LMFDB - Embedded newform 950.2.u.h.149.1

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:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.1
Character	$\chi$	$=$	950.149
Dual form			950.2.u.h.899.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 + 0.766044i) q^{2} +(-0.934611 - 2.56782i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.56782 + 0.934611i) q^{6} +(1.85059 - 1.06844i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-3.42208 + 2.87147i) q^{9} +O(q^{10})$	\(q+(-0.642788 + 0.766044i) q^{2} +(-0.934611 - 2.56782i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.56782 + 0.934611i) q^{6} +(1.85059 - 1.06844i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-3.42208 + 2.87147i) q^{9} +(0.926593 - 1.60491i) q^{11} +(-2.36652 + 1.36631i) q^{12} +(1.88555 - 5.18051i) q^{13} +(-0.371065 + 2.10441i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(2.37433 - 2.82962i) q^{17} -4.46721i q^{18} +(-1.21370 + 4.18652i) q^{19} +(-4.47314 - 3.75341i) q^{21} +(0.633827 + 1.74143i) q^{22} +(2.89878 - 0.511133i) q^{23} +(0.474515 - 2.69111i) q^{24} +(2.75649 + 4.77438i) q^{26} +(3.47219 + 2.00467i) q^{27} +(-1.37356 - 1.63694i) q^{28} +(5.36998 - 4.50595i) q^{29} +(2.12807 + 3.68592i) q^{31} +(0.342020 - 0.939693i) q^{32} +(-4.98712 - 0.879364i) q^{33} +(0.641422 + 3.63769i) q^{34} +(3.42208 + 2.87147i) q^{36} +3.49650i q^{37} +(-2.42690 - 3.62079i) q^{38} -15.0649 q^{39} +(1.47464 - 0.536727i) q^{41} +(5.75056 - 1.01398i) q^{42} +(2.29458 + 0.404597i) q^{43} +(-1.74143 - 0.633827i) q^{44} +(-1.47175 + 2.54915i) q^{46} +(-7.20983 - 8.59234i) q^{47} +(1.75649 + 2.09331i) q^{48} +(-1.21688 + 2.10770i) q^{49} +(-9.48504 - 3.45227i) q^{51} +(-5.42923 - 0.957319i) q^{52} +(-6.32356 + 1.11501i) q^{53} +(-3.76755 + 1.37127i) q^{54} +2.13688 q^{56} +(11.8846 - 0.796188i) q^{57} +7.01002i q^{58} +(-10.8207 - 9.07963i) q^{59} +(-0.0461045 - 0.261472i) q^{61} +(-4.19148 - 0.739071i) q^{62} +(-3.26488 + 8.97020i) q^{63} +(0.500000 + 0.866025i) q^{64} +(3.87929 - 3.25511i) q^{66} +(-9.49761 - 11.3188i) q^{67} +(-3.19893 - 1.84690i) q^{68} +(-4.02173 - 6.96585i) q^{69} +(0.722627 - 4.09822i) q^{71} +(-4.39935 + 0.775724i) q^{72} +(5.27085 + 14.4815i) q^{73} +(-2.67848 - 2.24751i) q^{74} +(4.33367 + 0.468284i) q^{76} -3.96003i q^{77} +(9.68352 - 11.5404i) q^{78} +(-2.70762 + 0.985493i) q^{79} +(-0.424681 + 2.40849i) q^{81} +(-0.536727 + 1.47464i) q^{82} +(-12.1408 + 7.00947i) q^{83} +(-2.91964 + 5.05696i) q^{84} +(-1.78487 + 1.49768i) q^{86} +(-16.5893 - 9.57786i) q^{87} +(1.60491 - 0.926593i) q^{88} +(1.86003 + 0.676995i) q^{89} +(-2.04567 - 11.6016i) q^{91} +(-1.00674 - 2.76599i) q^{92} +(7.47588 - 8.90941i) q^{93} +11.2165 q^{94} -2.73262 q^{96} +(6.94855 - 8.28096i) q^{97} +(-0.832394 - 2.28698i) q^{98} +(1.43756 + 8.15281i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) $ 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * 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
$3$	−0.934611	−	2.56782i	−0.539598	−	1.48253i	−0.847333	−	0.531061i	$-0.821793\pi$
$3$	−0.934611	−	2.56782i	−0.539598	−	1.48253i	0.307735	−	0.951472i	$-0.400429\pi$
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	2.56782	+	0.934611i	1.04831	+	0.381553i
$7$	1.85059	−	1.06844i	0.699457	−	0.403832i	−0.107688	−	0.994185i	$-0.534345\pi$
$7$	1.85059	−	1.06844i	0.699457	−	0.403832i	0.807145	+	0.590353i	$0.201011\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−3.42208	+	2.87147i	−1.14069	+	0.957157i
$10$		0			0
$11$	0.926593	−	1.60491i	0.279378	−	0.483898i	−0.691852	−	0.722039i	$-0.743205\pi$
$11$	0.926593	−	1.60491i	0.279378	−	0.483898i	0.971230	+	0.238142i	$0.0765383\pi$
$12$	−2.36652	+	1.36631i	−0.683155	+	0.394420i
$13$	1.88555	−	5.18051i	0.522958	−	1.43681i	−0.344255	−	0.938876i	$-0.611869\pi$
$13$	1.88555	−	5.18051i	0.522958	−	1.43681i	0.867213	−	0.497938i	$-0.165909\pi$
$14$	−0.371065	+	2.10441i	−0.0991712	+	0.562428i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	2.37433	−	2.82962i	0.575860	−	0.686283i	−0.396963	−	0.917835i	$-0.629936\pi$
$17$	2.37433	−	2.82962i	0.575860	−	0.686283i	0.972823	+	0.231551i	$0.0743802\pi$
$18$		−	4.46721i		−	1.05293i
$19$	−1.21370	+	4.18652i	−0.278443	+	0.960453i
$19$	−1.21370	+	4.18652i	−0.278443	+	0.960453i
$20$		0			0
$21$	−4.47314	−	3.75341i	−0.976120	−	0.819062i
$22$	0.633827	+	1.74143i	0.135132	+	0.371273i
$23$	2.89878	−	0.511133i	0.604438	−	0.106579i	0.136950	−	0.990578i	$-0.456270\pi$
$23$	2.89878	−	0.511133i	0.604438	−	0.106579i	0.467488	+	0.883999i	$0.345159\pi$
$24$	0.474515	−	2.69111i	0.0968599	−	0.549320i
$25$		0			0
$26$	2.75649	+	4.77438i	0.540592	+	0.936333i
$27$	3.47219	+	2.00467i	0.668223	+	0.385799i
$28$	−1.37356	−	1.63694i	−0.259578	−	0.309353i
$29$	5.36998	−	4.50595i	0.997181	−	0.836734i	0.0105895	−	0.999944i	$-0.496629\pi$
$29$	5.36998	−	4.50595i	0.997181	−	0.836734i	0.986591	+	0.163210i	$0.0521848\pi$
$30$		0			0
$31$	2.12807	+	3.68592i	0.382213	+	0.662012i	0.991378	−	0.131031i	$-0.0418289\pi$
$31$	2.12807	+	3.68592i	0.382213	+	0.662012i	−0.609166	+	0.793043i	$0.708496\pi$
$32$	0.342020	−	0.939693i	0.0604612	−	0.166116i
$33$	−4.98712	−	0.879364i	−0.868146	−	0.153078i
$34$	0.641422	+	3.63769i	0.110003	+	0.623858i
$35$		0			0
$36$	3.42208	+	2.87147i	0.570347	+	0.478578i
$37$			3.49650i			0.574822i	0.957807	+	0.287411i	$0.0927945\pi$
$37$			3.49650i			0.574822i	−0.957807	+	0.287411i	$0.907205\pi$
$38$	−2.42690	−	3.62079i	−0.393696	−	0.587370i
$39$	−15.0649			−2.41231
$40$		0			0
$41$	1.47464	−	0.536727i	0.230301	−	0.0838227i	−0.224292	−	0.974522i	$-0.572007\pi$
$41$	1.47464	−	0.536727i	0.230301	−	0.0838227i	0.454593	+	0.890699i	$0.349785\pi$
$42$	5.75056	−	1.01398i	0.887331	−	0.156460i
$43$	2.29458	+	0.404597i	0.349921	+	0.0617005i	0.345846	−	0.938291i	$-0.387592\pi$
$43$	2.29458	+	0.404597i	0.349921	+	0.0617005i	0.00407464	+	0.999992i	$0.498703\pi$
$44$	−1.74143	−	0.633827i	−0.262530	−	0.0955531i
$45$		0			0
$46$	−1.47175	+	2.54915i	−0.216998	+	0.375851i
$47$	−7.20983	−	8.59234i	−1.05166	−	1.25332i	−0.966422	−	0.256961i	$-0.917279\pi$
$47$	−7.20983	−	8.59234i	−1.05166	−	1.25332i	−0.0852401	−	0.996360i	$-0.527166\pi$
$48$	1.75649	+	2.09331i	0.253528	+	0.302143i
$49$	−1.21688	+	2.10770i	−0.173840	+	0.301099i
$50$		0			0
$51$	−9.48504	−	3.45227i	−1.32817	−	0.483415i
$52$	−5.42923	−	0.957319i	−0.752898	−	0.132756i
$53$	−6.32356	+	1.11501i	−0.868607	+	0.153159i	−0.590154	−	0.807291i	$-0.700933\pi$
$53$	−6.32356	+	1.11501i	−0.868607	+	0.153159i	−0.278453	+	0.960450i	$0.589822\pi$
$54$	−3.76755	+	1.37127i	−0.512698	+	0.186607i
$55$		0			0
$56$	2.13688			0.285552
$57$	11.8846	−	0.796188i	1.57415	−	0.105458i
$58$			7.01002i			0.920460i
$59$	−10.8207	−	9.07963i	−1.40873	−	1.18207i	−0.957062	−	0.289883i	$-0.906383\pi$
$59$	−10.8207	−	9.07963i	−1.40873	−	1.18207i	−0.451672	−	0.892184i	$-0.649172\pi$
$60$		0			0
$61$	−0.0461045	−	0.261472i	−0.00590308	−	0.0334780i	0.981714	−	0.190362i	$-0.0609662\pi$
$61$	−0.0461045	−	0.261472i	−0.00590308	−	0.0334780i	−0.987617	+	0.156884i	$0.949855\pi$
$62$	−4.19148	−	0.739071i	−0.532318	−	0.0938621i
$63$	−3.26488	+	8.97020i	−0.411337	+	1.13014i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	3.87929	−	3.25511i	0.477508	−	0.400677i
$67$	−9.49761	−	11.3188i	−1.16032	−	1.38281i	−0.909979	−	0.414654i	$-0.863903\pi$
$67$	−9.49761	−	11.3188i	−1.16032	−	1.38281i	−0.250338	−	0.968158i	$-0.580542\pi$
$68$	−3.19893	−	1.84690i	−0.387927	−	0.223970i
$69$	−4.02173	−	6.96585i	−0.484160	−	0.838589i
$70$		0			0
$71$	0.722627	−	4.09822i	0.0857601	−	0.486370i	−0.911430	−	0.411455i	$-0.865021\pi$
$71$	0.722627	−	4.09822i	0.0857601	−	0.486370i	0.997190	−	0.0749143i	$-0.0238683\pi$
$72$	−4.39935	+	0.775724i	−0.518468	+	0.0914199i
$73$	5.27085	+	14.4815i	0.616906	+	1.69494i	0.714434	+	0.699703i	$0.246684\pi$
$73$	5.27085	+	14.4815i	0.616906	+	1.69494i	−0.0975282	+	0.995233i	$0.531094\pi$
$74$	−2.67848	−	2.24751i	−0.311367	−	0.261268i
$75$		0			0
$76$	4.33367	+	0.468284i	0.497106	+	0.0537159i
$77$		−	3.96003i		−	0.451288i
$78$	9.68352	−	11.5404i	1.09644	−	1.30669i
$79$	−2.70762	+	0.985493i	−0.304631	+	0.110877i	−0.489813	−	0.871828i	$-0.662935\pi$
$79$	−2.70762	+	0.985493i	−0.304631	+	0.110877i	0.185182	+	0.982704i	$0.440713\pi$
$80$		0			0
$81$	−0.424681	+	2.40849i	−0.0471868	+	0.267610i
$82$	−0.536727	+	1.47464i	−0.0592716	+	0.162847i
$83$	−12.1408	+	7.00947i	−1.33262	+	0.769389i	−0.985701	−	0.168505i	$-0.946106\pi$
$83$	−12.1408	+	7.00947i	−1.33262	+	0.769389i	−0.346921	+	0.937894i	$0.612773\pi$
$84$	−2.91964	+	5.05696i	−0.318558	+	0.551759i
$85$		0			0
$86$	−1.78487	+	1.49768i	−0.192467	+	0.161499i
$87$	−16.5893	−	9.57786i	−1.77856	−	1.02685i
$88$	1.60491	−	0.926593i	0.171084	−	0.0987752i
$89$	1.86003	+	0.676995i	0.197163	+	0.0717613i	0.438714	−	0.898627i	$-0.355434\pi$
$89$	1.86003	+	0.676995i	0.197163	+	0.0717613i	−0.241552	+	0.970388i	$0.577656\pi$
$90$		0			0
$91$	−2.04567	−	11.6016i	−0.214445	−	1.21618i
$92$	−1.00674	−	2.76599i	−0.104960	−	0.288374i
$93$	7.47588	−	8.90941i	0.775213	−	0.923863i
$94$	11.2165			1.15689
$95$		0			0
$96$	−2.73262			−0.278897
$97$	6.94855	−	8.28096i	0.705519	−	0.840805i	−0.287620	−	0.957745i	$-0.592864\pi$
$97$	6.94855	−	8.28096i	0.705519	−	0.840805i	0.993139	+	0.116940i	$0.0373085\pi$
$98$	−0.832394	−	2.28698i	−0.0840845	−	0.231020i
$99$	1.43756	+	8.15281i	0.144480	+	0.819388i
$100$		0			0
$101$	−9.37445	−	3.41202i	−0.932792	−	0.339509i	−0.169477	−	0.985534i	$-0.554208\pi$
$101$	−9.37445	−	3.41202i	−0.932792	−	0.339509i	−0.763316	+	0.646026i	$0.776430\pi$
$102$	8.74146	−	5.04688i	0.865533	−	0.499716i
$103$	−7.59952	−	4.38758i	−0.748803	−	0.432322i	0.0764583	−	0.997073i	$-0.475639\pi$
$103$	−7.59952	−	4.38758i	−0.748803	−	0.432322i	−0.825261	+	0.564751i	$0.808972\pi$
$104$	4.22319	−	3.54368i	0.414118	−	0.347486i
$105$		0			0
$106$	3.21055	−	5.56084i	0.311837	−	0.540117i
$107$	4.93917	−	2.85163i	0.477487	−	0.275677i	−0.241882	−	0.970306i	$-0.577765\pi$
$107$	4.93917	−	2.85163i	0.477487	−	0.275677i	0.719369	+	0.694628i	$0.244431\pi$
$108$	1.37127	−	3.76755i	0.131951	−	0.362532i
$109$	−0.137722	+	0.781060i	−0.0131914	+	0.0748119i	−0.990693	−	0.136117i	$-0.956538\pi$
$109$	−0.137722	+	0.781060i	−0.0131914	+	0.0748119i	0.977501	+	0.210929i	$0.0676488\pi$
$110$		0			0
$111$	8.97841	−	3.26787i	0.852193	−	0.310173i
$112$	−1.37356	+	1.63694i	−0.129789	+	0.154677i
$113$			4.98604i			0.469047i	0.972110	+	0.234523i	$0.0753530\pi$
$113$			4.98604i			0.469047i	−0.972110	+	0.234523i	$0.924647\pi$
$114$	−7.02934	+	9.61589i	−0.658358	+	0.900611i
$115$		0			0
$116$	−5.36998	−	4.50595i	−0.498590	−	0.418367i
$117$	8.42316	+	23.1424i	0.778721	+	2.13952i
$118$	13.9108	−	2.45285i	1.28059	−	0.225803i
$119$	1.37064	−	7.77329i	0.125646	−	0.712576i
$120$		0			0
$121$	3.78285	+	6.55209i	0.343895	+	0.595644i
$122$	0.229934	+	0.132753i	0.0208173	+	0.0120189i
$123$	−2.75644	−	3.28500i	−0.248540	−	0.296198i
$124$	3.26039	−	2.73579i	0.292792	−	0.245682i
$125$		0			0
$126$	−4.77294	−	8.26698i	−0.425208	−	0.736481i
$127$	−5.30620	+	14.5787i	−0.470849	+	1.29365i	0.446221	+	0.894923i	$0.352769\pi$
$127$	−5.30620	+	14.5787i	−0.470849	+	1.29365i	−0.917071	+	0.398725i	$0.869453\pi$
$128$	−0.984808	−	0.173648i	−0.0870455	−	0.0153485i
$129$	−1.10561	−	6.27023i	−0.0973436	−	0.552063i
$130$		0			0
$131$	16.8928	+	14.1748i	1.47593	+	1.23846i	0.910399	+	0.413732i	$0.135775\pi$
$131$	16.8928	+	14.1748i	1.47593	+	1.23846i	0.565535	+	0.824724i	$0.308670\pi$
$132$			5.06406i			0.440770i
$133$	2.22697	+	9.04429i	0.193103	+	0.784240i
$134$	14.7757			1.27642
$135$		0			0
$136$	3.47104	−	1.26336i	0.297639	−	0.108332i
$137$	13.7309	−	2.42112i	1.17311	−	0.206851i	0.447066	−	0.894501i	$-0.352469\pi$
$137$	13.7309	−	2.42112i	1.17311	−	0.206851i	0.726042	+	0.687650i	$0.241358\pi$
$138$	7.92127	+	1.39673i	0.674303	+	0.118898i
$139$	11.5850	+	4.21658i	0.982623	+	0.357646i	0.782860	−	0.622198i	$-0.213760\pi$
$139$	11.5850	+	4.21658i	0.982623	+	0.357646i	0.199764	+	0.979844i	$0.435983\pi$
$140$		0			0
$141$	−15.3252	+	26.5441i	−1.29062	+	2.23541i
$142$	2.67493	+	3.18785i	0.224475	+	0.267519i
$143$	−6.56709	−	7.82636i	−0.549168	−	0.654473i
$144$	2.23361	−	3.86872i	0.186134	−	0.322393i
$145$		0			0
$146$	−14.4815	−	5.27085i	−1.19850	−	0.436218i
$147$	6.54950	+	1.15485i	0.540194	+	0.0952507i
$148$	3.44339	−	0.607162i	0.283045	−	0.0499084i
$149$	21.1569	−	7.70049i	1.73324	−	0.630849i	0.734389	−	0.678729i	$-0.237469\pi$
$149$	21.1569	−	7.70049i	1.73324	−	0.630849i	0.998853	+	0.0478803i	$0.0152466\pi$
$150$		0			0
$151$	22.6452			1.84284			0.921420	−	0.388568i	$-0.127030\pi$
$151$	22.6452			1.84284			0.921420	+	0.388568i	$0.127030\pi$
$152$	−3.14436	+	3.01878i	−0.255041	+	0.244855i
$153$			16.5010i			1.33403i
$154$	3.03356	+	2.54546i	0.244451	+	0.205119i
$155$		0			0
$156$	2.61599	+	14.8360i	0.209447	+	1.18783i
$157$	−14.6588	−	2.58475i	−1.16990	−	0.206285i	−0.445253	−	0.895405i	$-0.646886\pi$
$157$	−14.6588	−	2.58475i	−1.16990	−	0.206285i	−0.724648	+	0.689119i	$0.757998\pi$
$158$	0.985493	−	2.70762i	0.0784016	−	0.215407i
$159$	8.77322	+	15.1957i	0.695762	+	1.20510i
$160$		0			0
$161$	4.81834	−	4.04307i	0.379738	−	0.318638i
$162$	−1.57203	−	1.87347i	−0.123510	−	0.147194i
$163$	9.58148	+	5.53187i	0.750479	+	0.433289i	0.825867	−	0.563865i	$-0.190686\pi$
$163$	9.58148	+	5.53187i	0.750479	+	0.433289i	−0.0753878	+	0.997154i	$0.524019\pi$
$164$	−0.784642	−	1.35904i	−0.0612703	−	0.106123i
$165$		0			0
$166$	2.43436	−	13.8060i	0.188943	−	1.07155i
$167$	−19.4224	+	3.42470i	−1.50295	+	0.265011i	−0.863708	−	0.503992i	$-0.831864\pi$
$167$	−19.4224	+	3.42470i	−1.50295	+	0.265011i	−0.639245	+	0.769003i	$0.720753\pi$
$168$	−1.99715	−	5.48712i	−0.154083	−	0.423341i
$169$	−13.3238	−	11.1800i	−1.02491	−	0.859998i
$170$		0			0
$171$	−7.86806	−	17.8117i	−0.601685	−	1.36210i
$172$		−	2.32998i		−	0.177659i
$173$	3.89388	−	4.64055i	0.296047	−	0.352815i	−0.597433	−	0.801919i	$-0.703812\pi$
$173$	3.89388	−	4.64055i	0.296047	−	0.352815i	0.893479	+	0.449105i	$0.148257\pi$
$174$	18.0005	−	6.55164i	1.36461	−	0.496678i
$175$		0			0
$176$	−0.321803	+	1.82503i	−0.0242568	+	0.137567i
$177$	−13.2018	+	36.2715i	−0.992305	+	2.72634i
$178$	−1.71421	+	0.989700i	−0.128486	+	0.0741812i
$179$	−0.625049	+	1.08262i	−0.0467184	+	0.0809186i	−0.888439	−	0.458995i	$-0.848210\pi$
$179$	−0.625049	+	1.08262i	−0.0467184	+	0.0809186i	0.841721	+	0.539913i	$0.181543\pi$
$180$		0			0
$181$	12.0955	−	10.1494i	0.899054	−	0.754396i	−0.0709510	−	0.997480i	$-0.522603\pi$
$181$	12.0955	−	10.1494i	0.899054	−	0.754396i	0.970005	+	0.243084i	$0.0781590\pi$
$182$	10.2023	+	5.89028i	0.756242	+	0.436617i
$183$	−0.628323	+	0.362763i	−0.0464470	+	0.0268162i
$184$	2.76599	+	1.00674i	0.203911	+	0.0742176i
$185$		0			0
$186$	2.01960	+	11.4537i	0.148084	+	0.839827i
$187$	−2.34123	−	6.43249i	−0.171208	−	0.470390i
$188$	−7.20983	+	8.59234i	−0.525831	+	0.626661i
$189$	8.56746			0.623191
$190$		0			0
$191$	−2.05105			−0.148409			−0.0742045	−	0.997243i	$-0.523642\pi$
$191$	−2.05105			−0.148409			−0.0742045	+	0.997243i	$0.523642\pi$
$192$	1.75649	−	2.09331i	0.126764	−	0.151072i
$193$	0.281445	+	0.773263i	0.0202588	+	0.0556607i	0.949410	−	0.314040i	$-0.101683\pi$
$193$	0.281445	+	0.773263i	0.0202588	+	0.0556607i	−0.929151	+	0.369700i	$0.879460\pi$
$194$	1.87714	+	10.6458i	0.134771	+	0.764324i
$195$		0			0
$196$	2.28698	+	0.832394i	0.163356	+	0.0594567i
$197$	11.0002	−	6.35099i	0.783734	−	0.452489i	−0.0540180	−	0.998540i	$-0.517203\pi$
$197$	11.0002	−	6.35099i	0.783734	−	0.452489i	0.837752	+	0.546051i	$0.183869\pi$
$198$	−7.16946	−	4.13929i	−0.509511	−	0.294167i
$199$	3.91363	−	3.28392i	0.277430	−	0.232791i	−0.493446	−	0.869776i	$-0.664263\pi$
$199$	3.91363	−	3.28392i	0.277430	−	0.232791i	0.770876	+	0.636985i	$0.219819\pi$
$200$		0			0
$201$	−20.1881	+	34.9669i	−1.42396	+	2.46637i
$202$	8.63954	−	4.98804i	0.607876	−	0.350957i
$203$	5.12330	−	14.0762i	0.359585	−	0.987953i
$204$	−1.75276	+	9.94042i	−0.122718	+	0.695969i
$205$		0			0
$206$	8.24596	−	3.00128i	0.574523	−	0.209109i
$207$	−8.45217	+	10.0729i	−0.587466	+	0.700115i
$208$			5.51298i			0.382256i
$209$	5.59436	+	5.82708i	0.386970	+	0.403068i
$210$		0			0
$211$	−14.9318	−	12.5293i	−1.02795	−	0.862551i	−0.0373426	−	0.999303i	$-0.511889\pi$
$211$	−14.9318	−	12.5293i	−1.02795	−	0.862551i	−0.990605	+	0.136752i	$0.956334\pi$
$212$	2.19615	+	6.03387i	0.150832	+	0.414408i
$213$	−11.1989	+	1.97467i	−0.767335	+	0.135302i
$214$	−0.990360	+	5.61661i	−0.0676996	+	0.383944i
$215$		0			0
$216$	2.00467	+	3.47219i	0.136400	+	0.236253i
$217$	7.87637	+	4.54742i	0.534683	+	0.308699i
$218$	−0.509800	−	0.607556i	−0.0345280	−	0.0411489i
$219$	32.2598	−	27.0692i	2.17992	−	1.82917i
$220$		0			0
$221$	−10.1819	−	17.6356i	−0.684911	−	1.18630i
$222$	−3.26787	+	8.97841i	−0.219325	+	0.602591i
$223$	−2.40931	−	0.424827i	−0.161340	−	0.0284485i	0.0923948	−	0.995722i	$-0.470548\pi$
$223$	−2.40931	−	0.424827i	−0.161340	−	0.0284485i	−0.253734	+	0.967274i	$0.581659\pi$
$224$	−0.371065	−	2.10441i	−0.0247928	−	0.140607i
$225$		0			0
$226$	−3.81953	−	3.20496i	−0.254071	−	0.213191i
$227$		−	19.2300i		−	1.27634i	−0.769897	−	0.638169i	$-0.779692\pi$
$227$		−	19.2300i		−	1.27634i	0.769897	−	0.638169i	$-0.220308\pi$
$228$	−2.84783	−	11.5658i	−0.188602	−	0.765962i
$229$	−20.3871			−1.34722			−0.673609	−	0.739088i	$-0.735257\pi$
$229$	−20.3871			−1.34722			−0.673609	+	0.739088i	$0.735257\pi$
$230$		0			0
$231$	−10.1687	+	3.70109i	−0.669049	+	0.243514i
$232$	6.90352	−	1.21728i	0.453238	−	0.0799181i
$233$	−8.29121	−	1.46196i	−0.543175	−	0.0957764i	−0.104673	−	0.994507i	$-0.533380\pi$
$233$	−8.29121	−	1.46196i	−0.543175	−	0.0957764i	−0.438502	+	0.898730i	$0.644491\pi$
$234$	−23.1424	−	8.42316i	−1.51287	−	0.550639i
$235$		0			0
$236$	−7.06270	+	12.2330i	−0.459743	+	0.796298i
$237$	5.06114	+	6.03163i	0.328756	+	0.391797i
$238$	5.07365	+	6.04655i	0.328876	+	0.391939i
$239$	−6.60300	+	11.4367i	−0.427113	+	0.739781i	−0.996615	−	0.0822090i	$-0.973803\pi$
$239$	−6.60300	+	11.4367i	−0.427113	+	0.739781i	0.569503	+	0.821990i	$0.307136\pi$
$240$		0			0
$241$	6.63066	+	2.41336i	0.427118	+	0.155458i	0.546630	−	0.837375i	$-0.315911\pi$
$241$	6.63066	+	2.41336i	0.427118	+	0.155458i	−0.119511	+	0.992833i	$0.538133\pi$
$242$	−7.45076	−	1.31377i	−0.478953	−	0.0844523i
$243$	18.4268	−	3.24914i	1.18208	−	0.208432i
$244$	−0.249493	+	0.0908082i	−0.0159722	+	0.00581340i
$245$		0			0
$246$	4.28826			0.273409
$247$	19.3998	+	14.1815i	1.23438	+	0.902347i
$248$			4.25614i			0.270265i
$249$	29.3460	+	24.6242i	1.85973	+	1.56049i
$250$		0			0
$251$	−0.405222	−	2.29813i	−0.0255774	−	0.145057i	0.969345	−	0.245705i	$-0.0790194\pi$
$251$	−0.405222	−	2.29813i	−0.0255774	−	0.145057i	−0.994922	+	0.100648i	$0.967908\pi$
$252$	9.40086	+	1.65763i	0.592199	+	0.104421i
$253$	1.86567	−	5.12589i	0.117294	−	0.322262i
$254$	−7.75715	−	13.4358i	−0.486727	−	0.843035i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−3.56140	−	4.24431i	−0.222154	−	0.264753i	0.643443	−	0.765494i	$-0.277505\pi$
$257$	−3.56140	−	4.24431i	−0.222154	−	0.264753i	−0.865597	+	0.500741i	$0.833061\pi$
$258$	5.51395	+	3.18348i	0.343283	+	0.198195i
$259$	3.73580	+	6.47060i	0.232131	+	0.402063i
$260$		0			0
$261$	−5.43783	+	30.8395i	−0.336593	+	1.90892i
$262$	−21.7170	+	3.82930i	−1.34168	+	0.236575i
$263$	−0.606559	−	1.66651i	−0.0374020	−	0.102761i	0.919586	−	0.392889i	$-0.128524\pi$
$263$	−0.606559	−	1.66651i	−0.0374020	−	0.102761i	−0.956988	+	0.290128i	$0.906302\pi$
$264$	−3.87929	−	3.25511i	−0.238754	−	0.200338i
$265$		0			0
$266$	−8.35980	−	4.10760i	−0.512572	−	0.251853i
$267$		−	5.40895i		−	0.331022i
$268$	−9.49761	+	11.3188i	−0.580159	+	0.691406i
$269$	−14.9736	+	5.44995i	−0.912957	+	0.332289i	−0.755433	−	0.655226i	$-0.772573\pi$
$269$	−14.9736	+	5.44995i	−0.912957	+	0.332289i	−0.157524	+	0.987515i	$0.550351\pi$
$270$		0			0
$271$	2.44844	−	13.8858i	0.148732	−	0.843502i	−0.815562	−	0.578669i	$-0.803572\pi$
$271$	2.44844	−	13.8858i	0.148732	−	0.843502i	0.964294	−	0.264832i	$-0.0853166\pi$
$272$	−1.26336	+	3.47104i	−0.0766022	+	0.210463i
$273$	−27.8789	+	16.0959i	−1.68731	+	0.974168i
$274$	−6.97135	+	12.0747i	−0.421155	+	0.729461i
$275$		0			0
$276$	−6.16165	+	5.17024i	−0.370888	+	0.311212i
$277$	19.2828	+	11.1329i	1.15859	+	0.668912i	0.950965	−	0.309297i	$-0.100094\pi$
$277$	19.2828	+	11.1329i	1.15859	+	0.668912i	0.207623	+	0.978209i	$0.433427\pi$
$278$	−10.6768	+	6.16423i	−0.640349	+	0.369706i
$279$	−17.8665	−	6.50286i	−1.06964	−	0.389316i
$280$		0			0
$281$	−1.26898	−	7.19674i	−0.0757009	−	0.429321i	−0.998979	−	0.0451879i	$-0.985611\pi$
$281$	−1.26898	−	7.19674i	−0.0757009	−	0.429321i	0.923278	−	0.384133i	$-0.125500\pi$
$282$	−10.4831	−	28.8020i	−0.624258	−	1.71513i
$283$	6.62536	−	7.89580i	0.393837	−	0.469357i	−0.532294	−	0.846560i	$-0.678670\pi$
$283$	6.62536	−	7.89580i	0.393837	−	0.469357i	0.926131	+	0.377203i	$0.123114\pi$
$284$	−4.16145			−0.246936
$285$		0			0
$286$	10.2166			0.604119
$287$	2.15550	−	2.56883i	0.127235	−	0.151633i
$288$	1.52788	+	4.19781i	0.0900310	+	0.247358i
$289$	0.582730	+	3.30482i	0.0342782	+	0.194401i
$290$		0			0
$291$	−27.7582	−	10.1032i	−1.62722	−	0.592259i
$292$	13.3463	−	7.70546i	0.781030	−	0.450928i
$293$	26.5315	+	15.3180i	1.54999	+	0.894887i	0.998141	+	0.0609422i	$0.0194105\pi$
$293$	26.5315	+	15.3180i	1.54999	+	0.894887i	0.551848	+	0.833945i	$0.313923\pi$
$294$	−5.09461	+	4.27488i	−0.297123	+	0.249316i
$295$		0			0
$296$	−1.74825	+	3.02806i	−0.101615	+	0.176003i
$297$	6.43461	−	3.71503i	0.373374	−	0.215568i
$298$	−7.70049	+	21.1569i	−0.446077	+	1.22559i
$299$	2.81787	−	15.9809i	0.162962	−	0.924201i
$300$		0			0
$301$	4.67862	−	1.70288i	0.269671	−	0.0981523i
$302$	−14.5561	+	17.3472i	−0.837607	+	0.998221i
$303$			27.2608i			1.56609i
$304$	−0.291364	−	4.34915i	−0.0167109	−	0.249441i
$305$		0			0
$306$	−12.6405	−	10.6066i	−0.722610	−	0.606342i
$307$	2.73189	+	7.50580i	0.155917	+	0.428379i	0.992915	−	0.118828i	$-0.0379136\pi$
$307$	2.73189	+	7.50580i	0.155917	+	0.428379i	−0.836998	+	0.547206i	$0.815691\pi$
$308$	−3.89987	+	0.687652i	−0.222216	+	0.0391826i
$309$	−4.16395	+	23.6149i	−0.236879	+	1.34341i
$310$		0			0
$311$	13.3155	+	23.0631i	0.755052	+	1.30779i	0.945348	+	0.326062i	$0.105722\pi$
$311$	13.3155	+	23.0631i	0.755052	+	1.30779i	−0.190296	+	0.981727i	$0.560945\pi$
$312$	−13.0466	−	7.53244i	−0.738617	−	0.426440i
$313$	4.92589	+	5.87045i	0.278428	+	0.331817i	0.887076	−	0.461622i	$-0.152733\pi$
$313$	4.92589	+	5.87045i	0.278428	+	0.331817i	−0.608649	+	0.793440i	$0.708288\pi$
$314$	11.4025	−	9.56787i	0.643482	−	0.539946i
$315$		0			0
$316$	1.44069	+	2.49535i	0.0810454	+	0.140375i
$317$	−1.01446	+	2.78721i	−0.0569779	+	0.156545i	−0.964916	−	0.262559i	$-0.915434\pi$
$317$	−1.01446	+	2.78721i	−0.0569779	+	0.156545i	0.907938	+	0.419104i	$0.137656\pi$
$318$	−17.2799	−	3.04691i	−0.969008	−	0.170862i
$319$	−2.25584	−	12.7935i	−0.126303	−	0.716299i
$320$		0			0
$321$	−11.9387	−	10.0177i	−0.666352	−	0.559136i
$322$			6.28990i			0.350522i
$323$	8.96451	+	13.3745i	0.498799	+	0.744177i
$324$	2.44564			0.135869
$325$		0			0
$326$	−10.3965	+	3.78402i	−0.575810	+	0.209578i
$327$	2.13434	−	0.376342i	0.118029	−	0.0208117i
$328$	1.54544	+	0.272503i	0.0853328	+	0.0150465i
$329$	−22.5228	−	8.19764i	−1.24172	−	0.451950i
$330$		0			0
$331$	−1.33020	+	2.30397i	−0.0731143	+	0.126638i	−0.900265	−	0.435343i	$-0.856627\pi$
$331$	−1.33020	+	2.30397i	−0.0731143	+	0.126638i	0.827150	+	0.561981i	$0.189960\pi$
$332$	9.01120	+	10.7391i	0.494554	+	0.589386i
$333$	−10.0401	−	11.9653i	−0.550194	−	0.655696i
$334$	9.86103	−	17.0798i	0.539572	−	0.934565i
$335$		0			0
$336$	5.48712	+	1.99715i	0.299347	+	0.108953i
$337$	30.8485	+	5.43943i	1.68043	+	0.296304i	0.930792	−	0.365549i	$-0.119119\pi$
$337$	30.8485	+	5.43943i	1.68043	+	0.296304i	0.749634	+	0.661853i	$0.230230\pi$
$338$	17.1287	−	3.02025i	0.931679	−	0.164280i
$339$	12.8033	−	4.66001i	0.695378	−	0.253097i
$340$		0			0
$341$	7.88742			0.427128
$342$	18.7021	+	5.42188i	1.01129	+	0.293181i
$343$			20.1588i			1.08847i
$344$	1.78487	+	1.49768i	0.0962337	+	0.0807497i
$345$		0			0
$346$	1.05193	+	5.96578i	0.0565520	+	0.320722i
$347$	−10.4564	−	1.84375i	−0.561330	−	0.0989776i	−0.114218	−	0.993456i	$-0.536436\pi$
$347$	−10.4564	−	1.84375i	−0.561330	−	0.0989776i	−0.447112	+	0.894478i	$0.647547\pi$
$348$	−6.55164	+	18.0005i	−0.351205	+	0.964927i
$349$	18.4784	+	32.0056i	0.989128	+	1.71322i	0.621921	+	0.783080i	$0.286352\pi$
$349$	18.4784	+	32.0056i	0.989128	+	1.71322i	0.367206	+	0.930139i	$0.380314\pi$
$350$		0			0
$351$	16.9322	−	14.2078i	0.903773	−	0.758356i
$352$	−1.19121	−	1.41962i	−0.0634915	−	0.0756662i
$353$	−26.7210	−	15.4274i	−1.42222	−	0.821117i	−0.425729	−	0.904851i	$-0.639982\pi$
$353$	−26.7210	−	15.4274i	−1.42222	−	0.821117i	−0.996488	+	0.0837337i	$0.973315\pi$
$354$	−19.2997	−	33.4280i	−1.02577	−	1.77668i
$355$		0			0
$356$	0.343719	−	1.94933i	0.0182171	−	0.103314i
$357$	−21.2414	+	3.74544i	−1.12422	+	0.198230i
$358$	−0.427559	−	1.17471i	−0.0225972	−	0.0620853i
$359$	7.76753	+	6.51773i	0.409954	+	0.343993i	0.824326	−	0.566115i	$-0.191554\pi$
$359$	7.76753	+	6.51773i	0.409954	+	0.343993i	−0.414372	+	0.910108i	$0.635999\pi$
$360$		0			0
$361$	−16.0538	−	10.1624i	−0.844939	−	0.534862i
$362$			15.7896i			0.829883i
$363$	13.2891	−	15.8373i	0.697497	−	0.831245i
$364$	−11.0701	+	4.02919i	−0.580231	+	0.211187i
$365$		0			0
$366$	0.125986	−	0.714503i	0.00658540	−	0.0373477i
$367$	4.02729	−	11.0649i	0.210223	−	0.577583i	−0.789104	−	0.614259i	$-0.789455\pi$
$367$	4.02729	−	11.0649i	0.210223	−	0.577583i	0.999327	+	0.0366766i	$0.0116771\pi$
$368$	−2.54915	+	1.47175i	−0.132883	+	0.0767203i
$369$	−3.50516	+	6.07112i	−0.182472	+	0.316050i
$370$		0			0
$371$	−10.5110	+	8.81976i	−0.545703	+	0.457899i
$372$	−10.0722	−	5.81521i	−0.522221	−	0.301504i
$373$	16.9501	−	9.78613i	0.877641	−	0.506706i	0.00776129	−	0.999970i	$-0.497529\pi$
$373$	16.9501	−	9.78613i	0.877641	−	0.506706i	0.869880	+	0.493263i	$0.164196\pi$
$374$	6.43249	+	2.34123i	0.332616	+	0.121062i
$375$		0			0
$376$	−1.94773	−	11.0461i	−0.100446	−	0.569659i
$377$	−13.2177	−	36.3154i	−0.680748	−	1.87034i
$378$	−5.50706	+	6.56306i	−0.283252	+	0.337567i
$379$	−19.0901			−0.980591			−0.490296	−	0.871556i	$-0.663111\pi$
$379$	−19.0901			−0.980591			−0.490296	+	0.871556i	$0.663111\pi$
$380$		0			0
$381$	42.3947			2.17195
$382$	1.31839	−	1.57120i	0.0674548	−	0.0803894i
$383$	−6.72885	−	18.4874i	−0.343828	−	0.944660i	−0.984273	−	0.176655i	$-0.943472\pi$
$383$	−6.72885	−	18.4874i	−0.343828	−	0.944660i	0.640445	−	0.768004i	$-0.278750\pi$
$384$	0.474515	+	2.69111i	0.0242150	+	0.137330i
$385$		0			0
$386$	−0.773263	−	0.281445i	−0.0393580	−	0.0143252i
$387$	−9.01405	+	5.20426i	−0.458210	+	0.264548i
$388$	−9.36176	−	5.40502i	−0.475271	−	0.274398i
$389$	18.4221	−	15.4580i	0.934038	−	0.783751i	−0.0425001	−	0.999096i	$-0.513532\pi$
$389$	18.4221	−	15.4580i	0.934038	−	0.783751i	0.976538	+	0.215346i	$0.0690878\pi$
$390$		0			0
$391$	5.43636	−	9.41605i	0.274928	−	0.476190i
$392$	−2.10770	+	1.21688i	−0.106455	+	0.0614617i
$393$	20.6101	−	56.6257i	1.03964	−	2.85639i
$394$	−2.20567	+	12.5090i	−0.111120	+	0.630194i
$395$		0			0
$396$	7.77932	−	2.83144i	0.390926	−	0.142285i
$397$	1.63337	−	1.94657i	0.0819763	−	0.0976956i	−0.723497	−	0.690327i	$-0.757467\pi$
$397$	1.63337	−	1.94657i	0.0819763	−	0.0976956i	0.805474	+	0.592632i	$0.201911\pi$
$398$			5.10888i			0.256085i
$399$	21.1428	−	14.1714i	1.05846	−	0.709455i
$400$		0			0
$401$	1.13717	+	0.954196i	0.0567874	+	0.0476503i	0.670740	−	0.741693i	$-0.265977\pi$
$401$	1.13717	+	0.954196i	0.0567874	+	0.0476503i	−0.613952	+	0.789343i	$0.710421\pi$
$402$	−13.8095	−	37.9413i	−0.688755	−	1.89234i
$403$	23.1075	−	4.07448i	1.15107	−	0.202964i
$404$	−1.73233	+	9.82452i	−0.0861865	+	0.488788i
$405$		0			0
$406$	7.48977	+	12.9727i	0.371711	+	0.643822i
$407$	5.61156	+	3.23984i	0.278155	+	0.160593i
$408$	−6.48815	−	7.73227i	−0.321211	−	0.382805i
$409$	−9.40691	+	7.89333i	−0.465142	+	0.390300i	−0.845019	−	0.534737i	$-0.820411\pi$
$409$	−9.40691	+	7.89333i	−0.465142	+	0.390300i	0.379877	+	0.925037i	$0.375966\pi$
$410$		0			0
$411$	−19.0501	−	32.9957i	−0.939670	−	1.62756i
$412$	−3.00128	+	8.24596i	−0.147863	+	0.406249i
$413$	−29.7257	−	5.24144i	−1.46271	−	0.257914i
$414$	−2.28334	−	12.9495i	−0.112220	−	0.636432i
$415$		0			0
$416$	−4.22319	−	3.54368i	−0.207059	−	0.173743i
$417$		−	33.6890i		−	1.64976i
$418$	−8.05979	+	0.539953i	−0.394217	+	0.0264099i
$419$	2.95132			0.144182			0.0720908	−	0.997398i	$-0.477033\pi$
$419$	2.95132			0.144182			0.0720908	+	0.997398i	$0.477033\pi$
$420$		0			0
$421$	7.04747	−	2.56507i	0.343472	−	0.125014i	−0.164524	−	0.986373i	$-0.552609\pi$
$421$	7.04747	−	2.56507i	0.343472	−	0.125014i	0.507996	+	0.861359i	$0.330386\pi$
$422$	19.1960	−	3.38477i	0.934445	−	0.164768i
$423$	49.3453	+	8.70091i	2.39925	+	0.423053i
$424$	−6.03387	−	2.19615i	−0.293031	−	0.106654i
$425$		0			0
$426$	5.68583	−	9.84814i	0.275479	−	0.477144i
$427$	−0.364687	−	0.434617i	−0.0176484	−	0.0210326i
$428$	−3.66598	−	4.36895i	−0.177202	−	0.211181i
$429$	−13.9590	+	24.1777i	−0.673948	+	1.16731i
$430$		0			0
$431$	22.6407	+	8.24053i	1.09056	+	0.396933i	0.823829	−	0.566838i	$-0.191833\pi$
$431$	22.6407	+	8.24053i	1.09056	+	0.396933i	0.266734	+	0.963770i	$0.414056\pi$
$432$	−3.94843	−	0.696214i	−0.189969	−	0.0334966i
$433$	34.8458	−	6.14426i	1.67458	−	0.295274i	0.745875	−	0.666086i	$-0.232032\pi$
$433$	34.8458	−	6.14426i	1.67458	−	0.295274i	0.928708	+	0.370812i	$0.120920\pi$
$434$	−8.54636	+	3.11062i	−0.410238	+	0.149315i
$435$		0			0
$436$	0.793109			0.0379830
$437$	−1.37839	+	12.7562i	−0.0659375	+	0.610210i
$438$			42.1122i			2.01220i
$439$	−18.2221	−	15.2901i	−0.869692	−	0.729758i	0.0943411	−	0.995540i	$-0.469926\pi$
$439$	−18.2221	−	15.2901i	−0.869692	−	0.729758i	−0.964033	+	0.265782i	$0.914370\pi$
$440$		0			0
$441$	−1.88792	−	10.7069i	−0.0899011	−	0.509855i
$442$	20.0545	+	3.53615i	0.953895	+	0.168197i
$443$	4.68618	−	12.8752i	0.222647	−	0.611718i	−0.777199	−	0.629255i	$-0.783360\pi$
$443$	4.68618	−	12.8752i	0.222647	−	0.611718i	0.999846	+	0.0175367i	$0.00558239\pi$
$444$	−4.77731	−	8.27454i	−0.226721	−	0.392692i
$445$		0			0
$446$	1.87411	−	1.57257i	0.0887418	−	0.0744632i
$447$	−39.5470	−	47.1303i	−1.87051	−	2.22918i
$448$	1.85059	+	1.06844i	0.0874321	+	0.0504790i
$449$	7.58152	+	13.1316i	0.357794	+	0.619717i	0.987592	−	0.157042i	$-0.0501957\pi$
$449$	7.58152	+	13.1316i	0.357794	+	0.619717i	−0.629798	+	0.776759i	$0.716862\pi$
$450$		0			0
$451$	0.505000	−	2.86400i	0.0237795	−	0.134860i
$452$	4.91029	−	0.865816i	0.230961	−	0.0407246i
$453$	−21.1645	−	58.1489i	−0.994393	−	2.73207i
$454$	14.7310	+	12.3608i	0.691360	+	0.580120i
$455$		0			0
$456$	10.6904	+	5.25277i	0.500626	+	0.245983i
$457$			33.5768i			1.57066i	0.619079	+	0.785329i	$0.287506\pi$
$457$			33.5768i			1.57066i	−0.619079	+	0.785329i	$0.712494\pi$
$458$	13.1046	−	15.6174i	0.612337	−	0.729755i
$459$	13.9166	−	5.06522i	0.649570	−	0.236424i
$460$		0			0
$461$	4.57133	−	25.9253i	0.212908	−	1.20746i	−0.671591	−	0.740922i	$-0.734389\pi$
$461$	4.57133	−	25.9253i	0.212908	−	1.20746i	0.884500	−	0.466541i	$-0.154500\pi$
$462$	3.70109	−	10.1687i	0.172190	−	0.473089i
$463$	−9.13589	+	5.27461i	−0.424581	+	0.245132i	−0.697035	−	0.717037i	$-0.745498\pi$
$463$	−9.13589	+	5.27461i	−0.424581	+	0.245132i	0.272454	+	0.962169i	$0.412165\pi$
$464$	−3.50501	+	6.07085i	−0.162716	+	0.281832i
$465$		0			0
$466$	6.44942	−	5.41170i	0.298763	−	0.250692i
$467$	−26.4283	−	15.2584i	−1.22296	−	0.706074i	−0.257408	−	0.966303i	$-0.582869\pi$
$467$	−26.4283	−	15.2584i	−1.22296	−	0.706074i	−0.965547	+	0.260229i	$0.916202\pi$
$468$	21.3282	−	12.3138i	0.985895	−	0.569207i
$469$	−29.6696	−	10.7989i	−1.37002	−	0.498645i
$470$		0			0
$471$	7.06313	+	40.0570i	0.325452	+	1.84573i
$472$	−4.83117	−	13.2735i	−0.222373	−	0.610964i
$473$	2.77549	−	3.30770i	0.127617	−	0.152088i
$474$	−7.87374			−0.361653
$475$		0			0
$476$	−7.89321			−0.361784
$477$	18.4380	−	21.9736i	0.844219	−	1.00610i
$478$	−4.51672	−	12.4096i	−0.206590	−	0.567601i
$479$	−0.664874	−	3.77069i	−0.0303789	−	0.172287i	0.965843	−	0.259126i	$-0.0834345\pi$
$479$	−0.664874	−	3.77069i	−0.0303789	−	0.172287i	−0.996222	+	0.0868390i	$0.972323\pi$
$480$		0			0
$481$	18.1137	+	6.59284i	0.825912	+	0.300607i
$482$	−6.11085	+	3.52810i	−0.278341	+	0.160700i
$483$	−14.8852	−	8.59395i	−0.677298	−	0.391038i
$484$	5.79566	−	4.86314i	0.263439	−	0.221052i
$485$		0			0
$486$	−9.35551	+	16.2042i	−0.424375	+	0.735039i
$487$	−30.6951	+	17.7218i	−1.39093	+	0.803052i	−0.993418	−	0.114546i	$-0.963459\pi$
$487$	−30.6951	+	17.7218i	−1.39093	+	0.803052i	−0.397509	+	0.917598i	$0.630125\pi$
$488$	0.0908082	−	0.249493i	0.00411069	−	0.0112940i
$489$	5.24990	−	29.7737i	0.237409	−	1.34641i
$490$		0			0
$491$	−8.02415	+	2.92055i	−0.362125	+	0.131803i	−0.516673	−	0.856183i	$-0.672830\pi$
$491$	−8.02415	+	2.92055i	−0.362125	+	0.131803i	0.154549	+	0.987985i	$0.450608\pi$
$492$	−2.75644	+	3.28500i	−0.124270	+	0.148099i
$493$		−	25.8936i		−	1.16619i
$494$	−23.3336	+	5.74541i	−1.04983	+	0.258498i
$495$		0			0
$496$	−3.26039	−	2.73579i	−0.146396	−	0.122841i
$497$	−3.04141	−	8.35621i	−0.136426	−	0.374827i
$498$	−37.7265	+	6.65219i	−1.69056	+	0.298092i
$499$	−6.45368	+	36.6007i	−0.288907	+	1.63847i	0.402081	+	0.915604i	$0.368287\pi$
$499$	−6.45368	+	36.6007i	−0.288907	+	1.63847i	−0.690988	+	0.722866i	$0.742824\pi$
$500$		0			0
$501$	26.9465	+	46.6726i	1.20388	+	2.08518i
$502$	2.02094	+	1.16679i	0.0901991	+	0.0520765i
$503$	14.0913	+	16.7933i	0.628299	+	0.748778i	0.982474	−	0.186402i	$-0.0596826\pi$
$503$	14.0913	+	16.7933i	0.628299	+	0.748778i	−0.354175	+	0.935179i	$0.615238\pi$
$504$	−7.31257	+	6.13598i	−0.325728	+	0.273318i
$505$		0			0
$506$	2.72743	+	4.72404i	0.121249	+	0.210009i
$507$	−16.2556	+	44.6620i	−0.721939	+	1.98351i
$508$	15.2786	+	2.69403i	0.677878	+	0.119528i
$509$	1.71368	+	9.71877i	0.0759576	+	0.430777i	0.998944	+	0.0459444i	$0.0146297\pi$
$509$	1.71368	+	9.71877i	0.0759576	+	0.430777i	−0.922986	+	0.384833i	$0.874259\pi$
$510$		0			0
$511$	25.2268	+	21.1678i	1.11597	+	0.936408i
$512$			1.00000i			0.0441942i
$513$	−12.6068	+	12.1033i	−0.556603	+	0.534374i
$514$	5.54056			0.244384
$515$		0			0
$516$	−5.98298	+	2.17763i	−0.263386	+	0.0958647i
$517$	−20.4705	+	3.60950i	−0.900291	+	0.158746i
$518$	−7.35809	−	1.29743i	−0.323296	−	0.0570058i
$519$	−15.5554	−	5.66170i	−0.682805	−	0.248521i
$520$		0			0
$521$	2.86829	−	4.96802i	0.125662	−	0.217653i	−0.796330	−	0.604863i	$-0.793228\pi$
$521$	2.86829	−	4.96802i	0.125662	−	0.217653i	0.921991	+	0.387210i	$0.126561\pi$
$522$	−20.1290	−	23.9889i	−0.881024	−	1.04996i
$523$	−17.1734	−	20.4665i	−0.750941	−	0.894937i	0.246298	−	0.969194i	$-0.420786\pi$
$523$	−17.1734	−	20.4665i	−0.750941	−	0.894937i	−0.997239	+	0.0742573i	$0.976341\pi$
$524$	11.0260	−	19.0976i	0.481674	−	0.834283i
$525$		0			0
$526$	1.66651	+	0.606559i	0.0726632	+	0.0264472i
$527$	15.4825	+	2.72998i	0.674428	+	0.118920i
$528$	4.98712	−	0.879364i	0.217037	−	0.0382694i
$529$	−13.4713	+	4.90314i	−0.585707	+	0.213180i
$530$		0			0
$531$	63.1012			2.73836
$532$	8.52018	−	3.76366i	0.369397	−	0.163175i
$533$		−	8.65143i		−	0.374735i
$534$	4.14350	+	3.47681i	0.179307	+	0.150456i
$535$		0			0
$536$	−2.56577	−	14.5512i	−0.110824	−	0.628515i
$537$	3.36415	+	0.593190i	0.145174	+	0.0255980i
$538$	5.44995	−	14.9736i	0.234964	−	0.645558i
$539$	2.25510	+	3.90595i	0.0971342	+	0.168241i
$540$		0			0
$541$	23.7434	−	19.9231i	1.02081	−	0.856562i	0.0310814	−	0.999517i	$-0.490105\pi$
$541$	23.7434	−	19.9231i	1.02081	−	0.856562i	0.989729	+	0.142955i	$0.0456604\pi$
$542$	9.06330	+	10.8012i	0.389302	+	0.463952i
$543$	−37.3664	−	21.5735i	−1.60355	−	0.925807i
$544$	−1.84690	−	3.19893i	−0.0791853	−	0.137153i
$545$		0			0
$546$	5.59005	−	31.7027i	0.239232	−	1.35675i
$547$	17.1347	−	3.02131i	0.732627	−	0.129182i	0.205125	−	0.978736i	$-0.434240\pi$
$547$	17.1347	−	3.02131i	0.732627	−	0.129182i	0.527502	+	0.849554i	$0.323129\pi$
$548$	−4.76868	−	13.1019i	−0.203708	−	0.559683i
$549$	0.908582	+	0.762391i	0.0387773	+	0.0325380i
$550$		0			0
$551$	12.3467	+	27.9504i	0.525986	+	1.19073i
$552$		−	8.04347i		−	0.342353i
$553$	−3.95775	+	4.71667i	−0.168301	+	0.200573i
$554$	−20.9230	+	7.61536i	−0.888934	+	0.323546i
$555$		0			0
$556$	2.14081	−	12.1412i	0.0907907	−	0.514900i
$557$	−4.04009	+	11.1000i	−0.171184	+	0.470324i	−0.995384	−	0.0959752i	$-0.969403\pi$
$557$	−4.04009	+	11.1000i	−0.171184	+	0.470324i	0.824200	+	0.566299i	$0.191625\pi$
$558$	16.4658	−	9.50654i	0.697053	−	0.402444i
$559$	6.42257	−	11.1242i	0.271646	−	0.470504i
$560$		0			0
$561$	−14.3293	+	12.0238i	−0.604986	+	0.507643i
$562$	6.32870	+	3.65388i	0.266960	+	0.154130i
$563$	−27.1901	+	15.6982i	−1.14592	+	0.661600i	−0.947891	−	0.318595i	$-0.896789\pi$
$563$	−27.1901	+	15.6982i	−1.14592	+	0.661600i	−0.198034	+	0.980195i	$0.563456\pi$
$564$	28.8020	+	10.4831i	1.21278	+	0.441417i
$565$		0			0
$566$	1.78983	+	10.1506i	0.0752323	+	0.426663i
$567$	1.78741	+	4.91087i	0.0750642	+	0.206237i
$568$	2.67493	−	3.18785i	0.112237	−	0.133759i
$569$	−3.95114			−0.165640			−0.0828202	−	0.996565i	$-0.526393\pi$
$569$	−3.95114			−0.165640			−0.0828202	+	0.996565i	$0.526393\pi$
$570$		0			0
$571$	2.18380			0.0913891			0.0456946	−	0.998955i	$-0.485450\pi$
$571$	2.18380			0.0913891			0.0456946	+	0.998955i	$0.485450\pi$
$572$	−6.56709	+	7.82636i	−0.274584	+	0.327236i
$573$	1.91694	+	5.26674i	0.0800812	+	0.220021i
$574$	0.582306	+	3.30242i	0.0243050	+	0.137840i
$575$		0			0
$576$	−4.19781	−	1.52788i	−0.174909	−	0.0636615i
$577$	11.2886	−	6.51747i	0.469950	−	0.271326i	−0.246269	−	0.969202i	$-0.579205\pi$
$577$	11.2886	−	6.51747i	0.469950	−	0.271326i	0.716219	+	0.697876i	$0.245871\pi$
$578$	−2.90621	−	1.67790i	−0.120883	−	0.0697916i
$579$	1.72256	−	1.44540i	0.0715872	−	0.0600688i
$580$		0			0
$581$	−14.9784	+	25.9433i	−0.621408	+	1.07631i
$582$	25.5821	−	14.7699i	1.06041	−	0.612230i
$583$	−4.06987	+	11.1819i	−0.168557	+	0.463106i
$584$	−2.67608	+	15.1768i	−0.110737	+	0.628020i
$585$		0			0
$586$	−28.7884	+	10.4781i	−1.18924	+	0.432847i
$587$	24.9144	−	29.6918i	1.02833	−	1.22551i	0.0544318	−	0.998517i	$-0.482665\pi$
$587$	24.9144	−	29.6918i	1.02833	−	1.22551i	0.973896	−	0.226996i	$-0.0728903\pi$
$588$		−	6.65054i		−	0.274263i
$589$	−18.0140	+	4.43558i	−0.742255	+	0.182765i
$590$		0			0
$591$	−26.5891	−	22.3109i	−1.09373	−	0.917750i
$592$	−1.19588	−	3.28564i	−0.0491502	−	0.135039i
$593$	−17.1453	+	3.02318i	−0.704073	+	0.124147i	−0.514211	−	0.857664i	$-0.671915\pi$
$593$	−17.1453	+	3.02318i	−0.704073	+	0.124147i	−0.189862	+	0.981811i	$0.560804\pi$
$594$	−1.29022	+	7.31717i	−0.0529382	+	0.300227i
$595$		0			0
$596$	−11.2574	−	19.4983i	−0.461119	−	0.798682i
$597$	−12.0903	−	6.98031i	−0.494821	−	0.285685i
$598$	10.4308	+	12.4310i	0.426547	+	0.508339i
$599$	24.6574	−	20.6900i	1.00747	−	0.845370i	0.0194709	−	0.999810i	$-0.493802\pi$
$599$	24.6574	−	20.6900i	1.00747	−	0.845370i	0.988002	+	0.154440i	$0.0493574\pi$
$600$		0			0
$601$	−18.1105	−	31.3683i	−0.738742	−	1.27954i	−0.953062	−	0.302775i	$-0.902087\pi$
$601$	−18.1105	−	31.3683i	−0.738742	−	1.27954i	0.214321	−	0.976763i	$-0.431246\pi$
$602$	−1.70288	+	4.67862i	−0.0694042	+	0.190686i
$603$	65.0032	+	11.4618i	2.64714	+	0.466761i
$604$	−3.93230	−	22.3012i	−0.160003	−	0.907422i
$605$		0			0
$606$	−20.8830	−	17.5229i	−0.848314	−	0.711820i
$607$			30.3654i			1.23250i	0.787552	+	0.616248i	$0.211348\pi$
$607$			30.3654i			1.23250i	−0.787552	+	0.616248i	$0.788652\pi$
$608$	3.51893	+	2.57238i	0.142711	+	0.104324i
$609$	−40.9334			−1.65870
$610$		0			0
$611$	−58.1072	+	21.1493i	−2.35076	+	0.855608i
$612$	16.2503	−	2.86537i	0.656881	−	0.115826i
$613$	22.4794	+	3.96373i	0.907936	+	0.160094i	0.608066	−	0.793886i	$-0.291946\pi$
$613$	22.4794	+	3.96373i	0.907936	+	0.160094i	0.299870	+	0.953980i	$0.403057\pi$
$614$	−7.50580	−	2.73189i	−0.302910	−	0.110250i
$615$		0			0
$616$	1.98002	−	3.42949i	0.0797771	−	0.138178i
$617$	25.5214	+	30.4152i	1.02745	+	1.22447i	0.974153	+	0.225890i	$0.0725289\pi$
$617$	25.5214	+	30.4152i	1.02745	+	1.22447i	0.0532981	+	0.998579i	$0.483027\pi$
$618$	−15.4135	−	18.3691i	−0.620023	−	0.738915i
$619$	19.6707	−	34.0707i	0.790633	−	1.36942i	−0.134943	−	0.990853i	$-0.543085\pi$
$619$	19.6707	−	34.0707i	0.790633	−	1.36942i	0.925576	−	0.378562i	$-0.123581\pi$
$620$		0			0
$621$	11.0898	+	4.03635i	0.445017	+	0.161973i
$622$	−26.2264	−	4.62442i	−1.05158	−	0.185422i
$623$	4.16548	−	0.734486i	0.166886	−	0.0294266i
$624$	14.1564	−	5.15249i	0.566708	−	0.206265i
$625$		0			0
$626$	−7.66333			−0.306288
$627$	9.73436	−	19.8114i	0.388753	−	0.791190i
$628$			14.8850i			0.593974i
$629$	9.89378	+	8.30186i	0.394491	+	0.331017i
$630$		0			0
$631$	0.418513	+	2.37351i	0.0166607	+	0.0944878i	0.992004	−	0.126204i	$-0.0402795\pi$
$631$	0.418513	+	2.37351i	0.0166607	+	0.0944878i	−0.975344	+	0.220692i	$0.929168\pi$
$632$	−2.83761	−	0.500348i	−0.112874	−	0.0199028i
$633$	−18.2175	+	50.0522i	−0.724082	+	1.98940i
$634$	−1.48304	−	2.56871i	−0.0588992	−	0.102016i
$635$		0			0
$636$	13.4414	−	11.2786i	0.532985	−	0.447227i
$637$	8.62445	+	10.2782i	0.341713	+	0.407238i
$638$	11.2504	+	6.49543i	0.445408	+	0.257157i
$639$	9.29503	+	16.0995i	0.367706	+	0.636885i
$640$		0			0
$641$	−2.88094	+	16.3386i	−0.113790	+	0.645337i	0.873552	+	0.486731i	$0.161811\pi$
$641$	−2.88094	+	16.3386i	−0.113790	+	0.645337i	−0.987342	+	0.158606i	$0.949300\pi$
$642$	15.3481	−	2.70628i	0.605740	−	0.106808i
$643$	11.7811	+	32.3683i	0.464601	+	1.27648i	0.921990	+	0.387214i	$0.126562\pi$
$643$	11.7811	+	32.3683i	0.464601	+	1.27648i	−0.457389	+	0.889267i	$0.651215\pi$
$644$	−4.81834	−	4.04307i	−0.189869	−	0.159319i
$645$		0			0
$646$	−16.0077	−	1.72975i	−0.629816	−	0.0680561i
$647$		−	5.97186i		−	0.234778i	−0.993086	−	0.117389i	$-0.962548\pi$
$647$		−	5.97186i		−	0.234778i	0.993086	−	0.117389i	$-0.0374525\pi$
$648$	−1.57203	+	1.87347i	−0.0617551	+	0.0735969i
$649$	−24.5983	+	8.95307i	−0.965570	+	0.351439i
$650$		0			0
$651$	4.31564	−	24.4752i	0.169143	−	0.959258i
$652$	3.78402	−	10.3965i	0.148194	−	0.407159i
$653$	7.32332	−	4.22812i	0.286584	−	0.165459i	−0.349816	−	0.936818i	$-0.613756\pi$
$653$	7.32332	−	4.22812i	0.286584	−	0.165459i	0.636400	+	0.771359i	$0.280423\pi$
$654$	−1.08363	+	1.87691i	−0.0423734	+	0.0733928i
$655$		0			0
$656$	−1.20214	+	1.00872i	−0.0469357	+	0.0393838i
$657$	−59.6206	−	34.4220i	−2.32602	−	1.34293i
$658$	20.7571	−	11.9841i	0.809198	−	0.467191i
$659$	−21.5906	−	7.85832i	−0.841049	−	0.306117i	−0.114664	−	0.993404i	$-0.536579\pi$
$659$	−21.5906	−	7.85832i	−0.841049	−	0.306117i	−0.726385	+	0.687288i	$0.758801\pi$
$660$		0			0
$661$	4.06768	+	23.0690i	0.158214	+	0.897278i	0.955788	+	0.294057i	$0.0950054\pi$
$661$	4.06768	+	23.0690i	0.158214	+	0.897278i	−0.797574	+	0.603222i	$0.793883\pi$
$662$	−0.909909	−	2.49995i	−0.0353646	−	0.0971635i
$663$	−35.7690	+	42.6279i	−1.38915	+	1.65553i
$664$	−14.0189			−0.544040
$665$		0			0
$666$	15.6196			0.605249
$667$	13.2633	−	15.8065i	0.513556	−	0.612032i
$668$	6.74534	+	18.5327i	0.260985	+	0.717051i
$669$	1.16089	+	6.58374i	0.0448826	+	0.254542i
$670$		0			0
$671$	−0.462358	−	0.168285i	−0.0178491	−	0.00649655i
$672$	−5.05696	+	2.91964i	−0.195076	+	0.112627i
$673$	0.0327120	+	0.0188863i	0.00126095	+	0.000728012i	0.500630	−	0.865661i	$-0.333102\pi$
$673$	0.0327120	+	0.0188863i	0.00126095	+	0.000728012i	−0.499369	+	0.866389i	$0.666435\pi$
$674$	−23.9959	+	20.1349i	−0.924287	+	0.775569i
$675$		0			0
$676$	−8.69647	+	15.0627i	−0.334480	+	0.579336i
$677$	26.9197	−	15.5421i	1.03461	−	0.597332i	0.116307	−	0.993213i	$-0.462894\pi$
$677$	26.9197	−	15.5421i	1.03461	−	0.597332i	0.918302	+	0.395882i	$0.129561\pi$
$678$	−4.66001	+	12.8033i	−0.178966	+	0.491706i
$679$	4.01122	−	22.7488i	0.153937	−	0.873018i
$680$		0			0
$681$	−49.3791	+	17.9725i	−1.89221	+	0.688709i
$682$	−5.06994	+	6.04212i	−0.194138	+	0.231365i
$683$		−	22.0437i		−	0.843481i	−0.906717	−	0.421740i	$-0.861419\pi$
$683$		−	22.0437i		−	0.843481i	0.906717	−	0.421740i	$-0.138581\pi$
$684$	−16.1749	+	10.8415i	−0.618461	+	0.414535i
$685$		0			0
$686$	−15.4425	−	12.9578i	−0.589598	−	0.494732i
$687$	19.0540	+	52.3505i	0.726957	+	1.99730i
$688$	−2.29458	+	0.404597i	−0.0874802	+	0.0154251i
$689$	−6.14705	+	34.8616i	−0.234184	+	1.32812i
$690$		0			0
$691$	−4.10144	−	7.10391i	−0.156026	−	0.270245i	0.777406	−	0.628999i	$-0.216535\pi$
$691$	−4.10144	−	7.10391i	−0.156026	−	0.270245i	−0.933432	+	0.358754i	$0.883202\pi$
$692$	−5.24622	−	3.02890i	−0.199431	−	0.115142i
$693$	11.3711	+	13.5516i	0.431953	+	0.514781i
$694$	8.13364	−	6.82494i	0.308749	−	0.259071i
$695$		0			0
$696$	−9.57786	−	16.5893i	−0.363048	−	0.628817i
$697$	1.98256	−	5.44705i	0.0750950	−	0.206322i
$698$	−36.3954	−	6.41749i	−1.37759	−	0.242906i
$699$	3.99499	+	22.6567i	0.151104	+	0.856956i
$700$		0			0
$701$	2.73064	+	2.29128i	0.103135	+	0.0865405i	0.692897	−	0.721037i	$-0.256334\pi$
$701$	2.73064	+	2.29128i	0.103135	+	0.0865405i	−0.589762	+	0.807577i	$0.700778\pi$
$702$			22.1034i			0.834239i
$703$	−14.6382	−	4.24372i	−0.552089	−	0.160055i
$704$	1.85319			0.0698446
$705$		0			0
$706$	28.9940	−	10.5530i	1.09120	−	0.397166i
$707$	−20.9938	+	3.70177i	−0.789553	+	0.139219i
$708$	38.0130	+	6.70271i	1.42861	+	0.251903i
$709$	16.7368	+	6.09168i	0.628562	+	0.228778i	0.636605	−	0.771190i	$-0.280338\pi$
$709$	16.7368	+	6.09168i	0.628562	+	0.228778i	−0.00804307	+	0.999968i	$0.502560\pi$
$710$		0			0
$711$	6.43589	−	11.1473i	0.241365	−	0.418056i
$712$	1.27233	+	1.51631i	0.0476827	+	0.0568261i
$713$	8.05281	+	9.59696i	0.301580	+	0.359409i
$714$	10.7846	−	18.6794i	0.403602	−	0.699060i
$715$		0			0
$716$	1.17471	+	0.427559i	0.0439009	+	0.0159786i
$717$	35.5387	+	6.26644i	1.32722	+	0.234024i
$718$	−9.98574	+	1.76076i	−0.372664	+	0.0657108i
$719$	17.0854	−	6.21856i	0.637176	−	0.231913i	−0.00317562	−	0.999995i	$-0.501011\pi$
$719$	17.0854	−	6.21856i	0.637176	−	0.231913i	0.640352	+	0.768082i	$0.278789\pi$
$720$		0			0
$721$	−18.7515			−0.698341
$722$	18.1041	−	5.76570i	0.673763	−	0.214577i
$723$		−	19.2819i		−	0.717102i
$724$	−12.0955	−	10.1494i	−0.449527	−	0.377198i
$725$		0			0
$726$	3.59003	+	20.3601i	0.133239	+	0.755634i
$727$	−8.37743	−	1.47717i	−0.310702	−	0.0547851i	0.0161233	−	0.999870i	$-0.494868\pi$
$727$	−8.37743	−	1.47717i	−0.310702	−	0.0547851i	−0.326825	+	0.945085i	$0.605979\pi$
$728$	4.02919	−	11.0701i	0.149332	−	0.410285i
$729$	−21.8966	−	37.9260i	−0.810985	−	1.40467i
$730$		0			0
$731$	6.59296	−	5.53215i	0.243849	−	0.204614i
$732$	0.466359	+	0.555785i	0.0172371	+	0.0205424i
$733$	−44.1595	−	25.4955i	−1.63107	−	0.941698i	−0.983764	−	0.179468i	$-0.942562\pi$
$733$	−44.1595	−	25.4955i	−1.63107	−	0.941698i	−0.647306	−	0.762230i	$-0.724104\pi$
$734$	5.88751	+	10.1975i	0.217312	+	0.376395i
$735$		0			0
$736$	0.511133	−	2.89878i	0.0188406	−	0.106851i
$737$	−26.9661	+	4.75484i	−0.993307	+	0.175147i
$738$	−2.39767	−	6.58755i	−0.0882596	−	0.242491i
$739$	1.19013	+	0.998640i	0.0437798	+	0.0367356i	0.664415	−	0.747364i	$-0.268681\pi$
$739$	1.19013	+	0.998640i	0.0437798	+	0.0367356i	−0.620635	+	0.784099i	$0.713125\pi$
$740$		0			0
$741$	18.2843	−	63.0694i	0.671691	−	2.31691i
$742$		−	13.7211i		−	0.503718i
$743$	−6.37470	+	7.59707i	−0.233865	+	0.278710i	−0.870195	−	0.492707i	$-0.836007\pi$
$743$	−6.37470	+	7.59707i	−0.233865	+	0.278710i	0.636330	+	0.771417i	$0.280452\pi$
$744$	10.9290	−	3.97784i	0.400677	−	0.145835i
$745$		0			0
$746$	−3.39869	+	19.2749i	−0.124435	+	0.705704i
$747$	21.4192	−	58.8488i	0.783688	−	2.15317i
$748$	−5.92821	+	3.42266i	−0.216757	+	0.125145i
$749$	6.09358	−	10.5544i	0.222655	−	0.385649i
$750$		0			0
$751$	−3.53634	+	2.96734i	−0.129043	+	0.108280i	−0.705025	−	0.709183i	$-0.749064\pi$
$751$	−3.53634	+	2.96734i	−0.129043	+	0.108280i	0.575982	+	0.817462i	$0.304620\pi$
$752$	9.71378	+	5.60825i	0.354225	+	0.204512i
$753$	−5.52247	+	3.18840i	−0.201250	+	0.116192i
$754$	36.3154	+	13.2177i	1.32253	+	0.481362i
$755$		0			0
$756$	−1.48772	−	8.43730i	−0.0541080	−	0.306862i
$757$	7.94810	+	21.8372i	0.288879	+	0.793688i	0.996224	+	0.0868196i	$0.0276704\pi$
$757$	7.94810	+	21.8372i	0.288879	+	0.793688i	−0.707345	+	0.706868i	$0.750107\pi$
$758$	12.2709	−	14.6238i	0.445698	−	0.531162i
$759$	−14.9060			−0.541055
$760$		0			0
$761$	−25.6042			−0.928152			−0.464076	−	0.885795i	$-0.653614\pi$
$761$	−25.6042			−0.928152			−0.464076	+	0.885795i	$0.653614\pi$
$762$	−27.2508	+	32.4762i	−0.987191	+	1.17649i
$763$	0.579647	+	1.59257i	0.0209846	+	0.0576548i
$764$	0.356162	+	2.01989i	0.0128855	+	0.0730771i
$765$		0			0
$766$	18.4874	+	6.72885i	0.667975	+	0.243123i
$767$	−67.4401	+	38.9365i	−2.43512	+	1.40592i
$768$	−2.36652	−	1.36631i	−0.0853944	−	0.0493025i
$769$	−19.0328	+	15.9704i	−0.686339	+	0.575907i	−0.917851	−	0.396925i	$-0.870077\pi$
$769$	−19.0328	+	15.9704i	−0.686339	+	0.575907i	0.231512	+	0.972832i	$0.425633\pi$
$770$		0			0
$771$	−7.57012	+	13.1118i	−0.272631	+	0.472211i
$772$	0.712643	−	0.411445i	0.0256486	−	0.0148082i
$773$	−12.6153	+	34.6603i	−0.453741	+	1.24664i	0.476330	+	0.879266i	$0.341967\pi$
$773$	−12.6153	+	34.6603i	−0.453741	+	1.24664i	−0.930072	+	0.367378i	$0.880256\pi$
$774$	1.80742	−	10.2504i	0.0649664	−	0.368443i
$775$		0			0
$776$	10.1581	−	3.69725i	0.364655	−	0.132723i
$777$	13.1238	−	15.6404i	0.470815	−	0.561095i
$778$			24.0483i			0.862175i
$779$	0.457233	+	6.82505i	0.0163821	+	0.244533i
$780$		0			0
$781$	−5.90769	−	4.95714i	−0.211394	−	0.177380i
$782$	3.71869	+	10.2170i	0.132980	+	0.365359i
$783$	27.6785	−	4.88047i	0.989150	−	0.174414i
$784$	0.422618	−	2.39678i	0.0150935	−	0.0855994i
$785$		0			0
$786$	30.1299	+	52.1865i	1.07470	+	1.86143i
$787$	43.3382	+	25.0213i	1.54484	+	0.891914i	0.998523	+	0.0543351i	$0.0173039\pi$
$787$	43.3382	+	25.0213i	1.54484	+	0.891914i	0.546317	+	0.837579i	$0.316029\pi$
$788$	−8.16467	−	9.73028i	−0.290854	−	0.346627i
$789$	−3.71240	+	3.11507i	−0.132165	+	0.110900i
$790$		0			0
$791$	5.32727	+	9.22711i	0.189416	+	0.328078i
$792$	−2.83144	+	7.77932i	−0.100611	+	0.276426i
$793$	−1.44149	−	0.254173i	−0.0511888	−	0.00902596i
$794$	0.441252	+	2.50246i	0.0156594	+	0.0888091i
$795$		0			0
$796$	−3.91363	−	3.28392i	−0.138715	−	0.116396i
$797$			5.53339i			0.196003i	0.995186	+	0.0980013i	$0.0312449\pi$
$797$			5.53339i			0.196003i	−0.995186	+	0.0980013i	$0.968755\pi$
$798$	−2.73444	+	25.3055i	−0.0967981	+	0.895805i
$799$	−41.4316			−1.46574
$800$		0			0
$801$	−8.30914	+	3.02428i	−0.293589	+	0.106858i
$802$	−1.46191	+	0.257775i	−0.0516219	+	0.00910234i
$803$	28.1254	+	4.95928i	0.992525	+	0.175009i
$804$	37.9413	+	13.8095i	1.33809	+	0.487023i
$805$		0			0
$806$	−11.7320	+	20.3204i	−0.413242	+	0.715757i
$807$	27.9890	+	33.3560i	0.985260	+	1.17419i
$808$	−6.41250	−	7.64212i	−0.225591	−	0.268849i
$809$	6.93364	−	12.0094i	0.243774	−	0.422229i	−0.718012	−	0.696030i	$-0.754948\pi$
$809$	6.93364	−	12.0094i	0.243774	−	0.422229i	0.961786	+	0.273802i	$0.0882812\pi$
$810$		0			0
$811$	7.68087	+	2.79561i	0.269712	+	0.0981670i	0.473336	−	0.880882i	$-0.343050\pi$
$811$	7.68087	+	2.79561i	0.269712	+	0.0981670i	−0.203624	+	0.979049i	$0.565272\pi$
$812$	−14.7520	−	2.60117i	−0.517693	−	0.0912832i
$813$	−37.9446	+	6.69065i	−1.33077	+	0.234651i
$814$	−6.08890	+	2.21618i	−0.213416	+	0.0776771i
$815$		0			0
$816$	10.0938			0.353352
$817$	−4.47880	+	9.11526i	−0.156693	+	0.318902i
$818$		−	12.2798i		−	0.429355i
$819$	40.3141	+	33.8275i	1.40869	+	1.18203i
$820$		0			0
$821$	7.69213	+	43.6243i	0.268457	+	1.52250i	0.759006	+	0.651083i	$0.225685\pi$
$821$	7.69213	+	43.6243i	0.268457	+	1.52250i	−0.490549	+	0.871414i	$0.663204\pi$
$822$	37.5213	+	6.61601i	1.30871	+	0.230760i
$823$	−0.288286	+	0.792059i	−0.0100490	+	0.0276094i	−0.944616	−	0.328179i	$-0.893565\pi$
$823$	−0.288286	+	0.792059i	−0.0100490	+	0.0276094i	0.934567	+	0.355788i	$0.115787\pi$
$824$	−4.38758	−	7.59952i	−0.152849	−	0.264742i
$825$		0			0
$826$	23.1225	−	19.4021i	0.804534	−	0.675084i
$827$	−9.08627	−	10.8286i	−0.315961	−	0.376547i	0.584567	−	0.811345i	$-0.301264\pi$
$827$	−9.08627	−	10.8286i	−0.315961	−	0.376547i	−0.900528	+	0.434798i	$0.856820\pi$
$828$	11.3876	+	6.57462i	0.395746	+	0.228484i
$829$	23.8392	+	41.2907i	0.827969	+	1.43408i	0.899629	+	0.436655i	$0.143837\pi$
$829$	23.8392	+	41.2907i	0.827969	+	1.43408i	−0.0716603	+	0.997429i	$0.522830\pi$
$830$		0			0
$831$	10.5655	−	59.9197i	0.366511	−	2.07859i
$832$	5.42923	−	0.957319i	0.188225	−	0.0331891i
$833$	3.07470	+	8.44767i	0.106532	+	0.292695i
$834$	25.8073	+	21.6549i	0.893632	+	0.749847i
$835$		0			0
$836$	4.76710	−	6.52123i	0.164874	−	0.225541i
$837$			17.0643i			0.589828i
$838$	−1.89707	+	2.26085i	−0.0655333	+	0.0780996i
$839$	−0.221512	+	0.0806239i	−0.00764746	+	0.00278345i	−0.345841	−	0.938293i	$-0.612406\pi$
$839$	−0.221512	+	0.0806239i	−0.00764746	+	0.00278345i	0.338194	+	0.941077i	$0.390184\pi$
$840$		0			0
$841$	3.49733	−	19.8343i	0.120598	−	0.683943i
$842$	−2.56507	+	7.04747i	−0.0883981	+	0.242872i
$843$	−17.2939	+	9.98466i	−0.595635	+	0.343890i
$844$	−9.74604	+	16.8806i	−0.335473	+	0.581056i
$845$		0			0
$846$	−38.3838	+	32.2079i	−1.31966	+	1.10733i
$847$	14.0010	+	8.08348i	0.481080	+	0.277752i
$848$	5.56084	−	3.21055i	0.190960	−	0.110251i
$849$	−26.4672	−	9.63326i	−0.908350	−	0.330613i
$850$		0			0
$851$	1.78718	+	10.1356i	0.0612638	+	0.347444i
$852$	3.88933	+	10.6859i	0.133246	+	0.366091i
$853$	−2.45972	+	2.93138i	−0.0842191	+	0.100368i	−0.806508	−	0.591223i	$-0.798645\pi$
$853$	−2.45972	+	2.93138i	−0.0842191	+	0.100368i	0.722289	+	0.691591i	$0.243090\pi$
$854$	0.567352			0.0194144
$855$		0			0
$856$	5.70326			0.194933
$857$	7.97116	−	9.49966i	0.272290	−	0.324502i	−0.612520	−	0.790455i	$-0.709844\pi$
$857$	7.97116	−	9.49966i	0.272290	−	0.324502i	0.884809	+	0.465953i	$0.154288\pi$
$858$	−9.54853	−	26.2344i	−0.325982	−	0.895627i
$859$	−6.20007	−	35.1623i	−0.211544	−	1.19972i	−0.886805	−	0.462145i	$-0.847080\pi$
$859$	−6.20007	−	35.1623i	−0.211544	−	1.19972i	0.675261	−	0.737579i	$-0.264031\pi$
$860$		0			0
$861$	−8.61085	−	3.13409i	−0.293457	−	0.106810i
$862$	−20.8658	+	12.0469i	−0.710691	+	0.410317i
$863$	17.6983	+	10.2181i	0.602458	+	0.347830i	0.770008	−	0.638034i	$-0.220252\pi$
$863$	17.6983	+	10.2181i	0.602458	+	0.347830i	−0.167550	+	0.985864i	$0.553585\pi$
$864$	3.07133	−	2.57715i	0.104489	−	0.0876765i
$865$		0			0
$866$	−17.6917	+	30.6429i	−0.601188	+	1.04129i
$867$	7.94158	−	4.58507i	0.269710	−	0.155717i
$868$	3.11062	−	8.54636i	0.105581	−	0.290082i
$869$	−0.927238	+	5.25863i	−0.0314544	+	0.178387i
$870$		0			0
$871$	−76.5454	+	27.8602i	−2.59364	+	0.944008i
$872$	−0.509800	+	0.607556i	−0.0172640	+	0.0205745i
$873$			48.2907i			1.63439i
$874$	−8.88577	−	9.25541i	−0.300566	−	0.313069i
$875$		0			0
$876$	−32.2598	−	27.0692i	−1.08996	−	0.914584i
$877$	−18.0436	−	49.5744i	−0.609289	−	1.67401i	−0.731782	−	0.681539i	$-0.761311\pi$
$877$	−18.0436	−	49.5744i	−0.609289	−	1.67401i	0.122492	−	0.992469i	$-0.460911\pi$
$878$	23.4258	−	4.13061i	0.790584	−	0.139401i
$879$	14.5372	−	82.4447i	0.490328	−	2.78079i
$880$		0			0
$881$	−15.8483	−	27.4500i	−0.533941	−	0.924813i	−0.999214	−	0.0396459i	$-0.987377\pi$
$881$	−15.8483	−	27.4500i	−0.533941	−	0.924813i	0.465273	−	0.885167i	$-0.345956\pi$
$882$	9.41553	+	5.43606i	0.317037	+	0.183042i
$883$	−27.5683	−	32.8546i	−0.927746	−	1.10564i	−0.994167	−	0.107853i	$-0.965602\pi$
$883$	−27.5683	−	32.8546i	−0.927746	−	1.10564i	0.0664209	−	0.997792i	$-0.478842\pi$
$884$	−15.5996	+	13.0896i	−0.524672	+	0.440252i
$885$		0			0
$886$	6.85074	+	11.8658i	0.230155	+	0.398640i
$887$	10.0908	−	27.7243i	0.338816	−	0.930889i	−0.646915	−	0.762562i	$-0.723941\pi$
$887$	10.0908	−	27.7243i	0.338816	−	0.930889i	0.985731	−	0.168327i	$-0.0538366\pi$
$888$	9.40946	+	1.65914i	0.315761	+	0.0556772i
$889$	5.75681	+	32.6485i	0.193077	+	1.09499i
$890$		0			0
$891$	3.47189	+	2.91326i	0.116313	+	0.0975980i
$892$			2.44648i			0.0819142i
$893$	44.7226	−	19.7555i	1.49658	−	0.661093i
$894$	61.5242			2.05768
$895$		0			0
$896$	−2.00801	+	0.730855i	−0.0670828	+	0.0244161i
$897$	−43.6698	+	7.70016i	−1.45809	+	0.257101i
$898$	−14.9327	−	2.63303i	−0.498310	−	0.0878655i
$899$	28.0363	+	10.2044i	0.935063	+	0.340335i
$900$		0			0
$901$	−11.8592	+	20.5407i	−0.395086	+	0.684309i
$902$	1.86934	+	2.22779i	0.0622422	+	0.0741774i
$903$	−8.74538	−	10.4223i	−0.291028	−	0.346834i
$904$	−2.49302	+	4.31803i	−0.0829166	+	0.143616i
$905$		0			0
$906$	58.1489	+	21.1645i	1.93187	+	0.703142i
$907$	−27.3787	−	4.82761i	−0.909095	−	0.160298i	−0.300503	−	0.953781i	$-0.597154\pi$
$907$	−27.3787	−	4.82761i	−0.909095	−	0.160298i	−0.608593	+	0.793483i	$0.708266\pi$
$908$	−18.9378	+	3.33925i	−0.628473	+	0.110817i
$909$	41.8777	−	15.2422i	1.38899	−	0.505553i
$910$		0			0
$911$	14.5154			0.480915			0.240458	−	0.970660i	$-0.422703\pi$
$911$	14.5154			0.480915			0.240458	+	0.970660i	$0.422703\pi$
$912$	−10.8955	+	4.81294i	−0.360787	+	0.159372i
$913$			25.9797i			0.859803i
$914$	−25.7213	−	21.5828i	−0.850786	−	0.713894i
$915$		0			0
$916$	3.54019	+	20.0774i	0.116971	+	0.663376i
$917$	46.4066	+	8.18273i	1.53248	+	0.270218i
$918$	−5.06522	+	13.9166i	−0.167177	+	0.459315i
$919$	5.09200	+	8.81961i	0.167970	+	0.290932i	0.937706	−	0.347430i	$-0.112946\pi$
$919$	5.09200	+	8.81961i	0.167970	+	0.290932i	−0.769736	+	0.638362i	$0.779612\pi$
$920$		0			0
$921$	16.7203	−	14.0300i	0.550953	−	0.462305i
$922$	16.9216	+	20.1663i	0.557282	+	0.664142i
$923$	−19.8683	−	11.4710i	−0.653974	−	0.377572i
$924$	5.41063	+	9.37149i	0.177997	+	0.308299i
$925$		0			0
$926$	1.83185	−	10.3890i	0.0601984	−	0.341402i
$927$	38.6050	−	6.80710i	1.26795	−	0.223575i
$928$	−2.39757	−	6.58726i	−0.0787040	−	0.216237i
$929$	6.91896	+	5.80570i	0.227004	+	0.190479i	0.749195	−	0.662350i	$-0.230441\pi$
$929$	6.91896	+	5.80570i	0.227004	+	0.190479i	−0.522191	+	0.852829i	$0.674885\pi$
$930$		0			0
$931$	−7.34697	−	7.65260i	−0.240787	−	0.250804i
$932$			8.41911i			0.275777i
$933$	46.7772	−	55.7469i	1.53142	−	1.82507i
$934$	28.6764	−	10.4373i	0.938320	−	0.341520i
$935$		0			0
$936$	−4.27655	+	24.2535i	−0.139783	+	0.792751i
$937$	−13.4626	+	36.9882i	−0.439804	+	1.20835i	0.499816	+	0.866131i	$0.333401\pi$
$937$	−13.4626	+	36.9882i	−0.439804	+	1.20835i	−0.939620	+	0.342219i	$0.888821\pi$
$938$	27.3437	−	15.7869i	0.892802	−	0.515460i
$939$	10.4705	−	18.1354i	0.341691	−	0.591827i
$940$		0			0
$941$	33.3892	−	28.0169i	1.08846	−	0.913324i	0.0918617	−	0.995772i	$-0.470718\pi$
$941$	33.3892	−	28.0169i	1.08846	−	0.913324i	0.996595	+	0.0824478i	$0.0262738\pi$
$942$	−35.2255	−	20.3375i	−1.14771	−	0.662630i
$943$	4.00033	−	2.30959i	0.130269	−	0.0752107i
$944$	13.2735	+	4.83117i	0.432017	+	0.157241i
$945$		0			0
$946$	0.749794	+	4.25229i	0.0243779	+	0.138254i
$947$	9.00717	+	24.7470i	0.292694	+	0.804170i	0.995670	+	0.0929564i	$0.0296317\pi$
$947$	9.00717	+	24.7470i	0.292694	+	0.804170i	−0.702976	+	0.711213i	$0.748146\pi$
$948$	5.06114	−	6.03163i	0.164378	−	0.195898i
$949$	84.9601			2.75792
$950$		0			0
$951$	8.10520			0.262829
$952$	5.07365	−	6.04655i	0.164438	−	0.195970i
$953$	−0.328958	−	0.903804i	−0.0106560	−	0.0292771i	0.934251	−	0.356617i	$-0.116070\pi$
$953$	−0.328958	−	0.903804i	−0.0106560	−	0.0292771i	−0.944907	+	0.327340i	$0.893848\pi$
$954$	4.98100	+	28.2487i	0.161266	+	0.914585i
$955$		0			0
$956$	12.4096	+	4.51672i	0.401354	+	0.146081i
$957$	−30.7431	+	17.7496i	−0.993784	+	0.573762i
$958$	3.31589	+	1.91443i	0.107131	+	0.0618524i
$959$	22.8234	−	19.1511i	0.737006	−	0.618422i
$960$		0			0
$961$	6.44264	−	11.1590i	0.207827	−	0.359967i
$962$	−16.6936	+	9.63808i	−0.538225	+	0.310744i
$963$	−8.71388	+	23.9412i	−0.280801	+	0.771494i
$964$	1.22530	−	6.94900i	0.0394641	−	0.223812i
$965$		0			0
$966$	16.1513	−	5.87861i	0.519661	−	0.189141i
$967$	−11.5906	+	13.8131i	−0.372728	+	0.444200i	−0.919505	−	0.393078i	$-0.871410\pi$
$967$	−11.5906	+	13.8131i	−0.372728	+	0.444200i	0.546777	+	0.837278i	$0.315855\pi$
$968$			7.56570i			0.243171i
$969$	25.9650	−	35.5192i	0.834117	−	1.14104i
$970$		0			0
$971$	−8.19208	−	6.87397i	−0.262896	−	0.220596i	0.501806	−	0.864980i	$-0.332669\pi$
$971$	−8.19208	−	6.87397i	−0.262896	−	0.220596i	−0.764702	+	0.644384i	$0.777114\pi$
$972$	−6.39955	−	17.5826i	−0.205266	−	0.563963i
$973$	25.9442	−	4.57465i	0.831731	−	0.146657i
$974$	6.15472	−	34.9052i	0.197210	−	1.11843i
$975$		0			0
$976$	0.132753	+	0.229934i	0.00424931	+	0.00736002i
$977$	−43.6839	−	25.2209i	−1.39757	−	0.806889i	−0.403435	−	0.915008i	$-0.632184\pi$
$977$	−43.6839	−	25.2209i	−1.39757	−	0.806889i	−0.994138	+	0.108119i	$0.965517\pi$
$978$	19.4334	+	23.1598i	0.621411	+	0.740569i
$979$	2.81000	−	2.35787i	0.0898081	−	0.0753580i
$980$		0			0
$981$	−1.77149	−	3.06832i	−0.0565594	−	0.0979638i
$982$	2.92055	−	8.02415i	0.0931985	−	0.256061i
$983$	49.3325	+	8.69866i	1.57346	+	0.277444i	0.891182	−	0.453645i	$-0.149877\pi$
$983$	49.3325	+	8.69866i	1.57346	+	0.277444i	0.682282	+	0.731090i	$0.260988\pi$
$984$	−0.744648	−	4.22311i	−0.0237385	−	0.134628i
$985$		0			0
$986$	19.8357	+	16.6441i	0.631696	+	0.530056i
$987$			65.4962i			2.08477i
$988$	10.5973	−	21.5676i	0.337145	−	0.686158i
$989$	6.85830			0.218081
$990$		0			0
$991$	−13.6454	+	4.96651i	−0.433459	+	0.157766i	−0.549529	−	0.835475i	$-0.685193\pi$
$991$	−13.6454	+	4.96651i	−0.433459	+	0.157766i	0.116069	+	0.993241i	$0.462970\pi$
$992$	4.19148	−	0.739071i	0.133080	−	0.0234655i
$993$	7.15941	+	1.26240i	0.227197	+	0.0400609i
$994$	8.35621	+	3.04141i	0.265043	+	0.0964678i
$995$		0			0
$996$	19.1542	−	33.1761i	0.606925	−	1.05122i
$997$	15.4366	+	18.3966i	0.488882	+	0.582627i	0.952933	−	0.303182i	$-0.0980490\pi$
$997$	15.4366	+	18.3966i	0.488882	+	0.582627i	−0.464051	+	0.885809i	$0.653605\pi$
$998$	−23.8894	−	28.4703i	−0.756205	−	0.901210i
$999$	−7.00933	+	12.1405i	−0.221766	+	0.384109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.h.149.1		48
5.2	odd	4		950.2.l.j.301.1	yes	24
5.3	odd	4		950.2.l.k.301.4	yes	24
5.4	even	2	inner	950.2.u.h.149.8		48
19.6	even	9	inner	950.2.u.h.899.8		48
95.44	even	18	inner	950.2.u.h.899.1		48
95.63	odd	36		950.2.l.k.101.4	yes	24
95.82	odd	36		950.2.l.j.101.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.101.1	✓	24	95.82	odd	36
950.2.l.j.301.1	yes	24	5.2	odd	4
950.2.l.k.101.4	yes	24	95.63	odd	36
950.2.l.k.301.4	yes	24	5.3	odd	4
950.2.u.h.149.1		48	1.1	even	1	trivial
950.2.u.h.149.8		48	5.4	even	2	inner
950.2.u.h.899.1		48	95.44	even	18	inner
950.2.u.h.899.8		48	19.6	even	9	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)

\(f(q)\)	\(=\)	\(q+(-0.642788 + 0.766044i) q^{2} +(-0.934611 - 2.56782i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.56782 + 0.934611i) q^{6} +(1.85059 - 1.06844i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-3.42208 + 2.87147i) q^{9} +O(q^{10})\)	\(q+(-0.642788 + 0.766044i) q^{2} +(-0.934611 - 2.56782i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.56782 + 0.934611i) q^{6} +(1.85059 - 1.06844i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-3.42208 + 2.87147i) q^{9} +(0.926593 - 1.60491i) q^{11} +(-2.36652 + 1.36631i) q^{12} +(1.88555 - 5.18051i) q^{13} +(-0.371065 + 2.10441i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(2.37433 - 2.82962i) q^{17} -4.46721i q^{18} +(-1.21370 + 4.18652i) q^{19} +(-4.47314 - 3.75341i) q^{21} +(0.633827 + 1.74143i) q^{22} +(2.89878 - 0.511133i) q^{23} +(0.474515 - 2.69111i) q^{24} +(2.75649 + 4.77438i) q^{26} +(3.47219 + 2.00467i) q^{27} +(-1.37356 - 1.63694i) q^{28} +(5.36998 - 4.50595i) q^{29} +(2.12807 + 3.68592i) q^{31} +(0.342020 - 0.939693i) q^{32} +(-4.98712 - 0.879364i) q^{33} +(0.641422 + 3.63769i) q^{34} +(3.42208 + 2.87147i) q^{36} +3.49650i q^{37} +(-2.42690 - 3.62079i) q^{38} -15.0649 q^{39} +(1.47464 - 0.536727i) q^{41} +(5.75056 - 1.01398i) q^{42} +(2.29458 + 0.404597i) q^{43} +(-1.74143 - 0.633827i) q^{44} +(-1.47175 + 2.54915i) q^{46} +(-7.20983 - 8.59234i) q^{47} +(1.75649 + 2.09331i) q^{48} +(-1.21688 + 2.10770i) q^{49} +(-9.48504 - 3.45227i) q^{51} +(-5.42923 - 0.957319i) q^{52} +(-6.32356 + 1.11501i) q^{53} +(-3.76755 + 1.37127i) q^{54} +2.13688 q^{56} +(11.8846 - 0.796188i) q^{57} +7.01002i q^{58} +(-10.8207 - 9.07963i) q^{59} +(-0.0461045 - 0.261472i) q^{61} +(-4.19148 - 0.739071i) q^{62} +(-3.26488 + 8.97020i) q^{63} +(0.500000 + 0.866025i) q^{64} +(3.87929 - 3.25511i) q^{66} +(-9.49761 - 11.3188i) q^{67} +(-3.19893 - 1.84690i) q^{68} +(-4.02173 - 6.96585i) q^{69} +(0.722627 - 4.09822i) q^{71} +(-4.39935 + 0.775724i) q^{72} +(5.27085 + 14.4815i) q^{73} +(-2.67848 - 2.24751i) q^{74} +(4.33367 + 0.468284i) q^{76} -3.96003i q^{77} +(9.68352 - 11.5404i) q^{78} +(-2.70762 + 0.985493i) q^{79} +(-0.424681 + 2.40849i) q^{81} +(-0.536727 + 1.47464i) q^{82} +(-12.1408 + 7.00947i) q^{83} +(-2.91964 + 5.05696i) q^{84} +(-1.78487 + 1.49768i) q^{86} +(-16.5893 - 9.57786i) q^{87} +(1.60491 - 0.926593i) q^{88} +(1.86003 + 0.676995i) q^{89} +(-2.04567 - 11.6016i) q^{91} +(-1.00674 - 2.76599i) q^{92} +(7.47588 - 8.90941i) q^{93} +11.2165 q^{94} -2.73262 q^{96} +(6.94855 - 8.28096i) q^{97} +(-0.832394 - 2.28698i) q^{98} +(1.43756 + 8.15281i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) \) 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more