304	−	0.0659206i
$63$			19.1840i			0.0383644i
$64$	−70.9340	−	507.062i	−0.138543	−	0.990356i
$65$		−	233.619i		−	0.445798i
$66$	230.083	+	378.014i	0.429109	+	0.705005i
$67$	−13.3068	+	43.8665i	−0.0242639	+	0.0799873i	−0.968236	−	0.250037i	$-0.919557\pi$
$67$	−13.3068	+	43.8665i	−0.0242639	+	0.0799873i	0.943972	+	0.330025i	$0.107057\pi$
$68$	−750.596	−	63.6294i	−1.33858	−	0.113474i
$69$	−65.0783	+	660.751i	−0.113544	+	1.15283i
$70$	38.2443	−	9.85666i	0.0653010	−	0.0168299i
$71$	663.138	−	443.095i	1.10845	−	0.740643i	0.140076	−	0.990141i	$-0.455265\pi$
$71$	663.138	−	443.095i	1.10845	−	0.740643i	0.968375	+	0.249497i	$0.0802654\pi$
$72$	435.338	−	118.538i	0.712571	−	0.194026i
$73$	−604.413	+	904.568i	−0.969057	+	1.45030i	−0.0777097	+	0.996976i	$0.524761\pi$
$73$	−604.413	+	904.568i	−0.969057	+	1.45030i	−0.891348	+	0.453321i	$0.850239\pi$
$74$	187.760	+	390.097i	0.294955	+	0.612808i
$75$	−517.455	−	276.585i	−0.796674	−	0.425831i
$76$	496.391	−	213.569i	0.749210	−	0.322343i
$77$	−21.8649	+	2.15351i	−0.0323602	+	0.00318720i
$78$	282.880	+	131.445i	0.410640	+	0.190811i
$79$	−386.533	+	933.172i	−0.550485	+	1.32899i	0.366631	+	0.930367i	$0.380511\pi$
$79$	−386.533	+	933.172i	−0.550485	+	1.32899i	−0.917115	+	0.398622i	$0.869489\pi$
$80$	−459.986	−	806.964i	−0.642850	−	1.12777i
$81$	−332.850	−	803.570i	−0.456584	−	1.10229i
$82$	−42.5880	+	1006.57i	−0.0573544	+	1.35557i
$83$	758.509	+	622.493i	1.00310	+	0.823222i	0.984283	−	0.176601i	$-0.0565101\pi$
$83$	758.509	+	622.493i	1.00310	+	0.823222i	0.0188166	+	0.999823i	$0.494010\pi$
$84$	−9.58302	+	51.8544i	−0.0124475	+	0.0673545i
$85$	−1307.75	+	396.702i	−1.66877	+	0.506217i
$86$	−65.5174	−	1171.04i	−0.0821503	−	1.46833i
$87$	−743.090	+	147.810i	−0.915720	+	0.182148i
$88$	183.972	+	482.868i	0.222858	+	0.584931i
$89$	−123.388	+	620.316i	−0.146957	+	0.738801i	0.835083	+	0.550125i	$0.185420\pi$
$89$	−123.388	+	620.316i	−0.146957	+	0.738801i	−0.982039	+	0.188677i	$0.939580\pi$
$90$	654.121	−	492.061i	0.766115	−	0.576309i
$91$	−11.9713	+	9.82459i	−0.0137905	+	0.0113175i
$92$	−214.935	+	744.880i	−0.243571	+	0.844121i
$93$	70.6773	+	132.228i	0.0788053	+	0.147434i
$94$	−873.360	+	135.629i	−0.958300	+	0.148820i
$95$	693.214	−	693.214i	0.748656	−	0.748656i
$96$	1235.93	−	102.943i	1.31398	−	0.109444i
$97$	1226.56	+	1226.56i	1.28390	+	1.28390i	0.938432	+	0.345464i	$0.112279\pi$
$97$	1226.56	+	1226.56i	1.28390	+	1.28390i	0.345464	+	0.938432i	$0.387721\pi$
$98$	781.032	+	571.059i	0.805063	+	0.588629i
$99$	−401.586	+	214.652i	−0.407686	+	0.217913i
$100$	−535.463	−	427.385i	−0.535463	−	0.427385i
$101$	−239.271	−	291.553i	−0.235726	−	0.287234i	0.641689	−	0.766965i	$-0.278234\pi$
$101$	−239.271	−	291.553i	−0.235726	−	0.287234i	−0.877415	+	0.479732i	$0.840734\pi$
$102$	255.452	−	1806.71i	0.247976	−	1.75383i
$103$	−1315.09	−	261.588i	−1.25806	−	0.250243i	−0.479346	−	0.877626i	$-0.659126\pi$
$103$	−1315.09	−	261.588i	−1.25806	−	0.250243i	−0.778711	+	0.627383i	$0.784126\pi$
$104$	296.917	+	210.955i	0.279953	+	0.198903i
$105$	18.6635	+	93.8278i	0.0173464	+	0.0872063i
$106$	−586.393	+	655.897i	−0.537317	+	0.601004i
$107$	56.7851	+	187.195i	0.0513049	+	0.169130i	0.978849	−	0.204584i	$-0.0655842\pi$
$107$	56.7851	+	187.195i	0.0513049	+	0.169130i	−0.927544	+	0.373714i	$0.878084\pi$
$108$	−80.6498	−	378.469i	−0.0718568	−	0.337205i
$109$	1075.36	−	1310.33i	0.944961	−	1.15144i	−0.0433614	−	0.999059i	$-0.513807\pi$
$109$	1075.36	−	1310.33i	0.944961	−	1.15144i	0.988322	−	0.152379i	$-0.0486933\pi$
$110$	634.253	+	690.295i	0.549761	+	0.598337i
$111$	−968.858	+	401.314i	−0.828467	+	0.343162i
$112$	−22.0069	+	57.5070i	−0.0185666	+	0.0485169i
$113$	−537.107	−	222.477i	−0.447140	−	0.185211i	0.147740	−	0.989026i	$-0.452800\pi$
$113$	−537.107	−	222.477i	−0.447140	−	0.185211i	−0.594879	+	0.803815i	$0.702800\pi$
$114$	449.352	+	1229.42i	0.369172	+	1.01005i
$115$	137.859	+	1399.70i	0.111786	+	1.13498i
$116$	−884.599	+	12.0358i	−0.708043	+	0.00963358i
$117$	−151.303	+	283.068i	−0.119555	+	0.223672i
$118$	1314.25	+	460.186i	1.02531	+	0.359013i
$119$	75.3243	+	50.3301i	0.0580249	+	0.0387710i
$120$	2013.89	−	1003.29i	1.53202	−	0.763227i
$121$	449.735	+	673.076i	0.337892	+	0.505692i
$122$	667.568	+	393.977i	0.495400	+	0.292369i
$123$	−2428.63	−	239.199i	−1.78034	−	0.175349i
$124$	53.0947	+	166.825i	0.0384520	+	0.120817i
$125$	546.664	+	165.829i	0.391161	+	0.118657i
$126$	−52.7230	−	12.8259i	−0.0372773	−	0.00906843i
$127$	2608.58			1.82263			0.911314	−	0.411711i	$-0.135069\pi$
$127$	2608.58			1.82263			0.911314	+	0.411711i	$0.135069\pi$
$128$	1440.97	+	144.062i	0.995040	+	0.0994795i
$129$	2841.03			1.93906
$130$	642.049	+	156.191i	0.433165	+	0.105376i
$131$	2055.33	+	623.476i	1.37080	+	0.415827i	0.887976	−	0.459890i	$-0.152111\pi$
$131$	2055.33	+	623.476i	1.37080	+	0.415827i	0.482823	+	0.875718i	$0.339611\pi$
$132$	−1192.71	+	379.600i	−0.786457	+	0.250303i
$133$	−64.6747	−	6.36990i	−0.0421654	−	0.00415293i
$134$	−111.661	−	65.8985i	−0.0719852	−	0.0424833i
$135$	−390.024	−	583.713i	−0.248651	−	0.372133i
$136$	676.699	−	2020.30i	0.426665	−	1.27382i
$137$	−831.547	−	555.622i	−0.518568	−	0.346496i	0.268583	−	0.963257i	$-0.413445\pi$
$137$	−831.547	−	555.622i	−0.518568	−	0.346496i	−0.787151	+	0.616760i	$0.788445\pi$
$138$	−1772.42	−	620.613i	−1.09332	−	0.382826i
$139$	−755.277	+	1413.02i	−0.460876	+	0.862238i	0.538926	+	0.842353i	$0.318830\pi$
$139$	−755.277	+	1413.02i	−0.460876	+	0.862238i	−0.999802	+	0.0198852i	$0.993670\pi$
$140$	1.51972	+	111.696i	0.000917429	+	0.0674286i
$141$	−209.844	−	2130.58i	−0.125334	−	1.27253i
$142$	774.390	+	2118.73i	0.457644	+	1.25211i
$143$	−339.610	−	140.671i	−0.198599	−	0.0822623i
$144$	34.7200	+	1275.68i	0.0200926	+	0.738241i
$145$	−1482.80	+	614.194i	−0.849238	+	0.351766i
$146$	−2081.91	−	2265.86i	−1.18014	−	1.28441i
$147$	−1486.79	+	1811.66i	−0.834207	+	1.01648i
$148$	−1197.62	+	255.208i	−0.665163	+	0.141743i
$149$	−677.566	−	2233.63i	−0.372539	−	1.22810i	−0.920217	−	0.391408i	$-0.871988\pi$
$149$	−677.566	−	2233.63i	−0.372539	−	1.22810i	0.547678	−	0.836689i	$-0.315512\pi$
$150$	1106.09	−	1237.19i	0.602078	−	0.673441i
$151$	−408.406	−	2053.20i	−0.220103	−	1.10653i	−0.919888	−	0.392181i	$-0.871721\pi$
$151$	−408.406	−	2053.20i	−0.220103	−	1.10653i	0.699785	−	0.714354i	$-0.253279\pi$
$152$	255.074	+	1507.00i	0.136113	+	0.804173i
$153$	1841.48	+	366.294i	0.973040	+	0.193550i
$154$	8.69984	−	61.5305i	0.00455229	−	0.0321966i
$155$	201.489	+	245.515i	0.104413	+	0.127227i
$156$	−550.373	+	689.552i	−0.282469	+	0.353900i
$157$	1814.91	−	970.089i	0.922583	−	0.493131i	0.0595196	−	0.998227i	$-0.481043\pi$
$157$	1814.91	−	970.089i	0.922583	−	0.493131i	0.863063	+	0.505097i	$0.168543\pi$
$158$	−2306.19	−	1686.19i	−1.16121	−	0.849026i
$159$	−1506.95	−	1506.95i	−0.751627	−	0.751627i
$160$	2525.29	−	724.654i	1.24776	−	0.358056i
$161$	65.9273	−	65.9273i	0.0322721	−	0.0322721i
$162$	2430.96	−	377.518i	1.17898	−	0.183090i
$163$	−897.365	−	1678.85i	−0.431209	−	0.806735i	0.568666	−	0.822569i	$-0.307460\pi$
$163$	−897.365	−	1678.85i	−0.431209	−	0.806735i	−0.999875	+	0.0158337i	$0.994960\pi$
$164$	−2737.85	−	790.007i	−1.30360	−	0.376154i
$165$	−1755.30	+	1440.54i	−0.828183	+	0.679673i
$166$	−2217.90	+	1668.41i	−1.03700	+	0.780083i
$167$	−262.402	+	1319.18i	−0.121588	+	0.611266i	0.871154	+	0.491009i	$0.163372\pi$
$167$	−262.402	+	1319.18i	−0.121588	+	0.611266i	−0.992743	+	0.120257i	$0.961628\pi$
$168$	−136.103	−	61.0052i	−0.0625035	−	0.0280158i
$169$	1900.66	−	378.064i	0.865115	−	0.172082i
$170$	−215.920	−	3859.29i	−0.0974136	−	1.74114i
$171$	−1288.90	+	390.985i	−0.576403	+	0.174850i
$172$	3262.13	+	602.863i	1.44614	+	0.267255i
$173$	−1803.04	−	1479.71i	−0.792384	−	0.650293i	0.148542	−	0.988906i	$-0.452542\pi$
$173$	−1803.04	−	1479.71i	−0.792384	−	0.650293i	−0.940926	+	0.338614i	$0.890042\pi$
$174$	90.5874	−	2141.04i	0.0394679	−	0.932825i
$175$	31.5303	+	76.1210i	0.0136198	+	0.0328812i
$176$	−1450.05	+	182.774i	−0.621033	+	0.0782789i
$177$	−1290.80	+	3116.26i	−0.548147	+	1.32335i
$178$	−1622.30	−	753.831i	−0.683128	−	0.317427i
$179$	2161.86	−	212.924i	0.902708	−	0.0889090i	0.363998	−	0.931400i	$-0.381412\pi$
$179$	2161.86	−	212.924i	0.902708	−	0.0889090i	0.538711	+	0.842491i	$0.318912\pi$
$180$	914.993	+	2126.68i	0.378886	+	0.880631i
$181$	−194.016	−	103.704i	−0.0796747	−	0.0425870i	0.431078	−	0.902315i	$-0.358133\pi$
$181$	−194.016	−	103.704i	−0.0796747	−	0.0425870i	−0.510753	+	0.859728i	$0.670633\pi$
$182$	−18.9970	−	39.4689i	−0.00773709	−	0.0160749i
$183$	−1043.17	+	1561.21i	−0.421383	+	0.630644i
$184$	−1903.44	−	1088.71i	−0.762626	−	0.436199i
$185$	−1847.10	+	1234.19i	−0.734060	+	0.490484i
$186$	−410.652	+	105.837i	−0.161884	+	0.0417222i
$187$	−210.766	+	2139.94i	−0.0824209	+	0.836834i
$188$	211.159	−	2490.91i	0.0819168	−	0.966321i
$189$	−13.5090	+	44.5334i	−0.00519915	+	0.0171393i
$190$	1441.68	+	2368.61i	0.550476	+	0.904404i
$191$		−	2745.22i		−	1.03998i	−0.854171	−	0.519992i	$-0.825935\pi$
$191$		−	2745.22i		−	1.03998i	0.854171	−	0.519992i	$-0.174065\pi$
$192$	−543.394	+	3465.51i	−0.204250	+	1.30261i
$193$			4218.76i			1.57343i	0.617314	+	0.786717i	$0.288221\pi$
$193$			4218.76i			1.57343i	−0.617314	+	0.786717i	$0.711779\pi$
$194$	−4190.95	+	2550.87i	−1.55099	+	0.944031i
$195$	−464.626	+	1531.67i	−0.170628	+	0.562486i
$196$	−2091.60	+	1764.70i	−0.762246	+	0.643111i
$197$	238.479	−	2421.32i	0.0862485	−	0.875696i	−0.850566	−	0.525869i	$-0.823740\pi$
$197$	238.479	−	2421.32i	0.0862485	−	0.875696i	0.936814	−	0.349827i	$-0.113760\pi$
$198$	−321.434	−	1247.18i	−0.115370	−	0.447643i
$199$	1213.19	−	810.625i	0.432163	−	0.288762i	−0.320400	−	0.947282i	$-0.603817\pi$
$199$	1213.19	−	810.625i	0.432163	−	0.288762i	0.752563	+	0.658520i	$0.228817\pi$
$200$	1532.57	−	1185.86i	0.541844	−	0.419265i
$201$	174.485	−	261.135i	0.0612300	−	0.0916371i
$202$	961.237	−	462.659i	0.334814	−	0.161151i
$203$	93.8304	+	50.1534i	0.0324414	+	0.0173403i
$204$	4794.55	+	1909.97i	1.64552	+	0.655513i
$205$	−5144.70	+	506.709i	−1.75279	+	0.172634i
$206$	1598.15	−	3439.34i	0.540526	−	1.16325i
$207$	739.478	−	1785.26i	0.248296	−	0.599440i
$208$	−778.274	+	674.972i	−0.259440	+	0.225004i
$209$	−590.309	−	1425.13i	−0.195371	−	0.471667i
$210$	−270.342	−	11.4382i	−0.0888352	−	0.00375862i
$211$	2004.15	+	1644.77i	0.653893	+	0.536636i	0.901803	−	0.432147i	$-0.142244\pi$
$211$	2004.15	+	1644.77i	0.653893	+	0.536636i	−0.247910	+	0.968783i	$0.579744\pi$
$212$	−1410.54	−	2050.08i	−0.456964	−	0.664153i
$213$	−5228.94	+	1586.18i	−1.68207	+	0.510250i
$214$	−552.429	+	30.9074i	−0.176464	+	0.00987284i
$215$	5902.66	−	1174.11i	1.87236	−	0.372436i
$216$	1094.06	+	31.3859i	0.344635	+	0.00988675i
$217$	4.10748	−	20.6497i	0.00128495	−	0.00645987i
$218$	2882.19	+	3831.43i	0.895442	+	1.19035i
$219$	5761.71	−	4728.51i	1.77781	−	1.45901i
$220$	−2321.16	+	1281.59i	−0.711331	+	0.392749i
$221$	714.490	+	1336.72i	0.217474	+	0.406866i
$222$	−455.170	−	2930.99i	−0.137608	−	0.886105i
$223$	3232.41	−	3232.41i	0.970666	−	0.970666i	−0.0289163	−	0.999582i	$-0.509206\pi$
$223$	3232.41	−	3232.41i	0.970666	−	0.970666i	0.999582	+	0.0289163i	$0.00920562\pi$
$224$	−143.332	−	98.9286i	−0.0427534	−	0.0295087i
$225$	1207.48	+	1207.48i	0.357771	+	0.357771i
$226$	970.523	−	1327.38i	0.285656	−	0.390689i
$227$	2158.63	−	1153.81i	0.631160	−	0.337362i	−0.124604	−	0.992207i	$-0.539766\pi$
$227$	2158.63	−	1153.81i	0.631160	−	0.337362i	0.755763	+	0.654845i	$0.227266\pi$
$228$	−3679.22	+	412.984i	−1.06869	+	0.119958i
$229$	−1468.53	−	1789.41i	−0.423769	−	0.516364i	0.516735	−	0.856145i	$-0.327147\pi$
$229$	−1468.53	−	1789.41i	−0.423769	−	0.516364i	−0.940505	+	0.339781i	$0.889647\pi$
$230$	−3938.94	−	556.929i	−1.12924	−	0.159664i
$231$	147.635	+	29.3664i	0.0420505	+	0.00836436i
$232$	558.341	−	2439.17i	0.158004	−	0.690255i
$233$	−301.110	−	1513.78i	−0.0846625	−	0.425627i	−0.999750	−	0.0223711i	$-0.992878\pi$
$233$	−301.110	−	1513.78i	−0.0846625	−	0.425627i	0.915087	−	0.403256i	$-0.132122\pi$
$234$	−676.792	−	605.074i	−0.189074	−	0.169038i
$235$	−1316.49	−	4339.88i	−0.365439	−	1.20469i
$236$	−2143.39	+	3304.25i	−0.591198	+	0.911392i
$237$	4390.12	−	5349.37i	1.20324	−	1.46616i
$238$	−188.681	+	173.362i	−0.0513880	+	0.0472160i
$239$	3258.55	−	1349.74i	0.881918	−	0.365302i	0.104678	−	0.994506i	$-0.466619\pi$
$239$	3258.55	−	1349.74i	0.881918	−	0.365302i	0.777240	+	0.629204i	$0.216619\pi$
$240$	1410.88	+	6205.49i	0.379466	+	1.66901i
$241$	4928.66	+	2041.52i	1.31736	+	0.545667i	0.927023	−	0.375006i	$-0.122359\pi$
$241$	4928.66	+	2041.52i	1.31736	+	0.545667i	0.390335	+	0.920673i	$0.372359\pi$
$242$	−2150.48	+	785.995i	−0.571231	+	0.208784i
$243$	456.081	+	4630.66i	0.120402	+	1.22246i
$244$	−1529.07	+	1571.26i	−0.401184	+	0.412252i
$245$	−2340.33	+	4378.44i	−0.610278	+	1.14175i
$246$	2281.10	−	6514.62i	0.591210	−	1.68844i
$247$	−904.062	−	604.075i	−0.232891	−	0.155613i
$248$	−493.978	+	34.3844i	−0.126482	+	0.00880408i
$249$	−3734.96	−	5589.76i	−0.950575	−	1.42264i
$250$	−821.226	+	1391.51i	−0.207756	+	0.352028i
$251$	−1734.83	−	170.866i	−0.436262	−	0.0429681i	−0.122497	−	0.992469i	$-0.539090\pi$
$251$	−1734.83	−	170.866i	−0.436262	−	0.0429681i	−0.313765	+	0.949501i	$0.601590\pi$
$252$	70.4982	−	136.322i	0.0176229	−	0.0340773i
$253$	2117.75	+	642.412i	0.526252	+	0.159637i
$254$	−1744.02	+	7169.09i	−0.430826	+	1.77098i
$255$	9362.93			2.29933
$256$	−1359.31	+	3863.87i	−0.331864	+	0.943327i
$257$	3902.42			0.947184			0.473592	−	0.880744i	$-0.342957\pi$
$257$	3902.42			0.947184			0.473592	+	0.880744i	$0.342957\pi$
$258$	−1899.43	+	7807.92i	−0.458346	+	1.88411i
$259$	140.921	+	42.7479i	0.0338085	+	0.0102557i
$260$	−858.512	+	1660.10i	−0.204779	+	0.395981i
$261$	2194.44	+	216.133i	0.520430	+	0.0512579i
$262$	−3087.62	+	5231.76i	−0.728067	+	1.23366i
$263$	−1065.34	−	1594.39i	−0.249778	−	0.373818i	0.685301	−	0.728260i	$-0.259671\pi$
$263$	−1065.34	−	1594.39i	−0.249778	−	0.373818i	−0.935078	+	0.354442i	$0.884671\pi$
$264$	−245.831	−	3531.69i	−0.0573100	−	0.823336i
$265$	−3753.68	−	2508.13i	−0.870140	−	0.581409i
$266$	60.7459	−	173.485i	0.0140021	−	0.0399889i
$267$	2042.66	−	3821.55i	0.468198	−	0.875937i
$268$	255.760	−	262.816i	0.0582950	−	0.0599032i
$269$	336.674	+	3418.31i	0.0763099	+	0.774788i	0.954844	+	0.297108i	$0.0960221\pi$
$269$	336.674	+	3418.31i	0.0763099	+	0.774788i	−0.878534	+	0.477680i	$0.841478\pi$
$270$	1864.96	−	681.640i	0.420363	−	0.153642i
$271$	−423.818	−	175.551i	−0.0950004	−	0.0393505i	0.334677	−	0.942333i	$-0.391373\pi$
$271$	−423.818	−	175.551i	−0.0950004	−	0.0393505i	−0.429678	+	0.902982i	$0.641373\pi$
$272$	5099.93	+	3210.47i	1.13687	+	0.715675i
$273$	98.0262	−	40.6038i	0.0217319	−	0.00900166i
$274$	2082.95	−	1913.85i	0.459254	−	0.421969i
$275$	−1240.67	+	1511.76i	−0.272056	+	0.331501i
$276$	2890.60	−	4456.16i	0.630412	−	0.971845i
$277$	1467.81	+	4838.72i	0.318383	+	1.04957i	0.959402	+	0.282043i	$0.0910122\pi$
$277$	1467.81	+	4838.72i	0.318383	+	1.04957i	−0.641018	+	0.767526i	$0.721488\pi$
$278$	−3378.42	−	3020.42i	−0.728864	−	0.651628i
$279$	−85.1296	−	427.975i	−0.0182673	−	0.0918359i
$280$	−307.986	−	70.5000i	−0.0657347	−	0.0150471i
$281$	−4137.34	−	822.969i	−0.878339	−	0.174712i	−0.264730	−	0.964323i	$-0.585283\pi$
$281$	−4137.34	−	822.969i	−0.878339	−	0.174712i	−0.613609	+	0.789610i	$0.710283\pi$
$282$	5995.71	+	847.738i	1.26610	+	0.179014i
$283$	2167.58	+	2641.21i	0.455298	+	0.554783i	0.949175	−	0.314749i	$-0.101920\pi$
$283$	2167.58	+	2641.21i	0.455298	+	0.554783i	−0.493876	+	0.869532i	$0.664420\pi$
$284$	−6340.58	+	711.716i	−1.32480	+	0.148706i
$285$	−5923.57	+	3166.21i	−1.23116	+	0.658071i
$286$	613.657	−	839.293i	0.126875	−	0.173526i
$287$	242.320	+	242.320i	0.0498387	+	0.0498387i
$288$	−3529.13	−	757.464i	−0.722069	−	0.154979i
$289$	2795.41	−	2795.41i	0.568982	−	0.568982i
$290$	−696.618	−	4485.76i	−0.141058	−	0.908321i
$291$	−5602.22	−	10481.0i	−1.12855	−	2.11137i
$292$	7619.11	−	4206.76i	1.52697	−	0.843089i
$293$	842.258	−	691.223i	0.167936	−	0.137821i	−0.546672	−	0.837347i	$-0.684105\pi$
$293$	842.258	−	691.223i	0.167936	−	0.137821i	0.714607	+	0.699526i	$0.246605\pi$
$294$	−3984.91	−	5297.34i	−0.790493	−	1.05084i
$295$	−1393.96	+	7007.93i	−0.275118	+	1.38311i
$296$	99.3172	−	3462.02i	0.0195023	−	0.679818i
$297$	−1083.39	+	215.499i	−0.211665	+	0.0421028i
$298$	6591.64	−	368.790i	1.28135	−	0.0716895i
$299$	1492.75	−	452.820i	0.288722	−	0.0875828i
$300$	2660.64	+	3866.99i	0.512040	+	0.744202i
$301$	−308.395	−	253.093i	−0.0590551	−	0.0484652i
$302$	5915.79	+	250.298i	1.12720	+	0.0476921i
$303$	988.877	+	2387.36i	0.187490	+	0.452641i
$304$	−4312.20	−	306.528i	−0.813558	−	0.0578309i
$305$	−1522.13	+	3674.75i	−0.285761	+	0.689888i
$306$	−2237.84	+	4816.01i	−0.418068	+	0.899715i
$307$	−316.412	+	31.1639i	−0.0588227	+	0.00579353i	−0.127386	−	0.991853i	$-0.540659\pi$
$307$	−316.412	+	31.1639i	−0.0588227	+	0.00579353i	0.0685630	+	0.997647i	$0.478159\pi$
$308$	163.286	+	65.0471i	0.0302081	+	0.0120338i
$309$	8101.83	+	4330.52i	1.49158	+	0.797264i
$310$	−809.451	+	389.602i	−0.148302	+	0.0713803i
$311$	−5645.70	+	8449.39i	−1.02938	+	1.54058i	−0.201652	+	0.979457i	$0.564631\pi$
$311$	−5645.70	+	8449.39i	−1.02938	+	1.54058i	−0.827731	+	0.561125i	$0.810369\pi$
$312$	−1527.11	−	1973.59i	−0.277102	−	0.358118i
$313$	−6095.09	+	4072.61i	−1.10069	+	0.735455i	−0.966798	−	0.255541i	$-0.917746\pi$
$313$	−6095.09	+	4072.61i	−1.10069	+	0.735455i	−0.133889	+	0.990996i	$0.542746\pi$
$314$	1452.67	+	5636.44i	0.261080	+	1.01300i
$315$	27.2905	−	277.085i	0.00488141	−	0.0495618i
$316$	6175.97	−	5210.70i	1.09945	−	0.927610i
$317$	−1906.89	+	6286.17i	−0.337860	+	1.11378i	0.609280	+	0.792955i	$0.291459\pi$
$317$	−1906.89	+	6286.17i	−0.337860	+	1.11378i	−0.947140	+	0.320820i	$0.896041\pi$
$318$	5149.01	−	3134.00i	0.907993	−	0.552660i
$319$			2525.36i			0.443238i
$320$	303.209	+	7424.68i	0.0529684	+	1.29704i
$321$		−	1340.24i		−	0.233036i
$322$	137.109	+	225.263i	0.0237292	+	0.0389859i
$323$	−1846.33	+	6086.52i	−0.318057	+	1.04849i
$324$	−587.754	+	6933.36i	−0.100781	+	1.18885i
$325$	−135.118	+	1371.87i	−0.0230615	+	0.234147i
$326$	5213.90	−	1343.77i	0.885801	−	0.228296i
$327$	−9656.33	+	6452.16i	−1.63302	+	1.09115i
$328$	4001.61	−	6996.20i	0.673634	−	1.17775i
$329$	−167.024	+	249.969i	−0.0279889	+	0.0418883i
$330$	−2785.45	−	5787.16i	−0.464649	−	0.965372i
$331$	−2772.96	−	1482.18i	−0.460471	−	0.246127i	0.224814	−	0.974402i	$-0.427822\pi$
$331$	−2772.96	−	1482.18i	−0.460471	−	0.246127i	−0.685285	+	0.728275i	$0.740322\pi$
$332$	−3102.43	−	7210.85i	−0.512855	−	1.19201i
$333$	3037.38	−	299.156i	0.499843	−	0.0492302i
$334$	−3450.04	−	1603.12i	−0.565204	−	0.262631i
$335$	254.599	−	614.657i	0.0415231	−	0.100246i
$336$	258.654	−	333.263i	0.0419962	−	0.0541100i
$337$	−4108.24	−	9918.17i	−0.664065	−	1.60320i	−0.791374	−	0.611332i	$-0.790634\pi$
$337$	−4108.24	−	9918.17i	−0.664065	−	1.60320i	0.127309	−	0.991863i	$-0.459366\pi$
$338$	−231.702	+	5476.29i	−0.0372868	+	0.881275i
$339$	3078.94	+	2526.82i	0.493290	+	0.404833i
$340$	10750.7	+	1986.80i	1.71482	+	0.316910i
$341$	478.227	−	145.069i	0.0759456	−	0.0230378i
$342$	−212.808	−	3803.66i	−0.0336472	−	0.601399i
$343$	646.441	−	128.585i	0.101762	−	0.0202418i
$344$	−3837.80	+	8562.18i	−0.601513	+	1.34198i
$345$	1879.92	−	9450.99i	0.293367	−	1.47485i
$346$	5272.12	−	3965.95i	0.819165	−	0.616215i
$347$	−427.972	+	351.227i	−0.0662096	+	0.0543368i	−0.666916	−	0.745133i	$-0.732386\pi$
$347$	−427.972	+	351.227i	−0.0662096	+	0.0543368i	0.600706	+	0.799470i	$0.294886\pi$
$348$	5823.59	+	1680.40i	0.897061	+	0.258847i
$349$	−2588.85	−	4843.41i	−0.397072	−	0.742870i	0.601352	−	0.798984i	$-0.294629\pi$
$349$	−2588.85	−	4843.41i	−0.397072	−	0.742870i	−0.998424	+	0.0561143i	$0.982129\pi$
$350$	−230.282	+	35.7617i	−0.0351688	+	0.00546155i
$351$	−550.563	+	550.563i	−0.0837233	+	0.0837233i
$352$	467.153	−	4107.34i	0.0707367	−	0.621937i
$353$	4850.68	+	4850.68i	0.731376	+	0.731376i	0.970892	−	0.239516i	$-0.0769888\pi$
$353$	4850.68	+	4850.68i	0.731376	+	0.731376i	−0.239516	+	0.970892i	$0.576989\pi$
$354$	−7701.33	−	5630.90i	−1.15627	−	0.845421i
$355$	−10208.4	+	5456.49i	−1.52621	+	0.815777i
$356$	3156.36	−	3954.54i	0.469907	−	0.588737i
$357$	−393.748	−	479.783i	−0.0583735	−	0.0711283i
$358$	−860.183	+	6083.73i	−0.126989	+	0.898143i
$359$	−2050.93	−	407.955i	−0.301515	−	0.0599751i	0.0420143	−	0.999117i	$-0.486622\pi$
$359$	−2050.93	−	407.955i	−0.301515	−	0.0599751i	−0.343529	+	0.939142i	$0.611622\pi$
$360$	−6456.44	+	1092.81i	−0.945235	+	0.159989i
$361$	447.977	+	2252.13i	0.0653123	+	0.328347i
$362$	414.720	−	463.876i	0.0602133	−	0.0673503i
$363$	−1609.95	−	5307.30i	−0.232784	−	0.767385i
$364$	121.172	−	25.8212i	0.0174482	−	0.00371812i
$365$	10016.7	−	12205.3i	1.43643	−	1.75029i
$366$	−3593.20	−	3910.69i	−0.513168	−	0.558510i
$367$	−7973.83	+	3302.87i	−1.13414	+	0.469777i	−0.869187	−	0.494483i	$-0.835357\pi$
$367$	−7973.83	+	3302.87i	−1.13414	+	0.469777i	−0.264956	+	0.964261i	$0.585357\pi$
$368$	4264.65	−	4503.29i	0.604104	−	0.637908i
$369$	6561.83	+	2718.00i	0.925732	+	0.383451i
$370$	−2156.98	−	5901.47i	−0.303070	−	0.829197i
$371$	29.3333	+	297.826i	0.00410488	+	0.0416775i
$372$	−16.3182	−	1199.34i	−0.00227435	−	0.167159i
$373$	46.7031	−	87.3753i	0.00648309	−	0.0121290i	−0.878659	−	0.477450i	$-0.841561\pi$
$373$	46.7031	−	87.3753i	0.00648309	−	0.0121290i	0.885142	+	0.465321i	$0.154061\pi$
$374$	−5740.23	−	2009.95i	−0.793637	−	0.277893i
$375$	−3254.26	−	2174.43i	−0.448132	−	0.299432i
$376$	6704.53	+	2245.68i	0.919574	+	0.308011i
$377$	988.950	+	1480.07i	0.135102	+	0.202195i
$378$	−113.358	−	66.9003i	−0.0154246	−	0.00910313i
$379$	−3811.53	−	375.403i	−0.516583	−	0.0508790i	−0.163633	−	0.986521i	$-0.552321\pi$
$379$	−3811.53	−	375.403i	−0.516583	−	0.0508790i	−0.352950	+	0.935642i	$0.614821\pi$
$380$	−7473.45	+	2378.55i	−1.00889	+	0.321097i
$381$	−17102.5	−	5187.99i	−2.29971	−	0.697608i
$382$	7544.61	+	1835.38i	1.01051	+	0.245827i
$383$	13351.0			1.78121			0.890603	−	0.454781i	$-0.150282\pi$
$383$	13351.0			1.78121			0.890603	+	0.454781i	$0.150282\pi$
$384$	−9160.86	−	3810.34i	−1.21742	−	0.506368i
$385$	318.870			0.0422107
$386$	−11594.3	−	2820.54i	−1.52885	−	0.371922i
$387$	−7912.46	−	2400.22i	−1.03931	−	0.315271i
$388$	−4208.54	−	13223.3i	−0.550660	−	1.73019i
$389$	−2014.96	−	198.456i	−0.262629	−	0.0258667i	−0.0341541	−	0.999417i	$-0.510874\pi$
$389$	−2014.96	−	198.456i	−0.262629	−	0.0258667i	−0.228474	+	0.973550i	$0.573374\pi$
$390$	−3898.80	−	2300.95i	−0.506214	−	0.298751i
$391$	−5069.60	−	7587.19i	−0.655705	−	0.981331i
$392$	−3451.48	−	6928.12i	−0.444710	−	0.892661i
$393$	−12235.3	−	8175.34i	−1.57045	−	1.04934i
$394$	6495.02	+	2274.24i	0.830493	+	0.290798i
$395$	6910.39	−	12928.4i	0.880252	−	1.64683i
$396$	3642.49	−	49.5595i	0.462228	−	0.00628904i
$397$	809.673	+	8220.75i	0.102358	+	1.03926i	0.899929	+	0.436037i	$0.143618\pi$
$397$	809.673	+	8220.75i	0.102358	+	1.03926i	−0.797570	+	0.603226i	$0.793882\pi$
$398$	1416.72	+	3876.13i	0.178426	+	0.488173i
$399$	411.355	+	170.389i	0.0516128	+	0.0213787i
$400$	2234.44	+	5004.75i	0.279305	+	0.625594i
$401$	−3556.68	+	1473.23i	−0.442923	+	0.183465i	−0.592988	−	0.805211i	$-0.702052\pi$
$401$	−3556.68	+	1473.23i	−0.442923	+	0.183465i	0.150065	+	0.988676i	$0.452052\pi$
$402$	601.016	+	654.120i	0.0745670	+	0.0811556i
$403$	223.470	−	272.299i	0.0276224	−	0.0336580i
$404$	628.857	+	2951.06i	0.0774426	+	0.363418i
$405$	3664.39	+	12079.9i	0.449593	+	1.48211i
$406$	−200.568	+	224.341i	−0.0245173	+	0.0274232i
$407$	681.924	+	3428.26i	0.0830509	+	0.417525i
$408$	−8454.63	+	11899.8i	−1.02590	+	1.44394i
$409$	−2889.56	−	574.770i	−0.349339	−	0.0694879i	0.0173021	−	0.999850i	$-0.494492\pi$
$409$	−2889.56	−	574.770i	−0.349339	−	0.0694879i	−0.366641	+	0.930362i	$0.619492\pi$
$410$	2047.03	−	14477.8i	0.246574	−	1.74392i
$411$	4346.80	+	5296.59i	0.521683	+	0.635673i
$412$	8383.78	+	6691.60i	1.00252	+	0.800174i
$413$	417.728	−	223.280i	0.0497701	−	0.0266027i
$414$	4411.98	+	3225.86i	0.523761	+	0.382953i
$415$	−10070.0	−	10070.0i	−1.19113	−	1.19113i
$416$	−1334.67	−	2590.18i	−0.157302	−	0.305274i
$417$	7762.03	−	7762.03i	0.911531	−	0.911531i
$418$	4311.32	−	669.528i	0.504482	−	0.0783437i
$419$	2323.62	+	4347.20i	0.270922	+	0.506860i	0.980185	−	0.198084i	$-0.0634720\pi$
$419$	2323.62	+	4347.20i	0.270922	+	0.506860i	−0.709263	+	0.704944i	$0.750972\pi$
$420$	212.179	−	735.328i	0.0246506	−	0.0854294i
$421$	9102.18	−	7469.97i	1.05371	−	0.864760i	0.0626343	−	0.998037i	$-0.480050\pi$
$421$	9102.18	−	7469.97i	1.05371	−	0.864760i	0.991079	+	0.133276i	$0.0425498\pi$
$422$	−5860.19	+	4408.32i	−0.675994	+	0.508515i
$423$	−1215.57	+	6111.10i	−0.139724	+	0.702440i
$424$	6577.24	−	2505.92i	0.753347	−	0.287024i
$425$	7908.91	−	1573.18i	0.902679	−	0.179554i
$426$	−863.339	−	15431.0i	−0.0981899	−	1.75501i
$427$	252.316	−	76.5393i	0.0285959	−	0.00867447i
$428$	284.397	−	1538.89i	0.0321188	−	0.173797i
$429$	1946.80	+	1597.70i	0.219097	+	0.179808i
$430$	−719.571	+	17007.1i	−0.0806996	+	1.90734i
$431$	−2622.02	−	6330.11i	−0.293035	−	0.707450i	−1.00000		0.000200773i	$-0.999936\pi$
$431$	−2622.02	−	6330.11i	−0.293035	−	0.707450i	0.706965	−	0.707249i	$-0.250064\pi$
$432$	−817.712	+	2985.78i	−0.0910699	+	0.332531i
$433$	−4457.96	+	10762.5i	−0.494772	+	1.19448i	0.457494	+	0.889213i	$0.348747\pi$
$433$	−4457.96	+	10762.5i	−0.494772	+	1.19448i	−0.952265	+	0.305271i	$0.901253\pi$
$434$	54.0049	+	25.0943i	0.00597308	+	0.00277549i
$435$	10943.1	−	1077.80i	1.20617	−	0.118797i
$436$	−12456.8	+	5359.46i	−1.36828	+	0.588696i
$437$	5773.06	+	3085.77i	0.631952	+	0.337785i
$438$	9143.13	+	18996.1i	0.997433	+	2.07230i
$439$	5420.65	−	8112.58i	0.589325	−	0.881987i	−0.410225	−	0.911984i	$-0.634550\pi$
$439$	5420.65	−	8112.58i	0.589325	−	0.881987i	0.999550	+	0.0299973i	$0.00954987\pi$
$440$	−1970.29	−	7236.03i	−0.213478	−	0.784009i
$441$	5671.39	−	3789.50i	0.612395	−	0.409189i
$442$	−4151.35	+	1069.92i	−0.446742	+	0.115138i
$443$	83.7726	−	850.558i	0.00898455	−	0.0912217i	−0.989647	−	0.143525i	$-0.954156\pi$
$443$	83.7726	−	850.558i	0.00898455	−	0.0912217i	0.998631	+	0.0523033i	$0.0166563\pi$
$444$	8359.49	+	708.649i	0.893522	+	0.0757455i
$445$	2664.60	−	8784.01i	0.283852	−	0.935735i
$446$	6722.46	+	11044.7i	0.713717	+	1.17260i
$447$			15991.8i			1.69214i
$448$	367.710	−	327.774i	0.0387783	−	0.0345667i
$449$		−	413.161i		−	0.0434260i	−0.999764	−	0.0217130i	$-0.993088\pi$
$449$		−	413.161i		−	0.0434260i	0.999764	−	0.0217130i	$-0.00691201\pi$
$450$	−4125.77	+	2511.19i	−0.432201	+	0.263064i
$451$	−2361.23	+	7783.92i	−0.246532	+	0.812706i
$452$	2999.13	+	3554.71i	0.312095	+	0.369910i
$453$	−1405.82	+	14273.5i	−0.145808	+	1.48042i
$454$	1727.79	+	6703.91i	0.178611	+	0.693018i
$455$	186.884	−	124.872i	0.0192555	−	0.0128661i
$456$	1324.83	−	10387.6i	0.136054	−	1.06676i
$457$	−7922.79	+	11857.3i	−0.810968	+	1.21370i	0.162913	+	0.986640i	$0.447911\pi$
$457$	−7922.79	+	11857.3i	−0.810968	+	1.21370i	−0.973881	+	0.227059i	$0.927089\pi$
$458$	5899.60	−	2839.57i	0.601900	−	0.289704i
$459$	4016.84	+	2147.04i	0.408475	+	0.218334i
$460$	4164.06	−	10452.9i	0.422066	−	1.05950i
$461$	12822.2	−	1262.88i	1.29543	−	0.127588i	0.573297	−	0.819347i	$-0.305664\pi$
$461$	12822.2	−	1262.88i	1.29543	−	0.127588i	0.722128	+	0.691759i	$0.243164\pi$
$462$	−179.411	+	386.107i	−0.0180670	+	0.0388817i
$463$	−1954.88	+	4719.49i	−0.196222	+	0.473722i	−0.991112	−	0.133032i	$-0.957529\pi$
$463$	−1954.88	+	4719.49i	−0.196222	+	0.473722i	0.794890	+	0.606754i	$0.207529\pi$
$464$	6330.21	+	3165.23i	0.633346	+	0.316686i
$465$	−832.727	−	2010.38i	−0.0830468	−	0.200493i
$466$	4361.60	+	184.539i	0.433578	+	0.0183447i
$467$	3705.13	+	3040.73i	0.367137	+	0.301302i	0.799815	−	0.600247i	$-0.204931\pi$
$467$	3705.13	+	3040.73i	0.367137	+	0.301302i	−0.432677	+	0.901549i	$0.642431\pi$
$468$	2115.39	−	1455.47i	0.208940	−	0.143759i
$469$	−42.2037	+	12.8023i	−0.00415519	+	0.00126046i
$470$	12807.3	−	716.548i	1.25693	−	0.0703231i
$471$	−13828.3	+	2750.63i	−1.35282	+	0.269092i
$472$	−7647.98	−	8099.75i	−0.745820	−	0.789875i
$473$	1847.42	−	9287.63i	0.179587	−	0.902845i
$474$	11766.4	+	15641.7i	1.14019	+	1.51571i
$475$	−4471.68	+	3669.81i	−0.431946	+	0.354489i
$476$	−350.301	−	634.451i	−0.0337311	−	0.0610925i
$477$	2923.82	+	5470.09i	0.280655	+	0.525069i
$478$	1530.87	+	9857.80i	0.146486	+	0.943274i
$479$	−7059.33	+	7059.33i	−0.673380	+	0.673380i	−0.958494	−	0.285114i	$-0.907969\pi$
$479$	−7059.33	+	7059.33i	−0.673380	+	0.673380i	0.285114	+	0.958494i	$0.407969\pi$
$480$	−17997.7	−	271.329i	−1.71141	−	0.0258009i
$481$	1742.20	+	1742.20i	0.165150	+	0.165150i
$482$	−8905.82	+	12180.4i	−0.841596	+	1.15104i
$483$	−563.354	+	301.119i	−0.0530714	+	0.0283672i
$484$	−722.381	−	6435.59i	−0.0678419	−	0.604395i
$485$	−15970.9	−	19460.6i	−1.49526	−	1.82198i
$486$	−13031.3	−	1842.50i	−1.21628	−	0.171970i
$487$	1204.42	+	239.573i	0.112068	+	0.0222918i	0.250806	−	0.968037i	$-0.419304\pi$
$487$	1204.42	+	239.573i	0.112068	+	0.0222918i	−0.138738	+	0.990329i	$0.544304\pi$
$488$	−3295.95	−	5252.81i	−0.305739	−	0.487262i
$489$	2544.42	+	12791.7i	0.235302	+	1.18294i
$490$	−10468.5	−	9359.17i	−0.965139	−	0.862865i
$491$	1286.21	+	4240.07i	0.118220	+	0.389718i	0.996001	−	0.0893438i	$-0.0284770\pi$
$491$	1286.21	+	4240.07i	0.118220	+	0.389718i	−0.877781	+	0.479062i	$0.840977\pi$
$492$	16378.9	+	10624.6i	1.50085	+	0.973564i
$493$	6605.82	−	8049.21i	0.603471	−	0.735331i
$494$	2264.59	−	2080.74i	0.206253	−	0.189508i
$495$	6105.68	−	2529.05i	0.554404	−	0.229642i
$496$	235.762	−	1380.58i	0.0213428	−	0.124979i
$497$	708.909	+	293.640i	0.0639817	+	0.0265021i
$498$	17859.3	−	6527.53i	1.60701	−	0.587361i
$499$	−878.709	−	8921.68i	−0.0788305	−	0.800380i	−0.950591	−	0.310447i	$-0.899521\pi$
$499$	−878.709	−	8921.68i	−0.0788305	−	0.800380i	0.871760	−	0.489933i	$-0.162979\pi$
$500$	−3275.21	−	3187.28i	−0.292944	−	0.285079i
$501$	4343.99	−	8127.03i	0.387376	−	0.724729i
$502$	1629.45	−	4653.57i	0.144872	−	0.413743i
$503$	−17921.4	−	11974.7i	−1.58862	−	1.06148i	−0.958544	−	0.284944i	$-0.908025\pi$
$503$	−17921.4	−	11974.7i	−1.58862	−	1.06148i	−0.630073	−	0.776536i	$-0.716975\pi$
$504$	327.517	+	284.890i	0.0289460	+	0.0251785i
$505$	3041.17	+	4551.43i	0.267980	+	0.401061i
$506$	−3181.39	+	5390.66i	−0.279506	+	0.473605i
$507$	−13213.1	−	1301.38i	−1.15742	−	0.113996i
$508$	−18536.6	−	9586.10i	−1.61896	−	0.837233i
$509$	17487.2	+	5304.68i	1.52280	+	0.461936i	0.937238	−	0.348691i	$-0.113374\pi$
$509$	17487.2	+	5304.68i	1.52280	+	0.461936i	0.585562	+	0.810627i	$0.300874\pi$
$510$	−6259.79	+	25731.9i	−0.543506	+	2.23417i
$511$	−1046.68			−0.0906109
$512$	−9710.17	−	6319.04i	−0.838150	−	0.545439i
$513$	−3267.36			−0.281203
$514$	−2609.05	+	10724.9i	−0.223892	+	0.920343i
$515$	18622.4	+	5649.05i	1.59340	+	0.483354i
$516$	−20188.4	−	10440.3i	−1.72237	−	0.890715i
$517$	−7101.56	−	699.442i	−0.604112	−	0.0594999i
$518$	−211.699	+	358.710i	−0.0179566	+	0.0304262i
$519$	8878.29	+	13287.3i	0.750893	+	1.12379i
$520$	−3988.44	−	3469.32i	−0.336355	−	0.292577i
$521$	1323.42	+	884.280i	0.111286	+	0.0743590i	0.609968	−	0.792426i	$-0.291182\pi$
$521$	1323.42	+	884.280i	0.111286	+	0.0743590i	−0.498682	+	0.866785i	$0.666182\pi$
$522$	−2061.13	+	5886.41i	−0.172822	+	0.493565i
$523$	5090.73	−	9524.08i	0.425625	−	0.796289i	−0.574122	−	0.818770i	$-0.694656\pi$
$523$	5090.73	−	9524.08i	0.425625	−	0.796289i	0.999747	+	0.0224809i	$0.00715649\pi$
$524$	−12314.0	−	11983.4i	−1.02660	−	0.999043i
$525$	−55.3302	−	561.777i	−0.00459963	−	0.0467008i
$526$	5094.07	−	1861.87i	0.422266	−	0.154338i
$527$	−1903.75	−	788.558i	−0.157360	−	0.0651805i
$528$	9870.42	+	1685.58i	0.813551	+	0.138931i
$529$	2564.40	−	1062.21i	0.210767	−	0.0873025i
$530$	9402.64	−	8639.29i	0.770613	−	0.708050i
$531$	6227.70	−	7588.48i	0.508963	−	0.620173i
$532$	436.171	+	282.934i	0.0355459	+	0.0230578i
$533$	1664.37	+	5486.69i	0.135257	+	0.445882i
$534$	9137.00	+	8168.77i	0.740443	+	0.661980i
$535$	−553.880	−	2784.54i	−0.0447594	−	0.225021i
$536$	551.297	+	878.612i	0.0444261	+	0.0708027i
$537$	−14597.2	−	2903.55i	−1.17302	−	0.233329i
$538$	−9619.54	−	1360.11i	−0.770869	−	0.108994i
$539$	4955.71	+	6038.55i	0.396025	+	0.482558i
$540$	626.472	+	5581.15i	0.0499242	+	0.444768i
$541$	13033.7	−	6966.65i	1.03579	−	0.553641i	0.136338	−	0.990662i	$-0.456467\pi$
$541$	13033.7	−	6966.65i	1.03579	−	0.553641i	0.899451	+	0.437022i	$0.143967\pi$
$542$	765.816	−	1047.40i	0.0606912	−	0.0830068i
$543$	1065.77	+	1065.77i	0.0842296	+	0.0842296i
$544$	−12232.9	+	11869.6i	−0.964122	+	0.935484i
$545$	−17396.0	+	17396.0i	−1.36727	+	1.36727i
$546$	46.0527	+	296.549i	0.00360966	+	0.0232439i
$547$	−4191.04	−	7840.89i	−0.327598	−	0.612893i	0.663169	−	0.748470i	$-0.269211\pi$
$547$	−4191.04	−	7840.89i	−0.327598	−	0.612893i	−0.990767	+	0.135577i	$0.956711\pi$
$548$	3867.17	+	7004.06i	0.301455	+	0.545983i
$549$	4224.27	−	3466.77i	0.328392	−	0.269504i
$550$	−3325.26	−	4420.43i	−0.257799	−	0.342705i
$551$	−1457.29	+	7326.28i	−0.112673	+	0.566443i
$552$	10314.2	+	10923.4i	0.795290	+	0.842268i
$553$	−953.098	+	189.583i	−0.0732909	+	0.0145785i
$554$	−14279.5	+	798.911i	−1.09508	+	0.0612680i
$555$	14564.6	−	4418.13i	1.11393	−	0.337908i
$556$	10559.6	−	7265.46i	0.805447	−	0.554180i
$557$	9882.89	+	8110.68i	0.751798	+	0.616984i	0.930234	−	0.366967i	$-0.119604\pi$
$557$	9882.89	+	8110.68i	0.751798	+	0.616984i	−0.178436	+	0.983951i	$0.557104\pi$
$558$	1233.11	+	52.1729i	0.0935514	+	0.00395816i
$559$	−2554.36	−	6166.78i	−0.193270	−	0.466595i
$560$	399.665	−	799.297i	0.0301588	−	0.0603151i
$561$	5637.79	−	13610.8i	0.424291	−	1.02433i
$562$	5027.85	−	10820.3i	0.377379	−	0.812150i
$563$	18586.8	−	1830.64i	1.39137	−	0.137038i	0.625596	−	0.780147i	$-0.284856\pi$
$563$	18586.8	−	1830.64i	1.39137	−	0.137038i	0.765775	+	0.643109i	$0.222356\pi$
$564$	−6338.38	+	15911.1i	−0.473216	+	1.18790i
$565$	7441.23	+	3977.42i	0.554080	+	0.296162i
$566$	−8707.95	+	4191.28i	−0.646683	+	0.311259i
$567$	464.905	−	695.780i	0.0344342	−	0.0515344i
$568$	2283.14	−	17901.5i	0.168659	−	1.32241i
$569$	10375.5	−	6932.66i	0.764432	−	0.510777i	−0.111175	−	0.993801i	$-0.535462\pi$
$569$	10375.5	−	6932.66i	0.764432	−	0.510777i	0.875607	+	0.483024i	$0.160462\pi$
$570$	−4741.29	−	18396.4i	−0.348405	−	1.35183i
$571$	34.4158	−	349.430i	0.00252234	−	0.0256098i	−0.993841	−	0.110814i	$-0.964654\pi$
$571$	34.4158	−	349.430i	0.00252234	−	0.0256098i	0.996364	+	0.0852041i	$0.0271542\pi$
$572$	1896.33	+	2247.62i	0.138618	+	0.164297i
$573$	−5459.74	+	17998.3i	−0.398052	+	1.31220i
$574$	−827.970	+	503.953i	−0.0602070	+	0.0366457i
$575$		−	8299.17i		−	0.601912i
$576$	4441.20	−	9192.60i	0.321267	−	0.664974i
$577$		−	21595.0i		−	1.55808i	−0.626974	−	0.779040i	$-0.715707\pi$
$577$		−	21595.0i		−	1.55808i	0.626974	−	0.779040i	$-0.284293\pi$
$578$	5813.61	+	9551.47i	0.418364	+	0.687351i
$579$	8390.34	−	27659.3i	0.602229	−	1.98528i
$580$	12793.8	+	1084.56i	0.915923	+	0.0776446i
$581$	−92.5326	+	939.500i	−0.00660740	+	0.0670861i
$582$	32550.2	−	8389.12i	2.31830	−	0.597492i
$583$	−5906.29	+	3946.46i	−0.419577	+	0.280353i
$584$	6467.40	+	23751.9i	0.458259	+	1.68298i
$585$	2588.03	−	3873.26i	0.182909	−	0.273743i
$586$	1336.56	+	2776.89i	0.0942198	+	0.195755i
$587$	−15328.3	−	8193.13i	−1.07779	−	0.576093i	−0.165743	−	0.986169i	$-0.553002\pi$
$587$	−15328.3	−	8193.13i	−1.07779	−	0.576093i	−0.912051	+	0.410076i	$0.865502\pi$
$588$	17222.7	−	7409.98i	1.20791	−	0.519698i
$589$	1471.09	−	144.890i	0.102912	−	0.0101360i
$590$	−18327.8	−	8516.31i	−1.27888	−	0.594256i
$591$	−6379.10	+	15400.5i	−0.443995	+	1.07190i
$592$	9448.19	+	2587.56i	0.655943	+	0.179642i
$593$	−3734.31	−	9015.43i	−0.258600	−	0.624316i	0.740246	−	0.672336i	$-0.234709\pi$
$593$	−3734.31	−	9015.43i	−0.258600	−	0.624316i	−0.998846	+	0.0480199i	$0.984709\pi$
$594$	132.072	−	3121.52i	0.00912285	−	0.215619i
$595$	−1016.35	−	834.097i	−0.0700274	−	0.0574700i
$596$	−3393.45	+	18362.2i	−0.233223	+	1.26199i
$597$	−9566.14	+	2901.86i	−0.655806	+	0.198936i
$598$	246.464	+	4405.22i	0.0168540	+	0.301243i
$599$	19968.6	−	3972.00i	1.36209	−	0.270937i	0.540660	−	0.841241i	$-0.318175\pi$
$599$	19968.6	−	3972.00i	1.36209	−	0.270937i	0.821434	+	0.570304i	$0.193175\pi$
$600$	−12406.4	+	4726.81i	−0.844146	+	0.321619i
$601$	2819.15	−	14172.8i	0.191340	−	0.961933i	−0.759088	−	0.650988i	$-0.774355\pi$
$601$	2819.15	−	14172.8i	0.191340	−	0.961933i	0.950428	−	0.310945i	$-0.100645\pi$
$602$	901.753	−	678.342i	0.0610510	−	0.0459255i
$603$	−706.571	+	579.868i	−0.0477178	+	0.0391610i
$604$	−4643.02	+	16090.9i	−0.312785	+	1.08399i
$605$	−5538.26	−	10361.4i	−0.372169	−	0.696280i
$606$	−7222.26	+	1121.58i	−0.484132	+	0.0751835i
$607$	−11205.5	+	11205.5i	−0.749287	+	0.749287i	−0.974345	−	0.225058i	$-0.927743\pi$
$607$	−11205.5	+	11205.5i	−0.749287	+	0.749287i	0.225058	+	0.974345i	$0.427743\pi$
$608$	3725.44	−	11646.2i	0.248498	−	0.776833i
$609$	−515.430	−	515.430i	−0.0342960	−	0.0342960i
$610$	−9081.57	−	6640.08i	−0.602790	−	0.440736i
$611$	−4436.00	+	2371.09i	−0.293717	+	0.156995i
$612$	−11739.5	−	9370.04i	−0.775397	−	0.618891i
$613$	13985.0	+	17040.7i	0.921448	+	1.12279i	0.992120	+	0.125288i	$0.0399855\pi$
$613$	13985.0	+	17040.7i	0.921448	+	1.12279i	−0.0706723	+	0.997500i	$0.522514\pi$
$614$	125.897	−	890.422i	0.00827493	−	0.0585253i
$615$	34737.7	+	6909.76i	2.27766	+	0.453054i
$616$	−287.936	+	405.267i	−0.0188332	+	0.0265076i
$617$	4886.65	+	24566.8i	0.318848	+	1.60296i	0.724732	+	0.689031i	$0.241964\pi$
$617$	4886.65	+	24566.8i	0.318848	+	1.60296i	−0.405884	+	0.913925i	$0.633036\pi$
$618$	−17318.1	+	19370.8i	−1.12724	+	1.26085i
$619$	−1464.51	−	4827.85i	−0.0950949	−	0.313486i	0.896469	−	0.443107i	$-0.146124\pi$
$619$	−1464.51	−	4827.85i	−0.0950949	−	0.313486i	−0.991564	+	0.129621i	$0.958624\pi$
$620$	−529.556	−	2485.07i	−0.0343024	−	0.160972i
$621$	2973.75	−	3623.53i	0.192162	−	0.234150i
$622$	−19446.7	−	21165.0i	−1.25360	−	1.36437i
$623$	−562.175	+	232.860i	−0.0361526	+	0.0149749i
$624$	6444.96	−	2877.44i	0.413469	−	0.184599i
$625$	−17549.9	−	7269.39i	−1.12319	−	0.465241i
$626$	−7117.64	−	19473.8i	−0.454438	−	1.24334i
$627$	1035.89	+	10517.5i	0.0659799	+	0.669905i
$628$	−16461.7	+	223.977i	−1.04601	+	0.0142319i
$629$	6794.09	−	12710.9i	0.430681	−	0.805747i
$630$	743.260	+	260.253i	0.0470034	+	0.0164583i
$631$	−23988.3	−	16028.5i	−1.51340	−	1.01122i	−0.986951	−	0.161020i	$-0.948522\pi$
$631$	−23988.3	−	16028.5i	−1.51340	−	1.01122i	−0.526453	−	0.850204i	$-0.676478\pi$
$632$	10191.3	+	20457.0i	0.641440	+	1.28756i
$633$	−9868.59	−	14769.4i	−0.619655	−	0.927379i
$634$	−16001.2	−	9443.42i	−1.00235	−	0.591555i
$635$	−37677.1	−	3710.87i	−2.35460	−	0.231907i
$636$	5170.61	+	16246.2i	0.322371	+	1.01290i
$637$	5269.19	+	1598.39i	0.327744	+	0.0994201i
$638$	−6940.38	−	1688.39i	−0.430678	−	0.104771i
$639$	15903.0			0.984530
$640$	−20607.8	−	4130.63i	−1.27280	−	0.255121i
$641$	−10433.2			−0.642881			−0.321440	−	0.946930i	$-0.604167\pi$
$641$	−10433.2			−0.642881			−0.321440	+	0.946930i	$0.604167\pi$
$642$	3683.34	+	896.044i	0.226432	+	0.0550842i
$643$	19092.7	+	5791.69i	1.17098	+	0.355213i	0.815101	−	0.579318i	$-0.196681\pi$
$643$	19092.7	+	5791.69i	1.17098	+	0.355213i	0.355880	+	0.934532i	$0.384181\pi$
$644$	−710.753	+	226.209i	−0.0434901	+	0.0138414i
$645$	−41034.4	−	4041.54i	−2.50501	−	0.246722i
$646$	−15493.0	−	9143.49i	−0.943599	−	0.556882i
$647$	9238.31	+	13826.1i	0.561353	+	0.840124i	0.998235	−	0.0593951i	$-0.0189172\pi$
$647$	9238.31	+	13826.1i	0.561353	+	0.840124i	−0.436882	+	0.899519i	$0.643917\pi$
$648$	−18661.8	−	6250.76i	−1.13133	−	0.378940i
$649$	9348.02	+	6246.15i	0.565396	+	0.377785i
$650$	−3679.95	−	1288.54i	−0.222061	−	0.0777547i
$651$	−67.9982	+	127.216i	−0.00409379	+	0.00765895i
$652$	207.186	+	15227.6i	0.0124448	+	0.914662i
$653$	−731.812	−	7430.22i	−0.0438561	−	0.445278i	−0.991889	−	0.127106i	$-0.959431\pi$
$653$	−731.812	−	7430.22i	−0.0438561	−	0.445278i	0.948033	−	0.318172i	$-0.103069\pi$
$654$	−11276.3	−	30852.0i	−0.674220	−	1.84466i
$655$	−28799.2	−	11929.0i	−1.71798	−	0.711612i
$656$	16552.1	+	15675.0i	0.985139	+	0.932935i
$657$	−20041.6	+	8301.51i	−1.19010	+	0.492957i
$658$	−575.317	−	626.151i	−0.0340854	−	0.0370971i
$659$	−10264.9	+	12507.8i	−0.606773	+	0.739355i	−0.982271	−	0.187469i	$-0.939972\pi$
$659$	−10264.9	+	12507.8i	−0.606773	+	0.739355i	0.375498	+	0.926823i	$0.377472\pi$
$660$	17767.0	−	3786.06i	1.04785	−	0.223291i
$661$	3320.10	+	10944.9i	0.195366	+	0.644035i	0.998815	+	0.0486617i	$0.0154956\pi$
$661$	3320.10	+	10944.9i	0.195366	+	0.644035i	−0.803450	+	0.595373i	$0.797004\pi$
$662$	5927.37	−	6629.92i	0.347996	−	0.389244i
$663$	−2025.89	−	10184.9i	−0.118671	−	0.596602i
$664$	21891.6	−	3705.34i	1.27945	−	0.216559i
$665$	925.068	+	184.008i	0.0539438	+	0.0107301i
$666$	−1208.55	+	8547.57i	−0.0703157	+	0.497315i
$667$	−6798.58	−	8284.10i	−0.394666	−	0.480902i
$668$	6712.42	−	8409.86i	0.388789	−	0.487107i
$669$	−27621.2	+	14763.8i	−1.59626	+	0.853219i
$670$	1519.03	+	1110.65i	0.0875898	+	0.0640421i
$671$	4425.43	+	4425.43i	0.254608	+	0.254608i
$672$	742.968	+	933.662i	0.0426497	+	0.0535964i
$673$	21751.7	−	21751.7i	1.24587	−	1.24587i	0.288338	−	0.957529i	$-0.406897\pi$
$673$	21751.7	−	21751.7i	1.24587	−	1.24587i	0.957529	−	0.288338i	$-0.0931026\pi$
$674$	30004.5	−	4659.56i	1.71473	−	0.266290i
$675$	1952.73	+	3653.30i	0.111349	+	0.208319i
$676$	−14895.4	−	4298.08i	−0.847488	−	0.244542i
$677$	−10816.4	+	8876.79i	−0.614044	+	0.503933i	−0.889232	−	0.457457i	$-0.848760\pi$
$677$	−10816.4	+	8876.79i	−0.614044	+	0.503933i	0.275187	+	0.961391i	$0.411260\pi$
$678$	−9002.90	+	6772.42i	−0.509962	+	0.383618i
$679$	−325.578	+	1636.79i	−0.0184014	+	0.0925101i
$680$	−12647.9	+	28217.6i	−0.713273	+	1.59132i
$681$	−16447.2	+	3271.56i	−0.925491	+	0.184092i
$682$	78.9590	+	1411.29i	0.00443328	+	0.0792390i
$683$	21946.7	−	6657.46i	1.22953	−	0.372973i	0.392305	−	0.919835i	$-0.371678\pi$
$683$	21946.7	−	6657.46i	1.22953	−	0.372973i	0.837223	+	0.546862i	$0.184178\pi$
$684$	10595.8	+	1958.17i	0.592310	+	0.109463i
$685$	11220.1	+	9208.06i	0.625834	+	0.513609i
$686$	−78.8053	+	1862.57i	−0.00438600	+	0.103663i
$687$	6069.24	+	14652.5i	0.337054	+	0.813720i
$688$	−20965.4	−	16271.8i	−1.16177	−	0.901679i
$689$	−1916.11	+	4625.90i	−0.105948	+	0.255780i
$690$	24717.1	+	11485.2i	1.36371	+	0.633673i
$691$	14279.7	−	1406.43i	0.786144	−	0.0774285i	0.303025	−	0.952983i	$-0.402004\pi$
$691$	14279.7	−	1406.43i	0.786144	−	0.0774285i	0.483120	+	0.875554i	$0.339504\pi$
$692$	7374.71	+	17140.8i	0.405122	+	0.941609i
$693$	−386.364	−	206.516i	−0.0211786	−	0.0113202i
$694$	−679.139	−	1411.00i	−0.0371466	−	0.0771773i
$695$	12919.0	−	19334.6i	0.705100	−	1.05526i
$696$	−8511.68	+	14881.4i	−0.463555	+	0.810455i
$697$	27887.2	−	18633.6i	1.51550	−	1.01262i
$698$	15041.8	−	3876.72i	0.815676	−	0.210223i
$699$	−1036.48	+	10523.6i	−0.0560849	+	0.569440i
$700$	55.6770	−	656.786i	0.00300628	−	0.0354631i
$701$	7984.53	−	26321.5i	0.430202	−	1.41819i	−0.427489	−	0.904020i	$-0.640602\pi$
$701$	7984.53	−	26321.5i	0.430202	−	1.41819i	0.857691	−	0.514165i	$-0.171898\pi$
$702$	−1145.01	−	1881.19i	−0.0615605	−	0.101141i
$703$			10339.2i			0.554694i
$704$	10975.8	+	4029.92i	0.587592	+	0.215743i
$705$			31071.6i			1.65989i
$706$	−16574.0	+	10088.0i	−0.883530	+	0.537770i
$707$	105.335	−	347.243i	0.00560330	−	0.0184716i
$708$	20624.2	−	17400.7i	1.09478	−	0.923671i
$709$	185.643	−	1884.87i	0.00983355	−	0.0998417i	−0.989015	−	0.147815i	$-0.952776\pi$
$709$	185.643	−	1884.87i	0.00983355	−	0.0998417i	0.998849	+	0.0479729i	$0.0152761\pi$
$710$	−8170.90	−	31703.5i	−0.431899	−	1.67579i
$711$	−16746.2	+	11189.4i	−0.883305	+	0.590206i
$712$	8757.92	+	11318.4i	0.460979	+	0.595754i
$713$	−1178.22	+	1763.32i	−0.0618857	+	0.0926185i
$714$	1581.82	−	761.357i	0.0829107	−	0.0399063i
$715$	4705.05	+	2514.90i	0.246096	+	0.131541i
$716$	−16144.7	−	6431.43i	−0.842674	−	0.335690i
$717$	−24048.3	+	2368.55i	−1.25258	+	0.123368i
$718$	2492.37	−	5363.77i	0.129546	−	0.278794i
$719$	6556.38	−	15828.5i	0.340072	−	0.821006i	−0.657636	−	0.753336i	$-0.728444\pi$
$719$	6556.38	−	15828.5i	0.340072	−	0.821006i	0.997708	−	0.0676699i	$-0.0215565\pi$
$720$	1313.25	−	18474.7i	0.0679752	−	0.956266i
$721$	−493.673	−	1191.83i	−0.0254998	−	0.0615619i
$722$	−6488.98	−	274.549i	−0.334480	−	0.0141519i
$723$	−28253.4	−	23186.9i	−1.45333	−	1.19271i
$724$	997.589	+	1449.90i	0.0512087	+	0.0744270i
$725$	9062.61	−	2749.11i	0.464244	−	0.140827i
$726$	15662.3	−	876.276i	0.800663	−	0.0447957i
$727$	11080.0	−	2203.94i	0.565245	−	0.112434i	0.0958072	−	0.995400i	$-0.469457\pi$
$727$	11080.0	−	2203.94i	0.565245	−	0.112434i	0.469437	+	0.882966i	$0.344457\pi$
$728$	−10.0486	+	350.277i	−0.000511575	+	0.0178326i
$729$	1637.87	−	8234.11i	0.0832123	−	0.418336i
$730$	26846.7	+	35688.7i	1.36115	+	1.80945i
$731$	−30182.9	+	24770.5i	−1.52716	+	1.25331i
$732$	13149.9	−	7260.51i	0.663984	−	0.366607i
$733$	3370.46	+	6305.68i	0.169837	+	0.317743i	0.952412	−	0.304813i	$-0.0985941\pi$
$733$	3370.46	+	6305.68i	0.169837	+	0.317743i	−0.782575	+	0.622556i	$0.786094\pi$
$734$	−3746.11	−	24122.5i	−0.188381	−	1.21305i
$735$	24051.7	−	24051.7i	1.20702	−	1.20702i
$736$	9525.04	+	14731.2i	0.477035	+	0.737771i
$737$	−740.218	−	740.218i	−0.0369963	−	0.0369963i
$738$	−11856.9	+	16216.5i	−0.591405	+	0.808860i
$739$	−21652.2	+	11573.4i	−1.07780	+	0.576093i	−0.912052	−	0.410075i	$-0.865502\pi$
$739$	−21652.2	+	11573.4i	−1.07780	+	0.576093i	−0.165743	+	0.986169i	$0.553002\pi$
$740$	17661.0	−	1982.40i	0.877337	−	0.0984791i
$741$	4725.86	+	5758.48i	0.234290	+	0.285483i
$742$	−838.120	−	118.502i	−0.0414668	−	0.00586301i
$743$	37242.9	+	7408.07i	1.83891	+	0.365781i	0.987360	−	0.158495i	$-0.0506643\pi$
$743$	37242.9	+	7408.07i	1.83891	+	0.365781i	0.851548	+	0.524277i	$0.175664\pi$
$744$	3307.03	+	757.000i	0.162959	+	0.0373024i
$745$	6608.95	+	33225.4i	0.325011	+	1.63394i
$746$	208.907	+	186.770i	0.0102529	+	0.00916638i
$747$	5679.66	+	18723.3i	0.278190	+	0.917069i
$748$	9361.64	−	14431.9i	0.457614	−	0.705460i
$749$	−119.395	+	145.483i	−0.00582456	+	0.00709725i
$750$	8151.64	−	7489.84i	0.396874	−	0.364654i
$751$	−19453.2	+	8057.78i	−0.945216	+	0.391521i	−0.801431	−	0.598088i	$-0.795927\pi$
$751$	−19453.2	+	8057.78i	−0.945216	+	0.391521i	−0.143785	+	0.989609i	$0.545927\pi$
$752$	−10654.2	+	16924.5i	−0.516647	+	0.820709i
$753$	11034.2	+	4570.51i	0.534009	+	0.221194i
$754$	−4728.82	+	1728.37i	−0.228400	+	0.0834796i
$755$	2978.02	+	30236.4i	0.143551	+	1.45750i
$756$	259.649	−	266.811i	0.0124912	−	0.0128358i
$757$	4741.77	−	8871.23i	0.227665	−	0.425932i	−0.741989	−	0.670412i	$-0.766117\pi$
$757$	4741.77	−	8871.23i	0.227665	−	0.425932i	0.969654	+	0.244480i	$0.0786174\pi$
$758$	3579.99	−	10224.1i	0.171545	−	0.489918i
$759$	−12606.9	−	8423.64i	−0.602899	−	0.402844i
$760$	−1540.36	−	22129.3i	−0.0735193	−	1.05620i
$761$	14340.4	+	21462.0i	0.683101	+	1.02233i	0.997333	+	0.0729866i	$0.0232530\pi$
$761$	14340.4	+	21462.0i	0.683101	+	1.02233i	−0.314232	+	0.949346i	$0.601747\pi$
$762$	25692.3	−	43533.8i	1.22143	−	2.06964i
$763$	1622.99	+	159.851i	0.0770068	+	0.00758451i
$764$	−10088.2	+	19507.6i	−0.477722	+	0.923769i
$765$	−26076.4	−	7910.20i	−1.23241	−	0.373848i
$766$	−8926.08	+	36692.1i	−0.421034	+	1.73073i
$767$	7924.74			0.373072
$768$	16596.5	−	22629.1i	0.779787	−	1.06322i
$769$	15021.4			0.704400			0.352200	−	0.935925i	$-0.385434\pi$
$769$	15021.4			0.704400			0.352200	+	0.935925i	$0.385434\pi$
$770$	−213.187	+	876.342i	−0.00997759	+	0.0410145i
$771$	−25585.3	−	7761.21i	−1.19511	−	0.362533i
$772$	15503.3	−	29978.6i	0.722765	−	1.39761i
$773$	−31816.5	−	3133.65i	−1.48041	−	0.145808i	−0.674691	−	0.738101i	$-0.735723\pi$
$773$	−31816.5	−	3133.65i	−1.48041	−	0.145808i	−0.805723	+	0.592292i	$0.798223\pi$
$774$	11886.5	−	20140.9i	0.552005	−	0.935335i
$775$	−1041.20	−	1558.26i	−0.0482593	−	0.0722251i
$776$	39155.1	−	2725.47i	1.81132	−	0.126081i
$777$	−838.896	−	560.533i	−0.0387326	−	0.0258803i
$778$	1892.56	−	5404.98i	0.0872127	−	0.249072i
$779$	−11341.9	+	21219.2i	−0.521652	+	0.975941i
$780$	8930.26	−	9176.62i	0.409942	−	0.421251i
$781$	1785.20	+	18125.4i	0.0817918	+	0.830446i
$782$	24241.1	−	8860.06i	1.10851	−	0.405160i
$783$	4941.92	+	2047.01i	0.225555	+	0.0934280i
$784$	21347.9	−	4853.67i	0.972483	−	0.221104i
$785$	−27593.7	+	11429.7i	−1.25460	+	0.519672i
$786$	30648.2	−	28160.0i	1.39082	−	1.27791i
$787$	9739.52	−	11867.6i	0.441139	−	0.537529i	−0.504214	−	0.863579i	$-0.668218\pi$
$787$	9739.52	−	11867.6i	0.441139	−	0.537529i	0.945353	+	0.326050i	$0.105718\pi$
$788$	−10592.6	+	16329.6i	−0.478866	+	0.738221i
$789$	3813.67	+	12572.0i	0.172079	+	0.567268i
$790$	30910.8	+	27635.2i	1.39210	+	1.24458i
$791$	−109.119	−	548.576i	−0.00490494	−	0.0246588i
$792$	−2299.07	+	10043.7i	−0.103149	+	0.450616i
$793$	4326.69	+	860.632i	0.193752	+	0.0385397i
$794$	−23134.2	−	3270.96i	−1.03401	−	0.146199i
$795$	19621.9	+	23909.3i	0.875367	+	1.06664i
$796$	−11599.8	+	1302.06i	−0.516514	+	0.0579776i
$797$	−36437.7	+	19476.4i	−1.61943	+	0.865606i	−0.622912	+	0.782292i	$0.714050\pi$
$797$	−36437.7	+	19476.4i	−1.61943	+	0.865606i	−0.996523	+	0.0833137i	$0.973450\pi$
$798$	−743.296	+	1016.60i	−0.0329729	+	0.0450968i
$799$	20805.6	+	20805.6i	0.921211	+	0.921211i
$800$	−15248.3	+	2794.82i	−0.673886	+	0.123515i
$801$	−8917.56	+	8917.56i	−0.393367	+	0.393367i
$802$	−1670.93	−	10759.7i	−0.0735694	−	0.473738i
$803$	−11711.4	−	21910.4i	−0.514677	−	0.962893i
$804$	−2199.52	+	1214.43i	−0.0964817	+	0.0532707i
$805$	−1046.01	+	858.437i	−0.0457975	+	0.0375850i
$806$	598.947	+	796.209i	0.0261749	+	0.0347956i
$807$	4591.07	−	23080.9i	0.200264	−	1.00680i
$808$	−8530.77	−	244.727i	−0.371425	−	0.0106553i
$809$	−22899.3	+	4554.95i	−0.995175	+	0.197953i	−0.665706	−	0.746214i	$-0.731870\pi$
$809$	−22899.3	+	4554.95i	−0.995175	+	0.197953i	−0.329469	+	0.944167i	$0.606870\pi$
$810$	−35648.7	+	1994.48i	−1.54638	+	0.0865173i
$811$	13619.2	−	4131.35i	0.589687	−	0.178879i	0.0186808	−	0.999825i	$-0.494053\pi$
$811$	13619.2	−	4131.35i	0.589687	−	0.178879i	0.571006	+	0.820946i	$0.306553\pi$
$812$	−482.456	−	701.203i	−0.0208508	−	0.0303047i
$813$	2429.52	+	1993.86i	0.104806	+	0.0860118i
$814$	−9877.72	−	417.927i	−0.425324	−	0.0179955i
$815$	10572.8	+	25525.1i	0.454418	+	1.09706i
$816$	−27051.4	−	31191.5i	−1.16052	−	1.33814i
$817$	10719.1	−	25878.1i	0.459012	−	1.10815i
$818$	3511.51	−	7557.04i	0.150094	−	0.323014i
$819$	−307.314	+	30.2678i	−0.0131116	+	0.00129138i
$820$	38420.4	+	15305.3i	1.63622	+	0.651808i
$821$	−22902.7	−	12241.8i	−0.973582	−	0.520390i	−0.0937088	−	0.995600i	$-0.529872\pi$
$821$	−22902.7	−	12241.8i	−0.973582	−	0.520390i	−0.879873	+	0.475209i	$0.842372\pi$
$822$	−17462.6	+	8405.05i	−0.740973	+	0.356642i
$823$	3786.47	−	5666.86i	0.160374	−	0.240017i	−0.742576	−	0.669762i	$-0.766396\pi$
$823$	3786.47	−	5666.86i	0.160374	−	0.240017i	0.902951	+	0.429744i	$0.141396\pi$
$824$	−23995.5	+	18567.1i	−1.01447	+	0.784971i
$825$	11140.8	−	7444.03i	0.470148	−	0.314143i
$826$	334.354	+	1297.31i	0.0140843	+	0.0546480i
$827$	2151.87	−	21848.3i	0.0904811	−	0.918670i	−0.837598	−	0.546287i	$-0.816041\pi$
$827$	2151.87	−	21848.3i	0.0904811	−	0.918670i	0.928079	−	0.372383i	$-0.121459\pi$
$828$	−11815.3	+	9968.62i	−0.495905	+	0.418398i
$829$	−9987.09	+	32923.0i	−0.418415	+	1.37933i	0.454191	+	0.890904i	$0.349928\pi$
$829$	−9987.09	+	32923.0i	−0.418415	+	1.37933i	−0.872606	+	0.488425i	$0.837572\pi$
$830$	34407.7	−	20942.6i	1.43893	−	0.875818i
$831$		−	34643.1i		−	1.44616i
$832$	8010.85	−	1936.33i	0.333805	−	0.0806854i
$833$		−	32210.1i		−	1.33975i
$834$	16142.7	+	26521.7i	0.670236	+	1.10116i
$835$	5666.63	−	18680.4i	0.234852	−	0.774205i
$836$	−1042.38	+	12296.3i	−0.0431238	+	0.508704i
$837$	103.755	−	1053.44i	0.00428469	−	0.0435032i
$838$	−13500.8	+	3479.54i	−0.556536	+	0.143435i
$839$	23659.9	−	15809.0i	0.973575	−	0.650522i	0.0363837	−	0.999338i	$-0.488416\pi$
$839$	23659.9	−	15809.0i	0.973575	−	0.650522i	0.937191	+	0.348816i	$0.113416\pi$
$840$	1879.03	+	1074.75i	0.0771816	+	0.0441455i
$841$	−6755.70	+	10110.6i	−0.276998	+	0.414556i
$842$	14444.1	+	30009.5i	0.591182	+	1.22826i
$843$	25488.7	+	13624.0i	1.04137	+	0.556626i
$844$	−8197.30	−	19052.7i	−0.334316	−	0.777038i
$845$	−27990.0	+	2756.78i	−1.13951	+	0.112232i
$846$	−15982.3	−	7426.44i	−0.649506	−	0.301804i
$847$	−298.040	+	719.532i	−0.0120906	+	0.0291894i
$848$	2489.60	+	19751.5i	0.100817	+	0.799844i
$849$	−8958.35	−	21627.4i	−0.362132	−	0.874263i
$850$	−964.147	+	22787.7i	−0.0389058	+	0.919541i
$851$	−11466.3	−	9410.12i	−0.461879	−	0.379054i
$852$	42985.9	+	7944.07i	1.72849	+	0.319436i
$853$	15523.9	−	4709.13i	0.623129	−	0.189024i	0.0370963	−	0.999312i	$-0.488189\pi$
$853$	15523.9	−	4709.13i	0.623129	−	0.189024i	0.586032	+	0.810288i	$0.300689\pi$
$854$	41.6594	+	744.607i	0.00166927	+	0.0298360i
$855$	19172.5	−	3813.65i	0.766884	−	0.152543i
$856$	4039.15	+	1810.46i	0.161280	+	0.0722900i
$857$	−3751.76	+	18861.4i	−0.149542	+	0.751799i	0.831120	+	0.556093i	$0.187700\pi$
$857$	−3751.76	+	18861.4i	−0.149542	+	0.751799i	−0.980662	+	0.195707i	$0.937300\pi$
$858$	−5692.49	+	4282.17i	−0.226502	+	0.170385i
$859$	13414.7	−	11009.1i	0.532831	−	0.437283i	−0.329110	−	0.944292i	$-0.606749\pi$
$859$	13414.7	−	11009.1i	0.532831	−	0.437283i	0.861941	+	0.507008i	$0.169249\pi$
$860$	−46259.1	−	13348.1i	−1.83421	−	0.529261i
$861$	−1106.78	−	2070.64i	−0.0438084	−	0.0819597i
$862$	19149.9	−	2973.89i	0.756668	−	0.117507i
$863$	12791.4	−	12791.4i	0.504547	−	0.504547i	−0.408301	−	0.912848i	$-0.633878\pi$
$863$	12791.4	−	12791.4i	0.504547	−	0.504547i	0.912848	+	0.408301i	$0.133878\pi$
$864$	−7659.05	−	4243.51i	−0.301581	−	0.167092i
$865$	23937.2	+	23937.2i	0.940913	+	0.940913i
$866$	−26597.8	−	19447.2i	−1.04368	−	0.763098i
$867$	−23887.0	+	12767.8i	−0.935690	+	0.500137i
$868$	−105.072	+	131.643i	−0.00410873	+	0.00514775i
$869$	−14632.9	−	17830.3i	−0.571218	−	0.696031i
$870$	−4354.16	+	30795.3i	−0.169678	+	1.20007i
$871$	−723.704	−	143.954i	−0.0281536	−	0.00560009i
$872$	−6401.00	−	37817.8i	−0.248584	−	1.46866i
$873$	6747.78	+	33923.4i	0.261601	+	1.31516i
$874$	−12340.2	+	13802.9i	−0.477591	+	0.534199i
$875$	159.543	+	525.941i	0.00616403	+	0.0203201i
$876$	−58319.3	+	12427.6i	−2.24935	+	0.479324i
$877$	−4411.95	+	5375.98i	−0.169876	+	0.206994i	−0.850988	−	0.525184i	$-0.823996\pi$
$877$	−4411.95	+	5375.98i	−0.169876	+	0.206994i	0.681113	+	0.732179i	$0.261496\pi$
$878$	18671.5	+	20321.3i	0.717691	+	0.781105i
$879$	−6896.77	+	2856.74i	−0.264644	+	0.109619i
$880$	21203.9	−	577.104i	0.812253	−	0.0221070i
$881$	20166.5	+	8353.25i	0.771200	+	0.319442i	0.733359	−	0.679842i	$-0.237952\pi$
$881$	20166.5	+	8353.25i	0.771200	+	0.319442i	0.0378419	+	0.999284i	$0.487952\pi$
$882$	6622.85	+	18120.1i	0.252838	+	0.691763i
$883$	−1700.68	−	17267.3i	−0.0648160	−	0.658088i	−0.971622	−	0.236539i	$-0.923987\pi$
$883$	−1700.68	−	17267.3i	−0.0648160	−	0.658088i	0.906806	−	0.421548i	$-0.138513\pi$
$884$	−164.963	−	12124.4i	−0.00627638	−	0.461298i
$885$	23076.7	−	43173.5i	0.876514	−	1.63984i
$886$	2281.56	+	798.889i	0.0865129	+	0.0302926i
$887$	3274.18	+	2187.74i	0.123942	+	0.0828153i	0.615996	−	0.787749i	$-0.288754\pi$
$887$	3274.18	+	2187.74i	0.123942	+	0.0828153i	−0.492054	+	0.870565i	$0.663754\pi$
$888$	−7536.48	+	22500.4i	−0.284806	+	0.850297i
$889$	1394.31	+	2086.74i	0.0526026	+	0.0787254i
$890$	22359.4	+	13195.8i	0.842122	+	0.496994i
$891$	19766.9	+	1946.87i	0.743228	+	0.0732016i
$892$	−34848.2	+	11091.0i	−1.30808	+	0.416317i
$893$	−20198.6	−	6127.18i	−0.756910	−	0.229606i
$894$	−43949.9	−	10691.7i	−1.64419	−	0.399982i
$895$	−31527.7			−1.17749
$896$	654.972	+	1229.71i	0.0244208	+	0.0458501i
$897$	−10687.4			−0.397818
$898$	1135.48	+	276.228i	0.0421954	+	0.0102649i
$899$	−2315.82	−	702.495i	−0.0859141	−	0.0260618i
$900$	−4143.08	−	13017.7i	−0.153447	−	0.482135i
$901$	29148.5	+	2870.88i	1.07778	+	0.106152i
$902$	−19813.7	−	11693.4i	−0.731401	−	0.431650i
$903$	1518.56	+	2272.68i	0.0559628	+	0.0837543i
$904$	−11774.4	+	5865.85i	−0.433200	+	0.215813i
$905$	2654.75	+	1773.85i	0.0975105	+	0.0651544i
$906$	−38287.7	−	13406.5i	−1.40400	−	0.491611i
$907$	−18166.5	+	33987.1i	−0.665058	+	1.24424i	0.292574	+	0.956243i	$0.405488\pi$
$907$	−18166.5	+	33987.1i	−0.665058	+	1.24424i	−0.957632	+	0.287994i	$0.907012\pi$
$908$	−19579.3	+	266.395i	−0.715598	+	0.00973638i
$909$	−737.151	−	7484.42i	−0.0268974	−	0.273094i
$910$	218.237	+	597.094i	0.00794997	+	0.0217511i
$911$	−5366.75	−	2222.98i	−0.195179	−	0.0808459i	0.282953	−	0.959134i	$-0.408686\pi$
$911$	−5366.75	−	2222.98i	−0.195179	−	0.0808459i	−0.478132	+	0.878288i	$0.658686\pi$
$912$	27662.2	+	10585.9i	1.00437	+	0.384356i
$913$	−20702.3	+	8575.15i	−0.750432	+	0.310839i
$914$	−27290.1	−	29701.5i	−0.987612	−	1.07488i
$915$	17287.9	−	21065.4i	0.624613	−	0.761093i
$916$	3859.62	+	18112.2i	0.139220	+	0.653322i
$917$	599.842	+	1977.42i	0.0216015	+	0.0712105i
$918$	−8586.21	+	9603.92i	−0.308701	+	0.345290i
$919$	3850.63	+	19358.4i	0.138216	+	0.694859i	0.986295	+	0.164990i	$0.0527591\pi$
$919$	3850.63	+	19358.4i	0.138216	+	0.694859i	−0.848079	+	0.529870i	$0.822241\pi$
$920$	25943.6	+	18432.5i	0.929711	+	0.660546i
$921$	2136.46	+	424.968i	0.0764372	+	0.0152043i
$922$	−5101.85	+	36083.4i	−0.182235	+	1.28887i
$923$	8144.32	+	9923.88i	0.290437	+	0.353899i
$924$	−941.180	−	751.212i	−0.0335092	−	0.0267458i
$925$	11560.5	−	6179.20i	0.410925	−	0.219644i
$926$	−11663.5	−	8527.85i	−0.413915	−	0.302638i
$927$	−18905.6	−	18905.6i	−0.669838	−	0.669838i
$928$	−12931.1	+	15281.0i	−0.457419	+	0.540541i
$929$	−19865.9	+	19865.9i	−0.701594	+	0.701594i	−0.964753	−	0.263159i	$-0.915236\pi$
$929$	−19865.9	+	19865.9i	−0.701594	+	0.701594i	0.263159	+	0.964753i	$0.415236\pi$
$930$	6081.81	−	944.477i	0.214441	−	0.0333018i
$931$	10892.3	+	20378.1i	0.383439	+	0.717363i
$932$	−3423.21	+	11863.5i	−0.120312	+	0.416954i
$933$	53819.0	−	44168.1i	1.88848	−	1.54984i
$934$	−10833.9	+	8149.78i	−0.379546	+	0.285513i
$935$	6088.40	−	30608.4i	0.212954	−	1.07059i
$936$	2585.75	+	6786.77i	0.0902968	+	0.237000i
$937$	13961.4	−	2777.10i	0.486766	−	0.0968238i	0.0543948	−	0.998520i	$-0.482677\pi$
$937$	13961.4	−	2777.10i	0.486766	−	0.0968238i	0.432371	+	0.901696i	$0.357677\pi$
$938$	−6.96816	−	124.547i	−0.000242557	−	0.00433538i
$939$	48060.7	−	14579.0i	1.67029	−	0.506676i
$940$	−6593.36	+	35677.1i	−0.228778	+	1.23794i
$941$	−18535.2	−	15211.4i	−0.642115	−	0.526970i	0.256031	−	0.966669i	$-0.417585\pi$
$941$	−18535.2	−	15211.4i	−0.642115	−	0.526970i	−0.898145	+	0.439699i	$0.855085\pi$
$942$	1685.76	−	39843.0i	0.0583069	−	1.37809i
$943$	−13209.6	−	31890.8i	−0.456165	−	1.10128i
$944$	27373.6	−	15603.5i	0.943785	−	0.537977i
$945$	258.470	−	624.001i	0.00889738	−	0.0214802i
$946$	24289.8	+	11286.7i	0.834810	+	0.387909i
$947$	−27313.9	+	2690.18i	−0.937256	+	0.0923117i	−0.555098	−	0.831785i	$-0.687319\pi$
$947$	−27313.9	+	2690.18i	−0.937256	+	0.0923117i	−0.382158	+	0.924097i	$0.624819\pi$
$948$	−50854.3	+	21879.8i	−1.74227	+	0.749602i
$949$	−15444.1	−	8255.05i	−0.528280	−	0.282371i
$950$	−7096.00	−	14742.9i	−0.242342	−	0.503498i
$951$	25004.1	−	37421.3i	0.852591	−	1.27599i
$952$	1977.85	−	538.547i	0.0673344	−	0.0183345i
$953$	18728.2	−	12513.8i	0.636585	−	0.425353i	−0.194959	−	0.980811i	$-0.562457\pi$
$953$	18728.2	−	12513.8i	0.636585	−	0.425353i	0.831544	+	0.555459i	$0.187457\pi$
$954$	−16988.1	+	4378.32i	−0.576530	+	0.148588i
$955$	−3905.24	+	39650.6i	−0.132325	+	1.34352i
$956$	−28115.4	−	2383.40i	−0.951169	−	0.0806324i
$957$	5022.48	−	16556.9i	0.169649	−	0.559257i
$958$	−14681.3	−	24120.6i	−0.495126	−	0.813468i
$959$		−	962.183i		−	0.0323989i
$960$	12778.4	−	49281.1i	0.429606	−	1.65681i
$961$		−	29312.1i		−	0.983925i
$962$	−5952.82	+	3623.25i	−0.199508	+	0.121433i
$963$	−1132.29	+	3732.65i	−0.0378894	+	0.124904i
$964$	−27520.9	−	32619.1i	−0.919492	−	1.08983i
$965$	6001.45	−	60933.7i	0.200200	−	2.03267i
$966$	−450.915	−	1749.57i	−0.0150186	−	0.0582728i
$967$	−9552.86	+	6383.02i	−0.317683	+	0.212269i	−0.704180	−	0.710022i	$-0.748685\pi$
$967$	−9552.86	+	6383.02i	−0.317683	+	0.212269i	0.386497	+	0.922291i	$0.373685\pi$
$968$	18169.7	+	2317.36i	0.603303	+	0.0769449i
$969$	24210.0	−	36232.8i	0.802618	−	1.20120i
$970$	64160.9	−	30881.7i	2.12380	−	1.02222i
$971$	−22455.8	−	12002.9i	−0.742164	−	0.396695i	0.0565547	−	0.998399i	$-0.481988\pi$
$971$	−22455.8	−	12002.9i	−0.742164	−	0.396695i	−0.798719	+	0.601705i	$0.794488\pi$
$972$	13776.0	−	34581.6i	0.454595	−	1.14116i
$973$	−1534.05	+	151.091i	−0.0505442	+	0.00497817i
$974$	−1463.65	+	3149.89i	−0.0481503	+	0.103623i
$975$	3614.27	−	8725.63i	0.118717	−	0.286609i
$976$	16639.8	−	5546.29i	0.545723	−	0.181898i
$977$	15159.7	+	36598.7i	0.496419	+	1.19846i	0.951399	+	0.307960i	$0.0996463\pi$
$977$	15159.7	+	36598.7i	0.496419	+	1.19846i	−0.454980	+	0.890502i	$0.650354\pi$
$978$	−36856.2	−	1559.39i	−1.20504	−	0.0509853i
$979$	−11164.8	−	9162.71i	−0.364483	−	0.299123i
$980$	32720.5	−	22513.0i	1.06655	−	0.733828i
$981$	32344.6	−	9811.64i	1.05269	−	0.319329i
$982$	−12512.8	+	700.068i	−0.406618	+	0.0227496i
$983$	−34889.6	+	6939.97i	−1.13205	+	0.225179i	−0.725348	−	0.688382i	$-0.758321\pi$
$983$	−34889.6	+	6939.97i	−1.13205	+	0.225179i	−0.406702	+	0.913561i	$0.633321\pi$
$984$	−40149.7	+	37910.4i	−1.30074	+	1.22819i
$985$	−6888.97	+	34633.2i	−0.222843	+	1.12031i
$986$	17705.0	+	23536.1i	0.571847	+	0.760184i
$987$	1592.20	−	1306.68i	0.0513477	−	0.0421400i
$988$	4204.41	+	7614.85i	0.135385	+	0.245203i
$989$	18943.2	+	35440.3i	0.609059	+	1.13947i
$990$	2868.45	+	18470.9i	0.0920862	+	0.592974i
$991$	−27240.2	+	27240.2i	−0.873174	+	0.873174i	−0.992817	−	0.119643i	$-0.961825\pi$
$991$	−27240.2	+	27240.2i	−0.873174	+	0.873174i	0.119643	+	0.992817i	$0.461825\pi$
$992$	3636.58	+	1570.95i	0.116393	+	0.0502801i
$993$	15232.5	+	15232.5i	0.486796	+	0.486796i
$994$	−1280.96	+	1751.96i	−0.0408748	+	0.0559041i
$995$	−18675.8	+	9982.44i	−0.595039	+	0.318055i
$996$	5999.23	+	53446.3i	0.190856	+	1.70031i
$997$	13981.3	+	17036.3i	0.444125	+	0.541167i	0.946168	−	0.323675i	$-0.104918\pi$
$997$	13981.3	+	17036.3i	0.444125	+	0.541167i	−0.502044	+	0.864842i	$0.667418\pi$
$998$	25106.7	+	3549.86i	0.796332	+	0.112594i
$999$	7261.58	+	1444.42i	0.229976	+	0.0457451i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.k.a.5.20	✓	752
128.77	even	32	inner	128.4.k.a.77.20	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.4.k.a.5.20	✓	752	1.1	even	1	trivial
128.4.k.a.77.20	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)

\(f(q)\)	\(=\)	\(q+(-0.668572 + 2.74827i) q^{2} +(-6.55625 - 1.98882i) q^{3} +(-7.10602 - 3.67484i) q^{4} +(-14.4435 - 1.42256i) q^{5} +(9.84915 - 16.6887i) q^{6} +(0.534510 + 0.799951i) q^{7} +(14.8504 - 17.0724i) q^{8} +(16.5794 + 11.0780i) q^{9} +O(q^{10})\)	\(q+(-0.668572 + 2.74827i) q^{2} +(-6.55625 - 1.98882i) q^{3} +(-7.10602 - 3.67484i) q^{4} +(-14.4435 - 1.42256i) q^{5} +(9.84915 - 16.6887i) q^{6} +(0.534510 + 0.799951i) q^{7} +(14.8504 - 17.0724i) q^{8} +(16.5794 + 11.0780i) q^{9} +(13.5661 - 38.7437i) q^{10} +(-10.7650 + 20.1399i) q^{11} +(39.2803 + 38.2258i) q^{12} +(1.57776 + 16.0193i) q^{13} +(-2.55584 + 0.934156i) q^{14} +(91.8662 + 38.0522i) q^{15} +(36.9911 + 52.2270i) q^{16} +(86.9935 - 36.0339i) q^{17} +(-41.5299 + 38.1583i) q^{18} +(-42.8521 + 52.2154i) q^{19} +(97.4083 + 63.1864i) q^{20} +(-1.91343 - 6.30773i) q^{21} +(-48.1527 - 43.0501i) q^{22} +(-18.9060 - 95.0467i) q^{23} +(-131.317 + 82.3964i) q^{24} +(83.9935 + 16.7073i) q^{25} +(-45.0801 - 6.37391i) q^{26} +(30.6861 + 37.3911i) q^{27} +(-0.858551 - 7.64871i) q^{28} +(97.5274 - 52.1295i) q^{29} +(-165.997 + 227.033i) q^{30} +(-15.4742 - 15.4742i) q^{31} +(-168.265 + 66.7442i) q^{32} +(110.632 - 110.632i) q^{33} +(40.8696 + 263.173i) q^{34} +(-6.58223 - 12.3145i) q^{35} +(-77.1037 - 139.647i) q^{36} +(118.320 - 97.1029i) q^{37} +(-114.853 - 152.679i) q^{38} +(21.5152 - 108.164i) q^{39} +(-238.778 + 225.460i) q^{40} +(349.350 - 69.4901i) q^{41} +(18.6146 - 1.04146i) q^{42} +(-396.816 + 120.373i) q^{43} +(150.507 - 103.555i) q^{44} +(-223.706 - 183.591i) q^{45} +(273.854 + 11.5868i) q^{46} +(119.581 + 288.694i) q^{47} +(-138.653 - 415.982i) q^{48} +(130.906 - 316.036i) q^{49} +(-102.072 + 219.667i) q^{50} +(-642.016 + 63.2331i) q^{51} +(47.6566 - 119.631i) q^{52} +(274.329 + 146.632i) q^{53} +(-123.277 + 59.3352i) q^{54} +(184.134 - 275.577i) q^{55} +(21.5948 + 2.75418i) q^{56} +(384.796 - 257.112i) q^{57} +(78.0620 + 302.884i) q^{58} +(48.2557 - 489.948i) q^{59} +(-512.967 - 607.993i) q^{60} +(79.5550 - 262.258i) q^{61} +(52.8729 - 32.1817i) q^{62} +19.1840i q^{63} +(-70.9340 - 507.062i) q^{64} -233.619i q^{65} +(230.083 + 378.014i) q^{66} +(-13.3068 + 43.8665i) q^{67} +(-750.596 - 63.6294i) q^{68} +(-65.0783 + 660.751i) q^{69} +(38.2443 - 9.85666i) q^{70} +(663.138 - 443.095i) q^{71} +(435.338 - 118.538i) q^{72} +(-604.413 + 904.568i) q^{73} +(187.760 + 390.097i) q^{74} +(-517.455 - 276.585i) q^{75} +(496.391 - 213.569i) q^{76} +(-21.8649 + 2.15351i) q^{77} +(282.880 + 131.445i) q^{78} +(-386.533 + 933.172i) q^{79} +(-459.986 - 806.964i) q^{80} +(-332.850 - 803.570i) q^{81} +(-42.5880 + 1006.57i) q^{82} +(758.509 + 622.493i) q^{83} +(-9.58302 + 51.8544i) q^{84} +(-1307.75 + 396.702i) q^{85} +(-65.5174 - 1171.04i) q^{86} +(-743.090 + 147.810i) q^{87} +(183.972 + 482.868i) q^{88} +(-123.388 + 620.316i) q^{89} +(654.121 - 492.061i) q^{90} +(-11.9713 + 9.82459i) q^{91} +(-214.935 + 744.880i) q^{92} +(70.6773 + 132.228i) q^{93} +(-873.360 + 135.629i) q^{94} +(693.214 - 693.214i) q^{95} +(1235.93 - 102.943i) q^{96} +(1226.56 + 1226.56i) q^{97} +(781.032 + 571.059i) q^{98} +(-401.586 + 214.652i) 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

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