LMFDB - Embedded newform 460.2.w.a.167.51

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.w (of order $44$, degree $20$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			167.51
Character	$\chi$	$=$	460.167
Dual form			460.2.w.a.303.51

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965360 - 1.03348i) q^{2} +(-0.0994992 - 0.182219i) q^{3} +(-0.136158 - 1.99536i) q^{4} +(0.0408995 - 2.23569i) q^{5} +(-0.284372 - 0.0730769i) q^{6} +(2.09969 + 2.80485i) q^{7} +(-2.19360 - 1.78552i) q^{8} +(1.59862 - 2.48750i) q^{9} +O(q^{10})$	\(q+(0.965360 - 1.03348i) q^{2} +(-0.0994992 - 0.182219i) q^{3} +(-0.136158 - 1.99536i) q^{4} +(0.0408995 - 2.23569i) q^{5} +(-0.284372 - 0.0730769i) q^{6} +(2.09969 + 2.80485i) q^{7} +(-2.19360 - 1.78552i) q^{8} +(1.59862 - 2.48750i) q^{9} +(-2.27106 - 2.20052i) q^{10} +(0.956253 - 0.436706i) q^{11} +(-0.350045 + 0.223347i) q^{12} +(1.28177 + 0.959519i) q^{13} +(4.92571 + 0.537711i) q^{14} +(-0.411456 + 0.214997i) q^{15} +(-3.96292 + 0.543370i) q^{16} +(-3.78182 + 0.270481i) q^{17} +(-1.02754 - 4.05347i) q^{18} +(-1.55289 - 1.79213i) q^{19} +(-4.46658 + 0.222799i) q^{20} +(0.302181 - 0.661684i) q^{21} +(0.471802 - 1.40985i) q^{22} +(-2.44604 - 4.12516i) q^{23} +(-0.107095 + 0.577375i) q^{24} +(-4.99665 - 0.182877i) q^{25} +(2.22901 - 0.398398i) q^{26} +(-1.23359 - 0.0882281i) q^{27} +(5.31080 - 4.57153i) q^{28} +(4.94173 + 4.28203i) q^{29} +(-0.175008 + 0.632781i) q^{30} +(-0.00306293 - 0.0104314i) q^{31} +(-3.26409 + 4.62014i) q^{32} +(-0.174723 - 0.130796i) q^{33} +(-3.37128 + 4.16954i) q^{34} +(6.35666 - 4.57954i) q^{35} +(-5.18112 - 2.85113i) q^{36} +(2.06621 + 9.49822i) q^{37} +(-3.35123 - 0.125173i) q^{38} +(0.0473080 - 0.329034i) q^{39} +(-4.08160 + 4.83120i) q^{40} +(3.82402 - 2.45755i) q^{41} +(-0.392123 - 0.951061i) q^{42} +(2.54881 + 4.66780i) q^{43} +(-1.00159 - 1.84861i) q^{44} +(-5.49590 - 3.67576i) q^{45} +(-6.62457 - 1.45433i) q^{46} +(6.89925 - 6.89925i) q^{47} +(0.493320 + 0.668056i) q^{48} +(-1.48638 + 5.06216i) q^{49} +(-5.01257 + 4.98740i) q^{50} +(0.425575 + 0.662207i) q^{51} +(1.74006 - 2.68823i) q^{52} +(0.984405 + 1.31501i) q^{53} +(-1.28204 + 1.18972i) q^{54} +(-0.937231 - 2.15575i) q^{55} +(0.402252 - 9.90177i) q^{56} +(-0.172049 + 0.461282i) q^{57} +(9.19594 - 0.973469i) q^{58} +(0.811187 + 5.64193i) q^{59} +(0.485020 + 0.791729i) q^{60} +(0.228831 - 0.0671909i) q^{61} +(-0.0137374 - 0.00690456i) q^{62} +(10.3337 - 0.739078i) q^{63} +(1.62380 + 7.83347i) q^{64} +(2.19761 - 2.82640i) q^{65} +(-0.303845 + 0.0543072i) q^{66} +(5.38407 + 14.4353i) q^{67} +(1.05463 + 7.50926i) q^{68} +(-0.508304 + 0.856165i) q^{69} +(1.40362 - 10.9904i) q^{70} +(-0.804902 - 0.367587i) q^{71} +(-7.94823 + 2.60222i) q^{72} +(7.19833 + 0.514834i) q^{73} +(11.8108 + 7.03382i) q^{74} +(0.463840 + 0.928683i) q^{75} +(-3.36451 + 3.34259i) q^{76} +(3.23273 + 1.76520i) q^{77} +(-0.294381 - 0.366528i) q^{78} +(-1.38912 - 9.66155i) q^{79} +(1.05273 + 8.88210i) q^{80} +(-3.57835 - 7.83550i) q^{81} +(1.15173 - 6.32447i) q^{82} +(0.867471 + 3.98770i) q^{83} +(-1.36144 - 0.512866i) q^{84} +(0.450038 + 8.46605i) q^{85} +(7.28460 + 1.87197i) q^{86} +(0.288571 - 1.32654i) q^{87} +(-2.87739 - 0.749453i) q^{88} +(-1.49868 + 5.10402i) q^{89} +(-9.10435 + 2.13147i) q^{90} +5.60985i q^{91} +(-7.89812 + 5.44240i) q^{92} +(-0.00159604 + 0.00159604i) q^{93} +(-0.469968 - 13.7905i) q^{94} +(-4.07017 + 3.39849i) q^{95} +(1.16665 + 0.135079i) q^{96} +(-14.8509 - 3.23062i) q^{97} +(3.79674 + 6.42295i) q^{98} +(0.442378 - 3.07681i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.965360	−	1.03348i	0.682613	−	0.730780i
$2$	0.965360	−	1.03348i	0.682613	−	0.730780i
$3$	−0.0994992	−	0.182219i	−0.0574459	−	0.105204i	0.847378	−	0.530990i	$-0.178180\pi$
$3$	−0.0994992	−	0.182219i	−0.0574459	−	0.105204i	−0.904824	+	0.425785i	$0.859998\pi$
$4$	−0.136158	−	1.99536i	−0.0680791	−	0.997680i
$5$	0.0408995	−	2.23569i	0.0182908	−	0.999833i
$5$	0.0408995	−	2.23569i	0.0182908	−	0.999833i
$6$	−0.284372	−	0.0730769i	−0.116095	−	0.0298335i
$7$	2.09969	+	2.80485i	0.793606	+	1.06013i	0.996716	+	0.0809779i	$0.0258043\pi$
$7$	2.09969	+	2.80485i	0.793606	+	1.06013i	−0.203110	+	0.979156i	$0.565105\pi$
$8$	−2.19360	−	1.78552i	−0.775556	−	0.631278i
$9$	1.59862	−	2.48750i	0.532873	−	0.829166i
$10$	−2.27106	−	2.20052i	−0.718172	−	0.695865i
$11$	0.956253	−	0.436706i	0.288321	−	0.131672i	−0.266004	−	0.963972i	$-0.585704\pi$
$11$	0.956253	−	0.436706i	0.288321	−	0.131672i	0.554326	+	0.832300i	$0.312976\pi$
$12$	−0.350045	+	0.223347i	−0.101049	+	0.0644749i
$13$	1.28177	+	0.959519i	0.355498	+	0.266123i	0.762068	−	0.647497i	$-0.224184\pi$
$13$	1.28177	+	0.959519i	0.355498	+	0.266123i	−0.406570	+	0.913620i	$0.633275\pi$
$14$	4.92571	+	0.537711i	1.31645	+	0.143709i
$15$	−0.411456	+	0.214997i	−0.106237	+	0.0555120i
$16$	−3.96292	+	0.543370i	−0.990730	+	0.135842i
$17$	−3.78182	+	0.270481i	−0.917225	+	0.0656012i	−0.521964	−	0.852968i	$-0.674800\pi$
$17$	−3.78182	+	0.270481i	−0.917225	+	0.0656012i	−0.395261	+	0.918569i	$0.629346\pi$
$18$	−1.02754	−	4.05347i	−0.242192	−	0.955413i
$19$	−1.55289	−	1.79213i	−0.356257	−	0.411143i	0.549125	−	0.835740i	$-0.314961\pi$
$19$	−1.55289	−	1.79213i	−0.356257	−	0.411143i	−0.905382	+	0.424597i	$0.860416\pi$
$20$	−4.46658	+	0.222799i	−0.998758	+	0.0498194i
$21$	0.302181	−	0.661684i	0.0659413	−	0.144391i
$22$	0.471802	−	1.40985i	0.100589	−	0.300580i
$23$	−2.44604	−	4.12516i	−0.510034	−	0.860154i
$23$	−2.44604	−	4.12516i	−0.510034	−	0.860154i
$24$	−0.107095	+	0.577375i	−0.0218607	+	0.117856i
$25$	−4.99665	−	0.182877i	−0.999331	−	0.0365755i
$26$	2.22901	−	0.398398i	0.437145	−	0.0781323i
$27$	−1.23359	−	0.0882281i	−0.237404	−	0.0169795i
$28$	5.31080	−	4.57153i	1.00365	−	0.863938i
$29$	4.94173	+	4.28203i	0.917656	+	0.795154i	0.979189	−	0.202951i	$-0.0650533\pi$
$29$	4.94173	+	4.28203i	0.917656	+	0.795154i	−0.0615325	+	0.998105i	$0.519599\pi$
$30$	−0.175008	+	0.632781i	−0.0319520	+	0.115529i
$31$	−0.00306293	−	0.0104314i	−0.000550118	−	0.00187353i	0.959217	−	0.282669i	$-0.0912199\pi$
$31$	−0.00306293	−	0.0104314i	−0.000550118	−	0.00187353i	−0.959768	+	0.280796i	$0.909402\pi$
$32$	−3.26409	+	4.62014i	−0.577015	+	0.816734i
$33$	−0.174723	−	0.130796i	−0.0304153	−	0.0227686i
$34$	−3.37128	+	4.16954i	−0.578170	+	0.715070i
$35$	6.35666	−	4.57954i	1.07447	−	0.774083i
$36$	−5.18112	−	2.85113i	−0.863520	−	0.475188i
$37$	2.06621	+	9.49822i	0.339683	+	1.56150i	0.757419	+	0.652929i	$0.226460\pi$
$37$	2.06621	+	9.49822i	0.339683	+	1.56150i	−0.417736	+	0.908568i	$0.637176\pi$
$38$	−3.35123	−	0.125173i	−0.543641	−	0.0203057i
$39$	0.0473080	−	0.329034i	0.00757534	−	0.0526876i
$40$	−4.08160	+	4.83120i	−0.645358	+	0.763880i
$41$	3.82402	−	2.45755i	0.597212	−	0.383805i	−0.206830	−	0.978377i	$-0.566315\pi$
$41$	3.82402	−	2.45755i	0.597212	−	0.383805i	0.804042	+	0.594572i	$0.202678\pi$
$42$	−0.392123	−	0.951061i	−0.0605059	−	0.146752i
$43$	2.54881	+	4.66780i	0.388690	+	0.711833i	0.996619	−	0.0821582i	$-0.0261813\pi$
$43$	2.54881	+	4.66780i	0.388690	+	0.711833i	−0.607929	+	0.793991i	$0.707999\pi$
$44$	−1.00159	−	1.84861i	−0.150995	−	0.278688i
$45$	−5.49590	−	3.67576i	−0.819281	−	0.547950i
$46$	−6.62457	−	1.45433i	−0.976739	−	0.214430i
$47$	6.89925	−	6.89925i	1.00636	−	1.00636i	0.00637983	−	0.999980i	$-0.497969\pi$
$47$	6.89925	−	6.89925i	1.00636	−	1.00636i	0.999980	−	0.00637983i	$-0.00203078\pi$
$48$	0.493320	+	0.668056i	0.0712046	+	0.0964256i
$49$	−1.48638	+	5.06216i	−0.212340	+	0.723165i
$50$	−5.01257	+	4.98740i	−0.708885	+	0.705324i
$51$	0.425575	+	0.662207i	0.0595924	+	0.0927276i
$52$	1.74006	−	2.68823i	0.241303	−	0.372791i
$53$	0.984405	+	1.31501i	0.135218	+	0.180631i	0.863040	−	0.505136i	$-0.168558\pi$
$53$	0.984405	+	1.31501i	0.135218	+	0.180631i	−0.727821	+	0.685767i	$0.759467\pi$
$54$	−1.28204	+	1.18972i	−0.174464	+	0.161900i
$55$	−0.937231	−	2.15575i	−0.126376	−	0.290681i
$56$	0.402252	−	9.90177i	0.0537532	−	1.32318i
$57$	−0.172049	+	0.461282i	−0.0227885	+	0.0610983i
$58$	9.19594	−	0.973469i	1.20749	−	0.127823i
$59$	0.811187	+	5.64193i	0.105608	+	0.734517i	0.971971	+	0.235102i	$0.0755424\pi$
$59$	0.811187	+	5.64193i	0.105608	+	0.734517i	−0.866363	+	0.499415i	$0.833548\pi$
$60$	0.485020	+	0.791729i	0.0626158	+	0.102212i
$61$	0.228831	−	0.0671909i	0.0292988	−	0.00860291i	−0.267050	−	0.963683i	$-0.586049\pi$
$61$	0.228831	−	0.0671909i	0.0292988	−	0.00860291i	0.296349	+	0.955080i	$0.404231\pi$
$62$	−0.0137374	−	0.00690456i	−0.00174466	−	0.000876880i
$63$	10.3337	−	0.739078i	1.30192	−	0.0931151i
$64$	1.62380	+	7.83347i	0.202975	+	0.979184i
$65$	2.19761	−	2.82640i	0.272580	−	0.350571i
$66$	−0.303845	+	0.0543072i	−0.0374008	+	0.00668476i
$67$	5.38407	+	14.4353i	0.657769	+	1.76355i	0.645665	+	0.763621i	$0.276580\pi$
$67$	5.38407	+	14.4353i	0.657769	+	1.76355i	0.0121041	+	0.999927i	$0.496147\pi$
$68$	1.05463	+	7.50926i	0.127893	+	0.910631i
$69$	−0.508304	+	0.856165i	−0.0611926	+	0.103070i
$70$	1.40362	−	10.9904i	0.167764	−	1.31360i
$71$	−0.804902	−	0.367587i	−0.0955243	−	0.0436245i	0.367080	−	0.930189i	$-0.380358\pi$
$71$	−0.804902	−	0.367587i	−0.0955243	−	0.0436245i	−0.462604	+	0.886565i	$0.653085\pi$
$72$	−7.94823	+	2.60222i	−0.936708	+	0.306674i
$73$	7.19833	+	0.514834i	0.842500	+	0.0602568i	0.485915	−	0.874006i	$-0.338486\pi$
$73$	7.19833	+	0.514834i	0.842500	+	0.0602568i	0.356585	+	0.934263i	$0.383941\pi$
$74$	11.8108	+	7.03382i	1.37298	+	0.817665i
$75$	0.463840	+	0.928683i	0.0535596	+	0.107235i
$76$	−3.36451	+	3.34259i	−0.385935	+	0.383421i
$77$	3.23273	+	1.76520i	0.368403	+	0.201164i
$78$	−0.294381	−	0.366528i	−0.0333320	−	0.0415012i
$79$	−1.38912	−	9.66155i	−0.156288	−	1.08701i	−0.905398	−	0.424564i	$-0.860428\pi$
$79$	−1.38912	−	9.66155i	−0.156288	−	1.08701i	0.749110	−	0.662446i	$-0.230482\pi$
$80$	1.05273	+	8.88210i	0.117698	+	0.993049i
$81$	−3.57835	−	7.83550i	−0.397595	−	0.870611i
$82$	1.15173	−	6.32447i	0.127188	−	0.698421i
$83$	0.867471	+	3.98770i	0.0952174	+	0.437707i	0.999932	+	0.0116884i	$0.00372061\pi$
$83$	0.867471	+	3.98770i	0.0952174	+	0.437707i	−0.904714	+	0.426019i	$0.859916\pi$
$84$	−1.36144	−	0.512866i	−0.148545	−	0.0559582i
$85$	0.450038	+	8.46605i	0.0488135	+	0.918272i
$86$	7.28460	+	1.87197i	0.785519	+	0.201859i
$87$	0.288571	−	1.32654i	0.0309380	−	0.142220i
$88$	−2.87739	−	0.749453i	−0.306731	−	0.0798920i
$89$	−1.49868	+	5.10402i	−0.158859	+	0.541025i	0.841141	+	0.540816i	$0.181885\pi$
$89$	−1.49868	+	5.10402i	−0.158859	+	0.541025i	−1.00000		0.000208843i	$0.999934\pi$
$90$	−9.10435	+	2.13147i	−0.959683	+	0.224677i
$91$			5.60985i			0.588072i
$92$	−7.89812	+	5.44240i	−0.823436	+	0.567409i
$93$	−0.00159604	+	0.00159604i	−0.000165501	+	0.000165501i
$94$	−0.469968	−	13.7905i	−0.0484735	−	1.42238i
$95$	−4.07017	+	3.39849i	−0.417590	+	0.348678i
$96$	1.16665	+	0.135079i	0.119071	+	0.0137864i
$97$	−14.8509	−	3.23062i	−1.50788	−	0.328020i	−0.618721	−	0.785611i	$-0.712349\pi$
$97$	−14.8509	−	3.23062i	−1.50788	−	0.328020i	−0.889163	+	0.457590i	$0.848713\pi$
$98$	3.79674	+	6.42295i	0.383528	+	0.648816i
$99$	0.442378	−	3.07681i	0.0444607	−	0.309231i
$100$	0.315430	+	9.99502i	0.0315430	+	0.999502i
$101$	−9.25130	−	5.94545i	−0.920538	−	0.591594i	−0.00772465	−	0.999970i	$-0.502459\pi$
$101$	−9.25130	−	5.94545i	−0.920538	−	0.591594i	−0.912814	+	0.408376i	$0.866095\pi$
$102$	1.09521	+	0.199446i	0.108442	+	0.0197481i
$103$	−0.213379	+	0.572092i	−0.0210249	+	0.0563699i	−0.947038	−	0.321121i	$-0.895940\pi$
$103$	−0.213379	+	0.572092i	−0.0210249	+	0.0563699i	0.926013	+	0.377491i	$0.123213\pi$
$104$	−1.09845	−	4.39343i	−0.107711	−	0.430811i
$105$	−1.46696	−	0.702646i	−0.143161	−	0.0685712i
$106$	2.30934	+	0.252098i	0.224303	+	0.0244859i
$107$	2.74791	−	5.03242i	0.265651	−	0.486503i	−0.710471	−	0.703726i	$-0.751518\pi$
$107$	2.74791	−	5.03242i	0.265651	−	0.486503i	0.976122	+	0.217223i	$0.0697000\pi$
$108$	−0.00808331	+	2.47347i	−0.000777817	+	0.238010i
$109$	2.03462	+	1.76300i	0.194881	+	0.168865i	0.746835	−	0.665009i	$-0.231572\pi$
$109$	2.03462	+	1.76300i	0.194881	+	0.168865i	−0.551954	+	0.833874i	$0.686118\pi$
$110$	−3.13269	−	1.11247i	−0.298690	−	0.106070i
$111$	1.52517	−	1.32157i	0.144763	−	0.125438i
$112$	−9.84496	−	9.97450i	−0.930261	−	0.942502i
$113$	3.33854	+	8.95097i	0.314063	+	0.842036i	0.994061	+	0.108822i	$0.0347080\pi$
$113$	3.33854	+	8.95097i	0.314063	+	0.842036i	−0.679998	+	0.733214i	$0.738019\pi$
$114$	0.310636	+	0.623113i	0.0290937	+	0.0583599i
$115$	−9.32263	+	5.29987i	−0.869339	+	0.494216i
$116$	7.87134	−	10.4436i	0.730836	−	0.969661i
$117$	4.43586	−	1.65449i	0.410095	−	0.152958i
$118$	6.61390	+	4.60815i	0.608859	+	0.424215i
$119$	−8.69928	−	10.0395i	−0.797462	−	0.920320i
$120$	1.28645	+	0.263046i	0.117437	+	0.0240127i
$121$	−6.47976	+	7.47804i	−0.589069	+	0.679822i
$122$	0.151464	−	0.301356i	0.0137129	−	0.0272835i
$123$	−0.828301	−	0.452286i	−0.0746854	−	0.0407813i
$124$	−0.0203973	+	0.00753196i	−0.00183173	+	0.000676390i
$125$	−0.613218	+	11.1635i	−0.0548479	+	0.998495i
$126$	9.21189	−	11.3931i	0.820660	−	1.01498i
$127$	17.0479	+	6.35855i	1.51276	+	0.564230i	0.962623	−	0.270844i	$-0.0873028\pi$
$127$	17.0479	+	6.35855i	1.51276	+	0.564230i	0.550137	+	0.835074i	$0.314576\pi$
$128$	9.66328	+	5.88396i	0.854122	+	0.520073i
$129$	0.596959	−	0.928886i	0.0525593	−	0.0817838i
$130$	−0.799531	−	4.99968i	−0.0701235	−	0.438501i
$131$	−19.1885	−	2.75889i	−1.67651	−	0.241046i	−0.762572	−	0.646903i	$-0.776064\pi$
$131$	−19.1885	−	2.75889i	−1.67651	−	0.241046i	−0.913936	+	0.405858i	$0.866973\pi$
$132$	−0.237195	+	0.366444i	−0.0206452	+	0.0318948i
$133$	1.76608	−	8.11854i	0.153138	−	0.703966i
$134$	20.1161	+	8.37090i	1.73777	+	0.723136i
$135$	−0.247704	+	2.75432i	−0.0213190	+	0.237054i
$136$	8.77876	+	6.15920i	0.752772	+	0.528147i
$137$	10.4440	+	10.4440i	0.892289	+	0.892289i	0.994738	−	0.102449i	$-0.0326679\pi$
$137$	10.4440	+	10.4440i	0.892289	+	0.892289i	−0.102449	+	0.994738i	$0.532668\pi$
$138$	0.394132	+	1.35183i	0.0335507	+	0.115075i
$139$	19.4756			1.65190			0.825950	−	0.563743i	$-0.190639\pi$
$139$	19.4756			1.65190			0.825950	+	0.563743i	$0.190639\pi$
$140$	−10.0033	−	12.0603i	−0.845436	−	1.01928i
$141$	−1.94365	−	0.570706i	−0.163685	−	0.0480621i
$142$	−1.15691	+	0.476996i	−0.0970861	+	0.0400286i
$143$	1.64472	+	0.357787i	0.137539	+	0.0299197i
$144$	−4.98357	+	10.7264i	−0.415297	+	0.893867i
$145$	9.77543	−	10.8731i	0.811805	−	0.902959i
$146$	7.48105	−	6.94232i	0.619136	−	0.574550i
$147$	1.07032	−	0.232833i	0.0882782	−	0.0192037i
$148$	18.6710	−	5.41610i	1.53475	−	0.445200i
$149$	9.27799	−	4.23712i	0.760082	−	0.347118i	0.00261983	−	0.999997i	$-0.499166\pi$
$149$	9.27799	−	4.23712i	0.760082	−	0.347118i	0.757463	+	0.652879i	$0.226439\pi$
$150$	1.40755	+	0.417145i	0.114926	+	0.0340598i
$151$	−21.6150	+	3.10777i	−1.75900	+	0.252906i	−0.944794	−	0.327665i	$-0.893738\pi$
$151$	−21.6150	+	3.10777i	−1.75900	+	0.252906i	−0.814209	+	0.580572i	$0.802829\pi$
$152$	0.206533	+	6.70395i	0.0167520	+	0.543762i
$153$	−5.37286	+	9.83966i	−0.434370	+	0.795489i
$154$	4.94505	−	1.63690i	0.398483	−	0.131905i
$155$	−0.0234466	+	0.00642113i	−0.00188328	+	0.000515758i
$156$	−0.662983	−	0.0495957i	−0.0530811	−	0.00397083i
$157$	0.769778	−	10.7629i	0.0614350	−	0.858974i	−0.869533	−	0.493874i	$-0.835580\pi$
$157$	0.769778	−	10.7629i	0.0614350	−	0.858974i	0.930968	−	0.365100i	$-0.118965\pi$
$158$	−11.3260	−	7.89125i	−0.901049	−	0.627794i
$159$	0.141673	−	0.310220i	0.0112354	−	0.0246021i
$160$	10.1957	+	7.48646i	0.806043	+	0.591857i
$161$	6.43454	−	15.5223i	0.507113	−	1.22333i
$162$	−11.5522	−	3.86593i	−0.907629	−	0.303736i
$163$	−12.1545	+	4.53339i	−0.952013	+	0.355083i	−0.777012	−	0.629486i	$-0.783266\pi$
$163$	−12.1545	+	4.53339i	−0.952013	+	0.355083i	−0.175001	+	0.984568i	$0.555993\pi$
$164$	−5.42437	−	7.29569i	−0.423572	−	0.569698i
$165$	−0.299566	+	0.385277i	−0.0233211	+	0.0299938i
$166$	4.95863	+	2.95306i	0.384864	+	0.229202i
$167$	−0.208706	−	2.91809i	−0.0161501	−	0.225808i	−0.999117	−	0.0420234i	$-0.986620\pi$
$167$	−0.208706	−	2.91809i	−0.0161501	−	0.225808i	0.982967	−	0.183785i	$-0.0588350\pi$
$168$	−1.84432	+	0.911921i	−0.142292	+	0.0703562i
$169$	−2.94027	−	10.0136i	−0.226175	−	0.770281i
$170$	9.18393	+	7.70768i	0.704375	+	0.591152i
$171$	−6.94040	+	0.997879i	−0.530746	+	0.0763097i
$172$	8.96690	−	5.72136i	0.683720	−	0.436250i
$173$	−23.5375	−	8.77903i	−1.78952	−	0.667458i	−0.998445	−	0.0557421i	$-0.982248\pi$
$173$	−23.5375	−	8.77903i	−1.78952	−	0.667458i	−0.791078	−	0.611715i	$-0.790480\pi$
$174$	−1.09237	−	1.57882i	−0.0828127	−	0.119690i
$175$	−9.97846	−	14.3989i	−0.754300	−	1.08845i
$176$	−3.55226	+	2.25023i	−0.267762	+	0.169618i
$177$	0.947356	−	0.709182i	0.0712076	−	0.0533053i
$178$	3.82814	+	6.47607i	0.286931	+	0.485402i
$179$	12.4794	−	8.02003i	0.932755	−	0.599445i	0.0164233	−	0.999865i	$-0.494772\pi$
$179$	12.4794	−	8.02003i	0.932755	−	0.599445i	0.916332	+	0.400420i	$0.131136\pi$
$180$	−6.58615	+	11.4668i	−0.490903	+	0.854684i
$181$	8.94805	+	2.62738i	0.665103	+	0.195292i	0.596821	−	0.802374i	$-0.296430\pi$
$181$	8.94805	+	2.62738i	0.665103	+	0.195292i	0.0682818	+	0.997666i	$0.478248\pi$
$182$	5.79767	+	5.41553i	0.429752	+	0.401426i
$183$	−0.0350120	−	0.0350120i	−0.00258816	−	0.00258816i
$184$	−1.99993	+	13.4164i	−0.147437	+	0.989071i
$185$	21.3196	−	4.23094i	1.56745	−	0.311065i
$186$	0.000108720		0.00319022i	7.97173e−6		0.000233919i
$187$	−3.49825	+	1.91019i	−0.255818	+	0.139687i
$188$	−14.7059	−	12.8271i	−1.07254	−	0.935513i
$189$	−2.34268	−	3.64529i	−0.170405	−	0.265156i
$190$	−0.416911	+	7.48720i	−0.0302459	+	0.543179i
$191$	−0.400590	−	0.0575962i	−0.0289857	−	0.00416752i	0.127807	−	0.991799i	$-0.459206\pi$
$191$	−0.400590	−	0.0575962i	−0.0289857	−	0.00416752i	−0.156792	+	0.987632i	$0.550115\pi$
$192$	1.26584	−	1.07531i	0.0913543	−	0.0776040i
$193$	−8.57875	+	1.86619i	−0.617512	+	0.134331i	−0.510431	−	0.859919i	$-0.670514\pi$
$193$	−8.57875	+	1.86619i	−0.617512	+	0.134331i	−0.107081	+	0.994250i	$0.534150\pi$
$194$	−17.6753	+	12.2294i	−1.26901	+	0.878021i
$195$	−0.733685	−	0.119223i	−0.0525402	−	0.00853777i
$196$	10.3032	+	2.27661i	0.735943	+	0.162615i
$197$	−5.23206	+	6.98922i	−0.372769	+	0.497961i	−0.947223	−	0.320576i	$-0.896124\pi$
$197$	−5.23206	+	6.98922i	−0.372769	+	0.497961i	0.574454	+	0.818537i	$0.305214\pi$
$198$	−2.75276	−	3.42742i	−0.195630	−	0.243576i
$199$	−18.2692	+	5.36433i	−1.29507	+	0.380267i	−0.855436	−	0.517909i	$-0.826711\pi$
$199$	−18.2692	+	5.36433i	−1.29507	+	0.380267i	−0.439636	+	0.898176i	$0.644892\pi$
$200$	10.6342	+	9.32281i	0.751948	+	0.659222i
$201$	2.09467	−	2.41738i	0.147747	−	0.170509i
$202$	−15.0753	+	3.82152i	−1.06070	+	0.268881i
$203$	−1.63439	+	22.8517i	−0.114712	+	1.60388i
$204$	1.26340	−	0.939340i	0.0884554	−	0.0657669i
$205$	−5.33793	−	8.64986i	−0.372817	−	0.604132i
$206$	0.385257	+	0.772798i	0.0268421	+	0.0538434i
$207$	−14.1716	−	0.510036i	−0.984994	−	0.0354499i
$208$	−5.60092	−	3.10603i	−0.388354	−	0.215364i
$209$	−2.26759	−	1.03557i	−0.156853	−	0.0716322i
$210$	−2.14232	+	0.837769i	−0.147834	+	0.0578115i
$211$	−7.34437	+	6.36393i	−0.505607	+	0.438111i	−0.869940	−	0.493158i	$-0.835843\pi$
$211$	−7.34437	+	6.36393i	−0.505607	+	0.438111i	0.364333	+	0.931269i	$0.381297\pi$
$212$	2.48989	−	2.14329i	0.171006	−	0.147202i
$213$	0.0131058	+	0.183243i	0.000897996	+	0.0125556i
$214$	−2.54818	−	7.69801i	−0.174190	−	0.526225i
$215$	10.5400	−	5.50746i	0.718824	−	0.375605i
$216$	2.54847	+	2.39614i	0.173402	+	0.163037i
$217$	0.0228273	−	0.0304936i	0.00154962	−	0.00207004i
$218$	3.78616	−	0.400798i	0.256431	−	0.0271455i
$219$	−0.622415	−	1.36290i	−0.0420589	−	0.0920962i
$220$	−4.17389	+	2.16364i	−0.281403	+	0.145872i
$221$	−5.10694	−	3.28203i	−0.343530	−	0.220773i
$222$	0.106527	−	2.85202i	0.00714960	−	0.191415i
$223$	9.13488	−	6.83828i	0.611717	−	0.457925i	−0.247955	−	0.968771i	$-0.579759\pi$
$223$	9.13488	−	6.83828i	0.611717	−	0.457925i	0.859672	+	0.510846i	$0.170668\pi$
$224$	−19.8124	+	0.545571i	−1.32377	+	0.0364525i
$225$	−8.44265	+	12.1368i	−0.562843	+	0.809122i
$226$	12.4735	+	5.19060i	0.829727	+	0.345274i
$227$	14.1545	−	7.72894i	0.939467	−	0.512988i	0.0648998	−	0.997892i	$-0.479327\pi$
$227$	14.1545	−	7.72894i	0.939467	−	0.512988i	0.874567	+	0.484904i	$0.161145\pi$
$228$	0.943850	+	0.280493i	0.0625080	+	0.0185761i
$229$		−	11.4683i		−	0.757848i	−0.925428	−	0.378924i	$-0.876294\pi$
$229$		−	11.4683i		−	0.757848i	0.925428	−	0.378924i	$-0.123706\pi$
$230$	−3.52239	+	14.7510i	−0.232259	+	0.972654i
$231$		−	0.764701i		−	0.0503137i
$232$	−3.19453	−	18.2167i	−0.209731	−	1.19598i
$233$	3.94188	−	2.15243i	0.258241	−	0.141010i	−0.344914	−	0.938634i	$-0.612092\pi$
$233$	3.94188	−	2.15243i	0.258241	−	0.141010i	0.603155	+	0.797624i	$0.293910\pi$
$234$	2.57232	−	6.18155i	0.168158	−	0.404100i
$235$	−15.1424	−	15.7068i	−0.987784	−	1.02460i
$236$	11.1472	−	2.38681i	0.725623	−	0.155368i
$237$	−1.62230	+	1.21444i	−0.105380	+	0.0788865i
$238$	−18.7736	−	0.701216i	−1.21691	−	0.0454531i
$239$	−11.7760	−	7.56797i	−0.761725	−	0.489531i	0.101198	−	0.994866i	$-0.467733\pi$
$239$	−11.7760	−	7.56797i	−0.761725	−	0.489531i	−0.862923	+	0.505335i	$0.831369\pi$
$240$	1.51374	−	1.07559i	0.0977118	−	0.0694290i
$241$	−3.28924	−	7.20243i	−0.211878	−	0.463949i	0.773616	−	0.633654i	$-0.218446\pi$
$241$	−3.28924	−	7.20243i	−0.211878	−	0.463949i	−0.985495	+	0.169705i	$0.945718\pi$
$242$	1.47310	+	13.9157i	0.0946942	+	0.894535i
$243$	−3.29519	+	4.40186i	−0.211386	+	0.282379i
$244$	−0.165227	−	0.447452i	−0.0105776	−	0.0286452i
$245$	11.2566	+	3.53014i	0.719160	+	0.225532i
$246$	−1.26704	+	0.419412i	−0.0807833	+	0.0267407i
$247$	−0.270860	−	3.78712i	−0.0172344	−	0.240969i
$248$	−0.0119066	+	0.0283512i	−0.000756071	+	0.00180031i
$249$	0.640323	−	0.554843i	0.0405788	−	0.0351618i
$250$	10.9453	+	11.4106i	0.692240	+	0.721667i
$251$	−5.14420	−	2.34928i	−0.324699	−	0.148285i	0.246395	−	0.969169i	$-0.420754\pi$
$251$	−5.14420	−	2.34928i	−0.324699	−	0.148285i	−0.571095	+	0.820884i	$0.693481\pi$
$252$	−2.88174	−	20.5187i	−0.181533	−	1.29256i
$253$	−4.14051	−	2.87649i	−0.260312	−	0.180844i
$254$	23.0288	−	11.4804i	1.44496	−	0.720344i
$255$	1.49790	−	0.924371i	0.0938020	−	0.0578863i
$256$	15.4095	−	4.30666i	0.963094	−	0.269166i
$257$	−0.982487	+	13.7370i	−0.0612859	+	0.856888i	0.870105	+	0.492867i	$0.164051\pi$
$257$	−0.982487	+	13.7370i	−0.0612859	+	0.856888i	−0.931391	+	0.364021i	$0.881404\pi$
$258$	−0.383704	−	1.51365i	−0.0238884	−	0.0942360i
$259$	−22.3027	+	25.7387i	−1.38582	+	1.59932i
$260$	−5.93890	−	4.00019i	−0.368315	−	0.248081i
$261$	18.5515	−	5.44721i	1.14831	−	0.337174i
$262$	−21.3751	+	17.1676i	−1.32056	+	1.06062i
$263$	−0.612252	+	0.817873i	−0.0377531	+	0.0504322i	−0.819021	−	0.573764i	$-0.805483\pi$
$263$	−0.612252	+	0.817873i	−0.0377531	+	0.0504322i	0.781267	+	0.624196i	$0.214573\pi$
$264$	0.149734	+	0.598886i	0.00921546	+	0.0368589i
$265$	2.98022	−	2.14704i	0.183074	−	0.131892i
$266$	−6.68543	−	9.66252i	−0.409910	−	0.592447i
$267$	1.07917	−	0.234759i	0.0660440	−	0.0143670i
$268$	28.0704	−	12.7086i	1.71468	−	0.776304i
$269$	−7.33267	−	1.05428i	−0.447081	−	0.0642805i	−0.0849024	−	0.996389i	$-0.527058\pi$
$269$	−7.33267	−	1.05428i	−0.447081	−	0.0642805i	−0.362179	+	0.932109i	$0.617967\pi$
$270$	2.60741	+	2.91491i	0.158682	+	0.177396i
$271$	2.80311	+	4.36173i	0.170277	+	0.264956i	0.915895	−	0.401417i	$-0.131482\pi$
$271$	2.80311	+	4.36173i	0.170277	+	0.264956i	−0.745618	+	0.666373i	$0.767846\pi$
$272$	14.8401	−	3.12682i	0.899812	−	0.189591i
$273$	1.02222	−	0.558176i	0.0618678	−	0.0337824i
$274$	20.8758	−	0.711430i	1.26115	−	0.0429790i
$275$	−4.85793	+	2.00719i	−0.292944	+	0.121038i
$276$	1.77757	+	0.897675i	0.106997	+	0.0540337i
$277$	−13.2343	−	13.2343i	−0.795173	−	0.795173i	0.187157	−	0.982330i	$-0.440073\pi$
$277$	−13.2343	−	13.2343i	−0.795173	−	0.795173i	−0.982330	+	0.187157i	$0.940073\pi$
$278$	18.8010	−	20.1276i	1.12761	−	1.20718i
$279$	−0.0308445	−	0.00905676i	−0.00184661	−	0.000542214i
$280$	−22.1209	−	1.30429i	−1.32198	−	0.0779462i
$281$	4.48972	−	2.88536i	0.267834	−	0.172126i	−0.399830	−	0.916589i	$-0.630931\pi$
$281$	4.48972	−	2.88536i	0.267834	−	0.172126i	0.667664	+	0.744463i	$0.267294\pi$
$282$	−2.46613	+	1.45778i	−0.146856	+	0.0868096i
$283$	−26.5784	+	19.8964i	−1.57992	+	1.18272i	−0.692857	+	0.721075i	$0.743648\pi$
$283$	−26.5784	+	19.8964i	−1.57992	+	1.18272i	−0.887067	+	0.461641i	$0.847261\pi$
$284$	−0.623873	+	1.65612i	−0.0370201	+	0.0982726i
$285$	1.02425	+	0.403516i	0.0606713	+	0.0239022i
$286$	1.95752	−	1.35439i	0.115750	−	0.0800869i
$287$	14.9223	+	5.56573i	0.880836	+	0.328535i
$288$	6.27458	+	15.5053i	0.369733	+	0.913656i
$289$	−2.59799	+	0.373534i	−0.152823	+	0.0219726i
$290$	−1.80027	−	20.5991i	−0.105715	−	1.20962i
$291$	0.888975	+	3.02757i	0.0521127	+	0.177479i
$292$	0.0471683	−	14.4334i	0.00276031	−	0.844648i
$293$	−0.689994	−	9.64738i	−0.0403099	−	0.563606i	−0.976971	−	0.213370i	$-0.931556\pi$
$293$	−0.689994	−	9.64738i	−0.0403099	−	0.563606i	0.936662	−	0.350236i	$-0.113899\pi$
$294$	0.792613	−	1.33092i	0.0462261	−	0.0776207i
$295$	12.6468	−	1.58281i	0.736325	−	0.0921550i
$296$	12.4269	−	24.5246i	0.722296	−	1.42546i
$297$	−1.21815	+	0.454348i	−0.0706845	+	0.0263639i
$298$	4.57763	−	13.6790i	0.265175	−	0.792400i
$299$	0.822915	−	7.63451i	0.0475904	−	0.441515i
$300$	1.78990	−	1.05197i	0.103340	−	0.0607358i
$301$	−7.74079	+	16.9500i	−0.446171	+	0.976979i
$302$	−17.6544	+	25.3388i	−1.01590	+	1.45808i
$303$	−0.162878	+	2.27733i	−0.00935710	+	0.130829i
$304$	7.12777	+	6.25828i	0.408806	+	0.358937i
$305$	−0.140859	−	0.514344i	−0.00806557	−	0.0294513i
$306$	4.98234	+	15.0516i	0.284821	+	0.860440i
$307$	−12.1890	+	22.3226i	−0.695665	+	1.27402i	0.255940	+	0.966693i	$0.417615\pi$
$307$	−12.1890	+	22.3226i	−0.695665	+	1.27402i	−0.951605	+	0.307323i	$0.900567\pi$
$308$	3.08205	−	6.69080i	0.175616	−	0.381244i
$309$	0.125477	−	0.0180409i	0.00713815	−	0.00102631i
$310$	−0.0159983	+	0.0304303i	−0.000908645	+	0.00172833i
$311$	15.1955	−	6.93953i	0.861655	−	0.393505i	0.0649612	−	0.997888i	$-0.479308\pi$
$311$	15.1955	−	6.93953i	0.861655	−	0.393505i	0.796694	+	0.604383i	$0.206580\pi$
$312$	−0.691273	+	0.637301i	−0.0391357	+	0.0360801i
$313$	−33.2519	+	7.23350i	−1.87951	+	0.408862i	−0.997995	−	0.0632992i	$-0.979838\pi$
$313$	−33.2519	+	7.23350i	−1.87951	+	0.408862i	−0.881512	+	0.472161i	$0.843474\pi$
$314$	−10.3801	−	11.1856i	−0.585785	−	0.631242i
$315$	−1.22971	−	23.1331i	−0.0692864	−	1.30340i
$316$	−19.0891	+	4.08730i	−1.07385	+	0.229928i
$317$	1.72298	+	0.374811i	0.0967721	+	0.0210515i	0.260691	−	0.965422i	$-0.416050\pi$
$317$	1.72298	+	0.374811i	0.0967721	+	0.0210515i	−0.163918	+	0.986474i	$0.552413\pi$
$318$	−0.183841	−	0.445890i	−0.0103093	−	0.0250043i
$319$	6.59554	+	1.93662i	0.369279	+	0.108430i
$320$	17.5797	−	3.30994i	0.982733	−	0.185031i
$321$	−1.19042			−0.0664427
$322$	−9.83032	−	21.6346i	−0.547822	−	1.20565i
$323$	6.35748	+	6.35748i	0.353740	+	0.353740i
$324$	−15.1474	+	8.20697i	−0.841523	+	0.455943i
$325$	−6.22907	−	5.02879i	−0.345527	−	0.278947i
$326$	−7.04830	+	16.9378i	−0.390369	+	0.938096i
$327$	0.118811	−	0.546164i	0.00657024	−	0.0302029i
$328$	−12.7764	−	1.43699i	−0.705460	−	0.0793448i
$329$	33.8376	+	4.86512i	1.86553	+	0.268223i
$330$	0.108987	+	0.681526i	0.00599955	+	0.0375168i
$331$	−0.317148	+	0.493492i	−0.0174320	+	0.0271248i	−0.849860	−	0.527008i	$-0.823314\pi$
$331$	−0.317148	+	0.493492i	−0.0174320	+	0.0271248i	0.832428	+	0.554133i	$0.186950\pi$
$332$	7.83879	−	2.27388i	0.430209	−	0.124795i
$333$	26.9299	+	10.0443i	1.47575	+	0.550426i
$334$	−3.21726	−	2.60131i	−0.176040	−	0.142337i
$335$	32.4930	−	11.4467i	1.77528	−	0.625402i
$336$	−0.837980	+	2.78640i	−0.0457156	+	0.152010i
$337$	−7.26962	−	3.96951i	−0.396001	−	0.216233i	0.268894	−	0.963170i	$-0.413342\pi$
$337$	−7.26962	−	3.96951i	−0.396001	−	0.216233i	−0.664895	+	0.746937i	$0.731524\pi$
$338$	−13.1873	−	6.62807i	−0.717296	−	0.360520i
$339$	1.29886	−	1.49896i	0.0705442	−	0.0814124i
$340$	16.8315	−	2.05071i	0.912818	−	0.111215i
$341$	−0.00748438	−	0.00863744i	−0.000405302	−	0.000467743i
$342$	−5.66870	+	8.13608i	−0.306528	+	0.439949i
$343$	5.65996	−	2.11106i	0.305609	−	0.113986i
$344$	2.74339	−	14.7903i	0.147914	−	0.797439i
$345$	1.89333	+	1.17143i	0.101934	+	0.0630676i
$346$	−31.7951	+	15.8506i	−1.70932	+	0.852133i
$347$	−11.0243	−	29.5572i	−0.591814	−	1.58672i	−0.794363	−	0.607444i	$-0.792195\pi$
$347$	−11.0243	−	29.5572i	−0.591814	−	1.58672i	0.202548	−	0.979272i	$-0.435078\pi$
$348$	−2.68621	−	0.395183i	−0.143996	−	0.0211840i
$349$	7.32240	−	6.34489i	0.391959	−	0.339634i	−0.436480	−	0.899714i	$-0.643775\pi$
$349$	7.32240	−	6.34489i	0.391959	−	0.339634i	0.828439	+	0.560080i	$0.189229\pi$
$350$	−24.5137	−	3.58756i	−1.31031	−	0.191763i
$351$	−1.49652	−	1.29674i	−0.0798782	−	0.0692149i
$352$	−1.10365	+	5.84348i	−0.0588246	+	0.311458i
$353$	−6.48323	+	11.8731i	−0.345067	+	0.631944i	−0.991363	−	0.131143i	$-0.958135\pi$
$353$	−6.48323	+	11.8731i	−0.345067	+	0.631944i	0.646296	+	0.763087i	$0.276317\pi$
$354$	0.181615	−	1.66369i	0.00965275	−	0.0884240i
$355$	−0.854731	+	1.78448i	−0.0453644	+	0.0947104i
$356$	10.3884	+	2.29544i	0.550585	+	0.121658i
$357$	−0.963819	+	2.58410i	−0.0510107	+	0.136765i
$358$	3.75860	−	20.6394i	0.198648	−	1.09083i
$359$	−19.3452	−	12.4324i	−1.02100	−	0.656158i	−0.0807843	−	0.996732i	$-0.525743\pi$
$359$	−19.3452	−	12.4324i	−1.02100	−	0.656158i	−0.940218	+	0.340573i	$0.889379\pi$
$360$	5.49268	+	17.8762i	0.289490	+	0.942160i
$361$	1.90372	−	13.2406i	0.100196	−	0.696876i
$362$	11.3534	−	6.71125i	0.596723	−	0.352735i
$363$	2.00737	+	0.436678i	0.105360	+	0.0229196i
$364$	11.1937	−	0.763828i	0.586708	−	0.0400355i
$365$	1.44542	−	16.0722i	0.0756567	−	0.841257i
$366$	−0.0699834	+	0.00238497i	−0.00365809	+	0.000124664i
$367$	5.78428	−	5.78428i	0.301937	−	0.301937i	−0.539834	−	0.841771i	$-0.681513\pi$
$367$	5.78428	−	5.78428i	0.301937	−	0.301937i	0.841771	+	0.539834i	$0.181513\pi$
$368$	11.9349	+	15.0186i	0.622152	+	0.782897i
$369$		−	13.4409i		−	0.699708i
$370$	16.2085	−	26.1178i	0.842641	−	1.35780i
$371$	−1.62147	+	5.52222i	−0.0841825	+	0.286699i
$372$	0.00340198	+	0.00296736i	0.000176385	+	0.000153850i
$373$	3.38197	−	15.5467i	0.175112	−	0.804976i	−0.802848	−	0.596184i	$-0.796683\pi$
$373$	3.38197	−	15.5467i	0.175112	−	0.804976i	0.977960	−	0.208793i	$-0.0669534\pi$
$374$	−1.40293	+	5.45940i	−0.0725440	+	0.282299i
$375$	2.09522	−	0.999021i	0.108197	−	0.0515892i
$376$	−27.4530	+	2.81545i	−1.41578	+	0.145196i
$377$	2.22546	+	10.2303i	0.114617	+	0.526885i
$378$	−6.02886	−	1.09790i	−0.310091	−	0.0564699i
$379$	9.91044	+	21.7008i	0.509065	+	1.11470i	0.973416	+	0.229046i	$0.0735605\pi$
$379$	9.91044	+	21.7008i	0.509065	+	1.11470i	−0.464350	+	0.885652i	$0.653712\pi$
$380$	7.33540	+	7.65872i	0.376298	+	0.392884i
$381$	−0.537606	−	3.73913i	−0.0275424	−	0.191562i
$382$	−0.446239	+	0.358401i	−0.0228316	+	0.0183374i
$383$	15.6859	+	8.56517i	0.801514	+	0.437659i	0.827129	−	0.562012i	$-0.189973\pi$
$383$	15.6859	+	8.56517i	0.801514	+	0.437659i	−0.0256153	+	0.999672i	$0.508154\pi$
$384$	0.110681	−	2.34629i	0.00564816	−	0.119733i
$385$	4.07867	−	7.15519i	0.207868	−	0.364662i
$386$	−6.35291	+	10.6675i	−0.323355	+	0.542962i
$387$	15.6857	+	1.12187i	0.797351	+	0.0570277i
$388$	−4.42418	+	30.0728i	−0.224604	+	1.52672i
$389$	26.9380	+	12.3022i	1.36581	+	0.623745i	0.957323	−	0.289019i	$-0.0933292\pi$
$389$	26.9380	+	12.3022i	1.36581	+	0.623745i	0.408487	+	0.912764i	$0.366056\pi$
$390$	−0.831485	+	0.643154i	−0.0421039	+	0.0325674i
$391$	10.3662	+	14.9390i	0.524243	+	0.755496i
$392$	12.2991	−	8.45039i	0.621200	−	0.426809i
$393$	1.40652	+	3.77103i	0.0709495	+	0.190223i
$394$	2.17238	+	12.1543i	0.109443	+	0.612327i
$395$	−21.6571	+	2.71050i	−1.08969	+	0.136380i
$396$	−6.19957	−	0.463771i	−0.311540	−	0.0233054i
$397$	12.8042	−	0.915777i	0.642626	−	0.0459616i	0.253777	−	0.967263i	$-0.418327\pi$
$397$	12.8042	−	0.915777i	0.642626	−	0.0459616i	0.388850	+	0.921301i	$0.372873\pi$
$398$	−12.0925	+	24.0594i	−0.606141	+	1.20599i
$399$	−1.65508	+	0.485974i	−0.0828575	+	0.0243292i
$400$	19.9007	−	1.99030i	0.995036	−	0.0995151i
$401$	3.45563	+	24.0344i	0.172566	+	1.20022i	0.873438	+	0.486935i	$0.161885\pi$
$401$	3.45563	+	24.0344i	0.172566	+	1.20022i	−0.700872	+	0.713287i	$0.747206\pi$
$402$	−0.476198	−	4.49844i	−0.0237506	−	0.224362i
$403$	0.00608314	−	0.0163095i	0.000303023	−	0.000812435i
$404$	−10.6037	+	19.2692i	−0.527552	+	0.958678i
$405$	−17.6641	+	7.67963i	−0.877738	+	0.381604i
$406$	22.0390	+	23.7493i	1.09378	+	1.17866i
$407$	6.12375	+	8.18038i	0.303543	+	0.405486i
$408$	0.248845	−	2.21249i	0.0123196	−	0.109535i
$409$	−18.1982	−	28.3169i	−0.899841	−	1.40018i	−0.916377	−	0.400316i	$-0.868900\pi$
$409$	−18.1982	−	28.3169i	−0.899841	−	1.40018i	0.0165365	−	0.999863i	$-0.494736\pi$
$410$	−14.0925	−	2.83359i	−0.695978	−	0.139941i
$411$	0.863926	−	2.94226i	0.0426143	−	0.145131i
$412$	1.17058	+	0.347873i	0.0576705	+	0.0171385i
$413$	−14.1215	+	14.1215i	−0.694875	+	0.694875i
$414$	−14.2078	+	14.1537i	−0.698276	+	0.695616i
$415$	8.95076	−	1.77631i	0.439376	−	0.0871954i
$416$	−8.61692	+	2.79000i	−0.422479	+	0.136791i
$417$	−1.93781	−	3.54883i	−0.0948949	−	0.173787i
$418$	−3.25929	+	1.34381i	−0.159417	+	0.0657277i
$419$	12.0311	−	7.73192i	0.587758	−	0.377729i	−0.212701	−	0.977117i	$-0.568226\pi$
$419$	12.0311	−	7.73192i	0.587758	−	0.377729i	0.800458	+	0.599388i	$0.204590\pi$
$420$	−1.20229	+	3.02279i	−0.0586659	+	0.147497i
$421$	−2.59687	+	18.0617i	−0.126564	+	0.880271i	0.823300	+	0.567607i	$0.192131\pi$
$421$	−2.59687	+	18.0617i	−0.126564	+	0.880271i	−0.949864	+	0.312664i	$0.898778\pi$
$422$	−0.512973	+	13.7337i	−0.0249711	+	0.668548i
$423$	−6.13261	−	28.1912i	−0.298178	−	1.37070i
$424$	0.188590	−	4.64229i	0.00915872	−	0.225450i
$425$	18.9459	−	0.659891i	0.919011	−	0.0320094i
$426$	0.202030	+	0.163351i	0.00978838	+	0.00791439i
$427$	0.668934	+	0.500757i	0.0323720	+	0.0242333i
$428$	−10.4156	−	4.79787i	−0.503459	−	0.231914i
$429$	−0.0984529	−	0.335300i	−0.00475335	−	0.0161884i
$430$	4.48308	−	16.2096i	0.216193	−	0.781695i
$431$	21.7180	+	18.8187i	1.04612	+	0.906467i	0.995735	−	0.0922626i	$-0.0294099\pi$
$431$	21.7180	+	18.8187i	1.04612	+	0.906467i	0.0503843	+	0.998730i	$0.483955\pi$
$432$	4.93656	−	0.320654i	0.237510	−	0.0154275i
$433$	21.7132	+	1.55296i	1.04347	+	0.0746303i	0.582536	−	0.812805i	$-0.302061\pi$
$433$	21.7132	+	1.55296i	1.04347	+	0.0746303i	0.460932	+	0.887436i	$0.347515\pi$
$434$	−0.00947802	−	0.0530289i	−0.000454959	−	0.00254547i
$435$	−2.95393	−	0.699410i	−0.141630	−	0.0335342i
$436$	3.24080	−	4.29984i	0.155206	−	0.205925i
$437$	−3.59439	+	10.7895i	−0.171943	+	0.516133i
$438$	−2.00938	−	0.672436i	−0.0960120	−	0.0321302i
$439$	14.8180	−	32.4469i	0.707224	−	1.54860i	−0.123762	−	0.992312i	$-0.539496\pi$
$439$	14.8180	−	32.4469i	0.707224	−	1.54860i	0.830986	−	0.556293i	$-0.187777\pi$
$440$	−1.79323	+	6.40232i	−0.0854890	+	0.305218i
$441$	10.2159	+	11.7898i	0.486474	+	0.561421i
$442$	−8.32195	+	2.10957i	−0.395835	+	0.100342i
$443$	17.8662	−	1.27782i	0.848850	−	0.0607110i	0.359866	−	0.933004i	$-0.382822\pi$
$443$	17.8662	−	1.27782i	0.848850	−	0.0607110i	0.488984	+	0.872293i	$0.337368\pi$
$444$	−2.84467	−	2.86332i	−0.135002	−	0.135887i
$445$	11.3497	+	3.55933i	0.538029	+	0.168729i
$446$	1.75123	−	16.0421i	0.0829230	−	0.759616i
$447$	−1.69524	−	1.26904i	−0.0801820	−	0.0600235i
$448$	−18.5622	+	21.0023i	−0.876984	+	0.992268i
$449$	−25.3233	+	11.5647i	−1.19508	+	0.545774i	−0.910752	−	0.412954i	$-0.864497\pi$
$449$	−25.3233	+	11.5647i	−1.19508	+	0.545774i	−0.284326	+	0.958728i	$0.591770\pi$
$450$	4.39295	+	20.4417i	0.207086	+	0.963632i
$451$	2.58351	−	4.02002i	0.121653	−	0.189295i
$452$	17.4058	−	7.88034i	0.818702	−	0.370660i
$453$	2.71697	+	3.62945i	0.127654	+	0.170526i
$454$	5.67650	−	22.0896i	0.266411	−	1.03672i
$455$	12.5419	+	0.229440i	0.587974	+	0.0107563i
$456$	1.20104	−	0.704672i	0.0562438	−	0.0329993i
$457$	7.66862	+	14.0440i	0.358723	+	0.656952i	0.993256	−	0.115944i	$-0.0369893\pi$
$457$	7.66862	+	14.0440i	0.358723	+	0.656952i	−0.634533	+	0.772896i	$0.718807\pi$
$458$	−11.8523	−	11.0711i	−0.553820	−	0.517317i
$459$	4.68907			0.218867
$460$	11.8445	+	17.8804i	0.552253	+	0.833677i
$461$	−23.3258			−1.08639			−0.543195	−	0.839606i	$-0.682786\pi$
$461$	−23.3258			−1.08639			−0.543195	+	0.839606i	$0.682786\pi$
$462$	−0.790303	−	0.738213i	−0.0367682	−	0.0343448i
$463$	−13.6914	−	25.0740i	−0.636295	−	1.16529i	−0.974537	−	0.224227i	$-0.928014\pi$
$463$	−13.6914	−	25.0740i	−0.636295	−	1.16529i	0.338242	−	0.941059i	$-0.390168\pi$
$464$	−21.9104	−	14.2842i	−1.01717	−	0.663126i
$465$	0.00350298	+	0.00363353i	0.000162447	+	0.000168501i
$466$	1.58085	−	6.15173i	0.0732313	−	0.284973i
$467$	11.5063	+	15.3707i	0.532450	+	0.711270i	0.983435	−	0.181262i	$-0.0580181\pi$
$467$	11.5063	+	15.3707i	0.532450	+	0.711270i	−0.450985	+	0.892532i	$0.648927\pi$
$468$	−3.90528	−	8.62586i	−0.180522	−	0.398731i
$469$	−29.1839	+	45.4110i	−1.34759	+	2.09689i
$470$	−30.8506	+	0.486680i	−1.42303	+	0.0224489i
$471$	−2.03780	+	0.930633i	−0.0938969	+	0.0428813i
$472$	8.29438	−	13.8246i	0.381780	−	0.636327i
$473$	4.47577	+	3.35052i	0.205796	+	0.154057i
$474$	−0.311008	+	2.84899i	−0.0142851	+	0.130859i
$475$	7.43152	+	9.23865i	0.340981	+	0.423898i
$476$	−18.8479	+	18.7252i	−0.863894	+	0.858266i
$477$	4.84478	−	0.346505i	0.221827	−	0.0158654i
$478$	−19.1894	+	4.86442i	−0.877703	+	0.222493i
$479$	4.79851	+	5.53777i	0.219249	+	0.253027i	0.854710	−	0.519106i	$-0.173735\pi$
$479$	4.79851	+	5.53777i	0.219249	+	0.253027i	−0.635460	+	0.772134i	$0.719190\pi$
$480$	0.349710	−	2.60276i	0.0159620	−	0.118799i
$481$	−6.46532	+	14.1571i	−0.294793	+	0.645507i
$482$	−10.6189	−	3.55358i	−0.483676	−	0.161861i
$483$	−3.46869	+	0.371960i	−0.157831	+	0.0169248i
$484$	15.8037	+	11.9113i	0.718348	+	0.541421i
$485$	−7.83008	+	33.0700i	−0.355546	+	1.50163i
$486$	1.36818	+	7.65489i	0.0620620	+	0.347233i
$487$	36.6349	+	2.62018i	1.66009	+	0.118732i	0.869603	−	0.493752i	$-0.164375\pi$
$487$	36.6349	+	2.62018i	1.66009	+	0.118732i	0.790483	+	0.612484i	$0.209830\pi$
$488$	−0.621936	−	0.261193i	−0.0281537	−	0.0118237i
$489$	2.03543	+	1.76371i	0.0920455	+	0.0797579i
$490$	14.5150	−	8.22565i	0.655723	−	0.371597i
$491$	0.543353	+	1.85049i	0.0245212	+	0.0835114i	0.970845	−	0.239710i	$-0.0770523\pi$
$491$	0.543353	+	1.85049i	0.0245212	+	0.0835114i	−0.946323	+	0.323221i	$0.895234\pi$
$492$	−0.789694	+	1.71434i	−0.0356022	+	0.0772884i
$493$	−19.8469	−	14.8572i	−0.893861	−	0.669136i
$494$	−4.17539	−	3.37601i	−0.187860	−	0.151894i
$495$	−6.86070	−	1.11486i	−0.308366	−	0.0501093i
$496$	0.0178062	+	0.0396744i	0.000799523	+	0.00178143i
$497$	−0.659016	−	3.02945i	−0.0295609	−	0.135889i
$498$	0.0447238	−	1.19738i	0.00200412	−	0.0536561i
$499$	−3.71225	+	25.8193i	−0.166183	+	1.15583i	0.720501	+	0.693454i	$0.243912\pi$
$499$	−3.71225	+	25.8193i	−0.166183	+	1.15583i	−0.886684	+	0.462376i	$0.846997\pi$
$500$	22.3587	−	0.296413i	0.999912	−	0.0132560i
$501$	−0.510965	+	0.328377i	−0.0228282	+	0.0146708i
$502$	−7.39394	+	3.04853i	−0.330008	+	0.136062i
$503$	−17.5667	−	32.1711i	−0.783262	−	1.43444i	−0.897514	−	0.440985i	$-0.854629\pi$
$503$	−17.5667	−	32.1711i	−0.783262	−	1.43444i	0.114252	−	0.993452i	$-0.463553\pi$
$504$	−23.9876	−	16.8298i	−1.06849	−	0.749657i
$505$	−13.6706	+	20.4399i	−0.608333	+	0.909564i
$506$	−6.96988	+	1.50228i	−0.309849	+	0.0667845i
$507$	−1.53212	+	1.53212i	−0.0680441	+	0.0680441i
$508$	10.3664	−	34.8825i	0.459934	−	1.54766i
$509$	−2.25469	+	7.67876i	−0.0999372	+	0.340355i	−0.994250	−	0.107088i	$-0.965847\pi$
$509$	−2.25469	+	7.67876i	−0.0999372	+	0.340355i	0.894312	+	0.447443i	$0.147665\pi$
$510$	0.490694	−	2.44040i	0.0217283	−	0.108063i
$511$	13.6702	+	21.2712i	0.604733	+	0.940983i
$512$	10.4249	−	20.0829i	0.460719	−	0.887546i
$513$	1.75751	+	2.34776i	0.0775961	+	0.103656i
$514$	13.2484	+	14.2765i	0.584362	+	0.629710i
$515$	1.27030	+	0.500449i	0.0559759	+	0.0220524i
$516$	−1.93474	−	1.06467i	−0.0851723	−	0.0468696i
$517$	3.58449	−	9.61038i	0.157646	−	0.422664i
$518$	5.07025	+	47.8965i	0.222774	+	2.10445i
$519$	0.742254	+	5.16249i	0.0325814	+	0.226608i
$520$	−9.86730	+	2.27610i	−0.432710	+	0.0998136i
$521$	−37.1538	+	10.9093i	−1.62774	+	0.477947i	−0.963083	−	0.269205i	$-0.913239\pi$
$521$	−37.1538	+	10.9093i	−1.62774	+	0.477947i	−0.664654	+	0.747152i	$0.731421\pi$
$522$	12.2793	−	24.4311i	0.537451	−	1.06932i
$523$	−0.0247200	+	0.00176801i	−0.00108093	+	7.73098e-5i	−0.0718796	−	0.997413i	$-0.522900\pi$
$523$	−0.0247200	+	0.00176801i	−0.00108093	+	7.73098e-5i	0.0707987	+	0.997491i	$0.477445\pi$
$524$	−2.89231	+	38.6636i	−0.126351	+	1.68903i
$525$	−1.63090	+	3.25094i	−0.0711783	+	0.141883i
$526$	0.254211	+	1.42229i	0.0110841	+	0.0620149i
$527$	0.0144049	+	0.0386211i	0.000627488	+	0.00168236i
$528$	0.763483	+	0.423395i	0.0332263	+	0.0184259i
$529$	−11.0338	+	20.1806i	−0.479731	+	0.877416i
$530$	0.658064	−	5.15267i	0.0285845	−	0.223818i
$531$	15.3311	+	7.00147i	0.665312	+	0.303838i
$532$	−16.4399	−	2.41856i	−0.712759	−	0.104858i
$533$	7.25958	+	0.519215i	0.314447	+	0.0224897i
$534$	0.799168	−	1.34192i	0.0345834	−	0.0580708i
$535$	−11.1386	−	6.34931i	−0.481562	−	0.274505i
$536$	13.9640	−	41.2786i	0.603152	−	1.78297i
$537$	−2.70310	−	1.47600i	−0.116647	−	0.0636942i
$538$	−8.16825	+	6.56040i	−0.352158	+	0.282839i
$539$	0.789317	+	5.48982i	0.0339983	+	0.236463i
$540$	5.52959	+	0.119235i	0.237956	+	0.00513107i
$541$	−1.77561	−	3.88804i	−0.0763394	−	0.167160i	0.867614	−	0.497238i	$-0.165652\pi$
$541$	−1.77561	−	3.88804i	−0.0763394	−	0.167160i	−0.943954	+	0.330078i	$0.892925\pi$
$542$	7.21377	+	1.31368i	0.309858	+	0.0564275i
$543$	−0.411564	−	1.89193i	−0.0176619	−	0.0811904i
$544$	11.0945	−	18.3554i	0.475674	−	0.786982i
$545$	4.02475	−	4.47667i	0.172401	−	0.191760i
$546$	0.409951	−	1.59529i	0.0175443	−	0.0682720i
$547$	−6.07597	+	27.9308i	−0.259790	+	1.19423i	0.643582	+	0.765377i	$0.277447\pi$
$547$	−6.07597	+	27.9308i	−0.259790	+	1.19423i	−0.903372	+	0.428857i	$0.858916\pi$
$548$	19.4175	−	22.2615i	0.829473	−	0.950965i
$549$	0.198676	−	0.676630i	0.00847930	−	0.0288779i
$550$	−2.61526	+	6.95824i	−0.111515	+	0.296700i
$551$		−	15.5058i		−	0.660567i
$552$	2.64372	−	0.970498i	0.112524	−	0.0413071i
$553$	24.1825	−	24.1825i	1.02834	−	1.02834i
$554$	−26.4533	+	0.901504i	−1.12389	+	0.0383012i
$555$	−2.89225	−	3.46387i	−0.122769	−	0.147033i
$556$	−2.65177	−	38.8609i	−0.112460	−	1.64807i
$557$	28.1667	+	6.12729i	1.19346	+	0.259622i	0.765056	−	0.643964i	$-0.222711\pi$
$557$	28.1667	+	6.12729i	1.19346	+	0.259622i	0.428407	+	0.903586i	$0.359075\pi$
$558$	−0.0391360	+	0.0231341i	−0.00165676	+	0.000979344i
$559$	−1.21186	+	8.42867i	−0.0512562	+	0.356495i
$560$	−22.7026	+	21.6024i	−0.959359	+	0.912866i
$561$	0.696147	+	0.447387i	0.0293914	+	0.0188887i
$562$	1.35223	−	7.42544i	0.0570404	−	0.313223i
$563$	−11.9099	+	31.9317i	−0.501943	+	1.34576i	0.401030	+	0.916065i	$0.368652\pi$
$563$	−11.9099	+	31.9317i	−0.501943	+	1.34576i	−0.902973	+	0.429697i	$0.858620\pi$
$564$	−0.874121	+	3.95598i	−0.0368071	+	0.166577i
$565$	20.1482	−	7.09786i	0.847640	−	0.298609i
$566$	−5.09529	+	46.6754i	−0.214171	+	1.96191i
$567$	14.4640	−	26.4888i	0.607431	−	1.11243i
$568$	1.10930	+	2.24351i	0.0465453	+	0.0941357i
$569$	−23.7164	−	20.5504i	−0.994244	−	0.861517i	−0.00387811	−	0.999992i	$-0.501234\pi$
$569$	−23.7164	−	20.5504i	−0.994244	−	0.861517i	−0.990366	+	0.138475i	$0.955780\pi$
$570$	1.40579	−	0.669002i	0.0588823	−	0.0280214i
$571$	34.4116	−	29.8178i	1.44008	−	1.24784i	0.521123	−	0.853481i	$-0.325513\pi$
$571$	34.4116	−	29.8178i	1.44008	−	1.24784i	0.918958	−	0.394356i	$-0.129032\pi$
$572$	0.489972	−	3.33053i	0.0204868	−	0.139256i
$573$	0.0293633	+	0.0787261i	0.00122667	+	0.00328883i
$574$	20.1575	−	10.0490i	0.841357	−	0.419435i
$575$	11.4676	+	21.0593i	0.478232	+	0.878233i
$576$	22.0816	+	8.48353i	0.920066	+	0.353480i
$577$	2.54613	−	0.949658i	0.105997	−	0.0395348i	−0.295906	−	0.955217i	$-0.595622\pi$
$577$	2.54613	−	0.949658i	0.105997	−	0.0395348i	0.401903	+	0.915682i	$0.368349\pi$
$578$	−2.12196	+	3.04556i	−0.0882617	+	0.126679i
$579$	1.19363	+	1.37753i	0.0496058	+	0.0572481i
$580$	−23.0267	−	18.0250i	−0.956131	−	0.748449i
$581$	−9.36349	+	10.8060i	−0.388463	+	0.448310i
$582$	3.98711	+	2.00396i	0.165271	+	0.0830668i
$583$	1.51561	+	0.827588i	0.0627703	+	0.0342752i
$584$	−14.8710	−	13.9821i	−0.615368	−	0.578585i
$585$	−3.51751	−	9.98489i	−0.145431	−	0.412824i
$586$	−10.6365	−	8.60011i	−0.439388	−	0.355267i
$587$	−41.1214	−	15.3375i	−1.69726	−	0.633046i	−0.700515	−	0.713638i	$-0.747046\pi$
$587$	−41.1214	−	15.3375i	−1.69726	−	0.633046i	−0.996747	+	0.0805922i	$0.974319\pi$
$588$	−0.610318	−	2.10396i	−0.0251691	−	0.0867660i
$589$	−0.0139380	+	0.0216879i	−0.000574305	+	0.000893636i
$590$	10.5729	−	14.5982i	0.435280	−	0.600998i
$591$	1.79416	+	0.257961i	0.0738017	+	0.0106111i
$592$	−13.3493	−	36.5180i	−0.548652	−	1.50088i
$593$	8.30577	−	38.1810i	0.341077	−	1.56791i	−0.412757	−	0.910841i	$-0.635434\pi$
$593$	8.30577	−	38.1810i	0.341077	−	1.56791i	0.753834	−	0.657065i	$-0.228202\pi$
$594$	−0.706399	+	1.69755i	−0.0289839	+	0.0696512i
$595$	−22.8011	+	19.0383i	−0.934752	+	0.780495i
$596$	−9.71784	−	17.9360i	−0.398058	−	0.734687i
$597$	2.79526	+	2.79526i	0.114402	+	0.114402i
$598$	−7.09569	−	8.22052i	−0.290165	−	0.336162i
$599$	19.5805			0.800038			0.400019	−	0.916507i	$-0.369004\pi$
$599$	19.5805			0.800038			0.400019	+	0.916507i	$0.369004\pi$
$600$	0.640706	−	2.86536i	0.0261567	−	0.116978i
$601$	−11.9697	−	3.51461i	−0.488253	−	0.143364i	0.0283344	−	0.999599i	$-0.490980\pi$
$601$	−11.9697	−	3.51461i	−0.488253	−	0.143364i	−0.516587	+	0.856234i	$0.672798\pi$
$602$	10.0448	+	24.3628i	0.409395	+	0.992952i
$603$	44.5148	+	9.68360i	1.81278	+	0.394347i
$604$	9.14417	+	42.7065i	0.372071	+	1.73770i
$605$	16.4536	+	14.7926i	0.668934	+	0.601405i
$606$	2.19634	+	2.36678i	0.0892202	+	0.0961438i
$607$	−16.7286	+	3.63908i	−0.678991	+	0.147706i	−0.538819	−	0.842422i	$-0.681129\pi$
$607$	−16.7286	+	3.63908i	−0.678991	+	0.147706i	−0.140172	+	0.990127i	$0.544766\pi$
$608$	13.3487	−	1.32491i	0.541360	−	0.0537320i
$609$	4.32665	−	1.97591i	0.175325	−	0.0800681i
$610$	−0.667544	−	0.350953i	−0.0270281	−	0.0142097i
$611$	15.4632	−	2.22327i	0.625574	−	0.0899440i
$612$	20.3652	+	9.38104i	0.823215	+	0.379206i
$613$	8.30117	−	15.2025i	0.335281	−	0.614022i	−0.654591	−	0.755983i	$-0.727159\pi$
$613$	8.30117	−	15.2025i	0.335281	−	0.614022i	0.989872	+	0.141962i	$0.0453410\pi$
$614$	11.3031	+	34.1464i	0.456155	+	1.37804i
$615$	−1.04505	+	1.83333i	−0.0421405	+	0.0739269i
$616$	−3.93951	−	9.64427i	−0.158727	−	0.388579i
$617$	1.64379	−	22.9832i	0.0661766	−	0.925269i	−0.850586	−	0.525836i	$-0.823752\pi$
$617$	1.64379	−	22.9832i	0.0661766	−	0.925269i	0.916762	−	0.399433i	$-0.130793\pi$
$618$	0.102486	−	0.147094i	0.00412259	−	0.00591699i
$619$	−9.09622	+	19.9179i	−0.365608	+	0.800570i	0.634021	+	0.773316i	$0.281403\pi$
$619$	−9.09622	+	19.9179i	−0.365608	+	0.800570i	−0.999629	+	0.0272536i	$0.991324\pi$
$620$	0.0160049	+	0.0459102i	0.000642773	+	0.00184380i
$621$	2.65345	+	5.30456i	0.106479	+	0.212865i
$622$	7.49723	−	22.4033i	0.300611	−	0.898292i
$623$	−17.4628	+	6.51328i	−0.699631	+	0.260949i
$624$	−0.00869065	+	1.32964i	−0.000347904	+	0.0532283i
$625$	24.9331	+	1.82755i	0.997324	+	0.0731020i
$626$	−24.6244	+	41.3481i	−0.984188	+	1.65260i
$627$	0.0369220	+	0.516238i	0.00147452	+	0.0206165i
$628$	−21.5807	−	0.0705258i	−0.861163	−	0.00281429i
$629$	−10.3831	−	35.3616i	−0.414002	−	1.40996i
$630$	−25.0947	−	21.0609i	−0.999798	−	0.839087i
$631$	−13.7047	+	1.97044i	−0.545577	+	0.0784422i	−0.409592	−	0.912269i	$-0.634329\pi$
$631$	−13.7047	+	1.97044i	−0.545577	+	0.0784422i	−0.135985	+	0.990711i	$0.543420\pi$
$632$	−14.2038	+	23.6739i	−0.564995	+	0.941699i
$633$	1.89039	+	0.705079i	0.0751363	+	0.0280244i
$634$	2.05066	−	1.41883i	0.0814419	−	0.0563491i
$635$	14.9130	−	37.8539i	0.591806	−	1.50219i
$636$	−0.638291	−	0.240449i	−0.0253099	−	0.00953443i
$637$	−6.76243	+	5.06229i	−0.267937	+	0.200575i
$638$	8.36853	−	4.94681i	0.331313	−	0.195846i
$639$	−2.20110	+	1.41456i	−0.0870743	+	0.0559593i
$640$	13.5500	−	21.3635i	0.535609	−	0.844466i
$641$	10.8842	+	3.19589i	0.429901	+	0.126230i	0.489522	−	0.871991i	$-0.337171\pi$
$641$	10.8842	+	3.19589i	0.429901	+	0.126230i	−0.0596216	+	0.998221i	$0.518989\pi$
$642$	−1.14918	+	1.23027i	−0.0453547	+	0.0485550i
$643$	−21.9920	−	21.9920i	−0.867280	−	0.867280i	0.124891	−	0.992170i	$-0.460142\pi$
$643$	−21.9920	−	21.9920i	−0.867280	−	0.867280i	−0.992170	+	0.124891i	$0.960142\pi$
$644$	−31.8487	−	10.7257i	−1.25501	−	0.422653i
$645$	−2.05229	−	1.37261i	−0.0808088	−	0.0540464i
$646$	12.7076	−	0.433063i	0.499973	−	0.0170386i
$647$	−26.2913	+	14.3561i	−1.03362	+	0.564398i	−0.904163	−	0.427188i	$-0.859504\pi$
$647$	−26.2913	+	14.3561i	−1.03362	+	0.564398i	−0.129454	+	0.991585i	$0.541323\pi$
$648$	−6.14099	+	23.5772i	−0.241241	+	0.926201i
$649$	3.23957	+	5.04086i	0.127164	+	0.197871i
$650$	−11.2105	+	1.58302i	−0.439710	+	0.0620912i
$651$	−0.00782782	−	0.00112547i	−0.000306797	−	4.41107e-5i
$652$	10.7007	+	23.6353i	0.419071	+	0.925631i
$653$	21.7877	−	4.73961i	0.852617	−	0.185475i	0.235040	−	0.971986i	$-0.424478\pi$
$653$	21.7877	−	4.73961i	0.852617	−	0.185475i	0.617577	+	0.786510i	$0.288114\pi$
$654$	−0.449754	−	0.650033i	−0.0175868	−	0.0254183i
$655$	−6.95284	+	42.7868i	−0.271670	+	1.67182i
$656$	−13.8190	+	11.8169i	−0.539539	+	0.461374i
$657$	12.7880	−	17.0828i	0.498909	−	0.666464i
$658$	37.6935	−	30.2739i	1.46945	−	1.18020i
$659$	−22.8750	+	6.71671i	−0.891083	+	0.261646i	−0.695058	−	0.718953i	$-0.744622\pi$
$659$	−22.8750	+	6.71671i	−0.891083	+	0.261646i	−0.196025	+	0.980599i	$0.562803\pi$
$660$	0.809555	+	0.545282i	0.0315119	+	0.0212251i
$661$	10.3125	−	11.9012i	0.401108	−	0.462904i	−0.518881	−	0.854846i	$-0.673651\pi$
$661$	10.3125	−	11.9012i	0.401108	−	0.462904i	0.919990	+	0.391943i	$0.128197\pi$
$662$	0.203851	+	0.804163i	0.00792291	+	0.0312547i
$663$	−0.0899126	+	1.25714i	−0.00349192	+	0.0488234i
$664$	5.21725	−	10.2963i	0.202469	−	0.399575i
$665$	−18.0783	−	4.28046i	−0.701048	−	0.165989i
$666$	36.3777	−	18.1351i	1.40961	−	0.702720i
$667$	5.57640	−	30.8594i	0.215919	−	1.19488i
$668$	−5.79421	+	0.813764i	−0.224185	+	0.0314855i
$669$	−2.15498	−	0.984147i	−0.0833164	−	0.0380493i
$670$	19.5375	−	44.6311i	0.754800	−	1.72425i
$671$	0.189478	−	0.164183i	0.00731471	−	0.00633823i
$672$	2.07073	+	3.55591i	0.0798801	+	0.137172i
$673$	−1.86121	−	26.0231i	−0.0717444	−	1.00312i	−0.898049	−	0.439895i	$-0.855016\pi$
$673$	−1.86121	−	26.0231i	−0.0717444	−	1.00312i	0.826305	−	0.563223i	$-0.190439\pi$
$674$	−11.1202	+	3.68099i	−0.428334	+	0.141786i
$675$	6.14769	+	0.666441i	0.236625	+	0.0256513i
$676$	−19.5805	+	7.23034i	−0.753096	+	0.278090i
$677$	12.8954	−	17.2262i	0.495610	−	0.662057i	−0.481089	−	0.876672i	$-0.659759\pi$
$677$	12.8954	−	17.2262i	0.495610	−	0.662057i	0.976699	+	0.214615i	$0.0688496\pi$
$678$	−0.295280	−	2.78938i	−0.0113401	−	0.107125i
$679$	−22.1209	−	48.4380i	−0.848921	−	1.85888i
$680$	14.1291	−	19.3747i	0.541827	−	0.742986i
$681$	−2.81672	−	1.81020i	−0.107937	−	0.0693670i
$682$	−0.0161517		0.000603288i	−0.000618482		2.31011e-5i
$683$	7.10911	−	5.32181i	0.272022	−	0.203633i	−0.454554	−	0.890719i	$-0.650201\pi$
$683$	7.10911	−	5.32181i	0.272022	−	0.203633i	0.726576	+	0.687086i	$0.241110\pi$
$684$	2.93612	+	13.7127i	0.112265	+	0.524319i
$685$	23.7767	−	22.9224i	0.908460	−	0.875819i
$686$	3.28217	−	7.88738i	0.125314	−	0.301142i
$687$	−2.08975	+	1.14109i	−0.0797289	+	0.0435353i
$688$	−12.6371	−	17.1132i	−0.481785	−	0.652434i
$689$			2.63009i			0.100199i
$690$	3.03840	−	0.825869i	0.115670	−	0.0314403i
$691$		−	0.954482i		−	0.0363102i	−0.999835	−	0.0181551i	$-0.994221\pi$
$691$		−	0.954482i		−	0.0363102i	0.999835	−	0.0181551i	$-0.00577926\pi$
$692$	−14.3125	+	48.1611i	−0.544080	+	1.83081i
$693$	9.55884	−	5.21952i	0.363110	−	0.198273i
$694$	−41.1892	−	17.1400i	−1.56352	−	0.650627i
$695$	0.796542	−	43.5415i	0.0302146	−	1.65162i
$696$	−3.00158	+	2.39465i	−0.113774	+	0.0907689i
$697$	−13.7970	+	10.3283i	−0.522600	+	0.391213i
$698$	0.511438	−	13.6927i	0.0193582	−	0.518275i
$699$	−0.784429	−	0.504122i	−0.0296698	−	0.0190676i
$700$	−27.3722	+	21.8711i	−1.03457	+	0.826651i
$701$	9.74705	+	21.3431i	0.368141	+	0.806117i	0.999530	+	0.0306505i	$0.00975787\pi$
$701$	9.74705	+	21.3431i	0.368141	+	0.806117i	−0.631389	+	0.775466i	$0.717515\pi$
$702$	−2.78483	+	0.294798i	−0.105107	+	0.0111264i
$703$	13.8135	−	18.4526i	0.520984	−	0.695953i
$704$	4.97369	+	6.78166i	0.187453	+	0.255593i
$705$	−1.35542	+	4.32206i	−0.0510480	+	0.162778i
$706$	6.01199	+	18.1621i	0.226264	+	0.683541i
$707$	−2.74872	−	38.4321i	−0.103376	−	1.44539i
$708$	−1.54406	−	1.79375i	−0.0580294	−	0.0674134i
$709$	−10.5146	+	9.11095i	−0.394884	+	0.342169i	−0.829560	−	0.558418i	$-0.811408\pi$
$709$	−10.5146	+	9.11095i	−0.394884	+	0.342169i	0.434676	+	0.900587i	$0.356863\pi$
$710$	1.01910	+	2.60601i	0.0382462	+	0.0978020i
$711$	−26.2538	−	11.9897i	−0.984594	−	0.449649i
$712$	12.4009	−	8.52028i	0.464742	−	0.319311i
$713$	−0.0355390	+	0.0381506i	−0.00133095	+	0.00142875i
$714$	1.74018	+	3.49068i	0.0651246	+	0.130635i
$715$	0.867171	−	3.66246i	0.0324304	−	0.136968i
$716$	−17.7020	−	23.8089i	−0.661556	−	0.889781i
$717$	−0.207328	+	2.89882i	−0.00774279	+	0.108258i
$718$	−31.5238	+	7.99112i	−1.17646	+	0.298226i
$719$	−3.73264	+	4.30770i	−0.139204	+	0.160650i	−0.821071	−	0.570826i	$-0.806623\pi$
$719$	−3.73264	+	4.30770i	−0.139204	+	0.160650i	0.681867	+	0.731476i	$0.261168\pi$
$720$	23.7771	+	11.5804i	0.886121	+	0.431578i
$721$	−2.05266	+	0.602716i	−0.0764451	+	0.0224463i
$722$	−11.8462	−	14.7494i	−0.440868	−	0.548918i
$723$	−0.985144	+	1.31600i	−0.0366379	+	0.0489425i
$724$	4.02422	−	18.2123i	0.149559	−	0.676855i
$725$	−23.9090	−	22.2996i	−0.887959	−	0.828185i
$726$	2.38914	−	1.65303i	0.0886692	−	0.0613496i
$727$	−32.5899	+	7.08949i	−1.20869	+	0.262935i	−0.771380	−	0.636375i	$-0.780433\pi$
$727$	−32.5899	+	7.08949i	−1.20869	+	0.262935i	−0.437312	+	0.899310i	$0.644069\pi$
$728$	10.0165	−	12.3058i	0.371237	−	0.456083i
$729$	−24.4488	−	3.51520i	−0.905510	−	0.130193i
$730$	−15.2149	−	17.0093i	−0.563130	−	0.629542i
$731$	−10.9017	−	16.9634i	−0.403214	−	0.627413i
$732$	−0.0650944	+	0.0746287i	−0.00240596	+	0.00275836i
$733$	0.928928	−	0.507233i	0.0343107	−	0.0187351i	−0.462002	−	0.886879i	$-0.652869\pi$
$733$	0.928928	−	0.507233i	0.0343107	−	0.0187351i	0.496313	+	0.868144i	$0.334687\pi$
$734$	−0.394018	−	11.5619i	−0.0145435	−	0.426756i
$735$	−0.476768	−	2.40242i	−0.0175859	−	0.0886147i
$736$	27.0429	+	2.16382i	0.996814	+	0.0797596i
$737$	11.4525	+	11.4525i	0.421859	+	0.421859i
$738$	−13.8909	−	12.9754i	−0.511332	−	0.477629i
$739$	33.5116	+	9.83988i	1.23274	+	0.361966i	0.832284	−	0.554349i	$-0.187033\pi$
$739$	33.5116	+	9.83988i	1.23274	+	0.361966i	0.400458	+	0.916315i	$0.368851\pi$
$740$	−11.3451	−	41.9642i	−0.417054	−	1.54264i
$741$	−0.663136	+	0.426172i	−0.0243609	+	0.0156558i
$742$	4.14179	+	7.00669i	0.152050	+	0.257224i
$743$	−32.2883	+	24.1707i	−1.18454	+	0.886737i	−0.995456	−	0.0952232i	$-0.969644\pi$
$743$	−32.2883	+	24.1707i	−1.18454	+	0.886737i	−0.189086	+	0.981960i	$0.560553\pi$
$744$	0.00635084		0.000651311i	0.000232833		2.38782e-5i
$745$	−9.09343	−	20.9160i	−0.333157	−	0.766304i
$746$	−12.8023	−	18.5033i	−0.468727	−	0.677456i
$747$	11.3062	+	4.21698i	0.413671	+	0.154291i
$748$	4.28784	+	6.72019i	0.156779	+	0.245714i
$749$	19.8849	−	2.85902i	0.726580	−	0.104466i
$750$	0.990177	−	3.12978i	0.0361561	−	0.114284i
$751$	−6.21914	−	21.1804i	−0.226940	−	0.772885i	−0.991700	−	0.128571i	$-0.958961\pi$
$751$	−6.21914	−	21.1804i	−0.226940	−	0.772885i	0.764761	−	0.644314i	$-0.222857\pi$
$752$	−23.5924	+	31.0900i	−0.860325	+	1.13374i
$753$	0.0837605	+	1.17112i	0.00305240	+	0.0426781i
$754$	12.7211	+	7.57592i	0.463276	+	0.275899i
$755$	6.06397	+	48.4516i	0.220691	+	1.76333i
$756$	−6.95468	+	5.17083i	−0.252939	+	0.188061i
$757$	−16.6615	+	6.21444i	−0.605574	+	0.225867i	−0.633500	−	0.773743i	$-0.718382\pi$
$757$	−16.6615	+	6.21444i	−0.605574	+	0.225867i	0.0279261	+	0.999610i	$0.491110\pi$
$758$	31.9945	+	10.7069i	1.16209	+	0.388892i
$759$	−0.112175	+	1.04069i	−0.00407169	+	0.0377747i
$760$	14.9964	−	0.187557i	0.543978	−	0.00680340i
$761$	7.68418	−	16.8260i	0.278551	−	0.609942i	−0.717709	−	0.696343i	$-0.754809\pi$
$761$	7.68418	−	16.8260i	0.278551	−	0.609942i	0.996260	+	0.0864006i	$0.0275365\pi$
$762$	−4.38330	−	3.05401i	−0.158790	−	0.110635i
$763$	−0.672912	+	9.40855i	−0.0243611	+	0.340612i
$764$	−0.0603815	+	0.807164i	−0.00218452	+	0.0292022i
$765$	21.7787	+	12.4145i	0.787411	+	0.448848i
$766$	23.9945	−	7.94261i	0.866956	−	0.286978i
$767$	−4.37378	+	8.00999i	−0.157928	+	0.289224i
$768$	−2.31799	−	2.37940i	−0.0836433	−	0.0858591i
$769$	40.3454	−	5.80079i	1.45489	−	0.209182i	0.630936	−	0.775835i	$-0.282671\pi$
$769$	40.3454	−	5.80079i	1.45489	−	0.209182i	0.823956	+	0.566653i	$0.191762\pi$
$770$	−3.45736	−	11.1226i	−0.124594	−	0.400829i
$771$	2.60090	−	1.18779i	0.0936690	−	0.0427772i
$772$	4.89179	+	16.8636i	0.176059	+	0.606934i
$773$	−36.9718	+	8.04272i	−1.32978	+	0.289277i	−0.820660	−	0.571417i	$-0.806394\pi$
$773$	−36.9718	+	8.04272i	−1.32978	+	0.289277i	−0.509123	+	0.860694i	$0.670030\pi$
$774$	16.3018	−	15.1279i	0.585957	−	0.543760i
$775$	0.0133967	+	0.0526821i	0.000481225	+	0.00189240i
$776$	26.8087	+	33.6034i	0.962377	+	1.20629i
$777$	6.90918	+	1.50300i	0.247866	+	0.0539199i
$778$	38.7189	−	15.9638i	1.38814	−	0.572331i
$779$	−10.3425	−	3.03684i	−0.370560	−	0.108806i
$780$	−0.137996	+	1.48020i	−0.00494106	+	0.0529996i
$781$	−0.930218			−0.0332858
$782$	25.4463	+	3.70820i	0.909957	+	0.132605i
$783$	−5.71827	−	5.71827i	−0.204354	−	0.204354i
$784$	3.13980	−	20.8686i	0.112136	−	0.745307i
$785$	−24.0311	−	2.16119i	−0.857706	−	0.0771360i
$786$	5.25507	+	2.18679i	0.187442	+	0.0780002i
$787$	−7.41236	+	34.0741i	−0.264222	+	1.21461i	0.633393	+	0.773830i	$0.281662\pi$
$787$	−7.41236	+	34.0741i	−0.264222	+	1.21461i	−0.897615	+	0.440779i	$0.854702\pi$
$788$	14.6584	+	9.48821i	0.522184	+	0.338003i
$789$	0.209951	+	0.0301864i	0.00747445	+	0.00107466i
$790$	−18.1057	+	24.9988i	−0.644170	+	0.889416i
$791$	−18.0963	+	28.1583i	−0.643429	+	1.00119i
$792$	−6.46412	+	5.95942i	−0.229692	+	0.211759i
$793$	0.357779	+	0.133445i	0.0127051	+	0.00473876i
$794$	11.4143	−	14.1170i	0.405077	−	0.500993i
$795$	−0.687763	−	0.329425i	−0.0243924	−	0.0116835i
$796$	13.1913	+	35.7233i	0.467552	+	1.26618i
$797$	−24.5884	−	13.4263i	−0.870966	−	0.475583i	−0.0193885	−	0.999812i	$-0.506172\pi$
$797$	−24.5884	−	13.4263i	−0.870966	−	0.475583i	−0.851578	+	0.524229i	$0.824354\pi$
$798$	−1.09550	+	2.17963i	−0.0387803	+	0.0771580i
$799$	−24.2256	+	27.9578i	−0.857040	+	0.989077i
$800$	17.1544	−	22.4883i	0.606501	−	0.795083i
$801$	10.3004	+	11.8873i	0.363948	+	0.420019i
$802$	28.1750	+	19.6306i	0.994894	+	0.693179i
$803$	7.10826	−	2.65124i	0.250845	−	0.0935603i
$804$	−5.10875	−	3.85048i	−0.180172	−	0.135796i
$805$	−34.4399	−	15.0205i	−1.21385	−	0.529403i
$806$	−0.0109831	−	0.0220314i	−0.000386864	−	0.000776022i
$807$	0.537485	+	1.44105i	0.0189204	+	0.0507275i
$808$	9.67794	+	29.5604i	0.340469	+	1.03993i
$809$	13.7211	−	11.8894i	0.482406	−	0.418008i	−0.379409	−	0.925229i	$-0.623873\pi$
$809$	13.7211	−	11.8894i	0.482406	−	0.418008i	0.861816	+	0.507221i	$0.169327\pi$
$810$	−9.11551	+	25.6691i	−0.320286	+	0.901921i
$811$	−19.9862	−	17.3181i	−0.701810	−	0.608122i	0.229086	−	0.973406i	$-0.426426\pi$
$811$	−19.9862	−	17.3181i	−0.701810	−	0.608122i	−0.930896	+	0.365284i	$0.880972\pi$
$812$	45.8200	+	0.149740i	1.60797	+	0.00525484i
$813$	0.515884	−	0.944770i	0.0180928	−	0.0331345i
$814$	14.3659	+	1.56824i	0.503524	+	0.0549668i
$815$	9.63816	+	27.3591i	0.337610	+	0.958349i
$816$	−2.04634	−	2.39303i	−0.0716363	−	0.0837728i
$817$	4.40729	−	11.8164i	0.154191	−	0.413403i
$818$	−46.8327	−	8.52858i	−1.63747	−	0.298195i
$819$	13.9545	+	8.96802i	0.487610	+	0.313368i
$820$	−16.5328	+	11.8288i	−0.577350	+	0.413081i
$821$	3.72652	−	25.9185i	0.130056	−	0.904562i	−0.815420	−	0.578870i	$-0.803494\pi$
$821$	3.72652	−	25.9185i	0.130056	−	0.904562i	0.945476	−	0.325692i	$-0.105597\pi$
$822$	−2.20677	−	3.73319i	−0.0769698	−	0.130210i
$823$	24.7062	+	5.37451i	0.861204	+	0.187344i	0.621415	−	0.783481i	$-0.286558\pi$
$823$	24.7062	+	5.37451i	0.861204	+	0.187344i	0.239789	+	0.970825i	$0.422922\pi$
$824$	1.48955	−	0.873950i	0.0518911	−	0.0304455i
$825$	0.849110	+	0.685495i	0.0295622	+	0.0238659i
$826$	0.961940	+	28.2267i	0.0334702	+	0.982132i
$827$	−2.53023	+	2.53023i	−0.0879847	+	0.0879847i	−0.749729	−	0.661745i	$-0.769816\pi$
$827$	−2.53023	+	2.53023i	−0.0879847	+	0.0879847i	0.661745	+	0.749729i	$0.269816\pi$
$828$	0.911876	+	28.3469i	0.0316899	+	0.985122i
$829$		−	10.2843i		−	0.357188i	−0.983923	−	0.178594i	$-0.942845\pi$
$829$		−	10.2843i		−	0.357188i	0.983923	−	0.178594i	$-0.0571548\pi$
$830$	6.80493	−	10.9652i	0.236203	−	0.380608i
$831$	−1.09474	+	3.72835i	−0.0379762	+	0.129335i
$832$	−5.43503	+	11.5988i	−0.188426	+	0.402114i
$833$	4.25201	−	19.5462i	0.147323	−	0.677235i
$834$	−5.53833	−	1.42322i	−0.191777	−	0.0492820i
$835$	−6.53248	+	0.347254i	−0.226066	+	0.0120172i
$836$	−1.75759	+	4.66566i	−0.0607876	+	0.161365i
$837$	0.00285805	+	0.0131383i	9.87888e−5	+	0.000454125i
$838$	3.62357	−	19.8980i	0.125174	−	0.687364i
$839$	−13.7243	−	30.0519i	−0.473814	−	1.03751i	−0.984118	−	0.177514i	$-0.943195\pi$
$839$	−13.7243	−	30.0519i	−0.473814	−	1.03751i	0.510304	−	0.859994i	$-0.329533\pi$
$840$	1.96334	+	4.16063i	0.0677418	+	0.143555i
$841$	1.95776	+	13.6165i	0.0675089	+	0.469534i
$842$	16.1594	+	20.1198i	0.556891	+	0.693375i
$843$	−0.972492	−	0.531021i	−0.0334944	−	0.0182893i
$844$	13.6983	+	13.7882i	0.471516	+	0.474608i
$845$	−22.5077	+	6.16400i	−0.774289	+	0.212048i
$846$	−35.0552	−	20.8767i	−1.20522	−	0.717756i
$847$	−34.5802	−	2.47323i	−1.18819	−	0.0849811i
$848$	−4.61566	−	4.67639i	−0.158502	−	0.160588i
$849$	6.27003	+	2.86343i	0.215187	+	0.0982726i
$850$	17.6076	−	20.2172i	0.603937	−	0.693445i
$851$	34.1276	−	31.7564i	1.16988	−	1.08860i
$852$	0.363852	−	0.0511009i	0.0124654	−	0.00175069i
$853$	18.5950	+	49.8552i	0.636682	+	1.70701i	0.704870	+	0.709337i	$0.251006\pi$
$853$	18.5950	+	49.8552i	0.636682	+	1.70701i	−0.0681879	+	0.997672i	$0.521722\pi$
$854$	1.16328	−	0.207917i	0.0398068	−	0.00711479i
$855$	1.94709	+	15.5574i	0.0665892	+	0.532053i
$856$	−15.0133	+	6.13268i	−0.513146	+	0.209611i
$857$	33.1035	−	2.36761i	1.13079	−	0.0808759i	0.506626	−	0.862166i	$-0.330893\pi$
$857$	33.1035	−	2.36761i	1.13079	−	0.0808759i	0.624168	+	0.781290i	$0.285438\pi$
$858$	−0.441568	−	0.221936i	−0.0150749	−	0.00757677i
$859$	8.83142	−	2.59314i	0.301324	−	0.0884768i	−0.127576	−	0.991829i	$-0.540720\pi$
$859$	8.83142	−	2.59314i	0.301324	−	0.0884768i	0.428900	+	0.903352i	$0.358901\pi$
$860$	−12.4245	−	20.2813i	−0.423671	−	0.691585i
$861$	−0.470575	−	3.27292i	−0.0160371	−	0.111541i
$862$	40.4145	−	4.27822i	1.37652	−	0.145717i
$863$	−1.47883	+	3.96491i	−0.0503401	+	0.134967i	−0.959686	−	0.281073i	$-0.909310\pi$
$863$	−1.47883	+	3.96491i	−0.0503401	+	0.134967i	0.909346	+	0.416040i	$0.136582\pi$
$864$	4.43417	−	5.41138i	0.150854	−	0.184099i
$865$	−20.5899	+	52.2636i	−0.700078	+	1.77702i
$866$	22.5660	−	20.9409i	0.766823	−	0.711602i
$867$	0.326563	+	0.436237i	0.0110907	+	0.0148154i
$868$	−0.0639539	−	0.0413966i	−0.00217074	−	0.00140509i
$869$	−5.54761	−	8.63226i	−0.188190	−	0.292829i
$870$	−3.57443	+	2.37764i	−0.121185	+	0.0806096i
$871$	−6.94977	+	23.6688i	−0.235484	+	0.801985i
$872$	−1.31525	−	7.50019i	−0.0445401	−	0.253988i
$873$	−31.7772	+	31.7772i	−1.07549	+	1.07549i
$874$	7.68087	+	14.1305i	0.259809	+	0.477972i
$875$	−32.5995	+	21.7199i	−1.10207	+	0.734266i
$876$	−2.63473	+	1.42751i	−0.0890192	+	0.0482312i
$877$	17.2076	+	31.5133i	0.581058	+	1.06413i	0.988546	+	0.150918i	$0.0482229\pi$
$877$	17.2076	+	31.5133i	0.581058	+	1.06413i	−0.407488	+	0.913210i	$0.633595\pi$
$878$	−19.2285	−	46.6370i	−0.648929	−	1.57392i
$879$	−1.68929	+	1.08564i	−0.0569782	+	0.0366176i
$880$	4.88554	+	8.03381i	0.164692	+	0.270820i
$881$	−0.868316	+	6.03927i	−0.0292543	+	0.203468i	−0.999207	−	0.0398270i	$-0.987319\pi$
$881$	−0.868316	+	6.03927i	−0.0292543	+	0.203468i	0.969952	+	0.243295i	$0.0782284\pi$
$882$	22.0466	+	0.823469i	0.742348	+	0.0277277i
$883$	0.513019	+	2.35831i	0.0172645	+	0.0793635i	0.984973	−	0.172708i	$-0.0552518\pi$
$883$	0.513019	+	2.35831i	0.0172645	+	0.0793635i	−0.967709	+	0.252072i	$0.918888\pi$
$884$	−5.85348	+	10.6371i	−0.196874	+	0.357763i
$885$	−1.54677	−	2.14700i	−0.0519940	−	0.0721707i
$886$	15.9268	−	19.6979i	0.535070	−	0.661765i
$887$	−27.1476	−	20.3225i	−0.911528	−	0.682362i	0.0369115	−	0.999319i	$-0.488248\pi$
$887$	−27.1476	−	20.3225i	−0.911528	−	0.682362i	−0.948440	+	0.316957i	$0.897339\pi$
$888$	−5.70532	+	0.175768i	−0.191458	+	0.00589837i
$889$	17.9605	+	61.1679i	0.602376	+	2.05151i
$890$	14.6351	−	8.29368i	0.490569	−	0.278005i
$891$	−6.84362	−	5.93003i	−0.229270	−	0.198664i
$892$	−14.8886	−	17.2963i	−0.498508	−	0.579122i
$893$	−23.0781	−	1.65058i	−0.772281	−	0.0552346i
$894$	−2.94804	+	0.526912i	−0.0985972	+	0.0176226i
$895$	−17.4199	−	28.2282i	−0.582284	−	0.943563i
$896$	3.78623	+	39.4585i	0.126489	+	1.31822i
$897$	−1.47303	+	0.609677i	−0.0491832	+	0.0203565i
$898$	−12.4941	+	37.3352i	−0.416935	+	1.24589i
$899$	0.0295313	−	0.0646646i	0.000984925	−	0.00215668i
$900$	25.3669	+	15.1936i	0.845562	+	0.506453i
$901$	−4.07852	−	4.70687i	−0.135875	−	0.156809i
$902$	−1.66059	−	6.55077i	−0.0552915	−	0.218117i
$903$	3.85881	−	0.275988i	0.128413	−	0.00918429i
$904$	8.65874	−	25.5959i	0.287986	−	0.851308i
$905$	6.24000	−	19.8976i	0.207424	−	0.661420i
$906$	6.37381	+	0.695793i	0.211756	+	0.0231162i
$907$	−16.6637	−	12.4743i	−0.553308	−	0.414201i	0.285701	−	0.958319i	$-0.407774\pi$
$907$	−16.6637	−	12.4743i	−0.553308	−	0.414201i	−0.839009	+	0.544117i	$0.816865\pi$
$908$	−17.3493	−	27.1910i	−0.575756	−	0.902364i
$909$	−29.5786	+	13.5081i	−0.981060	+	0.448035i
$910$	12.3446	−	12.7403i	0.409219	−	0.422337i
$911$	0.0519912	−	0.0808999i	0.00172255	−	0.00268033i	−0.840391	−	0.541980i	$-0.817675\pi$
$911$	0.0519912	−	0.0808999i	0.00172255	−	0.00268033i	0.842114	+	0.539300i	$0.181311\pi$
$912$	0.431171	−	1.92151i	0.0142775	−	0.0636276i
$913$	2.57098	+	3.43442i	0.0850869	+	0.113663i
$914$	21.9172	+	5.63219i	0.724956	+	0.186296i
$915$	−0.0797081	+	0.0768441i	−0.00263507	+	0.00254039i
$916$	−22.8834	+	1.56151i	−0.756089	+	0.0515936i
$917$	−32.5516	−	59.6137i	−1.07495	−	1.96862i
$918$	4.52665	−	4.84606i	0.149402	−	0.159944i
$919$	59.7163			1.96986			0.984930	−	0.172956i	$-0.0553317\pi$
$919$	59.7163			1.96986			0.984930	+	0.172956i	$0.0553317\pi$
$920$	29.9132	+	5.01995i	0.986209	+	0.165503i
$921$	5.28040			0.173995
$922$	−22.5178	+	24.1067i	−0.741584	+	0.793913i
$923$	−0.678991	−	1.24348i	−0.0223493	−	0.0409296i
$924$	−1.52585	+	0.104120i	−0.0501969	+	0.00342531i
$925$	−8.58713	−	47.8372i	−0.282343	−	1.57288i
$926$	−39.1306	−	10.0556i	−1.28591	−	0.330448i
$927$	1.08197	+	1.44534i	0.0355364	+	0.0474711i
$928$	−35.9139	+	8.85458i	−1.17893	+	0.290666i
$929$	−5.12899	+	7.98086i	−0.168277	+	0.261843i	−0.915142	−	0.403132i	$-0.867922\pi$
$929$	−5.12899	+	7.98086i	−0.168277	+	0.261843i	0.746865	+	0.664975i	$0.231558\pi$
$930$	0.00713681		0.000112586i	0.000234025		3.69185e-6i
$931$	11.3802	−	5.19718i	0.372972	−	0.170331i
$932$	−4.83160	−	7.57241i	−0.158264	−	0.248042i
$933$	−2.77645	−	2.07843i	−0.0908970	−	0.0680446i
$934$	26.9930	+	2.94668i	0.883239	+	0.0964182i
$935$	4.12753	+	7.89915i	0.134985	+	0.258330i
$936$	−12.6847	−	4.29104i	−0.414611	−	0.140257i
$937$	−33.5973	+	2.40292i	−1.09758	+	0.0785001i	−0.608359	−	0.793662i	$-0.708172\pi$
$937$	−33.5973	+	2.40292i	−1.09758	+	0.0785001i	−0.489216	+	0.872162i	$0.662717\pi$
$938$	18.7584	+	73.9989i	0.612482	+	2.41615i
$939$	4.62662	+	5.33940i	0.150984	+	0.174245i
$940$	−29.2789	+	32.3532i	−0.954974	+	1.05525i
$941$	16.5436	−	36.2253i	0.539305	−	1.18091i	−0.422296	−	0.906458i	$-0.638776\pi$
$941$	16.5436	−	36.2253i	0.539305	−	1.18091i	0.961600	−	0.274454i	$-0.0884972\pi$
$942$	−1.00542	+	3.00442i	−0.0327585	+	0.0978894i
$943$	−19.4915	−	9.76343i	−0.634730	−	0.317941i
$944$	−6.28032	−	21.9177i	−0.204407	−	0.713362i
$945$	−8.24556	+	5.08843i	−0.268228	+	0.165527i
$946$	7.78342	−	1.39116i	0.253061	−	0.0452304i
$947$	−30.3038	−	2.16737i	−0.984740	−	0.0704300i	−0.430328	−	0.902672i	$-0.641602\pi$
$947$	−30.3038	−	2.16737i	−0.984740	−	0.0704300i	−0.554412	+	0.832242i	$0.687057\pi$
$948$	2.64414	+	3.07172i	0.0858776	+	0.0997650i
$949$	8.73258	+	7.56683i	0.283472	+	0.245630i
$950$	16.7220	+	1.23831i	0.542535	+	0.0401760i
$951$	−0.103137	−	0.351253i	−0.00334446	−	0.0113902i
$952$	1.15700	+	37.5555i	0.0374985	+	1.21718i
$953$	−22.4437	−	16.8012i	−0.727023	−	0.544243i	0.170421	−	0.985371i	$-0.445487\pi$
$953$	−22.4437	−	16.8012i	−0.727023	−	0.544243i	−0.897444	+	0.441129i	$0.854578\pi$
$954$	4.31885	−	5.34148i	0.139828	−	0.172937i
$955$	−0.145151	+	0.893242i	−0.00469699	+	0.0289046i
$956$	−13.4974	+	24.5278i	−0.436538	+	0.793285i
$957$	−0.303361	−	1.39453i	−0.00980626	−	0.0450787i
$958$	10.3555	+	0.386790i	0.334570	+	0.0124966i
$959$	−7.36473	+	51.2228i	−0.237820	+	1.65407i
$960$	−2.35230	−	2.87402i	−0.0759201	−	0.0927584i
$961$	26.0788	−	16.7598i	0.841250	−	0.540639i
$962$	8.38968	+	20.3485i	0.270494	+	0.656060i
$963$	−8.12529	−	14.8804i	−0.261834	−	0.479513i
$964$	−13.9236	+	7.54388i	−0.448448	+	0.242972i
$965$	3.82137	+	19.2558i	0.123014	+	0.619865i
$966$	−2.96413	+	3.94390i	−0.0953692	+	0.126893i
$967$	9.95033	−	9.95033i	0.319981	−	0.319981i	−0.528779	−	0.848760i	$-0.677350\pi$
$967$	9.95033	−	9.95033i	0.319981	−	0.319981i	0.848760	+	0.528779i	$0.177350\pi$
$968$	27.5663	−	4.83409i	0.886013	−	0.155374i
$969$	0.525891	−	1.79102i	0.0168941	−	0.0575359i
$970$	26.6183	+	40.0167i	0.854663	+	1.28486i
$971$	1.90331	+	2.96160i	0.0610801	+	0.0950424i	0.870450	−	0.492256i	$-0.163828\pi$
$971$	1.90331	+	2.96160i	0.0610801	+	0.0950424i	−0.809370	+	0.587299i	$0.800191\pi$
$972$	9.23195	+	5.97574i	0.296115	+	0.191672i
$973$	40.8927	+	54.6262i	1.31096	+	1.75124i
$974$	38.0738	−	35.3320i	1.21996	−	1.13211i
$975$	−0.296554	+	1.63542i	−0.00949734	+	0.0523753i
$976$	−0.870330	+	0.390612i	−0.0278586	+	0.0125032i
$977$	−2.34828	+	6.29598i	−0.0751281	+	0.201426i	−0.969085	−	0.246726i	$-0.920645\pi$
$977$	−2.34828	+	6.29598i	−0.0751281	+	0.201426i	0.893957	+	0.448153i	$0.147918\pi$
$978$	3.78769	−	0.400959i	0.121117	−	0.0128213i
$979$	0.795845	+	5.53522i	0.0254353	+	0.176906i
$980$	5.51121	−	22.9417i	0.176049	−	0.732846i
$981$	7.63804	−	2.24273i	0.243864	−	0.0716049i
$982$	2.43697	+	1.22485i	0.0777670	+	0.0390864i
$983$	3.48782	−	0.249454i	0.111244	−	0.00795635i	−0.0156060	−	0.999878i	$-0.504968\pi$
$983$	3.48782	−	0.249454i	0.111244	−	0.00795635i	0.126850	+	0.991922i	$0.459513\pi$
$984$	1.00940	+	2.47109i	0.0321784	+	0.0787754i
$985$	15.4118	+	11.9831i	0.491060	+	0.381815i
$986$	−34.5141	+	6.16881i	−1.09915	+	0.196455i
$987$	−2.48030	−	6.64994i	−0.0789488	−	0.211670i
$988$	−7.51979	+	1.05611i	−0.239236	+	0.0335994i
$989$	13.0209	−	21.9319i	0.414041	−	0.697393i
$990$	−7.77524	+	6.01415i	−0.247113	+	0.191142i
$991$	8.22765	+	3.75744i	0.261360	+	0.119359i	0.541786	−	0.840517i	$-0.317748\pi$
$991$	8.22765	+	3.75744i	0.261360	+	0.119359i	−0.280426	+	0.959876i	$0.590476\pi$
$992$	0.0581921	+	0.0198977i	0.00184760	+	0.000631754i
$993$	0.121480	+	0.00868840i	0.00385504	+	0.000275718i
$994$	−3.76706	−	2.24343i	−0.119484	−	0.0711573i
$995$	11.2458	+	41.0638i	0.356516	+	1.30181i
$996$	−1.19430	−	1.20213i	−0.0378428	−	0.0380909i
$997$	−20.8418	−	11.3805i	−0.660067	−	0.360424i	0.114042	−	0.993476i	$-0.463620\pi$
$997$	−20.8418	−	11.3805i	−0.660067	−	0.360424i	−0.774109	+	0.633052i	$0.781802\pi$
$998$	23.1000	+	28.7614i	0.731219	+	0.910428i
$999$	−1.71085	−	11.8992i	−0.0541288	−	0.376474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.167.51	yes	1360
4.3	odd	2	inner	460.2.w.a.167.67	yes	1360
5.3	odd	4	inner	460.2.w.a.443.16	yes	1360
20.3	even	4	inner	460.2.w.a.443.36	yes	1360
23.4	even	11	inner	460.2.w.a.27.36	yes	1360
92.27	odd	22	inner	460.2.w.a.27.16	✓	1360
115.73	odd	44	inner	460.2.w.a.303.67	yes	1360
460.303	even	44	inner	460.2.w.a.303.51	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.27.16	✓	1360	92.27	odd	22	inner
460.2.w.a.27.36	yes	1360	23.4	even	11	inner
460.2.w.a.167.51	yes	1360	1.1	even	1	trivial
460.2.w.a.167.67	yes	1360	4.3	odd	2	inner
460.2.w.a.303.51	yes	1360	460.303	even	44	inner
460.2.w.a.303.67	yes	1360	115.73	odd	44	inner
460.2.w.a.443.16	yes	1360	5.3	odd	4	inner
460.2.w.a.443.36	yes	1360	20.3	even	4	inner

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965360 - 1.03348i) q^{2} +(-0.0994992 - 0.182219i) q^{3} +(-0.136158 - 1.99536i) q^{4} +(0.0408995 - 2.23569i) q^{5} +(-0.284372 - 0.0730769i) q^{6} +(2.09969 + 2.80485i) q^{7} +(-2.19360 - 1.78552i) q^{8} +(1.59862 - 2.48750i) q^{9} +O(q^{10})\)	\(q+(0.965360 - 1.03348i) q^{2} +(-0.0994992 - 0.182219i) q^{3} +(-0.136158 - 1.99536i) q^{4} +(0.0408995 - 2.23569i) q^{5} +(-0.284372 - 0.0730769i) q^{6} +(2.09969 + 2.80485i) q^{7} +(-2.19360 - 1.78552i) q^{8} +(1.59862 - 2.48750i) q^{9} +(-2.27106 - 2.20052i) q^{10} +(0.956253 - 0.436706i) q^{11} +(-0.350045 + 0.223347i) q^{12} +(1.28177 + 0.959519i) q^{13} +(4.92571 + 0.537711i) q^{14} +(-0.411456 + 0.214997i) q^{15} +(-3.96292 + 0.543370i) q^{16} +(-3.78182 + 0.270481i) q^{17} +(-1.02754 - 4.05347i) q^{18} +(-1.55289 - 1.79213i) q^{19} +(-4.46658 + 0.222799i) q^{20} +(0.302181 - 0.661684i) q^{21} +(0.471802 - 1.40985i) q^{22} +(-2.44604 - 4.12516i) q^{23} +(-0.107095 + 0.577375i) q^{24} +(-4.99665 - 0.182877i) q^{25} +(2.22901 - 0.398398i) q^{26} +(-1.23359 - 0.0882281i) q^{27} +(5.31080 - 4.57153i) q^{28} +(4.94173 + 4.28203i) q^{29} +(-0.175008 + 0.632781i) q^{30} +(-0.00306293 - 0.0104314i) q^{31} +(-3.26409 + 4.62014i) q^{32} +(-0.174723 - 0.130796i) q^{33} +(-3.37128 + 4.16954i) q^{34} +(6.35666 - 4.57954i) q^{35} +(-5.18112 - 2.85113i) q^{36} +(2.06621 + 9.49822i) q^{37} +(-3.35123 - 0.125173i) q^{38} +(0.0473080 - 0.329034i) q^{39} +(-4.08160 + 4.83120i) q^{40} +(3.82402 - 2.45755i) q^{41} +(-0.392123 - 0.951061i) q^{42} +(2.54881 + 4.66780i) q^{43} +(-1.00159 - 1.84861i) q^{44} +(-5.49590 - 3.67576i) q^{45} +(-6.62457 - 1.45433i) q^{46} +(6.89925 - 6.89925i) q^{47} +(0.493320 + 0.668056i) q^{48} +(-1.48638 + 5.06216i) q^{49} +(-5.01257 + 4.98740i) q^{50} +(0.425575 + 0.662207i) q^{51} +(1.74006 - 2.68823i) q^{52} +(0.984405 + 1.31501i) q^{53} +(-1.28204 + 1.18972i) q^{54} +(-0.937231 - 2.15575i) q^{55} +(0.402252 - 9.90177i) q^{56} +(-0.172049 + 0.461282i) q^{57} +(9.19594 - 0.973469i) q^{58} +(0.811187 + 5.64193i) q^{59} +(0.485020 + 0.791729i) q^{60} +(0.228831 - 0.0671909i) q^{61} +(-0.0137374 - 0.00690456i) q^{62} +(10.3337 - 0.739078i) q^{63} +(1.62380 + 7.83347i) q^{64} +(2.19761 - 2.82640i) q^{65} +(-0.303845 + 0.0543072i) q^{66} +(5.38407 + 14.4353i) q^{67} +(1.05463 + 7.50926i) q^{68} +(-0.508304 + 0.856165i) q^{69} +(1.40362 - 10.9904i) q^{70} +(-0.804902 - 0.367587i) q^{71} +(-7.94823 + 2.60222i) q^{72} +(7.19833 + 0.514834i) q^{73} +(11.8108 + 7.03382i) q^{74} +(0.463840 + 0.928683i) q^{75} +(-3.36451 + 3.34259i) q^{76} +(3.23273 + 1.76520i) q^{77} +(-0.294381 - 0.366528i) q^{78} +(-1.38912 - 9.66155i) q^{79} +(1.05273 + 8.88210i) q^{80} +(-3.57835 - 7.83550i) q^{81} +(1.15173 - 6.32447i) q^{82} +(0.867471 + 3.98770i) q^{83} +(-1.36144 - 0.512866i) q^{84} +(0.450038 + 8.46605i) q^{85} +(7.28460 + 1.87197i) q^{86} +(0.288571 - 1.32654i) q^{87} +(-2.87739 - 0.749453i) q^{88} +(-1.49868 + 5.10402i) q^{89} +(-9.10435 + 2.13147i) q^{90} +5.60985i q^{91} +(-7.89812 + 5.44240i) q^{92} +(-0.00159604 + 0.00159604i) q^{93} +(-0.469968 - 13.7905i) q^{94} +(-4.07017 + 3.39849i) q^{95} +(1.16665 + 0.135079i) q^{96} +(-14.8509 - 3.23062i) q^{97} +(3.79674 + 6.42295i) q^{98} +(0.442378 - 3.07681i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Introduction

L-functions

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