LMFDB - Embedded newform 950.2.u.g.149.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.6
Character	$\chi$	$=$	950.149
Dual form			950.2.u.g.899.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 - 0.766044i) q^{2} +(0.613893 + 1.68666i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.68666 + 0.613893i) q^{6} +(1.17907 - 0.680736i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.169813 + 0.142490i) q^{9} +O(q^{10})$	\(q+(0.642788 - 0.766044i) q^{2} +(0.613893 + 1.68666i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.68666 + 0.613893i) q^{6} +(1.17907 - 0.680736i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.169813 + 0.142490i) q^{9} +(-3.22960 + 5.59384i) q^{11} +(1.55443 - 0.897451i) q^{12} +(-2.01005 + 5.52256i) q^{13} +(0.236417 - 1.34079i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(1.64480 - 1.96020i) q^{17} +0.221676i q^{18} +(3.83851 + 2.06538i) q^{19} +(1.87199 + 1.57079i) q^{21} +(2.20918 + 6.06967i) q^{22} +(8.29626 - 1.46285i) q^{23} +(0.311682 - 1.76763i) q^{24} +(2.93849 + 5.08962i) q^{26} +(4.31871 + 2.49341i) q^{27} +(-0.875137 - 1.04295i) q^{28} +(-3.41558 + 2.86601i) q^{29} +(0.701264 + 1.21462i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-11.4175 - 2.01322i) q^{33} +(-0.444341 - 2.51998i) q^{34} +(0.169813 + 0.142490i) q^{36} -4.42962i q^{37} +(4.04953 - 1.61287i) q^{38} -10.5486 q^{39} +(5.15407 - 1.87593i) q^{41} +(2.40658 - 0.424346i) q^{42} +(-6.74986 - 1.19018i) q^{43} +(6.06967 + 2.20918i) q^{44} +(4.21212 - 7.29560i) q^{46} +(-6.11821 - 7.29140i) q^{47} +(-1.15374 - 1.37498i) q^{48} +(-2.57320 + 4.45691i) q^{49} +(4.31591 + 1.57086i) q^{51} +(5.78770 + 1.02053i) q^{52} +(4.35841 - 0.768506i) q^{53} +(4.68608 - 1.70559i) q^{54} -1.36147 q^{56} +(-1.12716 + 7.74218i) q^{57} +4.45872i q^{58} +(7.87687 + 6.60948i) q^{59} +(1.12233 + 6.36503i) q^{61} +(1.38122 + 0.243546i) q^{62} +(-0.103223 + 0.283604i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-8.88125 + 7.45226i) q^{66} +(-4.31929 - 5.14753i) q^{67} +(-2.21604 - 1.27943i) q^{68} +(7.56034 + 13.0949i) q^{69} +(0.336459 - 1.90815i) q^{71} +(0.218308 - 0.0384936i) q^{72} +(-2.14907 - 5.90451i) q^{73} +(-3.39328 - 2.84730i) q^{74} +(1.36746 - 4.13885i) q^{76} +8.79403i q^{77} +(-6.78052 + 8.08071i) q^{78} +(-3.37355 + 1.22787i) q^{79} +(-1.66978 + 9.46980i) q^{81} +(1.87593 - 5.15407i) q^{82} +(11.6908 - 6.74970i) q^{83} +(1.22185 - 2.11631i) q^{84} +(-5.25046 + 4.40566i) q^{86} +(-6.93077 - 4.00148i) q^{87} +(5.59384 - 3.22960i) q^{88} +(-1.78165 - 0.648469i) q^{89} +(1.38942 + 7.87979i) q^{91} +(-2.88126 - 7.91619i) q^{92} +(-1.61815 + 1.92844i) q^{93} -9.51825 q^{94} -1.79490 q^{96} +(0.0793596 - 0.0945771i) q^{97} +(1.76017 + 4.83603i) q^{98} +(-0.248638 - 1.41010i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 36 q^{9}+O(q^{10}) $ 36 * q + 36 * q^9	$ 36 q + 36 q^{9} - 24 q^{11} - 12 q^{14} + 24 q^{21} - 18 q^{26} + 12 q^{29} - 12 q^{31} - 36 q^{34} - 36 q^{36} - 96 q^{39} - 42 q^{41} - 6 q^{44} + 36 q^{46} + 78 q^{49} + 84 q^{51} + 108 q^{54} + 60 q^{59} + 96 q^{61} + 18 q^{64} + 48 q^{66} + 60 q^{69} + 60 q^{71} + 6 q^{74} - 42 q^{76} - 60 q^{79} + 36 q^{81} - 12 q^{84} + 72 q^{86} - 60 q^{89} - 120 q^{91} - 12 q^{94} - 342 q^{99}+O(q^{100}) $ 36 * q + 36 * q^9 - 24 * q^11 - 12 * q^14 + 24 * q^21 - 18 * q^26 + 12 * q^29 - 12 * q^31 - 36 * q^34 - 36 * q^36 - 96 * q^39 - 42 * q^41 - 6 * q^44 + 36 * q^46 + 78 * q^49 + 84 * q^51 + 108 * q^54 + 60 * q^59 + 96 * q^61 + 18 * q^64 + 48 * q^66 + 60 * q^69 + 60 * q^71 + 6 * q^74 - 42 * q^76 - 60 * q^79 + 36 * q^81 - 12 * q^84 + 72 * q^86 - 60 * q^89 - 120 * q^91 - 12 * q^94 - 342 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	0.613893	+	1.68666i	0.354431	+	0.973792i	0.980929	+	0.194368i	$0.0622657\pi$
$3$	0.613893	+	1.68666i	0.354431	+	0.973792i	−0.626497	+	0.779423i	$0.715512\pi$
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	1.68666	+	0.613893i	0.688575	+	0.250621i
$7$	1.17907	−	0.680736i	0.445646	−	0.257294i	−0.260343	−	0.965516i	$-0.583836\pi$
$7$	1.17907	−	0.680736i	0.445646	−	0.257294i	0.705990	+	0.708222i	$0.250502\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	−0.169813	+	0.142490i	−0.0566045	+	0.0474968i
$10$		0			0
$11$	−3.22960	+	5.59384i	−0.973762	+	1.68661i	−0.289803	+	0.957086i	$0.593590\pi$
$11$	−3.22960	+	5.59384i	−0.973762	+	1.68661i	−0.683960	+	0.729520i	$0.739744\pi$
$12$	1.55443	−	0.897451i	0.448726	−	0.259072i
$13$	−2.01005	+	5.52256i	−0.557487	+	1.53168i	0.265784	+	0.964033i	$0.414369\pi$
$13$	−2.01005	+	5.52256i	−0.557487	+	1.53168i	−0.823270	+	0.567650i	$0.807853\pi$
$14$	0.236417	−	1.34079i	0.0631851	−	0.358341i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	1.64480	−	1.96020i	0.398923	−	0.475418i	−0.528768	−	0.848766i	$-0.677346\pi$
$17$	1.64480	−	1.96020i	0.398923	−	0.475418i	0.927691	+	0.373348i	$0.121790\pi$
$18$			0.221676i			0.0522494i
$19$	3.83851	+	2.06538i	0.880615	+	0.473832i
$19$	3.83851	+	2.06538i	0.880615	+	0.473832i
$20$		0			0
$21$	1.87199	+	1.57079i	0.408502	+	0.342774i
$22$	2.20918	+	6.06967i	0.470999	+	1.29406i
$23$	8.29626	−	1.46285i	1.72989	−	0.305026i	0.781918	−	0.623382i	$-0.214242\pi$
$23$	8.29626	−	1.46285i	1.72989	−	0.305026i	0.947971	+	0.318356i	$0.103131\pi$
$24$	0.311682	−	1.76763i	0.0636217	−	0.360817i
$25$		0			0
$26$	2.93849	+	5.08962i	0.576286	+	0.998156i
$27$	4.31871	+	2.49341i	0.831137	+	0.479857i
$28$	−0.875137	−	1.04295i	−0.165385	−	0.197099i
$29$	−3.41558	+	2.86601i	−0.634257	+	0.532205i	−0.902248	−	0.431217i	$-0.858084\pi$
$29$	−3.41558	+	2.86601i	−0.634257	+	0.532205i	0.267992	+	0.963421i	$0.413640\pi$
$30$		0			0
$31$	0.701264	+	1.21462i	0.125951	+	0.218153i	0.922104	−	0.386942i	$-0.126469\pi$
$31$	0.701264	+	1.21462i	0.125951	+	0.218153i	−0.796153	+	0.605095i	$0.793135\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	−11.4175	−	2.01322i	−1.98753	−	0.350456i
$34$	−0.444341	−	2.51998i	−0.0762038	−	0.432173i
$35$		0			0
$36$	0.169813	+	0.142490i	0.0283022	+	0.0237484i
$37$		−	4.42962i		−	0.728225i	−0.931355	−	0.364112i	$-0.881372\pi$
$37$		−	4.42962i		−	0.728225i	0.931355	−	0.364112i	$-0.118628\pi$
$38$	4.04953	−	1.61287i	0.656920	−	0.261642i
$39$	−10.5486			−1.68913
$40$		0			0
$41$	5.15407	−	1.87593i	0.804931	−	0.292971i	0.0934025	−	0.995628i	$-0.470226\pi$
$41$	5.15407	−	1.87593i	0.804931	−	0.292971i	0.711528	+	0.702658i	$0.248003\pi$
$42$	2.40658	−	0.424346i	0.371344	−	0.0654780i
$43$	−6.74986	−	1.19018i	−1.02934	−	0.181501i	−0.366625	−	0.930369i	$-0.619487\pi$
$43$	−6.74986	−	1.19018i	−1.02934	−	0.181501i	−0.662719	+	0.748868i	$0.730598\pi$
$44$	6.06967	+	2.20918i	0.915037	+	0.333046i
$45$		0			0
$46$	4.21212	−	7.29560i	0.621043	−	1.07568i
$47$	−6.11821	−	7.29140i	−0.892433	−	1.06356i	−0.997609	−	0.0691065i	$-0.977985\pi$
$47$	−6.11821	−	7.29140i	−0.892433	−	1.06356i	0.105176	−	0.994454i	$-0.466459\pi$
$48$	−1.15374	−	1.37498i	−0.166528	−	0.198461i
$49$	−2.57320	+	4.45691i	−0.367600	+	0.636701i
$50$		0			0
$51$	4.31591	+	1.57086i	0.604349	+	0.219965i
$52$	5.78770	+	1.02053i	0.802610	+	0.141522i
$53$	4.35841	−	0.768506i	0.598674	−	0.105562i	0.133905	−	0.990994i	$-0.457248\pi$
$53$	4.35841	−	0.768506i	0.598674	−	0.105562i	0.464769	+	0.885432i	$0.346137\pi$
$54$	4.68608	−	1.70559i	0.637695	−	0.232102i
$55$		0			0
$56$	−1.36147			−0.181934
$57$	−1.12716	+	7.74218i	−0.149296	+	1.02548i
$58$			4.45872i			0.585458i
$59$	7.87687	+	6.60948i	1.02548	+	0.860481i	0.990306	−	0.138900i	$-0.0443566\pi$
$59$	7.87687	+	6.60948i	1.02548	+	0.860481i	0.0351753	+	0.999381i	$0.488801\pi$
$60$		0			0
$61$	1.12233	+	6.36503i	0.143699	+	0.814958i	0.968402	+	0.249393i	$0.0802310\pi$
$61$	1.12233	+	6.36503i	0.143699	+	0.814958i	−0.824703	+	0.565566i	$0.808658\pi$
$62$	1.38122	+	0.243546i	0.175415	+	0.0309304i
$63$	−0.103223	+	0.283604i	−0.0130049	+	0.0357307i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	−8.88125	+	7.45226i	−1.09321	+	0.917309i
$67$	−4.31929	−	5.14753i	−0.527685	−	0.628871i	0.434695	−	0.900578i	$-0.356856\pi$
$67$	−4.31929	−	5.14753i	−0.527685	−	0.628871i	−0.962380	+	0.271707i	$0.912412\pi$
$68$	−2.21604	−	1.27943i	−0.268734	−	0.155153i
$69$	7.56034	+	13.0949i	0.910158	+	1.57644i
$70$		0			0
$71$	0.336459	−	1.90815i	0.0399303	−	0.226456i	−0.958312	−	0.285725i	$-0.907766\pi$
$71$	0.336459	−	1.90815i	0.0399303	−	0.226456i	0.998242	+	0.0592685i	$0.0188768\pi$
$72$	0.218308	−	0.0384936i	0.0257278	−	0.00453651i
$73$	−2.14907	−	5.90451i	−0.251529	−	0.691071i	−0.999622	−	0.0274772i	$-0.991253\pi$
$73$	−2.14907	−	5.90451i	−0.251529	−	0.691071i	0.748093	−	0.663594i	$-0.230970\pi$
$74$	−3.39328	−	2.84730i	−0.394461	−	0.330992i
$75$		0			0
$76$	1.36746	−	4.13885i	0.156858	−	0.474758i
$77$			8.79403i			1.00217i
$78$	−6.78052	+	8.08071i	−0.767743	+	0.914960i
$79$	−3.37355	+	1.22787i	−0.379554	+	0.138146i	−0.524750	−	0.851257i	$-0.675841\pi$
$79$	−3.37355	+	1.22787i	−0.379554	+	0.138146i	0.145195	+	0.989403i	$0.453619\pi$
$80$		0			0
$81$	−1.66978	+	9.46980i	−0.185531	+	1.05220i
$82$	1.87593	−	5.15407i	0.207162	−	0.569172i
$83$	11.6908	−	6.74970i	1.28323	−	0.740876i	0.305797	−	0.952097i	$-0.401077\pi$
$83$	11.6908	−	6.74970i	1.28323	−	0.740876i	0.977438	+	0.211221i	$0.0677439\pi$
$84$	1.22185	−	2.11631i	0.133315	−	0.230909i
$85$		0			0
$86$	−5.25046	+	4.40566i	−0.566172	+	0.475074i
$87$	−6.93077	−	4.00148i	−0.743057	−	0.429004i
$88$	5.59384	−	3.22960i	0.596305	−	0.344277i
$89$	−1.78165	−	0.648469i	−0.188855	−	0.0687376i	0.245861	−	0.969305i	$-0.420929\pi$
$89$	−1.78165	−	0.648469i	−0.188855	−	0.0687376i	−0.434716	+	0.900567i	$0.643151\pi$
$90$		0			0
$91$	1.38942	+	7.87979i	0.145651	+	0.826026i
$92$	−2.88126	−	7.91619i	−0.300392	−	0.825320i
$93$	−1.61815	+	1.92844i	−0.167795	+	0.199970i
$94$	−9.51825			−0.981732
$95$		0			0
$96$	−1.79490			−0.183191
$97$	0.0793596	−	0.0945771i	0.00805774	−	0.00960285i	−0.762001	−	0.647576i	$-0.775783\pi$
$97$	0.0793596	−	0.0945771i	0.00805774	−	0.00960285i	0.770058	+	0.637974i	$0.220227\pi$
$98$	1.76017	+	4.83603i	0.177804	+	0.488513i
$99$	−0.248638	−	1.41010i	−0.0249891	−	0.141720i
$100$		0			0
$101$	−12.8307	−	4.66998i	−1.27670	−	0.464680i	−0.387359	−	0.921929i	$-0.626613\pi$
$101$	−12.8307	−	4.66998i	−1.27670	−	0.464680i	−0.889339	+	0.457249i	$0.848835\pi$
$102$	3.97757	−	2.29645i	0.393838	−	0.227382i
$103$	−5.95330	−	3.43714i	−0.586596	−	0.338672i	0.177154	−	0.984183i	$-0.443311\pi$
$103$	−5.95330	−	3.43714i	−0.586596	−	0.338672i	−0.763751	+	0.645512i	$0.776644\pi$
$104$	4.50203	−	3.77765i	0.441460	−	0.370429i
$105$		0			0
$106$	2.21282	−	3.83272i	0.214929	−	0.372267i
$107$	7.65580	−	4.42008i	0.740114	−	0.427305i	−0.0819969	−	0.996633i	$-0.526130\pi$
$107$	7.65580	−	4.42008i	0.740114	−	0.427305i	0.822111	+	0.569328i	$0.192796\pi$
$108$	1.70559	−	4.68608i	0.164121	−	0.450918i
$109$	1.65245	−	9.37152i	0.158276	−	0.897629i	−0.797453	−	0.603381i	$-0.793820\pi$
$109$	1.65245	−	9.37152i	0.158276	−	0.897629i	0.955729	−	0.294248i	$-0.0950691\pi$
$110$		0			0
$111$	7.47124	−	2.71931i	0.709139	−	0.258106i
$112$	−0.875137	+	1.04295i	−0.0826927	+	0.0985493i
$113$			11.0799i			1.04231i	0.853462	+	0.521154i	$0.174498\pi$
$113$			11.0799i			1.04231i	−0.853462	+	0.521154i	$0.825502\pi$
$114$	5.20633	+	5.84003i	0.487617	+	0.546969i
$115$		0			0
$116$	3.41558	+	2.86601i	0.317128	+	0.266102i
$117$	−0.445578	−	1.22422i	−0.0411937	−	0.113179i
$118$	10.1263	−	1.78554i	0.932203	−	0.164373i
$119$	0.604958	−	3.43088i	0.0554564	−	0.314509i
$120$		0			0
$121$	−15.3607	−	26.6055i	−1.39643	−	2.41868i
$122$	5.59731	+	3.23161i	0.506757	+	0.292576i
$123$	6.32809	+	7.54153i	0.570585	+	0.679997i
$124$	1.07440	−	0.901527i	0.0964838	−	0.0809595i
$125$		0			0
$126$	0.150903	+	0.261371i	0.0134435	+	0.0232848i
$127$	3.14395	−	8.63792i	0.278980	−	0.766491i	−0.718499	−	0.695528i	$-0.755170\pi$
$127$	3.14395	−	8.63792i	0.278980	−	0.766491i	0.997479	−	0.0709633i	$-0.0226073\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	−2.13626	−	12.1153i	−0.188087	−	1.06670i
$130$		0			0
$131$	0.0847217	+	0.0710900i	0.00740217	+	0.00621116i	0.646481	−	0.762930i	$-0.276240\pi$
$131$	0.0847217	+	0.0710900i	0.00740217	+	0.00621116i	−0.639079	+	0.769141i	$0.720684\pi$
$132$			11.5937i			1.00910i
$133$	5.93185	−	0.177782i	0.514357	−	0.0154157i
$134$	−6.71962			−0.580487
$135$		0			0
$136$	−2.40454	+	0.875181i	−0.206188	+	0.0750461i
$137$	−13.4434	+	2.37043i	−1.14855	+	0.202520i	−0.715341	−	0.698776i	$-0.753729\pi$
$137$	−13.4434	+	2.37043i	−1.14855	+	0.202520i	−0.433205	+	0.901295i	$0.642617\pi$
$138$	14.8910	+	2.62568i	1.26760	+	0.223513i
$139$	2.27126	+	0.826670i	0.192645	+	0.0701172i	0.436541	−	0.899684i	$-0.356203\pi$
$139$	2.27126	+	0.826670i	0.192645	+	0.0701172i	−0.243896	+	0.969801i	$0.578425\pi$
$140$		0			0
$141$	8.54216	−	14.7955i	0.719380	−	1.24600i
$142$	−1.24546	−	1.48428i	−0.104517	−	0.124558i
$143$	−24.4007	−	29.0796i	−2.04048	−	2.43176i
$144$	0.110838	−	0.191977i	0.00923648	−	0.0159981i
$145$		0			0
$146$	−5.90451	−	2.14907i	−0.488661	−	0.177858i
$147$	−9.09694	−	1.60404i	−0.750303	−	0.132299i
$148$	−4.36232	+	0.769195i	−0.358581	+	0.0632274i
$149$	−2.08531	+	0.758990i	−0.170835	+	0.0621789i	−0.426022	−	0.904713i	$-0.640085\pi$
$149$	−2.08531	+	0.758990i	−0.170835	+	0.0621789i	0.255187	+	0.966892i	$0.417863\pi$
$150$		0			0
$151$	−11.6771			−0.950267			−0.475133	−	0.879914i	$-0.657600\pi$
$151$	−11.6771			−0.950267			−0.475133	+	0.879914i	$0.657600\pi$
$152$	−2.29156	−	3.70793i	−0.185870	−	0.300753i
$153$			0.567236i			0.0458583i
$154$	6.73662	+	5.65269i	0.542852	+	0.455507i
$155$		0			0
$156$	1.83175	+	10.3884i	0.146657	+	0.831734i
$157$	−4.10004	−	0.722948i	−0.327219	−	0.0576975i	0.00762562	−	0.999971i	$-0.497573\pi$
$157$	−4.10004	−	0.722948i	−0.327219	−	0.0576975i	−0.334844	+	0.942273i	$0.608684\pi$
$158$	−1.22787	+	3.37355i	−0.0976843	+	0.268385i
$159$	3.97181	+	6.87937i	0.314985	+	0.545569i
$160$		0			0
$161$	8.78604	−	7.37236i	0.692437	−	0.581024i
$162$	6.18097	+	7.36620i	0.485623	+	0.578743i
$163$	4.15894	+	2.40117i	0.325753	+	0.188074i	0.653954	−	0.756534i	$-0.273109\pi$
$163$	4.15894	+	2.40117i	0.325753	+	0.188074i	−0.328201	+	0.944608i	$0.606442\pi$
$164$	−2.74242	−	4.75002i	−0.214147	−	0.370914i
$165$		0			0
$166$	2.34415	−	13.2943i	0.181941	−	1.03184i
$167$	3.80840	−	0.671525i	0.294703	−	0.0519641i	−0.0243418	−	0.999704i	$-0.507749\pi$
$167$	3.80840	−	0.671525i	0.294703	−	0.0519641i	0.319045	+	0.947740i	$0.396638\pi$
$168$	−0.835798	−	2.29634i	−0.0644832	−	0.177166i
$169$	−16.4998	−	13.8450i	−1.26921	−	1.06500i
$170$		0			0
$171$	−0.946128	+	0.196221i	−0.0723522	+	0.0150054i
$172$			6.85399i			0.522612i
$173$	7.41704	−	8.83929i	0.563907	−	0.672039i	−0.406461	−	0.913668i	$-0.633237\pi$
$173$	7.41704	−	8.83929i	0.563907	−	0.672039i	0.970369	+	0.241629i	$0.0776818\pi$
$174$	−7.52033	+	2.73718i	−0.570115	+	0.207505i
$175$		0			0
$176$	1.12163	−	6.36108i	0.0845460	−	0.479484i
$177$	−6.31237	+	17.3431i	−0.474467	+	1.30359i
$178$	−1.64198	+	0.947998i	−0.123072	+	0.0710555i
$179$	4.18981	−	7.25696i	0.313161	−	0.542411i	−0.665884	−	0.746055i	$-0.731945\pi$
$179$	4.18981	−	7.25696i	0.313161	−	0.542411i	0.979045	+	0.203645i	$0.0652788\pi$
$180$		0			0
$181$	−8.13969	+	6.83001i	−0.605018	+	0.507671i	−0.893054	−	0.449949i	$-0.851442\pi$
$181$	−8.13969	+	6.83001i	−0.605018	+	0.507671i	0.288036	+	0.957620i	$0.406998\pi$
$182$	6.92937	+	4.00067i	0.513639	+	0.296550i
$183$	−10.0466	+	5.80042i	−0.742668	+	0.428780i
$184$	−7.91619	−	2.88126i	−0.583590	−	0.212409i
$185$		0			0
$186$	0.437142	+	2.47915i	0.0320528	+	0.181780i
$187$	5.65298	+	15.5314i	0.413386	+	1.13577i
$188$	−6.11821	+	7.29140i	−0.446216	+	0.531780i
$189$	6.78942			0.493857
$190$		0			0
$191$	10.8514			0.785179			0.392589	−	0.919714i	$-0.371579\pi$
$191$	10.8514			0.785179			0.392589	+	0.919714i	$0.371579\pi$
$192$	−1.15374	+	1.37498i	−0.0832641	+	0.0992303i
$193$	0.662240	+	1.81949i	0.0476691	+	0.130970i	0.961243	−	0.275704i	$-0.0889109\pi$
$193$	0.662240	+	1.81949i	0.0476691	+	0.130970i	−0.913574	+	0.406674i	$0.866689\pi$
$194$	−0.0214389	−	0.121586i	−0.00153922	−	0.00872936i
$195$		0			0
$196$	4.83603	+	1.76017i	0.345431	+	0.125726i
$197$	10.6122	−	6.12697i	0.756090	−	0.436529i	−0.0718004	−	0.997419i	$-0.522874\pi$
$197$	10.6122	−	6.12697i	0.756090	−	0.436529i	0.827890	+	0.560890i	$0.189541\pi$
$198$	−1.24002	−	0.715925i	−0.0881242	−	0.0508785i
$199$	0.331678	−	0.278311i	0.0235121	−	0.0197290i	−0.630956	−	0.775819i	$-0.717337\pi$
$199$	0.331678	−	0.278311i	0.0235121	−	0.0197290i	0.654468	+	0.756090i	$0.272893\pi$
$200$		0			0
$201$	6.03053	−	10.4452i	0.425361	−	0.736747i
$202$	−11.8248	+	6.82705i	−0.831990	+	0.480350i
$203$	−2.07621	+	5.70433i	−0.145721	+	0.400365i
$204$	0.797549	−	4.52312i	0.0558396	−	0.316682i
$205$		0			0
$206$	−6.45971	+	2.35114i	−0.450070	+	0.163812i
$207$	−1.20037	+	1.43055i	−0.0834317	+	0.0994300i
$208$		−	5.87698i		−	0.407496i
$209$	−23.9503	+	14.8017i	−1.65668	+	1.02385i
$210$		0			0
$211$	−10.5293	−	8.83513i	−0.724867	−	0.608235i	0.203860	−	0.979000i	$-0.434651\pi$
$211$	−10.5293	−	8.83513i	−0.724867	−	0.608235i	−0.928727	+	0.370765i	$0.879096\pi$
$212$	−1.51366	−	4.15875i	−0.103959	−	0.285624i
$213$	3.42495	−	0.603911i	0.234674	−	0.0413793i
$214$	1.53508	−	8.70585i	0.104936	−	0.595120i
$215$		0			0
$216$	−2.49341	−	4.31871i	−0.169655	−	0.293851i
$217$	1.65368	+	0.954751i	0.112259	+	0.0648127i
$218$	−6.11683	−	7.28975i	−0.414284	−	0.493724i
$219$	8.63959	−	7.24948i	0.583809	−	0.489874i
$220$		0			0
$221$	7.51918	+	13.0236i	0.505795	+	0.876062i
$222$	2.71931	−	7.47124i	0.182508	−	0.501437i
$223$	22.1729	+	3.90968i	1.48481	+	0.261812i	0.856497	−	0.516151i	$-0.172636\pi$
$223$	22.1729	+	3.90968i	1.48481	+	0.261812i	0.628310	+	0.777963i	$0.283747\pi$
$224$	0.236417	+	1.34079i	0.0157963	+	0.0895852i
$225$		0			0
$226$	8.48769	+	7.12202i	0.564593	+	0.473750i
$227$		−	18.8403i		−	1.25048i	−0.780433	−	0.625239i	$-0.785002\pi$
$227$		−	18.8403i		−	1.25048i	0.780433	−	0.625239i	$-0.214998\pi$
$228$	7.82029	−	0.234380i	0.517911	−	0.0155222i
$229$	4.51829			0.298577			0.149289	−	0.988794i	$-0.452302\pi$
$229$	4.51829			0.298577			0.149289	+	0.988794i	$0.452302\pi$
$230$		0			0
$231$	−14.8325	+	5.39859i	−0.975908	+	0.355201i
$232$	4.39098	−	0.774248i	0.288282	−	0.0508319i
$233$	10.5997	+	1.86901i	0.694406	+	0.122443i	0.509701	−	0.860351i	$-0.329756\pi$
$233$	10.5997	+	1.86901i	0.694406	+	0.122443i	0.184705	+	0.982794i	$0.440867\pi$
$234$	−1.22422	−	0.445578i	−0.0800295	−	0.0291284i
$235$		0			0
$236$	5.14126	−	8.90493i	0.334668	−	0.579662i
$237$	−4.14200	−	4.93624i	−0.269052	−	0.320643i
$238$	−2.23935	−	2.66875i	−0.145156	−	0.172990i
$239$	11.7010	−	20.2668i	0.756876	−	1.31095i	−0.187560	−	0.982253i	$-0.560058\pi$
$239$	11.7010	−	20.2668i	0.756876	−	1.31095i	0.944436	−	0.328695i	$-0.106609\pi$
$240$		0			0
$241$	19.6353	+	7.14665i	1.26482	+	0.460356i	0.885383	−	0.464862i	$-0.153896\pi$
$241$	19.6353	+	7.14665i	1.26482	+	0.460356i	0.379435	+	0.925218i	$0.376118\pi$
$242$	−30.2547	−	5.33471i	−1.94484	−	0.342928i
$243$	−2.26419	+	0.399237i	−0.145248	+	0.0256111i
$244$	6.07344	−	2.21055i	0.388812	−	0.141516i
$245$		0			0
$246$	9.84477			0.627679
$247$	−19.1218	+	17.0469i	−1.21669	+	1.08467i
$248$		−	1.40253i		−	0.0890606i
$249$	18.5613	+	15.5748i	1.17628	+	0.987014i
$250$		0			0
$251$	−3.10917	−	17.6330i	−0.196249	−	1.11298i	−0.910628	−	0.413226i	$-0.864402\pi$
$251$	−3.10917	−	17.6330i	−0.196249	−	1.11298i	0.714379	−	0.699759i	$-0.246709\pi$
$252$	0.297220	+	0.0524079i	0.0187231	+	0.00330139i
$253$	−18.6107	+	51.1324i	−1.17004	+	3.21466i
$254$	−4.59614	−	7.96075i	−0.288388	−	0.499502i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−0.312965	−	0.372978i	−0.0195222	−	0.0232657i	0.756195	−	0.654346i	$-0.227056\pi$
$257$	−0.312965	−	0.372978i	−0.0195222	−	0.0232657i	−0.775717	+	0.631081i	$0.782612\pi$
$258$	−10.6541	−	6.15112i	−0.663292	−	0.382952i
$259$	−3.01540	−	5.22282i	−0.187368	−	0.324531i
$260$		0			0
$261$	0.171632	−	0.973373i	0.0106238	−	0.0602503i
$262$	0.108916	−	0.0192049i	0.00672886	−	0.00118648i
$263$	−7.54785	−	20.7375i	−0.465420	−	1.27873i	−0.921356	−	0.388719i	$-0.872918\pi$
$263$	−7.54785	−	20.7375i	−0.465420	−	1.27873i	0.455936	−	0.890013i	$-0.349305\pi$
$264$	8.88125	+	7.45226i	0.546603	+	0.458655i
$265$		0			0
$266$	3.67673	−	4.65834i	0.225435	−	0.285621i
$267$		−	3.40313i		−	0.208268i
$268$	−4.31929	+	5.14753i	−0.263843	+	0.314435i
$269$	16.6789	−	6.07061i	1.01693	−	0.370131i	0.220838	−	0.975310i	$-0.429121\pi$
$269$	16.6789	−	6.07061i	1.01693	−	0.370131i	0.796089	+	0.605179i	$0.206899\pi$
$270$		0			0
$271$	1.89657	−	10.7560i	0.115208	−	0.653380i	−0.871438	−	0.490505i	$-0.836812\pi$
$271$	1.89657	−	10.7560i	0.115208	−	0.653380i	0.986647	−	0.162875i	$-0.0520766\pi$
$272$	−0.875181	+	2.40454i	−0.0530656	+	0.145797i
$273$	−12.4375	+	7.18082i	−0.752755	+	0.434603i
$274$	−6.82538	+	11.8219i	−0.412337	+	0.714188i
$275$		0			0
$276$	11.5831	−	9.71939i	0.697222	−	0.585039i
$277$	−7.84590	−	4.52983i	−0.471414	−	0.272171i	0.245417	−	0.969418i	$-0.421075\pi$
$277$	−7.84590	−	4.52983i	−0.471414	−	0.272171i	−0.716832	+	0.697246i	$0.754408\pi$
$278$	2.09320	−	1.20851i	0.125542	−	0.0724816i
$279$	−0.292156	−	0.106336i	−0.0174909	−	0.00636618i
$280$		0			0
$281$	2.65688	+	15.0679i	0.158496	+	0.898876i	0.955520	+	0.294928i	$0.0952956\pi$
$281$	2.65688	+	15.0679i	0.158496	+	0.898876i	−0.797023	+	0.603948i	$0.793593\pi$
$282$	−5.84318	−	16.0540i	−0.347957	−	0.956003i
$283$	−6.33163	+	7.54574i	−0.376376	+	0.448548i	−0.920667	−	0.390349i	$-0.872354\pi$
$283$	−6.33163	+	7.54574i	−0.376376	+	0.448548i	0.544291	+	0.838897i	$0.316799\pi$
$284$	−1.93759			−0.114975
$285$		0			0
$286$	−37.9607			−2.24466
$287$	4.79999	−	5.72041i	0.283335	−	0.337665i
$288$	−0.0758175	−	0.208307i	−0.00446759	−	0.0122746i
$289$	1.81501	+	10.2935i	0.106766	+	0.605498i
$290$		0			0
$291$	0.208237	+	0.0757922i	0.0122071	+	0.00444302i
$292$	−5.44163	+	3.14173i	−0.318447	+	0.183856i
$293$	7.08299	+	4.08936i	0.413792	+	0.238903i	0.692418	−	0.721497i	$-0.256545\pi$
$293$	7.08299	+	4.08936i	0.413792	+	0.238903i	−0.278625	+	0.960400i	$0.589879\pi$
$294$	−7.07617	+	5.93761i	−0.412690	+	0.346288i
$295$		0			0
$296$	−2.21481	+	3.83616i	−0.128733	+	0.222972i
$297$	−27.8955	+	16.1055i	−1.61866	+	0.934534i
$298$	−0.758990	+	2.08531i	−0.0439671	+	0.120799i
$299$	−8.59717	+	48.7570i	−0.497187	+	2.81969i
$300$		0			0
$301$	−8.76875	+	3.19157i	−0.505423	+	0.183959i
$302$	−7.50588	+	8.94516i	−0.431915	+	0.514736i
$303$		−	24.5078i		−	1.40794i
$304$	−4.31343	−	0.627978i	−0.247392	−	0.0360170i
$305$		0			0
$306$	0.434528	+	0.364612i	0.0248403	+	0.0208435i
$307$	2.06799	+	5.68175i	0.118026	+	0.324275i	0.984612	−	0.174753i	$-0.0559128\pi$
$307$	2.06799	+	5.68175i	0.118026	+	0.324275i	−0.866586	+	0.499028i	$0.833691\pi$
$308$	8.66043	−	1.52707i	0.493474	−	0.0870127i
$309$	2.14259	−	12.1512i	0.121888	−	0.691259i
$310$		0			0
$311$	−16.5582	−	28.6797i	−0.938932	−	1.62628i	−0.767468	−	0.641087i	$-0.778484\pi$
$311$	−16.5582	−	28.6797i	−0.938932	−	1.62628i	−0.171463	−	0.985191i	$-0.554849\pi$
$312$	9.13537	+	5.27431i	0.517188	+	0.298599i
$313$	3.96728	+	4.72802i	0.224244	+	0.267244i	0.866423	−	0.499312i	$-0.166414\pi$
$313$	3.96728	+	4.72802i	0.224244	+	0.267244i	−0.642179	+	0.766555i	$0.721969\pi$
$314$	−3.18927	+	2.67611i	−0.179981	+	0.151022i
$315$		0			0
$316$	1.79503	+	3.10908i	0.100978	+	0.174900i
$317$	−5.61135	+	15.4171i	−0.315165	+	0.865908i	0.676428	+	0.736509i	$0.263527\pi$
$317$	−5.61135	+	15.4171i	−0.315165	+	0.865908i	−0.991593	+	0.129399i	$0.958695\pi$
$318$	7.82293	+	1.37939i	0.438688	+	0.0773525i
$319$	−5.00103	−	28.3623i	−0.280004	−	1.58798i
$320$		0			0
$321$	12.1550	+	10.1992i	0.678425	+	0.569266i
$322$		−	11.4694i		−	0.639163i
$323$	10.3622	−	4.12710i	0.576566	−	0.229638i
$324$	9.61589			0.534216
$325$		0			0
$326$	4.51272	−	1.64249i	0.249936	−	0.0909694i
$327$	16.8210	−	2.96599i	0.930202	−	0.164020i
$328$	−5.40152	−	0.952434i	−0.298249	−	0.0525894i
$329$	−12.1773	−	4.43218i	−0.671357	−	0.244354i
$330$		0			0
$331$	−8.53392	+	14.7812i	−0.469066	+	0.812447i	−0.999375	−	0.0353579i	$-0.988743\pi$
$331$	−8.53392	+	14.7812i	−0.469066	+	0.812447i	0.530308	+	0.847805i	$0.322076\pi$
$332$	−8.67725	−	10.3411i	−0.476226	−	0.567544i
$333$	0.631178	+	0.752208i	0.0345883	+	0.0412208i
$334$	1.93358	−	3.34906i	0.105801	−	0.183252i
$335$		0			0
$336$	−2.29634	−	0.835798i	−0.125275	−	0.0455965i
$337$	18.5701	+	3.27441i	1.01158	+	0.178368i	0.654785	−	0.755816i	$-0.272759\pi$
$337$	18.5701	+	3.27441i	1.01158	+	0.178368i	0.356792	+	0.934184i	$0.383870\pi$
$338$	−21.2117	+	3.74020i	−1.15377	+	0.203440i
$339$	−18.6880	+	6.80187i	−1.01499	+	0.369427i
$340$		0			0
$341$	−9.05922			−0.490584
$342$	−0.457845	+	0.850905i	−0.0247574	+	0.0460117i
$343$			16.5370i			0.892913i
$344$	5.25046	+	4.40566i	0.283086	+	0.237537i
$345$		0			0
$346$	−2.00370	−	11.3636i	−0.107720	−	0.610909i
$347$	5.32560	+	0.939047i	0.285893	+	0.0504107i	0.314756	−	0.949173i	$-0.398077\pi$
$347$	5.32560	+	0.939047i	0.285893	+	0.0504107i	−0.0288626	+	0.999583i	$0.509189\pi$
$348$	−2.73718	+	7.52033i	−0.146728	+	0.403132i
$349$	−18.1540	−	31.4436i	−0.971761	−	1.68314i	−0.690235	−	0.723586i	$-0.742493\pi$
$349$	−18.1540	−	31.4436i	−0.971761	−	1.68314i	−0.281526	−	0.959554i	$-0.590841\pi$
$350$		0			0
$351$	−22.4508	+	18.8385i	−1.19834	+	1.00552i
$352$	−4.15190	−	4.94804i	−0.221297	−	0.263731i
$353$	−1.06514	−	0.614958i	−0.0566916	−	0.0327309i	0.471386	−	0.881927i	$-0.343754\pi$
$353$	−1.06514	−	0.614958i	−0.0566916	−	0.0327309i	−0.528078	+	0.849196i	$0.677087\pi$
$354$	9.22807	+	15.9835i	0.490466	+	0.849513i
$355$		0			0
$356$	−0.329236	+	1.86719i	−0.0174495	+	0.0989610i
$357$	6.15810	−	1.08584i	0.325921	−	0.0574687i
$358$	−2.86600	−	7.87426i	−0.151473	−	0.416168i
$359$	11.5897	+	9.72494i	0.611683	+	0.513263i	0.895177	−	0.445711i	$-0.147049\pi$
$359$	11.5897	+	9.72494i	0.611683	+	0.513263i	−0.283494	+	0.958974i	$0.591494\pi$
$360$		0			0
$361$	10.4684	+	15.8560i	0.550967	+	0.834527i
$362$			10.6256i			0.558470i
$363$	35.4445	−	42.2411i	1.86036	−	2.21709i
$364$	7.51881	−	2.73662i	0.394093	−	0.143438i
$365$		0			0
$366$	−2.01447	+	11.4246i	−0.105298	+	0.597174i
$367$	−0.723196	+	1.98697i	−0.0377505	+	0.103719i	−0.957136	−	0.289640i	$-0.906465\pi$
$367$	−0.723196	+	1.98697i	−0.0377505	+	0.103719i	0.919385	+	0.393358i	$0.128687\pi$
$368$	−7.29560	+	4.21212i	−0.380310	+	0.219572i
$369$	−0.607928	+	1.05296i	−0.0316475	+	0.0548151i
$370$		0			0
$371$	4.61572	−	3.87305i	0.239636	−	0.201079i
$372$	2.18013	+	1.25870i	0.113035	+	0.0652605i
$373$	−4.36262	+	2.51876i	−0.225888	+	0.130416i	−0.608674	−	0.793421i	$-0.708298\pi$
$373$	−4.36262	+	2.51876i	−0.225888	+	0.130416i	0.382786	+	0.923837i	$0.374965\pi$
$374$	15.5314	+	5.65298i	0.803111	+	0.292308i
$375$		0			0
$376$	1.65283	+	9.37364i	0.0852380	+	0.483409i
$377$	−8.96223	−	24.6235i	−0.461579	−	1.26818i
$378$	4.36415	−	5.20100i	0.224468	−	0.267510i
$379$	−37.2812			−1.91501			−0.957503	−	0.288423i	$-0.906869\pi$
$379$	−37.2812			−1.91501			−0.957503	+	0.288423i	$0.906869\pi$
$380$		0			0
$381$	16.4993			0.845282
$382$	6.97514	−	8.31264i	0.356879	−	0.425312i
$383$	5.09082	+	13.9869i	0.260129	+	0.714698i	0.999158	+	0.0410250i	$0.0130623\pi$
$383$	5.09082	+	13.9869i	0.260129	+	0.714698i	−0.739029	+	0.673673i	$0.764715\pi$
$384$	0.311682	+	1.76763i	0.0159054	+	0.0902042i
$385$		0			0
$386$	1.81949	+	0.662240i	0.0926096	+	0.0337071i
$387$	1.31581	−	0.759681i	0.0668862	−	0.0386168i
$388$	−0.106921	−	0.0617308i	−0.00542808	−	0.00313391i
$389$	−23.6259	+	19.8245i	−1.19788	+	1.00514i	−0.198191	+	0.980163i	$0.563507\pi$
$389$	−23.6259	+	19.8245i	−1.19788	+	1.00514i	−0.999688	+	0.0249764i	$0.992049\pi$
$390$		0			0
$391$	10.7782	−	18.6684i	0.545078	−	0.944102i
$392$	4.45691	−	2.57320i	0.225108	−	0.129966i
$393$	−0.0678943	+	0.186538i	−0.00342482	+	0.00940960i
$394$	2.12787	−	12.0678i	0.107201	−	0.607966i
$395$		0			0
$396$	−1.34550	+	0.489721i	−0.0676138	+	0.0246094i
$397$	14.2405	−	16.9711i	0.714708	−	0.851756i	−0.279397	−	0.960176i	$-0.590135\pi$
$397$	14.2405	−	16.9711i	0.714708	−	0.851756i	0.994105	+	0.108420i	$0.0345790\pi$
$398$		−	0.432975i		−	0.0217031i
$399$	3.94138	+	9.89586i	0.197316	+	0.495413i
$400$		0			0
$401$	23.8011	+	19.9715i	1.18857	+	0.997330i	0.999883	+	0.0152927i	$0.00486799\pi$
$401$	23.8011	+	19.9715i	1.18857	+	0.997330i	0.188688	+	0.982037i	$0.439576\pi$
$402$	−4.12513	−	11.3337i	−0.205743	−	0.565273i
$403$	−8.11741	+	1.43132i	−0.404357	+	0.0712990i
$404$	−2.37101	+	13.4467i	−0.117962	+	0.668997i
$405$		0			0
$406$	3.03521	+	5.25714i	0.150635	+	0.260907i
$407$	24.7786	+	14.3059i	1.22823	+	0.709118i
$408$	−2.95226	−	3.51836i	−0.146159	−	0.174185i
$409$	−1.56037	+	1.30931i	−0.0771554	+	0.0647411i	−0.680550	−	0.732702i	$-0.738259\pi$
$409$	−1.56037	+	1.30931i	−0.0771554	+	0.0647411i	0.603394	+	0.797443i	$0.293815\pi$
$410$		0			0
$411$	−12.2509	−	21.2192i	−0.604292	−	1.04667i
$412$	−2.35114	+	6.45971i	−0.115833	+	0.318247i
$413$	13.7867	+	2.43097i	0.678399	+	0.119620i
$414$	0.324279	+	1.83908i	0.0159374	+	0.0903857i
$415$		0			0
$416$	−4.50203	−	3.77765i	−0.220730	−	0.185215i
$417$			4.33832i			0.212448i
$418$	−4.05624	+	27.8613i	−0.198397	+	1.36274i
$419$	11.2236			0.548308			0.274154	−	0.961686i	$-0.411602\pi$
$419$	11.2236			0.548308			0.274154	+	0.961686i	$0.411602\pi$
$420$		0			0
$421$	9.19144	−	3.34541i	0.447964	−	0.163045i	−0.108181	−	0.994131i	$-0.534502\pi$
$421$	9.19144	−	3.34541i	0.447964	−	0.163045i	0.556144	+	0.831086i	$0.312280\pi$
$422$	−13.5362	+	2.38680i	−0.658932	+	0.116187i
$423$	2.07791	+	0.366391i	0.101031	+	0.0178146i
$424$	−4.15875	−	1.51366i	−0.201967	−	0.0735099i
$425$		0			0
$426$	1.73889	−	3.01185i	0.0842496	−	0.145925i
$427$	5.65620	+	6.74080i	0.273723	+	0.326210i
$428$	−5.68234	−	6.77195i	−0.274666	−	0.327335i
$429$	34.0679	−	59.0073i	1.64481	−	2.84890i
$430$		0			0
$431$	4.58045	+	1.66715i	0.220633	+	0.0803037i	0.449971	−	0.893043i	$-0.351434\pi$
$431$	4.58045	+	1.66715i	0.220633	+	0.0803037i	−0.229339	+	0.973347i	$0.573656\pi$
$432$	−4.91106	−	0.865953i	−0.236284	−	0.0416632i
$433$	−19.6135	+	3.45838i	−0.942563	+	0.166199i	−0.623755	−	0.781620i	$-0.714394\pi$
$433$	−19.6135	+	3.45838i	−0.942563	+	0.166199i	−0.318808	+	0.947819i	$0.603283\pi$
$434$	1.79434	−	0.653088i	0.0861313	−	0.0313492i
$435$		0			0
$436$	−9.51609			−0.455738
$437$	34.8666	+	11.5198i	1.66790	+	0.551066i
$438$		−	11.2782i		−	0.538892i
$439$	16.3249	+	13.6982i	0.779145	+	0.653780i	0.943033	−	0.332699i	$-0.107959\pi$
$439$	16.3249	+	13.6982i	0.779145	+	0.653780i	−0.163888	+	0.986479i	$0.552404\pi$
$440$		0			0
$441$	−0.198103	−	1.12350i	−0.00943348	−	0.0534999i
$442$	14.8099	+	2.61138i	0.704435	+	0.124211i
$443$	2.11541	−	5.81205i	0.100506	−	0.276139i	−0.879241	−	0.476377i	$-0.841950\pi$
$443$	2.11541	−	5.81205i	0.100506	−	0.276139i	0.979747	+	0.200239i	$0.0641718\pi$
$444$	−3.97537	−	6.88554i	−0.188662	−	0.326773i
$445$		0			0
$446$	17.2475	−	14.4723i	0.816691	−	0.685285i
$447$	−2.56031	−	3.05126i	−0.121099	−	0.144320i
$448$	1.17907	+	0.680736i	0.0557058	+	0.0321617i
$449$	20.3687	+	35.2797i	0.961260	+	1.66495i	0.719345	+	0.694653i	$0.244442\pi$
$449$	20.3687	+	35.2797i	0.961260	+	1.66495i	0.241914	+	0.970298i	$0.422225\pi$
$450$		0			0
$451$	−6.15197	+	34.8896i	−0.289685	+	1.64288i
$452$	10.9116	−	1.92400i	0.513237	−	0.0904975i
$453$	−7.16847	−	19.6952i	−0.336804	−	0.925362i
$454$	−14.4325	−	12.1103i	−0.677353	−	0.568366i
$455$		0			0
$456$	4.84724	−	6.14134i	0.226993	−	0.287595i
$457$			14.7073i			0.687978i	0.938974	+	0.343989i	$0.111778\pi$
$457$			14.7073i			0.687978i	−0.938974	+	0.343989i	$0.888222\pi$
$458$	2.90430	−	3.46121i	0.135709	−	0.161732i
$459$	11.9910	−	4.36437i	0.559692	−	0.203711i
$460$		0			0
$461$	−2.43148	+	13.7896i	−0.113245	+	0.642245i	0.874359	+	0.485280i	$0.161282\pi$
$461$	−2.43148	+	13.7896i	−0.113245	+	0.642245i	−0.987604	+	0.156966i	$0.949829\pi$
$462$	−5.39859	+	14.8325i	−0.251165	+	0.690071i
$463$	−1.96929	+	1.13697i	−0.0915206	+	0.0528394i	−0.545062	−	0.838396i	$-0.683494\pi$
$463$	−1.96929	+	1.13697i	−0.0915206	+	0.0528394i	0.453541	+	0.891235i	$0.350160\pi$
$464$	2.22936	−	3.86136i	0.103495	−	0.179259i
$465$		0			0
$466$	8.24507	−	6.91843i	0.381945	−	0.320490i
$467$	25.5178	+	14.7327i	1.18082	+	0.681749i	0.956205	−	0.292698i	$-0.0945531\pi$
$467$	25.5178	+	14.7327i	1.18082	+	0.681749i	0.224618	+	0.974447i	$0.427886\pi$
$468$	−1.12824	+	0.651392i	−0.0521531	+	0.0301106i
$469$	−8.59685	−	3.12900i	−0.396966	−	0.144484i
$470$		0			0
$471$	−1.29762	−	7.35917i	−0.0597912	−	0.339093i
$472$	−3.51683	−	9.66242i	−0.161875	−	0.444749i
$473$	28.4571	−	33.9138i	1.30846	−	1.55936i
$474$	−6.44381			−0.295974
$475$		0			0
$476$	−3.48381			−0.159680
$477$	−0.630612	+	0.751534i	−0.0288738	+	0.0344104i
$478$	−8.00397	−	21.9907i	−0.366093	−	1.00583i
$479$	−3.55187	−	20.1437i	−0.162289	−	0.920387i	−0.951816	−	0.306671i	$-0.900785\pi$
$479$	−3.55187	−	20.1437i	−0.162289	−	0.920387i	0.789527	−	0.613716i	$-0.210326\pi$
$480$		0			0
$481$	24.4628	+	8.90374i	1.11541	+	0.405976i
$482$	18.0960	−	10.4477i	0.824248	−	0.475880i
$483$	17.8283	+	10.2932i	0.811217	+	0.468357i
$484$	−23.5339	+	19.7473i	−1.06972	+	0.897606i
$485$		0			0
$486$	−1.14956	+	1.99109i	−0.0521450	+	0.0903178i
$487$	25.2182	−	14.5597i	1.14275	−	0.659765i	0.195637	−	0.980676i	$-0.437323\pi$
$487$	25.2182	−	14.5597i	1.14275	−	0.659765i	0.947109	+	0.320912i	$0.103989\pi$
$488$	2.21055	−	6.07344i	0.100067	−	0.274932i
$489$	−1.49680	+	8.48877i	−0.0676876	+	0.383875i
$490$		0			0
$491$	−15.6448	+	5.69426i	−0.706042	+	0.256978i	−0.669988	−	0.742372i	$-0.733701\pi$
$491$	−15.6448	+	5.69426i	−0.706042	+	0.256978i	−0.0360537	+	0.999350i	$0.511479\pi$
$492$	6.32809	−	7.54153i	0.285293	−	0.339998i
$493$			11.4092i			0.513846i
$494$	0.767422	+	25.6057i	0.0345279	+	1.15205i
$495$		0			0
$496$	−1.07440	−	0.901527i	−0.0482419	−	0.0404798i
$497$	−0.902240	−	2.47888i	−0.0404710	−	0.111193i
$498$	23.8620	−	4.20752i	1.06928	−	0.188543i
$499$	−5.09005	+	28.8671i	−0.227862	+	1.29227i	0.629276	+	0.777182i	$0.283351\pi$
$499$	−5.09005	+	28.8671i	−0.227862	+	1.29227i	−0.857138	+	0.515087i	$0.827760\pi$
$500$		0			0
$501$	3.47058	+	6.01123i	0.155054	+	0.268562i
$502$	−15.5062	−	8.95251i	−0.692075	−	0.399570i
$503$	−4.54061	−	5.41129i	−0.202456	−	0.241277i	0.655258	−	0.755405i	$-0.272560\pi$
$503$	−4.54061	−	5.41129i	−0.202456	−	0.241277i	−0.857713	+	0.514128i	$0.828116\pi$
$504$	0.231196	−	0.193997i	0.0102983	−	0.00864129i
$505$		0			0
$506$	27.2070	+	47.1238i	1.20950	+	2.09491i
$507$	13.2226	−	36.3288i	0.587237	−	1.61342i
$508$	−9.05263	−	1.59622i	−0.401646	−	0.0708209i
$509$	−2.11320	−	11.9846i	−0.0936661	−	0.531207i	−0.995148	−	0.0983900i	$-0.968631\pi$
$509$	−2.11320	−	11.9846i	−0.0936661	−	0.531207i	0.901482	−	0.432817i	$-0.142480\pi$
$510$		0			0
$511$	−6.55331	−	5.49888i	−0.289901	−	0.243256i
$512$		−	1.00000i		−	0.0441942i
$513$	11.4276	+	18.4908i	0.504540	+	0.816389i
$514$	−0.486888			−0.0214757
$515$		0			0
$516$	−11.5603	+	4.20761i	−0.508915	+	0.185230i
$517$	60.5463	−	10.6760i	2.66282	−	0.469528i
$518$	−5.93918	−	1.04724i	−0.260952	−	0.0460130i
$519$	19.4621	+	7.08363i	0.854292	+	0.310937i
$520$		0			0
$521$	−12.6575	+	21.9234i	−0.554535	+	0.960483i	0.443405	+	0.896322i	$0.353770\pi$
$521$	−12.6575	+	21.9234i	−0.554535	+	0.960483i	−0.997940	+	0.0641611i	$0.979563\pi$
$522$	−0.635324	−	0.757150i	−0.0278074	−	0.0331396i
$523$	−27.7800	−	33.1069i	−1.21473	−	1.44766i	−0.858150	−	0.513399i	$-0.828386\pi$
$523$	−27.7800	−	33.1069i	−1.21473	−	1.44766i	−0.356583	−	0.934263i	$-0.616058\pi$
$524$	0.0552982	−	0.0957793i	0.00241571	−	0.00418414i
$525$		0			0
$526$	−20.7375	−	7.54785i	−0.904200	−	0.329102i
$527$	3.53434	+	0.623200i	0.153958	+	0.0271470i
$528$	11.4175	−	2.01322i	0.496884	−	0.0876140i
$529$	45.0750	−	16.4060i	1.95978	−	0.713302i
$530$		0			0
$531$	−2.27939			−0.0989169
$532$	−1.20514	−	5.81086i	−0.0522493	−	0.251933i
$533$			32.2344i			1.39623i
$534$	−2.60695	−	2.18749i	−0.112814	−	0.0946619i
$535$		0			0
$536$	1.16685	+	6.61753i	0.0504002	+	0.285834i
$537$	14.8121	+	2.61177i	0.639189	+	0.112706i
$538$	6.07061	−	16.6789i	0.261722	−	0.719076i
$539$	−16.6208	−	28.7881i	−0.715909	−	1.23999i
$540$		0			0
$541$	−16.8919	+	14.1740i	−0.726240	+	0.609388i	−0.929104	−	0.369819i	$-0.879420\pi$
$541$	−16.8919	+	14.1740i	−0.726240	+	0.609388i	0.202864	+	0.979207i	$0.434975\pi$
$542$	−7.02047	−	8.36667i	−0.301555	−	0.359379i
$543$	−16.5168	−	9.53597i	−0.708803	−	0.409228i
$544$	1.27943	+	2.21604i	0.0548550	+	0.0950117i
$545$		0			0
$546$	−2.49387	+	14.1435i	−0.106728	+	0.605284i
$547$	−23.6615	+	4.17215i	−1.01169	+	0.178388i	−0.654836	−	0.755771i	$-0.727262\pi$
$547$	−23.6615	+	4.17215i	−1.01169	+	0.178388i	−0.356855	+	0.934160i	$0.616151\pi$
$548$	4.66884	+	12.8275i	0.199443	+	0.547965i
$549$	−1.09754	−	0.920946i	−0.0468419	−	0.0393050i
$550$		0			0
$551$	−19.0301	+	3.94673i	−0.810712	+	0.168137i
$552$		−	15.1207i		−	0.643579i
$553$	−3.14179	+	3.74424i	−0.133603	+	0.159221i
$554$	−8.51330	+	3.09859i	−0.361695	+	0.131646i
$555$		0			0
$556$	0.419711	−	2.38030i	0.0177997	−	0.100947i
$557$	1.55843	−	4.28175i	0.0660328	−	0.181424i	−0.902288	−	0.431135i	$-0.858113\pi$
$557$	1.55843	−	4.28175i	0.0660328	−	0.181424i	0.968320	+	0.249711i	$0.0803356\pi$
$558$	−0.269253	+	0.155453i	−0.0113984	+	0.00658085i
$559$	20.1404	−	34.8842i	0.851848	−	1.47544i
$560$		0			0
$561$	−22.7259	+	19.0693i	−0.959486	+	0.805105i
$562$	13.2505	+	7.65018i	0.558939	+	0.322703i
$563$	19.9237	−	11.5030i	0.839684	−	0.484792i	−0.0174729	−	0.999847i	$-0.505562\pi$
$563$	19.9237	−	11.5030i	0.839684	−	0.484792i	0.857157	+	0.515056i	$0.172229\pi$
$564$	−16.0540	−	5.84318i	−0.675996	−	0.246042i
$565$		0			0
$566$	1.71048	+	9.70062i	0.0718969	+	0.407747i
$567$	4.47765	+	12.3022i	0.188043	+	0.516645i
$568$	−1.24546	+	1.48428i	−0.0522583	+	0.0622790i
$569$	39.2546			1.64564			0.822819	−	0.568303i	$-0.192400\pi$
$569$	39.2546			1.64564			0.822819	+	0.568303i	$0.192400\pi$
$570$		0			0
$571$	−20.4203			−0.854563			−0.427282	−	0.904119i	$-0.640529\pi$
$571$	−20.4203			−0.854563			−0.427282	+	0.904119i	$0.640529\pi$
$572$	−24.4007	+	29.0796i	−1.02024	+	1.21588i
$573$	6.66159	+	18.3026i	0.278292	+	0.764601i
$574$	−1.29671	−	7.35402i	−0.0541237	−	0.306951i
$575$		0			0
$576$	−0.208307	−	0.0758175i	−0.00867946	−	0.00315906i
$577$	−19.1093	+	11.0328i	−0.795531	+	0.459300i	−0.841906	−	0.539624i	$-0.818566\pi$
$577$	−19.1093	+	11.0328i	−0.795531	+	0.459300i	0.0463754	+	0.998924i	$0.485233\pi$
$578$	9.05191	+	5.22613i	0.376510	+	0.217378i
$579$	−2.66231	+	2.23394i	−0.110642	+	0.0928396i
$580$		0			0
$581$	9.18953	−	15.9167i	0.381246	−	0.660337i
$582$	0.191913	−	0.110801i	0.00795503	−	0.00459284i
$583$	−9.77706	+	26.8622i	−0.404924	+	1.11252i
$584$	−1.09111	+	6.18799i	−0.0451504	+	0.256061i
$585$		0			0
$586$	7.68549	−	2.79729i	0.317485	−	0.115555i
$587$	1.82311	−	2.17270i	0.0752478	−	0.0896768i	−0.727107	−	0.686524i	$-0.759136\pi$
$587$	1.82311	−	2.17270i	0.0752478	−	0.0896768i	0.802355	+	0.596847i	$0.203580\pi$
$588$			9.23728i			0.380939i
$589$	0.183143	+	6.11073i	0.00754629	+	0.251788i
$590$		0			0
$591$	16.8489	+	14.1379i	0.693070	+	0.581554i
$592$	1.51502	+	4.16248i	0.0622669	+	0.171077i
$593$	−41.3185	+	7.28557i	−1.69675	+	0.299183i	−0.936557	−	0.350515i	$-0.886006\pi$
$593$	−41.3185	+	7.28557i	−1.69675	+	0.299183i	−0.760192	+	0.649698i	$0.774895\pi$
$594$	−5.59337	+	31.7216i	−0.229499	+	1.30155i
$595$		0			0
$596$	1.10957	+	1.92183i	0.0454498	+	0.0787213i
$597$	0.673031	+	0.388574i	0.0275453	+	0.0159033i
$598$	31.8238	+	37.9262i	1.30137	+	1.55092i
$599$	23.2333	−	19.4950i	0.949286	−	0.796546i	−0.0298911	−	0.999553i	$-0.509516\pi$
$599$	23.2333	−	19.4950i	0.949286	−	0.796546i	0.979177	+	0.203008i	$0.0650716\pi$
$600$		0			0
$601$	−16.4125	−	28.4274i	−0.669482	−	1.15958i	−0.978049	−	0.208374i	$-0.933183\pi$
$601$	−16.4125	−	28.4274i	−0.669482	−	1.15958i	0.308568	−	0.951202i	$-0.400150\pi$
$602$	−3.19157	+	8.76875i	−0.130078	+	0.357388i
$603$	1.46695	+	0.258662i	0.0597387	+	0.0105335i
$604$	2.02770	+	11.4997i	0.0825060	+	0.467915i
$605$		0			0
$606$	−18.7741	−	15.7533i	−0.762644	−	0.639934i
$607$		−	7.07201i		−	0.287044i	−0.989647	−	0.143522i	$-0.954157\pi$
$607$		−	7.07201i		−	0.287044i	0.989647	−	0.143522i	$-0.0458428\pi$
$608$	−3.25368	+	2.90062i	−0.131954	+	0.117636i
$609$	−10.8958			−0.441521
$610$		0			0
$611$	52.5651	−	19.1321i	2.12656	−	0.774003i
$612$	0.558619	−	0.0984995i	0.0225808	−	0.00398161i
$613$	20.7853	+	3.66501i	0.839510	+	0.148028i	0.576840	−	0.816857i	$-0.304286\pi$
$613$	20.7853	+	3.66501i	0.839510	+	0.148028i	0.262670	+	0.964886i	$0.415397\pi$
$614$	5.68175	+	2.06799i	0.229297	+	0.0834572i
$615$		0			0
$616$	4.39702	−	7.61585i	0.177161	−	0.306852i
$617$	−18.8083	−	22.4149i	−0.757195	−	0.902390i	0.240472	−	0.970656i	$-0.422698\pi$
$617$	−18.8083	−	22.4149i	−0.757195	−	0.902390i	−0.997667	+	0.0682659i	$0.978253\pi$
$618$	−7.93114	−	9.45197i	−0.319037	−	0.380214i
$619$	−8.81402	+	15.2663i	−0.354265	+	0.613606i	−0.986992	−	0.160770i	$-0.948602\pi$
$619$	−8.81402	+	15.2663i	−0.354265	+	0.613606i	0.632727	+	0.774375i	$0.281936\pi$
$620$		0			0
$621$	39.4767	+	14.3683i	1.58414	+	0.576581i
$622$	−32.6134	−	5.75062i	−1.30768	−	0.230579i
$623$	−2.54213	+	0.448246i	−0.101848	+	0.0179586i
$624$	9.91246	−	3.60784i	0.396816	−	0.144429i
$625$		0			0
$626$	6.17199			0.246682
$627$	−39.6682	−	31.3093i	−1.58420	−	1.25037i
$628$			4.16329i			0.166133i
$629$	−8.68293	−	7.28584i	−0.346211	−	0.290505i
$630$		0			0
$631$	5.98586	+	33.9475i	0.238293	+	1.35143i	0.835566	+	0.549390i	$0.185140\pi$
$631$	5.98586	+	33.9475i	0.238293	+	1.35143i	−0.597273	+	0.802038i	$0.703749\pi$
$632$	3.53552	+	0.623407i	0.140635	+	0.0247978i
$633$	8.43797	−	23.1831i	0.335379	−	0.921447i
$634$	8.20325	+	14.2084i	0.325793	+	0.564289i
$635$		0			0
$636$	6.08516	−	5.10605i	0.241292	−	0.202468i
$637$	−19.4413	−	23.1692i	−0.770292	−	0.917998i
$638$	−24.9414	−	14.3999i	−0.987438	−	0.570097i
$639$	0.214758	+	0.371972i	0.00849570	+	0.0147150i
$640$		0			0
$641$	8.27820	−	46.9480i	0.326969	−	1.85434i	−0.168489	−	0.985704i	$-0.553889\pi$
$641$	8.27820	−	46.9480i	0.326969	−	1.85434i	0.495458	−	0.868632i	$-0.335000\pi$
$642$	15.6262	−	2.75531i	0.616715	−	0.108744i
$643$	−3.24102	−	8.90463i	−0.127813	−	0.351164i	0.859236	−	0.511579i	$-0.170939\pi$
$643$	−3.24102	−	8.90463i	−0.127813	−	0.351164i	−0.987050	+	0.160414i	$0.948717\pi$
$644$	−8.78604	−	7.37236i	−0.346219	−	0.290512i
$645$		0			0
$646$	3.49912	−	10.5907i	0.137671	−	0.416686i
$647$			16.8594i			0.662810i	0.943489	+	0.331405i	$0.107523\pi$
$647$			16.8594i			0.662810i	−0.943489	+	0.331405i	$0.892477\pi$
$648$	6.18097	−	7.36620i	0.242812	−	0.289372i
$649$	−62.4116	+	22.7160i	−2.44987	+	0.891679i
$650$		0			0
$651$	−0.595156	+	3.37530i	−0.0233260	+	0.132288i
$652$	1.64249	−	4.51272i	0.0643250	−	0.176732i
$653$	−9.34245	+	5.39386i	−0.365598	+	0.211078i	−0.671534	−	0.740974i	$-0.734364\pi$
$653$	−9.34245	+	5.39386i	−0.365598	+	0.211078i	0.305936	+	0.952052i	$0.401031\pi$
$654$	8.54023	−	14.7921i	0.333949	−	0.578417i
$655$		0			0
$656$	−4.20164	+	3.52559i	−0.164046	+	0.137651i
$657$	1.20628	+	0.696444i	0.0470613	+	0.0271709i
$658$	−11.2227	+	6.47941i	−0.437505	+	0.252594i
$659$	−18.6209	−	6.77745i	−0.725367	−	0.264012i	−0.0471644	−	0.998887i	$-0.515018\pi$
$659$	−18.6209	−	6.77745i	−0.725367	−	0.264012i	−0.678202	+	0.734875i	$0.737241\pi$
$660$		0			0
$661$	−4.06094	−	23.0307i	−0.157952	−	0.895792i	−0.956037	−	0.293247i	$-0.905264\pi$
$661$	−4.06094	−	23.0307i	−0.157952	−	0.895792i	0.798084	−	0.602546i	$-0.205847\pi$
$662$	5.83754	+	16.0385i	0.226883	+	0.623355i
$663$	−17.3504	+	20.6774i	−0.673833	+	0.803043i
$664$	−13.4994			−0.523878
$665$		0			0
$666$	0.981938			0.0380493
$667$	−24.1439	+	28.7736i	−0.934857	+	1.11412i
$668$	−1.32265	−	3.63394i	−0.0511747	−	0.140601i
$669$	7.01750	+	39.7982i	0.271312	+	1.53869i
$670$		0			0
$671$	−39.2296	−	14.2784i	−1.51444	−	0.551212i
$672$	−2.11631	+	1.22185i	−0.0816386	+	0.0471341i
$673$	−19.0320	−	10.9881i	−0.733628	−	0.423560i	0.0861200	−	0.996285i	$-0.472553\pi$
$673$	−19.0320	−	10.9881i	−0.733628	−	0.423560i	−0.819748	+	0.572724i	$0.805887\pi$
$674$	14.4450	−	12.1208i	0.556399	−	0.466874i
$675$		0			0
$676$	−10.7695	+	18.6533i	−0.414210	+	0.717434i
$677$	−40.2317	+	23.2278i	−1.54623	+	0.892716i	−0.547804	+	0.836607i	$0.684536\pi$
$677$	−40.2317	+	23.2278i	−1.54623	+	0.892716i	−0.998425	+	0.0561091i	$0.982131\pi$
$678$	−6.80187	+	18.6880i	−0.261224	+	0.717707i
$679$	0.0291884	−	0.165536i	0.00112015	−	0.00635268i
$680$		0			0
$681$	31.7772	−	11.5660i	1.21770	−	0.443208i
$682$	−5.82315	+	6.93976i	−0.222980	+	0.265737i
$683$			13.4198i			0.513496i	0.966478	+	0.256748i	$0.0826511\pi$
$683$			13.4198i			0.513496i	−0.966478	+	0.256748i	$0.917349\pi$
$684$	0.357534	+	0.897681i	0.0136706	+	0.0343237i
$685$		0			0
$686$	12.6681	+	10.6298i	0.483669	+	0.405846i
$687$	2.77375	+	7.62081i	0.105825	+	0.290752i
$688$	6.74986	−	1.19018i	0.257336	−	0.0453753i
$689$	−4.51650	+	25.6143i	−0.172065	+	0.975828i
$690$		0			0
$691$	20.9252	+	36.2436i	0.796033	+	1.37877i	0.922181	+	0.386759i	$0.126405\pi$
$691$	20.9252	+	36.2436i	0.796033	+	1.37877i	−0.126148	+	0.992011i	$0.540261\pi$
$692$	−9.99296	−	5.76944i	−0.379875	−	0.219321i
$693$	−1.25306	−	1.49334i	−0.0476000	−	0.0567275i
$694$	4.14258	−	3.47604i	0.157250	−	0.131949i
$695$		0			0
$696$	4.00148	+	6.93077i	0.151676	+	0.262710i
$697$	4.80023	−	13.1885i	0.181822	−	0.499551i
$698$	−35.7564	−	6.30481i	−1.35340	−	0.238641i
$699$	3.35468	+	19.0253i	0.126886	+	0.719605i
$700$		0			0
$701$	20.5106	+	17.2104i	0.774674	+	0.650028i	0.941901	−	0.335890i	$-0.109037\pi$
$701$	20.5106	+	17.2104i	0.774674	+	0.650028i	−0.167228	+	0.985918i	$0.553481\pi$
$702$			29.3075i			1.10614i
$703$	9.14886	−	17.0031i	0.345056	−	0.641286i
$704$	−6.45921			−0.243441
$705$		0			0
$706$	−1.15574	+	0.420656i	−0.0434970	+	0.0158316i
$707$	−18.3073	+	3.22806i	−0.688515	+	0.121404i
$708$	18.1757	+	3.20488i	0.683086	+	0.120447i
$709$	−17.7455	−	6.45882i	−0.666445	−	0.242566i	−0.0134283	−	0.999910i	$-0.504274\pi$
$709$	−17.7455	−	6.45882i	−0.666445	−	0.242566i	−0.653016	+	0.757344i	$0.726497\pi$
$710$		0			0
$711$	0.397914	−	0.689208i	0.0149230	−	0.0258473i
$712$	1.21872	+	1.45242i	0.0456736	+	0.0544317i
$713$	7.59468	+	9.05099i	0.284423	+	0.338962i
$714$	3.12655	−	5.41535i	0.117008	−	0.202664i
$715$		0			0
$716$	−7.87426	−	2.86600i	−0.294275	−	0.107107i
$717$	41.3662	+	7.29398i	1.54485	+	0.272399i
$718$	14.8995	−	2.62718i	0.556044	−	0.0980455i
$719$	30.3154	−	11.0339i	1.13057	−	0.411496i	0.292074	−	0.956396i	$-0.405655\pi$
$719$	30.3154	−	11.0339i	1.13057	−	0.411496i	0.838501	+	0.544900i	$0.183432\pi$
$720$		0			0
$721$	−9.35914			−0.348553
$722$	18.8754	+	2.17281i	0.702468	+	0.0808637i
$723$			37.5052i			1.39483i
$724$	8.13969	+	6.83001i	0.302509	+	0.253835i
$725$		0			0
$726$	−9.57529	−	54.3042i	−0.355372	−	2.01542i
$727$	−17.6378	−	3.11002i	−0.654150	−	0.115344i	−0.163284	−	0.986579i	$-0.552209\pi$
$727$	−17.6378	−	3.11002i	−0.654150	−	0.115344i	−0.490866	+	0.871235i	$0.663320\pi$
$728$	2.73662	−	7.51881i	0.101426	−	0.278666i
$729$	12.3605	+	21.4090i	0.457796	+	0.792926i
$730$		0			0
$731$	−13.4352	+	11.2735i	−0.496918	+	0.416964i
$732$	7.45688	+	8.88676i	0.275614	+	0.328464i
$733$	−41.4082	−	23.9071i	−1.52945	−	0.883027i	−0.999385	−	0.0350693i	$-0.988835\pi$
$733$	−41.4082	−	23.9071i	−1.52945	−	0.883027i	−0.530063	−	0.847958i	$-0.677832\pi$
$734$	1.05724	+	1.83120i	0.0390235	+	0.0675907i
$735$		0			0
$736$	−1.46285	+	8.29626i	−0.0539215	+	0.305804i
$737$	42.7440	−	7.53693i	1.57450	−	0.277626i
$738$	0.415848	+	1.14253i	0.0153076	+	0.0420572i
$739$	2.75913	+	2.31519i	0.101496	+	0.0851656i	0.692124	−	0.721779i	$-0.256675\pi$
$739$	2.75913	+	2.31519i	0.101496	+	0.0851656i	−0.590627	+	0.806944i	$0.701120\pi$
$740$		0			0
$741$	−40.4910	−	21.7870i	−1.48747	−	0.800364i
$742$		−	6.02540i		−	0.221199i
$743$	−1.99911	+	2.38245i	−0.0733403	+	0.0874036i	−0.801467	−	0.598039i	$-0.795947\pi$
$743$	−1.99911	+	2.38245i	−0.0733403	+	0.0874036i	0.728127	+	0.685443i	$0.240391\pi$
$744$	2.36558	−	0.861001i	0.0867264	−	0.0315658i
$745$		0			0
$746$	−0.874756	+	4.96099i	−0.0320271	+	0.181635i
$747$	−1.02349	+	2.81202i	−0.0374476	+	0.102886i
$748$	14.3138	−	8.26410i	0.523366	−	0.302165i
$749$	6.01781	−	10.4231i	0.219886	−	0.380854i
$750$		0			0
$751$	15.5562	−	13.0532i	0.567654	−	0.476318i	−0.313213	−	0.949683i	$-0.601405\pi$
$751$	15.5562	−	13.0532i	0.567654	−	0.476318i	0.880866	+	0.473365i	$0.156961\pi$
$752$	8.24304	+	4.75912i	0.300593	+	0.173547i
$753$	27.8321	−	16.0689i	1.01426	−	0.585582i
$754$	−24.6235	−	8.96223i	−0.896736	−	0.326385i
$755$		0			0
$756$	−1.17897	−	6.68627i	−0.0428787	−	0.243177i
$757$	13.3721	+	36.7396i	0.486018	+	1.33532i	0.904258	+	0.426987i	$0.140425\pi$
$757$	13.3721	+	36.7396i	0.486018	+	1.33532i	−0.418239	+	0.908337i	$0.637353\pi$
$758$	−23.9639	+	28.5591i	−0.870408	+	1.03731i
$759$	−97.6677			−3.54511
$760$		0			0
$761$	4.22431			0.153131			0.0765656	−	0.997065i	$-0.475605\pi$
$761$	4.22431			0.153131			0.0765656	+	0.997065i	$0.475605\pi$
$762$	10.6055	−	12.6392i	0.384197	−	0.457868i
$763$	−4.43118	−	12.1746i	−0.160419	−	0.440748i
$764$	−1.88432	−	10.6865i	−0.0681724	−	0.386625i
$765$		0			0
$766$	13.9869	+	5.09082i	0.505368	+	0.183939i
$767$	−52.3341	+	30.2151i	−1.88968	+	1.09101i
$768$	1.55443	+	0.897451i	0.0560907	+	0.0323840i
$769$	−28.9268	+	24.2725i	−1.04313	+	0.875288i	−0.992354	−	0.123422i	$-0.960613\pi$
$769$	−28.9268	+	24.2725i	−1.04313	+	0.875288i	−0.0507735	+	0.998710i	$0.516169\pi$
$770$		0			0
$771$	0.436958	−	0.756833i	0.0157367	−	0.0272567i
$772$	1.67685	−	0.968131i	0.0603512	−	0.0348438i
$773$	−1.32574	+	3.64243i	−0.0476834	+	0.131009i	−0.961248	−	0.275684i	$-0.911096\pi$
$773$	−1.32574	+	3.64243i	−0.0476834	+	0.131009i	0.913565	+	0.406693i	$0.133318\pi$
$774$	0.263834	−	1.49628i	0.00948333	−	0.0537827i
$775$		0			0
$776$	−0.116016	+	0.0422263i	−0.00416473	+	0.00151584i
$777$	6.95798	−	8.29220i	0.249616	−	0.297481i
$778$			30.8414i			1.10572i
$779$	23.6585	+	3.44436i	0.847653	+	0.123407i
$780$		0			0
$781$	9.58727	+	8.04468i	0.343060	+	0.287861i
$782$	−7.37273	−	20.2564i	−0.263648	−	0.724368i
$783$	−21.8970	+	3.86104i	−0.782536	+	0.137982i
$784$	0.893662	−	5.06821i	0.0319165	−	0.181007i
$785$		0			0
$786$	0.0992549	+	0.171914i	0.00354030	+	0.00613199i
$787$	−5.91530	−	3.41520i	−0.210858	−	0.121739i	0.390852	−	0.920453i	$-0.372180\pi$
$787$	−5.91530	−	3.41520i	−0.210858	−	0.121739i	−0.601710	+	0.798715i	$0.705514\pi$
$788$	−7.87668	−	9.38706i	−0.280595	−	0.334400i
$789$	30.3436	−	25.4613i	1.08026	−	0.906445i
$790$		0			0
$791$	7.54248	+	13.0640i	0.268180	+	0.464501i
$792$	−0.489721	+	1.34550i	−0.0174015	+	0.0478102i
$793$	−37.4072	−	6.59589i	−1.32837	−	0.234227i
$794$	−3.84704	−	21.8176i	−0.136526	−	0.774279i
$795$		0			0
$796$	−0.331678	−	0.278311i	−0.0117560	−	0.00986448i
$797$		−	26.0356i		−	0.922229i	−0.887341	−	0.461114i	$-0.847450\pi$
$797$		−	26.0356i		−	0.922229i	0.887341	−	0.461114i	$-0.152550\pi$
$798$	10.1141	+	3.34167i	0.358037	+	0.118294i
$799$	−24.3558			−0.861647
$800$		0			0
$801$	0.394949	−	0.143750i	0.0139548	−	0.00507915i
$802$	30.5981	−	5.39528i	1.08046	−	0.190514i
$803$	39.9695	+	7.04771i	1.41049	+	0.248708i
$804$	−11.3337	−	4.12513i	−0.399709	−	0.145482i
$805$		0			0
$806$	−4.12131	+	7.13833i	−0.145167	+	0.251437i
$807$	20.4781	+	24.4048i	0.720862	+	0.859089i
$808$	8.77669	+	10.4596i	0.308763	+	0.367969i
$809$	1.43475	−	2.48505i	0.0504430	−	0.0873698i	−0.839701	−	0.543048i	$-0.817270\pi$
$809$	1.43475	−	2.48505i	0.0504430	−	0.0873698i	0.890144	+	0.455679i	$0.150603\pi$
$810$		0			0
$811$	−14.8021	−	5.38752i	−0.519772	−	0.189181i	0.0687939	−	0.997631i	$-0.478085\pi$
$811$	−14.8021	−	5.38752i	−0.519772	−	0.189181i	−0.588566	+	0.808449i	$0.700307\pi$
$812$	5.97820	+	1.05412i	0.209794	+	0.0369923i
$813$	19.3060	−	3.40416i	0.677089	−	0.119389i
$814$	26.8863	−	9.78582i	0.942365	−	0.342993i
$815$		0			0
$816$	−4.59290			−0.160784
$817$	−23.4512	−	18.5096i	−0.820455	−	0.647569i
$818$			2.03692i			0.0712193i
$819$	−1.35874	−	1.14011i	−0.0474781	−	0.0398388i
$820$		0			0
$821$	−2.78936	−	15.8192i	−0.0973493	−	0.552095i	−0.994002	−	0.109361i	$-0.965120\pi$
$821$	−2.78936	−	15.8192i	−0.0973493	−	0.552095i	0.896653	−	0.442734i	$-0.145992\pi$
$822$	−24.1296	−	4.25469i	−0.841615	−	0.148399i
$823$	13.9542	−	38.3389i	0.486413	−	1.33641i	−0.417494	−	0.908680i	$-0.637092\pi$
$823$	13.9542	−	38.3389i	0.486413	−	1.33641i	0.903907	−	0.427729i	$-0.140686\pi$
$824$	3.43714	+	5.95330i	0.119738	+	0.207393i
$825$		0			0
$826$	10.7241	−	8.99862i	0.373141	−	0.313102i
$827$	−15.6560	−	18.6581i	−0.544413	−	0.648806i	0.421758	−	0.906708i	$-0.361413\pi$
$827$	−15.6560	−	18.6581i	−0.544413	−	0.648806i	−0.966171	+	0.257903i	$0.916969\pi$
$828$	1.61726	+	0.933724i	0.0562036	+	0.0324492i
$829$	7.31291	+	12.6663i	0.253988	+	0.439920i	0.964620	−	0.263644i	$-0.0849243\pi$
$829$	7.31291	+	12.6663i	0.253988	+	0.439920i	−0.710632	+	0.703564i	$0.751591\pi$
$830$		0			0
$831$	2.82373	−	16.0142i	0.0979541	−	0.555525i
$832$	−5.78770	+	1.02053i	−0.200652	+	0.0353804i
$833$	4.50402	+	12.3747i	0.156055	+	0.428758i
$834$	3.32334	+	2.78862i	0.115078	+	0.0965619i
$835$		0			0
$836$	18.7357	+	21.0162i	0.647988	+	0.726860i
$837$			6.99415i			0.241753i
$838$	7.21438	−	8.59776i	0.249217	−	0.297005i
$839$	49.0332	−	17.8466i	1.69282	−	0.616134i	0.697840	−	0.716254i	$-0.254145\pi$
$839$	49.0332	−	17.8466i	1.69282	−	0.616134i	0.994975	+	0.100119i	$0.0319224\pi$
$840$		0			0
$841$	−1.58364	+	8.98128i	−0.0546083	+	0.309699i
$842$	3.34541	−	9.19144i	0.115291	−	0.316758i
$843$	−23.7834	+	13.7313i	−0.819142	+	0.472932i
$844$	−6.87251	+	11.9035i	−0.236562	+	0.409737i
$845$		0			0
$846$	1.61633	−	1.35626i	0.0555704	−	0.0466291i
$847$	−36.2226	−	20.9132i	−1.24462	−	0.718584i
$848$	−3.83272	+	2.21282i	−0.131616	+	0.0759887i
$849$	−16.6140	−	6.04701i	−0.570192	−	0.207533i
$850$		0			0
$851$	−6.47988	−	36.7492i	−0.222127	−	1.25975i
$852$	−1.18947	−	3.26805i	−0.0407507	−	0.111962i
$853$	−7.19445	+	8.57401i	−0.246333	+	0.293569i	−0.875017	−	0.484093i	$-0.839150\pi$
$853$	−7.19445	+	8.57401i	−0.246333	+	0.293569i	0.628683	+	0.777661i	$0.283594\pi$
$854$	8.79949			0.301112
$855$		0			0
$856$	−8.84015			−0.302150
$857$	−21.2831	+	25.3642i	−0.727016	+	0.866424i	−0.995292	−	0.0969180i	$-0.969102\pi$
$857$	−21.2831	+	25.3642i	−0.727016	+	0.866424i	0.268276	+	0.963342i	$0.413546\pi$
$858$	−23.3038	−	64.0266i	−0.795578	−	2.18583i
$859$	−1.64149	−	9.30936i	−0.0560070	−	0.317631i	0.943914	−	0.330191i	$-0.107113\pi$
$859$	−1.64149	−	9.30936i	−0.0560070	−	0.317631i	−0.999921	+	0.0125596i	$0.996002\pi$
$860$		0			0
$861$	12.5951	+	4.58422i	0.429238	+	0.156230i
$862$	4.22137	−	2.43721i	0.143780	−	0.0830117i
$863$	47.6935	+	27.5359i	1.62351	+	0.937332i	0.985972	+	0.166910i	$0.0533791\pi$
$863$	47.6935	+	27.5359i	1.62351	+	0.937332i	0.637535	+	0.770422i	$0.279954\pi$
$864$	−3.82013	+	3.20547i	−0.129963	+	0.109052i
$865$		0			0
$866$	−9.95802	+	17.2478i	−0.338387	+	0.586104i
$867$	−16.2473	+	9.38039i	−0.551787	+	0.318575i
$868$	0.653088	−	1.79434i	0.0221672	−	0.0609040i
$869$	4.02672	−	22.8367i	0.136597	−	0.774680i
$870$		0			0
$871$	37.1095	−	13.5068i	1.25741	−	0.457659i
$872$	−6.11683	+	7.28975i	−0.207142	+	0.246862i
$873$			0.0273684i			0.000926281i
$874$	31.2365	−	19.3046i	1.05659	−	0.652989i
$875$		0			0
$876$	−8.63959	−	7.24948i	−0.291905	−	0.244937i
$877$	6.07221	+	16.6833i	0.205044	+	0.563354i	0.999004	−	0.0446161i	$-0.0142065\pi$
$877$	6.07221	+	16.6833i	0.205044	+	0.563354i	−0.793960	+	0.607970i	$0.791984\pi$
$878$	20.9869	−	3.70055i	0.708273	−	0.124888i
$879$	−2.54916	+	14.4570i	−0.0859810	+	0.487622i
$880$		0			0
$881$	−9.17773	−	15.8963i	−0.309206	−	0.535560i	0.668983	−	0.743278i	$-0.266730\pi$
$881$	−9.17773	−	15.8963i	−0.309206	−	0.535560i	−0.978189	+	0.207718i	$0.933396\pi$
$882$	−0.987988	−	0.570415i	−0.0332673	−	0.0192069i
$883$	−15.1814	−	18.0924i	−0.510893	−	0.608859i	0.447509	−	0.894279i	$-0.352311\pi$
$883$	−15.1814	−	18.0924i	−0.510893	−	0.608859i	−0.958402	+	0.285421i	$0.907867\pi$
$884$	11.5201	−	9.66647i	0.387461	−	0.325119i
$885$		0			0
$886$	−3.09253	−	5.35641i	−0.103895	−	0.179952i
$887$	1.24604	−	3.42345i	0.0418378	−	0.114948i	−0.917014	−	0.398854i	$-0.869408\pi$
$887$	1.24604	−	3.42345i	0.0418378	−	0.114948i	0.958852	+	0.283906i	$0.0916303\pi$
$888$	−7.82994	−	1.38063i	−0.262756	−	0.0463309i
$889$	−2.17321	−	12.3249i	−0.0728872	−	0.413364i
$890$		0			0
$891$	−47.5798	−	39.9242i	−1.59398	−	1.33751i
$892$		−	22.5150i		−	0.753856i
$893$	−8.42529	−	40.6246i	−0.281942	−	1.35945i
$894$	−3.98314			−0.133216
$895$		0			0
$896$	1.27936	−	0.465651i	0.0427406	−	0.0155563i
$897$	−87.5140	+	15.4311i	−2.92201	+	0.515229i
$898$	40.1186	+	7.07398i	1.33877	+	0.236062i
$899$	−5.87634	−	2.13881i	−0.195987	−	0.0713334i
$900$		0			0
$901$	5.66230	−	9.80740i	0.188639	−	0.326732i
$902$	22.7725	+	27.1393i	0.758243	+	0.903638i
$903$	−10.7662	−	12.8306i	−0.358275	−	0.426976i
$904$	5.53995	−	9.59547i	0.184256	−	0.319141i
$905$		0			0
$906$	−19.6952	−	7.16847i	−0.654330	−	0.238156i
$907$	−1.02035	−	0.179915i	−0.0338801	−	0.00597397i	0.156682	−	0.987649i	$-0.449920\pi$
$907$	−1.02035	−	0.179915i	−0.0338801	−	0.00597397i	−0.190563	+	0.981675i	$0.561031\pi$
$908$	−18.5541	+	3.27159i	−0.615740	+	0.108572i
$909$	2.84424	−	1.03522i	0.0943376	−	0.0343361i
$910$		0			0
$911$	−20.4703			−0.678210			−0.339105	−	0.940749i	$-0.610124\pi$
$911$	−20.4703			−0.678210			−0.339105	+	0.940749i	$0.610124\pi$
$912$	−1.58880	−	7.66078i	−0.0526104	−	0.253674i
$913$			87.1955i			2.88575i
$914$	11.2664	+	9.45366i	0.372660	+	0.312699i
$915$		0			0
$916$	−0.784593	−	4.44965i	−0.0259237	−	0.147021i
$917$	0.148286	+	0.0261469i	0.00489684	+	0.000863446i
$918$	4.36437	−	11.9910i	0.144046	−	0.395762i
$919$	−21.9810	−	38.0723i	−0.725088	−	1.25589i	−0.958938	−	0.283616i	$-0.908466\pi$
$919$	−21.9810	−	38.0723i	−0.725088	−	1.25589i	0.233850	−	0.972273i	$-0.424868\pi$
$920$		0			0
$921$	−8.31364	+	6.97597i	−0.273944	+	0.229866i
$922$	9.00052	+	10.7264i	0.296416	+	0.353255i
$923$	9.86159	+	5.69359i	0.324598	+	0.187407i
$924$	7.89222	+	13.6697i	0.259635	+	0.449701i
$925$		0			0
$926$	−0.394865	+	2.23939i	−0.0129761	+	0.0735910i
$927$	1.50071	−	0.264616i	0.0492898	−	0.00869112i
$928$	−1.52497	−	4.18982i	−0.0500596	−	0.137538i
$929$	−5.62577	−	4.72058i	−0.184576	−	0.154877i	0.545818	−	0.837904i	$-0.316219\pi$
$929$	−5.62577	−	4.72058i	−0.184576	−	0.154877i	−0.730394	+	0.683026i	$0.760663\pi$
$930$		0			0
$931$	−19.0825	+	11.7933i	−0.625403	+	0.386508i
$932$		−	10.7632i		−	0.352559i
$933$	38.2078	−	45.5343i	1.25087	−	1.49073i
$934$	27.6884	−	10.0778i	0.905994	−	0.329755i
$935$		0			0
$936$	−0.226226	+	1.28299i	−0.00739443	+	0.0419359i
$937$	0.159172	−	0.437322i	0.00519993	−	0.0142867i	−0.937066	−	0.349154i	$-0.886469\pi$
$937$	0.159172	−	0.437322i	0.00519993	−	0.0142867i	0.942265	+	0.334867i	$0.108691\pi$
$938$	−7.92290	+	4.57429i	−0.258692	+	0.149356i
$939$	−5.53906	+	9.59394i	−0.180761	+	0.313086i
$940$		0			0
$941$	31.9901	−	26.8429i	1.04285	−	0.875054i	0.0505251	−	0.998723i	$-0.483911\pi$
$941$	31.9901	−	26.8429i	1.04285	−	0.875054i	0.992324	+	0.123669i	$0.0394661\pi$
$942$	−6.47155	−	3.73635i	−0.210854	−	0.121737i
$943$	40.0153	−	23.1028i	1.30308	−	0.752332i
$944$	−9.66242	−	3.51683i	−0.314485	−	0.114463i
$945$		0			0
$946$	−7.68764	−	43.5988i	−0.249947	−	1.41752i
$947$	12.0353	+	33.0668i	0.391096	+	1.07453i	0.966502	+	0.256659i	$0.0826218\pi$
$947$	12.0353	+	33.0668i	0.391096	+	1.07453i	−0.575406	+	0.817868i	$0.695156\pi$
$948$	−4.14200	+	4.93624i	−0.134526	+	0.160322i
$949$	36.9277			1.19873
$950$		0			0
$951$	−29.4481			−0.954919
$952$	−2.23935	+	2.66875i	−0.0725778	+	0.0864948i
$953$	3.24820	+	8.92435i	0.105219	+	0.289088i	0.981119	−	0.193406i	$-0.0619534\pi$
$953$	3.24820	+	8.92435i	0.105219	+	0.289088i	−0.875899	+	0.482494i	$0.839731\pi$
$954$	0.170359	+	0.966154i	0.00551558	+	0.0312804i
$955$		0			0
$956$	−21.9907	−	8.00397i	−0.711231	−	0.258867i
$957$	44.7673	−	25.8464i	1.44712	−	0.835496i
$958$	−17.7140	−	10.2272i	−0.572314	−	0.330426i
$959$	−14.2370	+	11.9463i	−0.459738	+	0.385766i
$960$		0			0
$961$	14.5165	−	25.1432i	0.468273	−	0.811072i
$962$	22.5451	−	13.0164i	0.726882	−	0.419665i
$963$	−0.670238	+	1.84146i	−0.0215981	+	0.0593404i
$964$	3.62845	−	20.5780i	0.116864	−	0.662771i
$965$		0			0
$966$	19.3449	−	7.04096i	0.622411	−	0.226539i
$967$	13.8461	−	16.5011i	0.445260	−	0.530641i	−0.496000	−	0.868323i	$-0.665198\pi$
$967$	13.8461	−	16.5011i	0.445260	−	0.530641i	0.941260	+	0.337682i	$0.109643\pi$
$968$			30.7214i			0.987423i
$969$	13.3223	+	14.9438i	0.427972	+	0.480064i
$970$		0			0
$971$	−16.6642	−	13.9829i	−0.534779	−	0.448733i	0.334969	−	0.942229i	$-0.391274\pi$
$971$	−16.6642	−	13.9829i	−0.534779	−	0.448733i	−0.869748	+	0.493496i	$0.835719\pi$
$972$	0.786344	+	2.16046i	0.0252220	+	0.0692968i
$973$	3.24071	−	0.571425i	0.103892	−	0.0183190i
$974$	5.05654	−	28.6771i	0.162022	−	0.918873i
$975$		0			0
$976$	−3.23161	−	5.59731i	−0.103441	−	0.179166i
$977$	−36.6442	−	21.1566i	−1.17235	−	0.676859i	−0.218120	−	0.975922i	$-0.569992\pi$
$977$	−36.6442	−	21.1566i	−1.17235	−	0.676859i	−0.954233	+	0.299063i	$0.903326\pi$
$978$	5.54065	+	6.60309i	0.177170	+	0.211143i
$979$	9.38147	−	7.87199i	0.299833	−	0.251590i
$980$		0			0
$981$	1.05474	+	1.82687i	0.0336753	+	0.0583274i
$982$	−5.69426	+	15.6448i	−0.181711	+	0.499247i
$983$	12.2561	+	2.16108i	0.390908	+	0.0689276i	0.365648	−	0.930753i	$-0.380847\pi$
$983$	12.2561	+	2.16108i	0.390908	+	0.0689276i	0.0252602	+	0.999681i	$0.491959\pi$
$984$	−1.70953	−	9.69520i	−0.0544977	−	0.309072i
$985$		0			0
$986$	8.73997	+	7.33371i	0.278337	+	0.233553i
$987$		−	23.2598i		−	0.740369i
$988$	20.1084	+	15.8711i	0.639733	+	0.504928i
$989$	−57.7396			−1.83601
$990$		0			0
$991$	11.7729	−	4.28498i	0.373978	−	0.136117i	−0.148191	−	0.988959i	$-0.547345\pi$
$991$	11.7729	−	4.28498i	0.373978	−	0.136117i	0.522169	+	0.852842i	$0.325123\pi$
$992$	−1.38122	+	0.243546i	−0.0438538	+	0.00773260i
$993$	−30.1697	−	5.31973i	−0.957406	−	0.168817i
$994$	−2.47888	−	0.902240i	−0.0786254	−	0.0286173i
$995$		0			0
$996$	12.1151	−	20.9839i	0.383880	−	0.664900i
$997$	−14.2610	−	16.9956i	−0.451651	−	0.538257i	0.491387	−	0.870941i	$-0.336490\pi$
$997$	−14.2610	−	16.9956i	−0.451651	−	0.538257i	−0.943038	+	0.332684i	$0.892046\pi$
$998$	18.8417	+	22.4546i	0.596422	+	0.710788i
$999$	11.0449	−	19.1303i	0.349444	−	0.605254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.g.149.6		36
5.2	odd	4		950.2.l.i.301.3		18
5.3	odd	4		190.2.k.d.111.1	yes	18
5.4	even	2	inner	950.2.u.g.149.1		36
19.6	even	9	inner	950.2.u.g.899.1		36
95.33	even	36		3610.2.a.bj.1.3		9
95.43	odd	36		3610.2.a.bi.1.7		9
95.44	even	18	inner	950.2.u.g.899.6		36
95.63	odd	36		190.2.k.d.101.1	✓	18
95.82	odd	36		950.2.l.i.101.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.101.1	✓	18	95.63	odd	36
190.2.k.d.111.1	yes	18	5.3	odd	4
950.2.l.i.101.3		18	95.82	odd	36
950.2.l.i.301.3		18	5.2	odd	4
950.2.u.g.149.1		36	5.4	even	2	inner
950.2.u.g.149.6		36	1.1	even	1	trivial
950.2.u.g.899.1		36	19.6	even	9	inner
950.2.u.g.899.6		36	95.44	even	18	inner
3610.2.a.bi.1.7		9	95.43	odd	36
3610.2.a.bj.1.3		9	95.33	even	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.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 - 0.766044i) q^{2} +(0.613893 + 1.68666i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.68666 + 0.613893i) q^{6} +(1.17907 - 0.680736i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.169813 + 0.142490i) q^{9} +O(q^{10})\)	\(q+(0.642788 - 0.766044i) q^{2} +(0.613893 + 1.68666i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.68666 + 0.613893i) q^{6} +(1.17907 - 0.680736i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.169813 + 0.142490i) q^{9} +(-3.22960 + 5.59384i) q^{11} +(1.55443 - 0.897451i) q^{12} +(-2.01005 + 5.52256i) q^{13} +(0.236417 - 1.34079i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(1.64480 - 1.96020i) q^{17} +0.221676i q^{18} +(3.83851 + 2.06538i) q^{19} +(1.87199 + 1.57079i) q^{21} +(2.20918 + 6.06967i) q^{22} +(8.29626 - 1.46285i) q^{23} +(0.311682 - 1.76763i) q^{24} +(2.93849 + 5.08962i) q^{26} +(4.31871 + 2.49341i) q^{27} +(-0.875137 - 1.04295i) q^{28} +(-3.41558 + 2.86601i) q^{29} +(0.701264 + 1.21462i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-11.4175 - 2.01322i) q^{33} +(-0.444341 - 2.51998i) q^{34} +(0.169813 + 0.142490i) q^{36} -4.42962i q^{37} +(4.04953 - 1.61287i) q^{38} -10.5486 q^{39} +(5.15407 - 1.87593i) q^{41} +(2.40658 - 0.424346i) q^{42} +(-6.74986 - 1.19018i) q^{43} +(6.06967 + 2.20918i) q^{44} +(4.21212 - 7.29560i) q^{46} +(-6.11821 - 7.29140i) q^{47} +(-1.15374 - 1.37498i) q^{48} +(-2.57320 + 4.45691i) q^{49} +(4.31591 + 1.57086i) q^{51} +(5.78770 + 1.02053i) q^{52} +(4.35841 - 0.768506i) q^{53} +(4.68608 - 1.70559i) q^{54} -1.36147 q^{56} +(-1.12716 + 7.74218i) q^{57} +4.45872i q^{58} +(7.87687 + 6.60948i) q^{59} +(1.12233 + 6.36503i) q^{61} +(1.38122 + 0.243546i) q^{62} +(-0.103223 + 0.283604i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-8.88125 + 7.45226i) q^{66} +(-4.31929 - 5.14753i) q^{67} +(-2.21604 - 1.27943i) q^{68} +(7.56034 + 13.0949i) q^{69} +(0.336459 - 1.90815i) q^{71} +(0.218308 - 0.0384936i) q^{72} +(-2.14907 - 5.90451i) q^{73} +(-3.39328 - 2.84730i) q^{74} +(1.36746 - 4.13885i) q^{76} +8.79403i q^{77} +(-6.78052 + 8.08071i) q^{78} +(-3.37355 + 1.22787i) q^{79} +(-1.66978 + 9.46980i) q^{81} +(1.87593 - 5.15407i) q^{82} +(11.6908 - 6.74970i) q^{83} +(1.22185 - 2.11631i) q^{84} +(-5.25046 + 4.40566i) q^{86} +(-6.93077 - 4.00148i) q^{87} +(5.59384 - 3.22960i) q^{88} +(-1.78165 - 0.648469i) q^{89} +(1.38942 + 7.87979i) q^{91} +(-2.88126 - 7.91619i) q^{92} +(-1.61815 + 1.92844i) q^{93} -9.51825 q^{94} -1.79490 q^{96} +(0.0793596 - 0.0945771i) q^{97} +(1.76017 + 4.83603i) q^{98} +(-0.248638 - 1.41010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 36 q^{9}+O(q^{10}) \) 36 * q + 36 * q^9	\( 36 q + 36 q^{9} - 24 q^{11} - 12 q^{14} + 24 q^{21} - 18 q^{26} + 12 q^{29} - 12 q^{31} - 36 q^{34} - 36 q^{36} - 96 q^{39} - 42 q^{41} - 6 q^{44} + 36 q^{46} + 78 q^{49} + 84 q^{51} + 108 q^{54} + 60 q^{59} + 96 q^{61} + 18 q^{64} + 48 q^{66} + 60 q^{69} + 60 q^{71} + 6 q^{74} - 42 q^{76} - 60 q^{79} + 36 q^{81} - 12 q^{84} + 72 q^{86} - 60 q^{89} - 120 q^{91} - 12 q^{94} - 342 q^{99}+O(q^{100}) \) 36 * q + 36 * q^9 - 24 * q^11 - 12 * q^14 + 24 * q^21 - 18 * q^26 + 12 * q^29 - 12 * q^31 - 36 * q^34 - 36 * q^36 - 96 * q^39 - 42 * q^41 - 6 * q^44 + 36 * q^46 + 78 * q^49 + 84 * q^51 + 108 * q^54 + 60 * q^59 + 96 * q^61 + 18 * q^64 + 48 * q^66 + 60 * q^69 + 60 * q^71 + 6 * q^74 - 42 * q^76 - 60 * q^79 + 36 * q^81 - 12 * q^84 + 72 * q^86 - 60 * q^89 - 120 * q^91 - 12 * q^94 - 342 * q^99

Introduction

L-functions

Modular forms

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