LMFDB - Embedded newform 950.2.l.l.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:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(-0.419293 - 2.37793i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.419293 - 2.37793i) q^{6} +(-1.31398 + 2.27588i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.65966 + 0.968036i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(-0.419293 - 2.37793i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.419293 - 2.37793i) q^{6} +(-1.31398 + 2.27588i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.65966 + 0.968036i) q^{9} +(-2.09427 - 3.62738i) q^{11} +(1.20731 - 2.09111i) q^{12} +(0.544100 - 3.08575i) q^{13} +(-2.01313 + 1.68922i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-7.14407 - 2.60023i) q^{17} -2.83035 q^{18} +(2.25570 - 3.72986i) q^{19} +(5.96281 + 2.17029i) q^{21} +(-0.727333 - 4.12491i) q^{22} +(-4.50159 - 3.77729i) q^{23} +(1.84970 - 1.55208i) q^{24} +(1.56667 - 2.71356i) q^{26} +(-0.204821 - 0.354760i) q^{27} +(-2.46947 + 0.898814i) q^{28} +(5.18892 - 1.88861i) q^{29} +(-0.321502 + 0.556858i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-7.74754 + 6.50096i) q^{33} +(-5.82390 - 4.88683i) q^{34} +(-2.65966 - 0.968036i) q^{36} +8.83349 q^{37} +(3.39535 - 2.73342i) q^{38} -7.56582 q^{39} +(0.611926 + 3.47041i) q^{41} +(4.86093 + 4.07881i) q^{42} +(2.48078 - 2.08162i) q^{43} +(0.727333 - 4.12491i) q^{44} +(-2.93821 - 5.08912i) q^{46} +(-7.14264 + 2.59971i) q^{47} +(2.26899 - 0.825846i) q^{48} +(0.0469220 + 0.0812713i) q^{49} +(-3.18770 + 18.0783i) q^{51} +(2.40028 - 2.01408i) q^{52} +(-4.83483 - 4.05691i) q^{53} +(-0.0711336 - 0.403419i) q^{54} -2.62796 q^{56} +(-9.81513 - 3.79999i) q^{57} +5.52193 q^{58} +(3.20401 + 1.16616i) q^{59} +(-2.95060 - 2.47585i) q^{61} +(-0.492569 + 0.413315i) q^{62} +(1.29160 - 7.32503i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-9.50377 + 3.45909i) q^{66} +(2.95249 - 1.07462i) q^{67} +(-3.80128 - 6.58401i) q^{68} +(-7.09463 + 12.2883i) q^{69} +(1.14572 - 0.961372i) q^{71} +(-2.16817 - 1.81931i) q^{72} +(0.900476 + 5.10685i) q^{73} +(8.30076 + 3.02123i) q^{74} +(4.12547 - 1.40730i) q^{76} +11.0073 q^{77} +(-7.10955 - 2.58766i) q^{78} +(0.0835983 + 0.474109i) q^{79} +(-7.26223 + 6.09374i) q^{81} +(-0.611926 + 3.47041i) q^{82} +(-5.16686 + 8.94927i) q^{83} +(3.17275 + 5.49536i) q^{84} +(3.04312 - 1.10761i) q^{86} +(-6.66666 - 11.5470i) q^{87} +(2.09427 - 3.62738i) q^{88} +(-2.65216 + 15.0411i) q^{89} +(6.30784 + 5.29291i) q^{91} +(-1.02043 - 5.78714i) q^{92} +(1.45897 + 0.531022i) q^{93} -7.60104 q^{94} +2.41461 q^{96} +(7.20537 + 2.62254i) q^{97} +(0.0162959 + 0.0924184i) q^{98} +(9.08148 + 7.62027i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) $ 30 * q - 12 * q^7 + 15 * q^8	$ 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) $ 30 * q - 12 * q^7 + 15 * q^8 + 6 * q^11 + 6 * q^14 - 30 * q^18 + 24 * q^19 + 24 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^26 - 18 * q^27 + 3 * q^28 + 12 * q^29 - 30 * q^33 + 24 * q^37 - 12 * q^38 - 24 * q^39 - 3 * q^41 + 12 * q^42 + 6 * q^43 - 3 * q^44 + 48 * q^47 + 15 * q^49 - 90 * q^51 - 18 * q^53 + 18 * q^54 - 24 * q^56 - 42 * q^57 + 36 * q^58 - 18 * q^59 - 60 * q^61 - 24 * q^62 - 21 * q^63 - 15 * q^64 - 78 * q^66 - 30 * q^67 - 12 * q^68 + 24 * q^69 + 30 * q^73 - 9 * q^74 - 3 * q^76 + 78 * q^77 - 6 * q^79 + 60 * q^81 + 3 * q^82 - 42 * q^83 - 6 * q^84 + 12 * q^86 - 54 * q^87 - 6 * q^88 - 30 * q^89 - 6 * q^91 - 6 * q^92 + 72 * q^93 - 78 * q^94 - 42 * q^97 + 6 * q^98 - 99 * 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
$3$	−0.419293	−	2.37793i	−0.242079	−	1.37290i	−0.827180	−	0.561937i	$-0.810056\pi$
$3$	−0.419293	−	2.37793i	−0.242079	−	1.37290i	0.585101	−	0.810960i	$-0.301055\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$		0			0
$5$		0			0
$6$	0.419293	−	2.37793i	0.171176	−	0.970785i
$7$	−1.31398	+	2.27588i	−0.496637	+	0.860201i	−0.999992	−	0.00387878i	$-0.998765\pi$
$7$	−1.31398	+	2.27588i	−0.496637	+	0.860201i	0.503355	+	0.864079i	$0.332099\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−2.65966	+	0.968036i	−0.886553	+	0.322679i
$10$		0			0
$11$	−2.09427	−	3.62738i	−0.631446	−	1.09370i	−0.987256	−	0.159139i	$-0.949128\pi$
$11$	−2.09427	−	3.62738i	−0.631446	−	1.09370i	0.355810	−	0.934558i	$-0.384205\pi$
$12$	1.20731	−	2.09111i	0.348519	−	0.603653i
$13$	0.544100	−	3.08575i	0.150906	−	0.855832i	−0.811527	−	0.584315i	$-0.801363\pi$
$13$	0.544100	−	3.08575i	0.150906	−	0.855832i	0.962434	−	0.271517i	$-0.0875255\pi$
$14$	−2.01313	+	1.68922i	−0.538032	+	0.451462i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−7.14407	−	2.60023i	−1.73269	−	0.630648i	−0.733875	−	0.679284i	$-0.762290\pi$
$17$	−7.14407	−	2.60023i	−1.73269	−	0.630648i	−0.998817	+	0.0486363i	$0.984512\pi$
$18$	−2.83035			−0.667120
$19$	2.25570	−	3.72986i	0.517493	−	0.855688i
$19$	2.25570	−	3.72986i	0.517493	−	0.855688i
$20$		0			0
$21$	5.96281	+	2.17029i	1.30119	+	0.473595i
$22$	−0.727333	−	4.12491i	−0.155068	−	0.879433i
$23$	−4.50159	−	3.77729i	−0.938647	−	0.787619i	0.0387022	−	0.999251i	$-0.487678\pi$
$23$	−4.50159	−	3.77729i	−0.938647	−	0.787619i	−0.977349	+	0.211632i	$0.932122\pi$
$24$	1.84970	−	1.55208i	0.377568	−	0.316817i
$25$		0			0
$26$	1.56667	−	2.71356i	0.307250	−	0.532173i
$27$	−0.204821	−	0.354760i	−0.0394178	−	0.0682737i
$28$	−2.46947	+	0.898814i	−0.466686	+	0.169860i
$29$	5.18892	−	1.88861i	0.963558	−	0.350707i	0.188131	−	0.982144i	$-0.439757\pi$
$29$	5.18892	−	1.88861i	0.963558	−	0.350707i	0.775427	+	0.631437i	$0.217535\pi$
$30$		0			0
$31$	−0.321502	+	0.556858i	−0.0577434	+	0.100015i	−0.893452	−	0.449158i	$-0.851724\pi$
$31$	−0.321502	+	0.556858i	−0.0577434	+	0.100015i	0.835709	+	0.549173i	$0.185057\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−7.74754	+	6.50096i	−1.34867	+	1.13167i
$34$	−5.82390	−	4.88683i	−0.998791	−	0.838085i
$35$		0			0
$36$	−2.65966	−	0.968036i	−0.443276	−	0.161339i
$37$	8.83349			1.45222			0.726108	−	0.687580i	$-0.241327\pi$
$37$	8.83349			1.45222			0.726108	+	0.687580i	$0.241327\pi$
$38$	3.39535	−	2.73342i	0.550798	−	0.443420i
$39$	−7.56582			−1.21150
$40$		0			0
$41$	0.611926	+	3.47041i	0.0955668	+	0.541986i	0.994572	+	0.104049i	$0.0331798\pi$
$41$	0.611926	+	3.47041i	0.0955668	+	0.541986i	−0.899005	+	0.437938i	$0.855709\pi$
$42$	4.86093	+	4.07881i	0.750058	+	0.629373i
$43$	2.48078	−	2.08162i	0.378315	−	0.317444i	−0.433726	−	0.901045i	$-0.642801\pi$
$43$	2.48078	−	2.08162i	0.378315	−	0.317444i	0.812040	+	0.583601i	$0.198357\pi$
$44$	0.727333	−	4.12491i	0.109650	−	0.621853i
$45$		0			0
$46$	−2.93821	−	5.08912i	−0.433215	−	0.750350i
$47$	−7.14264	+	2.59971i	−1.04186	+	0.379206i	−0.805585	−	0.592480i	$-0.798149\pi$
$47$	−7.14264	+	2.59971i	−1.04186	+	0.379206i	−0.236276	+	0.971686i	$0.575927\pi$
$48$	2.26899	−	0.825846i	0.327501	−	0.119201i
$49$	0.0469220	+	0.0812713i	0.00670315	+	0.0116102i
$50$		0			0
$51$	−3.18770	+	18.0783i	−0.446367	+	2.53147i
$52$	2.40028	−	2.01408i	0.332860	−	0.279302i
$53$	−4.83483	−	4.05691i	−0.664115	−	0.557259i	0.247202	−	0.968964i	$-0.420489\pi$
$53$	−4.83483	−	4.05691i	−0.664115	−	0.557259i	−0.911317	+	0.411705i	$0.864933\pi$
$54$	−0.0711336	−	0.403419i	−0.00968006	−	0.0548983i
$55$		0			0
$56$	−2.62796			−0.351175
$57$	−9.81513	−	3.79999i	−1.30005	−	0.503321i
$58$	5.52193			0.725065
$59$	3.20401	+	1.16616i	0.417127	+	0.151822i	0.542053	−	0.840344i	$-0.317647\pi$
$59$	3.20401	+	1.16616i	0.417127	+	0.151822i	−0.124926	+	0.992166i	$0.539869\pi$
$60$		0			0
$61$	−2.95060	−	2.47585i	−0.377786	−	0.317000i	0.434047	−	0.900890i	$-0.357085\pi$
$61$	−2.95060	−	2.47585i	−0.377786	−	0.317000i	−0.811832	+	0.583891i	$0.801530\pi$
$62$	−0.492569	+	0.413315i	−0.0625564	+	0.0524910i
$63$	1.29160	−	7.32503i	0.162726	−	0.922867i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	−9.50377	+	3.45909i	−1.16983	+	0.425784i
$67$	2.95249	−	1.07462i	0.360703	−	0.131285i	−0.155310	−	0.987866i	$-0.549638\pi$
$67$	2.95249	−	1.07462i	0.360703	−	0.131285i	0.516014	+	0.856580i	$0.327415\pi$
$68$	−3.80128	−	6.58401i	−0.460973	−	0.798429i
$69$	−7.09463	+	12.2883i	−0.854093	+	1.47933i
$70$		0			0
$71$	1.14572	−	0.961372i	0.135972	−	0.114094i	−0.572265	−	0.820069i	$-0.693935\pi$
$71$	1.14572	−	0.961372i	0.135972	−	0.114094i	0.708237	+	0.705975i	$0.249491\pi$
$72$	−2.16817	−	1.81931i	−0.255522	−	0.214408i
$73$	0.900476	+	5.10685i	0.105393	+	0.597712i	0.991063	+	0.133397i	$0.0425884\pi$
$73$	0.900476	+	5.10685i	0.105393	+	0.597712i	−0.885670	+	0.464315i	$0.846300\pi$
$74$	8.30076	+	3.02123i	0.964944	+	0.351211i
$75$		0			0
$76$	4.12547	−	1.40730i	0.473224	−	0.161428i
$77$	11.0073			1.25440
$78$	−7.10955	−	2.58766i	−0.804997	−	0.292995i
$79$	0.0835983	+	0.474109i	0.00940554	+	0.0533415i	0.989149	−	0.146914i	$-0.0469340\pi$
$79$	0.0835983	+	0.474109i	0.00940554	+	0.0533415i	−0.979744	+	0.200255i	$0.935823\pi$
$80$		0			0
$81$	−7.26223	+	6.09374i	−0.806915	+	0.677082i
$82$	−0.611926	+	3.47041i	−0.0675759	+	0.383242i
$83$	−5.16686	+	8.94927i	−0.567137	+	0.982310i	0.429711	+	0.902967i	$0.358616\pi$
$83$	−5.16686	+	8.94927i	−0.567137	+	0.982310i	−0.996847	+	0.0793430i	$0.974718\pi$
$84$	3.17275	+	5.49536i	0.346175	+	0.599593i
$85$		0			0
$86$	3.04312	−	1.10761i	0.328148	−	0.119436i
$87$	−6.66666	−	11.5470i	−0.714741	−	1.23797i
$88$	2.09427	−	3.62738i	0.223250	−	0.386680i
$89$	−2.65216	+	15.0411i	−0.281128	+	1.59436i	0.437669	+	0.899136i	$0.355804\pi$
$89$	−2.65216	+	15.0411i	−0.281128	+	1.59436i	−0.718797	+	0.695220i	$0.755307\pi$
$90$		0			0
$91$	6.30784	+	5.29291i	0.661242	+	0.554848i
$92$	−1.02043	−	5.78714i	−0.106387	−	0.603351i
$93$	1.45897	+	0.531022i	0.151288	+	0.0550644i
$94$	−7.60104			−0.783987
$95$		0			0
$96$	2.41461			0.246440
$97$	7.20537	+	2.62254i	0.731594	+	0.266278i	0.680839	−	0.732433i	$-0.261615\pi$
$97$	7.20537	+	2.62254i	0.731594	+	0.266278i	0.0507546	+	0.998711i	$0.483837\pi$
$98$	0.0162959	+	0.0924184i	0.00164613	+	0.00933566i
$99$	9.08148	+	7.62027i	0.912723	+	0.765866i
$100$		0			0
$101$	2.01961	−	11.4538i	0.200959	−	1.13970i	−0.702714	−	0.711472i	$-0.748029\pi$
$101$	2.01961	−	11.4538i	0.200959	−	1.13970i	0.903673	−	0.428223i	$-0.140860\pi$
$102$	−9.17862	+	15.8978i	−0.908818	+	1.57412i
$103$	−6.05517	−	10.4879i	−0.596634	−	1.03340i	−0.993314	−	0.115443i	$-0.963171\pi$
$103$	−6.05517	−	10.4879i	−0.596634	−	1.03340i	0.396680	−	0.917957i	$-0.370162\pi$
$104$	2.94438	−	1.07167i	0.288721	−	0.105086i
$105$		0			0
$106$	−3.15571	−	5.46586i	−0.306510	−	0.530891i
$107$	1.25896	−	2.18059i	0.121709	−	0.210805i	−0.798733	−	0.601686i	$-0.794496\pi$
$107$	1.25896	−	2.18059i	0.121709	−	0.210805i	0.920442	+	0.390880i	$0.127829\pi$
$108$	0.0711336	−	0.403419i	0.00684483	−	0.0388190i
$109$	8.09487	−	6.79241i	0.775348	−	0.650594i	−0.166724	−	0.986004i	$-0.553319\pi$
$109$	8.09487	−	6.79241i	0.775348	−	0.650594i	0.942073	+	0.335409i	$0.108875\pi$
$110$		0			0
$111$	−3.70382	−	21.0054i	−0.351551	−	1.99374i
$112$	−2.46947	−	0.898814i	−0.233343	−	0.0849299i
$113$	11.8896			1.11848			0.559240	−	0.829006i	$-0.311093\pi$
$113$	11.8896			1.11848			0.559240	+	0.829006i	$0.311093\pi$
$114$	−7.92353	−	6.92779i	−0.742107	−	0.648847i
$115$		0			0
$116$	5.18892	+	1.88861i	0.481779	+	0.175353i
$117$	1.53999	+	8.73374i	0.142372	+	0.807434i
$118$	2.61193	+	2.19167i	0.240448	+	0.201760i
$119$	15.3050	−	12.8424i	1.40300	−	1.17726i
$120$		0			0
$121$	−3.27194	+	5.66716i	−0.297449	+	0.515197i
$122$	−1.92587	−	3.33570i	−0.174360	−	0.302000i
$123$	7.99580	−	2.91023i	0.720957	−	0.262407i
$124$	−0.604226	+	0.219920i	−0.0542611	+	0.0197494i
$125$		0			0
$126$	3.71902	−	6.44153i	0.331316	−	0.573857i
$127$	0.988026	−	5.60337i	0.0876731	−	0.497219i	−0.909075	−	0.416633i	$-0.863210\pi$
$127$	0.988026	−	5.60337i	0.0876731	−	0.497219i	0.996748	−	0.0805855i	$-0.0256790\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	−5.99011	−	5.02630i	−0.527400	−	0.442541i
$130$		0			0
$131$	11.9076	+	4.33401i	1.04037	+	0.378665i	0.805021	−	0.593246i	$-0.202154\pi$
$131$	11.9076	+	4.33401i	1.04037	+	0.378665i	0.235351	+	0.971910i	$0.424376\pi$
$132$	−10.1137			−0.880285
$133$	5.52475	+	10.0346i	0.479057	+	0.870114i
$134$	3.14197			0.271425
$135$		0			0
$136$	−1.32017	−	7.48706i	−0.113204	−	0.642010i
$137$	9.71510	+	8.15193i	0.830017	+	0.696467i	0.955295	−	0.295655i	$-0.0955379\pi$
$137$	9.71510	+	8.15193i	0.830017	+	0.696467i	−0.125278	+	0.992122i	$0.539982\pi$
$138$	−10.8696	+	9.12068i	−0.925282	+	0.776404i
$139$	2.89061	−	16.3935i	0.245178	−	1.39047i	−0.574900	−	0.818224i	$-0.694959\pi$
$139$	2.89061	−	16.3935i	0.245178	−	1.39047i	0.820078	−	0.572251i	$-0.193930\pi$
$140$		0			0
$141$	9.17678	+	15.8946i	0.772824	+	1.33857i
$142$	1.40543	−	0.511535i	0.117941	−	0.0429271i
$143$	−12.3327	+	4.48873i	−1.03131	+	0.375366i
$144$	−1.41517	−	2.45115i	−0.117931	−	0.204263i
$145$		0			0
$146$	−0.900476	+	5.10685i	−0.0745239	+	0.422646i
$147$	0.173583	−	0.145654i	0.0143169	−	0.0120133i
$148$	6.76684	+	5.67806i	0.556231	+	0.466733i
$149$	2.81557	+	15.9679i	0.230661	+	1.30814i	0.851563	+	0.524253i	$0.175655\pi$
$149$	2.81557	+	15.9679i	0.230661	+	1.30814i	−0.620902	+	0.783888i	$0.713234\pi$
$150$		0			0
$151$	5.40405			0.439775			0.219888	−	0.975525i	$-0.429431\pi$
$151$	5.40405			0.439775			0.219888	+	0.975525i	$0.429431\pi$
$152$	4.35800	+	0.0885648i	0.353480	+	0.00718356i
$153$	21.5179			1.73962
$154$	10.3435	+	3.76472i	0.833502	+	0.303370i
$155$		0			0
$156$	−5.79575	−	4.86322i	−0.464032	−	0.389369i
$157$	1.11974	−	0.939575i	0.0893652	−	0.0749863i	−0.597011	−	0.802233i	$-0.703645\pi$
$157$	1.11974	−	0.939575i	0.0893652	−	0.0749863i	0.686376	+	0.727247i	$0.259201\pi$
$158$	−0.0835983	+	0.474109i	−0.00665072	+	0.0377181i
$159$	−7.61982	+	13.1979i	−0.604291	+	1.04666i
$160$		0			0
$161$	14.5116	−	5.28180i	1.14368	−	0.416264i
$162$	−8.90845	+	3.24241i	−0.699914	+	0.254748i
$163$	−3.20939	−	5.55882i	−0.251379	−	0.435401i	0.712527	−	0.701645i	$-0.247551\pi$
$163$	−3.20939	−	5.55882i	−0.251379	−	0.435401i	−0.963906	+	0.266244i	$0.914217\pi$
$164$	−1.76197	+	3.05182i	−0.137587	+	0.238307i
$165$		0			0
$166$	−7.91609	+	6.64239i	−0.614408	+	0.515549i
$167$	−2.51622	−	2.11136i	−0.194711	−	0.163382i	0.540220	−	0.841524i	$-0.318341\pi$
$167$	−2.51622	−	2.11136i	−0.194711	−	0.163382i	−0.734931	+	0.678142i	$0.762785\pi$
$168$	1.10188	+	6.24909i	0.0850122	+	0.482128i
$169$	2.99022	+	1.08835i	0.230017	+	0.0837193i
$170$		0			0
$171$	−2.38875	+	12.1037i	−0.182672	+	0.925596i
$172$	3.23842			0.246928
$173$	8.34198	+	3.03623i	0.634229	+	0.230840i	0.639071	−	0.769148i	$-0.279319\pi$
$173$	8.34198	+	3.03623i	0.634229	+	0.230840i	−0.00484204	+	0.999988i	$0.501541\pi$
$174$	−2.31531	−	13.1308i	−0.175523	−	0.995441i
$175$		0			0
$176$	3.20861	−	2.69234i	0.241858	−	0.202943i
$177$	1.42964	−	8.10787i	0.107458	−	0.609425i
$178$	−7.63658	+	13.2269i	−0.572386	+	0.991401i
$179$	−10.7539	−	18.6263i	−0.803786	−	1.39220i	−0.917108	−	0.398639i	$-0.869483\pi$
$179$	−10.7539	−	18.6263i	−0.803786	−	1.39220i	0.113322	−	0.993558i	$-0.463851\pi$
$180$		0			0
$181$	−5.36536	+	1.95283i	−0.398804	+	0.145153i	−0.533633	−	0.845716i	$-0.679174\pi$
$181$	−5.36536	+	1.95283i	−0.398804	+	0.145153i	0.134829	+	0.990869i	$0.456951\pi$
$182$	4.11715	+	7.13112i	0.305184	+	0.528594i
$183$	−4.65022	+	8.05442i	−0.343754	+	0.595400i
$184$	1.02043	−	5.78714i	0.0752270	−	0.426633i
$185$		0			0
$186$	1.18936	+	0.997995i	0.0872084	+	0.0731765i
$187$	5.52959	+	31.3599i	0.404364	+	2.29326i
$188$	−7.14264	−	2.59971i	−0.520930	−	0.189603i
$189$	1.07652			0.0783054
$190$		0			0
$191$	11.7437			0.849743			0.424872	−	0.905254i	$-0.360319\pi$
$191$	11.7437			0.849743			0.424872	+	0.905254i	$0.360319\pi$
$192$	2.26899	+	0.825846i	0.163750	+	0.0596003i
$193$	1.66874	+	9.46388i	0.120118	+	0.681225i	0.984088	+	0.177681i	$0.0568596\pi$
$193$	1.66874	+	9.46388i	0.120118	+	0.681225i	−0.863970	+	0.503544i	$0.832029\pi$
$194$	5.87387	+	4.92876i	0.421719	+	0.353864i
$195$		0			0
$196$	−0.0162959	+	0.0924184i	−0.00116399	+	0.00660131i
$197$	5.66035	−	9.80402i	0.403284	−	0.698508i	−0.590836	−	0.806791i	$-0.701202\pi$
$197$	5.66035	−	9.80402i	0.403284	−	0.698508i	0.994120	+	0.108284i	$0.0345355\pi$
$198$	5.92752	+	10.2668i	0.421250	+	0.729627i
$199$	12.9735	−	4.72197i	0.919667	−	0.334731i	0.161561	−	0.986863i	$-0.448347\pi$
$199$	12.9735	−	4.72197i	0.919667	−	0.334731i	0.758106	+	0.652131i	$0.226125\pi$
$200$		0			0
$201$	−3.79332	−	6.57022i	−0.267560	−	0.463427i
$202$	5.81525	−	10.0723i	0.409159	−	0.708685i
$203$	−2.51988	+	14.2909i	−0.176861	+	1.00303i
$204$	−14.0625	+	11.7998i	−0.984569	+	0.826151i
$205$		0			0
$206$	−2.10294	−	11.9264i	−0.146519	−	0.830949i
$207$	15.6292	+	5.68858i	1.08631	+	0.395384i
$208$	3.13335			0.217259
$209$	−18.2537	−	0.370958i	−1.26263	−	0.0256597i
$210$		0			0
$211$	0.911125	+	0.331623i	0.0627245	+	0.0228298i	0.373192	−	0.927754i	$-0.378263\pi$
$211$	0.911125	+	0.331623i	0.0627245	+	0.0228298i	−0.310467	+	0.950584i	$0.600486\pi$
$212$	−1.09597	−	6.21554i	−0.0752714	−	0.426885i
$213$	−2.76646	−	2.32134i	−0.189555	−	0.159056i
$214$	1.92884	−	1.61849i	0.131853	−	0.110638i
$215$		0			0
$216$	0.204821	−	0.354760i	0.0139363	−	0.0241384i
$217$	−0.844893	−	1.46340i	−0.0573551	−	0.0993419i
$218$	9.92983	−	3.61416i	0.672533	−	0.244782i
$219$	11.7662	−	4.28253i	0.795084	−	0.289387i
$220$		0			0
$221$	−11.9107	+	20.6300i	−0.801203	+	1.38772i
$222$	3.70382	−	21.0054i	0.248584	−	1.40979i
$223$	17.4098	−	14.6086i	1.16585	−	0.978262i	0.165878	−	0.986146i	$-0.446954\pi$
$223$	17.4098	−	14.6086i	1.16585	−	0.978262i	0.999969	+	0.00788479i	$0.00250983\pi$
$224$	−2.01313	−	1.68922i	−0.134508	−	0.112866i
$225$		0			0
$226$	11.1726	+	4.06648i	0.743188	+	0.270498i
$227$	−27.1606			−1.80271			−0.901356	−	0.433078i	$-0.857427\pi$
$227$	−27.1606			−1.80271			−0.901356	+	0.433078i	$0.857427\pi$
$228$	−5.07624	−	9.22000i	−0.336182	−	0.610610i
$229$	−29.6919			−1.96210			−0.981048	−	0.193764i	$-0.937931\pi$
$229$	−29.6919			−1.96210			−0.981048	+	0.193764i	$0.937931\pi$
$230$		0			0
$231$	−4.61528	−	26.1746i	−0.303663	−	1.72216i
$232$	4.23005	+	3.54943i	0.277716	+	0.233032i
$233$	9.46840	−	7.94493i	0.620296	−	0.520490i	−0.277601	−	0.960697i	$-0.589539\pi$
$233$	9.46840	−	7.94493i	0.620296	−	0.520490i	0.897897	+	0.440207i	$0.145095\pi$
$234$	−1.53999	+	8.73374i	−0.100673	+	0.570942i
$235$		0			0
$236$	1.70482	+	2.95283i	0.110974	+	0.192213i
$237$	1.09235	−	0.397581i	0.0709555	−	0.0258257i
$238$	18.7743	−	6.83329i	1.21696	−	0.442936i
$239$	−6.41730	−	11.1151i	−0.415101	−	0.718975i	0.580338	−	0.814375i	$-0.302920\pi$
$239$	−6.41730	−	11.1151i	−0.415101	−	0.718975i	−0.995439	+	0.0954000i	$0.969587\pi$
$240$		0			0
$241$	0.635063	−	3.60162i	0.0409080	−	0.232001i	−0.957498	−	0.288440i	$-0.906863\pi$
$241$	0.635063	−	3.60162i	0.0409080	−	0.232001i	0.998406	+	0.0564389i	$0.0179746\pi$
$242$	−5.01290	+	4.20632i	−0.322241	+	0.270393i
$243$	16.5941	+	13.9241i	1.06451	+	0.893229i
$244$	−0.668847	−	3.79322i	−0.0428185	−	0.242836i
$245$		0			0
$246$	8.50895			0.542511
$247$	−10.2821	−	8.98993i	−0.654232	−	0.572016i
$248$	−0.643004			−0.0408308
$249$	23.4471	+	8.53406i	1.48590	+	0.540824i
$250$		0			0
$251$	−19.6141	−	16.4582i	−1.23803	−	1.03883i	−0.997675	−	0.0681491i	$-0.978291\pi$
$251$	−19.6141	−	16.4582i	−1.23803	−	1.03883i	−0.240358	−	0.970684i	$-0.577265\pi$
$252$	5.69786	−	4.78108i	0.358932	−	0.301179i
$253$	−4.27411	+	24.2397i	−0.268711	+	1.52393i
$254$	2.84491	−	4.92752i	0.178505	−	0.309180i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−14.1074	+	5.13469i	−0.879998	+	0.320293i	−0.742209	−	0.670169i	$-0.766222\pi$
$257$	−14.1074	+	5.13469i	−0.879998	+	0.320293i	−0.137789	+	0.990462i	$0.544000\pi$
$258$	−3.90977	−	6.77192i	−0.243412	−	0.421601i
$259$	−11.6070	+	20.1039i	−0.721225	+	1.24920i
$260$		0			0
$261$	−11.9725	+	10.0461i	−0.741080	+	0.621840i
$262$	9.70717	+	8.14528i	0.599711	+	0.503217i
$263$	−0.572564	−	3.24717i	−0.0353058	−	0.200229i	0.962053	−	0.272863i	$-0.0879706\pi$
$263$	−0.572564	−	3.24717i	−0.0353058	−	0.200229i	−0.997359	+	0.0726339i	$0.976860\pi$
$264$	−9.50377	−	3.45909i	−0.584917	−	0.212892i
$265$		0			0
$266$	1.75952	+	11.3191i	0.107883	+	0.694016i
$267$	36.8788			2.25694
$268$	2.95249	+	1.07462i	0.180352	+	0.0656427i
$269$	−4.78685	−	27.1476i	−0.291859	−	1.65522i	−0.679700	−	0.733490i	$-0.737890\pi$
$269$	−4.78685	−	27.1476i	−0.291859	−	1.65522i	0.387841	−	0.921726i	$-0.373221\pi$
$270$		0			0
$271$	−7.98760	+	6.70239i	−0.485212	+	0.407141i	−0.852307	−	0.523042i	$-0.824797\pi$
$271$	−7.98760	+	6.70239i	−0.485212	+	0.407141i	0.367095	+	0.930184i	$0.380352\pi$
$272$	1.32017	−	7.48706i	0.0800471	−	0.453970i
$273$	9.94132	−	17.2189i	0.601676	−	1.04213i
$274$	6.34108	+	10.9831i	0.383079	+	0.663512i
$275$		0			0
$276$	−13.3335	+	4.85301i	−0.802585	+	0.292117i
$277$	6.73535	+	11.6660i	0.404688	+	0.700940i	0.994285	−	0.106758i	$-0.0340469\pi$
$277$	6.73535	+	11.6660i	0.404688	+	0.700940i	−0.589597	+	0.807697i	$0.700714\pi$
$278$	8.32318	−	14.4162i	0.499191	−	0.864624i
$279$	0.316027	−	1.79228i	0.0189200	−	0.107301i
$280$		0			0
$281$	−5.51826	−	4.63037i	−0.329192	−	0.276225i	0.463179	−	0.886265i	$-0.346709\pi$
$281$	−5.51826	−	4.63037i	−0.329192	−	0.276225i	−0.792370	+	0.610040i	$0.791153\pi$
$282$	3.18706	+	18.0747i	0.189787	+	1.07633i
$283$	15.0119	+	5.46388i	0.892363	+	0.324794i	0.747188	−	0.664612i	$-0.231403\pi$
$283$	15.0119	+	5.46388i	0.892363	+	0.324794i	0.145175	+	0.989406i	$0.453626\pi$
$284$	1.49563			0.0887492
$285$		0			0
$286$	−13.1242			−0.776048
$287$	−8.70227	−	3.16737i	−0.513679	−	0.186964i
$288$	−0.491485	−	2.78735i	−0.0289610	−	0.164246i
$289$	31.2538	+	26.2251i	1.83846	+	1.54265i
$290$		0			0
$291$	3.21505	−	18.2335i	0.188470	−	1.06886i
$292$	−2.59282	+	4.49089i	−0.151733	+	0.262809i
$293$	−13.5727	−	23.5086i	−0.792927	−	1.37339i	−0.924147	−	0.382036i	$-0.875223\pi$
$293$	−13.5727	−	23.5086i	−0.792927	−	1.37339i	0.131220	−	0.991353i	$-0.458110\pi$
$294$	0.212931	−	0.0775007i	0.0124184	−	0.00451993i
$295$		0			0
$296$	4.41674	+	7.65002i	0.256718	+	0.444649i
$297$	−0.857901	+	1.48593i	−0.0497805	+	0.0862223i
$298$	−2.81557	+	15.9679i	−0.163102	+	0.924995i
$299$	−14.1051	+	11.8356i	−0.815717	+	0.684468i
$300$		0			0
$301$	1.47782	+	8.38115i	0.0851803	+	0.483081i
$302$	5.07815	+	1.84829i	0.292214	+	0.106357i
$303$	−28.0831			−1.61333
$304$	4.06489	+	1.57375i	0.233137	+	0.0902606i
$305$		0			0
$306$	20.2202	+	7.35955i	1.15591	+	0.420718i
$307$	5.18541	+	29.4079i	0.295947	+	1.67840i	0.663329	+	0.748328i	$0.269143\pi$
$307$	5.18541	+	29.4079i	0.295947	+	1.67840i	−0.367382	+	0.930070i	$0.619746\pi$
$308$	8.43208	+	7.07536i	0.480463	+	0.403156i
$309$	−22.4005	+	18.7963i	−1.27432	+	1.06928i
$310$		0			0
$311$	−4.62942	+	8.01840i	−0.262511	+	0.454682i	−0.966908	−	0.255124i	$-0.917884\pi$
$311$	−4.62942	+	8.01840i	−0.262511	+	0.454682i	0.704398	+	0.709805i	$0.251217\pi$
$312$	−3.78291	−	6.55219i	−0.214165	−	0.370945i
$313$	−3.80836	+	1.38613i	−0.215261	+	0.0783486i	−0.447400	−	0.894334i	$-0.647650\pi$
$313$	−3.80836	+	1.38613i	−0.215261	+	0.0783486i	0.232139	+	0.972683i	$0.425428\pi$
$314$	1.37357	−	0.499938i	0.0775149	−	0.0282131i
$315$		0			0
$316$	−0.240712	+	0.416925i	−0.0135411	+	0.0234539i
$317$	−2.66460	+	15.1117i	−0.149659	+	0.848759i	0.813848	+	0.581077i	$0.197369\pi$
$317$	−2.66460	+	15.1117i	−0.149659	+	0.848759i	−0.963507	+	0.267682i	$0.913742\pi$
$318$	−11.6742	+	9.79585i	−0.654659	+	0.549324i
$319$	−17.7177	−	14.8669i	−0.992002	−	0.832389i
$320$		0			0
$321$	−5.71316	−	2.07942i	−0.318877	−	0.116062i
$322$	15.4430			0.860602
$323$	−25.8134	+	20.7810i	−1.43629	+	1.15629i
$324$	−9.48017			−0.526676
$325$		0			0
$326$	−1.11461	−	6.32126i	−0.0617325	−	0.350102i
$327$	−19.5460	−	16.4010i	−1.08089	−	0.906979i
$328$	−2.69950	+	2.26515i	−0.149055	+	0.125072i
$329$	3.46866	−	19.6717i	0.191233	−	1.08454i
$330$		0			0
$331$	−15.4633	−	26.7832i	−0.849941	−	1.47214i	−0.881260	−	0.472631i	$-0.843304\pi$
$331$	−15.4633	−	26.7832i	−0.849941	−	1.47214i	0.0313199	−	0.999509i	$-0.490029\pi$
$332$	−9.71052	+	3.53434i	−0.532934	+	0.193972i
$333$	−23.4941	+	8.55114i	−1.28747	+	0.468599i
$334$	−1.64234	−	2.84462i	−0.0898650	−	0.155651i
$335$		0			0
$336$	−1.10188	+	6.24909i	−0.0601127	+	0.340916i
$337$	−8.69365	+	7.29484i	−0.473573	+	0.397375i	−0.848096	−	0.529843i	$-0.822251\pi$
$337$	−8.69365	+	7.29484i	−0.473573	+	0.397375i	0.374523	+	0.927218i	$0.377807\pi$
$338$	2.43765	+	2.04543i	0.132591	+	0.111257i
$339$	−4.98523	−	28.2726i	−0.270760	−	1.53556i
$340$		0			0
$341$	2.69325			0.145848
$342$	−6.38441	+	10.5568i	−0.345230	+	0.570846i
$343$	−18.6423			−1.00659
$344$	3.04312	+	1.10761i	0.164074	+	0.0597181i
$345$		0			0
$346$	6.80044	+	5.70625i	0.365594	+	0.306770i
$347$	7.01695	−	5.88792i	0.376690	−	0.316080i	−0.434712	−	0.900570i	$-0.643150\pi$
$347$	7.01695	−	5.88792i	0.376690	−	0.316080i	0.811401	+	0.584490i	$0.198705\pi$
$348$	2.31531	−	13.1308i	0.124114	−	0.703883i
$349$	−10.8033	+	18.7119i	−0.578290	+	1.00163i	0.417386	+	0.908729i	$0.362946\pi$
$349$	−10.8033	+	18.7119i	−0.578290	+	1.00163i	−0.995676	+	0.0928978i	$0.970387\pi$
$350$		0			0
$351$	−1.20614	+	0.439000i	−0.0643792	+	0.0234321i
$352$	3.93594	−	1.43257i	0.209786	−	0.0763560i
$353$	10.8892	+	18.8607i	0.579576	+	1.00385i	0.995528	+	0.0944680i	$0.0301150\pi$
$353$	10.8892	+	18.8607i	0.579576	+	1.00385i	−0.415952	+	0.909386i	$0.636552\pi$
$354$	4.11647	−	7.12994i	0.218788	−	0.378952i
$355$		0			0
$356$	−11.6999	+	9.81740i	−0.620095	+	0.520321i
$357$	−36.9555	−	31.0094i	−1.95589	−	1.64119i
$358$	−3.73480	−	21.1811i	−0.197390	−	1.11946i
$359$	16.6127	+	6.04653i	0.876785	+	0.319124i	0.740912	−	0.671602i	$-0.234394\pi$
$359$	16.6127	+	6.04653i	0.876785	+	0.319124i	0.135874	+	0.990726i	$0.456616\pi$
$360$		0			0
$361$	−8.82364	−	16.8269i	−0.464402	−	0.885624i
$362$	−5.70969			−0.300095
$363$	14.8480	+	5.40423i	0.779318	+	0.283649i
$364$	1.42987	+	8.10921i	0.0749457	+	0.425038i
$365$		0			0
$366$	−7.12455	+	5.97821i	−0.372406	+	0.312486i
$367$	3.87570	−	21.9802i	0.202310	−	1.14736i	−0.699307	−	0.714822i	$-0.746508\pi$
$367$	3.87570	−	21.9802i	0.202310	−	1.14736i	0.901617	−	0.432536i	$-0.142381\pi$
$368$	2.93821	−	5.08912i	0.153165	−	0.265289i
$369$	−4.98699	−	8.63772i	−0.259612	−	0.449662i
$370$		0			0
$371$	15.5859	−	5.67280i	0.809179	−	0.294517i
$372$	0.776302	+	1.34459i	0.0402494	+	0.0697140i
$373$	6.84812	−	11.8613i	0.354582	−	0.614154i	−0.632464	−	0.774590i	$-0.717956\pi$
$373$	6.84812	−	11.8613i	0.354582	−	0.614154i	0.987046	+	0.160435i	$0.0512898\pi$
$374$	−5.52959	+	31.3599i	−0.285928	+	1.62158i
$375$		0			0
$376$	−5.82273	−	4.88585i	−0.300285	−	0.251969i
$377$	−3.00449	−	17.0393i	−0.154739	−	0.877568i
$378$	1.01160	+	0.368192i	0.0520311	+	0.0189378i
$379$	−1.22701			−0.0630273			−0.0315136	−	0.999503i	$-0.510033\pi$
$379$	−1.22701			−0.0630273			−0.0315136	+	0.999503i	$0.510033\pi$
$380$		0			0
$381$	−13.7387			−0.703854
$382$	11.0355	+	4.01658i	0.564623	+	0.205506i
$383$	3.38041	+	19.1713i	0.172731	+	0.979606i	0.940730	+	0.339156i	$0.110141\pi$
$383$	3.38041	+	19.1713i	0.172731	+	0.979606i	−0.767999	+	0.640451i	$0.778748\pi$
$384$	1.84970	+	1.55208i	0.0943921	+	0.0792044i
$385$		0			0
$386$	−1.66874	+	9.46388i	−0.0849365	+	0.481699i
$387$	−4.58294	+	7.93788i	−0.232964	+	0.403505i
$388$	3.83389	+	6.64050i	0.194637	+	0.337120i
$389$	19.2716	−	7.01431i	0.977111	−	0.355639i	0.196395	−	0.980525i	$-0.437077\pi$
$389$	19.2716	−	7.01431i	0.977111	−	0.355639i	0.780716	+	0.624885i	$0.214854\pi$
$390$		0			0
$391$	22.3379	+	38.6904i	1.12968	+	1.95666i
$392$	−0.0469220	+	0.0812713i	−0.00236992	+	0.00410482i
$393$	5.31320	−	30.1327i	0.268015	−	1.51999i
$394$	8.67217	−	7.27681i	0.436897	−	0.366600i
$395$		0			0
$396$	2.05860	+	11.6749i	0.103449	+	0.586687i
$397$	26.0078	+	9.46605i	1.30529	+	0.475088i	0.898717	−	0.438530i	$-0.144501\pi$
$397$	26.0078	+	9.46605i	1.30529	+	0.475088i	0.406576	+	0.913617i	$0.366723\pi$
$398$	13.8061			0.692037
$399$	21.5452	−	17.3449i	1.07861	−	0.868332i
$400$		0			0
$401$	21.7646	+	7.92166i	1.08687	+	0.395589i	0.822461	−	0.568822i	$-0.192601\pi$
$401$	21.7646	+	7.92166i	1.08687	+	0.395589i	0.264410	+	0.964410i	$0.414823\pi$
$402$	−1.31741	−	7.47138i	−0.0657062	−	0.372638i
$403$	1.54339	+	1.29506i	0.0768818	+	0.0645115i
$404$	8.90947	−	7.47594i	0.443263	−	0.371942i
$405$		0			0
$406$	−7.25570	+	12.5672i	−0.360094	+	0.623702i
$407$	−18.4997	−	32.0424i	−0.916997	−	1.58828i
$408$	−17.2502	+	6.27854i	−0.854010	+	0.310834i
$409$	−6.92206	+	2.51942i	−0.342274	+	0.124577i	−0.507437	−	0.861689i	$-0.669407\pi$
$409$	−6.92206	+	2.51942i	−0.342274	+	0.124577i	0.165163	+	0.986266i	$0.447185\pi$
$410$		0			0
$411$	15.3112	−	26.5198i	0.755248	−	1.30813i
$412$	2.10294	−	11.9264i	0.103604	−	0.587570i
$413$	−6.86405	+	5.75962i	−0.337758	+	0.283412i
$414$	12.7411	+	10.6910i	0.626190	+	0.525436i
$415$		0			0
$416$	2.94438	+	1.07167i	0.144360	+	0.0525429i
$417$	−40.1945			−1.96833
$418$	−17.0260	−	6.59171i	−0.832767	−	0.322411i
$419$	−3.84884			−0.188028			−0.0940141	−	0.995571i	$-0.529970\pi$
$419$	−3.84884			−0.188028			−0.0940141	+	0.995571i	$0.529970\pi$
$420$		0			0
$421$	−0.211425	−	1.19905i	−0.0103042	−	0.0584382i	0.979222	−	0.202791i	$-0.0650011\pi$
$421$	−0.211425	−	1.19905i	−0.0103042	−	0.0584382i	−0.989526	+	0.144353i	$0.953890\pi$
$422$	0.742756	+	0.623246i	0.0361568	+	0.0303392i
$423$	16.4804	−	13.8287i	0.801303	−	0.672373i
$424$	1.09597	−	6.21554i	0.0532249	−	0.301853i
$425$		0			0
$426$	−1.80568	−	3.12753i	−0.0874855	−	0.151529i
$427$	9.51175	−	3.46199i	0.460306	−	0.167538i
$428$	2.36608	−	0.861181i	0.114369	−	0.0416268i
$429$	15.8449	+	27.4441i	0.764998	+	1.32501i
$430$		0			0
$431$	−4.08214	+	23.1510i	−0.196630	+	1.11514i	0.713449	+	0.700708i	$0.247132\pi$
$431$	−4.08214	+	23.1510i	−0.196630	+	1.11514i	−0.910079	+	0.414436i	$0.863979\pi$
$432$	0.313804	−	0.263313i	0.0150979	−	0.0126686i
$433$	−11.3412	−	9.51639i	−0.545023	−	0.457328i	0.328229	−	0.944598i	$-0.393548\pi$
$433$	−11.3412	−	9.51639i	−0.545023	−	0.457328i	−0.873251	+	0.487270i	$0.837993\pi$
$434$	−0.293428	−	1.66411i	−0.0140850	−	0.0798800i
$435$		0			0
$436$	10.5671			0.506073
$437$	−24.2430	+	8.26988i	−1.15970	+	0.395602i
$438$	12.5213			0.598290
$439$	18.3446	+	6.67691i	0.875542	+	0.318671i	0.740409	−	0.672156i	$-0.234632\pi$
$439$	18.3446	+	6.67691i	0.875542	+	0.318671i	0.135133	+	0.990827i	$0.456854\pi$
$440$		0			0
$441$	−0.203470	−	0.170732i	−0.00968905	−	0.00813008i
$442$	−18.2483	+	15.3121i	−0.867984	+	0.728325i
$443$	2.53648	−	14.3851i	0.120512	−	0.683457i	−0.863361	−	0.504587i	$-0.831645\pi$
$443$	2.53648	−	14.3851i	0.120512	−	0.683457i	0.983873	−	0.178870i	$-0.0572441\pi$
$444$	10.6647	−	18.4718i	0.506125	−	0.876635i
$445$		0			0
$446$	21.3563	−	7.77305i	1.01125	−	0.368065i
$447$	36.7900	−	13.3904i	1.74010	−	0.633346i
$448$	−1.31398	−	2.27588i	−0.0620796	−	0.107525i
$449$	3.23511	−	5.60337i	0.152674	−	0.264439i	−0.779536	−	0.626358i	$-0.784545\pi$
$449$	3.23511	−	5.60337i	0.152674	−	0.264439i	0.932210	+	0.361919i	$0.117878\pi$
$450$		0			0
$451$	11.3069	−	9.48766i	0.532423	−	0.446756i
$452$	9.10796	+	7.64249i	0.428403	+	0.359472i
$453$	−2.26588	−	12.8504i	−0.106460	−	0.603767i
$454$	−25.5226	−	9.28947i	−1.19784	−	0.435977i
$455$		0			0
$456$	−1.61668	−	10.4001i	−0.0757078	−	0.487031i
$457$	21.2793			0.995402			0.497701	−	0.867349i	$-0.334178\pi$
$457$	21.2793			0.995402			0.497701	+	0.867349i	$0.334178\pi$
$458$	−27.9013	−	10.1552i	−1.30374	−	0.474523i
$459$	0.540798	+	3.06702i	0.0252423	+	0.143156i
$460$		0			0
$461$	12.3861	−	10.3932i	0.576880	−	0.484060i	−0.307041	−	0.951696i	$-0.599339\pi$
$461$	12.3861	−	10.3932i	0.576880	−	0.484060i	0.883921	+	0.467636i	$0.154894\pi$
$462$	4.61528	−	26.1746i	0.214722	−	1.21775i
$463$	4.72305	−	8.18056i	0.219499	−	0.380183i	−0.735156	−	0.677898i	$-0.762891\pi$
$463$	4.72305	−	8.18056i	0.219499	−	0.380183i	0.954655	+	0.297715i	$0.0962245\pi$
$464$	2.76097	+	4.78214i	0.128175	+	0.222005i
$465$		0			0
$466$	11.6147	−	4.22741i	0.538041	−	0.195831i
$467$	10.4497	+	18.0994i	0.483554	+	0.837541i	0.999822	−	0.0188868i	$-0.00601221\pi$
$467$	10.4497	+	18.0994i	0.483554	+	0.837541i	−0.516267	+	0.856428i	$0.672679\pi$
$468$	−4.43423	+	7.68032i	−0.204973	+	0.355023i
$469$	−1.43381	+	8.13152i	−0.0662070	+	0.375479i
$470$		0			0
$471$	−2.70374	−	2.26871i	−0.124582	−	0.104537i
$472$	0.592077	+	3.35784i	0.0272526	+	0.154557i
$473$	−12.7462	−	4.63926i	−0.586073	−	0.213313i
$474$	1.16245			0.0533931
$475$		0			0
$476$	19.9792			0.915745
$477$	16.7862	+	6.10969i	0.768589	+	0.279743i
$478$	−2.22870	−	12.6396i	−0.101939	−	0.578122i
$479$	−28.4241	−	23.8506i	−1.29873	−	1.08976i	−0.990363	−	0.138494i	$-0.955774\pi$
$479$	−28.4241	−	23.8506i	−1.29873	−	1.08976i	−0.308365	−	0.951268i	$-0.599782\pi$
$480$		0			0
$481$	4.80630	−	27.2579i	0.219149	−	1.24285i
$482$	1.82859	−	3.16721i	0.0832901	−	0.144263i
$483$	−18.6444	−	32.2930i	−0.848348	−	1.46938i
$484$	−6.14923	+	2.23814i	−0.279511	+	0.101734i
$485$		0			0
$486$	10.8310	+	18.7598i	0.491304	+	0.850964i
$487$	−2.37539	+	4.11429i	−0.107639	+	0.186436i	−0.914813	−	0.403877i	$-0.867662\pi$
$487$	−2.37539	+	4.11429i	−0.107639	+	0.186436i	0.807174	+	0.590313i	$0.200996\pi$
$488$	0.668847	−	3.79322i	0.0302773	−	0.171711i
$489$	−11.8728	+	9.96247i	−0.536907	+	0.450518i
$490$		0			0
$491$	−0.423756	−	2.40324i	−0.0191239	−	0.108457i	0.973752	−	0.227613i	$-0.0730921\pi$
$491$	−0.423756	−	2.40324i	−0.0191239	−	0.108457i	−0.992876	+	0.119156i	$0.961981\pi$
$492$	7.99580	+	2.91023i	0.360478	+	0.131203i
$493$	−41.9808			−1.89072
$494$	−6.58724	−	11.9644i	−0.296374	−	0.538306i
$495$		0			0
$496$	−0.604226	−	0.219920i	−0.0271305	−	0.00987471i
$497$	0.682515	+	3.87073i	0.0306150	+	0.173626i
$498$	19.1143	+	16.0388i	0.856532	+	0.718715i
$499$	16.8213	−	14.1147i	0.753024	−	0.631863i	−0.183276	−	0.983061i	$-0.558670\pi$
$499$	16.8213	−	14.1147i	0.753024	−	0.631863i	0.936301	+	0.351199i	$0.114226\pi$
$500$		0			0
$501$	−3.96562	+	6.86866i	−0.177171	+	0.306869i
$502$	−12.8022	−	22.1741i	−0.571391	−	0.989678i
$503$	2.78331	−	1.01304i	0.124102	−	0.0451693i	−0.279223	−	0.960226i	$-0.590077\pi$
$503$	2.78331	−	1.01304i	0.124102	−	0.0451693i	0.403324	+	0.915057i	$0.367855\pi$
$504$	6.98947	−	2.54396i	0.311336	−	0.113317i
$505$		0			0
$506$	−12.3068	+	21.3160i	−0.547104	+	0.947612i
$507$	1.33424	−	7.56687i	0.0592558	−	0.336056i
$508$	4.35865	−	3.65734i	0.193384	−	0.162268i
$509$	19.2998	+	16.1945i	0.855450	+	0.717808i	0.960983	−	0.276608i	$-0.0892102\pi$
$509$	19.2998	+	16.1945i	0.855450	+	0.717808i	−0.105532	+	0.994416i	$0.533655\pi$
$510$		0			0
$511$	−12.8058	−	4.66092i	−0.566494	−	0.206187i
$512$	−1.00000			−0.0441942
$513$	−1.78522	−	0.0362799i	−0.0788194	−	0.00160180i
$514$	−15.0128			−0.662187
$515$		0			0
$516$	−1.35785	−	7.70074i	−0.0597759	−	0.339006i
$517$	24.3888	+	20.4646i	1.07262	+	0.900032i
$518$	−17.7830	+	14.9217i	−0.781339	+	0.655621i
$519$	3.72221	−	21.1097i	0.163387	−	0.926613i
$520$		0			0
$521$	−10.9008	−	18.8808i	−0.477574	−	0.827182i	0.522096	−	0.852887i	$-0.325150\pi$
$521$	−10.9008	−	18.8808i	−0.477574	−	0.827182i	−0.999670	+	0.0257045i	$0.991817\pi$
$522$	−14.6865	+	5.34543i	−0.642809	+	0.233963i
$523$	20.6027	−	7.49878i	0.900895	−	0.327899i	0.150283	−	0.988643i	$-0.451981\pi$
$523$	20.6027	−	7.49878i	0.900895	−	0.327899i	0.750611	+	0.660744i	$0.229759\pi$
$524$	6.33591	+	10.9741i	0.276785	+	0.479406i
$525$		0			0
$526$	0.572564	−	3.24717i	0.0249650	−	0.141583i
$527$	3.74479	−	3.14225i	0.163126	−	0.136879i
$528$	−7.74754	−	6.50096i	−0.337169	−	0.282918i
$529$	2.00255	+	11.3570i	0.0870675	+	0.493784i
$530$		0			0
$531$	−9.65046			−0.418794
$532$	−2.21794	+	11.2382i	−0.0961598	+	0.487239i
$533$	11.0417			0.478271
$534$	34.6547	+	12.6133i	1.49966	+	0.545830i
$535$		0			0
$536$	2.40689	+	2.01962i	0.103962	+	0.0872342i
$537$	−39.7830	+	33.3819i	−1.71676	+	1.44054i
$538$	4.78685	−	27.1476i	0.206376	−	1.17041i
$539$	0.196535	−	0.340408i	0.00846536	−	0.0146624i
$540$		0			0
$541$	−29.0124	+	10.5597i	−1.24734	+	0.453995i	−0.879503	−	0.475894i	$-0.842125\pi$
$541$	−29.0124	+	10.5597i	−1.24734	+	0.453995i	−0.367839	+	0.929889i	$0.619902\pi$
$542$	−9.79824	+	3.56627i	−0.420870	+	0.153184i
$543$	6.89334	+	11.9396i	0.295822	+	0.512378i
$544$	3.80128	−	6.58401i	0.162979	−	0.282287i
$545$		0			0
$546$	15.2310	−	12.7803i	0.651826	−	0.546947i
$547$	23.7195	+	19.9030i	1.01417	+	0.850991i	0.988884	−	0.148689i	$-0.0475055\pi$
$547$	23.7195	+	19.9030i	1.01417	+	0.850991i	0.0252874	+	0.999680i	$0.491950\pi$
$548$	2.20223	+	12.4895i	0.0940748	+	0.533524i
$549$	10.2443	+	3.72862i	0.437216	+	0.159134i
$550$		0			0
$551$	4.66039	−	23.6141i	0.198539	−	1.00599i
$552$	−14.1893			−0.603935
$553$	−1.18886	−	0.432710i	−0.0505555	−	0.0184007i
$554$	2.33916	+	13.2660i	0.0993814	+	0.563620i
$555$		0			0
$556$	12.7518	−	10.7001i	0.540799	−	0.453784i
$557$	2.39170	−	13.5640i	0.101339	−	0.574725i	−0.891280	−	0.453454i	$-0.850192\pi$
$557$	2.39170	−	13.5640i	0.101339	−	0.574725i	0.992619	−	0.121271i	$-0.0386971\pi$
$558$	0.909962	−	1.57610i	0.0385218	−	0.0667217i
$559$	−5.07356	−	8.78766i	−0.214589	−	0.371678i
$560$		0			0
$561$	72.2530	−	26.2979i	3.05052	−	1.11030i
$562$	−3.60179	−	6.23848i	−0.151932	−	0.263154i
$563$	12.7232	−	22.0372i	0.536219	−	0.928759i	−0.462884	−	0.886419i	$-0.653185\pi$
$563$	12.7232	−	22.0372i	0.536219	−	0.928759i	0.999103	−	0.0423402i	$-0.0134813\pi$
$564$	−3.18706	+	18.0747i	−0.134199	+	0.761083i
$565$		0			0
$566$	12.2378	+	10.2687i	0.514393	+	0.431627i
$567$	−4.32618	−	24.5350i	−0.181683	−	1.03037i
$568$	1.40543	+	0.511535i	0.0589706	+	0.0214635i
$569$	−7.29395			−0.305778			−0.152889	−	0.988243i	$-0.548858\pi$
$569$	−7.29395			−0.305778			−0.152889	+	0.988243i	$0.548858\pi$
$570$		0			0
$571$	−14.9184			−0.624317			−0.312159	−	0.950030i	$-0.601052\pi$
$571$	−14.9184			−0.624317			−0.312159	+	0.950030i	$0.601052\pi$
$572$	−12.3327	−	4.48873i	−0.515655	−	0.187683i
$573$	−4.92404	−	27.9256i	−0.205705	−	1.16661i
$574$	−7.09416	−	5.95271i	−0.296104	−	0.248461i
$575$		0			0
$576$	0.491485	−	2.78735i	0.0204785	−	0.116140i
$577$	6.40570	−	11.0950i	0.266673	−	0.461891i	−0.701328	−	0.712839i	$-0.747409\pi$
$577$	6.40570	−	11.0950i	0.266673	−	0.461891i	0.968001	+	0.250948i	$0.0807424\pi$
$578$	20.3995	+	35.3329i	0.848506	+	1.46966i
$579$	21.8047	−	7.93627i	0.906174	−	0.329820i
$580$		0			0
$581$	−13.5783	−	23.5183i	−0.563322	−	0.975703i
$582$	9.25737	−	16.0342i	0.383730	−	0.664640i
$583$	−4.59051	+	26.0341i	−0.190119	+	1.07822i
$584$	−3.97243	+	3.33326i	−0.164380	+	0.137931i
$585$		0			0
$586$	−4.71376	−	26.7330i	−0.194723	−	1.10433i
$587$	−29.2853	−	10.6590i	−1.20873	−	0.439943i	−0.342470	−	0.939529i	$-0.611264\pi$
$587$	−29.2853	−	10.6590i	−1.20873	−	0.439943i	−0.866265	+	0.499585i	$0.833486\pi$
$588$	0.226597			0.00934470
$589$	1.35179	+	2.45526i	0.0556994	+	0.101167i
$590$		0			0
$591$	−25.6866	−	9.34916i	−1.05661	−	0.384573i
$592$	1.53392	+	8.69929i	0.0630437	+	0.357538i
$593$	−12.1181	−	10.1683i	−0.497631	−	0.417562i	0.359121	−	0.933291i	$-0.383077\pi$
$593$	−12.1181	−	10.1683i	−0.497631	−	0.417562i	−0.856752	+	0.515729i	$0.827521\pi$
$594$	−1.31438	+	1.10290i	−0.0539297	+	0.0452524i
$595$		0			0
$596$	−8.10711	+	14.0419i	−0.332080	+	0.575180i
$597$	−16.6682	−	28.8701i	−0.682184	−	1.18158i
$598$	−17.3024	+	6.29757i	−0.707549	+	0.257527i
$599$	−22.5757	+	8.21689i	−0.922418	+	0.335733i	−0.759200	−	0.650857i	$-0.774410\pi$
$599$	−22.5757	+	8.21689i	−0.922418	+	0.335733i	−0.163218	+	0.986590i	$0.552187\pi$
$600$		0			0
$601$	−7.19170	+	12.4564i	−0.293356	+	0.508107i	−0.974601	−	0.223948i	$-0.928105\pi$
$601$	−7.19170	+	12.4564i	−0.293356	+	0.508107i	0.681245	+	0.732055i	$0.261439\pi$
$602$	−1.47782	+	8.38115i	−0.0602315	+	0.341590i
$603$	−6.81233	+	5.71623i	−0.277420	+	0.232783i
$604$	4.13974	+	3.47366i	0.168444	+	0.141341i
$605$		0			0
$606$	−26.3895	−	9.60499i	−1.07200	−	0.390176i
$607$	−1.60889			−0.0653027			−0.0326513	−	0.999467i	$-0.510395\pi$
$607$	−1.60889			−0.0653027			−0.0326513	+	0.999467i	$0.510395\pi$
$608$	3.28149	+	2.86911i	0.133082	+	0.116358i
$609$	35.0394			1.41987
$610$		0			0
$611$	4.13573	+	23.4549i	0.167314	+	0.948883i
$612$	16.4837	+	13.8314i	0.666313	+	0.559103i
$613$	−12.9632	+	10.8774i	−0.523578	+	0.439334i	−0.865877	−	0.500257i	$-0.833239\pi$
$613$	−12.9632	+	10.8774i	−0.523578	+	0.439334i	0.342299	+	0.939591i	$0.388794\pi$
$614$	−5.18541	+	29.4079i	−0.209266	+	1.18681i
$615$		0			0
$616$	5.50365	+	9.53261i	0.221748	+	0.384080i
$617$	25.3826	−	9.23850i	1.02186	−	0.371928i	0.223886	−	0.974615i	$-0.428126\pi$
$617$	25.3826	−	9.23850i	1.02186	−	0.371928i	0.797977	+	0.602687i	$0.205903\pi$
$618$	−27.4783	+	10.0013i	−1.10534	+	0.402310i
$619$	6.19112	+	10.7233i	0.248842	+	0.431007i	0.963205	−	0.268768i	$-0.0866166\pi$
$619$	6.19112	+	10.7233i	0.248842	+	0.431007i	−0.714363	+	0.699776i	$0.753283\pi$
$620$		0			0
$621$	−0.418010	+	2.37065i	−0.0167742	+	0.0951311i
$622$	−7.09269	+	5.95147i	−0.284391	+	0.238632i
$623$	−30.7469	−	25.7997i	−1.23185	−	1.03364i
$624$	−1.31379	−	7.45088i	−0.0525937	−	0.298274i
$625$		0			0
$626$	−4.05277			−0.161981
$627$	6.77152	+	43.5614i	0.270428	+	1.73968i
$628$	1.46172			0.0583290
$629$	−63.1071	−	22.9691i	−2.51624	−	0.915838i
$630$		0			0
$631$	13.2651	+	11.1307i	0.528074	+	0.443107i	0.867436	−	0.497549i	$-0.165767\pi$
$631$	13.2651	+	11.1307i	0.528074	+	0.443107i	−0.339361	+	0.940656i	$0.610211\pi$
$632$	−0.368792	+	0.309453i	−0.0146697	+	0.0123094i
$633$	0.406546	−	2.30564i	0.0161588	−	0.0916409i
$634$	−7.67242	+	13.2890i	−0.304711	+	0.527775i
$635$		0			0
$636$	−14.3206	+	5.21226i	−0.567848	+	0.206680i
$637$	0.276313	−	0.100570i	0.0109479	−	0.00398472i
$638$	−11.5644	−	20.0302i	−0.457840	−	0.793002i
$639$	−2.11658	+	3.66602i	−0.0837304	+	0.145025i
$640$		0			0
$641$	−38.2255	+	32.0750i	−1.50982	+	1.26689i	−0.645708	+	0.763585i	$0.723438\pi$
$641$	−38.2255	+	32.0750i	−1.50982	+	1.26689i	−0.864110	+	0.503303i	$0.832118\pi$
$642$	−4.65741	−	3.90803i	−0.183813	−	0.154238i
$643$	7.42037	+	42.0830i	0.292631	+	1.65959i	0.676678	+	0.736279i	$0.263419\pi$
$643$	7.42037	+	42.0830i	0.292631	+	1.65959i	−0.384047	+	0.923314i	$0.625470\pi$
$644$	14.5116	+	5.28180i	0.571839	+	0.208132i
$645$		0			0
$646$	−31.3641	+	10.6991i	−1.23401	+	0.420950i
$647$	24.1311			0.948693			0.474346	−	0.880338i	$-0.342684\pi$
$647$	24.1311			0.948693			0.474346	+	0.880338i	$0.342684\pi$
$648$	−8.90845	−	3.24241i	−0.349957	−	0.127374i
$649$	−2.47994	−	14.0644i	−0.0973462	−	0.552078i
$650$		0			0
$651$	−3.12560	+	2.62269i	−0.122502	+	0.102791i
$652$	1.11461	−	6.32126i	0.0436514	−	0.247560i
$653$	7.62526	−	13.2073i	0.298400	−	0.516843i	−0.677370	−	0.735642i	$-0.736881\pi$
$653$	7.62526	−	13.2073i	0.298400	−	0.516843i	0.975770	+	0.218799i	$0.0702138\pi$
$654$	−12.7577	−	22.0970i	−0.498867	−	0.864062i
$655$		0			0
$656$	−3.31142	+	1.20526i	−0.129289	+	0.0470575i
$657$	−7.33857	−	12.7108i	−0.286305	−	0.495895i
$658$	9.98760	−	17.2990i	0.389357	−	0.674386i
$659$	−4.91316	+	27.8639i	−0.191390	+	1.08542i	0.726078	+	0.687613i	$0.241341\pi$
$659$	−4.91316	+	27.8639i	−0.191390	+	1.08542i	−0.917467	+	0.397812i	$0.869770\pi$
$660$		0			0
$661$	9.28101	+	7.78769i	0.360989	+	0.302906i	0.805185	−	0.593024i	$-0.202066\pi$
$661$	9.28101	+	7.78769i	0.360989	+	0.302906i	−0.444196	+	0.895930i	$0.646510\pi$
$662$	−5.37035	−	30.4568i	−0.208725	−	1.18374i
$663$	54.0508	+	19.6729i	2.09916	+	0.764031i
$664$	−10.3337			−0.401026
$665$		0			0
$666$	−25.0018			−0.968802
$667$	−30.4922	−	11.0983i	−1.18066	−	0.429727i
$668$	−0.570380	−	3.23478i	−0.0220687	−	0.125158i
$669$	−42.0379	−	35.2740i	−1.62528	−	1.36377i
$670$		0			0
$671$	−2.80149	+	15.8881i	−0.108150	+	0.613352i
$672$	−3.17275	+	5.49536i	−0.122391	+	0.211988i
$673$	−1.40545	−	2.43431i	−0.0541760	−	0.0938356i	0.837666	−	0.546183i	$-0.183920\pi$
$673$	−1.40545	−	2.43431i	−0.0541760	−	0.0938356i	−0.891842	+	0.452348i	$0.850587\pi$
$674$	−10.6643	+	3.88150i	−0.410775	+	0.149510i
$675$		0			0
$676$	1.59106	+	2.75580i	0.0611947	+	0.105992i
$677$	12.7127	−	22.0190i	0.488589	−	0.846261i	−0.511325	−	0.859387i	$-0.670845\pi$
$677$	12.7127	−	22.0190i	0.488589	−	0.846261i	0.999914	+	0.0131267i	$0.00417848\pi$
$678$	4.98523	−	28.2726i	0.191456	−	1.08580i
$679$	−15.4363	+	12.9526i	−0.592390	+	0.497074i
$680$		0			0
$681$	11.3882	+	64.5860i	0.436399	+	2.47494i
$682$	2.53083	+	0.921145i	0.0969103	+	0.0352725i
$683$	6.05107			0.231538			0.115769	−	0.993276i	$-0.463067\pi$
$683$	6.05107			0.231538			0.115769	+	0.993276i	$0.463067\pi$
$684$	−9.61002	+	7.73654i	−0.367448	+	0.295814i
$685$		0			0
$686$	−17.5180	−	6.37605i	−0.668842	−	0.243439i
$687$	12.4496	+	70.6052i	0.474982	+	2.69376i
$688$	2.48078	+	2.08162i	0.0945787	+	0.0793610i
$689$	−15.1492	+	12.7117i	−0.577139	+	0.484277i
$690$		0			0
$691$	15.6028	−	27.0249i	0.593559	−	1.02807i	−0.400190	−	0.916432i	$-0.631056\pi$
$691$	15.6028	−	27.0249i	0.593559	−	1.02807i	0.993749	−	0.111642i	$-0.0356109\pi$
$692$	4.43867	+	7.68801i	0.168733	+	0.292254i
$693$	−29.2757	+	10.6555i	−1.11209	+	0.404768i
$694$	8.60756	−	3.13290i	0.326739	−	0.118923i
$695$		0			0
$696$	6.66666	−	11.5470i	0.252699	−	0.437688i
$697$	4.65221	−	26.3840i	0.176215	−	0.999364i
$698$	−16.5517	+	13.8885i	−0.626490	+	0.525688i
$699$	−22.8625	−	19.1839i	−0.864740	−	0.725603i
$700$		0			0
$701$	−36.3729	−	13.2387i	−1.37379	−	0.500017i	−0.453498	−	0.891257i	$-0.649824\pi$
$701$	−36.3729	−	13.2387i	−1.37379	−	0.500017i	−0.920289	+	0.391240i	$0.872046\pi$
$702$	−1.28355			−0.0484445
$703$	19.9257	−	32.9476i	0.751512	−	1.24264i
$704$	4.18854			0.157862
$705$		0			0
$706$	3.78179	+	21.4476i	0.142330	+	0.807191i
$707$	23.4137	+	19.6464i	0.880563	+	0.738880i
$708$	6.30680	−	5.29204i	0.237024	−	0.198887i
$709$	−3.25118	+	18.4384i	−0.122101	+	0.692468i	0.860887	+	0.508796i	$0.169909\pi$
$709$	−3.25118	+	18.4384i	−0.122101	+	0.692468i	−0.982988	+	0.183671i	$0.941202\pi$
$710$		0			0
$711$	−0.681298	−	1.18004i	−0.0255507	−	0.0442551i
$712$	−14.3521	+	5.22373i	−0.537867	+	0.195768i
$713$	3.55068	−	1.29234i	0.132974	−	0.0483986i
$714$	−24.1210	−	41.7788i	−0.902706	−	1.56353i
$715$		0			0
$716$	3.73480	−	21.1811i	0.139576	−	0.791574i
$717$	−23.7402	+	19.9204i	−0.886592	+	0.743939i
$718$	13.5428	+	11.3638i	0.505413	+	0.424092i
$719$	1.60832	+	9.12122i	0.0599801	+	0.340164i	1.00000		0.000956817i	$-0.000304564\pi$
$719$	1.60832	+	9.12122i	0.0599801	+	0.340164i	−0.940019	+	0.341121i	$0.889193\pi$
$720$		0			0
$721$	31.8255			1.18524
$722$	−2.53639	−	18.8299i	−0.0943946	−	0.700778i
$723$	−8.83068			−0.328416
$724$	−5.36536	−	1.95283i	−0.199402	−	0.0725764i
$725$		0			0
$726$	12.1042	+	10.1566i	0.449229	+	0.376948i
$727$	−8.54305	+	7.16847i	−0.316844	+	0.265864i	−0.787314	−	0.616552i	$-0.788529\pi$
$727$	−8.54305	+	7.16847i	−0.316844	+	0.265864i	0.470470	+	0.882416i	$0.344084\pi$
$728$	−1.42987	+	8.10921i	−0.0529946	+	0.300547i
$729$	11.9324	−	20.6675i	0.441941	−	0.765464i
$730$		0			0
$731$	−23.1355	+	8.42065i	−0.855699	+	0.311449i
$732$	−8.73956	+	3.18094i	−0.323023	+	0.117571i
$733$	16.1024	+	27.8901i	0.594755	+	1.03015i	0.993581	+	0.113120i	$0.0360843\pi$
$733$	16.1024	+	27.8901i	0.594755	+	1.03015i	−0.398826	+	0.917026i	$0.630582\pi$
$734$	11.1596	−	19.3291i	0.411910	−	0.713449i
$735$		0			0
$736$	4.50159	−	3.77729i	0.165931	−	0.139233i
$737$	−10.0813	−	8.45926i	−0.371351	−	0.311601i
$738$	−1.73196	−	9.82246i	−0.0637545	−	0.361570i
$739$	12.5191	+	4.55660i	0.460524	+	0.167617i	0.561855	−	0.827236i	$-0.310088\pi$
$739$	12.5191	+	4.55660i	0.460524	+	0.167617i	−0.101331	+	0.994853i	$0.532310\pi$
$740$		0			0
$741$	−17.0662	+	28.2194i	−0.626943	+	1.03667i
$742$	16.5862			0.608897
$743$	28.8694	+	10.5076i	1.05912	+	0.385487i	0.812097	−	0.583523i	$-0.198326\pi$
$743$	28.8694	+	10.5076i	1.05912	+	0.385487i	0.247021	+	0.969010i	$0.420548\pi$
$744$	0.269607	+	1.52902i	0.00988427	+	0.0560565i
$745$		0			0
$746$	10.4919	−	8.80377i	0.384137	−	0.322329i
$747$	5.07887	−	28.8037i	0.185826	−	1.05387i
$748$	−15.9218	+	27.5774i	−0.582159	+	1.00833i
$749$	3.30850	+	5.73049i	0.120890	+	0.209388i
$750$		0			0
$751$	−1.70586	+	0.620884i	−0.0622479	+	0.0226564i	−0.372956	−	0.927849i	$-0.621656\pi$
$751$	−1.70586	+	0.620884i	−0.0622479	+	0.0226564i	0.310709	+	0.950505i	$0.399434\pi$
$752$	−3.80052	−	6.58269i	−0.138591	−	0.240046i
$753$	−30.9124	+	53.5418i	−1.12651	+	1.95117i
$754$	3.00449	−	17.0393i	0.109417	−	0.620534i
$755$		0			0
$756$	0.824663	+	0.691975i	0.0299927	+	0.0251669i
$757$	−6.77770	−	38.4383i	−0.246340	−	1.39706i	−0.817360	−	0.576127i	$-0.804564\pi$
$757$	−6.77770	−	38.4383i	−0.246340	−	1.39706i	0.571021	−	0.820936i	$-0.306548\pi$
$758$	−1.15301	−	0.419662i	−0.0418793	−	0.0152428i
$759$	59.4323			2.15726
$760$		0			0
$761$	2.12158			0.0769071			0.0384535	−	0.999260i	$-0.487757\pi$
$761$	2.12158			0.0769071			0.0384535	+	0.999260i	$0.487757\pi$
$762$	−12.9101	−	4.69891i	−0.467685	−	0.170223i
$763$	4.82219	+	27.3480i	0.174575	+	0.990065i
$764$	8.99619	+	7.54870i	0.325471	+	0.273102i
$765$		0			0
$766$	−3.38041	+	19.1713i	−0.122139	+	0.692686i
$767$	5.34179	−	9.25225i	0.192881	−	0.334080i
$768$	1.20731	+	2.09111i	0.0435649	+	0.0754566i
$769$	−28.8954	+	10.5171i	−1.04200	+	0.379255i	−0.805636	−	0.592411i	$-0.798176\pi$
$769$	−28.8954	+	10.5171i	−1.04200	+	0.379255i	−0.236359	+	0.971666i	$0.575954\pi$
$770$		0			0
$771$	18.1251	+	31.3935i	0.652758	+	1.13061i
$772$	−4.80494	+	8.32240i	−0.172933	+	0.299530i
$773$	9.20062	−	52.1793i	0.330923	−	1.87676i	−0.133352	−	0.991069i	$-0.542574\pi$
$773$	9.20062	−	52.1793i	0.330923	−	1.87676i	0.464275	−	0.885691i	$-0.346315\pi$
$774$	−7.02146	+	5.89171i	−0.252381	+	0.211773i
$775$		0			0
$776$	1.33150	+	7.55130i	0.0477980	+	0.271076i
$777$	52.6724	+	19.1712i	1.88961	+	0.687763i
$778$	20.5085			0.735264
$779$	14.3244	+	5.54579i	0.513226	+	0.198699i
$780$		0			0
$781$	−5.88671	−	2.14259i	−0.210643	−	0.0766678i
$782$	7.75787	+	43.9971i	0.277421	+	1.57333i
$783$	−1.73281	−	1.45400i	−0.0619254	−	0.0519616i
$784$	−0.0718887	+	0.0603218i	−0.00256745	+	0.00215435i
$785$		0			0
$786$	15.2987	−	26.4982i	0.545688	−	0.945160i
$787$	3.97851	+	6.89098i	0.141818	+	0.245637i	0.928181	−	0.372128i	$-0.121372\pi$
$787$	3.97851	+	6.89098i	0.141818	+	0.245637i	−0.786363	+	0.617765i	$0.788038\pi$
$788$	10.6380	−	3.87191i	0.378963	−	0.137931i
$789$	−7.48147	+	2.72303i	−0.266347	+	0.0969425i
$790$		0			0
$791$	−15.6227	+	27.0593i	−0.555479	+	0.962117i
$792$	−2.05860	+	11.6749i	−0.0731493	+	0.414850i
$793$	−9.24526	+	7.75769i	−0.328309	+	0.275484i
$794$	21.2017	+	17.7904i	0.752421	+	0.631356i
$795$		0			0
$796$	12.9735	+	4.72197i	0.459833	+	0.167366i
$797$	−1.79168			−0.0634645			−0.0317323	−	0.999496i	$-0.510102\pi$
$797$	−1.79168			−0.0634645			−0.0317323	+	0.999496i	$0.510102\pi$
$798$	26.1781	−	8.93001i	0.926696	−	0.316119i
$799$	57.7874			2.04437
$800$		0			0
$801$	−7.50653	−	42.5716i	−0.265230	−	1.50419i
$802$	17.7426	+	14.8878i	0.626515	+	0.525708i
$803$	16.6387	−	13.9615i	0.587166	−	0.492691i
$804$	1.31741	−	7.47138i	0.0464613	−	0.263495i
$805$		0			0
$806$	1.00738	+	1.74483i	0.0354834	+	0.0614590i
$807$	−62.5479	+	22.7656i	−2.20179	+	0.801386i
$808$	10.9291	−	3.97786i	0.384484	−	0.139941i
$809$	−11.4608	−	19.8506i	−0.402939	−	0.697910i	0.591140	−	0.806569i	$-0.298678\pi$
$809$	−11.4608	−	19.8506i	−0.402939	−	0.697910i	−0.994079	+	0.108658i	$0.965345\pi$
$810$		0			0
$811$	4.12315	−	23.3835i	0.144783	−	0.821107i	−0.822757	−	0.568393i	$-0.807565\pi$
$811$	4.12315	−	23.3835i	0.144783	−	0.821107i	0.967541	−	0.252715i	$-0.0813234\pi$
$812$	−11.1164	+	9.32775i	−0.390108	+	0.327340i
$813$	19.2869	+	16.1837i	0.676422	+	0.567586i
$814$	−6.42488	−	36.4373i	−0.225192	−	1.27713i
$815$		0			0
$816$	−18.3572			−0.642632
$817$	−2.16825	−	13.9484i	−0.0758575	−	0.487994i
$818$	−7.36630			−0.257557
$819$	−21.9004	−	7.97111i	−0.765263	−	0.278533i
$820$		0			0
$821$	−7.97863	−	6.69486i	−0.278456	−	0.233652i	0.492854	−	0.870112i	$-0.335954\pi$
$821$	−7.97863	−	6.69486i	−0.278456	−	0.233652i	−0.771310	+	0.636460i	$0.780398\pi$
$822$	23.4582	−	19.6838i	0.818198	−	0.686550i
$823$	0.145646	−	0.826000i	0.00507690	−	0.0287926i	−0.982164	−	0.188026i	$-0.939791\pi$
$823$	0.145646	−	0.826000i	0.00507690	−	0.0287926i	0.987241	+	0.159233i	$0.0509022\pi$
$824$	6.05517	−	10.4879i	0.210942	−	0.365362i
$825$		0			0
$826$	−8.42000	+	3.06463i	−0.292969	+	0.106632i
$827$	−16.6120	+	6.04628i	−0.577656	+	0.210250i	−0.614292	−	0.789079i	$-0.710558\pi$
$827$	−16.6120	+	6.04628i	−0.577656	+	0.210250i	0.0366356	+	0.999329i	$0.488336\pi$
$828$	8.31615	+	14.4040i	0.289006	+	0.500573i
$829$	−1.55946	+	2.70107i	−0.0541624	+	0.0938121i	−0.891835	−	0.452360i	$-0.850582\pi$
$829$	−1.55946	+	2.70107i	−0.0541624	+	0.0938121i	0.837673	+	0.546172i	$0.183916\pi$
$830$		0			0
$831$	24.9167	−	20.9076i	0.864352	−	0.725277i
$832$	2.40028	+	2.01408i	0.0832149	+	0.0698256i
$833$	−0.123890	−	0.702616i	−0.00429254	−	0.0243442i
$834$	−37.7704	−	13.7473i	−1.30788	−	0.476031i
$835$		0			0
$836$	−13.7447	−	12.0174i	−0.475369	−	0.415630i
$837$	0.263401			0.00910448
$838$	−3.61673	−	1.31638i	−0.124938	−	0.0454737i
$839$	−0.425740	−	2.41449i	−0.0146982	−	0.0833576i	0.976576	−	0.215171i	$-0.0690310\pi$
$839$	−0.425740	−	2.41449i	−0.0146982	−	0.0833576i	−0.991274	+	0.131814i	$0.957920\pi$
$840$		0			0
$841$	1.14275	−	0.958883i	0.0394053	−	0.0330649i
$842$	0.211425	−	1.19905i	0.00728619	−	0.0413220i
$843$	−8.69692	+	15.0635i	−0.299538	+	0.518814i
$844$	0.484800	+	0.839698i	0.0166875	+	0.0289036i
$845$		0			0
$846$	20.2162	−	7.35808i	0.695046	−	0.252976i
$847$	−8.59851	−	14.8931i	−0.295448	−	0.511732i
$848$	3.15571	−	5.46586i	0.108368	−	0.187698i
$849$	6.69833	−	37.9881i	0.229886	−	1.30375i
$850$		0			0
$851$	−39.7648	−	33.3666i	−1.36312	−	1.14379i
$852$	−0.627106	−	3.55650i	−0.0214843	−	0.121844i
$853$	−7.42940	−	2.70408i	−0.254378	−	0.0925859i	0.211684	−	0.977338i	$-0.432105\pi$
$853$	−7.42940	−	2.70408i	−0.254378	−	0.0925859i	−0.466062	+	0.884752i	$0.654327\pi$
$854$	10.1222			0.346374
$855$		0			0
$856$	2.51793			0.0860609
$857$	30.2588	+	11.0133i	1.03362	+	0.376207i	0.802458	−	0.596709i	$-0.203525\pi$
$857$	30.2588	+	11.0133i	1.03362	+	0.376207i	0.231162	+	0.972915i	$0.425747\pi$
$858$	5.50287	+	31.2083i	0.187865	+	1.06543i
$859$	−24.5504	−	20.6002i	−0.837649	−	0.702871i	0.119385	−	0.992848i	$-0.461908\pi$
$859$	−24.5504	−	20.6002i	−0.837649	−	0.702871i	−0.957034	+	0.289977i	$0.906352\pi$
$860$		0			0
$861$	−3.88297	+	22.0214i	−0.132331	+	0.750488i
$862$	−11.7541	+	20.3586i	−0.400345	+	0.693418i
$863$	8.90361	+	15.4215i	0.303082	+	0.524954i	0.976833	−	0.214005i	$-0.0686509\pi$
$863$	8.90361	+	15.4215i	0.303082	+	0.524954i	−0.673750	+	0.738959i	$0.735318\pi$
$864$	0.384938	−	0.140106i	0.0130958	−	0.00476650i
$865$		0			0
$866$	−7.40244	−	12.8214i	−0.251545	−	0.435689i
$867$	49.2568	−	85.3153i	1.67285	−	2.89746i
$868$	0.293428	−	1.66411i	0.00995960	−	0.0564837i
$869$	1.54470	−	1.29616i	0.0524003	−	0.0439691i
$870$		0			0
$871$	−1.70955	−	9.69532i	−0.0579258	−	0.328513i
$872$	9.92983	+	3.61416i	0.336267	+	0.122391i
$873$	−21.7025			−0.734519
$874$	−25.6094	−	0.520444i	−0.866251	−	0.0176043i
$875$		0			0
$876$	11.7662	+	4.28253i	0.397542	+	0.144693i
$877$	−0.779526	−	4.42091i	−0.0263227	−	0.149283i	0.968814	−	0.247790i	$-0.0797044\pi$
$877$	−0.779526	−	4.42091i	−0.0263227	−	0.149283i	−0.995136	+	0.0985069i	$0.968593\pi$
$878$	14.9547	+	12.5485i	0.504697	+	0.423491i
$879$	−50.2109	+	42.1320i	−1.69357	+	1.42108i
$880$		0			0
$881$	4.32560	−	7.49216i	0.145733	−	0.252417i	−0.783913	−	0.620871i	$-0.786779\pi$
$881$	4.32560	−	7.49216i	0.145733	−	0.252417i	0.929646	+	0.368453i	$0.120113\pi$
$882$	−0.132806	−	0.230026i	−0.00447180	−	0.00774539i
$883$	16.8319	−	6.12632i	0.566440	−	0.206167i	−0.0428960	−	0.999080i	$-0.513658\pi$
$883$	16.8319	−	6.12632i	0.566440	−	0.206167i	0.609336	+	0.792912i	$0.291436\pi$
$884$	−22.3849	+	8.14742i	−0.752884	+	0.274028i
$885$		0			0
$886$	7.30351	−	12.6500i	0.245366	−	0.424987i
$887$	2.04573	−	11.6019i	0.0686889	−	0.389554i	−0.931009	−	0.364995i	$-0.881071\pi$
$887$	2.04573	−	11.6019i	0.0686889	−	0.389554i	0.999698	−	0.0245592i	$-0.00781822\pi$
$888$	16.3393	−	13.7103i	0.548311	−	0.460088i
$889$	11.4543	+	9.61133i	0.384166	+	0.322354i
$890$		0			0
$891$	37.3134	+	13.5810i	1.25005	+	0.454980i
$892$	22.7269			0.760952
$893$	−6.41511	+	32.5052i	−0.214673	+	1.08774i
$894$	39.1510			1.30941
$895$		0			0
$896$	−0.456340	−	2.58803i	−0.0152452	−	0.0864601i
$897$	34.0582	+	28.5783i	1.13717	+	0.954200i
$898$	4.95647	−	4.15898i	0.165400	−	0.138787i
$899$	−0.616559	+	3.49668i	−0.0205634	+	0.116621i
$900$		0			0
$901$	23.9915	+	41.5545i	0.799273	+	1.38438i
$902$	13.8700	−	5.04828i	0.461821	−	0.168089i
$903$	19.3101	−	7.02831i	0.642601	−	0.233888i
$904$	5.94480	+	10.2967i	0.197721	+	0.342463i
$905$		0			0
$906$	2.26588	−	12.8504i	0.0752788	−	0.426927i
$907$	−26.2931	+	22.0626i	−0.873049	+	0.732575i	−0.964738	−	0.263213i	$-0.915218\pi$
$907$	−26.2931	+	22.0626i	−0.873049	+	0.732575i	0.0916889	+	0.995788i	$0.470773\pi$
$908$	−20.8062	−	17.4585i	−0.690479	−	0.579381i
$909$	5.71621	+	32.4182i	0.189595	+	1.07525i
$910$		0			0
$911$	9.15384			0.303280			0.151640	−	0.988436i	$-0.451545\pi$
$911$	9.15384			0.303280			0.151640	+	0.988436i	$0.451545\pi$
$912$	2.03788	−	10.3259i	0.0674809	−	0.341924i
$913$	43.2832			1.43247
$914$	19.9960	+	7.27794i	0.661408	+	0.240733i
$915$		0			0
$916$	−22.7453	−	19.0856i	−0.751527	−	0.630606i
$917$	−25.5100	+	21.4055i	−0.842415	+	0.706870i
$918$	−0.540798	+	3.06702i	−0.0178490	+	0.101227i
$919$	−13.9008	+	24.0769i	−0.458546	+	0.794225i	−0.998884	−	0.0472229i	$-0.984963\pi$
$919$	−13.9008	+	24.0769i	−0.458546	+	0.794225i	0.540338	+	0.841448i	$0.318296\pi$
$920$		0			0
$921$	67.7557	−	24.6611i	2.23263	−	0.812609i
$922$	15.1939	−	5.53011i	0.500383	−	0.182124i
$923$	−2.34316	−	4.05848i	−0.0771262	−	0.133586i
$924$	13.2892	−	23.0175i	0.437182	−	0.757221i
$925$		0			0
$926$	7.23613	−	6.07183i	0.237794	−	0.199533i
$927$	26.2573	+	22.0325i	0.862404	+	0.723642i
$928$	0.958874	+	5.43804i	0.0314766	+	0.178513i
$929$	51.4451	+	18.7245i	1.68786	+	0.614330i	0.994353	−	0.106122i	$-0.0338434\pi$
$929$	51.4451	+	18.7245i	1.68786	+	0.614330i	0.693505	+	0.720452i	$0.256066\pi$
$930$		0			0
$931$	0.408972	+	0.00831129i	0.0134035	+	0.000272391i
$932$	12.3601			0.404869
$933$	21.0083	+	7.64638i	0.687779	+	0.250331i
$934$	3.62914	+	20.5819i	0.118749	+	0.673460i
$935$		0			0
$936$	−6.79364	+	5.70054i	−0.222057	+	0.186328i
$937$	4.98266	−	28.2581i	0.162777	−	0.923152i	−0.788551	−	0.614970i	$-0.789168\pi$
$937$	4.98266	−	28.2581i	0.162777	−	0.923152i	0.951327	−	0.308182i	$-0.0997206\pi$
$938$	−4.12848	+	7.15074i	−0.134800	+	0.233480i
$939$	4.89293	+	8.47480i	0.159675	+	0.276565i
$940$		0			0
$941$	−2.92418	+	1.06431i	−0.0953255	+	0.0346957i	−0.389243	−	0.921135i	$-0.627263\pi$
$941$	−2.92418	+	1.06431i	−0.0953255	+	0.0346957i	0.293917	+	0.955831i	$0.405041\pi$
$942$	−1.76474	−	3.05662i	−0.0574984	−	0.0995902i
$943$	10.3541	−	17.9338i	0.337175	−	0.584004i
$944$	−0.592077	+	3.35784i	−0.0192705	+	0.109288i
$945$		0			0
$946$	−10.3908	−	8.71895i	−0.337835	−	0.283477i
$947$	8.90235	+	50.4877i	0.289287	+	1.64063i	0.689556	+	0.724232i	$0.257806\pi$
$947$	8.90235	+	50.4877i	0.289287	+	1.64063i	−0.400269	+	0.916398i	$0.631083\pi$
$948$	1.09235	+	0.397581i	0.0354777	+	0.0129128i
$949$	16.2484			0.527445
$950$		0			0
$951$	37.0518			1.20149
$952$	18.7743	+	6.83329i	0.608479	+	0.221468i
$953$	7.98914	+	45.3086i	0.258793	+	1.46769i	0.786144	+	0.618043i	$0.212074\pi$
$953$	7.98914	+	45.3086i	0.258793	+	1.46769i	−0.527351	+	0.849648i	$0.676815\pi$
$954$	13.6843	+	11.4825i	0.443044	+	0.371758i
$955$		0			0
$956$	2.22870	−	12.6396i	0.0720815	−	0.408794i
$957$	−27.9236	+	48.3651i	−0.902642	+	1.56342i
$958$	−18.5525	−	32.1338i	−0.599404	−	1.03820i
$959$	−31.3182	+	11.3989i	−1.01132	+	0.368090i
$960$		0			0
$961$	15.2933	+	26.4887i	0.493331	+	0.854475i
$962$	13.8392	−	23.9702i	0.446194	−	0.772830i
$963$	−1.23752	+	7.01834i	−0.0398786	+	0.226163i
$964$	2.80156	−	2.35079i	0.0902323	−	0.0757139i
$965$		0			0
$966$	−6.47512	−	36.7222i	−0.208334	−	1.18152i
$967$	−32.4866	−	11.8241i	−1.04470	−	0.380239i	−0.238038	−	0.971256i	$-0.576504\pi$
$967$	−32.4866	−	11.8241i	−1.04470	−	0.380239i	−0.806659	+	0.591017i	$0.798727\pi$
$968$	−6.54388			−0.210328
$969$	60.2391	+	52.6690i	1.93516	+	1.69197i
$970$		0			0
$971$	−3.02317	−	1.10034i	−0.0970182	−	0.0353117i	0.293055	−	0.956096i	$-0.405328\pi$
$971$	−3.02317	−	1.10034i	−0.0970182	−	0.0353117i	−0.390073	+	0.920784i	$0.627550\pi$
$972$	3.76157	+	21.3329i	0.120652	+	0.684253i
$973$	33.5113	+	28.1193i	1.07432	+	0.901464i
$974$	−3.63930	+	3.05374i	−0.116611	+	0.0978480i
$975$		0			0
$976$	1.92587	−	3.33570i	0.0616455	−	0.106773i
$977$	9.87128	+	17.0976i	0.315810	+	0.546999i	0.979609	−	0.200912i	$-0.0643904\pi$
$977$	9.87128	+	17.0976i	0.315810	+	0.546999i	−0.663799	+	0.747911i	$0.731057\pi$
$978$	−14.5642	+	5.30092i	−0.465710	+	0.169505i
$979$	60.1143	−	21.8798i	1.92126	−	0.699282i
$980$		0			0
$981$	−14.9543	+	25.9016i	−0.477454	+	0.826975i
$982$	0.423756	−	2.40324i	0.0135226	−	0.0766905i
$983$	−9.34361	+	7.84022i	−0.298015	+	0.250064i	−0.779517	−	0.626380i	$-0.784536\pi$
$983$	−9.34361	+	7.84022i	−0.298015	+	0.250064i	0.481503	+	0.876445i	$0.340091\pi$
$984$	6.51823	+	5.46945i	0.207794	+	0.174360i
$985$		0			0
$986$	−39.4491	−	14.3583i	−1.25631	−	0.457261i
$987$	−48.2323			−1.53525
$988$	−2.09790	−	13.4959i	−0.0667431	−	0.429361i
$989$	−19.0303			−0.605129
$990$		0			0
$991$	−3.35524	−	19.0285i	−0.106583	−	0.604460i	−0.990576	−	0.136961i	$-0.956266\pi$
$991$	−3.35524	−	19.0285i	−0.106583	−	0.604460i	0.883994	−	0.467499i	$-0.154845\pi$
$992$	−0.492569	−	0.413315i	−0.0156391	−	0.0131228i
$993$	−57.2050	+	48.0007i	−1.81535	+	1.52326i
$994$	−0.682515	+	3.87073i	−0.0216481	+	0.122772i
$995$		0			0
$996$	12.4760	+	21.6090i	0.395316	+	0.684707i
$997$	21.0342	−	7.65581i	0.666159	−	0.242462i	0.0132655	−	0.999912i	$-0.495777\pi$
$997$	21.0342	−	7.65581i	0.666159	−	0.242462i	0.652893	+	0.757450i	$0.273555\pi$
$998$	20.6344	−	7.51030i	0.653170	−	0.237734i
$999$	−1.80928	−	3.13377i	−0.0572432	−	0.0991482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.l.251.1		30
5.2	odd	4		190.2.p.a.99.1	✓	60
5.3	odd	4		190.2.p.a.99.10	yes	60
5.4	even	2		950.2.l.m.251.5		30
19.5	even	9	inner	950.2.l.l.651.1		30
95.24	even	18		950.2.l.m.651.5		30
95.43	odd	36		190.2.p.a.119.1	yes	60
95.62	odd	36		190.2.p.a.119.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.p.a.99.1	✓	60	5.2	odd	4
190.2.p.a.99.10	yes	60	5.3	odd	4
190.2.p.a.119.1	yes	60	95.43	odd	36
190.2.p.a.119.10	yes	60	95.62	odd	36
950.2.l.l.251.1		30	1.1	even	1	trivial
950.2.l.l.651.1		30	19.5	even	9	inner
950.2.l.m.251.5		30	5.4	even	2
950.2.l.m.651.5		30	95.24	even	18

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)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.419293 - 2.37793i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.419293 - 2.37793i) q^{6} +(-1.31398 + 2.27588i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.65966 + 0.968036i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.419293 - 2.37793i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.419293 - 2.37793i) q^{6} +(-1.31398 + 2.27588i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.65966 + 0.968036i) q^{9} +(-2.09427 - 3.62738i) q^{11} +(1.20731 - 2.09111i) q^{12} +(0.544100 - 3.08575i) q^{13} +(-2.01313 + 1.68922i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-7.14407 - 2.60023i) q^{17} -2.83035 q^{18} +(2.25570 - 3.72986i) q^{19} +(5.96281 + 2.17029i) q^{21} +(-0.727333 - 4.12491i) q^{22} +(-4.50159 - 3.77729i) q^{23} +(1.84970 - 1.55208i) q^{24} +(1.56667 - 2.71356i) q^{26} +(-0.204821 - 0.354760i) q^{27} +(-2.46947 + 0.898814i) q^{28} +(5.18892 - 1.88861i) q^{29} +(-0.321502 + 0.556858i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-7.74754 + 6.50096i) q^{33} +(-5.82390 - 4.88683i) q^{34} +(-2.65966 - 0.968036i) q^{36} +8.83349 q^{37} +(3.39535 - 2.73342i) q^{38} -7.56582 q^{39} +(0.611926 + 3.47041i) q^{41} +(4.86093 + 4.07881i) q^{42} +(2.48078 - 2.08162i) q^{43} +(0.727333 - 4.12491i) q^{44} +(-2.93821 - 5.08912i) q^{46} +(-7.14264 + 2.59971i) q^{47} +(2.26899 - 0.825846i) q^{48} +(0.0469220 + 0.0812713i) q^{49} +(-3.18770 + 18.0783i) q^{51} +(2.40028 - 2.01408i) q^{52} +(-4.83483 - 4.05691i) q^{53} +(-0.0711336 - 0.403419i) q^{54} -2.62796 q^{56} +(-9.81513 - 3.79999i) q^{57} +5.52193 q^{58} +(3.20401 + 1.16616i) q^{59} +(-2.95060 - 2.47585i) q^{61} +(-0.492569 + 0.413315i) q^{62} +(1.29160 - 7.32503i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-9.50377 + 3.45909i) q^{66} +(2.95249 - 1.07462i) q^{67} +(-3.80128 - 6.58401i) q^{68} +(-7.09463 + 12.2883i) q^{69} +(1.14572 - 0.961372i) q^{71} +(-2.16817 - 1.81931i) q^{72} +(0.900476 + 5.10685i) q^{73} +(8.30076 + 3.02123i) q^{74} +(4.12547 - 1.40730i) q^{76} +11.0073 q^{77} +(-7.10955 - 2.58766i) q^{78} +(0.0835983 + 0.474109i) q^{79} +(-7.26223 + 6.09374i) q^{81} +(-0.611926 + 3.47041i) q^{82} +(-5.16686 + 8.94927i) q^{83} +(3.17275 + 5.49536i) q^{84} +(3.04312 - 1.10761i) q^{86} +(-6.66666 - 11.5470i) q^{87} +(2.09427 - 3.62738i) q^{88} +(-2.65216 + 15.0411i) q^{89} +(6.30784 + 5.29291i) q^{91} +(-1.02043 - 5.78714i) q^{92} +(1.45897 + 0.531022i) q^{93} -7.60104 q^{94} +2.41461 q^{96} +(7.20537 + 2.62254i) q^{97} +(0.0162959 + 0.0924184i) q^{98} +(9.08148 + 7.62027i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) \) 30 * q - 12 * q^7 + 15 * q^8	\( 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) \) 30 * q - 12 * q^7 + 15 * q^8 + 6 * q^11 + 6 * q^14 - 30 * q^18 + 24 * q^19 + 24 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^26 - 18 * q^27 + 3 * q^28 + 12 * q^29 - 30 * q^33 + 24 * q^37 - 12 * q^38 - 24 * q^39 - 3 * q^41 + 12 * q^42 + 6 * q^43 - 3 * q^44 + 48 * q^47 + 15 * q^49 - 90 * q^51 - 18 * q^53 + 18 * q^54 - 24 * q^56 - 42 * q^57 + 36 * q^58 - 18 * q^59 - 60 * q^61 - 24 * q^62 - 21 * q^63 - 15 * q^64 - 78 * q^66 - 30 * q^67 - 12 * q^68 + 24 * q^69 + 30 * q^73 - 9 * q^74 - 3 * q^76 + 78 * q^77 - 6 * q^79 + 60 * q^81 + 3 * q^82 - 42 * q^83 - 6 * q^84 + 12 * q^86 - 54 * q^87 - 6 * q^88 - 30 * q^89 - 6 * q^91 - 6 * q^92 + 72 * q^93 - 78 * q^94 - 42 * q^97 + 6 * q^98 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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