LMFDB - Embedded newform 588.2.x.a.139.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(55,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 0, 9]))

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

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

chi := DirichletCharacter("588.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.x (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			139.15
Character	$\chi$	$=$	588.139
Dual form			588.2.x.a.55.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0809236 + 1.41190i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(-1.98690 + 0.228511i) q^{4} +(-0.881995 - 1.83148i) q^{5} +(-0.685509 - 1.23696i) q^{6} +(-1.70818 + 2.02043i) q^{7} +(-0.483422 - 2.78681i) q^{8} +(0.623490 - 0.781831i) q^{9} +O(q^{10})$	\(q+(0.0809236 + 1.41190i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(-1.98690 + 0.228511i) q^{4} +(-0.881995 - 1.83148i) q^{5} +(-0.685509 - 1.23696i) q^{6} +(-1.70818 + 2.02043i) q^{7} +(-0.483422 - 2.78681i) q^{8} +(0.623490 - 0.781831i) q^{9} +(2.51449 - 1.39349i) q^{10} +(3.11985 - 2.48800i) q^{11} +(1.69099 - 1.06797i) q^{12} +(1.46088 - 1.16501i) q^{13} +(-2.99087 - 2.24827i) q^{14} +(1.58930 + 1.26742i) q^{15} +(3.89557 - 0.908060i) q^{16} +(1.45920 - 0.333054i) q^{17} +(1.15432 + 0.817034i) q^{18} -5.08805 q^{19} +(2.17095 + 3.43743i) q^{20} +(0.662382 - 2.56149i) q^{21} +(3.76526 + 4.20357i) q^{22} +(5.98730 + 1.36656i) q^{23} +(1.64470 + 2.30108i) q^{24} +(0.541042 - 0.678446i) q^{25} +(1.76310 + 1.96833i) q^{26} +(-0.222521 + 0.974928i) q^{27} +(2.93229 - 4.40473i) q^{28} +(0.581766 + 2.54888i) q^{29} +(-1.66086 + 2.34649i) q^{30} +7.17708 q^{31} +(1.59733 + 5.42665i) q^{32} +(-1.73139 + 3.59526i) q^{33} +(0.588321 + 2.03329i) q^{34} +(5.20698 + 1.34648i) q^{35} +(-1.06016 + 1.69590i) q^{36} +(-1.48774 - 6.51823i) q^{37} +(-0.411743 - 7.18380i) q^{38} +(-0.810727 + 1.68349i) q^{39} +(-4.67761 + 3.34333i) q^{40} +(4.31387 + 8.95784i) q^{41} +(3.67017 + 0.727930i) q^{42} +(5.51444 - 11.4509i) q^{43} +(-5.63030 + 5.65633i) q^{44} +(-1.98182 - 0.452338i) q^{45} +(-1.44493 + 8.56403i) q^{46} +(-6.29117 - 7.88888i) q^{47} +(-3.11579 + 2.50836i) q^{48} +(-1.16427 - 6.90250i) q^{49} +(1.00168 + 0.708994i) q^{50} +(-1.17019 + 0.933196i) q^{51} +(-2.63641 + 2.64859i) q^{52} +(-0.0266545 + 0.116781i) q^{53} +(-1.39450 - 0.235282i) q^{54} +(-7.30841 - 3.51954i) q^{55} +(6.45632 + 3.78364i) q^{56} +(4.58417 - 2.20762i) q^{57} +(-3.55168 + 1.02766i) q^{58} +(4.65159 + 2.24009i) q^{59} +(-3.44740 - 2.15507i) q^{60} +(-5.32332 + 1.21501i) q^{61} +(0.580795 + 10.1333i) q^{62} +(0.514604 + 2.59522i) q^{63} +(-7.53261 + 2.69441i) q^{64} +(-3.42218 - 1.64804i) q^{65} +(-5.21624 - 2.15360i) q^{66} -7.66604i q^{67} +(-2.82319 + 0.995190i) q^{68} +(-5.98730 + 1.36656i) q^{69} +(-1.47973 + 7.46068i) q^{70} +(10.2617 + 2.34216i) q^{71} +(-2.48022 - 1.35959i) q^{72} +(-0.170928 - 0.136311i) q^{73} +(9.08267 - 2.62802i) q^{74} +(-0.193096 + 0.846008i) q^{75} +(10.1095 - 1.16268i) q^{76} +(-0.302432 + 10.5534i) q^{77} +(-2.44252 - 1.00843i) q^{78} +2.43942i q^{79} +(-5.09896 - 6.33375i) q^{80} +(-0.222521 - 0.974928i) q^{81} +(-12.2984 + 6.81564i) q^{82} +(4.29245 - 5.38256i) q^{83} +(-0.730759 + 5.24080i) q^{84} +(-1.89699 - 2.37875i) q^{85} +(16.6137 + 6.85918i) q^{86} +(-1.63007 - 2.04405i) q^{87} +(-8.44177 - 7.49167i) q^{88} +(-6.92689 - 5.52401i) q^{89} +(0.478279 - 2.83473i) q^{90} +(-0.141615 + 4.94165i) q^{91} +(-12.2085 - 1.34706i) q^{92} +(-6.46633 + 3.11402i) q^{93} +(10.6292 - 9.52088i) q^{94} +(4.48763 + 9.31866i) q^{95} +(-3.79368 - 4.19619i) q^{96} -14.2689i q^{97} +(9.65140 - 2.20240i) q^{98} -3.99044i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) $ 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9	$ 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9} + 20 q^{10} - 12 q^{14} + 36 q^{16} + 12 q^{19} - 25 q^{20} + 2 q^{21} - 6 q^{22} - 15 q^{24} + 32 q^{25} + 6 q^{26} - 28 q^{27} - 66 q^{28} - 8 q^{30} - 4 q^{31} + 25 q^{32} - 68 q^{34} - 12 q^{35} - 10 q^{37} + 35 q^{38} + 14 q^{39} + 16 q^{40} + 9 q^{42} + 20 q^{44} - 28 q^{46} - 8 q^{47} + 8 q^{48} - 8 q^{49} + 114 q^{50} + 20 q^{52} - 8 q^{53} - q^{56} + 12 q^{57} - 6 q^{58} + 20 q^{59} + 10 q^{60} - 14 q^{61} - 16 q^{62} - 12 q^{63} + 42 q^{64} - 8 q^{65} - 6 q^{66} - 16 q^{68} + 59 q^{70} + 28 q^{71} - 15 q^{72} + 22 q^{74} + 18 q^{75} + 7 q^{76} + 8 q^{77} + 6 q^{78} + 26 q^{80} - 28 q^{81} + 12 q^{82} + 10 q^{83} + 11 q^{84} - 24 q^{85} - 6 q^{86} - 242 q^{88} + 20 q^{90} - 16 q^{91} + 7 q^{92} - 4 q^{93} - 53 q^{94} - 10 q^{96} - 118 q^{98}+O(q^{100}) $ 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9 + 20 * q^10 - 12 * q^14 + 36 * q^16 + 12 * q^19 - 25 * q^20 + 2 * q^21 - 6 * q^22 - 15 * q^24 + 32 * q^25 + 6 * q^26 - 28 * q^27 - 66 * q^28 - 8 * q^30 - 4 * q^31 + 25 * q^32 - 68 * q^34 - 12 * q^35 - 10 * q^37 + 35 * q^38 + 14 * q^39 + 16 * q^40 + 9 * q^42 + 20 * q^44 - 28 * q^46 - 8 * q^47 + 8 * q^48 - 8 * q^49 + 114 * q^50 + 20 * q^52 - 8 * q^53 - q^56 + 12 * q^57 - 6 * q^58 + 20 * q^59 + 10 * q^60 - 14 * q^61 - 16 * q^62 - 12 * q^63 + 42 * q^64 - 8 * q^65 - 6 * q^66 - 16 * q^68 + 59 * q^70 + 28 * q^71 - 15 * q^72 + 22 * q^74 + 18 * q^75 + 7 * q^76 + 8 * q^77 + 6 * q^78 + 26 * q^80 - 28 * q^81 + 12 * q^82 + 10 * q^83 + 11 * q^84 - 24 * q^85 - 6 * q^86 - 242 * q^88 + 20 * q^90 - 16 * q^91 + 7 * q^92 - 4 * q^93 - 53 * q^94 - 10 * q^96 - 118 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{14}\right)$

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 $

$2$	0.0809236	+	1.41190i	0.0572216	+	0.998362i
$2$	0.0809236	+	1.41190i	0.0572216	+	0.998362i
$3$	−0.900969	+	0.433884i	−0.520175	+	0.250503i
$3$	−0.900969	+	0.433884i	−0.520175	+	0.250503i
$4$	−1.98690	+	0.228511i	−0.993451	+	0.114256i
$5$	−0.881995	−	1.83148i	−0.394440	−	0.819063i	−0.999734	−	0.0230611i	$-0.992659\pi$
$5$	−0.881995	−	1.83148i	−0.394440	−	0.819063i	0.605294	−	0.796002i	$-0.293056\pi$
$6$	−0.685509	−	1.23696i	−0.279858	−	0.504988i
$7$	−1.70818	+	2.02043i	−0.645630	+	0.763650i
$7$	−1.70818	+	2.02043i	−0.645630	+	0.763650i
$8$	−0.483422	−	2.78681i	−0.170915	−	0.985286i
$9$	0.623490	−	0.781831i	0.207830	−	0.260610i
$10$	2.51449	−	1.39349i	0.795150	−	0.440662i
$11$	3.11985	−	2.48800i	0.940670	−	0.750159i	−0.0277162	−	0.999616i	$-0.508823\pi$
$11$	3.11985	−	2.48800i	0.940670	−	0.750159i	0.968386	+	0.249457i	$0.0802520\pi$
$12$	1.69099	−	1.06797i	0.488147	−	0.308295i
$13$	1.46088	−	1.16501i	0.405175	−	0.323116i	−0.399607	−	0.916686i	$-0.630854\pi$
$13$	1.46088	−	1.16501i	0.405175	−	0.323116i	0.804782	+	0.593570i	$0.202282\pi$
$14$	−2.99087	−	2.24827i	−0.799343	−	0.600875i
$15$	1.58930	+	1.26742i	0.410355	+	0.327247i
$16$	3.89557	−	0.908060i	0.973891	−	0.227015i
$17$	1.45920	−	0.333054i	0.353909	−	0.0807774i	−0.0418705	−	0.999123i	$-0.513332\pi$
$17$	1.45920	−	0.333054i	0.353909	−	0.0807774i	0.395779	+	0.918346i	$0.370475\pi$
$18$	1.15432	+	0.817034i	0.272076	+	0.192577i
$19$	−5.08805			−1.16728			−0.583639	−	0.812013i	$-0.698372\pi$
$19$	−5.08805			−1.16728			−0.583639	+	0.812013i	$0.698372\pi$
$20$	2.17095	+	3.43743i	0.485440	+	0.768632i
$21$	0.662382	−	2.56149i	0.144544	−	0.558964i
$22$	3.76526	+	4.20357i	0.802757	+	0.896203i
$23$	5.98730	+	1.36656i	1.24844	+	0.284948i	0.795148	−	0.606415i	$-0.207393\pi$
$23$	5.98730	+	1.36656i	1.24844	+	0.284948i	0.453290	+	0.891363i	$0.350250\pi$
$24$	1.64470	+	2.30108i	0.335723	+	0.469706i
$25$	0.541042	−	0.678446i	0.108208	−	0.135689i
$26$	1.76310	+	1.96833i	0.345772	+	0.386022i
$27$	−0.222521	+	0.974928i	−0.0428242	+	0.187625i
$28$	2.93229	−	4.40473i	0.554151	−	0.832416i
$29$	0.581766	+	2.54888i	0.108031	+	0.473316i	0.999784	+	0.0207925i	$0.00661892\pi$
$29$	0.581766	+	2.54888i	0.108031	+	0.473316i	−0.891753	+	0.452523i	$0.850524\pi$
$30$	−1.66086	+	2.34649i	−0.303230	+	0.428409i
$31$	7.17708			1.28904			0.644521	−	0.764587i	$-0.277057\pi$
$31$	7.17708			1.28904			0.644521	+	0.764587i	$0.277057\pi$
$32$	1.59733	+	5.42665i	0.282371	+	0.959305i
$33$	−1.73139	+	3.59526i	−0.301395	+	0.625854i
$34$	0.588321	+	2.03329i	0.100896	+	0.348707i
$35$	5.20698	+	1.34648i	0.880140	+	0.227597i
$36$	−1.06016	+	1.69590i	−0.176693	+	0.282650i
$37$	−1.48774	−	6.51823i	−0.244583	−	1.07159i	−0.936790	−	0.349891i	$-0.886219\pi$
$37$	−1.48774	−	6.51823i	−0.244583	−	1.07159i	0.692207	−	0.721699i	$-0.256639\pi$
$38$	−0.411743	−	7.18380i	−0.0667935	−	1.16537i
$39$	−0.810727	+	1.68349i	−0.129820	+	0.269574i
$40$	−4.67761	+	3.34333i	−0.739595	+	0.528627i
$41$	4.31387	+	8.95784i	0.673713	+	1.39898i	0.904711	+	0.426026i	$0.140087\pi$
$41$	4.31387	+	8.95784i	0.673713	+	1.39898i	−0.230998	+	0.972954i	$0.574199\pi$
$42$	3.67017	+	0.727930i	0.566319	+	0.112322i
$43$	5.51444	−	11.4509i	0.840945	−	1.74624i	0.198197	−	0.980162i	$-0.436491\pi$
$43$	5.51444	−	11.4509i	0.840945	−	1.74624i	0.642748	−	0.766078i	$-0.277794\pi$
$44$	−5.63030	+	5.65633i	−0.848800	+	0.852723i
$45$	−1.98182	−	0.452338i	−0.295433	−	0.0674306i
$46$	−1.44493	+	8.56403i	−0.213043	+	1.26270i
$47$	−6.29117	−	7.88888i	−0.917661	−	1.15071i	−0.988195	−	0.153202i	$-0.951042\pi$
$47$	−6.29117	−	7.88888i	−0.917661	−	1.15071i	0.0705335	−	0.997509i	$-0.477530\pi$
$48$	−3.11579	+	2.50836i	−0.449726	+	0.362050i
$49$	−1.16427	−	6.90250i	−0.166324	−	0.986071i
$50$	1.00168	+	0.708994i	0.141659	+	0.100267i
$51$	−1.17019	+	0.933196i	−0.163859	+	0.130674i
$52$	−2.63641	+	2.64859i	−0.365604	+	0.367294i
$53$	−0.0266545	+	0.116781i	−0.00366128	+	0.0160411i	−0.976726	−	0.214493i	$-0.931190\pi$
$53$	−0.0266545	+	0.116781i	−0.00366128	+	0.0160411i	0.973064	+	0.230534i	$0.0740473\pi$
$54$	−1.39450	−	0.235282i	−0.189768	−	0.0320178i
$55$	−7.30841	−	3.51954i	−0.985465	−	0.474575i
$56$	6.45632	+	3.78364i	0.862762	+	0.505610i
$57$	4.58417	−	2.20762i	0.607188	−	0.292407i
$58$	−3.55168	+	1.02766i	−0.466359	+	0.134938i
$59$	4.65159	+	2.24009i	0.605586	+	0.291635i	0.711440	−	0.702747i	$-0.248043\pi$
$59$	4.65159	+	2.24009i	0.605586	+	0.291635i	−0.105854	+	0.994382i	$0.533758\pi$
$60$	−3.44740	−	2.15507i	−0.445058	−	0.278219i
$61$	−5.32332	+	1.21501i	−0.681581	+	0.155566i	−0.549274	−	0.835642i	$-0.685096\pi$
$61$	−5.32332	+	1.21501i	−0.681581	+	0.155566i	−0.132307	+	0.991209i	$0.542239\pi$
$62$	0.580795	+	10.1333i	0.0737611	+	1.28693i
$63$	0.514604	+	2.59522i	0.0648341	+	0.326967i
$64$	−7.53261	+	2.69441i	−0.941576	+	0.336801i
$65$	−3.42218	−	1.64804i	−0.424470	−	0.204414i
$66$	−5.21624	−	2.15360i	−0.642075	−	0.265089i
$67$		−	7.66604i		−	0.936556i	−0.883581	−	0.468278i	$-0.844875\pi$
$67$		−	7.66604i		−	0.936556i	0.883581	−	0.468278i	$-0.155125\pi$
$68$	−2.82319	+	0.995190i	−0.342362	+	0.120685i
$69$	−5.98730	+	1.36656i	−0.720786	+	0.164515i
$70$	−1.47973	+	7.46068i	−0.176861	+	0.891721i
$71$	10.2617	+	2.34216i	1.21784	+	0.277964i	0.782699	−	0.622400i	$-0.213842\pi$
$71$	10.2617	+	2.34216i	1.21784	+	0.277964i	0.435138	+	0.900364i	$0.356699\pi$
$72$	−2.48022	−	1.35959i	−0.292297	−	0.160230i
$73$	−0.170928	−	0.136311i	−0.0200056	−	0.0159539i	0.613436	−	0.789744i	$-0.289787\pi$
$73$	−0.170928	−	0.136311i	−0.0200056	−	0.0159539i	−0.633442	+	0.773791i	$0.718358\pi$
$74$	9.08267	−	2.62802i	1.05584	−	0.305501i
$75$	−0.193096	+	0.846008i	−0.0222968	+	0.0976886i
$76$	10.1095	−	1.16268i	1.15963	−	0.133368i
$77$	−0.302432	+	10.5534i	−0.0344653	+	1.20267i
$78$	−2.44252	−	1.00843i	−0.276561	−	0.114182i
$79$			2.43942i			0.274456i	0.990539	+	0.137228i	$0.0438193\pi$
$79$			2.43942i			0.274456i	−0.990539	+	0.137228i	$0.956181\pi$
$80$	−5.09896	−	6.33375i	−0.570081	−	0.708135i
$81$	−0.222521	−	0.974928i	−0.0247245	−	0.108325i
$82$	−12.2984	+	6.81564i	−1.35814	+	0.752661i
$83$	4.29245	−	5.38256i	0.471157	−	0.590813i	−0.488297	−	0.872678i	$-0.662382\pi$
$83$	4.29245	−	5.38256i	0.471157	−	0.590813i	0.959454	+	0.281865i	$0.0909530\pi$
$84$	−0.730759	+	5.24080i	−0.0797323	+	0.571818i
$85$	−1.89699	−	2.37875i	−0.205758	−	0.258012i
$86$	16.6137	+	6.85918i	1.79150	+	0.739644i
$87$	−1.63007	−	2.04405i	−0.174762	−	0.219145i
$88$	−8.44177	−	7.49167i	−0.899896	−	0.798615i
$89$	−6.92689	−	5.52401i	−0.734249	−	0.585544i	0.183352	−	0.983047i	$-0.441305\pi$
$89$	−6.92689	−	5.52401i	−0.734249	−	0.585544i	−0.917601	+	0.397504i	$0.869877\pi$
$90$	0.478279	−	2.83473i	0.0504150	−	0.298807i
$91$	−0.141615	+	4.94165i	−0.0148453	+	0.518025i
$92$	−12.2085	−	1.34706i	−1.27282	−	0.140441i
$93$	−6.46633	+	3.11402i	−0.670527	+	0.322909i
$94$	10.6292	−	9.52088i	1.09632	−	0.982003i
$95$	4.48763	+	9.31866i	0.460421	+	0.956074i
$96$	−3.79368	−	4.19619i	−0.387191	−	0.428272i
$97$		−	14.2689i		−	1.44879i	−0.689385	−	0.724395i	$-0.742119\pi$
$97$		−	14.2689i		−	1.44879i	0.689385	−	0.724395i	$-0.257881\pi$
$98$	9.65140	−	2.20240i	0.974938	−	0.222476i
$99$		−	3.99044i		−	0.401054i
$100$	−0.919966	+	1.47164i	−0.0919966	+	0.147164i
$101$	−3.17124	−	6.58515i	−0.315550	−	0.655247i	0.681515	−	0.731804i	$-0.261322\pi$
$101$	−3.17124	−	6.58515i	−0.315550	−	0.655247i	−0.997065	+	0.0765572i	$0.975607\pi$
$102$	−1.41227	−	1.57667i	−0.139836	−	0.156114i
$103$	−12.7888	+	6.15875i	−1.26011	+	0.606839i	−0.940205	−	0.340609i	$-0.889367\pi$
$103$	−12.7888	+	6.15875i	−1.26011	+	0.606839i	−0.319910	+	0.947448i	$0.603653\pi$
$104$	−3.95289	−	3.50800i	−0.387612	−	0.343988i
$105$	−5.27554	+	1.04608i	−0.514840	+	0.102087i
$106$	−0.167040	−	0.0281830i	−0.0162243	−	0.00273738i
$107$	−2.43839	−	1.94455i	−0.235728	−	0.187986i	0.498500	−	0.866889i	$-0.333884\pi$
$107$	−2.43839	−	1.94455i	−0.235728	−	0.187986i	−0.734228	+	0.678903i	$0.762456\pi$
$108$	0.219345	−	1.98794i	0.0211065	−	0.191289i
$109$	8.88746	+	11.1445i	0.851264	+	1.06745i	0.996944	+	0.0781196i	$0.0248916\pi$
$109$	8.88746	+	11.1445i	0.851264	+	1.06745i	−0.145680	+	0.989332i	$0.546537\pi$
$110$	4.37781	−	10.6035i	0.417408	−	1.01101i
$111$	4.16856	+	5.22721i	0.395662	+	0.496145i
$112$	−4.81964	+	9.42184i	−0.455413	+	0.890280i
$113$	6.06767	−	7.60861i	0.570798	−	0.715758i	−0.409715	−	0.912214i	$-0.634372\pi$
$113$	6.06767	−	7.60861i	0.570798	−	0.715758i	0.980513	+	0.196456i	$0.0629432\pi$
$114$	3.48790	+	6.29373i	0.326672	+	0.589462i
$115$	−2.77793	−	12.1709i	−0.259044	−	1.13494i
$116$	−1.73836	−	4.93144i	−0.161403	−	0.457873i
$117$		−	1.86853i		−	0.172746i
$118$	−2.78635	+	6.74884i	−0.256504	+	0.621281i
$119$	−1.81967	+	3.51713i	−0.166808	+	0.322415i
$120$	2.76377	−	5.04177i	0.252296	−	0.460249i
$121$	1.09560	−	4.80014i	0.0996000	−	0.436376i
$122$	−2.14625	−	7.41765i	−0.194313	−	0.671563i
$123$	−7.77332	−	6.19902i	−0.700897	−	0.558947i
$124$	−14.2602	+	1.64005i	−1.28060	+	0.147280i
$125$	−11.6289	−	2.65421i	−1.04012	−	0.237400i
$126$	−3.62254	+	0.936583i	−0.322722	+	0.0834374i
$127$	6.25693	−	1.42810i	0.555213	−	0.126724i	0.0642973	−	0.997931i	$-0.479519\pi$
$127$	6.25693	−	1.42810i	0.555213	−	0.126724i	0.490916	+	0.871207i	$0.336662\pi$
$128$	−4.41379	−	10.4172i	−0.390128	−	0.920761i
$129$			12.7095i			1.11901i
$130$	2.04992	−	4.96513i	0.179790	−	0.435471i
$131$	−3.06962	−	1.47825i	−0.268194	−	0.129155i	0.294954	−	0.955511i	$-0.404696\pi$
$131$	−3.06962	−	1.47825i	−0.268194	−	0.129155i	−0.563148	+	0.826356i	$0.690410\pi$
$132$	2.61854	−	7.53907i	0.227914	−	0.656192i
$133$	8.69128	−	10.2800i	0.753630	−	0.891392i
$134$	10.8237	−	0.620364i	0.935022	−	0.0535913i
$135$	1.98182	−	0.452338i	0.170568	−	0.0389311i
$136$	−1.63357	−	3.90552i	−0.140077	−	0.334895i
$137$	6.36340	+	3.06445i	0.543662	+	0.261814i	0.685496	−	0.728077i	$-0.259586\pi$
$137$	6.36340	+	3.06445i	0.543662	+	0.261814i	−0.141834	+	0.989890i	$0.545300\pi$
$138$	−2.41396	−	8.34286i	−0.205490	−	0.710191i
$139$	9.91716	−	4.77585i	0.841163	−	0.405083i	0.0368731	−	0.999320i	$-0.488260\pi$
$139$	9.91716	−	4.77585i	0.841163	−	0.405083i	0.804290	+	0.594237i	$0.202546\pi$
$140$	−10.6534	−	1.48548i	−0.900381	−	0.125546i
$141$	9.09100	+	4.37800i	0.765601	+	0.368694i
$142$	−2.47648	+	14.6780i	−0.207821	+	1.23175i
$143$	1.65918	−	7.26932i	0.138747	−	0.607891i
$144$	1.71890	−	3.61184i	0.143241	−	0.300987i
$145$	4.15512	−	3.31359i	0.345064	−	0.275179i
$146$	0.178624	−	0.252363i	0.0147831	−	0.0208857i
$147$	4.04385	+	5.71378i	0.333531	+	0.471265i
$148$	4.44549	+	12.6111i	0.365417	+	1.03663i
$149$	−2.98984	−	3.74914i	−0.244937	−	0.307142i	0.644132	−	0.764914i	$-0.277219\pi$
$149$	−2.98984	−	3.74914i	−0.244937	−	0.307142i	−0.889069	+	0.457773i	$0.848647\pi$
$150$	−1.21010	−	0.204169i	−0.0988044	−	0.0166704i
$151$	−8.31757	−	1.89843i	−0.676875	−	0.154492i	−0.129754	−	0.991546i	$-0.541419\pi$
$151$	−8.31757	−	1.89843i	−0.676875	−	0.154492i	−0.547120	+	0.837054i	$0.684276\pi$
$152$	2.45967	+	14.1794i	0.199506	+	1.15010i
$153$	0.649407	−	1.34851i	0.0525014	−	0.109020i
$154$	−14.9247	+	0.427014i	−1.20267	+	0.0344098i
$155$	−6.33015	−	13.1447i	−0.508450	−	1.05581i
$156$	1.22614	−	3.53019i	0.0981696	−	0.282642i
$157$	0.773651	−	1.60650i	0.0617441	−	0.128213i	−0.867813	−	0.496890i	$-0.834475\pi$
$157$	0.773651	−	1.60650i	0.0617441	−	0.128213i	0.929557	+	0.368678i	$0.120189\pi$
$158$	−3.44421	+	0.197407i	−0.274006	+	0.0157048i
$159$	−0.0266545	−	0.116781i	−0.00211384	−	0.00926133i
$160$	8.52997	−	7.71175i	0.674353	−	0.609668i
$161$	−12.9884	+	9.76259i	−1.02363	+	0.769400i
$162$	1.35849	−	0.393071i	0.106733	−	0.0308826i
$163$	−9.35275	+	19.4212i	−0.732564	+	1.52119i	0.116671	+	0.993171i	$0.462778\pi$
$163$	−9.35275	+	19.4212i	−0.732564	+	1.52119i	−0.849235	+	0.528014i	$0.822937\pi$
$164$	−10.6182	−	16.8126i	−0.829143	−	1.31284i
$165$	8.11172			0.631496
$166$	7.94698	+	5.62492i	0.616805	+	0.436578i
$167$	2.35952	+	10.3377i	0.182585	+	0.799959i	0.980394	+	0.197048i	$0.0631354\pi$
$167$	2.35952	+	10.3377i	0.182585	+	0.799959i	−0.797809	+	0.602911i	$0.794007\pi$
$168$	−7.45860	−	0.607652i	−0.575444	−	0.0468813i
$169$	−2.11586	+	9.27018i	−0.162758	+	0.713091i
$170$	3.20504	−	2.87085i	0.245815	−	0.220184i
$171$	−3.17235	+	3.97800i	−0.242595	+	0.304205i
$172$	−8.34001	+	24.0119i	−0.635920	+	1.83089i
$173$	23.2084	+	5.29716i	1.76450	+	0.402735i	0.976942	−	0.213506i	$-0.0684883\pi$
$173$	23.2084	+	5.29716i	1.76450	+	0.402735i	0.787557	+	0.616242i	$0.211345\pi$
$174$	2.75407	−	2.46690i	0.208785	−	0.187016i
$175$	0.446556	+	2.25204i	0.0337564	+	0.170238i
$176$	9.89432	−	12.5252i	0.745813	−	0.944119i
$177$	−5.16288			−0.388066
$178$	7.23878	−	10.2271i	0.542569	−	0.766551i
$179$	23.1918	−	5.29338i	1.73344	−	0.395646i	0.764828	−	0.644235i	$-0.222824\pi$
$179$	23.1918	−	5.29338i	1.73344	−	0.395646i	0.968609	+	0.248589i	$0.0799669\pi$
$180$	4.04106	+	0.445883i	0.301202	+	0.0332342i
$181$	−0.658981	−	0.525519i	−0.0489816	−	0.0390616i	0.598693	−	0.800979i	$-0.295687\pi$
$181$	−0.658981	−	0.525519i	−0.0489816	−	0.0390616i	−0.647675	+	0.761917i	$0.724258\pi$
$182$	−6.98855	+	0.199951i	−0.518026	+	0.0148213i
$183$	4.26897	−	3.40439i	0.315571	−	0.251660i
$184$	0.913957	−	17.3461i	0.0673778	−	1.27877i
$185$	−10.6258	+	8.47381i	−0.781226	+	0.623007i
$186$	−4.91995	−	8.87779i	−0.360748	−	0.650951i
$187$	3.72386	−	4.66957i	0.272315	−	0.341473i
$188$	14.3026	+	14.2368i	1.04313	+	1.03833i
$189$	−1.58967	−	2.11494i	−0.115631	−	0.153839i
$190$	−12.7938	+	7.09017i	−0.928162	+	0.514375i
$191$	4.48933	+	9.32218i	0.324836	+	0.674529i	0.997881	−	0.0650728i	$-0.0207280\pi$
$191$	4.48933	+	9.32218i	0.324836	+	0.674529i	−0.673044	+	0.739602i	$0.735014\pi$
$192$	5.61758	−	5.69585i	0.405414	−	0.411063i
$193$	−15.7490	+	7.58431i	−1.13364	+	0.545930i	−0.904079	−	0.427365i	$-0.859442\pi$
$193$	−15.7490	+	7.58431i	−1.13364	+	0.545930i	−0.229557	+	0.973295i	$0.573728\pi$
$194$	20.1463	−	1.15469i	1.44642	−	0.0829021i
$195$	3.79834			0.272005
$196$	3.89058	+	13.4485i	0.277899	+	0.960610i
$197$	−1.96307			−0.139863			−0.0699315	−	0.997552i	$-0.522278\pi$
$197$	−1.96307			−0.139863			−0.0699315	+	0.997552i	$0.522278\pi$
$198$	5.63408	−	0.322920i	0.400397	−	0.0229490i
$199$	−17.9159	+	8.62786i	−1.27003	+	0.611613i	−0.942808	−	0.333336i	$-0.891826\pi$
$199$	−17.9159	+	8.62786i	−1.27003	+	0.611613i	−0.327219	+	0.944948i	$0.606112\pi$
$200$	−2.15225	−	1.17981i	−0.152187	−	0.0834249i
$201$	3.32617	+	6.90687i	0.234610	+	0.487173i
$202$	9.04092	−	5.01036i	0.636117	−	0.352528i
$203$	−6.14360	−	3.17853i	−0.431196	−	0.223089i
$204$	2.11181	−	2.12157i	0.147856	−	0.148540i
$205$	12.6013	−	15.8015i	0.880113	−	1.10363i
$206$	−9.73042	−	17.5580i	−0.677951	−	1.22333i
$207$	4.80144	−	3.82902i	0.333723	−	0.266135i
$208$	4.63305	−	5.86495i	0.321244	−	0.406661i
$209$	−15.8739	+	12.6590i	−1.09802	+	0.875644i
$210$	−1.90388	−	7.36387i	−0.131380	−	0.508155i
$211$	−11.7062	−	9.33540i	−0.805889	−	0.642675i	0.131360	−	0.991335i	$-0.458066\pi$
$211$	−11.7062	−	9.33540i	−0.805889	−	0.642675i	−0.937249	+	0.348659i	$0.886637\pi$
$212$	0.0262741	−	0.238123i	0.00180451	−	0.0163544i
$213$	−10.2617	+	2.34216i	−0.703119	+	0.160482i
$214$	2.54818	−	3.60011i	0.174190	−	0.246098i
$215$	−25.8357			−1.76198
$216$	2.82451	+	0.148822i	0.192184	+	0.0101261i
$217$	−12.2597	+	14.5008i	−0.832244	+	0.984377i
$218$	−15.0157	+	13.4500i	−1.01699	+	0.910951i
$219$	0.213144	+	0.0486487i	0.0144029	+	0.00328737i
$220$	15.3253	+	5.32294i	1.03323	+	0.358872i
$221$	1.74371	−	2.18654i	0.117294	−	0.147083i
$222$	−7.04295	+	6.30858i	−0.472692	+	0.423404i
$223$	−3.69444	+	16.1864i	−0.247398	+	1.08392i	0.686710	+	0.726932i	$0.259054\pi$
$223$	−3.69444	+	16.1864i	−0.247398	+	1.08392i	−0.934108	+	0.356991i	$0.883803\pi$
$224$	−13.6927	−	6.04239i	−0.914881	−	0.403724i
$225$	−0.193096	−	0.846008i	−0.0128731	−	0.0564005i
$226$	11.2336	+	7.95120i	0.747247	+	0.528906i
$227$	−7.38162			−0.489935			−0.244968	−	0.969531i	$-0.578777\pi$
$227$	−7.38162			−0.489935			−0.244968	+	0.969531i	$0.578777\pi$
$228$	−8.60384	+	5.43386i	−0.569803	+	0.359866i
$229$	9.22294	−	19.1516i	0.609469	−	1.26557i	−0.336612	−	0.941644i	$-0.609281\pi$
$229$	9.22294	−	19.1516i	0.609469	−	1.26557i	0.946081	−	0.323931i	$-0.105005\pi$
$230$	16.9593	−	4.90707i	1.11826	−	0.323563i
$231$	−4.30645	−	9.63948i	−0.283344	−	0.634231i
$232$	6.82201	−	2.85346i	0.447887	−	0.187339i
$233$	−5.46681	−	23.9517i	−0.358143	−	1.56913i	−0.757816	−	0.652468i	$-0.773733\pi$
$233$	−5.46681	−	23.9517i	−0.358143	−	1.56913i	0.399673	−	0.916658i	$-0.369124\pi$
$234$	2.63818	−	0.151208i	0.172463	−	0.00988481i
$235$	−8.89955	+	18.4801i	−0.580543	+	1.20551i
$236$	−9.75415	−	3.38790i	−0.634941	−	0.220533i
$237$	−1.05842	−	2.19784i	−0.0687521	−	0.142765i
$238$	−5.11308	−	2.28456i	−0.331432	−	0.148086i
$239$	−8.03789	+	16.6909i	−0.519928	+	1.07964i	0.461381	+	0.887202i	$0.347354\pi$
$239$	−8.03789	+	16.6909i	−0.519928	+	1.07964i	−0.981309	+	0.192439i	$0.938360\pi$
$240$	7.34212	+	3.49415i	0.473932	+	0.225547i
$241$	12.7401	+	2.90785i	0.820663	+	0.187311i	0.612183	−	0.790716i	$-0.290291\pi$
$241$	12.7401	+	2.90785i	0.820663	+	0.187311i	0.208480	+	0.978027i	$0.433149\pi$
$242$	6.86595	+	1.15843i	0.441360	+	0.0744666i
$243$	0.623490	+	0.781831i	0.0399969	+	0.0501545i
$244$	10.2993	−	3.63055i	0.659344	−	0.232422i
$245$	−11.6149	+	8.22030i	−0.742050	+	0.525176i
$246$	8.12333	−	11.4768i	0.517924	−	0.731732i
$247$	−7.43302	+	5.92764i	−0.472952	+	0.377166i
$248$	−3.46956	−	20.0012i	−0.220317	−	1.27007i
$249$	−1.53196	+	6.71194i	−0.0970838	+	0.425352i
$250$	2.80643	−	16.6336i	0.177494	−	1.05200i
$251$	4.40925	+	2.12338i	0.278310	+	0.134027i	0.567832	−	0.823144i	$-0.307782\pi$
$251$	4.40925	+	2.12338i	0.278310	+	0.134027i	−0.289523	+	0.957171i	$0.593497\pi$
$252$	−1.61551	−	5.03886i	−0.101767	−	0.317419i
$253$	22.0795	−	10.6329i	1.38812	−	0.668486i
$254$	2.52267	+	8.71857i	0.158286	+	0.547052i
$255$	2.74123	+	1.32011i	0.171663	+	0.0826683i
$256$	14.3509	−	7.07481i	0.896928	−	0.442176i
$257$	6.18147	−	1.41088i	0.385590	−	0.0880083i	−0.0253318	−	0.999679i	$-0.508064\pi$
$257$	6.18147	−	1.41088i	0.385590	−	0.0880083i	0.410921	+	0.911671i	$0.365207\pi$
$258$	−17.9445	+	1.02850i	−1.11718	+	0.0640315i
$259$	15.7109	+	8.12840i	0.976230	+	0.505074i
$260$	7.17614	+	2.49248i	0.445045	+	0.154577i
$261$	2.35552	+	1.13436i	0.145803	+	0.0702151i
$262$	1.83873	−	4.45361i	0.113597	−	0.275145i
$263$		−	3.56408i		−	0.219771i	−0.993944	−	0.109885i	$-0.964952\pi$
$263$		−	3.56408i		−	0.219771i	0.993944	−	0.109885i	$-0.0350484\pi$
$264$	10.8563	+	3.08701i	0.668158	+	0.189993i
$265$	0.237391	−	0.0541830i	0.0145828	−	0.00332843i
$266$	15.2177	+	11.4393i	0.933056	+	0.701388i
$267$	8.63769	+	1.97150i	0.528618	+	0.120654i
$268$	1.75178	+	15.2317i	0.107007	+	0.930423i
$269$	6.14404	+	4.89971i	0.374609	+	0.298741i	0.792637	−	0.609693i	$-0.208707\pi$
$269$	6.14404	+	4.89971i	0.374609	+	0.298741i	−0.418029	+	0.908434i	$0.637279\pi$
$270$	0.799031	+	2.76152i	0.0486275	+	0.168061i
$271$	−1.00264	+	4.39285i	−0.0609060	+	0.266847i	−0.996208	−	0.0870039i	$-0.972271\pi$
$271$	−1.00264	+	4.39285i	−0.0609060	+	0.266847i	0.935302	+	0.353851i	$0.115128\pi$
$272$	5.38199	−	2.62248i	0.326331	−	0.159011i
$273$	−2.01651	−	4.51372i	−0.122045	−	0.273182i
$274$	−3.81174	+	9.23245i	−0.230276	+	0.557752i
$275$		−	3.46276i		−	0.208812i
$276$	11.5839	−	4.08339i	0.697269	−	0.245791i
$277$	5.34188	+	23.4043i	0.320962	+	1.40623i	0.835844	+	0.548967i	$0.184979\pi$
$277$	5.34188	+	23.4043i	0.320962	+	1.40623i	−0.514882	+	0.857261i	$0.672164\pi$
$278$	7.54554	+	13.6155i	0.452552	+	0.816605i
$279$	4.47484	−	5.61127i	0.267902	−	0.335938i
$280$	1.23523	−	15.1618i	0.0738190	−	0.906089i
$281$	10.3265	+	12.9490i	0.616027	+	0.772473i	0.987779	−	0.155859i	$-0.0498145\pi$
$281$	10.3265	+	12.9490i	0.616027	+	0.772473i	−0.371753	+	0.928332i	$0.621243\pi$
$282$	−5.44560	+	13.1898i	−0.324281	+	0.785443i
$283$	−8.15166	−	10.2219i	−0.484566	−	0.607627i	0.478104	−	0.878303i	$-0.341324\pi$
$283$	−8.15166	−	10.2219i	−0.484566	−	0.607627i	−0.962670	+	0.270676i	$0.912753\pi$
$284$	−20.9242	−	2.30874i	−1.24162	−	0.136998i
$285$	−8.08643	−	6.44871i	−0.478999	−	0.381989i
$286$	10.3978	+	1.75432i	0.614835	+	0.103735i
$287$	−25.4675	−	6.58571i	−1.50330	−	0.388742i
$288$	5.23865	+	2.13462i	0.308690	+	0.125784i
$289$	−13.2981	+	6.40404i	−0.782242	+	0.376708i
$290$	5.01470	+	5.59845i	0.294473	+	0.328752i
$291$	6.19106	+	12.8559i	0.362926	+	0.753624i
$292$	0.370766	+	0.231777i	0.0216974	+	0.0135637i
$293$			7.11193i			0.415483i	0.978184	+	0.207742i	$0.0666113\pi$
$293$			7.11193i			0.415483i	−0.978184	+	0.207742i	$0.933389\pi$
$294$	−7.74002	+	6.17188i	−0.451407	+	0.359951i
$295$		−	10.4950i		−	0.611045i
$296$	−17.4458	+	7.29711i	−1.01402	+	0.424136i
$297$	1.73139	+	3.59526i	0.100465	+	0.208618i
$298$	5.05145	−	4.52474i	0.292623	−	0.262111i
$299$	10.3388	−	4.97890i	0.597907	−	0.287937i
$300$	0.190340	−	1.72506i	0.0109893	−	0.0995964i
$301$	13.7160	+	30.7016i	0.790578	+	1.76961i
$302$	2.00730	−	11.8972i	0.115507	−	0.684606i
$303$	5.71438	+	4.55707i	0.328283	+	0.261797i
$304$	−19.8208	+	4.62025i	−1.13680	+	0.264990i
$305$	6.92041	+	8.67792i	0.396262	+	0.496896i
$306$	1.95650	+	0.807769i	0.111846	+	0.0461771i
$307$	−10.9157	−	13.6879i	−0.622993	−	0.781209i	0.365769	−	0.930706i	$-0.380806\pi$
$307$	−10.9157	−	13.6879i	−0.622993	−	0.781209i	−0.988762	+	0.149497i	$0.952235\pi$
$308$	−1.81066	−	21.0376i	−0.103172	−	1.19873i
$309$	8.85010	−	11.0977i	0.503465	−	0.631325i
$310$	18.0467	−	10.0012i	1.02498	−	0.568032i
$311$	6.83003	+	29.9243i	0.387296	+	1.69685i	0.673915	+	0.738809i	$0.264611\pi$
$311$	6.83003	+	29.9243i	0.387296	+	1.69685i	−0.286620	+	0.958044i	$0.592532\pi$
$312$	5.08349	+	1.44550i	0.287796	+	0.0818355i
$313$		−	12.2847i		−	0.694370i	−0.937797	−	0.347185i	$-0.887138\pi$
$313$		−	12.2847i		−	0.694370i	0.937797	−	0.347185i	$-0.112862\pi$
$314$	2.33082	+	0.962311i	0.131536	+	0.0543064i
$315$	4.29922	−	3.23146i	0.242234	−	0.182072i
$316$	−0.557435	−	4.84689i	−0.0313582	−	0.272659i
$317$	−6.40582	+	28.0658i	−0.359787	+	1.57633i	0.393936	+	0.919138i	$0.371113\pi$
$317$	−6.40582	+	28.0658i	−0.359787	+	1.57633i	−0.753723	+	0.657192i	$0.771744\pi$
$318$	0.162726	−	0.0470837i	0.00912520	−	0.00264032i
$319$	8.15663	+	6.50470i	0.456684	+	0.364193i
$320$	11.5785	+	11.4194i	0.647256	+	0.638362i
$321$	3.04062	+	0.694001i	0.169711	+	0.0387354i
$322$	−14.8348	−	17.5483i	−0.826713	−	0.977926i
$323$	−7.42450	+	1.69459i	−0.413110	+	0.0942897i
$324$	0.664910	+	1.88624i	0.0369394	+	0.104791i
$325$		−	1.62145i		−	0.0899418i
$326$	−28.1776	−	11.6335i	−1.56061	−	0.644319i
$327$	−12.8427	−	6.18474i	−0.710206	−	0.342017i
$328$	22.8784	−	16.3523i	1.26325	−	0.902907i
$329$	26.6853	+	0.764732i	1.47121	+	0.0421610i
$330$	0.656429	+	11.4529i	0.0361352	+	0.630462i
$331$	−12.0360	+	2.74713i	−0.661556	+	0.150996i	−0.540100	−	0.841601i	$-0.681614\pi$
$331$	−12.0360	+	2.74713i	−0.661556	+	0.150996i	−0.121456	+	0.992597i	$0.538756\pi$
$332$	−7.29870	+	11.6755i	−0.400568	+	0.640776i
$333$	−6.02375	−	2.90088i	−0.330099	−	0.158967i
$334$	−14.4049	+	4.16797i	−0.788200	+	0.228061i
$335$	−14.0402	+	6.76141i	−0.767099	+	0.369415i
$336$	0.254364	−	10.5799i	0.0138767	−	0.577183i
$337$	1.66810	+	0.803315i	0.0908673	+	0.0437594i	0.478765	−	0.877943i	$-0.341084\pi$
$337$	1.66810	+	0.803315i	0.0908673	+	0.0437594i	−0.387898	+	0.921702i	$0.626799\pi$
$338$	−13.2598	−	2.23720i	−0.721236	−	0.121687i
$339$	−2.16552	+	9.48778i	−0.117615	+	0.515306i
$340$	4.31271	+	4.29286i	0.233889	+	0.232813i
$341$	22.3914	−	17.8566i	1.21256	−	0.966987i
$342$	−5.87323	−	4.15711i	−0.317588	−	0.224791i
$343$	15.9348	+	9.43837i	0.860397	+	0.509624i
$344$	−34.5772	−	9.83211i	−1.86428	−	0.530112i
$345$	7.78360	+	9.76032i	0.419055	+	0.525478i
$346$	−5.60093	+	33.1965i	−0.301108	+	1.78465i
$347$	6.78072	+	1.54766i	0.364008	+	0.0830825i	0.400613	−	0.916247i	$-0.368797\pi$
$347$	6.78072	+	1.54766i	0.364008	+	0.0830825i	−0.0366048	+	0.999330i	$0.511654\pi$
$348$	3.70588	+	3.68883i	0.198656	+	0.197742i
$349$	−6.72576	+	13.9662i	−0.360022	+	0.747593i	−0.999780	−	0.0209836i	$-0.993320\pi$
$349$	−6.72576	+	13.9662i	−0.360022	+	0.747593i	0.639758	+	0.768576i	$0.279035\pi$
$350$	−3.14351	+	0.812734i	−0.168028	+	0.0434424i
$351$	0.810727	+	1.68349i	0.0432734	+	0.0898581i
$352$	18.4849	+	12.9562i	0.985249	+	0.690567i
$353$	5.21745	−	10.8342i	0.277697	−	0.576644i	−0.714741	−	0.699389i	$-0.753456\pi$
$353$	5.21745	−	10.8342i	0.277697	−	0.576644i	0.992438	+	0.122745i	$0.0391698\pi$
$354$	−0.417799	−	7.28945i	−0.0222057	−	0.387430i
$355$	−4.76112	−	20.8598i	−0.252694	−	1.10713i
$356$	15.0254	+	9.39279i	0.796342	+	0.497817i
$357$	0.113436	−	3.95835i	0.00600366	−	0.209498i
$358$	9.35047	+	32.3161i	0.494187	+	1.70796i
$359$	−10.3283	+	21.4469i	−0.545105	+	1.13192i	0.428470	+	0.903556i	$0.359053\pi$
$359$	−10.3283	+	21.4469i	−0.545105	+	1.13192i	−0.973575	+	0.228366i	$0.926662\pi$
$360$	−0.302524	+	5.74163i	−0.0159444	+	0.302611i
$361$	6.88822			0.362538
$362$	0.688652	−	0.972939i	0.0361947	−	0.0511365i
$363$	1.09560	+	4.80014i	0.0575041	+	0.251942i
$364$	−0.847848	−	9.85093i	−0.0444393	−	0.516329i
$365$	−0.0988925	+	0.433277i	−0.00517627	+	0.0226787i
$366$	5.15211	+	5.75185i	0.269305	+	0.300654i
$367$	13.5016	−	16.9305i	0.704779	−	0.883765i	−0.292592	−	0.956238i	$-0.594518\pi$
$367$	13.5016	−	16.9305i	0.704779	−	0.883765i	0.997370	+	0.0724728i	$0.0230890\pi$
$368$	24.5648	−	0.113295i	1.28053	−	0.00590593i
$369$	9.69318	+	2.21240i	0.504607	+	0.115173i
$370$	−12.8240	−	14.3168i	−0.666689	−	0.744297i
$371$	−0.190417	−	0.253336i	−0.00988596	−	0.0131525i
$372$	12.1364	−	7.66488i	0.629242	−	0.397406i
$373$	12.5704			0.650868			0.325434	−	0.945565i	$-0.394490\pi$
$373$	12.5704			0.650868			0.325434	+	0.945565i	$0.394490\pi$
$374$	6.89430	+	4.87982i	0.356496	+	0.252330i
$375$	11.6289	−	2.65421i	0.600513	−	0.137063i
$376$	−18.9435	+	21.3459i	−0.976937	+	1.10083i
$377$	3.81937	+	3.04585i	0.196708	+	0.156869i
$378$	2.85743	−	2.41559i	0.146970	−	0.124245i
$379$	7.72721	−	6.16224i	0.396920	−	0.316533i	−0.404608	−	0.914490i	$-0.632592\pi$
$379$	7.72721	−	6.16224i	0.396920	−	0.316533i	0.801528	+	0.597957i	$0.204021\pi$
$380$	−11.0459	−	17.4898i	−0.566643	−	0.897208i
$381$	−5.01767	+	4.00146i	−0.257063	+	0.205001i
$382$	−12.7987	+	7.09285i	−0.654837	+	0.362902i
$383$	−0.939167	+	1.17768i	−0.0479892	+	0.0601765i	−0.805247	−	0.592940i	$-0.797967\pi$
$383$	−0.939167	+	1.17768i	−0.0479892	+	0.0601765i	0.757258	+	0.653116i	$0.226539\pi$
$384$	8.49655	+	7.47052i	0.433588	+	0.381228i
$385$	19.5950	−	8.75412i	0.998655	−	0.446151i
$386$	−11.9827	−	21.6222i	−0.609904	−	1.10054i
$387$	−5.51444	−	11.4509i	−0.280315	−	0.582080i
$388$	3.26061	+	28.3510i	0.165533	+	1.43930i
$389$	15.6260	−	7.52506i	0.792267	−	0.381536i	0.00643809	−	0.999979i	$-0.497951\pi$
$389$	15.6260	−	7.52506i	0.792267	−	0.381536i	0.785829	+	0.618443i	$0.212236\pi$
$390$	0.307375	+	5.36286i	0.0155645	+	0.271559i
$391$	9.19183			0.464851
$392$	−18.6731	+	6.58141i	−0.943135	+	0.332411i
$393$	3.40702			0.171862
$394$	−0.158859	−	2.77165i	−0.00800319	−	0.139634i
$395$	4.46775	−	2.15155i	0.224797	−	0.108256i
$396$	0.911860	+	7.92861i	0.0458227	+	0.398428i
$397$	−13.9977	−	29.0665i	−0.702524	−	1.45881i	−0.880144	−	0.474707i	$-0.842554\pi$
$397$	−13.9977	−	29.0665i	−0.702524	−	1.45881i	0.177620	−	0.984099i	$-0.443160\pi$
$398$	−13.6315	−	24.5973i	−0.683284	−	1.23295i
$399$	−3.37023	+	13.0330i	−0.168723	+	0.652466i
$400$	1.49160	−	3.13423i	0.0745798	−	0.156711i
$401$	20.4847	−	25.6870i	1.02296	−	1.28275i	0.0643754	−	0.997926i	$-0.479494\pi$
$401$	20.4847	−	25.6870i	1.02296	−	1.28275i	0.958581	−	0.284821i	$-0.0919341\pi$
$402$	−9.48262	+	5.25514i	−0.472950	+	0.262103i
$403$	10.4848	−	8.36139i	0.522287	−	0.416510i
$404$	7.80573	+	12.3594i	0.388350	+	0.614903i
$405$	−1.58930	+	1.26742i	−0.0789729	+	0.0629788i
$406$	3.99059	−	8.93134i	0.198049	−	0.443255i
$407$	−20.8589	−	16.6344i	−1.03394	−	0.824536i
$408$	3.16633	+	2.80997i	0.156757	+	0.139114i
$409$	−19.6670	+	4.48887i	−0.972472	+	0.221960i	−0.679106	−	0.734040i	$-0.737633\pi$
$409$	−19.6670	+	4.48887i	−0.972472	+	0.221960i	−0.293366	+	0.956000i	$0.594775\pi$
$410$	23.3299	+	16.5130i	1.15218	+	0.815520i
$411$	−7.06284			−0.348384
$412$	24.0027	−	15.1592i	1.18253	−	0.746841i
$413$	−12.4717	+	5.57175i	−0.613691	+	0.274168i
$414$	5.79473	+	6.46928i	0.284796	+	0.317948i
$415$	−13.6440	−	3.11415i	−0.669756	−	0.152867i
$416$	8.65562	+	6.06677i	0.424377	+	0.297448i
$417$	−6.86289	+	8.60579i	−0.336077	+	0.421427i
$418$	−19.1578	−	21.3879i	−0.937040	−	1.04612i
$419$	−4.54257	+	19.9023i	−0.221919	+	0.972291i	0.734112	+	0.679028i	$0.237598\pi$
$419$	−4.54257	+	19.9023i	−0.221919	+	0.972291i	−0.956032	+	0.293264i	$0.905259\pi$
$420$	10.2429	−	3.28399i	0.499805	−	0.160242i
$421$	−6.56481	−	28.7623i	−0.319949	−	1.40179i	−0.837640	−	0.546222i	$-0.816066\pi$
$421$	−6.56481	−	28.7623i	−0.319949	−	1.40179i	0.517691	−	0.855568i	$-0.326792\pi$
$422$	12.2333	−	17.2834i	0.595508	−	0.841344i
$423$	−10.0903			−0.490605
$424$	0.338332	+	0.0178265i	0.0164308	+	0.000865732i
$425$	0.563532	−	1.17019i	0.0273353	−	0.0567624i
$426$	−4.13730	−	14.2989i	−0.200453	−	0.692784i
$427$	6.63832	−	12.8308i	0.321251	−	0.620928i
$428$	5.28919	+	3.30643i	0.255662	+	0.159822i
$429$	1.65918	+	7.26932i	0.0801057	+	0.350966i
$430$	−2.09072	−	36.4774i	−0.100823	−	1.75910i
$431$	3.08962	−	6.41567i	0.148822	−	0.309032i	−0.813209	−	0.581971i	$-0.802282\pi$
$431$	3.08962	−	6.41567i	0.148822	−	0.309032i	0.962031	+	0.272939i	$0.0879958\pi$
$432$	0.0184482	+	3.99996i	0.000887589	+	0.192448i
$433$	−5.94580	−	12.3466i	−0.285737	−	0.593339i	0.707856	−	0.706357i	$-0.249662\pi$
$433$	−5.94580	−	12.3466i	−0.285737	−	0.593339i	−0.993593	+	0.113018i	$0.963948\pi$
$434$	−21.4657	−	16.1360i	−1.03039	−	0.774553i
$435$	−2.30592	+	4.78828i	−0.110560	+	0.229581i
$436$	−20.2052	−	20.1122i	−0.967652	−	0.963199i
$437$	−30.4637	−	6.95313i	−1.45727	−	0.332613i
$438$	−0.0514385	+	0.304874i	−0.00245783	+	0.0145674i
$439$	1.63197	+	2.04643i	0.0778898	+	0.0976707i	0.819250	−	0.573437i	$-0.194390\pi$
$439$	1.63197	+	2.04643i	0.0778898	+	0.0976707i	−0.741360	+	0.671108i	$0.765819\pi$
$440$	−6.27525	+	22.0686i	−0.299161	+	1.05208i
$441$	−6.12250	−	3.39338i	−0.291548	−	0.161589i
$442$	3.22828	+	2.28499i	0.153553	+	0.108686i
$443$	7.73835	−	6.17113i	0.367660	−	0.293199i	−0.422180	−	0.906512i	$-0.638735\pi$
$443$	7.73835	−	6.17113i	0.367660	−	0.293199i	0.789840	+	0.613313i	$0.210164\pi$
$444$	−9.47701	−	9.43340i	−0.449759	−	0.447689i
$445$	−4.00764	+	17.5586i	−0.189980	+	0.832358i
$446$	−23.1525	−	3.90631i	−1.09630	−	0.184969i
$447$	4.32044	+	2.08062i	0.204350	+	0.0984098i
$448$	7.42316	−	19.8216i	0.350711	−	0.936484i
$449$	−3.28488	+	1.58191i	−0.155023	+	0.0746551i	−0.509787	−	0.860301i	$-0.670276\pi$
$449$	−3.28488	+	1.58191i	−0.155023	+	0.0746551i	0.354764	+	0.934956i	$0.384561\pi$
$450$	1.17885	−	0.341093i	0.0555715	−	0.0160793i
$451$	35.7457	+	17.2142i	1.68320	+	0.810586i
$452$	−10.3172	+	16.5041i	−0.485281	+	0.776288i
$453$	8.31757	−	1.89843i	0.390794	−	0.0891961i
$454$	−0.597347	−	10.4221i	−0.0280349	−	0.489133i
$455$	9.17544	−	4.09914i	0.430151	−	0.192171i
$456$	−8.36831	−	11.7080i	−0.391882	−	0.548277i
$457$	11.0064	+	5.30039i	0.514857	+	0.247942i	0.673224	−	0.739438i	$-0.264909\pi$
$457$	11.0064	+	5.30039i	0.514857	+	0.247942i	−0.158368	+	0.987380i	$0.550623\pi$
$458$	27.7865	+	11.4720i	1.29838	+	0.536052i
$459$			1.49673i			0.0698614i
$460$	8.30068	+	23.5477i	0.387021	+	1.09792i
$461$	−6.45982	+	1.47441i	−0.300864	+	0.0686702i	−0.370288	−	0.928917i	$-0.620741\pi$
$461$	−6.45982	+	1.47441i	−0.300864	+	0.0686702i	0.0694242	+	0.997587i	$0.477884\pi$
$462$	13.2614	−	6.86033i	0.616978	−	0.319171i
$463$	−4.20716	−	0.960257i	−0.195523	−	0.0446269i	0.123638	−	0.992327i	$-0.460544\pi$
$463$	−4.20716	−	0.960257i	−0.195523	−	0.0446269i	−0.319161	+	0.947700i	$0.603401\pi$
$464$	4.58085	+	9.40106i	0.212660	+	0.436433i
$465$	11.4065	+	9.09640i	0.528965	+	0.421836i
$466$	33.3749	−	9.65683i	1.54606	−	0.447344i
$467$	−2.43193	+	10.6550i	−0.112536	+	0.493054i	0.886976	+	0.461816i	$0.152802\pi$
$467$	−2.43193	+	10.6550i	−0.112536	+	0.493054i	−0.999512	+	0.0312379i	$0.990055\pi$
$468$	0.426981	+	3.71260i	0.0197372	+	0.171615i
$469$	15.4887	+	13.0950i	0.715202	+	0.604669i
$470$	−26.8122	−	11.0698i	−1.23675	−	0.510610i
$471$			1.78308i			0.0821602i
$472$	3.99402	−	14.0460i	0.183840	−	0.646520i
$473$	−11.2855	−	49.4449i	−0.518906	−	2.27348i
$474$	3.01747	−	1.67224i	0.138597	−	0.0768087i
$475$	−2.75285	+	3.45196i	−0.126309	+	0.158387i
$476$	2.81179	−	7.40401i	0.128878	−	0.339362i
$477$	0.0746842	+	0.0936510i	0.00341956	+	0.00428799i
$478$	−24.2162	−	9.99798i	−1.10762	−	0.457297i
$479$	5.37748	+	6.74315i	0.245703	+	0.308102i	0.889356	−	0.457216i	$-0.151153\pi$
$479$	5.37748	+	6.74315i	0.245703	+	0.308102i	−0.643653	+	0.765318i	$0.722582\pi$
$480$	−4.33923	+	10.6491i	−0.198058	+	0.486061i
$481$	−9.76722	−	7.78910i	−0.445347	−	0.355152i
$482$	−3.07460	+	18.2230i	−0.140044	+	0.830037i
$483$	7.46632	−	14.4312i	0.339729	−	0.656644i
$484$	−1.07996	+	9.78776i	−0.0490893	+	0.444898i
$485$	−26.1333	+	12.5851i	−1.18665	+	0.571461i
$486$	−1.05341	+	0.943572i	−0.0477836	+	0.0428013i
$487$	−11.1495	−	23.1522i	−0.505233	−	1.04913i	−0.985131	−	0.171803i	$-0.945041\pi$
$487$	−11.1495	−	23.1522i	−0.505233	−	1.04913i	0.479899	−	0.877324i	$-0.340673\pi$
$488$	5.95942	+	14.2477i	0.269770	+	0.644964i
$489$		−	21.5559i		−	0.974791i
$490$	−12.5461	−	15.7338i	−0.566776	−	0.710782i
$491$		−	38.0587i		−	1.71756i	−0.512341	−	0.858782i	$-0.671222\pi$
$491$		−	38.0587i		−	1.71756i	0.512341	−	0.858782i	$-0.328778\pi$
$492$	16.8614	+	10.5406i	0.760170	+	0.475205i
$493$	1.69783	+	3.52558i	0.0764664	+	0.158784i
$494$	−8.97071	−	10.0150i	−0.403612	−	0.450595i
$495$	−7.30841	+	3.51954i	−0.328488	+	0.158192i
$496$	27.9588	−	6.51722i	1.25539	−	0.292632i
$497$	−22.2609	+	16.7322i	−0.998540	+	0.750541i
$498$	−9.60054	−	1.61981i	−0.430210	−	0.0725854i
$499$	−11.0300	−	8.79609i	−0.493768	−	0.393767i	0.344704	−	0.938712i	$-0.387979\pi$
$499$	−11.0300	−	8.79609i	−0.493768	−	0.393767i	−0.838472	+	0.544944i	$0.816551\pi$
$500$	23.7120	+	2.61634i	1.06043	+	0.117006i
$501$	−6.61123	−	8.29023i	−0.295368	−	0.370380i
$502$	−2.64119	+	6.39724i	−0.117882	+	0.285523i
$503$	−9.13636	−	11.4566i	−0.407370	−	0.510826i	0.535250	−	0.844694i	$-0.320217\pi$
$503$	−9.13636	−	11.4566i	−0.407370	−	0.510826i	−0.942620	+	0.333868i	$0.891646\pi$
$504$	6.98362	−	2.68869i	0.311075	−	0.119764i
$505$	−9.26356	+	11.6161i	−0.412223	+	0.516911i
$506$	16.7993	+	30.3135i	0.746821	+	1.34760i
$507$	−2.11586	−	9.27018i	−0.0939686	−	0.411703i
$508$	−12.1056	+	4.26729i	−0.537098	+	0.189330i
$509$			26.9727i			1.19554i	0.801666	+	0.597772i	$0.203947\pi$
$509$			26.9727i			1.19554i	−0.801666	+	0.597772i	$0.796053\pi$
$510$	−1.64202	+	3.97716i	−0.0727101	+	0.176112i
$511$	0.567381	−	0.112505i	0.0250995	−	0.00497695i
$512$	11.1502	+	19.6894i	0.492775	+	0.870157i
$513$	1.13220	−	4.96048i	0.0499877	−	0.219010i
$514$	2.49224	+	8.61342i	0.109928	+	0.379922i
$515$	22.5592	+	17.9904i	0.994079	+	0.792752i
$516$	−2.90427	−	25.2525i	−0.127853	−	1.11168i
$517$	−39.2550	−	8.95970i	−1.72643	−	0.394047i
$518$	−10.2051	+	22.8400i	−0.448385	+	1.00353i
$519$	−23.2084	+	5.29716i	−1.01873	+	0.232519i
$520$	−2.93841	+	10.3337i	−0.128858	+	0.453161i
$521$		−	39.4201i		−	1.72703i	−0.504325	−	0.863514i	$-0.668259\pi$
$521$		−	39.4201i		−	1.72703i	0.504325	−	0.863514i	$-0.331741\pi$
$522$	−1.41098	+	3.41755i	−0.0617570	+	0.149582i
$523$	38.0371	+	18.3177i	1.66325	+	0.800977i	0.998548	+	0.0538657i	$0.0171543\pi$
$523$	38.0371	+	18.3177i	1.66325	+	0.800977i	0.664699	+	0.747112i	$0.268560\pi$
$524$	6.43683	+	2.23570i	0.281194	+	0.0976669i
$525$	−1.37946	−	1.83527i	−0.0602045	−	0.0800976i
$526$	5.03211	−	0.288418i	0.219411	−	0.0125756i
$527$	10.4728	−	2.39035i	0.456203	−	0.104125i
$528$	−3.48001	+	15.5778i	−0.151448	+	0.677935i
$529$	13.2580	+	6.38471i	0.576434	+	0.277596i
$530$	0.0957113	+	0.330787i	0.00415743	+	0.0143685i
$531$	4.65159	−	2.24009i	0.201862	−	0.0972116i
$532$	−14.9196	+	22.4115i	−0.646848	+	0.971661i
$533$	16.7380	+	8.06061i	0.725005	+	0.349144i
$534$	−2.08456	+	12.3551i	−0.0902075	+	0.534656i
$535$	−1.41076	+	6.18094i	−0.0609924	+	0.267225i
$536$	−21.3638	+	3.70593i	−0.922776	+	0.160072i
$537$	−18.5984	+	14.8317i	−0.802579	+	0.640036i
$538$	−6.42068	+	9.07125i	−0.276815	+	0.391089i
$539$	−20.8057	−	18.6381i	−0.896166	−	0.802798i
$540$	−3.83433	+	1.35162i	−0.165003	+	0.0581645i
$541$	−16.4108	−	20.5785i	−0.705555	−	0.884738i	0.291870	−	0.956458i	$-0.405723\pi$
$541$	−16.4108	−	20.5785i	−0.705555	−	0.884738i	−0.997425	+	0.0717198i	$0.977151\pi$
$542$	−6.28339	−	1.06014i	−0.269895	−	0.0455368i
$543$	0.821735	+	0.187556i	0.0352640	+	0.00804879i
$544$	4.13819	+	7.38659i	0.177424	+	0.316697i
$545$	12.5723	−	26.1066i	0.538537	−	1.11828i
$546$	6.20972	−	3.21237i	0.265751	−	0.137477i
$547$	1.66177	+	3.45070i	0.0710521	+	0.147541i	0.933470	−	0.358656i	$-0.116765\pi$
$547$	1.66177	+	3.45070i	0.0710521	+	0.147541i	−0.862418	+	0.506197i	$0.831051\pi$
$548$	−13.3437	−	4.63466i	−0.570015	−	0.197983i
$549$	−2.36910	+	4.91949i	−0.101111	+	0.209959i
$550$	4.88906	−	0.280219i	0.208470	−	0.0119486i
$551$	−2.96005	−	12.9688i	−0.126102	−	0.552491i
$552$	6.70274	+	16.0248i	0.285288	+	0.682062i
$553$	−4.92867	−	4.16696i	−0.209589	−	0.177197i
$554$	−32.6122	+	9.43614i	−1.38556	+	0.400903i
$555$	5.89689	−	12.2450i	0.250309	−	0.519772i
$556$	−18.6131	+	11.7553i	−0.789371	+	0.498538i
$557$	23.9590			1.01518			0.507589	−	0.861600i	$-0.330537\pi$
$557$	23.9590			1.01518			0.507589	+	0.861600i	$0.330537\pi$
$558$	8.28465	+	5.86392i	0.350717	+	0.248240i
$559$	−5.28446	−	23.1527i	−0.223509	−	0.979256i
$560$	21.5068	+	0.517069i	0.908829	+	0.0218502i
$561$	−1.32903	+	5.82286i	−0.0561117	+	0.245841i
$562$	−17.4470	+	15.6278i	−0.735957	+	0.659219i
$563$	−17.1249	+	21.4739i	−0.721728	+	0.905019i	−0.998434	−	0.0559359i	$-0.982186\pi$
$563$	−17.1249	+	21.4739i	−0.721728	+	0.905019i	0.276706	+	0.960955i	$0.410757\pi$
$564$	−19.0634	−	6.62126i	−0.802712	−	0.278805i
$565$	−19.2867	−	4.40206i	−0.811396	−	0.185196i
$566$	13.7725	−	12.3365i	0.578903	−	0.518542i
$567$	2.34988	+	1.21576i	0.0986856	+	0.0510572i
$568$	1.56644	−	29.7296i	0.0657263	−	1.24743i
$569$	−20.9060			−0.876424			−0.438212	−	0.898872i	$-0.644388\pi$
$569$	−20.9060			−0.876424			−0.438212	+	0.898872i	$0.644388\pi$
$570$	8.45053	−	11.9391i	0.353954	−	0.500072i
$571$	31.9756	−	7.29823i	1.33814	−	0.305421i	0.507220	−	0.861817i	$-0.330673\pi$
$571$	31.9756	−	7.29823i	1.33814	−	0.305421i	0.830918	+	0.556395i	$0.187816\pi$
$572$	−1.63550	+	14.8226i	−0.0683836	+	0.619763i
$573$	−8.08949	−	6.45115i	−0.337943	−	0.269501i
$574$	7.23741	−	36.4905i	0.302084	−	1.52308i
$575$	4.16652	−	3.32269i	0.173756	−	0.138566i
$576$	−2.58993	+	7.56917i	−0.107914	+	0.315382i
$577$	−27.4119	+	21.8602i	−1.14117	+	0.910053i	−0.996837	−	0.0794760i	$-0.974675\pi$
$577$	−27.4119	+	21.8602i	−1.14117	+	0.910053i	−0.144334	+	0.989529i	$0.546104\pi$
$578$	−10.1180	−	18.2573i	−0.420852	−	0.759405i
$579$	10.8986	−	13.6665i	0.452932	−	0.567958i
$580$	−7.49862	+	7.53328i	−0.311363	+	0.312802i
$581$	3.54282	+	17.8669i	0.146981	+	0.741246i
$582$	−17.6501	+	9.78148i	−0.731622	+	0.405455i
$583$	0.207393	+	0.430655i	0.00858932	+	0.0178359i
$584$	−0.297241	+	0.542239i	−0.0122999	+	0.0224380i
$585$	−3.42218	+	1.64804i	−0.141490	+	0.0681379i
$586$	−10.0413	+	0.575523i	−0.414803	+	0.0237746i
$587$	25.3805			1.04756			0.523782	−	0.851852i	$-0.324521\pi$
$587$	25.3805			1.04756			0.523782	+	0.851852i	$0.324521\pi$
$588$	−9.34040	−	10.4287i	−0.385192	−	0.430071i
$589$	−36.5173			−1.50467
$590$	14.8179	−	0.849297i	0.610044	−	0.0349650i
$591$	1.76867	−	0.851745i	0.0727532	−	0.0350361i
$592$	−11.7145	−	24.0412i	−0.481465	−	0.988088i
$593$	6.15741	+	12.7860i	0.252855	+	0.525058i	0.988299	−	0.152527i	$-0.0487410\pi$
$593$	6.15741	+	12.7860i	0.252855	+	0.525058i	−0.735445	+	0.677585i	$0.763027\pi$
$594$	−4.93602	+	2.73548i	−0.202527	+	0.112238i
$595$	8.04649	+	0.230591i	0.329874	+	0.00945332i
$596$	6.79724	+	6.76596i	0.278426	+	0.277145i
$597$	12.3982	−	15.5469i	0.507425	−	0.636291i
$598$	7.86634	+	14.1944i	0.321678	+	0.580451i
$599$	−12.9746	+	10.3469i	−0.530128	+	0.422763i	−0.851628	−	0.524147i	$-0.824384\pi$
$599$	−12.9746	+	10.3469i	−0.530128	+	0.422763i	0.321500	+	0.946909i	$0.395813\pi$
$600$	2.45101	+	0.129142i	0.100062	+	0.00527222i
$601$	−8.98051	+	7.16171i	−0.366322	+	0.292132i	−0.789300	−	0.614008i	$-0.789556\pi$
$601$	−8.98051	+	7.16171i	−0.366322	+	0.292132i	0.422978	+	0.906140i	$0.360985\pi$
$602$	−42.2376	+	21.8501i	−1.72148	+	0.890542i
$603$	−5.99356	−	4.77970i	−0.244076	−	0.194644i
$604$	16.9600	+	1.87134i	0.690094	+	0.0761437i
$605$	−9.75767	+	2.22712i	−0.396706	+	0.0905455i
$606$	−5.97168	+	8.43689i	−0.242583	+	0.342725i
$607$	20.0156			0.812409			0.406205	−	0.913782i	$-0.366852\pi$
$607$	20.0156			0.812409			0.406205	+	0.913782i	$0.366852\pi$
$608$	−8.12729	−	27.6111i	−0.329605	−	1.11978i
$609$	6.91430	+	0.198146i	0.280182	+	0.00802927i
$610$	−11.6923	+	10.4732i	−0.473408	+	0.424046i
$611$	−18.3813	−	4.19541i	−0.743627	−	0.169728i
$612$	−0.982159	+	2.82775i	−0.0397014	+	0.114305i
$613$	−30.8347	+	38.6654i	−1.24540	+	1.56168i	−0.583360	+	0.812214i	$0.698262\pi$
$613$	−30.8347	+	38.6654i	−1.24540	+	1.56168i	−0.662040	+	0.749468i	$0.730309\pi$
$614$	18.4425	−	16.5195i	0.744280	−	0.666675i
$615$	−4.49735	+	19.7042i	−0.181351	+	0.794550i
$616$	29.5564	−	4.25891i	1.19086	−	0.171596i
$617$	0.0797970	+	0.349614i	0.00321251	+	0.0140749i	0.976509	−	0.215478i	$-0.0691309\pi$
$617$	0.0797970	+	0.349614i	0.00321251	+	0.0140749i	−0.973296	+	0.229553i	$0.926274\pi$
$618$	16.3850	+	11.5974i	0.659099	+	0.466514i
$619$	4.87903			0.196105			0.0980524	−	0.995181i	$-0.468739\pi$
$619$	4.87903			0.196105			0.0980524	+	0.995181i	$0.468739\pi$
$620$	15.5811	+	24.6707i	0.625752	+	0.990799i
$621$	−2.66460	+	5.53310i	−0.106927	+	0.222036i
$622$	−41.6973	+	12.0649i	−1.67191	+	0.483758i
$623$	22.9932	−	4.55930i	0.921204	−	0.182665i
$624$	−1.62953	+	7.29434i	−0.0652333	+	0.292007i
$625$	4.42998	+	19.4090i	0.177199	+	0.776361i
$626$	17.3447	−	0.994118i	0.693232	−	0.0397330i
$627$	8.80937	−	18.2928i	0.351812	−	0.730546i
$628$	−1.17007	+	3.36875i	−0.0466907	+	0.134428i
$629$	−4.34184	−	9.01592i	−0.173120	−	0.359488i
$630$	4.91040	+	5.80855i	0.195635	+	0.231418i
$631$	7.10816	−	14.7602i	0.282971	−	0.587596i	−0.710235	−	0.703965i	$-0.751411\pi$
$631$	7.10816	−	14.7602i	0.282971	−	0.587596i	0.993206	+	0.116369i	$0.0371255\pi$
$632$	6.79820	−	1.17927i	0.270418	−	0.0469088i
$633$	14.5974	+	3.33176i	0.580195	+	0.132426i
$634$	−40.1443	−	6.77318i	−1.59433	−	0.268997i
$635$	−8.13413	−	10.1999i	−0.322793	−	0.404770i
$636$	0.0796457	+	0.225942i	0.00315816	+	0.00895916i
$637$	−9.74235	−	8.72733i	−0.386006	−	0.345789i
$638$	−8.52390	+	12.0427i	−0.337464	+	0.476775i
$639$	8.22923	−	6.56259i	0.325543	−	0.259612i
$640$	−15.1860	+	17.2717i	−0.600279	+	0.682724i
$641$	3.37841	−	14.8018i	0.133439	−	0.584636i	−0.863353	−	0.504601i	$-0.831640\pi$
$641$	3.37841	−	14.8018i	0.133439	−	0.584636i	0.996792	−	0.0800350i	$-0.0255032\pi$
$642$	−0.733800	+	4.34920i	−0.0289608	+	0.171649i
$643$	2.32224	+	1.11833i	0.0915803	+	0.0441028i	0.479113	−	0.877753i	$-0.340958\pi$
$643$	2.32224	+	1.11833i	0.0915803	+	0.0441028i	−0.387533	+	0.921856i	$0.626673\pi$
$644$	23.5758	−	22.3653i	0.929018	−	0.881317i
$645$	23.2772	−	11.2097i	0.916539	−	0.441382i
$646$	−2.99341	−	10.3455i	−0.117774	−	0.407038i
$647$	−18.6363	−	8.97476i	−0.732668	−	0.352834i	0.0300651	−	0.999548i	$-0.490429\pi$
$647$	−18.6363	−	8.97476i	−0.732668	−	0.352834i	−0.762733	+	0.646714i	$0.776143\pi$
$648$	−2.60937	+	1.09142i	−0.102506	+	0.0428752i
$649$	20.0856	−	4.58441i	0.788429	−	0.179954i
$650$	2.28932	−	0.131213i	0.0897944	−	0.00514661i
$651$	4.75397	−	18.3840i	0.186323	−	0.720528i
$652$	14.1450	−	40.7252i	0.553963	−	1.59492i
$653$	−39.1849	−	18.8704i	−1.53342	−	0.738457i	−0.538840	−	0.842408i	$-0.681137\pi$
$653$	−39.1849	−	18.8704i	−1.53342	−	0.738457i	−0.994582	+	0.103951i	$0.966852\pi$
$654$	7.69293	−	18.6331i	0.300818	−	0.728613i
$655$			6.92576i			0.270612i
$656$	24.9392	+	30.9786i	0.973713	+	1.20951i
$657$	−0.213144	+	0.0486487i	−0.00831553	+	0.00189797i
$658$	1.07975	+	37.7388i	0.0420931	+	1.47121i
$659$	21.7213	+	4.95774i	0.846141	+	0.193126i	0.623548	−	0.781785i	$-0.285691\pi$
$659$	21.7213	+	4.95774i	0.846141	+	0.193126i	0.222593	+	0.974911i	$0.428548\pi$
$660$	−16.1172	+	1.85362i	−0.627361	+	0.0721521i
$661$	15.2529	+	12.1638i	0.593269	+	0.473116i	0.873505	−	0.486815i	$-0.161841\pi$
$661$	15.2529	+	12.1638i	0.593269	+	0.473116i	−0.280236	+	0.959931i	$0.590413\pi$
$662$	−4.85265	−	16.7712i	−0.188604	−	0.651832i
$663$	−0.622322	+	2.72657i	−0.0241690	+	0.105891i
$664$	−17.0752	−	9.36019i	−0.662647	−	0.363246i
$665$	−26.4934	−	6.85098i	−1.02737	−	0.265669i
$666$	3.60828	−	8.73966i	0.139818	−	0.338655i
$667$			16.0560i			0.621689i
$668$	−7.05043	−	20.0009i	−0.272789	−	0.773858i
$669$	−3.69444	−	16.1864i	−0.142835	−	0.625803i
$670$	−10.6826	−	19.2762i	−0.412705	−	0.744703i
$671$	−13.5850	+	17.0351i	−0.524443	+	0.657631i
$672$	14.9584	−	0.497031i	0.577032	−	0.0191734i
$673$	12.7712	+	16.0146i	0.492293	+	0.617316i	0.964471	−	0.264187i	$-0.0851036\pi$
$673$	12.7712	+	16.0146i	0.492293	+	0.617316i	−0.472178	+	0.881503i	$0.656532\pi$
$674$	−0.999209	+	2.42019i	−0.0384881	+	0.0932224i
$675$	0.541042	+	0.678446i	0.0208247	+	0.0261134i
$676$	2.08566	−	18.9024i	0.0802178	−	0.727017i
$677$	−22.0079	−	17.5507i	−0.845833	−	0.674529i	0.101480	−	0.994838i	$-0.467642\pi$
$677$	−22.0079	−	17.5507i	−0.845833	−	0.674529i	−0.947313	+	0.320308i	$0.896214\pi$
$678$	−13.5710	−	2.28971i	−0.521191	−	0.0879358i
$679$	28.8294	+	24.3739i	1.10637	+	0.935383i
$680$	−5.71208	+	6.43649i	−0.219048	+	0.246828i
$681$	6.65061	−	3.20276i	0.254852	−	0.122730i
$682$	27.0236	+	30.1693i	1.03479	+	1.15524i
$683$	−17.3776	−	36.0850i	−0.664936	−	1.38075i	−0.911367	−	0.411594i	$-0.864972\pi$
$683$	−17.3776	−	36.0850i	−0.664936	−	1.38075i	0.246431	−	0.969160i	$-0.420742\pi$
$684$	5.39412	−	8.62881i	0.206250	−	0.329931i
$685$		−	14.3573i		−	0.548563i
$686$	−12.0365	+	23.2620i	−0.459556	+	0.888149i
$687$			21.2567i			0.810994i
$688$	11.0838	−	49.6150i	0.422566	−	1.89155i
$689$	0.0971122	+	0.201656i	0.00369968	+	0.00768247i
$690$	−13.1507	+	11.7795i	−0.500638	+	0.448437i
$691$	16.7027	−	8.04357i	0.635399	−	0.305992i	−0.0883145	−	0.996093i	$-0.528148\pi$
$691$	16.7027	−	8.04357i	0.635399	−	0.305992i	0.723713	+	0.690101i	$0.242434\pi$
$692$	−47.3232	−	5.22156i	−1.79896	−	0.198494i
$693$	8.06239	+	6.81637i	0.306265	+	0.258932i
$694$	−1.63641	+	9.69892i	−0.0621173	+	0.368166i
$695$	−17.4938	−	13.9508i	−0.663577	−	0.529185i
$696$	−4.90835	+	5.53084i	−0.186051	+	0.209646i
$697$	9.27825	+	11.6346i	0.351439	+	0.440690i
$698$	−20.2631	−	8.36588i	−0.766969	−	0.316653i
$699$	15.3177	+	19.2078i	0.579367	+	0.726504i
$700$	−1.40188	−	4.37255i	−0.0529861	−	0.165267i
$701$	−11.5427	+	14.4741i	−0.435962	+	0.546679i	−0.950474	−	0.310804i	$-0.899402\pi$
$701$	−11.5427	+	14.4741i	−0.435962	+	0.546679i	0.514512	+	0.857483i	$0.327973\pi$
$702$	−2.31131	+	1.28090i	−0.0872347	+	0.0483443i
$703$	7.56971	+	33.1650i	0.285497	+	1.25084i
$704$	−16.7969	+	27.1472i	−0.633058	+	1.02315i
$705$		−	20.5114i		−	0.772503i
$706$	15.7189	+	6.48976i	0.591589	+	0.244246i
$707$	18.7219	+	4.84133i	0.704109	+	0.182077i
$708$	10.2581	−	1.17978i	0.385524	−	0.0443387i
$709$	−5.29682	+	23.2069i	−0.198926	+	0.871553i	0.772651	+	0.634831i	$0.218930\pi$
$709$	−5.29682	+	23.2069i	−0.198926	+	0.871553i	−0.971577	+	0.236722i	$0.923927\pi$
$710$	29.0667	−	8.41027i	1.09085	−	0.315632i
$711$	1.90722	+	1.52095i	0.0715262	+	0.0570402i
$712$	−12.0457	+	21.9743i	−0.451433	+	0.823523i
$713$	42.9713	+	9.80793i	1.60929	+	0.367310i
$714$	5.59796	−	0.160164i	0.209498	−	0.00599399i
$715$	−14.7770	+	3.37276i	−0.552629	+	0.126134i
$716$	−44.8703	+	15.8170i	−1.67688	+	0.591110i
$717$		−	18.5254i		−	0.691846i
$718$	−31.1165	−	12.8469i	−1.16126	−	0.479441i
$719$	47.0030	+	22.6355i	1.75292	+	0.844160i	0.976974	+	0.213356i	$0.0684396\pi$
$719$	47.0030	+	22.6355i	1.75292	+	0.844160i	0.775942	+	0.630804i	$0.217275\pi$
$720$	−8.13107	+	0.0375013i	−0.303027	+	0.00139759i
$721$	9.40216	−	36.3590i	0.350155	−	1.35408i
$722$	0.557420	+	9.72546i	0.0207450	+	0.361944i
$723$	−12.7401	+	2.90785i	−0.473810	+	0.108144i
$724$	1.42942	+	0.893572i	0.0531239	+	0.0332093i
$725$	2.04404	+	0.984357i	0.0759137	+	0.0365581i
$726$	−6.68863	+	1.93532i	−0.248238	+	0.0718264i
$727$	−2.47862	+	1.19364i	−0.0919271	+	0.0442698i	−0.479282	−	0.877661i	$-0.659103\pi$
$727$	−2.47862	+	1.19364i	−0.0919271	+	0.0442698i	0.387355	+	0.921931i	$0.373389\pi$
$728$	13.8399	−	1.99425i	0.512940	−	0.0739117i
$729$	−0.900969	−	0.433884i	−0.0333692	−	0.0160698i
$730$	−0.619744	−	0.104564i	−0.0229378	−	0.00387008i
$731$	4.23294	−	18.5457i	0.156561	−	0.685939i
$732$	−7.70409	+	7.73970i	−0.284751	+	0.286068i
$733$	29.2741	−	23.3453i	1.08126	−	0.862279i	0.0902339	−	0.995921i	$-0.471239\pi$
$733$	29.2741	−	23.3453i	1.08126	−	0.862279i	0.991030	+	0.133642i	$0.0426671\pi$
$734$	24.9967	+	17.6928i	0.922645	+	0.653054i
$735$	6.89802	−	12.4458i	0.254437	−	0.459069i
$736$	2.14784	+	34.6738i	0.0791703	+	1.27809i
$737$	−19.0731	−	23.9169i	−0.702566	−	0.880990i
$738$	−2.33928	+	13.8648i	−0.0861100	+	0.510370i
$739$	−36.7956	−	8.39835i	−1.35355	−	0.308938i	−0.516602	−	0.856226i	$-0.672803\pi$
$739$	−36.7956	−	8.39835i	−1.35355	−	0.308938i	−0.836945	+	0.547288i	$0.815660\pi$
$740$	19.1761	−	19.2648i	0.704928	−	0.708187i
$741$	4.12502	−	8.56568i	0.151536	−	0.314668i
$742$	0.342275	−	0.289350i	0.0125653	−	0.0106224i
$743$	0.272580	+	0.566019i	0.0100000	+	0.0207652i	0.905909	−	0.423472i	$-0.139189\pi$
$743$	0.272580	+	0.566019i	0.0100000	+	0.0207652i	−0.895909	+	0.444238i	$0.853475\pi$
$744$	11.8041	+	16.5150i	0.432761	+	0.605471i
$745$	−4.22946	+	8.78255i	−0.154955	+	0.321768i
$746$	1.01724	+	17.7480i	0.0372437	+	0.649802i
$747$	−1.53196	−	6.71194i	−0.0560514	−	0.245577i
$748$	−6.33189	+	10.1289i	−0.231517	+	0.370350i
$749$	8.09401	−	1.60495i	0.295749	−	0.0586438i
$750$	4.68853	+	16.2040i	0.171201	+	0.591686i
$751$	−5.86847	+	12.1860i	−0.214143	+	0.444673i	−0.980176	−	0.198128i	$-0.936514\pi$
$751$	−5.86847	+	12.1860i	−0.214143	+	0.444673i	0.766033	+	0.642802i	$0.222228\pi$
$752$	−31.6712	−	25.0189i	−1.15493	−	0.912345i
$753$	−4.89390			−0.178344
$754$	−3.99134	+	5.63903i	−0.145356	+	0.205362i
$755$	3.85911	+	16.9079i	0.140448	+	0.615341i
$756$	3.64180	+	3.83892i	0.132451	+	0.139620i
$757$	−2.19896	+	9.63429i	−0.0799227	+	0.350164i	−0.999039	−	0.0438211i	$-0.986047\pi$
$757$	−2.19896	+	9.63429i	−0.0799227	+	0.350164i	0.919117	+	0.393985i	$0.128904\pi$
$758$	9.32576	+	10.4113i	0.338727	+	0.378157i
$759$	−15.2795	+	19.1598i	−0.554610	+	0.695458i
$760$	23.7999	−	17.0110i	0.863313	−	0.617054i
$761$	16.4819	+	3.76188i	0.597467	+	0.136368i	0.510551	−	0.859848i	$-0.329442\pi$
$761$	16.4819	+	3.76188i	0.597467	+	0.136368i	0.0869163	+	0.996216i	$0.472299\pi$
$762$	−6.05569	−	6.76062i	−0.219375	−	0.244911i
$763$	−37.6981	−	1.08033i	−1.36476	−	0.0391105i
$764$	−11.0501	−	17.4964i	−0.399778	−	0.632998i
$765$	−3.04254			−0.110003
$766$	−1.73876	−	1.23070i	−0.0628239	−	0.0444672i
$767$	9.40514	−	2.14666i	0.339600	−	0.0775115i
$768$	−9.86003	+	12.6008i	−0.355793	+	0.454692i
$769$	23.5446	+	18.7762i	0.849038	+	0.677086i	0.948092	−	0.317997i	$-0.103010\pi$
$769$	23.5446	+	18.7762i	0.849038	+	0.677086i	−0.0990535	+	0.995082i	$0.531581\pi$
$770$	13.9456	+	26.9577i	0.502565	+	0.971490i
$771$	−4.95715	+	3.95320i	−0.178528	+	0.142371i
$772$	29.5586	−	18.6681i	1.06384	−	0.671880i
$773$	−2.90090	+	2.31339i	−0.104338	+	0.0832068i	−0.674269	−	0.738486i	$-0.735541\pi$
$773$	−2.90090	+	2.31339i	−0.104338	+	0.0832068i	0.569931	+	0.821692i	$0.306970\pi$
$774$	15.7212	−	8.71247i	0.565086	−	0.313163i
$775$	3.88311	−	4.86926i	0.139485	−	0.174909i
$776$	−39.7648	+	6.89791i	−1.42747	+	0.247621i
$777$	−17.6819	−	0.506715i	−0.634333	−	0.0181783i
$778$	11.8891	+	21.4533i	0.426246	+	0.769137i
$779$	−21.9492	−	45.5779i	−0.786411	−	1.63300i
$780$	−7.54693	+	0.867964i	−0.270223	+	0.0310781i
$781$	37.8422	−	18.2238i	1.35410	−	0.652100i
$782$	0.743836	+	12.9779i	0.0265995	+	0.464089i
$783$	−2.61443			−0.0934322
$784$	−10.8034	−	25.8319i	−0.385834	−	0.922568i
$785$	−3.62463			−0.129369
$786$	0.275708	+	4.81036i	0.00983419	+	0.171580i
$787$	40.0839	−	19.3034i	1.42884	−	0.688091i	0.450055	−	0.893001i	$-0.351404\pi$
$787$	40.0839	−	19.3034i	1.42884	−	0.688091i	0.978781	+	0.204910i	$0.0656901\pi$
$788$	3.90043	−	0.448584i	0.138947	−	0.0159802i
$789$	1.54640	+	3.21113i	0.0550532	+	0.114319i
$790$	3.39932	+	6.13389i	0.120942	+	0.218234i
$791$	5.00802	+	25.2561i	0.178065	+	0.898005i
$792$	−11.1206	+	1.92906i	−0.395153	+	0.0685463i
$793$	−6.36122	+	7.97672i	−0.225894	+	0.283262i
$794$	39.9061	−	22.1155i	1.41622	−	0.784848i
$795$	−0.190373	+	0.151817i	−0.00675183	+	0.00538441i
$796$	33.6257	−	21.2367i	1.19183	−	0.752716i
$797$	−6.51515	+	5.19566i	−0.230778	+	0.184040i	−0.732051	−	0.681250i	$-0.761437\pi$
$797$	−6.51515	+	5.19566i	−0.230778	+	0.184040i	0.501273	+	0.865289i	$0.332865\pi$
$798$	−18.6740	−	3.70374i	−0.661052	−	0.131111i
$799$	−11.8075	−	9.41618i	−0.417720	−	0.333121i
$800$	4.54591	+	1.85235i	0.160722	+	0.0654904i
$801$	−8.63769	+	1.97150i	−0.305198	+	0.0696594i
$802$	37.9250	+	26.8436i	1.33918	+	0.947879i
$803$	−0.872410			−0.0307867
$804$	−8.18708	−	12.9632i	−0.288736	−	0.457177i
$805$	29.3357	+	15.1775i	1.03395	+	0.534935i
$806$	12.6539	+	14.1269i	0.445714	+	0.497598i
$807$	−7.66149	−	1.74869i	−0.269697	−	0.0615567i
$808$	−16.8185	+	12.0211i	−0.591673	+	0.422899i
$809$	32.5014	−	40.7555i	1.14269	−	1.43289i	0.258345	−	0.966053i	$-0.416823\pi$
$809$	32.5014	−	40.7555i	1.14269	−	1.43289i	0.884345	−	0.466835i	$-0.154606\pi$
$810$	−1.91808	−	2.14136i	−0.0673946	−	0.0752398i
$811$	−6.31976	+	27.6887i	−0.221917	+	0.972281i	0.734117	+	0.679024i	$0.237597\pi$
$811$	−6.31976	+	27.6887i	−0.221917	+	0.972281i	−0.956033	+	0.293258i	$0.905261\pi$
$812$	12.9331	+	4.91154i	0.453861	+	0.172361i
$813$	−1.00264	−	4.39285i	−0.0351641	−	0.154064i
$814$	21.7981	−	30.7967i	0.764021	−	1.07942i
$815$	43.8186			1.53490
$816$	−3.71115	+	4.69793i	−0.129916	+	0.164460i
$817$	−28.0578	+	58.2625i	−0.981616	+	2.03835i
$818$	−7.92935	−	27.4046i	−0.277243	−	0.958178i
$819$	3.77524	+	3.19179i	0.131918	+	0.111530i
$820$	−21.4267	+	34.2757i	−0.748254	+	1.19696i
$821$	1.71151	+	7.49860i	0.0597320	+	0.261703i	0.995973	−	0.0896560i	$-0.0285768\pi$
$821$	1.71151	+	7.49860i	0.0597320	+	0.261703i	−0.936241	+	0.351359i	$0.885720\pi$
$822$	−0.571550	−	9.97200i	−0.0199351	−	0.347813i
$823$	−20.2503	+	42.0502i	−0.705882	+	1.46578i	0.171100	+	0.985254i	$0.445268\pi$
$823$	−20.2503	+	42.0502i	−0.705882	+	1.46578i	−0.876981	+	0.480525i	$0.840446\pi$
$824$	23.3456	+	32.6626i	0.813283	+	1.13785i
$825$	1.50244	+	3.11984i	0.0523081	+	0.108619i
$826$	−8.87598	−	17.1578i	−0.308835	−	0.596997i
$827$	−22.9906	+	47.7404i	−0.799460	+	1.66010i	−0.0493520	+	0.998781i	$0.515716\pi$
$827$	−22.9906	+	47.7404i	−0.799460	+	1.66010i	−0.750108	+	0.661315i	$0.769999\pi$
$828$	−8.66502	+	8.70508i	−0.301130	+	0.302522i
$829$	−8.53354	−	1.94772i	−0.296382	−	0.0676473i	0.0717443	−	0.997423i	$-0.477143\pi$
$829$	−8.53354	−	1.94772i	−0.296382	−	0.0676473i	−0.368126	+	0.929776i	$0.620001\pi$
$830$	3.29273	−	19.5159i	0.114292	−	0.677406i
$831$	−14.9676	−	18.7688i	−0.519221	−	0.651082i
$832$	−7.86521	+	12.7118i	−0.272677	+	0.440702i
$833$	−3.99780	−	9.68439i	−0.138516	−	0.335544i
$834$	−12.7059	−	8.99328i	−0.439968	−	0.311412i
$835$	16.8523	−	13.4393i	0.583197	−	0.465084i
$836$	28.6472	−	28.7797i	0.990785	−	0.995365i
$837$	−1.59705	+	6.99714i	−0.0552022	+	0.241856i
$838$	−28.4676	−	4.80308i	−0.983397	−	0.165919i
$839$	−10.6175	−	5.11313i	−0.366558	−	0.176525i	0.241533	−	0.970393i	$-0.422350\pi$
$839$	−10.6175	−	5.11313i	−0.366558	−	0.176525i	−0.608090	+	0.793868i	$0.708064\pi$
$840$	5.46555	+	14.1962i	0.188579	+	0.489817i
$841$	19.9697	−	9.61692i	0.688612	−	0.331618i
$842$	40.0782	−	11.5964i	1.38118	−	0.399638i
$843$	−14.9222	−	7.18616i	−0.513948	−	0.247504i
$844$	25.3924	+	15.8735i	0.874041	+	0.546389i
$845$	18.8443	−	4.30110i	0.648265	−	0.147962i
$846$	−0.816539	−	14.2464i	−0.0280732	−	0.489801i
$847$	7.82686	+	10.4131i	0.268934	+	0.357797i
$848$	0.00220980	+	0.479132i	7.58849e−5	+	0.0164534i
$849$	11.7795	+	5.67271i	0.404271	+	0.194687i
$850$	1.69779	+	0.700953i	0.0582336	+	0.0240425i
$851$		−	41.0597i		−	1.40751i
$852$	19.8538	−	6.99856i	0.680178	−	0.239767i
$853$	−25.6765	+	5.86050i	−0.879147	+	0.200660i	−0.638193	−	0.769877i	$-0.720318\pi$
$853$	−25.6765	+	5.86050i	−0.879147	+	0.200660i	−0.240955	+	0.970536i	$0.577461\pi$
$854$	18.6530	+	8.33431i	0.638293	+	0.285194i
$855$	10.0836	+	2.30152i	0.344852	+	0.0787103i
$856$	−4.24031	+	7.73535i	−0.144931	+	0.264389i
$857$	34.7737	+	27.7311i	1.18785	+	0.947275i	0.999394	−	0.0348070i	$-0.0110816\pi$
$857$	34.7737	+	27.7311i	1.18785	+	0.947275i	0.188452	+	0.982082i	$0.439653\pi$
$858$	−10.1293	+	2.93084i	−0.345807	+	0.100057i
$859$	3.12090	−	13.6735i	0.106484	−	0.466535i	−0.893368	−	0.449325i	$-0.851664\pi$
$859$	3.12090	−	13.6735i	0.106484	−	0.466535i	0.999852	−	0.0172100i	$-0.00547837\pi$
$860$	51.3331	−	5.90376i	1.75044	−	0.201317i
$861$	25.8029	−	5.11643i	0.879360	−	0.174368i
$862$	9.30829	+	3.84305i	0.317041	+	0.130895i
$863$		−	34.1919i		−	1.16391i	−0.813222	−	0.581953i	$-0.802289\pi$
$863$		−	34.1919i		−	1.16391i	0.813222	−	0.581953i	$-0.197711\pi$
$864$	−5.64603	+	0.349738i	−0.192082	+	0.0118983i
$865$	−10.7680	−	47.1777i	−0.366123	−	1.60409i
$866$	16.9509	−	9.39398i	0.576016	−	0.319220i
$867$	9.20259	−	11.5397i	0.312536	−	0.391908i
$868$	21.0453	−	31.6131i	0.714323	−	1.07302i
$869$	6.06927	+	7.61062i	0.205886	+	0.258173i
$870$	−6.94716	−	2.86823i	−0.235531	−	0.0972421i
$871$	−8.93103	−	11.1992i	−0.302617	−	0.379469i
$872$	26.7613	−	30.1551i	0.906250	−	1.02118i
$873$	−11.1559	−	8.89654i	−0.377570	−	0.301102i
$874$	7.35187	−	43.5742i	0.248681	−	1.47392i
$875$	25.2268	−	18.9615i	0.852822	−	0.641014i
$876$	−0.434613	−	0.0479544i	−0.0146842	−	0.00162023i
$877$	29.3084	−	14.1142i	0.989674	−	0.476602i	0.132252	−	0.991216i	$-0.457779\pi$
$877$	29.3084	−	14.1142i	0.989674	−	0.476602i	0.857422	+	0.514614i	$0.172065\pi$
$878$	−2.75728	+	2.46978i	−0.0930536	+	0.0833510i
$879$	−3.08575	−	6.40763i	−0.104080	−	0.216124i
$880$	−31.6663	−	7.07414i	−1.06747	−	0.238469i
$881$		−	25.2740i		−	0.851501i	−0.904841	−	0.425751i	$-0.860010\pi$
$881$		−	25.2740i		−	0.851501i	0.904841	−	0.425751i	$-0.139990\pi$
$882$	4.29564	−	8.91894i	0.144642	−	0.300316i
$883$			48.3765i			1.62800i	0.580866	+	0.813999i	$0.302714\pi$
$883$			48.3765i			1.62800i	−0.580866	+	0.813999i	$0.697286\pi$
$884$	−2.96493	+	4.74290i	−0.0997213	+	0.159521i
$885$	4.55363	+	9.45571i	0.153069	+	0.317850i
$886$	9.33921	+	10.4264i	0.313757	+	0.350280i
$887$	14.1572	−	6.81777i	0.475354	−	0.228918i	−0.180837	−	0.983513i	$-0.557881\pi$
$887$	14.1572	−	6.81777i	0.475354	−	0.228918i	0.656191	+	0.754595i	$0.272166\pi$
$888$	12.5521	−	14.1439i	0.421220	−	0.474639i
$889$	−7.80256	+	15.0811i	−0.261690	+	0.505805i
$890$	−25.1152	−	4.23746i	−0.841865	−	0.142040i
$891$	−3.11985	−	2.48800i	−0.104519	−	0.0833510i
$892$	3.64172	−	33.0050i	0.121934	−	1.10509i
$893$	32.0098	+	40.1390i	1.07117	+	1.34320i
$894$	−2.58799	+	6.26839i	−0.0865553	+	0.209646i
$895$	−30.1498	−	37.8066i	−1.00780	−	1.26374i
$896$	28.5868	+	8.87670i	0.955017	+	0.296550i
$897$	−7.15466	+	8.97166i	−0.238887	+	0.299555i
$898$	−2.49932	−	4.50989i	−0.0834034	−	0.150497i
$899$	4.17538	+	18.2935i	0.139257	+	0.610124i
$900$	0.576985	+	1.63681i	0.0192328	+	0.0545604i
$901$			0.179285i			0.00597283i
$902$	−21.4120	+	51.8622i	−0.712942	+	1.72682i
$903$	−25.6786	−	21.7101i	−0.854532	−	0.722466i
$904$	−24.1370	−	13.2313i	−0.802784	−	0.440065i
$905$	−0.381261	+	1.67042i	−0.0126736	+	0.0555265i
$906$	3.35348	+	11.5899i	0.111412	+	0.385049i
$907$	−32.1627	−	25.6489i	−1.06794	−	0.851657i	−0.0785501	−	0.996910i	$-0.525029\pi$
$907$	−32.1627	−	25.6489i	−1.06794	−	0.851657i	−0.989395	+	0.145253i	$0.953600\pi$
$908$	14.6666	−	1.68678i	0.486727	−	0.0559779i
$909$	−7.12572	−	1.62640i	−0.236345	−	0.0539442i
$910$	6.53007	+	12.6230i	0.216470	+	0.418450i
$911$	10.3852	−	2.37035i	0.344077	−	0.0785333i	−0.0469905	−	0.998895i	$-0.514963\pi$
$911$	10.3852	−	2.37035i	0.344077	−	0.0785333i	0.391067	+	0.920362i	$0.372106\pi$
$912$	15.8533	−	12.7626i	0.524955	−	0.422613i
$913$		−	27.4724i		−	0.909203i
$914$	−6.59293	+	15.9688i	−0.218075	+	0.528201i
$915$	−10.0003	−	4.81588i	−0.330599	−	0.159208i
$916$	−13.9487	+	40.1600i	−0.460878	+	1.32692i
$917$	8.23016	−	3.67684i	0.271784	−	0.121420i
$918$	−2.11323	+	0.121121i	−0.0697469	+	0.00399758i
$919$	−21.3471	+	4.87232i	−0.704174	+	0.160723i	−0.559590	−	0.828769i	$-0.689041\pi$
$919$	−21.3471	+	4.87232i	−0.704174	+	0.160723i	−0.144584	+	0.989493i	$0.546184\pi$
$920$	−32.5751	+	13.6253i	−1.07397	+	0.449212i
$921$	15.7737	+	7.59620i	0.519760	+	0.250303i
$922$	−2.60447	−	9.00128i	−0.0857735	−	0.296441i
$923$	17.7197	−	8.53337i	0.583252	−	0.280879i
$924$	10.7592	+	18.1686i	0.353953	+	0.597704i
$925$	−5.22720	−	2.51728i	−0.171869	−	0.0827678i
$926$	1.01533	−	6.01778i	0.0333657	−	0.197757i
$927$	−3.15856	+	13.8386i	−0.103741	+	0.454519i
$928$	−12.9026	+	7.22845i	−0.423550	+	0.237285i
$929$	−2.10664	+	1.67999i	−0.0691167	+	0.0551188i	−0.657439	−	0.753508i	$-0.728360\pi$
$929$	−2.10664	+	1.67999i	−0.0691167	+	0.0551188i	0.588322	+	0.808627i	$0.299789\pi$
$930$	−11.9201	+	16.8410i	−0.390876	+	0.552237i
$931$	5.92384	+	35.1202i	0.194146	+	1.15102i
$932$	16.3353	+	46.3404i	0.535079	+	1.51793i
$933$	−19.1373	−	23.9974i	−0.626528	−	0.785641i
$934$	−15.2405	−	2.57140i	−0.498686	−	0.0841387i
$935$	−11.8366	−	2.70164i	−0.387100	−	0.0883530i
$936$	−5.20725	+	0.903290i	−0.170204	+	0.0295250i
$937$	−14.1418	+	29.3658i	−0.461994	+	0.959340i	0.531670	+	0.846951i	$0.321565\pi$
$937$	−14.1418	+	29.3658i	−0.461994	+	0.959340i	−0.993664	+	0.112389i	$0.964150\pi$
$938$	−17.2353	+	22.9281i	−0.562753	+	0.748630i
$939$	5.33011	+	11.0681i	0.173942	+	0.361193i
$940$	13.4596	−	38.7518i	0.439004	−	1.26394i
$941$	−9.68579	+	20.1127i	−0.315748	+	0.655657i	−0.997084	−	0.0763138i	$-0.975685\pi$
$941$	−9.68579	+	20.1127i	−0.315748	+	0.655657i	0.681336	+	0.731971i	$0.261399\pi$
$942$	−2.51753	+	0.144294i	−0.0820255	+	0.00470134i
$943$	13.5870	+	59.5285i	0.442453	+	1.93851i
$944$	20.1547	+	4.50249i	0.655980	+	0.146543i
$945$	−2.47139	+	4.77681i	−0.0803942	+	0.155390i
$946$	68.8978	−	19.9352i	2.24006	−	0.648148i
$947$	6.84809	−	14.2202i	0.222533	−	0.462094i	−0.759573	−	0.650422i	$-0.774592\pi$
$947$	6.84809	−	14.2202i	0.222533	−	0.462094i	0.982106	+	0.188327i	$0.0603066\pi$
$948$	2.60522	+	4.12503i	0.0846136	+	0.133975i
$949$	−0.408509			−0.0132608
$950$	−5.09659	−	3.60739i	−0.165355	−	0.117039i
$951$	−6.40582	−	28.0658i	−0.207723	−	0.910094i
$952$	10.6812	+	3.37080i	0.346181	+	0.109248i
$953$	6.77201	−	29.6701i	0.219367	−	0.961109i	−0.738580	−	0.674165i	$-0.764504\pi$
$953$	6.77201	−	29.6701i	0.219367	−	0.961109i	0.957947	−	0.286944i	$-0.0926394\pi$
$954$	−0.126182	+	0.113025i	−0.00408529	+	0.00365932i
$955$	13.1138	−	16.4442i	0.424354	−	0.532123i
$956$	12.1565	−	34.9998i	0.393168	−	1.13198i
$957$	−10.1712	−	2.32150i	−0.328787	−	0.0750434i
$958$	−9.08546	+	8.13813i	−0.293538	+	0.262931i
$959$	−17.0613	+	7.62217i	−0.550939	+	0.246133i
$960$	−15.3865	−	5.26479i	−0.496598	−	0.169920i
$961$	20.5105			0.661629
$962$	10.2070	−	14.4206i	0.329087	−	0.464940i
$963$	−3.04062	+	0.694001i	−0.0979825	+	0.0223639i
$964$	−25.9778	−	2.86635i	−0.836690	−	0.0923189i
$965$	27.7810	+	22.1546i	0.894303	+	0.713183i
$966$	20.9796	+	9.37385i	0.675008	+	0.301599i
$967$	44.3017	−	35.3294i	1.42465	−	1.13612i	0.455323	−	0.890326i	$-0.349524\pi$
$967$	44.3017	−	35.3294i	1.42465	−	1.13612i	0.969323	−	0.245791i	$-0.0790478\pi$
$968$	−13.9067	−	0.732737i	−0.446978	−	0.0235511i
$969$	5.95398	−	4.74814i	0.191269	−	0.152532i
$970$	−19.8837	−	35.8790i	−0.638427	−	1.15201i
$971$	−35.1852	+	44.1208i	−1.12915	+	1.41590i	−0.232814	+	0.972521i	$0.574793\pi$
$971$	−35.1852	+	44.1208i	−1.12915	+	1.41590i	−0.896332	+	0.443383i	$0.853778\pi$
$972$	−1.41747	−	1.41095i	−0.0454654	−	0.0452562i
$973$	−7.29099	+	28.1949i	−0.233738	+	0.903888i
$974$	31.7863	−	17.6155i	1.01850	−	0.564438i
$975$	0.703520	+	1.46087i	0.0225307	+	0.0467854i
$976$	−19.6340	+	9.56706i	−0.628470	+	0.306234i
$977$	−41.5636	+	20.0160i	−1.32974	+	0.640368i	−0.957678	−	0.287841i	$-0.907063\pi$
$977$	−41.5636	+	20.0160i	−1.32974	+	0.640368i	−0.372060	+	0.928209i	$0.621348\pi$
$978$	30.4347	−	1.74438i	0.973194	−	0.0557791i
$979$	−35.3546			−1.12994
$980$	21.1993	−	18.9871i	0.677186	−	0.606520i
$981$	14.2544			0.455107
$982$	53.7349	−	3.07984i	1.71475	−	0.0982818i
$983$	31.3657	−	15.1049i	1.00041	−	0.481772i	0.139332	−	0.990246i	$-0.455505\pi$
$983$	31.3657	−	15.1049i	1.00041	−	0.481772i	0.861077	+	0.508474i	$0.169790\pi$
$984$	−13.5177	+	24.6595i	−0.430928	+	0.786116i
$985$	1.73142	+	3.59533i	0.0551676	+	0.114557i
$986$	−4.84036	+	2.68246i	−0.154148	+	0.0854270i
$987$	−24.3745	+	10.8893i	−0.775848	+	0.346611i
$988$	13.4142	−	13.4762i	0.426761	−	0.428734i
$989$	48.6649	−	61.0239i	1.54746	−	1.94045i
$990$	−5.56065	−	10.0339i	−0.176729	−	0.318898i
$991$	−31.6182	+	25.2146i	−1.00438	+	0.800970i	−0.980053	−	0.198734i	$-0.936317\pi$
$991$	−31.6182	+	25.2146i	−1.00438	+	0.800970i	−0.0243307	+	0.999704i	$0.507745\pi$
$992$	11.4642	+	38.9475i	0.363988	+	1.23658i
$993$	9.65209	−	7.69728i	0.306300	−	0.244266i
$994$	−25.4255	−	30.0761i	−0.806449	−	0.953956i
$995$	31.6035	+	25.2030i	1.00190	+	0.798988i
$996$	1.51009	−	13.6860i	0.0478492	−	0.433659i
$997$	−30.6498	+	6.99562i	−0.970690	+	0.221554i	−0.678332	−	0.734756i	$-0.737297\pi$
$997$	−30.6498	+	6.99562i	−0.970690	+	0.221554i	−0.292358	+	0.956309i	$0.594440\pi$
$998$	11.5266	−	16.2850i	0.364868	−	0.515491i
$999$	6.68586			0.211531

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.x.a.139.15	yes	168
4.3	odd	2		588.2.x.b.139.26	yes	168
49.6	odd	14		588.2.x.b.55.26	yes	168
196.55	even	14	inner	588.2.x.a.55.15	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.x.a.55.15	✓	168	196.55	even	14	inner
588.2.x.a.139.15	yes	168	1.1	even	1	trivial
588.2.x.b.55.26	yes	168	49.6	odd	14
588.2.x.b.139.26	yes	168	4.3	odd	2

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.x (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0809236 + 1.41190i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(-1.98690 + 0.228511i) q^{4} +(-0.881995 - 1.83148i) q^{5} +(-0.685509 - 1.23696i) q^{6} +(-1.70818 + 2.02043i) q^{7} +(-0.483422 - 2.78681i) q^{8} +(0.623490 - 0.781831i) q^{9} +O(q^{10})\)	\(q+(0.0809236 + 1.41190i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(-1.98690 + 0.228511i) q^{4} +(-0.881995 - 1.83148i) q^{5} +(-0.685509 - 1.23696i) q^{6} +(-1.70818 + 2.02043i) q^{7} +(-0.483422 - 2.78681i) q^{8} +(0.623490 - 0.781831i) q^{9} +(2.51449 - 1.39349i) q^{10} +(3.11985 - 2.48800i) q^{11} +(1.69099 - 1.06797i) q^{12} +(1.46088 - 1.16501i) q^{13} +(-2.99087 - 2.24827i) q^{14} +(1.58930 + 1.26742i) q^{15} +(3.89557 - 0.908060i) q^{16} +(1.45920 - 0.333054i) q^{17} +(1.15432 + 0.817034i) q^{18} -5.08805 q^{19} +(2.17095 + 3.43743i) q^{20} +(0.662382 - 2.56149i) q^{21} +(3.76526 + 4.20357i) q^{22} +(5.98730 + 1.36656i) q^{23} +(1.64470 + 2.30108i) q^{24} +(0.541042 - 0.678446i) q^{25} +(1.76310 + 1.96833i) q^{26} +(-0.222521 + 0.974928i) q^{27} +(2.93229 - 4.40473i) q^{28} +(0.581766 + 2.54888i) q^{29} +(-1.66086 + 2.34649i) q^{30} +7.17708 q^{31} +(1.59733 + 5.42665i) q^{32} +(-1.73139 + 3.59526i) q^{33} +(0.588321 + 2.03329i) q^{34} +(5.20698 + 1.34648i) q^{35} +(-1.06016 + 1.69590i) q^{36} +(-1.48774 - 6.51823i) q^{37} +(-0.411743 - 7.18380i) q^{38} +(-0.810727 + 1.68349i) q^{39} +(-4.67761 + 3.34333i) q^{40} +(4.31387 + 8.95784i) q^{41} +(3.67017 + 0.727930i) q^{42} +(5.51444 - 11.4509i) q^{43} +(-5.63030 + 5.65633i) q^{44} +(-1.98182 - 0.452338i) q^{45} +(-1.44493 + 8.56403i) q^{46} +(-6.29117 - 7.88888i) q^{47} +(-3.11579 + 2.50836i) q^{48} +(-1.16427 - 6.90250i) q^{49} +(1.00168 + 0.708994i) q^{50} +(-1.17019 + 0.933196i) q^{51} +(-2.63641 + 2.64859i) q^{52} +(-0.0266545 + 0.116781i) q^{53} +(-1.39450 - 0.235282i) q^{54} +(-7.30841 - 3.51954i) q^{55} +(6.45632 + 3.78364i) q^{56} +(4.58417 - 2.20762i) q^{57} +(-3.55168 + 1.02766i) q^{58} +(4.65159 + 2.24009i) q^{59} +(-3.44740 - 2.15507i) q^{60} +(-5.32332 + 1.21501i) q^{61} +(0.580795 + 10.1333i) q^{62} +(0.514604 + 2.59522i) q^{63} +(-7.53261 + 2.69441i) q^{64} +(-3.42218 - 1.64804i) q^{65} +(-5.21624 - 2.15360i) q^{66} -7.66604i q^{67} +(-2.82319 + 0.995190i) q^{68} +(-5.98730 + 1.36656i) q^{69} +(-1.47973 + 7.46068i) q^{70} +(10.2617 + 2.34216i) q^{71} +(-2.48022 - 1.35959i) q^{72} +(-0.170928 - 0.136311i) q^{73} +(9.08267 - 2.62802i) q^{74} +(-0.193096 + 0.846008i) q^{75} +(10.1095 - 1.16268i) q^{76} +(-0.302432 + 10.5534i) q^{77} +(-2.44252 - 1.00843i) q^{78} +2.43942i q^{79} +(-5.09896 - 6.33375i) q^{80} +(-0.222521 - 0.974928i) q^{81} +(-12.2984 + 6.81564i) q^{82} +(4.29245 - 5.38256i) q^{83} +(-0.730759 + 5.24080i) q^{84} +(-1.89699 - 2.37875i) q^{85} +(16.6137 + 6.85918i) q^{86} +(-1.63007 - 2.04405i) q^{87} +(-8.44177 - 7.49167i) q^{88} +(-6.92689 - 5.52401i) q^{89} +(0.478279 - 2.83473i) q^{90} +(-0.141615 + 4.94165i) q^{91} +(-12.2085 - 1.34706i) q^{92} +(-6.46633 + 3.11402i) q^{93} +(10.6292 - 9.52088i) q^{94} +(4.48763 + 9.31866i) q^{95} +(-3.79368 - 4.19619i) q^{96} -14.2689i q^{97} +(9.65140 - 2.20240i) q^{98} -3.99044i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) \) 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9} + 20 q^{10} - 12 q^{14} + 36 q^{16} + 12 q^{19} - 25 q^{20} + 2 q^{21} - 6 q^{22} - 15 q^{24} + 32 q^{25} + 6 q^{26} - 28 q^{27} - 66 q^{28} - 8 q^{30} - 4 q^{31} + 25 q^{32} - 68 q^{34} - 12 q^{35} - 10 q^{37} + 35 q^{38} + 14 q^{39} + 16 q^{40} + 9 q^{42} + 20 q^{44} - 28 q^{46} - 8 q^{47} + 8 q^{48} - 8 q^{49} + 114 q^{50} + 20 q^{52} - 8 q^{53} - q^{56} + 12 q^{57} - 6 q^{58} + 20 q^{59} + 10 q^{60} - 14 q^{61} - 16 q^{62} - 12 q^{63} + 42 q^{64} - 8 q^{65} - 6 q^{66} - 16 q^{68} + 59 q^{70} + 28 q^{71} - 15 q^{72} + 22 q^{74} + 18 q^{75} + 7 q^{76} + 8 q^{77} + 6 q^{78} + 26 q^{80} - 28 q^{81} + 12 q^{82} + 10 q^{83} + 11 q^{84} - 24 q^{85} - 6 q^{86} - 242 q^{88} + 20 q^{90} - 16 q^{91} + 7 q^{92} - 4 q^{93} - 53 q^{94} - 10 q^{96} - 118 q^{98}+O(q^{100}) \) 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9 + 20 * q^10 - 12 * q^14 + 36 * q^16 + 12 * q^19 - 25 * q^20 + 2 * q^21 - 6 * q^22 - 15 * q^24 + 32 * q^25 + 6 * q^26 - 28 * q^27 - 66 * q^28 - 8 * q^30 - 4 * q^31 + 25 * q^32 - 68 * q^34 - 12 * q^35 - 10 * q^37 + 35 * q^38 + 14 * q^39 + 16 * q^40 + 9 * q^42 + 20 * q^44 - 28 * q^46 - 8 * q^47 + 8 * q^48 - 8 * q^49 + 114 * q^50 + 20 * q^52 - 8 * q^53 - q^56 + 12 * q^57 - 6 * q^58 + 20 * q^59 + 10 * q^60 - 14 * q^61 - 16 * q^62 - 12 * q^63 + 42 * q^64 - 8 * q^65 - 6 * q^66 - 16 * q^68 + 59 * q^70 + 28 * q^71 - 15 * q^72 + 22 * q^74 + 18 * q^75 + 7 * q^76 + 8 * q^77 + 6 * q^78 + 26 * q^80 - 28 * q^81 + 12 * q^82 + 10 * q^83 + 11 * q^84 - 24 * q^85 - 6 * q^86 - 242 * q^88 + 20 * q^90 - 16 * q^91 + 7 * q^92 - 4 * q^93 - 53 * q^94 - 10 * q^96 - 118 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more