LMFDB - Embedded newform 950.2.l.e.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.e.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	0.0503837	−	0.998730i	$-0.483956\pi$
$3$	1.26604	−	0.460802i	0.730951	−	0.266044i	0.680567	+	0.732685i	$0.261733\pi$
$4$	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	$0.0164821\pi$
$7$	1.43969	+	2.49362i	0.544153	+	0.942500i	−0.454507	+	0.890743i	$0.650185\pi$
$8$	−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	0.410425	−	0.911894i	$-0.365380\pi$
$13$	0.500000	+	0.181985i	0.138675	+	0.0504736i	−0.271750	+	0.962368i	$0.587602\pi$
$14$	−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	0.783276	−	0.621674i	$-0.213547\pi$
$17$	1.26604	+	1.06234i	0.307061	+	0.257655i	−0.476215	+	0.879329i	$0.657992\pi$
$18$	−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	0.957776	−	0.287516i	$-0.0928295\pi$
$23$	−0.194593	−	1.10359i	−0.0405754	−	0.230114i	−0.998351	+	0.0574018i	$0.981718\pi$
$24$	−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	$-0.431542\pi$
$37$	2.59627			0.426824			0.213412	+	0.976962i	$0.431542\pi$
$38$	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	$-0.633675\pi$
$43$	1.88666	−	10.6998i	0.287713	−	1.63170i	0.695431	−	0.718593i	$-0.255213\pi$
$44$	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	−0.535715	−	0.844399i	$-0.679958\pi$
$47$	1.39053	−	1.16679i	0.202830	−	0.170194i	0.738545	+	0.674205i	$0.235513\pi$
$48$	−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	$-0.746902\pi$
$53$	−2.08512	−	11.8253i	−0.286414	−	1.62433i	0.413779	−	0.910378i	$-0.364209\pi$
$54$	−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	−0.516567	−	0.856247i	$-0.672790\pi$
$67$	1.93969	−	1.62760i	0.236971	−	0.198842i	0.753538	+	0.657405i	$0.228346\pi$
$68$	−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	−0.0529835	−	0.998595i	$-0.516873\pi$
$73$	4.68479	−	1.70513i	0.548313	−	0.199570i	0.601297	+	0.799026i	$0.294651\pi$
$74$	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	$-0.967792\pi$
$83$	−5.32888	−	9.22989i	−0.584920	−	1.01311i	0.409965	−	0.912101i	$-0.365541\pi$
$84$	−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	0.0681291	−	0.997677i	$-0.478297\pi$
$97$	−8.88919	−	7.45891i	−0.902560	−	0.757338i	−0.970689	+	0.240339i	$0.922741\pi$
$98$	−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	−0.824239	−	0.566243i	$-0.808397\pi$
$103$	0.794263	−	1.37570i	0.0782611	−	0.135552i	0.902500	+	0.430690i	$0.141730\pi$
$104$	−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	0.717790	−	0.696259i	$-0.245154\pi$
$107$	−2.52481	−	4.37311i	−0.244083	−	0.422764i	−0.961873	+	0.273495i	$0.911820\pi$
$108$	−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	$-0.393434\pi$
$113$	6.98545			0.657136			0.328568	+	0.944480i	$0.393434\pi$
$114$	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	−0.604808	−	0.796371i	$-0.706750\pi$
$127$	−17.8059	−	6.48081i	−1.58002	−	0.575079i	−0.975208	+	0.221292i	$0.928972\pi$
$128$	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	0.954181	−	0.299229i	$-0.0967294\pi$
$137$	−0.524348	−	2.97373i	−0.0447981	−	0.254063i	−0.998979	+	0.0451662i	$0.985618\pi$
$138$	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	$-0.734830\pi$
$157$	2.66297	−	15.1025i	0.212528	−	1.20531i	0.885145	−	0.465316i	$-0.154059\pi$
$158$	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	−0.981157	−	0.193212i	$-0.938110\pi$
$163$	−4.12701	+	7.14819i	−0.323252	+	0.559890i	0.657905	+	0.753101i	$0.271443\pi$
$164$	−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	$-0.820599\pi$
$167$	−3.02007	−	17.1277i	−0.233700	−	1.32538i	0.611635	−	0.791140i	$-0.290512\pi$
$168$	−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	0.999530	−	0.0306582i	$-0.00976034\pi$
$173$	15.0326	+	12.6138i	1.14290	+	0.959010i	0.143374	+	0.989669i	$0.454205\pi$
$174$	−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	−0.158094	−	0.987424i	$-0.550535\pi$
$193$	4.93882	−	1.79758i	0.355504	−	0.129393i	0.513597	+	0.858031i	$0.328313\pi$
$194$	−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	$0.174255\pi$
$197$	12.3191	+	21.3373i	0.877698	+	1.52022i	0.0238373	+	0.999716i	$0.492412\pi$
$198$	−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	$0.295505\pi$
$223$	−3.54963	+	20.1310i	−0.237701	+	1.34807i	−0.836851	+	0.547431i	$0.815606\pi$
$224$	−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	$-0.416788\pi$
$227$	7.78787			0.516899			0.258449	+	0.966025i	$0.416788\pi$
$228$	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	−0.955719	−	0.294282i	$-0.904919\pi$
$233$	0.656574	−	3.72362i	0.0430136	−	0.243942i	0.998732	+	0.0503401i	$0.0160305\pi$
$234$	−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	−0.282520	−	0.959261i	$-0.591170\pi$
$257$	9.82888	−	8.24741i	0.613109	−	0.514459i	0.895629	+	0.444802i	$0.146726\pi$
$258$	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	−0.196371	−	0.980530i	$-0.562916\pi$
$263$	4.59714	−	1.67322i	0.283472	−	0.103175i	0.479843	+	0.877354i	$0.340694\pi$
$264$	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	−0.985658	−	0.168757i	$-0.946025\pi$
$277$	−5.76991	+	9.99379i	−0.346681	+	0.600468i	0.638977	+	0.769226i	$0.279358\pi$
$278$	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	0.528347	−	0.849028i	$-0.322812\pi$
$283$	−3.63429	−	3.04953i	−0.216036	−	0.181276i	−0.744383	+	0.667753i	$0.767256\pi$
$284$	−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	−0.621369	−	0.783518i	$-0.713423\pi$
$293$	6.29679	−	10.9064i	0.367862	−	0.637156i	0.989231	+	0.146362i	$0.0467564\pi$
$294$	−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	−0.983213	−	0.182461i	$-0.941594\pi$
$307$	−28.3692	+	10.3255i	−1.61911	+	0.589309i	−0.635901	+	0.771770i	$0.719371\pi$
$308$	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	−0.802553	−	0.596581i	$-0.796525\pi$
$313$	−6.26991	+	5.26108i	−0.354397	+	0.297374i	0.448156	+	0.893955i	$0.352081\pi$
$314$	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	0.212287	−	0.977207i	$-0.431909\pi$
$317$	−4.50862	−	1.64100i	−0.253229	−	0.0921679i	−0.465516	+	0.885040i	$0.654131\pi$
$318$	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	$0.123446\pi$
$337$	−1.34952	+	7.65350i	−0.0735129	+	0.416913i	−0.999249	+	0.0387428i	$0.987665\pi$
$338$	−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	−0.965518	−	0.260337i	$-0.916166\pi$
$347$	0.573978	−	3.25519i	0.0308128	−	0.174748i	0.996330	+	0.0855895i	$0.0272774\pi$
$348$	−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	$-0.556097\pi$
$353$	14.3721	−	24.8932i	0.764950	−	1.32493i	0.940273	−	0.340422i	$-0.110570\pi$
$354$	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	−0.0843402	−	0.996437i	$-0.526878\pi$
$367$	−15.1236	−	5.50454i	−0.789446	−	0.287335i	−0.705106	+	0.709102i	$0.749100\pi$
$368$	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	$0.0932515\pi$
$373$	14.0753	+	24.3792i	0.728793	+	1.26231i	−0.228601	+	0.973520i	$0.573415\pi$
$374$	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	−0.733953	−	0.679200i	$-0.762327\pi$
$383$	−16.8229	+	6.12305i	−0.859613	+	0.312873i	−0.125659	+	0.992073i	$0.540105\pi$
$384$	−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	0.898417	−	0.439143i	$-0.144718\pi$
$397$	12.3923	+	10.3984i	0.621954	+	0.521881i	−0.276463	+	0.961024i	$0.589162\pi$
$398$	−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	$-0.897907\pi$
$433$	−3.43464	−	19.4788i	−0.165058	−	0.936092i	0.783946	−	0.620829i	$-0.213204\pi$
$434$	−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	−0.0676432	−	0.997710i	$-0.521548\pi$
$443$	−16.0125	−	5.82807i	−0.760776	−	0.276900i	−0.693133	+	0.720810i	$0.743770\pi$
$444$	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	$-0.382539\pi$
$457$	15.4216			0.721391			0.360696	+	0.932684i	$0.382539\pi$
$458$	−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	0.909988	−	0.414636i	$-0.136091\pi$
$463$	2.06371	+	3.57445i	0.0959088	+	0.166119i	−0.814079	+	0.580755i	$0.802758\pi$
$464$	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	$0.375554\pi$
$467$	−13.1853	+	22.8375i	−0.610141	+	1.05680i	−0.991216	+	0.132251i	$0.957779\pi$
$468$	−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	0.600786	−	0.799410i	$-0.294854\pi$
$487$	−8.64883	−	14.9802i	−0.391916	−	0.678819i	−0.992702	+	0.120591i	$0.961521\pi$
$488$	−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	−0.994858	−	0.101276i	$-0.967707\pi$
$503$	−23.9500	+	20.0964i	−1.06788	+	0.896054i	−0.0730176	+	0.997331i	$0.523263\pi$
$504$	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	−0.370558	−	0.928809i	$-0.620834\pi$
$523$	10.9725	−	9.20702i	0.479794	−	0.402595i	0.850352	+	0.526215i	$0.176389\pi$
$524$	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	$0.157614\pi$
$547$	5.04205	+	28.5949i	0.215583	+	1.22263i	−0.664310	+	0.747457i	$0.731275\pi$
$548$	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	0.835260	−	0.549856i	$-0.185317\pi$
$557$	26.4722	+	9.63511i	1.12167	+	0.408253i	0.286406	+	0.958108i	$0.407540\pi$
$558$	−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	0.953939	−	0.300001i	$-0.0969871\pi$
$563$	5.15270	+	8.92474i	0.217161	+	0.376133i	−0.736778	+	0.676135i	$0.763654\pi$
$564$	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	$0.0704036\pi$
$577$	16.2815	+	28.2004i	0.677809	+	1.17400i	−0.297831	+	0.954619i	$0.596263\pi$
$578$	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	0.126465	−	0.991971i	$-0.459637\pi$
$587$	−20.0724	−	16.8427i	−0.828476	−	0.695174i	−0.954941	+	0.296797i	$0.904081\pi$
$588$	−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	$-0.624619\pi$
$593$	−8.25893	−	46.8387i	−0.339154	−	1.92344i	0.0424244	−	0.999100i	$-0.486492\pi$
$594$	−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	$-0.268568\pi$
$607$	32.7520			1.32936			0.664681	+	0.747128i	$0.268568\pi$
$608$	−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	$0.290570\pi$
$613$	−5.78729	+	32.8214i	−0.233747	+	1.32564i	−0.845237	+	0.534391i	$0.820541\pi$
$614$	−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	$-0.443912\pi$
$617$	29.1937	−	24.4964i	1.17529	−	0.986189i	0.999999	−	0.00167362i	$-0.000532729\pi$
$618$	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	0.193238	−	0.981152i	$-0.438101\pi$
$643$	24.6459	−	8.97037i	0.971939	−	0.353757i	0.778701	+	0.627395i	$0.215879\pi$
$644$	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	$-0.460402\pi$
$647$	6.31221			0.248159			0.124079	+	0.992272i	$0.460402\pi$
$648$	−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	0.658980	−	0.752161i	$-0.270988\pi$
$653$	−8.22580	−	14.2475i	−0.321901	−	0.557548i	−0.980880	+	0.194613i	$0.937655\pi$
$654$	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	$-0.620700\pi$
$673$	16.0692	−	27.8327i	0.619423	−	1.07287i	0.989591	−	0.143908i	$-0.0459669\pi$
$674$	−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	0.985585	−	0.169184i	$-0.0541132\pi$
$677$	9.00980	+	15.6054i	0.346275	+	0.599765i	−0.639310	+	0.768949i	$0.720780\pi$
$678$	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	$-0.677214\pi$
$683$	−27.6195			−1.05683			−0.528415	+	0.848986i	$0.677214\pi$
$684$	−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	−0.951053	−	0.309029i	$-0.899996\pi$
$727$	1.30335	−	7.39165i	0.0483385	−	0.274141i	0.999391	+	0.0348873i	$0.0111072\pi$
$728$	−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	−0.683370	−	0.730072i	$-0.739486\pi$
$733$	7.86706	−	13.6261i	0.290576	−	0.503293i	0.973946	+	0.226779i	$0.0728196\pi$
$734$	−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	0.938395	−	0.345564i	$-0.112312\pi$
$743$	20.7442	+	17.4065i	0.761032	+	0.638581i	−0.177363	+	0.984145i	$0.556757\pi$
$744$	−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	−0.668515	−	0.743699i	$-0.733070\pi$
$757$	−19.3307	+	7.03580i	−0.702586	+	0.255720i	−0.0340713	+	0.999419i	$0.510847\pi$
$758$	−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	0.604549	−	0.796568i	$-0.293353\pi$
$773$	15.4483	+	5.62273i	0.555637	+	0.202235i	−0.0489122	+	0.998803i	$0.515575\pi$
$774$	−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	$-0.483548\pi$
$787$	24.9873	−	43.2792i	0.890700	−	1.54274i	0.839038	−	0.544073i	$-0.183118\pi$
$788$	−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	$-0.567775\pi$
$797$	−11.9314			−0.422631			−0.211316	+	0.977418i	$0.567775\pi$
$798$	−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	0.163716	−	0.986508i	$-0.447652\pi$
$823$	−9.89693	−	3.60219i	−0.344985	−	0.125564i	−0.508701	+	0.860943i	$0.669874\pi$
$824$	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	$0.595846\pi$
$827$	−37.0565	+	31.0941i	−1.28858	+	1.08125i	−0.992000	+	0.126240i	$0.959709\pi$
$828$	−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	0.876001	−	0.482309i	$-0.160202\pi$
$853$	16.1550	+	13.5556i	0.553136	+	0.464136i	−0.322865	+	0.946445i	$0.604646\pi$
$854$	−17.9932			−0.615714
$855$		0			0
$856$	5.04963			0.172593
$857$	−23.6909	−	19.8791i	−0.809267	−	0.679056i	0.141166	−	0.989986i	$-0.454915\pi$
$857$	−23.6909	−	19.8791i	−0.809267	−	0.679056i	−0.950433	+	0.310930i	$0.899359\pi$
$858$	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	$0.415082\pi$
$863$	−20.6689	+	35.7996i	−0.703578	+	1.21863i	−0.967202	+	0.254007i	$0.918251\pi$
$864$	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	−0.378998	−	0.925398i	$-0.623731\pi$
$877$	−2.20604	+	0.802934i	−0.0744927	+	0.0271131i	0.304505	+	0.952511i	$0.401509\pi$
$878$	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	−0.652671	−	0.757642i	$-0.726352\pi$
$883$	−0.590585	+	0.495560i	−0.0198748	+	0.0166769i	0.632796	+	0.774318i	$0.281907\pi$
$884$	−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	0.411911	−	0.911224i	$-0.364862\pi$
$887$	4.22106	+	1.53634i	0.141729	+	0.0515852i	−0.270182	+	0.962809i	$0.587084\pi$
$888$	−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	$-0.848455\pi$
$907$	3.10653	−	17.6180i	0.103151	−	0.584997i	0.991943	−	0.126686i	$-0.0404342\pi$
$908$	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	−0.572813	−	0.819686i	$-0.694148\pi$
$937$	−47.0941	−	17.1409i	−1.53850	−	0.559967i	−0.965684	+	0.259719i	$0.916370\pi$
$938$	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	−0.693795	−	0.720173i	$-0.744063\pi$
$947$	−23.4602	+	8.53882i	−0.762355	+	0.277475i	−0.0685599	+	0.997647i	$0.521840\pi$
$948$	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	0.0784473	−	0.996918i	$-0.475004\pi$
$953$	24.0590	−	8.75677i	0.779348	−	0.283660i	0.700901	+	0.713259i	$0.252782\pi$
$954$	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	$0.0311679\pi$
$967$	39.3155	+	32.9896i	1.26430	+	1.06088i	0.269092	+	0.963115i	$0.413277\pi$
$968$	−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	−0.734162	−	0.678974i	$-0.762425\pi$
$977$	6.90554	−	11.9608i	0.220928	−	0.382658i	0.955090	+	0.296316i	$0.0957581\pi$
$978$	−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	−0.996820	−	0.0796878i	$-0.974608\pi$
$983$	−1.03028	+	5.84300i	−0.0328608	+	0.186363i	0.963959	+	0.266050i	$0.0857188\pi$
$984$	−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	−0.949984	−	0.312299i	$-0.898901\pi$
$997$	−25.4937	+	21.3917i	−0.807392	+	0.677483i	0.142592	+	0.989782i	$0.454456\pi$
$998$	−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.e.301.1	yes	6
5.2	odd	4		950.2.u.d.149.1		12
5.3	odd	4		950.2.u.d.149.2		12
5.4	even	2		950.2.l.b.301.1	yes	6
19.6	even	9	inner	950.2.l.e.101.1	yes	6
95.44	even	18		950.2.l.b.101.1	✓	6
95.63	odd	36		950.2.u.d.899.1		12
95.82	odd	36		950.2.u.d.899.2		12

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

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Database

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