LMFDB - Embedded newform 950.2.u.d.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not 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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.2
Root			$-0.984808 + 0.173648i$ of defining polynomial
Character	$\chi$	$=$	950.149
Dual form			950.2.u.d.899.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 - 0.766044i) q^{2} +(0.460802 + 1.26604i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.26604 + 0.460802i) q^{6} +(2.49362 - 1.43969i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.907604 - 0.761570i) q^{9} +O(q^{10})$	\(q+(0.642788 - 0.766044i) q^{2} +(0.460802 + 1.26604i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.26604 + 0.460802i) q^{6} +(2.49362 - 1.43969i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.907604 - 0.761570i) q^{9} +(0.500000 - 0.866025i) q^{11} +(1.16679 - 0.673648i) q^{12} +(-0.181985 + 0.500000i) q^{13} +(0.500000 - 2.83564i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(1.06234 - 1.26604i) q^{17} -1.18479i q^{18} +(-3.79086 - 2.15160i) q^{19} +(2.97178 + 2.49362i) q^{21} +(-0.342020 - 0.939693i) q^{22} +(1.10359 - 0.194593i) q^{23} +(0.233956 - 1.32683i) q^{24} +(0.266044 + 0.460802i) q^{26} +(4.88279 + 2.81908i) q^{27} +(-1.85083 - 2.20574i) q^{28} +(1.81521 - 1.52314i) q^{29} +(0.847296 + 1.46756i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(1.32683 + 0.233956i) q^{33} +(-0.286989 - 1.62760i) q^{34} +(-0.907604 - 0.761570i) q^{36} -2.59627i q^{37} +(-4.08494 + 1.52094i) q^{38} -0.716881 q^{39} +(-4.85844 + 1.76833i) q^{41} +(3.82045 - 0.673648i) q^{42} +(10.6998 + 1.88666i) q^{43} +(-0.939693 - 0.342020i) q^{44} +(0.560307 - 0.970481i) q^{46} +(-1.16679 - 1.39053i) q^{47} +(-0.866025 - 1.03209i) q^{48} +(0.645430 - 1.11792i) q^{49} +(2.09240 + 0.761570i) q^{51} +(0.524005 + 0.0923963i) q^{52} +(11.8253 - 2.08512i) q^{53} +(5.29813 - 1.92836i) q^{54} -2.87939 q^{56} +(0.977185 - 5.79086i) q^{57} -2.36959i q^{58} +(-6.72668 - 5.64436i) q^{59} +(1.08512 + 6.15403i) q^{61} +(1.66885 + 0.294263i) q^{62} +(1.16679 - 3.20574i) q^{63} +(0.500000 + 0.866025i) q^{64} +(1.03209 - 0.866025i) q^{66} +(-1.62760 - 1.93969i) q^{67} +(-1.43128 - 0.826352i) q^{68} +(0.754900 + 1.30753i) q^{69} +(-1.02229 + 5.79769i) q^{71} +(-1.16679 + 0.205737i) q^{72} +(1.70513 + 4.68479i) q^{73} +(-1.98886 - 1.66885i) q^{74} +(-1.46064 + 4.10689i) q^{76} -2.87939i q^{77} +(-0.460802 + 0.549163i) q^{78} +(-8.05690 + 2.93247i) q^{79} +(-0.701867 + 3.98048i) q^{81} +(-1.76833 + 4.85844i) q^{82} +(9.22989 - 5.32888i) q^{83} +(1.93969 - 3.35965i) q^{84} +(8.32295 - 6.98378i) q^{86} +(2.76481 + 1.59627i) q^{87} +(-0.866025 + 0.500000i) q^{88} +(0.694593 + 0.252811i) q^{89} +(0.266044 + 1.50881i) q^{91} +(-0.383273 - 1.05303i) q^{92} +(-1.46756 + 1.74897i) q^{93} -1.81521 q^{94} -1.34730 q^{96} +(-7.45891 + 8.88919i) q^{97} +(-0.441500 - 1.21301i) q^{98} +(-0.205737 - 1.16679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{6} + 18 q^{9}+O(q^{10}) $ 12 * q + 6 * q^6 + 18 * q^9	$ 12 q + 6 q^{6} + 18 q^{9} + 6 q^{11} + 6 q^{14} + 18 q^{19} + 6 q^{21} + 12 q^{24} - 6 q^{26} + 36 q^{29} + 6 q^{31} + 12 q^{34} - 18 q^{36} + 24 q^{39} - 42 q^{41} + 18 q^{46} - 24 q^{49} + 18 q^{51} + 36 q^{54} - 12 q^{56} - 54 q^{59} - 30 q^{61} + 6 q^{64} - 6 q^{66} + 12 q^{69} + 12 q^{71} - 36 q^{74} - 24 q^{79} - 36 q^{81} + 12 q^{84} + 18 q^{86} - 6 q^{91} - 36 q^{94} - 12 q^{96} + 18 q^{99}+O(q^{100}) $ 12 * q + 6 * q^6 + 18 * q^9 + 6 * q^11 + 6 * q^14 + 18 * q^19 + 6 * q^21 + 12 * q^24 - 6 * q^26 + 36 * q^29 + 6 * q^31 + 12 * q^34 - 18 * q^36 + 24 * q^39 - 42 * q^41 + 18 * q^46 - 24 * q^49 + 18 * q^51 + 36 * q^54 - 12 * q^56 - 54 * q^59 - 30 * q^61 + 6 * q^64 - 6 * q^66 + 12 * q^69 + 12 * q^71 - 36 * q^74 - 24 * q^79 - 36 * q^81 + 12 * q^84 + 18 * q^86 - 6 * q^91 - 36 * q^94 - 12 * q^96 + 18 * 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 $

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	0.460802	+	1.26604i	0.266044	+	0.730951i	0.998730	+	0.0503837i	$0.0160444\pi$
$3$	0.460802	+	1.26604i	0.266044	+	0.730951i	−0.732685	+	0.680567i	$0.761733\pi$
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	1.26604	+	0.460802i	0.516860	+	0.188122i
$7$	2.49362	−	1.43969i	0.942500	−	0.544153i	0.0517569	−	0.998660i	$-0.483518\pi$
$7$	2.49362	−	1.43969i	0.942500	−	0.544153i	0.890743	+	0.454507i	$0.150185\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	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	$0.118496\pi$
$12$	1.16679	−	0.673648i	0.336824	−	0.194465i
$13$	−0.181985	+	0.500000i	−0.0504736	+	0.138675i	−0.962368	−	0.271750i	$-0.912398\pi$
$13$	−0.181985	+	0.500000i	−0.0504736	+	0.138675i	0.911894	+	0.410425i	$0.134620\pi$
$14$	0.500000	−	2.83564i	0.133631	−	0.757857i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	1.06234	−	1.26604i	0.257655	−	0.307061i	−0.621674	−	0.783276i	$-0.713547\pi$
$17$	1.06234	−	1.26604i	0.257655	−	0.307061i	0.879329	+	0.476215i	$0.157992\pi$
$18$		−	1.18479i		−	0.279258i
$19$	−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
$22$	−0.342020	−	0.939693i	−0.0729189	−	0.200343i
$23$	1.10359	−	0.194593i	0.230114	−	0.0405754i	−0.0574018	−	0.998351i	$-0.518282\pi$
$23$	1.10359	−	0.194593i	0.230114	−	0.0405754i	0.287516	+	0.957776i	$0.407170\pi$
$24$	0.233956	−	1.32683i	0.0477560	−	0.270838i
$25$		0			0
$26$	0.266044	+	0.460802i	0.0521756	+	0.0903708i
$27$	4.88279	+	2.81908i	0.939693	+	0.542532i
$28$	−1.85083	−	2.20574i	−0.349775	−	0.416845i
$29$	1.81521	−	1.52314i	0.337076	−	0.282840i	−0.458500	−	0.888694i	$-0.651613\pi$
$29$	1.81521	−	1.52314i	0.337076	−	0.282840i	0.795575	+	0.605854i	$0.207169\pi$
$30$		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	$0.784704\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	1.32683	+	0.233956i	0.230971	+	0.0407264i
$34$	−0.286989	−	1.62760i	−0.0492182	−	0.279130i
$35$		0			0
$36$	−0.907604	−	0.761570i	−0.151267	−	0.126928i
$37$		−	2.59627i		−	0.426824i	−0.976962	−	0.213412i	$-0.931542\pi$
$37$		−	2.59627i		−	0.426824i	0.976962	−	0.213412i	$-0.0684576\pi$
$38$	−4.08494	+	1.52094i	−0.662665	+	0.246730i
$39$	−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	$0.521175\pi$
$42$	3.82045	−	0.673648i	0.589508	−	0.103946i
$43$	10.6998	+	1.88666i	1.63170	+	0.287713i	0.913108	−	0.407718i	$-0.133675\pi$
$43$	10.6998	+	1.88666i	1.63170	+	0.287713i	0.718593	+	0.695431i	$0.244787\pi$
$44$	−0.939693	−	0.342020i	−0.141664	−	0.0515615i
$45$		0			0
$46$	0.560307	−	0.970481i	0.0826128	−	0.143090i
$47$	−1.16679	−	1.39053i	−0.170194	−	0.202830i	0.674205	−	0.738545i	$-0.264487\pi$
$47$	−1.16679	−	1.39053i	−0.170194	−	0.202830i	−0.844399	+	0.535715i	$0.820042\pi$
$48$	−0.866025	−	1.03209i	−0.125000	−	0.148969i
$49$	0.645430	−	1.11792i	0.0922042	−	0.159702i
$50$		0			0
$51$	2.09240	+	0.761570i	0.292994	+	0.106641i
$52$	0.524005	+	0.0923963i	0.0726665	+	0.0128131i
$53$	11.8253	−	2.08512i	1.62433	−	0.286414i	0.713955	−	0.700192i	$-0.246902\pi$
$53$	11.8253	−	2.08512i	1.62433	−	0.286414i	0.910378	+	0.413779i	$0.135791\pi$
$54$	5.29813	−	1.92836i	0.720985	−	0.262417i
$55$		0			0
$56$	−2.87939			−0.384774
$57$	0.977185	−	5.79086i	0.129431	−	0.767018i
$58$		−	2.36959i		−	0.311142i
$59$	−6.72668	−	5.64436i	−0.875739	−	0.734833i	0.0895592	−	0.995982i	$-0.471454\pi$
$59$	−6.72668	−	5.64436i	−0.875739	−	0.734833i	−0.965299	+	0.261149i	$0.915899\pi$
$60$		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	$0.813437\pi$
$62$	1.66885	+	0.294263i	0.211944	+	0.0373714i
$63$	1.16679	−	3.20574i	0.147002	−	0.403885i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	1.03209	−	0.866025i	0.127041	−	0.106600i
$67$	−1.62760	−	1.93969i	−0.198842	−	0.236971i	0.657405	−	0.753538i	$-0.271654\pi$
$67$	−1.62760	−	1.93969i	−0.198842	−	0.236971i	−0.856247	+	0.516567i	$0.827210\pi$
$68$	−1.43128	−	0.826352i	−0.173569	−	0.100210i
$69$	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	$0.941963\pi$
$72$	−1.16679	+	0.205737i	−0.137508	+	0.0242463i
$73$	1.70513	+	4.68479i	0.199570	+	0.548313i	0.998595	−	0.0529835i	$-0.0168731\pi$
$73$	1.70513	+	4.68479i	0.199570	+	0.548313i	−0.799026	+	0.601297i	$0.794651\pi$
$74$	−1.98886	−	1.66885i	−0.231200	−	0.194000i
$75$		0			0
$76$	−1.46064	+	4.10689i	−0.167547	+	0.471093i
$77$		−	2.87939i		−	0.328136i
$78$	−0.460802	+	0.549163i	−0.0521756	+	0.0621805i
$79$	−8.05690	+	2.93247i	−0.906472	+	0.329929i	−0.752843	−	0.658200i	$-0.771318\pi$
$79$	−8.05690	+	2.93247i	−0.906472	+	0.329929i	−0.153629	+	0.988129i	$0.549096\pi$
$80$		0			0
$81$	−0.701867	+	3.98048i	−0.0779852	+	0.442276i
$82$	−1.76833	+	4.85844i	−0.195279	+	0.536525i
$83$	9.22989	−	5.32888i	1.01311	−	0.584920i	0.101011	−	0.994885i	$-0.467792\pi$
$83$	9.22989	−	5.32888i	1.01311	−	0.584920i	0.912101	+	0.409965i	$0.134459\pi$
$84$	1.93969	−	3.35965i	0.211638	−	0.366567i
$85$		0			0
$86$	8.32295	−	6.98378i	0.897487	−	0.753081i
$87$	2.76481	+	1.59627i	0.296419	+	0.171138i
$88$	−0.866025	+	0.500000i	−0.0923186	+	0.0533002i
$89$	0.694593	+	0.252811i	0.0736267	+	0.0267979i	0.378571	−	0.925572i	$-0.376416\pi$
$89$	0.694593	+	0.252811i	0.0736267	+	0.0267979i	−0.304944	+	0.952370i	$0.598638\pi$
$90$		0			0
$91$	0.266044	+	1.50881i	0.0278890	+	0.158167i
$92$	−0.383273	−	1.05303i	−0.0399590	−	0.109786i
$93$	−1.46756	+	1.74897i	−0.152179	+	0.181360i
$94$	−1.81521			−0.187224
$95$		0			0
$96$	−1.34730			−0.137508
$97$	−7.45891	+	8.88919i	−0.757338	+	0.902560i	−0.997677	−	0.0681291i	$-0.978297\pi$
$97$	−7.45891	+	8.88919i	−0.757338	+	0.902560i	0.240339	+	0.970689i	$0.422741\pi$
$98$	−0.441500	−	1.21301i	−0.0445982	−	0.122533i
$99$	−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	$0.862714\pi$
$102$	1.92836	−	1.11334i	0.190936	−	0.110237i
$103$	1.37570	+	0.794263i	0.135552	+	0.0782611i	0.566243	−	0.824239i	$-0.308397\pi$
$103$	1.37570	+	0.794263i	0.135552	+	0.0782611i	−0.430690	+	0.902500i	$0.641730\pi$
$104$	0.407604	−	0.342020i	0.0399688	−	0.0335378i
$105$		0			0
$106$	6.00387	−	10.3990i	0.583147	−	1.01004i
$107$	−4.37311	+	2.52481i	−0.422764	+	0.244083i	−0.696259	−	0.717790i	$-0.745154\pi$
$107$	−4.37311	+	2.52481i	−0.422764	+	0.244083i	0.273495	+	0.961873i	$0.411820\pi$
$108$	1.92836	−	5.29813i	0.185557	−	0.509813i
$109$	−0.688196	+	3.90295i	−0.0659172	+	0.373835i	0.933948	+	0.357409i	$0.116340\pi$
$109$	−0.688196	+	3.90295i	−0.0659172	+	0.373835i	−0.999865	+	0.0164259i	$0.994771\pi$
$110$		0			0
$111$	3.28699	−	1.19637i	0.311987	−	0.113554i
$112$	−1.85083	+	2.20574i	−0.174887	+	0.208423i
$113$			6.98545i			0.657136i	0.944480	+	0.328568i	$0.106566\pi$
$113$			6.98545i			0.657136i	−0.944480	+	0.328568i	$0.893434\pi$
$114$	−3.80793	−	4.47086i	−0.356646	−	0.418734i
$115$		0			0
$116$	−1.81521	−	1.52314i	−0.168538	−	0.141420i
$117$	0.215615	+	0.592396i	0.0199336	+	0.0547671i
$118$	−8.64766	+	1.52481i	−0.796081	+	0.140371i
$119$	0.826352	−	4.68647i	0.0757515	−	0.429608i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	5.41177	+	3.12449i	0.489958	+	0.282878i
$123$	−4.47756	−	5.33615i	−0.403728	−	0.481145i
$124$	1.29813	−	1.08926i	0.116576	−	0.0978187i
$125$		0			0
$126$	−1.70574	−	2.95442i	−0.151959	−	0.263201i
$127$	−6.48081	+	17.8059i	−0.575079	+	1.58002i	0.221292	+	0.975208i	$0.428972\pi$
$127$	−6.48081	+	17.8059i	−0.575079	+	1.58002i	−0.796371	+	0.604808i	$0.793250\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	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	$0.982990\pi$
$132$		−	1.34730i		−	0.117267i
$133$	−12.5506	+	0.0923963i	−1.08828	+	0.00801177i
$134$	−2.53209			−0.218739
$135$		0			0
$136$	−1.55303	+	0.565258i	−0.133172	+	0.0484705i
$137$	−2.97373	+	0.524348i	−0.254063	+	0.0447981i	−0.299229	−	0.954181i	$-0.596729\pi$
$137$	−2.97373	+	0.524348i	−0.254063	+	0.0447981i	0.0451662	+	0.998979i	$0.485618\pi$
$138$	1.48686	+	0.262174i	0.126570	+	0.0223177i
$139$	−11.6309	−	4.23329i	−0.986519	−	0.359063i	−0.202147	−	0.979355i	$-0.564792\pi$
$139$	−11.6309	−	4.23329i	−0.986519	−	0.359063i	−0.784371	+	0.620292i	$0.787014\pi$
$140$		0			0
$141$	1.22281	−	2.11797i	0.102979	−	0.178365i
$142$	3.78417	+	4.50980i	0.317561	+	0.378454i
$143$	0.342020	+	0.407604i	0.0286012	+	0.0340855i
$144$	−0.592396	+	1.02606i	−0.0493664	+	0.0855050i
$145$		0			0
$146$	4.68479	+	1.70513i	0.387716	+	0.141117i
$147$	1.71275	+	0.302004i	0.141265	+	0.0249088i
$148$	−2.55682	+	0.450837i	−0.210170	+	0.0370586i
$149$	8.76517	−	3.19026i	0.718070	−	0.261356i	0.0429640	−	0.999077i	$-0.486320\pi$
$149$	8.76517	−	3.19026i	0.718070	−	0.261356i	0.675106	+	0.737720i	$0.264098\pi$
$150$		0			0
$151$	−4.76651			−0.387893			−0.193947	−	0.981012i	$-0.562129\pi$
$151$	−4.76651			−0.387893			−0.193947	+	0.981012i	$0.562129\pi$
$152$	2.20718	+	3.75877i	0.179026	+	0.304877i
$153$		−	1.95811i		−	0.158304i
$154$	−2.20574	−	1.85083i	−0.177743	−	0.149144i
$155$		0			0
$156$	0.124485	+	0.705990i	0.00996679	+	0.0565245i
$157$	−15.1025	−	2.66297i	−1.20531	−	0.212528i	−0.465316	−	0.885145i	$-0.654059\pi$
$157$	−15.1025	−	2.66297i	−1.20531	−	0.212528i	−0.739991	+	0.672616i	$0.765170\pi$
$158$	−2.93247	+	8.05690i	−0.233295	+	0.640973i
$159$	8.08899	+	14.0105i	0.641499	+	1.11111i
$160$		0			0
$161$	2.47178	−	2.07407i	0.194804	−	0.163460i
$162$	2.59808	+	3.09627i	0.204124	+	0.243266i
$163$	−7.14819	−	4.12701i	−0.559890	−	0.323252i	0.193212	−	0.981157i	$-0.438110\pi$
$163$	−7.14819	−	4.12701i	−0.559890	−	0.323252i	−0.753101	+	0.657905i	$0.771443\pi$
$164$	2.58512	+	4.47756i	0.201864	+	0.349639i
$165$		0			0
$166$	1.85070	−	10.4958i	0.143642	−	0.814635i
$167$	−17.1277	+	3.02007i	−1.32538	+	0.233700i	−0.791140	−	0.611635i	$-0.790512\pi$
$167$	−17.1277	+	3.02007i	−1.32538	+	0.233700i	−0.534237	+	0.845335i	$0.679401\pi$
$168$	−1.32683	−	3.64543i	−0.102367	−	0.281251i
$169$	9.74170	+	8.17425i	0.749361	+	0.628789i
$170$		0			0
$171$	−5.07919	+	0.934204i	−0.388416	+	0.0714404i
$172$		−	10.8648i		−	0.828436i
$173$	−12.6138	+	15.0326i	−0.959010	+	1.14290i	0.0306582	+	0.999530i	$0.490240\pi$
$173$	−12.6138	+	15.0326i	−0.959010	+	1.14290i	−0.989669	+	0.143374i	$0.954205\pi$
$174$	3.00000	−	1.09191i	0.227429	−	0.0827775i
$175$		0			0
$176$	−0.173648	+	0.984808i	−0.0130892	+	0.0742327i
$177$	4.04633	−	11.1172i	0.304141	−	0.835621i
$178$	0.640140	−	0.369585i	0.0479805	−	0.0277016i
$179$	−9.66297	+	16.7368i	−0.722244	+	1.25096i	0.237854	+	0.971301i	$0.423556\pi$
$179$	−9.66297	+	16.7368i	−0.722244	+	1.25096i	−0.960098	+	0.279663i	$0.909777\pi$
$180$		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	$-0.161821\pi$
$182$	1.32683	+	0.766044i	0.0983510	+	0.0567830i
$183$	−7.29125	+	4.20961i	−0.538985	+	0.311183i
$184$	−1.05303	−	0.383273i	−0.0776307	−	0.0282552i
$185$		0			0
$186$	0.396459	+	2.24843i	0.0290698	+	0.164863i
$187$	−0.565258	−	1.55303i	−0.0413358	−	0.113569i
$188$	−1.16679	+	1.39053i	−0.0850971	+	0.101415i
$189$	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	$0.879875\pi$
$192$	−0.866025	+	1.03209i	−0.0625000	+	0.0744846i
$193$	1.79758	+	4.93882i	0.129393	+	0.355504i	0.987424	−	0.158094i	$-0.0505348\pi$
$193$	1.79758	+	4.93882i	0.129393	+	0.355504i	−0.858031	+	0.513597i	$0.828313\pi$
$194$	2.01501	+	11.4277i	0.144670	+	0.820462i
$195$		0			0
$196$	−1.21301	−	0.441500i	−0.0866436	−	0.0315357i
$197$	21.3373	−	12.3191i	1.52022	−	0.877698i	0.520502	−	0.853861i	$-0.325745\pi$
$197$	21.3373	−	12.3191i	1.52022	−	0.877698i	0.999716	−	0.0238373i	$-0.00758836\pi$
$198$	−1.02606	−	0.592396i	−0.0729189	−	0.0420998i
$199$	7.50181	−	6.29477i	0.531789	−	0.446224i	−0.336929	−	0.941530i	$-0.609388\pi$
$199$	7.50181	−	6.29477i	0.531789	−	0.446224i	0.868719	+	0.495306i	$0.164944\pi$
$200$		0			0
$201$	1.70574	−	2.95442i	0.120313	−	0.208389i
$202$	−12.3704	+	7.14203i	−0.870375	+	0.502511i
$203$	2.33359	−	6.41147i	0.163786	−	0.449997i
$204$	0.386659	−	2.19285i	0.0270716	−	0.153530i
$205$		0			0
$206$	1.49273	−	0.543308i	0.104003	−	0.0378541i
$207$	0.853427	−	1.01707i	0.0593172	−	0.0706915i
$208$		−	0.532089i		−	0.0368937i
$209$	−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	$0.456287\pi$
$212$	−4.10689	−	11.2836i	−0.282062	−	0.774960i
$213$	−7.81120	+	1.37733i	−0.535215	+	0.0943728i
$214$	−0.876859	+	4.97291i	−0.0599408	+	0.339941i
$215$		0			0
$216$	−2.81908	−	4.88279i	−0.191814	−	0.332232i
$217$	4.22567	+	2.43969i	0.286857	+	0.165617i
$218$	2.54747	+	3.03596i	0.172537	+	0.205621i
$219$	−5.14543	+	4.31753i	−0.347696	+	0.291752i
$220$		0			0
$221$	0.439693	+	0.761570i	0.0295769	+	0.0512287i
$222$	1.19637	−	3.28699i	0.0802948	−	0.220608i
$223$	−20.1310	−	3.54963i	−1.34807	−	0.237701i	−0.547431	−	0.836851i	$-0.684394\pi$
$223$	−20.1310	−	3.54963i	−1.34807	−	0.237701i	−0.800637	+	0.599150i	$0.795505\pi$
$224$	0.500000	+	2.83564i	0.0334077	+	0.189464i
$225$		0			0
$226$	5.35117	+	4.49016i	0.355954	+	0.298681i
$227$		−	7.78787i		−	0.516899i	−0.966025	−	0.258449i	$-0.916788\pi$
$227$		−	7.78787i		−	0.516899i	0.966025	−	0.258449i	$-0.0832115\pi$
$228$	−5.87257	+	0.0432332i	−0.388920	+	0.00286319i
$229$	8.02734			0.530462			0.265231	−	0.964185i	$-0.414552\pi$
$229$	8.02734			0.530462			0.265231	+	0.964185i	$0.414552\pi$
$230$		0			0
$231$	3.64543	−	1.32683i	0.239852	−	0.0872989i
$232$	−2.33359	+	0.411474i	−0.153207	+	0.0270146i
$233$	3.72362	+	0.656574i	0.243942	+	0.0430136i	0.294282	−	0.955719i	$-0.404919\pi$
$233$	3.72362	+	0.656574i	0.243942	+	0.0430136i	−0.0503401	+	0.998732i	$0.516031\pi$
$234$	0.592396	+	0.215615i	0.0387262	+	0.0140952i
$235$		0			0
$236$	−4.39053	+	7.60462i	−0.285799	+	0.495019i
$237$	−7.42528	−	8.84911i	−0.482324	−	0.574811i
$238$	−3.05888	−	3.64543i	−0.198278	−	0.236298i
$239$	3.39053	−	5.87257i	0.219315	−	0.379865i	−0.735284	−	0.677760i	$-0.762951\pi$
$239$	3.39053	−	5.87257i	0.219315	−	0.379865i	0.954599	+	0.297895i	$0.0962844\pi$
$240$		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	$0.548762\pi$
$242$	9.84808	+	1.73648i	0.633058	+	0.111625i
$243$	11.2946	−	1.99154i	0.724549	−	0.127758i
$244$	5.87211	−	2.13727i	0.375923	−	0.136825i
$245$		0			0
$246$	−6.96585			−0.444126
$247$	1.76568	−	1.50387i	0.112348	−	0.0956890i
$248$		−	1.69459i		−	0.107607i
$249$	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	$-0.113275\pi$
$252$	−3.35965	−	0.592396i	−0.211638	−	0.0373175i
$253$	0.383273	−	1.05303i	0.0240962	−	0.0662036i
$254$	9.47431	+	16.4100i	0.594471	+	1.02965i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−8.24741	−	9.82888i	−0.514459	−	0.613109i	0.444802	−	0.895629i	$-0.353274\pi$
$257$	−8.24741	−	9.82888i	−0.514459	−	0.613109i	−0.959261	+	0.282520i	$0.908830\pi$
$258$	12.6770	+	7.31908i	0.789236	+	0.455666i
$259$	−3.73783	−	6.47410i	−0.232257	−	0.402281i
$260$		0			0
$261$	0.487511	−	2.76481i	0.0301762	−	0.171138i
$262$	−16.4705	+	2.90420i	−1.01755	+	0.179422i
$263$	1.67322	+	4.59714i	0.103175	+	0.283472i	0.980530	−	0.196371i	$-0.0629158\pi$
$263$	1.67322	+	4.59714i	0.103175	+	0.283472i	−0.877354	+	0.479843i	$0.840694\pi$
$264$	−1.03209	−	0.866025i	−0.0635207	−	0.0533002i
$265$		0			0
$266$	−7.99660	+	9.67372i	−0.490303	+	0.593134i
$267$			0.995881i			0.0609469i
$268$	−1.62760	+	1.93969i	−0.0994212	+	0.118486i
$269$	−14.9290	+	5.43372i	−0.910238	+	0.331300i	−0.754348	−	0.656475i	$-0.772047\pi$
$269$	−14.9290	+	5.43372i	−0.910238	+	0.331300i	−0.155890	+	0.987774i	$0.549825\pi$
$270$		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	$0.789546\pi$
$272$	−0.565258	+	1.55303i	−0.0342738	+	0.0941665i
$273$	−1.78763	+	1.03209i	−0.108192	+	0.0624649i
$274$	−1.50980	+	2.61505i	−0.0912104	+	0.157981i
$275$		0			0
$276$	1.15657	−	0.970481i	0.0696176	−	0.0584161i
$277$	9.99379	+	5.76991i	0.600468	+	0.346681i	0.769226	−	0.638977i	$-0.220642\pi$
$277$	9.99379	+	5.76991i	0.600468	+	0.346681i	−0.168757	+	0.985658i	$0.553975\pi$
$278$	−10.7191	+	6.18866i	−0.642888	+	0.371171i
$279$	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	$-0.131121\pi$
$282$	−0.836452	−	2.29813i	−0.0498100	−	0.136852i
$283$	3.04953	−	3.63429i	0.181276	−	0.216036i	−0.667753	−	0.744383i	$-0.732744\pi$
$283$	3.04953	−	3.63429i	0.181276	−	0.216036i	0.849028	+	0.528347i	$0.177188\pi$
$284$	5.88713			0.349337
$285$		0			0
$286$	0.532089			0.0314631
$287$	−9.56926	+	11.4042i	−0.564856	+	0.673169i
$288$	0.405223	+	1.11334i	0.0238780	+	0.0656042i
$289$	2.47771	+	14.0518i	0.145748	+	0.826576i
$290$		0			0
$291$	−14.6912	−	5.34716i	−0.861213	−	0.313456i
$292$	4.31753	−	2.49273i	0.252664	−	0.145876i
$293$	10.9064	+	6.29679i	0.637156	+	0.367862i	0.783518	−	0.621369i	$-0.213423\pi$
$293$	10.9064	+	6.29679i	0.637156	+	0.367862i	−0.146362	+	0.989231i	$0.546756\pi$
$294$	1.33228	−	1.11792i	0.0777002	−	0.0651982i
$295$		0			0
$296$	−1.29813	+	2.24843i	−0.0754525	+	0.130688i
$297$	4.88279	−	2.81908i	0.283328	−	0.163579i
$298$	3.19026	−	8.76517i	0.184807	−	0.507752i
$299$	−0.103541	+	0.587208i	−0.00598791	+	0.0339591i
$300$		0			0
$301$	29.3974	−	10.6998i	1.69444	−	0.616725i
$302$	−3.06385	+	3.65136i	−0.176305	+	0.210112i
$303$		−	19.2449i		−	1.10559i
$304$	4.29813	+	0.725293i	0.246515	+	0.0415984i
$305$		0			0
$306$	−1.50000	−	1.25865i	−0.0857493	−	0.0719522i
$307$	10.3255	+	28.3692i	0.589309	+	1.61911i	0.771770	+	0.635901i	$0.219371\pi$
$307$	10.3255	+	28.3692i	0.589309	+	1.61911i	−0.182461	+	0.983213i	$0.558406\pi$
$308$	−2.83564	+	0.500000i	−0.161576	+	0.0284901i
$309$	−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	$0.935096\pi$
$312$	0.620838	+	0.358441i	0.0351480	+	0.0202927i
$313$	−5.26108	−	6.26991i	−0.297374	−	0.354397i	0.596581	−	0.802553i	$-0.296525\pi$
$313$	−5.26108	−	6.26991i	−0.297374	−	0.354397i	−0.893955	+	0.448156i	$0.852081\pi$
$314$	−11.7476	+	9.85743i	−0.662957	+	0.556287i
$315$		0			0
$316$	4.28699	+	7.42528i	0.241162	+	0.417705i
$317$	−1.64100	+	4.50862i	−0.0921679	+	0.253229i	−0.977207	−	0.212287i	$-0.931909\pi$
$317$	−1.64100	+	4.50862i	−0.0921679	+	0.253229i	0.885040	+	0.465516i	$0.154131\pi$
$318$	15.9322	+	2.80928i	0.893434	+	0.157536i
$319$	−0.411474	−	2.33359i	−0.0230381	−	0.130656i
$320$		0			0
$321$	−5.21167	−	4.37311i	−0.290887	−	0.244083i
$322$		−	3.22668i		−	0.179816i
$323$	−6.75119	+	2.51367i	−0.375646	+	0.139864i
$324$	4.04189			0.224549
$325$		0			0
$326$	−7.75624	+	2.82304i	−0.429579	+	0.156354i
$327$	−5.25844	+	0.927204i	−0.290792	+	0.0512745i
$328$	5.09170	+	0.897804i	0.281142	+	0.0495729i
$329$	−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	$0.0438164\pi$
$332$	−6.85067	−	8.16431i	−0.375980	−	0.448075i
$333$	−1.97724	−	2.35638i	−0.108352	−	0.129129i
$334$	−8.69594	+	15.0618i	−0.475820	+	0.824145i
$335$		0			0
$336$	−3.64543	−	1.32683i	−0.198874	−	0.0723844i
$337$	7.65350	+	1.34952i	0.416913	+	0.0735129i	0.378170	−	0.925736i	$-0.376554\pi$
$337$	7.65350	+	1.34952i	0.416913	+	0.0735129i	0.0387428	+	0.999249i	$0.487665\pi$
$338$	12.5237	−	2.20826i	0.681199	−	0.120114i
$339$	−8.84389	+	3.21891i	−0.480334	+	0.174827i
$340$		0			0
$341$	1.69459			0.0917673
$342$	−2.54920	+	4.49138i	−0.137845	+	0.242866i
$343$			16.4388i			0.887613i
$344$	−8.32295	−	6.98378i	−0.448743	−	0.376540i
$345$		0			0
$346$	3.40760	+	19.3255i	0.183194	+	1.03894i
$347$	−3.25519	−	0.573978i	−0.174748	−	0.0308128i	0.0855895	−	0.996330i	$-0.472723\pi$
$347$	−3.25519	−	0.573978i	−0.174748	−	0.0308128i	−0.260337	+	0.965518i	$0.583834\pi$
$348$	1.09191	−	3.00000i	0.0585326	−	0.160817i
$349$	−12.0851	−	20.9320i	−0.646902	−	1.12047i	−0.983859	−	0.178947i	$-0.942731\pi$
$349$	−12.0851	−	20.9320i	−0.646902	−	1.12047i	0.336957	−	0.941520i	$-0.390602\pi$
$350$		0			0
$351$	−2.29813	+	1.92836i	−0.122665	+	0.102928i
$352$	0.642788	+	0.766044i	0.0342607	+	0.0408303i
$353$	24.8932	+	14.3721i	1.32493	+	0.764950i	0.984511	−	0.175323i	$-0.0560968\pi$
$353$	24.8932	+	14.3721i	1.32493	+	0.764950i	0.340422	+	0.940273i	$0.389430\pi$
$354$	−5.91534	−	10.2457i	−0.314397	−	0.544552i
$355$		0			0
$356$	0.128356	−	0.727940i	0.00680283	−	0.0385808i
$357$	6.31407	−	1.11334i	0.334176	−	0.0589242i
$358$	6.60986	+	18.1604i	0.349342	+	0.959809i
$359$	9.98751	+	8.38052i	0.527121	+	0.442307i	0.867106	−	0.498124i	$-0.165978\pi$
$359$	9.98751	+	8.38052i	0.527121	+	0.442307i	−0.339985	+	0.940431i	$0.610422\pi$
$360$		0			0
$361$	9.74123	+	16.3128i	0.512696	+	0.858570i
$362$		−	26.4243i		−	1.38883i
$363$	−8.66025	+	10.3209i	−0.454545	+	0.541706i
$364$	1.43969	−	0.524005i	0.0754604	−	0.0274653i
$365$		0			0
$366$	−1.46198	+	8.29131i	−0.0764190	+	0.433394i
$367$	−5.50454	+	15.1236i	−0.287335	+	0.789446i	0.709102	+	0.705106i	$0.249100\pi$
$367$	−5.50454	+	15.1236i	−0.287335	+	0.789446i	−0.996437	+	0.0843402i	$0.973122\pi$
$368$	−0.970481	+	0.560307i	−0.0505898	+	0.0292080i
$369$	−3.06283	+	5.30498i	−0.159445	+	0.276166i
$370$		0			0
$371$	26.4859	−	22.2243i	1.37508	−	1.15383i
$372$	1.97724	+	1.14156i	0.102515	+	0.0591871i
$373$	−24.3792	+	14.0753i	−1.26231	+	0.728793i	−0.973520	−	0.228601i	$-0.926585\pi$
$373$	−24.3792	+	14.0753i	−1.26231	+	0.728793i	−0.288786	+	0.957394i	$0.593251\pi$
$374$	−1.55303	−	0.565258i	−0.0803054	−	0.0292288i
$375$		0			0
$376$	0.315207	+	1.78763i	0.0162556	+	0.0921900i
$377$	0.431229	+	1.18479i	0.0222094	+	0.0610199i
$378$	10.4353	−	12.4363i	0.536733	−	0.639654i
$379$	11.7510			0.603610			0.301805	−	0.953370i	$-0.402411\pi$
$379$	11.7510			0.603610			0.301805	+	0.953370i	$0.402411\pi$
$380$		0			0
$381$	−25.5294			−1.30791
$382$	−16.5168	+	19.6839i	−0.845071	+	1.00712i
$383$	−6.12305	−	16.8229i	−0.312873	−	0.859613i	−0.992073	−	0.125659i	$-0.959895\pi$
$383$	−6.12305	−	16.8229i	−0.312873	−	0.859613i	0.679200	−	0.733953i	$-0.262327\pi$
$384$	0.233956	+	1.32683i	0.0119390	+	0.0677094i
$385$		0			0
$386$	4.93882	+	1.79758i	0.251379	+	0.0914945i
$387$	11.1480	−	6.43629i	0.566684	−	0.327175i
$388$	10.0494	+	5.80200i	0.510179	+	0.294552i
$389$	20.1832	−	16.9357i	1.02333	−	0.858675i	0.0332867	−	0.999446i	$-0.489403\pi$
$389$	20.1832	−	16.9357i	1.02333	−	0.858675i	0.990042	+	0.140771i	$0.0449581\pi$
$390$		0			0
$391$	0.926022	−	1.60392i	0.0468309	−	0.0811136i
$392$	−1.11792	+	0.645430i	−0.0564633	+	0.0325991i
$393$	7.70675	−	21.1741i	0.388754	−	1.06809i
$394$	4.27837	−	24.2638i	0.215541	−	1.22239i
$395$		0			0
$396$	−1.11334	+	0.405223i	−0.0559475	+	0.0203632i
$397$	10.3984	−	12.3923i	0.521881	−	0.621954i	−0.439143	−	0.898417i	$-0.644718\pi$
$397$	10.3984	−	12.3923i	0.521881	−	0.621954i	0.961024	+	0.276463i	$0.0891624\pi$
$398$		−	9.79292i		−	0.490875i
$399$	−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	$0.462136\pi$
$402$	−1.16679	−	3.20574i	−0.0581943	−	0.159888i
$403$	−0.887975	+	0.156574i	−0.0442332	+	0.00779951i
$404$	−2.48040	+	14.0670i	−0.123404	+	0.699862i
$405$		0			0
$406$	−3.41147	−	5.90885i	−0.169309	−	0.293251i
$407$	−2.24843	−	1.29813i	−0.111451	−	0.0643461i
$408$	−1.43128	−	1.70574i	−0.0708591	−	0.0844466i
$409$	18.7606	−	15.7420i	0.927651	−	0.778392i	−0.0477432	−	0.998860i	$-0.515203\pi$
$409$	18.7606	−	15.7420i	0.927651	−	0.778392i	0.975394	+	0.220468i	$0.0707585\pi$
$410$		0			0
$411$	−2.03415	−	3.52325i	−0.100337	−	0.173789i
$412$	0.543308	−	1.49273i	0.0267669	−	0.0735413i
$413$	−24.8999	−	4.39053i	−1.22525	−	0.216044i
$414$	−0.230552	−	1.30753i	−0.0113310	−	0.0642614i
$415$		0			0
$416$	−0.407604	−	0.342020i	−0.0199844	−	0.0167689i
$417$		−	16.6759i		−	0.816624i
$418$	−0.725293	+	4.29813i	−0.0354752	+	0.210229i
$419$	−14.5972			−0.713120			−0.356560	−	0.934272i	$-0.616050\pi$
$419$	−14.5972			−0.713120			−0.356560	+	0.934272i	$0.616050\pi$
$420$		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	$0.264793\pi$
$422$	21.2176	−	3.74123i	1.03285	−	0.182120i
$423$	−2.11797	−	0.373455i	−0.102979	−	0.0181580i
$424$	−11.2836	−	4.10689i	−0.547979	−	0.199448i
$425$		0			0
$426$	−3.96585	+	6.86906i	−0.192146	+	0.332807i
$427$	11.5658	+	13.7836i	0.559708	+	0.667034i
$428$	3.24584	+	3.86824i	0.156894	+	0.186978i
$429$	−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	$0.970767\pi$
$432$	−5.55250	−	0.979055i	−0.267145	−	0.0471048i
$433$	19.4788	−	3.43464i	0.936092	−	0.165058i	0.315263	−	0.949004i	$-0.397907\pi$
$433$	19.4788	−	3.43464i	0.936092	−	0.165058i	0.620829	+	0.783946i	$0.286796\pi$
$434$	4.58512	−	1.66885i	0.220093	−	0.0801073i
$435$		0			0
$436$	3.96316			0.189801
$437$	−4.60224	−	1.63681i	−0.220155	−	0.0782993i
$438$			6.71688i			0.320945i
$439$	−14.6120	−	12.2609i	−0.697393	−	0.585182i	0.223638	−	0.974672i	$-0.428207\pi$
$439$	−14.6120	−	12.2609i	−0.697393	−	0.585182i	−0.921031	+	0.389490i	$0.872651\pi$
$440$		0			0
$441$	−0.265578	−	1.50617i	−0.0126466	−	0.0717222i
$442$	0.866025	+	0.152704i	0.0411926	+	0.00726337i
$443$	5.82807	−	16.0125i	0.276900	−	0.760776i	−0.720810	−	0.693133i	$-0.756230\pi$
$443$	5.82807	−	16.0125i	0.276900	−	0.760776i	0.997710	−	0.0676432i	$-0.0215480\pi$
$444$	−1.74897	−	3.02931i	−0.0830025	−	0.143764i
$445$		0			0
$446$	−15.6591	+	13.1395i	−0.741480	+	0.622176i
$447$	8.07802	+	9.62701i	0.382077	+	0.455342i
$448$	2.49362	+	1.43969i	0.117813	+	0.0680191i
$449$	−19.9368	−	34.5315i	−0.940874	−	1.62964i	−0.763810	−	0.645442i	$-0.776673\pi$
$449$	−19.9368	−	34.5315i	−0.940874	−	1.62964i	−0.177064	−	0.984199i	$-0.556660\pi$
$450$		0			0
$451$	−0.897804	+	5.09170i	−0.0422759	+	0.239759i
$452$	6.87933	−	1.21301i	0.323576	−	0.0570552i
$453$	−2.19642	−	6.03462i	−0.103197	−	0.283531i
$454$	−5.96585	−	5.00594i	−0.279991	−	0.234941i
$455$		0			0
$456$	−3.74170	+	4.52644i	−0.175221	+	0.211970i
$457$		−	15.4216i		−	0.721391i	−0.932684	−	0.360696i	$-0.882539\pi$
$457$		−	15.4216i		−	0.721391i	0.932684	−	0.360696i	$-0.117461\pi$
$458$	5.15988	−	6.14930i	0.241105	−	0.287338i
$459$	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	$0.987540\pi$
$462$	1.32683	−	3.64543i	0.0617296	−	0.169601i
$463$	−3.57445	+	2.06371i	−0.166119	+	0.0959088i	−0.580755	−	0.814079i	$-0.697242\pi$
$463$	−3.57445	+	2.06371i	−0.166119	+	0.0959088i	0.414636	+	0.909988i	$0.363909\pi$
$464$	−1.18479	+	2.05212i	−0.0550026	+	0.0952673i
$465$		0			0
$466$	2.89646	−	2.43042i	0.134176	−	0.112587i
$467$	22.8375	+	13.1853i	1.05680	+	0.610141i	0.924544	−	0.381075i	$-0.124446\pi$
$467$	22.8375	+	13.1853i	1.05680	+	0.610141i	0.132251	+	0.991216i	$0.457779\pi$
$468$	0.545955	−	0.315207i	0.0252368	−	0.0145705i
$469$	−6.85117	−	2.49362i	−0.316357	−	0.115145i
$470$		0			0
$471$	−3.58781	−	20.3475i	−0.165318	−	0.937563i
$472$	3.00330	+	8.25150i	0.138238	+	0.379806i
$473$	6.98378	−	8.32295i	0.321115	−	0.382690i
$474$	−11.5517			−0.530587
$475$		0			0
$476$	−4.75877			−0.218118
$477$	9.14473	−	10.8983i	0.418709	−	0.498998i
$478$	−2.31926	−	6.37211i	−0.106080	−	0.291454i
$479$	−2.82207	−	16.0048i	−0.128944	−	0.731276i	−0.978887	−	0.204402i	$-0.934475\pi$
$479$	−2.82207	−	16.0048i	−0.128944	−	0.731276i	0.849943	−	0.526874i	$-0.176636\pi$
$480$		0			0
$481$	1.29813	+	0.472482i	0.0591898	+	0.0215433i
$482$	5.23324	−	3.02141i	0.238367	−	0.137622i
$483$	3.76487	+	2.17365i	0.171307	+	0.0989044i
$484$	7.66044	−	6.42788i	0.348202	−	0.292176i
$485$		0			0
$486$	5.73442	−	9.93231i	0.260119	−	0.450539i
$487$	−14.9802	+	8.64883i	−0.678819	+	0.391916i	−0.799410	−	0.600786i	$-0.794854\pi$
$487$	−14.9802	+	8.64883i	−0.678819	+	0.391916i	0.120591	+	0.992702i	$0.461521\pi$
$488$	2.13727	−	5.87211i	0.0967498	−	0.265818i
$489$	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	$0.274357\pi$
$492$	−4.47756	+	5.33615i	−0.201864	+	0.240572i
$493$		−	3.91622i		−	0.176378i
$494$	−0.0170741	−	2.31926i	−0.000768202	−	0.104348i
$495$		0			0
$496$	−1.29813	−	1.08926i	−0.0582879	−	0.0489094i
$497$	5.79769	+	15.9290i	0.260062	+	0.714514i
$498$	14.1410	−	2.49344i	0.633674	−	0.111734i
$499$	6.52394	−	36.9991i	0.292052	−	1.65631i	−0.386899	−	0.922122i	$-0.626454\pi$
$499$	6.52394	−	36.9991i	0.292052	−	1.65631i	0.678950	−	0.734184i	$-0.262435\pi$
$500$		0			0
$501$	−11.7160	−	20.2927i	−0.523432	−	0.906612i
$502$	−4.94864	−	2.85710i	−0.220868	−	0.127518i
$503$	−20.0964	−	23.9500i	−0.896054	−	1.06788i	−0.997331	−	0.0730176i	$-0.976737\pi$
$503$	−20.0964	−	23.9500i	−0.896054	−	1.06788i	0.101276	−	0.994858i	$-0.467707\pi$
$504$	−2.61334	+	2.19285i	−0.116407	+	0.0976774i
$505$		0			0
$506$	−0.560307	−	0.970481i	−0.0249087	−	0.0431431i
$507$	−5.85997	+	16.1001i	−0.260250	+	0.715032i
$508$	18.6607	+	3.29039i	0.827937	+	0.145988i
$509$	−4.05438	−	22.9935i	−0.179707	−	1.01917i	−0.932569	−	0.360991i	$-0.882438\pi$
$509$	−4.05438	−	22.9935i	−0.179707	−	1.01917i	0.752862	−	0.658178i	$-0.228673\pi$
$510$		0			0
$511$	10.9966	+	9.22724i	0.486461	+	0.408189i
$512$		−	1.00000i		−	0.0441942i
$513$	−12.4444	−	21.1925i	−0.549435	−	0.935673i
$514$	−12.8307			−0.565937
$515$		0			0
$516$	13.7554	−	5.00654i	0.605546	−	0.220401i
$517$	−1.78763	+	0.315207i	−0.0786199	+	0.0138628i
$518$	−7.36208	−	1.29813i	−0.323471	−	0.0570367i
$519$	−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	$0.231065\pi$
$522$	−1.80460	−	2.15064i	−0.0789854	−	0.0941311i
$523$	9.20702	+	10.9725i	0.402595	+	0.479794i	0.928809	−	0.370558i	$-0.120834\pi$
$523$	9.20702	+	10.9725i	0.402595	+	0.479794i	−0.526215	+	0.850352i	$0.676389\pi$
$524$	−8.36231	+	14.4839i	−0.365309	+	0.632734i
$525$		0			0
$526$	4.59714	+	1.67322i	0.200445	+	0.0729560i
$527$	2.75811	+	0.486329i	0.120145	+	0.0211848i
$528$	−1.32683	+	0.233956i	−0.0577428	+	0.0101816i
$529$	−20.4329	+	7.43696i	−0.888386	+	0.323346i
$530$		0			0
$531$	−10.4037			−0.451484
$532$	2.27038	+	12.3439i	0.0984336	+	0.535176i
$533$		−	2.75103i		−	0.119160i
$534$	0.762889	+	0.640140i	0.0330134	+	0.0277016i
$535$		0			0
$536$	0.439693	+	2.49362i	0.0189918	+	0.107708i
$537$	−25.6422	−	4.52141i	−1.10654	−	0.195113i
$538$	−5.43372	+	14.9290i	−0.234264	+	0.643636i
$539$	−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	$0.526614\pi$
$542$	15.6981	+	18.7083i	0.674291	+	0.803589i
$543$	30.8316	+	17.8007i	1.32311	+	0.763899i
$544$	0.826352	+	1.43128i	0.0354295	+	0.0613658i
$545$		0			0
$546$	−0.358441	+	2.03282i	−0.0153398	+	0.0869966i
$547$	28.5949	−	5.04205i	1.22263	−	0.215583i	0.475172	−	0.879893i	$-0.342386\pi$
$547$	28.5949	−	5.04205i	1.22263	−	0.215583i	0.747457	+	0.664310i	$0.231275\pi$
$548$	1.03276	+	2.83750i	0.0441175	+	0.121212i
$549$	5.67159	+	4.75903i	0.242058	+	0.203110i
$550$		0			0
$551$	−10.1584	+	1.86841i	−0.432762	+	0.0795968i
$552$		−	1.50980i		−	0.0642614i
$553$	−15.8690	+	18.9119i	−0.674819	+	0.804218i
$554$	10.8439	−	3.94685i	0.460713	−	0.167686i
$555$		0			0
$556$	−2.14930	+	12.1893i	−0.0911506	+	0.516941i
$557$	9.63511	−	26.4722i	0.408253	−	1.12167i	−0.549856	−	0.835260i	$-0.685317\pi$
$557$	9.63511	−	26.4722i	0.408253	−	1.12167i	0.958108	−	0.286406i	$-0.0924605\pi$
$558$	1.73875	−	1.00387i	0.0736073	−	0.0424972i
$559$	−2.89053	+	5.00654i	−0.122256	+	0.211754i
$560$		0			0
$561$	1.70574	−	1.43128i	0.0720163	−	0.0604288i
$562$	−6.82812	−	3.94222i	−0.288027	−	0.166292i
$563$	−8.92474	+	5.15270i	−0.376133	+	0.217161i	−0.676135	−	0.736778i	$-0.736346\pi$
$563$	−8.92474	+	5.15270i	−0.376133	+	0.217161i	0.300001	+	0.953939i	$0.403013\pi$
$564$	−2.29813	−	0.836452i	−0.0967689	−	0.0352210i
$565$		0			0
$566$	−0.823826	−	4.67215i	−0.0346280	−	0.196385i
$567$	3.98048	+	10.9363i	0.167165	+	0.459281i
$568$	3.78417	−	4.50980i	0.158780	−	0.189227i
$569$	24.3723			1.02174			0.510869	−	0.859658i	$-0.329324\pi$
$569$	24.3723			1.02174			0.510869	+	0.859658i	$0.329324\pi$
$570$		0			0
$571$	−40.7844			−1.70677			−0.853386	−	0.521279i	$-0.825455\pi$
$571$	−40.7844			−1.70677			−0.853386	+	0.521279i	$0.825455\pi$
$572$	0.342020	−	0.407604i	0.0143006	−	0.0170428i
$573$	−11.8406	−	32.5317i	−0.494647	−	1.35903i
$574$	2.58512	+	14.6610i	0.107901	+	0.611937i
$575$		0			0
$576$	1.11334	+	0.405223i	0.0463892	+	0.0168843i
$577$	28.2004	−	16.2815i	1.17400	−	0.677809i	0.219381	−	0.975639i	$-0.429596\pi$
$577$	28.2004	−	16.2815i	1.17400	−	0.677809i	0.954619	+	0.297831i	$0.0962630\pi$
$578$	12.3569	+	7.13429i	0.513981	+	0.296747i
$579$	−5.42443	+	4.55164i	−0.225432	+	0.189160i
$580$		0			0
$581$	15.3439	−	26.5764i	0.636572	−	1.10257i
$582$	−13.5395	+	7.81702i	−0.561229	+	0.324026i
$583$	4.10689	−	11.2836i	0.170090	−	0.467318i
$584$	0.865715	−	4.90971i	0.0358235	−	0.203165i
$585$		0			0
$586$	11.8341	−	4.30726i	0.488862	−	0.177931i
$587$	−16.8427	+	20.0724i	−0.695174	+	0.828476i	−0.991971	−	0.126465i	$-0.959637\pi$
$587$	−16.8427	+	20.0724i	−0.695174	+	0.828476i	0.296797	+	0.954941i	$0.404081\pi$
$588$		−	1.73917i		−	0.0717222i
$589$	−0.0543776	−	7.38636i	−0.00224059	−	0.304350i
$590$		0			0
$591$	25.4288	+	21.3373i	1.04600	+	0.877698i
$592$	0.887975	+	2.43969i	0.0364956	+	0.100271i
$593$	46.8387	−	8.25893i	1.92344	−	0.339154i	0.924337	−	0.381578i	$-0.124619\pi$
$593$	46.8387	−	8.25893i	1.92344	−	0.339154i	0.999100	+	0.0424244i	$0.0135082\pi$
$594$	0.979055	−	5.55250i	0.0401711	−	0.227822i
$595$		0			0
$596$	−4.66385	−	8.07802i	−0.191039	−	0.330889i
$597$	11.4263	+	6.59698i	0.467648	+	0.269996i
$598$	0.383273	+	0.456767i	0.0156732	+	0.0186786i
$599$	11.9474	−	10.0251i	0.488159	−	0.409614i	−0.365207	−	0.930926i	$-0.619002\pi$
$599$	11.9474	−	10.0251i	0.488159	−	0.409614i	0.853366	+	0.521312i	$0.174557\pi$
$600$		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	$0.553369\pi$
$602$	10.6998	−	29.3974i	0.436090	−	1.19815i
$603$	−2.95442	−	0.520945i	−0.120313	−	0.0212145i
$604$	0.827696	+	4.69410i	0.0336785	+	0.191000i
$605$		0			0
$606$	−14.7424	−	12.3704i	−0.598870	−	0.502511i
$607$		−	32.7520i		−	1.32936i	−0.747128	−	0.664681i	$-0.768568\pi$
$607$		−	32.7520i		−	1.32936i	0.747128	−	0.664681i	$-0.231432\pi$
$608$	3.31839	−	2.82635i	0.134579	−	0.114624i
$609$	9.19253			0.372500
$610$		0			0
$611$	0.907604	−	0.330341i	0.0367177	−	0.0133642i
$612$	−1.92836	+	0.340022i	−0.0779494	+	0.0137446i
$613$	−32.8214	−	5.78729i	−1.32564	−	0.233747i	−0.534391	−	0.845237i	$-0.679459\pi$
$613$	−32.8214	−	5.78729i	−1.32564	−	0.233747i	−0.791252	+	0.611491i	$0.790570\pi$
$614$	28.3692	+	10.3255i	1.14489	+	0.416705i
$615$		0			0
$616$	−1.43969	+	2.49362i	−0.0580069	+	0.100471i
$617$	−24.4964	−	29.1937i	−0.986189	−	1.17529i	−0.984516	−	0.175296i	$-0.943912\pi$
$617$	−24.4964	−	29.1937i	−0.986189	−	1.17529i	−0.00167362	−	0.999999i	$-0.500533\pi$
$618$	1.37570	+	1.63950i	0.0553389	+	0.0659504i
$619$	−12.0312	+	20.8387i	−0.483575	+	0.837577i	−0.999822	−	0.0188630i	$-0.993995\pi$
$619$	−12.0312	+	20.8387i	−0.483575	+	0.837577i	0.516247	+	0.856440i	$0.327329\pi$
$620$		0			0
$621$	5.93717	+	2.16095i	0.238250	+	0.0867160i
$622$	−10.9163	−	1.92484i	−0.437704	−	0.0771791i
$623$	2.09602	−	0.369585i	0.0839753	−	0.0148071i
$624$	0.673648	−	0.245188i	0.0269675	−	0.00981537i
$625$		0			0
$626$	−8.18479			−0.327130
$627$	−4.52644	−	3.74170i	−0.180769	−	0.149429i
$628$			15.3354i			0.611951i
$629$	−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	$0.764149\pi$
$632$	8.44372	+	1.48886i	0.335873	+	0.0592235i
$633$	−9.92794	+	27.2768i	−0.394600	+	1.08415i
$634$	2.39899	+	4.15516i	0.0952759	+	0.165023i
$635$		0			0
$636$	12.3931	−	10.3990i	0.491417	−	0.412348i
$637$	0.441500	+	0.526159i	0.0174929	+	0.0208472i
$638$	−2.05212	−	1.18479i	−0.0812442	−	0.0469064i
$639$	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	$0.0289547\pi$
$642$	−6.69999	+	1.18139i	−0.264428	+	0.0466257i
$643$	8.97037	+	24.6459i	0.353757	+	0.971939i	0.981152	+	0.193238i	$0.0618990\pi$
$643$	8.97037	+	24.6459i	0.353757	+	0.971939i	−0.627395	+	0.778701i	$0.715879\pi$
$644$	−2.47178	−	2.07407i	−0.0974018	−	0.0817298i
$645$		0			0
$646$	−2.41400	+	6.78747i	−0.0949776	+	0.267049i
$647$		−	6.31221i		−	0.248159i	−0.992272	−	0.124079i	$-0.960402\pi$
$647$		−	6.31221i		−	0.248159i	0.992272	−	0.124079i	$-0.0395977\pi$
$648$	2.59808	−	3.09627i	0.102062	−	0.121633i
$649$	−8.25150	+	3.00330i	−0.323900	+	0.117890i
$650$		0			0
$651$	−1.14156	+	6.47410i	−0.0447412	+	0.253740i
$652$	−2.82304	+	7.75624i	−0.110559	+	0.303758i
$653$	14.2475	−	8.22580i	0.557548	−	0.321901i	−0.194613	−	0.980880i	$-0.562345\pi$
$653$	14.2475	−	8.22580i	0.557548	−	0.321901i	0.752161	+	0.658980i	$0.229012\pi$
$654$	−2.66978	+	4.62419i	−0.104397	+	0.180820i
$655$		0			0
$656$	3.96064	−	3.32337i	0.154637	−	0.129756i
$657$	5.11538	+	2.95336i	0.199570	+	0.115222i
$658$	−4.52644	+	2.61334i	−0.176459	+	0.101879i
$659$	33.6168	+	12.2355i	1.30952	+	0.476628i	0.900087	−	0.435710i	$-0.143503\pi$
$659$	33.6168	+	12.2355i	1.30952	+	0.476628i	0.409438	+	0.912338i	$0.365725\pi$
$660$		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	$0.750429\pi$
$662$	−4.68475	−	12.8712i	−0.182078	−	0.500255i
$663$	−0.761570	+	0.907604i	−0.0295769	+	0.0352484i
$664$	−10.6578			−0.413601
$665$		0			0
$666$	−3.07604			−0.119194
$667$	1.70685	−	2.03415i	0.0660896	−	0.0787625i
$668$	5.94837	+	16.3430i	0.230149	+	0.632330i
$669$	−4.78240	−	27.1224i	−0.184898	−	1.04861i
$670$		0			0
$671$	5.87211	+	2.13727i	0.226690	+	0.0825085i
$672$	−3.35965	+	1.93969i	−0.129601	+	0.0748253i
$673$	27.8327	+	16.0692i	1.07287	+	0.619423i	0.928965	−	0.370168i	$-0.120700\pi$
$673$	27.8327	+	16.0692i	1.07287	+	0.619423i	0.143908	+	0.989591i	$0.454033\pi$
$674$	5.95336	−	4.99546i	0.229315	−	0.192418i
$675$		0			0
$676$	6.35844	−	11.0131i	0.244555	−	0.423582i
$677$	15.6054	−	9.00980i	0.599765	−	0.346275i	−0.169184	−	0.985585i	$-0.554113\pi$
$677$	15.6054	−	9.00980i	0.599765	−	0.346275i	0.768949	+	0.639310i	$0.220780\pi$
$678$	−3.21891	+	8.84389i	−0.123622	+	0.339648i
$679$	−5.80200	+	32.9048i	−0.222660	+	1.26277i
$680$		0			0
$681$	9.85978	−	3.58867i	0.377828	−	0.137518i
$682$	1.08926	−	1.29813i	0.0417100	−	0.0497081i
$683$		−	27.6195i		−	1.05683i	−0.848986	−	0.528415i	$-0.822786\pi$
$683$		−	27.6195i		−	1.05683i	0.848986	−	0.528415i	$-0.177214\pi$
$684$	1.80200	+	4.83981i	0.0689013	+	0.185055i
$685$		0			0
$686$	12.5929	+	10.5667i	0.480798	+	0.403437i
$687$	3.69902	+	10.1630i	0.141126	+	0.387742i
$688$	−10.6998	+	1.88666i	−0.407925	+	0.0719282i
$689$	−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	$-0.357157\pi$
$692$	16.9945	+	9.81180i	0.646036	+	0.372989i
$693$	−2.19285	−	2.61334i	−0.0832996	−	0.0992726i
$694$	−2.53209	+	2.12467i	−0.0961168	+	0.0806516i
$695$		0			0
$696$	−1.59627	−	2.76481i	−0.0605063	−	0.104800i
$697$	−2.92252	+	8.02956i	−0.110698	+	0.304141i
$698$	−23.8030	−	4.19712i	−0.900959	−	0.158863i
$699$	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	$0.558758\pi$
$702$			3.00000i			0.113228i
$703$	−5.58613	+	9.84208i	−0.210685	+	0.371201i
$704$	1.00000			0.0376889
$705$		0			0
$706$	27.0107	−	9.83110i	1.01656	−	0.369998i
$707$	−40.5044	+	7.14203i	−1.52333	+	0.268604i
$708$	−11.6510	−	2.05438i	−0.437870	−	0.0772082i
$709$	27.9932	+	10.1887i	1.05131	+	0.382644i	0.809156	−	0.587594i	$-0.199925\pi$
$709$	27.9932	+	10.1887i	1.05131	+	0.382644i	0.242151	+	0.970239i	$0.422147\pi$
$710$		0			0
$711$	−5.07919	+	8.79742i	−0.190485	+	0.329929i
$712$	−0.475129	−	0.566237i	−0.0178062	−	0.0212206i
$713$	1.22064	+	1.45471i	0.0457135	+	0.0544792i
$714$	3.20574	−	5.55250i	0.119972	−	0.207797i
$715$		0			0
$716$	18.1604	+	6.60986i	0.678688	+	0.247022i
$717$	8.99730	+	1.58647i	0.336010	+	0.0592477i
$718$	12.8397	−	2.26399i	0.479173	−	0.0844912i
$719$	−14.2007	+	5.16863i	−0.529596	+	0.192757i	−0.592958	−	0.805233i	$-0.702040\pi$
$719$	−14.2007	+	5.16863i	−0.529596	+	0.192757i	0.0633618	+	0.997991i	$0.479818\pi$
$720$		0			0
$721$	4.57398			0.170344
$722$	18.7579	+	3.02347i	0.698097	+	0.112522i
$723$			8.14147i			0.302785i
$724$	−20.2422	−	16.9852i	−0.752294	−	0.631250i
$725$		0			0
$726$	2.33956	+	13.2683i	0.0868291	+	0.492432i
$727$	−7.39165	−	1.30335i	−0.274141	−	0.0483385i	0.0348873	−	0.999391i	$-0.488893\pi$
$727$	−7.39165	−	1.30335i	−0.274141	−	0.0483385i	−0.309029	+	0.951053i	$0.600004\pi$
$728$	0.524005	−	1.43969i	0.0194209	−	0.0533586i
$729$	13.7888	+	23.8829i	0.510696	+	0.884552i
$730$		0			0
$731$	13.7554	−	11.5421i	0.508761	−	0.426901i
$732$	5.41177	+	6.44949i	0.200025	+	0.238380i
$733$	13.6261	+	7.86706i	0.503293	+	0.290576i	0.730072	−	0.683370i	$-0.239486\pi$
$733$	13.6261	+	7.86706i	0.503293	+	0.290576i	−0.226779	+	0.973946i	$0.572820\pi$
$734$	8.04710	+	13.9380i	0.297024	+	0.514461i
$735$		0			0
$736$	−0.194593	+	1.10359i	−0.00717278	+	0.0406789i
$737$	−2.49362	+	0.439693i	−0.0918537	+	0.0161963i
$738$	2.09510	+	5.75624i	0.0771218	+	0.211890i
$739$	16.6570	+	13.9769i	0.612739	+	0.514149i	0.895512	−	0.445038i	$-0.146810\pi$
$739$	16.6570	+	13.9769i	0.612739	+	0.514149i	−0.282773	+	0.959187i	$0.591254\pi$
$740$		0			0
$741$	2.71760	+	1.54244i	0.0998334	+	0.0566630i
$742$		−	34.5749i		−	1.26928i
$743$	−17.4065	+	20.7442i	−0.638581	+	0.761032i	−0.984145	−	0.177363i	$-0.943243\pi$
$743$	−17.4065	+	20.7442i	−0.638581	+	0.761032i	0.345564	+	0.938395i	$0.387688\pi$
$744$	2.14543	−	0.780873i	0.0786553	−	0.0286282i
$745$		0			0
$746$	−4.88831	+	27.7230i	−0.178974	+	1.01501i
$747$	4.31877	−	11.8657i	0.158015	−	0.434144i
$748$	−1.43128	+	0.826352i	−0.0523329	+	0.0302144i
$749$	−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	$0.0466897\pi$
$752$	1.57202	+	0.907604i	0.0573255	+	0.0330969i
$753$	6.66728	−	3.84936i	0.242969	−	0.140278i
$754$	1.18479	+	0.431229i	0.0431476	+	0.0157044i
$755$		0			0
$756$	−2.81908	−	15.9878i	−0.102529	−	0.581470i
$757$	7.03580	+	19.3307i	0.255720	+	0.702586i	0.999419	+	0.0340713i	$0.0108473\pi$
$757$	7.03580	+	19.3307i	0.255720	+	0.702586i	−0.743699	+	0.668515i	$0.766930\pi$
$758$	7.55342	−	9.00181i	0.274352	−	0.326960i
$759$	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	$0.831089\pi$
$762$	−16.4100	+	19.5567i	−0.594471	+	0.708463i
$763$	3.90295	+	10.7233i	0.141296	+	0.388209i
$764$	4.46198	+	25.3052i	0.161429	+	0.915508i
$765$		0			0
$766$	−16.8229	−	6.12305i	−0.607838	−	0.221235i
$767$	4.04633	−	2.33615i	0.146105	−	0.0843536i
$768$	1.16679	+	0.673648i	0.0421030	+	0.0243082i
$769$	−12.2215	+	10.2550i	−0.440717	+	0.369806i	−0.835978	−	0.548763i	$-0.815099\pi$
$769$	−12.2215	+	10.2550i	−0.440717	+	0.369806i	0.395260	+	0.918569i	$0.370654\pi$
$770$		0			0
$771$	8.64337	−	14.9708i	0.311283	−	0.539159i
$772$	4.55164	−	2.62789i	0.163817	−	0.0945798i
$773$	−5.62273	+	15.4483i	−0.202235	+	0.555637i	−0.998803	−	0.0489122i	$-0.984425\pi$
$773$	−5.62273	+	15.4483i	−0.202235	+	0.555637i	0.796568	+	0.604549i	$0.206647\pi$
$774$	2.23530	−	12.6770i	0.0803462	−	0.455666i
$775$		0			0
$776$	10.9042	−	3.96880i	0.391438	−	0.142472i
$777$	6.47410	−	7.71554i	0.232257	−	0.276793i
$778$		−	26.3473i		−	0.944596i
$779$	22.2224	+	3.74994i	0.796200	+	0.134356i
$780$		0			0
$781$	4.50980	+	3.78417i	0.161373	+	0.135408i
$782$	−0.633436	−	1.74035i	−0.0226516	−	0.0622349i
$783$	13.1571	−	2.31996i	0.470197	−	0.0829084i
$784$	−0.224155	+	1.27125i	−0.00800555	+	0.0454017i
$785$		0			0
$786$	−11.2665	−	19.5142i	−0.401863	−	0.696047i
$787$	−43.2792	−	24.9873i	−1.54274	−	0.890700i	−0.998665	−	0.0516616i	$-0.983548\pi$
$787$	−43.2792	−	24.9873i	−1.54274	−	0.890700i	−0.544073	−	0.839038i	$-0.683118\pi$
$788$	−15.8371	−	18.8739i	−0.564173	−	0.672356i
$789$	−5.04916	+	4.23675i	−0.179755	+	0.150832i
$790$		0			0
$791$	10.0569	+	17.4191i	0.357582	+	0.619351i
$792$	−0.405223	+	1.11334i	−0.0143990	+	0.0395608i
$793$	−3.27449	−	0.577382i	−0.116281	−	0.0205034i
$794$	−2.80912	−	15.9313i	−0.0996918	−	0.565380i
$795$		0			0
$796$	−7.50181	−	6.29477i	−0.265895	−	0.223112i
$797$			11.9314i			0.422631i	0.977418	+	0.211316i	$0.0677748\pi$
$797$			11.9314i			0.422631i	−0.977418	+	0.211316i	$0.932225\pi$
$798$	−15.9322	−	5.66637i	−0.563994	−	0.200587i
$799$	−3.00000			−0.106132
$800$		0			0
$801$	0.822948	−	0.299529i	0.0290774	−	0.0105833i
$802$	28.7590	−	5.07098i	1.01552	−	0.179063i
$803$	4.90971	+	0.865715i	0.173260	+	0.0305504i
$804$	−3.20574	−	1.16679i	−0.113058	−	0.0411496i
$805$		0			0
$806$	−0.450837	+	0.780873i	−0.0158801	+	0.0275051i
$807$	−13.7587	−	16.3969i	−0.484328	−	0.577199i
$808$	9.18161	+	10.9422i	0.323008	+	0.384946i
$809$	−25.0744	+	43.4302i	−0.881571	+	1.52692i	−0.0319760	+	0.999489i	$0.510180\pi$
$809$	−25.0744	+	43.4302i	−0.881571	+	1.52692i	−0.849595	+	0.527436i	$0.823153\pi$
$810$		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	$0.751561\pi$
$812$	−6.71929	−	1.18479i	−0.235801	−	0.0415781i
$813$	−32.4037	+	5.71364i	−1.13645	+	0.200386i
$814$	−2.43969	+	0.887975i	−0.0855112	+	0.0311235i
$815$		0			0
$816$	−2.22668			−0.0779494
$817$	−36.5020	−	30.1737i	−1.27704	−	1.05564i
$818$		−	24.4902i		−	0.856280i
$819$	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	$-0.309663\pi$
$822$	−4.00649	−	0.706452i	−0.139742	−	0.0246404i
$823$	3.60219	−	9.89693i	0.125564	−	0.344985i	−0.860943	−	0.508701i	$-0.830126\pi$
$823$	3.60219	−	9.89693i	0.125564	−	0.344985i	0.986508	+	0.163716i	$0.0523481\pi$
$824$	−0.794263	−	1.37570i	−0.0276695	−	0.0479249i
$825$		0			0
$826$	−19.3687	+	16.2523i	−0.673924	+	0.565489i
$827$	31.0941	+	37.0565i	1.08125	+	1.28858i	0.955008	+	0.296581i	$0.0958464\pi$
$827$	31.0941	+	37.0565i	1.08125	+	1.28858i	0.126240	+	0.992000i	$0.459709\pi$
$828$	−1.14982	−	0.663848i	−0.0399590	−	0.0230703i
$829$	−11.1279	−	19.2741i	−0.386488	−	0.669416i	0.605487	−	0.795855i	$-0.292978\pi$
$829$	−11.1279	−	19.2741i	−0.386488	−	0.669416i	−0.991974	+	0.126439i	$0.959645\pi$
$830$		0			0
$831$	−2.69981	+	15.3114i	−0.0936553	+	0.531145i
$832$	−0.524005	+	0.0923963i	−0.0181666	+	0.00320326i
$833$	−0.729669	−	2.00475i	−0.0252815	−	0.0694604i
$834$	−12.7745	−	10.7191i	−0.442345	−	0.371171i
$835$		0			0
$836$	2.82635	+	3.31839i	0.0977514	+	0.114769i
$837$			9.55438i			0.330248i
$838$	−9.38290	+	11.1821i	−0.324127	+	0.386279i
$839$	13.6638	−	4.97323i	0.471728	−	0.171695i	−0.0952067	−	0.995458i	$-0.530351\pi$
$839$	13.6638	−	4.97323i	0.471728	−	0.171695i	0.566935	+	0.823762i	$0.308129\pi$
$840$		0			0
$841$	−4.06077	+	23.0298i	−0.140027	+	0.794131i
$842$	5.33424	−	14.6557i	0.183830	−	0.505069i
$843$	9.19951	−	5.31134i	0.316848	−	0.182932i
$844$	10.7724	−	18.6584i	0.370803	−	0.642249i
$845$		0			0
$846$	−1.64749	+	1.38241i	−0.0566418	+	0.0475281i
$847$	24.9362	+	14.3969i	0.856818	+	0.494684i
$848$	−10.3990	+	6.00387i	−0.357103	+	0.206174i
$849$	6.00640	+	2.18615i	0.206139	+	0.0750285i
$850$		0			0
$851$	−0.505215	−	2.86521i	−0.0173185	−	0.0982183i
$852$	2.71280	+	7.45336i	0.0929391	+	0.255348i
$853$	−13.5556	+	16.1550i	−0.464136	+	0.553136i	−0.946445	−	0.322865i	$-0.895354\pi$
$853$	−13.5556	+	16.1550i	−0.464136	+	0.553136i	0.482309	+	0.876001i	$0.339798\pi$
$854$	17.9932			0.615714
$855$		0			0
$856$	5.04963			0.172593
$857$	−19.8791	+	23.6909i	−0.679056	+	0.809267i	−0.989986	−	0.141166i	$-0.954915\pi$
$857$	−19.8791	+	23.6909i	−0.679056	+	0.809267i	0.310930	+	0.950433i	$0.399359\pi$
$858$	0.245188	+	0.673648i	0.00837058	+	0.0229980i
$859$	3.27110	+	18.5513i	0.111608	+	0.632963i	0.988374	+	0.152044i	$0.0485856\pi$
$859$	3.27110	+	18.5513i	0.111608	+	0.632963i	−0.876765	+	0.480918i	$0.840303\pi$
$860$		0			0
$861$	−18.8478	−	6.86002i	−0.642330	−	0.233789i
$862$	−32.5195	+	18.7751i	−1.10762	+	0.639483i
$863$	−35.7996	−	20.6689i	−1.21863	−	0.703578i	−0.254007	−	0.967202i	$-0.581749\pi$
$863$	−35.7996	−	20.6689i	−1.21863	−	0.703578i	−0.964625	+	0.263625i	$0.915082\pi$
$864$	−4.31908	+	3.62414i	−0.146938	+	0.123296i
$865$		0			0
$866$	9.88965	−	17.1294i	0.336064	−	0.582080i
$867$	−16.6485	+	9.61200i	−0.565412	+	0.326441i
$868$	1.66885	−	4.58512i	0.0566444	−	0.155629i
$869$	−1.48886	+	8.44372i	−0.0505060	+	0.286434i
$870$		0			0
$871$	1.26604	−	0.460802i	0.0428983	−	0.0156137i
$872$	2.54747	−	3.03596i	0.0862683	−	0.102811i
$873$			13.7483i			0.465311i
$874$	−4.21213	+	2.47340i	−0.142478	+	0.0836640i
$875$		0			0
$876$	5.14543	+	4.31753i	0.173848	+	0.145876i
$877$	0.802934	+	2.20604i	0.0271131	+	0.0744927i	0.952511	−	0.304505i	$-0.0984910\pi$
$877$	0.802934	+	2.20604i	0.0271131	+	0.0744927i	−0.925398	+	0.378998i	$0.876269\pi$
$878$	−18.7848	+	3.31227i	−0.633957	+	0.111784i
$879$	−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	$0.985793\pi$
$882$	−1.32450	−	0.764700i	−0.0445982	−	0.0257488i
$883$	−0.495560	−	0.590585i	−0.0166769	−	0.0198748i	0.757642	−	0.652671i	$-0.226352\pi$
$883$	−0.495560	−	0.590585i	−0.0166769	−	0.0198748i	−0.774318	+	0.632796i	$0.781907\pi$
$884$	0.673648	−	0.565258i	0.0226572	−	0.0190117i
$885$		0			0
$886$	−8.52007	−	14.7572i	−0.286237	−	0.495777i
$887$	1.53634	−	4.22106i	0.0515852	−	0.141729i	−0.911224	−	0.411911i	$-0.864862\pi$
$887$	1.53634	−	4.22106i	0.0515852	−	0.141729i	0.962809	+	0.270182i	$0.0870837\pi$
$888$	−3.44480	−	0.607411i	−0.115600	−	0.0203834i
$889$	9.47431	+	53.7315i	0.317758	+	1.80210i
$890$		0			0
$891$	3.09627	+	2.59808i	0.103729	+	0.0870388i
$892$			20.4415i			0.684432i
$893$	1.43128	+	7.78177i	0.0478961	+	0.260407i
$894$	12.5672			0.420309
$895$		0			0
$896$	2.70574	−	0.984808i	0.0903923	−	0.0329001i
$897$	−0.791143	+	0.139500i	−0.0264155	+	0.00465777i
$898$	−39.2677	−	6.92396i	−1.31038	−	0.231056i
$899$	3.77332	+	1.37338i	0.125847	+	0.0458046i
$900$		0			0
$901$	9.92262	−	17.1865i	0.330570	−	0.572565i
$902$	3.32337	+	3.96064i	0.110656	+	0.131875i
$903$	27.0928	+	32.2879i	0.901591	+	1.07447i
$904$	3.49273	−	6.04958i	0.116166	−	0.201206i
$905$		0			0
$906$	−6.03462	−	2.19642i	−0.200487	−	0.0729712i
$907$	−17.6180	−	3.10653i	−0.584997	−	0.103151i	−0.126686	−	0.991943i	$-0.540434\pi$
$907$	−17.6180	−	3.10653i	−0.584997	−	0.103151i	−0.458311	+	0.888792i	$0.651545\pi$
$908$	−7.66955	+	1.35235i	−0.254523	+	0.0448793i
$909$	−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	$0.614448\pi$
$912$	1.06234	+	5.77584i	0.0351775	+	0.191257i
$913$		−	10.6578i		−	0.352720i
$914$	−11.8136	−	9.91280i	−0.390760	−	0.327886i
$915$		0			0
$916$	−1.39393	−	7.90539i	−0.0460568	−	0.261201i
$917$	−47.4250	−	8.36231i	−1.56611	−	0.276148i
$918$	3.18701	−	8.75624i	0.105187	−	0.288999i
$919$	6.68913	+	11.5859i	0.220654	+	0.382184i	0.955007	−	0.296584i	$-0.0958475\pi$
$919$	6.68913	+	11.5859i	0.220654	+	0.382184i	−0.734353	+	0.678768i	$0.762514\pi$
$920$		0			0
$921$	−31.1586	+	26.1452i	−1.02671	+	0.861513i
$922$	5.85327	+	6.97565i	0.192767	+	0.229731i
$923$	−2.71280	−	1.56624i	−0.0892930	−	0.0515533i
$924$	−1.93969	−	3.35965i	−0.0638112	−	0.110524i
$925$		0			0
$926$	−0.716719	+	4.06472i	−0.0235529	+	0.133575i
$927$	1.85348	−	0.326819i	0.0608763	−	0.0107341i
$928$	0.810446	+	2.22668i	0.0266042	+	0.0730944i
$929$	8.74241	+	7.33575i	0.286829	+	0.240678i	0.774837	−	0.632161i	$-0.217832\pi$
$929$	8.74241	+	7.33575i	0.286829	+	0.240678i	−0.488008	+	0.872839i	$0.662276\pi$
$930$		0			0
$931$	−4.85204	+	2.84916i	−0.159019	+	0.0933774i
$932$		−	3.78106i		−	0.123853i
$933$	9.59964	−	11.4404i	0.314278	−	0.374542i
$934$	24.7802	−	9.01925i	0.810832	−	0.295119i
$935$		0			0
$936$	0.109470	−	0.620838i	0.00357815	−	0.0202927i
$937$	−17.1409	+	47.0941i	−0.559967	+	1.53850i	0.259719	+	0.965684i	$0.416370\pi$
$937$	−17.1409	+	47.0941i	−0.559967	+	1.53850i	−0.819686	+	0.572813i	$0.805852\pi$
$938$	−6.31407	+	3.64543i	−0.206162	+	0.119027i
$939$	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	$0.106773\pi$
$942$	−17.8933	−	10.3307i	−0.582995	−	0.336592i
$943$	−5.01762	+	2.89693i	−0.163396	+	0.0943369i
$944$	8.25150	+	3.00330i	0.268563	+	0.0977491i
$945$		0			0
$946$	−1.88666	−	10.6998i	−0.0613406	−	0.347880i
$947$	8.53882	+	23.4602i	0.277475	+	0.762355i	0.997647	+	0.0685599i	$0.0218404\pi$
$947$	8.53882	+	23.4602i	0.277475	+	0.762355i	−0.720173	+	0.693795i	$0.755937\pi$
$948$	−7.42528	+	8.84911i	−0.241162	+	0.287406i
$949$	−2.65270			−0.0861104
$950$		0			0
$951$	−6.46429			−0.209619
$952$	−3.05888	+	3.64543i	−0.0991388	+	0.118149i
$953$	8.75677	+	24.0590i	0.283660	+	0.779348i	0.996918	+	0.0784473i	$0.0249962\pi$
$953$	8.75677	+	24.0590i	0.283660	+	0.779348i	−0.713259	+	0.700901i	$0.752782\pi$
$954$	−2.47044	−	14.0105i	−0.0799834	−	0.453608i
$955$		0			0
$956$	−6.37211	−	2.31926i	−0.206089	−	0.0750102i
$957$	2.76481	−	1.59627i	0.0893738	−	0.0516000i
$958$	−14.0743	−	8.12583i	−0.454722	−	0.262534i
$959$	−6.66044	+	5.58878i	−0.215077	+	0.180471i
$960$		0			0
$961$	14.0642	−	24.3599i	0.453683	−	0.785802i
$962$	1.19637	−	0.690722i	0.0385724	−	0.0222698i
$963$	−2.04623	+	5.62196i	−0.0659387	+	0.181165i
$964$	1.04933	−	5.95102i	0.0337965	−	0.191669i
$965$		0			0
$966$	4.08512	−	1.48686i	0.131437	−	0.0478390i
$967$	32.9896	−	39.3155i	1.06088	−	1.26430i	0.0977605	−	0.995210i	$-0.468832\pi$
$967$	32.9896	−	39.3155i	1.06088	−	1.26430i	0.963115	−	0.269092i	$-0.0867235\pi$
$968$		−	10.0000i		−	0.321412i
$969$	−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	$0.632667\pi$
$972$	−3.92258	−	10.7772i	−0.125817	−	0.345678i
$973$	−35.0977	+	6.18866i	−1.12518	+	0.198399i
$974$	−3.00371	+	17.0349i	−0.0962450	+	0.545833i
$975$		0			0
$976$	−3.12449	−	5.41177i	−0.100012	−	0.173226i
$977$	−11.9608	−	6.90554i	−0.382658	−	0.220928i	0.296316	−	0.955090i	$-0.404242\pi$
$977$	−11.9608	−	6.90554i	−0.382658	−	0.220928i	−0.678974	+	0.734162i	$0.737575\pi$
$978$	−7.14819	−	8.51889i	−0.228574	−	0.272404i
$979$	0.566237	−	0.475129i	0.0180970	−	0.0151852i
$980$		0			0
$981$	2.34776	+	4.06645i	0.0749583	+	0.129832i
$982$	5.33688	−	14.6630i	0.170307	−	0.467914i
$983$	−5.84300	−	1.03028i	−0.186363	−	0.0328608i	0.0796878	−	0.996820i	$-0.474608\pi$
$983$	−5.84300	−	1.03028i	−0.186363	−	0.0328608i	−0.266050	+	0.963959i	$0.585719\pi$
$984$	1.20961	+	6.86002i	0.0385609	+	0.218690i
$985$		0			0
$986$	−3.00000	−	2.51730i	−0.0955395	−	0.0801671i
$987$		−	7.04189i		−	0.224146i
$988$	−1.78763	−	1.47771i	−0.0568721	−	0.0470123i
$989$	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	$0.557475\pi$
$992$	−1.66885	+	0.294263i	−0.0529860	+	0.00934286i
$993$	18.1739	+	3.20456i	0.576732	+	0.101693i
$994$	15.9290	+	5.79769i	0.505238	+	0.183891i
$995$		0			0
$996$	7.17958	−	12.4354i	0.227494	−	0.394031i
$997$	21.3917	+	25.4937i	0.677483	+	0.807392i	0.989782	−	0.142592i	$-0.0455435\pi$
$997$	21.3917	+	25.4937i	0.677483	+	0.807392i	−0.312299	+	0.949984i	$0.601099\pi$
$998$	−24.1494	−	28.7802i	−0.764437	−	0.911021i
$999$	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.u.d.149.2		12
5.2	odd	4		950.2.l.e.301.1	yes	6
5.3	odd	4		950.2.l.b.301.1	yes	6
5.4	even	2	inner	950.2.u.d.149.1		12
19.6	even	9	inner	950.2.u.d.899.1		12
95.44	even	18	inner	950.2.u.d.899.2		12
95.63	odd	36		950.2.l.b.101.1	✓	6
95.82	odd	36		950.2.l.e.101.1	yes	6

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 - 0.766044i) q^{2} +(0.460802 + 1.26604i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.26604 + 0.460802i) q^{6} +(2.49362 - 1.43969i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.907604 - 0.761570i) q^{9} +O(q^{10})\)	\(q+(0.642788 - 0.766044i) q^{2} +(0.460802 + 1.26604i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.26604 + 0.460802i) q^{6} +(2.49362 - 1.43969i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.907604 - 0.761570i) q^{9} +(0.500000 - 0.866025i) q^{11} +(1.16679 - 0.673648i) q^{12} +(-0.181985 + 0.500000i) q^{13} +(0.500000 - 2.83564i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(1.06234 - 1.26604i) q^{17} -1.18479i q^{18} +(-3.79086 - 2.15160i) q^{19} +(2.97178 + 2.49362i) q^{21} +(-0.342020 - 0.939693i) q^{22} +(1.10359 - 0.194593i) q^{23} +(0.233956 - 1.32683i) q^{24} +(0.266044 + 0.460802i) q^{26} +(4.88279 + 2.81908i) q^{27} +(-1.85083 - 2.20574i) q^{28} +(1.81521 - 1.52314i) q^{29} +(0.847296 + 1.46756i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(1.32683 + 0.233956i) q^{33} +(-0.286989 - 1.62760i) q^{34} +(-0.907604 - 0.761570i) q^{36} -2.59627i q^{37} +(-4.08494 + 1.52094i) q^{38} -0.716881 q^{39} +(-4.85844 + 1.76833i) q^{41} +(3.82045 - 0.673648i) q^{42} +(10.6998 + 1.88666i) q^{43} +(-0.939693 - 0.342020i) q^{44} +(0.560307 - 0.970481i) q^{46} +(-1.16679 - 1.39053i) q^{47} +(-0.866025 - 1.03209i) q^{48} +(0.645430 - 1.11792i) q^{49} +(2.09240 + 0.761570i) q^{51} +(0.524005 + 0.0923963i) q^{52} +(11.8253 - 2.08512i) q^{53} +(5.29813 - 1.92836i) q^{54} -2.87939 q^{56} +(0.977185 - 5.79086i) q^{57} -2.36959i q^{58} +(-6.72668 - 5.64436i) q^{59} +(1.08512 + 6.15403i) q^{61} +(1.66885 + 0.294263i) q^{62} +(1.16679 - 3.20574i) q^{63} +(0.500000 + 0.866025i) q^{64} +(1.03209 - 0.866025i) q^{66} +(-1.62760 - 1.93969i) q^{67} +(-1.43128 - 0.826352i) q^{68} +(0.754900 + 1.30753i) q^{69} +(-1.02229 + 5.79769i) q^{71} +(-1.16679 + 0.205737i) q^{72} +(1.70513 + 4.68479i) q^{73} +(-1.98886 - 1.66885i) q^{74} +(-1.46064 + 4.10689i) q^{76} -2.87939i q^{77} +(-0.460802 + 0.549163i) q^{78} +(-8.05690 + 2.93247i) q^{79} +(-0.701867 + 3.98048i) q^{81} +(-1.76833 + 4.85844i) q^{82} +(9.22989 - 5.32888i) q^{83} +(1.93969 - 3.35965i) q^{84} +(8.32295 - 6.98378i) q^{86} +(2.76481 + 1.59627i) q^{87} +(-0.866025 + 0.500000i) q^{88} +(0.694593 + 0.252811i) q^{89} +(0.266044 + 1.50881i) q^{91} +(-0.383273 - 1.05303i) q^{92} +(-1.46756 + 1.74897i) q^{93} -1.81521 q^{94} -1.34730 q^{96} +(-7.45891 + 8.88919i) q^{97} +(-0.441500 - 1.21301i) q^{98} +(-0.205737 - 1.16679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{6} + 18 q^{9}+O(q^{10}) \) 12 * q + 6 * q^6 + 18 * q^9	\( 12 q + 6 q^{6} + 18 q^{9} + 6 q^{11} + 6 q^{14} + 18 q^{19} + 6 q^{21} + 12 q^{24} - 6 q^{26} + 36 q^{29} + 6 q^{31} + 12 q^{34} - 18 q^{36} + 24 q^{39} - 42 q^{41} + 18 q^{46} - 24 q^{49} + 18 q^{51} + 36 q^{54} - 12 q^{56} - 54 q^{59} - 30 q^{61} + 6 q^{64} - 6 q^{66} + 12 q^{69} + 12 q^{71} - 36 q^{74} - 24 q^{79} - 36 q^{81} + 12 q^{84} + 18 q^{86} - 6 q^{91} - 36 q^{94} - 12 q^{96} + 18 q^{99}+O(q^{100}) \) 12 * q + 6 * q^6 + 18 * q^9 + 6 * q^11 + 6 * q^14 + 18 * q^19 + 6 * q^21 + 12 * q^24 - 6 * q^26 + 36 * q^29 + 6 * q^31 + 12 * q^34 - 18 * q^36 + 24 * q^39 - 42 * q^41 + 18 * q^46 - 24 * q^49 + 18 * q^51 + 36 * q^54 - 12 * q^56 - 54 * q^59 - 30 * q^61 + 6 * q^64 - 6 * q^66 + 12 * q^69 + 12 * q^71 - 36 * q^74 - 24 * q^79 - 36 * q^81 + 12 * q^84 + 18 * q^86 - 6 * q^91 - 36 * q^94 - 12 * q^96 + 18 * q^99

Introduction

L-functions

Modular forms

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