LMFDB - Embedded newform 555.2.bi.a.47.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(47,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("555.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.bi (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:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$72$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.10
Character	$\chi$	$=$	555.47
Dual form			555.2.bi.a.248.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.578972 - 2.16075i) q^{2} +(-0.231467 - 1.71651i) q^{3} +(-2.60160 + 1.50203i) q^{4} +(2.08250 + 0.814371i) q^{5} +(-3.57495 + 1.49396i) q^{6} +(-1.33384 + 4.97795i) q^{7} +(1.58821 + 1.58821i) q^{8} +(-2.89285 + 0.794631i) q^{9} +O(q^{10})$	\(q+(-0.578972 - 2.16075i) q^{2} +(-0.231467 - 1.71651i) q^{3} +(-2.60160 + 1.50203i) q^{4} +(2.08250 + 0.814371i) q^{5} +(-3.57495 + 1.49396i) q^{6} +(-1.33384 + 4.97795i) q^{7} +(1.58821 + 1.58821i) q^{8} +(-2.89285 + 0.794631i) q^{9} +(0.553946 - 4.97126i) q^{10} +4.64526i q^{11} +(3.18044 + 4.11801i) q^{12} +(1.76715 + 0.473506i) q^{13} +11.5284 q^{14} +(0.915851 - 3.76314i) q^{15} +(-0.491864 + 0.851934i) q^{16} +(-0.363752 - 1.35754i) q^{17} +(3.39188 + 5.79066i) q^{18} +(-2.85167 + 1.64641i) q^{19} +(-6.64103 + 1.00932i) q^{20} +(8.85347 + 1.13732i) q^{21} +(10.0373 - 2.68947i) q^{22} +(2.68378 + 2.68378i) q^{23} +(2.35857 - 3.09380i) q^{24} +(3.67360 + 3.39185i) q^{25} -4.09252i q^{26} +(2.03359 + 4.78168i) q^{27} +(-4.00694 - 14.9541i) q^{28} -6.85013 q^{29} +(-8.66147 + 0.199824i) q^{30} -3.07108 q^{31} +(6.46466 + 1.73220i) q^{32} +(7.97365 - 1.07522i) q^{33} +(-2.72271 + 1.57196i) q^{34} +(-6.83162 + 9.28034i) q^{35} +(6.33245 - 6.41246i) q^{36} +(-1.19974 - 5.96327i) q^{37} +(5.20853 + 5.20853i) q^{38} +(0.403744 - 3.14294i) q^{39} +(2.01405 + 4.60083i) q^{40} +(-3.26251 + 1.88361i) q^{41} +(-2.66844 - 19.7886i) q^{42} +(-6.22168 + 6.22168i) q^{43} +(-6.97732 - 12.0851i) q^{44} +(-6.67147 - 0.701031i) q^{45} +(4.24516 - 7.35283i) q^{46} +(6.62567 - 6.62567i) q^{47} +(1.57621 + 0.647098i) q^{48} +(-16.9387 - 9.77957i) q^{49} +(5.20204 - 9.90153i) q^{50} +(-2.24604 + 0.938611i) q^{51} +(-5.30863 + 1.42244i) q^{52} +(2.55036 - 0.683368i) q^{53} +(9.15464 - 7.16256i) q^{54} +(-3.78296 + 9.67374i) q^{55} +(-10.0244 + 5.78762i) q^{56} +(3.48616 + 4.51385i) q^{57} +(3.96604 + 14.8015i) q^{58} +(0.812581 - 1.40743i) q^{59} +(3.26968 + 11.1658i) q^{60} +(1.47736 + 2.55885i) q^{61} +(1.77807 + 6.63584i) q^{62} +(-0.0970482 - 15.4604i) q^{63} -13.0040i q^{64} +(3.29447 + 2.42519i) q^{65} +(-6.93981 - 16.6066i) q^{66} +(0.808241 - 3.01640i) q^{67} +(2.98540 + 2.98540i) q^{68} +(3.98555 - 5.22796i) q^{69} +(24.0078 + 9.38838i) q^{70} +(8.81440 - 5.08900i) q^{71} +(-5.85649 - 3.33240i) q^{72} +(-2.08180 + 2.08180i) q^{73} +(-12.1905 + 6.04490i) q^{74} +(4.97185 - 7.09089i) q^{75} +(4.94593 - 8.56660i) q^{76} +(-23.1239 - 6.19602i) q^{77} +(-7.02487 + 0.947281i) q^{78} +(0.0724067 - 0.0418040i) q^{79} +(-1.71810 + 1.37359i) q^{80} +(7.73712 - 4.59749i) q^{81} +(5.95893 + 5.95893i) q^{82} +(3.46712 - 0.929013i) q^{83} +(-24.7414 + 10.3393i) q^{84} +(0.348029 - 3.12330i) q^{85} +(17.0457 + 9.84134i) q^{86} +(1.58558 + 11.7584i) q^{87} +(-7.37764 + 7.37764i) q^{88} +(-4.94716 + 8.56874i) q^{89} +(2.34784 + 14.8213i) q^{90} +(-4.71418 + 8.16520i) q^{91} +(-11.0133 - 2.95099i) q^{92} +(0.710851 + 5.27155i) q^{93} +(-18.1525 - 10.4804i) q^{94} +(-7.27939 + 1.10634i) q^{95} +(1.47700 - 11.4976i) q^{96} +(2.90386 + 2.90386i) q^{97} +(-11.3242 + 42.2625i) q^{98} +(-3.69127 - 13.4380i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 16 q^{6} - 4 q^{7}+O(q^{10}) $ 288 * q - 16 * q^6 - 4 * q^7	$ 288 q - 16 q^{6} - 4 q^{7} - 16 q^{10} - 18 q^{12} - 20 q^{13} + 6 q^{15} + 112 q^{16} + 20 q^{18} - 4 q^{21} - 12 q^{22} - 36 q^{25} + 48 q^{27} - 28 q^{28} - 16 q^{30} - 80 q^{31} + 2 q^{33} - 16 q^{36} - 36 q^{37} + 8 q^{40} - 32 q^{42} - 16 q^{43} + 76 q^{45} - 24 q^{46} + 112 q^{48} + 48 q^{55} + 2 q^{57} - 60 q^{58} - 56 q^{60} + 16 q^{61} - 36 q^{63} - 36 q^{70} - 58 q^{72} - 48 q^{73} - 88 q^{75} + 16 q^{76} + 20 q^{78} - 56 q^{81} - 136 q^{82} + 144 q^{85} + 16 q^{87} + 144 q^{88} - 42 q^{90} - 22 q^{93} - 80 q^{96} + 56 q^{97}+O(q^{100}) $ 288 * q - 16 * q^6 - 4 * q^7 - 16 * q^10 - 18 * q^12 - 20 * q^13 + 6 * q^15 + 112 * q^16 + 20 * q^18 - 4 * q^21 - 12 * q^22 - 36 * q^25 + 48 * q^27 - 28 * q^28 - 16 * q^30 - 80 * q^31 + 2 * q^33 - 16 * q^36 - 36 * q^37 + 8 * q^40 - 32 * q^42 - 16 * q^43 + 76 * q^45 - 24 * q^46 + 112 * q^48 + 48 * q^55 + 2 * q^57 - 60 * q^58 - 56 * q^60 + 16 * q^61 - 36 * q^63 - 36 * q^70 - 58 * q^72 - 48 * q^73 - 88 * q^75 + 16 * q^76 + 20 * q^78 - 56 * q^81 - 136 * q^82 + 144 * q^85 + 16 * q^87 + 144 * q^88 - 42 * q^90 - 22 * q^93 - 80 * q^96 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.578972	−	2.16075i	−0.409395	−	1.52788i	−0.795803	−	0.605555i	$-0.792951\pi$
$2$	−0.578972	−	2.16075i	−0.409395	−	1.52788i	0.386408	−	0.922328i	$-0.373716\pi$
$3$	−0.231467	−	1.71651i	−0.133637	−	0.991030i
$3$	−0.231467	−	1.71651i	−0.133637	−	0.991030i
$4$	−2.60160	+	1.50203i	−1.30080	+	0.751016i
$5$	2.08250	+	0.814371i	0.931322	+	0.364198i
$5$	2.08250	+	0.814371i	0.931322	+	0.364198i
$6$	−3.57495	+	1.49396i	−1.45947	+	0.609905i
$7$	−1.33384	+	4.97795i	−0.504144	+	1.88149i	−0.0329552	+	0.999457i	$0.510492\pi$
$7$	−1.33384	+	4.97795i	−0.504144	+	1.88149i	−0.471188	+	0.882033i	$0.656175\pi$
$8$	1.58821	+	1.58821i	0.561517	+	0.561517i
$9$	−2.89285	+	0.794631i	−0.964282	+	0.264877i
$10$	0.553946	−	4.97126i	0.175173	−	1.57205i
$11$			4.64526i			1.40060i	0.713850	+	0.700299i	$0.246950\pi$
$11$			4.64526i			1.40060i	−0.713850	+	0.700299i	$0.753050\pi$
$12$	3.18044	+	4.11801i	0.918115	+	1.18877i
$13$	1.76715	+	0.473506i	0.490119	+	0.131327i	0.495410	−	0.868659i	$-0.335018\pi$
$13$	1.76715	+	0.473506i	0.490119	+	0.131327i	−0.00529159	+	0.999986i	$0.501684\pi$
$14$	11.5284			3.08109
$15$	0.915851	−	3.76314i	0.236472	−	0.971638i
$16$	−0.491864	+	0.851934i	−0.122966	+	0.212984i
$17$	−0.363752	−	1.35754i	−0.0882228	−	0.329252i	0.907682	−	0.419658i	$-0.137850\pi$
$17$	−0.363752	−	1.35754i	−0.0882228	−	0.329252i	−0.995905	+	0.0904064i	$0.971183\pi$
$18$	3.39188	+	5.79066i	0.799474	+	1.36487i
$19$	−2.85167	+	1.64641i	−0.654218	+	0.377713i	−0.790071	−	0.613016i	$-0.789956\pi$
$19$	−2.85167	+	1.64641i	−0.654218	+	0.377713i	0.135852	+	0.990729i	$0.456623\pi$
$20$	−6.64103	+	1.00932i	−1.48498	+	0.225690i
$21$	8.85347	+	1.13732i	1.93199	+	0.248184i
$22$	10.0373	−	2.68947i	2.13995	−	0.573398i
$23$	2.68378	+	2.68378i	0.559608	+	0.559608i	0.929196	−	0.369588i	$-0.120501\pi$
$23$	2.68378	+	2.68378i	0.559608	+	0.559608i	−0.369588	+	0.929196i	$0.620501\pi$
$24$	2.35857	−	3.09380i	0.481441	−	0.631520i
$25$	3.67360	+	3.39185i	0.734720	+	0.678370i
$26$		−	4.09252i		−	0.802609i
$27$	2.03359	+	4.78168i	0.391365	+	0.920235i
$28$	−4.00694	−	14.9541i	−0.757240	−	2.82606i
$29$	−6.85013			−1.27204			−0.636019	−	0.771673i	$-0.719420\pi$
$29$	−6.85013			−1.27204			−0.636019	+	0.771673i	$0.719420\pi$
$30$	−8.66147	+	0.199824i	−1.58136	+	0.0364828i
$31$	−3.07108			−0.551582			−0.275791	−	0.961218i	$-0.588940\pi$
$31$	−3.07108			−0.551582			−0.275791	+	0.961218i	$0.588940\pi$
$32$	6.46466	+	1.73220i	1.14280	+	0.306213i
$33$	7.97365	−	1.07522i	1.38803	−	0.187172i
$34$	−2.72271	+	1.57196i	−0.466941	+	0.269588i
$35$	−6.83162	+	9.28034i	−1.15475	+	1.56866i
$36$	6.33245	−	6.41246i	1.05541	−	1.06874i
$37$	−1.19974	−	5.96327i	−0.197236	−	0.980356i
$37$	−1.19974	−	5.96327i	−0.197236	−	0.980356i
$38$	5.20853	+	5.20853i	0.844935	+	0.844935i
$39$	0.403744	−	3.14294i	0.0646508	−	0.503273i
$40$	2.01405	+	4.60083i	0.318450	+	0.727456i
$41$	−3.26251	+	1.88361i	−0.509519	+	0.294171i	−0.732636	−	0.680621i	$-0.761710\pi$
$41$	−3.26251	+	1.88361i	−0.509519	+	0.294171i	0.223117	+	0.974792i	$0.428377\pi$
$42$	−2.66844	−	19.7886i	−0.411748	−	3.05345i
$43$	−6.22168	+	6.22168i	−0.948798	+	0.948798i	−0.998752	−	0.0499535i	$-0.984093\pi$
$43$	−6.22168	+	6.22168i	−0.948798	+	0.948798i	0.0499535	+	0.998752i	$0.484093\pi$
$44$	−6.97732	−	12.0851i	−1.05187	−	1.82189i
$45$	−6.67147	−	0.701031i	−0.994525	−	0.104504i
$46$	4.24516	−	7.35283i	0.625915	−	1.08412i
$47$	6.62567	−	6.62567i	0.966454	−	0.966454i	−0.0330015	−	0.999455i	$-0.510507\pi$
$47$	6.62567	−	6.62567i	0.966454	−	0.966454i	0.999455	+	0.0330015i	$0.0105066\pi$
$48$	1.57621	+	0.647098i	0.227506	+	0.0934006i
$49$	−16.9387	−	9.77957i	−2.41982	−	1.39708i
$50$	5.20204	−	9.90153i	0.735680	−	1.40029i
$51$	−2.24604	+	0.938611i	−0.314509	+	0.131432i
$52$	−5.30863	+	1.42244i	−0.736174	+	0.197257i
$53$	2.55036	−	0.683368i	0.350319	−	0.0938678i	−0.0793683	−	0.996845i	$-0.525290\pi$
$53$	2.55036	−	0.683368i	0.350319	−	0.0938678i	0.429688	+	0.902978i	$0.358624\pi$
$54$	9.15464	−	7.16256i	1.24579	−	0.974700i
$55$	−3.78296	+	9.67374i	−0.510094	+	1.30441i
$56$	−10.0244	+	5.78762i	−1.33957	+	0.773403i
$57$	3.48616	+	4.51385i	0.461753	+	0.597874i
$58$	3.96604	+	14.8015i	0.520766	+	1.94353i
$59$	0.812581	−	1.40743i	0.105789	−	0.183232i	−0.808271	−	0.588810i	$-0.799597\pi$
$59$	0.812581	−	1.40743i	0.105789	−	0.183232i	0.914060	+	0.405578i	$0.132930\pi$
$60$	3.26968	+	11.1658i	0.422114	+	1.44150i
$61$	1.47736	+	2.55885i	0.189156	+	0.327628i	0.944969	−	0.327160i	$-0.106092\pi$
$61$	1.47736	+	2.55885i	0.189156	+	0.327628i	−0.755813	+	0.654787i	$0.772758\pi$
$62$	1.77807	+	6.63584i	0.225815	+	0.842752i
$63$	−0.0970482	−	15.4604i	−0.0122269	−	1.94782i
$64$		−	13.0040i		−	1.62550i
$65$	3.29447	+	2.42519i	0.408629	+	0.300808i
$66$	−6.93981	−	16.6066i	−0.854231	−	2.04413i
$67$	0.808241	−	3.01640i	0.0987424	−	0.368512i	−0.898818	−	0.438322i	$-0.855573\pi$
$67$	0.808241	−	3.01640i	0.0987424	−	0.368512i	0.997560	+	0.0698107i	$0.0222395\pi$
$68$	2.98540	+	2.98540i	0.362033	+	0.362033i
$69$	3.98555	−	5.22796i	0.479804	−	0.629373i
$70$	24.0078	+	9.38838i	2.86949	+	1.12213i
$71$	8.81440	−	5.08900i	1.04608	−	0.603953i	0.124529	−	0.992216i	$-0.460258\pi$
$71$	8.81440	−	5.08900i	1.04608	−	0.603953i	0.921549	+	0.388263i	$0.126925\pi$
$72$	−5.85649	−	3.33240i	−0.690193	−	0.392728i
$73$	−2.08180	+	2.08180i	−0.243657	+	0.243657i	−0.818361	−	0.574704i	$-0.805117\pi$
$73$	−2.08180	+	2.08180i	−0.243657	+	0.243657i	0.574704	+	0.818361i	$0.305117\pi$
$74$	−12.1905	+	6.04490i	−1.41712	+	0.702706i
$75$	4.97185	−	7.09089i	0.574100	−	0.818785i
$76$	4.94593	−	8.56660i	0.567337	−	0.982657i
$77$	−23.1239	−	6.19602i	−2.63521	−	0.706102i
$78$	−7.02487	+	0.947281i	−0.795410	+	0.107258i
$79$	0.0724067	−	0.0418040i	0.00814639	−	0.00470332i	−0.495921	−	0.868367i	$-0.665170\pi$
$79$	0.0724067	−	0.0418040i	0.00814639	−	0.00470332i	0.504068	+	0.863664i	$0.331836\pi$
$80$	−1.71810	+	1.37359i	−0.192089	+	0.153572i
$81$	7.73712	−	4.59749i	0.859680	−	0.510833i
$82$	5.95893	+	5.95893i	0.658054	+	0.658054i
$83$	3.46712	−	0.929013i	0.380566	−	0.101972i	−0.0634642	−	0.997984i	$-0.520215\pi$
$83$	3.46712	−	0.929013i	0.380566	−	0.101972i	0.444030	+	0.896012i	$0.353548\pi$
$84$	−24.7414	+	10.3393i	−2.69951	+	1.12811i
$85$	0.348029	−	3.12330i	0.0377490	−	0.338770i
$86$	17.0457	+	9.84134i	1.83809	+	1.06122i
$87$	1.58558	+	11.7584i	0.169992	+	1.26063i
$88$	−7.37764	+	7.37764i	−0.786459	+	0.786459i
$89$	−4.94716	+	8.56874i	−0.524398	+	0.908285i	0.475198	+	0.879879i	$0.342376\pi$
$89$	−4.94716	+	8.56874i	−0.524398	+	0.908285i	−0.999596	+	0.0284058i	$0.990957\pi$
$90$	2.34784	+	14.8213i	0.247484	+	1.56230i
$91$	−4.71418	+	8.16520i	−0.494180	+	0.855946i
$92$	−11.0133	−	2.95099i	−1.14821	−	0.307662i
$93$	0.710851	+	5.27155i	0.0737119	+	0.546634i
$94$	−18.1525	−	10.4804i	−1.87229	−	1.08097i
$95$	−7.27939	+	1.10634i	−0.746850	+	0.113508i
$96$	1.47700	−	11.4976i	0.150745	−	1.17347i
$97$	2.90386	+	2.90386i	0.294842	+	0.294842i	0.838990	−	0.544147i	$-0.183147\pi$
$97$	2.90386	+	2.90386i	0.294842	+	0.294842i	−0.544147	+	0.838990i	$0.683147\pi$
$98$	−11.3242	+	42.2625i	−1.14392	+	4.26916i
$99$	−3.69127	−	13.4380i	−0.370986	−	1.35057i
$100$	−14.6519	−	3.30636i	−1.46519	−	0.330636i
$101$		−	11.0072i		−	1.09525i	−0.836723	−	0.547627i	$-0.815531\pi$
$101$		−	11.0072i		−	1.09525i	0.836723	−	0.547627i	$-0.184469\pi$
$102$	3.32850	+	4.30971i	0.329571	+	0.426725i
$103$	−10.8165	+	10.8165i	−1.06578	+	1.06578i	−0.0681002	+	0.997678i	$0.521694\pi$
$103$	−10.8165	+	10.8165i	−1.06578	+	1.06578i	−0.997678	+	0.0681002i	$0.978306\pi$
$104$	2.05457	+	3.55863i	0.201468	+	0.348952i
$105$	17.5111	+	9.57848i	1.70891	+	0.934764i
$106$	−2.95318	−	5.11506i	−0.286838	−	0.496818i
$107$	12.6335	+	3.38514i	1.22133	+	0.327254i	0.811197	−	0.584772i	$-0.198816\pi$
$107$	12.6335	+	3.38514i	1.22133	+	0.327254i	0.410131	+	0.912027i	$0.365483\pi$
$108$	−12.4728	−	9.38548i	−1.20020	−	0.903119i
$109$	8.78870	+	5.07416i	0.841805	+	0.486016i	0.857877	−	0.513855i	$-0.171783\pi$
$109$	8.78870	+	5.07416i	0.841805	+	0.486016i	−0.0160725	+	0.999871i	$0.505116\pi$
$110$	23.0928	+	2.57322i	2.20181	+	0.245347i
$111$	−9.95835	+	3.43966i	−0.945205	+	0.326479i
$112$	−3.58482	−	3.58482i	−0.338734	−	0.338734i
$113$	18.1130	−	4.85336i	1.70393	−	0.456566i	0.730003	−	0.683443i	$-0.239518\pi$
$113$	18.1130	−	4.85336i	1.70393	−	0.456566i	0.973923	+	0.226878i	$0.0728517\pi$
$114$	7.73492	−	10.1461i	0.724442	−	0.950272i
$115$	3.40338	+	7.77457i	0.317367	+	0.724983i
$116$	17.8213	−	10.2891i	1.65466	−	0.955321i
$117$	−5.48835	+	0.0344516i	−0.507398	+	0.00318505i
$118$	−3.51157	−	0.940923i	−0.323267	−	0.0866190i
$119$	7.24296			0.663961
$120$	7.43121	−	4.52209i	0.678374	−	0.412808i
$121$	−10.5784			−0.961673
$122$	4.67370	−	4.67370i	0.423137	−	0.423137i
$123$	3.98841	+	5.16416i	0.359623	+	0.465637i
$124$	7.98970	−	4.61285i	0.717496	−	0.414247i
$125$	4.88804	+	10.0552i	0.437200	+	0.899364i
$126$	−33.3498	+	9.16082i	−2.97104	+	0.816110i
$127$	14.7060	−	3.94046i	1.30495	−	0.349660i	0.461628	−	0.887073i	$-0.347265\pi$
$127$	14.7060	−	3.94046i	1.30495	−	0.349660i	0.843319	+	0.537414i	$0.180599\pi$
$128$	−15.1691	+	4.06454i	−1.34077	+	0.359258i
$129$	12.1197	+	9.23950i	1.06708	+	0.813493i
$130$	3.33283	−	8.52266i	0.292308	−	0.747487i
$131$	−3.48392	−	2.01144i	−0.304392	−	0.175741i	0.340022	−	0.940417i	$-0.389565\pi$
$131$	−3.48392	−	2.01144i	−0.304392	−	0.175741i	−0.644414	+	0.764677i	$0.722899\pi$
$132$	−19.1292	+	14.7740i	−1.66498	+	1.28591i
$133$	−4.39210	−	16.3915i	−0.380843	−	1.42133i
$134$	−6.98564			−0.603467
$135$	0.340892	+	11.6139i	0.0293393	+	0.999570i
$136$	1.57834	−	2.73377i	0.135342	−	0.234419i
$137$	0.292333	−	0.292333i	0.0249757	−	0.0249757i	−0.694509	−	0.719484i	$-0.744378\pi$
$137$	0.292333	−	0.292333i	0.0249757	−	0.0249757i	0.719484	+	0.694509i	$0.244378\pi$
$138$	−13.6039	−	5.58495i	−1.15804	−	0.475422i
$139$	17.3866	+	10.0381i	1.47471	+	0.851425i	0.999594	−	0.0284980i	$-0.00907243\pi$
$139$	17.3866	+	10.0381i	1.47471	+	0.851425i	0.475117	+	0.879923i	$0.342406\pi$
$140$	3.83374	−	34.4050i	0.324010	−	2.90775i
$141$	−12.9067	−	9.83944i	−1.08694	−	0.828631i
$142$	−16.0994	−	16.0994i	−1.35103	−	1.35103i
$143$	−2.19956	+	8.20886i	−0.183936	+	0.686459i
$144$	0.745915	−	2.85537i	0.0621595	−	0.237947i
$145$	−14.2654	−	5.57855i	−1.18468	−	0.463273i
$146$	5.70357	+	3.29296i	0.472031	+	0.272527i
$147$	−12.8660	+	31.3392i	−1.06117	+	2.58481i
$148$	12.0783	+	13.7120i	0.992827	+	1.12712i
$149$	2.47602			0.202843			0.101422	−	0.994844i	$-0.467661\pi$
$149$	2.47602			0.202843			0.101422	+	0.994844i	$0.467661\pi$
$150$	−18.2002	−	6.63751i	−1.48604	−	0.541951i
$151$	7.90477	+	13.6915i	0.643281	+	1.11420i	0.984696	+	0.174283i	$0.0557607\pi$
$151$	7.90477	+	13.6915i	0.643281	+	1.11420i	−0.341414	+	0.939913i	$0.610906\pi$
$152$	−7.14390	−	1.91420i	−0.579447	−	0.155262i
$153$	2.13102	+	3.63811i	0.172283	+	0.294124i
$154$			53.5523i			4.31537i
$155$	−6.39551	−	2.50100i	−0.513700	−	0.200885i
$156$	3.67041	+	8.78309i	0.293868	+	0.703210i
$157$	13.3835	−	3.58611i	1.06812	−	0.286202i	0.318401	−	0.947956i	$-0.396854\pi$
$157$	13.3835	−	3.58611i	1.06812	−	0.286202i	0.749721	+	0.661754i	$0.230188\pi$
$158$	−0.132250	−	0.132250i	−0.0105212	−	0.0105212i
$159$	−1.76334	−	4.21956i	−0.139842	−	0.334633i
$160$	12.0520	+	8.87194i	0.952794	+	0.701388i
$161$	−16.9395	+	9.78002i	−1.33502	+	0.770774i
$162$	−14.4136	−	14.0562i	−1.13244	−	1.10436i
$163$	−2.41715	−	9.02093i	−0.189326	−	0.706574i	−0.993663	−	0.112401i	$-0.964146\pi$
$163$	−2.41715	−	9.02093i	−0.189326	−	0.706574i	0.804337	−	0.594173i	$-0.202521\pi$
$164$	5.65850	−	9.80080i	0.441854	−	0.765314i
$165$	17.4807	+	4.25436i	1.36087	+	0.331202i
$166$	−4.01473	−	6.95372i	−0.311604	−	0.539714i
$167$	−2.21997	−	0.594840i	−0.171787	−	0.0460301i	0.171900	−	0.985114i	$-0.445009\pi$
$167$	−2.21997	−	0.594840i	−0.171787	−	0.0460301i	−0.343687	+	0.939084i	$0.611676\pi$
$168$	12.2549	+	15.8675i	0.945482	+	1.22420i
$169$	−8.35973	−	4.82649i	−0.643056	−	0.371268i
$170$	−6.95019	+	1.05630i	−0.533055	+	0.0810147i
$171$	6.94116	−	7.02885i	0.530804	−	0.537510i
$172$	6.84114	−	25.5315i	0.521632	−	1.94676i
$173$	−9.76916	+	2.61764i	−0.742736	+	0.199015i	−0.610294	−	0.792175i	$-0.708949\pi$
$173$	−9.76916	+	2.61764i	−0.742736	+	0.199015i	−0.132442	+	0.991191i	$0.542282\pi$
$174$	24.4889	−	10.2338i	1.85650	−	0.775822i
$175$	−21.7845	+	13.7628i	−1.64675	+	1.04037i
$176$	−3.95745	−	2.28484i	−0.298304	−	0.172226i
$177$	−2.60396	−	1.06903i	−0.195726	−	0.0803535i
$178$	21.3792	+	5.72854i	1.60244	+	0.429372i
$179$	4.39631			0.328596			0.164298	−	0.986411i	$-0.447464\pi$
$179$	4.39631			0.328596			0.164298	+	0.986411i	$0.447464\pi$
$180$	18.4094	−	8.19697i	1.37216	−	0.610966i
$181$	6.28722	+	10.8898i	0.467325	+	0.809431i	0.999303	−	0.0373271i	$-0.0118843\pi$
$181$	6.28722	+	10.8898i	0.467325	+	0.809431i	−0.531978	+	0.846758i	$0.678551\pi$
$182$	20.3724	+	5.45876i	1.51010	+	0.404630i
$183$	4.05035	−	3.12819i	0.299411	−	0.231243i
$184$			8.52482i			0.628458i
$185$	2.35787	−	13.3955i	0.173354	−	0.984860i
$186$	10.9790	−	4.58805i	0.805016	−	0.336412i
$187$	6.30612	−	1.68972i	0.461149	−	0.123565i
$188$	−7.28535	+	27.1893i	−0.531339	+	1.98298i
$189$	−26.5155	+	3.74514i	−1.92872	+	0.272419i
$190$	6.60508	+	15.0884i	0.479183	+	1.09463i
$191$			10.7222i			0.775831i	0.921695	+	0.387916i	$0.126805\pi$
$191$			10.7222i			0.775831i	−0.921695	+	0.387916i	$0.873195\pi$
$192$	−22.3215	+	3.00999i	−1.61092	+	0.217227i
$193$	−5.72710	+	5.72710i	−0.412246	+	0.412246i	−0.882520	−	0.470275i	$-0.844155\pi$
$193$	−5.72710	+	5.72710i	−0.412246	+	0.412246i	0.470275	+	0.882520i	$0.344155\pi$
$194$	4.59327	−	7.95578i	0.329778	−	0.571192i
$195$	3.40031	−	6.21636i	0.243502	−	0.445163i
$196$	58.7569			4.19692
$197$	−6.61428	−	24.6848i	−0.471248	−	1.75872i	−0.635295	−	0.772270i	$-0.719121\pi$
$197$	−6.61428	−	24.6848i	−0.471248	−	1.75872i	0.164047	−	0.986453i	$-0.447545\pi$
$198$	−26.8991	+	15.7562i	−1.91164	+	1.11974i
$199$			7.60467i			0.539081i	0.962989	+	0.269540i	$0.0868718\pi$
$199$			7.60467i			0.539081i	−0.962989	+	0.269540i	$0.913128\pi$
$200$	0.447474	+	11.2214i	0.0316412	+	0.793474i
$201$	−5.36477	−	0.689163i	−0.378402	−	0.0486098i
$202$	−23.7838	+	6.37284i	−1.67342	+	0.448391i
$203$	9.13697	−	34.0996i	0.641290	−	2.39333i
$204$	4.43347	−	5.81551i	0.310405	−	0.407167i
$205$	−8.32814	+	1.26573i	−0.581663	+	0.0884021i
$206$	29.6342	+	17.1093i	2.06471	+	1.19206i
$207$	−9.89640	−	5.63116i	−0.687847	−	0.391393i
$208$	−1.27259	+	1.27259i	−0.0882385	+	0.0882385i
$209$	−7.64801	−	13.2467i	−0.529024	−	0.916297i
$210$	10.5583	−	43.3829i	0.728591	−	2.99371i
$211$	6.09168			0.419369			0.209684	−	0.977769i	$-0.432756\pi$
$211$	6.09168			0.419369			0.209684	+	0.977769i	$0.432756\pi$
$212$	−5.60857	+	5.60857i	−0.385199	+	0.385199i
$213$	−10.7756	−	13.9521i	−0.738331	−	0.955984i
$214$		−	29.2578i		−	2.00002i
$215$	−18.0234	+	7.88989i	−1.22919	+	0.538086i
$216$	−4.36454	+	10.8241i	−0.296969	+	0.736486i
$217$	4.09632	−	15.2877i	0.278076	−	1.03779i
$218$	5.87559	−	21.9280i	0.397945	−	1.48515i
$219$	4.05531	+	3.09158i	0.274033	+	0.208910i
$220$	−4.68853	−	30.8493i	−0.316101	−	2.07986i
$221$		−	2.57121i		−	0.172959i
$222$	13.1979	+	19.5261i	0.885783	+	1.31050i
$223$	12.8009	−	12.8009i	0.857212	−	0.857212i	−0.133797	−	0.991009i	$-0.542717\pi$
$223$	12.8009	−	12.8009i	0.857212	−	0.857212i	0.991009	+	0.133797i	$0.0427170\pi$
$224$	−17.2456	+	29.8703i	−1.15227	+	1.99579i
$225$	−13.3224	−	6.89295i	−0.888162	−	0.459530i
$226$	−20.9738	−	36.3277i	−1.39516	−	2.41649i
$227$	−1.98066	−	0.530716i	−0.131461	−	0.0352248i	0.192489	−	0.981299i	$-0.438344\pi$
$227$	−1.98066	−	0.530716i	−0.131461	−	0.0352248i	−0.323950	+	0.946074i	$0.605011\pi$
$228$	−15.8495	−	6.50688i	−1.04966	−	0.430929i
$229$	−8.88036	+	5.12708i	−0.586830	+	0.338807i	−0.763843	−	0.645402i	$-0.776690\pi$
$229$	−8.88036	+	5.12708i	−0.586830	+	0.338807i	0.177013	+	0.984209i	$0.443357\pi$
$230$	14.8285	−	11.8551i	0.977761	−	0.781704i
$231$	−5.28316	+	41.1266i	−0.347607	+	2.70593i
$232$	−10.8794	−	10.8794i	−0.714271	−	0.714271i
$233$	−5.97240	−	5.97240i	−0.391265	−	0.391265i	0.483873	−	0.875138i	$-0.339230\pi$
$233$	−5.97240	−	5.97240i	−0.391265	−	0.391265i	−0.875138	+	0.483873i	$0.839230\pi$
$234$	3.25204	+	11.8390i	0.212593	+	0.773941i
$235$	19.1937	−	8.40220i	1.25206	−	0.548099i
$236$			4.88209i			0.317797i
$237$	−0.0885170	−	0.114611i	−0.00574980	−	0.00744478i
$238$	−4.19347	−	15.6502i	−0.271822	−	1.01445i
$239$	0.917410	−	1.58900i	0.0593423	−	0.102784i	−0.834828	−	0.550511i	$-0.814433\pi$
$239$	0.917410	−	1.58900i	0.0593423	−	0.102784i	0.894170	+	0.447727i	$0.147766\pi$
$240$	2.75547	+	2.63120i	0.177865	+	0.169843i
$241$	1.00505	+	1.74080i	0.0647411	+	0.112135i	0.896579	−	0.442884i	$-0.146045\pi$
$241$	1.00505	+	1.74080i	0.0647411	+	0.112135i	−0.831838	+	0.555018i	$0.812711\pi$
$242$	6.12460	+	22.8573i	0.393704	+	1.46932i
$243$	−9.68255	−	12.2167i	−0.621136	−	0.783703i
$244$	−7.68696	−	4.43807i	−0.492107	−	0.284118i
$245$	−27.3106	−	34.1603i	−1.74481	−	2.18242i
$246$	8.84930	−	11.6079i	0.564211	−	0.740092i
$247$	−5.81891	+	1.55917i	−0.370249	+	0.0992078i
$248$	−4.87751	−	4.87751i	−0.309722	−	0.309722i
$249$	−2.39719	−	5.73633i	−0.151916	−	0.363525i
$250$	18.8968	−	16.3835i	1.19514	−	1.03619i
$251$		−	5.85930i		−	0.369836i	−0.982754	−	0.184918i	$-0.940798\pi$
$251$		−	5.85930i		−	0.369836i	0.982754	−	0.184918i	$-0.0592019\pi$
$252$	23.4744	+	40.0758i	1.47875	+	2.52454i
$253$	−12.4669	+	12.4669i	−0.783785	+	0.783785i
$254$	−17.0287	−	29.4946i	−1.06848	−	1.85066i
$255$	−5.44176	+	0.125544i	−0.340776	+	0.00786187i
$256$	4.56095	+	7.89981i	0.285060	+	0.493738i
$257$	−0.234205	−	0.874065i	−0.0146093	−	0.0545227i	0.958236	−	0.285977i	$-0.0923182\pi$
$257$	−0.234205	−	0.874065i	−0.0146093	−	0.0545227i	−0.972846	+	0.231455i	$0.925652\pi$
$258$	12.9473	−	31.5372i	0.806064	−	1.96342i
$259$	31.2852	+	1.98181i	1.94396	+	0.123144i
$260$	−12.2136	−	1.36096i	−0.757455	−	0.0844030i
$261$	19.8164	−	5.44333i	1.22660	−	0.336934i
$262$	−2.32914	+	8.69247i	−0.143895	+	0.537023i
$263$	−5.15214	+	19.2280i	−0.317695	+	1.18565i	0.603760	+	0.797166i	$0.293669\pi$
$263$	−5.15214	+	19.2280i	−0.317695	+	1.18565i	−0.921455	+	0.388486i	$0.872998\pi$
$264$	14.3715	+	10.9561i	0.884505	+	0.674304i
$265$	5.86764	+	0.653829i	0.360447	+	0.0401644i
$266$	−32.8752	+	18.9805i	−2.01571	+	1.16377i
$267$	15.8535	+	6.50851i	0.970217	+	0.398314i
$268$	2.42801	+	9.06145i	0.148314	+	0.553516i
$269$	10.5111			0.640876			0.320438	−	0.947270i	$-0.396170\pi$
$269$	10.5111			0.640876			0.320438	+	0.947270i	$0.396170\pi$
$270$	24.8975	−	7.46074i	1.51521	−	0.454046i
$271$	−12.5624	+	21.7588i	−0.763114	+	1.32175i	0.178123	+	0.984008i	$0.442997\pi$
$271$	−12.5624	+	21.7588i	−0.763114	+	1.32175i	−0.941238	+	0.337745i	$0.890336\pi$
$272$	1.33545	+	0.357833i	0.0809737	+	0.0216968i
$273$	15.1069	+	6.20199i	0.914309	+	0.375362i
$274$	−0.800912	−	0.462407i	−0.0483849	−	0.0279350i
$275$	−15.7560	+	17.0648i	−0.950124	+	1.02905i
$276$	−2.51622	+	19.5875i	−0.151459	+	1.17903i
$277$	−3.71851	+	13.8777i	−0.223424	+	0.833829i	0.759606	+	0.650383i	$0.225392\pi$
$277$	−3.71851	+	13.8777i	−0.223424	+	0.833829i	−0.983030	+	0.183446i	$0.941275\pi$
$278$	11.6236	−	43.3799i	0.697138	−	2.60176i
$279$	8.88415	−	2.44037i	0.531880	−	0.146101i
$280$	−25.5892	+	3.88909i	−1.52924	+	0.232417i
$281$	6.68407	+	3.85905i	0.398738	+	0.230212i	0.685940	−	0.727659i	$-0.259391\pi$
$281$	6.68407	+	3.85905i	0.398738	+	0.230212i	−0.287201	+	0.957870i	$0.592725\pi$
$282$	−13.7880	+	33.5849i	−0.821063	+	1.99995i
$283$	16.4366	+	4.40417i	0.977053	+	0.261801i	0.711803	−	0.702379i	$-0.247879\pi$
$283$	16.4366	+	4.40417i	0.977053	+	0.261801i	0.265250	+	0.964180i	$0.414546\pi$
$284$	−15.2877	+	26.4790i	−0.907157	+	1.57124i
$285$	3.58398	+	12.2391i	0.212296	+	0.724982i
$286$	19.0108			1.12413
$287$	−5.02487	−	18.7531i	−0.296609	−	1.10696i
$288$	−20.0777	+	0.126033i	−1.18309	+	0.00742654i
$289$	13.0118	−	7.51238i	0.765402	−	0.441905i
$290$	−3.79461	+	34.0538i	−0.222827	+	1.99971i
$291$	4.31237	−	5.65667i	0.252796	−	0.331600i
$292$	2.28908	−	8.54295i	0.133958	−	0.499938i
$293$	4.00232	−	14.9369i	0.233818	−	0.872621i	−0.744860	−	0.667221i	$-0.767484\pi$
$293$	4.00232	−	14.9369i	0.233818	−	0.872621i	0.978678	−	0.205400i	$-0.0658495\pi$
$294$	75.1654	+	9.65580i	4.38373	+	0.563138i
$295$	2.83837	−	2.26923i	0.165256	−	0.132120i
$296$	7.56549	−	11.3764i	0.439735	−	0.661237i
$297$	−22.2121	+	9.44656i	−1.28888	+	0.548145i
$298$	−1.43355	−	5.35007i	−0.0830431	−	0.309921i
$299$	3.47186	+	6.01343i	0.200783	+	0.347766i
$300$	−2.28400	+	25.9155i	−0.131867	+	1.49623i
$301$	−22.6725	−	39.2700i	−1.30682	−	2.26348i
$302$	25.0072	−	25.0072i	1.43900	−	1.43900i
$303$	−18.8940	+	2.54779i	−1.08543	+	0.146367i
$304$		−	3.23925i		−	0.185784i
$305$	0.992733	+	6.53192i	0.0568437	+	0.374017i
$306$	6.62725	−	6.71098i	0.378855	−	0.383641i
$307$	−7.51301	−	7.51301i	−0.428790	−	0.428790i	0.459426	−	0.888216i	$-0.348055\pi$
$307$	−7.51301	−	7.51301i	−0.428790	−	0.428790i	−0.888216	+	0.459426i	$0.848055\pi$
$308$	69.4656	−	18.6132i	3.95817	−	1.06059i
$309$	21.0703	+	16.0630i	1.19865	+	0.913791i
$310$	−1.70121	+	15.2671i	−0.0966223	+	0.867115i
$311$	−17.4851	−	10.0950i	−0.991488	−	0.572436i	−0.0857694	−	0.996315i	$-0.527335\pi$
$311$	−17.4851	−	10.0950i	−0.991488	−	0.572436i	−0.905719	+	0.423879i	$0.860668\pi$
$312$	5.63287	−	4.35041i	0.318899	−	0.246294i
$313$	4.80126	+	17.9185i	0.271383	+	1.01282i	0.958226	+	0.286011i	$0.0923292\pi$
$313$	4.80126	+	17.9185i	0.271383	+	1.01282i	−0.686843	+	0.726806i	$0.741004\pi$
$314$	−15.4974	−	26.8423i	−0.874568	−	1.51480i
$315$	12.3884	−	32.2752i	0.698005	−	1.81850i
$316$	−0.125582	+	0.217514i	−0.00706454	+	0.0122361i
$317$	−3.34715	−	12.4917i	−0.187995	−	0.701606i	−0.993970	−	0.109656i	$-0.965025\pi$
$317$	−3.34715	−	12.4917i	−0.187995	−	0.701606i	0.805975	−	0.591950i	$-0.201642\pi$
$318$	−8.09651	+	6.25314i	−0.454030	+	0.350659i
$319$		−	31.8206i		−	1.78161i
$320$	10.5901	−	27.0808i	0.592003	−	1.51386i
$321$	2.88641	−	22.4692i	0.161104	−	1.25411i
$322$	30.9397	+	30.9397i	1.72420	+	1.72420i
$323$	3.27237	+	3.27237i	0.182080	+	0.182080i
$324$	−13.2233	+	23.5822i	−0.734627	+	1.31012i
$325$	4.88573	+	7.73338i	0.271012	+	0.428971i
$326$	−18.0926	+	10.4457i	−1.00205	+	0.578536i
$327$	6.67558	−	16.2604i	0.369160	−	0.899204i
$328$	−8.17313	−	2.18998i	−0.451285	−	0.120922i
$329$	24.1447	+	41.8199i	1.33114	+	2.30560i
$330$	−0.928235	−	40.2347i	−0.0510977	−	2.21485i
$331$	−9.79893	+	16.9722i	−0.538598	+	0.932879i	0.460382	+	0.887721i	$0.347712\pi$
$331$	−9.79893	+	16.9722i	−0.538598	+	0.932879i	−0.998980	+	0.0451577i	$0.985621\pi$
$332$	−7.62464	+	7.62464i	−0.418457	+	0.418457i
$333$	8.20926	+	16.2975i	0.449865	+	0.893097i
$334$			5.14121i			0.281314i
$335$	4.13963	−	5.62343i	0.226172	−	0.307241i
$336$	−5.32363	+	6.98316i	−0.290428	+	0.380963i
$337$	−1.01611	+	3.79217i	−0.0553510	+	0.206573i	−0.988063	−	0.154049i	$-0.950769\pi$
$337$	−1.01611	+	3.79217i	−0.0553510	+	0.206573i	0.932712	+	0.360622i	$0.117435\pi$
$338$	−5.58881	+	20.8577i	−0.303991	+	1.13451i
$339$	−12.5234	−	29.9678i	−0.680179	−	1.62763i
$340$	3.78587	+	8.64833i	0.205318	+	0.469021i
$341$		−	14.2659i		−	0.772544i
$342$	−19.2063	−	10.9286i	−1.03856	−	0.590952i
$343$	45.7670	−	45.7670i	2.47118	−	2.47118i
$344$	−19.7627			−1.06553
$345$	12.5574	−	7.64151i	0.676068	−	0.411405i
$346$	11.3121	+	19.5932i	0.608145	+	1.05334i
$347$	−20.0966	+	20.0966i	−1.07884	+	1.07884i	−0.0822276	+	0.996614i	$0.526203\pi$
$347$	−20.0966	+	20.0966i	−1.07884	+	1.07884i	−0.996614	+	0.0822276i	$0.973797\pi$
$348$	−21.7865	−	28.2089i	−1.16788	−	1.51216i
$349$	−1.73516	−	1.00180i	−0.0928811	−	0.0536249i	0.452840	−	0.891592i	$-0.350411\pi$
$349$	−1.73516	−	1.00180i	−0.0928811	−	0.0536249i	−0.545721	+	0.837967i	$0.683744\pi$
$350$	42.3507	+	39.1026i	2.26374	+	2.09012i
$351$	1.32951	+	9.41286i	0.0709638	+	0.502421i
$352$	−8.04652	+	30.0300i	−0.428881	+	1.60061i
$353$	18.2339	−	4.88576i	0.970494	−	0.260043i	0.261457	−	0.965215i	$-0.415797\pi$
$353$	18.2339	−	4.88576i	0.970494	−	0.260043i	0.709036	+	0.705172i	$0.249130\pi$
$354$	−0.802297	+	6.24546i	−0.0426416	+	0.331943i
$355$	22.5003	−	3.41964i	1.19419	−	0.181495i
$356$		−	29.7232i		−	1.57533i
$357$	−1.67650	−	12.4326i	−0.0887299	−	0.658005i
$358$	−2.54534	−	9.49935i	−0.134526	−	0.502056i
$359$	−11.1059			−0.586145			−0.293073	−	0.956090i	$-0.594678\pi$
$359$	−11.1059			−0.586145			−0.293073	+	0.956090i	$0.594678\pi$
$360$	−9.48231	−	11.7091i	−0.499762	−	0.617123i
$361$	−4.07865	+	7.06442i	−0.214666	+	0.371812i
$362$	19.8900	−	19.8900i	1.04540	−	1.04540i
$363$	2.44855	+	18.1580i	0.128515	+	0.953047i
$364$		−	28.3234i		−	1.48455i
$365$	−6.03071	+	2.63999i	−0.315662	+	0.138184i
$366$	−9.10429	−	6.94068i	−0.475889	−	0.362795i
$367$	−7.38604	+	27.5651i	−0.385548	+	1.43889i	0.451753	+	0.892143i	$0.350799\pi$
$367$	−7.38604	+	27.5651i	−0.385548	+	1.43889i	−0.837301	+	0.546742i	$0.815868\pi$
$368$	−3.60647	+	0.966350i	−0.188000	+	0.0503745i
$369$	7.94117	−	8.04150i	0.413401	−	0.418624i
$370$	−30.3096	+	2.66088i	−1.57572	+	0.138332i
$371$			13.6071i			0.706445i
$372$	−9.76738	−	12.6467i	−0.506415	−	0.655702i
$373$	−22.0904	−	5.91911i	−1.14380	−	0.306480i	−0.363321	−	0.931664i	$-0.618357\pi$
$373$	−22.0904	−	5.91911i	−1.14380	−	0.306480i	−0.780477	+	0.625184i	$0.785024\pi$
$374$	−7.30214	−	12.6477i	−0.377585	−	0.653996i
$375$	16.1285	−	10.7178i	0.832871	−	0.553467i
$376$	21.0459			1.08536
$377$	−12.1052	−	3.24358i	−0.623450	−	0.167053i
$378$	23.4441	+	55.1251i	1.20583	+	2.83533i
$379$	−5.72889	−	3.30758i	−0.294273	−	0.169899i	0.345594	−	0.938384i	$-0.387677\pi$
$379$	−5.72889	−	3.30758i	−0.294273	−	0.169899i	−0.639867	+	0.768485i	$0.721011\pi$
$380$	17.2763	−	13.8121i	0.886255	−	0.708547i
$381$	−10.1678	−	24.3310i	−0.520913	−	1.24651i
$382$	23.1680	−	6.20786i	1.18538	−	0.317622i
$383$	−4.97918	+	18.5826i	−0.254424	+	0.949524i	0.713986	+	0.700160i	$0.246888\pi$
$383$	−4.97918	+	18.5826i	−0.254424	+	0.949524i	−0.968410	+	0.249364i	$0.919779\pi$
$384$	10.4880	+	25.0971i	0.535212	+	1.28073i
$385$	−43.1096	−	31.7346i	−2.19707	−	1.61735i
$386$	15.6907	+	9.05902i	0.798634	+	0.461092i
$387$	13.0544	−	22.9423i	0.663594	−	1.16622i
$388$	−11.9164	−	3.19298i	−0.604961	−	0.162099i
$389$	7.79118	+	13.4947i	0.395029	+	0.684210i	0.993105	−	0.117230i	$-0.0374013\pi$
$389$	7.79118	+	13.4947i	0.395029	+	0.684210i	−0.598076	+	0.801439i	$0.704068\pi$
$390$	−15.4007	−	3.74814i	−0.779846	−	0.189794i
$391$	2.66711	−	4.61958i	0.134882	−	0.233622i
$392$	−11.3702	−	42.4342i	−0.574283	−	2.14325i
$393$	−2.64626	+	6.44579i	−0.133486	+	0.325147i
$394$	−49.5084	+	28.5837i	−2.49420	+	1.44002i
$395$	0.184831	−	0.0280909i	0.00929985	−	0.00141341i
$396$	29.7875	+	29.4159i	1.49688	+	1.47820i
$397$	5.66077	+	5.66077i	0.284106	+	0.284106i	0.834744	−	0.550638i	$-0.185616\pi$
$397$	5.66077	+	5.66077i	0.284106	+	0.284106i	−0.550638	+	0.834744i	$0.685616\pi$
$398$	16.4318	−	4.40289i	0.823653	−	0.220697i
$399$	−27.1197	+	11.3332i	−1.35768	+	0.567369i
$400$	−4.69655	+	1.46133i	−0.234827	+	0.0730667i
$401$			20.7039i			1.03390i	0.856015	+	0.516951i	$0.172933\pi$
$401$			20.7039i			1.03390i	−0.856015	+	0.516951i	$0.827067\pi$
$402$	1.61694	+	11.9910i	0.0806457	+	0.598054i
$403$	−5.42705	−	1.45417i	−0.270340	−	0.0724375i
$404$	16.5331	+	28.6362i	0.822553	+	1.42470i
$405$	19.8566	−	3.27339i	0.986683	−	0.162656i
$406$	−78.9710			−3.91926
$407$	27.7009	−	5.57309i	1.37308	−	0.276248i
$408$	−5.05789	−	2.07647i	−0.250403	−	0.102801i
$409$	−15.8024	−	9.12355i	−0.781381	−	0.451130i	0.0555386	−	0.998457i	$-0.482312\pi$
$409$	−15.8024	−	9.12355i	−0.781381	−	0.451130i	−0.836919	+	0.547326i	$0.815646\pi$
$410$	7.55668	+	17.2622i	0.373198	+	0.852521i
$411$	−0.569459	−	0.434129i	−0.0280894	−	0.0214140i
$412$	11.8934	−	44.3868i	0.585946	−	2.18678i
$413$	5.92228	+	5.92228i	0.291416	+	0.291416i
$414$	−6.43780	+	24.6440i	−0.316401	+	1.21118i
$415$	7.97684	+	0.888856i	0.391568	+	0.0436322i
$416$	10.6038	+	6.12211i	0.519895	+	0.300161i
$417$	13.2062	−	32.1678i	0.646711	−	1.57527i
$418$	−24.1950	+	24.1950i	−1.18341	+	1.18341i
$419$	7.48610	−	12.9663i	0.365720	−	0.633446i	−0.623171	−	0.782085i	$-0.714156\pi$
$419$	7.48610	−	12.9663i	0.365720	−	0.633446i	0.988891	+	0.148640i	$0.0474895\pi$
$420$	−59.9441	+	1.38294i	−2.92497	+	0.0674806i
$421$	8.41951			0.410342			0.205171	−	0.978726i	$-0.434225\pi$
$421$	8.41951			0.410342			0.205171	+	0.978726i	$0.434225\pi$
$422$	−3.52691	−	13.1626i	−0.171687	−	0.640746i
$423$	−13.9021	+	24.4320i	−0.675943	+	1.18793i
$424$	5.13584	+	2.96518i	0.249419	+	0.144002i
$425$	3.26830	−	6.22085i	0.158536	−	0.301756i
$426$	−23.9083	+	31.3613i	−1.15836	+	1.51946i
$427$	−14.7084	+	3.94111i	−0.711790	+	0.190723i
$428$	−37.9519	+	10.1692i	−1.83447	+	0.491546i
$429$	14.5997	+	1.87550i	0.704882	+	0.0905498i
$430$	27.4832	+	34.3761i	1.32536	+	1.65776i
$431$	−10.0688	+	5.81323i	−0.484997	+	0.280013i	−0.722497	−	0.691374i	$-0.757006\pi$
$431$	−10.0688	+	5.81323i	−0.484997	+	0.280013i	0.237500	+	0.971388i	$0.423672\pi$
$432$	−5.07393	−	0.619452i	−0.244120	−	0.0298034i
$433$	11.4297	−	11.4297i	0.549276	−	0.549276i	−0.376955	−	0.926231i	$-0.623029\pi$
$433$	11.4297	−	11.4297i	0.549276	−	0.549276i	0.926231	+	0.376955i	$0.123029\pi$
$434$	−35.4045			−1.69947
$435$	−6.27370	+	25.7780i	−0.300801	+	1.23596i
$436$	−30.4862			−1.46002
$437$	−12.0719	−	3.23465i	−0.577477	−	0.154734i
$438$	4.33222	−	10.5525i	0.207002	−	0.504217i
$439$	−28.1667	+	16.2621i	−1.34432	+	0.776146i	−0.987439	−	0.158002i	$-0.949495\pi$
$439$	−28.1667	+	16.2621i	−1.34432	+	0.776146i	−0.356886	+	0.934148i	$0.616162\pi$
$440$	−21.3721	+	9.35579i	−1.01887	+	0.446020i
$441$	56.7723	+	14.8308i	2.70344	+	0.706227i
$442$	−5.55576	+	1.48866i	−0.264261	+	0.0708084i
$443$	13.4205	+	13.4205i	0.637625	+	0.637625i	0.949969	−	0.312344i	$-0.101114\pi$
$443$	13.4205	+	13.4205i	0.637625	+	0.637625i	−0.312344	+	0.949969i	$0.601114\pi$
$444$	20.7411	−	23.9064i	0.984329	−	1.13455i
$445$	−17.2806	+	13.8156i	−0.819179	+	0.654920i
$446$	−35.0710	−	20.2482i	−1.66066	−	0.958781i
$447$	−0.573116	−	4.25013i	−0.0271074	−	0.201024i
$448$	64.7332	+	17.3452i	3.05836	+	0.819484i
$449$	−6.90028	−	11.9516i	−0.325644	−	0.564033i	0.655998	−	0.754762i	$-0.272248\pi$
$449$	−6.90028	−	11.9516i	−0.325644	−	0.564033i	−0.981643	+	0.190730i	$0.938915\pi$
$450$	−7.18065	+	32.7773i	−0.338499	+	1.54514i
$451$	−8.74987	−	15.1552i	−0.412015	−	0.713631i
$452$	−39.8328	+	39.8328i	−1.87358	+	1.87358i
$453$	21.6719	−	16.7378i	1.01824	−	0.786409i
$454$			4.58698i			0.215278i
$455$	−16.4668	+	13.1649i	−0.771974	+	0.617181i
$456$	−1.63218	+	12.7057i	−0.0764340	+	0.594998i
$457$	4.07635	−	15.2131i	0.190683	−	0.711640i	−0.802659	−	0.596439i	$-0.796582\pi$
$457$	4.07635	−	15.2131i	0.190683	−	0.711640i	0.993342	−	0.115202i	$-0.0367514\pi$
$458$	16.2198	+	16.2198i	0.757903	+	0.757903i
$459$	5.75160	−	4.50003i	0.268462	−	0.210044i
$460$	−20.5319	−	15.1143i	−0.957304	−	0.704708i
$461$	12.9850	+	7.49688i	0.604770	+	0.349164i	0.770916	−	0.636937i	$-0.219799\pi$
$461$	12.9850	+	7.49688i	0.604770	+	0.349164i	−0.166146	+	0.986101i	$0.553132\pi$
$462$	91.9233	−	12.3956i	4.27666	−	0.576694i
$463$	−10.6491	−	2.85340i	−0.494903	−	0.132609i	0.00273025	−	0.999996i	$-0.499131\pi$
$463$	−10.6491	−	2.85340i	−0.494903	−	0.132609i	−0.497634	+	0.867387i	$0.665798\pi$
$464$	3.36934	−	5.83586i	0.156418	−	0.270923i
$465$	−2.81265	+	11.5569i	−0.130433	+	0.535938i
$466$	−9.44703	+	16.3627i	−0.437625	+	0.757989i
$467$	22.3558	−	22.3558i	1.03450	−	1.03450i	0.0351186	−	0.999383i	$-0.488819\pi$
$467$	22.3558	−	22.3558i	1.03450	−	1.03450i	0.999383	−	0.0351186i	$-0.0111809\pi$
$468$	14.2267	−	8.33331i	0.657630	−	0.385207i
$469$	13.9374	+	8.04677i	0.643570	+	0.371565i
$470$	−29.2677	−	36.6082i	−1.35002	−	1.68861i
$471$	−9.25344	−	22.1430i	−0.426376	−	1.02029i
$472$	3.52584	−	0.944747i	0.162290	−	0.0434855i
$473$	−28.9013	−	28.9013i	−1.32888	−	1.32888i
$474$	−0.196397	+	0.257620i	−0.00902082	+	0.0118329i
$475$	−16.0603	−	3.62419i	−0.736897	−	0.166289i
$476$	−18.8432	+	10.8792i	−0.863679	+	0.498645i
$477$	−6.83479	+	4.00348i	−0.312943	+	0.183307i
$478$	−3.96459	−	1.06231i	−0.181336	−	0.0485889i
$479$	−2.64211	+	4.57626i	−0.120721	+	0.209095i	−0.920052	−	0.391796i	$-0.871854\pi$
$479$	−2.64211	+	4.57626i	−0.120721	+	0.209095i	0.799331	+	0.600891i	$0.205187\pi$
$480$	12.4392	−	22.7410i	0.567768	−	1.03798i
$481$	0.703532	−	11.1061i	0.0320783	−	0.506393i
$482$	3.17955	−	3.17955i	0.144824	−	0.144824i
$483$	20.7085	+	26.8131i	0.942268	+	1.22004i
$484$	27.5207	−	15.8891i	1.25094	−	0.722232i
$485$	3.68246	+	8.41210i	0.167212	+	0.381974i
$486$	−20.7914	+	27.9947i	−0.943116	+	1.26987i
$487$	−24.0416	−	24.0416i	−1.08943	−	1.08943i	−0.995587	−	0.0938440i	$-0.970085\pi$
$487$	−24.0416	−	24.0416i	−1.08943	−	1.08943i	−0.0938440	−	0.995587i	$-0.529915\pi$
$488$	−1.71765	+	6.41034i	−0.0777542	+	0.290183i
$489$	−14.9251	+	6.23712i	−0.674935	+	0.282052i
$490$	−58.0000	+	78.7895i	−2.62017	+	3.55935i
$491$		−	20.8392i		−	0.940461i	−0.882544	−	0.470231i	$-0.844171\pi$
$491$		−	20.8392i		−	0.940461i	0.882544	−	0.470231i	$-0.155829\pi$
$492$	−18.1330	−	7.44433i	−0.817498	−	0.335616i
$493$	2.49175	+	9.29933i	0.112223	+	0.418821i
$494$	6.73798	+	11.6705i	0.303156	+	0.525081i
$495$	3.25647	−	30.9907i	0.146367	−	1.39293i
$496$	1.51055	−	2.61635i	0.0678258	−	0.117478i
$497$	13.5758	+	50.6656i	0.608958	+	2.27266i
$498$	−11.0069	+	8.50091i	−0.493231	+	0.380935i
$499$	13.3179	−	7.68909i	0.596191	−	0.344211i	−0.171351	−	0.985210i	$-0.554813\pi$
$499$	13.3179	−	7.68909i	0.596191	−	0.344211i	0.767541	+	0.640999i	$0.221480\pi$
$500$	−27.8199	−	18.8176i	−1.24415	−	0.841547i
$501$	−0.507202	+	3.94830i	−0.0226601	+	0.176397i
$502$	−12.6605	+	3.39237i	−0.565066	+	0.151409i
$503$	−19.3248	+	5.17807i	−0.861652	+	0.230879i	−0.662474	−	0.749084i	$-0.730494\pi$
$503$	−19.3248	+	5.17807i	−0.861652	+	0.230879i	−0.199177	+	0.979963i	$0.563827\pi$
$504$	24.4002	−	24.7084i	1.08687	−	1.10060i
$505$	8.96391	−	22.9224i	0.398889	−	1.02003i
$506$	34.1558	+	19.7199i	1.51841	+	0.876655i
$507$	−6.34974	+	15.4668i	−0.282002	+	0.686903i
$508$	−32.3404	+	32.3404i	−1.43487	+	1.43487i
$509$	−22.0946	+	38.2689i	−0.979325	+	1.69624i	−0.314470	+	0.949268i	$0.601827\pi$
$509$	−22.0946	+	38.2689i	−0.979325	+	1.69624i	−0.664855	+	0.746972i	$0.731507\pi$
$510$	3.42189	+	11.6856i	0.151524	+	0.517447i
$511$	−7.58633	−	13.1399i	−0.335599	−	0.581275i
$512$	−7.78019	+	7.78019i	−0.343839	+	0.343839i
$513$	−13.6718	−	10.2877i	−0.603623	−	0.454211i
$514$	−1.75304	+	1.01212i	−0.0773233	+	0.0446426i
$515$	−31.3339	+	13.7167i	−1.38074	+	0.604429i
$516$	−45.4087	−	5.83323i	−1.99900	−	0.256794i
$517$	30.7779	+	30.7779i	1.35361	+	1.35361i
$518$	−13.8310	−	68.7469i	−0.607701	−	3.02057i
$519$	6.75445	+	16.1630i	0.296488	+	0.709478i
$520$	1.38061	+	9.08402i	0.0605436	+	0.398361i
$521$	18.3700	−	10.6059i	0.804804	−	0.464654i	−0.0403444	−	0.999186i	$-0.512846\pi$
$521$	18.3700	−	10.6059i	0.804804	−	0.464654i	0.845148	+	0.534532i	$0.179512\pi$
$522$	−23.2348	−	39.6668i	−1.01696	−	1.73617i
$523$	−9.53115	−	2.55386i	−0.416768	−	0.111673i	0.0443404	−	0.999016i	$-0.485881\pi$
$523$	−9.53115	−	2.55386i	−0.416768	−	0.111673i	−0.461108	+	0.887344i	$0.652548\pi$
$524$	12.0850			0.527936
$525$	28.6665	+	34.2077i	1.25111	+	1.49295i
$526$	44.5300			1.94160
$527$	1.11711	+	4.16911i	0.0486621	+	0.181609i
$528$	−3.00594	+	7.32189i	−0.130817	+	0.318644i
$529$		−	8.59460i		−	0.373678i
$530$	−1.98444	−	13.0571i	−0.0861985	−	0.567163i
$531$	−1.23228	+	4.71719i	−0.0534765	+	0.204708i
$532$	36.0471	+	36.0471i	1.56284	+	1.56284i
$533$	−6.65725	+	1.78380i	−0.288357	+	0.0772652i
$534$	4.88455	−	38.0237i	0.211375	−	1.64545i
$535$	23.5525	+	17.3379i	1.01826	+	0.749584i
$536$	6.07432	−	3.50701i	0.262371	−	0.151480i
$537$	−1.01760	−	7.54634i	−0.0439127	−	0.325649i
$538$	−6.08566	−	22.7120i	−0.262371	−	0.979184i
$539$	45.4286	−	78.6847i	1.95675	−	3.38919i
$540$	−18.3314	−	29.7028i	−0.788857	−	1.27820i
$541$	40.1861			1.72773			0.863867	−	0.503720i	$-0.168036\pi$
$541$	40.1861			1.72773			0.863867	+	0.503720i	$0.168036\pi$
$542$	54.2887	+	14.5466i	2.33190	+	0.624831i
$543$	17.2372	−	13.3127i	0.739719	−	0.571304i
$544$		−	9.40613i		−	0.403285i
$545$	14.1702	+	17.7242i	0.606985	+	0.759221i
$546$	4.65452	−	36.2330i	0.199195	−	1.55063i
$547$	4.97802	+	4.97802i	0.212845	+	0.212845i	0.805475	−	0.592630i	$-0.201910\pi$
$547$	4.97802	+	4.97802i	0.212845	+	0.212845i	−0.592630	+	0.805475i	$0.701910\pi$
$548$	−0.321439	+	1.19963i	−0.0137312	+	0.0512455i
$549$	−6.30711	−	6.22842i	−0.269181	−	0.265822i
$550$	45.9951	+	24.1648i	1.96124	+	1.03039i
$551$	19.5343	−	11.2782i	0.832191	−	0.480465i
$552$	14.6330	−	1.97321i	0.622821	−	0.0839854i
$553$	0.111520	+	0.416197i	0.00474230	+	0.0176985i
$554$	32.1392			1.36546
$555$	−23.5394	−	0.946693i	−0.999192	−	0.0401849i
$556$	−60.3105			−2.55773
$557$	9.35959	+	34.9305i	0.396578	+	1.48005i	0.819075	+	0.573687i	$0.194487\pi$
$557$	9.35959	+	34.9305i	0.396578	+	1.48005i	−0.422496	+	0.906365i	$0.638846\pi$
$558$	−10.4167	−	17.7836i	−0.440975	−	0.752838i
$559$	−13.9406	+	8.04863i	−0.589626	+	0.340421i
$560$	−4.54601	−	10.3848i	−0.192104	−	0.438836i
$561$	−4.36009	−	10.4334i	−0.184083	−	0.440500i
$562$	4.46857	−	16.6769i	0.188495	−	0.703473i
$563$	−9.28169	−	9.28169i	−0.391177	−	0.391177i	0.483930	−	0.875107i	$-0.339209\pi$
$563$	−9.28169	−	9.28169i	−0.391177	−	0.391177i	−0.875107	+	0.483930i	$0.839209\pi$
$564$	48.3571	+	6.21200i	2.03620	+	0.261572i
$565$	41.6727	+	4.64358i	1.75318	+	0.195357i
$566$		−	38.0653i		−	1.60000i
$567$	12.5660	+	44.6473i	0.527724	+	1.87501i
$568$	22.0815	+	5.91672i	0.926519	+	0.248260i
$569$	31.1450			1.30567			0.652833	−	0.757502i	$-0.273580\pi$
$569$	31.1450			1.30567			0.652833	+	0.757502i	$0.273580\pi$
$570$	24.3707	−	14.8302i	1.02078	−	0.621168i
$571$	−0.745666	+	1.29153i	−0.0312052	+	0.0540489i	−0.881206	−	0.472732i	$-0.843268\pi$
$571$	−0.745666	+	1.29153i	−0.0312052	+	0.0540489i	0.850001	+	0.526781i	$0.176601\pi$
$572$	−6.60761	−	24.6599i	−0.276278	−	1.03108i
$573$	18.4048	−	2.48183i	0.768872	−	0.103680i
$574$	−37.6115	+	21.7150i	−1.56987	+	0.906367i
$575$	0.756150	+	18.9622i	0.0315336	+	0.790777i
$576$	10.3334	+	37.6185i	0.430557	+	1.56744i
$577$	−27.5159	+	7.37287i	−1.14550	+	0.306937i	−0.781162	−	0.624329i	$-0.785373\pi$
$577$	−27.5159	+	7.37287i	−1.14550	+	0.306937i	−0.364342	+	0.931265i	$0.618706\pi$
$578$	−23.7659	−	23.7659i	−0.988531	−	0.988531i
$579$	11.1563	+	8.50502i	0.463639	+	0.353456i
$580$	45.4919	−	6.91395i	1.88895	−	0.287086i
$581$			18.4983i			0.767440i
$582$	−14.7194	−	6.04292i	−0.610139	−	0.250487i
$583$	3.17442	+	11.8471i	0.131471	+	0.490656i
$584$	−6.61268			−0.273635
$585$	−11.4575	−	4.39781i	−0.473711	−	0.181827i
$586$	−34.5921			−1.42899
$587$	−11.3083	−	3.03004i	−0.466743	−	0.125063i	0.0177802	−	0.999842i	$-0.494340\pi$
$587$	−11.3083	−	3.03004i	−0.466743	−	0.125063i	−0.484523	+	0.874779i	$0.661007\pi$
$588$	−13.6003	−	100.857i	−0.560865	−	4.15928i
$589$	8.75770	−	5.05626i	0.360855	−	0.208340i
$590$	−6.54659	−	4.81920i	−0.269519	−	0.198403i
$591$	−40.8409	+	17.0672i	−1.67997	+	0.702052i
$592$	5.67042	+	1.91103i	0.233053	+	0.0785427i
$593$	9.58272	+	9.58272i	0.393515	+	0.393515i	0.875938	−	0.482423i	$-0.160243\pi$
$593$	9.58272	+	9.58272i	0.393515	+	0.393515i	−0.482423	+	0.875938i	$0.660243\pi$
$594$	33.2719	+	42.5257i	1.36516	+	1.74485i
$595$	15.0835	+	5.89846i	0.618361	+	0.241813i
$596$	−6.44160	+	3.71906i	−0.263858	+	0.152339i
$597$	13.0535	−	1.76023i	0.534246	−	0.0720413i
$598$	10.9834	−	10.9834i	0.449146	−	0.449146i
$599$	−1.62038	−	2.80658i	−0.0662069	−	0.114674i	0.831022	−	0.556240i	$-0.187756\pi$
$599$	−1.62038	−	2.80658i	−0.0662069	−	0.114674i	−0.897229	+	0.441566i	$0.854423\pi$
$600$	19.1582	−	3.36548i	0.782128	−	0.137395i
$601$	12.0905	−	20.9414i	0.493182	−	0.854217i	−0.506787	−	0.862071i	$-0.669167\pi$
$601$	12.0905	−	20.9414i	0.493182	−	0.854217i	0.999969	+	0.00785470i	$0.00250025\pi$
$602$	−71.7260	+	71.7260i	−2.92333	+	2.92333i
$603$	0.0588065	+	9.36823i	0.00239479	+	0.381504i
$604$	−41.1300	−	23.7464i	−1.67356	−	0.966229i
$605$	−22.0295	−	8.61474i	−0.895627	−	0.350239i
$606$	16.4442	+	39.3501i	0.668001	+	1.59849i
$607$	5.23979	−	1.40400i	0.212676	−	0.0569865i	−0.150908	−	0.988548i	$-0.548220\pi$
$607$	5.23979	−	1.40400i	0.212676	−	0.0569865i	0.363584	+	0.931561i	$0.381553\pi$
$608$	−21.2870	+	5.70384i	−0.863303	+	0.231321i
$609$	−60.6475	−	7.79082i	−2.45756	−	0.315700i
$610$	13.5391	−	5.92685i	0.548183	−	0.239971i
$611$	14.8458	−	8.57125i	0.600599	−	0.346756i
$612$	−11.0086	−	6.26402i	−0.444997	−	0.253208i
$613$	1.97778	+	7.38116i	0.0798816	+	0.298122i	0.994296	−	0.106658i	$-0.0340149\pi$
$613$	1.97778	+	7.38116i	0.0798816	+	0.298122i	−0.914414	+	0.404780i	$0.867348\pi$
$614$	−11.8839	+	20.5836i	−0.479597	+	0.830686i
$615$	4.10032	+	14.0024i	0.165341	+	0.564631i
$616$	−26.8850	−	46.5661i	−1.08323	−	1.87620i
$617$	−9.03792	−	33.7300i	−0.363853	−	1.35792i	−0.868969	−	0.494866i	$-0.835217\pi$
$617$	−9.03792	−	33.7300i	−0.363853	−	1.35792i	0.505116	−	0.863051i	$-0.331450\pi$
$618$	22.5090	−	54.8277i	0.905446	−	2.20549i
$619$		−	11.9809i		−	0.481553i	−0.970581	−	0.240777i	$-0.922598\pi$
$619$		−	11.9809i		−	0.481553i	0.970581	−	0.240777i	$-0.0774021\pi$
$620$	20.3951	−	3.09968i	0.819087	−	0.124486i
$621$	−7.37528	+	18.2907i	−0.295960	+	0.733982i
$622$	−11.6895	+	43.6257i	−0.468705	+	1.74923i
$623$	−36.0561	−	36.0561i	−1.44456	−	1.44456i
$624$	2.47899	+	1.88986i	0.0992389	+	0.0756550i
$625$	1.99067	+	24.9206i	0.0796270	+	0.996825i
$626$	35.9378	−	20.7487i	1.43636	−	0.829284i
$627$	−20.9680	+	16.1941i	−0.837380	+	0.646730i
$628$	−29.4321	+	29.4321i	−1.17447	+	1.17447i
$629$	−7.65898	+	3.79784i	−0.305383	+	0.151430i
$630$	−76.9113	−	8.08176i	−3.06422	−	0.321985i
$631$	−1.66068	+	2.87638i	−0.0661106	+	0.114507i	−0.897186	−	0.441653i	$-0.854392\pi$
$631$	−1.66068	+	2.87638i	−0.0661106	+	0.114507i	0.831076	+	0.556160i	$0.187726\pi$
$632$	0.181391	+	0.0486034i	0.00721533	+	0.00193334i
$633$	−1.41002	−	10.4565i	−0.0560433	−	0.415607i
$634$	−25.0536	+	14.4647i	−0.995007	+	0.574468i
$635$	33.8342	+	3.77014i	1.34267	+	0.149613i
$636$	10.9254	+	8.32900i	0.433220	+	0.330267i
$637$	−25.3025	−	25.3025i	−1.00252	−	1.00252i
$638$	−68.7565	+	18.4233i	−2.72210	+	0.729384i
$639$	−21.4548	+	21.7259i	−0.848740	+	0.859463i
$640$	−34.8996	−	3.88885i	−1.37953	−	0.153720i
$641$	12.5508	+	7.24618i	0.495725	+	0.286207i	0.726946	−	0.686694i	$-0.240939\pi$
$641$	12.5508	+	7.24618i	0.495725	+	0.286207i	−0.231221	+	0.972901i	$0.574272\pi$
$642$	−50.2215	+	6.77221i	−1.98208	+	0.267278i
$643$	−8.05928	+	8.05928i	−0.317827	+	0.317827i	−0.847932	−	0.530105i	$-0.822152\pi$
$643$	−8.05928	+	8.05928i	−0.317827	+	0.317827i	0.530105	+	0.847932i	$0.322152\pi$
$644$	29.3798	−	50.8873i	1.15773	−	2.00524i
$645$	17.7149	+	29.1112i	0.697525	+	1.14625i
$646$	5.17618	−	8.96541i	0.203654	−	0.352739i
$647$	−42.6638	−	11.4317i	−1.67729	−	0.449428i	−0.710227	−	0.703973i	$-0.751408\pi$
$647$	−42.6638	−	11.4317i	−1.67729	−	0.449428i	−0.967061	+	0.254545i	$0.918074\pi$
$648$	19.5899	+	4.98639i	0.769566	+	0.195884i
$649$	6.53788	+	3.77465i	0.256634	+	0.148168i
$650$	13.8812	−	15.0343i	0.544466	−	0.589693i
$651$	−27.1897	−	3.49281i	−1.06565	−	0.136894i
$652$	19.8382	+	19.8382i	0.776923	+	0.776923i
$653$	−1.00561	+	3.75299i	−0.0393526	+	0.146866i	−0.982807	−	0.184637i	$-0.940889\pi$
$653$	−1.00561	+	3.75299i	−0.0393526	+	0.146866i	0.943454	+	0.331503i	$0.107556\pi$
$654$	−38.9998	−	5.00994i	−1.52501	−	0.195904i
$655$	−5.61720	−	7.02604i	−0.219482	−	0.274530i
$656$		−	3.70593i		−	0.144692i
$657$	4.36807	−	7.67660i	0.170415	−	0.299493i
$658$	76.3833	−	76.3833i	2.97773	−	2.97773i
$659$	4.94454	+	8.56419i	0.192612	+	0.333613i	0.946115	−	0.323831i	$-0.104971\pi$
$659$	4.94454	+	8.56419i	0.192612	+	0.333613i	−0.753503	+	0.657444i	$0.771638\pi$
$660$	−51.8680	+	15.1885i	−2.01896	+	0.591212i
$661$	−1.47448	−	2.55387i	−0.0573505	−	0.0993340i	0.835925	−	0.548844i	$-0.184932\pi$
$661$	−1.47448	−	2.55387i	−0.0573505	−	0.0993340i	−0.893275	+	0.449510i	$0.851599\pi$
$662$	42.3461	+	11.3466i	1.64583	+	0.440999i
$663$	−4.41353	+	0.595150i	−0.171407	+	0.0231137i
$664$	6.98198	+	4.03105i	0.270953	+	0.156435i
$665$	4.20225	−	37.7122i	0.162956	−	1.46241i
$666$	30.4619	−	27.1740i	1.18038	−	1.05297i
$667$	−18.3843	−	18.3843i	−0.711842	−	0.711842i
$668$	6.66893	−	1.78694i	0.258029	−	0.0691386i
$669$	−24.9359	−	19.0100i	−0.964078	−	0.734967i
$670$	−14.5476	−	5.68890i	−0.562022	−	0.219781i
$671$	−11.8865	+	6.86269i	−0.458874	+	0.264931i
$672$	55.2646	+	22.6884i	2.13188	+	0.875224i
$673$	36.8157	+	9.86473i	1.41914	+	0.380258i	0.885179	−	0.465251i	$-0.154036\pi$
$673$	36.8157	+	9.86473i	1.41914	+	0.380258i	0.533962	+	0.845509i	$0.320703\pi$
$674$	8.78225			0.338280
$675$	−8.74815	+	24.4636i	−0.336717	+	0.941606i
$676$	28.9982			1.11531
$677$	19.7378	−	19.7378i	0.758584	−	0.758584i	−0.217481	−	0.976065i	$-0.569784\pi$
$677$	19.7378	−	19.7378i	0.758584	−	0.758584i	0.976065	+	0.217481i	$0.0697839\pi$
$678$	−57.5024	+	44.4106i	−2.20837	+	1.70558i
$679$	−18.3286	+	10.5820i	−0.703386	+	0.406100i
$680$	5.51320	−	4.40772i	0.211422	−	0.169028i
$681$	−0.452525	+	3.52267i	−0.0173408	+	0.134989i
$682$	−30.8252	+	8.25958i	−1.18036	+	0.316276i
$683$	32.2794	−	8.64924i	1.23514	−	0.330954i	0.418559	−	0.908189i	$-0.362535\pi$
$683$	32.2794	−	8.64924i	1.23514	−	0.330954i	0.816578	+	0.577236i	$0.195869\pi$
$684$	−7.50053	+	28.7121i	−0.286790	+	1.09783i
$685$	0.846851	−	0.370716i	0.0323565	−	0.0141643i
$686$	−125.389	−	72.3933i	−4.78737	−	2.76399i
$687$	10.8562	+	14.0565i	0.414190	+	0.536290i
$688$	−2.24024	−	8.36069i	−0.0854084	−	0.318748i
$689$	4.83045			0.184025
$690$	−23.7818	−	22.7092i	−0.905358	−	0.864526i
$691$	−8.66554	+	15.0092i	−0.329653	+	0.570975i	−0.982443	−	0.186563i	$-0.940265\pi$
$691$	−8.66554	+	15.0092i	−0.329653	+	0.570975i	0.652790	+	0.757539i	$0.273598\pi$
$692$	21.4836	−	21.4836i	0.816685	−	0.816685i
$693$	71.8174	−	0.450814i	2.72812	−	0.0171250i
$694$	55.0591	+	31.7884i	2.09002	+	1.20667i
$695$	28.0328	+	35.0636i	1.06334	+	1.33004i
$696$	−16.1565	+	21.1930i	−0.612411	+	0.803317i
$697$	3.74383	+	3.74383i	0.141808	+	0.141808i
$698$	−1.16002	+	4.32927i	−0.0439076	+	0.163865i
$699$	−8.86930	+	11.6341i	−0.335468	+	0.440043i
$700$	36.0022	−	68.5263i	1.36075	−	2.59005i
$701$	−9.58105	−	5.53162i	−0.361871	−	0.208926i	0.308030	−	0.951377i	$-0.400330\pi$
$701$	−9.58105	−	5.53162i	−0.361871	−	0.208926i	−0.669901	+	0.742450i	$0.733664\pi$
$702$	19.5691	−	8.32252i	0.738589	−	0.314113i
$703$	13.2393	+	15.0300i	0.499329	+	0.566869i
$704$	60.4068			2.27667
$705$	−18.8652	−	31.0015i	−0.710505	−	1.16758i
$706$	−21.1139	−	36.5703i	−0.794631	−	1.37634i
$707$	54.7931	+	14.6818i	2.06071	+	0.552165i
$708$	8.38018	−	1.13004i	0.314946	−	0.0424695i
$709$		−	33.1729i		−	1.24583i	−0.782288	−	0.622917i	$-0.785948\pi$
$709$		−	33.1729i		−	1.24583i	0.782288	−	0.622917i	$-0.214052\pi$
$710$	−20.4160	−	46.6378i	−0.766201	−	1.75028i
$711$	−0.176243	+	0.178469i	−0.00660962	+	0.00669312i
$712$	−21.4661	+	5.75182i	−0.804475	+	0.215559i
$713$	−8.24211	−	8.24211i	−0.308669	−	0.308669i
$714$	−25.8932	+	10.8207i	−0.969030	+	0.404953i
$715$	−11.2656	+	15.3037i	−0.421311	+	0.572325i
$716$	−11.4374	+	6.60340i	−0.427437	+	0.246781i
$717$	−2.93989	−	1.20695i	−0.109792	−	0.0450743i
$718$	6.42999	+	23.9970i	0.239965	+	0.895562i
$719$	9.27779	−	16.0696i	0.346003	−	0.599295i	−0.639532	−	0.768764i	$-0.720872\pi$
$719$	9.27779	−	16.0696i	0.346003	−	0.599295i	0.985535	+	0.169469i	$0.0542054\pi$
$720$	3.87869	−	5.33884i	0.144550	−	0.198967i
$721$	−39.4165	−	68.2713i	−1.46795	−	2.54256i
$722$	17.6259	+	4.72284i	0.655968	+	0.175766i
$723$	2.75548	−	2.12812i	0.102477	−	0.0791458i
$724$	−32.7136	−	18.8872i	−1.21579	−	0.701938i
$725$	−25.1647	−	23.2346i	−0.934592	−	0.862913i
$726$	37.8173	−	15.8037i	1.40353	−	0.586529i
$727$	10.7761	−	40.2171i	0.399665	−	1.49157i	−0.414023	−	0.910266i	$-0.635877\pi$
$727$	10.7761	−	40.2171i	0.399665	−	1.49157i	0.813688	−	0.581302i	$-0.197457\pi$
$728$	−20.4552	+	5.48094i	−0.758118	+	0.203137i
$729$	−18.7290	+	19.4480i	−0.693666	+	0.720296i
$730$	9.19599	+	11.5024i	0.340359	+	0.425723i
$731$	10.7093	+	6.18304i	0.396099	+	0.228688i
$732$	−5.83874	+	14.2220i	−0.215806	+	0.525662i
$733$	17.7977	+	4.76888i	0.657373	+	0.176143i	0.572060	−	0.820211i	$-0.306144\pi$
$733$	17.7977	+	4.76888i	0.657373	+	0.176143i	0.0853131	+	0.996354i	$0.472811\pi$
$734$	63.8376			2.35629
$735$	−52.3152	+	54.7861i	−1.92968	+	2.02082i
$736$	12.7009	+	21.9986i	0.468162	+	0.810880i
$737$	14.0119	+	3.75449i	0.516136	+	0.138298i
$738$	−21.9734	−	12.5031i	−0.808853	−	0.460246i
$739$			33.4071i			1.22890i	0.788955	+	0.614451i	$0.210622\pi$
$739$			33.4071i			1.22890i	−0.788955	+	0.614451i	$0.789378\pi$
$740$	13.9863	+	38.3914i	0.514147	+	1.41129i
$741$	4.02323	+	9.62736i	0.147797	+	0.353670i
$742$	29.4016	−	7.87813i	1.07937	−	0.289215i
$743$	12.4725	−	46.5479i	0.457571	−	1.70768i	−0.222847	−	0.974854i	$-0.571535\pi$
$743$	12.4725	−	46.5479i	0.457571	−	1.70768i	0.680418	−	0.732825i	$-0.261798\pi$
$744$	−7.24334	+	9.50130i	−0.265554	+	0.348335i
$745$	5.15631	+	2.01640i	0.188913	+	0.0738751i
$746$			51.1589i			1.87306i
$747$	−9.29163	+	5.44258i	−0.339963	+	0.199133i
$748$	−13.8680	+	13.8680i	−0.507063	+	0.507063i
$749$	−33.7022	+	58.3738i	−1.23145	+	2.13293i
$750$	−32.4965	−	28.6443i	−1.18661	−	1.04594i
$751$	29.7538			1.08573			0.542867	−	0.839819i	$-0.317339\pi$
$751$	29.7538			1.08573			0.542867	+	0.839819i	$0.317339\pi$
$752$	2.38570	+	8.90357i	0.0869977	+	0.324680i
$753$	−10.0576	+	1.35623i	−0.366518	+	0.0494238i
$754$			28.0343i			1.02095i
$755$	5.31174	+	34.9499i	0.193314	+	1.27196i
$756$	63.3572	−	49.5704i	2.30428	−	1.80286i
$757$	49.7827	−	13.3392i	1.80938	−	0.484823i	0.814006	−	0.580856i	$-0.197282\pi$
$757$	49.7827	−	13.3392i	1.80938	−	0.484823i	0.995378	+	0.0960332i	$0.0306155\pi$
$758$	−3.82999	+	14.2937i	−0.139111	+	0.519171i
$759$	24.2852	+	18.5139i	0.881498	+	0.672012i
$760$	−13.3183	−	9.80411i	−0.483105	−	0.355632i
$761$	−10.5346	−	6.08214i	−0.381878	−	0.220477i	0.296757	−	0.954953i	$-0.404095\pi$
$761$	−10.5346	−	6.08214i	−0.381878	−	0.220477i	−0.678635	+	0.734476i	$0.737428\pi$
$762$	−46.6864	+	36.0571i	−1.69127	+	1.30621i
$763$	−36.9816	+	36.9816i	−1.33882	+	1.33882i
$764$	−16.1051	−	27.8948i	−0.582662	−	1.00920i
$765$	1.47508	+	9.31180i	0.0533317	+	0.336669i
$766$	43.0351			1.55492
$767$	2.10238	−	2.10238i	0.0759125	−	0.0759125i
$768$	12.5044	−	9.65749i	0.451215	−	0.348485i
$769$		−	11.4788i		−	0.413936i	−0.978348	−	0.206968i	$-0.933640\pi$
$769$		−	11.4788i		−	0.413936i	0.978348	−	0.206968i	$-0.0663596\pi$
$770$	−43.6114	+	111.523i	−1.57165	+	4.01899i
$771$	−1.44613	+	0.604333i	−0.0520813	+	0.0217645i
$772$	6.29731	−	23.5019i	0.226645	−	0.845851i
$773$	12.6949	−	47.3779i	0.456603	−	1.70406i	−0.226730	−	0.973958i	$-0.572803\pi$
$773$	12.6949	−	47.3779i	0.456603	−	1.70406i	0.683333	−	0.730107i	$-0.260530\pi$
$774$	−57.1309	−	14.9244i	−2.05353	−	0.536448i
$775$	−11.2819	−	10.4166i	−0.405258	−	0.374177i
$776$			9.22387i			0.331118i
$777$	−3.83966	−	54.1602i	−0.137747	−	1.94298i
$778$	24.6479	−	24.6479i	0.883670	−	0.883670i
$779$	6.20241	−	10.7429i	0.222225	−	0.384904i
$780$	0.490937	+	21.2798i	0.0175784	+	0.761941i
$781$	23.6397	+	40.9452i	0.845895	+	1.46513i
$782$	−11.5260	−	3.08837i	−0.412167	−	0.110440i
$783$	−13.9304	−	32.7552i	−0.497832	−	1.17057i
$784$	16.6631	−	9.62045i	0.595111	−	0.343587i
$785$	30.7916	+	3.43110i	1.09900	+	0.122461i
$786$	15.4599	+	1.98599i	0.551435	+	0.0708379i
$787$	22.0720	+	22.0720i	0.786782	+	0.786782i	0.980965	−	0.194183i	$-0.0622055\pi$
$787$	22.0720	+	22.0720i	0.786782	+	0.786782i	−0.194183	+	0.980965i	$0.562206\pi$
$788$	54.2851	+	54.2851i	1.93383	+	1.93383i
$789$	34.1978	+	4.39308i	1.21747	+	0.156398i
$790$	−0.167709	−	0.383110i	−0.00596683	−	0.0136304i
$791$			96.6392i			3.43609i
$792$	15.4799	−	27.2049i	0.550053	−	0.966683i
$793$	1.39907	+	5.22141i	0.0496825	+	0.185418i
$794$	8.95410	−	15.5090i	0.317769	−	0.550392i
$795$	−0.235855	−	10.2232i	−0.00836492	−	0.362581i
$796$	−11.4225	−	19.7843i	−0.404858	−	0.701235i
$797$	4.74737	+	17.7174i	0.168160	+	0.627583i	0.997616	+	0.0690104i	$0.0219842\pi$
$797$	4.74737	+	17.7174i	0.168160	+	0.627583i	−0.829456	+	0.558573i	$0.811349\pi$
$798$	40.1898	+	52.0374i	1.42270	+	1.84210i
$799$	−11.4047	−	6.58452i	−0.403470	−	0.232944i
$800$	17.8732	+	28.2906i	0.631914	+	1.00022i
$801$	7.50240	−	28.7192i	0.265084	−	1.01474i
$802$	44.7359	−	11.9870i	1.57968	−	0.423274i
$803$	−9.67051	−	9.67051i	−0.341265	−	0.341265i
$804$	14.9921	−	6.26513i	0.528731	−	0.220954i
$805$	−43.2410	+	6.57185i	−1.52405	+	0.231627i
$806$			12.5684i			0.442704i
$807$	−2.43298	−	18.0425i	−0.0856449	−	0.635127i
$808$	17.4817	−	17.4817i	0.615003	−	0.615003i
$809$	−4.87626	−	8.44593i	−0.171440	−	0.296943i	0.767483	−	0.641069i	$-0.221509\pi$
$809$	−4.87626	−	8.44593i	−0.171440	−	0.296943i	−0.938924	+	0.344126i	$0.888175\pi$
$810$	−18.5694	−	41.0100i	−0.652462	−	1.44095i
$811$	−11.1202	−	19.2607i	−0.390482	−	0.676335i	0.602031	−	0.798473i	$-0.294358\pi$
$811$	−11.1202	−	19.2607i	−0.390482	−	0.676335i	−0.992513	+	0.122138i	$0.961025\pi$
$812$	27.4480	+	102.438i	0.963238	+	3.59485i
$813$	40.2571	+	16.5272i	1.41188	+	0.579634i
$814$	−28.0801	−	56.6282i	−0.984208	−	1.98482i
$815$	2.31267	−	20.7545i	0.0810093	−	0.727000i
$816$	0.305114	−	2.37515i	0.0106811	−	0.0831468i
$817$	7.49874	−	27.9857i	0.262348	−	0.979095i
$818$	−10.5646	+	39.4275i	−0.369381	+	1.37855i
$819$	7.14908	−	27.3667i	0.249809	−	0.956270i
$820$	19.7653	−	15.8020i	0.690234	−	0.551831i
$821$	4.58715	−	2.64839i	0.160093	−	0.0924296i	−0.417813	−	0.908533i	$-0.637203\pi$
$821$	4.58715	−	2.64839i	0.160093	−	0.0924296i	0.577906	+	0.816103i	$0.303870\pi$
$822$	−0.608344	+	1.48181i	−0.0212184	+	0.0516841i
$823$	−8.61210	−	32.1408i	−0.300199	−	1.12036i	−0.937000	−	0.349329i	$-0.886409\pi$
$823$	−8.61210	−	32.1408i	−0.300199	−	1.12036i	0.636801	−	0.771028i	$-0.280257\pi$
$824$	−34.3576			−1.19691
$825$	32.9390	+	23.0955i	1.14679	+	0.804083i
$826$	9.36774	−	16.2254i	0.325946	−	0.564554i
$827$	−36.9581	−	9.90290i	−1.28516	−	0.344357i	−0.449339	−	0.893361i	$-0.648341\pi$
$827$	−36.9581	−	9.90290i	−1.28516	−	0.344357i	−0.835820	+	0.549004i	$0.815007\pi$
$828$	34.2046	−	0.214710i	1.18869	−	0.00746169i
$829$	17.6908	+	10.2138i	0.614427	+	0.354740i	0.774696	−	0.632334i	$-0.217903\pi$
$829$	17.6908	+	10.2138i	0.614427	+	0.354740i	−0.160269	+	0.987073i	$0.551236\pi$
$830$	−2.69777	−	17.7506i	−0.0936409	−	0.616133i
$831$	24.6820	+	3.17066i	0.856207	+	0.109989i
$832$	6.15746	−	22.9800i	0.213472	−	0.796687i
$833$	−7.11467	+	26.5523i	−0.246509	+	0.919984i
$834$	−77.1528	−	9.91111i	−2.67158	−	0.343194i
$835$	−4.13867	−	3.04663i	−0.143224	−	0.105433i
$836$	39.7941	+	22.9751i	1.37631	+	0.794611i
$837$	−6.24532	−	14.6849i	−0.215870	−	0.507585i
$838$	−32.3512	−	8.66849i	−1.11755	−	0.299448i
$839$	−19.8997	+	34.4673i	−0.687014	+	1.18994i	0.285785	+	0.958294i	$0.407746\pi$
$839$	−19.8997	+	34.4673i	−0.687014	+	1.18994i	−0.972799	+	0.231650i	$0.925588\pi$
$840$	12.5987	+	43.0240i	0.434697	+	1.48447i
$841$	17.9243			0.618081
$842$	−4.87466	−	18.1925i	−0.167992	−	0.626955i
$843$	5.07698	−	12.3666i	0.174861	−	0.425927i
$844$	−15.8481	+	9.14990i	−0.545514	+	0.314952i
$845$	−13.4786	−	16.8591i	−0.463677	−	0.579970i
$846$	60.8405	+	15.8935i	2.09174	+	0.546430i
$847$	14.1099	−	52.6588i	0.484821	−	1.80938i
$848$	−0.672249	+	2.50887i	−0.0230851	+	0.0861548i
$849$	3.75530	−	29.2330i	0.128882	−	1.00328i
$850$	−15.3340	−	3.46029i	−0.525951	−	0.118687i
$851$	12.7843	−	19.2240i	0.438240	−	0.658990i
$852$	48.9902	+	20.1125i	1.67838	+	0.689043i
$853$	−11.7665	−	43.9131i	−0.402877	−	1.50356i	−0.807938	−	0.589268i	$-0.799416\pi$
$853$	−11.7665	−	43.9131i	−0.402877	−	1.50356i	0.405061	−	0.914290i	$-0.367250\pi$
$854$	17.0315	+	29.4995i	0.582806	+	1.00945i
$855$	20.1790	−	8.98489i	0.690109	−	0.307277i
$856$	14.6884	+	25.4410i	0.502038	+	0.869555i
$857$	−12.3601	+	12.3601i	−0.422213	+	0.422213i	−0.885965	−	0.463752i	$-0.846503\pi$
$857$	−12.3601	+	12.3601i	−0.422213	+	0.422213i	0.463752	+	0.885965i	$0.346503\pi$
$858$	−4.40036	−	32.6323i	−0.150226	−	1.11405i
$859$		−	15.8602i		−	0.541144i	−0.962700	−	0.270572i	$-0.912787\pi$
$859$		−	15.8602i		−	0.541144i	0.962700	−	0.270572i	$-0.0872127\pi$
$860$	35.0388	−	47.5980i	1.19481	−	1.62308i
$861$	−31.0269	+	12.9660i	−1.05739	+	0.441879i
$862$	18.3905	+	18.3905i	0.626383	+	0.626383i
$863$	−3.30345	+	0.885156i	−0.112451	+	0.0301310i	−0.314606	−	0.949223i	$-0.601872\pi$
$863$	−3.30345	+	0.885156i	−0.112451	+	0.0301310i	0.202155	+	0.979354i	$0.435206\pi$
$864$	4.86366	+	34.4346i	0.165465	+	1.17149i
$865$	−22.4760	−	2.50449i	−0.764207	−	0.0851553i
$866$	−31.3142	−	18.0793i	−1.06410	−	0.614359i
$867$	−15.9069	−	20.5961i	−0.540227	−	0.699481i
$868$	12.3056	+	45.9251i	0.417679	+	1.55880i
$869$	0.194190	+	0.336348i	0.00658746	+	0.0114098i
$870$	59.3322	−	1.36882i	2.01155	−	0.0464075i
$871$	2.85656	−	4.94771i	0.0967910	−	0.167647i
$872$	5.89947	+	22.0171i	0.199781	+	0.745594i
$873$	−10.7079	−	6.09292i	−0.362408	−	0.206214i
$874$			27.9572i			0.945665i
$875$	−56.5742	+	10.9204i	−1.91256	+	0.369178i
$876$	−15.1939	−	1.95183i	−0.513356	−	0.0659461i
$877$	35.4226	+	35.4226i	1.19614	+	1.19614i	0.975314	+	0.220824i	$0.0708746\pi$
$877$	35.4226	+	35.4226i	1.19614	+	1.19614i	0.220824	+	0.975314i	$0.429125\pi$
$878$	51.4461	+	51.4461i	1.73622	+	1.73622i
$879$	−26.5657	−	3.41266i	−0.896040	−	0.115106i
$880$	−6.38068	−	7.98100i	−0.215093	−	0.269040i
$881$	47.8677	−	27.6364i	1.61270	−	0.931095i	0.623964	−	0.781453i	$-0.285521\pi$
$881$	47.8677	−	27.6364i	1.61270	−	0.931095i	0.988740	−	0.149643i	$-0.0478123\pi$
$882$	−0.823933	−	131.257i	−0.0277433	−	4.41967i
$883$	41.7101	+	11.1762i	1.40366	+	0.376109i	0.879657	−	0.475608i	$-0.157772\pi$
$883$	41.7101	+	11.1762i	1.40366	+	0.376109i	0.524001	+	0.851718i	$0.324439\pi$
$884$	3.86205	+	6.68926i	0.129895	+	0.224984i
$885$	−4.55216	−	4.34685i	−0.153019	−	0.146118i
$886$	21.2282	−	36.7683i	0.713176	−	1.23526i
$887$	33.9438	−	33.9438i	1.13972	−	1.13972i	0.151220	−	0.988500i	$-0.451680\pi$
$887$	33.9438	−	33.9438i	1.13972	−	1.13972i	0.988500	−	0.151220i	$-0.0483203\pi$
$888$	−21.2788	−	10.3530i	−0.714071	−	0.347425i
$889$			78.4618i			2.63152i
$890$	39.8570	+	29.3403i	1.33601	+	0.983488i
$891$	21.3565	+	35.9409i	0.715471	+	1.20407i
$892$	−14.0754	+	52.5301i	−0.471279	+	1.75884i
$893$	−7.98565	+	29.8028i	−0.267230	+	0.997314i
$894$	−8.85165	+	3.69907i	−0.296044	+	0.123715i
$895$	9.15532	+	3.58023i	0.306029	+	0.119674i
$896$		−	80.9324i		−	2.70376i
$897$	9.51853	−	7.35140i	0.317814	−	0.245456i
$898$	−21.8295	+	21.8295i	−0.728459	+	0.728459i
$899$	21.0373			0.701633
$900$	45.0130	−	2.07805i	1.50043	−	0.0692684i
$901$	−1.85540	−	3.21365i	−0.0618123	−	0.107062i
$902$	−27.6808	+	27.6808i	−0.921668	+	0.921668i
$903$	−62.1596	+	48.0074i	−2.06854	+	1.59759i
$904$	36.4754	+	21.0591i	1.21315	+	0.700414i
$905$	4.22480	+	27.7981i	0.140437	+	0.924040i
$906$	−48.7136	−	37.1370i	−1.61840	−	1.23379i
$907$	−7.00192	+	26.1315i	−0.232495	+	0.867683i	0.746767	+	0.665086i	$0.231605\pi$
$907$	−7.00192	+	26.1315i	−0.232495	+	0.867683i	−0.979262	+	0.202597i	$0.935062\pi$
$908$	5.95002	−	1.59430i	0.197458	−	0.0529088i
$909$	8.74664	+	31.8420i	0.290108	+	1.05613i
$910$	37.9800	+	27.9585i	1.25902	+	0.926816i
$911$			57.9138i			1.91877i	0.282100	+	0.959385i	$0.408969\pi$
$911$			57.9138i			1.91877i	−0.282100	+	0.959385i	$0.591031\pi$
$912$	−5.56022	+	0.749778i	−0.184117	+	0.0248276i
$913$	4.31550	+	16.1057i	0.142822	+	0.533020i
$914$	−35.2319			−1.16537
$915$	10.9824	−	3.21596i	0.363066	−	0.106316i
$916$	15.4021	−	26.6772i	0.508899	−	0.881438i
$917$	14.6599	−	14.6599i	0.484112	−	0.484112i
$918$	−13.0535	−	9.82241i	−0.430829	−	0.324188i
$919$			30.8933i			1.01908i	0.860448	+	0.509538i	$0.170184\pi$
$919$			30.8933i			1.01908i	−0.860448	+	0.509538i	$0.829816\pi$
$920$	−6.94237	+	17.7529i	−0.228883	+	0.585297i
$921$	−11.1572	+	14.6352i	−0.367642	+	0.482246i
$922$	8.68096	−	32.3978i	0.285892	−	1.06696i
$923$	17.9860	−	4.81934i	0.592017	−	0.158631i
$924$	−48.0289	−	114.930i	−1.58003	−	3.78093i
$925$	15.8192	−	25.9760i	0.520132	−	0.854086i
$926$			24.6620i			0.810444i
$927$	22.6953	−	39.8855i	0.745411	−	1.31001i
$928$	−44.2838	−	11.8658i	−1.45369	−	0.389514i
$929$	−6.11253	−	10.5872i	−0.200546	−	0.347355i	0.748159	−	0.663520i	$-0.230938\pi$
$929$	−6.11253	−	10.5872i	−0.200546	−	0.347355i	−0.948704	+	0.316164i	$0.897605\pi$
$930$	26.6000	−	0.613676i	0.872249	−	0.0201232i
$931$	64.4049			2.11078
$932$	24.5085	+	6.56703i	0.802803	+	0.215110i
$933$	−13.2810	+	32.3501i	−0.434802	+	1.05909i
$934$	−61.2487	−	35.3619i	−2.00412	−	1.15708i
$935$	14.5086	+	1.61668i	0.474480	+	0.0528712i
$936$	−8.77137	−	8.66193i	−0.286701	−	0.283124i
$937$	−8.23539	+	2.20667i	−0.269038	+	0.0720886i	−0.390816	−	0.920469i	$-0.627807\pi$
$937$	−8.23539	+	2.20667i	−0.269038	+	0.0720886i	0.121778	+	0.992557i	$0.461140\pi$
$938$	9.31771	−	34.7742i	0.304234	−	1.13542i
$939$	29.6461	−	12.3890i	0.967465	−	0.404299i
$940$	−37.3139	+	50.6887i	−1.21705	+	1.65328i
$941$	−32.3751	−	18.6918i	−1.05540	−	0.609335i	−0.131243	−	0.991350i	$-0.541897\pi$
$941$	−32.3751	−	18.6918i	−1.05540	−	0.609335i	−0.924156	+	0.382016i	$0.875230\pi$
$942$	−42.4880	+	32.8146i	−1.38433	+	1.06916i
$943$	−13.8111	−	3.70067i	−0.449751	−	0.120511i
$944$	0.799359	+	1.38453i	0.0260169	+	0.0450626i
$945$	−58.2684	−	13.7942i	−1.89547	−	0.448725i
$946$	−45.7156	+	79.1817i	−1.48634	+	2.57442i
$947$	−4.80911	−	17.9478i	−0.156275	−	0.583226i	−0.998993	−	0.0448708i	$-0.985712\pi$
$947$	−4.80911	−	17.9478i	−0.156275	−	0.583226i	0.842718	−	0.538356i	$-0.180954\pi$
$948$	0.402435	+	0.165216i	0.0130705	+	0.00536597i
$949$	−4.66460	+	2.69311i	−0.151419	+	0.0874220i
$950$	1.46749	+	36.8006i	0.0476117	+	1.19397i
$951$	−20.6675	+	8.63685i	−0.670189	+	0.280069i
$952$	11.5033	+	11.5033i	0.372825	+	0.372825i
$953$	17.2064	−	4.61043i	0.557369	−	0.149347i	0.0308718	−	0.999523i	$-0.490172\pi$
$953$	17.2064	−	4.61043i	0.557369	−	0.149347i	0.526497	+	0.850177i	$0.323505\pi$
$954$	12.6077	+	12.4504i	0.408189	+	0.403096i
$955$	−8.73185	+	22.3290i	−0.282556	+	0.722548i
$956$			5.51192i			0.178268i
$957$	−54.6206	+	7.36541i	−1.76563	+	0.238090i
$958$	11.4179	+	3.05941i	0.368895	+	0.0988451i
$959$	1.06530	+	1.84515i	0.0344002	+	0.0595829i
$960$	−48.9358	−	11.9097i	−1.57940	−	0.384384i
$961$	−21.5685			−0.695758
$962$	−24.4048	+	4.90995i	−0.786843	+	0.158303i
$963$	−39.2368	+	0.246298i	−1.26439	+	0.00793685i
$964$	−5.22948	−	3.01924i	−0.168430	−	0.0972432i
$965$	−16.5907	+	7.26269i	−0.534072	+	0.233794i
$966$	45.9470	−	60.2700i	1.47832	−	1.93915i
$967$	1.30537	−	4.87171i	0.0419779	−	0.156664i	−0.941755	−	0.336298i	$-0.890825\pi$
$967$	1.30537	−	4.87171i	0.0419779	−	0.156664i	0.983733	+	0.179635i	$0.0574916\pi$
$968$	−16.8007	−	16.8007i	−0.539995	−	0.539995i
$969$	4.85963	−	6.37452i	0.156114	−	0.204779i
$970$	16.0444	−	12.8273i	0.515156	−	0.411859i
$971$	−35.9579	−	20.7603i	−1.15394	−	0.666229i	−0.204098	−	0.978950i	$-0.565426\pi$
$971$	−35.9579	−	20.7603i	−1.15394	−	0.666229i	−0.949845	+	0.312721i	$0.898759\pi$
$972$	43.5400	+	17.2395i	1.39655	+	0.552956i
$973$	−73.1603	+	73.1603i	−2.34541	+	2.34541i
$974$	−38.0286	+	65.8675i	−1.21852	+	2.11053i
$975$	12.1436	−	10.1765i	0.388906	−	0.325907i
$976$	−2.90663			−0.0930391
$977$	15.4097	+	57.5097i	0.492999	+	1.83990i	0.540960	+	0.841048i	$0.318061\pi$
$977$	15.4097	+	57.5097i	0.492999	+	1.83990i	−0.0479614	+	0.998849i	$0.515272\pi$
$978$	22.1181	+	28.6383i	0.707258	+	0.915752i
$979$	−39.8040	−	22.9808i	−1.27214	−	0.734471i
$980$	122.361	+	47.8499i	3.90868	+	1.52851i
$981$	−29.4564	−	7.69498i	−0.940472	−	0.245682i
$982$	−45.0284	+	12.0653i	−1.43691	+	0.385020i
$983$	13.6544	−	3.65868i	0.435508	−	0.116694i	−0.0344028	−	0.999408i	$-0.510953\pi$
$983$	13.6544	−	3.65868i	0.435508	−	0.116694i	0.469910	+	0.882714i	$0.344286\pi$
$984$	−1.86733	+	14.5362i	−0.0595284	+	0.463397i
$985$	6.32838	−	56.7926i	0.201639	−	1.80956i
$986$	18.6509	−	10.7681i	0.593966	−	0.342926i
$987$	66.1957	−	51.1247i	2.10703	−	1.62732i
$988$	12.7965	−	12.7965i	0.407112	−	0.407112i
$989$	−33.3953			−1.06191
$990$	−68.8487	+	10.9063i	−2.18815	+	0.346626i
$991$	45.4771			1.44463			0.722314	−	0.691565i	$-0.243079\pi$
$991$	45.4771			1.44463			0.722314	+	0.691565i	$0.243079\pi$
$992$	−19.8535	−	5.31972i	−0.630348	−	0.168901i
$993$	31.4012	+	12.8915i	0.996488	+	0.409099i
$994$	101.616	−	58.6679i	3.22306	−	1.86083i
$995$	−6.19302	+	15.8367i	−0.196332	+	0.502058i
$996$	14.8527	+	11.3230i	0.470625	+	0.358782i
$997$	32.1629	−	8.61802i	1.01861	−	0.272936i	0.289387	−	0.957212i	$-0.406549\pi$
$997$	32.1629	−	8.61802i	1.01861	−	0.272936i	0.729222	+	0.684277i	$0.239882\pi$
$998$	−24.3249	−	24.3249i	−0.769991	−	0.769991i
$999$	26.0747	−	17.8636i	0.824967	−	0.565181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.bi.a.47.10	✓	288
3.2	odd	2	inner	555.2.bi.a.47.63	yes	288
5.3	odd	4	inner	555.2.bi.a.158.10	yes	288
15.8	even	4	inner	555.2.bi.a.158.63	yes	288
37.26	even	3	inner	555.2.bi.a.137.63	yes	288
111.26	odd	6	inner	555.2.bi.a.137.10	yes	288
185.63	odd	12	inner	555.2.bi.a.248.63	yes	288
555.248	even	12	inner	555.2.bi.a.248.10	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.bi.a.47.10	✓	288	1.1	even	1	trivial
555.2.bi.a.47.63	yes	288	3.2	odd	2	inner
555.2.bi.a.137.10	yes	288	111.26	odd	6	inner
555.2.bi.a.137.63	yes	288	37.26	even	3	inner
555.2.bi.a.158.10	yes	288	5.3	odd	4	inner
555.2.bi.a.158.63	yes	288	15.8	even	4	inner
555.2.bi.a.248.10	yes	288	555.248	even	12	inner
555.2.bi.a.248.63	yes	288	185.63	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:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.bi (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.578972 - 2.16075i) q^{2} +(-0.231467 - 1.71651i) q^{3} +(-2.60160 + 1.50203i) q^{4} +(2.08250 + 0.814371i) q^{5} +(-3.57495 + 1.49396i) q^{6} +(-1.33384 + 4.97795i) q^{7} +(1.58821 + 1.58821i) q^{8} +(-2.89285 + 0.794631i) q^{9} +O(q^{10})\)	\(q+(-0.578972 - 2.16075i) q^{2} +(-0.231467 - 1.71651i) q^{3} +(-2.60160 + 1.50203i) q^{4} +(2.08250 + 0.814371i) q^{5} +(-3.57495 + 1.49396i) q^{6} +(-1.33384 + 4.97795i) q^{7} +(1.58821 + 1.58821i) q^{8} +(-2.89285 + 0.794631i) q^{9} +(0.553946 - 4.97126i) q^{10} +4.64526i q^{11} +(3.18044 + 4.11801i) q^{12} +(1.76715 + 0.473506i) q^{13} +11.5284 q^{14} +(0.915851 - 3.76314i) q^{15} +(-0.491864 + 0.851934i) q^{16} +(-0.363752 - 1.35754i) q^{17} +(3.39188 + 5.79066i) q^{18} +(-2.85167 + 1.64641i) q^{19} +(-6.64103 + 1.00932i) q^{20} +(8.85347 + 1.13732i) q^{21} +(10.0373 - 2.68947i) q^{22} +(2.68378 + 2.68378i) q^{23} +(2.35857 - 3.09380i) q^{24} +(3.67360 + 3.39185i) q^{25} -4.09252i q^{26} +(2.03359 + 4.78168i) q^{27} +(-4.00694 - 14.9541i) q^{28} -6.85013 q^{29} +(-8.66147 + 0.199824i) q^{30} -3.07108 q^{31} +(6.46466 + 1.73220i) q^{32} +(7.97365 - 1.07522i) q^{33} +(-2.72271 + 1.57196i) q^{34} +(-6.83162 + 9.28034i) q^{35} +(6.33245 - 6.41246i) q^{36} +(-1.19974 - 5.96327i) q^{37} +(5.20853 + 5.20853i) q^{38} +(0.403744 - 3.14294i) q^{39} +(2.01405 + 4.60083i) q^{40} +(-3.26251 + 1.88361i) q^{41} +(-2.66844 - 19.7886i) q^{42} +(-6.22168 + 6.22168i) q^{43} +(-6.97732 - 12.0851i) q^{44} +(-6.67147 - 0.701031i) q^{45} +(4.24516 - 7.35283i) q^{46} +(6.62567 - 6.62567i) q^{47} +(1.57621 + 0.647098i) q^{48} +(-16.9387 - 9.77957i) q^{49} +(5.20204 - 9.90153i) q^{50} +(-2.24604 + 0.938611i) q^{51} +(-5.30863 + 1.42244i) q^{52} +(2.55036 - 0.683368i) q^{53} +(9.15464 - 7.16256i) q^{54} +(-3.78296 + 9.67374i) q^{55} +(-10.0244 + 5.78762i) q^{56} +(3.48616 + 4.51385i) q^{57} +(3.96604 + 14.8015i) q^{58} +(0.812581 - 1.40743i) q^{59} +(3.26968 + 11.1658i) q^{60} +(1.47736 + 2.55885i) q^{61} +(1.77807 + 6.63584i) q^{62} +(-0.0970482 - 15.4604i) q^{63} -13.0040i q^{64} +(3.29447 + 2.42519i) q^{65} +(-6.93981 - 16.6066i) q^{66} +(0.808241 - 3.01640i) q^{67} +(2.98540 + 2.98540i) q^{68} +(3.98555 - 5.22796i) q^{69} +(24.0078 + 9.38838i) q^{70} +(8.81440 - 5.08900i) q^{71} +(-5.85649 - 3.33240i) q^{72} +(-2.08180 + 2.08180i) q^{73} +(-12.1905 + 6.04490i) q^{74} +(4.97185 - 7.09089i) q^{75} +(4.94593 - 8.56660i) q^{76} +(-23.1239 - 6.19602i) q^{77} +(-7.02487 + 0.947281i) q^{78} +(0.0724067 - 0.0418040i) q^{79} +(-1.71810 + 1.37359i) q^{80} +(7.73712 - 4.59749i) q^{81} +(5.95893 + 5.95893i) q^{82} +(3.46712 - 0.929013i) q^{83} +(-24.7414 + 10.3393i) q^{84} +(0.348029 - 3.12330i) q^{85} +(17.0457 + 9.84134i) q^{86} +(1.58558 + 11.7584i) q^{87} +(-7.37764 + 7.37764i) q^{88} +(-4.94716 + 8.56874i) q^{89} +(2.34784 + 14.8213i) q^{90} +(-4.71418 + 8.16520i) q^{91} +(-11.0133 - 2.95099i) q^{92} +(0.710851 + 5.27155i) q^{93} +(-18.1525 - 10.4804i) q^{94} +(-7.27939 + 1.10634i) q^{95} +(1.47700 - 11.4976i) q^{96} +(2.90386 + 2.90386i) q^{97} +(-11.3242 + 42.2625i) q^{98} +(-3.69127 - 13.4380i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 16 q^{6} - 4 q^{7}+O(q^{10}) \) 288 * q - 16 * q^6 - 4 * q^7	\( 288 q - 16 q^{6} - 4 q^{7} - 16 q^{10} - 18 q^{12} - 20 q^{13} + 6 q^{15} + 112 q^{16} + 20 q^{18} - 4 q^{21} - 12 q^{22} - 36 q^{25} + 48 q^{27} - 28 q^{28} - 16 q^{30} - 80 q^{31} + 2 q^{33} - 16 q^{36} - 36 q^{37} + 8 q^{40} - 32 q^{42} - 16 q^{43} + 76 q^{45} - 24 q^{46} + 112 q^{48} + 48 q^{55} + 2 q^{57} - 60 q^{58} - 56 q^{60} + 16 q^{61} - 36 q^{63} - 36 q^{70} - 58 q^{72} - 48 q^{73} - 88 q^{75} + 16 q^{76} + 20 q^{78} - 56 q^{81} - 136 q^{82} + 144 q^{85} + 16 q^{87} + 144 q^{88} - 42 q^{90} - 22 q^{93} - 80 q^{96} + 56 q^{97}+O(q^{100}) \) 288 * q - 16 * q^6 - 4 * q^7 - 16 * q^10 - 18 * q^12 - 20 * q^13 + 6 * q^15 + 112 * q^16 + 20 * q^18 - 4 * q^21 - 12 * q^22 - 36 * q^25 + 48 * q^27 - 28 * q^28 - 16 * q^30 - 80 * q^31 + 2 * q^33 - 16 * q^36 - 36 * q^37 + 8 * q^40 - 32 * q^42 - 16 * q^43 + 76 * q^45 - 24 * q^46 + 112 * q^48 + 48 * q^55 + 2 * q^57 - 60 * q^58 - 56 * q^60 + 16 * q^61 - 36 * q^63 - 36 * q^70 - 58 * q^72 - 48 * q^73 - 88 * q^75 + 16 * q^76 + 20 * q^78 - 56 * q^81 - 136 * q^82 + 144 * q^85 + 16 * q^87 + 144 * q^88 - 42 * q^90 - 22 * q^93 - 80 * q^96 + 56 * q^97

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