LMFDB - Embedded newform 555.2.bi.a.248.10

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			248.10
Character	$\chi$	$=$	555.248
Dual form			555.2.bi.a.47.10

$q$-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 $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

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

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	0.386408	+	0.922328i	$0.373716\pi$
$2$	−0.578972	+	2.16075i	−0.409395	+	1.52788i	−0.795803	+	0.605555i	$0.792951\pi$
$3$	−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	−0.471188	−	0.882033i	$-0.656175\pi$
$7$	−1.33384	−	4.97795i	−0.504144	−	1.88149i	−0.0329552	−	0.999457i	$-0.510492\pi$
$8$	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	$-0.753050\pi$
$11$		−	4.64526i		−	1.40060i	0.713850	−	0.700299i	$-0.246950\pi$
$12$	3.18044	−	4.11801i	0.918115	−	1.18877i
$13$	1.76715	−	0.473506i	0.490119	−	0.131327i	−0.00529159	−	0.999986i	$-0.501684\pi$
$13$	1.76715	−	0.473506i	0.490119	−	0.131327i	0.495410	+	0.868659i	$0.335018\pi$
$14$	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	−0.995905	−	0.0904064i	$-0.971183\pi$
$17$	−0.363752	+	1.35754i	−0.0882228	+	0.329252i	0.907682	+	0.419658i	$0.137850\pi$
$18$	3.39188	−	5.79066i	0.799474	−	1.36487i
$19$	−2.85167	−	1.64641i	−0.654218	−	0.377713i	0.135852	−	0.990729i	$-0.456623\pi$
$19$	−2.85167	−	1.64641i	−0.654218	−	0.377713i	−0.790071	+	0.613016i	$0.789956\pi$
$20$	−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	−0.369588	−	0.929196i	$-0.620501\pi$
$23$	2.68378	−	2.68378i	0.559608	−	0.559608i	0.929196	+	0.369588i	$0.120501\pi$
$24$	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	0.223117	−	0.974792i	$-0.428377\pi$
$41$	−3.26251	−	1.88361i	−0.509519	−	0.294171i	−0.732636	+	0.680621i	$0.761710\pi$
$42$	−2.66844	+	19.7886i	−0.411748	+	3.05345i
$43$	−6.22168	−	6.22168i	−0.948798	−	0.948798i	0.0499535	−	0.998752i	$-0.484093\pi$
$43$	−6.22168	−	6.22168i	−0.948798	−	0.948798i	−0.998752	+	0.0499535i	$0.984093\pi$
$44$	−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	0.999455	−	0.0330015i	$-0.0105066\pi$
$47$	6.62567	+	6.62567i	0.966454	+	0.966454i	−0.0330015	+	0.999455i	$0.510507\pi$
$48$	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	0.429688	−	0.902978i	$-0.358624\pi$
$53$	2.55036	+	0.683368i	0.350319	+	0.0938678i	−0.0793683	+	0.996845i	$0.525290\pi$
$54$	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	0.914060	−	0.405578i	$-0.132930\pi$
$59$	0.812581	+	1.40743i	0.105789	+	0.183232i	−0.808271	+	0.588810i	$0.799597\pi$
$60$	3.26968	−	11.1658i	0.422114	−	1.44150i
$61$	1.47736	−	2.55885i	0.189156	−	0.327628i	−0.755813	−	0.654787i	$-0.772758\pi$
$61$	1.47736	−	2.55885i	0.189156	−	0.327628i	0.944969	+	0.327160i	$0.106092\pi$
$62$	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	0.997560	−	0.0698107i	$-0.0222395\pi$
$67$	0.808241	+	3.01640i	0.0987424	+	0.368512i	−0.898818	+	0.438322i	$0.855573\pi$
$68$	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	0.921549	−	0.388263i	$-0.126925\pi$
$71$	8.81440	+	5.08900i	1.04608	+	0.603953i	0.124529	+	0.992216i	$0.460258\pi$
$72$	−5.85649	+	3.33240i	−0.690193	+	0.392728i
$73$	−2.08180	−	2.08180i	−0.243657	−	0.243657i	0.574704	−	0.818361i	$-0.305117\pi$
$73$	−2.08180	−	2.08180i	−0.243657	−	0.243657i	−0.818361	+	0.574704i	$0.805117\pi$
$74$	−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	0.504068	−	0.863664i	$-0.331836\pi$
$79$	0.0724067	+	0.0418040i	0.00814639	+	0.00470332i	−0.495921	+	0.868367i	$0.665170\pi$
$80$	−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	0.444030	−	0.896012i	$-0.353548\pi$
$83$	3.46712	+	0.929013i	0.380566	+	0.101972i	−0.0634642	+	0.997984i	$0.520215\pi$
$84$	−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	−0.999596	−	0.0284058i	$-0.990957\pi$
$89$	−4.94716	−	8.56874i	−0.524398	−	0.908285i	0.475198	−	0.879879i	$-0.342376\pi$
$90$	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	−0.544147	−	0.838990i	$-0.683147\pi$
$97$	2.90386	−	2.90386i	0.294842	−	0.294842i	0.838990	+	0.544147i	$0.183147\pi$
$98$	−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	$0.184469\pi$
$101$			11.0072i			1.09525i	−0.836723	+	0.547627i	$0.815531\pi$
$102$	3.32850	−	4.30971i	0.329571	−	0.426725i
$103$	−10.8165	−	10.8165i	−1.06578	−	1.06578i	−0.997678	−	0.0681002i	$-0.978306\pi$
$103$	−10.8165	−	10.8165i	−1.06578	−	1.06578i	−0.0681002	−	0.997678i	$-0.521694\pi$
$104$	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	0.410131	−	0.912027i	$-0.365483\pi$
$107$	12.6335	−	3.38514i	1.22133	−	0.327254i	0.811197	+	0.584772i	$0.198816\pi$
$108$	−12.4728	+	9.38548i	−1.20020	+	0.903119i
$109$	8.78870	−	5.07416i	0.841805	−	0.486016i	−0.0160725	−	0.999871i	$-0.505116\pi$
$109$	8.78870	−	5.07416i	0.841805	−	0.486016i	0.857877	+	0.513855i	$0.171783\pi$
$110$	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	0.973923	−	0.226878i	$-0.0728517\pi$
$113$	18.1130	+	4.85336i	1.70393	+	0.456566i	0.730003	+	0.683443i	$0.239518\pi$
$114$	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	0.843319	−	0.537414i	$-0.180599\pi$
$127$	14.7060	+	3.94046i	1.30495	+	0.349660i	0.461628	+	0.887073i	$0.347265\pi$
$128$	−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	−0.644414	−	0.764677i	$-0.722899\pi$
$131$	−3.48392	+	2.01144i	−0.304392	+	0.175741i	0.340022	+	0.940417i	$0.389565\pi$
$132$	−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	0.719484	−	0.694509i	$-0.244378\pi$
$137$	0.292333	+	0.292333i	0.0249757	+	0.0249757i	−0.694509	+	0.719484i	$0.744378\pi$
$138$	−13.6039	+	5.58495i	−1.15804	+	0.475422i
$139$	17.3866	−	10.0381i	1.47471	−	0.851425i	0.475117	−	0.879923i	$-0.342406\pi$
$139$	17.3866	−	10.0381i	1.47471	−	0.851425i	0.999594	+	0.0284980i	$0.00907243\pi$
$140$	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	−0.341414	−	0.939913i	$-0.610906\pi$
$151$	7.90477	−	13.6915i	0.643281	−	1.11420i	0.984696	−	0.174283i	$-0.0557607\pi$
$152$	−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	0.749721	−	0.661754i	$-0.230188\pi$
$157$	13.3835	+	3.58611i	1.06812	+	0.286202i	0.318401	+	0.947956i	$0.396854\pi$
$158$	−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	0.804337	+	0.594173i	$0.202521\pi$
$163$	−2.41715	+	9.02093i	−0.189326	+	0.706574i	−0.993663	+	0.112401i	$0.964146\pi$
$164$	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	−0.343687	−	0.939084i	$-0.611676\pi$
$167$	−2.21997	+	0.594840i	−0.171787	+	0.0460301i	0.171900	+	0.985114i	$0.445009\pi$
$168$	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	−0.132442	−	0.991191i	$-0.542282\pi$
$173$	−9.76916	−	2.61764i	−0.742736	−	0.199015i	−0.610294	+	0.792175i	$0.708949\pi$
$174$	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	−0.531978	−	0.846758i	$-0.678551\pi$
$181$	6.28722	−	10.8898i	0.467325	−	0.809431i	0.999303	+	0.0373271i	$0.0118843\pi$
$182$	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	$-0.873195\pi$
$191$		−	10.7222i		−	0.775831i	0.921695	−	0.387916i	$-0.126805\pi$
$192$	−22.3215	−	3.00999i	−1.61092	−	0.217227i
$193$	−5.72710	−	5.72710i	−0.412246	−	0.412246i	0.470275	−	0.882520i	$-0.344155\pi$
$193$	−5.72710	−	5.72710i	−0.412246	−	0.412246i	−0.882520	+	0.470275i	$0.844155\pi$
$194$	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	0.164047	+	0.986453i	$0.447545\pi$
$197$	−6.61428	+	24.6848i	−0.471248	+	1.75872i	−0.635295	+	0.772270i	$0.719121\pi$
$198$	−26.8991	−	15.7562i	−1.91164	−	1.11974i
$199$		−	7.60467i		−	0.539081i	−0.962989	−	0.269540i	$-0.913128\pi$
$199$		−	7.60467i		−	0.539081i	0.962989	−	0.269540i	$-0.0868718\pi$
$200$	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	0.991009	−	0.133797i	$-0.0427170\pi$
$223$	12.8009	+	12.8009i	0.857212	+	0.857212i	−0.133797	+	0.991009i	$0.542717\pi$
$224$	−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	−0.323950	−	0.946074i	$-0.605011\pi$
$227$	−1.98066	+	0.530716i	−0.131461	+	0.0352248i	0.192489	+	0.981299i	$0.438344\pi$
$228$	−15.8495	+	6.50688i	−1.04966	+	0.430929i
$229$	−8.88036	−	5.12708i	−0.586830	−	0.338807i	0.177013	−	0.984209i	$-0.443357\pi$
$229$	−8.88036	−	5.12708i	−0.586830	−	0.338807i	−0.763843	+	0.645402i	$0.776690\pi$
$230$	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	−0.875138	−	0.483873i	$-0.839230\pi$
$233$	−5.97240	+	5.97240i	−0.391265	+	0.391265i	0.483873	+	0.875138i	$0.339230\pi$
$234$	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	0.894170	−	0.447727i	$-0.147766\pi$
$239$	0.917410	+	1.58900i	0.0593423	+	0.102784i	−0.834828	+	0.550511i	$0.814433\pi$
$240$	2.75547	−	2.63120i	0.177865	−	0.169843i
$241$	1.00505	−	1.74080i	0.0647411	−	0.112135i	−0.831838	−	0.555018i	$-0.812711\pi$
$241$	1.00505	−	1.74080i	0.0647411	−	0.112135i	0.896579	+	0.442884i	$0.146045\pi$
$242$	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	$0.0592019\pi$
$251$			5.85930i			0.369836i	−0.982754	+	0.184918i	$0.940798\pi$
$252$	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	−0.972846	−	0.231455i	$-0.925652\pi$
$257$	−0.234205	+	0.874065i	−0.0146093	+	0.0545227i	0.958236	+	0.285977i	$0.0923182\pi$
$258$	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	−0.921455	−	0.388486i	$-0.872998\pi$
$263$	−5.15214	−	19.2280i	−0.317695	−	1.18565i	0.603760	−	0.797166i	$-0.293669\pi$
$264$	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	−0.941238	−	0.337745i	$-0.890336\pi$
$271$	−12.5624	−	21.7588i	−0.763114	−	1.32175i	0.178123	−	0.984008i	$-0.442997\pi$
$272$	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	−0.983030	−	0.183446i	$-0.941275\pi$
$277$	−3.71851	−	13.8777i	−0.223424	−	0.833829i	0.759606	−	0.650383i	$-0.225392\pi$
$278$	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	−0.287201	−	0.957870i	$-0.592725\pi$
$281$	6.68407	−	3.85905i	0.398738	−	0.230212i	0.685940	+	0.727659i	$0.259391\pi$
$282$	−13.7880	−	33.5849i	−0.821063	−	1.99995i
$283$	16.4366	−	4.40417i	0.977053	−	0.261801i	0.265250	−	0.964180i	$-0.414546\pi$
$283$	16.4366	−	4.40417i	0.977053	−	0.261801i	0.711803	+	0.702379i	$0.247879\pi$
$284$	−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	0.978678	+	0.205400i	$0.0658495\pi$
$293$	4.00232	+	14.9369i	0.233818	+	0.872621i	−0.744860	+	0.667221i	$0.767484\pi$
$294$	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	−0.888216	−	0.459426i	$-0.848055\pi$
$307$	−7.51301	+	7.51301i	−0.428790	+	0.428790i	0.459426	+	0.888216i	$0.348055\pi$
$308$	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	−0.905719	−	0.423879i	$-0.860668\pi$
$311$	−17.4851	+	10.0950i	−0.991488	+	0.572436i	−0.0857694	+	0.996315i	$0.527335\pi$
$312$	5.63287	+	4.35041i	0.318899	+	0.246294i
$313$	4.80126	−	17.9185i	0.271383	−	1.01282i	−0.686843	−	0.726806i	$-0.741004\pi$
$313$	4.80126	−	17.9185i	0.271383	−	1.01282i	0.958226	−	0.286011i	$-0.0923292\pi$
$314$	−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	0.805975	+	0.591950i	$0.201642\pi$
$317$	−3.34715	+	12.4917i	−0.187995	+	0.701606i	−0.993970	+	0.109656i	$0.965025\pi$
$318$	−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	−0.998980	−	0.0451577i	$-0.985621\pi$
$331$	−9.79893	−	16.9722i	−0.538598	−	0.932879i	0.460382	−	0.887721i	$-0.347712\pi$
$332$	−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	0.932712	−	0.360622i	$-0.117435\pi$
$337$	−1.01611	−	3.79217i	−0.0553510	−	0.206573i	−0.988063	+	0.154049i	$0.950769\pi$
$338$	−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	−0.996614	−	0.0822276i	$-0.973797\pi$
$347$	−20.0966	−	20.0966i	−1.07884	−	1.07884i	−0.0822276	−	0.996614i	$-0.526203\pi$
$348$	−21.7865	+	28.2089i	−1.16788	+	1.51216i
$349$	−1.73516	+	1.00180i	−0.0928811	+	0.0536249i	−0.545721	−	0.837967i	$-0.683744\pi$
$349$	−1.73516	+	1.00180i	−0.0928811	+	0.0536249i	0.452840	+	0.891592i	$0.350411\pi$
$350$	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	0.709036	−	0.705172i	$-0.249130\pi$
$353$	18.2339	+	4.88576i	0.970494	+	0.260043i	0.261457	+	0.965215i	$0.415797\pi$
$354$	−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	−0.837301	−	0.546742i	$-0.815868\pi$
$367$	−7.38604	−	27.5651i	−0.385548	−	1.43889i	0.451753	−	0.892143i	$-0.350799\pi$
$368$	−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	−0.780477	−	0.625184i	$-0.785024\pi$
$373$	−22.0904	+	5.91911i	−1.14380	+	0.306480i	−0.363321	+	0.931664i	$0.618357\pi$
$374$	−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	−0.639867	−	0.768485i	$-0.721011\pi$
$379$	−5.72889	+	3.30758i	−0.294273	+	0.169899i	0.345594	+	0.938384i	$0.387677\pi$
$380$	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	−0.968410	−	0.249364i	$-0.919779\pi$
$383$	−4.97918	−	18.5826i	−0.254424	−	0.949524i	0.713986	−	0.700160i	$-0.246888\pi$
$384$	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	−0.598076	−	0.801439i	$-0.704068\pi$
$389$	7.79118	−	13.4947i	0.395029	−	0.684210i	0.993105	+	0.117230i	$0.0374013\pi$
$390$	−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	−0.550638	−	0.834744i	$-0.685616\pi$
$397$	5.66077	−	5.66077i	0.284106	−	0.284106i	0.834744	+	0.550638i	$0.185616\pi$
$398$	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	$-0.827067\pi$
$401$		−	20.7039i		−	1.03390i	0.856015	−	0.516951i	$-0.172933\pi$
$402$	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	−0.836919	−	0.547326i	$-0.815646\pi$
$409$	−15.8024	+	9.12355i	−0.781381	+	0.451130i	0.0555386	+	0.998457i	$0.482312\pi$
$410$	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	0.988891	−	0.148640i	$-0.0474895\pi$
$419$	7.48610	+	12.9663i	0.365720	+	0.633446i	−0.623171	+	0.782085i	$0.714156\pi$
$420$	−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	0.237500	−	0.971388i	$-0.423672\pi$
$431$	−10.0688	−	5.81323i	−0.484997	−	0.280013i	−0.722497	+	0.691374i	$0.757006\pi$
$432$	−5.07393	+	0.619452i	−0.244120	+	0.0298034i
$433$	11.4297	+	11.4297i	0.549276	+	0.549276i	0.926231	−	0.376955i	$-0.123029\pi$
$433$	11.4297	+	11.4297i	0.549276	+	0.549276i	−0.376955	+	0.926231i	$0.623029\pi$
$434$	−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	−0.356886	−	0.934148i	$-0.616162\pi$
$439$	−28.1667	−	16.2621i	−1.34432	−	0.776146i	−0.987439	+	0.158002i	$0.949495\pi$
$440$	−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	−0.312344	−	0.949969i	$-0.601114\pi$
$443$	13.4205	−	13.4205i	0.637625	−	0.637625i	0.949969	+	0.312344i	$0.101114\pi$
$444$	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	−0.981643	−	0.190730i	$-0.938915\pi$
$449$	−6.90028	+	11.9516i	−0.325644	+	0.564033i	0.655998	+	0.754762i	$0.272248\pi$
$450$	−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	0.993342	+	0.115202i	$0.0367514\pi$
$457$	4.07635	+	15.2131i	0.190683	+	0.711640i	−0.802659	+	0.596439i	$0.796582\pi$
$458$	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	−0.166146	−	0.986101i	$-0.553132\pi$
$461$	12.9850	−	7.49688i	0.604770	−	0.349164i	0.770916	+	0.636937i	$0.219799\pi$
$462$	91.9233	+	12.3956i	4.27666	+	0.576694i
$463$	−10.6491	+	2.85340i	−0.494903	+	0.132609i	−0.497634	−	0.867387i	$-0.665798\pi$
$463$	−10.6491	+	2.85340i	−0.494903	+	0.132609i	0.00273025	+	0.999996i	$0.499131\pi$
$464$	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	0.999383	+	0.0351186i	$0.0111809\pi$
$467$	22.3558	+	22.3558i	1.03450	+	1.03450i	0.0351186	+	0.999383i	$0.488819\pi$
$468$	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	0.799331	−	0.600891i	$-0.205187\pi$
$479$	−2.64211	−	4.57626i	−0.120721	−	0.209095i	−0.920052	+	0.391796i	$0.871854\pi$
$480$	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	−0.0938440	+	0.995587i	$0.529915\pi$
$487$	−24.0416	+	24.0416i	−1.08943	+	1.08943i	−0.995587	+	0.0938440i	$0.970085\pi$
$488$	−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	$0.155829\pi$
$491$			20.8392i			0.940461i	−0.882544	+	0.470231i	$0.844171\pi$
$492$	−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	0.767541	−	0.640999i	$-0.221480\pi$
$499$	13.3179	+	7.68909i	0.596191	+	0.344211i	−0.171351	+	0.985210i	$0.554813\pi$
$500$	−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	−0.199177	−	0.979963i	$-0.563827\pi$
$503$	−19.3248	−	5.17807i	−0.861652	−	0.230879i	−0.662474	+	0.749084i	$0.730494\pi$
$504$	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	−0.664855	−	0.746972i	$-0.731507\pi$
$509$	−22.0946	−	38.2689i	−0.979325	−	1.69624i	−0.314470	−	0.949268i	$-0.601827\pi$
$510$	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	0.845148	−	0.534532i	$-0.179512\pi$
$521$	18.3700	+	10.6059i	0.804804	+	0.464654i	−0.0403444	+	0.999186i	$0.512846\pi$
$522$	−23.2348	+	39.6668i	−1.01696	+	1.73617i
$523$	−9.53115	+	2.55386i	−0.416768	+	0.111673i	−0.461108	−	0.887344i	$-0.652548\pi$
$523$	−9.53115	+	2.55386i	−0.416768	+	0.111673i	0.0443404	+	0.999016i	$0.485881\pi$
$524$	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	−0.592630	−	0.805475i	$-0.701910\pi$
$547$	4.97802	−	4.97802i	0.212845	−	0.212845i	0.805475	+	0.592630i	$0.201910\pi$
$548$	−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	−0.422496	−	0.906365i	$-0.638846\pi$
$557$	9.35959	−	34.9305i	0.396578	−	1.48005i	0.819075	−	0.573687i	$-0.194487\pi$
$558$	−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	−0.875107	−	0.483930i	$-0.839209\pi$
$563$	−9.28169	+	9.28169i	−0.391177	+	0.391177i	0.483930	+	0.875107i	$0.339209\pi$
$564$	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	0.850001	−	0.526781i	$-0.176601\pi$
$571$	−0.745666	−	1.29153i	−0.0312052	−	0.0540489i	−0.881206	+	0.472732i	$0.843268\pi$
$572$	−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	−0.364342	−	0.931265i	$-0.618706\pi$
$577$	−27.5159	−	7.37287i	−1.14550	−	0.306937i	−0.781162	+	0.624329i	$0.785373\pi$
$578$	−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	−0.484523	−	0.874779i	$-0.661007\pi$
$587$	−11.3083	+	3.03004i	−0.466743	+	0.125063i	0.0177802	+	0.999842i	$0.494340\pi$
$588$	−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	−0.482423	−	0.875938i	$-0.660243\pi$
$593$	9.58272	−	9.58272i	0.393515	−	0.393515i	0.875938	+	0.482423i	$0.160243\pi$
$594$	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	−0.897229	−	0.441566i	$-0.854423\pi$
$599$	−1.62038	+	2.80658i	−0.0662069	+	0.114674i	0.831022	+	0.556240i	$0.187756\pi$
$600$	19.1582	+	3.36548i	0.782128	+	0.137395i
$601$	12.0905	+	20.9414i	0.493182	+	0.854217i	0.999969	−	0.00785470i	$-0.00250025\pi$
$601$	12.0905	+	20.9414i	0.493182	+	0.854217i	−0.506787	+	0.862071i	$0.669167\pi$
$602$	−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	0.363584	−	0.931561i	$-0.381553\pi$
$607$	5.23979	+	1.40400i	0.212676	+	0.0569865i	−0.150908	+	0.988548i	$0.548220\pi$
$608$	−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	−0.914414	−	0.404780i	$-0.867348\pi$
$613$	1.97778	−	7.38116i	0.0798816	−	0.298122i	0.994296	+	0.106658i	$0.0340149\pi$
$614$	−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	0.505116	+	0.863051i	$0.331450\pi$
$617$	−9.03792	+	33.7300i	−0.363853	+	1.35792i	−0.868969	+	0.494866i	$0.835217\pi$
$618$	22.5090	+	54.8277i	0.905446	+	2.20549i
$619$			11.9809i			0.481553i	0.970581	+	0.240777i	$0.0774021\pi$
$619$			11.9809i			0.481553i	−0.970581	+	0.240777i	$0.922598\pi$
$620$	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	0.831076	−	0.556160i	$-0.187726\pi$
$631$	−1.66068	−	2.87638i	−0.0661106	−	0.114507i	−0.897186	+	0.441653i	$0.854392\pi$
$632$	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	−0.231221	−	0.972901i	$-0.574272\pi$
$641$	12.5508	−	7.24618i	0.495725	−	0.286207i	0.726946	+	0.686694i	$0.240939\pi$
$642$	−50.2215	−	6.77221i	−1.98208	−	0.267278i
$643$	−8.05928	−	8.05928i	−0.317827	−	0.317827i	0.530105	−	0.847932i	$-0.322152\pi$
$643$	−8.05928	−	8.05928i	−0.317827	−	0.317827i	−0.847932	+	0.530105i	$0.822152\pi$
$644$	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	−0.967061	−	0.254545i	$-0.918074\pi$
$647$	−42.6638	+	11.4317i	−1.67729	+	0.449428i	−0.710227	+	0.703973i	$0.751408\pi$
$648$	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	0.943454	−	0.331503i	$-0.107556\pi$
$653$	−1.00561	−	3.75299i	−0.0393526	−	0.146866i	−0.982807	+	0.184637i	$0.940889\pi$
$654$	−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	−0.753503	−	0.657444i	$-0.771638\pi$
$659$	4.94454	−	8.56419i	0.192612	−	0.333613i	0.946115	+	0.323831i	$0.104971\pi$
$660$	−51.8680	−	15.1885i	−2.01896	−	0.591212i
$661$	−1.47448	+	2.55387i	−0.0573505	+	0.0993340i	−0.893275	−	0.449510i	$-0.851599\pi$
$661$	−1.47448	+	2.55387i	−0.0573505	+	0.0993340i	0.835925	+	0.548844i	$0.184932\pi$
$662$	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	0.533962	−	0.845509i	$-0.320703\pi$
$673$	36.8157	−	9.86473i	1.41914	−	0.380258i	0.885179	+	0.465251i	$0.154036\pi$
$674$	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	0.976065	−	0.217481i	$-0.0697839\pi$
$677$	19.7378	+	19.7378i	0.758584	+	0.758584i	−0.217481	+	0.976065i	$0.569784\pi$
$678$	−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	0.816578	−	0.577236i	$-0.195869\pi$
$683$	32.2794	+	8.64924i	1.23514	+	0.330954i	0.418559	+	0.908189i	$0.362535\pi$
$684$	−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	0.652790	−	0.757539i	$-0.273598\pi$
$691$	−8.66554	−	15.0092i	−0.329653	−	0.570975i	−0.982443	+	0.186563i	$0.940265\pi$
$692$	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	−0.669901	−	0.742450i	$-0.733664\pi$
$701$	−9.58105	+	5.53162i	−0.361871	+	0.208926i	0.308030	+	0.951377i	$0.400330\pi$
$702$	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	$0.214052\pi$
$709$			33.1729i			1.24583i	−0.782288	+	0.622917i	$0.785948\pi$
$710$	−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	0.985535	−	0.169469i	$-0.0542054\pi$
$719$	9.27779	+	16.0696i	0.346003	+	0.599295i	−0.639532	+	0.768764i	$0.720872\pi$
$720$	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	0.813688	+	0.581302i	$0.197457\pi$
$727$	10.7761	+	40.2171i	0.399665	+	1.49157i	−0.414023	+	0.910266i	$0.635877\pi$
$728$	−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	0.0853131	−	0.996354i	$-0.472811\pi$
$733$	17.7977	−	4.76888i	0.657373	−	0.176143i	0.572060	+	0.820211i	$0.306144\pi$
$734$	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	$-0.789378\pi$
$739$		−	33.4071i		−	1.22890i	0.788955	−	0.614451i	$-0.210622\pi$
$740$	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	0.680418	+	0.732825i	$0.261798\pi$
$743$	12.4725	+	46.5479i	0.457571	+	1.70768i	−0.222847	+	0.974854i	$0.571535\pi$
$744$	−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	0.995378	−	0.0960332i	$-0.0306155\pi$
$757$	49.7827	+	13.3392i	1.80938	+	0.484823i	0.814006	+	0.580856i	$0.197282\pi$
$758$	−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	−0.678635	−	0.734476i	$-0.737428\pi$
$761$	−10.5346	+	6.08214i	−0.381878	+	0.220477i	0.296757	+	0.954953i	$0.404095\pi$
$762$	−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	$0.0663596\pi$
$769$			11.4788i			0.413936i	−0.978348	+	0.206968i	$0.933640\pi$
$770$	−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	0.683333	+	0.730107i	$0.260530\pi$
$773$	12.6949	+	47.3779i	0.456603	+	1.70406i	−0.226730	+	0.973958i	$0.572803\pi$
$774$	−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	−0.194183	−	0.980965i	$-0.562206\pi$
$787$	22.0720	−	22.0720i	0.786782	−	0.786782i	0.980965	+	0.194183i	$0.0622055\pi$
$788$	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	−0.829456	−	0.558573i	$-0.811349\pi$
$797$	4.74737	−	17.7174i	0.168160	−	0.627583i	0.997616	−	0.0690104i	$-0.0219842\pi$
$798$	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	−0.938924	−	0.344126i	$-0.888175\pi$
$809$	−4.87626	+	8.44593i	−0.171440	+	0.296943i	0.767483	+	0.641069i	$0.221509\pi$
$810$	−18.5694	+	41.0100i	−0.652462	+	1.44095i
$811$	−11.1202	+	19.2607i	−0.390482	+	0.676335i	−0.992513	−	0.122138i	$-0.961025\pi$
$811$	−11.1202	+	19.2607i	−0.390482	+	0.676335i	0.602031	+	0.798473i	$0.294358\pi$
$812$	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	0.577906	−	0.816103i	$-0.303870\pi$
$821$	4.58715	+	2.64839i	0.160093	+	0.0924296i	−0.417813	+	0.908533i	$0.637203\pi$
$822$	−0.608344	−	1.48181i	−0.0212184	−	0.0516841i
$823$	−8.61210	+	32.1408i	−0.300199	+	1.12036i	0.636801	+	0.771028i	$0.280257\pi$
$823$	−8.61210	+	32.1408i	−0.300199	+	1.12036i	−0.937000	+	0.349329i	$0.886409\pi$
$824$	−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	−0.835820	−	0.549004i	$-0.815007\pi$
$827$	−36.9581	+	9.90290i	−1.28516	+	0.344357i	−0.449339	+	0.893361i	$0.648341\pi$
$828$	34.2046	+	0.214710i	1.18869	+	0.00746169i
$829$	17.6908	−	10.2138i	0.614427	−	0.354740i	−0.160269	−	0.987073i	$-0.551236\pi$
$829$	17.6908	−	10.2138i	0.614427	−	0.354740i	0.774696	+	0.632334i	$0.217903\pi$
$830$	−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	−0.972799	−	0.231650i	$-0.925588\pi$
$839$	−19.8997	−	34.4673i	−0.687014	−	1.18994i	0.285785	−	0.958294i	$-0.407746\pi$
$840$	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	0.405061	+	0.914290i	$0.367250\pi$
$853$	−11.7665	+	43.9131i	−0.402877	+	1.50356i	−0.807938	+	0.589268i	$0.799416\pi$
$854$	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	0.463752	−	0.885965i	$-0.346503\pi$
$857$	−12.3601	−	12.3601i	−0.422213	−	0.422213i	−0.885965	+	0.463752i	$0.846503\pi$
$858$	−4.40036	+	32.6323i	−0.150226	+	1.11405i
$859$			15.8602i			0.541144i	0.962700	+	0.270572i	$0.0872127\pi$
$859$			15.8602i			0.541144i	−0.962700	+	0.270572i	$0.912787\pi$
$860$	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	0.202155	−	0.979354i	$-0.435206\pi$
$863$	−3.30345	−	0.885156i	−0.112451	−	0.0301310i	−0.314606	+	0.949223i	$0.601872\pi$
$864$	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	0.220824	−	0.975314i	$-0.429125\pi$
$877$	35.4226	−	35.4226i	1.19614	−	1.19614i	0.975314	−	0.220824i	$-0.0708746\pi$
$878$	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	0.988740	+	0.149643i	$0.0478123\pi$
$881$	47.8677	+	27.6364i	1.61270	+	0.931095i	0.623964	+	0.781453i	$0.285521\pi$
$882$	−0.823933	+	131.257i	−0.0277433	+	4.41967i
$883$	41.7101	−	11.1762i	1.40366	−	0.376109i	0.524001	−	0.851718i	$-0.324439\pi$
$883$	41.7101	−	11.1762i	1.40366	−	0.376109i	0.879657	+	0.475608i	$0.157772\pi$
$884$	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	0.988500	+	0.151220i	$0.0483203\pi$
$887$	33.9438	+	33.9438i	1.13972	+	1.13972i	0.151220	+	0.988500i	$0.451680\pi$
$888$	−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	−0.979262	−	0.202597i	$-0.935062\pi$
$907$	−7.00192	−	26.1315i	−0.232495	−	0.867683i	0.746767	−	0.665086i	$-0.231605\pi$
$908$	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	$-0.591031\pi$
$911$		−	57.9138i		−	1.91877i	0.282100	−	0.959385i	$-0.408969\pi$
$912$	−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	$-0.829816\pi$
$919$		−	30.8933i		−	1.01908i	0.860448	−	0.509538i	$-0.170184\pi$
$920$	−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	−0.948704	−	0.316164i	$-0.897605\pi$
$929$	−6.11253	+	10.5872i	−0.200546	+	0.347355i	0.748159	+	0.663520i	$0.230938\pi$
$930$	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	0.121778	−	0.992557i	$-0.461140\pi$
$937$	−8.23539	−	2.20667i	−0.269038	−	0.0720886i	−0.390816	+	0.920469i	$0.627807\pi$
$938$	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	−0.924156	−	0.382016i	$-0.875230\pi$
$941$	−32.3751	+	18.6918i	−1.05540	+	0.609335i	−0.131243	+	0.991350i	$0.541897\pi$
$942$	−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	0.842718	+	0.538356i	$0.180954\pi$
$947$	−4.80911	+	17.9478i	−0.156275	+	0.583226i	−0.998993	+	0.0448708i	$0.985712\pi$
$948$	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	0.526497	−	0.850177i	$-0.323505\pi$
$953$	17.2064	+	4.61043i	0.557369	+	0.149347i	0.0308718	+	0.999523i	$0.490172\pi$
$954$	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	0.983733	−	0.179635i	$-0.0574916\pi$
$967$	1.30537	+	4.87171i	0.0419779	+	0.156664i	−0.941755	+	0.336298i	$0.890825\pi$
$968$	−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	−0.949845	−	0.312721i	$-0.898759\pi$
$971$	−35.9579	+	20.7603i	−1.15394	+	0.666229i	−0.204098	+	0.978950i	$0.565426\pi$
$972$	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	−0.0479614	−	0.998849i	$-0.515272\pi$
$977$	15.4097	−	57.5097i	0.492999	−	1.83990i	0.540960	−	0.841048i	$-0.318061\pi$
$978$	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	0.469910	−	0.882714i	$-0.344286\pi$
$983$	13.6544	+	3.65868i	0.435508	+	0.116694i	−0.0344028	+	0.999408i	$0.510953\pi$
$984$	−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	0.729222	−	0.684277i	$-0.239882\pi$
$997$	32.1629	+	8.61802i	1.01861	+	0.272936i	0.289387	+	0.957212i	$0.406549\pi$
$998$	−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.248.10	yes	288
3.2	odd	2	inner	555.2.bi.a.248.63	yes	288
5.2	odd	4	inner	555.2.bi.a.137.10	yes	288
15.2	even	4	inner	555.2.bi.a.137.63	yes	288
37.10	even	3	inner	555.2.bi.a.158.63	yes	288
111.47	odd	6	inner	555.2.bi.a.158.10	yes	288
185.47	odd	12	inner	555.2.bi.a.47.63	yes	288
555.47	even	12	inner	555.2.bi.a.47.10	✓	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.bi.a.47.10	✓	288	555.47	even	12	inner
555.2.bi.a.47.63	yes	288	185.47	odd	12	inner
555.2.bi.a.137.10	yes	288	5.2	odd	4	inner
555.2.bi.a.137.63	yes	288	15.2	even	4	inner
555.2.bi.a.158.10	yes	288	111.47	odd	6	inner
555.2.bi.a.158.63	yes	288	37.10	even	3	inner
555.2.bi.a.248.10	yes	288	1.1	even	1	trivial
555.2.bi.a.248.63	yes	288	3.2	odd	2	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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