LMFDB - Embedded newform 256.2.m.a.101.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			101.14
Character	$\chi$	$=$	256.101
Dual form			256.2.m.a.109.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.399439 + 1.35663i) q^{2} +(2.51580 - 0.630174i) q^{3} +(-1.68090 - 1.08378i) q^{4} +(2.55024 + 1.20617i) q^{5} +(-0.149994 + 3.66472i) q^{6} +(-0.0344414 - 0.113538i) q^{7} +(2.14171 - 1.84745i) q^{8} +(3.28634 - 1.75659i) q^{9} +O(q^{10})$	\(q+(-0.399439 + 1.35663i) q^{2} +(2.51580 - 0.630174i) q^{3} +(-1.68090 - 1.08378i) q^{4} +(2.55024 + 1.20617i) q^{5} +(-0.149994 + 3.66472i) q^{6} +(-0.0344414 - 0.113538i) q^{7} +(2.14171 - 1.84745i) q^{8} +(3.28634 - 1.75659i) q^{9} +(-2.65500 + 2.97794i) q^{10} +(-5.03330 + 0.746619i) q^{11} +(-4.91176 - 1.66732i) q^{12} +(1.80747 - 5.05153i) q^{13} +(0.167786 - 0.00137268i) q^{14} +(7.17598 + 1.42739i) q^{15} +(1.65082 + 3.64346i) q^{16} +(-4.56733 + 0.908499i) q^{17} +(1.07035 + 5.16001i) q^{18} +(5.03822 + 4.56638i) q^{19} +(-2.97946 - 4.79136i) q^{20} +(-0.158196 - 0.263934i) q^{21} +(0.997611 - 7.12656i) q^{22} +(-3.35215 + 0.330158i) q^{23} +(4.22389 - 5.99746i) q^{24} +(1.87690 + 2.28701i) q^{25} +(6.13109 + 4.46985i) q^{26} +(1.39580 - 1.26508i) q^{27} +(-0.0651583 + 0.228173i) q^{28} +(1.45575 + 1.96285i) q^{29} +(-4.80281 + 9.16500i) q^{30} +(-5.35108 - 2.21649i) q^{31} +(-5.60223 + 0.784219i) q^{32} +(-12.1922 + 5.05019i) q^{33} +(0.591875 - 6.55908i) q^{34} +(0.0491128 - 0.331092i) q^{35} +(-7.42776 - 0.609046i) q^{36} +(0.258533 - 5.26256i) q^{37} +(-8.20735 + 5.01102i) q^{38} +(1.36387 - 13.8476i) q^{39} +(7.69023 - 2.12816i) q^{40} +(-3.74252 + 4.56028i) q^{41} +(0.421251 - 0.109188i) q^{42} +(-2.09078 + 8.34687i) q^{43} +(9.26963 + 4.20002i) q^{44} +(10.4997 - 0.515818i) q^{45} +(0.891078 - 4.67951i) q^{46} +(2.41317 + 1.61243i) q^{47} +(6.44915 + 8.12589i) q^{48} +(5.80858 - 3.88117i) q^{49} +(-3.85234 + 1.63274i) q^{50} +(-10.9180 + 5.16381i) q^{51} +(-8.51293 + 6.53220i) q^{52} +(3.76278 - 5.07352i) q^{53} +(1.15871 + 2.39890i) q^{54} +(-13.7367 - 4.16697i) q^{55} +(-0.283519 - 0.179537i) q^{56} +(15.5527 + 8.31312i) q^{57} +(-3.24435 + 1.19087i) q^{58} +(-2.43736 - 6.81196i) q^{59} +(-10.5151 - 10.1765i) q^{60} +(1.05402 - 1.75853i) q^{61} +(5.14439 - 6.37409i) q^{62} +(-0.312626 - 0.312626i) q^{63} +(1.17386 - 7.91341i) q^{64} +(10.7025 - 10.7025i) q^{65} +(-1.98119 - 18.5576i) q^{66} +(-9.27917 - 5.56172i) q^{67} +(8.66183 + 3.42291i) q^{68} +(-8.22527 + 2.94305i) q^{69} +(0.429552 + 0.198879i) q^{70} +(0.928952 - 1.73795i) q^{71} +(3.79319 - 9.83346i) q^{72} +(2.65278 - 8.74506i) q^{73} +(7.03608 + 2.45281i) q^{74} +(6.16312 + 4.57088i) q^{75} +(-3.51976 - 13.1360i) q^{76} +(0.258123 + 0.545756i) q^{77} +(18.2414 + 7.38157i) q^{78} +(-0.925099 - 1.38451i) q^{79} +(-0.184645 + 11.2829i) q^{80} +(-3.49642 + 5.23276i) q^{81} +(-4.69170 - 6.89878i) q^{82} +(-0.164961 - 3.35785i) q^{83} +(-0.0201365 + 0.615097i) q^{84} +(-12.7436 - 3.19211i) q^{85} +(-10.4885 - 6.17049i) q^{86} +(4.89930 + 4.02075i) q^{87} +(-9.40053 + 10.8978i) q^{88} +(14.3812 + 1.41642i) q^{89} +(-3.49423 + 14.4503i) q^{90} +(-0.635793 - 0.0312345i) q^{91} +(5.99244 + 3.07805i) q^{92} +(-14.8590 - 2.20412i) q^{93} +(-3.15138 + 2.62971i) q^{94} +(7.34083 + 17.7223i) q^{95} +(-13.5999 + 5.50331i) q^{96} +(-2.28341 + 5.51265i) q^{97} +(2.94514 + 9.43040i) q^{98} +(-15.2296 + 11.2951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{9}{64}\right)$	$1$

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 $

$2$	−0.399439	+	1.35663i	−0.282446	+	0.959283i
$2$	−0.399439	+	1.35663i	−0.282446	+	0.959283i
$3$	2.51580	−	0.630174i	1.45250	−	0.363831i	0.565170	−	0.824975i	$-0.308811\pi$
$3$	2.51580	−	0.630174i	1.45250	−	0.363831i	0.887326	+	0.461144i	$0.152561\pi$
$4$	−1.68090	−	1.08378i	−0.840448	−	0.541892i
$5$	2.55024	+	1.20617i	1.14050	+	0.539417i	0.902005	−	0.431726i	$-0.142095\pi$
$5$	2.55024	+	1.20617i	1.14050	+	0.539417i	0.238497	+	0.971143i	$0.423345\pi$
$6$	−0.149994	+	3.66472i	−0.0612350	+	1.49612i
$7$	−0.0344414	−	0.113538i	−0.0130176	−	0.0429133i	0.950191	−	0.311668i	$-0.100888\pi$
$7$	−0.0344414	−	0.113538i	−0.0130176	−	0.0429133i	−0.963209	+	0.268755i	$0.913388\pi$
$8$	2.14171	−	1.84745i	0.757209	−	0.653172i
$9$	3.28634	−	1.75659i	1.09545	−	0.585529i
$10$	−2.65500	+	2.97794i	−0.839585	+	0.941708i
$11$	−5.03330	+	0.746619i	−1.51760	+	0.225114i	−0.852930	−	0.522026i	$-0.825176\pi$
$11$	−5.03330	+	0.746619i	−1.51760	+	0.225114i	−0.664667	+	0.747140i	$0.731426\pi$
$12$	−4.91176	−	1.66732i	−1.41790	−	0.481314i
$13$	1.80747	−	5.05153i	0.501301	−	1.40104i	−0.378456	−	0.925619i	$-0.623545\pi$
$13$	1.80747	−	5.05153i	0.501301	−	1.40104i	0.879757	−	0.475424i	$-0.157705\pi$
$14$	0.167786	−	0.00137268i	0.0448428	−	0.000366865i
$15$	7.17598	+	1.42739i	1.85283	+	0.368551i
$16$	1.65082	+	3.64346i	0.412706	+	0.910864i
$17$	−4.56733	+	0.908499i	−1.10774	+	0.220343i	−0.714875	−	0.699252i	$-0.753516\pi$
$17$	−4.56733	+	0.908499i	−1.10774	+	0.220343i	−0.392866	+	0.919596i	$0.628516\pi$
$18$	1.07035	+	5.16001i	0.252283	+	1.21623i
$19$	5.03822	+	4.56638i	1.15585	+	1.04760i	0.998192	+	0.0601046i	$0.0191434\pi$
$19$	5.03822	+	4.56638i	1.15585	+	1.04760i	0.157655	+	0.987494i	$0.449607\pi$
$20$	−2.97946	−	4.79136i	−0.666227	−	1.07138i
$21$	−0.158196	−	0.263934i	−0.0345212	−	0.0575952i
$22$	0.997611	−	7.12656i	0.212691	−	1.51939i
$23$	−3.35215	+	0.330158i	−0.698972	+	0.0688427i	−0.441260	−	0.897379i	$-0.645468\pi$
$23$	−3.35215	+	0.330158i	−0.698972	+	0.0688427i	−0.257711	+	0.966222i	$0.582968\pi$
$24$	4.22389	−	5.99746i	0.862199	−	1.22423i
$25$	1.87690	+	2.28701i	0.375381	+	0.457403i
$26$	6.13109	+	4.46985i	1.20241	+	0.876609i
$27$	1.39580	−	1.26508i	0.268621	−	0.243464i
$28$	−0.0651583	+	0.228173i	−0.0123138	+	0.0431206i
$29$	1.45575	+	1.96285i	0.270326	+	0.364492i	0.917422	−	0.397917i	$-0.130267\pi$
$29$	1.45575	+	1.96285i	0.270326	+	0.364492i	−0.647096	+	0.762409i	$0.724017\pi$
$30$	−4.80281	+	9.16500i	−0.876870	+	1.67329i
$31$	−5.35108	−	2.21649i	−0.961083	−	0.398093i	−0.153697	−	0.988118i	$-0.549118\pi$
$31$	−5.35108	−	2.21649i	−0.961083	−	0.398093i	−0.807385	+	0.590025i	$0.799118\pi$
$32$	−5.60223	+	0.784219i	−0.990344	+	0.138632i
$33$	−12.1922	+	5.05019i	−2.12240	+	0.879126i
$34$	0.591875	−	6.55908i	0.101506	−	1.12487i
$35$	0.0491128	−	0.331092i	0.00830158	−	0.0559647i
$36$	−7.42776	−	0.609046i	−1.23796	−	0.101508i
$37$	0.258533	−	5.26256i	0.0425025	−	0.865159i	−0.879008	−	0.476806i	$-0.841794\pi$
$37$	0.258533	−	5.26256i	0.0425025	−	0.865159i	0.921511	−	0.388353i	$-0.126956\pi$
$38$	−8.20735	+	5.01102i	−1.33141	+	0.812894i
$39$	1.36387	−	13.8476i	0.218395	−	2.21740i
$40$	7.69023	−	2.12816i	1.21593	−	0.336492i
$41$	−3.74252	+	4.56028i	−0.584484	+	0.712195i	−0.978346	−	0.206974i	$-0.933639\pi$
$41$	−3.74252	+	4.56028i	−0.584484	+	0.712195i	0.393863	+	0.919169i	$0.371139\pi$
$42$	0.421251	−	0.109188i	0.0650005	−	0.0168481i
$43$	−2.09078	+	8.34687i	−0.318841	+	1.27289i	0.572632	+	0.819812i	$0.305922\pi$
$43$	−2.09078	+	8.34687i	−0.318841	+	1.27289i	−0.891474	+	0.453073i	$0.850328\pi$
$44$	9.26963	+	4.20002i	1.39745	+	0.633177i
$45$	10.4997	−	0.515818i	1.56521	−	0.0768936i
$46$	0.891078	−	4.67951i	0.131382	−	0.689956i
$47$	2.41317	+	1.61243i	0.351996	+	0.235197i	0.718980	−	0.695031i	$-0.244609\pi$
$47$	2.41317	+	1.61243i	0.351996	+	0.235197i	−0.366983	+	0.930228i	$0.619609\pi$
$48$	6.44915	+	8.12589i	0.930854	+	1.17287i
$49$	5.80858	−	3.88117i	0.829798	−	0.554453i
$50$	−3.85234	+	1.63274i	−0.544804	+	0.230905i
$51$	−10.9180	+	5.16381i	−1.52882	+	0.723078i
$52$	−8.51293	+	6.53220i	−1.18053	+	0.905853i
$53$	3.76278	−	5.07352i	0.516857	−	0.696902i	−0.465259	−	0.885174i	$-0.654039\pi$
$53$	3.76278	−	5.07352i	0.516857	−	0.696902i	0.982117	+	0.188273i	$0.0602889\pi$
$54$	1.15871	+	2.39890i	0.157680	+	0.326450i
$55$	−13.7367	−	4.16697i	−1.85225	−	0.561875i
$56$	−0.283519	−	0.179537i	−0.0378869	−	0.0239916i
$57$	15.5527	+	8.31312i	2.06001	+	1.10110i
$58$	−3.24435	+	1.19087i	−0.426003	+	0.156369i
$59$	−2.43736	−	6.81196i	−0.317317	−	0.886841i	−0.989251	−	0.146230i	$-0.953286\pi$
$59$	−2.43736	−	6.81196i	−0.317317	−	0.886841i	0.671934	−	0.740611i	$-0.265464\pi$
$60$	−10.5151	−	10.1765i	−1.35749	−	1.31378i
$61$	1.05402	−	1.75853i	0.134953	−	0.225156i	−0.782832	−	0.622233i	$-0.786226\pi$
$61$	1.05402	−	1.75853i	0.134953	−	0.225156i	0.917785	+	0.397077i	$0.129976\pi$
$62$	5.14439	−	6.37409i	0.653339	−	0.809510i
$63$	−0.312626	−	0.312626i	−0.0393871	−	0.0393871i
$64$	1.17386	−	7.91341i	0.146732	−	0.989176i
$65$	10.7025	−	10.7025i	1.32748	−	1.32748i
$66$	−1.98119	−	18.5576i	−0.243867	−	2.28429i
$67$	−9.27917	−	5.56172i	−1.13363	−	0.679473i	−0.180965	−	0.983490i	$-0.557922\pi$
$67$	−9.27917	−	5.56172i	−1.13363	−	0.679473i	−0.952667	+	0.304017i	$0.901672\pi$
$68$	8.66183	+	3.42291i	1.05040	+	0.415089i
$69$	−8.22527	+	2.94305i	−0.990206	+	0.354301i
$70$	0.429552	+	0.198879i	0.0513412	+	0.0237706i
$71$	0.928952	−	1.73795i	0.110246	−	0.206256i	−0.820748	−	0.571291i	$-0.806443\pi$
$71$	0.928952	−	1.73795i	0.110246	−	0.206256i	0.930994	+	0.365035i	$0.118943\pi$
$72$	3.79319	−	9.83346i	0.447032	−	1.15888i
$73$	2.65278	−	8.74506i	0.310485	−	1.02353i	−0.653356	−	0.757051i	$-0.726639\pi$
$73$	2.65278	−	8.74506i	0.310485	−	1.02353i	0.963840	−	0.266480i	$-0.0858607\pi$
$74$	7.03608	+	2.45281i	0.817928	+	0.285133i
$75$	6.16312	+	4.57088i	0.711656	+	0.527800i
$76$	−3.51976	−	13.1360i	−0.403744	−	1.50680i
$77$	0.258123	+	0.545756i	0.0294159	+	0.0621947i
$78$	18.2414	+	7.38157i	2.06543	+	0.835798i
$79$	−0.925099	−	1.38451i	−0.104082	−	0.155769i	0.775773	−	0.631012i	$-0.217360\pi$
$79$	−0.925099	−	1.38451i	−0.104082	−	0.155769i	−0.879855	+	0.475243i	$0.842360\pi$
$80$	−0.184645	+	11.2829i	−0.0206439	+	1.26146i
$81$	−3.49642	+	5.23276i	−0.388491	+	0.581418i
$82$	−4.69170	−	6.89878i	−0.518112	−	0.761842i
$83$	−0.164961	−	3.35785i	−0.0181068	−	0.368572i	−0.990700	−	0.136061i	$-0.956556\pi$
$83$	−0.164961	−	3.35785i	−0.0181068	−	0.368572i	0.972594	−	0.232511i	$-0.0746943\pi$
$84$	−0.0201365	+	0.615097i	−0.00219708	+	0.0671126i
$85$	−12.7436	−	3.19211i	−1.38224	−	0.346233i
$86$	−10.4885	−	6.17049i	−1.13100	−	0.665381i
$87$	4.89930	+	4.02075i	0.525260	+	0.431070i
$88$	−9.40053	+	10.8978i	−1.00210	+	1.16171i
$89$	14.3812	+	1.41642i	1.52440	+	0.150140i	0.825223	−	0.564807i	$-0.191049\pi$
$89$	14.3812	+	1.41642i	1.52440	+	0.150140i	0.699179	+	0.714947i	$0.253549\pi$
$90$	−3.49423	+	14.4503i	−0.368324	+	1.52319i
$91$	−0.635793	−	0.0312345i	−0.0666492	−	0.00327426i
$92$	5.99244	+	3.07805i	0.624755	+	0.320908i
$93$	−14.8590	−	2.20412i	−1.54081	−	0.228557i
$94$	−3.15138	+	2.62971i	−0.325040	+	0.271234i
$95$	7.34083	+	17.7223i	0.753153	+	1.81827i
$96$	−13.5999	+	5.50331i	−1.38803	+	0.561680i
$97$	−2.28341	+	5.51265i	−0.231845	+	0.559725i	−0.996394	−	0.0848411i	$-0.972962\pi$
$97$	−2.28341	+	5.51265i	−0.231845	+	0.559725i	0.764549	+	0.644566i	$0.222962\pi$
$98$	2.94514	+	9.43040i	0.297504	+	0.952614i
$99$	−15.2296	+	11.2951i	−1.53064	+	1.13520i
$100$	−0.676251	−	5.87839i	−0.0676251	−	0.587839i
$101$	7.87623	+	8.69008i	0.783714	+	0.864695i	0.993591	−	0.113033i	$-0.0360565\pi$
$101$	7.87623	+	8.69008i	0.783714	+	0.864695i	−0.209877	+	0.977728i	$0.567306\pi$
$102$	−2.64432	−	16.8743i	−0.261827	−	1.67080i
$103$	14.4075	−	11.8239i	1.41961	−	1.16504i	0.458564	−	0.888661i	$-0.348364\pi$
$103$	14.4075	−	11.8239i	1.41961	−	1.16504i	0.961047	−	0.276384i	$-0.0891360\pi$
$104$	−5.46138	−	14.1581i	−0.535532	−	1.38832i
$105$	−0.0850875	−	0.863908i	−0.00830369	−	0.0843088i
$106$	5.37989	+	7.13127i	0.522541	+	0.692650i
$107$	−8.90961	+	5.34022i	−0.861325	+	0.516258i	−0.875264	−	0.483645i	$-0.839313\pi$
$107$	−8.90961	+	5.34022i	−0.861325	+	0.516258i	0.0139397	+	0.999903i	$0.495563\pi$
$108$	−3.71726	+	0.613720i	−0.357694	+	0.0590553i
$109$	−6.88822	+	7.59998i	−0.659771	+	0.727946i	−0.975279	−	0.220977i	$-0.929075\pi$
$109$	−6.88822	+	7.59998i	−0.659771	+	0.727946i	0.315507	+	0.948923i	$0.397825\pi$
$110$	11.1400	−	16.9711i	1.06216	−	1.61813i
$111$	−2.66591	−	13.4024i	−0.253037	−	1.27210i
$112$	0.356814	−	0.312917i	0.0337158	−	0.0295679i
$113$	−2.29354	+	11.5304i	−0.215758	+	1.08469i	0.709313	+	0.704894i	$0.249005\pi$
$113$	−2.29354	+	11.5304i	−0.215758	+	1.08469i	−0.925071	+	0.379794i	$0.875995\pi$
$114$	−17.4902	+	17.7788i	−1.63811	+	1.66513i
$115$	−8.94702	−	3.20129i	−0.834313	−	0.298522i
$116$	−0.319657	−	4.87706i	−0.0296794	−	0.452824i
$117$	−2.93350	−	19.7760i	−0.271202	−	1.82830i
$118$	10.2149	−	0.585630i	0.940357	−	0.0539116i
$119$	0.260454	+	0.487276i	0.0238758	+	0.0446685i
$120$	18.0059	−	10.2002i	1.64371	−	0.931147i
$121$	14.2503	−	4.32278i	1.29548	−	0.392980i
$122$	1.96465	+	2.13234i	0.177871	+	0.193053i
$123$	−6.54165	+	13.8312i	−0.589841	+	1.24711i
$124$	6.59242	+	9.52511i	0.592016	+	0.855380i
$125$	−1.39933	−	5.58645i	−0.125160	−	0.499667i
$126$	0.548993	−	0.299243i	0.0489082	−	0.0266587i
$127$			17.9427i			1.59216i	0.605191	+	0.796081i	$0.293097\pi$
$127$			17.9427i			1.59216i	−0.605191	+	0.796081i	$0.706903\pi$
$128$	10.2667	+	4.75342i	0.907456	+	0.420147i
$129$			22.3166i			1.96486i
$130$	10.2443	+	18.7943i	0.898488	+	1.64837i
$131$	0.00584834	+	0.0233479i	0.000510972	+	0.00203992i	0.970286	−	0.241960i	$-0.0777903\pi$
$131$	0.00584834	+	0.0233479i	0.000510972	+	0.00203992i	−0.969775	+	0.244000i	$0.921540\pi$
$132$	25.9672	+	4.72491i	2.26016	+	0.411251i
$133$	0.344934	−	0.729302i	0.0299096	−	0.0632385i
$134$	11.2517	−	10.3668i	0.971997	−	0.895559i
$135$	5.08552	−	1.54268i	0.437692	−	0.132772i
$136$	−8.10350	+	10.3837i	−0.694870	+	0.890392i
$137$	−0.849221	−	1.58878i	−0.0725539	−	0.135739i	0.843029	−	0.537868i	$-0.180770\pi$
$137$	−0.849221	−	1.58878i	−0.0725539	−	0.135739i	−0.915583	+	0.402129i	$0.868270\pi$
$138$	−0.707134	−	12.3342i	−0.0601952	−	1.04996i
$139$	0.0278576	+	0.187801i	0.00236285	+	0.0159291i	0.990326	−	0.138761i	$-0.0443120\pi$
$139$	0.0278576	+	0.187801i	0.00236285	+	0.0159291i	−0.987963	+	0.154690i	$0.950562\pi$
$140$	−0.441385	+	0.503303i	−0.0373039	+	0.0425369i
$141$	7.08714	+	2.53582i	0.596845	+	0.213555i
$142$	1.98669	+	1.95445i	0.166720	+	0.164014i
$143$	−5.32595	+	26.7754i	−0.445378	+	2.23907i
$144$	11.8252	+	9.07383i	0.985435	+	0.756153i
$145$	1.34497	+	6.76162i	0.111694	+	0.561522i
$146$	10.8042	+	7.09197i	0.894161	+	0.586936i
$147$	12.1674	−	13.4246i	1.00355	−	1.10725i
$148$	−6.13804	+	8.56562i	−0.504544	+	0.704089i
$149$	−9.16424	+	5.49283i	−0.750764	+	0.449990i	−0.837636	−	0.546229i	$-0.816063\pi$
$149$	−9.16424	+	5.49283i	−0.750764	+	0.449990i	0.0868722	+	0.996219i	$0.472313\pi$
$150$	−8.66280	+	6.53529i	−0.707314	+	0.533604i
$151$	−0.662013	−	6.72153i	−0.0538739	−	0.546991i	−0.983803	−	0.179252i	$-0.942632\pi$
$151$	−0.662013	−	6.72153i	−0.0538739	−	0.546991i	0.929929	−	0.367738i	$-0.119868\pi$
$152$	19.2266	+	0.472002i	1.55948	+	0.0382844i
$153$	−13.4140	+	11.0086i	−1.08445	+	0.889989i
$154$	−0.843494	+	0.132182i	−0.0679707	+	0.0106515i
$155$	−10.9731	−	12.1069i	−0.881378	−	0.972451i
$156$	−17.3004	+	21.7983i	−1.38514	+	1.74526i
$157$	9.20252	−	6.82506i	0.734441	−	0.544699i	−0.162575	−	0.986696i	$-0.551980\pi$
$157$	9.20252	−	6.82506i	0.734441	−	0.544699i	0.897016	+	0.441997i	$0.145730\pi$
$158$	2.24779	−	0.701991i	0.178825	−	0.0558474i
$159$	6.26918	−	15.1351i	0.497179	−	1.20030i
$160$	−15.2329	−	4.75732i	−1.20427	−	0.376099i
$161$	0.152938	+	0.369225i	0.0120532	+	0.0290990i
$162$	−5.70232	−	6.83352i	−0.448016	−	0.536892i
$163$	−1.46395	−	0.217157i	−0.114666	−	0.0170091i	0.0891510	−	0.996018i	$-0.471585\pi$
$163$	−1.46395	−	0.217157i	−0.114666	−	0.0170091i	−0.203817	+	0.979009i	$0.565335\pi$
$164$	11.2331	−	3.60927i	0.877161	−	0.281836i
$165$	−37.1846	−	1.82676i	−2.89482	−	0.142213i
$166$	4.62126	+	1.11747i	0.358679	+	0.0867324i
$167$	6.84815	+	0.674484i	0.529926	+	0.0521931i	0.359442	−	0.933167i	$-0.382967\pi$
$167$	6.84815	+	0.674484i	0.529926	+	0.0521931i	0.170484	+	0.985361i	$0.445467\pi$
$168$	−0.826416	−	0.273012i	−0.0637594	−	0.0210633i
$169$	−12.2019	−	10.0138i	−0.938608	−	0.770295i
$170$	9.42081	−	16.0133i	0.722543	−	1.22817i
$171$	24.5786	+	6.15661i	1.87957	+	0.470808i
$172$	12.5606	−	11.7643i	0.957736	−	0.897016i
$173$	0.0135221	+	0.275248i	0.00102806	+	0.0209267i	0.999255	−	0.0386016i	$-0.0122903\pi$
$173$	0.0135221	+	0.275248i	0.00102806	+	0.0209267i	−0.998227	+	0.0595283i	$0.981040\pi$
$174$	−7.41165	+	5.04050i	−0.561876	+	0.382119i
$175$	0.195020	−	0.291868i	0.0147421	−	0.0220631i
$176$	−11.0294	−	17.1061i	−0.831370	−	1.28942i
$177$	−10.4246	−	15.6015i	−0.783561	−	1.17268i
$178$	−7.66597	+	18.9442i	−0.574589	+	1.41993i
$179$	6.68462	+	14.1334i	0.499632	+	1.05638i	0.983444	+	0.181211i	$0.0580017\pi$
$179$	6.68462	+	14.1334i	0.499632	+	1.05638i	−0.483812	+	0.875172i	$0.660748\pi$
$180$	−18.2080	−	10.5124i	−1.35714	−	0.783547i
$181$	6.81076	+	5.05121i	0.506240	+	0.375453i	0.818466	−	0.574555i	$-0.194825\pi$
$181$	6.81076	+	5.05121i	0.506240	+	0.375453i	−0.312226	+	0.950008i	$0.601075\pi$
$182$	0.296334	−	0.850060i	0.0219658	−	0.0630106i
$183$	1.54352	−	5.08831i	0.114100	−	0.376138i
$184$	−6.56939	+	6.90003i	−0.484302	+	0.508677i
$185$	7.00688	−	13.1089i	0.515156	−	0.963789i
$186$	8.92546	−	19.2778i	0.654446	−	1.41351i
$187$	22.3104	−	7.98280i	1.63150	−	0.583760i
$188$	−2.30876	−	5.32567i	−0.168384	−	0.388415i
$189$	−0.191708	−	0.114905i	−0.0139447	−	0.00835812i
$190$	−26.9749	+	2.87980i	−1.95696	+	0.208923i
$191$	4.92571	−	4.92571i	0.356412	−	0.356412i	−0.506077	−	0.862488i	$-0.668905\pi$
$191$	4.92571	−	4.92571i	0.356412	−	0.356412i	0.862488	+	0.506077i	$0.168905\pi$
$192$	−2.03364	−	20.6483i	−0.146765	−	1.49016i
$193$	3.45701	+	3.45701i	0.248841	+	0.248841i	0.820495	−	0.571654i	$-0.193698\pi$
$193$	3.45701	+	3.45701i	0.248841	+	0.248841i	−0.571654	+	0.820495i	$0.693698\pi$
$194$	−6.56654	−	5.29972i	−0.471450	−	0.380498i
$195$	20.1809	−	33.6697i	1.44518	−	2.41114i
$196$	−13.9700	+	0.228596i	−0.997855	+	0.0163283i
$197$	1.33415	+	3.72869i	0.0950539	+	0.265658i	0.979654	−	0.200692i	$-0.0643189\pi$
$197$	1.33415	+	3.72869i	0.0950539	+	0.265658i	−0.884601	+	0.466350i	$0.845569\pi$
$198$	−9.23993	−	25.1727i	−0.656653	−	1.78895i
$199$	17.0880	+	9.13375i	1.21134	+	0.647474i	0.948320	−	0.317316i	$-0.102782\pi$
$199$	17.0880	+	9.13375i	1.21134	+	0.647474i	0.263020	+	0.964790i	$0.415282\pi$
$200$	8.24493	+	1.43064i	0.583005	+	0.101161i
$201$	−26.8494	−	8.14466i	−1.89381	−	0.574480i
$202$	−14.9353	+	7.21397i	−1.05084	+	0.507573i
$203$	0.172720	−	0.232886i	0.0121226	−	0.0163454i
$204$	23.9484	+	3.15288i	1.67672	+	0.220746i
$205$	−15.0448	+	7.11567i	−1.05078	+	0.496980i
$206$	10.2858	+	24.2686i	0.716644	+	1.69087i
$207$	−10.4364	+	6.97336i	−0.725377	+	0.484682i
$208$	21.3888	−	1.75376i	1.48305	−	0.121601i
$209$	−28.7682	−	19.2223i	−1.98994	−	1.32963i
$210$	1.20599	+	0.229647i	0.0832214	+	0.0158471i
$211$	−17.2274	+	0.846326i	−1.18598	+	0.0582635i	−0.632474	−	0.774581i	$-0.717961\pi$
$211$	−17.2274	+	0.846326i	−1.18598	+	0.0582635i	−0.553507	+	0.832845i	$0.686711\pi$
$212$	−11.8234	+	4.45002i	−0.812037	+	0.305629i
$213$	1.24184	−	4.95772i	0.0850898	−	0.339697i
$214$	−3.68585	−	14.2202i	−0.251960	−	0.972070i
$215$	−15.3998	+	18.7647i	−1.05026	+	1.27974i
$216$	0.652229	−	5.28810i	0.0443786	−	0.359809i
$217$	−0.0673573	+	0.683890i	−0.00457251	+	0.0464255i
$218$	−7.55894	−	12.3805i	−0.511956	−	0.838513i
$219$	1.16295	−	23.6725i	0.0785852	−	1.59964i
$220$	18.5738	+	21.8918i	1.25225	+	1.47595i
$221$	−3.66599	+	24.7141i	−0.246601	+	1.66245i
$222$	19.2470	+	1.73681i	1.29178	+	0.116567i
$223$	25.5646	−	10.5892i	1.71194	−	0.709107i	0.711959	−	0.702221i	$-0.247808\pi$
$223$	25.5646	−	10.5892i	1.71194	−	0.709107i	0.999976	−	0.00688593i	$-0.00219188\pi$
$224$	0.281987	+	0.609057i	0.0188411	+	0.0406943i
$225$	10.1855	+	4.21897i	0.679033	+	0.281265i
$226$	−14.7264	−	7.71718i	−0.979583	−	0.513339i
$227$	−3.60708	−	4.86358i	−0.239410	−	0.322807i	0.667118	−	0.744952i	$-0.267528\pi$
$227$	−3.60708	−	4.86358i	−0.239410	−	0.322807i	−0.906529	+	0.422144i	$0.861278\pi$
$228$	−17.1329	−	30.8293i	−1.13466	−	2.04172i
$229$	−19.6621	+	17.8207i	−1.29931	+	1.17763i	−0.326713	+	0.945123i	$0.605941\pi$
$229$	−19.6621	+	17.8207i	−1.29931	+	1.17763i	−0.972596	+	0.232502i	$0.925309\pi$
$230$	7.91677	−	10.8591i	0.522016	−	0.716026i
$231$	0.993307	+	1.21035i	0.0653548	+	0.0796351i
$232$	6.74406	+	1.51443i	0.442769	+	0.0994275i
$233$	1.10579	−	0.108911i	0.0724429	−	0.00713501i	−0.0617307	−	0.998093i	$-0.519662\pi$
$233$	1.10579	−	0.108911i	0.0724429	−	0.00713501i	0.134174	+	0.990958i	$0.457162\pi$
$234$	28.0005	+	3.91966i	1.83045	+	0.256236i
$235$	4.20929	+	7.02277i	0.274584	+	0.458115i
$236$	−3.28575	+	14.0918i	−0.213884	+	0.917295i
$237$	−3.19984	−	2.90017i	−0.207852	−	0.188386i
$238$	−0.765090	+	0.158703i	−0.0495934	+	0.0102872i
$239$	0.382150	−	0.0760144i	0.0247192	−	0.00491696i	−0.182715	−	0.983166i	$-0.558489\pi$
$239$	0.382150	−	0.0760144i	0.0247192	−	0.00491696i	0.207434	+	0.978249i	$0.433489\pi$
$240$	6.64564	+	28.5018i	0.428974	+	1.83978i
$241$	25.0550	+	4.98376i	1.61394	+	0.321032i	0.917851	−	0.396926i	$-0.129923\pi$
$241$	25.0550	+	4.98376i	1.61394	+	0.321032i	0.696086	+	0.717958i	$0.254923\pi$
$242$	0.172287	+	21.0591i	0.0110750	+	1.35373i
$243$	−7.40261	+	20.6889i	−0.474878	+	1.32719i
$244$	−3.67756	+	1.81357i	−0.235432	+	0.116102i
$245$	19.4946	−	2.89176i	1.24547	−	0.184748i
$246$	−16.1508	−	14.3993i	−1.02974	−	0.918067i
$247$	32.1736	−	17.1972i	2.04716	−	1.09423i
$248$	−15.5553	+	5.13877i	−0.987764	+	0.326312i
$249$	−2.53104	−	8.34372i	−0.160398	−	0.528762i
$250$	8.13770	+	0.333070i	0.514673	+	0.0210652i
$251$	18.2303	+	8.62227i	1.15068	+	0.544233i	0.905124	−	0.425148i	$-0.139778\pi$
$251$	18.2303	+	8.62227i	1.15068	+	0.544233i	0.245560	+	0.969381i	$0.421028\pi$
$252$	0.186673	+	0.864310i	0.0117593	+	0.0544464i
$253$	16.6259	−	4.16456i	1.04526	−	0.261824i
$254$	−24.3417	−	7.16704i	−1.52733	−	0.449700i
$255$	−34.0719			−2.13366
$256$	−10.5496	+	12.0294i	−0.659347	+	0.751838i
$257$	4.40932			0.275046			0.137523	−	0.990499i	$-0.456086\pi$
$257$	4.40932			0.275046			0.137523	+	0.990499i	$0.456086\pi$
$258$	−30.2753	−	8.91412i	−1.88486	−	0.554969i
$259$	−0.606405	+	0.151896i	−0.0376802	+	0.00943839i
$260$	−29.5890	+	6.39059i	−1.83503	+	0.396328i
$261$	8.23200	+	3.89345i	0.509548	+	0.240998i
$262$	−0.0340105	−	0.00139203i	−0.00210118	−	8.59997e-5i
$263$	0.647409	+	2.13422i	0.0399209	+	0.131602i	0.974636	−	0.223797i	$-0.0718452\pi$
$263$	0.647409	+	2.13422i	0.0399209	+	0.131602i	−0.934715	+	0.355398i	$0.884345\pi$
$264$	−16.7823	+	33.3406i	−1.03288	+	2.05197i
$265$	15.7155	−	8.40013i	0.965398	−	0.516016i
$266$	0.851614	+	0.759261i	0.0522158	+	0.0465533i
$267$	37.0727	−	5.49921i	2.26881	−	0.336546i
$268$	9.56962	+	19.4053i	0.584558	+	1.18537i
$269$	8.01906	−	22.4118i	0.488931	−	1.36647i	−0.403373	−	0.915036i	$-0.632162\pi$
$269$	8.01906	−	22.4118i	0.488931	−	1.36647i	0.892304	−	0.451435i	$-0.149088\pi$
$270$	0.0614844	+	7.51538i	0.00374182	+	0.457372i
$271$	−0.566972	−	0.112778i	−0.0344411	−	0.00685076i	0.177840	−	0.984059i	$-0.443089\pi$
$271$	−0.566972	−	0.112778i	−0.0344411	−	0.00685076i	−0.212281	+	0.977209i	$0.568089\pi$
$272$	−10.8499	−	15.1411i	−0.657874	−	0.918065i
$273$	−1.61921	+	0.322080i	−0.0979989	+	0.0194932i
$274$	2.49460	−	0.517458i	0.150704	−	0.0312608i
$275$	−11.1545	−	10.1099i	−0.672644	−	0.609649i
$276$	17.0154	+	3.96746i	1.02421	+	0.238813i
$277$	−14.4590	−	24.1234i	−0.868757	−	1.44943i	−0.893164	−	0.449731i	$-0.851520\pi$
$277$	−14.4590	−	24.1234i	−0.868757	−	1.44943i	0.0244068	−	0.999702i	$-0.492230\pi$
$278$	−0.265904	−	0.0372225i	−0.0159479	−	0.00223246i
$279$	−21.4789	+	2.11549i	−1.28591	+	0.126651i
$280$	−0.506490	−	0.799836i	−0.0302685	−	0.0477994i
$281$	11.0383	+	13.4502i	0.658490	+	0.802373i	0.989998	−	0.141080i	$-0.0450574\pi$
$281$	11.0383	+	13.4502i	0.658490	+	0.802373i	−0.331508	+	0.943452i	$0.607557\pi$
$282$	−6.27106	+	8.60173i	−0.373436	+	0.512226i
$283$	2.74774	−	2.49041i	0.163336	−	0.148039i	−0.585799	−	0.810456i	$-0.699219\pi$
$283$	2.74774	−	2.49041i	0.163336	−	0.148039i	0.749135	+	0.662417i	$0.230469\pi$
$284$	−3.44503	+	1.91453i	−0.204425	+	0.113606i
$285$	29.6362	+	39.9598i	1.75550	+	2.36701i
$286$	−34.1969	−	17.9205i	−2.02210	−	1.05966i
$287$	0.646662	+	0.267856i	0.0381713	+	0.0158111i
$288$	−17.0333	+	12.4180i	−1.00370	+	0.731739i
$289$	4.32920	−	1.79321i	0.254659	−	0.105483i
$290$	−9.71026	−	0.876230i	−0.570206	−	0.0514540i
$291$	−2.27067	+	15.3076i	−0.133109	+	0.897350i
$292$	−13.9368	+	11.8245i	−0.815590	+	0.691976i
$293$	0.255924	−	5.20946i	0.0149513	−	0.304340i	−0.979660	−	0.200665i	$-0.935690\pi$
$293$	0.255924	−	5.20946i	0.0149513	−	0.304340i	0.994611	−	0.103675i	$-0.0330602\pi$
$294$	13.3522	+	21.8690i	0.778714	+	1.27543i
$295$	2.00056	−	20.3120i	0.116477	−	1.18261i
$296$	−9.16861	−	11.7485i	−0.532915	−	0.682868i
$297$	−6.08093	+	7.40964i	−0.352852	+	0.429951i
$298$	−3.79119	−	14.6265i	−0.219618	−	0.847293i
$299$	−4.39110	+	17.5302i	−0.253944	+	1.01380i
$300$	−5.40572	−	14.3627i	−0.312099	−	0.829229i
$301$	1.01970	−	0.0500945i	0.0587743	−	0.00288740i
$302$	9.38308	+	1.78674i	0.539935	+	0.102815i
$303$	25.2912	+	16.8991i	1.45294	+	0.970826i
$304$	−8.32018	+	25.8948i	−0.477195	+	1.48517i
$305$	4.80909	−	3.21333i	0.275368	−	0.183995i
$306$	−9.57648	−	22.5951i	−0.547451	−	1.29167i
$307$	9.17685	−	4.34033i	0.523751	−	0.247716i	−0.147347	−	0.989085i	$-0.547073\pi$
$307$	9.17685	−	4.34033i	0.523751	−	0.247716i	0.671097	+	0.741369i	$0.265823\pi$
$308$	0.157603	−	1.19711i	0.00898027	−	0.0682116i
$309$	28.7952	−	38.8258i	1.63810	−	2.20872i
$310$	20.8077	−	10.0504i	1.18180	−	0.570826i
$311$	−13.9294	−	4.22544i	−0.789865	−	0.239603i	−0.130522	−	0.991445i	$-0.541665\pi$
$311$	−13.9294	−	4.22544i	−0.789865	−	0.239603i	−0.659343	+	0.751843i	$0.729165\pi$
$312$	−22.6618	−	32.1773i	−1.28297	−	1.82168i
$313$	−26.9391	−	14.3993i	−1.52269	−	0.813894i	−0.523418	−	0.852076i	$-0.675343\pi$
$313$	−26.9391	−	14.3993i	−1.52269	−	0.813894i	−0.999271	+	0.0381821i	$0.987843\pi$
$314$	5.58323	+	15.2106i	0.315080	+	0.858385i
$315$	−0.420190	−	1.17435i	−0.0236750	−	0.0661672i
$316$	0.0544871	+	3.32982i	0.00306514	+	0.187317i
$317$	−5.80120	+	9.67873i	−0.325828	+	0.543611i	−0.976437	−	0.215801i	$-0.930764\pi$
$317$	−5.80120	+	9.67873i	−0.325828	+	0.543611i	0.650609	+	0.759413i	$0.274514\pi$
$318$	18.0287	+	14.5505i	1.01100	+	0.815954i
$319$	−8.79271	−	8.79271i	−0.492297	−	0.492297i
$320$	12.5386	−	18.7652i	0.700927	−	1.04901i
$321$	−19.0495	+	19.0495i	−1.06324	+	1.06324i
$322$	−0.561992	+	0.0599975i	−0.0313186	+	0.00334353i
$323$	−27.1598	−	16.2789i	−1.51121	−	0.905785i
$324$	11.5483	−	5.00636i	0.641572	−	0.278131i
$325$	14.9454	−	5.34754i	0.829020	−	0.296628i
$326$	0.879363	−	1.89930i	0.0487034	−	0.105193i
$327$	−12.5400	+	23.4608i	−0.693466	+	1.29738i
$328$	0.409480	+	16.6809i	0.0226097	+	0.921050i
$329$	0.0999589	−	0.329520i	0.00551091	−	0.0181670i
$330$	17.3312	−	49.7161i	0.954053	−	2.73678i
$331$	−20.4514	−	15.1678i	−1.12411	−	0.833696i	−0.136501	−	0.990640i	$-0.543586\pi$
$331$	−20.4514	−	15.1678i	−1.12411	−	0.833696i	−0.987608	+	0.156944i	$0.949836\pi$
$332$	−3.36191	+	5.82299i	−0.184509	+	0.319578i
$333$	−8.39451	−	17.7487i	−0.460016	−	0.972623i
$334$	−3.65045	+	9.02100i	−0.199744	+	0.493607i
$335$	−16.9557	−	25.3760i	−0.926390	−	1.38644i
$336$	0.700480	−	1.01209i	0.0382143	−	0.0552141i
$337$	9.70445	−	14.5237i	0.528635	−	0.791158i	−0.467023	−	0.884245i	$-0.654674\pi$
$337$	9.70445	−	14.5237i	0.528635	−	0.791158i	0.995658	+	0.0930871i	$0.0296735\pi$
$338$	18.4590	−	12.5536i	1.00404	−	0.682823i
$339$	1.49608	+	30.4534i	0.0812560	+	1.65400i
$340$	17.9611	+	19.1769i	0.974078	+	1.04001i
$341$	28.5885	+	7.16104i	1.54815	+	0.387792i
$342$	−18.1699	+	30.8849i	−0.982516	+	1.67006i
$343$	−1.28272	−	1.05270i	−0.0692606	−	0.0568407i
$344$	10.9426	+	21.7392i	0.589984	+	1.17210i
$345$	−24.5262	−	2.41562i	−1.32045	−	0.130053i
$346$	−0.378811	−	0.0916004i	−0.0203650	−	0.00492447i
$347$	−10.5503	−	0.518304i	−0.566371	−	0.0278240i	−0.236131	−	0.971721i	$-0.575880\pi$
$347$	−10.5503	−	0.518304i	−0.566371	−	0.0278240i	−0.330240	+	0.943897i	$0.607130\pi$
$348$	−3.87759	−	12.0683i	−0.207861	−	0.646926i
$349$	−25.1359	−	3.72856i	−1.34549	−	0.199585i	−0.565177	−	0.824970i	$-0.691192\pi$
$349$	−25.1359	−	3.72856i	−1.34549	−	0.199585i	−0.780317	+	0.625384i	$0.784942\pi$
$350$	0.318058	+	0.381154i	0.0170009	+	0.0203735i
$351$	−3.86772	−	9.33750i	−0.206444	−	0.498399i
$352$	27.6122	−	8.12994i	1.47173	−	0.433327i
$353$	3.98085	−	9.61062i	0.211879	−	0.511522i	−0.781833	−	0.623488i	$-0.785715\pi$
$353$	3.98085	−	9.61062i	0.211879	−	0.511522i	0.993712	+	0.111967i	$0.0357149\pi$
$354$	25.3295	−	7.91048i	1.34625	−	0.420437i
$355$	4.46532	−	3.31170i	0.236994	−	0.175767i
$356$	−22.6382	−	17.9670i	−1.19982	−	0.952247i
$357$	0.962319	+	1.06176i	0.0509313	+	0.0561940i
$358$	−21.8440	+	3.42311i	−1.15449	+	0.180917i
$359$	−14.8041	+	12.1494i	−0.781329	+	0.641220i	−0.938080	−	0.346418i	$-0.887398\pi$
$359$	−14.8041	+	12.1494i	−0.781329	+	0.641220i	0.156751	+	0.987638i	$0.449898\pi$
$360$	21.5344	−	20.5024i	1.13496	−	1.08057i
$361$	2.66954	+	27.1043i	0.140502	+	1.42654i
$362$	−9.57311	+	7.22204i	−0.503152	+	0.379582i
$363$	33.1267	−	19.8554i	1.73870	−	1.04214i
$364$	1.03485	+	0.741564i	0.0542409	+	0.0388685i
$365$	17.3133	−	19.1023i	0.906219	−	0.999859i
$366$	6.28641	+	4.12646i	0.328596	+	0.215693i
$367$	3.12216	+	15.6962i	0.162976	+	0.819333i	0.972618	+	0.232410i	$0.0746611\pi$
$367$	3.12216	+	15.6962i	0.162976	+	0.819333i	−0.809642	+	0.586923i	$0.800339\pi$
$368$	−6.73673	−	11.6684i	−0.351176	−	0.608256i
$369$	−4.28869	+	21.5607i	−0.223260	+	1.12241i
$370$	14.9852	+	14.7420i	0.779043	+	0.766399i
$371$	−0.705633	−	0.252479i	−0.0366346	−	0.0131081i
$372$	22.5876	+	19.8089i	1.17111	+	1.02704i
$373$	4.42830	+	29.8532i	0.229289	+	1.54574i	0.732011	+	0.681292i	$0.238582\pi$
$373$	4.42830	+	29.8532i	0.229289	+	1.54574i	−0.502723	+	0.864448i	$0.667668\pi$
$374$	1.91805	+	33.4557i	0.0991799	+	1.72995i
$375$	−7.04087	−	13.1725i	−0.363589	−	0.680227i
$376$	8.14718	−	1.00485i	0.420159	−	0.0518213i
$377$	12.5466	−	3.80597i	0.646183	−	0.196018i
$378$	0.232459	−	0.214179i	0.0119564	−	0.0110162i
$379$	−7.49287	+	15.8423i	−0.384883	+	0.813766i	0.614803	+	0.788681i	$0.289236\pi$
$379$	−7.49287	+	15.8423i	−0.384883	+	0.813766i	−0.999685	+	0.0250851i	$0.992014\pi$
$380$	6.86801	−	37.7453i	0.352321	−	1.93629i
$381$	11.3071	+	45.1403i	0.579278	+	2.31261i
$382$	4.71484	+	8.64989i	0.241232	+	0.442567i
$383$		−	31.3630i		−	1.60257i	−0.598280	−	0.801287i	$-0.704149\pi$
$383$		−	31.3630i		−	1.60257i	0.598280	−	0.801287i	$-0.295851\pi$
$384$	28.8244	+	5.48883i	1.47094	+	0.280101i
$385$			1.70315i			0.0868006i
$386$	−6.07075	+	3.30902i	−0.308993	+	0.168425i
$387$	7.79097	+	31.1033i	0.396037	+	1.58107i
$388$	9.81270	−	6.79146i	0.498164	−	0.344784i
$389$	12.7364	−	26.9289i	0.645761	−	1.36535i	−0.269701	−	0.962944i	$-0.586925\pi$
$389$	12.7364	−	26.9289i	0.645761	−	1.36535i	0.915462	−	0.402404i	$-0.131825\pi$
$390$	37.6164	+	40.8270i	1.90478	+	2.06736i
$391$	15.0104	−	4.55337i	0.759110	−	0.230274i
$392$	5.27004	−	19.0434i	0.266177	−	0.961838i
$393$	0.0294265	+	0.0550531i	0.00148437	+	0.00277706i
$394$	−5.59136	+	0.320559i	−0.281689	+	0.0161495i
$395$	−0.689267	−	4.64666i	−0.0346808	−	0.233799i
$396$	37.8409	−	2.48020i	1.90158	−	0.124635i
$397$	−26.5641	−	9.50480i	−1.33322	−	0.477032i	−0.428690	−	0.903452i	$-0.641025\pi$
$397$	−26.5641	−	9.50480i	−1.33322	−	0.477032i	−0.904525	+	0.426420i	$0.859775\pi$
$398$	−19.2168	+	19.5338i	−0.963250	+	0.979141i
$399$	0.408197	−	2.05214i	0.0204354	−	0.102736i
$400$	−5.23420	+	10.6139i	−0.261710	+	0.530694i
$401$	4.15857	+	20.9065i	0.207669	+	1.04402i	0.934162	+	0.356849i	$0.116149\pi$
$401$	4.15857	+	20.9065i	0.207669	+	1.04402i	−0.726493	+	0.687174i	$0.758851\pi$
$402$	21.7740	−	33.1714i	1.08599	−	1.65444i
$403$	−20.8686	+	23.0249i	−1.03954	+	1.14695i
$404$	−3.82095	−	23.1432i	−0.190099	−	1.15142i
$405$	−15.2283	+	9.12751i	−0.756701	+	0.453549i
$406$	0.246949	+	0.327341i	0.0122559	+	0.0162457i
$407$	2.62785	+	26.6810i	0.130258	+	1.32253i
$408$	−13.8432	+	31.2298i	−0.685343	+	1.54610i
$409$	0.815115	−	0.668947i	0.0403048	−	0.0330773i	−0.614025	−	0.789286i	$-0.710451\pi$
$409$	0.815115	−	0.668947i	0.0403048	−	0.0330773i	0.654330	+	0.756209i	$0.272951\pi$
$410$	−3.64384	−	23.2525i	−0.179957	−	1.14836i
$411$	−3.13768	−	3.46189i	−0.154770	−	0.170763i
$412$	−37.0321	+	4.26017i	−1.82444	+	0.209884i
$413$	−0.689470	+	0.511346i	−0.0339266	+	0.0251617i
$414$	−5.29158	−	16.9437i	−0.260067	−	0.832739i
$415$	3.62947	−	8.76231i	0.178164	−	0.430125i
$416$	−6.16434	+	29.7173i	−0.302232	+	1.45701i
$417$	0.188431	+	0.454913i	0.00922752	+	0.0222772i
$418$	37.5687	−	31.3497i	1.83755	−	1.53336i
$419$	−8.95499	−	1.32835i	−0.437480	−	0.0648940i	−0.0756420	−	0.997135i	$-0.524101\pi$
$419$	−8.95499	−	1.32835i	−0.437480	−	0.0648940i	−0.361838	+	0.932241i	$0.617851\pi$
$420$	−0.793267	+	1.54436i	−0.0387075	+	0.0753569i
$421$	−4.17364	−	0.205038i	−0.203411	−	0.00999294i	−0.0528928	−	0.998600i	$-0.516844\pi$
$421$	−4.17364	−	0.205038i	−0.203411	−	0.00999294i	−0.150518	+	0.988607i	$0.548094\pi$
$422$	5.73314	−	23.7092i	0.279085	−	1.15415i
$423$	10.7629	+	1.06005i	0.523308	+	0.0515414i
$424$	−1.31429	−	17.8176i	−0.0638274	−	0.865297i
$425$	−10.6502	−	8.74039i	−0.516610	−	0.423971i
$426$	6.22976	+	3.66503i	0.301833	+	0.177571i
$427$	−0.235961	−	0.0591053i	−0.0114190	−	0.00286030i
$428$	20.7638	+	0.679747i	1.00366	+	0.0328568i
$429$	3.47413	+	70.7176i	0.167733	+	3.41428i
$430$	−19.3055	−	28.3871i	−0.930992	−	1.36895i
$431$	−6.34073	+	9.48957i	−0.305422	+	0.457096i	−0.952153	−	0.305622i	$-0.901136\pi$
$431$	−6.34073	+	9.48957i	−0.305422	+	0.457096i	0.646731	+	0.762718i	$0.276136\pi$
$432$	6.91347	+	2.99711i	0.332624	+	0.144198i
$433$	9.54189	+	14.2804i	0.458554	+	0.686274i	0.986640	−	0.162917i	$-0.0520901\pi$
$433$	9.54189	+	14.2804i	0.458554	+	0.686274i	−0.528086	+	0.849191i	$0.677090\pi$
$434$	−0.900882	−	0.364552i	−0.0432437	−	0.0174990i
$435$	7.64467	+	16.1633i	0.366534	+	0.774971i
$436$	19.8151	−	5.30943i	0.948972	−	0.254276i
$437$	−18.3965	−	13.6438i	−0.880024	−	0.652670i
$438$	31.6503	+	11.0334i	1.51231	+	0.527197i
$439$	−1.78094	+	5.87097i	−0.0849996	+	0.280206i	−0.989129	−	0.147054i	$-0.953021\pi$
$439$	−1.78094	+	5.87097i	−0.0849996	+	0.280206i	0.904129	+	0.427260i	$0.140521\pi$
$440$	−37.1183	+	16.4534i	−1.76954	+	0.784383i
$441$	12.2714	−	22.9581i	0.584352	−	1.09324i
$442$	−32.0636	−	14.8452i	−1.52511	−	0.706114i
$443$	14.6772	−	5.25159i	0.697336	−	0.249511i	0.0357289	−	0.999362i	$-0.488625\pi$
$443$	14.6772	−	5.25159i	0.697336	−	0.249511i	0.661607	+	0.749851i	$0.269875\pi$
$444$	−10.0442	+	25.4174i	−0.476678	+	1.20626i
$445$	34.9670	+	20.9584i	1.65760	+	0.993524i
$446$	4.15414	+	38.9116i	0.196704	+	1.84252i
$447$	−19.5939	+	19.5939i	−0.926760	+	0.926760i
$448$	−0.938902	+	0.139271i	−0.0443590	+	0.00657995i
$449$	−26.5158	−	26.5158i	−1.25136	−	1.25136i	−0.955111	−	0.296248i	$-0.904264\pi$
$449$	−26.5158	−	26.5158i	−1.25136	−	1.25136i	−0.296248	−	0.955111i	$-0.595736\pi$
$450$	−9.79207	+	12.1327i	−0.461603	+	0.571942i
$451$	15.4324	−	25.7475i	0.726685	−	1.21240i
$452$	16.3517	−	16.8957i	0.769117	−	0.794706i
$453$	−5.90122	−	16.4928i	−0.277264	−	0.774900i
$454$	8.03890	−	2.95077i	0.377284	−	0.138486i
$455$	−1.58375	−	0.846532i	−0.0742473	−	0.0396860i
$456$	48.6676	−	10.9286i	2.27907	−	0.511780i
$457$	11.2458	+	3.41137i	0.526055	+	0.159577i	0.542131	−	0.840294i	$-0.317618\pi$
$457$	11.2458	+	3.41137i	0.526055	+	0.159577i	−0.0160765	+	0.999871i	$0.505118\pi$
$458$	−16.3223	−	33.7925i	−0.762691	−	1.57902i
$459$	−5.22575	+	7.04611i	−0.243917	+	0.328884i
$460$	11.5695	+	15.0777i	0.539430	+	0.703000i
$461$	5.23441	−	2.47569i	0.243791	−	0.115304i	−0.301755	−	0.953386i	$-0.597572\pi$
$461$	5.23441	−	2.47569i	0.243791	−	0.115304i	0.545546	+	0.838081i	$0.316322\pi$
$462$	−2.03876	+	0.864090i	−0.0948518	+	0.0402011i
$463$	4.34392	−	2.90252i	0.201879	−	0.134891i	−0.450522	−	0.892766i	$-0.648762\pi$
$463$	4.34392	−	2.90252i	0.201879	−	0.134891i	0.652401	+	0.757874i	$0.273762\pi$
$464$	−4.74837	+	8.54427i	−0.220438	+	0.396658i
$465$	−35.2355	−	23.5436i	−1.63401	−	1.09181i
$466$	−0.293945	+	1.54366i	−0.0136168	+	0.0715085i
$467$	25.4349	−	1.24954i	1.17699	−	0.0578217i	0.548848	−	0.835922i	$-0.315067\pi$
$467$	25.4349	−	1.24954i	1.17699	−	0.0578217i	0.628139	+	0.778101i	$0.283817\pi$
$468$	−16.5021	+	36.4208i	−0.762808	+	1.68355i
$469$	−0.311879	+	1.24509i	−0.0144013	+	0.0574930i
$470$	−11.2087	+	2.90528i	−0.517017	+	0.134010i
$471$	18.8507	−	22.9696i	0.868594	−	1.05838i
$472$	−17.8049	−	10.0863i	−0.819535	−	0.464262i
$473$	4.29159	−	43.5733i	0.197328	−	2.00350i
$474$	5.21260	−	3.18256i	0.239423	−	0.146180i
$475$	−0.987112	+	20.0931i	−0.0452918	+	0.921936i
$476$	0.0903051	−	1.10134i	0.00413913	−	0.0504797i
$477$	3.45370	−	23.2830i	0.158134	−	1.06605i
$478$	−0.0495224	+	0.548800i	−0.00226510	+	0.0251015i
$479$	−20.9818	+	8.69093i	−0.958681	+	0.397099i	−0.806487	−	0.591252i	$-0.798634\pi$
$479$	−20.9818	+	8.69093i	−0.958681	+	0.397099i	−0.152194	+	0.988351i	$0.548634\pi$
$480$	−41.3209	−	2.36904i	−1.88603	−	0.108131i
$481$	−26.1167	−	10.8179i	−1.19082	−	0.493253i
$482$	−16.7691	+	31.9997i	−0.763811	+	1.45755i
$483$	0.617437	+	0.832518i	0.0280944	+	0.0378809i
$484$	−28.6382	−	8.17810i	−1.30174	−	0.371732i
$485$	−12.4725	+	11.3044i	−0.566345	+	0.513306i
$486$	−25.1103	−	18.3066i	−1.13903	−	0.830404i
$487$	−18.3963	−	22.4159i	−0.833614	−	1.01576i	−0.999561	−	0.0296268i	$-0.990568\pi$
$487$	−18.3963	−	22.4159i	−0.833614	−	1.01576i	0.165947	−	0.986135i	$-0.446932\pi$
$488$	−0.991382	−	5.71350i	−0.0448777	−	0.258638i
$489$	−3.81985	+	0.376223i	−0.172740	+	0.0170134i
$490$	−3.86388	+	27.6021i	−0.174552	+	1.24694i
$491$	3.04403	+	5.07865i	0.137375	+	0.229196i	0.918726	−	0.394895i	$-0.129219\pi$
$491$	3.04403	+	5.07865i	0.137375	+	0.229196i	−0.781351	+	0.624092i	$0.785469\pi$
$492$	25.9858	−	16.1590i	1.17153	−	0.728504i
$493$	−8.43213	−	7.64244i	−0.379764	−	0.344198i
$494$	10.4788	+	50.5170i	0.471463	+	2.27287i
$495$	−52.4631	+	10.4356i	−2.35804	+	0.469043i
$496$	−0.758006	−	23.1555i	−0.0340355	−	1.03971i
$497$	−0.229317	−	0.0456141i	−0.0102863	−	0.00204607i
$498$	12.3303	−	0.100876i	0.552536	−	0.00452037i
$499$	1.93196	−	5.39947i	0.0864865	−	0.241714i	−0.890512	−	0.454960i	$-0.849654\pi$
$499$	1.93196	−	5.39947i	0.0864865	−	0.241714i	0.976998	+	0.213246i	$0.0684036\pi$
$500$	−3.70237	+	10.9068i	−0.165575	+	0.487767i
$501$	17.6536	−	2.61866i	0.788704	−	0.116993i
$502$	−18.9791	+	21.2877i	−0.847080	+	0.950115i
$503$	−26.8007	+	14.3253i	−1.19498	+	0.638731i	−0.944219	−	0.329317i	$-0.893181\pi$
$503$	−26.8007	+	14.3253i	−1.19498	+	0.638731i	−0.250763	+	0.968049i	$0.580681\pi$
$504$	−1.24711	−	0.0919937i	−0.0555509	−	0.00409773i
$505$	9.60453	+	31.6619i	0.427396	+	1.40894i
$506$	−0.991252	+	24.2187i	−0.0440665	+	1.07665i
$507$	−37.0079	−	17.5035i	−1.64358	−	0.777356i
$508$	19.4461	−	30.1599i	0.862780	−	1.33813i
$509$	−21.2166	+	5.31449i	−0.940411	+	0.235561i	−0.682731	−	0.730670i	$-0.739208\pi$
$509$	−21.2166	+	5.31449i	−0.940411	+	0.235561i	−0.257680	+	0.966230i	$0.582958\pi$
$510$	13.6097	−	46.2230i	0.602646	−	2.04679i
$511$	−1.08426			−0.0479649
$512$	−12.1056	−	19.1169i	−0.534995	−	0.844855i
$513$	12.8092			0.565538
$514$	−1.76126	+	5.98182i	−0.0776857	+	0.263847i
$515$	51.0042	−	12.7759i	2.24752	−	0.562973i
$516$	24.1863	−	37.5118i	1.06474	−	1.65137i
$517$	−13.3501	−	6.31410i	−0.587135	−	0.277694i
$518$	0.0361545	−	0.883341i	0.00158854	−	0.0388118i
$519$	0.207473	+	0.683946i	0.00910704	+	0.0300219i
$520$	3.14933	−	42.6940i	0.138107	−	1.87226i
$521$	−9.40835	+	5.02887i	−0.412187	+	0.220319i	−0.664438	−	0.747343i	$-0.731329\pi$
$521$	−9.40835	+	5.02887i	−0.412187	+	0.220319i	0.252251	+	0.967662i	$0.418829\pi$
$522$	−8.57016	+	9.61260i	−0.375106	+	0.420732i
$523$	39.4875	−	5.85742i	1.72667	−	0.256127i	0.791713	−	0.610893i	$-0.209189\pi$
$523$	39.4875	−	5.85742i	1.72667	−	0.256127i	0.934955	+	0.354766i	$0.115439\pi$
$524$	0.0154736	−	0.0455837i	0.000675968	−	0.00199133i
$525$	0.306703	−	0.857176i	0.0133856	−	0.0374102i
$526$	−3.15395	+	0.0258029i	−0.137519	+	0.00112506i
$527$	26.4538	+	5.26200i	1.15235	+	0.229216i
$528$	−38.5274	−	36.0849i	−1.67669	−	1.57040i
$529$	−11.4302	+	2.27360i	−0.496963	+	0.0988522i
$530$	5.11847	+	24.6755i	0.222332	+	1.07184i
$531$	−19.9758	−	18.1050i	−0.866875	−	0.785690i
$532$	−1.37020	+	0.852047i	−0.0594059	+	0.0369409i
$533$	16.2719	+	27.1480i	0.704814	+	1.17591i
$534$	−7.34789	+	52.4906i	−0.317974	+	2.27149i
$535$	−29.1629	+	2.87229i	−1.26082	+	0.124180i
$536$	−30.1483	+	5.23120i	−1.30221	+	0.225954i
$537$	25.7237	+	31.3444i	1.11006	+	1.35261i
$538$	27.2014	+	19.8311i	1.17274	+	0.854978i
$539$	−26.3386	+	23.8719i	−1.13448	+	1.02824i
$540$	−10.2202	−	2.91853i	−0.439806	−	0.125594i
$541$	−3.36619	−	4.53878i	−0.144724	−	0.195137i	0.724898	−	0.688857i	$-0.241887\pi$
$541$	−3.36619	−	4.53878i	−0.144724	−	0.195137i	−0.869621	+	0.493719i	$0.835637\pi$
$542$	0.379469	−	0.724124i	0.0162996	−	0.0311038i
$543$	20.3176	+	8.41584i	0.871913	+	0.361158i
$544$	24.8748	−	8.67141i	1.06650	−	0.371784i
$545$	−26.7335	+	11.0734i	−1.14514	+	0.474331i
$546$	0.209831	−	2.32532i	0.00897994	−	0.0995145i
$547$	3.77440	−	25.4449i	0.161382	−	1.08795i	−0.745483	−	0.666525i	$-0.767781\pi$
$547$	3.77440	−	25.4449i	0.161382	−	1.08795i	0.906865	−	0.421422i	$-0.138469\pi$
$548$	−0.294443	+	3.59095i	−0.0125780	+	0.153398i
$549$	0.374867	−	7.63060i	0.0159989	−	0.325666i
$550$	18.1710	−	11.0943i	0.774812	−	0.473063i
$551$	−1.62873	+	16.5368i	−0.0693862	+	0.704490i
$552$	−12.1790	+	21.4989i	−0.518373	+	0.915055i
$553$	−0.125333	+	0.152718i	−0.00532969	+	0.00649425i
$554$	38.5020	−	9.97970i	1.63579	−	0.423997i
$555$	9.36696	−	37.3950i	0.397605	−	1.58733i
$556$	0.156710	−	0.345865i	0.00664597	−	0.0146680i
$557$	−0.896359	+	0.0440353i	−0.0379799	+	0.00186583i	−0.0680488	−	0.997682i	$-0.521677\pi$
$557$	−0.896359	+	0.0440353i	−0.0379799	+	0.00186583i	0.0300688	+	0.999548i	$0.490427\pi$
$558$	5.70960	−	29.9840i	0.241707	−	1.26932i
$559$	38.3854	+	25.6483i	1.62353	+	1.08481i
$560$	1.28739	−	0.367634i	0.0544024	−	0.0155354i
$561$	51.0980	−	34.1426i	2.15736	−	1.44150i
$562$	−22.6561	+	9.60236i	−0.955691	+	0.405051i
$563$	8.60622	−	4.07044i	0.362709	−	0.171549i	−0.237508	−	0.971385i	$-0.576331\pi$
$563$	8.60622	−	4.07044i	0.362709	−	0.171549i	0.600217	+	0.799837i	$0.295081\pi$
$564$	−9.16447	−	11.9434i	−0.385894	−	0.502907i
$565$	−19.7567	+	26.6389i	−0.831172	+	1.12071i
$566$	2.28101	+	4.72244i	0.0958780	+	0.198499i
$567$	0.714539	+	0.216753i	0.0300078	+	0.00910277i
$568$	−1.22122	−	5.43837i	−0.0512414	−	0.228189i
$569$	−20.6475	−	11.0363i	−0.865589	−	0.462667i	−0.0220635	−	0.999757i	$-0.507024\pi$
$569$	−20.6475	−	11.0363i	−0.865589	−	0.462667i	−0.843525	+	0.537090i	$0.819524\pi$
$570$	−66.0485	+	24.2439i	−2.76647	+	1.01546i
$571$	−1.88822	−	5.27723i	−0.0790196	−	0.220845i	0.895537	−	0.444988i	$-0.146792\pi$
$571$	−1.88822	−	5.27723i	−0.0790196	−	0.220845i	−0.974556	+	0.224142i	$0.928042\pi$
$572$	37.9711	−	39.2344i	1.58765	−	1.64047i
$573$	9.28802	−	15.4961i	0.388012	−	0.647360i
$574$	−0.621685	+	0.770290i	−0.0259486	+	0.0321513i
$575$	−7.04674	−	7.04674i	−0.293869	−	0.293869i
$576$	−10.0429	−	28.0682i	−0.418454	−	1.16951i
$577$	−11.1202	+	11.1202i	−0.462941	+	0.462941i	−0.899618	−	0.436677i	$-0.856155\pi$
$577$	−11.1202	+	11.1202i	−0.462941	+	0.462941i	0.436677	+	0.899618i	$0.356155\pi$
$578$	0.703476	+	6.58941i	0.0292608	+	0.274083i
$579$	10.8756	+	6.51861i	0.451976	+	0.270904i
$580$	5.06738	−	12.8232i	0.210412	−	0.532456i
$581$	−0.375563	+	0.134378i	−0.0155810	+	0.00557496i
$582$	−19.8598	−	9.19494i	−0.823216	−	0.381143i
$583$	−15.1512	+	28.3459i	−0.627499	+	1.17397i
$584$	−10.4746	−	23.6303i	−0.433440	−	0.977828i
$585$	16.3722	−	53.9720i	0.676908	−	2.23147i
$586$	6.96509	+	2.42806i	0.287725	+	0.100302i
$587$	−36.2557	−	26.8891i	−1.49643	−	1.10983i	−0.964843	−	0.262828i	$-0.915345\pi$
$587$	−36.2557	−	26.8891i	−1.49643	−	1.10983i	−0.531590	−	0.847002i	$-0.678405\pi$
$588$	−35.0015	+	9.37861i	−1.44344	+	0.386768i
$589$	−16.8386	−	35.6022i	−0.693822	−	1.46696i
$590$	26.7568	+	10.8274i	1.10156	+	0.445758i
$591$	5.70616	+	8.53987i	0.234720	+	0.351283i
$592$	19.6007	−	7.74560i	0.805584	−	0.318342i
$593$	22.6663	−	33.9224i	0.930791	−	1.39303i	0.0112921	−	0.999936i	$-0.496406\pi$
$593$	22.6663	−	33.9224i	0.930791	−	1.39303i	0.919499	−	0.393092i	$-0.128594\pi$
$594$	−7.62318	−	11.2093i	−0.312783	−	0.459923i
$595$	0.0764819	+	1.55682i	0.00313545	+	0.0638236i
$596$	21.3572	+	0.699174i	0.874824	+	0.0286393i
$597$	48.7459	+	12.2102i	1.99504	+	0.499731i
$598$	−22.0281	−	12.9594i	−0.900796	−	0.529948i
$599$	−3.65635	−	3.00069i	−0.149394	−	0.122605i	0.556727	−	0.830695i	$-0.312057\pi$
$599$	−3.65635	−	3.00069i	−0.149394	−	0.122605i	−0.706122	+	0.708091i	$0.749557\pi$
$600$	21.6441	−	1.59655i	0.883617	−	0.0651788i
$601$	27.9262	+	2.75049i	1.13913	+	0.112195i	0.649943	−	0.759983i	$-0.274793\pi$
$601$	27.9262	+	2.75049i	1.13913	+	0.112195i	0.489189	+	0.872178i	$0.337293\pi$
$602$	−0.339347	+	1.40336i	−0.0138308	+	0.0571967i
$603$	−40.2642	−	1.97805i	−1.63969	−	0.0805526i
$604$	−6.17192	+	12.0157i	−0.251132	+	0.488911i
$605$	41.5557	+	6.16421i	1.68948	+	0.250611i
$606$	−33.0281	+	27.5607i	−1.34168	+	1.11958i
$607$	−1.59151	−	3.84226i	−0.0645976	−	0.155952i	0.888284	−	0.459294i	$-0.151898\pi$
$607$	−1.59151	−	3.84226i	−0.0645976	−	0.155952i	−0.952882	+	0.303342i	$0.901898\pi$
$608$	−31.8063	−	21.6308i	−1.28992	−	0.877246i
$609$	0.287770	−	0.694737i	0.0116610	−	0.0281522i
$610$	2.43837	+	7.80769i	0.0987265	+	0.316124i
$611$	12.5069	−	9.27578i	0.505977	−	0.375258i
$612$	34.4784	−	3.96640i	1.39371	−	0.160332i
$613$	19.3122	+	21.3078i	0.780013	+	0.860612i	0.993203	−	0.116399i	$-0.0371350\pi$
$613$	19.3122	+	21.3078i	0.780013	+	0.860612i	−0.213189	+	0.977011i	$0.568385\pi$
$614$	2.22263	+	14.1833i	0.0896979	+	0.572391i
$615$	−33.3656	+	27.3824i	−1.34543	+	1.10417i
$616$	1.56108	+	0.691982i	0.0628978	+	0.0278808i
$617$	2.57045	+	26.0982i	0.103482	+	1.05067i	0.896971	+	0.442089i	$0.145762\pi$
$617$	2.57045	+	26.0982i	0.103482	+	1.05067i	−0.793489	+	0.608585i	$0.791738\pi$
$618$	41.1703	+	54.5729i	1.65611	+	2.19525i
$619$	15.1674	−	9.09102i	0.609631	−	0.365399i	−0.175728	−	0.984439i	$-0.556228\pi$
$619$	15.1674	−	9.09102i	0.609631	−	0.365399i	0.785360	+	0.619040i	$0.212478\pi$
$620$	5.32331	+	32.2429i	0.213789	+	1.29491i
$621$	−4.26125	+	4.70156i	−0.170998	+	0.188667i
$622$	11.2963	−	17.2093i	0.452941	−	0.690029i
$623$	−0.334490	−	1.68159i	−0.0134011	−	0.0673717i
$624$	52.7048	−	17.8908i	2.10988	−	0.716205i
$625$	6.05555	−	30.4433i	0.242222	−	1.21773i
$626$	30.2950	−	30.7948i	1.21083	−	1.23081i
$627$	−84.4883	−	30.2304i	−3.37414	−	1.20729i
$628$	−22.8654	+	1.49866i	−0.912428	+	0.0598032i
$629$	3.60022	+	24.2707i	0.143550	+	0.967737i
$630$	1.76100	−	0.100960i	0.0701600	−	0.00402235i
$631$	−11.5732	−	21.6519i	−0.460720	−	0.861947i	−0.999806	−	0.0196963i	$-0.993730\pi$
$631$	−11.5732	−	21.6519i	−0.460720	−	0.861947i	0.539086	−	0.842251i	$-0.318770\pi$
$632$	−4.53911	−	1.25614i	−0.180556	−	0.0499667i
$633$	−42.8072	+	12.9854i	−1.70143	+	0.516124i
$634$	−10.8132	−	11.7362i	−0.429448	−	0.466102i
$635$	−21.6421	+	45.7583i	−0.858839	+	1.81586i
$636$	−26.9411	+	18.6462i	−1.06828	+	0.739369i
$637$	−9.10704	−	36.3573i	−0.360834	−	1.44053i
$638$	15.4406	−	8.41631i	0.611300	−	0.333205i
$639$		−	7.34328i		−	0.290496i
$640$	20.4491	+	24.5058i	0.808321	+	0.968676i
$641$			17.4972i			0.691097i	0.938401	+	0.345548i	$0.112307\pi$
$641$			17.4972i			0.691097i	−0.938401	+	0.345548i	$0.887693\pi$
$642$	−18.2340	−	33.4523i	−0.719639	−	1.32026i
$643$	1.03513	+	4.13247i	0.0408215	+	0.162969i	0.987014	−	0.160637i	$-0.0513549\pi$
$643$	1.03513	+	4.13247i	0.0408215	+	0.162969i	−0.946192	+	0.323606i	$0.895105\pi$
$644$	0.143087	−	0.786382i	0.00563843	−	0.0309878i
$645$	−26.9177	+	56.9126i	−1.05988	+	2.24093i
$646$	32.9332	−	30.3433i	1.29574	−	1.19384i
$647$	20.3285	−	6.16658i	0.799195	−	0.242433i	0.135833	−	0.990732i	$-0.456629\pi$
$647$	20.3285	−	6.16658i	0.799195	−	0.242433i	0.663362	+	0.748299i	$0.269129\pi$
$648$	2.17894	+	17.6665i	0.0855969	+	0.694006i
$649$	17.3539	+	32.4668i	0.681199	+	1.27443i
$650$	1.28487	+	22.4114i	0.0503966	+	0.879046i
$651$	0.261513	+	1.76297i	0.0102495	+	0.0690964i
$652$	2.22540	+	1.95163i	0.0871535	+	0.0764317i
$653$	−19.5360	−	6.99008i	−0.764501	−	0.273543i	−0.0743734	−	0.997230i	$-0.523696\pi$
$653$	−19.5360	−	6.99008i	−0.764501	−	0.273543i	−0.690128	+	0.723688i	$0.742446\pi$
$654$	−26.8186	−	26.3834i	−1.04869	−	1.03167i
$655$	−0.0132469	+	0.0665969i	−0.000517601	+	0.00260216i
$656$	−22.7934	−	6.10750i	−0.889933	−	0.238458i
$657$	−6.64349	−	33.3991i	−0.259187	−	1.30302i
$658$	0.407110	+	0.267231i	0.0158708	+	0.0104177i
$659$	13.7391	−	15.1588i	0.535201	−	0.590503i	−0.411984	−	0.911191i	$-0.635164\pi$
$659$	13.7391	−	15.1588i	0.535201	−	0.590503i	0.947185	+	0.320688i	$0.103914\pi$
$660$	60.5236	+	43.3706i	2.35588	+	1.68820i
$661$	−34.1405	+	20.4630i	−1.32791	+	0.795918i	−0.989424	−	0.145053i	$-0.953665\pi$
$661$	−34.1405	+	20.4630i	−1.32791	+	0.795918i	−0.338486	+	0.940972i	$0.609915\pi$
$662$	28.7461	−	21.6864i	1.11725	−	0.842864i
$663$	6.35130	+	64.4858i	0.246664	+	2.50442i
$664$	−6.55677	−	6.88680i	−0.254452	−	0.267260i
$665$	1.75933	−	1.44385i	0.0682239	−	0.0559899i
$666$	27.4315	−	4.29872i	1.06295	−	0.166572i
$667$	−5.52794	−	6.09914i	−0.214043	−	0.236160i
$668$	−10.7800	−	8.55565i	−0.417092	−	0.331028i
$669$	57.6424	−	42.7505i	2.22858	−	1.65283i
$670$	41.1987	−	12.8665i	1.59164	−	0.497075i
$671$	−3.99225	+	9.63813i	−0.154119	+	0.372076i
$672$	1.09323	+	1.35456i	0.0421724	+	0.0522533i
$673$	5.37373	+	12.9733i	0.207142	+	0.500085i	0.992971	−	0.118359i	$-0.0377633\pi$
$673$	5.37373	+	12.9733i	0.207142	+	0.500085i	−0.785829	+	0.618444i	$0.787763\pi$
$674$	15.8270	+	18.9667i	0.609634	+	0.730570i
$675$	5.51303	+	0.817780i	0.212197	+	0.0314764i
$676$	9.65729	+	30.0565i	0.371434	+	1.15602i
$677$	−28.2811	−	1.38936i	−1.08693	−	0.0533975i	−0.502297	−	0.864695i	$-0.667512\pi$
$677$	−28.2811	−	1.38936i	−1.08693	−	0.0533975i	−0.584633	+	0.811298i	$0.698762\pi$
$678$	−41.9117	−	10.1347i	−1.60961	−	0.389220i
$679$	0.704539	+	0.0693910i	0.0270377	+	0.00266298i
$680$	−33.1904	+	16.7066i	−1.27279	+	0.640669i
$681$	−12.1396	−	9.96269i	−0.465189	−	0.381771i
$682$	−21.1342	+	35.9236i	−0.809272	+	1.37559i
$683$	3.90321	+	0.977703i	0.149352	+	0.0374108i	0.316935	−	0.948447i	$-0.397346\pi$
$683$	3.90321	+	0.977703i	0.149352	+	0.0374108i	−0.167583	+	0.985858i	$0.553596\pi$
$684$	−34.6416	−	36.9865i	−1.32455	−	1.41421i
$685$	−0.249372	−	5.07608i	−0.00952801	−	0.193947i
$686$	1.94050	−	1.31969i	0.0740887	−	0.0503860i
$687$	−38.2357	+	57.2238i	−1.45878	+	2.18322i
$688$	−33.8630	+	6.16154i	−1.29101	+	0.234906i
$689$	−18.8280	−	28.1780i	−0.717288	−	1.07350i
$690$	13.0739	−	32.3082i	0.497713	−	1.22995i
$691$	−4.59934	−	9.72449i	−0.174967	−	0.369937i	0.797380	−	0.603478i	$-0.206219\pi$
$691$	−4.59934	−	9.72449i	−0.174967	−	0.369937i	−0.972347	+	0.233541i	$0.924969\pi$
$692$	0.275580	−	0.477318i	0.0104760	−	0.0181449i
$693$	1.80695	+	1.34013i	0.0686404	+	0.0509072i
$694$	4.91736	−	14.1059i	0.186661	−	0.535451i
$695$	−0.155477	+	0.512538i	−0.00589757	+	0.0194417i
$696$	17.9210	−	0.439921i	0.679295	−	0.0166752i
$697$	12.9503	−	24.2284i	0.490529	−	0.917715i
$698$	15.0985	−	32.6108i	0.571489	−	1.23434i
$699$	2.71332	−	0.970840i	0.102627	−	0.0367206i
$700$	−0.644130	+	0.279240i	−0.0243458	+	0.0105543i
$701$	−42.4703	−	25.4557i	−1.60408	−	0.961450i	−0.984264	−	0.176703i	$-0.943457\pi$
$701$	−42.4703	−	25.4557i	−1.60408	−	0.961450i	−0.619817	−	0.784746i	$-0.712793\pi$
$702$	14.2125	−	1.51730i	0.536415	−	0.0572669i
$703$	25.3334	−	25.3334i	0.955466	−	0.955466i
$704$	−6.84114e−5		40.7070i	−2.57835e−6		1.53420i
$705$	15.0153	+	15.0153i	0.565508	+	0.565508i
$706$	11.4480	+	9.23941i	0.430850	+	0.347730i
$707$	0.715386	−	1.19355i	0.0269049	−	0.0448881i
$708$	0.613995	+	37.5226i	0.0230754	+	1.41018i
$709$	12.3964	+	34.6456i	0.465556	+	1.30114i	0.913412	+	0.407036i	$0.133438\pi$
$709$	12.3964	+	34.6456i	0.465556	+	1.30114i	−0.447857	+	0.894105i	$0.647812\pi$
$710$	2.70914	+	7.38061i	0.101672	+	0.276990i
$711$	−5.47221	−	2.92495i	−0.205224	−	0.109694i
$712$	33.4171	−	23.5349i	1.25236	−	0.882009i
$713$	18.6694	+	5.66331i	0.699175	+	0.212092i
$714$	−1.82480	+	0.881405i	−0.0682914	+	0.0329857i
$715$	−45.8782	+	61.8596i	−1.71575	+	2.31342i
$716$	4.08145	−	31.0015i	0.152531	−	1.15858i
$717$	0.913510	−	0.432058i	0.0341156	−	0.0161355i
$718$	−10.5689	−	24.9366i	−0.394428	−	0.930626i
$719$	24.5937	−	16.4330i	0.917192	−	0.612848i	−0.00482900	−	0.999988i	$-0.501537\pi$
$719$	24.5937	−	16.4330i	0.917192	−	0.612848i	0.922021	+	0.387140i	$0.126537\pi$
$720$	19.2125	+	37.4037i	0.716009	+	1.39395i
$721$	−1.83868	−	1.22857i	−0.0684759	−	0.0457542i
$722$	−37.8369	−	7.20495i	−1.40814	−	0.268141i
$723$	66.1740	−	3.25092i	2.46104	−	0.120903i
$724$	−5.97377	−	15.8719i	−0.222013	−	0.589876i
$725$	−1.75676	+	7.01340i	−0.0652446	+	0.260471i
$726$	13.7043	+	52.8718i	0.508615	+	1.96226i
$727$	21.3153	−	25.9728i	0.790541	−	0.963277i	−0.209353	−	0.977840i	$-0.567136\pi$
$727$	21.3153	−	25.9728i	0.790541	−	0.963277i	0.999894	+	0.0145627i	$0.00463563\pi$
$728$	−1.41939	+	1.10770i	−0.0526060	+	0.0410541i
$729$	−3.73526	+	37.9248i	−0.138343	+	1.40462i
$730$	18.9991	+	31.1180i	0.703189	+	1.15173i
$731$	1.96617	−	40.0224i	0.0727216	−	1.48028i
$732$	−8.10912	+	6.88007i	−0.299722	+	0.254295i
$733$	3.92913	−	26.4880i	0.145126	−	0.978357i	−0.787190	−	0.616711i	$-0.788465\pi$
$733$	3.92913	−	26.4880i	0.145126	−	0.978357i	0.932315	−	0.361646i	$-0.117785\pi$
$734$	−22.5410	−	2.03405i	−0.832004	−	0.0750781i
$735$	47.2222	−	19.5601i	1.74182	−	0.721485i
$736$	18.5206	−	4.47844i	0.682679	−	0.165077i
$737$	50.8573	+	21.0658i	1.87335	+	0.775969i
$738$	−27.5368	−	14.4304i	−1.01365	−	0.531189i
$739$	0.115482	+	0.155709i	0.00424807	+	0.00572786i	0.805326	−	0.592832i	$-0.201990\pi$
$739$	0.115482	+	0.155709i	0.00424807	+	0.00572786i	−0.801078	+	0.598559i	$0.795740\pi$
$740$	−25.9851	+	14.4408i	−0.955232	+	0.530856i
$741$	70.1050	−	63.5395i	2.57537	−	2.33418i
$742$	0.624379	−	0.856433i	0.0229217	−	0.0314407i
$743$	2.42834	+	2.95894i	0.0890871	+	0.108553i	0.815646	−	0.578551i	$-0.196382\pi$
$743$	2.42834	+	2.95894i	0.0890871	+	0.108553i	−0.726559	+	0.687104i	$0.758882\pi$
$744$	−35.8957	+	22.7307i	−1.31600	+	0.833346i
$745$	−29.9963	+	2.95438i	−1.09898	+	0.108240i
$746$	−42.2686	−	5.91697i	−1.54756	−	0.216636i
$747$	−6.44048	−	10.7453i	−0.235645	−	0.393150i
$748$	−46.1532	−	10.7614i	−1.68753	−	0.393477i
$749$	0.913177	+	0.827656i	0.0333668	+	0.0302419i
$750$	20.6827	−	4.29023i	0.755224	−	0.156657i
$751$	15.5005	−	3.08325i	0.565623	−	0.112509i	0.0960077	−	0.995381i	$-0.469393\pi$
$751$	15.5005	−	3.08325i	0.565623	−	0.112509i	0.469615	+	0.882871i	$0.344393\pi$
$752$	−1.89109	+	11.4541i	−0.0689611	+	0.417688i
$753$	51.2972	+	10.2036i	1.86937	+	0.371841i
$754$	0.151689	+	18.5414i	0.00552421	+	0.675237i
$755$	6.41904	−	17.9400i	0.233613	−	0.652904i
$756$	0.197708	+	0.400913i	0.00719058	+	0.0145811i
$757$	22.2967	−	3.30741i	0.810389	−	0.120210i	0.271339	−	0.962484i	$-0.412533\pi$
$757$	22.2967	−	3.30741i	0.810389	−	0.120210i	0.539050	+	0.842274i	$0.318783\pi$
$758$	−18.4993	−	16.4931i	−0.671923	−	0.599057i
$759$	39.2029	−	20.9544i	1.42297	−	0.760596i
$760$	48.4631	+	24.3943i	1.75794	+	0.884874i
$761$	8.41461	+	27.7392i	0.305029	+	1.00555i	0.966734	+	0.255783i	$0.0823331\pi$
$761$	8.41461	+	27.7392i	0.305029	+	1.00555i	−0.661705	+	0.749764i	$0.730167\pi$
$762$	−65.7552	−	2.69131i	−2.38206	−	0.0974959i
$763$	1.10013	+	0.520321i	0.0398272	+	0.0188369i
$764$	−13.6180	+	2.94120i	−0.492682	+	0.106409i
$765$	−47.4871	+	11.8949i	−1.71690	+	0.430061i
$766$	42.5480	+	12.5276i	1.53732	+	0.452641i
$767$	−38.8162			−1.40157
$768$	−18.9599	+	36.9116i	−0.684157	+	1.33193i
$769$	3.82715			0.138011			0.0690053	−	0.997616i	$-0.478017\pi$
$769$	3.82715			0.138011			0.0690053	+	0.997616i	$0.478017\pi$
$770$	−2.31055	−	0.680306i	−0.0832664	−	0.0245165i
$771$	11.0929	−	2.77864i	0.399503	−	0.100070i
$772$	−2.06422	−	9.55752i	−0.0742929	−	0.343983i
$773$	10.6441	+	5.03427i	0.382840	+	0.181070i	0.609280	−	0.792955i	$-0.291459\pi$
$773$	10.6441	+	5.03427i	0.382840	+	0.181070i	−0.226440	+	0.974025i	$0.572709\pi$
$774$	−45.3077	−	1.85441i	−1.62855	−	0.0666555i
$775$	−4.97432	−	16.3981i	−0.178683	−	0.589039i
$776$	5.29393	+	16.0250i	0.190041	+	0.575264i
$777$	−1.42987	+	0.764281i	−0.0512963	+	0.0274184i
$778$	31.4451	+	28.0351i	1.12736	+	1.00511i
$779$	−39.6796	+	5.88591i	−1.42167	+	0.210885i
$780$	−70.4127	+	34.7236i	−2.52118	+	1.24331i
$781$	−3.37811	+	9.44118i	−0.120878	+	0.337832i
$782$	0.181477	+	22.1824i	0.00648962	+	0.793242i
$783$	4.51508	+	0.898106i	0.161356	+	0.0320957i
$784$	23.7298	+	14.7562i	0.847494	+	0.527007i
$785$	31.7009	−	6.30569i	1.13145	−	0.225060i
$786$	−0.0864408	+	0.0179305i	−0.00308324	+	0.000639560i
$787$	26.6100	+	24.1179i	0.948544	+	0.859710i	0.990233	−	0.139420i	$-0.0445239\pi$
$787$	26.6100	+	24.1179i	0.948544	+	0.859710i	−0.0416890	+	0.999131i	$0.513274\pi$
$788$	1.79853	−	7.71346i	0.0640700	−	0.274781i
$789$	2.97368	+	4.96128i	0.105866	+	0.176626i
$790$	6.57913	+	0.920979i	0.234075	+	0.0327670i
$791$	1.38813	−	0.136719i	0.0493562	−	0.00486117i
$792$	−11.7504	+	52.3268i	−0.417533	+	1.85935i
$793$	−6.97814	−	8.50289i	−0.247801	−	0.301946i
$794$	23.5053	−	32.2411i	0.834171	−	1.14419i
$795$	34.2435	−	31.0365i	1.21449	−	1.10075i
$796$	−18.8242	−	33.8726i	−0.667207	−	1.20058i
$797$	13.1118	+	17.6792i	0.464443	+	0.626229i	0.971885	−	0.235457i	$-0.0756587\pi$
$797$	13.1118	+	17.6792i	0.464443	+	0.626229i	−0.507442	+	0.861686i	$0.669409\pi$
$798$	2.62095	+	1.37348i	0.0927807	+	0.0486206i
$799$	−12.4866	−	5.17213i	−0.441745	−	0.182977i
$800$	−12.3084	−	11.3405i	−0.435167	−	0.400947i
$801$	49.7496	−	20.6069i	1.75781	−	0.728110i
$802$	−30.0236	−	2.70925i	−1.06017	−	0.0956671i
$803$	−6.82302	+	45.9971i	−0.240779	+	1.62320i
$804$	36.3039	+	42.7892i	1.28034	+	1.50906i
$805$	−0.0553209	+	1.12608i	−0.00194981	+	0.0396892i
$806$	−22.9006	−	37.5080i	−0.806639	−	1.32116i
$807$	6.05100	−	61.4369i	0.213005	−	2.16268i
$808$	32.9231	+	4.06070i	1.15823	+	0.142855i
$809$	−9.68441	+	11.8005i	−0.340486	+	0.414883i	−0.914899	−	0.403682i	$-0.867730\pi$
$809$	−9.68441	+	11.8005i	−0.340486	+	0.414883i	0.574414	+	0.818565i	$0.305230\pi$
$810$	−6.29986	−	24.3051i	−0.221355	−	0.853994i
$811$	1.21491	−	4.85020i	0.0426613	−	0.170314i	−0.944956	−	0.327199i	$-0.893895\pi$
$811$	1.21491	−	4.85020i	0.0426613	−	0.170314i	0.987617	+	0.156885i	$0.0501453\pi$
$812$	−0.542723	+	0.204266i	−0.0190458	+	0.00716833i
$813$	−1.49746	+	0.0735653i	−0.0525181	+	0.00258005i
$814$	−37.2460	−	7.09243i	−1.30547	−	0.248590i
$815$	−3.47150	−	2.31959i	−0.121602	−	0.0812515i
$816$	−36.8378	−	31.2546i	−1.28958	−	1.09413i
$817$	−48.6488	+	32.5061i	−1.70200	+	1.13724i
$818$	0.581926	+	1.37301i	0.0203466	+	0.0480063i
$819$	−2.14430	+	1.01418i	−0.0749279	+	0.0354382i
$820$	33.0006	+	4.34463i	1.15243	+	0.151721i
$821$	−10.6607	+	14.3743i	−0.372061	+	0.501666i	−0.949067	−	0.315074i	$-0.897971\pi$
$821$	−10.6607	+	14.3743i	−0.372061	+	0.501666i	0.577006	+	0.816740i	$0.304221\pi$
$822$	5.94982	−	2.87385i	0.207524	−	0.100237i
$823$	9.79084	+	2.97002i	0.341287	+	0.103528i	0.456276	−	0.889838i	$-0.349183\pi$
$823$	9.79084	+	2.97002i	0.341287	+	0.103528i	−0.114988	+	0.993367i	$0.536683\pi$
$824$	9.01258	−	51.9405i	0.313968	−	1.80943i
$825$	−34.4335	−	18.4051i	−1.19882	−	0.640784i
$826$	−0.418306	−	1.13961i	−0.0145547	−	0.0396520i
$827$	13.4057	+	37.4663i	0.466161	+	1.30283i	0.912906	+	0.408171i	$0.133833\pi$
$827$	13.4057	+	37.4663i	0.466161	+	1.30283i	−0.446745	+	0.894661i	$0.647417\pi$
$828$	25.1001	−	0.410721i	0.872287	−	0.0142736i
$829$	−7.10176	+	11.8486i	−0.246654	+	0.411518i	−0.956011	−	0.293332i	$-0.905236\pi$
$829$	−7.10176	+	11.8486i	−0.246654	+	0.411518i	0.709356	+	0.704850i	$0.248986\pi$
$830$	10.4375	+	8.42386i	0.362290	+	0.292396i
$831$	−51.5778	−	51.5778i	−1.78921	−	1.78921i
$832$	−37.8531	−	20.2330i	−1.31232	−	0.701453i
$833$	−23.0037	+	23.0037i	−0.797031	+	0.797031i
$834$	−0.692416	+	0.0739214i	−0.0239764	+	0.00255969i
$835$	16.6509	+	9.98016i	0.576228	+	0.345378i
$836$	27.5236	+	63.4892i	0.951922	+	2.19582i
$837$	−10.2731	+	3.67576i	−0.355089	+	0.127053i
$838$	5.37905	−	11.6180i	0.185816	−	0.401338i
$839$	12.3809	−	23.1630i	0.427435	−	0.799675i	−0.572358	−	0.820004i	$-0.693971\pi$
$839$	12.3809	−	23.1630i	0.427435	−	0.799675i	0.999793	+	0.0203286i	$0.00647125\pi$
$840$	−1.77826	−	1.69305i	−0.0613558	−	0.0584157i
$841$	6.68468	−	22.0364i	0.230506	−	0.759877i
$842$	1.94528	−	5.58019i	0.0670387	−	0.192306i
$843$	36.2461	+	26.8819i	1.24838	+	0.925863i
$844$	29.8747	+	17.2482i	1.02833	+	0.593706i
$845$	−19.0393	−	40.2553i	−0.654973	−	1.38482i
$846$	−5.73721	+	14.1778i	−0.197249	+	0.487443i
$847$	−0.981600	−	1.46907i	−0.0337282	−	0.0504778i
$848$	24.6968	+	5.33404i	0.848093	+	0.183172i
$849$	5.34337	−	7.99692i	0.183384	−	0.274453i
$850$	16.1116	−	10.9571i	0.552623	−	0.375826i
$851$	0.870834	+	17.7262i	0.0298518	+	0.607648i
$852$	−7.46051	+	6.98752i	−0.255593	+	0.239389i
$853$	−5.50014	−	1.37771i	−0.188321	−	0.0471720i	0.147672	−	0.989036i	$-0.452822\pi$
$853$	−5.50014	−	1.37771i	−0.188321	−	0.0471720i	−0.335993	+	0.941864i	$0.609072\pi$
$854$	0.174436	−	0.296504i	0.00596909	−	0.0101461i
$855$	55.2553	+	45.3469i	1.88969	+	1.55083i
$856$	−9.21604	+	27.8973i	−0.314998	+	0.953509i
$857$	−2.69985	−	0.265912i	−0.0922251	−	0.00908338i	0.0517993	−	0.998658i	$-0.483504\pi$
$857$	−2.69985	−	0.265912i	−0.0922251	−	0.00908338i	−0.144024	+	0.989574i	$0.546004\pi$
$858$	−97.3254	−	23.5343i	−3.32263	−	0.803447i
$859$	−8.60969	−	0.422967i	−0.293759	−	0.0144315i	−0.0983453	−	0.995152i	$-0.531355\pi$
$859$	−8.60969	−	0.422967i	−0.293759	−	0.0144315i	−0.195414	+	0.980721i	$0.562605\pi$
$860$	46.2223	−	14.8514i	1.57617	−	0.506430i
$861$	1.79567	+	0.266362i	0.0611961	+	0.00907759i
$862$	−10.3411	−	12.3925i	−0.352219	−	0.422091i
$863$	6.23768	+	15.0591i	0.212333	+	0.512617i	0.993781	−	0.111353i	$-0.0355185\pi$
$863$	6.23768	+	15.0591i	0.212333	+	0.512617i	−0.781448	+	0.623971i	$0.785518\pi$
$864$	−6.82748	+	8.18187i	−0.232276	+	0.278353i
$865$	−0.297512	+	0.718258i	−0.0101157	+	0.0244215i
$866$	−23.1847	+	7.24065i	−0.787848	+	0.246047i
$867$	9.76135	−	7.23951i	0.331513	−	0.245867i
$868$	0.854410	−	1.07655i	0.0290006	−	0.0365404i
$869$	5.69000	+	6.27795i	0.193020	+	0.212965i
$870$	−24.9812	+	3.91474i	−0.846942	+	0.132722i
$871$	−44.8670	+	36.8214i	−1.52026	+	1.24765i
$872$	−0.711998	+	29.0026i	−0.0241113	+	0.982152i
$873$	2.17937	+	22.1275i	0.0737603	+	0.748901i
$874$	25.8579	−	19.5074i	0.874655	−	0.659848i
$875$	−0.586079	+	0.351282i	−0.0198131	+	0.0118755i
$876$	−27.6107	+	38.5306i	−0.932878	+	1.30183i
$877$	−19.4682	+	21.4799i	−0.657396	+	0.725325i	−0.974828	−	0.222956i	$-0.928429\pi$
$877$	−19.4682	+	21.4799i	−0.657396	+	0.725325i	0.317433	+	0.948281i	$0.397179\pi$
$878$	−7.25337	−	4.76118i	−0.244789	−	0.160682i
$879$	−2.63901	−	13.2672i	−0.0890117	−	0.447492i
$880$	−7.49464	−	56.9279i	−0.252644	−	1.91904i
$881$	1.43834	−	7.23103i	0.0484589	−	0.243619i	−0.948962	−	0.315390i	$-0.897865\pi$
$881$	1.43834	−	7.23103i	0.0484589	−	0.243619i	0.997421	+	0.0717701i	$0.0228648\pi$
$882$	26.2441	+	25.8181i	0.883683	+	0.869342i
$883$	11.7549	+	4.20599i	0.395586	+	0.141543i	0.527165	−	0.849763i	$-0.323255\pi$
$883$	11.7549	+	4.20599i	0.395586	+	0.141543i	−0.131580	+	0.991306i	$0.542005\pi$
$884$	32.9469	−	37.5687i	1.10812	−	1.26357i
$885$	−7.76710	−	52.3615i	−0.261088	−	1.76011i
$886$	1.26181	+	22.0093i	0.0423915	+	0.739416i
$887$	7.95086	+	14.8750i	0.266964	+	0.499454i	0.979308	−	0.202376i	$-0.0648664\pi$
$887$	7.95086	+	14.8750i	0.266964	+	0.499454i	−0.712344	+	0.701831i	$0.752366\pi$
$888$	−30.4699	−	23.7790i	−1.02250	−	0.797972i
$889$	2.03718	−	0.617973i	0.0683250	−	0.0207262i
$890$	−42.4000	+	39.0657i	−1.42125	+	1.30949i
$891$	13.6916	−	28.9485i	0.458687	−	0.969812i
$892$	−54.4480	−	9.90717i	−1.82305	−	0.331717i
$893$	4.79512	+	19.1432i	0.160463	+	0.640602i
$894$	−18.7551	−	34.4083i	−0.627265	−	1.15079i
$895$			44.1065i			1.47432i
$896$	0.186095	−	1.32937i	0.00621699	−	0.0444113i
$897$			46.8697i			1.56493i
$898$	46.5637	−	25.3807i	1.55385	−	0.846966i
$899$	−3.43919	−	13.7300i	−0.114703	−	0.457922i
$900$	−12.5483	−	18.1305i	−0.418277	−	0.604351i
$901$	−12.5766	+	26.5909i	−0.418987	+	0.885873i
$902$	28.7655	+	31.2207i	0.957786	+	1.03953i
$903$	2.53378	−	0.768613i	0.0843189	−	0.0255778i
$904$	16.3897	+	28.9320i	0.545114	+	0.962263i
$905$	11.2764	+	21.0968i	0.374842	+	0.701280i
$906$	24.7319	−	1.41790i	0.821661	−	0.0471067i
$907$	6.33188	+	42.6861i	0.210247	+	1.41737i	0.795223	+	0.606317i	$0.207354\pi$
$907$	6.33188	+	42.6861i	0.210247	+	1.41737i	−0.584977	+	0.811050i	$0.698896\pi$
$908$	0.792051	+	12.0845i	0.0262851	+	0.401037i
$909$	41.1489	+	14.7233i	1.36482	+	0.488341i
$910$	1.78104	−	1.81043i	0.0590410	−	0.0600150i
$911$	1.56857	−	7.88574i	0.0519691	−	0.261266i	−0.946062	−	0.323985i	$-0.894977\pi$
$911$	1.56857	−	7.88574i	0.0519691	−	0.261266i	0.998031	+	0.0627190i	$0.0199772\pi$
$912$	−4.61363	+	70.3893i	−0.152773	+	2.33082i
$913$	3.33734	+	16.7779i	0.110450	+	0.555268i
$914$	−9.11997	+	13.8937i	−0.301662	+	0.459563i
$915$	10.0737	−	11.1146i	0.333027	−	0.367439i
$916$	52.3638	−	8.64526i	1.73015	−	0.285648i
$917$	0.00244945	−	0.00146814i	8.08879e−5	−	4.84824e-5i
$918$	−7.47160	−	9.90391i	−0.246600	−	0.326878i
$919$	−4.95627	−	50.3219i	−0.163492	−	1.65996i	−0.630856	−	0.775900i	$-0.717296\pi$
$919$	−4.95627	−	50.3219i	−0.163492	−	1.65996i	0.467364	−	0.884065i	$-0.345204\pi$
$920$	−25.0762	+	9.67292i	−0.826736	+	0.318907i
$921$	20.3519	−	16.7024i	0.670619	−	0.550362i
$922$	1.26777	+	8.09005i	0.0417518	+	0.266432i
$923$	−7.10024	−	7.83391i	−0.233707	−	0.257856i
$924$	−0.357890	−	3.11100i	−0.0117737	−	0.102344i
$925$	12.5208	−	9.28605i	0.411681	−	0.305323i
$926$	2.20251	+	7.05248i	0.0723790	+	0.231759i
$927$	26.5782	−	64.1654i	0.872943	−	2.10747i
$928$	−9.69474	−	9.85471i	−0.318245	−	0.323497i
$929$	−17.7031	−	42.7390i	−0.580820	−	1.40222i	−0.892071	−	0.451895i	$-0.850748\pi$
$929$	−17.7031	−	42.7390i	−0.580820	−	1.40222i	0.311251	−	0.950328i	$-0.399252\pi$
$930$	46.0144	−	38.3973i	1.50887	−	1.25910i
$931$	46.9878	+	6.96998i	1.53996	+	0.228432i
$932$	−1.97676	−	1.01537i	−0.0647509	−	0.0332597i
$933$	−37.7063	−	1.85239i	−1.23445	−	0.0606446i
$934$	−8.46454	+	35.0049i	−0.276968	+	1.14540i
$935$	66.5256	+	6.55220i	2.17562	+	0.214280i
$936$	−42.8180	−	36.9351i	−1.39955	−	1.20726i
$937$	17.0489	+	13.9916i	0.556962	+	0.457087i	0.870277	−	0.492562i	$-0.163940\pi$
$937$	17.0489	+	13.9916i	0.556962	+	0.457087i	−0.313315	+	0.949649i	$0.601440\pi$
$938$	−1.56455	−	0.920445i	−0.0510845	−	0.0300536i
$939$	−76.8473	−	19.2493i	−2.50782	−	0.628176i
$940$	0.535793	−	16.3665i	0.0174756	−	0.533817i
$941$	−2.71796	−	55.3254i	−0.0886030	−	1.80356i	−0.473706	−	0.880683i	$-0.657084\pi$
$941$	−2.71796	−	55.3254i	−0.0886030	−	1.80356i	0.385103	−	0.922873i	$-0.374166\pi$
$942$	23.6316	+	34.7484i	0.769960	+	1.13216i
$943$	11.0399	−	16.5224i	0.359508	−	0.538042i
$944$	20.7954	−	20.1257i	0.676833	−	0.655037i
$945$	−0.350305	−	0.524268i	−0.0113954	−	0.0170544i
$946$	57.3986	+	23.2270i	1.86619	+	0.755175i
$947$	−15.1495	−	32.0310i	−0.492294	−	1.04087i	−0.985299	−	0.170841i	$-0.945352\pi$
$947$	−15.1495	−	32.0310i	−0.492294	−	1.04087i	0.493005	−	0.870027i	$-0.335898\pi$
$948$	2.23545	+	8.34282i	0.0726039	+	0.270962i
$949$	−39.3811	−	29.2070i	−1.27836	−	0.948100i
$950$	−26.8647	−	9.36514i	−0.871605	−	0.303845i
$951$	−8.49536	+	28.0055i	−0.275481	+	0.908139i
$952$	1.45804	+	0.562428i	0.0472552	+	0.0182284i
$953$	8.65348	−	16.1895i	0.280314	−	0.524430i	−0.701881	−	0.712294i	$-0.747656\pi$
$953$	8.65348	−	16.1895i	0.280314	−	0.524430i	0.982195	+	0.187864i	$0.0601563\pi$
$954$	30.2069	+	13.9855i	0.977984	+	0.452799i
$955$	18.5030	−	6.62048i	0.598743	−	0.214234i
$956$	−0.724738	−	0.286396i	−0.0234397	−	0.00926271i
$957$	−27.6616	−	16.5797i	−0.894173	−	0.535947i
$958$	−3.40944	−	31.9360i	−0.110154	−	1.03181i
$959$	−0.151139	+	0.151139i	−0.00488052	+	0.00488052i
$960$	19.7191	−	55.1109i	0.636432	−	1.77870i
$961$	1.80093	+	1.80093i	0.0580946	+	0.0580946i
$962$	25.1079	−	31.1096i	0.809512	−	1.00301i
$963$	−19.8995	+	33.2003i	−0.641252	+	1.06986i
$964$	−36.7136	−	35.5314i	−1.18247	−	1.14439i
$965$	4.64645	+	12.9859i	0.149574	+	0.418032i
$966$	−1.37605	+	0.505094i	−0.0442736	+	0.0162511i
$967$	21.7714	+	11.6370i	0.700119	+	0.374222i	0.782731	−	0.622360i	$-0.213826\pi$
$967$	21.7714	+	11.6370i	0.700119	+	0.374222i	−0.0826115	+	0.996582i	$0.526326\pi$
$968$	22.5339	−	35.5849i	0.724267	−	1.14374i
$969$	−78.5870	−	23.8391i	−2.52458	−	0.765823i
$970$	−10.3539	−	21.4359i	−0.332443	−	0.688267i
$971$	−21.3901	+	28.8412i	−0.686441	+	0.925558i	−0.999709	−	0.0241064i	$-0.992326\pi$
$971$	−21.3901	+	28.8412i	−0.686441	+	0.925558i	0.313269	+	0.949665i	$0.398576\pi$
$972$	34.8653	−	26.7531i	1.11831	−	0.858106i
$973$	0.0203631	−	0.00963102i	0.000652810	−	0.000308756i
$974$	37.7583	−	16.0031i	1.20985	−	0.512774i
$975$	34.2296	−	22.8715i	1.09622	−	0.732474i
$976$	8.14711	+	0.937259i	0.260783	+	0.0300009i
$977$	27.2487	+	18.2070i	0.871763	+	0.582493i	0.908992	−	0.416814i	$-0.136853\pi$
$977$	27.2487	+	18.2070i	0.871763	+	0.582493i	−0.0372293	+	0.999307i	$0.511853\pi$
$978$	1.01541	−	5.33241i	0.0324691	−	0.170512i
$979$	−73.4423	+	3.60799i	−2.34723	+	0.115312i
$980$	−35.9025	−	16.2672i	−1.14686	−	0.519638i
$981$	−9.28703	+	37.0759i	−0.296512	+	1.18374i
$982$	−8.10576	+	2.10101i	−0.258665	+	0.0670458i
$983$	12.6682	−	15.4362i	0.404053	−	0.492339i	−0.530739	−	0.847535i	$-0.678086\pi$
$983$	12.6682	−	15.4362i	0.404053	−	0.492339i	0.934792	+	0.355196i	$0.115586\pi$
$984$	11.5420	+	41.7077i	0.367947	+	1.32959i
$985$	−1.09505	+	11.1183i	−0.0348913	+	0.354257i
$986$	13.7361	−	8.38660i	0.437446	−	0.267084i
$987$	0.0438210	−	0.891997i	0.00139484	−	0.0283926i
$988$	−72.7185	−	5.96262i	−2.31348	−	0.189696i
$989$	4.25283	−	28.6702i	0.135232	−	0.911660i
$990$	6.79863	−	75.3414i	0.216074	−	2.39451i
$991$	−15.0479	+	6.23303i	−0.478011	+	0.197999i	−0.608662	−	0.793430i	$-0.708293\pi$
$991$	−15.0479	+	6.23303i	−0.478011	+	0.197999i	0.130651	+	0.991428i	$0.458293\pi$
$992$	31.7162	+	8.22088i	1.00699	+	0.261013i
$993$	−61.0098	−	25.2711i	−1.93609	−	0.801954i
$994$	0.153480	−	0.292879i	0.00486809	−	0.00928956i
$995$	32.5617	+	43.9044i	1.03228	+	1.39186i
$996$	−4.78838	+	16.7680i	−0.151726	+	0.531315i
$997$	18.1473	−	16.4477i	0.574729	−	0.520904i	−0.331631	−	0.943409i	$-0.607599\pi$
$997$	18.1473	−	16.4477i	0.574729	−	0.520904i	0.906361	+	0.422505i	$0.138849\pi$
$998$	6.55339	+	4.77772i	0.207444	+	0.151236i
$999$	−6.29668	−	7.67253i	−0.199218	−	0.242748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.101.14	✓	992
256.109	even	64	inner	256.2.m.a.109.14	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.101.14	✓	992	1.1	even	1	trivial
256.2.m.a.109.14	yes	992	256.109	even	64	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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.399439 + 1.35663i) q^{2} +(2.51580 - 0.630174i) q^{3} +(-1.68090 - 1.08378i) q^{4} +(2.55024 + 1.20617i) q^{5} +(-0.149994 + 3.66472i) q^{6} +(-0.0344414 - 0.113538i) q^{7} +(2.14171 - 1.84745i) q^{8} +(3.28634 - 1.75659i) q^{9} +O(q^{10})\)	\(q+(-0.399439 + 1.35663i) q^{2} +(2.51580 - 0.630174i) q^{3} +(-1.68090 - 1.08378i) q^{4} +(2.55024 + 1.20617i) q^{5} +(-0.149994 + 3.66472i) q^{6} +(-0.0344414 - 0.113538i) q^{7} +(2.14171 - 1.84745i) q^{8} +(3.28634 - 1.75659i) q^{9} +(-2.65500 + 2.97794i) q^{10} +(-5.03330 + 0.746619i) q^{11} +(-4.91176 - 1.66732i) q^{12} +(1.80747 - 5.05153i) q^{13} +(0.167786 - 0.00137268i) q^{14} +(7.17598 + 1.42739i) q^{15} +(1.65082 + 3.64346i) q^{16} +(-4.56733 + 0.908499i) q^{17} +(1.07035 + 5.16001i) q^{18} +(5.03822 + 4.56638i) q^{19} +(-2.97946 - 4.79136i) q^{20} +(-0.158196 - 0.263934i) q^{21} +(0.997611 - 7.12656i) q^{22} +(-3.35215 + 0.330158i) q^{23} +(4.22389 - 5.99746i) q^{24} +(1.87690 + 2.28701i) q^{25} +(6.13109 + 4.46985i) q^{26} +(1.39580 - 1.26508i) q^{27} +(-0.0651583 + 0.228173i) q^{28} +(1.45575 + 1.96285i) q^{29} +(-4.80281 + 9.16500i) q^{30} +(-5.35108 - 2.21649i) q^{31} +(-5.60223 + 0.784219i) q^{32} +(-12.1922 + 5.05019i) q^{33} +(0.591875 - 6.55908i) q^{34} +(0.0491128 - 0.331092i) q^{35} +(-7.42776 - 0.609046i) q^{36} +(0.258533 - 5.26256i) q^{37} +(-8.20735 + 5.01102i) q^{38} +(1.36387 - 13.8476i) q^{39} +(7.69023 - 2.12816i) q^{40} +(-3.74252 + 4.56028i) q^{41} +(0.421251 - 0.109188i) q^{42} +(-2.09078 + 8.34687i) q^{43} +(9.26963 + 4.20002i) q^{44} +(10.4997 - 0.515818i) q^{45} +(0.891078 - 4.67951i) q^{46} +(2.41317 + 1.61243i) q^{47} +(6.44915 + 8.12589i) q^{48} +(5.80858 - 3.88117i) q^{49} +(-3.85234 + 1.63274i) q^{50} +(-10.9180 + 5.16381i) q^{51} +(-8.51293 + 6.53220i) q^{52} +(3.76278 - 5.07352i) q^{53} +(1.15871 + 2.39890i) q^{54} +(-13.7367 - 4.16697i) q^{55} +(-0.283519 - 0.179537i) q^{56} +(15.5527 + 8.31312i) q^{57} +(-3.24435 + 1.19087i) q^{58} +(-2.43736 - 6.81196i) q^{59} +(-10.5151 - 10.1765i) q^{60} +(1.05402 - 1.75853i) q^{61} +(5.14439 - 6.37409i) q^{62} +(-0.312626 - 0.312626i) q^{63} +(1.17386 - 7.91341i) q^{64} +(10.7025 - 10.7025i) q^{65} +(-1.98119 - 18.5576i) q^{66} +(-9.27917 - 5.56172i) q^{67} +(8.66183 + 3.42291i) q^{68} +(-8.22527 + 2.94305i) q^{69} +(0.429552 + 0.198879i) q^{70} +(0.928952 - 1.73795i) q^{71} +(3.79319 - 9.83346i) q^{72} +(2.65278 - 8.74506i) q^{73} +(7.03608 + 2.45281i) q^{74} +(6.16312 + 4.57088i) q^{75} +(-3.51976 - 13.1360i) q^{76} +(0.258123 + 0.545756i) q^{77} +(18.2414 + 7.38157i) q^{78} +(-0.925099 - 1.38451i) q^{79} +(-0.184645 + 11.2829i) q^{80} +(-3.49642 + 5.23276i) q^{81} +(-4.69170 - 6.89878i) q^{82} +(-0.164961 - 3.35785i) q^{83} +(-0.0201365 + 0.615097i) q^{84} +(-12.7436 - 3.19211i) q^{85} +(-10.4885 - 6.17049i) q^{86} +(4.89930 + 4.02075i) q^{87} +(-9.40053 + 10.8978i) q^{88} +(14.3812 + 1.41642i) q^{89} +(-3.49423 + 14.4503i) q^{90} +(-0.635793 - 0.0312345i) q^{91} +(5.99244 + 3.07805i) q^{92} +(-14.8590 - 2.20412i) q^{93} +(-3.15138 + 2.62971i) q^{94} +(7.34083 + 17.7223i) q^{95} +(-13.5999 + 5.50331i) q^{96} +(-2.28341 + 5.51265i) q^{97} +(2.94514 + 9.43040i) q^{98} +(-15.2296 + 11.2951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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