LMFDB - Embedded newform 950.2.l.b.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			301.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	950.301
Dual form			950.2.l.b.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(-1.26604 + 0.460802i) q^{3} +(0.173648 + 0.984808i) q^{4} +(1.26604 + 0.460802i) q^{6} +(-1.43969 - 2.49362i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.907604 + 0.761570i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.26604 + 0.460802i) q^{3} +(0.173648 + 0.984808i) q^{4} +(1.26604 + 0.460802i) q^{6} +(-1.43969 - 2.49362i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.907604 + 0.761570i) q^{9} +(0.500000 - 0.866025i) q^{11} +(-0.673648 - 1.16679i) q^{12} +(-0.500000 - 0.181985i) q^{13} +(-0.500000 + 2.83564i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-1.26604 - 1.06234i) q^{17} +1.18479 q^{18} +(3.79086 + 2.15160i) q^{19} +(2.97178 + 2.49362i) q^{21} +(-0.939693 + 0.342020i) q^{22} +(0.194593 + 1.10359i) q^{23} +(-0.233956 + 1.32683i) q^{24} +(0.266044 + 0.460802i) q^{26} +(2.81908 - 4.88279i) q^{27} +(2.20574 - 1.85083i) q^{28} +(-1.81521 + 1.52314i) q^{29} +(0.847296 + 1.46756i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.233956 + 1.32683i) q^{33} +(0.286989 + 1.62760i) q^{34} +(-0.907604 - 0.761570i) q^{36} -2.59627 q^{37} +(-1.52094 - 4.08494i) q^{38} +0.716881 q^{39} +(-4.85844 + 1.76833i) q^{41} +(-0.673648 - 3.82045i) q^{42} +(-1.88666 + 10.6998i) q^{43} +(0.939693 + 0.342020i) q^{44} +(0.560307 - 0.970481i) q^{46} +(-1.39053 + 1.16679i) q^{47} +(1.03209 - 0.866025i) q^{48} +(-0.645430 + 1.11792i) q^{49} +(2.09240 + 0.761570i) q^{51} +(0.0923963 - 0.524005i) q^{52} +(2.08512 + 11.8253i) q^{53} +(-5.29813 + 1.92836i) q^{54} -2.87939 q^{56} +(-5.79086 - 0.977185i) q^{57} +2.36959 q^{58} +(6.72668 + 5.64436i) q^{59} +(1.08512 + 6.15403i) q^{61} +(0.294263 - 1.66885i) q^{62} +(3.20574 + 1.16679i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.03209 - 0.866025i) q^{66} +(-1.93969 + 1.62760i) q^{67} +(0.826352 - 1.43128i) q^{68} +(-0.754900 - 1.30753i) q^{69} +(-1.02229 + 5.79769i) q^{71} +(0.205737 + 1.16679i) q^{72} +(-4.68479 + 1.70513i) q^{73} +(1.98886 + 1.66885i) q^{74} +(-1.46064 + 4.10689i) q^{76} -2.87939 q^{77} +(-0.549163 - 0.460802i) q^{78} +(8.05690 - 2.93247i) q^{79} +(-0.701867 + 3.98048i) q^{81} +(4.85844 + 1.76833i) q^{82} +(5.32888 + 9.22989i) q^{83} +(-1.93969 + 3.35965i) q^{84} +(8.32295 - 6.98378i) q^{86} +(1.59627 - 2.76481i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-0.694593 - 0.252811i) q^{89} +(0.266044 + 1.50881i) q^{91} +(-1.05303 + 0.383273i) q^{92} +(-1.74897 - 1.46756i) q^{93} +1.81521 q^{94} -1.34730 q^{96} +(8.88919 + 7.45891i) q^{97} +(1.21301 - 0.441500i) q^{98} +(0.205737 + 1.16679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} + 3 q^{6} - 3 q^{7} + 3 q^{8} - 9 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 + 3 * q^6 - 3 * q^7 + 3 * q^8 - 9 * q^9	$ 6 q - 3 q^{3} + 3 q^{6} - 3 q^{7} + 3 q^{8} - 9 q^{9} + 3 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} - 3 q^{17} - 9 q^{19} + 3 q^{21} - 3 q^{23} - 6 q^{24} - 3 q^{26} + 3 q^{28} - 18 q^{29} + 3 q^{31} - 6 q^{33} - 6 q^{34} - 9 q^{36} + 12 q^{37} - 6 q^{38} - 12 q^{39} - 21 q^{41} - 3 q^{42} - 18 q^{43} + 9 q^{46} + 9 q^{47} - 3 q^{48} + 12 q^{49} + 9 q^{51} - 3 q^{52} - 9 q^{53} - 18 q^{54} - 6 q^{56} - 3 q^{57} + 27 q^{59} - 15 q^{61} + 12 q^{62} + 9 q^{63} - 3 q^{64} - 3 q^{66} - 6 q^{67} + 6 q^{68} - 6 q^{69} + 6 q^{71} - 9 q^{72} - 21 q^{73} + 18 q^{74} - 6 q^{77} - 15 q^{78} + 12 q^{79} - 18 q^{81} + 21 q^{82} + 18 q^{83} - 6 q^{84} + 9 q^{86} - 18 q^{87} - 3 q^{88} - 3 q^{91} + 6 q^{92} + 15 q^{93} + 18 q^{94} - 6 q^{96} + 45 q^{97} + 15 q^{98} - 9 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 + 3 * q^6 - 3 * q^7 + 3 * q^8 - 9 * q^9 + 3 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 - 3 * q^17 - 9 * q^19 + 3 * q^21 - 3 * q^23 - 6 * q^24 - 3 * q^26 + 3 * q^28 - 18 * q^29 + 3 * q^31 - 6 * q^33 - 6 * q^34 - 9 * q^36 + 12 * q^37 - 6 * q^38 - 12 * q^39 - 21 * q^41 - 3 * q^42 - 18 * q^43 + 9 * q^46 + 9 * q^47 - 3 * q^48 + 12 * q^49 + 9 * q^51 - 3 * q^52 - 9 * q^53 - 18 * q^54 - 6 * q^56 - 3 * q^57 + 27 * q^59 - 15 * q^61 + 12 * q^62 + 9 * q^63 - 3 * q^64 - 3 * q^66 - 6 * q^67 + 6 * q^68 - 6 * q^69 + 6 * q^71 - 9 * q^72 - 21 * q^73 + 18 * q^74 - 6 * q^77 - 15 * q^78 + 12 * q^79 - 18 * q^81 + 21 * q^82 + 18 * q^83 - 6 * q^84 + 9 * q^86 - 18 * q^87 - 3 * q^88 - 3 * q^91 + 6 * q^92 + 15 * q^93 + 18 * q^94 - 6 * q^96 + 45 * q^97 + 15 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	−1.26604	+	0.460802i	−0.730951	+	0.266044i	−0.680567	−	0.732685i	$-0.738267\pi$
$3$	−1.26604	+	0.460802i	−0.730951	+	0.266044i	−0.0503837	+	0.998730i	$0.516044\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$		0			0
$5$		0			0
$6$	1.26604	+	0.460802i	0.516860	+	0.188122i
$7$	−1.43969	−	2.49362i	−0.544153	−	0.942500i	−0.998660	−	0.0517569i	$-0.983518\pi$
$7$	−1.43969	−	2.49362i	−0.544153	−	0.942500i	0.454507	−	0.890743i	$-0.349815\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.907604	+	0.761570i	−0.302535	+	0.253857i
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	−0.780750	−	0.624844i	$-0.785163\pi$
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	0.931505	+	0.363727i	$0.118496\pi$
$12$	−0.673648	−	1.16679i	−0.194465	−	0.336824i
$13$	−0.500000	−	0.181985i	−0.138675	−	0.0504736i	0.271750	−	0.962368i	$-0.412398\pi$
$13$	−0.500000	−	0.181985i	−0.138675	−	0.0504736i	−0.410425	+	0.911894i	$0.634620\pi$
$14$	−0.500000	+	2.83564i	−0.133631	+	0.757857i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−1.26604	−	1.06234i	−0.307061	−	0.257655i	0.476215	−	0.879329i	$-0.342008\pi$
$17$	−1.26604	−	1.06234i	−0.307061	−	0.257655i	−0.783276	+	0.621674i	$0.786453\pi$
$18$	1.18479			0.279258
$19$	3.79086	+	2.15160i	0.869683	+	0.493611i
$19$	3.79086	+	2.15160i	0.869683	+	0.493611i
$20$		0			0
$21$	2.97178	+	2.49362i	0.648496	+	0.544153i
$22$	−0.939693	+	0.342020i	−0.200343	+	0.0729189i
$23$	0.194593	+	1.10359i	0.0405754	+	0.230114i	0.998351	−	0.0574018i	$-0.0182816\pi$
$23$	0.194593	+	1.10359i	0.0405754	+	0.230114i	−0.957776	+	0.287516i	$0.907170\pi$
$24$	−0.233956	+	1.32683i	−0.0477560	+	0.270838i
$25$		0			0
$26$	0.266044	+	0.460802i	0.0521756	+	0.0903708i
$27$	2.81908	−	4.88279i	0.542532	−	0.939693i
$28$	2.20574	−	1.85083i	0.416845	−	0.349775i
$29$	−1.81521	+	1.52314i	−0.337076	+	0.282840i	−0.795575	−	0.605854i	$-0.792831\pi$
$29$	−1.81521	+	1.52314i	−0.337076	+	0.282840i	0.458500	+	0.888694i	$0.348387\pi$
$30$		0			0
$31$	0.847296	+	1.46756i	0.152179	+	0.263582i	0.932028	−	0.362386i	$-0.118038\pi$
$31$	0.847296	+	1.46756i	0.152179	+	0.263582i	−0.779849	+	0.625967i	$0.784704\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	−0.233956	+	1.32683i	−0.0407264	+	0.230971i
$34$	0.286989	+	1.62760i	0.0492182	+	0.279130i
$35$		0			0
$36$	−0.907604	−	0.761570i	−0.151267	−	0.126928i
$37$	−2.59627			−0.426824			−0.213412	−	0.976962i	$-0.568458\pi$
$37$	−2.59627			−0.426824			−0.213412	+	0.976962i	$0.568458\pi$
$38$	−1.52094	−	4.08494i	−0.246730	−	0.662665i
$39$	0.716881			0.114793
$40$		0			0
$41$	−4.85844	+	1.76833i	−0.758761	+	0.276166i	−0.692288	−	0.721622i	$-0.743397\pi$
$41$	−4.85844	+	1.76833i	−0.758761	+	0.276166i	−0.0664735	+	0.997788i	$0.521175\pi$
$42$	−0.673648	−	3.82045i	−0.103946	−	0.589508i
$43$	−1.88666	+	10.6998i	−0.287713	+	1.63170i	0.407718	+	0.913108i	$0.366325\pi$
$43$	−1.88666	+	10.6998i	−0.287713	+	1.63170i	−0.695431	+	0.718593i	$0.744787\pi$
$44$	0.939693	+	0.342020i	0.141664	+	0.0515615i
$45$		0			0
$46$	0.560307	−	0.970481i	0.0826128	−	0.143090i
$47$	−1.39053	+	1.16679i	−0.202830	+	0.170194i	−0.738545	−	0.674205i	$-0.764487\pi$
$47$	−1.39053	+	1.16679i	−0.202830	+	0.170194i	0.535715	+	0.844399i	$0.320042\pi$
$48$	1.03209	−	0.866025i	0.148969	−	0.125000i
$49$	−0.645430	+	1.11792i	−0.0922042	+	0.159702i
$50$		0			0
$51$	2.09240	+	0.761570i	0.292994	+	0.106641i
$52$	0.0923963	−	0.524005i	0.0128131	−	0.0726665i
$53$	2.08512	+	11.8253i	0.286414	+	1.62433i	0.700192	+	0.713955i	$0.253098\pi$
$53$	2.08512	+	11.8253i	0.286414	+	1.62433i	−0.413779	+	0.910378i	$0.635791\pi$
$54$	−5.29813	+	1.92836i	−0.720985	+	0.262417i
$55$		0			0
$56$	−2.87939			−0.384774
$57$	−5.79086	−	0.977185i	−0.767018	−	0.129431i
$58$	2.36959			0.311142
$59$	6.72668	+	5.64436i	0.875739	+	0.734833i	0.965299	−	0.261149i	$-0.0841014\pi$
$59$	6.72668	+	5.64436i	0.875739	+	0.734833i	−0.0895592	+	0.995982i	$0.528546\pi$
$60$		0			0
$61$	1.08512	+	6.15403i	0.138936	+	0.787943i	0.972038	+	0.234824i	$0.0754515\pi$
$61$	1.08512	+	6.15403i	0.138936	+	0.787943i	−0.833102	+	0.553119i	$0.813437\pi$
$62$	0.294263	−	1.66885i	0.0373714	−	0.211944i
$63$	3.20574	+	1.16679i	0.403885	+	0.147002i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	1.03209	−	0.866025i	0.127041	−	0.106600i
$67$	−1.93969	+	1.62760i	−0.236971	+	0.198842i	−0.753538	−	0.657405i	$-0.771654\pi$
$67$	−1.93969	+	1.62760i	−0.236971	+	0.198842i	0.516567	+	0.856247i	$0.327210\pi$
$68$	0.826352	−	1.43128i	0.100210	−	0.173569i
$69$	−0.754900	−	1.30753i	−0.0908793	−	0.157408i
$70$		0			0
$71$	−1.02229	+	5.79769i	−0.121323	+	0.688059i	0.862101	+	0.506737i	$0.169149\pi$
$71$	−1.02229	+	5.79769i	−0.121323	+	0.688059i	−0.983424	+	0.181322i	$0.941963\pi$
$72$	0.205737	+	1.16679i	0.0242463	+	0.137508i
$73$	−4.68479	+	1.70513i	−0.548313	+	0.199570i	−0.601297	−	0.799026i	$-0.705349\pi$
$73$	−4.68479	+	1.70513i	−0.548313	+	0.199570i	0.0529835	+	0.998595i	$0.483127\pi$
$74$	1.98886	+	1.66885i	0.231200	+	0.194000i
$75$		0			0
$76$	−1.46064	+	4.10689i	−0.167547	+	0.471093i
$77$	−2.87939			−0.328136
$78$	−0.549163	−	0.460802i	−0.0621805	−	0.0521756i
$79$	8.05690	−	2.93247i	0.906472	−	0.329929i	0.153629	−	0.988129i	$-0.450904\pi$
$79$	8.05690	−	2.93247i	0.906472	−	0.329929i	0.752843	+	0.658200i	$0.228682\pi$
$80$		0			0
$81$	−0.701867	+	3.98048i	−0.0779852	+	0.442276i
$82$	4.85844	+	1.76833i	0.536525	+	0.195279i
$83$	5.32888	+	9.22989i	0.584920	+	1.01311i	0.994885	+	0.101011i	$0.0322076\pi$
$83$	5.32888	+	9.22989i	0.584920	+	1.01311i	−0.409965	+	0.912101i	$0.634459\pi$
$84$	−1.93969	+	3.35965i	−0.211638	+	0.366567i
$85$		0			0
$86$	8.32295	−	6.98378i	0.897487	−	0.753081i
$87$	1.59627	−	2.76481i	0.171138	−	0.296419i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−0.694593	−	0.252811i	−0.0736267	−	0.0267979i	0.304944	−	0.952370i	$-0.401362\pi$
$89$	−0.694593	−	0.252811i	−0.0736267	−	0.0267979i	−0.378571	+	0.925572i	$0.623584\pi$
$90$		0			0
$91$	0.266044	+	1.50881i	0.0278890	+	0.158167i
$92$	−1.05303	+	0.383273i	−0.109786	+	0.0399590i
$93$	−1.74897	−	1.46756i	−0.181360	−	0.152179i
$94$	1.81521			0.187224
$95$		0			0
$96$	−1.34730			−0.137508
$97$	8.88919	+	7.45891i	0.902560	+	0.757338i	0.970689	−	0.240339i	$-0.0772585\pi$
$97$	8.88919	+	7.45891i	0.902560	+	0.757338i	−0.0681291	+	0.997677i	$0.521703\pi$
$98$	1.21301	−	0.441500i	0.122533	−	0.0445982i
$99$	0.205737	+	1.16679i	0.0206774	+	0.117267i
$100$		0			0
$101$	−13.4226	−	4.88543i	−1.33560	−	0.486119i	−0.427176	−	0.904168i	$-0.640492\pi$
$101$	−13.4226	−	4.88543i	−1.33560	−	0.486119i	−0.908424	+	0.418050i	$0.862714\pi$
$102$	−1.11334	−	1.92836i	−0.110237	−	0.190936i
$103$	−0.794263	+	1.37570i	−0.0782611	+	0.135552i	−0.902500	−	0.430690i	$-0.858270\pi$
$103$	−0.794263	+	1.37570i	−0.0782611	+	0.135552i	0.824239	+	0.566243i	$0.191603\pi$
$104$	−0.407604	+	0.342020i	−0.0399688	+	0.0335378i
$105$		0			0
$106$	6.00387	−	10.3990i	0.583147	−	1.01004i
$107$	2.52481	+	4.37311i	0.244083	+	0.422764i	0.961873	−	0.273495i	$-0.0881797\pi$
$107$	2.52481	+	4.37311i	0.244083	+	0.422764i	−0.717790	+	0.696259i	$0.754846\pi$
$108$	5.29813	+	1.92836i	0.509813	+	0.185557i
$109$	0.688196	−	3.90295i	0.0659172	−	0.373835i	−0.933948	−	0.357409i	$-0.883660\pi$
$109$	0.688196	−	3.90295i	0.0659172	−	0.373835i	0.999865	−	0.0164259i	$-0.00522876\pi$
$110$		0			0
$111$	3.28699	−	1.19637i	0.311987	−	0.113554i
$112$	2.20574	+	1.85083i	0.208423	+	0.174887i
$113$	−6.98545			−0.657136			−0.328568	−	0.944480i	$-0.606566\pi$
$113$	−6.98545			−0.657136			−0.328568	+	0.944480i	$0.606566\pi$
$114$	3.80793	+	4.47086i	0.356646	+	0.418734i
$115$		0			0
$116$	−1.81521	−	1.52314i	−0.168538	−	0.141420i
$117$	0.592396	−	0.215615i	0.0547671	−	0.0199336i
$118$	−1.52481	−	8.64766i	−0.140371	−	0.796081i
$119$	−0.826352	+	4.68647i	−0.0757515	+	0.429608i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	3.12449	−	5.41177i	0.282878	−	0.489958i
$123$	5.33615	−	4.47756i	0.481145	−	0.403728i
$124$	−1.29813	+	1.08926i	−0.116576	+	0.0978187i
$125$		0			0
$126$	−1.70574	−	2.95442i	−0.151959	−	0.263201i
$127$	17.8059	+	6.48081i	1.58002	+	0.575079i	0.975208	−	0.221292i	$-0.0710275\pi$
$127$	17.8059	+	6.48081i	1.58002	+	0.575079i	0.604808	+	0.796371i	$0.293250\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	−2.54189	−	14.4158i	−0.223801	−	1.26924i
$130$		0			0
$131$	−12.8118	−	10.7504i	−1.11937	−	0.939265i	−0.120800	−	0.992677i	$-0.538546\pi$
$131$	−12.8118	−	10.7504i	−1.11937	−	0.939265i	−0.998573	+	0.0534118i	$0.982990\pi$
$132$	−1.34730			−0.117267
$133$	−0.0923963	−	12.5506i	−0.00801177	−	1.08828i
$134$	2.53209			0.218739
$135$		0			0
$136$	−1.55303	+	0.565258i	−0.133172	+	0.0484705i
$137$	0.524348	+	2.97373i	0.0447981	+	0.254063i	0.998979	−	0.0451662i	$-0.0143817\pi$
$137$	0.524348	+	2.97373i	0.0447981	+	0.254063i	−0.954181	+	0.299229i	$0.903271\pi$
$138$	−0.262174	+	1.48686i	−0.0223177	+	0.126570i
$139$	11.6309	+	4.23329i	0.986519	+	0.359063i	0.784371	−	0.620292i	$-0.212986\pi$
$139$	11.6309	+	4.23329i	0.986519	+	0.359063i	0.202147	+	0.979355i	$0.435208\pi$
$140$		0			0
$141$	1.22281	−	2.11797i	0.102979	−	0.178365i
$142$	4.50980	−	3.78417i	0.378454	−	0.317561i
$143$	−0.407604	+	0.342020i	−0.0340855	+	0.0286012i
$144$	0.592396	−	1.02606i	0.0493664	−	0.0855050i
$145$		0			0
$146$	4.68479	+	1.70513i	0.387716	+	0.141117i
$147$	0.302004	−	1.71275i	0.0249088	−	0.141265i
$148$	−0.450837	−	2.55682i	−0.0370586	−	0.210170i
$149$	−8.76517	+	3.19026i	−0.718070	+	0.261356i	−0.675106	−	0.737720i	$-0.735902\pi$
$149$	−8.76517	+	3.19026i	−0.718070	+	0.261356i	−0.0429640	+	0.999077i	$0.513680\pi$
$150$		0			0
$151$	−4.76651			−0.387893			−0.193947	−	0.981012i	$-0.562129\pi$
$151$	−4.76651			−0.387893			−0.193947	+	0.981012i	$0.562129\pi$
$152$	3.75877	−	2.20718i	0.304877	−	0.179026i
$153$	1.95811			0.158304
$154$	2.20574	+	1.85083i	0.177743	+	0.149144i
$155$		0			0
$156$	0.124485	+	0.705990i	0.00996679	+	0.0565245i
$157$	−2.66297	+	15.1025i	−0.212528	+	1.20531i	0.672616	+	0.739991i	$0.265170\pi$
$157$	−2.66297	+	15.1025i	−0.212528	+	1.20531i	−0.885145	+	0.465316i	$0.845941\pi$
$158$	−8.05690	−	2.93247i	−0.640973	−	0.233295i
$159$	−8.08899	−	14.0105i	−0.641499	−	1.11111i
$160$		0			0
$161$	2.47178	−	2.07407i	0.194804	−	0.163460i
$162$	3.09627	−	2.59808i	0.243266	−	0.204124i
$163$	4.12701	−	7.14819i	0.323252	−	0.559890i	−0.657905	−	0.753101i	$-0.728557\pi$
$163$	4.12701	−	7.14819i	0.323252	−	0.559890i	0.981157	+	0.193212i	$0.0618904\pi$
$164$	−2.58512	−	4.47756i	−0.201864	−	0.349639i
$165$		0			0
$166$	1.85070	−	10.4958i	0.143642	−	0.814635i
$167$	3.02007	+	17.1277i	0.233700	+	1.32538i	0.845335	+	0.534237i	$0.179401\pi$
$167$	3.02007	+	17.1277i	0.233700	+	1.32538i	−0.611635	+	0.791140i	$0.709488\pi$
$168$	3.64543	−	1.32683i	0.281251	−	0.102367i
$169$	−9.74170	−	8.17425i	−0.749361	−	0.628789i
$170$		0			0
$171$	−5.07919	+	0.934204i	−0.388416	+	0.0714404i
$172$	−10.8648			−0.828436
$173$	−15.0326	−	12.6138i	−1.14290	−	0.959010i	−0.143374	−	0.989669i	$-0.545795\pi$
$173$	−15.0326	−	12.6138i	−1.14290	−	0.959010i	−0.999530	+	0.0306582i	$0.990240\pi$
$174$	−3.00000	+	1.09191i	−0.227429	+	0.0827775i
$175$		0			0
$176$	−0.173648	+	0.984808i	−0.0130892	+	0.0742327i
$177$	−11.1172	−	4.04633i	−0.835621	−	0.304141i
$178$	0.369585	+	0.640140i	0.0277016	+	0.0479805i
$179$	9.66297	−	16.7368i	0.722244	−	1.25096i	−0.237854	−	0.971301i	$-0.576444\pi$
$179$	9.66297	−	16.7368i	0.722244	−	1.25096i	0.960098	−	0.279663i	$-0.0902227\pi$
$180$		0			0
$181$	20.2422	−	16.9852i	1.50459	−	1.26250i	0.631052	−	0.775741i	$-0.282624\pi$
$181$	20.2422	−	16.9852i	1.50459	−	1.26250i	0.873537	−	0.486758i	$-0.161821\pi$
$182$	0.766044	−	1.32683i	0.0567830	−	0.0983510i
$183$	−4.20961	−	7.29125i	−0.311183	−	0.538985i
$184$	1.05303	+	0.383273i	0.0776307	+	0.0282552i
$185$		0			0
$186$	0.396459	+	2.24843i	0.0290698	+	0.164863i
$187$	−1.55303	+	0.565258i	−0.113569	+	0.0413358i
$188$	−1.39053	−	1.16679i	−0.101415	−	0.0850971i
$189$	−16.2344			−1.18088
$190$		0			0
$191$	−25.6955			−1.85926			−0.929632	−	0.368490i	$-0.879875\pi$
$191$	−25.6955			−1.85926			−0.929632	+	0.368490i	$0.879875\pi$
$192$	1.03209	+	0.866025i	0.0744846	+	0.0625000i
$193$	−4.93882	+	1.79758i	−0.355504	+	0.129393i	−0.513597	−	0.858031i	$-0.671687\pi$
$193$	−4.93882	+	1.79758i	−0.355504	+	0.129393i	0.158094	+	0.987424i	$0.449465\pi$
$194$	−2.01501	−	11.4277i	−0.144670	−	0.820462i
$195$		0			0
$196$	−1.21301	−	0.441500i	−0.0866436	−	0.0315357i
$197$	−12.3191	−	21.3373i	−0.877698	−	1.52022i	−0.853861	−	0.520502i	$-0.825745\pi$
$197$	−12.3191	−	21.3373i	−0.877698	−	1.52022i	−0.0238373	−	0.999716i	$-0.507588\pi$
$198$	0.592396	−	1.02606i	0.0420998	−	0.0729189i
$199$	−7.50181	+	6.29477i	−0.531789	+	0.446224i	−0.868719	−	0.495306i	$-0.835056\pi$
$199$	−7.50181	+	6.29477i	−0.531789	+	0.446224i	0.336929	+	0.941530i	$0.390612\pi$
$200$		0			0
$201$	1.70574	−	2.95442i	0.120313	−	0.208389i
$202$	7.14203	+	12.3704i	0.502511	+	0.870375i
$203$	6.41147	+	2.33359i	0.449997	+	0.163786i
$204$	−0.386659	+	2.19285i	−0.0270716	+	0.153530i
$205$		0			0
$206$	1.49273	−	0.543308i	0.104003	−	0.0378541i
$207$	−1.01707	−	0.853427i	−0.0706915	−	0.0593172i
$208$	0.532089			0.0368937
$209$	3.75877	−	2.20718i	0.260000	−	0.152674i
$210$		0			0
$211$	16.5043	+	13.8488i	1.13621	+	0.953390i	0.999308	−	0.0371957i	$-0.0118425\pi$
$211$	16.5043	+	13.8488i	1.13621	+	0.953390i	0.136897	+	0.990585i	$0.456287\pi$
$212$	−11.2836	+	4.10689i	−0.774960	+	0.282062i
$213$	−1.37733	−	7.81120i	−0.0943728	−	0.535215i
$214$	0.876859	−	4.97291i	0.0599408	−	0.339941i
$215$		0			0
$216$	−2.81908	−	4.88279i	−0.191814	−	0.332232i
$217$	2.43969	−	4.22567i	0.165617	−	0.286857i
$218$	−3.03596	+	2.54747i	−0.205621	+	0.172537i
$219$	5.14543	−	4.31753i	0.347696	−	0.291752i
$220$		0			0
$221$	0.439693	+	0.761570i	0.0295769	+	0.0512287i
$222$	−3.28699	−	1.19637i	−0.220608	−	0.0802948i
$223$	3.54963	−	20.1310i	0.237701	−	1.34807i	−0.599150	−	0.800637i	$-0.704495\pi$
$223$	3.54963	−	20.1310i	0.237701	−	1.34807i	0.836851	−	0.547431i	$-0.184394\pi$
$224$	−0.500000	−	2.83564i	−0.0334077	−	0.189464i
$225$		0			0
$226$	5.35117	+	4.49016i	0.355954	+	0.298681i
$227$	−7.78787			−0.516899			−0.258449	−	0.966025i	$-0.583212\pi$
$227$	−7.78787			−0.516899			−0.258449	+	0.966025i	$0.583212\pi$
$228$	−0.0432332	−	5.87257i	−0.00286319	−	0.388920i
$229$	−8.02734			−0.530462			−0.265231	−	0.964185i	$-0.585448\pi$
$229$	−8.02734			−0.530462			−0.265231	+	0.964185i	$0.585448\pi$
$230$		0			0
$231$	3.64543	−	1.32683i	0.239852	−	0.0872989i
$232$	0.411474	+	2.33359i	0.0270146	+	0.153207i
$233$	−0.656574	+	3.72362i	−0.0430136	+	0.243942i	−0.998732	−	0.0503401i	$-0.983969\pi$
$233$	−0.656574	+	3.72362i	−0.0430136	+	0.243942i	0.955719	+	0.294282i	$0.0950806\pi$
$234$	−0.592396	−	0.215615i	−0.0387262	−	0.0140952i
$235$		0			0
$236$	−4.39053	+	7.60462i	−0.285799	+	0.495019i
$237$	−8.84911	+	7.42528i	−0.574811	+	0.482324i
$238$	3.64543	−	3.05888i	0.236298	−	0.198278i
$239$	−3.39053	+	5.87257i	−0.219315	+	0.379865i	−0.954599	−	0.297895i	$-0.903716\pi$
$239$	−3.39053	+	5.87257i	−0.219315	+	0.379865i	0.735284	+	0.677760i	$0.237049\pi$
$240$		0			0
$241$	5.67840	+	2.06677i	0.365778	+	0.133132i	0.518369	−	0.855157i	$-0.326540\pi$
$241$	5.67840	+	2.06677i	0.365778	+	0.133132i	−0.152591	+	0.988289i	$0.548762\pi$
$242$	1.73648	−	9.84808i	0.111625	−	0.633058i
$243$	1.99154	+	11.2946i	0.127758	+	0.724549i
$244$	−5.87211	+	2.13727i	−0.375923	+	0.136825i
$245$		0			0
$246$	−6.96585			−0.444126
$247$	−1.50387	−	1.76568i	−0.0956890	−	0.112348i
$248$	1.69459			0.107607
$249$	−10.9998	−	9.22989i	−0.697081	−	0.584920i
$250$		0			0
$251$	−0.992259	−	5.62738i	−0.0626308	−	0.355197i	−0.999977	−	0.00679744i	$-0.997836\pi$
$251$	−0.992259	−	5.62738i	−0.0626308	−	0.355197i	0.937346	−	0.348400i	$-0.113275\pi$
$252$	−0.592396	+	3.35965i	−0.0373175	+	0.211638i
$253$	1.05303	+	0.383273i	0.0662036	+	0.0240962i
$254$	−9.47431	−	16.4100i	−0.594471	−	1.02965i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−9.82888	+	8.24741i	−0.613109	+	0.514459i	−0.895629	−	0.444802i	$-0.853274\pi$
$257$	−9.82888	+	8.24741i	−0.613109	+	0.514459i	0.282520	+	0.959261i	$0.408830\pi$
$258$	−7.31908	+	12.6770i	−0.455666	+	0.789236i
$259$	3.73783	+	6.47410i	0.232257	+	0.402281i
$260$		0			0
$261$	0.487511	−	2.76481i	0.0301762	−	0.171138i
$262$	2.90420	+	16.4705i	0.179422	+	1.01755i
$263$	−4.59714	+	1.67322i	−0.283472	+	0.103175i	−0.479843	−	0.877354i	$-0.659306\pi$
$263$	−4.59714	+	1.67322i	−0.283472	+	0.103175i	0.196371	+	0.980530i	$0.437084\pi$
$264$	1.03209	+	0.866025i	0.0635207	+	0.0533002i
$265$		0			0
$266$	−7.99660	+	9.67372i	−0.490303	+	0.593134i
$267$	0.995881			0.0609469
$268$	−1.93969	−	1.62760i	−0.118486	−	0.0994212i
$269$	14.9290	−	5.43372i	0.910238	−	0.331300i	0.155890	−	0.987774i	$-0.450175\pi$
$269$	14.9290	−	5.43372i	0.910238	−	0.331300i	0.754348	+	0.656475i	$0.227953\pi$
$270$		0			0
$271$	−4.24082	+	24.0509i	−0.257611	+	1.46099i	0.531668	+	0.846953i	$0.321565\pi$
$271$	−4.24082	+	24.0509i	−0.257611	+	1.46099i	−0.789279	+	0.614034i	$0.789546\pi$
$272$	1.55303	+	0.565258i	0.0941665	+	0.0342738i
$273$	−1.03209	−	1.78763i	−0.0624649	−	0.108192i
$274$	1.50980	−	2.61505i	0.0912104	−	0.157981i
$275$		0			0
$276$	1.15657	−	0.970481i	0.0696176	−	0.0584161i
$277$	5.76991	−	9.99379i	0.346681	−	0.600468i	−0.638977	−	0.769226i	$-0.720642\pi$
$277$	5.76991	−	9.99379i	0.346681	−	0.600468i	0.985658	+	0.168757i	$0.0539755\pi$
$278$	−6.18866	−	10.7191i	−0.371171	−	0.642888i
$279$	−1.88666	−	0.686688i	−0.112951	−	0.0411109i
$280$		0			0
$281$	−1.36912	−	7.76466i	−0.0816747	−	0.463201i	−0.998025	−	0.0628223i	$-0.979990\pi$
$281$	−1.36912	−	7.76466i	−0.0816747	−	0.463201i	0.916350	−	0.400378i	$-0.131121\pi$
$282$	−2.29813	+	0.836452i	−0.136852	+	0.0498100i
$283$	3.63429	+	3.04953i	0.216036	+	0.181276i	0.744383	−	0.667753i	$-0.232744\pi$
$283$	3.63429	+	3.04953i	0.216036	+	0.181276i	−0.528347	+	0.849028i	$0.677188\pi$
$284$	−5.88713			−0.349337
$285$		0			0
$286$	0.532089			0.0314631
$287$	11.4042	+	9.56926i	0.673169	+	0.564856i
$288$	−1.11334	+	0.405223i	−0.0656042	+	0.0238780i
$289$	−2.47771	−	14.0518i	−0.145748	−	0.826576i
$290$		0			0
$291$	−14.6912	−	5.34716i	−0.861213	−	0.313456i
$292$	−2.49273	−	4.31753i	−0.145876	−	0.252664i
$293$	−6.29679	+	10.9064i	−0.367862	+	0.637156i	−0.989231	−	0.146362i	$-0.953244\pi$
$293$	−6.29679	+	10.9064i	−0.367862	+	0.637156i	0.621369	+	0.783518i	$0.286577\pi$
$294$	−1.33228	+	1.11792i	−0.0777002	+	0.0651982i
$295$		0			0
$296$	−1.29813	+	2.24843i	−0.0754525	+	0.130688i
$297$	−2.81908	−	4.88279i	−0.163579	−	0.283328i
$298$	8.76517	+	3.19026i	0.507752	+	0.184807i
$299$	0.103541	−	0.587208i	0.00598791	−	0.0339591i
$300$		0			0
$301$	29.3974	−	10.6998i	1.69444	−	0.616725i
$302$	3.65136	+	3.06385i	0.210112	+	0.176305i
$303$	19.2449			1.10559
$304$	−4.29813	−	0.725293i	−0.246515	−	0.0415984i
$305$		0			0
$306$	−1.50000	−	1.25865i	−0.0857493	−	0.0719522i
$307$	28.3692	−	10.3255i	1.61911	−	0.589309i	0.635901	−	0.771770i	$-0.280629\pi$
$307$	28.3692	−	10.3255i	1.61911	−	0.589309i	0.983213	+	0.182461i	$0.0584063\pi$
$308$	−0.500000	−	2.83564i	−0.0284901	−	0.161576i
$309$	0.371644	−	2.10770i	0.0211421	−	0.119903i
$310$		0			0
$311$	−5.54236	−	9.59964i	−0.314278	−	0.544346i	0.665006	−	0.746838i	$-0.268429\pi$
$311$	−5.54236	−	9.59964i	−0.314278	−	0.544346i	−0.979284	+	0.202493i	$0.935096\pi$
$312$	0.358441	−	0.620838i	0.0202927	−	0.0351480i
$313$	6.26991	−	5.26108i	0.354397	−	0.297374i	−0.448156	−	0.893955i	$-0.647919\pi$
$313$	6.26991	−	5.26108i	0.354397	−	0.297374i	0.802553	+	0.596581i	$0.203475\pi$
$314$	11.7476	−	9.85743i	0.662957	−	0.556287i
$315$		0			0
$316$	4.28699	+	7.42528i	0.241162	+	0.417705i
$317$	4.50862	+	1.64100i	0.253229	+	0.0921679i	0.465516	−	0.885040i	$-0.345869\pi$
$317$	4.50862	+	1.64100i	0.253229	+	0.0921679i	−0.212287	+	0.977207i	$0.568091\pi$
$318$	−2.80928	+	15.9322i	−0.157536	+	0.893434i
$319$	0.411474	+	2.33359i	0.0230381	+	0.130656i
$320$		0			0
$321$	−5.21167	−	4.37311i	−0.290887	−	0.244083i
$322$	−3.22668			−0.179816
$323$	−2.51367	−	6.75119i	−0.139864	−	0.375646i
$324$	−4.04189			−0.224549
$325$		0			0
$326$	−7.75624	+	2.82304i	−0.429579	+	0.156354i
$327$	0.927204	+	5.25844i	0.0512745	+	0.290792i
$328$	−0.897804	+	5.09170i	−0.0495729	+	0.281142i
$329$	4.91147	+	1.78763i	0.270778	+	0.0985553i
$330$		0			0
$331$	6.84864	−	11.8622i	0.376435	−	0.652005i	−0.614105	−	0.789224i	$-0.710483\pi$
$331$	6.84864	−	11.8622i	0.376435	−	0.652005i	0.990541	+	0.137219i	$0.0438164\pi$
$332$	−8.16431	+	6.85067i	−0.448075	+	0.375980i
$333$	2.35638	−	1.97724i	0.129129	−	0.108352i
$334$	8.69594	−	15.0618i	0.475820	−	0.824145i
$335$		0			0
$336$	−3.64543	−	1.32683i	−0.198874	−	0.0723844i
$337$	1.34952	−	7.65350i	0.0735129	−	0.416913i	−0.925736	−	0.378170i	$-0.876554\pi$
$337$	1.34952	−	7.65350i	0.0735129	−	0.416913i	0.999249	−	0.0387428i	$-0.0123353\pi$
$338$	2.20826	+	12.5237i	0.120114	+	0.681199i
$339$	8.84389	−	3.21891i	0.480334	−	0.174827i
$340$		0			0
$341$	1.69459			0.0917673
$342$	4.49138	+	2.54920i	0.242866	+	0.137845i
$343$	−16.4388			−0.887613
$344$	8.32295	+	6.98378i	0.448743	+	0.376540i
$345$		0			0
$346$	3.40760	+	19.3255i	0.183194	+	1.03894i
$347$	−0.573978	+	3.25519i	−0.0308128	+	0.174748i	−0.996330	−	0.0855895i	$-0.972723\pi$
$347$	−0.573978	+	3.25519i	−0.0308128	+	0.174748i	0.965518	+	0.260337i	$0.0838338\pi$
$348$	3.00000	+	1.09191i	0.160817	+	0.0585326i
$349$	12.0851	+	20.9320i	0.646902	+	1.12047i	0.983859	+	0.178947i	$0.0572690\pi$
$349$	12.0851	+	20.9320i	0.646902	+	1.12047i	−0.336957	+	0.941520i	$0.609398\pi$
$350$		0			0
$351$	−2.29813	+	1.92836i	−0.122665	+	0.102928i
$352$	0.766044	−	0.642788i	0.0408303	−	0.0342607i
$353$	−14.3721	+	24.8932i	−0.764950	+	1.32493i	0.175323	+	0.984511i	$0.443903\pi$
$353$	−14.3721	+	24.8932i	−0.764950	+	1.32493i	−0.940273	+	0.340422i	$0.889430\pi$
$354$	5.91534	+	10.2457i	0.314397	+	0.544552i
$355$		0			0
$356$	0.128356	−	0.727940i	0.00680283	−	0.0385808i
$357$	−1.11334	−	6.31407i	−0.0589242	−	0.334176i
$358$	−18.1604	+	6.60986i	−0.959809	+	0.349342i
$359$	−9.98751	−	8.38052i	−0.527121	−	0.442307i	0.339985	−	0.940431i	$-0.389578\pi$
$359$	−9.98751	−	8.38052i	−0.527121	−	0.442307i	−0.867106	+	0.498124i	$0.834022\pi$
$360$		0			0
$361$	9.74123	+	16.3128i	0.512696	+	0.858570i
$362$	−26.4243			−1.38883
$363$	−10.3209	−	8.66025i	−0.541706	−	0.454545i
$364$	−1.43969	+	0.524005i	−0.0754604	+	0.0274653i
$365$		0			0
$366$	−1.46198	+	8.29131i	−0.0764190	+	0.433394i
$367$	15.1236	+	5.50454i	0.789446	+	0.287335i	0.705106	−	0.709102i	$-0.250900\pi$
$367$	15.1236	+	5.50454i	0.789446	+	0.287335i	0.0843402	+	0.996437i	$0.473122\pi$
$368$	−0.560307	−	0.970481i	−0.0292080	−	0.0505898i
$369$	3.06283	−	5.30498i	0.159445	−	0.276166i
$370$		0			0
$371$	26.4859	−	22.2243i	1.37508	−	1.15383i
$372$	1.14156	−	1.97724i	0.0591871	−	0.102515i
$373$	−14.0753	−	24.3792i	−0.728793	−	1.26231i	−0.957394	−	0.288786i	$-0.906749\pi$
$373$	−14.0753	−	24.3792i	−0.728793	−	1.26231i	0.228601	−	0.973520i	$-0.426585\pi$
$374$	1.55303	+	0.565258i	0.0803054	+	0.0292288i
$375$		0			0
$376$	0.315207	+	1.78763i	0.0162556	+	0.0921900i
$377$	1.18479	−	0.431229i	0.0610199	−	0.0222094i
$378$	12.4363	+	10.4353i	0.639654	+	0.536733i
$379$	−11.7510			−0.603610			−0.301805	−	0.953370i	$-0.597589\pi$
$379$	−11.7510			−0.603610			−0.301805	+	0.953370i	$0.597589\pi$
$380$		0			0
$381$	−25.5294			−1.30791
$382$	19.6839	+	16.5168i	1.00712	+	0.845071i
$383$	16.8229	−	6.12305i	0.859613	−	0.312873i	0.125659	−	0.992073i	$-0.459895\pi$
$383$	16.8229	−	6.12305i	0.859613	−	0.312873i	0.733953	+	0.679200i	$0.237673\pi$
$384$	−0.233956	−	1.32683i	−0.0119390	−	0.0677094i
$385$		0			0
$386$	4.93882	+	1.79758i	0.251379	+	0.0914945i
$387$	−6.43629	−	11.1480i	−0.327175	−	0.566684i
$388$	−5.80200	+	10.0494i	−0.294552	+	0.510179i
$389$	−20.1832	+	16.9357i	−1.02333	+	0.858675i	−0.990042	−	0.140771i	$-0.955042\pi$
$389$	−20.1832	+	16.9357i	−1.02333	+	0.858675i	−0.0332867	+	0.999446i	$0.510597\pi$
$390$		0			0
$391$	0.926022	−	1.60392i	0.0468309	−	0.0811136i
$392$	0.645430	+	1.11792i	0.0325991	+	0.0564633i
$393$	21.1741	+	7.70675i	1.06809	+	0.388754i
$394$	−4.27837	+	24.2638i	−0.215541	+	1.22239i
$395$		0			0
$396$	−1.11334	+	0.405223i	−0.0559475	+	0.0203632i
$397$	−12.3923	−	10.3984i	−0.621954	−	0.521881i	0.276463	−	0.961024i	$-0.410838\pi$
$397$	−12.3923	−	10.3984i	−0.621954	−	0.521881i	−0.898417	+	0.439143i	$0.855282\pi$
$398$	9.79292			0.490875
$399$	5.90033	+	15.8471i	0.295386	+	0.793345i
$400$		0			0
$401$	22.3705	+	18.7711i	1.11713	+	0.937384i	0.998456	−	0.0555495i	$-0.0176911\pi$
$401$	22.3705	+	18.7711i	1.11713	+	0.937384i	0.118674	+	0.992933i	$0.462136\pi$
$402$	−3.20574	+	1.16679i	−0.159888	+	0.0581943i
$403$	−0.156574	−	0.887975i	−0.00779951	−	0.0442332i
$404$	2.48040	−	14.0670i	0.123404	−	0.699862i
$405$		0			0
$406$	−3.41147	−	5.90885i	−0.169309	−	0.293251i
$407$	−1.29813	+	2.24843i	−0.0643461	+	0.111451i
$408$	1.70574	−	1.43128i	0.0844466	−	0.0708591i
$409$	−18.7606	+	15.7420i	−0.927651	+	0.778392i	−0.975394	−	0.220468i	$-0.929242\pi$
$409$	−18.7606	+	15.7420i	−0.927651	+	0.778392i	0.0477432	+	0.998860i	$0.484797\pi$
$410$		0			0
$411$	−2.03415	−	3.52325i	−0.100337	−	0.173789i
$412$	−1.49273	−	0.543308i	−0.0735413	−	0.0267669i
$413$	4.39053	−	24.8999i	0.216044	−	1.22525i
$414$	0.230552	+	1.30753i	0.0113310	+	0.0642614i
$415$		0			0
$416$	−0.407604	−	0.342020i	−0.0199844	−	0.0167689i
$417$	−16.6759			−0.816624
$418$	−4.29813	−	0.725293i	−0.210229	−	0.0354752i
$419$	14.5972			0.713120			0.356560	−	0.934272i	$-0.383950\pi$
$419$	14.5972			0.713120			0.356560	+	0.934272i	$0.383950\pi$
$420$		0			0
$421$	14.6557	−	5.33424i	0.714275	−	0.259975i	0.0407816	−	0.999168i	$-0.487015\pi$
$421$	14.6557	−	5.33424i	0.714275	−	0.259975i	0.673493	+	0.739193i	$0.264793\pi$
$422$	−3.74123	−	21.2176i	−0.182120	−	1.03285i
$423$	0.373455	−	2.11797i	0.0181580	−	0.102979i
$424$	11.2836	+	4.10689i	0.547979	+	0.199448i
$425$		0			0
$426$	−3.96585	+	6.86906i	−0.192146	+	0.332807i
$427$	13.7836	−	11.5658i	0.667034	−	0.559708i
$428$	−3.86824	+	3.24584i	−0.186978	+	0.156894i
$429$	0.358441	−	0.620838i	0.0173057	−	0.0299743i
$430$		0			0
$431$	−35.2857	−	12.8429i	−1.69965	−	0.618623i	−0.703867	−	0.710332i	$-0.748545\pi$
$431$	−35.2857	−	12.8429i	−1.69965	−	0.618623i	−0.995786	+	0.0917093i	$0.970767\pi$
$432$	−0.979055	+	5.55250i	−0.0471048	+	0.267145i
$433$	3.43464	+	19.4788i	0.165058	+	0.936092i	0.949004	+	0.315263i	$0.102093\pi$
$433$	3.43464	+	19.4788i	0.165058	+	0.936092i	−0.783946	+	0.620829i	$0.786796\pi$
$434$	−4.58512	+	1.66885i	−0.220093	+	0.0801073i
$435$		0			0
$436$	3.96316			0.189801
$437$	−1.63681	+	4.60224i	−0.0782993	+	0.220155i
$438$	−6.71688			−0.320945
$439$	14.6120	+	12.2609i	0.697393	+	0.585182i	0.921031	−	0.389490i	$-0.127349\pi$
$439$	14.6120	+	12.2609i	0.697393	+	0.585182i	−0.223638	+	0.974672i	$0.571793\pi$
$440$		0			0
$441$	−0.265578	−	1.50617i	−0.0126466	−	0.0717222i
$442$	0.152704	−	0.866025i	0.00726337	−	0.0411926i
$443$	16.0125	+	5.82807i	0.760776	+	0.276900i	0.693133	−	0.720810i	$-0.256230\pi$
$443$	16.0125	+	5.82807i	0.760776	+	0.276900i	0.0676432	+	0.997710i	$0.478452\pi$
$444$	1.74897	+	3.02931i	0.0830025	+	0.143764i
$445$		0			0
$446$	−15.6591	+	13.1395i	−0.741480	+	0.622176i
$447$	9.62701	−	8.07802i	0.455342	−	0.382077i
$448$	−1.43969	+	2.49362i	−0.0680191	+	0.117813i
$449$	19.9368	+	34.5315i	0.940874	+	1.62964i	0.763810	+	0.645442i	$0.223327\pi$
$449$	19.9368	+	34.5315i	0.940874	+	1.62964i	0.177064	+	0.984199i	$0.443340\pi$
$450$		0			0
$451$	−0.897804	+	5.09170i	−0.0422759	+	0.239759i
$452$	−1.21301	−	6.87933i	−0.0570552	−	0.323576i
$453$	6.03462	−	2.19642i	0.283531	−	0.103197i
$454$	5.96585	+	5.00594i	0.279991	+	0.234941i
$455$		0			0
$456$	−3.74170	+	4.52644i	−0.175221	+	0.211970i
$457$	−15.4216			−0.721391			−0.360696	−	0.932684i	$-0.617461\pi$
$457$	−15.4216			−0.721391			−0.360696	+	0.932684i	$0.617461\pi$
$458$	6.14930	+	5.15988i	0.287338	+	0.241105i
$459$	−8.75624	+	3.18701i	−0.408706	+	0.148757i
$460$		0			0
$461$	−1.58125	+	8.96773i	−0.0736462	+	0.417669i	0.925588	+	0.378533i	$0.123571\pi$
$461$	−1.58125	+	8.96773i	−0.0736462	+	0.417669i	−0.999234	+	0.0391353i	$0.987540\pi$
$462$	−3.64543	−	1.32683i	−0.169601	−	0.0617296i
$463$	−2.06371	−	3.57445i	−0.0959088	−	0.166119i	0.814079	−	0.580755i	$-0.197242\pi$
$463$	−2.06371	−	3.57445i	−0.0959088	−	0.166119i	−0.909988	+	0.414636i	$0.863909\pi$
$464$	1.18479	−	2.05212i	0.0550026	−	0.0952673i
$465$		0			0
$466$	2.89646	−	2.43042i	0.134176	−	0.112587i
$467$	13.1853	−	22.8375i	0.610141	−	1.05680i	−0.381075	−	0.924544i	$-0.624446\pi$
$467$	13.1853	−	22.8375i	0.610141	−	1.05680i	0.991216	−	0.132251i	$-0.0422206\pi$
$468$	0.315207	+	0.545955i	0.0145705	+	0.0252368i
$469$	6.85117	+	2.49362i	0.316357	+	0.115145i
$470$		0			0
$471$	−3.58781	−	20.3475i	−0.165318	−	0.937563i
$472$	8.25150	−	3.00330i	0.379806	−	0.138238i
$473$	8.32295	+	6.98378i	0.382690	+	0.321115i
$474$	11.5517			0.530587
$475$		0			0
$476$	−4.75877			−0.218118
$477$	−10.8983	−	9.14473i	−0.498998	−	0.418709i
$478$	6.37211	−	2.31926i	0.291454	−	0.106080i
$479$	2.82207	+	16.0048i	0.128944	+	0.731276i	0.978887	+	0.204402i	$0.0655250\pi$
$479$	2.82207	+	16.0048i	0.128944	+	0.731276i	−0.849943	+	0.526874i	$0.823364\pi$
$480$		0			0
$481$	1.29813	+	0.472482i	0.0591898	+	0.0215433i
$482$	−3.02141	−	5.23324i	−0.137622	−	0.238367i
$483$	−2.17365	+	3.76487i	−0.0989044	+	0.171307i
$484$	−7.66044	+	6.42788i	−0.348202	+	0.292176i
$485$		0			0
$486$	5.73442	−	9.93231i	0.260119	−	0.450539i
$487$	8.64883	+	14.9802i	0.391916	+	0.678819i	0.992702	−	0.120591i	$-0.0384790\pi$
$487$	8.64883	+	14.9802i	0.391916	+	0.678819i	−0.600786	+	0.799410i	$0.705146\pi$
$488$	5.87211	+	2.13727i	0.265818	+	0.0967498i
$489$	−1.93107	+	10.9517i	−0.0873262	+	0.495252i
$490$		0			0
$491$	14.6630	−	5.33688i	0.661731	−	0.240850i	0.0107472	−	0.999942i	$-0.496579\pi$
$491$	14.6630	−	5.33688i	0.661731	−	0.240850i	0.650983	+	0.759092i	$0.274357\pi$
$492$	5.33615	+	4.47756i	0.240572	+	0.201864i
$493$	3.91622			0.176378
$494$	0.0170741	+	2.31926i	0.000768202	+	0.104348i
$495$		0			0
$496$	−1.29813	−	1.08926i	−0.0582879	−	0.0489094i
$497$	15.9290	−	5.79769i	0.714514	−	0.260062i
$498$	2.49344	+	14.1410i	0.111734	+	0.633674i
$499$	−6.52394	+	36.9991i	−0.292052	+	1.65631i	0.386899	+	0.922122i	$0.373546\pi$
$499$	−6.52394	+	36.9991i	−0.292052	+	1.65631i	−0.678950	+	0.734184i	$0.737565\pi$
$500$		0			0
$501$	−11.7160	−	20.2927i	−0.523432	−	0.906612i
$502$	−2.85710	+	4.94864i	−0.127518	+	0.220868i
$503$	23.9500	−	20.0964i	1.06788	−	0.896054i	0.0730176	−	0.997331i	$-0.476737\pi$
$503$	23.9500	−	20.0964i	1.06788	−	0.896054i	0.994858	+	0.101276i	$0.0322926\pi$
$504$	2.61334	−	2.19285i	0.116407	−	0.0976774i
$505$		0			0
$506$	−0.560307	−	0.970481i	−0.0249087	−	0.0431431i
$507$	16.1001	+	5.85997i	0.715032	+	0.260250i
$508$	−3.29039	+	18.6607i	−0.145988	+	0.827937i
$509$	4.05438	+	22.9935i	0.179707	+	1.01917i	0.932569	+	0.360991i	$0.117562\pi$
$509$	4.05438	+	22.9935i	0.179707	+	1.01917i	−0.752862	+	0.658178i	$0.771327\pi$
$510$		0			0
$511$	10.9966	+	9.22724i	0.486461	+	0.408189i
$512$	−1.00000			−0.0441942
$513$	21.1925	−	12.4444i	0.935673	−	0.549435i
$514$	12.8307			0.565937
$515$		0			0
$516$	13.7554	−	5.00654i	0.605546	−	0.220401i
$517$	0.315207	+	1.78763i	0.0138628	+	0.0786199i
$518$	1.29813	−	7.36208i	0.0570367	−	0.323471i
$519$	24.8444	+	9.04261i	1.09055	+	0.396926i
$520$		0			0
$521$	−4.58647	+	7.94399i	−0.200937	+	0.348033i	−0.948831	−	0.315786i	$-0.897732\pi$
$521$	−4.58647	+	7.94399i	−0.200937	+	0.348033i	0.747894	+	0.663818i	$0.231065\pi$
$522$	−2.15064	+	1.80460i	−0.0941311	+	0.0789854i
$523$	−10.9725	+	9.20702i	−0.479794	+	0.402595i	−0.850352	−	0.526215i	$-0.823611\pi$
$523$	−10.9725	+	9.20702i	−0.479794	+	0.402595i	0.370558	+	0.928809i	$0.379166\pi$
$524$	8.36231	−	14.4839i	0.365309	−	0.632734i
$525$		0			0
$526$	4.59714	+	1.67322i	0.200445	+	0.0729560i
$527$	0.486329	−	2.75811i	0.0211848	−	0.120145i
$528$	−0.233956	−	1.32683i	−0.0101816	−	0.0577428i
$529$	20.4329	−	7.43696i	0.888386	−	0.323346i
$530$		0			0
$531$	−10.4037			−0.451484
$532$	12.3439	−	2.27038i	0.535176	−	0.0984336i
$533$	2.75103			0.119160
$534$	−0.762889	−	0.640140i	−0.0330134	−	0.0277016i
$535$		0			0
$536$	0.439693	+	2.49362i	0.0189918	+	0.107708i
$537$	−4.52141	+	25.6422i	−0.195113	+	1.10654i
$538$	−14.9290	−	5.43372i	−0.643636	−	0.234264i
$539$	0.645430	+	1.11792i	0.0278006	+	0.0481521i
$540$		0			0
$541$	−25.1058	+	21.0663i	−1.07938	+	0.905710i	−0.995869	−	0.0907964i	$-0.971059\pi$
$541$	−25.1058	+	21.0663i	−1.07938	+	0.905710i	−0.0835140	+	0.996507i	$0.526614\pi$
$542$	18.7083	−	15.6981i	0.803589	−	0.674291i
$543$	−17.8007	+	30.8316i	−0.763899	+	1.32311i
$544$	−0.826352	−	1.43128i	−0.0354295	−	0.0613658i
$545$		0			0
$546$	−0.358441	+	2.03282i	−0.0153398	+	0.0869966i
$547$	−5.04205	−	28.5949i	−0.215583	−	1.22263i	−0.879893	−	0.475172i	$-0.842386\pi$
$547$	−5.04205	−	28.5949i	−0.215583	−	1.22263i	0.664310	−	0.747457i	$-0.268725\pi$
$548$	−2.83750	+	1.03276i	−0.121212	+	0.0441175i
$549$	−5.67159	−	4.75903i	−0.242058	−	0.203110i
$550$		0			0
$551$	−10.1584	+	1.86841i	−0.432762	+	0.0795968i
$552$	−1.50980			−0.0642614
$553$	−18.9119	−	15.8690i	−0.804218	−	0.674819i
$554$	−10.8439	+	3.94685i	−0.460713	+	0.167686i
$555$		0			0
$556$	−2.14930	+	12.1893i	−0.0911506	+	0.516941i
$557$	−26.4722	−	9.63511i	−1.12167	−	0.408253i	−0.286406	−	0.958108i	$-0.592460\pi$
$557$	−26.4722	−	9.63511i	−1.12167	−	0.408253i	−0.835260	+	0.549856i	$0.814683\pi$
$558$	1.00387	+	1.73875i	0.0424972	+	0.0736073i
$559$	2.89053	−	5.00654i	0.122256	−	0.211754i
$560$		0			0
$561$	1.70574	−	1.43128i	0.0720163	−	0.0604288i
$562$	−3.94222	+	6.82812i	−0.166292	+	0.288027i
$563$	−5.15270	−	8.92474i	−0.217161	−	0.376133i	0.736778	−	0.676135i	$-0.236346\pi$
$563$	−5.15270	−	8.92474i	−0.217161	−	0.376133i	−0.953939	+	0.300001i	$0.903013\pi$
$564$	2.29813	+	0.836452i	0.0967689	+	0.0352210i
$565$		0			0
$566$	−0.823826	−	4.67215i	−0.0346280	−	0.196385i
$567$	10.9363	−	3.98048i	0.459281	−	0.167165i
$568$	4.50980	+	3.78417i	0.189227	+	0.158780i
$569$	−24.3723			−1.02174			−0.510869	−	0.859658i	$-0.670676\pi$
$569$	−24.3723			−1.02174			−0.510869	+	0.859658i	$0.670676\pi$
$570$		0			0
$571$	−40.7844			−1.70677			−0.853386	−	0.521279i	$-0.825455\pi$
$571$	−40.7844			−1.70677			−0.853386	+	0.521279i	$0.825455\pi$
$572$	−0.407604	−	0.342020i	−0.0170428	−	0.0143006i
$573$	32.5317	−	11.8406i	1.35903	−	0.494647i
$574$	−2.58512	−	14.6610i	−0.107901	−	0.611937i
$575$		0			0
$576$	1.11334	+	0.405223i	0.0463892	+	0.0168843i
$577$	−16.2815	−	28.2004i	−0.677809	−	1.17400i	−0.975639	−	0.219381i	$-0.929596\pi$
$577$	−16.2815	−	28.2004i	−0.677809	−	1.17400i	0.297831	−	0.954619i	$-0.403737\pi$
$578$	−7.13429	+	12.3569i	−0.296747	+	0.513981i
$579$	5.42443	−	4.55164i	0.225432	−	0.189160i
$580$		0			0
$581$	15.3439	−	26.5764i	0.636572	−	1.10257i
$582$	7.81702	+	13.5395i	0.324026	+	0.561229i
$583$	11.2836	+	4.10689i	0.467318	+	0.170090i
$584$	−0.865715	+	4.90971i	−0.0358235	+	0.203165i
$585$		0			0
$586$	11.8341	−	4.30726i	0.488862	−	0.177931i
$587$	20.0724	+	16.8427i	0.828476	+	0.695174i	0.954941	−	0.296797i	$-0.0959185\pi$
$587$	20.0724	+	16.8427i	0.828476	+	0.695174i	−0.126465	+	0.991971i	$0.540363\pi$
$588$	1.73917			0.0717222
$589$	0.0543776	+	7.38636i	0.00224059	+	0.304350i
$590$		0			0
$591$	25.4288	+	21.3373i	1.04600	+	0.877698i
$592$	2.43969	−	0.887975i	0.100271	−	0.0364956i
$593$	8.25893	+	46.8387i	0.339154	+	1.92344i	0.381578	+	0.924337i	$0.375381\pi$
$593$	8.25893	+	46.8387i	0.339154	+	1.92344i	−0.0424244	+	0.999100i	$0.513508\pi$
$594$	−0.979055	+	5.55250i	−0.0401711	+	0.227822i
$595$		0			0
$596$	−4.66385	−	8.07802i	−0.191039	−	0.330889i
$597$	6.59698	−	11.4263i	0.269996	−	0.467648i
$598$	−0.456767	+	0.383273i	−0.0186786	+	0.0156732i
$599$	−11.9474	+	10.0251i	−0.488159	+	0.409614i	−0.853366	−	0.521312i	$-0.825443\pi$
$599$	−11.9474	+	10.0251i	−0.488159	+	0.409614i	0.365207	+	0.930926i	$0.380998\pi$
$600$		0			0
$601$	18.8876	+	32.7143i	0.770441	+	1.33444i	0.937321	+	0.348466i	$0.113297\pi$
$601$	18.8876	+	32.7143i	0.770441	+	1.33444i	−0.166881	+	0.985977i	$0.553369\pi$
$602$	−29.3974	−	10.6998i	−1.19815	−	0.436090i
$603$	0.520945	−	2.95442i	0.0212145	−	0.120313i
$604$	−0.827696	−	4.69410i	−0.0336785	−	0.191000i
$605$		0			0
$606$	−14.7424	−	12.3704i	−0.598870	−	0.502511i
$607$	−32.7520			−1.32936			−0.664681	−	0.747128i	$-0.731432\pi$
$607$	−32.7520			−1.32936			−0.664681	+	0.747128i	$0.731432\pi$
$608$	2.82635	+	3.31839i	0.114624	+	0.134579i
$609$	−9.19253			−0.372500
$610$		0			0
$611$	0.907604	−	0.330341i	0.0367177	−	0.0133642i
$612$	0.340022	+	1.92836i	0.0137446	+	0.0779494i
$613$	5.78729	−	32.8214i	0.233747	−	1.32564i	−0.611491	−	0.791252i	$-0.709430\pi$
$613$	5.78729	−	32.8214i	0.233747	−	1.32564i	0.845237	−	0.534391i	$-0.179459\pi$
$614$	−28.3692	−	10.3255i	−1.14489	−	0.416705i
$615$		0			0
$616$	−1.43969	+	2.49362i	−0.0580069	+	0.100471i
$617$	−29.1937	+	24.4964i	−1.17529	+	0.986189i	−0.175296	+	0.984516i	$0.556088\pi$
$617$	−29.1937	+	24.4964i	−1.17529	+	0.986189i	−0.999999	+	0.00167362i	$0.999467\pi$
$618$	−1.63950	+	1.37570i	−0.0659504	+	0.0553389i
$619$	12.0312	−	20.8387i	0.483575	−	0.837577i	−0.516247	−	0.856440i	$-0.672671\pi$
$619$	12.0312	−	20.8387i	0.483575	−	0.837577i	0.999822	+	0.0188630i	$0.00600463\pi$
$620$		0			0
$621$	5.93717	+	2.16095i	0.238250	+	0.0867160i
$622$	−1.92484	+	10.9163i	−0.0771791	+	0.437704i
$623$	0.369585	+	2.09602i	0.0148071	+	0.0839753i
$624$	−0.673648	+	0.245188i	−0.0269675	+	0.00981537i
$625$		0			0
$626$	−8.18479			−0.327130
$627$	−3.74170	+	4.52644i	−0.149429	+	0.180769i
$628$	−15.3354			−0.611951
$629$	3.28699	+	2.75811i	0.131061	+	0.109973i
$630$		0			0
$631$	4.68139	+	26.5495i	0.186363	+	1.05692i	0.924191	+	0.381930i	$0.124740\pi$
$631$	4.68139	+	26.5495i	0.186363	+	1.05692i	−0.737828	+	0.674988i	$0.764149\pi$
$632$	1.48886	−	8.44372i	0.0592235	−	0.335873i
$633$	−27.2768	−	9.92794i	−1.08415	−	0.394600i
$634$	−2.39899	−	4.15516i	−0.0952759	−	0.165023i
$635$		0			0
$636$	12.3931	−	10.3990i	0.491417	−	0.412348i
$637$	0.526159	−	0.441500i	0.0208472	−	0.0174929i
$638$	1.18479	−	2.05212i	0.0469064	−	0.0812442i
$639$	−3.48751	−	6.04055i	−0.137964	−	0.238960i
$640$		0			0
$641$	0.733956	−	4.16247i	0.0289895	−	0.164408i	−0.966876	−	0.255246i	$-0.917844\pi$
$641$	0.733956	−	4.16247i	0.0289895	−	0.164408i	0.995866	+	0.0908384i	$0.0289547\pi$
$642$	1.18139	+	6.69999i	0.0466257	+	0.264428i
$643$	−24.6459	+	8.97037i	−0.971939	+	0.353757i	−0.778701	−	0.627395i	$-0.784121\pi$
$643$	−24.6459	+	8.97037i	−0.971939	+	0.353757i	−0.193238	+	0.981152i	$0.561899\pi$
$644$	2.47178	+	2.07407i	0.0974018	+	0.0817298i
$645$		0			0
$646$	−2.41400	+	6.78747i	−0.0949776	+	0.267049i
$647$	−6.31221			−0.248159			−0.124079	−	0.992272i	$-0.539598\pi$
$647$	−6.31221			−0.248159			−0.124079	+	0.992272i	$0.539598\pi$
$648$	3.09627	+	2.59808i	0.121633	+	0.102062i
$649$	8.25150	−	3.00330i	0.323900	−	0.117890i
$650$		0			0
$651$	−1.14156	+	6.47410i	−0.0447412	+	0.253740i
$652$	7.75624	+	2.82304i	0.303758	+	0.110559i
$653$	8.22580	+	14.2475i	0.321901	+	0.557548i	0.980880	−	0.194613i	$-0.0623450\pi$
$653$	8.22580	+	14.2475i	0.321901	+	0.557548i	−0.658980	+	0.752161i	$0.729012\pi$
$654$	2.66978	−	4.62419i	0.104397	−	0.180820i
$655$		0			0
$656$	3.96064	−	3.32337i	0.154637	−	0.129756i
$657$	2.95336	−	5.11538i	0.115222	−	0.199570i
$658$	−2.61334	−	4.52644i	−0.101879	−	0.176459i
$659$	−33.6168	−	12.2355i	−1.30952	−	0.476628i	−0.409438	−	0.912338i	$-0.634275\pi$
$659$	−33.6168	−	12.2355i	−1.30952	−	0.476628i	−0.900087	+	0.435710i	$0.856497\pi$
$660$		0			0
$661$	5.11159	+	28.9892i	0.198818	+	1.12755i	0.906876	+	0.421397i	$0.138460\pi$
$661$	5.11159	+	28.9892i	0.198818	+	1.12755i	−0.708059	+	0.706154i	$0.750429\pi$
$662$	−12.8712	+	4.68475i	−0.500255	+	0.182078i
$663$	−0.907604	−	0.761570i	−0.0352484	−	0.0295769i
$664$	10.6578			0.413601
$665$		0			0
$666$	−3.07604			−0.119194
$667$	−2.03415	−	1.70685i	−0.0787625	−	0.0660896i
$668$	−16.3430	+	5.94837i	−0.632330	+	0.230149i
$669$	4.78240	+	27.1224i	0.184898	+	1.04861i
$670$		0			0
$671$	5.87211	+	2.13727i	0.226690	+	0.0825085i
$672$	1.93969	+	3.35965i	0.0748253	+	0.129601i
$673$	−16.0692	+	27.8327i	−0.619423	+	1.07287i	0.370168	+	0.928965i	$0.379300\pi$
$673$	−16.0692	+	27.8327i	−0.619423	+	1.07287i	−0.989591	+	0.143908i	$0.954033\pi$
$674$	−5.95336	+	4.99546i	−0.229315	+	0.192418i
$675$		0			0
$676$	6.35844	−	11.0131i	0.244555	−	0.423582i
$677$	−9.00980	−	15.6054i	−0.346275	−	0.599765i	0.639310	−	0.768949i	$-0.279220\pi$
$677$	−9.00980	−	15.6054i	−0.346275	−	0.599765i	−0.985585	+	0.169184i	$0.945887\pi$
$678$	−8.84389	−	3.21891i	−0.339648	−	0.123622i
$679$	5.80200	−	32.9048i	0.222660	−	1.26277i
$680$		0			0
$681$	9.85978	−	3.58867i	0.377828	−	0.137518i
$682$	−1.29813	−	1.08926i	−0.0497081	−	0.0417100i
$683$	27.6195			1.05683			0.528415	−	0.848986i	$-0.322786\pi$
$683$	27.6195			1.05683			0.528415	+	0.848986i	$0.322786\pi$
$684$	−1.80200	−	4.83981i	−0.0689013	−	0.185055i
$685$		0			0
$686$	12.5929	+	10.5667i	0.480798	+	0.403437i
$687$	10.1630	−	3.69902i	0.387742	−	0.141126i
$688$	−1.88666	−	10.6998i	−0.0719282	−	0.407925i
$689$	1.10947	−	6.29212i	0.0422675	−	0.239711i
$690$		0			0
$691$	−14.8089	−	25.6497i	−0.563356	−	0.975761i	−0.997201	−	0.0747733i	$-0.976177\pi$
$691$	−14.8089	−	25.6497i	−0.563356	−	0.975761i	0.433845	−	0.900988i	$-0.357157\pi$
$692$	9.81180	−	16.9945i	0.372989	−	0.646036i
$693$	2.61334	−	2.19285i	0.0992726	−	0.0832996i
$694$	2.53209	−	2.12467i	0.0961168	−	0.0806516i
$695$		0			0
$696$	−1.59627	−	2.76481i	−0.0605063	−	0.104800i
$697$	8.02956	+	2.92252i	0.304141	+	0.110698i
$698$	4.19712	−	23.8030i	0.158863	−	0.900959i
$699$	−0.884600	−	5.01681i	−0.0334586	−	0.189753i
$700$		0			0
$701$	19.9277	+	16.7213i	0.752658	+	0.631555i	0.936204	−	0.351456i	$-0.114313\pi$
$701$	19.9277	+	16.7213i	0.752658	+	0.631555i	−0.183547	+	0.983011i	$0.558758\pi$
$702$	3.00000			0.113228
$703$	−9.84208	−	5.58613i	−0.371201	−	0.210685i
$704$	−1.00000			−0.0376889
$705$		0			0
$706$	27.0107	−	9.83110i	1.01656	−	0.369998i
$707$	7.14203	+	40.5044i	0.268604	+	1.52333i
$708$	2.05438	−	11.6510i	0.0772082	−	0.437870i
$709$	−27.9932	−	10.1887i	−1.05131	−	0.382644i	−0.242151	−	0.970239i	$-0.577853\pi$
$709$	−27.9932	−	10.1887i	−1.05131	−	0.382644i	−0.809156	+	0.587594i	$0.800075\pi$
$710$		0			0
$711$	−5.07919	+	8.79742i	−0.190485	+	0.329929i
$712$	−0.566237	+	0.475129i	−0.0212206	+	0.0178062i
$713$	−1.45471	+	1.22064i	−0.0544792	+	0.0457135i
$714$	−3.20574	+	5.55250i	−0.119972	+	0.207797i
$715$		0			0
$716$	18.1604	+	6.60986i	0.678688	+	0.247022i
$717$	1.58647	−	8.99730i	0.0592477	−	0.336010i
$718$	2.26399	+	12.8397i	0.0844912	+	0.479173i
$719$	14.2007	−	5.16863i	0.529596	−	0.192757i	−0.0633618	−	0.997991i	$-0.520182\pi$
$719$	14.2007	−	5.16863i	0.529596	−	0.192757i	0.592958	+	0.805233i	$0.297960\pi$
$720$		0			0
$721$	4.57398			0.170344
$722$	3.02347	−	18.7579i	0.112522	−	0.698097i
$723$	−8.14147			−0.302785
$724$	20.2422	+	16.9852i	0.752294	+	0.631250i
$725$		0			0
$726$	2.33956	+	13.2683i	0.0868291	+	0.492432i
$727$	−1.30335	+	7.39165i	−0.0483385	+	0.274141i	−0.999391	−	0.0348873i	$-0.988893\pi$
$727$	−1.30335	+	7.39165i	−0.0483385	+	0.274141i	0.951053	+	0.309029i	$0.100004\pi$
$728$	1.43969	+	0.524005i	0.0533586	+	0.0194209i
$729$	−13.7888	−	23.8829i	−0.510696	−	0.884552i
$730$		0			0
$731$	13.7554	−	11.5421i	0.508761	−	0.426901i
$732$	6.44949	−	5.41177i	0.238380	−	0.200025i
$733$	−7.86706	+	13.6261i	−0.290576	+	0.503293i	−0.973946	−	0.226779i	$-0.927180\pi$
$733$	−7.86706	+	13.6261i	−0.290576	+	0.503293i	0.683370	+	0.730072i	$0.260514\pi$
$734$	−8.04710	−	13.9380i	−0.297024	−	0.514461i
$735$		0			0
$736$	−0.194593	+	1.10359i	−0.00717278	+	0.0406789i
$737$	0.439693	+	2.49362i	0.0161963	+	0.0918537i
$738$	−5.75624	+	2.09510i	−0.211890	+	0.0771218i
$739$	−16.6570	−	13.9769i	−0.612739	−	0.514149i	0.282773	−	0.959187i	$-0.408746\pi$
$739$	−16.6570	−	13.9769i	−0.612739	−	0.514149i	−0.895512	+	0.445038i	$0.853190\pi$
$740$		0			0
$741$	2.71760	+	1.54244i	0.0998334	+	0.0566630i
$742$	−34.5749			−1.26928
$743$	−20.7442	−	17.4065i	−0.761032	−	0.638581i	0.177363	−	0.984145i	$-0.443243\pi$
$743$	−20.7442	−	17.4065i	−0.761032	−	0.638581i	−0.938395	+	0.345564i	$0.887688\pi$
$744$	−2.14543	+	0.780873i	−0.0786553	+	0.0286282i
$745$		0			0
$746$	−4.88831	+	27.7230i	−0.178974	+	1.01501i
$747$	−11.8657	−	4.31877i	−0.434144	−	0.158015i
$748$	−0.826352	−	1.43128i	−0.0302144	−	0.0523329i
$749$	7.26991	−	12.5919i	0.265637	−	0.460097i
$750$		0			0
$751$	27.8733	−	23.3885i	1.01711	−	0.853457i	0.0278492	−	0.999612i	$-0.491134\pi$
$751$	27.8733	−	23.3885i	1.01711	−	0.853457i	0.989262	+	0.146155i	$0.0466897\pi$
$752$	0.907604	−	1.57202i	0.0330969	−	0.0573255i
$753$	3.84936	+	6.66728i	0.140278	+	0.242969i
$754$	−1.18479	−	0.431229i	−0.0431476	−	0.0157044i
$755$		0			0
$756$	−2.81908	−	15.9878i	−0.102529	−	0.581470i
$757$	19.3307	−	7.03580i	0.702586	−	0.255720i	0.0340713	−	0.999419i	$-0.489153\pi$
$757$	19.3307	−	7.03580i	0.702586	−	0.255720i	0.668515	+	0.743699i	$0.266930\pi$
$758$	9.00181	+	7.55342i	0.326960	+	0.274352i
$759$	−1.50980			−0.0548023
$760$		0			0
$761$	−47.5850			−1.72496			−0.862478	−	0.506095i	$-0.831089\pi$
$761$	−47.5850			−1.72496			−0.862478	+	0.506095i	$0.831089\pi$
$762$	19.5567	+	16.4100i	0.708463	+	0.594471i
$763$	−10.7233	+	3.90295i	−0.388209	+	0.141296i
$764$	−4.46198	−	25.3052i	−0.161429	−	0.915508i
$765$		0			0
$766$	−16.8229	−	6.12305i	−0.607838	−	0.221235i
$767$	−2.33615	−	4.04633i	−0.0843536	−	0.146105i
$768$	−0.673648	+	1.16679i	−0.0243082	+	0.0421030i
$769$	12.2215	−	10.2550i	0.440717	−	0.369806i	−0.395260	−	0.918569i	$-0.629346\pi$
$769$	12.2215	−	10.2550i	0.440717	−	0.369806i	0.835978	+	0.548763i	$0.184901\pi$
$770$		0			0
$771$	8.64337	−	14.9708i	0.311283	−	0.539159i
$772$	−2.62789	−	4.55164i	−0.0945798	−	0.163817i
$773$	−15.4483	−	5.62273i	−0.555637	−	0.202235i	0.0489122	−	0.998803i	$-0.484425\pi$
$773$	−15.4483	−	5.62273i	−0.555637	−	0.202235i	−0.604549	+	0.796568i	$0.706647\pi$
$774$	−2.23530	+	12.6770i	−0.0803462	+	0.455666i
$775$		0			0
$776$	10.9042	−	3.96880i	0.391438	−	0.142472i
$777$	−7.71554	−	6.47410i	−0.276793	−	0.232257i
$778$	26.3473			0.944596
$779$	−22.2224	−	3.74994i	−0.796200	−	0.134356i
$780$		0			0
$781$	4.50980	+	3.78417i	0.161373	+	0.135408i
$782$	−1.74035	+	0.633436i	−0.0622349	+	0.0226516i
$783$	2.31996	+	13.1571i	0.0829084	+	0.470197i
$784$	0.224155	−	1.27125i	0.00800555	−	0.0454017i
$785$		0			0
$786$	−11.2665	−	19.5142i	−0.401863	−	0.696047i
$787$	−24.9873	+	43.2792i	−0.890700	+	1.54274i	−0.0516616	+	0.998665i	$0.516452\pi$
$787$	−24.9873	+	43.2792i	−0.890700	+	1.54274i	−0.839038	+	0.544073i	$0.816882\pi$
$788$	18.8739	−	15.8371i	0.672356	−	0.564173i
$789$	5.04916	−	4.23675i	0.179755	−	0.150832i
$790$		0			0
$791$	10.0569	+	17.4191i	0.357582	+	0.619351i
$792$	1.11334	+	0.405223i	0.0395608	+	0.0143990i
$793$	0.577382	−	3.27449i	0.0205034	−	0.116281i
$794$	2.80912	+	15.9313i	0.0996918	+	0.565380i
$795$		0			0
$796$	−7.50181	−	6.29477i	−0.265895	−	0.223112i
$797$	11.9314			0.422631			0.211316	−	0.977418i	$-0.432225\pi$
$797$	11.9314			0.422631			0.211316	+	0.977418i	$0.432225\pi$
$798$	5.66637	−	15.9322i	0.200587	−	0.563994i
$799$	3.00000			0.106132
$800$		0			0
$801$	0.822948	−	0.299529i	0.0290774	−	0.0105833i
$802$	−5.07098	−	28.7590i	−0.179063	−	1.01552i
$803$	−0.865715	+	4.90971i	−0.0305504	+	0.173260i
$804$	3.20574	+	1.16679i	0.113058	+	0.0411496i
$805$		0			0
$806$	−0.450837	+	0.780873i	−0.0158801	+	0.0275051i
$807$	−16.3969	+	13.7587i	−0.577199	+	0.484328i
$808$	−10.9422	+	9.18161i	−0.384946	+	0.323008i
$809$	25.0744	−	43.4302i	0.881571	−	1.52692i	0.0319760	−	0.999489i	$-0.489820\pi$
$809$	25.0744	−	43.4302i	0.881571	−	1.52692i	0.849595	−	0.527436i	$-0.176847\pi$
$810$		0			0
$811$	−22.8567	−	8.31915i	−0.802607	−	0.292125i	−0.0920405	−	0.995755i	$-0.529339\pi$
$811$	−22.8567	−	8.31915i	−0.802607	−	0.292125i	−0.710566	+	0.703630i	$0.751561\pi$
$812$	−1.18479	+	6.71929i	−0.0415781	+	0.235801i
$813$	−5.71364	−	32.4037i	−0.200386	−	1.13645i
$814$	2.43969	−	0.887975i	0.0855112	−	0.0311235i
$815$		0			0
$816$	−2.22668			−0.0779494
$817$	−30.1737	+	36.5020i	−1.05564	+	1.27704i
$818$	24.4902			0.856280
$819$	−1.39053	−	1.16679i	−0.0485890	−	0.0407710i
$820$		0			0
$821$	−7.12671	−	40.4176i	−0.248724	−	1.41058i	−0.811683	−	0.584098i	$-0.801448\pi$
$821$	−7.12671	−	40.4176i	−0.248724	−	1.41058i	0.562959	−	0.826485i	$-0.309663\pi$
$822$	−0.706452	+	4.00649i	−0.0246404	+	0.139742i
$823$	9.89693	+	3.60219i	0.344985	+	0.125564i	0.508701	−	0.860943i	$-0.330126\pi$
$823$	9.89693	+	3.60219i	0.344985	+	0.125564i	−0.163716	+	0.986508i	$0.552348\pi$
$824$	0.794263	+	1.37570i	0.0276695	+	0.0479249i
$825$		0			0
$826$	−19.3687	+	16.2523i	−0.673924	+	0.565489i
$827$	37.0565	−	31.0941i	1.28858	−	1.08125i	0.296581	−	0.955008i	$-0.404154\pi$
$827$	37.0565	−	31.0941i	1.28858	−	1.08125i	0.992000	−	0.126240i	$-0.0402908\pi$
$828$	0.663848	−	1.14982i	0.0230703	−	0.0399590i
$829$	11.1279	+	19.2741i	0.386488	+	0.669416i	0.991974	−	0.126439i	$-0.0403549\pi$
$829$	11.1279	+	19.2741i	0.386488	+	0.669416i	−0.605487	+	0.795855i	$0.707022\pi$
$830$		0			0
$831$	−2.69981	+	15.3114i	−0.0936553	+	0.531145i
$832$	0.0923963	+	0.524005i	0.00320326	+	0.0181666i
$833$	2.00475	−	0.729669i	0.0694604	−	0.0252815i
$834$	12.7745	+	10.7191i	0.442345	+	0.371171i
$835$		0			0
$836$	2.82635	+	3.31839i	0.0977514	+	0.114769i
$837$	9.55438			0.330248
$838$	−11.1821	−	9.38290i	−0.386279	−	0.324127i
$839$	−13.6638	+	4.97323i	−0.471728	+	0.171695i	−0.566935	−	0.823762i	$-0.691871\pi$
$839$	−13.6638	+	4.97323i	−0.471728	+	0.171695i	0.0952067	+	0.995458i	$0.469649\pi$
$840$		0			0
$841$	−4.06077	+	23.0298i	−0.140027	+	0.794131i
$842$	−14.6557	−	5.33424i	−0.505069	−	0.183830i
$843$	5.31134	+	9.19951i	0.182932	+	0.316848i
$844$	−10.7724	+	18.6584i	−0.370803	+	0.642249i
$845$		0			0
$846$	−1.64749	+	1.38241i	−0.0566418	+	0.0475281i
$847$	14.3969	−	24.9362i	0.494684	−	0.856818i
$848$	−6.00387	−	10.3990i	−0.206174	−	0.357103i
$849$	−6.00640	−	2.18615i	−0.206139	−	0.0750285i
$850$		0			0
$851$	−0.505215	−	2.86521i	−0.0173185	−	0.0982183i
$852$	7.45336	−	2.71280i	0.255348	−	0.0929391i
$853$	−16.1550	−	13.5556i	−0.553136	−	0.464136i	0.322865	−	0.946445i	$-0.395354\pi$
$853$	−16.1550	−	13.5556i	−0.553136	−	0.464136i	−0.876001	+	0.482309i	$0.839798\pi$
$854$	−17.9932			−0.615714
$855$		0			0
$856$	5.04963			0.172593
$857$	23.6909	+	19.8791i	0.809267	+	0.679056i	0.950433	−	0.310930i	$-0.100641\pi$
$857$	23.6909	+	19.8791i	0.809267	+	0.679056i	−0.141166	+	0.989986i	$0.545085\pi$
$858$	−0.673648	+	0.245188i	−0.0229980	+	0.00837058i
$859$	−3.27110	−	18.5513i	−0.111608	−	0.632963i	−0.988374	−	0.152044i	$-0.951414\pi$
$859$	−3.27110	−	18.5513i	−0.111608	−	0.632963i	0.876765	−	0.480918i	$-0.159697\pi$
$860$		0			0
$861$	−18.8478	−	6.86002i	−0.642330	−	0.233789i
$862$	18.7751	+	32.5195i	0.639483	+	1.10762i
$863$	20.6689	−	35.7996i	0.703578	−	1.21863i	−0.263625	−	0.964625i	$-0.584918\pi$
$863$	20.6689	−	35.7996i	0.703578	−	1.21863i	0.967202	−	0.254007i	$-0.0817486\pi$
$864$	4.31908	−	3.62414i	0.146938	−	0.123296i
$865$		0			0
$866$	9.88965	−	17.1294i	0.336064	−	0.582080i
$867$	9.61200	+	16.6485i	0.326441	+	0.565412i
$868$	4.58512	+	1.66885i	0.155629	+	0.0566444i
$869$	1.48886	−	8.44372i	0.0505060	−	0.286434i
$870$		0			0
$871$	1.26604	−	0.460802i	0.0428983	−	0.0156137i
$872$	−3.03596	−	2.54747i	−0.102811	−	0.0862683i
$873$	−13.7483			−0.465311
$874$	4.21213	−	2.47340i	0.142478	−	0.0836640i
$875$		0			0
$876$	5.14543	+	4.31753i	0.173848	+	0.145876i
$877$	2.20604	−	0.802934i	0.0744927	−	0.0271131i	−0.304505	−	0.952511i	$-0.598491\pi$
$877$	2.20604	−	0.802934i	0.0744927	−	0.0271131i	0.378998	+	0.925398i	$0.376269\pi$
$878$	−3.31227	−	18.7848i	−0.111784	−	0.633957i
$879$	2.94634	−	16.7095i	0.0993775	−	0.563598i
$880$		0			0
$881$	−13.6792	−	23.6930i	−0.460863	−	0.798238i	0.538141	−	0.842855i	$-0.319127\pi$
$881$	−13.6792	−	23.6930i	−0.460863	−	0.798238i	−0.999004	+	0.0446167i	$0.985793\pi$
$882$	−0.764700	+	1.32450i	−0.0257488	+	0.0445982i
$883$	0.590585	−	0.495560i	0.0198748	−	0.0166769i	−0.632796	−	0.774318i	$-0.718093\pi$
$883$	0.590585	−	0.495560i	0.0198748	−	0.0166769i	0.652671	+	0.757642i	$0.273648\pi$
$884$	−0.673648	+	0.565258i	−0.0226572	+	0.0190117i
$885$		0			0
$886$	−8.52007	−	14.7572i	−0.286237	−	0.495777i
$887$	−4.22106	−	1.53634i	−0.141729	−	0.0515852i	0.270182	−	0.962809i	$-0.412916\pi$
$887$	−4.22106	−	1.53634i	−0.141729	−	0.0515852i	−0.411911	+	0.911224i	$0.635138\pi$
$888$	0.607411	−	3.44480i	0.0203834	−	0.115600i
$889$	−9.47431	−	53.7315i	−0.317758	−	1.80210i
$890$		0			0
$891$	3.09627	+	2.59808i	0.103729	+	0.0870388i
$892$	20.4415			0.684432
$893$	−7.78177	+	1.43128i	−0.260407	+	0.0478961i
$894$	−12.5672			−0.420309
$895$		0			0
$896$	2.70574	−	0.984808i	0.0903923	−	0.0329001i
$897$	0.139500	+	0.791143i	0.00465777	+	0.0264155i
$898$	6.92396	−	39.2677i	0.231056	−	1.31038i
$899$	−3.77332	−	1.37338i	−0.125847	−	0.0458046i
$900$		0			0
$901$	9.92262	−	17.1865i	0.330570	−	0.572565i
$902$	3.96064	−	3.32337i	0.131875	−	0.110656i
$903$	−32.2879	+	27.0928i	−1.07447	+	0.901591i
$904$	−3.49273	+	6.04958i	−0.116166	+	0.201206i
$905$		0			0
$906$	−6.03462	−	2.19642i	−0.200487	−	0.0729712i
$907$	−3.10653	+	17.6180i	−0.103151	+	0.584997i	0.888792	+	0.458311i	$0.151545\pi$
$907$	−3.10653	+	17.6180i	−0.103151	+	0.584997i	−0.991943	+	0.126686i	$0.959566\pi$
$908$	−1.35235	−	7.66955i	−0.0448793	−	0.254523i
$909$	15.9030	−	5.78823i	0.527470	−	0.191983i
$910$		0			0
$911$	−21.2398			−0.703706			−0.351853	−	0.936055i	$-0.614448\pi$
$911$	−21.2398			−0.703706			−0.351853	+	0.936055i	$0.614448\pi$
$912$	5.77584	−	1.06234i	0.191257	−	0.0351775i
$913$	10.6578			0.352720
$914$	11.8136	+	9.91280i	0.390760	+	0.327886i
$915$		0			0
$916$	−1.39393	−	7.90539i	−0.0460568	−	0.261201i
$917$	−8.36231	+	47.4250i	−0.276148	+	1.56611i
$918$	8.75624	+	3.18701i	0.288999	+	0.105187i
$919$	−6.68913	−	11.5859i	−0.220654	−	0.382184i	0.734353	−	0.678768i	$-0.237486\pi$
$919$	−6.68913	−	11.5859i	−0.220654	−	0.382184i	−0.955007	+	0.296584i	$0.904153\pi$
$920$		0			0
$921$	−31.1586	+	26.1452i	−1.02671	+	0.861513i
$922$	6.97565	−	5.85327i	0.229731	−	0.192767i
$923$	1.56624	−	2.71280i	0.0515533	−	0.0892930i
$924$	1.93969	+	3.35965i	0.0638112	+	0.110524i
$925$		0			0
$926$	−0.716719	+	4.06472i	−0.0235529	+	0.133575i
$927$	−0.326819	−	1.85348i	−0.0107341	−	0.0608763i
$928$	−2.22668	+	0.810446i	−0.0730944	+	0.0266042i
$929$	−8.74241	−	7.33575i	−0.286829	−	0.240678i	0.488008	−	0.872839i	$-0.337724\pi$
$929$	−8.74241	−	7.33575i	−0.286829	−	0.240678i	−0.774837	+	0.632161i	$0.782168\pi$
$930$		0			0
$931$	−4.85204	+	2.84916i	−0.159019	+	0.0933774i
$932$	−3.78106			−0.123853
$933$	11.4404	+	9.59964i	0.374542	+	0.314278i
$934$	−24.7802	+	9.01925i	−0.810832	+	0.295119i
$935$		0			0
$936$	0.109470	−	0.620838i	0.00357815	−	0.0202927i
$937$	47.0941	+	17.1409i	1.53850	+	0.559967i	0.965684	−	0.259719i	$-0.0836299\pi$
$937$	47.0941	+	17.1409i	1.53850	+	0.559967i	0.572813	+	0.819686i	$0.305852\pi$
$938$	−3.64543	−	6.31407i	−0.119027	−	0.206162i
$939$	−5.51367	+	9.54996i	−0.179932	+	0.311651i
$940$		0			0
$941$	24.0514	−	20.1816i	0.784055	−	0.657900i	−0.160212	−	0.987083i	$-0.551218\pi$
$941$	24.0514	−	20.1816i	0.784055	−	0.657900i	0.944266	+	0.329183i	$0.106773\pi$
$942$	−10.3307	+	17.8933i	−0.336592	+	0.582995i
$943$	−2.89693	−	5.01762i	−0.0943369	−	0.163396i
$944$	−8.25150	−	3.00330i	−0.268563	−	0.0977491i
$945$		0			0
$946$	−1.88666	−	10.6998i	−0.0613406	−	0.347880i
$947$	23.4602	−	8.53882i	0.762355	−	0.277475i	0.0685599	−	0.997647i	$-0.478160\pi$
$947$	23.4602	−	8.53882i	0.762355	−	0.277475i	0.693795	+	0.720173i	$0.255937\pi$
$948$	−8.84911	−	7.42528i	−0.287406	−	0.241162i
$949$	2.65270			0.0861104
$950$		0			0
$951$	−6.46429			−0.209619
$952$	3.64543	+	3.05888i	0.118149	+	0.0991388i
$953$	−24.0590	+	8.75677i	−0.779348	+	0.283660i	−0.700901	−	0.713259i	$-0.747218\pi$
$953$	−24.0590	+	8.75677i	−0.779348	+	0.283660i	−0.0784473	+	0.996918i	$0.524996\pi$
$954$	2.47044	+	14.0105i	0.0799834	+	0.453608i
$955$		0			0
$956$	−6.37211	−	2.31926i	−0.206089	−	0.0750102i
$957$	−1.59627	−	2.76481i	−0.0516000	−	0.0893738i
$958$	8.12583	−	14.0743i	0.262534	−	0.454722i
$959$	6.66044	−	5.58878i	0.215077	−	0.180471i
$960$		0			0
$961$	14.0642	−	24.3599i	0.453683	−	0.785802i
$962$	−0.690722	−	1.19637i	−0.0222698	−	0.0385724i
$963$	−5.62196	−	2.04623i	−0.181165	−	0.0659387i
$964$	−1.04933	+	5.95102i	−0.0337965	+	0.191669i
$965$		0			0
$966$	4.08512	−	1.48686i	0.131437	−	0.0478390i
$967$	−39.3155	−	32.9896i	−1.26430	−	1.06088i	−0.995210	−	0.0977605i	$-0.968832\pi$
$967$	−39.3155	−	32.9896i	−1.26430	−	1.06088i	−0.269092	−	0.963115i	$-0.586723\pi$
$968$	10.0000			0.321412
$969$	6.29339	+	7.38901i	0.202173	+	0.237369i
$970$		0			0
$971$	13.2554	+	11.1226i	0.425385	+	0.356940i	0.830207	−	0.557455i	$-0.188222\pi$
$971$	13.2554	+	11.1226i	0.425385	+	0.356940i	−0.404822	+	0.914395i	$0.632667\pi$
$972$	−10.7772	+	3.92258i	−0.345678	+	0.125817i
$973$	−6.18866	−	35.0977i	−0.198399	−	1.12518i
$974$	3.00371	−	17.0349i	0.0962450	−	0.545833i
$975$		0			0
$976$	−3.12449	−	5.41177i	−0.100012	−	0.173226i
$977$	−6.90554	+	11.9608i	−0.220928	+	0.382658i	−0.955090	−	0.296316i	$-0.904242\pi$
$977$	−6.90554	+	11.9608i	−0.220928	+	0.382658i	0.734162	+	0.678974i	$0.237575\pi$
$978$	8.51889	−	7.14819i	0.272404	−	0.228574i
$979$	−0.566237	+	0.475129i	−0.0180970	+	0.0151852i
$980$		0			0
$981$	2.34776	+	4.06645i	0.0749583	+	0.129832i
$982$	−14.6630	−	5.33688i	−0.467914	−	0.170307i
$983$	1.03028	−	5.84300i	0.0328608	−	0.186363i	−0.963959	−	0.266050i	$-0.914281\pi$
$983$	1.03028	−	5.84300i	0.0328608	−	0.186363i	0.996820	+	0.0796878i	$0.0253923\pi$
$984$	−1.20961	−	6.86002i	−0.0385609	−	0.218690i
$985$		0			0
$986$	−3.00000	−	2.51730i	−0.0955395	−	0.0801671i
$987$	−7.04189			−0.224146
$988$	1.47771	−	1.78763i	0.0470123	−	0.0568721i
$989$	−12.1753			−0.387152
$990$		0			0
$991$	−29.8901	+	10.8791i	−0.949491	+	0.345586i	−0.769907	−	0.638156i	$-0.779697\pi$
$991$	−29.8901	+	10.8791i	−0.949491	+	0.345586i	−0.179584	+	0.983743i	$0.557475\pi$
$992$	0.294263	+	1.66885i	0.00934286	+	0.0529860i
$993$	−3.20456	+	18.1739i	−0.101693	+	0.576732i
$994$	−15.9290	−	5.79769i	−0.505238	−	0.183891i
$995$		0			0
$996$	7.17958	−	12.4354i	0.227494	−	0.394031i
$997$	25.4937	−	21.3917i	0.807392	−	0.677483i	−0.142592	−	0.989782i	$-0.545544\pi$
$997$	25.4937	−	21.3917i	0.807392	−	0.677483i	0.949984	+	0.312299i	$0.101099\pi$
$998$	28.7802	−	24.1494i	0.911021	−	0.764437i
$999$	−7.31908	+	12.6770i	−0.231565	+	0.401083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.b.301.1	yes	6
5.2	odd	4		950.2.u.d.149.2		12
5.3	odd	4		950.2.u.d.149.1		12
5.4	even	2		950.2.l.e.301.1	yes	6
19.6	even	9	inner	950.2.l.b.101.1	✓	6
95.44	even	18		950.2.l.e.101.1	yes	6
95.63	odd	36		950.2.u.d.899.2		12
95.82	odd	36		950.2.u.d.899.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.b.101.1	✓	6	19.6	even	9	inner
950.2.l.b.301.1	yes	6	1.1	even	1	trivial
950.2.l.e.101.1	yes	6	95.44	even	18
950.2.l.e.301.1	yes	6	5.4	even	2
950.2.u.d.149.1		12	5.3	odd	4
950.2.u.d.149.2		12	5.2	odd	4
950.2.u.d.899.1		12	95.82	odd	36
950.2.u.d.899.2		12	95.63	odd	36

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.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.26604 + 0.460802i) q^{3} +(0.173648 + 0.984808i) q^{4} +(1.26604 + 0.460802i) q^{6} +(-1.43969 - 2.49362i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.907604 + 0.761570i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.26604 + 0.460802i) q^{3} +(0.173648 + 0.984808i) q^{4} +(1.26604 + 0.460802i) q^{6} +(-1.43969 - 2.49362i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.907604 + 0.761570i) q^{9} +(0.500000 - 0.866025i) q^{11} +(-0.673648 - 1.16679i) q^{12} +(-0.500000 - 0.181985i) q^{13} +(-0.500000 + 2.83564i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-1.26604 - 1.06234i) q^{17} +1.18479 q^{18} +(3.79086 + 2.15160i) q^{19} +(2.97178 + 2.49362i) q^{21} +(-0.939693 + 0.342020i) q^{22} +(0.194593 + 1.10359i) q^{23} +(-0.233956 + 1.32683i) q^{24} +(0.266044 + 0.460802i) q^{26} +(2.81908 - 4.88279i) q^{27} +(2.20574 - 1.85083i) q^{28} +(-1.81521 + 1.52314i) q^{29} +(0.847296 + 1.46756i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.233956 + 1.32683i) q^{33} +(0.286989 + 1.62760i) q^{34} +(-0.907604 - 0.761570i) q^{36} -2.59627 q^{37} +(-1.52094 - 4.08494i) q^{38} +0.716881 q^{39} +(-4.85844 + 1.76833i) q^{41} +(-0.673648 - 3.82045i) q^{42} +(-1.88666 + 10.6998i) q^{43} +(0.939693 + 0.342020i) q^{44} +(0.560307 - 0.970481i) q^{46} +(-1.39053 + 1.16679i) q^{47} +(1.03209 - 0.866025i) q^{48} +(-0.645430 + 1.11792i) q^{49} +(2.09240 + 0.761570i) q^{51} +(0.0923963 - 0.524005i) q^{52} +(2.08512 + 11.8253i) q^{53} +(-5.29813 + 1.92836i) q^{54} -2.87939 q^{56} +(-5.79086 - 0.977185i) q^{57} +2.36959 q^{58} +(6.72668 + 5.64436i) q^{59} +(1.08512 + 6.15403i) q^{61} +(0.294263 - 1.66885i) q^{62} +(3.20574 + 1.16679i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.03209 - 0.866025i) q^{66} +(-1.93969 + 1.62760i) q^{67} +(0.826352 - 1.43128i) q^{68} +(-0.754900 - 1.30753i) q^{69} +(-1.02229 + 5.79769i) q^{71} +(0.205737 + 1.16679i) q^{72} +(-4.68479 + 1.70513i) q^{73} +(1.98886 + 1.66885i) q^{74} +(-1.46064 + 4.10689i) q^{76} -2.87939 q^{77} +(-0.549163 - 0.460802i) q^{78} +(8.05690 - 2.93247i) q^{79} +(-0.701867 + 3.98048i) q^{81} +(4.85844 + 1.76833i) q^{82} +(5.32888 + 9.22989i) q^{83} +(-1.93969 + 3.35965i) q^{84} +(8.32295 - 6.98378i) q^{86} +(1.59627 - 2.76481i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-0.694593 - 0.252811i) q^{89} +(0.266044 + 1.50881i) q^{91} +(-1.05303 + 0.383273i) q^{92} +(-1.74897 - 1.46756i) q^{93} +1.81521 q^{94} -1.34730 q^{96} +(8.88919 + 7.45891i) q^{97} +(1.21301 - 0.441500i) q^{98} +(0.205737 + 1.16679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} + 3 q^{6} - 3 q^{7} + 3 q^{8} - 9 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 + 3 * q^6 - 3 * q^7 + 3 * q^8 - 9 * q^9	\( 6 q - 3 q^{3} + 3 q^{6} - 3 q^{7} + 3 q^{8} - 9 q^{9} + 3 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} - 3 q^{17} - 9 q^{19} + 3 q^{21} - 3 q^{23} - 6 q^{24} - 3 q^{26} + 3 q^{28} - 18 q^{29} + 3 q^{31} - 6 q^{33} - 6 q^{34} - 9 q^{36} + 12 q^{37} - 6 q^{38} - 12 q^{39} - 21 q^{41} - 3 q^{42} - 18 q^{43} + 9 q^{46} + 9 q^{47} - 3 q^{48} + 12 q^{49} + 9 q^{51} - 3 q^{52} - 9 q^{53} - 18 q^{54} - 6 q^{56} - 3 q^{57} + 27 q^{59} - 15 q^{61} + 12 q^{62} + 9 q^{63} - 3 q^{64} - 3 q^{66} - 6 q^{67} + 6 q^{68} - 6 q^{69} + 6 q^{71} - 9 q^{72} - 21 q^{73} + 18 q^{74} - 6 q^{77} - 15 q^{78} + 12 q^{79} - 18 q^{81} + 21 q^{82} + 18 q^{83} - 6 q^{84} + 9 q^{86} - 18 q^{87} - 3 q^{88} - 3 q^{91} + 6 q^{92} + 15 q^{93} + 18 q^{94} - 6 q^{96} + 45 q^{97} + 15 q^{98} - 9 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 + 3 * q^6 - 3 * q^7 + 3 * q^8 - 9 * q^9 + 3 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 - 3 * q^17 - 9 * q^19 + 3 * q^21 - 3 * q^23 - 6 * q^24 - 3 * q^26 + 3 * q^28 - 18 * q^29 + 3 * q^31 - 6 * q^33 - 6 * q^34 - 9 * q^36 + 12 * q^37 - 6 * q^38 - 12 * q^39 - 21 * q^41 - 3 * q^42 - 18 * q^43 + 9 * q^46 + 9 * q^47 - 3 * q^48 + 12 * q^49 + 9 * q^51 - 3 * q^52 - 9 * q^53 - 18 * q^54 - 6 * q^56 - 3 * q^57 + 27 * q^59 - 15 * q^61 + 12 * q^62 + 9 * q^63 - 3 * q^64 - 3 * q^66 - 6 * q^67 + 6 * q^68 - 6 * q^69 + 6 * q^71 - 9 * q^72 - 21 * q^73 + 18 * q^74 - 6 * q^77 - 15 * q^78 + 12 * q^79 - 18 * q^81 + 21 * q^82 + 18 * q^83 - 6 * q^84 + 9 * q^86 - 18 * q^87 - 3 * q^88 - 3 * q^91 + 6 * q^92 + 15 * q^93 + 18 * q^94 - 6 * q^96 + 45 * q^97 + 15 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

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Database

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