LMFDB - Embedded newform 169.2.k.a.127.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(4,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("169.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.k (of order $78$, degree $24$, 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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			127.10
Character	$\chi$	$=$	169.127
Dual form			169.2.k.a.4.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.596805 - 0.0240504i) q^{2} +(0.703900 + 2.43014i) q^{3} +(-1.63792 + 0.132226i) q^{4} +(3.70001 - 1.40323i) q^{5} +(0.478537 + 1.43339i) q^{6} +(-0.324840 + 0.762428i) q^{7} +(-2.16021 + 0.262296i) q^{8} +(-2.87456 + 1.81776i) q^{9} +O(q^{10})$	\(q+(0.596805 - 0.0240504i) q^{2} +(0.703900 + 2.43014i) q^{3} +(-1.63792 + 0.132226i) q^{4} +(3.70001 - 1.40323i) q^{5} +(0.478537 + 1.43339i) q^{6} +(-0.324840 + 0.762428i) q^{7} +(-2.16021 + 0.262296i) q^{8} +(-2.87456 + 1.81776i) q^{9} +(2.17443 - 0.926440i) q^{10} +(-0.896359 + 1.41748i) q^{11} +(-1.47426 - 3.88730i) q^{12} +(-2.52376 - 2.57500i) q^{13} +(-0.175530 + 0.462833i) q^{14} +(6.01448 + 8.00382i) q^{15} +(1.96102 - 0.318697i) q^{16} +(6.43696 + 2.74253i) q^{17} +(-1.67183 + 1.15398i) q^{18} +(-6.17486 - 3.56505i) q^{19} +(-5.87476 + 2.78761i) q^{20} +(-2.08147 - 0.252736i) q^{21} +(-0.500860 + 0.867515i) q^{22} +(-1.23179 - 2.13353i) q^{23} +(-2.15799 - 5.06498i) q^{24} +(7.97846 - 7.06830i) q^{25} +(-1.56812 - 1.47608i) q^{26} +(-0.759544 - 0.672898i) q^{27} +(0.431248 - 1.29175i) q^{28} +(-0.333794 - 8.28302i) q^{29} +(3.78197 + 4.63207i) q^{30} +(0.422119 - 0.476474i) q^{31} +(5.42687 - 1.10790i) q^{32} +(-4.07562 - 1.18052i) q^{33} +(3.90757 + 1.48195i) q^{34} +(-0.132051 + 3.27682i) q^{35} +(4.46793 - 3.35743i) q^{36} +(-4.24111 - 0.865829i) q^{37} +(-3.77092 - 1.97913i) q^{38} +(4.48116 - 7.94564i) q^{39} +(-7.62472 + 4.00176i) q^{40} +(-3.37479 + 0.977520i) q^{41} +(-1.24831 - 0.100774i) q^{42} +(0.218974 + 1.07261i) q^{43} +(1.28073 - 2.44023i) q^{44} +(-8.08515 + 10.7594i) q^{45} +(-0.786451 - 1.24367i) q^{46} +(-1.62013 - 1.11829i) q^{47} +(2.15484 + 4.54123i) q^{48} +(4.37330 + 4.55308i) q^{49} +(4.59159 - 4.41028i) q^{50} +(-2.13377 + 17.5732i) q^{51} +(4.47419 + 3.88393i) q^{52} +(-0.146967 - 1.21038i) q^{53} +(-0.469483 - 0.383321i) q^{54} +(-1.32749 + 6.50248i) q^{55} +(0.501739 - 1.73221i) q^{56} +(4.31712 - 17.5152i) q^{57} +(-0.398420 - 4.93532i) q^{58} +(-1.82780 + 11.2469i) q^{59} +(-10.9095 - 12.3143i) q^{60} +(-1.57425 - 1.18297i) q^{61} +(0.240463 - 0.294514i) q^{62} +(-0.452139 - 2.78212i) q^{63} +(-0.645897 + 0.159199i) q^{64} +(-12.9512 - 5.98612i) q^{65} +(-2.46074 - 0.606519i) q^{66} +(-0.248094 + 3.07320i) q^{67} +(-10.9058 - 3.64091i) q^{68} +(4.31772 - 4.49522i) q^{69} +1.95880i q^{70} +(-2.34131 - 2.24886i) q^{71} +(5.73284 - 4.68072i) q^{72} +(4.05158 + 7.71964i) q^{73} +(-2.55194 - 0.414731i) q^{74} +(22.7930 + 14.4134i) q^{75} +(10.5853 + 5.02279i) q^{76} +(-0.789552 - 1.14386i) q^{77} +(2.48328 - 4.84977i) q^{78} +(-3.06556 + 4.44123i) q^{79} +(6.80859 - 3.93094i) q^{80} +(-3.27346 + 6.89866i) q^{81} +(-1.99058 + 0.664553i) q^{82} +(-1.84811 - 7.49807i) q^{83} +(3.44269 + 0.138736i) q^{84} +(27.6652 + 1.11487i) q^{85} +(0.156481 + 0.634870i) q^{86} +(19.8940 - 6.64159i) q^{87} +(1.56452 - 3.29715i) q^{88} +(-14.6210 + 8.44146i) q^{89} +(-4.56649 + 6.61570i) q^{90} +(2.78307 - 1.08772i) q^{91} +(2.29968 + 3.33166i) q^{92} +(1.45503 + 0.690420i) q^{93} +(-0.993795 - 0.628438i) q^{94} +(-27.8496 - 4.52600i) q^{95} +(6.51234 + 12.4082i) q^{96} +(-0.0230764 + 0.0188413i) q^{97} +(2.71951 + 2.61212i) q^{98} -5.70399i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9}+O(q^{10}) $ 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9} - 27 q^{10} - 26 q^{11} - 14 q^{12} - 34 q^{13} - 30 q^{14} - 84 q^{15} - 13 q^{16} - 31 q^{17} + 52 q^{18} - 33 q^{19} - 29 q^{20} - 26 q^{21} - 33 q^{22} + 57 q^{23} + 58 q^{24} + 2 q^{25} - 29 q^{26} - 30 q^{27} - 26 q^{28} - 19 q^{29} + 178 q^{30} - 78 q^{31} - 30 q^{32} - 26 q^{33} - 91 q^{34} - 18 q^{35} - 51 q^{36} - 41 q^{37} + 25 q^{38} + 12 q^{39} - 134 q^{40} - 17 q^{41} + 250 q^{42} - 28 q^{43} + 42 q^{45} + 18 q^{46} + 117 q^{47} - 57 q^{48} - 117 q^{49} - 20 q^{50} - 59 q^{51} + 37 q^{52} - 75 q^{53} + 118 q^{54} + 64 q^{55} - 42 q^{56} - 104 q^{57} - 87 q^{58} + 170 q^{59} + 78 q^{60} - 15 q^{61} + 19 q^{62} + 39 q^{63} + 32 q^{64} - 17 q^{65} + 73 q^{66} + 20 q^{67} - 76 q^{68} - 11 q^{69} + 46 q^{71} - 198 q^{72} - 26 q^{73} + 29 q^{74} - 70 q^{75} + 58 q^{76} + 6 q^{77} + 128 q^{78} - 54 q^{79} - 24 q^{80} - 7 q^{81} + 81 q^{82} + 234 q^{83} - 273 q^{84} - 74 q^{85} + 52 q^{86} - 112 q^{87} + 256 q^{88} - 27 q^{89} + 28 q^{90} - 78 q^{91} - 34 q^{92} + 51 q^{93} + 28 q^{94} - 11 q^{95} + 143 q^{96} + 40 q^{97} - 47 q^{98}+O(q^{100}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9 - 27 * q^10 - 26 * q^11 - 14 * q^12 - 34 * q^13 - 30 * q^14 - 84 * q^15 - 13 * q^16 - 31 * q^17 + 52 * q^18 - 33 * q^19 - 29 * q^20 - 26 * q^21 - 33 * q^22 + 57 * q^23 + 58 * q^24 + 2 * q^25 - 29 * q^26 - 30 * q^27 - 26 * q^28 - 19 * q^29 + 178 * q^30 - 78 * q^31 - 30 * q^32 - 26 * q^33 - 91 * q^34 - 18 * q^35 - 51 * q^36 - 41 * q^37 + 25 * q^38 + 12 * q^39 - 134 * q^40 - 17 * q^41 + 250 * q^42 - 28 * q^43 + 42 * q^45 + 18 * q^46 + 117 * q^47 - 57 * q^48 - 117 * q^49 - 20 * q^50 - 59 * q^51 + 37 * q^52 - 75 * q^53 + 118 * q^54 + 64 * q^55 - 42 * q^56 - 104 * q^57 - 87 * q^58 + 170 * q^59 + 78 * q^60 - 15 * q^61 + 19 * q^62 + 39 * q^63 + 32 * q^64 - 17 * q^65 + 73 * q^66 + 20 * q^67 - 76 * q^68 - 11 * q^69 + 46 * q^71 - 198 * q^72 - 26 * q^73 + 29 * q^74 - 70 * q^75 + 58 * q^76 + 6 * q^77 + 128 * q^78 - 54 * q^79 - 24 * q^80 - 7 * q^81 + 81 * q^82 + 234 * q^83 - 273 * q^84 - 74 * q^85 + 52 * q^86 - 112 * q^87 + 256 * q^88 - 27 * q^89 + 28 * q^90 - 78 * q^91 - 34 * q^92 + 51 * q^93 + 28 * q^94 - 11 * q^95 + 143 * q^96 + 40 * q^97 - 47 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{77}{78}\right)$

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 $

$2$	0.596805	−	0.0240504i	0.422005	−	0.0170062i	0.171644	−	0.985159i	$-0.445092\pi$
$2$	0.596805	−	0.0240504i	0.422005	−	0.0170062i	0.250360	+	0.968153i	$0.419451\pi$
$3$	0.703900	+	2.43014i	0.406397	+	1.40304i	0.859294	+	0.511482i	$0.170903\pi$
$3$	0.703900	+	2.43014i	0.406397	+	1.40304i	−0.452897	+	0.891563i	$0.649610\pi$
$4$	−1.63792	+	0.132226i	−0.818959	+	0.0661132i
$5$	3.70001	−	1.40323i	1.65469	−	0.627543i	0.662144	−	0.749377i	$-0.269647\pi$
$5$	3.70001	−	1.40323i	1.65469	−	0.627543i	0.992550	+	0.121834i	$0.0388776\pi$
$6$	0.478537	+	1.43339i	0.195362	+	0.585180i
$7$	−0.324840	+	0.762428i	−0.122778	+	0.288171i	−0.970015	−	0.243044i	$-0.921854\pi$
$7$	−0.324840	+	0.762428i	−0.122778	+	0.288171i	0.847237	+	0.531215i	$0.178264\pi$
$8$	−2.16021	+	0.262296i	−0.763748	+	0.0927358i
$9$	−2.87456	+	1.81776i	−0.958186	+	0.605920i
$10$	2.17443	−	0.926440i	0.687617	−	0.292966i
$11$	−0.896359	+	1.41748i	−0.270262	+	0.427386i	−0.952861	−	0.303408i	$-0.901875\pi$
$11$	−0.896359	+	1.41748i	−0.270262	+	0.427386i	0.682598	+	0.730794i	$0.260850\pi$
$12$	−1.47426	−	3.88730i	−0.425582	−	1.12217i
$13$	−2.52376	−	2.57500i	−0.699965	−	0.714177i
$13$	−2.52376	−	2.57500i	−0.699965	−	0.714177i
$14$	−0.175530	+	0.462833i	−0.0469122	+	0.123697i
$15$	6.01448	+	8.00382i	1.55293	+	2.06658i
$16$	1.96102	−	0.318697i	0.490255	−	0.0796742i
$17$	6.43696	+	2.74253i	1.56119	+	0.665162i	0.988027	−	0.154278i	$-0.0493051\pi$
$17$	6.43696	+	2.74253i	1.56119	+	0.665162i	0.573165	+	0.819440i	$0.305715\pi$
$18$	−1.67183	+	1.15398i	−0.394054	+	0.271996i
$19$	−6.17486	−	3.56505i	−1.41661	−	0.817880i	−0.420610	−	0.907242i	$-0.638184\pi$
$19$	−6.17486	−	3.56505i	−1.41661	−	0.817880i	−0.995999	+	0.0893619i	$0.971517\pi$
$20$	−5.87476	+	2.78761i	−1.31364	+	0.623329i
$21$	−2.08147	−	0.252736i	−0.454213	−	0.0551514i
$22$	−0.500860	+	0.867515i	−0.106784	+	0.184955i
$23$	−1.23179	−	2.13353i	−0.256846	−	0.444871i	0.708549	−	0.705662i	$-0.249350\pi$
$23$	−1.23179	−	2.13353i	−0.256846	−	0.444871i	−0.965395	+	0.260791i	$0.916017\pi$
$24$	−2.15799	−	5.06498i	−0.440497	−	1.03388i
$25$	7.97846	−	7.06830i	1.59569	−	1.41366i
$26$	−1.56812	−	1.47608i	−0.307534	−	0.289482i
$27$	−0.759544	−	0.672898i	−0.146174	−	0.129499i
$28$	0.431248	−	1.29175i	0.0814983	−	0.244117i
$29$	−0.333794	−	8.28302i	−0.0619841	−	1.53812i	−0.668900	−	0.743352i	$-0.733235\pi$
$29$	−0.333794	−	8.28302i	−0.0619841	−	1.53812i	0.606916	−	0.794766i	$-0.292406\pi$
$30$	3.78197	+	4.63207i	0.690490	+	0.845696i
$31$	0.422119	−	0.476474i	0.0758148	−	0.0855772i	−0.709379	−	0.704827i	$-0.751025\pi$
$31$	0.422119	−	0.476474i	0.0758148	−	0.0855772i	0.785194	+	0.619250i	$0.212563\pi$
$32$	5.42687	−	1.10790i	0.959344	−	0.195851i
$33$	−4.07562	−	1.18052i	−0.709475	−	0.205502i
$34$	3.90757	+	1.48195i	0.670142	+	0.254152i
$35$	−0.132051	+	3.27682i	−0.0223207	+	0.553883i
$36$	4.46793	−	3.35743i	0.744655	−	0.559572i
$37$	−4.24111	−	0.865829i	−0.697235	−	0.142341i	−0.161681	−	0.986843i	$-0.551692\pi$
$37$	−4.24111	−	0.865829i	−0.697235	−	0.142341i	−0.535553	+	0.844502i	$0.679897\pi$
$38$	−3.77092	−	1.97913i	−0.611725	−	0.321058i
$39$	4.48116	−	7.94564i	0.717559	−	1.27232i
$40$	−7.62472	+	4.00176i	−1.20557	+	0.632734i
$41$	−3.37479	+	0.977520i	−0.527054	+	0.152663i	−0.531068	−	0.847329i	$-0.678209\pi$
$41$	−3.37479	+	0.977520i	−0.527054	+	0.152663i	0.00401474	+	0.999992i	$0.498722\pi$
$42$	−1.24831	−	0.100774i	−0.192618	−	0.0155497i
$43$	0.218974	+	1.07261i	0.0333932	+	0.163571i	0.993068	−	0.117542i	$-0.0375015\pi$
$43$	0.218974	+	1.07261i	0.0333932	+	0.163571i	−0.959675	+	0.281113i	$0.909296\pi$
$44$	1.28073	−	2.44023i	0.193078	−	0.367879i
$45$	−8.08515	+	10.7594i	−1.20526	+	1.60391i
$46$	−0.786451	−	1.24367i	−0.115956	−	0.183370i
$47$	−1.62013	−	1.11829i	−0.236320	−	0.163120i	0.444019	−	0.896017i	$-0.353552\pi$
$47$	−1.62013	−	1.11829i	−0.236320	−	0.163120i	−0.680339	+	0.732897i	$0.738168\pi$
$48$	2.15484	+	4.54123i	0.311024	+	0.655470i
$49$	4.37330	+	4.55308i	0.624756	+	0.650440i
$50$	4.59159	−	4.41028i	0.649349	−	0.623708i
$51$	−2.13377	+	17.5732i	−0.298788	+	2.46074i
$52$	4.47419	+	3.88393i	0.620459	+	0.538605i
$53$	−0.146967	−	1.21038i	−0.0201874	−	0.166258i	0.979128	−	0.203242i	$-0.0651480\pi$
$53$	−0.146967	−	1.21038i	−0.0201874	−	0.166258i	−0.999316	+	0.0369841i	$0.988225\pi$
$54$	−0.469483	−	0.383321i	−0.0638886	−	0.0521634i
$55$	−1.32749	+	6.50248i	−0.178999	+	0.876794i
$56$	0.501739	−	1.73221i	0.0670478	−	0.231476i
$57$	4.31712	−	17.5152i	0.571816	−	2.31995i
$58$	−0.398420	−	4.93532i	−0.0523151	−	0.648039i
$59$	−1.82780	+	11.2469i	−0.237960	+	1.46423i	0.543047	+	0.839702i	$0.317271\pi$
$59$	−1.82780	+	11.2469i	−0.237960	+	1.46423i	−0.781007	+	0.624523i	$0.785294\pi$
$60$	−10.9095	−	12.3143i	−1.40842	−	1.58977i
$61$	−1.57425	−	1.18297i	−0.201562	−	0.151464i	0.495169	−	0.868797i	$-0.335106\pi$
$61$	−1.57425	−	1.18297i	−0.201562	−	0.151464i	−0.696730	+	0.717333i	$0.745363\pi$
$62$	0.240463	−	0.294514i	0.0305388	−	0.0374033i
$63$	−0.452139	−	2.78212i	−0.0569642	−	0.350515i
$64$	−0.645897	+	0.159199i	−0.0807371	+	0.0198999i
$65$	−12.9512	−	5.98612i	−1.60640	−	0.742487i
$66$	−2.46074	−	0.606519i	−0.302897	−	0.0746573i
$67$	−0.248094	+	3.07320i	−0.0303095	+	0.375451i	0.963765	+	0.266752i	$0.0859504\pi$
$67$	−0.248094	+	3.07320i	−0.0303095	+	0.375451i	−0.994075	+	0.108699i	$0.965332\pi$
$68$	−10.9058	−	3.64091i	−1.32253	−	0.441525i
$69$	4.31772	−	4.49522i	0.519792	−	0.541161i
$70$			1.95880i			0.234121i
$71$	−2.34131	−	2.24886i	−0.277862	−	0.266890i	0.540819	−	0.841139i	$-0.318115\pi$
$71$	−2.34131	−	2.24886i	−0.277862	−	0.266890i	−0.818681	+	0.574249i	$0.805294\pi$
$72$	5.73284	−	4.68072i	0.675622	−	0.551628i
$73$	4.05158	+	7.71964i	0.474201	+	0.903515i	0.998643	+	0.0520689i	$0.0165816\pi$
$73$	4.05158	+	7.71964i	0.474201	+	0.903515i	−0.524442	+	0.851446i	$0.675726\pi$
$74$	−2.55194	−	0.414731i	−0.296657	−	0.0482114i
$75$	22.7930	+	14.4134i	2.63191	+	1.66432i
$76$	10.5853	+	5.02279i	1.21422	+	0.576153i
$77$	−0.789552	−	1.14386i	−0.0899778	−	0.130355i
$78$	2.48328	−	4.84977i	0.281176	−	0.549128i
$79$	−3.06556	+	4.44123i	−0.344903	+	0.499678i	−0.956596	−	0.291417i	$-0.905873\pi$
$79$	−3.06556	+	4.44123i	−0.344903	+	0.499678i	0.611693	+	0.791095i	$0.290489\pi$
$80$	6.80859	−	3.93094i	0.761223	−	0.439492i
$81$	−3.27346	+	6.89866i	−0.363717	+	0.766518i
$82$	−1.99058	+	0.664553i	−0.219823	+	0.0733877i
$83$	−1.84811	−	7.49807i	−0.202856	−	0.823020i	−0.980853	−	0.194751i	$-0.937610\pi$
$83$	−1.84811	−	7.49807i	−0.202856	−	0.823020i	0.777997	−	0.628269i	$-0.216236\pi$
$84$	3.44269	+	0.138736i	0.375628	+	0.0151373i
$85$	27.6652	+	1.11487i	3.00071	+	0.120925i
$86$	0.156481	+	0.634870i	0.0168738	+	0.0684597i
$87$	19.8940	−	6.64159i	2.13286	−	0.712053i
$88$	1.56452	−	3.29715i	0.166778	−	0.351478i
$89$	−14.6210	+	8.44146i	−1.54983	+	0.894793i	−0.551673	+	0.834060i	$0.686010\pi$
$89$	−14.6210	+	8.44146i	−1.54983	+	0.894793i	−0.998154	+	0.0607327i	$0.980656\pi$
$90$	−4.56649	+	6.61570i	−0.481350	+	0.697356i
$91$	2.78307	−	1.08772i	0.291745	−	0.114024i
$92$	2.29968	+	3.33166i	0.239758	+	0.347350i
$93$	1.45503	+	0.690420i	0.150879	+	0.0715932i
$94$	−0.993795	−	0.628438i	−0.102502	−	0.0648184i
$95$	−27.8496	−	4.52600i	−2.85731	−	0.464358i
$96$	6.51234	+	12.4082i	0.664663	+	1.26641i
$97$	−0.0230764	+	0.0188413i	−0.00234305	+	0.00191304i	−0.633616	−	0.773648i	$-0.718430\pi$
$97$	−0.0230764	+	0.0188413i	−0.00234305	+	0.00191304i	0.631273	+	0.775561i	$0.282533\pi$
$98$	2.71951	+	2.61212i	0.274712	+	0.263864i
$99$		−	5.70399i		−	0.573272i
$100$	−12.1334	+	12.6323i	−1.21334	+	1.26323i
$101$	−3.57391	−	1.19315i	−0.355618	−	0.118723i	0.133246	−	0.991083i	$-0.457460\pi$
$101$	−3.57391	−	1.19315i	−0.355618	−	0.118723i	−0.488863	+	0.872360i	$0.662588\pi$
$102$	−0.850804	+	10.5391i	−0.0842421	+	1.04353i
$103$	8.48507	+	2.09138i	0.836058	+	0.206070i	0.634029	−	0.773309i	$-0.281400\pi$
$103$	8.48507	+	2.09138i	0.836058	+	0.206070i	0.202030	+	0.979379i	$0.435246\pi$
$104$	6.12725	+	4.90056i	0.600826	+	0.480540i
$105$	−8.05609	+	1.98565i	−0.786194	+	0.193779i
$106$	−0.116821	−	0.718825i	−0.0113466	−	0.0698185i
$107$	6.44814	−	7.89753i	0.623365	−	0.763483i	−0.362325	−	0.932052i	$-0.618017\pi$
$107$	6.44814	−	7.89753i	0.623365	−	0.763483i	0.985690	+	0.168568i	$0.0539144\pi$
$108$	1.33305	+	1.00172i	0.128272	+	0.0963904i
$109$	2.13815	+	2.41347i	0.204798	+	0.231169i	0.841932	−	0.539584i	$-0.181419\pi$
$109$	2.13815	+	2.41347i	0.204798	+	0.231169i	−0.637134	+	0.770753i	$0.719880\pi$
$110$	−0.635865	+	3.91264i	−0.0606274	+	0.373055i
$111$	−0.881228	−	10.9160i	−0.0836425	−	1.03610i
$112$	−0.394035	+	1.59866i	−0.0372328	+	0.151059i
$113$	−2.01280	+	6.94901i	−0.189349	+	0.653707i	0.808521	+	0.588467i	$0.200268\pi$
$113$	−2.01280	+	6.94901i	−0.189349	+	0.653707i	−0.997870	+	0.0652400i	$0.979219\pi$
$114$	2.15523	−	10.5570i	0.201856	−	0.988754i
$115$	−7.55147	−	6.16558i	−0.704178	−	0.574943i
$116$	1.64196	+	13.5228i	0.152452	+	1.25556i
$117$	11.9354	+	2.81441i	1.10343	+	0.260192i
$118$	−0.820349	+	6.75618i	−0.0755192	+	0.621957i
$119$	−4.18197	+	4.01684i	−0.383360	+	0.368223i
$120$	−15.0919	−	15.7123i	−1.37769	−	1.43433i
$121$	3.50983	+	7.39682i	0.319076	+	0.672438i
$122$	−0.967968	−	0.668140i	−0.0876357	−	0.0604906i
$123$	−4.75103	−	7.51315i	−0.428386	−	0.677438i
$124$	−0.628393	+	0.836239i	−0.0564314	+	0.0750965i
$125$	10.4070	−	19.8289i	0.930832	−	1.77355i
$126$	−0.336750	−	1.64951i	−0.0300001	−	0.146950i
$127$	−15.1340	−	1.22174i	−1.34292	−	0.108412i	−0.611993	−	0.790863i	$-0.709632\pi$
$127$	−15.1340	−	1.22174i	−1.34292	−	0.108412i	−0.730931	+	0.682451i	$0.760914\pi$
$128$	−11.0219	+	3.19253i	−0.974207	+	0.282182i
$129$	−2.45245	+	1.28715i	−0.215926	+	0.113327i
$130$	−7.87333	−	3.26106i	−0.690537	−	0.286014i
$131$	8.69381	+	4.56286i	0.759582	+	0.398659i	0.799595	−	0.600540i	$-0.205048\pi$
$131$	8.69381	+	4.56286i	0.759582	+	0.398659i	−0.0400131	+	0.999199i	$0.512740\pi$
$132$	6.83163	+	1.39469i	0.594617	+	0.121392i
$133$	4.72394	−	3.54981i	0.409618	−	0.307808i
$134$	−0.0741521	+	1.84006i	−0.00640576	+	0.158957i
$135$	−3.75455	−	1.42391i	−0.323140	−	0.122551i
$136$	−14.6245	−	4.23604i	−1.25404	−	0.363238i
$137$	2.53524	−	0.517573i	0.216600	−	0.0442193i	−0.0904998	−	0.995896i	$-0.528846\pi$
$137$	2.53524	−	0.517573i	0.216600	−	0.0442193i	0.307100	+	0.951677i	$0.400641\pi$
$138$	2.46872	−	2.78661i	0.210152	−	0.237212i
$139$	−4.33081	−	5.30428i	−0.367334	−	0.449903i	0.557555	−	0.830140i	$-0.311740\pi$
$139$	−4.33081	−	5.30428i	−0.367334	−	0.449903i	−0.924889	+	0.380237i	$0.875842\pi$
$140$	−0.216992	−	5.38461i	−0.0183392	−	0.455083i
$141$	1.57721	−	4.72431i	0.132825	−	0.397859i
$142$	−1.45139	−	1.28582i	−0.121798	−	0.107903i
$143$	5.91220	−	1.26925i	0.494403	−	0.106140i
$144$	−5.05775	+	4.48077i	−0.421479	+	0.373398i
$145$	−12.8580	−	30.1789i	−1.06780	−	2.50622i
$146$	2.60366	+	4.50967i	0.215481	+	0.373223i
$147$	−7.98629	+	13.8327i	−0.658698	+	1.14090i
$148$	7.06108	+	0.857370i	0.580417	+	0.0704754i
$149$	4.62535	−	2.19476i	0.378923	−	0.179801i	−0.229698	−	0.973262i	$-0.573774\pi$
$149$	4.62535	−	2.19476i	0.378923	−	0.179801i	0.608622	+	0.793460i	$0.291723\pi$
$150$	13.9496	+	8.05383i	1.13898	+	0.657592i
$151$	15.8714	−	10.9553i	1.29160	−	0.891526i	0.293673	−	0.955906i	$-0.405122\pi$
$151$	15.8714	−	10.9553i	1.29160	−	0.891526i	0.997925	+	0.0643796i	$0.0205069\pi$
$152$	14.2741	+	6.08161i	1.15778	+	0.493283i
$153$	−23.4887	+	3.81728i	−1.89895	+	0.308609i
$154$	−0.498719	−	0.663674i	−0.0401879	−	0.0534804i
$155$	0.893242	−	2.35529i	0.0717469	−	0.189181i
$156$	−6.28914	+	13.6068i	−0.503534	+	1.08942i
$157$	−3.72482	−	9.82155i	−0.297273	−	0.783845i	−0.997549	−	0.0699728i	$-0.977709\pi$
$157$	−3.72482	−	9.82155i	−0.297273	−	0.783845i	0.700276	−	0.713873i	$-0.253060\pi$
$158$	−1.72273	+	2.72428i	−0.137053	+	0.216732i
$159$	2.83795	−	1.20914i	0.225064	−	0.0958907i
$160$	18.5248	−	11.7144i	1.46452	−	0.926104i
$161$	2.02680	−	0.246098i	0.159734	−	0.0193952i
$162$	−1.78770	+	4.19588i	−0.140455	+	0.329660i
$163$	−1.04738	−	3.13728i	−0.0820370	−	0.245731i	0.899527	−	0.436866i	$-0.143911\pi$
$163$	−1.04738	−	3.13728i	−0.0820370	−	0.245731i	−0.981564	+	0.191135i	$0.938783\pi$
$164$	5.39837	−	2.04733i	0.421542	−	0.159870i
$165$	−16.7364	+	1.35110i	−1.30293	+	0.105183i
$166$	−1.28329	−	4.43043i	−0.0996027	−	0.343868i
$167$	−7.66565	+	0.308915i	−0.593186	+	0.0239046i	−0.335044	−	0.942202i	$-0.608751\pi$
$167$	−7.66565	+	0.308915i	−0.593186	+	0.0239046i	−0.258142	+	0.966107i	$0.583110\pi$
$168$	4.56268			0.352019
$169$	−0.261281	+	12.9974i	−0.0200985	+	0.999798i
$170$	16.5375			1.26837
$171$	24.2304	−	0.976451i	1.85294	−	0.0746711i
$172$	−0.500488	−	1.72788i	−0.0381618	−	0.131750i
$173$	−11.7219	+	0.946291i	−0.891201	+	0.0719452i	−0.517579	−	0.855636i	$-0.673167\pi$
$173$	−11.7219	+	0.946291i	−0.891201	+	0.0719452i	−0.373623	+	0.927581i	$0.621884\pi$
$174$	11.7131	−	4.44219i	0.887967	−	0.336761i
$175$	2.79735	+	8.37907i	0.211459	+	0.633398i
$176$	−1.30603	+	3.06537i	−0.0984458	+	0.231061i
$177$	−28.6182	+	3.47488i	−2.15108	+	0.261188i
$178$	−8.52289	+	5.38955i	−0.638817	+	0.403964i
$179$	4.93785	−	2.10382i	0.369072	−	0.157247i	−0.199464	−	0.979905i	$-0.563920\pi$
$179$	4.93785	−	2.10382i	0.369072	−	0.157247i	0.568536	+	0.822658i	$0.307510\pi$
$180$	11.8201	−	18.6921i	0.881021	−	1.39322i
$181$	9.25186	+	24.3951i	0.687685	+	1.81328i	0.572452	+	0.819938i	$0.305992\pi$
$181$	9.25186	+	24.3951i	0.687685	+	1.81328i	0.115233	+	0.993338i	$0.463238\pi$
$182$	1.63479	−	0.716091i	0.121179	−	0.0530802i
$183$	1.76667	−	4.65834i	0.130596	−	0.344354i
$184$	3.22054	+	4.28576i	0.237421	+	0.315950i
$185$	−16.9071	+	2.74767i	−1.24304	+	0.202013i
$186$	0.884973	+	0.377052i	0.0648894	+	0.0276468i
$187$	−9.65731	+	6.66596i	−0.706212	+	0.487463i
$188$	2.80150	+	1.61745i	0.204320	+	0.117964i
$189$	0.759767	−	0.360514i	0.0552649	−	0.0262235i
$190$	−16.7296	−	2.03134i	−1.21369	−	0.147369i
$191$	8.65735	−	14.9950i	0.626424	−	1.08500i	−0.361840	−	0.932240i	$-0.617851\pi$
$191$	8.65735	−	14.9950i	0.626424	−	1.08500i	0.988264	−	0.152757i	$-0.0488153\pi$
$192$	−0.841524	−	1.45756i	−0.0607318	−	0.105190i
$193$	−6.72766	−	15.7904i	−0.484267	−	1.13662i	−0.965589	−	0.260073i	$-0.916253\pi$
$193$	−6.72766	−	15.7904i	−0.484267	−	1.13662i	0.481322	−	0.876544i	$-0.340157\pi$
$194$	−0.0133190	+	0.0117996i	−0.000956246	+	0.000847160i
$195$	5.43076	−	35.6870i	0.388905	−	2.55560i
$196$	−7.76513	−	6.87931i	−0.554652	−	0.491379i
$197$	0.213116	−	0.638360i	0.0151839	−	0.0454812i	−0.940672	−	0.339318i	$-0.889804\pi$
$197$	0.213116	−	0.638360i	0.0151839	−	0.0454812i	0.955856	+	0.293836i	$0.0949321\pi$
$198$	−0.137183	−	3.40417i	−0.00974919	−	0.241924i
$199$	0.373580	+	0.457553i	0.0264824	+	0.0324351i	0.787676	−	0.616089i	$-0.211284\pi$
$199$	0.373580	+	0.457553i	0.0264824	+	0.0324351i	−0.761194	+	0.648524i	$0.775386\pi$
$200$	−15.3811	+	17.3617i	−1.08761	+	1.22766i
$201$	−7.64294	+	1.56032i	−0.539092	+	0.110056i
$202$	−2.16162	−	0.626122i	−0.152091	−	0.0440538i
$203$	6.42364	+	2.43616i	0.450851	+	0.170985i
$204$	1.17130	−	29.0656i	0.0820077	−	2.03500i
$205$	−11.1151	+	8.35243i	−0.776310	+	0.583359i
$206$	5.11423	+	1.04408i	0.356325	+	0.0727443i
$207$	7.41909	+	3.89384i	0.515663	+	0.270641i
$208$	−5.76979	−	4.24532i	−0.400063	−	0.294360i
$209$	10.5883	−	5.55715i	0.732406	−	0.384396i
$210$	−4.76016	+	1.37880i	−0.328482	+	0.0951459i
$211$	18.8950	+	1.52536i	1.30079	+	0.105010i	0.711370	−	0.702818i	$-0.248075\pi$
$211$	18.8950	+	1.52536i	1.30079	+	0.105010i	0.589418	+	0.807828i	$0.299357\pi$
$212$	0.400763	+	1.96307i	0.0275245	+	0.134824i
$213$	3.81700	−	7.27268i	0.261536	−	0.498316i
$214$	3.65834	−	4.86837i	0.250079	−	0.332795i
$215$	2.31532	+	3.66138i	0.157903	+	0.249704i
$216$	1.81727	+	1.25437i	0.123650	+	0.0853491i
$217$	0.226156	+	0.476613i	0.0153524	+	0.0323546i
$218$	1.33410	+	1.38895i	0.0903569	+	0.0940715i
$219$	−15.9079	+	15.2798i	−1.07496	+	1.03251i
$220$	1.31452	−	10.8260i	0.0886249	−	0.729892i
$221$	−9.18331	−	23.4967i	−0.617736	−	1.58056i
$222$	−0.788455	−	6.49351i	−0.0529176	−	0.435816i
$223$	7.99217	+	6.52540i	0.535195	+	0.436973i	0.861105	−	0.508428i	$-0.169773\pi$
$223$	7.99217	+	6.52540i	0.535195	+	0.436973i	−0.325910	+	0.945401i	$0.605671\pi$
$224$	−0.918169	+	4.49749i	−0.0613477	+	0.300501i
$225$	−10.0861	+	34.8212i	−0.672405	+	2.32141i
$226$	−1.03412	+	4.19561i	−0.0687889	+	0.279088i
$227$	1.68507	+	20.8734i	0.111842	+	1.38542i	0.772637	+	0.634849i	$0.218938\pi$
$227$	1.68507	+	20.8734i	0.111842	+	1.38542i	−0.660794	+	0.750567i	$0.729780\pi$
$228$	−4.75511	+	29.2593i	−0.314915	+	1.93775i
$229$	−3.80883	−	4.29928i	−0.251695	−	0.284104i	0.609061	−	0.793124i	$-0.291547\pi$
$229$	−3.80883	−	4.29928i	−0.251695	−	0.284104i	−0.860755	+	0.509019i	$0.830008\pi$
$230$	−4.65504	−	3.49803i	−0.306944	−	0.230653i
$231$	2.22399	−	2.72389i	0.146328	−	0.179219i
$232$	2.89367	+	17.8055i	0.189979	+	1.16899i
$233$	−13.3788	+	3.29759i	−0.876477	+	0.216032i	−0.651791	−	0.758399i	$-0.725982\pi$
$233$	−13.3788	+	3.29759i	−0.876477	+	0.216032i	−0.224686	+	0.974431i	$0.572136\pi$
$234$	7.19081	+	1.39260i	0.470078	+	0.0910370i
$235$	−7.56370	−	1.86429i	−0.493402	−	0.121613i
$236$	1.50665	−	18.6632i	0.0980746	−	1.21487i
$237$	−12.9507	−	4.32357i	−0.841237	−	0.280846i
$238$	−2.39921	+	2.49784i	−0.155518	+	0.161911i
$239$			12.0681i			0.780623i	0.920683	+	0.390312i	$0.127633\pi$
$239$			12.0681i			0.780623i	−0.920683	+	0.390312i	$0.872367\pi$
$240$	14.3453	+	13.7789i	0.925986	+	0.889422i
$241$	−0.690176	+	0.563511i	−0.0444582	+	0.0362990i	−0.654414	−	0.756136i	$-0.727085\pi$
$241$	−0.690176	+	0.563511i	−0.0444582	+	0.0362990i	0.609956	+	0.792435i	$0.291187\pi$
$242$	2.27258	+	4.33004i	0.146087	+	0.278346i
$243$	−22.0737	−	3.58733i	−1.41603	−	0.230127i
$244$	2.73490	+	1.72945i	0.175084	+	0.110717i
$245$	22.5702	+	10.7097i	1.44196	+	0.684219i
$246$	−3.01613	−	4.36962i	−0.192301	−	0.278597i
$247$	6.40382	+	24.8976i	0.407465	+	1.58420i
$248$	−0.786886	+	1.14000i	−0.0499673	+	0.0723901i
$249$	16.9205	−	9.76906i	1.07229	−	0.619089i
$250$	5.73407	−	12.0843i	0.362654	−	0.764277i
$251$	12.8958	−	4.30524i	0.813974	−	0.271744i	0.120950	−	0.992659i	$-0.461406\pi$
$251$	12.8958	−	4.30524i	0.813974	−	0.271744i	0.693024	+	0.720914i	$0.256278\pi$
$252$	1.10844	+	4.49711i	0.0698250	+	0.283291i
$253$	4.12835	+	0.166367i	0.259547	+	0.0104594i
$254$	−9.06142	−	0.365163i	−0.568564	−	0.0229123i
$255$	16.7642	+	68.0152i	1.04982	+	4.25928i
$256$	−5.23915	+	1.74909i	−0.327447	+	0.109318i
$257$	12.1540	−	25.6141i	0.758147	−	1.59776i	−0.0428420	−	0.999082i	$-0.513641\pi$
$257$	12.1540	−	25.6141i	0.758147	−	1.59776i	0.800989	−	0.598679i	$-0.204308\pi$
$258$	−1.43268	+	0.827157i	−0.0891946	+	0.0514965i
$259$	2.03782	−	2.95229i	0.126624	−	0.183446i
$260$	22.0046	+	8.09228i	1.36467	+	0.501862i
$261$	16.0161	+	23.2033i	0.991369	+	1.43625i
$262$	5.29825	+	2.51405i	0.327327	+	0.155318i
$263$	8.01836	+	5.07050i	0.494433	+	0.312661i	0.758308	−	0.651896i	$-0.226026\pi$
$263$	8.01836	+	5.07050i	0.494433	+	0.312661i	−0.263875	+	0.964557i	$0.585001\pi$
$264$	9.11383	+	1.48114i	0.560917	+	0.0911579i
$265$	−2.24222	−	4.27219i	−0.137738	−	0.262438i
$266$	2.73390	−	2.23216i	0.167626	−	0.136862i
$267$	−30.8057	−	29.5893i	−1.88528	−	1.81084i
$268$		−	5.06645i		−	0.309482i
$269$	−11.2902	+	11.7544i	−0.688378	+	0.716677i	−0.970069	−	0.242828i	$-0.921925\pi$
$269$	−11.2902	+	11.7544i	−0.688378	+	0.716677i	0.281691	+	0.959505i	$0.409105\pi$
$270$	−2.27498	−	0.759500i	−0.138451	−	0.0462217i
$271$	1.48422	−	18.3854i	0.0901601	−	1.11683i	−0.780569	−	0.625070i	$-0.785070\pi$
$271$	1.48422	−	18.3854i	0.0901601	−	1.11683i	0.870729	−	0.491763i	$-0.163647\pi$
$272$	13.4970	+	3.32672i	0.818379	+	0.201712i
$273$	4.60232	+	5.99762i	0.278545	+	0.362993i
$274$	1.50060	−	0.369864i	0.0906544	−	0.0223443i
$275$	2.86760	+	17.6450i	0.172923	+	1.06404i
$276$	−6.47768	+	7.93372i	−0.389910	+	0.477554i
$277$	18.8669	+	14.1775i	1.13360	+	0.851846i	0.990452	−	0.137855i	$-0.0440209\pi$
$277$	18.8669	+	14.1775i	1.13360	+	0.851846i	0.143149	+	0.989701i	$0.454277\pi$
$278$	−2.71222	−	3.06146i	−0.162668	−	0.183614i
$279$	−0.347290	+	2.13696i	−0.0207917	+	0.127937i
$280$	−0.574239	−	7.11323i	−0.0343174	−	0.425097i
$281$	3.47530	−	14.0998i	0.207319	−	0.841125i	−0.771472	−	0.636263i	$-0.780479\pi$
$281$	3.47530	−	14.0998i	0.207319	−	0.841125i	0.978791	−	0.204862i	$-0.0656746\pi$
$282$	0.827662	−	2.85742i	0.0492866	−	0.170157i
$283$	3.60804	−	17.6733i	0.214475	−	1.05057i	−0.719845	−	0.694135i	$-0.755787\pi$
$283$	3.60804	−	17.6733i	0.214475	−	1.05057i	0.934320	−	0.356435i	$-0.116008\pi$
$284$	4.13222	+	3.37386i	0.245202	+	0.200202i
$285$	−8.60450	−	70.8644i	−0.509687	−	4.19765i
$286$	3.49791	−	0.899683i	0.206835	−	0.0531994i
$287$	0.350979	−	2.89057i	0.0207176	−	0.170625i
$288$	−13.5859	+	13.0495i	−0.800559	+	0.768948i
$289$	22.1367	+	23.0467i	1.30216	+	1.35569i
$290$	−8.39954	−	17.7016i	−0.493238	−	1.03948i
$291$	−0.0620306	−	0.0428166i	−0.00363630	−	0.00250995i
$292$	−7.65689	−	12.1084i	−0.448085	−	0.708590i
$293$	5.03801	−	6.70437i	0.294324	−	0.391674i	−0.627923	−	0.778275i	$-0.716095\pi$
$293$	5.03801	−	6.70437i	0.294324	−	0.391674i	0.922247	+	0.386602i	$0.126351\pi$
$294$	−4.43357	+	8.44747i	−0.258571	+	0.492666i
$295$	9.01912	+	44.1785i	0.525113	+	2.57217i
$296$	9.38878	+	0.757940i	0.545712	+	0.0440544i
$297$	1.63464	−	0.473480i	0.0948515	−	0.0274741i
$298$	2.70765	−	1.42108i	0.156850	−	0.0823211i
$299$	−2.38509	+	8.55637i	−0.137933	+	0.494828i
$300$	−39.2389	−	20.5942i	−2.26546	−	1.18901i
$301$	−0.888916	−	0.181474i	−0.0512363	−	0.0104600i
$302$	9.20867	−	6.91986i	0.529899	−	0.398193i
$303$	0.383844	−	9.52498i	0.0220512	−	0.547196i
$304$	−13.2452	−	5.02324i	−0.759664	−	0.288102i
$305$	−7.48470	−	2.16797i	−0.428573	−	0.124138i
$306$	−13.9263	+	2.84308i	−0.796116	+	0.162528i
$307$	13.7755	−	15.5494i	0.786211	−	0.887449i	−0.209702	−	0.977765i	$-0.567249\pi$
$307$	13.7755	−	15.5494i	0.786211	−	0.887449i	0.995913	+	0.0903167i	$0.0287879\pi$
$308$	1.44447	+	1.76915i	0.0823063	+	0.100807i
$309$	0.890280	+	22.0921i	0.0506462	+	1.25677i
$310$	0.476445	−	1.42713i	0.0270603	−	0.0810554i
$311$	6.61585	+	5.86114i	0.375151	+	0.332354i	0.829539	−	0.558449i	$-0.188604\pi$
$311$	6.61585	+	5.86114i	0.375151	+	0.332354i	−0.454388	+	0.890804i	$0.650142\pi$
$312$	−7.59610	+	18.3396i	−0.430045	+	1.03828i
$313$	17.8929	−	15.8517i	1.01137	−	0.895994i	0.0167764	−	0.999859i	$-0.494660\pi$
$313$	17.8929	−	15.8517i	1.01137	−	0.895994i	0.994591	+	0.103866i	$0.0331212\pi$
$314$	−2.45921	−	5.77197i	−0.138781	−	0.325731i
$315$	−5.57688	−	9.65943i	−0.314221	−	0.544247i
$316$	4.43389	−	7.67972i	0.249426	−	0.432018i
$317$	−15.9927	−	1.94187i	−0.898242	−	0.109066i	−0.341626	−	0.939836i	$-0.610978\pi$
$317$	−15.9927	−	1.94187i	−0.898242	−	0.109066i	−0.556616	+	0.830770i	$0.687901\pi$
$318$	1.66462	−	0.789872i	0.0933472	−	0.0442938i
$319$	12.0402	+	6.95141i	0.674122	+	0.389204i
$320$	−2.16643	+	1.49538i	−0.121107	+	0.0835942i
$321$	23.7310	+	10.1108i	1.32453	+	0.564332i
$322$	1.20368	−	0.195617i	0.0670786	−	0.0109013i
$323$	−29.9700	−	39.8829i	−1.66758	−	2.21914i
$324$	4.44946	−	11.7323i	0.247192	−	0.651793i
$325$	−38.3366	−	2.70588i	−2.12653	−	0.150095i
$326$	−0.700533	−	1.84715i	−0.0387989	−	0.102304i
$327$	−4.36005	+	6.89486i	−0.241111	+	0.381287i
$328$	7.03384	−	2.99684i	0.388379	−	0.165473i
$329$	1.37890	−	0.871964i	0.0760212	−	0.0480729i
$330$	−9.95586	+	1.20886i	−0.548052	+	0.0665455i
$331$	11.1221	−	26.1044i	0.611323	−	1.43483i	−0.270254	−	0.962789i	$-0.587108\pi$
$331$	11.1221	−	26.1044i	0.611323	−	1.43483i	0.881577	−	0.472040i	$-0.156482\pi$
$332$	4.01849	+	12.0368i	0.220543	+	0.660608i
$333$	13.7652	−	5.22045i	0.754328	−	0.286079i
$334$	−4.56747	+	0.368724i	−0.249921	+	0.0201757i
$335$	3.39445	+	11.7190i	0.185458	+	0.640277i
$336$	−4.16234	+	0.167737i	−0.227074	+	0.00915078i
$337$	−5.53405			−0.301459			−0.150730	−	0.988575i	$-0.548162\pi$
$337$	−5.53405			−0.301459			−0.150730	+	0.988575i	$0.548162\pi$
$338$	0.156658	+	7.76318i	0.00852109	+	0.422261i
$339$	−18.3039			−0.994131
$340$	−45.4607	+	1.83201i	−2.46545	+	0.0993544i
$341$	0.297021	+	1.02544i	0.0160846	+	0.0555304i
$342$	14.4373	−	1.16550i	0.780681	−	0.0630231i
$343$	−10.3162	+	3.91244i	−0.557025	+	0.211252i
$344$	−0.754369	−	2.25961i	−0.0406729	−	0.121830i
$345$	9.66778	−	22.6911i	0.520496	−	1.22165i
$346$	−6.97294	+	0.846668i	−0.374868	+	0.0455172i
$347$	−7.21382	+	4.56174i	−0.387258	+	0.244887i	−0.713880	−	0.700268i	$-0.753064\pi$
$347$	−7.21382	+	4.56174i	−0.387258	+	0.244887i	0.326622	+	0.945155i	$0.394090\pi$
$348$	−31.7065	+	13.5089i	−1.69965	+	0.724152i
$349$	4.08332	−	6.45726i	0.218575	−	0.345649i	−0.718044	−	0.695998i	$-0.754962\pi$
$349$	4.08332	−	6.45726i	0.218575	−	0.345649i	0.936619	+	0.350348i	$0.113937\pi$
$350$	1.87099	+	4.93339i	0.100009	+	0.263701i
$351$	0.184194	+	3.65406i	0.00983153	+	0.195039i
$352$	−3.29399	+	8.68555i	−0.175570	+	0.462941i
$353$	3.01731	+	4.01531i	0.160595	+	0.213713i	0.872567	−	0.488495i	$-0.162454\pi$
$353$	3.01731	+	4.01531i	0.160595	+	0.213713i	−0.711972	+	0.702208i	$0.752198\pi$
$354$	−16.9959	+	2.76211i	−0.903324	+	0.146804i
$355$	−11.8185	−	5.03540i	−0.627262	−	0.267251i
$356$	22.8319	−	15.7597i	1.21009	−	0.835262i
$357$	−12.7052	−	7.33534i	−0.672429	−	0.388227i
$358$	2.89633	−	1.37433i	0.153076	−	0.0726355i
$359$	−18.7273	−	2.27391i	−0.988392	−	0.120012i	−0.389657	−	0.920960i	$-0.627406\pi$
$359$	−18.7273	−	2.27391i	−0.988392	−	0.120012i	−0.598734	+	0.800948i	$0.704330\pi$
$360$	14.6434	−	25.3632i	0.771777	−	1.33676i
$361$	15.9192	+	27.5729i	0.837854	+	1.45121i
$362$	6.10827	+	14.3366i	0.321043	+	0.753516i
$363$	−15.5048	+	13.7360i	−0.813789	+	0.720954i
$364$	−4.41462	+	2.14959i	−0.231389	+	0.112669i
$365$	25.8233	+	22.8774i	1.35165	+	1.19746i
$366$	0.942325	−	2.82261i	0.0492561	−	0.147540i
$367$	0.357589	+	8.87348i	0.0186660	+	0.463192i	0.981311	+	0.192427i	$0.0616357\pi$
$367$	0.357589	+	8.87348i	0.0186660	+	0.463192i	−0.962645	+	0.270765i	$0.912723\pi$
$368$	−3.09552	−	3.79132i	−0.161365	−	0.197636i
$369$	7.92413	−	8.94449i	0.412514	−	0.465632i
$370$	−10.0242	+	2.04645i	−0.521131	+	0.106390i
$371$	0.970568	+	0.281128i	0.0503894	+	0.0145955i
$372$	−2.47451	−	0.938457i	−0.128297	−	0.0486567i
$373$	−0.235174	+	5.83579i	−0.0121769	+	0.302166i	0.981612	+	0.190886i	$0.0611361\pi$
$373$	−0.235174	+	5.83579i	−0.0121769	+	0.302166i	−0.993789	+	0.111280i	$0.964505\pi$
$374$	−5.60321	+	4.21054i	−0.289735	+	0.217722i
$375$	55.5126	+	11.3330i	2.86666	+	0.585233i
$376$	3.79313	+	1.99079i	0.195616	+	0.102667i
$377$	−20.4864	+	21.7639i	−1.05510	+	1.12090i
$378$	0.444762	−	0.233429i	0.0228761	−	0.0120063i
$379$	−27.5302	+	7.97422i	−1.41413	+	0.409608i	−0.895375	−	0.445313i	$-0.853092\pi$
$379$	−27.5302	+	7.97422i	−1.41413	+	0.409608i	−0.518757	+	0.854922i	$0.673605\pi$
$380$	46.2138	+	3.73076i	2.37072	+	0.191384i
$381$	−7.68380	−	37.6377i	−0.393653	−	1.92824i
$382$	4.80611	−	9.15728i	0.245902	−	0.468527i
$383$	9.78915	−	13.0270i	0.500202	−	0.665648i	−0.476767	−	0.879030i	$-0.658191\pi$
$383$	9.78915	−	13.0270i	0.500202	−	0.665648i	0.976969	+	0.213382i	$0.0684477\pi$
$384$	−15.5166	−	24.5376i	−0.791829	−	1.25218i
$385$	−4.52645	−	3.12438i	−0.230689	−	0.159233i
$386$	−4.39486	−	9.26198i	−0.223693	−	0.471422i
$387$	−2.57919	−	2.68522i	−0.131108	−	0.136498i
$388$	0.0353059	−	0.0339118i	0.00179239	−	0.00172161i
$389$	−0.443898	+	3.65583i	−0.0225065	+	0.185358i	−0.999626	−	0.0273313i	$-0.991299\pi$
$389$	−0.443898	+	3.65583i	−0.0225065	+	0.185358i	0.977120	+	0.212689i	$0.0682222\pi$
$390$	2.38282	−	21.4288i	0.120659	−	1.08509i
$391$	−2.07773	−	17.1117i	−0.105075	−	0.865374i
$392$	−10.6415	−	8.68849i	−0.537475	−	0.438835i
$393$	−4.96884	+	24.3390i	−0.250645	+	1.22774i
$394$	0.111836	−	0.386102i	0.00563420	−	0.0194515i
$395$	−5.11054	+	20.7343i	−0.257139	+	1.04325i
$396$	0.754217	+	9.34266i	0.0379008	+	0.469486i
$397$	2.15430	−	13.2559i	0.108121	−	0.665296i	−0.875248	−	0.483675i	$-0.839302\pi$
$397$	2.15430	−	13.2559i	0.108121	−	0.665296i	0.983369	−	0.181621i	$-0.0581343\pi$
$398$	0.233959	+	0.264085i	0.0117273	+	0.0132374i
$399$	11.9517	+	8.98115i	0.598335	+	0.449620i
$400$	13.3933	−	16.4038i	0.669664	−	0.820189i
$401$	4.07738	+	25.0891i	0.203615	+	1.25289i	0.864588	+	0.502482i	$0.167580\pi$
$401$	4.07738	+	25.0891i	0.203615	+	1.25289i	−0.660973	+	0.750410i	$0.729856\pi$
$402$	−4.52382	+	1.11502i	−0.225628	+	0.0556122i
$403$	−2.29225	+	0.115547i	−0.114185	+	0.00575583i
$404$	6.01154	+	1.48171i	0.299085	+	0.0737179i
$405$	−2.43142	+	30.1185i	−0.120818	+	1.49660i
$406$	3.89225	+	1.29942i	0.193169	+	0.0644893i
$407$	5.02885	−	5.23559i	0.249271	−	0.259519i
$408$		−	38.5214i		−	1.90710i
$409$	−11.6503	−	11.1902i	−0.576069	−	0.553322i	0.347045	−	0.937849i	$-0.387185\pi$
$409$	−11.6503	−	11.1902i	−0.576069	−	0.553322i	−0.923114	+	0.384527i	$0.874365\pi$
$410$	−6.43265	+	5.25209i	−0.317686	+	0.259382i
$411$	3.04233	+	5.79668i	0.150067	+	0.285929i
$412$	−14.1744	−	2.30356i	−0.698321	−	0.113488i
$413$	−7.98123	−	5.04702i	−0.392731	−	0.248348i
$414$	4.52140	+	2.14543i	0.222215	+	0.105442i
$415$	−17.3595	−	25.1496i	−0.852145	−	1.23454i
$416$	−16.5490	−	11.1781i	−0.811380	−	0.548053i
$417$	9.84170	−	14.2582i	0.481950	−	0.698225i
$418$	6.18548	−	3.57119i	0.302542	−	0.174673i
$419$	9.36613	−	19.7387i	0.457565	−	0.964299i	−0.535256	−	0.844690i	$-0.679785\pi$
$419$	9.36613	−	19.7387i	0.457565	−	0.964299i	0.992821	−	0.119609i	$-0.0381640\pi$
$420$	12.9326	−	4.31755i	0.631049	−	0.210675i
$421$	−1.70880	−	6.93287i	−0.0832818	−	0.337887i	0.914490	−	0.404609i	$-0.132592\pi$
$421$	−1.70880	−	6.93287i	−0.0832818	−	0.337887i	−0.997772	+	0.0667214i	$0.978746\pi$
$422$	11.3133	+	0.455912i	0.550724	+	0.0221934i
$423$	6.68994	+	0.269595i	0.325276	+	0.0131082i
$424$	0.634956	+	2.57612i	0.0308362	+	0.125107i
$425$	70.7421	−	23.6172i	3.43150	−	1.14560i
$426$	2.10309	−	4.43217i	0.101895	−	0.214739i
$427$	1.41331	−	0.815973i	0.0683947	−	0.0394877i
$428$	−9.51725	+	13.7881i	−0.460034	+	0.666474i
$429$	7.24605	+	13.4741i	0.349843	+	0.650535i
$430$	1.46985	+	2.12944i	0.0708824	+	0.102691i
$431$	−26.3769	−	12.5160i	−1.27053	−	0.602875i	−0.330451	−	0.943823i	$-0.607201\pi$
$431$	−26.3769	−	12.5160i	−1.27053	−	0.602875i	−0.940082	+	0.340948i	$0.889252\pi$
$432$	−1.70393	−	1.07750i	−0.0819805	−	0.0518413i
$433$	−13.2259	−	2.14942i	−0.635595	−	0.103294i	−0.165928	−	0.986138i	$-0.553062\pi$
$433$	−13.2259	−	2.14942i	−0.635595	−	0.103294i	−0.469667	+	0.882844i	$0.655626\pi$
$434$	0.146434	+	0.279006i	0.00702903	+	0.0133927i
$435$	64.2882	−	52.4897i	3.08239	−	2.51669i
$436$	−3.82124	−	3.67035i	−0.183004	−	0.175778i
$437$			17.5656i			0.840278i
$438$	−9.12644	+	9.50163i	−0.436078	+	0.454005i
$439$	26.3794	+	8.80673i	1.25902	+	0.420323i	0.866387	−	0.499373i	$-0.166436\pi$
$439$	26.3794	+	8.80673i	1.25902	+	0.420323i	0.392633	+	0.919695i	$0.371564\pi$
$440$	1.16207	−	14.3949i	0.0553997	−	0.686249i
$441$	−20.8477	−	5.13850i	−0.992747	−	0.244690i
$442$	−6.04575	−	13.8021i	−0.287567	−	0.656498i
$443$	−16.0778	+	3.96281i	−0.763877	+	0.188279i	−0.601961	−	0.798526i	$-0.705614\pi$
$443$	−16.0778	+	3.96281i	−0.763877	+	0.188279i	−0.161916	+	0.986804i	$0.551768\pi$
$444$	2.88676	+	17.7629i	0.136999	+	0.842992i
$445$	−42.2527	+	51.7501i	−2.00297	+	2.45319i
$446$	4.92670	+	3.70218i	0.233286	+	0.175303i
$447$	8.58936	+	9.69538i	0.406263	+	0.458576i
$448$	0.0884353	−	0.544164i	0.00417817	−	0.0257093i
$449$	2.44403	+	30.2748i	0.115341	+	1.42876i	0.752789	+	0.658262i	$0.228708\pi$
$449$	2.44403	+	30.2748i	0.115341	+	1.42876i	−0.637448	+	0.770493i	$0.720010\pi$
$450$	−5.18195	+	21.0240i	−0.244280	+	0.991081i
$451$	1.63941	−	5.65990i	0.0771968	−	0.266514i
$452$	2.37796	−	11.6480i	0.111850	−	0.547878i
$453$	37.7948	+	30.8585i	1.77575	+	1.44986i
$454$	1.50767	+	12.4168i	0.0707587	+	0.582750i
$455$	8.77108	−	7.92986i	0.411194	−	0.371758i
$456$	−4.73168	+	38.9689i	−0.221581	+	1.82488i
$457$	−2.62498	+	2.52133i	−0.122792	+	0.117943i	−0.751605	−	0.659613i	$-0.770720\pi$
$457$	−2.62498	+	2.52133i	−0.122792	+	0.117943i	0.628814	+	0.777556i	$0.283541\pi$
$458$	−2.37653	−	2.47423i	−0.111048	−	0.115613i
$459$	−3.04371	−	6.41449i	−0.142068	−	0.299403i
$460$	13.1839	+	9.10021i	0.614704	+	0.424299i
$461$	5.45872	+	8.63227i	0.254238	+	0.402045i	0.948055	−	0.318106i	$-0.103047\pi$
$461$	5.45872	+	8.63227i	0.254238	+	0.402045i	−0.693817	+	0.720151i	$0.744072\pi$
$462$	1.26178	−	1.67912i	0.0587031	−	0.0781196i
$463$	−14.8084	+	28.2151i	−0.688206	+	1.31127i	0.251025	+	0.967981i	$0.419232\pi$
$463$	−14.8084	+	28.2151i	−0.688206	+	1.31127i	−0.939231	+	0.343286i	$0.888460\pi$
$464$	−3.29435	−	16.1368i	−0.152936	−	0.749132i
$465$	6.35244	+	0.512822i	0.294587	+	0.0237815i
$466$	−7.90525	+	2.28978i	−0.366203	+	0.106072i
$467$	−35.8485	+	18.8147i	−1.65887	+	0.870643i	−0.666761	+	0.745271i	$0.732320\pi$
$467$	−35.8485	+	18.8147i	−1.65887	+	0.870643i	−0.992110	+	0.125371i	$0.959988\pi$
$468$	−19.9214	−	3.03159i	−0.920866	−	0.140135i
$469$	−2.26250	−	1.18745i	−0.104473	−	0.0548314i
$470$	−4.55889	−	0.930704i	−0.210286	−	0.0429302i
$471$	21.2459	−	15.9653i	0.978959	−	0.735640i
$472$	0.998402	−	24.7751i	0.0459552	−	1.14037i
$473$	−1.71667	−	0.651048i	−0.0789327	−	0.0299352i
$474$	−7.83301	−	2.26886i	−0.359782	−	0.104212i
$475$	−74.4647	+	15.2021i	−3.41668	+	0.697519i
$476$	6.31859	−	7.13221i	0.289612	−	0.326904i
$477$	2.62264	+	3.21215i	0.120083	+	0.147074i
$478$	0.290244	+	7.20233i	0.0132754	+	0.329427i
$479$	−6.11407	+	18.3139i	−0.279359	+	0.836782i	0.711596	+	0.702588i	$0.247972\pi$
$479$	−6.11407	+	18.3139i	−0.279359	+	0.836782i	−0.990955	+	0.134193i	$0.957156\pi$
$480$	41.5073	+	36.7722i	1.89454	+	1.67842i
$481$	8.47403	+	13.1060i	0.386383	+	0.597583i
$482$	−0.398348	+	0.352905i	−0.0181442	+	0.0160744i
$483$	2.02471	+	4.75218i	0.0921277	+	0.216232i
$484$	−6.72687	−	11.6513i	−0.305767	−	0.529604i
$485$	−0.0589442	+	0.102094i	−0.00267652	+	0.00463587i
$486$	−13.2600	−	1.61005i	−0.601485	−	0.0730335i
$487$	2.59942	−	1.23344i	0.117791	−	0.0558925i	−0.368885	−	0.929475i	$-0.620260\pi$
$487$	2.59942	−	1.23344i	0.117791	−	0.0558925i	0.486676	+	0.873582i	$0.338209\pi$
$488$	3.71098	+	2.14254i	0.167988	+	0.0969881i
$489$	6.88679	−	4.75361i	0.311432	−	0.214966i
$490$	13.7276	+	5.84878i	0.620150	+	0.264221i
$491$	−36.3663	+	5.91010i	−1.64119	+	0.266719i	−0.909741	−	0.415177i	$-0.863720\pi$
$491$	−36.3663	+	5.91010i	−1.64119	+	0.266719i	−0.731449	+	0.681896i	$0.761155\pi$
$492$	8.77523	+	11.6777i	0.395618	+	0.526472i
$493$	20.5678	−	54.2329i	0.926329	−	2.44253i
$494$	4.42063	+	14.7050i	0.198894	+	0.661609i
$495$	−8.00399	−	21.1048i	−0.359753	−	0.948590i
$496$	0.675933	−	1.06890i	0.0303503	−	0.0479951i
$497$	2.47514	−	1.05456i	0.111025	−	0.0473034i
$498$	9.86329	−	6.23716i	0.441984	−	0.279494i
$499$	21.9894	−	2.66999i	0.984380	−	0.119525i	0.387512	−	0.921865i	$-0.373335\pi$
$499$	21.9894	−	2.66999i	0.984380	−	0.119525i	0.596868	+	0.802339i	$0.296412\pi$
$500$	−14.4239	+	33.8542i	−0.645058	+	1.51401i
$501$	−6.14656	−	18.4112i	−0.274608	−	0.822552i
$502$	7.59272	−	2.87954i	0.338879	−	0.128520i
$503$	−15.8695	+	1.28112i	−0.707585	+	0.0571222i	−0.429020	−	0.903295i	$-0.641141\pi$
$503$	−15.8695	+	1.28112i	−0.707585	+	0.0571222i	−0.278565	+	0.960417i	$0.589859\pi$
$504$	1.70645	+	5.89137i	0.0760115	+	0.262422i
$505$	−14.8978	+	0.600359i	−0.662942	+	0.0267156i
$506$	2.46782			0.109708
$507$	−31.7694	+	8.51390i	−1.41093	+	0.378116i
$508$	24.9498			1.10697
$509$	34.8656	−	1.40504i	1.54539	−	0.0622772i	0.747167	−	0.664636i	$-0.231413\pi$
$509$	34.8656	−	1.40504i	1.54539	−	0.0622772i	0.798225	+	0.602359i	$0.205772\pi$
$510$	11.6408	+	40.1886i	0.515462	+	1.77958i
$511$	−7.20178	+	0.581388i	−0.318588	+	0.0257191i
$512$	18.3738	−	6.96828i	0.812016	−	0.307957i
$513$	2.29116	+	6.86286i	0.101157	+	0.303003i
$514$	6.63755	−	15.5789i	0.292770	−	0.687156i
$515$	34.3295	−	4.16836i	1.51274	−	0.183680i
$516$	3.84672	−	2.43252i	0.169342	−	0.107086i
$517$	3.03737	−	1.29410i	0.133583	−	0.0569146i
$518$	1.14517	−	1.81095i	0.0503161	−	0.0795685i
$519$	−10.5507	−	27.8199i	−0.463124	−	1.22116i
$520$	29.5475	+	9.53419i	1.29574	+	0.418102i
$521$	−4.33967	+	11.4428i	−0.190125	+	0.501317i	−0.995854	−	0.0909666i	$-0.971004\pi$
$521$	−4.33967	+	11.4428i	−0.190125	+	0.501317i	0.805729	+	0.592284i	$0.201774\pi$
$522$	10.1165	+	13.4626i	0.442787	+	0.589243i
$523$	−18.2775	+	2.97038i	−0.799219	+	0.129886i	−0.546287	−	0.837598i	$-0.683959\pi$
$523$	−18.2775	+	2.97038i	−0.799219	+	0.129886i	−0.252932	+	0.967484i	$0.581395\pi$
$524$	−14.8431	−	6.32404i	−0.648422	−	0.276267i
$525$	−18.3933	+	12.6960i	−0.802750	+	0.554098i
$526$	4.90734	+	2.83326i	0.213970	+	0.123536i
$527$	4.02391	−	1.90937i	0.175284	−	0.0831734i
$528$	−8.36860	−	1.01613i	−0.364197	−	0.0442215i
$529$	8.46538	−	14.6625i	0.368060	−	0.637498i
$530$	−1.44091	−	2.49573i	−0.0625893	−	0.108408i
$531$	−15.1901	−	35.6524i	−0.659194	−	1.54718i
$532$	−7.26804	+	6.43892i	−0.315110	+	0.279163i
$533$	11.0343	+	6.22307i	0.477947	+	0.269551i
$534$	−19.0966	−	16.9181i	−0.826392	−	0.732120i
$535$	12.7761	−	38.2692i	0.552360	−	1.65452i
$536$	−0.270154	−	6.70381i	−0.0116689	−	0.289560i
$537$	8.58834	+	10.5188i	0.370614	+	0.453920i
$538$	−6.45537	+	7.28661i	−0.278311	+	0.314148i
$539$	−10.3739	+	2.11785i	−0.446837	+	0.0912224i
$540$	6.33792	+	1.83580i	0.272741	+	0.0790003i
$541$	−35.0371	−	13.2878i	−1.50636	−	0.571288i	−0.543057	−	0.839696i	$-0.682733\pi$
$541$	−35.0371	−	13.2878i	−1.50636	−	0.571288i	−0.963305	+	0.268407i	$0.913503\pi$
$542$	0.443615	−	11.0082i	0.0190549	−	0.472842i
$543$	−52.7713	+	39.6551i	−2.26464	+	1.70176i
$544$	37.9710	+	7.75184i	1.62799	+	0.332357i
$545$	11.2978	+	5.92956i	0.483946	+	0.253994i
$546$	2.89093	+	3.46872i	0.123721	+	0.148448i
$547$	−9.21786	+	4.83791i	−0.394127	+	0.206854i	−0.650131	−	0.759822i	$-0.725286\pi$
$547$	−9.21786	+	4.83791i	−0.394127	+	0.206854i	0.256004	+	0.966676i	$0.417594\pi$
$548$	−4.08408	+	1.18297i	−0.174463	+	0.0505339i
$549$	6.67561	+	0.538911i	0.284908	+	0.0230002i
$550$	2.13576	+	10.4617i	0.0910693	+	0.446087i
$551$	−27.4683	+	52.3365i	−1.17019	+	2.22961i
$552$	−8.14808	+	10.8431i	−0.346805	+	0.461514i
$553$	−2.39030	−	3.77996i	−0.101646	−	0.160740i
$554$	11.6008	+	8.00747i	0.492872	+	0.340205i
$555$	−18.5782	−	39.1526i	−0.788599	−	1.66194i
$556$	7.79487	+	8.11532i	0.330576	+	0.344166i
$557$	10.0923	−	9.69375i	0.427623	−	0.410737i	−0.447771	−	0.894148i	$-0.647782\pi$
$557$	10.0923	−	9.69375i	0.427623	−	0.410737i	0.875393	+	0.483411i	$0.160602\pi$
$558$	−0.155870	+	1.28370i	−0.00659848	+	0.0543434i
$559$	2.20932	−	3.27086i	0.0934445	−	0.138342i
$560$	0.785356	+	6.46798i	0.0331873	+	0.273322i
$561$	−22.9970	−	18.7765i	−0.970935	−	0.792744i
$562$	1.73497	−	8.49843i	0.0731851	−	0.358485i
$563$	10.4076	−	35.9312i	0.438628	−	1.51432i	−0.371706	−	0.928351i	$-0.621227\pi$
$563$	10.4076	−	35.9312i	0.438628	−	1.51432i	0.810334	−	0.585969i	$-0.199286\pi$
$564$	−1.95865	+	7.94657i	−0.0824742	+	0.334611i
$565$	2.30365	+	28.5358i	0.0969152	+	1.20051i
$566$	1.72824	−	10.6343i	0.0726434	−	0.446993i
$567$	−4.19638	−	4.73674i	−0.176232	−	0.198924i
$568$	5.64757	+	4.24387i	0.236967	+	0.178069i
$569$	9.15370	−	11.2112i	0.383743	−	0.470000i	−0.546226	−	0.837638i	$-0.683936\pi$
$569$	9.15370	−	11.2112i	0.383743	−	0.470000i	0.929969	+	0.367638i	$0.119833\pi$
$570$	−6.83952	−	42.0853i	−0.286476	−	1.76276i
$571$	2.71476	−	0.669129i	0.113609	−	0.0280022i	−0.182101	−	0.983280i	$-0.558290\pi$
$571$	2.71476	−	0.669129i	0.113609	−	0.0280022i	0.295710	+	0.955278i	$0.404444\pi$
$572$	−9.51587	+	2.86067i	−0.397879	+	0.119611i
$573$	42.5338	+	10.4836i	1.77688	+	0.437961i
$574$	0.139946	−	1.73355i	0.00584125	−	0.0723569i
$575$	−24.9082	−	8.31558i	−1.03874	−	0.346784i
$576$	1.56728	−	1.63171i	0.0653034	−	0.0679880i
$577$			17.4959i			0.728363i	0.931328	+	0.364181i	$0.118651\pi$
$577$			17.4959i			0.728363i	−0.931328	+	0.364181i	$0.881349\pi$
$578$	13.7656	+	13.2220i	0.572572	+	0.549962i
$579$	33.6373	−	27.4640i	1.39792	−	1.14137i
$580$	25.0508	+	47.7303i	1.04018	+	1.98189i
$581$	6.31708	+	1.02662i	0.262076	+	0.0425916i
$582$	−0.0380499	−	0.0240613i	−0.00157722	−	0.000997373i
$583$	1.84742	+	0.876612i	0.0765123	+	0.0363056i
$584$	−10.7771	−	15.6133i	−0.445958	−	0.646082i
$585$	48.1104	−	6.33480i	1.98912	−	0.261912i
$586$	2.84547	−	4.12237i	0.117545	−	0.170293i
$587$	23.6521	−	13.6555i	0.976225	−	0.563624i	0.0750967	−	0.997176i	$-0.476073\pi$
$587$	23.6521	−	13.6555i	0.976225	−	0.563624i	0.901128	+	0.433553i	$0.142740\pi$
$588$	11.2518	−	23.7127i	0.464018	−	0.977897i
$589$	−4.30518	+	1.43728i	−0.177392	+	0.0592221i
$590$	6.44516	+	26.1491i	0.265343	+	1.07654i
$591$	1.70132	+	0.0685608i	0.0699829	+	0.00282021i
$592$	−8.59284	−	0.346280i	−0.353164	−	0.0142320i
$593$	−2.38260	−	9.66657i	−0.0978415	−	0.396959i	0.901518	−	0.432741i	$-0.142454\pi$
$593$	−2.38260	−	9.66657i	−0.0978415	−	0.396959i	−0.999360	+	0.0357828i	$0.988608\pi$
$594$	0.964175	−	0.321889i	0.0395606	−	0.0132073i
$595$	−9.83678	+	20.7306i	−0.403269	+	0.849871i
$596$	−7.28574	+	4.20642i	−0.298435	+	0.172302i
$597$	−0.848956	+	1.22993i	−0.0347455	+	0.0503375i
$598$	−1.21765	+	5.16385i	−0.0497934	+	0.211165i
$599$	0.542710	+	0.786250i	0.0221745	+	0.0321253i	0.833914	−	0.551894i	$-0.186095\pi$
$599$	0.542710	+	0.786250i	0.0221745	+	0.0321253i	−0.811740	+	0.584019i	$0.801479\pi$
$600$	−53.0182	−	25.1575i	−2.16446	−	1.02705i
$601$	14.8450	+	9.38738i	0.605538	+	0.382919i	0.801765	−	0.597639i	$-0.203895\pi$
$601$	14.8450	+	9.38738i	0.605538	+	0.382919i	−0.196227	+	0.980559i	$0.562869\pi$
$602$	−0.534874	−	0.0869255i	−0.0217998	−	0.00354282i
$603$	−4.87317	−	9.28505i	−0.198451	−	0.378117i
$604$	−24.5475	+	20.0424i	−0.998824	+	0.815515i
$605$	23.3658	+	22.4432i	0.949956	+	0.912445i
$606$		−	5.69378i		−	0.231294i
$607$	11.0908	−	11.5468i	0.450162	−	0.468669i	−0.456989	−	0.889472i	$-0.651072\pi$
$607$	11.0908	−	11.5468i	0.450162	−	0.468669i	0.907152	+	0.420803i	$0.138252\pi$
$608$	−37.4599	−	12.5059i	−1.51920	−	0.507183i
$609$	−1.39863	+	17.3252i	−0.0566755	+	0.702052i
$610$	−4.51905	−	1.11384i	−0.182971	−	0.0450983i
$611$	1.20920	+	6.99413i	0.0489191	+	0.282952i
$612$	37.9678	−	9.35821i	1.53476	−	0.378283i
$613$	1.75125	+	10.7759i	0.0707322	+	0.435233i	0.998128	+	0.0611522i	$0.0194775\pi$
$613$	1.75125	+	10.7759i	0.0707322	+	0.435233i	−0.927396	+	0.374080i	$0.877958\pi$
$614$	7.84733	−	9.61124i	0.316693	−	0.387878i
$615$	−28.1215	−	21.1319i	−1.13397	−	0.852122i
$616$	2.00562	+	2.26388i	0.0808089	+	0.0912144i
$617$	6.32854	−	38.9411i	0.254778	−	1.56771i	−0.472478	−	0.881342i	$-0.656640\pi$
$617$	6.32854	−	38.9411i	0.254778	−	1.56771i	0.727256	−	0.686367i	$-0.240796\pi$
$618$	1.06265	+	13.1632i	0.0427459	+	0.529503i
$619$	4.55502	−	18.4804i	0.183082	−	0.742791i	−0.805562	−	0.592512i	$-0.798136\pi$
$619$	4.55502	−	18.4804i	0.183082	−	0.742791i	0.988644	−	0.150280i	$-0.0480174\pi$
$620$	−1.15163	+	3.97587i	−0.0462504	+	0.159675i
$621$	−0.500044	+	2.44938i	−0.0200661	+	0.0982901i
$622$	4.08934	+	3.33884i	0.163967	+	0.133875i
$623$	−1.68651	−	13.8896i	−0.0675684	−	0.556476i
$624$	6.25538	−	17.0097i	0.250416	−	0.680933i
$625$	4.25749	−	35.0636i	0.170300	−	1.40254i
$626$	10.2973	−	9.89073i	0.411564	−	0.395313i
$627$	20.9578	+	21.8194i	0.836973	+	0.871381i
$628$	7.39962	+	15.5944i	0.295277	+	0.622283i
$629$	−24.9253	−	17.2047i	−0.993837	−	0.685996i
$630$	−3.56062	−	5.63067i	−0.141858	−	0.224331i
$631$	−14.3061	+	19.0380i	−0.569517	+	0.757889i	−0.988683	−	0.150020i	$-0.952066\pi$
$631$	−14.3061	+	19.0380i	−0.569517	+	0.757889i	0.419166	+	0.907910i	$0.362322\pi$
$632$	5.45732	−	10.3981i	0.217081	−	0.413613i
$633$	9.59336	+	46.9914i	0.381302	+	1.86774i
$634$	−9.59125	−	0.774286i	−0.380917	−	0.0307508i
$635$	−57.7102	+	16.7160i	−2.29016	+	0.663353i
$636$	−4.48844	+	2.35572i	−0.177978	+	0.0934102i
$637$	0.687058	−	22.7521i	0.0272222	−	0.901472i
$638$	7.35283	+	3.85906i	0.291101	+	0.152782i
$639$	10.8181	+	2.20853i	0.427957	+	0.0873681i
$640$	−36.3012	+	27.2786i	−1.43493	+	1.07828i
$641$	−1.59713	+	39.6324i	−0.0630829	+	1.56539i	0.589563	+	0.807722i	$0.299300\pi$
$641$	−1.59713	+	39.6324i	−0.0630829	+	1.56539i	−0.652646	+	0.757663i	$0.726341\pi$
$642$	14.4059	+	5.46345i	0.568557	+	0.215625i
$643$	28.3238	+	8.20409i	1.11698	+	0.323538i	0.784844	−	0.619693i	$-0.212743\pi$
$643$	28.3238	+	8.20409i	1.11698	+	0.323538i	0.332138	+	0.943231i	$0.392230\pi$
$644$	−3.28718	+	0.671083i	−0.129533	+	0.0264444i
$645$	−7.26793	+	8.20380i	−0.286174	+	0.323024i
$646$	−18.8455	−	23.0815i	−0.741465	−	0.908129i
$647$	0.532911	+	13.2241i	0.0209509	+	0.519891i	0.975259	+	0.221066i	$0.0709537\pi$
$647$	0.532911	+	13.2241i	0.0209509	+	0.519891i	−0.954308	+	0.298825i	$0.903405\pi$
$648$	5.26184	−	15.7611i	0.206705	−	0.619156i
$649$	−14.3039	−	12.6722i	−0.561477	−	0.497425i
$650$	−22.9445	−	0.692869i	−0.899959	−	0.0271766i
$651$	−0.999048	+	0.885079i	−0.0391558	+	0.0346890i
$652$	2.13035	+	5.00011i	0.0834309	+	0.195820i
$653$	−7.60819	−	13.1778i	−0.297731	−	0.515686i	0.677885	−	0.735168i	$-0.262897\pi$
$653$	−7.60819	−	13.1778i	−0.297731	−	0.515686i	−0.975617	+	0.219482i	$0.929563\pi$
$654$	−2.43627	+	4.21975i	−0.0952658	+	0.165005i
$655$	38.5699	+	4.68323i	1.50705	+	0.182989i
$656$	−6.30650	+	2.99247i	−0.246227	+	0.116836i
$657$	−25.6789	−	14.8257i	−1.00183	−	0.578407i
$658$	0.801963	−	0.553555i	0.0312638	−	0.0215798i
$659$	−40.0454	−	17.0617i	−1.55995	−	0.664631i	−0.572118	−	0.820172i	$-0.693878\pi$
$659$	−40.0454	−	17.0617i	−1.55995	−	0.664631i	−0.987830	+	0.155540i	$0.950288\pi$
$660$	27.2341	−	4.42598i	1.06009	−	0.172281i
$661$	19.0799	+	25.3908i	0.742123	+	0.987586i	0.999772	+	0.0213477i	$0.00679570\pi$
$661$	19.0799	+	25.3908i	0.742123	+	0.987586i	−0.257649	+	0.966239i	$0.582948\pi$
$662$	6.00987	−	15.8467i	0.233580	−	0.615901i
$663$	50.6362	−	38.8561i	1.96655	−	1.50905i
$664$	5.95901	+	15.7126i	0.231254	+	0.609767i
$665$	12.4974	−	19.7631i	0.484629	−	0.766380i
$666$	8.08958	−	3.44665i	0.313465	−	0.133555i
$667$	−17.2609	+	10.9151i	−0.668344	+	0.422635i
$668$	12.5149	−	1.51958i	0.484214	−	0.0587943i
$669$	−10.2320	+	24.0154i	−0.395591	+	0.928487i
$670$	2.30767	+	6.91231i	0.0891530	+	0.267046i
$671$	3.08792	−	1.17109i	0.119208	−	0.0452096i
$672$	−11.5758	+	0.934499i	−0.446548	+	0.0360491i
$673$	−10.2312	−	35.3221i	−0.394383	−	1.36157i	−0.874782	−	0.484517i	$-0.838995\pi$
$673$	−10.2312	−	35.3221i	−0.394383	−	1.36157i	0.480399	−	0.877050i	$-0.340492\pi$
$674$	−3.30275	+	0.133096i	−0.127217	+	0.00512668i
$675$	−10.8162			−0.416317
$676$	−1.29064	−	21.3232i	−0.0496399	−	0.820122i
$677$	28.2190			1.08454			0.542272	−	0.840203i	$-0.317564\pi$
$677$	28.2190			1.08454			0.542272	+	0.840203i	$0.317564\pi$
$678$	−10.9239	+	0.440216i	−0.419528	+	0.0169064i
$679$	−0.00686899	−	0.0237145i	−0.000263608	−	0.000910079i
$680$	−60.0550	+	4.84814i	−2.30300	+	0.185918i
$681$	−49.5392	+	18.7878i	−1.89835	+	0.719948i
$682$	0.201926	+	0.604841i	0.00773213	+	0.0231606i
$683$	5.08466	−	11.9341i	0.194559	−	0.456647i	−0.793917	−	0.608027i	$-0.791961\pi$
$683$	5.08466	−	11.9341i	0.194559	−	0.456647i	0.988476	+	0.151380i	$0.0483716\pi$
$684$	−39.5583	+	4.80324i	−1.51255	+	0.183657i
$685$	8.65414	−	5.47255i	0.330658	−	0.209095i
$686$	−6.06269	+	2.58307i	−0.231475	+	0.0986221i
$687$	7.76684	−	12.2823i	0.296323	−	0.468598i
$688$	0.771248	+	2.03361i	0.0294036	+	0.0775308i
$689$	−2.74582	+	3.43314i	−0.104607	+	0.130792i
$690$	5.22404	−	13.7747i	0.198876	−	0.524393i
$691$	4.18825	+	5.57354i	0.159328	+	0.212028i	0.872047	−	0.489423i	$-0.162793\pi$
$691$	4.18825	+	5.57354i	0.159328	+	0.212028i	−0.712718	+	0.701450i	$0.752536\pi$
$692$	19.0744	−	3.09989i	0.725100	−	0.117840i
$693$	4.34888	+	1.85288i	0.165200	+	0.0703853i
$694$	−4.19553	+	2.89597i	−0.159260	+	0.109929i
$695$	−23.4671	−	13.5488i	−0.890159	−	0.513934i
$696$	−41.2330	+	19.5653i	−1.56293	+	0.741621i
$697$	−24.4043	−	2.96321i	−0.924378	−	0.112240i
$698$	2.28165	−	3.95193i	0.0863616	−	0.149583i
$699$	−17.4310	−	30.1913i	−0.659300	−	1.14194i
$700$	−5.68975	−	13.3543i	−0.215052	−	0.504747i
$701$	−4.88998	+	4.33214i	−0.184692	+	0.163623i	−0.750403	−	0.660981i	$-0.770140\pi$
$701$	−4.88998	+	4.33214i	−0.184692	+	0.163623i	0.565711	+	0.824604i	$0.308602\pi$
$702$	0.197809	+	2.17633i	0.00746583	+	0.0821403i
$703$	23.1015	+	20.4662i	0.871291	+	0.771896i
$704$	0.353294	−	1.05824i	0.0133153	−	0.0398841i
$705$	−0.793607	−	19.6932i	−0.0298890	−	0.741687i
$706$	1.89731	+	2.32379i	0.0714063	+	0.0874569i
$707$	2.07064	−	2.33727i	0.0778744	−	0.0879020i
$708$	46.4148	−	9.47566i	1.74438	−	0.356117i
$709$	39.0057	+	11.2981i	1.46489	+	0.424310i	0.912431	−	0.409231i	$-0.134203\pi$
$709$	39.0057	+	11.2981i	1.46489	+	0.424310i	0.552458	+	0.833541i	$0.313690\pi$
$710$	−7.17445	−	2.72091i	−0.269252	−	0.102114i
$711$	0.739038	−	18.3390i	0.0277161	−	0.687767i
$712$	29.3703	−	22.0703i	1.10070	−	0.827121i
$713$	−1.53653	−	0.313685i	−0.0575436	−	0.0117476i
$714$	−7.75893	−	4.07220i	−0.290371	−	0.152398i
$715$	20.0942	−	12.9924i	0.751479	−	0.485888i
$716$	−7.80961	+	4.09880i	−0.291859	+	0.153179i
$717$	−29.3273	+	8.49477i	−1.09525	+	0.317243i
$718$	−11.2313	−	0.906681i	−0.419147	−	0.0338370i
$719$	−1.01967	−	4.99465i	−0.0380271	−	0.186269i	0.956341	−	0.292255i	$-0.0944054\pi$
$719$	−1.01967	−	4.99465i	−0.0380271	−	0.186269i	−0.994368	+	0.105985i	$0.966200\pi$
$720$	−12.4262	+	23.6761i	−0.463096	+	0.882356i
$721$	−4.35082	+	5.78989i	−0.162033	+	0.215627i
$722$	10.1638	+	16.0728i	0.378258	+	0.598167i
$723$	−1.85523	−	1.28057i	−0.0689967	−	0.0476250i
$724$	−18.3795	−	38.7339i	−0.683067	−	1.43953i
$725$	−61.2100	−	63.7264i	−2.27328	−	2.36674i
$726$	−8.92296	+	8.57062i	−0.331162	+	0.318086i
$727$	−3.28409	+	27.0469i	−0.121800	+	1.00312i	0.795786	+	0.605578i	$0.207058\pi$
$727$	−3.28409	+	27.0469i	−0.121800	+	1.00312i	−0.917586	+	0.397537i	$0.869865\pi$
$728$	−5.72670	+	3.07969i	−0.212246	+	0.114141i
$729$	−4.05875	−	33.4268i	−0.150324	−	1.23803i
$730$	15.9617	+	13.0323i	0.590768	+	0.482347i
$731$	−1.53213	+	7.50486i	−0.0566678	+	0.277577i
$732$	−2.27771	+	7.86357i	−0.0841866	+	0.290646i
$733$	9.92446	−	40.2651i	0.366568	−	1.48723i	−0.441030	−	0.897492i	$-0.645387\pi$
$733$	9.92446	−	40.2651i	0.366568	−	1.48723i	0.807598	−	0.589733i	$-0.200767\pi$
$734$	0.426822	+	5.28713i	0.0157543	+	0.195152i
$735$	−10.1390	+	62.3875i	−0.373981	+	2.30120i
$736$	−9.04851	−	10.2137i	−0.333533	−	0.376481i
$737$	−4.13381	−	3.10635i	−0.152271	−	0.114424i
$738$	4.51404	−	5.52869i	0.166164	−	0.203514i
$739$	3.54166	+	21.7927i	0.130282	+	0.801657i	0.967141	+	0.254239i	$0.0818251\pi$
$739$	3.54166	+	21.7927i	0.130282	+	0.801657i	−0.836859	+	0.547418i	$0.815611\pi$
$740$	27.3291	−	6.73602i	1.00464	−	0.247621i
$741$	−55.9971	+	33.0876i	−2.05711	+	1.21550i
$742$	0.586001	+	0.144436i	0.0215128	+	0.00530242i
$743$	−3.09791	+	38.3745i	−0.113651	+	1.40782i	0.648889	+	0.760883i	$0.275234\pi$
$743$	−3.09791	+	38.3745i	−0.113651	+	1.40782i	−0.762540	+	0.646941i	$0.776048\pi$
$744$	−3.32426	−	1.10980i	−0.121873	−	0.0406872i
$745$	14.0341	−	14.6110i	0.514169	−	0.535307i
$746$			3.48849i			0.127723i
$747$	18.9422	+	18.1942i	0.693058	+	0.665691i
$748$	14.9365	−	12.1952i	0.546131	−	0.445902i
$749$	3.92669	+	7.48168i	0.143478	+	0.273375i
$750$	33.4028	+	5.42848i	1.21970	+	0.198220i
$751$	42.3783	+	26.7984i	1.54641	+	0.977889i	0.989044	+	0.147620i	$0.0471613\pi$
$751$	42.3783	+	26.7984i	1.54641	+	0.977889i	0.557363	+	0.830269i	$0.311813\pi$
$752$	−3.53350	−	1.67667i	−0.128853	−	0.0611417i
$753$	19.5397	+	28.3081i	0.712066	+	1.03161i
$754$	−11.7029	+	13.4815i	−0.426196	+	0.490967i
$755$	43.3517	−	62.8058i	1.57773	−	2.28574i
$756$	−1.19677	+	0.690953i	−0.0435259	+	0.0251297i
$757$	15.5053	−	32.6768i	0.563551	−	1.18766i	−0.399099	−	0.916908i	$-0.630677\pi$
$757$	15.5053	−	32.6768i	0.563551	−	1.18766i	0.962650	−	0.270751i	$-0.0872719\pi$
$758$	−16.2384	+	5.42117i	−0.589804	+	0.196906i
$759$	2.50165	+	10.1496i	0.0908042	+	0.368407i
$760$	61.3480	+	2.47224i	2.22533	+	0.0896776i
$761$	−14.2485	−	0.574196i	−0.516509	−	0.0208146i	−0.219357	−	0.975645i	$-0.570396\pi$
$761$	−14.2485	−	0.574196i	−0.516509	−	0.0208146i	−0.297152	+	0.954830i	$0.596037\pi$
$762$	−5.49093	−	22.2776i	−0.198915	−	0.807032i
$763$	−2.53466	+	0.846193i	−0.0917608	+	0.0306343i
$764$	−12.1973	+	25.7052i	−0.441282	+	0.929983i
$765$	−81.5518	+	47.0840i	−2.94851	+	1.70232i
$766$	5.52891	−	8.01001i	0.199768	−	0.289413i

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.k (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.596805 - 0.0240504i) q^{2} +(0.703900 + 2.43014i) q^{3} +(-1.63792 + 0.132226i) q^{4} +(3.70001 - 1.40323i) q^{5} +(0.478537 + 1.43339i) q^{6} +(-0.324840 + 0.762428i) q^{7} +(-2.16021 + 0.262296i) q^{8} +(-2.87456 + 1.81776i) q^{9} +O(q^{10})\)	\(q+(0.596805 - 0.0240504i) q^{2} +(0.703900 + 2.43014i) q^{3} +(-1.63792 + 0.132226i) q^{4} +(3.70001 - 1.40323i) q^{5} +(0.478537 + 1.43339i) q^{6} +(-0.324840 + 0.762428i) q^{7} +(-2.16021 + 0.262296i) q^{8} +(-2.87456 + 1.81776i) q^{9} +(2.17443 - 0.926440i) q^{10} +(-0.896359 + 1.41748i) q^{11} +(-1.47426 - 3.88730i) q^{12} +(-2.52376 - 2.57500i) q^{13} +(-0.175530 + 0.462833i) q^{14} +(6.01448 + 8.00382i) q^{15} +(1.96102 - 0.318697i) q^{16} +(6.43696 + 2.74253i) q^{17} +(-1.67183 + 1.15398i) q^{18} +(-6.17486 - 3.56505i) q^{19} +(-5.87476 + 2.78761i) q^{20} +(-2.08147 - 0.252736i) q^{21} +(-0.500860 + 0.867515i) q^{22} +(-1.23179 - 2.13353i) q^{23} +(-2.15799 - 5.06498i) q^{24} +(7.97846 - 7.06830i) q^{25} +(-1.56812 - 1.47608i) q^{26} +(-0.759544 - 0.672898i) q^{27} +(0.431248 - 1.29175i) q^{28} +(-0.333794 - 8.28302i) q^{29} +(3.78197 + 4.63207i) q^{30} +(0.422119 - 0.476474i) q^{31} +(5.42687 - 1.10790i) q^{32} +(-4.07562 - 1.18052i) q^{33} +(3.90757 + 1.48195i) q^{34} +(-0.132051 + 3.27682i) q^{35} +(4.46793 - 3.35743i) q^{36} +(-4.24111 - 0.865829i) q^{37} +(-3.77092 - 1.97913i) q^{38} +(4.48116 - 7.94564i) q^{39} +(-7.62472 + 4.00176i) q^{40} +(-3.37479 + 0.977520i) q^{41} +(-1.24831 - 0.100774i) q^{42} +(0.218974 + 1.07261i) q^{43} +(1.28073 - 2.44023i) q^{44} +(-8.08515 + 10.7594i) q^{45} +(-0.786451 - 1.24367i) q^{46} +(-1.62013 - 1.11829i) q^{47} +(2.15484 + 4.54123i) q^{48} +(4.37330 + 4.55308i) q^{49} +(4.59159 - 4.41028i) q^{50} +(-2.13377 + 17.5732i) q^{51} +(4.47419 + 3.88393i) q^{52} +(-0.146967 - 1.21038i) q^{53} +(-0.469483 - 0.383321i) q^{54} +(-1.32749 + 6.50248i) q^{55} +(0.501739 - 1.73221i) q^{56} +(4.31712 - 17.5152i) q^{57} +(-0.398420 - 4.93532i) q^{58} +(-1.82780 + 11.2469i) q^{59} +(-10.9095 - 12.3143i) q^{60} +(-1.57425 - 1.18297i) q^{61} +(0.240463 - 0.294514i) q^{62} +(-0.452139 - 2.78212i) q^{63} +(-0.645897 + 0.159199i) q^{64} +(-12.9512 - 5.98612i) q^{65} +(-2.46074 - 0.606519i) q^{66} +(-0.248094 + 3.07320i) q^{67} +(-10.9058 - 3.64091i) q^{68} +(4.31772 - 4.49522i) q^{69} +1.95880i q^{70} +(-2.34131 - 2.24886i) q^{71} +(5.73284 - 4.68072i) q^{72} +(4.05158 + 7.71964i) q^{73} +(-2.55194 - 0.414731i) q^{74} +(22.7930 + 14.4134i) q^{75} +(10.5853 + 5.02279i) q^{76} +(-0.789552 - 1.14386i) q^{77} +(2.48328 - 4.84977i) q^{78} +(-3.06556 + 4.44123i) q^{79} +(6.80859 - 3.93094i) q^{80} +(-3.27346 + 6.89866i) q^{81} +(-1.99058 + 0.664553i) q^{82} +(-1.84811 - 7.49807i) q^{83} +(3.44269 + 0.138736i) q^{84} +(27.6652 + 1.11487i) q^{85} +(0.156481 + 0.634870i) q^{86} +(19.8940 - 6.64159i) q^{87} +(1.56452 - 3.29715i) q^{88} +(-14.6210 + 8.44146i) q^{89} +(-4.56649 + 6.61570i) q^{90} +(2.78307 - 1.08772i) q^{91} +(2.29968 + 3.33166i) q^{92} +(1.45503 + 0.690420i) q^{93} +(-0.993795 - 0.628438i) q^{94} +(-27.8496 - 4.52600i) q^{95} +(6.51234 + 12.4082i) q^{96} +(-0.0230764 + 0.0188413i) q^{97} +(2.71951 + 2.61212i) q^{98} -5.70399i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9}+O(q^{10}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9	\( 360 q - 23 q^{2} - 24 q^{3} - 41 q^{4} - 26 q^{5} - 32 q^{6} - 26 q^{7} - 26 q^{8} - 11 q^{9} - 27 q^{10} - 26 q^{11} - 14 q^{12} - 34 q^{13} - 30 q^{14} - 84 q^{15} - 13 q^{16} - 31 q^{17} + 52 q^{18} - 33 q^{19} - 29 q^{20} - 26 q^{21} - 33 q^{22} + 57 q^{23} + 58 q^{24} + 2 q^{25} - 29 q^{26} - 30 q^{27} - 26 q^{28} - 19 q^{29} + 178 q^{30} - 78 q^{31} - 30 q^{32} - 26 q^{33} - 91 q^{34} - 18 q^{35} - 51 q^{36} - 41 q^{37} + 25 q^{38} + 12 q^{39} - 134 q^{40} - 17 q^{41} + 250 q^{42} - 28 q^{43} + 42 q^{45} + 18 q^{46} + 117 q^{47} - 57 q^{48} - 117 q^{49} - 20 q^{50} - 59 q^{51} + 37 q^{52} - 75 q^{53} + 118 q^{54} + 64 q^{55} - 42 q^{56} - 104 q^{57} - 87 q^{58} + 170 q^{59} + 78 q^{60} - 15 q^{61} + 19 q^{62} + 39 q^{63} + 32 q^{64} - 17 q^{65} + 73 q^{66} + 20 q^{67} - 76 q^{68} - 11 q^{69} + 46 q^{71} - 198 q^{72} - 26 q^{73} + 29 q^{74} - 70 q^{75} + 58 q^{76} + 6 q^{77} + 128 q^{78} - 54 q^{79} - 24 q^{80} - 7 q^{81} + 81 q^{82} + 234 q^{83} - 273 q^{84} - 74 q^{85} + 52 q^{86} - 112 q^{87} + 256 q^{88} - 27 q^{89} + 28 q^{90} - 78 q^{91} - 34 q^{92} + 51 q^{93} + 28 q^{94} - 11 q^{95} + 143 q^{96} + 40 q^{97} - 47 q^{98}+O(q^{100}) \) 360 * q - 23 * q^2 - 24 * q^3 - 41 * q^4 - 26 * q^5 - 32 * q^6 - 26 * q^7 - 26 * q^8 - 11 * q^9 - 27 * q^10 - 26 * q^11 - 14 * q^12 - 34 * q^13 - 30 * q^14 - 84 * q^15 - 13 * q^16 - 31 * q^17 + 52 * q^18 - 33 * q^19 - 29 * q^20 - 26 * q^21 - 33 * q^22 + 57 * q^23 + 58 * q^24 + 2 * q^25 - 29 * q^26 - 30 * q^27 - 26 * q^28 - 19 * q^29 + 178 * q^30 - 78 * q^31 - 30 * q^32 - 26 * q^33 - 91 * q^34 - 18 * q^35 - 51 * q^36 - 41 * q^37 + 25 * q^38 + 12 * q^39 - 134 * q^40 - 17 * q^41 + 250 * q^42 - 28 * q^43 + 42 * q^45 + 18 * q^46 + 117 * q^47 - 57 * q^48 - 117 * q^49 - 20 * q^50 - 59 * q^51 + 37 * q^52 - 75 * q^53 + 118 * q^54 + 64 * q^55 - 42 * q^56 - 104 * q^57 - 87 * q^58 + 170 * q^59 + 78 * q^60 - 15 * q^61 + 19 * q^62 + 39 * q^63 + 32 * q^64 - 17 * q^65 + 73 * q^66 + 20 * q^67 - 76 * q^68 - 11 * q^69 + 46 * q^71 - 198 * q^72 - 26 * q^73 + 29 * q^74 - 70 * q^75 + 58 * q^76 + 6 * q^77 + 128 * q^78 - 54 * q^79 - 24 * q^80 - 7 * q^81 + 81 * q^82 + 234 * q^83 - 273 * q^84 - 74 * q^85 + 52 * q^86 - 112 * q^87 + 256 * q^88 - 27 * q^89 + 28 * q^90 - 78 * q^91 - 34 * q^92 + 51 * q^93 + 28 * q^94 - 11 * q^95 + 143 * q^96 + 40 * q^97 - 47 * q^98

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