LMFDB - Embedded newform 1155.2.k.b.769.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(769,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.769");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.k (of order $2$, degree $1$, 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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			769.5
Character	$\chi$	$=$	1155.769
Dual form			1155.2.k.b.769.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.43104 q^{2} +1.00000 q^{3} +3.90997 q^{4} +(2.21714 + 0.290295i) q^{5} -2.43104 q^{6} +(1.43522 + 2.22265i) q^{7} -4.64322 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.43104 q^{2} +1.00000 q^{3} +3.90997 q^{4} +(2.21714 + 0.290295i) q^{5} -2.43104 q^{6} +(1.43522 + 2.22265i) q^{7} -4.64322 q^{8} +1.00000 q^{9} +(-5.38997 - 0.705719i) q^{10} +(-1.89585 - 2.72135i) q^{11} +3.90997 q^{12} +2.23538i q^{13} +(-3.48907 - 5.40335i) q^{14} +(2.21714 + 0.290295i) q^{15} +3.46794 q^{16} +4.51862i q^{17} -2.43104 q^{18} +0.900450 q^{19} +(8.66897 + 1.13504i) q^{20} +(1.43522 + 2.22265i) q^{21} +(4.60889 + 6.61572i) q^{22} +2.09062i q^{23} -4.64322 q^{24} +(4.83146 + 1.28725i) q^{25} -5.43431i q^{26} +1.00000 q^{27} +(5.61165 + 8.69048i) q^{28} -3.99148i q^{29} +(-5.38997 - 0.705719i) q^{30} +8.71349i q^{31} +0.855744 q^{32} +(-1.89585 - 2.72135i) q^{33} -10.9850i q^{34} +(2.53686 + 5.34456i) q^{35} +3.90997 q^{36} +7.32857i q^{37} -2.18903 q^{38} +2.23538i q^{39} +(-10.2947 - 1.34790i) q^{40} -0.222345 q^{41} +(-3.48907 - 5.40335i) q^{42} +4.66125 q^{43} +(-7.41272 - 10.6404i) q^{44} +(2.21714 + 0.290295i) q^{45} -5.08239i q^{46} -6.60502 q^{47} +3.46794 q^{48} +(-2.88031 + 6.37995i) q^{49} +(-11.7455 - 3.12936i) q^{50} +4.51862i q^{51} +8.74028i q^{52} -3.38806i q^{53} -2.43104 q^{54} +(-3.41338 - 6.58398i) q^{55} +(-6.66403 - 10.3202i) q^{56} +0.900450 q^{57} +9.70346i q^{58} -8.40349i q^{59} +(8.66897 + 1.13504i) q^{60} +2.18474 q^{61} -21.1829i q^{62} +(1.43522 + 2.22265i) q^{63} -9.01623 q^{64} +(-0.648919 + 4.95617i) q^{65} +(4.60889 + 6.61572i) q^{66} -11.5990i q^{67} +17.6677i q^{68} +2.09062i q^{69} +(-6.16721 - 12.9929i) q^{70} +2.71126 q^{71} -4.64322 q^{72} -4.36305i q^{73} -17.8161i q^{74} +(4.83146 + 1.28725i) q^{75} +3.52073 q^{76} +(3.32765 - 8.11953i) q^{77} -5.43431i q^{78} +4.44023i q^{79} +(7.68892 + 1.00672i) q^{80} +1.00000 q^{81} +0.540529 q^{82} +7.79488i q^{83} +(5.61165 + 8.69048i) q^{84} +(-1.31173 + 10.0184i) q^{85} -11.3317 q^{86} -3.99148i q^{87} +(8.80285 + 12.6358i) q^{88} -1.90097i q^{89} +(-5.38997 - 0.705719i) q^{90} +(-4.96846 + 3.20826i) q^{91} +8.17426i q^{92} +8.71349i q^{93} +16.0571 q^{94} +(1.99643 + 0.261396i) q^{95} +0.855744 q^{96} +12.7447 q^{97} +(7.00216 - 15.5099i) q^{98} +(-1.89585 - 2.72135i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9}+O(q^{10}) $ 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9	$ 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9} + 48 q^{12} - 4 q^{15} + 40 q^{16} - 18 q^{20} + 20 q^{25} + 48 q^{27} + 48 q^{36} - 20 q^{38} - 16 q^{44} - 4 q^{45} + 8 q^{47} + 40 q^{48} + 24 q^{49} - 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} + 20 q^{75} - 32 q^{77} - 46 q^{80} + 48 q^{81} - 32 q^{82} - 16 q^{86} + 68 q^{97}+O(q^{100}) $ 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9 + 48 * q^12 - 4 * q^15 + 40 * q^16 - 18 * q^20 + 20 * q^25 + 48 * q^27 + 48 * q^36 - 20 * q^38 - 16 * q^44 - 4 * q^45 + 8 * q^47 + 40 * q^48 + 24 * q^49 - 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 + 20 * q^75 - 32 * q^77 - 46 * q^80 + 48 * q^81 - 32 * q^82 - 16 * q^86 + 68 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−2.43104			−1.71901			−0.859504	−	0.511130i	$-0.829227\pi$
$2$	−2.43104			−1.71901			−0.859504	+	0.511130i	$0.829227\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	3.90997			1.95499
$5$	2.21714	+	0.290295i	0.991537	+	0.129824i
$5$	2.21714	+	0.290295i	0.991537	+	0.129824i
$6$	−2.43104			−0.992469
$7$	1.43522	+	2.22265i	0.542461	+	0.840081i
$7$	1.43522	+	2.22265i	0.542461	+	0.840081i
$8$	−4.64322			−1.64163
$9$	1.00000			0.333333
$10$	−5.38997	−	0.705719i	−1.70446	−	0.223168i
$11$	−1.89585	−	2.72135i	−0.571620	−	0.820518i
$11$	−1.89585	−	2.72135i	−0.571620	−	0.820518i
$12$	3.90997			1.12871
$13$			2.23538i			0.619984i	0.950739	+	0.309992i	$0.100326\pi$
$13$			2.23538i			0.619984i	−0.950739	+	0.309992i	$0.899674\pi$
$14$	−3.48907	−	5.40335i	−0.932494	−	1.44411i
$15$	2.21714	+	0.290295i	0.572464	+	0.0749537i
$16$	3.46794			0.866984
$17$			4.51862i			1.09593i	0.836502	+	0.547963i	$0.184597\pi$
$17$			4.51862i			1.09593i	−0.836502	+	0.547963i	$0.815403\pi$
$18$	−2.43104			−0.573002
$19$	0.900450			0.206577			0.103289	−	0.994651i	$-0.467063\pi$
$19$	0.900450			0.206577			0.103289	+	0.994651i	$0.467063\pi$
$20$	8.66897	+	1.13504i	1.93844	+	0.253803i
$21$	1.43522	+	2.22265i	0.313190	+	0.485021i
$22$	4.60889	+	6.61572i	0.982619	+	1.41048i
$23$			2.09062i			0.435924i	0.975957	+	0.217962i	$0.0699409\pi$
$23$			2.09062i			0.435924i	−0.975957	+	0.217962i	$0.930059\pi$
$24$	−4.64322			−0.947794
$25$	4.83146	+	1.28725i	0.966292	+	0.257450i
$26$		−	5.43431i		−	1.06576i
$27$	1.00000			0.192450
$28$	5.61165	+	8.69048i	1.06050	+	1.64235i
$29$		−	3.99148i		−	0.741199i	−0.928793	−	0.370600i	$-0.879152\pi$
$29$		−	3.99148i		−	0.741199i	0.928793	−	0.370600i	$-0.120848\pi$
$30$	−5.38997	−	0.705719i	−0.984070	−	0.128846i
$31$			8.71349i			1.56499i	0.622657	+	0.782495i	$0.286053\pi$
$31$			8.71349i			1.56499i	−0.622657	+	0.782495i	$0.713947\pi$
$32$	0.855744			0.151276
$33$	−1.89585	−	2.72135i	−0.330025	−	0.473727i
$34$		−	10.9850i		−	1.88391i
$35$	2.53686	+	5.34456i	0.428807	+	0.903396i
$36$	3.90997			0.651662
$37$			7.32857i			1.20481i	0.798191	+	0.602405i	$0.205791\pi$
$37$			7.32857i			1.20481i	−0.798191	+	0.602405i	$0.794209\pi$
$38$	−2.18903			−0.355108
$39$			2.23538i			0.357948i
$40$	−10.2947	−	1.34790i	−1.62773	−	0.213122i
$41$	−0.222345			−0.0347244			−0.0173622	−	0.999849i	$-0.505527\pi$
$41$	−0.222345			−0.0347244			−0.0173622	+	0.999849i	$0.505527\pi$
$42$	−3.48907	−	5.40335i	−0.538375	−	0.833755i
$43$	4.66125			0.710833			0.355417	−	0.934708i	$-0.384339\pi$
$43$	4.66125			0.710833			0.355417	+	0.934708i	$0.384339\pi$
$44$	−7.41272	−	10.6404i	−1.11751	−	1.60410i
$45$	2.21714	+	0.290295i	0.330512	+	0.0432746i
$46$		−	5.08239i		−	0.749357i
$47$	−6.60502			−0.963441			−0.481721	−	0.876325i	$-0.659988\pi$
$47$	−6.60502			−0.963441			−0.481721	+	0.876325i	$0.659988\pi$
$48$	3.46794			0.500554
$49$	−2.88031	+	6.37995i	−0.411473	+	0.911422i
$50$	−11.7455	−	3.12936i	−1.66106	−	0.442558i
$51$			4.51862i			0.632734i
$52$			8.74028i			1.21206i
$53$		−	3.38806i		−	0.465386i	−0.972550	−	0.232693i	$-0.925246\pi$
$53$		−	3.38806i		−	0.465386i	0.972550	−	0.232693i	$-0.0747537\pi$
$54$	−2.43104			−0.330823
$55$	−3.41338	−	6.58398i	−0.460260	−	0.887784i
$56$	−6.66403	−	10.3202i	−0.890518	−	1.37910i
$57$	0.900450			0.119268
$58$			9.70346i			1.27413i
$59$		−	8.40349i		−	1.09404i	−0.837119	−	0.547020i	$-0.815762\pi$
$59$		−	8.40349i		−	1.09404i	0.837119	−	0.547020i	$-0.184238\pi$
$60$	8.66897	+	1.13504i	1.11916	+	0.146533i
$61$	2.18474			0.279727			0.139863	−	0.990171i	$-0.455334\pi$
$61$	2.18474			0.279727			0.139863	+	0.990171i	$0.455334\pi$
$62$		−	21.1829i		−	2.69023i
$63$	1.43522	+	2.22265i	0.180820	+	0.280027i
$64$	−9.01623			−1.12703
$65$	−0.648919	+	4.95617i	−0.0804885	+	0.614737i
$66$	4.60889	+	6.61572i	0.567315	+	0.814339i
$67$		−	11.5990i		−	1.41704i	−0.705690	−	0.708521i	$-0.749363\pi$
$67$		−	11.5990i		−	1.41704i	0.705690	−	0.708521i	$-0.250637\pi$
$68$			17.6677i			2.14252i
$69$			2.09062i			0.251681i
$70$	−6.16721	−	12.9929i	−0.737123	−	1.55294i
$71$	2.71126			0.321767			0.160884	−	0.986973i	$-0.448566\pi$
$71$	2.71126			0.321767			0.160884	+	0.986973i	$0.448566\pi$
$72$	−4.64322			−0.547209
$73$		−	4.36305i		−	0.510656i	−0.966854	−	0.255328i	$-0.917816\pi$
$73$		−	4.36305i		−	0.510656i	0.966854	−	0.255328i	$-0.0821835\pi$
$74$		−	17.8161i		−	2.07108i
$75$	4.83146	+	1.28725i	0.557889	+	0.148639i
$76$	3.52073			0.403856
$77$	3.32765	−	8.11953i	0.379221	−	0.925306i
$78$		−	5.43431i		−	0.615315i
$79$			4.44023i			0.499565i	0.968302	+	0.249783i	$0.0803592\pi$
$79$			4.44023i			0.499565i	−0.968302	+	0.249783i	$0.919641\pi$
$80$	7.68892	+	1.00672i	0.859647	+	0.112555i
$81$	1.00000			0.111111
$82$	0.540529			0.0596915
$83$			7.79488i			0.855599i	0.903874	+	0.427800i	$0.140711\pi$
$83$			7.79488i			0.855599i	−0.903874	+	0.427800i	$0.859289\pi$
$84$	5.61165	+	8.69048i	0.612282	+	0.948210i
$85$	−1.31173	+	10.0184i	−0.142277	+	1.08665i
$86$	−11.3317			−1.22193
$87$		−	3.99148i		−	0.427932i
$88$	8.80285	+	12.6358i	0.938387	+	1.34699i
$89$		−	1.90097i		−	0.201502i	−0.994912	−	0.100751i	$-0.967875\pi$
$89$		−	1.90097i		−	0.201502i	0.994912	−	0.100751i	$-0.0321246\pi$
$90$	−5.38997	−	0.705719i	−0.568153	−	0.0743893i
$91$	−4.96846	+	3.20826i	−0.520837	+	0.336317i
$92$			8.17426i			0.852226i
$93$			8.71349i			0.903547i
$94$	16.0571			1.65616
$95$	1.99643	+	0.261396i	0.204829	+	0.0268186i
$96$	0.855744			0.0873390
$97$	12.7447			1.29403			0.647014	−	0.762478i	$-0.276017\pi$
$97$	12.7447			1.29403			0.647014	+	0.762478i	$0.276017\pi$
$98$	7.00216	−	15.5099i	0.707325	−	1.56674i
$99$	−1.89585	−	2.72135i	−0.190540	−	0.273506i
$100$	18.8909	+	5.03311i	1.88909	+	0.503311i
$101$	0.859985			0.0855717			0.0427858	−	0.999084i	$-0.486377\pi$
$101$	0.859985			0.0855717			0.0427858	+	0.999084i	$0.486377\pi$
$102$		−	10.9850i		−	1.08767i
$103$	−1.85324			−0.182605			−0.0913026	−	0.995823i	$-0.529103\pi$
$103$	−1.85324			−0.182605			−0.0913026	+	0.995823i	$0.529103\pi$
$104$		−	10.3794i		−	1.01778i
$105$	2.53686	+	5.34456i	0.247572	+	0.521576i
$106$			8.23652i			0.800001i
$107$	−9.90730			−0.957775			−0.478887	−	0.877876i	$-0.658960\pi$
$107$	−9.90730			−0.957775			−0.478887	+	0.877876i	$0.658960\pi$
$108$	3.90997			0.376237
$109$		−	9.26520i		−	0.887445i	−0.896164	−	0.443723i	$-0.853658\pi$
$109$		−	9.26520i		−	0.887445i	0.896164	−	0.443723i	$-0.146342\pi$
$110$	8.29807	+	16.0060i	0.791190	+	1.52611i
$111$			7.32857i			0.695597i
$112$	4.97724	+	7.70800i	0.470305	+	0.728337i
$113$			17.4516i			1.64171i	0.571137	+	0.820855i	$0.306503\pi$
$113$			17.4516i			1.64171i	−0.571137	+	0.820855i	$0.693497\pi$
$114$	−2.18903			−0.205022
$115$	−0.606895	+	4.63521i	−0.0565933	+	0.432235i
$116$		−	15.6066i		−	1.44903i
$117$			2.23538i			0.206661i
$118$			20.4292i			1.88066i
$119$	−10.0433	+	6.48520i	−0.920668	+	0.594497i
$120$	−10.2947	−	1.34790i	−0.939773	−	0.123046i
$121$	−3.81151	+	10.3185i	−0.346501	+	0.938050i
$122$	−5.31119			−0.480853
$123$	−0.222345			−0.0200481
$124$			34.0695i			3.05953i
$125$	10.3384	+	4.25656i	0.924691	+	0.380719i
$126$	−3.48907	−	5.40335i	−0.310831	−	0.481369i
$127$	−22.1655			−1.96687			−0.983433	−	0.181271i	$-0.941979\pi$
$127$	−22.1655			−1.96687			−0.983433	+	0.181271i	$0.941979\pi$
$128$	20.2073			1.78609
$129$	4.66125			0.410400
$130$	1.57755	−	12.0487i	0.138360	−	1.05674i
$131$	16.0202			1.39969			0.699847	−	0.714293i	$-0.253252\pi$
$131$	16.0202			1.39969			0.699847	+	0.714293i	$0.253252\pi$
$132$	−7.41272	−	10.6404i	−0.645194	−	0.926129i
$133$	1.29234	+	2.00138i	0.112060	+	0.173542i
$134$			28.1976i			2.43590i
$135$	2.21714	+	0.290295i	0.190821	+	0.0249846i
$136$		−	20.9810i		−	1.79910i
$137$		−	14.9090i		−	1.27377i	−0.770961	−	0.636883i	$-0.780224\pi$
$137$		−	14.9090i		−	1.27377i	0.770961	−	0.636883i	$-0.219776\pi$
$138$		−	5.08239i		−	0.432641i
$139$	18.2709			1.54972			0.774858	−	0.632135i	$-0.217821\pi$
$139$	18.2709			1.54972			0.774858	+	0.632135i	$0.217821\pi$
$140$	9.91905	+	20.8971i	0.838312	+	1.76613i
$141$	−6.60502			−0.556243
$142$	−6.59119			−0.553121
$143$	6.08326	−	4.23795i	0.508708	−	0.354395i
$144$	3.46794			0.288995
$145$	1.15871	−	8.84969i	0.0962252	−	0.734927i
$146$			10.6068i			0.877822i
$147$	−2.88031	+	6.37995i	−0.237564	+	0.526210i
$148$			28.6545i			2.35539i
$149$			8.97699i			0.735424i	0.929940	+	0.367712i	$0.119859\pi$
$149$			8.97699i			0.735424i	−0.929940	+	0.367712i	$0.880141\pi$
$150$	−11.7455	−	3.12936i	−0.959015	−	0.255511i
$151$			10.7566i			0.875357i	0.899132	+	0.437678i	$0.144199\pi$
$151$			10.7566i			0.875357i	−0.899132	+	0.437678i	$0.855801\pi$
$152$	−4.18099			−0.339123
$153$			4.51862i			0.365309i
$154$	−8.08966	+	19.7389i	−0.651884	+	1.59061i
$155$	−2.52948	+	19.3191i	−0.203173	+	1.55174i
$156$			8.74028i			0.699783i
$157$	19.0721			1.52212			0.761059	−	0.648683i	$-0.224680\pi$
$157$	19.0721			1.52212			0.761059	+	0.648683i	$0.224680\pi$
$158$		−	10.7944i		−	0.858756i
$159$		−	3.38806i		−	0.268691i
$160$	1.89731	+	0.248418i	0.149995	+	0.0196392i
$161$	−4.64671	+	3.00049i	−0.366212	+	0.236472i
$162$	−2.43104			−0.191001
$163$		−	3.29902i		−	0.258399i	−0.991619	−	0.129199i	$-0.958759\pi$
$163$		−	3.29902i		−	0.258399i	0.991619	−	0.129199i	$-0.0412407\pi$
$164$	−0.869361			−0.0678857
$165$	−3.41338	−	6.58398i	−0.265731	−	0.512563i
$166$		−	18.9497i		−	1.47078i
$167$		−	6.00033i		−	0.464320i	−0.972678	−	0.232160i	$-0.925421\pi$
$167$		−	6.00033i		−	0.464320i	0.972678	−	0.232160i	$-0.0745793\pi$
$168$	−6.66403	−	10.3202i	−0.514141	−	0.796224i
$169$	8.00306			0.615620
$170$	3.18888	−	24.3553i	0.244576	−	1.86796i
$171$	0.900450			0.0688591
$172$	18.2253			1.38967
$173$			23.8329i			1.81198i	0.423299	+	0.905990i	$0.360872\pi$
$173$			23.8329i			1.81198i	−0.423299	+	0.905990i	$0.639128\pi$
$174$			9.70346i			0.735618i
$175$	4.07308	+	12.5861i	0.307896	+	0.951420i
$176$	−6.57469	−	9.43748i	−0.495586	−	0.711377i
$177$		−	8.40349i		−	0.631645i
$178$			4.62133i			0.346384i
$179$	11.5323			0.861968			0.430984	−	0.902360i	$-0.358167\pi$
$179$	11.5323			0.861968			0.430984	+	0.902360i	$0.358167\pi$
$180$	8.66897	+	1.13504i	0.646147	+	0.0846012i
$181$		−	16.7900i		−	1.24799i	−0.781427	−	0.623997i	$-0.785508\pi$
$181$		−	16.7900i		−	1.24799i	0.781427	−	0.623997i	$-0.214492\pi$
$182$	12.0786	−	7.79941i	0.895322	−	0.578131i
$183$	2.18474			0.161500
$184$		−	9.70722i		−	0.715626i
$185$	−2.12744	+	16.2485i	−0.156413	+	1.19461i
$186$		−	21.1829i		−	1.55320i
$187$	12.2968	−	8.56662i	0.899228	−	0.626454i
$188$	−25.8254			−1.88351
$189$	1.43522	+	2.22265i	0.104397	+	0.161674i
$190$	−4.85340	−	0.635464i	−0.352103	−	0.0461014i
$191$	−8.47885			−0.613508			−0.306754	−	0.951789i	$-0.599243\pi$
$191$	−8.47885			−0.613508			−0.306754	+	0.951789i	$0.599243\pi$
$192$	−9.01623			−0.650690
$193$	16.4453			1.18376			0.591881	−	0.806026i	$-0.298386\pi$
$193$	16.4453			1.18376			0.591881	+	0.806026i	$0.298386\pi$
$194$	−30.9829			−2.22444
$195$	−0.648919	+	4.95617i	−0.0464701	+	0.354918i
$196$	−11.2619	+	24.9454i	−0.804424	+	1.78182i
$197$	−14.8948			−1.06121			−0.530604	−	0.847620i	$-0.678035\pi$
$197$	−14.8948			−1.06121			−0.530604	+	0.847620i	$0.678035\pi$
$198$	4.60889	+	6.61572i	0.327540	+	0.470159i
$199$		−	15.3446i		−	1.08775i	−0.839166	−	0.543875i	$-0.816957\pi$
$199$		−	15.3446i		−	1.08775i	0.839166	−	0.543875i	$-0.183043\pi$
$200$	−22.4335	−	5.97699i	−1.58629	−	0.422637i
$201$		−	11.5990i		−	0.818129i
$202$	−2.09066			−0.147098
$203$	8.87165	−	5.72864i	0.622668	−	0.402071i
$204$			17.6677i			1.23699i
$205$	−0.492970	−	0.0645454i	−0.0344305	−	0.00450805i
$206$	4.50531			0.313900
$207$			2.09062i			0.145308i
$208$			7.75217i			0.537516i
$209$	−1.70712	−	2.45044i	−0.118084	−	0.169501i
$210$	−6.16721	−	12.9929i	−0.425578	−	0.896593i
$211$		−	26.7512i		−	1.84163i	−0.390005	−	0.920813i	$-0.627527\pi$
$211$		−	26.7512i		−	1.84163i	0.390005	−	0.920813i	$-0.372473\pi$
$212$		−	13.2472i		−	0.909822i
$213$	2.71126			0.185773
$214$	24.0851			1.64642
$215$	10.3347	+	1.35313i	0.704818	+	0.0922830i
$216$	−4.64322			−0.315931
$217$	−19.3670	+	12.5057i	−1.31472	+	0.848945i
$218$			22.5241i			1.52553i
$219$		−	4.36305i		−	0.294828i
$220$	−13.3462	−	25.7432i	−0.899801	−	1.73561i
$221$	−10.1008			−0.679457
$222$		−	17.8161i		−	1.19574i
$223$	−26.8433			−1.79756			−0.898779	−	0.438402i	$-0.855545\pi$
$223$	−26.8433			−1.79756			−0.898779	+	0.438402i	$0.855545\pi$
$224$	1.22818	+	1.90202i	0.0820610	+	0.127084i
$225$	4.83146	+	1.28725i	0.322097	+	0.0858167i
$226$		−	42.4256i		−	2.82211i
$227$		−	3.82354i		−	0.253777i	−0.991917	−	0.126889i	$-0.959501\pi$
$227$		−	3.82354i		−	0.253777i	0.991917	−	0.126889i	$-0.0404991\pi$
$228$	3.52073			0.233166
$229$			6.29821i			0.416197i	0.978108	+	0.208099i	$0.0667275\pi$
$229$			6.29821i			0.416197i	−0.978108	+	0.208099i	$0.933273\pi$
$230$	1.47539	−	11.2684i	0.0972843	−	0.743015i
$231$	3.32765	−	8.11953i	0.218943	−	0.534226i
$232$			18.5333i			1.21677i
$233$	0.623619			0.0408546			0.0204273	−	0.999791i	$-0.493497\pi$
$233$	0.623619			0.0408546			0.0204273	+	0.999791i	$0.493497\pi$
$234$		−	5.43431i		−	0.355252i
$235$	−14.6443	−	1.91740i	−0.955288	−	0.125077i
$236$		−	32.8574i		−	2.13883i
$237$			4.44023i			0.288424i
$238$	24.4157	−	15.7658i	1.58263	−	1.02194i
$239$		−	13.6468i		−	0.882738i	−0.897326	−	0.441369i	$-0.854493\pi$
$239$		−	13.6468i		−	0.882738i	0.897326	−	0.441369i	$-0.145507\pi$
$240$	7.68892	+	1.00672i	0.496317	+	0.0649837i
$241$	−2.04549			−0.131761			−0.0658807	−	0.997828i	$-0.520986\pi$
$241$	−2.04549			−0.131761			−0.0658807	+	0.997828i	$0.520986\pi$
$242$	9.26595	−	25.0848i	0.595638	−	1.61251i
$243$	1.00000			0.0641500
$244$	8.54226			0.546862
$245$	−8.23813	+	13.3091i	−0.526315	+	0.850290i
$246$	0.540529			0.0344629
$247$			2.01285i			0.128075i
$248$		−	40.4587i		−	2.56913i
$249$			7.79488i			0.493981i
$250$	−25.1330	−	10.3479i	−1.58955	−	0.654458i
$251$			15.4429i			0.974748i	0.873193	+	0.487374i	$0.162045\pi$
$251$			15.4429i			0.974748i	−0.873193	+	0.487374i	$0.837955\pi$
$252$	5.61165	+	8.69048i	0.353501	+	0.547449i
$253$	5.68931	−	3.96350i	0.357684	−	0.249183i
$254$	53.8852			3.38106
$255$	−1.31173	+	10.0184i	−0.0821438	+	0.627379i
$256$	−31.0925			−1.94328
$257$	−12.2672			−0.765206			−0.382603	−	0.923913i	$-0.624972\pi$
$257$	−12.2672			−0.765206			−0.382603	+	0.923913i	$0.624972\pi$
$258$	−11.3317			−0.705480
$259$	−16.2888	+	10.5181i	−1.01214	+	0.653562i
$260$	−2.53726	+	19.3785i	−0.157354	+	1.20180i
$261$		−	3.99148i		−	0.247066i
$262$	−38.9459			−2.40608
$263$	29.9141			1.84458			0.922290	−	0.386499i	$-0.126316\pi$
$263$	29.9141			1.84458			0.922290	+	0.386499i	$0.126316\pi$
$264$	8.80285	+	12.6358i	0.541778	+	0.777683i
$265$	0.983535	−	7.51182i	0.0604181	−	0.461447i
$266$	−3.14174	−	4.86545i	−0.192632	−	0.298320i
$267$		−	1.90097i		−	0.116337i
$268$		−	45.3517i		−	2.77030i
$269$		−	24.3142i		−	1.48247i	−0.671248	−	0.741233i	$-0.734241\pi$
$269$		−	24.3142i		−	1.48247i	0.671248	−	0.741233i	$-0.265759\pi$
$270$	−5.38997	−	0.705719i	−0.328023	−	0.0429487i
$271$	−5.68827			−0.345538			−0.172769	−	0.984962i	$-0.555271\pi$
$271$	−5.68827			−0.345538			−0.172769	+	0.984962i	$0.555271\pi$
$272$			15.6703i			0.950151i
$273$	−4.96846	+	3.20826i	−0.300705	+	0.194173i
$274$			36.2445i			2.18961i
$275$	−5.65666	−	15.5885i	−0.341109	−	0.940024i
$276$			8.17426i			0.492033i
$277$	−17.3410			−1.04192			−0.520961	−	0.853580i	$-0.674426\pi$
$277$	−17.3410			−1.04192			−0.520961	+	0.853580i	$0.674426\pi$
$278$	−44.4173			−2.66397
$279$			8.71349i			0.521663i
$280$	−11.7792	−	24.8160i	−0.703942	−	1.48304i
$281$			8.03999i			0.479625i	0.970819	+	0.239813i	$0.0770860\pi$
$281$			8.03999i			0.479625i	−0.970819	+	0.239813i	$0.922914\pi$
$282$	16.0571			0.956186
$283$		−	21.8263i		−	1.29744i	−0.761028	−	0.648718i	$-0.775305\pi$
$283$		−	21.8263i		−	1.29744i	0.761028	−	0.648718i	$-0.224695\pi$
$284$	10.6010			0.629051
$285$	1.99643	+	0.261396i	0.118258	+	0.0154837i
$286$	−14.7887	+	10.3026i	−0.874473	+	0.609208i
$287$	−0.319112	−	0.494193i	−0.0188366	−	0.0291713i
$288$	0.855744			0.0504252
$289$	−3.41794			−0.201055
$290$	−2.81686	+	21.5140i	−0.165412	+	1.26334i
$291$	12.7447			0.747108
$292$		−	17.0594i		−	0.998326i
$293$			6.81797i			0.398310i	0.979968	+	0.199155i	$0.0638198\pi$
$293$			6.81797i			0.398310i	−0.979968	+	0.199155i	$0.936180\pi$
$294$	7.00216	−	15.5099i	0.408374	−	0.904558i
$295$	2.43949	−	18.6317i	0.142032	−	1.08478i
$296$		−	34.0282i		−	1.97785i
$297$	−1.89585	−	2.72135i	−0.110008	−	0.157909i
$298$		−	21.8234i		−	1.26420i
$299$	−4.67333			−0.270266
$300$	18.8909	+	5.03311i	1.09066	+	0.290587i
$301$	6.68989	+	10.3603i	0.385599	+	0.597158i
$302$		−	26.1497i		−	1.50474i
$303$	0.859985			0.0494048
$304$	3.12270			0.179099
$305$	4.84388	+	0.634217i	0.277360	+	0.0363152i
$306$		−	10.9850i		−	0.627969i
$307$		−	18.2117i		−	1.03940i	−0.854349	−	0.519699i	$-0.826044\pi$
$307$		−	18.2117i		−	1.03940i	0.854349	−	0.519699i	$-0.173956\pi$
$308$	13.0110	−	31.7471i	0.741372	−	1.80896i
$309$	−1.85324			−0.105427
$310$	6.14927	−	46.9655i	0.349255	−	2.66746i
$311$			3.37193i			0.191205i	0.995420	+	0.0956024i	$0.0304777\pi$
$311$			3.37193i			0.191205i	−0.995420	+	0.0956024i	$0.969522\pi$
$312$		−	10.3794i		−	0.587617i
$313$	2.14358			0.121163			0.0605813	−	0.998163i	$-0.480705\pi$
$313$	2.14358			0.121163			0.0605813	+	0.998163i	$0.480705\pi$
$314$	−46.3651			−2.61653
$315$	2.53686	+	5.34456i	0.142936	+	0.301132i
$316$			17.3612i			0.976643i
$317$			27.5818i			1.54915i	0.632484	+	0.774574i	$0.282036\pi$
$317$			27.5818i			1.54915i	−0.632484	+	0.774574i	$0.717964\pi$
$318$			8.23652i			0.461881i
$319$	−10.8622	+	7.56725i	−0.608168	+	0.423684i
$320$	−19.9903	−	2.61736i	−1.11749	−	0.146315i
$321$	−9.90730			−0.552972
$322$	11.2963	−	7.29432i	0.629521	−	0.406497i
$323$			4.06879i			0.226394i
$324$	3.90997			0.217221
$325$	−2.87750	+	10.8002i	−0.159615	+	0.599085i
$326$			8.02005i			0.444190i
$327$		−	9.26520i		−	0.512367i
$328$	1.03240			0.0570045
$329$	−9.47963	−	14.6806i	−0.522629	−	0.809369i
$330$	8.29807	+	16.0060i	0.456794	+	0.881099i
$331$	34.7927			1.91238			0.956190	−	0.292746i	$-0.0945692\pi$
$331$	34.7927			1.91238			0.956190	+	0.292746i	$0.0945692\pi$
$332$			30.4778i			1.67268i
$333$			7.32857i			0.401603i
$334$			14.5871i			0.798169i
$335$	3.36712	−	25.7166i	0.183966	−	1.40505i
$336$	4.97724	+	7.70800i	0.271531	+	0.420506i
$337$	−22.2249			−1.21067			−0.605335	−	0.795971i	$-0.706961\pi$
$337$	−22.2249			−1.21067			−0.605335	+	0.795971i	$0.706961\pi$
$338$	−19.4558			−1.05826
$339$			17.4516i			0.947842i
$340$	−5.12883	+	39.1718i	−0.278150	+	2.12439i
$341$	23.7125	−	16.5195i	1.28410	−	0.894579i
$342$	−2.18903			−0.118369
$343$	−18.3142	+	2.75470i	−0.988876	+	0.148740i
$344$	−21.6432			−1.16692
$345$	−0.606895	+	4.63521i	−0.0326742	+	0.249551i
$346$		−	57.9388i		−	3.11481i
$347$	19.6744			1.05618			0.528089	−	0.849189i	$-0.322909\pi$
$347$	19.6744			1.05618			0.528089	+	0.849189i	$0.322909\pi$
$348$		−	15.6066i		−	0.836600i
$349$	−11.5710			−0.619384			−0.309692	−	0.950837i	$-0.600226\pi$
$349$	−11.5710			−0.619384			−0.309692	+	0.950837i	$0.600226\pi$
$350$	−9.90184	−	30.5974i	−0.529276	−	1.63550i
$351$			2.23538i			0.119316i
$352$	−1.62236	−	2.32878i	−0.0864722	−	0.124124i
$353$	6.04199			0.321582			0.160791	−	0.986988i	$-0.448595\pi$
$353$	6.04199			0.321582			0.160791	+	0.986988i	$0.448595\pi$
$354$			20.4292i			1.08580i
$355$	6.01126	+	0.787064i	0.319044	+	0.0417730i
$356$		−	7.43273i		−	0.393934i
$357$	−10.0433	+	6.48520i	−0.531548	+	0.343233i
$358$	−28.0356			−1.48173
$359$		−	33.7239i		−	1.77988i	−0.456079	−	0.889939i	$-0.650747\pi$
$359$		−	33.7239i		−	1.77988i	0.456079	−	0.889939i	$-0.349253\pi$
$360$	−10.2947	−	1.34790i	−0.542578	−	0.0710407i
$361$	−18.1892			−0.957326
$362$			40.8173i			2.14531i
$363$	−3.81151	+	10.3185i	−0.200053	+	0.541583i
$364$	−19.4266	+	12.5442i	−1.01823	+	0.657494i
$365$	1.26657	−	9.67351i	0.0662953	−	0.506335i
$366$	−5.31119			−0.277620
$367$	2.50137			0.130570			0.0652852	−	0.997867i	$-0.479204\pi$
$367$	2.50137			0.130570			0.0652852	+	0.997867i	$0.479204\pi$
$368$			7.25014i			0.377940i
$369$	−0.222345			−0.0115748
$370$	5.17191	−	39.5008i	0.268875	−	2.05355i
$371$	7.53046	−	4.86259i	0.390962	−	0.252453i
$372$			34.0695i			1.76642i
$373$	−35.4822			−1.83720			−0.918599	−	0.395190i	$-0.870679\pi$
$373$	−35.4822			−1.83720			−0.918599	+	0.395190i	$0.870679\pi$
$374$	−29.8940	+	20.8258i	−1.54578	+	1.07688i
$375$	10.3384	+	4.25656i	0.533871	+	0.219808i
$376$	30.6686			1.58161
$377$	8.92249			0.459532
$378$	−3.48907	−	5.40335i	−0.179458	−	0.277918i
$379$	9.73935			0.500277			0.250138	−	0.968210i	$-0.419524\pi$
$379$	9.73935			0.500277			0.250138	+	0.968210i	$0.419524\pi$
$380$	7.80598	+	1.02205i	0.400438	+	0.0524301i
$381$	−22.1655			−1.13557
$382$	20.6125			1.05462
$383$	−5.18157			−0.264766			−0.132383	−	0.991199i	$-0.542263\pi$
$383$	−5.18157			−0.264766			−0.132383	+	0.991199i	$0.542263\pi$
$384$	20.2073			1.03120
$385$	9.73494	−	17.0362i	0.496138	−	0.868244i
$386$	−39.9793			−2.03489
$387$	4.66125			0.236944
$388$	49.8314			2.52981
$389$	−14.9906			−0.760056			−0.380028	−	0.924975i	$-0.624086\pi$
$389$	−14.9906			−0.760056			−0.380028	+	0.924975i	$0.624086\pi$
$390$	1.57755	−	12.0487i	0.0798824	−	0.610107i
$391$	−9.44672			−0.477741
$392$	13.3739	−	29.6236i	0.675486	−	1.49622i
$393$	16.0202			0.808114
$394$	36.2098			1.82423
$395$	−1.28898	+	9.84464i	−0.0648554	+	0.495337i
$396$	−7.41272	−	10.6404i	−0.372503	−	0.534701i
$397$	23.1431			1.16152			0.580759	−	0.814076i	$-0.302756\pi$
$397$	23.1431			1.16152			0.580759	+	0.814076i	$0.302756\pi$
$398$			37.3034i			1.86985i
$399$	1.29234	+	2.00138i	0.0646979	+	0.100194i
$400$	16.7552	+	4.46410i	0.837760	+	0.223205i
$401$	1.67429			0.0836099			0.0418050	−	0.999126i	$-0.486689\pi$
$401$	1.67429			0.0836099			0.0418050	+	0.999126i	$0.486689\pi$
$402$			28.1976i			1.40637i
$403$	−19.4780			−0.970268
$404$	3.36252			0.167291
$405$	2.21714	+	0.290295i	0.110171	+	0.0144249i
$406$	−21.5674	+	13.9266i	−1.07037	+	0.691164i
$407$	19.9436	−	13.8939i	0.988569	−	0.688693i
$408$		−	20.9810i		−	1.03871i
$409$	26.0758			1.28937			0.644684	−	0.764449i	$-0.276989\pi$
$409$	26.0758			1.28937			0.644684	+	0.764449i	$0.276989\pi$
$410$	1.19843	+	0.156913i	0.0591863	+	0.00774936i
$411$		−	14.9090i		−	0.735409i
$412$	−7.24611			−0.356990
$413$	18.6780	−	12.0608i	0.919083	−	0.593474i
$414$		−	5.08239i		−	0.249786i
$415$	−2.26281	+	17.2824i	−0.111077	+	0.848359i
$416$			1.91292i			0.0937884i
$417$	18.2709			0.894729
$418$	4.15008	+	5.95713i	0.202987	+	0.291373i
$419$		−	8.14345i		−	0.397833i	−0.980016	−	0.198917i	$-0.936258\pi$
$419$		−	8.14345i		−	0.397833i	0.980016	−	0.198917i	$-0.0637423\pi$
$420$	9.91905	+	20.8971i	0.484000	+	1.01967i
$421$	7.65839			0.373247			0.186624	−	0.982431i	$-0.440246\pi$
$421$	7.65839			0.373247			0.186624	+	0.982431i	$0.440246\pi$
$422$			65.0332i			3.16577i
$423$	−6.60502			−0.321147
$424$			15.7315i			0.763990i
$425$	−5.81660	+	21.8315i	−0.282146	+	1.05898i
$426$	−6.59119			−0.319344
$427$	3.13557	+	4.85590i	0.151741	+	0.234993i
$428$	−38.7373			−1.87244
$429$	6.08326	−	4.23795i	0.293703	−	0.204610i
$430$	−25.1240	−	3.28953i	−1.21159	−	0.158635i
$431$			13.8325i			0.666288i	0.942876	+	0.333144i	$0.108109\pi$
$431$			13.8325i			0.666288i	−0.942876	+	0.333144i	$0.891891\pi$
$432$	3.46794			0.166851
$433$	27.4999			1.32156			0.660780	−	0.750580i	$-0.270226\pi$
$433$	27.4999			1.32156			0.660780	+	0.750580i	$0.270226\pi$
$434$	47.0820	−	30.4020i	2.26001	−	1.45934i
$435$	1.15871	−	8.84969i	0.0555557	−	0.424310i
$436$		−	36.2267i		−	1.73494i
$437$			1.88250i			0.0900521i
$438$			10.6068i			0.506811i
$439$	−40.1343			−1.91551			−0.957753	−	0.287591i	$-0.907146\pi$
$439$	−40.1343			−1.91551			−0.957753	+	0.287591i	$0.907146\pi$
$440$	15.8491	+	30.5709i	0.755575	+	1.45741i
$441$	−2.88031	+	6.37995i	−0.137158	+	0.303807i
$442$	24.5556			1.16799
$443$			33.7067i			1.60145i	0.599029	+	0.800727i	$0.295553\pi$
$443$			33.7067i			1.60145i	−0.599029	+	0.800727i	$0.704447\pi$
$444$			28.6545i			1.35988i
$445$	0.551840	−	4.21472i	0.0261597	−	0.199797i
$446$	65.2571			3.09001
$447$			8.97699i			0.424597i
$448$	−12.9402	−	20.0399i	−0.611368	−	0.946795i
$449$	−12.4875			−0.589320			−0.294660	−	0.955602i	$-0.595206\pi$
$449$	−12.4875			−0.589320			−0.294660	+	0.955602i	$0.595206\pi$
$450$	−11.7455	−	3.12936i	−0.553687	−	0.147519i
$451$	0.421532	+	0.605078i	0.0198491	+	0.0284920i
$452$			68.2353i			3.20952i
$453$			10.7566i			0.505387i
$454$			9.29519i			0.436245i
$455$	−11.9471	+	5.67085i	−0.560091	+	0.265854i
$456$	−4.18099			−0.195793
$457$	−5.91499			−0.276691			−0.138346	−	0.990384i	$-0.544179\pi$
$457$	−5.91499			−0.276691			−0.138346	+	0.990384i	$0.544179\pi$
$458$		−	15.3112i		−	0.715446i
$459$			4.51862i			0.210911i
$460$	−2.37294	+	18.1235i	−0.110639	+	0.845014i
$461$	24.6797			1.14945			0.574725	−	0.818346i	$-0.305109\pi$
$461$	24.6797			1.14945			0.574725	+	0.818346i	$0.305109\pi$
$462$	−8.08966	+	19.7389i	−0.376365	+	0.918338i
$463$		−	21.0685i		−	0.979137i	−0.871965	−	0.489568i	$-0.837154\pi$
$463$		−	21.0685i		−	0.979137i	0.871965	−	0.489568i	$-0.162846\pi$
$464$		−	13.8422i		−	0.642608i
$465$	−2.52948	+	19.3191i	−0.117302	+	0.895900i
$466$	−1.51604			−0.0702294
$467$	11.2951			0.522674			0.261337	−	0.965248i	$-0.415837\pi$
$467$	11.2951			0.522674			0.261337	+	0.965248i	$0.415837\pi$
$468$			8.74028i			0.404020i
$469$	25.7804	−	16.6470i	1.19043	−	0.768689i
$470$	35.6009	+	4.66129i	1.64215	+	0.215009i
$471$	19.0721			0.878795
$472$			39.0193i			1.79601i
$473$	−8.83702	−	12.6849i	−0.406327	−	0.583252i
$474$		−	10.7944i		−	0.495803i
$475$	4.35049	+	1.15910i	0.199614	+	0.0531834i
$476$	−39.2690	+	25.3569i	−1.79989	+	1.16223i
$477$		−	3.38806i		−	0.155129i
$478$			33.1759i			1.51743i
$479$	−26.9493			−1.23135			−0.615673	−	0.788002i	$-0.711116\pi$
$479$	−26.9493			−1.23135			−0.615673	+	0.788002i	$0.711116\pi$
$480$	1.89731	+	0.248418i	0.0865999	+	0.0113387i
$481$	−16.3822			−0.746962
$482$	4.97267			0.226499
$483$	−4.64671	+	3.00049i	−0.211433	+	0.136527i
$484$	−14.9029	+	40.3452i	−0.677405	+	1.83387i
$485$	28.2569	+	3.69972i	1.28308	+	0.167996i
$486$	−2.43104			−0.110274
$487$		−	40.3226i		−	1.82719i	−0.406626	−	0.913595i	$-0.633295\pi$
$487$		−	40.3226i		−	1.82719i	0.406626	−	0.913595i	$-0.366705\pi$
$488$	−10.1442			−0.459208
$489$		−	3.29902i		−	0.149187i
$490$	20.0273	−	32.3551i	0.904739	−	1.46165i
$491$			15.3176i			0.691275i	0.938368	+	0.345637i	$0.112337\pi$
$491$			15.3176i			0.691275i	−0.938368	+	0.345637i	$0.887663\pi$
$492$	−0.869361			−0.0391938
$493$	18.0360			0.812300
$494$		−	4.89333i		−	0.220161i
$495$	−3.41338	−	6.58398i	−0.153420	−	0.295928i
$496$			30.2178i			1.35682i
$497$	3.89124	+	6.02617i	0.174546	+	0.270311i
$498$		−	18.9497i		−	0.849156i
$499$	−35.2565			−1.57830			−0.789150	−	0.614201i	$-0.789478\pi$
$499$	−35.2565			−1.57830			−0.789150	+	0.614201i	$0.789478\pi$
$500$	40.4227	+	16.6430i	1.80776	+	0.744300i
$501$		−	6.00033i		−	0.268075i
$502$		−	37.5424i		−	1.67560i
$503$			4.01005i			0.178799i	0.995996	+	0.0893995i	$0.0284948\pi$
$503$			4.01005i			0.178799i	−0.995996	+	0.0893995i	$0.971505\pi$
$504$	−6.66403	−	10.3202i	−0.296839	−	0.459700i
$505$	1.90671	+	0.249649i	0.0848475	+	0.0111092i
$506$	−13.8310	+	9.63544i	−0.614861	+	0.428347i
$507$	8.00306			0.355429
$508$	−86.6663			−3.84520
$509$		−	22.0928i		−	0.979245i	−0.871934	−	0.489623i	$-0.837135\pi$
$509$		−	22.0928i		−	0.979245i	0.871934	−	0.489623i	$-0.162865\pi$
$510$	3.18888	−	24.3553i	0.141206	−	1.07847i
$511$	9.69752	−	6.26192i	0.428993	−	0.277011i
$512$	35.1725			1.55442
$513$	0.900450			0.0397558
$514$	29.8221			1.31539
$515$	−4.10890	−	0.537985i	−0.181060	−	0.0237065i
$516$	18.2253			0.802326
$517$	12.5221	+	17.9746i	0.550722	+	0.790521i
$518$	39.5988	−	25.5699i	1.73987	−	1.12348i
$519$			23.8329i			1.04615i
$520$	3.01308	−	23.0126i	0.132132	−	1.00917i
$521$			11.5287i			0.505083i	0.967586	+	0.252542i	$0.0812665\pi$
$521$			11.5287i			0.505083i	−0.967586	+	0.252542i	$0.918734\pi$
$522$			9.70346i			0.424709i
$523$		−	7.86287i		−	0.343819i	−0.985113	−	0.171910i	$-0.945006\pi$
$523$		−	7.86287i		−	0.343819i	0.985113	−	0.171910i	$-0.0549937\pi$
$524$	62.6387			2.73638
$525$	4.07308	+	12.5861i	0.177764	+	0.549303i
$526$	−72.7224			−3.17085
$527$	−39.3730			−1.71511
$528$	−6.57469	−	9.43748i	−0.286126	−	0.410713i
$529$	18.6293			0.809970
$530$	−2.39102	+	18.2615i	−0.103859	+	0.793231i
$531$		−	8.40349i		−	0.364680i
$532$	5.05301	+	7.82535i	0.219076	+	0.339272i
$533$		−	0.497025i		−	0.0215285i
$534$			4.62133i			0.199985i
$535$	−21.9659	−	2.87604i	−0.949669	−	0.124342i
$536$			53.8567i			2.32626i
$537$	11.5323			0.497657
$538$			59.1090i			2.54837i
$539$	22.8227	−	4.25709i	0.983045	−	0.183366i
$540$	8.66897	+	1.13504i	0.373053	+	0.0488445i
$541$		−	19.9882i		−	0.859358i	−0.902982	−	0.429679i	$-0.858627\pi$
$541$		−	19.9882i		−	0.859358i	0.902982	−	0.429679i	$-0.141373\pi$
$542$	13.8284			0.593982
$543$		−	16.7900i		−	0.720530i
$544$			3.86678i			0.165787i
$545$	2.68964	−	20.5423i	0.115211	−	0.879935i
$546$	12.0786	−	7.79941i	0.516914	−	0.333784i
$547$	19.6243			0.839074			0.419537	−	0.907738i	$-0.362193\pi$
$547$	19.6243			0.839074			0.419537	+	0.907738i	$0.362193\pi$
$548$		−	58.2939i		−	2.49019i
$549$	2.18474			0.0932423
$550$	13.7516	+	37.8964i	0.586369	+	1.61591i
$551$		−	3.59413i		−	0.153115i
$552$		−	9.70722i		−	0.413167i
$553$	−9.86907	+	6.37269i	−0.419675	+	0.270994i
$554$	42.1568			1.79107
$555$	−2.12744	+	16.2485i	−0.0903050	+	0.689710i
$556$	71.4387			3.02967
$557$	−7.42645			−0.314669			−0.157334	−	0.987545i	$-0.550290\pi$
$557$	−7.42645			−0.314669			−0.157334	+	0.987545i	$0.550290\pi$
$558$		−	21.1829i		−	0.896743i
$559$			10.4197i			0.440705i
$560$	8.79767	+	18.5346i	0.371769	+	0.783230i
$561$	12.2968	−	8.56662i	0.519170	−	0.361683i
$562$		−	19.5456i		−	0.824479i
$563$		−	22.7910i		−	0.960527i	−0.877124	−	0.480263i	$-0.840541\pi$
$563$		−	22.7910i		−	0.960527i	0.877124	−	0.480263i	$-0.159459\pi$
$564$	−25.8254			−1.08745
$565$	−5.06611	+	38.6927i	−0.213133	+	1.62782i
$566$			53.0606i			2.23030i
$567$	1.43522	+	2.22265i	0.0602734	+	0.0933424i
$568$	−12.5890			−0.528222
$569$		−	24.5518i		−	1.02927i	−0.857411	−	0.514633i	$-0.827928\pi$
$569$		−	24.5518i		−	1.02927i	0.857411	−	0.514633i	$-0.172072\pi$
$570$	−4.85340	−	0.635464i	−0.203287	−	0.0266167i
$571$			27.0927i			1.13379i	0.823789	+	0.566897i	$0.191856\pi$
$571$			27.0927i			1.13379i	−0.823789	+	0.566897i	$0.808144\pi$
$572$	23.7854	−	16.5703i	0.994517	−	0.692837i
$573$	−8.47885			−0.354209
$574$	0.775776	+	1.20141i	0.0323803	+	0.0501457i
$575$	−2.69115	+	10.1007i	−0.112229	+	0.421230i
$576$	−9.01623			−0.375676
$577$	−7.09032			−0.295174			−0.147587	−	0.989049i	$-0.547151\pi$
$577$	−7.09032			−0.295174			−0.147587	+	0.989049i	$0.547151\pi$
$578$	8.30917			0.345616
$579$	16.4453			0.683445
$580$	4.53051	−	34.6020i	0.188119	−	1.43677i
$581$	−17.3253	+	11.1873i	−0.718773	+	0.464129i
$582$	−30.9829			−1.28428
$583$	−9.22010	+	6.42325i	−0.381858	+	0.266024i
$584$			20.2586i			0.838308i
$585$	−0.648919	+	4.95617i	−0.0268295	+	0.204912i
$586$		−	16.5748i		−	0.684698i
$587$	−44.8736			−1.85213			−0.926067	−	0.377360i	$-0.876832\pi$
$587$	−44.8736			−1.85213			−0.926067	+	0.377360i	$0.876832\pi$
$588$	−11.2619	+	24.9454i	−0.464435	+	1.02873i
$589$			7.84606i			0.323291i
$590$	−5.93050	+	45.2946i	−0.244155	+	1.86475i
$591$	−14.8948			−0.612689
$592$			25.4150i			1.04455i
$593$		−	5.62319i		−	0.230917i	−0.993312	−	0.115458i	$-0.963166\pi$
$593$		−	5.62319i		−	0.230917i	0.993312	−	0.115458i	$-0.0368337\pi$
$594$	4.60889	+	6.61572i	0.189105	+	0.271446i
$595$	−24.1501	+	11.4631i	−0.990056	+	0.469941i
$596$			35.0998i			1.43774i
$597$		−	15.3446i		−	0.628013i
$598$	11.3611			0.464589
$599$	−28.4239			−1.16137			−0.580685	−	0.814128i	$-0.697215\pi$
$599$	−28.4239			−1.16137			−0.580685	+	0.814128i	$0.697215\pi$
$600$	−22.4335	−	5.97699i	−0.915846	−	0.244010i
$601$	−3.53417			−0.144162			−0.0720809	−	0.997399i	$-0.522964\pi$
$601$	−3.53417			−0.144162			−0.0720809	+	0.997399i	$0.522964\pi$
$602$	−16.2634	−	25.1863i	−0.662848	−	1.02652i
$603$		−	11.5990i		−	0.472347i
$604$			42.0579i			1.71131i
$605$	−11.4461	+	21.7712i	−0.465350	+	0.885127i
$606$	−2.09066			−0.0849273
$607$		−	2.43587i		−	0.0988688i	−0.998777	−	0.0494344i	$-0.984258\pi$
$607$		−	2.43587i		−	0.0988688i	0.998777	−	0.0494344i	$-0.0157419\pi$
$608$	0.770555			0.0312501
$609$	8.87165	−	5.72864i	0.359497	−	0.232136i
$610$	−11.7757	−	1.54181i	−0.476783	−	0.0624261i
$611$		−	14.7647i		−	0.597318i
$612$			17.6677i			0.714174i
$613$	12.3836			0.500167			0.250084	−	0.968224i	$-0.419542\pi$
$613$	12.3836			0.500167			0.250084	+	0.968224i	$0.419542\pi$
$614$			44.2735i			1.78673i
$615$	−0.492970	−	0.0645454i	−0.0198785	−	0.00260272i
$616$	−15.4510	+	37.7008i	−0.622540	+	1.51901i
$617$		−	38.2622i		−	1.54038i	−0.637815	−	0.770190i	$-0.720162\pi$
$617$		−	38.2622i		−	1.54038i	0.637815	−	0.770190i	$-0.279838\pi$
$618$	4.50531			0.181230
$619$		−	32.4381i		−	1.30380i	−0.758307	−	0.651898i	$-0.773973\pi$
$619$		−	32.4381i		−	1.30380i	0.758307	−	0.651898i	$-0.226027\pi$
$620$	−9.89019	+	75.5370i	−0.397200	+	3.03364i
$621$			2.09062i			0.0838937i
$622$		−	8.19731i		−	0.328682i
$623$	4.22518	−	2.72830i	0.169278	−	0.109307i
$624$			7.75217i			0.310335i
$625$	21.6860	+	12.4386i	0.867439	+	0.497543i
$626$	−5.21115			−0.208279
$627$	−1.70712	−	2.45044i	−0.0681757	−	0.0978612i
$628$	74.5713			2.97572
$629$	−33.1150			−1.32038
$630$	−6.16721	−	12.9929i	−0.245708	−	0.517648i
$631$	15.2295			0.606275			0.303138	−	0.952947i	$-0.401966\pi$
$631$	15.2295			0.606275			0.303138	+	0.952947i	$0.401966\pi$
$632$		−	20.6170i		−	0.820100i
$633$		−	26.7512i		−	1.06326i
$634$		−	67.0525i		−	2.66300i
$635$	−49.1440	−	6.43451i	−1.95022	−	0.255346i
$636$		−	13.2472i		−	0.525286i
$637$	−14.2616	−	6.43860i	−0.565067	−	0.255107i
$638$	26.4065	−	18.3963i	1.04544	−	0.728317i
$639$	2.71126			0.107256
$640$	44.8026	+	5.86608i	1.77098	+	0.231877i
$641$	2.85005			0.112570			0.0562850	−	0.998415i	$-0.482074\pi$
$641$	2.85005			0.112570			0.0562850	+	0.998415i	$0.482074\pi$
$642$	24.0851			0.950562
$643$	−40.5687			−1.59987			−0.799937	−	0.600084i	$-0.795134\pi$
$643$	−40.5687			−1.59987			−0.799937	+	0.600084i	$0.795134\pi$
$644$	−18.1685	+	11.7318i	−0.715939	+	0.462299i
$645$	10.3347	+	1.35313i	0.406927	+	0.0532796i
$646$		−	9.89141i		−	0.389172i
$647$	−8.32972			−0.327475			−0.163737	−	0.986504i	$-0.552355\pi$
$647$	−8.32972			−0.327475			−0.163737	+	0.986504i	$0.552355\pi$
$648$	−4.64322			−0.182403
$649$	−22.8688	+	15.9317i	−0.897681	+	0.625376i
$650$	6.99532	−	26.2557i	0.274379	−	1.02983i
$651$	−19.3670	+	12.5057i	−0.759053	+	0.490139i
$652$		−	12.8991i		−	0.505166i
$653$			8.10570i			0.317201i	0.987343	+	0.158600i	$0.0506981\pi$
$653$			8.10570i			0.317201i	−0.987343	+	0.158600i	$0.949302\pi$
$654$			22.5241i			0.880762i
$655$	35.5192	+	4.65059i	1.38785	+	0.181713i
$656$	−0.771077			−0.0301055
$657$		−	4.36305i		−	0.170219i
$658$	23.0454	+	35.6892i	0.898403	+	1.39131i
$659$		−	26.8215i		−	1.04482i	−0.852695	−	0.522409i	$-0.825034\pi$
$659$		−	26.8215i		−	1.04482i	0.852695	−	0.522409i	$-0.174966\pi$
$660$	−13.3462	−	25.7432i	−0.519500	−	1.00205i
$661$		−	33.5147i		−	1.30357i	−0.758404	−	0.651785i	$-0.774020\pi$
$661$		−	33.5147i		−	1.30357i	0.758404	−	0.651785i	$-0.225980\pi$
$662$	−84.5826			−3.28740
$663$	−10.1008			−0.392284
$664$		−	36.1934i		−	1.40458i
$665$	2.28431	+	4.81251i	0.0885819	+	0.186621i
$666$		−	17.8161i		−	0.690359i
$667$	8.34467			0.323107
$668$		−	23.4611i		−	0.907739i
$669$	−26.8433			−1.03782
$670$	−8.18562	+	62.5182i	−0.316238	+	2.41529i
$671$	−4.14193	−	5.94544i	−0.159898	−	0.229521i
$672$	1.22818	+	1.90202i	0.0473780	+	0.0733719i
$673$	29.6119			1.14145			0.570727	−	0.821140i	$-0.306661\pi$
$673$	29.6119			1.14145			0.570727	+	0.821140i	$0.306661\pi$
$674$	54.0298			2.08115
$675$	4.83146	+	1.28725i	0.185963	+	0.0495463i
$676$	31.2918			1.20353
$677$		−	36.4537i		−	1.40103i	−0.713638	−	0.700515i	$-0.752954\pi$
$677$		−	36.4537i		−	1.40103i	0.713638	−	0.700515i	$-0.247046\pi$
$678$		−	42.4256i		−	1.62935i
$679$	18.2914	+	28.3270i	0.701960	+	1.08709i
$680$	6.09066	−	46.5179i	0.233566	−	1.78388i
$681$		−	3.82354i		−	0.146518i
$682$	−57.6461	+	40.1595i	−2.20738	+	1.53779i
$683$		−	50.6338i		−	1.93745i	−0.248140	−	0.968724i	$-0.579819\pi$
$683$		−	50.6338i		−	1.93745i	0.248140	−	0.968724i	$-0.420181\pi$
$684$	3.52073			0.134619
$685$	4.32801	−	33.0555i	0.165365	−	1.26299i
$686$	44.5227	−	6.69678i	1.69989	−	0.255684i
$687$			6.29821i			0.240292i
$688$	16.1649			0.616281
$689$	7.57361			0.288531
$690$	1.47539	−	11.2684i	0.0561671	−	0.428980i
$691$			37.3838i			1.42215i	0.703117	+	0.711074i	$0.251791\pi$
$691$			37.3838i			1.42215i	−0.703117	+	0.711074i	$0.748209\pi$
$692$			93.1859i			3.54240i
$693$	3.32765	−	8.11953i	0.126407	−	0.308435i
$694$	−47.8293			−1.81558
$695$	40.5092	+	5.30394i	1.53660	+	0.201190i
$696$			18.5333i			0.702505i
$697$		−	1.00469i		−	0.0380554i
$698$	28.1297			1.06473
$699$	0.623619			0.0235874
$700$	15.9256	+	49.2113i	0.601933	+	1.86001i
$701$		−	10.3258i		−	0.390001i	−0.980803	−	0.195001i	$-0.937529\pi$
$701$		−	10.3258i		−	0.390001i	0.980803	−	0.195001i	$-0.0624709\pi$
$702$		−	5.43431i		−	0.205105i
$703$			6.59901i			0.248886i
$704$	17.0934	+	24.5363i	0.644232	+	0.924747i
$705$	−14.6443	−	1.91740i	−0.551536	−	0.0722135i
$706$	−14.6883			−0.552803
$707$	1.23426	+	1.91144i	0.0464193	+	0.0718872i
$708$		−	32.8574i		−	1.23486i
$709$	−32.1746			−1.20834			−0.604170	−	0.796855i	$-0.706495\pi$
$709$	−32.1746			−1.20834			−0.604170	+	0.796855i	$0.706495\pi$
$710$	−14.6136	−	1.91339i	−0.548440	−	0.0718082i
$711$			4.44023i			0.166522i
$712$			8.82662i			0.330791i
$713$	−18.2166			−0.682217
$714$	24.4157	−	15.7658i	0.913734	−	0.590020i
$715$	14.7177	−	7.63020i	0.550412	−	0.285353i
$716$	45.0911			1.68514
$717$		−	13.6468i		−	0.509649i
$718$			81.9842i			3.05962i
$719$		−	18.9928i		−	0.708311i	−0.935187	−	0.354156i	$-0.884768\pi$
$719$		−	18.9928i		−	0.708311i	0.935187	−	0.354156i	$-0.115232\pi$
$720$	7.68892	+	1.00672i	0.286549	+	0.0375184i
$721$	−2.65980	−	4.11910i	−0.0990561	−	0.153403i
$722$	44.2187			1.64565
$723$	−2.04549			−0.0760725
$724$		−	65.6486i		−	2.43981i
$725$	5.13803	−	19.2847i	0.190822	−	0.716215i
$726$	9.26595	−	25.0848i	0.343892	−	0.930985i
$727$	2.78810			0.103405			0.0517025	−	0.998663i	$-0.483535\pi$
$727$	2.78810			0.103405			0.0517025	+	0.998663i	$0.483535\pi$
$728$	23.0697	−	14.8967i	0.855020	−	0.552107i
$729$	1.00000			0.0370370
$730$	−3.07909	+	23.5167i	−0.113962	+	0.870393i
$731$			21.0624i			0.779021i
$732$	8.54226			0.315731
$733$			37.8437i			1.39779i	0.715225	+	0.698894i	$0.246324\pi$
$733$			37.8437i			1.39779i	−0.715225	+	0.698894i	$0.753676\pi$
$734$	−6.08094			−0.224452
$735$	−8.23813	+	13.3091i	−0.303868	+	0.490915i
$736$			1.78904i			0.0659447i
$737$	−31.5649	+	21.9899i	−1.16271	+	0.810009i
$738$	0.540529			0.0198972
$739$		−	30.5762i		−	1.12476i	−0.826878	−	0.562381i	$-0.809885\pi$
$739$		−	30.5762i		−	1.12476i	0.826878	−	0.562381i	$-0.190115\pi$
$740$	−8.31825	+	63.5312i	−0.305785	+	2.33545i
$741$			2.01285i			0.0739439i
$742$	−18.3069	+	11.8212i	−0.672066	+	0.433969i
$743$	−30.0083			−1.10090			−0.550448	−	0.834869i	$-0.685543\pi$
$743$	−30.0083			−1.10090			−0.550448	+	0.834869i	$0.685543\pi$
$744$		−	40.4587i		−	1.48329i
$745$	−2.60597	+	19.9033i	−0.0954754	+	0.729200i
$746$	86.2588			3.15816
$747$			7.79488i			0.285200i
$748$	48.0800	−	33.4953i	1.75798	−	1.22471i
$749$	−14.2191	−	22.0204i	−0.519555	−	0.804609i
$750$	−25.1330	−	10.3479i	−0.917727	−	0.377852i
$751$	43.9821			1.60493			0.802465	−	0.596699i	$-0.203521\pi$
$751$	43.9821			1.60493			0.802465	+	0.596699i	$0.203521\pi$
$752$	−22.9058			−0.835288
$753$			15.4429i			0.562771i
$754$	−21.6910			−0.789938
$755$	−3.12257	+	23.8489i	−0.113642	+	0.867949i
$756$	5.61165	+	8.69048i	0.204094	+	0.316070i
$757$			19.6883i			0.715583i	0.933801	+	0.357792i	$0.116470\pi$
$757$			19.6883i			0.715583i	−0.933801	+	0.357792i	$0.883530\pi$
$758$	−23.6768			−0.859979
$759$	5.68931	−	3.96350i	0.206509	−	0.143866i
$760$	−9.26986	−	1.21372i	−0.336253	−	0.0440262i
$761$	6.41086			0.232393			0.116197	−	0.993226i	$-0.462930\pi$
$761$	6.41086			0.232393			0.116197	+	0.993226i	$0.462930\pi$
$762$	53.8852			1.95205
$763$	20.5933	−	13.2976i	0.745526	−	0.481404i
$764$	−33.1521			−1.19940
$765$	−1.31173	+	10.0184i	−0.0474257	+	0.362217i
$766$	12.5966			0.455135
$767$	18.7850			0.678287
$768$	−31.0925			−1.12195
$769$	49.6557			1.79063			0.895314	−	0.445435i	$-0.146951\pi$
$769$	49.6557			1.79063			0.895314	+	0.445435i	$0.146951\pi$
$770$	−23.6661	+	41.4157i	−0.852865	+	1.49252i
$771$	−12.2672			−0.441792
$772$	64.3008			2.31424
$773$	−32.8350			−1.18099			−0.590497	−	0.807040i	$-0.701068\pi$
$773$	−32.8350			−1.18099			−0.590497	+	0.807040i	$0.701068\pi$
$774$	−11.3317			−0.407309
$775$	−11.2164	+	42.0989i	−0.402906	+	1.51224i
$776$	−59.1765			−2.12431
$777$	−16.2888	+	10.5181i	−0.584358	+	0.377334i
$778$	36.4429			1.30654
$779$	−0.200210			−0.00717327
$780$	−2.53726	+	19.3785i	−0.0908484	+	0.693861i
$781$	−5.14014	−	7.37830i	−0.183929	−	0.264016i
$782$	22.9654			0.821240
$783$		−	3.99148i		−	0.142644i
$784$	−9.98874	+	22.1253i	−0.356741	+	0.790188i
$785$	42.2856	+	5.53652i	1.50924	+	0.197607i
$786$	−38.9459			−1.38915
$787$		−	55.7000i		−	1.98549i	−0.120239	−	0.992745i	$-0.538366\pi$
$787$		−	55.7000i		−	1.98549i	0.120239	−	0.992745i	$-0.461634\pi$
$788$	−58.2381			−2.07465
$789$	29.9141			1.06497
$790$	3.13356	−	23.9327i	0.111487	−	0.851489i
$791$	−38.7888	+	25.0468i	−1.37917	+	0.890563i
$792$	8.80285	+	12.6358i	0.312796	+	0.448995i
$793$			4.88372i			0.173426i
$794$	−56.2618			−1.99666
$795$	0.983535	−	7.51182i	0.0348824	−	0.266417i
$796$		−	59.9970i		−	2.12654i
$797$	40.5772			1.43732			0.718659	−	0.695363i	$-0.244756\pi$
$797$	40.5772			1.43732			0.718659	+	0.695363i	$0.244756\pi$
$798$	−3.14174	−	4.86545i	−0.111216	−	0.172235i
$799$		−	29.8456i		−	1.05586i
$800$	4.13449	+	1.10156i	0.146176	+	0.0389459i
$801$		−	1.90097i		−	0.0671674i
$802$	−4.07027			−0.143726
$803$	−11.8734	+	8.27168i	−0.419003	+	0.291901i
$804$		−	45.3517i		−	1.59943i
$805$	−11.1734	+	5.30361i	−0.393812	+	0.186928i
$806$	47.3518			1.66790
$807$		−	24.3142i		−	0.855902i
$808$	−3.99310			−0.140477
$809$			29.5534i			1.03904i	0.854458	+	0.519521i	$0.173889\pi$
$809$			29.5534i			1.03904i	−0.854458	+	0.519521i	$0.826111\pi$
$810$	−5.38997	−	0.705719i	−0.189384	−	0.0247964i
$811$	−23.1028			−0.811248			−0.405624	−	0.914040i	$-0.632946\pi$
$811$	−23.1028			−0.811248			−0.405624	+	0.914040i	$0.632946\pi$
$812$	34.6879	−	22.3988i	1.21731	−	0.786044i
$813$	−5.68827			−0.199496
$814$	−48.4838	+	33.7766i	−1.69936	+	1.18387i
$815$	0.957686	−	7.31439i	0.0335463	−	0.256212i
$816$			15.6703i			0.548570i
$817$	4.19722			0.146842
$818$	−63.3915			−2.21643
$819$	−4.96846	+	3.20826i	−0.173612	+	0.112106i
$820$	−1.92750	−	0.252371i	−0.0673112	−	0.00881317i
$821$		−	2.22635i		−	0.0777003i	−0.999245	−	0.0388501i	$-0.987631\pi$
$821$		−	2.22635i		−	0.0777003i	0.999245	−	0.0388501i	$-0.0123695\pi$
$822$			36.2445i			1.26417i
$823$			19.2519i			0.671080i	0.942026	+	0.335540i	$0.108919\pi$
$823$			19.2519i			0.671080i	−0.942026	+	0.335540i	$0.891081\pi$
$824$	8.60501			0.299770
$825$	−5.65666	−	15.5885i	−0.196939	−	0.542723i
$826$	−45.4070	+	29.3204i	−1.57991	+	1.02019i
$827$	6.05218			0.210455			0.105227	−	0.994448i	$-0.466443\pi$
$827$	6.05218			0.210455			0.105227	+	0.994448i	$0.466443\pi$
$828$			8.17426i			0.284075i
$829$			0.890443i			0.0309264i	0.999880	+	0.0154632i	$0.00492228\pi$
$829$			0.890443i			0.0309264i	−0.999880	+	0.0154632i	$0.995078\pi$
$830$	5.50099	−	42.0142i	0.190942	−	1.45833i
$831$	−17.3410			−0.601554
$832$		−	20.1547i		−	0.698739i
$833$	−28.8286	−	13.0150i	−0.998852	−	0.450944i
$834$	−44.4173			−1.53805
$835$	1.74186	−	13.3036i	0.0602797	−	0.460390i
$836$	−6.67478	−	9.58116i	−0.230852	−	0.331371i
$837$			8.71349i			0.301182i
$838$			19.7971i			0.683878i
$839$		−	28.2528i		−	0.975394i	−0.873013	−	0.487697i	$-0.837837\pi$
$839$		−	28.2528i		−	0.975394i	0.873013	−	0.487697i	$-0.162163\pi$
$840$	−11.7792	−	24.8160i	−0.406421	−	0.856234i
$841$	13.0681			0.450623
$842$	−18.6179			−0.641615
$843$			8.03999i			0.276912i
$844$		−	104.596i		−	3.60035i
$845$	17.7439	+	2.32325i	0.610410	+	0.0799221i
$846$	16.0571			0.552054
$847$	−28.4048	+	6.33769i	−0.976001	+	0.217766i
$848$		−	11.7496i		−	0.403482i
$849$		−	21.8263i		−	0.749076i
$850$	14.1404	−	53.0734i	0.485012	−	1.82040i
$851$	−15.3213			−0.525206
$852$	10.6010			0.363183
$853$		−	26.7330i		−	0.915319i	−0.889127	−	0.457660i	$-0.848688\pi$
$853$		−	26.7330i		−	0.915319i	0.889127	−	0.457660i	$-0.151312\pi$
$854$	−7.62271	−	11.8049i	−0.260844	−	0.403955i
$855$	1.99643	+	0.261396i	0.0682764	+	0.00893955i
$856$	46.0018			1.57231
$857$			43.2637i			1.47786i	0.673783	+	0.738929i	$0.264668\pi$
$857$			43.2637i			1.47786i	−0.673783	+	0.738929i	$0.735332\pi$
$858$	−14.7887	+	10.3026i	−0.504877	+	0.351726i
$859$			24.4844i			0.835398i	0.908586	+	0.417699i	$0.137163\pi$
$859$			24.4844i			0.835398i	−0.908586	+	0.417699i	$0.862837\pi$
$860$	40.4082	+	5.29072i	1.37791	+	0.180412i
$861$	−0.319112	−	0.494193i	−0.0108753	−	0.0168421i
$862$		−	33.6274i		−	1.14535i
$863$		−	9.43459i		−	0.321157i	−0.987023	−	0.160579i	$-0.948664\pi$
$863$		−	9.43459i		−	0.321157i	0.987023	−	0.160579i	$-0.0513360\pi$
$864$	0.855744			0.0291130
$865$	−6.91855	+	52.8409i	−0.235238	+	1.79665i
$866$	−66.8534			−2.27177
$867$	−3.41794			−0.116079
$868$	−75.7244	+	48.8971i	−2.57026	+	1.65968i
$869$	12.0834	−	8.41801i	0.409902	−	0.285561i
$870$	−2.81686	+	21.5140i	−0.0955006	+	0.729392i
$871$	25.9282			0.878543
$872$			43.0204i			1.45686i
$873$	12.7447			0.431343
$874$		−	4.57644i		−	0.154800i
$875$	5.37694	+	29.0876i	0.181774	+	0.983340i
$876$		−	17.0594i		−	0.576384i
$877$	−0.638445			−0.0215588			−0.0107794	−	0.999942i	$-0.503431\pi$
$877$	−0.638445			−0.0215588			−0.0107794	+	0.999942i	$0.503431\pi$
$878$	97.5683			3.29277
$879$			6.81797i			0.229964i
$880$	−11.8374	−	22.8328i	−0.399038	−	0.769695i
$881$			28.7520i			0.968681i	0.874880	+	0.484340i	$0.160940\pi$
$881$			28.7520i			0.968681i	−0.874880	+	0.484340i	$0.839060\pi$
$882$	7.00216	−	15.5099i	0.235775	−	0.522247i
$883$		−	47.7250i		−	1.60607i	−0.595929	−	0.803037i	$-0.703216\pi$
$883$		−	47.7250i		−	1.60607i	0.595929	−	0.803037i	$-0.296784\pi$
$884$	−39.4940			−1.32833
$885$	2.43949	−	18.6317i	0.0820024	−	0.626299i
$886$		−	81.9425i		−	2.75291i
$887$		−	44.1371i		−	1.48198i	−0.671518	−	0.740989i	$-0.734357\pi$
$887$		−	44.1371i		−	1.48198i	0.671518	−	0.740989i	$-0.265643\pi$
$888$		−	34.0282i		−	1.14191i
$889$	−31.8122	−	49.2660i	−1.06695	−	1.65233i
$890$	−1.34155	+	10.2462i	−0.0449688	+	0.343452i
$891$	−1.89585	−	2.72135i	−0.0635133	−	0.0911687i
$892$	−104.956			−3.51420
$893$	−5.94749			−0.199025
$894$		−	21.8234i		−	0.729885i
$895$	25.5689	+	3.34778i	0.854673	+	0.111904i
$896$	29.0019	+	44.9138i	0.968886	+	1.50046i
$897$	−4.67333			−0.156038
$898$	30.3576			1.01305
$899$	34.7797			1.15997
$900$	18.8909	+	5.03311i	0.629696	+	0.167770i
$901$	15.3094			0.510029
$902$	−1.02476	−	1.47097i	−0.0341208	−	0.0489779i
$903$	6.68989	+	10.3603i	0.222626	+	0.344769i
$904$		−	81.0318i		−	2.69508i
$905$	4.87406	−	37.2260i	0.162019	−	1.23743i
$906$		−	26.1497i		−	0.868765i
$907$		−	1.88919i		−	0.0627295i	−0.999508	−	0.0313647i	$-0.990015\pi$
$907$		−	1.88919i		−	0.0627295i	0.999508	−	0.0313647i	$-0.00998534\pi$
$908$		−	14.9499i		−	0.496131i
$909$	0.859985			0.0285239
$910$	29.0440	−	13.7861i	0.962800	−	0.457004i
$911$	−34.4840			−1.14251			−0.571253	−	0.820774i	$-0.693542\pi$
$911$	−34.4840			−1.14251			−0.571253	+	0.820774i	$0.693542\pi$
$912$	3.12270			0.103403
$913$	21.2126	−	14.7779i	0.702035	−	0.489078i
$914$	14.3796			0.475635
$915$	4.84388	+	0.634217i	0.160134	+	0.0209666i
$916$			24.6258i			0.813660i
$917$	22.9925	+	35.6073i	0.759279	+	1.17586i
$918$		−	10.9850i		−	0.362558i
$919$			31.2719i			1.03156i	0.856720	+	0.515782i	$0.172499\pi$
$919$			31.2719i			1.03156i	−0.856720	+	0.515782i	$0.827501\pi$
$920$	2.81795	−	21.5223i	0.0929051	−	0.709569i
$921$		−	18.2117i		−	0.600097i
$922$	−59.9975			−1.97591
$923$			6.06071i			0.199491i
$924$	13.0110	−	31.7471i	0.428031	−	1.04440i
$925$	−9.43370	+	35.4077i	−0.310178	+	1.16420i
$926$			51.2185i			1.68314i
$927$	−1.85324			−0.0608684
$928$		−	3.41569i		−	0.112125i
$929$			20.2079i			0.663000i	0.943455	+	0.331500i	$0.107555\pi$
$929$			20.2079i			0.663000i	−0.943455	+	0.331500i	$0.892445\pi$
$930$	6.14927	−	46.9655i	0.201643	−	1.54006i
$931$	−2.59358	+	5.74483i	−0.0850011	+	0.188279i
$932$	2.43833			0.0798702
$933$			3.37193i			0.110392i
$934$	−27.4588			−0.898481
$935$	29.7505	−	15.4238i	0.972947	−	0.504411i
$936$		−	10.3794i		−	0.339261i
$937$		−	7.50320i		−	0.245119i	−0.992461	−	0.122559i	$-0.960890\pi$
$937$		−	7.50320i		−	0.245119i	0.992461	−	0.122559i	$-0.0391102\pi$
$938$	−62.6734	+	40.4697i	−2.04636	+	1.32138i
$939$	2.14358			0.0699532
$940$	−57.2587	−	7.49699i	−1.86757	−	0.244525i
$941$	−27.6846			−0.902493			−0.451246	−	0.892399i	$-0.649020\pi$
$941$	−27.6846			−0.902493			−0.451246	+	0.892399i	$0.649020\pi$
$942$	−46.3651			−1.51066
$943$		−	0.464838i		−	0.0151372i
$944$		−	29.1428i		−	0.948516i
$945$	2.53686	+	5.34456i	0.0825240	+	0.173859i
$946$	21.4832	+	30.8375i	0.698478	+	1.00261i
$947$		−	25.2758i		−	0.821352i	−0.911781	−	0.410676i	$-0.865293\pi$
$947$		−	25.2758i		−	0.821352i	0.911781	−	0.410676i	$-0.134707\pi$
$948$			17.3612i			0.563865i
$949$	9.75309			0.316599
$950$	−10.5762	−	2.81783i	−0.343138	−	0.0914226i
$951$			27.5818i			0.894401i
$952$	46.6333	−	30.1122i	1.51139	−	0.975943i
$953$	0.370486			0.0120012			0.00600062	−	0.999982i	$-0.498090\pi$
$953$	0.370486			0.0120012			0.00600062	+	0.999982i	$0.498090\pi$
$954$			8.23652i			0.266667i
$955$	−18.7988	−	2.46136i	−0.608316	−	0.0796479i
$956$		−	53.3586i		−	1.72574i
$957$	−10.8622	+	7.56725i	−0.351126	+	0.244614i
$958$	65.5150			2.11669
$959$	33.1375	−	21.3977i	1.07007	−	0.690967i
$960$	−19.9903	−	2.61736i	−0.645183	−	0.0844750i
$961$	−44.9249			−1.44919
$962$	39.8257			1.28403
$963$	−9.90730			−0.319258
$964$	−7.99780			−0.257592
$965$	36.4617	+	4.77399i	1.17374	+	0.153680i
$966$	11.2963	−	7.29432i	0.363454	−	0.234691i
$967$	26.9429			0.866424			0.433212	−	0.901292i	$-0.357380\pi$
$967$	26.9429			0.866424			0.433212	+	0.901292i	$0.357380\pi$
$968$	17.6977	−	47.9113i	0.568826	−	1.53993i
$969$			4.06879i			0.130708i
$970$	−68.6936	−	8.99418i	−2.20562	−	0.288786i
$971$		−	47.1845i		−	1.51422i	−0.653286	−	0.757111i	$-0.726610\pi$
$971$		−	47.1845i		−	1.51422i	0.653286	−	0.757111i	$-0.273390\pi$
$972$	3.90997			0.125412
$973$	26.2227	+	40.6097i	0.840660	+	1.30189i
$974$			98.0259i			3.14095i
$975$	−2.87750	+	10.8002i	−0.0921536	+	0.345882i
$976$	7.57653			0.242519
$977$		−	43.8326i		−	1.40233i	−0.712999	−	0.701165i	$-0.752664\pi$
$977$		−	43.8326i		−	1.40233i	0.712999	−	0.701165i	$-0.247336\pi$
$978$			8.02005i			0.256453i
$979$	−5.17320	+	3.60395i	−0.165336	+	0.115183i
$980$	−32.2109	+	52.0384i	−1.02894	+	1.66230i
$981$		−	9.26520i		−	0.295815i
$982$		−	37.2378i		−	1.18831i
$983$	−10.2359			−0.326475			−0.163238	−	0.986587i	$-0.552194\pi$
$983$	−10.2359			−0.326475			−0.163238	+	0.986587i	$0.552194\pi$
$984$	1.03240			0.0329116
$985$	−33.0239	−	4.32387i	−1.05223	−	0.137770i
$986$	−43.8463			−1.39635
$987$	−9.47963	−	14.6806i	−0.301740	−	0.467289i
$988$			7.87019i			0.250384i
$989$			9.74489i			0.309870i
$990$	8.29807	+	16.0060i	0.263730	+	0.508703i
$991$	31.3439			0.995673			0.497837	−	0.867271i	$-0.334128\pi$
$991$	31.3439			0.995673			0.497837	+	0.867271i	$0.334128\pi$
$992$			7.45652i			0.236745i
$993$	34.7927			1.10411
$994$	−9.45978	−	14.6499i	−0.300046	−	0.464666i
$995$	4.45445	−	34.0212i	0.141216	−	1.07854i
$996$			30.4778i			0.965725i
$997$			46.4651i			1.47156i	0.677219	+	0.735782i	$0.263185\pi$
$997$			46.4651i			1.47156i	−0.677219	+	0.735782i	$0.736815\pi$
$998$	85.7102			2.71311
$999$			7.32857i			0.231866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.k.b.769.5	yes	48
5.4	even	2		1155.2.k.a.769.44	yes	48
7.6	odd	2		1155.2.k.a.769.6	yes	48
11.10	odd	2	inner	1155.2.k.b.769.44	yes	48
35.34	odd	2	inner	1155.2.k.b.769.43	yes	48
55.54	odd	2		1155.2.k.a.769.5	✓	48
77.76	even	2		1155.2.k.a.769.43	yes	48
385.384	even	2	inner	1155.2.k.b.769.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.k.a.769.5	✓	48	55.54	odd	2
1155.2.k.a.769.6	yes	48	7.6	odd	2
1155.2.k.a.769.43	yes	48	77.76	even	2
1155.2.k.a.769.44	yes	48	5.4	even	2
1155.2.k.b.769.5	yes	48	1.1	even	1	trivial
1155.2.k.b.769.6	yes	48	385.384	even	2	inner
1155.2.k.b.769.43	yes	48	35.34	odd	2	inner
1155.2.k.b.769.44	yes	48	11.10	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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.43104 q^{2} +1.00000 q^{3} +3.90997 q^{4} +(2.21714 + 0.290295i) q^{5} -2.43104 q^{6} +(1.43522 + 2.22265i) q^{7} -4.64322 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.43104 q^{2} +1.00000 q^{3} +3.90997 q^{4} +(2.21714 + 0.290295i) q^{5} -2.43104 q^{6} +(1.43522 + 2.22265i) q^{7} -4.64322 q^{8} +1.00000 q^{9} +(-5.38997 - 0.705719i) q^{10} +(-1.89585 - 2.72135i) q^{11} +3.90997 q^{12} +2.23538i q^{13} +(-3.48907 - 5.40335i) q^{14} +(2.21714 + 0.290295i) q^{15} +3.46794 q^{16} +4.51862i q^{17} -2.43104 q^{18} +0.900450 q^{19} +(8.66897 + 1.13504i) q^{20} +(1.43522 + 2.22265i) q^{21} +(4.60889 + 6.61572i) q^{22} +2.09062i q^{23} -4.64322 q^{24} +(4.83146 + 1.28725i) q^{25} -5.43431i q^{26} +1.00000 q^{27} +(5.61165 + 8.69048i) q^{28} -3.99148i q^{29} +(-5.38997 - 0.705719i) q^{30} +8.71349i q^{31} +0.855744 q^{32} +(-1.89585 - 2.72135i) q^{33} -10.9850i q^{34} +(2.53686 + 5.34456i) q^{35} +3.90997 q^{36} +7.32857i q^{37} -2.18903 q^{38} +2.23538i q^{39} +(-10.2947 - 1.34790i) q^{40} -0.222345 q^{41} +(-3.48907 - 5.40335i) q^{42} +4.66125 q^{43} +(-7.41272 - 10.6404i) q^{44} +(2.21714 + 0.290295i) q^{45} -5.08239i q^{46} -6.60502 q^{47} +3.46794 q^{48} +(-2.88031 + 6.37995i) q^{49} +(-11.7455 - 3.12936i) q^{50} +4.51862i q^{51} +8.74028i q^{52} -3.38806i q^{53} -2.43104 q^{54} +(-3.41338 - 6.58398i) q^{55} +(-6.66403 - 10.3202i) q^{56} +0.900450 q^{57} +9.70346i q^{58} -8.40349i q^{59} +(8.66897 + 1.13504i) q^{60} +2.18474 q^{61} -21.1829i q^{62} +(1.43522 + 2.22265i) q^{63} -9.01623 q^{64} +(-0.648919 + 4.95617i) q^{65} +(4.60889 + 6.61572i) q^{66} -11.5990i q^{67} +17.6677i q^{68} +2.09062i q^{69} +(-6.16721 - 12.9929i) q^{70} +2.71126 q^{71} -4.64322 q^{72} -4.36305i q^{73} -17.8161i q^{74} +(4.83146 + 1.28725i) q^{75} +3.52073 q^{76} +(3.32765 - 8.11953i) q^{77} -5.43431i q^{78} +4.44023i q^{79} +(7.68892 + 1.00672i) q^{80} +1.00000 q^{81} +0.540529 q^{82} +7.79488i q^{83} +(5.61165 + 8.69048i) q^{84} +(-1.31173 + 10.0184i) q^{85} -11.3317 q^{86} -3.99148i q^{87} +(8.80285 + 12.6358i) q^{88} -1.90097i q^{89} +(-5.38997 - 0.705719i) q^{90} +(-4.96846 + 3.20826i) q^{91} +8.17426i q^{92} +8.71349i q^{93} +16.0571 q^{94} +(1.99643 + 0.261396i) q^{95} +0.855744 q^{96} +12.7447 q^{97} +(7.00216 - 15.5099i) q^{98} +(-1.89585 - 2.72135i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9}+O(q^{10}) \) 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9	\( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9} + 48 q^{12} - 4 q^{15} + 40 q^{16} - 18 q^{20} + 20 q^{25} + 48 q^{27} + 48 q^{36} - 20 q^{38} - 16 q^{44} - 4 q^{45} + 8 q^{47} + 40 q^{48} + 24 q^{49} - 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} + 20 q^{75} - 32 q^{77} - 46 q^{80} + 48 q^{81} - 32 q^{82} - 16 q^{86} + 68 q^{97}+O(q^{100}) \) 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9 + 48 * q^12 - 4 * q^15 + 40 * q^16 - 18 * q^20 + 20 * q^25 + 48 * q^27 + 48 * q^36 - 20 * q^38 - 16 * q^44 - 4 * q^45 + 8 * q^47 + 40 * q^48 + 24 * q^49 - 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 + 20 * q^75 - 32 * q^77 - 46 * q^80 + 48 * q^81 - 32 * q^82 - 16 * q^86 + 68 * q^97

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