LMFDB - Embedded newform 169.2.k.a.4.10

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			4.10
Character	$\chi$	$=$	169.4
Dual form			169.2.k.a.127.10

$q$-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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{78}\right)$

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	0.250360	−	0.968153i	$-0.419451\pi$
$2$	0.596805	+	0.0240504i	0.422005	+	0.0170062i	0.171644	+	0.985159i	$0.445092\pi$
$3$	0.703900	−	2.43014i	0.406397	−	1.40304i	−0.452897	−	0.891563i	$-0.649610\pi$
$3$	0.703900	−	2.43014i	0.406397	−	1.40304i	0.859294	−	0.511482i	$-0.170903\pi$
$4$	−1.63792	−	0.132226i	−0.818959	−	0.0661132i
$5$	3.70001	+	1.40323i	1.65469	+	0.627543i	0.992550	−	0.121834i	$-0.0388776\pi$
$5$	3.70001	+	1.40323i	1.65469	+	0.627543i	0.662144	+	0.749377i	$0.269647\pi$
$6$	0.478537	−	1.43339i	0.195362	−	0.585180i
$7$	−0.324840	−	0.762428i	−0.122778	−	0.288171i	0.847237	−	0.531215i	$-0.178264\pi$
$7$	−0.324840	−	0.762428i	−0.122778	−	0.288171i	−0.970015	+	0.243044i	$0.921854\pi$
$8$	−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	0.682598	−	0.730794i	$-0.260850\pi$
$11$	−0.896359	−	1.41748i	−0.270262	−	0.427386i	−0.952861	+	0.303408i	$0.901875\pi$
$12$	−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	0.573165	−	0.819440i	$-0.305715\pi$
$17$	6.43696	−	2.74253i	1.56119	−	0.665162i	0.988027	+	0.154278i	$0.0493051\pi$
$18$	−1.67183	−	1.15398i	−0.394054	−	0.271996i
$19$	−6.17486	+	3.56505i	−1.41661	+	0.817880i	−0.995999	−	0.0893619i	$-0.971517\pi$
$19$	−6.17486	+	3.56505i	−1.41661	+	0.817880i	−0.420610	+	0.907242i	$0.638184\pi$
$20$	−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	−0.965395	−	0.260791i	$-0.916017\pi$
$23$	−1.23179	+	2.13353i	−0.256846	+	0.444871i	0.708549	+	0.705662i	$0.249350\pi$
$24$	−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	0.606916	+	0.794766i	$0.292406\pi$
$29$	−0.333794	+	8.28302i	−0.0619841	+	1.53812i	−0.668900	+	0.743352i	$0.733235\pi$
$30$	3.78197	−	4.63207i	0.690490	−	0.845696i
$31$	0.422119	+	0.476474i	0.0758148	+	0.0855772i	0.785194	−	0.619250i	$-0.212563\pi$
$31$	0.422119	+	0.476474i	0.0758148	+	0.0855772i	−0.709379	+	0.704827i	$0.751025\pi$
$32$	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	−0.535553	−	0.844502i	$-0.679897\pi$
$37$	−4.24111	+	0.865829i	−0.697235	+	0.142341i	−0.161681	+	0.986843i	$0.551692\pi$
$38$	−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	0.00401474	−	0.999992i	$-0.498722\pi$
$41$	−3.37479	−	0.977520i	−0.527054	−	0.152663i	−0.531068	+	0.847329i	$0.678209\pi$
$42$	−1.24831	+	0.100774i	−0.192618	+	0.0155497i
$43$	0.218974	−	1.07261i	0.0333932	−	0.163571i	−0.959675	−	0.281113i	$-0.909296\pi$
$43$	0.218974	−	1.07261i	0.0333932	−	0.163571i	0.993068	+	0.117542i	$0.0375015\pi$
$44$	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	−0.680339	−	0.732897i	$-0.738168\pi$
$47$	−1.62013	+	1.11829i	−0.236320	+	0.163120i	0.444019	+	0.896017i	$0.353552\pi$
$48$	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	−0.999316	−	0.0369841i	$-0.988225\pi$
$53$	−0.146967	+	1.21038i	−0.0201874	+	0.166258i	0.979128	+	0.203242i	$0.0651480\pi$
$54$	−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	−0.781007	−	0.624523i	$-0.785294\pi$
$59$	−1.82780	−	11.2469i	−0.237960	−	1.46423i	0.543047	−	0.839702i	$-0.317271\pi$
$60$	−10.9095	+	12.3143i	−1.40842	+	1.58977i
$61$	−1.57425	+	1.18297i	−0.201562	+	0.151464i	−0.696730	−	0.717333i	$-0.745363\pi$
$61$	−1.57425	+	1.18297i	−0.201562	+	0.151464i	0.495169	+	0.868797i	$0.335106\pi$
$62$	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	−0.994075	−	0.108699i	$-0.965332\pi$
$67$	−0.248094	−	3.07320i	−0.0303095	−	0.375451i	0.963765	−	0.266752i	$-0.0859504\pi$
$68$	−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	−0.818681	−	0.574249i	$-0.805294\pi$
$71$	−2.34131	+	2.24886i	−0.277862	+	0.266890i	0.540819	+	0.841139i	$0.318115\pi$
$72$	5.73284	+	4.68072i	0.675622	+	0.551628i
$73$	4.05158	−	7.71964i	0.474201	−	0.903515i	−0.524442	−	0.851446i	$-0.675726\pi$
$73$	4.05158	−	7.71964i	0.474201	−	0.903515i	0.998643	−	0.0520689i	$-0.0165816\pi$
$74$	−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	0.611693	−	0.791095i	$-0.290489\pi$
$79$	−3.06556	−	4.44123i	−0.344903	−	0.499678i	−0.956596	+	0.291417i	$0.905873\pi$
$80$	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	0.777997	+	0.628269i	$0.216236\pi$
$83$	−1.84811	+	7.49807i	−0.202856	+	0.823020i	−0.980853	+	0.194751i	$0.937610\pi$
$84$	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	−0.998154	−	0.0607327i	$-0.980656\pi$
$89$	−14.6210	−	8.44146i	−1.54983	−	0.894793i	−0.551673	−	0.834060i	$-0.686010\pi$
$90$	−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	0.631273	−	0.775561i	$-0.282533\pi$
$97$	−0.0230764	−	0.0188413i	−0.00234305	−	0.00191304i	−0.633616	+	0.773648i	$0.718430\pi$
$98$	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	−0.488863	−	0.872360i	$-0.662588\pi$
$101$	−3.57391	+	1.19315i	−0.355618	+	0.118723i	0.133246	+	0.991083i	$0.457460\pi$
$102$	−0.850804	−	10.5391i	−0.0842421	−	1.04353i
$103$	8.48507	−	2.09138i	0.836058	−	0.206070i	0.202030	−	0.979379i	$-0.435246\pi$
$103$	8.48507	−	2.09138i	0.836058	−	0.206070i	0.634029	+	0.773309i	$0.281400\pi$
$104$	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	0.985690	−	0.168568i	$-0.0539144\pi$
$107$	6.44814	+	7.89753i	0.623365	+	0.763483i	−0.362325	+	0.932052i	$0.618017\pi$
$108$	1.33305	−	1.00172i	0.128272	−	0.0963904i
$109$	2.13815	−	2.41347i	0.204798	−	0.231169i	−0.637134	−	0.770753i	$-0.719880\pi$
$109$	2.13815	−	2.41347i	0.204798	−	0.231169i	0.841932	+	0.539584i	$0.181419\pi$
$110$	−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	−0.997870	−	0.0652400i	$-0.979219\pi$
$113$	−2.01280	−	6.94901i	−0.189349	−	0.653707i	0.808521	−	0.588467i	$-0.200268\pi$
$114$	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	−0.730931	−	0.682451i	$-0.760914\pi$
$127$	−15.1340	+	1.22174i	−1.34292	+	0.108412i	−0.611993	+	0.790863i	$0.709632\pi$
$128$	−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	−0.0400131	−	0.999199i	$-0.512740\pi$
$131$	8.69381	−	4.56286i	0.759582	−	0.398659i	0.799595	+	0.600540i	$0.205048\pi$
$132$	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	0.307100	−	0.951677i	$-0.400641\pi$
$137$	2.53524	+	0.517573i	0.216600	+	0.0442193i	−0.0904998	+	0.995896i	$0.528846\pi$
$138$	2.46872	+	2.78661i	0.210152	+	0.237212i
$139$	−4.33081	+	5.30428i	−0.367334	+	0.449903i	−0.924889	−	0.380237i	$-0.875842\pi$
$139$	−4.33081	+	5.30428i	−0.367334	+	0.449903i	0.557555	+	0.830140i	$0.311740\pi$
$140$	−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	0.608622	−	0.793460i	$-0.291723\pi$
$149$	4.62535	+	2.19476i	0.378923	+	0.179801i	−0.229698	+	0.973262i	$0.573774\pi$
$150$	13.9496	−	8.05383i	1.13898	−	0.657592i
$151$	15.8714	+	10.9553i	1.29160	+	0.891526i	0.997925	−	0.0643796i	$-0.0205069\pi$
$151$	15.8714	+	10.9553i	1.29160	+	0.891526i	0.293673	+	0.955906i	$0.405122\pi$
$152$	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	0.700276	+	0.713873i	$0.253060\pi$
$157$	−3.72482	+	9.82155i	−0.297273	+	0.783845i	−0.997549	+	0.0699728i	$0.977709\pi$
$158$	−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	−0.981564	−	0.191135i	$-0.938783\pi$
$163$	−1.04738	+	3.13728i	−0.0820370	+	0.245731i	0.899527	+	0.436866i	$0.143911\pi$
$164$	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	−0.258142	−	0.966107i	$-0.583110\pi$
$167$	−7.66565	−	0.308915i	−0.593186	−	0.0239046i	−0.335044	+	0.942202i	$0.608751\pi$
$168$	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	−0.373623	−	0.927581i	$-0.621884\pi$
$173$	−11.7219	−	0.946291i	−0.891201	−	0.0719452i	−0.517579	+	0.855636i	$0.673167\pi$
$174$	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	0.568536	−	0.822658i	$-0.307510\pi$
$179$	4.93785	+	2.10382i	0.369072	+	0.157247i	−0.199464	+	0.979905i	$0.563920\pi$
$180$	11.8201	+	18.6921i	0.881021	+	1.39322i
$181$	9.25186	−	24.3951i	0.687685	−	1.81328i	0.115233	−	0.993338i	$-0.463238\pi$
$181$	9.25186	−	24.3951i	0.687685	−	1.81328i	0.572452	−	0.819938i	$-0.305992\pi$
$182$	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	0.988264	+	0.152757i	$0.0488153\pi$
$191$	8.65735	+	14.9950i	0.626424	+	1.08500i	−0.361840	+	0.932240i	$0.617851\pi$
$192$	−0.841524	+	1.45756i	−0.0607318	+	0.105190i
$193$	−6.72766	+	15.7904i	−0.484267	+	1.13662i	0.481322	+	0.876544i	$0.340157\pi$
$193$	−6.72766	+	15.7904i	−0.484267	+	1.13662i	−0.965589	+	0.260073i	$0.916253\pi$
$194$	−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	0.955856	−	0.293836i	$-0.0949321\pi$
$197$	0.213116	+	0.638360i	0.0151839	+	0.0454812i	−0.940672	+	0.339318i	$0.889804\pi$
$198$	−0.137183	+	3.40417i	−0.00974919	+	0.241924i
$199$	0.373580	−	0.457553i	0.0264824	−	0.0324351i	−0.761194	−	0.648524i	$-0.775386\pi$
$199$	0.373580	−	0.457553i	0.0264824	−	0.0324351i	0.787676	+	0.616089i	$0.211284\pi$
$200$	−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	0.589418	−	0.807828i	$-0.299357\pi$
$211$	18.8950	−	1.52536i	1.30079	−	0.105010i	0.711370	+	0.702818i	$0.248075\pi$
$212$	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	−0.325910	−	0.945401i	$-0.605671\pi$
$223$	7.99217	−	6.52540i	0.535195	−	0.436973i	0.861105	+	0.508428i	$0.169773\pi$
$224$	−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	−0.660794	−	0.750567i	$-0.729780\pi$
$227$	1.68507	−	20.8734i	0.111842	−	1.38542i	0.772637	−	0.634849i	$-0.218938\pi$
$228$	−4.75511	−	29.2593i	−0.314915	−	1.93775i
$229$	−3.80883	+	4.29928i	−0.251695	+	0.284104i	−0.860755	−	0.509019i	$-0.830008\pi$
$229$	−3.80883	+	4.29928i	−0.251695	+	0.284104i	0.609061	+	0.793124i	$0.291547\pi$
$230$	−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	−0.224686	−	0.974431i	$-0.572136\pi$
$233$	−13.3788	−	3.29759i	−0.876477	−	0.216032i	−0.651791	+	0.758399i	$0.725982\pi$
$234$	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	$-0.872367\pi$
$239$		−	12.0681i		−	0.780623i	0.920683	−	0.390312i	$-0.127633\pi$
$240$	14.3453	−	13.7789i	0.925986	−	0.889422i
$241$	−0.690176	−	0.563511i	−0.0444582	−	0.0362990i	0.609956	−	0.792435i	$-0.291187\pi$
$241$	−0.690176	−	0.563511i	−0.0444582	−	0.0362990i	−0.654414	+	0.756136i	$0.727085\pi$
$242$	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	0.693024	−	0.720914i	$-0.256278\pi$
$251$	12.8958	+	4.30524i	0.813974	+	0.271744i	0.120950	+	0.992659i	$0.461406\pi$
$252$	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	0.800989	+	0.598679i	$0.204308\pi$
$257$	12.1540	+	25.6141i	0.758147	+	1.59776i	−0.0428420	+	0.999082i	$0.513641\pi$
$258$	−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	−0.263875	−	0.964557i	$-0.585001\pi$
$263$	8.01836	−	5.07050i	0.494433	−	0.312661i	0.758308	+	0.651896i	$0.226026\pi$
$264$	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	0.281691	−	0.959505i	$-0.409105\pi$
$269$	−11.2902	−	11.7544i	−0.688378	−	0.716677i	−0.970069	+	0.242828i	$0.921925\pi$
$270$	−2.27498	+	0.759500i	−0.138451	+	0.0462217i
$271$	1.48422	+	18.3854i	0.0901601	+	1.11683i	0.870729	+	0.491763i	$0.163647\pi$
$271$	1.48422	+	18.3854i	0.0901601	+	1.11683i	−0.780569	+	0.625070i	$0.785070\pi$
$272$	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	0.143149	−	0.989701i	$-0.454277\pi$
$277$	18.8669	−	14.1775i	1.13360	−	0.851846i	0.990452	+	0.137855i	$0.0440209\pi$
$278$	−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	0.978791	+	0.204862i	$0.0656746\pi$
$281$	3.47530	+	14.0998i	0.207319	+	0.841125i	−0.771472	+	0.636263i	$0.780479\pi$
$282$	0.827662	+	2.85742i	0.0492866	+	0.170157i
$283$	3.60804	+	17.6733i	0.214475	+	1.05057i	0.934320	+	0.356435i	$0.116008\pi$
$283$	3.60804	+	17.6733i	0.214475	+	1.05057i	−0.719845	+	0.694135i	$0.755787\pi$
$284$	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	0.922247	−	0.386602i	$-0.126351\pi$
$293$	5.03801	+	6.70437i	0.294324	+	0.391674i	−0.627923	+	0.778275i	$0.716095\pi$
$294$	−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	0.995913	−	0.0903167i	$-0.0287879\pi$
$307$	13.7755	+	15.5494i	0.786211	+	0.887449i	−0.209702	+	0.977765i	$0.567249\pi$
$308$	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	−0.454388	−	0.890804i	$-0.650142\pi$
$311$	6.61585	−	5.86114i	0.375151	−	0.332354i	0.829539	+	0.558449i	$0.188604\pi$
$312$	−7.59610	−	18.3396i	−0.430045	−	1.03828i
$313$	17.8929	+	15.8517i	1.01137	+	0.895994i	0.994591	−	0.103866i	$-0.0331212\pi$
$313$	17.8929	+	15.8517i	1.01137	+	0.895994i	0.0167764	+	0.999859i	$0.494660\pi$
$314$	−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	−0.556616	−	0.830770i	$-0.687901\pi$
$317$	−15.9927	+	1.94187i	−0.898242	+	0.109066i	−0.341626	+	0.939836i	$0.610978\pi$
$318$	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	0.881577	+	0.472040i	$0.156482\pi$
$331$	11.1221	+	26.1044i	0.611323	+	1.43483i	−0.270254	+	0.962789i	$0.587108\pi$
$332$	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	0.326622	−	0.945155i	$-0.394090\pi$
$347$	−7.21382	−	4.56174i	−0.387258	−	0.244887i	−0.713880	+	0.700268i	$0.753064\pi$
$348$	−31.7065	−	13.5089i	−1.69965	−	0.724152i
$349$	4.08332	+	6.45726i	0.218575	+	0.345649i	0.936619	−	0.350348i	$-0.113937\pi$
$349$	4.08332	+	6.45726i	0.218575	+	0.345649i	−0.718044	+	0.695998i	$0.754962\pi$
$350$	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	−0.711972	−	0.702208i	$-0.752198\pi$
$353$	3.01731	−	4.01531i	0.160595	−	0.213713i	0.872567	+	0.488495i	$0.162454\pi$
$354$	−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	−0.598734	−	0.800948i	$-0.704330\pi$
$359$	−18.7273	+	2.27391i	−0.988392	+	0.120012i	−0.389657	+	0.920960i	$0.627406\pi$
$360$	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	−0.962645	−	0.270765i	$-0.912723\pi$
$367$	0.357589	−	8.87348i	0.0186660	−	0.463192i	0.981311	−	0.192427i	$-0.0616357\pi$
$368$	−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	−0.993789	−	0.111280i	$-0.964505\pi$
$373$	−0.235174	−	5.83579i	−0.0121769	−	0.302166i	0.981612	−	0.190886i	$-0.0611361\pi$
$374$	−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	−0.518757	−	0.854922i	$-0.673605\pi$
$379$	−27.5302	−	7.97422i	−1.41413	−	0.409608i	−0.895375	+	0.445313i	$0.853092\pi$
$380$	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	0.976969	−	0.213382i	$-0.0684477\pi$
$383$	9.78915	+	13.0270i	0.500202	+	0.665648i	−0.476767	+	0.879030i	$0.658191\pi$
$384$	−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	0.977120	−	0.212689i	$-0.0682222\pi$
$389$	−0.443898	−	3.65583i	−0.0225065	−	0.185358i	−0.999626	+	0.0273313i	$0.991299\pi$
$390$	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	0.983369	+	0.181621i	$0.0581343\pi$
$397$	2.15430	+	13.2559i	0.108121	+	0.665296i	−0.875248	+	0.483675i	$0.839302\pi$
$398$	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	−0.660973	−	0.750410i	$-0.729856\pi$
$401$	4.07738	−	25.0891i	0.203615	−	1.25289i	0.864588	−	0.502482i	$-0.167580\pi$
$402$	−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	−0.923114	−	0.384527i	$-0.874365\pi$
$409$	−11.6503	+	11.1902i	−0.576069	+	0.553322i	0.347045	+	0.937849i	$0.387185\pi$
$410$	−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	0.992821	+	0.119609i	$0.0381640\pi$
$419$	9.36613	+	19.7387i	0.457565	+	0.964299i	−0.535256	+	0.844690i	$0.679785\pi$
$420$	12.9326	+	4.31755i	0.631049	+	0.210675i
$421$	−1.70880	+	6.93287i	−0.0832818	+	0.337887i	−0.997772	−	0.0667214i	$-0.978746\pi$
$421$	−1.70880	+	6.93287i	−0.0832818	+	0.337887i	0.914490	+	0.404609i	$0.132592\pi$
$422$	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	−0.940082	−	0.340948i	$-0.889252\pi$
$431$	−26.3769	+	12.5160i	−1.27053	+	0.602875i	−0.330451	+	0.943823i	$0.607201\pi$
$432$	−1.70393	+	1.07750i	−0.0819805	+	0.0518413i
$433$	−13.2259	+	2.14942i	−0.635595	+	0.103294i	−0.469667	−	0.882844i	$-0.655626\pi$
$433$	−13.2259	+	2.14942i	−0.635595	+	0.103294i	−0.165928	+	0.986138i	$0.553062\pi$
$434$	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	0.392633	−	0.919695i	$-0.371564\pi$
$439$	26.3794	−	8.80673i	1.25902	−	0.420323i	0.866387	+	0.499373i	$0.166436\pi$
$440$	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	−0.161916	−	0.986804i	$-0.551768\pi$
$443$	−16.0778	−	3.96281i	−0.763877	−	0.188279i	−0.601961	+	0.798526i	$0.705614\pi$
$444$	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	−0.637448	−	0.770493i	$-0.720010\pi$
$449$	2.44403	−	30.2748i	0.115341	−	1.42876i	0.752789	−	0.658262i	$-0.228708\pi$
$450$	−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	0.628814	−	0.777556i	$-0.283541\pi$
$457$	−2.62498	−	2.52133i	−0.122792	−	0.117943i	−0.751605	+	0.659613i	$0.770720\pi$
$458$	−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	−0.693817	−	0.720151i	$-0.744072\pi$
$461$	5.45872	−	8.63227i	0.254238	−	0.402045i	0.948055	+	0.318106i	$0.103047\pi$
$462$	1.26178	+	1.67912i	0.0587031	+	0.0781196i
$463$	−14.8084	−	28.2151i	−0.688206	−	1.31127i	−0.939231	−	0.343286i	$-0.888460\pi$
$463$	−14.8084	−	28.2151i	−0.688206	−	1.31127i	0.251025	−	0.967981i	$-0.419232\pi$
$464$	−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	−0.992110	−	0.125371i	$-0.959988\pi$
$467$	−35.8485	−	18.8147i	−1.65887	−	0.870643i	−0.666761	−	0.745271i	$-0.732320\pi$
$468$	−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	−0.990955	−	0.134193i	$-0.957156\pi$
$479$	−6.11407	−	18.3139i	−0.279359	−	0.836782i	0.711596	−	0.702588i	$-0.247972\pi$
$480$	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	0.486676	−	0.873582i	$-0.338209\pi$
$487$	2.59942	+	1.23344i	0.117791	+	0.0558925i	−0.368885	+	0.929475i	$0.620260\pi$
$488$	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	−0.731449	−	0.681896i	$-0.761155\pi$
$491$	−36.3663	−	5.91010i	−1.64119	−	0.266719i	−0.909741	+	0.415177i	$0.863720\pi$
$492$	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	0.596868	−	0.802339i	$-0.296412\pi$
$499$	21.9894	+	2.66999i	0.984380	+	0.119525i	0.387512	+	0.921865i	$0.373335\pi$
$500$	−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	−0.278565	−	0.960417i	$-0.589859\pi$
$503$	−15.8695	−	1.28112i	−0.707585	−	0.0571222i	−0.429020	+	0.903295i	$0.641141\pi$
$504$	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	0.798225	−	0.602359i	$-0.205772\pi$
$509$	34.8656	+	1.40504i	1.54539	+	0.0622772i	0.747167	+	0.664636i	$0.231413\pi$
$510$	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	0.805729	−	0.592284i	$-0.201774\pi$
$521$	−4.33967	−	11.4428i	−0.190125	−	0.501317i	−0.995854	+	0.0909666i	$0.971004\pi$
$522$	10.1165	−	13.4626i	0.442787	−	0.589243i
$523$	−18.2775	−	2.97038i	−0.799219	−	0.129886i	−0.252932	−	0.967484i	$-0.581395\pi$
$523$	−18.2775	−	2.97038i	−0.799219	−	0.129886i	−0.546287	+	0.837598i	$0.683959\pi$
$524$	−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	−0.963305	−	0.268407i	$-0.913503\pi$
$541$	−35.0371	+	13.2878i	−1.50636	+	0.571288i	−0.543057	+	0.839696i	$0.682733\pi$
$542$	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	0.256004	−	0.966676i	$-0.417594\pi$
$547$	−9.21786	−	4.83791i	−0.394127	−	0.206854i	−0.650131	+	0.759822i	$0.725286\pi$
$548$	−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	0.875393	−	0.483411i	$-0.160602\pi$
$557$	10.0923	+	9.69375i	0.427623	+	0.410737i	−0.447771	+	0.894148i	$0.647782\pi$
$558$	−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	0.810334	+	0.585969i	$0.199286\pi$
$563$	10.4076	+	35.9312i	0.438628	+	1.51432i	−0.371706	+	0.928351i	$0.621227\pi$
$564$	−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	0.929969	−	0.367638i	$-0.119833\pi$
$569$	9.15370	+	11.2112i	0.383743	+	0.470000i	−0.546226	+	0.837638i	$0.683936\pi$
$570$	−6.83952	+	42.0853i	−0.286476	+	1.76276i
$571$	2.71476	+	0.669129i	0.113609	+	0.0280022i	0.295710	−	0.955278i	$-0.404444\pi$
$571$	2.71476	+	0.669129i	0.113609	+	0.0280022i	−0.182101	+	0.983280i	$0.558290\pi$
$572$	−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	$-0.881349\pi$
$577$		−	17.4959i		−	0.728363i	0.931328	−	0.364181i	$-0.118651\pi$
$578$	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	0.901128	−	0.433553i	$-0.142740\pi$
$587$	23.6521	+	13.6555i	0.976225	+	0.563624i	0.0750967	+	0.997176i	$0.476073\pi$
$588$	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	−0.999360	−	0.0357828i	$-0.988608\pi$
$593$	−2.38260	+	9.66657i	−0.0978415	+	0.396959i	0.901518	+	0.432741i	$0.142454\pi$
$594$	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	−0.811740	−	0.584019i	$-0.801479\pi$
$599$	0.542710	−	0.786250i	0.0221745	−	0.0321253i	0.833914	+	0.551894i	$0.186095\pi$
$600$	−53.0182	+	25.1575i	−2.16446	+	1.02705i
$601$	14.8450	−	9.38738i	0.605538	−	0.382919i	−0.196227	−	0.980559i	$-0.562869\pi$
$601$	14.8450	−	9.38738i	0.605538	−	0.382919i	0.801765	+	0.597639i	$0.203895\pi$
$602$	−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	0.907152	−	0.420803i	$-0.138252\pi$
$607$	11.0908	+	11.5468i	0.450162	+	0.468669i	−0.456989	+	0.889472i	$0.651072\pi$
$608$	−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	−0.927396	−	0.374080i	$-0.877958\pi$
$613$	1.75125	−	10.7759i	0.0707322	−	0.435233i	0.998128	−	0.0611522i	$-0.0194775\pi$
$614$	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	0.727256	+	0.686367i	$0.240796\pi$
$617$	6.32854	+	38.9411i	0.254778	+	1.56771i	−0.472478	+	0.881342i	$0.656640\pi$
$618$	1.06265	−	13.1632i	0.0427459	−	0.529503i
$619$	4.55502	+	18.4804i	0.183082	+	0.742791i	0.988644	+	0.150280i	$0.0480174\pi$
$619$	4.55502	+	18.4804i	0.183082	+	0.742791i	−0.805562	+	0.592512i	$0.798136\pi$
$620$	−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	0.419166	−	0.907910i	$-0.362322\pi$
$631$	−14.3061	−	19.0380i	−0.569517	−	0.757889i	−0.988683	+	0.150020i	$0.952066\pi$
$632$	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	−0.652646	−	0.757663i	$-0.726341\pi$
$641$	−1.59713	−	39.6324i	−0.0630829	−	1.56539i	0.589563	−	0.807722i	$-0.299300\pi$
$642$	14.4059	−	5.46345i	0.568557	−	0.215625i
$643$	28.3238	−	8.20409i	1.11698	−	0.323538i	0.332138	−	0.943231i	$-0.392230\pi$
$643$	28.3238	−	8.20409i	1.11698	−	0.323538i	0.784844	+	0.619693i	$0.212743\pi$
$644$	−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	−0.954308	−	0.298825i	$-0.903405\pi$
$647$	0.532911	−	13.2241i	0.0209509	−	0.519891i	0.975259	−	0.221066i	$-0.0709537\pi$
$648$	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	−0.975617	−	0.219482i	$-0.929563\pi$
$653$	−7.60819	+	13.1778i	−0.297731	+	0.515686i	0.677885	+	0.735168i	$0.262897\pi$
$654$	−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	−0.987830	−	0.155540i	$-0.950288\pi$
$659$	−40.0454	+	17.0617i	−1.55995	+	0.664631i	−0.572118	+	0.820172i	$0.693878\pi$
$660$	27.2341	+	4.42598i	1.06009	+	0.172281i
$661$	19.0799	−	25.3908i	0.742123	−	0.987586i	−0.257649	−	0.966239i	$-0.582948\pi$
$661$	19.0799	−	25.3908i	0.742123	−	0.987586i	0.999772	−	0.0213477i	$-0.00679570\pi$
$662$	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	0.480399	+	0.877050i	$0.340492\pi$
$673$	−10.2312	+	35.3221i	−0.394383	+	1.36157i	−0.874782	+	0.484517i	$0.838995\pi$
$674$	−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	0.988476	−	0.151380i	$-0.0483716\pi$
$683$	5.08466	+	11.9341i	0.194559	+	0.456647i	−0.793917	+	0.608027i	$0.791961\pi$
$684$	−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	−0.712718	−	0.701450i	$-0.752536\pi$
$691$	4.18825	−	5.57354i	0.159328	−	0.212028i	0.872047	+	0.489423i	$0.162793\pi$
$692$	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	0.565711	−	0.824604i	$-0.308602\pi$
$701$	−4.88998	−	4.33214i	−0.184692	−	0.163623i	−0.750403	+	0.660981i	$0.770140\pi$
$702$	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	0.552458	−	0.833541i	$-0.313690\pi$
$709$	39.0057	−	11.2981i	1.46489	−	0.424310i	0.912431	+	0.409231i	$0.134203\pi$
$710$	−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	−0.994368	−	0.105985i	$-0.966200\pi$
$719$	−1.01967	+	4.99465i	−0.0380271	+	0.186269i	0.956341	+	0.292255i	$0.0944054\pi$
$720$	−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	−0.917586	−	0.397537i	$-0.869865\pi$
$727$	−3.28409	−	27.0469i	−0.121800	−	1.00312i	0.795786	−	0.605578i	$-0.207058\pi$
$728$	−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	0.807598	+	0.589733i	$0.200767\pi$
$733$	9.92446	+	40.2651i	0.366568	+	1.48723i	−0.441030	+	0.897492i	$0.645387\pi$
$734$	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	−0.836859	−	0.547418i	$-0.815611\pi$
$739$	3.54166	−	21.7927i	0.130282	−	0.801657i	0.967141	−	0.254239i	$-0.0818251\pi$
$740$	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	−0.762540	−	0.646941i	$-0.776048\pi$
$743$	−3.09791	−	38.3745i	−0.113651	−	1.40782i	0.648889	−	0.760883i	$-0.275234\pi$
$744$	−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	0.557363	−	0.830269i	$-0.311813\pi$
$751$	42.3783	−	26.7984i	1.54641	−	0.977889i	0.989044	−	0.147620i	$-0.0471613\pi$
$752$	−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	0.962650	+	0.270751i	$0.0872719\pi$
$757$	15.5053	+	32.6768i	0.563551	+	1.18766i	−0.399099	+	0.916908i	$0.630677\pi$
$758$	−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	−0.297152	−	0.954830i	$-0.596037\pi$
$761$	−14.2485	+	0.574196i	−0.516509	+	0.0208146i	−0.219357	+	0.975645i	$0.570396\pi$
$762$	−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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