LMFDB - Embedded newform 950.2.l.k.251.1

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			251.1
Character	$\chi$	$=$	950.251
Dual form			950.2.l.k.651.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(-0.443457 - 2.51497i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.443457 + 2.51497i) q^{6} +(2.28243 - 3.95328i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-3.30934 + 1.20450i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.443457 - 2.51497i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.443457 + 2.51497i) q^{6} +(2.28243 - 3.95328i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-3.30934 + 1.20450i) q^{9} +(-1.71245 - 2.96606i) q^{11} +(1.27688 - 2.21163i) q^{12} +(0.141697 - 0.803603i) q^{13} +(-3.49688 + 2.93423i) q^{14} +(0.173648 + 0.984808i) q^{16} +(3.99445 + 1.45386i) q^{17} +3.52173 q^{18} +(4.31207 - 0.637234i) q^{19} +(-10.9545 - 3.98712i) q^{21} +(0.594729 + 3.37288i) q^{22} +(-3.70262 - 3.10687i) q^{23} +(-1.95630 + 1.64153i) q^{24} +(-0.408000 + 0.706677i) q^{26} +(0.666183 + 1.15386i) q^{27} +(4.28956 - 1.56127i) q^{28} +(-2.25311 + 0.820065i) q^{29} +(3.45137 - 5.97794i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-6.70015 + 5.62209i) q^{33} +(-3.25630 - 2.73236i) q^{34} +(-3.30934 - 1.20450i) q^{36} +3.82859 q^{37} +(-4.26997 - 0.876010i) q^{38} -2.08387 q^{39} +(2.12597 + 12.0570i) q^{41} +(8.93022 + 7.49334i) q^{42} +(-3.38122 + 2.83718i) q^{43} +(0.594729 - 3.37288i) q^{44} +(2.41672 + 4.18588i) q^{46} +(6.98859 - 2.54364i) q^{47} +(2.39976 - 0.873440i) q^{48} +(-6.91895 - 11.9840i) q^{49} +(1.88505 - 10.6906i) q^{51} +(0.625092 - 0.524515i) q^{52} +(-8.64770 - 7.25628i) q^{53} +(-0.231363 - 1.31212i) q^{54} -4.56485 q^{56} +(-3.51484 - 10.5621i) q^{57} +2.39771 q^{58} +(5.29935 + 1.92881i) q^{59} +(7.36453 + 6.17958i) q^{61} +(-5.28780 + 4.43699i) q^{62} +(-2.79160 + 15.8319i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(8.21895 - 2.99145i) q^{66} +(-5.29642 + 1.92774i) q^{67} +(2.12540 + 3.68130i) q^{68} +(-6.17173 + 10.6898i) q^{69} +(-11.7667 + 9.87343i) q^{71} +(2.69780 + 2.26372i) q^{72} +(1.61551 + 9.16200i) q^{73} +(-3.59769 - 1.30945i) q^{74} +(3.71284 + 2.28359i) q^{76} -15.6342 q^{77} +(1.95820 + 0.712727i) q^{78} +(-0.376083 - 2.13287i) q^{79} +(-5.48689 + 4.60405i) q^{81} +(2.12597 - 12.0570i) q^{82} +(-0.240255 + 0.416134i) q^{83} +(-5.82879 - 10.0958i) q^{84} +(4.14768 - 1.50963i) q^{86} +(3.06159 + 5.30284i) q^{87} +(-1.71245 + 2.96606i) q^{88} +(-0.474094 + 2.68872i) q^{89} +(-2.85346 - 2.39433i) q^{91} +(-0.839317 - 4.76000i) q^{92} +(-16.5649 - 6.02912i) q^{93} -7.43710 q^{94} -2.55377 q^{96} +(1.87426 + 0.682176i) q^{97} +(2.40292 + 13.6277i) q^{98} +(9.23972 + 7.75304i) 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	−0.443457	−	2.51497i	−0.256030	−	1.45202i	−0.793415	−	0.608681i	$-0.791699\pi$
$3$	−0.443457	−	2.51497i	−0.256030	−	1.45202i	0.537385	−	0.843337i	$-0.319412\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$		0			0
$5$		0			0
$6$	−0.443457	+	2.51497i	−0.181041	+	1.02673i
$7$	2.28243	−	3.95328i	0.862676	−	1.49420i	−0.00665977	−	0.999978i	$-0.502120\pi$
$7$	2.28243	−	3.95328i	0.862676	−	1.49420i	0.869336	−	0.494221i	$-0.164547\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−3.30934	+	1.20450i	−1.10311	+	0.401500i
$10$		0			0
$11$	−1.71245	−	2.96606i	−0.516324	−	0.894300i	−0.999820	−	0.0189536i	$-0.993967\pi$
$11$	−1.71245	−	2.96606i	−0.516324	−	0.894300i	0.483496	−	0.875347i	$-0.339367\pi$
$12$	1.27688	−	2.21163i	0.368605	−	0.638442i
$13$	0.141697	−	0.803603i	0.0392997	−	0.222879i	−0.958832	−	0.283973i	$-0.908348\pi$
$13$	0.141697	−	0.803603i	0.0392997	−	0.222879i	0.998132	+	0.0610931i	$0.0194587\pi$
$14$	−3.49688	+	2.93423i	−0.934581	+	0.784206i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	3.99445	+	1.45386i	0.968796	+	0.352613i	0.777474	−	0.628915i	$-0.216501\pi$
$17$	3.99445	+	1.45386i	0.968796	+	0.352613i	0.191321	+	0.981527i	$0.438723\pi$
$18$	3.52173			0.830079
$19$	4.31207	−	0.637234i	0.989256	−	0.146191i
$19$	4.31207	−	0.637234i	0.989256	−	0.146191i
$20$		0			0
$21$	−10.9545	−	3.98712i	−2.39048	−	0.870062i
$22$	0.594729	+	3.37288i	0.126797	+	0.719100i
$23$	−3.70262	−	3.10687i	−0.772051	−	0.647827i	0.169183	−	0.985585i	$-0.445887\pi$
$23$	−3.70262	−	3.10687i	−0.772051	−	0.647827i	−0.941233	+	0.337757i	$0.890332\pi$
$24$	−1.95630	+	1.64153i	−0.399328	+	0.335076i
$25$		0			0
$26$	−0.408000	+	0.706677i	−0.0800154	+	0.138591i
$27$	0.666183	+	1.15386i	0.128207	+	0.222061i
$28$	4.28956	−	1.56127i	0.810651	−	0.295053i
$29$	−2.25311	+	0.820065i	−0.418392	+	0.152282i	−0.542633	−	0.839970i	$-0.682573\pi$
$29$	−2.25311	+	0.820065i	−0.418392	+	0.152282i	0.124241	+	0.992252i	$0.460350\pi$
$30$		0			0
$31$	3.45137	−	5.97794i	0.619884	−	1.07367i	−0.369623	−	0.929182i	$-0.620513\pi$
$31$	3.45137	−	5.97794i	0.619884	−	1.07367i	0.989506	−	0.144488i	$-0.0461536\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	−6.70015	+	5.62209i	−1.16635	+	0.978680i
$34$	−3.25630	−	2.73236i	−0.558451	−	0.468596i
$35$		0			0
$36$	−3.30934	−	1.20450i	−0.551557	−	0.200750i
$37$	3.82859			0.629416			0.314708	−	0.949189i	$-0.398093\pi$
$37$	3.82859			0.629416			0.314708	+	0.949189i	$0.398093\pi$
$38$	−4.26997	−	0.876010i	−0.692680	−	0.142108i
$39$	−2.08387			−0.333687
$40$		0			0
$41$	2.12597	+	12.0570i	0.332020	+	1.88298i	0.454874	+	0.890556i	$0.349684\pi$
$41$	2.12597	+	12.0570i	0.332020	+	1.88298i	−0.122853	+	0.992425i	$0.539204\pi$
$42$	8.93022	+	7.49334i	1.37796	+	1.15625i
$43$	−3.38122	+	2.83718i	−0.515631	+	0.432666i	−0.863106	−	0.505024i	$-0.831484\pi$
$43$	−3.38122	+	2.83718i	−0.515631	+	0.432666i	0.347474	+	0.937689i	$0.387039\pi$
$44$	0.594729	−	3.37288i	0.0896588	−	0.508480i
$45$		0			0
$46$	2.41672	+	4.18588i	0.356325	+	0.617174i
$47$	6.98859	−	2.54364i	1.01939	−	0.371028i	0.222358	−	0.974965i	$-0.428625\pi$
$47$	6.98859	−	2.54364i	1.01939	−	0.371028i	0.797032	+	0.603937i	$0.206402\pi$
$48$	2.39976	−	0.873440i	0.346375	−	0.126070i
$49$	−6.91895	−	11.9840i	−0.988421	−	1.71200i
$50$		0			0
$51$	1.88505	−	10.6906i	0.263960	−	1.49699i
$52$	0.625092	−	0.524515i	0.0866847	−	0.0727371i
$53$	−8.64770	−	7.25628i	−1.18785	−	0.996727i	−0.999894	−	0.0145501i	$-0.995368\pi$
$53$	−8.64770	−	7.25628i	−1.18785	−	0.996727i	−0.187959	−	0.982177i	$-0.560187\pi$
$54$	−0.231363	−	1.31212i	−0.0314845	−	0.178558i
$55$		0			0
$56$	−4.56485			−0.610004
$57$	−3.51484	−	10.5621i	−0.465552	−	1.39899i
$58$	2.39771			0.314835
$59$	5.29935	+	1.92881i	0.689917	+	0.251109i	0.663100	−	0.748531i	$-0.269241\pi$
$59$	5.29935	+	1.92881i	0.689917	+	0.251109i	0.0268173	+	0.999640i	$0.491463\pi$
$60$		0			0
$61$	7.36453	+	6.17958i	0.942932	+	0.791214i	0.978093	−	0.208168i	$-0.0667501\pi$
$61$	7.36453	+	6.17958i	0.942932	+	0.791214i	−0.0351615	+	0.999382i	$0.511195\pi$
$62$	−5.28780	+	4.43699i	−0.671551	+	0.563499i
$63$	−2.79160	+	15.8319i	−0.351708	+	1.99464i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	8.21895	−	2.99145i	1.01168	−	0.368222i
$67$	−5.29642	+	1.92774i	−0.647061	+	0.235511i	−0.644640	−	0.764486i	$-0.722993\pi$
$67$	−5.29642	+	1.92774i	−0.647061	+	0.235511i	−0.00242072	+	0.999997i	$0.500771\pi$
$68$	2.12540	+	3.68130i	0.257743	+	0.446424i
$69$	−6.17173	+	10.6898i	−0.742989	+	1.28689i
$70$		0			0
$71$	−11.7667	+	9.87343i	−1.39645	+	1.17176i	−0.433800	+	0.901009i	$0.642828\pi$
$71$	−11.7667	+	9.87343i	−1.39645	+	1.17176i	−0.962649	+	0.270751i	$0.912728\pi$
$72$	2.69780	+	2.26372i	0.317939	+	0.266782i
$73$	1.61551	+	9.16200i	0.189081	+	1.07233i	0.920599	+	0.390509i	$0.127701\pi$
$73$	1.61551	+	9.16200i	0.189081	+	1.07233i	−0.731518	+	0.681822i	$0.761188\pi$
$74$	−3.59769	−	1.30945i	−0.418223	−	0.152221i
$75$		0			0
$76$	3.71284	+	2.28359i	0.425892	+	0.261946i
$77$	−15.6342			−1.78168
$78$	1.95820	+	0.712727i	0.221723	+	0.0807004i
$79$	−0.376083	−	2.13287i	−0.0423127	−	0.239967i	0.956315	−	0.292338i	$-0.0944333\pi$
$79$	−0.376083	−	2.13287i	−0.0423127	−	0.239967i	−0.998628	+	0.0523710i	$0.983322\pi$
$80$		0			0
$81$	−5.48689	+	4.60405i	−0.609654	+	0.511561i
$82$	2.12597	−	12.0570i	0.234774	−	1.33147i
$83$	−0.240255	+	0.416134i	−0.0263714	+	0.0456767i	−0.878910	−	0.476988i	$-0.841729\pi$
$83$	−0.240255	+	0.416134i	−0.0263714	+	0.0456767i	0.852538	+	0.522664i	$0.175062\pi$
$84$	−5.82879	−	10.0958i	−0.635973	−	1.10154i
$85$		0			0
$86$	4.14768	−	1.50963i	0.447256	−	0.162788i
$87$	3.06159	+	5.30284i	0.328237	+	0.568524i
$88$	−1.71245	+	2.96606i	−0.182548	+	0.316183i
$89$	−0.474094	+	2.68872i	−0.0502539	+	0.285004i	−0.999570	−	0.0293186i	$-0.990666\pi$
$89$	−0.474094	+	2.68872i	−0.0502539	+	0.285004i	0.949316	+	0.314323i	$0.101777\pi$
$90$		0			0
$91$	−2.85346	−	2.39433i	−0.299123	−	0.250994i
$92$	−0.839317	−	4.76000i	−0.0875048	−	0.496265i
$93$	−16.5649	−	6.02912i	−1.71770	−	0.625191i
$94$	−7.43710			−0.767078
$95$		0			0
$96$	−2.55377			−0.260643
$97$	1.87426	+	0.682176i	0.190303	+	0.0692645i	0.435414	−	0.900231i	$-0.356602\pi$
$97$	1.87426	+	0.682176i	0.190303	+	0.0692645i	−0.245111	+	0.969495i	$0.578824\pi$
$98$	2.40292	+	13.6277i	0.242732	+	1.37660i
$99$	9.23972	+	7.75304i	0.928626	+	0.779210i
$100$		0			0
$101$	−0.698250	+	3.95997i	−0.0694784	+	0.394032i	0.930160	+	0.367154i	$0.119668\pi$
$101$	−0.698250	+	3.95997i	−0.0694784	+	0.394032i	−0.999639	+	0.0268781i	$0.991443\pi$
$102$	−5.42778	+	9.40119i	−0.537430	+	0.930856i
$103$	−2.51914	−	4.36328i	−0.248218	−	0.429926i	0.714813	−	0.699315i	$-0.246512\pi$
$103$	−2.51914	−	4.36328i	−0.248218	−	0.429926i	−0.963031	+	0.269389i	$0.913178\pi$
$104$	−0.766789	+	0.279088i	−0.0751899	+	0.0273669i
$105$		0			0
$106$	5.64439	+	9.77636i	0.548231	+	0.949564i
$107$	−2.31512	+	4.00990i	−0.223811	+	0.387651i	−0.955962	−	0.293491i	$-0.905183\pi$
$107$	−2.31512	+	4.00990i	−0.223811	+	0.387651i	0.732151	+	0.681142i	$0.238516\pi$
$108$	−0.231363	+	1.31212i	−0.0222629	+	0.126259i
$109$	−13.7948	+	11.5752i	−1.32130	+	1.10870i	−0.335275	+	0.942120i	$0.608829\pi$
$109$	−13.7948	+	11.5752i	−1.32130	+	1.10870i	−0.986027	+	0.166584i	$0.946726\pi$
$110$		0			0
$111$	−1.69781	−	9.62878i	−0.161149	−	0.913923i
$112$	4.28956	+	1.56127i	0.405325	+	0.147526i
$113$	3.77177			0.354818			0.177409	−	0.984137i	$-0.443228\pi$
$113$	3.77177			0.354818			0.177409	+	0.984137i	$0.443228\pi$
$114$	−0.309593	+	11.1273i	−0.0289960	+	1.04217i
$115$		0			0
$116$	−2.25311	−	0.820065i	−0.209196	−	0.0761411i
$117$	0.499018	+	2.83007i	0.0461342	+	0.261640i
$118$	−4.32007	−	3.62497i	−0.397695	−	0.333706i
$119$	14.8645	−	12.4728i	1.36263	−	1.14338i
$120$		0			0
$121$	−0.365002	+	0.632201i	−0.0331820	+	0.0574728i
$122$	−4.80686	−	8.32572i	−0.435192	−	0.753775i
$123$	29.3801	−	10.6935i	2.64912	−	0.964199i
$124$	6.48645	−	2.36087i	0.582500	−	0.212013i
$125$		0			0
$126$	8.03808	−	13.9224i	0.716089	−	1.24030i
$127$	−3.07313	+	17.4286i	−0.272696	+	1.54653i	0.473491	+	0.880798i	$0.342994\pi$
$127$	−3.07313	+	17.4286i	−0.272696	+	1.54653i	−0.746187	+	0.665736i	$0.768118\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	8.63485	+	7.24550i	0.760256	+	0.637930i
$130$		0			0
$131$	4.37918	+	1.59389i	0.382611	+	0.139259i	0.526163	−	0.850384i	$-0.323630\pi$
$131$	4.37918	+	1.59389i	0.382611	+	0.139259i	−0.143552	+	0.989643i	$0.545852\pi$
$132$	−8.74642			−0.761278
$133$	7.32282	−	18.5013i	0.634969	−	1.60426i
$134$	5.63633			0.486905
$135$		0			0
$136$	−0.738144	−	4.18622i	−0.0632953	−	0.358966i
$137$	5.37802	+	4.51269i	0.459475	+	0.385546i	0.842938	−	0.538011i	$-0.180824\pi$
$137$	5.37802	+	4.51269i	0.459475	+	0.385546i	−0.383463	+	0.923556i	$0.625269\pi$
$138$	9.45564	−	7.93422i	0.804918	−	0.675406i
$139$	3.36353	−	19.0755i	0.285291	−	1.61797i	−0.418953	−	0.908008i	$-0.637603\pi$
$139$	3.36353	−	19.0755i	0.285291	−	1.61797i	0.704244	−	0.709958i	$-0.251286\pi$
$140$		0			0
$141$	−9.49631	−	16.4481i	−0.799733	−	1.38518i
$142$	14.4340	−	5.25354i	1.21127	−	0.440867i
$143$	−2.62618	+	0.955853i	−0.219613	+	0.0799324i
$144$	−1.76086	−	3.04990i	−0.146739	−	0.254159i
$145$		0			0
$146$	1.61551	−	9.16200i	0.133700	−	0.758252i
$147$	−27.0711	+	22.7153i	−2.23278	+	1.87353i
$148$	2.93287	+	2.46097i	0.241080	+	0.202290i
$149$	−3.31009	−	18.7725i	−0.271173	−	1.53790i	−0.750861	−	0.660461i	$-0.770361\pi$
$149$	−3.31009	−	18.7725i	−0.271173	−	1.53790i	0.479687	−	0.877440i	$-0.340750\pi$
$150$		0			0
$151$	18.2844			1.48796			0.743980	−	0.668202i	$-0.232936\pi$
$151$	18.2844			1.48796			0.743980	+	0.668202i	$0.232936\pi$
$152$	−2.70789	−	3.41574i	−0.219639	−	0.277053i
$153$	−14.9702			−1.21027
$154$	14.6914	+	5.34721i	1.18386	+	0.430891i
$155$		0			0
$156$	−1.59634	−	1.33949i	−0.127810	−	0.107245i
$157$	9.24679	−	7.75898i	0.737974	−	0.619234i	−0.194319	−	0.980938i	$-0.562250\pi$
$157$	9.24679	−	7.75898i	0.737974	−	0.619234i	0.932293	+	0.361705i	$0.117805\pi$
$158$	−0.376083	+	2.13287i	−0.0299196	+	0.169682i
$159$	−14.4144	+	24.9666i	−1.14314	+	1.97998i
$160$		0			0
$161$	−20.7333	+	7.54630i	−1.63401	+	0.594732i
$162$	6.73067	−	2.44976i	0.528811	−	0.192471i
$163$	−7.46264	−	12.9257i	−0.584519	−	1.01242i	−0.994935	−	0.100519i	$-0.967950\pi$
$163$	−7.46264	−	12.9257i	−0.584519	−	1.01242i	0.410416	−	0.911898i	$-0.365384\pi$
$164$	−6.12148	+	10.6027i	−0.478007	+	0.827933i
$165$		0			0
$166$	0.368092	−	0.308866i	0.0285695	−	0.0239727i
$167$	−9.00653	−	7.55738i	−0.696946	−	0.584807i	0.223957	−	0.974599i	$-0.428103\pi$
$167$	−9.00653	−	7.55738i	−0.696946	−	0.584807i	−0.920903	+	0.389792i	$0.872547\pi$
$168$	2.02432	+	11.4805i	0.156179	+	0.885737i
$169$	11.5903	+	4.21853i	0.891562	+	0.324502i
$170$		0			0
$171$	−13.5026	+	7.30272i	−1.03257	+	0.558453i
$172$	−4.41387			−0.336554
$173$	−7.22448	−	2.62950i	−0.549267	−	0.199917i	0.0524536	−	0.998623i	$-0.483296\pi$
$173$	−7.22448	−	2.62950i	−0.549267	−	0.199917i	−0.601721	+	0.798706i	$0.705518\pi$
$174$	−1.06328	−	6.03016i	−0.0806071	−	0.457146i
$175$		0			0
$176$	2.62363	−	2.20149i	0.197764	−	0.165943i
$177$	2.50085	−	14.1831i	0.187976	−	1.06606i
$178$	1.36510	−	2.36442i	0.102319	−	0.177221i
$179$	10.2549	+	17.7620i	0.766488	+	1.32760i	0.939456	+	0.342669i	$0.111331\pi$
$179$	10.2549	+	17.7620i	0.766488	+	1.32760i	−0.172968	+	0.984928i	$0.555336\pi$
$180$		0			0
$181$	24.9617	−	9.08531i	1.85539	−	0.675306i	0.873211	−	0.487342i	$-0.162033\pi$
$181$	24.9617	−	9.08531i	1.85539	−	0.675306i	0.982176	−	0.187964i	$-0.0601888\pi$
$182$	1.86246	+	3.22588i	0.138055	+	0.239118i
$183$	12.2756	−	21.2619i	0.907438	−	1.57173i
$184$	−0.839317	+	4.76000i	−0.0618753	+	0.350912i
$185$		0			0
$186$	13.5038	+	11.3310i	0.990148	+	0.830832i
$187$	−2.52808	−	14.3374i	−0.184871	−	1.04846i
$188$	6.98859	+	2.54364i	0.509695	+	0.185514i
$189$	6.08206			0.442405
$190$		0			0
$191$	17.6682			1.27842			0.639212	−	0.769031i	$-0.279261\pi$
$191$	17.6682			1.27842			0.639212	+	0.769031i	$0.279261\pi$
$192$	2.39976	+	0.873440i	0.173187	+	0.0630351i
$193$	−2.55837	−	14.5092i	−0.184156	−	1.04440i	−0.927036	−	0.374974i	$-0.877652\pi$
$193$	−2.55837	−	14.5092i	−0.184156	−	1.04440i	0.742880	−	0.669425i	$-0.233459\pi$
$194$	−1.52791	−	1.28207i	−0.109698	−	0.0920474i
$195$		0			0
$196$	2.40292	−	13.6277i	0.171637	−	0.973405i
$197$	2.88336	−	4.99412i	0.205431	−	0.355816i	−0.744839	−	0.667244i	$-0.767474\pi$
$197$	2.88336	−	4.99412i	0.205431	−	0.355816i	0.950270	+	0.311428i	$0.100807\pi$
$198$	−6.03080	−	10.4456i	−0.428590	−	0.742340i
$199$	4.99379	−	1.81759i	0.354000	−	0.128846i	−0.158898	−	0.987295i	$-0.550794\pi$
$199$	4.99379	−	1.81759i	0.354000	−	0.128846i	0.512898	+	0.858449i	$0.328572\pi$
$200$		0			0
$201$	7.19694	+	12.4655i	0.507633	+	0.879246i
$202$	2.01053	−	3.48234i	0.141460	−	0.245017i
$203$	−1.90061	+	10.7789i	−0.133397	+	0.756531i
$204$	8.31584	−	6.97782i	0.582225	−	0.488545i
$205$		0			0
$206$	0.874888	+	4.96174i	0.0609563	+	0.345700i
$207$	15.9955	+	5.82188i	1.11176	+	0.404648i
$208$	0.816000			0.0565794
$209$	−9.27429	−	11.6986i	−0.641516	−	0.809210i
$210$		0			0
$211$	−17.6700	−	6.43135i	−1.21645	−	0.442752i	−0.347515	−	0.937675i	$-0.612974\pi$
$211$	−17.6700	−	6.43135i	−1.21645	−	0.442752i	−0.868937	+	0.494922i	$0.835196\pi$
$212$	−1.96027	−	11.1173i	−0.134632	−	0.763537i
$213$	30.0494	+	25.2144i	2.05895	+	1.72766i
$214$	3.54696	−	2.97625i	0.242465	−	0.203453i
$215$		0			0
$216$	0.666183	−	1.15386i	0.0453280	−	0.0785105i
$217$	−15.7550	−	27.2884i	−1.06952	−	1.85246i
$218$	16.9218	−	6.15904i	1.14609	−	0.417143i
$219$	22.3257	−	8.12590i	1.50863	−	0.549098i
$220$		0			0
$221$	1.73433	−	3.00394i	0.116663	−	0.202067i
$222$	−1.69781	+	9.62878i	−0.113950	+	0.646241i
$223$	−8.23688	+	6.91157i	−0.551583	+	0.462833i	−0.875476	−	0.483261i	$-0.839452\pi$
$223$	−8.23688	+	6.91157i	−0.551583	+	0.462833i	0.323894	+	0.946093i	$0.395008\pi$
$224$	−3.49688	−	2.93423i	−0.233645	−	0.196052i
$225$		0			0
$226$	−3.54430	−	1.29002i	−0.235764	−	0.0858109i
$227$	−20.8415			−1.38330			−0.691648	−	0.722235i	$-0.743115\pi$
$227$	−20.8415			−1.38330			−0.691648	+	0.722235i	$0.743115\pi$
$228$	4.09669	−	10.3504i	0.271310	−	0.685469i
$229$	19.1888			1.26803			0.634015	−	0.773321i	$-0.281406\pi$
$229$	19.1888			1.26803			0.634015	+	0.773321i	$0.281406\pi$
$230$		0			0
$231$	6.93310	+	39.3196i	0.456164	+	2.58704i
$232$	1.83675	+	1.54122i	0.120589	+	0.101186i
$233$	16.1774	−	13.5744i	1.05981	−	0.889290i	0.0657234	−	0.997838i	$-0.479064\pi$
$233$	16.1774	−	13.5744i	1.05981	−	0.889290i	0.994091	+	0.108548i	$0.0346200\pi$
$234$	0.499018	−	2.83007i	0.0326218	−	0.185007i
$235$		0			0
$236$	2.81973	+	4.88391i	0.183549	+	0.317915i
$237$	−5.19734	+	1.89168i	−0.337603	+	0.122878i
$238$	−18.2341	+	6.63666i	−1.18194	+	0.430191i
$239$	3.07893	+	5.33286i	0.199159	+	0.344954i	0.948256	−	0.317507i	$-0.102846\pi$
$239$	3.07893	+	5.33286i	0.199159	+	0.344954i	−0.749097	+	0.662461i	$0.769512\pi$
$240$		0			0
$241$	3.98528	−	22.6017i	0.256715	−	1.45590i	−0.534918	−	0.844904i	$-0.679657\pi$
$241$	3.98528	−	22.6017i	0.256715	−	1.45590i	0.791633	−	0.610997i	$-0.209231\pi$
$242$	0.559215	−	0.469237i	0.0359477	−	0.0301637i
$243$	17.0742	+	14.3269i	1.09531	+	0.919074i
$244$	1.66940	+	9.46766i	0.106873	+	0.606105i
$245$		0			0
$246$	−31.2657			−1.99343
$247$	0.0989236	−	3.55549i	0.00629436	−	0.226230i
$248$	−6.90273			−0.438324
$249$	1.15311	+	0.419697i	0.0730753	+	0.0265972i
$250$		0			0
$251$	−12.4104	−	10.4136i	−0.783341	−	0.657301i	0.160747	−	0.986996i	$-0.448610\pi$
$251$	−12.4104	−	10.4136i	−0.783341	−	0.657301i	−0.944088	+	0.329695i	$0.893054\pi$
$252$	−12.3151	+	10.3336i	−0.775776	+	0.650953i
$253$	−2.87458	+	16.3026i	−0.180724	+	1.02493i
$254$	8.84871	−	15.3264i	0.555218	−	0.961665i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	3.15450	−	1.14814i	0.196772	−	0.0716192i	−0.241754	−	0.970338i	$-0.577723\pi$
$257$	3.15450	−	1.14814i	0.196772	−	0.0716192i	0.438526	+	0.898718i	$0.355501\pi$
$258$	−5.63600	−	9.76183i	−0.350882	−	0.607745i
$259$	8.73847	−	15.1355i	0.542982	−	0.940472i
$260$		0			0
$261$	6.46853	−	5.42775i	0.400392	−	0.335969i
$262$	−3.56994	−	2.99554i	−0.220552	−	0.185065i
$263$	3.62047	+	20.5327i	0.223248	+	1.26610i	0.866007	+	0.500032i	$0.166678\pi$
$263$	3.62047	+	20.5327i	0.223248	+	1.26610i	−0.642760	+	0.766068i	$0.722211\pi$
$264$	8.21895	+	2.99145i	0.505841	+	0.184111i
$265$		0			0
$266$	−13.2090	+	14.8809i	−0.809896	+	0.912409i
$267$	6.97230			0.426698
$268$	−5.29642	−	1.92774i	−0.323530	−	0.117755i
$269$	−1.97588	−	11.2058i	−0.120472	−	0.683228i	−0.983895	−	0.178748i	$-0.942795\pi$
$269$	−1.97588	−	11.2058i	−0.120472	−	0.683228i	0.863423	−	0.504480i	$-0.168316\pi$
$270$		0			0
$271$	4.51353	−	3.78730i	0.274177	−	0.230062i	−0.495322	−	0.868709i	$-0.664950\pi$
$271$	4.51353	−	3.78730i	0.274177	−	0.230062i	0.769500	+	0.638647i	$0.220506\pi$
$272$	−0.738144	+	4.18622i	−0.0447566	+	0.253827i
$273$	−4.75629	+	8.23814i	−0.287864	+	0.498595i
$274$	−3.51025	−	6.07994i	−0.212062	−	0.367302i
$275$		0			0
$276$	−11.5991	+	4.22171i	−0.698181	+	0.254117i
$277$	−6.35228	−	11.0025i	−0.381672	−	0.661075i	0.609630	−	0.792686i	$-0.291318\pi$
$277$	−6.35228	−	11.0025i	−0.381672	−	0.661075i	−0.991301	+	0.131612i	$0.957985\pi$
$278$	−9.68490	+	16.7747i	−0.580862	+	1.00608i
$279$	−4.22131	+	23.9402i	−0.252723	+	1.43326i
$280$		0			0
$281$	10.0997	+	8.47462i	0.602495	+	0.505554i	0.892247	−	0.451548i	$-0.149128\pi$
$281$	10.0997	+	8.47462i	0.602495	+	0.505554i	−0.289751	+	0.957102i	$0.593573\pi$
$282$	3.29803	+	18.7041i	0.196395	+	1.11381i
$283$	15.7302	+	5.72532i	0.935062	+	0.340335i	0.764214	−	0.644963i	$-0.223127\pi$
$283$	15.7302	+	5.72532i	0.935062	+	0.340335i	0.170848	+	0.985297i	$0.445349\pi$
$284$	−15.3603			−0.911468
$285$		0			0
$286$	2.79473			0.165256
$287$	52.5169	+	19.1146i	3.09997	+	1.12830i
$288$	0.611541	+	3.46822i	0.0360354	+	0.204367i
$289$	0.819145	+	0.687345i	0.0481850	+	0.0404320i
$290$		0			0
$291$	0.884497	−	5.01623i	0.0518502	−	0.294057i
$292$	−4.65167	+	8.05693i	−0.272218	+	0.471496i
$293$	3.42172	+	5.92659i	0.199899	+	0.346235i	0.948495	−	0.316791i	$-0.102605\pi$
$293$	3.42172	+	5.92659i	0.199899	+	0.346235i	−0.748597	+	0.663026i	$0.769272\pi$
$294$	33.2076	−	12.0866i	1.93670	−	0.704903i
$295$		0			0
$296$	−1.91429	−	3.31565i	−0.111266	−	0.192718i
$297$	2.28162	−	3.95188i	0.132393	−	0.229311i
$298$	−3.31009	+	18.7725i	−0.191748	+	1.08746i
$299$	−3.02134	+	2.53521i	−0.174729	+	0.146615i
$300$		0			0
$301$	3.49878	+	19.8426i	0.201666	+	1.14371i
$302$	−17.1817	−	6.25362i	−0.988694	−	0.359855i
$303$	10.2688			0.589930
$304$	1.37634	+	4.13590i	0.0789383	+	0.237210i
$305$		0			0
$306$	14.0673	+	5.12010i	0.804177	+	0.292696i
$307$	4.29767	+	24.3733i	0.245281	+	1.39106i	0.819839	+	0.572594i	$0.194063\pi$
$307$	4.29767	+	24.3733i	0.245281	+	1.39106i	−0.574558	+	0.818464i	$0.694826\pi$
$308$	−11.9765	−	10.0495i	−0.682424	−	0.572622i
$309$	−9.85638	+	8.27048i	−0.560710	+	0.470491i
$310$		0			0
$311$	5.82580	−	10.0906i	0.330351	−	0.572184i	−0.652230	−	0.758021i	$-0.726166\pi$
$311$	5.82580	−	10.0906i	0.330351	−	0.572184i	0.982581	+	0.185837i	$0.0594997\pi$
$312$	1.04194	+	1.80469i	0.0589881	+	0.102170i
$313$	−14.5483	+	5.29514i	−0.822317	+	0.299299i	−0.718702	−	0.695319i	$-0.755263\pi$
$313$	−14.5483	+	5.29514i	−0.822317	+	0.299299i	−0.103615	+	0.994617i	$0.533041\pi$
$314$	−11.3429	+	4.12847i	−0.640115	+	0.232983i
$315$		0			0
$316$	1.08289	−	1.87562i	0.0609173	−	0.105512i
$317$	−1.31336	+	7.44843i	−0.0737656	+	0.418346i	0.925454	+	0.378859i	$0.123683\pi$
$317$	−1.31336	+	7.44843i	−0.0737656	+	0.418346i	−0.999220	+	0.0394868i	$0.987428\pi$
$318$	22.0842	−	18.5309i	1.23842	−	1.03916i
$319$	6.29071	+	5.27853i	0.352212	+	0.295541i
$320$		0			0
$321$	11.1114	+	4.04423i	0.620179	+	0.225727i
$322$	22.0639			1.22957
$323$	18.1508	+	3.72375i	1.00994	+	0.207195i
$324$	−7.16262			−0.397924
$325$		0			0
$326$	2.59175	+	14.6985i	0.143544	+	0.814077i
$327$	35.2287	+	29.5604i	1.94815	+	1.63469i
$328$	9.37865	−	7.86962i	0.517849	−	0.434527i
$329$	5.89523	−	33.4335i	0.325014	−	1.84325i
$330$		0			0
$331$	−4.69302	−	8.12854i	−0.257952	−	0.446785i	0.707741	−	0.706472i	$-0.249714\pi$
$331$	−4.69302	−	8.12854i	−0.257952	−	0.446785i	−0.965693	+	0.259686i	$0.916381\pi$
$332$	−0.451532	+	0.164344i	−0.0247811	+	0.00901956i
$333$	−12.6701	+	4.61154i	−0.694317	+	0.252711i
$334$	5.87860	+	10.1820i	0.321662	+	0.557136i
$335$		0			0
$336$	2.02432	−	11.4805i	0.110436	−	0.626311i
$337$	−6.52647	+	5.47636i	−0.355520	+	0.298316i	−0.803002	−	0.595976i	$-0.796765\pi$
$337$	−6.52647	+	5.47636i	−0.355520	+	0.298316i	0.447482	+	0.894293i	$0.352321\pi$
$338$	−9.44850	−	7.92823i	−0.513931	−	0.431239i
$339$	−1.67262	−	9.48589i	−0.0908441	−	0.515203i
$340$		0			0
$341$	−23.6412			−1.28024
$342$	15.1859	−	2.24416i	0.821161	−	0.121350i
$343$	−31.2140			−1.68540
$344$	4.14768	+	1.50963i	0.223628	+	0.0813939i
$345$		0			0
$346$	5.88945	+	4.94184i	0.316619	+	0.265675i
$347$	−5.21162	+	4.37307i	−0.279774	+	0.234759i	−0.771867	−	0.635784i	$-0.780677\pi$
$347$	−5.21162	+	4.37307i	−0.279774	+	0.234759i	0.492092	+	0.870543i	$0.336232\pi$
$348$	−1.06328	+	6.03016i	−0.0569978	+	0.323251i
$349$	1.90811	−	3.30495i	0.102139	−	0.176910i	−0.810427	−	0.585840i	$-0.800765\pi$
$349$	1.90811	−	3.30495i	0.102139	−	0.176910i	0.912566	+	0.408930i	$0.134098\pi$
$350$		0			0
$351$	1.02164	−	0.371848i	0.0545313	−	0.0198478i
$352$	−3.21836	+	1.17139i	−0.171539	+	0.0624352i
$353$	1.88034	+	3.25685i	0.100081	+	0.173345i	0.911718	−	0.410817i	$-0.134757\pi$
$353$	1.88034	+	3.25685i	0.100081	+	0.173345i	−0.811637	+	0.584162i	$0.801423\pi$
$354$	−7.20092	+	12.4724i	−0.382725	+	0.662899i
$355$		0			0
$356$	−2.09146	+	1.75494i	−0.110847	+	0.0930116i
$357$	−37.9606	−	31.8527i	−2.00909	−	1.68582i
$358$	−3.56149	−	20.1982i	−0.188231	−	1.06751i
$359$	13.6016	+	4.95058i	0.717865	+	0.261281i	0.675019	−	0.737800i	$-0.264135\pi$
$359$	13.6016	+	4.95058i	0.717865	+	0.261281i	0.0428458	+	0.999082i	$0.486358\pi$
$360$		0			0
$361$	18.1879	−	5.49559i	0.957256	−	0.289242i
$362$	−26.5637			−1.39616
$363$	1.75183	+	0.637614i	0.0919472	+	0.0334660i
$364$	−0.646826	−	3.66833i	−0.0339029	−	0.192273i
$365$		0			0
$366$	−18.8073	+	15.7812i	−0.983073	+	0.824896i
$367$	1.52775	−	8.66431i	0.0797479	−	0.452273i	−0.918619	−	0.395145i	$-0.870694\pi$
$367$	1.52775	−	8.66431i	0.0797479	−	0.452273i	0.998367	−	0.0571284i	$-0.0181944\pi$
$368$	2.41672	−	4.18588i	0.125980	−	0.218204i
$369$	−21.5582	−	37.3399i	−1.12227	−	1.94383i
$370$		0			0
$371$	−48.4239	+	17.6248i	−2.51404	+	0.915036i
$372$	−8.81399	−	15.2663i	−0.456984	−	0.791519i
$373$	−3.35359	+	5.80859i	−0.173642	+	0.300757i	−0.939691	−	0.342026i	$-0.888887\pi$
$373$	−3.35359	+	5.80859i	−0.173642	+	0.300757i	0.766048	+	0.642783i	$0.222220\pi$
$374$	−2.52808	+	14.3374i	−0.130724	+	0.741371i
$375$		0			0
$376$	−5.69715	−	4.78047i	−0.293808	−	0.246534i
$377$	0.339748	+	1.92681i	0.0174979	+	0.0992356i
$378$	−5.71527	−	2.08019i	−0.293962	−	0.106993i
$379$	−16.8707			−0.866591			−0.433295	−	0.901252i	$-0.642649\pi$
$379$	−16.8707			−0.866591			−0.433295	+	0.901252i	$0.642649\pi$
$380$		0			0
$381$	45.1951			2.31542
$382$	−16.6026	−	6.04287i	−0.849465	−	0.309180i
$383$	−1.21387	−	6.88419i	−0.0620258	−	0.351766i	−0.999987	−	0.00502655i	$-0.998400\pi$
$383$	−1.21387	−	6.88419i	−0.0620258	−	0.351766i	0.937962	−	0.346739i	$-0.112711\pi$
$384$	−1.95630	−	1.64153i	−0.0998320	−	0.0837690i
$385$		0			0
$386$	−2.55837	+	14.5092i	−0.130218	+	0.738501i
$387$	7.77222	−	13.4619i	0.395084	−	0.684306i
$388$	0.997275	+	1.72733i	0.0506290	+	0.0876920i
$389$	−11.1144	+	4.04531i	−0.563523	+	0.205106i	−0.608045	−	0.793903i	$-0.708046\pi$
$389$	−11.1144	+	4.04531i	−0.563523	+	0.205106i	0.0445218	+	0.999008i	$0.485824\pi$
$390$		0			0
$391$	−10.2730	−	17.7933i	−0.519527	−	0.899847i
$392$	−6.91895	+	11.9840i	−0.349460	+	0.605282i
$393$	2.06661	−	11.7203i	0.104247	−	0.591212i
$394$	−4.41756	+	3.70677i	−0.222553	+	0.186744i
$395$		0			0
$396$	2.09447	+	11.8783i	0.105251	+	0.596909i
$397$	27.9894	+	10.1873i	1.40475	+	0.511286i	0.929583	−	0.368612i	$-0.120167\pi$
$397$	27.9894	+	10.1873i	1.40475	+	0.511286i	0.475163	+	0.879898i	$0.342389\pi$
$398$	−5.31428			−0.266381
$399$	−49.7774	−	10.2122i	−2.49199	−	0.511247i
$400$		0			0
$401$	−17.1199	−	6.23113i	−0.854927	−	0.311168i	−0.122879	−	0.992422i	$-0.539213\pi$
$401$	−17.1199	−	6.23113i	−0.854927	−	0.311168i	−0.732047	+	0.681254i	$0.761435\pi$
$402$	−2.49947	−	14.1752i	−0.124662	−	0.706995i
$403$	−4.31485	−	3.62059i	−0.214938	−	0.180354i
$404$	−3.08031	+	2.58469i	−0.153251	+	0.128593i
$405$		0			0
$406$	5.47259	−	9.47881i	0.271600	−	0.470426i
$407$	−6.55628	−	11.3558i	−0.324983	−	0.562887i
$408$	−10.2009	+	3.71282i	−0.505019	+	0.183812i
$409$	−17.3500	+	6.31489i	−0.857903	+	0.312251i	−0.733258	−	0.679950i	$-0.762001\pi$
$409$	−17.3500	+	6.31489i	−0.857903	+	0.312251i	−0.124645	+	0.992201i	$0.539779\pi$
$410$		0			0
$411$	8.96437	−	15.5267i	0.442180	−	0.765878i
$412$	0.874888	−	4.96174i	0.0431026	−	0.244447i
$413$	19.7205	−	16.5475i	0.970382	−	0.814247i
$414$	−13.0396	−	10.9415i	−0.640863	−	0.537748i
$415$		0			0
$416$	−0.766789	−	0.279088i	−0.0375949	−	0.0136834i
$417$	−49.4660			−2.42236
$418$	4.71382	+	14.1651i	0.230561	+	0.692837i
$419$	−38.4546			−1.87863			−0.939314	−	0.343057i	$-0.888537\pi$
$419$	−38.4546			−1.87863			−0.939314	+	0.343057i	$0.888537\pi$
$420$		0			0
$421$	1.36999	+	7.76960i	0.0667692	+	0.378667i	0.999821	+	0.0189248i	$0.00602430\pi$
$421$	1.36999	+	7.76960i	0.0667692	+	0.378667i	−0.933052	+	0.359742i	$0.882865\pi$
$422$	14.4047	+	12.0870i	0.701210	+	0.588385i
$423$	−20.0638	+	16.8355i	−0.975535	+	0.818571i
$424$	−1.96027	+	11.1173i	−0.0951993	+	0.539902i
$425$		0			0
$426$	−19.6134	−	33.9713i	−0.950270	−	1.64592i
$427$	41.2386	−	15.0096i	1.99568	−	0.726366i
$428$	−4.35099	+	1.58363i	−0.210313	+	0.0765477i
$429$	3.56854	+	6.18089i	0.172291	+	0.298416i
$430$		0			0
$431$	0.372953	−	2.11512i	0.0179645	−	0.101882i	−0.974507	−	0.224357i	$-0.927972\pi$
$431$	0.372953	−	2.11512i	0.0179645	−	0.101882i	0.992472	+	0.122475i	$0.0390831\pi$
$432$	−1.02065	+	0.856429i	−0.0491061	+	0.0412049i
$433$	6.72774	+	5.64524i	0.323314	+	0.271293i	0.789969	−	0.613147i	$-0.210096\pi$
$433$	6.72774	+	5.64524i	0.323314	+	0.271293i	−0.466655	+	0.884440i	$0.654541\pi$
$434$	5.47165	+	31.0313i	0.262648	+	1.48955i
$435$		0			0
$436$	−18.0078			−0.862419
$437$	−17.9458	−	11.0376i	−0.858463	−	0.528000i
$438$	−23.7586			−1.13523
$439$	−2.27368	−	0.827552i	−0.108517	−	0.0394969i	0.287191	−	0.957873i	$-0.407279\pi$
$439$	−2.27368	−	0.827552i	−0.108517	−	0.0394969i	−0.395708	+	0.918376i	$0.629501\pi$
$440$		0			0
$441$	37.3318	+	31.3251i	1.77771	+	1.49167i
$442$	−2.65714	+	2.22961i	−0.126387	+	0.106052i
$443$	5.72598	−	32.4737i	0.272050	−	1.54287i	−0.476130	−	0.879375i	$-0.657961\pi$
$443$	5.72598	−	32.4737i	0.272050	−	1.54287i	0.748180	−	0.663496i	$-0.230928\pi$
$444$	4.88866	−	8.46740i	0.232005	−	0.401845i
$445$		0			0
$446$	10.1040	−	3.67757i	0.478440	−	0.174138i
$447$	−45.7443	+	16.6496i	−2.16363	+	0.787497i
$448$	2.28243	+	3.95328i	0.107835	+	0.186775i
$449$	9.54580	−	16.5338i	0.450494	−	0.780279i	−0.547923	−	0.836529i	$-0.684581\pi$
$449$	9.54580	−	16.5338i	0.450494	−	0.780279i	0.998417	+	0.0562503i	$0.0179145\pi$
$450$		0			0
$451$	32.1210	−	26.9527i	1.51252	−	1.26916i
$452$	2.88934	+	2.42445i	0.135903	+	0.114036i
$453$	−8.10833	−	45.9846i	−0.380962	−	2.16054i
$454$	19.5846	+	7.12820i	0.919149	+	0.334543i
$455$		0			0
$456$	−7.38966	+	8.32501i	−0.346052	+	0.389854i
$457$	17.3344			0.810867			0.405434	−	0.914125i	$-0.367121\pi$
$457$	17.3344			0.810867			0.405434	+	0.914125i	$0.367121\pi$
$458$	−18.0315	−	6.56294i	−0.842559	−	0.306666i
$459$	0.983478	+	5.57758i	0.0459048	+	0.260339i
$460$		0			0
$461$	9.33023	−	7.82900i	0.434552	−	0.364633i	−0.399114	−	0.916901i	$-0.630682\pi$
$461$	9.33023	−	7.82900i	0.434552	−	0.364633i	0.833666	+	0.552269i	$0.186238\pi$
$462$	6.93310	−	39.3196i	0.322557	−	1.82931i
$463$	4.15240	−	7.19217i	0.192979	−	0.334249i	−0.753257	−	0.657726i	$-0.771519\pi$
$463$	4.15240	−	7.19217i	0.192979	−	0.334249i	0.946236	+	0.323477i	$0.104852\pi$
$464$	−1.19885	−	2.07648i	−0.0556554	−	0.0963980i
$465$		0			0
$466$	−19.8445	+	7.22280i	−0.919278	+	0.334590i
$467$	−4.05543	−	7.02421i	−0.187663	−	0.325042i	0.756808	−	0.653638i	$-0.226758\pi$
$467$	−4.05543	−	7.02421i	−0.187663	−	0.325042i	−0.944471	+	0.328596i	$0.893425\pi$
$468$	−1.43686	+	2.48872i	−0.0664191	+	0.115041i
$469$	−4.46780	+	25.3382i	−0.206304	+	1.17001i
$470$		0			0
$471$	−23.6142	−	19.8146i	−1.08808	−	0.913010i
$472$	−0.979281	−	5.55378i	−0.0450750	−	0.255633i
$473$	14.2054	+	5.17035i	0.653166	+	0.237733i
$474$	5.53089			0.254042
$475$		0			0
$476$	19.4043			0.889394
$477$	37.3584	+	13.5973i	1.71052	+	0.622579i
$478$	−1.06930	−	6.06431i	−0.0489087	−	0.277375i
$479$	24.1256	+	20.2438i	1.10233	+	0.924962i	0.997579	−	0.0695374i	$-0.0221523\pi$
$479$	24.1256	+	20.2438i	1.10233	+	0.924962i	0.104747	+	0.994499i	$0.466597\pi$
$480$		0			0
$481$	0.542499	−	3.07666i	0.0247358	−	0.140284i
$482$	−11.4752	+	19.8756i	−0.522680	+	0.905308i
$483$	28.1731	+	48.7972i	1.28192	+	2.22035i
$484$	−0.685978	+	0.249676i	−0.0311808	+	0.0113489i
$485$		0			0
$486$	−11.1444	−	19.3026i	−0.505520	−	0.875586i
$487$	7.83611	−	13.5725i	0.355088	−	0.615030i	−0.632045	−	0.774932i	$-0.717784\pi$
$487$	7.83611	−	13.5725i	0.355088	−	0.615030i	0.987133	+	0.159901i	$0.0511176\pi$
$488$	1.66940	−	9.46766i	0.0755704	−	0.428581i
$489$	−29.1983	+	24.5003i	−1.32039	+	1.10794i
$490$		0			0
$491$	−2.50123	−	14.1852i	−0.112879	−	0.640168i	−0.987779	−	0.155864i	$-0.950184\pi$
$491$	−2.50123	−	14.1852i	−0.112879	−	0.640168i	0.874900	−	0.484304i	$-0.160927\pi$
$492$	29.3801	+	10.6935i	1.32456	+	0.482100i
$493$	−10.1922			−0.459033
$494$	−1.30901	+	3.30723i	−0.0588949	+	0.148799i
$495$		0			0
$496$	6.48645	+	2.36087i	0.291250	+	0.106006i
$497$	12.1758	+	69.0524i	0.546159	+	3.09742i
$498$	−0.940022	−	0.788772i	−0.0421234	−	0.0353457i
$499$	−17.3717	+	14.5766i	−0.777666	+	0.652539i	−0.942660	−	0.333756i	$-0.891684\pi$
$499$	−17.3717	+	14.5766i	−0.777666	+	0.652539i	0.164994	+	0.986295i	$0.447240\pi$
$500$		0			0
$501$	−15.0126	+	26.0025i	−0.670712	+	1.16171i
$502$	8.10035	+	14.0302i	0.361536	+	0.626199i
$503$	−25.4664	+	9.26902i	−1.13549	+	0.413285i	−0.840283	−	0.542148i	$-0.817611\pi$
$503$	−25.4664	+	9.26902i	−1.13549	+	0.413285i	−0.295208	+	0.955433i	$0.595389\pi$
$504$	15.1067	−	5.49837i	0.672904	−	0.244917i
$505$		0			0
$506$	8.27704	−	14.3362i	0.367959	−	0.637324i
$507$	5.46966	−	31.0200i	0.242916	−	1.37765i
$508$	−13.5570	+	11.3757i	−0.601495	+	0.504714i
$509$	−5.88641	−	4.93928i	−0.260910	−	0.218930i	0.502943	−	0.864320i	$-0.332251\pi$
$509$	−5.88641	−	4.93928i	−0.260910	−	0.218930i	−0.763853	+	0.645390i	$0.776695\pi$
$510$		0			0
$511$	39.9072	+	14.5250i	1.76539	+	0.642550i
$512$	1.00000			0.0441942
$513$	3.60791	+	4.55102i	0.159293	+	0.200933i
$514$	−3.35695			−0.148069
$515$		0			0
$516$	1.95736	+	11.1007i	0.0861680	+	0.488683i
$517$	−19.5122	−	16.3727i	−0.858146	−	0.720070i
$518$	−13.3881	+	11.2340i	−0.588240	+	0.493592i
$519$	−3.40936	+	19.3354i	−0.149654	+	0.848731i
$520$		0			0
$521$	−6.14900	−	10.6504i	−0.269393	−	0.466602i	0.699312	−	0.714816i	$-0.253490\pi$
$521$	−6.14900	−	10.6504i	−0.269393	−	0.466602i	−0.968705	+	0.248214i	$0.920156\pi$
$522$	−7.93483	+	2.88804i	−0.347298	+	0.126406i
$523$	−13.8543	+	5.04254i	−0.605805	+	0.220495i	−0.626667	−	0.779287i	$-0.715581\pi$
$523$	−13.8543	+	5.04254i	−0.605805	+	0.220495i	0.0208617	+	0.999782i	$0.493359\pi$
$524$	2.33011	+	4.03588i	0.101791	+	0.176308i
$525$		0			0
$526$	3.62047	−	20.5327i	0.157860	−	0.895268i
$527$	22.4774	−	18.8608i	0.979131	−	0.821588i
$528$	−6.70015	−	5.62209i	−0.291586	−	0.244670i
$529$	0.0628742	+	0.356577i	0.00273366	+	0.0155033i
$530$		0			0
$531$	−19.8606			−0.861877
$532$	17.5020	−	9.46576i	0.758807	−	0.410393i
$533$	9.99026			0.432726
$534$	−6.55182	−	2.38467i	−0.283525	−	0.103195i
$535$		0			0
$536$	4.31768	+	3.62297i	0.186495	+	0.156488i
$537$	40.1234	−	33.6675i	1.73145	−	1.45286i
$538$	−1.97588	+	11.2058i	−0.0851863	+	0.483115i
$539$	−23.6968	+	41.0440i	−1.02069	+	1.76789i
$540$		0			0
$541$	−30.4211	+	11.0724i	−1.30790	+	0.476038i	−0.899563	−	0.436791i	$-0.856115\pi$
$541$	−30.4211	+	11.0724i	−1.30790	+	0.476038i	−0.408341	+	0.912829i	$0.633893\pi$
$542$	−5.53666	+	2.01518i	−0.237820	+	0.0865594i
$543$	−33.9187	−	58.7489i	−1.45559	−	2.52116i
$544$	2.12540	−	3.68130i	0.0911258	−	0.157835i
$545$		0			0
$546$	7.28706	−	6.11457i	0.311857	−	0.261679i
$547$	23.8367	+	20.0014i	1.01918	+	0.855196i	0.989525	−	0.144364i	$-0.0461136\pi$
$547$	23.8367	+	20.0014i	1.01918	+	0.855196i	0.0296585	+	0.999560i	$0.490558\pi$
$548$	1.21910	+	6.91385i	0.0520773	+	0.295345i
$549$	−31.8150	−	11.5797i	−1.35783	−	0.494211i
$550$		0			0
$551$	−9.19299	+	4.97193i	−0.391634	+	0.211811i
$552$	12.3435			0.525373
$553$	−9.29023	−	3.38137i	−0.395061	−	0.143790i
$554$	2.20612	+	12.5116i	0.0937292	+	0.531565i
$555$		0			0
$556$	14.8381	−	12.4507i	0.629277	−	0.528026i
$557$	−0.866290	+	4.91297i	−0.0367059	+	0.208169i	−0.997645	−	0.0685909i	$-0.978150\pi$
$557$	−0.866290	+	4.91297i	−0.0367059	+	0.208169i	0.960939	+	0.276760i	$0.0892608\pi$
$558$	12.1548	−	21.0527i	0.514552	−	0.891231i
$559$	1.80086	+	3.11918i	0.0761682	+	0.131927i
$560$		0			0
$561$	−34.9371	+	12.7161i	−1.47505	+	0.536873i
$562$	−6.59209	−	11.4178i	−0.278070	−	0.481632i
$563$	−13.0247	+	22.5594i	−0.548924	+	0.950764i	0.449425	+	0.893318i	$0.351629\pi$
$563$	−13.0247	+	22.5594i	−0.548924	+	0.950764i	−0.998349	+	0.0574458i	$0.981704\pi$
$564$	3.29803	−	18.7041i	0.138872	−	0.787584i
$565$		0			0
$566$	−12.8234	−	10.7601i	−0.539006	−	0.452280i
$567$	5.67766	+	32.1996i	0.238439	+	1.35226i
$568$	14.4340	+	5.25354i	0.605637	+	0.220434i
$569$	33.8230			1.41793			0.708967	−	0.705242i	$-0.249162\pi$
$569$	33.8230			1.41793			0.708967	+	0.705242i	$0.249162\pi$
$570$		0			0
$571$	41.6528			1.74312			0.871558	−	0.490293i	$-0.163110\pi$
$571$	41.6528			1.74312			0.871558	+	0.490293i	$0.163110\pi$
$572$	−2.62618	−	0.955853i	−0.109806	−	0.0399662i
$573$	−7.83507	−	44.4349i	−0.327315	−	1.85630i
$574$	−42.8122	−	35.9237i	−1.78695	−	1.49943i
$575$		0			0
$576$	0.611541	−	3.46822i	0.0254809	−	0.144509i
$577$	−18.0943	+	31.3403i	−0.753276	+	1.30471i	0.192951	+	0.981208i	$0.438194\pi$
$577$	−18.0943	+	31.3403i	−0.753276	+	1.30471i	−0.946227	+	0.323504i	$0.895139\pi$
$578$	−0.534659	−	0.926057i	−0.0222389	−	0.0385189i
$579$	−35.3558	+	12.8685i	−1.46934	+	0.534795i
$580$		0			0
$581$	1.09673	+	1.89959i	0.0455000	+	0.0788084i
$582$	−2.54681	+	4.41120i	−0.105569	+	0.182850i
$583$	−6.71376	+	38.0756i	−0.278056	+	1.57693i
$584$	7.12677	−	5.98007i	0.294908	−	0.247457i
$585$		0			0
$586$	−1.18835	−	6.73947i	−0.0490903	−	0.278405i
$587$	−26.6275	−	9.69163i	−1.09904	−	0.400016i	−0.272075	−	0.962276i	$-0.587710\pi$
$587$	−26.6275	−	9.69163i	−1.09904	−	0.400016i	−0.826961	+	0.562260i	$0.809932\pi$
$588$	−35.3388			−1.45735
$589$	11.0732	−	27.9766i	0.456263	−	1.15276i
$590$		0			0
$591$	−13.8387	−	5.03687i	−0.569248	−	0.207189i
$592$	0.664827	+	3.77042i	0.0273242	+	0.154963i
$593$	34.2107	+	28.7061i	1.40486	+	1.17882i	0.958892	+	0.283773i	$0.0915862\pi$
$593$	34.2107	+	28.7061i	1.40486	+	1.17882i	0.445972	+	0.895047i	$0.352858\pi$
$594$	−3.49564	+	2.93319i	−0.143428	+	0.120350i
$595$		0			0
$596$	9.53103	−	16.5082i	0.390406	−	0.676203i
$597$	−6.78572	−	11.7532i	−0.277721	−	0.481027i
$598$	3.70622	−	1.34896i	0.151559	−	0.0551629i
$599$	−10.8852	+	3.96190i	−0.444759	+	0.161879i	−0.554684	−	0.832061i	$-0.687161\pi$
$599$	−10.8852	+	3.96190i	−0.444759	+	0.161879i	0.109926	+	0.993940i	$0.464939\pi$
$600$		0			0
$601$	1.22575	−	2.12305i	0.0499992	−	0.0866012i	−0.839943	−	0.542675i	$-0.817411\pi$
$601$	1.22575	−	2.12305i	0.0499992	−	0.0866012i	0.889942	+	0.456074i	$0.150745\pi$
$602$	3.49878	−	19.8426i	0.142600	−	0.808722i
$603$	15.2057	−	12.7591i	0.619224	−	0.519590i
$604$	14.0066	+	11.7530i	0.569922	+	0.478221i
$605$		0			0
$606$	−9.64956	−	3.51215i	−0.391987	−	0.142671i
$607$	22.4395			0.910790			0.455395	−	0.890290i	$-0.349498\pi$
$607$	22.4395			0.910790			0.455395	+	0.890290i	$0.349498\pi$
$608$	0.121230	−	4.35721i	0.00491652	−	0.176708i
$609$	27.9515			1.13265
$610$		0			0
$611$	−1.05381	−	5.97648i	−0.0426328	−	0.241782i
$612$	−11.4678	−	9.62263i	−0.463559	−	0.388972i
$613$	17.6927	−	14.8459i	0.714602	−	0.599622i	−0.211284	−	0.977425i	$-0.567765\pi$
$613$	17.6927	−	14.8459i	0.714602	−	0.599622i	0.925886	+	0.377802i	$0.123320\pi$
$614$	4.29767	−	24.3733i	0.173440	−	0.983626i
$615$		0			0
$616$	7.81711	+	13.5396i	0.314960	+	0.545527i
$617$	−15.3738	+	5.59562i	−0.618928	+	0.225271i	−0.632405	−	0.774638i	$-0.717932\pi$
$617$	−15.3738	+	5.59562i	−0.618928	+	0.225271i	0.0134772	+	0.999909i	$0.495710\pi$
$618$	12.0906	−	4.40063i	0.486357	−	0.177019i
$619$	−5.96422	−	10.3303i	−0.239722	−	0.415211i	0.720912	−	0.693026i	$-0.243723\pi$
$619$	−5.96422	−	10.3303i	−0.239722	−	0.415211i	−0.960635	+	0.277815i	$0.910390\pi$
$620$		0			0
$621$	1.11828	−	6.34207i	0.0448749	−	0.254498i
$622$	−8.92564	+	7.48950i	−0.357886	+	0.300302i
$623$	9.54719	+	8.01104i	0.382500	+	0.320956i
$624$	−0.361861	−	2.05222i	−0.0144860	−	0.0821544i
$625$		0			0
$626$	15.4819			0.618783
$627$	−25.3089	+	28.5124i	−1.01074	+	1.13868i
$628$	12.0708			0.481678
$629$	15.2931	+	5.56623i	0.609775	+	0.221940i
$630$		0			0
$631$	21.5749	+	18.1035i	0.858883	+	0.720688i	0.961727	−	0.274009i	$-0.0883499\pi$
$631$	21.5749	+	18.1035i	0.858883	+	0.720688i	−0.102844	+	0.994697i	$0.532794\pi$
$632$	−1.65908	+	1.39214i	−0.0659947	+	0.0553762i
$633$	−8.33877	+	47.2915i	−0.331436	+	1.87967i
$634$	3.78167	−	6.55004i	0.150189	−	0.260135i
$635$		0			0
$636$	−27.0903	+	9.86006i	−1.07420	+	0.390977i
$637$	−10.6107	+	3.86200i	−0.420413	+	0.153018i
$638$	−4.10597	−	7.11174i	−0.162557	−	0.281557i
$639$	27.0474	−	46.8475i	1.06998	−	1.85326i
$640$		0			0
$641$	−9.66506	+	8.10994i	−0.381747	+	0.320324i	−0.813388	−	0.581722i	$-0.802379\pi$
$641$	−9.66506	+	8.10994i	−0.381747	+	0.320324i	0.431641	+	0.902045i	$0.357935\pi$
$642$	−9.05811	−	7.60066i	−0.357495	−	0.299974i
$643$	−0.605419	−	3.43350i	−0.0238754	−	0.135404i	0.970540	−	0.240939i	$-0.0774555\pi$
$643$	−0.605419	−	3.43350i	−0.0238754	−	0.135404i	−0.994416	+	0.105535i	$0.966344\pi$
$644$	−20.7333	−	7.54630i	−0.817006	−	0.297366i
$645$		0			0
$646$	−15.7826	−	9.70711i	−0.620956	−	0.381921i
$647$	41.3497			1.62562			0.812812	−	0.582526i	$-0.197936\pi$
$647$	41.3497			1.62562			0.812812	+	0.582526i	$0.197936\pi$
$648$	6.73067	+	2.44976i	0.264405	+	0.0962357i
$649$	−3.35395	−	19.0212i	−0.131654	−	0.746647i
$650$		0			0
$651$	−61.6429	+	51.7246i	−2.41598	+	2.02725i
$652$	2.59175	−	14.6985i	0.101501	−	0.575639i
$653$	12.3851	−	21.4517i	0.484668	−	0.839469i	−0.515177	−	0.857084i	$-0.672274\pi$
$653$	12.3851	−	21.4517i	0.484668	−	0.839469i	0.999845	+	0.0176147i	$0.00560722\pi$
$654$	−22.9939	−	39.8266i	−0.899133	−	1.55734i
$655$		0			0
$656$	−11.5046	+	4.18734i	−0.449180	+	0.163488i
$657$	−16.3819	−	28.3743i	−0.639119	−	1.10699i
$658$	−16.9746	+	29.4009i	−0.661740	+	1.14617i
$659$	5.30246	−	30.0718i	0.206555	−	1.17143i	−0.688420	−	0.725312i	$-0.741695\pi$
$659$	5.30246	−	30.0718i	0.206555	−	1.17143i	0.894975	−	0.446117i	$-0.147194\pi$
$660$		0			0
$661$	5.85365	+	4.91180i	0.227681	+	0.191047i	0.749491	−	0.662015i	$-0.230299\pi$
$661$	5.85365	+	4.91180i	0.227681	+	0.191047i	−0.521810	+	0.853062i	$0.674743\pi$
$662$	1.62987	+	9.24344i	0.0633466	+	0.359256i
$663$	−8.32393	−	3.02966i	−0.323274	−	0.117662i
$664$	0.480511			0.0186474
$665$		0			0
$666$	13.4832			0.522465
$667$	10.8903	+	3.96373i	0.421672	+	0.153476i
$668$	−2.04161	−	11.5786i	−0.0789924	−	0.447988i
$669$	21.0351	+	17.6505i	0.813263	+	0.682409i
$670$		0			0
$671$	5.71756	−	32.4259i	0.220724	−	1.25179i
$672$	−5.82879	+	10.0958i	−0.224850	+	0.389452i
$673$	13.8374	+	23.9670i	0.533392	+	0.923861i	0.999239	+	0.0389966i	$0.0124161\pi$
$673$	13.8374	+	23.9670i	0.533392	+	0.923861i	−0.465848	+	0.884865i	$0.654251\pi$
$674$	8.00591	−	2.91391i	0.308376	−	0.112240i
$675$		0			0
$676$	6.16707	+	10.6817i	0.237195	+	0.410834i
$677$	8.70125	−	15.0710i	0.334416	−	0.579226i	−0.648956	−	0.760826i	$-0.724794\pi$
$677$	8.70125	−	15.0710i	0.334416	−	0.579226i	0.983373	+	0.181600i	$0.0581275\pi$
$678$	−1.67262	+	9.48589i	−0.0642365	+	0.364303i
$679$	6.97471	−	5.85247i	0.267665	−	0.224597i
$680$		0			0
$681$	9.24229	+	52.4156i	0.354165	+	2.00857i
$682$	22.2155	+	8.08578i	0.850675	+	0.309621i
$683$	16.0345			0.613545			0.306772	−	0.951783i	$-0.400751\pi$
$683$	16.0345			0.613545			0.306772	+	0.951783i	$0.400751\pi$
$684$	−15.0376	−	3.08507i	−0.574979	−	0.117961i
$685$		0			0
$686$	29.3315	+	10.6758i	1.11988	+	0.407604i
$687$	−8.50939	−	48.2592i	−0.324654	−	1.84120i
$688$	−3.38122	−	2.83718i	−0.128908	−	0.108166i
$689$	−7.05652	+	5.92113i	−0.268832	+	0.225577i
$690$		0			0
$691$	−22.9510	+	39.7524i	−0.873099	+	1.51225i	−0.0143239	+	0.999897i	$0.504560\pi$
$691$	−22.9510	+	39.7524i	−0.873099	+	1.51225i	−0.858775	+	0.512354i	$0.828774\pi$
$692$	−3.84407	−	6.65812i	−0.146130	−	0.253104i
$693$	51.7389	−	18.8314i	1.96540	−	0.715347i
$694$	6.39300	−	2.32686i	0.242675	−	0.0883264i
$695$		0			0
$696$	3.06159	−	5.30284i	0.116049	−	0.201004i
$697$	−9.03707	+	51.2518i	−0.342303	+	1.94130i
$698$	−2.92340	+	2.45303i	−0.110652	+	0.0928484i
$699$	−41.3132	−	34.6659i	−1.56261	−	1.31119i
$700$		0			0
$701$	−22.3326	−	8.12842i	−0.843492	−	0.307006i	−0.116108	−	0.993237i	$-0.537042\pi$
$701$	−22.3326	−	8.12842i	−0.843492	−	0.307006i	−0.727384	+	0.686231i	$0.759264\pi$
$702$	−1.08721			−0.0410341
$703$	16.5091	−	2.43970i	0.622653	−	0.0920152i
$704$	3.42491			0.129081
$705$		0			0
$706$	−0.653037	−	3.70356i	−0.0245774	−	0.139385i
$707$	14.0612	+	11.7987i	0.528825	+	0.443737i
$708$	11.0325	−	9.25733i	0.414625	−	0.347912i
$709$	−2.18071	+	12.3674i	−0.0818984	+	0.464469i	0.916084	+	0.400985i	$0.131332\pi$
$709$	−2.18071	+	12.3674i	−0.0818984	+	0.464469i	−0.997983	+	0.0634836i	$0.979779\pi$
$710$		0			0
$711$	3.81364	+	6.60542i	0.143023	+	0.247722i
$712$	2.56555	−	0.933784i	0.0961480	−	0.0349950i
$713$	−31.3518	+	11.4111i	−1.17413	+	0.427350i
$714$	24.7770	+	42.9151i	0.927257	+	1.60606i
$715$		0			0
$716$	−3.56149	+	20.1982i	−0.133099	+	0.754844i
$717$	12.0466	−	10.1083i	0.449889	−	0.377502i
$718$	−11.0881	−	9.30404i	−0.413805	−	0.347224i
$719$	1.20794	+	6.85055i	0.0450485	+	0.255483i	0.999012	−	0.0444399i	$-0.0141503\pi$
$719$	1.20794	+	6.85055i	0.0450485	+	0.255483i	−0.953964	+	0.299922i	$0.903039\pi$
$720$		0			0
$721$	−22.9990			−0.856528
$722$	−18.9706	−	1.05645i	−0.706013	−	0.0393169i
$723$	−58.6098			−2.17972
$724$	24.9617	+	9.08531i	0.927694	+	0.337653i
$725$		0			0
$726$	−1.42810	−	1.19832i	−0.0530019	−	0.0444739i
$727$	−40.0035	+	33.5669i	−1.48365	+	1.24493i	−0.581468	+	0.813569i	$0.697521\pi$
$727$	−40.0035	+	33.5669i	−1.48365	+	1.24493i	−0.902180	+	0.431359i	$0.858034\pi$
$728$	−0.646826	+	3.66833i	−0.0239730	+	0.135957i
$729$	17.7162	−	30.6854i	0.656157	−	1.13650i
$730$		0			0
$731$	−17.6310	+	6.41715i	−0.652105	+	0.237347i
$732$	23.0706	−	8.39700i	0.852713	−	0.310362i
$733$	−14.2340	−	24.6540i	−0.525744	−	0.910615i	−0.999550	−	0.0299862i	$-0.990454\pi$
$733$	−14.2340	−	24.6540i	−0.525744	−	0.910615i	0.473806	−	0.880629i	$-0.342880\pi$
$734$	−4.39898	+	7.61926i	−0.162369	+	0.281232i
$735$		0			0
$736$	−3.70262	+	3.10687i	−0.136481	+	0.114521i
$737$	14.7877	+	12.4083i	0.544711	+	0.457067i
$738$	7.48707	+	42.4613i	0.275603	+	1.56302i
$739$	7.54033	+	2.74446i	0.277376	+	0.100956i	0.476962	−	0.878924i	$-0.341738\pi$
$739$	7.54033	+	2.74446i	0.277376	+	0.100956i	−0.199587	+	0.979880i	$0.563960\pi$
$740$		0			0
$741$	−8.98581	+	1.32792i	−0.330102	+	0.0487822i
$742$	51.5316			1.89178
$743$	−16.1528	−	5.87914i	−0.592589	−	0.215685i	0.0282789	−	0.999600i	$-0.490997\pi$
$743$	−16.1528	−	5.87914i	−0.592589	−	0.215685i	−0.620868	+	0.783915i	$0.713220\pi$
$744$	3.06107	+	17.3602i	0.112224	+	0.636455i
$745$		0			0
$746$	5.13800	−	4.31129i	0.188115	−	0.157848i
$747$	0.293852	−	1.66652i	0.0107515	−	0.0609747i
$748$	7.27931	−	12.6081i	0.266158	−	0.460999i
$749$	10.5682	+	18.3046i	0.386152	+	0.668835i
$750$		0			0
$751$	39.3470	−	14.3211i	1.43579	−	0.522585i	0.497206	−	0.867633i	$-0.334359\pi$
$751$	39.3470	−	14.3211i	1.43579	−	0.522585i	0.938585	+	0.345048i	$0.112137\pi$
$752$	3.71855	+	6.44072i	0.135602	+	0.234869i
$753$	−20.6864	+	35.8299i	−0.753854	+	1.30571i
$754$	0.339748	−	1.92681i	0.0123729	−	0.0701701i
$755$		0			0
$756$	4.65913	+	3.90947i	0.169451	+	0.142186i
$757$	−7.08380	−	40.1742i	−0.257465	−	1.46016i	−0.789665	−	0.613538i	$-0.789746\pi$
$757$	−7.08380	−	40.1742i	−0.257465	−	1.46016i	0.532200	−	0.846619i	$-0.321365\pi$
$758$	15.8533	+	5.77013i	0.575817	+	0.209580i
$759$	42.2752			1.53449
$760$		0			0
$761$	28.2817			1.02521			0.512606	−	0.858624i	$-0.328680\pi$
$761$	28.2817			1.02521			0.512606	+	0.858624i	$0.328680\pi$
$762$	−42.4695	−	15.4576i	−1.53851	−	0.559971i
$763$	14.2744	+	80.9543i	0.516769	+	2.93074i
$764$	13.5346	+	11.3569i	0.489665	+	0.410878i
$765$		0			0
$766$	−1.21387	+	6.88419i	−0.0438589	+	0.248736i
$767$	2.30090	−	3.98527i	0.0830806	−	0.143900i
$768$	1.27688	+	2.21163i	0.0460756	+	0.0798052i
$769$	−30.8544	+	11.2301i	−1.11264	+	0.404967i	−0.831961	−	0.554835i	$-0.812782\pi$
$769$	−30.8544	+	11.2301i	−1.11264	+	0.404967i	−0.280678	+	0.959802i	$0.590559\pi$
$770$		0			0
$771$	−4.28643	−	7.42431i	−0.154372	−	0.267380i
$772$	7.36654	−	12.7592i	0.265127	−	0.459214i
$773$	2.57843	−	14.6230i	0.0927397	−	0.525953i	−0.902677	−	0.430319i	$-0.858401\pi$
$773$	2.57843	−	14.6230i	0.0927397	−	0.525953i	0.995417	−	0.0956341i	$-0.0304879\pi$
$774$	−11.9077	+	9.99177i	−0.428014	+	0.359147i
$775$		0			0
$776$	−0.346350	−	1.96425i	−0.0124332	−	0.0705124i
$777$	−41.9404	−	15.2651i	−1.50460	−	0.547631i
$778$	11.8277			0.424044
$779$	16.8504	+	50.6357i	0.603729	+	1.81421i
$780$		0			0
$781$	49.4351	+	17.9929i	1.76893	+	0.643837i
$782$	3.56777	+	20.2338i	0.127583	+	0.723560i
$783$	−2.44723	−	2.05347i	−0.0874567	−	0.0733849i
$784$	10.6004	−	8.89483i	0.378587	−	0.317672i
$785$		0			0
$786$	−5.95057	+	10.3067i	−0.212250	+	0.367627i
$787$	9.53904	+	16.5221i	0.340030	+	0.588949i	0.984438	−	0.175733i	$-0.0562294\pi$
$787$	9.53904	+	16.5221i	0.340030	+	0.588949i	−0.644408	+	0.764682i	$0.722896\pi$
$788$	5.41894	−	1.97233i	0.193042	−	0.0702614i
$789$	50.0336	−	18.2107i	1.78124	−	0.648319i
$790$		0			0
$791$	8.60879	−	14.9109i	0.306093	−	0.530169i
$792$	2.09447	−	11.8783i	0.0744239	−	0.422079i
$793$	6.00946	−	5.04253i	0.213402	−	0.179066i
$794$	−22.8171	−	19.1459i	−0.809750	−	0.679461i
$795$		0			0
$796$	4.99379	+	1.81759i	0.177000	+	0.0644228i
$797$	5.02894			0.178134			0.0890672	−	0.996026i	$-0.471611\pi$
$797$	5.02894			0.178134			0.0890672	+	0.996026i	$0.471611\pi$
$798$	43.2827	+	26.6212i	1.53219	+	0.942379i
$799$	31.6136			1.11841
$800$		0			0
$801$	−1.66963	−	9.46895i	−0.0589935	−	0.334569i
$802$	13.9563	+	11.7107i	0.492813	+	0.413519i
$803$	24.4085	−	20.4812i	0.861359	−	0.722766i
$804$	−2.49947	+	14.1752i	−0.0881496	+	0.499921i
$805$		0			0
$806$	2.81632	+	4.87800i	0.0992005	+	0.171820i
$807$	−27.3060	+	9.93856i	−0.961216	+	0.349854i
$808$	3.77856	−	1.37528i	0.132929	−	0.0483823i
$809$	11.3894	+	19.7270i	0.400429	+	0.693564i	0.993778	−	0.111382i	$-0.0355276\pi$
$809$	11.3894	+	19.7270i	0.400429	+	0.693564i	−0.593348	+	0.804946i	$0.702194\pi$
$810$		0			0
$811$	4.11323	−	23.3273i	0.144435	−	0.819132i	−0.823384	−	0.567485i	$-0.807917\pi$
$811$	4.11323	−	23.3273i	0.144435	−	0.819132i	0.967819	−	0.251647i	$-0.0809723\pi$
$812$	−8.38450	+	7.03543i	−0.294238	+	0.246895i
$813$	−11.5265	−	9.67188i	−0.404252	−	0.339208i
$814$	2.27697	+	12.9133i	0.0798078	+	0.452613i
$815$		0			0
$816$	10.8556			0.380021
$817$	−12.7721	+	14.3887i	−0.446839	+	0.503398i
$818$	18.4635			0.645561
$819$	12.3270	+	4.48667i	0.430741	+	0.156777i
$820$		0			0
$821$	−4.27500	−	3.58715i	−0.149199	−	0.125192i	0.565133	−	0.825000i	$-0.308825\pi$
$821$	−4.27500	−	3.58715i	−0.149199	−	0.125192i	−0.714332	+	0.699807i	$0.753269\pi$
$822$	−13.7342	+	11.5244i	−0.479036	+	0.401959i
$823$	−0.0595499	+	0.337724i	−0.00207578	+	0.0117723i	−0.985828	−	0.167759i	$-0.946347\pi$
$823$	−0.0595499	+	0.337724i	−0.00207578	+	0.0117723i	0.983752	+	0.179531i	$0.0574581\pi$
$824$	−2.51914	+	4.36328i	−0.0877584	+	0.152002i
$825$		0			0
$826$	−24.1908	+	8.80472i	−0.841705	+	0.306355i
$827$	39.1878	−	14.2632i	1.36269	−	0.495980i	0.445807	−	0.895129i	$-0.352917\pi$
$827$	39.1878	−	14.2632i	1.36269	−	0.495980i	0.916886	+	0.399149i	$0.130694\pi$
$828$	8.51101	+	14.7415i	0.295778	+	0.512303i
$829$	2.81234	−	4.87112i	0.0976766	−	0.169181i	−0.813046	−	0.582200i	$-0.802192\pi$
$829$	2.81234	−	4.87112i	0.0976766	−	0.169181i	0.910723	+	0.413019i	$0.135526\pi$
$830$		0			0
$831$	−24.8539	+	20.8549i	−0.862173	+	0.723449i
$832$	0.625092	+	0.524515i	0.0216712	+	0.0181843i
$833$	−10.2144	−	57.9285i	−0.353907	−	2.00710i
$834$	46.4828	+	16.9184i	1.60957	+	0.585835i
$835$		0			0
$836$	0.415201	−	14.9231i	0.0143600	−	0.516125i
$837$	9.19697			0.317894
$838$	36.1355	+	13.1522i	1.24828	+	0.454337i
$839$	−5.64367	−	32.0068i	−0.194841	−	1.10500i	−0.912645	−	0.408753i	$-0.865964\pi$
$839$	−5.64367	−	32.0068i	−0.194841	−	1.10500i	0.717804	−	0.696245i	$-0.245147\pi$
$840$		0			0
$841$	−17.8113	+	14.9455i	−0.614183	+	0.515360i
$842$	1.36999	−	7.76960i	0.0472130	−	0.267758i
$843$	16.8347	−	29.1585i	0.579816	−	1.00427i
$844$	−9.40200	−	16.2847i	−0.323630	−	0.560544i
$845$		0			0
$846$	24.6119	−	8.95799i	0.846174	−	0.307982i
$847$	1.66618	+	2.88591i	0.0572506	+	0.0991609i
$848$	5.64439	−	9.77636i	0.193829	−	0.335722i
$849$	7.42334	−	42.0999i	0.254768	−	1.44486i
$850$		0			0
$851$	−14.1758	−	11.8949i	−0.485941	−	0.407753i
$852$	6.81165	+	38.6308i	0.233363	+	1.32347i
$853$	−5.81701	−	2.11722i	−0.199170	−	0.0724921i	0.240509	−	0.970647i	$-0.422686\pi$
$853$	−5.81701	−	2.11722i	−0.199170	−	0.0724921i	−0.439679	+	0.898155i	$0.644908\pi$
$854$	−43.8852			−1.50172
$855$		0			0
$856$	4.63023			0.158258
$857$	−25.5378	−	9.29500i	−0.872355	−	0.317511i	−0.133234	−	0.991085i	$-0.542536\pi$
$857$	−25.5378	−	9.29500i	−0.872355	−	0.317511i	−0.739120	+	0.673573i	$0.764759\pi$
$858$	−1.23934	−	7.02865i	−0.0423104	−	0.239954i
$859$	−7.91500	−	6.64147i	−0.270056	−	0.226604i	0.497695	−	0.867352i	$-0.334180\pi$
$859$	−7.91500	−	6.64147i	−0.270056	−	0.226604i	−0.767751	+	0.640748i	$0.778624\pi$
$860$		0			0
$861$	24.7836	−	140.555i	0.844624	−	4.79010i
$862$	−1.07388	+	1.86001i	−0.0365764	+	0.0633521i
$863$	8.76039	+	15.1734i	0.298207	+	0.516510i	0.975726	−	0.218996i	$-0.0702781\pi$
$863$	8.76039	+	15.1734i	0.298207	+	0.516510i	−0.677519	+	0.735505i	$0.736945\pi$
$864$	1.25202	−	0.455696i	0.0425944	−	0.0155031i
$865$		0			0
$866$	−4.39122	−	7.60582i	−0.149220	−	0.258456i
$867$	1.36539	−	2.36493i	0.0463712	−	0.0803173i
$868$	5.47165	−	31.0313i	0.185720	−	1.05327i
$869$	−5.68221	+	4.76794i	−0.192756	+	0.161741i
$870$		0			0
$871$	0.798651	+	4.52938i	0.0270613	+	0.153472i
$872$	16.9218	+	6.15904i	0.573045	+	0.208571i
$873$	−7.02426			−0.237735
$874$	13.0884	+	16.5098i	0.442723	+	0.558451i
$875$		0			0
$876$	22.3257	+	8.12590i	0.754317	+	0.274549i
$877$	−5.22646	−	29.6407i	−0.176485	−	1.00090i	−0.936416	−	0.350892i	$-0.885878\pi$
$877$	−5.22646	−	29.6407i	−0.176485	−	1.00090i	0.759931	−	0.650004i	$-0.225233\pi$
$878$	1.85352	+	1.55529i	0.0625533	+	0.0524884i
$879$	13.3878	−	11.2337i	0.451560	−	0.378904i
$880$		0			0
$881$	−8.38802	+	14.5285i	−0.282600	+	0.489477i	−0.972024	−	0.234881i	$-0.924530\pi$
$881$	−8.38802	+	14.5285i	−0.282600	+	0.489477i	0.689425	+	0.724357i	$0.257863\pi$
$882$	−24.3666	−	42.2042i	−0.820467	−	1.42109i
$883$	−44.3132	+	16.1287i	−1.49126	+	0.542774i	−0.953781	−	0.300504i	$-0.902845\pi$
$883$	−44.3132	+	16.1287i	−1.49126	+	0.542774i	−0.537478	+	0.843278i	$0.680623\pi$
$884$	3.25947	−	1.18635i	0.109628	−	0.0399013i
$885$		0			0
$886$	−16.4873	+	28.5569i	−0.553902	+	0.959386i
$887$	3.83168	−	21.7305i	0.128655	−	0.729640i	−0.850414	−	0.526114i	$-0.823649\pi$
$887$	3.83168	−	21.7305i	0.128655	−	0.729640i	0.979070	−	0.203526i	$-0.0652402\pi$
$888$	−7.48986	+	6.28474i	−0.251343	+	0.210902i
$889$	61.8858	+	51.9283i	2.07558	+	1.74162i
$890$		0			0
$891$	23.0519	+	8.39021i	0.772268	+	0.281083i
$892$	−10.7525			−0.360020
$893$	28.5144	−	15.4217i	0.954197	−	0.516068i
$894$	48.6801			1.62810
$895$		0			0
$896$	−0.792679	−	4.49550i	−0.0264815	−	0.150184i
$897$	7.71580	+	6.47433i	0.257623	+	0.216172i
$898$	−14.6250	+	12.2718i	−0.488043	+	0.409517i
$899$	−2.87401	+	16.2993i	−0.0958535	+	0.543612i
$900$		0			0
$901$	−23.9932	−	41.5574i	−0.799328	−	1.38448i
$902$	−39.4023	+	14.3413i	−1.31195	+	0.477512i
$903$	48.3519	−	17.5986i	1.60905	−	0.585646i
$904$	−1.88589	−	3.26645i	−0.0627236	−	0.108640i
$905$		0			0
$906$	−8.10833	+	45.9846i	−0.269381	+	1.52774i
$907$	−24.7890	+	20.8005i	−0.823106	+	0.690668i	−0.953697	−	0.300768i	$-0.902757\pi$
$907$	−24.7890	+	20.8005i	−0.823106	+	0.690668i	0.130591	+	0.991436i	$0.458312\pi$
$908$	−15.9655	−	13.3966i	−0.529833	−	0.444583i
$909$	−2.45904	−	13.9459i	−0.0815613	−	0.462557i
$910$		0			0
$911$	0.987475			0.0327165			0.0163583	−	0.999866i	$-0.494793\pi$
$911$	0.987475			0.0327165			0.0163583	+	0.999866i	$0.494793\pi$
$912$	9.79133	−	5.29554i	0.324223	−	0.175353i
$913$	1.64571			0.0544649
$914$	−16.2890	−	5.92870i	−0.538791	−	0.196104i
$915$		0			0
$916$	14.6994	+	12.3343i	0.485683	+	0.407537i
$917$	16.2963	−	13.6742i	0.538150	−	0.451561i
$918$	0.983478	−	5.57758i	0.0324596	−	0.184088i
$919$	−18.5503	+	32.1300i	−0.611917	+	1.05987i	0.379000	+	0.925396i	$0.376268\pi$
$919$	−18.5503	+	32.1300i	−0.611917	+	1.05987i	−0.990917	+	0.134474i	$0.957065\pi$
$920$		0			0
$921$	59.3923	−	21.6170i	1.95704	−	0.712305i
$922$	−11.4452	+	4.16572i	−0.376928	+	0.137191i
$923$	6.26702	+	10.8548i	0.206281	+	0.357290i
$924$	−19.9631	+	34.5770i	−0.656737	+	1.13750i
$925$		0			0
$926$	−6.36185	+	5.33823i	−0.209063	+	0.175425i
$927$	13.5923	+	11.4053i	0.446428	+	0.374598i
$928$	0.416358	+	2.36128i	0.0136676	+	0.0775129i
$929$	−51.4497	−	18.7261i	−1.68801	−	0.614385i	−0.693636	−	0.720326i	$-0.743992\pi$
$929$	−51.4497	−	18.7261i	−1.68801	−	0.614385i	−0.994372	+	0.105941i	$0.966215\pi$
$930$		0			0
$931$	−37.4716	−	47.2667i	−1.22808	−	1.54910i
$932$	21.1181			0.691745
$933$	−27.9610	−	10.1770i	−0.915402	−	0.333179i
$934$	1.40844	+	7.98763i	0.0460854	+	0.261363i
$935$		0			0
$936$	2.20140	−	1.84720i	0.0719551	−	0.0603775i
$937$	−3.20513	+	18.1772i	−0.104707	+	0.593822i	0.886630	+	0.462479i	$0.153040\pi$
$937$	−3.20513	+	18.1772i	−0.104707	+	0.593822i	−0.991337	+	0.131343i	$0.958071\pi$
$938$	12.8645	−	22.2820i	0.420041	−	0.727533i
$939$	19.7686	+	34.2403i	0.645125	+	1.11739i
$940$		0			0
$941$	5.45017	−	1.98370i	0.177671	−	0.0646668i	−0.251653	−	0.967818i	$-0.580974\pi$
$941$	5.45017	−	1.98370i	0.177671	−	0.0646668i	0.429324	+	0.903151i	$0.358752\pi$
$942$	15.4130	+	26.6962i	0.502184	+	0.869808i
$943$	29.5878	−	51.2475i	0.963510	−	1.66885i
$944$	−0.979281	+	5.55378i	−0.0318729	+	0.180760i
$945$		0			0
$946$	−11.5804	−	9.71708i	−0.376510	−	0.315930i
$947$	−5.80578	−	32.9262i	−0.188663	−	1.06996i	−0.921159	−	0.389187i	$-0.872756\pi$
$947$	−5.80578	−	32.9262i	−0.188663	−	1.06996i	0.732496	−	0.680771i	$-0.238355\pi$
$948$	−5.19734	−	1.89168i	−0.168802	−	0.0614388i
$949$	7.59152			0.246431
$950$		0			0
$951$	19.3150			0.626332
$952$	−18.2341	−	6.63666i	−0.590970	−	0.215095i
$953$	5.39450	+	30.5937i	0.174745	+	0.991027i	0.938438	+	0.345448i	$0.112273\pi$
$953$	5.39450	+	30.5937i	0.174745	+	0.991027i	−0.763693	+	0.645579i	$0.776616\pi$
$954$	−30.4548	−	25.5546i	−0.986012	−	0.827362i
$955$		0			0
$956$	−1.06930	+	6.06431i	−0.0345837	+	0.196134i
$957$	10.4857	−	18.1617i	0.338954	−	0.587086i
$958$	−15.7469	−	27.2744i	−0.508758	−	0.881195i
$959$	30.1149	−	10.9609i	0.972460	−	0.353947i
$960$		0			0
$961$	−8.32387	−	14.4174i	−0.268512	−	0.465076i
$962$	−1.56206	+	2.70557i	−0.0503629	+	0.0872312i
$963$	2.83158	−	16.0587i	0.0912463	−	0.517483i
$964$	17.5810	−	14.7522i	0.566245	−	0.475136i
$965$		0			0
$966$	−9.78440	−	55.4901i	−0.314808	−	1.78536i
$967$	−13.4086	−	4.88033i	−0.431191	−	0.156941i	0.117301	−	0.993096i	$-0.462576\pi$
$967$	−13.4086	−	4.88033i	−0.431191	−	0.156941i	−0.548492	+	0.836156i	$0.684798\pi$
$968$	0.730003			0.0234632
$969$	1.31602	−	47.3000i	0.0422766	−	1.51949i
$970$		0			0
$971$	31.2960	+	11.3908i	1.00434	+	0.365549i	0.791255	−	0.611486i	$-0.209428\pi$
$971$	31.2960	+	11.3908i	1.00434	+	0.365549i	0.213081	+	0.977035i	$0.431650\pi$
$972$	3.87040	+	21.9502i	0.124143	+	0.704052i
$973$	−67.7339	−	56.8355i	−2.17145	−	1.82206i
$974$	−12.0056	+	10.0739i	−0.384685	+	0.322789i
$975$		0			0
$976$	−4.80686	+	8.32572i	−0.153864	+	0.266500i
$977$	6.31564	+	10.9390i	0.202055	+	0.349970i	0.949191	−	0.314702i	$-0.101905\pi$
$977$	6.31564	+	10.9390i	0.202055	+	0.349970i	−0.747135	+	0.664672i	$0.768571\pi$
$978$	35.8170	−	13.0363i	1.14530	−	0.416856i
$979$	8.78678	−	3.19812i	0.280827	−	0.102213i
$980$		0			0
$981$	31.7093	−	54.9222i	1.01240	−	1.75353i
$982$	−2.50123	+	14.1852i	−0.0798174	+	0.452667i
$983$	26.9174	−	22.5864i	0.858532	−	0.720394i	−0.103119	−	0.994669i	$-0.532882\pi$
$983$	26.9174	−	22.5864i	0.858532	−	0.720394i	0.961651	+	0.274275i	$0.0884379\pi$
$984$	−23.9509	−	20.0972i	−0.763526	−	0.640675i
$985$		0			0
$986$	9.57752	+	3.48593i	0.305010	+	0.111015i
$987$	−86.6985			−2.75964
$988$	2.36120	−	2.66007i	0.0751199	−	0.0846282i
$989$	21.3341			0.678386
$990$		0			0
$991$	6.83350	+	38.7547i	0.217073	+	1.23108i	0.877272	+	0.479993i	$0.159361\pi$
$991$	6.83350	+	38.7547i	0.217073	+	1.23108i	−0.660199	+	0.751091i	$0.729528\pi$
$992$	−5.28780	−	4.43699i	−0.167888	−	0.140875i
$993$	−18.3619	+	15.4075i	−0.582697	+	0.488941i
$994$	12.1758	−	69.0524i	0.386193	−	2.19021i
$995$		0			0
$996$	0.613556	+	1.06271i	0.0194413	+	0.0336733i
$997$	−58.0784	+	21.1388i	−1.83936	+	0.669472i	−0.849470	+	0.527637i	$0.823078\pi$
$997$	−58.0784	+	21.1388i	−1.83936	+	0.669472i	−0.989890	+	0.141835i	$0.954700\pi$
$998$	21.3096	−	7.75605i	0.674543	−	0.245514i
$999$	2.55054	+	4.41766i	0.0806955	+	0.139769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.k.251.1	yes	24
5.2	odd	4		950.2.u.h.99.5		48
5.3	odd	4		950.2.u.h.99.4		48
5.4	even	2		950.2.l.j.251.4	✓	24
19.5	even	9	inner	950.2.l.k.651.1	yes	24
95.24	even	18		950.2.l.j.651.4	yes	24
95.43	odd	36		950.2.u.h.499.5		48
95.62	odd	36		950.2.u.h.499.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.251.4	✓	24	5.4	even	2
950.2.l.j.651.4	yes	24	95.24	even	18
950.2.l.k.251.1	yes	24	1.1	even	1	trivial
950.2.l.k.651.1	yes	24	19.5	even	9	inner
950.2.u.h.99.4		48	5.3	odd	4
950.2.u.h.99.5		48	5.2	odd	4
950.2.u.h.499.4		48	95.62	odd	36
950.2.u.h.499.5		48	95.43	odd	36

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.443457 - 2.51497i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.443457 + 2.51497i) q^{6} +(2.28243 - 3.95328i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-3.30934 + 1.20450i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.443457 - 2.51497i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.443457 + 2.51497i) q^{6} +(2.28243 - 3.95328i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-3.30934 + 1.20450i) q^{9} +(-1.71245 - 2.96606i) q^{11} +(1.27688 - 2.21163i) q^{12} +(0.141697 - 0.803603i) q^{13} +(-3.49688 + 2.93423i) q^{14} +(0.173648 + 0.984808i) q^{16} +(3.99445 + 1.45386i) q^{17} +3.52173 q^{18} +(4.31207 - 0.637234i) q^{19} +(-10.9545 - 3.98712i) q^{21} +(0.594729 + 3.37288i) q^{22} +(-3.70262 - 3.10687i) q^{23} +(-1.95630 + 1.64153i) q^{24} +(-0.408000 + 0.706677i) q^{26} +(0.666183 + 1.15386i) q^{27} +(4.28956 - 1.56127i) q^{28} +(-2.25311 + 0.820065i) q^{29} +(3.45137 - 5.97794i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-6.70015 + 5.62209i) q^{33} +(-3.25630 - 2.73236i) q^{34} +(-3.30934 - 1.20450i) q^{36} +3.82859 q^{37} +(-4.26997 - 0.876010i) q^{38} -2.08387 q^{39} +(2.12597 + 12.0570i) q^{41} +(8.93022 + 7.49334i) q^{42} +(-3.38122 + 2.83718i) q^{43} +(0.594729 - 3.37288i) q^{44} +(2.41672 + 4.18588i) q^{46} +(6.98859 - 2.54364i) q^{47} +(2.39976 - 0.873440i) q^{48} +(-6.91895 - 11.9840i) q^{49} +(1.88505 - 10.6906i) q^{51} +(0.625092 - 0.524515i) q^{52} +(-8.64770 - 7.25628i) q^{53} +(-0.231363 - 1.31212i) q^{54} -4.56485 q^{56} +(-3.51484 - 10.5621i) q^{57} +2.39771 q^{58} +(5.29935 + 1.92881i) q^{59} +(7.36453 + 6.17958i) q^{61} +(-5.28780 + 4.43699i) q^{62} +(-2.79160 + 15.8319i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(8.21895 - 2.99145i) q^{66} +(-5.29642 + 1.92774i) q^{67} +(2.12540 + 3.68130i) q^{68} +(-6.17173 + 10.6898i) q^{69} +(-11.7667 + 9.87343i) q^{71} +(2.69780 + 2.26372i) q^{72} +(1.61551 + 9.16200i) q^{73} +(-3.59769 - 1.30945i) q^{74} +(3.71284 + 2.28359i) q^{76} -15.6342 q^{77} +(1.95820 + 0.712727i) q^{78} +(-0.376083 - 2.13287i) q^{79} +(-5.48689 + 4.60405i) q^{81} +(2.12597 - 12.0570i) q^{82} +(-0.240255 + 0.416134i) q^{83} +(-5.82879 - 10.0958i) q^{84} +(4.14768 - 1.50963i) q^{86} +(3.06159 + 5.30284i) q^{87} +(-1.71245 + 2.96606i) q^{88} +(-0.474094 + 2.68872i) q^{89} +(-2.85346 - 2.39433i) q^{91} +(-0.839317 - 4.76000i) q^{92} +(-16.5649 - 6.02912i) q^{93} -7.43710 q^{94} -2.55377 q^{96} +(1.87426 + 0.682176i) q^{97} +(2.40292 + 13.6277i) q^{98} +(9.23972 + 7.75304i) 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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