LMFDB - Embedded newform 950.2.u.g.899.6

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			899.6
Character	$\chi$	$=$	950.899
Dual form			950.2.u.g.149.6

$q$-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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.642788	+	0.766044i	0.454519	+	0.541675i
$2$	0.642788	+	0.766044i	0.454519	+	0.541675i
$3$	0.613893	−	1.68666i	0.354431	−	0.973792i	−0.626497	−	0.779423i	$-0.715512\pi$
$3$	0.613893	−	1.68666i	0.354431	−	0.973792i	0.980929	−	0.194368i	$-0.0622657\pi$
$4$	−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	0.705990	−	0.708222i	$-0.250502\pi$
$7$	1.17907	+	0.680736i	0.445646	+	0.257294i	−0.260343	+	0.965516i	$0.583836\pi$
$8$	−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	−0.683960	−	0.729520i	$-0.739744\pi$
$11$	−3.22960	−	5.59384i	−0.973762	−	1.68661i	−0.289803	−	0.957086i	$-0.593590\pi$
$12$	1.55443	+	0.897451i	0.448726	+	0.259072i
$13$	−2.01005	−	5.52256i	−0.557487	−	1.53168i	−0.823270	−	0.567650i	$-0.807853\pi$
$13$	−2.01005	−	5.52256i	−0.557487	−	1.53168i	0.265784	−	0.964033i	$-0.414369\pi$
$14$	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	0.927691	−	0.373348i	$-0.121790\pi$
$17$	1.64480	+	1.96020i	0.398923	+	0.475418i	−0.528768	+	0.848766i	$0.677346\pi$
$18$		−	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	0.947971	−	0.318356i	$-0.103131\pi$
$23$	8.29626	+	1.46285i	1.72989	+	0.305026i	0.781918	+	0.623382i	$0.214242\pi$
$24$	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	0.267992	−	0.963421i	$-0.413640\pi$
$29$	−3.41558	−	2.86601i	−0.634257	−	0.532205i	−0.902248	+	0.431217i	$0.858084\pi$
$30$		0			0
$31$	0.701264	−	1.21462i	0.125951	−	0.218153i	−0.796153	−	0.605095i	$-0.793135\pi$
$31$	0.701264	−	1.21462i	0.125951	−	0.218153i	0.922104	+	0.386942i	$0.126469\pi$
$32$	−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	$0.118628\pi$
$37$			4.42962i			0.728225i	−0.931355	+	0.364112i	$0.881372\pi$
$38$	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	0.711528	−	0.702658i	$-0.248003\pi$
$41$	5.15407	+	1.87593i	0.804931	+	0.292971i	0.0934025	+	0.995628i	$0.470226\pi$
$42$	2.40658	+	0.424346i	0.371344	+	0.0654780i
$43$	−6.74986	+	1.19018i	−1.02934	+	0.181501i	−0.662719	−	0.748868i	$-0.730598\pi$
$43$	−6.74986	+	1.19018i	−1.02934	+	0.181501i	−0.366625	+	0.930369i	$0.619487\pi$
$44$	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	0.105176	+	0.994454i	$0.466459\pi$
$47$	−6.11821	+	7.29140i	−0.892433	+	1.06356i	−0.997609	+	0.0691065i	$0.977985\pi$
$48$	−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	0.464769	−	0.885432i	$-0.346137\pi$
$53$	4.35841	+	0.768506i	0.598674	+	0.105562i	0.133905	+	0.990994i	$0.457248\pi$
$54$	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	0.0351753	−	0.999381i	$-0.488801\pi$
$59$	7.87687	−	6.60948i	1.02548	−	0.860481i	0.990306	+	0.138900i	$0.0443566\pi$
$60$		0			0
$61$	1.12233	−	6.36503i	0.143699	−	0.814958i	−0.824703	−	0.565566i	$-0.808658\pi$
$61$	1.12233	−	6.36503i	0.143699	−	0.814958i	0.968402	−	0.249393i	$-0.0802310\pi$
$62$	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	−0.962380	−	0.271707i	$-0.912412\pi$
$67$	−4.31929	+	5.14753i	−0.527685	+	0.628871i	0.434695	+	0.900578i	$0.356856\pi$
$68$	−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	0.998242	−	0.0592685i	$-0.0188768\pi$
$71$	0.336459	+	1.90815i	0.0399303	+	0.226456i	−0.958312	+	0.285725i	$0.907766\pi$
$72$	0.218308	+	0.0384936i	0.0257278	+	0.00453651i
$73$	−2.14907	+	5.90451i	−0.251529	+	0.691071i	0.748093	+	0.663594i	$0.230970\pi$
$73$	−2.14907	+	5.90451i	−0.251529	+	0.691071i	−0.999622	+	0.0274772i	$0.991253\pi$
$74$	−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	0.145195	−	0.989403i	$-0.453619\pi$
$79$	−3.37355	−	1.22787i	−0.379554	−	0.138146i	−0.524750	+	0.851257i	$0.675841\pi$
$80$		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	0.977438	−	0.211221i	$-0.0677439\pi$
$83$	11.6908	+	6.74970i	1.28323	+	0.740876i	0.305797	+	0.952097i	$0.401077\pi$
$84$	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	−0.434716	−	0.900567i	$-0.643151\pi$
$89$	−1.78165	+	0.648469i	−0.188855	+	0.0687376i	0.245861	+	0.969305i	$0.420929\pi$
$90$		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	0.770058	−	0.637974i	$-0.220227\pi$
$97$	0.0793596	+	0.0945771i	0.00805774	+	0.00960285i	−0.762001	+	0.647576i	$0.775783\pi$
$98$	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	−0.889339	−	0.457249i	$-0.848835\pi$
$101$	−12.8307	+	4.66998i	−1.27670	+	0.464680i	−0.387359	+	0.921929i	$0.626613\pi$
$102$	3.97757	+	2.29645i	0.393838	+	0.227382i
$103$	−5.95330	+	3.43714i	−0.586596	+	0.338672i	−0.763751	−	0.645512i	$-0.776644\pi$
$103$	−5.95330	+	3.43714i	−0.586596	+	0.338672i	0.177154	+	0.984183i	$0.443311\pi$
$104$	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	0.822111	−	0.569328i	$-0.192796\pi$
$107$	7.65580	+	4.42008i	0.740114	+	0.427305i	−0.0819969	+	0.996633i	$0.526130\pi$
$108$	1.70559	+	4.68608i	0.164121	+	0.450918i
$109$	1.65245	+	9.37152i	0.158276	+	0.897629i	0.955729	+	0.294248i	$0.0950691\pi$
$109$	1.65245	+	9.37152i	0.158276	+	0.897629i	−0.797453	+	0.603381i	$0.793820\pi$
$110$		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	$-0.825502\pi$
$113$		−	11.0799i		−	1.04231i	0.853462	−	0.521154i	$-0.174498\pi$
$114$	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	0.997479	+	0.0709633i	$0.0226073\pi$
$127$	3.14395	+	8.63792i	0.278980	+	0.766491i	−0.718499	+	0.695528i	$0.755170\pi$
$128$	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	−0.639079	−	0.769141i	$-0.720684\pi$
$131$	0.0847217	−	0.0710900i	0.00740217	−	0.00621116i	0.646481	+	0.762930i	$0.276240\pi$
$132$		−	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	−0.433205	−	0.901295i	$-0.642617\pi$
$137$	−13.4434	−	2.37043i	−1.14855	−	0.202520i	−0.715341	+	0.698776i	$0.753729\pi$
$138$	14.8910	−	2.62568i	1.26760	−	0.223513i
$139$	2.27126	−	0.826670i	0.192645	−	0.0701172i	−0.243896	−	0.969801i	$-0.578425\pi$
$139$	2.27126	−	0.826670i	0.192645	−	0.0701172i	0.436541	+	0.899684i	$0.356203\pi$
$140$		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	0.255187	−	0.966892i	$-0.417863\pi$
$149$	−2.08531	−	0.758990i	−0.170835	−	0.0621789i	−0.426022	+	0.904713i	$0.640085\pi$
$150$		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	−0.334844	−	0.942273i	$-0.608684\pi$
$157$	−4.10004	+	0.722948i	−0.327219	+	0.0576975i	0.00762562	+	0.999971i	$0.497573\pi$
$158$	−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	−0.328201	−	0.944608i	$-0.606442\pi$
$163$	4.15894	−	2.40117i	0.325753	−	0.188074i	0.653954	+	0.756534i	$0.273109\pi$
$164$	−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	0.319045	−	0.947740i	$-0.396638\pi$
$167$	3.80840	+	0.671525i	0.294703	+	0.0519641i	−0.0243418	+	0.999704i	$0.507749\pi$
$168$	−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	0.970369	−	0.241629i	$-0.0776818\pi$
$173$	7.41704	+	8.83929i	0.563907	+	0.672039i	−0.406461	+	0.913668i	$0.633237\pi$
$174$	−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	0.979045	−	0.203645i	$-0.0652788\pi$
$179$	4.18981	+	7.25696i	0.313161	+	0.542411i	−0.665884	+	0.746055i	$0.731945\pi$
$180$		0			0
$181$	−8.13969	−	6.83001i	−0.605018	−	0.507671i	0.288036	−	0.957620i	$-0.406998\pi$
$181$	−8.13969	−	6.83001i	−0.605018	−	0.507671i	−0.893054	+	0.449949i	$0.851442\pi$
$182$	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	−0.913574	−	0.406674i	$-0.866689\pi$
$193$	0.662240	−	1.81949i	0.0476691	−	0.130970i	0.961243	+	0.275704i	$0.0889109\pi$
$194$	−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	0.827890	−	0.560890i	$-0.189541\pi$
$197$	10.6122	+	6.12697i	0.756090	+	0.436529i	−0.0718004	+	0.997419i	$0.522874\pi$
$198$	−1.24002	+	0.715925i	−0.0881242	+	0.0508785i
$199$	0.331678	+	0.278311i	0.0235121	+	0.0197290i	0.654468	−	0.756090i	$-0.272893\pi$
$199$	0.331678	+	0.278311i	0.0235121	+	0.0197290i	−0.630956	+	0.775819i	$0.717337\pi$
$200$		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	−0.928727	−	0.370765i	$-0.879096\pi$
$211$	−10.5293	+	8.83513i	−0.724867	+	0.608235i	0.203860	+	0.979000i	$0.434651\pi$
$212$	−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	0.628310	−	0.777963i	$-0.283747\pi$
$223$	22.1729	−	3.90968i	1.48481	−	0.261812i	0.856497	+	0.516151i	$0.172636\pi$
$224$	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	$0.214998\pi$
$227$			18.8403i			1.25048i	−0.780433	+	0.625239i	$0.785002\pi$
$228$	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	0.184705	−	0.982794i	$-0.440867\pi$
$233$	10.5997	−	1.86901i	0.694406	−	0.122443i	0.509701	+	0.860351i	$0.329756\pi$
$234$	−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	0.944436	+	0.328695i	$0.106609\pi$
$239$	11.7010	+	20.2668i	0.756876	+	1.31095i	−0.187560	+	0.982253i	$0.560058\pi$
$240$		0			0
$241$	19.6353	−	7.14665i	1.26482	−	0.460356i	0.379435	−	0.925218i	$-0.376118\pi$
$241$	19.6353	−	7.14665i	1.26482	−	0.460356i	0.885383	+	0.464862i	$0.153896\pi$
$242$	−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	0.714379	+	0.699759i	$0.246709\pi$
$251$	−3.10917	+	17.6330i	−0.196249	+	1.11298i	−0.910628	+	0.413226i	$0.864402\pi$
$252$	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	−0.775717	−	0.631081i	$-0.782612\pi$
$257$	−0.312965	+	0.372978i	−0.0195222	+	0.0232657i	0.756195	+	0.654346i	$0.227056\pi$
$258$	−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	0.455936	+	0.890013i	$0.349305\pi$
$263$	−7.54785	+	20.7375i	−0.465420	+	1.27873i	−0.921356	+	0.388719i	$0.872918\pi$
$264$	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	0.796089	−	0.605179i	$-0.206899\pi$
$269$	16.6789	+	6.07061i	1.01693	+	0.370131i	0.220838	+	0.975310i	$0.429121\pi$
$270$		0			0
$271$	1.89657	+	10.7560i	0.115208	+	0.653380i	0.986647	+	0.162875i	$0.0520766\pi$
$271$	1.89657	+	10.7560i	0.115208	+	0.653380i	−0.871438	+	0.490505i	$0.836812\pi$
$272$	−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	−0.716832	−	0.697246i	$-0.754408\pi$
$277$	−7.84590	+	4.52983i	−0.471414	+	0.272171i	0.245417	+	0.969418i	$0.421075\pi$
$278$	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	−0.797023	−	0.603948i	$-0.793593\pi$
$281$	2.65688	−	15.0679i	0.158496	−	0.898876i	0.955520	−	0.294928i	$-0.0952956\pi$
$282$	−5.84318	+	16.0540i	−0.347957	+	0.956003i
$283$	−6.33163	−	7.54574i	−0.376376	−	0.448548i	0.544291	−	0.838897i	$-0.316799\pi$
$283$	−6.33163	−	7.54574i	−0.376376	−	0.448548i	−0.920667	+	0.390349i	$0.872354\pi$
$284$	−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	−0.278625	−	0.960400i	$-0.589879\pi$
$293$	7.08299	−	4.08936i	0.413792	−	0.238903i	0.692418	+	0.721497i	$0.256545\pi$
$294$	−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	−0.866586	−	0.499028i	$-0.833691\pi$
$307$	2.06799	−	5.68175i	0.118026	−	0.324275i	0.984612	+	0.174753i	$0.0559128\pi$
$308$	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	−0.171463	+	0.985191i	$0.554849\pi$
$311$	−16.5582	+	28.6797i	−0.938932	+	1.62628i	−0.767468	+	0.641087i	$0.778484\pi$
$312$	9.13537	−	5.27431i	0.517188	−	0.298599i
$313$	3.96728	−	4.72802i	0.224244	−	0.267244i	−0.642179	−	0.766555i	$-0.721969\pi$
$313$	3.96728	−	4.72802i	0.224244	−	0.267244i	0.866423	+	0.499312i	$0.166414\pi$
$314$	−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	−0.991593	−	0.129399i	$-0.958695\pi$
$317$	−5.61135	−	15.4171i	−0.315165	−	0.865908i	0.676428	−	0.736509i	$-0.263527\pi$
$318$	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	0.530308	−	0.847805i	$-0.322076\pi$
$331$	−8.53392	−	14.7812i	−0.469066	−	0.812447i	−0.999375	+	0.0353579i	$0.988743\pi$
$332$	−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	0.356792	−	0.934184i	$-0.383870\pi$
$337$	18.5701	−	3.27441i	1.01158	−	0.178368i	0.654785	+	0.755816i	$0.272759\pi$
$338$	−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	−0.0288626	−	0.999583i	$-0.509189\pi$
$347$	5.32560	−	0.939047i	0.285893	−	0.0504107i	0.314756	+	0.949173i	$0.398077\pi$
$348$	−2.73718	−	7.52033i	−0.146728	−	0.403132i
$349$	−18.1540	+	31.4436i	−0.971761	+	1.68314i	−0.281526	+	0.959554i	$0.590841\pi$
$349$	−18.1540	+	31.4436i	−0.971761	+	1.68314i	−0.690235	+	0.723586i	$0.742493\pi$
$350$		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	−0.528078	−	0.849196i	$-0.677087\pi$
$353$	−1.06514	+	0.614958i	−0.0566916	+	0.0327309i	0.471386	+	0.881927i	$0.343754\pi$
$354$	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	−0.283494	−	0.958974i	$-0.591494\pi$
$359$	11.5897	−	9.72494i	0.611683	−	0.513263i	0.895177	+	0.445711i	$0.147049\pi$
$360$		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	0.919385	−	0.393358i	$-0.128687\pi$
$367$	−0.723196	−	1.98697i	−0.0377505	−	0.103719i	−0.957136	+	0.289640i	$0.906465\pi$
$368$	−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	0.382786	−	0.923837i	$-0.374965\pi$
$373$	−4.36262	−	2.51876i	−0.225888	−	0.130416i	−0.608674	+	0.793421i	$0.708298\pi$
$374$	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	−0.739029	−	0.673673i	$-0.764715\pi$
$383$	5.09082	−	13.9869i	0.260129	−	0.714698i	0.999158	−	0.0410250i	$-0.0130623\pi$
$384$	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	−0.999688	−	0.0249764i	$-0.992049\pi$
$389$	−23.6259	−	19.8245i	−1.19788	−	1.00514i	−0.198191	−	0.980163i	$-0.563507\pi$
$390$		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	0.994105	−	0.108420i	$-0.0345790\pi$
$397$	14.2405	+	16.9711i	0.714708	+	0.851756i	−0.279397	+	0.960176i	$0.590135\pi$
$398$			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	0.188688	−	0.982037i	$-0.439576\pi$
$401$	23.8011	−	19.9715i	1.18857	−	0.997330i	0.999883	−	0.0152927i	$-0.00486799\pi$
$402$	−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	0.603394	−	0.797443i	$-0.293815\pi$
$409$	−1.56037	−	1.30931i	−0.0771554	−	0.0647411i	−0.680550	+	0.732702i	$0.738259\pi$
$410$		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	0.556144	−	0.831086i	$-0.312280\pi$
$421$	9.19144	+	3.34541i	0.447964	+	0.163045i	−0.108181	+	0.994131i	$0.534502\pi$
$422$	−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	−0.229339	−	0.973347i	$-0.573656\pi$
$431$	4.58045	−	1.66715i	0.220633	−	0.0803037i	0.449971	+	0.893043i	$0.351434\pi$
$432$	−4.91106	+	0.865953i	−0.236284	+	0.0416632i
$433$	−19.6135	−	3.45838i	−0.942563	−	0.166199i	−0.318808	−	0.947819i	$-0.603283\pi$
$433$	−19.6135	−	3.45838i	−0.942563	−	0.166199i	−0.623755	+	0.781620i	$0.714394\pi$
$434$	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	−0.163888	−	0.986479i	$-0.552404\pi$
$439$	16.3249	−	13.6982i	0.779145	−	0.653780i	0.943033	+	0.332699i	$0.107959\pi$
$440$		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	0.979747	−	0.200239i	$-0.0641718\pi$
$443$	2.11541	+	5.81205i	0.100506	+	0.276139i	−0.879241	+	0.476377i	$0.841950\pi$
$444$	−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	0.241914	−	0.970298i	$-0.422225\pi$
$449$	20.3687	−	35.2797i	0.961260	−	1.66495i	0.719345	−	0.694653i	$-0.244442\pi$
$450$		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	$-0.888222\pi$
$457$		−	14.7073i		−	0.687978i	0.938974	−	0.343989i	$-0.111778\pi$
$458$	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	−0.987604	−	0.156966i	$-0.949829\pi$
$461$	−2.43148	−	13.7896i	−0.113245	−	0.642245i	0.874359	−	0.485280i	$-0.161282\pi$
$462$	−5.39859	−	14.8325i	−0.251165	−	0.690071i
$463$	−1.96929	−	1.13697i	−0.0915206	−	0.0528394i	0.453541	−	0.891235i	$-0.350160\pi$
$463$	−1.96929	−	1.13697i	−0.0915206	−	0.0528394i	−0.545062	+	0.838396i	$0.683494\pi$
$464$	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	0.224618	−	0.974447i	$-0.427886\pi$
$467$	25.5178	−	14.7327i	1.18082	−	0.681749i	0.956205	+	0.292698i	$0.0945531\pi$
$468$	−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	0.789527	+	0.613716i	$0.210326\pi$
$479$	−3.55187	+	20.1437i	−0.162289	+	0.920387i	−0.951816	+	0.306671i	$0.900785\pi$
$480$		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	0.947109	−	0.320912i	$-0.103989\pi$
$487$	25.2182	+	14.5597i	1.14275	+	0.659765i	0.195637	+	0.980676i	$0.437323\pi$
$488$	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	−0.0360537	−	0.999350i	$-0.511479\pi$
$491$	−15.6448	−	5.69426i	−0.706042	−	0.256978i	−0.669988	+	0.742372i	$0.733701\pi$
$492$	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	−0.857138	−	0.515087i	$-0.827760\pi$
$499$	−5.09005	−	28.8671i	−0.227862	−	1.29227i	0.629276	−	0.777182i	$-0.283351\pi$
$500$		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	−0.857713	−	0.514128i	$-0.828116\pi$
$503$	−4.54061	+	5.41129i	−0.202456	+	0.241277i	0.655258	+	0.755405i	$0.272560\pi$
$504$	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	0.901482	+	0.432817i	$0.142480\pi$
$509$	−2.11320	+	11.9846i	−0.0936661	+	0.531207i	−0.995148	+	0.0983900i	$0.968631\pi$
$510$		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	−0.997940	−	0.0641611i	$-0.979563\pi$
$521$	−12.6575	−	21.9234i	−0.554535	−	0.960483i	0.443405	−	0.896322i	$-0.353770\pi$
$522$	−0.635324	+	0.757150i	−0.0278074	+	0.0331396i
$523$	−27.7800	+	33.1069i	−1.21473	+	1.44766i	−0.356583	+	0.934263i	$0.616058\pi$
$523$	−27.7800	+	33.1069i	−1.21473	+	1.44766i	−0.858150	+	0.513399i	$0.828386\pi$
$524$	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	0.202864	−	0.979207i	$-0.434975\pi$
$541$	−16.8919	−	14.1740i	−0.726240	−	0.609388i	−0.929104	+	0.369819i	$0.879420\pi$
$542$	−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	−0.356855	−	0.934160i	$-0.616151\pi$
$547$	−23.6615	−	4.17215i	−1.01169	−	0.178388i	−0.654836	+	0.755771i	$0.727262\pi$
$548$	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	0.968320	−	0.249711i	$-0.0803356\pi$
$557$	1.55843	+	4.28175i	0.0660328	+	0.181424i	−0.902288	+	0.431135i	$0.858113\pi$
$558$	−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	0.857157	−	0.515056i	$-0.172229\pi$
$563$	19.9237	+	11.5030i	0.839684	+	0.484792i	−0.0174729	+	0.999847i	$0.505562\pi$
$564$	−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	0.0463754	−	0.998924i	$-0.485233\pi$
$577$	−19.1093	−	11.0328i	−0.795531	−	0.459300i	−0.841906	+	0.539624i	$0.818566\pi$
$578$	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	0.802355	−	0.596847i	$-0.203580\pi$
$587$	1.82311	+	2.17270i	0.0752478	+	0.0896768i	−0.727107	+	0.686524i	$0.759136\pi$
$588$		−	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	−0.760192	−	0.649698i	$-0.774895\pi$
$593$	−41.3185	−	7.28557i	−1.69675	−	0.299183i	−0.936557	+	0.350515i	$0.886006\pi$
$594$	−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	0.979177	−	0.203008i	$-0.0650716\pi$
$599$	23.2333	+	19.4950i	0.949286	+	0.796546i	−0.0298911	+	0.999553i	$0.509516\pi$
$600$		0			0
$601$	−16.4125	+	28.4274i	−0.669482	+	1.15958i	0.308568	+	0.951202i	$0.400150\pi$
$601$	−16.4125	+	28.4274i	−0.669482	+	1.15958i	−0.978049	+	0.208374i	$0.933183\pi$
$602$	−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	$0.0458428\pi$
$607$			7.07201i			0.287044i	−0.989647	+	0.143522i	$0.954157\pi$
$608$	−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	0.262670	−	0.964886i	$-0.415397\pi$
$613$	20.7853	−	3.66501i	0.839510	−	0.148028i	0.576840	+	0.816857i	$0.304286\pi$
$614$	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	−0.997667	−	0.0682659i	$-0.978253\pi$
$617$	−18.8083	+	22.4149i	−0.757195	+	0.902390i	0.240472	+	0.970656i	$0.422698\pi$
$618$	−7.93114	+	9.45197i	−0.319037	+	0.380214i
$619$	−8.81402	−	15.2663i	−0.354265	−	0.613606i	0.632727	−	0.774375i	$-0.281936\pi$
$619$	−8.81402	−	15.2663i	−0.354265	−	0.613606i	−0.986992	+	0.160770i	$0.948602\pi$
$620$		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	−0.597273	−	0.802038i	$-0.703749\pi$
$631$	5.98586	−	33.9475i	0.238293	−	1.35143i	0.835566	−	0.549390i	$-0.185140\pi$
$632$	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	0.495458	+	0.868632i	$0.335000\pi$
$641$	8.27820	+	46.9480i	0.326969	+	1.85434i	−0.168489	+	0.985704i	$0.553889\pi$
$642$	15.6262	+	2.75531i	0.616715	+	0.108744i
$643$	−3.24102	+	8.90463i	−0.127813	+	0.351164i	−0.987050	−	0.160414i	$-0.948717\pi$
$643$	−3.24102	+	8.90463i	−0.127813	+	0.351164i	0.859236	+	0.511579i	$0.170939\pi$
$644$	−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	$-0.892477\pi$
$647$		−	16.8594i		−	0.662810i	0.943489	−	0.331405i	$-0.107523\pi$
$648$	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	0.305936	−	0.952052i	$-0.401031\pi$
$653$	−9.34245	−	5.39386i	−0.365598	−	0.211078i	−0.671534	+	0.740974i	$0.734364\pi$
$654$	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	−0.678202	−	0.734875i	$-0.737241\pi$
$659$	−18.6209	+	6.77745i	−0.725367	+	0.264012i	−0.0471644	+	0.998887i	$0.515018\pi$
$660$		0			0
$661$	−4.06094	+	23.0307i	−0.157952	+	0.895792i	0.798084	+	0.602546i	$0.205847\pi$
$661$	−4.06094	+	23.0307i	−0.157952	+	0.895792i	−0.956037	+	0.293247i	$0.905264\pi$
$662$	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	−0.819748	−	0.572724i	$-0.805887\pi$
$673$	−19.0320	+	10.9881i	−0.733628	+	0.423560i	0.0861200	+	0.996285i	$0.472553\pi$
$674$	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	−0.998425	−	0.0561091i	$-0.982131\pi$
$677$	−40.2317	−	23.2278i	−1.54623	−	0.892716i	−0.547804	−	0.836607i	$-0.684536\pi$
$678$	−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	$-0.917349\pi$
$683$		−	13.4198i		−	0.513496i	0.966478	−	0.256748i	$-0.0826511\pi$
$684$	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	−0.126148	−	0.992011i	$-0.540261\pi$
$691$	20.9252	−	36.2436i	0.796033	−	1.37877i	0.922181	−	0.386759i	$-0.126405\pi$
$692$	−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	−0.167228	−	0.985918i	$-0.553481\pi$
$701$	20.5106	−	17.2104i	0.774674	−	0.650028i	0.941901	+	0.335890i	$0.109037\pi$
$702$		−	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	−0.653016	−	0.757344i	$-0.726497\pi$
$709$	−17.7455	+	6.45882i	−0.666445	+	0.242566i	−0.0134283	+	0.999910i	$0.504274\pi$
$710$		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	0.838501	−	0.544900i	$-0.183432\pi$
$719$	30.3154	+	11.0339i	1.13057	+	0.411496i	0.292074	+	0.956396i	$0.405655\pi$
$720$		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	−0.490866	−	0.871235i	$-0.663320\pi$
$727$	−17.6378	+	3.11002i	−0.654150	+	0.115344i	−0.163284	+	0.986579i	$0.552209\pi$
$728$	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	−0.530063	+	0.847958i	$0.677832\pi$
$733$	−41.4082	+	23.9071i	−1.52945	+	0.883027i	−0.999385	+	0.0350693i	$0.988835\pi$
$734$	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	−0.590627	−	0.806944i	$-0.701120\pi$
$739$	2.75913	−	2.31519i	0.101496	−	0.0851656i	0.692124	+	0.721779i	$0.256675\pi$
$740$		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	0.728127	−	0.685443i	$-0.240391\pi$
$743$	−1.99911	−	2.38245i	−0.0733403	−	0.0874036i	−0.801467	+	0.598039i	$0.795947\pi$
$744$	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	0.880866	−	0.473365i	$-0.156961\pi$
$751$	15.5562	+	13.0532i	0.567654	+	0.476318i	−0.313213	+	0.949683i	$0.601405\pi$
$752$	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	−0.418239	−	0.908337i	$-0.637353\pi$
$757$	13.3721	−	36.7396i	0.486018	−	1.33532i	0.904258	−	0.426987i	$-0.140425\pi$
$758$	−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	−0.0507735	−	0.998710i	$-0.516169\pi$
$769$	−28.9268	−	24.2725i	−1.04313	−	0.875288i	−0.992354	+	0.123422i	$0.960613\pi$
$770$		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	0.913565	−	0.406693i	$-0.133318\pi$
$773$	−1.32574	−	3.64243i	−0.0476834	−	0.131009i	−0.961248	+	0.275684i	$0.911096\pi$
$774$	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	−0.601710	−	0.798715i	$-0.705514\pi$
$787$	−5.91530	+	3.41520i	−0.210858	+	0.121739i	0.390852	+	0.920453i	$0.372180\pi$
$788$	−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	$0.152550\pi$
$797$			26.0356i			0.922229i	−0.887341	+	0.461114i	$0.847450\pi$
$798$	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	0.890144	−	0.455679i	$-0.150603\pi$
$809$	1.43475	+	2.48505i	0.0504430	+	0.0873698i	−0.839701	+	0.543048i	$0.817270\pi$
$810$		0			0
$811$	−14.8021	+	5.38752i	−0.519772	+	0.189181i	−0.588566	−	0.808449i	$-0.700307\pi$
$811$	−14.8021	+	5.38752i	−0.519772	+	0.189181i	0.0687939	+	0.997631i	$0.478085\pi$
$812$	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	0.896653	+	0.442734i	$0.145992\pi$
$821$	−2.78936	+	15.8192i	−0.0973493	+	0.552095i	−0.994002	+	0.109361i	$0.965120\pi$
$822$	−24.1296	+	4.25469i	−0.841615	+	0.148399i
$823$	13.9542	+	38.3389i	0.486413	+	1.33641i	0.903907	+	0.427729i	$0.140686\pi$
$823$	13.9542	+	38.3389i	0.486413	+	1.33641i	−0.417494	+	0.908680i	$0.637092\pi$
$824$	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	−0.966171	−	0.257903i	$-0.916969\pi$
$827$	−15.6560	+	18.6581i	−0.544413	+	0.648806i	0.421758	+	0.906708i	$0.361413\pi$
$828$	1.61726	−	0.933724i	0.0562036	−	0.0324492i
$829$	7.31291	−	12.6663i	0.253988	−	0.439920i	−0.710632	−	0.703564i	$-0.751591\pi$
$829$	7.31291	−	12.6663i	0.253988	−	0.439920i	0.964620	+	0.263644i	$0.0849243\pi$
$830$		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	0.994975	−	0.100119i	$-0.0319224\pi$
$839$	49.0332	+	17.8466i	1.69282	+	0.616134i	0.697840	+	0.716254i	$0.254145\pi$
$840$		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	0.628683	−	0.777661i	$-0.283594\pi$
$853$	−7.19445	−	8.57401i	−0.246333	−	0.293569i	−0.875017	+	0.484093i	$0.839150\pi$
$854$	8.79949			0.301112
$855$		0			0
$856$	−8.84015			−0.302150
$857$	−21.2831	−	25.3642i	−0.727016	−	0.866424i	0.268276	−	0.963342i	$-0.413546\pi$
$857$	−21.2831	−	25.3642i	−0.727016	−	0.866424i	−0.995292	+	0.0969180i	$0.969102\pi$
$858$	−23.3038	+	64.0266i	−0.795578	+	2.18583i
$859$	−1.64149	+	9.30936i	−0.0560070	+	0.317631i	−0.999921	−	0.0125596i	$-0.996002\pi$
$859$	−1.64149	+	9.30936i	−0.0560070	+	0.317631i	0.943914	+	0.330191i	$0.107113\pi$
$860$		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	0.637535	−	0.770422i	$-0.279954\pi$
$863$	47.6935	−	27.5359i	1.62351	−	0.937332i	0.985972	−	0.166910i	$-0.0533791\pi$
$864$	−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	−0.793960	−	0.607970i	$-0.791984\pi$
$877$	6.07221	−	16.6833i	0.205044	−	0.563354i	0.999004	+	0.0446161i	$0.0142065\pi$
$878$	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	−0.978189	−	0.207718i	$-0.933396\pi$
$881$	−9.17773	+	15.8963i	−0.309206	+	0.535560i	0.668983	+	0.743278i	$0.266730\pi$
$882$	−0.987988	+	0.570415i	−0.0332673	+	0.0192069i
$883$	−15.1814	+	18.0924i	−0.510893	+	0.608859i	−0.958402	−	0.285421i	$-0.907867\pi$
$883$	−15.1814	+	18.0924i	−0.510893	+	0.608859i	0.447509	+	0.894279i	$0.352311\pi$
$884$	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	0.958852	−	0.283906i	$-0.0916303\pi$
$887$	1.24604	+	3.42345i	0.0418378	+	0.114948i	−0.917014	+	0.398854i	$0.869408\pi$
$888$	−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	−0.190563	−	0.981675i	$-0.561031\pi$
$907$	−1.02035	+	0.179915i	−0.0338801	+	0.00597397i	0.156682	+	0.987649i	$0.449920\pi$
$908$	−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	0.233850	+	0.972273i	$0.424868\pi$
$919$	−21.9810	+	38.0723i	−0.725088	+	1.25589i	−0.958938	+	0.283616i	$0.908466\pi$
$920$		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	−0.730394	−	0.683026i	$-0.760663\pi$
$929$	−5.62577	+	4.72058i	−0.184576	+	0.154877i	0.545818	+	0.837904i	$0.316219\pi$
$930$		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	0.942265	−	0.334867i	$-0.108691\pi$
$937$	0.159172	+	0.437322i	0.00519993	+	0.0142867i	−0.937066	+	0.349154i	$0.886469\pi$
$938$	−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	0.992324	−	0.123669i	$-0.0394661\pi$
$941$	31.9901	+	26.8429i	1.04285	+	0.875054i	0.0505251	+	0.998723i	$0.483911\pi$
$942$	−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	−0.575406	−	0.817868i	$-0.695156\pi$
$947$	12.0353	−	33.0668i	0.391096	−	1.07453i	0.966502	−	0.256659i	$-0.0826218\pi$
$948$	−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	−0.875899	−	0.482494i	$-0.839731\pi$
$953$	3.24820	−	8.92435i	0.105219	−	0.289088i	0.981119	+	0.193406i	$0.0619534\pi$
$954$	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	0.941260	−	0.337682i	$-0.109643\pi$
$967$	13.8461	+	16.5011i	0.445260	+	0.530641i	−0.496000	+	0.868323i	$0.665198\pi$
$968$		−	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	−0.869748	−	0.493496i	$-0.835719\pi$
$971$	−16.6642	+	13.9829i	−0.534779	+	0.448733i	0.334969	+	0.942229i	$0.391274\pi$
$972$	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	−0.954233	−	0.299063i	$-0.903326\pi$
$977$	−36.6442	+	21.1566i	−1.17235	+	0.676859i	−0.218120	+	0.975922i	$0.569992\pi$
$978$	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	0.0252602	−	0.999681i	$-0.491959\pi$
$983$	12.2561	−	2.16108i	0.390908	−	0.0689276i	0.365648	+	0.930753i	$0.380847\pi$
$984$	−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	0.522169	−	0.852842i	$-0.325123\pi$
$991$	11.7729	+	4.28498i	0.373978	+	0.136117i	−0.148191	+	0.988959i	$0.547345\pi$
$992$	−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	−0.943038	−	0.332684i	$-0.892046\pi$
$997$	−14.2610	+	16.9956i	−0.451651	+	0.538257i	0.491387	+	0.870941i	$0.336490\pi$
$998$	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.899.6		36
5.2	odd	4		190.2.k.d.101.1	✓	18
5.3	odd	4		950.2.l.i.101.3		18
5.4	even	2	inner	950.2.u.g.899.1		36
19.16	even	9	inner	950.2.u.g.149.1		36
95.42	odd	36		3610.2.a.bi.1.7		9
95.54	even	18	inner	950.2.u.g.149.6		36
95.72	even	36		3610.2.a.bj.1.3		9
95.73	odd	36		950.2.l.i.301.3		18
95.92	odd	36		190.2.k.d.111.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.101.1	✓	18	5.2	odd	4
190.2.k.d.111.1	yes	18	95.92	odd	36
950.2.l.i.101.3		18	5.3	odd	4
950.2.l.i.301.3		18	95.73	odd	36
950.2.u.g.149.1		36	19.16	even	9	inner
950.2.u.g.149.6		36	95.54	even	18	inner
950.2.u.g.899.1		36	5.4	even	2	inner
950.2.u.g.899.6		36	1.1	even	1	trivial
3610.2.a.bi.1.7		9	95.42	odd	36
3610.2.a.bj.1.3		9	95.72	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

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