LMFDB - Embedded newform 950.2.l.j.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			101.1
Character	$\chi$	$=$	950.101
Dual form			950.2.l.j.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-2.56782 - 0.934611i) q^{3} +(0.173648 - 0.984808i) q^{4} +(2.56782 - 0.934611i) q^{6} +(1.06844 - 1.85059i) q^{7} +(0.500000 + 0.866025i) q^{8} +(3.42208 + 2.87147i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-2.56782 - 0.934611i) q^{3} +(0.173648 - 0.984808i) q^{4} +(2.56782 - 0.934611i) q^{6} +(1.06844 - 1.85059i) q^{7} +(0.500000 + 0.866025i) q^{8} +(3.42208 + 2.87147i) q^{9} +(0.926593 + 1.60491i) q^{11} +(-1.36631 + 2.36652i) q^{12} +(-5.18051 + 1.88555i) q^{13} +(0.371065 + 2.10441i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(2.82962 - 2.37433i) q^{17} -4.46721 q^{18} +(1.21370 + 4.18652i) q^{19} +(-4.47314 + 3.75341i) q^{21} +(-1.74143 - 0.633827i) q^{22} +(-0.511133 + 2.89878i) q^{23} +(-0.474515 - 2.69111i) q^{24} +(2.75649 - 4.77438i) q^{26} +(-2.00467 - 3.47219i) q^{27} +(-1.63694 - 1.37356i) q^{28} +(-5.36998 - 4.50595i) q^{29} +(2.12807 - 3.68592i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.879364 - 4.98712i) q^{33} +(-0.641422 + 3.63769i) q^{34} +(3.42208 - 2.87147i) q^{36} -3.49650 q^{37} +(-3.62079 - 2.42690i) q^{38} +15.0649 q^{39} +(1.47464 + 0.536727i) q^{41} +(1.01398 - 5.75056i) q^{42} +(0.404597 + 2.29458i) q^{43} +(1.74143 - 0.633827i) q^{44} +(-1.47175 - 2.54915i) q^{46} +(8.59234 + 7.20983i) q^{47} +(2.09331 + 1.75649i) q^{48} +(1.21688 + 2.10770i) q^{49} +(-9.48504 + 3.45227i) q^{51} +(0.957319 + 5.42923i) q^{52} +(1.11501 - 6.32356i) q^{53} +(3.76755 + 1.37127i) q^{54} +2.13688 q^{56} +(0.796188 - 11.8846i) q^{57} +7.01002 q^{58} +(10.8207 - 9.07963i) q^{59} +(-0.0461045 + 0.261472i) q^{61} +(0.739071 + 4.19148i) q^{62} +(8.97020 - 3.26488i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(3.87929 + 3.25511i) q^{66} +(11.3188 + 9.49761i) q^{67} +(-1.84690 - 3.19893i) q^{68} +(4.02173 - 6.96585i) q^{69} +(0.722627 + 4.09822i) q^{71} +(-0.775724 + 4.39935i) q^{72} +(14.4815 + 5.27085i) q^{73} +(2.67848 - 2.24751i) q^{74} +(4.33367 - 0.468284i) q^{76} +3.96003 q^{77} +(-11.5404 + 9.68352i) q^{78} +(2.70762 + 0.985493i) q^{79} +(-0.424681 - 2.40849i) q^{81} +(-1.47464 + 0.536727i) q^{82} +(7.00947 - 12.1408i) q^{83} +(2.91964 + 5.05696i) q^{84} +(-1.78487 - 1.49768i) q^{86} +(9.57786 + 16.5893i) q^{87} +(-0.926593 + 1.60491i) q^{88} +(-1.86003 + 0.676995i) q^{89} +(-2.04567 + 11.6016i) q^{91} +(2.76599 + 1.00674i) q^{92} +(-8.90941 + 7.47588i) q^{93} -11.2165 q^{94} -2.73262 q^{96} +(8.28096 - 6.94855i) q^{97} +(-2.28698 - 0.832394i) q^{98} +(-1.43756 + 8.15281i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{7} + 12 q^{8}+O(q^{10}) $ 24 * q - 3 * q^7 + 12 * q^8	$ 24 q - 3 q^{7} + 12 q^{8} - 6 q^{11} + 3 q^{12} - 24 q^{13} - 15 q^{14} + 9 q^{17} - 30 q^{18} - 15 q^{19} - 18 q^{21} - 12 q^{23} - 9 q^{26} + 21 q^{27} - 12 q^{28} - 12 q^{29} + 9 q^{31} + 42 q^{33} - 9 q^{34} - 66 q^{37} - 6 q^{38} + 66 q^{39} + 18 q^{41} - 9 q^{42} + 3 q^{43} - 3 q^{46} + 12 q^{47} - 27 q^{49} - 3 q^{51} + 12 q^{52} + 45 q^{53} + 27 q^{54} - 6 q^{56} + 27 q^{57} + 18 q^{58} + 36 q^{59} + 12 q^{61} + 24 q^{62} + 63 q^{63} - 12 q^{64} + 48 q^{66} + 54 q^{67} - 3 q^{68} + 21 q^{69} - 39 q^{71} - 48 q^{73} + 18 q^{74} + 6 q^{76} - 48 q^{77} + 12 q^{78} - 42 q^{79} - 36 q^{81} - 18 q^{82} + 3 q^{83} + 9 q^{84} - 39 q^{86} + 24 q^{87} + 6 q^{88} - 36 q^{89} + 12 q^{91} + 15 q^{92} + 6 q^{93} + 12 q^{94} + 6 q^{96} + 54 q^{97} - 3 q^{98} + 51 q^{99}+O(q^{100}) $ 24 * q - 3 * q^7 + 12 * q^8 - 6 * q^11 + 3 * q^12 - 24 * q^13 - 15 * q^14 + 9 * q^17 - 30 * q^18 - 15 * q^19 - 18 * q^21 - 12 * q^23 - 9 * q^26 + 21 * q^27 - 12 * q^28 - 12 * q^29 + 9 * q^31 + 42 * q^33 - 9 * q^34 - 66 * q^37 - 6 * q^38 + 66 * q^39 + 18 * q^41 - 9 * q^42 + 3 * q^43 - 3 * q^46 + 12 * q^47 - 27 * q^49 - 3 * q^51 + 12 * q^52 + 45 * q^53 + 27 * q^54 - 6 * q^56 + 27 * q^57 + 18 * q^58 + 36 * q^59 + 12 * q^61 + 24 * q^62 + 63 * q^63 - 12 * q^64 + 48 * q^66 + 54 * q^67 - 3 * q^68 + 21 * q^69 - 39 * q^71 - 48 * q^73 + 18 * q^74 + 6 * q^76 - 48 * q^77 + 12 * q^78 - 42 * q^79 - 36 * q^81 - 18 * q^82 + 3 * q^83 + 9 * q^84 - 39 * q^86 + 24 * q^87 + 6 * q^88 - 36 * q^89 + 12 * q^91 + 15 * q^92 + 6 * q^93 + 12 * q^94 + 6 * q^96 + 54 * q^97 - 3 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−2.56782	−	0.934611i	−1.48253	−	0.539598i	−0.531061	−	0.847333i	$-0.678207\pi$
$3$	−2.56782	−	0.934611i	−1.48253	−	0.539598i	−0.951472	+	0.307735i	$0.900429\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	2.56782	−	0.934611i	1.04831	−	0.381553i
$7$	1.06844	−	1.85059i	0.403832	−	0.699457i	−0.590353	−	0.807145i	$-0.701011\pi$
$7$	1.06844	−	1.85059i	0.403832	−	0.699457i	0.994185	+	0.107688i	$0.0343448\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	3.42208	+	2.87147i	1.14069	+	0.957157i
$10$		0			0
$11$	0.926593	+	1.60491i	0.279378	+	0.483898i	0.971230	−	0.238142i	$-0.0765383\pi$
$11$	0.926593	+	1.60491i	0.279378	+	0.483898i	−0.691852	+	0.722039i	$0.743205\pi$
$12$	−1.36631	+	2.36652i	−0.394420	+	0.683155i
$13$	−5.18051	+	1.88555i	−1.43681	+	0.522958i	−0.938876	−	0.344255i	$-0.888131\pi$
$13$	−5.18051	+	1.88555i	−1.43681	+	0.522958i	−0.497938	+	0.867213i	$0.665909\pi$
$14$	0.371065	+	2.10441i	0.0991712	+	0.562428i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	2.82962	−	2.37433i	0.686283	−	0.575860i	−0.231551	−	0.972823i	$-0.574380\pi$
$17$	2.82962	−	2.37433i	0.686283	−	0.575860i	0.917835	+	0.396963i	$0.129936\pi$
$18$	−4.46721			−1.05293
$19$	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
$22$	−1.74143	−	0.633827i	−0.371273	−	0.135132i
$23$	−0.511133	+	2.89878i	−0.106579	+	0.604438i	0.883999	+	0.467488i	$0.154841\pi$
$23$	−0.511133	+	2.89878i	−0.106579	+	0.604438i	−0.990578	+	0.136950i	$0.956270\pi$
$24$	−0.474515	−	2.69111i	−0.0968599	−	0.549320i
$25$		0			0
$26$	2.75649	−	4.77438i	0.540592	−	0.936333i
$27$	−2.00467	−	3.47219i	−0.385799	−	0.668223i
$28$	−1.63694	−	1.37356i	−0.309353	−	0.259578i
$29$	−5.36998	−	4.50595i	−0.997181	−	0.836734i	−0.0105895	−	0.999944i	$-0.503371\pi$
$29$	−5.36998	−	4.50595i	−0.997181	−	0.836734i	−0.986591	+	0.163210i	$0.947815\pi$
$30$		0			0
$31$	2.12807	−	3.68592i	0.382213	−	0.662012i	−0.609166	−	0.793043i	$-0.708496\pi$
$31$	2.12807	−	3.68592i	0.382213	−	0.662012i	0.991378	+	0.131031i	$0.0418289\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−0.879364	−	4.98712i	−0.153078	−	0.868146i
$34$	−0.641422	+	3.63769i	−0.110003	+	0.623858i
$35$		0			0
$36$	3.42208	−	2.87147i	0.570347	−	0.478578i
$37$	−3.49650			−0.574822			−0.287411	−	0.957807i	$-0.592795\pi$
$37$	−3.49650			−0.574822			−0.287411	+	0.957807i	$0.592795\pi$
$38$	−3.62079	−	2.42690i	−0.587370	−	0.393696i
$39$	15.0649			2.41231
$40$		0			0
$41$	1.47464	+	0.536727i	0.230301	+	0.0838227i	0.454593	−	0.890699i	$-0.349785\pi$
$41$	1.47464	+	0.536727i	0.230301	+	0.0838227i	−0.224292	+	0.974522i	$0.572007\pi$
$42$	1.01398	−	5.75056i	0.156460	−	0.887331i
$43$	0.404597	+	2.29458i	0.0617005	+	0.349921i	0.999992	+	0.00407464i	$0.00129700\pi$
$43$	0.404597	+	2.29458i	0.0617005	+	0.349921i	−0.938291	+	0.345846i	$0.887592\pi$
$44$	1.74143	−	0.633827i	0.262530	−	0.0955531i
$45$		0			0
$46$	−1.47175	−	2.54915i	−0.216998	−	0.375851i
$47$	8.59234	+	7.20983i	1.25332	+	1.05166i	0.996360	+	0.0852401i	$0.0271657\pi$
$47$	8.59234	+	7.20983i	1.25332	+	1.05166i	0.256961	+	0.966422i	$0.417279\pi$
$48$	2.09331	+	1.75649i	0.302143	+	0.253528i
$49$	1.21688	+	2.10770i	0.173840	+	0.301099i
$50$		0			0
$51$	−9.48504	+	3.45227i	−1.32817	+	0.483415i
$52$	0.957319	+	5.42923i	0.132756	+	0.752898i
$53$	1.11501	−	6.32356i	0.153159	−	0.868607i	−0.807291	−	0.590154i	$-0.799067\pi$
$53$	1.11501	−	6.32356i	0.153159	−	0.868607i	0.960450	−	0.278453i	$-0.0898218\pi$
$54$	3.76755	+	1.37127i	0.512698	+	0.186607i
$55$		0			0
$56$	2.13688			0.285552
$57$	0.796188	−	11.8846i	0.105458	−	1.57415i
$58$	7.01002			0.920460
$59$	10.8207	−	9.07963i	1.40873	−	1.18207i	0.451672	−	0.892184i	$-0.350828\pi$
$59$	10.8207	−	9.07963i	1.40873	−	1.18207i	0.957062	−	0.289883i	$-0.0936165\pi$
$60$		0			0
$61$	−0.0461045	+	0.261472i	−0.00590308	+	0.0334780i	−0.987617	−	0.156884i	$-0.949855\pi$
$61$	−0.0461045	+	0.261472i	−0.00590308	+	0.0334780i	0.981714	+	0.190362i	$0.0609662\pi$
$62$	0.739071	+	4.19148i	0.0938621	+	0.532318i
$63$	8.97020	−	3.26488i	1.13014	−	0.411337i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	3.87929	+	3.25511i	0.477508	+	0.400677i
$67$	11.3188	+	9.49761i	1.38281	+	1.16032i	0.968158	+	0.250338i	$0.0805418\pi$
$67$	11.3188	+	9.49761i	1.38281	+	1.16032i	0.414654	+	0.909979i	$0.363903\pi$
$68$	−1.84690	−	3.19893i	−0.223970	−	0.387927i
$69$	4.02173	−	6.96585i	0.484160	−	0.838589i
$70$		0			0
$71$	0.722627	+	4.09822i	0.0857601	+	0.486370i	0.997190	+	0.0749143i	$0.0238683\pi$
$71$	0.722627	+	4.09822i	0.0857601	+	0.486370i	−0.911430	+	0.411455i	$0.865021\pi$
$72$	−0.775724	+	4.39935i	−0.0914199	+	0.518468i
$73$	14.4815	+	5.27085i	1.69494	+	0.616906i	0.995233	−	0.0975282i	$-0.0310936\pi$
$73$	14.4815	+	5.27085i	1.69494	+	0.616906i	0.699703	+	0.714434i	$0.253316\pi$
$74$	2.67848	−	2.24751i	0.311367	−	0.261268i
$75$		0			0
$76$	4.33367	−	0.468284i	0.497106	−	0.0537159i
$77$	3.96003			0.451288
$78$	−11.5404	+	9.68352i	−1.30669	+	1.09644i
$79$	2.70762	+	0.985493i	0.304631	+	0.110877i	0.489813	−	0.871828i	$-0.337065\pi$
$79$	2.70762	+	0.985493i	0.304631	+	0.110877i	−0.185182	+	0.982704i	$0.559287\pi$
$80$		0			0
$81$	−0.424681	−	2.40849i	−0.0471868	−	0.267610i
$82$	−1.47464	+	0.536727i	−0.162847	+	0.0592716i
$83$	7.00947	−	12.1408i	0.769389	−	1.33262i	−0.168505	−	0.985701i	$-0.553894\pi$
$83$	7.00947	−	12.1408i	0.769389	−	1.33262i	0.937894	−	0.346921i	$-0.112773\pi$
$84$	2.91964	+	5.05696i	0.318558	+	0.551759i
$85$		0			0
$86$	−1.78487	−	1.49768i	−0.192467	−	0.161499i
$87$	9.57786	+	16.5893i	1.02685	+	1.77856i
$88$	−0.926593	+	1.60491i	−0.0987752	+	0.171084i
$89$	−1.86003	+	0.676995i	−0.197163	+	0.0717613i	−0.438714	−	0.898627i	$-0.644566\pi$
$89$	−1.86003	+	0.676995i	−0.197163	+	0.0717613i	0.241552	+	0.970388i	$0.422344\pi$
$90$		0			0
$91$	−2.04567	+	11.6016i	−0.214445	+	1.21618i
$92$	2.76599	+	1.00674i	0.288374	+	0.104960i
$93$	−8.90941	+	7.47588i	−0.923863	+	0.775213i
$94$	−11.2165			−1.15689
$95$		0			0
$96$	−2.73262			−0.278897
$97$	8.28096	−	6.94855i	0.840805	−	0.705519i	−0.116940	−	0.993139i	$-0.537309\pi$
$97$	8.28096	−	6.94855i	0.840805	−	0.705519i	0.957745	+	0.287620i	$0.0928641\pi$
$98$	−2.28698	−	0.832394i	−0.231020	−	0.0840845i
$99$	−1.43756	+	8.15281i	−0.144480	+	0.819388i
$100$		0			0
$101$	−9.37445	+	3.41202i	−0.932792	+	0.339509i	−0.763316	−	0.646026i	$-0.776430\pi$
$101$	−9.37445	+	3.41202i	−0.932792	+	0.339509i	−0.169477	+	0.985534i	$0.554208\pi$
$102$	5.04688	−	8.74146i	0.499716	−	0.865533i
$103$	−4.38758	−	7.59952i	−0.432322	−	0.748803i	0.564751	−	0.825261i	$-0.308972\pi$
$103$	−4.38758	−	7.59952i	−0.432322	−	0.748803i	−0.997073	+	0.0764583i	$0.975639\pi$
$104$	−4.22319	−	3.54368i	−0.414118	−	0.347486i
$105$		0			0
$106$	3.21055	+	5.56084i	0.311837	+	0.540117i
$107$	2.85163	−	4.93917i	0.275677	−	0.477487i	−0.694628	−	0.719369i	$-0.744431\pi$
$107$	2.85163	−	4.93917i	0.275677	−	0.477487i	0.970306	+	0.241882i	$0.0777645\pi$
$108$	−3.76755	+	1.37127i	−0.362532	+	0.131951i
$109$	0.137722	+	0.781060i	0.0131914	+	0.0748119i	0.990693	−	0.136117i	$-0.0434623\pi$
$109$	0.137722	+	0.781060i	0.0131914	+	0.0748119i	−0.977501	+	0.210929i	$0.932351\pi$
$110$		0			0
$111$	8.97841	+	3.26787i	0.852193	+	0.310173i
$112$	−1.63694	+	1.37356i	−0.154677	+	0.129789i
$113$	4.98604			0.469047			0.234523	−	0.972110i	$-0.424647\pi$
$113$	4.98604			0.469047			0.234523	+	0.972110i	$0.424647\pi$
$114$	7.02934	+	9.61589i	0.658358	+	0.900611i
$115$		0			0
$116$	−5.36998	+	4.50595i	−0.498590	+	0.418367i
$117$	−23.1424	−	8.42316i	−2.13952	−	0.778721i
$118$	−2.45285	+	13.9108i	−0.225803	+	1.28059i
$119$	−1.37064	−	7.77329i	−0.125646	−	0.712576i
$120$		0			0
$121$	3.78285	−	6.55209i	0.343895	−	0.595644i
$122$	−0.132753	−	0.229934i	−0.0120189	−	0.0208173i
$123$	−3.28500	−	2.75644i	−0.296198	−	0.248540i
$124$	−3.26039	−	2.73579i	−0.292792	−	0.245682i
$125$		0			0
$126$	−4.77294	+	8.26698i	−0.425208	+	0.736481i
$127$	−14.5787	+	5.30620i	−1.29365	+	0.470849i	−0.894923	−	0.446221i	$-0.852769\pi$
$127$	−14.5787	+	5.30620i	−1.29365	+	0.470849i	−0.398725	+	0.917071i	$0.630547\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	1.10561	−	6.27023i	0.0973436	−	0.552063i
$130$		0			0
$131$	16.8928	−	14.1748i	1.47593	−	1.23846i	0.565535	−	0.824724i	$-0.308670\pi$
$131$	16.8928	−	14.1748i	1.47593	−	1.23846i	0.910399	−	0.413732i	$-0.135775\pi$
$132$	−5.06406			−0.440770
$133$	9.04429	+	2.22697i	0.784240	+	0.193103i
$134$	−14.7757			−1.27642
$135$		0			0
$136$	3.47104	+	1.26336i	0.297639	+	0.108332i
$137$	2.42112	−	13.7309i	0.206851	−	1.17311i	−0.687650	−	0.726042i	$-0.741358\pi$
$137$	2.42112	−	13.7309i	0.206851	−	1.17311i	0.894501	−	0.447066i	$-0.147531\pi$
$138$	1.39673	+	7.92127i	0.118898	+	0.674303i
$139$	−11.5850	+	4.21658i	−0.982623	+	0.357646i	−0.782860	−	0.622198i	$-0.786240\pi$
$139$	−11.5850	+	4.21658i	−0.982623	+	0.357646i	−0.199764	+	0.979844i	$0.564017\pi$
$140$		0			0
$141$	−15.3252	−	26.5441i	−1.29062	−	2.23541i
$142$	−3.18785	−	2.67493i	−0.267519	−	0.224475i
$143$	−7.82636	−	6.56709i	−0.654473	−	0.549168i
$144$	−2.23361	−	3.86872i	−0.186134	−	0.322393i
$145$		0			0
$146$	−14.4815	+	5.27085i	−1.19850	+	0.436218i
$147$	−1.15485	−	6.54950i	−0.0952507	−	0.540194i
$148$	−0.607162	+	3.44339i	−0.0499084	+	0.283045i
$149$	−21.1569	−	7.70049i	−1.73324	−	0.630849i	−0.734389	−	0.678729i	$-0.762531\pi$
$149$	−21.1569	−	7.70049i	−1.73324	−	0.630849i	−0.998853	+	0.0478803i	$0.984753\pi$
$150$		0			0
$151$	22.6452			1.84284			0.921420	−	0.388568i	$-0.127030\pi$
$151$	22.6452			1.84284			0.921420	+	0.388568i	$0.127030\pi$
$152$	−3.01878	+	3.14436i	−0.244855	+	0.255041i
$153$	16.5010			1.33403
$154$	−3.03356	+	2.54546i	−0.244451	+	0.205119i
$155$		0			0
$156$	2.61599	−	14.8360i	0.209447	−	1.18783i
$157$	2.58475	+	14.6588i	0.206285	+	1.16990i	0.895405	+	0.445253i	$0.146886\pi$
$157$	2.58475	+	14.6588i	0.206285	+	1.16990i	−0.689119	+	0.724648i	$0.742002\pi$
$158$	−2.70762	+	0.985493i	−0.215407	+	0.0784016i
$159$	−8.77322	+	15.1957i	−0.695762	+	1.20510i
$160$		0			0
$161$	4.81834	+	4.04307i	0.379738	+	0.318638i
$162$	1.87347	+	1.57203i	0.147194	+	0.123510i
$163$	5.53187	+	9.58148i	0.433289	+	0.750479i	0.997154	−	0.0753878i	$-0.0240195\pi$
$163$	5.53187	+	9.58148i	0.433289	+	0.750479i	−0.563865	+	0.825867i	$0.690686\pi$
$164$	0.784642	−	1.35904i	0.0612703	−	0.106123i
$165$		0			0
$166$	2.43436	+	13.8060i	0.188943	+	1.07155i
$167$	−3.42470	+	19.4224i	−0.265011	+	1.50295i	0.503992	+	0.863708i	$0.331864\pi$
$167$	−3.42470	+	19.4224i	−0.265011	+	1.50295i	−0.769003	+	0.639245i	$0.779247\pi$
$168$	−5.48712	−	1.99715i	−0.423341	−	0.154083i
$169$	13.3238	−	11.1800i	1.02491	−	0.859998i
$170$		0			0
$171$	−7.86806	+	17.8117i	−0.601685	+	1.36210i
$172$	2.32998			0.177659
$173$	−4.64055	+	3.89388i	−0.352815	+	0.296047i	−0.801919	−	0.597433i	$-0.796188\pi$
$173$	−4.64055	+	3.89388i	−0.352815	+	0.296047i	0.449105	+	0.893479i	$0.351743\pi$
$174$	−18.0005	−	6.55164i	−1.36461	−	0.496678i
$175$		0			0
$176$	−0.321803	−	1.82503i	−0.0242568	−	0.137567i
$177$	−36.2715	+	13.2018i	−2.72634	+	0.992305i
$178$	0.989700	−	1.71421i	0.0741812	−	0.128486i
$179$	0.625049	+	1.08262i	0.0467184	+	0.0809186i	0.888439	−	0.458995i	$-0.151790\pi$
$179$	0.625049	+	1.08262i	0.0467184	+	0.0809186i	−0.841721	+	0.539913i	$0.818457\pi$
$180$		0			0
$181$	12.0955	+	10.1494i	0.899054	+	0.754396i	0.970005	−	0.243084i	$-0.0781590\pi$
$181$	12.0955	+	10.1494i	0.899054	+	0.754396i	−0.0709510	+	0.997480i	$0.522603\pi$
$182$	−5.89028	−	10.2023i	−0.436617	−	0.756242i
$183$	0.362763	−	0.628323i	0.0268162	−	0.0464470i
$184$	−2.76599	+	1.00674i	−0.203911	+	0.0742176i
$185$		0			0
$186$	2.01960	−	11.4537i	0.148084	−	0.839827i
$187$	6.43249	+	2.34123i	0.470390	+	0.171208i
$188$	8.59234	−	7.20983i	0.626661	−	0.525831i
$189$	−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	$0.523642\pi$
$192$	2.09331	−	1.75649i	0.151072	−	0.126764i
$193$	0.773263	+	0.281445i	0.0556607	+	0.0202588i	0.369700	−	0.929151i	$-0.379460\pi$
$193$	0.773263	+	0.281445i	0.0556607	+	0.0202588i	−0.314040	+	0.949410i	$0.601683\pi$
$194$	−1.87714	+	10.6458i	−0.134771	+	0.764324i
$195$		0			0
$196$	2.28698	−	0.832394i	0.163356	−	0.0594567i
$197$	6.35099	−	11.0002i	0.452489	−	0.783734i	−0.546051	−	0.837752i	$-0.683869\pi$
$197$	6.35099	−	11.0002i	0.452489	−	0.783734i	0.998540	+	0.0540180i	$0.0172028\pi$
$198$	−4.13929	−	7.16946i	−0.294167	−	0.509511i
$199$	−3.91363	−	3.28392i	−0.277430	−	0.232791i	0.493446	−	0.869776i	$-0.335737\pi$
$199$	−3.91363	−	3.28392i	−0.277430	−	0.232791i	−0.770876	+	0.636985i	$0.780181\pi$
$200$		0			0
$201$	−20.1881	−	34.9669i	−1.42396	−	2.46637i
$202$	4.98804	−	8.63954i	0.350957	−	0.607876i
$203$	−14.0762	+	5.12330i	−0.987953	+	0.359585i
$204$	1.75276	+	9.94042i	0.122718	+	0.695969i
$205$		0			0
$206$	8.24596	+	3.00128i	0.574523	+	0.209109i
$207$	−10.0729	+	8.45217i	−0.700115	+	0.587466i
$208$	5.51298			0.382256
$209$	−5.59436	+	5.82708i	−0.386970	+	0.403068i
$210$		0			0
$211$	−14.9318	+	12.5293i	−1.02795	+	0.862551i	−0.990605	−	0.136752i	$-0.956334\pi$
$211$	−14.9318	+	12.5293i	−1.02795	+	0.862551i	−0.0373426	+	0.999303i	$0.511889\pi$
$212$	−6.03387	−	2.19615i	−0.414408	−	0.150832i
$213$	1.97467	−	11.1989i	0.135302	−	0.767335i
$214$	0.990360	+	5.61661i	0.0676996	+	0.383944i
$215$		0			0
$216$	2.00467	−	3.47219i	0.136400	−	0.236253i
$217$	−4.54742	−	7.87637i	−0.308699	−	0.534683i
$218$	−0.607556	−	0.509800i	−0.0411489	−	0.0345280i
$219$	−32.2598	−	27.0692i	−2.17992	−	1.82917i
$220$		0			0
$221$	−10.1819	+	17.6356i	−0.684911	+	1.18630i
$222$	−8.97841	+	3.26787i	−0.602591	+	0.219325i
$223$	−0.424827	−	2.40931i	−0.0284485	−	0.161340i	0.967274	−	0.253734i	$-0.0816589\pi$
$223$	−0.424827	−	2.40931i	−0.0284485	−	0.161340i	−0.995722	+	0.0923948i	$0.970548\pi$
$224$	0.371065	−	2.10441i	0.0247928	−	0.140607i
$225$		0			0
$226$	−3.81953	+	3.20496i	−0.254071	+	0.213191i
$227$	19.2300			1.27634			0.638169	−	0.769897i	$-0.279692\pi$
$227$	19.2300			1.27634			0.638169	+	0.769897i	$0.279692\pi$
$228$	−11.5658	−	2.84783i	−0.765962	−	0.188602i
$229$	20.3871			1.34722			0.673609	−	0.739088i	$-0.264743\pi$
$229$	20.3871			1.34722			0.673609	+	0.739088i	$0.264743\pi$
$230$		0			0
$231$	−10.1687	−	3.70109i	−0.669049	−	0.243514i
$232$	1.21728	−	6.90352i	0.0799181	−	0.453238i
$233$	−1.46196	−	8.29121i	−0.0957764	−	0.543175i	−0.994507	−	0.104673i	$-0.966620\pi$
$233$	−1.46196	−	8.29121i	−0.0957764	−	0.543175i	0.898730	−	0.438502i	$-0.144491\pi$
$234$	23.1424	−	8.42316i	1.51287	−	0.550639i
$235$		0			0
$236$	−7.06270	−	12.2330i	−0.459743	−	0.796298i
$237$	−6.03163	−	5.06114i	−0.391797	−	0.328756i
$238$	6.04655	+	5.07365i	0.391939	+	0.328876i
$239$	6.60300	+	11.4367i	0.427113	+	0.739781i	0.996615	−	0.0822090i	$-0.0261975\pi$
$239$	6.60300	+	11.4367i	0.427113	+	0.739781i	−0.569503	+	0.821990i	$0.692864\pi$
$240$		0			0
$241$	6.63066	−	2.41336i	0.427118	−	0.155458i	−0.119511	−	0.992833i	$-0.538133\pi$
$241$	6.63066	−	2.41336i	0.427118	−	0.155458i	0.546630	+	0.837375i	$0.315911\pi$
$242$	1.31377	+	7.45076i	0.0844523	+	0.478953i
$243$	−3.24914	+	18.4268i	−0.208432	+	1.18208i
$244$	0.249493	+	0.0908082i	0.0159722	+	0.00581340i
$245$		0			0
$246$	4.28826			0.273409
$247$	−14.1815	−	19.3998i	−0.902347	−	1.23438i
$248$	4.25614			0.270265
$249$	−29.3460	+	24.6242i	−1.85973	+	1.56049i
$250$		0			0
$251$	−0.405222	+	2.29813i	−0.0255774	+	0.145057i	−0.994922	−	0.100648i	$-0.967908\pi$
$251$	−0.405222	+	2.29813i	−0.0255774	+	0.145057i	0.969345	+	0.245705i	$0.0790194\pi$
$252$	−1.65763	−	9.40086i	−0.104421	−	0.592199i
$253$	−5.12589	+	1.86567i	−0.322262	+	0.117294i
$254$	7.75715	−	13.4358i	0.486727	−	0.843035i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	4.24431	+	3.56140i	0.264753	+	0.222154i	0.765494	−	0.643443i	$-0.222495\pi$
$257$	4.24431	+	3.56140i	0.264753	+	0.222154i	−0.500741	+	0.865597i	$0.666939\pi$
$258$	3.18348	+	5.51395i	0.198195	+	0.343283i
$259$	−3.73580	+	6.47060i	−0.232131	+	0.402063i
$260$		0			0
$261$	−5.43783	−	30.8395i	−0.336593	−	1.90892i
$262$	−3.82930	+	21.7170i	−0.236575	+	1.34168i
$263$	−1.66651	−	0.606559i	−0.102761	−	0.0374020i	0.290128	−	0.956988i	$-0.406302\pi$
$263$	−1.66651	−	0.606559i	−0.102761	−	0.0374020i	−0.392889	+	0.919586i	$0.628524\pi$
$264$	3.87929	−	3.25511i	0.238754	−	0.200338i
$265$		0			0
$266$	−8.35980	+	4.10760i	−0.512572	+	0.251853i
$267$	5.40895			0.331022
$268$	11.3188	−	9.49761i	0.691406	−	0.580159i
$269$	14.9736	+	5.44995i	0.912957	+	0.332289i	0.755433	−	0.655226i	$-0.227427\pi$
$269$	14.9736	+	5.44995i	0.912957	+	0.332289i	0.157524	+	0.987515i	$0.449649\pi$
$270$		0			0
$271$	2.44844	+	13.8858i	0.148732	+	0.843502i	0.964294	+	0.264832i	$0.0853166\pi$
$271$	2.44844	+	13.8858i	0.148732	+	0.843502i	−0.815562	+	0.578669i	$0.803572\pi$
$272$	−3.47104	+	1.26336i	−0.210463	+	0.0766022i
$273$	16.0959	−	27.8789i	0.974168	−	1.68731i
$274$	6.97135	+	12.0747i	0.421155	+	0.729461i
$275$		0			0
$276$	−6.16165	−	5.17024i	−0.370888	−	0.311212i
$277$	−11.1329	−	19.2828i	−0.668912	−	1.15859i	−0.978209	−	0.207623i	$-0.933427\pi$
$277$	−11.1329	−	19.2828i	−0.668912	−	1.15859i	0.309297	−	0.950965i	$-0.399906\pi$
$278$	6.16423	−	10.6768i	0.369706	−	0.640349i
$279$	17.8665	−	6.50286i	1.06964	−	0.389316i
$280$		0			0
$281$	−1.26898	+	7.19674i	−0.0757009	+	0.429321i	0.923278	+	0.384133i	$0.125500\pi$
$281$	−1.26898	+	7.19674i	−0.0757009	+	0.429321i	−0.998979	+	0.0451879i	$0.985611\pi$
$282$	28.8020	+	10.4831i	1.71513	+	0.624258i
$283$	−7.89580	+	6.62536i	−0.469357	+	0.393837i	−0.846560	−	0.532294i	$-0.821330\pi$
$283$	−7.89580	+	6.62536i	−0.469357	+	0.393837i	0.377203	+	0.926131i	$0.376886\pi$
$284$	4.16145			0.246936
$285$		0			0
$286$	10.2166			0.604119
$287$	2.56883	−	2.15550i	0.151633	−	0.127235i
$288$	4.19781	+	1.52788i	0.247358	+	0.0900310i
$289$	−0.582730	+	3.30482i	−0.0342782	+	0.194401i
$290$		0			0
$291$	−27.7582	+	10.1032i	−1.62722	+	0.592259i
$292$	7.70546	−	13.3463i	0.450928	−	0.781030i
$293$	15.3180	+	26.5315i	0.894887	+	1.54999i	0.833945	+	0.551848i	$0.186077\pi$
$293$	15.3180	+	26.5315i	0.894887	+	1.54999i	0.0609422	+	0.998141i	$0.480589\pi$
$294$	5.09461	+	4.27488i	0.297123	+	0.249316i
$295$		0			0
$296$	−1.74825	−	3.02806i	−0.101615	−	0.176003i
$297$	3.71503	−	6.43461i	0.215568	−	0.373374i
$298$	21.1569	−	7.70049i	1.22559	−	0.446077i
$299$	−2.81787	−	15.9809i	−0.162962	−	0.924201i
$300$		0			0
$301$	4.67862	+	1.70288i	0.269671	+	0.0981523i
$302$	−17.3472	+	14.5561i	−0.998221	+	0.837607i
$303$	27.2608			1.56609
$304$	0.291364	−	4.34915i	0.0167109	−	0.249441i
$305$		0			0
$306$	−12.6405	+	10.6066i	−0.722610	+	0.606342i
$307$	−7.50580	−	2.73189i	−0.428379	−	0.155917i	0.118828	−	0.992915i	$-0.462086\pi$
$307$	−7.50580	−	2.73189i	−0.428379	−	0.155917i	−0.547206	+	0.836998i	$0.684309\pi$
$308$	0.687652	−	3.89987i	0.0391826	−	0.222216i
$309$	4.16395	+	23.6149i	0.236879	+	1.34341i
$310$		0			0
$311$	13.3155	−	23.0631i	0.755052	−	1.30779i	−0.190296	−	0.981727i	$-0.560945\pi$
$311$	13.3155	−	23.0631i	0.755052	−	1.30779i	0.945348	−	0.326062i	$-0.105722\pi$
$312$	7.53244	+	13.0466i	0.426440	+	0.738617i
$313$	5.87045	+	4.92589i	0.331817	+	0.278428i	0.793440	−	0.608649i	$-0.208288\pi$
$313$	5.87045	+	4.92589i	0.331817	+	0.278428i	−0.461622	+	0.887076i	$0.652733\pi$
$314$	−11.4025	−	9.56787i	−0.643482	−	0.539946i
$315$		0			0
$316$	1.44069	−	2.49535i	0.0810454	−	0.140375i
$317$	−2.78721	+	1.01446i	−0.156545	+	0.0569779i	−0.419104	−	0.907938i	$-0.637656\pi$
$317$	−2.78721	+	1.01446i	−0.156545	+	0.0569779i	0.262559	+	0.964916i	$0.415434\pi$
$318$	−3.04691	−	17.2799i	−0.170862	−	0.969008i
$319$	2.25584	−	12.7935i	0.126303	−	0.716299i
$320$		0			0
$321$	−11.9387	+	10.0177i	−0.666352	+	0.559136i
$322$	−6.28990			−0.350522
$323$	13.3745	+	8.96451i	0.744177	+	0.498799i
$324$	−2.44564			−0.135869
$325$		0			0
$326$	−10.3965	−	3.78402i	−0.575810	−	0.209578i
$327$	0.376342	−	2.13434i	0.0208117	−	0.118029i
$328$	0.272503	+	1.54544i	0.0150465	+	0.0853328i
$329$	22.5228	−	8.19764i	1.24172	−	0.451950i
$330$		0			0
$331$	−1.33020	−	2.30397i	−0.0731143	−	0.126638i	0.827150	−	0.561981i	$-0.189960\pi$
$331$	−1.33020	−	2.30397i	−0.0731143	−	0.126638i	−0.900265	+	0.435343i	$0.856627\pi$
$332$	−10.7391	−	9.01120i	−0.589386	−	0.494554i
$333$	−11.9653	−	10.0401i	−0.655696	−	0.550194i
$334$	−9.86103	−	17.0798i	−0.539572	−	0.934565i
$335$		0			0
$336$	5.48712	−	1.99715i	0.299347	−	0.108953i
$337$	−5.43943	−	30.8485i	−0.296304	−	1.68043i	−0.661853	−	0.749634i	$-0.730230\pi$
$337$	−5.43943	−	30.8485i	−0.296304	−	1.68043i	0.365549	−	0.930792i	$-0.380881\pi$
$338$	−3.02025	+	17.1287i	−0.164280	+	0.931679i
$339$	−12.8033	−	4.66001i	−0.695378	−	0.253097i
$340$		0			0
$341$	7.88742			0.427128
$342$	−5.42188	−	18.7021i	−0.293181	−	1.01129i
$343$	20.1588			1.08847
$344$	−1.78487	+	1.49768i	−0.0962337	+	0.0807497i
$345$		0			0
$346$	1.05193	−	5.96578i	0.0565520	−	0.320722i
$347$	1.84375	+	10.4564i	0.0989776	+	0.561330i	0.993456	+	0.114218i	$0.0364362\pi$
$347$	1.84375	+	10.4564i	0.0989776	+	0.561330i	−0.894478	+	0.447112i	$0.852453\pi$
$348$	18.0005	−	6.55164i	0.964927	−	0.351205i
$349$	−18.4784	+	32.0056i	−0.989128	+	1.71322i	−0.367206	+	0.930139i	$0.619686\pi$
$349$	−18.4784	+	32.0056i	−0.989128	+	1.71322i	−0.621921	+	0.783080i	$0.713648\pi$
$350$		0			0
$351$	16.9322	+	14.2078i	0.903773	+	0.758356i
$352$	1.41962	+	1.19121i	0.0756662	+	0.0634915i
$353$	−15.4274	−	26.7210i	−0.821117	−	1.42222i	−0.904851	−	0.425729i	$-0.860018\pi$
$353$	−15.4274	−	26.7210i	−0.821117	−	1.42222i	0.0837337	−	0.996488i	$-0.473315\pi$
$354$	19.2997	−	33.4280i	1.02577	−	1.77668i
$355$		0			0
$356$	0.343719	+	1.94933i	0.0182171	+	0.103314i
$357$	−3.74544	+	21.2414i	−0.198230	+	1.12422i
$358$	−1.17471	−	0.427559i	−0.0620853	−	0.0225972i
$359$	−7.76753	+	6.51773i	−0.409954	+	0.343993i	−0.824326	−	0.566115i	$-0.808446\pi$
$359$	−7.76753	+	6.51773i	−0.409954	+	0.343993i	0.414372	+	0.910108i	$0.364001\pi$
$360$		0			0
$361$	−16.0538	+	10.1624i	−0.844939	+	0.534862i
$362$	−15.7896			−0.829883
$363$	−15.8373	+	13.2891i	−0.831245	+	0.697497i
$364$	11.0701	+	4.02919i	0.580231	+	0.211187i
$365$		0			0
$366$	0.125986	+	0.714503i	0.00658540	+	0.0373477i
$367$	11.0649	−	4.02729i	0.577583	−	0.210223i	−0.0366766	−	0.999327i	$-0.511677\pi$
$367$	11.0649	−	4.02729i	0.577583	−	0.210223i	0.614259	+	0.789104i	$0.289455\pi$
$368$	1.47175	−	2.54915i	0.0767203	−	0.132883i
$369$	3.50516	+	6.07112i	0.182472	+	0.316050i
$370$		0			0
$371$	−10.5110	−	8.81976i	−0.545703	−	0.457899i
$372$	5.81521	+	10.0722i	0.301504	+	0.522221i
$373$	−9.78613	+	16.9501i	−0.506706	+	0.877641i	0.493263	+	0.869880i	$0.335804\pi$
$373$	−9.78613	+	16.9501i	−0.506706	+	0.877641i	−0.999970	+	0.00776129i	$0.997529\pi$
$374$	−6.43249	+	2.34123i	−0.332616	+	0.121062i
$375$		0			0
$376$	−1.94773	+	11.0461i	−0.100446	+	0.569659i
$377$	36.3154	+	13.2177i	1.87034	+	0.680748i
$378$	6.56306	−	5.50706i	0.337567	−	0.283252i
$379$	19.0901			0.980591			0.490296	−	0.871556i	$-0.336889\pi$
$379$	19.0901			0.980591			0.490296	+	0.871556i	$0.336889\pi$
$380$		0			0
$381$	42.3947			2.17195
$382$	1.57120	−	1.31839i	0.0803894	−	0.0674548i
$383$	−18.4874	−	6.72885i	−0.944660	−	0.343828i	−0.176655	−	0.984273i	$-0.556528\pi$
$383$	−18.4874	−	6.72885i	−0.944660	−	0.343828i	−0.768004	+	0.640445i	$0.778750\pi$
$384$	−0.474515	+	2.69111i	−0.0242150	+	0.137330i
$385$		0			0
$386$	−0.773263	+	0.281445i	−0.0393580	+	0.0143252i
$387$	−5.20426	+	9.01405i	−0.264548	+	0.458210i
$388$	−5.40502	−	9.36176i	−0.274398	−	0.475271i
$389$	−18.4221	−	15.4580i	−0.934038	−	0.783751i	0.0425001	−	0.999096i	$-0.486468\pi$
$389$	−18.4221	−	15.4580i	−0.934038	−	0.783751i	−0.976538	+	0.215346i	$0.930912\pi$
$390$		0			0
$391$	5.43636	+	9.41605i	0.274928	+	0.476190i
$392$	−1.21688	+	2.10770i	−0.0614617	+	0.106455i
$393$	−56.6257	+	20.6101i	−2.85639	+	1.03964i
$394$	2.20567	+	12.5090i	0.111120	+	0.630194i
$395$		0			0
$396$	7.77932	+	2.83144i	0.390926	+	0.142285i
$397$	1.94657	−	1.63337i	0.0976956	−	0.0819763i	−0.592632	−	0.805474i	$-0.701911\pi$
$397$	1.94657	−	1.63337i	0.0976956	−	0.0819763i	0.690327	+	0.723497i	$0.257467\pi$
$398$	5.10888			0.256085
$399$	−21.1428	−	14.1714i	−1.05846	−	0.709455i
$400$		0			0
$401$	1.13717	−	0.954196i	0.0567874	−	0.0476503i	−0.613952	−	0.789343i	$-0.710421\pi$
$401$	1.13717	−	0.954196i	0.0567874	−	0.0476503i	0.670740	+	0.741693i	$0.265977\pi$
$402$	37.9413	+	13.8095i	1.89234	+	0.688755i
$403$	−4.07448	+	23.1075i	−0.202964	+	1.15107i
$404$	1.73233	+	9.82452i	0.0861865	+	0.488788i
$405$		0			0
$406$	7.48977	−	12.9727i	0.371711	−	0.643822i
$407$	−3.23984	−	5.61156i	−0.160593	−	0.278155i
$408$	−7.73227	−	6.48815i	−0.382805	−	0.321211i
$409$	9.40691	+	7.89333i	0.465142	+	0.390300i	0.845019	−	0.534737i	$-0.179589\pi$
$409$	9.40691	+	7.89333i	0.465142	+	0.390300i	−0.379877	+	0.925037i	$0.624034\pi$
$410$		0			0
$411$	−19.0501	+	32.9957i	−0.939670	+	1.62756i
$412$	−8.24596	+	3.00128i	−0.406249	+	0.147863i
$413$	−5.24144	−	29.7257i	−0.257914	−	1.46271i
$414$	2.28334	−	12.9495i	0.112220	−	0.636432i
$415$		0			0
$416$	−4.22319	+	3.54368i	−0.207059	+	0.173743i
$417$	33.6890			1.64976
$418$	0.539953	−	8.05979i	0.0264099	−	0.394217i
$419$	−2.95132			−0.144182			−0.0720908	−	0.997398i	$-0.522967\pi$
$419$	−2.95132			−0.144182			−0.0720908	+	0.997398i	$0.522967\pi$
$420$		0			0
$421$	7.04747	+	2.56507i	0.343472	+	0.125014i	0.507996	−	0.861359i	$-0.330386\pi$
$421$	7.04747	+	2.56507i	0.343472	+	0.125014i	−0.164524	+	0.986373i	$0.552609\pi$
$422$	3.38477	−	19.1960i	0.164768	−	0.934445i
$423$	8.70091	+	49.3453i	0.423053	+	2.39925i
$424$	6.03387	−	2.19615i	0.293031	−	0.106654i
$425$		0			0
$426$	5.68583	+	9.84814i	0.275479	+	0.477144i
$427$	0.434617	+	0.364687i	0.0210326	+	0.0176484i
$428$	−4.36895	−	3.66598i	−0.211181	−	0.177202i
$429$	13.9590	+	24.1777i	0.673948	+	1.16731i
$430$		0			0
$431$	22.6407	−	8.24053i	1.09056	−	0.396933i	0.266734	−	0.963770i	$-0.414056\pi$
$431$	22.6407	−	8.24053i	1.09056	−	0.396933i	0.823829	+	0.566838i	$0.191833\pi$
$432$	0.696214	+	3.94843i	0.0334966	+	0.189969i
$433$	−6.14426	+	34.8458i	−0.295274	+	1.67458i	0.370812	+	0.928708i	$0.379080\pi$
$433$	−6.14426	+	34.8458i	−0.295274	+	1.67458i	−0.666086	+	0.745875i	$0.732032\pi$
$434$	8.54636	+	3.11062i	0.410238	+	0.149315i
$435$		0			0
$436$	0.793109			0.0379830
$437$	−12.7562	+	1.37839i	−0.610210	+	0.0659375i
$438$	42.1122			2.01220
$439$	18.2221	−	15.2901i	0.869692	−	0.729758i	−0.0943411	−	0.995540i	$-0.530074\pi$
$439$	18.2221	−	15.2901i	0.869692	−	0.729758i	0.964033	+	0.265782i	$0.0856300\pi$
$440$		0			0
$441$	−1.88792	+	10.7069i	−0.0899011	+	0.509855i
$442$	−3.53615	−	20.0545i	−0.168197	−	0.953895i
$443$	−12.8752	+	4.68618i	−0.611718	+	0.222647i	−0.629255	−	0.777199i	$-0.716640\pi$
$443$	−12.8752	+	4.68618i	−0.611718	+	0.222647i	0.0175367	+	0.999846i	$0.494418\pi$
$444$	4.77731	−	8.27454i	0.226721	−	0.392692i
$445$		0			0
$446$	1.87411	+	1.57257i	0.0887418	+	0.0744632i
$447$	47.1303	+	39.5470i	2.22918	+	1.87051i
$448$	1.06844	+	1.85059i	0.0504790	+	0.0874321i
$449$	−7.58152	+	13.1316i	−0.357794	+	0.619717i	−0.987592	−	0.157042i	$-0.949804\pi$
$449$	−7.58152	+	13.1316i	−0.357794	+	0.619717i	0.629798	+	0.776759i	$0.283138\pi$
$450$		0			0
$451$	0.505000	+	2.86400i	0.0237795	+	0.134860i
$452$	0.865816	−	4.91029i	0.0407246	−	0.230961i
$453$	−58.1489	−	21.1645i	−2.73207	−	0.994393i
$454$	−14.7310	+	12.3608i	−0.691360	+	0.580120i
$455$		0			0
$456$	10.6904	−	5.25277i	0.500626	−	0.245983i
$457$	−33.5768			−1.57066			−0.785329	−	0.619079i	$-0.787506\pi$
$457$	−33.5768			−1.57066			−0.785329	+	0.619079i	$0.787506\pi$
$458$	−15.6174	+	13.1046i	−0.729755	+	0.612337i
$459$	−13.9166	−	5.06522i	−0.649570	−	0.236424i
$460$		0			0
$461$	4.57133	+	25.9253i	0.212908	+	1.20746i	0.884500	+	0.466541i	$0.154500\pi$
$461$	4.57133	+	25.9253i	0.212908	+	1.20746i	−0.671591	+	0.740922i	$0.734389\pi$
$462$	10.1687	−	3.70109i	0.473089	−	0.172190i
$463$	5.27461	−	9.13589i	0.245132	−	0.424581i	−0.717037	−	0.697035i	$-0.754502\pi$
$463$	5.27461	−	9.13589i	0.245132	−	0.424581i	0.962169	+	0.272454i	$0.0878354\pi$
$464$	3.50501	+	6.07085i	0.162716	+	0.281832i
$465$		0			0
$466$	6.44942	+	5.41170i	0.298763	+	0.250692i
$467$	15.2584	+	26.4283i	0.706074	+	1.22296i	0.966303	+	0.257408i	$0.0828686\pi$
$467$	15.2584	+	26.4283i	0.706074	+	1.22296i	−0.260229	+	0.965547i	$0.583798\pi$
$468$	−12.3138	+	21.3282i	−0.569207	+	0.985895i
$469$	29.6696	−	10.7989i	1.37002	−	0.498645i
$470$		0			0
$471$	7.06313	−	40.0570i	0.325452	−	1.84573i
$472$	13.2735	+	4.83117i	0.610964	+	0.222373i
$473$	−3.30770	+	2.77549i	−0.152088	+	0.127617i
$474$	7.87374			0.361653
$475$		0			0
$476$	−7.89321			−0.361784
$477$	21.9736	−	18.4380i	1.00610	−	0.844219i
$478$	−12.4096	−	4.51672i	−0.567601	−	0.206590i
$479$	0.664874	−	3.77069i	0.0303789	−	0.172287i	−0.965843	−	0.259126i	$-0.916565\pi$
$479$	0.664874	−	3.77069i	0.0303789	−	0.172287i	0.996222	+	0.0868390i	$0.0276766\pi$
$480$		0			0
$481$	18.1137	−	6.59284i	0.825912	−	0.300607i
$482$	−3.52810	+	6.11085i	−0.160700	+	0.278341i
$483$	−8.59395	−	14.8852i	−0.391038	−	0.677298i
$484$	−5.79566	−	4.86314i	−0.263439	−	0.221052i
$485$		0			0
$486$	−9.35551	−	16.2042i	−0.424375	−	0.735039i
$487$	−17.7218	+	30.6951i	−0.803052	+	1.39093i	0.114546	+	0.993418i	$0.463459\pi$
$487$	−17.7218	+	30.6951i	−0.803052	+	1.39093i	−0.917598	+	0.397509i	$0.869875\pi$
$488$	−0.249493	+	0.0908082i	−0.0112940	+	0.00411069i
$489$	−5.24990	−	29.7737i	−0.237409	−	1.34641i
$490$		0			0
$491$	−8.02415	−	2.92055i	−0.362125	−	0.131803i	0.154549	−	0.987985i	$-0.450608\pi$
$491$	−8.02415	−	2.92055i	−0.362125	−	0.131803i	−0.516673	+	0.856183i	$0.672830\pi$
$492$	−3.28500	+	2.75644i	−0.148099	+	0.124270i
$493$	−25.8936			−1.16619
$494$	23.3336	+	5.74541i	1.04983	+	0.258498i
$495$		0			0
$496$	−3.26039	+	2.73579i	−0.146396	+	0.122841i
$497$	8.35621	+	3.04141i	0.374827	+	0.136426i
$498$	6.65219	−	37.7265i	0.298092	−	1.69056i
$499$	6.45368	+	36.6007i	0.288907	+	1.63847i	0.690988	+	0.722866i	$0.257176\pi$
$499$	6.45368	+	36.6007i	0.288907	+	1.63847i	−0.402081	+	0.915604i	$0.631713\pi$
$500$		0			0
$501$	26.9465	−	46.6726i	1.20388	−	2.08518i
$502$	−1.16679	−	2.02094i	−0.0520765	−	0.0901991i
$503$	16.7933	+	14.0913i	0.748778	+	0.628299i	0.935179	−	0.354175i	$-0.115238\pi$
$503$	16.7933	+	14.0913i	0.748778	+	0.628299i	−0.186402	+	0.982474i	$0.559683\pi$
$504$	7.31257	+	6.13598i	0.325728	+	0.273318i
$505$		0			0
$506$	2.72743	−	4.72404i	0.121249	−	0.210009i
$507$	−44.6620	+	16.2556i	−1.98351	+	0.721939i
$508$	2.69403	+	15.2786i	0.119528	+	0.677878i
$509$	−1.71368	+	9.71877i	−0.0759576	+	0.430777i	0.922986	+	0.384833i	$0.125741\pi$
$509$	−1.71368	+	9.71877i	−0.0759576	+	0.430777i	−0.998944	+	0.0459444i	$0.985370\pi$
$510$		0			0
$511$	25.2268	−	21.1678i	1.11597	−	0.936408i
$512$	−1.00000			−0.0441942
$513$	12.1033	−	12.6068i	0.534374	−	0.556603i
$514$	−5.54056			−0.244384
$515$		0			0
$516$	−5.98298	−	2.17763i	−0.263386	−	0.0958647i
$517$	−3.60950	+	20.4705i	−0.158746	+	0.900291i
$518$	−1.29743	−	7.35809i	−0.0570058	−	0.323296i
$519$	15.5554	−	5.66170i	0.682805	−	0.248521i
$520$		0			0
$521$	2.86829	+	4.96802i	0.125662	+	0.217653i	0.921991	−	0.387210i	$-0.126561\pi$
$521$	2.86829	+	4.96802i	0.125662	+	0.217653i	−0.796330	+	0.604863i	$0.793228\pi$
$522$	23.9889	+	20.1290i	1.04996	+	0.881024i
$523$	−20.4665	−	17.1734i	−0.894937	−	0.750941i	0.0742573	−	0.997239i	$-0.476341\pi$
$523$	−20.4665	−	17.1734i	−0.894937	−	0.750941i	−0.969194	+	0.246298i	$0.920786\pi$
$524$	−11.0260	−	19.0976i	−0.481674	−	0.834283i
$525$		0			0
$526$	1.66651	−	0.606559i	0.0726632	−	0.0264472i
$527$	−2.72998	−	15.4825i	−0.118920	−	0.674428i
$528$	−0.879364	+	4.98712i	−0.0382694	+	0.217037i
$529$	13.4713	+	4.90314i	0.585707	+	0.213180i
$530$		0			0
$531$	63.1012			2.73836
$532$	3.76366	−	8.52018i	0.163175	−	0.369397i
$533$	−8.65143			−0.374735
$534$	−4.14350	+	3.47681i	−0.179307	+	0.150456i
$535$		0			0
$536$	−2.56577	+	14.5512i	−0.110824	+	0.628515i
$537$	−0.593190	−	3.36415i	−0.0255980	−	0.145174i
$538$	−14.9736	+	5.44995i	−0.645558	+	0.234964i
$539$	−2.25510	+	3.90595i	−0.0971342	+	0.168241i
$540$		0			0
$541$	23.7434	+	19.9231i	1.02081	+	0.856562i	0.989729	−	0.142955i	$-0.0456604\pi$
$541$	23.7434	+	19.9231i	1.02081	+	0.856562i	0.0310814	+	0.999517i	$0.490105\pi$
$542$	−10.8012	−	9.06330i	−0.463952	−	0.389302i
$543$	−21.5735	−	37.3664i	−0.925807	−	1.60355i
$544$	1.84690	−	3.19893i	0.0791853	−	0.137153i
$545$		0			0
$546$	5.59005	+	31.7027i	0.239232	+	1.35675i
$547$	3.02131	−	17.1347i	0.129182	−	0.732627i	−0.849554	−	0.527502i	$-0.823129\pi$
$547$	3.02131	−	17.1347i	0.129182	−	0.732627i	0.978736	−	0.205125i	$-0.0657601\pi$
$548$	−13.1019	−	4.76868i	−0.559683	−	0.203708i
$549$	−0.908582	+	0.762391i	−0.0387773	+	0.0325380i
$550$		0			0
$551$	12.3467	−	27.9504i	0.525986	−	1.19073i
$552$	8.04347			0.342353
$553$	4.71667	−	3.95775i	0.200573	−	0.168301i
$554$	20.9230	+	7.61536i	0.888934	+	0.323546i
$555$		0			0
$556$	2.14081	+	12.1412i	0.0907907	+	0.514900i
$557$	−11.1000	+	4.04009i	−0.470324	+	0.171184i	−0.566299	−	0.824200i	$-0.691625\pi$
$557$	−11.1000	+	4.04009i	−0.470324	+	0.171184i	0.0959752	+	0.995384i	$0.469403\pi$
$558$	−9.50654	+	16.4658i	−0.402444	+	0.697053i
$559$	−6.42257	−	11.1242i	−0.271646	−	0.470504i
$560$		0			0
$561$	−14.3293	−	12.0238i	−0.604986	−	0.507643i
$562$	−3.65388	−	6.32870i	−0.154130	−	0.266960i
$563$	15.6982	−	27.1901i	0.661600	−	1.14592i	−0.318595	−	0.947891i	$-0.603211\pi$
$563$	15.6982	−	27.1901i	0.661600	−	1.14592i	0.980195	−	0.198034i	$-0.0634556\pi$
$564$	−28.8020	+	10.4831i	−1.21278	+	0.441417i
$565$		0			0
$566$	1.78983	−	10.1506i	0.0752323	−	0.426663i
$567$	−4.91087	−	1.78741i	−0.206237	−	0.0750642i
$568$	−3.18785	+	2.67493i	−0.133759	+	0.112237i
$569$	3.95114			0.165640			0.0828202	−	0.996565i	$-0.473607\pi$
$569$	3.95114			0.165640			0.0828202	+	0.996565i	$0.473607\pi$
$570$		0			0
$571$	2.18380			0.0913891			0.0456946	−	0.998955i	$-0.485450\pi$
$571$	2.18380			0.0913891			0.0456946	+	0.998955i	$0.485450\pi$
$572$	−7.82636	+	6.56709i	−0.327236	+	0.274584i
$573$	5.26674	+	1.91694i	0.220021	+	0.0800812i
$574$	−0.582306	+	3.30242i	−0.0243050	+	0.137840i
$575$		0			0
$576$	−4.19781	+	1.52788i	−0.174909	+	0.0636615i
$577$	6.51747	−	11.2886i	0.271326	−	0.469950i	−0.697876	−	0.716219i	$-0.745871\pi$
$577$	6.51747	−	11.2886i	0.271326	−	0.469950i	0.969202	+	0.246269i	$0.0792046\pi$
$578$	−1.67790	−	2.90621i	−0.0697916	−	0.120883i
$579$	−1.72256	−	1.44540i	−0.0715872	−	0.0600688i
$580$		0			0
$581$	−14.9784	−	25.9433i	−0.621408	−	1.07631i
$582$	14.7699	−	25.5821i	0.612230	−	1.06041i
$583$	11.1819	−	4.06987i	0.463106	−	0.168557i
$584$	2.67608	+	15.1768i	0.110737	+	0.628020i
$585$		0			0
$586$	−28.7884	−	10.4781i	−1.18924	−	0.432847i
$587$	29.6918	−	24.9144i	1.22551	−	1.02833i	0.226996	−	0.973896i	$-0.427110\pi$
$587$	29.6918	−	24.9144i	1.22551	−	1.02833i	0.998517	−	0.0544318i	$-0.0173348\pi$
$588$	−6.65054			−0.274263
$589$	18.0140	+	4.43558i	0.742255	+	0.182765i
$590$		0			0
$591$	−26.5891	+	22.3109i	−1.09373	+	0.917750i
$592$	3.28564	+	1.19588i	0.135039	+	0.0491502i
$593$	3.02318	−	17.1453i	0.124147	−	0.704073i	−0.857664	−	0.514211i	$-0.828085\pi$
$593$	3.02318	−	17.1453i	0.124147	−	0.704073i	0.981811	−	0.189862i	$-0.0608040\pi$
$594$	1.29022	+	7.31717i	0.0529382	+	0.300227i
$595$		0			0
$596$	−11.2574	+	19.4983i	−0.461119	+	0.798682i
$597$	6.98031	+	12.0903i	0.285685	+	0.494821i
$598$	12.4310	+	10.4308i	0.508339	+	0.426547i
$599$	−24.6574	−	20.6900i	−1.00747	−	0.845370i	−0.0194709	−	0.999810i	$-0.506198\pi$
$599$	−24.6574	−	20.6900i	−1.00747	−	0.845370i	−0.988002	+	0.154440i	$0.950643\pi$
$600$		0			0
$601$	−18.1105	+	31.3683i	−0.738742	+	1.27954i	0.214321	+	0.976763i	$0.431246\pi$
$601$	−18.1105	+	31.3683i	−0.738742	+	1.27954i	−0.953062	+	0.302775i	$0.902087\pi$
$602$	−4.67862	+	1.70288i	−0.190686	+	0.0694042i
$603$	11.4618	+	65.0032i	0.466761	+	2.64714i
$604$	3.93230	−	22.3012i	0.160003	−	0.907422i
$605$		0			0
$606$	−20.8830	+	17.5229i	−0.848314	+	0.711820i
$607$	−30.3654			−1.23250			−0.616248	−	0.787552i	$-0.711348\pi$
$607$	−30.3654			−1.23250			−0.616248	+	0.787552i	$0.711348\pi$
$608$	2.57238	+	3.51893i	0.104324	+	0.142711i
$609$	40.9334			1.65870
$610$		0			0
$611$	−58.1072	−	21.1493i	−2.35076	−	0.855608i
$612$	2.86537	−	16.2503i	0.115826	−	0.656881i
$613$	3.96373	+	22.4794i	0.160094	+	0.907936i	0.953980	+	0.299870i	$0.0969434\pi$
$613$	3.96373	+	22.4794i	0.160094	+	0.907936i	−0.793886	+	0.608066i	$0.791946\pi$
$614$	7.50580	−	2.73189i	0.302910	−	0.110250i
$615$		0			0
$616$	1.98002	+	3.42949i	0.0797771	+	0.138178i
$617$	−30.4152	−	25.5214i	−1.22447	−	1.02745i	−0.998579	−	0.0532981i	$-0.983027\pi$
$617$	−30.4152	−	25.5214i	−1.22447	−	1.02745i	−0.225890	−	0.974153i	$-0.572529\pi$
$618$	−18.3691	−	15.4135i	−0.738915	−	0.620023i
$619$	−19.6707	−	34.0707i	−0.790633	−	1.36942i	−0.925576	−	0.378562i	$-0.876419\pi$
$619$	−19.6707	−	34.0707i	−0.790633	−	1.36942i	0.134943	−	0.990853i	$-0.456915\pi$
$620$		0			0
$621$	11.0898	−	4.03635i	0.445017	−	0.161973i
$622$	4.62442	+	26.2264i	0.185422	+	1.05158i
$623$	−0.734486	+	4.16548i	−0.0294266	+	0.166886i
$624$	−14.1564	−	5.15249i	−0.566708	−	0.206265i
$625$		0			0
$626$	−7.66333			−0.306288
$627$	19.8114	−	9.73436i	0.791190	−	0.388753i
$628$	14.8850			0.593974
$629$	−9.89378	+	8.30186i	−0.394491	+	0.331017i
$630$		0			0
$631$	0.418513	−	2.37351i	0.0166607	−	0.0944878i	−0.975344	−	0.220692i	$-0.929168\pi$
$631$	0.418513	−	2.37351i	0.0166607	−	0.0944878i	0.992004	+	0.126204i	$0.0402795\pi$
$632$	0.500348	+	2.83761i	0.0199028	+	0.112874i
$633$	50.0522	−	18.2175i	1.98940	−	0.724082i
$634$	1.48304	−	2.56871i	0.0588992	−	0.102016i
$635$		0			0
$636$	13.4414	+	11.2786i	0.532985	+	0.447227i
$637$	−10.2782	−	8.62445i	−0.407238	−	0.341713i
$638$	6.49543	+	11.2504i	0.257157	+	0.445408i
$639$	−9.29503	+	16.0995i	−0.367706	+	0.636885i
$640$		0			0
$641$	−2.88094	−	16.3386i	−0.113790	−	0.645337i	−0.987342	−	0.158606i	$-0.949300\pi$
$641$	−2.88094	−	16.3386i	−0.113790	−	0.645337i	0.873552	−	0.486731i	$-0.161811\pi$
$642$	2.70628	−	15.3481i	0.106808	−	0.605740i
$643$	32.3683	+	11.7811i	1.27648	+	0.464601i	0.889267	−	0.457389i	$-0.151215\pi$
$643$	32.3683	+	11.7811i	1.27648	+	0.464601i	0.387214	+	0.921990i	$0.373438\pi$
$644$	4.81834	−	4.04307i	0.189869	−	0.159319i
$645$		0			0
$646$	−16.0077	+	1.72975i	−0.629816	+	0.0680561i
$647$	5.97186			0.234778			0.117389	−	0.993086i	$-0.462548\pi$
$647$	5.97186			0.234778			0.117389	+	0.993086i	$0.462548\pi$
$648$	1.87347	−	1.57203i	0.0735969	−	0.0617551i
$649$	24.5983	+	8.95307i	0.965570	+	0.351439i
$650$		0			0
$651$	4.31564	+	24.4752i	0.169143	+	0.959258i
$652$	10.3965	−	3.78402i	0.407159	−	0.148194i
$653$	−4.22812	+	7.32332i	−0.165459	+	0.286584i	−0.936818	−	0.349816i	$-0.886244\pi$
$653$	−4.22812	+	7.32332i	−0.165459	+	0.286584i	0.771359	+	0.636400i	$0.219577\pi$
$654$	1.08363	+	1.87691i	0.0423734	+	0.0733928i
$655$		0			0
$656$	−1.20214	−	1.00872i	−0.0469357	−	0.0393838i
$657$	34.4220	+	59.6206i	1.34293	+	2.32602i
$658$	−11.9841	+	20.7571i	−0.467191	+	0.809198i
$659$	21.5906	−	7.85832i	0.841049	−	0.306117i	0.114664	−	0.993404i	$-0.463421\pi$
$659$	21.5906	−	7.85832i	0.841049	−	0.306117i	0.726385	+	0.687288i	$0.241199\pi$
$660$		0			0
$661$	4.06768	−	23.0690i	0.158214	−	0.897278i	−0.797574	−	0.603222i	$-0.793883\pi$
$661$	4.06768	−	23.0690i	0.158214	−	0.897278i	0.955788	−	0.294057i	$-0.0950054\pi$
$662$	2.49995	+	0.909909i	0.0971635	+	0.0353646i
$663$	42.6279	−	35.7690i	1.65553	−	1.38915i
$664$	14.0189			0.544040
$665$		0			0
$666$	15.6196			0.605249
$667$	15.8065	−	13.2633i	0.612032	−	0.513556i
$668$	18.5327	+	6.74534i	0.717051	+	0.260985i
$669$	−1.16089	+	6.58374i	−0.0448826	+	0.254542i
$670$		0			0
$671$	−0.462358	+	0.168285i	−0.0178491	+	0.00649655i
$672$	−2.91964	+	5.05696i	−0.112627	+	0.195076i
$673$	0.0188863	+	0.0327120i	0.000728012	+	0.00126095i	0.866389	−	0.499369i	$-0.166435\pi$
$673$	0.0188863	+	0.0327120i	0.000728012	+	0.00126095i	−0.865661	+	0.500630i	$0.833102\pi$
$674$	23.9959	+	20.1349i	0.924287	+	0.775569i
$675$		0			0
$676$	−8.69647	−	15.0627i	−0.334480	−	0.579336i
$677$	15.5421	−	26.9197i	0.597332	−	1.03461i	−0.395882	−	0.918302i	$-0.629561\pi$
$677$	15.5421	−	26.9197i	0.597332	−	1.03461i	0.993213	−	0.116307i	$-0.0371057\pi$
$678$	12.8033	−	4.66001i	0.491706	−	0.178966i
$679$	−4.01122	−	22.7488i	−0.153937	−	0.873018i
$680$		0			0
$681$	−49.3791	−	17.9725i	−1.89221	−	0.688709i
$682$	−6.04212	+	5.06994i	−0.231365	+	0.194138i
$683$	−22.0437			−0.843481			−0.421740	−	0.906717i	$-0.638581\pi$
$683$	−22.0437			−0.843481			−0.421740	+	0.906717i	$0.638581\pi$
$684$	16.1749	+	10.8415i	0.618461	+	0.414535i
$685$		0			0
$686$	−15.4425	+	12.9578i	−0.589598	+	0.494732i
$687$	−52.3505	−	19.0540i	−1.99730	−	0.726957i
$688$	0.404597	−	2.29458i	0.0154251	−	0.0874802i
$689$	6.14705	+	34.8616i	0.234184	+	1.32812i
$690$		0			0
$691$	−4.10144	+	7.10391i	−0.156026	+	0.270245i	−0.933432	−	0.358754i	$-0.883202\pi$
$691$	−4.10144	+	7.10391i	−0.156026	+	0.270245i	0.777406	+	0.628999i	$0.216535\pi$
$692$	3.02890	+	5.24622i	0.115142	+	0.199431i
$693$	13.5516	+	11.3711i	0.514781	+	0.431953i
$694$	−8.13364	−	6.82494i	−0.308749	−	0.259071i
$695$		0			0
$696$	−9.57786	+	16.5893i	−0.363048	+	0.628817i
$697$	5.44705	−	1.98256i	0.206322	−	0.0750950i
$698$	−6.41749	−	36.3954i	−0.242906	−	1.37759i
$699$	−3.99499	+	22.6567i	−0.151104	+	0.856956i
$700$		0			0
$701$	2.73064	−	2.29128i	0.103135	−	0.0865405i	−0.589762	−	0.807577i	$-0.700778\pi$
$701$	2.73064	−	2.29128i	0.103135	−	0.0865405i	0.692897	+	0.721037i	$0.256334\pi$
$702$	−22.1034			−0.834239
$703$	−4.24372	−	14.6382i	−0.160055	−	0.552089i
$704$	−1.85319			−0.0698446
$705$		0			0
$706$	28.9940	+	10.5530i	1.09120	+	0.397166i
$707$	−3.70177	+	20.9938i	−0.139219	+	0.789553i
$708$	6.70271	+	38.0130i	0.251903	+	1.42861i
$709$	−16.7368	+	6.09168i	−0.628562	+	0.228778i	−0.636605	−	0.771190i	$-0.719662\pi$
$709$	−16.7368	+	6.09168i	−0.628562	+	0.228778i	0.00804307	+	0.999968i	$0.497440\pi$
$710$		0			0
$711$	6.43589	+	11.1473i	0.241365	+	0.418056i
$712$	−1.51631	−	1.27233i	−0.0568261	−	0.0476827i
$713$	9.59696	+	8.05281i	0.359409	+	0.301580i
$714$	−10.7846	−	18.6794i	−0.403602	−	0.699060i
$715$		0			0
$716$	1.17471	−	0.427559i	0.0439009	−	0.0159786i
$717$	−6.26644	−	35.5387i	−0.234024	−	1.32722i
$718$	1.76076	−	9.98574i	0.0657108	−	0.372664i
$719$	−17.0854	−	6.21856i	−0.637176	−	0.231913i	0.00317562	−	0.999995i	$-0.498989\pi$
$719$	−17.0854	−	6.21856i	−0.637176	−	0.231913i	−0.640352	+	0.768082i	$0.721211\pi$
$720$		0			0
$721$	−18.7515			−0.698341
$722$	5.76570	−	18.1041i	0.214577	−	0.673763i
$723$	−19.2819			−0.717102
$724$	12.0955	−	10.1494i	0.449527	−	0.377198i
$725$		0			0
$726$	3.59003	−	20.3601i	0.133239	−	0.755634i
$727$	1.47717	+	8.37743i	0.0547851	+	0.310702i	0.999870	−	0.0161233i	$-0.00513242\pi$
$727$	1.47717	+	8.37743i	0.0547851	+	0.310702i	−0.945085	+	0.326825i	$0.894021\pi$
$728$	−11.0701	+	4.02919i	−0.410285	+	0.149332i
$729$	21.8966	−	37.9260i	0.810985	−	1.40467i
$730$		0			0
$731$	6.59296	+	5.53215i	0.243849	+	0.204614i
$732$	−0.555785	−	0.466359i	−0.0205424	−	0.0172371i
$733$	−25.4955	−	44.1595i	−0.941698	−	1.63107i	−0.762230	−	0.647306i	$-0.775896\pi$
$733$	−25.4955	−	44.1595i	−0.941698	−	1.63107i	−0.179468	−	0.983764i	$-0.557438\pi$
$734$	−5.88751	+	10.1975i	−0.217312	+	0.376395i
$735$		0			0
$736$	0.511133	+	2.89878i	0.0188406	+	0.106851i
$737$	−4.75484	+	26.9661i	−0.175147	+	0.993307i
$738$	−6.58755	−	2.39767i	−0.242491	−	0.0882596i
$739$	−1.19013	+	0.998640i	−0.0437798	+	0.0367356i	−0.664415	−	0.747364i	$-0.731319\pi$
$739$	−1.19013	+	0.998640i	−0.0437798	+	0.0367356i	0.620635	+	0.784099i	$0.286875\pi$
$740$		0			0
$741$	18.2843	+	63.0694i	0.671691	+	2.31691i
$742$	13.7211			0.503718
$743$	7.59707	−	6.37470i	0.278710	−	0.233865i	−0.492707	−	0.870195i	$-0.663993\pi$
$743$	7.59707	−	6.37470i	0.278710	−	0.233865i	0.771417	+	0.636330i	$0.219548\pi$
$744$	−10.9290	−	3.97784i	−0.400677	−	0.145835i
$745$		0			0
$746$	−3.39869	−	19.2749i	−0.124435	−	0.705704i
$747$	58.8488	−	21.4192i	2.15317	−	0.783688i
$748$	3.42266	−	5.92821i	0.125145	−	0.216757i
$749$	−6.09358	−	10.5544i	−0.222655	−	0.385649i
$750$		0			0
$751$	−3.53634	−	2.96734i	−0.129043	−	0.108280i	0.575982	−	0.817462i	$-0.304620\pi$
$751$	−3.53634	−	2.96734i	−0.129043	−	0.108280i	−0.705025	+	0.709183i	$0.749064\pi$
$752$	−5.60825	−	9.71378i	−0.204512	−	0.354225i
$753$	3.18840	−	5.52247i	0.116192	−	0.201250i
$754$	−36.3154	+	13.2177i	−1.32253	+	0.481362i
$755$		0			0
$756$	−1.48772	+	8.43730i	−0.0541080	+	0.306862i
$757$	−21.8372	−	7.94810i	−0.793688	−	0.288879i	−0.0868196	−	0.996224i	$-0.527670\pi$
$757$	−21.8372	−	7.94810i	−0.793688	−	0.288879i	−0.706868	+	0.707345i	$0.749893\pi$
$758$	−14.6238	+	12.2709i	−0.531162	+	0.445698i
$759$	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	$0.653614\pi$
$762$	−32.4762	+	27.2508i	−1.17649	+	0.987191i
$763$	1.59257	+	0.579647i	0.0576548	+	0.0209846i
$764$	−0.356162	+	2.01989i	−0.0128855	+	0.0730771i
$765$		0			0
$766$	18.4874	−	6.72885i	0.667975	−	0.243123i
$767$	−38.9365	+	67.4401i	−1.40592	+	2.43512i
$768$	−1.36631	−	2.36652i	−0.0493025	−	0.0853944i
$769$	19.0328	+	15.9704i	0.686339	+	0.575907i	0.917851	−	0.396925i	$-0.129923\pi$
$769$	19.0328	+	15.9704i	0.686339	+	0.575907i	−0.231512	+	0.972832i	$0.574367\pi$
$770$		0			0
$771$	−7.57012	−	13.1118i	−0.272631	−	0.472211i
$772$	0.411445	−	0.712643i	0.0148082	−	0.0256486i
$773$	34.6603	−	12.6153i	1.24664	−	0.453741i	0.367378	−	0.930072i	$-0.380256\pi$
$773$	34.6603	−	12.6153i	1.24664	−	0.453741i	0.879266	+	0.476330i	$0.158033\pi$
$774$	−1.80742	−	10.2504i	−0.0649664	−	0.368443i
$775$		0			0
$776$	10.1581	+	3.69725i	0.364655	+	0.132723i
$777$	15.6404	−	13.1238i	0.561095	−	0.470815i
$778$	24.0483			0.862175
$779$	−0.457233	+	6.82505i	−0.0163821	+	0.244533i
$780$		0			0
$781$	−5.90769	+	4.95714i	−0.211394	+	0.177380i
$782$	−10.2170	−	3.71869i	−0.365359	−	0.132980i
$783$	−4.88047	+	27.6785i	−0.174414	+	0.989150i
$784$	−0.422618	−	2.39678i	−0.0150935	−	0.0855994i
$785$		0			0
$786$	30.1299	−	52.1865i	1.07470	−	1.86143i
$787$	−25.0213	−	43.3382i	−0.891914	−	1.54484i	−0.837579	−	0.546317i	$-0.816029\pi$
$787$	−25.0213	−	43.3382i	−0.891914	−	1.54484i	−0.0543351	−	0.998523i	$-0.517304\pi$
$788$	−9.73028	−	8.16467i	−0.346627	−	0.290854i
$789$	3.71240	+	3.11507i	0.132165	+	0.110900i
$790$		0			0
$791$	5.32727	−	9.22711i	0.189416	−	0.328078i
$792$	−7.77932	+	2.83144i	−0.276426	+	0.100611i
$793$	−0.254173	−	1.44149i	−0.00902596	−	0.0511888i
$794$	−0.441252	+	2.50246i	−0.0156594	+	0.0888091i
$795$		0			0
$796$	−3.91363	+	3.28392i	−0.138715	+	0.116396i
$797$	−5.53339			−0.196003			−0.0980013	−	0.995186i	$-0.531245\pi$
$797$	−5.53339			−0.196003			−0.0980013	+	0.995186i	$0.531245\pi$
$798$	25.3055	−	2.73444i	0.895805	−	0.0967981i
$799$	41.4316			1.46574
$800$		0			0
$801$	−8.30914	−	3.02428i	−0.293589	−	0.106858i
$802$	−0.257775	+	1.46191i	−0.00910234	+	0.0516219i
$803$	4.95928	+	28.1254i	0.175009	+	0.992525i
$804$	−37.9413	+	13.8095i	−1.33809	+	0.487023i
$805$		0			0
$806$	−11.7320	−	20.3204i	−0.413242	−	0.715757i
$807$	−33.3560	−	27.9890i	−1.17419	−	0.985260i
$808$	−7.64212	−	6.41250i	−0.268849	−	0.225591i
$809$	−6.93364	−	12.0094i	−0.243774	−	0.422229i	0.718012	−	0.696030i	$-0.245052\pi$
$809$	−6.93364	−	12.0094i	−0.243774	−	0.422229i	−0.961786	+	0.273802i	$0.911719\pi$
$810$		0			0
$811$	7.68087	−	2.79561i	0.269712	−	0.0981670i	−0.203624	−	0.979049i	$-0.565272\pi$
$811$	7.68087	−	2.79561i	0.269712	−	0.0981670i	0.473336	+	0.880882i	$0.343050\pi$
$812$	2.60117	+	14.7520i	0.0912832	+	0.517693i
$813$	6.69065	−	37.9446i	0.234651	−	1.33077i
$814$	6.08890	+	2.21618i	0.213416	+	0.0776771i
$815$		0			0
$816$	10.0938			0.353352
$817$	−9.11526	+	4.47880i	−0.318902	+	0.156693i
$818$	−12.2798			−0.429355
$819$	−40.3141	+	33.8275i	−1.40869	+	1.18203i
$820$		0			0
$821$	7.69213	−	43.6243i	0.268457	−	1.52250i	−0.490549	−	0.871414i	$-0.663204\pi$
$821$	7.69213	−	43.6243i	0.268457	−	1.52250i	0.759006	−	0.651083i	$-0.225685\pi$
$822$	−6.61601	−	37.5213i	−0.230760	−	1.30871i
$823$	0.792059	−	0.288286i	0.0276094	−	0.0100490i	−0.328179	−	0.944616i	$-0.606435\pi$
$823$	0.792059	−	0.288286i	0.0276094	−	0.0100490i	0.355788	+	0.934567i	$0.384213\pi$
$824$	4.38758	−	7.59952i	0.152849	−	0.264742i
$825$		0			0
$826$	23.1225	+	19.4021i	0.804534	+	0.675084i
$827$	10.8286	+	9.08627i	0.376547	+	0.315961i	0.811345	−	0.584567i	$-0.198736\pi$
$827$	10.8286	+	9.08627i	0.376547	+	0.315961i	−0.434798	+	0.900528i	$0.643180\pi$
$828$	6.57462	+	11.3876i	0.228484	+	0.395746i
$829$	−23.8392	+	41.2907i	−0.827969	+	1.43408i	0.0716603	+	0.997429i	$0.477170\pi$
$829$	−23.8392	+	41.2907i	−0.827969	+	1.43408i	−0.899629	+	0.436655i	$0.856163\pi$
$830$		0			0
$831$	10.5655	+	59.9197i	0.366511	+	2.07859i
$832$	0.957319	−	5.42923i	0.0331891	−	0.188225i
$833$	8.44767	+	3.07470i	0.292695	+	0.106532i
$834$	−25.8073	+	21.6549i	−0.893632	+	0.749847i
$835$		0			0
$836$	4.76710	+	6.52123i	0.164874	+	0.225541i
$837$	−17.0643			−0.589828
$838$	2.26085	−	1.89707i	0.0780996	−	0.0655333i
$839$	0.221512	+	0.0806239i	0.00764746	+	0.00278345i	0.345841	−	0.938293i	$-0.387594\pi$
$839$	0.221512	+	0.0806239i	0.00764746	+	0.00278345i	−0.338194	+	0.941077i	$0.609816\pi$
$840$		0			0
$841$	3.49733	+	19.8343i	0.120598	+	0.683943i
$842$	−7.04747	+	2.56507i	−0.242872	+	0.0883981i
$843$	9.98466	−	17.2939i	0.343890	−	0.595635i
$844$	9.74604	+	16.8806i	0.335473	+	0.581056i
$845$		0			0
$846$	−38.3838	−	32.2079i	−1.31966	−	1.10733i
$847$	−8.08348	−	14.0010i	−0.277752	−	0.481080i
$848$	−3.21055	+	5.56084i	−0.110251	+	0.190960i
$849$	26.4672	−	9.63326i	0.908350	−	0.330613i
$850$		0			0
$851$	1.78718	−	10.1356i	0.0612638	−	0.347444i
$852$	−10.6859	−	3.88933i	−0.366091	−	0.133246i
$853$	2.93138	−	2.45972i	0.100368	−	0.0842191i	−0.591223	−	0.806508i	$-0.701355\pi$
$853$	2.93138	−	2.45972i	0.100368	−	0.0842191i	0.691591	+	0.722289i	$0.256910\pi$
$854$	−0.567352			−0.0194144
$855$		0			0
$856$	5.70326			0.194933
$857$	9.49966	−	7.97116i	0.324502	−	0.272290i	−0.465953	−	0.884809i	$-0.654288\pi$
$857$	9.49966	−	7.97116i	0.324502	−	0.272290i	0.790455	+	0.612520i	$0.209844\pi$
$858$	−26.2344	−	9.54853i	−0.895627	−	0.325982i
$859$	6.20007	−	35.1623i	0.211544	−	1.19972i	−0.675261	−	0.737579i	$-0.735969\pi$
$859$	6.20007	−	35.1623i	0.211544	−	1.19972i	0.886805	−	0.462145i	$-0.152920\pi$
$860$		0			0
$861$	−8.61085	+	3.13409i	−0.293457	+	0.106810i
$862$	−12.0469	+	20.8658i	−0.410317	+	0.710691i
$863$	10.2181	+	17.6983i	0.347830	+	0.602458i	0.985864	−	0.167550i	$-0.0535855\pi$
$863$	10.2181	+	17.6983i	0.347830	+	0.602458i	−0.638034	+	0.770008i	$0.720252\pi$
$864$	−3.07133	−	2.57715i	−0.104489	−	0.0876765i
$865$		0			0
$866$	−17.6917	−	30.6429i	−0.601188	−	1.04129i
$867$	4.58507	−	7.94158i	0.155717	−	0.269710i
$868$	−8.54636	+	3.11062i	−0.290082	+	0.105581i
$869$	0.927238	+	5.25863i	0.0314544	+	0.178387i
$870$		0			0
$871$	−76.5454	−	27.8602i	−2.59364	−	0.944008i
$872$	−0.607556	+	0.509800i	−0.0205745	+	0.0172640i
$873$	48.2907			1.63439
$874$	8.88577	−	9.25541i	0.300566	−	0.313069i
$875$		0			0
$876$	−32.2598	+	27.0692i	−1.08996	+	0.914584i
$877$	49.5744	+	18.0436i	1.67401	+	0.609289i	0.992469	−	0.122492i	$-0.0390886\pi$
$877$	49.5744	+	18.0436i	1.67401	+	0.609289i	0.681539	+	0.731782i	$0.261311\pi$
$878$	−4.13061	+	23.4258i	−0.139401	+	0.790584i
$879$	−14.5372	−	82.4447i	−0.490328	−	2.78079i
$880$		0			0
$881$	−15.8483	+	27.4500i	−0.533941	+	0.924813i	0.465273	+	0.885167i	$0.345956\pi$
$881$	−15.8483	+	27.4500i	−0.533941	+	0.924813i	−0.999214	+	0.0396459i	$0.987377\pi$
$882$	−5.43606	−	9.41553i	−0.183042	−	0.317037i
$883$	−32.8546	−	27.5683i	−1.10564	−	0.927746i	−0.107853	−	0.994167i	$-0.534398\pi$
$883$	−32.8546	−	27.5683i	−1.10564	−	0.927746i	−0.997792	+	0.0664209i	$0.978842\pi$
$884$	15.5996	+	13.0896i	0.524672	+	0.440252i
$885$		0			0
$886$	6.85074	−	11.8658i	0.230155	−	0.398640i
$887$	27.7243	−	10.0908i	0.930889	−	0.338816i	0.168327	−	0.985731i	$-0.446163\pi$
$887$	27.7243	−	10.0908i	0.930889	−	0.338816i	0.762562	+	0.646915i	$0.223941\pi$
$888$	1.65914	+	9.40946i	0.0556772	+	0.315761i
$889$	−5.75681	+	32.6485i	−0.193077	+	1.09499i
$890$		0			0
$891$	3.47189	−	2.91326i	0.116313	−	0.0975980i
$892$	−2.44648			−0.0819142
$893$	−19.7555	+	44.7226i	−0.661093	+	1.49658i
$894$	−61.5242			−2.05768
$895$		0			0
$896$	−2.00801	−	0.730855i	−0.0670828	−	0.0244161i
$897$	−7.70016	+	43.6698i	−0.257101	+	1.45809i
$898$	−2.63303	−	14.9327i	−0.0878655	−	0.498310i
$899$	−28.0363	+	10.2044i	−0.935063	+	0.340335i
$900$		0			0
$901$	−11.8592	−	20.5407i	−0.395086	−	0.684309i
$902$	−2.22779	−	1.86934i	−0.0741774	−	0.0622422i
$903$	−10.4223	−	8.74538i	−0.346834	−	0.291028i
$904$	2.49302	+	4.31803i	0.0829166	+	0.143616i
$905$		0			0
$906$	58.1489	−	21.1645i	1.93187	−	0.703142i
$907$	4.82761	+	27.3787i	0.160298	+	0.909095i	0.953781	+	0.300503i	$0.0971545\pi$
$907$	4.82761	+	27.3787i	0.160298	+	0.909095i	−0.793483	+	0.608593i	$0.791734\pi$
$908$	3.33925	−	18.9378i	0.110817	−	0.628473i
$909$	−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	$0.422703\pi$
$912$	−4.81294	+	10.8955i	−0.159372	+	0.360787i
$913$	25.9797			0.859803
$914$	25.7213	−	21.5828i	0.850786	−	0.713894i
$915$		0			0
$916$	3.54019	−	20.0774i	0.116971	−	0.663376i
$917$	−8.18273	−	46.4066i	−0.270218	−	1.53248i
$918$	13.9166	−	5.06522i	0.459315	−	0.167177i
$919$	−5.09200	+	8.81961i	−0.167970	+	0.290932i	−0.937706	−	0.347430i	$-0.887054\pi$
$919$	−5.09200	+	8.81961i	−0.167970	+	0.290932i	0.769736	+	0.638362i	$0.220388\pi$
$920$		0			0
$921$	16.7203	+	14.0300i	0.550953	+	0.462305i
$922$	−20.1663	−	16.9216i	−0.664142	−	0.557282i
$923$	−11.4710	−	19.8683i	−0.377572	−	0.653974i
$924$	−5.41063	+	9.37149i	−0.177997	+	0.308299i
$925$		0			0
$926$	1.83185	+	10.3890i	0.0601984	+	0.341402i
$927$	6.80710	−	38.6050i	0.223575	−	1.26795i
$928$	−6.58726	−	2.39757i	−0.216237	−	0.0787040i
$929$	−6.91896	+	5.80570i	−0.227004	+	0.190479i	−0.749195	−	0.662350i	$-0.769559\pi$
$929$	−6.91896	+	5.80570i	−0.227004	+	0.190479i	0.522191	+	0.852829i	$0.325115\pi$
$930$		0			0
$931$	−7.34697	+	7.65260i	−0.240787	+	0.250804i
$932$	−8.41911			−0.275777
$933$	−55.7469	+	46.7772i	−1.82507	+	1.53142i
$934$	−28.6764	−	10.4373i	−0.938320	−	0.341520i
$935$		0			0
$936$	−4.27655	−	24.2535i	−0.139783	−	0.792751i
$937$	−36.9882	+	13.4626i	−1.20835	+	0.439804i	−0.866131	−	0.499816i	$-0.833401\pi$
$937$	−36.9882	+	13.4626i	−1.20835	+	0.439804i	−0.342219	+	0.939620i	$0.611179\pi$
$938$	−15.7869	+	27.3437i	−0.515460	+	0.892802i
$939$	−10.4705	−	18.1354i	−0.341691	−	0.591827i
$940$		0			0
$941$	33.3892	+	28.0169i	1.08846	+	0.913324i	0.996595	−	0.0824478i	$-0.0262738\pi$
$941$	33.3892	+	28.0169i	1.08846	+	0.913324i	0.0918617	+	0.995772i	$0.470718\pi$
$942$	20.3375	+	35.2255i	0.662630	+	1.14771i
$943$	−2.30959	+	4.00033i	−0.0752107	+	0.130269i
$944$	−13.2735	+	4.83117i	−0.432017	+	0.157241i
$945$		0			0
$946$	0.749794	−	4.25229i	0.0243779	−	0.138254i
$947$	−24.7470	−	9.00717i	−0.804170	−	0.292694i	−0.0929564	−	0.995670i	$-0.529632\pi$
$947$	−24.7470	−	9.00717i	−0.804170	−	0.292694i	−0.711213	+	0.702976i	$0.751854\pi$
$948$	−6.03163	+	5.06114i	−0.195898	+	0.164378i
$949$	−84.9601			−2.75792
$950$		0			0
$951$	8.10520			0.262829
$952$	6.04655	−	5.07365i	0.195970	−	0.164438i
$953$	−0.903804	−	0.328958i	−0.0292771	−	0.0106560i	0.327340	−	0.944907i	$-0.393848\pi$
$953$	−0.903804	−	0.328958i	−0.0292771	−	0.0106560i	−0.356617	+	0.934251i	$0.616070\pi$
$954$	−4.98100	+	28.2487i	−0.161266	+	0.914585i
$955$		0			0
$956$	12.4096	−	4.51672i	0.401354	−	0.146081i
$957$	−17.7496	+	30.7431i	−0.573762	+	0.993784i
$958$	1.91443	+	3.31589i	0.0618524	+	0.107131i
$959$	−22.8234	−	19.1511i	−0.737006	−	0.618422i
$960$		0			0
$961$	6.44264	+	11.1590i	0.207827	+	0.359967i
$962$	−9.63808	+	16.6936i	−0.310744	+	0.538225i
$963$	23.9412	−	8.71388i	0.771494	−	0.280801i
$964$	−1.22530	−	6.94900i	−0.0394641	−	0.223812i
$965$		0			0
$966$	16.1513	+	5.87861i	0.519661	+	0.189141i
$967$	−13.8131	+	11.5906i	−0.444200	+	0.372728i	−0.837278	−	0.546777i	$-0.815855\pi$
$967$	−13.8131	+	11.5906i	−0.444200	+	0.372728i	0.393078	+	0.919505i	$0.371410\pi$
$968$	7.56570			0.243171
$969$	−25.9650	−	35.5192i	−0.834117	−	1.14104i
$970$		0			0
$971$	−8.19208	+	6.87397i	−0.262896	+	0.220596i	−0.764702	−	0.644384i	$-0.777114\pi$
$971$	−8.19208	+	6.87397i	−0.262896	+	0.220596i	0.501806	+	0.864980i	$0.332669\pi$
$972$	17.5826	+	6.39955i	0.563963	+	0.205266i
$973$	−4.57465	+	25.9442i	−0.146657	+	0.831731i
$974$	−6.15472	−	34.9052i	−0.197210	−	1.11843i
$975$		0			0
$976$	0.132753	−	0.229934i	0.00424931	−	0.00736002i
$977$	25.2209	+	43.6839i	0.806889	+	1.39757i	0.915008	+	0.403435i	$0.132184\pi$
$977$	25.2209	+	43.6839i	0.806889	+	1.39757i	−0.108119	+	0.994138i	$0.534483\pi$
$978$	23.1598	+	19.4334i	0.740569	+	0.621411i
$979$	−2.81000	−	2.35787i	−0.0898081	−	0.0753580i
$980$		0			0
$981$	−1.77149	+	3.06832i	−0.0565594	+	0.0979638i
$982$	8.02415	−	2.92055i	0.256061	−	0.0931985i
$983$	8.69866	+	49.3325i	0.277444	+	1.57346i	0.731090	+	0.682282i	$0.239012\pi$
$983$	8.69866	+	49.3325i	0.277444	+	1.57346i	−0.453645	+	0.891182i	$0.649877\pi$
$984$	0.744648	−	4.22311i	0.0237385	−	0.134628i
$985$		0			0
$986$	19.8357	−	16.6441i	0.631696	−	0.530056i
$987$	−65.4962			−2.08477
$988$	−21.5676	+	10.5973i	−0.686158	+	0.337145i
$989$	−6.85830			−0.218081
$990$		0			0
$991$	−13.6454	−	4.96651i	−0.433459	−	0.157766i	0.116069	−	0.993241i	$-0.462970\pi$
$991$	−13.6454	−	4.96651i	−0.433459	−	0.157766i	−0.549529	+	0.835475i	$0.685193\pi$
$992$	0.739071	−	4.19148i	0.0234655	−	0.133080i
$993$	1.26240	+	7.15941i	0.0400609	+	0.227197i
$994$	−8.35621	+	3.04141i	−0.265043	+	0.0964678i
$995$		0			0
$996$	19.1542	+	33.1761i	0.606925	+	1.05122i
$997$	−18.3966	−	15.4366i	−0.582627	−	0.488882i	0.303182	−	0.952933i	$-0.401951\pi$
$997$	−18.3966	−	15.4366i	−0.582627	−	0.488882i	−0.885809	+	0.464051i	$0.846395\pi$
$998$	−28.4703	−	23.8894i	−0.901210	−	0.756205i
$999$	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.l.j.101.1	✓	24
5.2	odd	4		950.2.u.h.899.1		48
5.3	odd	4		950.2.u.h.899.8		48
5.4	even	2		950.2.l.k.101.4	yes	24
19.16	even	9	inner	950.2.l.j.301.1	yes	24
95.54	even	18		950.2.l.k.301.4	yes	24
95.73	odd	36		950.2.u.h.149.1		48
95.92	odd	36		950.2.u.h.149.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.101.1	✓	24	1.1	even	1	trivial
950.2.l.j.301.1	yes	24	19.16	even	9	inner
950.2.l.k.101.4	yes	24	5.4	even	2
950.2.l.k.301.4	yes	24	95.54	even	18
950.2.u.h.149.1		48	95.73	odd	36
950.2.u.h.149.8		48	95.92	odd	36
950.2.u.h.899.1		48	5.2	odd	4
950.2.u.h.899.8		48	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-2.56782 - 0.934611i) q^{3} +(0.173648 - 0.984808i) q^{4} +(2.56782 - 0.934611i) q^{6} +(1.06844 - 1.85059i) q^{7} +(0.500000 + 0.866025i) q^{8} +(3.42208 + 2.87147i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-2.56782 - 0.934611i) q^{3} +(0.173648 - 0.984808i) q^{4} +(2.56782 - 0.934611i) q^{6} +(1.06844 - 1.85059i) q^{7} +(0.500000 + 0.866025i) q^{8} +(3.42208 + 2.87147i) q^{9} +(0.926593 + 1.60491i) q^{11} +(-1.36631 + 2.36652i) q^{12} +(-5.18051 + 1.88555i) q^{13} +(0.371065 + 2.10441i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(2.82962 - 2.37433i) q^{17} -4.46721 q^{18} +(1.21370 + 4.18652i) q^{19} +(-4.47314 + 3.75341i) q^{21} +(-1.74143 - 0.633827i) q^{22} +(-0.511133 + 2.89878i) q^{23} +(-0.474515 - 2.69111i) q^{24} +(2.75649 - 4.77438i) q^{26} +(-2.00467 - 3.47219i) q^{27} +(-1.63694 - 1.37356i) q^{28} +(-5.36998 - 4.50595i) q^{29} +(2.12807 - 3.68592i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.879364 - 4.98712i) q^{33} +(-0.641422 + 3.63769i) q^{34} +(3.42208 - 2.87147i) q^{36} -3.49650 q^{37} +(-3.62079 - 2.42690i) q^{38} +15.0649 q^{39} +(1.47464 + 0.536727i) q^{41} +(1.01398 - 5.75056i) q^{42} +(0.404597 + 2.29458i) q^{43} +(1.74143 - 0.633827i) q^{44} +(-1.47175 - 2.54915i) q^{46} +(8.59234 + 7.20983i) q^{47} +(2.09331 + 1.75649i) q^{48} +(1.21688 + 2.10770i) q^{49} +(-9.48504 + 3.45227i) q^{51} +(0.957319 + 5.42923i) q^{52} +(1.11501 - 6.32356i) q^{53} +(3.76755 + 1.37127i) q^{54} +2.13688 q^{56} +(0.796188 - 11.8846i) q^{57} +7.01002 q^{58} +(10.8207 - 9.07963i) q^{59} +(-0.0461045 + 0.261472i) q^{61} +(0.739071 + 4.19148i) q^{62} +(8.97020 - 3.26488i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(3.87929 + 3.25511i) q^{66} +(11.3188 + 9.49761i) q^{67} +(-1.84690 - 3.19893i) q^{68} +(4.02173 - 6.96585i) q^{69} +(0.722627 + 4.09822i) q^{71} +(-0.775724 + 4.39935i) q^{72} +(14.4815 + 5.27085i) q^{73} +(2.67848 - 2.24751i) q^{74} +(4.33367 - 0.468284i) q^{76} +3.96003 q^{77} +(-11.5404 + 9.68352i) q^{78} +(2.70762 + 0.985493i) q^{79} +(-0.424681 - 2.40849i) q^{81} +(-1.47464 + 0.536727i) q^{82} +(7.00947 - 12.1408i) q^{83} +(2.91964 + 5.05696i) q^{84} +(-1.78487 - 1.49768i) q^{86} +(9.57786 + 16.5893i) q^{87} +(-0.926593 + 1.60491i) q^{88} +(-1.86003 + 0.676995i) q^{89} +(-2.04567 + 11.6016i) q^{91} +(2.76599 + 1.00674i) q^{92} +(-8.90941 + 7.47588i) q^{93} -11.2165 q^{94} -2.73262 q^{96} +(8.28096 - 6.94855i) q^{97} +(-2.28698 - 0.832394i) q^{98} +(-1.43756 + 8.15281i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{7} + 12 q^{8}+O(q^{10}) \) 24 * q - 3 * q^7 + 12 * q^8	\( 24 q - 3 q^{7} + 12 q^{8} - 6 q^{11} + 3 q^{12} - 24 q^{13} - 15 q^{14} + 9 q^{17} - 30 q^{18} - 15 q^{19} - 18 q^{21} - 12 q^{23} - 9 q^{26} + 21 q^{27} - 12 q^{28} - 12 q^{29} + 9 q^{31} + 42 q^{33} - 9 q^{34} - 66 q^{37} - 6 q^{38} + 66 q^{39} + 18 q^{41} - 9 q^{42} + 3 q^{43} - 3 q^{46} + 12 q^{47} - 27 q^{49} - 3 q^{51} + 12 q^{52} + 45 q^{53} + 27 q^{54} - 6 q^{56} + 27 q^{57} + 18 q^{58} + 36 q^{59} + 12 q^{61} + 24 q^{62} + 63 q^{63} - 12 q^{64} + 48 q^{66} + 54 q^{67} - 3 q^{68} + 21 q^{69} - 39 q^{71} - 48 q^{73} + 18 q^{74} + 6 q^{76} - 48 q^{77} + 12 q^{78} - 42 q^{79} - 36 q^{81} - 18 q^{82} + 3 q^{83} + 9 q^{84} - 39 q^{86} + 24 q^{87} + 6 q^{88} - 36 q^{89} + 12 q^{91} + 15 q^{92} + 6 q^{93} + 12 q^{94} + 6 q^{96} + 54 q^{97} - 3 q^{98} + 51 q^{99}+O(q^{100}) \) 24 * q - 3 * q^7 + 12 * q^8 - 6 * q^11 + 3 * q^12 - 24 * q^13 - 15 * q^14 + 9 * q^17 - 30 * q^18 - 15 * q^19 - 18 * q^21 - 12 * q^23 - 9 * q^26 + 21 * q^27 - 12 * q^28 - 12 * q^29 + 9 * q^31 + 42 * q^33 - 9 * q^34 - 66 * q^37 - 6 * q^38 + 66 * q^39 + 18 * q^41 - 9 * q^42 + 3 * q^43 - 3 * q^46 + 12 * q^47 - 27 * q^49 - 3 * q^51 + 12 * q^52 + 45 * q^53 + 27 * q^54 - 6 * q^56 + 27 * q^57 + 18 * q^58 + 36 * q^59 + 12 * q^61 + 24 * q^62 + 63 * q^63 - 12 * q^64 + 48 * q^66 + 54 * q^67 - 3 * q^68 + 21 * q^69 - 39 * q^71 - 48 * q^73 + 18 * q^74 + 6 * q^76 - 48 * q^77 + 12 * q^78 - 42 * q^79 - 36 * q^81 - 18 * q^82 + 3 * q^83 + 9 * q^84 - 39 * q^86 + 24 * q^87 + 6 * q^88 - 36 * q^89 + 12 * q^91 + 15 * q^92 + 6 * q^93 + 12 * q^94 + 6 * q^96 + 54 * q^97 - 3 * q^98 + 51 * q^99

Introduction

L-functions

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