LMFDB - Embedded newform 961.2.g.m.338.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(235,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.235"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,4,-3,6,-3,-11,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			338.1
Root			$0.176392i$ of defining polynomial
Character	$\chi$	$=$	961.338
Dual form			961.2.g.m.816.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.996848 + 0.724253i) q^{2} +(0.216894 - 2.06361i) q^{3} +(-0.148869 + 0.458173i) q^{4} +(0.772811 - 1.33855i) q^{5} +(1.27836 + 2.21419i) q^{6} +(3.72064 - 0.790846i) q^{7} +(-0.944957 - 2.90828i) q^{8} +(-1.27699 - 0.271433i) q^{9} +(0.199072 + 1.89404i) q^{10} +(2.51695 + 2.79536i) q^{11} +(0.913200 + 0.406583i) q^{12} +(2.40725 - 1.07178i) q^{13} +(-3.13614 + 3.48303i) q^{14} +(-2.59462 - 1.88510i) q^{15} +(2.26882 + 1.64839i) q^{16} +(-2.52553 + 2.80488i) q^{17} +(1.46955 - 0.654287i) q^{18} +(5.57109 + 2.48041i) q^{19} +(0.498239 + 0.553350i) q^{20} +(-0.825012 - 7.84947i) q^{21} +(-4.53356 - 0.963639i) q^{22} +(-0.281158 - 0.865316i) q^{23} +(-6.20650 + 1.31923i) q^{24} +(1.30553 + 2.26124i) q^{25} +(-1.62343 + 2.81186i) q^{26} +(1.08650 - 3.34392i) q^{27} +(-0.191545 + 1.82243i) q^{28} +(-5.50827 + 4.00199i) q^{29} +3.95173 q^{30} +2.66037 q^{32} +(6.31443 - 4.58770i) q^{33} +(0.486124 - 4.62516i) q^{34} +(1.81676 - 5.59143i) q^{35} +(0.314468 - 0.544675i) q^{36} +(-0.907032 - 1.57103i) q^{37} +(-7.34997 + 1.56228i) q^{38} +(-1.68961 - 5.20008i) q^{39} +(-4.62315 - 0.982680i) q^{40} +(-0.0352412 - 0.335298i) q^{41} +(6.50741 + 7.22721i) q^{42} +(-3.54821 - 1.57976i) q^{43} +(-1.65545 + 0.737056i) q^{44} +(-1.35020 + 1.49955i) q^{45} +(0.906980 + 0.658959i) q^{46} +(0.962040 + 0.698963i) q^{47} +(3.89373 - 4.32442i) q^{48} +(6.82288 - 3.03774i) q^{49} +(-2.93912 - 1.30858i) q^{50} +(5.24040 + 5.82006i) q^{51} +(0.132693 + 1.26249i) q^{52} +(-2.29290 - 0.487371i) q^{53} +(1.33876 + 4.12028i) q^{54} +(5.68685 - 1.20878i) q^{55} +(-5.81584 - 10.0733i) q^{56} +(6.32692 - 10.9586i) q^{57} +(2.59245 - 7.97875i) q^{58} +(-0.813109 + 7.73622i) q^{59} +(1.24996 - 0.908151i) q^{60} +2.72343 q^{61} -4.96588 q^{63} +(-7.18962 + 5.22357i) q^{64} +(0.425725 - 4.05050i) q^{65} +(-2.97187 + 9.14649i) q^{66} +(3.71059 - 6.42693i) q^{67} +(-0.909147 - 1.57469i) q^{68} +(-1.84665 + 0.392519i) q^{69} +(2.23857 + 6.88960i) q^{70} +(4.98677 + 1.05997i) q^{71} +(0.417300 + 3.97034i) q^{72} +(-3.60778 - 4.00685i) q^{73} +(2.04199 + 0.909154i) q^{74} +(4.94947 - 2.20364i) q^{75} +(-1.96582 + 2.18326i) q^{76} +(11.5754 + 8.40999i) q^{77} +(5.45046 + 3.95999i) q^{78} +(6.51548 - 7.23617i) q^{79} +(3.95982 - 1.76303i) q^{80} +(-10.2428 - 4.56040i) q^{81} +(0.277970 + 0.308717i) q^{82} +(-0.877532 - 8.34916i) q^{83} +(3.71923 + 0.790547i) q^{84} +(1.80271 + 5.54818i) q^{85} +(4.68117 - 0.995014i) q^{86} +(7.06383 + 12.2349i) q^{87} +(5.75127 - 9.96149i) q^{88} +(-1.57463 + 4.84620i) q^{89} +(0.259892 - 2.47271i) q^{90} +(8.10889 - 5.89146i) q^{91} +0.438320 q^{92} -1.46523 q^{94} +(7.62555 - 5.54028i) q^{95} +(0.577018 - 5.48996i) q^{96} +(3.37268 - 10.3800i) q^{97} +(-4.60129 + 7.96966i) q^{98} +(-2.45537 - 4.25283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 11 q^{6} - 3 q^{7} - 8 q^{8} + 5 q^{9} + 18 q^{10} + 2 q^{11} + 20 q^{12} + 27 q^{13} - 6 q^{14} - 4 q^{15} - 2 q^{16} + 16 q^{17} + 22 q^{18} - 4 q^{19} - 18 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 3 * q^3 + 6 * q^4 - 3 * q^5 - 11 * q^6 - 3 * q^7 - 8 * q^8 + 5 * q^9 + 18 * q^10 + 2 * q^11 + 20 * q^12 + 27 * q^13 - 6 * q^14 - 4 * q^15 - 2 * q^16 + 16 * q^17 + 22 * q^18 - 4 * q^19 - 18 * q^20 - 29 * q^21 - 4 * q^22 - 21 * q^23 + 25 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 - 40 * q^28 - 26 * q^29 + 22 * q^30 - 42 * q^32 + 7 * q^33 - 28 * q^34 + 21 * q^35 + q^36 + 8 * q^37 - 27 * q^38 + 2 * q^39 - 16 * q^40 - 3 * q^41 + 51 * q^42 - 8 * q^43 - 4 * q^44 + 25 * q^45 + 16 * q^46 + 4 * q^47 + 86 * q^48 + 27 * q^49 - 27 * q^50 + 13 * q^51 - 24 * q^52 - 66 * q^53 - 39 * q^54 + 52 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 - 51 * q^59 - 35 * q^60 + 60 * q^61 - 46 * q^63 - 32 * q^64 - 18 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 + 48 * q^69 + 27 * q^70 - 24 * q^71 + 2 * q^72 - 27 * q^73 - 28 * q^74 + 32 * q^75 + 18 * q^76 + 42 * q^77 + 15 * q^78 - 8 * q^79 - 39 * q^80 - 7 * q^81 + 29 * q^82 - 4 * q^83 + 27 * q^84 + 63 * q^85 - 34 * q^86 + 15 * q^87 + 17 * q^88 - 26 * q^89 + 57 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 + 28 * q^95 + 62 * q^96 - 37 * q^97 - 10 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{8}{15}\right)$

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 $

$2$	−0.996848	+	0.724253i	−0.704878	+	0.512124i	−0.881517	−	0.472152i	$-0.843477\pi$
$2$	−0.996848	+	0.724253i	−0.704878	+	0.512124i	0.176639	+	0.984276i	$0.443477\pi$
$3$	0.216894	−	2.06361i	0.125224	−	1.19142i	−0.733755	−	0.679414i	$-0.762234\pi$
$3$	0.216894	−	2.06361i	0.125224	−	1.19142i	0.858979	−	0.512011i	$-0.171099\pi$
$4$	−0.148869	+	0.458173i	−0.0744347	+	0.229086i
$5$	0.772811	−	1.33855i	0.345612	−	0.598617i	−0.639853	−	0.768497i	$-0.721005\pi$
$5$	0.772811	−	1.33855i	0.345612	−	0.598617i	0.985465	+	0.169880i	$0.0543381\pi$
$6$	1.27836	+	2.21419i	0.521890	+	0.903939i
$7$	3.72064	−	0.790846i	1.40627	−	0.298912i	0.558600	−	0.829437i	$-0.311339\pi$
$7$	3.72064	−	0.790846i	1.40627	−	0.298912i	0.847669	+	0.530526i	$0.178005\pi$
$8$	−0.944957	−	2.90828i	−0.334093	−	1.02823i
$9$	−1.27699	−	0.271433i	−0.425664	−	0.0904776i
$10$	0.199072	+	1.89404i	0.0629520	+	0.598948i
$11$	2.51695	+	2.79536i	0.758889	+	0.842832i	0.991550	−	0.129726i	$-0.0414098\pi$
$11$	2.51695	+	2.79536i	0.758889	+	0.842832i	−0.232661	+	0.972558i	$0.574743\pi$
$12$	0.913200	+	0.406583i	0.263618	+	0.117370i
$13$	2.40725	−	1.07178i	0.667651	−	0.297257i	−0.0447827	−	0.998997i	$-0.514260\pi$
$13$	2.40725	−	1.07178i	0.667651	−	0.297257i	0.712434	+	0.701739i	$0.247593\pi$
$14$	−3.13614	+	3.48303i	−0.838168	+	0.930880i
$15$	−2.59462	−	1.88510i	−0.669928	−	0.486731i
$16$	2.26882	+	1.64839i	0.567204	+	0.412098i
$17$	−2.52553	+	2.80488i	−0.612530	+	0.680284i	−0.966998	−	0.254785i	$-0.917995\pi$
$17$	−2.52553	+	2.80488i	−0.612530	+	0.680284i	0.354468	+	0.935068i	$0.384662\pi$
$18$	1.46955	−	0.654287i	0.346377	−	0.154217i
$19$	5.57109	+	2.48041i	1.27810	+	0.569045i	0.929705	−	0.368305i	$-0.120062\pi$
$19$	5.57109	+	2.48041i	1.27810	+	0.569045i	0.348390	+	0.937350i	$0.386728\pi$
$20$	0.498239	+	0.553350i	0.111410	+	0.123733i
$21$	−0.825012	−	7.84947i	−0.180032	−	1.71289i
$22$	−4.53356	−	0.963639i	−0.966559	−	0.205448i
$23$	−0.281158	−	0.865316i	−0.0586255	−	0.180431i	0.917455	−	0.397839i	$-0.130240\pi$
$23$	−0.281158	−	0.865316i	−0.0586255	−	0.180431i	−0.976081	+	0.217408i	$0.930240\pi$
$24$	−6.20650	+	1.31923i	−1.26690	+	0.269287i
$25$	1.30553	+	2.26124i	0.261105	+	0.452247i
$26$	−1.62343	+	2.81186i	−0.318380	+	0.551450i
$27$	1.08650	−	3.34392i	0.209098	−	0.643537i
$28$	−0.191545	+	1.82243i	−0.0361986	+	0.344407i
$29$	−5.50827	+	4.00199i	−1.02286	+	0.743151i	−0.966867	−	0.255280i	$-0.917832\pi$
$29$	−5.50827	+	4.00199i	−1.02286	+	0.743151i	−0.0559922	+	0.998431i	$0.517832\pi$
$30$	3.95173			0.721485
$31$		0			0
$31$		0			0
$32$	2.66037			0.470292
$33$	6.31443	−	4.58770i	1.09920	−	0.798617i
$34$	0.486124	−	4.62516i	0.0833696	−	0.793208i
$35$	1.81676	−	5.59143i	0.307089	−	0.945124i
$36$	0.314468	−	0.544675i	0.0524114	−	0.0907792i
$37$	−0.907032	−	1.57103i	−0.149115	−	0.258275i	0.781786	−	0.623547i	$-0.214309\pi$
$37$	−0.907032	−	1.57103i	−0.149115	−	0.258275i	−0.930901	+	0.365272i	$0.880976\pi$
$38$	−7.34997	+	1.56228i	−1.19232	+	0.253436i
$39$	−1.68961	−	5.20008i	−0.270554	−	0.832680i
$40$	−4.62315	−	0.982680i	−0.730984	−	0.155375i
$41$	−0.0352412	−	0.335298i	−0.00550375	−	0.0523647i	0.991425	−	0.130675i	$-0.0417143\pi$
$41$	−0.0352412	−	0.335298i	−0.00550375	−	0.0523647i	−0.996929	+	0.0783099i	$0.975048\pi$
$42$	6.50741	+	7.22721i	1.00411	+	1.11518i
$43$	−3.54821	−	1.57976i	−0.541096	−	0.240912i	0.117943	−	0.993020i	$-0.462370\pi$
$43$	−3.54821	−	1.57976i	−0.541096	−	0.240912i	−0.659039	+	0.752109i	$0.729037\pi$
$44$	−1.65545	+	0.737056i	−0.249569	+	0.111115i
$45$	−1.35020	+	1.49955i	−0.201276	+	0.223540i
$46$	0.906980	+	0.658959i	0.133727	+	0.0971582i
$47$	0.962040	+	0.698963i	0.140328	+	0.101954i	0.655735	−	0.754992i	$-0.272359\pi$
$47$	0.962040	+	0.698963i	0.140328	+	0.101954i	−0.515407	+	0.856946i	$0.672359\pi$
$48$	3.89373	−	4.32442i	0.562011	−	0.624177i
$49$	6.82288	−	3.03774i	0.974698	−	0.433963i
$50$	−2.93912	−	1.30858i	−0.415654	−	0.185061i
$51$	5.24040	+	5.82006i	0.733803	+	0.814971i
$52$	0.132693	+	1.26249i	0.0184012	+	0.175076i
$53$	−2.29290	−	0.487371i	−0.314954	−	0.0669456i	0.0477225	−	0.998861i	$-0.484804\pi$
$53$	−2.29290	−	0.487371i	−0.314954	−	0.0669456i	−0.362677	+	0.931915i	$0.618137\pi$
$54$	1.33876	+	4.12028i	0.182182	+	0.560699i
$55$	5.68685	−	1.20878i	0.766815	−	0.162991i
$56$	−5.81584	−	10.0733i	−0.777175	−	1.34611i
$57$	6.32692	−	10.9586i	0.838022	−	1.45150i
$58$	2.59245	−	7.97875i	0.340406	−	1.04766i
$59$	−0.813109	+	7.73622i	−0.105858	+	1.00717i	0.804670	+	0.593722i	$0.202342\pi$
$59$	−0.813109	+	7.73622i	−0.105858	+	1.00717i	−0.910528	+	0.413448i	$0.864324\pi$
$60$	1.24996	−	0.908151i	0.161369	−	0.117242i
$61$	2.72343			0.348700			0.174350	−	0.984684i	$-0.444218\pi$
$61$	2.72343			0.348700			0.174350	+	0.984684i	$0.444218\pi$
$62$		0			0
$63$	−4.96588			−0.625642
$64$	−7.18962	+	5.22357i	−0.898703	+	0.652946i
$65$	0.425725	−	4.05050i	0.0528047	−	0.502403i
$66$	−2.97187	+	9.14649i	−0.365812	+	1.12586i
$67$	3.71059	−	6.42693i	0.453321	−	0.785175i	−0.545269	−	0.838261i	$-0.683573\pi$
$67$	3.71059	−	6.42693i	0.453321	−	0.785175i	0.998590	+	0.0530864i	$0.0169059\pi$
$68$	−0.909147	−	1.57469i	−0.110250	−	0.190959i
$69$	−1.84665	+	0.392519i	−0.222311	+	0.0472537i
$70$	2.23857	+	6.88960i	0.267560	+	0.823465i
$71$	4.98677	+	1.05997i	0.591821	+	0.125795i	0.494080	−	0.869416i	$-0.335505\pi$
$71$	4.98677	+	1.05997i	0.591821	+	0.125795i	0.0977410	+	0.995212i	$0.468838\pi$
$72$	0.417300	+	3.97034i	0.0491792	+	0.467909i
$73$	−3.60778	−	4.00685i	−0.422259	−	0.468966i	0.494053	−	0.869432i	$-0.335515\pi$
$73$	−3.60778	−	4.00685i	−0.422259	−	0.468966i	−0.916312	+	0.400466i	$0.868848\pi$
$74$	2.04199	+	0.909154i	0.237377	+	0.105687i
$75$	4.94947	−	2.20364i	0.571515	−	0.254455i
$76$	−1.96582	+	2.18326i	−0.225495	+	0.250438i
$77$	11.5754	+	8.40999i	1.31913	+	0.958407i
$78$	5.45046	+	3.95999i	0.617143	+	0.448380i
$79$	6.51548	−	7.23617i	0.733048	−	0.814133i	−0.255216	−	0.966884i	$-0.582147\pi$
$79$	6.51548	−	7.23617i	0.733048	−	0.814133i	0.988265	+	0.152751i	$0.0488134\pi$
$80$	3.95982	−	1.76303i	0.442721	−	0.197112i
$81$	−10.2428	−	4.56040i	−1.13809	−	0.506711i
$82$	0.277970	+	0.308717i	0.0306967	+	0.0340921i
$83$	−0.877532	−	8.34916i	−0.0963216	−	0.916439i	−0.930832	−	0.365447i	$-0.880916\pi$
$83$	−0.877532	−	8.34916i	−0.0963216	−	0.916439i	0.834511	−	0.550992i	$-0.185751\pi$
$84$	3.71923	+	0.790547i	0.405801	+	0.0862558i
$85$	1.80271	+	5.54818i	0.195532	+	0.601785i
$86$	4.68117	−	0.995014i	0.504784	−	0.107295i
$87$	7.06383	+	12.2349i	0.757322	+	1.31172i
$88$	5.75127	−	9.96149i	0.613087	−	1.06190i
$89$	−1.57463	+	4.84620i	−0.166910	+	0.513696i	−0.999172	−	0.0406863i	$-0.987046\pi$
$89$	−1.57463	+	4.84620i	−0.166910	+	0.513696i	0.832262	+	0.554383i	$0.187046\pi$
$90$	0.259892	−	2.47271i	0.0273950	−	0.260646i
$91$	8.10889	−	5.89146i	0.850043	−	0.617592i
$92$	0.438320			0.0456980
$93$		0			0
$94$	−1.46523			−0.151127
$95$	7.62555	−	5.54028i	0.782365	−	0.568421i
$96$	0.577018	−	5.48996i	0.0588917	−	0.560317i
$97$	3.37268	−	10.3800i	0.342444	−	1.05393i	−0.620494	−	0.784211i	$-0.713068\pi$
$97$	3.37268	−	10.3800i	0.342444	−	1.05393i	0.962938	−	0.269723i	$-0.0869320\pi$
$98$	−4.60129	+	7.96966i	−0.464800	+	0.805057i
$99$	−2.45537	−	4.25283i	−0.246774	−	0.427426i
$100$	−1.23039	+	0.261527i	−0.123039	+	0.0261527i
$101$	−0.123213	−	0.379212i	−0.0122602	−	0.0377330i	0.944739	−	0.327823i	$-0.106315\pi$
$101$	−0.123213	−	0.379212i	−0.0122602	−	0.0377330i	−0.956999	+	0.290090i	$0.906315\pi$
$102$	−9.43908	−	2.00634i	−0.934608	−	0.198657i
$103$	−0.342519	−	3.25885i	−0.0337494	−	0.321104i	−0.998352	−	0.0573947i	$-0.981721\pi$
$103$	−0.342519	−	3.25885i	−0.0337494	−	0.321104i	0.964602	−	0.263709i	$-0.0849460\pi$
$104$	−5.39177	−	5.98817i	−0.528707	−	0.587189i
$105$	−11.1445	−	4.96184i	−1.08759	−	0.484226i
$106$	2.63865	−	1.17480i	0.256289	−	0.114107i
$107$	2.11234	−	2.34599i	0.204208	−	0.226796i	−0.632338	−	0.774693i	$-0.717905\pi$
$107$	2.11234	−	2.34599i	0.204208	−	0.226796i	0.836546	+	0.547897i	$0.184571\pi$
$108$	1.37035	+	0.995614i	0.131862	+	0.0958030i
$109$	−5.62770	−	4.08876i	−0.539036	−	0.391632i	0.284691	−	0.958619i	$-0.408109\pi$
$109$	−5.62770	−	4.08876i	−0.539036	−	0.391632i	−0.823727	+	0.566987i	$0.808109\pi$
$110$	−4.79347	+	5.32368i	−0.457039	+	0.507593i
$111$	−3.43871	+	1.53101i	−0.326388	+	0.145317i
$112$	9.74507	+	4.33878i	0.920822	+	0.409977i
$113$	−10.2021	−	11.3306i	−0.959732	−	1.06589i	−0.997779	−	0.0666144i	$-0.978780\pi$
$113$	−10.2021	−	11.3306i	−0.959732	−	1.06589i	0.0380468	−	0.999276i	$-0.487886\pi$
$114$	1.62978	+	15.5063i	0.152643	+	1.45230i
$115$	−1.37555	−	0.292382i	−0.128271	−	0.0272648i
$116$	−1.01359	−	3.11951i	−0.0941096	−	0.289639i
$117$	−3.36495	+	0.715243i	−0.311090	+	0.0661242i
$118$	−4.79243	−	8.30073i	−0.441179	−	0.764144i
$119$	−7.17834	+	12.4332i	−0.658037	+	1.13975i
$120$	−3.03060	+	9.32722i	−0.276655	+	0.851455i
$121$	−0.329167	+	3.13181i	−0.0299243	+	0.284710i
$122$	−2.71485	+	1.97245i	−0.245791	+	0.178578i
$123$	−0.699567			−0.0630778
$124$		0			0
$125$	11.7638			1.05219
$126$	4.95023	−	3.59655i	0.441002	−	0.320407i
$127$	−2.11423	+	20.1156i	−0.187608	+	1.78497i	0.344997	+	0.938604i	$0.387880\pi$
$127$	−2.11423	+	20.1156i	−0.187608	+	1.78497i	−0.532605	+	0.846364i	$0.678787\pi$
$128$	1.73958	−	5.35388i	0.153759	−	0.473220i
$129$	−4.02960	+	6.97946i	−0.354786	+	0.614508i
$130$	2.50920	+	4.34607i	0.220072	+	0.381175i
$131$	−12.3748	+	2.63035i	−1.08119	+	0.229815i	−0.713870	−	0.700279i	$-0.753059\pi$
$131$	−12.3748	+	2.63035i	−1.08119	+	0.229815i	−0.367323	+	0.930093i	$0.619726\pi$
$132$	1.16194	+	3.57607i	0.101134	+	0.311257i
$133$	22.6896	+	4.82283i	1.96744	+	0.418192i
$134$	0.955826	+	9.09408i	0.0825708	+	0.785609i
$135$	−3.63633	−	4.03856i	−0.312966	−	0.347584i
$136$	10.5439	+	4.69444i	0.904131	+	0.402545i
$137$	9.02401	−	4.01775i	0.770974	−	0.343260i	0.0167349	−	0.999860i	$-0.494673\pi$
$137$	9.02401	−	4.01775i	0.770974	−	0.343260i	0.754239	+	0.656600i	$0.228006\pi$
$138$	1.55655	−	1.72873i	0.132502	−	0.147159i
$139$	−12.5389	−	9.11007i	−1.06354	−	0.772706i	−0.0887990	−	0.996050i	$-0.528303\pi$
$139$	−12.5389	−	9.11007i	−1.06354	−	0.772706i	−0.974740	+	0.223343i	$0.928303\pi$
$140$	2.29138	+	1.66479i	0.193657	+	0.140700i
$141$	1.65105	−	1.83367i	0.139043	−	0.154423i
$142$	−5.73874	+	2.55505i	−0.481585	+	0.214415i
$143$	9.05493	+	4.03151i	0.757211	+	0.337132i
$144$	−2.44983	−	2.72081i	−0.204153	−	0.226735i
$145$	1.10001	+	10.4659i	0.0913506	+	0.869143i
$146$	6.49838	+	1.38127i	0.537810	+	0.114315i
$147$	−4.78887	−	14.7386i	−0.394979	−	1.21562i
$148$	0.854831	−	0.181700i	0.0702666	−	0.0149356i
$149$	7.62162	+	13.2010i	0.624388	+	1.08147i	0.988659	+	0.150178i	$0.0479848\pi$
$149$	7.62162	+	13.2010i	0.624388	+	1.08147i	−0.364271	+	0.931293i	$0.618682\pi$
$150$	−3.33787	+	5.78136i	−0.272536	+	0.472046i
$151$	0.0809093	−	0.249013i	0.00658430	−	0.0202644i	−0.947710	−	0.319132i	$-0.896609\pi$
$151$	0.0809093	−	0.249013i	0.00658430	−	0.0202644i	0.954295	+	0.298867i	$0.0966088\pi$
$152$	1.94928	−	18.5462i	0.158107	−	1.50429i
$153$	3.98641	−	2.89630i	0.322282	−	0.234152i
$154$	−17.6298			−1.42065
$155$		0			0
$156$	2.63407			0.210894
$157$	−12.8848	+	9.36138i	−1.02832	+	0.747120i	−0.967972	−	0.251058i	$-0.919222\pi$
$157$	−12.8848	+	9.36138i	−1.02832	+	0.747120i	−0.0603497	+	0.998177i	$0.519222\pi$
$158$	−1.25413	+	11.9322i	−0.0997729	+	0.949276i
$159$	−1.50306	+	4.62594i	−0.119200	+	0.366861i
$160$	2.05597	−	3.56104i	0.162538	−	0.281525i
$161$	−1.73042	−	2.99717i	−0.136376	−	0.236210i
$162$	13.5134	−	2.87237i	1.06172	−	0.225675i
$163$	−0.0411534	−	0.126657i	−0.00322339	−	0.00992056i	0.949432	−	0.313973i	$-0.101660\pi$
$163$	−0.0411534	−	0.126657i	−0.00322339	−	0.00992056i	−0.952655	+	0.304053i	$0.901660\pi$
$164$	0.158871	+	0.0337690i	0.0124057	+	0.00263692i
$165$	−1.26100	−	11.9976i	−0.0981686	−	0.934012i
$166$	6.92166	+	7.68729i	0.537225	+	0.596649i
$167$	3.60739	+	1.60611i	0.279148	+	0.124285i	0.541536	−	0.840678i	$-0.317843\pi$
$167$	3.60739	+	1.60611i	0.279148	+	0.124285i	−0.262387	+	0.964963i	$0.584510\pi$
$168$	−22.0488	+	9.81677i	−1.70110	+	0.757380i
$169$	−4.05255	+	4.50081i	−0.311735	+	0.346216i
$170$	−5.81532	−	4.22508i	−0.446015	−	0.324049i
$171$	−6.44097	−	4.67964i	−0.492553	−	0.357861i
$172$	1.25202	−	1.39051i	0.0954659	−	0.106026i
$173$	−13.2071	+	5.88017i	−1.00412	+	0.447061i	−0.841865	−	0.539689i	$-0.818542\pi$
$173$	−13.2071	+	5.88017i	−1.00412	+	0.447061i	−0.162250	+	0.986750i	$0.551875\pi$
$174$	−15.9027	−	7.08035i	−1.20558	−	0.536760i
$175$	6.64567	+	7.38077i	0.502366	+	0.557934i
$176$	1.10266	+	10.4911i	0.0831159	+	0.790795i
$177$	15.7882	+	3.35588i	1.18671	+	0.252243i
$178$	−1.94021	−	5.97136i	−0.145425	−	0.447572i
$179$	−17.3327	+	3.68417i	−1.29550	+	0.275368i	−0.803542	−	0.595248i	$-0.797054\pi$
$179$	−17.3327	+	3.68417i	−1.29550	+	0.275368i	−0.491962	+	0.870616i	$0.663720\pi$
$180$	−0.486049	−	0.841862i	−0.0362280	−	0.0627487i
$181$	−6.02958	+	10.4435i	−0.448175	+	0.776262i	−0.998267	−	0.0588418i	$-0.981259\pi$
$181$	−6.02958	+	10.4435i	−0.448175	+	0.776262i	0.550092	+	0.835104i	$0.314593\pi$
$182$	−3.81643	+	11.7458i	−0.282893	+	0.870655i
$183$	0.590696	−	5.62010i	0.0436655	−	0.415450i
$184$	−2.25090	+	1.63537i	−0.165938	+	0.120561i
$185$	−2.80386			−0.206144
$186$		0			0
$187$	−14.1973			−1.03821
$188$	−0.463464	+	0.336727i	−0.0338016	+	0.0245583i
$189$	1.39797	−	13.3008i	0.101687	−	0.967488i
$190$	−3.58895	+	11.0456i	−0.260370	+	0.801335i
$191$	−2.53576	+	4.39207i	−0.183481	+	0.317799i	−0.943064	−	0.332612i	$-0.892070\pi$
$191$	−2.53576	+	4.39207i	−0.183481	+	0.317799i	0.759583	+	0.650411i	$0.225403\pi$
$192$	9.22001	+	15.9695i	0.665397	+	1.15250i
$193$	19.6038	−	4.16691i	1.41111	−	0.299941i	0.561555	−	0.827439i	$-0.310203\pi$
$193$	19.6038	−	4.16691i	1.41111	−	0.299941i	0.849556	+	0.527498i	$0.176870\pi$
$194$	4.15572	+	12.7900i	0.298364	+	0.918269i
$195$	−8.26631	−	1.75706i	−0.591963	−	0.125826i
$196$	0.376093	+	3.57829i	0.0268638	+	0.255592i
$197$	−14.5257	−	16.1325i	−1.03492	−	1.14939i	−0.988616	−	0.150462i	$-0.951924\pi$
$197$	−14.5257	−	16.1325i	−1.03492	−	1.14939i	−0.0462995	−	0.998928i	$-0.514743\pi$
$198$	5.52776	+	2.46112i	0.392841	+	0.174904i
$199$	−13.8544	+	6.16837i	−0.982111	+	0.437264i	−0.834035	−	0.551712i	$-0.813975\pi$
$199$	−13.8544	+	6.16837i	−0.982111	+	0.437264i	−0.148076	+	0.988976i	$0.547308\pi$
$200$	5.34264	−	5.93360i	0.377782	−	0.419569i
$201$	−12.4579	−	9.05117i	−0.878710	−	0.638420i
$202$	0.397470	+	0.288779i	0.0279659	+	0.0203184i
$203$	−17.3293	+	19.2461i	−1.21628	+	1.35081i
$204$	−3.44673	+	1.53458i	−0.241319	+	0.107442i
$205$	−0.476047	−	0.211950i	−0.0332486	−	0.0148032i
$206$	2.70167	+	3.00051i	0.188234	+	0.209055i
$207$	0.124161	+	1.18132i	0.00862981	+	0.0821072i
$208$	7.22832	+	1.53643i	0.501194	+	0.106532i
$209$	7.08853	+	21.8162i	0.490324	+	1.50906i
$210$	14.7030	−	3.12521i	1.01460	−	0.215660i
$211$	−3.15220	−	5.45978i	−0.217007	−	0.375867i	0.736885	−	0.676018i	$-0.236296\pi$
$211$	−3.15220	−	5.45978i	−0.217007	−	0.375867i	−0.953891	+	0.300152i	$0.902963\pi$
$212$	0.564643	−	0.977990i	0.0387798	−	0.0671687i
$213$	3.26897	−	10.0608i	0.223986	−	0.689358i
$214$	−0.406593	+	3.86847i	−0.0277941	+	0.264443i
$215$	−4.85668	+	3.52859i	−0.331223	+	0.240648i
$216$	−10.7517			−0.731564
$217$		0			0
$218$	8.57126			0.580519
$219$	−9.05107	+	6.57598i	−0.611614	+	0.444364i
$220$	−0.292769	+	2.78551i	−0.0197385	+	0.187799i
$221$	−3.07337	+	9.45885i	−0.206737	+	0.636271i
$222$	2.31903	−	4.01668i	0.155643	−	0.269582i
$223$	3.69455	+	6.39915i	0.247406	+	0.428519i	0.962805	−	0.270196i	$-0.0870887\pi$
$223$	3.69455	+	6.39915i	0.247406	+	0.428519i	−0.715400	+	0.698716i	$0.753755\pi$
$224$	9.89828	−	2.10394i	0.661356	−	0.140576i
$225$	−1.05337	−	3.24194i	−0.0702247	−	0.216129i
$226$	18.3761	+	3.90597i	1.22236	+	0.259821i
$227$	−2.01111	−	19.1344i	−0.133482	−	1.26999i	−0.832151	−	0.554549i	$-0.812891\pi$
$227$	−2.01111	−	19.1344i	−0.133482	−	1.26999i	0.698669	−	0.715445i	$-0.253776\pi$
$228$	4.07903	+	4.53022i	0.270140	+	0.300021i
$229$	5.56085	+	2.47585i	0.367471	+	0.163609i	0.582161	−	0.813074i	$-0.302207\pi$
$229$	5.56085	+	2.47585i	0.367471	+	0.163609i	−0.214690	+	0.976682i	$0.568874\pi$
$230$	1.58297	−	0.704785i	0.104378	−	0.0464721i
$231$	19.8655	−	22.0629i	1.30706	−	1.45163i
$232$	16.8440	+	12.2379i	1.10586	+	0.803455i
$233$	−14.1805	−	10.3027i	−0.928995	−	0.674954i	0.0167519	−	0.999860i	$-0.494667\pi$
$233$	−14.1805	−	10.3027i	−0.928995	−	0.674954i	−0.945746	+	0.324906i	$0.894667\pi$
$234$	2.83633	−	3.15007i	0.185417	−	0.205926i
$235$	1.67907	−	0.747571i	0.109531	−	0.0487662i
$236$	−3.42348	−	1.52423i	−0.222849	−	0.0992190i
$237$	−13.5194	−	15.0149i	−0.878183	−	0.975320i
$238$	−1.84910	−	17.5930i	−0.119859	−	1.14038i
$239$	−27.3021	−	5.80324i	−1.76603	−	0.375380i	−0.793572	−	0.608476i	$-0.791781\pi$
$239$	−27.3021	−	5.80324i	−1.76603	−	0.375380i	−0.972454	+	0.233096i	$0.925114\pi$
$240$	−2.77933	−	8.55391i	−0.179405	−	0.552152i
$241$	22.2526	−	4.72994i	1.43342	−	0.304682i	0.575218	−	0.818000i	$-0.304917\pi$
$241$	22.2526	−	4.72994i	1.43342	−	0.304682i	0.858198	+	0.513318i	$0.171584\pi$
$242$	−1.94010	−	3.36034i	−0.124714	−	0.216011i
$243$	−6.35849	+	11.0132i	−0.407897	+	0.706499i
$244$	−0.405436	+	1.24780i	−0.0259554	+	0.0798824i
$245$	1.20663	−	11.4804i	0.0770891	−	0.733453i
$246$	0.697362	−	0.506663i	0.0444622	−	0.0323037i
$247$	16.0694			1.02247
$248$		0			0
$249$	−17.4197			−1.10393
$250$	−11.7267	+	8.51997i	−0.741664	+	0.538850i
$251$	−1.69697	+	16.1456i	−0.107112	+	1.01910i	0.800513	+	0.599316i	$0.204561\pi$
$251$	−1.69697	+	16.1456i	−0.107112	+	1.01910i	−0.907624	+	0.419783i	$0.862106\pi$
$252$	0.739268	−	2.27523i	0.0465695	−	0.143326i
$253$	1.71121	−	2.96390i	0.107583	−	0.186339i
$254$	−12.4612	−	21.5834i	−0.781884	−	1.35426i
$255$	11.8403	−	2.51673i	0.741467	−	0.157604i
$256$	−3.34892	−	10.3069i	−0.209307	−	0.644182i
$257$	−22.8418	−	4.85518i	−1.42483	−	0.302858i	−0.569950	−	0.821679i	$-0.693037\pi$
$257$	−22.8418	−	4.85518i	−1.42483	−	0.302858i	−0.854882	+	0.518822i	$0.826371\pi$
$258$	−1.03800	−	9.87591i	−0.0646231	−	0.614847i
$259$	−4.61718	−	5.12789i	−0.286897	−	0.318632i
$260$	1.79245	+	0.798052i	0.111163	+	0.0494931i
$261$	8.12028	−	3.61538i	0.502633	−	0.223786i
$262$	10.4308	−	11.5846i	0.644416	−	0.715696i
$263$	−8.40921	−	6.10965i	−0.518534	−	0.376737i	0.297517	−	0.954716i	$-0.403841\pi$
$263$	−8.40921	−	6.10965i	−0.518534	−	0.376737i	−0.816051	+	0.577979i	$0.803841\pi$
$264$	−19.3092	−	14.0289i	−1.18840	−	0.863422i
$265$	−2.42435	+	2.69251i	−0.148927	+	0.165400i
$266$	−26.1110	+	11.6254i	−1.60097	+	0.712798i
$267$	9.65913	+	4.30052i	0.591129	+	0.263188i
$268$	2.39225	+	2.65687i	0.146130	+	0.162294i
$269$	−0.461812	−	4.39384i	−0.0281571	−	0.267897i	−0.999539	−	0.0303726i	$-0.990331\pi$
$269$	−0.461812	−	4.39384i	−0.0281571	−	0.267897i	0.971381	−	0.237525i	$-0.0763361\pi$
$270$	6.54981	+	1.39220i	0.398609	+	0.0847269i
$271$	−1.90134	−	5.85172i	−0.115498	−	0.355467i	0.876552	−	0.481306i	$-0.159838\pi$
$271$	−1.90134	−	5.85172i	−0.115498	−	0.355467i	−0.992051	+	0.125840i	$0.959838\pi$
$272$	−10.3535	+	2.20070i	−0.627773	+	0.133437i
$273$	−10.3989	−	18.0114i	−0.629369	−	1.09010i
$274$	−6.08571	+	10.5408i	−0.367651	+	0.636790i
$275$	−3.03502	+	9.34083i	−0.183019	+	0.563273i
$276$	0.0950690	−	0.904521i	0.00572248	−	0.0544458i
$277$	17.8367	−	12.9591i	1.07171	−	0.778639i	0.0954872	−	0.995431i	$-0.469559\pi$
$277$	17.8367	−	12.9591i	1.07171	−	0.778639i	0.976218	+	0.216791i	$0.0695591\pi$
$278$	19.0974			1.14539
$279$		0			0
$280$	−17.9782			−1.07440
$281$	24.8963	−	18.0882i	1.48519	−	1.07905i	0.509353	−	0.860557i	$-0.329885\pi$
$281$	24.8963	−	18.0882i	1.48519	−	1.07905i	0.975838	−	0.218497i	$-0.0701154\pi$
$282$	−0.317800	+	3.02367i	−0.0189247	+	0.180057i
$283$	−6.59605	+	20.3005i	−0.392094	+	1.20674i	0.539107	+	0.842237i	$0.318762\pi$
$283$	−6.59605	+	20.3005i	−0.392094	+	1.20674i	−0.931202	+	0.364505i	$0.881238\pi$
$284$	−1.22803	+	2.12701i	−0.0728701	+	0.126215i
$285$	−9.77904	−	16.9378i	−0.579260	−	1.00331i
$286$	−11.9462	+	2.53925i	−0.706395	+	0.150149i
$287$	−0.396289	−	1.21965i	−0.0233922	−	0.0719937i
$288$	−3.39727	−	0.722112i	−0.200186	−	0.0425509i
$289$	0.287909	+	2.73927i	0.0169358	+	0.161134i
$290$	−8.67647	−	9.63619i	−0.509500	−	0.565857i
$291$	−20.6888	−	9.21126i	−1.21280	−	0.539974i
$292$	2.37292	−	1.05649i	0.138864	−	0.0618264i
$293$	−1.20378	+	1.33694i	−0.0703258	+	0.0781047i	−0.777281	−	0.629154i	$-0.783402\pi$
$293$	−1.20378	+	1.33694i	−0.0703258	+	0.0781047i	0.706955	+	0.707258i	$0.250068\pi$
$294$	15.4483	+	11.2238i	0.900961	+	0.654587i
$295$	9.72692	+	7.06702i	0.566323	+	0.411458i
$296$	−3.71187	+	4.12245i	−0.215748	+	0.239613i
$297$	12.0821	−	5.37931i	0.701076	−	0.312139i
$298$	−17.1585	−	7.63945i	−0.993965	−	0.442542i
$299$	−1.60424	−	1.78169i	−0.0927758	−	0.103038i
$300$	0.272826	+	2.59577i	0.0157516	+	0.149867i
$301$	−14.4509	−	3.07164i	−0.832938	−	0.177046i
$302$	0.0996942	+	0.306827i	0.00573676	+	0.0176559i
$303$	−0.809269	+	0.172015i	−0.0464913	+	0.00988203i
$304$	8.55109	+	14.8109i	0.490439	+	0.849465i
$305$	2.10470	−	3.64545i	0.120515	−	0.208738i
$306$	−1.87620	+	5.77434i	−0.107255	+	0.330097i
$307$	−2.79816	+	26.6228i	−0.159700	+	1.51944i	0.561943	+	0.827176i	$0.310054\pi$
$307$	−2.79816	+	26.6228i	−0.159700	+	1.51944i	−0.721643	+	0.692265i	$0.756613\pi$
$308$	−5.57645	+	4.05153i	−0.317748	+	0.230857i
$309$	−6.79928			−0.386798
$310$		0			0
$311$	4.18114			0.237090			0.118545	−	0.992949i	$-0.462177\pi$
$311$	4.18114			0.237090			0.118545	+	0.992949i	$0.462177\pi$
$312$	−13.5267	+	9.82771i	−0.765798	+	0.556384i
$313$	−1.18565	+	11.2807i	−0.0670168	+	0.637622i	0.908528	+	0.417823i	$0.137207\pi$
$313$	−1.18565	+	11.2807i	−0.0670168	+	0.637622i	−0.975545	+	0.219799i	$0.929460\pi$
$314$	6.06422	−	18.6638i	0.342224	−	1.05326i
$315$	−3.83769	+	6.64708i	−0.216229	+	0.374520i
$316$	2.34546	+	4.06246i	0.131943	+	0.228531i
$317$	−25.3158	+	5.38103i	−1.42188	+	0.302229i	−0.853737	−	0.520704i	$-0.825669\pi$
$317$	−25.3158	+	5.38103i	−1.42188	+	0.302229i	−0.568138	+	0.822933i	$0.692336\pi$
$318$	−1.85203	−	5.69996i	−0.103857	−	0.319638i
$319$	−25.0510	−	5.32476i	−1.40259	−	0.298129i
$320$	1.43578	+	13.6605i	0.0802623	+	0.763644i
$321$	−4.38306	−	4.86788i	−0.244638	−	0.271698i
$322$	3.89568	+	1.73447i	0.217098	+	0.0966581i
$323$	−21.0272	+	9.36190i	−1.16998	+	0.520910i
$324$	3.61430	−	4.01408i	0.200794	−	0.223005i
$325$	5.56627	+	4.04413i	0.308761	+	0.224328i
$326$	0.132756	+	0.0964526i	0.00735265	+	0.00534202i
$327$	−9.65822	+	10.7265i	−0.534101	+	0.593179i
$328$	−0.941838	+	0.419333i	−0.0520043	+	0.0231538i
$329$	4.13217	+	1.83976i	0.227814	+	0.101429i
$330$	9.94632	+	11.0465i	0.547527	+	0.608090i
$331$	0.0800466	+	0.761593i	0.00439976	+	0.0418609i	0.996502	−	0.0835749i	$-0.0266338\pi$
$331$	0.0800466	+	0.761593i	0.00439976	+	0.0418609i	−0.992102	+	0.125436i	$0.959967\pi$
$332$	3.95600	+	0.840873i	0.217113	+	0.0461489i
$333$	0.731844	+	2.25238i	0.0401048	+	0.123430i
$334$	−4.75925	+	1.01161i	−0.260415	+	0.0553528i
$335$	−5.73517	−	9.93361i	−0.313346	−	0.542731i
$336$	11.0672	−	19.1689i	0.603765	−	1.04575i
$337$	−0.739892	+	2.27715i	−0.0403045	+	0.124044i	−0.969184	−	0.246337i	$-0.920773\pi$
$337$	−0.739892	+	2.27715i	−0.0403045	+	0.124044i	0.928880	+	0.370381i	$0.120773\pi$
$338$	0.780052	−	7.42170i	0.0424292	−	0.403687i
$339$	−25.5946	+	18.5956i	−1.39011	+	1.00997i
$340$	−2.81040			−0.152415
$341$		0			0
$342$	9.80991			0.530459
$343$	1.44195	−	1.04764i	0.0778580	−	0.0565672i
$344$	−1.24149	+	11.8120i	−0.0669366	+	0.636859i
$345$	−0.901710	+	2.77518i	−0.0485465	+	0.149411i
$346$	8.90672	−	15.4269i	0.478828	−	0.829355i
$347$	2.82890	+	4.89980i	0.151863	+	0.263035i	0.931912	−	0.362683i	$-0.118139\pi$
$347$	2.82890	+	4.89980i	0.151863	+	0.263035i	−0.780049	+	0.625718i	$0.784806\pi$
$348$	−6.65729	+	1.41505i	−0.356868	+	0.0758547i
$349$	8.98238	+	27.6449i	0.480816	+	1.47980i	0.837950	+	0.545746i	$0.183754\pi$
$349$	8.98238	+	27.6449i	0.480816	+	1.47980i	−0.357134	+	0.934053i	$0.616246\pi$
$350$	−11.9703	−	2.54436i	−0.639838	−	0.136002i
$351$	−0.968445	−	9.21414i	−0.0516918	−	0.491814i
$352$	6.69603	+	7.43669i	0.356899	+	0.396377i
$353$	17.6088	+	7.83993i	0.937220	+	0.417277i	0.817759	−	0.575561i	$-0.195216\pi$
$353$	17.6088	+	7.83993i	0.937220	+	0.417277i	0.119462	+	0.992839i	$0.461883\pi$
$354$	−18.1689	+	8.08932i	−0.965666	+	0.429942i
$355$	5.27266	−	5.85588i	0.279844	−	0.310798i
$356$	−1.98598	−	1.44290i	−0.105257	−	0.0764737i
$357$	24.1004	+	17.5100i	1.27553	+	0.926726i
$358$	14.6098	−	16.2258i	0.772150	−	0.857560i
$359$	9.44996	−	4.20739i	0.498750	−	0.222058i	−0.141914	−	0.989879i	$-0.545326\pi$
$359$	9.44996	−	4.20739i	0.498750	−	0.222058i	0.640664	+	0.767821i	$0.278659\pi$
$360$	5.63699	+	2.50975i	0.297095	+	0.132275i
$361$	12.1711	+	13.5174i	0.640585	+	0.711441i
$362$	−1.55318	−	14.7776i	−0.0816336	−	0.776691i
$363$	6.39144	+	1.35854i	0.335464	+	0.0713050i
$364$	1.49214	+	4.59233i	0.0782094	+	0.240704i
$365$	−8.15149	+	1.73265i	−0.426669	+	0.0906912i
$366$	3.48154	+	6.03020i	0.181983	+	0.315203i
$367$	−0.0682819	+	0.118268i	−0.00356428	+	0.00617352i	−0.867802	−	0.496910i	$-0.834468\pi$
$367$	−0.0682819	+	0.118268i	−0.00356428	+	0.00617352i	0.864238	+	0.503084i	$0.167801\pi$
$368$	0.788484	−	2.42670i	0.0411025	−	0.126501i
$369$	−0.0460081	+	0.437738i	−0.00239509	+	0.0227877i
$370$	2.79502	−	2.03070i	0.145306	−	0.105571i
$371$	−8.91649			−0.462921
$372$		0			0
$373$	−7.36393			−0.381290			−0.190645	−	0.981659i	$-0.561058\pi$
$373$	−7.36393			−0.381290			−0.190645	+	0.981659i	$0.561058\pi$
$374$	14.1525	−	10.2824i	0.731810	−	0.531691i
$375$	2.55150	−	24.2759i	0.131759	−	1.25360i
$376$	1.12369	−	3.45837i	0.0579500	−	0.178352i
$377$	−8.97053	+	15.5374i	−0.462006	+	0.800218i
$378$	8.23955	+	14.2713i	0.423797	+	0.734038i
$379$	4.50744	−	0.958085i	0.231531	−	0.0492135i	−0.0906847	−	0.995880i	$-0.528906\pi$
$379$	4.50744	−	0.958085i	0.231531	−	0.0492135i	0.322216	+	0.946666i	$0.395572\pi$
$380$	1.40320	+	4.31860i	0.0719825	+	0.221539i
$381$	41.0521	+	8.72589i	2.10316	+	0.447041i
$382$	−0.653197	−	6.21475i	−0.0334205	−	0.317974i
$383$	21.6094	+	23.9997i	1.10419	+	1.22633i	0.971969	+	0.235107i	$0.0755441\pi$
$383$	21.6094	+	23.9997i	1.10419	+	1.22633i	0.132221	+	0.991220i	$0.457789\pi$
$384$	−10.6710	−	4.75103i	−0.544552	−	0.242450i
$385$	20.2027	−	8.99484i	1.02963	−	0.458420i
$386$	−16.5241	+	18.3519i	−0.841055	+	0.934086i
$387$	4.10223	+	2.98044i	0.208528	+	0.151504i
$388$	4.25377	+	3.09054i	0.215952	+	0.156898i
$389$	23.6011	−	26.2117i	1.19662	−	1.32898i	0.265573	−	0.964091i	$-0.414439\pi$
$389$	23.6011	−	26.2117i	1.19662	−	1.32898i	0.931049	−	0.364893i	$-0.118895\pi$
$390$	9.51281	−	4.23538i	0.481700	−	0.214467i
$391$	3.13718	+	1.39676i	0.158654	+	0.0706373i
$392$	−15.2819	−	16.9723i	−0.771854	−	0.857231i
$393$	2.74399	+	26.1073i	0.138416	+	1.31694i
$394$	26.1639	+	5.56131i	1.31812	+	0.280175i
$395$	−4.65073	−	14.3135i	−0.234004	−	0.720189i
$396$	2.31406	−	0.491869i	0.116286	−	0.0247174i
$397$	2.01701	+	3.49356i	0.101231	+	0.175337i	0.912192	−	0.409763i	$-0.134389\pi$
$397$	2.01701	+	3.49356i	0.101231	+	0.175337i	−0.810961	+	0.585100i	$0.801055\pi$
$398$	9.34326	−	16.1830i	0.468335	−	0.811181i
$399$	14.8737	−	45.7764i	0.744614	−	2.29169i
$400$	−0.765406	+	7.28235i	−0.0382703	+	0.364117i
$401$	20.1309	−	14.6260i	1.00529	−	0.730387i	0.0420750	−	0.999114i	$-0.486603\pi$
$401$	20.1309	−	14.6260i	1.00529	−	0.730387i	0.963216	+	0.268728i	$0.0866032\pi$
$402$	18.9739			0.946334
$403$		0			0
$404$	0.192087			0.00955671
$405$	−14.0201	+	10.1862i	−0.696664	+	0.506156i
$406$	3.33562	−	31.7363i	0.165544	−	1.57504i
$407$	2.10862	−	6.48967i	0.104521	−	0.321681i
$408$	11.9744	−	20.7403i	0.592821	−	1.02680i
$409$	1.75361	+	3.03734i	0.0867105	+	0.150187i	0.906119	−	0.423023i	$-0.139031\pi$
$409$	1.75361	+	3.03734i	0.0867105	+	0.150187i	−0.819408	+	0.573210i	$0.805698\pi$
$410$	0.628052	−	0.133497i	0.0310173	−	0.00659293i
$411$	−6.33381	−	19.4935i	−0.312424	−	0.961541i
$412$	1.54411	+	0.328210i	0.0760728	+	0.0161698i
$413$	3.09287	+	29.4267i	0.152190	+	1.44799i
$414$	−0.979342	−	1.08767i	−0.0481320	−	0.0534560i
$415$	−11.8539	−	5.27770i	−0.581886	−	0.259072i
$416$	6.40418	−	2.85132i	0.313991	−	0.139798i
$417$	−21.5192	+	23.8995i	−1.05380	+	1.17037i
$418$	−22.8667	−	16.6136i	−1.11844	−	0.812598i
$419$	−3.33340	−	2.42186i	−0.162847	−	0.118316i	0.503377	−	0.864067i	$-0.332091\pi$
$419$	−3.33340	−	2.42186i	−0.162847	−	0.118316i	−0.666224	+	0.745751i	$0.732091\pi$
$420$	3.93245	−	4.36743i	0.191884	−	0.213109i
$421$	25.2151	−	11.2265i	1.22891	−	0.547146i	0.313469	−	0.949598i	$-0.398509\pi$
$421$	25.2151	−	11.2265i	1.22891	−	0.547146i	0.915441	+	0.402452i	$0.131842\pi$
$422$	7.09653	+	3.15958i	0.345454	+	0.153806i
$423$	−1.03880	−	1.15370i	−0.0505080	−	0.0560948i
$424$	0.749282	+	7.12894i	0.0363883	+	0.346212i
$425$	−9.63964	−	2.04897i	−0.467591	−	0.0993895i
$426$	4.02793	+	12.3967i	0.195154	+	0.600622i
$427$	10.1329	−	2.15382i	0.490366	−	0.104230i
$428$	0.760408	+	1.31706i	0.0367557	+	0.0636627i
$429$	10.2834	−	17.8114i	0.496488	−	0.859943i
$430$	2.28579	−	7.03493i	0.110230	−	0.339255i
$431$	1.55475	−	14.7925i	0.0748897	−	0.712528i	−0.891075	−	0.453855i	$-0.850048\pi$
$431$	1.55475	−	14.7925i	0.0748897	−	0.712528i	0.965965	−	0.258672i	$-0.0832850\pi$
$432$	7.97717	−	5.79575i	0.383802	−	0.278848i
$433$	−9.26195			−0.445101			−0.222550	−	0.974921i	$-0.571438\pi$
$433$	−9.26195			−0.445101			−0.222550	+	0.974921i	$0.571438\pi$
$434$		0			0
$435$	21.8360			1.04696
$436$	2.71115	−	1.96977i	0.129841	−	0.0943348i
$437$	0.579980	−	5.51814i	0.0277442	−	0.263968i
$438$	4.25987	−	13.1105i	0.203544	−	0.626445i
$439$	−8.85909	+	15.3444i	−0.422821	+	0.732348i	−0.996214	−	0.0869324i	$-0.972294\pi$
$439$	−8.85909	+	15.3444i	−0.422821	+	0.732348i	0.573393	+	0.819281i	$0.305627\pi$
$440$	−8.88929	−	15.3967i	−0.423780	−	0.734009i
$441$	−9.53731	+	2.02722i	−0.454158	+	0.0965342i
$442$	−3.78692	−	11.6549i	−0.180125	−	0.554369i
$443$	18.0471	+	3.83602i	0.857441	+	0.182255i	0.615598	−	0.788060i	$-0.288915\pi$
$443$	18.0471	+	3.83602i	0.857441	+	0.182255i	0.241843	+	0.970315i	$0.422248\pi$
$444$	−0.189550	−	1.80344i	−0.00899563	−	0.0855877i
$445$	5.26999	+	5.85291i	0.249821	+	0.277455i
$446$	−8.31751	−	3.70320i	−0.393846	−	0.175351i
$447$	28.8949	−	12.8648i	1.36668	−	0.608485i
$448$	−22.6189	+	25.1209i	−1.06864	+	1.18685i
$449$	18.3730	+	13.3487i	0.867073	+	0.629966i	0.929800	−	0.368065i	$-0.119980\pi$
$449$	18.3730	+	13.3487i	0.867073	+	0.629966i	−0.0627268	+	0.998031i	$0.519980\pi$
$450$	3.39804	+	2.46882i	0.160185	+	0.116381i
$451$	0.848577	−	0.942440i	0.0399579	−	0.0443778i
$452$	6.71014	−	2.98755i	0.315618	−	0.140522i
$453$	−0.496317	−	0.220974i	−0.0233190	−	0.0103823i
$454$	15.8629	+	17.6175i	0.744483	+	0.826832i
$455$	−1.61935	−	15.4071i	−0.0759165	−	0.722297i
$456$	−37.8492	−	8.04510i	−1.77245	−	0.376746i
$457$	4.99429	+	15.3708i	0.233623	+	0.719018i	0.997301	+	0.0734205i	$0.0233915\pi$
$457$	4.99429	+	15.3708i	0.233623	+	0.719018i	−0.763678	+	0.645597i	$0.776608\pi$
$458$	−7.33646	+	1.55941i	−0.342810	+	0.0728666i
$459$	6.63529	+	11.4927i	0.309709	+	0.536432i
$460$	0.338739	−	0.586713i	0.0157938	−	0.0273556i
$461$	−6.65584	+	20.4846i	−0.309993	+	0.954062i	0.667773	+	0.744365i	$0.267248\pi$
$461$	−6.65584	+	20.4846i	−0.309993	+	0.954062i	−0.977766	+	0.209697i	$0.932752\pi$
$462$	−3.82380	+	36.3811i	−0.177899	+	1.69260i
$463$	−14.1657	+	10.2920i	−0.658337	+	0.478310i	−0.866101	−	0.499869i	$-0.833381\pi$
$463$	−14.1657	+	10.2920i	−0.658337	+	0.478310i	0.207764	+	0.978179i	$0.433381\pi$
$464$	−19.0941			−0.886421
$465$		0			0
$466$	21.5976			1.00049
$467$	9.55176	−	6.93976i	0.442003	−	0.321134i	−0.344427	−	0.938813i	$-0.611927\pi$
$467$	9.55176	−	6.93976i	0.442003	−	0.321134i	0.786430	+	0.617679i	$0.211927\pi$
$468$	0.173234	−	1.64821i	0.00800773	−	0.0761885i
$469$	8.72305	−	26.8468i	0.402793	−	1.23967i
$470$	−1.13235	+	1.96129i	−0.0522314	+	0.0904674i
$471$	16.5236	+	28.6197i	0.761366	+	1.31872i
$472$	23.2674	−	4.94565i	1.07097	−	0.227642i
$473$	−4.51466	−	13.8947i	−0.207584	−	0.638879i
$474$	24.3514	+	5.17605i	1.11850	+	0.237744i
$475$	1.66441	+	15.8358i	0.0763683	+	0.726595i
$476$	−4.62794	−	5.13985i	−0.212121	−	0.235585i
$477$	2.79573	+	1.24474i	0.128008	+	0.0569926i
$478$	31.4191	−	13.9887i	1.43707	−	0.639827i
$479$	−10.5781	+	11.7482i	−0.483326	+	0.536787i	−0.934648	−	0.355573i	$-0.884286\pi$
$479$	−10.5781	+	11.7482i	−0.483326	+	0.536787i	0.451323	+	0.892361i	$0.350952\pi$
$480$	−6.90266	−	5.01507i	−0.315062	−	0.228906i
$481$	−3.86724	−	2.80972i	−0.176331	−	0.128112i
$482$	−18.7568	+	20.8315i	−0.854349	+	0.948850i
$483$	−6.56031	+	2.92084i	−0.298504	+	0.132903i
$484$	−1.38591	−	0.617047i	−0.0629959	−	0.0280476i
$485$	−11.2877	−	12.5363i	−0.512550	−	0.569245i
$486$	−1.63791	−	15.5837i	−0.0742971	−	0.706890i
$487$	12.5121	+	2.65953i	0.566978	+	0.120515i	0.482477	−	0.875909i	$-0.339737\pi$
$487$	12.5121	+	2.65953i	0.566978	+	0.120515i	0.0845007	+	0.996423i	$0.473070\pi$
$488$	−2.57353	−	7.92050i	−0.116498	−	0.358544i
$489$	−0.270297	+	0.0574534i	−0.0122232	+	0.00259813i
$490$	7.11185	+	12.3181i	0.321281	+	0.556475i
$491$	−9.26410	+	16.0459i	−0.418083	+	0.724141i	−0.995747	−	0.0921341i	$-0.970631\pi$
$491$	−9.26410	+	16.0459i	−0.418083	+	0.724141i	0.577664	+	0.816275i	$0.303964\pi$
$492$	0.104144	−	0.320523i	0.00469518	−	0.0144503i
$493$	2.68617	−	25.5572i	0.120979	−	1.15104i
$494$	−16.0188	+	11.6383i	−0.720720	+	0.523634i
$495$	−7.59016			−0.341152
$496$		0			0
$497$	19.3922			0.869861
$498$	17.3648	−	12.6163i	0.778136	−	0.565349i
$499$	4.27388	−	40.6633i	0.191325	−	1.82034i	−0.305169	−	0.952298i	$-0.598713\pi$
$499$	4.27388	−	40.6633i	0.191325	−	1.82034i	0.496495	−	0.868040i	$-0.334620\pi$
$500$	−1.75127	+	5.38986i	−0.0783193	+	0.241042i
$501$	4.09681	−	7.09588i	0.183032	−	0.317021i
$502$	−10.0018	−	17.3237i	−0.446404	−	0.773195i
$503$	−19.6384	+	4.17426i	−0.875631	+	0.186121i	−0.623738	−	0.781634i	$-0.714387\pi$
$503$	−19.6384	+	4.17426i	−0.875631	+	0.186121i	−0.251894	+	0.967755i	$0.581053\pi$
$504$	4.69255	+	14.4422i	0.209023	+	0.643306i
$505$	−0.602814	−	0.128132i	−0.0268249	−	0.00570181i
$506$	0.440797	+	4.19390i	0.0195958	+	0.186442i
$507$	8.40894	+	9.33907i	0.373454	+	0.414763i
$508$	−8.90166	−	3.96328i	−0.394947	−	0.175842i
$509$	29.1523	−	12.9795i	1.29215	−	0.575304i	0.358517	−	0.933523i	$-0.383282\pi$
$509$	29.1523	−	12.9795i	1.29215	−	0.575304i	0.933638	+	0.358219i	$0.116616\pi$
$510$	−9.98021	+	11.0841i	−0.441931	+	0.490814i
$511$	−16.5920	−	12.0548i	−0.733989	−	0.533274i
$512$	19.9117	+	14.4667i	0.879983	+	0.639345i
$513$	14.3473	−	15.9343i	0.633448	−	0.703516i
$514$	26.2862	−	11.7034i	1.15943	−	0.516213i
$515$	−4.62683	−	2.06000i	−0.203883	−	0.0907744i
$516$	−2.59792	−	2.88528i	−0.114367	−	0.127017i
$517$	0.467556	+	4.44850i	0.0205631	+	0.195645i
$518$	8.31651	+	1.76773i	0.365407	+	0.0776696i
$519$	9.26983	+	28.5296i	0.406900	+	1.25231i
$520$	−12.1823	+	2.58942i	−0.534228	+	0.113554i
$521$	−1.05378	−	1.82520i	−0.0461670	−	0.0799635i	0.842019	−	0.539449i	$-0.181367\pi$
$521$	−1.05378	−	1.82520i	−0.0461670	−	0.0799635i	−0.888185	+	0.459485i	$0.848034\pi$
$522$	−5.47624	+	9.48512i	−0.239688	+	0.415152i
$523$	−1.51658	+	4.66757i	−0.0663156	+	0.204098i	−0.978723	−	0.205184i	$-0.934221\pi$
$523$	−1.51658	+	4.66757i	−0.0663156	+	0.204098i	0.912408	+	0.409282i	$0.134221\pi$
$524$	0.637077	−	6.06139i	0.0278309	−	0.264793i
$525$	16.6724	−	12.1132i	0.727644	−	0.528664i
$526$	12.8076			0.558440
$527$		0			0
$528$	21.8886			0.952580
$529$	17.9377	−	13.0325i	0.779899	−	0.566630i
$530$	0.466649	−	4.43987i	0.0202699	−	0.192856i
$531$	3.13820	−	9.65838i	0.136186	−	0.419138i
$532$	−5.58748	+	9.67780i	−0.242248	+	0.419586i
$533$	−0.444199	−	0.769375i	−0.0192404	−	0.0333253i
$534$	−12.7434	+	2.70868i	−0.551459	+	0.117216i
$535$	−1.50778	−	4.64048i	−0.0651872	−	0.200626i
$536$	−22.1977	−	4.71826i	−0.958793	−	0.203798i
$537$	3.84334	+	36.5669i	0.165852	+	1.57798i
$538$	3.64261	+	4.04553i	0.157044	+	0.174415i
$539$	25.6644	+	11.4265i	1.10545	+	0.492176i
$540$	2.39170	−	1.06485i	0.102922	−	0.0458239i
$541$	−8.32199	+	9.24251i	−0.357790	+	0.397366i	−0.894988	−	0.446090i	$-0.852816\pi$
$541$	−8.32199	+	9.24251i	−0.357790	+	0.397366i	0.537198	+	0.843456i	$0.319483\pi$
$542$	6.13347	+	4.45623i	0.263455	+	0.191411i
$543$	20.2436	+	14.7078i	0.868736	+	0.631173i
$544$	−6.71884	+	7.46203i	−0.288068	+	0.319932i
$545$	−9.82216	+	4.37311i	−0.420735	+	0.187323i
$546$	23.4109	+	10.4232i	1.00189	+	0.446072i
$547$	−9.34442	−	10.3780i	−0.399538	−	0.443732i	0.509484	−	0.860480i	$-0.329836\pi$
$547$	−9.34442	−	10.3780i	−0.399538	−	0.443732i	−0.909022	+	0.416748i	$0.863170\pi$
$548$	0.497425	+	4.73268i	0.0212489	+	0.202170i
$549$	−3.47780	−	0.739229i	−0.148429	−	0.0315495i
$550$	−3.73967	−	11.5095i	−0.159460	−	0.490767i
$551$	−40.6136	+	8.63269i	−1.73020	+	0.367765i
$552$	2.88656	+	4.99967i	0.122860	+	0.212800i
$553$	18.5190	−	32.0759i	0.787509	−	1.36401i
$554$	−8.39482	+	25.8366i	−0.356662	+	1.09769i
$555$	−0.608140	+	5.78606i	−0.0258141	+	0.245605i
$556$	6.04065	−	4.38879i	0.256181	−	0.186126i
$557$	37.2207			1.57709			0.788546	−	0.614976i	$-0.210834\pi$
$557$	37.2207			1.57709			0.788546	+	0.614976i	$0.210834\pi$
$558$		0			0
$559$	−10.2346			−0.432876
$560$	13.3388	−	9.69119i	0.563666	−	0.409527i
$561$	−3.07930	+	29.2976i	−0.130008	+	1.23695i
$562$	−11.7174	+	36.0625i	−0.494269	+	1.52120i
$563$	15.0134	−	26.0039i	0.632738	−	1.09593i	−0.354252	−	0.935150i	$-0.615264\pi$
$563$	15.0134	−	26.0039i	0.632738	−	1.09593i	0.986990	−	0.160784i	$-0.0514023\pi$
$564$	0.594349	+	1.02944i	0.0250266	+	0.0433474i
$565$	−23.0508	+	4.89960i	−0.969755	+	0.206128i
$566$	−8.12746	−	25.0138i	−0.341623	−	1.05141i
$567$	−41.7164	−	8.86710i	−1.75193	−	0.372383i
$568$	−1.62959	−	15.5046i	−0.0683763	−	0.650557i
$569$	27.0137	+	30.0017i	1.13247	+	1.25774i	0.962201	+	0.272341i	$0.0877978\pi$
$569$	27.0137	+	30.0017i	1.13247	+	1.25774i	0.170272	+	0.985397i	$0.445536\pi$
$570$	22.0155	+	9.80191i	0.922126	+	0.410557i
$571$	−38.9184	+	17.3276i	−1.62869	+	0.725138i	−0.998676	−	0.0514487i	$-0.983616\pi$
$571$	−38.9184	+	17.3276i	−1.62869	+	0.725138i	−0.630011	+	0.776587i	$0.716949\pi$
$572$	−3.19513	+	3.54855i	−0.133595	+	0.148373i
$573$	8.51351	+	6.18543i	0.355657	+	0.258400i
$574$	1.27837	+	0.928794i	0.0533583	+	0.0387671i
$575$	1.58962	−	1.76546i	0.0662919	−	0.0736246i
$576$	10.5989	−	4.71895i	0.441622	−	0.196623i
$577$	−5.97255	−	2.65915i	−0.248640	−	0.110702i	0.278633	−	0.960398i	$-0.410119\pi$
$577$	−5.97255	−	2.65915i	−0.248640	−	0.110702i	−0.527273	+	0.849696i	$0.676785\pi$
$578$	−2.27093	−	2.52212i	−0.0944582	−	0.104906i
$579$	−4.34693	−	41.3583i	−0.180652	−	1.71879i
$580$	−4.95893	−	1.05405i	−0.205908	−	0.0437672i
$581$	−9.86787	−	30.3702i	−0.409388	−	1.25997i
$582$	27.2949	−	5.80171i	1.13141	−	0.240489i
$583$	−4.40874	−	7.63617i	−0.182591	−	0.316258i
$584$	−8.24383	+	14.2787i	−0.341132	+	0.590858i
$585$	−1.64309	+	5.05690i	−0.0679333	+	0.209077i
$586$	0.231709	−	2.20457i	0.00957183	−	0.0910699i
$587$	−17.2949	+	12.5655i	−0.713838	+	0.518634i	−0.884410	−	0.466712i	$-0.845439\pi$
$587$	−17.2949	+	12.5655i	−0.713838	+	0.518634i	0.170572	+	0.985345i	$0.445439\pi$
$588$	7.46576			0.307883
$589$		0			0
$590$	−14.8146			−0.609907
$591$	−36.4416	+	26.4764i	−1.49901	+	1.08909i
$592$	0.531776	−	5.05951i	0.0218559	−	0.207945i
$593$	8.03153	−	24.7185i	0.329816	−	1.01507i	−0.639404	−	0.768871i	$-0.720819\pi$
$593$	8.03153	−	24.7185i	0.329816	−	1.01507i	0.969220	−	0.246197i	$-0.0791811\pi$
$594$	−8.14807	+	14.1129i	−0.334319	+	0.579058i
$595$	11.0950	+	19.2171i	0.454851	+	0.787824i
$596$	−7.18299	+	1.52679i	−0.294227	+	0.0625398i
$597$	9.72416	+	29.9279i	0.397983	+	1.22487i
$598$	2.88958	+	0.614200i	0.118164	+	0.0251165i
$599$	0.960403	+	9.13762i	0.0392410	+	0.373353i	0.996465	+	0.0840061i	$0.0267715\pi$
$599$	0.960403	+	9.13762i	0.0392410	+	0.373353i	−0.957224	+	0.289347i	$0.906562\pi$
$600$	−11.0858	−	12.3121i	−0.452578	−	0.502638i
$601$	−30.4385	−	13.5521i	−1.24161	−	0.552801i	−0.322414	−	0.946599i	$-0.604494\pi$
$601$	−30.4385	−	13.5521i	−1.24161	−	0.552801i	−0.919197	+	0.393798i	$0.871161\pi$
$602$	16.6300	−	7.40417i	0.677790	−	0.301771i
$603$	−6.48287	+	7.19996i	−0.264003	+	0.293205i
$604$	0.102046	+	0.0741409i	0.00415220	+	0.00301675i
$605$	3.93770	+	2.86091i	0.160090	+	0.116312i
$606$	0.682136	−	0.757589i	0.0277099	−	0.0307749i
$607$	−44.4904	+	19.8084i	−1.80581	+	0.803998i	−0.841003	+	0.541030i	$0.818035\pi$
$607$	−44.4904	+	19.8084i	−1.80581	+	0.803998i	−0.964805	+	0.262968i	$0.915299\pi$
$608$	14.8212	+	6.59881i	0.601078	+	0.267617i
$609$	35.9579	+	39.9352i	1.45709	+	1.61826i
$610$	0.542158	+	5.15829i	0.0219513	+	0.208853i
$611$	3.06500	+	0.651487i	0.123997	+	0.0263563i
$612$	0.733551	+	2.25764i	0.0296520	+	0.0912595i
$613$	20.4570	−	4.34827i	0.826250	−	0.175625i	0.224667	−	0.974436i	$-0.427870\pi$
$613$	20.4570	−	4.34827i	0.826250	−	0.175625i	0.601582	+	0.798811i	$0.294537\pi$
$614$	−16.4923	−	28.5654i	−0.665573	−	1.15281i
$615$	−0.540633	+	0.936404i	−0.0218004	+	0.0377594i
$616$	13.5204	−	41.6114i	0.544752	−	1.67657i
$617$	−4.74392	+	45.1353i	−0.190983	+	1.81708i	0.309019	+	0.951056i	$0.399999\pi$
$617$	−4.74392	+	45.1353i	−0.190983	+	1.81708i	−0.500001	+	0.866025i	$0.666667\pi$
$618$	6.77785	−	4.92440i	0.272645	−	0.198088i
$619$	10.2462			0.411832			0.205916	−	0.978570i	$-0.433983\pi$
$619$	10.2462			0.411832			0.205916	+	0.978570i	$0.433983\pi$
$620$		0			0
$621$	−3.19902			−0.128372
$622$	−4.16796	+	3.02820i	−0.167120	+	0.121420i
$623$	−2.02601	+	19.2762i	−0.0811706	+	0.772286i
$624$	4.73836	−	14.5832i	0.189686	−	0.583794i
$625$	2.56358	−	4.44025i	0.102543	−	0.177610i
$626$	−6.98816	−	12.1038i	−0.279303	−	0.483767i
$627$	46.5576	−	9.89613i	1.85933	−	0.395213i
$628$	−2.37097	−	7.29711i	−0.0946121	−	0.291186i
$629$	6.69727	+	1.42355i	0.267038	+	0.0567606i
$630$	−0.988567	−	9.40558i	−0.0393854	−	0.374727i
$631$	7.14429	+	7.93453i	0.284410	+	0.315869i	0.868373	−	0.495911i	$-0.165166\pi$
$631$	7.14429	+	7.93453i	0.284410	+	0.315869i	−0.583964	+	0.811780i	$0.698499\pi$
$632$	−27.2016	−	12.1110i	−1.08202	−	0.481748i
$633$	−11.9505	+	5.32072i	−0.474991	+	0.211480i
$634$	21.3388	−	23.6991i	0.847470	−	0.941211i
$635$	25.2918	+	18.3755i	1.00367	+	0.729211i
$636$	−1.89572	−	1.37732i	−0.0751702	−	0.0546144i
$637$	13.1686	−	14.6252i	0.521759	−	0.579472i
$638$	28.8285	−	12.8353i	1.14133	−	0.508154i
$639$	−6.08036	−	2.70715i	−0.240535	−	0.107093i
$640$	−5.82206	−	6.46605i	−0.230137	−	0.255593i
$641$	2.49427	+	23.7314i	0.0985177	+	0.937333i	0.926428	+	0.376472i	$0.122863\pi$
$641$	2.49427	+	23.7314i	0.0985177	+	0.937333i	−0.827910	+	0.560861i	$0.810470\pi$
$642$	7.89482	+	1.67810i	0.311584	+	0.0662291i
$643$	2.45337	+	7.55069i	0.0967513	+	0.297770i	0.987706	−	0.156322i	$-0.0499637\pi$
$643$	2.45337	+	7.55069i	0.0967513	+	0.297770i	−0.890955	+	0.454092i	$0.849964\pi$
$644$	1.63083	−	0.346644i	0.0642637	−	0.0136597i
$645$	6.22823	+	10.7876i	0.245237	+	0.424762i
$646$	14.1805	−	24.5614i	0.557925	−	0.966355i
$647$	−0.765625	+	2.35635i	−0.0300998	+	0.0926377i	−0.964978	−	0.262331i	$-0.915509\pi$
$647$	−0.765625	+	2.35635i	−0.0300998	+	0.0926377i	0.934878	+	0.354969i	$0.115509\pi$
$648$	−3.58389	+	34.0984i	−0.140788	+	1.33951i
$649$	−23.6721	+	17.1988i	−0.929209	+	0.675110i
$650$	−8.47769			−0.332523
$651$		0			0
$652$	0.0641574			0.00251260
$653$	−18.1981	+	13.2217i	−0.712145	+	0.517404i	−0.883865	−	0.467742i	$-0.845068\pi$
$653$	−18.1981	+	13.2217i	−0.712145	+	0.517404i	0.171720	+	0.985146i	$0.445068\pi$
$654$	1.85905	−	17.6877i	0.0726948	−	0.691644i
$655$	−6.04255	+	18.5971i	−0.236102	+	0.726647i
$656$	0.472746	−	0.818821i	0.0184576	−	0.0319696i
$657$	3.51952	+	6.09598i	0.137309	+	0.237827i
$658$	−5.45160	+	1.15877i	−0.212526	+	0.0451737i
$659$	−3.69573	−	11.3743i	−0.143965	−	0.443079i	0.852911	−	0.522056i	$-0.174835\pi$
$659$	−3.69573	−	11.3743i	−0.143965	−	0.443079i	−0.996876	+	0.0789765i	$0.974835\pi$
$660$	5.68470	+	1.20832i	0.221277	+	0.0470338i
$661$	−2.49154	−	23.7054i	−0.0969096	−	0.922033i	−0.929668	−	0.368397i	$-0.879907\pi$
$661$	−2.49154	−	23.7054i	−0.0969096	−	0.922033i	0.832759	−	0.553636i	$-0.186760\pi$
$662$	−0.631380	−	0.701218i	−0.0245393	−	0.0272536i
$663$	18.8528	+	8.39379i	0.732181	+	0.325988i
$664$	−23.4524	+	10.4417i	−0.910131	+	0.405217i
$665$	23.9904	−	26.6440i	0.930307	−	1.03321i
$666$	−2.36083	−	1.71525i	−0.0914804	−	0.0664644i
$667$	5.01168	+	3.64120i	0.194053	+	0.140988i
$668$	−1.27291	+	1.41371i	−0.0492503	+	0.0546980i
$669$	14.0067	−	6.23617i	0.541529	−	0.241104i
$670$	12.9115	+	5.74859i	0.498816	+	0.222087i
$671$	6.85475	+	7.61297i	0.264625	+	0.293895i
$672$	−2.19484	−	20.8825i	−0.0846677	−	0.805560i
$673$	3.41777	+	0.726469i	0.131745	+	0.0280033i	0.273312	−	0.961925i	$-0.411881\pi$
$673$	3.41777	+	0.726469i	0.131745	+	0.0280033i	−0.141567	+	0.989929i	$0.545214\pi$
$674$	−0.911675	−	2.80585i	−0.0351164	−	0.108077i
$675$	8.97985	−	1.90873i	0.345634	−	0.0734669i
$676$	−1.45885	−	2.52680i	−0.0561096	−	0.0971847i
$677$	−9.62287	+	16.6673i	−0.369837	+	0.640576i	−0.989540	−	0.144260i	$-0.953920\pi$
$677$	−9.62287	+	16.6673i	−0.369837	+	0.640576i	0.619703	+	0.784836i	$0.287253\pi$
$678$	12.0461	−	37.0740i	0.462626	−	1.42382i
$679$	4.33951	−	41.2876i	0.166535	−	1.58447i
$680$	14.4322	−	10.4856i	0.553449	−	0.402104i
$681$	−39.9221			−1.52982
$682$		0			0
$683$	−39.8738			−1.52573			−0.762865	−	0.646558i	$-0.776208\pi$
$683$	−39.8738			−1.52573			−0.762865	+	0.646558i	$0.776208\pi$
$684$	3.10295	−	2.25442i	0.118644	−	0.0862000i
$685$	1.59591	−	15.1840i	0.0609765	−	0.580152i
$686$	−0.678651	+	2.08867i	−0.0259110	+	0.0797459i
$687$	6.31529	−	10.9384i	0.240944	−	0.417326i
$688$	−5.44616	−	9.43303i	−0.207633	−	0.359631i
$689$	−6.04194	+	1.28425i	−0.230180	+	0.0489262i
$690$	−1.11106	−	3.41950i	−0.0422974	−	0.130178i
$691$	−37.5711	−	7.98598i	−1.42927	−	0.303801i	−0.572673	−	0.819784i	$-0.694093\pi$
$691$	−37.5711	−	7.98598i	−1.42927	−	0.303801i	−0.856599	+	0.515983i	$0.827427\pi$
$692$	−0.728005	−	6.92650i	−0.0276746	−	0.263306i
$693$	−12.4989	−	13.8814i	−0.474793	−	0.527311i
$694$	−6.36868	−	2.83552i	−0.241752	−	0.107635i
$695$	−21.8845	+	9.74361i	−0.830127	+	0.369596i
$696$	28.9075	−	32.1050i	1.09574	−	1.21694i
$697$	1.02947	+	0.747956i	0.0389941	+	0.0283308i
$698$	−28.9760	−	21.0523i	−1.09676	−	0.796841i
$699$	−24.3364	+	27.0284i	−0.920489	+	1.02231i
$700$	−4.37101	+	1.94610i	−0.165209	+	0.0735556i
$701$	−32.3628	−	14.4088i	−1.22233	−	0.544214i	−0.308851	−	0.951111i	$-0.599944\pi$
$701$	−32.3628	−	14.4088i	−1.22233	−	0.544214i	−0.913474	+	0.406896i	$0.866611\pi$
$702$	7.63876	+	8.48370i	0.288306	+	0.320197i
$703$	−1.15637	−	11.0021i	−0.0436133	−	0.414953i
$704$	−32.6977	−	6.95010i	−1.23234	−	0.261942i
$705$	−1.17851	−	3.62709i	−0.0443854	−	0.136604i
$706$	−23.2314	+	4.93798i	−0.874324	+	0.185843i
$707$	−0.758331	−	1.31347i	−0.0285200	−	0.0493980i
$708$	−3.88795	+	6.73412i	−0.146118	+	0.253084i
$709$	7.97551	−	24.5461i	0.299526	−	0.921848i	−0.682137	−	0.731225i	$-0.738949\pi$
$709$	7.97551	−	24.5461i	0.299526	−	0.921848i	0.981663	−	0.190623i	$-0.0610508\pi$
$710$	−1.01490	+	9.65616i	−0.0380886	+	0.362389i
$711$	−10.2843	+	7.47201i	−0.385693	+	0.280222i
$712$	15.5821			0.583962
$713$		0			0
$714$	−36.7061			−1.37369
$715$	12.3941	−	9.00486i	0.463514	−	0.336763i
$716$	0.892316	−	8.48982i	0.0333474	−	0.317279i
$717$	−17.8973	+	55.0821i	−0.668386	+	2.05708i
$718$	−6.37296	+	11.0383i	−0.237837	+	0.411945i
$719$	−19.5234	−	33.8155i	−0.728099	−	1.26110i	−0.957686	−	0.287816i	$-0.907071\pi$
$719$	−19.5234	−	33.8155i	−0.728099	−	1.26110i	0.229587	−	0.973288i	$-0.426262\pi$
$720$	−5.53520	+	1.17654i	−0.206285	+	0.0438472i
$721$	−3.85164	−	11.8541i	−0.143443	−	0.441471i
$722$	−21.9228	−	4.65983i	−0.815880	−	0.173421i
$723$	−4.93428	−	46.9465i	−0.183508	−	1.74596i
$724$	−3.88733	−	4.31731i	−0.144471	−	0.160452i
$725$	−16.2406	−	7.23079i	−0.603162	−	0.268545i
$726$	−7.35523	+	3.27476i	−0.272978	+	0.121538i
$727$	16.7173	−	18.5665i	0.620011	−	0.688592i	−0.348572	−	0.937282i	$-0.613333\pi$
$727$	16.7173	−	18.5665i	0.620011	−	0.688592i	0.968583	+	0.248690i	$0.0800000\pi$
$728$	−24.7966	−	18.0158i	−0.919021	−	0.667708i
$729$	−5.86467	−	4.26093i	−0.217210	−	0.157812i
$730$	6.87092	−	7.63093i	0.254304	−	0.282433i
$731$	13.3921	−	5.96256i	0.495326	−	0.220533i
$732$	2.48704	+	1.10730i	0.0919236	+	0.0409270i
$733$	−11.3411	−	12.5956i	−0.418894	−	0.465229i	0.496354	−	0.868120i	$-0.334672\pi$
$733$	−11.3411	−	12.5956i	−0.418894	−	0.465229i	−0.915248	+	0.402891i	$0.868005\pi$
$734$	−0.0175890	−	0.167348i	−0.000649222	−	0.00617694i
$735$	−23.4293	−	4.98004i	−0.864201	−	0.183692i
$736$	−0.747985	−	2.30206i	−0.0275711	−	0.0848551i
$737$	27.3049	−	5.80385i	1.00579	−	0.213787i
$738$	−0.271170	−	0.469680i	−0.00998190	−	0.0172892i
$739$	7.19107	−	12.4553i	0.264528	−	0.458175i	−0.702912	−	0.711277i	$-0.748117\pi$
$739$	7.19107	−	12.4553i	0.264528	−	0.458175i	0.967440	+	0.253101i	$0.0814506\pi$
$740$	0.417409	−	1.28465i	0.0153442	−	0.0472247i
$741$	3.48537	−	33.1610i	0.128038	−	1.21820i
$742$	8.88838	−	6.45779i	0.326303	−	0.237073i
$743$	27.7705			1.01880			0.509400	−	0.860530i	$-0.329867\pi$
$743$	27.7705			1.01880			0.509400	+	0.860530i	$0.329867\pi$
$744$		0			0
$745$	23.5603			0.863183
$746$	7.34072	−	5.33334i	0.268763	−	0.195268i
$747$	−1.14564	+	10.9000i	−0.0419166	+	0.398810i
$748$	2.11354	−	6.50480i	0.0772786	−	0.237839i
$749$	6.00394	−	10.3991i	0.219379	−	0.379976i
$750$	15.0384	+	26.0473i	0.549126	+	0.951113i
$751$	42.6181	−	9.05875i	1.55516	−	0.330559i	0.651443	−	0.758698i	$-0.274164\pi$
$751$	42.6181	−	9.05875i	1.55516	−	0.330559i	0.903713	+	0.428139i	$0.140831\pi$
$752$	1.03053	+	3.17164i	0.0375795	+	0.115658i
$753$	32.9501	+	7.00375i	1.20077	+	0.255231i
$754$	−2.31076	−	21.9854i	−0.0841528	−	0.800660i
$755$	−0.270789	−	0.300741i	−0.00985501	−	0.0109451i
$756$	5.88593	+	2.62059i	0.214069	+	0.0953098i
$757$	−23.0370	+	10.2567i	−0.837293	+	0.372787i	−0.780160	−	0.625580i	$-0.784862\pi$
$757$	−23.0370	+	10.2567i	−0.837293	+	0.372787i	−0.0571327	+	0.998367i	$0.518196\pi$
$758$	−3.79933	+	4.21959i	−0.137998	+	0.153262i
$759$	−5.74517	−	4.17411i	−0.208536	−	0.151511i
$760$	−23.3185	−	16.9419i	−0.845851	−	0.614547i
$761$	1.75040	−	1.94402i	0.0634519	−	0.0704705i	−0.710583	−	0.703613i	$-0.751569\pi$
$761$	1.75040	−	1.94402i	0.0634519	−	0.0704705i	0.774035	+	0.633143i	$0.218235\pi$
$762$	−47.2424	+	21.0337i	−1.71141	+	0.761970i
$763$	−24.1722	−	10.7622i	−0.875093	−	0.389616i
$764$	−1.63483	−	1.81566i	−0.0591460	−	0.0656883i
$765$	−0.796091	−	7.57430i	−0.0287827	−	0.273849i
$766$	−38.9232	−	8.27337i	−1.40635	−	0.298929i
$767$	6.33414	+	19.4945i	0.228713	+	0.703905i
$768$	−21.9958	+	4.67535i	−0.793705	+	0.168707i
$769$	−5.67534	−	9.82998i	−0.204658	−	0.354478i	0.745366	−	0.666656i	$-0.232275\pi$
$769$	−5.67534	−	9.82998i	−0.204658	−	0.354478i	−0.950024	+	0.312178i	$0.898942\pi$
$770$	−13.6245	+	23.5984i	−0.490994	+	0.850427i
$771$	−14.9734	+	46.0835i	−0.539255	+	1.65966i
$772$	−1.00924	+	9.60225i	−0.0363232	+	0.345593i
$773$	−9.23685	+	6.71097i	−0.332226	+	0.241377i	−0.741375	−	0.671091i	$-0.765826\pi$
$773$	−9.23685	+	6.71097i	−0.332226	+	0.241377i	0.409148	+	0.912468i	$0.365826\pi$
$774$	−6.24789			−0.224576
$775$		0			0
$776$	−33.3751			−1.19810
$777$	−11.5834	+	8.41583i	−0.415552	+	0.301916i
$778$	−4.54284	+	43.2222i	−0.162869	+	1.54959i
$779$	0.635343	−	1.95539i	0.0227635	−	0.0700590i
$780$	2.03564	−	3.52583i	0.0728875	−	0.126245i
$781$	9.58846	+	16.6077i	0.343102	+	0.594270i
$782$	−4.13890	+	0.879751i	−0.148007	+	0.0314598i
$783$	7.39756	+	22.7674i	0.264367	+	0.813639i
$784$	20.4873	+	4.35470i	0.731688	+	0.155525i
$785$	2.57312	+	24.4816i	0.0918384	+	0.873784i
$786$	−21.6436	−	24.0377i	−0.772002	−	0.857395i
$787$	24.7472	+	11.0182i	0.882143	+	0.392755i	0.797260	−	0.603635i	$-0.206282\pi$
$787$	24.7472	+	11.0182i	0.882143	+	0.392755i	0.0848828	+	0.996391i	$0.472948\pi$
$788$	9.55389	−	4.25367i	0.340343	−	0.151531i
$789$	−14.4318	+	16.0282i	−0.513787	+	0.570618i
$790$	15.0026	+	10.9001i	0.533770	+	0.387807i
$791$	−46.9190	−	34.0887i	−1.66825	−	1.21205i
$792$	−10.0482	+	11.1597i	−0.357047	+	0.396541i
$793$	6.55598	−	2.91891i	0.232810	−	0.103654i
$794$	−4.54087	−	2.02173i	−0.161150	−	0.0717484i
$795$	5.03046	+	5.58690i	0.178412	+	0.198147i
$796$	−0.763686	−	7.26598i	−0.0270681	−	0.257536i
$797$	47.5926	+	10.1161i	1.68582	+	0.358331i	0.948392	−	0.317100i	$-0.102709\pi$
$797$	47.5926	+	10.1161i	1.68582	+	0.358331i	0.737423	+	0.675431i	$0.236042\pi$
$798$	18.3269	+	56.4044i	0.648766	+	1.99670i
$799$	−4.39017	+	0.933159i	−0.155313	+	0.0330128i
$800$	3.47318	+	6.01573i	0.122796	+	0.212688i
$801$	3.32620	−	5.76115i	0.117526	−	0.203560i
$802$	−9.47458	+	29.1598i	−0.334559	+	1.02967i
$803$	2.11996	−	20.1701i	0.0748118	−	0.711786i
$804$	6.00159	−	4.36041i	0.211660	−	0.153780i
$805$	−5.34915			−0.188533
$806$		0			0
$807$	−9.16733			−0.322705
$808$	−0.986423	+	0.716678i	−0.0347022	+	0.0252127i
$809$	−1.96609	+	18.7061i	−0.0691240	+	0.657671i	0.904023	+	0.427485i	$0.140600\pi$
$809$	−1.96609	+	18.7061i	−0.0691240	+	0.657671i	−0.973147	+	0.230186i	$0.926066\pi$
$810$	6.59853	−	20.3082i	0.231849	−	0.713557i
$811$	19.7693	−	34.2414i	0.694193	−	1.20238i	−0.276259	−	0.961083i	$-0.589095\pi$
$811$	19.7693	−	34.2414i	0.694193	−	1.20238i	0.970452	−	0.241294i	$-0.0775720\pi$
$812$	−6.23826	−	10.8050i	−0.218920	−	0.379180i
$813$	−12.4880	+	2.65442i	−0.437975	+	0.0930944i
$814$	2.59819	+	7.99639i	0.0910664	+	0.280273i
$815$	−0.201341	−	0.0427963i	−0.00705266	−	0.00149909i
$816$	2.29578	+	21.8429i	0.0803684	+	0.764654i
$817$	−15.8489	−	17.6020i	−0.554483	−	0.615816i
$818$	−3.94789	−	1.75771i	−0.138035	−	0.0614570i
$819$	−11.9541	+	5.32232i	−0.417711	+	0.185977i
$820$	0.167979	−	0.186559i	0.00586606	−	0.00651492i
$821$	−11.8414	−	8.60325i	−0.413266	−	0.300255i	0.361657	−	0.932311i	$-0.382211\pi$
$821$	−11.8414	−	8.60325i	−0.413266	−	0.300255i	−0.774923	+	0.632056i	$0.782211\pi$
$822$	20.4320	+	14.8447i	0.712649	+	0.517770i
$823$	−27.9608	+	31.0536i	−0.974651	+	1.08246i	0.0219236	+	0.999760i	$0.493021\pi$
$823$	−27.9608	+	31.0536i	−0.974651	+	1.08246i	−0.996574	+	0.0826999i	$0.973646\pi$
$824$	−9.15398	+	4.07562i	−0.318894	+	0.141981i
$825$	18.6175	+	8.28906i	0.648179	+	0.288588i
$826$	−24.3955	−	27.0939i	−0.848828	−	0.942719i
$827$	−0.983208	−	9.35460i	−0.0341895	−	0.325291i	−0.998227	−	0.0595246i	$-0.981042\pi$
$827$	−0.983208	−	9.35460i	−0.0341895	−	0.325291i	0.964037	−	0.265767i	$-0.0856251\pi$
$828$	−0.559731	−	0.118975i	−0.0194520	−	0.00413465i
$829$	−12.4629	−	38.3568i	−0.432854	−	1.33219i	−0.895270	−	0.445524i	$-0.853017\pi$
$829$	−12.4629	−	38.3568i	−0.432854	−	1.33219i	0.462416	−	0.886663i	$-0.346983\pi$
$830$	15.6389	−	3.32416i	0.542836	−	0.115383i
$831$	−22.8739	−	39.6188i	−0.793487	−	1.37436i
$832$	−11.7087	+	20.2801i	−0.405927	+	0.703086i
$833$	−8.71086	+	26.8093i	−0.301813	+	0.928886i
$834$	4.14211	−	39.4096i	0.143430	−	1.36464i
$835$	4.93769	−	3.58744i	0.170876	−	0.124149i
$836$	−11.0509			−0.382203
$837$		0			0
$838$	5.07693			0.175380
$839$	−5.78419	+	4.20246i	−0.199692	+	0.145085i	−0.683138	−	0.730290i	$-0.739385\pi$
$839$	−5.78419	+	4.20246i	−0.199692	+	0.145085i	0.483445	+	0.875374i	$0.339385\pi$
$840$	−3.89936	+	37.0999i	−0.134541	+	1.28007i
$841$	5.36358	−	16.5074i	0.184951	−	0.569221i
$842$	−17.0048	+	29.4532i	−0.586025	+	1.01503i
$843$	−31.9272	−	55.2995i	−1.09963	−	1.90462i
$844$	2.97079	−	0.631461i	0.102259	−	0.0217358i
$845$	2.89270	+	8.90281i	0.0995119	+	0.306266i
$846$	1.87109	+	0.397713i	0.0643295	+	0.0136736i
$847$	1.25207	+	11.9127i	0.0430217	+	0.409324i
$848$	−4.39879	−	4.88536i	−0.151055	−	0.167764i
$849$	40.4617	+	18.0147i	1.38864	+	0.618263i
$850$	11.0932	−	4.93902i	0.380494	−	0.169407i
$851$	−1.10441	+	1.22658i	−0.0378588	+	0.0420465i
$852$	4.12296	+	2.99550i	0.141250	+	0.102624i
$853$	−0.911496	−	0.662240i	−0.0312090	−	0.0226747i	0.572071	−	0.820204i	$-0.306140\pi$
$853$	−0.911496	−	0.662240i	−0.0312090	−	0.0226747i	−0.603280	+	0.797529i	$0.706140\pi$
$854$	−8.54106	+	9.48581i	−0.292269	+	0.324598i
$855$	−11.2416	+	5.00507i	−0.384454	+	0.171170i
$856$	−8.81888	−	3.92642i	−0.301423	−	0.134202i
$857$	−15.9615	−	17.7270i	−0.545233	−	0.605543i	0.406054	−	0.913849i	$-0.366904\pi$
$857$	−15.9615	−	17.7270i	−0.545233	−	0.605543i	−0.951287	+	0.308306i	$0.900238\pi$
$858$	2.64895	+	25.2031i	0.0904337	+	0.860419i
$859$	31.7562	+	6.75000i	1.08351	+	0.230307i	0.714864	−	0.699264i	$-0.246489\pi$
$859$	31.7562	+	6.75000i	1.08351	+	0.230307i	0.368645	+	0.929570i	$0.379822\pi$
$860$	−0.893692	−	2.75050i	−0.0304746	−	0.0937913i
$861$	−2.60283	+	0.553249i	−0.0887043	+	0.0188547i
$862$	9.16363	+	15.8719i	0.312114	+	0.540598i
$863$	−11.9209	+	20.6476i	−0.405793	+	0.702853i	−0.994413	−	0.105556i	$-0.966338\pi$
$863$	−11.9209	+	20.6476i	−0.405793	+	0.702853i	0.588621	+	0.808409i	$0.299671\pi$
$864$	2.89051	−	8.89606i	0.0983370	−	0.302650i
$865$	−2.33569	+	22.2226i	−0.0794157	+	0.755590i
$866$	9.23276	−	6.70799i	0.313742	−	0.227947i
$867$	5.71523			0.194099
$868$		0			0
$869$	36.6268			1.24248
$870$	−21.7672	+	15.8148i	−0.737977	+	0.536172i
$871$	2.04408	−	19.4482i	0.0692611	−	0.658976i
$872$	−6.57333	+	20.2306i	−0.222601	+	0.685095i
$873$	−7.12437	+	12.3398i	−0.241123	+	0.417638i
$874$	3.41837	+	5.92080i	0.115628	+	0.200274i
$875$	43.7689	−	9.30336i	1.47966	−	0.314511i
$876$	−1.66551	−	5.12592i	−0.0562724	−	0.173189i
$877$	−28.6349	−	6.08654i	−0.966932	−	0.205528i	−0.302726	−	0.953077i	$-0.597897\pi$
$877$	−28.6349	−	6.08654i	−0.966932	−	0.205528i	−0.664206	+	0.747550i	$0.731230\pi$
$878$	−2.28205	−	21.7123i	−0.0770155	−	0.732753i
$879$	2.49782	+	2.77411i	0.0842494	+	0.0935685i
$880$	14.8950	+	6.63166i	0.502109	+	0.223553i
$881$	−8.24939	+	3.67286i	−0.277929	+	0.123742i	−0.540968	−	0.841043i	$-0.681942\pi$
$881$	−8.24939	+	3.67286i	−0.277929	+	0.123742i	0.263039	+	0.964785i	$0.415275\pi$
$882$	8.03903	−	8.92825i	0.270688	−	0.300630i
$883$	17.3191	+	12.5831i	0.582834	+	0.423454i	0.839745	−	0.542981i	$-0.182705\pi$
$883$	17.3191	+	12.5831i	0.582834	+	0.423454i	−0.256911	+	0.966435i	$0.582705\pi$
$884$	−3.87626	−	2.81627i	−0.130373	−	0.0947213i
$885$	16.6933	−	18.5398i	0.561138	−	0.623207i
$886$	−20.7684	+	9.24670i	−0.697729	+	0.310649i
$887$	22.4687	+	10.0037i	0.754424	+	0.335891i	0.747656	−	0.664086i	$-0.231179\pi$
$887$	22.4687	+	10.0037i	0.754424	+	0.335891i	0.00676752	+	0.999977i	$0.497846\pi$
$888$	7.70204	+	8.55399i	0.258464	+	0.287053i
$889$	8.04202	+	76.5148i	0.269721	+	2.56622i
$890$	−9.49237	−	2.01766i	−0.318185	−	0.0676323i
$891$	−13.0328	−	40.1107i	−0.436614	−	1.34376i
$892$	−3.48193	+	0.740106i	−0.116583	+	0.0247806i
$893$	3.62590	+	6.28024i	0.121336	+	0.210160i
$894$	−19.4864	+	33.7514i	−0.651723	+	1.12882i
$895$	−8.46344	+	26.0478i	−0.282902	+	0.870681i
$896$	2.23825	−	21.2956i	0.0747749	−	0.711435i
$897$	−4.02467	+	2.92409i	−0.134380	+	0.0976326i
$898$	−27.9829			−0.933801
$899$		0			0
$900$	1.64218			0.0547395
$901$	7.15780	−	5.20044i	0.238461	−	0.173252i
$902$	−0.163338	+	1.55405i	−0.00543855	+	0.0517443i
$903$	−9.47298	+	29.1548i	−0.315241	+	0.970212i
$904$	−23.3119	+	40.3774i	−0.775343	+	1.34293i
$905$	9.31946	+	16.1418i	0.309789	+	0.536571i
$906$	0.654794	−	0.139181i	0.0217541	−	0.00462397i
$907$	−6.10812	−	18.7989i	−0.202817	−	0.624206i	−0.999796	−	0.0201992i	$-0.993570\pi$
$907$	−6.10812	−	18.7989i	−0.202817	−	0.624206i	0.796979	−	0.604007i	$-0.206430\pi$
$908$	9.06625	+	1.92709i	0.300874	+	0.0639528i
$909$	0.0544119	+	0.517695i	0.00180473	+	0.0171708i
$910$	12.7729	+	14.1858i	0.423418	+	0.470253i
$911$	32.5419	+	14.4886i	1.07816	+	0.480029i	0.867453	−	0.497520i	$-0.165756\pi$
$911$	32.5419	+	14.4886i	1.07816	+	0.480029i	0.210710	+	0.977549i	$0.432422\pi$
$912$	32.4186	−	14.4337i	1.07349	−	0.477948i
$913$	21.1302	−	23.4674i	0.699307	−	0.776659i
$914$	−16.1109	−	11.7053i	−0.532902	−	0.387176i
$915$	−7.06628	−	5.13395i	−0.233604	−	0.169723i
$916$	−1.96221	+	2.17925i	−0.0648331	+	0.0720045i
$917$	−43.9620	+	19.5732i	−1.45175	+	0.646362i
$918$	−14.9380	−	6.65082i	−0.493027	−	0.219510i
$919$	−11.4798	−	12.7496i	−0.378685	−	0.420572i	0.523430	−	0.852069i	$-0.324652\pi$
$919$	−11.4798	−	12.7496i	−0.378685	−	0.420572i	−0.902114	+	0.431497i	$0.857986\pi$
$920$	0.449507	+	4.27677i	0.0148198	+	0.141001i
$921$	54.3320	+	11.5486i	1.79030	+	0.380540i
$922$	−8.20114	−	25.2405i	−0.270090	−	0.831252i
$923$	13.1405	−	2.79309i	0.432524	−	0.0919357i
$924$	7.15126	+	12.3863i	0.235259	+	0.407481i
$925$	2.36831	−	4.10203i	0.0778694	−	0.134874i
$926$	6.66707	−	20.5191i	0.219094	−	0.674301i
$927$	−0.447166	+	4.25450i	−0.0146868	+	0.139736i
$928$	−14.6540	+	10.6468i	−0.481042	+	0.349498i
$929$	−45.5222			−1.49353			−0.746767	−	0.665086i	$-0.768395\pi$
$929$	−45.5222			−1.49353			−0.746767	+	0.665086i	$0.768395\pi$
$930$		0			0
$931$	45.5457			1.49270
$932$	6.83147	−	4.96335i	0.223772	−	0.162580i
$933$	0.906863	−	8.62823i	0.0296894	−	0.282475i
$934$	−4.49552	+	13.8358i	−0.147098	+	0.452720i
$935$	−10.9718	+	19.0037i	−0.358817	+	0.621489i
$936$	5.25986	+	9.11035i	0.171924	+	0.297781i
$937$	−25.0577	+	5.32617i	−0.818599	+	0.173999i	−0.598134	−	0.801396i	$-0.704091\pi$
$937$	−25.0577	+	5.32617i	−0.818599	+	0.173999i	−0.220465	+	0.975395i	$0.570757\pi$
$938$	10.7483	+	33.0799i	0.350944	+	1.08010i
$939$	23.0218	+	4.89343i	0.751287	+	0.159691i
$940$	0.0925543	+	0.880596i	0.00301879	+	0.0287219i
$941$	−8.11243	−	9.00977i	−0.264458	−	0.293710i	0.596261	−	0.802790i	$-0.296652\pi$
$941$	−8.11243	−	9.00977i	−0.264458	−	0.293710i	−0.860719	+	0.509080i	$0.829986\pi$
$942$	−37.1994	−	16.5622i	−1.21202	−	0.539627i
$943$	−0.280230	+	0.124766i	−0.00912555	+	0.00406296i
$944$	−14.5971	+	16.2117i	−0.475096	+	0.527647i
$945$	−16.7233	−	12.1502i	−0.544011	−	0.395247i
$946$	14.5637	+	10.5811i	0.473507	+	0.344023i
$947$	18.2011	−	20.2143i	0.591455	−	0.656878i	−0.370900	−	0.928673i	$-0.620951\pi$
$947$	18.2011	−	20.2143i	0.591455	−	0.656878i	0.962355	+	0.271795i	$0.0876174\pi$
$948$	8.89204	−	3.95899i	0.288800	−	0.128582i
$949$	−12.9793	−	5.77875i	−0.421325	−	0.187586i
$950$	−13.1283	−	14.5804i	−0.425937	−	0.473051i
$951$	5.61350	+	53.4089i	0.182030	+	1.73190i
$952$	42.9426	+	9.12772i	1.39178	+	0.295831i
$953$	−7.69226	−	23.6743i	−0.249177	−	0.766887i	−0.994921	−	0.100655i	$-0.967906\pi$
$953$	−7.69226	−	23.6743i	−0.249177	−	0.766887i	0.745745	−	0.666232i	$-0.232094\pi$
$954$	−3.68842	+	0.783998i	−0.119417	+	0.0253829i
$955$	3.91933	+	6.78848i	0.126826	+	0.219670i
$956$	6.72333	−	11.6452i	0.217448	−	0.376631i
$957$	−16.4216	+	50.5406i	−0.530836	+	1.63374i
$958$	2.03612	−	19.3724i	0.0657839	−	0.625892i
$959$	30.3977	−	22.0852i	0.981592	−	0.713168i
$960$	28.5013			0.919876
$961$		0			0
$962$	5.89000			0.189901
$963$	−3.33422	+	2.42246i	−0.107444	+	0.0780625i
$964$	−1.14560	+	10.8997i	−0.0368974	+	0.351055i
$965$	9.57241	−	29.4609i	0.308147	−	0.948378i
$966$	4.42421	−	7.66295i	0.142347	−	0.246551i
$967$	26.0999	+	45.2064i	0.839316	+	1.45374i	0.890467	+	0.455048i	$0.150378\pi$
$967$	26.0999	+	45.2064i	0.839316	+	1.45374i	−0.0511507	+	0.998691i	$0.516289\pi$
$968$	9.41924	−	2.00212i	0.302746	−	0.0643506i
$969$	14.7586	+	45.4224i	0.474115	+	1.45918i
$970$	20.3316	+	4.32162i	0.652809	+	0.138759i
$971$	2.08648	+	19.8515i	0.0669582	+	0.637065i	0.975610	+	0.219510i	$0.0704460\pi$
$971$	2.08648	+	19.8515i	0.0669582	+	0.637065i	−0.908652	+	0.417554i	$0.862887\pi$
$972$	−4.09938	−	4.55282i	−0.131488	−	0.146032i
$973$	−53.8575	−	23.9789i	−1.72659	−	0.768728i
$974$	−14.3989	+	6.41078i	−0.461369	+	0.205415i
$975$	9.55279	−	10.6094i	0.305934	−	0.339774i
$976$	6.17897	+	4.48929i	0.197784	+	0.143699i
$977$	48.7438	+	35.4144i	1.55945	+	1.13301i	0.936458	+	0.350781i	$0.114084\pi$
$977$	48.7438	+	35.4144i	1.55945	+	1.13301i	0.622994	+	0.782227i	$0.285916\pi$
$978$	0.227834	−	0.253036i	0.00728534	−	0.00809118i
$979$	−17.5101	+	7.79601i	−0.559626	+	0.249162i
$980$	5.08036	+	2.26192i	0.162286	+	0.0722545i
$981$	6.07670	+	6.74886i	0.194014	+	0.215474i
$982$	−2.38638	−	22.7049i	−0.0761524	−	0.724541i
$983$	−11.2866	−	2.39904i	−0.359986	−	0.0765174i	0.0243684	−	0.999703i	$-0.492243\pi$
$983$	−11.2866	−	2.39904i	−0.359986	−	0.0765174i	−0.384354	+	0.923186i	$0.625576\pi$
$984$	0.661060	+	2.03453i	0.0210738	+	0.0648586i
$985$	−32.8197	+	6.97605i	−1.04572	+	0.222275i
$986$	15.8321	+	27.4221i	0.504198	+	0.873297i
$987$	4.69279	−	8.12816i	0.149373	−	0.258722i
$988$	−2.39225	+	7.36259i	−0.0761076	+	0.234235i
$989$	−0.369387	+	3.51448i	−0.0117458	+	0.111754i
$990$	7.56624	−	5.49719i	0.240471	−	0.174712i
$991$	−37.3423			−1.18622			−0.593109	−	0.805122i	$-0.702100\pi$
$991$	−37.3423			−1.18622			−0.593109	+	0.805122i	$0.702100\pi$
$992$		0			0
$993$	1.58899			0.0504251
$994$	−19.3311	+	14.0449i	−0.613146	+	0.445477i
$995$	−2.45016	+	23.3117i	−0.0776754	+	0.739032i
$996$	2.59326	−	7.98124i	0.0821707	−	0.252895i
$997$	−10.4012	+	18.0154i	−0.329410	+	0.570555i	−0.982395	−	0.186816i	$-0.940183\pi$
$997$	−10.4012	+	18.0154i	−0.329410	+	0.570555i	0.652985	+	0.757371i	$0.273516\pi$
$998$	25.1901	+	43.6305i	0.797378	+	1.38110i
$999$	−6.23887	+	1.32611i	−0.197389	+	0.0419564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.m.338.1		16
31.2	even	5		961.2.g.n.732.1		16
31.3	odd	30		961.2.d.o.531.3		16
31.4	even	5		961.2.g.j.448.2		16
31.5	even	3		961.2.g.n.235.1		16
31.6	odd	6		961.2.d.p.388.2		16
31.7	even	15		961.2.d.n.628.3		16
31.8	even	5		961.2.c.i.521.5		16
31.9	even	15		961.2.c.i.439.5		16
31.10	even	15	inner	961.2.g.m.816.1		16
31.11	odd	30		31.2.g.a.9.2	yes	16
31.12	odd	30		961.2.d.p.374.2		16
31.13	odd	30		961.2.g.k.547.2		16
31.14	even	15		961.2.a.j.1.5		8
31.15	odd	10		31.2.g.a.7.2	✓	16
31.16	even	5		961.2.g.l.844.2		16
31.17	odd	30		961.2.a.i.1.5		8
31.18	even	15		961.2.g.j.547.2		16
31.19	even	15		961.2.d.q.374.2		16
31.20	even	15		961.2.g.l.846.2		16
31.21	odd	30		961.2.g.s.816.1		16
31.22	odd	30		961.2.c.j.439.5		16
31.23	odd	10		961.2.c.j.521.5		16
31.24	odd	30		961.2.d.o.628.3		16
31.25	even	3		961.2.d.q.388.2		16
31.26	odd	6		961.2.g.t.235.1		16
31.27	odd	10		961.2.g.k.448.2		16
31.28	even	15		961.2.d.n.531.3		16
31.29	odd	10		961.2.g.t.732.1		16
31.30	odd	2		961.2.g.s.338.1		16
93.11	even	30		279.2.y.c.226.1		16
93.14	odd	30		8649.2.a.be.1.4		8
93.17	even	30		8649.2.a.bf.1.4		8
93.77	even	10		279.2.y.c.100.1		16
124.11	even	30		496.2.bg.c.257.2		16
124.15	even	10		496.2.bg.c.193.2		16
155.42	even	60		775.2.ck.a.474.3		32
155.73	even	60		775.2.ck.a.474.2		32
155.77	even	20		775.2.ck.a.224.2		32
155.104	odd	30		775.2.bl.a.226.1		16
155.108	even	20		775.2.ck.a.224.3		32
155.139	odd	10		775.2.bl.a.751.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.7.2	✓	16	31.15	odd	10
31.2.g.a.9.2	yes	16	31.11	odd	30
279.2.y.c.100.1		16	93.77	even	10
279.2.y.c.226.1		16	93.11	even	30
496.2.bg.c.193.2		16	124.15	even	10
496.2.bg.c.257.2		16	124.11	even	30
775.2.bl.a.226.1		16	155.104	odd	30
775.2.bl.a.751.1		16	155.139	odd	10
775.2.ck.a.224.2		32	155.77	even	20
775.2.ck.a.224.3		32	155.108	even	20
775.2.ck.a.474.2		32	155.73	even	60
775.2.ck.a.474.3		32	155.42	even	60
961.2.a.i.1.5		8	31.17	odd	30
961.2.a.j.1.5		8	31.14	even	15
961.2.c.i.439.5		16	31.9	even	15
961.2.c.i.521.5		16	31.8	even	5
961.2.c.j.439.5		16	31.22	odd	30
961.2.c.j.521.5		16	31.23	odd	10
961.2.d.n.531.3		16	31.28	even	15
961.2.d.n.628.3		16	31.7	even	15
961.2.d.o.531.3		16	31.3	odd	30
961.2.d.o.628.3		16	31.24	odd	30
961.2.d.p.374.2		16	31.12	odd	30
961.2.d.p.388.2		16	31.6	odd	6
961.2.d.q.374.2		16	31.19	even	15
961.2.d.q.388.2		16	31.25	even	3
961.2.g.j.448.2		16	31.4	even	5
961.2.g.j.547.2		16	31.18	even	15
961.2.g.k.448.2		16	31.27	odd	10
961.2.g.k.547.2		16	31.13	odd	30
961.2.g.l.844.2		16	31.16	even	5
961.2.g.l.846.2		16	31.20	even	15
961.2.g.m.338.1		16	1.1	even	1	trivial
961.2.g.m.816.1		16	31.10	even	15	inner
961.2.g.n.235.1		16	31.5	even	3
961.2.g.n.732.1		16	31.2	even	5
961.2.g.s.338.1		16	31.30	odd	2
961.2.g.s.816.1		16	31.21	odd	30
961.2.g.t.235.1		16	31.26	odd	6
961.2.g.t.732.1		16	31.29	odd	10
8649.2.a.be.1.4		8	93.14	odd	30
8649.2.a.bf.1.4		8	93.17	even	30

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.996848 + 0.724253i) q^{2} +(0.216894 - 2.06361i) q^{3} +(-0.148869 + 0.458173i) q^{4} +(0.772811 - 1.33855i) q^{5} +(1.27836 + 2.21419i) q^{6} +(3.72064 - 0.790846i) q^{7} +(-0.944957 - 2.90828i) q^{8} +(-1.27699 - 0.271433i) q^{9} +(0.199072 + 1.89404i) q^{10} +(2.51695 + 2.79536i) q^{11} +(0.913200 + 0.406583i) q^{12} +(2.40725 - 1.07178i) q^{13} +(-3.13614 + 3.48303i) q^{14} +(-2.59462 - 1.88510i) q^{15} +(2.26882 + 1.64839i) q^{16} +(-2.52553 + 2.80488i) q^{17} +(1.46955 - 0.654287i) q^{18} +(5.57109 + 2.48041i) q^{19} +(0.498239 + 0.553350i) q^{20} +(-0.825012 - 7.84947i) q^{21} +(-4.53356 - 0.963639i) q^{22} +(-0.281158 - 0.865316i) q^{23} +(-6.20650 + 1.31923i) q^{24} +(1.30553 + 2.26124i) q^{25} +(-1.62343 + 2.81186i) q^{26} +(1.08650 - 3.34392i) q^{27} +(-0.191545 + 1.82243i) q^{28} +(-5.50827 + 4.00199i) q^{29} +3.95173 q^{30} +2.66037 q^{32} +(6.31443 - 4.58770i) q^{33} +(0.486124 - 4.62516i) q^{34} +(1.81676 - 5.59143i) q^{35} +(0.314468 - 0.544675i) q^{36} +(-0.907032 - 1.57103i) q^{37} +(-7.34997 + 1.56228i) q^{38} +(-1.68961 - 5.20008i) q^{39} +(-4.62315 - 0.982680i) q^{40} +(-0.0352412 - 0.335298i) q^{41} +(6.50741 + 7.22721i) q^{42} +(-3.54821 - 1.57976i) q^{43} +(-1.65545 + 0.737056i) q^{44} +(-1.35020 + 1.49955i) q^{45} +(0.906980 + 0.658959i) q^{46} +(0.962040 + 0.698963i) q^{47} +(3.89373 - 4.32442i) q^{48} +(6.82288 - 3.03774i) q^{49} +(-2.93912 - 1.30858i) q^{50} +(5.24040 + 5.82006i) q^{51} +(0.132693 + 1.26249i) q^{52} +(-2.29290 - 0.487371i) q^{53} +(1.33876 + 4.12028i) q^{54} +(5.68685 - 1.20878i) q^{55} +(-5.81584 - 10.0733i) q^{56} +(6.32692 - 10.9586i) q^{57} +(2.59245 - 7.97875i) q^{58} +(-0.813109 + 7.73622i) q^{59} +(1.24996 - 0.908151i) q^{60} +2.72343 q^{61} -4.96588 q^{63} +(-7.18962 + 5.22357i) q^{64} +(0.425725 - 4.05050i) q^{65} +(-2.97187 + 9.14649i) q^{66} +(3.71059 - 6.42693i) q^{67} +(-0.909147 - 1.57469i) q^{68} +(-1.84665 + 0.392519i) q^{69} +(2.23857 + 6.88960i) q^{70} +(4.98677 + 1.05997i) q^{71} +(0.417300 + 3.97034i) q^{72} +(-3.60778 - 4.00685i) q^{73} +(2.04199 + 0.909154i) q^{74} +(4.94947 - 2.20364i) q^{75} +(-1.96582 + 2.18326i) q^{76} +(11.5754 + 8.40999i) q^{77} +(5.45046 + 3.95999i) q^{78} +(6.51548 - 7.23617i) q^{79} +(3.95982 - 1.76303i) q^{80} +(-10.2428 - 4.56040i) q^{81} +(0.277970 + 0.308717i) q^{82} +(-0.877532 - 8.34916i) q^{83} +(3.71923 + 0.790547i) q^{84} +(1.80271 + 5.54818i) q^{85} +(4.68117 - 0.995014i) q^{86} +(7.06383 + 12.2349i) q^{87} +(5.75127 - 9.96149i) q^{88} +(-1.57463 + 4.84620i) q^{89} +(0.259892 - 2.47271i) q^{90} +(8.10889 - 5.89146i) q^{91} +0.438320 q^{92} -1.46523 q^{94} +(7.62555 - 5.54028i) q^{95} +(0.577018 - 5.48996i) q^{96} +(3.37268 - 10.3800i) q^{97} +(-4.60129 + 7.96966i) q^{98} +(-2.45537 - 4.25283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 11 q^{6} - 3 q^{7} - 8 q^{8} + 5 q^{9} + 18 q^{10} + 2 q^{11} + 20 q^{12} + 27 q^{13} - 6 q^{14} - 4 q^{15} - 2 q^{16} + 16 q^{17} + 22 q^{18} - 4 q^{19} - 18 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 3 * q^3 + 6 * q^4 - 3 * q^5 - 11 * q^6 - 3 * q^7 - 8 * q^8 + 5 * q^9 + 18 * q^10 + 2 * q^11 + 20 * q^12 + 27 * q^13 - 6 * q^14 - 4 * q^15 - 2 * q^16 + 16 * q^17 + 22 * q^18 - 4 * q^19 - 18 * q^20 - 29 * q^21 - 4 * q^22 - 21 * q^23 + 25 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 - 40 * q^28 - 26 * q^29 + 22 * q^30 - 42 * q^32 + 7 * q^33 - 28 * q^34 + 21 * q^35 + q^36 + 8 * q^37 - 27 * q^38 + 2 * q^39 - 16 * q^40 - 3 * q^41 + 51 * q^42 - 8 * q^43 - 4 * q^44 + 25 * q^45 + 16 * q^46 + 4 * q^47 + 86 * q^48 + 27 * q^49 - 27 * q^50 + 13 * q^51 - 24 * q^52 - 66 * q^53 - 39 * q^54 + 52 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 - 51 * q^59 - 35 * q^60 + 60 * q^61 - 46 * q^63 - 32 * q^64 - 18 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 + 48 * q^69 + 27 * q^70 - 24 * q^71 + 2 * q^72 - 27 * q^73 - 28 * q^74 + 32 * q^75 + 18 * q^76 + 42 * q^77 + 15 * q^78 - 8 * q^79 - 39 * q^80 - 7 * q^81 + 29 * q^82 - 4 * q^83 + 27 * q^84 + 63 * q^85 - 34 * q^86 + 15 * q^87 + 17 * q^88 - 26 * q^89 + 57 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 + 28 * q^95 + 62 * q^96 - 37 * q^97 - 10 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

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