LMFDB - Embedded newform 770.2.bd.a.263.5

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			263.5
Character	$\chi$	$=$	770.263
Dual form			770.2.bd.a.527.5

$q$-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} +(-2.91274 - 1.58617i) 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} +(2.28599 - 2.40297i) 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} +(6.27987 + 1.51589i) 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} +(1.72943 + 2.83003i) 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} +(3.48711 + 6.54523i) 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} +(-3.08959 + 5.67355i) 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} +(2.26991 + 8.47629i) 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} +(-3.18121 + 0.938033i) 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
$11$	−2.91274	−	1.58617i	−0.878225	−	0.478247i
$11$	−2.91274	−	1.58617i	−0.878225	−	0.478247i
$12$	1.88147	+	0.504137i	0.543132	+	0.145532i
$13$	0.386358	−	0.386358i	0.107156	−	0.107156i	−0.651496	−	0.758652i	$-0.725858\pi$
$13$	0.386358	−	0.386358i	0.107156	−	0.107156i	0.758652	+	0.651496i	$0.225858\pi$
$14$	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	−0.665304	−	0.746573i	$-0.731698\pi$
$17$	−3.57963	+	0.959159i	−0.868188	+	0.232630i	−0.202884	+	0.979203i	$0.565031\pi$
$18$	0.205519	+	0.767009i	0.0484414	+	0.180786i
$19$	3.63284	+	6.29226i	0.833430	+	1.44354i	0.895302	+	0.445459i	$0.146960\pi$
$19$	3.63284	+	6.29226i	0.833430	+	1.44354i	−0.0618721	+	0.998084i	$0.519707\pi$
$20$	1.00186	+	1.99907i	0.224023	+	0.447005i
$21$	4.39702	+	2.68788i	0.959508	+	0.586543i
$22$	2.28599	−	2.40297i	0.487375	−	0.512314i
$23$	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	$-0.326250\pi$
$29$	5.59137			1.03829			0.519145	+	0.854686i	$0.326250\pi$
$30$	−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
$33$	6.27987	+	1.51589i	1.09319	+	0.263883i
$34$		−	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	$0.184956\pi$
$41$			7.02946i			1.09782i	−0.835882	+	0.548908i	$0.815044\pi$
$42$	−3.73432	+	3.55152i	−0.576219	+	0.548011i
$43$	−5.80892	+	5.80892i	−0.885853	+	0.885853i	−0.994122	−	0.108269i	$-0.965469\pi$
$43$	−5.80892	+	5.80892i	−0.885853	+	0.885853i	0.108269	+	0.994122i	$0.465469\pi$
$44$	1.72943	+	2.83003i	0.260721	+	0.426643i
$45$	−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
$55$	3.48711	+	6.54523i	0.470202	+	0.882559i
$56$	−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	−0.598362	−	0.801226i	$-0.704182\pi$
$61$	−1.59065	+	0.918360i	−0.203661	+	0.117584i	0.394701	+	0.918810i	$0.370848\pi$
$62$	−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
$66$	−3.08959	+	5.67355i	−0.380302	+	0.698366i
$67$	−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	$0.247015\pi$
$73$	3.80926	+	14.2164i	0.445841	+	1.66390i	−0.267867	+	0.963456i	$0.586319\pi$
$74$	0.968191	−	1.67696i	0.112550	−	0.194942i
$75$	−6.02769	−	7.64974i	−0.696018	−	0.883316i
$76$		−	7.26568i		−	0.833430i
$77$	2.26991	+	8.47629i	0.258680	+	0.965963i
$78$	−0.752562	−	0.752562i	−0.0852108	−	0.0852108i
$79$	−1.67078	−	2.89388i	−0.187978	−	0.325587i	0.756598	−	0.653880i	$-0.226860\pi$
$79$	−1.67078	−	2.89388i	−0.187978	−	0.325587i	−0.944576	+	0.328293i	$0.893527\pi$
$80$	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	−0.887980	−	0.459882i	$-0.847892\pi$
$83$	−3.90016	+	3.90016i	−0.428098	+	0.428098i	0.459882	+	0.887980i	$0.347892\pi$
$84$	−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
$88$	−3.18121	+	0.938033i	−0.339118	+	0.0999947i
$89$	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	0.162987	−	0.986628i	$-0.447887\pi$
$101$	−6.13007	−	3.53920i	−0.609964	−	0.352163i	−0.772952	+	0.634465i	$0.781220\pi$
$102$	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	−0.894438	−	0.447191i	$-0.852424\pi$
$107$	1.07334	−	4.00576i	0.103764	−	0.387251i	0.998202	+	0.0599402i	$0.0190910\pi$
$108$	−4.15039	+	1.11209i	−0.399371	+	0.107011i
$109$	3.18395	−	5.51476i	0.304967	−	0.528218i	−0.672287	−	0.740291i	$-0.734688\pi$
$109$	3.18395	−	5.51476i	0.304967	−	0.528218i	0.977254	+	0.212072i	$0.0680213\pi$
$110$	−7.22474	+	1.67426i	−0.688852	+	0.159634i
$111$	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
$121$	5.96816	+	9.24019i	0.542560	+	0.840017i
$122$	−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	0.367202	−	0.930141i	$-0.380316\pi$
$127$	−6.34400	−	6.34400i	−0.562939	−	0.562939i	−0.930141	+	0.367202i	$0.880316\pi$
$128$	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	−0.129764	−	0.991545i	$-0.541422\pi$
$131$	7.60049	−	4.38814i	0.664058	−	0.383394i	0.793821	+	0.608151i	$0.208088\pi$
$132$	−4.68058	−	4.45274i	−0.407392	−	0.387561i
$133$	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	$-0.311782\pi$
$139$	13.1443			1.11489			0.557444	+	0.830215i	$0.311782\pi$
$140$	2.00584	−	5.56566i	0.169524	−	0.470384i
$141$	8.26289			0.695861
$142$	−3.65509	+	13.6410i	−0.306728	+	1.14472i
$143$	−1.73819	+	0.512534i	−0.145355	+	0.0428603i
$144$	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	0.997965	−	0.0637661i	$-0.0203111\pi$
$149$	5.41677	+	9.38213i	0.443759	+	0.768614i	−0.554205	+	0.832380i	$0.686978\pi$
$150$	8.94917	−	3.84240i	0.730696	−	0.313731i
$151$	19.7106	+	11.3799i	1.60403	+	0.926086i	0.990670	+	0.136281i	$0.0435149\pi$
$151$	19.7106	+	11.3799i	1.60403	+	0.926086i	0.613358	+	0.789805i	$0.289818\pi$
$152$	7.01810	+	1.88050i	0.569243	+	0.152528i
$153$	−2.08083	+	2.08083i	−0.168225	+	0.168225i
$154$	−8.77496	−	0.00125896i	−0.707107	−	0.000101450i
$155$	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
$165$	−9.86057	−	10.5566i	−0.767644	−	0.821834i
$166$	−2.75783	−	4.77670i	−0.214049	−	0.370744i
$167$	4.35793	+	4.35793i	0.337227	+	0.337227i	0.855323	−	0.518096i	$-0.173359\pi$
$167$	4.35793	+	4.35793i	0.337227	+	0.337227i	−0.518096	+	0.855323i	$0.673359\pi$
$168$	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	−0.372698	−	0.927953i	$-0.621567\pi$
$173$	−15.2500	−	4.08624i	−1.15944	−	0.310671i	−0.786742	+	0.617282i	$0.788234\pi$
$174$		−	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
$187$	11.9479	+	2.88410i	0.873719	+	0.210906i
$188$	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	0.954993	−	0.296628i	$-0.0958622\pi$
$193$	−0.282979	−	1.05609i	−0.0203693	−	0.0760193i	−0.975362	+	0.220609i	$0.929196\pi$
$194$	−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	0.721066	−	0.692867i	$-0.243653\pi$
$197$	0.395788	+	0.395788i	0.0281987	+	0.0281987i	−0.692867	+	0.721066i	$0.743653\pi$
$198$	0.617977	−	2.56009i	0.0439177	−	0.181938i
$199$	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	$0.138478\pi$
$211$			12.2438i			0.842896i	−0.906852	+	0.421448i	$0.861522\pi$
$212$	−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
$220$	0.252692	−	7.41189i	0.0170365	−	0.499710i
$221$	−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	−0.545835	−	0.837893i	$-0.683788\pi$
$227$	−9.03383	+	2.42061i	−0.599596	+	0.160661i	−0.0537609	+	0.998554i	$0.517121\pi$
$228$	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
$231$	−8.54397	−	14.8035i	−0.562152	−	0.973999i
$232$	3.95369	−	3.95369i	0.259573	−	0.259573i
$233$	2.13770	+	0.572794i	0.140045	+	0.0375250i	0.328161	−	0.944622i	$-0.393571\pi$
$233$	2.13770	+	0.572794i	0.140045	+	0.0375250i	−0.188115	+	0.982147i	$0.560238\pi$
$234$	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	$-0.689249\pi$
$239$	−17.3188			−1.12026			−0.560130	+	0.828404i	$0.689249\pi$
$240$	0.877159	+	4.26625i	0.0566204	+	0.275385i
$241$	15.2676	+	8.81473i	0.983470	+	0.567807i	0.903316	−	0.428976i	$-0.141125\pi$
$241$	15.2676	+	8.81473i	0.983470	+	0.567807i	0.0801541	+	0.996782i	$0.474459\pi$
$242$	−10.4700	+	3.37326i	−0.673038	+	0.216842i
$243$	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
$253$	−14.4618	+	15.2018i	−0.909206	+	0.955730i
$254$	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	$0.152314\pi$
$263$	5.66235	+	21.1322i	0.349155	+	1.30307i	−0.538527	+	0.842608i	$0.681019\pi$
$264$	5.51244	−	3.36864i	0.339267	−	0.207326i
$265$	−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	−0.915896	−	0.401416i	$-0.868518\pi$
$271$	−16.8935	+	9.75347i	−1.02621	+	0.592481i	−0.110311	+	0.993897i	$0.535185\pi$
$272$	−2.62047	−	2.62047i	−0.158889	−	0.158889i
$273$	2.73730	−	0.660340i	0.165669	−	0.0399656i
$274$	−0.519409			−0.0313786
$275$	1.54167	−	16.5113i	0.0929662	−	0.995669i
$276$	6.16127	−	10.6716i	0.370865	−	0.642357i
$277$	−17.7363	+	4.75243i	−1.06567	+	0.285546i	−0.748714	−	0.662894i	$-0.769328\pi$
$277$	−17.7363	+	4.75243i	−1.06567	+	0.285546i	−0.316958	+	0.948439i	$0.602662\pi$
$278$	−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	$-0.844640\pi$
$281$		−	15.7214i		−	0.937860i	0.883235	−	0.468930i	$-0.155360\pi$
$282$	−2.13859	+	7.98134i	−0.127351	+	0.475282i
$283$	−0.738594	−	2.75647i	−0.0439049	−	0.163855i	0.940493	−	0.339814i	$-0.110364\pi$
$283$	−0.738594	−	2.75647i	−0.0439049	−	0.163855i	−0.984398	+	0.175959i	$0.943697\pi$
$284$	−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	−0.247219	−	0.968960i	$-0.579517\pi$
$293$	12.3542	−	12.3542i	0.721741	−	0.721741i	0.968960	+	0.247219i	$0.0795167\pi$
$294$	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
$297$	−13.6690	+	4.03054i	−0.793157	+	0.233876i
$298$	−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	0.833548	−	0.552448i	$-0.186306\pi$
$307$	4.92527	+	4.92527i	0.281100	+	0.281100i	−0.552448	+	0.833548i	$0.686306\pi$
$308$	2.27234	−	8.47564i	0.129479	−	0.482944i
$309$		−	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
$319$	−16.2862	−	8.86883i	−0.911854	−	0.496559i
$320$	−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
$330$	12.7490	−	6.79232i	0.701812	−	0.373905i
$331$	−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	$0.00738440\pi$
$337$	18.7785	+	18.7785i	1.02293	+	1.02293i	0.0231967	+	0.999731i	$0.492616\pi$
$338$	−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
$341$	8.69521	−	5.31363i	0.470872	−	0.287749i
$342$	−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	−0.750445	−	0.660933i	$-0.770161\pi$
$347$	−19.9297	+	5.34014i	−1.06988	+	0.286674i	−0.319437	+	0.947607i	$0.603494\pi$
$348$	10.5200	+	2.81882i	0.563929	+	0.151104i
$349$	−11.4208			−0.611343			−0.305672	−	0.952137i	$-0.598881\pi$
$349$	−11.4208			−0.611343			−0.305672	+	0.952137i	$0.598881\pi$
$350$	10.3958	+	8.18088i	0.555680	+	0.437286i
$351$		−	2.34774i		−	0.125313i
$352$	3.22402	+	0.778244i	0.171841	+	0.0414806i
$353$	−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	0.984140	−	0.177393i	$-0.0567664\pi$
$359$	6.41258	+	11.1069i	0.338443	+	0.586201i	−0.645697	+	0.763594i	$0.723433\pi$
$360$	−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
$363$	−15.8872	−	14.3763i	−0.833862	−	0.754561i
$364$	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	0.946801	−	0.321821i	$-0.104295\pi$
$373$	31.0140	+	8.31017i	1.60584	+	0.430284i	0.659043	+	0.752105i	$0.270962\pi$
$374$	−5.87818	+	10.7944i	−0.303953	+	0.558163i
$375$	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
$385$	6.19019	−	18.6194i	0.315481	−	0.948932i
$386$	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
$396$	2.31291	+	1.25952i	0.116228	+	0.0632932i
$397$	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
$407$	4.65306	+	4.42655i	0.230644	+	0.219416i
$408$	1.86828	−	6.97253i	0.0924939	−	0.345192i
$409$	8.41009	−	14.5667i	0.415852	−	0.720277i	−0.579665	−	0.814855i	$-0.696817\pi$
$409$	8.41009	−	14.5667i	0.415852	−	0.720277i	0.995517	+	0.0945777i	$0.0301501\pi$
$410$	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
$418$	23.4247	+	5.65447i	1.14574	+	0.276569i
$419$		−	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
$429$	3.01195	−	1.84060i	0.145418	−	0.0888650i
$430$	−1.08355	+	18.3374i	−0.0522536	+	0.884310i
$431$	−8.33767	−	4.81375i	−0.401611	−	0.231870i	0.285568	−	0.958359i	$-0.407818\pi$
$431$	−8.33767	−	4.81375i	−0.401611	−	0.231870i	−0.687179	+	0.726488i	$0.741151\pi$
$432$	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	0.655146	−	0.755503i	$-0.272607\pi$
$439$	−6.84537	−	11.8565i	−0.326712	−	0.565881i	−0.981857	+	0.189621i	$0.939274\pi$
$440$	7.09394	+	2.16242i	0.338190	+	0.103089i
$441$	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
$451$	11.1499	−	20.4750i	0.525027	−	0.964131i
$452$	−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	−0.974833	−	0.222938i	$-0.928435\pi$
$457$	−0.409034	+	1.52654i	−0.0191338	+	0.0714084i	0.955699	+	0.294346i	$0.0951019\pi$
$458$	−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	$-0.963546\pi$
$461$		−	4.90705i		−	0.228544i	0.993449	−	0.114272i	$-0.0364536\pi$
$462$	16.5104	−	4.42142i	0.768135	−	0.205703i
$463$	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
$473$	26.1338	−	7.70600i	1.20163	−	0.354322i
$474$	−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	$0.346361\pi$
$479$	−11.7094	+	20.2812i	−0.535015	+	0.926674i	−0.999163	+	0.0409157i	$0.986972\pi$
$480$	−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	$-0.979328\pi$
$491$		−	2.87607i		−	0.129795i	0.997892	−	0.0648976i	$-0.0206721\pi$
$492$	−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
$495$	4.99669	+	3.11654i	0.224585	+	0.140078i
$496$	−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	−0.648864	−	0.760905i	$-0.724755\pi$
$503$	2.51282	−	2.51282i	0.112041	−	0.112041i	0.760905	+	0.648864i	$0.224755\pi$
$504$	−1.84521	+	1.00448i	−0.0821921	+	0.0447433i
$505$	7.09155	+	14.1502i	0.315570	+	0.629675i
$506$	−10.9408	−	17.9036i	−0.486380	−	0.795910i
$507$	−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
$517$	10.1936	+	9.69737i	0.448313	+	0.426490i
$518$	−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	0.816253	−	0.577695i	$-0.196048\pi$
$523$	28.2275	+	7.56353i	1.23430	+	0.330730i	0.418048	+	0.908425i	$0.362714\pi$
$524$	−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
$528$	1.82714	+	6.19647i	0.0795158	+	0.269667i
$529$	−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
$539$	12.1117	−	19.8067i	0.521687	−	0.853137i
$540$	9.11771	+	3.02982i	0.392364	+	0.130383i
$541$	1.95940	−	1.13126i	0.0842410	−	0.0486366i	−0.457288	−	0.889319i	$-0.651179\pi$
$541$	1.95940	−	1.13126i	0.0842410	−	0.0486366i	0.541529	+	0.840682i	$0.317846\pi$
$542$	−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	0.676608	−	0.736344i	$-0.263449\pi$
$547$	−1.39712	−	1.39712i	−0.0597363	−	0.0597363i	−0.736344	+	0.676608i	$0.763449\pi$
$548$	0.134433	−	0.501711i	0.00574269	−	0.0214320i
$549$	−0.729238	+	1.26308i	−0.0311231	+	0.0539068i
$550$	15.5497	+	5.76258i	0.663041	+	0.245717i
$551$	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	−0.128425	−	0.991719i	$-0.540992\pi$
$557$	6.04688	−	1.62026i	0.256215	−	0.0686525i	0.384640	+	0.923067i	$0.374326\pi$
$558$	−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	$0.0285617\pi$
$563$	4.22921	+	15.7836i	0.178240	+	0.665201i	−0.817737	+	0.575592i	$0.804772\pi$
$564$	−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	0.977241	−	0.212133i	$-0.0680410\pi$
$569$	7.27318	+	12.5975i	0.304908	+	0.528116i	−0.672333	+	0.740249i	$0.734708\pi$
$570$	−31.5905	−	1.86667i	−1.32318	−	0.0781863i
$571$	28.9266	+	16.7008i	1.21054	+	0.698906i	0.962877	−	0.269940i	$-0.0870039\pi$
$571$	28.9266	+	16.7008i	1.21054	+	0.698906i	0.247663	+	0.968846i	$0.420337\pi$
$572$	1.76158	+	0.425227i	0.0736555	+	0.0177796i
$573$	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
$583$	−46.4014	−	11.2008i	−1.92175	−	0.463889i
$584$	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	−0.279950	−	0.960015i	$-0.590318\pi$
$593$	−24.4101	−	6.54066i	−1.00240	−	0.268593i	−0.722451	+	0.691422i	$0.756985\pi$
$594$	−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	$-0.722776\pi$
$601$		−	37.5047i		−	1.52985i	0.644120	−	0.764924i	$-0.277224\pi$
$602$	−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
$605$	0.224765	−	24.5957i	0.00913799	−	0.999958i
$606$	−6.89377	+	11.9404i	−0.280040	+	0.485044i
$607$	4.39076	−	16.3865i	0.178215	−	0.665109i	−0.817766	−	0.575551i	$-0.804788\pi$
$607$	4.39076	−	16.3865i	0.178215	−	0.665109i	0.995982	−	0.0895583i	$-0.0285455\pi$
$608$	−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	0.943723	−	0.330738i	$-0.107298\pi$
$613$	−0.963961	−	3.59755i	−0.0389340	−	0.145304i	−0.982657	+	0.185434i	$0.940631\pi$
$614$	−6.03220	+	3.48269i	−0.243440	+	0.140550i
$615$	−9.65485	+	29.0546i	−0.389321	+	1.17159i
$616$	7.59871	+	4.38857i	0.306161	+	0.176821i
$617$	−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
$627$	13.2754	+	45.0216i	0.530167	+	1.79799i
$628$	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
$638$	12.7818	−	13.4359i	0.506037	−	0.531931i
$639$	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
$649$	10.4350	+	17.0757i	0.409608	+	0.670282i
$650$	−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	$-0.371613\pi$
$659$	20.1514			0.784986			0.392493	+	0.919755i	$0.371613\pi$
$660$	3.26118	+	14.0726i	0.126941	+	0.547776i
$661$	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	−0.102948	−	0.994687i	$-0.532828\pi$
$673$	23.1337	−	23.1337i	0.891739	−	0.891739i	0.994687	+	0.102948i	$0.0328275\pi$
$674$	−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	$-0.536270\pi$
$677$	12.5289	−	46.7585i	0.481525	−	1.79707i	0.595224	−	0.803560i	$-0.297063\pi$
$678$	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
$682$	2.88209	+	9.77420i	0.110361	+	0.374273i
$683$	−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
$693$	4.92634	+	4.92776i	0.187136	+	0.187190i
$694$		−	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	$-0.984777\pi$
$701$		−	2.53145i		−	0.0956117i	0.998857	−	0.0478058i	$-0.0152229\pi$
$702$	2.26774	+	0.607639i	0.0855903	+	0.0229339i
$703$	−3.64136	−	13.5897i	−0.137336	−	0.512546i
$704$	−1.58617	+	2.91274i	−0.0597808	+	0.109778i
$705$	−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
$715$	3.87607	+	1.18153i	0.144957	+	0.0441867i
$716$	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
$726$	17.9984	−	11.6250i	0.667982	−	0.431444i
$727$	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	−0.252636	−	0.967561i	$-0.581298\pi$
$733$	−25.8612	−	6.92950i	−0.955207	−	0.255947i	−0.702570	+	0.711614i	$0.747964\pi$
$734$	−1.39426			−0.0514631
$735$	−11.0532	+	28.4143i	−0.407705	+	1.04808i
$736$			6.32628i			0.233190i
$737$	−9.34504	+	38.7136i	−0.344229	+	1.42603i
$738$	−5.39166	+	1.44469i	−0.198470	+	0.0531798i
$739$	−10.6878	+	18.5119i	−0.393158	+	0.680970i	−0.992864	−	0.119250i	$-0.961951\pi$
$739$	−10.6878	+	18.5119i	−0.393158	+	0.680970i	0.599706	+	0.800220i	$0.295284\pi$
$740$	−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	−0.979796	−	0.200002i	$-0.935905\pi$
$743$	−21.2556	+	21.2556i	−0.779794	+	0.779794i	0.200002	+	0.979796i	$0.435905\pi$
$744$	−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
$748$	−8.90516	−	8.47167i	−0.325605	−	0.309755i
$749$	−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
$759$	19.5456	−	35.8924i	0.709460	−	1.30281i
$760$	−10.7904	−	12.1457i	−0.391409	−	0.440570i
$761$	−31.2865	+	18.0633i	−1.13414	+	0.654794i	−0.944972	−	0.327152i	$-0.893911\pi$
$761$	−31.2865	+	18.0633i	−1.13414	+	0.654794i	−0.189164	+	0.981946i	$0.560578\pi$
$762$	−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	$-0.627103\pi$
$769$	−21.5623			−0.777557			−0.388779	+	0.921331i	$0.627103\pi$
$770$	16.3828	+	10.7983i	0.590395	+	0.389144i
$771$	−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
$781$	−41.1343	−	22.4001i	−1.47190	−	0.801538i
$782$	−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	0.606991	−	0.794708i	$-0.292376\pi$
$787$	42.9223	−	11.5010i	1.53002	−	0.409966i	0.923024	+	0.384742i	$0.125710\pi$
$788$	−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
$792$	−1.81523	+	1.90811i	−0.0645013	+	0.0678018i
$793$	−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
$803$	11.4541	−	47.4508i	0.404206	−	1.67450i
$804$		−	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	$-0.619531\pi$
$809$	17.7001	−	30.6574i	0.622302	−	1.07786i	0.989056	−	0.147540i	$-0.0471356\pi$
$810$	4.84174	+	23.5488i	0.170121	+	0.827422i
$811$		−	34.4635i		−	1.21018i	−0.796158	−	0.605089i	$-0.793137\pi$
$811$		−	34.4635i		−	1.21018i	0.796158	−	0.605089i	$-0.206863\pi$
$812$	3.46919	+	14.3808i	0.121745	+	0.504668i
$813$	26.8674	−	26.8674i	0.942283	−	0.942283i
$814$	−5.48002	+	3.34883i	−0.192075	+	0.117377i
$815$	−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	−0.665320	−	0.746558i	$-0.731705\pi$
$821$	−10.0699	+	5.81385i	−0.351441	+	0.202905i	0.313879	+	0.949463i	$0.398371\pi$
$822$	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
$825$	5.42336	+	31.8427i	0.188817	+	1.10862i
$826$	−15.9588	−	0.400410i	−0.555278	−	0.0139320i
$827$	28.7023	+	28.7023i	0.998077	+	0.998077i	0.999998	−	0.00192148i	$-0.000611626\pi$
$827$	28.7023	+	28.7023i	0.998077	+	0.998077i	−0.00192148	+	0.999998i	$0.500612\pi$
$828$	−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
$836$	−11.5246	+	21.1631i	−0.398585	+	0.731940i
$837$	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
$847$	6.83312	−	28.2897i	0.234789	−	0.972046i
$848$	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	−0.571033	−	0.820927i	$-0.693457\pi$
$853$	7.29843	−	7.29843i	0.249894	−	0.249894i	0.820927	+	0.571033i	$0.193457\pi$
$854$	−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	−0.0141089	−	0.999900i	$-0.504491\pi$
$857$	13.8651	−	3.71514i	0.473623	−	0.126907i	0.487732	+	0.872994i	$0.337824\pi$
$858$	0.998333	+	3.38571i	0.0340825	+	0.115586i
$859$	−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	−0.999534	−	0.0305400i	$-0.990277\pi$
$877$	−3.51349	+	13.1125i	−0.118642	+	0.442778i	0.880891	+	0.473318i	$0.156944\pi$
$878$	13.2242	−	3.54343i	0.446297	−	0.119585i
$879$	−17.0158	+	29.4722i	−0.573929	+	0.994074i
$880$	−3.92478	+	6.29254i	−0.132304	+	0.212122i
$881$	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	$0.419150\pi$
$887$	−13.4109	+	50.0501i	−0.450293	+	1.68052i	−0.701569	+	0.712602i	$0.747517\pi$
$888$	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
$891$	30.4275	−	18.5942i	1.01936	−	0.622930i
$892$	−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
$902$	16.8915	+	16.0693i	0.562427	+	0.535049i
$903$	−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
$913$	17.5465	−	5.17387i	0.580703	−	0.171230i
$914$	−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	0.996692	−	0.0812739i	$-0.0258989\pi$
$919$	12.9736	+	22.4710i	0.427961	+	0.741249i	−0.568731	+	0.822523i	$0.692566\pi$
$920$	−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
$924$	−0.00245224	+	17.0922i	−8.06729e−5	+	0.562292i
$925$	−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
$935$	−18.7605	−	20.0848i	−0.613533	−	0.656844i
$936$	−0.216936	−	0.375744i	−0.00709077	−	0.0122816i
$937$	9.42731	+	9.42731i	0.307977	+	0.307977i	0.844124	−	0.536148i	$-0.180121\pi$
$937$	9.42731	+	9.42731i	0.307977	+	0.307977i	−0.536148	+	0.844124i	$0.680121\pi$
$938$	−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	0.964114	−	0.265487i	$-0.0855329\pi$
$941$	37.3094	+	21.5406i	1.21625	+	0.702204i	0.252138	+	0.967691i	$0.418866\pi$
$942$	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	−0.994275	−	0.106854i	$-0.965922\pi$
$953$	−27.3953	+	27.3953i	−0.887421	+	0.887421i	0.106854	+	0.994275i	$0.465922\pi$
$954$	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
$957$	35.1131	+	8.47591i	1.13504	+	0.273987i
$958$	−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	0.572042	−	0.820224i	$-0.306151\pi$
$967$	−7.71762	−	7.71762i	−0.248182	−	0.248182i	−0.820224	+	0.572042i	$0.806151\pi$
$968$	10.7539	+	2.31367i	0.345644	+	0.0743642i
$969$	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
$990$	−4.30358	+	4.01981i	−0.136777	+	0.127758i
$991$	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	−0.520011	−	0.854160i	$-0.674072\pi$
$997$	−17.1540	+	4.59641i	−0.543274	+	0.145570i	−0.0232629	+	0.999729i	$0.507405\pi$
$998$	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.263.5	✓	192
5.2	odd	4	inner	770.2.bd.a.417.20	yes	192
7.2	even	3	inner	770.2.bd.a.373.44	yes	192
11.10	odd	2	inner	770.2.bd.a.263.29	yes	192
35.2	odd	12	inner	770.2.bd.a.527.29	yes	192
55.32	even	4	inner	770.2.bd.a.417.44	yes	192
77.65	odd	6	inner	770.2.bd.a.373.20	yes	192
385.142	even	12	inner	770.2.bd.a.527.5	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bd.a.263.5	✓	192	1.1	even	1	trivial
770.2.bd.a.263.29	yes	192	11.10	odd	2	inner
770.2.bd.a.373.20	yes	192	77.65	odd	6	inner
770.2.bd.a.373.44	yes	192	7.2	even	3	inner
770.2.bd.a.417.20	yes	192	5.2	odd	4	inner
770.2.bd.a.417.44	yes	192	55.32	even	4	inner
770.2.bd.a.527.5	yes	192	385.142	even	12	inner
770.2.bd.a.527.29	yes	192	35.2	odd	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} +(-2.91274 - 1.58617i) 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} +(2.28599 - 2.40297i) 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} +(6.27987 + 1.51589i) 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} +(1.72943 + 2.83003i) 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} +(3.48711 + 6.54523i) 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} +(-3.08959 + 5.67355i) 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} +(2.26991 + 8.47629i) 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} +(-3.18121 + 0.938033i) 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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