LMFDB - Embedded newform 483.2.q.c.463.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 40 x^{18} - 117 x^{17} + 295 x^{16} - 575 x^{15} + 1777 x^{14} - 1560 x^{13} + \cdots + 2374681 $ x^20 - 8x^19 + 40x^18 - 117x^17 + 295x^16 - 575x^15 + 1777x^14 - 1560x^13 + 4383x^12 - 6446x^11 + 7261x^10 + 7700x^9 + 7852x^8 - 39430x^7 - 101709x^6 + 156742x^5 + 999838x^4 + 2029154x^3 + 3616480x^2 + 4299390*x + 2374681
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			463.1
Root			$0.216617 - 1.50661i$ of defining polynomial
Character	$\chi$	$=$	483.463
Dual form			483.2.q.c.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.186393 + 1.29639i) q^{2} +(0.415415 - 0.909632i) q^{3} +(0.273100 - 0.0801894i) q^{4} +(-0.810370 + 0.935217i) q^{5} +(1.25667 + 0.368991i) q^{6} +(0.841254 - 0.540641i) q^{7} +(1.24302 + 2.72183i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-1.36345 - 0.876238i) q^{10} +(-0.722222 + 5.02317i) q^{11} +(0.0405070 - 0.281733i) q^{12} +(-1.31805 - 0.847057i) q^{13} +(0.857685 + 0.989821i) q^{14} +(0.514063 + 1.12564i) q^{15} +(-2.81797 + 1.81100i) q^{16} +(5.77863 + 1.69676i) q^{17} +(0.857685 - 0.989821i) q^{18} +(5.51952 - 1.62068i) q^{19} +(-0.146318 + 0.320391i) q^{20} +(-0.142315 - 0.989821i) q^{21} -6.64660 q^{22} +(2.46012 - 4.11677i) q^{23} +2.99223 q^{24} +(0.493643 + 3.43336i) q^{25} +(0.852443 - 1.86659i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(0.186393 - 0.215109i) q^{28} +(-4.19162 - 1.23077i) q^{29} +(-1.36345 + 0.876238i) q^{30} +(1.03303 + 2.26202i) q^{31} +(1.04598 + 1.20712i) q^{32} +(4.26921 + 2.74365i) q^{33} +(-1.12257 + 7.80763i) q^{34} +(-0.176110 + 1.22487i) q^{35} +(-0.239446 - 0.153882i) q^{36} +(-5.56318 - 6.42026i) q^{37} +(3.12983 + 6.85337i) q^{38} +(-1.31805 + 0.847057i) q^{39} +(-3.55280 - 1.04320i) q^{40} +(3.91794 - 4.52155i) q^{41} +(1.25667 - 0.368991i) q^{42} +(-0.842640 + 1.84512i) q^{43} +(0.205566 + 1.42974i) q^{44} +1.23747 q^{45} +(5.79549 + 2.42195i) q^{46} -2.38197 q^{47} +(0.476716 + 3.31563i) q^{48} +(0.415415 - 0.909632i) q^{49} +(-4.35897 + 1.27991i) q^{50} +(3.94396 - 4.55157i) q^{51} +(-0.427884 - 0.125638i) q^{52} +(-5.44615 + 3.50003i) q^{53} +(-0.544078 - 1.19136i) q^{54} +(-4.11248 - 4.74606i) q^{55} +(2.51722 + 1.61772i) q^{56} +(0.818672 - 5.69399i) q^{57} +(0.814272 - 5.66339i) q^{58} +(-10.4019 - 6.68489i) q^{59} +(0.230655 + 0.266190i) q^{60} +(-1.36641 - 2.99203i) q^{61} +(-2.73991 + 1.76083i) q^{62} +(-0.959493 - 0.281733i) q^{63} +(-5.75714 + 6.64410i) q^{64} +(1.86029 - 0.546230i) q^{65} +(-2.76110 + 6.04596i) q^{66} +(-1.72856 - 12.0224i) q^{67} +1.71421 q^{68} +(-2.72277 - 3.94798i) q^{69} -1.62074 q^{70} +(1.16690 + 8.11596i) q^{71} +(1.24302 - 2.72183i) q^{72} +(-4.18826 + 1.22978i) q^{73} +(7.28622 - 8.40875i) q^{74} +(3.32816 + 0.977237i) q^{75} +(1.37742 - 0.885215i) q^{76} +(2.10816 + 4.61622i) q^{77} +(-1.34379 - 1.55082i) q^{78} +(-4.51918 - 2.90430i) q^{79} +(0.589921 - 4.10299i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(6.59197 + 4.23640i) q^{82} +(2.21220 + 2.55301i) q^{83} +(-0.118239 - 0.258908i) q^{84} +(-6.26967 + 4.02927i) q^{85} +(-2.54906 - 0.748472i) q^{86} +(-2.86081 + 3.30155i) q^{87} +(-14.5699 + 4.27811i) q^{88} +(2.88880 - 6.32558i) q^{89} +(0.230655 + 1.60424i) q^{90} -1.56677 q^{91} +(0.341739 - 1.32157i) q^{92} +2.48674 q^{93} +(-0.443981 - 3.08796i) q^{94} +(-2.95717 + 6.47530i) q^{95} +(1.53255 - 0.449997i) q^{96} +(11.2146 - 12.9424i) q^{97} +(1.25667 + 0.368991i) q^{98} +(4.26921 - 2.74365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9} + 9 q^{10} + 3 q^{11} + 18 q^{12} - 2 q^{13} + 18 q^{14} - q^{15} + 8 q^{16} + 8 q^{17} + 18 q^{18} + 6 q^{19} - 2 q^{20} - 2 q^{21}+ \cdots + 14 q^{99}+O(q^{100}) $ 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9 + 9 * q^10 + 3 * q^11 + 18 * q^12 - 2 * q^13 + 18 * q^14 - q^15 + 8 * q^16 + 8 * q^17 + 18 * q^18 + 6 * q^19 - 2 * q^20 - 2 * q^21 + 6 * q^22 + 11 * q^23 + 9 * q^25 + 7 * q^26 - 2 * q^27 - 4 * q^28 + 23 * q^29 + 9 * q^30 + q^31 - 28 * q^32 + 14 * q^33 - 28 * q^34 + 10 * q^35 - 4 * q^36 - 9 * q^37 + 34 * q^38 - 2 * q^39 - 15 * q^41 - 4 * q^42 - 23 * q^43 - 16 * q^44 - 12 * q^45 + 11 * q^46 - 66 * q^47 - 36 * q^48 - 2 * q^49 - 26 * q^50 - 14 * q^51 + 7 * q^52 + 9 * q^53 - 4 * q^54 - 62 * q^55 + 22 * q^56 - 27 * q^57 - 20 * q^58 + 49 * q^59 - 2 * q^60 + 46 * q^61 - 9 * q^62 - 2 * q^63 + 16 * q^64 + 11 * q^65 - 16 * q^66 + 14 * q^67 + 38 * q^68 + 11 * q^69 - 2 * q^70 + 36 * q^71 - q^73 + 4 * q^74 - 2 * q^75 + 34 * q^76 - 8 * q^77 - 15 * q^78 - 22 * q^79 + 15 * q^80 - 2 * q^81 - 30 * q^82 + 8 * q^83 - 4 * q^84 - 32 * q^85 - 68 * q^86 + q^87 - 11 * q^88 - 2 * q^89 - 2 * q^90 - 24 * q^91 + 11 * q^92 - 32 * q^93 + 33 * q^94 - 107 * q^95 + 16 * q^96 + 18 * q^97 - 4 * q^98 + 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	0.186393	+	1.29639i	0.131800	+	0.916686i	0.943207	+	0.332205i	$0.107793\pi$
$2$	0.186393	+	1.29639i	0.131800	+	0.916686i	−0.811407	+	0.584481i	$0.801298\pi$
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$	0.273100	−	0.0801894i	0.136550	−	0.0400947i
$5$	−0.810370	+	0.935217i	−0.362408	+	0.418242i	−0.907445	−	0.420171i	$-0.861970\pi$
$5$	−0.810370	+	0.935217i	−0.362408	+	0.418242i	0.545037	+	0.838412i	$0.316516\pi$
$6$	1.25667	+	0.368991i	0.513033	+	0.150640i
$7$	0.841254	−	0.540641i	0.317964	−	0.204343i
$7$	0.841254	−	0.540641i	0.317964	−	0.204343i
$8$	1.24302	+	2.72183i	0.439473	+	0.962311i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	−1.36345	−	0.876238i	−0.431162	−	0.277091i
$11$	−0.722222	+	5.02317i	−0.217758	+	1.51454i	0.528528	+	0.848916i	$0.322744\pi$
$11$	−0.722222	+	5.02317i	−0.217758	+	1.51454i	−0.746286	+	0.665625i	$0.768165\pi$
$12$	0.0405070	−	0.281733i	0.0116934	−	0.0813292i
$13$	−1.31805	−	0.847057i	−0.365560	−	0.234931i	0.344945	−	0.938623i	$-0.387897\pi$
$13$	−1.31805	−	0.847057i	−0.365560	−	0.234931i	−0.710506	+	0.703691i	$0.751534\pi$
$14$	0.857685	+	0.989821i	0.229226	+	0.264541i
$15$	0.514063	+	1.12564i	0.132731	+	0.290639i
$16$	−2.81797	+	1.81100i	−0.704492	+	0.452750i
$17$	5.77863	+	1.69676i	1.40152	+	0.411525i	0.893207	−	0.449645i	$-0.148450\pi$
$17$	5.77863	+	1.69676i	1.40152	+	0.411525i	0.508317	+	0.861170i	$0.330268\pi$
$18$	0.857685	−	0.989821i	0.202158	−	0.233303i
$19$	5.51952	−	1.62068i	1.26626	−	0.371809i	0.421442	−	0.906855i	$-0.361524\pi$
$19$	5.51952	−	1.62068i	1.26626	−	0.371809i	0.844823	+	0.535046i	$0.179706\pi$
$20$	−0.146318	+	0.320391i	−0.0327176	+	0.0716416i
$21$	−0.142315	−	0.989821i	−0.0310556	−	0.215997i
$22$	−6.64660			−1.41706
$23$	2.46012	−	4.11677i	0.512971	−	0.858406i
$23$	2.46012	−	4.11677i	0.512971	−	0.858406i
$24$	2.99223			0.610786
$25$	0.493643	+	3.43336i	0.0987287	+	0.686673i
$26$	0.852443	−	1.86659i	0.167178	−	0.366068i
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$	0.186393	−	0.215109i	0.0352249	−	0.0406517i
$29$	−4.19162	−	1.23077i	−0.778365	−	0.228548i	−0.131666	−	0.991294i	$-0.542033\pi$
$29$	−4.19162	−	1.23077i	−0.778365	−	0.228548i	−0.646699	+	0.762746i	$0.723851\pi$
$30$	−1.36345	+	0.876238i	−0.248931	+	0.159978i
$31$	1.03303	+	2.26202i	0.185538	+	0.406271i	0.979429	−	0.201789i	$-0.0646755\pi$
$31$	1.03303	+	2.26202i	0.185538	+	0.406271i	−0.793891	+	0.608060i	$0.791948\pi$
$32$	1.04598	+	1.20712i	0.184904	+	0.213391i
$33$	4.26921	+	2.74365i	0.743174	+	0.477609i
$34$	−1.12257	+	7.80763i	−0.192519	+	1.33900i
$35$	−0.176110	+	1.22487i	−0.0297681	+	0.207041i
$36$	−0.239446	−	0.153882i	−0.0399076	−	0.0256471i
$37$	−5.56318	−	6.42026i	−0.914582	−	1.05548i	−0.998259	−	0.0589905i	$-0.981212\pi$
$37$	−5.56318	−	6.42026i	−0.914582	−	1.05548i	0.0836769	−	0.996493i	$-0.473334\pi$
$38$	3.12983	+	6.85337i	0.507725	+	1.11176i
$39$	−1.31805	+	0.847057i	−0.211056	+	0.135638i
$40$	−3.55280	−	1.04320i	−0.561747	−	0.164944i
$41$	3.91794	−	4.52155i	0.611880	−	0.706147i	−0.362264	−	0.932075i	$-0.617996\pi$
$41$	3.91794	−	4.52155i	0.611880	−	0.706147i	0.974144	+	0.225929i	$0.0725416\pi$
$42$	1.25667	−	0.368991i	0.193908	−	0.0569366i
$43$	−0.842640	+	1.84512i	−0.128501	+	0.281379i	−0.962937	−	0.269727i	$-0.913067\pi$
$43$	−0.842640	+	1.84512i	−0.128501	+	0.281379i	0.834435	+	0.551106i	$0.185794\pi$
$44$	0.205566	+	1.42974i	0.0309902	+	0.215542i
$45$	1.23747			0.184471
$46$	5.79549	+	2.42195i	0.854498	+	0.357096i
$47$	−2.38197			−0.347446			−0.173723	−	0.984795i	$-0.555580\pi$
$47$	−2.38197			−0.347446			−0.173723	+	0.984795i	$0.555580\pi$
$48$	0.476716	+	3.31563i	0.0688080	+	0.478570i
$49$	0.415415	−	0.909632i	0.0593450	−	0.129947i
$50$	−4.35897	+	1.27991i	−0.616451	+	0.181006i
$51$	3.94396	−	4.55157i	0.552265	−	0.637347i
$52$	−0.427884	−	0.125638i	−0.0593368	−	0.0174229i
$53$	−5.44615	+	3.50003i	−0.748086	+	0.480766i	−0.858304	−	0.513142i	$-0.828482\pi$
$53$	−5.44615	+	3.50003i	−0.748086	+	0.480766i	0.110218	+	0.993907i	$0.464845\pi$
$54$	−0.544078	−	1.19136i	−0.0740396	−	0.162124i
$55$	−4.11248	−	4.74606i	−0.554527	−	0.639958i
$56$	2.51722	+	1.61772i	0.336378	+	0.216177i
$57$	0.818672	−	5.69399i	0.108436	−	0.754187i
$58$	0.814272	−	5.66339i	0.106919	−	0.743639i
$59$	−10.4019	−	6.68489i	−1.35421	−	0.870299i	−0.356267	−	0.934384i	$-0.615951\pi$
$59$	−10.4019	−	6.68489i	−1.35421	−	0.870299i	−0.997944	+	0.0640850i	$0.979587\pi$
$60$	0.230655	+	0.266190i	0.0297775	+	0.0343650i
$61$	−1.36641	−	2.99203i	−0.174951	−	0.383090i	0.801760	−	0.597645i	$-0.203897\pi$
$61$	−1.36641	−	2.99203i	−0.174951	−	0.383090i	−0.976712	+	0.214556i	$0.931170\pi$
$62$	−2.73991	+	1.76083i	−0.347969	+	0.223626i
$63$	−0.959493	−	0.281733i	−0.120885	−	0.0354950i
$64$	−5.75714	+	6.64410i	−0.719643	+	0.830512i
$65$	1.86029	−	0.546230i	0.230740	−	0.0677515i
$66$	−2.76110	+	6.04596i	−0.339868	+	0.744206i
$67$	−1.72856	−	12.0224i	−0.211178	−	1.46877i	−0.769232	−	0.638969i	$-0.779361\pi$
$67$	−1.72856	−	12.0224i	−0.211178	−	1.46877i	0.558055	−	0.829804i	$-0.311548\pi$
$68$	1.71421			0.207878
$69$	−2.72277	−	3.94798i	−0.327783	−	0.475280i
$70$	−1.62074			−0.193715
$71$	1.16690	+	8.11596i	0.138485	+	0.963187i	0.934005	+	0.357260i	$0.116289\pi$
$71$	1.16690	+	8.11596i	0.138485	+	0.963187i	−0.795520	+	0.605928i	$0.792802\pi$
$72$	1.24302	−	2.72183i	0.146491	−	0.320770i
$73$	−4.18826	+	1.22978i	−0.490199	+	0.143935i	−0.517485	−	0.855692i	$-0.673132\pi$
$73$	−4.18826	+	1.22978i	−0.490199	+	0.143935i	0.0272863	+	0.999628i	$0.491313\pi$
$74$	7.28622	−	8.40875i	0.847006	−	0.977497i
$75$	3.32816	+	0.977237i	0.384303	+	0.112842i
$76$	1.37742	−	0.885215i	0.158001	−	0.101541i
$77$	2.10816	+	4.61622i	0.240247	+	0.526067i
$78$	−1.34379	−	1.55082i	−0.152154	−	0.175596i
$79$	−4.51918	−	2.90430i	−0.508447	−	0.326759i	0.261140	−	0.965301i	$-0.415902\pi$
$79$	−4.51918	−	2.90430i	−0.508447	−	0.326759i	−0.769587	+	0.638542i	$0.779538\pi$
$80$	0.589921	−	4.10299i	0.0659552	−	0.458728i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	6.59197	+	4.23640i	0.727961	+	0.467832i
$83$	2.21220	+	2.55301i	0.242820	+	0.280229i	0.864058	−	0.503393i	$-0.167915\pi$
$83$	2.21220	+	2.55301i	0.242820	+	0.280229i	−0.621237	+	0.783622i	$0.713370\pi$
$84$	−0.118239	−	0.258908i	−0.0129010	−	0.0282492i
$85$	−6.26967	+	4.02927i	−0.680041	+	0.437036i
$86$	−2.54906	−	0.748472i	−0.274873	−	0.0807099i
$87$	−2.86081	+	3.30155i	−0.306711	+	0.353964i
$88$	−14.5699	+	4.27811i	−1.55316	+	0.456049i
$89$	2.88880	−	6.32558i	0.306212	−	0.670510i	−0.692491	−	0.721426i	$-0.743487\pi$
$89$	2.88880	−	6.32558i	0.306212	−	0.670510i	0.998703	+	0.0509161i	$0.0162141\pi$
$90$	0.230655	+	1.60424i	0.0243132	+	0.169102i
$91$	−1.56677			−0.164242
$92$	0.341739	−	1.32157i	0.0356288	−	0.137783i
$93$	2.48674			0.257863
$94$	−0.443981	−	3.08796i	−0.0457932	−	0.318499i
$95$	−2.95717	+	6.47530i	−0.303399	+	0.664351i
$96$	1.53255	−	0.449997i	0.156415	−	0.0459276i
$97$	11.2146	−	12.9424i	1.13867	−	1.31410i	0.195916	−	0.980621i	$-0.437232\pi$
$97$	11.2146	−	12.9424i	1.13867	−	1.31410i	0.942758	−	0.333479i	$-0.108223\pi$
$98$	1.25667	+	0.368991i	0.126943	+	0.0372737i
$99$	4.26921	−	2.74365i	0.429072	−	0.275748i
$100$	0.410134	+	0.898067i	0.0410134	+	0.0898067i
$101$	−3.26390	−	3.76674i	−0.324770	−	0.374805i	0.569761	−	0.821810i	$-0.307036\pi$
$101$	−3.26390	−	3.76674i	−0.324770	−	0.374805i	−0.894531	+	0.447006i	$0.852490\pi$
$102$	6.63574	+	4.26453i	0.657036	+	0.422251i
$103$	−0.861017	+	5.98851i	−0.0848385	+	0.590065i	0.902410	+	0.430878i	$0.141796\pi$
$103$	−0.861017	+	5.98851i	−0.0848385	+	0.590065i	−0.987249	+	0.159187i	$0.949113\pi$
$104$	0.667189	−	4.64040i	0.0654233	−	0.455029i
$105$	1.04103	+	0.669026i	0.101594	+	0.0652903i
$106$	−5.55253	−	6.40796i	−0.539309	−	0.622396i
$107$	−7.01150	−	15.3531i	−0.677828	−	1.48424i	−0.864929	−	0.501895i	$-0.832636\pi$
$107$	−7.01150	−	15.3531i	−0.677828	−	1.48424i	0.187101	−	0.982341i	$-0.440091\pi$
$108$	−0.239446	+	0.153882i	−0.0230407	+	0.0148073i
$109$	8.59687	+	2.52427i	0.823430	+	0.241781i	0.666193	−	0.745780i	$-0.267923\pi$
$109$	8.59687	+	2.52427i	0.823430	+	0.241781i	0.157238	+	0.987561i	$0.449741\pi$
$110$	5.38620	−	6.21601i	0.513554	−	0.592673i
$111$	−8.15110	+	2.39338i	−0.773668	+	0.227169i
$112$	−1.39153	+	3.04702i	−0.131487	+	0.287916i
$113$	2.43496	+	16.9355i	0.229062	+	1.59316i	0.702074	+	0.712104i	$0.252258\pi$
$113$	2.43496	+	16.9355i	0.229062	+	1.59316i	−0.473012	+	0.881056i	$0.656833\pi$
$114$	7.53422			0.705645
$115$	1.85646	+	5.63686i	0.173116	+	0.525639i
$116$	−1.24343			−0.115449
$117$	0.222974	+	1.55082i	0.0206140	+	0.143373i
$118$	6.72739	−	14.7309i	0.619307	−	1.35609i
$119$	5.77863	−	1.69676i	0.529727	−	0.155542i
$120$	−2.42481	+	2.79838i	−0.221354	+	0.255456i
$121$	−14.1562	−	4.15662i	−1.28692	−	0.377875i
$122$	3.62415	−	2.32910i	0.328115	−	0.210867i
$123$	−2.48537	−	5.44220i	−0.224098	−	0.490707i
$124$	0.463511	+	0.534920i	0.0416245	+	0.0480372i
$125$	−8.81610	−	5.66576i	−0.788536	−	0.506761i
$126$	0.186393	−	1.29639i	0.0166052	−	0.115492i
$127$	0.941452	−	6.54794i	0.0835404	−	0.581036i	−0.904457	−	0.426565i	$-0.859724\pi$
$127$	0.941452	−	6.54794i	0.0835404	−	0.581036i	0.987997	−	0.154471i	$-0.0493673\pi$
$128$	−6.99906	−	4.49802i	−0.618635	−	0.397573i
$129$	1.32834	+	1.53298i	0.116954	+	0.134972i
$130$	1.05487	+	2.30985i	0.0925183	+	0.202587i
$131$	2.84475	−	1.82821i	0.248547	−	0.159731i	−0.410436	−	0.911890i	$-0.634623\pi$
$131$	2.84475	−	1.82821i	0.248547	−	0.159731i	0.658983	+	0.752158i	$0.270987\pi$
$132$	1.38593	+	0.406947i	0.120630	+	0.0354202i
$133$	3.76711	−	4.34748i	0.326650	−	0.376974i
$134$	15.2636	−	4.48179i	1.31857	−	0.387168i
$135$	0.514063	−	1.12564i	0.0442435	−	0.0968798i
$136$	2.56465	+	17.8375i	0.219917	+	1.52956i
$137$	13.7505			1.17478			0.587392	−	0.809302i	$-0.300155\pi$
$137$	13.7505			1.17478			0.587392	+	0.809302i	$0.300155\pi$
$138$	4.61061	−	4.26565i	0.392481	−	0.363116i
$139$	3.33313			0.282712			0.141356	−	0.989959i	$-0.454854\pi$
$139$	3.33313			0.282712			0.141356	+	0.989959i	$0.454854\pi$
$140$	0.0501262	+	0.348635i	0.00423644	+	0.0294651i
$141$	−0.989505	+	2.16671i	−0.0833313	+	0.182470i
$142$	−10.3040	+	3.02551i	−0.864688	+	0.253895i
$143$	5.20683	−	6.00900i	0.435417	−	0.502498i
$144$	3.21404	+	0.943727i	0.267837	+	0.0786439i
$145$	4.54780	−	2.92270i	0.377674	−	0.242717i
$146$	−2.37494	−	5.20039i	−0.196551	−	0.430388i
$147$	−0.654861	−	0.755750i	−0.0540120	−	0.0623332i
$148$	−2.03414	−	1.30726i	−0.167206	−	0.107456i
$149$	2.40658	−	16.7381i	0.197154	−	1.37124i	−0.615337	−	0.788265i	$-0.710980\pi$
$149$	2.40658	−	16.7381i	0.197154	−	1.37124i	0.812491	−	0.582974i	$-0.198111\pi$
$150$	−0.646535	+	4.49675i	−0.0527894	+	0.367158i
$151$	−10.3876	−	6.67573i	−0.845334	−	0.543263i	0.0447823	−	0.998997i	$-0.485741\pi$
$151$	−10.3876	−	6.67573i	−0.845334	−	0.543263i	−0.890116	+	0.455734i	$0.849377\pi$
$152$	11.2721	+	13.0086i	0.914285	+	1.05514i
$153$	−2.50188	−	5.47834i	−0.202265	−	0.442898i
$154$	−5.59148	+	3.59342i	−0.450574	+	0.289566i
$155$	−2.95261	−	0.866966i	−0.237160	−	0.0696364i
$156$	−0.292034	+	0.337025i	−0.0233814	+	0.0269836i
$157$	19.5221	−	5.73221i	1.55803	−	0.457480i	0.614545	−	0.788882i	$-0.289340\pi$
$157$	19.5221	−	5.73221i	1.55803	−	0.457480i	0.943490	+	0.331402i	$0.107522\pi$
$158$	2.92276	−	6.39996i	0.232522	−	0.509153i
$159$	0.921325	+	6.40796i	0.0730658	+	0.508184i
$160$	−1.97655			−0.156260
$161$	−0.156105	−	4.79329i	−0.0123028	−	0.377764i
$162$	−1.30972			−0.102901
$163$	1.11633	+	7.76423i	0.0874376	+	0.608142i	0.985678	+	0.168638i	$0.0539367\pi$
$163$	1.11633	+	7.76423i	0.0874376	+	0.608142i	−0.898241	+	0.439504i	$0.855154\pi$
$164$	0.707410	−	1.54901i	0.0552395	−	0.120958i
$165$	−6.02555	+	1.76926i	−0.469089	+	0.137737i
$166$	−2.89736	+	3.34373i	−0.224879	+	0.259524i
$167$	−1.92671	−	0.565732i	−0.149093	−	0.0437777i	0.206334	−	0.978482i	$-0.433847\pi$
$167$	−1.92671	−	0.565732i	−0.149093	−	0.0437777i	−0.355427	+	0.934704i	$0.615665\pi$
$168$	2.51722	−	1.61772i	0.194208	−	0.124810i
$169$	−4.38065	−	9.59229i	−0.336973	−	0.737869i
$170$	−6.39213	−	7.37691i	−0.490254	−	0.565783i
$171$	−4.83934	−	3.11006i	−0.370074	−	0.237832i
$172$	−0.0821656	+	0.571475i	−0.00626507	+	0.0435745i
$173$	0.342875	−	2.38475i	0.0260683	−	0.181309i	−0.972627	−	0.232371i	$-0.925352\pi$
$173$	0.342875	−	2.38475i	0.0260683	−	0.181309i	0.998695	+	0.0510621i	$0.0162607\pi$
$174$	−4.81334	−	3.09334i	−0.364898	−	0.234506i
$175$	2.27150	+	2.62145i	0.171709	+	0.198163i
$176$	−7.06175	−	15.4631i	−0.532299	−	1.16557i
$177$	−10.4019	+	6.68489i	−0.781855	+	0.502467i
$178$	8.73887	+	2.56596i	0.655006	+	0.192327i
$179$	−16.8898	+	19.4919i	−1.26240	+	1.45689i	−0.429892	+	0.902880i	$0.641448\pi$
$179$	−16.8898	+	19.4919i	−1.26240	+	1.45689i	−0.832510	+	0.554010i	$0.813097\pi$
$180$	0.337953	−	0.0992320i	0.0251895	−	0.00739631i
$181$	4.56559	−	9.99726i	0.339358	−	0.743090i	−0.660613	−	0.750727i	$-0.729704\pi$
$181$	4.56559	−	9.99726i	0.339358	−	0.743090i	0.999971	+	0.00763653i	$0.00243081\pi$
$182$	−0.292034	−	2.03114i	−0.0216470	−	0.150558i
$183$	−3.28927			−0.243150
$184$	14.2631	+	1.57882i	1.05149	+	0.116392i
$185$	10.5126			0.772899
$186$	0.463511	+	3.22379i	0.0339863	+	0.236380i
$187$	−12.6966	+	27.8016i	−0.928465	+	2.03305i
$188$	−0.650516	+	0.191009i	−0.0474437	+	0.0139307i
$189$	−0.654861	+	0.755750i	−0.0476341	+	0.0549727i
$190$	−8.94571	−	2.62670i	−0.648990	−	0.190561i
$191$	−9.28500	+	5.96711i	−0.671839	+	0.431765i	−0.831588	−	0.555393i	$-0.812568\pi$
$191$	−9.28500	+	5.96711i	−0.671839	+	0.431765i	0.159749	+	0.987158i	$0.448931\pi$
$192$	3.65208	+	7.99694i	0.263566	+	0.577130i
$193$	12.4297	+	14.3446i	0.894706	+	1.03255i	0.999277	+	0.0380285i	$0.0121078\pi$
$193$	12.4297	+	14.3446i	0.894706	+	1.03255i	−0.104570	+	0.994517i	$0.533347\pi$
$194$	18.8687	+	12.1262i	1.35469	+	0.870609i
$195$	0.275923	−	1.91909i	0.0197593	−	0.137429i
$196$	0.0405070	−	0.281733i	0.00289336	−	0.0201238i
$197$	10.7634	+	6.91721i	0.766859	+	0.492830i	0.864649	−	0.502377i	$-0.167541\pi$
$197$	10.7634	+	6.91721i	0.766859	+	0.492830i	−0.0977897	+	0.995207i	$0.531177\pi$
$198$	4.35260	+	5.02317i	0.309326	+	0.356981i
$199$	−0.519802	−	1.13821i	−0.0368478	−	0.0806854i	0.890313	−	0.455349i	$-0.150486\pi$
$199$	−0.519802	−	1.13821i	−0.0368478	−	0.0806854i	−0.927161	+	0.374664i	$0.877758\pi$
$200$	−8.73142	+	5.61134i	−0.617404	+	0.396782i
$201$	−11.6541	−	3.42194i	−0.822014	−	0.241365i
$202$	4.27480	−	4.93338i	0.300774	−	0.347111i
$203$	−4.19162	+	1.23077i	−0.294194	+	0.0863832i
$204$	0.712108	−	1.55930i	0.0498575	−	0.109173i
$205$	1.05364	+	7.32825i	0.0735896	+	0.511827i
$206$	−7.92393			−0.552086
$207$	−4.72229	+	0.836672i	−0.328222	+	0.0581528i
$208$	5.24824			0.363900
$209$	4.15461	+	28.8960i	0.287380	+	1.99877i
$210$	−0.673280	+	1.47428i	−0.0464607	+	0.101735i
$211$	−2.23052	+	0.654941i	−0.153556	+	0.0450880i	−0.357607	−	0.933872i	$-0.616407\pi$
$211$	−2.23052	+	0.654941i	−0.153556	+	0.0450880i	0.204051	+	0.978960i	$0.434589\pi$
$212$	−1.20668	+	1.39258i	−0.0828751	+	0.0956429i
$213$	7.86728	+	2.31004i	0.539057	+	0.158282i
$214$	18.5967	−	11.9513i	1.27124	−	0.816977i
$215$	−1.04274	−	2.28328i	−0.0711143	−	0.155719i
$216$	−1.95949	−	2.26138i	−0.133327	−	0.153867i
$217$	2.09198	+	1.34443i	0.142013	+	0.0912661i
$218$	−1.67004	+	11.6154i	−0.113110	+	0.786694i
$219$	−0.621215	+	4.32064i	−0.0419778	+	0.291962i
$220$	−1.50370	−	0.966371i	−0.101380	−	0.0651527i
$221$	−6.17926	−	7.13124i	−0.415662	−	0.479699i
$222$	−4.62206	−	10.1209i	−0.310212	−	0.679270i
$223$	−16.7091	+	10.7383i	−1.11893	+	0.719090i	−0.963220	−	0.268713i	$-0.913402\pi$
$223$	−16.7091	+	10.7383i	−1.11893	+	0.719090i	−0.155706	+	0.987803i	$0.549765\pi$
$224$	1.53255	+	0.449997i	0.102398	+	0.0300667i
$225$	2.27150	−	2.62145i	0.151433	−	0.174763i
$226$	−21.5012	+	6.31332i	−1.43024	+	0.419956i
$227$	6.45719	−	14.1393i	0.428579	−	0.938457i	−0.564976	−	0.825107i	$-0.691115\pi$
$227$	6.45719	−	14.1393i	0.428579	−	0.938457i	0.993555	−	0.113350i	$-0.0361581\pi$
$228$	−0.233018	−	1.62068i	−0.0154320	−	0.107332i
$229$	−4.10506			−0.271270			−0.135635	−	0.990759i	$-0.543307\pi$
$229$	−4.10506			−0.271270			−0.135635	+	0.990759i	$0.543307\pi$
$230$	−6.96153	+	3.45737i	−0.459030	+	0.227972i
$231$	5.07482			0.333899
$232$	−1.86031	−	12.9387i	−0.122135	−	0.849470i
$233$	−6.40472	+	14.0244i	−0.419587	+	0.918768i	0.575316	+	0.817931i	$0.304879\pi$
$233$	−6.40472	+	14.0244i	−0.419587	+	0.918768i	−0.994903	+	0.100837i	$0.967848\pi$
$234$	−1.96890	+	0.578123i	−0.128711	+	0.0377931i
$235$	1.93027	−	2.22766i	0.125917	−	0.145316i
$236$	−3.37682	−	0.991523i	−0.219812	−	0.0645427i
$237$	−4.51918	+	2.90430i	−0.293552	+	0.188654i
$238$	3.27676	+	7.17510i	0.212401	+	0.465093i
$239$	−13.6319	−	15.7321i	−0.881775	−	1.01762i	−0.999697	−	0.0245994i	$-0.992169\pi$
$239$	−13.6319	−	15.7321i	−0.881775	−	1.01762i	0.117923	−	0.993023i	$-0.462376\pi$
$240$	−3.48715	−	2.24106i	−0.225095	−	0.144659i
$241$	−3.99284	+	27.7708i	−0.257202	+	1.78888i	0.295341	+	0.955392i	$0.404567\pi$
$241$	−3.99284	+	27.7708i	−0.257202	+	1.78888i	−0.552543	+	0.833485i	$0.686342\pi$
$242$	2.75000	−	19.1267i	0.176777	−	1.22951i
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$	−0.613097	−	0.707551i	−0.0392495	−	0.0452963i
$245$	0.514063	+	1.12564i	0.0328423	+	0.0719146i
$246$	6.59197	−	4.23640i	0.420288	−	0.270103i
$247$	−8.64779	−	2.53922i	−0.550246	−	0.161567i
$248$	−4.87275	+	5.62346i	−0.309420	+	0.357090i
$249$	3.24128	−	0.951726i	0.205408	−	0.0603132i
$250$	5.70178	−	12.4852i	0.360612	−	0.789631i
$251$	0.502591	+	3.49560i	0.0317233	+	0.220640i	0.999516	−	0.0311081i	$-0.00990360\pi$
$251$	0.502591	+	3.49560i	0.0317233	+	0.220640i	−0.967793	+	0.251748i	$0.918995\pi$
$252$	−0.284630			−0.0179300
$253$	18.9025	+	15.3308i	1.18839	+	0.963841i
$254$	8.66417			0.543638
$255$	1.06064	+	7.37691i	0.0664198	+	0.461960i
$256$	−2.77755	+	6.08198i	−0.173597	+	0.380124i
$257$	−20.2053	+	5.93280i	−1.26037	+	0.370078i	−0.842632	−	0.538490i	$-0.818995\pi$
$257$	−20.2053	+	5.93280i	−1.26037	+	0.370078i	−0.417737	+	0.908568i	$0.637177\pi$
$258$	−1.73975	+	2.00778i	−0.108312	+	0.124999i
$259$	−8.15110	−	2.39338i	−0.506485	−	0.148717i
$260$	0.464243	−	0.298351i	0.0287911	−	0.0185029i
$261$	1.81477	+	3.97380i	0.112332	+	0.245972i
$262$	2.90031	+	3.34714i	0.179182	+	0.206787i
$263$	20.8890	+	13.4245i	1.28807	+	0.827793i	0.991860	−	0.127329i	$-0.0406405\pi$
$263$	20.8890	+	13.4245i	1.28807	+	0.827793i	0.296211	+	0.955123i	$0.404277\pi$
$264$	−2.16105	+	15.0305i	−0.133004	+	0.925061i
$265$	1.14011	−	7.92965i	0.0700365	−	0.487115i
$266$	6.33819	+	4.07331i	0.388619	+	0.249751i
$267$	−4.55390	−	5.25548i	−0.278694	−	0.321630i
$268$	−1.43614	−	3.14471i	−0.0877264	−	0.192094i
$269$	−21.5571	+	13.8539i	−1.31436	+	0.844687i	−0.994697	−	0.102844i	$-0.967206\pi$
$269$	−21.5571	+	13.8539i	−1.31436	+	0.844687i	−0.319662	+	0.947532i	$0.603569\pi$
$270$	1.55509	+	0.456615i	0.0946397	+	0.0277887i
$271$	2.53472	−	2.92523i	0.153973	−	0.177695i	−0.673522	−	0.739167i	$-0.735219\pi$
$271$	2.53472	−	2.92523i	0.153973	−	0.177695i	0.827496	+	0.561472i	$0.189765\pi$
$272$	−19.3568	+	5.68368i	−1.17368	+	0.344624i
$273$	−0.650858	+	1.42518i	−0.0393917	+	0.0862558i
$274$	2.56299	+	17.8260i	0.154836	+	1.07691i
$275$	−17.6029			−1.06149
$276$	−1.06018	−	0.859855i	−0.0638151	−	0.0517572i
$277$	22.2525			1.33702			0.668512	−	0.743701i	$-0.266931\pi$
$277$	22.2525			1.33702			0.668512	+	0.743701i	$0.266931\pi$
$278$	0.621271	+	4.32103i	0.0372614	+	0.259158i
$279$	1.03303	−	2.26202i	0.0618459	−	0.135424i
$280$	−3.55280	+	1.04320i	−0.212320	+	0.0623429i
$281$	−5.21094	+	6.01375i	−0.310859	+	0.358750i	−0.889583	−	0.456773i	$-0.849005\pi$
$281$	−5.21094	+	6.01375i	−0.310859	+	0.358750i	0.578725	+	0.815523i	$0.303551\pi$
$282$	−2.99334	−	0.878925i	−0.178251	−	0.0523392i
$283$	18.1352	−	11.6548i	1.07803	−	0.692807i	0.123927	−	0.992291i	$-0.460451\pi$
$283$	18.1352	−	11.6548i	1.07803	−	0.692807i	0.954101	+	0.299485i	$0.0968148\pi$
$284$	0.969495	+	2.12290i	0.0575289	+	0.125971i
$285$	4.66168	+	5.37987i	0.276134	+	0.318676i
$286$	8.76053	+	5.63005i	0.518021	+	0.332912i
$287$	0.851450	−	5.92197i	0.0502595	−	0.349563i
$288$	0.227312	−	1.58099i	0.0133945	−	0.0931608i
$289$	16.2123	+	10.4190i	0.953665	+	0.612884i
$290$	4.63663	+	5.35096i	0.272272	+	0.314219i
$291$	−7.11408	−	15.5777i	−0.417034	−	0.913178i
$292$	−1.04520	+	0.671708i	−0.0611656	+	0.0393087i
$293$	−27.7947	−	8.16126i	−1.62378	−	0.476786i	−0.661752	−	0.749723i	$-0.730187\pi$
$293$	−27.7947	−	8.16126i	−1.62378	−	0.476786i	−0.962032	+	0.272937i	$0.912005\pi$
$294$	0.857685	−	0.989821i	0.0500212	−	0.0577276i
$295$	14.6812	−	4.31079i	0.854773	−	0.250984i
$296$	10.5597	−	23.1225i	0.613770	−	1.34397i
$297$	−0.722222	−	5.02317i	−0.0419076	−	0.291474i
$298$	22.1477			1.28298
$299$	−6.72970	+	3.34223i	−0.389189	+	0.193286i
$300$	0.987287			0.0570010
$301$	0.288676	+	2.00778i	0.0166390	+	0.115727i
$302$	6.71817	−	14.7107i	0.386587	−	0.846508i
$303$	−4.78222	+	1.40419i	−0.274731	+	0.0806684i
$304$	−12.6188	+	14.5629i	−0.723738	+	0.835238i
$305$	3.90549	+	1.14676i	0.223628	+	0.0656631i
$306$	6.63574	−	4.26453i	0.379340	−	0.243787i
$307$	−5.49019	−	12.0218i	−0.313342	−	0.686123i	0.685789	−	0.727800i	$-0.259457\pi$
$307$	−5.49019	−	12.0218i	−0.313342	−	0.686123i	−0.999131	+	0.0416775i	$0.986730\pi$
$308$	0.945910	+	1.09164i	0.0538982	+	0.0622019i
$309$	5.08966	+	3.27092i	0.289540	+	0.186076i
$310$	0.573580	−	3.98934i	0.0325772	−	0.226579i
$311$	2.29477	−	15.9605i	0.130124	−	0.905034i	−0.815264	−	0.579089i	$-0.803408\pi$
$311$	2.29477	−	15.9605i	0.130124	−	0.905034i	0.945389	−	0.325945i	$-0.105683\pi$
$312$	−3.94390	−	2.53459i	−0.223279	−	0.143493i
$313$	4.28466	+	4.94476i	0.242183	+	0.279495i	0.863808	−	0.503820i	$-0.168073\pi$
$313$	4.28466	+	4.94476i	0.242183	+	0.279495i	−0.621625	+	0.783315i	$0.713527\pi$
$314$	11.0700	+	24.2398i	0.624714	+	1.36793i
$315$	1.04103	−	0.669026i	0.0586551	−	0.0376954i
$316$	−1.46708	−	0.430774i	−0.0825298	−	0.0242329i
$317$	10.5478	−	12.1728i	0.592424	−	0.683694i	−0.377804	−	0.925885i	$-0.623321\pi$
$317$	10.5478	−	12.1728i	0.592424	−	0.683694i	0.970228	+	0.242192i	$0.0778663\pi$
$318$	−8.13549	+	2.38879i	−0.456215	+	0.133957i
$319$	9.20965	−	20.1663i	0.515641	−	1.12910i
$320$	−1.54826	−	10.7684i	−0.0865501	−	0.601969i
$321$	−16.8783			−0.942055
$322$	6.18488	−	1.09581i	0.344670	−	0.0610670i
$323$	34.6452			1.92771
$324$	0.0405070	+	0.281733i	0.00225039	+	0.0156518i
$325$	2.25761	−	4.94348i	0.125230	−	0.274215i
$326$	−9.85740	+	2.89439i	−0.545951	+	0.160306i
$327$	5.86742	−	6.77137i	0.324469	−	0.374457i
$328$	17.1769	+	5.04360i	0.948438	+	0.278486i
$329$	−2.00384	+	1.28779i	−0.110475	+	0.0709981i
$330$	−3.41677	−	7.48169i	−0.188087	−	0.411853i
$331$	−6.68170	−	7.71110i	−0.367260	−	0.423840i	0.541799	−	0.840508i	$-0.317743\pi$
$331$	−6.68170	−	7.71110i	−0.367260	−	0.423840i	−0.909059	+	0.416668i	$0.863198\pi$
$332$	0.808876	+	0.519833i	0.0443928	+	0.0285295i
$333$	−1.20900	+	8.40875i	−0.0662525	+	0.460796i
$334$	0.374285	−	2.60321i	0.0204800	−	0.142441i
$335$	12.6444	+	8.12603i	0.690835	+	0.443973i
$336$	2.19360	+	2.53155i	0.119671	+	0.138108i
$337$	10.0645	+	22.0381i	0.548246	+	1.20049i	0.957596	+	0.288113i	$0.0930280\pi$
$337$	10.0645	+	22.0381i	0.548246	+	1.20049i	−0.409351	+	0.912377i	$0.634245\pi$
$338$	11.6188	−	7.46697i	0.631981	−	0.406150i
$339$	16.4166	+	4.82035i	0.891628	+	0.261806i
$340$	−1.38914	+	1.60316i	−0.0753368	+	0.0869434i
$341$	−12.1086	+	3.55540i	−0.655716	+	0.192536i
$342$	3.12983	−	6.85337i	0.169242	−	0.370588i
$343$	−0.142315	−	0.989821i	−0.00768428	−	0.0534453i
$344$	−6.06952			−0.327247
$345$	5.89867	+	0.652938i	0.317573	+	0.0351530i
$346$	3.15548			0.169639
$347$	0.640065	+	4.45175i	0.0343605	+	0.238983i	0.999763	−	0.0217828i	$-0.00693422\pi$
$347$	0.640065	+	4.45175i	0.0343605	+	0.238983i	−0.965402	+	0.260765i	$0.916025\pi$
$348$	−0.516538	+	1.13106i	−0.0276894	+	0.0606313i
$349$	20.2000	−	5.93127i	1.08128	−	0.317493i	0.307891	−	0.951422i	$-0.400377\pi$
$349$	20.2000	−	5.93127i	1.08128	−	0.317493i	0.773392	+	0.633928i	$0.218558\pi$
$350$	−2.97503	+	3.43336i	−0.159022	+	0.183521i
$351$	1.50330	+	0.441409i	0.0802402	+	0.0235607i
$352$	−6.81899	+	4.38230i	−0.363453	+	0.233577i
$353$	12.7699	+	27.9622i	0.679675	+	1.48828i	0.862987	+	0.505225i	$0.168591\pi$
$353$	12.7699	+	27.9622i	0.679675	+	1.48828i	−0.183313	+	0.983055i	$0.558682\pi$
$354$	−10.6051	−	12.2389i	−0.563653	−	0.650490i
$355$	−8.53580	−	5.48563i	−0.453033	−	0.291147i
$356$	0.281686	−	1.95917i	0.0149293	−	0.103836i
$357$	0.857104	−	5.96129i	0.0453628	−	0.315505i
$358$	−28.4172	−	18.2626i	−1.50190	−	0.965210i
$359$	−8.50587	−	9.81630i	−0.448923	−	0.518084i	0.485507	−	0.874233i	$-0.338635\pi$
$359$	−8.50587	−	9.81630i	−0.448923	−	0.518084i	−0.934429	+	0.356149i	$0.884090\pi$
$360$	1.53819	+	3.36818i	0.0810700	+	0.177518i
$361$	11.8547	−	7.61855i	0.623931	−	0.400976i
$362$	13.8113	+	4.05538i	0.725908	+	0.213146i
$363$	−9.66168	+	11.1502i	−0.507107	+	0.585232i
$364$	−0.427884	+	0.125638i	−0.0224272	+	0.00658522i
$365$	2.24392	−	4.91351i	0.117452	−	0.257185i
$366$	−0.613097	−	4.26418i	−0.0320471	−	0.222892i
$367$	−5.19518			−0.271186			−0.135593	−	0.990765i	$-0.543294\pi$
$367$	−5.19518			−0.271186			−0.135593	+	0.990765i	$0.543294\pi$
$368$	0.522909	+	16.0562i	0.0272585	+	0.836988i
$369$	−5.98286			−0.311455
$370$	1.95947	+	13.6284i	0.101868	+	0.708506i
$371$	−2.68934	+	5.88882i	−0.139623	+	0.305732i
$372$	0.679130	−	0.199410i	0.0352112	−	0.0103389i
$373$	−7.20454	+	8.31448i	−0.373037	+	0.430507i	−0.910965	−	0.412483i	$-0.864662\pi$
$373$	−7.20454	+	8.31448i	−0.373037	+	0.430507i	0.537928	+	0.842991i	$0.319207\pi$
$374$	−38.4083	−	11.2777i	−1.98604	−	0.583155i
$375$	−8.81610	+	5.66576i	−0.455261	+	0.292579i
$376$	−2.96082	−	6.48330i	−0.152693	−	0.334351i
$377$	4.48222	+	5.17276i	0.230846	+	0.266411i
$378$	−1.10181	−	0.708089i	−0.0566709	−	0.0364202i
$379$	3.36674	−	23.4162i	0.172938	−	1.20281i	−0.699698	−	0.714438i	$-0.746682\pi$
$379$	3.36674	−	23.4162i	0.172938	−	1.20281i	0.872636	−	0.488371i	$-0.162409\pi$
$380$	−0.288353	+	2.00554i	−0.0147922	+	0.102882i
$381$	−5.56512	−	3.57649i	−0.285110	−	0.183229i
$382$	−9.46636	−	10.9248i	−0.484341	−	0.558959i
$383$	−8.94526	−	19.5874i	−0.457081	−	1.00087i	−0.988143	−	0.153536i	$-0.950934\pi$
$383$	−8.94526	−	19.5874i	−0.457081	−	1.00087i	0.531062	−	0.847333i	$-0.321793\pi$
$384$	−6.99906	+	4.49802i	−0.357169	+	0.229539i
$385$	−6.02555	−	1.76926i	−0.307091	−	0.0901699i
$386$	−16.2794	+	18.7874i	−0.828599	+	0.956254i
$387$	1.94626	−	0.571475i	0.0989341	−	0.0290497i
$388$	2.02488	−	4.43386i	0.102798	−	0.225095i
$389$	4.91397	+	34.1774i	0.249148	+	1.73286i	0.603158	+	0.797621i	$0.293909\pi$
$389$	4.91397	+	34.1774i	0.249148	+	1.73286i	−0.354010	+	0.935242i	$0.615182\pi$
$390$	2.53932			0.128583
$391$	21.2013	−	19.6151i	1.07220	−	0.991976i
$392$	2.99223			0.151130
$393$	−0.481246	−	3.34714i	−0.0242757	−	0.168841i
$394$	−6.96118	+	15.2429i	−0.350699	+	0.767924i
$395$	6.37835	−	1.87285i	0.320930	−	0.0942335i
$396$	0.945910	−	1.09164i	0.0475338	−	0.0548569i
$397$	16.4741	+	4.83725i	0.826814	+	0.242774i	0.667648	−	0.744477i	$-0.267301\pi$
$397$	16.4741	+	4.83725i	0.826814	+	0.242774i	0.159166	+	0.987252i	$0.449119\pi$
$398$	1.37867	−	0.886021i	0.0691067	−	0.0444122i
$399$	−2.38969	−	5.23269i	−0.119634	−	0.261962i
$400$	−7.60889	−	8.78113i	−0.380445	−	0.439056i
$401$	8.84134	+	5.68199i	0.441516	+	0.283745i	0.742452	−	0.669899i	$-0.233663\pi$
$401$	8.84134	+	5.68199i	0.441516	+	0.283745i	−0.300936	+	0.953644i	$0.597299\pi$
$402$	2.26394	−	15.7460i	0.112915	−	0.785341i
$403$	0.554479	−	3.85648i	0.0276206	−	0.192105i
$404$	−1.19342	−	0.766967i	−0.0593751	−	0.0381580i
$405$	−0.810370	−	0.935217i	−0.0402676	−	0.0464713i
$406$	−2.37685	−	5.20457i	−0.117961	−	0.258299i
$407$	36.2679	−	23.3079i	1.79773	−	1.15533i
$408$	17.2910	+	5.07709i	0.856032	+	0.251354i
$409$	20.8200	−	24.0276i	1.02948	−	1.18809i	0.0475471	−	0.998869i	$-0.484860\pi$
$409$	20.8200	−	24.0276i	1.02948	−	1.18809i	0.981935	−	0.189217i	$-0.0605950\pi$
$410$	−9.30388	+	2.73187i	−0.459486	+	0.134917i
$411$	5.71216	−	12.5079i	0.281760	−	0.616969i
$412$	0.245071	+	1.70451i	0.0120738	+	0.0839750i
$413$	−12.3648			−0.608430
$414$	−1.96485	−	5.96598i	−0.0965673	−	0.293212i
$415$	−4.18032			−0.205204
$416$	−0.356145	−	2.47704i	−0.0174614	−	0.121447i
$417$	1.38463	−	3.03192i	0.0678057	−	0.148474i
$418$	−36.6860	+	10.7720i	−1.79437	+	0.526876i
$419$	−9.00481	+	10.3921i	−0.439914	+	0.507687i	−0.931800	−	0.362972i	$-0.881762\pi$
$419$	−9.00481	+	10.3921i	−0.439914	+	0.507687i	0.491886	+	0.870659i	$0.336308\pi$
$420$	0.337953	+	0.0992320i	0.0164904	+	0.00484202i
$421$	9.14507	−	5.87718i	0.445704	−	0.286436i	−0.298474	−	0.954418i	$-0.596478\pi$
$421$	9.14507	−	5.87718i	0.445704	−	0.286436i	0.744178	+	0.667981i	$0.232841\pi$
$422$	−1.26481	−	2.76955i	−0.0615701	−	0.134820i
$423$	1.55986	+	1.80017i	0.0758428	+	0.0875273i
$424$	−16.2961	−	10.4729i	−0.791410	−	0.508608i
$425$	−2.97301	+	20.6778i	−0.144212	+	1.00302i
$426$	−1.52831	+	10.6296i	−0.0740470	+	0.515008i
$427$	−2.76711	−	1.77832i	−0.133910	−	0.0860587i
$428$	−3.14600	−	3.63067i	−0.152067	−	0.175495i
$429$	−3.30299	−	7.23253i	−0.159470	−	0.349190i
$430$	2.76567	−	1.77739i	0.133372	−	0.0857132i
$431$	−7.39486	−	2.17133i	−0.356198	−	0.104589i	0.0987377	−	0.995113i	$-0.468520\pi$
$431$	−7.39486	−	2.17133i	−0.356198	−	0.104589i	−0.454935	+	0.890524i	$0.650338\pi$
$432$	2.19360	−	2.53155i	0.105540	−	0.121799i
$433$	34.7859	−	10.2141i	1.67170	−	0.490856i	0.697510	−	0.716575i	$-0.254291\pi$
$433$	34.7859	−	10.2141i	1.67170	−	0.490856i	0.974192	+	0.225719i	$0.0724731\pi$
$434$	−1.35298	+	2.96262i	−0.0649452	+	0.142210i
$435$	−0.769352	−	5.35096i	−0.0368876	−	0.256559i
$436$	2.55023			0.122134
$437$	6.90675	−	26.7097i	0.330395	−	1.27770i
$438$	−5.71703			−0.273170
$439$	5.05375	+	35.1496i	0.241202	+	1.67760i	0.646113	+	0.763242i	$0.276393\pi$
$439$	5.05375	+	35.1496i	0.241202	+	1.67760i	−0.404911	+	0.914356i	$0.632698\pi$
$440$	7.80606	−	17.0929i	0.372139	−	0.814872i
$441$	−0.959493	+	0.281733i	−0.0456901	+	0.0134158i
$442$	8.09311	−	9.33994i	0.384950	−	0.444256i
$443$	16.0351	+	4.70833i	0.761850	+	0.223699i	0.639504	−	0.768788i	$-0.279140\pi$
$443$	16.0351	+	4.70833i	0.761850	+	0.223699i	0.122347	+	0.992487i	$0.460958\pi$
$444$	−2.03414	+	1.30726i	−0.0965362	+	0.0620400i
$445$	3.57480	+	7.82771i	0.169462	+	0.371069i
$446$	−17.0355	−	19.6600i	−0.806655	−	0.930929i
$447$	−14.2258	−	9.14236i	−0.672856	−	0.432419i
$448$	−1.25115	+	8.70192i	−0.0591111	+	0.411127i
$449$	3.04200	−	21.1575i	0.143561	−	0.998486i	−0.782914	−	0.622130i	$-0.786268\pi$
$449$	3.04200	−	21.1575i	0.143561	−	0.998486i	0.926475	−	0.376357i	$-0.122823\pi$
$450$	3.82181	+	2.45613i	0.180162	+	0.115783i
$451$	19.8829	+	22.9460i	0.936247	+	1.08049i
$452$	2.02304	+	4.42984i	0.0951557	+	0.208362i
$453$	−10.3876	+	6.67573i	−0.488054	+	0.313653i
$454$	19.5336	+	5.73558i	0.916757	+	0.269184i
$455$	1.26966	−	1.46527i	0.0595226	−	0.0686927i
$456$	16.5157	−	4.84944i	0.773417	−	0.227096i
$457$	−4.45265	+	9.74994i	−0.208286	+	0.456083i	−0.984727	−	0.174108i	$-0.944296\pi$
$457$	−4.45265	+	9.74994i	−0.208286	+	0.456083i	0.776441	+	0.630191i	$0.217023\pi$
$458$	−0.765154	−	5.32177i	−0.0357533	−	0.248670i
$459$	−6.02259			−0.281111
$460$	0.959016	+	1.39056i	0.0447144	+	0.0648351i
$461$	−33.0490			−1.53924			−0.769622	−	0.638500i	$-0.779555\pi$
$461$	−33.0490			−1.53924			−0.769622	+	0.638500i	$0.779555\pi$
$462$	0.945910	+	6.57895i	0.0440077	+	0.306080i
$463$	−0.336321	+	0.736440i	−0.0156301	+	0.0342253i	−0.917286	−	0.398229i	$-0.869625\pi$
$463$	−0.336321	+	0.736440i	−0.0156301	+	0.0342253i	0.901656	+	0.432454i	$0.142352\pi$
$464$	14.0408	−	4.12275i	0.651827	−	0.191394i
$465$	−2.01518	+	2.32564i	−0.0934518	+	0.107849i
$466$	−19.3749	−	5.68898i	−0.897524	−	0.263537i
$467$	−0.800368	+	0.514365i	−0.0370366	+	0.0238020i	−0.559028	−	0.829149i	$-0.688826\pi$
$467$	−0.800368	+	0.514365i	−0.0370366	+	0.0238020i	0.521992	+	0.852951i	$0.325189\pi$
$468$	0.185253	+	0.405649i	0.00856335	+	0.0187511i
$469$	−7.95398	−	9.17938i	−0.367280	−	0.423864i
$470$	3.24770	+	2.08717i	0.149805	+	0.0962740i
$471$	2.89558	−	20.1392i	0.133421	−	0.927965i
$472$	5.26539	−	36.6216i	0.242359	−	1.68565i
$473$	−8.65979	−	5.56531i	−0.398178	−	0.255893i
$474$	−4.60745	−	5.31728i	−0.211627	−	0.244231i
$475$	8.28905	+	18.1505i	0.380328	+	0.832802i
$476$	1.44208	−	0.926771i	0.0660978	−	0.0424785i
$477$	6.21162	+	1.82389i	0.284410	+	0.0835104i
$478$	17.8540	−	20.6046i	0.816623	−	0.942433i
$479$	−9.99872	+	2.93589i	−0.456853	+	0.134144i	−0.502059	−	0.864833i	$-0.667424\pi$
$479$	−9.99872	+	2.93589i	−0.456853	+	0.134144i	0.0452055	+	0.998978i	$0.485606\pi$
$480$	−0.821087	+	1.79793i	−0.0374773	+	0.0820638i
$481$	1.89421	+	13.1745i	0.0863686	+	0.600707i
$482$	−36.7461			−1.67374
$483$	−4.42498	−	1.84921i	−0.201343	−	0.0841418i
$484$	−4.19937			−0.190880
$485$	3.01593	+	20.9762i	0.136946	+	0.952482i
$486$	−0.544078	+	1.19136i	−0.0246799	+	0.0540414i
$487$	−14.8598	+	4.36324i	−0.673364	+	0.197717i	−0.600500	−	0.799625i	$-0.705032\pi$
$487$	−14.8598	+	4.36324i	−0.673364	+	0.197717i	−0.0728634	+	0.997342i	$0.523214\pi$
$488$	6.44531	−	7.43828i	0.291765	−	0.336715i
$489$	7.52633	+	2.20993i	0.340353	+	0.0999365i
$490$	−1.36345	+	0.876238i	−0.0615945	+	0.0395844i
$491$	0.509450	+	1.11554i	0.0229911	+	0.0503436i	0.920779	−	0.390084i	$-0.127554\pi$
$491$	0.509450	+	1.11554i	0.0229911	+	0.0503436i	−0.897788	+	0.440428i	$0.854827\pi$
$492$	−1.11516	−	1.28697i	−0.0502754	−	0.0580209i
$493$	−22.1335	−	14.2244i	−0.996844	−	0.640633i
$494$	1.67994	−	11.6842i	0.0755839	−	0.525697i
$495$	−0.893728	+	6.21601i	−0.0401701	+	0.279389i
$496$	−7.00756	−	4.50349i	−0.314649	−	0.202213i
$497$	5.36948	+	6.19671i	0.240854	+	0.277960i
$498$	1.83796	+	4.02457i	0.0823609	+	0.180345i
$499$	−3.32849	+	2.13909i	−0.149004	+	0.0957588i	−0.613018	−	0.790069i	$-0.710045\pi$
$499$	−3.32849	+	2.13909i	−0.149004	+	0.0957588i	0.464015	+	0.885827i	$0.346408\pi$
$500$	−2.86201	−	0.840363i	−0.127993	−	0.0375822i
$501$	−1.31499	+	1.51758i	−0.0587495	+	0.0678005i
$502$	−4.43798	+	1.30311i	−0.198077	+	0.0581606i
$503$	−1.25095	+	2.73920i	−0.0557771	+	0.122135i	−0.935468	−	0.353410i	$-0.885022\pi$
$503$	−1.25095	+	2.73920i	−0.0557771	+	0.122135i	0.879691	+	0.475545i	$0.157749\pi$
$504$	−0.425839	−	2.96177i	−0.0189684	−	0.131928i
$505$	6.16768			0.274458
$506$	−16.3515	+	27.3625i	−0.726911	+	1.21641i
$507$	−10.5452			−0.468331
$508$	−0.267965	−	1.86374i	−0.0118890	−	0.0826900i
$509$	10.4783	−	22.9444i	0.464444	−	1.01699i	−0.522008	−	0.852941i	$-0.674817\pi$
$509$	10.4783	−	22.9444i	0.464444	−	1.01699i	0.986452	−	0.164051i	$-0.0524560\pi$
$510$	−9.36566	+	2.75001i	−0.414719	+	0.121772i
$511$	−2.85852	+	3.29890i	−0.126453	+	0.145935i
$512$	−24.3679	−	7.15506i	−1.07692	−	0.316212i
$513$	−4.83934	+	3.11006i	−0.213662	+	0.137312i
$514$	−11.4573	−	25.0881i	−0.505361	−	1.10659i
$515$	−4.90281	−	5.65814i	−0.216044	−	0.249328i
$516$	0.485699	+	0.312140i	0.0213817	+	0.0137412i
$517$	1.72031	−	11.9650i	0.0756591	−	0.526221i
$518$	1.58345	−	11.0131i	0.0695727	−	0.483889i
$519$	−2.02681	−	1.30255i	−0.0889670	−	0.0571756i
$520$	3.79911	+	4.38441i	0.166602	+	0.192269i
$521$	−9.68150	−	21.1995i	−0.424154	−	0.928768i	−0.994239	−	0.107183i	$-0.965817\pi$
$521$	−9.68150	−	21.1995i	−0.424154	−	0.928768i	0.570085	−	0.821586i	$-0.306910\pi$
$522$	−4.81334	+	3.09334i	−0.210674	+	0.135392i
$523$	−43.0007	−	12.6261i	−1.88029	−	0.552103i	−0.996437	−	0.0843350i	$-0.973123\pi$
$523$	−43.0007	−	12.6261i	−1.88029	−	0.552103i	−0.883851	−	0.467768i	$-0.845058\pi$
$524$	0.630299	−	0.727403i	0.0275347	−	0.0317768i
$525$	3.32816	−	0.977237i	0.145253	−	0.0426501i
$526$	−13.5099	+	29.5825i	−0.589059	+	1.28986i
$527$	2.13140	+	14.8242i	0.0928451	+	0.645752i
$528$	−16.9993			−0.739798
$529$	−10.8956	−	20.2555i	−0.473721	−	0.880675i
$530$	10.4924			0.455762
$531$	1.75969	+	12.2389i	0.0763640	+	0.531123i
$532$	0.680177	−	1.48938i	0.0294894	−	0.0645728i
$533$	−8.99404	+	2.64089i	−0.389575	+	0.114390i
$534$	5.96434	−	6.88322i	0.258102	−	0.297866i
$535$	20.0403	+	5.88438i	0.866420	+	0.254404i
$536$	30.5743	−	19.6489i	1.32061	−	0.848705i
$537$	10.7141	+	23.4607i	0.462350	+	1.01240i
$538$	−21.9782	−	25.3641i	−0.947545	−	1.09353i
$539$	4.26921	+	2.74365i	0.183888	+	0.118178i
$540$	0.0501262	−	0.348635i	0.00215709	−	0.0150029i
$541$	−3.08437	+	21.4522i	−0.132607	+	0.922304i	0.809531	+	0.587078i	$0.199722\pi$
$541$	−3.08437	+	21.4522i	−0.132607	+	0.922304i	−0.942138	+	0.335226i	$0.891187\pi$
$542$	4.26469	+	2.74075i	0.183184	+	0.117725i
$543$	−7.19721	−	8.30602i	−0.308862	−	0.356445i
$544$	3.99612	+	8.75027i	0.171332	+	0.375165i
$545$	−9.32738	+	5.99434i	−0.399541	+	0.256769i
$546$	−1.96890	−	0.578123i	−0.0842614	−	0.0247414i
$547$	−16.6646	+	19.2319i	−0.712525	+	0.822298i	−0.990387	−	0.138323i	$-0.955829\pi$
$547$	−16.6646	+	19.2319i	−0.712525	+	0.822298i	0.277862	+	0.960621i	$0.410374\pi$
$548$	3.75526	−	1.10264i	0.160417	−	0.0471027i
$549$	−1.36641	+	2.99203i	−0.0583171	+	0.127697i
$550$	−3.28105	−	22.8202i	−0.139904	−	0.973057i
$551$	−25.1304			−1.07059
$552$	7.36125	−	12.3183i	0.313316	−	0.524302i
$553$	−5.37195			−0.228439
$554$	4.14771	+	28.8480i	0.176219	+	1.22563i
$555$	4.36708	−	9.56257i	0.185372	−	0.405908i
$556$	0.910278	−	0.267282i	0.0386044	−	0.0113353i
$557$	−4.68482	+	5.40657i	−0.198502	+	0.229084i	−0.846270	−	0.532754i	$-0.821157\pi$
$557$	−4.68482	+	5.40657i	−0.198502	+	0.229084i	0.647768	+	0.761838i	$0.275703\pi$
$558$	3.12501	+	0.917586i	0.132292	+	0.0388445i
$559$	2.67356	−	1.71820i	0.113080	−	0.0726719i
$560$	−1.72197	−	3.77059i	−0.0727666	−	0.159337i
$561$	20.0149	+	23.0984i	0.845029	+	0.975215i
$562$	−8.76744	−	5.63449i	−0.369832	−	0.237677i
$563$	0.493281	−	3.43085i	0.0207893	−	0.144593i	−0.976783	−	0.214231i	$-0.931275\pi$
$563$	0.493281	−	3.43085i	0.0207893	−	0.144593i	0.997572	+	0.0696382i	$0.0221845\pi$
$564$	−0.0964864	+	0.671078i	−0.00406281	+	0.0282575i
$565$	−17.8116	−	11.4468i	−0.749340	−	0.481572i
$566$	18.4895	+	21.3380i	0.777170	+	0.896902i
$567$	0.415415	+	0.909632i	0.0174458	+	0.0382010i
$568$	−20.6398	+	13.2644i	−0.866025	+	0.556561i
$569$	10.7227	+	3.14847i	0.449520	+	0.131991i	0.498654	−	0.866801i	$-0.333828\pi$
$569$	10.7227	+	3.14847i	0.449520	+	0.131991i	−0.0491341	+	0.998792i	$0.515646\pi$
$570$	−6.10551	+	7.04613i	−0.255732	+	0.295130i
$571$	−36.1496	+	10.6145i	−1.51281	+	0.444202i	−0.929740	−	0.368217i	$-0.879968\pi$
$571$	−36.1496	+	10.6145i	−1.51281	+	0.444202i	−0.583074	+	0.812419i	$0.698150\pi$
$572$	0.940128	−	2.05859i	0.0393087	−	0.0860741i
$573$	1.57074	+	10.9248i	0.0656187	+	0.456388i
$574$	7.83588			0.327064
$575$	15.3488	+	6.41429i	0.640089	+	0.267494i
$576$	8.79140			0.366308
$577$	4.40027	+	30.6045i	0.183185	+	1.27408i	0.849171	+	0.528118i	$0.177102\pi$
$577$	4.40027	+	30.6045i	0.183185	+	1.27408i	−0.665986	+	0.745965i	$0.731989\pi$
$578$	−10.4853	+	22.9595i	−0.436129	+	0.954990i
$579$	18.2118	−	5.34746i	0.756855	−	0.222233i
$580$	1.00764	−	1.16287i	0.0418398	−	0.0482857i
$581$	3.24128	+	0.951726i	0.134471	+	0.0394842i
$582$	18.8687	−	12.1262i	0.782133	−	0.502646i
$583$	−13.6479	−	29.8847i	−0.565238	−	1.23770i
$584$	−8.55333	−	9.87107i	−0.353939	−	0.408468i
$585$	−1.63104	−	1.04821i	−0.0674353	−	0.0433380i
$586$	5.39945	−	37.5540i	0.223049	−	1.55134i
$587$	1.92027	−	13.3557i	0.0792579	−	0.551251i	−0.911043	−	0.412311i	$-0.864722\pi$
$587$	1.92027	−	13.3557i	0.0792579	−	0.551251i	0.990301	−	0.138939i	$-0.0443693\pi$
$588$	−0.239446	−	0.153882i	−0.00987458	−	0.00634600i
$589$	9.36783	+	10.8111i	0.385995	+	0.445462i
$590$	8.32494	+	18.2291i	0.342732	+	0.750479i
$591$	10.7634	−	6.91721i	0.442746	−	0.284536i
$592$	27.3040	+	8.01716i	1.12219	+	0.329503i
$593$	17.6057	−	20.3180i	0.722978	−	0.834361i	−0.268684	−	0.963228i	$-0.586589\pi$
$593$	17.6057	−	20.3180i	0.722978	−	0.834361i	0.991662	+	0.128867i	$0.0411342\pi$
$594$	6.37737	−	1.87256i	0.261667	−	0.0768322i
$595$	−3.09599	+	6.77928i	−0.126923	+	0.277923i
$596$	−0.684983	−	4.76416i	−0.0280580	−	0.195148i
$597$	−1.25128			−0.0512117
$598$	−5.58720	−	8.10135i	−0.228478	−	0.331289i
$599$	3.51729			0.143713			0.0718563	−	0.997415i	$-0.477108\pi$
$599$	3.51729			0.143713			0.0718563	+	0.997415i	$0.477108\pi$
$600$	1.47709	+	10.2734i	0.0603021	+	0.419410i
$601$	−14.9738	+	32.7881i	−0.610796	+	1.33746i	0.311232	+	0.950334i	$0.399258\pi$
$601$	−14.9738	+	32.7881i	−0.610796	+	1.33746i	−0.922028	+	0.387123i	$0.873469\pi$
$602$	−2.54906	+	0.748472i	−0.103892	+	0.0305055i
$603$	−7.95398	+	9.17938i	−0.323911	+	0.373813i
$604$	−3.37219	−	0.990164i	−0.137212	−	0.0402892i
$605$	15.3591	−	9.87068i	0.624435	−	0.401300i
$606$	−2.71174	−	5.93789i	−0.110157	−	0.241210i
$607$	−4.59837	−	5.30680i	−0.186642	−	0.215396i	0.654715	−	0.755875i	$-0.272788\pi$
$607$	−4.59837	−	5.30680i	−0.186642	−	0.215396i	−0.841357	+	0.540479i	$0.818243\pi$
$608$	7.72963	+	4.96753i	0.313478	+	0.201460i
$609$	−0.621714	+	4.32411i	−0.0251931	+	0.175222i
$610$	−0.758688	+	5.27679i	−0.0307184	+	0.213651i
$611$	3.13954	+	2.01766i	0.127012	+	0.0816259i
$612$	−1.12257	−	1.29551i	−0.0453771	−	0.0523680i
$613$	14.0309	+	30.7233i	0.566701	+	1.24090i	0.948535	+	0.316672i	$0.102565\pi$
$613$	14.0309	+	30.7233i	0.566701	+	1.24090i	−0.381834	+	0.924231i	$0.624707\pi$
$614$	14.5617	−	9.35821i	0.587661	−	0.377667i
$615$	7.10371	+	2.08584i	0.286449	+	0.0841091i
$616$	−9.94407	+	11.4761i	−0.400658	+	0.462384i
$617$	−9.96521	+	2.92605i	−0.401184	+	0.117798i	−0.476099	−	0.879392i	$-0.657950\pi$
$617$	−9.96521	+	2.92605i	−0.401184	+	0.117798i	0.0749150	+	0.997190i	$0.476131\pi$
$618$	−3.29172	+	7.20786i	−0.132412	+	0.289943i
$619$	1.10133	+	7.65991i	0.0442661	+	0.307878i	0.999911	+	0.0133556i	$0.00425136\pi$
$619$	1.10133	+	7.65991i	0.0442661	+	0.307878i	−0.955645	+	0.294522i	$0.904840\pi$
$620$	−0.875881			−0.0351762
$621$	−1.20064	+	4.64311i	−0.0481802	+	0.186322i
$622$	21.1187			0.846783
$623$	−0.989657	−	6.88322i	−0.0396498	−	0.275770i
$624$	2.18020	−	4.77396i	0.0872777	−	0.191111i
$625$	−4.19781	+	1.23259i	−0.167912	+	0.0493035i
$626$	−5.61172	+	6.47626i	−0.224289	+	0.258844i
$627$	28.0106	+	8.22465i	1.11863	+	0.328461i
$628$	4.87183	−	3.13094i	0.194407	−	0.124938i
$629$	−21.2540	−	46.5397i	−0.847451	−	1.85566i
$630$	1.06136	+	1.22487i	0.0422855	+	0.0488001i
$631$	8.27780	+	5.31982i	0.329534	+	0.211779i	0.694937	−	0.719071i	$-0.255432\pi$
$631$	8.27780	+	5.31982i	0.329534	+	0.211779i	−0.365403	+	0.930849i	$0.619069\pi$
$632$	2.28759	−	15.9105i	0.0909953	−	0.632886i
$633$	−0.330838	+	2.30103i	−0.0131496	+	0.0914577i
$634$	17.7468	+	11.4052i	0.704814	+	0.452957i
$635$	5.36082	+	6.18672i	0.212738	+	0.245512i
$636$	0.765465	+	1.67613i	0.0303526	+	0.0664630i
$637$	−1.31805	+	0.847057i	−0.0522229	+	0.0335616i
$638$	27.8600	+	8.18045i	1.10299	+	0.323867i
$639$	5.36948	−	6.19671i	0.212413	−	0.245138i
$640$	9.87845	−	2.90057i	0.390480	−	0.114655i
$641$	15.2971	−	33.4960i	0.604200	−	1.32301i	−0.322271	−	0.946647i	$-0.604446\pi$
$641$	15.2971	−	33.4960i	0.604200	−	1.32301i	0.926471	−	0.376366i	$-0.122827\pi$
$642$	−3.14600	−	21.8809i	−0.124163	−	0.863569i
$643$	35.9019			1.41583			0.707916	−	0.706297i	$-0.249636\pi$
$643$	35.9019			1.41583			0.707916	+	0.706297i	$0.249636\pi$
$644$	−0.427004	−	1.29653i	−0.0168263	−	0.0510905i
$645$	−2.51012			−0.0988358
$646$	6.45761	+	44.9137i	0.254071	+	1.76711i
$647$	−2.90327	+	6.35727i	−0.114139	+	0.249930i	−0.958077	−	0.286511i	$-0.907504\pi$
$647$	−2.90327	+	6.35727i	−0.114139	+	0.249930i	0.843938	+	0.536441i	$0.180232\pi$
$648$	−2.87102	+	0.843008i	−0.112784	+	0.0331165i
$649$	41.0918	−	47.4225i	1.61299	−	1.86149i
$650$	6.82948	+	2.00532i	0.267874	+	0.0786550i
$651$	2.09198	−	1.34443i	0.0819912	−	0.0526925i
$652$	0.927479	+	2.03090i	0.0363229	+	0.0795360i
$653$	9.32812	+	10.7652i	0.365038	+	0.421276i	0.908321	−	0.418273i	$-0.137365\pi$
$653$	9.32812	+	10.7652i	0.365038	+	0.421276i	−0.543284	+	0.839549i	$0.682819\pi$
$654$	9.87198	+	6.34434i	0.386025	+	0.248083i
$655$	−0.595527	+	4.14198i	−0.0232692	+	0.161841i
$656$	−2.85213	+	19.8370i	−0.111357	+	0.774503i
$657$	3.67213	+	2.35994i	0.143264	+	0.0920699i
$658$	−2.04298	−	2.35772i	−0.0796436	−	0.0919136i
$659$	4.94239	+	10.8223i	0.192528	+	0.421578i	0.981136	−	0.193319i	$-0.0619251\pi$
$659$	4.94239	+	10.8223i	0.192528	+	0.421578i	−0.788608	+	0.614896i	$0.789198\pi$
$660$	−1.50370	+	0.966371i	−0.0585316	+	0.0376159i
$661$	−22.0859	−	6.48502i	−0.859044	−	0.252238i	−0.177595	−	0.984104i	$-0.556832\pi$
$661$	−22.0859	−	6.48502i	−0.859044	−	0.252238i	−0.681449	+	0.731866i	$0.738650\pi$
$662$	8.75117	−	10.0994i	0.340124	−	0.392524i
$663$	−9.05377	+	2.65843i	−0.351619	+	0.103245i
$664$	−4.19906	+	9.19465i	−0.162955	+	0.356822i
$665$	1.01308	+	7.04613i	0.0392856	+	0.273237i
$666$	−11.1264			−0.431138
$667$	−15.3787	+	14.2281i	−0.595466	+	0.550914i
$668$	−0.571550			−0.0221139
$669$	2.82668	+	19.6600i	0.109286	+	0.760100i
$670$	−8.17769	+	17.9066i	−0.315932	+	0.691794i
$671$	16.0163	−	4.70281i	0.618303	−	0.181550i
$672$	1.04598	−	1.20712i	0.0403494	−	0.0465657i
$673$	0.725833	+	0.213124i	0.0279788	+	0.00821532i	0.295692	−	0.955283i	$-0.404450\pi$
$673$	0.725833	+	0.213124i	0.0279788	+	0.00821532i	−0.267713	+	0.963499i	$0.586268\pi$
$674$	−26.6940	+	17.1552i	−1.02821	+	0.660793i
$675$	−1.44094	−	3.15521i	−0.0554617	−	0.121444i
$676$	−1.96556	−	2.26837i	−0.0755984	−	0.0872452i
$677$	20.2601	+	13.0204i	0.778659	+	0.500413i	0.868588	−	0.495535i	$-0.165028\pi$
$677$	20.2601	+	13.0204i	0.778659	+	0.500413i	−0.0899296	+	0.995948i	$0.528664\pi$
$678$	−3.18912	+	22.1808i	−0.122477	+	0.851849i
$679$	2.43717	−	16.9509i	0.0935301	−	0.650516i
$680$	−18.7603	−	12.0565i	−0.719424	−	0.462346i
$681$	−10.1791	−	11.7473i	−0.390065	−	0.450159i
$682$	−6.86614	−	15.0347i	−0.262918	−	0.575710i
$683$	11.9849	−	7.70225i	0.458591	−	0.294718i	−0.290875	−	0.956761i	$-0.593947\pi$
$683$	11.9849	−	7.70225i	0.458591	−	0.294718i	0.749466	+	0.662042i	$0.230310\pi$
$684$	−1.57102	−	0.461293i	−0.0600694	−	0.0176380i
$685$	−11.1430	+	12.8597i	−0.425752	+	0.491344i
$686$	1.25667	−	0.368991i	0.0479798	−	0.0140881i
$687$	−1.70531	+	3.73410i	−0.0650615	+	0.142465i
$688$	−0.966984	−	6.72552i	−0.0368659	−	0.256408i
$689$	10.1430			0.386418
$690$	0.253006	+	7.76868i	0.00963176	+	0.295748i
$691$	−42.3183			−1.60986			−0.804932	−	0.593367i	$-0.797798\pi$
$691$	−42.3183			−1.60986			−0.804932	+	0.593367i	$0.797798\pi$
$692$	−0.0975925	−	0.678771i	−0.00370991	−	0.0258030i
$693$	2.10816	−	4.61622i	0.0800822	−	0.175356i
$694$	−5.65190	+	1.65955i	−0.214543	+	0.0629956i
$695$	−2.70107	+	3.11720i	−0.102457	+	0.118242i
$696$	−12.5423	−	3.68275i	−0.475414	−	0.139594i
$697$	30.3123	−	19.4806i	1.14816	−	0.737879i
$698$	11.4544	+	25.0816i	0.433555	+	0.949352i
$699$	10.0964	+	11.6519i	0.381881	+	0.440715i
$700$	0.830558	+	0.533767i	0.0313922	+	0.0201745i
$701$	−1.87982	+	13.0744i	−0.0709998	+	0.493815i	0.923032	+	0.384723i	$0.125703\pi$
$701$	−1.87982	+	13.0744i	−0.0709998	+	0.493815i	−0.994032	+	0.109091i	$0.965206\pi$
$702$	−0.292034	+	2.03114i	−0.0110221	+	0.0766604i
$703$	−41.1113	−	26.4206i	−1.55054	−	0.996472i
$704$	−29.2165	−	33.7176i	−1.10114	−	1.27078i
$705$	−1.22448	−	2.68124i	−0.0461166	−	0.100981i
$706$	−33.8698	+	21.7668i	−1.27471	+	0.819203i
$707$	−4.78222	−	1.40419i	−0.179854	−	0.0528099i
$708$	−2.30470	+	2.65977i	−0.0866160	+	0.0999602i
$709$	22.9380	−	6.73521i	0.861456	−	0.252946i	0.178978	−	0.983853i	$-0.442721\pi$
$709$	22.9380	−	6.73521i	0.861456	−	0.252946i	0.682477	+	0.730907i	$0.260903\pi$
$710$	5.52050	−	12.0882i	0.207181	−	0.453663i
$711$	0.764509	+	5.31728i	0.0286713	+	0.199413i
$712$	20.8080			0.779811
$713$	11.8536	+	1.31210i	0.443921	+	0.0491387i
$714$	7.88792			0.295198
$715$	1.40026	+	9.73903i	0.0523668	+	0.364219i
$716$	−3.04956	+	6.67761i	−0.113968	+	0.249554i
$717$	−19.9733	+	5.86468i	−0.745916	+	0.219021i
$718$	11.1403	−	12.8566i	0.415753	−	0.479805i
$719$	−25.4193	−	7.46378i	−0.947980	−	0.278352i	−0.229035	−	0.973418i	$-0.573557\pi$
$719$	−25.4193	−	7.46378i	−0.947980	−	0.278352i	−0.718946	+	0.695066i	$0.755375\pi$
$720$	−3.48715	+	2.24106i	−0.129958	+	0.0835192i
$721$	2.51330	+	5.50335i	0.0936001	+	0.204956i
$722$	12.0862	+	13.9483i	0.449803	+	0.519101i
$723$	23.6025	+	15.1684i	0.877788	+	0.564120i
$724$	0.445190	−	3.09636i	0.0165454	−	0.115075i
$725$	2.15652	−	14.9989i	0.0800911	−	0.557046i
$726$	−16.2558	−	10.4470i	−0.603311	−	0.387725i
$727$	12.7965	+	14.7680i	0.474596	+	0.547713i	0.941684	−	0.336498i	$-0.109242\pi$
$727$	12.7965	+	14.7680i	0.474596	+	0.547713i	−0.467088	+	0.884211i	$0.654697\pi$
$728$	−1.94752	−	4.26446i	−0.0721797	−	0.158052i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	6.78808	+	1.99316i	0.251238	+	0.0737701i
$731$	−8.00004	+	9.23254i	−0.295892	+	0.341478i
$732$	−0.898301	+	0.263765i	−0.0332022	+	0.00974903i
$733$	−3.10247	+	6.79347i	−0.114592	+	0.250922i	−0.958235	−	0.285984i	$-0.907680\pi$
$733$	−3.10247	+	6.79347i	−0.114592	+	0.250922i	0.843642	+	0.536906i	$0.180407\pi$
$734$	−0.968344	−	6.73498i	−0.0357422	−	0.248593i
$735$	1.23747			0.0456447
$736$	7.54266	−	1.33637i	0.278026	−	0.0492594i
$737$	61.6391			2.27050
$738$	−1.11516	−	7.75613i	−0.0410497	−	0.285507i
$739$	−15.0021	+	32.8501i	−0.551862	+	1.20841i	0.404045	+	0.914739i	$0.367604\pi$
$739$	−15.0021	+	32.8501i	−0.551862	+	1.20841i	−0.955907	+	0.293670i	$0.905123\pi$
$740$	2.87098	−	0.842997i	0.105539	−	0.0309892i
$741$	−5.90218	+	6.81148i	−0.216822	+	0.250226i
$742$	−8.13549	−	2.38879i	−0.298663	−	0.0876954i
$743$	8.48702	−	5.45428i	0.311358	−	0.200098i	−0.375624	−	0.926772i	$-0.622571\pi$
$743$	8.48702	−	5.45428i	0.311358	−	0.200098i	0.686982	+	0.726674i	$0.258935\pi$
$744$	3.09106	+	6.76848i	0.113324	+	0.248145i
$745$	13.7035	+	15.8147i	0.502059	+	0.579407i
$746$	−12.1217	−	7.79013i	−0.443806	−	0.285217i
$747$	0.480756	−	3.34373i	0.0175899	−	0.122341i
$748$	−1.23804	+	8.61075i	−0.0452672	+	0.314840i
$749$	−14.1989	−	9.12510i	−0.518818	−	0.333424i
$750$	−8.98830	−	10.3730i	−0.328206	−	0.378770i
$751$	7.04358	+	15.4233i	0.257024	+	0.562804i	0.993523	−	0.113635i	$-0.0362494\pi$
$751$	7.04358	+	15.4233i	0.257024	+	0.562804i	−0.736499	+	0.676439i	$0.763522\pi$
$752$	6.71231	−	4.31374i	0.244773	−	0.157306i
$753$	3.38849	+	0.994951i	0.123484	+	0.0362580i
$754$	−5.87046	+	6.77487i	−0.213790	+	0.246726i
$755$	14.6611	−	4.30488i	0.533571	−	0.156671i
$756$	−0.118239	+	0.258908i	−0.00430033	+	0.00941640i
$757$	−0.718352	−	4.99625i	−0.0261090	−	0.181592i	0.972594	−	0.232511i	$-0.0746941\pi$
$757$	−0.718352	−	4.99625i	−0.0261090	−	0.181592i	−0.998703	+	0.0509189i	$0.983785\pi$
$758$	30.9841			1.12539
$759$	21.7978	−	10.8256i	0.791209	−	0.392945i
$760$	−21.3004			−0.772648
$761$	−5.22083	−	36.3117i	−0.189255	−	1.31630i	−0.833943	−	0.551851i	$-0.813922\pi$
$761$	−5.22083	−	36.3117i	−0.189255	−	1.31630i	0.644688	−	0.764446i	$-0.276987\pi$
$762$	3.59923	−	7.88121i	0.130386	−	0.285506i
$763$	8.59687	−	2.52427i	0.311227	−	0.0913846i
$764$	−2.05724	+	2.37418i	−0.0744282	+	0.0858947i
$765$	7.15088	+	2.09969i	0.258541	+	0.0759144i
$766$	23.7256	−	15.2475i	0.857240	−	0.550915i
$767$	8.04770	+	17.6220i	0.290586	+	0.636294i
$768$	4.37853	+	5.05309i	0.157996	+	0.182338i
$769$	−4.44668	−	2.85771i	−0.160351	−	0.103052i	0.458004	−	0.888950i	$-0.348564\pi$
$769$	−4.44668	−	2.85771i	−0.160351	−	0.103052i	−0.618356	+	0.785898i	$0.712201\pi$
$770$	1.17053	−	8.14124i	0.0421831	−	0.293390i
$771$	−2.99690	+	20.8439i	−0.107931	+	0.750675i
$772$	4.54483	+	2.92078i	0.163572	+	0.105121i
$773$	18.9646	+	21.8864i	0.682110	+	0.787197i	0.986220	−	0.165440i	$-0.0529043\pi$
$773$	18.9646	+	21.8864i	0.682110	+	0.787197i	−0.304109	+	0.952637i	$0.598359\pi$
$774$	1.10362	+	2.41660i	0.0396689	+	0.0868628i
$775$	−7.25639	+	4.66340i	−0.260657	+	0.167514i
$776$	49.1669	+	14.4367i	1.76499	+	0.518247i
$777$	−5.56318	+	6.42026i	−0.199578	+	0.230325i
$778$	−43.3913	+	12.7408i	−1.55565	+	0.456781i
$779$	14.2972	−	31.3065i	0.512250	−	1.12167i
$780$	−0.0785360	−	0.546230i	−0.00281204	−	0.0195582i
$781$	−41.6106			−1.48894
$782$	29.3806	+	23.8291i	1.05065	+	0.852127i
$783$	4.36858			0.156120
$784$	0.476716	+	3.31563i	0.0170256	+	0.118415i
$785$	−10.4593	+	22.9026i	−0.373308	+	0.817430i
$786$	4.24950	−	1.24777i	0.151575	−	0.0445063i
$787$	−20.2363	+	23.3539i	−0.721346	+	0.832477i	−0.991468	−	0.130349i	$-0.958390\pi$
$787$	−20.2363	+	23.3539i	−0.721346	+	0.832477i	0.270122	+	0.962826i	$0.412936\pi$
$788$	3.49417	+	1.02598i	0.124475	+	0.0365490i
$789$	20.8890	−	13.4245i	0.743668	−	0.477927i
$790$	3.61683	+	7.91975i	0.128681	+	0.281772i
$791$	11.2045	+	12.9306i	0.398385	+	0.459760i
$792$	12.7745	+	8.20964i	0.453920	+	0.291717i
$793$	−0.733422	+	5.10106i	−0.0260446	+	0.181144i
$794$	−3.20030	+	22.2586i	−0.113574	+	0.789927i
$795$	−6.73944	−	4.33118i	−0.239023	−	0.153611i
$796$	−0.233230	−	0.269162i	−0.00826663	−	0.00954020i
$797$	−8.23345	−	18.0287i	−0.291644	−	0.638611i	0.705926	−	0.708286i	$-0.250531\pi$
$797$	−8.23345	−	18.0287i	−0.291644	−	0.638611i	−0.997570	+	0.0696749i	$0.977804\pi$
$798$	6.33819	−	4.07331i	0.224370	−	0.144194i
$799$	−13.7645	−	4.04163i	−0.486954	−	0.142982i
$800$	−3.62814	+	4.18710i	−0.128274	+	0.148036i
$801$	−6.67231	+	1.95917i	−0.235755	+	0.0692238i
$802$	−5.71811	+	12.5209i	−0.201914	+	0.442129i
$803$	−3.15255	−	21.9265i	−0.111251	−	0.773769i
$804$	−3.45713			−0.121924
$805$	4.60927	+	3.73835i	0.162455	+	0.131759i
$806$	5.10286			0.179741
$807$	3.64681	+	25.3641i	0.128374	+	0.892860i
$808$	6.19533	−	13.5659i	0.217951	−	0.477246i
$809$	−31.4284	+	9.22821i	−1.10496	+	0.324446i	−0.782822	−	0.622245i	$-0.786221\pi$
$809$	−31.4284	+	9.22821i	−1.10496	+	0.324446i	−0.322141	+	0.946692i	$0.604402\pi$
$810$	1.06136	−	1.22487i	0.0372923	−	0.0430377i
$811$	−12.9958	−	3.81590i	−0.456343	−	0.133994i	0.0454791	−	0.998965i	$-0.485519\pi$
$811$	−12.9958	−	3.81590i	−0.456343	−	0.133994i	−0.501822	+	0.864971i	$0.667337\pi$
$812$	−1.04604	+	0.672248i	−0.0367087	+	0.0235913i
$813$	−1.60792	−	3.52085i	−0.0563921	−	0.123482i
$814$	36.9763	+	42.6729i	1.29602	+	1.49568i
$815$	−8.16588	−	5.24789i	−0.286038	−	0.183826i
$816$	−2.87106	+	19.9687i	−0.100507	+	0.699044i
$817$	−1.66062	+	11.5498i	−0.0580976	+	0.404078i
$818$	35.0298	+	22.5123i	1.22479	+	0.787123i
$819$	1.02601	+	1.18408i	0.0358518	+	0.0413752i
$820$	0.875399	+	1.91686i	0.0305702	+	0.0669395i
$821$	−3.61915	+	2.32589i	−0.126309	+	0.0811740i	−0.602270	−	0.798293i	$-0.705737\pi$
$821$	−3.61915	+	2.32589i	−0.126309	+	0.0811740i	0.475961	+	0.879467i	$0.342100\pi$
$822$	17.2798	+	5.07381i	0.602703	+	0.176970i
$823$	35.8522	−	41.3757i	1.24973	−	1.44226i	0.398755	−	0.917058i	$-0.369442\pi$
$823$	35.8522	−	41.3757i	1.24973	−	1.44226i	0.850975	−	0.525207i	$-0.176012\pi$
$824$	−17.3699	+	5.10027i	−0.605110	+	0.177676i
$825$	−7.31250	+	16.0121i	−0.254589	+	0.557471i
$826$	−2.30470	−	16.0296i	−0.0801908	−	0.557740i
$827$	−50.4636			−1.75479			−0.877395	−	0.479768i	$-0.840721\pi$
$827$	−50.4636			−1.75479			−0.877395	+	0.479768i	$0.840721\pi$
$828$	−1.22256	+	0.607173i	−0.0424871	+	0.0211007i
$829$	−53.4164			−1.85523			−0.927614	−	0.373540i	$-0.878144\pi$
$829$	−53.4164			−1.85523			−0.927614	+	0.373540i	$0.878144\pi$
$830$	−0.779181	−	5.41932i	−0.0270458	−	0.188107i
$831$	9.24403	−	20.2416i	0.320672	−	0.702174i
$832$	13.2161	−	3.88060i	0.458187	−	0.134536i
$833$	3.94396	−	4.55157i	0.136650	−	0.157703i
$834$	4.18864	+	1.22989i	0.145041	+	0.0425878i
$835$	2.09043	−	1.34344i	0.0723422	−	0.0464915i
$836$	3.45178	+	7.55833i	0.119382	+	0.261410i
$837$	−1.62847	−	1.87935i	−0.0562881	−	0.0649600i
$838$	−15.1507	−	9.73673i	−0.523371	−	0.336350i
$839$	6.67522	−	46.4272i	0.230454	−	1.60284i	−0.465694	−	0.884946i	$-0.654195\pi$
$839$	6.67522	−	46.4272i	0.230454	−	1.60284i	0.696148	−	0.717898i	$-0.254896\pi$
$840$	−0.526962	+	3.66510i	−0.0181819	+	0.126458i
$841$	−8.34145	−	5.36073i	−0.287636	−	0.184853i
$842$	9.32370	+	10.7601i	0.321316	+	0.370818i
$843$	3.30559	+	7.23824i	0.113851	+	0.249298i
$844$	−0.556637	+	0.357729i	−0.0191602	+	0.0123135i
$845$	12.5208	+	3.67645i	0.430729	+	0.126474i
$846$	−2.04298	+	2.35772i	−0.0702390	+	0.0810601i
$847$	−14.1562	+	4.15662i	−0.486412	+	0.142823i
$848$	9.00854	−	19.7259i	0.309354	−	0.677392i
$849$	−3.06794	−	21.3380i	−0.105291	−	0.732318i
$850$	−27.3606			−0.938460
$851$	−40.1168	+	7.10771i	−1.37519	+	0.243649i
$852$	2.33380			0.0799546
$853$	−7.36750	−	51.2421i	−0.252258	−	1.75450i	−0.584587	−	0.811331i	$-0.698743\pi$
$853$	−7.36750	−	51.2421i	−0.252258	−	1.75450i	0.332328	−	0.943164i	$-0.392166\pi$
$854$	1.78962	−	3.91872i	0.0612396	−	0.134096i
$855$	6.83024	−	2.00554i	0.233589	−	0.0685880i
$856$	33.0729	−	38.1682i	1.13041	−	1.30456i
$857$	−2.90673	−	0.853494i	−0.0992921	−	0.0291548i	0.231709	−	0.972785i	$-0.425568\pi$
$857$	−2.90673	−	0.853494i	−0.0992921	−	0.0291548i	−0.331001	+	0.943630i	$0.607386\pi$
$858$	8.76053	−	5.63005i	0.299080	−	0.192207i
$859$	2.87498	+	6.29533i	0.0980932	+	0.214794i	0.952316	−	0.305112i	$-0.0986941\pi$
$859$	2.87498	+	6.29533i	0.0980932	+	0.214794i	−0.854223	+	0.519906i	$0.825967\pi$
$860$	−0.467868	−	0.539948i	−0.0159542	−	0.0184121i
$861$	−5.03310	−	3.23458i	−0.171528	−	0.110234i
$862$	1.43654	−	9.99134i	0.0489287	−	0.340306i
$863$	−3.31894	+	23.0837i	−0.112978	+	0.785780i	0.852017	+	0.523513i	$0.175379\pi$
$863$	−3.31894	+	23.0837i	−0.112978	+	0.785780i	−0.964995	+	0.262266i	$0.915530\pi$
$864$	−1.34369	−	0.863538i	−0.0457133	−	0.0293781i
$865$	1.95240	+	2.25319i	0.0663837	+	0.0766108i
$866$	19.7252	+	43.1922i	0.670291	+	1.46773i
$867$	16.2123	−	10.4190i	0.550599	−	0.353848i
$868$	0.679130	+	0.199410i	0.0230512	+	0.00676843i
$869$	17.8526	−	20.6030i	0.605609	−	0.698910i
$870$	6.79353	−	1.99476i	0.230322	−	0.0676287i
$871$	−7.90536	+	17.3103i	−0.267863	+	0.586538i
$872$	3.81543	+	26.5369i	0.129207	+	0.898652i
$873$	−17.1252			−0.579601
$874$	35.9135	+	3.97536i	1.21479	+	0.134469i
$875$	−10.4797			−0.354279
$876$	0.176816	+	1.22978i	0.00597406	+	0.0415505i
$877$	−14.1687	+	31.0252i	−0.478444	+	1.04765i	0.504445	+	0.863444i	$0.331697\pi$
$877$	−14.1687	+	31.0252i	−0.478444	+	1.04765i	−0.982888	+	0.184202i	$0.941030\pi$
$878$	−44.6256	+	13.1033i	−1.50604	+	0.442213i
$879$	−18.9701	+	21.8926i	−0.639845	+	0.738420i
$880$	20.1839	+	5.92654i	0.680401	+	0.199784i
$881$	−21.0254	+	13.5122i	−0.708364	+	0.455238i	−0.844572	−	0.535442i	$-0.820145\pi$
$881$	−21.0254	+	13.5122i	−0.708364	+	0.455238i	0.136208	+	0.990680i	$0.456509\pi$
$882$	−0.544078	−	1.19136i	−0.0183201	−	0.0401153i
$883$	1.25826	+	1.45211i	0.0423437	+	0.0488673i	0.776526	−	0.630085i	$-0.216980\pi$
$883$	1.25826	+	1.45211i	0.0423437	+	0.0488673i	−0.734183	+	0.678952i	$0.762434\pi$
$884$	−2.25941	−	1.45203i	−0.0759921	−	0.0488371i
$885$	2.17756	−	15.1453i	0.0731979	−	0.509103i
$886$	−3.11501	+	21.6653i	−0.104651	+	0.727861i
$887$	−35.8364	−	23.0307i	−1.20327	−	0.773295i	−0.223751	−	0.974646i	$-0.571830\pi$
$887$	−35.8364	−	23.0307i	−1.20327	−	0.773295i	−0.979519	+	0.201352i	$0.935467\pi$
$888$	−16.6463	−	19.2109i	−0.558614	−	0.644675i
$889$	−2.74808	−	6.01747i	−0.0921678	−	0.201819i
$890$	−9.48145	+	6.09336i	−0.317819	+	0.204250i
$891$	−4.86925	−	1.42974i	−0.163126	−	0.0478982i
$892$	−3.70217	+	4.27253i	−0.123958	+	0.143055i
$893$	−13.1473	+	3.86040i	−0.439958	+	0.129183i
$894$	9.20048	−	20.1462i	0.307710	−	0.673791i
$895$	−4.54213	−	31.5912i	−0.151827	−	1.05598i
$896$	−8.31979			−0.277945
$897$	0.244580	+	7.50996i	0.00816629	+	0.250750i
$898$	27.9954			0.934220
$899$	−1.54604	−	10.7530i	−0.0515634	−	0.358631i
$900$	0.410134	−	0.898067i	0.0136711	−	0.0299356i
$901$	−37.4100	+	10.9846i	−1.24631	+	0.365949i
$902$	−26.0410	+	30.0529i	−0.867070	+	1.00065i
$903$	1.94626	+	0.571475i	0.0647676	+	0.0190175i
$904$	−43.0689	+	27.6787i	−1.43245	+	0.920579i
$905$	5.64978	+	12.3713i	0.187805	+	0.411236i
$906$	−10.5905	−	12.2221i	−0.351847	−	0.406053i
$907$	47.5268	+	30.5436i	1.57810	+	1.01418i	0.976535	+	0.215360i	$0.0690926\pi$
$907$	47.5268	+	30.5436i	1.57810	+	1.01418i	0.601566	+	0.798823i	$0.294544\pi$
$908$	0.629639	−	4.37924i	0.0208953	−	0.145330i
$909$	−0.709313	+	4.93338i	−0.0235264	+	0.163630i
$910$	2.13621	+	1.37286i	0.0708147	+	0.0455099i
$911$	26.0325	+	30.0431i	0.862494	+	0.995371i	0.999988	+	0.00486818i	$0.00154960\pi$
$911$	26.0325	+	30.0431i	0.862494	+	0.995371i	−0.137495	+	0.990503i	$0.543905\pi$
$912$	8.00481	+	17.5281i	0.265066	+	0.580413i
$913$	−14.4219	+	9.26839i	−0.477295	+	0.306739i
$914$	−13.4697	−	3.95505i	−0.445537	−	0.130821i
$915$	2.66553	−	3.07618i	0.0881196	−	0.101695i
$916$	−1.12109	+	0.329183i	−0.0370420	+	0.0108765i
$917$	1.40475	−	3.07598i	0.0463890	−	0.101578i
$918$	−1.12257	−	7.80763i	−0.0370503	−	0.257690i
$919$	−50.8429			−1.67715			−0.838577	−	0.544783i	$-0.816612\pi$
$919$	−50.8429			−1.67715			−0.838577	+	0.544783i	$0.816612\pi$
$920$	−13.0349	+	12.0597i	−0.429749	+	0.397596i
$921$	−13.2162			−0.435487
$922$	−6.16009	−	42.8444i	−0.202872	−	1.41100i
$923$	5.33666	−	11.6856i	0.175658	−	0.384638i
$924$	1.38593	−	0.406947i	0.0455939	−	0.0133876i
$925$	19.2968	−	22.2697i	0.634476	−	0.732225i
$926$	−1.01740	−	0.298736i	−0.0334339	−	0.00981707i
$927$	5.08966	−	3.27092i	0.167166	−	0.107431i
$928$	−2.89864	−	6.34715i	−0.0951527	−	0.208355i
$929$	4.77995	+	5.51635i	0.156825	+	0.180986i	0.828725	−	0.559656i	$-0.189067\pi$
$929$	4.77995	+	5.51635i	0.156825	+	0.180986i	−0.671900	+	0.740642i	$0.734521\pi$
$930$	−3.39056	−	2.17898i	−0.111181	−	0.0714515i
$931$	0.818672	−	5.69399i	0.0268309	−	0.186613i
$932$	−0.624523	+	4.34365i	−0.0204569	+	0.142281i
$933$	−13.5649	−	8.71761i	−0.444094	−	0.285402i
$934$	−0.816001	−	0.941715i	−0.0267004	−	0.0308139i
$935$	−15.7116	−	34.4036i	−0.513824	−	1.12512i
$936$	−3.94390	+	2.53459i	−0.128910	+	0.0828456i
$937$	31.9260	+	9.37433i	1.04298	+	0.306246i	0.757977	−	0.652281i	$-0.226188\pi$
$937$	31.9260	+	9.37433i	1.04298	+	0.306246i	0.285001	+	0.958527i	$0.408006\pi$
$938$	10.4175	−	12.0224i	0.340143	−	0.392546i
$939$	6.27783	−	1.84334i	0.204869	−	0.0601550i
$940$	0.348524	−	0.763161i	0.0113676	−	0.0248916i
$941$	5.68918	+	39.5691i	0.185462	+	1.28992i	0.843581	+	0.537002i	$0.180443\pi$
$941$	5.68918	+	39.5691i	0.185462	+	1.28992i	−0.658119	+	0.752914i	$0.728648\pi$
$942$	26.6480			0.868238
$943$	−8.97554	−	27.2528i	−0.292284	−	0.887474i
$944$	41.4186			1.34806
$945$	−0.176110	−	1.22487i	−0.00572887	−	0.0398451i
$946$	5.60069	−	12.2638i	0.182094	−	0.398731i
$947$	37.2766	−	10.9454i	1.21133	−	0.355678i	0.387154	−	0.922015i	$-0.373458\pi$
$947$	37.2766	−	10.9454i	1.21133	−	0.355678i	0.824173	+	0.566338i	$0.191640\pi$
$948$	−1.00129	+	1.15555i	−0.0325205	+	0.0375307i
$949$	6.56202	+	1.92678i	0.213012	+	0.0625460i
$950$	−21.9851	+	14.1290i	−0.713291	+	0.458404i
$951$	−6.69107	−	14.6514i	−0.216973	−	0.475104i
$952$	11.8012	+	13.6193i	0.382480	+	0.441405i
$953$	5.95424	+	3.82656i	0.192877	+	0.123954i	0.633515	−	0.773730i	$-0.281611\pi$
$953$	5.95424	+	3.82656i	0.192877	+	0.123954i	−0.440638	+	0.897685i	$0.645248\pi$
$954$	−1.20668	+	8.39264i	−0.0390677	+	0.271722i
$955$	1.94375	−	13.5190i	0.0628981	−	0.437466i
$956$	−4.98442	−	3.20329i	−0.161208	−	0.103602i
$957$	−14.5181	−	16.7548i	−0.469304	−	0.541605i
$958$	−5.66975	−	12.4150i	−0.183181	−	0.401111i
$959$	11.5677	−	7.43408i	0.373539	−	0.240059i
$960$	−10.4384	−	3.06499i	−0.336898	−	0.0989222i
$961$	16.2511	−	18.7548i	0.524229	−	0.604993i
$962$	−16.7263	+	4.91128i	−0.539277	+	0.158346i
$963$	−7.01150	+	15.3531i	−0.225943	+	0.494745i
$964$	1.13648	+	7.90440i	0.0366036	+	0.254584i
$965$	−23.4879			−0.756103
$966$	1.57251	−	6.08118i	0.0505947	−	0.195659i
$967$	−23.3017			−0.749334			−0.374667	−	0.927160i	$-0.622243\pi$
$967$	−23.3017			−0.749334			−0.374667	+	0.927160i	$0.622243\pi$
$968$	−6.28273	−	43.6974i	−0.201935	−	1.40449i
$969$	14.3921	−	31.5144i	0.462342	−	1.01239i
$970$	−26.6312	+	7.81964i	−0.855078	+	0.251073i
$971$	−6.84185	+	7.89591i	−0.219565	+	0.253392i	−0.854837	−	0.518897i	$-0.826343\pi$
$971$	−6.84185	+	7.89591i	−0.219565	+	0.253392i	0.635271	+	0.772289i	$0.280888\pi$
$972$	0.273100	+	0.0801894i	0.00875969	+	0.00257208i
$973$	2.80401	−	1.80202i	0.0898923	−	0.0577703i
$974$	−8.42623	−	18.4509i	−0.269994	−	0.591204i
$975$	−3.55890	−	4.10719i	−0.113976	−	0.131535i
$976$	9.26907	+	5.95687i	0.296696	+	0.190675i
$977$	−0.813665	+	5.65917i	−0.0260315	+	0.181053i	−0.998689	−	0.0511920i	$-0.983698\pi$
$977$	−0.813665	+	5.65917i	−0.0260315	+	0.181053i	0.972657	+	0.232245i	$0.0746070\pi$
$978$	−1.46208	+	10.1690i	−0.0467521	+	0.325168i
$979$	29.6881	+	19.0794i	0.948835	+	0.609780i
$980$	0.230655	+	0.266190i	0.00736801	+	0.00850314i
$981$	−3.72204	−	8.15012i	−0.118835	−	0.260213i
$982$	−1.35122	+	0.868374i	−0.0431191	+	0.0277109i
$983$	−7.75211	−	2.27623i	−0.247254	−	0.0726003i	0.155757	−	0.987795i	$-0.450218\pi$
$983$	−7.75211	−	2.27623i	−0.247254	−	0.0726003i	−0.403011	+	0.915195i	$0.632036\pi$
$984$	11.7234	−	13.5295i	0.373728	−	0.431305i
$985$	−15.1914	+	4.46060i	−0.484038	+	0.142127i
$986$	14.3148	−	31.3450i	0.455876	−	0.998228i
$987$	0.338989	+	2.35772i	0.0107901	+	0.0750471i
$988$	−2.56533			−0.0816141
$989$	5.52295	+	8.00819i	0.175620	+	0.254646i
$990$	−8.22496			−0.261406
$991$	−3.15246	−	21.9258i	−0.100141	−	0.696497i	−0.976607	−	0.215033i	$-0.931014\pi$
$991$	−3.15246	−	21.9258i	−0.100141	−	0.696497i	0.876466	−	0.481464i	$-0.159895\pi$
$992$	−1.65001	+	3.61301i	−0.0523877	+	0.114713i
$993$	−9.78994	+	2.87459i	−0.310674	+	0.0912222i
$994$	−7.03252	+	8.11596i	−0.223058	+	0.257423i
$995$	1.48570	+	0.436242i	0.0471000	+	0.0138298i
$996$	0.808876	−	0.519833i	0.0256302	−	0.0164715i
$997$	−25.8681	−	56.6433i	−0.819252	−	1.79391i	−0.560955	−	0.827847i	$-0.689566\pi$
$997$	−25.8681	−	56.6433i	−0.819252	−	1.79391i	−0.258298	−	0.966065i	$-0.583162\pi$
$998$	−3.39350	−	3.91631i	−0.107419	−	0.123969i
$999$	7.14663	+	4.59286i	0.226109	+	0.145312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.c.463.1	yes	20
23.8	even	11	inner	483.2.q.c.169.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.c.169.1	✓	20	23.8	even	11	inner
483.2.q.c.463.1	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.186393 + 1.29639i) q^{2} +(0.415415 - 0.909632i) q^{3} +(0.273100 - 0.0801894i) q^{4} +(-0.810370 + 0.935217i) q^{5} +(1.25667 + 0.368991i) q^{6} +(0.841254 - 0.540641i) q^{7} +(1.24302 + 2.72183i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-1.36345 - 0.876238i) q^{10} +(-0.722222 + 5.02317i) q^{11} +(0.0405070 - 0.281733i) q^{12} +(-1.31805 - 0.847057i) q^{13} +(0.857685 + 0.989821i) q^{14} +(0.514063 + 1.12564i) q^{15} +(-2.81797 + 1.81100i) q^{16} +(5.77863 + 1.69676i) q^{17} +(0.857685 - 0.989821i) q^{18} +(5.51952 - 1.62068i) q^{19} +(-0.146318 + 0.320391i) q^{20} +(-0.142315 - 0.989821i) q^{21} -6.64660 q^{22} +(2.46012 - 4.11677i) q^{23} +2.99223 q^{24} +(0.493643 + 3.43336i) q^{25} +(0.852443 - 1.86659i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(0.186393 - 0.215109i) q^{28} +(-4.19162 - 1.23077i) q^{29} +(-1.36345 + 0.876238i) q^{30} +(1.03303 + 2.26202i) q^{31} +(1.04598 + 1.20712i) q^{32} +(4.26921 + 2.74365i) q^{33} +(-1.12257 + 7.80763i) q^{34} +(-0.176110 + 1.22487i) q^{35} +(-0.239446 - 0.153882i) q^{36} +(-5.56318 - 6.42026i) q^{37} +(3.12983 + 6.85337i) q^{38} +(-1.31805 + 0.847057i) q^{39} +(-3.55280 - 1.04320i) q^{40} +(3.91794 - 4.52155i) q^{41} +(1.25667 - 0.368991i) q^{42} +(-0.842640 + 1.84512i) q^{43} +(0.205566 + 1.42974i) q^{44} +1.23747 q^{45} +(5.79549 + 2.42195i) q^{46} -2.38197 q^{47} +(0.476716 + 3.31563i) q^{48} +(0.415415 - 0.909632i) q^{49} +(-4.35897 + 1.27991i) q^{50} +(3.94396 - 4.55157i) q^{51} +(-0.427884 - 0.125638i) q^{52} +(-5.44615 + 3.50003i) q^{53} +(-0.544078 - 1.19136i) q^{54} +(-4.11248 - 4.74606i) q^{55} +(2.51722 + 1.61772i) q^{56} +(0.818672 - 5.69399i) q^{57} +(0.814272 - 5.66339i) q^{58} +(-10.4019 - 6.68489i) q^{59} +(0.230655 + 0.266190i) q^{60} +(-1.36641 - 2.99203i) q^{61} +(-2.73991 + 1.76083i) q^{62} +(-0.959493 - 0.281733i) q^{63} +(-5.75714 + 6.64410i) q^{64} +(1.86029 - 0.546230i) q^{65} +(-2.76110 + 6.04596i) q^{66} +(-1.72856 - 12.0224i) q^{67} +1.71421 q^{68} +(-2.72277 - 3.94798i) q^{69} -1.62074 q^{70} +(1.16690 + 8.11596i) q^{71} +(1.24302 - 2.72183i) q^{72} +(-4.18826 + 1.22978i) q^{73} +(7.28622 - 8.40875i) q^{74} +(3.32816 + 0.977237i) q^{75} +(1.37742 - 0.885215i) q^{76} +(2.10816 + 4.61622i) q^{77} +(-1.34379 - 1.55082i) q^{78} +(-4.51918 - 2.90430i) q^{79} +(0.589921 - 4.10299i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(6.59197 + 4.23640i) q^{82} +(2.21220 + 2.55301i) q^{83} +(-0.118239 - 0.258908i) q^{84} +(-6.26967 + 4.02927i) q^{85} +(-2.54906 - 0.748472i) q^{86} +(-2.86081 + 3.30155i) q^{87} +(-14.5699 + 4.27811i) q^{88} +(2.88880 - 6.32558i) q^{89} +(0.230655 + 1.60424i) q^{90} -1.56677 q^{91} +(0.341739 - 1.32157i) q^{92} +2.48674 q^{93} +(-0.443981 - 3.08796i) q^{94} +(-2.95717 + 6.47530i) q^{95} +(1.53255 - 0.449997i) q^{96} +(11.2146 - 12.9424i) q^{97} +(1.25667 + 0.368991i) q^{98} +(4.26921 - 2.74365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9} + 9 q^{10} + 3 q^{11} + 18 q^{12} - 2 q^{13} + 18 q^{14} - q^{15} + 8 q^{16} + 8 q^{17} + 18 q^{18} + 6 q^{19} - 2 q^{20} - 2 q^{21}+ \cdots + 14 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9 + 9 * q^10 + 3 * q^11 + 18 * q^12 - 2 * q^13 + 18 * q^14 - q^15 + 8 * q^16 + 8 * q^17 + 18 * q^18 + 6 * q^19 - 2 * q^20 - 2 * q^21 + 6 * q^22 + 11 * q^23 + 9 * q^25 + 7 * q^26 - 2 * q^27 - 4 * q^28 + 23 * q^29 + 9 * q^30 + q^31 - 28 * q^32 + 14 * q^33 - 28 * q^34 + 10 * q^35 - 4 * q^36 - 9 * q^37 + 34 * q^38 - 2 * q^39 - 15 * q^41 - 4 * q^42 - 23 * q^43 - 16 * q^44 - 12 * q^45 + 11 * q^46 - 66 * q^47 - 36 * q^48 - 2 * q^49 - 26 * q^50 - 14 * q^51 + 7 * q^52 + 9 * q^53 - 4 * q^54 - 62 * q^55 + 22 * q^56 - 27 * q^57 - 20 * q^58 + 49 * q^59 - 2 * q^60 + 46 * q^61 - 9 * q^62 - 2 * q^63 + 16 * q^64 + 11 * q^65 - 16 * q^66 + 14 * q^67 + 38 * q^68 + 11 * q^69 - 2 * q^70 + 36 * q^71 - q^73 + 4 * q^74 - 2 * q^75 + 34 * q^76 - 8 * q^77 - 15 * q^78 - 22 * q^79 + 15 * q^80 - 2 * q^81 - 30 * q^82 + 8 * q^83 - 4 * q^84 - 32 * q^85 - 68 * q^86 + q^87 - 11 * q^88 - 2 * q^89 - 2 * q^90 - 24 * q^91 + 11 * q^92 - 32 * q^93 + 33 * q^94 - 107 * q^95 + 16 * q^96 + 18 * q^97 - 4 * q^98 + 14 * q^99

Introduction

L-functions

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