LMFDB - Embedded newform 430.2.q.a.271.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			271.3
Character	$\chi$	$=$	430.271
Dual form			430.2.q.a.311.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.222521 + 0.974928i) q^{2} +(2.06188 - 1.91315i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.988831 - 0.149042i) q^{5} +(1.40637 + 2.43590i) q^{6} +(-0.0872858 + 0.151183i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.367035 - 4.89775i) q^{9} +O(q^{10})$	\(q+(-0.222521 + 0.974928i) q^{2} +(2.06188 - 1.91315i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.988831 - 0.149042i) q^{5} +(1.40637 + 2.43590i) q^{6} +(-0.0872858 + 0.151183i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.367035 - 4.89775i) q^{9} +(0.365341 - 0.930874i) q^{10} +(3.45126 - 1.66204i) q^{11} +(-2.68777 + 0.829068i) q^{12} +(-1.25376 - 3.19454i) q^{13} +(-0.127970 - 0.118739i) q^{14} +(-2.32399 + 1.58447i) q^{15} +(0.623490 + 0.781831i) q^{16} +(1.30349 - 0.196470i) q^{17} +(4.69328 + 1.44768i) q^{18} +(-0.0478401 - 0.638381i) q^{19} +(0.826239 + 0.563320i) q^{20} +(0.109263 + 0.478713i) q^{21} +(0.852390 + 3.73457i) q^{22} +(2.61406 + 1.78223i) q^{23} +(-0.210196 - 2.80487i) q^{24} +(0.955573 + 0.294755i) q^{25} +(3.39343 - 0.511478i) q^{26} +(-3.35219 - 4.20351i) q^{27} +(0.144238 - 0.0983397i) q^{28} +(-3.48654 - 3.23504i) q^{29} +(-1.02761 - 2.61830i) q^{30} +(-1.65492 + 0.510477i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(3.93636 - 10.0297i) q^{33} +(-0.0985102 + 1.31453i) q^{34} +(0.108844 - 0.136486i) q^{35} +(-2.45574 + 4.25347i) q^{36} +(0.805651 + 1.39543i) q^{37} +(0.633021 + 0.0954126i) q^{38} +(-8.69673 - 4.18813i) q^{39} +(-0.733052 + 0.680173i) q^{40} +(0.795835 - 3.48678i) q^{41} -0.491024 q^{42} +(2.31958 + 6.13348i) q^{43} -3.83061 q^{44} +(-1.09291 + 4.78834i) q^{45} +(-2.31923 + 2.15193i) q^{46} +(-6.56928 - 3.16360i) q^{47} +(2.78132 + 0.419216i) q^{48} +(3.48476 + 6.03579i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(2.31177 - 2.89886i) q^{51} +(-0.256456 + 3.42217i) q^{52} +(-2.60764 + 6.64416i) q^{53} +(4.84405 - 2.33277i) q^{54} +(-3.66042 + 1.12909i) q^{55} +(0.0637782 + 0.162504i) q^{56} +(-1.31996 - 1.22474i) q^{57} +(3.92976 - 2.67926i) q^{58} +(5.47921 + 6.87071i) q^{59} +(2.78132 - 0.419216i) q^{60} +(2.74944 + 0.848090i) q^{61} +(-0.129423 - 1.72702i) q^{62} +(0.708421 + 0.482993i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(0.763639 + 3.34572i) q^{65} +(8.90230 + 6.06948i) q^{66} +(0.109298 + 1.45848i) q^{67} +(-1.25965 - 0.388550i) q^{68} +(8.79955 - 1.32632i) q^{69} +(0.108844 + 0.136486i) q^{70} +(0.335101 - 0.228468i) q^{71} +(-3.60037 - 3.34065i) q^{72} +(5.87190 + 14.9614i) q^{73} +(-1.53972 + 0.474940i) q^{74} +(2.53419 - 1.22040i) q^{75} +(-0.233881 + 0.595919i) q^{76} +(-0.0499732 + 0.666845i) q^{77} +(6.01833 - 7.54674i) q^{78} +(-6.67332 + 11.5585i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.383861 - 0.0578578i) q^{81} +(3.22227 + 1.55176i) q^{82} +(-0.868930 + 0.806249i) q^{83} +(0.109263 - 0.478713i) q^{84} -1.31821 q^{85} +(-6.49585 + 0.896593i) q^{86} -13.3779 q^{87} +(0.852390 - 3.73457i) q^{88} +(10.9799 - 10.1879i) q^{89} +(-4.42509 - 2.13101i) q^{90} +(0.592397 + 0.0892895i) q^{91} +(-1.58190 - 2.73994i) q^{92} +(-2.43564 + 4.21865i) q^{93} +(4.54608 - 5.70061i) q^{94} +(-0.0478401 + 0.638381i) q^{95} +(-1.02761 + 2.61830i) q^{96} +(-16.8041 + 8.09242i) q^{97} +(-6.65989 + 2.05430i) q^{98} +(-6.87351 - 17.5134i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

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 $

$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$3$	2.06188	−	1.91315i	1.19043	−	1.10456i	0.198194	−	0.980163i	$-0.436492\pi$
$3$	2.06188	−	1.91315i	1.19043	−	1.10456i	0.992233	−	0.124393i	$-0.0396982\pi$
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	−0.988831	−	0.149042i	−0.442219	−	0.0666537i
$5$	−0.988831	−	0.149042i	−0.442219	−	0.0666537i
$6$	1.40637	+	2.43590i	0.574147	+	0.994452i
$7$	−0.0872858	+	0.151183i	−0.0329909	+	0.0571420i	−0.882049	−	0.471157i	$-0.843837\pi$
$7$	−0.0872858	+	0.151183i	−0.0329909	+	0.0571420i	0.849059	+	0.528299i	$0.177170\pi$
$8$	0.623490	−	0.781831i	0.220437	−	0.276419i
$9$	0.367035	−	4.89775i	0.122345	−	1.63258i
$10$	0.365341	−	0.930874i	0.115531	−	0.294368i
$11$	3.45126	−	1.66204i	1.04059	−	0.501123i	0.166074	−	0.986113i	$-0.446891\pi$
$11$	3.45126	−	1.66204i	1.04059	−	0.501123i	0.874520	+	0.484990i	$0.161177\pi$
$12$	−2.68777	+	0.829068i	−0.775893	+	0.239331i
$13$	−1.25376	−	3.19454i	−0.347732	−	0.886006i	−0.992569	−	0.121686i	$-0.961170\pi$
$13$	−1.25376	−	3.19454i	−0.347732	−	0.886006i	0.644837	−	0.764320i	$-0.276925\pi$
$14$	−0.127970	−	0.118739i	−0.0342014	−	0.0317343i
$15$	−2.32399	+	1.58447i	−0.600052	+	0.409108i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	1.30349	−	0.196470i	0.316143	−	0.0476509i	0.0109458	−	0.999940i	$-0.496516\pi$
$17$	1.30349	−	0.196470i	0.316143	−	0.0476509i	0.305197	+	0.952289i	$0.401278\pi$
$18$	4.69328	+	1.44768i	1.10622	+	0.341222i
$19$	−0.0478401	−	0.638381i	−0.0109753	−	0.146455i	0.989024	−	0.147756i	$-0.0472049\pi$
$19$	−0.0478401	−	0.638381i	−0.0109753	−	0.146455i	−0.999999	+	0.00130099i	$0.999586\pi$
$20$	0.826239	+	0.563320i	0.184753	+	0.125962i
$21$	0.109263	+	0.478713i	0.0238432	+	0.104464i
$22$	0.852390	+	3.73457i	0.181730	+	0.796212i
$23$	2.61406	+	1.78223i	0.545069	+	0.371622i	0.804327	−	0.594186i	$-0.202526\pi$
$23$	2.61406	+	1.78223i	0.545069	+	0.371622i	−0.259259	+	0.965808i	$0.583478\pi$
$24$	−0.210196	−	2.80487i	−0.0429061	−	0.572542i
$25$	0.955573	+	0.294755i	0.191115	+	0.0589510i
$26$	3.39343	−	0.511478i	0.665507	−	0.100309i
$27$	−3.35219	−	4.20351i	−0.645128	−	0.808965i
$28$	0.144238	−	0.0983397i	0.0272584	−	0.0185845i
$29$	−3.48654	−	3.23504i	−0.647435	−	0.600732i	0.286541	−	0.958068i	$-0.407495\pi$
$29$	−3.48654	−	3.23504i	−0.647435	−	0.600732i	−0.933976	+	0.357336i	$0.883685\pi$
$30$	−1.02761	−	2.61830i	−0.187615	−	0.478034i
$31$	−1.65492	+	0.510477i	−0.297233	+	0.0916843i	−0.439785	−	0.898103i	$-0.644945\pi$
$31$	−1.65492	+	0.510477i	−0.297233	+	0.0916843i	0.142552	+	0.989787i	$0.454469\pi$
$32$	−0.900969	+	0.433884i	−0.159270	+	0.0767005i
$33$	3.93636	−	10.0297i	0.685233	−	1.74594i
$34$	−0.0985102	+	1.31453i	−0.0168944	+	0.225440i
$35$	0.108844	−	0.136486i	0.0183979	−	0.0230703i
$36$	−2.45574	+	4.25347i	−0.409290	+	0.708911i
$37$	0.805651	+	1.39543i	0.132448	+	0.229407i	0.924620	−	0.380891i	$-0.124383\pi$
$37$	0.805651	+	1.39543i	0.132448	+	0.229407i	−0.792172	+	0.610298i	$0.791050\pi$
$38$	0.633021	+	0.0954126i	0.102690	+	0.0154780i
$39$	−8.69673	−	4.18813i	−1.39259	−	0.670637i
$40$	−0.733052	+	0.680173i	−0.115906	+	0.107545i
$41$	0.795835	−	3.48678i	0.124289	−	0.544544i	−0.873993	−	0.485939i	$-0.838478\pi$
$41$	0.795835	−	3.48678i	0.124289	−	0.544544i	0.998281	−	0.0586047i	$-0.0186652\pi$
$42$	−0.491024			−0.0757666
$43$	2.31958	+	6.13348i	0.353732	+	0.935347i
$43$	2.31958	+	6.13348i	0.353732	+	0.935347i
$44$	−3.83061			−0.577486
$45$	−1.09291	+	4.78834i	−0.162921	+	0.713803i
$46$	−2.31923	+	2.15193i	−0.341952	+	0.317285i
$47$	−6.56928	−	3.16360i	−0.958228	−	0.461458i	−0.111665	−	0.993746i	$-0.535618\pi$
$47$	−6.56928	−	3.16360i	−0.958228	−	0.461458i	−0.846564	+	0.532288i	$0.821333\pi$
$48$	2.78132	+	0.419216i	0.401449	+	0.0605087i
$49$	3.48476	+	6.03579i	0.497823	+	0.862255i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	2.31177	−	2.89886i	0.323712	−	0.405922i
$52$	−0.256456	+	3.42217i	−0.0355641	+	0.474569i
$53$	−2.60764	+	6.64416i	−0.358187	+	0.912646i	0.632260	+	0.774756i	$0.282127\pi$
$53$	−2.60764	+	6.64416i	−0.358187	+	0.912646i	−0.990448	+	0.137890i	$0.955968\pi$
$54$	4.84405	−	2.33277i	0.659191	−	0.317450i
$55$	−3.66042	+	1.12909i	−0.493572	+	0.152247i
$56$	0.0637782	+	0.162504i	0.00852272	+	0.0217155i
$57$	−1.31996	−	1.22474i	−0.174833	−	0.162221i
$58$	3.92976	−	2.67926i	0.516003	−	0.351805i
$59$	5.47921	+	6.87071i	0.713333	+	0.894491i	0.997940	−	0.0641534i	$-0.0204347\pi$
$59$	5.47921	+	6.87071i	0.713333	+	0.894491i	−0.284608	+	0.958644i	$0.591863\pi$
$60$	2.78132	−	0.419216i	0.359067	−	0.0541206i
$61$	2.74944	+	0.848090i	0.352030	+	0.108587i	0.465727	−	0.884929i	$-0.345793\pi$
$61$	2.74944	+	0.848090i	0.352030	+	0.108587i	−0.113697	+	0.993515i	$0.536269\pi$
$62$	−0.129423	−	1.72702i	−0.0164367	−	0.219332i
$63$	0.708421	+	0.482993i	0.0892527	+	0.0608514i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	0.763639	+	3.34572i	0.0947178	+	0.414986i
$66$	8.90230	+	6.06948i	1.09580	+	0.747102i
$67$	0.109298	+	1.45848i	0.0133528	+	0.178181i	0.999893	+	0.0146594i	$0.00466640\pi$
$67$	0.109298	+	1.45848i	0.0133528	+	0.178181i	−0.986540	+	0.163522i	$0.947715\pi$
$68$	−1.25965	−	0.388550i	−0.152755	−	0.0471187i
$69$	8.79955	−	1.32632i	1.05934	−	0.159670i
$70$	0.108844	+	0.136486i	0.0130093	+	0.0163131i
$71$	0.335101	−	0.228468i	0.0397692	−	0.0271142i	−0.543272	−	0.839557i	$-0.682815\pi$
$71$	0.335101	−	0.228468i	0.0397692	−	0.0271142i	0.583041	+	0.812442i	$0.301863\pi$
$72$	−3.60037	−	3.34065i	−0.424308	−	0.393700i
$73$	5.87190	+	14.9614i	0.687254	+	1.75109i	0.659764	+	0.751473i	$0.270656\pi$
$73$	5.87190	+	14.9614i	0.687254	+	1.75109i	0.0274898	+	0.999622i	$0.491249\pi$
$74$	−1.53972	+	0.474940i	−0.178988	+	0.0552106i
$75$	2.53419	−	1.22040i	0.292623	−	0.140920i
$76$	−0.233881	+	0.595919i	−0.0268280	+	0.0683565i
$77$	−0.0499732	+	0.666845i	−0.00569497	+	0.0759941i
$78$	6.01833	−	7.54674i	0.681441	−	0.854500i
$79$	−6.67332	+	11.5585i	−0.750807	+	1.30044i	0.196625	+	0.980479i	$0.437002\pi$
$79$	−6.67332	+	11.5585i	−0.750807	+	1.30044i	−0.947432	+	0.319957i	$0.896331\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.383861	−	0.0578578i	−0.0426512	−	0.00642864i
$82$	3.22227	+	1.55176i	0.355840	+	0.171364i
$83$	−0.868930	+	0.806249i	−0.0953775	+	0.0884974i	−0.726421	−	0.687250i	$-0.758818\pi$
$83$	−0.868930	+	0.806249i	−0.0953775	+	0.0884974i	0.631043	+	0.775748i	$0.282627\pi$
$84$	0.109263	−	0.478713i	0.0119216	−	0.0522318i
$85$	−1.31821			−0.142980
$86$	−6.49585	+	0.896593i	−0.700466	+	0.0966821i
$87$	−13.3779			−1.43427
$88$	0.852390	−	3.73457i	0.0908651	−	0.398106i
$89$	10.9799	−	10.1879i	1.16387	−	1.07991i	0.168316	−	0.985733i	$-0.446167\pi$
$89$	10.9799	−	10.1879i	1.16387	−	1.07991i	0.995555	−	0.0941818i	$-0.0300235\pi$
$90$	−4.42509	−	2.13101i	−0.466446	−	0.224628i
$91$	0.592397	+	0.0892895i	0.0621001	+	0.00936008i
$92$	−1.58190	−	2.73994i	−0.164925	−	0.285658i
$93$	−2.43564	+	4.21865i	−0.252564	+	0.437454i
$94$	4.54608	−	5.70061i	0.468893	−	0.587973i
$95$	−0.0478401	+	0.638381i	−0.00490829	+	0.0654965i
$96$	−1.02761	+	2.61830i	−0.104880	+	0.267229i
$97$	−16.8041	+	8.09242i	−1.70620	+	0.821661i	−0.713550	+	0.700604i	$0.752914\pi$
$97$	−16.8041	+	8.09242i	−1.70620	+	0.821661i	−0.992646	+	0.121056i	$0.961372\pi$
$98$	−6.65989	+	2.05430i	−0.672750	+	0.207516i
$99$	−6.87351	−	17.5134i	−0.690814	−	1.76016i
$100$	−0.733052	−	0.680173i	−0.0733052	−	0.0680173i
$101$	3.04050	−	2.07298i	0.302541	−	0.206269i	−0.402528	−	0.915408i	$-0.631868\pi$
$101$	3.04050	−	2.07298i	0.302541	−	0.206269i	0.705069	+	0.709139i	$0.250916\pi$
$102$	2.31177	+	2.89886i	0.228899	+	0.287030i
$103$	−12.3882	+	1.86723i	−1.22065	+	0.183983i	−0.727589	−	0.686013i	$-0.759359\pi$
$103$	−12.3882	+	1.86723i	−1.22065	+	0.183983i	−0.493059	+	0.869996i	$0.664121\pi$
$104$	−3.27930	−	1.01153i	−0.321562	−	0.0991887i
$105$	−0.0366942	−	0.489651i	−0.00358099	−	0.0477850i
$106$	−5.89733	−	4.02073i	−0.572799	−	0.390528i
$107$	−0.392172	−	1.71822i	−0.0379127	−	0.166106i	0.952427	−	0.304765i	$-0.0985780\pi$
$107$	−0.392172	−	1.71822i	−0.0379127	−	0.166106i	−0.990340	+	0.138659i	$0.955721\pi$
$108$	1.19638	+	5.24169i	0.115122	+	0.504382i
$109$	12.2190	+	8.33077i	1.17037	+	0.797943i	0.982866	−	0.184322i	$-0.0590088\pi$
$109$	12.2190	+	8.33077i	1.17037	+	0.797943i	0.187501	+	0.982264i	$0.439961\pi$
$110$	−0.286262	−	3.81990i	−0.0272940	−	0.364213i
$111$	4.33081	+	1.33588i	0.411063	+	0.126796i
$112$	−0.172622	+	0.0260185i	−0.0163112	+	0.00245852i
$113$	−12.8300	−	16.0883i	−1.20694	−	1.51346i	−0.799998	−	0.600003i	$-0.795166\pi$
$113$	−12.8300	−	16.0883i	−1.20694	−	1.51346i	−0.406944	−	0.913453i	$-0.633405\pi$
$114$	1.48775	−	1.01433i	0.139341	−	0.0950009i
$115$	−2.31923	−	2.15193i	−0.216270	−	0.200669i
$116$	1.73764	+	4.42742i	0.161335	+	0.411076i
$117$	−16.1062	+	4.96811i	−1.48902	+	0.459302i
$118$	−7.91769	+	3.81296i	−0.728882	+	0.351011i
$119$	−0.0840733	+	0.214215i	−0.00770698	+	0.0196371i
$120$	−0.210196	+	2.80487i	−0.0191882	+	0.256048i
$121$	2.29042	−	2.87210i	0.208220	−	0.261100i
$122$	−1.43863	+	2.49179i	−0.130248	+	0.225596i
$123$	−5.02980	−	8.71188i	−0.453522	−	0.785524i
$124$	1.71252	+	0.258121i	0.153789	+	0.0231800i
$125$	−0.900969	−	0.433884i	−0.0805851	−	0.0388077i
$126$	−0.628522	+	0.583183i	−0.0559932	+	0.0519541i
$127$	3.23753	−	14.1845i	0.287284	−	1.25867i	−0.600951	−	0.799286i	$-0.705211\pi$
$127$	3.23753	−	14.1845i	0.287284	−	1.25867i	0.888235	−	0.459388i	$-0.151931\pi$
$128$	1.00000			0.0883883
$129$	16.5169	+	8.20881i	1.45423	+	0.722746i
$130$	−3.43176			−0.300986
$131$	3.87896	−	16.9948i	0.338906	−	1.48485i	−0.462443	−	0.886649i	$-0.653027\pi$
$131$	3.87896	−	16.9948i	0.338906	−	1.48485i	0.801349	−	0.598197i	$-0.204116\pi$
$132$	−7.89826	+	7.32851i	−0.687455	+	0.637865i
$133$	0.100688	+	0.0484890i	0.00873079	+	0.00420453i
$134$	−1.44623	−	0.217984i	−0.124935	−	0.0188310i
$135$	2.68824	+	4.65618i	0.231367	+	0.400740i
$136$	0.659107	−	1.14161i	0.0565180	−	0.0978920i
$137$	−9.18534	+	11.5181i	−0.784757	+	0.984054i	0.215215	+	0.976567i	$0.430955\pi$
$137$	−9.18534	+	11.5181i	−0.784757	+	0.984054i	−0.999972	+	0.00748721i	$0.997617\pi$
$138$	−0.665019	+	8.87406i	−0.0566102	+	0.755410i
$139$	−2.09559	+	5.33948i	−0.177746	+	0.452889i	−0.991784	−	0.127922i	$-0.959169\pi$
$139$	−2.09559	+	5.33948i	−0.177746	+	0.452889i	0.814038	+	0.580811i	$0.197264\pi$
$140$	−0.157284	+	0.0757438i	−0.0132929	+	0.00640152i
$141$	−19.5975	+	6.04503i	−1.65041	+	0.509083i
$142$	0.148173	+	0.377538i	0.0124344	+	0.0316823i
$143$	−9.63651	−	8.94138i	−0.805846	−	0.747715i
$144$	4.05806	−	2.76674i	0.338171	−	0.230561i
$145$	2.96544	+	3.71855i	0.246267	+	0.308809i
$146$	−15.8929	+	2.39546i	−1.31530	+	0.198250i
$147$	18.7325	+	5.77821i	1.54503	+	0.476579i
$148$	−0.120413	−	1.60680i	−0.00989787	−	0.132078i
$149$	6.72683	+	4.58628i	0.551084	+	0.375722i	0.806614	−	0.591079i	$-0.201298\pi$
$149$	6.72683	+	4.58628i	0.551084	+	0.375722i	−0.255530	+	0.966801i	$0.582250\pi$
$150$	0.625892	+	2.74221i	0.0511039	+	0.223901i
$151$	2.36305	+	10.3532i	0.192302	+	0.842532i	0.975366	+	0.220591i	$0.0707986\pi$
$151$	2.36305	+	10.3532i	0.192302	+	0.842532i	−0.783064	+	0.621941i	$0.786344\pi$
$152$	−0.528934	−	0.360621i	−0.0429022	−	0.0292502i
$153$	−0.483831	−	6.45628i	−0.0391154	−	0.521959i
$154$	−0.639006	−	0.197107i	−0.0514926	−	0.0158834i
$155$	1.71252	−	0.258121i	0.137553	−	0.0207328i
$156$	6.01833	+	7.54674i	0.481852	+	0.604223i
$157$	−16.4667	+	11.2268i	−1.31419	+	0.895998i	−0.998600	−	0.0528985i	$-0.983154\pi$
$157$	−16.4667	+	11.2268i	−1.31419	+	0.895998i	−0.315588	+	0.948896i	$0.602202\pi$
$158$	−9.78378	−	9.07802i	−0.778356	−	0.722209i
$159$	7.33461	+	18.6883i	0.581672	+	1.48208i
$160$	0.955573	−	0.294755i	0.0755447	−	0.0233024i
$161$	−0.497614	+	0.239638i	−0.0392175	+	0.0188862i
$162$	0.141824	−	0.361362i	0.0111428	−	0.0283913i
$163$	0.857286	−	11.4397i	0.0671478	−	0.896025i	−0.857325	−	0.514776i	$-0.827875\pi$
$163$	0.857286	−	11.4397i	0.0671478	−	0.896025i	0.924472	−	0.381249i	$-0.124506\pi$
$164$	−2.22988	+	2.79618i	−0.174124	+	0.218345i
$165$	−5.38724	+	9.33098i	−0.419396	+	0.726416i
$166$	−0.592680	−	1.02655i	−0.0460009	−	0.0796759i
$167$	16.8070	+	2.53325i	1.30057	+	0.196029i	0.762564	−	0.646913i	$-0.223940\pi$
$167$	16.8070	+	2.53325i	1.30057	+	0.196029i	0.538004	+	0.842942i	$0.319178\pi$
$168$	0.442397	+	0.213047i	0.0341317	+	0.0164369i
$169$	0.896517	−	0.831846i	0.0689629	−	0.0639882i
$170$	0.293330	−	1.28516i	0.0224974	−	0.0985675i
$171$	−3.14419			−0.240442
$172$	0.571350	−	6.53250i	0.0435650	−	0.498098i
$173$	−4.10785			−0.312314			−0.156157	−	0.987732i	$-0.549911\pi$
$173$	−4.10785			−0.312314			−0.156157	+	0.987732i	$0.549911\pi$
$174$	2.97687	−	13.0425i	0.225676	−	0.988751i
$175$	−0.127970	+	0.118739i	−0.00967362	+	0.00897581i
$176$	3.45126	+	1.66204i	0.260148	+	0.125281i
$177$	24.4422	+	3.68406i	1.83719	+	0.276911i
$178$	7.48920	+	12.9717i	0.561339	+	0.972268i
$179$	9.73146	−	16.8554i	0.727363	−	1.25983i	−0.230631	−	0.973041i	$-0.574079\pi$
$179$	9.73146	−	16.8554i	0.727363	−	1.25983i	0.957994	−	0.286789i	$-0.0925877\pi$
$180$	3.06226	−	3.83995i	0.228247	−	0.286213i
$181$	1.47133	−	19.6336i	0.109363	−	1.45935i	−0.625015	−	0.780613i	$-0.714907\pi$
$181$	1.47133	−	19.6336i	0.109363	−	1.45935i	0.734378	−	0.678741i	$-0.237474\pi$
$182$	−0.218872	+	0.557676i	−0.0162238	+	0.0413377i
$183$	7.29154	−	3.51142i	0.539006	−	0.259572i
$184$	3.02325	−	0.932548i	0.222877	−	0.0687483i
$185$	−0.588675	−	1.49992i	−0.0432802	−	0.110276i
$186$	−3.57090	−	3.31331i	−0.261831	−	0.242944i
$187$	4.17214	−	2.84452i	0.305097	−	0.208012i
$188$	4.54608	+	5.70061i	0.331557	+	0.415760i
$189$	0.928099	−	0.139888i	0.0675093	−	0.0101754i
$190$	−0.611730	−	0.188694i	−0.0443796	−	0.0136893i
$191$	−0.297670	−	3.97213i	−0.0215387	−	0.287413i	−0.997564	−	0.0697566i	$-0.977778\pi$
$191$	−0.297670	−	3.97213i	−0.0215387	−	0.287413i	0.976025	−	0.217657i	$-0.0698413\pi$
$192$	−2.32399	−	1.58447i	−0.167720	−	0.114349i
$193$	1.79257	+	7.85374i	0.129032	+	0.565325i	0.997568	+	0.0696994i	$0.0222040\pi$
$193$	1.79257	+	7.85374i	0.129032	+	0.565325i	−0.868536	+	0.495626i	$0.834939\pi$
$194$	−4.15026	−	18.1835i	−0.297972	−	1.30550i
$195$	7.97539	+	5.43753i	0.571130	+	0.389390i
$196$	−0.520833	−	6.95004i	−0.0372024	−	0.496431i
$197$	11.6455	+	3.59216i	0.829706	+	0.255930i	0.680382	−	0.732858i	$-0.261814\pi$
$197$	11.6455	+	3.59216i	0.829706	+	0.255930i	0.149324	+	0.988788i	$0.452290\pi$
$198$	18.6038	−	2.80407i	1.32212	−	0.199277i
$199$	−5.99710	−	7.52012i	−0.425123	−	0.533087i	0.522432	−	0.852681i	$-0.325025\pi$
$199$	−5.99710	−	7.52012i	−0.425123	−	0.533087i	−0.947555	+	0.319594i	$0.896454\pi$
$200$	0.826239	−	0.563320i	0.0584239	−	0.0398327i
$201$	3.01564	+	2.79810i	0.212707	+	0.197363i
$202$	1.34443	+	3.42555i	0.0945937	+	0.241021i
$203$	0.793410	−	0.244735i	0.0556865	−	0.0171770i
$204$	−3.34060	+	1.60875i	−0.233889	+	0.112635i
$205$	−1.30662	+	3.32922i	−0.0912586	+	0.232523i
$206$	0.936230	−	12.4931i	0.0652303	−	0.870437i
$207$	9.68839	−	12.1489i	0.673389	−	0.844404i
$208$	1.71588	−	2.97200i	0.118975	−	0.206071i
$209$	−1.22612	−	2.12371i	−0.0848127	−	0.146900i
$210$	0.485539	+	0.0731833i	0.0335054	+	0.00505013i
$211$	−15.0068	−	7.22690i	−1.03311	−	0.497520i	−0.161065	−	0.986944i	$-0.551493\pi$
$211$	−15.0068	−	7.22690i	−1.03311	−	0.497520i	−0.872046	+	0.489424i	$0.837207\pi$
$212$	5.23220	−	4.85477i	0.359349	−	0.333427i
$213$	0.253846	−	1.11217i	0.0173932	−	0.0762047i
$214$	1.76241			0.120476
$215$	−1.37952	−	6.41069i	−0.0940826	−	0.437205i
$216$	−5.37649			−0.365824
$217$	0.0672758	−	0.294754i	0.00456698	−	0.0200092i
$218$	−10.8409	+	10.0589i	−0.734237	+	0.681272i
$219$	40.7304	+	19.6147i	2.75231	+	1.32544i
$220$	3.78782	+	0.570922i	0.255375	+	0.0384916i
$221$	−2.26190	−	3.91773i	−0.152152	−	0.263535i
$222$	−2.26608	+	3.92497i	−0.152090	+	0.263427i
$223$	7.32135	−	9.18068i	0.490274	−	0.614784i	−0.473731	−	0.880670i	$-0.657093\pi$
$223$	7.32135	−	9.18068i	0.490274	−	0.614784i	0.964004	+	0.265886i	$0.0856645\pi$
$224$	0.0130458	−	0.174083i	0.000871656	−	0.0116314i
$225$	1.79437	−	4.57197i	0.119624	−	0.304798i
$226$	18.5398	−	8.92831i	1.23325	−	0.593903i
$227$	−1.92109	+	0.592577i	−0.127507	+	0.0393307i	−0.357852	−	0.933778i	$-0.616491\pi$
$227$	−1.92109	+	0.592577i	−0.127507	+	0.0393307i	0.230345	+	0.973109i	$0.426015\pi$
$228$	0.657845	+	1.67616i	0.0435668	+	0.111006i
$229$	11.9800	+	11.1158i	0.791663	+	0.734556i	0.968319	−	0.249717i	$-0.0803376\pi$
$229$	11.9800	+	11.1158i	0.791663	+	0.734556i	−0.176656	+	0.984273i	$0.556528\pi$
$230$	2.61406	−	1.78223i	0.172366	−	0.117517i
$231$	1.17273	+	1.47056i	0.0771602	+	0.0967559i
$232$	−4.70308	+	0.708875i	−0.308772	+	0.0465399i
$233$	13.1322	+	4.05074i	0.860317	+	0.265373i	0.693360	−	0.720592i	$-0.256130\pi$
$233$	13.1322	+	4.05074i	0.860317	+	0.265373i	0.166957	+	0.985964i	$0.446606\pi$
$234$	−1.25958	−	16.8079i	−0.0823413	−	1.09877i
$235$	6.02440	+	4.10737i	0.392988	+	0.267935i
$236$	−1.95551	−	8.56764i	−0.127293	−	0.557706i
$237$	8.35356	+	36.5993i	0.542622	+	2.37738i
$238$	−0.190136	−	0.129633i	−0.0123247	−	0.00840284i
$239$	−0.185755	−	2.47873i	−0.0120155	−	0.160336i	−0.999984	−	0.00567979i	$-0.998192\pi$
$239$	−0.185755	−	2.47873i	−0.0120155	−	0.160336i	0.987968	−	0.154656i	$-0.0494270\pi$
$240$	−2.68777	−	0.829068i	−0.173495	−	0.0535161i
$241$	15.3745	−	2.31733i	0.990356	−	0.149272i	0.366170	−	0.930548i	$-0.380669\pi$
$241$	15.3745	−	2.31733i	0.990356	−	0.149272i	0.624186	+	0.781276i	$0.285431\pi$
$242$	2.29042	+	2.87210i	0.147234	+	0.184626i
$243$	12.4246	−	8.47096i	0.797040	−	0.543413i
$244$	−2.10919	−	1.95704i	−0.135027	−	0.125287i
$245$	−2.54625	−	6.48775i	−0.162674	−	0.414487i
$246$	9.61269	−	2.96512i	0.612883	−	0.189049i
$247$	−1.97935	+	0.953206i	−0.125943	+	0.0606511i
$248$	−0.632722	+	1.61215i	−0.0401779	+	0.102372i
$249$	−0.249158	+	3.32478i	−0.0157897	+	0.210699i
$250$	0.623490	−	0.781831i	0.0394330	−	0.0494474i
$251$	−7.42189	+	12.8551i	−0.468465	+	0.811406i	−0.999350	−	0.0360381i	$-0.988526\pi$
$251$	−7.42189	+	12.8551i	−0.468465	+	0.811406i	0.530885	+	0.847444i	$0.321860\pi$
$252$	−0.428702	−	0.742534i	−0.0270057	−	0.0467753i
$253$	11.9839	+	1.80629i	0.753423	+	0.113560i
$254$	13.1085	+	6.31271i	0.822499	+	0.396095i
$255$	−2.71800	+	2.52194i	−0.170208	+	0.157930i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	−30.5475			−1.90550			−0.952752	−	0.303751i	$-0.901761\pi$
$257$	−30.5475			−1.90550			−0.952752	+	0.303751i	$0.901761\pi$
$258$	−11.6784	+	14.2762i	−0.727063	+	0.888796i
$259$	−0.281287			−0.0174784
$260$	0.763639	−	3.34572i	0.0473589	−	0.207493i
$261$	−17.1241	+	15.8888i	−1.05995	+	0.983494i
$262$	15.7056	+	7.56341i	0.970295	+	0.467269i
$263$	−16.8174	−	2.53481i	−1.03700	−	0.156303i	−0.391593	−	0.920138i	$-0.628076\pi$
$263$	−16.8174	−	2.53481i	−1.03700	−	0.156303i	−0.645411	+	0.763835i	$0.723314\pi$
$264$	−5.38724	−	9.33098i	−0.331562	−	0.574282i
$265$	3.56878	−	6.18131i	0.219228	−	0.379715i
$266$	−0.0696785	+	0.0873741i	−0.00427227	+	0.00535725i
$267$	3.14840	−	42.0125i	0.192679	−	2.57112i
$268$	0.534336	−	1.36146i	0.0326397	−	0.0831647i
$269$	−13.5408	+	6.52088i	−0.825594	+	0.397585i	−0.798461	−	0.602047i	$-0.794352\pi$
$269$	−13.5408	+	6.52088i	−0.825594	+	0.397585i	−0.0271333	+	0.999632i	$0.508638\pi$
$270$	−5.13763	+	1.58475i	−0.312666	+	0.0964447i
$271$	−7.82816	−	19.9458i	−0.475527	−	1.21162i	−0.944530	−	0.328427i	$-0.893482\pi$
$271$	−7.82816	−	19.9458i	−0.475527	−	1.21162i	0.469002	−	0.883197i	$-0.344614\pi$
$272$	0.966319	+	0.896613i	0.0585917	+	0.0543652i
$273$	1.39228	−	0.949238i	0.0842644	−	0.0574505i
$274$	−9.18534	−	11.5181i	−0.554907	−	0.695831i
$275$	3.78782	−	0.570922i	0.228414	−	0.0344279i
$276$	−8.50359	−	2.62301i	−0.511856	−	0.157887i
$277$	1.57199	+	20.9767i	0.0944516	+	1.26037i	0.820067	+	0.572268i	$0.193936\pi$
$277$	1.57199	+	20.9767i	0.0944516	+	1.26037i	−0.725615	+	0.688101i	$0.758445\pi$
$278$	−4.73930	−	3.23120i	−0.284244	−	0.193794i
$279$	1.89277	+	8.29276i	0.113317	+	0.496475i
$280$	−0.0388458	−	0.170195i	−0.00232148	−	0.0101711i
$281$	−0.254993	−	0.173852i	−0.0152116	−	0.0103711i	0.555690	−	0.831389i	$-0.312454\pi$
$281$	−0.254993	−	0.173852i	−0.0152116	−	0.0103711i	−0.570902	+	0.821018i	$0.693406\pi$
$282$	−1.53261	−	20.4513i	−0.0912658	−	1.21786i
$283$	20.3012	+	6.26208i	1.20678	+	0.372242i	0.831950	−	0.554851i	$-0.187225\pi$
$283$	20.3012	+	6.26208i	1.20678	+	0.372242i	0.374830	+	0.927094i	$0.377701\pi$
$284$	−0.401044	+	0.0604477i	−0.0237976	+	0.00358691i
$285$	1.12268	+	1.40779i	0.0665016	+	0.0833903i
$286$	10.8615	−	7.40526i	0.642255	−	0.437882i
$287$	0.457678	+	0.424664i	0.0270159	+	0.0250671i
$288$	1.79437	+	4.57197i	0.105734	+	0.269406i
$289$	−14.5843	+	4.49865i	−0.857897	+	0.264626i
$290$	−4.28519	+	2.06364i	−0.251635	+	0.121181i
$291$	−19.1660	+	48.8343i	−1.12353	+	2.86271i
$292$	1.20109	−	16.0274i	0.0702885	−	0.937935i
$293$	11.6010	−	14.5472i	0.677738	−	0.849856i	−0.317406	−	0.948290i	$-0.602812\pi$
$293$	11.6010	−	14.5472i	0.677738	−	0.849856i	0.995144	+	0.0984335i	$0.0313832\pi$
$294$	−9.80171	+	16.9771i	−0.571648	+	0.990123i
$295$	−4.39399	−	7.61061i	−0.255828	−	0.443107i
$296$	1.59330	+	0.240152i	0.0926090	+	0.0139586i
$297$	−18.5556	−	8.93593i	−1.07671	−	0.518515i
$298$	−5.96815	+	5.53763i	−0.345726	+	0.320787i
$299$	2.41601	−	10.5852i	0.139721	−	0.612159i
$300$	−2.81274			−0.162393
$301$	−1.12975	−	0.184684i	−0.0651175	−	0.0106450i
$302$	−10.6195			−0.611081
$303$	2.30324	−	10.0912i	0.132318	−	0.579722i
$304$	0.469279	−	0.435427i	0.0269150	−	0.0249735i
$305$	−2.59233	−	1.24840i	−0.148436	−	0.0714832i
$306$	6.40207	+	0.964956i	0.365982	+	0.0551629i
$307$	−0.634683	−	1.09930i	−0.0362233	−	0.0627406i	0.847345	−	0.531042i	$-0.178199\pi$
$307$	−0.634683	−	1.09930i	−0.0362233	−	0.0627406i	−0.883569	+	0.468302i	$0.844866\pi$
$308$	0.334358	−	0.579124i	0.0190518	−	0.0329987i
$309$	−21.9708	+	27.5505i	−1.24987	+	1.56729i
$310$	−0.129423	+	1.72702i	−0.00735071	+	0.0980884i
$311$	4.54984	−	11.5928i	0.257998	−	0.657367i	−0.741916	−	0.670493i	$-0.766083\pi$
$311$	4.54984	−	11.5928i	0.257998	−	0.657367i	0.999914	+	0.0131253i	$0.00417804\pi$
$312$	−8.69673	+	4.18813i	−0.492356	+	0.237106i
$313$	−28.3377	+	8.74103i	−1.60174	+	0.494072i	−0.961662	−	0.274236i	$-0.911575\pi$
$313$	−28.3377	+	8.74103i	−1.60174	+	0.494072i	−0.640080	+	0.768308i	$0.721099\pi$
$314$	−7.28115	−	18.5521i	−0.410899	−	1.04695i
$315$	−0.628522	−	0.583183i	−0.0354132	−	0.0328587i
$316$	11.0275	−	7.51843i	0.620346	−	0.422945i
$317$	3.16165	+	3.96459i	0.177576	+	0.222673i	0.862652	−	0.505799i	$-0.168802\pi$
$317$	3.16165	+	3.96459i	0.177576	+	0.222673i	−0.685075	+	0.728472i	$0.740231\pi$
$318$	−19.8518	+	2.99218i	−1.11324	+	0.167793i
$319$	−17.4097	−	5.37019i	−0.974757	−	0.300673i
$320$	0.0747301	+	0.997204i	0.00417754	+	0.0557454i
$321$	−4.09582	−	2.79248i	−0.228606	−	0.155861i
$322$	−0.122901	−	0.538463i	−0.00684898	−	0.0300074i
$323$	−0.187782	−	0.822725i	−0.0104484	−	0.0457776i
$324$	0.320743	+	0.218679i	0.0178191	+	0.0121488i
$325$	−0.256456	−	3.42217i	−0.0142256	−	0.189828i
$326$	10.9621	+	3.38136i	0.607135	+	0.187276i
$327$	41.1321	−	6.19966i	2.27461	−	0.342842i
$328$	−2.22988	−	2.79618i	−0.123125	−	0.154393i
$329$	1.05169	−	0.717029i	0.0579815	−	0.0395311i
$330$	−7.89826	−	7.32851i	−0.434785	−	0.403421i
$331$	1.22557	+	3.12270i	0.0673633	+	0.171639i	0.960591	−	0.277966i	$-0.0896601\pi$
$331$	1.22557	+	3.12270i	0.0673633	+	0.171639i	−0.893228	+	0.449605i	$0.851565\pi$
$332$	1.13270	−	0.349391i	0.0621649	−	0.0191753i
$333$	7.13016	−	3.43370i	0.390730	−	0.188166i
$334$	−6.20966	+	15.8220i	−0.339777	+	0.865739i
$335$	0.109298	−	1.45848i	0.00597157	−	0.0796851i
$336$	−0.306148	+	0.383898i	−0.0167018	+	0.0209433i
$337$	5.57560	−	9.65722i	0.303722	−	0.526062i	−0.673254	−	0.739411i	$-0.735104\pi$
$337$	5.57560	−	9.65722i	0.303722	−	0.526062i	0.976976	+	0.213349i	$0.0684372\pi$
$338$	0.611496	+	1.05914i	0.0332610	+	0.0576098i
$339$	−57.2330	−	8.62649i	−3.10847	−	0.468527i
$340$	1.18767	+	0.571952i	0.0644104	+	0.0310184i
$341$	−4.86314	+	4.51233i	−0.263354	+	0.244357i
$342$	0.699648	−	3.06536i	0.0378326	−	0.165756i
$343$	−2.43868			−0.131676
$344$	6.24158	+	2.01064i	0.336523	+	0.108407i
$345$	−8.89895			−0.479103
$346$	0.914082	−	4.00486i	0.0491414	−	0.215302i
$347$	−0.831592	+	0.771604i	−0.0446422	+	0.0414219i	−0.702178	−	0.712001i	$-0.747789\pi$
$347$	−0.831592	+	0.771604i	−0.0446422	+	0.0414219i	0.657536	+	0.753423i	$0.271599\pi$
$348$	12.0531	+	5.80447i	0.646114	+	0.311152i
$349$	23.8880	+	3.60053i	1.27869	+	0.192732i	0.753045	−	0.657969i	$-0.228584\pi$
$349$	23.8880	+	3.60053i	1.27869	+	0.192732i	0.525649	+	0.850702i	$0.323823\pi$
$350$	−0.0872858	−	0.151183i	−0.00466562	−	0.00808109i
$351$	−9.22542	+	15.9789i	−0.492416	+	0.852890i
$352$	−2.38834	+	2.99489i	−0.127299	+	0.159628i
$353$	0.836223	−	11.1586i	0.0445076	−	0.593913i	−0.929708	−	0.368296i	$-0.879941\pi$
$353$	0.836223	−	11.1586i	0.0445076	−	0.593913i	0.974216	−	0.225617i	$-0.0724398\pi$
$354$	−9.03059	+	23.0096i	−0.479970	+	1.22294i
$355$	−0.365409	+	0.175972i	−0.0193939	+	0.00933962i
$356$	−14.3129	+	4.41496i	−0.758585	+	0.233992i
$357$	0.236476	+	0.602531i	0.0125156	+	0.0318893i
$358$	14.2673	+	13.2381i	0.754051	+	0.699658i
$359$	−20.3889	+	13.9009i	−1.07608	+	0.733661i	−0.965552	−	0.260212i	$-0.916208\pi$
$359$	−20.3889	+	13.9009i	−1.07608	+	0.733661i	−0.110532	+	0.993873i	$0.535255\pi$
$360$	3.06226	+	3.83995i	0.161395	+	0.202383i
$361$	18.3825	−	2.77072i	0.967502	−	0.145828i
$362$	18.8139	+	5.80333i	0.988838	+	0.305016i
$363$	−0.772166	−	10.3038i	−0.0405282	−	0.540811i
$364$	−0.494990	−	0.337479i	−0.0259445	−	0.0176887i
$365$	−3.57644	−	15.6694i	−0.187200	−	0.820175i
$366$	1.80086	+	7.89009i	0.0941325	+	0.412421i
$367$	−23.7160	−	16.1693i	−1.23796	−	0.844030i	−0.245843	−	0.969310i	$-0.579065\pi$
$367$	−23.7160	−	16.1693i	−1.23796	−	0.844030i	−0.992121	+	0.125280i	$0.960017\pi$
$368$	0.236431	+	3.15496i	0.0123248	+	0.164464i
$369$	−16.7853	−	5.17757i	−0.873806	−	0.269534i
$370$	1.59330	−	0.240152i	0.0828320	−	0.0124849i
$371$	−0.776877	−	0.974173i	−0.0403335	−	0.0505766i
$372$	4.02484	−	2.74409i	0.208678	−	0.142274i
$373$	24.4153	+	22.6541i	1.26418	+	1.17298i	0.976562	+	0.215237i	$0.0690524\pi$
$373$	24.4153	+	22.6541i	1.26418	+	1.17298i	0.287614	+	0.957746i	$0.407138\pi$
$374$	1.84481	+	4.70050i	0.0953929	+	0.243057i
$375$	−2.68777	+	0.829068i	−0.138796	+	0.0428129i
$376$	−6.56928	+	3.16360i	−0.338785	+	0.163150i
$377$	−5.96316	+	15.1939i	−0.307118	+	0.782525i
$378$	−0.0701403	+	0.935958i	−0.00360763	+	0.0481405i
$379$	−8.49899	+	10.6574i	−0.436564	+	0.547434i	−0.950634	−	0.310314i	$-0.899566\pi$
$379$	−8.49899	+	10.6574i	−0.436564	+	0.547434i	0.514070	+	0.857748i	$0.328137\pi$
$380$	0.320086	−	0.554405i	0.0164200	−	0.0284404i
$381$	−20.4617	−	35.4407i	−1.04828	−	1.81568i
$382$	3.93878	+	0.593675i	0.201525	+	0.0303751i
$383$	−24.6885	−	11.8893i	−1.26152	−	0.607517i	−0.320945	−	0.947098i	$-0.604000\pi$
$383$	−24.6885	−	11.8893i	−1.26152	−	0.607517i	−0.940577	+	0.339581i	$0.889715\pi$
$384$	2.06188	−	1.91315i	0.105220	−	0.0976298i
$385$	0.148803	−	0.651949i	0.00758371	−	0.0332264i
$386$	−8.05572			−0.410025
$387$	30.8916	−	9.10950i	1.57031	−	0.463062i
$388$	18.6511			0.946867
$389$	−2.95470	+	12.9454i	−0.149809	+	0.656358i	0.843127	+	0.537714i	$0.180712\pi$
$389$	−2.95470	+	12.9454i	−0.149809	+	0.656358i	−0.992937	+	0.118644i	$0.962145\pi$
$390$	−7.07589	+	6.56547i	−0.358302	+	0.332455i
$391$	3.75755	+	1.80954i	0.190028	+	0.0915125i
$392$	6.89168	+	1.03875i	0.348082	+	0.0524650i
$393$	−24.5156	−	42.4623i	−1.23665	−	2.14194i
$394$	−6.09346	+	10.5542i	−0.306984	+	0.531712i
$395$	8.32149	−	10.4348i	0.418700	−	0.525033i
$396$	−1.40597	+	18.7613i	−0.0706526	+	0.942793i
$397$	5.92820	−	15.1048i	0.297528	−	0.758089i	−0.701443	−	0.712726i	$-0.747460\pi$
$397$	5.92820	−	15.1048i	0.297528	−	0.758089i	0.998971	−	0.0453629i	$-0.0144444\pi$
$398$	8.66606	−	4.17335i	0.434390	−	0.209191i
$399$	0.300374	−	0.0926531i	0.0150375	−	0.00463846i
$400$	0.365341	+	0.930874i	0.0182671	+	0.0465437i
$401$	20.2076	+	18.7499i	1.00912	+	0.936326i	0.997975	−	0.0636122i	$-0.0202621\pi$
$401$	20.2076	+	18.7499i	1.00912	+	0.936326i	0.0111445	+	0.999938i	$0.496453\pi$
$402$	−3.39899	+	2.31739i	−0.169526	+	0.115581i
$403$	3.70562	+	4.64670i	0.184590	+	0.231469i
$404$	−3.63883	+	0.548465i	−0.181038	+	0.0272871i
$405$	0.370951	+	0.114423i	0.0184327	+	0.00568573i
$406$	0.0620482	+	0.827976i	0.00307940	+	0.0410918i
$407$	5.09976	+	3.47696i	0.252786	+	0.172347i
$408$	−0.825060	−	3.61482i	−0.0408466	−	0.178960i
$409$	−1.45069	−	6.35590i	−0.0717321	−	0.314279i	0.926315	−	0.376751i	$-0.122959\pi$
$409$	−1.45069	−	6.35590i	−0.0717321	−	0.314279i	−0.998047	+	0.0624720i	$0.980102\pi$
$410$	−2.95500	−	2.01469i	−0.145937	−	0.0994983i
$411$	3.09664	+	41.3218i	0.152746	+	2.03825i
$412$	11.9716	+	3.69274i	0.589797	+	0.181928i
$413$	−1.51700	+	0.228650i	−0.0746465	+	0.0112511i
$414$	9.68839	+	12.1489i	0.476158	+	0.597083i
$415$	0.979390	−	0.667737i	0.0480764	−	0.0327779i
$416$	2.51566	+	2.33419i	0.123340	+	0.114443i
$417$	5.89435	+	15.0185i	0.288647	+	0.735461i
$418$	2.34330	−	0.722812i	0.114614	−	0.0353539i
$419$	11.1261	−	5.35804i	0.543545	−	0.261757i	−0.141901	−	0.989881i	$-0.545321\pi$
$419$	11.1261	−	5.35804i	0.543545	−	0.261757i	0.685446	+	0.728123i	$0.259607\pi$
$420$	−0.179391	+	0.457081i	−0.00875339	+	0.0223033i
$421$	1.61233	−	21.5150i	0.0785801	−	1.04858i	−0.808965	−	0.587857i	$-0.799972\pi$
$421$	1.61233	−	21.5150i	0.0785801	−	1.04858i	0.887545	−	0.460722i	$-0.152409\pi$
$422$	10.3850	−	13.0224i	0.505535	−	0.633921i
$423$	−17.9057	+	31.0135i	−0.870603	+	1.50793i
$424$	3.56878	+	6.18131i	0.173315	+	0.300191i
$425$	1.30349	+	0.196470i	0.0632286	+	0.00953017i
$426$	1.02780	+	0.494962i	0.0497971	+	0.0239810i
$427$	−0.368204	+	0.341644i	−0.0178186	+	0.0165333i
$428$	−0.392172	+	1.71822i	−0.0189564	+	0.0830532i
$429$	−36.9755			−1.78519
$430$	6.55693	+	0.0815780i	0.316203	+	0.00393404i
$431$	27.4160			1.32058			0.660290	−	0.751010i	$-0.270433\pi$
$431$	27.4160			1.32058			0.660290	+	0.751010i	$0.270433\pi$
$432$	1.19638	−	5.24169i	0.0575609	−	0.252191i
$433$	20.5161	−	19.0361i	0.985939	−	0.914818i	−0.0104309	−	0.999946i	$-0.503320\pi$
$433$	20.5161	−	19.0361i	0.985939	−	0.914818i	0.996370	+	0.0851278i	$0.0271299\pi$
$434$	0.272394	+	0.131178i	0.0130753	+	0.00629675i
$435$	13.2285	+	1.99388i	0.634259	+	0.0955992i
$436$	−7.39435	−	12.8074i	−0.354125	−	0.613362i
$437$	1.01269	−	1.75403i	0.0484435	−	0.0839065i
$438$	−28.1863	+	35.3445i	−1.34679	+	1.68883i
$439$	0.506681	−	6.76118i	0.0241826	−	0.322694i	−0.971973	−	0.235092i	$-0.924461\pi$
$439$	0.506681	−	6.76118i	0.0241826	−	0.322694i	0.996156	−	0.0876014i	$-0.0279202\pi$
$440$	−1.39948	+	3.56581i	−0.0667175	+	0.169993i
$441$	30.8408	−	14.8521i	1.46861	−	0.707245i
$442$	4.32282	−	1.33341i	0.205616	−	0.0634240i
$443$	2.98792	+	7.61310i	0.141960	+	0.361709i	0.984116	−	0.177525i	$-0.0568090\pi$
$443$	2.98792	+	7.61310i	0.141960	+	0.361709i	−0.842156	+	0.539234i	$0.818714\pi$
$444$	−3.32231	−	3.08266i	−0.157670	−	0.146296i
$445$	−12.3757	+	8.43763i	−0.586666	+	0.399982i
$446$	7.32135	+	9.18068i	0.346676	+	0.434718i
$447$	22.6441	−	3.41306i	1.07103	−	0.161432i
$448$	0.166816	+	0.0514559i	0.00788131	+	0.00243106i
$449$	−1.90772	−	25.4568i	−0.0900311	−	1.20138i	−0.840997	−	0.541040i	$-0.818031\pi$
$449$	−1.90772	−	25.4568i	−0.0900311	−	1.20138i	0.750966	−	0.660341i	$-0.229588\pi$
$450$	4.05806	+	2.76674i	0.191299	+	0.130425i
$451$	−3.04853	−	13.3565i	−0.143550	−	0.628933i
$452$	4.57896	+	20.0617i	0.215376	+	0.943625i
$453$	24.6795	+	16.8262i	1.15955	+	0.790565i
$454$	−0.150238	−	2.00478i	−0.00705101	−	0.0940891i
$455$	−0.572473	−	0.176584i	−0.0268379	−	0.00827841i
$456$	−1.78052	+	0.268370i	−0.0833805	+	0.0125676i
$457$	−10.8139	−	13.5602i	−0.505852	−	0.634318i	0.461686	−	0.887043i	$-0.347245\pi$
$457$	−10.8139	−	13.5602i	−0.505852	−	0.634318i	−0.967538	+	0.252725i	$0.918673\pi$
$458$	−13.5030	+	9.20616i	−0.630952	+	0.430176i
$459$	−5.19540	−	4.82063i	−0.242501	−	0.225008i
$460$	1.15587	+	2.94510i	0.0538926	+	0.137316i
$461$	−3.96982	+	1.22453i	−0.184893	+	0.0570320i	−0.385819	−	0.922574i	$-0.626081\pi$
$461$	−3.96982	+	1.22453i	−0.184893	+	0.0570320i	0.200926	+	0.979606i	$0.435605\pi$
$462$	−1.69465	+	0.816100i	−0.0788422	+	0.0379684i
$463$	−12.3183	+	31.3866i	−0.572481	+	1.45866i	0.292209	+	0.956354i	$0.405610\pi$
$463$	−12.3183	+	31.3866i	−0.572481	+	1.45866i	−0.864691	+	0.502304i	$0.832486\pi$
$464$	0.355431	−	4.74290i	0.0165005	−	0.220184i
$465$	3.03719	−	3.80852i	0.140847	−	0.176616i
$466$	−6.87136	+	11.9015i	−0.318309	+	0.551328i
$467$	−19.2343	−	33.3148i	−0.890057	−	1.54162i	−0.839805	−	0.542888i	$-0.817331\pi$
$467$	−19.2343	−	33.3148i	−0.890057	−	1.54162i	−0.0502520	−	0.998737i	$-0.516002\pi$
$468$	16.6668	+	2.51211i	0.770422	+	0.116123i
$469$	−0.230038	−	0.110780i	−0.0106222	−	0.00511536i
$470$	−5.34494	+	4.95938i	−0.246544	+	0.228759i
$471$	−12.4739	+	54.6516i	−0.574766	+	2.51821i
$472$	8.78797			0.404499
$473$	18.1995	+	17.3130i	0.836816	+	0.796052i
$474$	−37.5406			−1.72430
$475$	0.142451	−	0.624121i	0.00653612	−	0.0286366i
$476$	0.168692	−	0.156523i	0.00773198	−	0.00717423i
$477$	31.5843	+	15.2102i	1.44615	+	0.696428i
$478$	2.45792	+	0.370472i	0.112423	+	0.0169450i
$479$	6.89217	+	11.9376i	0.314911	+	0.545443i	0.979419	−	0.201839i	$-0.0646919\pi$
$479$	6.89217	+	11.9376i	0.314911	+	0.545443i	−0.664507	+	0.747282i	$0.731359\pi$
$480$	1.40637	−	2.43590i	0.0641916	−	0.111183i
$481$	3.44765	−	4.32322i	0.157199	−	0.197122i
$482$	−1.16191	+	15.5046i	−0.0529236	+	0.706217i
$483$	−0.567558	+	1.44612i	−0.0258248	+	0.0658005i
$484$	−3.30976	+	1.59390i	−0.150444	+	0.0724498i
$485$	17.8225	−	5.49751i	0.809278	−	0.249629i
$486$	5.49384	+	13.9981i	0.249206	+	0.634966i
$487$	−0.999698	−	0.927584i	−0.0453006	−	0.0420328i	0.657198	−	0.753718i	$-0.271742\pi$
$487$	−0.999698	−	0.927584i	−0.0453006	−	0.0420328i	−0.702498	+	0.711685i	$0.747932\pi$
$488$	2.37731	−	1.62082i	0.107616	−	0.0733712i
$489$	−20.1182	−	25.2274i	−0.909775	−	1.14082i
$490$	6.89168	−	1.03875i	0.311334	−	0.0469261i
$491$	−24.5024	−	7.55800i	−1.10578	−	0.341088i	−0.312483	−	0.949924i	$-0.601161\pi$
$491$	−24.5024	−	7.55800i	−1.10578	−	0.341088i	−0.793296	+	0.608836i	$0.791637\pi$
$492$	0.751756	+	10.0315i	0.0338918	+	0.452254i
$493$	−5.18026	−	3.53184i	−0.233307	−	0.159066i
$494$	−0.488860	−	2.14184i	−0.0219949	−	0.0963657i
$495$	4.18650	+	18.3422i	0.188169	+	0.824423i
$496$	−1.43094	−	0.975595i	−0.0642509	−	0.0438055i
$497$	0.00529102	+	0.0706037i	0.000237335	+	0.00316701i
$498$	−3.18598	−	0.982744i	−0.142767	−	0.0440378i
$499$	−20.6219	+	3.10825i	−0.923162	+	0.139144i	−0.593389	−	0.804916i	$-0.702210\pi$
$499$	−20.6219	+	3.10825i	−0.923162	+	0.139144i	−0.329773	+	0.944060i	$0.606972\pi$
$500$	0.623490	+	0.781831i	0.0278833	+	0.0349646i
$501$	39.5006	−	26.9311i	1.76476	−	1.20319i
$502$	−10.8813	−	10.0963i	−0.485654	−	0.450621i
$503$	6.31921	+	16.1011i	0.281760	+	0.717912i	0.999761	+	0.0218700i	$0.00696200\pi$
$503$	6.31921	+	16.1011i	0.281760	+	0.717912i	−0.718001	+	0.696042i	$0.754943\pi$
$504$	0.819313	−	0.252725i	0.0364951	−	0.0112572i
$505$	−3.31550	+	1.59666i	−0.147538	+	0.0710505i
$506$	−4.42768	+	11.2815i	−0.196834	+	0.501525i
$507$	0.257068	−	3.43034i	0.0114168	−	0.152347i
$508$	−9.07135	+	11.3751i	−0.402476	+	0.504689i
$509$	−4.41799	+	7.65219i	−0.195824	+	0.339177i	−0.947170	−	0.320731i	$-0.896071\pi$
$509$	−4.41799	+	7.65219i	−0.195824	+	0.339177i	0.751346	+	0.659908i	$0.229405\pi$
$510$	−1.85389	−	3.21104i	−0.0820918	−	0.142187i
$511$	−2.77444	−	0.418180i	−0.122734	−	0.0184992i
$512$	−0.900969	−	0.433884i	−0.0398176	−	0.0191751i
$513$	−2.52307	+	2.34107i	−0.111396	+	0.103361i
$514$	6.79747	−	29.7816i	0.299823	−	1.31361i
$515$	12.5282			0.552057
$516$	−11.3196	−	14.5623i	−0.498316	−	0.641070i
$517$	−27.9303			−1.22837
$518$	0.0625924	−	0.274235i	0.00275015	−	0.0120492i
$519$	−8.46989	+	7.85891i	−0.371787	+	0.344968i
$520$	3.09191	+	1.48899i	0.135589	+	0.0652964i
$521$	8.81044	+	1.32796i	0.385992	+	0.0581790i	0.339172	−	0.940724i	$-0.389853\pi$
$521$	8.81044	+	1.32796i	0.385992	+	0.0581790i	0.0468202	+	0.998903i	$0.485091\pi$
$522$	−11.6800	−	20.2304i	−0.511220	−	0.885458i
$523$	−7.24231	+	12.5441i	−0.316684	+	0.548513i	−0.979794	−	0.200009i	$-0.935903\pi$
$523$	−7.24231	+	12.5441i	−0.316684	+	0.548513i	0.663110	+	0.748522i	$0.269236\pi$
$524$	−10.8686	+	13.6288i	−0.474797	+	0.595377i
$525$	−0.0366942	+	0.489651i	−0.00160147	+	0.0213701i
$526$	6.21348	−	15.8317i	0.270921	−	0.690294i
$527$	−2.05689	+	0.990544i	−0.0895993	+	0.0431488i
$528$	10.2958	−	3.17584i	0.448067	−	0.138210i
$529$	−4.74590	−	12.0924i	−0.206344	−	0.525755i
$530$	5.23220	+	4.85477i	0.227272	+	0.210878i
$531$	35.6621	−	24.3140i	1.54760	−	1.05514i
$532$	−0.0696785	−	0.0873741i	−0.00302095	−	0.00378815i
$533$	−12.1365	+	1.82928i	−0.525688	+	0.0792347i
$534$	40.2585	+	12.4181i	1.74216	+	0.537384i
$535$	0.131705	+	1.75748i	0.00569409	+	0.0759824i
$536$	1.20843	+	0.823893i	0.0521962	+	0.0355868i
$537$	−12.1817	−	53.3715i	−0.525679	−	2.30315i
$538$	−3.34429	−	14.6523i	−0.144183	−	0.631705i
$539$	22.0585	+	15.0392i	0.950128	+	0.647786i
$540$	−0.401785	−	5.36145i	−0.0172901	−	0.230720i
$541$	−35.8224	−	11.0497i	−1.54012	−	0.475066i	−0.595538	−	0.803327i	$-0.703061\pi$
$541$	−35.8224	−	11.0497i	−1.54012	−	0.475066i	−0.944587	+	0.328262i	$0.893537\pi$
$542$	21.1877	−	3.19353i	0.910089	−	0.137174i
$543$	−34.5282	−	43.2970i	−1.48175	−	1.85805i
$544$	−1.08916	+	0.742576i	−0.0466973	+	0.0318377i
$545$	−10.8409	−	10.0589i	−0.464372	−	0.430874i
$546$	0.615628	+	1.56859i	0.0263464	+	0.0671296i
$547$	−11.5768	+	3.57097i	−0.494989	+	0.152684i	−0.532192	−	0.846624i	$-0.678631\pi$
$547$	−11.5768	+	3.57097i	−0.494989	+	0.152684i	0.0372028	+	0.999308i	$0.488155\pi$
$548$	13.2732	−	6.39204i	0.567003	−	0.273054i
$549$	5.16287	−	13.1548i	0.220346	−	0.561432i
$550$	−0.286262	+	3.81990i	−0.0122062	+	0.162881i
$551$	−1.89839	+	2.38051i	−0.0808742	+	0.101413i
$552$	4.44947	−	7.70671i	0.189382	−	0.328019i
$553$	−1.16497	−	2.01779i	−0.0495397	−	0.0858052i
$554$	−20.8006	−	3.13518i	−0.883732	−	0.133201i
$555$	−4.08334	−	1.96643i	−0.173328	−	0.0834704i
$556$	4.20478	−	3.90146i	0.178322	−	0.165459i
$557$	−6.93550	+	30.3864i	−0.293866	+	1.28751i	0.585229	+	0.810868i	$0.301005\pi$
$557$	−6.93550	+	30.3864i	−0.293866	+	1.28751i	−0.879096	+	0.476645i	$0.841853\pi$
$558$	−8.50603			−0.360089
$559$	16.6854	−	15.0999i	0.705719	−	0.638658i
$560$	0.174572			0.00737700
$561$	3.16048	−	13.8470i	0.133436	−	0.584620i
$562$	0.226234	−	0.209915i	0.00954311	−	0.00885471i
$563$	−16.8896	−	8.13358i	−0.711810	−	0.342790i	0.0426911	−	0.999088i	$-0.486407\pi$
$563$	−16.8896	−	8.13358i	−0.711810	−	0.342790i	−0.754501	+	0.656299i	$0.772121\pi$
$564$	20.2796	+	3.05666i	0.853924	+	0.128708i
$565$	10.2888	+	17.8208i	0.432854	+	0.749726i
$566$	−10.6225	+	18.3987i	−0.446498	+	0.773357i
$567$	0.0422528	−	0.0529833i	0.00177445	−	0.00222509i
$568$	0.0303086	−	0.404440i	0.00127172	−	0.0169699i
$569$	−1.25074	+	3.18682i	−0.0524336	+	0.133599i	−0.954691	−	0.297600i	$-0.903814\pi$
$569$	−1.25074	+	3.18682i	−0.0524336	+	0.133599i	0.902257	+	0.431198i	$0.141909\pi$
$570$	−1.62231	+	0.781265i	−0.0679512	+	0.0327236i
$571$	−38.1375	+	11.7639i	−1.59601	+	0.492303i	−0.960145	−	0.279501i	$-0.909831\pi$
$571$	−38.1375	+	11.7639i	−1.59601	+	0.492303i	−0.635861	+	0.771804i	$0.719355\pi$
$572$	4.80268	+	12.2370i	0.200810	+	0.511656i
$573$	−8.21303	−	7.62058i	−0.343104	−	0.318354i
$574$	−0.515859	+	0.351707i	−0.0215316	+	0.0146800i
$575$	1.97260	+	2.47356i	0.0822631	+	0.103155i
$576$	−4.85662	+	0.732018i	−0.202359	+	0.0305008i
$577$	37.4774	+	11.5602i	1.56020	+	0.481259i	0.950331	−	0.311241i	$-0.100744\pi$
$577$	37.4774	+	11.5602i	1.56020	+	0.481259i	0.609872	+	0.792500i	$0.291221\pi$
$578$	−1.14055	−	15.2196i	−0.0474408	−	0.633053i
$579$	18.7214	+	12.7640i	0.778036	+	0.530456i
$580$	−1.05835	−	4.63696i	−0.0439458	−	0.192539i
$581$	−0.0460463	−	0.201742i	−0.00191032	−	0.00836967i
$582$	−43.3450	−	29.5521i	−1.79671	−	1.22498i
$583$	2.04321	+	27.2647i	0.0846211	+	1.12919i
$584$	15.3583	+	4.73742i	0.635532	+	0.196036i
$585$	16.6668	−	2.51211i	0.689087	−	0.103863i
$586$	11.6010	+	14.5472i	0.479233	+	0.600939i
$587$	−6.29478	+	4.29171i	−0.259813	+	0.177138i	−0.686220	−	0.727394i	$-0.740731\pi$
$587$	−6.29478	+	4.29171i	−0.259813	+	0.177138i	0.426407	+	0.904531i	$0.359779\pi$
$588$	−14.3703	−	13.3337i	−0.592622	−	0.549873i
$589$	0.405050	+	1.03205i	0.0166898	+	0.0425249i
$590$	8.39755	−	2.59030i	0.345722	−	0.106641i
$591$	30.8839	−	14.8729i	1.27039	−	0.611790i
$592$	−0.588675	+	1.49992i	−0.0241944	+	0.0616463i
$593$	0.277649	−	3.70497i	0.0114017	−	0.152145i	−0.988597	−	0.150585i	$-0.951884\pi$
$593$	0.277649	−	3.70497i	0.0114017	−	0.152145i	0.999999	−	0.00156012i	$-0.000496600\pi$
$594$	12.8409	−	16.1020i	0.526869	−	0.660673i
$595$	0.115061	−	0.199292i	0.00471706	−	0.00817018i
$596$	−4.07076	−	7.05076i	−0.166745	−	0.288810i
$597$	−26.7524	−	4.03228i	−1.09490	−	0.165030i
$598$	9.78221	+	4.71086i	0.400024	+	0.192642i
$599$	−11.7862	+	10.9360i	−0.481570	+	0.446832i	−0.883218	−	0.468962i	$-0.844628\pi$
$599$	−11.7862	+	10.9360i	−0.481570	+	0.446832i	0.401648	+	0.915794i	$0.368438\pi$
$600$	0.625892	−	2.74221i	0.0255520	−	0.111950i
$601$	−34.0494			−1.38891			−0.694453	−	0.719538i	$-0.744353\pi$
$601$	−34.0494			−1.38891			−0.694453	+	0.719538i	$0.744353\pi$
$602$	0.431446	−	1.06033i	0.0175844	−	0.0432156i
$603$	7.18337			0.292529
$604$	2.36305	−	10.3532i	0.0961512	−	0.421266i
$605$	−2.69291	+	2.49865i	−0.109482	+	0.101585i
$606$	9.32563	+	4.49099i	0.378828	+	0.182434i
$607$	−5.52783	−	0.833186i	−0.224368	−	0.0338180i	0.0358962	−	0.999356i	$-0.488571\pi$
$607$	−5.52783	−	0.833186i	−0.224368	−	0.0338180i	−0.260264	+	0.965538i	$0.583810\pi$
$608$	0.320086	+	0.554405i	0.0129812	+	0.0224841i
$609$	1.16770	−	2.02252i	0.0473178	−	0.0819568i
$610$	1.79395	−	2.24954i	0.0726348	−	0.0910812i
$611$	−1.86991	+	24.9522i	−0.0756485	+	1.00946i
$612$	−2.36536	+	6.02683i	−0.0956139	+	0.243620i
$613$	11.1436	−	5.36647i	0.450085	−	0.216750i	−0.195088	−	0.980786i	$-0.562499\pi$
$613$	11.1436	−	5.36647i	0.450085	−	0.216750i	0.645173	+	0.764036i	$0.276785\pi$
$614$	1.21297	−	0.374152i	0.0489516	−	0.0150996i
$615$	3.67519	+	9.36423i	0.148198	+	0.377602i
$616$	0.490203	+	0.454842i	0.0197508	+	0.0183261i
$617$	−26.1971	+	17.8609i	−1.05465	+	0.719051i	−0.960998	−	0.276554i	$-0.910808\pi$
$617$	−26.1971	+	17.8609i	−1.05465	+	0.719051i	−0.0936556	+	0.995605i	$0.529855\pi$
$618$	−21.9708	−	27.5505i	−0.883794	−	1.10824i
$619$	−10.3278	+	1.55666i	−0.415109	+	0.0625675i	−0.353276	−	0.935519i	$-0.614932\pi$
$619$	−10.3278	+	1.55666i	−0.415109	+	0.0625675i	−0.0618322	+	0.998087i	$0.519694\pi$
$620$	−1.65492	−	0.510477i	−0.0664634	−	0.0205012i
$621$	−1.27117	−	16.9626i	−0.0510103	−	0.680685i
$622$	10.2897	+	7.01540i	0.412580	+	0.281292i
$623$	0.581848	+	2.54924i	0.0233113	+	0.102133i
$624$	−2.14792	−	9.41063i	−0.0859854	−	0.376727i
$625$	0.826239	+	0.563320i	0.0330496	+	0.0225328i
$626$	−2.21614	−	29.5723i	−0.0885746	−	1.18195i
$627$	−6.59108	−	2.03308i	−0.263222	−	0.0811933i
$628$	19.7071	−	2.97037i	0.786401	−	0.118531i
$629$	1.32432	+	1.66064i	0.0528040	+	0.0662141i
$630$	0.708421	−	0.482993i	0.0282242	−	0.0192429i
$631$	−22.3183	−	20.7084i	−0.888478	−	0.824387i	0.0968074	−	0.995303i	$-0.469137\pi$
$631$	−22.3183	−	20.7084i	−0.888478	−	0.824387i	−0.985286	+	0.170916i	$0.945327\pi$
$632$	4.87608	+	12.4240i	0.193960	+	0.494202i
$633$	−44.7684	+	13.8092i	−1.77938	+	0.548867i
$634$	−4.56872	+	2.20018i	−0.181447	+	0.0873803i
$635$	−5.31546	+	13.5436i	−0.210938	+	0.537461i
$636$	1.50029	−	20.0199i	0.0594902	−	0.793842i
$637$	14.9125	−	18.6997i	0.590854	−	0.740908i
$638$	9.10957	−	15.7782i	0.360651	−	0.624667i
$639$	−0.995984	−	1.72510i	−0.0394005	−	0.0682437i
$640$	−0.988831	−	0.149042i	−0.0390870	−	0.00589141i
$641$	32.5975	+	15.6981i	1.28752	+	0.620039i	0.947313	−	0.320311i	$-0.103787\pi$
$641$	32.5975	+	15.6981i	1.28752	+	0.620039i	0.340211	+	0.940349i	$0.389502\pi$
$642$	3.63387	−	3.37174i	0.143417	−	0.133072i
$643$	−1.87911	+	8.23290i	−0.0741047	+	0.324674i	−0.998370	−	0.0570774i	$-0.981822\pi$
$643$	−1.87911	+	8.23290i	−0.0741047	+	0.324674i	0.924265	+	0.381751i	$0.124679\pi$
$644$	0.552310			0.0217641
$645$	−15.1090	−	10.5788i	−0.594916	−	0.416542i
$646$	0.843883			0.0332021
$647$	0.738839	−	3.23706i	0.0290468	−	0.127262i	−0.958326	−	0.285678i	$-0.907781\pi$
$647$	0.738839	−	3.23706i	0.0290468	−	0.127262i	0.987373	+	0.158415i	$0.0506385\pi$
$648$	−0.284569	+	0.264041i	−0.0111789	+	0.0103725i
$649$	30.3296	+	14.6059i	1.19054	+	0.573334i
$650$	3.39343	+	0.511478i	0.133101	+	0.0200618i
$651$	−0.425194	−	0.736457i	−0.0166647	−	0.0288640i
$652$	−5.73588	+	9.93484i	−0.224634	+	0.389078i
$653$	−16.6236	+	20.8453i	−0.650530	+	0.815739i	−0.992276	−	0.124053i	$-0.960411\pi$
$653$	−16.6236	+	20.8453i	−0.650530	+	0.815739i	0.341745	+	0.939793i	$0.388982\pi$
$654$	−3.10852	+	41.4804i	−0.121553	+	1.62201i
$655$	−6.36858	+	16.2269i	−0.248841	+	0.634037i
$656$	3.22227	−	1.55176i	0.125809	−	0.0605862i
$657$	75.4321	−	23.2677i	2.94289	−	0.907761i
$658$	0.465029	+	1.18487i	0.0181287	+	0.0461912i
$659$	14.8256	+	13.7562i	0.577525	+	0.535865i	0.913940	−	0.405849i	$-0.133024\pi$
$659$	14.8256	+	13.7562i	0.577525	+	0.535865i	−0.336415	+	0.941714i	$0.609215\pi$
$660$	8.90230	−	6.06948i	0.346521	−	0.236254i
$661$	−1.27623	−	1.60034i	−0.0496395	−	0.0622460i	0.756392	−	0.654119i	$-0.226960\pi$
$661$	−1.27623	−	1.60034i	−0.0496395	−	0.0622460i	−0.806032	+	0.591873i	$0.798389\pi$
$662$	−3.31712	+	0.499975i	−0.128924	+	0.0194321i
$663$	−12.1589	−	3.75054i	−0.472214	−	0.145659i
$664$	0.0885821	+	1.18205i	0.00343765	+	0.0458723i
$665$	−0.0923369	−	0.0629542i	−0.00358067	−	0.00244126i
$666$	1.76100	+	7.71546i	0.0682375	+	0.298968i
$667$	−3.34843	−	14.6704i	−0.129652	−	0.568041i
$668$	−14.0435	−	9.57469i	−0.543359	−	0.370456i
$669$	−2.46823	−	32.9363i	−0.0954274	−	1.27339i
$670$	1.39759	+	0.431099i	0.0539936	+	0.0166548i
$671$	10.8986	−	1.64270i	0.420735	−	0.0634156i
$672$	−0.306148	−	0.383898i	−0.0118099	−	0.0148092i
$673$	9.31468	−	6.35064i	0.359055	−	0.244799i	−0.370334	−	0.928899i	$-0.620757\pi$
$673$	9.31468	−	6.35064i	0.359055	−	0.244799i	0.729389	+	0.684099i	$0.239804\pi$
$674$	8.17441	+	7.58474i	0.314866	+	0.292153i
$675$	−1.96425	−	5.00483i	−0.0756041	−	0.192636i
$676$	−1.16866	+	0.360483i	−0.0449484	+	0.0138647i
$677$	29.2744	−	14.0978i	1.12510	−	0.541822i	0.223639	−	0.974672i	$-0.428206\pi$
$677$	29.2744	−	14.0978i	1.12510	−	0.541822i	0.901466	+	0.432850i	$0.142492\pi$
$678$	21.1458	−	53.8785i	0.812098	−	2.06919i
$679$	0.243318	−	3.24685i	0.00933768	−	0.124603i
$680$	−0.821893	+	1.03062i	−0.0315182	+	0.0395225i
$681$	−2.82737	+	4.89715i	−0.108345	+	0.187659i
$682$	−3.31705	−	5.74530i	−0.127016	−	0.219999i
$683$	−5.00425	−	0.754269i	−0.191482	−	0.0288613i	0.0526009	−	0.998616i	$-0.483249\pi$
$683$	−5.00425	−	0.754269i	−0.191482	−	0.0288613i	−0.244083	+	0.969754i	$0.578487\pi$
$684$	2.83282	+	1.36421i	0.108315	+	0.0521620i
$685$	10.7994	−	10.0204i	0.412625	−	0.382860i
$686$	0.542658	−	2.37754i	0.0207188	−	0.0907749i
$687$	45.9676			1.75377
$688$	−3.34911	+	5.63768i	−0.127684	+	0.214935i
$689$	24.4944			0.933163
$690$	1.98020	−	8.67583i	0.0753850	−	0.330283i
$691$	−3.36689	+	3.12402i	−0.128083	+	0.118843i	−0.741614	−	0.670827i	$-0.765939\pi$
$691$	−3.36689	+	3.12402i	−0.128083	+	0.118843i	0.613531	+	0.789671i	$0.289749\pi$
$692$	3.70104	+	1.78233i	0.140693	+	0.0677540i
$693$	3.24770	+	0.489512i	0.123370	+	0.0185950i
$694$	−0.567212	−	0.982440i	−0.0215311	−	0.0372929i
$695$	2.86799	−	4.96751i	0.108789	−	0.188428i
$696$	−8.34101	+	10.4593i	−0.316165	+	0.396459i
$697$	0.352317	−	4.70134i	0.0133450	−	0.178076i
$698$	−8.82583	+	22.4879i	−0.334063	+	0.851178i
$699$	34.8266	−	16.7716i	1.31726	−	0.634361i
$700$	0.166816	−	0.0514559i	0.00630505	−	0.00194485i
$701$	13.6265	+	34.7198i	0.514666	+	1.31135i	0.918104	+	0.396340i	$0.129720\pi$
$701$	13.6265	+	34.7198i	0.514666	+	1.31135i	−0.403438	+	0.915007i	$0.632185\pi$
$702$	−13.5254	−	12.5498i	−0.510484	−	0.473660i
$703$	0.852273	−	0.581070i	0.0321441	−	0.0219155i
$704$	−2.38834	−	2.99489i	−0.0900141	−	0.112874i
$705$	20.2796	−	3.05666i	0.763773	−	0.115120i
$706$	10.6928	+	3.29828i	0.402428	+	0.124133i
$707$	0.0480074	+	0.640615i	0.00180551	+	0.0240928i
$708$	−20.4232	−	13.9243i	−0.767550	−	0.523307i
$709$	7.07887	+	31.0146i	0.265853	+	1.16478i	0.914789	+	0.403933i	$0.132357\pi$
$709$	7.07887	+	31.0146i	0.265853	+	1.16478i	−0.648936	+	0.760843i	$0.724786\pi$
$710$	−0.0902487	−	0.395405i	−0.00338697	−	0.0148393i
$711$	54.1614	+	36.9266i	2.03121	+	1.38486i
$712$	−1.11934	−	14.9365i	−0.0419489	−	0.559769i
$713$	−5.23586	−	1.61505i	−0.196084	−	0.0604840i
$714$	−0.640045	+	0.0964712i	−0.0239531	+	0.00361034i
$715$	8.19624	+	10.2778i	0.306522	+	0.384366i
$716$	−16.0810	+	10.9638i	−0.600976	+	0.409738i
$717$	−5.12519	−	4.75548i	−0.191404	−	0.177597i
$718$	−9.01542	−	22.9709i	−0.336452	−	0.857267i
$719$	32.1297	−	9.91068i	1.19823	−	0.369606i	0.369490	−	0.929235i	$-0.379532\pi$
$719$	32.1297	−	9.91068i	1.19823	−	0.369606i	0.828744	+	0.559628i	$0.189056\pi$
$720$	−4.42509	+	2.13101i	−0.164913	+	0.0794181i
$721$	0.799023	−	2.03588i	0.0297572	−	0.0758200i
$722$	−1.38925	+	18.5382i	−0.0517024	+	0.689920i
$723$	27.2669	−	34.1916i	1.01407	−	1.27160i
$724$	−9.84432	+	17.0509i	−0.365861	+	0.633691i
$725$	−2.37810	−	4.11899i	−0.0883205	−	0.152976i
$726$	10.2173	+	1.54001i	0.379201	+	0.0571553i
$727$	−41.8872	−	20.1718i	−1.55351	−	0.748131i	−0.556914	−	0.830570i	$-0.688015\pi$
$727$	−41.8872	−	20.1718i	−1.55351	−	0.748131i	−0.996596	+	0.0824393i	$0.973729\pi$
$728$	0.439163	−	0.407484i	0.0162765	−	0.0151024i
$729$	9.67105	−	42.3716i	0.358187	−	1.56932i
$730$	16.0724			0.594866
$731$	4.22859	+	7.53920i	0.156400	+	0.278848i
$732$	−8.09300			−0.299126
$733$	2.46601	−	10.8043i	0.0910841	−	0.399065i	−0.908749	−	0.417343i	$-0.862961\pi$
$733$	2.46601	−	10.8043i	0.0910841	−	0.399065i	0.999833	+	0.0182780i	$0.00581838\pi$
$734$	21.0412	−	19.5234i	0.776644	−	0.720621i
$735$	−17.6621	−	8.50561i	−0.651476	−	0.313734i
$736$	−3.12847	−	0.471541i	−0.115317	−	0.0173812i
$737$	2.80126	+	4.85192i	0.103186	+	0.178723i
$738$	8.78283	−	15.2123i	0.323301	−	0.559973i
$739$	−10.7532	+	13.4841i	−0.395563	+	0.496020i	−0.939234	−	0.343279i	$-0.888462\pi$
$739$	−10.7532	+	13.4841i	−0.395563	+	0.496020i	0.543671	+	0.839298i	$0.317034\pi$
$740$	−0.120413	+	1.60680i	−0.00442646	+	0.0590670i
$741$	−2.25757	+	5.75219i	−0.0829338	+	0.211312i
$742$	1.12262	−	0.540625i	0.0412127	−	0.0198470i
$743$	−10.9788	+	3.38651i	−0.402773	+	0.124239i	−0.489521	−	0.871991i	$-0.662829\pi$
$743$	−10.9788	+	3.38651i	−0.402773	+	0.124239i	0.0867486	+	0.996230i	$0.472352\pi$
$744$	1.77968	+	4.53455i	0.0652462	+	0.166245i
$745$	−5.96815	−	5.53763i	−0.218656	−	0.202883i
$746$	−27.5190	+	18.7621i	−1.00754	+	0.686931i
$747$	3.62988	+	4.55172i	0.132810	+	0.166539i
$748$	−4.99316	+	0.752598i	−0.182568	+	0.0275177i
$749$	0.293997	+	0.0906861i	0.0107424	+	0.00331360i
$750$	−0.210196	−	2.80487i	−0.00767527	−	0.102419i
$751$	−16.7396	−	11.4129i	−0.610837	−	0.416462i	0.218002	−	0.975948i	$-0.430046\pi$
$751$	−16.7396	−	11.4129i	−0.610837	−	0.416462i	−0.828839	+	0.559486i	$0.810998\pi$
$752$	−1.62248	−	7.10854i	−0.0591657	−	0.259222i
$753$	9.29061	+	40.7048i	0.338569	+	1.48337i
$754$	−13.4860	−	9.19460i	−0.491131	−	0.334848i
$755$	−0.793593	−	10.5898i	−0.0288818	−	0.385401i
$756$	−0.896883	−	0.276652i	−0.0326193	−	0.0100617i
$757$	20.0441	−	3.02116i	0.728515	−	0.109806i	0.225696	−	0.974198i	$-0.427534\pi$
$757$	20.0441	−	3.02116i	0.728515	−	0.109806i	0.502819	+	0.864392i	$0.332296\pi$
$758$	−8.49899	−	10.6574i	−0.308697	−	0.387094i
$759$	28.1651	−	19.2027i	1.02233	−	0.697012i
$760$	0.469279	+	0.435427i	0.0170225	+	0.0157946i
$761$	−16.1144	−	41.0587i	−0.584145	−	1.48838i	−0.851277	−	0.524717i	$-0.824171\pi$
$761$	−16.1144	−	41.0587i	−0.584145	−	1.48838i	0.267132	−	0.963660i	$-0.413924\pi$
$762$	39.1053	−	12.0624i	1.41663	−	0.436974i
$763$	−2.32602	+	1.12015i	−0.0842075	+	0.0405522i
$764$	−1.45525	+	3.70792i	−0.0526492	+	0.134148i
$765$	−0.483831	+	6.45628i	−0.0174930	+	0.233427i
$766$	17.0849	−	21.4238i	0.617304	−	0.774075i
$767$	15.0791	−	26.1178i	0.544476	−	0.943060i
$768$	1.40637	+	2.43590i	0.0507479	+	0.0878980i
$769$	1.11050	+	0.167381i	0.0400457	+	0.00603591i	0.169035	−	0.985610i	$-0.445935\pi$
$769$	1.11050	+	0.167381i	0.0400457	+	0.00603591i	−0.128989	+	0.991646i	$0.541173\pi$
$770$	0.602492	+	0.290145i	0.0217123	+	0.0104561i
$771$	−62.9854	+	58.4419i	−2.26836	+	2.10473i
$772$	1.79257	−	7.85374i	0.0645159	−	0.282662i
$773$	0.203153			0.00730691			0.00365346	−	0.999993i	$-0.498837\pi$
$773$	0.203153			0.00730691			0.00365346	+	0.999993i	$0.498837\pi$
$774$	2.00708	+	32.1441i	0.0721429	+	1.15540i
$775$	−1.73187			−0.0622105
$776$	−4.15026	+	18.1835i	−0.148986	+	0.652750i
$777$	−0.579981	+	0.538144i	−0.0208067	+	0.0193058i
$778$	−11.9633	−	5.76124i	−0.428907	−	0.206551i
$779$	−2.26397	−	0.341238i	−0.0811151	−	0.0122261i
$780$	−4.82632	−	8.35944i	−0.172810	−	0.299316i
$781$	0.776797	−	1.34545i	0.0277960	−	0.0481441i
$782$	−2.60031	+	3.26068i	−0.0929868	+	0.116602i
$783$	−1.91097	+	25.5002i	−0.0682926	+	0.911302i
$784$	−2.54625	+	6.48775i	−0.0909376	+	0.231705i
$785$	17.9561	−	8.64719i	0.640880	−	0.308631i
$786$	46.8530	−	14.4522i	1.67119	−	0.515494i
$787$	14.8293	+	37.7843i	0.528606	+	1.34687i	0.906965	+	0.421207i	$0.138393\pi$
$787$	14.8293	+	37.7843i	0.528606	+	1.34687i	−0.378359	+	0.925659i	$0.623511\pi$
$788$	−8.93364	−	8.28920i	−0.318248	−	0.295291i
$789$	−39.5249	+	26.9476i	−1.40712	+	0.959361i
$790$	8.32149	+	10.4348i	0.296065	+	0.371254i
$791$	3.55215	−	0.535401i	0.126300	−	0.0190367i
$792$	−17.9781	−	5.54551i	−0.638824	−	0.197051i
$793$	−0.737893	−	9.84650i	−0.0262034	−	0.349659i
$794$	13.4070	+	9.14071i	0.475795	+	0.324392i
$795$	−4.46734	−	19.5727i	−0.158440	−	0.694173i
$796$	2.14034	+	9.37744i	0.0758623	+	0.332375i
$797$	−15.7052	−	10.7076i	−0.556307	−	0.379284i	0.252285	−	0.967653i	$-0.418818\pi$
$797$	−15.7052	−	10.7076i	−0.556307	−	0.379284i	−0.808592	+	0.588369i	$0.799770\pi$
$798$	0.0234906	+	0.313460i	0.000831558	+	0.0110964i
$799$	−9.18455	−	2.83306i	−0.324926	−	0.100226i
$800$	−0.988831	+	0.149042i	−0.0349604	+	0.00526944i
$801$	−45.8677	−	57.5163i	−1.62066	−	2.03224i
$802$	−22.7764	+	15.5287i	−0.804263	+	0.548338i
$803$	45.1318	+	41.8762i	1.59267	+	1.47778i
$804$	−1.50294	−	3.82944i	−0.0530048	−	0.135054i
$805$	0.527773	−	0.162796i	0.0186015	−	0.00573782i
$806$	−5.35478	+	2.57873i	−0.188614	+	0.0908318i
$807$	−15.4440	+	39.3507i	−0.543655	+	1.38521i
$808$	0.275001	−	3.66964i	0.00967452	−	0.129097i
$809$	−2.61624	+	3.28066i	−0.0919822	+	0.115342i	−0.825693	−	0.564120i	$-0.809215\pi$
$809$	−2.61624	+	3.28066i	−0.0919822	+	0.115342i	0.733710	+	0.679462i	$0.237787\pi$
$810$	−0.194099	+	0.336189i	−0.00681993	+	0.0118125i
$811$	−3.91266	−	6.77692i	−0.137392	−	0.237970i	0.789117	−	0.614243i	$-0.210539\pi$
$811$	−3.91266	−	6.77692i	−0.137392	−	0.237970i	−0.926509	+	0.376273i	$0.877205\pi$
$812$	−0.821024	−	0.123749i	−0.0288123	−	0.00434276i
$813$	−54.3000	−	26.1495i	−1.90439	−	0.917104i
$814$	−4.52459	+	4.19821i	−0.158587	+	0.147147i
$815$	−2.55271	+	11.1841i	−0.0894174	+	0.391763i
$816$	3.70779			0.129798
$817$	3.80453	−	1.77420i	0.133104	−	0.0620714i
$818$	6.51935			0.227944
$819$	0.654748	−	2.86864i	0.0228788	−	0.100238i
$820$	2.62172	−	2.43260i	0.0915546	−	0.0849502i
$821$	12.8711	+	6.19837i	0.449203	+	0.216325i	0.644787	−	0.764362i	$-0.276946\pi$
$821$	12.8711	+	6.19837i	0.449203	+	0.216325i	−0.195584	+	0.980687i	$0.562660\pi$
$822$	−40.9748	−	6.17596i	−1.42916	−	0.215411i
$823$	17.6417	+	30.5563i	0.614951	+	1.06513i	0.990393	+	0.138280i	$0.0441574\pi$
$823$	17.6417	+	30.5563i	0.614951	+	1.06513i	−0.375442	+	0.926846i	$0.622509\pi$
$824$	−6.26408	+	10.8497i	−0.218220	+	0.377967i
$825$	6.71778	−	8.42383i	0.233883	−	0.293280i
$826$	0.114646	−	1.52984i	0.00398903	−	0.0532300i
$827$	−14.5773	+	37.1423i	−0.506901	+	1.29156i	0.416991	+	0.908911i	$0.363085\pi$
$827$	−14.5773	+	37.1423i	−0.506901	+	1.29156i	−0.923892	+	0.382653i	$0.875011\pi$
$828$	−14.0001	+	6.74210i	−0.486538	+	0.234304i
$829$	−24.4036	+	7.52752i	−0.847573	+	0.261441i	−0.687969	−	0.725740i	$-0.741498\pi$
$829$	−24.4036	+	7.52752i	−0.847573	+	0.261441i	−0.159603	+	0.987181i	$0.551021\pi$
$830$	0.433061	+	1.10342i	0.0150318	+	0.0383003i
$831$	43.3728	+	40.2440i	1.50458	+	1.39605i
$832$	−2.83546	+	1.93318i	−0.0983018	+	0.0670210i
$833$	5.72820	+	7.18294i	0.198470	+	0.248874i
$834$	−15.9536	+	2.40462i	−0.552429	+	0.0832652i
$835$	−16.2418	−	5.00992i	−0.562069	−	0.173375i
$836$	0.183256	+	2.44539i	0.00633806	+	0.0845755i
$837$	7.69341	+	5.24528i	0.265923	+	0.181303i
$838$	2.74792	+	12.0394i	0.0949252	+	0.415895i
$839$	−3.05468	−	13.3834i	−0.105459	−	0.462047i	−0.999890	−	0.0148402i	$-0.995276\pi$
$839$	−3.05468	−	13.3834i	−0.105459	−	0.462047i	0.894431	−	0.447206i	$-0.147581\pi$
$840$	−0.405703	−	0.276603i	−0.0139981	−	0.00954373i
$841$	−0.476668	−	6.36070i	−0.0164368	−	0.219334i
$842$	20.6168	+	6.35945i	0.710503	+	0.219161i
$843$	−0.858369	+	0.129378i	−0.0295638	+	0.00445603i
$844$	10.3850	+	13.0224i	0.357468	+	0.448250i
$845$	−1.01048	+	0.688936i	−0.0347617	+	0.0237001i
$846$	−26.2516	−	24.3579i	−0.902547	−	0.837442i
$847$	0.234293	+	0.596968i	0.00805039	+	0.0205120i
$848$	−6.82046	+	2.10383i	−0.234215	+	0.0722459i
$849$	53.8389	−	25.9274i	1.84775	−	0.889827i
$850$	−0.481598	+	1.22709i	−0.0165187	+	0.0420889i
$851$	−0.380962	+	5.08359i	−0.0130592	+	0.174263i
$852$	−0.711260	+	0.891892i	−0.0243674	+	0.0305557i
$853$	−7.86411	+	13.6210i	−0.269262	+	0.466375i	−0.968671	−	0.248346i	$-0.920113\pi$
$853$	−7.86411	+	13.6210i	−0.269262	+	0.466375i	0.699410	+	0.714721i	$0.253446\pi$
$854$	−0.251145	−	0.434995i	−0.00859399	−	0.0148852i
$855$	3.10907	+	0.468617i	0.106328	+	0.0160264i
$856$	−1.58787	−	0.764679i	−0.0542724	−	0.0261362i
$857$	−6.71808	+	6.23347i	−0.229485	+	0.212931i	−0.786531	−	0.617550i	$-0.788125\pi$
$857$	−6.71808	+	6.23347i	−0.229485	+	0.212931i	0.557046	+	0.830482i	$0.311935\pi$
$858$	8.22782	−	36.0484i	0.280893	−	1.23067i
$859$	−40.3228			−1.37580			−0.687899	−	0.725807i	$-0.741467\pi$
$859$	−40.3228			−1.37580			−0.687899	+	0.725807i	$0.741467\pi$
$860$	−1.53859	+	6.37438i	−0.0524654	+	0.217365i
$861$	1.75612			0.0598485
$862$	−6.10063	+	26.7286i	−0.207788	+	0.910379i
$863$	3.69595	−	3.42934i	0.125811	−	0.116736i	−0.614758	−	0.788716i	$-0.710746\pi$
$863$	3.69595	−	3.42934i	0.125811	−	0.116736i	0.740569	+	0.671980i	$0.234556\pi$
$864$	4.84405	+	2.33277i	0.164798	+	0.0793625i
$865$	4.06197	+	0.612243i	0.138111	+	0.0208169i
$866$	13.9936	+	24.2376i	0.475522	+	0.823628i
$867$	−21.4644	+	37.1775i	−0.728970	+	1.26261i
$868$	−0.188503	+	0.236375i	−0.00639819	+	0.00802308i
$869$	−3.82063	+	50.9828i	−0.129606	+	1.72947i
$870$	−4.88751	+	12.4532i	−0.165702	+	0.422202i
$871$	4.52213	−	2.17774i	0.153226	−	0.0737900i
$872$	14.1317	−	4.35904i	0.478559	−	0.147616i
$873$	33.4669	+	85.2723i	1.13268	+	2.88603i
$874$	1.48471	+	1.37761i	0.0502209	+	0.0465982i
$875$	0.144238	−	0.0983397i	0.00487613	−	0.00332449i
$876$	−28.1863	−	35.3445i	−0.952328	−	1.19418i
$877$	22.6189	−	3.40926i	0.763787	−	0.115122i	0.244415	−	0.969671i	$-0.421404\pi$
$877$	22.6189	−	3.40926i	0.763787	−	0.115122i	0.519372	+	0.854548i	$0.326166\pi$
$878$	6.47892	+	1.99848i	0.218653	+	0.0674455i
$879$	−3.91102	−	52.1890i	−0.131916	−	1.76029i
$880$	−3.16500	−	2.15786i	−0.106692	−	0.0727414i
$881$	−2.38020	−	10.4283i	−0.0801909	−	0.351339i	0.918875	−	0.394548i	$-0.129099\pi$
$881$	−2.38020	−	10.4283i	−0.0801909	−	0.351339i	−0.999066	+	0.0432091i	$0.986242\pi$
$882$	7.61704	+	33.3724i	0.256479	+	1.12371i
$883$	32.7363	+	22.3192i	1.10166	+	0.751101i	0.970702	−	0.240287i	$-0.0772414\pi$
$883$	32.7363	+	22.3192i	1.10166	+	0.751101i	0.130961	+	0.991388i	$0.458194\pi$
$884$	0.338064	+	4.51115i	0.0113703	+	0.151726i
$885$	−23.6201	−	7.28583i	−0.793980	−	0.244910i
$886$	−8.08710	+	1.21893i	−0.271691	+	0.0409509i
$887$	−26.4133	−	33.1213i	−0.886872	−	1.11210i	−0.993043	−	0.117755i	$-0.962430\pi$
$887$	−26.4133	−	33.1213i	−0.886872	−	1.11210i	0.106170	−	0.994348i	$-0.466141\pi$
$888$	3.74465	−	2.55306i	0.125662	−	0.0856751i
$889$	1.86188	+	1.72757i	0.0624453	+	0.0579408i
$890$	−5.47222	−	13.9430i	−0.183429	−	0.467370i
$891$	−1.42097	+	0.438310i	−0.0476042	+	0.0146839i
$892$	−10.5797	+	5.09489i	−0.354233	+	0.170590i
$893$	−1.70531	+	4.34505i	−0.0570659	+	0.145402i
$894$	−1.71131	+	22.8359i	−0.0572349	+	0.763746i
$895$	−12.1349	+	15.2167i	−0.405626	+	0.508639i
$896$	−0.0872858	+	0.151183i	−0.00291601	+	0.00505068i
$897$	−15.2695	−	26.4476i	−0.509835	−	0.883060i
$898$	25.2431	+	3.80478i	0.842372	+	0.126967i
$899$	7.42138	+	3.57395i	0.247517	+	0.119198i
$900$	−3.60037	+	3.34065i	−0.120012	+	0.111355i
$901$	−2.09366	+	9.17293i	−0.0697500	+	0.305595i
$902$	13.7000			0.456159
$903$	−2.68273	+	1.78057i	−0.0892757	+	0.0592538i
$904$	−20.5777			−0.684403
$905$	−4.38114	+	19.1950i	−0.145634	+	0.638064i
$906$	−21.8961	+	20.3166i	−0.727448	+	0.674973i
$907$	−47.2084	−	22.7343i	−1.56753	−	0.754882i	−0.569770	−	0.821805i	$-0.692968\pi$
$907$	−47.2084	−	22.7343i	−1.56753	−	0.754882i	−0.997758	+	0.0669230i	$0.978682\pi$
$908$	1.98795	+	0.299635i	0.0659724	+	0.00994375i
$909$	−9.03695	−	15.6525i	−0.299737	−	0.519159i
$910$	0.299544	−	0.518826i	0.00992980	−	0.0171989i
$911$	20.1443	−	25.2602i	0.667411	−	0.836907i	−0.326716	−	0.945122i	$-0.605942\pi$
$911$	20.1443	−	25.2602i	0.667411	−	0.836907i	0.994127	+	0.108215i	$0.0345136\pi$
$912$	0.134561	−	1.79560i	0.00445577	−	0.0594582i
$913$	−1.65889	+	4.22677i	−0.0549011	+	0.139886i
$914$	15.6265	−	7.52533i	0.516879	−	0.248916i
$915$	−7.73345	+	2.38545i	−0.255660	+	0.0788606i
$916$	−5.97065	−	15.2130i	−0.197276	−	0.502651i
$917$	2.23076	+	2.06984i	0.0736662	+	0.0683522i
$918$	5.85585	−	3.99245i	0.193272	−	0.131771i
$919$	−21.3927	−	26.8256i	−0.705680	−	0.884894i	0.291754	−	0.956493i	$-0.405761\pi$
$919$	−21.3927	−	26.8256i	−0.705680	−	0.884894i	−0.997433	+	0.0715993i	$0.977190\pi$
$920$	−3.12847	+	0.471541i	−0.103143	+	0.0155462i
$921$	−3.41177	−	1.05239i	−0.112422	−	0.0346775i
$922$	−0.310458	−	4.14277i	−0.0102244	−	0.136435i
$923$	−1.14999	−	0.784048i	−0.0378523	−	0.0258073i
$924$	−0.418544	−	1.83376i	−0.0137691	−	0.0603263i
$925$	0.358548	+	1.57090i	0.0117890	+	0.0516510i
$926$	−27.8586	−	18.9937i	−0.915490	−	0.624170i
$927$	4.59828	+	61.3597i	0.151027	+	2.01532i
$928$	4.54490	+	1.40192i	0.149194	+	0.0460201i
$929$	−7.59662	+	1.14501i	−0.249237	+	0.0375664i	−0.272472	−	0.962164i	$-0.587841\pi$
$929$	−7.59662	+	1.14501i	−0.249237	+	0.0375664i	0.0232354	+	0.999730i	$0.492603\pi$
$930$	3.03719	+	3.80852i	0.0995935	+	0.124886i
$931$	3.68642	−	2.51336i	0.120818	−	0.0823720i
$932$	−10.0741	−	9.34742i	−0.329989	−	0.306185i
$933$	−12.7975	−	32.6075i	−0.418971	−	1.06752i
$934$	36.7595	−	11.3388i	1.20281	−	0.371017i
$935$	−4.54950	+	2.19092i	−0.148784	+	0.0716508i
$936$	−6.15784	+	15.6899i	−0.201275	+	0.512841i
$937$	−2.16911	+	28.9448i	−0.0708618	+	0.945585i	0.842568	+	0.538589i	$0.181043\pi$
$937$	−2.16911	+	28.9448i	−0.0708618	+	0.945585i	−0.913430	+	0.406996i	$0.866576\pi$
$938$	0.159191	−	0.199619i	0.00519777	−	0.00651780i
$939$	−41.7061	+	72.2371i	−1.36103	+	2.35737i
$940$	−3.64568	−	6.31450i	−0.118909	−	0.205956i
$941$	18.0301	+	2.71760i	0.587765	+	0.0885913i	0.436190	−	0.899854i	$-0.356327\pi$
$941$	18.0301	+	2.71760i	0.587765	+	0.0885913i	0.151575	+	0.988446i	$0.451566\pi$
$942$	−50.5057	−	24.3223i	−1.64556	−	0.792462i
$943$	8.29462	−	7.69628i	0.270110	−	0.250626i
$944$	−1.95551	+	8.56764i	−0.0636464	+	0.278853i
$945$	−0.938582			−0.0305321
$946$	−20.9287	+	13.8907i	−0.680451	+	0.451627i
$947$	−51.9842			−1.68926			−0.844630	−	0.535350i	$-0.820180\pi$
$947$	−51.9842			−1.68926			−0.844630	+	0.535350i	$0.820180\pi$
$948$	8.35356	−	36.5993i	0.271311	−	1.18869i
$949$	40.4327	−	37.5160i	1.31250	−	1.21782i
$950$	0.576774	+	0.277760i	0.0187130	+	0.00901172i
$951$	14.1038	+	2.12580i	0.457347	+	0.0689339i
$952$	0.115061	+	0.199292i	0.00372916	+	0.00645909i
$953$	9.29498	−	16.0994i	0.301094	−	0.521510i	−0.675290	−	0.737552i	$-0.735982\pi$
$953$	9.29498	−	16.0994i	0.301094	−	0.521510i	0.976384	+	0.216042i	$0.0693149\pi$
$954$	−21.8570	+	27.4079i	−0.707648	+	0.887362i
$955$	−0.297670	+	3.97213i	−0.00963238	+	0.128535i
$956$	−0.908123	+	2.31386i	−0.0293708	+	0.0748355i
$957$	−46.1707	+	22.2346i	−1.49249	+	0.718744i
$958$	−13.1719	+	4.06301i	−0.425566	+	0.131270i
$959$	−0.939589	−	2.39403i	−0.0303409	−	0.0773074i
$960$	2.06188	+	1.91315i	0.0665469	+	0.0617465i
$961$	−23.1352	+	15.7733i	−0.746297	+	0.508817i
$962$	3.44765	+	4.32322i	0.111157	+	0.139386i
$963$	−8.55934	+	1.29011i	−0.275821	+	0.0415733i
$964$	−14.8574	−	4.58289i	−0.478523	−	0.147605i
$965$	−0.602005	−	8.03319i	−0.0193792	−	0.258598i
$966$	−1.28356	−	0.875119i	−0.0412980	−	0.0281565i
$967$	−3.10848	−	13.6191i	−0.0999619	−	0.437962i	−0.999998	−	0.00214569i	$-0.999317\pi$
$967$	−3.10848	−	13.6191i	−0.0999619	−	0.437962i	0.900036	−	0.435816i	$-0.143540\pi$
$968$	−0.817443	−	3.58145i	−0.0262736	−	0.115112i
$969$	−1.96118	−	1.33711i	−0.0630020	−	0.0429541i
$970$	1.39380	+	18.5990i	0.0447522	+	0.597177i
$971$	−23.1830	−	7.15101i	−0.743978	−	0.229487i	−0.100485	−	0.994939i	$-0.532039\pi$
$971$	−23.1830	−	7.15101i	−0.743978	−	0.229487i	−0.643493	+	0.765452i	$0.722516\pi$
$972$	−14.8696	+	2.24123i	−0.476943	+	0.0718876i
$973$	−0.624326	−	0.782880i	−0.0200150	−	0.0250980i
$974$	1.12678	−	0.768226i	0.0361044	−	0.0246156i
$975$	−7.07589	−	6.56547i	−0.226610	−	0.210263i
$976$	1.05118	+	2.67837i	0.0336476	+	0.0857327i
$977$	48.9874	−	15.1106i	1.56725	−	0.483432i	0.614940	−	0.788574i	$-0.289180\pi$
$977$	48.9874	−	15.1106i	1.56725	−	0.483432i	0.952307	+	0.305142i	$0.0987041\pi$
$978$	29.0716	−	14.0001i	0.929607	−	0.447675i
$979$	20.9619	−	53.4101i	0.669946	−	1.70700i
$980$	−0.520833	+	6.95004i	−0.0166374	+	0.222011i
$981$	45.2868	−	56.7878i	1.44590	−	1.81310i
$982$	12.8208	−	22.2063i	0.409128	−	0.708631i
$983$	24.7080	+	42.7956i	0.788064	+	1.36497i	0.927151	+	0.374687i	$0.122250\pi$
$983$	24.7080	+	42.7956i	0.788064	+	1.36497i	−0.139087	+	0.990280i	$0.544417\pi$
$984$	−9.94725	−	1.49931i	−0.317107	−	0.0477962i
$985$	−10.9800	−	5.28770i	−0.349853	−	0.168480i
$986$	4.59601	−	4.26447i	0.146367	−	0.135809i
$987$	0.796675	−	3.49046i	0.0253585	−	0.111103i
$988$	2.19692			0.0698932
$989$	−4.86779	+	20.1673i	−0.154787	+	0.641283i
$990$	−18.8140			−0.597947
$991$	1.80987	−	7.92955i	0.0574923	−	0.251890i	−0.938012	−	0.346602i	$-0.887336\pi$
$991$	1.80987	−	7.92955i	0.0574923	−	0.251890i	0.995505	+	0.0947111i	$0.0301927\pi$
$992$	1.26955	−	1.17797i	0.0403082	−	0.0374005i
$993$	8.50115	+	4.09394i	0.269776	+	0.129917i
$994$	−0.0700109	−	0.0105524i	−0.00222061	−	0.000334703i
$995$	4.80930	+	8.32995i	0.152465	+	0.264077i
$996$	1.66705	−	2.88742i	0.0528226	−	0.0914914i
$997$	12.2314	−	15.3377i	0.387374	−	0.485751i	−0.549463	−	0.835518i	$-0.685168\pi$
$997$	12.2314	−	15.3377i	0.387374	−	0.485751i	0.936837	+	0.349767i	$0.113739\pi$
$998$	1.55848	−	20.7965i	0.0493329	−	0.658301i
$999$	3.16500	−	8.06429i	0.100136	−	0.255143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.a.271.3	✓	36
43.10	even	21	inner	430.2.q.a.311.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.a.271.3	✓	36	1.1	even	1	trivial
430.2.q.a.311.3	yes	36	43.10	even	21	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.222521 + 0.974928i) q^{2} +(2.06188 - 1.91315i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.988831 - 0.149042i) q^{5} +(1.40637 + 2.43590i) q^{6} +(-0.0872858 + 0.151183i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.367035 - 4.89775i) q^{9} +O(q^{10})\)	\(q+(-0.222521 + 0.974928i) q^{2} +(2.06188 - 1.91315i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.988831 - 0.149042i) q^{5} +(1.40637 + 2.43590i) q^{6} +(-0.0872858 + 0.151183i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.367035 - 4.89775i) q^{9} +(0.365341 - 0.930874i) q^{10} +(3.45126 - 1.66204i) q^{11} +(-2.68777 + 0.829068i) q^{12} +(-1.25376 - 3.19454i) q^{13} +(-0.127970 - 0.118739i) q^{14} +(-2.32399 + 1.58447i) q^{15} +(0.623490 + 0.781831i) q^{16} +(1.30349 - 0.196470i) q^{17} +(4.69328 + 1.44768i) q^{18} +(-0.0478401 - 0.638381i) q^{19} +(0.826239 + 0.563320i) q^{20} +(0.109263 + 0.478713i) q^{21} +(0.852390 + 3.73457i) q^{22} +(2.61406 + 1.78223i) q^{23} +(-0.210196 - 2.80487i) q^{24} +(0.955573 + 0.294755i) q^{25} +(3.39343 - 0.511478i) q^{26} +(-3.35219 - 4.20351i) q^{27} +(0.144238 - 0.0983397i) q^{28} +(-3.48654 - 3.23504i) q^{29} +(-1.02761 - 2.61830i) q^{30} +(-1.65492 + 0.510477i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(3.93636 - 10.0297i) q^{33} +(-0.0985102 + 1.31453i) q^{34} +(0.108844 - 0.136486i) q^{35} +(-2.45574 + 4.25347i) q^{36} +(0.805651 + 1.39543i) q^{37} +(0.633021 + 0.0954126i) q^{38} +(-8.69673 - 4.18813i) q^{39} +(-0.733052 + 0.680173i) q^{40} +(0.795835 - 3.48678i) q^{41} -0.491024 q^{42} +(2.31958 + 6.13348i) q^{43} -3.83061 q^{44} +(-1.09291 + 4.78834i) q^{45} +(-2.31923 + 2.15193i) q^{46} +(-6.56928 - 3.16360i) q^{47} +(2.78132 + 0.419216i) q^{48} +(3.48476 + 6.03579i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(2.31177 - 2.89886i) q^{51} +(-0.256456 + 3.42217i) q^{52} +(-2.60764 + 6.64416i) q^{53} +(4.84405 - 2.33277i) q^{54} +(-3.66042 + 1.12909i) q^{55} +(0.0637782 + 0.162504i) q^{56} +(-1.31996 - 1.22474i) q^{57} +(3.92976 - 2.67926i) q^{58} +(5.47921 + 6.87071i) q^{59} +(2.78132 - 0.419216i) q^{60} +(2.74944 + 0.848090i) q^{61} +(-0.129423 - 1.72702i) q^{62} +(0.708421 + 0.482993i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(0.763639 + 3.34572i) q^{65} +(8.90230 + 6.06948i) q^{66} +(0.109298 + 1.45848i) q^{67} +(-1.25965 - 0.388550i) q^{68} +(8.79955 - 1.32632i) q^{69} +(0.108844 + 0.136486i) q^{70} +(0.335101 - 0.228468i) q^{71} +(-3.60037 - 3.34065i) q^{72} +(5.87190 + 14.9614i) q^{73} +(-1.53972 + 0.474940i) q^{74} +(2.53419 - 1.22040i) q^{75} +(-0.233881 + 0.595919i) q^{76} +(-0.0499732 + 0.666845i) q^{77} +(6.01833 - 7.54674i) q^{78} +(-6.67332 + 11.5585i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.383861 - 0.0578578i) q^{81} +(3.22227 + 1.55176i) q^{82} +(-0.868930 + 0.806249i) q^{83} +(0.109263 - 0.478713i) q^{84} -1.31821 q^{85} +(-6.49585 + 0.896593i) q^{86} -13.3779 q^{87} +(0.852390 - 3.73457i) q^{88} +(10.9799 - 10.1879i) q^{89} +(-4.42509 - 2.13101i) q^{90} +(0.592397 + 0.0892895i) q^{91} +(-1.58190 - 2.73994i) q^{92} +(-2.43564 + 4.21865i) q^{93} +(4.54608 - 5.70061i) q^{94} +(-0.0478401 + 0.638381i) q^{95} +(-1.02761 + 2.61830i) q^{96} +(-16.8041 + 8.09242i) q^{97} +(-6.65989 + 2.05430i) q^{98} +(-6.87351 - 17.5134i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Introduction

L-functions

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