LMFDB - Embedded newform 234.2.y.a.149.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(11,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			149.13
Character	$\chi$	$=$	234.149
Dual form			234.2.y.a.11.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +(1.25580 + 1.19288i) q^{3} +1.00000i q^{4} +(0.650628 - 0.174335i) q^{5} +(0.0444876 + 1.73148i) q^{6} +(-1.73068 + 0.463733i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.154059 + 2.99604i) q^{9} +(0.583337 + 0.336790i) q^{10} +(0.696978 - 0.696978i) q^{11} +(-1.19288 + 1.25580i) q^{12} +(0.391864 - 3.58419i) q^{13} +(-1.55168 - 0.895864i) q^{14} +(1.02502 + 0.557194i) q^{15} -1.00000 q^{16} +(-1.20946 - 2.09485i) q^{17} +(-2.00959 + 2.22746i) q^{18} +(6.33213 + 1.69669i) q^{19} +(0.174335 + 0.650628i) q^{20} +(-2.72656 - 1.48214i) q^{21} +0.985676 q^{22} +(-3.16302 - 5.47852i) q^{23} +(-1.73148 + 0.0444876i) q^{24} +(-3.93720 + 2.27315i) q^{25} +(2.81150 - 2.25732i) q^{26} +(-3.38046 + 3.94620i) q^{27} +(-0.463733 - 1.73068i) q^{28} -4.29257i q^{29} +(0.330803 + 1.11879i) q^{30} +(1.49861 + 5.59289i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.70668 - 0.0438503i) q^{33} +(0.626062 - 2.33650i) q^{34} +(-1.04518 + 0.603436i) q^{35} +(-2.99604 + 0.154059i) q^{36} +(6.83094 - 1.83034i) q^{37} +(3.27775 + 5.67724i) q^{38} +(4.76763 - 4.03358i) q^{39} +(-0.336790 + 0.583337i) q^{40} +(1.28786 - 4.80634i) q^{41} +(-0.879938 - 2.97600i) q^{42} +(-0.772736 - 0.446139i) q^{43} +(0.696978 + 0.696978i) q^{44} +(0.622551 + 1.92245i) q^{45} +(1.63730 - 6.11049i) q^{46} +(-3.66378 - 0.981707i) q^{47} +(-1.25580 - 1.19288i) q^{48} +(-3.28199 + 1.89486i) q^{49} +(-4.39138 - 1.17667i) q^{50} +(0.980069 - 4.07345i) q^{51} +(3.58419 + 0.391864i) q^{52} -9.00014i q^{53} +(-5.18073 + 0.400036i) q^{54} +(0.331966 - 0.574981i) q^{55} +(0.895864 - 1.55168i) q^{56} +(5.92793 + 9.68420i) q^{57} +(3.03531 - 3.03531i) q^{58} +(-3.33959 + 3.33959i) q^{59} +(-0.557194 + 1.02502i) q^{60} +(-2.38199 + 4.12572i) q^{61} +(-2.89509 + 5.01445i) q^{62} +(-1.65599 - 5.11374i) q^{63} -1.00000i q^{64} +(-0.369894 - 2.40029i) q^{65} +(1.23781 + 1.17580i) q^{66} +(10.6950 + 2.86571i) q^{67} +(2.09485 - 1.20946i) q^{68} +(2.56311 - 10.6530i) q^{69} +(-1.16575 - 0.312361i) q^{70} +(-1.70900 + 6.37808i) q^{71} +(-2.22746 - 2.00959i) q^{72} +(-8.01788 - 8.01788i) q^{73} +(6.12445 + 3.53595i) q^{74} +(-7.65593 - 1.84201i) q^{75} +(-1.69669 + 6.33213i) q^{76} +(-0.883031 + 1.52946i) q^{77} +(6.22339 + 0.519052i) q^{78} +(-0.807117 - 1.39797i) q^{79} +(-0.650628 + 0.174335i) q^{80} +(-8.95253 + 0.923132i) q^{81} +(4.30925 - 2.48795i) q^{82} +(-1.95885 + 7.31055i) q^{83} +(1.48214 - 2.72656i) q^{84} +(-1.15211 - 1.15211i) q^{85} +(-0.230939 - 0.861875i) q^{86} +(5.12054 - 5.39061i) q^{87} +0.985676i q^{88} +(-0.440877 - 1.64537i) q^{89} +(-0.919169 + 1.79959i) q^{90} +(0.983920 + 6.38480i) q^{91} +(5.47852 - 3.16302i) q^{92} +(-4.78971 + 8.81121i) q^{93} +(-1.89651 - 3.28485i) q^{94} +4.41566 q^{95} +(-0.0444876 - 1.73148i) q^{96} +(-0.497183 - 1.85551i) q^{97} +(-3.66058 - 0.980849i) q^{98} +(2.19555 + 1.98080i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	1.25580	+	1.19288i	0.725035	+	0.688712i
$3$	1.25580	+	1.19288i	0.725035	+	0.688712i
$4$			1.00000i			0.500000i
$5$	0.650628	−	0.174335i	0.290970	−	0.0779651i	−0.110382	−	0.993889i	$-0.535207\pi$
$5$	0.650628	−	0.174335i	0.290970	−	0.0779651i	0.401351	+	0.915924i	$0.368541\pi$
$6$	0.0444876	+	1.73148i	0.0181620	+	0.706873i
$7$	−1.73068	+	0.463733i	−0.654134	+	0.175275i	−0.570597	−	0.821230i	$-0.693288\pi$
$7$	−1.73068	+	0.463733i	−0.654134	+	0.175275i	−0.0835368	+	0.996505i	$0.526622\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.154059	+	2.99604i	0.0513529	+	0.998681i
$10$	0.583337	+	0.336790i	0.184467	+	0.106502i
$11$	0.696978	−	0.696978i	0.210147	−	0.210147i	−0.594183	−	0.804330i	$-0.702525\pi$
$11$	0.696978	−	0.696978i	0.210147	−	0.210147i	0.804330	+	0.594183i	$0.202525\pi$
$12$	−1.19288	+	1.25580i	−0.344356	+	0.362518i
$13$	0.391864	−	3.58419i	0.108684	−	0.994076i
$13$	0.391864	−	3.58419i	0.108684	−	0.994076i
$14$	−1.55168	−	0.895864i	−0.414704	−	0.239430i
$15$	1.02502	+	0.557194i	0.264659	+	0.143867i
$16$	−1.00000			−0.250000
$17$	−1.20946	−	2.09485i	−0.293337	−	0.508075i	0.681260	−	0.732042i	$-0.261432\pi$
$17$	−1.20946	−	2.09485i	−0.293337	−	0.508075i	−0.974597	+	0.223967i	$0.928099\pi$
$18$	−2.00959	+	2.22746i	−0.473664	+	0.525017i
$19$	6.33213	+	1.69669i	1.45269	+	0.389247i	0.896959	−	0.442114i	$-0.145771\pi$
$19$	6.33213	+	1.69669i	1.45269	+	0.389247i	0.555732	+	0.831361i	$0.312438\pi$
$20$	0.174335	+	0.650628i	0.0389826	+	0.145485i
$21$	−2.72656	−	1.48214i	−0.594984	−	0.323429i
$22$	0.985676			0.210147
$23$	−3.16302	−	5.47852i	−0.659536	−	1.14235i	−0.980736	−	0.195338i	$-0.937420\pi$
$23$	−3.16302	−	5.47852i	−0.659536	−	1.14235i	0.321200	−	0.947011i	$-0.395914\pi$
$24$	−1.73148	+	0.0444876i	−0.353437	+	0.00908098i
$25$	−3.93720	+	2.27315i	−0.787441	+	0.454629i
$26$	2.81150	−	2.25732i	0.551380	−	0.442696i
$27$	−3.38046	+	3.94620i	−0.650570	+	0.759446i
$28$	−0.463733	−	1.73068i	−0.0876374	−	0.327067i
$29$		−	4.29257i		−	0.797111i	−0.917144	−	0.398555i	$-0.869512\pi$
$29$		−	4.29257i		−	0.797111i	0.917144	−	0.398555i	$-0.130488\pi$
$30$	0.330803	+	1.11879i	0.0603961	+	0.204263i
$31$	1.49861	+	5.59289i	0.269158	+	1.00451i	0.959656	+	0.281178i	$0.0907250\pi$
$31$	1.49861	+	5.59289i	0.269158	+	1.00451i	−0.690498	+	0.723335i	$0.742608\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	1.70668	−	0.0438503i	0.297094	−	0.00763336i
$34$	0.626062	−	2.33650i	0.107369	−	0.400706i
$35$	−1.04518	+	0.603436i	−0.176668	+	0.101999i
$36$	−2.99604	+	0.154059i	−0.499340	+	0.0256764i
$37$	6.83094	−	1.83034i	1.12300	−	0.300907i	0.350902	−	0.936412i	$-0.385875\pi$
$37$	6.83094	−	1.83034i	1.12300	−	0.300907i	0.772096	+	0.635505i	$0.219208\pi$
$38$	3.27775	+	5.67724i	0.531722	+	0.920969i
$39$	4.76763	−	4.03358i	0.763431	−	0.645889i
$40$	−0.336790	+	0.583337i	−0.0532512	+	0.0922337i
$41$	1.28786	−	4.80634i	0.201129	−	0.750625i	−0.789465	−	0.613795i	$-0.789642\pi$
$41$	1.28786	−	4.80634i	0.201129	−	0.750625i	0.990595	−	0.136830i	$-0.0436913\pi$
$42$	−0.879938	−	2.97600i	−0.135777	−	0.459207i
$43$	−0.772736	−	0.446139i	−0.117841	−	0.0680356i	0.439921	−	0.898037i	$-0.355006\pi$
$43$	−0.772736	−	0.446139i	−0.117841	−	0.0680356i	−0.557762	+	0.830001i	$0.688340\pi$
$44$	0.696978	+	0.696978i	0.105073	+	0.105073i
$45$	0.622551	+	1.92245i	0.0928044	+	0.286582i
$46$	1.63730	−	6.11049i	0.241407	−	0.900943i
$47$	−3.66378	−	0.981707i	−0.534417	−	0.143197i	−0.0184899	−	0.999829i	$-0.505886\pi$
$47$	−3.66378	−	0.981707i	−0.534417	−	0.143197i	−0.515927	+	0.856632i	$0.672553\pi$
$48$	−1.25580	−	1.19288i	−0.181259	−	0.172178i
$49$	−3.28199	+	1.89486i	−0.468855	+	0.270694i
$50$	−4.39138	−	1.17667i	−0.621035	−	0.166406i
$51$	0.980069	−	4.07345i	0.137237	−	0.570397i
$52$	3.58419	+	0.391864i	0.497038	+	0.0543418i
$53$		−	9.00014i		−	1.23626i	−0.786074	−	0.618132i	$-0.787890\pi$
$53$		−	9.00014i		−	1.23626i	0.786074	−	0.618132i	$-0.212110\pi$
$54$	−5.18073	+	0.400036i	−0.705008	+	0.0544380i
$55$	0.331966	−	0.574981i	0.0447622	−	0.0775305i
$56$	0.895864	−	1.55168i	0.119715	−	0.207352i
$57$	5.92793	+	9.68420i	0.785173	+	1.28270i
$58$	3.03531	−	3.03531i	0.398555	−	0.398555i
$59$	−3.33959	+	3.33959i	−0.434777	+	0.434777i	−0.890250	−	0.455473i	$-0.849470\pi$
$59$	−3.33959	+	3.33959i	−0.434777	+	0.434777i	0.455473	+	0.890250i	$0.349470\pi$
$60$	−0.557194	+	1.02502i	−0.0719334	+	0.132329i
$61$	−2.38199	+	4.12572i	−0.304982	+	0.528245i	−0.977257	−	0.212057i	$-0.931984\pi$
$61$	−2.38199	+	4.12572i	−0.304982	+	0.528245i	0.672275	+	0.740301i	$0.265317\pi$
$62$	−2.89509	+	5.01445i	−0.367677	+	0.636835i
$63$	−1.65599	−	5.11374i	−0.208635	−	0.644270i
$64$		−	1.00000i		−	0.125000i
$65$	−0.369894	−	2.40029i	−0.0458797	−	0.297720i
$66$	1.23781	+	1.17580i	0.152364	+	0.144730i
$67$	10.6950	+	2.86571i	1.30660	+	0.350102i	0.843942	−	0.536434i	$-0.180229\pi$
$67$	10.6950	+	2.86571i	1.30660	+	0.350102i	0.462658	+	0.886537i	$0.346896\pi$
$68$	2.09485	−	1.20946i	0.254037	−	0.146669i
$69$	2.56311	−	10.6530i	0.308562	−	1.28247i
$70$	−1.16575	−	0.312361i	−0.139334	−	0.0373343i
$71$	−1.70900	+	6.37808i	−0.202821	+	0.756939i	0.787281	+	0.616594i	$0.211488\pi$
$71$	−1.70900	+	6.37808i	−0.202821	+	0.756939i	−0.990103	+	0.140345i	$0.955179\pi$
$72$	−2.22746	−	2.00959i	−0.262508	−	0.236832i
$73$	−8.01788	−	8.01788i	−0.938421	−	0.938421i	0.0597896	−	0.998211i	$-0.480957\pi$
$73$	−8.01788	−	8.01788i	−0.938421	−	0.938421i	−0.998211	+	0.0597896i	$0.980957\pi$
$74$	6.12445	+	3.53595i	0.711953	+	0.411046i
$75$	−7.65593	−	1.84201i	−0.884031	−	0.212697i
$76$	−1.69669	+	6.33213i	−0.194624	+	0.726346i
$77$	−0.883031	+	1.52946i	−0.100631	+	0.174298i
$78$	6.22339	+	0.519052i	0.704660	+	0.0587711i
$79$	−0.807117	−	1.39797i	−0.0908078	−	0.157284i	0.817043	−	0.576576i	$-0.195612\pi$
$79$	−0.807117	−	1.39797i	−0.0908078	−	0.157284i	−0.907851	+	0.419292i	$0.862278\pi$
$80$	−0.650628	+	0.174335i	−0.0727424	+	0.0194913i
$81$	−8.95253	+	0.923132i	−0.994726	+	0.102570i
$82$	4.30925	−	2.48795i	0.475877	−	0.274748i
$83$	−1.95885	+	7.31055i	−0.215012	+	0.802437i	0.771150	+	0.636653i	$0.219682\pi$
$83$	−1.95885	+	7.31055i	−0.215012	+	0.802437i	−0.986162	+	0.165783i	$0.946985\pi$
$84$	1.48214	−	2.72656i	0.161715	−	0.297492i
$85$	−1.15211	−	1.15211i	−0.124964	−	0.124964i
$86$	−0.230939	−	0.861875i	−0.0249028	−	0.0929384i
$87$	5.12054	−	5.39061i	0.548979	−	0.577934i
$88$			0.985676i			0.105073i
$89$	−0.440877	−	1.64537i	−0.0467329	−	0.174409i	0.938615	−	0.344967i	$-0.112110\pi$
$89$	−0.440877	−	1.64537i	−0.0467329	−	0.174409i	−0.985348	+	0.170557i	$0.945443\pi$
$90$	−0.919169	+	1.79959i	−0.0968889	+	0.189693i
$91$	0.983920	+	6.38480i	0.103143	+	0.669309i
$92$	5.47852	−	3.16302i	0.571175	−	0.329768i
$93$	−4.78971	+	8.81121i	−0.496670	+	0.913679i
$94$	−1.89651	−	3.28485i	−0.195610	−	0.338807i
$95$	4.41566			0.453037
$96$	−0.0444876	−	1.73148i	−0.00454049	−	0.176718i
$97$	−0.497183	−	1.85551i	−0.0504812	−	0.188399i	0.936081	−	0.351785i	$-0.114425\pi$
$97$	−0.497183	−	1.85551i	−0.0504812	−	0.188399i	−0.986562	+	0.163386i	$0.947758\pi$
$98$	−3.66058	−	0.980849i	−0.369774	−	0.0990807i
$99$	2.19555	+	1.98080i	0.220661	+	0.199078i
$100$	−2.27315	−	3.93720i	−0.227315	−	0.393720i
$101$	−14.8919			−1.48180			−0.740902	−	0.671613i	$-0.765602\pi$
$101$	−14.8919			−1.48180			−0.740902	+	0.671613i	$0.765602\pi$
$102$	3.57338	−	2.18735i	0.353817	−	0.216580i
$103$	9.08751	+	5.24668i	0.895419	+	0.516971i	0.875711	−	0.482835i	$-0.160393\pi$
$103$	9.08751	+	5.24668i	0.895419	+	0.516971i	0.0197081	+	0.999806i	$0.493726\pi$
$104$	2.25732	+	2.81150i	0.221348	+	0.275690i
$105$	−2.03237	−	0.488986i	−0.198339	−	0.0477202i
$106$	6.36406	−	6.36406i	0.618132	−	0.618132i
$107$	−1.87899	−	1.08484i	−0.181649	−	0.104875i	0.406418	−	0.913687i	$-0.366778\pi$
$107$	−1.87899	−	1.08484i	−0.181649	−	0.104875i	−0.588067	+	0.808812i	$0.700111\pi$
$108$	−3.94620	−	3.38046i	−0.379723	−	0.325285i
$109$	−8.28528	+	8.28528i	−0.793586	+	0.793586i	−0.982075	−	0.188489i	$-0.939641\pi$
$109$	−8.28528	+	8.28528i	−0.793586	+	0.793586i	0.188489	+	0.982075i	$0.439641\pi$
$110$	0.641308	−	0.171838i	0.0611463	−	0.0163841i
$111$	10.7617	+	5.84997i	1.02145	+	0.555254i
$112$	1.73068	−	0.463733i	0.163534	−	0.0438187i
$113$			11.0857i			1.04285i	0.853296	+	0.521427i	$0.174600\pi$
$113$			11.0857i			1.04285i	−0.853296	+	0.521427i	$0.825400\pi$
$114$	−2.65608	+	11.0394i	−0.248765	+	1.03394i
$115$	−3.01305	−	3.01305i	−0.280968	−	0.280968i
$116$	4.29257			0.398555
$117$	10.7988	+	0.621865i	0.998346	+	0.0574915i
$118$	−4.72289			−0.434777
$119$	3.06463	+	3.06463i	0.280934	+	0.280934i
$120$	−1.11879	+	0.330803i	−0.102131	+	0.0301980i
$121$			10.0284i			0.911677i
$122$	−4.60165	+	1.23301i	−0.416614	+	0.111631i
$123$	7.35070	−	4.49954i	0.662790	−	0.405710i
$124$	−5.59289	+	1.49861i	−0.502256	+	0.134579i
$125$	−4.54683	+	4.54683i	−0.406681	+	0.406681i
$126$	2.44500	−	4.78692i	0.217818	−	0.426453i
$127$	4.33197	+	2.50106i	0.384400	+	0.221933i	0.679731	−	0.733462i	$-0.262097\pi$
$127$	4.33197	+	2.50106i	0.384400	+	0.221933i	−0.295331	+	0.955395i	$0.595430\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−0.438208	−	1.48204i	−0.0385821	−	0.130487i
$130$	1.43571	−	1.95882i	0.125920	−	0.171800i
$131$	19.0361	+	10.9905i	1.66319	+	0.960242i	0.971178	+	0.238354i	$0.0766080\pi$
$131$	19.0361	+	10.9905i	1.66319	+	0.960242i	0.692010	+	0.721888i	$0.256725\pi$
$132$	0.0438503	+	1.70668i	0.00381668	+	0.148547i
$133$	−11.7457			−1.01848
$134$	5.53613	+	9.58886i	0.478249	+	0.828351i
$135$	−1.51146	+	3.15684i	−0.130086	+	0.271698i
$136$	2.33650	+	0.626062i	0.200353	+	0.0536844i
$137$	3.25829	+	12.1601i	0.278374	+	1.03891i	0.953546	+	0.301246i	$0.0974026\pi$
$137$	3.25829	+	12.1601i	0.278374	+	1.03891i	−0.675172	+	0.737660i	$0.735931\pi$
$138$	9.34522	−	5.72044i	0.795518	−	0.486956i
$139$	−19.6965			−1.67063			−0.835316	−	0.549770i	$-0.814715\pi$
$139$	−19.6965			−1.67063			−0.835316	+	0.549770i	$0.814715\pi$
$140$	−0.603436	−	1.04518i	−0.0509996	−	0.0883340i
$141$	−3.42991	−	5.60329i	−0.288850	−	0.471882i
$142$	−5.71843	+	3.30154i	−0.479880	+	0.277059i
$143$	−2.22498	−	2.77122i	−0.186062	−	0.231741i
$144$	−0.154059	−	2.99604i	−0.0128382	−	0.249670i
$145$	−0.748347	−	2.79287i	−0.0621468	−	0.231935i
$146$		−	11.3390i		−	0.938421i
$147$	−6.38185	−	1.53547i	−0.526366	−	0.126643i
$148$	1.83034	+	6.83094i	0.150453	+	0.561499i
$149$	−6.83755	−	6.83755i	−0.560154	−	0.560154i	0.369197	−	0.929351i	$-0.379633\pi$
$149$	−6.83755	−	6.83755i	−0.560154	−	0.560154i	−0.929351	+	0.369197i	$0.879633\pi$
$150$	−4.11106	−	6.71606i	−0.335667	−	0.548364i
$151$	−1.28698	+	4.80308i	−0.104733	+	0.390869i	−0.998315	−	0.0580316i	$-0.981518\pi$
$151$	−1.28698	+	4.80308i	−0.104733	+	0.390869i	0.893582	+	0.448900i	$0.148184\pi$
$152$	−5.67724	+	3.27775i	−0.460485	+	0.265861i
$153$	6.08992	−	3.94632i	0.492341	−	0.319041i
$154$	−1.70589	+	0.457091i	−0.137464	+	0.0368334i
$155$	1.95008	+	3.37763i	0.156634	+	0.271298i
$156$	4.03358	+	4.76763i	0.322945	+	0.381716i
$157$	−4.86181	+	8.42090i	−0.388015	+	0.672061i	−0.992182	−	0.124796i	$-0.960172\pi$
$157$	−4.86181	+	8.42090i	−0.388015	+	0.672061i	0.604168	+	0.796857i	$0.293506\pi$
$158$	0.417795	−	1.55923i	0.0332380	−	0.124046i
$159$	10.7361	−	11.3024i	0.851429	−	0.896335i
$160$	−0.583337	−	0.336790i	−0.0461169	−	0.0266256i
$161$	8.01474	+	8.01474i	0.631650	+	0.631650i
$162$	−6.98315	−	5.67764i	−0.548648	−	0.446078i
$163$	1.24717	−	4.65451i	0.0976861	−	0.364570i	−0.899727	−	0.436453i	$-0.856234\pi$
$163$	1.24717	−	4.65451i	0.0976861	−	0.364570i	0.997413	+	0.0718838i	$0.0229011\pi$
$164$	4.80634	+	1.28786i	0.375312	+	0.100565i
$165$	1.10277	−	0.326064i	0.0858503	−	0.0253841i
$166$	−6.55446	+	3.78422i	−0.508724	+	0.293712i
$167$	13.6676	+	3.66224i	1.05763	+	0.283392i	0.745403	−	0.666614i	$-0.232257\pi$
$167$	13.6676	+	3.66224i	1.05763	+	0.283392i	0.312231	+	0.950006i	$0.398924\pi$
$168$	2.97600	−	0.879938i	0.229603	−	0.0678887i
$169$	−12.6929	−	2.80903i	−0.976376	−	0.216079i
$170$		−	1.62934i		−	0.124964i
$171$	−4.10784	+	19.2327i	−0.314134	+	1.47076i
$172$	0.446139	−	0.772736i	0.0340178	−	0.0589206i
$173$	11.5989	−	20.0900i	0.881852	−	1.52741i	0.0325714	−	0.999469i	$-0.489630\pi$
$173$	11.5989	−	20.0900i	0.881852	−	1.52741i	0.849280	−	0.527942i	$-0.177036\pi$
$174$	7.43250	−	0.190966i	0.563456	−	0.0144771i
$175$	5.75989	−	5.75989i	0.435407	−	0.435407i
$176$	−0.696978	+	0.696978i	−0.0525367	+	0.0525367i
$177$	−8.17759	+	0.210110i	−0.614665	+	0.0157928i
$178$	0.851709	−	1.47520i	0.0638383	−	0.110571i
$179$	−2.78545	+	4.82455i	−0.208194	+	0.360603i	−0.951146	−	0.308742i	$-0.900092\pi$
$179$	−2.78545	+	4.82455i	−0.208194	+	0.360603i	0.742951	+	0.669345i	$0.233425\pi$
$180$	−1.92245	+	0.622551i	−0.143291	+	0.0464022i
$181$		−	20.8410i		−	1.54910i	−0.632514	−	0.774549i	$-0.717977\pi$
$181$		−	20.8410i		−	1.54910i	0.632514	−	0.774549i	$-0.282023\pi$
$182$	−3.81900	+	5.21047i	−0.283083	+	0.386226i
$183$	−7.91281	+	2.33964i	−0.584931	+	0.172951i
$184$	6.11049	+	1.63730i	0.450471	+	0.120703i
$185$	4.12531	−	2.38175i	0.303298	−	0.175109i
$186$	−9.61730	+	2.84363i	−0.705175	+	0.208505i
$187$	−2.30303	−	0.617094i	−0.168414	−	0.0451264i
$188$	0.981707	−	3.66378i	0.0715983	−	0.267209i
$189$	4.02050	−	8.39722i	0.292448	−	0.610808i
$190$	3.12234	+	3.12234i	0.226518	+	0.226518i
$191$	−15.6514	−	9.03635i	−1.13250	−	0.653847i	−0.187935	−	0.982181i	$-0.560179\pi$
$191$	−15.6514	−	9.03635i	−1.13250	−	0.653847i	−0.944562	+	0.328334i	$0.893513\pi$
$192$	1.19288	−	1.25580i	0.0860889	−	0.0906294i
$193$	1.90556	−	7.11166i	0.137165	−	0.511908i	−0.862814	−	0.505521i	$-0.831300\pi$
$193$	1.90556	−	7.11166i	0.137165	−	0.511908i	0.999980	−	0.00638720i	$-0.00203312\pi$
$194$	0.960483	−	1.66361i	0.0689587	−	0.119440i
$195$	2.39876	−	3.45552i	0.171779	−	0.247455i
$196$	−1.89486	−	3.28199i	−0.135347	−	0.234428i
$197$	23.6473	−	6.33628i	1.68480	−	0.451441i	0.715761	−	0.698345i	$-0.246080\pi$
$197$	23.6473	−	6.33628i	1.68480	−	0.451441i	0.969040	+	0.246904i	$0.0794132\pi$
$198$	0.151852	+	2.95313i	0.0107916	+	0.209869i
$199$	−6.97794	+	4.02871i	−0.494653	+	0.285588i	−0.726503	−	0.687164i	$-0.758856\pi$
$199$	−6.97794	+	4.02871i	−0.494653	+	0.285588i	0.231850	+	0.972752i	$0.425522\pi$
$200$	1.17667	−	4.39138i	0.0832029	−	0.310517i
$201$	10.0123	+	16.3566i	0.706212	+	1.15371i
$202$	−10.5302	−	10.5302i	−0.740902	−	0.740902i
$203$	1.99061	+	7.42905i	0.139713	+	0.521417i
$204$	4.07345	+	0.980069i	0.285198	+	0.0686186i
$205$		−	3.35166i		−	0.234090i
$206$	2.71588	+	10.1358i	0.189224	+	0.706195i
$207$	15.9266	−	10.3206i	1.10697	−	0.717329i
$208$	−0.391864	+	3.58419i	−0.0271709	+	0.248519i
$209$	5.59591	−	3.23080i	0.387077	−	0.223479i
$210$	−1.09133	−	1.78287i	−0.0753092	−	0.123029i
$211$	7.04091	+	12.1952i	0.484716	+	0.839553i	0.999846	−	0.0175594i	$-0.00558961\pi$
$211$	7.04091	+	12.1952i	0.484716	+	0.839553i	−0.515130	+	0.857112i	$0.672256\pi$
$212$	9.00014			0.618132
$213$	−9.75447	+	5.97094i	−0.668365	+	0.409122i
$214$	−0.561553	−	2.09574i	−0.0383870	−	0.143262i
$215$	−0.580542	−	0.155556i	−0.0395926	−	0.0106088i
$216$	−0.400036	−	5.18073i	−0.0272190	−	0.352504i
$217$	−5.18722	−	8.98452i	−0.352131	−	0.609909i
$218$	−11.7172			−0.793586
$219$	−0.504444	−	19.6332i	−0.0340872	−	1.32669i
$220$	0.574981	+	0.331966i	0.0387652	+	0.0223811i
$221$	−7.98227	+	3.51404i	−0.536946	+	0.236380i
$222$	3.47309	+	11.7462i	0.233099	+	0.788353i
$223$	16.7879	−	16.7879i	1.12420	−	1.12420i	0.133096	−	0.991103i	$-0.457508\pi$
$223$	16.7879	−	16.7879i	1.12420	−	1.12420i	0.991103	−	0.133096i	$-0.0424918\pi$
$224$	1.55168	+	0.895864i	0.103676	+	0.0598574i
$225$	−7.41700	−	11.4458i	−0.494466	−	0.763055i
$226$	−7.83876	+	7.83876i	−0.521427	+	0.521427i
$227$	−23.1257	+	6.19651i	−1.53491	+	0.411277i	−0.924616	−	0.380901i	$-0.875614\pi$
$227$	−23.1257	+	6.19651i	−1.53491	+	0.411277i	−0.610291	+	0.792178i	$0.708947\pi$
$228$	−9.68420	+	5.92793i	−0.641352	+	0.392587i
$229$	−19.8362	+	5.31509i	−1.31081	+	0.351231i	−0.845529	−	0.533930i	$-0.820714\pi$
$229$	−19.8362	+	5.31509i	−1.31081	+	0.351231i	−0.465284	+	0.885161i	$0.654048\pi$
$230$		−	4.26110i		−	0.280968i
$231$	−2.93337	+	0.867334i	−0.193002	+	0.0570664i
$232$	3.03531	+	3.03531i	0.199278	+	0.199278i
$233$	2.79071			0.182825			0.0914126	−	0.995813i	$-0.470862\pi$
$233$	2.79071			0.182825			0.0914126	+	0.995813i	$0.470862\pi$
$234$	7.19615	+	8.07560i	0.470427	+	0.527919i
$235$	−2.55490			−0.166664
$236$	−3.33959	−	3.33959i	−0.217389	−	0.217389i
$237$	0.654036	−	2.71836i	0.0424842	−	0.176577i
$238$			4.33405i			0.280934i
$239$	7.58852	−	2.03334i	0.490861	−	0.131526i	−0.00489453	−	0.999988i	$-0.501558\pi$
$239$	7.58852	−	2.03334i	0.490861	−	0.131526i	0.495755	+	0.868462i	$0.334891\pi$
$240$	−1.02502	−	0.557194i	−0.0661647	−	0.0359667i
$241$	22.4869	−	6.02534i	1.44851	−	0.388126i	0.553002	−	0.833180i	$-0.313482\pi$
$241$	22.4869	−	6.02534i	1.44851	−	0.388126i	0.895504	+	0.445054i	$0.146815\pi$
$242$	−7.09118	+	7.09118i	−0.455838	+	0.455838i
$243$	−12.3438	−	9.52006i	−0.791853	−	0.610712i
$244$	−4.12572	−	2.38199i	−0.264122	−	0.152491i
$245$	−1.80501	+	1.80501i	−0.115318	+	0.115318i
$246$	8.37938	+	2.01607i	0.534250	+	0.128540i
$247$	8.56260	−	22.0307i	0.544825	−	1.40178i
$248$	−5.01445	−	2.89509i	−0.318418	−	0.183839i
$249$	−11.1806	+	6.84388i	−0.708539	+	0.433714i
$250$	−6.43019			−0.406681
$251$	−13.0241	−	22.5583i	−0.822071	−	1.42387i	−0.904138	−	0.427241i	$-0.859485\pi$
$251$	−13.0241	−	22.5583i	−0.822071	−	1.42387i	0.0820668	−	0.996627i	$-0.473848\pi$
$252$	5.11374	−	1.65599i	0.322135	−	0.104318i
$253$	−6.02296	−	1.61385i	−0.378660	−	0.101462i
$254$	1.29465	+	4.83168i	0.0812333	+	0.303167i
$255$	−0.0724851	−	2.82116i	−0.00453920	−	0.176668i
$256$	1.00000			0.0625000
$257$	−3.60078	−	6.23673i	−0.224610	−	0.389036i	0.731592	−	0.681743i	$-0.238778\pi$
$257$	−3.60078	−	6.23673i	−0.224610	−	0.389036i	−0.956202	+	0.292706i	$0.905444\pi$
$258$	0.738104	−	1.35782i	0.0459523	−	0.0845344i
$259$	−10.9733	+	6.33546i	−0.681851	+	0.393667i
$260$	2.40029	−	0.369894i	0.148860	−	0.0229398i
$261$	12.8607	−	0.661308i	0.796059	−	0.0409339i
$262$	5.68909	+	21.2320i	0.351473	+	1.31172i
$263$		−	11.4549i		−	0.706342i	−0.935559	−	0.353171i	$-0.885103\pi$
$263$		−	11.4549i		−	0.706342i	0.935559	−	0.353171i	$-0.114897\pi$
$264$	−1.17580	+	1.23781i	−0.0723652	+	0.0761819i
$265$	−1.56904	−	5.85574i	−0.0963855	−	0.359715i
$266$	−8.30546	−	8.30546i	−0.509240	−	0.509240i
$267$	1.40909	−	2.59217i	0.0862348	−	0.158638i
$268$	−2.86571	+	10.6950i	−0.175051	+	0.653300i
$269$	21.7795	−	12.5744i	1.32792	−	0.766674i	0.342941	−	0.939357i	$-0.388577\pi$
$269$	21.7795	−	12.5744i	1.32792	−	0.766674i	0.984977	+	0.172683i	$0.0552437\pi$
$270$	−3.30099	+	1.16346i	−0.200892	+	0.0708058i
$271$	6.17248	−	1.65391i	0.374952	−	0.100468i	−0.0664215	−	0.997792i	$-0.521158\pi$
$271$	6.17248	−	1.65391i	0.374952	−	0.100468i	0.441373	+	0.897324i	$0.354492\pi$
$272$	1.20946	+	2.09485i	0.0733343	+	0.127019i
$273$	−6.38072	+	9.19172i	−0.386178	+	0.556308i
$274$	−6.29452	+	10.9024i	−0.380266	+	0.658640i
$275$	−1.15981	+	4.32848i	−0.0699393	+	0.261017i
$276$	10.6530	+	2.56311i	0.641237	+	0.154281i
$277$	16.8380	+	9.72143i	1.01170	+	0.584104i	0.911688	−	0.410882i	$-0.134779\pi$
$277$	16.8380	+	9.72143i	1.01170	+	0.584104i	0.100010	+	0.994986i	$0.468113\pi$
$278$	−13.9275	−	13.9275i	−0.835316	−	0.835316i
$279$	−16.5257	+	5.35153i	−0.989365	+	0.320388i
$280$	0.312361	−	1.16575i	0.0186672	−	0.0696668i
$281$	28.7919	+	7.71478i	1.71758	+	0.460225i	0.977263	−	0.212030i	$-0.0680074\pi$
$281$	28.7919	+	7.71478i	1.71758	+	0.460225i	0.740320	+	0.672255i	$0.234674\pi$
$282$	1.53681	−	6.38743i	0.0915158	−	0.380366i
$283$	19.1183	−	11.0380i	1.13647	−	0.656139i	0.190914	−	0.981607i	$-0.438855\pi$
$283$	19.1183	−	11.0380i	1.13647	−	0.656139i	0.945553	+	0.325467i	$0.105522\pi$
$284$	−6.37808	−	1.70900i	−0.378470	−	0.101411i
$285$	5.54518	+	5.26736i	0.328468	+	0.312012i
$286$	0.386251	−	3.53285i	0.0228395	−	0.208902i
$287$			8.91545i			0.526262i
$288$	2.00959	−	2.22746i	0.118416	−	0.131254i
$289$	5.57442	−	9.65517i	0.327907	−	0.567951i
$290$	1.44570	−	2.50402i	0.0848941	−	0.147041i
$291$	1.58905	−	2.92323i	0.0931516	−	0.171363i
$292$	8.01788	−	8.01788i	0.469211	−	0.469211i
$293$	−6.70889	+	6.70889i	−0.391938	+	0.391938i	−0.875378	−	0.483440i	$-0.839387\pi$
$293$	−6.70889	+	6.70889i	−0.391938	+	0.391938i	0.483440	+	0.875378i	$0.339387\pi$
$294$	−3.42691	−	5.59839i	−0.199861	−	0.326505i
$295$	−1.59062	+	2.75504i	−0.0926096	+	0.160404i
$296$	−3.53595	+	6.12445i	−0.205523	+	0.355976i
$297$	0.394306	+	5.10652i	0.0228799	+	0.296310i
$298$		−	9.66976i		−	0.560154i
$299$	−20.8755	+	9.19005i	−1.20726	+	0.531475i
$300$	1.84201	−	7.65593i	0.106349	−	0.442015i
$301$	1.54425	+	0.413779i	0.0890088	+	0.0238498i
$302$	−4.30632	+	2.48626i	−0.247801	+	0.143068i
$303$	−18.7013	−	17.7643i	−1.07436	−	1.02054i
$304$	−6.33213	−	1.69669i	−0.363173	−	0.0973119i
$305$	−0.830529	+	3.09958i	−0.0475560	+	0.177481i
$306$	7.09669	+	1.51575i	0.405691	+	0.0866498i
$307$	3.35703	+	3.35703i	0.191596	+	0.191596i	0.796385	−	0.604790i	$-0.206743\pi$
$307$	3.35703	+	3.35703i	0.191596	+	0.191596i	−0.604790	+	0.796385i	$0.706743\pi$
$308$	−1.52946	−	0.883031i	−0.0871488	−	0.0503154i
$309$	5.15341	+	17.4291i	0.293167	+	0.991508i
$310$	−1.00943	+	3.76726i	−0.0573320	+	0.213966i
$311$	−10.5634	+	18.2964i	−0.598996	+	1.03749i	0.393973	+	0.919122i	$0.371100\pi$
$311$	−10.5634	+	18.2964i	−0.598996	+	1.03749i	−0.992970	+	0.118370i	$0.962233\pi$
$312$	−0.519052	+	6.22339i	−0.0293856	+	0.352330i
$313$	−5.16590	−	8.94760i	−0.291994	−	0.505748i	0.682287	−	0.731084i	$-0.260985\pi$
$313$	−5.16590	−	8.94760i	−0.291994	−	0.505748i	−0.974281	+	0.225336i	$0.927652\pi$
$314$	−9.39229	+	2.51666i	−0.530038	+	0.142023i
$315$	−1.96894	−	3.03844i	−0.110937	−	0.171197i
$316$	1.39797	−	0.807117i	0.0786419	−	0.0454039i
$317$	−4.33708	+	16.1862i	−0.243595	+	0.909108i	0.730490	+	0.682924i	$0.239292\pi$
$317$	−4.33708	+	16.1862i	−0.243595	+	0.909108i	−0.974084	+	0.226185i	$0.927375\pi$
$318$	15.5836	−	0.400394i	0.873882	−	0.0224530i
$319$	−2.99183	−	2.99183i	−0.167510	−	0.167510i
$320$	−0.174335	−	0.650628i	−0.00974564	−	0.0363712i
$321$	−1.06555	−	3.60376i	−0.0594733	−	0.201142i
$322$			11.3346i			0.631650i
$323$	−4.10416	−	15.3169i	−0.228361	−	0.852256i
$324$	−0.923132	−	8.95253i	−0.0512851	−	0.497363i
$325$	6.60454	+	15.0025i	0.366354	+	0.832187i
$326$	4.17312	−	2.40935i	0.231128	−	0.133442i
$327$	−20.2880	+	0.521267i	−1.12193	+	0.0288262i
$328$	2.48795	+	4.30925i	0.137374	+	0.237939i
$329$	6.79607			0.374679
$330$	1.01034	+	0.549212i	0.0556172	+	0.0302331i
$331$	3.81878	+	14.2519i	0.209899	+	0.783354i	0.987900	+	0.155091i	$0.0495671\pi$
$331$	3.81878	+	14.2519i	0.209899	+	0.783354i	−0.778001	+	0.628263i	$0.783766\pi$
$332$	−7.31055	−	1.95885i	−0.401218	−	0.107506i
$333$	6.53615	+	20.1838i	0.358179	+	1.10606i
$334$	7.07490	+	12.2541i	0.387121	+	0.670513i
$335$	7.45805			0.407477
$336$	2.72656	+	1.48214i	0.148746	+	0.0808573i
$337$	3.36489	+	1.94272i	0.183297	+	0.105827i	0.588841	−	0.808249i	$-0.299584\pi$
$337$	3.36489	+	1.94272i	0.183297	+	0.105827i	−0.405544	+	0.914076i	$0.632918\pi$
$338$	−6.98894	−	10.9615i	−0.380148	−	0.596228i
$339$	−13.2239	+	13.9214i	−0.718225	+	0.756106i
$340$	1.15211	−	1.15211i	0.0624822	−	0.0624822i
$341$	4.94262	+	2.85362i	0.267658	+	0.154532i
$342$	−16.5043	+	10.6949i	−0.892449	+	0.578315i
$343$	13.6699	−	13.6699i	0.738108	−	0.738108i
$344$	0.861875	−	0.230939i	0.0464692	−	0.0124514i
$345$	−0.189566	−	7.37800i	−0.0102059	−	0.397218i
$346$	22.4074	−	6.00406i	1.20463	−	0.322780i
$347$			32.3179i			1.73492i	0.497510	+	0.867459i	$0.334248\pi$
$347$			32.3179i			1.73492i	−0.497510	+	0.867459i	$0.665752\pi$
$348$	5.39061	+	5.12054i	0.288967	+	0.274490i
$349$	13.4101	+	13.4101i	0.717828	+	0.717828i	0.968160	−	0.250332i	$-0.0805399\pi$
$349$	13.4101	+	13.4101i	0.717828	+	0.717828i	−0.250332	+	0.968160i	$0.580540\pi$
$350$	8.14572			0.435407
$351$	12.8193	+	13.6626i	0.684241	+	0.729256i
$352$	−0.985676			−0.0525367
$353$	−13.8574	−	13.8574i	−0.737554	−	0.737554i	0.234550	−	0.972104i	$-0.424638\pi$
$353$	−13.8574	−	13.8574i	−0.737554	−	0.737554i	−0.972104	+	0.234550i	$0.924638\pi$
$354$	−5.93100	−	5.63386i	−0.315229	−	0.299436i
$355$			4.44770i			0.236059i
$356$	1.64537	−	0.440877i	0.0872047	−	0.0233664i
$357$	0.192811	+	7.50431i	0.0102046	+	0.397170i
$358$	−5.38108	+	1.44186i	−0.284399	+	0.0762045i
$359$	19.2085	−	19.2085i	1.01379	−	1.01379i	0.0138835	−	0.999904i	$-0.495581\pi$
$359$	19.2085	−	19.2085i	1.01379	−	1.01379i	0.999904	−	0.0138835i	$-0.00441940\pi$
$360$	−1.79959	−	0.919169i	−0.0948466	−	0.0484444i
$361$	20.7627	+	11.9873i	1.09277	+	0.630913i
$362$	14.7368	−	14.7368i	0.774549	−	0.774549i
$363$	−11.9628	+	12.5937i	−0.627882	+	0.660998i
$364$	−6.38480	+	0.983920i	−0.334654	+	0.0515714i
$365$	−6.61445	−	3.81886i	−0.346216	−	0.199888i
$366$	−7.24958	−	3.94082i	−0.378941	−	0.205990i
$367$	7.69429			0.401639			0.200819	−	0.979628i	$-0.435640\pi$
$367$	7.69429			0.401639			0.200819	+	0.979628i	$0.435640\pi$
$368$	3.16302	+	5.47852i	0.164884	+	0.285587i
$369$	14.5984	+	3.11801i	0.759963	+	0.162317i
$370$	4.60118	+	1.23288i	0.239204	+	0.0640945i
$371$	4.17366	+	15.5763i	0.216686	+	0.808683i
$372$	−8.81121	−	4.78971i	−0.456840	−	0.248335i
$373$	−16.0980			−0.833521			−0.416760	−	0.909016i	$-0.636835\pi$
$373$	−16.0980			−0.833521			−0.416760	+	0.909016i	$0.636835\pi$
$374$	−1.19213	−	2.06484i	−0.0616438	−	0.106770i
$375$	−11.1337	+	0.286063i	−0.574944	+	0.0147722i
$376$	3.28485	−	1.89651i	0.169403	−	0.0978051i
$377$	−15.3854	−	1.68210i	−0.792389	−	0.0866328i
$378$	8.78066	−	3.09481i	0.451628	−	0.159180i
$379$	6.71919	+	25.0764i	0.345142	+	1.28809i	0.892446	+	0.451153i	$0.148987\pi$
$379$	6.71919	+	25.0764i	0.345142	+	1.28809i	−0.547305	+	0.836933i	$0.684346\pi$
$380$			4.41566i			0.226518i
$381$	2.45660	+	8.30836i	0.125856	+	0.425650i
$382$	−4.67756	−	17.4569i	−0.239325	−	0.893172i
$383$	−22.2443	−	22.2443i	−1.13663	−	1.13663i	−0.989050	−	0.147581i	$-0.952851\pi$
$383$	−22.2443	−	22.2443i	−1.13663	−	1.13663i	−0.147581	−	0.989050i	$-0.547149\pi$
$384$	1.73148	−	0.0444876i	0.0883592	−	0.00227025i
$385$	−0.307887	+	1.14905i	−0.0156914	+	0.0585610i
$386$	6.37614	−	3.68127i	0.324537	−	0.187372i
$387$	1.21761	−	2.38388i	0.0618944	−	0.121179i
$388$	1.85551	−	0.497183i	0.0941993	−	0.0252406i
$389$	12.6984	+	21.9943i	0.643836	+	1.11516i	0.984569	+	0.174997i	$0.0559915\pi$
$389$	12.6984	+	21.9943i	0.643836	+	1.11516i	−0.340733	+	0.940160i	$0.610675\pi$
$390$	4.13960	−	0.747246i	0.209617	−	0.0378383i
$391$	−7.65110	+	13.2521i	−0.386933	+	0.670187i
$392$	0.980849	−	3.66058i	0.0495404	−	0.184887i
$393$	10.7951	+	36.5096i	0.544541	+	1.84167i
$394$	21.2016	+	12.2407i	1.06812	+	0.616680i
$395$	−0.768848	−	0.768848i	−0.0386850	−	0.0386850i
$396$	−1.98080	+	2.19555i	−0.0995389	+	0.110331i
$397$	0.337126	−	1.25817i	0.0169199	−	0.0631458i	−0.956950	−	0.290254i	$-0.906260\pi$
$397$	0.337126	−	1.25817i	0.0169199	−	0.0631458i	0.973870	+	0.227108i	$0.0729270\pi$
$398$	−7.78288	−	2.08542i	−0.390120	−	0.104532i
$399$	−14.7502	−	14.0112i	−0.738434	−	0.701439i
$400$	3.93720	−	2.27315i	0.196860	−	0.113657i
$401$	1.38859	+	0.372073i	0.0693431	+	0.0185804i	0.293324	−	0.956013i	$-0.405239\pi$
$401$	1.38859	+	0.372073i	0.0693431	+	0.0185804i	−0.223981	+	0.974594i	$0.571905\pi$
$402$	−4.48613	+	18.6456i	−0.223748	+	0.929960i
$403$	20.6332	−	3.17966i	1.02782	−	0.158390i
$404$		−	14.8919i		−	0.740902i
$405$	−5.66383	+	2.16136i	−0.281438	+	0.107399i
$406$	−3.84556	+	6.66071i	−0.190852	+	0.330565i
$407$	3.48530	−	6.03672i	0.172760	−	0.299229i
$408$	2.18735	+	3.57338i	0.108290	+	0.176908i
$409$	16.2435	−	16.2435i	0.803189	−	0.803189i	−0.180404	−	0.983593i	$-0.557741\pi$
$409$	16.2435	−	16.2435i	0.803189	−	0.803189i	0.983593	+	0.180404i	$0.0577405\pi$
$410$	2.36998	−	2.36998i	0.117045	−	0.117045i
$411$	−10.4138	+	19.1574i	−0.513676	+	0.944963i
$412$	−5.24668	+	9.08751i	−0.258485	+	0.447710i
$413$	4.23107	−	7.32842i	0.208197	−	0.360608i
$414$	18.5595	+	3.96405i	0.912151	+	0.194822i
$415$			5.09794i			0.250248i
$416$	−2.81150	+	2.25732i	−0.137845	+	0.110674i
$417$	−24.7348	−	23.4956i	−1.21127	−	1.15058i
$418$	6.24143	+	1.67239i	0.305278	+	0.0817991i
$419$	−5.72052	+	3.30274i	−0.279466	+	0.161350i	−0.633182	−	0.774003i	$-0.718251\pi$
$419$	−5.72052	+	3.30274i	−0.279466	+	0.161350i	0.353716	+	0.935353i	$0.384918\pi$
$420$	0.488986	−	2.03237i	0.0238601	−	0.0991693i
$421$	9.08681	+	2.43480i	0.442864	+	0.118665i	0.473359	−	0.880870i	$-0.343042\pi$
$421$	9.08681	+	2.43480i	0.442864	+	0.118665i	−0.0304944	+	0.999535i	$0.509708\pi$
$422$	−3.64464	+	13.6020i	−0.177418	+	0.662134i
$423$	2.37680	−	11.1281i	0.115564	−	0.541066i
$424$	6.36406	+	6.36406i	0.309066	+	0.309066i
$425$	9.52378	+	5.49855i	0.461971	+	0.266719i
$426$	−11.1195	−	2.67536i	−0.538744	−	0.129621i
$427$	2.20921	−	8.24490i	0.106911	−	0.398999i
$428$	1.08484	−	1.87899i	0.0524376	−	0.0908246i
$429$	0.511617	−	6.13424i	0.0247011	−	0.296164i
$430$	−0.300510	−	0.520499i	−0.0144919	−	0.0251007i
$431$	−1.92865	+	0.516780i	−0.0928998	+	0.0248924i	−0.304970	−	0.952362i	$-0.598646\pi$
$431$	−1.92865	+	0.516780i	−0.0928998	+	0.0248924i	0.212070	+	0.977255i	$0.431980\pi$
$432$	3.38046	−	3.94620i	0.162643	−	0.189862i
$433$	−27.7623	+	16.0286i	−1.33417	+	0.770285i	−0.985936	−	0.167122i	$-0.946553\pi$
$433$	−27.7623	+	16.0286i	−1.33417	+	0.770285i	−0.348236	+	0.937407i	$0.613219\pi$
$434$	2.68510	−	10.0209i	0.128889	−	0.481020i
$435$	2.39179	−	4.39997i	0.114678	−	0.210962i
$436$	−8.28528	−	8.28528i	−0.396793	−	0.396793i
$437$	−10.7333	−	40.0574i	−0.513445	−	1.91620i
$438$	13.5261	−	14.2395i	0.646302	−	0.680389i
$439$		−	26.1293i		−	1.24708i	−0.781790	−	0.623542i	$-0.785693\pi$
$439$		−	26.1293i		−	1.24708i	0.781790	−	0.623542i	$-0.214307\pi$
$440$	0.171838	+	0.641308i	0.00819206	+	0.0305732i
$441$	−6.18268	−	9.54105i	−0.294414	−	0.454336i
$442$	−8.12912	−	3.15952i	−0.386663	−	0.150283i
$443$	9.85727	−	5.69110i	0.468333	−	0.270392i	−0.247209	−	0.968962i	$-0.579513\pi$
$443$	9.85727	−	5.69110i	0.468333	−	0.270392i	0.715542	+	0.698570i	$0.246180\pi$
$444$	−5.84997	+	10.7617i	−0.277627	+	0.510726i
$445$	−0.573694	−	0.993667i	−0.0271957	−	0.0471043i
$446$	23.7416			1.12420
$447$	−0.430184	−	16.7430i	−0.0203470	−	0.791916i
$448$	0.463733	+	1.73068i	0.0219093	+	0.0817668i
$449$	13.3760	+	3.58409i	0.631253	+	0.169144i	0.560238	−	0.828331i	$-0.310710\pi$
$449$	13.3760	+	3.58409i	0.631253	+	0.169144i	0.0710148	+	0.997475i	$0.477376\pi$
$450$	2.84881	−	13.3380i	0.134294	−	0.628761i
$451$	−2.45231	−	4.24752i	−0.115475	−	0.200008i
$452$	−11.0857			−0.521427
$453$	−7.34570	+	4.49648i	−0.345131	+	0.211263i
$454$	−20.7339	−	11.9707i	−0.973092	−	0.561815i
$455$	1.75326	+	3.98260i	0.0821942	+	0.186707i
$456$	−11.0394	−	2.65608i	−0.516969	−	0.124382i
$457$	23.8139	−	23.8139i	1.11397	−	1.11397i	0.121357	−	0.992609i	$-0.461276\pi$
$457$	23.8139	−	23.8139i	1.11397	−	1.11397i	0.992609	−	0.121357i	$-0.0387244\pi$
$458$	−17.7846	−	10.2680i	−0.831022	−	0.479791i
$459$	12.3552	+	2.30878i	0.576692	+	0.107765i
$460$	3.01305	−	3.01305i	0.140484	−	0.140484i
$461$	8.68738	−	2.32778i	0.404612	−	0.108415i	−0.0507728	−	0.998710i	$-0.516168\pi$
$461$	8.68738	−	2.32778i	0.404612	−	0.108415i	0.455385	+	0.890295i	$0.349502\pi$
$462$	−2.68750	−	1.46091i	−0.125034	−	0.0679676i
$463$	−18.3164	+	4.90786i	−0.851234	+	0.228087i	−0.657956	−	0.753057i	$-0.728579\pi$
$463$	−18.3164	+	4.90786i	−0.851234	+	0.228087i	−0.193278	+	0.981144i	$0.561912\pi$
$464$			4.29257i			0.199278i
$465$	−1.58022	+	6.56783i	−0.0732808	+	0.304576i
$466$	1.97333	+	1.97333i	0.0914126	+	0.0914126i
$467$	−33.1417			−1.53362			−0.766808	−	0.641877i	$-0.778156\pi$
$467$	−33.1417			−1.53362			−0.766808	+	0.641877i	$0.778156\pi$
$468$	−0.621865	+	10.7988i	−0.0287457	+	0.499173i
$469$	−19.8385			−0.916056
$470$	−1.80659	−	1.80659i	−0.0833318	−	0.0833318i
$471$	−16.1506	+	4.77538i	−0.744180	+	0.220038i
$472$		−	4.72289i		−	0.217389i
$473$	−0.849529	+	0.227631i	−0.0390614	+	0.0104665i
$474$	2.38465	−	1.45970i	0.109530	−	0.0670462i
$475$	−28.7877	+	7.71365i	−1.32087	+	0.353926i
$476$	−3.06463	+	3.06463i	−0.140467	+	0.140467i
$477$	26.9648	−	1.38655i	1.23463	−	0.0634857i
$478$	6.80368	+	3.92811i	0.311193	+	0.179667i
$479$	−21.8028	+	21.8028i	−0.996195	+	0.996195i	−0.999993	−	0.00379781i	$-0.998791\pi$
$479$	−21.8028	+	21.8028i	−0.996195	+	0.996195i	0.00379781	+	0.999993i	$0.498791\pi$
$480$	−0.330803	−	1.11879i	−0.0150990	−	0.0510657i
$481$	−3.88351	−	25.2006i	−0.177073	−	1.14905i
$482$	20.1612	+	11.6401i	0.918316	+	0.530190i
$483$	0.504247	+	19.6255i	0.0229440	+	0.892993i
$484$	−10.0284			−0.455838
$485$	−0.646962	−	1.12057i	−0.0293770	−	0.0508825i
$486$	−1.99666	−	15.4601i	−0.0905703	−	0.701282i
$487$	−19.5417	−	5.23619i	−0.885520	−	0.237274i	−0.212733	−	0.977110i	$-0.568236\pi$
$487$	−19.5417	−	5.23619i	−0.885520	−	0.237274i	−0.672787	+	0.739836i	$0.734903\pi$
$488$	−1.23301	−	4.60165i	−0.0558156	−	0.208307i
$489$	7.11849	−	4.35740i	0.321909	−	0.197048i
$490$	−2.55267			−0.115318
$491$	−7.55120	−	13.0791i	−0.340781	−	0.590250i	0.643797	−	0.765196i	$-0.277358\pi$
$491$	−7.55120	−	13.0791i	−0.340781	−	0.590250i	−0.984578	+	0.174946i	$0.944025\pi$
$492$	4.49954	+	7.35070i	0.202855	+	0.331395i
$493$	−8.99228	+	5.19169i	−0.404992	+	0.233822i
$494$	21.6327	−	9.52340i	0.973303	−	0.428478i
$495$	1.77381	+	0.906002i	0.0797268	+	0.0407218i
$496$	−1.49861	−	5.59289i	−0.0672896	−	0.251128i
$497$		−	11.8309i		−	0.530689i
$498$	−12.7452	−	3.06649i	−0.571126	−	0.137413i
$499$	−10.8485	−	40.4871i	−0.485645	−	1.81245i	−0.577140	−	0.816645i	$-0.695831\pi$
$499$	−10.8485	−	40.4871i	−0.485645	−	1.81245i	0.0914956	−	0.995805i	$-0.470835\pi$
$500$	−4.54683	−	4.54683i	−0.203340	−	0.203340i
$501$	12.7952	+	20.9029i	0.571647	+	0.933875i
$502$	6.74174	−	25.1605i	0.300899	−	1.12297i
$503$	−10.9025	+	6.29458i	−0.486120	+	0.280661i	−0.722963	−	0.690886i	$-0.757220\pi$
$503$	−10.9025	+	6.29458i	−0.486120	+	0.280661i	0.236843	+	0.971548i	$0.423887\pi$
$504$	4.78692	+	2.44500i	0.213226	+	0.108909i
$505$	−9.68912	+	2.59619i	−0.431160	+	0.115529i
$506$	−3.11771	−	5.40004i	−0.138599	−	0.240061i
$507$	−12.5889	−	18.6687i	−0.559091	−	0.829107i
$508$	−2.50106	+	4.33197i	−0.110967	+	0.192200i
$509$	8.59675	−	32.0835i	0.381044	−	1.42208i	−0.463264	−	0.886220i	$-0.653322\pi$
$509$	8.59675	−	32.0835i	0.381044	−	1.42208i	0.844309	−	0.535857i	$-0.180011\pi$
$510$	1.94361	−	2.04612i	0.0860644	−	0.0906035i
$511$	17.5945	+	10.1582i	0.778335	+	0.449372i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−28.1010	+	19.2523i	−1.24069	+	0.850008i
$514$	1.86390	−	6.95616i	0.0822130	−	0.306823i
$515$	6.82727	+	1.82936i	0.300846	+	0.0806113i
$516$	1.48204	−	0.438208i	0.0652434	−	0.0192910i
$517$	−3.23780	+	1.86935i	−0.142398	+	0.0822137i
$518$	−12.2392	−	3.27948i	−0.537759	−	0.144092i
$519$	38.5309	−	11.3928i	1.69132	−	0.500086i
$520$	1.95882	+	1.43571i	0.0858998	+	0.0629600i
$521$			17.5549i			0.769094i	0.923105	+	0.384547i	$0.125642\pi$
$521$			17.5549i			0.769094i	−0.923105	+	0.384547i	$0.874358\pi$
$522$	9.56152	+	8.62629i	0.418496	+	0.377563i
$523$	−4.19432	+	7.26477i	−0.183405	+	0.317666i	−0.943038	−	0.332686i	$-0.892045\pi$
$523$	−4.19432	+	7.26477i	−0.183405	+	0.317666i	0.759633	+	0.650352i	$0.225379\pi$
$524$	−10.9905	+	19.0361i	−0.480121	+	0.831594i
$525$	14.1041	−	0.362383i	0.615555	−	0.0158157i
$526$	8.09986	−	8.09986i	0.353171	−	0.353171i
$527$	9.90373	−	9.90373i	0.431413	−	0.431413i
$528$	−1.70668	+	0.0438503i	−0.0742736	+	0.00190834i
$529$	−8.50943	+	14.7388i	−0.369975	+	0.640816i
$530$	3.03116	−	5.25012i	0.131665	−	0.228050i
$531$	−10.5200	−	9.49105i	−0.456531	−	0.411876i
$532$		−	11.7457i		−	0.509240i
$533$	−16.7222	−	6.49936i	−0.724319	−	0.281518i
$534$	2.82932	−	0.836568i	0.122437	−	0.0362018i
$535$	−1.41165	−	0.378251i	−0.0610310	−	0.0163532i
$536$	−9.58886	+	5.53613i	−0.414176	+	0.239124i
$537$	−9.25309	+	2.73594i	−0.399300	+	0.118064i
$538$	24.2918	+	6.50898i	1.04730	+	0.280622i
$539$	−0.966799	+	3.60814i	−0.0416430	+	0.155414i
$540$	−3.15684	−	1.51146i	−0.135849	−	0.0650430i
$541$	1.43745	+	1.43745i	0.0618007	+	0.0618007i	0.737332	−	0.675531i	$-0.236086\pi$
$541$	1.43745	+	1.43745i	0.0618007	+	0.0618007i	−0.675531	+	0.737332i	$0.736086\pi$
$542$	5.53410	+	3.19511i	0.237710	+	0.137242i
$543$	24.8608	−	26.1721i	1.06688	−	1.12315i
$544$	−0.626062	+	2.33650i	−0.0268422	+	0.100176i
$545$	−3.94622	+	6.83505i	−0.169037	+	0.292781i
$546$	−11.0114	+	1.98768i	−0.471243	+	0.0850649i
$547$	5.93332	+	10.2768i	0.253691	+	0.439405i	0.964539	−	0.263940i	$-0.0850222\pi$
$547$	5.93332	+	10.2768i	0.253691	+	0.439405i	−0.710848	+	0.703345i	$0.751689\pi$
$548$	−12.1601	+	3.25829i	−0.519453	+	0.139187i
$549$	−12.7278	−	6.50093i	−0.543210	−	0.277453i
$550$	−3.88080	+	2.24058i	−0.165478	+	0.0955388i
$551$	7.28317	−	27.1811i	0.310273	−	1.15796i
$552$	5.72044	+	9.34522i	0.243478	+	0.397759i
$553$	2.04514	+	2.04514i	0.0869683	+	0.0869683i
$554$	5.03218	+	18.7804i	0.213797	+	0.797901i
$555$	8.02170	+	1.93002i	0.340502	+	0.0819246i
$556$		−	19.6965i		−	0.835316i
$557$	9.18337	+	34.2728i	0.389112	+	1.45219i	0.831582	+	0.555402i	$0.187436\pi$
$557$	9.18337	+	34.2728i	0.389112	+	1.45219i	−0.442470	+	0.896783i	$0.645898\pi$
$558$	−15.4695	−	7.90130i	−0.654876	−	0.334489i
$559$	−1.90186	+	2.59481i	−0.0804400	+	0.109749i
$560$	1.04518	−	0.603436i	0.0441670	−	0.0254998i
$561$	−2.15602	−	3.52219i	−0.0910271	−	0.148707i
$562$	14.9038	+	25.8141i	0.628679	+	1.08890i
$563$	36.9752			1.55832			0.779159	−	0.626826i	$-0.215647\pi$
$563$	36.9752			1.55832			0.779159	+	0.626826i	$0.215647\pi$
$564$	5.60329	−	3.42991i	0.235941	−	0.144425i
$565$	1.93263	+	7.21266i	0.0813062	+	0.303439i
$566$	21.3237	+	5.71368i	0.896303	+	0.240164i
$567$	15.0658	−	5.74923i	0.632706	−	0.241445i
$568$	−3.30154	−	5.71843i	−0.138529	−	0.239940i
$569$	24.5310			1.02840			0.514198	−	0.857672i	$-0.328090\pi$
$569$	24.5310			1.02840			0.514198	+	0.857672i	$0.328090\pi$
$570$	0.196442	+	7.64562i	0.00822804	+	0.320240i
$571$	−7.42838	−	4.28878i	−0.310868	−	0.179480i	0.336447	−	0.941702i	$-0.390775\pi$
$571$	−7.42838	−	4.28878i	−0.310868	−	0.179480i	−0.647315	+	0.762223i	$0.724108\pi$
$572$	2.77122	−	2.22498i	0.115871	−	0.0930312i
$573$	−8.87571	−	30.0181i	−0.370788	−	1.25403i
$574$	−6.30417	+	6.30417i	−0.263131	+	0.263131i
$575$	24.9069	+	14.3800i	1.03869	+	0.599688i
$576$	2.99604	−	0.154059i	0.124835	−	0.00641911i
$577$	−0.991168	+	0.991168i	−0.0412629	+	0.0412629i	−0.727437	−	0.686174i	$-0.759289\pi$
$577$	−0.991168	+	0.991168i	−0.0412629	+	0.0412629i	0.686174	+	0.727437i	$0.259289\pi$
$578$	10.7689	−	2.88553i	0.447929	−	0.120022i
$579$	10.8764	−	6.65770i	0.452007	−	0.276684i
$580$	2.79287	−	0.748347i	0.115968	−	0.0310734i
$581$		−	13.5606i		−	0.562587i
$582$	3.19066	−	0.943408i	0.132257	−	0.0391055i
$583$	−6.27290	−	6.27290i	−0.259797	−	0.259797i
$584$	11.3390			0.469211
$585$	7.13439	−	1.47800i	0.294971	−	0.0611079i
$586$	−9.48781			−0.391938
$587$	−26.9762	−	26.9762i	−1.11343	−	1.11343i	−0.992684	−	0.120743i	$-0.961472\pi$
$587$	−26.9762	−	26.9762i	−1.11343	−	1.11343i	−0.120743	−	0.992684i	$-0.538528\pi$
$588$	1.53547	−	6.38185i	0.0633217	−	0.263183i
$589$			37.9576i			1.56402i
$590$	−3.07284	+	0.823366i	−0.126507	+	0.0338975i
$591$	37.2547	+	20.2514i	1.53245	+	0.833031i
$592$	−6.83094	+	1.83034i	−0.280750	+	0.0752267i
$593$	−22.4411	+	22.4411i	−0.921547	+	0.921547i	−0.997139	−	0.0755923i	$-0.975915\pi$
$593$	−22.4411	+	22.4411i	−0.921547	+	0.921547i	0.0755923	+	0.997139i	$0.475915\pi$
$594$	−3.33204	+	3.88967i	−0.136715	+	0.159595i
$595$	2.52821	+	1.45966i	0.103647	+	0.0598403i
$596$	6.83755	−	6.83755i	0.280077	−	0.280077i
$597$	−13.5687	−	3.26461i	−0.555329	−	0.133612i
$598$	−21.2596	−	8.26289i	−0.869369	−	0.337895i
$599$	12.9383	+	7.46992i	0.528644	+	0.305213i	0.740464	−	0.672096i	$-0.234606\pi$
$599$	12.9383	+	7.46992i	0.528644	+	0.305213i	−0.211820	+	0.977309i	$0.567939\pi$
$600$	6.71606	−	4.11106i	0.274182	−	0.167833i
$601$	−9.43517			−0.384869			−0.192434	−	0.981310i	$-0.561638\pi$
$601$	−9.43517			−0.384869			−0.192434	+	0.981310i	$0.561638\pi$
$602$	0.799360	+	1.38453i	0.0325795	+	0.0564293i
$603$	−6.93814	+	32.4841i	−0.282543	+	1.32285i
$604$	−4.80308	−	1.28698i	−0.195434	−	0.0523665i
$605$	1.74831	+	6.52479i	0.0710790	+	0.265270i
$606$	−0.662506	−	25.7851i	−0.0269125	−	1.04745i
$607$	8.22930			0.334017			0.167008	−	0.985955i	$-0.446589\pi$
$607$	8.22930			0.334017			0.167008	+	0.985955i	$0.446589\pi$
$608$	−3.27775	−	5.67724i	−0.132930	−	0.230242i
$609$	−6.36219	+	11.7040i	−0.257809	+	0.474268i
$610$	−2.77901	+	1.60446i	−0.112519	+	0.0649627i
$611$	−4.95433	+	12.7470i	−0.200431	+	0.515688i
$612$	3.94632	+	6.08992i	0.159521	+	0.246170i
$613$	−5.26589	−	19.6526i	−0.212687	−	0.793760i	−0.986968	−	0.160918i	$-0.948555\pi$
$613$	−5.26589	−	19.6526i	−0.212687	−	0.793760i	0.774280	−	0.632843i	$-0.218112\pi$
$614$			4.74755i			0.191596i
$615$	3.99814	−	4.20901i	0.161221	−	0.169724i
$616$	−0.457091	−	1.70589i	−0.0184167	−	0.0687321i
$617$	23.1593	+	23.1593i	0.932360	+	0.932360i	0.997853	−	0.0654935i	$-0.0208622\pi$
$617$	23.1593	+	23.1593i	0.932360	+	0.932360i	−0.0654935	+	0.997853i	$0.520862\pi$
$618$	−8.68023	+	15.9683i	−0.349170	+	0.642337i
$619$	2.50985	−	9.36687i	0.100879	−	0.376486i	−0.896966	−	0.442100i	$-0.854234\pi$
$619$	2.50985	−	9.36687i	0.100879	−	0.376486i	0.997845	+	0.0656133i	$0.0209004\pi$
$620$	−3.37763	+	1.95008i	−0.135649	+	0.0783169i
$621$	32.3118	+	6.03800i	1.29663	+	0.242297i
$622$	−20.4069	+	5.46802i	−0.818244	+	0.219248i
$623$	1.52603	+	2.64316i	0.0611391	+	0.105896i
$624$	−4.76763	+	4.03358i	−0.190858	+	0.161472i
$625$	9.20010	−	15.9350i	0.368004	−	0.637402i
$626$	2.67407	−	9.97975i	0.106877	−	0.398871i
$627$	10.8813	+	2.61804i	0.434558	+	0.104554i
$628$	−8.42090	−	4.86181i	−0.336030	−	0.194007i
$629$	−12.0960	−	12.0960i	−0.482300	−	0.482300i
$630$	0.756254	−	3.54075i	0.0301299	−	0.141067i
$631$	−5.85572	+	21.8539i	−0.233113	+	0.869988i	0.745878	+	0.666083i	$0.232030\pi$
$631$	−5.85572	+	21.8539i	−0.233113	+	0.869988i	−0.978991	+	0.203906i	$0.934636\pi$
$632$	1.55923	+	0.417795i	0.0620229	+	0.0166190i
$633$	−5.70550	+	23.7137i	−0.226773	+	0.942535i
$634$	−14.5122	+	8.37860i	−0.576352	+	0.332757i
$635$	3.25452	+	0.872047i	0.129152	+	0.0346061i
$636$	11.3024	+	10.7361i	0.448168	+	0.425715i
$637$	5.50544	+	12.5058i	0.218133	+	0.495498i
$638$		−	4.23108i		−	0.167510i
$639$	−19.3723	−	4.13764i	−0.766356	−	0.163683i
$640$	0.336790	−	0.583337i	0.0133128	−	0.0230584i
$641$	5.39399	−	9.34267i	0.213050	−	0.369013i	−0.739618	−	0.673027i	$-0.764994\pi$
$641$	5.39399	−	9.34267i	0.213050	−	0.369013i	0.952668	+	0.304014i	$0.0983270\pi$
$642$	1.79478	−	3.30170i	0.0708344	−	0.130308i
$643$	7.58253	−	7.58253i	0.299026	−	0.299026i	−0.541606	−	0.840632i	$-0.682184\pi$
$643$	7.58253	−	7.58253i	0.299026	−	0.299026i	0.840632	+	0.541606i	$0.182184\pi$
$644$	−8.01474	+	8.01474i	−0.315825	+	0.315825i
$645$	−0.543483	−	0.887865i	−0.0213996	−	0.0349596i
$646$	7.92862	−	13.7328i	0.311947	−	0.540309i
$647$	2.44136	−	4.22856i	0.0959799	−	0.166242i	−0.814037	−	0.580813i	$-0.802735\pi$
$647$	2.44136	−	4.22856i	0.0959799	−	0.166242i	0.910017	+	0.414571i	$0.136068\pi$
$648$	5.67764	−	6.98315i	0.223039	−	0.274324i
$649$			4.65524i			0.182734i
$650$	−5.93822	+	15.2785i	−0.232916	+	0.599270i
$651$	4.20339	−	17.4705i	0.164744	−	0.684723i
$652$	4.65451	+	1.24717i	0.182285	+	0.0488431i
$653$	−19.0037	+	10.9718i	−0.743673	+	0.429360i	−0.823403	−	0.567457i	$-0.807927\pi$
$653$	−19.0037	+	10.9718i	−0.743673	+	0.429360i	0.0797303	+	0.996816i	$0.474594\pi$
$654$	−14.7144	−	13.9772i	−0.575378	−	0.546552i
$655$	14.3014	+	3.83206i	0.558803	+	0.149731i
$656$	−1.28786	+	4.80634i	−0.0502823	+	0.187656i
$657$	22.7867	−	25.2571i	0.888993	−	0.985374i
$658$	4.80554	+	4.80554i	0.187340	+	0.187340i
$659$	36.6396	+	21.1539i	1.42728	+	0.824038i	0.996905	−	0.0786138i	$-0.0250494\pi$
$659$	36.6396	+	21.1539i	1.42728	+	0.824038i	0.430371	+	0.902652i	$0.358383\pi$
$660$	0.326064	+	1.10277i	0.0126920	+	0.0429252i
$661$	−8.10585	+	30.2514i	−0.315281	+	1.17664i	0.608447	+	0.793595i	$0.291793\pi$
$661$	−8.10585	+	30.2514i	−0.315281	+	1.17664i	−0.923728	+	0.383050i	$0.874874\pi$
$662$	−7.37732	+	12.7779i	−0.286728	+	0.496627i
$663$	−14.2160	−	5.10899i	−0.552103	−	0.198417i
$664$	−3.78422	−	6.55446i	−0.146856	−	0.254362i
$665$	−7.64207	+	2.04769i	−0.296347	+	0.0794059i
$666$	−9.65034	+	18.8938i	−0.373943	+	0.732122i
$667$	−23.5169	+	13.5775i	−0.910579	+	0.525723i
$668$	−3.66224	+	13.6676i	−0.141696	+	0.528817i
$669$	41.1082	−	1.05621i	1.58933	−	0.0408353i
$670$	5.27364	+	5.27364i	0.203738	+	0.203738i
$671$	1.21535	+	4.53573i	0.0469179	+	0.175100i
$672$	0.879938	+	2.97600i	0.0339444	+	0.114802i
$673$		−	38.0352i		−	1.46615i	−0.680148	−	0.733075i	$-0.738085\pi$
$673$		−	38.0352i		−	1.46615i	0.680148	−	0.733075i	$-0.261915\pi$
$674$	1.00563	+	3.75304i	0.0387352	+	0.144562i
$675$	4.33928	−	23.2213i	0.167019	−	0.893787i
$676$	2.80903	−	12.6929i	0.108040	−	0.488188i
$677$	−4.73877	+	2.73593i	−0.182126	+	0.105150i	−0.588291	−	0.808649i	$-0.700199\pi$
$677$	−4.73877	+	2.73593i	−0.182126	+	0.105150i	0.406165	+	0.913800i	$0.366866\pi$
$678$	−19.1946	+	0.493175i	−0.737166	+	0.0189403i
$679$	1.72092	+	2.98073i	0.0660430	+	0.114390i
$680$	1.62934			0.0624822
$681$	−36.4329	−	19.8047i	−1.39611	−	0.758917i
$682$	1.47714	+	5.51277i	0.0565627	+	0.211095i
$683$	−24.9699	−	6.69067i	−0.955447	−	0.256011i	−0.252775	−	0.967525i	$-0.581343\pi$
$683$	−24.9699	−	6.69067i	−0.955447	−	0.256011i	−0.702672	+	0.711514i	$0.748010\pi$
$684$	−19.2327	−	4.10784i	−0.735382	−	0.157067i
$685$	4.23986	+	7.34366i	0.161997	+	0.280587i
$686$	19.3322			0.738108
$687$	−31.2505	−	16.9876i	−1.19228	−	0.648117i
$688$	0.772736	+	0.446139i	0.0294603	+	0.0170089i
$689$	−32.2582	−	3.52683i	−1.22894	−	0.134362i
$690$	5.08299	−	5.35108i	0.193506	−	0.203712i
$691$	−23.9424	+	23.9424i	−0.910811	+	0.910811i	−0.996336	−	0.0855252i	$-0.972743\pi$
$691$	−23.9424	+	23.9424i	−0.910811	+	0.910811i	0.0855252	+	0.996336i	$0.472743\pi$
$692$	20.0900	+	11.5989i	0.763706	+	0.440926i
$693$	−4.71835	−	2.40997i	−0.179235	−	0.0915473i
$694$	−22.8522	+	22.8522i	−0.867459	+	0.867459i
$695$	−12.8151	+	3.43379i	−0.486103	+	0.130251i
$696$	0.190966	+	7.43250i	0.00723855	+	0.281728i
$697$	−11.6262	+	3.11522i	−0.440372	+	0.117997i
$698$			18.9648i			0.717828i
$699$	3.50456	+	3.32899i	0.132555	+	0.125914i
$700$	5.75989	+	5.75989i	0.217703	+	0.217703i
$701$	−29.4689			−1.11303			−0.556513	−	0.830839i	$-0.687861\pi$
$701$	−29.4689			−1.11303			−0.556513	+	0.830839i	$0.687861\pi$
$702$	−0.596336	+	18.7255i	−0.0225073	+	0.706748i
$703$	46.3599			1.74850
$704$	−0.696978	−	0.696978i	−0.0262683	−	0.0262683i
$705$	−3.20844	−	3.04770i	−0.120837	−	0.114783i
$706$		−	19.5973i		−	0.737554i
$707$	25.7731	−	6.90589i	0.969298	−	0.259723i
$708$	−0.210110	−	8.17759i	−0.00789641	−	0.307332i
$709$	−12.5359	+	3.35900i	−0.470797	+	0.126150i	−0.486414	−	0.873728i	$-0.661695\pi$
$709$	−12.5359	+	3.35900i	−0.470797	+	0.126150i	0.0156169	+	0.999878i	$0.495029\pi$
$710$	−3.14500	+	3.14500i	−0.118030	+	0.118030i
$711$	4.06403	−	2.63353i	0.152413	−	0.0987649i
$712$	1.47520	+	0.851709i	0.0552856	+	0.0319191i
$713$	25.9006	−	25.9006i	0.969985	−	0.969985i
$714$	−5.17001	+	5.44269i	−0.193483	+	0.203687i
$715$	−1.93076	−	1.41514i	−0.0722063	−	0.0529234i
$716$	−4.82455	−	2.78545i	−0.180302	−	0.104097i
$717$	11.9552	+	6.49876i	0.446475	+	0.242701i
$718$	27.1650			1.01379
$719$	1.46802	+	2.54269i	0.0547480	+	0.0948263i	0.892101	−	0.451837i	$-0.149231\pi$
$719$	1.46802	+	2.54269i	0.0547480	+	0.0948263i	−0.837353	+	0.546663i	$0.815898\pi$
$720$	−0.622551	−	1.92245i	−0.0232011	−	0.0716455i
$721$	−18.1606	−	4.86612i	−0.676336	−	0.181224i
$722$	6.20510	+	23.1578i	0.230930	+	0.861843i
$723$	35.4265	+	19.2576i	1.31753	+	0.716198i
$724$	20.8410			0.774549
$725$	9.75764	+	16.9007i	0.362390	+	0.627677i
$726$	−17.3640	+	0.446141i	−0.644440	+	0.0165578i
$727$	−34.7895	+	20.0857i	−1.29027	+	0.744938i	−0.978702	−	0.205285i	$-0.934188\pi$
$727$	−34.7895	+	20.0857i	−1.29027	+	0.744938i	−0.311569	+	0.950224i	$0.600854\pi$
$728$	−5.21047	−	3.81900i	−0.193113	−	0.141541i
$729$	−4.14496	−	26.6799i	−0.153517	−	0.988146i
$730$	−1.97679	−	7.37746i	−0.0731641	−	0.273052i
$731$			2.15835i			0.0798294i
$732$	−2.33964	−	7.91281i	−0.0864757	−	0.292466i
$733$	−3.39197	−	12.6590i	−0.125285	−	0.467571i	0.874564	−	0.484909i	$-0.161147\pi$
$733$	−3.39197	−	12.6590i	−0.125285	−	0.467571i	−0.999850	+	0.0173384i	$0.994481\pi$
$734$	5.44068	+	5.44068i	0.200819	+	0.200819i
$735$	−4.41990	+	0.113562i	−0.163030	+	0.00418880i
$736$	−1.63730	+	6.11049i	−0.0603517	+	0.225236i
$737$	9.45150	−	5.45683i	0.348151	−	0.201005i
$738$	8.11787	+	12.5274i	0.298823	+	0.461140i
$739$	−20.2177	+	5.41732i	−0.743721	+	0.199279i	−0.610731	−	0.791838i	$-0.709124\pi$
$739$	−20.2177	+	5.41732i	−0.743721	+	0.199279i	−0.132990	+	0.991117i	$0.542458\pi$
$740$	2.38175	+	4.12531i	0.0875547	+	0.151649i
$741$	37.0330	−	17.4520i	1.36044	−	0.641114i
$742$	−8.06290	+	13.9654i	−0.295998	+	0.512684i
$743$	−4.33508	+	16.1787i	−0.159039	+	0.593540i	0.839687	+	0.543071i	$0.182738\pi$
$743$	−4.33508	+	16.1787i	−0.159039	+	0.593540i	−0.998726	+	0.0504696i	$0.983928\pi$
$744$	−2.84363	−	9.61730i	−0.104252	−	0.352587i
$745$	−5.64073	−	3.25668i	−0.206660	−	0.119315i
$746$	−11.3830	−	11.3830i	−0.416760	−	0.416760i
$747$	−22.2045	−	4.74256i	−0.812419	−	0.173521i
$748$	0.617094	−	2.30303i	0.0225632	−	0.0842070i
$749$	3.75500	+	1.00615i	0.137205	+	0.0367639i
$750$	−8.07502	−	7.67046i	−0.294858	−	0.280086i
$751$	−8.11367	+	4.68443i	−0.296072	+	0.170937i	−0.640677	−	0.767810i	$-0.721346\pi$
$751$	−8.11367	+	4.68443i	−0.296072	+	0.170937i	0.344605	+	0.938748i	$0.388013\pi$
$752$	3.66378	+	0.981707i	0.133604	+	0.0357992i
$753$	10.5539	−	43.8649i	0.384604	−	1.59852i
$754$	−9.68970	−	12.0686i	−0.352878	−	0.439511i
$755$			3.34938i			0.121897i
$756$	8.39722	+	4.02050i	0.305404	+	0.146224i
$757$	1.46922	−	2.54477i	0.0533999	−	0.0924913i	−0.838090	−	0.545532i	$-0.816328\pi$
$757$	1.46922	−	2.54477i	0.0533999	−	0.0924913i	0.891490	+	0.453041i	$0.149661\pi$
$758$	−12.9805	+	22.4829i	−0.471472	+	0.816614i
$759$	−5.63849	−	9.21136i	−0.204664	−	0.334351i
$760$	−3.12234	+	3.12234i	−0.113259	+	0.113259i
$761$	−7.31204	+	7.31204i	−0.265061	+	0.265061i	−0.827106	−	0.562045i	$-0.810015\pi$
$761$	−7.31204	+	7.31204i	−0.265061	+	0.265061i	0.562045	+	0.827106i	$0.310015\pi$
$762$	−4.13782	+	7.61198i	−0.149897	+	0.275753i
$763$	10.4970	−	18.1813i	0.380016	−	0.658207i
$764$	9.03635	−	15.6514i	0.326924	−	0.566248i
$765$	3.27429	−	3.62927i	0.118382	−	0.131217i
$766$		−	31.4582i		−	1.13663i
$767$	10.6611	+	13.2784i	0.384949	+	0.479455i
$768$	1.25580	+	1.19288i	0.0453147	+	0.0430445i
$769$	−0.0675077	−	0.0180886i	−0.00243439	−	0.000652292i	0.257602	−	0.966251i	$-0.417068\pi$
$769$	−0.0675077	−	0.0180886i	−0.00243439	−	0.000652292i	−0.260036	+	0.965599i	$0.583734\pi$
$770$	−1.03021	+	0.594792i	−0.0371262	+	0.0214348i
$771$	2.91784	−	12.1274i	0.105083	−	0.436757i
$772$	7.11166	+	1.90556i	0.255954	+	0.0685827i
$773$	−6.52883	+	24.3659i	−0.234826	+	0.876382i	0.743402	+	0.668845i	$0.233211\pi$
$773$	−6.52883	+	24.3659i	−0.234826	+	0.876382i	−0.978227	+	0.207536i	$0.933456\pi$
$774$	2.54663	−	0.824681i	0.0915369	−	0.0296426i
$775$	−18.6138	−	18.6138i	−0.668627	−	0.668627i
$776$	1.66361	+	0.960483i	0.0597199	+	0.0344793i
$777$	−21.3378	−	5.13386i	−0.765489	−	0.184176i
$778$	−6.57319	+	24.5315i	−0.235660	+	0.879496i
$779$	16.3098	−	28.2493i	0.584358	−	1.01214i
$780$	3.45552	+	2.39876i	0.123728	+	0.0858893i
$781$	3.25425	+	5.63652i	0.116446	+	0.201691i
$782$	−14.7808	+	3.96050i	−0.528560	+	0.141627i
$783$	16.9393	+	14.5109i	0.605363	+	0.518577i
$784$	3.28199	−	1.89486i	0.117214	−	0.0676734i
$785$	−1.69517	+	6.32646i	−0.0605032	+	0.225801i
$786$	−18.1829	+	33.4495i	−0.648563	+	1.19310i
$787$	21.2801	+	21.2801i	0.758554	+	0.758554i	0.976059	−	0.217506i	$-0.0697920\pi$
$787$	21.2801	+	21.2801i	0.758554	+	0.758554i	−0.217506	+	0.976059i	$0.569792\pi$
$788$	6.33628	+	23.6473i	0.225721	+	0.842401i
$789$	13.6644	−	14.3851i	0.486466	−	0.512123i
$790$		−	1.08732i		−	0.0386850i
$791$	−5.14080	−	19.1857i	−0.182786	−	0.682166i
$792$	−2.95313	+	0.151852i	−0.104935	+	0.00539582i
$793$	13.8540	+	10.1542i	0.491969	+	0.360587i
$794$	1.12805	−	0.651278i	0.0400329	−	0.0231130i
$795$	5.01482	−	9.22532i	0.177857	−	0.327188i
$796$	−4.02871	−	6.97794i	−0.142794	−	0.247326i
$797$	−27.5921			−0.977363			−0.488682	−	0.872462i	$-0.662522\pi$
$797$	−27.5921			−0.977363			−0.488682	+	0.872462i	$0.662522\pi$
$798$	−0.522537	−	20.3374i	−0.0184976	−	0.719937i
$799$	2.37467	+	8.86239i	0.0840098	+	0.313529i
$800$	4.39138	+	1.17667i	0.155259	+	0.0416014i
$801$	4.86169	−	1.57437i	0.171779	−	0.0556276i
$802$	0.718789	+	1.24498i	0.0253813	+	0.0439618i
$803$	−11.1766			−0.394412
$804$	−16.3566	+	10.0123i	−0.576854	+	0.353106i
$805$	6.61187	+	3.81736i	0.233038	+	0.134544i
$806$	16.8383	+	12.3415i	0.593102	+	0.434713i
$807$	42.3504	+	10.1895i	1.49080	+	0.358687i
$808$	10.5302	−	10.5302i	0.370451	−	0.370451i
$809$	31.3309	+	18.0889i	1.10154	+	0.635972i	0.936624	−	0.350336i	$-0.113933\pi$
$809$	31.3309	+	18.0889i	1.10154	+	0.635972i	0.164912	+	0.986308i	$0.447266\pi$
$810$	−5.53325	−	2.47663i	−0.194418	−	0.0870197i
$811$	0.803239	−	0.803239i	0.0282055	−	0.0282055i	−0.692863	−	0.721069i	$-0.743651\pi$
$811$	0.803239	−	0.803239i	0.0282055	−	0.0282055i	0.721069	+	0.692863i	$0.243651\pi$
$812$	−7.42905	+	1.99061i	−0.260709	+	0.0698567i
$813$	9.72432	+	5.28607i	0.341047	+	0.185391i
$814$	6.73309	−	1.80412i	0.235995	−	0.0632345i
$815$		−	3.24578i		−	0.113695i
$816$	−0.980069	+	4.07345i	−0.0343093	+	0.142599i
$817$	−4.13611	−	4.13611i	−0.144704	−	0.144704i
$818$	22.9718			0.803189
$819$	−18.9775	+	3.93150i	−0.663129	+	0.137378i
$820$	3.35166			0.117045
$821$	−34.2693	−	34.2693i	−1.19601	−	1.19601i	−0.975352	−	0.220656i	$-0.929180\pi$
$821$	−34.2693	−	34.2693i	−1.19601	−	1.19601i	−0.220656	−	0.975352i	$-0.570820\pi$
$822$	−20.9100	+	6.18263i	−0.729319	+	0.215644i
$823$			28.2827i			0.985873i	0.870065	+	0.492937i	$0.164077\pi$
$823$			28.2827i			0.985873i	−0.870065	+	0.492937i	$0.835923\pi$
$824$	−10.1358	+	2.71588i	−0.353098	+	0.0946122i
$825$	−6.61986	+	4.05217i	−0.230474	+	0.141079i
$826$	8.17379	−	2.19016i	0.284403	−	0.0762055i
$827$	13.1080	−	13.1080i	0.455810	−	0.455810i	−0.441467	−	0.897277i	$-0.645542\pi$
$827$	13.1080	−	13.1080i	0.455810	−	0.455810i	0.897277	+	0.441467i	$0.145542\pi$
$828$	10.3206	+	15.9266i	0.358664	+	0.553487i
$829$	46.5863	+	26.8966i	1.61801	+	0.934159i	0.987434	+	0.158032i	$0.0505148\pi$
$829$	46.5863	+	26.8966i	1.61801	+	0.934159i	0.630577	+	0.776127i	$0.282818\pi$
$830$	−3.60479	+	3.60479i	−0.125124	+	0.125124i
$831$	9.54861	+	32.2939i	0.331238	+	1.12026i
$832$	−3.58419	−	0.391864i	−0.124260	−	0.0135854i
$833$	7.93886	+	4.58350i	0.275065	+	0.158809i
$834$	−0.876248	−	34.1040i	−0.0303420	−	1.18093i
$835$	9.53101			0.329834
$836$	3.23080	+	5.59591i	0.111740	+	0.193539i
$837$	−27.1366	−	12.9927i	−0.937979	−	0.449095i
$838$	−6.38041	−	1.70963i	−0.220408	−	0.0590581i
$839$	−1.12772	−	4.20871i	−0.0389332	−	0.145301i	0.943723	−	0.330736i	$-0.107297\pi$
$839$	−1.12772	−	4.20871i	−0.0389332	−	0.145301i	−0.982656	+	0.185436i	$0.940630\pi$
$840$	1.78287	−	1.09133i	0.0615147	−	0.0376546i
$841$	10.5738			0.364614
$842$	4.70368	+	8.14701i	0.162100	+	0.280765i
$843$	26.9540	+	44.0336i	0.928346	+	1.51660i
$844$	−12.1952	+	7.04091i	−0.419776	+	0.242358i
$845$	−8.74806	+	0.385182i	−0.300942	+	0.0132507i
$846$	9.54939	−	6.18809i	0.328315	−	0.212751i
$847$	−4.65052	−	17.3560i	−0.159794	−	0.596359i
$848$			9.00014i			0.309066i
$849$	37.1758	+	8.94447i	1.27587	+	0.306973i
$850$	2.84626	+	10.6224i	0.0976260	+	0.364345i
$851$	−31.6340	−	31.6340i	−1.08440	−	1.08440i
$852$	−5.97094	−	9.75447i	−0.204561	−	0.334183i
$853$	2.92390	−	10.9121i	0.100112	−	0.373625i	−0.897632	−	0.440745i	$-0.854714\pi$
$853$	2.92390	−	10.9121i	0.100112	−	0.373625i	0.997745	+	0.0671200i	$0.0213810\pi$
$854$	7.39218	−	4.26788i	0.252955	−	0.146044i
$855$	0.680270	+	13.2295i	0.0232647	+	0.452439i
$856$	2.09574	−	0.561553i	0.0716311	−	0.0191935i
$857$	−8.91122	−	15.4347i	−0.304401	−	0.527239i	0.672726	−	0.739891i	$-0.265123\pi$
$857$	−8.91122	−	15.4347i	−0.304401	−	0.527239i	−0.977128	+	0.212653i	$0.931790\pi$
$858$	4.69933	−	3.97580i	0.160433	−	0.135731i
$859$	−12.6436	+	21.8993i	−0.431393	+	0.747194i	−0.996994	−	0.0774851i	$-0.975311\pi$
$859$	−12.6436	+	21.8993i	−0.431393	+	0.747194i	0.565601	+	0.824679i	$0.308644\pi$
$860$	0.155556	−	0.580542i	0.00530440	−	0.0197963i
$861$	−10.6351	+	11.1960i	−0.362443	+	0.381559i
$862$	−1.72918	−	0.998343i	−0.0588961	−	0.0340037i
$863$	9.09474	+	9.09474i	0.309589	+	0.309589i	0.844750	−	0.535161i	$-0.179749\pi$
$863$	9.09474	+	9.09474i	0.309589	+	0.309589i	−0.535161	+	0.844750i	$0.679749\pi$
$864$	5.18073	−	0.400036i	0.176252	−	0.0136095i
$865$	4.04421	−	15.0932i	0.137507	−	0.513184i
$866$	−30.9649	−	8.29701i	−1.05223	−	0.281944i
$867$	18.5178	−	5.47532i	0.628899	−	0.185952i
$868$	8.98452	−	5.18722i	0.304955	−	0.176066i
$869$	−1.53690	−	0.411810i	−0.0521356	−	0.0139697i
$870$	4.80250	−	1.42000i	0.162820	−	0.0481423i
$871$	14.4622	−	37.2099i	0.490034	−	1.26081i
$872$		−	11.7172i		−	0.396793i
$873$	5.48259	−	1.77544i	0.185558	−	0.0600894i
$874$	20.7352	−	35.9145i	0.701379	−	1.21482i
$875$	5.76057	−	9.97761i	0.194743	−	0.337305i
$876$	19.6332	−	0.504444i	0.663345	−	0.0170436i
$877$	36.5154	−	36.5154i	1.23304	−	1.23304i	0.270247	−	0.962791i	$-0.412895\pi$
$877$	36.5154	−	36.5154i	1.23304	−	1.23304i	0.962791	−	0.270247i	$-0.0871052\pi$
$878$	18.4762	−	18.4762i	0.623542	−	0.623542i
$879$	−16.4279	+	0.422089i	−0.554101	+	0.0142367i
$880$	−0.331966	+	0.574981i	−0.0111906	+	0.0193826i
$881$	−21.3121	+	36.9136i	−0.718023	+	1.24365i	0.243759	+	0.969836i	$0.421619\pi$
$881$	−21.3121	+	36.9136i	−0.718023	+	1.24365i	−0.961782	+	0.273816i	$0.911714\pi$
$882$	2.37472	−	11.1184i	0.0799610	−	0.374375i
$883$		−	33.4740i		−	1.12649i	−0.826290	−	0.563245i	$-0.809553\pi$
$883$		−	33.4740i		−	1.12649i	0.826290	−	0.563245i	$-0.190447\pi$
$884$	−3.51404	−	7.98227i	−0.118190	−	0.268473i
$885$	−5.28394	+	1.56235i	−0.177618	+	0.0525177i
$886$	10.9944	+	2.94593i	0.369363	+	0.0989704i
$887$	−4.08001	+	2.35559i	−0.136993	+	0.0790931i	−0.566930	−	0.823766i	$-0.691869\pi$
$887$	−4.08001	+	2.35559i	−0.136993	+	0.0790931i	0.429937	+	0.902859i	$0.358536\pi$
$888$	−11.7462	+	3.47309i	−0.394177	+	0.116549i
$889$	−8.65706	−	2.31965i	−0.290349	−	0.0777987i
$890$	0.296966	−	1.10829i	0.00995431	−	0.0371500i
$891$	−5.59631	+	6.88312i	−0.187484	+	0.230593i
$892$	16.7879	+	16.7879i	0.562099	+	0.562099i
$893$	−21.5339	−	12.4326i	−0.720604	−	0.416041i
$894$	11.5349	−	12.1433i	0.385785	−	0.406132i
$895$	−0.971205	+	3.62459i	−0.0324638	+	0.121157i
$896$	−0.895864	+	1.55168i	−0.0299287	+	0.0518381i
$897$	−37.1781	−	13.3612i	−1.24134	−	0.446118i
$898$	6.92393	+	11.9926i	0.231055	+	0.400198i
$899$	24.0079	−	6.43289i	0.800708	−	0.214549i
$900$	11.4458	−	7.41700i	0.381528	−	0.247233i
$901$	−18.8539	+	10.8853i	−0.628115	+	0.362642i
$902$	1.26941	−	4.73750i	0.0422667	−	0.157741i
$903$	1.44567	+	2.36173i	0.0481089	+	0.0785934i
$904$	−7.83876	−	7.83876i	−0.260713	−	0.260713i
$905$	−3.63332	−	13.5597i	−0.120776	−	0.450740i
$906$	−8.37368	−	2.01470i	−0.278197	−	0.0669340i
$907$			2.22688i			0.0739424i	0.999316	+	0.0369712i	$0.0117710\pi$
$907$			2.22688i			0.0739424i	−0.999316	+	0.0369712i	$0.988229\pi$
$908$	−6.19651	−	23.1257i	−0.205638	−	0.767453i
$909$	−2.29423	−	44.6169i	−0.0760948	−	1.47985i
$910$	−1.57638	+	4.05587i	−0.0522564	+	0.134451i
$911$	−10.3509	+	5.97609i	−0.342940	+	0.197997i	−0.661571	−	0.749882i	$-0.730110\pi$
$911$	−10.3509	+	5.97609i	−0.342940	+	0.197997i	0.318631	+	0.947879i	$0.396777\pi$
$912$	−5.92793	−	9.68420i	−0.196293	−	0.320676i
$913$	3.73001	+	6.46057i	0.123445	+	0.213814i
$914$	33.6779			1.11397
$915$	−4.74041	+	2.90172i	−0.156713	+	0.0959279i
$916$	−5.31509	−	19.8362i	−0.175616	−	0.655406i
$917$	−38.0419	−	10.1933i	−1.25625	−	0.336612i
$918$	7.10390	+	10.3690i	0.234464	+	0.342228i
$919$	2.28777	+	3.96254i	0.0754667	+	0.130712i	0.901289	−	0.433218i	$-0.142622\pi$
$919$	2.28777	+	3.96254i	0.0754667	+	0.130712i	−0.825822	+	0.563930i	$0.809289\pi$
$920$	4.26110			0.140484
$921$	0.211207	+	8.22029i	0.00695951	+	0.270868i
$922$	7.78890	+	4.49692i	0.256514	+	0.148098i
$923$	22.1906	+	8.62473i	0.730412	+	0.283887i
$924$	−0.867334	−	2.93337i	−0.0285332	−	0.0965008i
$925$	−22.7341	+	22.7341i	−0.747494	+	0.747494i
$926$	−16.4220	−	9.48125i	−0.539661	−	0.311573i
$927$	−14.3193	+	28.0349i	−0.470306	+	0.920786i
$928$	−3.03531	+	3.03531i	−0.0996388	+	0.0996388i
$929$	45.6232	−	12.2247i	1.49685	−	0.401079i	0.584805	−	0.811174i	$-0.301171\pi$
$929$	45.6232	−	12.2247i	1.49685	−	0.401079i	0.912043	+	0.410095i	$0.134505\pi$
$930$	−5.76154	+	3.52678i	−0.188928	+	0.115648i
$931$	−23.9970	+	6.42997i	−0.786469	+	0.210734i
$932$			2.79071i			0.0914126i
$933$	−35.0909	+	10.3756i	−1.14883	+	0.339683i
$934$	−23.4347	−	23.4347i	−0.766808	−	0.766808i
$935$	−1.60600			−0.0525217
$936$	−8.07560	+	7.19615i	−0.263959	+	0.235214i
$937$	34.1939			1.11707			0.558533	−	0.829482i	$-0.311365\pi$
$937$	34.1939			1.11707			0.558533	+	0.829482i	$0.311365\pi$
$938$	−14.0279	−	14.0279i	−0.458028	−	0.458028i
$939$	4.18611	−	17.3987i	0.136609	−	0.567785i
$940$		−	2.55490i		−	0.0833318i
$941$	−28.2319	+	7.56472i	−0.920334	+	0.246603i	−0.687728	−	0.725968i	$-0.741392\pi$
$941$	−28.2319	+	7.56472i	−0.920334	+	0.246603i	−0.232606	+	0.972571i	$0.574725\pi$
$942$	−14.7969	−	8.04350i	−0.482109	−	0.262071i
$943$	−30.4052	+	8.14704i	−0.990128	+	0.265304i
$944$	3.33959	−	3.33959i	0.108694	−	0.108694i
$945$	1.15192	−	6.16439i	0.0374719	−	0.200527i
$946$	−0.761667	−	0.439749i	−0.0247639	−	0.0142975i
$947$	−19.5151	+	19.5151i	−0.634154	+	0.634154i	−0.949107	−	0.314953i	$-0.898011\pi$
$947$	−19.5151	+	19.5151i	−0.634154	+	0.634154i	0.314953	+	0.949107i	$0.398011\pi$
$948$	2.71836	+	0.654036i	0.0882883	+	0.0212421i
$949$	−31.8795	+	25.5957i	−1.03485	+	0.830872i
$950$	−25.8104	−	14.9016i	−0.837399	−	0.483472i
$951$	−24.7548	+	15.1530i	−0.802728	+	0.491369i
$952$	−4.33405			−0.140467
$953$	−8.06765	−	13.9736i	−0.261337	−	0.452649i	0.705261	−	0.708948i	$-0.250830\pi$
$953$	−8.06765	−	13.9736i	−0.261337	−	0.452649i	−0.966597	+	0.256299i	$0.917497\pi$
$954$	20.0474	+	18.0866i	0.649059	+	0.585574i
$955$	−11.7586	−	3.15071i	−0.380500	−	0.101955i
$956$	2.03334	+	7.58852i	0.0657629	+	0.245430i
$957$	−0.188231	−	7.32604i	−0.00608463	−	0.236817i
$958$	−30.8338			−0.996195
$959$	−11.2781	−	19.5342i	−0.364188	−	0.630792i
$960$	0.557194	−	1.02502i	0.0179833	−	0.0330824i
$961$	−2.18777	+	1.26311i	−0.0705733	+	0.0407455i
$962$	15.0735	−	20.5656i	0.485989	−	0.663061i
$963$	2.96074	−	5.79667i	0.0954086	−	0.186795i
$964$	6.02534	+	22.4869i	0.194063	+	0.724253i
$965$		−	4.95925i		−	0.159644i
$966$	−13.5208	+	14.2339i	−0.435025	+	0.457969i
$967$	−8.38995	−	31.3117i	−0.269803	−	1.00692i	−0.959245	−	0.282576i	$-0.908811\pi$
$967$	−8.38995	−	31.3117i	−0.269803	−	1.00692i	0.689442	−	0.724341i	$-0.257856\pi$
$968$	−7.09118	−	7.09118i	−0.227919	−	0.227919i
$969$	13.1173	−	24.1307i	0.421389	−	0.775191i
$970$	0.334892	−	1.24983i	0.0107527	−	0.0401298i
$971$	23.3310	−	13.4701i	0.748727	−	0.432278i	−0.0765068	−	0.997069i	$-0.524377\pi$
$971$	23.3310	−	13.4701i	0.748727	−	0.432278i	0.825234	+	0.564791i	$0.191043\pi$
$972$	9.52006	−	12.3438i	0.305356	−	0.395926i
$973$	34.0882	−	9.13391i	1.09282	−	0.292820i
$974$	−10.1155	−	17.5206i	−0.324123	−	0.561397i
$975$	−9.60221	+	26.7185i	−0.307517	+	0.855677i
$976$	2.38199	−	4.12572i	0.0762456	−	0.132061i
$977$	3.95573	−	14.7630i	0.126555	−	0.472310i	−0.873335	−	0.487120i	$-0.838048\pi$
$977$	3.95573	−	14.7630i	0.126555	−	0.472310i	0.999890	+	0.0148095i	$0.00471418\pi$
$978$	8.11468	+	1.95239i	0.259479	+	0.0624304i
$979$	−1.45407	−	0.839508i	−0.0464723	−	0.0268308i
$980$	−1.80501	−	1.80501i	−0.0576590	−	0.0576590i
$981$	−26.0995	−	23.5466i	−0.833292	−	0.751786i
$982$	3.90879	−	14.5878i	0.124735	−	0.465516i
$983$	−2.82359	−	0.756578i	−0.0900584	−	0.0241311i	0.213508	−	0.976941i	$-0.431511\pi$
$983$	−2.82359	−	0.756578i	−0.0900584	−	0.0241311i	−0.303567	+	0.952810i	$0.598178\pi$
$984$	−2.01607	+	8.37938i	−0.0642701	+	0.267125i
$985$	14.2810	−	8.24512i	0.455030	−	0.262711i
$986$	−10.0296	−	2.68742i	−0.319407	−	0.0855848i
$987$	8.53449	+	8.10691i	0.271656	+	0.258046i
$988$	22.0307	+	8.56260i	0.700891	+	0.272413i
$989$			5.64460i			0.179488i
$990$	0.613633	+	1.89491i	0.0195025	+	0.0602243i
$991$	20.0775	−	34.7753i	0.637784	−	1.10467i	−0.348134	−	0.937445i	$-0.613185\pi$
$991$	20.0775	−	34.7753i	0.637784	−	1.10467i	0.985918	−	0.167229i	$-0.0534821\pi$
$992$	2.89509	−	5.01445i	0.0919193	−	0.159209i
$993$	−12.2052	+	22.4528i	−0.387321	+	0.712520i
$994$	8.36572	−	8.36572i	0.265345	−	0.265345i
$995$	−3.83769	+	3.83769i	−0.121663	+	0.121663i
$996$	−6.84388	−	11.1806i	−0.216857	−	0.354269i
$997$	−7.81967	+	13.5441i	−0.247651	+	0.428945i	−0.962874	−	0.269952i	$-0.912992\pi$
$997$	−7.81967	+	13.5441i	−0.247651	+	0.428945i	0.715222	+	0.698897i	$0.246325\pi$
$998$	20.9577	−	36.2997i	0.663403	−	1.14905i
$999$	−15.8688	+	33.1436i	−0.502067	+	1.04862i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.y.a.149.13	yes	56
3.2	odd	2		702.2.bb.a.71.4		56
9.2	odd	6		234.2.z.a.227.1	yes	56
9.7	even	3		702.2.bc.a.305.11		56
13.11	odd	12		234.2.z.a.167.1	yes	56
39.11	even	12		702.2.bc.a.557.11		56
117.11	even	12	inner	234.2.y.a.11.13	✓	56
117.115	odd	12		702.2.bb.a.89.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.13	✓	56	117.11	even	12	inner
234.2.y.a.149.13	yes	56	1.1	even	1	trivial
234.2.z.a.167.1	yes	56	13.11	odd	12
234.2.z.a.227.1	yes	56	9.2	odd	6
702.2.bb.a.71.4		56	3.2	odd	2
702.2.bb.a.89.4		56	117.115	odd	12
702.2.bc.a.305.11		56	9.7	even	3
702.2.bc.a.557.11		56	39.11	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.25580 + 1.19288i) q^{3} +1.00000i q^{4} +(0.650628 - 0.174335i) q^{5} +(0.0444876 + 1.73148i) q^{6} +(-1.73068 + 0.463733i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.154059 + 2.99604i) q^{9} +(0.583337 + 0.336790i) q^{10} +(0.696978 - 0.696978i) q^{11} +(-1.19288 + 1.25580i) q^{12} +(0.391864 - 3.58419i) q^{13} +(-1.55168 - 0.895864i) q^{14} +(1.02502 + 0.557194i) q^{15} -1.00000 q^{16} +(-1.20946 - 2.09485i) q^{17} +(-2.00959 + 2.22746i) q^{18} +(6.33213 + 1.69669i) q^{19} +(0.174335 + 0.650628i) q^{20} +(-2.72656 - 1.48214i) q^{21} +0.985676 q^{22} +(-3.16302 - 5.47852i) q^{23} +(-1.73148 + 0.0444876i) q^{24} +(-3.93720 + 2.27315i) q^{25} +(2.81150 - 2.25732i) q^{26} +(-3.38046 + 3.94620i) q^{27} +(-0.463733 - 1.73068i) q^{28} -4.29257i q^{29} +(0.330803 + 1.11879i) q^{30} +(1.49861 + 5.59289i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.70668 - 0.0438503i) q^{33} +(0.626062 - 2.33650i) q^{34} +(-1.04518 + 0.603436i) q^{35} +(-2.99604 + 0.154059i) q^{36} +(6.83094 - 1.83034i) q^{37} +(3.27775 + 5.67724i) q^{38} +(4.76763 - 4.03358i) q^{39} +(-0.336790 + 0.583337i) q^{40} +(1.28786 - 4.80634i) q^{41} +(-0.879938 - 2.97600i) q^{42} +(-0.772736 - 0.446139i) q^{43} +(0.696978 + 0.696978i) q^{44} +(0.622551 + 1.92245i) q^{45} +(1.63730 - 6.11049i) q^{46} +(-3.66378 - 0.981707i) q^{47} +(-1.25580 - 1.19288i) q^{48} +(-3.28199 + 1.89486i) q^{49} +(-4.39138 - 1.17667i) q^{50} +(0.980069 - 4.07345i) q^{51} +(3.58419 + 0.391864i) q^{52} -9.00014i q^{53} +(-5.18073 + 0.400036i) q^{54} +(0.331966 - 0.574981i) q^{55} +(0.895864 - 1.55168i) q^{56} +(5.92793 + 9.68420i) q^{57} +(3.03531 - 3.03531i) q^{58} +(-3.33959 + 3.33959i) q^{59} +(-0.557194 + 1.02502i) q^{60} +(-2.38199 + 4.12572i) q^{61} +(-2.89509 + 5.01445i) q^{62} +(-1.65599 - 5.11374i) q^{63} -1.00000i q^{64} +(-0.369894 - 2.40029i) q^{65} +(1.23781 + 1.17580i) q^{66} +(10.6950 + 2.86571i) q^{67} +(2.09485 - 1.20946i) q^{68} +(2.56311 - 10.6530i) q^{69} +(-1.16575 - 0.312361i) q^{70} +(-1.70900 + 6.37808i) q^{71} +(-2.22746 - 2.00959i) q^{72} +(-8.01788 - 8.01788i) q^{73} +(6.12445 + 3.53595i) q^{74} +(-7.65593 - 1.84201i) q^{75} +(-1.69669 + 6.33213i) q^{76} +(-0.883031 + 1.52946i) q^{77} +(6.22339 + 0.519052i) q^{78} +(-0.807117 - 1.39797i) q^{79} +(-0.650628 + 0.174335i) q^{80} +(-8.95253 + 0.923132i) q^{81} +(4.30925 - 2.48795i) q^{82} +(-1.95885 + 7.31055i) q^{83} +(1.48214 - 2.72656i) q^{84} +(-1.15211 - 1.15211i) q^{85} +(-0.230939 - 0.861875i) q^{86} +(5.12054 - 5.39061i) q^{87} +0.985676i q^{88} +(-0.440877 - 1.64537i) q^{89} +(-0.919169 + 1.79959i) q^{90} +(0.983920 + 6.38480i) q^{91} +(5.47852 - 3.16302i) q^{92} +(-4.78971 + 8.81121i) q^{93} +(-1.89651 - 3.28485i) q^{94} +4.41566 q^{95} +(-0.0444876 - 1.73148i) q^{96} +(-0.497183 - 1.85551i) q^{97} +(-3.66058 - 0.980849i) q^{98} +(2.19555 + 1.98080i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more