LMFDB - Embedded newform 770.2.bd.a.263.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(263,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 8, 6]))

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

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

chi := DirichletCharacter("770.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bd (of order $12$, degree $4$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			263.29
Character	$\chi$	$=$	770.263
Dual form			770.2.bd.a.527.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-1.88147 + 0.504137i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.86717 - 1.23031i) q^{5} +1.94784i q^{6} +(1.82332 + 1.91716i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.687681 - 0.397033i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-1.88147 + 0.504137i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.86717 - 1.23031i) q^{5} +1.94784i q^{6} +(1.82332 + 1.91716i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.687681 - 0.397033i) q^{9} +(-1.67165 + 1.48512i) q^{10} +(2.83003 + 1.72943i) q^{11} +(1.88147 + 0.504137i) q^{12} +(-0.386358 + 0.386358i) q^{13} +(2.32375 - 1.26499i) q^{14} +(4.13326 + 1.37348i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.57963 - 0.959159i) q^{17} +(-0.205519 - 0.767009i) q^{18} +(-3.63284 - 6.29226i) q^{19} +(1.00186 + 1.99907i) q^{20} +(-4.39702 - 2.68788i) q^{21} +(2.40297 - 2.28599i) q^{22} +(1.63736 - 6.11071i) q^{23} +(0.973918 - 1.68688i) q^{24} +(1.97265 + 4.59441i) q^{25} +(0.273196 + 0.473190i) q^{26} +(3.03830 - 3.03830i) q^{27} +(-0.620455 - 2.57197i) q^{28} -5.59137 q^{29} +(2.39645 - 3.63694i) q^{30} +(-1.53624 + 2.66084i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-6.19647 - 1.82714i) q^{33} -3.70591i q^{34} +(-1.04572 - 5.82293i) q^{35} -0.794066 q^{36} +(-1.87040 - 0.501172i) q^{37} +(-7.01810 + 1.88050i) q^{38} +(0.532141 - 0.921696i) q^{39} +(2.19025 - 0.450325i) q^{40} -7.02946i q^{41} +(-3.73432 + 3.55152i) q^{42} +(5.80892 - 5.80892i) q^{43} +(-1.58617 - 2.91274i) q^{44} +(-1.77249 - 0.104736i) q^{45} +(-5.47872 - 3.16314i) q^{46} +(-4.09754 - 1.09793i) q^{47} +(-1.37733 - 1.37733i) q^{48} +(-0.351042 + 6.99119i) q^{49} +(4.94842 - 0.716313i) q^{50} +(-6.25140 + 3.60925i) q^{51} +(0.527774 - 0.141417i) q^{52} +(13.9020 - 3.72502i) q^{53} +(-2.14840 - 3.72114i) q^{54} +(-3.15641 - 6.71097i) q^{55} +(-2.64492 - 0.0663616i) q^{56} +(10.0072 + 10.0072i) q^{57} +(-1.44715 + 5.40085i) q^{58} +(-5.22539 - 3.01688i) q^{59} +(-2.89277 - 3.25610i) q^{60} +(1.59065 - 0.918360i) q^{61} +(2.17257 + 2.17257i) q^{62} +(2.01504 + 0.594482i) q^{63} -1.00000i q^{64} +(1.19674 - 0.246054i) q^{65} +(-3.36864 + 5.51244i) q^{66} +(-3.10786 - 11.5987i) q^{67} +(-3.57963 - 0.959159i) q^{68} +12.3225i q^{69} +(-5.89517 - 0.496991i) q^{70} +14.1222 q^{71} +(-0.205519 + 0.767009i) q^{72} +(-3.80926 - 14.2164i) q^{73} +(-0.968191 + 1.67696i) q^{74} +(-6.02769 - 7.64974i) q^{75} +7.26568i q^{76} +(1.84444 + 8.57893i) q^{77} +(-0.752562 - 0.752562i) q^{78} +(1.67078 + 2.89388i) q^{79} +(0.131899 - 2.23217i) q^{80} +(-5.37583 + 9.31121i) q^{81} +(-6.78994 - 1.81936i) q^{82} +(3.90016 - 3.90016i) q^{83} +(2.46399 + 4.52628i) q^{84} +(-7.86385 - 2.61316i) q^{85} +(-4.10753 - 7.11445i) q^{86} +(10.5200 - 2.81882i) q^{87} +(-3.22402 + 0.778244i) q^{88} +(11.7521 - 6.78506i) q^{89} +(-0.559922 + 1.68499i) q^{90} +(-1.44516 - 0.0362595i) q^{91} +(-4.47335 + 4.47335i) q^{92} +(1.54895 - 5.78076i) q^{93} +(-2.12104 + 3.67375i) q^{94} +(-0.958332 + 16.2183i) q^{95} +(-1.68688 + 0.973918i) q^{96} +(-1.09060 + 1.09060i) q^{97} +(6.66212 + 2.14853i) q^{98} +(2.63280 + 0.0656795i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{5}+O(q^{10}) $ 192 * q + 8 * q^5	$ 192 q + 8 q^{5} + 4 q^{11} + 16 q^{15} + 96 q^{16} + 24 q^{22} - 8 q^{23} + 24 q^{25} - 8 q^{26} - 16 q^{33} - 160 q^{36} - 40 q^{37} - 40 q^{42} + 32 q^{45} - 40 q^{47} + 40 q^{53} + 8 q^{55} + 16 q^{56} + 32 q^{58} - 48 q^{67} - 72 q^{70} + 32 q^{71} - 48 q^{75} - 72 q^{77} - 8 q^{80} + 64 q^{81} + 16 q^{82} - 12 q^{88} - 112 q^{91} - 16 q^{92} + 80 q^{93} - 64 q^{97}+O(q^{100}) $ 192 * q + 8 * q^5 + 4 * q^11 + 16 * q^15 + 96 * q^16 + 24 * q^22 - 8 * q^23 + 24 * q^25 - 8 * q^26 - 16 * q^33 - 160 * q^36 - 40 * q^37 - 40 * q^42 + 32 * q^45 - 40 * q^47 + 40 * q^53 + 8 * q^55 + 16 * q^56 + 32 * q^58 - 48 * q^67 - 72 * q^70 + 32 * q^71 - 48 * q^75 - 72 * q^77 - 8 * q^80 + 64 * q^81 + 16 * q^82 - 12 * q^88 - 112 * q^91 - 16 * q^92 + 80 * q^93 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−1.88147	+	0.504137i	−1.08626	+	0.291064i	−0.757160	−	0.653230i	$-0.773414\pi$
$3$	−1.88147	+	0.504137i	−1.08626	+	0.291064i	−0.329105	+	0.944293i	$0.606747\pi$
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−1.86717	−	1.23031i	−0.835024	−	0.550213i
$5$	−1.86717	−	1.23031i	−0.835024	−	0.550213i
$6$			1.94784i			0.795201i
$7$	1.82332	+	1.91716i	0.689148	+	0.724620i
$7$	1.82332	+	1.91716i	0.689148	+	0.724620i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.687681	−	0.397033i	0.229227	−	0.132344i
$10$	−1.67165	+	1.48512i	−0.528623	+	0.469636i
$11$	2.83003	+	1.72943i	0.853287	+	0.521442i
$11$	2.83003	+	1.72943i	0.853287	+	0.521442i
$12$	1.88147	+	0.504137i	0.543132	+	0.145532i
$13$	−0.386358	+	0.386358i	−0.107156	+	0.107156i	−0.758652	−	0.651496i	$-0.774142\pi$
$13$	−0.386358	+	0.386358i	−0.107156	+	0.107156i	0.651496	+	0.758652i	$0.274142\pi$
$14$	2.32375	−	1.26499i	0.621048	−	0.338082i
$15$	4.13326	+	1.37348i	1.06720	+	0.354632i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.57963	−	0.959159i	0.868188	−	0.232630i	0.202884	−	0.979203i	$-0.434969\pi$
$17$	3.57963	−	0.959159i	0.868188	−	0.232630i	0.665304	+	0.746573i	$0.268302\pi$
$18$	−0.205519	−	0.767009i	−0.0484414	−	0.180786i
$19$	−3.63284	−	6.29226i	−0.833430	−	1.44354i	−0.895302	−	0.445459i	$-0.853040\pi$
$19$	−3.63284	−	6.29226i	−0.833430	−	1.44354i	0.0618721	−	0.998084i	$-0.480293\pi$
$20$	1.00186	+	1.99907i	0.224023	+	0.447005i
$21$	−4.39702	−	2.68788i	−0.959508	−	0.586543i
$22$	2.40297	−	2.28599i	0.512314	−	0.487375i
$23$	1.63736	−	6.11071i	0.341413	−	1.27417i	−0.555333	−	0.831628i	$-0.687409\pi$
$23$	1.63736	−	6.11071i	0.341413	−	1.27417i	0.896747	−	0.442544i	$-0.145924\pi$
$24$	0.973918	−	1.68688i	0.198800	−	0.344332i
$25$	1.97265	+	4.59441i	0.394530	+	0.918883i
$26$	0.273196	+	0.473190i	0.0535782	+	0.0928001i
$27$	3.03830	−	3.03830i	0.584720	−	0.584720i
$28$	−0.620455	−	2.57197i	−0.117255	−	0.486057i
$29$	−5.59137			−1.03829			−0.519145	−	0.854686i	$-0.673750\pi$
$29$	−5.59137			−1.03829			−0.519145	+	0.854686i	$0.673750\pi$
$30$	2.39645	−	3.63694i	0.437530	−	0.664012i
$31$	−1.53624	+	2.66084i	−0.275917	+	0.477902i	−0.970366	−	0.241640i	$-0.922315\pi$
$31$	−1.53624	+	2.66084i	−0.275917	+	0.477902i	0.694449	+	0.719542i	$0.255648\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−6.19647	−	1.82714i	−1.07867	−	0.318063i
$34$		−	3.70591i		−	0.635558i
$35$	−1.04572	−	5.82293i	−0.176760	−	0.984254i
$36$	−0.794066			−0.132344
$37$	−1.87040	−	0.501172i	−0.307492	−	0.0823922i	0.101773	−	0.994808i	$-0.467548\pi$
$37$	−1.87040	−	0.501172i	−0.307492	−	0.0823922i	−0.409265	+	0.912415i	$0.634215\pi$
$38$	−7.01810	+	1.88050i	−1.13849	+	0.305057i
$39$	0.532141	−	0.921696i	0.0852108	−	0.147589i
$40$	2.19025	−	0.450325i	0.346309	−	0.0712026i
$41$		−	7.02946i		−	1.09782i	−0.835882	−	0.548908i	$-0.815044\pi$
$41$		−	7.02946i		−	1.09782i	0.835882	−	0.548908i	$-0.184956\pi$
$42$	−3.73432	+	3.55152i	−0.576219	+	0.548011i
$43$	5.80892	−	5.80892i	0.885853	−	0.885853i	−0.108269	−	0.994122i	$-0.534531\pi$
$43$	5.80892	−	5.80892i	0.885853	−	0.885853i	0.994122	+	0.108269i	$0.0345308\pi$
$44$	−1.58617	−	2.91274i	−0.239123	−	0.439113i
$45$	−1.77249	−	0.104736i	−0.264228	−	0.0156131i
$46$	−5.47872	−	3.16314i	−0.807793	−	0.466379i
$47$	−4.09754	−	1.09793i	−0.597688	−	0.160150i	−0.0527234	−	0.998609i	$-0.516790\pi$
$47$	−4.09754	−	1.09793i	−0.597688	−	0.160150i	−0.544964	+	0.838459i	$0.683457\pi$
$48$	−1.37733	−	1.37733i	−0.198800	−	0.198800i
$49$	−0.351042	+	6.99119i	−0.0501489	+	0.998742i
$50$	4.94842	−	0.716313i	0.699813	−	0.101302i
$51$	−6.25140	+	3.60925i	−0.875372	+	0.505396i
$52$	0.527774	−	0.141417i	0.0731891	−	0.0196110i
$53$	13.9020	−	3.72502i	1.90958	−	0.511671i	0.915607	−	0.402075i	$-0.131711\pi$
$53$	13.9020	−	3.72502i	1.90958	−	0.511671i	0.993976	−	0.109596i	$-0.0349558\pi$
$54$	−2.14840	−	3.72114i	−0.292360	−	0.506383i
$55$	−3.15641	−	6.71097i	−0.425610	−	0.904907i
$56$	−2.64492	−	0.0663616i	−0.353442	−	0.00886794i
$57$	10.0072	+	10.0072i	1.32549	+	1.32549i
$58$	−1.44715	+	5.40085i	−0.190020	+	0.709166i
$59$	−5.22539	−	3.01688i	−0.680288	−	0.392765i	0.119675	−	0.992813i	$-0.461815\pi$
$59$	−5.22539	−	3.01688i	−0.680288	−	0.392765i	−0.799964	+	0.600048i	$0.795148\pi$
$60$	−2.89277	−	3.25610i	−0.373455	−	0.420361i
$61$	1.59065	−	0.918360i	0.203661	−	0.117584i	−0.394701	−	0.918810i	$-0.629152\pi$
$61$	1.59065	−	0.918360i	0.203661	−	0.117584i	0.598362	+	0.801226i	$0.295818\pi$
$62$	2.17257	+	2.17257i	0.275917	+	0.275917i
$63$	2.01504	+	0.594482i	0.253871	+	0.0748977i
$64$		−	1.00000i		−	0.125000i
$65$	1.19674	−	0.246054i	0.148437	−	0.0305193i
$66$	−3.36864	+	5.51244i	−0.414651	+	0.678534i
$67$	−3.10786	−	11.5987i	−0.379686	−	1.41701i	−0.846376	−	0.532585i	$-0.821221\pi$
$67$	−3.10786	−	11.5987i	−0.379686	−	1.41701i	0.466691	−	0.884421i	$-0.345446\pi$
$68$	−3.57963	−	0.959159i	−0.434094	−	0.116315i
$69$			12.3225i			1.48346i
$70$	−5.89517	−	0.496991i	−0.704607	−	0.0594018i
$71$	14.1222			1.67599			0.837997	−	0.545675i	$-0.183727\pi$
$71$	14.1222			1.67599			0.837997	+	0.545675i	$0.183727\pi$
$72$	−0.205519	+	0.767009i	−0.0242207	+	0.0903928i
$73$	−3.80926	−	14.2164i	−0.445841	−	1.66390i	−0.713707	−	0.700444i	$-0.752985\pi$
$73$	−3.80926	−	14.2164i	−0.445841	−	1.66390i	0.267867	−	0.963456i	$-0.413681\pi$
$74$	−0.968191	+	1.67696i	−0.112550	+	0.194942i
$75$	−6.02769	−	7.64974i	−0.696018	−	0.883316i
$76$			7.26568i			0.833430i
$77$	1.84444	+	8.57893i	0.210194	+	0.977660i
$78$	−0.752562	−	0.752562i	−0.0852108	−	0.0852108i
$79$	1.67078	+	2.89388i	0.187978	+	0.325587i	0.944576	−	0.328293i	$-0.106473\pi$
$79$	1.67078	+	2.89388i	0.187978	+	0.325587i	−0.756598	+	0.653880i	$0.773140\pi$
$80$	0.131899	−	2.23217i	0.0147467	−	0.249565i
$81$	−5.37583	+	9.31121i	−0.597314	+	1.03458i
$82$	−6.78994	−	1.81936i	−0.749823	−	0.200914i
$83$	3.90016	−	3.90016i	0.428098	−	0.428098i	−0.459882	−	0.887980i	$-0.652108\pi$
$83$	3.90016	−	3.90016i	0.428098	−	0.428098i	0.887980	+	0.459882i	$0.152108\pi$
$84$	2.46399	+	4.52628i	0.268843	+	0.493858i
$85$	−7.86385	−	2.61316i	−0.852954	−	0.283437i
$86$	−4.10753	−	7.11445i	−0.442926	−	0.767171i
$87$	10.5200	−	2.81882i	1.12786	−	0.302209i
$88$	−3.22402	+	0.778244i	−0.343682	+	0.0829611i
$89$	11.7521	−	6.78506i	1.24572	−	0.719215i	0.275465	−	0.961311i	$-0.411168\pi$
$89$	11.7521	−	6.78506i	1.24572	−	0.719215i	0.970252	+	0.242096i	$0.0778348\pi$
$90$	−0.559922	+	1.68499i	−0.0590210	+	0.177613i
$91$	−1.44516	−	0.0362595i	−0.151494	−	0.00380102i
$92$	−4.47335	+	4.47335i	−0.466379	+	0.466379i
$93$	1.54895	−	5.78076i	0.160619	−	0.599437i
$94$	−2.12104	+	3.67375i	−0.218769	+	0.378919i
$95$	−0.958332	+	16.2183i	−0.0983228	+	1.66396i
$96$	−1.68688	+	0.973918i	−0.172166	+	0.0994001i
$97$	−1.09060	+	1.09060i	−0.110733	+	0.110733i	−0.760302	−	0.649569i	$-0.774949\pi$
$97$	−1.09060	+	1.09060i	−0.110733	+	0.110733i	0.649569	+	0.760302i	$0.274949\pi$
$98$	6.66212	+	2.14853i	0.672975	+	0.217035i
$99$	2.63280	+	0.0656795i	0.264606	+	0.00660104i
$100$	0.588841	−	4.96521i	0.0588841	−	0.496521i
$101$	6.13007	+	3.53920i	0.609964	+	0.352163i	0.772952	−	0.634465i	$-0.218780\pi$
$101$	6.13007	+	3.53920i	0.609964	+	0.352163i	−0.162987	+	0.986628i	$0.552113\pi$
$102$	1.86828	+	6.97253i	0.184988	+	0.690384i
$103$	−1.22437	+	4.56942i	−0.120641	+	0.450238i	−0.999647	−	0.0265726i	$-0.991541\pi$
$103$	−1.22437	+	4.56942i	−0.120641	+	0.450238i	0.879006	+	0.476811i	$0.158207\pi$
$104$		−	0.546392i		−	0.0535782i
$105$	4.90305	+	10.4284i	0.478488	+	1.01771i
$106$		−	14.3924i		−	1.39791i
$107$	−1.07334	+	4.00576i	−0.103764	+	0.387251i	−0.998202	−	0.0599402i	$-0.980909\pi$
$107$	−1.07334	+	4.00576i	−0.103764	+	0.387251i	0.894438	+	0.447191i	$0.147576\pi$
$108$	−4.15039	+	1.11209i	−0.399371	+	0.107011i
$109$	−3.18395	+	5.51476i	−0.304967	+	0.528218i	−0.977254	−	0.212072i	$-0.931979\pi$
$109$	−3.18395	+	5.51476i	−0.304967	+	0.528218i	0.672287	+	0.740291i	$0.265312\pi$
$110$	−7.29924	+	1.31193i	−0.695955	+	0.125088i
$111$	3.77175			0.357999
$112$	−0.748656	+	2.53762i	−0.0707413	+	0.239783i
$113$	14.6138	+	14.6138i	1.37475	+	1.37475i	0.853246	+	0.521509i	$0.174631\pi$
$113$	14.6138	+	14.6138i	1.37475	+	1.37475i	0.521509	+	0.853246i	$0.325369\pi$
$114$	12.2563	−	7.07617i	1.14791	−	0.662744i
$115$	−10.5753	+	9.39527i	−0.986155	+	0.876114i
$116$	4.84227	+	2.79568i	0.449593	+	0.259573i
$117$	−0.112294	+	0.419088i	−0.0103816	+	0.0387447i
$118$	−4.26652	+	4.26652i	−0.392765	+	0.392765i
$119$	8.36566	+	5.11389i	0.766879	+	0.468790i
$120$	−3.89386	+	1.95146i	−0.355459	+	0.178143i
$121$	5.01816	+	9.78867i	0.456196	+	0.889879i
$122$	−0.475378	−	1.77414i	−0.0430387	−	0.160623i
$123$	3.54381	+	13.2257i	0.319535	+	1.19252i
$124$	2.66084	−	1.53624i	0.238951	−	0.137958i
$125$	1.96930	−	11.0055i	0.176139	−	0.984365i
$126$	1.09576	−	1.79251i	0.0976177	−	0.159690i
$127$	6.34400	+	6.34400i	0.562939	+	0.562939i	0.930141	−	0.367202i	$-0.119684\pi$
$127$	6.34400	+	6.34400i	0.562939	+	0.562939i	−0.367202	+	0.930141i	$0.619684\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−8.00079	+	13.8578i	−0.704431	+	1.22011i
$130$	0.0720683	−	1.21964i	0.00632081	−	0.106970i
$131$	−7.60049	+	4.38814i	−0.664058	+	0.383394i	−0.793821	−	0.608151i	$-0.791912\pi$
$131$	−7.60049	+	4.38814i	−0.664058	+	0.383394i	0.129764	+	0.991545i	$0.458578\pi$
$132$	4.45274	+	4.68058i	0.387561	+	0.407392i
$133$	5.43949	−	18.4375i	0.471664	−	1.59874i
$134$	−12.0079			−1.03732
$135$	−9.41107	+	1.93496i	−0.809976	+	0.166535i
$136$	−1.85295	+	3.20941i	−0.158889	+	0.275205i
$137$	0.134433	+	0.501711i	0.0114854	+	0.0428640i	0.971431	−	0.237323i	$-0.0762701\pi$
$137$	0.134433	+	0.501711i	0.0114854	+	0.0428640i	−0.959945	+	0.280187i	$0.909603\pi$
$138$	11.9027	+	3.18931i	1.01322	+	0.271492i
$139$	−13.1443			−1.11489			−0.557444	−	0.830215i	$-0.688218\pi$
$139$	−13.1443			−1.11489			−0.557444	+	0.830215i	$0.688218\pi$
$140$	−2.00584	+	5.56566i	−0.169524	+	0.470384i
$141$	8.26289			0.695861
$142$	3.65509	−	13.6410i	0.306728	−	1.14472i
$143$	−1.76158	+	0.425227i	−0.147311	+	0.0355592i
$144$	0.687681	+	0.397033i	0.0573068	+	0.0330861i
$145$	10.4400	+	6.87914i	0.866998	+	0.571282i
$146$	−14.7179			−1.21806
$147$	−2.86405	−	13.3307i	−0.236223	−	1.09949i
$148$	1.36923	+	1.36923i	0.112550	+	0.112550i
$149$	−5.41677	−	9.38213i	−0.443759	−	0.768614i	0.554205	−	0.832380i	$-0.313022\pi$
$149$	−5.41677	−	9.38213i	−0.443759	−	0.768614i	−0.997965	+	0.0637661i	$0.979689\pi$
$150$	−8.94917	+	3.84240i	−0.730696	+	0.313731i
$151$	−19.7106	−	11.3799i	−1.60403	−	0.926086i	−0.990670	−	0.136281i	$-0.956485\pi$
$151$	−19.7106	−	11.3799i	−1.60403	−	0.926086i	−0.613358	−	0.789805i	$-0.710182\pi$
$152$	7.01810	+	1.88050i	0.569243	+	0.152528i
$153$	2.08083	−	2.08083i	0.168225	−	0.168225i
$154$	8.76399	+	0.438797i	0.706222	+	0.0353593i
$155$	6.14210	−	3.07819i	0.493345	−	0.247246i
$156$	−0.921696	+	0.532141i	−0.0737947	+	0.0426054i
$157$	0.0124513	+	0.0464689i	0.000993722	+	0.00370862i	0.966421	−	0.256964i	$-0.0827223\pi$
$157$	0.0124513	+	0.0464689i	0.000993722	+	0.00370862i	−0.965427	+	0.260673i	$0.916056\pi$
$158$	3.22770	−	0.864861i	0.256782	−	0.0688046i
$159$	−24.2782	+	14.0170i	−1.92538	+	1.11162i
$160$	−2.12198	−	0.705133i	−0.167757	−	0.0557457i
$161$	14.7007	−	8.00267i	1.15858	−	0.630699i
$162$	7.60257	+	7.60257i	0.597314	+	0.597314i
$163$	3.36225	−	12.5481i	0.263352	−	0.982843i	−0.699899	−	0.714241i	$-0.746772\pi$
$163$	3.36225	−	12.5481i	0.263352	−	0.982843i	0.963251	−	0.268601i	$-0.0865615\pi$
$164$	−3.51473	+	6.08769i	−0.274454	+	0.475369i
$165$	9.32192	+	11.0352i	0.725711	+	0.859088i
$166$	−2.75783	−	4.77670i	−0.214049	−	0.370744i
$167$	−4.35793	−	4.35793i	−0.337227	−	0.337227i	0.518096	−	0.855323i	$-0.326641\pi$
$167$	−4.35793	−	4.35793i	−0.337227	−	0.337227i	−0.855323	+	0.518096i	$0.826641\pi$
$168$	5.00978	−	1.20854i	0.386513	−	0.0932413i
$169$			12.7015i			0.977035i
$170$	−4.55943	+	6.91956i	−0.349692	+	0.530706i
$171$	−4.99647	−	2.88471i	−0.382089	−	0.220599i
$172$	−7.93514	+	2.12621i	−0.605049	+	0.162122i
$173$	15.2500	+	4.08624i	1.15944	+	0.310671i	0.786742	−	0.617282i	$-0.211766\pi$
$173$	15.2500	+	4.08624i	1.15944	+	0.310671i	0.372698	+	0.927953i	$0.378433\pi$
$174$		−	10.8911i		−	0.825650i
$175$	−5.21148	+	12.1590i	−0.393951	+	0.919131i
$176$	−0.0827129	+	3.31559i	−0.00623472	+	0.249922i
$177$	11.3523	+	3.04184i	0.853292	+	0.228639i
$178$	−3.51221	−	13.1077i	−0.263251	−	0.982466i
$179$	−18.1187	−	10.4608i	−1.35426	−	0.781880i	−0.365414	−	0.930845i	$-0.619072\pi$
$179$	−18.1187	−	10.4608i	−1.35426	−	0.781880i	−0.988842	+	0.148965i	$0.952406\pi$
$180$	1.48266	+	0.976951i	0.110511	+	0.0728176i
$181$	−3.97842			−0.295714			−0.147857	−	0.989009i	$-0.547237\pi$
$181$	−3.97842			−0.295714			−0.147857	+	0.989009i	$0.547237\pi$
$182$	−0.409060	+	1.38654i	−0.0303215	+	0.102777i
$183$	−2.52977	+	2.52977i	−0.187006	+	0.187006i
$184$	3.16314	+	5.47872i	0.233190	+	0.403896i
$185$	2.87576	+	3.23696i	0.211430	+	0.237986i
$186$	−5.18289	−	2.99234i	−0.380028	−	0.219409i
$187$	11.7893	+	3.47626i	0.862116	+	0.254210i
$188$	2.99961	+	2.99961i	0.218769	+	0.218769i
$189$	11.3647	+	0.285142i	0.826659	+	0.0207411i
$190$	15.4176	+	5.12327i	1.11851	+	0.371681i
$191$	−4.85802	−	8.41434i	−0.351514	−	0.608840i	0.635001	−	0.772511i	$-0.281000\pi$
$191$	−4.85802	−	8.41434i	−0.351514	−	0.608840i	−0.986515	+	0.163671i	$0.947666\pi$
$192$	0.504137	+	1.88147i	0.0363830	+	0.135783i
$193$	0.282979	+	1.05609i	0.0203693	+	0.0760193i	0.975362	−	0.220609i	$-0.0708045\pi$
$193$	0.282979	+	1.05609i	0.0203693	+	0.0760193i	−0.954993	+	0.296628i	$0.904138\pi$
$194$	0.771167	+	1.33570i	0.0553666	+	0.0958978i
$195$	−2.12757	+	1.06626i	−0.152359	+	0.0763566i
$196$	3.79961	−	5.87903i	0.271401	−	0.419931i
$197$	−0.395788	−	0.395788i	−0.0281987	−	0.0281987i	0.692867	−	0.721066i	$-0.256347\pi$
$197$	−0.395788	−	0.395788i	−0.0281987	−	0.0281987i	−0.721066	+	0.692867i	$0.756347\pi$
$198$	0.744860	−	2.52609i	0.0529349	−	0.179521i
$199$	8.47056	+	4.89048i	0.600462	+	0.346677i	0.769223	−	0.638980i	$-0.220643\pi$
$199$	8.47056	+	4.89048i	0.600462	+	0.346677i	−0.168761	+	0.985657i	$0.553977\pi$
$200$	−4.64362	−	1.85387i	−0.328353	−	0.131088i
$201$	11.6947	+	20.2558i	0.824878	+	1.42873i
$202$	5.00518	−	5.00518i	0.352163	−	0.352163i
$203$	−10.1948	−	10.7196i	−0.715537	−	0.752367i
$204$	7.21850			0.505396
$205$	−8.64845	+	13.1252i	−0.604034	+	0.916704i
$206$	4.09683	+	2.36531i	0.285440	+	0.164799i
$207$	−1.30017	−	4.85231i	−0.0903682	−	0.337259i
$208$	−0.527774	−	0.141417i	−0.0365946	−	0.00980549i
$209$	0.600965	−	24.0900i	0.0415696	−	1.66634i
$210$	11.3421	−	2.03690i	0.782680	−	0.140559i
$211$		−	12.2438i		−	0.842896i	−0.906852	−	0.421448i	$-0.861522\pi$
$211$		−	12.2438i		−	0.842896i	0.906852	−	0.421448i	$-0.138478\pi$
$212$	−13.9020	−	3.72502i	−0.954791	−	0.255836i
$213$	−26.5704	+	7.11951i	−1.82057	+	0.487821i
$214$	3.59146	+	2.07353i	0.245507	+	0.141744i
$215$	−17.9931	+	3.69945i	−1.22712	+	0.252300i
$216$			4.29680i			0.292360i
$217$	−7.90232	+	1.90633i	−0.536445	+	0.129410i
$218$	4.50278	+	4.50278i	0.304967	+	0.304967i
$219$	14.3340	+	24.8272i	0.968602	+	1.67767i
$220$	−0.621952	+	7.39007i	−0.0419320	+	0.498239i
$221$	−1.01244	+	1.75360i	−0.0681040	+	0.117960i
$222$	0.976202	−	3.64323i	0.0655184	−	0.244518i
$223$	2.37934	+	2.37934i	0.159332	+	0.159332i	0.782271	−	0.622938i	$-0.214061\pi$
$223$	2.37934	+	2.37934i	0.159332	+	0.159332i	−0.622938	+	0.782271i	$0.714061\pi$
$224$	2.25739	+	1.37993i	0.150828	+	0.0922005i
$225$	3.18069	+	2.37628i	0.212046	+	0.158419i
$226$	17.8982	−	10.3335i	1.19057	−	0.687377i
$227$	9.03383	−	2.42061i	0.599596	−	0.160661i	0.0537609	−	0.998554i	$-0.482879\pi$
$227$	9.03383	−	2.42061i	0.599596	−	0.160661i	0.545835	+	0.837893i	$0.316212\pi$
$228$	−3.66290	−	13.6701i	−0.242581	−	0.905326i
$229$	−7.06247	+	4.07752i	−0.466701	+	0.269450i	−0.714858	−	0.699270i	$-0.753509\pi$
$229$	−7.06247	+	4.07752i	−0.466701	+	0.269450i	0.248157	+	0.968720i	$0.420175\pi$
$230$	6.33804	+	12.6467i	0.417918	+	0.833896i
$231$	−7.79521	−	15.2111i	−0.512887	−	1.00082i
$232$	3.95369	−	3.95369i	0.259573	−	0.259573i
$233$	−2.13770	−	0.572794i	−0.140045	−	0.0375250i	0.188115	−	0.982147i	$-0.439762\pi$
$233$	−2.13770	−	0.572794i	−0.140045	−	0.0375250i	−0.328161	+	0.944622i	$0.606429\pi$
$234$	0.375744	+	0.216936i	0.0245631	+	0.0141815i
$235$	6.30001	+	7.09129i	0.410967	+	0.462585i
$236$	3.01688	+	5.22539i	0.196382	+	0.340144i
$237$	−4.60243	−	4.60243i	−0.298960	−	0.298960i
$238$	7.10483	−	6.75704i	0.460538	−	0.437994i
$239$	17.3188			1.12026			0.560130	−	0.828404i	$-0.310751\pi$
$239$	17.3188			1.12026			0.560130	+	0.828404i	$0.310751\pi$
$240$	0.877159	+	4.26625i	0.0566204	+	0.275385i
$241$	−15.2676	−	8.81473i	−0.983470	−	0.567807i	−0.0801541	−	0.996782i	$-0.525541\pi$
$241$	−15.2676	−	8.81473i	−0.983470	−	0.567807i	−0.903316	+	0.428976i	$0.858875\pi$
$242$	10.7539	−	2.31367i	0.691289	−	0.148728i
$243$	2.08403	−	7.77770i	0.133691	−	0.498940i
$244$	−1.83672			−0.117584
$245$	9.25682	−	12.6219i	0.591397	−	0.806381i
$246$	13.6922			0.872985
$247$	3.83464	+	1.02749i	0.243992	+	0.0653775i
$248$	−0.795216	−	2.96779i	−0.0504963	−	0.188455i
$249$	−5.37180	+	9.30423i	−0.340424	+	0.589631i
$250$	−10.1208	−	4.75064i	−0.640098	−	0.300457i
$251$	−15.4378			−0.974428			−0.487214	−	0.873283i	$-0.661987\pi$
$251$	−15.4378			−0.974428			−0.487214	+	0.873283i	$0.661987\pi$
$252$	−1.44783	−	1.52236i	−0.0912049	−	0.0958994i
$253$	15.2018	−	14.4618i	0.955730	−	0.909206i
$254$	7.76978	−	4.48589i	0.487520	−	0.281470i
$255$	16.1129	+	0.952109i	1.00903	+	0.0596234i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.0712	+	2.96651i	0.690600	+	0.185046i	0.587016	−	0.809575i	$-0.300302\pi$
$257$	11.0712	+	2.96651i	0.690600	+	0.185046i	0.103584	+	0.994621i	$0.466969\pi$
$258$	11.3148	+	11.3148i	0.704431	+	0.704431i
$259$	−2.44950	−	4.49966i	−0.152205	−	0.279595i
$260$	−1.15943	−	0.385279i	−0.0719049	−	0.0238940i
$261$	−3.84508	+	2.21996i	−0.238004	+	0.137412i
$262$	2.27147	+	8.47724i	0.140332	+	0.523726i
$263$	−5.66235	−	21.1322i	−0.349155	−	1.30307i	−0.887682	−	0.460457i	$-0.847686\pi$
$263$	−5.66235	−	21.1322i	−0.349155	−	1.30307i	0.538527	−	0.842608i	$-0.318981\pi$
$264$	5.67355	−	3.08959i	0.349183	−	0.190151i
$265$	−30.5403	−	10.1486i	−1.87608	−	0.623420i
$266$	−16.4014	−	10.0261i	−1.00564	−	0.614741i
$267$	−18.6905	+	18.6905i	−1.14384	+	1.14384i
$268$	−3.10786	+	11.5987i	−0.189843	+	0.708503i
$269$	24.1121	+	13.9211i	1.47014	+	0.848786i	0.999439	−	0.0335059i	$-0.0106672\pi$
$269$	24.1121	+	13.9211i	1.47014	+	0.848786i	0.470702	+	0.882292i	$0.344001\pi$
$270$	−0.566741	+	9.59120i	−0.0344908	+	0.583702i
$271$	16.8935	−	9.75347i	1.02621	−	0.592481i	0.110311	−	0.993897i	$-0.464815\pi$
$271$	16.8935	−	9.75347i	1.02621	−	0.592481i	0.915896	+	0.401416i	$0.131482\pi$
$272$	2.62047	+	2.62047i	0.158889	+	0.158889i
$273$	2.73730	−	0.660340i	0.165669	−	0.0399656i
$274$	0.519409			0.0313786
$275$	−2.36304	+	16.4139i	−0.142497	+	0.989795i
$276$	6.16127	−	10.6716i	0.370865	−	0.642357i
$277$	17.7363	−	4.75243i	1.06567	−	0.285546i	0.316958	−	0.948439i	$-0.397338\pi$
$277$	17.7363	−	4.75243i	1.06567	−	0.285546i	0.748714	+	0.662894i	$0.230672\pi$
$278$	−3.40200	+	12.6964i	−0.204039	+	0.761482i
$279$			2.43975i			0.146064i
$280$	4.85687	+	3.37799i	0.290253	+	0.201874i
$281$			15.7214i			0.937860i	0.883235	+	0.468930i	$0.155360\pi$
$281$			15.7214i			0.937860i	−0.883235	+	0.468930i	$0.844640\pi$
$282$	2.13859	−	7.98134i	0.127351	−	0.475282i
$283$	0.738594	+	2.75647i	0.0439049	+	0.163855i	0.984398	−	0.175959i	$-0.0563025\pi$
$283$	0.738594	+	2.75647i	0.0439049	+	0.163855i	−0.940493	+	0.339814i	$0.889636\pi$
$284$	−12.2302	−	7.06108i	−0.725726	−	0.418998i
$285$	−6.37316	−	30.9972i	−0.377513	−	1.83612i
$286$	−0.0451937	+	1.81161i	−0.00267236	+	0.107123i
$287$	13.4766	−	12.8169i	0.795500	−	0.756559i
$288$	0.561489	−	0.561489i	0.0330861	−	0.0330861i
$289$	−2.82866	+	1.63313i	−0.166392	+	0.0960664i
$290$	9.34682	−	8.30385i	0.548864	−	0.487619i
$291$	1.50211	−	2.60173i	0.0880551	−	0.152516i
$292$	−3.80926	+	14.2164i	−0.222920	+	0.831950i
$293$	−12.3542	+	12.3542i	−0.721741	+	0.721741i	−0.968960	−	0.247219i	$-0.920483\pi$
$293$	−12.3542	+	12.3542i	−0.721741	+	0.721741i	0.247219	+	0.968960i	$0.420483\pi$
$294$	−13.6177	−	0.683772i	−0.794200	−	0.0398784i
$295$	6.04499	+	12.0619i	0.351953	+	0.702272i
$296$	1.67696	−	0.968191i	0.0974711	−	0.0562749i
$297$	13.8530	−	3.34396i	0.803832	−	0.194036i
$298$	−10.4644	+	2.80393i	−0.606187	+	0.162427i
$299$	1.72831	+	2.99353i	0.0999510	+	0.173120i
$300$	1.39526	+	9.63872i	0.0805554	+	0.556492i
$301$	21.7282	+	0.545164i	1.25239	+	0.0314227i
$302$	−16.0937	+	16.0937i	−0.926086	+	0.926086i
$303$	−13.3177	−	3.56848i	−0.765085	−	0.205004i
$304$	3.63284	−	6.29226i	0.208358	−	0.360886i
$305$	−4.09988	−	0.242261i	−0.234758	−	0.0138718i
$306$	−1.47137	−	2.54848i	−0.0841124	−	0.145687i
$307$	−4.92527	−	4.92527i	−0.281100	−	0.281100i	0.552448	−	0.833548i	$-0.313694\pi$
$307$	−4.92527	−	4.92527i	−0.281100	−	0.281100i	−0.833548	+	0.552448i	$0.813694\pi$
$308$	2.69213	−	8.35179i	0.153398	−	0.475888i
$309$		−	9.21445i		−	0.524192i
$310$	−1.38361	−	6.72950i	−0.0785840	−	0.382210i
$311$	6.00343	−	10.3983i	0.340424	−	0.589631i	−0.644088	−	0.764952i	$-0.722763\pi$
$311$	6.00343	−	10.3983i	0.340424	−	0.589631i	0.984511	+	0.175321i	$0.0560962\pi$
$312$	0.275457	+	1.02802i	0.0155947	+	0.0582001i
$313$	−5.26844	+	19.6621i	−0.297790	+	1.11137i	0.641186	+	0.767385i	$0.278443\pi$
$313$	−5.26844	+	19.6621i	−0.297790	+	1.11137i	−0.938976	+	0.343982i	$0.888224\pi$
$314$	0.0481081			0.00271490
$315$	−3.03102	−	3.58913i	−0.170779	−	0.202225i
$316$		−	3.34156i		−	0.187978i
$317$	−7.81683	−	2.09451i	−0.439037	−	0.117640i	0.0325282	−	0.999471i	$-0.489644\pi$
$317$	−7.81683	−	2.09451i	−0.439037	−	0.117640i	−0.471565	+	0.881831i	$0.656311\pi$
$318$	7.25573	+	27.0788i	0.406881	+	1.51850i
$319$	−15.8237	−	9.66987i	−0.885960	−	0.541409i
$320$	−1.23031	+	1.86717i	−0.0687767	+	0.104378i
$321$		−	8.07780i		−	0.450859i
$322$	−3.92517	−	16.2710i	−0.218741	−	0.906747i
$323$	−19.0395	−	19.0395i	−1.05939	−	1.05939i
$324$	9.31121	−	5.37583i	0.517289	−	0.298657i
$325$	−2.53724	−	1.01294i	−0.140741	−	0.0561877i
$326$	−11.2503	−	6.49537i	−0.623097	−	0.359745i
$327$	3.21029	−	11.9810i	0.177530	−	0.662549i
$328$	4.97058	+	4.97058i	0.274454	+	0.274454i
$329$	−5.36619	−	9.85754i	−0.295848	−	0.543464i
$330$	13.0719	−	6.14817i	0.719582	−	0.338446i
$331$	−9.20843	−	15.9495i	−0.506141	−	0.876662i	−0.999975	−	0.00710573i	$-0.997738\pi$
$331$	−9.20843	−	15.9495i	−0.506141	−	0.876662i	0.493834	−	0.869556i	$-0.335595\pi$
$332$	−5.32772	+	1.42756i	−0.292396	+	0.0783474i
$333$	−1.48522	+	0.397964i	−0.0813896	+	0.0218083i
$334$	−5.33736	+	3.08152i	−0.292047	+	0.168614i
$335$	−8.46714	+	25.4804i	−0.462609	+	1.39214i
$336$	0.129261	−	5.15187i	0.00705179	−	0.281057i
$337$	−18.7785	−	18.7785i	−1.02293	−	1.02293i	−0.999731	−	0.0231967i	$-0.992616\pi$
$337$	−18.7785	−	18.7785i	−1.02293	−	1.02293i	−0.0231967	−	0.999731i	$-0.507384\pi$
$338$	12.2687	+	3.28738i	0.667327	+	0.178810i
$339$	−34.8628	−	20.1281i	−1.89349	−	1.09321i
$340$	5.50371	+	6.19499i	0.298481	+	0.335970i
$341$	−8.94934	+	4.87346i	−0.484634	+	0.263912i
$342$	−4.07960	+	4.07960i	−0.220599	+	0.220599i
$343$	−14.0433	+	12.0741i	−0.758268	+	0.651942i
$344$			8.21506i			0.442926i
$345$	15.1606	−	23.0083i	0.816220	−	1.23873i
$346$	7.89401	−	13.6728i	0.424384	−	0.735055i
$347$	19.9297	−	5.34014i	1.06988	−	0.286674i	0.319437	−	0.947607i	$-0.396506\pi$
$347$	19.9297	−	5.34014i	1.06988	−	0.286674i	0.750445	+	0.660933i	$0.229839\pi$
$348$	−10.5200	−	2.81882i	−0.563929	−	0.151104i
$349$	11.4208			0.611343			0.305672	−	0.952137i	$-0.401119\pi$
$349$	11.4208			0.611343			0.305672	+	0.952137i	$0.401119\pi$
$350$	10.3958	+	8.18088i	0.555680	+	0.437286i
$351$			2.34774i			0.125313i
$352$	3.18121	+	0.938033i	0.169559	+	0.0499973i
$353$	−17.7005	+	4.74284i	−0.942103	+	0.252436i	−0.697008	−	0.717063i	$-0.745486\pi$
$353$	−17.7005	+	4.74284i	−0.942103	+	0.252436i	−0.245095	+	0.969499i	$0.578819\pi$
$354$	5.87639	−	10.1782i	0.312327	−	0.540966i
$355$	−26.3685	−	17.3747i	−1.39949	−	0.922154i
$356$	−13.5701			−0.719215
$357$	−18.3178	−	5.40417i	−0.969481	−	0.286019i
$358$	−14.7939	+	14.7939i	−0.781880	+	0.781880i
$359$	−6.41258	−	11.1069i	−0.338443	−	0.586201i	0.645697	−	0.763594i	$-0.276567\pi$
$359$	−6.41258	−	11.1069i	−0.338443	−	0.586201i	−0.984140	+	0.177393i	$0.943234\pi$
$360$	1.32740	−	1.17928i	0.0699602	−	0.0621536i
$361$	−16.8950	+	29.2630i	−0.889212	+	1.54016i
$362$	−1.02969	+	3.84286i	−0.0541194	+	0.201976i
$363$	−14.3763	−	15.8872i	−0.754561	−	0.833862i
$364$	1.23342	+	0.753983i	0.0646487	+	0.0395195i
$365$	−10.3781	+	31.2310i	−0.543213	+	1.63470i
$366$	1.78881	+	3.09832i	0.0935028	+	0.161952i
$367$	0.360861	+	1.34675i	0.0188368	+	0.0702999i	0.974704	−	0.223498i	$-0.0717475\pi$
$367$	0.360861	+	1.34675i	0.0188368	+	0.0702999i	−0.955868	+	0.293798i	$0.905081\pi$
$368$	6.11071	−	1.63736i	0.318543	−	0.0853533i
$369$	−2.79093	−	4.83403i	−0.145290	−	0.251649i
$370$	3.87096	−	1.93998i	0.201242	−	0.100855i
$371$	32.4892	+	19.8605i	1.68675	+	1.03110i
$372$	−4.23181	+	4.23181i	−0.219409	+	0.219409i
$373$	−31.0140	−	8.31017i	−1.60584	−	0.430284i	−0.659043	−	0.752105i	$-0.729038\pi$
$373$	−31.0140	−	8.31017i	−1.60584	−	0.430284i	−0.946801	+	0.321821i	$0.895705\pi$
$374$	6.40910	−	10.4878i	0.331407	−	0.542313i
$375$	1.84313	+	21.6993i	0.0951789	+	1.12055i
$376$	3.67375	−	2.12104i	0.189459	−	0.109384i
$377$	2.16027	−	2.16027i	0.111259	−	0.111259i
$378$	3.21682	−	10.9036i	0.165456	−	0.560823i
$379$			37.9317i			1.94842i	0.225643	+	0.974210i	$0.427552\pi$
$379$			37.9317i			1.94842i	−0.225643	+	0.974210i	$0.572448\pi$
$380$	8.93907	−	13.5663i	0.458564	−	0.695934i
$381$	−15.1343	−	8.73777i	−0.775352	−	0.447650i
$382$	−9.38498	+	2.51470i	−0.480177	+	0.128663i
$383$	−6.14426	+	22.9307i	−0.313957	+	1.17170i	0.610999	+	0.791631i	$0.290768\pi$
$383$	−6.14426	+	22.9307i	−0.313957	+	1.17170i	−0.924956	+	0.380073i	$0.875899\pi$
$384$	1.94784			0.0994001
$385$	7.11090	−	18.2876i	0.362405	−	0.932021i
$386$	1.09335			0.0556500
$387$	1.68835	−	6.30102i	0.0858238	−	0.320299i
$388$	1.48978	−	0.399186i	0.0756322	−	0.0202656i
$389$	8.51106	+	4.91386i	0.431528	+	0.249143i	0.699997	−	0.714145i	$-0.253184\pi$
$389$	8.51106	+	4.91386i	0.431528	+	0.249143i	−0.268469	+	0.963288i	$0.586518\pi$
$390$	0.479273	+	2.33105i	0.0242689	+	0.118037i
$391$		−	23.4446i		−	1.18564i
$392$	−4.69530	−	5.19174i	−0.237148	−	0.262223i
$393$	12.0878	−	12.0878i	0.609750	−	0.609750i
$394$	−0.484739	+	0.279864i	−0.0244208	+	0.0140994i
$395$	0.440747	−	7.45896i	0.0221764	−	0.375301i
$396$	−2.24723	−	1.37328i	−0.112928	−	0.0690099i
$397$	15.4014	+	4.12678i	0.772972	+	0.207117i	0.623684	−	0.781677i	$-0.285635\pi$
$397$	15.4014	+	4.12678i	0.772972	+	0.207117i	0.149288	+	0.988794i	$0.452302\pi$
$398$	6.91619	−	6.91619i	0.346677	−	0.346677i
$399$	−0.939172	+	37.4318i	−0.0470174	+	1.87393i
$400$	−2.99255	+	4.00557i	−0.149628	+	0.200279i
$401$	−3.08656	−	5.34608i	−0.154135	−	0.266970i	0.778608	−	0.627510i	$-0.215926\pi$
$401$	−3.08656	−	5.34608i	−0.154135	−	0.266970i	−0.932744	+	0.360540i	$0.882593\pi$
$402$	22.5924	−	6.05360i	1.12680	−	0.301926i
$403$	−0.434500	−	1.62158i	−0.0216440	−	0.0807764i
$404$	−3.53920	−	6.13007i	−0.176082	−	0.304982i
$405$	21.4933	−	10.7717i	1.06801	−	0.535248i
$406$	−12.9929	+	7.07302i	−0.644828	+	0.351028i
$407$	−4.42655	−	4.65306i	−0.219416	−	0.230644i
$408$	1.86828	−	6.97253i	0.0924939	−	0.345192i
$409$	−8.41009	+	14.5667i	−0.415852	+	0.720277i	−0.995517	−	0.0945777i	$-0.969850\pi$
$409$	−8.41009	+	14.5667i	−0.415852	+	0.720277i	0.579665	+	0.814855i	$0.303183\pi$
$410$	10.4396	+	11.7508i	0.515574	+	0.580331i
$411$	−0.505862	−	0.876178i	−0.0249523	−	0.0432187i
$412$	3.34505	−	3.34505i	0.164799	−	0.164799i
$413$	−3.74368	−	15.5187i	−0.184214	−	0.763624i
$414$	−5.02348			−0.246891
$415$	−12.0807	+	2.48384i	−0.593017	+	0.121927i
$416$	−0.273196	+	0.473190i	−0.0133945	+	0.0232000i
$417$	24.7306	−	6.62654i	1.21106	−	0.324503i
$418$	−23.1136	−	6.81545i	−1.13052	−	0.333354i
$419$		−	3.07735i		−	0.150338i	−0.997171	−	0.0751691i	$-0.976050\pi$
$419$		−	3.07735i		−	0.150338i	0.997171	−	0.0751691i	$-0.0239497\pi$
$420$	0.968058	−	11.4828i	0.0472364	−	0.560304i
$421$	−7.58703			−0.369769			−0.184885	−	0.982760i	$-0.559191\pi$
$421$	−7.58703			−0.369769			−0.184885	+	0.982760i	$0.559191\pi$
$422$	−11.8266	−	3.16892i	−0.575709	−	0.154261i
$423$	−3.25372	+	0.871831i	−0.158201	+	0.0423899i
$424$	−7.19619	+	12.4642i	−0.349478	+	0.605314i
$425$	11.4681	+	14.5542i	0.556286	+	0.705983i
$426$			27.5077i			1.33275i
$427$	4.66090	+	1.37507i	0.225557	+	0.0665443i
$428$	2.93242	−	2.93242i	0.141744	−	0.141744i
$429$	3.09998	−	1.68813i	0.149669	−	0.0815036i
$430$	−1.08355	+	18.3374i	−0.0522536	+	0.884310i
$431$	8.33767	+	4.81375i	0.401611	+	0.231870i	0.687179	−	0.726488i	$-0.258849\pi$
$431$	8.33767	+	4.81375i	0.401611	+	0.231870i	−0.285568	+	0.958359i	$0.592182\pi$
$432$	4.15039	+	1.11209i	0.199686	+	0.0535056i
$433$	1.29749	+	1.29749i	0.0623534	+	0.0623534i	0.737596	−	0.675242i	$-0.235961\pi$
$433$	1.29749	+	1.29749i	0.0623534	+	0.0623534i	−0.675242	+	0.737596i	$0.735961\pi$
$434$	−0.203894	+	8.12645i	−0.00978725	+	0.390082i
$435$	−23.1106	−	7.67966i	−1.10807	−	0.368211i
$436$	5.51476	−	3.18395i	0.264109	−	0.152483i
$437$	−44.3985	+	11.8965i	−2.12387	+	0.569088i
$438$	27.6912	−	7.41982i	1.32313	−	0.354533i
$439$	6.84537	+	11.8565i	0.326712	+	0.565881i	0.981857	−	0.189621i	$-0.0607260\pi$
$439$	6.84537	+	11.8565i	0.326712	+	0.565881i	−0.655146	+	0.755503i	$0.727393\pi$
$440$	6.97729	+	2.51345i	0.332629	+	0.119824i
$441$	2.53433	+	4.94709i	0.120682	+	0.235576i
$442$	1.43181	+	1.43181i	0.0681040	+	0.0681040i
$443$	−6.44475	+	24.0521i	−0.306199	+	1.14275i	0.625709	+	0.780057i	$0.284810\pi$
$443$	−6.44475	+	24.0521i	−0.306199	+	1.14275i	−0.931908	+	0.362695i	$0.881857\pi$
$444$	−3.26643	−	1.88588i	−0.155018	−	0.0894998i
$445$	−30.2909	−	1.78988i	−1.43593	−	0.0848484i
$446$	2.91408	−	1.68245i	0.137986	−	0.0796662i
$447$	14.9214	+	14.9214i	0.705756	+	0.705756i
$448$	1.91716	−	1.82332i	0.0905775	−	0.0861436i
$449$		−	26.5851i		−	1.25463i	−0.778766	−	0.627314i	$-0.784154\pi$
$449$		−	26.5851i		−	1.25463i	0.778766	−	0.627314i	$-0.215846\pi$
$450$	3.11854	−	2.45728i	0.147009	−	0.115837i
$451$	12.1569	−	19.8936i	0.572448	−	0.936752i
$452$	−5.34904	−	19.9629i	−0.251598	−	0.938975i
$453$	42.8219	+	11.4741i	2.01195	+	0.539100i
$454$		−	9.35250i		−	0.438935i
$455$	2.65376	+	1.84571i	0.124410	+	0.0865281i
$456$	−14.1523			−0.662744
$457$	0.409034	−	1.52654i	0.0191338	−	0.0714084i	−0.955699	−	0.294346i	$-0.904898\pi$
$457$	0.409034	−	1.52654i	0.0191338	−	0.0714084i	0.974833	+	0.222938i	$0.0715647\pi$
$458$	2.11068	+	7.87716i	0.0986255	+	0.368075i
$459$	7.96177	−	13.7902i	0.371623	−	0.643671i
$460$	13.8561	−	2.84888i	0.646046	−	0.132830i
$461$			4.90705i			0.228544i	0.993449	+	0.114272i	$0.0364536\pi$
$461$			4.90705i			0.228544i	−0.993449	+	0.114272i	$0.963546\pi$
$462$	−16.7103	+	3.59267i	−0.777436	+	0.167146i
$463$	1.32933	+	1.32933i	0.0617790	+	0.0617790i	0.737321	−	0.675542i	$-0.236090\pi$
$463$	1.32933	+	1.32933i	0.0617790	+	0.0617790i	−0.675542	+	0.737321i	$0.736090\pi$
$464$	−2.79568	−	4.84227i	−0.129786	−	0.224797i
$465$	−10.0043	+	8.88797i	−0.463939	+	0.412170i
$466$	−1.10655	+	1.91661i	−0.0512601	+	0.0887851i
$467$	40.5540	+	10.8664i	1.87661	+	0.502837i	0.999756	+	0.0220859i	$0.00703072\pi$
$467$	40.5540	+	10.8664i	1.87661	+	0.502837i	0.876857	+	0.480751i	$0.159636\pi$
$468$	0.306793	−	0.306793i	0.0141815	−	0.0141815i
$469$	16.5700	−	27.1064i	0.765131	−	1.25166i
$470$	8.48022	−	4.24998i	0.391164	−	0.196037i
$471$	−0.0468534	−	0.0811524i	−0.00215889	−	0.00373931i
$472$	5.82817	−	1.56165i	0.268263	−	0.0718809i
$473$	26.4856	−	6.39332i	1.21781	−	0.293965i
$474$	−5.63680	+	3.25441i	−0.258907	+	0.149480i
$475$	21.7429	−	29.1032i	0.997634	−	1.33535i
$476$	−4.68793	−	8.61159i	−0.214871	−	0.394712i
$477$	8.08117	−	8.08117i	0.370011	−	0.370011i
$478$	4.48244	−	16.7287i	0.205022	−	0.765152i
$479$	11.7094	−	20.2812i	0.535015	−	0.926674i	−0.464147	−	0.885758i	$-0.653639\pi$
$479$	11.7094	−	20.2812i	0.535015	−	0.926674i	0.999163	−	0.0409157i	$-0.0130275\pi$
$480$	4.34791	+	0.256917i	0.198454	+	0.0117266i
$481$	0.916276	−	0.529012i	0.0417786	−	0.0241209i
$482$	−12.4659	+	12.4659i	−0.567807	+	0.567807i
$483$	−23.6244	+	22.4679i	−1.07495	+	1.02232i
$484$	0.548485	−	10.9863i	0.0249311	−	0.499378i
$485$	3.37810	−	0.694552i	0.153392	−	0.0315380i
$486$	−6.97330	−	4.02604i	−0.316315	−	0.182625i
$487$	0.265878	+	0.992271i	0.0120481	+	0.0449641i	0.971688	−	0.236267i	$-0.0759240\pi$
$487$	0.265878	+	0.992271i	0.0120481	+	0.0449641i	−0.959640	+	0.281231i	$0.909257\pi$
$488$	−0.475378	+	1.77414i	−0.0215194	+	0.0803113i
$489$			25.3038i			1.14428i
$490$	−9.79593	−	12.2082i	−0.442535	−	0.551509i
$491$			2.87607i			0.129795i	0.997892	+	0.0648976i	$0.0206721\pi$
$491$			2.87607i			0.129795i	−0.997892	+	0.0648976i	$0.979328\pi$
$492$	3.54381	−	13.2257i	0.159767	−	0.596260i
$493$	−20.0150	+	5.36301i	−0.901432	+	0.241538i
$494$	1.98495	−	3.43804i	0.0893073	−	0.154685i
$495$	−4.83508	−	3.36181i	−0.217321	−	0.151102i
$496$	−3.07248			−0.137958
$497$	25.7492	+	27.0745i	1.15501	+	1.21446i
$498$	7.59687	+	7.59687i	0.340424	+	0.340424i
$499$	28.1258	−	16.2385i	1.25908	−	0.726933i	0.286188	−	0.958173i	$-0.407612\pi$
$499$	28.1258	−	16.2385i	1.25908	−	0.726933i	0.972897	+	0.231241i	$0.0742785\pi$
$500$	−7.20823	+	8.54643i	−0.322362	+	0.382208i
$501$	10.3963	+	6.00230i	0.464472	+	0.268163i
$502$	−3.99561	+	14.9118i	−0.178333	+	0.665547i
$503$	−2.51282	+	2.51282i	−0.112041	+	0.112041i	−0.760905	−	0.648864i	$-0.775245\pi$
$503$	−2.51282	+	2.51282i	−0.112041	+	0.112041i	0.648864	+	0.760905i	$0.275245\pi$
$504$	−1.84521	+	1.00448i	−0.0821921	+	0.0447433i
$505$	−7.09155	−	14.1502i	−0.315570	−	0.629675i
$506$	−10.0345	−	18.4268i	−0.446089	−	0.819172i
$507$	−6.40327	−	23.8973i	−0.284379	−	1.06132i
$508$	−2.32207	−	8.66607i	−0.103025	−	0.384495i
$509$	−22.3536	+	12.9058i	−0.990804	+	0.572041i	−0.905515	−	0.424315i	$-0.860515\pi$
$509$	−22.3536	+	12.9058i	−0.990804	+	0.572041i	−0.0852895	+	0.996356i	$0.527182\pi$
$510$	5.09000	−	15.3175i	0.225389	−	0.678270i
$511$	20.3096	−	33.2239i	0.898445	−	1.46974i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−30.1554	−	8.08011i	−1.33139	−	0.356746i
$514$	5.73085	−	9.92613i	0.252777	−	0.437823i
$515$	7.90793	−	7.02552i	0.348465	−	0.309581i
$516$	13.8578	−	8.00079i	0.610055	−	0.352215i
$517$	−9.69737	−	10.1936i	−0.426490	−	0.448313i
$518$	−4.98032	+	1.20144i	−0.218823	+	0.0527881i
$519$	−30.7525			−1.34988
$520$	−0.672234	+	1.02021i	−0.0294794	+	0.0447391i
$521$	−10.6777	+	18.4944i	−0.467800	+	0.810253i	−0.999323	−	0.0367909i	$-0.988286\pi$
$521$	−10.6777	+	18.4944i	−0.467800	+	0.810253i	0.531523	+	0.847044i	$0.321620\pi$
$522$	1.14913	+	4.28863i	0.0502962	+	0.187708i
$523$	−28.2275	−	7.56353i	−1.23430	−	0.330730i	−0.418048	−	0.908425i	$-0.637286\pi$
$523$	−28.2275	−	7.56353i	−1.23430	−	0.330730i	−0.816253	+	0.577695i	$0.803952\pi$
$524$	8.77629			0.383394
$525$	3.67544	−	25.5040i	0.160409	−	1.11308i
$526$	−21.8776			−0.953910
$527$	−2.94700	+	10.9983i	−0.128373	+	0.479095i
$528$	−1.51589	−	6.27987i	−0.0659707	−	0.273296i
$529$	−14.7413	−	8.51088i	−0.640925	−	0.370038i
$530$	−17.7072	+	26.8730i	−0.769150	+	1.16729i
$531$	−4.79121			−0.207921
$532$	−13.9295	+	13.2476i	−0.603920	+	0.574357i
$533$	2.71589	+	2.71589i	0.117638	+	0.117638i
$534$	13.2162	+	22.8911i	0.571921	+	0.990596i
$535$	6.93245	−	6.15888i	0.299716	−	0.266272i
$536$	10.3991	+	6.00393i	0.449173	+	0.259330i
$537$	39.3634	+	10.5474i	1.69866	+	0.455154i
$538$	19.6874	−	19.6874i	0.848786	−	0.848786i
$539$	−13.0842	+	19.1782i	−0.563577	+	0.826063i
$540$	9.11771	+	3.02982i	0.392364	+	0.130383i
$541$	−1.95940	+	1.13126i	−0.0842410	+	0.0486366i	−0.541529	−	0.840682i	$-0.682154\pi$
$541$	−1.95940	+	1.13126i	−0.0842410	+	0.0486366i	0.457288	+	0.889319i	$0.348821\pi$
$542$	−5.04877	−	18.8422i	−0.216863	−	0.809344i
$543$	7.48526	−	2.00567i	0.321223	−	0.0860715i
$544$	3.20941	−	1.85295i	0.137602	−	0.0794447i
$545$	12.7299	−	6.37974i	0.545287	−	0.273278i
$546$	0.0706275	−	2.81494i	0.00302258	−	0.120468i
$547$	1.39712	+	1.39712i	0.0597363	+	0.0597363i	0.736344	−	0.676608i	$-0.236551\pi$
$547$	1.39712	+	1.39712i	0.0597363	+	0.0597363i	−0.676608	+	0.736344i	$0.736551\pi$
$548$	0.134433	−	0.501711i	0.00574269	−	0.0214320i
$549$	0.729238	−	1.26308i	0.0311231	−	0.0539068i
$550$	15.2430	+	6.53075i	0.649964	+	0.278472i
$551$	20.3125	+	35.1823i	0.865343	+	1.49882i
$552$	−8.71336	−	8.71336i	−0.370865	−	0.370865i
$553$	−2.50168	+	8.47962i	−0.106382	+	0.360590i
$554$		−	18.3620i		−	0.780126i
$555$	−7.04251	−	4.64044i	−0.298938	−	0.196976i
$556$	11.3833	+	6.57217i	0.482760	+	0.278722i
$557$	−6.04688	+	1.62026i	−0.256215	+	0.0686525i	−0.384640	−	0.923067i	$-0.625674\pi$
$557$	−6.04688	+	1.62026i	−0.256215	+	0.0686525i	0.128425	+	0.991719i	$0.459008\pi$
$558$	2.35662	+	0.631454i	0.0997636	+	0.0267316i
$559$			4.48864i			0.189849i
$560$	4.51994	−	3.81709i	0.191002	−	0.161301i
$561$	−23.9336	−	0.597063i	−1.01048	−	0.0252080i
$562$	15.1857	+	4.06900i	0.640570	+	0.171640i
$563$	−4.22921	−	15.7836i	−0.178240	−	0.665201i	−0.995977	−	0.0896089i	$-0.971438\pi$
$563$	−4.22921	−	15.7836i	−0.178240	−	0.665201i	0.817737	−	0.575592i	$-0.195228\pi$
$564$	−7.15587	−	4.13145i	−0.301317	−	0.173965i
$565$	−9.30691	−	45.2662i	−0.391545	−	1.90436i
$566$	2.85371			0.119950
$567$	−27.6530	+	6.67092i	−1.16131	+	0.280152i
$568$	−9.98588	+	9.98588i	−0.418998	+	0.418998i
$569$	−7.27318	−	12.5975i	−0.304908	−	0.528116i	0.672333	−	0.740249i	$-0.265292\pi$
$569$	−7.27318	−	12.5975i	−0.304908	−	0.528116i	−0.977241	+	0.212133i	$0.931959\pi$
$570$	−31.5905	−	1.86667i	−1.32318	−	0.0781863i
$571$	−28.9266	−	16.7008i	−1.21054	−	0.698906i	−0.247663	−	0.968846i	$-0.579663\pi$
$571$	−28.9266	−	16.7008i	−1.21054	−	0.698906i	−0.962877	+	0.269940i	$0.912996\pi$
$572$	1.73819	+	0.512534i	0.0726773	+	0.0214301i
$573$	13.3822	+	13.3822i	0.559049	+	0.559049i
$574$	−8.89218	−	16.3347i	−0.371153	−	0.681797i
$575$	31.3051	−	4.53159i	1.30551	−	0.188981i
$576$	−0.397033	−	0.687681i	−0.0165430	−	0.0286534i
$577$	1.03675	+	3.86920i	0.0431604	+	0.161077i	0.984143	−	0.177379i	$-0.0567620\pi$
$577$	1.03675	+	3.86920i	0.0431604	+	0.161077i	−0.940982	+	0.338456i	$0.890095\pi$
$578$	0.845370	+	3.15496i	0.0351628	+	0.131229i
$579$	−1.06483	−	1.84434i	−0.0442529	−	0.0766483i
$580$	−5.60177	−	11.1775i	−0.232601	−	0.464122i
$581$	14.5885	+	0.366028i	0.605232	+	0.0151854i
$582$	−2.12430	−	2.12430i	−0.0880551	−	0.0880551i
$583$	45.7852	+	13.5005i	1.89623	+	0.559135i
$584$	12.7460	+	7.35893i	0.527435	+	0.304515i
$585$	0.725282	−	0.644351i	0.0299867	−	0.0266406i
$586$	8.73575	+	15.1308i	0.360870	+	0.625046i
$587$	6.17604	−	6.17604i	0.254912	−	0.254912i	−0.568069	−	0.822981i	$-0.692309\pi$
$587$	6.17604	−	6.17604i	0.254912	−	0.254912i	0.822981	+	0.568069i	$0.192309\pi$
$588$	−4.18499	+	12.9767i	−0.172586	+	0.535151i
$589$	22.3236			0.919829
$590$	13.2155	−	2.71716i	0.544072	−	0.111864i
$591$	0.944193	+	0.545130i	0.0388389	+	0.0224237i
$592$	−0.501172	−	1.87040i	−0.0205981	−	0.0768730i
$593$	24.4101	+	6.54066i	1.00240	+	0.268593i	0.722451	−	0.691422i	$-0.243015\pi$
$593$	24.4101	+	6.54066i	1.00240	+	0.268593i	0.279950	+	0.960015i	$0.409682\pi$
$594$	0.355401	−	14.2464i	0.0145823	−	0.584538i
$595$	−9.32842	−	19.8409i	−0.382428	−	0.813398i
$596$			10.8335i			0.443759i
$597$	−18.4025	−	4.93095i	−0.753166	−	0.201810i
$598$	3.33885	−	0.894641i	0.136536	−	0.0365846i
$599$	−9.26663	−	5.35009i	−0.378624	−	0.218599i	0.298595	−	0.954380i	$-0.403482\pi$
$599$	−9.26663	−	5.35009i	−0.378624	−	0.218599i	−0.677220	+	0.735781i	$0.736815\pi$
$600$	9.67141	+	1.14697i	0.394834	+	0.0468247i
$601$			37.5047i			1.52985i	0.644120	+	0.764924i	$0.277224\pi$
$601$			37.5047i			1.52985i	−0.644120	+	0.764924i	$0.722776\pi$
$602$	6.15025	−	20.8467i	0.250666	−	0.849648i
$603$	−6.74228	−	6.74228i	−0.274567	−	0.274567i
$604$	11.3799	+	19.7106i	0.463043	+	0.802014i
$605$	2.67339	−	24.4510i	0.108689	−	0.994076i
$606$	−6.89377	+	11.9404i	−0.280040	+	0.485044i
$607$	−4.39076	+	16.3865i	−0.178215	+	0.665109i	0.817766	+	0.575551i	$0.195212\pi$
$607$	−4.39076	+	16.3865i	−0.178215	+	0.665109i	−0.995982	+	0.0895583i	$0.971454\pi$
$608$	−5.13761	−	5.13761i	−0.208358	−	0.208358i
$609$	24.5853	+	15.0289i	0.996249	+	0.609002i
$610$	−1.29513	+	3.89748i	−0.0524384	+	0.157804i
$611$	2.00731	−	1.15892i	0.0812071	−	0.0468850i
$612$	−2.84246	+	0.761635i	−0.114900	+	0.0307873i
$613$	0.963961	+	3.59755i	0.0389340	+	0.145304i	0.982657	−	0.185434i	$-0.0593691\pi$
$613$	0.963961	+	3.59755i	0.0389340	+	0.145304i	−0.943723	+	0.330738i	$0.892702\pi$
$614$	−6.03220	+	3.48269i	−0.243440	+	0.140550i
$615$	9.65485	−	29.0546i	0.389321	−	1.17159i
$616$	−7.37044	−	4.76200i	−0.296963	−	0.191867i
$617$	−1.51321	+	1.51321i	−0.0609196	+	0.0609196i	−0.736910	−	0.675991i	$-0.763716\pi$
$617$	−1.51321	+	1.51321i	−0.0609196	+	0.0609196i	0.675991	+	0.736910i	$0.263716\pi$
$618$	−8.90048	−	2.38488i	−0.358030	−	0.0959338i
$619$	20.2956	+	11.7177i	0.815748	+	0.470972i	0.848948	−	0.528476i	$-0.177236\pi$
$619$	20.2956	+	11.7177i	0.815748	+	0.470972i	−0.0331998	+	0.999449i	$0.510570\pi$
$620$	−6.85831	−	0.405255i	−0.275436	−	0.0162754i
$621$	−13.5914	−	23.5409i	−0.545403	−	0.944665i
$622$	−8.49014	−	8.49014i	−0.340424	−	0.340424i
$623$	34.4358	+	10.1594i	1.37964	+	0.407026i
$624$	1.06428			0.0426054
$625$	−17.2173	+	18.1264i	−0.688692	+	0.725054i
$626$	17.6286	+	10.1779i	0.704579	+	0.406789i
$627$	11.0140	+	45.6275i	0.439856	+	1.82219i
$628$	0.0124513	−	0.0464689i	0.000496861	−	0.00185431i
$629$	−7.17605			−0.286128
$630$	−4.25132	+	1.99880i	−0.169377	+	0.0796343i
$631$	26.0471			1.03692			0.518459	−	0.855103i	$-0.326506\pi$
$631$	26.0471			1.03692			0.518459	+	0.855103i	$0.326506\pi$
$632$	−3.22770	−	0.864861i	−0.128391	−	0.0344023i
$633$	6.17254	+	23.0362i	0.245337	+	0.915608i
$634$	−4.04629	+	7.00838i	−0.160699	+	0.278338i
$635$	−4.04021	−	19.6505i	−0.160331	−	0.779804i
$636$	28.0340			1.11162
$637$	−2.56547	−	2.83673i	−0.101648	−	0.112395i
$638$	−13.4359	+	12.7818i	−0.531931	+	0.506037i
$639$	9.71155	−	5.60697i	0.384183	−	0.221808i
$640$	1.48512	+	1.67165i	0.0587045	+	0.0660778i
$641$	7.22923	−	12.5214i	0.285537	−	0.494565i	−0.687202	−	0.726466i	$-0.741161\pi$
$641$	7.22923	−	12.5214i	0.285537	−	0.494565i	0.972739	+	0.231901i	$0.0744946\pi$
$642$	−7.80255	−	2.09069i	−0.307942	−	0.0825129i
$643$	−1.26582	−	1.26582i	−0.0499190	−	0.0499190i	0.681707	−	0.731626i	$-0.261238\pi$
$643$	−1.26582	−	1.26582i	−0.0499190	−	0.0499190i	−0.731626	+	0.681707i	$0.761238\pi$
$644$	−16.7325	−	0.419822i	−0.659352	−	0.0165433i
$645$	31.9883	−	16.0313i	1.25954	−	0.631234i
$646$	−23.3185	+	13.4630i	−0.917455	+	0.529693i
$647$	4.07153	+	15.1952i	0.160068	+	0.597384i	0.998618	+	0.0525581i	$0.0167375\pi$
$647$	4.07153	+	15.1952i	0.160068	+	0.597384i	−0.838549	+	0.544826i	$0.816596\pi$
$648$	−2.78273	−	10.3853i	−0.109316	−	0.407973i
$649$	−9.57055	−	17.5748i	−0.375677	−	0.689872i
$650$	−1.63511	+	2.18861i	−0.0641342	+	0.0858445i
$651$	13.9069	−	7.57056i	0.545054	−	0.296714i
$652$	−9.18584	+	9.18584i	−0.359745	+	0.359745i
$653$	4.46960	−	16.6808i	0.174909	−	0.652769i	−0.821658	−	0.569980i	$-0.806951\pi$
$653$	4.46960	−	16.6808i	0.174909	−	0.652769i	0.996567	−	0.0827884i	$-0.0263826\pi$
$654$	−10.7418	−	6.20181i	−0.420039	−	0.242510i
$655$	19.5902	+	1.15758i	0.765453	+	0.0452304i
$656$	6.08769	−	3.51473i	0.237684	−	0.137227i
$657$	−8.26393	−	8.26393i	−0.322406	−	0.322406i
$658$	−10.9105	+	2.63202i	−0.425337	+	0.102607i
$659$	−20.1514			−0.784986			−0.392493	−	0.919755i	$-0.628387\pi$
$659$	−20.1514			−0.784986			−0.392493	+	0.919755i	$0.628387\pi$
$660$	−2.55543	−	14.2177i	−0.0994700	−	0.553424i
$661$	8.58081	−	14.8624i	0.333755	−	0.578080i	−0.649490	−	0.760370i	$-0.725018\pi$
$661$	8.58081	−	14.8624i	0.333755	−	0.578080i	0.983245	+	0.182290i	$0.0583509\pi$
$662$	−17.7893	+	4.76663i	−0.691402	+	0.185261i
$663$	1.02082	−	3.80974i	0.0396452	−	0.147958i
$664$			5.51566i			0.214049i
$665$	−32.8404	+	27.7337i	−1.27350	+	1.07547i
$666$			1.53761i			0.0595813i
$667$	−9.15509	+	34.1672i	−0.354486	+	1.32296i
$668$	1.59511	+	5.95305i	0.0617168	+	0.230330i
$669$	−5.67616	−	3.27713i	−0.219453	−	0.126701i
$670$	22.4207	+	14.7734i	0.866187	+	0.570748i
$671$	6.08982	+	0.151920i	0.235095	+	0.00586483i
$672$	−4.94287	−	1.45826i	−0.190675	−	0.0562536i
$673$	−23.1337	+	23.1337i	−0.891739	+	0.891739i	−0.994687	−	0.102948i	$-0.967172\pi$
$673$	−23.1337	+	23.1337i	−0.891739	+	0.891739i	0.102948	+	0.994687i	$0.467172\pi$
$674$	−22.9988	+	13.2784i	−0.885881	+	0.511464i
$675$	19.9527	+	7.96569i	0.767979	+	0.306600i
$676$	6.35073	−	10.9998i	0.244259	−	0.423069i
$677$	−12.5289	+	46.7585i	−0.481525	+	1.79707i	0.113700	+	0.993515i	$0.463730\pi$
$677$	−12.5289	+	46.7585i	−0.481525	+	1.79707i	−0.595224	+	0.803560i	$0.702937\pi$
$678$	−28.4654	+	28.4654i	−1.09321	+	1.09321i
$679$	−4.07935	−	0.102352i	−0.156551	−	0.00392790i
$680$	7.40836	−	3.71280i	0.284098	−	0.142379i
$681$	−15.7765	+	9.10857i	−0.604557	+	0.349041i
$682$	2.39114	+	9.90574i	0.0915614	+	0.379311i
$683$	−17.5159	+	4.69338i	−0.670229	+	0.179587i	−0.577858	−	0.816137i	$-0.696111\pi$
$683$	−17.5159	+	4.69338i	−0.670229	+	0.179587i	−0.0923708	+	0.995725i	$0.529445\pi$
$684$	2.88471	+	4.99647i	0.110300	+	0.191045i
$685$	0.366253	−	1.10217i	0.0139938	−	0.0421119i
$686$	8.02805	+	16.6898i	0.306512	+	0.637221i
$687$	11.2322	−	11.2322i	0.428533	−	0.428533i
$688$	7.93514	+	2.12621i	0.302524	+	0.0810611i
$689$	−3.93194	+	6.81033i	−0.149795	+	0.259453i
$690$	−18.3005	−	20.5990i	−0.696686	−	0.784191i
$691$	−7.12026	−	12.3326i	−0.270867	−	0.469156i	0.698217	−	0.715886i	$-0.253977\pi$
$691$	−7.12026	−	12.3326i	−0.270867	−	0.469156i	−0.969084	+	0.246730i	$0.920644\pi$
$692$	−11.1638	−	11.1638i	−0.424384	−	0.424384i
$693$	4.67451	+	5.16726i	0.177570	+	0.196288i
$694$		−	20.6327i		−	0.783208i
$695$	24.5427	+	16.1717i	0.930958	+	0.613426i
$696$	−5.44553	+	9.43194i	−0.206412	+	0.357517i
$697$	−6.74237	−	25.1629i	−0.255385	−	0.953111i
$698$	2.95593	−	11.0317i	0.111884	−	0.417555i
$699$	4.31077			0.163048
$700$	10.5928	−	7.92423i	0.400369	−	0.299508i
$701$			2.53145i			0.0956117i	0.998857	+	0.0478058i	$0.0152229\pi$
$701$			2.53145i			0.0956117i	−0.998857	+	0.0478058i	$0.984777\pi$
$702$	2.26774	+	0.607639i	0.0855903	+	0.0229339i
$703$	3.64136	+	13.5897i	0.137336	+	0.512546i
$704$	1.72943	−	2.83003i	0.0651803	−	0.106661i
$705$	−15.4282	−	10.1660i	−0.581061	−	0.382872i
$706$			18.3249i			0.689667i
$707$	4.39182	+	18.2054i	0.165172	+	0.684685i
$708$	−8.31047	−	8.31047i	−0.312327	−	0.312327i
$709$	28.2548	−	16.3129i	1.06113	−	0.612644i	0.135386	−	0.990793i	$-0.456773\pi$
$709$	28.2548	−	16.3129i	1.06113	−	0.612644i	0.925745	+	0.378149i	$0.123439\pi$
$710$	−23.6074	+	20.9731i	−0.885968	+	0.787107i
$711$	2.29793	+	1.32671i	0.0861791	+	0.0497556i
$712$	−3.51221	+	13.1077i	−0.131626	+	0.491233i
$713$	13.7443	+	13.7443i	0.514727	+	0.514727i
$714$	−9.96102	+	16.2949i	−0.372782	+	0.609823i
$715$	3.81234	+	1.37333i	0.142573	+	0.0513596i
$716$	10.4608	+	18.1187i	0.390940	+	0.677128i
$717$	−32.5847	+	8.73106i	−1.21690	+	0.326067i
$718$	−12.3882	+	3.31940i	−0.462322	+	0.123879i
$719$	7.00294	−	4.04315i	0.261166	−	0.150784i	−0.363700	−	0.931516i	$-0.618487\pi$
$719$	7.00294	−	4.04315i	0.261166	−	0.150784i	0.624866	+	0.780732i	$0.285153\pi$
$720$	−0.795543	−	1.58739i	−0.0296481	−	0.0591586i
$721$	−10.9927	+	5.98417i	−0.409391	+	0.222862i
$722$	23.8932	+	23.8932i	0.889212	+	0.889212i
$723$	33.1692	+	8.88767i	1.23358	+	0.330536i
$724$	3.44541	+	1.98921i	0.128048	+	0.0739284i
$725$	−11.0298	−	25.6891i	−0.409637	−	0.954068i
$726$	−19.0667	+	9.77455i	−0.707633	+	0.362767i
$727$	8.40403	−	8.40403i	0.311688	−	0.311688i	−0.533875	−	0.845563i	$-0.679265\pi$
$727$	8.40403	−	8.40403i	0.311688	−	0.311688i	0.845563	+	0.533875i	$0.179265\pi$
$728$	1.04752	−	0.996245i	0.0388238	−	0.0369233i
$729$		−	16.5709i		−	0.613735i
$730$	27.4808	+	18.1076i	1.01711	+	0.670193i
$731$	15.2221	−	26.3655i	0.563010	−	0.975163i
$732$	3.45572	−	0.925959i	0.127727	−	0.0342244i
$733$	25.8612	+	6.92950i	0.955207	+	0.255947i	0.702570	−	0.711614i	$-0.252036\pi$
$733$	25.8612	+	6.92950i	0.955207	+	0.255947i	0.252636	+	0.967561i	$0.418702\pi$
$734$	1.39426			0.0514631
$735$	−11.0532	+	28.4143i	−0.407705	+	1.04808i
$736$		−	6.32628i		−	0.233190i
$737$	11.2638	−	38.1995i	0.414906	−	1.40710i
$738$	−5.39166	+	1.44469i	−0.198470	+	0.0531798i
$739$	10.6878	−	18.5119i	0.393158	−	0.680970i	−0.599706	−	0.800220i	$-0.704716\pi$
$739$	10.6878	−	18.5119i	0.393158	−	0.680970i	0.992864	+	0.119250i	$0.0380491\pi$
$740$	−0.872001	−	4.24116i	−0.0320554	−	0.155908i
$741$	−7.73273			−0.284069
$742$	27.5926	−	26.2419i	1.01296	−	0.963369i
$743$	21.2556	−	21.2556i	0.779794	−	0.779794i	−0.200002	−	0.979796i	$-0.564095\pi$
$743$	21.2556	−	21.2556i	0.779794	−	0.779794i	0.979796	+	0.200002i	$0.0640948\pi$
$744$	2.99234	+	5.18289i	0.109705	+	0.190014i
$745$	−1.42893	+	24.1824i	−0.0523519	+	0.885973i
$746$	−16.0540	+	27.8064i	−0.587780	+	1.01806i
$747$	1.13357	−	4.23056i	0.0414753	−	0.154788i
$748$	−8.47167	−	8.90516i	−0.309755	−	0.325605i
$749$	−9.63673	+	5.24599i	−0.352118	+	0.191684i
$750$	21.4370	+	3.83587i	0.782768	+	0.140066i
$751$	18.9952	+	32.9007i	0.693145	+	1.20056i	0.970802	+	0.239882i	$0.0771088\pi$
$751$	18.9952	+	32.9007i	0.693145	+	1.20056i	−0.277657	+	0.960680i	$0.589558\pi$
$752$	−1.09793	−	4.09754i	−0.0400375	−	0.149422i
$753$	29.0458	−	7.78279i	1.05849	−	0.283621i
$754$	−1.52754	−	2.64578i	−0.0556297	−	0.0963535i
$755$	22.8022	+	45.4986i	0.829857	+	1.65586i
$756$	−9.69953	−	5.92928i	−0.352769	−	0.215646i
$757$	−30.7167	+	30.7167i	−1.11642	+	1.11642i	−0.124156	+	0.992263i	$0.539622\pi$
$757$	−30.7167	+	30.7167i	−1.11642	+	1.11642i	−0.992263	+	0.124156i	$0.960378\pi$
$758$	36.6392	+	9.81744i	1.33080	+	0.356586i
$759$	−21.3110	+	34.8732i	−0.773539	+	1.26582i
$760$	−10.7904	−	12.1457i	−0.391409	−	0.440570i
$761$	31.2865	−	18.0633i	1.13414	−	0.654794i	0.189164	−	0.981946i	$-0.439422\pi$
$761$	31.2865	−	18.0633i	1.13414	−	0.654794i	0.944972	+	0.327152i	$0.106089\pi$
$762$	−12.3571	+	12.3571i	−0.447650	+	0.447650i
$763$	−16.3780	+	3.95099i	−0.592925	+	0.143036i
$764$			9.71604i			0.351514i
$765$	−6.44533	+	1.32519i	−0.233031	+	0.0479122i
$766$	20.5591	+	11.8698i	0.742831	+	0.428874i
$767$	3.18447	−	0.853275i	0.114984	−	0.0308100i
$768$	0.504137	−	1.88147i	0.0181915	−	0.0678915i
$769$	21.5623			0.777557			0.388779	−	0.921331i	$-0.372897\pi$
$769$	21.5623			0.777557			0.388779	+	0.921331i	$0.372897\pi$
$770$	−15.8240	−	11.6018i	−0.570257	−	0.418099i
$771$	−22.3255			−0.804034
$772$	0.282979	−	1.05609i	0.0101847	−	0.0380096i
$773$	25.0017	−	6.69919i	0.899250	−	0.240953i	0.220556	−	0.975374i	$-0.429213\pi$
$773$	25.0017	−	6.69919i	0.899250	−	0.240953i	0.678694	+	0.734421i	$0.262546\pi$
$774$	−5.64934	−	3.26165i	−0.203061	−	0.117238i
$775$	−15.2555	−	1.80920i	−0.547993	−	0.0649884i
$776$		−	1.54233i		−	0.0553666i
$777$	6.87710	+	7.23107i	0.246714	+	0.259413i
$778$	6.94925	−	6.94925i	0.249143	−	0.249143i
$779$	−44.2312	+	25.5369i	−1.58475	+	0.914954i
$780$	2.37566	+	0.140377i	0.0850624	+	0.00502631i
$781$	39.9662	+	24.4233i	1.43010	+	0.873934i
$782$	−22.6457	−	6.06791i	−0.809810	−	0.216988i
$783$	−16.9882	+	16.9882i	−0.607110	+	0.607110i
$784$	−6.23007	+	3.19158i	−0.222503	+	0.113985i
$785$	0.0339226	−	0.102084i	0.00121075	−	0.00364355i
$786$	−8.54739	−	14.8045i	−0.304875	−	0.528059i
$787$	−42.9223	+	11.5010i	−1.53002	+	0.409966i	−0.923024	−	0.384742i	$-0.874290\pi$
$787$	−42.9223	+	11.5010i	−1.53002	+	0.409966i	−0.606991	+	0.794708i	$0.707624\pi$
$788$	0.144869	+	0.540657i	0.00516073	+	0.0192601i
$789$	21.3070	+	36.9048i	0.758550	+	1.31385i
$790$	−7.09072	−	2.35625i	−0.252277	−	0.0838316i
$791$	−1.37150	+	54.6628i	−0.0487650	+	1.94358i
$792$	−1.90811	+	1.81523i	−0.0678018	+	0.0645013i
$793$	−0.259743	+	0.969374i	−0.00922374	+	0.0344235i
$794$	7.97233	−	13.8085i	0.282927	−	0.490045i
$795$	62.5768	+	3.69764i	2.21937	+	0.131142i
$796$	−4.89048	−	8.47056i	−0.173339	−	0.300231i
$797$	−2.16707	+	2.16707i	−0.0767615	+	0.0767615i	−0.744445	−	0.667684i	$-0.767286\pi$
$797$	−2.16707	+	2.16707i	−0.0767615	+	0.0767615i	0.667684	+	0.744445i	$0.267286\pi$
$798$	35.9133	+	10.5952i	1.27132	+	0.375067i
$799$	−15.7208			−0.556161
$800$	3.09456	+	3.92730i	0.109409	+	0.138851i
$801$	5.38779	−	9.33192i	0.190368	−	0.329727i
$802$	−5.96278	+	1.59772i	−0.210553	+	0.0564175i
$803$	13.8058	−	46.8206i	0.487198	−	1.65226i
$804$		−	23.3893i		−	0.824878i
$805$	−37.2945	−	3.14411i	−1.31446	−	0.110815i
$806$	−1.67878			−0.0591324
$807$	−52.3842	−	14.0363i	−1.84401	−	0.494102i
$808$	−6.83720	+	1.83202i	−0.240532	+	0.0644503i
$809$	−17.7001	+	30.6574i	−0.622302	+	1.07786i	0.366754	+	0.930318i	$0.380469\pi$
$809$	−17.7001	+	30.6574i	−0.622302	+	1.07786i	−0.989056	+	0.147540i	$0.952864\pi$
$810$	−4.84174	−	23.5488i	−0.170121	−	0.827422i
$811$			34.4635i			1.21018i	0.796158	+	0.605089i	$0.206863\pi$
$811$			34.4635i			1.21018i	−0.796158	+	0.605089i	$0.793137\pi$
$812$	3.46919	+	14.3808i	0.121745	+	0.504668i
$813$	−26.8674	+	26.8674i	−0.942283	+	0.942283i
$814$	−5.64018	+	3.07142i	−0.197688	+	0.107653i
$815$	−21.7160	+	19.2928i	−0.760679	+	0.675798i
$816$	−6.25140	−	3.60925i	−0.218843	−	0.126349i
$817$	−57.6541	−	15.4484i	−2.01706	−	0.540470i
$818$	11.8937	+	11.8937i	0.415852	+	0.415852i
$819$	−1.00821	+	0.548842i	−0.0352296	+	0.0191781i
$820$	14.0524	−	7.04253i	0.490730	−	0.245936i
$821$	10.0699	−	5.81385i	0.351441	−	0.202905i	−0.313879	−	0.949463i	$-0.601629\pi$
$821$	10.0699	−	5.81385i	0.351441	−	0.202905i	0.665320	+	0.746558i	$0.268295\pi$
$822$	−0.977250	+	0.261853i	−0.0340855	+	0.00913318i
$823$	40.0870	−	10.7413i	1.39734	−	0.374417i	0.519954	−	0.854195i	$-0.325949\pi$
$823$	40.0870	−	10.7413i	1.39734	−	0.374417i	0.877390	+	0.479777i	$0.159283\pi$
$824$	−2.36531	−	4.09683i	−0.0823993	−	0.142720i
$825$	−3.82887	−	32.0735i	−0.133304	−	1.11666i
$826$	−15.9588	−	0.400410i	−0.555278	−	0.0139320i
$827$	−28.7023	−	28.7023i	−0.998077	−	0.998077i	0.00192148	−	0.999998i	$-0.499388\pi$
$827$	−28.7023	−	28.7023i	−0.998077	−	0.998077i	−0.999998	+	0.00192148i	$0.999388\pi$
$828$	−1.30017	+	4.85231i	−0.0451841	+	0.168629i
$829$	35.5852	+	20.5451i	1.23592	+	0.713561i	0.968259	−	0.249951i	$-0.0804145\pi$
$829$	35.5852	+	20.5451i	1.23592	+	0.713561i	0.267665	+	0.963512i	$0.413748\pi$
$830$	−0.727507	+	12.3119i	−0.0252521	+	0.427353i
$831$	−30.9744	+	17.8831i	−1.07449	+	0.620357i
$832$	0.386358	+	0.386358i	0.0133945	+	0.0133945i
$833$	5.44907	+	25.3626i	0.188799	+	0.878762i
$834$		−	25.6030i		−	0.886559i
$835$	2.77538	+	13.4986i	0.0960458	+	0.467140i
$836$	−12.5655	+	20.5621i	−0.434586	+	0.711155i
$837$	3.41688	+	12.7520i	0.118105	+	0.440773i
$838$	−2.97249	−	0.796476i	−0.102683	−	0.0275138i
$839$		−	53.8142i		−	1.85787i	−0.370239	−	0.928936i	$-0.620724\pi$
$839$		−	53.8142i		−	1.85787i	0.370239	−	0.928936i	$-0.379276\pi$
$840$	−10.8410	−	3.90704i	−0.374050	−	0.134806i
$841$	2.26340			0.0780481
$842$	−1.96367	+	7.32851i	−0.0676725	+	0.252557i
$843$	−7.92574	−	29.5793i	−0.272977	−	1.01876i
$844$	−6.12189	+	10.6034i	−0.210724	+	0.364985i
$845$	15.6268	−	23.7158i	0.537578	−	0.815848i
$846$			3.36850i			0.115811i
$847$	−9.61682	+	27.4685i	−0.330438	+	0.943828i
$848$	10.1770	+	10.1770i	0.349478	+	0.349478i
$849$	−2.77928	−	4.81385i	−0.0953846	−	0.165211i
$850$	17.0265	−	7.31046i	0.584003	−	0.250747i
$851$	−6.12504	+	10.6089i	−0.209964	+	0.363668i
$852$	26.5704	+	7.11951i	0.910286	+	0.243910i
$853$	−7.29843	+	7.29843i	−0.249894	+	0.249894i	−0.820927	−	0.571033i	$-0.806543\pi$
$853$	−7.29843	+	7.29843i	−0.249894	+	0.249894i	0.571033	+	0.820927i	$0.306543\pi$
$854$	2.53455	−	4.14619i	0.0867304	−	0.141880i
$855$	5.78015	+	11.5335i	0.197677	+	0.394437i
$856$	−2.07353	−	3.59146i	−0.0708718	−	0.122754i
$857$	−13.8651	+	3.71514i	−0.473623	+	0.126907i	−0.487732	−	0.872994i	$-0.662176\pi$
$857$	−13.8651	+	3.71514i	−0.473623	+	0.126907i	0.0141089	+	0.999900i	$0.495509\pi$
$858$	−0.828272	−	3.43127i	−0.0282767	−	0.117142i
$859$	−4.28018	+	2.47116i	−0.146038	+	0.0843150i	−0.571238	−	0.820784i	$-0.693537\pi$
$859$	−4.28018	+	2.47116i	−0.146038	+	0.0843150i	0.425201	+	0.905099i	$0.360204\pi$
$860$	17.4322	+	5.79271i	0.594432	+	0.197530i
$861$	−18.8943	+	30.9087i	−0.643917	+	1.05336i
$862$	6.80768	−	6.80768i	0.231870	−	0.231870i
$863$	−11.2894	+	42.1326i	−0.384296	+	1.43421i	0.454978	+	0.890503i	$0.349647\pi$
$863$	−11.2894	+	42.1326i	−0.384296	+	1.43421i	−0.839274	+	0.543709i	$0.817020\pi$
$864$	2.14840	−	3.72114i	0.0730900	−	0.126596i
$865$	−23.4471	−	26.3921i	−0.797225	−	0.897357i
$866$	1.58909	−	0.917464i	0.0539996	−	0.0311767i
$867$	4.49871	−	4.49871i	0.152784	−	0.152784i
$868$	7.79678	+	2.30023i	0.264640	+	0.0780748i
$869$	−0.276391	+	11.0793i	−0.00937591	+	0.375838i
$870$	−13.3994	+	20.3355i	−0.454284	+	0.689437i
$871$	5.68199	+	3.28050i	0.192527	+	0.111155i
$872$	−1.64813	−	6.15091i	−0.0558128	−	0.208296i
$873$	−0.316980	+	1.18298i	−0.0107281	+	0.0400379i
$874$			45.9647i			1.55478i
$875$	24.6901	−	16.2911i	0.834677	−	0.550740i
$876$		−	28.6680i		−	0.968602i
$877$	3.51349	−	13.1125i	0.118642	−	0.442778i	−0.880891	−	0.473318i	$-0.843056\pi$
$877$	3.51349	−	13.1125i	0.118642	−	0.442778i	0.999534	+	0.0305400i	$0.00972269\pi$
$878$	13.2242	−	3.54343i	0.446297	−	0.119585i
$879$	17.0158	−	29.4722i	0.573929	−	0.994074i
$880$	4.23366	−	6.08902i	0.142717	−	0.205261i
$881$	25.4735			0.858223			0.429112	−	0.903251i	$-0.358827\pi$
$881$	25.4735			0.858223			0.429112	+	0.903251i	$0.358827\pi$
$882$	5.43445	−	1.16757i	0.182987	−	0.0393142i
$883$	−6.51338	−	6.51338i	−0.219193	−	0.219193i	0.588965	−	0.808158i	$-0.299535\pi$
$883$	−6.51338	−	6.51338i	−0.219193	−	0.219193i	−0.808158	+	0.588965i	$0.799535\pi$
$884$	1.75360	−	1.01244i	0.0589798	−	0.0340520i
$885$	−17.4543	−	19.6466i	−0.586719	−	0.660412i
$886$	21.5646	+	12.4503i	0.724475	+	0.418276i
$887$	13.4109	−	50.0501i	0.450293	−	1.68052i	−0.251276	−	0.967916i	$-0.580850\pi$
$887$	13.4109	−	50.0501i	0.450293	−	1.68052i	0.701569	−	0.712602i	$-0.252483\pi$
$888$	−2.66703	+	2.66703i	−0.0894998	+	0.0894998i
$889$	−0.595381	+	23.7296i	−0.0199684	+	0.795866i
$890$	−9.56875	+	28.7955i	−0.320745	+	0.965227i
$891$	−31.3168	+	17.0539i	−1.04915	+	0.571327i
$892$	−0.870899	−	3.25024i	−0.0291598	−	0.108826i
$893$	7.97722	+	29.7714i	0.266948	+	0.996262i
$894$	18.2748	−	10.5510i	0.611202	−	0.352878i
$895$	20.9606	+	41.8239i	0.700636	+	1.39802i
$896$	−1.26499	−	2.32375i	−0.0422603	−	0.0776310i
$897$	−4.76091	−	4.76091i	−0.158962	−	0.158962i
$898$	−25.6792	−	6.88073i	−0.856927	−	0.229613i
$899$	8.58968	−	14.8778i	0.286482	−	0.496201i
$900$	−1.56642	−	3.64827i	−0.0522138	−	0.121609i
$901$	46.1910	−	26.6684i	1.53885	−	0.888454i
$902$	−16.0693	−	16.8915i	−0.535049	−	0.562427i
$903$	−41.1556	+	9.92827i	−1.36957	+	0.330392i
$904$	−20.6671			−0.687377
$905$	7.42839	+	4.89471i	0.246928	+	0.162706i
$906$	22.1662	−	38.3931i	0.736424	−	1.27552i
$907$	−6.09313	−	22.7399i	−0.202319	−	0.755064i	−0.990250	−	0.139301i	$-0.955514\pi$
$907$	−6.09313	−	22.7399i	−0.202319	−	0.755064i	0.787931	−	0.615763i	$-0.211152\pi$
$908$	−9.03383	−	2.42061i	−0.299798	−	0.0803306i
$909$	5.62071			0.186427
$910$	2.46966	−	2.08563i	0.0818684	−	0.0691379i
$911$	−13.0385			−0.431986			−0.215993	−	0.976395i	$-0.569299\pi$
$911$	−13.0385			−0.431986			−0.215993	+	0.976395i	$0.569299\pi$
$912$	−3.66290	+	13.6701i	−0.121291	+	0.452663i
$913$	17.7826	−	4.29253i	0.588519	−	0.142062i
$914$	−1.36866	−	0.790194i	−0.0452711	−	0.0261373i
$915$	7.83591	−	1.61110i	0.259047	−	0.0532612i
$916$	8.15503			0.269450
$917$	−22.2709	−	6.57042i	−0.735449	−	0.216974i
$918$	−11.2596	−	11.2596i	−0.371623	−	0.371623i
$919$	−12.9736	−	22.4710i	−0.427961	−	0.741249i	0.568731	−	0.822523i	$-0.307434\pi$
$919$	−12.9736	−	22.4710i	−0.427961	−	0.741249i	−0.996692	+	0.0812739i	$0.974101\pi$
$920$	0.834426	−	14.1214i	0.0275102	−	0.465567i
$921$	11.7497	+	6.78371i	0.387167	+	0.223531i
$922$	4.73985	+	1.27004i	0.156099	+	0.0418265i
$923$	−5.45621	+	5.45621i	−0.179593	+	0.179593i
$924$	−0.854705	+	17.0708i	−0.0281177	+	0.561588i
$925$	−1.38706	−	9.58204i	−0.0456061	−	0.315055i
$926$	1.62808	−	0.939975i	0.0535022	−	0.0308895i
$927$	0.972232	+	3.62842i	0.0319323	+	0.119173i
$928$	−5.40085	+	1.44715i	−0.177291	+	0.0475051i
$929$	−43.0975	+	24.8823i	−1.41398	+	0.816363i	−0.995761	−	0.0919815i	$-0.970680\pi$
$929$	−43.0975	+	24.8823i	−1.41398	+	0.816363i	−0.418222	+	0.908345i	$0.637347\pi$
$930$	5.99581	+	11.9638i	0.196610	+	0.392308i
$931$	45.2657	−	23.1890i	1.48352	−	0.759989i
$932$	1.56490	+	1.56490i	0.0512601	+	0.0512601i
$933$	−6.05311	+	22.5905i	−0.198170	+	0.739580i
$934$	20.9923	−	36.3597i	0.686888	−	1.18973i
$935$	−17.7357	−	20.9953i	−0.580018	−	0.686619i
$936$	−0.216936	−	0.375744i	−0.00709077	−	0.0122816i
$937$	−9.42731	−	9.42731i	−0.307977	−	0.307977i	0.536148	−	0.844124i	$-0.319879\pi$
$937$	−9.42731	−	9.42731i	−0.307977	−	0.307977i	−0.844124	+	0.536148i	$0.819879\pi$
$938$	−21.8941	−	23.0210i	−0.714868	−	0.751663i
$939$		−	39.6496i		−	1.29391i
$940$	−1.91032	−	9.29124i	−0.0623077	−	0.303047i
$941$	−37.3094	−	21.5406i	−1.21625	−	0.702204i	−0.252138	−	0.967691i	$-0.581134\pi$
$941$	−37.3094	−	21.5406i	−1.21625	−	0.702204i	−0.964114	+	0.265487i	$0.914467\pi$
$942$	−0.0905138	+	0.0242531i	−0.00294910	+	0.000790208i
$943$	−42.9550	−	11.5098i	−1.39881	−	0.374809i
$944$		−	6.03376i		−	0.196382i
$945$	−20.8690	−	14.5145i	−0.678868	−	0.472158i
$946$	0.679492	−	27.2378i	0.0220922	−	0.885577i
$947$	22.9294	+	6.14390i	0.745104	+	0.199650i	0.611345	−	0.791364i	$-0.290629\pi$
$947$	22.9294	+	6.14390i	0.745104	+	0.199650i	0.133759	+	0.991014i	$0.457295\pi$
$948$	1.68461	+	6.28704i	0.0547135	+	0.204193i
$949$	6.96434	+	4.02086i	0.226072	+	0.130523i
$950$	−22.4840	−	28.5345i	−0.729479	−	0.925782i
$951$	15.7630			0.511151
$952$	−9.53148	+	2.29935i	−0.308917	+	0.0745223i
$953$	27.3953	−	27.3953i	0.887421	−	0.887421i	−0.106854	−	0.994275i	$-0.534078\pi$
$953$	27.3953	−	27.3953i	0.887421	−	0.887421i	0.994275	+	0.106854i	$0.0340778\pi$
$954$	−5.71425	−	9.89737i	−0.185006	−	0.320439i
$955$	−1.28153	+	21.6879i	−0.0414694	+	0.701804i
$956$	−14.9985	−	8.65941i	−0.485087	−	0.280065i
$957$	34.6468	+	10.2162i	1.11997	+	0.330242i
$958$	−16.5596	−	16.5596i	−0.535015	−	0.535015i
$959$	−0.716748	+	1.17251i	−0.0231450	+	0.0378622i
$960$	1.37348	−	4.13326i	0.0443290	−	0.133401i
$961$	10.7799	+	18.6714i	0.347740	+	0.602303i
$962$	−0.273837	−	1.02197i	−0.00882885	−	0.0329497i
$963$	0.852302	+	3.18083i	0.0274650	+	0.102501i
$964$	8.81473	+	15.2676i	0.283903	+	0.491735i
$965$	0.770957	−	2.32006i	0.0248180	−	0.0746854i
$966$	15.5879	+	28.6345i	0.501532	+	0.921300i
$967$	7.71762	+	7.71762i	0.248182	+	0.248182i	0.820224	−	0.572042i	$-0.193849\pi$
$967$	7.71762	+	7.71762i	0.248182	+	0.248182i	−0.572042	+	0.820224i	$0.693849\pi$
$968$	−10.4700	−	3.37326i	−0.336519	−	0.108421i
$969$	45.4207	+	26.2236i	1.45912	+	0.842424i
$970$	0.203432	−	3.44276i	0.00653180	−	0.110540i
$971$	−3.94661	−	6.83573i	−0.126653	−	0.219369i	0.795725	−	0.605658i	$-0.207090\pi$
$971$	−3.94661	−	6.83573i	−0.126653	−	0.219369i	−0.922378	+	0.386289i	$0.873757\pi$
$972$	−5.69367	+	5.69367i	−0.182625	+	0.182625i
$973$	−23.9663	−	25.1998i	−0.768323	−	0.807870i
$974$	1.02727			0.0329160
$975$	5.28438	+	0.626693i	0.169236	+	0.0200702i
$976$	1.59065	+	0.918360i	0.0509153	+	0.0293960i
$977$	1.45176	+	5.41802i	0.0464458	+	0.173338i	0.985253	−	0.171106i	$-0.0547341\pi$
$977$	1.45176	+	5.41802i	0.0464458	+	0.173338i	−0.938807	+	0.344444i	$0.888067\pi$
$978$	24.4416	+	6.54912i	0.781557	+	0.209418i
$979$	44.9930	+	1.12243i	1.43798	+	0.0358729i
$980$	−14.3276	+	6.30244i	−0.457677	+	0.201324i
$981$			5.05653i			0.161443i
$982$	2.77807	+	0.744381i	0.0886517	+	0.0237542i
$983$	−32.3794	+	8.67602i	−1.03274	+	0.276722i	−0.735102	−	0.677956i	$-0.762866\pi$
$983$	−32.3794	+	8.67602i	−1.03274	+	0.276722i	−0.297639	+	0.954678i	$0.596199\pi$
$984$	−11.8578	−	6.84612i	−0.378014	−	0.218246i
$985$	0.252060	+	1.22595i	0.00803130	+	0.0390619i
$986$			20.7211i			0.659894i
$987$	15.0659	+	15.8413i	0.479551	+	0.504235i
$988$	−2.80715	−	2.80715i	−0.0893073	−	0.0893073i
$989$	−25.9854	−	45.0080i	−0.826286	−	1.43117i
$990$	−4.49867	+	3.80023i	−0.142977	+	0.120779i
$991$	17.0214	−	29.4819i	0.540702	−	0.936523i	−0.458162	−	0.888869i	$-0.651492\pi$
$991$	17.0214	−	29.4819i	0.540702	−	0.936523i	0.998864	−	0.0476545i	$-0.0151747\pi$
$992$	−0.795216	+	2.96779i	−0.0252481	+	0.0942273i
$993$	25.3661	+	25.3661i	0.804968	+	0.804968i
$994$	32.8164	−	17.8644i	1.04087	−	0.566624i
$995$	−9.79915	−	19.5528i	−0.310654	−	0.619866i
$996$	9.30423	−	5.37180i	0.294816	−	0.170212i
$997$	17.1540	−	4.59641i	0.543274	−	0.145570i	0.0232629	−	0.999729i	$-0.492595\pi$
$997$	17.1540	−	4.59641i	0.543274	−	0.145570i	0.520011	+	0.854160i	$0.325928\pi$
$998$	−8.40564	−	31.3703i	−0.266076	−	0.993009i
$999$	−7.20554	+	4.16012i	−0.227973	+	0.131620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bd.a.263.29	yes	192
5.2	odd	4	inner	770.2.bd.a.417.44	yes	192
7.2	even	3	inner	770.2.bd.a.373.20	yes	192
11.10	odd	2	inner	770.2.bd.a.263.5	✓	192
35.2	odd	12	inner	770.2.bd.a.527.5	yes	192
55.32	even	4	inner	770.2.bd.a.417.20	yes	192
77.65	odd	6	inner	770.2.bd.a.373.44	yes	192
385.142	even	12	inner	770.2.bd.a.527.29	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bd.a.263.5	✓	192	11.10	odd	2	inner
770.2.bd.a.263.29	yes	192	1.1	even	1	trivial
770.2.bd.a.373.20	yes	192	7.2	even	3	inner
770.2.bd.a.373.44	yes	192	77.65	odd	6	inner
770.2.bd.a.417.20	yes	192	55.32	even	4	inner
770.2.bd.a.417.44	yes	192	5.2	odd	4	inner
770.2.bd.a.527.5	yes	192	35.2	odd	12	inner
770.2.bd.a.527.29	yes	192	385.142	even	12	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.88147 + 0.504137i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.86717 - 1.23031i) q^{5} +1.94784i q^{6} +(1.82332 + 1.91716i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.687681 - 0.397033i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.88147 + 0.504137i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.86717 - 1.23031i) q^{5} +1.94784i q^{6} +(1.82332 + 1.91716i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.687681 - 0.397033i) q^{9} +(-1.67165 + 1.48512i) q^{10} +(2.83003 + 1.72943i) q^{11} +(1.88147 + 0.504137i) q^{12} +(-0.386358 + 0.386358i) q^{13} +(2.32375 - 1.26499i) q^{14} +(4.13326 + 1.37348i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.57963 - 0.959159i) q^{17} +(-0.205519 - 0.767009i) q^{18} +(-3.63284 - 6.29226i) q^{19} +(1.00186 + 1.99907i) q^{20} +(-4.39702 - 2.68788i) q^{21} +(2.40297 - 2.28599i) q^{22} +(1.63736 - 6.11071i) q^{23} +(0.973918 - 1.68688i) q^{24} +(1.97265 + 4.59441i) q^{25} +(0.273196 + 0.473190i) q^{26} +(3.03830 - 3.03830i) q^{27} +(-0.620455 - 2.57197i) q^{28} -5.59137 q^{29} +(2.39645 - 3.63694i) q^{30} +(-1.53624 + 2.66084i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-6.19647 - 1.82714i) q^{33} -3.70591i q^{34} +(-1.04572 - 5.82293i) q^{35} -0.794066 q^{36} +(-1.87040 - 0.501172i) q^{37} +(-7.01810 + 1.88050i) q^{38} +(0.532141 - 0.921696i) q^{39} +(2.19025 - 0.450325i) q^{40} -7.02946i q^{41} +(-3.73432 + 3.55152i) q^{42} +(5.80892 - 5.80892i) q^{43} +(-1.58617 - 2.91274i) q^{44} +(-1.77249 - 0.104736i) q^{45} +(-5.47872 - 3.16314i) q^{46} +(-4.09754 - 1.09793i) q^{47} +(-1.37733 - 1.37733i) q^{48} +(-0.351042 + 6.99119i) q^{49} +(4.94842 - 0.716313i) q^{50} +(-6.25140 + 3.60925i) q^{51} +(0.527774 - 0.141417i) q^{52} +(13.9020 - 3.72502i) q^{53} +(-2.14840 - 3.72114i) q^{54} +(-3.15641 - 6.71097i) q^{55} +(-2.64492 - 0.0663616i) q^{56} +(10.0072 + 10.0072i) q^{57} +(-1.44715 + 5.40085i) q^{58} +(-5.22539 - 3.01688i) q^{59} +(-2.89277 - 3.25610i) q^{60} +(1.59065 - 0.918360i) q^{61} +(2.17257 + 2.17257i) q^{62} +(2.01504 + 0.594482i) q^{63} -1.00000i q^{64} +(1.19674 - 0.246054i) q^{65} +(-3.36864 + 5.51244i) q^{66} +(-3.10786 - 11.5987i) q^{67} +(-3.57963 - 0.959159i) q^{68} +12.3225i q^{69} +(-5.89517 - 0.496991i) q^{70} +14.1222 q^{71} +(-0.205519 + 0.767009i) q^{72} +(-3.80926 - 14.2164i) q^{73} +(-0.968191 + 1.67696i) q^{74} +(-6.02769 - 7.64974i) q^{75} +7.26568i q^{76} +(1.84444 + 8.57893i) q^{77} +(-0.752562 - 0.752562i) q^{78} +(1.67078 + 2.89388i) q^{79} +(0.131899 - 2.23217i) q^{80} +(-5.37583 + 9.31121i) q^{81} +(-6.78994 - 1.81936i) q^{82} +(3.90016 - 3.90016i) q^{83} +(2.46399 + 4.52628i) q^{84} +(-7.86385 - 2.61316i) q^{85} +(-4.10753 - 7.11445i) q^{86} +(10.5200 - 2.81882i) q^{87} +(-3.22402 + 0.778244i) q^{88} +(11.7521 - 6.78506i) q^{89} +(-0.559922 + 1.68499i) q^{90} +(-1.44516 - 0.0362595i) q^{91} +(-4.47335 + 4.47335i) q^{92} +(1.54895 - 5.78076i) q^{93} +(-2.12104 + 3.67375i) q^{94} +(-0.958332 + 16.2183i) q^{95} +(-1.68688 + 0.973918i) q^{96} +(-1.09060 + 1.09060i) q^{97} +(6.66212 + 2.14853i) q^{98} +(2.63280 + 0.0656795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{5}+O(q^{10}) \) 192 * q + 8 * q^5	\( 192 q + 8 q^{5} + 4 q^{11} + 16 q^{15} + 96 q^{16} + 24 q^{22} - 8 q^{23} + 24 q^{25} - 8 q^{26} - 16 q^{33} - 160 q^{36} - 40 q^{37} - 40 q^{42} + 32 q^{45} - 40 q^{47} + 40 q^{53} + 8 q^{55} + 16 q^{56} + 32 q^{58} - 48 q^{67} - 72 q^{70} + 32 q^{71} - 48 q^{75} - 72 q^{77} - 8 q^{80} + 64 q^{81} + 16 q^{82} - 12 q^{88} - 112 q^{91} - 16 q^{92} + 80 q^{93} - 64 q^{97}+O(q^{100}) \) 192 * q + 8 * q^5 + 4 * q^11 + 16 * q^15 + 96 * q^16 + 24 * q^22 - 8 * q^23 + 24 * q^25 - 8 * q^26 - 16 * q^33 - 160 * q^36 - 40 * q^37 - 40 * q^42 + 32 * q^45 - 40 * q^47 + 40 * q^53 + 8 * q^55 + 16 * q^56 + 32 * q^58 - 48 * q^67 - 72 * q^70 + 32 * q^71 - 48 * q^75 - 72 * q^77 - 8 * q^80 + 64 * q^81 + 16 * q^82 - 12 * q^88 - 112 * q^91 - 16 * q^92 + 80 * q^93 - 64 * q^97

Introduction

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