LMFDB - Embedded newform 950.2.bb.b.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			193.2
Character	$\chi$	$=$	950.193
Dual form			950.2.bb.b.507.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0871557 - 0.996195i) q^{2} +(0.794263 - 1.70330i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(3.18056 + 0.852228i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-0.342020 - 0.407604i) q^{9} +O(q^{10})$	\(q+(-0.0871557 - 0.996195i) q^{2} +(0.794263 - 1.70330i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(3.18056 + 0.852228i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-0.342020 - 0.407604i) q^{9} +(0.892233 - 1.54539i) q^{11} +(-0.486421 + 1.81535i) q^{12} +(0.0794377 - 0.0370424i) q^{13} +(0.571781 - 3.24273i) q^{14} +(0.939693 - 0.342020i) q^{16} +(4.66301 - 0.407961i) q^{17} +(-0.376244 + 0.376244i) q^{18} +(-2.36507 - 3.66148i) q^{19} +(3.97780 - 4.74056i) q^{21} +(-1.61728 - 0.754148i) q^{22} +(-2.70748 + 3.86668i) q^{23} +(1.85083 + 0.326352i) q^{24} +(-0.0438249 - 0.0759070i) q^{26} +(4.48011 - 1.20044i) q^{27} +(-3.28023 - 0.286983i) q^{28} +(1.51413 - 1.27051i) q^{29} +(6.29770 - 3.63598i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(-1.92360 - 2.74719i) q^{33} +(-0.812817 - 4.60971i) q^{34} +(0.407604 + 0.342020i) q^{36} +(0.443988 + 0.443988i) q^{37} +(-3.44142 + 2.67519i) q^{38} -0.164728i q^{39} +(-1.43910 - 3.95390i) q^{41} +(-5.06920 - 3.54950i) q^{42} +(-4.66363 + 3.26551i) q^{43} +(-0.610323 + 1.67685i) q^{44} +(4.08794 + 2.36017i) q^{46} +(0.0133439 - 0.152522i) q^{47} +(0.163799 - 1.87223i) q^{48} +(3.32748 + 1.92112i) q^{49} +(3.00878 - 8.26654i) q^{51} +(-0.0717985 + 0.0502739i) q^{52} +(-3.78609 - 2.65105i) q^{53} +(-1.58634 - 4.35844i) q^{54} +3.29276i q^{56} +(-8.11509 + 1.12026i) q^{57} +(-1.39764 - 1.39764i) q^{58} +(-10.0191 - 8.40702i) q^{59} +(2.37516 + 13.4702i) q^{61} +(-4.17103 - 5.95684i) q^{62} +(-0.740444 - 1.58789i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-2.56908 + 2.15572i) q^{66} +(-6.13787 - 0.536994i) q^{67} +(-4.52133 + 1.21149i) q^{68} +(4.43567 + 7.68281i) q^{69} +(-2.75320 - 0.485463i) q^{71} +(0.305194 - 0.435862i) q^{72} +(6.99705 + 3.26278i) q^{73} +(0.403603 - 0.480995i) q^{74} +(2.96495 + 3.19516i) q^{76} +(4.15483 - 4.15483i) q^{77} +(-0.164101 + 0.0143570i) q^{78} +(-12.5159 + 4.55541i) q^{79} +(1.79086 - 10.1565i) q^{81} +(-3.81343 + 1.77823i) q^{82} +(1.33654 - 4.98805i) q^{83} +(-3.09418 + 5.35927i) q^{84} +(3.65954 + 4.36127i) q^{86} +(-0.961438 - 3.58814i) q^{87} +(1.72366 + 0.461854i) q^{88} +(6.11897 + 2.22712i) q^{89} +(0.284225 - 0.0501165i) q^{91} +(1.99490 - 4.27808i) q^{92} +(-1.19114 - 13.6148i) q^{93} -0.153105 q^{94} -1.87939 q^{96} +(0.728294 + 8.32443i) q^{97} +(1.62380 - 3.48225i) q^{98} +(-0.935070 + 0.164878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{6}+O(q^{10}) $ 48 * q - 48 * q^6	$ 48 q - 48 q^{6} - 12 q^{11} + 36 q^{21} - 72 q^{31} + 48 q^{36} + 96 q^{41} + 72 q^{46} - 48 q^{51} - 108 q^{61} + 24 q^{66} - 60 q^{71} - 48 q^{76} - 168 q^{81} - 48 q^{86} + 252 q^{91}+O(q^{100}) $ 48 * q - 48 * q^6 - 12 * q^11 + 36 * q^21 - 72 * q^31 + 48 * q^36 + 96 * q^41 + 72 * q^46 - 48 * q^51 - 108 * q^61 + 24 * q^66 - 60 * q^71 - 48 * q^76 - 168 * q^81 - 48 * q^86 + 252 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$3$	0.794263	−	1.70330i	0.458568	−	0.983402i	−0.532047	−	0.846715i	$-0.678577\pi$
$3$	0.794263	−	1.70330i	0.458568	−	0.983402i	0.990614	−	0.136687i	$-0.0436453\pi$
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$		0			0
$5$		0			0
$6$	−1.76604	−	0.642788i	−0.720985	−	0.262417i
$7$	3.18056	+	0.852228i	1.20214	+	0.322112i	0.803673	−	0.595072i	$-0.202876\pi$
$7$	3.18056	+	0.852228i	1.20214	+	0.322112i	0.398465	+	0.917183i	$0.369543\pi$
$8$	0.258819	+	0.965926i	0.0915064	+	0.341506i
$9$	−0.342020	−	0.407604i	−0.114007	−	0.135868i
$10$		0			0
$11$	0.892233	−	1.54539i	0.269018	−	0.465954i	−0.699590	−	0.714544i	$-0.746634\pi$
$11$	0.892233	−	1.54539i	0.269018	−	0.465954i	0.968609	+	0.248591i	$0.0799674\pi$
$12$	−0.486421	+	1.81535i	−0.140418	+	0.524045i
$13$	0.0794377	−	0.0370424i	0.0220321	−	0.0102737i	−0.411571	−	0.911378i	$-0.635020\pi$
$13$	0.0794377	−	0.0370424i	0.0220321	−	0.0102737i	0.433603	+	0.901104i	$0.357242\pi$
$14$	0.571781	−	3.24273i	0.152815	−	0.866656i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	4.66301	−	0.407961i	1.13095	−	0.0989450i	0.493720	−	0.869621i	$-0.335637\pi$
$17$	4.66301	−	0.407961i	1.13095	−	0.0989450i	0.637227	+	0.770676i	$0.280081\pi$
$18$	−0.376244	+	0.376244i	−0.0886815	+	0.0886815i
$19$	−2.36507	−	3.66148i	−0.542585	−	0.840001i
$19$	−2.36507	−	3.66148i	−0.542585	−	0.840001i
$20$		0			0
$21$	3.97780	−	4.74056i	0.868027	−	1.03447i
$22$	−1.61728	−	0.754148i	−0.344804	−	0.160785i
$23$	−2.70748	+	3.86668i	−0.564548	+	0.806258i	−0.995364	−	0.0961816i	$-0.969337\pi$
$23$	−2.70748	+	3.86668i	−0.564548	+	0.806258i	0.430816	+	0.902440i	$0.358226\pi$
$24$	1.85083	+	0.326352i	0.377800	+	0.0666163i
$25$		0			0
$26$	−0.0438249	−	0.0759070i	−0.00859477	−	0.0148866i
$27$	4.48011	−	1.20044i	0.862198	−	0.231025i
$28$	−3.28023	−	0.286983i	−0.619904	−	0.0542346i
$29$	1.51413	−	1.27051i	0.281167	−	0.235927i	−0.491287	−	0.870998i	$-0.663473\pi$
$29$	1.51413	−	1.27051i	0.281167	−	0.235927i	0.772454	+	0.635071i	$0.219029\pi$
$30$		0			0
$31$	6.29770	−	3.63598i	1.13110	−	0.653042i	0.186890	−	0.982381i	$-0.440159\pi$
$31$	6.29770	−	3.63598i	1.13110	−	0.653042i	0.944212	+	0.329339i	$0.106826\pi$
$32$	−0.422618	−	0.906308i	−0.0747091	−	0.160214i
$33$	−1.92360	−	2.74719i	−0.334856	−	0.478224i
$34$	−0.812817	−	4.60971i	−0.139397	−	0.790559i
$35$		0			0
$36$	0.407604	+	0.342020i	0.0679340	+	0.0570034i
$37$	0.443988	+	0.443988i	0.0729912	+	0.0729912i	0.742660	−	0.669669i	$-0.233564\pi$
$37$	0.443988	+	0.443988i	0.0729912	+	0.0729912i	−0.669669	+	0.742660i	$0.733564\pi$
$38$	−3.44142	+	2.67519i	−0.558272	+	0.433973i
$39$		−	0.164728i		−	0.0263776i
$40$		0			0
$41$	−1.43910	−	3.95390i	−0.224750	−	0.617495i	0.775148	−	0.631779i	$-0.217675\pi$
$41$	−1.43910	−	3.95390i	−0.224750	−	0.617495i	−0.999898	+	0.0142845i	$0.995453\pi$
$42$	−5.06920	−	3.54950i	−0.782195	−	0.547699i
$43$	−4.66363	+	3.26551i	−0.711197	+	0.497985i	−0.872312	−	0.488950i	$-0.837380\pi$
$43$	−4.66363	+	3.26551i	−0.711197	+	0.497985i	0.161115	+	0.986936i	$0.448491\pi$
$44$	−0.610323	+	1.67685i	−0.0920097	+	0.252795i
$45$		0			0
$46$	4.08794	+	2.36017i	0.602734	+	0.347988i
$47$	0.0133439	−	0.152522i	0.00194641	−	0.0222476i	−0.995159	−	0.0982741i	$-0.968668\pi$
$47$	0.0133439	−	0.152522i	0.00194641	−	0.0222476i	0.997106	+	0.0760265i	$0.0242234\pi$
$48$	0.163799	−	1.87223i	0.0236424	−	0.270234i
$49$	3.32748	+	1.92112i	0.475354	+	0.274446i
$50$		0			0
$51$	3.00878	−	8.26654i	0.421313	−	1.15755i
$52$	−0.0717985	+	0.0502739i	−0.00995666	+	0.00697173i
$53$	−3.78609	−	2.65105i	−0.520059	−	0.364150i	0.283881	−	0.958860i	$-0.408378\pi$
$53$	−3.78609	−	2.65105i	−0.520059	−	0.364150i	−0.803940	+	0.594710i	$0.797267\pi$
$54$	−1.58634	−	4.35844i	−0.215874	−	0.593109i
$55$		0			0
$56$			3.29276i			0.440013i
$57$	−8.11509	+	1.12026i	−1.07487	+	0.148381i
$58$	−1.39764	−	1.39764i	−0.183519	−	0.183519i
$59$	−10.0191	−	8.40702i	−1.30437	−	1.09450i	−0.989372	−	0.145410i	$-0.953550\pi$
$59$	−10.0191	−	8.40702i	−1.30437	−	1.09450i	−0.315003	−	0.949091i	$-0.602006\pi$
$60$		0			0
$61$	2.37516	+	13.4702i	0.304108	+	1.72468i	0.627674	+	0.778476i	$0.284007\pi$
$61$	2.37516	+	13.4702i	0.304108	+	1.72468i	−0.323566	+	0.946206i	$0.604882\pi$
$62$	−4.17103	−	5.95684i	−0.529721	−	0.756520i
$63$	−0.740444	−	1.58789i	−0.0932871	−	0.200055i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$		0			0
$66$	−2.56908	+	2.15572i	−0.316232	+	0.265350i
$67$	−6.13787	−	0.536994i	−0.749861	−	0.0656043i	−0.294183	−	0.955749i	$-0.595048\pi$
$67$	−6.13787	−	0.536994i	−0.749861	−	0.0656043i	−0.455678	+	0.890145i	$0.650603\pi$
$68$	−4.52133	+	1.21149i	−0.548292	+	0.146914i
$69$	4.43567	+	7.68281i	0.533992	+	0.924902i
$70$		0			0
$71$	−2.75320	−	0.485463i	−0.326744	−	0.0576138i	0.00786993	−	0.999969i	$-0.497495\pi$
$71$	−2.75320	−	0.485463i	−0.326744	−	0.0576138i	−0.334614	+	0.942355i	$0.608606\pi$
$72$	0.305194	−	0.435862i	0.0359674	−	0.0513668i
$73$	6.99705	+	3.26278i	0.818943	+	0.381879i	0.786497	−	0.617594i	$-0.211893\pi$
$73$	6.99705	+	3.26278i	0.818943	+	0.381879i	0.0324460	+	0.999473i	$0.489670\pi$
$74$	0.403603	−	0.480995i	0.0469179	−	0.0559145i
$75$		0			0
$76$	2.96495	+	3.19516i	0.340103	+	0.366510i
$77$	4.15483	−	4.15483i	0.473486	−	0.473486i
$78$	−0.164101	+	0.0143570i	−0.0185808	+	0.00162561i
$79$	−12.5159	+	4.55541i	−1.40815	+	0.512523i	−0.930585	−	0.366075i	$-0.880701\pi$
$79$	−12.5159	+	4.55541i	−1.40815	+	0.512523i	−0.477561	+	0.878599i	$0.658479\pi$
$80$		0			0
$81$	1.79086	−	10.1565i	0.198984	−	1.12850i
$82$	−3.81343	+	1.77823i	−0.421122	+	0.196373i
$83$	1.33654	−	4.98805i	0.146705	−	0.547509i	−0.852969	−	0.521962i	$-0.825200\pi$
$83$	1.33654	−	4.98805i	0.146705	−	0.547509i	0.999674	−	0.0255477i	$-0.00813297\pi$
$84$	−3.09418	+	5.35927i	−0.337603	+	0.584745i
$85$		0			0
$86$	3.65954	+	4.36127i	0.394619	+	0.470288i
$87$	−0.961438	−	3.58814i	−0.103077	−	0.384689i
$88$	1.72366	+	0.461854i	0.183743	+	0.0492338i
$89$	6.11897	+	2.22712i	0.648610	+	0.236075i	0.645311	−	0.763920i	$-0.276728\pi$
$89$	6.11897	+	2.22712i	0.648610	+	0.236075i	0.00329858	+	0.999995i	$0.498950\pi$
$90$		0			0
$91$	0.284225	−	0.0501165i	0.0297949	−	0.00525364i
$92$	1.99490	−	4.27808i	0.207983	−	0.446021i
$93$	−1.19114	−	13.6148i	−0.123516	−	1.41179i
$94$	−0.153105			−0.0157915
$95$		0			0
$96$	−1.87939			−0.191814
$97$	0.728294	+	8.32443i	0.0739470	+	0.845218i	0.939085	+	0.343685i	$0.111675\pi$
$97$	0.728294	+	8.32443i	0.0739470	+	0.845218i	−0.865138	+	0.501534i	$0.832769\pi$
$98$	1.62380	−	3.48225i	0.164029	−	0.351761i
$99$	−0.935070	+	0.164878i	−0.0939781	+	0.0165709i
$100$		0			0
$101$	−11.0617	−	4.02612i	−1.10068	−	0.400614i	−0.273111	−	0.961982i	$-0.588053\pi$
$101$	−11.0617	−	4.02612i	−1.10068	−	0.400614i	−0.827566	+	0.561369i	$0.810275\pi$
$102$	−8.49732	−	2.27685i	−0.841360	−	0.225442i
$103$	2.88377	+	10.7624i	0.284146	+	1.06045i	0.949461	+	0.313885i	$0.101631\pi$
$103$	2.88377	+	10.7624i	0.284146	+	1.06045i	−0.665315	+	0.746563i	$0.731703\pi$
$104$	0.0563402	+	0.0671437i	0.00552461	+	0.00658398i
$105$		0			0
$106$	−2.31098	+	4.00274i	−0.224462	+	0.388780i
$107$	−4.08698	+	15.2528i	−0.395103	+	1.47454i	0.426501	+	0.904487i	$0.359746\pi$
$107$	−4.08698	+	15.2528i	−0.395103	+	1.47454i	−0.821605	+	0.570058i	$0.806921\pi$
$108$	−4.20360	+	1.96017i	−0.404491	+	0.188617i
$109$	0.837775	−	4.75126i	0.0802443	−	0.455088i	−0.918038	−	0.396494i	$-0.870227\pi$
$109$	0.837775	−	4.75126i	0.0802443	−	0.455088i	0.998282	−	0.0585947i	$-0.0186620\pi$
$110$		0			0
$111$	1.10889	−	0.403603i	0.105251	−	0.0383083i
$112$	3.28023	−	0.286983i	0.309952	−	0.0271173i
$113$	1.53763	−	1.53763i	0.144648	−	0.144648i	−0.631074	−	0.775722i	$-0.717386\pi$
$113$	1.53763	−	1.53763i	0.144648	−	0.144648i	0.775722	+	0.631074i	$0.217386\pi$
$114$	1.82327	+	7.98657i	0.170765	+	0.748011i
$115$		0			0
$116$	−1.27051	+	1.51413i	−0.117964	+	0.140584i
$117$	−0.0422679	−	0.0197099i	−0.00390767	−	0.00182218i
$118$	−7.50180	+	10.7137i	−0.690597	+	0.986275i
$119$	15.1787	+	2.67641i	1.39143	+	0.245346i
$120$		0			0
$121$	3.90784	+	6.76858i	0.355258	+	0.615325i
$122$	13.2119	−	3.54013i	1.19615	−	0.320508i
$123$	−7.87770	−	0.689210i	−0.710309	−	0.0621439i
$124$	−5.57065	+	4.67433i	−0.500259	+	0.419767i
$125$		0			0
$126$	−1.51731	+	0.876019i	−0.135173	+	0.0780420i
$127$	5.99452	+	12.8553i	0.531927	+	1.14072i	0.970295	+	0.241926i	$0.0777791\pi$
$127$	5.99452	+	12.8553i	0.531927	+	1.14072i	−0.438367	+	0.898796i	$0.644443\pi$
$128$	0.573576	+	0.819152i	0.0506975	+	0.0724035i
$129$	1.85800	+	10.5372i	0.163588	+	0.927752i
$130$		0			0
$131$	−1.39611	−	1.17148i	−0.121979	−	0.102353i	0.579758	−	0.814789i	$-0.303147\pi$
$131$	−1.39611	−	1.17148i	−0.121979	−	0.102353i	−0.701737	+	0.712436i	$0.747592\pi$
$132$	2.37142	+	2.37142i	0.206406	+	0.206406i
$133$	−4.40183	−	13.6611i	−0.381687	−	1.18457i
$134$			6.16132i			0.532257i
$135$		0			0
$136$	1.60094	+	4.39854i	0.137279	+	0.377171i
$137$	−0.186947	−	0.130902i	−0.0159719	−	0.0111837i	0.565563	−	0.824705i	$-0.308659\pi$
$137$	−0.186947	−	0.130902i	−0.0159719	−	0.0111837i	−0.581535	+	0.813521i	$0.697548\pi$
$138$	7.26698	−	5.08839i	0.618606	−	0.433153i
$139$	7.75531	−	21.3075i	0.657797	−	1.80728i	0.0711095	−	0.997469i	$-0.477346\pi$
$139$	7.75531	−	21.3075i	0.657797	−	1.80728i	0.586687	−	0.809814i	$-0.300432\pi$
$140$		0			0
$141$	−0.249192	−	0.143871i	−0.0209858	−	0.0121161i
$142$	−0.243659	+	2.78503i	−0.0204474	+	0.233715i
$143$	0.0136319	−	0.155813i	0.00113995	−	0.0130297i
$144$	−0.460802	−	0.266044i	−0.0384002	−	0.0221704i
$145$		0			0
$146$	2.64053	−	7.25480i	0.218532	−	0.600411i
$147$	5.91514	−	4.14182i	0.487872	−	0.341612i
$148$	−0.514341	−	0.360145i	−0.0422786	−	0.0296038i
$149$	0.939750	+	2.58194i	0.0769873	+	0.211521i	0.972216	−	0.234087i	$-0.0752099\pi$
$149$	0.939750	+	2.58194i	0.0769873	+	0.211521i	−0.895228	+	0.445607i	$0.852988\pi$
$150$		0			0
$151$		−	16.7726i		−	1.36494i	−0.730916	−	0.682468i	$-0.760907\pi$
$151$		−	16.7726i		−	1.36494i	0.730916	−	0.682468i	$-0.239093\pi$
$152$	2.92459	−	3.23215i	0.237216	−	0.262162i
$153$	−1.76113	−	1.76113i	−0.142379	−	0.142379i
$154$	−4.50113	−	3.77690i	−0.362712	−	0.304351i
$155$		0			0
$156$	0.0286047	+	0.162225i	0.00229021	+	0.0129884i
$157$	13.6138	+	19.4425i	1.08650	+	1.55168i	0.806085	+	0.591800i	$0.201583\pi$
$157$	13.6138	+	19.4425i	1.08650	+	1.55168i	0.280413	+	0.959879i	$0.409528\pi$
$158$	5.62890	+	12.0712i	0.447812	+	0.960335i
$159$	−7.52269	+	4.34322i	−0.596588	+	0.344440i
$160$		0			0
$161$	−11.9066	+	9.99081i	−0.938370	+	0.787386i
$162$	−10.2739	−	0.898850i	−0.807194	−	0.0706203i
$163$	9.13205	−	2.44692i	0.715277	−	0.191658i	0.117214	−	0.993107i	$-0.462604\pi$
$163$	9.13205	−	2.44692i	0.715277	−	0.191658i	0.598063	+	0.801449i	$0.295937\pi$
$164$	2.10382	+	3.64393i	0.164281	+	0.284543i
$165$		0			0
$166$	−5.08555	−	0.896721i	−0.394716	−	0.0695990i
$167$	13.7583	−	19.6489i	1.06465	−	1.52047i	0.227284	−	0.973829i	$-0.427015\pi$
$167$	13.7583	−	19.6489i	1.06465	−	1.52047i	0.837364	−	0.546646i	$-0.184096\pi$
$168$	5.60856	+	2.61531i	0.432709	+	0.201776i
$169$	−8.35130	+	9.95269i	−0.642408	+	0.765592i
$170$		0			0
$171$	−0.683530	+	2.21631i	−0.0522709	+	0.169486i
$172$	4.02573	−	4.02573i	0.306959	−	0.306959i
$173$	12.8023	−	1.12005i	0.973339	−	0.0851561i	0.410622	−	0.911806i	$-0.365312\pi$
$173$	12.8023	−	1.12005i	0.973339	−	0.0851561i	0.562717	+	0.826650i	$0.309756\pi$
$174$	−3.49069	+	1.27051i	−0.264628	+	0.0963168i
$175$		0			0
$176$	0.309869	−	1.75736i	0.0233573	−	0.132466i
$177$	−22.2775	+	10.3882i	−1.67448	+	0.780822i
$178$	1.68534	−	6.28979i	0.126322	−	0.471440i
$179$	4.62396	−	8.00894i	0.345611	−	0.598616i	−0.639853	−	0.768497i	$-0.721005\pi$
$179$	4.62396	−	8.00894i	0.345611	−	0.598616i	0.985465	+	0.169881i	$0.0543382\pi$
$180$		0			0
$181$	−5.60398	−	6.67856i	−0.416540	−	0.496413i	0.516449	−	0.856318i	$-0.327254\pi$
$181$	−5.60398	−	6.67856i	−0.416540	−	0.496413i	−0.932989	+	0.359905i	$0.882809\pi$
$182$	−0.0746976	−	0.278775i	−0.00553696	−	0.0206642i
$183$	24.8303	+	6.65326i	1.83551	+	0.491823i
$184$	−4.43567	−	1.61445i	−0.327002	−	0.119019i
$185$		0			0
$186$	−13.4592	+	2.37322i	−0.986876	+	0.174013i
$187$	3.53003	−	7.57018i	0.258142	−	0.553587i
$188$	0.0133439	+	0.152522i	0.000973207	+	0.0111238i
$189$	15.2723			1.11090
$190$		0			0
$191$	−11.8345			−0.856316			−0.428158	−	0.903704i	$-0.640837\pi$
$191$	−11.8345			−0.856316			−0.428158	+	0.903704i	$0.640837\pi$
$192$	0.163799	+	1.87223i	0.0118212	+	0.135117i
$193$	3.68982	−	7.91284i	0.265599	−	0.569579i	−0.727601	−	0.686001i	$-0.759365\pi$
$193$	3.68982	−	7.91284i	0.265599	−	0.569579i	0.993200	+	0.116422i	$0.0371425\pi$
$194$	8.22928	−	1.45104i	0.590828	−	0.104179i
$195$		0			0
$196$	−3.61053	−	1.31412i	−0.257895	−	0.0938660i
$197$	−16.6023	−	4.44858i	−1.18287	−	0.316948i	−0.386804	−	0.922162i	$-0.626421\pi$
$197$	−16.6023	−	4.44858i	−1.18287	−	0.316948i	−0.796063	+	0.605213i	$0.793088\pi$
$198$	0.245747	+	0.917142i	0.0174645	+	0.0651784i
$199$	−2.43291	−	2.89943i	−0.172465	−	0.205535i	0.672888	−	0.739745i	$-0.265054\pi$
$199$	−2.43291	−	2.89943i	−0.172465	−	0.205535i	−0.845352	+	0.534210i	$0.820609\pi$
$200$		0			0
$201$	−5.78975	+	10.0281i	−0.408377	+	0.707330i
$202$	−3.04671	+	11.3705i	−0.214366	+	0.800024i
$203$	5.89854	−	2.75054i	0.413996	−	0.193050i
$204$	−1.52760	+	8.66342i	−0.106953	+	0.606561i
$205$		0			0
$206$	10.4701	−	3.81080i	0.729485	−	0.265511i
$207$	2.50209	−	0.218904i	0.173907	−	0.0152149i
$208$	0.0619778	−	0.0619778i	0.00429739	−	0.00429739i
$209$	−7.76862	+	0.388073i	−0.537367	+	0.0268436i
$210$		0			0
$211$	−4.58000	+	5.45824i	−0.315301	+	0.375761i	−0.900298	−	0.435275i	$-0.856651\pi$
$211$	−4.58000	+	5.45824i	−0.315301	+	0.375761i	0.584997	+	0.811035i	$0.301096\pi$
$212$	4.18892	+	1.95333i	0.287696	+	0.134155i
$213$	−3.01365	+	4.30394i	−0.206492	+	0.294901i
$214$	15.5510	+	2.74206i	1.06304	+	0.187443i
$215$		0			0
$216$	2.31908	+	4.01676i	0.157793	+	0.273306i
$217$	23.1289	−	6.19737i	1.57009	−	0.420705i
$218$	−4.80620	−	0.420488i	−0.325517	−	0.0284790i
$219$	11.1150	−	9.32659i	0.751082	−	0.630232i
$220$		0			0
$221$	0.355307	−	0.205137i	0.0239005	−	0.0137990i
$222$	−0.498713	−	1.06949i	−0.0334714	−	0.0717797i
$223$	12.2512	+	17.4965i	0.820399	+	1.17165i	0.982754	+	0.184918i	$0.0592020\pi$
$223$	12.2512	+	17.4965i	0.820399	+	1.17165i	−0.162355	+	0.986732i	$0.551909\pi$
$224$	−0.571781	−	3.24273i	−0.0382037	−	0.216664i
$225$		0			0
$226$	−1.66579	−	1.39777i	−0.110807	−	0.0929780i
$227$	−15.2554	−	15.2554i	−1.01254	−	1.01254i	−0.999920	−	0.0126188i	$-0.995983\pi$
$227$	−15.2554	−	15.2554i	−1.01254	−	1.01254i	−0.0126188	−	0.999920i	$-0.504017\pi$
$228$	7.79728	−	2.51241i	0.516387	−	0.166388i
$229$			11.0502i			0.730219i	0.930965	+	0.365109i	$0.118968\pi$
$229$			11.0502i			0.730219i	−0.930965	+	0.365109i	$0.881032\pi$
$230$		0			0
$231$	−3.77690	−	10.3769i	−0.248502	−	0.682753i
$232$	1.61910	+	1.13371i	0.106299	+	0.0744315i
$233$	−0.638588	+	0.447144i	−0.0418353	+	0.0292934i	−0.594307	−	0.804238i	$-0.702574\pi$
$233$	−0.638588	+	0.447144i	−0.0418353	+	0.0292934i	0.552472	+	0.833532i	$0.313685\pi$
$234$	−0.0159510	+	0.0438249i	−0.00104275	+	0.00286492i
$235$		0			0
$236$	11.3267	+	6.53950i	0.737308	+	0.425685i
$237$	−2.18166	+	24.9365i	−0.141714	+	1.61980i
$238$	1.34332	−	15.3542i	0.0870742	−	0.995262i
$239$	20.7057	+	11.9544i	1.33934	+	0.773268i	0.986709	−	0.162495i	$-0.0519540\pi$
$239$	20.7057	+	11.9544i	1.33934	+	0.773268i	0.352630	+	0.935763i	$0.385287\pi$
$240$		0			0
$241$	−8.63802	+	23.7328i	−0.556424	+	1.52876i	0.268363	+	0.963318i	$0.413517\pi$
$241$	−8.63802	+	23.7328i	−0.556424	+	1.52876i	−0.824787	+	0.565443i	$0.808705\pi$
$242$	6.40223	−	4.48289i	0.411551	−	0.288171i
$243$	−4.47905	−	3.13626i	−0.287331	−	0.201191i
$244$	−4.67815	−	12.8531i	−0.299488	−	0.822836i
$245$		0			0
$246$			7.90779i			0.504183i
$247$	−0.323506	−	0.203252i	−0.0205842	−	0.0129326i
$248$	5.14205	+	5.14205i	0.326521	+	0.326521i
$249$	−7.43458	−	6.23836i	−0.471148	−	0.395340i
$250$		0			0
$251$	2.24897	+	12.7545i	0.141954	+	0.805059i	0.969763	+	0.244049i	$0.0784759\pi$
$251$	2.24897	+	12.7545i	0.141954	+	0.805059i	−0.827809	+	0.561010i	$0.810413\pi$
$252$	1.00493	+	1.43519i	0.0633045	+	0.0904082i
$253$	3.55984	+	7.63410i	0.223805	+	0.479952i
$254$	12.2839	−	7.09212i	0.770761	−	0.444999i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−23.6092	−	2.06554i	−1.47270	−	0.128845i	−0.677650	−	0.735384i	$-0.737002\pi$
$257$	−23.6092	−	2.06554i	−1.47270	−	0.128845i	−0.795053	+	0.606539i	$0.792557\pi$
$258$	10.3352	−	2.76931i	0.643442	−	0.172410i
$259$	1.03375	+	1.79051i	0.0642342	+	0.111257i
$260$		0			0
$261$	−1.03573	−	0.182627i	−0.0641099	−	0.0113043i
$262$	−1.04534	+	1.49290i	−0.0645814	+	0.0922318i
$263$	23.1913	+	10.8143i	1.43004	+	0.666838i	0.974708	−	0.223484i	$-0.0717431\pi$
$263$	23.1913	+	10.8143i	1.43004	+	0.666838i	0.455331	+	0.890322i	$0.349521\pi$
$264$	2.15572	−	2.56908i	0.132675	−	0.158116i
$265$		0			0
$266$	−13.2255	+	5.57573i	−0.810907	+	0.341870i
$267$	8.65353	−	8.65353i	0.529587	−	0.529587i
$268$	6.13787	−	0.536994i	0.374930	−	0.0328022i
$269$	−25.0224	+	9.10741i	−1.52564	+	0.555289i	−0.962550	−	0.271104i	$-0.912611\pi$
$269$	−25.0224	+	9.10741i	−1.52564	+	0.555289i	−0.563094	+	0.826393i	$0.690389\pi$
$270$		0			0
$271$	1.14223	−	6.47790i	0.0693854	−	0.393504i	−0.930261	−	0.366900i	$-0.880419\pi$
$271$	1.14223	−	6.47790i	0.0693854	−	0.393504i	0.999646	−	0.0266049i	$-0.00846960\pi$
$272$	4.24227	−	1.97820i	0.257225	−	0.119946i
$273$	0.140386	−	0.523926i	0.00849652	−	0.0317095i
$274$	−0.114110	+	0.197644i	−0.00689364	+	0.0119401i
$275$		0			0
$276$	−5.70239	−	6.79584i	−0.343244	−	0.409062i
$277$	3.35138	+	12.5075i	0.201365	+	0.751504i	0.990527	+	0.137319i	$0.0438484\pi$
$277$	3.35138	+	12.5075i	0.201365	+	0.751504i	−0.789162	+	0.614185i	$0.789485\pi$
$278$	−21.9024	−	5.86872i	−1.31362	−	0.351983i
$279$	−3.63598	−	1.32339i	−0.217681	−	0.0792292i
$280$		0			0
$281$	−1.45685	+	0.256882i	−0.0869085	+	0.0153243i	−0.216933	−	0.976186i	$-0.569605\pi$
$281$	−1.45685	+	0.256882i	−0.0869085	+	0.0153243i	0.130025	+	0.991511i	$0.458494\pi$
$282$	−0.121605	+	0.260783i	−0.00724149	+	0.0155294i
$283$	2.52467	+	28.8571i	0.150076	+	1.71538i	0.581767	+	0.813355i	$0.302361\pi$
$283$	2.52467	+	28.8571i	0.150076	+	1.71538i	−0.431691	+	0.902021i	$0.642083\pi$
$284$	2.79567			0.165892
$285$		0			0
$286$	−0.156408			−0.00924861
$287$	−1.20752	−	13.8020i	−0.0712778	−	0.814709i
$288$	−0.224870	+	0.482236i	−0.0132506	+	0.0284160i
$289$	4.83552	−	0.852633i	0.284442	−	0.0501549i
$290$		0			0
$291$	14.7575	+	5.37128i	0.865099	+	0.314870i
$292$	−7.45733	−	1.99818i	−0.436407	−	0.116935i
$293$	4.63618	+	17.3024i	0.270848	+	1.01082i	0.958573	+	0.284848i	$0.0919431\pi$
$293$	4.63618	+	17.3024i	0.270848	+	1.01082i	−0.687724	+	0.725972i	$0.741390\pi$
$294$	−4.64160	−	5.53165i	−0.270704	−	0.322612i
$295$		0			0
$296$	−0.313947	+	0.543773i	−0.0182478	+	0.0316061i
$297$	2.14215	−	7.99461i	0.124300	−	0.463895i
$298$	2.49021	−	1.16120i	0.144254	−	0.0672668i
$299$	−0.0718447	+	0.407452i	−0.00415489	+	0.0235635i
$300$		0			0
$301$	−17.6159	+	6.41166i	−1.01536	+	0.369562i
$302$	−16.7088	+	1.46183i	−0.961482	+	0.0841188i
$303$	−15.6436	+	15.6436i	−0.898699	+	0.898699i
$304$	−3.47474	−	2.63176i	−0.199290	−	0.150942i
$305$		0			0
$306$	−1.60094	+	1.90792i	−0.0915194	+	0.109069i
$307$	8.23752	+	3.84122i	0.470140	+	0.219230i	0.643225	−	0.765677i	$-0.277596\pi$
$307$	8.23752	+	3.84122i	0.470140	+	0.219230i	−0.173085	+	0.984907i	$0.555374\pi$
$308$	−3.37023	+	4.81318i	−0.192037	+	0.274257i
$309$	20.6220	+	3.63622i	1.17315	+	0.206857i
$310$		0			0
$311$	12.0787	+	20.9209i	0.684920	+	1.18632i	0.973462	+	0.228848i	$0.0734960\pi$
$311$	12.0787	+	20.9209i	0.684920	+	1.18632i	−0.288543	+	0.957467i	$0.593171\pi$
$312$	0.159115	−	0.0426347i	0.00900810	−	0.00241371i
$313$	−29.2902	−	2.56256i	−1.65558	−	0.144844i	−0.779300	−	0.626651i	$-0.784425\pi$
$313$	−29.2902	−	2.56256i	−1.65558	−	0.144844i	−0.876277	+	0.481807i	$0.839981\pi$
$314$	18.1820	−	15.2565i	1.02607	−	0.860974i
$315$		0			0
$316$	11.5347	−	6.65956i	0.648877	−	0.374630i
$317$	1.36206	+	2.92095i	0.0765010	+	0.164057i	0.940839	−	0.338855i	$-0.110040\pi$
$317$	1.36206	+	2.92095i	0.0765010	+	0.164057i	−0.864338	+	0.502912i	$0.832262\pi$
$318$	4.98234	+	7.11552i	0.279396	+	0.399019i
$319$	−0.612475	−	3.47352i	−0.0342920	−	0.194480i
$320$		0			0
$321$	22.7340	+	19.0761i	1.26889	+	1.06472i
$322$	10.9905	+	10.9905i	0.612478	+	0.612478i
$323$	−12.5221	−	16.1087i	−0.696748	−	0.896310i
$324$			10.3131i			0.572953i
$325$		0			0
$326$	−3.23352	−	8.88403i	−0.179088	−	0.492041i
$327$	−7.42742	−	5.20073i	−0.410737	−	0.287601i
$328$	3.44670	−	2.41341i	0.190312	−	0.133258i
$329$	0.172425	−	0.473733i	0.00950608	−	0.0261177i
$330$		0			0
$331$	13.8617	+	8.00303i	0.761906	+	0.439886i	0.829979	−	0.557794i	$-0.188352\pi$
$331$	13.8617	+	8.00303i	0.761906	+	0.439886i	−0.0680740	+	0.997680i	$0.521685\pi$
$332$	−0.450073	+	5.14436i	−0.0247010	+	0.282333i
$333$	0.0291184	−	0.332824i	0.00159568	−	0.0182387i
$334$	−20.7732	−	11.9934i	−1.13666	−	0.656250i
$335$		0			0
$336$	2.11654	−	5.81515i	0.115467	−	0.317243i
$337$	9.63404	−	6.74583i	0.524800	−	0.367469i	−0.280952	−	0.959722i	$-0.590650\pi$
$337$	9.63404	−	6.74583i	0.524800	−	0.367469i	0.805752	+	0.592253i	$0.201761\pi$
$338$	10.6427	+	7.45209i	0.578886	+	0.405340i
$339$	−1.39777	−	3.84033i	−0.0759163	−	0.208578i
$340$		0			0
$341$		−	12.9766i		−	0.702721i
$342$	2.26745	+	0.487765i	0.122610	+	0.0263753i
$343$	−7.35231	−	7.35231i	−0.396987	−	0.396987i
$344$	−4.36127	−	3.65954i	−0.235144	−	0.197309i
$345$		0			0
$346$	−2.23158	−	12.6559i	−0.119971	−	0.680387i
$347$	−18.3404	−	26.1928i	−0.984562	−	1.40610i	−0.912674	−	0.408688i	$-0.865986\pi$
$347$	−18.3404	−	26.1928i	−0.984562	−	1.40610i	−0.0718885	−	0.997413i	$-0.522903\pi$
$348$	1.56991	+	3.36667i	0.0841558	+	0.180473i
$349$	−7.53234	+	4.34880i	−0.403197	+	0.232786i	−0.687862	−	0.725841i	$-0.741451\pi$
$349$	−7.53234	+	4.34880i	−0.403197	+	0.232786i	0.284666	+	0.958627i	$0.408117\pi$
$350$		0			0
$351$	0.311423	−	0.261315i	0.0166225	−	0.0139479i
$352$	−1.77768	−	0.155527i	−0.0947505	−	0.00828959i
$353$	−33.7033	+	9.03078i	−1.79385	+	0.480660i	−0.992990	−	0.118197i	$-0.962289\pi$
$353$	−33.7033	+	9.03078i	−1.79385	+	0.480660i	−0.800856	+	0.598857i	$0.795622\pi$
$354$	12.2902	+	21.2873i	0.653219	+	1.13141i
$355$		0			0
$356$	−6.41275	−	1.13074i	−0.339875	−	0.0599291i
$357$	16.6146	−	23.7281i	0.879336	−	1.25582i
$358$	−8.38147	−	3.90834i	−0.442974	−	0.206562i
$359$	−19.2695	+	22.9644i	−1.01700	+	1.21202i	−0.0399103	+	0.999203i	$0.512707\pi$
$359$	−19.2695	+	22.9644i	−1.01700	+	1.21202i	−0.977093	+	0.212814i	$0.931737\pi$
$360$		0			0
$361$	−7.81286	+	17.3193i	−0.411203	+	0.911544i
$362$	−6.16473	+	6.16473i	−0.324011	+	0.324011i
$363$	14.6328	−	1.28020i	0.768022	−	0.0671932i
$364$	−0.271204	+	0.0987102i	−0.0142150	+	0.00517382i
$365$		0			0
$366$	4.46384	−	25.3157i	0.233329	−	1.32327i
$367$	−8.39093	+	3.91276i	−0.438003	+	0.204244i	−0.629096	−	0.777328i	$-0.716575\pi$
$367$	−8.39093	+	3.91276i	−0.438003	+	0.204244i	0.191093	+	0.981572i	$0.438797\pi$
$368$	−1.22171	+	4.55950i	−0.0636863	+	0.237680i
$369$	−1.11942	+	1.93890i	−0.0582748	+	0.100935i
$370$		0			0
$371$	−9.78258	−	11.6584i	−0.507886	−	0.605275i
$372$	3.53723	+	13.2011i	0.183397	+	0.684447i
$373$	1.82554	+	0.489152i	0.0945230	+	0.0253273i	0.305771	−	0.952105i	$-0.401086\pi$
$373$	1.82554	+	0.489152i	0.0945230	+	0.0253273i	−0.211248	+	0.977433i	$0.567753\pi$
$374$	−7.84904	−	2.85682i	−0.405864	−	0.147722i
$375$		0			0
$376$	0.150779	−	0.0265863i	0.00777581	−	0.00137109i
$377$	0.0732165	−	0.157013i	0.00377084	−	0.00808659i
$378$	−1.33107	−	15.2142i	−0.0684628	−	0.782534i
$379$	−23.8751			−1.22638			−0.613192	−	0.789934i	$-0.710115\pi$
$379$	−23.8751			−1.22638			−0.613192	+	0.789934i	$0.710115\pi$
$380$		0			0
$381$	26.6576			1.36571
$382$	1.03145	+	11.7895i	0.0527734	+	0.603203i
$383$	11.8960	−	25.5111i	0.607859	−	1.30356i	−0.325814	−	0.945434i	$-0.605638\pi$
$383$	11.8960	−	25.5111i	0.607859	−	1.30356i	0.933674	−	0.358125i	$-0.116584\pi$
$384$	1.85083	−	0.326352i	0.0944499	−	0.0166541i
$385$		0			0
$386$	−8.20432	−	2.98613i	−0.417589	−	0.151990i
$387$	2.92609	+	0.784043i	0.148741	+	0.0398551i
$388$	−2.16275	−	8.07150i	−0.109797	−	0.409768i
$389$	0.142159	+	0.169419i	0.00720777	+	0.00858988i	0.769636	−	0.638483i	$-0.220438\pi$
$389$	0.142159	+	0.169419i	0.00720777	+	0.00858988i	−0.762429	+	0.647072i	$0.775993\pi$
$390$		0			0
$391$	−11.0476	+	19.1349i	−0.558699	+	0.967694i
$392$	−0.994445	+	3.71132i	−0.0502271	+	0.187450i
$393$	−3.10426	+	1.44754i	−0.156589	+	0.0730188i
$394$	−2.98467	+	16.9269i	−0.150365	+	0.852764i
$395$		0			0
$396$	0.892233	−	0.324746i	0.0448364	−	0.0163191i
$397$	−5.55608	+	0.486094i	−0.278851	+	0.0243963i	−0.225724	−	0.974191i	$-0.572475\pi$
$397$	−5.55608	+	0.486094i	−0.278851	+	0.0243963i	−0.0531278	+	0.998588i	$0.516919\pi$
$398$	−2.67636	+	2.67636i	−0.134154	+	0.134154i
$399$	−26.7652	−	3.35287i	−1.33994	−	0.167853i
$400$		0			0
$401$	21.0921	−	25.1365i	1.05329	−	1.25526i	0.0874333	−	0.996170i	$-0.472134\pi$
$401$	21.0921	−	25.1365i	1.05329	−	1.25526i	0.965854	−	0.259088i	$-0.0834220\pi$
$402$	10.4946	+	4.89371i	0.523422	+	0.244076i
$403$	0.365590	−	0.522116i	0.0182113	−	0.0260085i
$404$	11.5927	+	2.04411i	0.576760	+	0.101698i
$405$		0			0
$406$	−3.25416	−	5.63637i	−0.161501	−	0.279728i
$407$	1.08228	−	0.289996i	0.0536465	−	0.0143745i
$408$	8.76360	+	0.766715i	0.433863	+	0.0379581i
$409$	−2.16162	+	1.81381i	−0.106885	+	0.0896872i	−0.694664	−	0.719334i	$-0.744447\pi$
$409$	−2.16162	+	1.81381i	−0.106885	+	0.0896872i	0.587779	+	0.809022i	$0.300002\pi$
$410$		0			0
$411$	−0.371450	+	0.214457i	−0.0183223	+	0.0105784i
$412$	−4.70882	−	10.0981i	−0.231987	−	0.497498i
$413$	−24.7016	−	35.2775i	−1.21549	−	1.73589i
$414$	−0.436142	−	2.47349i	−0.0214352	−	0.121565i
$415$		0			0
$416$	−0.0671437	−	0.0563402i	−0.00329199	−	0.00276231i
$417$	−30.1334	−	30.1334i	−1.47564	−	1.47564i
$418$	1.06368	+	7.70524i	0.0520261	+	0.376875i
$419$		−	34.6418i		−	1.69236i	−0.532897	−	0.846180i	$-0.678897\pi$
$419$		−	34.6418i		−	1.69236i	0.532897	−	0.846180i	$-0.321103\pi$
$420$		0			0
$421$	−6.22989	−	17.1165i	−0.303626	−	0.834206i	−0.993863	−	0.110622i	$-0.964716\pi$
$421$	−6.22989	−	17.1165i	−0.303626	−	0.834206i	0.690236	−	0.723584i	$-0.257507\pi$
$422$	5.83664	+	4.08686i	0.284123	+	0.198945i
$423$	−0.0667324	+	0.0467265i	−0.00324464	+	0.00227192i
$424$	1.58080	−	4.34322i	0.0767706	−	0.210926i
$425$		0			0
$426$	4.55022	+	2.62707i	0.220459	+	0.127282i
$427$	−3.92535	+	44.8669i	−0.189961	+	2.17126i
$428$	1.37627	−	15.7308i	0.0665243	−	0.760376i
$429$	−0.254569	−	0.146976i	−0.0122907	−	0.00709605i
$430$		0			0
$431$	−3.63707	+	9.99276i	−0.175191	+	0.481334i	−0.995947	−	0.0899455i	$-0.971331\pi$
$431$	−3.63707	+	9.99276i	−0.175191	+	0.481334i	0.820755	+	0.571280i	$0.193553\pi$
$432$	3.79935	−	2.66034i	0.182797	−	0.127996i
$433$	1.95053	+	1.36577i	0.0937364	+	0.0656349i	0.619505	−	0.784993i	$-0.287333\pi$
$433$	1.95053	+	1.36577i	0.0937364	+	0.0656349i	−0.525769	+	0.850628i	$0.676222\pi$
$434$	−8.18960	−	22.5007i	−0.393114	−	1.08007i
$435$		0			0
$436$			4.82456i			0.231054i
$437$	20.5612	+	0.768398i	0.983573	+	0.0367575i
$438$	−10.2598	−	10.2598i	−0.490234	−	0.490234i
$439$	−14.1862	−	11.9037i	−0.677071	−	0.568130i	0.238078	−	0.971246i	$-0.423483\pi$
$439$	−14.1862	−	11.9037i	−0.677071	−	0.568130i	−0.915149	+	0.403116i	$0.867927\pi$
$440$		0			0
$441$	−0.355009	−	2.01335i	−0.0169052	−	0.0958740i
$442$	−0.235323	−	0.336076i	−0.0111932	−	0.0159855i
$443$	−10.7264	−	23.0029i	−0.509628	−	1.09290i	−0.977853	−	0.209292i	$-0.932884\pi$
$443$	−10.7264	−	23.0029i	−0.509628	−	1.09290i	0.468225	−	0.883609i	$-0.344894\pi$
$444$	−1.02196	+	0.590028i	−0.0485000	+	0.0280015i
$445$		0			0
$446$	16.3621	−	13.7295i	0.774770	−	0.650109i
$447$	5.14423	+	0.450062i	0.243314	+	0.0212872i
$448$	−3.18056	+	0.852228i	−0.150267	+	0.0402640i
$449$	18.5442	+	32.1194i	0.875153	+	1.51581i	0.856600	+	0.515982i	$0.172573\pi$
$449$	18.5442	+	32.1194i	0.875153	+	1.51581i	0.0185532	+	0.999828i	$0.494094\pi$
$450$		0			0
$451$	−7.39434	−	1.30382i	−0.348186	−	0.0613946i
$452$	−1.24726	+	1.78128i	−0.0586664	+	0.0837843i
$453$	−28.5688	−	13.3219i	−1.34228	−	0.625915i
$454$	−13.8678	+	16.5270i	−0.650848	+	0.775650i
$455$		0			0
$456$	−3.18242	−	7.54863i	−0.149031	−	0.353497i
$457$	−13.9770	+	13.9770i	−0.653815	+	0.653815i	−0.953909	−	0.300095i	$-0.902982\pi$
$457$	−13.9770	+	13.9770i	−0.653815	+	0.653815i	0.300095	+	0.953909i	$0.402982\pi$
$458$	11.0082	−	0.963090i	0.514378	−	0.0450022i
$459$	20.4011	−	7.42539i	0.952242	−	0.346588i
$460$		0			0
$461$	4.60073	−	26.0920i	0.214277	−	1.21523i	−0.667879	−	0.744270i	$-0.732797\pi$
$461$	4.60073	−	26.0920i	0.214277	−	1.21523i	0.882156	−	0.470957i	$-0.156091\pi$
$462$	−10.0083	+	4.66694i	−0.465627	+	0.217126i
$463$	0.0934066	−	0.348598i	0.00434097	−	0.0162007i	−0.963721	−	0.266910i	$-0.913997\pi$
$463$	0.0934066	−	0.348598i	0.00434097	−	0.0162007i	0.968062	+	0.250710i	$0.0806639\pi$
$464$	0.988279	−	1.71175i	0.0458797	−	0.0794659i
$465$		0			0
$466$	0.501099	+	0.597187i	0.0232130	+	0.0276641i
$467$	2.46589	+	9.20282i	0.114108	+	0.425856i	0.999219	−	0.0395244i	$-0.0125843\pi$
$467$	2.46589	+	9.20282i	0.114108	+	0.425856i	−0.885111	+	0.465380i	$0.845918\pi$
$468$	0.0450484	+	0.0120707i	0.00208236	+	0.000557967i
$469$	−19.0642	−	6.93881i	−0.880304	−	0.320404i
$470$		0			0
$471$	43.9293	−	7.74593i	2.02416	−	0.356914i
$472$	5.52742	−	11.8536i	0.254420	−	0.545606i
$473$	0.885450	+	10.1207i	0.0407130	+	0.465352i
$474$	25.0318			1.14975
$475$		0			0
$476$	−15.4128			−0.706445
$477$	0.214342	+	2.44994i	0.00981403	+	0.112175i
$478$	10.1043	−	21.6688i	0.462161	−	0.991108i
$479$	5.24484	−	0.924808i	0.239643	−	0.0422555i	−0.0525366	−	0.998619i	$-0.516731\pi$
$479$	5.24484	−	0.924808i	0.239643	−	0.0422555i	0.292180	+	0.956363i	$0.405619\pi$
$480$		0			0
$481$	0.0517158	+	0.0188230i	0.00235804	+	0.000858256i
$482$	24.3953	+	6.53670i	1.11118	+	0.297739i
$483$	7.56041	+	28.2158i	0.344010	+	1.28386i
$484$	−5.02382	−	5.98716i	−0.228356	−	0.272144i
$485$		0			0
$486$	−2.73396	+	4.73535i	−0.124015	+	0.214800i
$487$	6.84995	−	25.5644i	0.310401	−	1.15843i	−0.617795	−	0.786340i	$-0.711974\pi$
$487$	6.84995	−	25.5644i	0.310401	−	1.15843i	0.928196	−	0.372093i	$-0.121360\pi$
$488$	−12.3965	+	5.78057i	−0.561162	+	0.261674i
$489$	3.08539	−	17.4981i	0.139526	−	0.791293i
$490$		0			0
$491$	−6.91431	+	2.51660i	−0.312038	+	0.113573i	−0.493292	−	0.869864i	$-0.664207\pi$
$491$	−6.91431	+	2.51660i	−0.312038	+	0.113573i	0.181254	+	0.983436i	$0.441984\pi$
$492$	7.87770	−	0.689210i	0.355154	−	0.0310720i
$493$	6.54209	−	6.54209i	0.294641	−	0.294641i
$494$	−0.174283	+	0.339990i	−0.00784135	+	0.0152969i
$495$		0			0
$496$	4.67433	−	5.57065i	0.209884	−	0.250129i
$497$	−8.34298	−	3.89039i	−0.374234	−	0.174508i
$498$	−5.56665	+	7.95000i	−0.249448	+	0.356248i
$499$	32.5920	+	5.74685i	1.45902	+	0.257265i	0.846161	−	0.532928i	$-0.178908\pi$
$499$	32.5920	+	5.74685i	1.45902	+	0.257265i	0.612859	+	0.790192i	$0.290019\pi$
$500$		0			0
$501$	−22.5402	−	39.0409i	−1.00702	−	1.74422i
$502$	12.5100	−	3.35204i	0.558348	−	0.149609i
$503$	2.67365	+	0.233914i	0.119212	+	0.0104297i	0.146606	−	0.989195i	$-0.453165\pi$
$503$	2.67365	+	0.233914i	0.119212	+	0.0104297i	−0.0273936	+	0.999625i	$0.508721\pi$
$504$	1.34214	−	1.12619i	0.0597836	−	0.0501644i
$505$		0			0
$506$	7.29479	−	4.21165i	0.324293	−	0.187231i
$507$	10.3193	+	22.1298i	0.458297	+	0.982820i
$508$	−8.13574	−	11.6190i	−0.360965	−	0.515512i
$509$	6.40712	+	36.3366i	0.283991	+	1.61059i	0.708869	+	0.705340i	$0.249206\pi$
$509$	6.40712	+	36.3366i	0.283991	+	1.61059i	−0.424878	+	0.905250i	$0.639683\pi$
$510$		0			0
$511$	19.4739	+	16.3405i	0.861475	+	0.722863i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−14.9912	−	13.5647i	−0.661877	−	0.598897i
$514$			23.6994i			1.04534i
$515$		0			0
$516$	−3.65954	−	10.0545i	−0.161102	−	0.442625i
$517$	−0.223801	−	0.156707i	−0.00984273	−	0.00689196i
$518$	1.69360	−	1.18587i	0.0744125	−	0.0521042i
$519$	8.26058	−	22.6957i	0.362599	−	0.996233i
$520$		0			0
$521$	6.83008	+	3.94335i	0.299231	+	0.172761i	0.642097	−	0.766623i	$-0.278064\pi$
$521$	6.83008	+	3.94335i	0.299231	+	0.172761i	−0.342866	+	0.939384i	$0.611398\pi$
$522$	−0.0916621	+	1.04770i	−0.00401194	+	0.0458567i
$523$	−0.410283	+	4.68956i	−0.0179404	+	0.205060i	0.981934	+	0.189223i	$0.0605969\pi$
$523$	−0.410283	+	4.68956i	−0.0179404	+	0.205060i	−0.999875	+	0.0158371i	$0.994959\pi$
$524$	1.57833	+	0.911249i	0.0689496	+	0.0398081i
$525$		0			0
$526$	8.75189	−	24.0456i	0.381600	−	1.04844i
$527$	27.8829	−	19.5238i	1.21460	−	0.850472i
$528$	−2.74719	−	1.92360i	−0.119556	−	0.0837141i
$529$	0.245691	+	0.675029i	0.0106822	+	0.0293491i
$530$		0			0
$531$			6.95919i			0.302003i
$532$	6.70719	+	12.6892i	0.290794	+	0.550147i
$533$	−0.260781	−	0.260781i	−0.0112957	−	0.0112957i
$534$	−9.37481	−	7.86640i	−0.405688	−	0.340412i
$535$		0			0
$536$	−1.06990	−	6.06772i	−0.0462127	−	0.262085i
$537$	−9.96900	−	14.2372i	−0.430194	−	0.614381i
$538$	11.2536	+	24.1334i	0.485177	+	1.04047i
$539$	5.93777	−	3.42817i	0.255758	−	0.147662i
$540$		0			0
$541$	−6.17988	+	5.18553i	−0.265694	+	0.222944i	−0.765895	−	0.642966i	$-0.777704\pi$
$541$	−6.17988	+	5.18553i	−0.265694	+	0.222944i	0.500201	+	0.865909i	$0.333259\pi$
$542$	−6.55280	−	0.573296i	−0.281467	−	0.0246252i
$543$	−15.8266	+	4.24073i	−0.679186	+	0.181987i
$544$	−2.34041	−	4.05371i	−0.100344	−	0.173802i
$545$		0			0
$546$	−0.534168	−	0.0941882i	−0.0228603	−	0.00403088i
$547$	−10.7454	+	15.3460i	−0.459439	+	0.656147i	−0.980305	−	0.197492i	$-0.936720\pi$
$547$	−10.7454	+	15.3460i	−0.459439	+	0.656147i	0.520865	+	0.853639i	$0.325609\pi$
$548$	0.206838	+	0.0964499i	0.00883566	+	0.00412014i
$549$	4.67815	−	5.57520i	0.199659	−	0.237944i
$550$		0			0
$551$	−8.23296	−	2.53912i	−0.350736	−	0.108170i
$552$	−6.27299	+	6.27299i	−0.266996	+	0.266996i
$553$	−43.6897	+	3.82236i	−1.85788	+	0.162543i
$554$	12.1678	−	4.42873i	0.516961	−	0.188159i
$555$		0			0
$556$	−3.93747	+	22.3305i	−0.166986	+	0.947025i
$557$	−27.2073	+	12.6870i	−1.15281	+	0.537564i	−0.902538	−	0.430611i	$-0.858298\pi$
$557$	−27.2073	+	12.6870i	−1.15281	+	0.537564i	−0.250273	+	0.968175i	$0.580520\pi$
$558$	−1.00146	+	3.73749i	−0.0423950	+	0.158220i
$559$	−0.249506	+	0.432157i	−0.0105530	+	0.0182783i
$560$		0			0
$561$	−10.0905	−	12.0254i	−0.426023	−	0.507714i
$562$	0.382878	+	1.42892i	0.0161507	+	0.0602753i
$563$	0.0968017	+	0.0259379i	0.00407971	+	0.00109315i	0.260858	−	0.965377i	$-0.415994\pi$
$563$	0.0968017	+	0.0259379i	0.00407971	+	0.00109315i	−0.256779	+	0.966470i	$0.582661\pi$
$564$	0.270389	+	0.0984137i	0.0113855	+	0.00414397i
$565$		0			0
$566$	28.5273	−	5.03012i	1.19909	−	0.211432i
$567$	14.3516	−	30.7770i	0.602709	−	1.29251i
$568$	−0.243659	−	2.78503i	−0.0102237	−	0.116857i
$569$	−26.3750			−1.10570			−0.552850	−	0.833281i	$-0.686460\pi$
$569$	−26.3750			−1.10570			−0.552850	+	0.833281i	$0.686460\pi$
$570$		0			0
$571$	−24.1697			−1.01147			−0.505735	−	0.862689i	$-0.668779\pi$
$571$	−24.1697			−1.01147			−0.505735	+	0.862689i	$0.668779\pi$
$572$	0.0136319	+	0.155813i	0.000569977	+	0.00651487i
$573$	−9.39971	+	20.1578i	−0.392679	+	0.842102i
$574$	−13.6443	+	2.40585i	−0.569501	+	0.100418i
$575$		0			0
$576$	0.500000	+	0.181985i	0.0208333	+	0.00758271i
$577$	−26.9664	−	7.22561i	−1.12262	−	0.300806i	−0.350679	−	0.936496i	$-0.614049\pi$
$577$	−26.9664	−	7.22561i	−1.12262	−	0.300806i	−0.771945	+	0.635689i	$0.780716\pi$
$578$	−1.27083	−	4.74281i	−0.0528596	−	0.197275i
$579$	−10.5473	−	12.5697i	−0.438329	−	0.522381i
$580$		0			0
$581$	8.50191	−	14.7257i	0.352719	−	0.610927i
$582$	4.06464	−	15.1695i	0.168485	−	0.628794i
$583$	−7.47499	+	3.48564i	−0.309582	+	0.144361i
$584$	−1.34063	+	7.60310i	−0.0554758	+	0.314619i
$585$		0			0
$586$	16.8325	−	6.12654i	0.695346	−	0.253085i
$587$	−12.3028	+	1.07636i	−0.507792	+	0.0444261i	−0.338174	−	0.941084i	$-0.609809\pi$
$587$	−12.3028	+	1.07636i	−0.507792	+	0.0444261i	−0.169619	+	0.985510i	$0.554254\pi$
$588$	−5.10605	+	5.10605i	−0.210570	+	0.210570i
$589$	−28.2076	−	14.4596i	−1.16227	−	0.595796i
$590$		0			0
$591$	−20.7639	+	24.7454i	−0.854112	+	1.01789i
$592$	0.569066	+	0.265360i	0.0233885	+	0.0109062i
$593$	15.4793	−	22.1067i	0.635659	−	0.907815i	−0.364063	−	0.931374i	$-0.618611\pi$
$593$	15.4793	−	22.1067i	0.635659	−	0.907815i	0.999722	+	0.0235590i	$0.00749976\pi$
$594$	−8.15089	−	1.43722i	−0.334435	−	0.0589699i
$595$		0			0
$596$	−1.37382	−	2.37953i	−0.0562739	−	0.0974693i
$597$	−6.87098	+	1.84107i	−0.281210	+	0.0753501i
$598$	0.412163	+	0.0360596i	0.0168546	+	0.00147459i
$599$	30.0738	−	25.2349i	1.22878	−	1.03107i	0.230465	−	0.973081i	$-0.425975\pi$
$599$	30.0738	−	25.2349i	1.22878	−	1.03107i	0.998317	−	0.0579896i	$-0.0184690\pi$
$600$		0			0
$601$	36.4203	−	21.0273i	1.48561	−	0.857720i	0.485748	−	0.874099i	$-0.338547\pi$
$601$	36.4203	−	21.0273i	1.48561	−	0.857720i	0.999866	+	0.0163790i	$0.00521382\pi$
$602$	7.92259	+	16.9901i	0.322901	+	0.692463i
$603$	1.88040	+	2.68548i	0.0765756	+	0.109361i
$604$	2.91253	+	16.5178i	0.118509	+	0.672099i
$605$		0			0
$606$	16.9475	+	14.2206i	0.688443	+	0.577672i
$607$	−13.5346	−	13.5346i	−0.549354	−	0.549354i	0.376900	−	0.926254i	$-0.376990\pi$
$607$	−13.5346	−	13.5346i	−0.549354	−	0.549354i	−0.926254	+	0.376900i	$0.876990\pi$
$608$	−2.31890	+	3.69089i	−0.0940440	+	0.149685i
$609$		−	12.2316i		−	0.495651i
$610$		0			0
$611$	−0.00458977	−	0.0126103i	−0.000185682	−	0.000510158i
$612$	2.04019	+	1.42856i	0.0824699	+	0.0577460i
$613$	−17.9877	+	12.5952i	−0.726518	+	0.508713i	−0.877353	−	0.479846i	$-0.840693\pi$
$613$	−17.9877	+	12.5952i	−0.726518	+	0.508713i	0.150835	+	0.988559i	$0.451804\pi$
$614$	3.10866	−	8.54096i	0.125455	−	0.344685i
$615$		0			0
$616$	5.08860	+	2.93791i	0.205026	+	0.118372i
$617$	−2.11867	+	24.2165i	−0.0852945	+	0.974921i	0.826137	+	0.563469i	$0.190534\pi$
$617$	−2.11867	+	24.2165i	−0.0852945	+	0.974921i	−0.911432	+	0.411452i	$0.865022\pi$
$618$	1.82505	−	20.8605i	0.0734145	−	0.839131i
$619$	−30.7908	−	17.7771i	−1.23759	−	0.714521i	−0.268986	−	0.963144i	$-0.586689\pi$
$619$	−30.7908	−	17.7771i	−1.23759	−	0.714521i	−0.968600	+	0.248623i	$0.920022\pi$
$620$		0			0
$621$	−7.48808	+	20.5733i	−0.300486	+	0.825580i
$622$	19.7886	−	13.8561i	0.793449	−	0.555579i
$623$	17.5637	+	12.2983i	0.703676	+	0.492719i
$624$	−0.0563402	−	0.154793i	−0.00225541	−	0.00619670i
$625$		0			0
$626$			29.4020i			1.17514i
$627$	−5.50932	+	13.5405i	−0.220021	+	0.540757i
$628$	−16.7831	−	16.7831i	−0.669719	−	0.669719i
$629$	2.25145	+	1.88919i	0.0897713	+	0.0753271i
$630$		0			0
$631$	1.31098	+	7.43493i	0.0521892	+	0.295980i	0.999719	−	0.0236864i	$-0.00754031\pi$
$631$	1.31098	+	7.43493i	0.0521892	+	0.295980i	−0.947530	+	0.319666i	$0.896429\pi$
$632$	−7.63953	−	10.9104i	−0.303884	−	0.433992i
$633$	5.65930	+	12.1364i	0.224937	+	0.482379i
$634$	2.79112	−	1.61146i	0.110850	−	0.0639991i
$635$		0			0
$636$	6.65421	−	5.58354i	0.263856	−	0.221402i
$637$	0.335490	+	0.0293516i	0.0132926	+	0.00116295i
$638$	−3.40692	+	0.912881i	−0.134881	+	0.0361413i
$639$	0.743772	+	1.28825i	0.0294232	+	0.0509624i
$640$		0			0
$641$	15.7180	+	2.77151i	0.620825	+	0.109468i	0.475209	−	0.879873i	$-0.342372\pi$
$641$	15.7180	+	2.77151i	0.620825	+	0.109468i	0.145616	+	0.989341i	$0.453484\pi$
$642$	17.0221	−	24.3101i	0.671809	−	0.959442i
$643$	3.25014	+	1.51557i	0.128173	+	0.0597681i	0.485647	−	0.874155i	$-0.338584\pi$
$643$	3.25014	+	1.51557i	0.128173	+	0.0597681i	−0.357474	+	0.933923i	$0.616362\pi$
$644$	9.99081	−	11.9066i	0.393693	−	0.469185i
$645$		0			0
$646$	−14.9560	+	13.8784i	−0.588436	+	0.546039i
$647$	8.30544	−	8.30544i	0.326520	−	0.326520i	−0.524741	−	0.851262i	$-0.675838\pi$
$647$	8.30544	−	8.30544i	0.326520	−	0.326520i	0.851262	+	0.524741i	$0.175838\pi$
$648$	10.2739	−	0.898850i	0.403597	−	0.0353102i
$649$	−21.9315	+	7.98242i	−0.860887	+	0.313337i
$650$		0			0
$651$	7.81443	−	44.3178i	0.306272	−	1.73695i
$652$	−8.56841	+	3.99551i	−0.335565	+	0.156476i
$653$	7.02165	−	26.2051i	0.274778	−	1.02549i	−0.681212	−	0.732087i	$-0.738547\pi$
$653$	7.02165	−	26.2051i	0.274778	−	1.02549i	0.955990	−	0.293400i	$-0.0947867\pi$
$654$	−4.53360	+	7.85243i	−0.177278	+	0.307054i
$655$		0			0
$656$	−2.70463	−	3.22325i	−0.105598	−	0.125847i
$657$	−1.06321	−	3.96796i	−0.0414798	−	0.154805i
$658$	−0.486958	−	0.130480i	−0.0189836	−	0.00508664i
$659$	−30.6896	−	11.1701i	−1.19550	−	0.435125i	−0.333846	−	0.942628i	$-0.608346\pi$
$659$	−30.6896	−	11.1701i	−1.19550	−	0.435125i	−0.861650	+	0.507503i	$0.830569\pi$
$660$		0			0
$661$	10.7233	−	1.89080i	0.417086	−	0.0735435i	0.0388330	−	0.999246i	$-0.487636\pi$
$661$	10.7233	−	1.89080i	0.417086	−	0.0735435i	0.378253	+	0.925702i	$0.376525\pi$
$662$	6.76445	−	14.5064i	0.262908	−	0.563808i
$663$	−0.0672025	−	0.768128i	−0.00260993	−	0.0298316i
$664$	5.16401			0.200402
$665$		0			0
$666$	−0.334096			−0.0129459
$667$	0.813166	+	9.29453i	0.0314859	+	0.359886i
$668$	−10.1373	+	21.7395i	−0.392223	+	0.841125i
$669$	39.5324	−	6.97063i	1.52841	−	0.269500i
$670$		0			0
$671$	22.9359	+	8.34800i	0.885432	+	0.322271i
$672$	−5.97749	−	1.60166i	−0.230587	−	0.0617856i
$673$	6.34446	+	23.6779i	0.244561	+	0.912714i	0.973604	+	0.228246i	$0.0732990\pi$
$673$	6.34446	+	23.6779i	0.244561	+	0.912714i	−0.729043	+	0.684468i	$0.760034\pi$
$674$	−7.55982	−	9.00944i	−0.291193	−	0.347031i
$675$		0			0
$676$	6.49616	−	11.2517i	0.249852	−	0.432757i
$677$	2.92231	−	10.9062i	0.112314	−	0.419160i	−0.886758	−	0.462233i	$-0.847048\pi$
$677$	2.92231	−	10.9062i	0.112314	−	0.419160i	0.999072	+	0.0430735i	$0.0137150\pi$
$678$	−3.70390	+	1.72715i	−0.142247	+	0.0663310i
$679$	−4.77793	+	27.0970i	−0.183360	+	1.03989i
$680$		0			0
$681$	−38.1014	+	13.8678i	−1.46005	+	0.531415i
$682$	−12.9272	+	1.13098i	−0.495008	+	0.0433076i
$683$	7.89889	−	7.89889i	0.302242	−	0.302242i	−0.539648	−	0.841891i	$-0.681443\pi$
$683$	7.89889	−	7.89889i	0.302242	−	0.302242i	0.841891	+	0.539648i	$0.181443\pi$
$684$	0.288287	−	2.30134i	0.0110229	−	0.0879937i
$685$		0			0
$686$	−6.68353	+	7.96512i	−0.255178	+	0.304110i
$687$	18.8218	+	8.77677i	0.718098	+	0.334855i
$688$	−3.26551	+	4.66363i	−0.124496	+	0.177799i
$689$	−0.398960	−	0.0703473i	−0.0151992	−	0.00268002i
$690$		0			0
$691$	−4.76158	−	8.24730i	−0.181139	−	0.313742i	0.761130	−	0.648600i	$-0.224645\pi$
$691$	−4.76158	−	8.24730i	−0.181139	−	0.313742i	−0.942269	+	0.334858i	$0.891312\pi$
$692$	−12.4133	+	3.32613i	−0.471882	+	0.126440i
$693$	−3.11456	−	0.272488i	−0.118312	−	0.0103510i
$694$	−24.4946	+	20.5534i	−0.929803	+	0.780197i
$695$		0			0
$696$	3.21704	−	1.85736i	0.121941	−	0.0704029i
$697$	−8.32358	−	17.8500i	−0.315278	−	0.676116i
$698$	4.98874	+	7.12465i	0.188826	+	0.269672i
$699$	0.254415	+	1.44286i	0.00962285	+	0.0545739i
$700$		0			0
$701$	5.00206	+	4.19723i	0.188925	+	0.158527i	0.732344	−	0.680934i	$-0.238426\pi$
$701$	5.00206	+	4.19723i	0.188925	+	0.158527i	−0.543419	+	0.839461i	$0.682871\pi$
$702$	−0.287463	−	0.287463i	−0.0108496	−	0.0108496i
$703$	0.575590	−	2.67572i	0.0217088	−	0.100917i
$704$			1.78447i			0.0672546i
$705$		0			0
$706$	11.9338	+	32.7880i	0.449136	+	1.23399i
$707$	−31.7511	−	22.2324i	−1.19412	−	0.836134i
$708$	20.1351	−	14.0988i	0.756725	−	0.529865i
$709$	10.2305	−	28.1080i	0.384214	−	1.05562i	−0.585350	−	0.810781i	$-0.699043\pi$
$709$	10.2305	−	28.1080i	0.384214	−	1.05562i	0.969564	−	0.244839i	$-0.0787349\pi$
$710$		0			0
$711$	6.13748	+	3.54348i	0.230174	+	0.132891i
$712$	−0.567530	+	6.48689i	−0.0212691	+	0.243107i
$713$	−2.99172	+	34.1955i	−0.112041	+	1.28063i
$714$	−25.0858	−	14.4833i	−0.938813	−	0.542024i
$715$		0			0
$716$	−3.16298	+	8.69021i	−0.118206	+	0.324768i
$717$	36.8078	−	25.7731i	1.37461	−	0.962513i
$718$	24.5565	+	17.1946i	0.916441	+	0.641699i
$719$	17.1193	+	47.0348i	0.638442	+	1.75410i	0.656567	+	0.754268i	$0.272008\pi$
$719$	17.1193	+	47.0348i	0.638442	+	1.75410i	−0.0181251	+	0.999836i	$0.505770\pi$
$720$		0			0
$721$			36.6880i			1.36633i
$722$	17.9344	+	6.27366i	0.667448	+	0.233481i
$723$	33.5632	+	33.5632i	1.24823	+	1.24823i
$724$	6.67856	+	5.60398i	0.248207	+	0.208270i
$725$		0			0
$726$	−2.55066	−	14.4655i	−0.0946639	−	0.536866i
$727$	4.15175	+	5.92932i	0.153980	+	0.219906i	0.888729	−	0.458433i	$-0.151589\pi$
$727$	4.15175	+	5.92932i	0.153980	+	0.219906i	−0.734749	+	0.678339i	$0.762700\pi$
$728$	0.121972	+	0.261569i	0.00452057	+	0.00969439i
$729$	17.8948	−	10.3316i	0.662770	−	0.382651i
$730$		0			0
$731$	−20.4144	+	17.1297i	−0.755052	+	0.633564i
$732$	−25.6084	−	2.24045i	−0.946514	−	0.0828092i
$733$	9.95924	−	2.66857i	0.367853	−	0.0985659i	−0.0701571	−	0.997536i	$-0.522350\pi$
$733$	9.95924	−	2.66857i	0.367853	−	0.0985659i	0.438010	+	0.898970i	$0.355683\pi$
$734$	4.62919	+	8.01798i	0.170866	+	0.295949i
$735$		0			0
$736$	4.64863	+	0.819679i	0.171351	+	0.0302138i
$737$	−6.30628	+	9.00631i	−0.232295	+	0.331752i
$738$	2.02908	+	0.946176i	0.0746915	+	0.0348292i
$739$	7.58687	−	9.04168i	0.279087	−	0.332603i	−0.608232	−	0.793760i	$-0.708121\pi$
$739$	7.58687	−	9.04168i	0.279087	−	0.332603i	0.887319	+	0.461156i	$0.152565\pi$
$740$		0			0
$741$	−0.603147	+	0.389593i	−0.0221572	+	0.0143121i
$742$	−10.7615	+	10.7615i	−0.395065	+	0.395065i
$743$	−6.66745	+	0.583326i	−0.244605	+	0.0214002i	−0.208799	−	0.977959i	$-0.566955\pi$
$743$	−6.66745	+	0.583326i	−0.244605	+	0.0214002i	−0.0358061	+	0.999359i	$0.511400\pi$
$744$	12.8426	−	4.67433i	0.470833	−	0.171369i
$745$		0			0
$746$	0.328185	−	1.86123i	0.0120157	−	0.0681444i
$747$	−2.49027	+	1.16123i	−0.0911143	+	0.0424873i
$748$	−2.16186	+	8.06816i	−0.0790453	+	0.295001i
$749$	−25.9977	+	45.0294i	−0.949937	+	1.64534i
$750$		0			0
$751$	−3.23061	−	3.85009i	−0.117887	−	0.140492i	0.703874	−	0.710325i	$-0.251452\pi$
$751$	−3.23061	−	3.85009i	−0.117887	−	0.140492i	−0.821760	+	0.569834i	$0.807008\pi$
$752$	−0.0396264	−	0.147888i	−0.00144503	−	0.00539291i
$753$	23.5111	+	6.29978i	0.856792	+	0.229577i
$754$	−0.162797	−	0.0592532i	−0.00592872	−	0.00215788i
$755$		0			0
$756$	−15.0403	+	2.65201i	−0.547010	+	0.0964527i
$757$	−11.5616	+	24.7939i	−0.420213	+	0.901149i	0.576263	+	0.817265i	$0.304511\pi$
$757$	−11.5616	+	24.7939i	−0.420213	+	0.901149i	−0.996475	+	0.0838847i	$0.973267\pi$
$758$	2.08086	+	23.7843i	0.0755801	+	0.863884i
$759$	15.8306			0.574615
$760$		0			0
$761$	5.14173			0.186388			0.0931938	−	0.995648i	$-0.470292\pi$
$761$	5.14173			0.186388			0.0931938	+	0.995648i	$0.470292\pi$
$762$	−2.32337	−	26.5562i	−0.0841667	−	0.962030i
$763$	6.71375	−	14.3977i	0.243054	−	0.521231i
$764$	11.6547	−	2.05504i	0.421653	−	0.0743488i
$765$		0			0
$766$	−26.4509	−	9.62733i	−0.955709	−	0.347850i
$767$	−1.10731	−	0.296703i	−0.0399826	−	0.0107133i
$768$	−0.486421	−	1.81535i	−0.0175522	−	0.0655057i
$769$	−8.74618	−	10.4233i	−0.315395	−	0.375873i	0.584935	−	0.811080i	$-0.301120\pi$
$769$	−8.74618	−	10.4233i	−0.315395	−	0.375873i	−0.900331	+	0.435206i	$0.856675\pi$
$770$		0			0
$771$	−22.2702	+	38.5731i	−0.802041	+	1.38918i
$772$	−2.25971	+	8.43335i	−0.0813288	+	0.303523i
$773$	31.0049	−	14.4578i	1.11517	−	0.520012i	0.224413	−	0.974494i	$-0.427954\pi$
$773$	31.0049	−	14.4578i	1.11517	−	0.520012i	0.890756	+	0.454483i	$0.150176\pi$
$774$	0.526034	−	2.98329i	0.0189079	−	0.107232i
$775$		0			0
$776$	−7.85229	+	2.85800i	−0.281881	+	0.102596i
$777$	3.87085	−	0.338655i	0.138866	−	0.0121492i
$778$	0.156384	−	0.156384i	0.00560665	−	0.00560665i
$779$	−11.0735	+	14.6205i	−0.396751	+	0.523834i
$780$		0			0
$781$	−3.20672	+	3.82163i	−0.114746	+	0.136749i
$782$	20.0250	+	9.33779i	0.716091	+	0.333919i
$783$	5.25831	−	7.50964i	0.187917	−	0.268373i
$784$	3.78387	+	0.667198i	0.135138	+	0.0238285i
$785$		0			0
$786$	1.71259	+	2.96629i	0.0610860	+	0.105804i
$787$	40.7244	−	10.9121i	1.45167	−	0.388973i	0.555065	−	0.831807i	$-0.312693\pi$
$787$	40.7244	−	10.9121i	1.45167	−	0.388973i	0.896604	+	0.442834i	$0.146027\pi$
$788$	17.1226	+	1.49803i	0.609967	+	0.0533652i
$789$	36.8400	−	30.9124i	1.31154	−	1.10051i
$790$		0			0
$791$	6.20094	−	3.58011i	0.220480	−	0.127294i
$792$	−0.401274	−	0.860535i	−0.0142586	−	0.0305778i
$793$	0.687646	+	0.982060i	0.0244190	+	0.0348740i
$794$	0.968488	+	5.49257i	0.0343703	+	0.194924i
$795$		0			0
$796$	2.89943	+	2.43291i	0.102768	+	0.0862323i
$797$	21.0090	+	21.0090i	0.744176	+	0.744176i	0.973379	−	0.229203i	$-0.0736120\pi$
$797$	21.0090	+	21.0090i	0.744176	+	0.744176i	−0.229203	+	0.973379i	$0.573612\pi$
$798$	−1.00737	+	26.9556i	−0.0356604	+	0.954218i
$799$		−	0.716656i		−	0.0253535i
$800$		0			0
$801$	−1.18503	−	3.25584i	−0.0418709	−	0.115039i
$802$	−26.8792	−	18.8210i	−0.949137	−	0.664593i
$803$	11.2853	−	7.90204i	0.398249	−	0.278857i
$804$	3.96042	−	10.8812i	0.139673	−	0.383749i
$805$		0			0
$806$	−0.551993	−	0.318693i	−0.0194431	−	0.0112255i
$807$	−4.36169	+	49.8544i	−0.153539	+	1.75496i
$808$	1.02596	−	11.7268i	0.0360932	−	0.412547i
$809$	−13.9609	−	8.06031i	−0.490838	−	0.283385i	0.234084	−	0.972216i	$-0.424791\pi$
$809$	−13.9609	−	8.06031i	−0.490838	−	0.283385i	−0.724922	+	0.688831i	$0.758124\pi$
$810$		0			0
$811$	−2.63474	+	7.23890i	−0.0925184	+	0.254192i	−0.977317	−	0.211781i	$-0.932074\pi$
$811$	−2.63474	+	7.23890i	−0.0925184	+	0.254192i	0.884799	+	0.465973i	$0.154296\pi$
$812$	−5.33130	+	3.73302i	−0.187092	+	0.131003i
$813$	−10.1266	−	7.09071i	−0.355155	−	0.248682i
$814$	−0.383219	−	1.05288i	−0.0134318	−	0.0369036i
$815$		0			0
$816$		−	8.79707i		−	0.307959i
$817$	22.9864	+	9.35262i	0.804193	+	0.327207i
$818$	1.99531	+	1.99531i	0.0697642	+	0.0697642i
$819$	−0.117638	−	0.0987102i	−0.00411061	−	0.00344922i
$820$		0			0
$821$	−3.07209	−	17.4227i	−0.107217	−	0.608055i	−0.990312	−	0.138862i	$-0.955656\pi$
$821$	−3.07209	−	17.4227i	−0.107217	−	0.608055i	0.883095	−	0.469194i	$-0.155455\pi$
$822$	0.246015	+	0.351345i	0.00858074	+	0.0122546i
$823$	−8.90378	−	19.0942i	−0.310366	−	0.665583i	0.687814	−	0.725887i	$-0.258571\pi$
$823$	−8.90378	−	19.0942i	−0.310366	−	0.665583i	−0.998180	+	0.0603045i	$0.980793\pi$
$824$	−9.64928	+	5.57101i	−0.336148	+	0.194075i
$825$		0			0
$826$	−32.9904	+	27.6822i	−1.14788	+	0.963189i
$827$	−23.9288	−	2.09350i	−0.832087	−	0.0727982i	−0.336852	−	0.941558i	$-0.609362\pi$
$827$	−23.9288	−	2.09350i	−0.832087	−	0.0727982i	−0.495234	+	0.868759i	$0.664918\pi$
$828$	−2.42606	+	0.650061i	−0.0843114	+	0.0225912i
$829$	−12.2908	−	21.2883i	−0.426876	−	0.739372i	0.569717	−	0.821841i	$-0.307053\pi$
$829$	−12.2908	−	21.2883i	−0.426876	−	0.739372i	−0.996594	+	0.0824691i	$0.973719\pi$
$830$		0			0
$831$	23.9659	+	4.22584i	0.831369	+	0.146593i
$832$	−0.0502739	+	0.0717985i	−0.00174293	+	0.00248917i
$833$	16.2998	+	7.60073i	0.564755	+	0.263350i
$834$	−27.3924	+	32.6450i	−0.948523	+	1.13041i
$835$		0			0
$836$	7.58321	−	1.73118i	0.262271	−	0.0598743i
$837$	23.8496	−	23.8496i	0.824364	−	0.824364i
$838$	−34.5099	+	3.01923i	−1.19213	+	0.104297i
$839$	−2.96152	+	1.07791i	−0.102243	+	0.0372135i	−0.392635	−	0.919694i	$-0.628436\pi$
$839$	−2.96152	+	1.07791i	−0.102243	+	0.0372135i	0.290392	+	0.956908i	$0.406214\pi$
$840$		0			0
$841$	−4.35739	+	24.7120i	−0.150255	+	0.852138i
$842$	−16.5084	+	7.69798i	−0.568916	+	0.265290i
$843$	−0.719575	+	2.68549i	−0.0247835	+	0.0924932i
$844$	3.56261	−	6.17062i	0.122630	−	0.212402i
$845$		0			0
$846$	0.0523648	+	0.0624060i	0.00180034	+	0.00214556i
$847$	6.66074	+	24.8582i	0.228866	+	0.854139i
$848$	−4.46447	−	1.19625i	−0.153311	−	0.0410795i
$849$	51.1576	+	18.6198i	1.75572	+	0.639031i
$850$		0			0
$851$	−2.91885	+	0.514672i	−0.100057	+	0.0176427i
$852$	2.22050	−	4.76187i	0.0760729	−	0.163139i
$853$	1.56658	+	17.9061i	0.0536386	+	0.613092i	0.974677	+	0.223619i	$0.0717872\pi$
$853$	1.56658	+	17.9061i	0.0536386	+	0.613092i	−0.921038	+	0.389473i	$0.872657\pi$
$854$	45.0383			1.54118
$855$		0			0
$856$	−15.7909			−0.539721
$857$	2.00787	+	22.9500i	0.0685875	+	0.783959i	0.950130	+	0.311854i	$0.100950\pi$
$857$	2.00787	+	22.9500i	0.0685875	+	0.783959i	−0.881543	+	0.472105i	$0.843494\pi$
$858$	−0.124229	+	0.266410i	−0.00424111	+	0.00909510i
$859$	46.8105	−	8.25396i	1.59715	−	0.281622i	0.696960	−	0.717110i	$-0.254535\pi$
$859$	46.8105	−	8.25396i	1.59715	−	0.281622i	0.900195	+	0.435488i	$0.143424\pi$
$860$		0			0
$861$	−24.4681	−	8.90567i	−0.833872	−	0.303504i
$862$	10.2717	+	2.75230i	0.349856	+	0.0937438i
$863$	−14.7185	−	54.9302i	−0.501024	−	1.86985i	−0.493269	−	0.869877i	$-0.664198\pi$
$863$	−14.7185	−	54.9302i	−0.501024	−	1.86985i	−0.00775464	−	0.999970i	$-0.502468\pi$
$864$	−2.98135	−	3.55303i	−0.101428	−	0.120877i
$865$		0			0
$866$	1.19058	−	2.06214i	0.0404575	−	0.0700744i
$867$	2.38838	−	8.91356i	0.0811137	−	0.302720i
$868$	−21.7014	+	10.1195i	−0.736592	+	0.343479i
$869$	−4.12719	+	23.4064i	−0.140005	+	0.794009i
$870$		0			0
$871$	−0.507470	+	0.184704i	−0.0171950	+	0.00625846i
$872$	4.80620	−	0.420488i	0.162758	−	0.0142395i
$873$	3.14398	−	3.14398i	0.106408	−	0.106408i
$874$	−1.02655	−	20.5499i	−0.0347235	−	0.695110i
$875$		0			0
$876$	−9.32659	+	11.1150i	−0.315116	+	0.375541i
$877$	40.6713	+	18.9653i	1.37337	+	0.640413i	0.962500	−	0.271280i	$-0.0874471\pi$
$877$	40.6713	+	18.9653i	1.37337	+	0.640413i	0.410870	+	0.911694i	$0.365225\pi$
$878$	−10.6219	+	15.1697i	−0.358473	+	0.511953i
$879$	33.1536	+	5.84588i	1.11824	+	0.197177i
$880$		0			0
$881$	0.668039	+	1.15708i	0.0225068	+	0.0389829i	0.877059	−	0.480382i	$-0.159502\pi$
$881$	0.668039	+	1.15708i	0.0225068	+	0.0389829i	−0.854553	+	0.519365i	$0.826169\pi$
$882$	−1.97475	+	0.529133i	−0.0664934	+	0.0178168i
$883$	56.2931	+	4.92501i	1.89441	+	0.165740i	0.974202	−	0.225679i	$-0.0724601\pi$
$883$	56.2931	+	4.92501i	1.89441	+	0.165740i	0.920213	+	0.391419i	$0.128016\pi$
$884$	−0.314288	+	0.263719i	−0.0105706	+	0.00886982i
$885$		0			0
$886$	−21.9805	+	12.6905i	−0.738450	+	0.426344i
$887$	−4.31811	−	9.26022i	−0.144988	−	0.310928i	0.820380	−	0.571818i	$-0.193762\pi$
$887$	−4.31811	−	9.26022i	−0.144988	−	0.310928i	−0.965368	+	0.260890i	$0.915984\pi$
$888$	0.676852	+	0.966645i	0.0227137	+	0.0324385i
$889$	8.11028	+	45.9957i	0.272010	+	1.54265i
$890$		0			0
$891$	−14.0979	−	11.8295i	−0.472297	−	0.396304i
$892$	−15.1033	−	15.1033i	−0.505695	−	0.505695i
$893$	−0.590015	+	0.311867i	−0.0197441	+	0.0104362i
$894$		−	5.16388i		−	0.172706i
$895$		0			0
$896$	1.12619	+	3.09418i	0.0376233	+	0.103369i
$897$	0.636950	+	0.445997i	0.0212671	+	0.0148914i
$898$	30.3810	−	21.2730i	1.01383	−	0.709889i
$899$	4.91601	−	13.5066i	0.163958	−	0.450471i
$900$		0			0
$901$	−18.7361	−	10.8173i	−0.624190	−	0.360376i
$902$	−0.654401	+	7.47984i	−0.0217892	+	0.249051i
$903$	−3.07065	+	35.0977i	−0.102185	+	1.16798i
$904$	1.88321	+	1.08727i	0.0626345	+	0.0361620i
$905$		0			0
$906$	−10.7812	+	29.6212i	−0.358182	+	0.984097i
$907$	3.70078	−	2.59132i	0.122883	−	0.0860433i	−0.510519	−	0.859866i	$-0.670547\pi$
$907$	3.70078	−	2.59132i	0.122883	−	0.0860433i	0.633402	+	0.773823i	$0.281658\pi$
$908$	17.6728	+	12.3746i	0.586491	+	0.410665i
$909$	2.14225	+	5.88579i	0.0710540	+	0.195219i
$910$		0			0
$911$		−	45.7057i		−	1.51430i	−0.653243	−	0.757148i	$-0.726592\pi$
$911$		−	45.7057i		−	1.51430i	0.653243	−	0.757148i	$-0.273408\pi$
$912$	−7.24254	+	3.82822i	−0.239825	+	0.126765i
$913$	−6.51599	−	6.51599i	−0.215648	−	0.215648i
$914$	15.1420	+	12.7056i	0.500851	+	0.420264i
$915$		0			0
$916$	−1.91885	−	10.8823i	−0.0634006	−	0.359563i
$917$	−3.44206	−	4.91576i	−0.113667	−	0.162333i
$918$	−9.17521	−	19.6763i	−0.302827	−	0.649415i
$919$	−17.3858	+	10.0377i	−0.573506	+	0.331114i	−0.758548	−	0.651617i	$-0.774091\pi$
$919$	−17.3858	+	10.0377i	−0.573506	+	0.331114i	0.185042	+	0.982731i	$0.440758\pi$
$920$		0			0
$921$	13.0855	−	10.9801i	0.431182	−	0.361805i
$922$	−26.3937	−	2.30915i	−0.869231	−	0.0760479i
$923$	−0.236690	+	0.0634210i	−0.00779076	+	0.00208753i
$924$	5.52146	+	9.56344i	0.181643	+	0.314614i
$925$		0			0
$926$	−0.355412	−	0.0626688i	−0.0116796	−	0.00205942i
$927$	3.40047	−	4.85638i	0.111686	−	0.159504i
$928$	−1.79137	−	0.835329i	−0.0588046	−	0.0274210i
$929$	−5.15730	+	6.14623i	−0.169206	+	0.201651i	−0.843983	−	0.536370i	$-0.819795\pi$
$929$	−5.15730	+	6.14623i	−0.169206	+	0.201651i	0.674777	+	0.738021i	$0.264240\pi$
$930$		0			0
$931$	−0.835584	−	16.7271i	−0.0273852	−	0.548208i
$932$	0.551241	−	0.551241i	0.0180565	−	0.0180565i
$933$	45.2282	−	3.95696i	1.48071	−	0.129545i
$934$	8.95288	−	3.25858i	0.292947	−	0.106624i
$935$		0			0
$936$	0.00809852	−	0.0459290i	0.000264708	−	0.00150124i
$937$	−11.4328	+	5.33119i	−0.373493	+	0.174162i	−0.600296	−	0.799778i	$-0.704950\pi$
$937$	−11.4328	+	5.33119i	−0.373493	+	0.174162i	0.226803	+	0.973941i	$0.427173\pi$
$938$	−5.25085	+	19.5964i	−0.171446	+	0.639846i
$939$	−27.6289	+	47.8546i	−0.901634	+	1.56168i
$940$		0			0
$941$	−13.7030	−	16.3306i	−0.446705	−	0.532363i	0.494959	−	0.868916i	$-0.335183\pi$
$941$	−13.7030	−	16.3306i	−0.446705	−	0.532363i	−0.941664	+	0.336554i	$0.890739\pi$
$942$	−11.5451	−	43.0871i	−0.376161	−	1.40385i
$943$	19.1848	+	5.14055i	0.624743	+	0.167399i
$944$	−12.2902	−	4.47328i	−0.400013	−	0.145593i
$945$		0			0
$946$	10.0051	−	1.76416i	0.325292	−	0.0573578i
$947$	−13.0264	+	27.9352i	−0.423300	+	0.907771i	0.572813	+	0.819686i	$0.305852\pi$
$947$	−13.0264	+	27.9352i	−0.423300	+	0.907771i	−0.996113	+	0.0880844i	$0.971925\pi$
$948$	−2.18166	−	24.9365i	−0.0708571	−	0.809900i
$949$	0.676691			0.0219663
$950$		0			0
$951$	6.05709			0.196415
$952$	1.34332	+	15.3542i	0.0435371	+	0.497631i
$953$	−2.86748	+	6.14934i	−0.0928869	+	0.199197i	−0.947262	−	0.320460i	$-0.896162\pi$
$953$	−2.86748	+	6.14934i	−0.0928869	+	0.199197i	0.854375	+	0.519657i	$0.173940\pi$
$954$	2.42193	−	0.427052i	0.0784130	−	0.0138263i
$955$		0			0
$956$	−22.4670	−	8.17731i	−0.726634	−	0.264473i
$957$	−6.40291	−	1.71565i	−0.206977	−	0.0554592i
$958$	−1.37841	−	5.14428i	−0.0445343	−	0.166204i
$959$	−0.483037	−	0.575661i	−0.0155981	−	0.0185891i
$960$		0			0
$961$	10.9407	−	18.9499i	0.352926	−	0.611287i
$962$	0.0142441	−	0.0531596i	0.000459247	−	0.00171393i
$963$	7.61493	−	3.55090i	0.245388	−	0.114426i
$964$	4.38564	−	24.8722i	0.141252	−	0.801079i
$965$		0			0
$966$	27.4495	−	9.99081i	0.883174	−	0.321449i
$967$	48.7531	−	4.26534i	1.56779	−	0.137164i	0.730114	−	0.683326i	$-0.239467\pi$
$967$	48.7531	−	4.26534i	1.56779	−	0.137164i	0.837680	+	0.546162i	$0.183912\pi$
$968$	−5.52652	+	5.52652i	−0.177629	+	0.177629i
$969$	−37.3838	+	8.53440i	−1.20094	+	0.274165i
$970$		0			0
$971$	−20.4328	+	24.3508i	−0.655718	+	0.781455i	−0.986764	−	0.162160i	$-0.948154\pi$
$971$	−20.4328	+	24.3508i	−0.655718	+	0.781455i	0.331046	+	0.943615i	$0.392598\pi$
$972$	4.95561	+	2.31084i	0.158951	+	0.0741202i
$973$	42.8251	−	61.1606i	1.37291	−	1.96072i
$974$	−26.0641	−	4.59580i	−0.835148	−	0.147259i
$975$		0			0
$976$	6.83900	+	11.8455i	0.218911	+	0.379165i
$977$	−8.13219	+	2.17901i	−0.260172	+	0.0697128i	−0.386547	−	0.922270i	$-0.626332\pi$
$977$	−8.13219	+	2.17901i	−0.260172	+	0.0697128i	0.126375	+	0.991983i	$0.459666\pi$
$978$	−17.7005	−	1.54859i	−0.565998	−	0.0495184i
$979$	8.90133	−	7.46910i	0.284488	−	0.238714i
$980$		0			0
$981$	−2.22317	+	1.28355i	−0.0709803	+	0.0409805i
$982$	3.10965	+	6.66866i	0.0992328	+	0.212805i
$983$	4.08228	+	5.83010i	0.130205	+	0.185951i	0.878961	−	0.476894i	$-0.158237\pi$
$983$	4.08228	+	5.83010i	0.130205	+	0.185951i	−0.748756	+	0.662846i	$0.769349\pi$
$984$	−1.37317	−	7.78766i	−0.0437752	−	0.248261i
$985$		0			0
$986$	−7.08738	−	5.94702i	−0.225708	−	0.189392i
$987$	−0.669959	−	0.669959i	−0.0213250	−	0.0213250i
$988$	0.353885	+	0.143987i	0.0112586	+	0.00458085i
$989$		−	26.8740i		−	0.854545i
$990$		0			0
$991$	2.23427	+	6.13860i	0.0709739	+	0.194999i	0.970108	−	0.242675i	$-0.0780247\pi$
$991$	2.23427	+	6.13860i	0.0709739	+	0.194999i	−0.899134	+	0.437674i	$0.855803\pi$
$992$	−5.95684	−	4.17103i	−0.189130	−	0.132430i
$993$	24.6414	−	17.2541i	0.781970	−	0.547541i
$994$	−3.14845	+	8.65030i	−0.0998628	+	0.274371i
$995$		0			0
$996$	8.40492	+	4.85258i	0.266320	+	0.153760i
$997$	1.98790	−	22.7218i	0.0629575	−	0.719608i	−0.897470	−	0.441076i	$-0.854597\pi$
$997$	1.98790	−	22.7218i	0.0629575	−	0.719608i	0.960427	−	0.278531i	$-0.0898476\pi$
$998$	2.88440	−	32.9689i	0.0913042	−	1.04361i
$999$	2.52210	+	1.45614i	0.0797958	+	0.0460701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.b.193.2	✓	48
5.2	odd	4	inner	950.2.bb.b.307.3	yes	48
5.3	odd	4	inner	950.2.bb.b.307.2	yes	48
5.4	even	2	inner	950.2.bb.b.193.3	yes	48
19.13	odd	18	inner	950.2.bb.b.393.3	yes	48
95.13	even	36	inner	950.2.bb.b.507.3	yes	48
95.32	even	36	inner	950.2.bb.b.507.2	yes	48
95.89	odd	18	inner	950.2.bb.b.393.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.b.193.2	✓	48	1.1	even	1	trivial
950.2.bb.b.193.3	yes	48	5.4	even	2	inner
950.2.bb.b.307.2	yes	48	5.3	odd	4	inner
950.2.bb.b.307.3	yes	48	5.2	odd	4	inner
950.2.bb.b.393.2	yes	48	95.89	odd	18	inner
950.2.bb.b.393.3	yes	48	19.13	odd	18	inner
950.2.bb.b.507.2	yes	48	95.32	even	36	inner
950.2.bb.b.507.3	yes	48	95.13	even	36	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(0.794263 - 1.70330i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(3.18056 + 0.852228i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-0.342020 - 0.407604i) q^{9} +O(q^{10})\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(0.794263 - 1.70330i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(3.18056 + 0.852228i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-0.342020 - 0.407604i) q^{9} +(0.892233 - 1.54539i) q^{11} +(-0.486421 + 1.81535i) q^{12} +(0.0794377 - 0.0370424i) q^{13} +(0.571781 - 3.24273i) q^{14} +(0.939693 - 0.342020i) q^{16} +(4.66301 - 0.407961i) q^{17} +(-0.376244 + 0.376244i) q^{18} +(-2.36507 - 3.66148i) q^{19} +(3.97780 - 4.74056i) q^{21} +(-1.61728 - 0.754148i) q^{22} +(-2.70748 + 3.86668i) q^{23} +(1.85083 + 0.326352i) q^{24} +(-0.0438249 - 0.0759070i) q^{26} +(4.48011 - 1.20044i) q^{27} +(-3.28023 - 0.286983i) q^{28} +(1.51413 - 1.27051i) q^{29} +(6.29770 - 3.63598i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(-1.92360 - 2.74719i) q^{33} +(-0.812817 - 4.60971i) q^{34} +(0.407604 + 0.342020i) q^{36} +(0.443988 + 0.443988i) q^{37} +(-3.44142 + 2.67519i) q^{38} -0.164728i q^{39} +(-1.43910 - 3.95390i) q^{41} +(-5.06920 - 3.54950i) q^{42} +(-4.66363 + 3.26551i) q^{43} +(-0.610323 + 1.67685i) q^{44} +(4.08794 + 2.36017i) q^{46} +(0.0133439 - 0.152522i) q^{47} +(0.163799 - 1.87223i) q^{48} +(3.32748 + 1.92112i) q^{49} +(3.00878 - 8.26654i) q^{51} +(-0.0717985 + 0.0502739i) q^{52} +(-3.78609 - 2.65105i) q^{53} +(-1.58634 - 4.35844i) q^{54} +3.29276i q^{56} +(-8.11509 + 1.12026i) q^{57} +(-1.39764 - 1.39764i) q^{58} +(-10.0191 - 8.40702i) q^{59} +(2.37516 + 13.4702i) q^{61} +(-4.17103 - 5.95684i) q^{62} +(-0.740444 - 1.58789i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-2.56908 + 2.15572i) q^{66} +(-6.13787 - 0.536994i) q^{67} +(-4.52133 + 1.21149i) q^{68} +(4.43567 + 7.68281i) q^{69} +(-2.75320 - 0.485463i) q^{71} +(0.305194 - 0.435862i) q^{72} +(6.99705 + 3.26278i) q^{73} +(0.403603 - 0.480995i) q^{74} +(2.96495 + 3.19516i) q^{76} +(4.15483 - 4.15483i) q^{77} +(-0.164101 + 0.0143570i) q^{78} +(-12.5159 + 4.55541i) q^{79} +(1.79086 - 10.1565i) q^{81} +(-3.81343 + 1.77823i) q^{82} +(1.33654 - 4.98805i) q^{83} +(-3.09418 + 5.35927i) q^{84} +(3.65954 + 4.36127i) q^{86} +(-0.961438 - 3.58814i) q^{87} +(1.72366 + 0.461854i) q^{88} +(6.11897 + 2.22712i) q^{89} +(0.284225 - 0.0501165i) q^{91} +(1.99490 - 4.27808i) q^{92} +(-1.19114 - 13.6148i) q^{93} -0.153105 q^{94} -1.87939 q^{96} +(0.728294 + 8.32443i) q^{97} +(1.62380 - 3.48225i) q^{98} +(-0.935070 + 0.164878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{6}+O(q^{10}) \) 48 * q - 48 * q^6	\( 48 q - 48 q^{6} - 12 q^{11} + 36 q^{21} - 72 q^{31} + 48 q^{36} + 96 q^{41} + 72 q^{46} - 48 q^{51} - 108 q^{61} + 24 q^{66} - 60 q^{71} - 48 q^{76} - 168 q^{81} - 48 q^{86} + 252 q^{91}+O(q^{100}) \) 48 * q - 48 * q^6 - 12 * q^11 + 36 * q^21 - 72 * q^31 + 48 * q^36 + 96 * q^41 + 72 * q^46 - 48 * q^51 - 108 * q^61 + 24 * q^66 - 60 * q^71 - 48 * q^76 - 168 * q^81 - 48 * q^86 + 252 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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